LMFDB - Embedded newform 324.3.j.a.199.27

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			199.27
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.51166 + 1.30953i) q^{2} +(0.570252 + 3.95914i) q^{4} +(-2.52245 + 0.918095i) q^{5} +(-1.85168 + 0.326500i) q^{7} +(-4.32259 + 6.73165i) q^{8} +O(q^{10})$	\(q+(1.51166 + 1.30953i) q^{2} +(0.570252 + 3.95914i) q^{4} +(-2.52245 + 0.918095i) q^{5} +(-1.85168 + 0.326500i) q^{7} +(-4.32259 + 6.73165i) q^{8} +(-5.01536 - 1.91537i) q^{10} +(-4.30945 + 11.8401i) q^{11} +(-7.78634 - 6.53352i) q^{13} +(-3.22667 - 1.93127i) q^{14} +(-15.3496 + 4.51542i) q^{16} +(-11.3753 + 19.7026i) q^{17} +(18.9400 - 10.9350i) q^{19} +(-5.07330 - 9.46317i) q^{20} +(-22.0194 + 12.2549i) q^{22} +(-1.40339 - 0.247456i) q^{23} +(-13.6313 + 11.4380i) q^{25} +(-3.21448 - 20.0729i) q^{26} +(-2.34858 - 7.14486i) q^{28} +(-20.6757 + 17.3490i) q^{29} +(32.6513 + 5.75731i) q^{31} +(-29.1166 - 13.2750i) q^{32} +(-42.9969 + 14.8874i) q^{34} +(4.37099 - 2.52359i) q^{35} +(18.4391 - 31.9375i) q^{37} +(42.9506 + 8.27247i) q^{38} +(4.72321 - 20.9488i) q^{40} +(-1.18844 - 0.997219i) q^{41} +(-7.41069 + 20.3607i) q^{43} +(-49.3342 - 10.3099i) q^{44} +(-1.79740 - 2.21186i) q^{46} +(70.2738 - 12.3912i) q^{47} +(-42.7228 + 15.5498i) q^{49} +(-35.5843 - 0.560187i) q^{50} +(21.4269 - 34.5530i) q^{52} +45.3136 q^{53} -33.8225i q^{55} +(5.80616 - 13.8762i) q^{56} +(-53.9739 - 0.849685i) q^{58} +(31.4169 + 86.3172i) q^{59} +(13.6397 + 77.3544i) q^{61} +(41.8184 + 51.4611i) q^{62} +(-26.6304 - 58.1964i) q^{64} +(25.6390 + 9.33183i) q^{65} +(69.7557 - 83.1316i) q^{67} +(-84.4923 - 33.8010i) q^{68} +(9.91220 + 1.90913i) q^{70} +(-29.5909 - 17.0843i) q^{71} +(20.6562 + 35.7776i) q^{73} +(69.6968 - 24.1321i) q^{74} +(54.0938 + 68.7504i) q^{76} +(4.11390 - 23.3311i) q^{77} +(-10.0229 - 11.9448i) q^{79} +(34.5730 - 25.4823i) q^{80} +(-0.490630 - 3.06376i) q^{82} +(49.5078 + 59.0011i) q^{83} +(10.6047 - 60.1424i) q^{85} +(-37.8654 + 21.0740i) q^{86} +(-61.0756 - 80.1897i) q^{88} +(-88.0911 - 152.578i) q^{89} +(16.5510 + 9.55571i) q^{91} +(0.179425 - 5.69734i) q^{92} +(122.457 + 73.2945i) q^{94} +(-37.7357 + 44.9717i) q^{95} +(-39.0324 - 14.2066i) q^{97} +(-84.9456 - 32.4408i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.51166	+	1.30953i	0.755832	+	0.654766i
$2$	1.51166	+	1.30953i	0.755832	+	0.654766i
$3$		0			0
$3$		0			0
$4$	0.570252	+	3.95914i	0.142563	+	0.989786i
$5$	−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	−0.304338	−	0.952564i	$-0.598435\pi$
$7$	−1.85168	+	0.326500i	−0.264525	+	0.0466429i	0.0398124	+	0.999207i	$0.487324\pi$
$8$	−4.32259	+	6.73165i	−0.540324	+	0.841457i
$9$		0			0
$10$	−5.01536	−	1.91537i	−0.501536	−	0.191537i
$11$	−4.30945	+	11.8401i	−0.391768	+	1.07637i	0.574426	+	0.818557i	$0.305225\pi$
$11$	−4.30945	+	11.8401i	−0.391768	+	1.07637i	−0.966194	+	0.257817i	$0.916997\pi$
$12$		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	$0.850071\pi$
$14$	−3.22667	−	1.93127i	−0.230477	−	0.137948i
$15$		0			0
$16$	−15.3496	+	4.51542i	−0.959352	+	0.282214i
$17$	−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	0.0895295	−	0.995984i	$-0.471464\pi$
$19$	18.9400	−	10.9350i	0.996842	−	0.575527i	0.907312	+	0.420457i	$0.138130\pi$
$20$	−5.07330	−	9.46317i	−0.253665	−	0.473159i
$21$		0			0
$22$	−22.0194	+	12.2549i	−1.00088	+	0.557041i
$23$	−1.40339	−	0.247456i	−0.0610170	−	0.0107589i	0.143056	−	0.989715i	$-0.454307\pi$
$23$	−1.40339	−	0.247456i	−0.0610170	−	0.0107589i	−0.204073	+	0.978956i	$0.565418\pi$
$24$		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	0.673368	−	0.739308i	$-0.264847\pi$
$31$	32.6513	+	5.75731i	1.05327	+	0.185720i	0.379901	+	0.925027i	$0.375958\pi$
$32$	−29.1166	−	13.2750i	−0.909892	−	0.414845i
$33$		0			0
$34$	−42.9969	+	14.8874i	−1.26461	+	0.437865i
$35$	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	$0.000604684\pi$
$38$	42.9506	+	8.27247i	1.13028	+	0.217697i
$39$		0			0
$40$	4.72321	−	20.9488i	0.118080	−	0.523720i
$41$	−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	−0.995550	−	0.0942347i	$-0.969960\pi$
$43$	−7.41069	+	20.3607i	−0.172342	+	0.473504i	0.823208	+	0.567739i	$0.192182\pi$
$44$	−49.3342	−	10.3099i	−1.12123	−	0.234315i
$45$		0			0
$46$	−1.79740	−	2.21186i	−0.0390740	−	0.0480838i
$47$	70.2738	−	12.3912i	1.49519	−	0.263642i	0.634559	−	0.772875i	$-0.281182\pi$
$47$	70.2738	−	12.3912i	1.49519	−	0.263642i	0.860629	+	0.509233i	$0.170071\pi$
$48$		0			0
$49$	−42.7228	+	15.5498i	−0.871895	+	0.317344i
$50$	−35.5843	−	0.560187i	−0.711687	−	0.0112037i
$51$		0			0
$52$	21.4269	−	34.5530i	0.412057	−	0.664480i
$53$	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
$56$	5.80616	−	13.8762i	0.103681	−	0.247789i
$57$		0			0
$58$	−53.9739	−	0.849685i	−0.930584	−	0.0146497i
$59$	31.4169	+	86.3172i	0.532490	+	1.46300i	0.856099	+	0.516812i	$0.172881\pi$
$59$	31.4169	+	86.3172i	0.532490	+	1.46300i	−0.323609	+	0.946191i	$0.604896\pi$
$60$		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	$0.721787\pi$
$62$	41.8184	+	51.4611i	0.674491	+	0.830017i
$63$		0			0
$64$	−26.6304	−	58.1964i	−0.416099	−	0.909319i
$65$	25.6390	+	9.33183i	0.394446	+	0.143567i
$66$		0			0
$67$	69.7557	−	83.1316i	1.04113	−	1.24077i	0.0711805	−	0.997463i	$-0.477323\pi$
$67$	69.7557	−	83.1316i	1.04113	−	1.24077i	0.969949	−	0.243307i	$-0.0782322\pi$
$68$	−84.4923	−	33.8010i	−1.24253	−	0.497074i
$69$		0			0
$70$	9.91220	+	1.90913i	0.141603	+	0.0272733i
$71$	−29.5909	−	17.0843i	−0.416774	−	0.240624i	0.276922	−	0.960892i	$-0.410686\pi$
$71$	−29.5909	−	17.0843i	−0.416774	−	0.240624i	−0.693696	+	0.720268i	$0.744019\pi$
$72$		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	$0.742016\pi$
$74$	69.6968	−	24.1321i	0.941849	−	0.326109i
$75$		0			0
$76$	54.0938	+	68.7504i	0.711761	+	0.904611i
$77$	4.11390	−	23.3311i	0.0534273	−	0.303001i
$78$		0			0
$79$	−10.0229	−	11.9448i	−0.126872	−	0.151200i	0.698869	−	0.715250i	$-0.253687\pi$
$79$	−10.0229	−	11.9448i	−0.126872	−	0.151200i	−0.825741	+	0.564050i	$0.809243\pi$
$80$	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	0.976837	−	0.213983i	$-0.0686436\pi$
$83$	49.5078	+	59.0011i	0.596480	+	0.710857i	−0.380358	+	0.924839i	$0.624199\pi$
$84$		0			0
$85$	10.6047	−	60.1424i	0.124762	−	0.707558i
$86$	−37.8654	+	21.0740i	−0.440296	+	0.245046i
$87$		0			0
$88$	−61.0756	−	80.1897i	−0.694041	−	0.911247i
$89$	−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
$92$	0.179425	−	5.69734i	0.00195028	−	0.0619276i
$93$		0			0
$94$	122.457	+	73.2945i	1.30273	+	0.779729i
$95$	−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	$0.679796\pi$
$98$	−84.9456	−	32.4408i	−0.866791	−	0.331029i
$99$		0			0
$100$	−53.0580	−	47.4456i	−0.530580	−	0.474456i
$101$	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	$0.209101\pi$
$103$	59.5132	+	163.511i	0.577798	+	1.58749i	−0.214085	+	0.976815i	$0.568677\pi$
$104$	77.6386	−	24.1732i	0.746525	−	0.232435i
$105$		0			0
$106$	68.4989	+	59.3396i	0.646216	+	0.559807i
$107$		−	15.1974i		−	0.142032i	−0.997475	−	0.0710159i	$-0.977376\pi$
$107$		−	15.1974i		−	0.142032i	0.997475	−	0.0710159i	$-0.0226241\pi$
$108$		0			0
$109$	191.484			1.75673			0.878367	−	0.477986i	$-0.158633\pi$
$109$	191.484			1.75673			0.878367	+	0.477986i	$0.158633\pi$
$110$	44.2917	−	51.1283i	0.402652	−	0.464802i
$111$		0			0
$112$	26.9482	−	13.3728i	0.240609	−	0.119400i
$113$	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
$116$	−80.4776	−	71.9649i	−0.693772	−	0.620387i
$117$		0			0
$118$	−65.5433	+	171.624i	−0.555452	+	1.45444i
$119$	14.6305	−	40.1969i	0.122945	−	0.337789i
$120$		0			0
$121$	−28.9256	−	24.2714i	−0.239054	−	0.200590i
$122$	−80.6794	+	134.795i	−0.661307	+	1.10488i
$123$		0			0
$124$	−4.17452	+	132.554i	−0.0336654	+	1.06899i
$125$	57.4371	−	99.4840i	0.459497	−	0.795872i
$126$		0			0
$127$	−5.73249	+	3.30965i	−0.0451377	+	0.0260603i	−0.522399	−	0.852701i	$-0.674963\pi$
$127$	−5.73249	+	3.30965i	−0.0451377	+	0.0260603i	0.477261	+	0.878761i	$0.341630\pi$
$128$	35.9539	−	122.847i	0.280890	−	0.959740i
$129$		0			0
$130$	26.5372	+	47.6817i	0.204132	+	0.366782i
$131$	−74.2972	−	13.1006i	−0.567154	−	0.100005i	−0.117284	−	0.993098i	$-0.537419\pi$
$131$	−74.2972	−	13.1006i	−0.567154	−	0.100005i	−0.449870	+	0.893094i	$0.648530\pi$
$132$		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	−0.161725	−	0.986836i	$-0.551706\pi$
$139$	−90.5189	−	15.9609i	−0.651215	−	0.114827i	−0.489490	+	0.872009i	$0.662817\pi$
$140$	12.4838	+	15.8663i	0.0891703	+	0.113331i
$141$		0			0
$142$	−22.3591	−	64.5760i	−0.157458	−	0.454761i
$143$	110.912	−	64.0353i	0.775611	−	0.447799i
$144$		0			0
$145$	36.2254	−	62.7442i	0.249830	−	0.432719i
$146$	−15.6267	+	81.1337i	−0.107032	+	0.555710i
$147$		0			0
$148$	136.960	+	54.7906i	0.925405	+	0.370207i
$149$	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	$0.347243\pi$
$151$	−69.7867	+	191.737i	−0.462164	+	1.26978i	−0.923855	+	0.382744i	$0.874979\pi$
$152$	−8.25919	+	174.765i	−0.0543368	+	1.14977i
$153$		0			0
$154$	36.7716	−	29.8815i	0.238777	−	0.194036i
$155$	−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	$0.452968\pi$
$158$	0.490880	−	31.1818i	0.00310683	−	0.197353i
$159$		0			0
$160$	85.6326	+	6.75376i	0.535204	+	0.0422110i
$161$	2.67942			0.0166424
$162$		0			0
$163$		−	53.0284i		−	0.325327i	−0.986682	−	0.162664i	$-0.947991\pi$
$163$		−	53.0284i		−	0.325327i	0.986682	−	0.162664i	$-0.0520085\pi$
$164$	3.27042	−	5.27386i	0.0199416	−	0.0321577i
$165$		0			0
$166$	−2.42469	+	154.022i	−0.0146066	+	0.927843i
$167$	−7.20265	−	19.7891i	−0.0431296	−	0.118498i	0.916258	−	0.400588i	$-0.131194\pi$
$167$	−7.20265	−	19.7891i	−0.0431296	−	0.118498i	−0.959388	+	0.282091i	$0.908972\pi$
$168$		0			0
$169$	−11.4063	−	64.6882i	−0.0674927	−	0.382770i
$170$	94.7892	−	77.0279i	0.557584	−	0.453105i
$171$		0			0
$172$	−84.8369	−	17.7292i	−0.493238	−	0.103077i
$173$	−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
$176$	12.6853	−	201.200i	0.0720757	−	1.14318i
$177$		0			0
$178$	66.6420	−	346.005i	0.374393	−	1.94385i
$179$	−58.2296	−	33.6189i	−0.325305	−	0.187815i	0.328450	−	0.944521i	$-0.393474\pi$
$179$	−58.2296	−	33.6189i	−0.325305	−	0.187815i	−0.653755	+	0.756707i	$0.726807\pi$
$180$		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	$0.752859\pi$
$182$	12.5060	+	36.1190i	0.0687143	+	0.198456i
$183$		0			0
$184$	7.73208	−	8.37750i	0.0420222	−	0.0455299i
$185$	−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	$-0.977812\pi$
$191$	−170.551	−	203.255i	−0.892937	−	1.06416i	0.104635	−	0.994511i	$-0.466633\pi$
$192$		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	$-0.111349\pi$
$194$	−40.3998	−	72.5898i	−0.208246	−	0.374174i
$195$		0			0
$196$	−85.9268	−	160.278i	−0.438402	−	0.817747i
$197$	−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	−0.0458104	−	0.998950i	$-0.514587\pi$
$199$	−185.833	−	107.290i	−0.933832	−	0.539148i	−0.888021	+	0.459802i	$0.847920\pi$
$200$	−18.0742	−	141.203i	−0.0903710	−	0.706015i
$201$		0			0
$202$	−50.4810	+	84.3412i	−0.249906	+	0.417531i
$203$	32.6203	−	38.8754i	0.160691	−	0.191504i
$204$		0			0
$205$	3.91331	+	1.42433i	0.0190893	+	0.00694795i
$206$	−124.159	+	325.108i	−0.602715	+	1.57820i
$207$		0			0
$208$	149.019	+	65.1284i	0.716437	+	0.313117i
$209$	47.8508	+	271.376i	0.228951	+	1.29845i
$210$		0			0
$211$	−26.5454	−	72.9330i	−0.125808	−	0.345654i	0.860759	−	0.509013i	$-0.169989\pi$
$211$	−26.5454	−	72.9330i	−0.125808	−	0.345654i	−0.986567	+	0.163359i	$0.947767\pi$
$212$	25.8402	+	179.403i	0.121888	+	0.846240i
$213$		0			0
$214$	19.9015	−	22.9733i	0.0929976	−	0.107352i
$215$		−	58.1624i		−	0.270523i
$216$		0			0
$217$	−62.3394			−0.287279
$218$	289.459	+	250.755i	1.32780	+	1.15025i
$219$		0			0
$220$	133.908	−	19.2874i	0.608674	−	0.0876699i
$221$	217.300	−	79.0906i	0.983256	−	0.357876i
$222$		0			0
$223$	177.451	−	31.2894i	0.795746	−	0.140311i	0.239027	−	0.971013i	$-0.423171\pi$
$223$	177.451	−	31.2894i	0.795746	−	0.140311i	0.556718	+	0.830701i	$0.312060\pi$
$224$	58.2487	+	15.0745i	0.260039	+	0.0672968i
$225$		0			0
$226$	176.151	+	67.2721i	0.779428	+	0.297664i
$227$	37.5673	−	103.215i	0.165495	−	0.454693i	−0.829029	−	0.559206i	$-0.811106\pi$
$227$	37.5673	−	103.215i	0.165495	−	0.454693i	0.994524	+	0.104513i	$0.0333283\pi$
$228$		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	$0.856227\pi$
$230$	6.56455	+	3.92910i	0.0285415	+	0.0170830i
$231$		0			0
$232$	−27.4147	−	214.175i	−0.118167	−	0.923167i
$233$	−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
$236$	−323.826	+	173.607i	−1.37215	+	0.735621i
$237$		0			0
$238$	74.7555	−	41.6051i	0.314099	−	0.174812i
$239$	−88.4519	−	15.5965i	−0.370092	−	0.0652571i	−0.0144906	−	0.999895i	$-0.504613\pi$
$239$	−88.4519	−	15.5965i	−0.370092	−	0.0652571i	−0.355601	+	0.934638i	$0.615724\pi$
$240$		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
$248$	−179.895	+	194.911i	−0.725382	+	0.785931i
$249$		0			0
$250$	217.103	−	75.1706i	0.868412	−	0.300682i
$251$	−121.486	+	70.1402i	−0.484009	+	0.279443i	−0.722086	−	0.691804i	$-0.756816\pi$
$251$	−121.486	+	70.1402i	−0.484009	+	0.279443i	0.238077	+	0.971246i	$0.423483\pi$
$252$		0			0
$253$	8.97775	−	15.5499i	0.0354852	−	0.0614621i
$254$	−12.9997	−	2.50379i	−0.0511799	−	0.00985745i
$255$		0			0
$256$	215.222	−	138.620i	0.840711	−	0.541485i
$257$	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
$260$	−22.3254	+	106.830i	−0.0858668	+	0.410885i
$261$		0			0
$262$	−95.1567	−	117.098i	−0.363194	−	0.446940i
$263$	−195.884	+	34.5397i	−0.744807	+	0.131330i	−0.533157	−	0.846016i	$-0.678995\pi$
$263$	−195.884	+	34.5397i	−0.744807	+	0.131330i	−0.211649	+	0.977346i	$0.567883\pi$
$264$		0			0
$265$	−114.301	+	41.6022i	−0.431325	+	0.156989i
$266$	−82.2316	−	1.29453i	−0.309141	−	0.00486667i
$267$		0			0
$268$	368.908	+	228.767i	1.37652	+	0.853607i
$269$	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	$0.291292\pi$
$271$			429.609i			1.58527i	−0.609694	+	0.792637i	$0.708708\pi$
$272$	85.6412	−	353.792i	0.314857	−	1.30071i
$273$		0			0
$274$	−465.372	−	7.32613i	−1.69844	−	0.0267377i
$275$	−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	$0.550439\pi$
$278$	−115.933	−	142.665i	−0.417024	−	0.513183i
$279$		0			0
$280$	−1.90607	+	40.3325i	−0.00680738	+	0.144045i
$281$	−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	−0.947221	−	0.320581i	$-0.896122\pi$
$283$	−132.169	+	157.512i	−0.467027	+	0.556581i	0.480194	+	0.877162i	$0.340566\pi$
$284$	50.7650	−	126.897i	0.178750	−	0.446821i
$285$		0			0
$286$	251.519	+	48.4435i	0.879435	+	0.169383i
$287$	2.52620	+	1.45850i	0.00880208	+	0.00508188i
$288$		0			0
$289$	−114.296	−	197.966i	−0.395487	−	0.685004i
$290$	136.926	−	47.4098i	0.472159	−	0.163482i
$291$		0			0
$292$	−129.869	+	102.183i	−0.444758	+	0.349942i
$293$	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
$302$	−356.580	+	198.455i	−1.18073	+	0.657134i
$303$		0			0
$304$	−241.346	+	253.370i	−0.793900	+	0.833455i
$305$	−105.424	−	182.600i	−0.345652	−	0.598687i
$306$		0			0
$307$	452.918	+	261.492i	1.47530	+	0.851766i	0.999612	−	0.0278473i	$-0.00886522\pi$
$307$	452.918	+	261.492i	1.47530	+	0.851766i	0.475690	+	0.879613i	$0.342199\pi$
$308$	94.7171	+	2.98291i	0.307523	+	0.00968478i
$309$		0			0
$310$	−152.731	−	91.4144i	−0.492680	−	0.294885i
$311$	86.2078	−	102.739i	0.277196	−	0.330349i	−0.609427	−	0.792842i	$-0.708601\pi$
$311$	86.2078	−	102.739i	0.277196	−	0.330349i	0.886623	+	0.462493i	$0.153045\pi$
$312$		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	$0.579004\pi$
$314$	−117.306	−	44.7995i	−0.373588	−	0.142673i
$315$		0			0
$316$	41.5756	−	46.4935i	0.131568	−	0.147131i
$317$	−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
$320$	120.603	+	122.348i	0.376886	+	0.382338i
$321$		0			0
$322$	4.05038	+	3.50879i	0.0125788	+	0.0108969i
$323$			497.557i			1.54042i
$324$		0			0
$325$	180.868			0.556517
$326$	69.4423	−	80.1610i	0.213013	−	0.245893i
$327$		0			0
$328$	11.8501	−	3.68959i	0.0361283	−	0.0112487i
$329$	−126.079	+	45.8889i	−0.383218	+	0.139480i
$330$		0			0
$331$	493.266	−	86.9762i	1.49023	−	0.262768i	0.631572	−	0.775317i	$-0.282410\pi$
$331$	493.266	−	86.9762i	1.49023	−	0.262768i	0.858658	+	0.512549i	$0.171299\pi$
$332$	−205.362	+	229.654i	−0.618560	+	0.691729i
$333$		0			0
$334$	15.0265	−	39.3466i	0.0449895	−	0.117804i
$335$	−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	$0.834317\pi$
$338$	67.4688	−	112.724i	0.199612	−	0.333502i
$339$		0			0
$340$	244.160	+	7.68929i	0.718117	+	0.0226156i
$341$	−208.876	+	361.785i	−0.612541	+	1.06095i
$342$		0			0
$343$	153.820	−	88.8082i	0.448456	−	0.258916i
$344$	−105.028	−	137.897i	−0.305313	−	0.400864i
$345$		0			0
$346$	−158.316	−	284.460i	−0.457560	−	0.822138i
$347$	518.270	+	91.3849i	1.49357	+	0.263357i	0.859987	−	0.510315i	$-0.170471\pi$
$347$	518.270	+	91.3849i	1.49357	+	0.263357i	0.633586	+	0.773673i	$0.281582\pi$
$348$		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
$356$	553.845	−	435.774i	1.55575	−	1.22408i
$357$		0			0
$358$	−43.9986	−	127.074i	−0.122901	−	0.354955i
$359$	359.255	−	207.416i	1.00071	−	0.577761i	0.0922526	−	0.995736i	$-0.470593\pi$
$359$	359.255	−	207.416i	1.00071	−	0.577761i	0.908459	+	0.417975i	$0.137260\pi$
$360$		0			0
$361$	58.6489	−	101.583i	0.162462	−	0.281393i
$362$	−34.2505	+	177.828i	−0.0946146	+	0.491238i
$363$		0			0
$364$	−28.3942	+	70.9768i	−0.0780060	+	0.194991i
$365$	−84.9514	−	71.2827i	−0.232744	−	0.195295i
$366$		0			0
$367$	−85.5131	+	234.945i	−0.233006	+	0.640178i	−0.999999	−	0.00147719i	$-0.999530\pi$
$367$	−85.5131	+	234.945i	−0.233006	+	0.640178i	0.766993	+	0.641655i	$0.221752\pi$
$368$	22.6589	−	2.53855i	0.0615731	−	0.00689823i
$369$		0			0
$370$	−153.651	+	124.860i	−0.415273	+	0.337460i
$371$	−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	$0.171090\pi$
$374$	9.02432	−	573.244i	0.0241292	−	1.53274i
$375$		0			0
$376$	−220.352	+	526.621i	−0.586043	+	1.40059i
$377$	274.338			0.727688
$378$		0			0
$379$		−	28.5744i		−	0.0753941i	−0.999289	−	0.0376970i	$-0.987998\pi$
$379$		−	28.5744i		−	0.0753941i	0.999289	−	0.0376970i	$-0.0120022\pi$
$380$	−199.568	−	123.756i	−0.525179	−	0.325673i
$381$		0			0
$382$	8.35290	−	530.595i	0.0218662	−	1.38899i
$383$	−52.2463	−	143.546i	−0.136413	−	0.374793i	0.852611	−	0.522546i	$-0.175018\pi$
$383$	−52.2463	−	143.546i	−0.136413	−	0.374793i	−0.989024	+	0.147754i	$0.952796\pi$
$384$		0			0
$385$	11.0431	+	62.6284i	0.0286833	+	0.162671i
$386$	299.950	−	243.747i	0.777074	−	0.631468i
$387$		0			0
$388$	33.9878	−	162.636i	0.0875973	−	0.419166i
$389$	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
$392$	79.9973	−	354.811i	0.204075	−	0.905130i
$393$		0			0
$394$	115.381	−	599.060i	0.292846	−	1.52046i
$395$	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	$0.753333\pi$
$398$	−140.416	−	405.541i	−0.352804	−	1.01895i
$399$		0			0
$400$	157.588	−	237.120i	0.393969	−	0.592800i
$401$	−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	$0.106742\pi$
$410$	4.05041	+	7.27771i	0.00987904	+	0.0177505i
$411$		0			0
$412$	−613.427	+	328.864i	−1.48890	+	0.798213i
$413$	−86.3565	−	149.574i	−0.209096	−	0.362164i
$414$		0			0
$415$	−179.049	−	103.374i	−0.431444	−	0.249094i
$416$	139.979	+	293.597i	0.336488	+	0.705763i
$417$		0			0
$418$	−283.041	+	472.891i	−0.677131	+	1.13132i
$419$	97.7496	−	116.493i	0.233293	−	0.278027i	−0.636679	−	0.771129i	$-0.719692\pi$
$419$	97.7496	−	116.493i	0.233293	−	0.278027i	0.869972	+	0.493101i	$0.164137\pi$
$420$		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	$0.633490\pi$
$422$	55.3803	−	145.012i	0.131233	−	0.343631i
$423$		0			0
$424$	−195.872	+	305.035i	−0.461963	+	0.719423i
$425$	−70.2986	−	398.683i	−0.165408	−	0.938078i
$426$		0			0
$427$	−50.5125	−	138.782i	−0.118296	−	0.325016i
$428$	60.1687	−	8.66635i	0.140581	−	0.0202485i
$429$		0			0
$430$	76.1656	−	87.9220i	0.177129	−	0.204470i
$431$			225.843i			0.523998i	0.965068	+	0.261999i	$0.0843818\pi$
$431$			225.843i			0.523998i	−0.965068	+	0.261999i	$0.915618\pi$
$432$		0			0
$433$	71.7938			0.165805			0.0829027	−	0.996558i	$-0.473581\pi$
$433$	71.7938			0.165805			0.0829027	+	0.996558i	$0.473581\pi$
$434$	−94.2362	−	81.6355i	−0.217134	−	0.188100i
$435$		0			0
$436$	109.194	+	758.113i	0.250446	+	1.73879i
$437$	−29.2862	+	10.6593i	−0.0670164	+	0.0243920i
$438$		0			0
$439$	663.291	−	116.956i	1.51091	−	0.266415i	0.644059	−	0.764976i	$-0.277249\pi$
$439$	663.291	−	116.956i	1.51091	−	0.266415i	0.866855	+	0.498561i	$0.166138\pi$
$440$	227.682	+	146.201i	0.517458	+	0.332275i
$441$		0			0
$442$	432.055	+	165.002i	0.977501	+	0.373309i
$443$	74.1027	−	203.596i	0.167275	−	0.459584i	−0.827526	−	0.561428i	$-0.810252\pi$
$443$	74.1027	−	203.596i	0.167275	−	0.459584i	0.994800	+	0.101844i	$0.0324744\pi$
$444$		0			0
$445$	362.286	+	303.994i	0.814127	+	0.683134i
$446$	309.221	+	185.079i	0.693321	+	0.414975i
$447$		0			0
$448$	68.3119	+	99.0661i	0.152482	+	0.221130i
$449$	−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
$452$	178.186	+	332.368i	0.394216	+	0.735327i
$453$		0			0
$454$	191.953	−	106.831i	0.422804	−	0.235311i
$455$	−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	0.992706	−	0.120562i	$-0.0384697\pi$
$463$	872.435	+	153.834i	1.88431	+	0.332255i	0.891604	+	0.452817i	$0.149581\pi$
$464$	239.027	−	359.661i	0.515144	−	0.775130i
$465$		0			0
$466$	−422.044	+	146.130i	−0.905674	+	0.313584i
$467$	−259.319	+	149.718i	−0.555287	+	0.320595i	−0.751252	−	0.660016i	$-0.770550\pi$
$467$	−259.319	+	149.718i	−0.555287	+	0.320595i	0.195964	+	0.980611i	$0.437216\pi$
$468$		0			0
$469$	−102.022	+	176.708i	−0.217532	+	0.376776i
$470$	−376.182	−	72.4543i	−0.800388	−	0.154158i
$471$		0			0
$472$	−716.860	−	161.627i	−1.51877	−	0.342429i
$473$	−209.137	−	175.487i	−0.442150	−	0.371008i
$474$		0			0
$475$	−133.102	+	365.694i	−0.280214	+	0.769882i
$476$	167.488	+	35.0018i	0.351867	+	0.0735332i
$477$		0			0
$478$	−113.285	−	139.407i	−0.236999	−	0.291647i
$479$	236.431	−	41.6891i	0.493592	−	0.0870337i	0.0786892	−	0.996899i	$-0.474927\pi$
$479$	236.431	−	41.6891i	0.493592	−	0.0870337i	0.414903	+	0.909866i	$0.363815\pi$
$480$		0			0
$481$	−352.237	+	128.204i	−0.732301	+	0.266536i
$482$	−854.947	−	13.4590i	−1.77375	−	0.0279233i
$483$		0			0
$484$	79.5992	−	128.361i	0.164461	−	0.265209i
$485$	111.500			0.229897
$486$		0			0
$487$		−	520.778i		−	1.06936i	−0.845055	−	0.534680i	$-0.820432\pi$
$487$		−	520.778i		−	1.06936i	0.845055	−	0.534680i	$-0.179568\pi$
$488$	−579.682	−	242.554i	−1.18787	−	0.497037i
$489$		0			0
$490$	244.054	+	3.84203i	0.498070	+	0.00784088i
$491$	120.820	+	331.951i	0.246070	+	0.676071i	0.999821	+	0.0189114i	$0.00602004\pi$
$491$	120.820	+	331.951i	0.246070	+	0.676071i	−0.753751	+	0.657160i	$0.771758\pi$
$492$		0			0
$493$	−106.628	−	604.717i	−0.216284	−	1.22661i
$494$	−280.380	−	345.031i	−0.567571	−	0.698443i
$495$		0			0
$496$	−527.182	+	59.0619i	−1.06287	+	0.119077i
$497$	60.3709	+	21.9732i	0.121471	+	0.0442117i
$498$		0			0
$499$	−201.989	+	240.721i	−0.404787	+	0.482406i	−0.929473	−	0.368889i	$-0.879738\pi$
$499$	−201.989	+	240.721i	−0.404787	+	0.482406i	0.524686	+	0.851296i	$0.324183\pi$
$500$	426.625	+	170.671i	0.853250	+	0.341341i
$501$		0			0
$502$	−275.497	−	53.0619i	−0.548799	−	0.105701i
$503$	527.110	+	304.327i	1.04793	+	0.605024i	0.922070	−	0.387024i	$-0.126497\pi$
$503$	527.110	+	304.327i	1.04793	+	0.605024i	0.125862	+	0.992048i	$0.459830\pi$
$504$		0			0
$505$	−65.9636	−	114.252i	−0.130621	−	0.226242i
$506$	33.9344	−	11.7496i	0.0670641	−	0.0232205i
$507$		0			0
$508$	−16.3723	−	20.8084i	−0.0322290	−	0.0409614i
$509$	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
$518$	−121.177	+	67.4409i	−0.233932	+	0.130195i
$519$		0			0
$520$	−173.646	+	132.255i	−0.333934	+	0.254337i
$521$	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	0.780142	−	0.625602i	$-0.215147\pi$
$523$	328.667	+	189.756i	0.628426	+	0.362822i	−0.151717	+	0.988424i	$0.548480\pi$
$524$	9.49900	−	301.624i	0.0181279	−	0.575618i
$525$		0			0
$526$	−341.342	−	204.304i	−0.648939	−	0.388411i
$527$	−484.853	+	577.826i	−0.920025	+	1.09644i
$528$		0			0
$529$	−495.189	−	180.234i	−0.936085	−	0.340707i
$530$	−227.264	−	86.7923i	−0.428800	−	0.163759i
$531$		0			0
$532$	−122.611	−	109.642i	−0.230472	−	0.206094i
$533$	2.73825	+	15.5294i	0.00513742	+	0.0291358i
$534$		0			0
$535$	13.9527	+	38.3346i	0.0260797	+	0.0716535i
$536$	258.088	+	828.916i	0.481507	+	1.54648i
$537$		0			0
$538$	367.064	+	317.982i	0.682274	+	0.591044i
$539$		−	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	$0.797009\pi$
$542$	−562.587	+	649.424i	−1.03798	+	1.19820i
$543$		0			0
$544$	592.763	−	422.665i	1.08964	−	0.776958i
$545$	−483.008	+	175.801i	−0.886253	+	0.322570i
$546$		0			0
$547$	419.101	−	73.8988i	0.766181	−	0.135098i	0.223119	−	0.974791i	$-0.428376\pi$
$547$	419.101	−	73.8988i	0.766181	−	0.135098i	0.543062	+	0.839693i	$0.317265\pi$
$548$	−693.892	−	620.494i	−1.26623	−	1.13229i
$549$		0			0
$550$	159.982	−	418.909i	0.290876	−	0.761652i
$551$	−201.887	+	554.680i	−0.366401	+	1.00668i
$552$		0			0
$553$	22.4591	+	18.8454i	0.0406132	+	0.0340785i
$554$	−537.777	+	898.493i	−0.970717	+	1.62183i
$555$		0			0
$556$	11.5730	−	367.479i	0.0208147	−	0.660933i
$557$	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
$560$	−55.6980	+	58.4731i	−0.0994607	+	0.104416i
$561$		0			0
$562$	−161.405	−	290.010i	−0.287197	−	0.516032i
$563$	141.923	+	25.0249i	0.252084	+	0.0444492i	0.298262	−	0.954484i	$-0.403593\pi$
$563$	141.923	+	25.0249i	0.252084	+	0.0444492i	−0.0461780	+	0.998933i	$0.514704\pi$
$564$		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	−0.173109	−	0.984903i	$-0.555381\pi$
$571$	−384.074	−	67.7226i	−0.672634	−	0.118604i	−0.499526	+	0.866299i	$0.666492\pi$
$572$	316.773	+	402.602i	0.553799	+	0.703849i
$573$		0			0
$574$	1.90881	+	5.51289i	0.00332545	+	0.00960435i
$575$	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	$0.830466\pi$
$578$	86.4662	−	448.932i	0.149595	−	0.776699i
$579$		0			0
$580$	269.071	+	107.641i	0.463915	+	0.185589i
$581$	−110.936	−	93.0866i	−0.190940	−	0.160218i
$582$		0			0
$583$	−195.277	+	536.518i	−0.334951	+	0.920271i
$584$	−330.131	−	15.6016i	−0.565293	−	0.0267151i
$585$		0			0
$586$	377.562	−	306.815i	0.644304	−	0.523576i
$587$	661.848	−	116.702i	1.12751	−	0.198810i	0.421374	−	0.906887i	$-0.361548\pi$
$587$	661.848	−	116.702i	1.12751	−	0.198810i	0.706136	+	0.708077i	$0.250437\pi$
$588$		0			0
$589$	681.372	−	247.999i	1.15683	−	0.421051i
$590$	7.76243	−	493.087i	0.0131567	−	0.835741i
$591$		0			0
$592$	−138.822	+	573.488i	−0.234497	+	0.968730i
$593$	−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
$596$	−486.148	+	783.961i	−0.815685	+	1.31537i
$597$		0			0
$598$	−0.455992	+	28.9656i	−0.000762529	+	0.0484375i
$599$	30.3539	+	83.3966i	0.0506743	+	0.139226i	0.962448	−	0.271467i	$-0.0875088\pi$
$599$	30.3539	+	83.3966i	0.0506743	+	0.139226i	−0.911773	+	0.410694i	$0.865287\pi$
$600$		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	$-0.193809\pi$
$602$	63.2339	−	51.3853i	0.105040	−	0.0853576i
$603$		0			0
$604$	−798.912	−	166.957i	−1.32270	−	0.276419i
$605$	95.2467	+	34.6670i	0.157433	+	0.0573008i
$606$		0			0
$607$	59.8471	−	71.3229i	0.0985948	−	0.117501i	−0.714491	−	0.699645i	$-0.753342\pi$
$607$	59.8471	−	71.3229i	0.0985948	−	0.117501i	0.813086	+	0.582144i	$0.197786\pi$
$608$	−696.630	+	66.9609i	−1.14577	+	0.110133i
$609$		0			0
$610$	79.7545	−	414.085i	0.130745	−	0.678828i
$611$	−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	$0.822293\pi$
$614$	342.227	+	988.398i	0.557373	+	1.60977i
$615$		0			0
$616$	139.274	+	128.544i	0.226094	+	0.208676i
$617$	−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	$-0.996470\pi$
$619$	−518.241	−	617.616i	−0.837224	−	0.997764i	0.162715	−	0.986673i	$-0.447975\pi$
$620$	−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
$626$	61.3103	+	110.162i	0.0979398	+	0.175977i
$627$		0			0
$628$	−118.662	−	221.338i	−0.188952	−	0.352450i
$629$	419.501	+	726.597i	0.666934	+	1.15516i
$630$		0			0
$631$	−960.558	−	554.578i	−1.52228	−	0.878888i	−0.999653	−	0.0263256i	$-0.991619\pi$
$631$	−960.558	−	554.578i	−1.52228	−	0.878888i	−0.522625	−	0.852562i	$-0.675047\pi$
$632$	123.733	−	15.8380i	0.195780	−	0.0250601i
$633$		0			0
$634$	182.459	−	304.844i	0.287790	−	0.480826i
$635$	11.4213	−	13.6114i	0.0179863	−	0.0214352i
$636$		0			0
$637$	434.250	+	158.054i	0.681711	+	0.248122i
$638$	242.658	−	635.395i	0.380342	−	0.995917i
$639$		0			0
$640$	22.0931	+	342.883i	0.0345205	+	0.535755i
$641$	−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	$0.0122291\pi$
$643$	166.197	+	456.624i	0.258472	+	0.710146i	−0.740790	+	0.671737i	$0.765549\pi$
$644$	1.52795	+	10.6082i	0.00237259	+	0.0164724i
$645$		0			0
$646$	−651.567	+	752.139i	−1.00862	+	1.16430i
$647$		−	208.039i		−	0.321544i	−0.986992	−	0.160772i	$-0.948602\pi$
$647$		−	208.039i		−	0.321544i	0.986992	−	0.160772i	$-0.0513984\pi$
$648$		0			0
$649$	−1157.39			−1.78335
$650$	273.412	+	236.853i	0.420633	+	0.364389i
$651$		0			0
$652$	209.947	−	30.2395i	0.322004	−	0.0463797i
$653$	−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
$656$	22.7450	+	9.94063i	0.0346722	+	0.0151534i
$657$		0			0
$658$	−250.681	−	95.7355i	−0.380975	−	0.145495i
$659$	122.012	−	335.225i	0.185147	−	0.508687i	−0.812043	−	0.583597i	$-0.801645\pi$
$659$	122.012	−	335.225i	0.185147	−	0.508687i	0.997190	+	0.0749099i	$0.0238669\pi$
$660$		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	$0.513694\pi$
$662$	859.551	+	514.469i	1.29841	+	0.777144i
$663$		0			0
$664$	−611.177	+	78.2316i	−0.920448	+	0.117819i
$665$	55.1910	−	95.5937i	0.0829941	−	0.143750i
$666$		0			0
$667$	33.3093	−	19.2311i	0.0499389	−	0.0288323i
$668$	74.2406	−	39.8011i	0.111139	−	0.0595825i
$669$		0			0
$670$	−509.078	+	283.327i	−0.759818	+	0.422876i
$671$	−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
$680$	359.018	+	331.359i	0.527968	+	0.487292i
$681$		0			0
$682$	−789.519	+	273.366i	−1.15765	+	0.400830i
$683$	−184.655	+	106.611i	−0.270359	+	0.156092i	−0.629051	−	0.777364i	$-0.716556\pi$
$683$	−184.655	+	106.611i	−0.270359	+	0.156092i	0.358692	+	0.933456i	$0.383223\pi$
$684$		0			0
$685$	312.342	−	540.992i	0.455974	−	0.789769i
$686$	348.822	+	67.1845i	0.508486	+	0.0979366i
$687$		0			0
$688$	21.8141	−	345.991i	0.0317066	−	0.502894i
$689$	−352.827	−	296.057i	−0.512085	−	0.429691i
$690$		0			0
$691$	−250.303	+	687.702i	−0.362233	+	0.995227i	0.616005	+	0.787742i	$0.288750\pi$
$691$	−250.303	+	687.702i	−0.362233	+	0.995227i	−0.978238	+	0.207485i	$0.933472\pi$
$692$	133.189	−	637.327i	0.192469	−	0.920992i
$693$		0			0
$694$	663.778	+	816.834i	0.956452	+	1.17699i
$695$	242.983	−	42.8444i	0.349615	−	0.0616466i
$696$		0			0
$697$	33.1667	−	12.0717i	0.0475849	−	0.0173195i
$698$	1296.11	+	20.4041i	1.85690	+	0.0292323i
$699$		0			0
$700$	113.737	+	70.5305i	0.162482	+	0.100758i
$701$	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
$704$	803.815	−	64.5119i	1.14178	−	0.0916363i
$705$		0			0
$706$	111.449	+	1.75449i	0.157860	+	0.00248511i
$707$	−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	$-0.165642\pi$
$710$	115.686	+	142.362i	0.162939	+	0.200510i
$711$		0			0
$712$	1407.89	+	66.5351i	1.97737	+	0.0934481i
$713$	−44.3979	−	16.1595i	−0.0622692	−	0.0226641i
$714$		0			0
$715$	−220.980	+	263.354i	−0.309063	+	0.368327i
$716$	99.8963	−	249.710i	0.139520	−	0.348758i
$717$		0			0
$718$	814.691	+	156.913i	1.13467	+	0.218542i
$719$	−1151.09	−	664.581i	−1.60096	−	0.924313i	−0.991296	−	0.131650i	$-0.957972\pi$
$719$	−1151.09	−	664.581i	−1.60096	−	0.924313i	−0.609661	−	0.792662i	$-0.708694\pi$
$720$		0			0
$721$	−163.586	−	283.339i	−0.226887	−	0.392980i
$722$	221.683	−	76.7565i	0.307041	−	0.106311i
$723$		0			0
$724$	−284.647	+	223.964i	−0.393159	+	0.309343i
$725$	83.3989	−	472.978i	0.115033	−	0.652384i
$726$		0			0
$727$	−350.736	−	417.991i	−0.482443	−	0.574953i	0.468836	−	0.883285i	$-0.344674\pi$
$727$	−350.736	−	417.991i	−0.482443	−	0.574953i	−0.951279	+	0.308332i	$0.900229\pi$
$728$	−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	$0.0870005\pi$
$734$	−436.936	+	243.176i	−0.595280	+	0.331303i
$735$		0			0
$736$	37.5769	+	25.8351i	0.0510556	+	0.0351021i
$737$	683.679	+	1184.17i	0.927651	+	1.60674i
$738$		0			0
$739$	−202.168	−	116.722i	−0.273570	−	0.157946i	0.356939	−	0.934128i	$-0.383820\pi$
$739$	−202.168	−	116.722i	−0.273570	−	0.157946i	−0.630509	+	0.776182i	$0.717154\pi$
$740$	−395.777	−	12.4641i	−0.534833	−	0.0168434i
$741$		0			0
$742$	−146.212	−	87.5127i	−0.197051	−	0.117942i
$743$	388.931	−	463.509i	0.523460	−	0.623835i	−0.437935	−	0.899006i	$-0.644290\pi$
$743$	388.931	−	463.509i	0.523460	−	0.623835i	0.961395	+	0.275171i	$0.0887346\pi$
$744$		0			0
$745$	−581.714	−	211.727i	−0.780825	−	0.284197i
$746$	881.002	+	336.456i	1.18097	+	0.451013i
$747$		0			0
$748$	764.324	−	854.735i	1.02182	−	1.14269i
$749$	4.96196	+	28.1407i	0.00662478	+	0.0375710i
$750$		0			0
$751$	−9.87280	−	27.1253i	−0.0131462	−	0.0361189i	0.932946	−	0.360016i	$-0.117229\pi$
$751$	−9.87280	−	27.1253i	−0.0131462	−	0.0361189i	−0.946092	+	0.323898i	$0.895007\pi$
$752$	−1022.73	+	507.516i	−1.36001	+	0.674888i
$753$		0			0
$754$	414.707	+	359.255i	0.550010	+	0.476465i
$755$		−	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	$0.285592\pi$
$758$	37.4190	−	43.1948i	0.0493655	−	0.0569852i
$759$		0			0
$760$	−139.618	−	448.418i	−0.183707	−	0.590024i
$761$	−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
$764$	707.457	−	791.142i	0.925991	−	1.03553i
$765$		0			0
$766$	108.999	−	285.411i	0.142296	−	0.372599i
$767$	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	$0.620789\pi$
$770$	−65.3204	+	109.134i	−0.0848317	+	0.141733i
$771$		0			0
$772$	772.618	+	24.3319i	1.00080	+	0.0315181i
$773$	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
$776$	264.355	−	201.343i	0.340664	−	0.259463i
$777$		0			0
$778$	417.433	+	750.037i	0.536546	+	0.964058i
$779$	−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	0.240422	−	0.970669i	$-0.422714\pi$
$787$	105.738	+	18.6445i	0.134356	+	0.0236906i	−0.106066	+	0.994359i	$0.533825\pi$
$788$	958.905	−	754.481i	1.21689	−	0.957463i
$789$		0			0
$790$	27.3896	+	79.1049i	0.0346704	+	0.100133i
$791$	−153.519	+	88.6342i	−0.194082	+	0.112053i
$792$		0			0
$793$	399.193	−	691.422i	0.503396	−	0.871907i
$794$	−74.6909	+	387.795i	−0.0940691	+	0.488406i
$795$		0			0
$796$	318.807	−	796.920i	0.400511	−	1.00116i
$797$	−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
$800$	548.736	−	152.080i	0.685920	−	0.190100i
$801$		0			0
$802$	−578.657	+	470.230i	−0.721517	+	0.586321i
$803$	−512.628	+	90.3902i	−0.638391	+	0.112566i
$804$		0			0
$805$	−6.75869	+	2.45996i	−0.00839589	+	0.00305585i
$806$	10.6091	−	673.915i	0.0131627	−	0.836122i
$807$		0			0
$808$	−362.706	−	151.766i	−0.448893	−	0.187829i
$809$	−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	$0.114330\pi$
$811$			570.142i			0.703011i	−0.936186	+	0.351506i	$0.885670\pi$
$812$	172.515	+	106.980i	0.212457	+	0.131748i
$813$		0			0
$814$	−14.6282	+	929.214i	−0.0179707	+	1.14154i
$815$	48.6851	+	133.761i	0.0597363	+	0.164124i
$816$		0			0
$817$	82.2860	+	466.667i	0.100717	+	0.571196i
$818$	−203.290	+	165.198i	−0.248521	+	0.201954i
$819$		0			0
$820$	−3.40755	+	16.3056i	−0.00415555	+	0.0198849i
$821$	−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	−0.504358	−	0.863494i	$-0.668271\pi$
$823$	356.852	−	425.279i	0.433599	−	0.516743i	0.937957	+	0.346752i	$0.112715\pi$
$824$	−1357.95	−	306.170i	−1.64800	−	0.371566i
$825$		0			0
$826$	65.3297	−	339.192i	0.0790917	−	0.410644i
$827$	917.032	+	529.449i	1.10887	+	0.640204i	0.938535	−	0.345183i	$-0.112183\pi$
$827$	917.032	+	529.449i	1.10887	+	0.640204i	0.170330	+	0.985387i	$0.445516\pi$
$828$		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	$0.822425\pi$
$830$	−135.291	−	390.738i	−0.163001	−	0.470769i
$831$		0			0
$832$	−172.874	+	627.127i	−0.207782	+	0.753758i
$833$	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	$0.0554532\pi$
$839$	826.031	+	984.425i	0.984542	+	1.17333i	−0.000321569		1.00000i	$0.500102\pi$
$840$		0			0
$841$	−19.5398	+	110.816i	−0.0232340	+	0.131767i
$842$	−57.5279	−	103.365i	−0.0683229	−	0.122762i
$843$		0			0
$844$	273.615	−	146.687i	0.324188	−	0.173800i
$845$	88.1616	+	152.700i	0.104333	+	0.180710i
$846$		0			0
$847$	61.4854	+	35.4986i	0.0725920	+	0.0419110i
$848$	−695.546	+	204.610i	−0.820220	+	0.241285i
$849$		0			0
$850$	415.820	−	694.733i	0.489200	−	0.817333i
$851$	−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	$0.509744\pi$
$854$	105.381	−	275.939i	0.123397	−	0.323114i
$855$		0			0
$856$	102.304	+	65.6922i	0.119514	+	0.0767432i
$857$	−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	0.919364	−	0.393407i	$-0.128704\pi$
$859$	−32.4589	−	89.1800i	−0.0377868	−	0.103818i	−0.957151	+	0.289589i	$0.906481\pi$
$860$	230.273	−	33.1673i	0.267760	−	0.0385666i
$861$		0			0
$862$	−295.749	+	341.399i	−0.343096	+	0.396055i
$863$		−	582.627i		−	0.675119i	−0.941304	−	0.337559i	$-0.890399\pi$
$863$		−	582.627i		−	0.675119i	0.941304	−	0.337559i	$-0.109601\pi$
$864$		0			0
$865$	436.938			0.505131
$866$	108.528	+	94.0162i	0.125321	+	0.108564i
$867$		0			0
$868$	−35.5492	−	246.811i	−0.0409553	−	0.284344i
$869$	184.621	−	67.1964i	0.212452	−	0.0773262i
$870$		0			0
$871$	−1086.28	+	191.541i	−1.24717	+	0.219909i
$872$	−827.708	+	1289.00i	−0.949206	+	1.47822i
$873$		0			0
$874$	−58.2295	−	22.2379i	−0.0666241	−	0.0254438i
$875$	−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	$0.888178\pi$
$878$	1155.83	+	691.802i	1.31644	+	0.787930i
$879$		0			0
$880$	152.723	+	519.163i	0.173549	+	0.589958i
$881$	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	−0.292757	−	0.956187i	$-0.594573\pi$
$883$	343.440	−	198.285i	0.388947	−	0.224559i	0.681704	+	0.731628i	$0.261239\pi$
$884$	437.046	+	815.218i	0.494396	+	0.922193i
$885$		0			0
$886$	378.633	−	210.728i	0.427351	−	0.237842i
$887$	−537.102	−	94.7055i	−0.605526	−	0.106771i	−0.137525	−	0.990498i	$-0.543915\pi$
$887$	−537.102	−	94.7055i	−0.605526	−	0.106771i	−0.468001	+	0.883728i	$0.655026\pi$
$888$		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
$896$	−26.4655	+	239.211i	−0.0295374	+	0.266977i
$897$		0			0
$898$	−812.060	+	281.171i	−0.904298	+	0.313108i
$899$	−774.974	+	447.432i	−0.862040	+	0.497699i
$900$		0			0
$901$	−515.456	+	892.797i	−0.572094	+	0.990895i
$902$	38.3896	+	7.39399i	0.0425605	+	0.00819733i
$903$		0			0
$904$	−165.890	+	735.768i	−0.183506	+	0.813903i
$905$	−186.196	−	156.237i	−0.205741	−	0.172638i
$906$		0			0
$907$	451.817	−	1241.36i	0.498144	−	1.36864i	−0.394922	−	0.918715i	$-0.629229\pi$
$907$	451.817	−	1241.36i	0.498144	−	1.36864i	0.893066	−	0.449925i	$-0.148549\pi$
$908$	430.067	+	89.8756i	0.473642	+	0.0989819i
$909$		0			0
$910$	−64.7064	−	79.6266i	−0.0711059	−	0.0875018i
$911$	−1111.55	+	195.997i	−1.22014	+	0.215144i	−0.746388	−	0.665511i	$-0.768213\pi$
$911$	−1111.55	+	195.997i	−1.22014	+	0.215144i	−0.473757	+	0.880656i	$0.657102\pi$
$912$		0			0
$913$	−911.931	+	331.916i	−0.998830	+	0.363544i
$914$	527.712	+	8.30752i	0.577366	+	0.00908919i
$915$		0			0
$916$	394.560	−	636.265i	0.430742	−	0.694613i
$917$	141.852			0.154691
$918$		0			0
$919$			62.0726i			0.0675436i	0.999430	+	0.0337718i	$0.0107519\pi$
$919$			62.0726i			0.0675436i	−0.999430	+	0.0337718i	$0.989248\pi$
$920$	−11.8124	+	28.2306i	−0.0128396	+	0.0306854i
$921$		0			0
$922$	453.195	+	7.13444i	0.491535	+	0.00773800i
$923$	118.784	+	326.357i	0.128694	+	0.353583i
$924$		0			0
$925$	113.952	+	646.255i	0.123192	+	0.698654i
$926$	1117.38	+	1375.03i	1.20667	+	1.48491i
$927$		0			0
$928$	832.315	−	230.672i	0.896891	−	0.248569i
$929$	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
$932$	−829.351	−	331.781i	−0.889862	−	0.355988i
$933$		0			0
$934$	−588.064	−	113.264i	−0.629619	−	0.121267i
$935$	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	$0.855675\pi$
$938$	−385.628	+	133.521i	−0.411118	+	0.142347i
$939$		0			0
$940$	−473.780	−	602.149i	−0.504021	−	0.640584i
$941$	−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	0.657125	−	0.753782i	$-0.271772\pi$
$947$	−188.750	−	224.943i	−0.199313	−	0.237533i	−0.856439	+	0.516249i	$0.827328\pi$
$948$		0			0
$949$	72.9173	−	413.534i	0.0768359	−	0.435758i
$950$	−680.093	+	378.505i	−0.715887	+	0.398426i
$951$		0			0
$952$	207.350	+	272.242i	0.217805	+	0.285969i
$953$	−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
$956$	11.3087	−	359.088i	0.0118292	−	0.375615i
$957$		0			0
$958$	411.997	+	246.594i	0.430060	+	0.257405i
$959$	281.258	−	335.191i	0.293283	−	0.349521i
$960$		0			0
$961$	129.918	+	47.2862i	0.135190	+	0.0492052i
$962$	−700.350	−	267.465i	−0.728015	−	0.278030i
$963$		0			0
$964$	−1274.77	−	1139.93i	−1.32237	−	1.18250i
$965$	90.0795	+	510.866i	0.0933467	+	0.529395i
$966$		0			0
$967$	206.167	+	566.439i	0.213203	+	0.585769i	0.999485	−	0.0320984i	$-0.0102190\pi$
$967$	206.167	+	566.439i	0.213203	+	0.585769i	−0.786282	+	0.617868i	$0.787997\pi$
$968$	288.421	−	89.8014i	0.297955	−	0.0927701i
$969$		0			0
$970$	168.551	+	146.013i	0.173764	+	0.150529i
$971$			1204.36i			1.24033i	0.784472	+	0.620165i	$0.212934\pi$
$971$			1204.36i			1.24033i	−0.784472	+	0.620165i	$0.787066\pi$
$972$		0			0
$973$	172.823			0.177619
$974$	681.976	−	787.242i	0.700181	−	0.808256i
$975$		0			0
$976$	−558.651	−	1125.77i	−0.572389	−	1.15345i
$977$	−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
$980$	363.897	+	325.405i	0.371323	+	0.332046i
$981$		0			0
$982$	−252.061	+	660.016i	−0.256681	+	0.672114i
$983$	−215.293	+	591.512i	−0.219016	+	0.601742i	−0.999732	−	0.0231441i	$-0.992632\pi$
$983$	−215.293	+	591.512i	−0.219016	+	0.601742i	0.780716	+	0.624886i	$0.214855\pi$
$984$		0			0
$985$	627.248	+	526.324i	0.636800	+	0.534339i
$986$	630.711	−	1053.76i	0.639666	−	1.06872i
$987$		0			0
$988$	27.9889	−	888.737i	0.0283288	−	0.899532i
$989$	15.4385	−	26.7402i	0.0156102	−	0.0270376i
$990$		0			0
$991$	−387.015	+	223.443i	−0.390529	+	0.225472i	−0.682389	−	0.730989i	$-0.739059\pi$
$991$	−387.015	+	223.443i	−0.390529	+	0.225472i	0.291860	+	0.956461i	$0.405726\pi$
$992$	−874.266	−	601.080i	−0.881316	−	0.605928i
$993$		0			0
$994$	62.4858	+	112.274i	0.0628630	+	0.112951i
$995$	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.199.27		204
3.2	odd	2		108.3.j.a.103.8	yes	204
4.3	odd	2	inner	324.3.j.a.199.12		204
12.11	even	2		108.3.j.a.103.23	yes	204
27.11	odd	18		108.3.j.a.43.23	yes	204
27.16	even	9	inner	324.3.j.a.127.12		204
108.11	even	18		108.3.j.a.43.8	✓	204
108.43	odd	18	inner	324.3.j.a.127.27		204

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

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)

\(f(q)\)	\(=\)	\(q+(1.51166 + 1.30953i) q^{2} +(0.570252 + 3.95914i) q^{4} +(-2.52245 + 0.918095i) q^{5} +(-1.85168 + 0.326500i) q^{7} +(-4.32259 + 6.73165i) q^{8} +O(q^{10})\)	\(q+(1.51166 + 1.30953i) q^{2} +(0.570252 + 3.95914i) q^{4} +(-2.52245 + 0.918095i) q^{5} +(-1.85168 + 0.326500i) q^{7} +(-4.32259 + 6.73165i) q^{8} +(-5.01536 - 1.91537i) q^{10} +(-4.30945 + 11.8401i) q^{11} +(-7.78634 - 6.53352i) q^{13} +(-3.22667 - 1.93127i) q^{14} +(-15.3496 + 4.51542i) q^{16} +(-11.3753 + 19.7026i) q^{17} +(18.9400 - 10.9350i) q^{19} +(-5.07330 - 9.46317i) q^{20} +(-22.0194 + 12.2549i) q^{22} +(-1.40339 - 0.247456i) q^{23} +(-13.6313 + 11.4380i) q^{25} +(-3.21448 - 20.0729i) q^{26} +(-2.34858 - 7.14486i) q^{28} +(-20.6757 + 17.3490i) q^{29} +(32.6513 + 5.75731i) q^{31} +(-29.1166 - 13.2750i) q^{32} +(-42.9969 + 14.8874i) q^{34} +(4.37099 - 2.52359i) q^{35} +(18.4391 - 31.9375i) q^{37} +(42.9506 + 8.27247i) q^{38} +(4.72321 - 20.9488i) q^{40} +(-1.18844 - 0.997219i) q^{41} +(-7.41069 + 20.3607i) q^{43} +(-49.3342 - 10.3099i) q^{44} +(-1.79740 - 2.21186i) q^{46} +(70.2738 - 12.3912i) q^{47} +(-42.7228 + 15.5498i) q^{49} +(-35.5843 - 0.560187i) q^{50} +(21.4269 - 34.5530i) q^{52} +45.3136 q^{53} -33.8225i q^{55} +(5.80616 - 13.8762i) q^{56} +(-53.9739 - 0.849685i) q^{58} +(31.4169 + 86.3172i) q^{59} +(13.6397 + 77.3544i) q^{61} +(41.8184 + 51.4611i) q^{62} +(-26.6304 - 58.1964i) q^{64} +(25.6390 + 9.33183i) q^{65} +(69.7557 - 83.1316i) q^{67} +(-84.4923 - 33.8010i) q^{68} +(9.91220 + 1.90913i) q^{70} +(-29.5909 - 17.0843i) q^{71} +(20.6562 + 35.7776i) q^{73} +(69.6968 - 24.1321i) q^{74} +(54.0938 + 68.7504i) q^{76} +(4.11390 - 23.3311i) q^{77} +(-10.0229 - 11.9448i) q^{79} +(34.5730 - 25.4823i) q^{80} +(-0.490630 - 3.06376i) q^{82} +(49.5078 + 59.0011i) q^{83} +(10.6047 - 60.1424i) q^{85} +(-37.8654 + 21.0740i) q^{86} +(-61.0756 - 80.1897i) q^{88} +(-88.0911 - 152.578i) q^{89} +(16.5510 + 9.55571i) q^{91} +(0.179425 - 5.69734i) q^{92} +(122.457 + 73.2945i) q^{94} +(-37.7357 + 44.9717i) q^{95} +(-39.0324 - 14.2066i) q^{97} +(-84.9456 - 32.4408i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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

Introduction

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