LMFDB - Embedded newform 324.3.j.a.199.23

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			199.23
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08010 + 1.68327i) q^{2} +(-1.66676 + 3.63619i) q^{4} +(-9.22169 + 3.35642i) q^{5} +(4.51251 - 0.795677i) q^{7} +(-7.92095 + 1.12185i) q^{8} +O(q^{10})$	\(q+(1.08010 + 1.68327i) q^{2} +(-1.66676 + 3.63619i) q^{4} +(-9.22169 + 3.35642i) q^{5} +(4.51251 - 0.795677i) q^{7} +(-7.92095 + 1.12185i) q^{8} +(-15.6101 - 11.8973i) q^{10} +(2.67518 - 7.34999i) q^{11} +(-5.33182 - 4.47393i) q^{13} +(6.21330 + 6.73633i) q^{14} +(-10.4438 - 12.1213i) q^{16} +(7.51307 - 13.0130i) q^{17} +(-18.4333 + 10.6425i) q^{19} +(3.16578 - 39.1262i) q^{20} +(15.2614 - 3.43570i) q^{22} +(-16.6774 - 2.94067i) q^{23} +(54.6229 - 45.8341i) q^{25} +(1.77190 - 13.8072i) q^{26} +(-4.62805 + 17.7346i) q^{28} +(-14.8391 + 12.4515i) q^{29} +(-14.8493 - 2.61834i) q^{31} +(9.12307 - 30.6720i) q^{32} +(30.0192 - 1.40889i) q^{34} +(-38.9423 + 22.4834i) q^{35} +(-14.9619 + 25.9148i) q^{37} +(-37.8239 - 19.5332i) q^{38} +(69.2791 - 36.9314i) q^{40} +(-29.3512 - 24.6286i) q^{41} +(-14.2890 + 39.2588i) q^{43} +(22.2671 + 21.9782i) q^{44} +(-13.0633 - 31.2487i) q^{46} +(-60.2645 + 10.6263i) q^{47} +(-26.3153 + 9.57799i) q^{49} +(136.149 + 42.4394i) q^{50} +(25.1550 - 11.9306i) q^{52} +24.8870 q^{53} +76.7584i q^{55} +(-34.8507 + 11.3649i) q^{56} +(-36.9868 - 11.5293i) q^{58} +(31.1472 + 85.5763i) q^{59} +(4.84636 + 27.4850i) q^{61} +(-11.6314 - 27.8234i) q^{62} +(61.4829 - 17.7723i) q^{64} +(64.1848 + 23.3614i) q^{65} +(25.2305 - 30.0686i) q^{67} +(34.7953 + 49.0086i) q^{68} +(-79.9071 - 41.2659i) q^{70} +(-34.2911 - 19.7980i) q^{71} +(-41.3131 - 71.5564i) q^{73} +(-59.7818 + 2.80573i) q^{74} +(-7.97413 - 84.7654i) q^{76} +(6.22354 - 35.2955i) q^{77} +(10.3986 + 12.3926i) q^{79} +(136.994 + 76.7255i) q^{80} +(9.75418 - 76.0073i) q^{82} +(-55.6540 - 66.3258i) q^{83} +(-25.6060 + 145.219i) q^{85} +(-81.5166 + 18.3512i) q^{86} +(-12.9443 + 61.2201i) q^{88} +(5.93712 + 10.2834i) q^{89} +(-27.6197 - 15.9462i) q^{91} +(38.4901 - 55.7408i) q^{92} +(-82.9785 - 89.9637i) q^{94} +(134.265 - 160.011i) q^{95} +(47.7745 + 17.3885i) q^{97} +(-44.5455 - 33.9505i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.08010	+	1.68327i	0.540051	+	0.841633i
$2$	1.08010	+	1.68327i	0.540051	+	0.841633i
$3$		0			0
$3$		0			0
$4$	−1.66676	+	3.63619i	−0.416691	+	0.909048i
$5$	−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	0.158238	−	0.987401i	$-0.449419\pi$
$7$	4.51251	−	0.795677i	0.644644	−	0.113668i	0.486406	+	0.873733i	$0.338308\pi$
$8$	−7.92095	+	1.12185i	−0.990119	+	0.140232i
$9$		0			0
$10$	−15.6101	−	11.8973i	−1.56101	−	1.18973i
$11$	2.67518	−	7.34999i	0.243198	−	0.668181i	−0.756698	−	0.653765i	$-0.773189\pi$
$11$	2.67518	−	7.34999i	0.243198	−	0.668181i	0.999896	−	0.0144166i	$-0.00458909\pi$
$12$		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	$0.808486\pi$
$14$	6.21330	+	6.73633i	0.443807	+	0.481167i
$15$		0			0
$16$	−10.4438	−	12.1213i	−0.652738	−	0.757584i
$17$	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	−0.899289	−	0.437355i	$-0.855915\pi$
$19$	−18.4333	+	10.6425i	−0.970173	+	0.560129i	−0.0708838	+	0.997485i	$0.522582\pi$
$20$	3.16578	−	39.1262i	0.158289	−	1.95631i
$21$		0			0
$22$	15.2614	−	3.43570i	0.693702	−	0.156168i
$23$	−16.6774	−	2.94067i	−0.725104	−	0.127855i	−0.201099	−	0.979571i	$-0.564451\pi$
$23$	−16.6774	−	2.94067i	−0.725104	−	0.127855i	−0.524005	+	0.851715i	$0.675563\pi$
$24$		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	−0.0710708	−	0.997471i	$-0.522642\pi$
$31$	−14.8493	−	2.61834i	−0.479011	−	0.0844625i	−0.407940	+	0.913009i	$0.633753\pi$
$32$	9.12307	−	30.6720i	0.285096	−	0.958499i
$33$		0			0
$34$	30.0192	−	1.40889i	0.882918	−	0.0414379i
$35$	−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	$0.299178\pi$
$38$	−37.8239	−	19.5332i	−0.995365	−	0.514031i
$39$		0			0
$40$	69.2791	−	36.9314i	1.73198	−	0.923285i
$41$	−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	$0.272581\pi$
$43$	−14.2890	+	39.2588i	−0.332303	+	0.912995i	−0.987511	+	0.157547i	$0.949641\pi$
$44$	22.2671	+	21.9782i	0.506071	+	0.499504i
$45$		0			0
$46$	−13.0633	−	31.2487i	−0.283986	−	0.679320i
$47$	−60.2645	+	10.6263i	−1.28222	+	0.226090i	−0.772924	−	0.634499i	$-0.781206\pi$
$47$	−60.2645	+	10.6263i	−1.28222	+	0.226090i	−0.509299	+	0.860589i	$0.670095\pi$
$48$		0			0
$49$	−26.3153	+	9.57799i	−0.537047	+	0.195469i
$50$	136.149	+	42.4394i	2.72298	+	0.848788i
$51$		0			0
$52$	25.1550	−	11.9306i	0.483749	−	0.229434i
$53$	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
$56$	−34.8507	+	11.3649i	−0.622334	+	0.202944i
$57$		0			0
$58$	−36.9868	−	11.5293i	−0.637703	−	0.198780i
$59$	31.1472	+	85.5763i	0.527919	+	1.45045i	0.861516	+	0.507730i	$0.169515\pi$
$59$	31.1472	+	85.5763i	0.527919	+	1.45045i	−0.333598	+	0.942716i	$0.608263\pi$
$60$		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	$0.870976\pi$
$62$	−11.6314	−	27.8234i	−0.187604	−	0.448765i
$63$		0			0
$64$	61.4829	−	17.7723i	0.960670	−	0.277692i
$65$	64.1848	+	23.3614i	0.987459	+	0.359406i
$66$		0			0
$67$	25.2305	−	30.0686i	0.376575	−	0.448785i	−0.544155	−	0.838985i	$-0.683150\pi$
$67$	25.2305	−	30.0686i	0.376575	−	0.448785i	0.920730	+	0.390200i	$0.127594\pi$
$68$	34.7953	+	49.0086i	0.511696	+	0.720714i
$69$		0			0
$70$	−79.9071	−	41.2659i	−1.14153	−	0.589513i
$71$	−34.2911	−	19.7980i	−0.482973	−	0.278845i	0.238682	−	0.971098i	$-0.423285\pi$
$71$	−34.2911	−	19.7980i	−0.482973	−	0.278845i	−0.721655	+	0.692253i	$0.756618\pi$
$72$		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	$-0.358151\pi$
$74$	−59.7818	+	2.80573i	−0.807862	+	0.0379153i
$75$		0			0
$76$	−7.97413	−	84.7654i	−0.104923	−	1.11533i
$77$	6.22354	−	35.2955i	0.0808252	−	0.458383i
$78$		0			0
$79$	10.3986	+	12.3926i	0.131628	+	0.156869i	0.827833	−	0.560975i	$-0.189574\pi$
$79$	10.3986	+	12.3926i	0.131628	+	0.156869i	−0.696204	+	0.717844i	$0.745129\pi$
$80$	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	0.318326	−	0.947981i	$-0.396879\pi$
$83$	−55.6540	−	66.3258i	−0.670530	−	0.799106i	−0.988856	+	0.148875i	$0.952435\pi$
$84$		0			0
$85$	−25.6060	+	145.219i	−0.301247	+	1.70846i
$86$	−81.5166	+	18.3512i	−0.947867	+	0.213387i
$87$		0			0
$88$	−12.9443	+	61.2201i	−0.147095	+	0.695683i
$89$	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
$92$	38.4901	−	55.7408i	0.418371	−	0.605878i
$93$		0			0
$94$	−82.9785	−	89.9637i	−0.882750	−	0.957060i
$95$	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	$0.526708\pi$
$98$	−44.5455	−	33.9505i	−0.454546	−	0.346433i
$99$		0			0
$100$	75.6180	+	275.014i	0.756180	+	2.75014i
$101$	−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	0.998922	−	0.0464265i	$-0.0147833\pi$
$103$	20.9977	+	57.6906i	0.203861	+	0.560103i	−0.795061	+	0.606530i	$0.792561\pi$
$104$	47.2522	+	29.4563i	0.454348	+	0.283233i
$105$		0			0
$106$	26.8804	+	41.8914i	0.253589	+	0.395201i
$107$			122.605i			1.14584i	0.819612	+	0.572919i	$0.194189\pi$
$107$			122.605i			1.14584i	−0.819612	+	0.572919i	$0.805811\pi$
$108$		0			0
$109$	−37.9855			−0.348491			−0.174245	−	0.984702i	$-0.555749\pi$
$109$	−37.9855			−0.348491			−0.174245	+	0.984702i	$0.555749\pi$
$110$	−129.205	+	82.9068i	−1.17459	+	0.753698i
$111$		0			0
$112$	−56.7724	−	46.3878i	−0.506896	−	0.414176i
$113$	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
$116$	−20.5427	−	74.7113i	−0.177092	−	0.644063i
$117$		0			0
$118$	−110.405	+	144.860i	−0.935639	+	1.22763i
$119$	23.5486	−	64.6993i	0.197888	−	0.543692i
$120$		0			0
$121$	45.8256	+	38.4522i	0.378724	+	0.317787i
$122$	−41.0301	+	37.8443i	−0.336312	+	0.310199i
$123$		0			0
$124$	34.2711	−	49.6309i	0.276380	−	0.400249i
$125$	−227.208	+	393.536i	−1.81766	+	3.14829i
$126$		0			0
$127$	−159.542	+	92.1119i	−1.25624	+	0.725290i	−0.972341	−	0.233564i	$-0.924961\pi$
$127$	−159.542	+	92.1119i	−1.25624	+	0.725290i	−0.283898	+	0.958854i	$0.591628\pi$
$128$	96.3232	+	84.2962i	0.752525	+	0.658564i
$129$		0			0
$130$	30.0027	+	133.273i	0.230790	+	1.02517i
$131$	−198.290	−	34.9638i	−1.51366	−	0.266900i	−0.645724	−	0.763571i	$-0.723444\pi$
$131$	−198.290	−	34.9638i	−1.51366	−	0.266900i	−0.867939	+	0.496671i	$0.834555\pi$
$132$		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	−0.450105	−	0.892975i	$-0.648614\pi$
$139$	−163.809	−	28.8839i	−1.17848	−	0.207798i	−0.728376	+	0.685177i	$0.759725\pi$
$140$	−16.8462	−	179.076i	−0.120330	−	1.27912i
$141$		0			0
$142$	−3.71261	−	79.1048i	−0.0261452	−	0.557076i
$143$	−47.1469	+	27.2203i	−0.329699	+	0.190352i
$144$		0			0
$145$	95.0490	−	164.630i	0.655510	−	1.13538i
$146$	75.8261	−	146.829i	0.519357	−	1.00568i
$147$		0			0
$148$	−69.2931	−	97.5981i	−0.468197	−	0.659447i
$149$	−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	−0.965506	−	0.260382i	$-0.916151\pi$
$151$	−8.83574	+	24.2760i	−0.0585148	+	0.160768i	0.906991	+	0.421151i	$0.138374\pi$
$152$	134.070	−	104.978i	0.882038	−	0.690643i
$153$		0			0
$154$	66.1337	−	27.6468i	0.429440	−	0.179525i
$155$	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	$0.401228\pi$
$158$	−9.62848	+	30.8890i	−0.0609397	+	0.195500i
$159$		0			0
$160$	18.8179	+	313.468i	0.117612	+	1.95918i
$161$	−77.5967			−0.481967
$162$		0			0
$163$		−	187.452i		−	1.15001i	−0.818148	−	0.575007i	$-0.804999\pi$
$163$		−	187.452i		−	1.15001i	0.818148	−	0.575007i	$-0.195001\pi$
$164$	138.476	−	65.6767i	0.844365	−	0.400468i
$165$		0			0
$166$	51.5320	−	165.319i	0.310434	−	0.995897i
$167$	71.8589	+	197.431i	0.430293	+	1.18222i	0.945634	+	0.325234i	$0.105443\pi$
$167$	71.8589	+	197.431i	0.430293	+	1.18222i	−0.515341	+	0.856985i	$0.672335\pi$
$168$		0			0
$169$	−20.9343	−	118.724i	−0.123871	−	0.702509i
$170$	−272.099	+	113.749i	−1.60058	+	0.669115i
$171$		0			0
$172$	−118.936	−	117.393i	−0.691489	−	0.682516i
$173$	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
$176$	−117.031	+	44.3351i	−0.664948	+	0.251904i
$177$		0			0
$178$	−10.8970	+	21.1008i	−0.0612190	+	0.118544i
$179$	273.877	+	158.123i	1.53004	+	0.883370i	0.999359	+	0.0357989i	$0.0113976\pi$
$179$	273.877	+	158.123i	1.53004	+	0.883370i	0.530682	+	0.847571i	$0.321936\pi$
$180$		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	$0.975637\pi$
$182$	−2.99032	−	63.7148i	−0.0164303	−	0.350081i
$183$		0			0
$184$	135.400	+	4.58336i	0.735868	+	0.0249096i
$185$	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	0.888000	−	0.459844i	$-0.152095\pi$
$191$	53.6600	+	63.9495i	0.280942	+	0.334814i	−0.607057	+	0.794658i	$0.707650\pi$
$192$		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	$0.110890\pi$
$194$	22.3318	+	99.1985i	0.115113	+	0.511332i
$195$		0			0
$196$	9.03397	−	111.652i	0.0460917	−	0.569652i
$197$	−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	0.649201	−	0.760617i	$-0.275103\pi$
$199$	62.7025	+	36.2013i	0.315088	+	0.181916i	−0.334113	+	0.942533i	$0.608437\pi$
$200$	−381.246	+	424.328i	−1.90623	+	2.12164i
$201$		0			0
$202$	3.74939	−	3.45827i	0.0185613	−	0.0171201i
$203$	−57.0541	+	67.9944i	−0.281054	+	0.334948i
$204$		0			0
$205$	353.332	+	128.602i	1.72357	+	0.627328i
$206$	−74.4290	+	97.6564i	−0.361306	+	0.474060i
$207$		0			0
$208$	1.45445	+	111.354i	0.00699255	+	0.535354i
$209$	28.9097	+	163.955i	0.138324	+	0.784473i
$210$		0			0
$211$	0.151632	+	0.416605i	0.000718634	+	0.00197443i	0.940051	−	0.341033i	$-0.110777\pi$
$211$	0.151632	+	0.416605i	0.000718634	+	0.00197443i	−0.939333	+	0.343007i	$0.888554\pi$
$212$	−41.4807	+	90.4938i	−0.195664	+	0.426858i
$213$		0			0
$214$	−206.376	+	132.425i	−0.964374	+	0.618810i
$215$		−	409.992i		−	1.90694i
$216$		0			0
$217$	−69.0911			−0.318392
$218$	−41.0282	−	63.9397i	−0.188203	−	0.293301i
$219$		0			0
$220$	−279.108	−	127.938i	−1.26867	−	0.581536i
$221$	−98.2777	+	35.7702i	−0.444695	+	0.161856i
$222$		0			0
$223$	25.9540	−	4.57639i	0.116386	−	0.0205219i	−0.115152	−	0.993348i	$-0.536735\pi$
$223$	25.9540	−	4.57639i	0.116386	−	0.0205219i	0.231538	+	0.972826i	$0.425624\pi$
$224$	16.7630	−	145.666i	0.0748347	−	0.650297i
$225$		0			0
$226$	173.011	+	131.860i	0.765534	+	0.583453i
$227$	5.75679	−	15.8167i	0.0253603	−	0.0696769i	−0.926366	−	0.376623i	$-0.877085\pi$
$227$	5.75679	−	15.8167i	0.0253603	−	0.0696769i	0.951727	+	0.306947i	$0.0993073\pi$
$228$		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	$0.911565\pi$
$230$	225.350	+	244.320i	0.979782	+	1.06226i
$231$		0			0
$232$	103.571	−	115.275i	0.446426	−	0.496873i
$233$	−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
$236$	−363.087	−	29.3781i	−1.53850	−	0.124483i
$237$		0			0
$238$	134.341	−	30.2432i	0.564458	−	0.127072i
$239$	304.381	+	53.6706i	1.27356	+	0.224563i	0.769244	−	0.638955i	$-0.220633\pi$
$239$	304.381	+	53.6706i	1.27356	+	0.224563i	0.504318	+	0.863518i	$0.331744\pi$
$240$		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
$248$	120.558	+	4.08096i	0.486122	+	0.0164555i
$249$		0			0
$250$	−907.833	+	42.6072i	−3.63133	+	0.170429i
$251$	184.422	−	106.476i	0.734748	−	0.424207i	−0.0854089	−	0.996346i	$-0.527220\pi$
$251$	184.422	−	106.476i	0.734748	−	0.424207i	0.820156	+	0.572139i	$0.193886\pi$
$252$		0			0
$253$	−66.2289	+	114.712i	−0.261774	+	0.453407i
$254$	−327.371	−	169.062i	−1.28886	−	0.665599i
$255$		0			0
$256$	−37.8540	+	253.186i	−0.147867	+	0.989007i
$257$	−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
$260$	−191.927	+	194.451i	−0.738182	+	0.747887i
$261$		0			0
$262$	−155.320	−	371.539i	−0.592823	−	1.41809i
$263$	19.1179	−	3.37100i	0.0726916	−	0.0128175i	−0.137184	−	0.990546i	$-0.543805\pi$
$263$	19.1179	−	3.37100i	0.0726916	−	0.0128175i	0.209876	+	0.977728i	$0.432694\pi$
$264$		0			0
$265$	−229.500	+	83.5311i	−0.866037	+	0.315212i
$266$	−186.223	−	58.0480i	−0.700085	−	0.218225i
$267$		0			0
$268$	67.2819	+	141.860i	0.251052	+	0.529330i
$269$	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	$0.129197\pi$
$271$			213.999i			0.789665i	−0.918753	+	0.394833i	$0.870803\pi$
$272$	−236.200	+	44.8369i	−0.868383	+	0.164841i
$273$		0			0
$274$	221.605	+	69.0771i	0.808777	+	0.252106i
$275$	−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	$-0.120193\pi$
$278$	−128.311	−	306.931i	−0.461550	−	1.10407i
$279$		0			0
$280$	283.237	−	221.777i	1.01156	−	0.792061i
$281$	−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	$0.570556\pi$
$283$	−323.295	+	385.288i	−1.14238	+	1.36144i	−0.922538	+	0.385907i	$0.873889\pi$
$284$	129.144	−	91.6905i	0.454733	−	0.322854i
$285$		0			0
$286$	−96.7424	−	49.9601i	−0.338260	−	0.174686i
$287$	−152.044	−	87.7827i	−0.529770	−	0.305863i
$288$		0			0
$289$	31.6076	+	54.7461i	0.109369	+	0.189433i
$290$	379.778	−	17.8241i	1.30958	−	0.0614622i
$291$		0			0
$292$	329.052	−	30.9549i	1.12689	−	0.106010i
$293$	−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
$302$	−50.4064	+	11.3476i	−0.166909	+	0.0375750i
$303$		0			0
$304$	321.514	+	112.288i	1.05761	+	0.369370i
$305$	−136.943	−	237.192i	−0.448993	−	0.777679i
$306$		0			0
$307$	−268.474	−	155.003i	−0.874507	−	0.504897i	−0.00566388	−	0.999984i	$-0.501803\pi$
$307$	−268.474	−	155.003i	−0.874507	−	0.504897i	−0.868843	+	0.495087i	$0.835136\pi$
$308$	117.968	+	81.4592i	0.383013	+	0.264478i
$309$		0			0
$310$	200.649	+	217.539i	0.647253	+	0.701739i
$311$	−275.480	+	328.304i	−0.885786	+	1.05564i	0.112292	+	0.993675i	$0.464181\pi$
$311$	−275.480	+	328.304i	−0.885786	+	1.05564i	−0.998078	+	0.0619638i	$0.980264\pi$
$312$		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	$0.580332\pi$
$314$	−19.3562	−	14.7524i	−0.0616440	−	0.0469821i
$315$		0			0
$316$	−62.3940	+	17.1559i	−0.197449	+	0.0542909i
$317$	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
$320$	−507.325	+	370.253i	−1.58539	+	1.15704i
$321$		0			0
$322$	−83.8123	−	130.616i	−0.260287	−	0.405639i
$323$			319.830i			0.990186i
$324$		0			0
$325$	−496.298			−1.52707
$326$	315.532	−	202.467i	0.967890	−	0.621066i
$327$		0			0
$328$	260.119	+	162.154i	0.793047	+	0.494373i
$329$	−263.489	+	95.9021i	−0.800878	+	0.291496i
$330$		0			0
$331$	270.454	−	47.6883i	0.817081	−	0.144073i	0.250539	−	0.968107i	$-0.419392\pi$
$331$	270.454	−	47.6883i	0.817081	−	0.144073i	0.566542	+	0.824033i	$0.308281\pi$
$332$	333.935	−	91.8192i	1.00583	−	0.276564i
$333$		0			0
$334$	−254.713	+	334.203i	−0.762614	+	1.00061i
$335$	−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	$0.398386\pi$
$338$	177.233	−	163.472i	0.524358	−	0.483645i
$339$		0			0
$340$	−485.365	−	335.154i	−1.42754	−	0.985747i
$341$	−58.9694	+	102.138i	−0.172931	+	0.299525i
$342$		0			0
$343$	−305.570	+	176.421i	−0.890876	+	0.514347i
$344$	69.1401	−	326.997i	0.200989	−	0.950573i
$345$		0			0
$346$	74.1670	+	329.451i	0.214355	+	0.952171i
$347$	−18.5984	−	3.27941i	−0.0535978	−	0.00945074i	0.146785	−	0.989168i	$-0.453107\pi$
$347$	−18.5984	−	3.27941i	−0.0535978	−	0.00945074i	−0.200383	+	0.979718i	$0.564219\pi$
$348$		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
$356$	−47.2881	+	4.44853i	−0.132832	+	0.0124959i
$357$		0			0
$358$	29.6520	+	631.797i	0.0828269	+	1.76480i
$359$	−32.9975	+	19.0511i	−0.0919150	+	0.0530671i	−0.545253	−	0.838272i	$-0.683566\pi$
$359$	−32.9975	+	19.0511i	−0.0919150	+	0.0530671i	0.453338	+	0.891339i	$0.350233\pi$
$360$		0			0
$361$	46.0239	−	79.7157i	0.127490	−	0.220819i
$362$	143.618	−	278.102i	0.396736	−	0.768237i
$363$		0			0
$364$	104.019	−	73.8520i	0.285767	−	0.202890i
$365$	621.150	+	521.207i	1.70178	+	1.42796i
$366$		0			0
$367$	−111.793	+	307.148i	−0.304612	+	0.836915i	0.689071	+	0.724694i	$0.258019\pi$
$367$	−111.793	+	307.148i	−0.304612	+	0.836915i	−0.993683	+	0.112222i	$0.964203\pi$
$368$	138.530	+	232.864i	0.376441	+	0.632783i
$369$		0			0
$370$	541.872	−	226.526i	1.46452	−	0.612233i
$371$	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	$0.311524\pi$
$374$	69.9515	−	224.410i	0.187036	−	0.600027i
$375$		0			0
$376$	465.431	−	151.778i	1.23785	−	0.403665i
$377$	134.826			0.357629
$378$		0			0
$379$		−	361.411i		−	0.953590i	−0.879014	−	0.476795i	$-0.841798\pi$
$379$		−	361.411i		−	0.953590i	0.879014	−	0.476795i	$-0.158202\pi$
$380$	358.043	+	754.916i	0.942219	+	1.98662i
$381$		0			0
$382$	−49.6857	+	159.396i	−0.130067	+	0.417267i
$383$	−119.450	−	328.187i	−0.311880	−	0.856884i	−0.992277	−	0.124040i	$-0.960415\pi$
$383$	−119.450	−	328.187i	−0.311880	−	0.856884i	0.680397	−	0.732844i	$-0.261807\pi$
$384$		0			0
$385$	61.0749	+	346.373i	0.158636	+	0.899669i
$386$	−123.197	+	51.5016i	−0.319162	+	0.133424i
$387$		0			0
$388$	−142.857	+	144.735i	−0.368187	+	0.373028i
$389$	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
$392$	197.697	−	105.389i	0.504330	−	0.268849i
$393$		0			0
$394$	254.810	−	493.413i	0.646726	−	1.25232i
$395$	−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	$0.840487\pi$
$398$	6.78865	+	144.646i	0.0170569	+	0.363432i
$399$		0			0
$400$	−1126.04	−	183.421i	−2.81510	−	0.458553i
$401$	−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	$-0.147440\pi$
$410$	165.162	+	733.655i	0.402835	+	1.78940i
$411$		0			0
$412$	−244.772	−	19.8050i	−0.594108	−	0.0480704i
$413$	208.643	+	361.380i	0.505189	+	0.875013i
$414$		0			0
$415$	735.841	+	424.838i	1.77311	+	1.02371i
$416$	−185.867	+	122.722i	−0.446795	+	0.295004i
$417$		0			0
$418$	−244.754	+	225.751i	−0.585536	+	0.540073i
$419$	−358.205	+	426.892i	−0.854905	+	1.01884i	0.144664	+	0.989481i	$0.453790\pi$
$419$	−358.205	+	426.892i	−0.854905	+	1.01884i	−0.999569	+	0.0293551i	$0.990655\pi$
$420$		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	$0.951564\pi$
$422$	−0.537479	+	0.705212i	−0.00127365	+	0.00167112i
$423$		0			0
$424$	−197.128	+	27.9195i	−0.464925	+	0.0658479i
$425$	−186.054	−	1055.16i	−0.437773	−	2.48274i
$426$		0			0
$427$	43.7384	+	120.170i	0.102432	+	0.281429i
$428$	−445.814	−	204.353i	−1.04162	−	0.477460i
$429$		0			0
$430$	690.126	−	442.833i	1.60494	−	1.02984i
$431$		−	623.656i		−	1.44700i	−0.690326	−	0.723499i	$-0.742533\pi$
$431$		−	623.656i		−	1.44700i	0.690326	−	0.723499i	$-0.257467\pi$
$432$		0			0
$433$	533.046			1.23105			0.615527	−	0.788116i	$-0.288943\pi$
$433$	533.046			1.23105			0.615527	+	0.788116i	$0.288943\pi$
$434$	−74.6253	−	116.299i	−0.171948	−	0.267969i
$435$		0			0
$436$	63.3128	−	138.123i	0.145213	−	0.316795i
$437$	338.715	−	123.282i	0.775092	−	0.282110i
$438$		0			0
$439$	491.828	−	86.7226i	1.12034	−	0.197546i	0.417349	−	0.908746i	$-0.362959\pi$
$439$	491.828	−	86.7226i	1.12034	−	0.197546i	0.702989	+	0.711201i	$0.251848\pi$
$440$	−86.1116	−	607.999i	−0.195708	−	1.38182i
$441$		0			0
$442$	−166.360	−	126.792i	−0.376381	−	0.286860i
$443$	3.57129	−	9.81203i	0.00806159	−	0.0221490i	−0.935597	−	0.353071i	$-0.885137\pi$
$443$	3.57129	−	9.81203i	0.00806159	−	0.0221490i	0.943658	+	0.330922i	$0.107360\pi$
$444$		0			0
$445$	−89.2656	−	74.9028i	−0.200597	−	0.168321i
$446$	35.7362	+	38.7445i	0.0801260	+	0.0868710i
$447$		0			0
$448$	263.301	−	129.118i	0.587725	−	0.288210i
$449$	−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
$452$	−35.0871	+	433.645i	−0.0776263	+	0.959392i
$453$		0			0
$454$	32.8416	−	7.39338i	0.0723382	−	0.0162850i
$455$	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	0.198820	−	0.980036i	$-0.436289\pi$
$463$	23.3623	+	4.11941i	0.0504586	+	0.00889720i	−0.148362	+	0.988933i	$0.547400\pi$
$464$	305.905	+	49.8289i	0.659277	+	0.107390i
$465$		0			0
$466$	−34.1257	+	1.60162i	−0.0732312	+	0.00343695i
$467$	7.22269	−	4.17002i	0.0154661	−	0.00892939i	−0.492247	−	0.870456i	$-0.663824\pi$
$467$	7.22269	−	4.17002i	0.0154661	−	0.00892939i	0.507713	+	0.861526i	$0.330491\pi$
$468$		0			0
$469$	89.9281	−	155.760i	0.191744	−	0.332111i
$470$	1067.16	+	551.106i	2.27055	+	1.17257i
$471$		0			0
$472$	−342.719	−	642.903i	−0.726101	−	1.36208i
$473$	250.326	+	210.049i	0.529231	+	0.444077i
$474$		0			0
$475$	−519.092	+	1426.19i	−1.09283	+	3.00251i
$476$	196.009	+	193.466i	0.411784	+	0.406441i
$477$		0			0
$478$	238.421	+	570.324i	0.498788	+	1.19315i
$479$	−464.091	+	81.8317i	−0.968874	+	0.170839i	−0.635623	−	0.772000i	$-0.719257\pi$
$479$	−464.091	+	81.8317i	−0.968874	+	0.170839i	−0.333251	+	0.942838i	$0.608146\pi$
$480$		0			0
$481$	195.715	−	71.2345i	0.406892	−	0.148097i
$482$	506.137	+	157.769i	1.05008	+	0.327322i
$483$		0			0
$484$	−216.200	+	102.540i	−0.446694	+	0.211859i
$485$	−498.925			−1.02871
$486$		0			0
$487$			218.971i			0.449633i	0.974401	+	0.224817i	$0.0721783\pi$
$487$			218.971i			0.449633i	−0.974401	+	0.224817i	$0.927822\pi$
$488$	−69.2219	−	212.271i	−0.141848	−	0.434981i
$489$		0			0
$490$	524.737	+	163.567i	1.07089	+	0.333810i
$491$	−41.7305	−	114.654i	−0.0849908	−	0.233510i	0.889916	−	0.456125i	$-0.150763\pi$
$491$	−41.7305	−	114.654i	−0.0849908	−	0.233510i	−0.974906	+	0.222615i	$0.928541\pi$
$492$		0			0
$493$	50.5441	+	286.650i	0.102523	+	0.581439i
$494$	114.280	+	273.369i	0.231337	+	0.553378i
$495$		0			0
$496$	123.346	+	207.339i	0.248681	+	0.418023i
$497$	−170.491	−	62.0538i	−0.343041	−	0.124857i
$498$		0			0
$499$	18.9123	−	22.5388i	0.0379004	−	0.0451680i	−0.746761	−	0.665092i	$-0.768392\pi$
$499$	18.9123	−	22.5388i	0.0379004	−	0.0451680i	0.784662	+	0.619924i	$0.212837\pi$
$500$	−1052.27	−	1482.10i	−2.10454	−	2.96421i
$501$		0			0
$502$	378.421	+	195.426i	0.753827	+	0.389294i
$503$	100.859	+	58.2311i	0.200515	+	0.115768i	0.596896	−	0.802319i	$-0.296401\pi$
$503$	100.859	+	58.2311i	0.200515	+	0.115768i	−0.396381	+	0.918086i	$0.629734\pi$
$504$		0			0
$505$	12.5140	+	21.6750i	0.0247803	+	0.0429207i
$506$	−264.624	+	12.4196i	−0.522973	+	0.0245446i
$507$		0			0
$508$	−69.0171	−	733.656i	−0.135861	−	1.44420i
$509$	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
$518$	−267.533	+	60.2278i	−0.516473	+	0.116270i
$519$		0			0
$520$	−534.613	−	113.038i	−1.02810	−	0.217381i
$521$	−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	0.164103	−	0.986443i	$-0.447527\pi$
$523$	−318.052	−	183.627i	−0.608130	−	0.351104i	−0.772233	+	0.635339i	$0.780860\pi$
$524$	457.637	−	662.744i	0.873354	−	1.26478i
$525$		0			0
$526$	26.3236	+	28.5395i	0.0500448	+	0.0542576i
$527$	−145.636	+	173.563i	−0.276350	+	0.329341i
$528$		0			0
$529$	−227.610	−	82.8431i	−0.430264	−	0.156603i
$530$	−388.488	−	296.087i	−0.732996	−	0.558655i
$531$		0			0
$532$	−103.429	−	376.160i	−0.194416	−	0.707067i
$533$	46.3089	+	262.631i	0.0868835	+	0.492741i
$534$		0			0
$535$	−411.513	−	1130.62i	−0.769182	−	2.11331i
$536$	−166.117	+	266.477i	−0.309920	+	0.497158i
$537$		0			0
$538$	454.745	+	708.690i	0.845251	+	1.31727i
$539$			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	$0.345603\pi$
$542$	−360.218	+	231.141i	−0.664608	+	0.426459i
$543$		0			0
$544$	−330.592	−	349.159i	−0.607707	−	0.641837i
$545$	350.291	−	127.495i	0.642735	−	0.233936i
$546$		0			0
$547$	−74.2886	+	13.0991i	−0.135811	+	0.0239472i	−0.241140	−	0.970490i	$-0.577521\pi$
$547$	−74.2886	+	13.0991i	−0.135811	+	0.0239472i	0.105329	+	0.994437i	$0.466410\pi$
$548$	123.081	+	447.630i	0.224600	+	0.816843i
$549$		0			0
$550$	676.152	−	887.162i	1.22937	−	1.61302i
$551$	141.019	−	387.445i	0.255932	−	0.703168i
$552$		0			0
$553$	56.7845	+	47.6478i	0.102684	+	0.0861624i
$554$	164.252	−	151.499i	0.296484	−	0.273463i
$555$		0			0
$556$	378.058	−	547.498i	0.679961	−	0.984709i
$557$	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
$560$	679.234	+	237.221i	1.21292	+	0.423610i
$561$		0			0
$562$	−22.1846	−	98.5443i	−0.0394743	−	0.175346i
$563$	−329.585	−	58.1147i	−0.585408	−	0.103223i	−0.126903	−	0.991915i	$-0.540504\pi$
$563$	−329.585	−	58.1147i	−0.585408	−	0.103223i	−0.458505	+	0.888692i	$0.651615\pi$
$564$		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	−0.319176	−	0.947696i	$-0.603406\pi$
$571$	−538.586	−	94.9673i	−0.943234	−	0.166318i	−0.624058	+	0.781378i	$0.714517\pi$
$572$	−20.3955	−	216.805i	−0.0356565	−	0.379030i
$573$		0			0
$574$	−16.4614	−	350.745i	−0.0286785	−	0.611053i
$575$	−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	$0.265943\pi$
$578$	−58.0127	+	112.335i	−0.100368	+	0.194352i
$579$		0			0
$580$	440.201	+	620.015i	0.758967	+	1.06899i
$581$	−303.913	−	255.013i	−0.523086	−	0.438921i
$582$		0			0
$583$	66.5771	−	182.919i	0.114197	−	0.313755i
$584$	407.515	+	520.447i	0.697799	+	0.891177i
$585$		0			0
$586$	−208.364	+	87.1054i	−0.355570	+	0.148644i
$587$	−729.661	+	128.659i	−1.24303	+	0.219180i	−0.756215	−	0.654323i	$-0.772954\pi$
$587$	−729.661	+	128.659i	−1.24303	+	0.219180i	−0.486818	+	0.873503i	$0.661843\pi$
$588$		0			0
$589$	301.587	−	109.769i	0.512033	−	0.186365i
$590$	531.913	−	1706.42i	0.901548	−	2.89224i
$591$		0			0
$592$	470.381	−	89.2904i	0.794562	−	0.150828i
$593$	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
$596$	328.821	−	155.954i	0.551712	−	0.261668i
$597$		0			0
$598$	−70.1531	+	225.057i	−0.117313	+	0.376350i
$599$	241.563	+	663.689i	0.403277	+	1.10799i	0.960657	+	0.277737i	$0.0895844\pi$
$599$	241.563	+	663.689i	0.403277	+	1.10799i	−0.557380	+	0.830257i	$0.688193\pi$
$600$		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	$-0.237787\pi$
$602$	−353.242	+	147.671i	−0.586781	+	0.245301i
$603$		0			0
$604$	−73.5451	−	72.5908i	−0.121763	−	0.120183i
$605$	−551.651	−	200.785i	−0.911820	−	0.331875i
$606$		0			0
$607$	−260.988	+	311.033i	−0.429963	+	0.512410i	−0.936912	−	0.349566i	$-0.886329\pi$
$607$	−260.988	+	311.033i	−0.429963	+	0.512410i	0.506948	+	0.861976i	$0.330773\pi$
$608$	158.257	+	662.477i	0.260291	+	1.08960i
$609$		0			0
$610$	251.345	−	486.703i	0.412041	−	0.797874i
$611$	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	$0.568636\pi$
$614$	−29.0670	−	619.332i	−0.0473404	−	1.00868i
$615$		0			0
$616$	−9.70006	+	286.556i	−0.0157469	+	0.465188i
$617$	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	0.434108	−	0.900861i	$-0.357064\pi$
$619$	−327.110	−	389.834i	−0.528448	−	0.629780i	−0.962557	+	0.271080i	$0.912619\pi$
$620$	−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
$626$	26.5467	+	117.921i	0.0424069	+	0.188372i
$627$		0			0
$628$	3.92550	−	48.5157i	0.00625080	−	0.0772543i
$629$	224.819	+	389.399i	0.357424	+	0.619076i
$630$		0			0
$631$	−1083.33	−	625.458i	−1.71684	−	0.991218i	−0.924540	−	0.381086i	$-0.875550\pi$
$631$	−1083.33	−	625.458i	−1.71684	−	0.991218i	−0.792300	−	0.610132i	$-0.791116\pi$
$632$	−96.2698	−	86.4956i	−0.152326	−	0.136860i
$633$		0			0
$634$	−481.170	+	443.810i	−0.758943	+	0.700016i
$635$	1162.08	−	1384.92i	1.83005	−	2.18097i
$636$		0			0
$637$	183.160	+	66.6648i	0.287535	+	0.104654i
$638$	−183.686	+	241.010i	−0.287909	+	0.377758i
$639$		0			0
$640$	−1171.20	−	454.052i	−1.82999	−	0.709456i
$641$	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	$0.0811250\pi$
$643$	249.775	+	686.251i	0.388453	+	1.06726i	−0.579246	+	0.815153i	$0.696653\pi$
$644$	129.335	−	282.157i	0.200831	−	0.438131i
$645$		0			0
$646$	−538.359	+	345.449i	−0.833373	+	0.534750i
$647$			1180.60i			1.82472i	0.409385	+	0.912362i	$0.365743\pi$
$647$			1180.60i			1.82472i	−0.409385	+	0.912362i	$0.634257\pi$
$648$		0			0
$649$	712.309			1.09755
$650$	−536.052	−	835.401i	−0.824696	−	1.28523i
$651$		0			0
$652$	681.613	+	312.439i	1.04542	+	0.479200i
$653$	−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
$656$	8.00662	+	612.993i	0.0122052	+	0.934440i
$657$		0			0
$658$	−446.023	−	339.938i	−0.677847	−	0.516622i
$659$	90.2708	−	248.017i	0.136982	−	0.376354i	−0.852168	−	0.523269i	$-0.824712\pi$
$659$	90.2708	−	248.017i	0.136982	−	0.376354i	0.989149	+	0.146915i	$0.0469345\pi$
$660$		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	$-0.599184\pi$
$662$	372.389	+	403.737i	0.562522	+	0.609875i
$663$		0			0
$664$	515.240	+	462.928i	0.775964	+	0.697181i
$665$	478.556	−	828.884i	0.719634	−	1.24644i
$666$		0			0
$667$	284.093	−	164.021i	0.425926	−	0.245908i
$668$	−837.667	−	67.7773i	−1.25399	−	0.101463i
$669$		0			0
$670$	−751.586	+	169.199i	−1.12177	+	0.252536i
$671$	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
$680$	39.9098	−	1179.00i	0.0586908	−	1.73382i
$681$		0			0
$682$	−235.618	+	11.0582i	−0.345481	+	0.0162144i
$683$	831.903	−	480.300i	1.21801	−	0.703220i	0.253521	−	0.967330i	$-0.418411\pi$
$683$	831.903	−	480.300i	1.21801	−	0.703220i	0.964493	+	0.264110i	$0.0850780\pi$
$684$		0			0
$685$	−569.482	+	986.372i	−0.831361	+	1.43996i
$686$	−627.011	−	323.803i	−0.914010	−	0.472017i
$687$		0			0
$688$	625.101	−	236.809i	0.908577	−	0.344199i
$689$	−132.693	−	111.343i	−0.192588	−	0.161600i
$690$		0			0
$691$	229.573	−	630.745i	0.332232	−	0.912801i	−0.655298	−	0.755371i	$-0.727457\pi$
$691$	229.573	−	630.745i	0.332232	−	0.912801i	0.987530	−	0.157430i	$-0.0503209\pi$
$692$	−474.446	+	480.683i	−0.685615	+	0.694629i
$693$		0			0
$694$	−14.5681	−	34.8482i	−0.0209915	−	0.0502135i
$695$	1607.54	−	283.453i	2.31301	−	0.407846i
$696$		0			0
$697$	−541.010	+	196.912i	−0.776198	+	0.282513i
$698$	98.1581	+	30.5971i	0.140628	+	0.0438354i
$699$		0			0
$700$	560.049	+	1180.83i	0.800070	+	1.68691i
$701$	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
$704$	33.8516	−	499.443i	0.0480847	−	0.709436i
$705$		0			0
$706$	−479.877	−	149.584i	−0.679712	−	0.211875i
$707$	−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	$-0.277317\pi$
$710$	299.745	+	717.019i	0.422177	+	1.00989i
$711$		0			0
$712$	−58.5640	−	74.7936i	−0.0822529	−	0.105047i
$713$	239.948	+	87.3341i	0.336534	+	0.122488i
$714$		0			0
$715$	343.412	−	409.262i	0.480296	−	0.572395i
$716$	−1031.46	+	732.317i	−1.44058	+	1.02279i
$717$		0			0
$718$	−67.7087	−	34.9664i	−0.0943018	−	0.0486997i
$719$	−826.808	−	477.358i	−1.14994	−	0.663919i	−0.201069	−	0.979577i	$-0.564442\pi$
$719$	−826.808	−	477.358i	−1.14994	−	0.663919i	−0.948873	+	0.315658i	$0.897775\pi$
$720$		0			0
$721$	140.655	+	243.622i	0.195084	+	0.337895i
$722$	183.893	−	8.63062i	0.254700	−	0.0119538i
$723$		0			0
$724$	623.242	−	58.6301i	0.860831	−	0.0809809i
$725$	−239.852	+	1360.27i	−0.330831	+	1.87623i
$726$		0			0
$727$	713.696	+	850.550i	0.981700	+	1.16994i	0.985452	+	0.169951i	$0.0543611\pi$
$727$	713.696	+	850.550i	0.981700	+	1.16994i	−0.00375251	+	0.999993i	$0.501194\pi$
$728$	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	$0.698009\pi$
$734$	−637.759	+	143.574i	−0.868881	+	0.195605i
$735$		0			0
$736$	−242.345	+	484.700i	−0.329274	+	0.658560i
$737$	−153.508	−	265.883i	−0.208287	−	0.360764i
$738$		0			0
$739$	1070.82	+	618.236i	1.44901	+	0.836585i	0.998422	−	0.0561488i	$-0.0178821\pi$
$739$	1070.82	+	618.236i	1.44901	+	0.836585i	0.450585	+	0.892734i	$0.351215\pi$
$740$	966.580	+	667.442i	1.30619	+	0.901949i
$741$		0			0
$742$	154.630	+	167.647i	0.208396	+	0.225939i
$743$	213.265	−	254.159i	0.287032	−	0.342071i	−0.603191	−	0.797597i	$-0.706104\pi$
$743$	213.265	−	254.159i	0.287032	−	0.342071i	0.890223	+	0.455526i	$0.150549\pi$
$744$		0			0
$745$	839.011	+	305.375i	1.12619	+	0.409899i
$746$	285.580	+	217.655i	0.382815	+	0.291763i
$747$		0			0
$748$	453.296	−	124.639i	0.606011	−	0.166629i
$749$	97.5536	+	553.254i	0.130245	+	0.738657i
$750$		0			0
$751$	−339.987	−	934.108i	−0.452713	−	1.24382i	−0.930807	−	0.365510i	$-0.880895\pi$
$751$	−339.987	−	934.108i	−0.452713	−	1.24382i	0.478095	−	0.878308i	$-0.341328\pi$
$752$	758.195	+	619.508i	1.00824	+	0.823814i
$753$		0			0
$754$	145.626	+	226.948i	0.193138	+	0.300992i
$755$		−	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	$0.445022\pi$
$758$	608.350	−	390.360i	0.802573	−	0.514987i
$759$		0			0
$760$	−884.001	+	1418.07i	−1.16316	+	1.86588i
$761$	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
$764$	−321.971	+	88.5295i	−0.421428	+	0.115876i
$765$		0			0
$766$	423.407	−	555.541i	0.552751	−	0.725250i
$767$	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	$0.677841\pi$
$770$	−517.070	+	476.923i	−0.671520	+	0.619380i
$771$		0			0
$772$	−219.756	−	151.745i	−0.284657	−	0.196562i
$773$	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
$776$	−397.927	−	84.1374i	−0.512792	−	0.108425i
$777$		0			0
$778$	0.250907	+	1.11453i	0.000322502	+	0.00143256i
$779$	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	0.895068	−	0.445929i	$-0.147127\pi$
$787$	1246.33	+	219.761i	1.58364	+	0.279239i	0.688573	+	0.725167i	$0.258238\pi$
$788$	1105.76	−	104.023i	1.40325	−	0.132008i
$789$		0			0
$790$	−14.8855	−	317.166i	−0.0188424	−	0.401475i
$791$	431.607	−	249.189i	0.545648	−	0.315030i
$792$		0			0
$793$	97.1263	−	168.228i	0.122480	−	0.212141i
$794$	16.3734	−	31.7054i	0.0206214	−	0.0399312i
$795$		0			0
$796$	−236.145	+	167.659i	−0.296665	+	0.210627i
$797$	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
$800$	−907.492	−	2093.54i	−1.13436	−	2.61692i
$801$		0			0
$802$	−718.885	+	300.526i	−0.896366	+	0.374720i
$803$	−636.459	+	112.225i	−0.792601	+	0.139757i
$804$		0			0
$805$	715.572	−	260.447i	0.888910	−	0.323537i
$806$	−62.4634	+	200.388i	−0.0774980	+	0.248620i
$807$		0			0
$808$	6.32560	+	19.3976i	0.00782871	+	0.0240069i
$809$	−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	$-0.822856\pi$
$811$		−	856.788i		−	1.05646i	0.849102	−	0.528229i	$-0.177144\pi$
$812$	−152.145	−	320.790i	−0.187371	−	0.395062i
$813$		0			0
$814$	−139.305	+	446.901i	−0.171136	+	0.549019i
$815$	629.169	+	1728.63i	0.771986	+	2.12102i
$816$		0			0
$817$	−154.416	−	875.739i	−0.189004	−	1.07190i
$818$	898.663	−	375.681i	1.09861	−	0.459267i
$819$		0			0
$820$	−1056.54	+	1070.43i	−1.28847	+	1.30541i
$821$	−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	$-0.502053\pi$
$823$	806.094	−	960.665i	0.979458	−	1.16727i	0.985907	−	0.167293i	$-0.0535026\pi$
$824$	−231.042	−	433.408i	−0.280391	−	0.525981i
$825$		0			0
$826$	−382.943	+	741.529i	−0.463612	+	0.897735i
$827$	−228.269	−	131.791i	−0.276020	−	0.159360i	0.355600	−	0.934638i	$-0.384276\pi$
$827$	−228.269	−	131.791i	−0.276020	−	0.159360i	−0.631620	+	0.775278i	$0.717610\pi$
$828$		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	$0.734715\pi$
$830$	79.6677	+	1697.48i	0.0959852	+	2.04516i
$831$		0			0
$832$	−407.328	−	180.312i	−0.489577	−	0.216721i
$833$	−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	$-0.951783\pi$
$839$	−810.051	−	965.381i	−0.965495	−	1.15063i	0.0230539	−	0.999734i	$-0.492661\pi$
$840$		0			0
$841$	−80.8790	+	458.687i	−0.0961700	+	0.545407i
$842$	−324.356	−	1440.80i	−0.385221	−	1.71116i
$843$		0			0
$844$	−1.76759	−	0.143019i	−0.00209430	−	0.000169454i
$845$	591.537	+	1024.57i	0.700044	+	1.21251i
$846$		0			0
$847$	237.384	+	137.054i	0.280264	+	0.161811i
$848$	−259.915	−	301.663i	−0.306503	−	0.355735i
$849$		0			0
$850$	1575.16	−	1452.86i	1.85313	−	1.70925i
$851$	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	$0.693467\pi$
$854$	−155.037	+	203.419i	−0.181542	+	0.238196i
$855$		0			0
$856$	−137.544	−	971.145i	−0.160683	−	1.13452i
$857$	−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	$-0.973793\pi$
$859$	−245.695	−	675.042i	−0.286025	−	0.785846i	0.710588	−	0.703608i	$-0.248429\pi$
$860$	1490.81	+	683.360i	1.73350	+	0.794605i
$861$		0			0
$862$	1049.78	−	673.611i	1.21784	−	0.781452i
$863$		−	564.987i		−	0.654678i	−0.944907	−	0.327339i	$-0.893848\pi$
$863$		−	564.987i		−	0.654678i	0.944907	−	0.327339i	$-0.106152\pi$
$864$		0			0
$865$	−1656.99			−1.91560
$866$	575.744	+	897.258i	0.664831	+	1.03609i
$867$		0			0
$868$	115.158	−	251.228i	0.132671	−	0.289434i
$869$	118.904	−	43.2775i	0.136828	−	0.0498015i
$870$		0			0
$871$	−269.050	+	47.4407i	−0.308897	+	0.0544669i
$872$	300.881	−	42.6141i	0.345047	−	0.0488694i
$873$		0			0
$874$	573.363	+	436.990i	0.656022	+	0.499989i
$875$	−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	$0.835128\pi$
$878$	677.202	+	734.208i	0.771300	+	0.836228i
$879$		0			0
$880$	930.415	−	801.649i	1.05729	−	0.910965i
$881$	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	−0.489093	−	0.872232i	$-0.662672\pi$
$883$	19.1924	−	11.0808i	0.0217355	−	0.0125490i	0.510828	+	0.859683i	$0.329339\pi$
$884$	33.7384	−	416.977i	0.0381656	−	0.471693i
$885$		0			0
$886$	20.3736	−	4.58656i	0.0229950	−	0.00517671i
$887$	−1621.95	−	285.993i	−1.82858	−	0.322428i	−0.849761	−	0.527168i	$-0.823254\pi$
$887$	−1621.95	−	285.993i	−1.82858	−	0.322428i	−0.978816	+	0.204740i	$0.934365\pi$
$888$		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
$896$	501.732	+	303.745i	0.559968	+	0.339001i
$897$		0			0
$898$	−727.253	+	34.1321i	−0.809859	+	0.0380090i
$899$	252.952	−	146.042i	0.281371	−	0.162450i
$900$		0			0
$901$	186.977	−	323.854i	0.207522	−	0.359439i
$902$	−532.559	−	275.026i	−0.590420	−	0.304907i
$903$		0			0
$904$	−767.838	+	409.320i	−0.849378	+	0.452788i
$905$	1176.49	+	987.193i	1.29999	+	1.09082i
$906$		0			0
$907$	−212.408	+	583.586i	−0.234188	+	0.643425i	0.765812	+	0.643064i	$0.222337\pi$
$907$	−212.408	+	583.586i	−0.234188	+	0.643425i	−1.00000		0.000360886i	$0.999885\pi$
$908$	47.9172	+	47.2954i	0.0527723	+	0.0520875i
$909$		0			0
$910$	241.430	+	577.522i	0.265307	+	0.634639i
$911$	935.459	−	164.947i	1.02685	−	0.181061i	0.365242	−	0.930913i	$-0.380986\pi$
$911$	935.459	−	164.947i	1.02685	−	0.181061i	0.661606	+	0.749851i	$0.269875\pi$
$912$		0			0
$913$	−636.378	+	231.623i	−0.697019	+	0.253694i
$914$	−481.266	−	150.017i	−0.526549	−	0.164132i
$915$		0			0
$916$	927.567	−	439.929i	1.01263	−	0.480271i
$917$	−922.604			−1.00611
$918$		0			0
$919$			1119.44i			1.21811i	0.793128	+	0.609055i	$0.208451\pi$
$919$			1119.44i			1.21811i	−0.793128	+	0.609055i	$0.791549\pi$
$920$	−1264.00	+	412.192i	−1.37391	+	0.448035i
$921$		0			0
$922$	−524.466	−	163.483i	−0.568835	−	0.177313i
$923$	94.2592	+	258.975i	0.102123	+	0.280580i
$924$		0			0
$925$	370.517	+	2101.30i	0.400558	+	2.27168i
$926$	18.2996	+	43.7743i	0.0197620	+	0.0472725i
$927$		0			0
$928$	246.533	+	568.739i	0.265660	+	0.612865i
$929$	−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
$932$	−39.5552	−	55.7127i	−0.0424412	−	0.0597776i
$933$		0			0
$934$	14.8205	+	7.65366i	0.0158678	+	0.00819450i
$935$	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	$0.889360\pi$
$938$	359.317	−	16.8638i	0.383067	−	0.0179784i
$939$		0			0
$940$	224.981	+	2391.56i	0.239342	+	2.54421i
$941$	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	0.879735	−	0.475465i	$-0.157720\pi$
$947$	245.016	+	291.999i	0.258729	+	0.308341i	−0.621006	+	0.783806i	$0.713276\pi$
$948$		0			0
$949$	−99.8642	+	566.358i	−0.105231	+	0.596795i
$950$	−2961.33	+	666.664i	−3.11719	+	0.701752i
$951$		0			0
$952$	−113.944	+	538.898i	−0.119689	+	0.566069i
$953$	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
$956$	−702.488	+	1017.33i	−0.734820	+	1.06416i
$957$		0			0
$958$	−639.009	−	692.801i	−0.667024	−	0.723174i
$959$	341.837	−	407.386i	0.356452	−	0.424803i
$960$		0			0
$961$	−689.398	−	250.920i	−0.717375	−	0.261103i
$962$	331.299	+	252.500i	0.344385	+	0.262474i
$963$		0			0
$964$	281.112	+	1022.37i	0.291610	+	1.06055i
$965$	−113.773	−	645.237i	−0.117899	−	0.668640i
$966$		0			0
$967$	620.108	+	1703.73i	0.641270	+	1.76188i	0.647699	+	0.761896i	$0.275731\pi$
$967$	620.108	+	1703.73i	0.641270	+	1.76188i	−0.00642855	+	0.999979i	$0.502046\pi$
$968$	−406.120	−	253.169i	−0.419545	−	0.261538i
$969$		0			0
$970$	−538.889	−	839.822i	−0.555556	−	0.865796i
$971$		−	284.479i		−	0.292976i	−0.989212	−	0.146488i	$-0.953203\pi$
$971$		−	284.479i		−	0.292976i	0.989212	−	0.146488i	$-0.0467969\pi$
$972$		0			0
$973$	−762.171			−0.783321
$974$	−368.587	+	236.511i	−0.378426	+	0.242825i
$975$		0			0
$976$	282.541	−	345.793i	0.289489	−	0.354296i
$977$	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
$980$	291.442	+	1059.94i	0.297390	+	1.08157i
$981$		0			0
$982$	147.919	−	194.081i	0.150630	−	0.197638i
$983$	258.620	−	710.553i	0.263093	−	0.722841i	−0.735862	−	0.677131i	$-0.763223\pi$
$983$	258.620	−	710.553i	0.263093	−	0.722841i	0.998955	−	0.0457097i	$-0.0145549\pi$
$984$		0			0
$985$	2087.35	+	1751.49i	2.11913	+	1.77816i
$986$	−427.915	+	394.690i	−0.433990	+	0.400294i
$987$		0			0
$988$	−336.718	+	487.630i	−0.340808	+	0.493553i
$989$	353.751	−	612.715i	0.357686	−	0.619530i
$990$		0			0
$991$	1351.75	−	780.435i	1.36403	−	0.787522i	0.373871	−	0.927481i	$-0.378030\pi$
$991$	1351.75	−	780.435i	1.36403	−	0.787522i	0.990157	+	0.139958i	$0.0446969\pi$
$992$	−215.781	+	431.571i	−0.217521	+	0.435051i
$993$		0			0
$994$	−79.6950	−	354.007i	−0.0801761	−	0.356144i
$995$	−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.199.23		204
3.2	odd	2		108.3.j.a.103.12	yes	204
4.3	odd	2	inner	324.3.j.a.199.8		204
12.11	even	2		108.3.j.a.103.27	yes	204
27.11	odd	18		108.3.j.a.43.27	yes	204
27.16	even	9	inner	324.3.j.a.127.8		204
108.11	even	18		108.3.j.a.43.12	✓	204
108.43	odd	18	inner	324.3.j.a.127.23		204

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

\(f(q)\)	\(=\)	\(q+(1.08010 + 1.68327i) q^{2} +(-1.66676 + 3.63619i) q^{4} +(-9.22169 + 3.35642i) q^{5} +(4.51251 - 0.795677i) q^{7} +(-7.92095 + 1.12185i) q^{8} +O(q^{10})\)	\(q+(1.08010 + 1.68327i) q^{2} +(-1.66676 + 3.63619i) q^{4} +(-9.22169 + 3.35642i) q^{5} +(4.51251 - 0.795677i) q^{7} +(-7.92095 + 1.12185i) q^{8} +(-15.6101 - 11.8973i) q^{10} +(2.67518 - 7.34999i) q^{11} +(-5.33182 - 4.47393i) q^{13} +(6.21330 + 6.73633i) q^{14} +(-10.4438 - 12.1213i) q^{16} +(7.51307 - 13.0130i) q^{17} +(-18.4333 + 10.6425i) q^{19} +(3.16578 - 39.1262i) q^{20} +(15.2614 - 3.43570i) q^{22} +(-16.6774 - 2.94067i) q^{23} +(54.6229 - 45.8341i) q^{25} +(1.77190 - 13.8072i) q^{26} +(-4.62805 + 17.7346i) q^{28} +(-14.8391 + 12.4515i) q^{29} +(-14.8493 - 2.61834i) q^{31} +(9.12307 - 30.6720i) q^{32} +(30.0192 - 1.40889i) q^{34} +(-38.9423 + 22.4834i) q^{35} +(-14.9619 + 25.9148i) q^{37} +(-37.8239 - 19.5332i) q^{38} +(69.2791 - 36.9314i) q^{40} +(-29.3512 - 24.6286i) q^{41} +(-14.2890 + 39.2588i) q^{43} +(22.2671 + 21.9782i) q^{44} +(-13.0633 - 31.2487i) q^{46} +(-60.2645 + 10.6263i) q^{47} +(-26.3153 + 9.57799i) q^{49} +(136.149 + 42.4394i) q^{50} +(25.1550 - 11.9306i) q^{52} +24.8870 q^{53} +76.7584i q^{55} +(-34.8507 + 11.3649i) q^{56} +(-36.9868 - 11.5293i) q^{58} +(31.1472 + 85.5763i) q^{59} +(4.84636 + 27.4850i) q^{61} +(-11.6314 - 27.8234i) q^{62} +(61.4829 - 17.7723i) q^{64} +(64.1848 + 23.3614i) q^{65} +(25.2305 - 30.0686i) q^{67} +(34.7953 + 49.0086i) q^{68} +(-79.9071 - 41.2659i) q^{70} +(-34.2911 - 19.7980i) q^{71} +(-41.3131 - 71.5564i) q^{73} +(-59.7818 + 2.80573i) q^{74} +(-7.97413 - 84.7654i) q^{76} +(6.22354 - 35.2955i) q^{77} +(10.3986 + 12.3926i) q^{79} +(136.994 + 76.7255i) q^{80} +(9.75418 - 76.0073i) q^{82} +(-55.6540 - 66.3258i) q^{83} +(-25.6060 + 145.219i) q^{85} +(-81.5166 + 18.3512i) q^{86} +(-12.9443 + 61.2201i) q^{88} +(5.93712 + 10.2834i) q^{89} +(-27.6197 - 15.9462i) q^{91} +(38.4901 - 55.7408i) q^{92} +(-82.9785 - 89.9637i) q^{94} +(134.265 - 160.011i) q^{95} +(47.7745 + 17.3885i) q^{97} +(-44.5455 - 33.9505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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