LMFDB - Embedded newform 819.2.et.b.136.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			136.2
Character	$\chi$	$=$	819.136
Dual form			819.2.et.b.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14693 + 1.14693i) q^{2} -0.630890i q^{4} +(-0.395109 + 1.47457i) q^{5} +(0.0531605 - 2.64522i) q^{7} +(-1.57027 - 1.57027i) q^{8} +O(q^{10})$	\(q+(-1.14693 + 1.14693i) q^{2} -0.630890i q^{4} +(-0.395109 + 1.47457i) q^{5} +(0.0531605 - 2.64522i) q^{7} +(-1.57027 - 1.57027i) q^{8} +(-1.23806 - 2.14439i) q^{10} +(0.745574 - 2.78252i) q^{11} +(-2.94467 + 2.08061i) q^{13} +(2.97290 + 3.09485i) q^{14} +4.86376 q^{16} +6.21574 q^{17} +(2.23387 - 0.598564i) q^{19} +(0.930289 + 0.249270i) q^{20} +(2.33623 + 4.04647i) q^{22} +5.62238i q^{23} +(2.31189 + 1.33477i) q^{25} +(0.991014 - 5.76363i) q^{26} +(-1.66884 - 0.0335384i) q^{28} +(-0.379237 + 0.656858i) q^{29} +(8.36292 - 2.24084i) q^{31} +(-2.43784 + 2.43784i) q^{32} +(-7.12901 + 7.12901i) q^{34} +(3.87955 + 1.12354i) q^{35} +(-4.26298 - 4.26298i) q^{37} +(-1.87558 + 3.24860i) q^{38} +(2.93590 - 1.69504i) q^{40} +(1.94919 - 0.522283i) q^{41} +(-2.24252 + 1.29472i) q^{43} +(-1.75546 - 0.470375i) q^{44} +(-6.44847 - 6.44847i) q^{46} +(2.13395 + 0.571791i) q^{47} +(-6.99435 - 0.281242i) q^{49} +(-4.18246 + 1.12069i) q^{50} +(1.31263 + 1.85776i) q^{52} +(-2.47328 + 4.28385i) q^{53} +(3.80843 + 2.19880i) q^{55} +(-4.23719 + 4.07023i) q^{56} +(-0.318411 - 1.18833i) q^{58} +(0.623268 - 0.623268i) q^{59} +(4.48249 + 2.58797i) q^{61} +(-7.02159 + 12.1617i) q^{62} +4.13546i q^{64} +(-1.90453 - 5.16418i) q^{65} +(15.1664 + 4.06383i) q^{67} -3.92145i q^{68} +(-5.73818 + 3.16095i) q^{70} +(10.3040 + 2.76095i) q^{71} +(1.80076 + 6.72052i) q^{73} +9.77867 q^{74} +(-0.377628 - 1.40933i) q^{76} +(-7.32073 - 2.12012i) q^{77} +(-4.24764 - 7.35713i) q^{79} +(-1.92172 + 7.17194i) q^{80} +(-1.63656 + 2.83460i) q^{82} +(1.51432 + 1.51432i) q^{83} +(-2.45590 + 9.16553i) q^{85} +(1.08706 - 4.05696i) q^{86} +(-5.54006 + 3.19856i) q^{88} +(5.91573 - 5.91573i) q^{89} +(5.34712 + 7.89989i) q^{91} +3.54710 q^{92} +(-3.10329 + 1.79169i) q^{94} +3.53049i q^{95} +(-0.933928 + 3.48547i) q^{97} +(8.34458 - 7.69945i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	$ 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.14693	+	1.14693i	−0.811001	+	0.811001i	−0.984784	−	0.173783i	$-0.944401\pi$
$2$	−1.14693	+	1.14693i	−0.811001	+	0.811001i	0.173783	+	0.984784i	$0.444401\pi$
$3$		0			0
$3$		0			0
$4$		−	0.630890i		−	0.315445i
$5$	−0.395109	+	1.47457i	−0.176698	+	0.659447i	0.819558	+	0.572996i	$0.194219\pi$
$5$	−0.395109	+	1.47457i	−0.176698	+	0.659447i	−0.996256	+	0.0864504i	$0.972448\pi$
$6$		0			0
$7$	0.0531605	−	2.64522i	0.0200928	−	0.999798i
$7$	0.0531605	−	2.64522i	0.0200928	−	0.999798i
$8$	−1.57027	−	1.57027i	−0.555175	−	0.555175i
$9$		0			0
$10$	−1.23806	−	2.14439i	−0.391509	−	0.678114i
$11$	0.745574	−	2.78252i	0.224799	−	0.838961i	−0.757686	−	0.652619i	$-0.773670\pi$
$11$	0.745574	−	2.78252i	0.224799	−	0.838961i	0.982485	−	0.186342i	$-0.0596632\pi$
$12$		0			0
$13$	−2.94467	+	2.08061i	−0.816704	+	0.577057i
$13$	−2.94467	+	2.08061i	−0.816704	+	0.577057i
$14$	2.97290	+	3.09485i	0.794542	+	0.827132i
$15$		0			0
$16$	4.86376			1.21594
$17$	6.21574			1.50754			0.753769	−	0.657139i	$-0.228234\pi$
$17$	6.21574			1.50754			0.753769	+	0.657139i	$0.228234\pi$
$18$		0			0
$19$	2.23387	−	0.598564i	0.512485	−	0.137320i	0.00669672	−	0.999978i	$-0.497868\pi$
$19$	2.23387	−	0.598564i	0.512485	−	0.137320i	0.505788	+	0.862658i	$0.331202\pi$
$20$	0.930289	+	0.249270i	0.208019	+	0.0557385i
$21$		0			0
$22$	2.33623	+	4.04647i	0.498086	+	0.862710i
$23$			5.62238i			1.17235i	0.810185	+	0.586174i	$0.199367\pi$
$23$			5.62238i			1.17235i	−0.810185	+	0.586174i	$0.800633\pi$
$24$		0			0
$25$	2.31189	+	1.33477i	0.462378	+	0.266954i
$26$	0.991014	−	5.76363i	0.194354	−	1.13034i
$27$		0			0
$28$	−1.66884	−	0.0335384i	−0.315381	−	0.00633816i
$29$	−0.379237	+	0.656858i	−0.0704225	+	0.121975i	−0.899087	−	0.437771i	$-0.855768\pi$
$29$	−0.379237	+	0.656858i	−0.0704225	+	0.121975i	0.828664	+	0.559746i	$0.189101\pi$
$30$		0			0
$31$	8.36292	−	2.24084i	1.50202	−	0.402466i	0.588247	−	0.808682i	$-0.299818\pi$
$31$	8.36292	−	2.24084i	1.50202	−	0.402466i	0.913777	+	0.406215i	$0.133152\pi$
$32$	−2.43784	+	2.43784i	−0.430953	+	0.430953i
$33$		0			0
$34$	−7.12901	+	7.12901i	−1.22261	+	1.22261i
$35$	3.87955	+	1.12354i	0.655763	+	0.189913i
$36$		0			0
$37$	−4.26298	−	4.26298i	−0.700830	−	0.700830i	0.263759	−	0.964589i	$-0.415038\pi$
$37$	−4.26298	−	4.26298i	−0.700830	−	0.700830i	−0.964589	+	0.263759i	$0.915038\pi$
$38$	−1.87558	+	3.24860i	−0.304259	+	0.526992i
$39$		0			0
$40$	2.93590	−	1.69504i	0.464207	−	0.268010i
$41$	1.94919	−	0.522283i	0.304412	−	0.0815669i	−0.103380	−	0.994642i	$-0.532966\pi$
$41$	1.94919	−	0.522283i	0.304412	−	0.0815669i	0.407792	+	0.913075i	$0.366299\pi$
$42$		0			0
$43$	−2.24252	+	1.29472i	−0.341981	+	0.197443i	−0.661148	−	0.750256i	$-0.729930\pi$
$43$	−2.24252	+	1.29472i	−0.341981	+	0.197443i	0.319167	+	0.947699i	$0.396597\pi$
$44$	−1.75546	−	0.470375i	−0.264646	−	0.0709116i
$45$		0			0
$46$	−6.44847	−	6.44847i	−0.950775	−	0.950775i
$47$	2.13395	+	0.571791i	0.311269	+	0.0834043i	0.411072	−	0.911603i	$-0.365155\pi$
$47$	2.13395	+	0.571791i	0.311269	+	0.0834043i	−0.0998029	+	0.995007i	$0.531821\pi$
$48$		0			0
$49$	−6.99435	−	0.281242i	−0.999193	−	0.0401774i
$50$	−4.18246	+	1.12069i	−0.591488	+	0.158489i
$51$		0			0
$52$	1.31263	+	1.85776i	0.182030	+	0.257625i
$53$	−2.47328	+	4.28385i	−0.339732	+	0.588433i	−0.984382	−	0.176045i	$-0.943670\pi$
$53$	−2.47328	+	4.28385i	−0.339732	+	0.588433i	0.644650	+	0.764477i	$0.277003\pi$
$54$		0			0
$55$	3.80843	+	2.19880i	0.513529	+	0.296486i
$56$	−4.23719	+	4.07023i	−0.566218	+	0.543908i
$57$		0			0
$58$	−0.318411	−	1.18833i	−0.0418094	−	0.156035i
$59$	0.623268	−	0.623268i	0.0811426	−	0.0811426i	−0.665371	−	0.746513i	$-0.731726\pi$
$59$	0.623268	−	0.623268i	0.0811426	−	0.0811426i	0.746513	+	0.665371i	$0.231726\pi$
$60$		0			0
$61$	4.48249	+	2.58797i	0.573924	+	0.331355i	0.758715	−	0.651423i	$-0.225828\pi$
$61$	4.48249	+	2.58797i	0.573924	+	0.331355i	−0.184791	+	0.982778i	$0.559161\pi$
$62$	−7.02159	+	12.1617i	−0.891742	+	1.54454i
$63$		0			0
$64$			4.13546i			0.516933i
$65$	−1.90453	−	5.16418i	−0.236228	−	0.640538i
$66$		0			0
$67$	15.1664	+	4.06383i	1.85287	+	0.496476i	0.999684	−	0.0251264i	$-0.00799882\pi$
$67$	15.1664	+	4.06383i	1.85287	+	0.496476i	0.853189	+	0.521602i	$0.174665\pi$
$68$		−	3.92145i		−	0.475545i
$69$		0			0
$70$	−5.73818	+	3.16095i	−0.685844	+	0.377805i
$71$	10.3040	+	2.76095i	1.22286	+	0.327665i	0.811796	−	0.583941i	$-0.198490\pi$
$71$	10.3040	+	2.76095i	1.22286	+	0.327665i	0.411066	+	0.911606i	$0.365157\pi$
$72$		0			0
$73$	1.80076	+	6.72052i	0.210763	+	0.786578i	0.987615	+	0.156895i	$0.0501484\pi$
$73$	1.80076	+	6.72052i	0.210763	+	0.786578i	−0.776852	+	0.629683i	$0.783185\pi$
$74$	9.77867			1.13675
$75$		0			0
$76$	−0.377628	−	1.40933i	−0.0433169	−	0.161661i
$77$	−7.32073	−	2.12012i	−0.834275	−	0.241611i
$78$		0			0
$79$	−4.24764	−	7.35713i	−0.477897	−	0.827742i	0.521782	−	0.853079i	$-0.325267\pi$
$79$	−4.24764	−	7.35713i	−0.477897	−	0.827742i	−0.999679	+	0.0253371i	$0.991934\pi$
$80$	−1.92172	+	7.17194i	−0.214854	+	0.801847i
$81$		0			0
$82$	−1.63656	+	2.83460i	−0.180727	+	0.313029i
$83$	1.51432	+	1.51432i	0.166218	+	0.166218i	0.785315	−	0.619096i	$-0.212501\pi$
$83$	1.51432	+	1.51432i	0.166218	+	0.166218i	−0.619096	+	0.785315i	$0.712501\pi$
$84$		0			0
$85$	−2.45590	+	9.16553i	−0.266379	+	0.994141i
$86$	1.08706	−	4.05696i	0.117221	−	0.437473i
$87$		0			0
$88$	−5.54006	+	3.19856i	−0.590573	+	0.340967i
$89$	5.91573	−	5.91573i	0.627066	−	0.627066i	−0.320263	−	0.947329i	$-0.603771\pi$
$89$	5.91573	−	5.91573i	0.627066	−	0.627066i	0.947329	+	0.320263i	$0.103771\pi$
$90$		0			0
$91$	5.34712	+	7.89989i	0.560531	+	0.828134i
$92$	3.54710			0.369811
$93$		0			0
$94$	−3.10329	+	1.79169i	−0.320080	+	0.184798i
$95$			3.53049i			0.362221i
$96$		0			0
$97$	−0.933928	+	3.48547i	−0.0948260	+	0.353896i	−0.996993	−	0.0774914i	$-0.975309\pi$
$97$	−0.933928	+	3.48547i	−0.0948260	+	0.353896i	0.902167	+	0.431387i	$0.141976\pi$
$98$	8.34458	−	7.69945i	0.842930	−	0.777762i
$99$		0			0
$100$	0.842092	−	1.45855i	0.0842092	−	0.145855i
$101$	−9.84474	−	17.0516i	−0.979589	−	1.69670i	−0.663876	−	0.747843i	$-0.731090\pi$
$101$	−9.84474	−	17.0516i	−0.979589	−	1.69670i	−0.315713	−	0.948855i	$-0.602244\pi$
$102$		0			0
$103$	−4.70130	−	8.14290i	−0.463233	−	0.802344i	0.535887	−	0.844290i	$-0.319977\pi$
$103$	−4.70130	−	8.14290i	−0.463233	−	0.802344i	−0.999120	+	0.0419464i	$0.986644\pi$
$104$	7.89105	+	1.35681i	0.773781	+	0.133046i
$105$		0			0
$106$	−2.07659	−	7.74995i	−0.201697	−	0.752742i
$107$	−0.0718412			−0.00694515			−0.00347258	−	0.999994i	$-0.501105\pi$
$107$	−0.0718412			−0.00694515			−0.00347258	+	0.999994i	$0.501105\pi$
$108$		0			0
$109$	1.89580	+	7.07523i	0.181585	+	0.677684i	0.995336	+	0.0964705i	$0.0307553\pi$
$109$	1.89580	+	7.07523i	0.181585	+	0.677684i	−0.813751	+	0.581214i	$0.802578\pi$
$110$	−6.88986	+	1.84613i	−0.656922	+	0.176022i
$111$		0			0
$112$	0.258560	−	12.8657i	0.0244316	−	1.21569i
$113$	8.15754	+	14.1293i	0.767396	+	1.32917i	0.938970	+	0.343998i	$0.111781\pi$
$113$	8.15754	+	14.1293i	0.767396	+	1.32917i	−0.171574	+	0.985171i	$0.554885\pi$
$114$		0			0
$115$	−8.29059	−	2.22146i	−0.773101	−	0.207152i
$116$	0.414405	+	0.239257i	0.0384765	+	0.0222144i
$117$		0			0
$118$			1.42969i			0.131613i
$119$	0.330432	−	16.4420i	0.0302906	−	1.50723i
$120$		0			0
$121$	2.33975	+	1.35085i	0.212704	+	0.122805i
$122$	−8.10931	+	2.17288i	−0.734182	+	0.196724i
$123$		0			0
$124$	−1.41372	−	5.27608i	−0.126956	−	0.473806i
$125$	−8.27895	+	8.27895i	−0.740492	+	0.740492i
$126$		0			0
$127$	14.9037	+	8.60464i	1.32249	+	0.763538i	0.984125	−	0.177478i	$-0.0567937\pi$
$127$	14.9037	+	8.60464i	1.32249	+	0.763538i	0.338362	+	0.941016i	$0.390127\pi$
$128$	−9.61876	−	9.61876i	−0.850186	−	0.850186i
$129$		0			0
$130$	8.10731	+	3.73858i	0.711058	+	0.327895i
$131$	−4.73734	+	2.73511i	−0.413904	+	0.238967i	−0.692466	−	0.721451i	$-0.743476\pi$
$131$	−4.73734	+	2.73511i	−0.413904	+	0.238967i	0.278562	+	0.960418i	$0.410142\pi$
$132$		0			0
$133$	−1.46458	−	5.94089i	−0.126995	−	0.515141i
$134$	−22.0557	+	12.7339i	−1.90532	+	1.10004i
$135$		0			0
$136$	−9.76040	−	9.76040i	−0.836947	−	0.836947i
$137$	1.24060	+	1.24060i	0.105991	+	0.105991i	0.758114	−	0.652122i	$-0.226121\pi$
$137$	1.24060	+	1.24060i	0.105991	+	0.105991i	−0.652122	+	0.758114i	$0.726121\pi$
$138$		0			0
$139$	7.13953	−	4.12201i	0.605567	−	0.349624i	−0.165662	−	0.986183i	$-0.552976\pi$
$139$	7.13953	−	4.12201i	0.605567	−	0.349624i	0.771228	+	0.636559i	$0.219643\pi$
$140$	0.708829	−	2.44757i	0.0599070	−	0.206857i
$141$		0			0
$142$	−14.9846	+	8.65135i	−1.25748	+	0.726005i
$143$	3.59387	+	9.74484i	0.300534	+	0.814904i
$144$		0			0
$145$	−0.818741	−	0.818741i	−0.0679927	−	0.0679927i
$146$	−9.77330	−	5.64262i	−0.808844	−	0.466986i
$147$		0			0
$148$	−2.68947	+	2.68947i	−0.221073	+	0.221073i
$149$	−1.15185	−	4.29875i	−0.0943628	−	0.352167i	0.902559	−	0.430566i	$-0.141686\pi$
$149$	−1.15185	−	4.29875i	−0.0943628	−	0.352167i	−0.996922	+	0.0783988i	$0.975019\pi$
$150$		0			0
$151$	−8.69443	+	2.32966i	−0.707542	+	0.189585i	−0.594606	−	0.804017i	$-0.702692\pi$
$151$	−8.69443	+	2.32966i	−0.707542	+	0.189585i	−0.112936	+	0.993602i	$0.536025\pi$
$152$	−4.44769	−	2.56788i	−0.360755	−	0.208282i
$153$		0			0
$154$	10.8280	−	5.96472i	0.872544	−	0.480651i
$155$			13.2171i			1.06162i
$156$		0			0
$157$	−4.21105	−	2.43125i	−0.336078	−	0.194035i	0.322458	−	0.946584i	$-0.395491\pi$
$157$	−4.21105	−	2.43125i	−0.336078	−	0.194035i	−0.658537	+	0.752549i	$0.728824\pi$
$158$	13.3098	+	3.56636i	1.05887	+	0.283724i
$159$		0			0
$160$	−2.63155	−	4.55797i	−0.208042	−	0.360339i
$161$	14.8724	+	0.298889i	1.17211	+	0.0235557i
$162$		0			0
$163$	6.17099	−	1.65351i	0.483349	−	0.129513i	−0.00891239	−	0.999960i	$-0.502837\pi$
$163$	6.17099	−	1.65351i	0.483349	−	0.129513i	0.492262	+	0.870447i	$0.336170\pi$
$164$	−0.329503	−	1.22972i	−0.0257299	−	0.0960252i
$165$		0			0
$166$	−3.47364			−0.269607
$167$	−2.62064	−	9.78037i	−0.202791	−	0.756828i	−0.990111	−	0.140283i	$-0.955199\pi$
$167$	−2.62064	−	9.78037i	−0.202791	−	0.756828i	0.787320	−	0.616544i	$-0.211468\pi$
$168$		0			0
$169$	4.34213	−	12.2534i	0.334010	−	0.942569i
$170$	−7.69547	−	13.3289i	−0.590215	−	1.02228i
$171$		0			0
$172$	0.816825	+	1.41478i	0.0622823	+	0.107876i
$173$	8.82380	−	15.2833i	0.670861	−	1.16197i	−0.306799	−	0.951774i	$-0.599258\pi$
$173$	8.82380	−	15.2833i	0.670861	−	1.16197i	0.977660	−	0.210192i	$-0.0674088\pi$
$174$		0			0
$175$	3.65366	−	6.04449i	0.276190	−	0.456920i
$176$	3.62629	−	13.5335i	0.273342	−	1.02013i
$177$		0			0
$178$			13.5698i			1.01710i
$179$	17.5138	−	10.1116i	1.30904	−	0.755775i	0.327105	−	0.944988i	$-0.393927\pi$
$179$	17.5138	−	10.1116i	1.30904	−	0.755775i	0.981936	+	0.189213i	$0.0605936\pi$
$180$		0			0
$181$	−17.4649			−1.29815			−0.649077	−	0.760722i	$-0.724845\pi$
$181$	−17.4649			−1.29815			−0.649077	+	0.760722i	$0.724845\pi$
$182$	−15.1934	−	2.92784i	−1.12621	−	0.217026i
$183$		0			0
$184$	8.82867	−	8.82867i	0.650858	−	0.650858i
$185$	7.97040	−	4.60171i	0.585995	−	0.338324i
$186$		0			0
$187$	4.63429	−	17.2954i	0.338893	−	1.26477i
$188$	0.360737	−	1.34629i	0.0263094	−	0.0981882i
$189$		0			0
$190$	−4.04922	−	4.04922i	−0.293761	−	0.293761i
$191$	0.0207944	−	0.0360170i	0.00150463	−	0.00260610i	−0.865272	−	0.501302i	$-0.832854\pi$
$191$	0.0207944	−	0.0360170i	0.00150463	−	0.00260610i	0.866777	+	0.498696i	$0.166188\pi$
$192$		0			0
$193$	3.23272	−	12.0647i	0.232696	−	0.868434i	−0.746478	−	0.665411i	$-0.768256\pi$
$193$	3.23272	−	12.0647i	0.232696	−	0.868434i	0.979174	−	0.203024i	$-0.0650769\pi$
$194$	−2.92643	−	5.06873i	−0.210106	−	0.363914i
$195$		0			0
$196$	−0.177433	+	4.41266i	−0.0126738	+	0.315190i
$197$	−0.962573	−	3.59237i	−0.0685805	−	0.255946i	0.923121	−	0.384510i	$-0.125630\pi$
$197$	−0.962573	−	3.59237i	−0.0685805	−	0.255946i	−0.991701	+	0.128565i	$0.958963\pi$
$198$		0			0
$199$	−8.77707			−0.622190			−0.311095	−	0.950379i	$-0.600696\pi$
$199$	−8.77707			−0.622190			−0.311095	+	0.950379i	$0.600696\pi$
$200$	−1.53434	−	5.72624i	−0.108494	−	0.404907i
$201$		0			0
$202$	30.8482	+	8.26575i	2.17047	+	0.581576i
$203$	1.71737	+	1.03808i	0.120536	+	0.0728591i
$204$		0			0
$205$			3.08057i			0.215156i
$206$	14.7314	+	3.94726i	1.02638	+	0.275019i
$207$		0			0
$208$	−14.3221	+	10.1196i	−0.993062	+	0.701666i
$209$		−	6.66206i		−	0.460824i
$210$		0			0
$211$	−3.33665	+	5.77924i	−0.229704	+	0.397859i	−0.957720	−	0.287701i	$-0.907109\pi$
$211$	−3.33665	+	5.77924i	−0.229704	+	0.397859i	0.728016	+	0.685560i	$0.240443\pi$
$212$	2.70264	+	1.56037i	0.185618	+	0.107167i
$213$		0			0
$214$	0.0823968	−	0.0823968i	0.00563253	−	0.00563253i
$215$	−1.02311	−	3.81830i	−0.0697756	−	0.260406i
$216$		0			0
$217$	−5.48292	−	22.2409i	−0.372205	−	1.50981i
$218$	−10.2891	−	5.94043i	−0.696868	−	0.402337i
$219$		0			0
$220$	1.38720	−	2.40270i	0.0935249	−	0.161990i
$221$	−18.3033	+	12.9325i	−1.23121	+	0.869936i
$222$		0			0
$223$	−6.10027	+	1.63456i	−0.408505	+	0.109458i	−0.457219	−	0.889354i	$-0.651154\pi$
$223$	−6.10027	+	1.63456i	−0.408505	+	0.109458i	0.0487142	+	0.998813i	$0.484488\pi$
$224$	6.31902	+	6.57821i	0.422207	+	0.439525i
$225$		0			0
$226$	−25.5614	−	6.84915i	−1.70032	−	0.455599i
$227$	−16.6512	−	16.6512i	−1.10518	−	1.10518i	−0.993775	−	0.111402i	$-0.964466\pi$
$227$	−16.6512	−	16.6512i	−1.10518	−	1.10518i	−0.111402	−	0.993775i	$-0.535534\pi$
$228$		0			0
$229$	18.2790	+	4.89785i	1.20791	+	0.323659i	0.805942	−	0.591995i	$-0.201659\pi$
$229$	18.2790	+	4.89785i	1.20791	+	0.323659i	0.401969	+	0.915653i	$0.368326\pi$
$230$	12.0566	−	6.96086i	0.794986	−	0.458985i
$231$		0			0
$232$	1.62695	−	0.435940i	0.106814	−	0.0286209i
$233$	−6.36747	+	3.67626i	−0.417147	+	0.240840i	−0.693856	−	0.720114i	$-0.744090\pi$
$233$	−6.36747	+	3.67626i	−0.417147	+	0.240840i	0.276709	+	0.960954i	$0.410756\pi$
$234$		0			0
$235$	−1.68629	+	2.92074i	−0.110001	+	0.190528i
$236$	−0.393214	−	0.393214i	−0.0255960	−	0.0255960i
$237$		0			0
$238$	18.4788	+	19.2368i	1.19780	+	1.24693i
$239$	4.08646	−	4.08646i	0.264331	−	0.264331i	−0.562480	−	0.826811i	$-0.690153\pi$
$239$	4.08646	−	4.08646i	0.264331	−	0.264331i	0.826811	+	0.562480i	$0.190153\pi$
$240$		0			0
$241$	20.3223	−	20.3223i	1.30907	−	1.30907i	0.386988	−	0.922085i	$-0.373515\pi$
$241$	20.3223	−	20.3223i	1.30907	−	1.30907i	0.922085	−	0.386988i	$-0.126485\pi$
$242$	−4.23286	+	1.13419i	−0.272098	+	0.0729086i
$243$		0			0
$244$	1.63272	−	2.82796i	0.104524	−	0.181041i
$245$	3.17824	−	10.2025i	0.203050	−	0.651815i
$246$		0			0
$247$	−5.33263	+	6.41038i	−0.339307	+	0.407883i
$248$	−16.6508	−	9.61333i	−1.05732	−	0.610447i
$249$		0			0
$250$		−	18.9907i		−	1.20108i
$251$	9.72695	+	16.8476i	0.613960	+	1.06341i	0.990566	+	0.137036i	$0.0437576\pi$
$251$	9.72695	+	16.8476i	0.613960	+	1.06341i	−0.376606	+	0.926373i	$0.622909\pi$
$252$		0			0
$253$	15.6444	+	4.19190i	0.983554	+	0.263543i
$254$	−26.9624	+	7.22454i	−1.69177	+	0.453308i
$255$		0			0
$256$	13.7931			0.862070
$257$	25.2048			1.57223			0.786116	−	0.618080i	$-0.212089\pi$
$257$	25.2048			1.57223			0.786116	+	0.618080i	$0.212089\pi$
$258$		0			0
$259$	−11.5031	+	11.0499i	−0.714770	+	0.686607i
$260$	−3.25803	+	1.20155i	−0.202054	+	0.0745170i
$261$		0			0
$262$	2.29642	−	8.57036i	0.141873	−	0.529479i
$263$	15.6393	+	27.0881i	0.964362	+	1.67032i	0.711320	+	0.702868i	$0.248098\pi$
$263$	15.6393	+	27.0881i	0.964362	+	1.67032i	0.253041	+	0.967455i	$0.418569\pi$
$264$		0			0
$265$	−5.33961	−	5.33961i	−0.328010	−	0.328010i
$266$	8.49354	+	5.13401i	0.520773	+	0.314787i
$267$		0			0
$268$	2.56383	−	9.56834i	0.156611	−	0.584479i
$269$		−	9.01798i		−	0.549836i	−0.961468	−	0.274918i	$-0.911349\pi$
$269$		−	9.01798i		−	0.549836i	0.961468	−	0.274918i	$-0.0886507\pi$
$270$		0			0
$271$	2.40845	−	2.40845i	0.146303	−	0.146303i	−0.630161	−	0.776464i	$-0.717011\pi$
$271$	2.40845	−	2.40845i	0.146303	−	0.146303i	0.776464	+	0.630161i	$0.217011\pi$
$272$	30.2318			1.83308
$273$		0			0
$274$	−2.84575			−0.171918
$275$	5.43770	−	5.43770i	0.327906	−	0.327906i
$276$		0			0
$277$		−	4.02905i		−	0.242082i	−0.992648	−	0.121041i	$-0.961377\pi$
$277$		−	4.02905i		−	0.242082i	0.992648	−	0.121041i	$-0.0386232\pi$
$278$	−3.46088	+	12.9162i	−0.207570	+	0.774661i
$279$		0			0
$280$	−4.32768	−	7.85620i	−0.258629	−	0.469498i
$281$	3.28511	+	3.28511i	0.195973	+	0.195973i	0.798271	−	0.602298i	$-0.205748\pi$
$281$	3.28511	+	3.28511i	0.195973	+	0.195973i	−0.602298	+	0.798271i	$0.705748\pi$
$282$		0			0
$283$	0.514830	+	0.891711i	0.0306035	+	0.0530067i	0.880921	−	0.473262i	$-0.156924\pi$
$283$	0.514830	+	0.891711i	0.0306035	+	0.0530067i	−0.850318	+	0.526269i	$0.823590\pi$
$284$	1.74186	−	6.50070i	0.103360	−	0.385745i
$285$		0			0
$286$	−15.2985	−	7.05473i	−0.904622	−	0.417155i
$287$	−1.27793	−	5.18379i	−0.0754340	−	0.305989i
$288$		0			0
$289$	21.6354			1.27267
$290$	1.87807			0.110284
$291$		0			0
$292$	4.23991	−	1.13608i	0.248122	−	0.0664840i
$293$	−24.6989	−	6.61806i	−1.44293	−	0.386631i	−0.549369	−	0.835580i	$-0.685132\pi$
$293$	−24.6989	−	6.61806i	−1.44293	−	0.386631i	−0.893558	+	0.448948i	$0.851799\pi$
$294$		0			0
$295$	0.672792	+	1.16531i	0.0391715	+	0.0678470i
$296$			13.3881i			0.778166i
$297$		0			0
$298$	6.25144	+	3.60927i	0.362136	+	0.209079i
$299$	−11.6980	−	16.5561i	−0.676512	−	0.957461i
$300$		0			0
$301$	3.30560	+	6.00078i	0.190532	+	0.345879i
$302$	7.29993	−	12.6438i	0.420064	−	0.727571i
$303$		0			0
$304$	10.8650	−	2.91127i	0.623151	−	0.166973i
$305$	−5.58721	+	5.58721i	−0.319922	+	0.319922i
$306$		0			0
$307$	−14.0195	+	14.0195i	−0.800136	+	0.800136i	−0.983117	−	0.182981i	$-0.941425\pi$
$307$	−14.0195	+	14.0195i	−0.800136	+	0.800136i	0.182981	+	0.983117i	$0.441425\pi$
$308$	−1.33756	+	4.61857i	−0.0762148	+	0.263168i
$309$		0			0
$310$	−15.1590	−	15.1590i	−0.860975	−	0.860975i
$311$	−3.20853	+	5.55733i	−0.181939	+	0.315127i	−0.942541	−	0.334091i	$-0.891571\pi$
$311$	−3.20853	+	5.55733i	−0.181939	+	0.315127i	0.760602	+	0.649219i	$0.224904\pi$
$312$		0			0
$313$	−21.8008	+	12.5867i	−1.23225	+	0.711441i	−0.967499	−	0.252875i	$-0.918624\pi$
$313$	−21.8008	+	12.5867i	−1.23225	+	0.711441i	−0.264753	+	0.964316i	$0.585291\pi$
$314$	7.61824	−	2.04130i	0.429922	−	0.115197i
$315$		0			0
$316$	−4.64154	+	2.67979i	−0.261107	+	0.150750i
$317$	−23.2745	−	6.23639i	−1.30723	−	0.350271i	−0.463049	−	0.886333i	$-0.653245\pi$
$317$	−23.2745	−	6.23639i	−1.30723	−	0.350271i	−0.844178	+	0.536062i	$0.819911\pi$
$318$		0			0
$319$	1.54497	+	1.54497i	0.0865017	+	0.0865017i
$320$	−6.09802	−	1.63396i	−0.340890	−	0.0913411i
$321$		0			0
$322$	−17.4004	+	16.7148i	−0.969687	+	0.931480i
$323$	13.8852	−	3.72052i	0.772591	−	0.207015i
$324$		0			0
$325$	−9.58488	+	0.879683i	−0.531673	+	0.0487960i
$326$	−5.18123	+	8.97415i	−0.286962	+	0.497032i
$327$		0			0
$328$	−3.88088	−	2.24063i	−0.214286	−	0.123718i
$329$	1.62595	−	5.61437i	0.0896417	−	0.309530i
$330$		0			0
$331$	−1.52989	−	5.70964i	−0.0840905	−	0.313830i	0.911050	−	0.412296i	$-0.135273\pi$
$331$	−1.52989	−	5.70964i	−0.0840905	−	0.313830i	−0.995140	+	0.0984660i	$0.968606\pi$
$332$	0.955370	−	0.955370i	0.0524328	−	0.0524328i
$333$		0			0
$334$	14.2231	+	8.21169i	0.778252	+	0.449324i
$335$	−11.9848	+	20.7583i	−0.654799	+	1.13414i
$336$		0			0
$337$			11.5318i			0.628179i	0.949393	+	0.314089i	$0.101699\pi$
$337$			11.5318i			0.628179i	−0.949393	+	0.314089i	$0.898301\pi$
$338$	9.07366	+	19.0339i	0.493542	+	1.03531i
$339$		0			0
$340$	5.78244	+	1.54940i	0.313597	+	0.0840280i
$341$		−	24.9407i		−	1.35061i
$342$		0			0
$343$	−1.11577	+	18.4866i	−0.0602459	+	0.998184i
$344$	5.55442	+	1.48830i	0.299474	+	0.0802439i
$345$		0			0
$346$	7.40855	+	27.6491i	0.398286	+	1.48642i
$347$	−9.07305			−0.487067			−0.243533	−	0.969893i	$-0.578307\pi$
$347$	−9.07305			−0.487067			−0.243533	+	0.969893i	$0.578307\pi$
$348$		0			0
$349$	−7.77792	−	29.0276i	−0.416342	−	1.55381i	−0.782132	−	0.623113i	$-0.785868\pi$
$349$	−7.77792	−	29.0276i	−0.416342	−	1.55381i	0.365789	−	0.930698i	$-0.380799\pi$
$350$	2.74212	+	11.1231i	0.146572	+	0.594554i
$351$		0			0
$352$	4.96574	+	8.60092i	0.264675	+	0.458431i
$353$	−7.50007	+	27.9907i	−0.399189	+	1.48979i	0.415338	+	0.909667i	$0.363663\pi$
$353$	−7.50007	+	27.9907i	−0.399189	+	1.48979i	−0.814527	+	0.580125i	$0.803004\pi$
$354$		0			0
$355$	−8.14242	+	14.1031i	−0.432155	+	0.748514i
$356$	−3.73217	−	3.73217i	−0.197805	−	0.197805i
$357$		0			0
$358$	−8.48978	+	31.6843i	−0.448699	+	1.67457i
$359$	−2.28482	+	8.52708i	−0.120588	+	0.450042i	−0.999644	−	0.0266770i	$-0.991507\pi$
$359$	−2.28482	+	8.52708i	−0.120588	+	0.450042i	0.879056	+	0.476719i	$0.158174\pi$
$360$		0			0
$361$	−11.8226	+	6.82577i	−0.622241	+	0.359251i
$362$	20.0310	−	20.0310i	1.05280	−	1.05280i
$363$		0			0
$364$	4.98396	−	3.37344i	0.261230	−	0.176816i
$365$	−10.6214			−0.555947
$366$		0			0
$367$	−11.5082	+	6.64427i	−0.600724	+	0.346828i	−0.769326	−	0.638856i	$-0.779408\pi$
$367$	−11.5082	+	6.64427i	−0.600724	+	0.346828i	0.168602	+	0.985684i	$0.446075\pi$
$368$			27.3459i			1.42550i
$369$		0			0
$370$	−3.86364	+	14.4193i	−0.200861	+	0.749624i
$371$	11.2002	+	6.77011i	0.581488	+	0.351486i
$372$		0			0
$373$	4.12496	−	7.14464i	0.213582	−	0.369935i	−0.739251	−	0.673430i	$-0.764820\pi$
$373$	4.12496	−	7.14464i	0.213582	−	0.369935i	0.952833	+	0.303495i	$0.0981535\pi$
$374$	14.5214	+	25.1518i	0.750884	+	1.30057i
$375$		0			0
$376$	−2.45302	−	4.24875i	−0.126505	−	0.219113i
$377$	−0.249937	−	2.72327i	−0.0128724	−	0.140256i
$378$		0			0
$379$	0.896568	+	3.34604i	0.0460536	+	0.171874i	0.985122	−	0.171855i	$-0.0549762\pi$
$379$	0.896568	+	3.34604i	0.0460536	+	0.171874i	−0.939069	+	0.343730i	$0.888310\pi$
$380$	2.22735			0.114261
$381$		0			0
$382$	0.0174592	+	0.0651586i	0.000893291	+	0.00333381i
$383$	−33.2559	+	8.91088i	−1.69930	+	0.455325i	−0.972762	−	0.231806i	$-0.925537\pi$
$383$	−33.2559	+	8.91088i	−1.69930	+	0.455325i	−0.726534	+	0.687131i	$0.758870\pi$
$384$		0			0
$385$	6.01876	−	9.95723i	0.306744	−	0.507468i
$386$	10.1296	+	17.5450i	0.515584	+	0.893018i
$387$		0			0
$388$	2.19894	+	0.589205i	0.111635	+	0.0299124i
$389$	8.07601	+	4.66269i	0.409470	+	0.236408i	0.690562	−	0.723273i	$-0.257363\pi$
$389$	8.07601	+	4.66269i	0.409470	+	0.236408i	−0.281092	+	0.959681i	$0.590697\pi$
$390$		0			0
$391$			34.9473i			1.76736i
$392$	10.5414	+	11.4247i	0.532421	+	0.577032i
$393$		0			0
$394$	5.22420	+	3.01619i	0.263191	+	0.151954i
$395$	12.5269	−	3.35656i	0.630295	−	0.168887i
$396$		0			0
$397$	−5.12022	−	19.1089i	−0.256977	−	0.959049i	−0.966980	−	0.254852i	$-0.917973\pi$
$397$	−5.12022	−	19.1089i	−0.256977	−	0.959049i	0.710004	−	0.704198i	$-0.248693\pi$
$398$	10.0667	−	10.0667i	0.504596	−	0.504596i
$399$		0			0
$400$	11.2445	+	6.49199i	0.562223	+	0.324600i
$401$	−8.51496	−	8.51496i	−0.425217	−	0.425217i	0.461778	−	0.886995i	$-0.347212\pi$
$401$	−8.51496	−	8.51496i	−0.425217	−	0.425217i	−0.886995	+	0.461778i	$0.847212\pi$
$402$		0			0
$403$	−19.9637	+	23.9985i	−0.994463	+	1.19545i
$404$	−10.7577	+	6.21095i	−0.535214	+	0.309006i
$405$		0			0
$406$	−3.16031	+	0.779094i	−0.156843	+	0.0386658i
$407$	−15.0402	+	8.68346i	−0.745514	+	0.430423i
$408$		0			0
$409$	−13.7865	−	13.7865i	−0.681696	−	0.681696i	0.278686	−	0.960382i	$-0.410101\pi$
$409$	−13.7865	−	13.7865i	−0.681696	−	0.681696i	−0.960382	+	0.278686i	$0.910101\pi$
$410$	−3.53319	−	3.53319i	−0.174492	−	0.174492i
$411$		0			0
$412$	−5.13727	+	2.96600i	−0.253095	+	0.146125i
$413$	−1.61555	−	1.68181i	−0.0794959	−	0.0827566i
$414$		0			0
$415$	−2.83129	+	1.63465i	−0.138983	+	0.0802417i
$416$	2.10644	−	12.2508i	0.103277	−	0.600645i
$417$		0			0
$418$	7.64091	+	7.64091i	0.373729	+	0.373729i
$419$	3.34749	+	1.93268i	0.163536	+	0.0944174i	0.579534	−	0.814948i	$-0.303235\pi$
$419$	3.34749	+	1.93268i	0.163536	+	0.0944174i	−0.415999	+	0.909365i	$0.636568\pi$
$420$		0			0
$421$	3.65782	−	3.65782i	0.178271	−	0.178271i	−0.612331	−	0.790602i	$-0.709768\pi$
$421$	3.65782	−	3.65782i	0.178271	−	0.178271i	0.790602	+	0.612331i	$0.209768\pi$
$422$	−2.80148	−	10.4553i	−0.136374	−	0.508955i
$423$		0			0
$424$	10.6105	−	2.84309i	0.515293	−	0.138072i
$425$	14.3701	+	8.29658i	0.697052	+	0.402443i
$426$		0			0
$427$	7.08403	−	11.7196i	0.342820	−	0.567150i
$428$			0.0453239i			0.00219081i
$429$		0			0
$430$	5.55275	+	3.20588i	0.267778	+	0.154601i
$431$	−9.71910	−	2.60423i	−0.468153	−	0.125441i	0.0170280	−	0.999855i	$-0.494580\pi$
$431$	−9.71910	−	2.60423i	−0.468153	−	0.125441i	−0.485181	+	0.874414i	$0.661246\pi$
$432$		0			0
$433$	−3.80951	−	6.59826i	−0.183073	−	0.317092i	0.759852	−	0.650096i	$-0.225271\pi$
$433$	−3.80951	−	6.59826i	−0.183073	−	0.317092i	−0.942926	+	0.333004i	$0.891938\pi$
$434$	31.7972	+	19.2201i	1.52631	+	0.922596i
$435$		0			0
$436$	4.46369	−	1.19604i	0.213772	−	0.0572800i
$437$	3.36536	+	12.5597i	0.160987	+	0.600811i
$438$		0			0
$439$	22.3628			1.06732			0.533658	−	0.845700i	$-0.320817\pi$
$439$	22.3628			1.06732			0.533658	+	0.845700i	$0.320817\pi$
$440$	−2.52756	−	9.43298i	−0.120497	−	0.449700i
$441$		0			0
$442$	6.15988	−	35.8252i	0.292996	−	1.70403i
$443$	12.8459	+	22.2497i	0.610326	+	1.05712i	0.991185	+	0.132483i	$0.0422951\pi$
$443$	12.8459	+	22.2497i	0.610326	+	1.05712i	−0.380859	+	0.924633i	$0.624372\pi$
$444$		0			0
$445$	6.38578	+	11.0605i	0.302715	+	0.524318i
$446$	5.12185	−	8.87130i	0.242527	−	0.420068i
$447$		0			0
$448$	10.9392	+	0.219843i	0.516828	+	0.0103866i
$449$	0.821652	−	3.06645i	0.0387761	−	0.144715i	−0.943824	−	0.330449i	$-0.892800\pi$
$449$	0.821652	−	3.06645i	0.0387761	−	0.144715i	0.982600	+	0.185735i	$0.0594665\pi$
$450$		0			0
$451$		−	5.81305i		−	0.273726i
$452$	8.91401	−	5.14650i	0.419280	−	0.242071i
$453$		0			0
$454$	38.1954			1.79260
$455$	−13.7616	+	4.76337i	−0.645155	+	0.223310i
$456$		0			0
$457$	−23.2165	+	23.2165i	−1.08602	+	1.08602i	−0.0900871	+	0.995934i	$0.528715\pi$
$457$	−23.2165	+	23.2165i	−1.08602	+	1.08602i	−0.995934	+	0.0900871i	$0.971285\pi$
$458$	−26.5822	+	15.3472i	−1.24210	+	0.717129i
$459$		0			0
$460$	−1.40149	+	5.23045i	−0.0653450	+	0.243871i
$461$	1.38662	−	5.17492i	0.0645811	−	0.241020i	−0.926088	−	0.377307i	$-0.876850\pi$
$461$	1.38662	−	5.17492i	0.0645811	−	0.241020i	0.990669	+	0.136287i	$0.0435169\pi$
$462$		0			0
$463$	−17.0182	−	17.0182i	−0.790903	−	0.790903i	0.190738	−	0.981641i	$-0.438912\pi$
$463$	−17.0182	−	17.0182i	−0.790903	−	0.790903i	−0.981641	+	0.190738i	$0.938912\pi$
$464$	−1.84452	+	3.19480i	−0.0856295	+	0.148315i
$465$		0			0
$466$	3.08663	−	11.5194i	0.142985	−	0.533628i
$467$	3.73447	+	6.46829i	0.172811	+	0.299317i	0.939401	−	0.342819i	$-0.111382\pi$
$467$	3.73447	+	6.46829i	0.172811	+	0.299317i	−0.766591	+	0.642136i	$0.778049\pi$
$468$		0			0
$469$	11.5560	−	39.9024i	0.533605	−	1.84252i
$470$	−1.41582	−	5.28393i	−0.0653071	−	0.243729i
$471$		0			0
$472$	−1.95740			−0.0900967
$473$	1.93062	+	7.20516i	0.0887698	+	0.331294i
$474$		0			0
$475$	5.96340	+	1.59789i	0.273620	+	0.0733162i
$476$	−10.3731	−	0.208466i	−0.475449	−	0.00955502i
$477$		0			0
$478$			9.37376i			0.428746i
$479$	20.1369	+	5.39566i	0.920078	+	0.246534i	0.687619	−	0.726072i	$-0.258656\pi$
$479$	20.1369	+	5.39566i	0.920078	+	0.246534i	0.232459	+	0.972606i	$0.425323\pi$
$480$		0			0
$481$	21.4227	+	3.68347i	0.976789	+	0.167952i
$482$			46.6164i			2.12332i
$483$		0			0
$484$	0.852240	−	1.47612i	0.0387382	−	0.0670965i
$485$	−4.77055	−	2.75428i	−0.216620	−	0.125065i
$486$		0			0
$487$	−13.2023	+	13.2023i	−0.598255	+	0.598255i	−0.939848	−	0.341593i	$-0.889034\pi$
$487$	−13.2023	+	13.2023i	−0.598255	+	0.598255i	0.341593	+	0.939848i	$0.389034\pi$
$488$	−2.97492	−	11.1025i	−0.134668	−	0.502588i
$489$		0			0
$490$	8.05634	+	15.3468i	0.363948	+	0.693297i
$491$	−26.9636	−	15.5675i	−1.21685	−	0.702550i	−0.252609	−	0.967569i	$-0.581289\pi$
$491$	−26.9636	−	15.5675i	−1.21685	−	0.702550i	−0.964243	+	0.265019i	$0.914622\pi$
$492$		0			0
$493$	−2.35724	+	4.08286i	−0.106165	+	0.183883i
$494$	−1.23611	−	13.4684i	−0.0556150	−	0.605972i
$495$		0			0
$496$	40.6752	−	10.8989i	1.82637	−	0.489374i
$497$	7.85109	−	27.1096i	0.352169	−	1.21603i
$498$		0			0
$499$	17.9002	+	4.79636i	0.801325	+	0.214714i	0.636166	−	0.771553i	$-0.280519\pi$
$499$	17.9002	+	4.79636i	0.801325	+	0.214714i	0.165159	+	0.986267i	$0.447186\pi$
$500$	5.22310	+	5.22310i	0.233584	+	0.233584i
$501$		0			0
$502$	−30.4791	−	8.16684i	−1.36035	−	0.364504i
$503$	22.0368	−	12.7230i	0.982573	−	0.567289i	0.0795268	−	0.996833i	$-0.474659\pi$
$503$	22.0368	−	12.7230i	0.982573	−	0.567289i	0.903046	+	0.429544i	$0.141326\pi$
$504$		0			0
$505$	29.0335	−	7.77950i	1.29197	−	0.346183i
$506$	−22.7508	+	13.1352i	−1.01140	+	0.583930i
$507$		0			0
$508$	5.42858	−	9.40257i	0.240854	−	0.417172i
$509$	17.5363	+	17.5363i	0.777285	+	0.777285i	0.979368	−	0.202084i	$-0.0647713\pi$
$509$	17.5363	+	17.5363i	0.777285	+	0.777285i	−0.202084	+	0.979368i	$0.564771\pi$
$510$		0			0
$511$	17.8730	−	4.40613i	0.790654	−	0.194916i
$512$	3.41779	−	3.41779i	0.151046	−	0.151046i
$513$		0			0
$514$	−28.9081	+	28.9081i	−1.27508	+	1.27508i
$515$	13.8648	−	3.71506i	0.610955	−	0.163705i
$516$		0			0
$517$	3.18204	−	5.51145i	0.139946	−	0.242393i
$518$	0.519839	−	25.8667i	0.0228404	−	1.13652i
$519$		0			0
$520$	−5.11853	+	11.0998i	−0.224462	+	0.486758i
$521$	3.53287	+	2.03970i	0.154778	+	0.0893610i	0.575389	−	0.817880i	$-0.304851\pi$
$521$	3.53287	+	2.03970i	0.154778	+	0.0893610i	−0.420611	+	0.907241i	$0.638184\pi$
$522$		0			0
$523$		−	29.4455i		−	1.28756i	−0.765209	−	0.643781i	$-0.777365\pi$
$523$		−	29.4455i		−	1.28756i	0.765209	−	0.643781i	$-0.222635\pi$
$524$	1.72555	+	2.98874i	0.0753810	+	0.130564i
$525$		0			0
$526$	−49.0053	−	13.1309i	−2.13673	−	0.572536i
$527$	51.9817	−	13.9285i	2.26436	−	0.606733i
$528$		0			0
$529$	−8.61121			−0.374400
$530$	12.2483			0.532033
$531$		0			0
$532$	−3.74805	+	0.923987i	−0.162498	+	0.0400599i
$533$	−4.65304	+	5.59345i	−0.201546	+	0.242279i
$534$		0			0
$535$	0.0283851	−	0.105935i	0.00122720	−	0.00457996i
$536$	−17.4341	−	30.1967i	−0.753038	−	1.30430i
$537$		0			0
$538$	10.3430	+	10.3430i	0.445917	+	0.445917i
$539$	−5.99736	+	19.2522i	−0.258325	+	0.829252i
$540$		0			0
$541$	−9.74099	+	36.3539i	−0.418798	+	1.56298i	0.358307	+	0.933604i	$0.383354\pi$
$541$	−9.74099	+	36.3539i	−0.418798	+	1.56298i	−0.777105	+	0.629371i	$0.783312\pi$
$542$			5.52463i			0.237303i
$543$		0			0
$544$	−15.1530	+	15.1530i	−0.649678	+	0.649678i
$545$	−11.1820			−0.478982
$546$		0			0
$547$	−36.7251			−1.57025			−0.785125	−	0.619337i	$-0.787401\pi$
$547$	−36.7251			−1.57025			−0.785125	+	0.619337i	$0.787401\pi$
$548$	0.782679	−	0.782679i	0.0334344	−	0.0334344i
$549$		0			0
$550$			12.4733i			0.531864i
$551$	−0.453995	+	1.69433i	−0.0193408	+	0.0721810i
$552$		0			0
$553$	−19.6870	+	10.8448i	−0.837177	+	0.461169i
$554$	4.62103	+	4.62103i	0.196329	+	0.196329i
$555$		0			0
$556$	−2.60053	−	4.50425i	−0.110287	−	0.191023i
$557$	5.17843	−	19.3262i	0.219417	−	0.818876i	−0.765148	−	0.643855i	$-0.777334\pi$
$557$	5.17843	−	19.3262i	0.219417	−	0.818876i	0.984565	−	0.175021i	$-0.0559993\pi$
$558$		0			0
$559$	3.90967	−	8.47832i	0.165361	−	0.358595i
$560$	18.8692	+	5.46462i	0.797368	+	0.230922i
$561$		0			0
$562$	−7.53556			−0.317869
$563$	−15.6920			−0.661340			−0.330670	−	0.943746i	$-0.607275\pi$
$563$	−15.6920			−0.661340			−0.330670	+	0.943746i	$0.607275\pi$
$564$		0			0
$565$	−24.0577	+	6.44624i	−1.01211	+	0.271195i
$566$	−1.61320	−	0.432256i	−0.0678079	−	0.0181691i
$567$		0			0
$568$	−11.8447	−	20.5155i	−0.496991	−	0.860813i
$569$		−	5.07533i		−	0.212769i	−0.994325	−	0.106385i	$-0.966073\pi$
$569$		−	5.07533i		−	0.212769i	0.994325	−	0.106385i	$-0.0339275\pi$
$570$		0			0
$571$	−17.5642	−	10.1407i	−0.735038	−	0.424374i	0.0852246	−	0.996362i	$-0.472839\pi$
$571$	−17.5642	−	10.1407i	−0.735038	−	0.424374i	−0.820262	+	0.571988i	$0.806173\pi$
$572$	6.14792	−	2.26733i	0.257057	−	0.0948020i
$573$		0			0
$574$	7.41113	+	4.47974i	0.309335	+	0.186981i
$575$	−7.50459	+	12.9983i	−0.312963	+	0.542068i
$576$		0			0
$577$	−25.2962	+	6.77811i	−1.05310	+	0.282176i	−0.743531	−	0.668702i	$-0.766850\pi$
$577$	−25.2962	+	6.77811i	−1.05310	+	0.282176i	−0.309566	+	0.950878i	$0.600184\pi$
$578$	−24.8143	+	24.8143i	−1.03214	+	1.03214i
$579$		0			0
$580$	−0.516535	+	0.516535i	−0.0214480	+	0.0214480i
$581$	4.08621	−	3.92521i	0.169525	−	0.162845i
$582$		0			0
$583$	10.0759	+	10.0759i	0.417301	+	0.417301i
$584$	7.72537	−	13.3807i	0.319678	−	0.553698i
$585$		0			0
$586$	35.9183	−	20.7375i	1.48377	−	0.856657i
$587$	−1.75410	+	0.470009i	−0.0723994	+	0.0193994i	−0.294837	−	0.955548i	$-0.595265\pi$
$587$	−1.75410	+	0.470009i	−0.0723994	+	0.0193994i	0.222438	+	0.974947i	$0.428599\pi$
$588$		0			0
$589$	17.3404	−	10.0115i	0.714498	−	0.412516i
$590$	−2.10817	−	0.564883i	−0.0867921	−	0.0232559i
$591$		0			0
$592$	−20.7341	−	20.7341i	−0.852166	−	0.852166i
$593$	−30.9506	−	8.29320i	−1.27099	−	0.340561i	−0.440580	−	0.897713i	$-0.645227\pi$
$593$	−30.9506	−	8.29320i	−1.27099	−	0.340561i	−0.830410	+	0.557153i	$0.811894\pi$
$594$		0			0
$595$	24.1143	+	6.98362i	0.988588	+	0.286301i
$596$	−2.71203	+	0.726687i	−0.111089	+	0.0297663i
$597$		0			0
$598$	32.4054	+	5.57186i	1.32515	+	0.227850i
$599$	−1.81349	+	3.14105i	−0.0740970	+	0.128340i	−0.900693	−	0.434456i	$-0.856941\pi$
$599$	−1.81349	+	3.14105i	−0.0740970	+	0.128340i	0.826596	+	0.562795i	$0.190274\pi$
$600$		0			0
$601$	22.0032	+	12.7035i	0.897529	+	0.518189i	0.876398	−	0.481588i	$-0.159940\pi$
$601$	22.0032	+	12.7035i	0.897529	+	0.518189i	0.0211313	+	0.999777i	$0.493273\pi$
$602$	−10.6737	−	3.09118i	−0.435030	−	0.125987i
$603$		0			0
$604$	1.46976	+	5.48522i	0.0598037	+	0.223191i
$605$	−2.91638	+	2.91638i	−0.118568	+	0.118568i
$606$		0			0
$607$	3.52942	+	2.03771i	0.143255	+	0.0827081i	0.569914	−	0.821704i	$-0.306976\pi$
$607$	3.52942	+	2.03771i	0.143255	+	0.0827081i	−0.426660	+	0.904412i	$0.640310\pi$
$608$	−3.98661	+	6.90502i	−0.161679	+	0.280035i
$609$		0			0
$610$		−	12.8162i		−	0.518915i
$611$	−7.47345	+	2.75619i	−0.302344	+	0.111503i
$612$		0			0
$613$	−22.4119	−	6.00524i	−0.905207	−	0.242550i	−0.223956	−	0.974599i	$-0.571897\pi$
$613$	−22.4119	−	6.00524i	−0.905207	−	0.242550i	−0.681251	+	0.732050i	$0.738564\pi$
$614$		−	32.1588i		−	1.29782i
$615$		0			0
$616$	8.16637	+	14.8247i	0.329032	+	0.597304i
$617$	−0.685439	−	0.183663i	−0.0275948	−	0.00739399i	0.244995	−	0.969524i	$-0.421214\pi$
$617$	−0.685439	−	0.183663i	−0.0275948	−	0.00739399i	−0.272590	+	0.962130i	$0.587880\pi$
$618$		0			0
$619$	−3.54491	−	13.2298i	−0.142482	−	0.531751i	−0.999855	−	0.0170541i	$-0.994571\pi$
$619$	−3.54491	−	13.2298i	−0.142482	−	0.531751i	0.857372	−	0.514697i	$-0.172095\pi$
$620$	8.33851			0.334882
$621$		0			0
$622$	−2.69391	−	10.0538i	−0.108016	−	0.403121i
$623$	−15.3339	−	15.9629i	−0.614340	−	0.639539i
$624$		0			0
$625$	−2.26294	−	3.91952i	−0.0905174	−	0.156781i
$626$	10.5679	−	39.4399i	0.422378	−	1.57634i
$627$		0			0
$628$	−1.53385	+	2.65671i	−0.0612073	+	0.106014i
$629$	−26.4976	−	26.4976i	−1.05653	−	1.05653i
$630$		0			0
$631$	−0.371814	+	1.38763i	−0.0148017	+	0.0552407i	−0.972932	−	0.231093i	$-0.925770\pi$
$631$	−0.371814	+	1.38763i	−0.0148017	+	0.0552407i	0.958130	+	0.286334i	$0.0924365\pi$
$632$	−4.88274	+	18.2226i	−0.194225	+	0.724858i
$633$		0			0
$634$	33.8469	−	19.5415i	1.34423	−	0.776093i
$635$	−18.5767	+	18.5767i	−0.737194	+	0.737194i
$636$		0			0
$637$	21.1812	−	13.7243i	0.839229	−	0.543778i
$638$	−3.54394			−0.140306
$639$		0			0
$640$	17.9840	−	10.3830i	0.710879	−	0.410426i
$641$			11.0407i			0.436083i	0.975939	+	0.218042i	$0.0699669\pi$
$641$			11.0407i			0.436083i	−0.975939	+	0.218042i	$0.930033\pi$
$642$		0			0
$643$	11.5604	−	43.1441i	0.455899	−	1.70144i	−0.229532	−	0.973301i	$-0.573719\pi$
$643$	11.5604	−	43.1441i	0.455899	−	1.70144i	0.685431	−	0.728138i	$-0.259614\pi$
$644$	0.188566	−	9.38286i	0.00743053	−	0.369736i
$645$		0			0
$646$	−11.6581	+	20.1924i	−0.458682	+	0.794461i
$647$	5.20304	+	9.01192i	0.204552	+	0.354295i	0.949990	−	0.312280i	$-0.101093\pi$
$647$	5.20304	+	9.01192i	0.204552	+	0.354295i	−0.745438	+	0.666575i	$0.767759\pi$
$648$		0			0
$649$	−1.26956	−	2.19895i	−0.0498347	−	0.0863163i
$650$	9.98423	−	12.0021i	0.391614	−	0.470761i
$651$		0			0
$652$	−1.04318	−	3.89321i	−0.0408542	−	0.152470i
$653$	10.4386			0.408493			0.204246	−	0.978920i	$-0.434526\pi$
$653$	10.4386			0.408493			0.204246	+	0.978920i	$0.434526\pi$
$654$		0			0
$655$	−2.16133	−	8.06620i	−0.0844502	−	0.315172i
$656$	9.48038	−	2.54026i	0.370146	−	0.0991804i
$657$		0			0
$658$	4.57443	+	8.30413i	0.178330	+	0.323729i
$659$	3.86557	+	6.69537i	0.150581	+	0.260815i	0.931441	−	0.363892i	$-0.118552\pi$
$659$	3.86557	+	6.69537i	0.150581	+	0.260815i	−0.780860	+	0.624706i	$0.785219\pi$
$660$		0			0
$661$	43.2687	+	11.5938i	1.68296	+	0.450947i	0.968558	−	0.248790i	$-0.0800328\pi$
$661$	43.2687	+	11.5938i	1.68296	+	0.450947i	0.714401	+	0.699737i	$0.246699\pi$
$662$	8.30322	+	4.79387i	0.322714	+	0.186319i
$663$		0			0
$664$		−	4.75580i		−	0.184561i
$665$	9.33892	+	0.187683i	0.362148	+	0.00727802i
$666$		0			0
$667$	−3.69311	−	2.13222i	−0.142998	−	0.0825597i
$668$	−6.17033	+	1.65334i	−0.238737	+	0.0639695i
$669$		0			0
$670$	−10.0625	−	37.5539i	−0.388750	−	1.45083i
$671$	10.5431	−	10.5431i	0.407012	−	0.407012i
$672$		0			0
$673$	−19.6804	−	11.3625i	−0.758625	−	0.437992i	0.0701768	−	0.997535i	$-0.477644\pi$
$673$	−19.6804	−	11.3625i	−0.758625	−	0.437992i	−0.828802	+	0.559542i	$0.810977\pi$
$674$	−13.2262	−	13.2262i	−0.509454	−	0.509454i
$675$		0			0
$676$	−7.73054	−	2.73941i	−0.297329	−	0.105362i
$677$	7.56955	−	4.37028i	0.290921	−	0.167964i	−0.347436	−	0.937704i	$-0.612948\pi$
$677$	7.56955	−	4.37028i	0.290921	−	0.167964i	0.638357	+	0.769740i	$0.279614\pi$
$678$		0			0
$679$	9.17017	+	2.65573i	0.351919	+	0.101918i
$680$	18.2488	−	10.5359i	0.699809	−	0.404035i
$681$		0			0
$682$	28.6052	+	28.6052i	1.09535	+	1.09535i
$683$	−1.57793	−	1.57793i	−0.0603777	−	0.0603777i	0.676273	−	0.736651i	$-0.263594\pi$
$683$	−1.57793	−	1.57793i	−0.0603777	−	0.0603777i	−0.736651	+	0.676273i	$0.763594\pi$
$684$		0			0
$685$	−2.31951	+	1.33917i	−0.0886240	+	0.0511671i
$686$	−19.9231	−	22.4825i	−0.760668	−	0.858387i
$687$		0			0
$688$	−10.9071	+	6.29720i	−0.415828	+	0.240078i
$689$	−1.63002	−	17.7605i	−0.0620990	−	0.676620i
$690$		0			0
$691$	−3.25857	−	3.25857i	−0.123962	−	0.123962i	0.642404	−	0.766366i	$-0.277937\pi$
$691$	−3.25857	−	3.25857i	−0.123962	−	0.123962i	−0.766366	+	0.642404i	$0.777937\pi$
$692$	−9.64206	−	5.56685i	−0.366536	−	0.211620i
$693$		0			0
$694$	10.4061	−	10.4061i	0.395012	−	0.395012i
$695$	3.25729	+	12.1564i	0.123556	+	0.461117i
$696$		0			0
$697$	12.1156	−	3.24638i	0.458913	−	0.122965i
$698$	42.2133	+	24.3718i	1.59780	+	0.922488i
$699$		0			0
$700$	−3.81341	−	2.30505i	−0.144133	−	0.0871228i
$701$			10.7910i			0.407569i	0.979016	+	0.203784i	$0.0653242\pi$
$701$			10.7910i			0.407569i	−0.979016	+	0.203784i	$0.934676\pi$
$702$		0			0
$703$	−12.0746	−	6.97128i	−0.455403	−	0.262927i
$704$	11.5070	+	3.08329i	0.433686	+	0.116206i
$705$		0			0
$706$	−23.5012	−	40.7053i	−0.884481	−	1.53197i
$707$	−45.6285	+	25.1350i	−1.71604	+	0.945300i
$708$		0			0
$709$	−22.3737	+	5.99502i	−0.840262	+	0.225148i	−0.653186	−	0.757198i	$-0.726568\pi$
$709$	−22.3737	+	5.99502i	−0.840262	+	0.225148i	−0.187076	+	0.982345i	$0.559901\pi$
$710$	−6.83646	−	25.5140i	−0.256568	−	0.957524i
$711$		0			0
$712$	−18.5786			−0.696262
$713$	12.5988	+	47.0195i	0.471830	+	1.76090i
$714$		0			0
$715$	−15.7894	+	1.44912i	−0.590490	+	0.0541941i
$716$	−6.37929	−	11.0493i	−0.238405	−	0.412930i
$717$		0			0
$718$	−7.15942	−	12.4005i	−0.267187	−	0.462782i
$719$	−17.9493	+	31.0890i	−0.669394	+	1.15942i	0.308679	+	0.951166i	$0.400113\pi$
$719$	−17.9493	+	31.0890i	−0.669394	+	1.15942i	−0.978074	+	0.208259i	$0.933220\pi$
$720$		0			0
$721$	−21.7897	+	12.0031i	−0.811489	+	0.447018i
$722$	5.73099	−	21.3883i	0.213285	−	0.795991i
$723$		0			0
$724$			11.0184i			0.409496i
$725$	−1.75351	+	1.01239i	−0.0651236	+	0.0375991i
$726$		0			0
$727$	40.7770			1.51234			0.756168	−	0.654377i	$-0.227069\pi$
$727$	40.7770			1.51234			0.756168	+	0.654377i	$0.227069\pi$
$728$	4.00854	−	20.8014i	0.148566	−	0.770952i
$729$		0			0
$730$	12.1819	−	12.1819i	0.450874	−	0.450874i
$731$	−13.9389	+	8.04764i	−0.515549	+	0.297653i
$732$		0			0
$733$	−6.43098	+	24.0007i	−0.237533	+	0.886487i	0.739457	+	0.673204i	$0.235082\pi$
$733$	−6.43098	+	24.0007i	−0.237533	+	0.886487i	−0.976990	+	0.213283i	$0.931584\pi$
$734$	5.57860	−	20.8196i	0.205910	−	0.768466i
$735$		0			0
$736$	−13.7065	−	13.7065i	−0.505227	−	0.505227i
$737$	22.6154	−	39.1710i	0.833048	−	1.44288i
$738$		0			0
$739$	−10.9878	+	41.0071i	−0.404194	+	1.50847i	0.401344	+	0.915927i	$0.368543\pi$
$739$	−10.9878	+	41.0071i	−0.404194	+	1.50847i	−0.805538	+	0.592544i	$0.798124\pi$
$740$	−2.90317	−	5.02844i	−0.106723	−	0.184849i
$741$		0			0
$742$	−20.6107	+	5.08105i	−0.756643	+	0.186531i
$743$	6.30753	+	23.5400i	0.231401	+	0.863600i	0.979738	+	0.200282i	$0.0641858\pi$
$743$	6.30753	+	23.5400i	0.231401	+	0.863600i	−0.748337	+	0.663318i	$0.769148\pi$
$744$		0			0
$745$	6.79390			0.248909
$746$	3.46336	+	12.9254i	0.126802	+	0.473233i
$747$		0			0
$748$	−10.9115	−	2.92373i	−0.398964	−	0.106902i
$749$	−0.00381912	+	0.190036i	−0.000139547	+	0.00694375i
$750$		0			0
$751$		−	28.4458i		−	1.03800i	−0.854774	−	0.519001i	$-0.826304\pi$
$751$		−	28.4458i		−	1.03800i	0.854774	−	0.519001i	$-0.173696\pi$
$752$	10.3790	+	2.78105i	0.378484	+	0.101415i
$753$		0			0
$754$	3.41006	+	2.83674i	0.124187	+	0.103308i
$755$		−	13.7410i		−	0.500086i
$756$		0			0
$757$	−26.0081	+	45.0474i	−0.945282	+	1.63728i	−0.190095	+	0.981766i	$0.560880\pi$
$757$	−26.0081	+	45.0474i	−0.945282	+	1.63728i	−0.755187	+	0.655510i	$0.772454\pi$
$758$	−4.86597	−	2.80937i	−0.176740	−	0.102041i
$759$		0			0
$760$	5.54383	−	5.54383i	0.201096	−	0.201096i
$761$	−1.53417	−	5.72561i	−0.0556137	−	0.207553i	0.932528	−	0.361098i	$-0.117598\pi$
$761$	−1.53417	−	5.72561i	−0.0556137	−	0.207553i	−0.988142	+	0.153544i	$0.950931\pi$
$762$		0			0
$763$	18.8163	−	4.63869i	0.681196	−	0.167932i
$764$	−0.0227228	−	0.0131190i	−0.000822080	−	0.000474628i
$765$		0			0
$766$	27.9220	−	48.3623i	1.00886	−	1.74740i
$767$	−0.538541	+	3.13210i	−0.0194456	+	0.113093i
$768$		0			0
$769$	0.310861	−	0.0832949i	0.0112099	−	0.00300369i	−0.253210	−	0.967411i	$-0.581486\pi$
$769$	0.310861	−	0.0832949i	0.0112099	−	0.00300369i	0.264420	+	0.964408i	$0.414820\pi$
$770$	4.51715	+	18.3233i	0.162787	+	0.660326i
$771$		0			0
$772$	−7.61148	−	2.03949i	−0.273943	−	0.0734028i
$773$	−22.4820	−	22.4820i	−0.808623	−	0.808623i	0.175802	−	0.984425i	$-0.443748\pi$
$773$	−22.4820	−	22.4820i	−0.808623	−	0.808623i	−0.984425	+	0.175802i	$0.943748\pi$
$774$		0			0
$775$	22.3251	+	5.98200i	0.801942	+	0.214880i
$776$	6.93965	−	4.00661i	0.249119	−	0.143829i
$777$		0			0
$778$	−14.6104	+	3.91484i	−0.523807	+	0.140354i
$779$	4.04161	−	2.33343i	0.144806	−	0.0836037i
$780$		0			0
$781$	15.3648	−	26.6126i	0.549796	−	0.952274i
$782$	−40.0820	−	40.0820i	−1.43333	−	1.43333i
$783$		0			0
$784$	−34.0188	−	1.36789i	−1.21496	−	0.0488533i
$785$	5.24887	−	5.24887i	0.187340	−	0.187340i
$786$		0			0
$787$	23.7400	−	23.7400i	0.846239	−	0.846239i	−0.143423	−	0.989662i	$-0.545811\pi$
$787$	23.7400	−	23.7400i	0.846239	−	0.846239i	0.989662	+	0.143423i	$0.0458108\pi$
$788$	−2.26639	+	0.607277i	−0.0807368	+	0.0216334i
$789$		0			0
$790$	−10.5177	+	18.2172i	−0.374202	+	0.648137i
$791$	37.8086	−	20.8273i	1.34432	−	0.740535i
$792$		0			0
$793$	−18.5840	+	1.70561i	−0.659937	+	0.0605678i
$794$	27.7891	+	16.0440i	0.986198	+	0.569382i
$795$		0			0
$796$			5.53736i			0.196267i
$797$	−6.34434	−	10.9887i	−0.224728	−	0.389240i	0.731510	−	0.681831i	$-0.238816\pi$
$797$	−6.34434	−	10.9887i	−0.224728	−	0.389240i	−0.956238	+	0.292591i	$0.905483\pi$
$798$		0			0
$799$	13.2641	+	3.55410i	0.469250	+	0.125735i
$800$	−8.88996	+	2.38206i	−0.314308	+	0.0842185i
$801$		0			0
$802$	19.5321			0.689703
$803$	20.0426			0.707287
$804$		0			0
$805$	−6.31697	+	21.8123i	−0.222644	+	0.768783i
$806$	−4.62759	−	50.4215i	−0.163000	−	1.77602i
$807$		0			0
$808$	−11.3167	+	42.2346i	−0.398121	+	1.48581i
$809$	−21.4022	−	37.0698i	−0.752463	−	1.30330i	−0.946626	−	0.322334i	$-0.895533\pi$
$809$	−21.4022	−	37.0698i	−0.752463	−	1.30330i	0.194163	−	0.980969i	$-0.437801\pi$
$810$		0			0
$811$	1.51360	+	1.51360i	0.0531496	+	0.0531496i	0.733182	−	0.680032i	$-0.238034\pi$
$811$	1.51360	+	1.51360i	0.0531496	+	0.0531496i	−0.680032	+	0.733182i	$0.738034\pi$
$812$	0.654916	−	1.08347i	0.0229830	−	0.0380224i
$813$		0			0
$814$	7.29072	−	27.2093i	0.255539	−	0.953686i
$815$			9.75286i			0.341628i
$816$		0			0
$817$	−4.23453	+	4.23453i	−0.148147	+	0.148147i
$818$	31.6242			1.10571
$819$		0			0
$820$	1.94350			0.0678699
$821$	−26.6039	+	26.6039i	−0.928481	+	0.928481i	−0.997608	−	0.0691268i	$-0.977979\pi$
$821$	−26.6039	+	26.6039i	−0.928481	+	0.928481i	0.0691268	+	0.997608i	$0.477979\pi$
$822$		0			0
$823$			44.4969i			1.55107i	0.631308	+	0.775533i	$0.282519\pi$
$823$			44.4969i			1.55107i	−0.631308	+	0.775533i	$0.717481\pi$
$824$	−5.40424	+	20.1689i	−0.188266	+	0.702616i
$825$		0			0
$826$	3.78184	+	0.0760030i	0.131587	+	0.00264448i
$827$	−12.3898	−	12.3898i	−0.430835	−	0.430835i	0.458077	−	0.888912i	$-0.348538\pi$
$827$	−12.3898	−	12.3898i	−0.430835	−	0.430835i	−0.888912	+	0.458077i	$0.848538\pi$
$828$		0			0
$829$	−21.1381	−	36.6122i	−0.734155	−	1.27159i	−0.955093	−	0.296306i	$-0.904245\pi$
$829$	−21.1381	−	36.6122i	−0.734155	−	1.27159i	0.220938	−	0.975288i	$-0.429088\pi$
$830$	1.37247	−	5.12212i	0.0476390	−	0.177791i
$831$		0			0
$832$	−8.60428	−	12.1776i	−0.298300	−	0.422181i
$833$	−43.4750	−	1.74813i	−1.50632	−	0.0605690i
$834$		0			0
$835$	15.4573			0.534920
$836$	−4.20302			−0.145365
$837$		0			0
$838$	−6.05597	+	1.62269i	−0.209200	+	0.0560550i
$839$	−25.6907	−	6.88379i	−0.886940	−	0.237655i	−0.213541	−	0.976934i	$-0.568500\pi$
$839$	−25.6907	−	6.88379i	−0.886940	−	0.237655i	−0.673399	+	0.739279i	$0.735166\pi$
$840$		0			0
$841$	14.2124	+	24.6165i	0.490081	+	0.848846i
$842$			8.39052i			0.289156i
$843$		0			0
$844$	3.64606	+	2.10506i	0.125503	+	0.0724590i
$845$	16.3529	+	11.2442i	0.562555	+	0.386812i
$846$		0			0
$847$	3.69769	−	6.11733i	0.127054	−	0.210194i
$848$	−12.0295	+	20.8356i	−0.413093	+	0.715498i
$849$		0			0
$850$	−25.9971	+	6.96589i	−0.891691	+	0.238928i
$851$	23.9681	−	23.9681i	0.821616	−	0.821616i
$852$		0			0
$853$	−0.950856	+	0.950856i	−0.0325567	+	0.0325567i	−0.723198	−	0.690641i	$-0.757328\pi$
$853$	−0.950856	+	0.950856i	−0.0325567	+	0.0325567i	0.690641	+	0.723198i	$0.257328\pi$
$854$	5.31665	+	21.5664i	0.181932	+	0.737987i
$855$		0			0
$856$	0.112810	+	0.112810i	0.00385578	+	0.00385578i
$857$	21.1903	−	36.7026i	0.723845	−	1.25374i	−0.235602	−	0.971850i	$-0.575706\pi$
$857$	21.1903	−	36.7026i	0.723845	−	1.25374i	0.959447	−	0.281887i	$-0.0909605\pi$
$858$		0			0
$859$	−5.83030	+	3.36613i	−0.198927	+	0.114851i	−0.596155	−	0.802869i	$-0.703306\pi$
$859$	−5.83030	+	3.36613i	−0.198927	+	0.114851i	0.397228	+	0.917720i	$0.369972\pi$
$860$	−2.40893	+	0.645470i	−0.0821437	+	0.0220103i
$861$		0			0
$862$	14.1340	−	8.16026i	0.481405	−	0.277939i
$863$	−17.8200	−	4.77484i	−0.606598	−	0.162537i	−0.0575702	−	0.998341i	$-0.518335\pi$
$863$	−17.8200	−	4.77484i	−0.606598	−	0.162537i	−0.549028	+	0.835804i	$0.685002\pi$
$864$		0			0
$865$	19.0499	+	19.0499i	0.647715	+	0.647715i
$866$	11.9370	+	3.19850i	0.405634	+	0.108689i
$867$		0			0
$868$	−14.0315	+	3.45912i	−0.476261	+	0.117410i
$869$	−23.6383	+	6.33386i	−0.801874	+	0.214861i
$870$		0			0
$871$	−53.1153	+	19.5888i	−1.79974	+	0.663740i
$872$	8.13311	−	14.0870i	0.275422	−	0.477045i
$873$		0			0
$874$	−18.2649	−	10.5452i	−0.617819	−	0.356698i
$875$	21.4595	+	22.3397i	0.725464	+	0.755221i
$876$		0			0
$877$	3.89991	+	14.5547i	0.131691	+	0.491476i	0.999990	−	0.00456529i	$-0.00145318\pi$
$877$	3.89991	+	14.5547i	0.131691	+	0.491476i	−0.868299	+	0.496041i	$0.834787\pi$
$878$	−25.6485	+	25.6485i	−0.865595	+	0.865595i
$879$		0			0
$880$	18.5233	+	10.6944i	0.624420	+	0.360509i
$881$	22.3633	−	38.7344i	0.753439	−	1.30500i	−0.192707	−	0.981256i	$-0.561727\pi$
$881$	22.3633	−	38.7344i	0.753439	−	1.30500i	0.946146	−	0.323739i	$-0.104940\pi$
$882$		0			0
$883$			46.5076i			1.56510i	0.622585	+	0.782552i	$0.286083\pi$
$883$			46.5076i			1.56510i	−0.622585	+	0.782552i	$0.713917\pi$
$884$	8.15899	+	11.5474i	0.274417	+	0.388380i
$885$		0			0
$886$	−40.2522	−	10.7855i	−1.35230	−	0.362347i
$887$			46.0518i			1.54627i	0.634244	+	0.773133i	$0.281312\pi$
$887$			46.0518i			1.54627i	−0.634244	+	0.773133i	$0.718688\pi$
$888$		0			0
$889$	23.5534	−	38.9660i	0.789957	−	1.30688i
$890$	−20.0096	−	5.36156i	−0.670724	−	0.179720i
$891$		0			0
$892$	1.03123	+	3.84860i	0.0345281	+	0.128861i
$893$	5.10923			0.170974
$894$		0			0
$895$	7.99036	+	29.8204i	0.267088	+	0.996787i
$896$	−25.9550	+	24.9324i	−0.867097	+	0.832932i
$897$		0			0
$898$	2.57462	+	4.45937i	0.0859161	+	0.148811i
$899$	−1.69962	+	6.34305i	−0.0566854	+	0.211553i
$900$		0			0
$901$	−15.3733	+	26.6273i	−0.512158	+	0.887085i
$902$	6.66715	+	6.66715i	0.221992	+	0.221992i
$903$		0			0
$904$	9.37724	−	34.9963i	0.311882	−	1.16396i
$905$	6.90054	−	25.7532i	0.229382	−	0.856064i
$906$		0			0
$907$	27.6067	−	15.9387i	0.916666	−	0.529237i	0.0340961	−	0.999419i	$-0.489145\pi$
$907$	27.6067	−	15.9387i	0.916666	−	0.529237i	0.882570	+	0.470181i	$0.155811\pi$
$908$	−10.5051	+	10.5051i	−0.348623	+	0.348623i
$909$		0			0
$910$	10.3203	−	21.2468i	0.342116	−	0.704326i
$911$	−34.8516			−1.15469			−0.577343	−	0.816502i	$-0.695910\pi$
$911$	−34.8516			−1.15469			−0.577343	+	0.816502i	$0.695910\pi$
$912$		0			0
$913$	5.34267	−	3.08459i	0.176817	−	0.102085i
$914$		−	53.2553i		−	1.76153i
$915$		0			0
$916$	3.09000	−	11.5320i	0.102096	−	0.381029i
$917$	6.98311	+	12.6767i	0.230603	+	0.418621i
$918$		0			0
$919$	1.90511	−	3.29975i	0.0628439	−	0.108849i	−0.832892	−	0.553436i	$-0.813316\pi$
$919$	1.90511	−	3.29975i	0.0628439	−	0.108849i	0.895736	+	0.444587i	$0.146650\pi$
$920$	9.53018	+	16.5068i	0.314201	+	0.544212i
$921$		0			0
$922$	4.34491	+	7.52561i	0.143092	+	0.247843i
$923$	−36.0864	+	13.3085i	−1.18780	+	0.438056i
$924$		0			0
$925$	−4.16544	−	15.5456i	−0.136959	−	0.511137i
$926$	39.0373			1.28285
$927$		0			0
$928$	−0.676794	−	2.52583i	−0.0222169	−	0.0829145i
$929$	−36.3444	+	9.73846i	−1.19242	+	0.319509i	−0.799843	−	0.600210i	$-0.795084\pi$
$929$	−36.3444	+	9.73846i	−1.19242	+	0.319509i	−0.392579	+	0.919718i	$0.628417\pi$
$930$		0			0
$931$	−15.7928	+	3.55830i	−0.517588	+	0.116619i
$932$	2.31931	+	4.01717i	0.0759717	+	0.131587i
$933$		0			0
$934$	−11.7018	−	3.13550i	−0.382895	−	0.102597i
$935$	23.6722	+	13.6672i	0.774164	+	0.446964i
$936$		0			0
$937$			38.0350i			1.24255i	0.783593	+	0.621275i	$0.213385\pi$
$937$			38.0350i			1.24255i	−0.783593	+	0.621275i	$0.786615\pi$
$938$	32.5114	+	59.0191i	1.06153	+	1.92704i
$939$		0			0
$940$	1.84266	+	1.06386i	0.0601010	+	0.0346993i
$941$	25.3679	−	6.79732i	0.826971	−	0.221586i	0.179579	−	0.983744i	$-0.442526\pi$
$941$	25.3679	−	6.79732i	0.826971	−	0.221586i	0.647392	+	0.762157i	$0.275860\pi$
$942$		0			0
$943$	2.93648	+	10.9591i	0.0956248	+	0.356877i
$944$	3.03143	−	3.03143i	0.0986645	−	0.0986645i
$945$		0			0
$946$	−10.4781	−	6.04952i	−0.340672	−	0.196687i
$947$	5.51091	+	5.51091i	0.179081	+	0.179081i	0.790955	−	0.611874i	$-0.209584\pi$
$947$	5.51091	+	5.51091i	0.179081	+	0.179081i	−0.611874	+	0.790955i	$0.709584\pi$
$948$		0			0
$949$	−19.2854	−	16.0430i	−0.626031	−	0.520779i
$950$	−8.67226	+	5.00693i	−0.281365	+	0.162446i
$951$		0			0
$952$	−26.3372	+	25.2995i	−0.853595	+	0.819962i
$953$	7.95143	−	4.59076i	0.257572	−	0.148709i	−0.365654	−	0.930751i	$-0.619155\pi$
$953$	7.95143	−	4.59076i	0.257572	−	0.148709i	0.623227	+	0.782041i	$0.285821\pi$
$954$		0			0
$955$	0.0448934	+	0.0448934i	0.00145272	+	0.00145272i
$956$	−2.57811	−	2.57811i	−0.0833820	−	0.0833820i
$957$		0			0
$958$	−29.2840	+	16.9071i	−0.946124	+	0.546245i
$959$	3.34759	−	3.21569i	0.108099	−	0.103840i
$960$		0			0
$961$	38.0702	−	21.9798i	1.22807	−	0.709027i
$962$	−28.7949	+	20.3456i	−0.928386	+	0.655968i
$963$		0			0
$964$	−12.8211	−	12.8211i	−0.412940	−	0.412940i
$965$	16.5129	+	9.53373i	0.531569	+	0.306902i
$966$		0			0
$967$	29.3315	−	29.3315i	0.943237	−	0.943237i	−0.0552359	−	0.998473i	$-0.517591\pi$
$967$	29.3315	−	29.3315i	0.943237	−	0.943237i	0.998473	+	0.0552359i	$0.0175911\pi$
$968$	−1.55283	−	5.79525i	−0.0499099	−	0.186266i
$969$		0			0
$970$	8.63045	−	2.31252i	0.277107	−	0.0742506i
$971$	−32.5158	−	18.7730i	−1.04348	−	0.602455i	−0.122665	−	0.992448i	$-0.539144\pi$
$971$	−32.5158	−	18.7730i	−1.04348	−	0.602455i	−0.920818	+	0.389993i	$0.872478\pi$
$972$		0			0
$973$	−10.5241	−	19.1047i	−0.337386	−	0.612469i
$974$		−	30.2843i		−	0.970371i
$975$		0			0
$976$	21.8017	+	12.5872i	0.697857	+	0.402908i
$977$	−27.8219	−	7.45485i	−0.890101	−	0.238502i	−0.215341	−	0.976539i	$-0.569086\pi$
$977$	−27.8219	−	7.45485i	−0.890101	−	0.238502i	−0.674760	+	0.738037i	$0.735753\pi$
$978$		0			0
$979$	−12.0500	−	20.8712i	−0.385120	−	0.667047i
$980$	−6.43666	−	2.00512i	−0.205612	−	0.0640512i
$981$		0			0
$982$	48.7801	−	13.0706i	1.55664	−	0.417099i
$983$	−5.09738	−	19.0237i	−0.162581	−	0.606762i	−0.998336	−	0.0576591i	$-0.981636\pi$
$983$	−5.09738	−	19.0237i	−0.162581	−	0.606762i	0.835755	−	0.549102i	$-0.185030\pi$
$984$		0			0
$985$	5.67752			0.180901
$986$	−1.97916	−	7.38633i	−0.0630293	−	0.235229i
$987$		0			0
$988$	4.04424	+	3.36430i	0.128665	+	0.107033i
$989$	−7.27941	−	12.6083i	−0.231472	−	0.400921i
$990$		0			0
$991$	−17.6102	−	30.5018i	−0.559407	−	0.968921i	−0.997546	−	0.0700140i	$-0.977696\pi$
$991$	−17.6102	−	30.5018i	−0.559407	−	0.968921i	0.438139	−	0.898907i	$-0.355638\pi$
$992$	−14.9246	+	25.8502i	−0.473858	+	0.820746i
$993$		0			0
$994$	22.0881	+	40.0974i	0.700593	+	1.27181i
$995$	3.46790	−	12.9424i	0.109940	−	0.410301i
$996$		0			0
$997$		−	36.6156i		−	1.15963i	−0.814749	−	0.579814i	$-0.803125\pi$
$997$		−	36.6156i		−	1.15963i	0.814749	−	0.579814i	$-0.196875\pi$
$998$	−26.0314	+	15.0292i	−0.824009	+	0.475742i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.b.136.2		28
3.2	odd	2		91.2.ba.a.45.6	yes	28
7.5	odd	6		819.2.gh.b.19.6		28
13.11	odd	12		819.2.gh.b.388.6		28
21.2	odd	6		637.2.x.a.19.2		28
21.5	even	6		91.2.w.a.19.2	✓	28
21.11	odd	6		637.2.bd.b.97.6		28
21.17	even	6		637.2.bd.a.97.6		28
21.20	even	2		637.2.bb.a.227.6		28
39.11	even	12		91.2.w.a.24.2	yes	28
91.89	even	12	inner	819.2.et.b.271.2		28
273.11	even	12		637.2.bd.a.440.6		28
273.89	odd	12		91.2.ba.a.89.6	yes	28
273.128	even	12		637.2.bb.a.362.6		28
273.167	odd	12		637.2.x.a.570.2		28
273.206	odd	12		637.2.bd.b.440.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.2	✓	28	21.5	even	6
91.2.w.a.24.2	yes	28	39.11	even	12
91.2.ba.a.45.6	yes	28	3.2	odd	2
91.2.ba.a.89.6	yes	28	273.89	odd	12
637.2.x.a.19.2		28	21.2	odd	6
637.2.x.a.570.2		28	273.167	odd	12
637.2.bb.a.227.6		28	21.20	even	2
637.2.bb.a.362.6		28	273.128	even	12
637.2.bd.a.97.6		28	21.17	even	6
637.2.bd.a.440.6		28	273.11	even	12
637.2.bd.b.97.6		28	21.11	odd	6
637.2.bd.b.440.6		28	273.206	odd	12
819.2.et.b.136.2		28	1.1	even	1	trivial
819.2.et.b.271.2		28	91.89	even	12	inner
819.2.gh.b.19.6		28	7.5	odd	6
819.2.gh.b.388.6		28	13.11	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14693 + 1.14693i) q^{2} -0.630890i q^{4} +(-0.395109 + 1.47457i) q^{5} +(0.0531605 - 2.64522i) q^{7} +(-1.57027 - 1.57027i) q^{8} +O(q^{10})\)	\(q+(-1.14693 + 1.14693i) q^{2} -0.630890i q^{4} +(-0.395109 + 1.47457i) q^{5} +(0.0531605 - 2.64522i) q^{7} +(-1.57027 - 1.57027i) q^{8} +(-1.23806 - 2.14439i) q^{10} +(0.745574 - 2.78252i) q^{11} +(-2.94467 + 2.08061i) q^{13} +(2.97290 + 3.09485i) q^{14} +4.86376 q^{16} +6.21574 q^{17} +(2.23387 - 0.598564i) q^{19} +(0.930289 + 0.249270i) q^{20} +(2.33623 + 4.04647i) q^{22} +5.62238i q^{23} +(2.31189 + 1.33477i) q^{25} +(0.991014 - 5.76363i) q^{26} +(-1.66884 - 0.0335384i) q^{28} +(-0.379237 + 0.656858i) q^{29} +(8.36292 - 2.24084i) q^{31} +(-2.43784 + 2.43784i) q^{32} +(-7.12901 + 7.12901i) q^{34} +(3.87955 + 1.12354i) q^{35} +(-4.26298 - 4.26298i) q^{37} +(-1.87558 + 3.24860i) q^{38} +(2.93590 - 1.69504i) q^{40} +(1.94919 - 0.522283i) q^{41} +(-2.24252 + 1.29472i) q^{43} +(-1.75546 - 0.470375i) q^{44} +(-6.44847 - 6.44847i) q^{46} +(2.13395 + 0.571791i) q^{47} +(-6.99435 - 0.281242i) q^{49} +(-4.18246 + 1.12069i) q^{50} +(1.31263 + 1.85776i) q^{52} +(-2.47328 + 4.28385i) q^{53} +(3.80843 + 2.19880i) q^{55} +(-4.23719 + 4.07023i) q^{56} +(-0.318411 - 1.18833i) q^{58} +(0.623268 - 0.623268i) q^{59} +(4.48249 + 2.58797i) q^{61} +(-7.02159 + 12.1617i) q^{62} +4.13546i q^{64} +(-1.90453 - 5.16418i) q^{65} +(15.1664 + 4.06383i) q^{67} -3.92145i q^{68} +(-5.73818 + 3.16095i) q^{70} +(10.3040 + 2.76095i) q^{71} +(1.80076 + 6.72052i) q^{73} +9.77867 q^{74} +(-0.377628 - 1.40933i) q^{76} +(-7.32073 - 2.12012i) q^{77} +(-4.24764 - 7.35713i) q^{79} +(-1.92172 + 7.17194i) q^{80} +(-1.63656 + 2.83460i) q^{82} +(1.51432 + 1.51432i) q^{83} +(-2.45590 + 9.16553i) q^{85} +(1.08706 - 4.05696i) q^{86} +(-5.54006 + 3.19856i) q^{88} +(5.91573 - 5.91573i) q^{89} +(5.34712 + 7.89989i) q^{91} +3.54710 q^{92} +(-3.10329 + 1.79169i) q^{94} +3.53049i q^{95} +(-0.933928 + 3.48547i) q^{97} +(8.34458 - 7.69945i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8	\( 28 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 4 q^{8} - 6 q^{10} - 2 q^{11} + 20 q^{14} + 4 q^{16} + 12 q^{17} + 14 q^{19} - 36 q^{20} - 8 q^{22} - 24 q^{26} + 2 q^{28} + 8 q^{29} - 4 q^{31} - 10 q^{32} - 12 q^{34} + 20 q^{35} - 10 q^{37} + 48 q^{40} + 18 q^{41} + 48 q^{43} + 6 q^{44} + 24 q^{46} + 6 q^{47} - 50 q^{49} - 10 q^{50} - 26 q^{52} - 12 q^{53} + 6 q^{55} - 54 q^{56} - 46 q^{58} - 42 q^{59} + 30 q^{61} - 36 q^{62} - 28 q^{65} - 10 q^{67} - 88 q^{70} + 42 q^{71} + 40 q^{73} - 12 q^{74} - 52 q^{76} + 4 q^{79} - 30 q^{80} - 54 q^{82} - 66 q^{83} - 54 q^{85} + 18 q^{86} - 6 q^{88} + 26 q^{91} + 156 q^{92} - 18 q^{94} - 62 q^{97} + 56 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 4 * q^8 - 6 * q^10 - 2 * q^11 + 20 * q^14 + 4 * q^16 + 12 * q^17 + 14 * q^19 - 36 * q^20 - 8 * q^22 - 24 * q^26 + 2 * q^28 + 8 * q^29 - 4 * q^31 - 10 * q^32 - 12 * q^34 + 20 * q^35 - 10 * q^37 + 48 * q^40 + 18 * q^41 + 48 * q^43 + 6 * q^44 + 24 * q^46 + 6 * q^47 - 50 * q^49 - 10 * q^50 - 26 * q^52 - 12 * q^53 + 6 * q^55 - 54 * q^56 - 46 * q^58 - 42 * q^59 + 30 * q^61 - 36 * q^62 - 28 * q^65 - 10 * q^67 - 88 * q^70 + 42 * q^71 + 40 * q^73 - 12 * q^74 - 52 * q^76 + 4 * q^79 - 30 * q^80 - 54 * q^82 - 66 * q^83 - 54 * q^85 + 18 * q^86 - 6 * q^88 + 26 * q^91 + 156 * q^92 - 18 * q^94 - 62 * q^97 + 56 * q^98

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