LMFDB - Embedded newform 891.2.u.c.215.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			215.2
Character	$\chi$	$=$	891.215
Dual form			891.2.u.c.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.460557 + 0.511500i) q^{2} +(0.159537 + 1.51789i) q^{4} +(-0.0298066 + 0.0268380i) q^{5} +(0.100402 - 0.225507i) q^{7} +(-1.96356 - 1.42661i) q^{8} +O(q^{10})$	\(q+(-0.460557 + 0.511500i) q^{2} +(0.159537 + 1.51789i) q^{4} +(-0.0298066 + 0.0268380i) q^{5} +(0.100402 - 0.225507i) q^{7} +(-1.96356 - 1.42661i) q^{8} -0.0276065i q^{10} +(-2.53364 - 2.14025i) q^{11} +(0.478513 - 2.25123i) q^{13} +(0.0691059 + 0.155214i) q^{14} +(-1.35177 + 0.287327i) q^{16} +(-1.32142 + 4.06692i) q^{17} +(-3.64429 + 5.01593i) q^{19} +(-0.0454925 - 0.0409616i) q^{20} +(2.26162 - 0.310248i) q^{22} +(-5.88883 - 3.39992i) q^{23} +(-0.522474 + 4.97101i) q^{25} +(0.931121 + 1.28158i) q^{26} +(0.358314 + 0.116423i) q^{28} +(-5.11196 - 2.27599i) q^{29} +(-4.69255 - 0.997431i) q^{31} +(2.90269 - 5.02760i) q^{32} +(-1.47164 - 2.54895i) q^{34} +(0.00305951 + 0.00941619i) q^{35} +(3.26102 - 2.36927i) q^{37} +(-0.887248 - 4.17418i) q^{38} +(0.0968143 - 0.0101756i) q^{40} +(8.77271 - 3.90586i) q^{41} +(0.893447 - 0.515832i) q^{43} +(2.84447 - 4.18724i) q^{44} +(4.45120 - 1.44628i) q^{46} +(-11.0653 - 1.16301i) q^{47} +(4.64314 + 5.15673i) q^{49} +(-2.30204 - 2.55668i) q^{50} +(3.49347 + 0.367178i) q^{52} +(-8.52885 + 2.77119i) q^{53} +(0.132959 - 0.00420408i) q^{55} +(-0.518855 + 0.299561i) q^{56} +(3.51852 - 1.56655i) q^{58} +(2.77304 - 0.291459i) q^{59} +(-1.76403 - 8.29909i) q^{61} +(2.67137 - 1.94086i) q^{62} +(0.380665 + 1.17156i) q^{64} +(0.0461556 + 0.0799438i) q^{65} +(-3.97294 + 6.88133i) q^{67} +(-6.38397 - 1.35695i) q^{68} +(-0.00622546 - 0.00277175i) q^{70} +(3.16559 + 1.02856i) q^{71} +(-6.96743 - 9.58984i) q^{73} +(-0.290003 + 2.75920i) q^{74} +(-8.19506 - 4.73142i) q^{76} +(-0.737025 + 0.356467i) q^{77} +(2.23761 + 2.01475i) q^{79} +(0.0325803 - 0.0448429i) q^{80} +(-2.04248 + 6.28611i) q^{82} +(5.17811 - 1.10064i) q^{83} +(-0.0697608 - 0.156685i) q^{85} +(-0.147635 + 0.694568i) q^{86} +(1.92164 + 7.81702i) q^{88} +8.54422i q^{89} +(-0.459624 - 0.333936i) q^{91} +(4.22123 - 9.48104i) q^{92} +(5.69106 - 5.12425i) q^{94} +(-0.0259937 - 0.247313i) q^{95} +(-2.02629 + 2.25042i) q^{97} -4.77610 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4}+O(q^{10}) $ 32 * q + 4 * q^4	$ 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) $ 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.460557	+	0.511500i	−0.325663	+	0.361685i	−0.883637	−	0.468173i	$-0.844912\pi$
$2$	−0.460557	+	0.511500i	−0.325663	+	0.361685i	0.557974	+	0.829859i	$0.311579\pi$
$3$		0			0
$3$		0			0
$4$	0.159537	+	1.51789i	0.0797686	+	0.758947i
$5$	−0.0298066	+	0.0268380i	−0.0133299	+	0.0120023i	−0.675769	−	0.737114i	$-0.736188\pi$
$5$	−0.0298066	+	0.0268380i	−0.0133299	+	0.0120023i	0.662439	+	0.749116i	$0.269521\pi$
$6$		0			0
$7$	0.100402	−	0.225507i	0.0379485	−	0.0852336i	−0.893577	−	0.448911i	$-0.851812\pi$
$7$	0.100402	−	0.225507i	0.0379485	−	0.0852336i	0.931525	+	0.363677i	$0.118479\pi$
$8$	−1.96356	−	1.42661i	−0.694222	−	0.504382i
$9$		0			0
$10$		−	0.0276065i		−	0.00872994i
$11$	−2.53364	−	2.14025i	−0.763921	−	0.645310i
$11$	−2.53364	−	2.14025i	−0.763921	−	0.645310i
$12$		0			0
$13$	0.478513	−	2.25123i	0.132716	−	0.624378i	−0.860632	−	0.509227i	$-0.829931\pi$
$13$	0.478513	−	2.25123i	0.132716	−	0.624378i	0.993348	−	0.115151i	$-0.0367353\pi$
$14$	0.0691059	+	0.155214i	0.0184693	+	0.0414828i
$15$		0			0
$16$	−1.35177	+	0.287327i	−0.337942	+	0.0718317i
$17$	−1.32142	+	4.06692i	−0.320492	+	0.986372i	0.652943	+	0.757407i	$0.273534\pi$
$17$	−1.32142	+	4.06692i	−0.320492	+	0.986372i	−0.973435	+	0.228965i	$0.926466\pi$
$18$		0			0
$19$	−3.64429	+	5.01593i	−0.836057	+	1.15073i	0.150708	+	0.988578i	$0.451845\pi$
$19$	−3.64429	+	5.01593i	−0.836057	+	1.15073i	−0.986765	+	0.162156i	$0.948155\pi$
$20$	−0.0454925	−	0.0409616i	−0.0101724	−	0.00915930i
$21$		0			0
$22$	2.26162	−	0.310248i	0.482180	−	0.0661451i
$23$	−5.88883	−	3.39992i	−1.22791	−	0.708932i	−0.261315	−	0.965254i	$-0.584156\pi$
$23$	−5.88883	−	3.39992i	−1.22791	−	0.708932i	−0.966592	+	0.256321i	$0.917489\pi$
$24$		0			0
$25$	−0.522474	+	4.97101i	−0.104495	+	0.994202i
$26$	0.931121	+	1.28158i	0.182608	+	0.251338i
$27$		0			0
$28$	0.358314	+	0.116423i	0.0677149	+	0.0220019i
$29$	−5.11196	−	2.27599i	−0.949268	−	0.422641i	−0.127102	−	0.991890i	$-0.540568\pi$
$29$	−5.11196	−	2.27599i	−0.949268	−	0.422641i	−0.822166	+	0.569248i	$0.807234\pi$
$30$		0			0
$31$	−4.69255	−	0.997431i	−0.842806	−	0.179144i	−0.233775	−	0.972291i	$-0.575108\pi$
$31$	−4.69255	−	0.997431i	−0.842806	−	0.179144i	−0.609031	+	0.793147i	$0.708441\pi$
$32$	2.90269	−	5.02760i	0.513128	−	0.888763i
$33$		0			0
$34$	−1.47164	−	2.54895i	−0.252384	−	0.437142i
$35$	0.00305951	+	0.00941619i	0.000517151	+	0.00159163i
$36$		0			0
$37$	3.26102	−	2.36927i	0.536109	−	0.389506i	−0.286529	−	0.958072i	$-0.592502\pi$
$37$	3.26102	−	2.36927i	0.536109	−	0.389506i	0.822638	+	0.568566i	$0.192502\pi$
$38$	−0.887248	−	4.17418i	−0.143931	−	0.677141i
$39$		0			0
$40$	0.0968143	−	0.0101756i	0.0153077	−	0.00160890i
$41$	8.77271	−	3.90586i	1.37007	−	0.609993i	0.415939	−	0.909392i	$-0.363453\pi$
$41$	8.77271	−	3.90586i	1.37007	−	0.609993i	0.954128	+	0.299399i	$0.0967862\pi$
$42$		0			0
$43$	0.893447	−	0.515832i	0.136249	−	0.0786636i	−0.430326	−	0.902674i	$-0.641601\pi$
$43$	0.893447	−	0.515832i	0.136249	−	0.0786636i	0.566575	+	0.824010i	$0.308268\pi$
$44$	2.84447	−	4.18724i	0.428820	−	0.631251i
$45$		0			0
$46$	4.45120	−	1.44628i	0.656294	−	0.213243i
$47$	−11.0653	−	1.16301i	−1.61403	−	0.169642i	−0.745930	−	0.666024i	$-0.767995\pi$
$47$	−11.0653	−	1.16301i	−1.61403	−	0.169642i	−0.868104	+	0.496382i	$0.834661\pi$
$48$		0			0
$49$	4.64314	+	5.15673i	0.663306	+	0.736676i
$50$	−2.30204	−	2.55668i	−0.325558	−	0.361569i
$51$		0			0
$52$	3.49347	+	0.367178i	0.484457	+	0.0509184i
$53$	−8.52885	+	2.77119i	−1.17153	+	0.380652i	−0.829213	−	0.558933i	$-0.811211\pi$
$53$	−8.52885	+	2.77119i	−1.17153	+	0.380652i	−0.342314	+	0.939585i	$0.611211\pi$
$54$		0			0
$55$	0.132959	−	0.00420408i	0.0179282	−	0.000566878i
$56$	−0.518855	+	0.299561i	−0.0693350	+	0.0400306i
$57$		0			0
$58$	3.51852	−	1.56655i	0.462004	−	0.205698i
$59$	2.77304	−	0.291459i	0.361020	−	0.0379447i	0.0777175	−	0.996975i	$-0.475237\pi$
$59$	2.77304	−	0.291459i	0.361020	−	0.0379447i	0.283302	+	0.959031i	$0.408570\pi$
$60$		0			0
$61$	−1.76403	−	8.29909i	−0.225860	−	1.06259i	−0.934209	−	0.356727i	$-0.883893\pi$
$61$	−1.76403	−	8.29909i	−0.225860	−	1.06259i	0.708348	−	0.705863i	$-0.249441\pi$
$62$	2.67137	−	1.94086i	0.339264	−	0.246490i
$63$		0			0
$64$	0.380665	+	1.17156i	0.0475831	+	0.146446i
$65$	0.0461556	+	0.0799438i	0.00572489	+	0.00991581i
$66$		0			0
$67$	−3.97294	+	6.88133i	−0.485372	+	0.840689i	−0.999859	−	0.0168095i	$-0.994649\pi$
$67$	−3.97294	+	6.88133i	−0.485372	+	0.840689i	0.514487	+	0.857498i	$0.327982\pi$
$68$	−6.38397	−	1.35695i	−0.774170	−	0.164555i
$69$		0			0
$70$	−0.00622546	−	0.00277175i	−0.000744084	−	0.000331288i
$71$	3.16559	+	1.02856i	0.375687	+	0.122068i	0.490773	−	0.871288i	$-0.336714\pi$
$71$	3.16559	+	1.02856i	0.375687	+	0.122068i	−0.115086	+	0.993355i	$0.536714\pi$
$72$		0			0
$73$	−6.96743	−	9.58984i	−0.815476	−	1.12241i	−0.990455	−	0.137834i	$-0.955986\pi$
$73$	−6.96743	−	9.58984i	−0.815476	−	1.12241i	0.174980	−	0.984572i	$-0.444014\pi$
$74$	−0.290003	+	2.75920i	−0.0337122	+	0.320750i
$75$		0			0
$76$	−8.19506	−	4.73142i	−0.940038	−	0.542731i
$77$	−0.737025	+	0.356467i	−0.0839917	+	0.0406232i
$78$		0			0
$79$	2.23761	+	2.01475i	0.251751	+	0.226678i	0.785337	−	0.619068i	$-0.212489\pi$
$79$	2.23761	+	2.01475i	0.251751	+	0.226678i	−0.533587	+	0.845745i	$0.679156\pi$
$80$	0.0325803	−	0.0448429i	0.00364259	−	0.00501359i
$81$		0			0
$82$	−2.04248	+	6.28611i	−0.225554	+	0.694185i
$83$	5.17811	−	1.10064i	0.568372	−	0.120811i	0.0852426	−	0.996360i	$-0.472833\pi$
$83$	5.17811	−	1.10064i	0.568372	−	0.120811i	0.483129	+	0.875549i	$0.339500\pi$
$84$		0			0
$85$	−0.0697608	−	0.156685i	−0.00756662	−	0.0169949i
$86$	−0.147635	+	0.694568i	−0.0159199	+	0.0748972i
$87$		0			0
$88$	1.92164	+	7.81702i	0.204848	+	0.833297i
$89$			8.54422i			0.905686i	0.891590	+	0.452843i	$0.149590\pi$
$89$			8.54422i			0.905686i	−0.891590	+	0.452843i	$0.850410\pi$
$90$		0			0
$91$	−0.459624	−	0.333936i	−0.0481817	−	0.0350060i
$92$	4.22123	−	9.48104i	0.440094	−	0.988467i
$93$		0			0
$94$	5.69106	−	5.12425i	0.586988	−	0.528526i
$95$	−0.0259937	−	0.247313i	−0.00266690	−	0.0253738i
$96$		0			0
$97$	−2.02629	+	2.25042i	−0.205738	+	0.228496i	−0.837180	−	0.546928i	$-0.815797\pi$
$97$	−2.02629	+	2.25042i	−0.205738	+	0.228496i	0.631441	+	0.775424i	$0.282464\pi$
$98$	−4.77610			−0.482459
$99$		0			0
$100$	−7.62882			−0.762882
$101$	−4.65178	+	5.16633i	−0.462869	+	0.514069i	−0.928713	−	0.370798i	$-0.879084\pi$
$101$	−4.65178	+	5.16633i	−0.462869	+	0.514069i	0.465844	+	0.884867i	$0.345751\pi$
$102$		0			0
$103$	−1.37135	−	13.0475i	−0.135123	−	1.28561i	−0.826425	−	0.563046i	$-0.809629\pi$
$103$	−1.37135	−	13.0475i	−0.135123	−	1.28561i	0.691302	−	0.722566i	$-0.257037\pi$
$104$	−4.15121	+	3.73776i	−0.407059	+	0.366518i
$105$		0			0
$106$	2.51055	−	5.63879i	0.243846	−	0.547688i
$107$	−1.10712	−	0.804368i	−0.107029	−	0.0777612i	0.532983	−	0.846126i	$-0.321071\pi$
$107$	−1.10712	−	0.804368i	−0.107029	−	0.0777612i	−0.640012	+	0.768365i	$0.721071\pi$
$108$		0			0
$109$		−	7.34454i		−	0.703480i	−0.936098	−	0.351740i	$-0.885590\pi$
$109$		−	7.34454i		−	0.703480i	0.936098	−	0.351740i	$-0.114410\pi$
$110$	−0.0590849	+	0.0699448i	−0.00563352	+	0.00666898i
$111$		0			0
$112$	−0.0709261	+	0.333681i	−0.00670189	+	0.0315299i
$113$	0.214978	+	0.482848i	0.0202234	+	0.0454225i	0.923375	−	0.383900i	$-0.125419\pi$
$113$	0.214978	+	0.482848i	0.0202234	+	0.0454225i	−0.903151	+	0.429322i	$0.858752\pi$
$114$		0			0
$115$	0.266773	−	0.0567044i	0.0248767	−	0.00528771i
$116$	2.63917	−	8.12253i	0.245041	−	0.754158i
$117$		0			0
$118$	−1.12806	+	1.55265i	−0.103847	+	0.142933i
$119$	0.784445	+	0.706317i	0.0719099	+	0.0647480i
$120$		0			0
$121$	1.83864	+	10.8452i	0.167149	+	0.985932i
$122$	5.05742	+	2.91990i	0.457877	+	0.264355i
$123$		0			0
$124$	0.765360	−	7.28192i	0.0687314	−	0.653935i
$125$	−0.235715	−	0.324434i	−0.0210830	−	0.0290183i
$126$		0			0
$127$	12.1468	+	3.94673i	1.07785	+	0.350215i	0.793541	−	0.608517i	$-0.208235\pi$
$127$	12.1468	+	3.94673i	1.07785	+	0.350215i	0.284311	+	0.958732i	$0.408235\pi$
$128$	9.83238	+	4.37766i	0.869067	+	0.386934i
$129$		0			0
$130$	−0.0621485	−	0.0132101i	−0.00545078	−	0.00115860i
$131$	−9.07668	+	15.7213i	−0.793033	+	1.37357i	0.131047	+	0.991376i	$0.458166\pi$
$131$	−9.07668	+	15.7213i	−0.793033	+	1.37357i	−0.924081	+	0.382198i	$0.875167\pi$
$132$		0			0
$133$	0.765233	+	1.32542i	0.0663542	+	0.114929i
$134$	−1.69004	−	5.20140i	−0.145997	−	0.449333i
$135$		0			0
$136$	8.39658	−	6.10048i	0.720001	−	0.523111i
$137$	3.34176	+	15.7217i	0.285506	+	1.34320i	0.853897	+	0.520441i	$0.174233\pi$
$137$	3.34176	+	15.7217i	0.285506	+	1.34320i	−0.568392	+	0.822758i	$0.692434\pi$
$138$		0			0
$139$	−3.83617	+	0.403198i	−0.325380	+	0.0341988i	−0.265810	−	0.964025i	$-0.585639\pi$
$139$	−3.83617	+	0.403198i	−0.325380	+	0.0341988i	−0.0595696	+	0.998224i	$0.518973\pi$
$140$	−0.0138047	+	0.00614624i	−0.00116671	+	0.000519452i
$141$		0			0
$142$	−1.98404	+	1.14549i	−0.166497	+	0.0961273i
$143$	−6.03057	+	4.67966i	−0.504302	+	0.391333i
$144$		0			0
$145$	0.213453	−	0.0693552i	0.0177263	−	0.00575964i
$146$	8.11410	+	0.852826i	0.671528	+	0.0705804i
$147$		0			0
$148$	4.11656	+	4.57190i	0.338379	+	0.375808i
$149$	6.87196	+	7.63209i	0.562973	+	0.625245i	0.955676	−	0.294420i	$-0.0951265\pi$
$149$	6.87196	+	7.63209i	0.562973	+	0.625245i	−0.392703	+	0.919665i	$0.628460\pi$
$150$		0			0
$151$	−8.72237	−	0.916758i	−0.709817	−	0.0746047i	−0.257262	−	0.966342i	$-0.582820\pi$
$151$	−8.72237	−	0.916758i	−0.709817	−	0.0746047i	−0.452554	+	0.891737i	$0.649487\pi$
$152$	14.3115	−	4.65010i	1.16082	−	0.377173i
$153$		0			0
$154$	0.157109	−	0.541161i	0.0126602	−	0.0436080i
$155$	0.166638	−	0.0962084i	0.0133847	−	0.00772765i
$156$		0			0
$157$	−11.9043	+	5.30012i	−0.950064	+	0.422996i	−0.822456	−	0.568829i	$-0.807397\pi$
$157$	−11.9043	+	5.30012i	−0.950064	+	0.422996i	−0.127608	+	0.991825i	$0.540730\pi$
$158$	−2.06109	+	0.216630i	−0.163972	+	0.0172341i
$159$		0			0
$160$	0.0484115	+	0.227758i	0.00382726	+	0.0180059i
$161$	−1.35796	+	0.986614i	−0.107022	+	0.0777561i
$162$		0			0
$163$	−2.83608	−	8.72855i	−0.222139	−	0.683673i	−0.998569	−	0.0534700i	$-0.982972\pi$
$163$	−2.83608	−	8.72855i	−0.222139	−	0.683673i	0.776431	−	0.630203i	$-0.217028\pi$
$164$	7.32826	+	12.6929i	0.572241	+	0.991151i
$165$		0			0
$166$	−1.82184	+	3.15551i	−0.141402	+	0.244915i
$167$	7.44305	+	1.58207i	0.575961	+	0.122424i	0.486677	−	0.873582i	$-0.338209\pi$
$167$	7.44305	+	1.58207i	0.575961	+	0.122424i	0.0892837	+	0.996006i	$0.471542\pi$
$168$		0			0
$169$	7.03704	+	3.13309i	0.541311	+	0.241007i
$170$	0.112273	+	0.0364798i	0.00861097	+	0.00279787i
$171$		0			0
$172$	0.925516	+	1.27386i	0.0705699	+	0.0971312i
$173$	1.73731	−	16.5294i	0.132085	−	1.25670i	−0.704832	−	0.709374i	$-0.748978\pi$
$173$	1.73731	−	16.5294i	0.132085	−	1.25670i	0.836917	−	0.547330i	$-0.184356\pi$
$174$		0			0
$175$	1.06854	+	0.616922i	0.0807740	+	0.0466349i
$176$	4.03984	+	2.16514i	0.304514	+	0.163204i
$177$		0			0
$178$	−4.37037	−	3.93510i	−0.327573	−	0.294948i
$179$	−4.14376	+	5.70340i	−0.309719	+	0.426292i	−0.935294	−	0.353872i	$-0.884865\pi$
$179$	−4.14376	+	5.70340i	−0.309719	+	0.426292i	0.625574	+	0.780165i	$0.284865\pi$
$180$		0			0
$181$	−6.52756	+	20.0898i	−0.485189	+	1.49326i	0.346517	+	0.938044i	$0.387364\pi$
$181$	−6.52756	+	20.0898i	−0.485189	+	1.49326i	−0.831706	+	0.555216i	$0.812636\pi$
$182$	0.382491	−	0.0813010i	0.0283521	−	0.00602643i
$183$		0			0
$184$	6.71271	+	15.0770i	0.494868	+	1.11149i
$185$	−0.0336135	+	0.158139i	−0.00247132	+	0.0116266i
$186$		0			0
$187$	12.0522	−	7.47592i	0.881347	−	0.546693i
$188$		−	16.9814i		−	1.23850i
$189$		0			0
$190$	0.138472	+	0.100606i	0.0100458	+	0.00729873i
$191$	−5.55938	+	12.4866i	−0.402263	+	0.903497i	0.592902	+	0.805275i	$0.297982\pi$
$191$	−5.55938	+	12.4866i	−0.402263	+	0.903497i	−0.995165	+	0.0982221i	$0.968684\pi$
$192$		0			0
$193$	18.6045	−	16.7516i	1.33918	−	1.20581i	0.379345	−	0.925255i	$-0.376149\pi$
$193$	18.6045	−	16.7516i	1.33918	−	1.20581i	0.959839	−	0.280552i	$-0.0905174\pi$
$194$	−0.217870	−	2.07289i	−0.0156421	−	0.148825i
$195$		0			0
$196$	−7.08662	+	7.87049i	−0.506187	+	0.562178i
$197$	21.0442			1.49934			0.749668	−	0.661814i	$-0.230213\pi$
$197$	21.0442			1.49934			0.749668	+	0.661814i	$0.230213\pi$
$198$		0			0
$199$	−10.3709			−0.735176			−0.367588	−	0.929989i	$-0.619816\pi$
$199$	−10.3709			−0.735176			−0.367588	+	0.929989i	$0.619816\pi$
$200$	8.11759	−	9.01550i	0.574000	−	0.637492i
$201$		0			0
$202$	−0.500167	−	4.75877i	−0.0351916	−	0.334826i
$203$	−1.02650	+	0.924269i	−0.0720465	+	0.0648710i
$204$		0			0
$205$	−0.156659	+	0.351862i	−0.0109416	+	0.0245751i
$206$	7.30540	+	5.30768i	0.508991	+	0.369804i
$207$		0			0
$208$			3.18062i			0.220537i
$209$	19.9687	−	4.90886i	1.38126	−	0.339553i
$210$		0			0
$211$	3.89702	−	18.3340i	0.268282	−	1.26217i	−0.613192	−	0.789934i	$-0.710115\pi$
$211$	3.89702	−	18.3340i	0.268282	−	1.26217i	0.881474	−	0.472233i	$-0.156552\pi$
$212$	−5.56704	−	12.5038i	−0.382346	−	0.858763i
$213$		0			0
$214$	0.921325	−	0.195834i	0.0629805	−	0.0133869i
$215$	−0.0127867	+	0.0393535i	−0.000872048	+	0.00268389i
$216$		0			0
$217$	−0.696069	+	0.958057i	−0.0472523	+	0.0650372i
$218$	3.75673	+	3.38258i	0.254438	+	0.229097i
$219$		0			0
$220$	0.0275933	+	0.201147i	0.00186034	+	0.0135613i
$221$	8.52324	+	4.92090i	0.573335	+	0.331015i
$222$		0			0
$223$	−1.01068	+	9.61597i	−0.0676801	+	0.643933i	0.907123	+	0.420866i	$0.138274\pi$
$223$	−1.01068	+	9.61597i	−0.0676801	+	0.643933i	−0.974803	+	0.223067i	$0.928393\pi$
$224$	−0.842323	−	1.15936i	−0.0562801	−	0.0774629i
$225$		0			0
$226$	−0.345986	−	0.112418i	−0.0230146	−	0.00747791i
$227$	10.7033	+	4.76540i	0.710401	+	0.316291i	0.729933	−	0.683518i	$-0.239551\pi$
$227$	10.7033	+	4.76540i	0.710401	+	0.316291i	−0.0195325	+	0.999809i	$0.506218\pi$
$228$		0			0
$229$	−20.0326	−	4.25807i	−1.32379	−	0.281381i	−0.508817	−	0.860875i	$-0.669917\pi$
$229$	−20.0326	−	4.25807i	−1.32379	−	0.281381i	−0.814977	+	0.579494i	$0.803250\pi$
$230$	−0.0938599	+	0.162570i	−0.00618894	+	0.0107196i
$231$		0			0
$232$	6.79068	+	11.7618i	0.445830	+	0.772201i
$233$	4.98842	+	15.3528i	0.326802	+	1.00579i	0.970621	+	0.240615i	$0.0773492\pi$
$233$	4.98842	+	15.3528i	0.326802	+	1.00579i	−0.643818	+	0.765178i	$0.722651\pi$
$234$		0			0
$235$	0.361031	−	0.262304i	0.0235510	−	0.0171108i
$236$	0.884807	+	4.16269i	0.0575960	+	0.270968i
$237$		0			0
$238$	−0.722562	+	0.0759444i	−0.0468368	+	0.00492274i
$239$	−25.9333	+	11.5462i	−1.67749	+	0.746865i	−0.677550	+	0.735476i	$0.736958\pi$
$239$	−25.9333	+	11.5462i	−1.67749	+	0.746865i	−0.999935	+	0.0113883i	$0.996375\pi$
$240$		0			0
$241$	−12.4408	+	7.18270i	−0.801383	+	0.462679i	−0.843954	−	0.536415i	$-0.819778\pi$
$241$	−12.4408	+	7.18270i	−0.801383	+	0.462679i	0.0425716	+	0.999093i	$0.486445\pi$
$242$	−6.39414	−	4.05439i	−0.411031	−	0.260626i
$243$		0			0
$244$	12.3157	−	4.00162i	0.788433	−	0.256177i
$245$	−0.276793	−	0.0290921i	−0.0176836	−	0.00185862i
$246$		0			0
$247$	9.54817	+	10.6043i	0.607535	+	0.674737i
$248$	7.79114	+	8.65294i	0.494738	+	0.549462i
$249$		0			0
$250$	0.274508	+	0.0288520i	0.0173614	+	0.00182476i
$251$	6.60298	−	2.14544i	0.416776	−	0.135419i	−0.0931196	−	0.995655i	$-0.529684\pi$
$251$	6.60298	−	2.14544i	0.416776	−	0.135419i	0.509896	+	0.860236i	$0.329684\pi$
$252$		0			0
$253$	7.64348	+	21.2178i	0.480542	+	1.33395i
$254$	−7.61303	+	4.39538i	−0.477684	+	0.275791i
$255$		0			0
$256$	−9.01825	+	4.01518i	−0.563641	+	0.250949i
$257$	10.3612	−	1.08901i	0.646315	−	0.0679305i	0.224301	−	0.974520i	$-0.427990\pi$
$257$	10.3612	−	1.08901i	0.646315	−	0.0679305i	0.422014	+	0.906589i	$0.361323\pi$
$258$		0			0
$259$	−0.206873	−	0.973263i	−0.0128545	−	0.0604756i
$260$	−0.113983	+	0.0828133i	−0.00706891	+	0.00513586i
$261$		0			0
$262$	−3.86110	−	11.8833i	−0.238540	−	0.734150i
$263$	2.13055	+	3.69022i	0.131375	+	0.227549i	0.924207	−	0.381892i	$-0.124727\pi$
$263$	2.13055	+	3.69022i	0.131375	+	0.227549i	−0.792832	+	0.609441i	$0.791394\pi$
$264$		0			0
$265$	0.179843	−	0.311497i	0.0110477	−	0.0191351i
$266$	−1.03039	−	0.219016i	−0.0631771	−	0.0134287i
$267$		0			0
$268$	−11.0790	−	4.93268i	−0.676756	−	0.301311i
$269$	−10.5223	−	3.41889i	−0.641553	−	0.208453i	−0.0298672	−	0.999554i	$-0.509508\pi$
$269$	−10.5223	−	3.41889i	−0.641553	−	0.208453i	−0.611686	+	0.791101i	$0.709508\pi$
$270$		0			0
$271$	9.34327	+	12.8599i	0.567563	+	0.781184i	0.992263	−	0.124150i	$-0.0396205\pi$
$271$	9.34327	+	12.8599i	0.567563	+	0.781184i	−0.424700	+	0.905334i	$0.639621\pi$
$272$	0.617719	−	5.87720i	0.0374547	−	0.356358i
$273$		0			0
$274$	−9.58074	−	5.53144i	−0.578794	−	0.334167i
$275$	11.9630	−	11.4765i	0.721395	−	0.692060i
$276$		0			0
$277$	−8.42804	−	7.58864i	−0.506392	−	0.455957i	0.375900	−	0.926660i	$-0.377334\pi$
$277$	−8.42804	−	7.58864i	−0.506392	−	0.455957i	−0.882292	+	0.470703i	$0.844000\pi$
$278$	1.56054	−	2.14790i	0.0935949	−	0.128822i
$279$		0			0
$280$	0.00742570	−	0.0228539i	0.000443770	−	0.00136578i
$281$	−1.52620	+	0.324404i	−0.0910454	+	0.0193523i	−0.253209	−	0.967412i	$-0.581486\pi$
$281$	−1.52620	+	0.324404i	−0.0910454	+	0.0193523i	0.162164	+	0.986764i	$0.448153\pi$
$282$		0			0
$283$	10.8051	+	24.2687i	0.642299	+	1.44263i	0.881750	+	0.471718i	$0.156366\pi$
$283$	10.8051	+	24.2687i	0.642299	+	1.44263i	−0.239451	+	0.970908i	$0.576967\pi$
$284$	−1.05622	+	4.96913i	−0.0626752	+	0.294863i
$285$		0			0
$286$	0.383777	−	5.23989i	0.0226932	−	0.309841i
$287$		−	2.37046i		−	0.139924i
$288$		0			0
$289$	−1.04038	−	0.755878i	−0.0611986	−	0.0444634i
$290$	−0.0628322	+	0.141123i	−0.00368963	+	0.00828705i
$291$		0			0
$292$	13.4448	−	12.1058i	0.786798	−	0.708436i
$293$	2.75271	+	26.1903i	0.160815	+	1.53005i	0.715867	+	0.698237i	$0.246032\pi$
$293$	2.75271	+	26.1903i	0.160815	+	1.53005i	−0.555052	+	0.831816i	$0.687302\pi$
$294$		0			0
$295$	−0.0748329	+	0.0831103i	−0.00435694	+	0.00483887i
$296$	−9.78322			−0.568638
$297$		0			0
$298$	−7.06874			−0.409481
$299$	−10.4719	+	11.6302i	−0.605604	+	0.672592i
$300$		0			0
$301$	−0.0266197	−	0.253269i	−0.00153433	−	0.0145982i
$302$	4.48607	−	4.03927i	0.258144	−	0.232434i
$303$		0			0
$304$	3.48502	−	7.82747i	0.199879	−	0.448936i
$305$	0.275310	+	0.200025i	0.0157642	+	0.0114534i
$306$		0			0
$307$		−	26.0083i		−	1.48437i	−0.670195	−	0.742185i	$-0.733789\pi$
$307$		−	26.0083i		−	1.48437i	0.670195	−	0.742185i	$-0.266211\pi$
$308$	−0.658662	−	1.06186i	−0.0375307	−	0.0605048i
$309$		0			0
$310$	−0.0275356	+	0.129545i	−0.00156392	+	0.00735765i
$311$	−5.41967	−	12.1728i	−0.307321	−	0.690255i	0.692183	−	0.721722i	$-0.256649\pi$
$311$	−5.41967	−	12.1728i	−0.307321	−	0.690255i	−0.999505	+	0.0314665i	$0.989982\pi$
$312$		0			0
$313$	11.0025	−	2.33866i	0.621899	−	0.132189i	0.113823	−	0.993501i	$-0.463690\pi$
$313$	11.0025	−	2.33866i	0.621899	−	0.132189i	0.508076	+	0.861312i	$0.330357\pi$
$314$	2.77158	−	8.53004i	0.156409	−	0.481378i
$315$		0			0
$316$	−2.70120	+	3.71788i	−0.151954	+	0.209147i
$317$	−8.13939	−	7.32874i	−0.457154	−	0.411623i	0.408116	−	0.912930i	$-0.366186\pi$
$317$	−8.13939	−	7.32874i	−0.457154	−	0.411623i	−0.865269	+	0.501307i	$0.832853\pi$
$318$		0			0
$319$	8.08067	+	16.7074i	0.452430	+	0.935437i
$320$	−0.0427888	−	0.0247041i	−0.00239196	−	0.00138100i
$321$		0			0
$322$	0.120763	−	1.14899i	0.00672988	−	0.0640305i
$323$	−15.5837	−	21.4492i	−0.867103	−	1.19346i
$324$		0			0
$325$	10.9409	+	3.55490i	0.606890	+	0.197191i
$326$	5.77083	+	2.56934i	0.319616	+	0.142302i
$327$		0			0
$328$	−22.7979	−	4.84583i	−1.25880	−	0.267566i
$329$	−1.37324	+	2.37852i	−0.0757093	+	0.131132i
$330$		0			0
$331$	−2.11643	−	3.66576i	−0.116329	−	0.201488i	0.801981	−	0.597349i	$-0.203779\pi$
$331$	−2.11643	−	3.66576i	−0.116329	−	0.201488i	−0.918310	+	0.395861i	$0.870446\pi$
$332$	2.49676	+	7.68424i	0.137027	+	0.421727i
$333$		0			0
$334$	−4.23718	+	3.07849i	−0.231848	+	0.168447i
$335$	−0.0662613	−	0.311735i	−0.00362024	−	0.0170319i
$336$		0			0
$337$	2.64780	−	0.278295i	0.144235	−	0.0151597i	−0.0321359	−	0.999484i	$-0.510231\pi$
$337$	2.64780	−	0.278295i	0.144235	−	0.0151597i	0.176371	+	0.984324i	$0.443564\pi$
$338$	−4.84353	+	2.15648i	−0.263453	+	0.117297i
$339$		0			0
$340$	0.226702	−	0.130887i	0.0122947	−	0.00709832i
$341$	9.75446	+	12.5704i	0.528233	+	0.680723i
$342$		0			0
$343$	3.27243	−	1.06328i	0.176694	−	0.0574115i
$344$	−2.49022	−	0.261733i	−0.134264	−	0.0141117i
$345$		0			0
$346$	7.65464	+	8.50134i	0.411516	+	0.457035i
$347$	−11.1097	−	12.3386i	−0.596399	−	0.662368i	0.367068	−	0.930194i	$-0.380362\pi$
$347$	−11.1097	−	12.3386i	−0.596399	−	0.662368i	−0.963467	+	0.267826i	$0.913695\pi$
$348$		0			0
$349$	13.6993	+	1.43985i	0.733307	+	0.0770736i	0.463819	−	0.885930i	$-0.346479\pi$
$349$	13.6993	+	1.43985i	0.733307	+	0.0770736i	0.269488	+	0.963004i	$0.413146\pi$
$350$	−0.807679	+	0.262431i	−0.0431722	+	0.0140275i
$351$		0			0
$352$	−18.1147	+	6.52564i	−0.965517	+	0.347818i
$353$	−9.54783	+	5.51244i	−0.508180	+	0.293398i	−0.732085	−	0.681213i	$-0.761453\pi$
$353$	−9.54783	+	5.51244i	−0.508180	+	0.293398i	0.223905	+	0.974611i	$0.428119\pi$
$354$		0			0
$355$	−0.121960	+	0.0543001i	−0.00647297	+	0.00288195i
$356$	−12.9692	+	1.36312i	−0.687368	+	0.0722453i
$357$		0			0
$358$	−1.00885	−	4.74627i	−0.0533195	−	0.250848i
$359$	−15.3828	+	11.1763i	−0.811875	+	0.589862i	−0.914374	−	0.404871i	$-0.867316\pi$
$359$	−15.3828	+	11.1763i	−0.811875	+	0.589862i	0.102499	+	0.994733i	$0.467316\pi$
$360$		0			0
$361$	−6.00743	−	18.4890i	−0.316180	−	0.973103i
$362$	−7.26960	−	12.5913i	−0.382082	−	0.661785i
$363$		0			0
$364$	0.433553	−	0.750936i	0.0227243	−	0.0393597i
$365$	0.465047	+	0.0988489i	0.0243417	+	0.00517399i
$366$		0			0
$367$	−5.20463	−	2.31725i	−0.271680	−	0.120960i	0.266375	−	0.963869i	$-0.414174\pi$
$367$	−5.20463	−	2.31725i	−0.271680	−	0.120960i	−0.538055	+	0.842910i	$0.680841\pi$
$368$	8.93722	+	2.90388i	0.465885	+	0.151375i
$369$		0			0
$370$	−0.0654073	−	0.0900254i	−0.00340036	−	0.00468020i
$371$	−0.231392	+	2.20155i	−0.0120133	+	0.114299i
$372$		0			0
$373$	−19.1906	−	11.0797i	−0.993651	−	0.573684i	−0.0872871	−	0.996183i	$-0.527820\pi$
$373$	−19.1906	−	11.0797i	−0.993651	−	0.573684i	−0.906364	+	0.422499i	$0.861153\pi$
$374$	−1.72680	+	9.60780i	−0.0892909	+	0.496808i
$375$		0			0
$376$	20.0681	+	18.0694i	1.03493	+	0.931859i
$377$	−7.56992	+	10.4191i	−0.389871	+	0.536611i
$378$		0			0
$379$	−0.117844	+	0.362687i	−0.00605325	+	0.0186300i	−0.954038	−	0.299687i	$-0.903118\pi$
$379$	−0.117844	+	0.362687i	−0.00605325	+	0.0186300i	0.947984	+	0.318317i	$0.103118\pi$
$380$	0.371249	−	0.0789113i	0.0190447	−	0.00404807i
$381$		0			0
$382$	−3.82647	−	8.59440i	−0.195779	−	0.439728i
$383$	2.63308	−	12.3877i	0.134544	−	0.632981i	−0.858258	−	0.513218i	$-0.828453\pi$
$383$	2.63308	−	12.3877i	0.134544	−	0.632981i	0.992803	−	0.119763i	$-0.0382135\pi$
$384$		0			0
$385$	0.0124013	−	0.0304053i	0.000632031	−	0.00154960i
$386$			17.2313i			0.877049i
$387$		0			0
$388$	−3.73917	−	2.71667i	−0.189828	−	0.137918i
$389$	9.67976	−	21.7411i	0.490783	−	1.10232i	−0.483161	−	0.875531i	$-0.660511\pi$
$389$	9.67976	−	21.7411i	0.490783	−	1.10232i	0.973945	−	0.226786i	$-0.0728219\pi$
$390$		0			0
$391$	21.6088	−	19.4567i	1.09281	−	0.983966i
$392$	−1.76044	−	16.7495i	−0.0889157	−	0.845976i
$393$		0			0
$394$	−9.69204	+	10.7641i	−0.488278	+	0.542288i
$395$	−0.120768			−0.00607647
$396$		0			0
$397$	5.00497			0.251192			0.125596	−	0.992081i	$-0.459916\pi$
$397$	5.00497			0.251192			0.125596	+	0.992081i	$0.459916\pi$
$398$	4.77641	−	5.30474i	0.239420	−	0.265902i
$399$		0			0
$400$	−0.722042	−	6.86977i	−0.0361021	−	0.343488i
$401$	3.15402	−	2.83989i	0.157504	−	0.141817i	−0.586611	−	0.809869i	$-0.699538\pi$
$401$	3.15402	−	2.83989i	0.157504	−	0.141817i	0.744115	+	0.668052i	$0.232871\pi$
$402$		0			0
$403$	−4.49089	+	10.0867i	−0.223707	+	0.502455i
$404$	−8.58407	−	6.23669i	−0.427073	−	0.310287i
$405$		0			0
$406$		−	0.950735i		−	0.0471842i
$407$	−13.3331	−	0.976535i	−0.660897	−	0.0484051i
$408$		0			0
$409$	2.45452	−	11.5476i	0.121368	−	0.570992i	−0.874872	−	0.484354i	$-0.839055\pi$
$409$	2.45452	−	11.5476i	0.121368	−	0.570992i	0.996240	−	0.0866372i	$-0.0276121\pi$
$410$	−0.107827	−	0.242184i	−0.00532520	−	0.0119606i
$411$		0			0
$412$	19.5860	−	4.16313i	0.964933	−	0.205103i
$413$	0.212694	−	0.654604i	0.0104660	−	0.0322109i
$414$		0			0
$415$	−0.124803	+	0.171777i	−0.00612634	+	0.00843218i
$416$	−9.92930	−	8.94039i	−0.486824	−	0.438338i
$417$		0			0
$418$	−6.68582	+	12.4748i	−0.327014	+	0.610162i
$419$	−18.1688	−	10.4898i	−0.887604	−	0.512459i	−0.0144463	−	0.999896i	$-0.504599\pi$
$419$	−18.1688	−	10.4898i	−0.887604	−	0.512459i	−0.873158	+	0.487437i	$0.837932\pi$
$420$		0			0
$421$	0.290566	−	2.76455i	0.0141613	−	0.134736i	−0.985157	−	0.171656i	$-0.945088\pi$
$421$	0.290566	−	2.76455i	0.0141613	−	0.134736i	0.999318	+	0.0369204i	$0.0117548\pi$
$422$	7.58306	+	10.4372i	0.369137	+	0.508074i
$423$		0			0
$424$	20.7003	+	6.72593i	1.00529	+	0.326640i
$425$	−19.5263	−	8.69366i	−0.947164	−	0.421704i
$426$		0			0
$427$	−2.04861	−	0.435446i	−0.0991394	−	0.0210727i
$428$	1.04432	−	1.80881i	0.0504791	−	0.0874324i
$429$		0			0
$430$	−0.0142403	−	0.0246649i	−0.000686729	−	0.00118945i
$431$	−8.63060	−	26.5623i	−0.415722	−	1.27946i	−0.911604	−	0.411070i	$-0.865155\pi$
$431$	−8.63060	−	26.5623i	−0.415722	−	1.27946i	0.495882	−	0.868390i	$-0.334845\pi$
$432$		0			0
$433$	7.41714	−	5.38887i	0.356445	−	0.258973i	−0.395123	−	0.918628i	$-0.629298\pi$
$433$	7.41714	−	5.38887i	0.356445	−	0.258973i	0.751568	+	0.659656i	$0.229298\pi$
$434$	−0.169467	−	0.797279i	−0.00813467	−	0.0382706i
$435$		0			0
$436$	11.1482	−	1.17173i	0.533904	−	0.0561156i
$437$	38.5144	−	17.1477i	1.84239	−	0.820286i
$438$		0			0
$439$	−2.53842	+	1.46556i	−0.121152	+	0.0699472i	−0.559351	−	0.828931i	$-0.688950\pi$
$439$	−2.53842	+	1.46556i	−0.121152	+	0.0699472i	0.438199	+	0.898878i	$0.355616\pi$
$440$	−0.267071	−	0.181426i	−0.0127321	−	0.00864913i
$441$		0			0
$442$	−6.44247	+	2.09329i	−0.306437	+	0.0995675i
$443$	−35.6451	−	3.74645i	−1.69355	−	0.177999i	−0.791953	−	0.610582i	$-0.790936\pi$
$443$	−35.6451	−	3.74645i	−1.69355	−	0.177999i	−0.901594	+	0.432583i	$0.857602\pi$
$444$		0			0
$445$	−0.229310	−	0.254674i	−0.0108703	−	0.0120727i
$446$	−4.45309	−	4.94566i	−0.210860	−	0.234184i
$447$		0			0
$448$	0.302416	+	0.0317852i	0.0142878	+	0.00150171i
$449$	−13.5184	+	4.39241i	−0.637974	+	0.207290i	−0.610104	−	0.792321i	$-0.708872\pi$
$449$	−13.5184	+	4.39241i	−0.637974	+	0.207290i	−0.0278700	+	0.999612i	$0.508872\pi$
$450$		0			0
$451$	−30.5864	−	8.87978i	−1.44026	−	0.418132i
$452$	−0.698615	+	0.403345i	−0.0328601	+	0.0189718i
$453$		0			0
$454$	−7.36696	+	3.27998i	−0.345749	+	0.153937i
$455$	0.0226620	−	0.00238187i	0.00106241	−	0.000111664i
$456$		0			0
$457$	−4.24125	−	19.9535i	−0.198397	−	0.933386i	−0.958833	−	0.283972i	$-0.908348\pi$
$457$	−4.24125	−	19.9535i	−0.198397	−	0.933386i	0.760435	−	0.649414i	$-0.224986\pi$
$458$	11.4042	−	8.28561i	0.532882	−	0.387161i
$459$		0			0
$460$	0.128631	+	0.395887i	0.00599747	+	0.0184583i
$461$	0.385177	+	0.667146i	0.0179395	+	0.0310721i	0.874856	−	0.484383i	$-0.160956\pi$
$461$	0.385177	+	0.667146i	0.0179395	+	0.0310721i	−0.856916	+	0.515456i	$0.827623\pi$
$462$		0			0
$463$	−18.8974	+	32.7312i	−0.878236	+	1.52115i	−0.0249608	+	0.999688i	$0.507946\pi$
$463$	−18.8974	+	32.7312i	−0.878236	+	1.52115i	−0.853275	+	0.521461i	$0.825387\pi$
$464$	7.56414	+	1.60781i	0.351156	+	0.0746406i
$465$		0			0
$466$	−10.1504	−	4.51925i	−0.470208	−	0.209350i
$467$	16.7411	+	5.43950i	0.774684	+	0.251710i	0.669569	−	0.742750i	$-0.266479\pi$
$467$	16.7411	+	5.43950i	0.774684	+	0.251710i	0.105115	+	0.994460i	$0.466479\pi$
$468$		0			0
$469$	1.15290	+	1.58683i	0.0532358	+	0.0732728i
$470$	−0.0321065	+	0.305473i	−0.00148096	+	0.0140904i
$471$		0			0
$472$	−5.86083	−	3.38375i	−0.269766	−	0.155750i
$473$	−3.36768	−	0.605271i	−0.154846	−	0.0278304i
$474$		0			0
$475$	−23.0302	−	20.7365i	−1.05670	−	0.951456i
$476$	−0.946967	+	1.30339i	−0.0434042	+	0.0597407i
$477$		0			0
$478$	6.03785	−	18.5826i	0.276165	−	0.849948i
$479$	−2.35329	+	0.500206i	−0.107524	+	0.0228550i	−0.261360	−	0.965242i	$-0.584171\pi$
$479$	−2.35329	+	0.500206i	−0.107524	+	0.0228550i	0.153835	+	0.988097i	$0.450838\pi$
$480$		0			0
$481$	−3.77333	−	8.47503i	−0.172049	−	0.386428i
$482$	2.05574	−	9.67152i	0.0936366	−	0.440525i
$483$		0			0
$484$	−16.1686	+	4.52108i	−0.734937	+	0.205504i
$485$		−	0.121459i		−	0.00551517i
$486$		0			0
$487$	−11.8099	−	8.58039i	−0.535157	−	0.388815i	0.287126	−	0.957893i	$-0.407300\pi$
$487$	−11.8099	−	8.58039i	−0.535157	−	0.388815i	−0.822283	+	0.569078i	$0.807300\pi$
$488$	−8.37578	+	18.8123i	−0.379154	+	0.851593i
$489$		0			0
$490$	0.142359	−	0.128181i	0.00643114	−	0.00579062i
$491$	−2.61764	−	24.9052i	−0.118132	−	1.12396i	−0.879587	−	0.475737i	$-0.842181\pi$
$491$	−2.61764	−	24.9052i	−0.118132	−	1.12396i	0.761455	−	0.648218i	$-0.224485\pi$
$492$		0			0
$493$	16.0113	−	17.7824i	0.721114	−	0.800879i
$494$	−9.82158			−0.441894
$495$		0			0
$496$	6.62982			0.297688
$497$	0.549780	−	0.610593i	0.0246610	−	0.0273888i
$498$		0			0
$499$	−2.37400	−	22.5871i	−0.106275	−	1.01114i	−0.909568	−	0.415555i	$-0.863587\pi$
$499$	−2.37400	−	22.5871i	−0.106275	−	1.01114i	0.803293	−	0.595584i	$-0.203079\pi$
$500$	0.454852	−	0.409550i	0.0203416	−	0.0183156i
$501$		0			0
$502$	−1.94365	+	4.36552i	−0.0867496	+	0.194843i
$503$	−8.41953	−	6.11715i	−0.375408	−	0.272750i	0.384042	−	0.923316i	$-0.374532\pi$
$503$	−8.41953	−	6.11715i	−0.375408	−	0.272750i	−0.759450	+	0.650566i	$0.774532\pi$
$504$		0			0
$505$		−	0.278835i		−	0.0124080i
$506$	−14.3731	−	5.86234i	−0.638964	−	0.260613i
$507$		0			0
$508$	−4.05285	+	19.0672i	−0.179816	+	0.845969i
$509$	3.28867	+	7.38647i	0.145768	+	0.327399i	0.971643	−	0.236454i	$-0.0759851\pi$
$509$	3.28867	+	7.38647i	0.145768	+	0.327399i	−0.825875	+	0.563853i	$0.809318\pi$
$510$		0			0
$511$	−2.86212	+	0.608363i	−0.126613	+	0.0269124i
$512$	−4.55217	+	14.0102i	−0.201180	+	0.619167i
$513$		0			0
$514$	−4.21490	+	5.80132i	−0.185911	+	0.255885i
$515$	0.391045	+	0.352098i	0.0172315	+	0.0155153i
$516$		0			0
$517$	25.5462	+	26.6291i	1.12352	+	1.17115i
$518$	0.593101	+	0.342427i	0.0260594	+	0.0150454i
$519$		0			0
$520$	0.0234193	−	0.222820i	0.00102701	−	0.00977131i
$521$	20.5846	+	28.3323i	0.901828	+	1.24126i	0.969881	+	0.243578i	$0.0783211\pi$
$521$	20.5846	+	28.3323i	0.901828	+	1.24126i	−0.0680535	+	0.997682i	$0.521679\pi$
$522$		0			0
$523$	41.1766	+	13.3791i	1.80052	+	0.585026i	0.999900	−	0.0141400i	$-0.00450104\pi$
$523$	41.1766	+	13.3791i	1.80052	+	0.585026i	0.800625	+	0.599166i	$0.204501\pi$
$524$	−25.3113	−	11.2693i	−1.10573	−	0.492302i
$525$		0			0
$526$	−2.86879	−	0.609779i	−0.125085	−	0.0265876i
$527$	10.2573	−	17.7662i	0.446815	−	0.773906i
$528$		0			0
$529$	11.6189	+	20.1245i	0.505170	+	0.874980i
$530$	0.0765028	+	0.235452i	0.00332307	+	0.0102274i
$531$		0			0
$532$	−1.88977	+	1.37300i	−0.0819319	+	0.0595270i
$533$	−4.59513	−	21.6184i	−0.199037	−	0.936396i
$534$		0			0
$535$	0.0545871	−	0.00573733i	0.00236000	−	0.000248046i
$536$	17.6181	−	7.84407i	0.760984	−	0.338812i
$537$		0			0
$538$	6.59486	−	3.80754i	0.284324	−	0.164155i
$539$	−0.727333	−	23.0028i	−0.0313284	−	0.990800i
$540$		0			0
$541$	−0.215252	+	0.0699396i	−0.00925440	+	0.00300694i	−0.313641	−	0.949542i	$-0.601549\pi$
$541$	−0.215252	+	0.0699396i	−0.00925440	+	0.00300694i	0.304386	+	0.952549i	$0.401549\pi$
$542$	−10.8809	−	1.14363i	−0.467377	−	0.0491233i
$543$		0			0
$544$	16.6112	+	18.4486i	0.712198	+	0.790976i
$545$	0.197113	+	0.218916i	0.00844338	+	0.00937733i
$546$		0			0
$547$	16.3731	+	1.72088i	0.700062	+	0.0735795i	0.447871	−	0.894098i	$-0.352182\pi$
$547$	16.3731	+	1.72088i	0.700062	+	0.0735795i	0.252191	+	0.967678i	$0.418849\pi$
$548$	−23.3308	+	7.58064i	−0.996643	+	0.323829i
$549$		0			0
$550$	0.360607	+	11.4046i	0.0153763	+	0.486296i
$551$	30.0457	−	17.3469i	1.27999	−	0.739003i
$552$		0			0
$553$	0.679002	−	0.302311i	0.0288741	−	0.0128556i
$554$	7.76318	−	0.815943i	0.329826	−	0.0346661i
$555$		0			0
$556$	−1.22402	−	5.75858i	−0.0519102	−	0.244218i
$557$	21.2624	−	15.4481i	0.900919	−	0.654556i	−0.0377832	−	0.999286i	$-0.512030\pi$
$557$	21.2624	−	15.4481i	0.900919	−	0.654556i	0.938702	+	0.344730i	$0.112030\pi$
$558$		0			0
$559$	−0.733729	−	2.25818i	−0.0310334	−	0.0955110i
$560$	−0.00684126	−	0.0118494i	−0.000289096	−	0.000500729i
$561$		0			0
$562$	0.536969	−	0.930057i	0.0226507	−	0.0392321i
$563$	−35.5711	−	7.56087i	−1.49914	−	0.318653i	−0.615996	−	0.787750i	$-0.711246\pi$
$563$	−35.5711	−	7.56087i	−1.49914	−	0.318653i	−0.883147	+	0.469097i	$0.844579\pi$
$564$		0			0
$565$	−0.0193664	−	0.00862248i	−0.000814751	−	0.000362750i
$566$	−17.3898	−	5.65030i	−0.730949	−	0.237500i
$567$		0			0
$568$	−4.74846	−	6.53570i	−0.199241	−	0.274232i
$569$	−2.11468	+	20.1198i	−0.0886520	+	0.843468i	0.856348	+	0.516399i	$0.172728\pi$
$569$	−2.11468	+	20.1198i	−0.0886520	+	0.843468i	−0.945000	+	0.327069i	$0.893939\pi$
$570$		0			0
$571$	−21.1312	−	12.2001i	−0.884313	−	0.510558i	−0.0122350	−	0.999925i	$-0.503895\pi$
$571$	−21.1312	−	12.2001i	−0.884313	−	0.510558i	−0.872078	+	0.489367i	$0.837228\pi$
$572$	−8.06533	−	8.40720i	−0.337228	−	0.351523i
$573$		0			0
$574$	1.21249	+	1.09173i	0.0506085	+	0.0455681i
$575$	19.9778	−	27.4971i	0.833132	−	1.14671i
$576$		0			0
$577$	−5.96494	+	18.3582i	−0.248324	+	0.764262i	0.746748	+	0.665107i	$0.231614\pi$
$577$	−5.96494	+	18.3582i	−0.248324	+	0.764262i	−0.995072	+	0.0991553i	$0.968386\pi$
$578$	0.865784	−	0.184028i	0.0360118	−	0.00765455i
$579$		0			0
$580$	0.139328	+	0.312935i	0.00578526	+	0.0129939i
$581$	0.271691	−	1.27821i	0.0112717	−	0.0530290i
$582$		0			0
$583$	27.5401	+	11.2327i	1.14059	+	0.465211i
$584$			28.7700i			1.19051i
$585$		0			0
$586$	−14.6641	−	10.6541i	−0.605769	−	0.440117i
$587$	7.78344	−	17.4819i	0.321257	−	0.721555i	−0.678660	−	0.734453i	$-0.737439\pi$
$587$	7.78344	−	17.4819i	0.321257	−	0.721555i	0.999917	+	0.0128978i	$0.00410562\pi$
$588$		0			0
$589$	22.1040	−	19.9026i	0.910781	−	0.820071i
$590$	−0.00804615	−	0.0765540i	−0.000331255	−	0.00315168i
$591$		0			0
$592$	−3.72739	+	4.13968i	−0.153195	+	0.170140i
$593$	−14.9885			−0.615503			−0.307751	−	0.951467i	$-0.599577\pi$
$593$	−14.9885			−0.615503			−0.307751	+	0.951467i	$0.599577\pi$
$594$		0			0
$595$	−0.0423378			−0.00173568
$596$	−10.4884	+	11.6485i	−0.429620	+	0.477142i
$597$		0			0
$598$	−1.12595	−	10.7127i	−0.0460437	−	0.438076i
$599$	−24.7771	+	22.3094i	−1.01236	+	0.911537i	−0.996091	−	0.0883306i	$-0.971847\pi$
$599$	−24.7771	+	22.3094i	−1.01236	+	0.911537i	−0.0162732	+	0.999868i	$0.505180\pi$
$600$		0			0
$601$	−17.1940	+	38.6183i	−0.701357	+	1.57527i	0.112133	+	0.993693i	$0.464232\pi$
$601$	−17.1940	+	38.6183i	−0.701357	+	1.57527i	−0.813490	+	0.581579i	$0.802435\pi$
$602$	0.141807	+	0.103029i	0.00577962	+	0.00419914i
$603$		0			0
$604$		−	13.3859i		−	0.544664i
$605$	−0.345868	−	0.273915i	−0.0140615	−	0.0111362i
$606$		0			0
$607$	6.42154	−	30.2110i	0.260642	−	1.22623i	−0.631824	−	0.775112i	$-0.717694\pi$
$607$	6.42154	−	30.2110i	0.260642	−	1.22623i	0.892467	−	0.451114i	$-0.148973\pi$
$608$	14.6399	+	32.8817i	0.593726	+	1.33353i
$609$		0			0
$610$	−0.229109	+	0.0486986i	−0.00927634	+	0.00197175i
$611$	−7.91306	+	24.3539i	−0.320128	+	0.985254i
$612$		0			0
$613$	−9.38958	+	12.9237i	−0.379242	+	0.521981i	−0.955383	−	0.295368i	$-0.904558\pi$
$613$	−9.38958	+	12.9237i	−0.379242	+	0.521981i	0.576142	+	0.817350i	$0.304558\pi$
$614$	13.3032	+	11.9783i	0.536875	+	0.483404i
$615$		0			0
$616$	1.95573	+	0.351502i	0.0787985	+	0.0141624i
$617$	−2.28088	−	1.31687i	−0.0918248	−	0.0530151i	0.453384	−	0.891315i	$-0.350216\pi$
$617$	−2.28088	−	1.31687i	−0.0918248	−	0.0530151i	−0.545209	+	0.838300i	$0.683550\pi$
$618$		0			0
$619$	−2.11664	+	20.1385i	−0.0850751	+	0.809436i	0.865910	+	0.500200i	$0.166740\pi$
$619$	−2.11664	+	20.1385i	−0.0850751	+	0.809436i	−0.950985	+	0.309236i	$0.899927\pi$
$620$	0.172619	+	0.237590i	0.00693255	+	0.00954184i
$621$		0			0
$622$	8.72244	+	2.83409i	0.349738	+	0.113637i
$623$	1.92678	+	0.857858i	0.0771949	+	0.0343694i
$624$		0			0
$625$	−24.4301	−	5.19278i	−0.977204	−	0.207711i
$626$	−3.87106	+	6.70487i	−0.154719	+	0.267980i
$627$		0			0
$628$	−9.94420	−	17.2239i	−0.396817	−	0.687307i
$629$	5.32645	+	16.3931i	0.212379	+	0.653636i
$630$		0			0
$631$	−6.82846	+	4.96116i	−0.271837	+	0.197501i	−0.715349	−	0.698767i	$-0.753732\pi$
$631$	−6.82846	+	4.96116i	−0.271837	+	0.197501i	0.443512	+	0.896268i	$0.353732\pi$
$632$	−1.51941	−	7.14828i	−0.0604390	−	0.284343i
$633$		0			0
$634$	7.49730	−	0.787998i	0.297756	−	0.0312954i
$635$	−0.467976	+	0.208356i	−0.0185711	+	0.00826837i
$636$		0			0
$637$	13.8308	−	7.98521i	0.547996	−	0.316385i
$638$	−12.2675	−	3.56146i	−0.485673	−	0.141000i
$639$		0			0
$640$	−0.410557	+	0.133398i	−0.0162287	+	0.00527302i
$641$	32.1374	+	3.37778i	1.26935	+	0.133414i	0.715152	−	0.698969i	$-0.246357\pi$
$641$	32.1374	+	3.37778i	1.26935	+	0.133414i	0.554200	+	0.832383i	$0.313024\pi$
$642$		0			0
$643$	9.21842	+	10.2381i	0.363539	+	0.403751i	0.896969	−	0.442093i	$-0.145764\pi$
$643$	9.21842	+	10.2381i	0.363539	+	0.403751i	−0.533430	+	0.845844i	$0.679097\pi$
$644$	−1.71422	−	1.90383i	−0.0675497	−	0.0750216i
$645$		0			0
$646$	18.1485	+	1.90748i	0.714042	+	0.0750488i
$647$	8.11003	−	2.63511i	0.318838	−	0.103597i	−0.145226	−	0.989399i	$-0.546391\pi$
$647$	8.11003	−	2.63511i	0.318838	−	0.103597i	0.464064	+	0.885802i	$0.346391\pi$
$648$		0			0
$649$	−7.64968	−	5.19656i	−0.300276	−	0.203983i
$650$	−6.85722	+	3.95902i	−0.268962	+	0.155285i
$651$		0			0
$652$	12.7966	−	5.69739i	0.501152	−	0.223127i
$653$	−1.20137	+	0.126269i	−0.0470132	+	0.00494129i	−0.128006	−	0.991773i	$-0.540858\pi$
$653$	−1.20137	+	0.126269i	−0.0470132	+	0.00494129i	0.0809927	+	0.996715i	$0.474191\pi$
$654$		0			0
$655$	−0.151382	−	0.712198i	−0.00591499	−	0.0278279i
$656$	−10.7364	+	7.80045i	−0.419186	+	0.304556i
$657$		0			0
$658$	−0.584160	−	1.79786i	−0.0227729	−	0.0700878i
$659$	4.70527	+	8.14977i	0.183291	+	0.317470i	0.942999	−	0.332794i	$-0.107991\pi$
$659$	4.70527	+	8.14977i	0.183291	+	0.317470i	−0.759708	+	0.650264i	$0.774658\pi$
$660$		0			0
$661$	−7.55133	+	13.0793i	−0.293713	+	0.508725i	−0.974685	−	0.223584i	$-0.928224\pi$
$661$	−7.55133	+	13.0793i	−0.293713	+	0.508725i	0.680972	+	0.732309i	$0.261558\pi$
$662$	2.84977	+	0.605737i	0.110759	+	0.0235426i
$663$		0			0
$664$	−11.7377	−	5.22596i	−0.455511	−	0.202807i
$665$	−0.0583807	−	0.0189690i	−0.00226391	−	0.000735588i
$666$		0			0
$667$	22.3653	+	30.7832i	0.865988	+	1.19193i
$668$	−1.21397	+	11.5502i	−0.0469700	+	0.446889i
$669$		0			0
$670$	0.189970	+	0.109679i	0.00733916	+	0.00423727i
$671$	−13.2927	+	24.8023i	−0.513161	+	0.957484i
$672$		0			0
$673$	−30.9140	−	27.8351i	−1.19165	−	1.07296i	−0.995727	−	0.0923433i	$-0.970564\pi$
$673$	−30.9140	−	27.8351i	−1.19165	−	1.07296i	−0.195919	−	0.980620i	$-0.562769\pi$
$674$	−1.07711	+	1.48252i	−0.0414888	+	0.0571045i
$675$		0			0
$676$	−3.63303	+	11.1813i	−0.139732	+	0.430051i
$677$	4.42177	−	0.939877i	0.169943	−	0.0361224i	−0.122154	−	0.992511i	$-0.538980\pi$
$677$	4.42177	−	0.939877i	0.169943	−	0.0361224i	0.292097	+	0.956389i	$0.405647\pi$
$678$		0			0
$679$	0.304042	+	0.682890i	0.0116681	+	0.0262069i
$680$	−0.0865492	+	0.407182i	−0.00331901	+	0.0156147i
$681$		0			0
$682$	−10.9222	−	0.799960i	−0.418233	−	0.0306320i
$683$		−	34.7783i		−	1.33075i	−0.746507	−	0.665377i	$-0.768271\pi$
$683$		−	34.7783i		−	1.33075i	0.746507	−	0.665377i	$-0.231729\pi$
$684$		0			0
$685$	−0.521547	−	0.378926i	−0.0199273	−	0.0144780i
$686$	−0.963272	+	2.16354i	−0.0367779	+	0.0826045i
$687$		0			0
$688$	−1.05952	+	0.953996i	−0.0403938	+	0.0363707i
$689$	2.15741	+	20.5264i	0.0821909	+	0.781995i
$690$		0			0
$691$	−11.9664	+	13.2900i	−0.455223	+	0.505576i	−0.926441	−	0.376441i	$-0.877148\pi$
$691$	−11.9664	+	13.2900i	−0.455223	+	0.505576i	0.471218	+	0.882017i	$0.343815\pi$
$692$	25.3670			0.964308
$693$		0			0
$694$	11.4278			0.433794
$695$	0.103522	−	0.114973i	0.00392682	−	0.00436118i
$696$		0			0
$697$	4.29237	+	40.8392i	0.162585	+	1.54689i
$698$	−7.04579	+	6.34406i	−0.266687	+	0.240126i
$699$		0			0
$700$	−0.765950	+	1.72035i	−0.0289502	+	0.0650232i
$701$	−14.1345	−	10.2693i	−0.533852	−	0.387866i	0.287945	−	0.957647i	$-0.407028\pi$
$701$	−14.1345	−	10.2693i	−0.533852	−	0.387866i	−0.821797	+	0.569781i	$0.807028\pi$
$702$		0			0
$703$			24.9914i			0.942568i
$704$	1.54298	−	3.78304i	0.0581532	−	0.142579i
$705$		0			0
$706$	1.57770	−	7.42251i	0.0593776	−	0.279350i
$707$	0.697994	+	1.56772i	0.0262507	+	0.0589601i
$708$		0			0
$709$	−8.15627	+	1.73367i	−0.306315	+	0.0651093i	−0.358505	−	0.933528i	$-0.616713\pi$
$709$	−8.15627	+	1.73367i	−0.306315	+	0.0651093i	0.0521896	+	0.998637i	$0.483380\pi$
$710$	0.0283950	−	0.0873909i	0.00106565	−	0.00327972i
$711$		0			0
$712$	12.1893	−	16.7771i	0.456812	−	0.628747i
$713$	24.2424	+	21.8280i	0.907886	+	0.817464i
$714$		0			0
$715$	0.0541584	−	0.301333i	0.00202541	−	0.0112692i
$716$	−9.31824	−	5.37989i	−0.348239	−	0.201056i
$717$		0			0
$718$	1.36800	−	13.0156i	0.0510532	−	0.485739i
$719$	−13.8736	−	19.0953i	−0.517397	−	0.712136i	0.467748	−	0.883862i	$-0.345066\pi$
$719$	−13.8736	−	19.0953i	−0.517397	−	0.712136i	−0.985145	+	0.171726i	$0.945066\pi$
$720$		0			0
$721$	−3.08000	−	1.00075i	−0.114705	−	0.0372699i
$722$	12.2239	+	5.44241i	0.454925	+	0.202546i
$723$		0			0
$724$	−31.5355	−	6.70308i	−1.17201	−	0.249118i
$725$	13.9849	−	24.2225i	0.519384	−	0.899600i
$726$		0			0
$727$	−0.952312	−	1.64945i	−0.0353193	−	0.0611748i	0.847825	−	0.530275i	$-0.177911\pi$
$727$	−0.952312	−	1.64945i	−0.0353193	−	0.0611748i	−0.883145	+	0.469101i	$0.844578\pi$
$728$	0.426102	+	1.31141i	0.0157924	+	0.0486039i
$729$		0			0
$730$	−0.264742	+	0.192346i	−0.00979854	+	0.00711905i
$731$	0.917225	+	4.31521i	0.0339248	+	0.159604i
$732$		0			0
$733$	17.5153	−	1.84093i	0.646943	−	0.0679964i	0.224626	−	0.974445i	$-0.427884\pi$
$733$	17.5153	−	1.84093i	0.646943	−	0.0679964i	0.422316	+	0.906449i	$0.361217\pi$
$734$	3.58230	−	1.59494i	0.132225	−	0.0588704i
$735$		0			0
$736$	−34.1869	+	19.7378i	−1.26015	+	0.727545i
$737$	24.7938	−	8.93171i	0.913291	−	0.329004i
$738$		0			0
$739$	−4.54355	+	1.47629i	−0.167137	+	0.0543062i	−0.391390	−	0.920225i	$-0.628006\pi$
$739$	−4.54355	+	1.47629i	−0.167137	+	0.0543062i	0.224253	+	0.974531i	$0.428006\pi$
$740$	−0.245401	−	0.0257927i	−0.00902113	−	0.000948159i
$741$		0			0
$742$	−1.01952	−	1.13229i	−0.0374278	−	0.0415678i
$743$	1.22970	+	1.36573i	0.0451135	+	0.0501036i	0.765279	−	0.643698i	$-0.222601\pi$
$743$	1.22970	+	1.36573i	0.0451135	+	0.0501036i	−0.720166	+	0.693802i	$0.755934\pi$
$744$		0			0
$745$	−0.409660	−	0.0430570i	−0.0150088	−	0.00157749i
$746$	14.5056	−	4.71316i	0.531088	−	0.172561i
$747$		0			0
$748$	13.2704	+	17.1013i	0.485215	+	0.625287i
$749$	−0.292548	+	0.168902i	−0.0106895	+	0.00617156i
$750$		0			0
$751$	−34.6641	+	15.4334i	−1.26491	+	0.563174i	−0.925957	−	0.377629i	$-0.876740\pi$
$751$	−34.6641	+	15.4334i	−1.26491	+	0.563174i	−0.338953	+	0.940803i	$0.610073\pi$
$752$	15.2918	−	1.60723i	0.557635	−	0.0586098i
$753$		0			0
$754$	−1.84299	−	8.67060i	−0.0671179	−	0.315765i
$755$	0.284588	−	0.206765i	0.0103572	−	0.00752497i
$756$		0			0
$757$	−9.46409	−	29.1275i	−0.343978	−	1.05866i	−0.962128	−	0.272596i	$-0.912118\pi$
$757$	−9.46409	−	29.1275i	−0.343978	−	1.05866i	0.618150	−	0.786060i	$-0.287882\pi$
$758$	−0.131240	−	0.227315i	−0.00476687	−	0.00825646i
$759$		0			0
$760$	−0.301779	+	0.522697i	−0.0109467	+	0.0189602i
$761$	30.1908	+	6.41724i	1.09441	+	0.232625i	0.719540	−	0.694451i	$-0.244353\pi$
$761$	30.1908	+	6.41724i	1.09441	+	0.232625i	0.374874	+	0.927076i	$0.377686\pi$
$762$		0			0
$763$	−1.65625	−	0.737408i	−0.0599601	−	0.0266960i
$764$	−19.8402	−	6.44648i	−0.717794	−	0.233225i
$765$		0			0
$766$	5.12362	+	7.05205i	0.185124	+	0.254801i
$767$	0.670798	−	6.38222i	0.0242211	−	0.230449i
$768$		0			0
$769$	16.7276	+	9.65771i	0.603214	+	0.348266i	0.770305	−	0.637676i	$-0.220104\pi$
$769$	16.7276	+	9.65771i	0.603214	+	0.348266i	−0.167091	+	0.985942i	$0.553437\pi$
$770$	0.00984080	+	0.0203467i	0.000354638	+	0.000733243i
$771$		0			0
$772$	28.3953	+	25.5672i	1.02197	+	0.920185i
$773$	−1.72928	+	2.38015i	−0.0621980	+	0.0856082i	−0.838983	−	0.544158i	$-0.816849\pi$
$773$	−1.72928	+	2.38015i	−0.0621980	+	0.0856082i	0.776785	+	0.629766i	$0.216849\pi$
$774$		0			0
$775$	7.40997	−	22.8056i	0.266174	−	0.819200i
$776$	7.18920	−	1.52811i	0.258077	−	0.0548560i
$777$		0			0
$778$	6.66249	+	14.9642i	0.238862	+	0.536493i
$779$	−12.3787	+	58.2374i	−0.443515	+	2.08657i
$780$		0			0
$781$	−5.81908	−	9.38117i	−0.208223	−	0.335685i
$782$			20.0138i			0.715693i
$783$		0			0
$784$	−7.75811	−	5.63660i	−0.277075	−	0.201307i
$785$	0.212581	−	0.477465i	0.00758735	−	0.0170415i
$786$		0			0
$787$	5.97911	−	5.38362i	0.213132	−	0.191905i	−0.555649	−	0.831417i	$-0.687530\pi$
$787$	5.97911	−	5.38362i	0.213132	−	0.191905i	0.768781	+	0.639512i	$0.220863\pi$
$788$	3.35733	+	31.9429i	0.119600	+	1.13792i
$789$		0			0
$790$	0.0556203	−	0.0617726i	0.00197888	−	0.00219777i
$791$	0.130470			0.00463897
$792$		0			0
$793$	−19.5272			−0.693433
$794$	−2.30507	+	2.56004i	−0.0818039	+	0.0908524i
$795$		0			0
$796$	−1.65455	−	15.7420i	−0.0586440	−	0.557960i
$797$	40.8149	−	36.7499i	1.44574	−	1.30175i	0.567634	−	0.823281i	$-0.307859\pi$
$797$	40.8149	−	36.7499i	1.44574	−	1.30175i	0.878105	−	0.478468i	$-0.158808\pi$
$798$		0			0
$799$	19.3517	−	43.4647i	0.684615	−	1.53767i
$800$	23.4757	+	17.0561i	0.829991	+	0.603024i
$801$		0			0
$802$			2.92121i			0.103152i
$803$	−2.87174	+	39.2092i	−0.101342	+	1.38366i
$804$		0			0
$805$	0.0139974	−	0.0658524i	0.000493342	−	0.00232099i
$806$	−3.09104	−	6.94259i	−0.108877	−	0.244542i
$807$		0			0
$808$	16.5044	−	3.50811i	0.580621	−	0.123415i
$809$	7.52538	−	23.1607i	0.264578	−	0.814288i	−0.727212	−	0.686413i	$-0.759184\pi$
$809$	7.52538	−	23.1607i	0.264578	−	0.814288i	0.991790	−	0.127875i	$-0.0408156\pi$
$810$		0			0
$811$	−12.2026	+	16.7955i	−0.428493	+	0.589770i	−0.967607	−	0.252463i	$-0.918759\pi$
$811$	−12.2026	+	16.7955i	−0.428493	+	0.589770i	0.539114	+	0.842233i	$0.318759\pi$
$812$	−1.56671	−	1.41067i	−0.0549807	−	0.0495048i
$813$		0			0
$814$	6.64014	−	6.37012i	0.232737	−	0.223273i
$815$	0.318790	+	0.184054i	0.0111667	+	0.00644712i
$816$		0			0
$817$	−0.668601	+	6.36131i	−0.0233914	+	0.222554i
$818$	4.77615	+	6.57380i	0.166994	+	0.229848i
$819$		0			0
$820$	−0.559083	−	0.181657i	−0.0195240	−	0.00634374i
$821$	26.1615	+	11.6478i	0.913042	+	0.406513i	0.808830	−	0.588043i	$-0.200101\pi$
$821$	26.1615	+	11.6478i	0.913042	+	0.406513i	0.104212	+	0.994555i	$0.466768\pi$
$822$		0			0
$823$	−2.43348	−	0.517251i	−0.0848256	−	0.0180302i	0.165303	−	0.986243i	$-0.447140\pi$
$823$	−2.43348	−	0.517251i	−0.0848256	−	0.0180302i	−0.250129	+	0.968213i	$0.580473\pi$
$824$	−15.9210	+	27.5760i	−0.554634	+	0.960654i
$825$		0			0
$826$	0.236872	+	0.410275i	0.00824184	+	0.0142753i
$827$	−7.36490	−	22.6668i	−0.256103	−	0.788202i	−0.993610	−	0.112864i	$-0.963998\pi$
$827$	−7.36490	−	22.6668i	−0.256103	−	0.788202i	0.737508	−	0.675338i	$-0.236002\pi$
$828$		0			0
$829$	32.8736	−	23.8841i	1.14175	−	0.829528i	0.154386	−	0.988011i	$-0.450660\pi$
$829$	32.8736	−	23.8841i	1.14175	−	0.829528i	0.987362	+	0.158482i	$0.0506601\pi$
$830$	−0.0303849	−	0.142950i	−0.00105467	−	0.00496185i
$831$		0			0
$832$	2.81961	−	0.296353i	0.0977525	−	0.0102742i
$833$	−27.1075	+	12.0691i	−0.939221	+	0.418168i
$834$		0			0
$835$	−0.264312	+	0.152600i	−0.00914688	+	0.00528096i
$836$	10.6369	+	29.5272i	0.367884	+	1.02122i
$837$		0			0
$838$	13.7333	−	4.46221i	0.474408	−	0.154145i
$839$	56.9097	+	5.98145i	1.96474	+	0.206503i	0.998661	−	0.0517373i	$-0.0164759\pi$
$839$	56.9097	+	5.98145i	1.96474	+	0.206503i	0.966081	+	0.258240i	$0.0831425\pi$
$840$		0			0
$841$	1.54724	+	1.71839i	0.0533532	+	0.0592548i
$842$	1.28025	+	1.42186i	0.0441202	+	0.0490004i
$843$		0			0
$844$	28.4508	+	2.99030i	0.979318	+	0.102930i
$845$	−0.293836	+	0.0954731i	−0.0101083	+	0.00328438i
$846$		0			0
$847$	2.63028	+	0.674260i	0.0903776	+	0.0231679i
$848$	10.7328	−	6.19657i	0.368565	−	0.212791i
$849$		0			0
$850$	13.4398	−	5.98377i	0.460980	−	0.205242i
$851$	−27.2589	+	2.86503i	−0.934425	+	0.0982120i
$852$		0			0
$853$	6.34987	+	29.8738i	0.217415	+	1.02286i	0.942502	+	0.334201i	$0.108466\pi$
$853$	6.34987	+	29.8738i	0.217415	+	1.02286i	−0.725087	+	0.688658i	$0.758200\pi$
$854$	1.16623	−	0.847318i	0.0399077	−	0.0289946i
$855$		0			0
$856$	1.02637	+	3.15885i	0.0350807	+	0.107967i
$857$	3.07390	+	5.32416i	0.105003	+	0.181870i	0.913739	−	0.406301i	$-0.133182\pi$
$857$	3.07390	+	5.32416i	0.105003	+	0.181870i	−0.808737	+	0.588171i	$0.799848\pi$
$858$		0			0
$859$	13.7994	−	23.9013i	0.470830	−	0.815501i	−0.528614	−	0.848863i	$-0.677288\pi$
$859$	13.7994	−	23.9013i	0.470830	−	0.815501i	0.999443	+	0.0333614i	$0.0106212\pi$
$860$	−0.0617744	−	0.0131306i	−0.00210649	−	0.000447748i
$861$		0			0
$862$	17.5615	+	7.81887i	0.598146	+	0.266312i
$863$	40.7061	+	13.2262i	1.38565	+	0.450226i	0.904523	−	0.426424i	$-0.140227\pi$
$863$	40.7061	+	13.2262i	1.38565	+	0.450226i	0.481129	+	0.876650i	$0.340227\pi$
$864$		0			0
$865$	0.391832	+	0.539310i	0.0133227	+	0.0183371i
$866$	−0.659608	+	6.27575i	−0.0224144	+	0.213259i
$867$		0			0
$868$	−1.56528	−	0.903714i	−0.0531290	−	0.0306741i
$869$	−1.35721	−	9.89371i	−0.0460403	−	0.335621i
$870$		0			0
$871$	13.5903	+	12.2368i	0.460491	+	0.414628i
$872$	−10.4778	+	14.4214i	−0.354822	+	0.488371i
$873$		0			0
$874$	−8.96700	+	27.5976i	−0.303313	+	0.933503i
$875$	−0.0968285	+	0.0205815i	−0.00327340	+	0.000695783i
$876$		0			0
$877$	4.56785	+	10.2596i	0.154245	+	0.346441i	0.974095	−	0.226138i	$-0.0726099\pi$
$877$	4.56785	+	10.2596i	0.154245	+	0.346441i	−0.819850	+	0.572578i	$0.805943\pi$
$878$	0.419453	−	1.97337i	0.0141559	−	0.0665981i
$879$		0			0
$880$	−0.178522	+	0.0438857i	−0.00601797	+	0.00147939i
$881$		−	47.3136i		−	1.59403i	−0.603957	−	0.797017i	$-0.706410\pi$
$881$		−	47.3136i		−	1.59403i	0.603957	−	0.797017i	$-0.293590\pi$
$882$		0			0
$883$	−14.7740	−	10.7340i	−0.497186	−	0.361227i	0.310755	−	0.950490i	$-0.399418\pi$
$883$	−14.7740	−	10.7340i	−0.497186	−	0.361227i	−0.807941	+	0.589263i	$0.799418\pi$
$884$	−6.10963	+	13.7224i	−0.205489	+	0.461536i
$885$		0			0
$886$	18.3329	−	16.5070i	0.615905	−	0.554563i
$887$	−4.25539	−	40.4873i	−0.142882	−	1.35943i	−0.797430	−	0.603411i	$-0.793808\pi$
$887$	−4.25539	−	40.4873i	−0.142882	−	1.35943i	0.654548	−	0.756020i	$-0.272859\pi$
$888$		0			0
$889$	2.10958	−	2.34292i	0.0707529	−	0.0785791i
$890$	0.235876			0.00790658
$891$		0			0
$892$	−14.7573			−0.494110
$893$	46.1586	−	51.2643i	1.54464	−	1.71549i
$894$		0			0
$895$	−0.0295563	−	0.281209i	−0.000987958	−	0.00939979i
$896$	1.97438	−	1.77774i	0.0659595	−	0.0593902i
$897$		0			0
$898$	3.97929	−	8.93763i	0.132791	−	0.298253i
$899$	21.7180	+	15.7790i	0.724335	+	0.526260i
$900$		0			0
$901$		−	38.3480i		−	1.27756i
$902$	18.6288	−	11.5553i	0.620270	−	0.384750i
$903$		0			0
$904$	0.266713	−	1.25479i	0.00887075	−	0.0417336i
$905$	−0.344604	−	0.773994i	−0.0114550	−	0.0257284i
$906$		0			0
$907$	−1.15589	+	0.245691i	−0.0383806	+	0.00815804i	−0.227062	−	0.973880i	$-0.572912\pi$
$907$	−1.15589	+	0.245691i	−0.0383806	+	0.00815804i	0.188681	+	0.982038i	$0.439579\pi$
$908$	−5.52581	+	17.0067i	−0.183380	+	0.564387i
$909$		0			0
$910$	−0.00921881	+	0.0126886i	−0.000305601	+	0.000420623i
$911$	−15.7280	−	14.1615i	−0.521092	−	0.469193i	0.366112	−	0.930571i	$-0.380689\pi$
$911$	−15.7280	−	14.1615i	−0.521092	−	0.469193i	−0.887204	+	0.461378i	$0.847355\pi$
$912$		0			0
$913$	−15.4751	−	8.29384i	−0.512152	−	0.274486i
$914$	12.1596	+	7.02032i	0.402202	+	0.232212i
$915$		0			0
$916$	3.26735	−	31.0867i	0.107956	−	1.02713i
$917$	2.63394	+	3.62530i	0.0869803	+	0.119718i
$918$		0			0
$919$	−13.4009	−	4.35422i	−0.442055	−	0.143633i	0.0795283	−	0.996833i	$-0.474659\pi$
$919$	−13.4009	−	4.35422i	−0.442055	−	0.143633i	−0.521584	+	0.853200i	$0.674659\pi$
$920$	−0.604719	−	0.269238i	−0.0199370	−	0.00887653i
$921$		0			0
$922$	−0.518641	−	0.110241i	−0.0170805	−	0.00363058i
$923$	3.83031	−	6.63429i	0.126076	−	0.218370i
$924$		0			0
$925$	10.0739	+	17.4485i	0.331227	+	0.573702i
$926$	−8.03871	−	24.7406i	−0.264168	−	0.813027i
$927$		0			0
$928$	−26.2812	+	19.0944i	−0.862723	+	0.626805i
$929$	7.08681	+	33.3408i	0.232511	+	1.09388i	0.927200	+	0.374567i	$0.122209\pi$
$929$	7.08681	+	33.3408i	0.232511	+	1.09388i	−0.694689	+	0.719310i	$0.744458\pi$
$930$		0			0
$931$	−42.7868	+	4.49707i	−1.40228	+	0.147386i
$932$	−22.5081	+	10.0212i	−0.737276	+	0.328256i
$933$		0			0
$934$	−10.4925	+	6.05786i	−0.343326	+	0.198219i
$935$	−0.158598	+	0.546290i	−0.00518669	+	0.0178656i
$936$		0			0
$937$	6.41974	−	2.08590i	0.209724	−	0.0681434i	−0.202271	−	0.979330i	$-0.564832\pi$
$937$	6.41974	−	2.08590i	0.209724	−	0.0681434i	0.411995	+	0.911186i	$0.364832\pi$
$938$	−1.34264	−	0.141117i	−0.0438386	−	0.00460763i
$939$		0			0
$940$	0.455748	+	0.506159i	0.0148648	+	0.0165091i
$941$	22.2806	+	24.7451i	0.726328	+	0.806669i	0.987332	−	0.158669i	$-0.0507203\pi$
$941$	22.2806	+	24.7451i	0.726328	+	0.806669i	−0.261004	+	0.965338i	$0.584054\pi$
$942$		0			0
$943$	−64.9407	−	6.82554i	−2.11476	−	0.222270i
$944$	−3.66476	+	1.19075i	−0.119278	+	0.0387557i
$945$		0			0
$946$	1.86060	−	1.44381i	0.0604934	−	0.0469422i
$947$	−0.650586	+	0.375616i	−0.0211412	+	0.0122059i	−0.510533	−	0.859858i	$-0.670552\pi$
$947$	−0.650586	+	0.375616i	−0.0211412	+	0.0122059i	0.489392	+	0.872064i	$0.337219\pi$
$948$		0			0
$949$	−24.9229	+	11.0964i	−0.809032	+	0.360204i
$950$	21.2134	−	2.22962i	0.688255	−	0.0723385i
$951$		0			0
$952$	−0.532664	−	2.50599i	−0.0172638	−	0.0812196i
$953$	−3.76491	+	2.73537i	−0.121957	+	0.0886073i	−0.647092	−	0.762412i	$-0.724015\pi$
$953$	−3.76491	+	2.73537i	−0.121957	+	0.0886073i	0.525134	+	0.851019i	$0.324015\pi$
$954$		0			0
$955$	−0.169408	−	0.521385i	−0.00548192	−	0.0168716i
$956$	−21.6633	−	37.5220i	−0.700641	−	1.21355i
$957$		0			0
$958$	0.827966	−	1.43408i	0.0267504	−	0.0463330i
$959$	3.88088	+	0.824907i	0.125320	+	0.0266376i
$960$		0			0
$961$	−7.29480	−	3.24785i	−0.235316	−	0.104769i
$962$	6.07281	+	1.97318i	0.195795	+	0.0636177i
$963$		0			0
$964$	−12.8874	−	17.7379i	−0.415074	−	0.571300i
$965$	−0.104959	+	0.998617i	−0.00337875	+	0.0321466i
$966$		0			0
$967$	−18.8385	−	10.8764i	−0.605807	−	0.349763i	0.165516	−	0.986207i	$-0.447071\pi$
$967$	−18.8385	−	10.8764i	−0.605807	−	0.349763i	−0.771323	+	0.636444i	$0.780404\pi$
$968$	11.8616	−	23.9183i	0.381248	−	0.768763i
$969$		0			0
$970$	0.0621263	+	0.0559387i	0.00199475	+	0.00179608i
$971$	3.45215	−	4.75147i	0.110785	−	0.152482i	−0.750024	−	0.661410i	$-0.769958\pi$
$971$	3.45215	−	4.75147i	0.110785	−	0.152482i	0.860809	+	0.508928i	$0.169958\pi$
$972$		0			0
$973$	−0.294236	+	0.905565i	−0.00943277	+	0.0290311i
$974$	9.82799	−	2.08900i	0.314909	−	0.0669360i
$975$		0			0
$976$	4.76910	+	10.7116i	0.152655	+	0.342869i
$977$	0.191277	−	0.899889i	0.00611950	−	0.0287900i	−0.974982	−	0.222284i	$-0.928649\pi$
$977$	0.191277	−	0.899889i	0.00611950	−	0.0287900i	0.981101	+	0.193494i	$0.0619821\pi$
$978$		0			0
$979$	18.2868	−	21.6480i	0.584448	−	0.691872i
$980$		−	0.424783i		−	0.0135692i
$981$		0			0
$982$	13.9446	+	10.1313i	0.444989	+	0.323304i
$983$	−18.9685	+	42.6040i	−0.605002	+	1.35886i	0.308188	+	0.951325i	$0.400277\pi$
$983$	−18.9685	+	42.6040i	−0.605002	+	1.35886i	−0.913191	+	0.407532i	$0.866389\pi$
$984$		0			0
$985$	−0.627256	+	0.564784i	−0.0199860	+	0.0179955i
$986$	1.72157	+	16.3796i	0.0548258	+	0.521633i
$987$		0			0
$988$	−14.5729	+	16.1849i	−0.463627	+	0.514910i
$989$	−7.01515			−0.223069
$990$		0			0
$991$	6.21090			0.197296			0.0986478	−	0.995122i	$-0.468548\pi$
$991$	6.21090			0.197296			0.0986478	+	0.995122i	$0.468548\pi$
$992$	−18.6357	+	20.6970i	−0.591683	+	0.657131i
$993$		0			0
$994$	0.0591133	+	0.562425i	0.00187496	+	0.0178390i
$995$	0.309123	−	0.278335i	0.00979984	−	0.00882382i
$996$		0			0
$997$	−11.6192	+	26.0971i	−0.367982	+	0.826502i	0.630741	+	0.775993i	$0.282751\pi$
$997$	−11.6192	+	26.0971i	−0.367982	+	0.826502i	−0.998724	+	0.0505088i	$0.983916\pi$
$998$	12.6467	+	9.18836i	0.400324	+	0.290852i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.c.215.2		32
3.2	odd	2	inner	891.2.u.c.215.3		32
9.2	odd	6	inner	891.2.u.c.512.2		32
9.4	even	3		99.2.j.a.17.2	✓	16
9.5	odd	6		99.2.j.a.17.3	yes	16
9.7	even	3	inner	891.2.u.c.512.3		32
11.2	odd	10	inner	891.2.u.c.134.2		32
33.2	even	10	inner	891.2.u.c.134.3		32
36.23	even	6		1584.2.cd.c.17.2		16
36.31	odd	6		1584.2.cd.c.17.3		16
99.2	even	30	inner	891.2.u.c.431.2		32
99.13	odd	30		99.2.j.a.35.3	yes	16
99.14	odd	30		1089.2.d.g.1088.11		16
99.41	even	30		1089.2.d.g.1088.5		16
99.58	even	15		1089.2.d.g.1088.6		16
99.68	even	30		99.2.j.a.35.2	yes	16
99.79	odd	30	inner	891.2.u.c.431.3		32
99.85	odd	30		1089.2.d.g.1088.12		16
396.167	odd	30		1584.2.cd.c.1025.3		16
396.211	even	30		1584.2.cd.c.1025.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.2	✓	16	9.4	even	3
99.2.j.a.17.3	yes	16	9.5	odd	6
99.2.j.a.35.2	yes	16	99.68	even	30
99.2.j.a.35.3	yes	16	99.13	odd	30
891.2.u.c.134.2		32	11.2	odd	10	inner
891.2.u.c.134.3		32	33.2	even	10	inner
891.2.u.c.215.2		32	1.1	even	1	trivial
891.2.u.c.215.3		32	3.2	odd	2	inner
891.2.u.c.431.2		32	99.2	even	30	inner
891.2.u.c.431.3		32	99.79	odd	30	inner
891.2.u.c.512.2		32	9.2	odd	6	inner
891.2.u.c.512.3		32	9.7	even	3	inner
1089.2.d.g.1088.5		16	99.41	even	30
1089.2.d.g.1088.6		16	99.58	even	15
1089.2.d.g.1088.11		16	99.14	odd	30
1089.2.d.g.1088.12		16	99.85	odd	30
1584.2.cd.c.17.2		16	36.23	even	6
1584.2.cd.c.17.3		16	36.31	odd	6
1584.2.cd.c.1025.2		16	396.211	even	30
1584.2.cd.c.1025.3		16	396.167	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.460557 + 0.511500i) q^{2} +(0.159537 + 1.51789i) q^{4} +(-0.0298066 + 0.0268380i) q^{5} +(0.100402 - 0.225507i) q^{7} +(-1.96356 - 1.42661i) q^{8} +O(q^{10})\)	\(q+(-0.460557 + 0.511500i) q^{2} +(0.159537 + 1.51789i) q^{4} +(-0.0298066 + 0.0268380i) q^{5} +(0.100402 - 0.225507i) q^{7} +(-1.96356 - 1.42661i) q^{8} -0.0276065i q^{10} +(-2.53364 - 2.14025i) q^{11} +(0.478513 - 2.25123i) q^{13} +(0.0691059 + 0.155214i) q^{14} +(-1.35177 + 0.287327i) q^{16} +(-1.32142 + 4.06692i) q^{17} +(-3.64429 + 5.01593i) q^{19} +(-0.0454925 - 0.0409616i) q^{20} +(2.26162 - 0.310248i) q^{22} +(-5.88883 - 3.39992i) q^{23} +(-0.522474 + 4.97101i) q^{25} +(0.931121 + 1.28158i) q^{26} +(0.358314 + 0.116423i) q^{28} +(-5.11196 - 2.27599i) q^{29} +(-4.69255 - 0.997431i) q^{31} +(2.90269 - 5.02760i) q^{32} +(-1.47164 - 2.54895i) q^{34} +(0.00305951 + 0.00941619i) q^{35} +(3.26102 - 2.36927i) q^{37} +(-0.887248 - 4.17418i) q^{38} +(0.0968143 - 0.0101756i) q^{40} +(8.77271 - 3.90586i) q^{41} +(0.893447 - 0.515832i) q^{43} +(2.84447 - 4.18724i) q^{44} +(4.45120 - 1.44628i) q^{46} +(-11.0653 - 1.16301i) q^{47} +(4.64314 + 5.15673i) q^{49} +(-2.30204 - 2.55668i) q^{50} +(3.49347 + 0.367178i) q^{52} +(-8.52885 + 2.77119i) q^{53} +(0.132959 - 0.00420408i) q^{55} +(-0.518855 + 0.299561i) q^{56} +(3.51852 - 1.56655i) q^{58} +(2.77304 - 0.291459i) q^{59} +(-1.76403 - 8.29909i) q^{61} +(2.67137 - 1.94086i) q^{62} +(0.380665 + 1.17156i) q^{64} +(0.0461556 + 0.0799438i) q^{65} +(-3.97294 + 6.88133i) q^{67} +(-6.38397 - 1.35695i) q^{68} +(-0.00622546 - 0.00277175i) q^{70} +(3.16559 + 1.02856i) q^{71} +(-6.96743 - 9.58984i) q^{73} +(-0.290003 + 2.75920i) q^{74} +(-8.19506 - 4.73142i) q^{76} +(-0.737025 + 0.356467i) q^{77} +(2.23761 + 2.01475i) q^{79} +(0.0325803 - 0.0448429i) q^{80} +(-2.04248 + 6.28611i) q^{82} +(5.17811 - 1.10064i) q^{83} +(-0.0697608 - 0.156685i) q^{85} +(-0.147635 + 0.694568i) q^{86} +(1.92164 + 7.81702i) q^{88} +8.54422i q^{89} +(-0.459624 - 0.333936i) q^{91} +(4.22123 - 9.48104i) q^{92} +(5.69106 - 5.12425i) q^{94} +(-0.0259937 - 0.247313i) q^{95} +(-2.02629 + 2.25042i) q^{97} -4.77610 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4}+O(q^{10}) \) 32 * q + 4 * q^4	\( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70} - 40 q^{73} - 24 q^{82} + 100 q^{85} + 12 q^{88} - 144 q^{91} + 80 q^{94} - 60 q^{97}+O(q^{100}) \) 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

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