LMFDB - Embedded newform 324.3.j.a.199.12

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			199.12
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02714 - 1.71610i) q^{2} +(-1.88997 + 3.52534i) q^{4} +(-2.52245 + 0.918095i) q^{5} +(1.85168 - 0.326500i) q^{7} +(7.99108 - 0.377649i) q^{8} +O(q^{10})$	\(q+(-1.02714 - 1.71610i) q^{2} +(-1.88997 + 3.52534i) q^{4} +(-2.52245 + 0.918095i) q^{5} +(1.85168 - 0.326500i) q^{7} +(7.99108 - 0.377649i) q^{8} +(4.16644 + 3.38575i) q^{10} +(4.30945 - 11.8401i) q^{11} +(-7.78634 - 6.53352i) q^{13} +(-2.46224 - 2.84229i) q^{14} +(-8.85604 - 13.3256i) q^{16} +(-11.3753 + 19.7026i) q^{17} +(-18.9400 + 10.9350i) q^{19} +(1.53075 - 10.6276i) q^{20} +(-24.7452 + 4.76602i) q^{22} +(1.40339 + 0.247456i) q^{23} +(-13.6313 + 11.4380i) q^{25} +(-3.21448 + 20.0729i) q^{26} +(-2.34858 + 7.14486i) q^{28} +(-20.6757 + 17.3490i) q^{29} +(-32.6513 - 5.75731i) q^{31} +(-13.7716 + 28.8850i) q^{32} +(45.4956 - 0.716216i) q^{34} +(-4.37099 + 2.52359i) q^{35} +(18.4391 - 31.9375i) q^{37} +(38.2195 + 21.2711i) q^{38} +(-19.8103 + 8.28917i) q^{40} +(-1.18844 - 0.997219i) q^{41} +(7.41069 - 20.3607i) q^{43} +(33.5957 + 37.5697i) q^{44} +(-1.01682 - 2.66253i) q^{46} +(-70.2738 + 12.3912i) q^{47} +(-42.7228 + 15.5498i) q^{49} +(33.6299 + 11.6442i) q^{50} +(37.7488 - 15.1014i) q^{52} +45.3136 q^{53} +33.8225i q^{55} +(14.6736 - 3.30837i) q^{56} +(51.0094 + 17.6617i) q^{58} +(-31.4169 - 86.3172i) q^{59} +(13.6397 + 77.3544i) q^{61} +(23.6574 + 61.9464i) q^{62} +(63.7148 - 6.03565i) q^{64} +(25.6390 + 9.33183i) q^{65} +(-69.7557 + 83.1316i) q^{67} +(-47.9595 - 77.3392i) q^{68} +(8.82035 + 4.90896i) q^{70} +(29.5909 + 17.0843i) q^{71} +(20.6562 + 35.7776i) q^{73} +(-73.7472 + 1.16097i) q^{74} +(-2.75363 - 87.4367i) q^{76} +(4.11390 - 23.3311i) q^{77} +(10.0229 + 11.9448i) q^{79} +(34.5730 + 25.4823i) q^{80} +(-0.490630 + 3.06376i) q^{82} +(-49.5078 - 59.0011i) q^{83} +(10.6047 - 60.1424i) q^{85} +(-42.5527 + 8.19583i) q^{86} +(29.9658 - 96.2428i) q^{88} +(-88.0911 - 152.578i) q^{89} +(-16.5510 - 9.55571i) q^{91} +(-3.52473 + 4.47975i) q^{92} +(93.4455 + 107.869i) q^{94} +(37.7357 - 44.9717i) q^{95} +(-39.0324 - 14.2066i) q^{97} +(70.5673 + 57.3446i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.02714	−	1.71610i	−0.513570	−	0.858048i
$2$	−1.02714	−	1.71610i	−0.513570	−	0.858048i
$3$		0			0
$3$		0			0
$4$	−1.88997	+	3.52534i	−0.472492	+	0.881335i
$5$	−2.52245	+	0.918095i	−0.504489	+	0.183619i	−0.581712	−	0.813395i	$-0.697617\pi$
$5$	−2.52245	+	0.918095i	−0.504489	+	0.183619i	0.0772229	+	0.997014i	$0.475395\pi$
$6$		0			0
$7$	1.85168	−	0.326500i	0.264525	−	0.0466429i	−0.0398124	−	0.999207i	$-0.512676\pi$
$7$	1.85168	−	0.326500i	0.264525	−	0.0466429i	0.304338	+	0.952564i	$0.401565\pi$
$8$	7.99108	−	0.377649i	0.998885	−	0.0472061i
$9$		0			0
$10$	4.16644	+	3.38575i	0.416644	+	0.338575i
$11$	4.30945	−	11.8401i	0.391768	−	1.07637i	−0.574426	−	0.818557i	$-0.694775\pi$
$11$	4.30945	−	11.8401i	0.391768	−	1.07637i	0.966194	−	0.257817i	$-0.0830032\pi$
$12$		0			0
$13$	−7.78634	−	6.53352i	−0.598949	−	0.502578i	0.292158	−	0.956370i	$-0.405627\pi$
$13$	−7.78634	−	6.53352i	−0.598949	−	0.502578i	−0.891108	+	0.453792i	$0.850071\pi$
$14$	−2.46224	−	2.84229i	−0.175874	−	0.203021i
$15$		0			0
$16$	−8.85604	−	13.3256i	−0.553502	−	0.832848i
$17$	−11.3753	+	19.7026i	−0.669136	+	1.15898i	0.309010	+	0.951059i	$0.400003\pi$
$17$	−11.3753	+	19.7026i	−0.669136	+	1.15898i	−0.978146	+	0.207919i	$0.933331\pi$
$18$		0			0
$19$	−18.9400	+	10.9350i	−0.996842	+	0.575527i	−0.907312	−	0.420457i	$-0.861870\pi$
$19$	−18.9400	+	10.9350i	−0.996842	+	0.575527i	−0.0895295	+	0.995984i	$0.528536\pi$
$20$	1.53075	−	10.6276i	0.0765373	−	0.531382i
$21$		0			0
$22$	−24.7452	+	4.76602i	−1.12478	+	0.216637i
$23$	1.40339	+	0.247456i	0.0610170	+	0.0107589i	0.204073	−	0.978956i	$-0.434582\pi$
$23$	1.40339	+	0.247456i	0.0610170	+	0.0107589i	−0.143056	+	0.989715i	$0.545693\pi$
$24$		0			0
$25$	−13.6313	+	11.4380i	−0.545251	+	0.457520i
$26$	−3.21448	+	20.0729i	−0.123634	+	0.772036i
$27$		0			0
$28$	−2.34858	+	7.14486i	−0.0838780	+	0.255174i
$29$	−20.6757	+	17.3490i	−0.712957	+	0.598242i	−0.925427	−	0.378926i	$-0.876294\pi$
$29$	−20.6757	+	17.3490i	−0.712957	+	0.598242i	0.212470	+	0.977168i	$0.431849\pi$
$30$		0			0
$31$	−32.6513	−	5.75731i	−1.05327	−	0.185720i	−0.379901	−	0.925027i	$-0.624042\pi$
$31$	−32.6513	−	5.75731i	−1.05327	−	0.185720i	−0.673368	+	0.739308i	$0.735153\pi$
$32$	−13.7716	+	28.8850i	−0.430361	+	0.902657i
$33$		0			0
$34$	45.4956	−	0.716216i	1.33811	−	0.0210652i
$35$	−4.37099	+	2.52359i	−0.124885	+	0.0721027i
$36$		0			0
$37$	18.4391	−	31.9375i	0.498354	−	0.863174i	−0.501644	−	0.865074i	$-0.667271\pi$
$37$	18.4391	−	31.9375i	0.498354	−	0.863174i	0.999998	+	0.00189967i	$0.000604684\pi$
$38$	38.2195	+	21.2711i	1.00578	+	0.559765i
$39$		0			0
$40$	−19.8103	+	8.28917i	−0.495259	+	0.207229i
$41$	−1.18844	−	0.997219i	−0.0289863	−	0.0243224i	0.628179	−	0.778069i	$-0.283800\pi$
$41$	−1.18844	−	0.997219i	−0.0289863	−	0.0243224i	−0.657166	+	0.753746i	$0.728245\pi$
$42$		0			0
$43$	7.41069	−	20.3607i	0.172342	−	0.473504i	−0.823208	−	0.567739i	$-0.807818\pi$
$43$	7.41069	−	20.3607i	0.172342	−	0.473504i	0.995550	+	0.0942347i	$0.0300404\pi$
$44$	33.5957	+	37.5697i	0.763539	+	0.853857i
$45$		0			0
$46$	−1.01682	−	2.66253i	−0.0221048	−	0.0578810i
$47$	−70.2738	+	12.3912i	−1.49519	+	0.263642i	−0.860629	−	0.509233i	$-0.829929\pi$
$47$	−70.2738	+	12.3912i	−1.49519	+	0.263642i	−0.634559	+	0.772875i	$0.718818\pi$
$48$		0			0
$49$	−42.7228	+	15.5498i	−0.871895	+	0.317344i
$50$	33.6299	+	11.6442i	0.672599	+	0.232883i
$51$		0			0
$52$	37.7488	−	15.1014i	0.725938	−	0.290411i
$53$	45.3136			0.854973			0.427487	−	0.904022i	$-0.359399\pi$
$53$	45.3136			0.854973			0.427487	+	0.904022i	$0.359399\pi$
$54$		0			0
$55$			33.8225i			0.614955i
$56$	14.6736	−	3.30837i	0.262028	−	0.0590781i
$57$		0			0
$58$	51.0094	+	17.6617i	0.879473	+	0.304512i
$59$	−31.4169	−	86.3172i	−0.532490	−	1.46300i	−0.856099	−	0.516812i	$-0.827119\pi$
$59$	−31.4169	−	86.3172i	−0.532490	−	1.46300i	0.323609	−	0.946191i	$-0.395104\pi$
$60$		0			0
$61$	13.6397	+	77.3544i	0.223601	+	1.26810i	0.865342	+	0.501183i	$0.167102\pi$
$61$	13.6397	+	77.3544i	0.223601	+	1.26810i	−0.641740	+	0.766922i	$0.721787\pi$
$62$	23.6574	+	61.9464i	0.381571	+	0.999135i
$63$		0			0
$64$	63.7148	−	6.03565i	0.995543	−	0.0943070i
$65$	25.6390	+	9.33183i	0.394446	+	0.143567i
$66$		0			0
$67$	−69.7557	+	83.1316i	−1.04113	+	1.24077i	−0.0711805	+	0.997463i	$0.522677\pi$
$67$	−69.7557	+	83.1316i	−1.04113	+	1.24077i	−0.969949	+	0.243307i	$0.921768\pi$
$68$	−47.9595	−	77.3392i	−0.705286	−	1.13734i
$69$		0			0
$70$	8.82035	+	4.90896i	0.126005	+	0.0701280i
$71$	29.5909	+	17.0843i	0.416774	+	0.240624i	0.693696	−	0.720268i	$-0.255981\pi$
$71$	29.5909	+	17.0843i	0.416774	+	0.240624i	−0.276922	+	0.960892i	$0.589314\pi$
$72$		0			0
$73$	20.6562	+	35.7776i	0.282962	+	0.490104i	0.972113	−	0.234513i	$-0.0753497\pi$
$73$	20.6562	+	35.7776i	0.282962	+	0.490104i	−0.689151	+	0.724618i	$0.742016\pi$
$74$	−73.7472	+	1.16097i	−0.996584	+	0.0156888i
$75$		0			0
$76$	−2.75363	−	87.4367i	−0.0362320	−	1.15048i
$77$	4.11390	−	23.3311i	0.0534273	−	0.303001i
$78$		0			0
$79$	10.0229	+	11.9448i	0.126872	+	0.151200i	0.825741	−	0.564050i	$-0.190757\pi$
$79$	10.0229	+	11.9448i	0.126872	+	0.151200i	−0.698869	+	0.715250i	$0.746313\pi$
$80$	34.5730	+	25.4823i	0.432162	+	0.318529i
$81$		0			0
$82$	−0.490630	+	3.06376i	−0.00598329	+	0.0373629i
$83$	−49.5078	−	59.0011i	−0.596480	−	0.710857i	0.380358	−	0.924839i	$-0.375801\pi$
$83$	−49.5078	−	59.0011i	−0.596480	−	0.710857i	−0.976837	+	0.213983i	$0.931356\pi$
$84$		0			0
$85$	10.6047	−	60.1424i	0.124762	−	0.707558i
$86$	−42.5527	+	8.19583i	−0.494799	+	0.0953003i
$87$		0			0
$88$	29.9658	−	96.2428i	0.340520	−	1.09367i
$89$	−88.0911	−	152.578i	−0.989788	−	1.71436i	−0.618343	−	0.785908i	$-0.712196\pi$
$89$	−88.0911	−	152.578i	−0.989788	−	1.71436i	−0.371445	−	0.928455i	$-0.621138\pi$
$90$		0			0
$91$	−16.5510	−	9.55571i	−0.181879	−	0.105008i
$92$	−3.52473	+	4.47975i	−0.0383123	+	0.0486929i
$93$		0			0
$94$	93.4455	+	107.869i	0.994101	+	1.14754i
$95$	37.7357	−	44.9717i	0.397218	−	0.473386i
$96$		0			0
$97$	−39.0324	−	14.2066i	−0.402396	−	0.146460i	0.132891	−	0.991131i	$-0.457574\pi$
$97$	−39.0324	−	14.2066i	−0.402396	−	0.146460i	−0.535286	+	0.844671i	$0.679796\pi$
$98$	70.5673	+	57.3446i	0.720075	+	0.585149i
$99$		0			0
$100$	−14.5602	−	69.6724i	−0.145602	−	0.696724i
$101$	8.53432	+	48.4005i	0.0844982	+	0.479213i	0.997464	+	0.0711764i	$0.0226753\pi$
$101$	8.53432	+	48.4005i	0.0844982	+	0.479213i	−0.912966	+	0.408037i	$0.866214\pi$
$102$		0			0
$103$	−59.5132	−	163.511i	−0.577798	−	1.58749i	−0.791883	−	0.610672i	$-0.790899\pi$
$103$	−59.5132	−	163.511i	−0.577798	−	1.58749i	0.214085	−	0.976815i	$-0.431323\pi$
$104$	−64.6887	−	49.2693i	−0.622006	−	0.473744i
$105$		0			0
$106$	−46.5434	−	77.7624i	−0.439088	−	0.733608i
$107$			15.1974i			0.142032i	0.997475	+	0.0710159i	$0.0226241\pi$
$107$			15.1974i			0.142032i	−0.997475	+	0.0710159i	$0.977376\pi$
$108$		0			0
$109$	191.484			1.75673			0.878367	−	0.477986i	$-0.158633\pi$
$109$	191.484			1.75673			0.878367	+	0.477986i	$0.158633\pi$
$110$	58.0427	−	34.7405i	0.527661	−	0.315822i
$111$		0			0
$112$	−20.7493	−	21.7831i	−0.185262	−	0.194492i
$113$	88.5939	−	32.2455i	0.784017	−	0.285359i	0.0811703	−	0.996700i	$-0.474134\pi$
$113$	88.5939	−	32.2455i	0.784017	−	0.285359i	0.702847	+	0.711341i	$0.251912\pi$
$114$		0			0
$115$	−3.76717	+	0.664253i	−0.0327580	+	0.00577611i
$116$	−22.0846	−	105.678i	−0.190385	−	0.911018i
$117$		0			0
$118$	−115.859	+	142.574i	−0.981856	+	1.20826i
$119$	−14.6305	+	40.1969i	−0.122945	+	0.337789i
$120$		0			0
$121$	−28.9256	−	24.2714i	−0.239054	−	0.200590i
$122$	118.738	−	102.861i	0.973260	−	0.843121i
$123$		0			0
$124$	82.0064	−	104.226i	0.661342	−	0.840531i
$125$	57.4371	−	99.4840i	0.459497	−	0.795872i
$126$		0			0
$127$	5.73249	−	3.30965i	0.0451377	−	0.0260603i	−0.477261	−	0.878761i	$-0.658370\pi$
$127$	5.73249	−	3.30965i	0.0451377	−	0.0260603i	0.522399	+	0.852701i	$0.325037\pi$
$128$	−75.8017	−	103.141i	−0.592201	−	0.805790i
$129$		0			0
$130$	−10.3205	−	53.5841i	−0.0793886	−	0.412185i
$131$	74.2972	+	13.1006i	0.567154	+	0.100005i	0.449870	−	0.893094i	$-0.351470\pi$
$131$	74.2972	+	13.1006i	0.567154	+	0.100005i	0.117284	+	0.993098i	$0.462581\pi$
$132$		0			0
$133$	−31.5004	+	26.4320i	−0.236845	+	0.198737i
$134$	214.311	+	34.3197i	1.59933	+	0.256117i
$135$		0			0
$136$	−83.4604	+	161.741i	−0.613680	+	1.18927i
$137$	−178.270	+	149.586i	−1.30124	+	1.09187i	−0.311312	+	0.950308i	$0.600768\pi$
$137$	−178.270	+	149.586i	−1.30124	+	1.09187i	−0.989929	+	0.141563i	$0.954787\pi$
$138$		0			0
$139$	90.5189	+	15.9609i	0.651215	+	0.114827i	0.489490	−	0.872009i	$-0.337183\pi$
$139$	90.5189	+	15.9609i	0.651215	+	0.114827i	0.161725	+	0.986836i	$0.448294\pi$
$140$	−0.635486	−	20.1787i	−0.00453919	−	0.144134i
$141$		0			0
$142$	−1.07567	−	68.3289i	−0.00757513	−	0.481189i
$143$	−110.912	+	64.0353i	−0.775611	+	0.447799i
$144$		0			0
$145$	36.2254	−	62.7442i	0.249830	−	0.432719i
$146$	40.1810	−	72.1967i	0.275212	−	0.494498i
$147$		0			0
$148$	77.7410	+	125.365i	0.525277	+	0.847060i
$149$	176.662	+	148.237i	1.18565	+	0.994877i	0.999925	+	0.0122747i	$0.00390724\pi$
$149$	176.662	+	148.237i	1.18565	+	0.994877i	0.185723	+	0.982602i	$0.440537\pi$
$150$		0			0
$151$	69.7867	−	191.737i	0.462164	−	1.26978i	−0.461691	−	0.887041i	$-0.652757\pi$
$151$	69.7867	−	191.737i	0.462164	−	1.26978i	0.923855	−	0.382744i	$-0.125021\pi$
$152$	−147.221	+	94.5352i	−0.968562	+	0.621942i
$153$		0			0
$154$	−44.2639	+	16.9044i	−0.287428	+	0.109769i
$155$	87.6469	−	15.4545i	0.565464	−	0.0997066i
$156$		0			0
$157$	−58.9986	+	21.4737i	−0.375787	+	0.136775i	−0.523007	−	0.852329i	$-0.675190\pi$
$157$	−58.9986	+	21.4737i	−0.375787	+	0.136775i	0.147220	+	0.989104i	$0.452968\pi$
$158$	10.2035	−	29.4692i	0.0645792	−	0.186514i
$159$		0			0
$160$	8.21879	−	85.5045i	0.0513675	−	0.534403i
$161$	2.67942			0.0166424
$162$		0			0
$163$			53.0284i			0.325327i	0.986682	+	0.162664i	$0.0520085\pi$
$163$			53.0284i			0.325327i	−0.986682	+	0.162664i	$0.947991\pi$
$164$	5.76165	−	2.30494i	0.0351320	−	0.0140545i
$165$		0			0
$166$	−50.4001	+	145.563i	−0.303615	+	0.876883i
$167$	7.20265	+	19.7891i	0.0431296	+	0.118498i	0.959388	−	0.282091i	$-0.0910279\pi$
$167$	7.20265	+	19.7891i	0.0431296	+	0.118498i	−0.916258	+	0.400588i	$0.868806\pi$
$168$		0			0
$169$	−11.4063	−	64.6882i	−0.0674927	−	0.382770i
$170$	−114.103	+	43.5759i	−0.671192	+	0.256329i
$171$		0			0
$172$	57.7724	+	64.6063i	0.335886	+	0.375618i
$173$	−152.957	−	55.6719i	−0.884146	−	0.321803i	−0.140264	−	0.990114i	$-0.544795\pi$
$173$	−152.957	−	55.6719i	−0.884146	−	0.321803i	−0.743882	+	0.668311i	$0.767017\pi$
$174$		0			0
$175$	−21.5062	+	25.6301i	−0.122893	+	0.146458i
$176$	−195.941	+	47.4307i	−1.11330	+	0.269492i
$177$		0			0
$178$	−171.357	+	307.892i	−0.962680	+	1.72973i
$179$	58.2296	+	33.6189i	0.325305	+	0.187815i	0.653755	−	0.756707i	$-0.273193\pi$
$179$	58.2296	+	33.6189i	0.325305	+	0.187815i	−0.328450	+	0.944521i	$0.606526\pi$
$180$		0			0
$181$	45.2742	+	78.4172i	0.250134	+	0.433244i	0.963562	−	0.267484i	$-0.0861922\pi$
$181$	45.2742	+	78.4172i	0.250134	+	0.433244i	−0.713429	+	0.700728i	$0.752859\pi$
$182$	0.601649	+	38.2181i	0.00330577	+	0.209990i
$183$		0			0
$184$	11.3081	+	1.44745i	0.0614569	+	0.00786658i
$185$	−17.1900	+	97.4893i	−0.0929189	+	0.526969i
$186$		0			0
$187$	184.260	+	219.593i	0.985348	+	1.17429i
$188$	89.1322	−	271.158i	0.474108	−	1.44233i
$189$		0			0
$190$	−115.936	−	18.5659i	−0.610187	−	0.0977153i
$191$	170.551	+	203.255i	0.892937	+	1.06416i	0.997571	+	0.0696500i	$0.0221882\pi$
$191$	170.551	+	203.255i	0.892937	+	1.06416i	−0.104635	+	0.994511i	$0.533367\pi$
$192$		0			0
$193$	33.5576	−	190.314i	0.173873	−	0.986085i	−0.765563	−	0.643361i	$-0.777539\pi$
$193$	33.5576	−	190.314i	0.173873	−	0.986085i	0.939436	−	0.342724i	$-0.111349\pi$
$194$	15.7118	+	81.5755i	0.0809886	+	0.420492i
$195$		0			0
$196$	25.9263	−	180.001i	0.132277	−	0.918374i
$197$	−152.517	−	264.168i	−0.774200	−	1.34095i	−0.935243	−	0.354007i	$-0.884819\pi$
$197$	−152.517	−	264.168i	−0.774200	−	1.34095i	0.161042	−	0.986947i	$-0.448514\pi$
$198$		0			0
$199$	185.833	+	107.290i	0.933832	+	0.539148i	0.888021	−	0.459802i	$-0.152080\pi$
$199$	185.833	+	107.290i	0.933832	+	0.539148i	0.0458104	+	0.998950i	$0.485413\pi$
$200$	−104.609	+	96.5498i	−0.523046	+	0.482749i
$201$		0			0
$202$	74.2940	−	64.3598i	0.367792	−	0.318613i
$203$	−32.6203	+	38.8754i	−0.160691	+	0.191504i
$204$		0			0
$205$	3.91331	+	1.42433i	0.0190893	+	0.00694795i
$206$	−219.472	+	270.079i	−1.06540	+	1.31106i
$207$		0			0
$208$	−18.1066	+	161.618i	−0.0870511	+	0.777012i
$209$	47.8508	+	271.376i	0.228951	+	1.29845i
$210$		0			0
$211$	26.5454	+	72.9330i	0.125808	+	0.345654i	0.986567	−	0.163359i	$-0.0522328\pi$
$211$	26.5454	+	72.9330i	0.125808	+	0.345654i	−0.860759	+	0.509013i	$0.830011\pi$
$212$	−85.6412	+	159.746i	−0.403968	+	0.753518i
$213$		0			0
$214$	26.0802	−	15.6098i	0.121870	−	0.0729432i
$215$			58.1624i			0.270523i
$216$		0			0
$217$	−62.3394			−0.287279
$218$	−196.681	−	328.605i	−0.902206	−	1.50736i
$219$		0			0
$220$	−119.236	−	63.9235i	−0.541981	−	0.290561i
$221$	217.300	−	79.0906i	0.983256	−	0.357876i
$222$		0			0
$223$	−177.451	+	31.2894i	−0.795746	+	0.140311i	−0.556718	−	0.830701i	$-0.687940\pi$
$223$	−177.451	+	31.2894i	−0.795746	+	0.140311i	−0.239027	+	0.971013i	$0.576829\pi$
$224$	−16.0695	+	57.9821i	−0.0717387	+	0.258849i
$225$		0			0
$226$	−146.335	−	118.915i	−0.647499	−	0.526172i
$227$	−37.5673	+	103.215i	−0.165495	+	0.454693i	−0.994524	−	0.104513i	$-0.966672\pi$
$227$	−37.5673	+	103.215i	−0.165495	+	0.454693i	0.829029	+	0.559206i	$0.188894\pi$
$228$		0			0
$229$	−143.379	−	120.309i	−0.626110	−	0.525368i	0.273608	−	0.961841i	$-0.411783\pi$
$229$	−143.379	−	120.309i	−0.626110	−	0.525368i	−0.899717	+	0.436473i	$0.856227\pi$
$230$	5.00933	+	5.78254i	0.0217797	+	0.0251415i
$231$		0			0
$232$	−158.670	+	146.446i	−0.683921	+	0.631231i
$233$	−111.657	+	193.395i	−0.479213	+	0.830022i	−0.999716	−	0.0238385i	$-0.992411\pi$
$233$	−111.657	+	193.395i	−0.479213	+	0.830022i	0.520503	+	0.853860i	$0.325745\pi$
$234$		0			0
$235$	165.886	−	95.7741i	0.705896	−	0.407549i
$236$	363.674	+	52.3816i	1.54099	+	0.221956i
$237$		0			0
$238$	84.0093	−	16.1805i	0.352980	−	0.0679855i
$239$	88.4519	+	15.5965i	0.370092	+	0.0652571i	0.355601	−	0.934638i	$-0.384276\pi$
$239$	88.4519	+	15.5965i	0.370092	+	0.0652571i	0.0144906	+	0.999895i	$0.495387\pi$
$240$		0			0
$241$	−327.504	+	274.809i	−1.35894	+	1.14028i	−0.382630	+	0.923902i	$0.624982\pi$
$241$	−327.504	+	274.809i	−1.35894	+	1.14028i	−0.976309	+	0.216383i	$0.930574\pi$
$242$	−11.9415	+	74.5692i	−0.0493451	+	0.308137i
$243$		0			0
$244$	−298.479	−	98.1129i	−1.22327	−	0.402102i
$245$	93.4898	−	78.4472i	0.381591	−	0.320193i
$246$		0			0
$247$	218.917	+	38.6010i	0.886305	+	0.156279i
$248$	−263.094	−	33.6764i	−1.06086	−	0.135792i
$249$		0			0
$250$	−229.720	+	3.61637i	−0.918880	+	0.0144655i
$251$	121.486	−	70.1402i	0.484009	−	0.279443i	−0.238077	−	0.971246i	$-0.576517\pi$
$251$	121.486	−	70.1402i	0.484009	−	0.279443i	0.722086	+	0.691804i	$0.243184\pi$
$252$		0			0
$253$	8.97775	−	15.5499i	0.0354852	−	0.0614621i
$254$	−11.5677	−	6.43802i	−0.0455423	−	0.0253465i
$255$		0			0
$256$	−99.1412	+	236.023i	−0.387270	+	0.921966i
$257$	32.0824	+	26.9203i	0.124834	+	0.104748i	0.703067	−	0.711123i	$-0.251813\pi$
$257$	32.0824	+	26.9203i	0.124834	+	0.104748i	−0.578233	+	0.815872i	$0.696258\pi$
$258$		0			0
$259$	23.7156	−	65.1582i	0.0915662	−	0.251576i
$260$	−81.3548	+	72.7493i	−0.312903	+	0.279805i
$261$		0			0
$262$	−53.8317	−	140.957i	−0.205465	−	0.538005i
$263$	195.884	−	34.5397i	0.744807	−	0.131330i	0.211649	−	0.977346i	$-0.432117\pi$
$263$	195.884	−	34.5397i	0.744807	−	0.131330i	0.533157	+	0.846016i	$0.321005\pi$
$264$		0			0
$265$	−114.301	+	41.6022i	−0.431325	+	0.156989i
$266$	77.7152	+	26.9084i	0.292162	+	0.101159i
$267$		0			0
$268$	−161.231	−	403.029i	−0.601608	−	1.50384i
$269$	242.821			0.902680			0.451340	−	0.892352i	$-0.350946\pi$
$269$	242.821			0.902680			0.451340	+	0.892352i	$0.350946\pi$
$270$		0			0
$271$		−	429.609i		−	1.58527i	−0.609694	−	0.792637i	$-0.708708\pi$
$271$		−	429.609i		−	1.58527i	0.609694	−	0.792637i	$-0.291292\pi$
$272$	363.289	−	22.9047i	1.33562	−	0.0842085i
$273$		0			0
$274$	439.813	+	152.282i	1.60516	+	0.555775i
$275$	76.6839	+	210.687i	0.278851	+	0.766136i
$276$		0			0
$277$	90.9166	+	515.614i	0.328219	+	1.86142i	0.486016	+	0.873950i	$0.338450\pi$
$277$	90.9166	+	515.614i	0.328219	+	1.86142i	−0.157797	+	0.987472i	$0.550439\pi$
$278$	−65.5851	−	171.733i	−0.235917	−	0.617745i
$279$		0			0
$280$	−33.9759	+	21.8169i	−0.121343	+	0.0779177i
$281$	−155.942	−	56.7582i	−0.554953	−	0.201986i	0.0492926	−	0.998784i	$-0.484303\pi$
$281$	−155.942	−	56.7582i	−0.554953	−	0.201986i	−0.604246	+	0.796798i	$0.706526\pi$
$282$		0			0
$283$	132.169	−	157.512i	0.467027	−	0.556581i	−0.480194	−	0.877162i	$-0.659434\pi$
$283$	132.169	−	157.512i	0.467027	−	0.556581i	0.947221	+	0.320581i	$0.103878\pi$
$284$	−116.154	+	72.0292i	−0.408993	+	0.253624i
$285$		0			0
$286$	223.813	+	124.563i	0.782564	+	0.435535i
$287$	−2.52620	−	1.45850i	−0.00880208	−	0.00508188i
$288$		0			0
$289$	−114.296	−	197.966i	−0.395487	−	0.685004i
$290$	−144.884	+	2.28083i	−0.499599	+	0.00786495i
$291$		0			0
$292$	−165.168	+	5.20161i	−0.565643	+	0.0178137i
$293$	42.2405	−	239.558i	0.144166	−	0.817603i	−0.823868	−	0.566782i	$-0.808188\pi$
$293$	42.2405	−	239.558i	0.144166	−	0.817603i	0.968033	−	0.250821i	$-0.0807007\pi$
$294$		0			0
$295$	158.495	+	188.887i	0.537270	+	0.640294i
$296$	135.287	−	262.178i	0.457051	−	0.885737i
$297$		0			0
$298$	72.9322	−	455.428i	0.244739	−	1.52828i
$299$	−9.31053	−	11.0959i	−0.0311389	−	0.0371099i
$300$		0			0
$301$	7.07441	−	40.1210i	0.0235030	−	0.133292i
$302$	−400.721	+	77.1804i	−1.32689	+	0.255564i
$303$		0			0
$304$	313.448	+	155.545i	1.03108	+	0.511662i
$305$	−105.424	−	182.600i	−0.345652	−	0.598687i
$306$		0			0
$307$	−452.918	−	261.492i	−1.47530	−	0.851766i	−0.475690	−	0.879613i	$-0.657801\pi$
$307$	−452.918	−	261.492i	−1.47530	−	0.851766i	−0.999612	+	0.0278473i	$0.991135\pi$
$308$	74.4749	+	58.5979i	0.241802	+	0.190253i
$309$		0			0
$310$	−116.547	−	134.537i	−0.375958	−	0.433989i
$311$	−86.2078	+	102.739i	−0.277196	+	0.330349i	−0.886623	−	0.462493i	$-0.846955\pi$
$311$	−86.2078	+	102.739i	−0.277196	+	0.330349i	0.609427	+	0.792842i	$0.291399\pi$
$312$		0			0
$313$	59.2351	+	21.5598i	0.189250	+	0.0688812i	0.434907	−	0.900476i	$-0.356781\pi$
$313$	59.2351	+	21.5598i	0.189250	+	0.0688812i	−0.245657	+	0.969357i	$0.579004\pi$
$314$	97.4507	+	79.1907i	0.310353	+	0.252200i
$315$		0			0
$316$	−61.0523	+	12.7587i	−0.193204	+	0.0403757i
$317$	−30.8465	−	174.939i	−0.0973077	−	0.551859i	−0.994016	−	0.109237i	$-0.965159\pi$
$317$	−30.8465	−	174.939i	−0.0973077	−	0.551859i	0.896708	−	0.442622i	$-0.145952\pi$
$318$		0			0
$319$	116.313	+	319.568i	0.364618	+	1.00178i
$320$	−155.176	+	73.7208i	−0.484924	+	0.230377i
$321$		0			0
$322$	−2.75214	−	4.59814i	−0.00854701	−	0.0142799i
$323$		−	497.557i		−	1.54042i
$324$		0			0
$325$	180.868			0.556517
$326$	91.0017	−	54.4675i	0.279146	−	0.167078i
$327$		0			0
$328$	−9.87351	−	7.52004i	−0.0301022	−	0.0229270i
$329$	−126.079	+	45.8889i	−0.383218	+	0.139480i
$330$		0			0
$331$	−493.266	+	86.9762i	−1.49023	+	0.262768i	−0.858658	−	0.512549i	$-0.828701\pi$
$331$	−493.266	+	86.9762i	−1.49023	+	0.262768i	−0.631572	+	0.775317i	$0.717590\pi$
$332$	301.567	−	63.0216i	0.908335	−	0.189824i
$333$		0			0
$334$	26.5619	−	32.6866i	0.0795266	−	0.0978641i
$335$	99.6322	−	273.737i	0.297410	−	0.817126i
$336$		0			0
$337$	−178.088	−	149.433i	−0.528450	−	0.443423i	0.339116	−	0.940745i	$-0.389872\pi$
$337$	−178.088	−	149.433i	−0.528450	−	0.443423i	−0.867566	+	0.497322i	$0.834317\pi$
$338$	−99.2953	+	86.0180i	−0.293773	+	0.254491i
$339$		0			0
$340$	191.980	+	151.053i	0.564647	+	0.444272i
$341$	−208.876	+	361.785i	−0.612541	+	1.06095i
$342$		0			0
$343$	−153.820	+	88.8082i	−0.448456	+	0.258916i
$344$	51.5302	−	165.503i	0.149797	−	0.481112i
$345$		0			0
$346$	61.5702	+	319.672i	0.177948	+	0.923908i
$347$	−518.270	−	91.3849i	−1.49357	−	0.263357i	−0.633586	−	0.773673i	$-0.718418\pi$
$347$	−518.270	−	91.3849i	−1.49357	−	0.263357i	−0.859987	+	0.510315i	$0.829529\pi$
$348$		0			0
$349$	496.502	−	416.615i	1.42264	−	1.19374i	0.472736	−	0.881204i	$-0.343266\pi$
$349$	496.502	−	416.615i	1.42264	−	1.19374i	0.949906	−	0.312535i	$-0.101178\pi$
$350$	66.0736	+	10.5810i	0.188782	+	0.0302315i
$351$		0			0
$352$	282.654	+	287.535i	0.802995	+	0.816862i
$353$	42.6928	−	35.8235i	0.120943	−	0.101483i	−0.580310	−	0.814395i	$-0.697069\pi$
$353$	42.6928	−	35.8235i	0.120943	−	0.101483i	0.701253	+	0.712912i	$0.252624\pi$
$354$		0			0
$355$	−90.3266	−	15.9270i	−0.254441	−	0.0448648i
$356$	704.380	−	22.1829i	1.97860	−	0.0623116i
$357$		0			0
$358$	−2.11672	−	134.459i	−0.00591263	−	0.375583i
$359$	−359.255	+	207.416i	−1.00071	+	0.577761i	−0.908459	−	0.417975i	$-0.862740\pi$
$359$	−359.255	+	207.416i	−1.00071	+	0.577761i	−0.0922526	+	0.995736i	$0.529407\pi$
$360$		0			0
$361$	58.6489	−	101.583i	0.162462	−	0.281393i
$362$	88.0684	−	158.240i	0.243283	−	0.437128i
$363$		0			0
$364$	64.9679	−	40.2878i	0.178483	−	0.110681i
$365$	−84.9514	−	71.2827i	−0.232744	−	0.195295i
$366$		0			0
$367$	85.5131	−	234.945i	0.233006	−	0.640178i	−0.766993	−	0.641655i	$-0.778248\pi$
$367$	85.5131	−	234.945i	0.233006	−	0.640178i	0.999999	+	0.00147719i	$0.000470204\pi$
$368$	−9.13100	−	20.8925i	−0.0248125	−	0.0567730i
$369$		0			0
$370$	184.957	−	70.6354i	0.499885	−	0.190907i
$371$	83.9061	−	14.7949i	0.226162	−	0.0398784i
$372$		0			0
$373$	443.095	−	161.273i	1.18792	−	0.432368i	0.328928	−	0.944355i	$-0.393313\pi$
$373$	443.095	−	161.273i	1.18792	−	0.432368i	0.858993	+	0.511987i	$0.171090\pi$
$374$	187.581	−	541.760i	0.501554	−	1.44856i
$375$		0			0
$376$	−556.884	+	125.558i	−1.48108	+	0.333930i
$377$	274.338			0.727688
$378$		0			0
$379$			28.5744i			0.0753941i	0.999289	+	0.0376970i	$0.0120022\pi$
$379$			28.5744i			0.0753941i	−0.999289	+	0.0376970i	$0.987998\pi$
$380$	87.2211	+	218.026i	0.229529	+	0.573753i
$381$		0			0
$382$	173.625	−	501.453i	0.454515	−	1.31270i
$383$	52.2463	+	143.546i	0.136413	+	0.374793i	0.989024	−	0.147754i	$-0.0472043\pi$
$383$	52.2463	+	143.546i	0.136413	+	0.374793i	−0.852611	+	0.522546i	$0.824982\pi$
$384$		0			0
$385$	11.0431	+	62.6284i	0.0286833	+	0.162671i
$386$	−361.066	+	137.891i	−0.935404	+	0.357232i
$387$		0			0
$388$	123.853	−	110.752i	0.319209	−	0.285444i
$389$	403.304	+	146.791i	1.03677	+	0.377354i	0.803655	−	0.595095i	$-0.202886\pi$
$389$	403.304	+	146.791i	1.03677	+	0.377354i	0.233116	+	0.972449i	$0.425108\pi$
$390$		0			0
$391$	−20.8396	+	24.8356i	−0.0532981	+	0.0635182i
$392$	−335.529	+	140.394i	−0.855942	+	0.358149i
$393$		0			0
$394$	−296.681	+	533.072i	−0.752997	+	1.35297i
$395$	−36.2486	−	20.9281i	−0.0917685	−	0.0529826i
$396$		0			0
$397$	98.7305	+	171.006i	0.248691	+	0.430746i	0.963163	−	0.268918i	$-0.0866661\pi$
$397$	98.7305	+	171.006i	0.248691	+	0.430746i	−0.714472	+	0.699665i	$0.753333\pi$
$398$	−6.75525	−	429.109i	−0.0169730	−	1.07816i
$399$		0			0
$400$	273.137	+	80.3491i	0.682842	+	0.200873i
$401$	−64.7384	+	367.150i	−0.161442	+	0.915585i	0.791215	+	0.611538i	$0.209449\pi$
$401$	−64.7384	+	367.150i	−0.161442	+	0.915585i	−0.952657	+	0.304047i	$0.901662\pi$
$402$		0			0
$403$	216.619	+	258.156i	0.537516	+	0.640586i
$404$	−186.758	−	61.3891i	−0.462272	−	0.151953i
$405$		0			0
$406$	100.220	+	16.0491i	0.246846	+	0.0395299i
$407$	−298.681	−	355.954i	−0.733859	−	0.874579i
$408$		0			0
$409$	−22.7435	+	128.985i	−0.0556075	+	0.315366i	−0.999906	−	0.0137248i	$-0.995631\pi$
$409$	−22.7435	+	128.985i	−0.0556075	+	0.315366i	0.944298	+	0.329091i	$0.106742\pi$
$410$	−1.57523	−	8.17860i	−0.00384203	−	0.0199478i
$411$		0			0
$412$	688.911	+	99.2268i	1.67211	+	0.240842i
$413$	−86.3565	−	149.574i	−0.209096	−	0.362164i
$414$		0			0
$415$	179.049	+	103.374i	0.431444	+	0.249094i
$416$	295.951	−	134.932i	0.711420	−	0.324356i
$417$		0			0
$418$	416.557	−	360.857i	0.996548	−	0.863295i
$419$	−97.7496	+	116.493i	−0.233293	+	0.278027i	−0.869972	−	0.493101i	$-0.835863\pi$
$419$	−97.7496	+	116.493i	−0.233293	+	0.278027i	0.636679	+	0.771129i	$0.280308\pi$
$420$		0			0
$421$	−55.5808	−	20.2297i	−0.132021	−	0.0480516i	0.275165	−	0.961397i	$-0.411268\pi$
$421$	−55.5808	−	20.2297i	−0.132021	−	0.0480516i	−0.407186	+	0.913345i	$0.633490\pi$
$422$	97.8941	−	120.467i	0.231977	−	0.285467i
$423$		0			0
$424$	362.104	−	17.1126i	0.854020	−	0.0403600i
$425$	−70.2986	−	398.683i	−0.165408	−	0.938078i
$426$		0			0
$427$	50.5125	+	138.782i	0.118296	+	0.325016i
$428$	−53.5760	−	28.7226i	−0.125178	−	0.0671089i
$429$		0			0
$430$	99.8123	−	59.7409i	0.232122	−	0.138932i
$431$		−	225.843i		−	0.523998i	−0.965068	−	0.261999i	$-0.915618\pi$
$431$		−	225.843i		−	0.523998i	0.965068	−	0.261999i	$-0.0843818\pi$
$432$		0			0
$433$	71.7938			0.165805			0.0829027	−	0.996558i	$-0.473581\pi$
$433$	71.7938			0.165805			0.0829027	+	0.996558i	$0.473581\pi$
$434$	64.0313	+	106.980i	0.147538	+	0.246499i
$435$		0			0
$436$	−361.899	+	675.046i	−0.830043	+	1.54827i
$437$	−29.2862	+	10.6593i	−0.0670164	+	0.0243920i
$438$		0			0
$439$	−663.291	+	116.956i	−1.51091	+	0.266415i	−0.866855	−	0.498561i	$-0.833862\pi$
$439$	−663.291	+	116.956i	−1.51091	+	0.266415i	−0.644059	+	0.764976i	$0.722751\pi$
$440$	12.7730	+	270.279i	0.0290296	+	0.614269i
$441$		0			0
$442$	−358.924	−	291.670i	−0.812045	−	0.659886i
$443$	−74.1027	+	203.596i	−0.167275	+	0.459584i	−0.994800	−	0.101844i	$-0.967526\pi$
$443$	−74.1027	+	203.596i	−0.167275	+	0.459584i	0.827526	+	0.561428i	$0.189748\pi$
$444$		0			0
$445$	362.286	+	303.994i	0.814127	+	0.683134i
$446$	235.963	+	272.385i	0.529065	+	0.610728i
$447$		0			0
$448$	116.008	−	31.9790i	0.258947	−	0.0713816i
$449$	−214.840	+	372.113i	−0.478485	+	0.828760i	−0.999696	−	0.0246676i	$-0.992147\pi$
$449$	−214.840	+	372.113i	−0.478485	+	0.828760i	0.521211	+	0.853428i	$0.325481\pi$
$450$		0			0
$451$	−16.9287	+	9.77379i	−0.0375359	+	0.0216714i
$452$	−53.7632	+	373.267i	−0.118945	+	0.825811i
$453$		0			0
$454$	215.714	−	41.5475i	0.475142	−	0.0915142i
$455$	50.5220	+	8.90839i	0.111037	+	0.0195789i
$456$		0			0
$457$	202.151	−	169.624i	0.442342	−	0.371169i	−0.394243	−	0.919006i	$-0.628993\pi$
$457$	202.151	−	169.624i	0.442342	−	0.371169i	0.836585	+	0.547837i	$0.184549\pi$
$458$	−59.1920	+	369.627i	−0.129240	+	0.807045i
$459$		0			0
$460$	4.77811	−	14.5360i	0.0103872	−	0.0315999i
$461$	173.605	−	145.672i	0.376584	−	0.315992i	−0.434775	−	0.900539i	$-0.643172\pi$
$461$	173.605	−	145.672i	0.376584	−	0.315992i	0.811360	+	0.584547i	$0.198728\pi$
$462$		0			0
$463$	−872.435	−	153.834i	−1.88431	−	0.332255i	−0.891604	−	0.452817i	$-0.850419\pi$
$463$	−872.435	−	153.834i	−1.88431	−	0.332255i	−0.992706	+	0.120562i	$0.961530\pi$
$464$	414.291	+	121.872i	0.892867	+	0.262656i
$465$		0			0
$466$	446.571	−	7.03016i	0.958308	−	0.0150862i
$467$	259.319	−	149.718i	0.555287	−	0.320595i	−0.195964	−	0.980611i	$-0.562784\pi$
$467$	259.319	−	149.718i	0.555287	−	0.320595i	0.751252	+	0.660016i	$0.229450\pi$
$468$		0			0
$469$	−102.022	+	176.708i	−0.217532	+	0.376776i
$470$	−334.745	−	186.302i	−0.712224	−	0.396388i
$471$		0			0
$472$	−283.652	−	677.903i	−0.600959	−	1.43624i
$473$	−209.137	−	175.487i	−0.442150	−	0.371008i
$474$		0			0
$475$	133.102	−	365.694i	0.280214	−	0.769882i
$476$	−114.057	−	127.548i	−0.239615	−	0.267959i
$477$		0			0
$478$	−64.0874	−	167.812i	−0.134074	−	0.351070i
$479$	−236.431	+	41.6891i	−0.493592	+	0.0870337i	−0.414903	−	0.909866i	$-0.636185\pi$
$479$	−236.431	+	41.6891i	−0.493592	+	0.0870337i	−0.0786892	+	0.996899i	$0.525073\pi$
$480$		0			0
$481$	−352.237	+	128.204i	−0.732301	+	0.266536i
$482$	807.990	+	279.762i	1.67633	+	0.580418i
$483$		0			0
$484$	140.234	−	56.1002i	0.289739	−	0.115910i
$485$	111.500			0.229897
$486$		0			0
$487$			520.778i			1.06936i	0.845055	+	0.534680i	$0.179568\pi$
$487$			520.778i			1.06936i	−0.845055	+	0.534680i	$0.820432\pi$
$488$	138.208	+	612.994i	0.283214	+	1.25614i
$489$		0			0
$490$	−230.650	−	79.8611i	−0.470714	−	0.162982i
$491$	−120.820	−	331.951i	−0.246070	−	0.676071i	−0.999821	−	0.0189114i	$-0.993980\pi$
$491$	−120.820	−	331.951i	−0.246070	−	0.676071i	0.753751	−	0.657160i	$-0.228242\pi$
$492$		0			0
$493$	−106.628	−	604.717i	−0.216284	−	1.22661i
$494$	−158.616	−	415.332i	−0.321084	−	0.840752i
$495$		0			0
$496$	212.442	+	486.084i	0.428310	+	0.980008i
$497$	60.3709	+	21.9732i	0.121471	+	0.0442117i
$498$		0			0
$499$	201.989	−	240.721i	0.404787	−	0.482406i	−0.524686	−	0.851296i	$-0.675817\pi$
$499$	201.989	−	240.721i	0.404787	−	0.482406i	0.929473	+	0.368889i	$0.120262\pi$
$500$	242.161	+	390.507i	0.484321	+	0.781014i
$501$		0			0
$502$	−245.151	−	136.438i	−0.488348	−	0.271790i
$503$	−527.110	−	304.327i	−1.04793	−	0.605024i	−0.125862	−	0.992048i	$-0.540170\pi$
$503$	−527.110	−	304.327i	−1.04793	−	0.605024i	−0.922070	+	0.387024i	$0.873503\pi$
$504$		0			0
$505$	−65.9636	−	114.252i	−0.130621	−	0.226242i
$506$	−35.9065	+	0.565260i	−0.0709616	+	0.00111711i
$507$		0			0
$508$	0.833430	+	26.4641i	0.00164061	+	0.0520947i
$509$	54.6196	−	309.763i	0.107308	−	0.608572i	−0.882966	−	0.469437i	$-0.844457\pi$
$509$	54.6196	−	309.763i	0.107308	−	0.608572i	0.990273	−	0.139135i	$-0.0444322\pi$
$510$		0			0
$511$	49.9300	+	59.5043i	0.0977104	+	0.116447i
$512$	506.870	−	72.2932i	0.989981	−	0.141198i
$513$		0			0
$514$	13.2448	−	82.7074i	0.0257680	−	0.160909i
$515$	300.238	+	357.809i	0.582986	+	0.694775i
$516$		0			0
$517$	−156.129	+	885.449i	−0.301990	+	1.71267i
$518$	−136.177	+	26.2282i	−0.262890	+	0.0506337i
$519$		0			0
$520$	208.408	+	64.8889i	0.400784	+	0.124786i
$521$	233.111	+	403.760i	0.447430	+	0.774972i	0.998218	−	0.0596735i	$-0.0190059\pi$
$521$	233.111	+	403.760i	0.447430	+	0.774972i	−0.550788	+	0.834645i	$0.685673\pi$
$522$		0			0
$523$	−328.667	−	189.756i	−0.628426	−	0.362822i	0.151717	−	0.988424i	$-0.451520\pi$
$523$	−328.667	−	189.756i	−0.628426	−	0.362822i	−0.780142	+	0.625602i	$0.784853\pi$
$524$	−186.603	+	237.163i	−0.356113	+	0.452601i
$525$		0			0
$526$	−260.474	−	300.679i	−0.495197	−	0.571633i
$527$	484.853	−	577.826i	0.920025	−	1.09644i
$528$		0			0
$529$	−495.189	−	180.234i	−0.936085	−	0.340707i
$530$	188.796	+	153.420i	0.356220	+	0.289472i
$531$		0			0
$532$	−33.6470	−	161.005i	−0.0632462	−	0.302642i
$533$	2.73825	+	15.5294i	0.00513742	+	0.0291358i
$534$		0			0
$535$	−13.9527	−	38.3346i	−0.0260797	−	0.0716535i
$536$	−526.029	+	690.655i	−0.981397	+	1.28853i
$537$		0			0
$538$	−249.411	−	416.704i	−0.463589	−	0.774543i
$539$			572.855i			1.06281i
$540$		0			0
$541$	−869.342			−1.60692			−0.803458	−	0.595361i	$-0.797009\pi$
$541$	−869.342			−1.60692			−0.803458	+	0.595361i	$0.797009\pi$
$542$	−737.250	+	441.268i	−1.36024	+	0.814148i
$543$		0			0
$544$	−412.455	−	599.912i	−0.758190	−	1.10278i
$545$	−483.008	+	175.801i	−0.886253	+	0.322570i
$546$		0			0
$547$	−419.101	+	73.8988i	−0.766181	+	0.135098i	−0.543062	−	0.839693i	$-0.682735\pi$
$547$	−419.101	+	73.8988i	−0.766181	+	0.135098i	−0.223119	+	0.974791i	$0.571624\pi$
$548$	−190.418	−	911.176i	−0.347478	−	1.66273i
$549$		0			0
$550$	282.795	−	348.002i	0.514172	−	0.632732i
$551$	201.887	−	554.680i	0.366401	−	1.00668i
$552$		0			0
$553$	22.4591	+	18.8454i	0.0406132	+	0.0340785i
$554$	791.458	−	685.629i	1.42863	−	1.23760i
$555$		0			0
$556$	−227.345	+	288.944i	−0.408895	+	0.519684i
$557$	336.696	−	583.174i	0.604481	−	1.04699i	−0.387653	−	0.921805i	$-0.626714\pi$
$557$	336.696	−	583.174i	0.604481	−	1.04699i	0.992133	−	0.125186i	$-0.0399527\pi$
$558$		0			0
$559$	−190.729	+	110.117i	−0.341197	+	0.196990i
$560$	72.3380	+	35.8969i	0.129175	+	0.0641016i
$561$		0			0
$562$	62.7716	+	325.910i	0.111693	+	0.579911i
$563$	−141.923	−	25.0249i	−0.252084	−	0.0444492i	0.0461780	−	0.998933i	$-0.485296\pi$
$563$	−141.923	−	25.0249i	−0.252084	−	0.0444492i	−0.298262	+	0.954484i	$0.596407\pi$
$564$		0			0
$565$	−193.869	+	162.675i	−0.343131	+	0.287921i
$566$	−406.062	−	65.0267i	−0.717424	−	0.114888i
$567$		0			0
$568$	242.915	+	125.347i	0.427668	+	0.220682i
$569$	−300.826	+	252.423i	−0.528692	+	0.443625i	−0.867649	−	0.497176i	$-0.834370\pi$
$569$	−300.826	+	252.423i	−0.528692	+	0.443625i	0.338957	+	0.940802i	$0.389926\pi$
$570$		0			0
$571$	384.074	+	67.7226i	0.672634	+	0.118604i	0.499526	−	0.866299i	$-0.333508\pi$
$571$	384.074	+	67.7226i	0.672634	+	0.118604i	0.173109	+	0.984903i	$0.444619\pi$
$572$	−16.1252	−	512.029i	−0.0281910	−	0.895155i
$573$		0			0
$574$	0.0918305	+	5.83328i	0.000159983	+	0.0101625i
$575$	−21.9604	+	12.6789i	−0.0381920	+	0.0220502i
$576$		0			0
$577$	−502.275	+	869.965i	−0.870494	+	1.50774i	−0.00900655	+	0.999959i	$0.502867\pi$
$577$	−502.275	+	869.965i	−0.870494	+	1.50774i	−0.861487	+	0.507780i	$0.830466\pi$
$578$	−222.331	+	399.481i	−0.384656	+	0.691144i
$579$		0			0
$580$	152.730	+	246.291i	0.263327	+	0.424640i
$581$	−110.936	−	93.0866i	−0.190940	−	0.160218i
$582$		0			0
$583$	195.277	−	536.518i	0.334951	−	0.920271i
$584$	178.577	+	278.101i	0.305782	+	0.476200i
$585$		0			0
$586$	−454.491	+	173.571i	−0.775582	+	0.296195i
$587$	−661.848	+	116.702i	−1.12751	+	0.198810i	−0.706136	−	0.708077i	$-0.749563\pi$
$587$	−661.848	+	116.702i	−1.12751	+	0.198810i	−0.421374	+	0.906887i	$0.638452\pi$
$588$		0			0
$589$	681.372	−	247.999i	1.15683	−	0.421051i
$590$	161.351	−	466.005i	0.273477	−	0.789839i
$591$		0			0
$592$	−588.882	+	37.1280i	−0.994733	+	0.0627161i
$593$	−479.407			−0.808443			−0.404221	−	0.914661i	$-0.632457\pi$
$593$	−479.407			−0.808443			−0.404221	+	0.914661i	$0.632457\pi$
$594$		0			0
$595$		−	114.827i		−	0.192986i
$596$	−856.469	+	342.629i	−1.43703	+	0.574881i
$597$		0			0
$598$	−9.47834	+	27.3747i	−0.0158501	+	0.0457772i
$599$	−30.3539	−	83.3966i	−0.0506743	−	0.139226i	0.911773	−	0.410694i	$-0.134713\pi$
$599$	−30.3539	−	83.3966i	−0.0506743	−	0.139226i	−0.962448	+	0.271467i	$0.912491\pi$
$600$		0			0
$601$	−87.8334	−	498.128i	−0.146145	−	0.828832i	−0.966440	−	0.256891i	$-0.917302\pi$
$601$	−87.8334	−	498.128i	−0.146145	−	0.828832i	0.820295	−	0.571941i	$-0.193809\pi$
$602$	−76.1179	+	29.0695i	−0.126442	+	0.0482882i
$603$		0			0
$604$	544.045	+	608.400i	0.900737	+	1.00728i
$605$	95.2467	+	34.6670i	0.157433	+	0.0573008i
$606$		0			0
$607$	−59.8471	+	71.3229i	−0.0985948	+	0.117501i	−0.813086	−	0.582144i	$-0.802214\pi$
$607$	−59.8471	+	71.3229i	−0.0985948	+	0.117501i	0.714491	+	0.699645i	$0.246658\pi$
$608$	−55.0249	−	697.674i	−0.0905015	−	1.14749i
$609$		0			0
$610$	−205.073	+	368.473i	−0.336186	+	0.604054i
$611$	628.134	+	362.653i	1.02804	+	0.593540i
$612$		0			0
$613$	21.2569	+	36.8180i	0.0346768	+	0.0600619i	0.882843	−	0.469668i	$-0.155626\pi$
$613$	21.2569	+	36.8180i	0.0346768	+	0.0600619i	−0.848166	+	0.529730i	$0.822293\pi$
$614$	16.4641	+	1045.84i	0.0268146	+	1.70332i
$615$		0			0
$616$	24.0636	−	187.994i	0.0390642	−	0.305185i
$617$	−94.4173	+	535.467i	−0.153026	+	0.867856i	0.807541	+	0.589811i	$0.200798\pi$
$617$	−94.4173	+	535.467i	−0.153026	+	0.867856i	−0.960568	+	0.278045i	$0.910313\pi$
$618$		0			0
$619$	518.241	+	617.616i	0.837224	+	0.997764i	0.999938	+	0.0110910i	$0.00353045\pi$
$619$	518.241	+	617.616i	0.837224	+	0.997764i	−0.162715	+	0.986673i	$0.552025\pi$
$620$	−111.168	+	338.194i	−0.179302	+	0.545474i
$621$		0			0
$622$	264.857	+	42.4141i	0.425814	+	0.0681899i
$623$	−212.933	−	253.764i	−0.341787	−	0.407326i
$624$		0			0
$625$	23.7028	−	134.425i	0.0379245	−	0.215080i
$626$	−23.8440	−	123.798i	−0.0380895	−	0.197761i
$627$		0			0
$628$	35.8033	−	248.575i	0.0570116	−	0.395819i
$629$	419.501	+	726.597i	0.666934	+	1.15516i
$630$		0			0
$631$	960.558	+	554.578i	1.52228	+	0.878888i	0.999653	+	0.0263256i	$0.00838068\pi$
$631$	960.558	+	554.578i	1.52228	+	0.878888i	0.522625	+	0.852562i	$0.324953\pi$
$632$	84.6045	+	91.6666i	0.133868	+	0.145042i
$633$		0			0
$634$	−268.529	+	232.623i	−0.423547	+	0.366913i
$635$	−11.4213	+	13.6114i	−0.0179863	+	0.0214352i
$636$		0			0
$637$	434.250	+	158.054i	0.681711	+	0.248122i
$638$	428.939	−	527.845i	0.672318	−	0.827344i
$639$		0			0
$640$	285.899	+	190.575i	0.446717	+	0.297773i
$641$	−12.8053	−	72.6225i	−0.0199771	−	0.113296i	0.973189	−	0.230008i	$-0.0738754\pi$
$641$	−12.8053	−	72.6225i	−0.0199771	−	0.113296i	−0.993166	+	0.116713i	$0.962764\pi$
$642$		0			0
$643$	−166.197	−	456.624i	−0.258472	−	0.710146i	−0.999262	−	0.0384093i	$-0.987771\pi$
$643$	−166.197	−	456.624i	−0.258472	−	0.710146i	0.740790	−	0.671737i	$-0.234451\pi$
$644$	−5.06402	+	9.44587i	−0.00786339	+	0.0146675i
$645$		0			0
$646$	−853.855	+	511.060i	−1.32176	+	0.791115i
$647$			208.039i			0.321544i	0.986992	+	0.160772i	$0.0513984\pi$
$647$			208.039i			0.321544i	−0.986992	+	0.160772i	$0.948602\pi$
$648$		0			0
$649$	−1157.39			−1.78335
$650$	−185.777	−	310.387i	−0.285811	−	0.477519i
$651$		0			0
$652$	−186.943	−	100.222i	−0.286722	−	0.153715i
$653$	−372.173	+	135.460i	−0.569943	+	0.207442i	−0.610885	−	0.791719i	$-0.709186\pi$
$653$	−372.173	+	135.460i	−0.569943	+	0.207442i	0.0409423	+	0.999162i	$0.486964\pi$
$654$		0			0
$655$	−199.438	+	35.1663i	−0.304486	+	0.0536891i
$656$	−2.76364	+	24.6680i	−0.00421286	+	0.0376037i
$657$		0			0
$658$	208.250	+	169.229i	0.316489	+	0.257186i
$659$	−122.012	+	335.225i	−0.185147	+	0.508687i	−0.997190	−	0.0749099i	$-0.976133\pi$
$659$	−122.012	+	335.225i	−0.185147	+	0.508687i	0.812043	+	0.583597i	$0.198355\pi$
$660$		0			0
$661$	616.990	+	517.716i	0.933419	+	0.783232i	0.976428	−	0.215843i	$-0.0692499\pi$
$661$	616.990	+	517.716i	0.933419	+	0.783232i	−0.0430087	+	0.999075i	$0.513694\pi$
$662$	655.913	+	757.155i	0.990805	+	1.14374i
$663$		0			0
$664$	−417.903	−	452.786i	−0.629372	−	0.681907i
$665$	55.1910	−	95.5937i	0.0829941	−	0.143750i
$666$		0			0
$667$	−33.3093	+	19.2311i	−0.0499389	+	0.0288323i
$668$	−83.3761	−	12.0090i	−0.124815	−	0.0179776i
$669$		0			0
$670$	−572.096	+	110.188i	−0.853874	+	0.164460i
$671$	974.664	+	171.860i	1.45255	+	0.256125i
$672$		0			0
$673$	658.151	−	552.254i	0.977936	−	0.820586i	−0.00584030	−	0.999983i	$-0.501859\pi$
$673$	658.151	−	552.254i	0.977936	−	0.820586i	0.983777	+	0.179397i	$0.0574146\pi$
$674$	−73.5210	+	459.105i	−0.109082	+	0.681164i
$675$		0			0
$676$	249.605	+	82.0476i	0.369239	+	0.121372i
$677$	610.168	−	511.992i	0.901282	−	0.756266i	−0.0691584	−	0.997606i	$-0.522031\pi$
$677$	610.168	−	511.992i	0.901282	−	0.756266i	0.970441	+	0.241340i	$0.0775869\pi$
$678$		0			0
$679$	−76.9138	−	13.5620i	−0.113275	−	0.0199735i
$680$	62.0306	−	484.608i	0.0912214	−	0.712659i
$681$		0			0
$682$	835.402	−	13.1513i	1.22493	−	0.0192835i
$683$	184.655	−	106.611i	0.270359	−	0.156092i	−0.358692	−	0.933456i	$-0.616777\pi$
$683$	184.655	−	106.611i	0.270359	−	0.156092i	0.629051	+	0.777364i	$0.283444\pi$
$684$		0			0
$685$	312.342	−	540.992i	0.455974	−	0.789769i
$686$	310.398	+	172.752i	0.452476	+	0.251825i
$687$		0			0
$688$	−336.947	+	81.5635i	−0.489749	+	0.118552i
$689$	−352.827	−	296.057i	−0.512085	−	0.429691i
$690$		0			0
$691$	250.303	−	687.702i	0.362233	−	0.995227i	−0.616005	−	0.787742i	$-0.711250\pi$
$691$	250.303	−	687.702i	0.362233	−	0.995227i	0.978238	−	0.207485i	$-0.0665277\pi$
$692$	485.347	−	434.008i	0.701368	−	0.627179i
$693$		0			0
$694$	375.510	+	983.266i	0.541081	+	1.41681i
$695$	−242.983	+	42.8444i	−0.349615	+	0.0616466i
$696$		0			0
$697$	33.1667	−	12.0717i	0.0475849	−	0.0173195i
$698$	−1224.93	−	424.124i	−1.75491	−	0.607627i
$699$		0			0
$700$	−49.7087	−	124.257i	−0.0710125	−	0.177510i
$701$	248.972			0.355166			0.177583	−	0.984106i	$-0.443172\pi$
$701$	248.972			0.355166			0.177583	+	0.984106i	$0.443172\pi$
$702$		0			0
$703$			806.527i			1.14726i
$704$	203.113	−	780.400i	0.288512	−	1.10852i
$705$		0			0
$706$	−105.328	−	36.4692i	−0.149190	−	0.0516560i
$707$	31.6056	+	86.8356i	0.0447038	+	0.122823i
$708$		0			0
$709$	−83.4714	−	473.390i	−0.117731	−	0.667687i	−0.985362	−	0.170477i	$-0.945469\pi$
$709$	−83.4714	−	473.390i	−0.117731	−	0.667687i	0.867630	−	0.497210i	$-0.165642\pi$
$710$	65.4457	+	171.368i	0.0921771	+	0.241364i
$711$		0			0
$712$	−761.565	−	1186.00i	−1.06961	−	1.66573i
$713$	−44.3979	−	16.1595i	−0.0622692	−	0.0226641i
$714$		0			0
$715$	220.980	−	263.354i	0.309063	−	0.368327i
$716$	−228.570	+	141.740i	−0.319232	+	0.197962i
$717$		0			0
$718$	724.951	+	403.471i	1.00968	+	0.561938i
$719$	1151.09	+	664.581i	1.60096	+	0.924313i	0.991296	+	0.131650i	$0.0420277\pi$
$719$	1151.09	+	664.581i	1.60096	+	0.924313i	0.609661	+	0.792662i	$0.291306\pi$
$720$		0			0
$721$	−163.586	−	283.339i	−0.226887	−	0.392980i
$722$	−234.567	+	3.69267i	−0.324884	+	0.00511450i
$723$		0			0
$724$	−362.014	+	11.4008i	−0.500019	+	0.0157470i
$725$	83.3989	−	472.978i	0.115033	−	0.652384i
$726$		0			0
$727$	350.736	+	417.991i	0.482443	+	0.574953i	0.951279	−	0.308332i	$-0.0997708\pi$
$727$	350.736	+	417.991i	0.482443	+	0.574953i	−0.468836	+	0.883285i	$0.655326\pi$
$728$	−135.869	−	70.1100i	−0.186633	−	0.0963049i
$729$		0			0
$730$	−35.0710	+	219.002i	−0.0480424	+	0.300003i
$731$	316.860	+	377.619i	0.433461	+	0.516579i
$732$		0			0
$733$	−25.1072	+	142.390i	−0.0342527	+	0.194257i	−0.997133	−	0.0756732i	$-0.975889\pi$
$733$	−25.1072	+	142.390i	−0.0342527	+	0.194257i	0.962880	+	0.269930i	$0.0870005\pi$
$734$	−491.023	+	94.5730i	−0.668968	+	0.128846i
$735$		0			0
$736$	−26.4746	+	37.1291i	−0.0359710	+	0.0504472i
$737$	683.679	+	1184.17i	0.927651	+	1.60674i
$738$		0			0
$739$	202.168	+	116.722i	0.273570	+	0.157946i	0.630509	−	0.776182i	$-0.282846\pi$
$739$	202.168	+	116.722i	0.273570	+	0.157946i	−0.356939	+	0.934128i	$0.616180\pi$
$740$	−311.194	−	244.852i	−0.420533	−	0.330881i
$741$		0			0
$742$	−111.573	−	128.794i	−0.150368	−	0.173577i
$743$	−388.931	+	463.509i	−0.523460	+	0.623835i	−0.961395	−	0.275171i	$-0.911265\pi$
$743$	−388.931	+	463.509i	−0.523460	+	0.623835i	0.437935	+	0.899006i	$0.355710\pi$
$744$		0			0
$745$	−581.714	−	211.727i	−0.780825	−	0.284197i
$746$	−731.880	−	594.743i	−0.981073	−	0.797242i
$747$		0			0
$748$	−1122.38	+	234.556i	−1.50051	+	0.313578i
$749$	4.96196	+	28.1407i	0.00662478	+	0.0375710i
$750$		0			0
$751$	9.87280	+	27.1253i	0.0131462	+	0.0361189i	0.946092	−	0.323898i	$-0.104993\pi$
$751$	9.87280	+	27.1253i	0.0131462	+	0.0361189i	−0.932946	+	0.360016i	$0.882771\pi$
$752$	787.467	+	826.701i	1.04716	+	1.09934i
$753$		0			0
$754$	−281.784	−	470.791i	−0.373719	−	0.624391i
$755$			547.718i			0.725454i
$756$		0			0
$757$	944.419			1.24758			0.623790	−	0.781592i	$-0.285592\pi$
$757$	944.419			1.24758			0.623790	+	0.781592i	$0.285592\pi$
$758$	49.0363	−	29.3498i	0.0646917	−	0.0387201i
$759$		0			0
$760$	284.566	−	373.623i	0.374429	−	0.491609i
$761$	−143.081	+	52.0772i	−0.188017	+	0.0684326i	−0.434313	−	0.900762i	$-0.643009\pi$
$761$	−143.081	+	52.0772i	−0.188017	+	0.0684326i	0.246296	+	0.969195i	$0.420787\pi$
$762$		0			0
$763$	354.566	−	62.5196i	0.464700	−	0.0819392i
$764$	−1038.88	+	217.105i	−1.35979	+	0.284169i
$765$		0			0
$766$	192.674	−	237.101i	0.251532	−	0.309531i
$767$	−319.332	+	877.358i	−0.416339	+	1.14388i
$768$		0			0
$769$	369.119	+	309.728i	0.479999	+	0.402767i	0.850426	−	0.526095i	$-0.176344\pi$
$769$	369.119	+	309.728i	0.479999	+	0.402767i	−0.370427	+	0.928862i	$0.620789\pi$
$770$	96.1335	−	83.2790i	0.124849	−	0.108155i
$771$		0			0
$772$	607.500	+	477.990i	0.786917	+	0.619158i
$773$	35.9726	−	62.3064i	0.0465364	−	0.0806033i	−0.841819	−	0.539760i	$-0.818515\pi$
$773$	35.9726	−	62.3064i	0.0465364	−	0.0806033i	0.888355	+	0.459157i	$0.151848\pi$
$774$		0			0
$775$	510.931	−	294.986i	0.659266	−	0.380628i
$776$	−317.276	−	98.7858i	−0.408861	−	0.127301i
$777$		0			0
$778$	−162.343	−	842.883i	−0.208667	−	1.08340i
$779$	33.4136	+	5.89172i	0.0428930	+	0.00756319i
$780$		0			0
$781$	329.801	−	276.736i	0.422281	−	0.354336i
$782$	64.0254	+	10.2530i	0.0818739	+	0.0131113i
$783$		0			0
$784$	585.565	+	431.596i	0.746895	+	0.550505i
$785$	129.106	−	108.333i	0.164466	−	0.138003i
$786$		0			0
$787$	−105.738	−	18.6445i	−0.134356	−	0.0236906i	0.106066	−	0.994359i	$-0.466175\pi$
$787$	−105.738	−	18.6445i	−0.134356	−	0.0236906i	−0.240422	+	0.970669i	$0.577286\pi$
$788$	1219.54	−	38.4066i	1.54763	−	0.0487394i
$789$		0			0
$790$	1.31768	+	83.7021i	0.00166795	+	0.105952i
$791$	153.519	−	88.6342i	0.194082	−	0.112053i
$792$		0			0
$793$	399.193	−	691.422i	0.503396	−	0.871907i
$794$	192.053	−	345.078i	0.241880	−	0.434607i
$795$		0			0
$796$	−729.453	+	452.347i	−0.916398	+	0.568275i
$797$	−329.502	−	276.485i	−0.413428	−	0.346908i	0.412228	−	0.911081i	$-0.364751\pi$
$797$	−329.502	−	276.485i	−0.413428	−	0.346908i	−0.825657	+	0.564173i	$0.809195\pi$
$798$		0			0
$799$	555.249	−	1525.53i	0.694929	−	1.90930i
$800$	−142.663	−	551.259i	−0.178329	−	0.689074i
$801$		0			0
$802$	696.559	−	266.017i	0.868528	−	0.331692i
$803$	512.628	−	90.3902i	0.638391	−	0.112566i
$804$		0			0
$805$	−6.75869	+	2.45996i	−0.00839589	+	0.00305585i
$806$	220.523	−	636.901i	0.273602	−	0.790200i
$807$		0			0
$808$	86.4768	+	383.549i	0.107026	+	0.474690i
$809$	−794.650			−0.982262			−0.491131	−	0.871086i	$-0.663416\pi$
$809$	−794.650			−0.982262			−0.491131	+	0.871086i	$0.663416\pi$
$810$		0			0
$811$		−	570.142i		−	0.703011i	−0.936186	−	0.351506i	$-0.885670\pi$
$811$		−	570.142i		−	0.703011i	0.936186	−	0.351506i	$-0.114330\pi$
$812$	−75.3976	−	188.471i	−0.0928541	−	0.232107i
$813$		0			0
$814$	−304.064	+	878.179i	−0.373543	+	1.07884i
$815$	−48.6851	−	133.761i	−0.0597363	−	0.164124i
$816$		0			0
$817$	82.2860	+	466.667i	0.100717	+	0.571196i
$818$	244.711	−	93.4553i	0.299157	−	0.114249i
$819$		0			0
$820$	−12.4173	+	11.1038i	−0.0151430	+	0.0135412i
$821$	−207.172	−	75.4043i	−0.252341	−	0.0918445i	0.212753	−	0.977106i	$-0.431757\pi$
$821$	−207.172	−	75.4043i	−0.252341	−	0.0918445i	−0.465094	+	0.885262i	$0.653979\pi$
$822$		0			0
$823$	−356.852	+	425.279i	−0.433599	+	0.516743i	−0.937957	−	0.346752i	$-0.887285\pi$
$823$	−356.852	+	425.279i	−0.433599	+	0.516743i	0.504358	+	0.863494i	$0.331729\pi$
$824$	−537.325	−	1284.16i	−0.652093	−	1.55844i
$825$		0			0
$826$	−167.983	+	301.829i	−0.203369	+	0.365411i
$827$	−917.032	−	529.449i	−1.10887	−	0.640204i	−0.170330	−	0.985387i	$-0.554484\pi$
$827$	−917.032	−	529.449i	−1.10887	−	0.640204i	−0.938535	+	0.345183i	$0.887817\pi$
$828$		0			0
$829$	28.4032	+	49.1958i	0.0342620	+	0.0593435i	0.882648	−	0.470035i	$-0.155759\pi$
$829$	28.4032	+	49.1958i	0.0342620	+	0.0593435i	−0.848386	+	0.529378i	$0.822425\pi$
$830$	−6.50868	−	413.446i	−0.00784178	−	0.498127i
$831$		0			0
$832$	−535.539	−	369.286i	−0.643676	−	0.443853i
$833$	179.613	−	1018.64i	0.215622	−	1.22285i
$834$		0			0
$835$	−36.3366	−	43.3042i	−0.0435168	−	0.0518613i
$836$	−1047.13	−	344.201i	−1.25254	−	0.411724i
$837$		0			0
$838$	300.316	+	48.0926i	0.358373	+	0.0573898i
$839$	−826.031	−	984.425i	−0.984542	−	1.17333i	−0.984864	−	0.173331i	$-0.944547\pi$
$839$	−826.031	−	984.425i	−0.984542	−	1.17333i	0.000321569	−	1.00000i	$-0.499898\pi$
$840$		0			0
$841$	−19.5398	+	110.816i	−0.0232340	+	0.131767i
$842$	22.3730	+	116.161i	0.0265713	+	0.137958i
$843$		0			0
$844$	−307.284	−	44.2594i	−0.364080	−	0.0524400i
$845$	88.1616	+	152.700i	0.104333	+	0.180710i
$846$		0			0
$847$	−61.4854	−	35.4986i	−0.0725920	−	0.0419110i
$848$	−401.299	−	603.829i	−0.473230	−	0.712062i
$849$		0			0
$850$	−611.972	+	530.142i	−0.719967	+	0.623697i
$851$	33.7804	−	40.2579i	0.0396949	−	0.0473066i
$852$		0			0
$853$	501.932	+	182.688i	0.588432	+	0.214172i	0.619040	−	0.785360i	$-0.287522\pi$
$853$	501.932	+	182.688i	0.588432	+	0.214172i	−0.0306077	+	0.999531i	$0.509744\pi$
$854$	186.280	−	229.233i	0.218126	−	0.268422i
$855$		0			0
$856$	5.73928	+	121.444i	0.00670477	+	0.141873i
$857$	−119.473	−	677.568i	−0.139409	−	0.790628i	−0.971687	−	0.236270i	$-0.924075\pi$
$857$	−119.473	−	677.568i	−0.139409	−	0.790628i	0.832278	−	0.554358i	$-0.187036\pi$
$858$		0			0
$859$	32.4589	+	89.1800i	0.0377868	+	0.103818i	0.957151	−	0.289589i	$-0.0935185\pi$
$859$	32.4589	+	89.1800i	0.0377868	+	0.103818i	−0.919364	+	0.393407i	$0.871296\pi$
$860$	−205.042	−	109.925i	−0.238421	−	0.127820i
$861$		0			0
$862$	−387.569	+	231.973i	−0.449616	+	0.269110i
$863$			582.627i			0.675119i	0.941304	+	0.337559i	$0.109601\pi$
$863$			582.627i			0.675119i	−0.941304	+	0.337559i	$0.890399\pi$
$864$		0			0
$865$	436.938			0.505131
$866$	−73.7422	−	123.205i	−0.0851527	−	0.142269i
$867$		0			0
$868$	117.820	−	219.768i	0.135737	−	0.253189i
$869$	184.621	−	67.1964i	0.212452	−	0.0773262i
$870$		0			0
$871$	1086.28	−	191.541i	1.24717	−	0.219909i
$872$	1530.16	−	72.3138i	1.75478	−	0.0829286i
$873$		0			0
$874$	48.3733	+	39.3093i	0.0553471	+	0.0449763i
$875$	73.8733	−	202.965i	0.0844267	−	0.231960i
$876$		0			0
$877$	−669.221	−	561.543i	−0.763080	−	0.640300i	0.175846	−	0.984418i	$-0.443734\pi$
$877$	−669.221	−	561.543i	−0.763080	−	0.640300i	−0.938927	+	0.344117i	$0.888178\pi$
$878$	882.000	+	1018.14i	1.00456	+	1.15961i
$879$		0			0
$880$	450.704	−	299.534i	0.512164	−	0.340379i
$881$	174.490	−	302.226i	0.198059	−	0.343049i	−0.749840	−	0.661619i	$-0.769870\pi$
$881$	174.490	−	302.226i	0.198059	−	0.343049i	0.947899	+	0.318571i	$0.103203\pi$
$882$		0			0
$883$	−343.440	+	198.285i	−0.388947	+	0.224559i	−0.681704	−	0.731628i	$-0.738761\pi$
$883$	−343.440	+	198.285i	−0.388947	+	0.224559i	0.292757	+	0.956187i	$0.405427\pi$
$884$	−131.868	+	915.533i	−0.149172	+	1.03567i
$885$		0			0
$886$	425.503	−	81.9537i	0.480252	−	0.0924985i
$887$	537.102	+	94.7055i	0.605526	+	0.106771i	0.468001	−	0.883728i	$-0.344974\pi$
$887$	537.102	+	94.7055i	0.605526	+	0.106771i	0.137525	+	0.990498i	$0.456085\pi$
$888$		0			0
$889$	9.53410	−	8.00006i	0.0107245	−	0.00899894i
$890$	149.565	−	933.963i	0.168050	−	1.04940i
$891$		0			0
$892$	225.071	−	684.712i	0.252322	−	0.767614i
$893$	1195.49	−	1003.13i	1.33873	−	1.12333i
$894$		0			0
$895$	−177.746	−	31.3415i	−0.198599	−	0.0350184i
$896$	−174.036	−	166.235i	−0.194236	−	0.185530i
$897$		0			0
$898$	859.253	−	13.5268i	0.956852	−	0.0150633i
$899$	774.974	−	447.432i	0.862040	−	0.497699i
$900$		0			0
$901$	−515.456	+	892.797i	−0.572094	+	0.990895i
$902$	34.1609	+	19.0122i	0.0378724	+	0.0210778i
$903$		0			0
$904$	695.784	−	291.134i	0.769672	−	0.322051i
$905$	−186.196	−	156.237i	−0.205741	−	0.172638i
$906$		0			0
$907$	−451.817	+	1241.36i	−0.498144	+	1.36864i	0.394922	+	0.918715i	$0.370771\pi$
$907$	−451.817	+	1241.36i	−0.498144	+	1.36864i	−0.893066	+	0.449925i	$0.851451\pi$
$908$	−292.868	−	327.511i	−0.322542	−	0.360695i
$909$		0			0
$910$	−36.6055	−	95.8507i	−0.0402258	−	0.105330i
$911$	1111.55	−	195.997i	1.22014	−	0.215144i	0.473757	−	0.880656i	$-0.342898\pi$
$911$	1111.55	−	195.997i	1.22014	−	0.215144i	0.746388	+	0.665511i	$0.231787\pi$
$912$		0			0
$913$	−911.931	+	331.916i	−0.998830	+	0.363544i
$914$	−498.729	−	172.682i	−0.545655	−	0.188930i
$915$		0			0
$916$	695.113	−	278.079i	0.758857	−	0.303580i
$917$	141.852			0.154691
$918$		0			0
$919$		−	62.0726i		−	0.0675436i	−0.999430	−	0.0337718i	$-0.989248\pi$
$919$		−	62.0726i		−	0.0675436i	0.999430	−	0.0337718i	$-0.0107519\pi$
$920$	−29.8529	+	6.73077i	−0.0324488	+	0.00731605i
$921$		0			0
$922$	−428.305	−	148.298i	−0.464539	−	0.160844i
$923$	−118.784	−	326.357i	−0.128694	−	0.353583i
$924$		0			0
$925$	113.952	+	646.255i	0.123192	+	0.698654i
$926$	632.119	+	1655.19i	0.682634	+	1.78746i
$927$		0			0
$928$	−216.389	−	836.142i	−0.233178	−	0.901015i
$929$	1010.07	+	367.635i	1.08726	+	0.395732i	0.822607	−	0.568611i	$-0.192519\pi$
$929$	1010.07	+	367.635i	1.08726	+	0.395732i	0.264657	+	0.964343i	$0.414741\pi$
$930$		0			0
$931$	639.133	−	761.689i	0.686501	−	0.818140i
$932$	−470.755	−	759.138i	−0.505102	−	0.814526i
$933$		0			0
$934$	−523.287	−	291.235i	−0.560265	−	0.311815i
$935$	−666.393	−	384.742i	−0.712719	−	0.411489i
$936$		0			0
$937$	−65.7114	−	113.816i	−0.0701296	−	0.121468i	0.828828	−	0.559503i	$-0.189008\pi$
$937$	−65.7114	−	113.816i	−0.0701296	−	0.121468i	−0.898958	+	0.438035i	$0.855675\pi$
$938$	408.039	−	6.42357i	0.435010	−	0.00684815i
$939$		0			0
$940$	24.1176	+	765.813i	0.0256571	+	0.814695i
$941$	−218.501	+	1239.18i	−0.232201	+	1.31688i	0.616228	+	0.787568i	$0.288660\pi$
$941$	−218.501	+	1239.18i	−0.232201	+	1.31688i	−0.848429	+	0.529309i	$0.822451\pi$
$942$		0			0
$943$	−1.42108	−	1.69357i	−0.00150697	−	0.00179594i
$944$	−871.996	+	1183.08i	−0.923724	+	1.25326i
$945$		0			0
$946$	−86.3392	+	539.148i	−0.0912676	+	0.569924i
$947$	188.750	+	224.943i	0.199313	+	0.237533i	0.856439	−	0.516249i	$-0.172672\pi$
$947$	188.750	+	224.943i	0.199313	+	0.237533i	−0.657125	+	0.753782i	$0.728228\pi$
$948$		0			0
$949$	72.9173	−	413.534i	0.0768359	−	0.435758i
$950$	−764.280	+	147.203i	−0.804505	+	0.154951i
$951$		0			0
$952$	−101.733	+	326.742i	−0.106862	+	0.343217i
$953$	−325.171	−	563.213i	−0.341208	−	0.590990i	0.643449	−	0.765489i	$-0.277503\pi$
$953$	−325.171	−	563.213i	−0.341208	−	0.590990i	−0.984657	+	0.174499i	$0.944169\pi$
$954$		0			0
$955$	−616.812	−	356.117i	−0.645877	−	0.372897i
$956$	−222.154	+	282.346i	−0.232379	+	0.295341i
$957$		0			0
$958$	314.390	+	362.917i	0.328173	+	0.378828i
$959$	−281.258	+	335.191i	−0.293283	+	0.349521i
$960$		0			0
$961$	129.918	+	47.2862i	0.135190	+	0.0492052i
$962$	581.806	+	472.789i	0.604788	+	0.491465i
$963$		0			0
$964$	−349.821	−	1673.94i	−0.362885	−	1.73646i
$965$	90.0795	+	510.866i	0.0933467	+	0.529395i
$966$		0			0
$967$	−206.167	−	566.439i	−0.213203	−	0.585769i	0.786282	−	0.617868i	$-0.212003\pi$
$967$	−206.167	−	566.439i	−0.213203	−	0.585769i	−0.999485	+	0.0320984i	$0.989781\pi$
$968$	−240.313	−	183.031i	−0.248257	−	0.189082i
$969$		0			0
$970$	−114.526	−	191.345i	−0.118068	−	0.197263i
$971$		−	1204.36i		−	1.24033i	−0.784472	−	0.620165i	$-0.787066\pi$
$971$		−	1204.36i		−	1.24033i	0.784472	−	0.620165i	$-0.212934\pi$
$972$		0			0
$973$	172.823			0.177619
$974$	893.706	−	534.912i	0.917562	−	0.549191i
$975$		0			0
$976$	909.997	−	866.809i	0.932374	−	0.888124i
$977$	−324.705	+	118.183i	−0.332349	+	0.120965i	−0.502804	−	0.864400i	$-0.667698\pi$
$977$	−324.705	+	118.183i	−0.332349	+	0.120965i	0.170455	+	0.985365i	$0.445476\pi$
$978$		0			0
$979$	−2186.17	+	385.481i	−2.23306	+	0.393749i
$980$	99.8604	+	477.846i	0.101898	+	0.487598i
$981$		0			0
$982$	−445.560	+	548.299i	−0.453727	+	0.558349i
$983$	215.293	−	591.512i	0.219016	−	0.601742i	−0.780716	−	0.624886i	$-0.785145\pi$
$983$	215.293	−	591.512i	0.219016	−	0.601742i	0.999732	+	0.0231441i	$0.00736765\pi$
$984$		0			0
$985$	627.248	+	526.324i	0.636800	+	0.534339i
$986$	−928.231	+	804.113i	−0.941410	+	0.815530i
$987$		0			0
$988$	−549.829	+	698.803i	−0.556507	+	0.707291i
$989$	15.4385	−	26.7402i	0.0156102	−	0.0270376i
$990$		0			0
$991$	387.015	−	223.443i	0.390529	−	0.225472i	−0.291860	−	0.956461i	$-0.594274\pi$
$991$	387.015	−	223.443i	0.390529	−	0.225472i	0.682389	+	0.730989i	$0.260941\pi$
$992$	615.959	−	863.847i	0.620927	−	0.870814i
$993$		0			0
$994$	−24.3012	−	126.172i	−0.0244479	−	0.126933i
$995$	−567.255	−	100.022i	−0.570106	−	0.100525i
$996$		0			0
$997$	−491.230	+	412.191i	−0.492708	+	0.413431i	−0.854996	−	0.518635i	$-0.826440\pi$
$997$	−491.230	+	412.191i	−0.492708	+	0.413431i	0.362287	+	0.932066i	$0.381996\pi$
$998$	−620.571	−	99.3781i	−0.621814	−	0.0995773i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.12		204
3.2	odd	2		108.3.j.a.103.23	yes	204
4.3	odd	2	inner	324.3.j.a.199.27		204
12.11	even	2		108.3.j.a.103.8	yes	204
27.11	odd	18		108.3.j.a.43.8	✓	204
27.16	even	9	inner	324.3.j.a.127.27		204
108.11	even	18		108.3.j.a.43.23	yes	204
108.43	odd	18	inner	324.3.j.a.127.12		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.8	✓	204	27.11	odd	18
108.3.j.a.43.23	yes	204	108.11	even	18
108.3.j.a.103.8	yes	204	12.11	even	2
108.3.j.a.103.23	yes	204	3.2	odd	2
324.3.j.a.127.12		204	108.43	odd	18	inner
324.3.j.a.127.27		204	27.16	even	9	inner
324.3.j.a.199.12		204	1.1	even	1	trivial
324.3.j.a.199.27		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)

\(f(q)\)	\(=\)	\(q+(-1.02714 - 1.71610i) q^{2} +(-1.88997 + 3.52534i) q^{4} +(-2.52245 + 0.918095i) q^{5} +(1.85168 - 0.326500i) q^{7} +(7.99108 - 0.377649i) q^{8} +O(q^{10})\)	\(q+(-1.02714 - 1.71610i) q^{2} +(-1.88997 + 3.52534i) q^{4} +(-2.52245 + 0.918095i) q^{5} +(1.85168 - 0.326500i) q^{7} +(7.99108 - 0.377649i) q^{8} +(4.16644 + 3.38575i) q^{10} +(4.30945 - 11.8401i) q^{11} +(-7.78634 - 6.53352i) q^{13} +(-2.46224 - 2.84229i) q^{14} +(-8.85604 - 13.3256i) q^{16} +(-11.3753 + 19.7026i) q^{17} +(-18.9400 + 10.9350i) q^{19} +(1.53075 - 10.6276i) q^{20} +(-24.7452 + 4.76602i) q^{22} +(1.40339 + 0.247456i) q^{23} +(-13.6313 + 11.4380i) q^{25} +(-3.21448 + 20.0729i) q^{26} +(-2.34858 + 7.14486i) q^{28} +(-20.6757 + 17.3490i) q^{29} +(-32.6513 - 5.75731i) q^{31} +(-13.7716 + 28.8850i) q^{32} +(45.4956 - 0.716216i) q^{34} +(-4.37099 + 2.52359i) q^{35} +(18.4391 - 31.9375i) q^{37} +(38.2195 + 21.2711i) q^{38} +(-19.8103 + 8.28917i) q^{40} +(-1.18844 - 0.997219i) q^{41} +(7.41069 - 20.3607i) q^{43} +(33.5957 + 37.5697i) q^{44} +(-1.01682 - 2.66253i) q^{46} +(-70.2738 + 12.3912i) q^{47} +(-42.7228 + 15.5498i) q^{49} +(33.6299 + 11.6442i) q^{50} +(37.7488 - 15.1014i) q^{52} +45.3136 q^{53} +33.8225i q^{55} +(14.6736 - 3.30837i) q^{56} +(51.0094 + 17.6617i) q^{58} +(-31.4169 - 86.3172i) q^{59} +(13.6397 + 77.3544i) q^{61} +(23.6574 + 61.9464i) q^{62} +(63.7148 - 6.03565i) q^{64} +(25.6390 + 9.33183i) q^{65} +(-69.7557 + 83.1316i) q^{67} +(-47.9595 - 77.3392i) q^{68} +(8.82035 + 4.90896i) q^{70} +(29.5909 + 17.0843i) q^{71} +(20.6562 + 35.7776i) q^{73} +(-73.7472 + 1.16097i) q^{74} +(-2.75363 - 87.4367i) q^{76} +(4.11390 - 23.3311i) q^{77} +(10.0229 + 11.9448i) q^{79} +(34.5730 + 25.4823i) q^{80} +(-0.490630 + 3.06376i) q^{82} +(-49.5078 - 59.0011i) q^{83} +(10.6047 - 60.1424i) q^{85} +(-42.5527 + 8.19583i) q^{86} +(29.9658 - 96.2428i) q^{88} +(-88.0911 - 152.578i) q^{89} +(-16.5510 - 9.55571i) q^{91} +(-3.52473 + 4.47975i) q^{92} +(93.4455 + 107.869i) q^{94} +(37.7357 - 44.9717i) q^{95} +(-39.0324 - 14.2066i) q^{97} +(70.5673 + 57.3446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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