LMFDB - Embedded newform 567.2.bd.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(17,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 3]))

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

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

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (of order $18$, degree $6$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50283 + 0.441316i) q^{2} +(4.19001 - 1.52504i) q^{4} +(0.437341 - 0.159179i) q^{5} +(-1.48170 + 2.19193i) q^{7} +(-5.41196 + 3.12460i) q^{8} +O(q^{10})$	\(q+(-2.50283 + 0.441316i) q^{2} +(4.19001 - 1.52504i) q^{4} +(0.437341 - 0.159179i) q^{5} +(-1.48170 + 2.19193i) q^{7} +(-5.41196 + 3.12460i) q^{8} +(-1.02434 + 0.591403i) q^{10} +(-0.845970 + 2.32428i) q^{11} +(-2.13324 - 5.86102i) q^{13} +(2.74112 - 6.13993i) q^{14} +(5.33482 - 4.47645i) q^{16} +(-0.336582 - 0.582978i) q^{17} +(0.628166 + 0.362672i) q^{19} +(1.58971 - 1.33392i) q^{20} +(1.09157 - 6.19062i) q^{22} +(-3.18900 - 0.562306i) q^{23} +(-3.66429 + 3.07471i) q^{25} +(7.92569 + 13.7277i) q^{26} +(-2.86558 + 11.4439i) q^{28} +(1.84864 - 5.07909i) q^{29} +(2.36874 + 6.50807i) q^{31} +(-3.34281 + 3.98381i) q^{32} +(1.09969 + 1.31055i) q^{34} +(-0.299100 + 1.19448i) q^{35} -7.40866 q^{37} +(-1.73225 - 0.630486i) q^{38} +(-1.86950 + 2.22798i) q^{40} +(-3.54917 + 1.29179i) q^{41} +(-1.41606 - 8.03089i) q^{43} +11.0289i q^{44} +8.22967 q^{46} +(8.57711 + 3.12181i) q^{47} +(-2.60911 - 6.49558i) q^{49} +(7.81418 - 9.31258i) q^{50} +(-17.8766 - 21.3045i) q^{52} +(-11.5438 - 6.66480i) q^{53} +1.15116i q^{55} +(1.17003 - 16.4924i) q^{56} +(-2.38534 + 13.5279i) q^{58} +(-8.34926 - 7.00586i) q^{59} +(0.319477 - 0.877757i) q^{61} +(-8.80068 - 15.2432i) q^{62} +(-0.355740 + 0.616160i) q^{64} +(-1.86590 - 2.22370i) q^{65} +(-0.00418019 + 0.0237070i) q^{67} +(-2.29935 - 1.92938i) q^{68} +(0.221455 - 3.12157i) q^{70} +(-8.62973 - 4.98238i) q^{71} -2.87796i q^{73} +(18.5426 - 3.26957i) q^{74} +(3.18511 + 0.561622i) q^{76} +(-3.84119 - 5.29820i) q^{77} +(0.191220 + 1.08446i) q^{79} +(1.62058 - 2.80692i) q^{80} +(8.31288 - 4.79945i) q^{82} +(-4.97140 - 1.80944i) q^{83} +(-0.239999 - 0.201383i) q^{85} +(7.08833 + 19.4750i) q^{86} +(-2.68409 - 15.2222i) q^{88} +(-5.10142 + 8.83591i) q^{89} +(16.0078 + 4.00839i) q^{91} +(-14.2195 + 2.50728i) q^{92} +(-22.8448 - 4.02815i) q^{94} +(0.332452 + 0.0586203i) q^{95} +(-18.3280 + 3.23172i) q^{97} +(9.39676 + 15.1059i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−2.50283	+	0.441316i	−1.76977	+	0.312058i	−0.961099	−	0.276205i	$-0.910923\pi$
$2$	−2.50283	+	0.441316i	−1.76977	+	0.312058i	−0.808669	+	0.588263i	$0.799812\pi$
$3$		0			0
$3$		0			0
$4$	4.19001	−	1.52504i	2.09501	−	0.762520i
$5$	0.437341	−	0.159179i	0.195585	−	0.0711870i	−0.242371	−	0.970184i	$-0.577925\pi$
$5$	0.437341	−	0.159179i	0.195585	−	0.0711870i	0.437955	+	0.898997i	$0.355703\pi$
$6$		0			0
$7$	−1.48170	+	2.19193i	−0.560031	+	0.828471i
$7$	−1.48170	+	2.19193i	−0.560031	+	0.828471i
$8$	−5.41196	+	3.12460i	−1.91342	+	1.10471i
$9$		0			0
$10$	−1.02434	+	0.591403i	−0.323925	+	0.187018i
$11$	−0.845970	+	2.32428i	−0.255069	+	0.700798i	0.744384	+	0.667751i	$0.232743\pi$
$11$	−0.845970	+	2.32428i	−0.255069	+	0.700798i	−0.999454	+	0.0330462i	$0.989479\pi$
$12$		0			0
$13$	−2.13324	−	5.86102i	−0.591653	−	1.62555i	−0.767436	−	0.641125i	$-0.778468\pi$
$13$	−2.13324	−	5.86102i	−0.591653	−	1.62555i	0.175783	−	0.984429i	$-0.443754\pi$
$14$	2.74112	−	6.13993i	0.732595	−	1.64096i
$15$		0			0
$16$	5.33482	−	4.47645i	1.33371	−	1.11911i
$17$	−0.336582	−	0.582978i	−0.0816332	−	0.141393i	0.822318	−	0.569028i	$-0.192680\pi$
$17$	−0.336582	−	0.582978i	−0.0816332	−	0.141393i	−0.903952	+	0.427635i	$0.859347\pi$
$18$		0			0
$19$	0.628166	+	0.362672i	0.144111	+	0.0832027i	0.570322	−	0.821421i	$-0.306818\pi$
$19$	0.628166	+	0.362672i	0.144111	+	0.0832027i	−0.426211	+	0.904624i	$0.640152\pi$
$20$	1.58971	−	1.33392i	0.355470	−	0.298274i
$21$		0			0
$22$	1.09157	−	6.19062i	0.232724	−	1.31985i
$23$	−3.18900	−	0.562306i	−0.664952	−	0.117249i	−0.169023	−	0.985612i	$-0.554061\pi$
$23$	−3.18900	−	0.562306i	−0.664952	−	0.117249i	−0.495929	+	0.868363i	$0.665172\pi$
$24$		0			0
$25$	−3.66429	+	3.07471i	−0.732859	+	0.614941i
$26$	7.92569	+	13.7277i	1.55436	+	2.69222i
$27$		0			0
$28$	−2.86558	+	11.4439i	−0.541543	+	2.16269i
$29$	1.84864	−	5.07909i	0.343284	−	0.943164i	−0.641151	−	0.767415i	$-0.721543\pi$
$29$	1.84864	−	5.07909i	0.343284	−	0.943164i	0.984435	−	0.175750i	$-0.0562349\pi$
$30$		0			0
$31$	2.36874	+	6.50807i	0.425439	+	1.16888i	0.948552	+	0.316620i	$0.102548\pi$
$31$	2.36874	+	6.50807i	0.425439	+	1.16888i	−0.523114	+	0.852263i	$0.675230\pi$
$32$	−3.34281	+	3.98381i	−0.590932	+	0.704245i
$33$		0			0
$34$	1.09969	+	1.31055i	0.188595	+	0.224758i
$35$	−0.299100	+	1.19448i	−0.0505571	+	0.201903i
$36$		0			0
$37$	−7.40866			−1.21798			−0.608988	−	0.793179i	$-0.708424\pi$
$37$	−7.40866			−1.21798			−0.608988	+	0.793179i	$0.708424\pi$
$38$	−1.73225	−	0.630486i	−0.281008	−	0.102278i
$39$		0			0
$40$	−1.86950	+	2.22798i	−0.295594	+	0.352275i
$41$	−3.54917	+	1.29179i	−0.554287	+	0.201744i	−0.603950	−	0.797022i	$-0.706408\pi$
$41$	−3.54917	+	1.29179i	−0.554287	+	0.201744i	0.0496629	+	0.998766i	$0.484185\pi$
$42$		0			0
$43$	−1.41606	−	8.03089i	−0.215948	−	1.22470i	−0.879254	−	0.476352i	$-0.841959\pi$
$43$	−1.41606	−	8.03089i	−0.215948	−	1.22470i	0.663307	−	0.748348i	$-0.269152\pi$
$44$			11.0289i			1.66267i
$45$		0			0
$46$	8.22967			1.21340
$47$	8.57711	+	3.12181i	1.25110	+	0.455363i	0.880773	−	0.473538i	$-0.157023\pi$
$47$	8.57711	+	3.12181i	1.25110	+	0.455363i	0.370327	+	0.928901i	$0.379246\pi$
$48$		0			0
$49$	−2.60911	−	6.49558i	−0.372730	−	0.927940i
$50$	7.81418	−	9.31258i	1.10509	−	1.31700i
$51$		0			0
$52$	−17.8766	−	21.3045i	−2.47904	−	2.95440i
$53$	−11.5438	−	6.66480i	−1.58566	−	0.915480i	−0.994011	−	0.109283i	$-0.965144\pi$
$53$	−11.5438	−	6.66480i	−1.58566	−	0.915480i	−0.591647	−	0.806197i	$-0.701522\pi$
$54$		0			0
$55$			1.15116i			0.155223i
$56$	1.17003	−	16.4924i	0.156351	−	2.20388i
$57$		0			0
$58$	−2.38534	+	13.5279i	−0.313211	+	1.77631i
$59$	−8.34926	−	7.00586i	−1.08698	−	0.912085i	−0.0904991	−	0.995897i	$-0.528846\pi$
$59$	−8.34926	−	7.00586i	−1.08698	−	0.912085i	−0.996482	+	0.0838114i	$0.973291\pi$
$60$		0			0
$61$	0.319477	−	0.877757i	0.0409049	−	0.112385i	−0.917559	−	0.397601i	$-0.869843\pi$
$61$	0.319477	−	0.877757i	0.0409049	−	0.112385i	0.958463	+	0.285215i	$0.0920652\pi$
$62$	−8.80068	−	15.2432i	−1.11769	−	1.93589i
$63$		0			0
$64$	−0.355740	+	0.616160i	−0.0444675	+	0.0770200i
$65$	−1.86590	−	2.22370i	−0.231437	−	0.275815i
$66$		0			0
$67$	−0.00418019	+	0.0237070i	−0.000510691	+	0.00289627i	−0.985062	−	0.172200i	$-0.944913\pi$
$67$	−0.00418019	+	0.0237070i	−0.000510691	+	0.00289627i	0.984551	+	0.175096i	$0.0560236\pi$
$68$	−2.29935	−	1.92938i	−0.278837	−	0.233972i
$69$		0			0
$70$	0.221455	−	3.12157i	0.0264689	−	0.373099i
$71$	−8.62973	−	4.98238i	−1.02416	−	0.591300i	−0.108854	−	0.994058i	$-0.534718\pi$
$71$	−8.62973	−	4.98238i	−1.02416	−	0.591300i	−0.915306	+	0.402758i	$0.868052\pi$
$72$		0			0
$73$		−	2.87796i		−	0.336840i	−0.985715	−	0.168420i	$-0.946133\pi$
$73$		−	2.87796i		−	0.336840i	0.985715	−	0.168420i	$-0.0538665\pi$
$74$	18.5426	−	3.26957i	2.15554	−	0.380079i
$75$		0			0
$76$	3.18511	+	0.561622i	0.365358	+	0.0644224i
$77$	−3.84119	−	5.29820i	−0.437744	−	0.603786i
$78$		0			0
$79$	0.191220	+	1.08446i	0.0215139	+	0.122011i	0.993673	−	0.112309i	$-0.0358247\pi$
$79$	0.191220	+	1.08446i	0.0215139	+	0.122011i	−0.972159	+	0.234320i	$0.924714\pi$
$80$	1.62058	−	2.80692i	0.181186	−	0.313824i
$81$		0			0
$82$	8.31288	−	4.79945i	0.918004	−	0.530010i
$83$	−4.97140	−	1.80944i	−0.545682	−	0.198612i	0.0544449	−	0.998517i	$-0.482661\pi$
$83$	−4.97140	−	1.80944i	−0.545682	−	0.198612i	−0.600127	+	0.799905i	$0.704883\pi$
$84$		0			0
$85$	−0.239999	−	0.201383i	−0.0260315	−	0.0218431i
$86$	7.08833	+	19.4750i	0.764354	+	2.10005i
$87$		0			0
$88$	−2.68409	−	15.2222i	−0.286125	−	1.62270i
$89$	−5.10142	+	8.83591i	−0.540749	+	0.936605i	0.458112	+	0.888894i	$0.348526\pi$
$89$	−5.10142	+	8.83591i	−0.540749	+	0.936605i	−0.998861	+	0.0477103i	$0.984808\pi$
$90$		0			0
$91$	16.0078	+	4.00839i	1.67807	+	0.420193i
$92$	−14.2195	+	2.50728i	−1.48248	+	0.261402i
$93$		0			0
$94$	−22.8448	−	4.02815i	−2.35626	−	0.415472i
$95$	0.332452	+	0.0586203i	0.0341089	+	0.00601432i
$96$		0			0
$97$	−18.3280	+	3.23172i	−1.86092	+	0.328131i	−0.987349	−	0.158559i	$-0.949315\pi$
$97$	−18.3280	+	3.23172i	−1.86092	+	0.328131i	−0.873575	+	0.486690i	$0.838204\pi$
$98$	9.39676	+	15.1059i	0.949216	+	1.52593i
$99$		0			0
$100$	−10.6644	+	18.4713i	−1.06644	+	1.84713i
$101$	0.185180	+	1.05021i	0.0184261	+	0.104500i	0.992634	−	0.121154i	$-0.0386594\pi$
$101$	0.185180	+	1.05021i	0.0184261	+	0.104500i	−0.974208	+	0.225653i	$0.927548\pi$
$102$		0			0
$103$	−1.93415	−	5.31403i	−0.190577	−	0.523607i	0.807197	−	0.590282i	$-0.200983\pi$
$103$	−1.93415	−	5.31403i	−0.190577	−	0.523607i	−0.997775	+	0.0666744i	$0.978761\pi$
$104$	29.8583	+	25.0541i	2.92785	+	2.45676i
$105$		0			0
$106$	31.8334	+	11.5864i	3.09193	+	1.12537i
$107$	−2.29684	+	1.32608i	−0.222044	+	0.128197i	−0.606897	−	0.794781i	$-0.707586\pi$
$107$	−2.29684	+	1.32608i	−0.222044	+	0.128197i	0.384852	+	0.922978i	$0.374252\pi$
$108$		0			0
$109$	5.69975	−	9.87226i	0.545937	−	0.945591i	−0.452610	−	0.891709i	$-0.649507\pi$
$109$	5.69975	−	9.87226i	0.545937	−	0.945591i	0.998547	−	0.0538826i	$-0.0171597\pi$
$110$	−0.508027	−	2.88117i	−0.0484385	−	0.274708i
$111$		0			0
$112$	1.90743	+	18.3263i	0.180235	+	1.73167i
$113$	6.99660	+	1.23369i	0.658184	+	0.116056i	0.492758	−	0.870166i	$-0.335989\pi$
$113$	6.99660	+	1.23369i	0.658184	+	0.116056i	0.165427	+	0.986222i	$0.447100\pi$
$114$		0			0
$115$	−1.48419	+	0.261702i	−0.138401	+	0.0244038i
$116$		−	24.1007i		−	2.23770i
$117$		0			0
$118$	23.9886	+	13.8498i	2.20833	+	1.27498i
$119$	1.77656	+	0.126036i	0.162857	+	0.0115537i
$120$		0			0
$121$	3.73986	+	3.13812i	0.339988	+	0.285283i
$122$	−0.412229	+	2.33787i	−0.0373215	+	0.211660i
$123$		0			0
$124$	19.8501	+	23.6565i	1.78259	+	2.12441i
$125$	−2.27664	+	3.94325i	−0.203628	+	0.352695i
$126$		0			0
$127$	−4.69551	−	8.13286i	−0.416659	−	0.721675i	0.578942	−	0.815369i	$-0.303466\pi$
$127$	−4.69551	−	8.13286i	−0.416659	−	0.721675i	−0.995601	+	0.0936941i	$0.970132\pi$
$128$	4.17579	−	11.4729i	0.369091	−	1.01407i
$129$		0			0
$130$	5.65139	+	4.74208i	0.495660	+	0.415908i
$131$	−1.41748	+	8.03890i	−0.123845	+	0.702362i	0.858141	+	0.513413i	$0.171619\pi$
$131$	−1.41748	+	8.03890i	−0.123845	+	0.702362i	−0.981987	+	0.188949i	$0.939492\pi$
$132$		0			0
$133$	−1.72571	+	0.839524i	−0.149638	+	0.0727959i
$134$		−	0.0611794i		−	0.00528510i
$135$		0			0
$136$	3.64314	+	2.10337i	0.312397	+	0.180362i
$137$	13.1537	+	15.6760i	1.12380	+	1.33929i	0.933919	+	0.357483i	$0.116365\pi$
$137$	13.1537	+	15.6760i	1.12380	+	1.33929i	0.189879	+	0.981807i	$0.439190\pi$
$138$		0			0
$139$	−0.533744	+	0.636091i	−0.0452715	+	0.0539525i	−0.788205	−	0.615413i	$-0.788989\pi$
$139$	−0.533744	+	0.636091i	−0.0452715	+	0.0539525i	0.742934	+	0.669365i	$0.233434\pi$
$140$	0.568390	+	5.46101i	0.0480377	+	0.461539i
$141$		0			0
$142$	23.7976	+	8.66160i	1.99705	+	0.726866i
$143$	15.4273			1.29010
$144$		0			0
$145$		−	2.51556i		−	0.208906i
$146$	1.27009	+	7.20305i	0.105114	+	0.596129i
$147$		0			0
$148$	−31.0424	+	11.2985i	−2.55167	+	0.928732i
$149$	1.43965	−	1.71571i	0.117941	−	0.140557i	−0.703843	−	0.710355i	$-0.748534\pi$
$149$	1.43965	−	1.71571i	0.117941	−	0.140557i	0.821784	+	0.569798i	$0.192979\pi$
$150$		0			0
$151$	2.76579	+	1.00666i	0.225077	+	0.0819212i	0.452097	−	0.891969i	$-0.350676\pi$
$151$	2.76579	+	1.00666i	0.225077	+	0.0819212i	−0.227020	+	0.973890i	$0.572898\pi$
$152$	−4.53282			−0.367660
$153$		0			0
$154$	11.9520	+	11.5653i	0.963121	+	0.931960i
$155$	2.07189	+	2.46919i	0.166419	+	0.198330i
$156$		0			0
$157$	−5.71959	+	6.81634i	−0.456473	+	0.544003i	−0.944364	−	0.328901i	$-0.893322\pi$
$157$	−5.71959	+	6.81634i	−0.456473	+	0.544003i	0.487891	+	0.872904i	$0.337766\pi$
$158$	−0.957180	−	2.62983i	−0.0761492	−	0.209218i
$159$		0			0
$160$	−0.827810	+	2.27439i	−0.0654441	+	0.179806i
$161$	5.95769	−	6.15689i	0.469531	−	0.485231i
$162$		0			0
$163$	0.888889	+	1.53960i	0.0696232	+	0.120591i	0.898735	−	0.438491i	$-0.144487\pi$
$163$	0.888889	+	1.53960i	0.0696232	+	0.120591i	−0.829112	+	0.559082i	$0.811154\pi$
$164$	−12.9010	+	10.8253i	−1.00740	+	0.845311i
$165$		0			0
$166$	13.2411	+	2.33476i	1.02771	+	0.181213i
$167$	1.50485	−	8.53440i	0.116448	−	0.660412i	−0.869574	−	0.493802i	$-0.835607\pi$
$167$	1.50485	−	8.53440i	0.116448	−	0.660412i	0.986023	−	0.166610i	$-0.0532821\pi$
$168$		0			0
$169$	−19.8423	+	16.6496i	−1.52633	+	1.28074i
$170$	0.689550	+	0.398112i	0.0528861	+	0.0305338i
$171$		0			0
$172$	−18.1808	−	31.4900i	−1.38627	−	2.40109i
$173$	−7.13977	+	5.99097i	−0.542826	+	0.455485i	−0.872503	−	0.488608i	$-0.837505\pi$
$173$	−7.13977	+	5.99097i	−0.542826	+	0.455485i	0.329677	+	0.944094i	$0.393060\pi$
$174$		0			0
$175$	−1.31014	−	12.5877i	−0.0990376	−	0.951539i
$176$	5.89143	+	16.1866i	0.444083	+	1.22011i
$177$		0			0
$178$	8.86854	−	24.3661i	0.664725	−	1.82632i
$179$	−9.93962	+	5.73864i	−0.742922	+	0.428926i	−0.823131	−	0.567852i	$-0.807775\pi$
$179$	−9.93962	+	5.73864i	−0.742922	+	0.428926i	0.0802086	+	0.996778i	$0.474441\pi$
$180$		0			0
$181$	−4.44357	+	2.56549i	−0.330288	+	0.190692i	−0.655969	−	0.754788i	$-0.727740\pi$
$181$	−4.44357	+	2.56549i	−0.330288	+	0.190692i	0.325681	+	0.945480i	$0.394406\pi$
$182$	−41.8337	−	2.96783i	−3.10092	−	0.219990i
$183$		0			0
$184$	19.0157	−	6.92115i	1.40186	−	0.510234i
$185$	−3.24011	+	1.17930i	−0.238218	+	0.0867041i
$186$		0			0
$187$	1.63974	−	0.289131i	0.119910	−	0.0211434i
$188$	40.6991			2.96829
$189$		0			0
$190$	−0.857942			−0.0622416
$191$	17.2558	−	3.04266i	1.24859	−	0.220159i	0.489994	−	0.871726i	$-0.336999\pi$
$191$	17.2558	−	3.04266i	1.24859	−	0.220159i	0.758592	+	0.651566i	$0.225888\pi$
$192$		0			0
$193$	6.97690	−	2.53938i	0.502208	−	0.182789i	−0.0784786	−	0.996916i	$-0.525006\pi$
$193$	6.97690	−	2.53938i	0.502208	−	0.182789i	0.580687	+	0.814127i	$0.302784\pi$
$194$	44.4456	−	16.1769i	3.19101	−	1.16143i
$195$		0			0
$196$	−20.8382	−	23.2376i	−1.48844	−	1.65983i
$197$	−4.10505	+	2.37005i	−0.292473	+	0.168859i	−0.639057	−	0.769160i	$-0.720675\pi$
$197$	−4.10505	+	2.37005i	−0.292473	+	0.168859i	0.346584	+	0.938019i	$0.387342\pi$
$198$		0			0
$199$	5.80701	−	3.35268i	0.411648	−	0.237665i	−0.279849	−	0.960044i	$-0.590285\pi$
$199$	5.80701	−	3.35268i	0.411648	−	0.237665i	0.691498	+	0.722379i	$0.256951\pi$
$200$	10.2238	−	28.0896i	0.722931	−	1.98624i
$201$		0			0
$202$	−0.926949	−	2.54677i	−0.0652199	−	0.179190i
$203$	8.39388	+	11.5778i	0.589135	+	0.812602i
$204$		0			0
$205$	−1.34657	+	1.12991i	−0.0940486	+	0.0789161i
$206$	7.18602	+	12.4466i	0.500674	+	0.867192i
$207$		0			0
$208$	−37.6170	−	21.7182i	−2.60827	−	1.50588i
$209$	−1.37436	+	1.15323i	−0.0950666	+	0.0797704i
$210$		0			0
$211$	1.74430	−	9.89241i	0.120082	−	0.681021i	−0.864025	−	0.503449i	$-0.832064\pi$
$211$	1.74430	−	9.89241i	0.120082	−	0.681021i	0.984108	−	0.177573i	$-0.0568245\pi$
$212$	−58.5326	−	10.3209i	−4.02004	−	0.708841i
$213$		0			0
$214$	5.16339	−	4.33260i	0.352962	−	0.296170i
$215$	−1.89765	−	3.28683i	−0.129419	−	0.224160i
$216$		0			0
$217$	−17.7750	−	4.45091i	−1.20665	−	0.302148i
$218$	−9.90872	+	27.2240i	−0.671103	+	1.84384i
$219$		0			0
$220$	1.75557	+	4.82339i	0.118361	+	0.325193i
$221$	−2.69883	+	3.21635i	−0.181543	+	0.216355i
$222$		0			0
$223$	18.4562	+	21.9953i	1.23592	+	1.47291i	0.828806	+	0.559536i	$0.189021\pi$
$223$	18.4562	+	21.9953i	1.23592	+	1.47291i	0.407114	+	0.913377i	$0.366535\pi$
$224$	−3.77917	−	13.2300i	−0.252507	−	0.883969i
$225$		0			0
$226$	−18.0557			−1.20105
$227$	−2.18774	−	0.796273i	−0.145206	−	0.0528505i	0.268395	−	0.963309i	$-0.413507\pi$
$227$	−2.18774	−	0.796273i	−0.145206	−	0.0528505i	−0.413601	+	0.910458i	$0.635729\pi$
$228$		0			0
$229$	7.24263	−	8.63143i	0.478607	−	0.570381i	−0.471675	−	0.881772i	$-0.656351\pi$
$229$	7.24263	−	8.63143i	0.478607	−	0.570381i	0.950282	+	0.311391i	$0.100795\pi$
$230$	3.59917	−	1.30999i	0.237322	−	0.0863782i
$231$		0			0
$232$	5.86536	+	33.2641i	0.385080	+	2.18390i
$233$			13.3846i			0.876856i	0.898766	+	0.438428i	$0.144465\pi$
$233$			13.3846i			0.876856i	−0.898766	+	0.438428i	$0.855535\pi$
$234$		0			0
$235$	4.24805			0.277112
$236$	−45.6677	−	16.6217i	−2.97271	−	1.08198i
$237$		0			0
$238$	−4.50205	+	0.468580i	−0.291825	+	0.0303735i
$239$	15.7161	−	18.7297i	1.01659	−	1.21152i	0.0393838	−	0.999224i	$-0.487461\pi$
$239$	15.7161	−	18.7297i	1.01659	−	1.21152i	0.977205	−	0.212299i	$-0.0680950\pi$
$240$		0			0
$241$	8.18673	+	9.75657i	0.527354	+	0.628476i	0.962303	−	0.271979i	$-0.0876781\pi$
$241$	8.18673	+	9.75657i	0.527354	+	0.628476i	−0.434949	+	0.900455i	$0.643234\pi$
$242$	−10.7451	−	6.20371i	−0.690724	−	0.398790i
$243$		0			0
$244$		−	4.16503i		−	0.266639i
$245$	−2.17503	−	2.42547i	−0.138957	−	0.154957i
$246$		0			0
$247$	0.785600	−	4.45536i	0.0499865	−	0.283488i
$248$	−33.1546	−	27.8200i	−2.10532	−	1.76657i
$249$		0			0
$250$	3.95781	−	10.8740i	0.250314	−	0.687732i
$251$	−2.40624	−	4.16774i	−0.151881	−	0.263065i	0.780038	−	0.625732i	$-0.215200\pi$
$251$	−2.40624	−	4.16774i	−0.151881	−	0.263065i	−0.931919	+	0.362667i	$0.881866\pi$
$252$		0			0
$253$	4.00475	−	6.93644i	0.251777	−	0.436090i
$254$	15.3412	+	18.2830i	0.962594	+	1.14717i
$255$		0			0
$256$	−5.14102	+	29.1562i	−0.321314	+	1.82226i
$257$	−0.549450	−	0.461043i	−0.0342738	−	0.0287591i	0.625490	−	0.780232i	$-0.284899\pi$
$257$	−0.549450	−	0.461043i	−0.0342738	−	0.0287591i	−0.659764	+	0.751473i	$0.729344\pi$
$258$		0			0
$259$	10.9774	−	16.2393i	0.682105	−	1.00906i
$260$	−11.2094	−	6.47174i	−0.695176	−	0.401360i
$261$		0			0
$262$		−	20.7456i		−	1.28167i
$263$	−15.9005	+	2.80368i	−0.980466	+	0.172883i	−0.640837	−	0.767677i	$-0.721413\pi$
$263$	−15.9005	+	2.80368i	−0.980466	+	0.172883i	−0.339629	+	0.940560i	$0.610301\pi$
$264$		0			0
$265$	−6.10945	−	1.07726i	−0.375301	−	0.0661756i
$266$	3.94866	−	2.86277i	0.242108	−	0.175528i
$267$		0			0
$268$	0.0186391	+	0.105708i	0.00113856	+	0.00645712i
$269$	8.30293	−	14.3811i	0.506238	−	0.876831i	−0.493736	−	0.869612i	$-0.664369\pi$
$269$	8.30293	−	14.3811i	0.506238	−	0.876831i	0.999974	−	0.00721846i	$-0.00229773\pi$
$270$		0			0
$271$	−12.6238	+	7.28836i	−0.766842	+	0.442736i	−0.831747	−	0.555155i	$-0.812659\pi$
$271$	−12.6238	+	7.28836i	−0.766842	+	0.442736i	0.0649049	+	0.997891i	$0.479326\pi$
$272$	−4.40528	−	1.60339i	−0.267109	−	0.0972198i
$273$		0			0
$274$	−39.8396	−	33.4294i	−2.40680	−	2.01954i
$275$	−4.04661	−	11.1180i	−0.244020	−	0.670438i
$276$		0			0
$277$	3.08714	+	17.5081i	0.185488	+	1.05196i	0.925326	+	0.379172i	$0.123791\pi$
$277$	3.08714	+	17.5081i	0.185488	+	1.05196i	−0.739838	+	0.672785i	$0.765098\pi$
$278$	1.05515	−	1.82758i	0.0632838	−	0.109611i
$279$		0			0
$280$	−2.11354	−	7.39902i	−0.126308	−	0.442176i
$281$	25.4750	−	4.49194i	1.51971	−	0.267967i	0.649393	−	0.760453i	$-0.275023\pi$
$281$	25.4750	−	4.49194i	1.51971	−	0.267967i	0.870320	+	0.492486i	$0.163912\pi$
$282$		0			0
$283$	2.37217	+	0.418277i	0.141011	+	0.0248640i	0.243708	−	0.969849i	$-0.421636\pi$
$283$	2.37217	+	0.418277i	0.141011	+	0.0248640i	−0.102697	+	0.994713i	$0.532747\pi$
$284$	−43.7570	−	7.71554i	−2.59650	−	0.457833i
$285$		0			0
$286$	−38.6120	+	6.80833i	−2.28317	+	0.402585i
$287$	2.42730	−	9.69359i	0.143279	−	0.572194i
$288$		0			0
$289$	8.27342	−	14.3300i	0.486672	−	0.842941i
$290$	1.11016	+	6.29602i	0.0651907	+	0.369715i
$291$		0			0
$292$	−4.38901	−	12.0587i	−0.256847	−	0.705682i
$293$	14.1349	+	11.8606i	0.825772	+	0.692905i	0.954316	−	0.298799i	$-0.0965859\pi$
$293$	14.1349	+	11.8606i	0.825772	+	0.692905i	−0.128544	+	0.991704i	$0.541030\pi$
$294$		0			0
$295$	−4.76665	−	1.73492i	−0.277525	−	0.101011i
$296$	40.0954	−	23.1491i	2.33050	−	1.34551i
$297$		0			0
$298$	−2.84604	+	4.92948i	−0.164867	+	0.285557i
$299$	3.50720	+	19.8903i	0.202827	+	1.15029i
$300$		0			0
$301$	19.7013	+	8.79550i	1.13557	+	0.506964i
$302$	−7.36655	−	1.29892i	−0.423897	−	0.0747446i
$303$		0			0
$304$	4.97464	−	0.877163i	0.285315	−	0.0503087i
$305$		−	0.434733i		−	0.0248927i
$306$		0			0
$307$	8.85587	+	5.11294i	0.505431	+	0.291811i	0.730954	−	0.682427i	$-0.239076\pi$
$307$	8.85587	+	5.11294i	0.505431	+	0.291811i	−0.225522	+	0.974238i	$0.572409\pi$
$308$	−24.1746	−	16.3416i	−1.37748	−	0.931148i
$309$		0			0
$310$	−6.27529	−	5.26560i	−0.356413	−	0.299066i
$311$	−4.30935	+	24.4395i	−0.244361	+	1.38584i	0.577612	+	0.816311i	$0.303985\pi$
$311$	−4.30935	+	24.4395i	−0.244361	+	1.38584i	−0.821973	+	0.569527i	$0.807126\pi$
$312$		0			0
$313$	−10.6819	−	12.7301i	−0.603775	−	0.719551i	0.374416	−	0.927261i	$-0.377843\pi$
$313$	−10.6819	−	12.7301i	−0.603775	−	0.719551i	−0.978190	+	0.207710i	$0.933399\pi$
$314$	11.3070	−	19.5843i	0.638091	−	1.10521i
$315$		0			0
$316$	2.45506	+	4.25229i	0.138108	+	0.239210i
$317$	−2.18194	+	5.99483i	−0.122550	+	0.336703i	−0.985764	−	0.168135i	$-0.946226\pi$
$317$	−2.18194	+	5.99483i	−0.122550	+	0.336703i	0.863214	+	0.504838i	$0.168448\pi$
$318$		0			0
$319$	10.2414	+	8.59352i	0.573406	+	0.481145i
$320$	−0.0574999	+	0.326098i	−0.00321434	+	0.0182294i
$321$		0			0
$322$	−12.1939	+	18.0389i	−0.679542	+	1.00527i
$323$		−	0.488276i		−	0.0271684i
$324$		0			0
$325$	25.8377	+	14.9174i	1.43322	+	0.827469i
$326$	−2.90419	−	3.46108i	−0.160848	−	0.191691i
$327$		0			0
$328$	15.1716	−	18.0809i	0.837714	−	0.998349i
$329$	−19.5515	+	14.1748i	−1.07791	+	0.781483i
$330$		0			0
$331$	−8.65398	−	3.14979i	−0.475666	−	0.173128i	0.0930516	−	0.995661i	$-0.470338\pi$
$331$	−8.65398	−	3.14979i	−0.475666	−	0.173128i	−0.568717	+	0.822533i	$0.692560\pi$
$332$	−23.5897			−1.29465
$333$		0			0
$334$			22.0243i			1.20511i
$335$	0.00194549	+	0.0110334i	0.000106294	+	0.000602821i
$336$		0			0
$337$	−4.60865	+	1.67741i	−0.251049	+	0.0913745i	−0.464480	−	0.885584i	$-0.653759\pi$
$337$	−4.60865	+	1.67741i	−0.251049	+	0.0913745i	0.213430	+	0.976958i	$0.431536\pi$
$338$	42.3141	−	50.4280i	2.30158	−	2.74292i
$339$		0			0
$340$	−1.31272	−	0.477789i	−0.0711920	−	0.0259118i
$341$	−17.1305			−0.927667
$342$		0			0
$343$	18.1038	+	3.90554i	0.977512	+	0.210879i
$344$	32.7570	+	39.0383i	1.76614	+	2.10480i
$345$		0			0
$346$	15.2257	−	18.1453i	0.818539	−	0.975497i
$347$	1.93235	+	5.30909i	0.103734	+	0.285007i	0.980692	−	0.195561i	$-0.0626528\pi$
$347$	1.93235	+	5.30909i	0.103734	+	0.285007i	−0.876958	+	0.480568i	$0.840431\pi$
$348$		0			0
$349$	1.55645	−	4.27631i	0.0833149	−	0.228906i	−0.891039	−	0.453927i	$-0.850023\pi$
$349$	1.55645	−	4.27631i	0.0833149	−	0.228906i	0.974354	+	0.225021i	$0.0722450\pi$
$350$	8.83422	+	30.9266i	0.472209	+	1.65310i
$351$		0			0
$352$	−6.43158	−	11.1398i	−0.342805	−	0.593755i
$353$	−7.64819	+	6.41759i	−0.407072	+	0.341574i	−0.823220	−	0.567723i	$-0.807824\pi$
$353$	−7.64819	+	6.41759i	−0.407072	+	0.341574i	0.416147	+	0.909297i	$0.363380\pi$
$354$		0			0
$355$	−4.56722	−	0.805324i	−0.242403	−	0.0427422i
$356$	−7.89988	+	44.8024i	−0.418693	+	2.37452i
$357$		0			0
$358$	22.3446	−	18.7494i	1.18095	−	0.990935i
$359$	−12.4498	−	7.18790i	−0.657075	−	0.379363i	0.134086	−	0.990970i	$-0.457190\pi$
$359$	−12.4498	−	7.18790i	−0.657075	−	0.379363i	−0.791162	+	0.611607i	$0.790523\pi$
$360$		0			0
$361$	−9.23694	−	15.9988i	−0.486155	−	0.842045i
$362$	9.98930	−	8.38202i	0.525026	−	0.440549i
$363$		0			0
$364$	73.1857	−	7.61728i	3.83597	−	0.399254i
$365$	−0.458111	−	1.25865i	−0.0239786	−	0.0658808i
$366$		0			0
$367$	−12.1475	+	33.3749i	−0.634092	+	1.74215i	0.0354422	+	0.999372i	$0.488716\pi$
$367$	−12.1475	+	33.3749i	−0.634092	+	1.74215i	−0.669534	+	0.742781i	$0.733506\pi$
$368$	−19.5299	+	11.2756i	−1.01806	+	0.587780i
$369$		0			0
$370$	7.58900	−	4.38151i	0.394533	−	0.227784i
$371$	31.7132	−	15.4279i	1.64647	−	0.800975i
$372$		0			0
$373$	3.20225	−	1.16553i	0.165806	−	0.0603486i	−0.257783	−	0.966203i	$-0.582992\pi$
$373$	3.20225	−	1.16553i	0.165806	−	0.0603486i	0.423590	+	0.905854i	$0.360770\pi$
$374$	−3.97640	+	1.44729i	−0.205615	+	0.0748377i
$375$		0			0
$376$	−56.1734	+	9.90489i	−2.89692	+	0.510806i
$377$	−33.7123			−1.73627
$378$		0			0
$379$	1.03172			0.0529960			0.0264980	−	0.999649i	$-0.491564\pi$
$379$	1.03172			0.0529960			0.0264980	+	0.999649i	$0.491564\pi$
$380$	1.48238	−	0.261383i	0.0760444	−	0.0134087i
$381$		0			0
$382$	−41.8455	+	15.2305i	−2.14100	+	0.779262i
$383$	3.09920	−	1.12802i	0.158362	−	0.0576390i	−0.261623	−	0.965170i	$-0.584258\pi$
$383$	3.09920	−	1.12802i	0.158362	−	0.0576390i	0.419985	+	0.907531i	$0.362035\pi$
$384$		0			0
$385$	−2.52327	−	1.70568i	−0.128598	−	0.0869297i
$386$	−16.3413	+	9.43467i	−0.831752	+	0.480212i
$387$		0			0
$388$	−71.8660	+	41.4918i	−3.64844	+	2.10643i
$389$	6.54841	−	17.9916i	0.332018	−	0.912211i	−0.655569	−	0.755135i	$-0.727571\pi$
$389$	6.54841	−	17.9916i	0.332018	−	0.912211i	0.987587	−	0.157076i	$-0.0502067\pi$
$390$		0			0
$391$	0.745548	+	2.04838i	0.0377040	+	0.103591i
$392$	34.4165	+	27.0014i	1.73829	+	1.36378i
$393$		0			0
$394$	9.22830	−	7.74347i	0.464915	−	0.390110i
$395$	0.256251	+	0.443840i	0.0128934	+	0.0223320i
$396$		0			0
$397$	13.6656	+	7.88983i	0.685856	+	0.395979i	0.802058	−	0.597246i	$-0.203739\pi$
$397$	13.6656	+	7.88983i	0.685856	+	0.395979i	−0.116202	+	0.993226i	$0.537072\pi$
$398$	−13.0544	+	10.9539i	−0.654357	+	0.549070i
$399$		0			0
$400$	−5.78459	+	32.8060i	−0.289229	+	1.64030i
$401$	−28.2579	−	4.98263i	−1.41113	−	0.248821i	−0.584423	−	0.811449i	$-0.698679\pi$
$401$	−28.2579	−	4.98263i	−1.41113	−	0.248821i	−0.826710	+	0.562629i	$0.809790\pi$
$402$		0			0
$403$	33.0908	−	27.7665i	1.64837	−	1.38315i
$404$	2.37752	+	4.11798i	0.118286	+	0.204877i
$405$		0			0
$406$	−26.1179	−	25.2729i	−1.29621	−	1.25427i
$407$	6.26751	−	17.2198i	0.310669	−	0.853555i
$408$		0			0
$409$	−0.287782	−	0.790673i	−0.0142299	−	0.0390963i	0.932374	−	0.361494i	$-0.117733\pi$
$409$	−0.287782	−	0.790673i	−0.0142299	−	0.0390963i	−0.946604	+	0.322398i	$0.895511\pi$
$410$	2.87159	−	3.42223i	0.141818	−	0.169012i
$411$		0			0
$412$	−16.2082	−	19.3162i	−0.798522	−	0.951642i
$413$	27.7275	−	7.92038i	1.36438	−	0.389736i
$414$		0			0
$415$	−2.46222			−0.120866
$416$	30.4802	+	11.0939i	1.49442	+	0.543923i
$417$		0			0
$418$	2.93086	−	3.49286i	0.143353	−	0.170841i
$419$	−14.6826	+	5.34404i	−0.717294	+	0.261073i	−0.674776	−	0.738022i	$-0.735760\pi$
$419$	−14.6826	+	5.34404i	−0.717294	+	0.261073i	−0.0425171	+	0.999096i	$0.513538\pi$
$420$		0			0
$421$	−5.15879	−	29.2570i	−0.251424	−	1.42590i	−0.805088	−	0.593156i	$-0.797882\pi$
$421$	−5.15879	−	29.2570i	−0.251424	−	1.42590i	0.553663	−	0.832740i	$-0.313229\pi$
$422$			25.5288i			1.24272i
$423$		0			0
$424$	83.2992			4.04537
$425$	3.02582	+	1.10131i	0.146774	+	0.0534214i
$426$		0			0
$427$	1.45061	+	2.00085i	0.0701999	+	0.0968278i
$428$	−7.60148	+	9.05909i	−0.367431	+	0.437888i
$429$		0			0
$430$	6.20003	+	7.38891i	0.298992	+	0.356325i
$431$	31.9989	+	18.4746i	1.54133	+	0.889889i	0.998755	+	0.0498828i	$0.0158848\pi$
$431$	31.9989	+	18.4746i	1.54133	+	0.889889i	0.542577	+	0.840006i	$0.317449\pi$
$432$		0			0
$433$		−	9.86033i		−	0.473857i	−0.971527	−	0.236929i	$-0.923859\pi$
$433$		−	9.86033i		−	0.473857i	0.971527	−	0.236929i	$-0.0761407\pi$
$434$	46.4521	+	3.29547i	2.22977	+	0.158188i
$435$		0			0
$436$	8.82644	−	50.0573i	0.422710	−	2.39731i
$437$	−1.79929	−	1.50978i	−0.0860716	−	0.0722227i
$438$		0			0
$439$	−12.1719	+	33.4421i	−0.580934	+	1.59610i	0.205655	+	0.978625i	$0.434068\pi$
$439$	−12.1719	+	33.4421i	−0.580934	+	1.59610i	−0.786589	+	0.617477i	$0.788155\pi$
$440$	−3.59692	−	6.23005i	−0.171477	−	0.297006i
$441$		0			0
$442$	5.33530	−	9.24101i	0.253774	−	0.439550i
$443$	8.55552	+	10.1961i	0.406485	+	0.484430i	0.929986	−	0.367595i	$-0.119819\pi$
$443$	8.55552	+	10.1961i	0.406485	+	0.484430i	−0.523501	+	0.852025i	$0.675374\pi$
$444$		0			0
$445$	−0.824565	+	4.67634i	−0.0390881	+	0.221680i
$446$	−55.8997	−	46.9054i	−2.64693	−	2.22104i
$447$		0			0
$448$	−0.823478	−	1.69272i	−0.0389057	−	0.0799737i
$449$	6.46903	+	3.73490i	0.305293	+	0.176261i	0.644818	−	0.764336i	$-0.276933\pi$
$449$	6.46903	+	3.73490i	0.305293	+	0.176261i	−0.339525	+	0.940597i	$0.610266\pi$
$450$		0			0
$451$		−	9.34210i		−	0.439902i
$452$	31.1973	−	5.50092i	1.46740	−	0.258741i
$453$		0			0
$454$	5.82696	+	1.02745i	0.273473	+	0.0482206i
$455$	7.63890	−	0.795068i	0.358117	−	0.0372733i
$456$		0			0
$457$	−4.50073	−	25.5249i	−0.210535	−	1.19400i	−0.888488	−	0.458899i	$-0.848244\pi$
$457$	−4.50073	−	25.5249i	−0.210535	−	1.19400i	0.677953	−	0.735105i	$-0.262867\pi$
$458$	−14.3179	+	24.7993i	−0.669031	+	1.15880i
$459$		0			0
$460$	−5.81965	+	3.35998i	−0.271343	+	0.156660i
$461$	−23.7286	−	8.63651i	−1.10515	−	0.402242i	−0.275939	−	0.961175i	$-0.588989\pi$
$461$	−23.7286	−	8.63651i	−1.10515	−	0.402242i	−0.829213	+	0.558933i	$0.811211\pi$
$462$		0			0
$463$	15.4294	+	12.9468i	0.717064	+	0.601688i	0.926571	−	0.376119i	$-0.122742\pi$
$463$	15.4294	+	12.9468i	0.717064	+	0.601688i	−0.209508	+	0.977807i	$0.567186\pi$
$464$	−12.8741	−	35.3714i	−0.597667	−	1.64208i
$465$		0			0
$466$	−5.90685	−	33.4994i	−0.273630	−	1.55183i
$467$	−2.15750	+	3.73690i	−0.0998373	+	0.172923i	−0.911617	−	0.411040i	$-0.865166\pi$
$467$	−2.15750	+	3.73690i	−0.0998373	+	0.172923i	0.811780	+	0.583964i	$0.198499\pi$
$468$		0			0
$469$	−0.0457703	−	0.0442894i	−0.00211348	−	0.00204510i
$470$	−10.6321	+	1.87473i	−0.490424	+	0.0864750i
$471$		0			0
$472$	67.0763	+	11.8274i	3.08744	+	0.544399i
$473$	19.8640	+	3.50256i	0.913348	+	0.161048i
$474$		0			0
$475$	−3.41690	+	0.602491i	−0.156778	+	0.0276442i
$476$	7.63602	−	2.18124i	0.349997	−	0.0999768i
$477$		0			0
$478$	−31.0689	+	53.8130i	−1.42106	+	2.46135i
$479$	−0.333083	−	1.88901i	−0.0152189	−	0.0863109i	0.976252	−	0.216637i	$-0.0695087\pi$
$479$	−0.333083	−	1.88901i	−0.0152189	−	0.0863109i	−0.991471	+	0.130326i	$0.958398\pi$
$480$		0			0
$481$	15.8044	+	43.4223i	0.720620	+	1.97989i
$482$	−24.7957	−	20.8061i	−1.12941	−	0.947692i
$483$		0			0
$484$	20.4558	+	7.44531i	0.929811	+	0.338423i
$485$	−7.50115	+	4.33079i	−0.340610	+	0.196651i
$486$		0			0
$487$	−10.2277	+	17.7149i	−0.463461	+	0.802738i	−0.999131	−	0.0416897i	$-0.986726\pi$
$487$	−10.2277	+	17.7149i	−0.463461	+	0.802738i	0.535670	+	0.844428i	$0.320059\pi$
$488$	1.01364	+	5.74862i	0.0458852	+	0.260228i
$489$		0			0
$490$	6.51412	+	5.11065i	0.294278	+	0.230876i
$491$	−27.9607	−	4.93023i	−1.26185	−	0.222498i	−0.497593	−	0.867411i	$-0.665783\pi$
$491$	−27.9607	−	4.93023i	−1.26185	−	0.222498i	−0.764256	+	0.644912i	$0.776894\pi$
$492$		0			0
$493$	−3.58322	+	0.631818i	−0.161380	+	0.0284557i
$494$			11.4977i			0.517306i
$495$		0			0
$496$	41.7698	+	24.1158i	1.87552	+	1.08283i
$497$	23.7077	−	11.5334i	1.06344	−	0.517342i
$498$		0			0
$499$	17.9357	+	15.0499i	0.802913	+	0.673724i	0.948905	−	0.315562i	$-0.102193\pi$
$499$	17.9357	+	15.0499i	0.802913	+	0.673724i	−0.145992	+	0.989286i	$0.546637\pi$
$500$	−3.52552	+	19.9942i	−0.157666	+	0.894169i
$501$		0			0
$502$	7.86171	+	9.36922i	0.350885	+	0.418169i
$503$	5.80401	−	10.0528i	0.258788	−	0.448234i	−0.707129	−	0.707084i	$-0.750010\pi$
$503$	5.80401	−	10.0528i	0.258788	−	0.448234i	0.965918	+	0.258850i	$0.0833435\pi$
$504$		0			0
$505$	0.248158	+	0.429822i	0.0110429	+	0.0191268i
$506$	−6.96206	+	19.1281i	−0.309501	+	0.850347i
$507$		0			0
$508$	−32.0772	−	26.9159i	−1.42319	−	1.19420i
$509$	−3.05982	+	17.3531i	−0.135624	+	0.769162i	0.838799	+	0.544441i	$0.183258\pi$
$509$	−3.05982	+	17.3531i	−0.135624	+	0.769162i	−0.974423	+	0.224721i	$0.927853\pi$
$510$		0			0
$511$	6.30829	+	4.26429i	0.279062	+	0.188641i
$512$		−	50.8234i		−	2.24610i
$513$		0			0
$514$	1.57865	+	0.911432i	0.0696311	+	0.0402015i
$515$	−1.69176	−	2.01617i	−0.0745481	−	0.0888429i
$516$		0			0
$517$	−14.5120	+	17.2947i	−0.638235	+	0.760619i
$518$	−20.3080	+	45.4887i	−0.892283	+	1.99866i
$519$		0			0
$520$	17.0463	+	6.20436i	0.747531	+	0.272079i
$521$	−25.9372			−1.13633			−0.568164	−	0.822916i	$-0.692346\pi$
$521$	−25.9372			−1.13633			−0.568164	+	0.822916i	$0.692346\pi$
$522$		0			0
$523$		−	3.68634i		−	0.161192i	−0.996747	−	0.0805962i	$-0.974318\pi$
$523$		−	3.68634i		−	0.161192i	0.996747	−	0.0805962i	$-0.0256824\pi$
$524$	6.32041	+	35.8448i	0.276108	+	1.56589i
$525$		0			0
$526$	38.5589	−	14.0343i	1.68125	−	0.611924i
$527$	2.99678	−	3.57143i	0.130542	−	0.155574i
$528$		0			0
$529$	−11.7594	−	4.28008i	−0.511279	−	0.186090i
$530$	15.7663			0.684846
$531$		0			0
$532$	−5.95043	+	6.14939i	−0.257984	+	0.266610i
$533$	15.1424	+	18.0461i	0.655892	+	0.781662i
$534$		0			0
$535$	−0.793419	+	0.945560i	−0.0343025	+	0.0408801i
$536$	−0.0514519	−	0.141363i	−0.00222238	−	0.00610594i
$537$		0			0
$538$	−14.4342	+	39.6576i	−0.622303	+	1.70976i
$539$	17.3048	−	0.569242i	0.745370	−	0.0245190i
$540$		0			0
$541$	−12.7616	−	22.1037i	−0.548663	−	0.950313i	−0.998366	−	0.0571349i	$-0.981803\pi$
$541$	−12.7616	−	22.1037i	−0.548663	−	0.950313i	0.449703	−	0.893178i	$-0.351530\pi$
$542$	28.3788	−	23.8126i	1.21897	−	1.02284i
$543$		0			0
$544$	3.44761	+	0.607906i	0.147815	+	0.0260638i
$545$	0.921277	−	5.22482i	0.0394632	−	0.223807i
$546$		0			0
$547$	−5.90120	+	4.95170i	−0.252317	+	0.211719i	−0.760169	−	0.649725i	$-0.774884\pi$
$547$	−5.90120	+	4.95170i	−0.252317	+	0.211719i	0.507852	+	0.861444i	$0.330440\pi$
$548$	79.0208	+	45.6227i	3.37560	+	1.94890i
$549$		0			0
$550$	15.0345	+	26.0405i	0.641074	+	1.11037i
$551$	3.00330	−	2.52007i	0.127945	−	0.107358i
$552$		0			0
$553$	−2.66039	−	1.18771i	−0.113131	−	0.0505065i
$554$	−15.4532	−	42.4573i	−0.656543	−	1.80384i
$555$		0			0
$556$	−1.26633	+	3.47921i	−0.0537043	+	0.147551i
$557$	1.34204	−	0.774828i	0.0568641	−	0.0328305i	−0.471298	−	0.881974i	$-0.656215\pi$
$557$	1.34204	−	0.774828i	0.0568641	−	0.0328305i	0.528163	+	0.849143i	$0.322881\pi$
$558$		0			0
$559$	−44.0484	+	25.4314i	−1.86305	+	1.07563i
$560$	3.75136	+	7.71122i	0.158524	+	0.325859i
$561$		0			0
$562$	−61.7773	+	22.4851i	−2.60592	+	0.948477i
$563$	23.1809	−	8.43716i	0.976959	−	0.355584i	0.196302	−	0.980544i	$-0.437107\pi$
$563$	23.1809	−	8.43716i	0.976959	−	0.355584i	0.780657	+	0.624960i	$0.214885\pi$
$564$		0			0
$565$	3.25627	−	0.574169i	0.136992	−	0.0241555i
$566$	−6.12172			−0.257315
$567$		0			0
$568$	62.2717			2.61286
$569$	−26.7591	+	4.71836i	−1.12180	+	0.197804i	−0.703631	−	0.710565i	$-0.748439\pi$
$569$	−26.7591	+	4.71836i	−1.12180	+	0.197804i	−0.418170	+	0.908369i	$0.637328\pi$
$570$		0			0
$571$	−14.8509	+	5.40528i	−0.621491	+	0.226204i	−0.633523	−	0.773723i	$-0.718392\pi$
$571$	−14.8509	+	5.40528i	−0.621491	+	0.226204i	0.0120327	+	0.999928i	$0.496170\pi$
$572$	64.6407	−	23.5273i	2.70276	−	0.983725i
$573$		0			0
$574$	−1.79718	+	25.3326i	−0.0750130	+	1.05736i
$575$	13.4144	−	7.74478i	0.559417	−	0.322980i
$576$		0			0
$577$	−14.1651	+	8.17820i	−0.589699	+	0.340463i	−0.764978	−	0.644056i	$-0.777250\pi$
$577$	−14.1651	+	8.17820i	−0.589699	+	0.340463i	0.175280	+	0.984519i	$0.443917\pi$
$578$	−14.3829	+	39.5167i	−0.598250	+	1.64368i
$579$		0			0
$580$	−3.83633	−	10.5402i	−0.159295	−	0.437659i
$581$	11.3323	−	8.21590i	0.470144	−	0.340853i
$582$		0			0
$583$	25.2565	−	21.1928i	1.04602	−	0.877714i
$584$	8.99248	+	15.5754i	0.372111	+	0.644516i
$585$		0			0
$586$	−40.6116	−	23.4471i	−1.67765	−	0.968593i
$587$	−2.06287	+	1.73095i	−0.0851436	+	0.0714439i	−0.684366	−	0.729139i	$-0.739921\pi$
$587$	−2.06287	+	1.73095i	−0.0851436	+	0.0714439i	0.599222	+	0.800583i	$0.295476\pi$
$588$		0			0
$589$	−0.872329	+	4.94723i	−0.0359437	+	0.203847i
$590$	12.6958	+	2.23861i	0.522677	+	0.0921620i
$591$		0			0
$592$	−39.5239	+	33.1645i	−1.62442	+	1.36305i
$593$	3.92320	+	6.79519i	0.161107	+	0.279045i	0.935266	−	0.353946i	$-0.115160\pi$
$593$	3.92320	+	6.79519i	0.161107	+	0.279045i	−0.774159	+	0.632991i	$0.781827\pi$
$594$		0			0
$595$	0.797025	−	0.227671i	0.0326748	−	0.00933359i
$596$	3.41564	−	9.38439i	0.139910	−	0.384400i
$597$		0			0
$598$	−17.5558	−	48.2343i	−0.717912	−	1.97245i
$599$	21.3812	−	25.4812i	0.873614	−	1.04113i	−0.125185	−	0.992133i	$-0.539952\pi$
$599$	21.3812	−	25.4812i	0.873614	−	1.04113i	0.998799	−	0.0489991i	$-0.0156032\pi$
$600$		0			0
$601$	−21.4176	−	25.5245i	−0.873642	−	1.04117i	−0.998797	−	0.0490291i	$-0.984387\pi$
$601$	−21.4176	−	25.5245i	−0.873642	−	1.04117i	0.125155	−	0.992137i	$-0.460057\pi$
$602$	−53.1907	−	13.3191i	−2.16789	−	0.542846i
$603$		0			0
$604$	13.1239			0.534003
$605$	2.13512	+	0.777119i	0.0868048	+	0.0315944i
$606$		0			0
$607$	8.33873	−	9.93771i	0.338459	−	0.403359i	−0.569790	−	0.821790i	$-0.692975\pi$
$607$	8.33873	−	9.93771i	0.338459	−	0.403359i	0.908249	+	0.418431i	$0.137420\pi$
$608$	−3.54466	+	1.29015i	−0.143755	+	0.0523225i
$609$		0			0
$610$	0.191855	+	1.08806i	0.00776797	+	0.0440543i
$611$		−	56.9302i		−	2.30315i
$612$		0			0
$613$	−41.0770			−1.65909			−0.829543	−	0.558443i	$-0.811399\pi$
$613$	−41.0770			−1.65909			−0.829543	+	0.558443i	$0.811399\pi$
$614$	−24.4212	−	8.88857i	−0.985558	−	0.358714i
$615$		0			0
$616$	37.3431	+	16.6715i	1.50460	+	0.671714i
$617$	14.4145	−	17.1786i	0.580307	−	0.691583i	−0.393405	−	0.919365i	$-0.628703\pi$
$617$	14.4145	−	17.1786i	0.580307	−	0.691583i	0.973712	+	0.227782i	$0.0731473\pi$
$618$		0			0
$619$	19.7531	+	23.5408i	0.793944	+	0.946186i	0.999473	−	0.0324651i	$-0.0103358\pi$
$619$	19.7531	+	23.5408i	0.793944	+	0.946186i	−0.205528	+	0.978651i	$0.565891\pi$
$620$	12.4469	+	7.18621i	0.499879	+	0.288605i
$621$		0			0
$622$		−	63.0698i		−	2.52887i
$623$	−11.8089	−	24.2741i	−0.473114	−	0.972523i
$624$		0			0
$625$	3.78516	−	21.4667i	0.151406	−	0.858668i
$626$	32.3529	+	27.1473i	1.29308	+	1.08502i
$627$		0			0
$628$	−13.5700	+	37.2832i	−0.541501	+	1.48776i
$629$	2.49363	+	4.31909i	0.0994274	+	0.172213i
$630$		0			0
$631$	−1.19417	+	2.06836i	−0.0475391	+	0.0823402i	−0.888816	−	0.458265i	$-0.848471\pi$
$631$	−1.19417	+	2.06836i	−0.0475391	+	0.0823402i	0.841277	+	0.540605i	$0.181805\pi$
$632$	−4.42337	−	5.27157i	−0.175952	−	0.209692i
$633$		0			0
$634$	2.81541	−	15.9670i	0.111814	−	0.634129i
$635$	−3.34812	−	2.80940i	−0.132866	−	0.111488i
$636$		0			0
$637$	−32.5049	+	29.1486i	−1.28789	+	1.15491i
$638$	−29.4248	−	16.9884i	−1.16494	−	0.672579i
$639$		0			0
$640$		−	5.68225i		−	0.224611i
$641$	−23.2187	+	4.09409i	−0.917084	+	0.161707i	−0.612218	−	0.790689i	$-0.709723\pi$
$641$	−23.2187	+	4.09409i	−0.917084	+	0.161707i	−0.304866	+	0.952395i	$0.598612\pi$
$642$		0			0
$643$	−35.0530	−	6.18079i	−1.38236	−	0.243746i	−0.567482	−	0.823386i	$-0.692082\pi$
$643$	−35.0530	−	6.18079i	−1.38236	−	0.243746i	−0.814873	+	0.579639i	$0.803193\pi$
$644$	15.5733	−	34.8831i	0.613673	−	1.37459i
$645$		0			0
$646$	0.215484	+	1.22207i	0.00847811	+	0.0480818i
$647$	8.19674	−	14.1972i	0.322247	−	0.558148i	−0.658704	−	0.752402i	$-0.728895\pi$
$647$	8.19674	−	14.1972i	0.322247	−	0.558148i	0.980951	+	0.194254i	$0.0622285\pi$
$648$		0			0
$649$	23.3468	−	13.4793i	0.916443	−	0.529108i
$650$	−71.2507	−	25.9331i	−2.79468	−	1.01718i
$651$		0			0
$652$	6.07241	+	5.09536i	0.237814	+	0.199550i
$653$	−1.18288	−	3.24993i	−0.0462896	−	0.127180i	0.914394	−	0.404826i	$-0.132668\pi$
$653$	−1.18288	−	3.24993i	−0.0462896	−	0.127180i	−0.960683	+	0.277646i	$0.910446\pi$
$654$		0			0
$655$	0.659705	+	3.74137i	0.0257768	+	0.146187i
$656$	−13.1516	+	22.7792i	−0.513482	+	0.889377i
$657$		0			0
$658$	42.6786	−	44.1056i	1.66378	−	1.71941i
$659$	−22.4506	+	3.95865i	−0.874551	+	0.154207i	−0.592867	−	0.805300i	$-0.702004\pi$
$659$	−22.4506	+	3.95865i	−0.874551	+	0.154207i	−0.281684	+	0.959507i	$0.590893\pi$
$660$		0			0
$661$	−12.6905	−	2.23768i	−0.493603	−	0.0870355i	−0.0786945	−	0.996899i	$-0.525075\pi$
$661$	−12.6905	−	2.23768i	−0.493603	−	0.0870355i	−0.414908	+	0.909863i	$0.636186\pi$
$662$	23.0495	+	4.06425i	0.895844	+	0.157961i
$663$		0			0
$664$	32.5588	−	5.74100i	1.26353	−	0.222794i
$665$	−0.621087	+	0.641854i	−0.0240847	+	0.0248900i
$666$		0			0
$667$	−8.75131	+	15.1577i	−0.338852	+	0.586909i
$668$	−6.70998	−	38.0542i	−0.259617	−	1.47236i
$669$		0			0
$670$	−0.00973847	−	0.0267562i	−0.000376230	−	0.00103368i
$671$	1.76989	+	1.48511i	0.0683257	+	0.0573321i
$672$		0			0
$673$	−7.15895	−	2.60564i	−0.275957	−	0.100440i	0.200334	−	0.979728i	$-0.435797\pi$
$673$	−7.15895	−	2.60564i	−0.275957	−	0.100440i	−0.476292	+	0.879287i	$0.658019\pi$
$674$	10.7944	−	6.23215i	0.415785	−	0.240054i
$675$		0			0
$676$	−57.7480	+	100.022i	−2.22108	+	3.84702i
$677$	−7.22216	−	40.9589i	−0.277570	−	1.57418i	−0.730677	−	0.682723i	$-0.760796\pi$
$677$	−7.22216	−	40.9589i	−0.277570	−	1.57418i	0.453107	−	0.891456i	$-0.350316\pi$
$678$		0			0
$679$	20.0729	−	44.9621i	0.770329	−	1.72549i
$680$	1.92811	+	0.339977i	0.0739395	+	0.0130375i
$681$		0			0
$682$	42.8747	−	7.55996i	1.64176	−	0.289486i
$683$		−	34.2304i		−	1.30979i	−0.755719	−	0.654896i	$-0.772713\pi$
$683$		−	34.2304i		−	1.30979i	0.755719	−	0.654896i	$-0.227287\pi$
$684$		0			0
$685$	8.24795	+	4.76195i	0.315138	+	0.181945i
$686$	−47.0343	−	1.78541i	−1.79578	−	0.0681674i
$687$		0			0
$688$	−43.5043	−	36.5045i	−1.65859	−	1.39172i
$689$	−14.4369	+	81.8758i	−0.550003	+	3.11922i
$690$		0			0
$691$	2.69005	+	3.20587i	0.102334	+	0.121957i	0.814781	−	0.579769i	$-0.196857\pi$
$691$	2.69005	+	3.20587i	0.102334	+	0.121957i	−0.712446	+	0.701726i	$0.752413\pi$
$692$	−20.7792	+	35.9907i	−0.789908	+	1.36816i
$693$		0			0
$694$	−7.17933	−	12.4350i	−0.272524	−	0.472025i
$695$	−0.132175	+	0.363149i	−0.00501370	+	0.0137750i
$696$		0			0
$697$	1.94768	+	1.63429i	0.0737735	+	0.0619033i
$698$	−2.00832	+	11.3898i	−0.0760162	+	0.431109i
$699$		0			0
$700$	−24.6862	−	50.7445i	−0.933052	−	1.91796i
$701$			12.5933i			0.475643i	0.971309	+	0.237821i	$0.0764333\pi$
$701$			12.5933i			0.475643i	−0.971309	+	0.237821i	$0.923567\pi$
$702$		0			0
$703$	−4.65387	−	2.68692i	−0.175524	−	0.101339i
$704$	−1.13118	−	1.34809i	−0.0426331	−	0.0508082i
$705$		0			0
$706$	16.3099	−	19.4374i	0.613832	−	0.731537i
$707$	−2.57637	−	1.15020i	−0.0968942	−	0.0432576i
$708$		0			0
$709$	7.07268	+	2.57424i	0.265620	+	0.0966778i	0.471397	−	0.881921i	$-0.343750\pi$
$709$	7.07268	+	2.57424i	0.265620	+	0.0966778i	−0.205777	+	0.978599i	$0.565972\pi$
$710$	11.7864			0.442335
$711$		0			0
$712$		−	63.7595i		−	2.38949i
$713$	−3.89439	−	22.0862i	−0.145846	−	0.827134i
$714$		0			0
$715$	6.74699	−	2.45570i	0.252323	−	0.0918381i
$716$	−32.8955	+	39.2033i	−1.22936	+	1.46510i
$717$		0			0
$718$	34.3319	+	12.4958i	1.28125	+	0.466338i
$719$	37.8930			1.41317			0.706585	−	0.707628i	$-0.250235\pi$
$719$	37.8930			1.41317			0.706585	+	0.707628i	$0.250235\pi$
$720$		0			0
$721$	14.5138	+	3.63430i	0.540523	+	0.135349i
$722$	30.1790	+	35.9660i	1.12315	+	1.33852i
$723$		0			0
$724$	−14.7061	+	17.5261i	−0.546549	+	0.651351i
$725$	8.84277	+	24.2953i	0.328412	+	0.902305i
$726$		0			0
$727$	6.98614	−	19.1943i	0.259102	−	0.711876i	−0.740122	−	0.672473i	$-0.765232\pi$
$727$	6.98614	−	19.1943i	0.259102	−	0.711876i	0.999223	−	0.0394032i	$-0.0125457\pi$
$728$	−99.1580	+	28.3246i	−3.67504	+	1.04978i
$729$		0			0
$730$	1.70204	+	2.94802i	0.0629952	+	0.109111i
$731$	−4.20521	+	3.52859i	−0.155535	+	0.130510i
$732$		0			0
$733$	−28.4107	−	5.00957i	−1.04937	−	0.185033i	−0.377736	−	0.925913i	$-0.623297\pi$
$733$	−28.4107	−	5.00957i	−1.04937	−	0.185033i	−0.671637	+	0.740881i	$0.734408\pi$
$734$	15.6741	−	88.8925i	0.578543	−	3.28108i
$735$		0			0
$736$	12.9004	−	10.8247i	0.475513	−	0.399003i
$737$	−0.0515655	−	0.0297714i	−0.00189944	−	0.00109664i
$738$		0			0
$739$	−13.2552	−	22.9587i	−0.487600	−	0.844548i	0.512298	−	0.858808i	$-0.328794\pi$
$739$	−13.2552	−	22.9587i	−0.487600	−	0.844548i	−0.999898	+	0.0142594i	$0.995461\pi$
$740$	−11.7776	+	9.88259i	−0.432954	+	0.363291i
$741$		0			0
$742$	−72.5642	+	52.6089i	−2.66391	+	1.93133i
$743$	−2.96176	−	8.13736i	−0.108656	−	0.298531i	0.873434	−	0.486943i	$-0.161888\pi$
$743$	−2.96176	−	8.13736i	−0.108656	−	0.298531i	−0.982090	+	0.188412i	$0.939666\pi$
$744$		0			0
$745$	0.356514	−	0.979514i	0.0130617	−	0.0358866i
$746$	−7.50033	+	4.33032i	−0.274607	+	0.158544i
$747$		0			0
$748$	6.42961	−	3.71214i	0.235090	−	0.135729i
$749$	0.496561	−	6.99939i	0.0181439	−	0.255752i
$750$		0			0
$751$	−5.98066	+	2.17678i	−0.218237	+	0.0794319i	−0.448825	−	0.893620i	$-0.648157\pi$
$751$	−5.98066	+	2.17678i	−0.218237	+	0.0794319i	0.230588	+	0.973052i	$0.425935\pi$
$752$	59.7320	−	21.7407i	2.17820	−	0.792801i
$753$		0			0
$754$	84.3760	−	14.8778i	3.07279	−	0.541817i
$755$	1.36983			0.0498532
$756$		0			0
$757$	19.8369			0.720983			0.360492	−	0.932762i	$-0.382609\pi$
$757$	19.8369			0.720983			0.360492	+	0.932762i	$0.382609\pi$
$758$	−2.58222	+	0.455316i	−0.0937906	+	0.0165378i
$759$		0			0
$760$	−1.98238	+	0.721529i	−0.0719086	+	0.0261726i
$761$	−47.2462	+	17.1962i	−1.71267	+	0.623362i	−0.997165	−	0.0752443i	$-0.976026\pi$
$761$	−47.2462	+	17.1962i	−1.71267	+	0.623362i	−0.715507	+	0.698606i	$0.753804\pi$
$762$		0			0
$763$	13.1940	+	27.1212i	0.477653	+	0.981854i
$764$	67.6618	−	39.0646i	2.44792	−	1.41331i
$765$		0			0
$766$	−7.25896	+	4.19096i	−0.262277	+	0.151426i
$767$	−23.2505	+	63.8803i	−0.839528	+	2.30658i
$768$		0			0
$769$	10.8973	+	29.9402i	0.392968	+	1.07967i	0.965640	+	0.259885i	$0.0836847\pi$
$769$	10.8973	+	29.9402i	0.392968	+	1.07967i	−0.572672	+	0.819785i	$0.694093\pi$
$770$	7.06806	+	3.15548i	0.254715	+	0.113715i
$771$		0			0
$772$	25.3606	−	21.2801i	0.912750	−	0.765888i
$773$	12.0759	+	20.9160i	0.434339	+	0.752298i	0.997241	−	0.0742258i	$-0.0236486\pi$
$773$	12.0759	+	20.9160i	0.434339	+	0.752298i	−0.562902	+	0.826524i	$0.690315\pi$
$774$		0			0
$775$	−28.6902	−	16.5643i	−1.03058	−	0.595006i
$776$	89.0925	−	74.7575i	3.19823	−	2.68364i
$777$		0			0
$778$	−8.44957	+	47.9199i	−0.302932	+	1.71801i
$779$	−2.69797	−	0.475724i	−0.0966647	−	0.0170446i
$780$		0			0
$781$	18.8809	−	15.8430i	0.675613	−	0.566907i
$782$	−2.76996	−	4.79772i	−0.0990537	−	0.171566i
$783$		0			0
$784$	−42.9963	−	22.9732i	−1.53558	−	0.820472i
$785$	−1.41639	+	3.89150i	−0.0505532	+	0.138894i
$786$		0			0
$787$	3.44103	+	9.45415i	0.122659	+	0.337004i	0.985791	−	0.167975i	$-0.0537226\pi$
$787$	3.44103	+	9.45415i	0.122659	+	0.337004i	−0.863132	+	0.504978i	$0.831500\pi$
$788$	−13.5858	+	16.1909i	−0.483974	+	0.576778i
$789$		0			0
$790$	−0.837228	−	0.997769i	−0.0297872	−	0.0354990i
$791$	−13.0710	+	13.5081i	−0.464753	+	0.480292i
$792$		0			0
$793$	−5.82607			−0.206890
$794$	−37.6845	−	13.7161i	−1.33737	−	0.486764i
$795$		0			0
$796$	19.2185	−	22.9037i	0.681181	−	0.811800i
$797$	21.8937	−	7.96866i	0.775515	−	0.282264i	0.0762137	−	0.997092i	$-0.475717\pi$
$797$	21.8937	−	7.96866i	0.775515	−	0.282264i	0.699301	+	0.714827i	$0.253495\pi$
$798$		0			0
$799$	−1.06696	−	6.05101i	−0.0377462	−	0.214069i
$800$		−	24.8760i		−	0.879501i
$801$		0			0
$802$	72.9236			2.57502
$803$	6.68920	+	2.43467i	0.236057	+	0.0859176i
$804$		0			0
$805$	1.62549	−	3.64099i	0.0572910	−	0.128328i
$806$	−70.5669	+	84.0983i	−2.48561	+	2.96224i
$807$		0			0
$808$	−4.28367	−	5.10507i	−0.150699	−	0.179596i
$809$	−36.9148	−	21.3128i	−1.29786	−	0.749317i	−0.317822	−	0.948150i	$-0.602951\pi$
$809$	−36.9148	−	21.3128i	−1.29786	−	0.749317i	−0.980033	+	0.198833i	$0.936285\pi$
$810$		0			0
$811$			33.7669i			1.18572i	0.805307	+	0.592859i	$0.202001\pi$
$811$			33.7669i			1.18572i	−0.805307	+	0.592859i	$0.797999\pi$
$812$	52.8271	+	35.7101i	1.85387	+	1.25318i
$813$		0			0
$814$	−8.08711	+	45.8643i	−0.283453	+	1.60754i
$815$	0.633819	+	0.531838i	0.0222017	+	0.0186295i
$816$		0			0
$817$	2.02306	−	5.55830i	0.0707778	−	0.194460i
$818$	1.06921	+	1.85192i	0.0373839	+	0.0647508i
$819$		0			0
$820$	−3.91899	+	6.78790i	−0.136857	+	0.237044i
$821$	−15.1489	−	18.0538i	−0.528702	−	0.630082i	0.433914	−	0.900954i	$-0.357132\pi$
$821$	−15.1489	−	18.0538i	−0.528702	−	0.630082i	−0.962615	+	0.270872i	$0.912688\pi$
$822$		0			0
$823$	−5.04491	+	28.6111i	−0.175854	+	0.997320i	0.761299	+	0.648401i	$0.224562\pi$
$823$	−5.04491	+	28.6111i	−0.175854	+	0.997320i	−0.937153	+	0.348918i	$0.886549\pi$
$824$	27.0718	+	22.7159i	0.943089	+	0.791346i
$825$		0			0
$826$	−65.9018	+	32.0599i	−2.29302	+	1.11551i
$827$	28.8450	+	16.6537i	1.00304	+	0.579105i	0.909146	−	0.416478i	$-0.136736\pi$
$827$	28.8450	+	16.6537i	1.00304	+	0.579105i	0.0938928	+	0.995582i	$0.470069\pi$
$828$		0			0
$829$		−	39.6583i		−	1.37739i	−0.725052	−	0.688694i	$-0.758184\pi$
$829$		−	39.6583i		−	1.37739i	0.725052	−	0.688694i	$-0.241816\pi$
$830$	6.16252	−	1.08662i	0.213904	−	0.0377171i
$831$		0			0
$832$	4.37020	+	0.770585i	0.151510	+	0.0267152i
$833$	−2.90860	+	3.70735i	−0.100777	+	0.128452i
$834$		0			0
$835$	−0.700367	−	3.97198i	−0.0242372	−	0.137456i
$836$	−3.99988	+	6.92799i	−0.138339	+	0.239610i
$837$		0			0
$838$	34.3897	−	19.8549i	1.18797	−	0.685877i
$839$	48.4005	+	17.6163i	1.67097	+	0.608184i	0.992029	−	0.126008i	$-0.0402164\pi$
$839$	48.4005	+	17.6163i	1.67097	+	0.608184i	0.678942	+	0.734192i	$0.262439\pi$
$840$		0			0
$841$	−0.164445	−	0.137985i	−0.00567050	−	0.00475812i
$842$	25.8231	+	70.9485i	0.889924	+	2.44505i
$843$		0			0
$844$	−7.77768	−	44.1094i	−0.267719	−	1.51831i
$845$	−6.02756	+	10.4400i	−0.207354	+	0.359148i
$846$		0			0
$847$	−12.4199	+	3.54776i	−0.426753	+	0.121902i
$848$	−91.4185	+	16.1196i	−3.13933	+	0.553548i
$849$		0			0
$850$	−8.05915	−	1.42104i	−0.276426	−	0.0487414i
$851$	23.6262	+	4.16594i	0.809896	+	0.142807i
$852$		0			0
$853$	37.1908	−	6.55774i	1.27339	−	0.224533i	0.504218	−	0.863576i	$-0.331781\pi$
$853$	37.1908	−	6.55774i	1.27339	−	0.224533i	0.769171	+	0.639044i	$0.220670\pi$
$854$	−4.51364	−	4.36760i	−0.154453	−	0.149456i
$855$		0			0
$856$	8.28696	−	14.3534i	0.283242	−	0.490590i
$857$	−7.70609	−	43.7034i	−0.263235	−	1.49288i	−0.774014	−	0.633168i	$-0.781754\pi$
$857$	−7.70609	−	43.7034i	−0.263235	−	1.49288i	0.510779	−	0.859712i	$-0.329357\pi$
$858$		0			0
$859$	3.58111	+	9.83903i	0.122186	+	0.335703i	0.985673	−	0.168668i	$-0.0539465\pi$
$859$	3.58111	+	9.83903i	0.122186	+	0.335703i	−0.863487	+	0.504371i	$0.831724\pi$
$860$	−12.9637	−	10.8779i	−0.442059	−	0.370932i
$861$		0			0
$862$	−88.2409	−	32.1171i	−3.00550	−	1.09391i
$863$	16.5153	−	9.53510i	0.562187	−	0.324579i	−0.191836	−	0.981427i	$-0.561444\pi$
$863$	16.5153	−	9.53510i	0.562187	−	0.324579i	0.754023	+	0.656848i	$0.228111\pi$
$864$		0			0
$865$	−2.16887	+	3.75660i	−0.0737439	+	0.127728i
$866$	4.35152	+	24.6787i	0.147871	+	0.838617i
$867$		0			0
$868$	−81.2653	+	8.45821i	−2.75832	+	0.287090i
$869$	−2.68236	−	0.472972i	−0.0909928	−	0.0160445i
$870$		0			0
$871$	0.147865	−	0.0260725i	0.00501020	−	0.000883434i
$872$			71.2377i			2.41241i
$873$		0			0
$874$	5.16960	+	2.98467i	0.174864	+	0.100958i
$875$	−5.27002	−	10.8330i	−0.178159	−	0.366221i
$876$		0			0
$877$	28.2729	+	23.7237i	0.954706	+	0.801094i	0.980084	−	0.198584i	$-0.0636343\pi$
$877$	28.2729	+	23.7237i	0.954706	+	0.801094i	−0.0253774	+	0.999678i	$0.508079\pi$
$878$	15.7057	−	89.0714i	0.530042	−	3.00602i
$879$		0			0
$880$	5.15312	+	6.14125i	0.173712	+	0.207022i
$881$	14.1834	−	24.5664i	0.477851	−	0.827662i	−0.521827	−	0.853052i	$-0.674749\pi$
$881$	14.1834	−	24.5664i	0.477851	−	0.827662i	0.999678	+	0.0253894i	$0.00808256\pi$
$882$		0			0
$883$	−1.51080	−	2.61677i	−0.0508423	−	0.0880615i	0.839484	−	0.543384i	$-0.182857\pi$
$883$	−1.51080	−	2.61677i	−0.0508423	−	0.0880615i	−0.890327	+	0.455323i	$0.849524\pi$
$884$	−6.40309	+	17.5924i	−0.215359	+	0.591695i
$885$		0			0
$886$	−25.9127	−	21.7433i	−0.870554	−	0.730482i
$887$	−0.0218494	+	0.123914i	−0.000733631	+	0.00416063i	−0.985172	−	0.171567i	$-0.945117\pi$
$887$	−0.0218494	+	0.123914i	−0.000733631	+	0.00416063i	0.984439	+	0.175728i	$0.0562280\pi$
$888$		0			0
$889$	24.7840	+	1.75826i	0.831229	+	0.0589703i
$890$		−	12.0680i		−	0.404520i
$891$		0			0
$892$	110.876	+	64.0140i	3.71239	+	2.14335i
$893$	4.25566	+	5.07170i	0.142410	+	0.169718i
$894$		0			0
$895$	−3.43353	+	4.09192i	−0.114770	+	0.136778i
$896$	18.9605	+	26.1524i	0.633424	+	0.873691i
$897$		0			0
$898$	−17.8392	−	6.49292i	−0.595301	−	0.216672i
$899$	37.4340			1.24850
$900$		0			0
$901$			8.97301i			0.298934i
$902$	4.12282	+	23.3817i	0.137275	+	0.778525i
$903$		0			0
$904$	−41.7201	+	15.1849i	−1.38759	+	0.505041i
$905$	−1.53498	+	1.82932i	−0.0510244	+	0.0608086i
$906$		0			0
$907$	7.24680	+	2.63762i	0.240626	+	0.0875808i	0.459518	−	0.888168i	$-0.348022\pi$
$907$	7.24680	+	2.63762i	0.240626	+	0.0875808i	−0.218892	+	0.975749i	$0.570244\pi$
$908$	−10.3810			−0.344506
$909$		0			0
$910$	−18.7680	+	5.36109i	−0.622153	+	0.177718i
$911$	−3.55791	−	4.24015i	−0.117879	−	0.140482i	0.703878	−	0.710321i	$-0.251450\pi$
$911$	−3.55791	−	4.24015i	−0.117879	−	0.140482i	−0.821757	+	0.569838i	$0.807006\pi$
$912$		0			0
$913$	8.41131	−	10.0242i	0.278374	−	0.331753i
$914$	22.5291	+	61.8982i	0.745197	+	2.04741i
$915$		0			0
$916$	17.1834	−	47.2111i	0.567757	−	1.55990i
$917$	−15.5204	−	15.0183i	−0.512530	−	0.495947i
$918$		0			0
$919$	0.511927	+	0.886684i	0.0168869	+	0.0292490i	0.874345	−	0.485304i	$-0.161291\pi$
$919$	0.511927	+	0.886684i	0.0168869	+	0.0292490i	−0.857458	+	0.514553i	$0.827958\pi$
$920$	7.21464	−	6.05380i	0.237860	−	0.199588i
$921$		0			0
$922$	63.2001	+	11.1439i	2.08138	+	0.367004i
$923$	−10.7926	+	61.2076i	−0.355241	+	2.01467i
$924$		0			0
$925$	27.1475	−	22.7795i	0.892605	−	0.748984i
$926$	−44.3307	−	25.5943i	−1.45680	−	0.841082i
$927$		0			0
$928$	14.0545	+	24.3431i	0.461361	+	0.799102i
$929$	17.1349	−	14.3779i	0.562177	−	0.471723i	−0.316862	−	0.948472i	$-0.602629\pi$
$929$	17.1349	−	14.3779i	0.562177	−	0.471723i	0.879040	+	0.476749i	$0.158185\pi$
$930$		0			0
$931$	0.716811	−	5.02656i	0.0234925	−	0.164739i
$932$	20.4121	+	56.0817i	0.668620	+	1.83702i
$933$		0			0
$934$	3.75071	−	10.3050i	0.122727	−	0.337189i
$935$	0.671103	−	0.387461i	0.0219474	−	0.0126713i
$936$		0			0
$937$	12.3038	−	7.10360i	0.401947	−	0.232064i	−0.285377	−	0.958415i	$-0.592119\pi$
$937$	12.3038	−	7.10360i	0.401947	−	0.232064i	0.687324	+	0.726351i	$0.258785\pi$
$938$	0.134101	+	0.0906498i	0.00437855	+	0.00295982i
$939$		0			0
$940$	17.7994	−	6.47844i	0.580551	−	0.211303i
$941$	30.1790	−	10.9843i	0.983807	−	0.358076i	0.200488	−	0.979696i	$-0.435747\pi$
$941$	30.1790	−	10.9843i	0.983807	−	0.358076i	0.783319	+	0.621620i	$0.213525\pi$
$942$		0			0
$943$	12.0447	−	2.12380i	0.392229	−	0.0691605i
$944$	−75.9032			−2.47044
$945$		0			0
$946$	−51.2620			−1.66667
$947$	−40.7828	+	7.19111i	−1.32526	+	0.233680i	−0.791093	−	0.611697i	$-0.790487\pi$
$947$	−40.7828	+	7.19111i	−1.32526	+	0.233680i	−0.534171	+	0.845376i	$0.679376\pi$
$948$		0			0
$949$	−16.8678	+	6.13938i	−0.547552	+	0.199293i
$950$	8.28602	−	3.01586i	0.268834	−	0.0978476i
$951$		0			0
$952$	−10.0085	+	4.86894i	−0.324377	+	0.157803i
$953$	−29.7841	+	17.1959i	−0.964803	+	0.557029i	−0.897648	−	0.440713i	$-0.854726\pi$
$953$	−29.7841	+	17.1959i	−0.964803	+	0.557029i	−0.0671552	+	0.997743i	$0.521392\pi$
$954$		0			0
$955$	7.06233	−	4.07744i	0.228532	−	0.131943i
$956$	37.2870	−	102.445i	1.20595	−	3.31332i
$957$		0			0
$958$	1.66730	+	4.58087i	0.0538680	+	0.148001i
$959$	−53.8506	+	5.60485i	−1.73893	+	0.180990i
$960$		0			0
$961$	−12.9966	+	10.9055i	−0.419246	+	0.351789i
$962$	−58.7188	−	101.704i	−1.89317	−	3.27907i
$963$		0			0
$964$	49.1817	+	28.3951i	1.58404	+	0.914543i
$965$	2.64707	−	2.22115i	0.0852121	−	0.0715014i
$966$		0			0
$967$	0.771534	−	4.37559i	0.0248109	−	0.140709i	−0.969886	−	0.243559i	$-0.921685\pi$
$967$	0.771534	−	4.37559i	0.0248109	−	0.140709i	0.994697	+	0.102850i	$0.0327961\pi$
$968$	−30.0454	−	5.29781i	−0.965694	−	0.170278i
$969$		0			0
$970$	16.8628	−	14.1496i	0.541433	−	0.454317i
$971$	19.3649	+	33.5409i	0.621448	+	1.07638i	0.989216	+	0.146462i	$0.0467888\pi$
$971$	19.3649	+	33.5409i	0.621448	+	1.07638i	−0.367768	+	0.929918i	$0.619878\pi$
$972$		0			0
$973$	−0.603416	−	2.11243i	−0.0193446	−	0.0677213i
$974$	17.7803	−	48.8510i	0.569718	−	1.56529i
$975$		0			0
$976$	−2.22488	−	6.11280i	−0.0712166	−	0.195666i
$977$	11.6518	−	13.8861i	0.372775	−	0.444256i	−0.546745	−	0.837299i	$-0.684133\pi$
$977$	11.6518	−	13.8861i	0.372775	−	0.444256i	0.919520	+	0.393043i	$0.128578\pi$
$978$		0			0
$979$	−16.2215	−	19.3320i	−0.518442	−	0.617855i
$980$	−12.8123	−	6.84572i	−0.409275	−	0.218679i
$981$		0			0
$982$	72.1567			2.30261
$983$	6.07153	+	2.20986i	0.193652	+	0.0704834i	0.437025	−	0.899449i	$-0.356032\pi$
$983$	6.07153	+	2.20986i	0.193652	+	0.0704834i	−0.243374	+	0.969933i	$0.578254\pi$
$984$		0			0
$985$	−1.41804	+	1.68996i	−0.0451826	+	0.0538465i
$986$	8.68936	−	3.16267i	0.276725	−	0.100720i
$987$		0			0
$988$	−3.50293	−	19.8661i	−0.111443	−	0.632024i
$989$			26.4068i			0.839686i
$990$		0			0
$991$	37.7750			1.19996			0.599981	−	0.800014i	$-0.295175\pi$
$991$	37.7750			1.19996			0.599981	+	0.800014i	$0.295175\pi$
$992$	−33.8452	−	12.3186i	−1.07459	−	0.391117i
$993$		0			0
$994$	−54.2466	+	39.3286i	−1.72060	+	1.24743i
$995$	2.00597	−	2.39062i	0.0635934	−	0.0757877i
$996$		0			0
$997$	27.4844	+	32.7546i	0.870438	+	1.03735i	0.998958	+	0.0456410i	$0.0145330\pi$
$997$	27.4844	+	32.7546i	0.870438	+	1.03735i	−0.128520	+	0.991707i	$0.541023\pi$
$998$	−51.5318	−	29.7519i	−1.63121	−	0.941780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.17.1		132
3.2	odd	2		189.2.bd.a.185.22	yes	132
7.5	odd	6		567.2.ba.a.341.22		132
21.5	even	6		189.2.ba.a.131.1	yes	132
27.7	even	9		189.2.ba.a.101.1	✓	132
27.20	odd	18		567.2.ba.a.143.22		132
189.47	even	18	inner	567.2.bd.a.467.1		132
189.61	odd	18		189.2.bd.a.47.22	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.1	✓	132	27.7	even	9
189.2.ba.a.131.1	yes	132	21.5	even	6
189.2.bd.a.47.22	yes	132	189.61	odd	18
189.2.bd.a.185.22	yes	132	3.2	odd	2
567.2.ba.a.143.22		132	27.20	odd	18
567.2.ba.a.341.22		132	7.5	odd	6
567.2.bd.a.17.1		132	1.1	even	1	trivial
567.2.bd.a.467.1		132	189.47	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.50283 + 0.441316i) q^{2} +(4.19001 - 1.52504i) q^{4} +(0.437341 - 0.159179i) q^{5} +(-1.48170 + 2.19193i) q^{7} +(-5.41196 + 3.12460i) q^{8} +O(q^{10})\)	\(q+(-2.50283 + 0.441316i) q^{2} +(4.19001 - 1.52504i) q^{4} +(0.437341 - 0.159179i) q^{5} +(-1.48170 + 2.19193i) q^{7} +(-5.41196 + 3.12460i) q^{8} +(-1.02434 + 0.591403i) q^{10} +(-0.845970 + 2.32428i) q^{11} +(-2.13324 - 5.86102i) q^{13} +(2.74112 - 6.13993i) q^{14} +(5.33482 - 4.47645i) q^{16} +(-0.336582 - 0.582978i) q^{17} +(0.628166 + 0.362672i) q^{19} +(1.58971 - 1.33392i) q^{20} +(1.09157 - 6.19062i) q^{22} +(-3.18900 - 0.562306i) q^{23} +(-3.66429 + 3.07471i) q^{25} +(7.92569 + 13.7277i) q^{26} +(-2.86558 + 11.4439i) q^{28} +(1.84864 - 5.07909i) q^{29} +(2.36874 + 6.50807i) q^{31} +(-3.34281 + 3.98381i) q^{32} +(1.09969 + 1.31055i) q^{34} +(-0.299100 + 1.19448i) q^{35} -7.40866 q^{37} +(-1.73225 - 0.630486i) q^{38} +(-1.86950 + 2.22798i) q^{40} +(-3.54917 + 1.29179i) q^{41} +(-1.41606 - 8.03089i) q^{43} +11.0289i q^{44} +8.22967 q^{46} +(8.57711 + 3.12181i) q^{47} +(-2.60911 - 6.49558i) q^{49} +(7.81418 - 9.31258i) q^{50} +(-17.8766 - 21.3045i) q^{52} +(-11.5438 - 6.66480i) q^{53} +1.15116i q^{55} +(1.17003 - 16.4924i) q^{56} +(-2.38534 + 13.5279i) q^{58} +(-8.34926 - 7.00586i) q^{59} +(0.319477 - 0.877757i) q^{61} +(-8.80068 - 15.2432i) q^{62} +(-0.355740 + 0.616160i) q^{64} +(-1.86590 - 2.22370i) q^{65} +(-0.00418019 + 0.0237070i) q^{67} +(-2.29935 - 1.92938i) q^{68} +(0.221455 - 3.12157i) q^{70} +(-8.62973 - 4.98238i) q^{71} -2.87796i q^{73} +(18.5426 - 3.26957i) q^{74} +(3.18511 + 0.561622i) q^{76} +(-3.84119 - 5.29820i) q^{77} +(0.191220 + 1.08446i) q^{79} +(1.62058 - 2.80692i) q^{80} +(8.31288 - 4.79945i) q^{82} +(-4.97140 - 1.80944i) q^{83} +(-0.239999 - 0.201383i) q^{85} +(7.08833 + 19.4750i) q^{86} +(-2.68409 - 15.2222i) q^{88} +(-5.10142 + 8.83591i) q^{89} +(16.0078 + 4.00839i) q^{91} +(-14.2195 + 2.50728i) q^{92} +(-22.8448 - 4.02815i) q^{94} +(0.332452 + 0.0586203i) q^{95} +(-18.3280 + 3.23172i) q^{97} +(9.39676 + 15.1059i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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