LMFDB - Embedded newform 324.3.j.a.199.8

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			199.8
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47013 - 1.35599i) q^{2} +(0.322594 + 3.98697i) q^{4} +(-9.22169 + 3.35642i) q^{5} +(-4.51251 + 0.795677i) q^{7} +(4.93203 - 6.29882i) q^{8} +O(q^{10})$	\(q+(-1.47013 - 1.35599i) q^{2} +(0.322594 + 3.98697i) q^{4} +(-9.22169 + 3.35642i) q^{5} +(-4.51251 + 0.795677i) q^{7} +(4.93203 - 6.29882i) q^{8} +(18.1084 + 7.57011i) q^{10} +(-2.67518 + 7.34999i) q^{11} +(-5.33182 - 4.47393i) q^{13} +(7.71292 + 4.94915i) q^{14} +(-15.7919 + 2.57234i) q^{16} +(7.51307 - 13.0130i) q^{17} +(18.4333 - 10.6425i) q^{19} +(-16.3568 - 35.6838i) q^{20} +(13.8994 - 7.17797i) q^{22} +(16.6774 + 2.94067i) q^{23} +(54.6229 - 45.8341i) q^{25} +(1.77190 + 13.8072i) q^{26} +(-4.62805 - 17.7346i) q^{28} +(-14.8391 + 12.4515i) q^{29} +(14.8493 + 2.61834i) q^{31} +(26.7042 + 17.6319i) q^{32} +(-28.6907 + 8.94326i) q^{34} +(38.9423 - 22.4834i) q^{35} +(-14.9619 + 25.9148i) q^{37} +(-41.5305 - 9.34945i) q^{38} +(-24.3401 + 74.6397i) q^{40} +(-29.3512 - 24.6286i) q^{41} +(14.2890 - 39.2588i) q^{43} +(-30.1672 - 8.29480i) q^{44} +(-20.5305 - 26.9375i) q^{46} +(60.2645 - 10.6263i) q^{47} +(-26.3153 + 9.57799i) q^{49} +(-142.453 - 6.68575i) q^{50} +(16.1174 - 22.7011i) q^{52} +24.8870 q^{53} -76.7584i q^{55} +(-17.2440 + 32.3478i) q^{56} +(38.6995 + 1.81628i) q^{58} +(-31.1472 - 85.5763i) q^{59} +(4.84636 + 27.4850i) q^{61} +(-18.2801 - 23.9848i) q^{62} +(-15.3502 - 62.1319i) q^{64} +(64.1848 + 23.3614i) q^{65} +(-25.2305 + 30.0686i) q^{67} +(54.3062 + 25.7565i) q^{68} +(-87.7376 - 19.7517i) q^{70} +(34.2911 + 19.7980i) q^{71} +(-41.3131 - 71.5564i) q^{73} +(57.1361 - 17.8100i) q^{74} +(48.3776 + 70.0598i) q^{76} +(6.22354 - 35.2955i) q^{77} +(-10.3986 - 12.3926i) q^{79} +(136.994 - 76.7255i) q^{80} +(9.75418 + 76.0073i) q^{82} +(55.6540 + 66.3258i) q^{83} +(-25.6060 + 145.219i) q^{85} +(-74.2413 + 38.3400i) q^{86} +(33.1022 + 53.1008i) q^{88} +(5.93712 + 10.2834i) q^{89} +(27.6197 + 15.9462i) q^{91} +(-6.34436 + 67.4409i) q^{92} +(-103.006 - 66.0959i) q^{94} +(-134.265 + 160.011i) q^{95} +(47.7745 + 17.3885i) q^{97} +(51.6747 + 21.6023i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.47013	−	1.35599i	−0.735067	−	0.677994i
$2$	−1.47013	−	1.35599i	−0.735067	−	0.677994i
$3$		0			0
$3$		0			0
$4$	0.322594	+	3.98697i	0.0806484	+	0.996743i
$5$	−9.22169	+	3.35642i	−1.84434	+	0.671284i	−0.856426	+	0.516270i	$0.827320\pi$
$5$	−9.22169	+	3.35642i	−1.84434	+	0.671284i	−0.987912	+	0.155014i	$0.950458\pi$
$6$		0			0
$7$	−4.51251	+	0.795677i	−0.644644	+	0.113668i	−0.486406	−	0.873733i	$-0.661692\pi$
$7$	−4.51251	+	0.795677i	−0.644644	+	0.113668i	−0.158238	+	0.987401i	$0.550581\pi$
$8$	4.93203	−	6.29882i	0.616503	−	0.787352i
$9$		0			0
$10$	18.1084	+	7.57011i	1.81084	+	0.757011i
$11$	−2.67518	+	7.34999i	−0.243198	+	0.668181i	0.756698	+	0.653765i	$0.226811\pi$
$11$	−2.67518	+	7.34999i	−0.243198	+	0.668181i	−0.999896	+	0.0144166i	$0.995411\pi$
$12$		0			0
$13$	−5.33182	−	4.47393i	−0.410140	−	0.344149i	0.414257	−	0.910160i	$-0.364041\pi$
$13$	−5.33182	−	4.47393i	−0.410140	−	0.344149i	−0.824397	+	0.566011i	$0.808486\pi$
$14$	7.71292	+	4.94915i	0.550923	+	0.353511i
$15$		0			0
$16$	−15.7919	+	2.57234i	−0.986992	+	0.160771i
$17$	7.51307	−	13.0130i	0.441945	−	0.765471i	−0.555889	−	0.831257i	$-0.687622\pi$
$17$	7.51307	−	13.0130i	0.441945	−	0.765471i	0.997834	+	0.0657853i	$0.0209553\pi$
$18$		0			0
$19$	18.4333	−	10.6425i	0.970173	−	0.560129i	0.0708838	−	0.997485i	$-0.477418\pi$
$19$	18.4333	−	10.6425i	0.970173	−	0.560129i	0.899289	+	0.437355i	$0.144085\pi$
$20$	−16.3568	−	35.6838i	−0.817840	−	1.78419i
$21$		0			0
$22$	13.8994	−	7.17797i	0.631790	−	0.326271i
$23$	16.6774	+	2.94067i	0.725104	+	0.127855i	0.524005	−	0.851715i	$-0.324437\pi$
$23$	16.6774	+	2.94067i	0.725104	+	0.127855i	0.201099	+	0.979571i	$0.435549\pi$
$24$		0			0
$25$	54.6229	−	45.8341i	2.18492	−	1.83336i
$26$	1.77190	+	13.8072i	0.0681501	+	0.531045i
$27$		0			0
$28$	−4.62805	−	17.7346i	−0.165287	−	0.633377i
$29$	−14.8391	+	12.4515i	−0.511692	+	0.429361i	−0.861724	−	0.507377i	$-0.830615\pi$
$29$	−14.8391	+	12.4515i	−0.511692	+	0.429361i	0.350032	+	0.936738i	$0.386171\pi$
$30$		0			0
$31$	14.8493	+	2.61834i	0.479011	+	0.0844625i	0.407940	−	0.913009i	$-0.366247\pi$
$31$	14.8493	+	2.61834i	0.479011	+	0.0844625i	0.0710708	+	0.997471i	$0.477358\pi$
$32$	26.7042	+	17.6319i	0.834507	+	0.550997i
$33$		0			0
$34$	−28.6907	+	8.94326i	−0.843844	+	0.263037i
$35$	38.9423	−	22.4834i	1.11264	−	0.642382i
$36$		0			0
$37$	−14.9619	+	25.9148i	−0.404376	+	0.700399i	−0.994249	−	0.107097i	$-0.965844\pi$
$37$	−14.9619	+	25.9148i	−0.404376	+	0.700399i	0.589873	+	0.807496i	$0.299178\pi$
$38$	−41.5305	−	9.34945i	−1.09291	−	0.246038i
$39$		0			0
$40$	−24.3401	+	74.6397i	−0.608504	+	1.86599i
$41$	−29.3512	−	24.6286i	−0.715884	−	0.600698i	0.210360	−	0.977624i	$-0.432537\pi$
$41$	−29.3512	−	24.6286i	−0.715884	−	0.600698i	−0.926243	+	0.376926i	$0.876981\pi$
$42$		0			0
$43$	14.2890	−	39.2588i	0.332303	−	0.912995i	−0.655208	−	0.755448i	$-0.727419\pi$
$43$	14.2890	−	39.2588i	0.332303	−	0.912995i	0.987511	−	0.157547i	$-0.0503586\pi$
$44$	−30.1672	−	8.29480i	−0.685618	−	0.188518i
$45$		0			0
$46$	−20.5305	−	26.9375i	−0.446315	−	0.585598i
$47$	60.2645	−	10.6263i	1.28222	−	0.226090i	0.509299	−	0.860589i	$-0.329905\pi$
$47$	60.2645	−	10.6263i	1.28222	−	0.226090i	0.772924	+	0.634499i	$0.218794\pi$
$48$		0			0
$49$	−26.3153	+	9.57799i	−0.537047	+	0.195469i
$50$	−142.453	−	6.68575i	−2.84907	−	0.133715i
$51$		0			0
$52$	16.1174	−	22.7011i	0.309950	−	0.436559i
$53$	24.8870			0.469565			0.234783	−	0.972048i	$-0.424562\pi$
$53$	24.8870			0.469565			0.234783	+	0.972048i	$0.424562\pi$
$54$		0			0
$55$		−	76.7584i		−	1.39561i
$56$	−17.2440	+	32.3478i	−0.307928	+	0.577639i
$57$		0			0
$58$	38.6995	+	1.81628i	0.667232	+	0.0313151i
$59$	−31.1472	−	85.5763i	−0.527919	−	1.45045i	−0.861516	−	0.507730i	$-0.830485\pi$
$59$	−31.1472	−	85.5763i	−0.527919	−	1.45045i	0.333598	−	0.942716i	$-0.391737\pi$
$60$		0			0
$61$	4.84636	+	27.4850i	0.0794484	+	0.450575i	0.998417	+	0.0562438i	$0.0179124\pi$
$61$	4.84636	+	27.4850i	0.0794484	+	0.450575i	−0.918969	+	0.394331i	$0.870976\pi$
$62$	−18.2801	−	23.9848i	−0.294840	−	0.386852i
$63$		0			0
$64$	−15.3502	−	62.1319i	−0.239847	−	0.970811i
$65$	64.1848	+	23.3614i	0.987459	+	0.359406i
$66$		0			0
$67$	−25.2305	+	30.0686i	−0.376575	+	0.448785i	−0.920730	−	0.390200i	$-0.872406\pi$
$67$	−25.2305	+	30.0686i	−0.376575	+	0.448785i	0.544155	+	0.838985i	$0.316850\pi$
$68$	54.3062	+	25.7565i	0.798620	+	0.378771i
$69$		0			0
$70$	−87.7376	−	19.7517i	−1.25339	−	0.282168i
$71$	34.2911	+	19.7980i	0.482973	+	0.278845i	0.721655	−	0.692253i	$-0.243382\pi$
$71$	34.2911	+	19.7980i	0.482973	+	0.278845i	−0.238682	+	0.971098i	$0.576715\pi$
$72$		0			0
$73$	−41.3131	−	71.5564i	−0.565933	−	0.980225i	−0.996962	−	0.0778868i	$-0.975183\pi$
$73$	−41.3131	−	71.5564i	−0.565933	−	0.980225i	0.431029	−	0.902338i	$-0.358151\pi$
$74$	57.1361	−	17.8100i	0.772110	−	0.240676i
$75$		0			0
$76$	48.3776	+	70.0598i	0.636548	+	0.921839i
$77$	6.22354	−	35.2955i	0.0808252	−	0.458383i
$78$		0			0
$79$	−10.3986	−	12.3926i	−0.131628	−	0.156869i	0.696204	−	0.717844i	$-0.254871\pi$
$79$	−10.3986	−	12.3926i	−0.131628	−	0.156869i	−0.827833	+	0.560975i	$0.810426\pi$
$80$	136.994	−	76.7255i	1.71242	−	0.959069i
$81$		0			0
$82$	9.75418	+	76.0073i	0.118953	+	0.926918i
$83$	55.6540	+	66.3258i	0.670530	+	0.799106i	0.988856	−	0.148875i	$-0.0475652\pi$
$83$	55.6540	+	66.3258i	0.670530	+	0.799106i	−0.318326	+	0.947981i	$0.603121\pi$
$84$		0			0
$85$	−25.6060	+	145.219i	−0.301247	+	1.70846i
$86$	−74.2413	+	38.3400i	−0.863270	+	0.445814i
$87$		0			0
$88$	33.1022	+	53.1008i	0.376161	+	0.603418i
$89$	5.93712	+	10.2834i	0.0667092	+	0.115544i	0.897451	−	0.441114i	$-0.145417\pi$
$89$	5.93712	+	10.2834i	0.0667092	+	0.115544i	−0.830742	+	0.556658i	$0.812083\pi$
$90$		0			0
$91$	27.6197	+	15.9462i	0.303513	+	0.175233i
$92$	−6.34436	+	67.4409i	−0.0689605	+	0.733053i
$93$		0			0
$94$	−103.006	−	66.0959i	−1.09581	−	0.703148i
$95$	−134.265	+	160.011i	−1.41332	+	1.68433i
$96$		0			0
$97$	47.7745	+	17.3885i	0.492521	+	0.179263i	0.576327	−	0.817219i	$-0.304486\pi$
$97$	47.7745	+	17.3885i	0.492521	+	0.179263i	−0.0838064	+	0.996482i	$0.526708\pi$
$98$	51.6747	+	21.6023i	0.527293	+	0.220432i
$99$		0			0
$100$	200.360	+	202.994i	2.00360	+	2.02994i
$101$	−0.442867	−	2.51162i	−0.00438482	−	0.0248676i	0.982537	−	0.186068i	$-0.0595745\pi$
$101$	−0.442867	−	2.51162i	−0.00438482	−	0.0248676i	−0.986922	+	0.161201i	$0.948463\pi$
$102$		0			0
$103$	−20.9977	−	57.6906i	−0.203861	−	0.560103i	0.795061	−	0.606530i	$-0.207439\pi$
$103$	−20.9977	−	57.6906i	−0.203861	−	0.560103i	−0.998922	+	0.0464265i	$0.985217\pi$
$104$	−54.4772	+	11.5186i	−0.523819	+	0.110756i
$105$		0			0
$106$	−36.5872	−	33.7464i	−0.345162	−	0.318362i
$107$		−	122.605i		−	1.14584i	−0.819612	−	0.572919i	$-0.805811\pi$
$107$		−	122.605i		−	1.14584i	0.819612	−	0.572919i	$-0.194189\pi$
$108$		0			0
$109$	−37.9855			−0.348491			−0.174245	−	0.984702i	$-0.555749\pi$
$109$	−37.9855			−0.348491			−0.174245	+	0.984702i	$0.555749\pi$
$110$	−104.083	+	112.845i	−0.946213	+	1.02587i
$111$		0			0
$112$	69.2142	−	24.1729i	0.617984	−	0.215830i
$113$	102.206	−	37.2000i	0.904480	−	0.329204i	0.152433	−	0.988314i	$-0.451289\pi$
$113$	102.206	−	37.2000i	0.904480	−	0.329204i	0.752047	+	0.659110i	$0.229067\pi$
$114$		0			0
$115$	−163.664	+	28.8584i	−1.42316	+	0.250942i
$116$	−54.4306	−	55.1462i	−0.469229	−	0.475398i
$117$		0			0
$118$	−70.2498	+	168.044i	−0.595337	+	1.42410i
$119$	−23.5486	+	64.6993i	−0.197888	+	0.543692i
$120$		0			0
$121$	45.8256	+	38.4522i	0.378724	+	0.317787i
$122$	30.1446	−	46.9783i	0.247087	−	0.385068i
$123$		0			0
$124$	−5.64894	+	60.0485i	−0.0455559	+	0.484262i
$125$	−227.208	+	393.536i	−1.81766	+	3.14829i
$126$		0			0
$127$	159.542	−	92.1119i	1.25624	−	0.725290i	0.283898	−	0.958854i	$-0.408372\pi$
$127$	159.542	−	92.1119i	1.25624	−	0.725290i	0.972341	+	0.233564i	$0.0750388\pi$
$128$	−61.6832	+	112.157i	−0.481900	+	0.876226i
$129$		0			0
$130$	−62.6826	−	121.378i	−0.482174	−	0.933678i
$131$	198.290	+	34.9638i	1.51366	+	0.266900i	0.867939	−	0.496671i	$-0.165445\pi$
$131$	198.290	+	34.9638i	1.51366	+	0.266900i	0.645724	+	0.763571i	$0.276556\pi$
$132$		0			0
$133$	−74.7123	+	62.6911i	−0.561747	+	0.471362i
$134$	77.8649	−	9.99257i	0.581082	−	0.0745714i
$135$		0			0
$136$	−44.9119	−	111.504i	−0.330235	−	0.819882i
$137$	88.9077	−	74.6024i	0.648961	−	0.544543i	−0.257794	−	0.966200i	$-0.582996\pi$
$137$	88.9077	−	74.6024i	0.648961	−	0.544543i	0.906756	+	0.421657i	$0.138551\pi$
$138$		0			0
$139$	163.809	+	28.8839i	1.17848	+	0.207798i	0.728376	−	0.685177i	$-0.240275\pi$
$139$	163.809	+	28.8839i	1.17848	+	0.207798i	0.450105	+	0.892975i	$0.351386\pi$
$140$	102.203	+	148.009i	0.730022	+	1.05721i
$141$		0			0
$142$	−23.5667	−	75.6040i	−0.165963	−	0.532422i
$143$	47.1469	−	27.2203i	0.329699	−	0.190352i
$144$		0			0
$145$	95.0490	−	164.630i	0.655510	−	1.13538i
$146$	−36.2938	+	161.218i	−0.248588	+	1.10423i
$147$		0			0
$148$	−108.148	−	51.2927i	−0.730730	−	0.346572i
$149$	−69.6965	−	58.4823i	−0.467762	−	0.392499i	0.378216	−	0.925718i	$-0.376538\pi$
$149$	−69.6965	−	58.4823i	−0.467762	−	0.392499i	−0.845977	+	0.533219i	$0.820982\pi$
$150$		0			0
$151$	8.83574	−	24.2760i	0.0585148	−	0.160768i	−0.906991	−	0.421151i	$-0.861626\pi$
$151$	8.83574	−	24.2760i	0.0585148	−	0.160768i	0.965506	+	0.260382i	$0.0838486\pi$
$152$	23.8785	−	168.597i	0.157096	−	1.10919i
$153$		0			0
$154$	−57.0097	+	43.4501i	−0.370193	+	0.282143i
$155$	−145.724	+	25.6951i	−0.940156	+	0.165775i
$156$		0			0
$157$	−11.4347	+	4.16190i	−0.0728326	+	0.0265089i	−0.378180	−	0.925732i	$-0.623450\pi$
$157$	−11.4347	+	4.16190i	−0.0728326	+	0.0265089i	0.305347	+	0.952241i	$0.401228\pi$
$158$	−1.51683	+	32.3193i	−0.00960022	+	0.204552i
$159$		0			0
$160$	−305.438	−	72.9652i	−1.90899	−	0.456032i
$161$	−77.5967			−0.481967
$162$		0			0
$163$			187.452i			1.15001i	0.818148	+	0.575007i	$0.195001\pi$
$163$			187.452i			1.15001i	−0.818148	+	0.575007i	$0.804999\pi$
$164$	88.7250	−	124.968i	0.541006	−	0.761997i
$165$		0			0
$166$	8.11816	−	172.974i	0.0489046	−	1.04201i
$167$	−71.8589	−	197.431i	−0.430293	−	1.18222i	−0.945634	−	0.325234i	$-0.894557\pi$
$167$	−71.8589	−	197.431i	−0.430293	−	1.18222i	0.515341	−	0.856985i	$-0.327665\pi$
$168$		0			0
$169$	−20.9343	−	118.724i	−0.123871	−	0.702509i
$170$	234.560	−	178.770i	1.37976	−	1.05159i
$171$		0			0
$172$	161.133	+	44.3053i	0.936821	+	0.257589i
$173$	158.665	+	57.7495i	0.917141	+	0.333812i	0.757100	−	0.653298i	$-0.226615\pi$
$173$	158.665	+	57.7495i	0.917141	+	0.333812i	0.160040	+	0.987110i	$0.448838\pi$
$174$		0			0
$175$	−210.017	+	250.289i	−1.20010	+	1.43022i
$176$	23.3394	−	122.952i	0.132610	−	0.698588i
$177$		0			0
$178$	5.21579	−	23.1686i	0.0293022	−	0.130161i
$179$	−273.877	−	158.123i	−1.53004	−	0.883370i	−0.999359	−	0.0357989i	$-0.988602\pi$
$179$	−273.877	−	158.123i	−1.53004	−	0.883370i	−0.530682	−	0.847571i	$-0.678064\pi$
$180$		0			0
$181$	−78.2492	−	135.532i	−0.432316	−	0.748793i	0.564757	−	0.825258i	$-0.308970\pi$
$181$	−78.2492	−	135.532i	−0.432316	−	0.748793i	−0.997072	+	0.0764647i	$0.975637\pi$
$182$	−18.9818	−	60.8951i	−0.104295	−	0.334588i
$183$		0			0
$184$	100.776	−	90.5444i	0.547696	−	0.492089i
$185$	50.9931	−	289.196i	0.275638	−	1.56322i
$186$		0			0
$187$	75.5468	+	90.0331i	0.403993	+	0.481461i
$188$	61.8075	+	236.845i	0.328763	+	1.25981i
$189$		0			0
$190$	414.362	−	53.1759i	2.18085	−	0.279873i
$191$	−53.6600	−	63.9495i	−0.280942	−	0.334814i	0.607057	−	0.794658i	$-0.292350\pi$
$191$	−53.6600	−	63.9495i	−0.280942	−	0.334814i	−0.888000	+	0.459844i	$0.847905\pi$
$192$		0			0
$193$	−11.5935	+	65.7498i	−0.0600698	+	0.340673i	−1.00000		0.000694602i	$-0.999779\pi$
$193$	−11.5935	+	65.7498i	−0.0600698	+	0.340673i	0.939930	+	0.341367i	$0.110890\pi$
$194$	−46.6564	−	90.3451i	−0.240497	−	0.465696i
$195$		0			0
$196$	−46.6763	−	101.829i	−0.238145	−	0.519534i
$197$	−138.831	−	240.462i	−0.704725	−	1.22062i	−0.966791	−	0.255570i	$-0.917737\pi$
$197$	−138.831	−	240.462i	−0.704725	−	1.22062i	0.262065	−	0.965050i	$-0.415596\pi$
$198$		0			0
$199$	−62.7025	−	36.2013i	−0.315088	−	0.181916i	0.334113	−	0.942533i	$-0.391563\pi$
$199$	−62.7025	−	36.2013i	−0.315088	−	0.181916i	−0.649201	+	0.760617i	$0.724897\pi$
$200$	−19.2987	−	570.114i	−0.0964935	−	2.85057i
$201$		0			0
$202$	−2.75466	+	4.29295i	−0.0136369	+	0.0212522i
$203$	57.0541	−	67.9944i	0.281054	−	0.334948i
$204$		0			0
$205$	353.332	+	128.602i	1.72357	+	0.627328i
$206$	−47.3584	+	113.286i	−0.229895	+	0.549930i
$207$		0			0
$208$	95.7079	+	56.9365i	0.460134	+	0.273733i
$209$	28.9097	+	163.955i	0.138324	+	0.784473i
$210$		0			0
$211$	−0.151632	−	0.416605i	−0.000718634	−	0.00197443i	0.939333	−	0.343007i	$-0.111446\pi$
$211$	−0.151632	−	0.416605i	−0.000718634	−	0.00197443i	−0.940051	+	0.341033i	$0.889223\pi$
$212$	8.02837	+	99.2236i	0.0378697	+	0.468036i
$213$		0			0
$214$	−166.250	+	180.245i	−0.776871	+	0.842268i
$215$			409.992i			1.90694i
$216$		0			0
$217$	−69.0911			−0.318392
$218$	55.8438	+	51.5079i	0.256164	+	0.236275i
$219$		0			0
$220$	306.033	−	24.7618i	1.39106	−	0.112553i
$221$	−98.2777	+	35.7702i	−0.444695	+	0.161856i
$222$		0			0
$223$	−25.9540	+	4.57639i	−0.116386	+	0.0205219i	−0.231538	−	0.972826i	$-0.574376\pi$
$223$	−25.9540	+	4.57639i	−0.116386	+	0.0205219i	0.115152	+	0.993348i	$0.463265\pi$
$224$	−134.532	−	58.3161i	−0.600591	−	0.260340i
$225$		0			0
$226$	−200.700	−	83.9014i	−0.888052	−	0.371245i
$227$	−5.75679	+	15.8167i	−0.0253603	+	0.0696769i	−0.951727	−	0.306947i	$-0.900693\pi$
$227$	−5.75679	+	15.8167i	−0.0253603	+	0.0696769i	0.926366	+	0.376623i	$0.122915\pi$
$228$		0			0
$229$	−196.606	−	164.972i	−0.858542	−	0.720403i	0.103111	−	0.994670i	$-0.467120\pi$
$229$	−196.606	−	164.972i	−0.858542	−	0.720403i	−0.961654	+	0.274267i	$0.911565\pi$
$230$	279.740	+	179.501i	1.21626	+	0.780437i
$231$		0			0
$232$	5.24276	+	154.880i	0.0225981	+	0.667584i
$233$	−8.54082	+	14.7931i	−0.0366559	+	0.0634899i	−0.883771	−	0.467919i	$-0.845004\pi$
$233$	−8.54082	+	14.7931i	−0.0366559	+	0.0634899i	0.847115	+	0.531409i	$0.178337\pi$
$234$		0			0
$235$	−520.074	+	300.265i	−2.21308	+	1.27772i
$236$	331.142	−	151.789i	1.40314	−	0.643175i
$237$		0			0
$238$	122.351	−	63.1850i	0.514080	−	0.265483i
$239$	−304.381	−	53.6706i	−1.27356	−	0.224563i	−0.504318	−	0.863518i	$-0.668256\pi$
$239$	−304.381	−	53.6706i	−1.27356	−	0.224563i	−0.769244	+	0.638955i	$0.779367\pi$
$240$		0			0
$241$	203.062	−	170.389i	0.842580	−	0.707009i	−0.115563	−	0.993300i	$-0.536867\pi$
$241$	203.062	−	170.389i	0.842580	−	0.707009i	0.958143	+	0.286292i	$0.0924226\pi$
$242$	−15.2290	−	118.669i	−0.0629299	−	0.490367i
$243$		0			0
$244$	−108.019	+	28.1888i	−0.442699	+	0.115528i
$245$	210.524	−	176.651i	0.859281	−	0.721023i
$246$		0			0
$247$	−145.897	−	25.7255i	−0.590675	−	0.104152i
$248$	89.7298	−	80.6195i	0.361814	−	0.325079i
$249$		0			0
$250$	867.657	−	270.460i	3.47063	−	1.08184i
$251$	−184.422	+	106.476i	−0.734748	+	0.424207i	−0.820156	−	0.572139i	$-0.806114\pi$
$251$	−184.422	+	106.476i	−0.734748	+	0.424207i	0.0854089	+	0.996346i	$0.472780\pi$
$252$		0			0
$253$	−66.2289	+	114.712i	−0.261774	+	0.453407i
$254$	−359.452	−	80.9207i	−1.41516	−	0.318586i
$255$		0			0
$256$	242.766	−	81.2442i	0.948305	−	0.317360i
$257$	−345.413	−	289.836i	−1.34402	−	1.12776i	−0.980574	−	0.196149i	$-0.937156\pi$
$257$	−345.413	−	289.836i	−1.34402	−	1.12776i	−0.363444	−	0.931616i	$-0.618399\pi$
$258$		0			0
$259$	46.8959	−	128.845i	0.181065	−	0.497472i
$260$	−72.4355	+	263.439i	−0.278598	+	1.01323i
$261$		0			0
$262$	−244.102	−	320.280i	−0.931688	−	1.22244i
$263$	−19.1179	+	3.37100i	−0.0726916	+	0.0128175i	−0.209876	−	0.977728i	$-0.567306\pi$
$263$	−19.1179	+	3.37100i	−0.0726916	+	0.0128175i	0.137184	+	0.990546i	$0.456195\pi$
$264$		0			0
$265$	−229.500	+	83.5311i	−0.866037	+	0.315212i
$266$	194.846	+	9.14466i	0.732502	+	0.0343784i
$267$		0			0
$268$	−128.022	−	90.8935i	−0.477693	−	0.339155i
$269$	421.021			1.56513			0.782567	−	0.622567i	$-0.213910\pi$
$269$	421.021			1.56513			0.782567	+	0.622567i	$0.213910\pi$
$270$		0			0
$271$		−	213.999i		−	0.789665i	−0.918753	−	0.394833i	$-0.870803\pi$
$271$		−	213.999i		−	0.789665i	0.918753	−	0.394833i	$-0.129197\pi$
$272$	−85.1714	+	224.826i	−0.313130	+	0.826566i
$273$		0			0
$274$	−231.866	−	10.8821i	−0.846227	−	0.0397159i
$275$	190.754	+	524.092i	0.693651	+	1.90579i
$276$		0			0
$277$	−19.4010	−	110.028i	−0.0700396	−	0.397214i	−0.999593	−	0.0285268i	$-0.990918\pi$
$277$	−19.4010	−	110.028i	−0.0700396	−	0.397214i	0.929553	−	0.368687i	$-0.120193\pi$
$278$	−201.655	−	264.586i	−0.725378	−	0.951749i
$279$		0			0
$280$	50.4460	−	356.179i	0.180164	−	1.27207i
$281$	−47.4594	−	17.2738i	−0.168895	−	0.0614727i	0.256189	−	0.966627i	$-0.417533\pi$
$281$	−47.4594	−	17.2738i	−0.168895	−	0.0614727i	−0.425084	+	0.905154i	$0.639755\pi$
$282$		0			0
$283$	323.295	−	385.288i	1.14238	−	1.36144i	0.219847	−	0.975534i	$-0.429444\pi$
$283$	323.295	−	385.288i	1.14238	−	1.36144i	0.922538	−	0.385907i	$-0.126111\pi$
$284$	−67.8718	+	143.104i	−0.238985	+	0.503888i
$285$		0			0
$286$	−106.223	−	23.9132i	−0.371408	−	0.0836125i
$287$	152.044	+	87.7827i	0.529770	+	0.305863i
$288$		0			0
$289$	31.6076	+	54.7461i	0.109369	+	0.189433i
$290$	−362.971	+	113.143i	−1.25162	+	0.390147i
$291$		0			0
$292$	271.966	−	187.798i	0.931390	−	0.643143i
$293$	−19.6082	+	111.204i	−0.0669222	+	0.379535i	0.932890	+	0.360161i	$0.117278\pi$
$293$	−19.6082	+	111.204i	−0.0669222	+	0.379535i	−0.999812	+	0.0193737i	$0.993833\pi$
$294$		0			0
$295$	574.460	+	684.615i	1.94732	+	2.32073i
$296$	89.4399	+	222.055i	0.302162	+	0.750184i
$297$		0			0
$298$	23.1620	+	180.485i	0.0777247	+	0.605653i
$299$	−75.7645	−	90.2927i	−0.253393	−	0.301982i
$300$		0			0
$301$	−33.2421	+	188.525i	−0.110439	+	0.626329i
$302$	−45.9077	+	23.7078i	−0.152012	+	0.0785028i
$303$		0			0
$304$	−263.720	+	215.481i	−0.867500	+	0.708819i
$305$	−136.943	−	237.192i	−0.448993	−	0.777679i
$306$		0			0
$307$	268.474	+	155.003i	0.874507	+	0.504897i	0.868843	−	0.495087i	$-0.164864\pi$
$307$	268.474	+	155.003i	0.874507	+	0.504897i	0.00566388	+	0.999984i	$0.498197\pi$
$308$	142.730	+	13.4270i	0.463408	+	0.0435941i
$309$		0			0
$310$	249.076	+	159.825i	0.803472	+	0.515564i
$311$	275.480	−	328.304i	0.885786	−	1.05564i	−0.112292	−	0.993675i	$-0.535819\pi$
$311$	275.480	−	328.304i	0.885786	−	1.05564i	0.998078	−	0.0619638i	$-0.0197363\pi$
$312$		0			0
$313$	56.7914	+	20.6704i	0.181442	+	0.0660395i	0.431144	−	0.902283i	$-0.358110\pi$
$313$	56.7914	+	20.6704i	0.181442	+	0.0660395i	−0.249701	+	0.968323i	$0.580332\pi$
$314$	22.4541	+	9.38679i	0.0715097	+	0.0298942i
$315$		0			0
$316$	46.0545	−	45.4569i	0.145742	−	0.143851i
$317$	56.8344	+	322.324i	0.179288	+	1.01680i	0.933077	+	0.359678i	$0.117113\pi$
$317$	56.8344	+	322.324i	0.179288	+	1.01680i	−0.753788	+	0.657117i	$0.771776\pi$
$318$		0			0
$319$	−51.8210	−	142.377i	−0.162448	−	0.446323i
$320$	350.096	+	521.439i	1.09405	+	1.62950i
$321$		0			0
$322$	114.078	+	105.220i	0.354278	+	0.326771i
$323$		−	319.830i		−	0.990186i
$324$		0			0
$325$	−496.298			−1.52707
$326$	254.183	−	275.580i	0.779703	−	0.845338i
$327$		0			0
$328$	−299.892	+	63.4091i	−0.914305	+	0.193320i
$329$	−263.489	+	95.9021i	−0.800878	+	0.291496i
$330$		0			0
$331$	−270.454	+	47.6883i	−0.817081	+	0.144073i	−0.566542	−	0.824033i	$-0.691719\pi$
$331$	−270.454	+	47.6883i	−0.817081	+	0.144073i	−0.250539	+	0.968107i	$0.580608\pi$
$332$	−246.485	+	243.287i	−0.742426	+	0.732792i
$333$		0			0
$334$	−162.071	+	387.689i	−0.485243	+	1.16075i
$335$	131.745	−	361.967i	0.393270	−	1.08050i
$336$		0			0
$337$	439.240	+	368.567i	1.30338	+	1.09367i	0.989550	+	0.144191i	$0.0460581\pi$
$337$	439.240	+	368.567i	1.30338	+	1.09367i	0.313834	+	0.949478i	$0.398386\pi$
$338$	−130.212	+	202.927i	−0.385243	+	0.600376i
$339$		0			0
$340$	−587.244	−	55.2438i	−1.72719	−	0.162482i
$341$	−58.9694	+	102.138i	−0.172931	+	0.299525i
$342$		0			0
$343$	305.570	−	176.421i	0.890876	−	0.514347i
$344$	−176.810	−	283.629i	−0.513983	−	0.824504i
$345$		0			0
$346$	−154.952	−	300.048i	−0.447838	−	0.867190i
$347$	18.5984	+	3.27941i	0.0535978	+	0.00945074i	0.200383	−	0.979718i	$-0.435781\pi$
$347$	18.5984	+	3.27941i	0.0535978	+	0.00945074i	−0.146785	+	0.989168i	$0.546893\pi$
$348$		0			0
$349$	39.3809	−	33.0445i	0.112839	−	0.0946834i	−0.584622	−	0.811306i	$-0.698757\pi$
$349$	39.3809	−	33.0445i	0.112839	−	0.0946834i	0.697462	+	0.716622i	$0.254313\pi$
$350$	648.142	−	83.1774i	1.85183	−	0.237650i
$351$		0			0
$352$	−201.033	+	149.107i	−0.571116	+	0.423601i
$353$	−192.526	+	161.549i	−0.545400	+	0.457645i	−0.873380	−	0.487040i	$-0.838077\pi$
$353$	−192.526	+	161.549i	−0.545400	+	0.457645i	0.327980	+	0.944685i	$0.393632\pi$
$354$		0			0
$355$	−382.672	−	67.4754i	−1.07795	−	0.190072i
$356$	−39.0843	+	26.9885i	−0.109787	+	0.0758103i
$357$		0			0
$358$	188.224	+	603.837i	0.525764	+	1.68670i
$359$	32.9975	−	19.0511i	0.0919150	−	0.0530671i	−0.453338	−	0.891339i	$-0.649767\pi$
$359$	32.9975	−	19.0511i	0.0919150	−	0.0530671i	0.545253	+	0.838272i	$0.316434\pi$
$360$		0			0
$361$	46.0239	−	79.7157i	0.127490	−	0.220819i
$362$	−68.7423	+	305.355i	−0.189896	+	0.843521i
$363$		0			0
$364$	−54.6672	+	115.263i	−0.150185	+	0.316657i
$365$	621.150	+	521.207i	1.70178	+	1.42796i
$366$		0			0
$367$	111.793	−	307.148i	0.304612	−	0.836915i	−0.689071	−	0.724694i	$-0.741981\pi$
$367$	111.793	−	307.148i	0.304612	−	0.836915i	0.993683	−	0.112222i	$-0.0357966\pi$
$368$	−270.932	−	3.53878i	−0.736227	−	0.00961626i
$369$		0			0
$370$	−467.113	+	356.012i	−1.26247	+	0.962193i
$371$	−112.303	+	19.8020i	−0.302702	+	0.0533746i
$372$		0			0
$373$	168.707	−	61.4042i	0.452297	−	0.164623i	−0.105819	−	0.994385i	$-0.533747\pi$
$373$	168.707	−	61.4042i	0.452297	−	0.164623i	0.558116	+	0.829763i	$0.311524\pi$
$374$	11.0199	−	234.801i	0.0294650	−	0.627811i
$375$		0			0
$376$	230.293	−	432.004i	0.612482	−	1.14895i
$377$	134.826			0.357629
$378$		0			0
$379$			361.411i			0.953590i	0.879014	+	0.476795i	$0.158202\pi$
$379$			361.411i			0.953590i	−0.879014	+	0.476795i	$0.841798\pi$
$380$	−681.273	−	483.694i	−1.79282	−	1.27288i
$381$		0			0
$382$	−7.82731	+	166.777i	−0.0204903	+	0.436588i
$383$	119.450	+	328.187i	0.311880	+	0.856884i	0.992277	+	0.124040i	$0.0395853\pi$
$383$	119.450	+	328.187i	0.311880	+	0.856884i	−0.680397	+	0.732844i	$0.738193\pi$
$384$		0			0
$385$	61.0749	+	346.373i	0.158636	+	0.899669i
$386$	106.200	−	80.9405i	0.275129	−	0.209690i
$387$		0			0
$388$	−53.9157	+	196.085i	−0.138958	+	0.505373i
$389$	0.536764	+	0.195366i	0.00137986	+	0.000502227i	0.342710	−	0.939441i	$-0.388655\pi$
$389$	0.536764	+	0.195366i	0.00137986	+	0.000502227i	−0.341330	+	0.939943i	$0.610877\pi$
$390$		0			0
$391$	163.565	−	194.930i	0.418326	−	0.498541i
$392$	−69.4579	+	212.994i	−0.177188	+	0.543353i
$393$		0			0
$394$	−121.964	+	541.765i	−0.309552	+	1.37504i
$395$	137.488	+	79.3787i	0.348071	+	0.200959i
$396$		0			0
$397$	−8.92090	−	15.4515i	−0.0224708	−	0.0389206i	0.854571	−	0.519334i	$-0.173820\pi$
$397$	−8.92090	−	15.4515i	−0.0224708	−	0.0389206i	−0.877042	+	0.480413i	$0.840487\pi$
$398$	43.0926	+	138.245i	0.108273	+	0.347348i
$399$		0			0
$400$	−744.697	+	864.314i	−1.86174	+	2.16079i
$401$	−67.6511	+	383.668i	−0.168706	+	0.956779i	0.776455	+	0.630173i	$0.217016\pi$
$401$	−67.6511	+	383.668i	−0.168706	+	0.956779i	−0.945161	+	0.326606i	$0.894095\pi$
$402$		0			0
$403$	−67.4598	−	80.3954i	−0.167394	−	0.199492i
$404$	9.87090	−	2.57593i	0.0244329	−	0.00637607i
$405$		0			0
$406$	−176.077	+	22.5963i	−0.433687	+	0.0556559i
$407$	−150.448	−	179.296i	−0.369650	−	0.440532i
$408$		0			0
$409$	84.5691	−	479.615i	0.206770	−	1.17265i	−0.687859	−	0.725844i	$-0.741449\pi$
$409$	84.5691	−	479.615i	0.206770	−	1.17265i	0.894629	−	0.446809i	$-0.147440\pi$
$410$	−345.062	−	668.176i	−0.841616	−	1.62970i
$411$		0			0
$412$	223.237	−	102.328i	0.541838	−	0.248368i
$413$	208.643	+	361.380i	0.505189	+	0.875013i
$414$		0			0
$415$	−735.841	−	424.838i	−1.77311	−	1.02371i
$416$	−63.4984	−	213.483i	−0.152640	−	0.513180i
$417$		0			0
$418$	179.820	−	280.237i	0.430191	−	0.670424i
$419$	358.205	−	426.892i	0.854905	−	1.01884i	−0.144664	−	0.989481i	$-0.546210\pi$
$419$	358.205	−	426.892i	0.854905	−	1.01884i	0.999569	−	0.0293551i	$-0.00934536\pi$
$420$		0			0
$421$	−693.894	−	252.557i	−1.64821	−	0.599898i	−0.659760	−	0.751476i	$-0.729342\pi$
$421$	−693.894	−	252.557i	−1.64821	−	0.599898i	−0.988445	+	0.151579i	$0.951564\pi$
$422$	−0.341992	+	0.818076i	−0.000810407	+	0.00193857i
$423$		0			0
$424$	122.743	−	156.758i	0.289489	−	0.369713i
$425$	−186.054	−	1055.16i	−0.437773	−	2.48274i
$426$		0			0
$427$	−43.7384	−	120.170i	−0.102432	−	0.281429i
$428$	488.821	−	39.5515i	1.14210	−	0.0924099i
$429$		0			0
$430$	555.945	−	602.744i	1.29289	−	1.40173i
$431$			623.656i			1.44700i	0.690326	+	0.723499i	$0.257467\pi$
$431$			623.656i			1.44700i	−0.690326	+	0.723499i	$0.742533\pi$
$432$		0			0
$433$	533.046			1.23105			0.615527	−	0.788116i	$-0.288943\pi$
$433$	533.046			1.23105			0.615527	+	0.788116i	$0.288943\pi$
$434$	101.573	+	93.6867i	0.234040	+	0.215868i
$435$		0			0
$436$	−12.2539	−	151.447i	−0.0281052	−	0.347356i
$437$	338.715	−	123.282i	0.775092	−	0.282110i
$438$		0			0
$439$	−491.828	+	86.7226i	−1.12034	+	0.197546i	−0.702989	−	0.711201i	$-0.748152\pi$
$439$	−491.828	+	86.7226i	−1.12034	+	0.197546i	−0.417349	+	0.908746i	$0.637041\pi$
$440$	−483.487	−	378.574i	−1.09883	−	0.860396i
$441$		0			0
$442$	192.985	+	80.6764i	0.436618	+	0.182526i
$443$	−3.57129	+	9.81203i	−0.00806159	+	0.0221490i	−0.943658	−	0.330922i	$-0.892640\pi$
$443$	−3.57129	+	9.81203i	−0.00806159	+	0.0221490i	0.935597	+	0.353071i	$0.114863\pi$
$444$		0			0
$445$	−89.2656	−	74.9028i	−0.200597	−	0.168321i
$446$	44.3614	+	28.4654i	0.0994650	+	0.0638237i
$447$		0			0
$448$	118.705	+	268.157i	0.264966	+	0.598564i
$449$	−182.013	+	315.257i	−0.405375	+	0.702131i	−0.994365	−	0.106010i	$-0.966192\pi$
$449$	−182.013	+	315.257i	−0.405375	+	0.702131i	0.588990	+	0.808140i	$0.299526\pi$
$450$		0			0
$451$	259.540	−	149.845i	0.575476	−	0.332251i
$452$	181.287	+	395.493i	0.401076	+	0.874984i
$453$		0			0
$454$	29.9105	−	15.4465i	0.0658821	−	0.0340231i
$455$	−308.223	−	54.3480i	−0.677412	−	0.119446i
$456$		0			0
$457$	−193.083	+	162.016i	−0.422502	+	0.354521i	−0.829114	−	0.559080i	$-0.811155\pi$
$457$	−193.083	+	162.016i	−0.422502	+	0.354521i	0.406612	+	0.913601i	$0.366710\pi$
$458$	65.3374	+	509.127i	0.142658	+	1.11163i
$459$		0			0
$460$	−167.854	−	643.214i	−0.364901	−	1.39829i
$461$	−210.415	+	176.559i	−0.456432	+	0.382992i	−0.841816	−	0.539764i	$-0.818513\pi$
$461$	−210.415	+	176.559i	−0.456432	+	0.382992i	0.385384	+	0.922756i	$0.374069\pi$
$462$		0			0
$463$	−23.3623	−	4.11941i	−0.0504586	−	0.00889720i	0.148362	−	0.988933i	$-0.452600\pi$
$463$	−23.3623	−	4.11941i	−0.0504586	−	0.00889720i	−0.198820	+	0.980036i	$0.563711\pi$
$464$	202.307	−	234.803i	0.436007	−	0.506041i
$465$		0			0
$466$	32.6155	−	10.1667i	0.0699903	−	0.0218169i
$467$	−7.22269	+	4.17002i	−0.0154661	+	0.00892939i	−0.507713	−	0.861526i	$-0.669509\pi$
$467$	−7.22269	+	4.17002i	−0.0154661	+	0.00892939i	0.492247	+	0.870456i	$0.336176\pi$
$468$		0			0
$469$	89.9281	−	155.760i	0.191744	−	0.332111i
$470$	1171.73	+	263.784i	2.49305	+	0.561243i
$471$		0			0
$472$	−692.648	−	225.874i	−1.46748	−	0.478546i
$473$	250.326	+	210.049i	0.529231	+	0.444077i
$474$		0			0
$475$	519.092	−	1426.19i	1.09283	−	3.00251i
$476$	−265.551	−	73.0161i	−0.557880	−	0.153395i
$477$		0			0
$478$	374.705	+	491.640i	0.783901	+	1.02854i
$479$	464.091	−	81.8317i	0.968874	−	0.170839i	0.333251	−	0.942838i	$-0.391854\pi$
$479$	464.091	−	81.8317i	0.968874	−	0.170839i	0.635623	+	0.772000i	$0.280743\pi$
$480$		0			0
$481$	195.715	−	71.2345i	0.406892	−	0.148097i
$482$	−529.574	−	24.8544i	−1.09870	−	0.0515651i
$483$		0			0
$484$	−138.525	+	195.110i	−0.286208	+	0.403119i
$485$	−498.925			−1.02871
$486$		0			0
$487$		−	218.971i		−	0.449633i	−0.974401	−	0.224817i	$-0.927822\pi$
$487$		−	218.971i		−	0.449633i	0.974401	−	0.224817i	$-0.0721783\pi$
$488$	197.026	+	105.031i	0.403741	+	0.215227i
$489$		0			0
$490$	−549.035	−	25.7678i	−1.12048	−	0.0525873i
$491$	41.7305	+	114.654i	0.0849908	+	0.233510i	0.974906	−	0.222615i	$-0.0714592\pi$
$491$	41.7305	+	114.654i	0.0849908	+	0.233510i	−0.889916	+	0.456125i	$0.849237\pi$
$492$		0			0
$493$	50.5441	+	286.650i	0.102523	+	0.581439i
$494$	179.604	+	235.654i	0.363571	+	0.477032i
$495$		0			0
$496$	−241.234	−	3.15089i	−0.486359	−	0.00635259i
$497$	−170.491	−	62.0538i	−0.343041	−	0.124857i
$498$		0			0
$499$	−18.9123	+	22.5388i	−0.0379004	+	0.0451680i	−0.784662	−	0.619924i	$-0.787163\pi$
$499$	−18.9123	+	22.5388i	−0.0379004	+	0.0451680i	0.746761	+	0.665092i	$0.231608\pi$
$500$	−1642.31	−	778.920i	−3.28462	−	1.55784i
$501$		0			0
$502$	415.505	+	93.5396i	0.827699	+	0.186334i
$503$	−100.859	−	58.2311i	−0.200515	−	0.115768i	0.396381	−	0.918086i	$-0.370266\pi$
$503$	−100.859	−	58.2311i	−0.200515	−	0.115768i	−0.596896	+	0.802319i	$0.703599\pi$
$504$		0			0
$505$	12.5140	+	21.6750i	0.0247803	+	0.0429207i
$506$	252.913	−	78.8363i	0.499829	−	0.155803i
$507$		0			0
$508$	418.715	+	606.376i	0.824242	+	1.19365i
$509$	10.6160	−	60.2066i	0.0208567	−	0.118284i	−0.972602	−	0.232477i	$-0.925317\pi$
$509$	10.6160	−	60.2066i	0.0208567	−	0.118284i	0.993459	+	0.114193i	$0.0364281\pi$
$510$		0			0
$511$	243.361	+	290.027i	0.476246	+	0.567567i
$512$	−467.065	−	209.748i	−0.912236	−	0.409664i
$513$		0			0
$514$	114.790	+	894.473i	0.223326	+	1.74022i
$515$	387.268	+	461.528i	0.751977	+	0.896171i
$516$		0			0
$517$	−83.1153	+	471.371i	−0.160765	+	0.911742i
$518$	−243.656	+	125.830i	−0.470378	+	0.242915i
$519$		0			0
$520$	463.710	−	289.070i	0.891751	−	0.555903i
$521$	−364.846	−	631.931i	−0.700280	−	1.21292i	−0.968368	−	0.249526i	$-0.919725\pi$
$521$	−364.846	−	631.931i	−0.700280	−	1.21292i	0.268089	−	0.963394i	$-0.413608\pi$
$522$		0			0
$523$	318.052	+	183.627i	0.608130	+	0.351104i	0.772233	−	0.635339i	$-0.219140\pi$
$523$	318.052	+	183.627i	0.608130	+	0.351104i	−0.164103	+	0.986443i	$0.552473\pi$
$524$	−75.4328	+	801.855i	−0.143956	+	1.53026i
$525$		0			0
$526$	32.6769	+	20.9678i	0.0621235	+	0.0398628i
$527$	145.636	−	173.563i	0.276350	−	0.329341i
$528$		0			0
$529$	−227.610	−	82.8431i	−0.430264	−	0.156603i
$530$	450.663	+	188.397i	0.850307	+	0.355466i
$531$		0			0
$532$	−274.049	−	277.652i	−0.515130	−	0.521903i
$533$	46.3089	+	262.631i	0.0868835	+	0.492741i
$534$		0			0
$535$	411.513	+	1130.62i	0.769182	+	2.11331i
$536$	64.9588	+	307.222i	0.121192	+	0.573175i
$537$		0			0
$538$	−618.958	−	570.899i	−1.15048	−	1.06115i
$539$		−	219.040i		−	0.406383i
$540$		0			0
$541$	504.486			0.932507			0.466254	−	0.884651i	$-0.345603\pi$
$541$	504.486			0.932507			0.466254	+	0.884651i	$0.345603\pi$
$542$	−290.180	+	314.608i	−0.535388	+	0.580457i
$543$		0			0
$544$	430.075	−	215.033i	0.790579	−	0.395281i
$545$	350.291	−	127.495i	0.642735	−	0.233936i
$546$		0			0
$547$	74.2886	−	13.0991i	0.135811	−	0.0239472i	−0.105329	−	0.994437i	$-0.533590\pi$
$547$	74.2886	−	13.0991i	0.135811	−	0.0239472i	0.241140	+	0.970490i	$0.422479\pi$
$548$	326.119	+	330.406i	0.595107	+	0.602931i
$549$		0			0
$550$	430.229	−	1029.15i	0.782234	−	1.87117i
$551$	−141.019	+	387.445i	−0.255932	+	0.703168i
$552$		0			0
$553$	56.7845	+	47.6478i	0.102684	+	0.0861624i
$554$	−120.675	+	188.064i	−0.217825	+	0.339466i
$555$		0			0
$556$	−62.3157	+	662.419i	−0.112079	+	1.19140i
$557$	366.474	−	634.751i	0.657942	−	1.13959i	−0.323206	−	0.946329i	$-0.604761\pi$
$557$	366.474	−	634.751i	0.657942	−	1.13959i	0.981148	−	0.193260i	$-0.0619061\pi$
$558$		0			0
$559$	−251.828	+	145.393i	−0.450497	+	0.260095i
$560$	−557.137	+	455.227i	−0.994887	+	0.812906i
$561$		0			0
$562$	46.3487	+	89.7493i	0.0824710	+	0.159696i
$563$	329.585	+	58.1147i	0.585408	+	0.103223i	0.458505	−	0.888692i	$-0.348385\pi$
$563$	329.585	+	58.1147i	0.585408	+	0.103223i	0.126903	+	0.991915i	$0.459496\pi$
$564$		0			0
$565$	−817.655	+	686.094i	−1.44718	+	1.21433i
$566$	−997.733	+	128.041i	−1.76278	+	0.226221i
$567$		0			0
$568$	293.828	−	118.349i	0.517303	−	0.208361i
$569$	115.616	−	97.0135i	0.203192	−	0.170498i	−0.535513	−	0.844527i	$-0.679882\pi$
$569$	115.616	−	97.0135i	0.203192	−	0.170498i	0.738705	+	0.674028i	$0.235437\pi$
$570$		0			0
$571$	538.586	+	94.9673i	0.943234	+	0.166318i	0.624058	−	0.781378i	$-0.285483\pi$
$571$	538.586	+	94.9673i	0.943234	+	0.166318i	0.319176	+	0.947696i	$0.396594\pi$
$572$	123.736	+	179.192i	0.216321	+	0.313273i
$573$		0			0
$574$	−104.493	−	335.222i	−0.182044	−	0.584011i
$575$	1045.75	−	603.764i	1.81870	−	1.05002i
$576$		0			0
$577$	−177.054	+	306.667i	−0.306853	+	0.531485i	−0.977672	−	0.210136i	$-0.932609\pi$
$577$	−177.054	+	306.667i	−0.306853	+	0.531485i	0.670819	+	0.741621i	$0.265943\pi$
$578$	27.7675	−	123.344i	0.0480406	−	0.213397i
$579$		0			0
$580$	687.036	+	325.849i	1.18454	+	0.561808i
$581$	−303.913	−	255.013i	−0.523086	−	0.438921i
$582$		0			0
$583$	−66.5771	+	182.919i	−0.114197	+	0.313755i
$584$	−654.478	−	92.6944i	−1.12068	−	0.158723i
$585$		0			0
$586$	179.618	−	136.896i	0.306515	−	0.233611i
$587$	729.661	−	128.659i	1.24303	−	0.219180i	0.486818	−	0.873503i	$-0.338157\pi$
$587$	729.661	−	128.659i	1.24303	−	0.219180i	0.756215	+	0.654323i	$0.227046\pi$
$588$		0			0
$589$	301.587	−	109.769i	0.512033	−	0.186365i
$590$	83.7956	−	1785.44i	0.142026	−	3.02616i
$591$		0			0
$592$	169.615	−	447.730i	0.286511	−	0.756300i
$593$	912.777			1.53925			0.769626	−	0.638495i	$-0.220443\pi$
$593$	912.777			1.53925			0.769626	+	0.638495i	$0.220443\pi$
$594$		0			0
$595$		−	675.676i		−	1.13559i
$596$	210.684	−	296.744i	0.353496	−	0.497893i
$597$		0			0
$598$	−11.0517	+	235.478i	−0.0184810	+	0.393776i
$599$	−241.563	−	663.689i	−0.403277	−	1.10799i	−0.960657	−	0.277737i	$-0.910416\pi$
$599$	−241.563	−	663.689i	−0.403277	−	1.10799i	0.557380	−	0.830257i	$-0.311807\pi$
$600$		0			0
$601$	−113.073	−	641.270i	−0.188142	−	1.06701i	−0.921852	−	0.387543i	$-0.873324\pi$
$601$	−113.073	−	641.270i	−0.188142	−	1.06701i	0.733710	−	0.679463i	$-0.237787\pi$
$602$	304.508	−	232.081i	0.505827	−	0.385517i
$603$		0			0
$604$	99.6380	+	27.3966i	0.164964	+	0.0453585i
$605$	−551.651	−	200.785i	−0.911820	−	0.331875i
$606$		0			0
$607$	260.988	−	311.033i	0.429963	−	0.512410i	−0.506948	−	0.861976i	$-0.669227\pi$
$607$	260.988	−	311.033i	0.429963	−	0.512410i	0.936912	+	0.349566i	$0.113671\pi$
$608$	679.893	+	40.8148i	1.11825	+	0.0671296i
$609$		0			0
$610$	−120.305	+	534.398i	−0.197221	+	0.876061i
$611$	−368.861	−	212.962i	−0.603700	−	0.348546i
$612$		0			0
$613$	453.001	+	784.621i	0.738990	+	1.27997i	0.952950	+	0.303126i	$0.0980303\pi$
$613$	453.001	+	784.621i	0.738990	+	1.27997i	−0.213960	+	0.976842i	$0.568636\pi$
$614$	−184.510	−	591.923i	−0.300505	−	0.964044i
$615$		0			0
$616$	−191.625	−	213.279i	−0.311080	−	0.346232i
$617$	70.9099	−	402.150i	0.114927	−	0.651783i	−0.871859	−	0.489756i	$-0.837086\pi$
$617$	70.9099	−	402.150i	0.114927	−	0.651783i	0.986786	−	0.162027i	$-0.0518031\pi$
$618$		0			0
$619$	327.110	+	389.834i	0.528448	+	0.629780i	0.962557	−	0.271080i	$-0.0873809\pi$
$619$	327.110	+	389.834i	0.528448	+	0.629780i	−0.434108	+	0.900861i	$0.642936\pi$
$620$	−149.455	−	572.709i	−0.241057	−	0.923724i
$621$		0			0
$622$	−850.168	+	109.104i	−1.36683	+	0.175408i
$623$	−34.9735	−	41.6798i	−0.0561373	−	0.0669018i
$624$		0			0
$625$	464.820	−	2636.13i	0.743712	−	4.21780i
$626$	−55.4622	−	107.397i	−0.0885978	−	0.171560i
$627$		0			0
$628$	−20.2821	−	44.2473i	−0.0322964	−	0.0704574i
$629$	224.819	+	389.399i	0.357424	+	0.619076i
$630$		0			0
$631$	1083.33	+	625.458i	1.71684	+	0.991218i	0.924540	+	0.381086i	$0.124450\pi$
$631$	1083.33	+	625.458i	1.71684	+	0.991218i	0.792300	+	0.610132i	$0.208884\pi$
$632$	−129.345	+	4.37841i	−0.204660	+	0.00692786i
$633$		0			0
$634$	353.513	−	550.927i	0.557592	−	0.868969i
$635$	−1162.08	+	1384.92i	−1.83005	+	2.18097i
$636$		0			0
$637$	183.160	+	66.6648i	0.287535	+	0.104654i
$638$	−116.878	+	279.582i	−0.183194	+	0.438216i
$639$		0			0
$640$	192.378	−	1241.31i	0.300590	−	1.93955i
$641$	5.31127	+	30.1217i	0.00828592	+	0.0469918i	0.988670	−	0.150103i	$-0.0479605\pi$
$641$	5.31127	+	30.1217i	0.00828592	+	0.0469918i	−0.980384	+	0.197095i	$0.936849\pi$
$642$		0			0
$643$	−249.775	−	686.251i	−0.388453	−	1.06726i	−0.967698	−	0.252112i	$-0.918875\pi$
$643$	−249.775	−	686.251i	−0.388453	−	1.06726i	0.579246	−	0.815153i	$-0.303347\pi$
$644$	−25.0322	−	309.376i	−0.0388699	−	0.480397i
$645$		0			0
$646$	−433.686	+	470.193i	−0.671340	+	0.727853i
$647$		−	1180.60i		−	1.82472i	−0.409385	−	0.912362i	$-0.634257\pi$
$647$		−	1180.60i		−	1.82472i	0.409385	−	0.912362i	$-0.365743\pi$
$648$		0			0
$649$	712.309			1.09755
$650$	729.625	+	672.974i	1.12250	+	1.03534i
$651$		0			0
$652$	−747.367	+	60.4709i	−1.14627	+	0.0927468i
$653$	−878.642	+	319.800i	−1.34555	+	0.489739i	−0.911555	−	0.411178i	$-0.865118\pi$
$653$	−878.642	+	319.800i	−1.34555	+	0.489739i	−0.433992	+	0.900917i	$0.642895\pi$
$654$		0			0
$655$	−1945.92	+	343.118i	−2.97087	+	0.523845i
$656$	526.864	+	313.430i	0.803146	+	0.477790i
$657$		0			0
$658$	517.406	+	216.299i	0.786332	+	0.328721i
$659$	−90.2708	+	248.017i	−0.136982	+	0.376354i	−0.989149	−	0.146915i	$-0.953065\pi$
$659$	−90.2708	+	248.017i	−0.136982	+	0.376354i	0.852168	+	0.523269i	$0.175288\pi$
$660$		0			0
$661$	−857.449	−	719.486i	−1.29720	−	1.08848i	−0.990621	−	0.136635i	$-0.956371\pi$
$661$	−857.449	−	719.486i	−1.29720	−	1.08848i	−0.306579	−	0.951845i	$-0.599184\pi$
$662$	462.268	+	296.624i	0.698290	+	0.448072i
$663$		0			0
$664$	692.261	−	23.4334i	1.04256	−	0.0352913i
$665$	478.556	−	828.884i	0.719634	−	1.24644i
$666$		0			0
$667$	−284.093	+	164.021i	−0.425926	+	0.245908i
$668$	763.969	−	350.189i	1.14367	−	0.524235i
$669$		0			0
$670$	−684.507	+	353.496i	−1.02165	+	0.527606i
$671$	−214.980	−	37.9067i	−0.320387	−	0.0564929i
$672$		0			0
$673$	155.205	−	130.232i	0.230616	−	0.193510i	−0.520156	−	0.854071i	$-0.674126\pi$
$673$	155.205	−	130.232i	0.230616	−	0.193510i	0.750772	+	0.660561i	$0.229682\pi$
$674$	−145.971	−	1137.45i	−0.216574	−	1.68761i
$675$		0			0
$676$	466.596	−	121.764i	0.690231	−	0.180124i
$677$	−945.200	+	793.117i	−1.39616	+	1.17152i	−0.433387	+	0.901208i	$0.642682\pi$
$677$	−945.200	+	793.117i	−1.39616	+	1.17152i	−0.962773	+	0.270310i	$0.912874\pi$
$678$		0			0
$679$	−229.418	−	40.4526i	−0.337877	−	0.0595768i
$680$	788.418	+	877.512i	1.15944	+	1.29046i
$681$		0			0
$682$	225.191	−	70.1948i	0.330192	−	0.102925i
$683$	−831.903	+	480.300i	−1.21801	+	0.703220i	−0.964493	−	0.264110i	$-0.914922\pi$
$683$	−831.903	+	480.300i	−1.21801	+	0.703220i	−0.253521	+	0.967330i	$0.581589\pi$
$684$		0			0
$685$	−569.482	+	986.372i	−0.831361	+	1.43996i
$686$	−688.455	−	154.987i	−1.00358	−	0.225928i
$687$		0			0
$688$	−124.663	+	656.726i	−0.181197	+	0.954544i
$689$	−132.693	−	111.343i	−0.192588	−	0.161600i
$690$		0			0
$691$	−229.573	+	630.745i	−0.332232	+	0.912801i	0.655298	+	0.755371i	$0.272543\pi$
$691$	−229.573	+	630.745i	−0.332232	+	0.912801i	−0.987530	+	0.157430i	$0.949679\pi$
$692$	−179.061	+	651.224i	−0.258759	+	0.941075i
$693$		0			0
$694$	−22.8954	−	30.0404i	−0.0329905	−	0.0432859i
$695$	−1607.54	+	283.453i	−2.31301	+	0.407846i
$696$		0			0
$697$	−541.010	+	196.912i	−0.776198	+	0.282513i
$698$	−102.703	−	4.82016i	−0.147139	−	0.00690567i
$699$		0			0
$700$	−1065.64	−	756.591i	−1.52235	−	1.08084i
$701$	83.2481			0.118756			0.0593781	−	0.998236i	$-0.481088\pi$
$701$	83.2481			0.118756			0.0593781	+	0.998236i	$0.481088\pi$
$702$		0			0
$703$			636.925i			0.906011i
$704$	497.733	+	53.3900i	0.707008	+	0.0758381i
$705$		0			0
$706$	502.097	+	23.5649i	0.711186	+	0.0333780i
$707$	3.99688	+	10.9813i	0.00565330	+	0.0155323i
$708$		0			0
$709$	−158.003	−	896.078i	−0.222853	−	1.26386i	−0.866748	−	0.498747i	$-0.833794\pi$
$709$	−158.003	−	896.078i	−0.222853	−	1.26386i	0.643895	−	0.765114i	$-0.277317\pi$
$710$	471.084	+	618.096i	0.663498	+	0.870558i
$711$		0			0
$712$	94.0552	+	13.3211i	0.132100	+	0.0187095i
$713$	239.948	+	87.3341i	0.336534	+	0.122488i
$714$		0			0
$715$	−343.412	+	409.262i	−0.480296	+	0.572395i
$716$	542.081	−	1142.95i	0.757097	−	1.59630i
$717$		0			0
$718$	−74.3438	−	16.7365i	−0.103543	−	0.0233099i
$719$	826.808	+	477.358i	1.14994	+	0.663919i	0.948873	−	0.315658i	$-0.102225\pi$
$719$	826.808	+	477.358i	1.14994	+	0.663919i	0.201069	+	0.979577i	$0.435558\pi$
$720$		0			0
$721$	140.655	+	243.622i	0.195084	+	0.337895i
$722$	−175.755	+	54.7850i	−0.243428	+	0.0758795i
$723$		0			0
$724$	515.117	−	355.699i	0.711488	−	0.491296i
$725$	−239.852	+	1360.27i	−0.330831	+	1.87623i
$726$		0			0
$727$	−713.696	−	850.550i	−0.981700	−	1.16994i	−0.985452	−	0.169951i	$-0.945639\pi$
$727$	−713.696	−	850.550i	−0.981700	−	1.16994i	0.00375251	−	0.999993i	$-0.498806\pi$
$728$	236.664	−	95.3241i	0.325087	−	0.130940i
$729$		0			0
$730$	−206.424	−	1608.52i	−0.282773	−	2.20345i
$731$	−403.521	−	480.897i	−0.552012	−	0.657862i
$732$		0			0
$733$	−229.498	+	1301.55i	−0.313094	+	1.77565i	0.269618	+	0.962967i	$0.413103\pi$
$733$	−229.498	+	1301.55i	−0.313094	+	1.77565i	−0.582712	+	0.812678i	$0.698009\pi$
$734$	−580.839	+	299.959i	−0.791334	+	0.408664i
$735$		0			0
$736$	393.507	+	372.582i	0.534657	+	0.506226i
$737$	−153.508	−	265.883i	−0.208287	−	0.360764i
$738$		0			0
$739$	−1070.82	−	618.236i	−1.44901	−	0.836585i	−0.450585	−	0.892734i	$-0.648785\pi$
$739$	−1070.82	−	618.236i	−1.44901	−	0.836585i	−0.998422	+	0.0561488i	$0.982118\pi$
$740$	1169.47	+	110.015i	1.58036	+	0.148669i
$741$		0			0
$742$	191.951	+	123.169i	0.258694	+	0.165996i
$743$	−213.265	+	254.159i	−0.287032	+	0.342071i	−0.890223	−	0.455526i	$-0.849451\pi$
$743$	−213.265	+	254.159i	−0.287032	+	0.342071i	0.603191	+	0.797597i	$0.293896\pi$
$744$		0			0
$745$	839.011	+	305.375i	1.12619	+	0.409899i
$746$	−331.285	−	138.492i	−0.444082	−	0.185646i
$747$		0			0
$748$	−334.588	+	330.247i	−0.447311	+	0.441506i
$749$	97.5536	+	553.254i	0.130245	+	0.738657i
$750$		0			0
$751$	339.987	+	934.108i	0.452713	+	1.24382i	0.930807	+	0.365510i	$0.119105\pi$
$751$	339.987	+	934.108i	0.452713	+	1.24382i	−0.478095	+	0.878308i	$0.658672\pi$
$752$	−924.354	+	322.829i	−1.22919	+	0.429294i
$753$		0			0
$754$	−198.213	−	182.823i	−0.262882	−	0.242471i
$755$			253.522i			0.335791i
$756$		0			0
$757$	260.196			0.343720			0.171860	−	0.985121i	$-0.445022\pi$
$757$	260.196			0.343720			0.171860	+	0.985121i	$0.445022\pi$
$758$	490.068	−	531.322i	0.646528	−	0.700953i
$759$		0			0
$760$	345.681	+	1634.89i	0.454844	+	2.15118i
$761$	274.656	−	99.9667i	0.360915	−	0.131362i	−0.155197	−	0.987884i	$-0.549601\pi$
$761$	274.656	−	99.9667i	0.360915	−	0.131362i	0.516112	+	0.856521i	$0.327379\pi$
$762$		0			0
$763$	171.410	−	30.2242i	0.224653	−	0.0396123i
$764$	237.654	−	234.571i	0.311066	−	0.307030i
$765$		0			0
$766$	269.409	−	644.452i	0.351709	−	0.841321i
$767$	−216.791	+	595.628i	−0.282648	+	0.776569i
$768$		0			0
$769$	163.739	+	137.394i	0.212925	+	0.178665i	0.743012	−	0.669278i	$-0.233396\pi$
$769$	163.739	+	137.394i	0.212925	+	0.178665i	−0.530087	+	0.847943i	$0.677841\pi$
$770$	379.889	−	592.031i	0.493362	−	0.768872i
$771$		0			0
$772$	−265.883	−	25.0124i	−0.344408	−	0.0323994i
$773$	365.228	−	632.593i	0.472481	−	0.818361i	−0.527023	−	0.849851i	$-0.676692\pi$
$773$	365.228	−	632.593i	0.472481	−	0.818361i	0.999504	+	0.0314897i	$0.0100251\pi$
$774$		0			0
$775$	931.123	−	537.584i	1.20145	−	0.693657i
$776$	345.152	−	215.162i	0.444784	−	0.277271i
$777$		0			0
$778$	−0.524202	−	1.01506i	−0.000673781	−	0.00130471i
$779$	−803.148	−	141.617i	−1.03100	−	0.181793i
$780$		0			0
$781$	−237.250	+	199.076i	−0.303777	+	0.254899i
$782$	−504.785	+	64.7802i	−0.645506	+	0.0828391i
$783$		0			0
$784$	390.930	−	218.946i	0.498635	−	0.279268i
$785$	91.4783	−	76.7594i	0.116533	−	0.0977827i
$786$		0			0
$787$	−1246.33	−	219.761i	−1.58364	−	0.279239i	−0.688573	−	0.725167i	$-0.741762\pi$
$787$	−1246.33	−	219.761i	−1.58364	−	0.279239i	−0.895068	+	0.445929i	$0.852873\pi$
$788$	913.929	−	631.086i	1.15981	−	0.800871i
$789$		0			0
$790$	−94.4893	−	303.129i	−0.119607	−	0.383708i
$791$	−431.607	+	249.189i	−0.545648	+	0.315030i
$792$		0			0
$793$	97.1263	−	168.228i	0.122480	−	0.212141i
$794$	−7.83706	+	34.8124i	−0.00987035	+	0.0438443i
$795$		0			0
$796$	124.106	−	261.671i	0.155912	−	0.328733i
$797$	233.897	+	196.263i	0.293472	+	0.246252i	0.777621	−	0.628734i	$-0.216426\pi$
$797$	233.897	+	196.263i	0.293472	+	0.246252i	−0.484149	+	0.874985i	$0.660871\pi$
$798$		0			0
$799$	314.491	−	864.058i	0.393606	−	1.08142i
$800$	2266.80	−	260.859i	2.83350	−	0.326073i
$801$		0			0
$802$	619.706	−	472.310i	0.772700	−	0.588915i
$803$	636.459	−	112.225i	0.792601	−	0.139757i
$804$		0			0
$805$	715.572	−	260.447i	0.888910	−	0.323537i
$806$	−9.84026	+	209.667i	−0.0122088	+	0.260132i
$807$		0			0
$808$	−18.0045	−	9.59786i	−0.0222828	−	0.0118785i
$809$	−63.8675			−0.0789462			−0.0394731	−	0.999221i	$-0.512568\pi$
$809$	−63.8675			−0.0789462			−0.0394731	+	0.999221i	$0.512568\pi$
$810$		0			0
$811$			856.788i			1.05646i	0.849102	+	0.528229i	$0.177144\pi$
$811$			856.788i			1.05646i	−0.849102	+	0.528229i	$0.822856\pi$
$812$	289.497	+	205.538i	0.356523	+	0.253126i
$813$		0			0
$814$	−21.9456	+	467.595i	−0.0269601	+	0.574441i
$815$	−629.169	−	1728.63i	−0.771986	−	2.12102i
$816$		0			0
$817$	−154.416	−	875.739i	−0.189004	−	1.07190i
$818$	−774.680	+	590.424i	−0.947042	+	0.721790i
$819$		0			0
$820$	−398.751	+	1450.21i	−0.486282	+	1.76855i
$821$	−630.914	−	229.634i	−0.768470	−	0.279700i	−0.0721137	−	0.997396i	$-0.522974\pi$
$821$	−630.914	−	229.634i	−0.768470	−	0.279700i	−0.696356	+	0.717696i	$0.745197\pi$
$822$		0			0
$823$	−806.094	+	960.665i	−0.979458	+	1.16727i	0.00644958	+	0.999979i	$0.497947\pi$
$823$	−806.094	+	960.665i	−0.979458	+	1.16727i	−0.985907	+	0.167293i	$0.946497\pi$
$824$	−466.944	−	152.271i	−0.566680	−	0.184795i
$825$		0			0
$826$	183.294	−	814.195i	0.221906	−	0.985709i
$827$	228.269	+	131.791i	0.276020	+	0.159360i	0.631620	−	0.775278i	$-0.282390\pi$
$827$	228.269	+	131.791i	0.276020	+	0.159360i	−0.355600	+	0.934638i	$0.615724\pi$
$828$		0			0
$829$	252.751	+	437.777i	0.304886	+	0.528078i	0.977236	−	0.212155i	$-0.0680483\pi$
$829$	252.751	+	437.777i	0.304886	+	0.528078i	−0.672350	+	0.740234i	$0.734715\pi$
$830$	505.710	+	1622.36i	0.609290	+	1.95465i
$831$		0			0
$832$	−196.129	+	399.952i	−0.235732	+	0.480712i
$833$	−73.0702	+	414.402i	−0.0877193	+	0.497481i
$834$		0			0
$835$	1325.32	+	1579.46i	1.58721	+	1.89156i
$836$	−644.357	+	168.153i	−0.770762	+	0.201140i
$837$		0			0
$838$	−1105.47	+	141.867i	−1.31918	+	0.169293i
$839$	810.051	+	965.381i	0.965495	+	1.15063i	0.988549	+	0.150898i	$0.0482166\pi$
$839$	810.051	+	965.381i	0.965495	+	1.15063i	−0.0230539	+	0.999734i	$0.507339\pi$
$840$		0			0
$841$	−80.8790	+	458.687i	−0.0961700	+	0.545407i
$842$	677.654	+	1312.21i	0.804815	+	1.55844i
$843$		0			0
$844$	1.61208	−	0.738945i	0.00191004	−	0.000875528i
$845$	591.537	+	1024.57i	0.700044	+	1.21251i
$846$		0			0
$847$	−237.384	−	137.054i	−0.280264	−	0.161811i
$848$	−393.012	+	64.0178i	−0.463457	+	0.0754927i
$849$		0			0
$850$	−1157.26	+	1803.52i	−1.36149	+	2.12179i
$851$	−325.732	+	388.193i	−0.382764	+	0.456160i
$852$		0			0
$853$	−410.158	−	149.285i	−0.480842	−	0.175012i	0.0902154	−	0.995922i	$-0.471244\pi$
$853$	−410.158	−	149.285i	−0.480842	−	0.175012i	−0.571057	+	0.820910i	$0.693467\pi$
$854$	−98.6481	+	235.975i	−0.115513	+	0.276318i
$855$		0			0
$856$	−772.264	−	604.689i	−0.902178	−	0.706413i
$857$	−25.9873	−	147.381i	−0.0303236	−	0.171974i	0.965885	−	0.258972i	$-0.0833837\pi$
$857$	−25.9873	−	147.381i	−0.0303236	−	0.171974i	−0.996208	+	0.0869982i	$0.972273\pi$
$858$		0			0
$859$	245.695	+	675.042i	0.286025	+	0.785846i	0.996613	+	0.0822378i	$0.0262067\pi$
$859$	245.695	+	675.042i	0.286025	+	0.785846i	−0.710588	+	0.703608i	$0.751571\pi$
$860$	−1634.63	+	132.261i	−1.90073	+	0.153792i
$861$		0			0
$862$	845.670	−	916.858i	0.981055	−	1.06364i
$863$			564.987i			0.654678i	0.944907	+	0.327339i	$0.106152\pi$
$863$			564.987i			0.654678i	−0.944907	+	0.327339i	$0.893848\pi$
$864$		0			0
$865$	−1656.99			−1.91560
$866$	−783.650	−	722.804i	−0.904907	−	0.834647i
$867$		0			0
$868$	−22.2883	−	275.464i	−0.0256778	−	0.317355i
$869$	118.904	−	43.2775i	0.136828	−	0.0498015i
$870$		0			0
$871$	269.050	−	47.4407i	0.308897	−	0.0544669i
$872$	−187.346	+	239.264i	−0.214846	+	0.274385i
$873$		0			0
$874$	−665.126	−	278.052i	−0.761014	−	0.318137i
$875$	712.151	−	1956.62i	0.813886	−	2.23613i
$876$		0			0
$877$	−466.664	−	391.577i	−0.532113	−	0.446496i	0.336717	−	0.941606i	$-0.390683\pi$
$877$	−466.664	−	391.577i	−0.532113	−	0.446496i	−0.868830	+	0.495110i	$0.835128\pi$
$878$	840.649	+	539.419i	0.957459	+	0.614373i
$879$		0			0
$880$	197.449	+	1212.16i	0.224374	+	1.37745i
$881$	215.603	−	373.436i	0.244726	−	0.423877i	−0.717329	−	0.696735i	$-0.754635\pi$
$881$	215.603	−	373.436i	0.244726	−	0.423877i	0.962054	+	0.272858i	$0.0879688\pi$
$882$		0			0
$883$	−19.1924	+	11.0808i	−0.0217355	+	0.0125490i	−0.510828	−	0.859683i	$-0.670661\pi$
$883$	−19.1924	+	11.0808i	−0.0217355	+	0.0125490i	0.489093	+	0.872232i	$0.337328\pi$
$884$	−174.318	−	380.291i	−0.197193	−	0.430193i
$885$		0			0
$886$	18.5553	−	9.58238i	0.0209427	−	0.0108153i
$887$	1621.95	+	285.993i	1.82858	+	0.322428i	0.978816	−	0.204740i	$-0.0656349\pi$
$887$	1621.95	+	285.993i	1.82858	+	0.322428i	0.849761	+	0.527168i	$0.176746\pi$
$888$		0			0
$889$	−646.645	+	542.600i	−0.727385	+	0.610348i
$890$	29.6653	+	231.160i	0.0333318	+	0.259731i
$891$		0			0
$892$	−26.6185	−	102.001i	−0.0298414	−	0.114351i
$893$	997.783	−	837.239i	1.11734	−	0.937558i
$894$		0			0
$895$	3056.34	+	538.915i	3.41491	+	0.602140i
$896$	189.105	−	555.189i	0.211055	−	0.619630i
$897$		0			0
$898$	695.069	−	216.662i	0.774018	−	0.241271i
$899$	−252.952	+	146.042i	−0.281371	+	0.162450i
$900$		0			0
$901$	186.977	−	323.854i	0.207522	−	0.359439i
$902$	−584.747	−	131.640i	−0.648278	−	0.145942i
$903$		0			0
$904$	269.768	−	827.250i	0.298416	−	0.915100i
$905$	1176.49	+	987.193i	1.29999	+	1.09082i
$906$		0			0
$907$	212.408	−	583.586i	0.234188	−	0.643425i	−0.765812	−	0.643064i	$-0.777663\pi$
$907$	212.408	−	583.586i	0.234188	−	0.643425i	1.00000		0.000360886i	$-0.000114874\pi$
$908$	−64.9177	−	17.8498i	−0.0714952	−	0.0196584i
$909$		0			0
$910$	379.434	+	497.845i	0.416960	+	0.547082i
$911$	−935.459	+	164.947i	−1.02685	+	0.181061i	−0.661606	−	0.749851i	$-0.730125\pi$
$911$	−935.459	+	164.947i	−1.02685	+	0.181061i	−0.365242	+	0.930913i	$0.619014\pi$
$912$		0			0
$913$	−636.378	+	231.623i	−0.697019	+	0.253694i
$914$	503.551	+	23.6331i	0.550931	+	0.0258567i
$915$		0			0
$916$	594.315	−	837.082i	0.648816	−	0.913845i
$917$	−922.604			−1.00611
$918$		0			0
$919$		−	1119.44i		−	1.21811i	−0.793128	−	0.609055i	$-0.791549\pi$
$919$		−	1119.44i		−	1.21811i	0.793128	−	0.609055i	$-0.208451\pi$
$920$	−625.421	+	1173.22i	−0.679806	+	1.27524i
$921$		0			0
$922$	548.751	+	25.7545i	0.595175	+	0.0279333i
$923$	−94.2592	−	258.975i	−0.102123	−	0.280580i
$924$		0			0
$925$	370.517	+	2101.30i	0.400558	+	2.27168i
$926$	28.7599	+	37.7351i	0.0310582	+	0.0407506i
$927$		0			0
$928$	−615.809	+	70.8658i	−0.663587	+	0.0763641i
$929$	−1350.81	−	491.654i	−1.45404	−	0.529229i	−0.510326	−	0.859981i	$-0.670475\pi$
$929$	−1350.81	−	491.654i	−1.45404	−	0.529229i	−0.943718	+	0.330752i	$0.892698\pi$
$930$		0			0
$931$	−383.144	+	456.614i	−0.411541	+	0.490455i
$932$	−61.7350	−	29.2798i	−0.0662393	−	0.0314161i
$933$		0			0
$934$	16.2728	+	3.66339i	0.0174227	+	0.00392226i
$935$	−998.858	−	576.691i	−1.06830	−	0.616782i
$936$		0			0
$937$	−164.072	−	284.182i	−0.175104	−	0.303289i	0.765093	−	0.643920i	$-0.222693\pi$
$937$	−164.072	−	284.182i	−0.175104	−	0.303289i	−0.940197	+	0.340630i	$0.889360\pi$
$938$	−343.415	+	107.047i	−0.366114	+	0.114122i
$939$		0			0
$940$	−1364.92	−	1976.66i	−1.45204	−	2.10283i
$941$	116.085	−	658.349i	0.123363	−	0.699627i	−0.858904	−	0.512137i	$-0.828854\pi$
$941$	116.085	−	658.349i	0.123363	−	0.699627i	0.982267	−	0.187489i	$-0.0600350\pi$
$942$		0			0
$943$	−417.077	−	497.053i	−0.442288	−	0.527098i
$944$	712.004	+	1271.29i	0.754242	+	1.34670i
$945$		0			0
$946$	−83.1899	−	648.239i	−0.0879386	−	0.685242i
$947$	−245.016	−	291.999i	−0.258729	−	0.308341i	0.621006	−	0.783806i	$-0.286724\pi$
$947$	−245.016	−	291.999i	−0.258729	−	0.308341i	−0.879735	+	0.475465i	$0.842280\pi$
$948$		0			0
$949$	−99.8642	+	566.358i	−0.105231	+	0.596795i
$950$	−2697.04	+	1392.81i	−2.83899	+	1.46612i
$951$		0			0
$952$	291.387	+	467.427i	0.306078	+	0.490995i
$953$	813.401	+	1408.85i	0.853517	+	1.47833i	0.878014	+	0.478634i	$0.158868\pi$
$953$	813.401	+	1408.85i	0.853517	+	1.47833i	−0.0244977	+	0.999700i	$0.507799\pi$
$954$		0			0
$955$	709.477	+	409.617i	0.742908	+	0.428918i
$956$	115.792	−	1230.87i	0.121121	−	1.28752i
$957$		0			0
$958$	−793.239	−	508.998i	−0.828015	−	0.531313i
$959$	−341.837	+	407.386i	−0.356452	+	0.424803i
$960$		0			0
$961$	−689.398	−	250.920i	−0.717375	−	0.261103i
$962$	−384.321	−	160.663i	−0.399502	−	0.167009i
$963$		0			0
$964$	744.843	+	754.635i	0.772658	+	0.782816i
$965$	−113.773	−	645.237i	−0.117899	−	0.668640i
$966$		0			0
$967$	−620.108	−	1703.73i	−0.641270	−	1.76188i	−0.647699	−	0.761896i	$-0.724269\pi$
$967$	−620.108	−	1703.73i	−0.641270	−	1.76188i	0.00642855	−	0.999979i	$-0.497954\pi$
$968$	468.217	−	98.9995i	0.483695	−	0.102272i
$969$		0			0
$970$	733.487	+	676.536i	0.756172	+	0.697460i
$971$			284.479i			0.292976i	0.989212	+	0.146488i	$0.0467969\pi$
$971$			284.479i			0.292976i	−0.989212	+	0.146488i	$0.953203\pi$
$972$		0			0
$973$	−762.171			−0.783321
$974$	−296.922	+	321.917i	−0.304849	+	0.330511i
$975$		0			0
$976$	−147.234	−	421.574i	−0.150854	−	0.431940i
$977$	558.491	−	203.274i	0.571638	−	0.208059i	−0.0399961	−	0.999200i	$-0.512735\pi$
$977$	558.491	−	203.274i	0.571638	−	0.208059i	0.611635	+	0.791140i	$0.290512\pi$
$978$		0			0
$979$	−91.4657	+	16.1279i	−0.0934276	+	0.0164738i
$980$	772.214	+	782.366i	0.787974	+	0.798333i
$981$		0			0
$982$	94.1194	−	225.142i	0.0958446	−	0.229269i
$983$	−258.620	+	710.553i	−0.263093	+	0.722841i	0.735862	+	0.677131i	$0.236777\pi$
$983$	−258.620	+	710.553i	−0.263093	+	0.722841i	−0.998955	+	0.0457097i	$0.985445\pi$
$984$		0			0
$985$	2087.35	+	1751.49i	2.11913	+	1.77816i
$986$	314.387	−	489.951i	0.318851	−	0.496907i
$987$		0			0
$988$	55.5015	−	589.984i	0.0561757	−	0.597150i
$989$	353.751	−	612.715i	0.357686	−	0.619530i
$990$		0			0
$991$	−1351.75	+	780.435i	−1.36403	+	0.787522i	−0.990157	−	0.139958i	$-0.955303\pi$
$991$	−1351.75	+	780.435i	−1.36403	+	0.787522i	−0.373871	+	0.927481i	$0.621970\pi$
$992$	350.374	+	331.743i	0.353199	+	0.334418i
$993$		0			0
$994$	166.501	+	322.412i	0.167506	+	0.324358i
$995$	699.730	+	123.381i	0.703246	+	0.124001i
$996$		0			0
$997$	1068.15	−	896.280i	1.07136	−	0.898977i	0.0761844	−	0.997094i	$-0.475726\pi$
$997$	1068.15	−	896.280i	1.07136	−	0.898977i	0.995175	+	0.0981166i	$0.0312818\pi$
$998$	58.3660	−	7.49023i	0.0584830	−	0.00750524i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.8		204
3.2	odd	2		108.3.j.a.103.27	yes	204
4.3	odd	2	inner	324.3.j.a.199.23		204
12.11	even	2		108.3.j.a.103.12	yes	204
27.11	odd	18		108.3.j.a.43.12	✓	204
27.16	even	9	inner	324.3.j.a.127.23		204
108.11	even	18		108.3.j.a.43.27	yes	204
108.43	odd	18	inner	324.3.j.a.127.8		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.12	✓	204	27.11	odd	18
108.3.j.a.43.27	yes	204	108.11	even	18
108.3.j.a.103.12	yes	204	12.11	even	2
108.3.j.a.103.27	yes	204	3.2	odd	2
324.3.j.a.127.8		204	108.43	odd	18	inner
324.3.j.a.127.23		204	27.16	even	9	inner
324.3.j.a.199.8		204	1.1	even	1	trivial
324.3.j.a.199.23		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)

\(f(q)\)	\(=\)	\(q+(-1.47013 - 1.35599i) q^{2} +(0.322594 + 3.98697i) q^{4} +(-9.22169 + 3.35642i) q^{5} +(-4.51251 + 0.795677i) q^{7} +(4.93203 - 6.29882i) q^{8} +O(q^{10})\)	\(q+(-1.47013 - 1.35599i) q^{2} +(0.322594 + 3.98697i) q^{4} +(-9.22169 + 3.35642i) q^{5} +(-4.51251 + 0.795677i) q^{7} +(4.93203 - 6.29882i) q^{8} +(18.1084 + 7.57011i) q^{10} +(-2.67518 + 7.34999i) q^{11} +(-5.33182 - 4.47393i) q^{13} +(7.71292 + 4.94915i) q^{14} +(-15.7919 + 2.57234i) q^{16} +(7.51307 - 13.0130i) q^{17} +(18.4333 - 10.6425i) q^{19} +(-16.3568 - 35.6838i) q^{20} +(13.8994 - 7.17797i) q^{22} +(16.6774 + 2.94067i) q^{23} +(54.6229 - 45.8341i) q^{25} +(1.77190 + 13.8072i) q^{26} +(-4.62805 - 17.7346i) q^{28} +(-14.8391 + 12.4515i) q^{29} +(14.8493 + 2.61834i) q^{31} +(26.7042 + 17.6319i) q^{32} +(-28.6907 + 8.94326i) q^{34} +(38.9423 - 22.4834i) q^{35} +(-14.9619 + 25.9148i) q^{37} +(-41.5305 - 9.34945i) q^{38} +(-24.3401 + 74.6397i) q^{40} +(-29.3512 - 24.6286i) q^{41} +(14.2890 - 39.2588i) q^{43} +(-30.1672 - 8.29480i) q^{44} +(-20.5305 - 26.9375i) q^{46} +(60.2645 - 10.6263i) q^{47} +(-26.3153 + 9.57799i) q^{49} +(-142.453 - 6.68575i) q^{50} +(16.1174 - 22.7011i) q^{52} +24.8870 q^{53} -76.7584i q^{55} +(-17.2440 + 32.3478i) q^{56} +(38.6995 + 1.81628i) q^{58} +(-31.1472 - 85.5763i) q^{59} +(4.84636 + 27.4850i) q^{61} +(-18.2801 - 23.9848i) q^{62} +(-15.3502 - 62.1319i) q^{64} +(64.1848 + 23.3614i) q^{65} +(-25.2305 + 30.0686i) q^{67} +(54.3062 + 25.7565i) q^{68} +(-87.7376 - 19.7517i) q^{70} +(34.2911 + 19.7980i) q^{71} +(-41.3131 - 71.5564i) q^{73} +(57.1361 - 17.8100i) q^{74} +(48.3776 + 70.0598i) q^{76} +(6.22354 - 35.2955i) q^{77} +(-10.3986 - 12.3926i) q^{79} +(136.994 - 76.7255i) q^{80} +(9.75418 + 76.0073i) q^{82} +(55.6540 + 66.3258i) q^{83} +(-25.6060 + 145.219i) q^{85} +(-74.2413 + 38.3400i) q^{86} +(33.1022 + 53.1008i) q^{88} +(5.93712 + 10.2834i) q^{89} +(27.6197 + 15.9462i) q^{91} +(-6.34436 + 67.4409i) q^{92} +(-103.006 - 66.0959i) q^{94} +(-134.265 + 160.011i) q^{95} +(47.7745 + 17.3885i) q^{97} +(51.6747 + 21.6023i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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