LMFDB - Embedded newform 567.2.ba.a.143.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (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			143.22
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63361 - 1.94686i) q^{2} +(-0.774283 - 4.39118i) q^{4} +(0.356523 - 0.299159i) q^{5} +(-2.41592 - 1.07857i) q^{7} +(-5.41196 - 3.12460i) q^{8} +O(q^{10})$	\(q+(1.63361 - 1.94686i) q^{2} +(-0.774283 - 4.39118i) q^{4} +(0.356523 - 0.299159i) q^{5} +(-2.41592 - 1.07857i) q^{7} +(-5.41196 - 3.12460i) q^{8} -1.18281i q^{10} +(-1.58990 + 1.89477i) q^{11} +(2.13324 - 5.86102i) q^{13} +(-6.04649 + 2.94150i) q^{14} +(-6.54413 + 2.38187i) q^{16} -0.673165 q^{17} -0.725344i q^{19} +(-1.58971 - 1.33392i) q^{20} +(1.09157 + 6.19062i) q^{22} +(1.10753 - 3.04291i) q^{23} +(-0.830628 + 4.71072i) q^{25} +(-7.92569 - 13.7277i) q^{26} +(-2.86558 + 11.4439i) q^{28} +(1.84864 + 5.07909i) q^{29} +(6.82052 - 1.20264i) q^{31} +(-1.77867 + 4.88687i) q^{32} +(-1.09969 + 1.31055i) q^{34} +(-1.18400 + 0.338210i) q^{35} +(3.70433 - 6.41609i) q^{37} +(-1.41214 - 1.18493i) q^{38} +(-2.86424 + 0.505043i) q^{40} +(3.54917 + 1.29179i) q^{41} +(-1.41606 + 8.03089i) q^{43} +(9.55132 + 5.51446i) q^{44} +(-4.11484 - 7.12711i) q^{46} +(1.58499 - 8.98890i) q^{47} +(4.67338 + 5.21148i) q^{49} +(7.81418 + 9.31258i) q^{50} +(-27.3885 - 4.82933i) q^{52} +(11.5438 + 6.66480i) q^{53} +1.15116i q^{55} +(9.70479 + 13.3860i) q^{56} +(12.9082 + 4.69821i) q^{58} +(-10.2419 - 3.72774i) q^{59} +(0.919898 + 0.162203i) q^{61} +(8.80068 - 15.2432i) q^{62} +(-0.355740 - 0.616160i) q^{64} +(-0.992826 - 2.72777i) q^{65} +(-0.0184408 + 0.0154737i) q^{67} +(0.521220 + 2.95599i) q^{68} +(-1.27574 + 2.85757i) q^{70} +(-8.62973 + 4.98238i) q^{71} +(-2.49239 + 1.43898i) q^{73} +(-6.43979 - 17.6932i) q^{74} +(-3.18511 + 0.561622i) q^{76} +(5.88473 - 2.86281i) q^{77} +(0.843560 + 0.707831i) q^{79} +(-1.62058 + 2.80692i) q^{80} +(8.31288 - 4.79945i) q^{82} +(4.97140 - 1.80944i) q^{83} +(-0.239999 + 0.201383i) q^{85} +(13.3217 + 15.8762i) q^{86} +(14.5249 - 5.28663i) q^{88} -10.2028 q^{89} +(-11.4753 + 11.8589i) q^{91} +(-14.2195 - 2.50728i) q^{92} +(-14.9109 - 17.7701i) q^{94} +(-0.216993 - 0.258602i) q^{95} +(18.3280 + 3.23172i) q^{97} +(17.7805 - 0.584889i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	1.63361	−	1.94686i	1.15513	−	1.37664i	0.241348	−	0.970439i	$-0.422410\pi$
$2$	1.63361	−	1.94686i	1.15513	−	1.37664i	0.913786	−	0.406197i	$-0.133145\pi$
$3$		0			0
$3$		0			0
$4$	−0.774283	−	4.39118i	−0.387142	−	2.19559i
$5$	0.356523	−	0.299159i	0.159442	−	0.133788i	−0.559576	−	0.828779i	$-0.689036\pi$
$5$	0.356523	−	0.299159i	0.159442	−	0.133788i	0.719018	+	0.694991i	$0.244592\pi$
$6$		0			0
$7$	−2.41592	−	1.07857i	−0.913133	−	0.407661i
$7$	−2.41592	−	1.07857i	−0.913133	−	0.407661i
$8$	−5.41196	−	3.12460i	−1.91342	−	1.10471i
$9$		0			0
$10$		−	1.18281i		−	0.374036i
$11$	−1.58990	+	1.89477i	−0.479374	+	0.571295i	−0.950482	−	0.310780i	$-0.899410\pi$
$11$	−1.58990	+	1.89477i	−0.479374	+	0.571295i	0.471108	+	0.882075i	$0.343854\pi$
$12$		0			0
$13$	2.13324	−	5.86102i	0.591653	−	1.62555i	−0.175783	−	0.984429i	$-0.556246\pi$
$13$	2.13324	−	5.86102i	0.591653	−	1.62555i	0.767436	−	0.641125i	$-0.221532\pi$
$14$	−6.04649	+	2.94150i	−1.61599	+	0.786149i
$15$		0			0
$16$	−6.54413	+	2.38187i	−1.63603	+	0.595467i
$17$	−0.673165			−0.163266			−0.0816332	−	0.996662i	$-0.526014\pi$
$17$	−0.673165			−0.163266			−0.0816332	+	0.996662i	$0.526014\pi$
$18$		0			0
$19$		−	0.725344i		−	0.166405i	−0.996533	−	0.0832027i	$-0.973485\pi$
$19$		−	0.725344i		−	0.166405i	0.996533	−	0.0832027i	$-0.0265149\pi$
$20$	−1.58971	−	1.33392i	−0.355470	−	0.298274i
$21$		0			0
$22$	1.09157	+	6.19062i	0.232724	+	1.31985i
$23$	1.10753	−	3.04291i	0.230935	−	0.634490i	−0.769054	−	0.639184i	$-0.779272\pi$
$23$	1.10753	−	3.04291i	0.230935	−	0.634490i	0.999989	+	0.00469449i	$0.00149431\pi$
$24$		0			0
$25$	−0.830628	+	4.71072i	−0.166126	+	0.942145i
$26$	−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	0.984435	+	0.175750i	$0.0562349\pi$
$29$	1.84864	+	5.07909i	0.343284	+	0.943164i	−0.641151	+	0.767415i	$0.721543\pi$
$30$		0			0
$31$	6.82052	−	1.20264i	1.22500	−	0.216001i	0.476525	−	0.879161i	$-0.341896\pi$
$31$	6.82052	−	1.20264i	1.22500	−	0.216001i	0.748478	+	0.663160i	$0.230785\pi$
$32$	−1.77867	+	4.88687i	−0.314428	+	0.863884i
$33$		0			0
$34$	−1.09969	+	1.31055i	−0.188595	+	0.224758i
$35$	−1.18400	+	0.338210i	−0.200132	+	0.0571678i
$36$		0			0
$37$	3.70433	−	6.41609i	0.608988	−	1.05480i	−0.382419	−	0.923989i	$-0.624909\pi$
$37$	3.70433	−	6.41609i	0.608988	−	1.05480i	0.991407	−	0.130810i	$-0.0417578\pi$
$38$	−1.41214	−	1.18493i	−0.229079	−	0.192220i
$39$		0			0
$40$	−2.86424	+	0.505043i	−0.452876	+	0.0798543i
$41$	3.54917	+	1.29179i	0.554287	+	0.201744i	0.603950	−	0.797022i	$-0.293592\pi$
$41$	3.54917	+	1.29179i	0.554287	+	0.201744i	−0.0496629	+	0.998766i	$0.515815\pi$
$42$		0			0
$43$	−1.41606	+	8.03089i	−0.215948	+	1.22470i	0.663307	+	0.748348i	$0.269152\pi$
$43$	−1.41606	+	8.03089i	−0.215948	+	1.22470i	−0.879254	+	0.476352i	$0.841959\pi$
$44$	9.55132	+	5.51446i	1.43992	+	0.831335i
$45$		0			0
$46$	−4.11484	−	7.12711i	−0.606700	−	1.05083i
$47$	1.58499	−	8.98890i	0.231194	−	1.31117i	−0.619289	−	0.785163i	$-0.712579\pi$
$47$	1.58499	−	8.98890i	0.231194	−	1.31117i	0.850483	−	0.526003i	$-0.176310\pi$
$48$		0			0
$49$	4.67338	+	5.21148i	0.667626	+	0.744497i
$50$	7.81418	+	9.31258i	1.10509	+	1.31700i
$51$		0			0
$52$	−27.3885	−	4.82933i	−3.79810	−	0.669708i
$53$	11.5438	+	6.66480i	1.58566	+	0.915480i	0.994011	+	0.109283i	$0.0348555\pi$
$53$	11.5438	+	6.66480i	1.58566	+	0.915480i	0.591647	+	0.806197i	$0.298478\pi$
$54$		0			0
$55$			1.15116i			0.155223i
$56$	9.70479	+	13.3860i	1.29686	+	1.78877i
$57$		0			0
$58$	12.9082	+	4.69821i	1.69493	+	0.616905i
$59$	−10.2419	−	3.72774i	−1.33338	−	0.485310i	−0.425658	−	0.904884i	$-0.639957\pi$
$59$	−10.2419	−	3.72774i	−1.33338	−	0.485310i	−0.907721	+	0.419574i	$0.862180\pi$
$60$		0			0
$61$	0.919898	+	0.162203i	0.117781	+	0.0207680i	0.232228	−	0.972661i	$-0.425398\pi$
$61$	0.919898	+	0.162203i	0.117781	+	0.0207680i	−0.114447	+	0.993429i	$0.536510\pi$
$62$	8.80068	−	15.2432i	1.11769	−	1.93589i
$63$		0			0
$64$	−0.355740	−	0.616160i	−0.0444675	−	0.0770200i
$65$	−0.992826	−	2.72777i	−0.123145	−	0.338338i
$66$		0			0
$67$	−0.0184408	+	0.0154737i	−0.00225290	+	0.00189041i	−0.643913	−	0.765098i	$-0.722690\pi$
$67$	−0.0184408	+	0.0154737i	−0.00225290	+	0.00189041i	0.641660	+	0.766989i	$0.278246\pi$
$68$	0.521220	+	2.95599i	0.0632072	+	0.358466i
$69$		0			0
$70$	−1.27574	+	2.85757i	−0.152480	+	0.341545i
$71$	−8.62973	+	4.98238i	−1.02416	+	0.591300i	−0.915306	−	0.402758i	$-0.868052\pi$
$71$	−8.62973	+	4.98238i	−1.02416	+	0.591300i	−0.108854	+	0.994058i	$0.534718\pi$
$72$		0			0
$73$	−2.49239	+	1.43898i	−0.291712	+	0.168420i	−0.638714	−	0.769444i	$-0.720533\pi$
$73$	−2.49239	+	1.43898i	−0.291712	+	0.168420i	0.347002	+	0.937865i	$0.387200\pi$
$74$	−6.43979	−	17.6932i	−0.748610	−	2.05679i
$75$		0			0
$76$	−3.18511	+	0.561622i	−0.365358	+	0.0644224i
$77$	5.88473	−	2.86281i	0.670627	−	0.326247i
$78$		0			0
$79$	0.843560	+	0.707831i	0.0949080	+	0.0796372i	0.689007	−	0.724755i	$-0.258047\pi$
$79$	0.843560	+	0.707831i	0.0949080	+	0.0796372i	−0.594099	+	0.804392i	$0.702491\pi$
$80$	−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	$-0.517339\pi$
$83$	4.97140	−	1.80944i	0.545682	−	0.198612i	0.600127	+	0.799905i	$0.295117\pi$
$84$		0			0
$85$	−0.239999	+	0.201383i	−0.0260315	+	0.0218431i
$86$	13.3217	+	15.8762i	1.43652	+	1.71197i
$87$		0			0
$88$	14.5249	−	5.28663i	1.54836	−	0.563557i
$89$	−10.2028			−1.08150			−0.540749	−	0.841184i	$-0.681859\pi$
$89$	−10.2028			−1.08150			−0.540749	+	0.841184i	$0.681859\pi$
$90$		0			0
$91$	−11.4753	+	11.8589i	−1.20293	+	1.24315i
$92$	−14.2195	−	2.50728i	−1.48248	−	0.261402i
$93$		0			0
$94$	−14.9109	−	17.7701i	−1.53794	−	1.83284i
$95$	−0.216993	−	0.258602i	−0.0222630	−	0.0265320i
$96$		0			0
$97$	18.3280	+	3.23172i	1.86092	+	0.328131i	0.987349	−	0.158559i	$-0.0506848\pi$
$97$	18.3280	+	3.23172i	1.86092	+	0.328131i	0.873575	+	0.486690i	$0.161796\pi$
$98$	17.7805	−	0.584889i	1.79610	−	0.0590828i
$99$		0			0
$100$	21.3288			2.13288
$101$	1.00210	−	0.364734i	0.0997124	−	0.0362924i	−0.291682	−	0.956515i	$-0.594215\pi$
$101$	1.00210	−	0.364734i	0.0997124	−	0.0362924i	0.391395	+	0.920223i	$0.371993\pi$
$102$		0			0
$103$	3.63501	+	4.33204i	0.358169	+	0.426849i	0.914798	−	0.403912i	$-0.132350\pi$
$103$	3.63501	+	4.33204i	0.358169	+	0.426849i	−0.556629	+	0.830761i	$0.687906\pi$
$104$	−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	−0.384852	−	0.922978i	$-0.625748\pi$
$107$	2.29684	−	1.32608i	0.222044	−	0.128197i	0.606897	+	0.794781i	$0.292414\pi$
$108$		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	$-0.0171597\pi$
$110$	2.24115	+	1.88055i	0.213685	+	0.179303i
$111$		0			0
$112$	18.3791	+	1.30388i	1.73666	+	0.123205i
$113$	6.99660	−	1.23369i	0.658184	−	0.116056i	0.165427	−	0.986222i	$-0.447100\pi$
$113$	6.99660	−	1.23369i	0.658184	−	0.116056i	0.492758	+	0.870166i	$0.335989\pi$
$114$		0			0
$115$	−0.515452	−	1.41619i	−0.0480662	−	0.132061i
$116$	20.8718	−	12.0504i	1.93790	−	1.11885i
$117$		0			0
$118$	−23.9886	+	13.8498i	−2.20833	+	1.27498i
$119$	1.62631	+	0.726054i	0.149084	+	0.0665573i
$120$		0			0
$121$	0.847758	+	4.80788i	0.0770689	+	0.437080i
$122$	1.81854	−	1.52593i	0.164643	−	0.138152i
$123$		0			0
$124$	−10.5620	−	29.0189i	−0.948498	−	2.60598i
$125$	2.27664	+	3.94325i	0.203628	+	0.352695i
$126$		0			0
$127$	−4.69551	+	8.13286i	−0.416659	+	0.721675i	−0.995601	−	0.0936941i	$-0.970132\pi$
$127$	−4.69551	+	8.13286i	−0.416659	+	0.721675i	0.578942	+	0.815369i	$0.303466\pi$
$128$	−12.0237	−	2.12010i	−1.06275	−	0.187392i
$129$		0			0
$130$	−6.93245	−	2.52321i	−0.608016	−	0.221300i
$131$	−7.67063	−	2.79188i	−0.670186	−	0.243928i	−0.0155582	−	0.999879i	$-0.504953\pi$
$131$	−7.67063	−	2.79188i	−0.670186	−	0.243928i	−0.654628	+	0.755951i	$0.727175\pi$
$132$		0			0
$133$	−0.782333	+	1.75238i	−0.0678369	+	0.151950i
$134$			0.0611794i			0.00528510i
$135$		0			0
$136$	3.64314	+	2.10337i	0.312397	+	0.180362i
$137$	−20.1527	−	3.55346i	−1.72176	−	0.303593i	−0.776549	−	0.630056i	$-0.783032\pi$
$137$	−20.1527	−	3.55346i	−1.72176	−	0.303593i	−0.945210	+	0.326464i	$0.894143\pi$
$138$		0			0
$139$	0.533744	+	0.636091i	0.0452715	+	0.0539525i	0.788205	−	0.615413i	$-0.211011\pi$
$139$	0.533744	+	0.636091i	0.0452715	+	0.0539525i	−0.742934	+	0.669365i	$0.766566\pi$
$140$	2.40189	+	4.93727i	0.202996	+	0.417275i
$141$		0			0
$142$	−4.39761	+	24.9401i	−0.369039	+	2.09293i
$143$	7.71366	+	13.3605i	0.645049	+	1.11726i
$144$		0			0
$145$	2.17854	+	1.25778i	0.180918	+	0.104453i
$146$	−1.27009	+	7.20305i	−0.105114	+	0.596129i
$147$		0			0
$148$	−31.0424	−	11.2985i	−2.55167	−	0.928732i
$149$	−2.20568	+	0.388921i	−0.180696	+	0.0318616i	−0.263264	−	0.964724i	$-0.584799\pi$
$149$	−2.20568	+	0.388921i	−0.180696	+	0.0318616i	0.0825677	+	0.996585i	$0.473688\pi$
$150$		0			0
$151$	−2.25469	−	1.89191i	−0.183484	−	0.153961i	0.546419	−	0.837512i	$-0.315991\pi$
$151$	−2.25469	−	1.89191i	−0.183484	−	0.153961i	−0.729903	+	0.683550i	$0.760435\pi$
$152$	−2.26641	+	3.92553i	−0.183830	+	0.318403i
$153$		0			0
$154$	4.03985	−	16.1334i	0.325541	−	1.30007i
$155$	2.07189	−	2.46919i	0.166419	−	0.198330i
$156$		0			0
$157$	3.04333	−	8.36148i	0.242884	−	0.667319i	−0.757019	−	0.653393i	$-0.773345\pi$
$157$	3.04333	−	8.36148i	0.242884	−	0.667319i	0.999903	−	0.0139259i	$-0.00443289\pi$
$158$	2.75609	−	0.485973i	0.219263	−	0.0386620i
$159$		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	$0.811154\pi$
$164$	2.92443	−	16.5853i	0.228359	−	1.29509i
$165$		0			0
$166$	4.59859	−	12.6345i	0.356920	−	0.980629i
$167$	−1.50485	−	8.53440i	−0.116448	−	0.660412i	−0.986023	−	0.166610i	$-0.946718\pi$
$167$	−1.50485	−	8.53440i	−0.116448	−	0.660412i	0.869574	−	0.493802i	$-0.164393\pi$
$168$		0			0
$169$	−19.8423	−	16.6496i	−1.52633	−	1.28074i
$170$			0.796224i			0.0610676i
$171$		0			0
$172$	36.3615			2.77254
$173$	−8.75822	+	3.18773i	−0.665875	+	0.242359i	−0.652771	−	0.757555i	$-0.726394\pi$
$173$	−8.75822	+	3.18773i	−0.665875	+	0.242359i	−0.0131042	+	0.999914i	$0.504171\pi$
$174$		0			0
$175$	7.08757	−	10.4849i	0.535770	−	0.792581i
$176$	5.89143	−	16.1866i	0.444083	−	1.22011i
$177$		0			0
$178$	−16.6674	+	19.8634i	−1.24928	+	1.48883i
$179$			11.4773i			0.857853i	0.903339	+	0.428926i	$0.141108\pi$
$179$			11.4773i			0.857853i	−0.903339	+	0.428926i	$0.858892\pi$
$180$		0			0
$181$	4.44357	+	2.56549i	0.330288	+	0.190692i	0.655969	−	0.754788i	$-0.272260\pi$
$181$	4.44357	+	2.56549i	0.330288	+	0.190692i	−0.325681	+	0.945480i	$0.605594\pi$
$182$	4.34160	+	41.7135i	0.321821	+	3.09201i
$183$		0			0
$184$	−15.5018	+	13.0075i	−1.14280	+	0.958927i
$185$	−0.598748	−	3.39567i	−0.0440208	−	0.249655i
$186$		0			0
$187$	1.07027	−	1.27549i	0.0782656	−	0.0932734i
$188$	−40.6991			−2.96829
$189$		0			0
$190$	−0.857942			−0.0622416
$191$	−11.2629	+	13.4226i	−0.814956	+	0.971227i	−0.999934	−	0.0115156i	$-0.996334\pi$
$191$	−11.2629	+	13.4226i	−0.814956	+	0.971227i	0.184977	+	0.982743i	$0.440779\pi$
$192$		0			0
$193$	−1.28928	−	7.31187i	−0.0928044	−	0.526320i	−0.995398	−	0.0958263i	$-0.969451\pi$
$193$	−1.28928	−	7.31187i	−0.0928044	−	0.526320i	0.902594	−	0.430493i	$-0.141660\pi$
$194$	36.2324	−	30.4026i	2.60133	−	2.18278i
$195$		0			0
$196$	19.2660	−	24.5568i	1.37614	−	1.75406i
$197$	−4.10505	−	2.37005i	−0.292473	−	0.168859i	0.346584	−	0.938019i	$-0.387342\pi$
$197$	−4.10505	−	2.37005i	−0.292473	−	0.168859i	−0.639057	+	0.769160i	$0.720675\pi$
$198$		0			0
$199$			6.70536i			0.475330i	0.971347	+	0.237665i	$0.0763821\pi$
$199$			6.70536i			0.475330i	−0.971347	+	0.237665i	$0.923618\pi$
$200$	19.2144	−	22.8989i	1.35867	−	1.61920i
$201$		0			0
$202$	0.926949	−	2.54677i	0.0652199	−	0.179190i
$203$	1.01198	−	14.2646i	0.0710271	−	1.00118i
$204$		0			0
$205$	1.65181	−	0.601211i	0.115368	−	0.0419904i
$206$	14.3720			1.00135
$207$		0			0
$208$			43.4364i			3.01177i
$209$	1.37436	+	1.15323i	0.0950666	+	0.0797704i
$210$		0			0
$211$	1.74430	+	9.89241i	0.120082	+	0.681021i	0.984108	+	0.177573i	$0.0568245\pi$
$211$	1.74430	+	9.89241i	0.120082	+	0.681021i	−0.864025	+	0.503449i	$0.832064\pi$
$212$	20.3282	−	55.8512i	1.39614	−	3.83587i
$213$		0			0
$214$	1.17045	−	6.63793i	0.0800100	−	0.453759i
$215$	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
$220$	5.05496	−	0.891326i	0.340806	−	0.0600932i
$221$	−1.43602	+	3.94543i	−0.0965971	+	0.265398i
$222$		0			0
$223$	−18.4562	+	21.9953i	−1.23592	+	1.47291i	−0.407114	+	0.913377i	$0.633465\pi$
$223$	−18.4562	+	21.9953i	−1.23592	+	1.47291i	−0.828806	+	0.559536i	$0.810979\pi$
$224$	9.56797	−	9.88788i	0.639287	−	0.660662i
$225$		0			0
$226$	9.02787	−	15.6367i	0.600525	−	1.04014i
$227$	−1.78346	−	1.49650i	−0.118373	−	0.0993265i	0.581680	−	0.813418i	$-0.302396\pi$
$227$	−1.78346	−	1.49650i	−0.118373	−	0.0993265i	−0.700053	+	0.714091i	$0.746840\pi$
$228$		0			0
$229$	11.0964	−	1.95659i	0.733268	−	0.129295i	0.205468	−	0.978664i	$-0.434128\pi$
$229$	11.0964	−	1.95659i	0.733268	−	0.129295i	0.527800	+	0.849369i	$0.323017\pi$
$230$	−3.59917	−	1.30999i	−0.237322	−	0.0863782i
$231$		0			0
$232$	5.86536	−	33.2641i	0.385080	−	2.18390i
$233$	11.5914	+	6.69231i	0.759379	+	0.438428i	0.829073	−	0.559141i	$-0.188869\pi$
$233$	11.5914	+	6.69231i	0.759379	+	0.438428i	−0.0696935	+	0.997568i	$0.522202\pi$
$234$		0			0
$235$	−2.12402	−	3.67892i	−0.138556	−	0.239986i
$236$	−8.43905	+	47.8602i	−0.549335	+	3.11544i
$237$		0			0
$238$	4.07028	−	1.98011i	0.263837	−	0.128352i
$239$	15.7161	+	18.7297i	1.01659	+	1.21152i	0.977205	+	0.212299i	$0.0680950\pi$
$239$	15.7161	+	18.7297i	1.01659	+	1.21152i	0.0393838	+	0.999224i	$0.487461\pi$
$240$		0			0
$241$	12.5428	+	2.21163i	0.807953	+	0.142464i	0.562342	−	0.826905i	$-0.309900\pi$
$241$	12.5428	+	2.21163i	0.807953	+	0.142464i	0.245611	+	0.969369i	$0.421011\pi$
$242$	10.7451	+	6.20371i	0.690724	+	0.398790i
$243$		0			0
$244$		−	4.16503i		−	0.266639i
$245$	3.22523	+	0.459933i	0.206052	+	0.0293840i
$246$		0			0
$247$	−4.25126	−	1.54733i	−0.270501	−	0.0984543i
$248$	−40.6702	−	14.8027i	−2.58256	−	0.939975i
$249$		0			0
$250$	11.3961	+	2.00943i	0.720750	+	0.127088i
$251$	2.40624	−	4.16774i	0.151881	−	0.263065i	−0.780038	−	0.625732i	$-0.784800\pi$
$251$	2.40624	−	4.16774i	0.151881	−	0.263065i	0.931919	+	0.362667i	$0.118134\pi$
$252$		0			0
$253$	4.00475	+	6.93644i	0.251777	+	0.436090i
$254$	8.16290	+	22.4274i	0.512186	+	1.40722i
$255$		0			0
$256$	−22.6795	+	19.0303i	−1.41747	+	1.18940i
$257$	0.124550	+	0.706359i	0.00776923	+	0.0440615i	0.988446	−	0.151574i	$-0.0484342\pi$
$257$	0.124550	+	0.706359i	0.00776923	+	0.0440615i	−0.980677	+	0.195635i	$0.937323\pi$
$258$		0			0
$259$	−15.8696	+	11.5054i	−0.986088	+	0.714912i
$260$	−11.2094	+	6.47174i	−0.695176	+	0.401360i
$261$		0			0
$262$	−17.9662	+	10.3728i	−1.10995	+	0.640833i
$263$	5.52218	+	15.1721i	0.340512	+	0.935550i	0.985246	+	0.171143i	$0.0547459\pi$
$263$	5.52218	+	15.1721i	0.340512	+	0.935550i	−0.644734	+	0.764407i	$0.723032\pi$
$264$		0			0
$265$	6.10945	−	1.07726i	0.375301	−	0.0661756i
$266$	2.13360	+	4.38578i	0.130819	+	0.268910i
$267$		0			0
$268$	0.0822259	+	0.0689958i	0.00502275	+	0.00421459i
$269$	−8.30293	+	14.3811i	−0.506238	+	0.876831i	0.493736	+	0.869612i	$0.335631\pi$
$269$	−8.30293	+	14.3811i	−0.506238	+	0.876831i	−0.999974	+	0.00721846i	$0.997702\pi$
$270$		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
$275$	−7.60513	−	9.06345i	−0.458607	−	0.546546i
$276$		0			0
$277$	−16.7060	+	6.08048i	−1.00377	+	0.365341i	−0.791036	−	0.611770i	$-0.790458\pi$
$277$	−16.7060	+	6.08048i	−1.00377	+	0.365341i	−0.212730	+	0.977111i	$0.568236\pi$
$278$	2.11030			0.126568
$279$		0			0
$280$	7.46451	+	1.86913i	0.446090	+	0.111702i
$281$	25.4750	+	4.49194i	1.51971	+	0.267967i	0.870320	−	0.492486i	$-0.163912\pi$
$281$	25.4750	+	4.49194i	1.51971	+	0.267967i	0.649393	+	0.760453i	$0.275023\pi$
$282$		0			0
$283$	1.54832	+	1.84522i	0.0920382	+	0.109687i	0.810098	−	0.586295i	$-0.199414\pi$
$283$	1.54832	+	1.84522i	0.0920382	+	0.109687i	−0.718060	+	0.695982i	$0.754970\pi$
$284$	28.5604	+	34.0369i	1.69475	+	2.01972i
$285$		0			0
$286$	38.6120	+	6.80833i	2.28317	+	0.402585i
$287$	−7.18124	−	6.94890i	−0.423895	−	0.410181i
$288$		0			0
$289$	−16.5468			−0.973344
$290$	6.00759	−	2.18658i	0.352778	−	0.128401i
$291$		0			0
$292$	8.24864	+	9.83035i	0.482715	+	0.575278i
$293$	−14.1349	+	11.8606i	−0.825772	+	0.692905i	−0.954316	−	0.298799i	$-0.903414\pi$
$293$	−14.1349	+	11.8606i	−0.825772	+	0.692905i	0.128544	+	0.991704i	$0.458970\pi$
$294$		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
$299$	−15.4719	−	12.9825i	−0.894764	−	0.750796i
$300$		0			0
$301$	12.0830	−	17.8747i	0.696451	−	1.03028i
$302$	−7.36655	+	1.29892i	−0.423897	+	0.0747446i
$303$		0			0
$304$	1.72767	+	4.74674i	0.0990889	+	0.272244i
$305$	0.376490	−	0.217366i	0.0215577	−	0.0124464i
$306$		0			0
$307$	−8.85587	+	5.11294i	−0.505431	+	0.291811i	−0.730954	−	0.682427i	$-0.760924\pi$
$307$	−8.85587	+	5.11294i	−0.505431	+	0.291811i	0.225522	+	0.974238i	$0.427591\pi$
$308$	−17.1275	−	23.6243i	−0.975932	−	1.34612i
$309$		0			0
$310$	−1.42249	−	8.06736i	−0.0807922	−	0.458195i
$311$	19.0106	−	15.9518i	1.07799	−	0.904542i	0.0822383	−	0.996613i	$-0.473793\pi$
$311$	19.0106	−	15.9518i	1.07799	−	0.904542i	0.995752	+	0.0920711i	$0.0293487\pi$
$312$		0			0
$313$	5.68370	+	15.6158i	0.321262	+	0.882659i	0.990239	+	0.139377i	$0.0445100\pi$
$313$	5.68370	+	15.6158i	0.321262	+	0.882659i	−0.668978	+	0.743283i	$0.733268\pi$
$314$	−11.3070	−	19.5843i	−0.638091	−	1.10521i
$315$		0			0
$316$	2.45506	−	4.25229i	0.138108	−	0.239210i
$317$	6.28264	+	1.10780i	0.352868	+	0.0622202i	0.347273	−	0.937764i	$-0.387108\pi$
$317$	6.28264	+	1.10780i	0.352868	+	0.0622202i	0.00559547	+	0.999984i	$0.498219\pi$
$318$		0			0
$319$	−12.5629	−	4.57252i	−0.703387	−	0.256012i
$320$	−0.311159	−	0.113253i	−0.0173943	−	0.00633102i
$321$		0			0
$322$	2.25406	+	21.6567i	0.125614	+	1.20688i
$323$			0.488276i			0.0271684i
$324$		0			0
$325$	25.8377	+	14.9174i	1.43322	+	0.827469i
$326$	4.44948	+	0.784563i	0.246434	+	0.0434529i
$327$		0			0
$328$	−15.1716	−	18.0809i	−0.837714	−	0.998349i
$329$	−13.5244	+	20.0070i	−0.745622	+	1.10302i
$330$		0			0
$331$	1.59919	−	9.06946i	0.0878994	−	0.498502i	−0.908794	−	0.417246i	$-0.862995\pi$
$331$	1.59919	−	9.06946i	0.0878994	−	0.498502i	0.996693	−	0.0812569i	$-0.0258934\pi$
$332$	−11.7949	−	20.4293i	−0.647327	−	1.12120i
$333$		0			0
$334$	−19.0736	−	11.0121i	−1.04366	−	0.602557i
$335$	−0.00194549	+	0.0110334i	−0.000106294	+	0.000602821i
$336$		0			0
$337$	−4.60865	−	1.67741i	−0.251049	−	0.0913745i	0.213430	−	0.976958i	$-0.431536\pi$
$337$	−4.60865	−	1.67741i	−0.251049	−	0.0913745i	−0.464480	+	0.885584i	$0.653759\pi$
$338$	−64.8289	+	11.4311i	−3.52623	+	0.621769i
$339$		0			0
$340$	1.07014	+	0.897950i	0.0580362	+	0.0486982i
$341$	−8.56524	+	14.8354i	−0.463834	+	0.803383i
$342$		0			0
$343$	−5.66959	−	17.6311i	−0.306129	−	0.951990i
$344$	32.7570	−	39.0383i	1.76614	−	2.10480i
$345$		0			0
$346$	−8.10143	+	22.2585i	−0.435535	+	1.19662i
$347$	−5.56398	+	0.981080i	−0.298690	+	0.0526671i	−0.320985	−	0.947084i	$-0.604014\pi$
$347$	−5.56398	+	0.981080i	−0.298690	+	0.0526671i	0.0222948	+	0.999751i	$0.492903\pi$
$348$		0			0
$349$	−1.55645	−	4.27631i	−0.0833149	−	0.228906i	0.891039	−	0.453927i	$-0.149977\pi$
$349$	−1.55645	−	4.27631i	−0.0833149	−	0.228906i	−0.974354	+	0.225021i	$0.927755\pi$
$350$	−8.83422	−	30.9266i	−0.472209	−	1.65310i
$351$		0			0
$352$	−6.43158	−	11.1398i	−0.342805	−	0.593755i
$353$	1.73370	−	9.83232i	0.0922758	−	0.523322i	−0.903272	−	0.429068i	$-0.858842\pi$
$353$	1.73370	−	9.83232i	0.0922758	−	0.523322i	0.995548	−	0.0942543i	$-0.0300467\pi$
$354$		0			0
$355$	−1.58618	+	4.35799i	−0.0841857	+	0.231298i
$356$	7.89988	+	44.8024i	0.418693	+	2.37452i
$357$		0			0
$358$	22.3446	+	18.7494i	1.18095	+	0.990935i
$359$		−	14.3758i		−	0.758725i	−0.925248	−	0.379363i	$-0.876143\pi$
$359$		−	14.3758i		−	0.758725i	0.925248	−	0.379363i	$-0.123857\pi$
$360$		0			0
$361$	18.4739			0.972309
$362$	12.2537	−	4.45998i	0.644039	−	0.234411i
$363$		0			0
$364$	60.9598	+	41.2077i	3.19516	+	2.15987i
$365$	−0.458111	+	1.25865i	−0.0239786	+	0.0658808i
$366$		0			0
$367$	22.8297	−	27.2074i	1.19170	−	1.42022i	0.308501	−	0.951224i	$-0.400173\pi$
$367$	22.8297	−	27.2074i	1.19170	−	1.42022i	0.883202	−	0.468992i	$-0.155383\pi$
$368$			22.5512i			1.17556i
$369$		0			0
$370$	−7.58900	−	4.38151i	−0.394533	−	0.227784i
$371$	−20.7004	−	28.5524i	−1.07471	−	1.48237i
$372$		0			0
$373$	−2.61050	+	2.19047i	−0.135167	+	0.113418i	−0.707865	−	0.706348i	$-0.750341\pi$
$373$	−2.61050	+	2.19047i	−0.135167	+	0.113418i	0.572698	+	0.819767i	$0.305897\pi$
$374$	−0.734809	−	4.16731i	−0.0379961	−	0.215486i
$375$		0			0
$376$	−36.6646	+	43.6952i	−1.89083	+	2.25341i
$377$	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	$0.491564\pi$
$380$	−0.967553	+	1.15309i	−0.0496344	+	0.0591520i
$381$		0			0
$382$	7.73274	+	43.8546i	0.395642	+	2.24380i
$383$	2.52649	−	2.11998i	0.129098	−	0.108326i	−0.575953	−	0.817483i	$-0.695369\pi$
$383$	2.52649	−	2.11998i	0.129098	−	0.108326i	0.705050	+	0.709157i	$0.250924\pi$
$384$		0			0
$385$	1.24161	−	2.78112i	0.0632783	−	0.141739i
$386$	−16.3413	−	9.43467i	−0.831752	−	0.480212i
$387$		0			0
$388$		−	82.9837i		−	4.21286i
$389$	12.3070	−	14.6669i	0.623989	−	0.743641i	−0.357762	−	0.933813i	$-0.616460\pi$
$389$	12.3070	−	14.6669i	0.623989	−	0.743641i	0.981751	+	0.190172i	$0.0609045\pi$
$390$		0			0
$391$	−0.745548	+	2.04838i	−0.0377040	+	0.103591i
$392$	−9.00837	−	42.8068i	−0.454991	−	2.16207i
$393$		0			0
$394$	−11.3202	+	4.12021i	−0.570303	+	0.207573i
$395$	0.512503			0.0257868
$396$		0			0
$397$		−	15.7797i		−	0.791958i	−0.918260	−	0.395979i	$-0.870405\pi$
$397$		−	15.7797i		−	0.791958i	0.918260	−	0.395979i	$-0.129595\pi$
$398$	13.0544	+	10.9539i	0.654357	+	0.549070i
$399$		0			0
$400$	−5.78459	−	32.8060i	−0.289229	−	1.64030i
$401$	9.81387	−	26.9634i	0.490081	−	1.34649i	−0.410525	−	0.911850i	$-0.634654\pi$
$401$	9.81387	−	26.9634i	0.490081	−	1.34649i	0.900606	−	0.434637i	$-0.143123\pi$
$402$		0			0
$403$	7.50108	−	42.5407i	0.373655	−	2.11911i
$404$	−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
$409$	−0.828634	+	0.146111i	−0.0409733	+	0.00722470i	−0.194097	−	0.980982i	$-0.562178\pi$
$409$	−0.828634	+	0.146111i	−0.0409733	+	0.00722470i	0.153124	+	0.988207i	$0.451067\pi$
$410$	1.52794	−	4.19798i	0.0754596	−	0.207324i
$411$		0			0
$412$	16.2082	−	19.3162i	0.798522	−	0.951642i
$413$	20.7230	+	20.0525i	1.01971	+	0.986719i
$414$		0			0
$415$	1.23111	−	2.13235i	0.0604328	−	0.104673i
$416$	24.8477	+	20.8497i	1.21826	+	1.02224i
$417$		0			0
$418$	4.49033	−	0.791767i	0.219629	−	0.0387266i
$419$	14.6826	+	5.34404i	0.717294	+	0.261073i	0.674776	−	0.738022i	$-0.264240\pi$
$419$	14.6826	+	5.34404i	0.717294	+	0.261073i	0.0425171	+	0.999096i	$0.486462\pi$
$420$		0			0
$421$	−5.15879	+	29.2570i	−0.251424	+	1.42590i	0.553663	+	0.832740i	$0.313229\pi$
$421$	−5.15879	+	29.2570i	−0.251424	+	1.42590i	−0.805088	+	0.593156i	$0.797882\pi$
$422$	22.1086	+	12.7644i	1.07623	+	0.621361i
$423$		0			0
$424$	−41.6496	−	72.1392i	−2.02268	−	3.50339i
$425$	0.559149	−	3.17109i	0.0271227	−	0.153821i
$426$		0			0
$427$	−2.04746	−	1.38404i	−0.0990834	−	0.0669786i
$428$	−7.60148	−	9.05909i	−0.367431	−	0.437888i
$429$		0			0
$430$	9.49900	+	1.67493i	0.458082	+	0.0807723i
$431$	−31.9989	−	18.4746i	−1.54133	−	0.889889i	−0.998755	−	0.0498828i	$-0.984115\pi$
$431$	−31.9989	−	18.4746i	−1.54133	−	0.889889i	−0.542577	−	0.840006i	$-0.682551\pi$
$432$		0			0
$433$		−	9.86033i		−	0.473857i	−0.971527	−	0.236929i	$-0.923859\pi$
$433$		−	9.86033i		−	0.473857i	0.971527	−	0.236929i	$-0.0761407\pi$
$434$	−37.7026	+	27.3343i	−1.80978	+	1.31209i
$435$		0			0
$436$	−47.7641	−	17.3847i	−2.28748	−	0.832576i
$437$	−2.20715	−	0.803338i	−0.105582	−	0.0384289i
$438$		0			0
$439$	−35.0476	−	6.17984i	−1.67273	−	0.294948i	−0.744686	−	0.667415i	$-0.767401\pi$
$439$	−35.0476	−	6.17984i	−1.67273	−	0.294948i	−0.928045	+	0.372467i	$0.878512\pi$
$440$	3.59692	−	6.23005i	0.171477	−	0.297006i
$441$		0			0
$442$	5.33530	+	9.24101i	0.253774	+	0.439550i
$443$	4.55230	+	12.5073i	0.216286	+	0.594241i	0.999626	−	0.0273526i	$-0.00870769\pi$
$443$	4.55230	+	12.5073i	0.216286	+	0.594241i	−0.783340	+	0.621594i	$0.786485\pi$
$444$		0			0
$445$	−3.63755	+	3.05226i	−0.172436	+	0.144691i
$446$	12.6714	+	71.8633i	0.600010	+	3.40282i
$447$		0			0
$448$	0.194870	+	1.87229i	0.00920676	+	0.0884572i
$449$	6.46903	−	3.73490i	0.305293	−	0.176261i	−0.339525	−	0.940597i	$-0.610266\pi$
$449$	6.46903	−	3.73490i	0.305293	−	0.176261i	0.644818	+	0.764336i	$0.276933\pi$
$450$		0			0
$451$	−8.09049	+	4.67105i	−0.380966	+	0.219951i
$452$	−10.8347	−	29.7681i	−0.509621	−	1.40017i
$453$		0			0
$454$	−5.82696	+	1.02745i	−0.273473	+	0.0482206i
$455$	−0.543492	+	7.66091i	−0.0254793	+	0.359149i
$456$		0			0
$457$	−19.8548	−	16.6602i	−0.928770	−	0.779331i	0.0468260	−	0.998903i	$-0.485089\pi$
$457$	−19.8548	−	16.6602i	−0.928770	−	0.779331i	−0.975596	+	0.219572i	$0.929534\pi$
$458$	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	$-0.411011\pi$
$461$	23.7286	−	8.63651i	1.10515	−	0.402242i	0.829213	+	0.558933i	$0.188789\pi$
$462$		0			0
$463$	15.4294	−	12.9468i	0.717064	−	0.601688i	−0.209508	−	0.977807i	$-0.567186\pi$
$463$	15.4294	−	12.9468i	0.717064	−	0.601688i	0.926571	+	0.376119i	$0.122742\pi$
$464$	−24.1955	−	28.8350i	−1.12325	−	1.33863i
$465$		0			0
$466$	31.9648	−	11.6342i	1.48074	−	0.538945i
$467$	−4.31501			−0.199675			−0.0998373	−	0.995004i	$-0.531832\pi$
$467$	−4.31501			−0.199675			−0.0998373	+	0.995004i	$0.531832\pi$
$468$		0			0
$469$	0.0612409	−	0.0174935i	0.00282784	−	0.000807776i
$470$	−10.6321	−	1.87473i	−0.490424	−	0.0864750i
$471$		0			0
$472$	43.7810	+	52.1761i	2.01518	+	2.40160i
$473$	−12.9653	−	15.4515i	−0.596146	−	0.710459i
$474$		0			0
$475$	3.41690	+	0.602491i	0.156778	+	0.0276442i
$476$	1.92901	−	7.70361i	0.0884158	−	0.353094i
$477$		0			0
$478$	62.1379			2.84212
$479$	−1.80247	+	0.656045i	−0.0823569	+	0.0299755i	−0.382870	−	0.923802i	$-0.625064\pi$
$479$	−1.80247	+	0.656045i	−0.0823569	+	0.0299755i	0.300513	+	0.953778i	$0.402842\pi$
$480$		0			0
$481$	−29.7026	−	35.3982i	−1.35432	−	1.61402i
$482$	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	$0.320059\pi$
$488$	−4.47163	−	3.75215i	−0.202421	−	0.169852i
$489$		0			0
$490$	6.16417	−	5.52770i	0.278469	−	0.249716i
$491$	−27.9607	+	4.93023i	−1.26185	+	0.222498i	−0.764256	−	0.644912i	$-0.776894\pi$
$491$	−27.9607	+	4.93023i	−1.26185	+	0.222498i	−0.497593	+	0.867411i	$0.665783\pi$
$492$		0			0
$493$	−1.24444	−	3.41907i	−0.0560467	−	0.153987i
$494$	−9.95731	+	5.74885i	−0.448000	+	0.258653i
$495$		0			0
$496$	−41.7698	+	24.1158i	−1.87552	+	1.08283i
$497$	26.2226	−	2.72929i	1.17625	−	0.122425i
$498$		0			0
$499$	4.06570	+	23.0577i	0.182006	+	1.03220i	0.929743	+	0.368210i	$0.120029\pi$
$499$	4.06570	+	23.0577i	0.182006	+	1.03220i	−0.747737	+	0.663995i	$0.768860\pi$
$500$	15.5527	−	13.0503i	0.695540	−	0.583627i
$501$		0			0
$502$	−4.18313	−	11.4930i	−0.186702	−	0.512960i
$503$	−5.80401	−	10.0528i	−0.258788	−	0.448234i	0.707129	−	0.707084i	$-0.249990\pi$
$503$	−5.80401	−	10.0528i	−0.258788	−	0.448234i	−0.965918	+	0.258850i	$0.916656\pi$
$504$		0			0
$505$	0.248158	−	0.429822i	0.0110429	−	0.0191268i
$506$	20.0464	+	3.53473i	0.891173	+	0.157138i
$507$		0			0
$508$	39.3485	+	14.3217i	1.74581	+	0.635422i
$509$	−16.5581	−	6.02667i	−0.733926	−	0.267127i	−0.0521003	−	0.998642i	$-0.516592\pi$
$509$	−16.5581	−	6.02667i	−0.733926	−	0.267127i	−0.681826	+	0.731515i	$0.738814\pi$
$510$		0			0
$511$	7.57347	−	0.788257i	0.335030	−	0.0348705i
$512$			50.8234i			2.24610i
$513$		0			0
$514$	1.57865	+	0.911432i	0.0696311	+	0.0402015i
$515$	2.59193	+	0.457028i	0.114214	+	0.0201391i
$516$		0			0
$517$	14.5120	+	17.2947i	0.638235	+	0.760619i
$518$	−3.52526	+	49.6911i	−0.154891	+	2.18330i
$519$		0			0
$520$	−3.15004	+	17.8647i	−0.138138	+	0.783421i
$521$	−12.9686	−	22.4622i	−0.568164	−	0.984088i	−0.996748	−	0.0805864i	$-0.974321\pi$
$521$	−12.9686	−	22.4622i	−0.568164	−	0.984088i	0.428584	−	0.903502i	$-0.359013\pi$
$522$		0			0
$523$	3.19247	+	1.84317i	0.139597	+	0.0805962i	0.568172	−	0.822910i	$-0.307651\pi$
$523$	3.19247	+	1.84317i	0.139597	+	0.0805962i	−0.428575	+	0.903506i	$0.640984\pi$
$524$	−6.32041	+	35.8448i	−0.276108	+	1.56589i
$525$		0			0
$526$	38.5589	+	14.0343i	1.68125	+	0.611924i
$527$	−4.59134	+	0.809576i	−0.200002	+	0.0352657i
$528$		0			0
$529$	9.58636	+	8.04391i	0.416798	+	0.349735i
$530$	7.88317	−	13.6540i	0.342423	−	0.593094i
$531$		0			0
$532$	8.30074	+	2.07853i	0.359883	+	0.0901157i
$533$	15.1424	−	18.0461i	0.655892	−	0.781662i
$534$		0			0
$535$	0.422169	−	1.15990i	0.0182520	−	0.0501469i
$536$	0.148150	−	0.0261228i	0.00639909	−	0.00112833i
$537$		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	$-0.351530\pi$
$542$	−6.43295	+	36.4831i	−0.276319	+	1.56708i
$543$		0			0
$544$	1.19734	−	3.28967i	0.0513356	−	0.141043i
$545$	−0.921277	−	5.22482i	−0.0394632	−	0.223807i
$546$		0			0
$547$	−5.90120	−	4.95170i	−0.252317	−	0.211719i	0.507852	−	0.861444i	$-0.330440\pi$
$547$	−5.90120	−	4.95170i	−0.252317	−	0.211719i	−0.760169	+	0.649725i	$0.774884\pi$
$548$			91.2454i			3.89781i
$549$		0			0
$550$	−30.0690			−1.28215
$551$	3.68409	−	1.34090i	0.156948	−	0.0571242i
$552$		0			0
$553$	−1.27453	−	2.61990i	−0.0541987	−	0.111410i
$554$	−15.4532	+	42.4573i	−0.656543	+	1.80384i
$555$		0			0
$556$	2.37992	−	2.83628i	0.100931	−	0.120285i
$557$		−	1.54966i		−	0.0656610i	−0.999461	−	0.0328305i	$-0.989548\pi$
$557$		−	1.54966i		−	0.0656610i	0.999461	−	0.0328305i	$-0.0104522\pi$
$558$		0			0
$559$	44.0484	+	25.4314i	1.86305	+	1.07563i
$560$	6.94265	−	5.03341i	0.293381	−	0.212700i
$561$		0			0
$562$	50.3613	−	42.2582i	2.12437	−	1.78255i
$563$	4.28366	+	24.2938i	0.180535	+	1.02386i	0.931559	+	0.363589i	$0.118449\pi$
$563$	4.28366	+	24.2938i	0.180535	+	1.02386i	−0.751025	+	0.660274i	$0.770440\pi$
$564$		0			0
$565$	2.12538	−	2.53293i	0.0894154	−	0.106561i
$566$	6.12172			0.257315
$567$		0			0
$568$	62.2717			2.61286
$569$	17.4658	−	20.8149i	0.732204	−	0.872606i	−0.263552	−	0.964645i	$-0.584894\pi$
$569$	17.4658	−	20.8149i	0.732204	−	0.872606i	0.995755	+	0.0920390i	$0.0293384\pi$
$570$		0			0
$571$	2.74433	+	15.5639i	0.114847	+	0.651329i	0.986826	+	0.161786i	$0.0517253\pi$
$571$	2.74433	+	15.5639i	0.114847	+	0.651329i	−0.871979	+	0.489543i	$0.837164\pi$
$572$	52.6956	−	44.2168i	2.20331	−	1.84880i
$573$		0			0
$574$	−25.2598	+	2.62908i	−1.05432	+	0.109736i
$575$	13.4144	+	7.74478i	0.559417	+	0.322980i
$576$		0			0
$577$		−	16.3564i		−	0.680925i	−0.940258	−	0.340463i	$-0.889416\pi$
$577$		−	16.3564i		−	0.680925i	0.940258	−	0.340463i	$-0.110584\pi$
$578$	−27.0310	+	32.2143i	−1.12434	+	1.33994i
$579$		0			0
$580$	3.83633	−	10.5402i	0.159295	−	0.437659i
$581$	−13.9621	−	0.990523i	−0.579247	−	0.0410938i
$582$		0			0
$583$	−30.9817	+	11.2764i	−1.28313	+	0.467022i
$584$	17.9850			0.744223
$585$		0			0
$586$			46.8943i			1.93719i
$587$	2.06287	+	1.73095i	0.0851436	+	0.0714439i	0.684366	−	0.729139i	$-0.260079\pi$
$587$	2.06287	+	1.73095i	0.0851436	+	0.0714439i	−0.599222	+	0.800583i	$0.704524\pi$
$588$		0			0
$589$	−0.872329	−	4.94723i	−0.0359437	−	0.203847i
$590$	−4.40920	+	12.1142i	−0.181524	+	0.498732i
$591$		0			0
$592$	−8.95934	+	50.8110i	−0.368227	+	2.08832i
$593$	−3.92320	−	6.79519i	−0.161107	−	0.279045i	0.774159	−	0.632991i	$-0.218173\pi$
$593$	−3.92320	−	6.79519i	−0.161107	−	0.279045i	−0.935266	+	0.353946i	$0.884840\pi$
$594$		0			0
$595$	0.797025	−	0.227671i	0.0326748	−	0.00933359i
$596$	3.41564	+	9.38439i	0.139910	+	0.384400i
$597$		0			0
$598$	−50.5500	+	8.91334i	−2.06714	+	0.364493i
$599$	11.3767	−	31.2573i	0.464840	−	1.27714i	−0.456965	−	0.889485i	$-0.651064\pi$
$599$	11.3767	−	31.2573i	0.464840	−	1.27714i	0.921805	−	0.387653i	$-0.126714\pi$
$600$		0			0
$601$	21.4176	−	25.5245i	0.873642	−	1.04117i	−0.125155	−	0.992137i	$-0.539943\pi$
$601$	21.4176	−	25.5245i	0.873642	−	1.04117i	0.998797	−	0.0490291i	$-0.0156127\pi$
$602$	−15.0607	−	52.7241i	−0.613827	−	2.14887i
$603$		0			0
$604$	−6.56194	+	11.3656i	−0.267002	+	0.462460i
$605$	1.74056	+	1.46051i	0.0707639	+	0.0593780i
$606$		0			0
$607$	12.7757	−	2.25270i	0.518549	−	0.0914341i	0.0917522	−	0.995782i	$-0.470753\pi$
$607$	12.7757	−	2.25270i	0.518549	−	0.0914341i	0.426796	+	0.904348i	$0.359642\pi$
$608$	3.54466	+	1.29015i	0.143755	+	0.0523225i
$609$		0			0
$610$	0.191855	−	1.08806i	0.00776797	−	0.0440543i
$611$	−49.3030	−	28.4651i	−1.99459	−	1.15157i
$612$		0			0
$613$	20.5385	+	35.5738i	0.829543	+	1.43681i	0.898397	+	0.439184i	$0.144732\pi$
$613$	20.5385	+	35.5738i	0.829543	+	1.43681i	−0.0688544	+	0.997627i	$0.521934\pi$
$614$	−4.51285	+	25.5936i	−0.182124	+	1.03287i
$615$		0			0
$616$	−40.7930	−	2.89400i	−1.64360	−	0.116603i
$617$	14.4145	+	17.1786i	0.580307	+	0.691583i	0.973712	−	0.227782i	$-0.0731473\pi$
$617$	14.4145	+	17.1786i	0.580307	+	0.691583i	−0.393405	+	0.919365i	$0.628703\pi$
$618$		0			0
$619$	30.2635	+	5.33627i	1.21639	+	0.214483i	0.744772	−	0.667318i	$-0.232558\pi$
$619$	30.2635	+	5.33627i	1.21639	+	0.214483i	0.471621	+	0.881801i	$0.343669\pi$
$620$	−12.4469	−	7.18621i	−0.499879	−	0.288605i
$621$		0			0
$622$		−	63.0698i		−	2.52887i
$623$	24.6493	+	11.0045i	0.987552	+	0.440884i
$624$		0			0
$625$	−20.4833	−	7.45530i	−0.819331	−	0.298212i
$626$	39.6867	+	14.4448i	1.58620	+	0.577330i
$627$		0			0
$628$	−39.0732	−	6.88965i	−1.55919	−	0.274927i
$629$	−2.49363	+	4.31909i	−0.0994274	+	0.172213i
$630$		0			0
$631$	−1.19417	−	2.06836i	−0.0475391	−	0.0823402i	0.841277	−	0.540605i	$-0.181805\pi$
$631$	−1.19417	−	2.06836i	−0.0475391	−	0.0823402i	−0.888816	+	0.458265i	$0.848471\pi$
$632$	−2.35363	−	6.46654i	−0.0936223	−	0.257225i
$633$		0			0
$634$	12.4201	−	10.4217i	0.493265	−	0.413898i
$635$	0.758956	+	4.30426i	0.0301183	+	0.170809i
$636$		0			0
$637$	40.5140	−	16.2734i	1.60522	−	0.644777i
$638$	−29.4248	+	16.9884i	−1.16494	+	0.672579i
$639$		0			0
$640$	−4.92097	+	2.84113i	−0.194519	+	0.112305i
$641$	8.06378	+	22.1550i	0.318500	+	0.875072i	0.990866	+	0.134852i	$0.0430560\pi$
$641$	8.06378	+	22.1550i	0.318500	+	0.875072i	−0.672366	+	0.740219i	$0.734722\pi$
$642$		0			0
$643$	35.0530	−	6.18079i	1.38236	−	0.243746i	0.567482	−	0.823386i	$-0.307918\pi$
$643$	35.0530	−	6.18079i	1.38236	−	0.243746i	0.814873	+	0.579639i	$0.196807\pi$
$644$	31.6489	+	21.3941i	1.24714	+	0.843045i
$645$		0			0
$646$	0.950603	+	0.797651i	0.0374010	+	0.0313832i
$647$	−8.19674	+	14.1972i	−0.322247	+	0.558148i	−0.980951	−	0.194254i	$-0.937772\pi$
$647$	−8.19674	+	14.1972i	−0.322247	+	0.558148i	0.658704	+	0.752402i	$0.271105\pi$
$648$		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
$653$	−2.22308	−	2.64937i	−0.0869960	−	0.103678i	0.720790	−	0.693153i	$-0.243779\pi$
$653$	−2.22308	−	2.64937i	−0.0869960	−	0.103678i	−0.807786	+	0.589475i	$0.799335\pi$
$654$		0			0
$655$	−3.56997	+	1.29936i	−0.139490	+	0.0507704i
$656$	−26.3031			−1.02696
$657$		0			0
$658$	16.8573	+	59.0135i	0.657165	+	2.30059i
$659$	−22.4506	−	3.95865i	−0.874551	−	0.154207i	−0.281684	−	0.959507i	$-0.590893\pi$
$659$	−22.4506	−	3.95865i	−0.874551	−	0.154207i	−0.592867	+	0.805300i	$0.702004\pi$
$660$		0			0
$661$	−8.28313	−	9.87145i	−0.322176	−	0.383955i	0.580511	−	0.814253i	$-0.302853\pi$
$661$	−8.28313	−	9.87145i	−0.322176	−	0.383955i	−0.902687	+	0.430298i	$0.858409\pi$
$662$	−15.0445	−	17.9293i	−0.584720	−	0.696843i
$663$		0			0
$664$	−32.5588	−	5.74100i	−1.26353	−	0.222794i
$665$	0.245318	+	0.858805i	0.00951303	+	0.0333030i
$666$		0			0
$667$	17.5026			0.677704
$668$	−36.3109	+	13.2161i	−1.40491	+	0.511346i
$669$		0			0
$670$	0.0183023	+	0.0218119i	0.000707081	+	0.000842667i
$671$	−1.76989	+	1.48511i	−0.0683257	+	0.0573321i
$672$		0			0
$673$	−7.15895	+	2.60564i	−0.275957	+	0.100440i	−0.476292	−	0.879287i	$-0.658019\pi$
$673$	−7.15895	+	2.60564i	−0.275957	+	0.100440i	0.200334	+	0.979728i	$0.435797\pi$
$674$	−10.7944	+	6.23215i	−0.415785	+	0.240054i
$675$		0			0
$676$	−57.7480	+	100.022i	−2.22108	+	3.84702i
$677$	31.8604	+	26.7340i	1.22449	+	1.02747i	0.998577	+	0.0533258i	$0.0169822\pi$
$677$	31.8604	+	26.7340i	1.22449	+	1.02747i	0.225917	+	0.974147i	$0.427462\pi$
$678$		0			0
$679$	−40.7934	−	27.5756i	−1.56551	−	1.05825i
$680$	1.92811	−	0.339977i	0.0739395	−	0.0130375i
$681$		0			0
$682$	14.8902	+	40.9105i	0.570176	+	1.56655i
$683$	29.6444	−	17.1152i	1.13431	−	0.654896i	0.189297	−	0.981920i	$-0.439379\pi$
$683$	29.6444	−	17.1152i	1.13431	−	0.654896i	0.945016	+	0.327024i	$0.106046\pi$
$684$		0			0
$685$	−8.24795	+	4.76195i	−0.315138	+	0.181945i
$686$	−43.5871	−	17.7644i	−1.66416	−	0.678248i
$687$		0			0
$688$	−9.86163	−	55.9281i	−0.375971	−	2.13224i
$689$	63.6881	−	53.4406i	2.42632	−	2.03593i
$690$		0			0
$691$	−1.43134	−	3.93259i	−0.0544509	−	0.149603i	0.909485	−	0.415736i	$-0.136476\pi$
$691$	−1.43134	−	3.93259i	−0.0544509	−	0.149603i	−0.963936	+	0.266134i	$0.914254\pi$
$692$	20.7792	+	35.9907i	0.789908	+	1.36816i
$693$		0			0
$694$	−7.17933	+	12.4350i	−0.272524	+	0.472025i
$695$	0.380584	+	0.0671072i	0.0144364	+	0.00254552i
$696$		0			0
$697$	−2.38918	−	0.869589i	−0.0904965	−	0.0329380i
$698$	−10.8680	−	3.95563i	−0.411360	−	0.149723i
$699$		0			0
$700$	−51.5287	−	23.0045i	−1.94760	−	0.869490i
$701$		−	12.5933i		−	0.475643i	−0.971309	−	0.237821i	$-0.923567\pi$
$701$		−	12.5933i		−	0.475643i	0.971309	−	0.237821i	$-0.0764333\pi$
$702$		0			0
$703$	−4.65387	−	2.68692i	−0.175524	−	0.101339i
$704$	1.73308	+	0.305588i	0.0653178	+	0.0115173i
$705$		0			0
$706$	−16.3099	−	19.4374i	−0.613832	−	0.731537i
$707$	−2.81438	−	0.199662i	−0.105846	−	0.00750907i
$708$		0			0
$709$	−1.30698	+	7.41224i	−0.0490846	+	0.278373i	−0.999465	−	0.0327188i	$-0.989583\pi$
$709$	−1.30698	+	7.41224i	−0.0490846	+	0.278373i	0.950380	+	0.311091i	$0.100695\pi$
$710$	5.89319	+	10.2073i	0.221168	+	0.383073i
$711$		0			0
$712$	55.2173	+	31.8797i	2.06936	+	1.19474i
$713$	3.89439	−	22.0862i	0.145846	−	0.827134i
$714$		0			0
$715$	6.74699	+	2.45570i	0.252323	+	0.0918381i
$716$	50.3988	−	8.88667i	1.88349	−	0.332110i
$717$		0			0
$718$	−27.9876	−	23.4844i	−1.04449	−	0.876430i
$719$	18.9465	−	32.8163i	0.706585	−	1.22384i	−0.259532	−	0.965735i	$-0.583568\pi$
$719$	18.9465	−	32.8163i	0.706585	−	1.22384i	0.966117	−	0.258106i	$-0.0830985\pi$
$720$		0			0
$721$	−4.10951	−	14.3865i	−0.153046	−	0.535781i
$722$	30.1790	−	35.9660i	1.12315	−	1.33852i
$723$		0			0
$724$	7.82496	−	21.4989i	0.290812	−	0.799001i
$725$	−25.4617	+	4.48959i	−0.945626	+	0.166739i
$726$		0			0
$727$	−6.98614	−	19.1943i	−0.259102	−	0.711876i	−0.999223	−	0.0394032i	$-0.987454\pi$
$727$	−6.98614	−	19.1943i	−0.259102	−	0.711876i	0.740122	−	0.672473i	$-0.234768\pi$
$728$	99.1580	−	28.3246i	3.67504	−	1.04978i
$729$		0			0
$730$	1.70204	+	2.94802i	0.0629952	+	0.109111i
$731$	0.953244	−	5.40612i	0.0352570	−	0.199952i
$732$		0			0
$733$	−9.86692	+	27.1092i	−0.364443	+	1.00130i	0.612997	+	0.790085i	$0.289964\pi$
$733$	−9.86692	+	27.1092i	−0.364443	+	1.00130i	−0.977440	+	0.211214i	$0.932258\pi$
$734$	−15.6741	−	88.8925i	−0.578543	−	3.28108i
$735$		0			0
$736$	12.9004	+	10.8247i	0.475513	+	0.399003i
$737$		−	0.0595427i		−	0.00219328i
$738$		0			0
$739$	26.5104			0.975200			0.487600	−	0.873067i	$-0.337872\pi$
$739$	26.5104			0.975200			0.487600	+	0.873067i	$0.337872\pi$
$740$	−14.4474	+	5.25842i	−0.531096	+	0.193303i
$741$		0			0
$742$	−89.4037	−	6.34261i	−3.28211	−	0.232845i
$743$	−2.96176	+	8.13736i	−0.108656	+	0.298531i	−0.982090	−	0.188412i	$-0.939666\pi$
$743$	−2.96176	+	8.13736i	−0.108656	+	0.298531i	0.873434	+	0.486943i	$0.161888\pi$
$744$		0			0
$745$	−0.670027	+	0.798507i	−0.0245479	+	0.0292550i
$746$			8.66064i			0.317089i
$747$		0			0
$748$	−6.42961	−	3.71214i	−0.235090	−	0.135729i
$749$	−6.97928	+	0.726413i	−0.255017	+	0.0265426i
$750$		0			0
$751$	4.87548	−	4.09101i	0.177909	−	0.149283i	−0.549485	−	0.835504i	$-0.685176\pi$
$751$	4.87548	−	4.09101i	0.177909	−	0.149283i	0.727394	+	0.686221i	$0.240732\pi$
$752$	11.0380	+	62.5998i	0.402515	+	2.28278i
$753$		0			0
$754$	55.0726	−	65.6329i	2.00562	−	2.39021i
$755$	−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	$0.382609\pi$
$758$	1.68543	−	2.00861i	0.0612174	−	0.0729561i
$759$		0			0
$760$	0.366330	+	2.07756i	0.0132882	+	0.0753610i
$761$	−38.5154	+	32.3183i	−1.39618	+	1.17154i	−0.433419	+	0.901192i	$0.642693\pi$
$761$	−38.5154	+	32.3183i	−1.39618	+	1.17154i	−0.962764	+	0.270344i	$0.912863\pi$
$762$		0			0
$763$	−24.4181	+	17.7031i	−0.883994	+	0.640894i
$764$	67.6618	+	39.0646i	2.44792	+	1.41331i
$765$		0			0
$766$		−	8.38193i		−	0.302851i
$767$	−43.6967	+	52.0757i	−1.57780	+	1.88034i
$768$		0			0
$769$	−10.8973	+	29.9402i	−0.392968	+	1.07967i	0.572672	+	0.819785i	$0.305907\pi$
$769$	−10.8973	+	29.9402i	−0.392968	+	1.07967i	−0.965640	+	0.259885i	$0.916315\pi$
$770$	−3.38615	−	6.96050i	−0.122028	−	0.250839i
$771$		0			0
$772$	−31.1094	+	11.3229i	−1.11965	+	0.407520i
$773$	24.1518			0.868679			0.434339	−	0.900749i	$-0.356982\pi$
$773$	24.1518			0.868679			0.434339	+	0.900749i	$0.356982\pi$
$774$		0			0
$775$			33.1286i			1.19001i
$776$	−89.0925	−	74.7575i	−3.19823	−	2.68364i
$777$		0			0
$778$	−8.44957	−	47.9199i	−0.302932	−	1.71801i
$779$	0.936994	−	2.57437i	0.0335713	−	0.0922364i
$780$		0			0
$781$	4.27996	−	24.2729i	0.153149	−	0.868552i
$782$	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
$787$	9.90805	−	1.74706i	0.353184	−	0.0622758i	0.00575824	−	0.999983i	$-0.498167\pi$
$787$	9.90805	−	1.74706i	0.353184	−	0.0622758i	0.347425	+	0.937708i	$0.387056\pi$
$788$	−7.22885	+	19.8611i	−0.257517	+	0.707523i
$789$		0			0
$790$	0.837228	−	0.997769i	0.0297872	−	0.0354990i
$791$	−18.2339	−	4.56581i	−0.648322	−	0.162342i
$792$		0			0
$793$	2.91304	−	5.04552i	0.103445	−	0.179172i
$794$	−30.7207	−	25.7777i	−1.09024	−	0.914818i
$795$		0			0
$796$	29.4444	−	5.19185i	1.04363	−	0.184020i
$797$	−21.8937	−	7.96866i	−0.775515	−	0.282264i	−0.0762137	−	0.997092i	$-0.524283\pi$
$797$	−21.8937	−	7.96866i	−0.775515	−	0.282264i	−0.699301	+	0.714827i	$0.746505\pi$
$798$		0			0
$799$	−1.06696	+	6.05101i	−0.0377462	+	0.214069i
$800$	−21.5433	−	12.4380i	−0.761670	−	0.439750i
$801$		0			0
$802$	−36.4618	−	63.1537i	−1.28751	−	2.23004i
$803$	1.23611	−	7.01035i	0.0436215	−	0.247390i
$804$		0			0
$805$	−0.282168	+	3.97737i	−0.00994513	+	0.140184i
$806$	−70.5669	−	84.0983i	−2.48561	−	2.96224i
$807$		0			0
$808$	−6.56296	−	1.15723i	−0.230884	−	0.0407111i
$809$	36.9148	+	21.3128i	1.29786	+	0.749317i	0.980033	−	0.198833i	$-0.0637153\pi$
$809$	36.9148	+	21.3128i	1.29786	+	0.749317i	0.317822	+	0.948150i	$0.397049\pi$
$810$		0			0
$811$			33.7669i			1.18572i	0.805307	+	0.592859i	$0.202001\pi$
$811$			33.7669i			1.18572i	−0.805307	+	0.592859i	$0.797999\pi$
$812$	−63.4219	+	6.60105i	−2.22567	+	0.231651i
$813$		0			0
$814$	43.7632	+	15.9285i	1.53390	+	0.558293i
$815$	0.777495	+	0.282985i	0.0272344	+	0.00991253i
$816$		0			0
$817$	5.82516	+	1.02713i	0.203797	+	0.0359348i
$818$	−1.06921	+	1.85192i	−0.0373839	+	0.0647508i
$819$		0			0
$820$	−3.91899	−	6.78790i	−0.136857	−	0.237044i
$821$	−8.06058	−	22.1463i	−0.281316	−	0.772910i	−0.997206	−	0.0746970i	$-0.976201\pi$
$821$	−8.06058	−	22.1463i	−0.281316	−	0.772910i	0.715890	−	0.698213i	$-0.246021\pi$
$822$		0			0
$823$	−22.2555	+	18.6746i	−0.775777	+	0.650954i	−0.942181	−	0.335103i	$-0.891229\pi$
$823$	−22.2555	+	18.6746i	−0.775777	+	0.650954i	0.166404	+	0.986058i	$0.446784\pi$
$824$	−6.13667	−	34.8028i	−0.213781	−	1.21241i
$825$		0			0
$826$	72.8925	−	7.58676i	2.53626	−	0.263977i
$827$	28.8450	−	16.6537i	1.00304	−	0.579105i	0.0938928	−	0.995582i	$-0.470069\pi$
$827$	28.8450	−	16.6537i	1.00304	−	0.579105i	0.909146	+	0.416478i	$0.136736\pi$
$828$		0			0
$829$	−34.3451	+	19.8291i	−1.19285	+	0.688694i	−0.958953	−	0.283566i	$-0.908482\pi$
$829$	−34.3451	+	19.8291i	−1.19285	+	0.688694i	−0.233901	+	0.972261i	$0.575149\pi$
$830$	−2.14022	−	5.88021i	−0.0742881	−	0.204105i
$831$		0			0
$832$	−4.37020	+	0.770585i	−0.151510	+	0.0267152i
$833$	−3.14595	−	3.50818i	−0.109001	−	0.121551i
$834$		0			0
$835$	−3.08965	−	2.59253i	−0.106922	−	0.0897180i
$836$	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	$-0.959784\pi$
$839$	−48.4005	+	17.6163i	−1.67097	+	0.608184i	−0.678942	+	0.734192i	$0.737561\pi$
$840$		0			0
$841$	−0.164445	+	0.137985i	−0.00567050	+	0.00475812i
$842$	48.5316	+	57.8378i	1.67251	+	1.99322i
$843$		0			0
$844$	42.0887	−	15.3190i	1.44875	−	0.527303i
$845$	−12.0551			−0.414709
$846$		0			0
$847$	3.13751	−	12.5298i	0.107806	−	0.430530i
$848$	−91.4185	−	16.1196i	−3.13933	−	0.553548i
$849$		0			0
$850$	−5.26023	−	6.26890i	−0.180425	−	0.215022i
$851$	−15.4209	−	18.3779i	−0.528622	−	0.629987i
$852$		0			0
$853$	−37.1908	−	6.55774i	−1.27339	−	0.224533i	−0.504218	−	0.863576i	$-0.668219\pi$
$853$	−37.1908	−	6.55774i	−1.27339	−	0.224533i	−0.769171	+	0.639044i	$0.779330\pi$
$854$	−6.03927	+	1.72512i	−0.206660	+	0.0590325i
$855$		0			0
$856$	−16.5739			−0.566485
$857$	−41.7013	+	15.1780i	−1.42449	+	0.518472i	−0.935347	−	0.353732i	$-0.884912\pi$
$857$	−41.7013	+	15.1780i	−1.42449	+	0.518472i	−0.489143	+	0.872204i	$0.662690\pi$
$858$		0			0
$859$	−6.73029	−	8.02085i	−0.229635	−	0.273668i	0.638907	−	0.769284i	$-0.279387\pi$
$859$	−6.73029	−	8.02085i	−0.229635	−	0.273668i	−0.868542	+	0.495616i	$0.834942\pi$
$860$	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	−0.754023	−	0.656848i	$-0.771889\pi$
$863$	−16.5153	+	9.53510i	−0.562187	+	0.324579i	0.191836	+	0.981427i	$0.438556\pi$
$864$		0			0
$865$	−2.16887	+	3.75660i	−0.0737439	+	0.127728i
$866$	−19.1966	−	16.1079i	−0.652328	−	0.547368i
$867$		0			0
$868$	−5.78186	+	81.4994i	−0.196249	+	2.76627i
$869$	−2.68236	+	0.472972i	−0.0909928	+	0.0160445i
$870$		0			0
$871$	0.0513528	+	0.141091i	0.00174002	+	0.00478068i
$872$	−61.6937	+	35.6189i	−2.08921	+	1.20621i
$873$		0			0
$874$	−5.16960	+	2.98467i	−0.174864	+	0.100958i
$875$	−1.24711	−	11.9821i	−0.0421602	−	0.405069i
$876$		0			0
$877$	6.40894	+	36.3469i	0.216414	+	1.22735i	0.878435	+	0.477862i	$0.158588\pi$
$877$	6.40894	+	36.3469i	0.216414	+	1.22735i	−0.662021	+	0.749485i	$0.730301\pi$
$878$	−69.2853	+	58.1372i	−2.33826	+	1.96204i
$879$		0			0
$880$	−2.74192	−	7.53336i	−0.0924301	−	0.253950i
$881$	−14.1834	−	24.5664i	−0.477851	−	0.827662i	0.521827	−	0.853052i	$-0.325251\pi$
$881$	−14.1834	−	24.5664i	−0.477851	−	0.827662i	−0.999678	+	0.0253894i	$0.991917\pi$
$882$		0			0
$883$	−1.51080	+	2.61677i	−0.0508423	+	0.0880615i	−0.890327	−	0.455323i	$-0.849524\pi$
$883$	−1.51080	+	2.61677i	−0.0508423	+	0.0880615i	0.839484	+	0.543384i	$0.182857\pi$
$884$	18.4370	+	3.25094i	0.620103	+	0.109341i
$885$		0			0
$886$	31.7866	+	11.5694i	1.06789	+	0.388681i
$887$	−0.118237	−	0.0430349i	−0.00397003	−	0.00144497i	0.340034	−	0.940413i	$-0.389561\pi$
$887$	−0.118237	−	0.0430349i	−0.00397003	−	0.00144497i	−0.344004	+	0.938968i	$0.611784\pi$
$888$		0			0
$889$	20.1158	−	14.5839i	0.674664	−	0.489130i
$890$			12.0680i			0.404520i
$891$		0			0
$892$	110.876	+	64.0140i	3.71239	+	2.14335i
$893$	−6.52005	−	1.14966i	−0.218185	−	0.0384719i
$894$		0			0
$895$	3.43353	+	4.09192i	0.114770	+	0.136778i
$896$	26.7617	+	18.0904i	0.894044	+	0.604357i
$897$		0			0
$898$	3.29654	−	18.6956i	0.110007	−	0.623881i
$899$	18.7170	+	32.4188i	0.624248	+	1.08123i
$900$		0			0
$901$	−7.77086	−	4.48651i	−0.258885	−	0.149467i
$902$	−4.12282	+	23.3817i	−0.137275	+	0.778525i
$903$		0			0
$904$	−41.7201	−	15.1849i	−1.38759	−	0.505041i
$905$	2.35172	−	0.414672i	0.0781740	−	0.0137842i
$906$		0			0
$907$	−5.90765	−	4.95711i	−0.196160	−	0.164598i	0.539417	−	0.842039i	$-0.318645\pi$
$907$	−5.90765	−	4.95711i	−0.196160	−	0.164598i	−0.735577	+	0.677441i	$0.763089\pi$
$908$	−5.19051	+	8.99023i	−0.172253	+	0.298351i
$909$		0			0
$910$	14.0268	+	13.5730i	0.464985	+	0.449941i
$911$	−3.55791	+	4.24015i	−0.117879	+	0.140482i	−0.821757	−	0.569838i	$-0.807006\pi$
$911$	−3.55791	+	4.24015i	−0.117879	+	0.140482i	0.703878	+	0.710321i	$0.251450\pi$
$912$		0			0
$913$	−4.47556	+	12.2965i	−0.148120	+	0.406955i
$914$	−64.8700	+	11.4383i	−2.14571	+	0.378346i
$915$		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	$0.827958\pi$
$920$	−1.63543	+	9.27496i	−0.0539184	+	0.305786i
$921$		0			0
$922$	21.9492	−	60.3048i	0.722857	−	1.98603i
$923$	10.7926	+	61.2076i	0.355241	+	2.01467i
$924$		0			0
$925$	27.1475	+	22.7795i	0.892605	+	0.748984i
$926$		−	51.1887i		−	1.68216i
$927$		0			0
$928$	−28.1090			−0.922723
$929$	21.0190	−	7.65030i	0.689612	−	0.250998i	0.0266431	−	0.999645i	$-0.491518\pi$
$929$	21.0190	−	7.65030i	0.689612	−	0.250998i	0.662969	+	0.748647i	$0.269296\pi$
$930$		0			0
$931$	3.78012	−	3.38981i	0.123888	−	0.111096i
$932$	20.4121	−	56.0817i	0.668620	−	1.83702i
$933$		0			0
$934$	−7.04902	+	8.40070i	−0.230651	+	0.274879i
$935$		−	0.774923i		−	0.0253427i
$936$		0			0
$937$	−12.3038	−	7.10360i	−0.401947	−	0.232064i	0.285377	−	0.958415i	$-0.407881\pi$
$937$	−12.3038	−	7.10360i	−0.401947	−	0.232064i	−0.687324	+	0.726351i	$0.741215\pi$
$938$	0.0659862	−	0.147805i	0.00215453	−	0.00482600i
$939$		0			0
$940$	−14.5102	+	12.1755i	−0.473270	+	0.397120i
$941$	5.57685	+	31.6279i	0.181800	+	1.03104i	0.929998	+	0.367564i	$0.119808\pi$
$941$	5.57685	+	31.6279i	0.181800	+	1.03104i	−0.748198	+	0.663475i	$0.769081\pi$
$942$		0			0
$943$	7.86161	−	9.36910i	0.256009	−	0.305100i
$944$	75.9032			2.47044
$945$		0			0
$946$	−51.2620			−1.66667
$947$	26.6191	−	31.7234i	0.865004	−	1.03087i	−0.134198	−	0.990954i	$-0.542846\pi$
$947$	26.6191	−	31.7234i	0.865004	−	1.03087i	0.999203	−	0.0399177i	$-0.0127096\pi$
$948$		0			0
$949$	3.11704	+	17.6776i	0.101184	+	0.573840i
$950$	6.75483	−	5.66797i	0.219155	−	0.183893i
$951$		0			0
$952$	−6.53293	−	9.01096i	−0.211733	−	0.292047i
$953$	−29.7841	−	17.1959i	−0.964803	−	0.557029i	−0.0671552	−	0.997743i	$-0.521392\pi$
$953$	−29.7841	−	17.1959i	−0.964803	−	0.557029i	−0.897648	+	0.440713i	$0.854726\pi$
$954$		0			0
$955$			8.15488i			0.263886i
$956$	70.0767	−	83.5142i	2.26644	−	2.70104i
$957$		0			0
$958$	−1.66730	+	4.58087i	−0.0538680	+	0.148001i
$959$	44.8547	+	30.3209i	1.44843	+	0.979114i
$960$		0			0
$961$	15.9427	−	5.80268i	0.514281	−	0.187183i
$962$	−117.438			−3.78634
$963$		0			0
$964$		−	56.7901i		−	1.82909i
$965$	−2.64707	−	2.22115i	−0.0852121	−	0.0715014i
$966$		0			0
$967$	0.771534	+	4.37559i	0.0248109	+	0.140709i	0.994697	−	0.102850i	$-0.0327961\pi$
$967$	0.771534	+	4.37559i	0.0248109	+	0.140709i	−0.969886	+	0.243559i	$0.921685\pi$
$968$	10.4346	−	28.6689i	0.335382	−	0.921455i
$969$		0			0
$970$	3.82250	−	21.6785i	0.122733	−	0.696053i
$971$	−19.3649	−	33.5409i	−0.621448	−	1.07638i	−0.989216	−	0.146462i	$-0.953211\pi$
$971$	−19.3649	−	33.5409i	−0.621448	−	1.07638i	0.367768	−	0.929918i	$-0.380122\pi$
$972$		0			0
$973$	−0.603416	−	2.11243i	−0.0193446	−	0.0677213i
$974$	17.7803	+	48.8510i	0.569718	+	1.56529i
$975$		0			0
$976$	−6.40628	+	1.12960i	−0.205060	+	0.0361576i
$977$	6.19981	−	17.0338i	0.198349	−	0.544961i	−0.800145	−	0.599806i	$-0.795244\pi$
$977$	6.19981	−	17.0338i	0.198349	−	0.544961i	0.998495	+	0.0548455i	$0.0174666\pi$
$978$		0			0
$979$	16.2215	−	19.3320i	0.518442	−	0.617855i
$980$	−0.477592	−	14.5187i	−0.0152561	−	0.463782i
$981$		0			0
$982$	−36.0784	+	62.4895i	−1.15131	+	1.99412i
$983$	4.94956	+	4.15317i	0.157866	+	0.132466i	0.718299	−	0.695734i	$-0.244921\pi$
$983$	4.94956	+	4.15317i	0.157866	+	0.132466i	−0.560433	+	0.828200i	$0.689365\pi$
$984$		0			0
$985$	−2.17257	+	0.383082i	−0.0692238	+	0.0122060i
$986$	−8.68936	−	3.16267i	−0.276725	−	0.100720i
$987$		0			0
$988$	−3.50293	+	19.8661i	−0.111443	+	0.632024i
$989$	22.8689	+	13.2034i	0.727190	+	0.419843i
$990$		0			0
$991$	−18.8875	−	32.7141i	−0.599981	−	1.03920i	−0.992823	−	0.119591i	$-0.961842\pi$
$991$	−18.8875	−	32.7141i	−0.599981	−	1.03920i	0.392842	−	0.919606i	$-0.371492\pi$
$992$	−6.25434	+	35.4701i	−0.198575	+	1.12618i
$993$		0			0
$994$	37.5239	−	55.5102i	1.19019	−	1.76068i
$995$	2.00597	+	2.39062i	0.0635934	+	0.0757877i
$996$		0			0
$997$	42.1085	+	7.42486i	1.33359	+	0.235148i	0.794584	−	0.607155i	$-0.207689\pi$
$997$	42.1085	+	7.42486i	1.33359	+	0.235148i	0.539005	+	0.842302i	$0.318800\pi$
$998$	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.ba.a.143.22		132
3.2	odd	2		189.2.ba.a.101.1	✓	132
7.5	odd	6		567.2.bd.a.467.1		132
21.5	even	6		189.2.bd.a.47.22	yes	132
27.4	even	9		189.2.bd.a.185.22	yes	132
27.23	odd	18		567.2.bd.a.17.1		132
189.131	even	18	inner	567.2.ba.a.341.22		132
189.166	odd	18		189.2.ba.a.131.1	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.1	✓	132	3.2	odd	2
189.2.ba.a.131.1	yes	132	189.166	odd	18
189.2.bd.a.47.22	yes	132	21.5	even	6
189.2.bd.a.185.22	yes	132	27.4	even	9
567.2.ba.a.143.22		132	1.1	even	1	trivial
567.2.ba.a.341.22		132	189.131	even	18	inner
567.2.bd.a.17.1		132	27.23	odd	18
567.2.bd.a.467.1		132	7.5	odd	6

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.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.63361 - 1.94686i) q^{2} +(-0.774283 - 4.39118i) q^{4} +(0.356523 - 0.299159i) q^{5} +(-2.41592 - 1.07857i) q^{7} +(-5.41196 - 3.12460i) q^{8} +O(q^{10})\)	\(q+(1.63361 - 1.94686i) q^{2} +(-0.774283 - 4.39118i) q^{4} +(0.356523 - 0.299159i) q^{5} +(-2.41592 - 1.07857i) q^{7} +(-5.41196 - 3.12460i) q^{8} -1.18281i q^{10} +(-1.58990 + 1.89477i) q^{11} +(2.13324 - 5.86102i) q^{13} +(-6.04649 + 2.94150i) q^{14} +(-6.54413 + 2.38187i) q^{16} -0.673165 q^{17} -0.725344i q^{19} +(-1.58971 - 1.33392i) q^{20} +(1.09157 + 6.19062i) q^{22} +(1.10753 - 3.04291i) q^{23} +(-0.830628 + 4.71072i) q^{25} +(-7.92569 - 13.7277i) q^{26} +(-2.86558 + 11.4439i) q^{28} +(1.84864 + 5.07909i) q^{29} +(6.82052 - 1.20264i) q^{31} +(-1.77867 + 4.88687i) q^{32} +(-1.09969 + 1.31055i) q^{34} +(-1.18400 + 0.338210i) q^{35} +(3.70433 - 6.41609i) q^{37} +(-1.41214 - 1.18493i) q^{38} +(-2.86424 + 0.505043i) q^{40} +(3.54917 + 1.29179i) q^{41} +(-1.41606 + 8.03089i) q^{43} +(9.55132 + 5.51446i) q^{44} +(-4.11484 - 7.12711i) q^{46} +(1.58499 - 8.98890i) q^{47} +(4.67338 + 5.21148i) q^{49} +(7.81418 + 9.31258i) q^{50} +(-27.3885 - 4.82933i) q^{52} +(11.5438 + 6.66480i) q^{53} +1.15116i q^{55} +(9.70479 + 13.3860i) q^{56} +(12.9082 + 4.69821i) q^{58} +(-10.2419 - 3.72774i) q^{59} +(0.919898 + 0.162203i) q^{61} +(8.80068 - 15.2432i) q^{62} +(-0.355740 - 0.616160i) q^{64} +(-0.992826 - 2.72777i) q^{65} +(-0.0184408 + 0.0154737i) q^{67} +(0.521220 + 2.95599i) q^{68} +(-1.27574 + 2.85757i) q^{70} +(-8.62973 + 4.98238i) q^{71} +(-2.49239 + 1.43898i) q^{73} +(-6.43979 - 17.6932i) q^{74} +(-3.18511 + 0.561622i) q^{76} +(5.88473 - 2.86281i) q^{77} +(0.843560 + 0.707831i) q^{79} +(-1.62058 + 2.80692i) q^{80} +(8.31288 - 4.79945i) q^{82} +(4.97140 - 1.80944i) q^{83} +(-0.239999 + 0.201383i) q^{85} +(13.3217 + 15.8762i) q^{86} +(14.5249 - 5.28663i) q^{88} -10.2028 q^{89} +(-11.4753 + 11.8589i) q^{91} +(-14.2195 - 2.50728i) q^{92} +(-14.9109 - 17.7701i) q^{94} +(-0.216993 - 0.258602i) q^{95} +(18.3280 + 3.23172i) q^{97} +(17.7805 - 0.584889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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