LMFDB - Embedded newform 324.3.j.a.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.3
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93271 - 0.514419i) q^{2} +(3.47075 + 1.98845i) q^{4} +(3.81867 - 1.38988i) q^{5} +(-5.53905 + 0.976684i) q^{7} +(-5.68506 - 5.62851i) q^{8} +O(q^{10})$	\(q+(-1.93271 - 0.514419i) q^{2} +(3.47075 + 1.98845i) q^{4} +(3.81867 - 1.38988i) q^{5} +(-5.53905 + 0.976684i) q^{7} +(-5.68506 - 5.62851i) q^{8} +(-8.09537 + 0.721846i) q^{10} +(-7.44387 + 20.4519i) q^{11} +(-15.1056 - 12.6751i) q^{13} +(11.2078 + 0.961743i) q^{14} +(8.09216 + 13.8028i) q^{16} +(3.04352 - 5.27153i) q^{17} +(8.89586 - 5.13603i) q^{19} +(16.0173 + 2.76929i) q^{20} +(24.9077 - 35.6983i) q^{22} +(-25.6005 - 4.51407i) q^{23} +(-6.50063 + 5.45468i) q^{25} +(22.6745 + 32.2680i) q^{26} +(-21.1667 - 7.62428i) q^{28} +(10.0865 - 8.46358i) q^{29} +(-37.2448 - 6.56727i) q^{31} +(-8.53940 - 30.8396i) q^{32} +(-8.59401 + 8.62270i) q^{34} +(-19.7943 + 11.4283i) q^{35} +(-13.6566 + 23.6539i) q^{37} +(-19.8352 + 5.35026i) q^{38} +(-29.5323 - 13.5919i) q^{40} +(32.5982 + 27.3531i) q^{41} +(-13.6950 + 37.6266i) q^{43} +(-66.5032 + 56.1815i) q^{44} +(47.1563 + 21.8938i) q^{46} +(-18.8590 + 3.32535i) q^{47} +(-16.3178 + 5.93919i) q^{49} +(15.3698 - 7.19827i) q^{50} +(-27.2240 - 74.0290i) q^{52} -84.3059 q^{53} +88.4451i q^{55} +(36.9871 + 25.6241i) q^{56} +(-23.8481 + 11.1690i) q^{58} +(5.90492 + 16.2236i) q^{59} +(3.64271 + 20.6588i) q^{61} +(68.6051 + 31.8521i) q^{62} +(0.639751 + 63.9968i) q^{64} +(-75.3005 - 27.4071i) q^{65} +(17.2385 - 20.5441i) q^{67} +(21.0454 - 12.2443i) q^{68} +(44.1357 - 11.9050i) q^{70} +(-15.0660 - 8.69838i) q^{71} +(-20.6995 - 35.8526i) q^{73} +(38.5622 - 38.6909i) q^{74} +(41.0880 - 0.136909i) q^{76} +(21.2570 - 120.554i) q^{77} +(-3.44549 - 4.10617i) q^{79} +(50.0856 + 41.4611i) q^{80} +(-48.9319 - 69.6348i) q^{82} +(-36.9625 - 44.0502i) q^{83} +(4.29539 - 24.3604i) q^{85} +(45.8242 - 65.6764i) q^{86} +(157.432 - 74.3721i) q^{88} +(-17.1351 - 29.6789i) q^{89} +(96.0505 + 55.4548i) q^{91} +(-79.8770 - 66.5725i) q^{92} +(38.1597 + 3.27449i) q^{94} +(26.8319 - 31.9770i) q^{95} +(146.828 + 53.4411i) q^{97} +(34.5928 - 3.08456i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.93271	−	0.514419i	−0.966356	−	0.257209i
$2$	−1.93271	−	0.514419i	−0.966356	−	0.257209i
$3$		0			0
$3$		0			0
$4$	3.47075	+	1.98845i	0.867687	+	0.497112i
$5$	3.81867	−	1.38988i	0.763734	−	0.277977i	0.0693611	−	0.997592i	$-0.477904\pi$
$5$	3.81867	−	1.38988i	0.763734	−	0.277977i	0.694373	+	0.719615i	$0.255682\pi$
$6$		0			0
$7$	−5.53905	+	0.976684i	−0.791293	+	0.139526i	−0.554665	−	0.832074i	$-0.687153\pi$
$7$	−5.53905	+	0.976684i	−0.791293	+	0.139526i	−0.236628	+	0.971600i	$0.576042\pi$
$8$	−5.68506	−	5.62851i	−0.710632	−	0.703564i
$9$		0			0
$10$	−8.09537	+	0.721846i	−0.809537	+	0.0721846i
$11$	−7.44387	+	20.4519i	−0.676715	+	1.85926i	−0.201208	+	0.979549i	$0.564487\pi$
$11$	−7.44387	+	20.4519i	−0.676715	+	1.85926i	−0.475507	+	0.879712i	$0.657735\pi$
$12$		0			0
$13$	−15.1056	−	12.6751i	−1.16197	−	0.975011i	−0.162042	−	0.986784i	$-0.551808\pi$
$13$	−15.1056	−	12.6751i	−1.16197	−	0.975011i	−0.999931	+	0.0117728i	$0.996253\pi$
$14$	11.2078	+	0.961743i	0.800558	+	0.0686959i
$15$		0			0
$16$	8.09216	+	13.8028i	0.505760	+	0.862674i
$17$	3.04352	−	5.27153i	0.179030	−	0.310090i	−0.762518	−	0.646967i	$-0.776037\pi$
$17$	3.04352	−	5.27153i	0.179030	−	0.310090i	0.941549	+	0.336877i	$0.109371\pi$
$18$		0			0
$19$	8.89586	−	5.13603i	0.468203	−	0.270317i	−0.247284	−	0.968943i	$-0.579538\pi$
$19$	8.89586	−	5.13603i	0.468203	−	0.270317i	0.715487	+	0.698626i	$0.246205\pi$
$20$	16.0173	+	2.76929i	0.800867	+	0.138465i
$21$		0			0
$22$	24.9077	−	35.6983i	1.13217	−	1.62265i
$23$	−25.6005	−	4.51407i	−1.11307	−	0.196264i	−0.413272	−	0.910608i	$-0.635614\pi$
$23$	−25.6005	−	4.51407i	−1.11307	−	0.196264i	−0.699795	+	0.714344i	$0.746725\pi$
$24$		0			0
$25$	−6.50063	+	5.45468i	−0.260025	+	0.218187i
$26$	22.6745	+	32.2680i	0.872097	+	1.24108i
$27$		0			0
$28$	−21.1667	−	7.62428i	−0.755954	−	0.272296i
$29$	10.0865	−	8.46358i	0.347810	−	0.291848i	−0.452100	−	0.891967i	$-0.649325\pi$
$29$	10.0865	−	8.46358i	0.347810	−	0.291848i	0.799910	+	0.600120i	$0.204880\pi$
$30$		0			0
$31$	−37.2448	−	6.56727i	−1.20145	−	0.211847i	−0.463122	−	0.886294i	$-0.653271\pi$
$31$	−37.2448	−	6.56727i	−1.20145	−	0.211847i	−0.738323	+	0.674447i	$0.764382\pi$
$32$	−8.53940	−	30.8396i	−0.266856	−	0.963736i
$33$		0			0
$34$	−8.59401	+	8.62270i	−0.252765	+	0.253609i
$35$	−19.7943	+	11.4283i	−0.565552	+	0.326522i
$36$		0			0
$37$	−13.6566	+	23.6539i	−0.369096	+	0.639294i	−0.989424	−	0.145049i	$-0.953666\pi$
$37$	−13.6566	+	23.6539i	−0.369096	+	0.639294i	0.620328	+	0.784342i	$0.286999\pi$
$38$	−19.8352	+	5.35026i	−0.521979	+	0.140796i
$39$		0			0
$40$	−29.5323	−	13.5919i	−0.738308	−	0.339797i
$41$	32.5982	+	27.3531i	0.795078	+	0.667150i	0.946997	−	0.321243i	$-0.104101\pi$
$41$	32.5982	+	27.3531i	0.795078	+	0.667150i	−0.151919	+	0.988393i	$0.548545\pi$
$42$		0			0
$43$	−13.6950	+	37.6266i	−0.318487	+	0.875037i	0.672381	+	0.740205i	$0.265272\pi$
$43$	−13.6950	+	37.6266i	−0.318487	+	0.875037i	−0.990869	+	0.134832i	$0.956951\pi$
$44$	−66.5032	+	56.1815i	−1.51144	+	1.27685i
$45$		0			0
$46$	47.1563	+	21.8938i	1.02514	+	0.475952i
$47$	−18.8590	+	3.32535i	−0.401256	+	0.0707522i	−0.370634	−	0.928779i	$-0.620860\pi$
$47$	−18.8590	+	3.32535i	−0.401256	+	0.0707522i	−0.0306214	+	0.999531i	$0.509749\pi$
$48$		0			0
$49$	−16.3178	+	5.93919i	−0.333016	+	0.121208i
$50$	15.3698	−	7.19827i	0.307397	−	0.143965i
$51$		0			0
$52$	−27.2240	−	74.0290i	−0.523539	−	1.42363i
$53$	−84.3059			−1.59068			−0.795339	−	0.606165i	$-0.792707\pi$
$53$	−84.3059			−1.59068			−0.795339	+	0.606165i	$0.792707\pi$
$54$		0			0
$55$			88.4451i			1.60809i
$56$	36.9871	+	25.6241i	0.660484	+	0.457573i
$57$		0			0
$58$	−23.8481	+	11.1690i	−0.411174	+	0.192568i
$59$	5.90492	+	16.2236i	0.100083	+	0.274977i	0.979622	−	0.200851i	$-0.0643707\pi$
$59$	5.90492	+	16.2236i	0.100083	+	0.274977i	−0.879538	+	0.475828i	$0.842148\pi$
$60$		0			0
$61$	3.64271	+	20.6588i	0.0597166	+	0.338670i	0.999999	−	0.00172713i	$-0.000549762\pi$
$61$	3.64271	+	20.6588i	0.0597166	+	0.338670i	−0.940282	+	0.340397i	$0.889439\pi$
$62$	68.6051	+	31.8521i	1.10653	+	0.513743i
$63$		0			0
$64$	0.639751	+	63.9968i	0.00999611	+	0.999950i
$65$	−75.3005	−	27.4071i	−1.15847	−	0.421648i
$66$		0			0
$67$	17.2385	−	20.5441i	0.257292	−	0.306628i	−0.621900	−	0.783097i	$-0.713639\pi$
$67$	17.2385	−	20.5441i	0.257292	−	0.306628i	0.879192	+	0.476469i	$0.158083\pi$
$68$	21.0454	−	12.2443i	0.309492	−	0.180063i
$69$		0			0
$70$	44.1357	−	11.9050i	0.630509	−	0.170071i
$71$	−15.0660	−	8.69838i	−0.212198	−	0.122512i	0.390135	−	0.920758i	$-0.372428\pi$
$71$	−15.0660	−	8.69838i	−0.212198	−	0.122512i	−0.602332	+	0.798245i	$0.705762\pi$
$72$		0			0
$73$	−20.6995	−	35.8526i	−0.283555	−	0.491131i	0.688703	−	0.725043i	$-0.258180\pi$
$73$	−20.6995	−	35.8526i	−0.283555	−	0.491131i	−0.972258	+	0.233913i	$0.924847\pi$
$74$	38.5622	−	38.6909i	0.521111	−	0.522850i
$75$		0			0
$76$	41.0880	−	0.136909i	0.540632	−	0.00180144i
$77$	21.2570	−	120.554i	0.276064	−	1.56564i
$78$		0			0
$79$	−3.44549	−	4.10617i	−0.0436138	−	0.0519769i	0.743797	−	0.668406i	$-0.233023\pi$
$79$	−3.44549	−	4.10617i	−0.0436138	−	0.0519769i	−0.787410	+	0.616429i	$0.788579\pi$
$80$	50.0856	+	41.4611i	0.626070	+	0.518264i
$81$		0			0
$82$	−48.9319	−	69.6348i	−0.596731	−	0.849205i
$83$	−36.9625	−	44.0502i	−0.445332	−	0.530726i	0.495949	−	0.868352i	$-0.334820\pi$
$83$	−36.9625	−	44.0502i	−0.445332	−	0.530726i	−0.941280	+	0.337626i	$0.890376\pi$
$84$		0			0
$85$	4.29539	−	24.3604i	0.0505340	−	0.286593i
$86$	45.8242	−	65.6764i	0.532840	−	0.763679i
$87$		0			0
$88$	157.432	−	74.3721i	1.78900	−	0.845138i
$89$	−17.1351	−	29.6789i	−0.192529	−	0.333471i	0.753558	−	0.657381i	$-0.228336\pi$
$89$	−17.1351	−	29.6789i	−0.192529	−	0.333471i	−0.946088	+	0.323910i	$0.895002\pi$
$90$		0			0
$91$	96.0505	+	55.4548i	1.05550	+	0.609393i
$92$	−79.8770	−	66.5725i	−0.868229	−	0.723614i
$93$		0			0
$94$	38.1597	+	3.27449i	0.405954	+	0.0348350i
$95$	26.8319	−	31.9770i	0.282441	−	0.336600i
$96$		0			0
$97$	146.828	+	53.4411i	1.51369	+	0.550939i	0.959564	−	0.281491i	$-0.0908291\pi$
$97$	146.828	+	53.4411i	1.51369	+	0.550939i	0.554129	+	0.832431i	$0.313051\pi$
$98$	34.5928	−	3.08456i	0.352988	−	0.0314751i
$99$		0			0
$100$	−33.4084	+	6.00565i	−0.334084	+	0.0600565i
$101$	3.69583	+	20.9601i	0.0365924	+	0.207526i	0.997622	−	0.0689187i	$-0.0219549\pi$
$101$	3.69583	+	20.9601i	0.0365924	+	0.207526i	−0.961030	+	0.276445i	$0.910844\pi$
$102$		0			0
$103$	6.44120	+	17.6971i	0.0625360	+	0.171816i	0.967025	−	0.254680i	$-0.0819701\pi$
$103$	6.44120	+	17.6971i	0.0625360	+	0.171816i	−0.904489	+	0.426496i	$0.859748\pi$
$104$	14.5343	+	157.081i	0.139753	+	1.51040i
$105$		0			0
$106$	162.939	+	43.3686i	1.53716	+	0.409137i
$107$			45.7984i			0.428023i	0.976831	+	0.214011i	$0.0686530\pi$
$107$			45.7984i			0.428023i	−0.976831	+	0.214011i	$0.931347\pi$
$108$		0			0
$109$	15.3619			0.140935			0.0704677	−	0.997514i	$-0.477551\pi$
$109$	15.3619			0.140935			0.0704677	+	0.997514i	$0.477551\pi$
$110$	45.4978	−	170.939i	0.413616	−	1.55399i
$111$		0			0
$112$	−58.3038	−	68.5508i	−0.520570	−	0.612061i
$113$	178.553	−	64.9880i	1.58012	−	0.575115i	0.604886	−	0.796312i	$-0.293219\pi$
$113$	178.553	−	64.9880i	1.58012	−	0.575115i	0.975229	+	0.221197i	$0.0709964\pi$
$114$		0			0
$115$	−104.034	+	18.3440i	−0.904644	+	0.159513i
$116$	51.8371	−	9.31847i	0.446871	−	0.0803317i
$117$		0			0
$118$	−3.06677	−	34.3932i	−0.0259895	−	0.291468i
$119$	−11.7096	+	32.1718i	−0.0983998	+	0.270351i
$120$		0			0
$121$	−270.176	−	226.705i	−2.23286	−	1.87359i
$122$	3.58699	−	41.8015i	0.0294015	−	0.342635i
$123$		0			0
$124$	−116.209	−	96.8526i	−0.937167	−	0.781069i
$125$	−68.0392	+	117.847i	−0.544314	+	0.942779i
$126$		0			0
$127$	20.3113	−	11.7267i	0.159931	−	0.0923364i	−0.417898	−	0.908494i	$-0.637233\pi$
$127$	20.3113	−	11.7267i	0.159931	−	0.0923364i	0.577830	+	0.816157i	$0.303900\pi$
$128$	31.6847	−	124.016i	0.247537	−	0.968879i
$129$		0			0
$130$	131.435	+	91.7061i	1.01104	+	0.705431i
$131$	22.5210	+	3.97106i	0.171916	+	0.0303134i	0.258943	−	0.965892i	$-0.416626\pi$
$131$	22.5210	+	3.97106i	0.171916	+	0.0303134i	−0.0870275	+	0.996206i	$0.527737\pi$
$132$		0			0
$133$	−44.2584	+	37.1372i	−0.332770	+	0.279227i
$134$	−43.8854	+	30.8380i	−0.327503	+	0.230134i
$135$		0			0
$136$	−46.9734	+	12.8385i	−0.345393	+	0.0944005i
$137$	−103.052	+	86.4710i	−0.752205	+	0.631175i	−0.936085	−	0.351774i	$-0.885579\pi$
$137$	−103.052	+	86.4710i	−0.752205	+	0.631175i	0.183880	+	0.982949i	$0.441134\pi$
$138$		0			0
$139$	115.591	+	20.3818i	0.831588	+	0.146631i	0.573206	−	0.819412i	$-0.305700\pi$
$139$	115.591	+	20.3818i	0.831588	+	0.146631i	0.258382	+	0.966043i	$0.416811\pi$
$140$	−91.4256	+	0.304640i	−0.653040	+	0.00217600i
$141$		0			0
$142$	24.6437	+	24.5617i	0.173547	+	0.172970i
$143$	371.675	−	214.587i	2.59912	−	1.50061i
$144$		0			0
$145$	26.7536	−	46.3387i	0.184508	−	0.319577i
$146$	21.5629	+	79.9408i	0.147691	+	0.547540i
$147$		0			0
$148$	−94.4329	+	54.9412i	−0.638060	+	0.371224i
$149$	72.4842	+	60.8215i	0.486471	+	0.408198i	0.852760	−	0.522303i	$-0.174927\pi$
$149$	72.4842	+	60.8215i	0.486471	+	0.408198i	−0.366288	+	0.930501i	$0.619372\pi$
$150$		0			0
$151$	73.2545	−	201.265i	0.485129	−	1.33288i	−0.419915	−	0.907564i	$-0.637940\pi$
$151$	73.2545	−	201.265i	0.485129	−	1.33288i	0.905044	−	0.425318i	$-0.139838\pi$
$152$	−79.4817	−	20.8718i	−0.522906	−	0.137315i
$153$		0			0
$154$	−103.099	+	222.061i	−0.669473	+	1.44196i
$155$	−151.353	+	26.6877i	−0.976474	+	0.172179i
$156$		0			0
$157$	140.989	−	51.3158i	0.898019	−	0.326852i	0.148561	−	0.988903i	$-0.452536\pi$
$157$	140.989	−	51.3158i	0.898019	−	0.326852i	0.749459	+	0.662051i	$0.230314\pi$
$158$	4.54684	+	9.70847i	0.0287775	+	0.0614460i
$159$		0			0
$160$	−75.4726	−	105.897i	−0.471703	−	0.661859i
$161$	146.211			0.908146
$162$		0			0
$163$		−	125.197i		−	0.768080i	−0.923316	−	0.384040i	$-0.874532\pi$
$163$		−	125.197i		−	0.768080i	0.923316	−	0.384040i	$-0.125468\pi$
$164$	58.7498	+	159.756i	0.358231	+	0.974119i
$165$		0			0
$166$	48.7776	+	104.151i	0.293841	+	0.627413i
$167$	94.4286	+	259.440i	0.565441	+	1.55354i	0.811544	+	0.584292i	$0.198628\pi$
$167$	94.4286	+	259.440i	0.565441	+	1.55354i	−0.246103	+	0.969244i	$0.579150\pi$
$168$		0			0
$169$	38.1748	+	216.500i	0.225886	+	1.28107i
$170$	−20.8332	+	44.8719i	−0.122548	+	0.263952i
$171$		0			0
$172$	−122.350	+	103.361i	−0.711338	+	0.600934i
$173$	133.982	+	48.7655i	0.774463	+	0.281881i	0.698862	−	0.715257i	$-0.253690\pi$
$173$	133.982	+	48.7655i	0.774463	+	0.281881i	0.0756008	+	0.997138i	$0.475913\pi$
$174$		0			0
$175$	30.6798	−	36.5628i	0.175313	−	0.208930i
$176$	−342.530	+	62.7537i	−1.94619	+	0.356555i
$177$		0			0
$178$	17.8498	+	66.1753i	0.100280	+	0.371771i
$179$	−169.609	−	97.9239i	−0.947537	−	0.547061i	−0.0552220	−	0.998474i	$-0.517587\pi$
$179$	−169.609	−	97.9239i	−0.947537	−	0.547061i	−0.892315	+	0.451413i	$0.850920\pi$
$180$		0			0
$181$	−3.70581	−	6.41865i	−0.0204741	−	0.0354622i	0.855607	−	0.517626i	$-0.173184\pi$
$181$	−3.70581	−	6.41865i	−0.0204741	−	0.0354622i	−0.876081	+	0.482164i	$0.839851\pi$
$182$	−157.111	−	156.588i	−0.863247	−	0.860375i
$183$		0			0
$184$	120.133	+	169.756i	0.652897	+	0.922585i
$185$	−19.2738	+	109.307i	−0.104183	+	0.590851i
$186$		0			0
$187$	85.1570	+	101.486i	0.455385	+	0.542707i
$188$	−72.0672	−	25.9587i	−0.383336	−	0.138078i
$189$		0			0
$190$	−68.3079	+	47.9995i	−0.359515	+	0.252629i
$191$	−87.5599	−	104.350i	−0.458429	−	0.546334i	0.486470	−	0.873697i	$-0.338284\pi$
$191$	−87.5599	−	104.350i	−0.458429	−	0.546334i	−0.944899	+	0.327363i	$0.893840\pi$
$192$		0			0
$193$	−47.2377	+	267.898i	−0.244755	+	1.38807i	0.576307	+	0.817234i	$0.304493\pi$
$193$	−47.2377	+	267.898i	−0.244755	+	1.38807i	−0.821061	+	0.570840i	$0.806618\pi$
$194$	−256.285	−	178.817i	−1.32106	−	0.921739i
$195$		0			0
$196$	−68.4446	−	11.8336i	−0.349207	−	0.0603756i
$197$	−185.008	−	320.442i	−0.939125	−	1.62661i	−0.767108	−	0.641518i	$-0.778305\pi$
$197$	−185.008	−	320.442i	−0.939125	−	1.62661i	−0.172016	−	0.985094i	$-0.555028\pi$
$198$		0			0
$199$	−157.019	−	90.6548i	−0.789038	−	0.455552i	0.0505855	−	0.998720i	$-0.483891\pi$
$199$	−157.019	−	90.6548i	−0.789038	−	0.455552i	−0.839624	+	0.543168i	$0.817225\pi$
$200$	67.6582	+	5.57872i	0.338291	+	0.0278936i
$201$		0			0
$202$	3.63930	−	42.4110i	0.0180163	−	0.209956i
$203$	−47.6034	+	56.7315i	−0.234499	+	0.279466i
$204$		0			0
$205$	162.499	+	59.1450i	0.792680	+	0.288512i
$206$	−3.34529	−	37.5168i	−0.0162393	−	0.182120i
$207$		0			0
$208$	52.7149	−	311.069i	0.253437	−	1.49553i
$209$	38.8217	+	220.169i	0.185750	+	1.05344i
$210$		0			0
$211$	−99.8063	−	274.215i	−0.473015	−	1.29960i	−0.915317	−	0.402733i	$-0.868060\pi$
$211$	−99.8063	−	274.215i	−0.473015	−	1.29960i	0.442302	−	0.896866i	$-0.354162\pi$
$212$	−292.605	−	167.638i	−1.38021	−	0.790744i
$213$		0			0
$214$	23.5596	−	88.5152i	0.110092	−	0.413622i
$215$			162.718i			0.756828i
$216$		0			0
$217$	212.715			0.980253
$218$	−29.6902	−	7.90248i	−0.136194	−	0.0362499i
$219$		0			0
$220$	−175.868	+	306.970i	−0.799401	+	1.39532i
$221$	−112.792	+	41.0528i	−0.510370	+	0.185759i
$222$		0			0
$223$	−325.450	+	57.3856i	−1.45942	+	0.257335i	−0.846321	−	0.532674i	$-0.821187\pi$
$223$	−325.450	+	57.3856i	−1.45942	+	0.257335i	−0.613096	+	0.790008i	$0.710076\pi$
$224$	77.4207	+	162.482i	0.345628	+	0.725364i
$225$		0			0
$226$	−378.522	+	33.7520i	−1.67488	+	0.149345i
$227$	43.2105	−	118.720i	0.190355	−	0.522995i	−0.807397	−	0.590008i	$-0.799125\pi$
$227$	43.2105	−	118.720i	0.190355	−	0.522995i	0.997752	+	0.0670126i	$0.0213468\pi$
$228$		0			0
$229$	99.8093	+	83.7500i	0.435849	+	0.365720i	0.834153	−	0.551533i	$-0.185957\pi$
$229$	99.8093	+	83.7500i	0.435849	+	0.365720i	−0.398305	+	0.917253i	$0.630401\pi$
$230$	210.504	+	18.0634i	0.915237	+	0.0785365i
$231$		0			0
$232$	−104.980	−	8.65604i	−0.452499	−	0.0373105i
$233$	−87.7066	+	151.912i	−0.376423	+	0.651984i	−0.990539	−	0.137232i	$-0.956179\pi$
$233$	−87.7066	+	151.912i	−0.376423	+	0.651984i	0.614116	+	0.789216i	$0.289513\pi$
$234$		0			0
$235$	−67.3946	+	38.9103i	−0.286785	+	0.165576i
$236$	−11.7654	+	68.0498i	−0.0498532	+	0.288347i
$237$		0			0
$238$	39.1810	−	56.1552i	0.164626	−	0.235946i
$239$	217.844	+	38.4118i	0.911483	+	0.160719i	0.609677	−	0.792650i	$-0.291299\pi$
$239$	217.844	+	38.4118i	0.911483	+	0.160719i	0.301806	+	0.953369i	$0.402410\pi$
$240$		0			0
$241$	−148.174	+	124.333i	−0.614829	+	0.515903i	−0.896173	−	0.443704i	$-0.853664\pi$
$241$	−148.174	+	124.333i	−0.614829	+	0.515903i	0.281344	+	0.959607i	$0.409220\pi$
$242$	405.551	+	577.138i	1.67583	+	2.38487i
$243$		0			0
$244$	−28.4361	+	78.9449i	−0.116541	+	0.323545i
$245$	−54.0575	+	45.3596i	−0.220643	+	0.185141i
$246$		0			0
$247$	−199.478	−	35.1733i	−0.807602	−	0.142402i
$248$	174.775	+	246.968i	0.704738	+	0.995839i
$249$		0			0
$250$	192.123	−	192.764i	0.768493	−	0.771057i
$251$	190.354	−	109.901i	0.758383	−	0.437853i	−0.0703317	−	0.997524i	$-0.522406\pi$
$251$	190.354	−	109.901i	0.758383	−	0.437853i	0.828715	+	0.559671i	$0.189072\pi$
$252$		0			0
$253$	282.888	−	489.977i	1.11814	−	1.93667i
$254$	−45.2883	+	12.2159i	−0.178300	+	0.0480939i
$255$		0			0
$256$	−125.034	+	223.389i	−0.488413	+	0.872612i
$257$	11.2364	+	9.42849i	0.0437215	+	0.0366867i	0.664387	−	0.747389i	$-0.268693\pi$
$257$	11.2364	+	9.42849i	0.0437215	+	0.0366867i	−0.620665	+	0.784076i	$0.713137\pi$
$258$		0			0
$259$	52.5420	−	144.358i	0.202865	−	0.557367i
$260$	−206.851	−	244.854i	−0.795582	−	0.941747i
$261$		0			0
$262$	−41.4838	−	19.2601i	−0.158335	−	0.0735120i
$263$	−7.69280	+	1.35645i	−0.0292502	+	0.00515760i	−0.188254	−	0.982120i	$-0.560283\pi$
$263$	−7.69280	+	1.35645i	−0.0292502	+	0.00515760i	0.159004	+	0.987278i	$0.449172\pi$
$264$		0			0
$265$	−321.937	+	117.175i	−1.21486	+	0.442171i
$266$	104.643	−	49.0081i	0.393394	−	0.184241i
$267$		0			0
$268$	100.681	−	37.0254i	0.375677	−	0.138155i
$269$	−72.1191			−0.268101			−0.134050	−	0.990975i	$-0.542798\pi$
$269$	−72.1191			−0.268101			−0.134050	+	0.990975i	$0.542798\pi$
$270$		0			0
$271$			213.834i			0.789057i	0.918884	+	0.394529i	$0.129092\pi$
$271$			213.834i			0.789057i	−0.918884	+	0.394529i	$0.870908\pi$
$272$	97.3904	−	0.649037i	0.358053	−	0.00238617i
$273$		0			0
$274$	243.652	−	114.111i	0.889242	−	0.416465i
$275$	−63.1685	−	173.554i	−0.229704	−	0.631105i
$276$		0			0
$277$	−64.3062	−	364.698i	−0.232152	−	1.31660i	−0.848529	−	0.529149i	$-0.822511\pi$
$277$	−64.3062	−	364.698i	−0.232152	−	1.31660i	0.616376	−	0.787452i	$-0.288600\pi$
$278$	−212.919	−	98.8541i	−0.765894	−	0.355590i
$279$		0			0
$280$	176.856	+	46.4423i	0.631629	+	0.165865i
$281$	328.252	+	119.474i	1.16816	+	0.425174i	0.852005	−	0.523534i	$-0.175387\pi$
$281$	328.252	+	119.474i	1.16816	+	0.425174i	0.316152	+	0.948708i	$0.397609\pi$
$282$		0			0
$283$	246.776	−	294.097i	0.872001	−	1.03921i	−0.126880	−	0.991918i	$-0.540496\pi$
$283$	246.776	−	294.097i	0.872001	−	1.03921i	0.998881	−	0.0472925i	$-0.0150593\pi$
$284$	−34.9941	−	60.1479i	−0.123219	−	0.211788i
$285$		0			0
$286$	−828.727	+	223.537i	−2.89765	+	0.781599i
$287$	−207.278	−	119.672i	−0.722224	−	0.416976i
$288$		0			0
$289$	125.974	+	218.193i	0.435896	+	0.754994i
$290$	−75.5446	+	75.7967i	−0.260499	+	0.261368i
$291$		0			0
$292$	−0.551779	−	165.595i	−0.00188966	−	0.567106i
$293$	38.4745	−	218.200i	0.131312	−	0.744709i	−0.846045	−	0.533112i	$-0.821022\pi$
$293$	38.4745	−	218.200i	0.131312	−	0.744709i	0.977357	−	0.211597i	$-0.0678665\pi$
$294$		0			0
$295$	45.0979	+	53.7456i	0.152874	+	0.182189i
$296$	210.774	−	57.6074i	0.712075	−	0.194620i
$297$		0			0
$298$	−108.803	−	154.838i	−0.365112	−	0.519589i
$299$	329.496	+	392.678i	1.10199	+	1.31331i
$300$		0			0
$301$	39.1078	−	221.791i	0.129926	−	0.736848i
$302$	−245.114	+	351.304i	−0.811637	+	1.16326i
$303$		0			0
$304$	142.878	+	81.2261i	0.469994	+	0.267191i
$305$	42.6237	+	73.8264i	0.139750	+	0.242054i
$306$		0			0
$307$	433.287	+	250.158i	1.41136	+	0.814847i	0.995516	−	0.0945902i	$-0.0301541\pi$
$307$	433.287	+	250.158i	1.41136	+	0.814847i	0.415841	+	0.909438i	$0.363487\pi$
$308$	313.493	−	376.145i	1.01783	−	1.22125i
$309$		0			0
$310$	306.251	+	26.2794i	0.987907	+	0.0847724i
$311$	−35.6895	+	42.5330i	−0.114757	+	0.136762i	−0.820365	−	0.571840i	$-0.806230\pi$
$311$	−35.6895	+	42.5330i	−0.114757	+	0.136762i	0.705608	+	0.708603i	$0.250674\pi$
$312$		0			0
$313$	−195.341	−	71.0983i	−0.624092	−	0.227151i	0.0105656	−	0.999944i	$-0.496637\pi$
$313$	−195.341	−	71.0983i	−0.624092	−	0.227151i	−0.634658	+	0.772793i	$0.718859\pi$
$314$	−298.889	+	26.6512i	−0.951876	+	0.0848766i
$315$		0			0
$316$	−3.79351	−	21.1027i	−0.0120048	−	0.0667806i
$317$	16.2685	+	92.2635i	0.0513203	+	0.291052i	0.999656	−	0.0262158i	$-0.00834571\pi$
$317$	16.2685	+	92.2635i	0.0513203	+	0.291052i	−0.948336	+	0.317268i	$0.897235\pi$
$318$		0			0
$319$	98.0134	+	269.289i	0.307252	+	0.844168i
$320$	91.3911	+	243.494i	0.285597	+	0.760918i
$321$		0			0
$322$	−282.585	−	75.2139i	−0.877592	−	0.233584i
$323$		−	62.5264i		−	0.193580i
$324$		0			0
$325$	167.335			0.514877
$326$	−64.4037	+	241.970i	−0.197558	+	0.742239i
$327$		0			0
$328$	−31.3652	−	338.983i	−0.0956257	−	1.03349i
$329$	101.213	−	36.8386i	0.307639	−	0.111971i
$330$		0			0
$331$	−274.896	+	48.4715i	−0.830501	+	0.146440i	−0.572707	−	0.819760i	$-0.694107\pi$
$331$	−274.896	+	48.4715i	−0.830501	+	0.146440i	−0.257794	+	0.966200i	$0.582996\pi$
$332$	−40.6961	−	226.385i	−0.122579	−	0.681883i
$333$		0			0
$334$	−49.0422	−	549.999i	−0.146833	−	1.64670i
$335$	37.2744	−	102.411i	0.111267	−	0.305704i
$336$		0			0
$337$	403.060	+	338.208i	1.19602	+	1.00358i	0.999735	+	0.0230374i	$0.00733369\pi$
$337$	403.060	+	338.208i	1.19602	+	1.00358i	0.196290	+	0.980546i	$0.437111\pi$
$338$	37.5908	−	438.070i	0.111215	−	1.29606i
$339$		0			0
$340$	63.3475	−	76.0075i	0.186316	−	0.223551i
$341$	411.558	−	712.840i	1.20692	−	2.09044i
$342$		0			0
$343$	323.261	−	186.635i	0.942453	−	0.544125i
$344$	289.638	−	136.827i	0.841971	−	0.397753i
$345$		0			0
$346$	−233.863	−	163.172i	−0.675904	−	0.471597i
$347$	−227.315	−	40.0818i	−0.655087	−	0.115510i	−0.163781	−	0.986497i	$-0.552369\pi$
$347$	−227.315	−	40.0818i	−0.655087	−	0.115510i	−0.491306	+	0.870987i	$0.663480\pi$
$348$		0			0
$349$	−266.323	+	223.471i	−0.763102	+	0.640319i	−0.938932	−	0.344102i	$-0.888184\pi$
$349$	−266.323	+	223.471i	−0.763102	+	0.640319i	0.175830	+	0.984421i	$0.443739\pi$
$350$	−78.1038	+	54.8830i	−0.223154	+	0.156809i
$351$		0			0
$352$	694.293	+	54.9190i	1.97242	+	0.156020i
$353$	−185.644	+	155.774i	−0.525903	+	0.441285i	−0.866684	−	0.498858i	$-0.833753\pi$
$353$	−185.644	+	155.774i	−0.525903	+	0.441285i	0.340781	+	0.940143i	$0.389309\pi$
$354$		0			0
$355$	−69.6219	−	12.2762i	−0.196118	−	0.0345809i
$356$	−0.456765	−	137.080i	−0.00128305	−	0.385056i
$357$		0			0
$358$	277.432	+	276.509i	0.774949	+	0.772371i
$359$	−286.224	+	165.252i	−0.797282	+	0.460311i	−0.842520	−	0.538665i	$-0.818929\pi$
$359$	−286.224	+	165.252i	−0.797282	+	0.460311i	0.0452381	+	0.998976i	$0.485595\pi$
$360$		0			0
$361$	−127.742	+	221.256i	−0.353857	+	0.612898i
$362$	3.86039	+	14.3117i	0.0106641	+	0.0395352i
$363$		0			0
$364$	223.098	+	383.461i	0.612907	+	1.05346i
$365$	−128.875	−	108.139i	−0.353083	−	0.296272i
$366$		0			0
$367$	−22.0119	+	60.4772i	−0.0599780	+	0.164788i	−0.966062	−	0.258309i	$-0.916835\pi$
$367$	−22.0119	+	60.4772i	−0.0599780	+	0.164788i	0.906084	+	0.423097i	$0.139057\pi$
$368$	−144.857	−	389.887i	−0.393633	−	1.05948i
$369$		0			0
$370$	93.4805	−	201.345i	0.252650	−	0.544175i
$371$	466.975	−	82.3403i	1.25869	−	0.221941i
$372$		0			0
$373$	−242.062	+	88.1032i	−0.648959	+	0.236202i	−0.645462	−	0.763792i	$-0.723335\pi$
$373$	−242.062	+	88.1032i	−0.648959	+	0.236202i	−0.00349656	+	0.999994i	$0.501113\pi$
$374$	−112.378	−	239.950i	−0.300475	−	0.641577i
$375$		0			0
$376$	125.931	+	87.2434i	0.334924	+	0.232030i
$377$	−259.640			−0.688701
$378$		0			0
$379$		−	299.350i		−	0.789843i	−0.918715	−	0.394921i	$-0.870772\pi$
$379$		−	299.350i		−	0.789843i	0.918715	−	0.394921i	$-0.129228\pi$
$380$	156.711	−	57.6303i	0.412398	−	0.151659i
$381$		0			0
$382$	115.548	+	246.720i	0.302483	+	0.645865i
$383$	−94.7246	−	260.254i	−0.247323	−	0.679513i	−0.999782	−	0.0208747i	$-0.993355\pi$
$383$	−94.7246	−	260.254i	−0.247323	−	0.679513i	0.752460	−	0.658639i	$-0.228867\pi$
$384$		0			0
$385$	−86.3829	−	489.902i	−0.224371	−	1.27247i
$386$	229.109	−	493.470i	0.593546	−	1.27842i
$387$		0			0
$388$	403.339	+	477.441i	1.03953	+	1.23052i
$389$	−346.254	−	126.026i	−0.890114	−	0.323975i	−0.143830	−	0.989602i	$-0.545942\pi$
$389$	−346.254	−	126.026i	−0.890114	−	0.323975i	−0.746284	+	0.665628i	$0.768164\pi$
$390$		0			0
$391$	−101.712	+	121.215i	−0.260132	+	0.310014i
$392$	126.196	+	58.0802i	0.321929	+	0.148164i
$393$		0			0
$394$	192.725	+	714.494i	0.489149	+	1.81344i
$395$	−18.8643	−	10.8913i	−0.0477577	−	0.0275729i
$396$		0			0
$397$	−226.740	−	392.726i	−0.571134	−	0.989233i	−0.996450	−	0.0841882i	$-0.973170\pi$
$397$	−226.740	−	392.726i	−0.571134	−	0.989233i	0.425316	−	0.905045i	$-0.360163\pi$
$398$	256.837	+	255.983i	0.645320	+	0.643173i
$399$		0			0
$400$	−127.894	−	45.5867i	−0.319735	−	0.113967i
$401$	−81.3303	+	461.247i	−0.202819	+	1.15024i	0.698017	+	0.716081i	$0.254066\pi$
$401$	−81.3303	+	461.247i	−0.202819	+	1.15024i	−0.900836	+	0.434160i	$0.857045\pi$
$402$		0			0
$403$	479.366	+	571.286i	1.18949	+	1.41758i
$404$	−28.8508	+	80.0962i	−0.0714127	+	0.198258i
$405$		0			0
$406$	121.187	−	85.1575i	0.298491	−	0.209748i
$407$	−382.108	−	455.378i	−0.938840	−	1.11887i
$408$		0			0
$409$	4.90627	−	27.8248i	0.0119958	−	0.0680313i	−0.978222	−	0.207560i	$-0.933448\pi$
$409$	4.90627	−	27.8248i	0.0119958	−	0.0680313i	0.990218	+	0.139529i	$0.0445588\pi$
$410$	−283.639	−	197.903i	−0.691803	−	0.482690i
$411$		0			0
$412$	−12.8339	+	74.2300i	−0.0311502	+	0.180170i
$413$	−48.5530	−	84.0963i	−0.117562	−	0.203623i
$414$		0			0
$415$	−202.372	−	116.840i	−0.487644	−	0.281542i
$416$	−261.903	+	574.090i	−0.629574	+	1.38002i
$417$		0			0
$418$	38.2279	−	445.494i	0.0914542	−	1.06577i
$419$	−85.6108	+	102.027i	−0.204322	+	0.243501i	−0.858468	−	0.512867i	$-0.828584\pi$
$419$	−85.6108	+	102.027i	−0.204322	+	0.243501i	0.654147	+	0.756368i	$0.273028\pi$
$420$		0			0
$421$	312.802	+	113.851i	0.742997	+	0.270429i	0.685656	−	0.727926i	$-0.259516\pi$
$421$	312.802	+	113.851i	0.742997	+	0.270429i	0.0573411	+	0.998355i	$0.481738\pi$
$422$	51.8351	+	581.322i	0.122832	+	1.37754i
$423$		0			0
$424$	479.284	+	474.517i	1.13039	+	1.11914i
$425$	8.96969	+	50.8697i	0.0211052	+	0.119693i
$426$		0			0
$427$	−40.3543	−	110.873i	−0.0945066	−	0.259655i
$428$	−91.0677	+	158.955i	−0.212775	+	0.371390i
$429$		0			0
$430$	83.7052	−	314.487i	0.194663	−	0.731365i
$431$			544.979i			1.26445i	0.774784	+	0.632226i	$0.217859\pi$
$431$			544.979i			1.26445i	−0.774784	+	0.632226i	$0.782141\pi$
$432$		0			0
$433$	−750.692			−1.73370			−0.866850	−	0.498568i	$-0.833859\pi$
$433$	−750.692			−1.73370			−0.866850	+	0.498568i	$0.833859\pi$
$434$	−411.117	−	109.425i	−0.947273	−	0.252130i
$435$		0			0
$436$	53.3174	+	30.5464i	0.122288	+	0.0700606i
$437$	−250.923	+	91.3286i	−0.574195	+	0.208990i
$438$		0			0
$439$	−52.3809	+	9.23616i	−0.119319	+	0.0210391i	−0.232989	−	0.972479i	$-0.574850\pi$
$439$	−52.3809	+	9.23616i	−0.119319	+	0.0210391i	0.113670	+	0.993519i	$0.463739\pi$
$440$	497.814	−	502.815i	1.13140	−	1.14276i
$441$		0			0
$442$	239.112	−	21.3211i	0.540978	−	0.0482377i
$443$	−141.718	+	389.368i	−0.319906	+	0.878934i	0.670644	+	0.741779i	$0.266018\pi$
$443$	−141.718	+	389.368i	−0.319906	+	0.878934i	−0.990550	+	0.137154i	$0.956204\pi$
$444$		0			0
$445$	−106.684	−	89.5181i	−0.239738	−	0.201164i
$446$	658.521	+	56.5078i	1.47650	+	0.126699i
$447$		0			0
$448$	−66.0483	−	353.857i	−0.147429	−	0.789858i
$449$	−124.462	+	215.575i	−0.277199	+	0.480122i	−0.970687	−	0.240345i	$-0.922739\pi$
$449$	−124.462	+	215.575i	−0.277199	+	0.480122i	0.693489	+	0.720467i	$0.256073\pi$
$450$		0			0
$451$	−802.079	+	463.081i	−1.77845	+	1.02679i
$452$	748.937	+	129.486i	1.65694	+	0.286474i
$453$		0			0
$454$	−144.585	+	207.223i	−0.318470	+	0.456439i
$455$	443.861	+	78.2647i	0.975519	+	0.172010i
$456$		0			0
$457$	−410.088	+	344.104i	−0.897347	+	0.752964i	−0.969670	−	0.244417i	$-0.921403\pi$
$457$	−410.088	+	344.104i	−0.897347	+	0.752964i	0.0723227	+	0.997381i	$0.476959\pi$
$458$	−149.820	−	213.208i	−0.327118	−	0.465520i
$459$		0			0
$460$	−397.552	−	143.199i	−0.864244	−	0.311302i
$461$	525.136	−	440.641i	1.13912	−	0.955838i	0.139713	−	0.990192i	$-0.455382\pi$
$461$	525.136	−	440.641i	1.13912	−	0.955838i	0.999410	+	0.0343542i	$0.0109374\pi$
$462$		0			0
$463$	909.043	+	160.289i	1.96338	+	0.346196i	0.995499	+	0.0947721i	$0.0302122\pi$
$463$	909.043	+	160.289i	1.96338	+	0.346196i	0.967877	+	0.251424i	$0.0808989\pi$
$464$	198.443	+	70.7331i	0.427678	+	0.152442i
$465$		0			0
$466$	247.658	−	248.485i	0.531455	−	0.533229i
$467$	−129.687	+	74.8750i	−0.277703	+	0.160332i	−0.632383	−	0.774656i	$-0.717923\pi$
$467$	−129.687	+	74.8750i	−0.277703	+	0.160332i	0.354680	+	0.934988i	$0.384590\pi$
$468$		0			0
$469$	−75.4200	+	130.631i	−0.160810	+	0.278532i
$470$	150.270	−	40.5333i	0.319724	−	0.0862410i
$471$		0			0
$472$	57.7451	−	125.468i	0.122341	−	0.265823i
$473$	−667.590	−	560.175i	−1.41140	−	1.18430i
$474$		0			0
$475$	−29.8133	+	81.9115i	−0.0627649	+	0.172445i
$476$	−104.613	+	88.3763i	−0.219775	+	0.185665i
$477$		0			0
$478$	−401.270	−	186.302i	−0.839478	−	0.389754i
$479$	−560.418	+	98.8168i	−1.16997	+	0.206298i	−0.724680	−	0.689086i	$-0.758012\pi$
$479$	−560.418	+	98.8168i	−1.16997	+	0.206298i	−0.445295	+	0.895384i	$0.646901\pi$
$480$		0			0
$481$	506.107	−	184.208i	1.05220	−	0.382969i
$482$	350.336	−	164.076i	0.726839	−	0.340406i
$483$		0			0
$484$	−486.923	−	1324.07i	−1.00604	−	2.73567i
$485$	634.966			1.30921
$486$		0			0
$487$			75.8835i			0.155818i	0.996960	+	0.0779091i	$0.0248244\pi$
$487$			75.8835i			0.155818i	−0.996960	+	0.0779091i	$0.975176\pi$
$488$	95.5695	−	137.950i	0.195839	−	0.282684i
$489$		0			0
$490$	127.811	−	59.8589i	0.260840	−	0.122161i
$491$	16.9685	+	46.6205i	0.0345590	+	0.0949502i	0.955772	−	0.294108i	$-0.0950226\pi$
$491$	16.9685	+	46.6205i	0.0345590	+	0.0949502i	−0.921213	+	0.389058i	$0.872800\pi$
$492$		0			0
$493$	−13.9175	−	78.9303i	−0.0282303	−	0.160102i
$494$	367.439	+	170.595i	0.743804	+	0.345334i
$495$		0			0
$496$	−210.745	−	567.226i	−0.424888	−	1.14360i
$497$	91.9470	+	33.4660i	0.185004	+	0.0673360i
$498$		0			0
$499$	−541.294	+	645.089i	−1.08476	+	1.29276i	−0.131266	+	0.991347i	$0.541904\pi$
$499$	−541.294	+	645.089i	−1.08476	+	1.29276i	−0.953492	+	0.301417i	$0.902540\pi$
$500$	−470.480	+	273.726i	−0.940960	+	0.547452i
$501$		0			0
$502$	−424.435	+	114.485i	−0.845488	+	0.228058i
$503$	−262.850	−	151.757i	−0.522565	−	0.301703i	0.215418	−	0.976522i	$-0.430889\pi$
$503$	−262.850	−	151.757i	−0.522565	−	0.301703i	−0.737984	+	0.674819i	$0.764222\pi$
$504$		0			0
$505$	43.2453	+	74.9030i	0.0856342	+	0.148323i
$506$	−798.794	+	801.461i	−1.57865	+	1.58391i
$507$		0			0
$508$	93.8132	−	0.312595i	0.184672	−	0.000615345i
$509$	18.5379	−	105.133i	0.0364202	−	0.206549i	−0.961168	−	0.275965i	$-0.911003\pi$
$509$	18.5379	−	105.133i	0.0364202	−	0.206549i	0.997588	+	0.0694162i	$0.0221136\pi$
$510$		0			0
$511$	149.672	+	178.372i	0.292900	+	0.349065i
$512$	356.570	−	367.426i	0.696425	−	0.717630i
$513$		0			0
$514$	−16.8666	−	24.0028i	−0.0328144	−	0.0466980i
$515$	49.1937	+	58.6268i	0.0955217	+	0.113838i
$516$		0			0
$517$	72.3744	−	410.456i	0.139989	−	0.793918i
$518$	−175.809	+	251.974i	−0.339400	+	0.486436i
$519$		0			0
$520$	273.826	+	579.641i	0.526589	+	1.11469i
$521$	227.354	+	393.788i	0.436380	+	0.755832i	0.997407	−	0.0719656i	$-0.0229272\pi$
$521$	227.354	+	393.788i	0.436380	+	0.755832i	−0.561028	+	0.827797i	$0.689594\pi$
$522$		0			0
$523$	−508.326	−	293.482i	−0.971943	−	0.561152i	−0.0721152	−	0.997396i	$-0.522975\pi$
$523$	−508.326	−	293.482i	−0.971943	−	0.561152i	−0.899828	+	0.436245i	$0.856308\pi$
$524$	70.2684	+	58.5643i	0.134100	+	0.111764i
$525$		0			0
$526$	15.5657	+	1.33570i	0.0295927	+	0.00253935i
$527$	−147.975	+	176.349i	−0.280787	+	0.334629i
$528$		0			0
$529$	137.914	+	50.1965i	0.260706	+	0.0948894i
$530$	682.488	−	60.8559i	1.28771	−	0.114822i
$531$		0			0
$532$	−227.455	+	40.8883i	−0.427547	+	0.0768578i
$533$	−145.712	−	826.374i	−0.273381	−	1.55042i
$534$		0			0
$535$	63.6545	+	174.889i	0.118980	+	0.326896i
$536$	−213.635	+	19.7670i	−0.398572	+	0.0368788i
$537$		0			0
$538$	139.385	+	37.0994i	0.259081	+	0.0689580i
$539$		−	377.940i		−	0.701187i
$540$		0			0
$541$	408.236			0.754595			0.377297	−	0.926092i	$-0.376853\pi$
$541$	408.236			0.754595			0.377297	+	0.926092i	$0.376853\pi$
$542$	110.000	−	413.280i	0.202953	−	0.762510i
$543$		0			0
$544$	−188.561	−	48.8451i	−0.346620	−	0.0897887i
$545$	58.6622	−	21.3513i	0.107637	−	0.0391767i
$546$		0			0
$547$	−332.257	+	58.5859i	−0.607417	+	0.107104i	−0.468893	−	0.883255i	$-0.655347\pi$
$547$	−332.257	+	58.5859i	−0.607417	+	0.107104i	−0.138524	+	0.990359i	$0.544236\pi$
$548$	−529.610	+	95.2053i	−0.966442	+	0.173732i
$549$		0			0
$550$	32.8070	+	367.925i	0.0596491	+	0.668954i
$551$	46.2589	−	127.095i	0.0839545	−	0.230663i
$552$		0			0
$553$	23.0952	+	19.3791i	0.0417634	+	0.0350437i
$554$	−63.3225	+	737.937i	−0.114300	+	1.33202i
$555$		0			0
$556$	360.658	+	300.586i	0.648665	+	0.540622i
$557$	−460.391	+	797.421i	−0.826555	+	1.43164i	0.0741701	+	0.997246i	$0.476369\pi$
$557$	−460.391	+	797.421i	−0.826555	+	1.43164i	−0.900725	+	0.434390i	$0.856964\pi$
$558$		0			0
$559$	683.794	−	394.788i	1.22324	−	0.706240i
$560$	−317.921	−	180.738i	−0.567716	−	0.322746i
$561$		0			0
$562$	−572.957	−	399.768i	−1.01950	−	0.711331i
$563$	−587.386	−	103.572i	−1.04332	−	0.183965i	−0.374372	−	0.927278i	$-0.622142\pi$
$563$	−587.386	−	103.572i	−1.04332	−	0.183965i	−0.668943	+	0.743314i	$0.733253\pi$
$564$		0			0
$565$	591.510	−	496.336i	1.04692	−	0.878470i
$566$	−628.236	+	441.457i	−1.10996	+	0.779960i
$567$		0			0
$568$	36.6923	+	134.250i	0.0645992	+	0.236356i
$569$	349.724	−	293.453i	0.614629	−	0.515735i	−0.281481	−	0.959567i	$-0.590826\pi$
$569$	349.724	−	293.453i	0.614629	−	0.515735i	0.896110	+	0.443832i	$0.146381\pi$
$570$		0			0
$571$	−518.842	−	91.4859i	−0.908656	−	0.160221i	−0.300263	−	0.953857i	$-0.597074\pi$
$571$	−518.842	−	91.4859i	−0.908656	−	0.160221i	−0.608393	+	0.793636i	$0.708185\pi$
$572$	1716.68	−	5.72016i	3.00119	−	0.0100003i
$573$		0			0
$574$	339.048	+	337.920i	0.590675	+	0.588710i
$575$	191.042	−	110.298i	0.332248	−	0.191823i
$576$		0			0
$577$	−529.613	+	917.317i	−0.917873	+	1.58980i	−0.115234	+	0.993338i	$0.536762\pi$
$577$	−529.613	+	917.317i	−0.917873	+	1.58980i	−0.802639	+	0.596465i	$0.796571\pi$
$578$	−131.229	−	486.508i	−0.227039	−	0.841710i
$579$		0			0
$580$	184.997	−	107.632i	0.318961	−	0.185572i
$581$	247.760	+	207.896i	0.426438	+	0.357824i
$582$		0			0
$583$	627.562	−	1724.21i	1.07644	−	2.95748i
$584$	−84.1187	+	320.331i	−0.144039	+	0.548512i
$585$		0			0
$586$	−186.606	+	401.925i	−0.318441	+	0.685879i
$587$	254.912	−	44.9479i	0.434262	−	0.0765722i	0.0477562	−	0.998859i	$-0.484793\pi$
$587$	254.912	−	44.9479i	0.434262	−	0.0765722i	0.386506	+	0.922287i	$0.373682\pi$
$588$		0			0
$589$	−365.054	+	132.869i	−0.619787	+	0.225584i
$590$	−59.5135	−	127.074i	−0.100870	−	0.215380i
$591$		0			0
$592$	−437.000	+	2.91229i	−0.738176	+	0.00491941i
$593$	676.112			1.14015			0.570077	−	0.821591i	$-0.306913\pi$
$593$	676.112			1.14015			0.570077	+	0.821591i	$0.306913\pi$
$594$		0			0
$595$			139.128i			0.233829i
$596$	130.634	+	355.227i	0.219185	+	0.596018i
$597$		0			0
$598$	−434.820	−	928.433i	−0.727124	−	1.55256i
$599$	−55.7448	−	153.158i	−0.0930631	−	0.255689i	0.884424	−	0.466684i	$-0.154552\pi$
$599$	−55.7448	−	153.158i	−0.0930631	−	0.255689i	−0.977487	+	0.210996i	$0.932329\pi$
$600$		0			0
$601$	−87.8381	−	498.155i	−0.146153	−	0.828876i	−0.966434	−	0.256915i	$-0.917294\pi$
$601$	−87.8381	−	498.155i	−0.146153	−	0.828876i	0.820281	−	0.571961i	$-0.193817\pi$
$602$	−189.678	+	408.540i	−0.315079	+	0.678639i
$603$		0			0
$604$	654.453	−	552.878i	1.08353	−	0.915360i
$605$	−1346.81	−	490.198i	−2.22613	−	0.810244i
$606$		0			0
$607$	−702.863	+	837.639i	−1.15793	+	1.37997i	−0.246176	+	0.969225i	$0.579174\pi$
$607$	−702.863	+	837.639i	−1.15793	+	1.37997i	−0.911752	+	0.410740i	$0.865270\pi$
$608$	−234.358	−	230.486i	−0.385458	−	0.379089i
$609$		0			0
$610$	−44.4016	−	164.612i	−0.0727895	−	0.269855i
$611$	327.027	+	188.809i	0.535233	+	0.309017i
$612$		0			0
$613$	123.629	+	214.132i	0.201679	+	0.349318i	0.949070	−	0.315067i	$-0.102027\pi$
$613$	123.629	+	214.132i	0.201679	+	0.349318i	−0.747391	+	0.664385i	$0.768694\pi$
$614$	−708.732	−	706.374i	−1.15429	−	1.15045i
$615$		0			0
$616$	−799.387	+	565.712i	−1.29771	+	0.918364i
$617$	−18.2921	+	103.739i	−0.0296468	+	0.168135i	−0.996036	−	0.0889467i	$-0.971650\pi$
$617$	−18.2921	+	103.739i	−0.0296468	+	0.168135i	0.966390	+	0.257082i	$0.0827610\pi$
$618$		0			0
$619$	181.659	+	216.492i	0.293471	+	0.349746i	0.892553	−	0.450942i	$-0.148912\pi$
$619$	181.659	+	216.492i	0.293471	+	0.349746i	−0.599082	+	0.800688i	$0.704468\pi$
$620$	−578.376	−	208.332i	−0.932865	−	0.336019i
$621$		0			0
$622$	90.8572	−	63.8448i	0.146073	−	0.102644i
$623$	123.899	+	147.657i	0.198875	+	0.237010i
$624$		0			0
$625$	−59.1861	+	335.661i	−0.0946977	+	0.537057i
$626$	340.963	+	237.900i	0.544670	+	0.380031i
$627$		0			0
$628$	591.376	+	102.245i	0.941682	+	0.162810i
$629$	83.1280	+	143.982i	0.132159	+	0.228906i
$630$		0			0
$631$	−205.862	−	118.855i	−0.326248	−	0.188359i	0.327926	−	0.944703i	$-0.393650\pi$
$631$	−205.862	−	118.855i	−0.326248	−	0.188359i	−0.654174	+	0.756344i	$0.726984\pi$
$632$	−3.52384	+	42.7368i	−0.00557569	+	0.0676215i
$633$		0			0
$634$	16.0197	−	186.688i	0.0252676	−	0.294460i
$635$	61.2633	−	73.0108i	0.0964777	−	0.114978i
$636$		0			0
$637$	321.771	+	117.115i	0.505135	+	0.183854i
$638$	−50.9040	−	570.879i	−0.0797868	−	0.894794i
$639$		0			0
$640$	−51.3748	−	517.616i	−0.0802732	−	0.808775i
$641$	−30.6876	−	174.038i	−0.0478746	−	0.271510i	0.951469	−	0.307746i	$-0.0995746\pi$
$641$	−30.6876	−	174.038i	−0.0478746	−	0.271510i	−0.999343	+	0.0362352i	$0.988463\pi$
$642$		0			0
$643$	158.986	+	436.809i	0.247256	+	0.679330i	0.999784	+	0.0207704i	$0.00661189\pi$
$643$	158.986	+	436.809i	0.247256	+	0.679330i	−0.752528	+	0.658560i	$0.771166\pi$
$644$	507.463	+	290.734i	0.787986	+	0.451450i
$645$		0			0
$646$	−32.1647	+	120.845i	−0.0497906	+	0.187067i
$647$			932.596i			1.44142i	0.693239	+	0.720708i	$0.256183\pi$
$647$			932.596i			1.44142i	−0.693239	+	0.720708i	$0.743817\pi$
$648$		0			0
$649$	−375.759			−0.578982
$650$	−323.410	−	86.0803i	−0.497554	−	0.132431i
$651$		0			0
$652$	248.948	−	434.527i	0.381822	−	0.666453i
$653$	−81.2175	+	29.5607i	−0.124376	+	0.0452691i	−0.403458	−	0.914998i	$-0.632192\pi$
$653$	−81.2175	+	29.5607i	−0.124376	+	0.0452691i	0.279082	+	0.960267i	$0.409970\pi$
$654$		0			0
$655$	91.5196	−	16.1374i	0.139725	−	0.0246372i
$656$	−113.760	+	671.292i	−0.173414	+	1.02331i
$657$		0			0
$658$	−214.566	+	19.1324i	−0.326089	+	0.0290766i
$659$	−62.6424	+	172.109i	−0.0950568	+	0.261166i	−0.978104	−	0.208119i	$-0.933266\pi$
$659$	−62.6424	+	172.109i	−0.0950568	+	0.261166i	0.883047	+	0.469285i	$0.155488\pi$
$660$		0			0
$661$	854.686	+	717.167i	1.29302	+	1.08497i	0.991306	+	0.131574i	$0.0420031\pi$
$661$	854.686	+	717.167i	1.29302	+	1.08497i	0.301714	+	0.953399i	$0.402441\pi$
$662$	556.229	+	47.7301i	0.840225	+	0.0720998i
$663$		0			0
$664$	−37.8031	+	458.472i	−0.0569323	+	0.690470i
$665$	−117.392	+	203.329i	−0.176529	+	0.305757i
$666$		0			0
$667$	−296.425	+	171.141i	−0.444415	+	0.256583i
$668$	−188.146	+	1088.22i	−0.281655	+	1.62907i
$669$		0			0
$670$	−124.723	+	178.756i	−0.186153	+	0.266799i
$671$	−449.628	−	79.2815i	−0.670086	−	0.118154i
$672$		0			0
$673$	−284.180	+	238.456i	−0.422259	+	0.354317i	−0.829022	−	0.559216i	$-0.811102\pi$
$673$	−284.180	+	238.456i	−0.422259	+	0.354317i	0.406763	+	0.913534i	$0.366658\pi$
$674$	−605.019	−	860.999i	−0.897654	−	1.27745i
$675$		0			0
$676$	−298.004	+	827.325i	−0.440834	+	1.22385i
$677$	−286.716	+	240.583i	−0.423509	+	0.355367i	−0.829496	−	0.558512i	$-0.811372\pi$
$677$	−286.716	+	240.583i	−0.423509	+	0.355367i	0.405987	+	0.913879i	$0.366928\pi$
$678$		0			0
$679$	−865.484	−	152.608i	−1.27464	−	0.224754i
$680$	−161.532	+	114.313i	−0.237547	+	0.168108i
$681$		0			0
$682$	−1162.12	+	1166.00i	−1.70399	+	1.70968i
$683$	4.35578	−	2.51481i	0.00637743	−	0.00368201i	−0.496808	−	0.867861i	$-0.665495\pi$
$683$	4.35578	−	2.51481i	0.00637743	−	0.00368201i	0.503185	+	0.864179i	$0.332161\pi$
$684$		0			0
$685$	−273.338	+	473.434i	−0.399033	+	0.691145i
$686$	−720.779	+	194.420i	−1.05070	+	0.283411i
$687$		0			0
$688$	−630.173	+	115.452i	−0.915950	+	0.167808i
$689$	1273.50	+	1068.59i	1.84833	+	1.55093i
$690$		0			0
$691$	312.035	−	857.308i	0.451570	−	1.24068i	−0.480049	−	0.877241i	$-0.659381\pi$
$691$	312.035	−	857.308i	0.451570	−	1.24068i	0.931619	−	0.363436i	$-0.118396\pi$
$692$	368.050	+	435.669i	0.531864	+	0.629579i
$693$		0			0
$694$	418.716	+	194.402i	0.603337	+	0.280118i
$695$	469.731	−	82.8263i	0.675872	−	0.119174i
$696$		0			0
$697$	243.406	−	88.5925i	0.349219	−	0.127105i
$698$	629.683	−	294.904i	0.902124	−	0.422499i
$699$		0			0
$700$	179.185	−	65.8950i	0.255979	−	0.0941357i
$701$	−540.204			−0.770619			−0.385310	−	0.922787i	$-0.625905\pi$
$701$	−540.204			−0.770619			−0.385310	+	0.922787i	$0.625905\pi$
$702$		0			0
$703$			280.562i			0.399092i
$704$	−1313.62	−	463.300i	−1.86593	−	0.658096i
$705$		0			0
$706$	438.929	−	205.567i	0.621712	−	0.291171i
$707$	−40.9428	−	112.489i	−0.0579106	−	0.159108i
$708$		0			0
$709$	−166.509	−	944.318i	−0.234850	−	1.33190i	−0.842929	−	0.538025i	$-0.819171\pi$
$709$	−166.509	−	944.318i	−0.234850	−	1.33190i	0.608079	−	0.793877i	$-0.291940\pi$
$710$	128.244	+	59.5412i	0.180625	+	0.0838609i
$711$		0			0
$712$	−69.6338	+	265.171i	−0.0978003	+	0.372432i
$713$	923.842	+	336.251i	1.29571	+	0.471600i
$714$		0			0
$715$	1121.05	−	1336.02i	1.56791	−	1.86856i
$716$	−393.954	−	677.128i	−0.550215	−	0.945709i
$717$		0			0
$718$	638.197	−	172.145i	0.888854	−	0.239756i
$719$	209.447	+	120.924i	0.291303	+	0.168184i	0.638529	−	0.769598i	$-0.279543\pi$
$719$	209.447	+	120.924i	0.291303	+	0.168184i	−0.347226	+	0.937781i	$0.612876\pi$
$720$		0			0
$721$	−52.9626	−	91.7339i	−0.0734571	−	0.127231i
$722$	360.708	−	361.912i	0.499595	−	0.501263i
$723$		0			0
$724$	−0.0987846	−	29.6463i	−0.000136443	−	0.0409480i
$725$	−19.4025	+	110.037i	−0.0267621	+	0.151775i
$726$		0			0
$727$	181.466	+	216.263i	0.249610	+	0.297473i	0.876271	−	0.481818i	$-0.160024\pi$
$727$	181.466	+	216.263i	0.249610	+	0.297473i	−0.626661	+	0.779292i	$0.715579\pi$
$728$	−233.925	−	855.885i	−0.321325	−	1.17567i
$729$		0			0
$730$	193.450	+	275.298i	0.265000	+	0.377120i
$731$	156.669	+	186.710i	0.214321	+	0.255418i
$732$		0			0
$733$	200.749	−	1138.50i	0.273873	−	1.55321i	−0.468645	−	0.883387i	$-0.655258\pi$
$733$	200.749	−	1138.50i	0.273873	−	1.55321i	0.742518	−	0.669826i	$-0.233631\pi$
$734$	73.6533	−	105.562i	0.100345	−	0.143817i
$735$		0			0
$736$	79.4015	+	828.057i	0.107883	+	1.12508i
$737$	291.844	+	505.488i	0.395988	+	0.685872i
$738$		0			0
$739$	−628.641	−	362.946i	−0.850664	−	0.491131i	0.0102107	−	0.999948i	$-0.496750\pi$
$739$	−628.641	−	362.946i	−0.850664	−	0.491131i	−0.860875	+	0.508817i	$0.830083\pi$
$740$	−284.246	+	341.053i	−0.384117	+	0.460883i
$741$		0			0
$742$	−944.885	−	81.0807i	−1.27343	−	0.109273i
$743$	819.405	−	976.528i	1.10283	−	1.31430i	0.157748	−	0.987479i	$-0.449577\pi$
$743$	819.405	−	976.528i	1.10283	−	1.31430i	0.945085	−	0.326825i	$-0.105979\pi$
$744$		0			0
$745$	361.328	+	131.513i	0.485004	+	0.176527i
$746$	513.157	−	45.7571i	0.687878	−	0.0613365i
$747$		0			0
$748$	93.7586	+	521.563i	0.125346	+	0.697277i
$749$	−44.7306	−	253.680i	−0.0597204	−	0.338691i
$750$		0			0
$751$	−184.174	−	506.015i	−0.245239	−	0.673789i	−0.999845	−	0.0176103i	$-0.994394\pi$
$751$	−184.174	−	506.015i	−0.245239	−	0.673789i	0.754606	−	0.656178i	$-0.227828\pi$
$752$	−198.509	−	233.398i	−0.263975	−	0.310369i
$753$		0			0
$754$	501.810	+	133.564i	0.665530	+	0.177140i
$755$		−	870.381i		−	1.15282i
$756$		0			0
$757$	−616.583			−0.814509			−0.407254	−	0.913315i	$-0.633514\pi$
$757$	−616.583			−0.814509			−0.407254	+	0.913315i	$0.633514\pi$
$758$	−153.991	+	578.558i	−0.203155	+	0.763269i
$759$		0			0
$760$	−332.524	+	30.7675i	−0.437531	+	0.0404836i
$761$	−883.018	+	321.392i	−1.16034	+	0.422329i	−0.849218	−	0.528042i	$-0.822926\pi$
$761$	−883.018	+	321.392i	−1.16034	+	0.422329i	−0.311120	+	0.950371i	$0.600704\pi$
$762$		0			0
$763$	−85.0906	+	15.0038i	−0.111521	+	0.0196642i
$764$	−96.4042	−	536.280i	−0.126183	−	0.701937i
$765$		0			0
$766$	49.1959	+	551.723i	0.0642244	+	0.720265i
$767$	116.439	−	319.914i	0.151811	−	0.417098i
$768$		0			0
$769$	−359.959	−	302.041i	−0.468087	−	0.392771i	0.378009	−	0.925802i	$-0.376609\pi$
$769$	−359.959	−	302.041i	−0.468087	−	0.392771i	−0.846096	+	0.533030i	$0.821053\pi$
$770$	−85.0614	+	991.275i	−0.110469	+	1.28737i
$771$		0			0
$772$	−696.651	+	835.877i	−0.902398	+	1.08274i
$773$	28.5783	−	49.4991i	0.0369707	−	0.0640351i	−0.846948	−	0.531676i	$-0.821563\pi$
$773$	28.5783	−	49.4991i	0.0369707	−	0.0640351i	0.883919	+	0.467641i	$0.154896\pi$
$774$		0			0
$775$	277.937	−	160.467i	0.358629	−	0.207054i
$776$	−533.933	−	1130.24i	−0.688058	−	1.45649i
$777$		0			0
$778$	604.379	+	421.692i	0.776837	+	0.542021i
$779$	430.476	+	75.9045i	0.552600	+	0.0974383i
$780$		0			0
$781$	290.048	−	243.379i	0.371380	−	0.311625i
$782$	258.935	−	181.952i	0.331119	−	0.232675i
$783$		0			0
$784$	−214.024	−	177.170i	−0.272989	−	0.225982i
$785$	467.068	−	391.917i	0.594991	−	0.499257i
$786$		0			0
$787$	886.857	+	156.377i	1.12688	+	0.198700i	0.705861	−	0.708350i	$-0.250560\pi$
$787$	886.857	+	156.377i	1.12688	+	0.198700i	0.421022	+	0.907050i	$0.361671\pi$
$788$	−4.93169	−	1480.05i	−0.00625849	−	1.87824i
$789$		0			0
$790$	30.8565	+	30.7539i	0.0390589	+	0.0389290i
$791$	−925.541	+	534.361i	−1.17009	+	0.675552i
$792$		0			0
$793$	206.828	−	358.237i	0.260818	−	0.451749i
$794$	236.198	+	875.665i	0.297479	+	1.10285i
$795$		0			0
$796$	−364.710	−	626.863i	−0.458178	−	0.787516i
$797$	−585.520	−	491.310i	−0.734655	−	0.616449i	0.196741	−	0.980455i	$-0.436964\pi$
$797$	−585.520	−	491.310i	−0.734655	−	0.616449i	−0.931396	+	0.364006i	$0.881409\pi$
$798$		0			0
$799$	−39.8681	+	109.537i	−0.0498975	+	0.137092i
$800$	223.731	+	153.897i	0.279664	+	0.192371i
$801$		0			0
$802$	394.462	−	849.619i	0.491848	−	1.05938i
$803$	887.336	−	156.461i	1.10503	−	0.194846i
$804$		0			0
$805$	558.334	−	203.217i	0.693582	−	0.252443i
$806$	−632.596	−	1350.73i	−0.784858	−	1.67584i
$807$		0			0
$808$	96.9632	−	139.961i	0.120004	−	0.173220i
$809$	−388.814			−0.480610			−0.240305	−	0.970697i	$-0.577247\pi$
$809$	−388.814			−0.480610			−0.240305	+	0.970697i	$0.577247\pi$
$810$		0			0
$811$		−	1206.55i		−	1.48774i	−0.668326	−	0.743869i	$-0.732989\pi$
$811$		−	1206.55i		−	1.48774i	0.668326	−	0.743869i	$-0.267011\pi$
$812$	−278.027	+	102.244i	−0.342398	+	0.125916i
$813$		0			0
$814$	504.249	+	1076.68i	0.619470	+	1.32270i
$815$	−174.009	−	478.087i	−0.213508	−	0.586609i
$816$		0			0
$817$	71.4228	+	405.059i	0.0874208	+	0.495788i
$818$	−23.7960	+	51.2535i	−0.0290905	+	0.0626570i
$819$		0			0
$820$	446.388	+	528.399i	0.544375	+	0.644389i
$821$	979.566	+	356.533i	1.19314	+	0.434266i	0.860824	−	0.508903i	$-0.169949\pi$
$821$	979.566	+	356.533i	1.19314	+	0.434266i	0.332313	+	0.943169i	$0.392171\pi$
$822$		0			0
$823$	136.341	−	162.485i	0.165663	−	0.197430i	−0.676826	−	0.736143i	$-0.736645\pi$
$823$	136.341	−	162.485i	0.165663	−	0.197430i	0.842489	+	0.538713i	$0.181089\pi$
$824$	62.9895	−	136.863i	0.0764435	−	0.166096i
$825$		0			0
$826$	50.5783	+	187.511i	0.0612328	+	0.227010i
$827$	1235.32	+	713.212i	1.49373	+	0.862408i	0.999974	−	0.00718959i	$-0.00228854\pi$
$827$	1235.32	+	713.212i	1.49373	+	0.862408i	0.493761	+	0.869598i	$0.335622\pi$
$828$		0			0
$829$	363.827	+	630.168i	0.438875	+	0.760154i	0.997603	−	0.0691970i	$-0.0220437\pi$
$829$	363.827	+	630.168i	0.438875	+	0.760154i	−0.558728	+	0.829351i	$0.688710\pi$
$830$	331.023	+	329.922i	0.398823	+	0.397496i
$831$		0			0
$832$	801.505	−	974.822i	0.963347	−	1.17166i
$833$	−18.3549	+	104.096i	−0.0220347	+	0.124965i
$834$		0			0
$835$	721.183	+	859.473i	0.863693	+	1.02931i
$836$	−303.054	+	841.345i	−0.362504	+	1.00639i
$837$		0			0
$838$	217.946	−	153.149i	0.260078	−	0.182755i
$839$	499.135	+	594.846i	0.594916	+	0.708994i	0.976543	−	0.215323i	$-0.0690804\pi$
$839$	499.135	+	594.846i	0.594916	+	0.708994i	−0.381627	+	0.924317i	$0.624636\pi$
$840$		0			0
$841$	−115.933	+	657.488i	−0.137851	+	0.781793i
$842$	−545.989	−	380.951i	−0.648442	−	0.452436i
$843$		0			0
$844$	198.860	−	1150.19i	0.235617	−	1.36279i
$845$	446.687	+	773.684i	0.528623	+	0.915602i
$846$		0			0
$847$	1717.94	+	991.852i	2.02826	+	1.17102i
$848$	−682.217	−	1163.66i	−0.804502	−	1.37224i
$849$		0			0
$850$	8.83248	−	102.931i	0.0103912	−	0.121095i
$851$	456.391	−	543.905i	0.536299	−	0.639136i
$852$		0			0
$853$	128.733	+	46.8551i	0.150918	+	0.0549298i	0.416375	−	0.909193i	$-0.363300\pi$
$853$	128.733	+	46.8551i	0.150918	+	0.0549298i	−0.265456	+	0.964123i	$0.585523\pi$
$854$	20.9583	+	235.044i	0.0245413	+	0.275227i
$855$		0			0
$856$	257.777	−	260.367i	0.301141	−	0.304167i
$857$	−177.241	−	1005.19i	−0.206816	−	1.17291i	−0.894556	−	0.446955i	$-0.852508\pi$
$857$	−177.241	−	1005.19i	−0.206816	−	1.17291i	0.687740	−	0.725957i	$-0.258603\pi$
$858$		0			0
$859$	−3.67086	−	10.0856i	−0.00427341	−	0.0117411i	0.937538	−	0.347884i	$-0.113100\pi$
$859$	−3.67086	−	10.0856i	−0.00427341	−	0.0117411i	−0.941811	+	0.336143i	$0.890877\pi$
$860$	−323.556	+	564.753i	−0.376228	+	0.656689i
$861$		0			0
$862$	280.347	−	1053.29i	0.325229	−	1.22191i
$863$		−	761.949i		−	0.882907i	−0.897284	−	0.441454i	$-0.854463\pi$
$863$		−	761.949i		−	0.882907i	0.897284	−	0.441454i	$-0.145537\pi$
$864$		0			0
$865$	579.412			0.669840
$866$	1450.87	+	386.170i	1.67537	+	0.445924i
$867$		0			0
$868$	738.280	+	422.972i	0.850553	+	0.487295i
$869$	109.627	−	39.9009i	0.126153	−	0.0459158i
$870$		0			0
$871$	−520.799	+	91.8309i	−0.597932	+	0.105432i
$872$	−87.3336	−	86.4649i	−0.100153	−	0.0991570i
$873$		0			0
$874$	531.944	−	47.4322i	0.608631	−	0.0542702i
$875$	261.773	−	719.215i	0.299169	−	0.821960i
$876$		0			0
$877$	11.1243	+	9.33437i	0.0126845	+	0.0106435i	0.649108	−	0.760696i	$-0.275142\pi$
$877$	11.1243	+	9.33437i	0.0126845	+	0.0106435i	−0.636423	+	0.771340i	$0.719587\pi$
$878$	105.988	+	9.09488i	0.120716	+	0.0103586i
$879$		0			0
$880$	−1220.79	+	715.712i	−1.38726	+	0.813309i
$881$	357.397	−	619.030i	0.405672	−	0.702645i	−0.588727	−	0.808332i	$-0.700371\pi$
$881$	357.397	−	619.030i	0.405672	−	0.702645i	0.994399	+	0.105687i	$0.0337042\pi$
$882$		0			0
$883$	396.493	−	228.915i	0.449029	−	0.259247i	−0.258391	−	0.966040i	$-0.583192\pi$
$883$	396.493	−	228.915i	0.449029	−	0.259247i	0.707420	+	0.706793i	$0.249859\pi$
$884$	−473.103	−	81.7963i	−0.535184	−	0.0925297i
$885$		0			0
$886$	474.199	−	679.633i	0.535213	−	0.767080i
$887$	−384.736	−	67.8393i	−0.433749	−	0.0764817i	−0.0474895	−	0.998872i	$-0.515122\pi$
$887$	−384.736	−	67.8393i	−0.433749	−	0.0764817i	−0.386260	+	0.922390i	$0.626233\pi$
$888$		0			0
$889$	−101.052	+	84.7926i	−0.113669	+	0.0953797i
$890$	160.139	+	227.893i	0.179931	+	0.256059i
$891$		0			0
$892$	−1243.66	−	447.969i	−1.39424	−	0.502207i
$893$	−150.688	+	126.442i	−0.168744	+	0.141593i
$894$		0			0
$895$	−783.784	−	138.202i	−0.875737	−	0.154416i
$896$	−54.3783	+	717.879i	−0.0606901	+	0.801204i
$897$		0			0
$898$	351.445	−	352.618i	0.391364	−	0.392671i
$899$	−431.252	+	248.984i	−0.479702	+	0.276956i
$900$		0			0
$901$	−256.587	+	444.421i	−0.284780	+	0.493253i
$902$	1788.41	−	482.397i	1.98271	−	0.534808i
$903$		0			0
$904$	−1380.87	−	635.527i	−1.52751	−	0.703017i
$905$	−23.0724	−	19.3601i	−0.0254944	−	0.0213924i
$906$		0			0
$907$	−237.421	+	652.309i	−0.261765	+	0.719194i	0.737283	+	0.675584i	$0.236108\pi$
$907$	−237.421	+	652.309i	−0.261765	+	0.719194i	−0.999049	+	0.0436106i	$0.986114\pi$
$908$	386.041	−	326.125i	0.425155	−	0.359169i
$909$		0			0
$910$	−817.595	−	379.594i	−0.898456	−	0.417136i
$911$	−662.597	+	116.834i	−0.727329	+	0.128248i	−0.525039	−	0.851078i	$-0.675949\pi$
$911$	−662.597	+	116.834i	−0.727329	+	0.128248i	−0.202290	+	0.979326i	$0.564838\pi$
$912$		0			0
$913$	1176.05	−	428.048i	1.28812	−	0.468837i
$914$	969.595	−	454.098i	1.06083	−	0.496825i
$915$		0			0
$916$	179.881	+	489.140i	0.196376	+	0.533996i
$917$	−128.623			−0.140265
$918$		0			0
$919$		−	128.381i		−	0.139696i	−0.997558	−	0.0698481i	$-0.977749\pi$
$919$		−	128.381i		−	0.139696i	0.997558	−	0.0698481i	$-0.0222514\pi$
$920$	694.689	+	481.270i	0.755097	+	0.523120i
$921$		0			0
$922$	−1241.61	+	581.493i	−1.34665	+	0.630686i
$923$	117.329	+	322.359i	0.127117	+	0.349251i
$924$		0			0
$925$	−40.2479	−	228.257i	−0.0435112	−	0.246765i
$926$	−1674.46	−	777.421i	−1.80827	−	0.839547i
$927$		0			0
$928$	−347.146	−	238.789i	−0.374079	−	0.257316i
$929$	−1149.47	−	418.374i	−1.23732	−	0.450349i	−0.361223	−	0.932479i	$-0.617641\pi$
$929$	−1149.47	−	418.374i	−1.23732	−	0.450349i	−0.876099	+	0.482131i	$0.839863\pi$
$930$		0			0
$931$	−114.657	+	136.643i	−0.123155	+	0.146770i
$932$	−606.477	+	352.849i	−0.650726	+	0.378593i
$933$		0			0
$934$	289.165	−	77.9982i	0.309599	−	0.0835099i
$935$	466.241	+	269.184i	0.498653	+	0.287897i
$936$		0			0
$937$	−274.344	−	475.177i	−0.292789	−	0.507126i	0.681679	−	0.731652i	$-0.261250\pi$
$937$	−274.344	−	475.177i	−0.292789	−	0.507126i	−0.974468	+	0.224525i	$0.927917\pi$
$938$	212.964	−	213.675i	0.227041	−	0.227799i
$939$		0			0
$940$	−311.280	+	1.03722i	−0.331149	+	0.00110342i
$941$	124.148	−	704.078i	0.131932	−	0.748224i	−0.845015	−	0.534742i	$-0.820409\pi$
$941$	124.148	−	704.078i	0.131932	−	0.748224i	0.976947	−	0.213481i	$-0.0684802\pi$
$942$		0			0
$943$	−711.058	−	847.406i	−0.754038	−	0.898627i
$944$	−176.148	+	212.789i	−0.186597	+	0.225412i
$945$		0			0
$946$	1002.09	+	1426.08i	1.05930	+	1.50748i
$947$	406.774	+	484.775i	0.429540	+	0.511906i	0.936789	−	0.349894i	$-0.113782\pi$
$947$	406.774	+	484.775i	0.429540	+	0.511906i	−0.507250	+	0.861799i	$0.669338\pi$
$948$		0			0
$949$	−141.757	+	803.945i	−0.149375	+	0.847150i
$950$	99.7574	−	142.975i	0.105008	−	0.150500i
$951$		0			0
$952$	247.649	−	116.991i	0.260135	−	0.122890i
$953$	−31.0794	−	53.8310i	−0.0326121	−	0.0564859i	0.849259	−	0.527977i	$-0.177049\pi$
$953$	−31.0794	−	53.8310i	−0.0326121	−	0.0564859i	−0.881871	+	0.471491i	$0.843716\pi$
$954$		0			0
$955$	−479.396	−	276.780i	−0.501986	−	0.289822i
$956$	679.703	+	566.490i	0.710986	+	0.592562i
$957$		0			0
$958$	1133.96	+	97.3052i	1.18367	+	0.101571i
$959$	486.356	−	579.616i	0.507149	−	0.604396i
$960$		0			0
$961$	441.002	+	160.512i	0.458899	+	0.167026i
$962$	−1072.92	+	95.6698i	−1.11530	+	0.0994488i
$963$		0			0
$964$	−761.503	+	136.891i	−0.789941	+	0.142003i
$965$	191.962	+	1088.67i	0.198924	+	1.12816i
$966$		0			0
$967$	311.692	+	856.368i	0.322329	+	0.885592i	0.989991	+	0.141128i	$0.0450729\pi$
$967$	311.692	+	856.368i	0.322329	+	0.885592i	−0.667662	+	0.744464i	$0.732705\pi$
$968$	259.957	+	2809.52i	0.268551	+	2.90239i
$969$		0			0
$970$	−1227.21	−	326.638i	−1.26516	−	0.336741i
$971$		−	1749.90i		−	1.80216i	−0.433655	−	0.901079i	$-0.642776\pi$
$971$		−	1749.90i		−	1.80216i	0.433655	−	0.901079i	$-0.357224\pi$
$972$		0			0
$973$	−660.169			−0.678488
$974$	39.0359	−	146.661i	0.0400779	−	0.150576i
$975$		0			0
$976$	−255.672	+	217.454i	−0.261959	+	0.222802i
$977$	342.599	−	124.696i	0.350664	−	0.127631i	−0.160682	−	0.987006i	$-0.551369\pi$
$977$	342.599	−	124.696i	0.350664	−	0.127631i	0.511346	+	0.859375i	$0.329147\pi$
$978$		0			0
$979$	734.540	−	129.519i	0.750296	−	0.132297i
$980$	−277.815	+	49.9413i	−0.283485	+	0.0509605i
$981$		0			0
$982$	−8.81271	−	98.8329i	−0.00897424	−	0.100645i
$983$	29.4082	−	80.7983i	0.0299168	−	0.0821956i	−0.923835	−	0.382791i	$-0.874963\pi$
$983$	29.4082	−	80.7983i	0.0299168	−	0.0821956i	0.953752	+	0.300595i	$0.0971853\pi$
$984$		0			0
$985$	−1151.86	−	966.526i	−1.16940	−	0.981245i
$986$	−13.7046	+	159.709i	−0.0138992	+	0.161977i
$987$		0			0
$988$	−622.396	−	518.728i	−0.629956	−	0.525029i
$989$	520.447	−	901.441i	0.526236	−	0.911467i
$990$		0			0
$991$	−576.512	+	332.849i	−0.581747	+	0.335872i	−0.761828	−	0.647780i	$-0.775698\pi$
$991$	−576.512	+	332.849i	−0.581747	+	0.335872i	0.180080	+	0.983652i	$0.442364\pi$
$992$	115.517	+	1204.69i	0.116448	+	1.21441i
$993$		0			0
$994$	−160.492	−	111.979i	−0.161460	−	0.112655i
$995$	−725.602	−	127.943i	−0.729248	−	0.128586i
$996$		0			0
$997$	−389.011	+	326.419i	−0.390181	+	0.327401i	−0.816684	−	0.577085i	$-0.804190\pi$
$997$	−389.011	+	326.419i	−0.390181	+	0.327401i	0.426503	+	0.904486i	$0.359746\pi$
$998$	1378.01	−	968.320i	1.38077	−	0.970260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.3		204
3.2	odd	2		108.3.j.a.103.32	yes	204
4.3	odd	2	inner	324.3.j.a.199.18		204
12.11	even	2		108.3.j.a.103.17	yes	204
27.11	odd	18		108.3.j.a.43.17	✓	204
27.16	even	9	inner	324.3.j.a.127.18		204
108.11	even	18		108.3.j.a.43.32	yes	204
108.43	odd	18	inner	324.3.j.a.127.3		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.17	✓	204	27.11	odd	18
108.3.j.a.43.32	yes	204	108.11	even	18
108.3.j.a.103.17	yes	204	12.11	even	2
108.3.j.a.103.32	yes	204	3.2	odd	2
324.3.j.a.127.3		204	108.43	odd	18	inner
324.3.j.a.127.18		204	27.16	even	9	inner
324.3.j.a.199.3		204	1.1	even	1	trivial
324.3.j.a.199.18		204	4.3	odd	2	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93271 - 0.514419i) q^{2} +(3.47075 + 1.98845i) q^{4} +(3.81867 - 1.38988i) q^{5} +(-5.53905 + 0.976684i) q^{7} +(-5.68506 - 5.62851i) q^{8} +O(q^{10})\)	\(q+(-1.93271 - 0.514419i) q^{2} +(3.47075 + 1.98845i) q^{4} +(3.81867 - 1.38988i) q^{5} +(-5.53905 + 0.976684i) q^{7} +(-5.68506 - 5.62851i) q^{8} +(-8.09537 + 0.721846i) q^{10} +(-7.44387 + 20.4519i) q^{11} +(-15.1056 - 12.6751i) q^{13} +(11.2078 + 0.961743i) q^{14} +(8.09216 + 13.8028i) q^{16} +(3.04352 - 5.27153i) q^{17} +(8.89586 - 5.13603i) q^{19} +(16.0173 + 2.76929i) q^{20} +(24.9077 - 35.6983i) q^{22} +(-25.6005 - 4.51407i) q^{23} +(-6.50063 + 5.45468i) q^{25} +(22.6745 + 32.2680i) q^{26} +(-21.1667 - 7.62428i) q^{28} +(10.0865 - 8.46358i) q^{29} +(-37.2448 - 6.56727i) q^{31} +(-8.53940 - 30.8396i) q^{32} +(-8.59401 + 8.62270i) q^{34} +(-19.7943 + 11.4283i) q^{35} +(-13.6566 + 23.6539i) q^{37} +(-19.8352 + 5.35026i) q^{38} +(-29.5323 - 13.5919i) q^{40} +(32.5982 + 27.3531i) q^{41} +(-13.6950 + 37.6266i) q^{43} +(-66.5032 + 56.1815i) q^{44} +(47.1563 + 21.8938i) q^{46} +(-18.8590 + 3.32535i) q^{47} +(-16.3178 + 5.93919i) q^{49} +(15.3698 - 7.19827i) q^{50} +(-27.2240 - 74.0290i) q^{52} -84.3059 q^{53} +88.4451i q^{55} +(36.9871 + 25.6241i) q^{56} +(-23.8481 + 11.1690i) q^{58} +(5.90492 + 16.2236i) q^{59} +(3.64271 + 20.6588i) q^{61} +(68.6051 + 31.8521i) q^{62} +(0.639751 + 63.9968i) q^{64} +(-75.3005 - 27.4071i) q^{65} +(17.2385 - 20.5441i) q^{67} +(21.0454 - 12.2443i) q^{68} +(44.1357 - 11.9050i) q^{70} +(-15.0660 - 8.69838i) q^{71} +(-20.6995 - 35.8526i) q^{73} +(38.5622 - 38.6909i) q^{74} +(41.0880 - 0.136909i) q^{76} +(21.2570 - 120.554i) q^{77} +(-3.44549 - 4.10617i) q^{79} +(50.0856 + 41.4611i) q^{80} +(-48.9319 - 69.6348i) q^{82} +(-36.9625 - 44.0502i) q^{83} +(4.29539 - 24.3604i) q^{85} +(45.8242 - 65.6764i) q^{86} +(157.432 - 74.3721i) q^{88} +(-17.1351 - 29.6789i) q^{89} +(96.0505 + 55.4548i) q^{91} +(-79.8770 - 66.5725i) q^{92} +(38.1597 + 3.27449i) q^{94} +(26.8319 - 31.9770i) q^{95} +(146.828 + 53.4411i) q^{97} +(34.5928 - 3.08456i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

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