LMFDB - Embedded newform 819.2.gh.d.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(19,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("819.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.gh (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	819.19
Dual form			819.2.gh.d.388.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14623 + 0.575080i) q^{2} +(2.54352 + 1.46850i) q^{4} +(-3.44337 + 0.922649i) q^{5} +(2.25660 + 1.38122i) q^{7} +(1.47218 + 1.47218i) q^{8} +O(q^{10})$	\(q+(2.14623 + 0.575080i) q^{2} +(2.54352 + 1.46850i) q^{4} +(-3.44337 + 0.922649i) q^{5} +(2.25660 + 1.38122i) q^{7} +(1.47218 + 1.47218i) q^{8} -7.92086 q^{10} +(2.44335 + 2.44335i) q^{11} +(-0.668132 + 3.54311i) q^{13} +(4.04887 + 4.26213i) q^{14} +(-0.624002 - 1.08080i) q^{16} +(-1.26366 + 2.18873i) q^{17} +(3.15731 + 3.15731i) q^{19} +(-10.1132 - 2.70983i) q^{20} +(3.83886 + 6.64910i) q^{22} +(-2.64388 + 1.52645i) q^{23} +(6.67542 - 3.85405i) q^{25} +(-3.47153 + 7.22008i) q^{26} +(3.71139 + 6.82698i) q^{28} +(1.12965 - 1.95662i) q^{29} +(-1.54238 + 5.75625i) q^{31} +(-1.79541 - 6.70056i) q^{32} +(-3.97081 + 3.97081i) q^{34} +(-9.04470 - 2.67399i) q^{35} +(2.71503 - 10.1326i) q^{37} +(4.96060 + 8.59202i) q^{38} +(-6.42756 - 3.71095i) q^{40} +(2.06529 - 0.553392i) q^{41} +(3.23658 - 1.86864i) q^{43} +(2.62665 + 9.80278i) q^{44} +(-6.55221 + 1.75566i) q^{46} +(-1.75541 - 6.55128i) q^{47} +(3.18448 + 6.23370i) q^{49} +(16.5433 - 4.43278i) q^{50} +(-6.90247 + 8.03082i) q^{52} +(2.54393 + 4.40622i) q^{53} +(-10.6677 - 6.15901i) q^{55} +(1.28872 + 5.35551i) q^{56} +(3.54971 - 3.54971i) q^{58} +(-2.20064 - 8.21290i) q^{59} -13.0938i q^{61} +(-6.62060 + 11.4672i) q^{62} -12.9174i q^{64} +(-0.968415 - 12.8167i) q^{65} +(-6.52131 + 6.52131i) q^{67} +(-6.42832 + 3.71139i) q^{68} +(-17.8742 - 10.9404i) q^{70} +(12.8101 + 3.43246i) q^{71} +(4.73040 + 1.26751i) q^{73} +(11.6541 - 20.1856i) q^{74} +(3.39417 + 12.6672i) q^{76} +(2.13887 + 8.88845i) q^{77} +(-4.45795 + 7.72140i) q^{79} +(3.14587 + 3.14587i) q^{80} +4.75082 q^{82} +(-0.573646 - 0.573646i) q^{83} +(2.33184 - 8.70254i) q^{85} +(8.02106 - 2.14924i) q^{86} +7.19408i q^{88} +(8.03851 + 2.15391i) q^{89} +(-6.40150 + 7.07254i) q^{91} -8.96637 q^{92} -15.0700i q^{94} +(-13.7849 - 7.95872i) q^{95} +(4.06679 - 15.1775i) q^{97} +(3.24975 + 15.2103i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^7	$ 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) $ 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.14623	+	0.575080i	1.51761	+	0.406643i	0.918955	−	0.394363i	$-0.129035\pi$
$2$	2.14623	+	0.575080i	1.51761	+	0.406643i	0.598657	+	0.801006i	$0.295701\pi$
$3$		0			0
$3$		0			0
$4$	2.54352	+	1.46850i	1.27176	+	0.734252i
$5$	−3.44337	+	0.922649i	−1.53992	+	0.412621i	−0.926241	−	0.376931i	$-0.876979\pi$
$5$	−3.44337	+	0.922649i	−1.53992	+	0.412621i	−0.613683	+	0.789553i	$0.710313\pi$
$6$		0			0
$7$	2.25660	+	1.38122i	0.852915	+	0.522051i
$7$	2.25660	+	1.38122i	0.852915	+	0.522051i
$8$	1.47218	+	1.47218i	0.520493	+	0.520493i
$9$		0			0
$10$	−7.92086			−2.50480
$11$	2.44335	+	2.44335i	0.736697	+	0.736697i	0.971937	−	0.235240i	$-0.0755877\pi$
$11$	2.44335	+	2.44335i	0.736697	+	0.736697i	−0.235240	+	0.971937i	$0.575588\pi$
$12$		0			0
$13$	−0.668132	+	3.54311i	−0.185307	+	0.982681i
$13$	−0.668132	+	3.54311i	−0.185307	+	0.982681i
$14$	4.04887	+	4.26213i	1.08210	+	1.13910i
$15$		0			0
$16$	−0.624002	−	1.08080i	−0.156000	−	0.270201i
$17$	−1.26366	+	2.18873i	−0.306484	+	0.530845i	−0.977591	−	0.210515i	$-0.932486\pi$
$17$	−1.26366	+	2.18873i	−0.306484	+	0.530845i	0.671107	+	0.741361i	$0.265819\pi$
$18$		0			0
$19$	3.15731	+	3.15731i	0.724337	+	0.724337i	0.969486	−	0.245148i	$-0.0788367\pi$
$19$	3.15731	+	3.15731i	0.724337	+	0.724337i	−0.245148	+	0.969486i	$0.578837\pi$
$20$	−10.1132	−	2.70983i	−2.26138	−	0.605936i
$21$		0			0
$22$	3.83886	+	6.64910i	0.818447	+	1.41759i
$23$	−2.64388	+	1.52645i	−0.551288	+	0.318286i	−0.749641	−	0.661844i	$-0.769774\pi$
$23$	−2.64388	+	1.52645i	−0.551288	+	0.318286i	0.198353	+	0.980131i	$0.436441\pi$
$24$		0			0
$25$	6.67542	−	3.85405i	1.33508	−	0.770811i
$26$	−3.47153	+	7.22008i	−0.680823	+	1.41597i
$27$		0			0
$28$	3.71139	+	6.82698i	0.701387	+	1.29018i
$29$	1.12965	−	1.95662i	0.209771	−	0.363335i	−0.741871	−	0.670543i	$-0.766061\pi$
$29$	1.12965	−	1.95662i	0.209771	−	0.363335i	0.951642	+	0.307208i	$0.0993947\pi$
$30$		0			0
$31$	−1.54238	+	5.75625i	−0.277020	+	1.03385i	0.677456	+	0.735564i	$0.263083\pi$
$31$	−1.54238	+	5.75625i	−0.277020	+	1.03385i	−0.954476	+	0.298289i	$0.903584\pi$
$32$	−1.79541	−	6.70056i	−0.317387	−	1.18450i
$33$		0			0
$34$	−3.97081	+	3.97081i	−0.680988	+	0.680988i
$35$	−9.04470	−	2.67399i	−1.52883	−	0.451987i
$36$		0			0
$37$	2.71503	−	10.1326i	0.446348	−	1.66579i	−0.266003	−	0.963972i	$-0.585703\pi$
$37$	2.71503	−	10.1326i	0.446348	−	1.66579i	0.712352	−	0.701823i	$-0.247630\pi$
$38$	4.96060	+	8.59202i	0.804716	+	1.39381i
$39$		0			0
$40$	−6.42756	−	3.71095i	−1.01629	−	0.586753i
$41$	2.06529	−	0.553392i	0.322544	−	0.0864254i	−0.0939142	−	0.995580i	$-0.529938\pi$
$41$	2.06529	−	0.553392i	0.322544	−	0.0864254i	0.416458	+	0.909155i	$0.363271\pi$
$42$		0			0
$43$	3.23658	−	1.86864i	0.493574	−	0.284965i	−0.232482	−	0.972601i	$-0.574685\pi$
$43$	3.23658	−	1.86864i	0.493574	−	0.284965i	0.726056	+	0.687635i	$0.241351\pi$
$44$	2.62665	+	9.80278i	0.395982	+	1.47782i
$45$		0			0
$46$	−6.55221	+	1.75566i	−0.966070	+	0.258858i
$47$	−1.75541	−	6.55128i	−0.256053	−	0.955603i	−0.967502	−	0.252865i	$-0.918627\pi$
$47$	−1.75541	−	6.55128i	−0.256053	−	0.955603i	0.711449	−	0.702738i	$-0.248039\pi$
$48$		0			0
$49$	3.18448	+	6.23370i	0.454926	+	0.890529i
$50$	16.5433	−	4.43278i	2.33958	−	0.626889i
$51$		0			0
$52$	−6.90247	+	8.03082i	−0.957201	+	1.11367i
$53$	2.54393	+	4.40622i	0.349436	+	0.605241i	0.986149	−	0.165860i	$-0.0530398\pi$
$53$	2.54393	+	4.40622i	0.349436	+	0.605241i	−0.636713	+	0.771101i	$0.719706\pi$
$54$		0			0
$55$	−10.6677	−	6.15901i	−1.43843	−	0.830480i
$56$	1.28872	+	5.35551i	0.172212	+	0.715660i
$57$		0			0
$58$	3.54971	−	3.54971i	0.466099	−	0.466099i
$59$	−2.20064	−	8.21290i	−0.286499	−	1.06923i	−0.947737	−	0.319052i	$-0.896635\pi$
$59$	−2.20064	−	8.21290i	−0.286499	−	1.06923i	0.661238	−	0.750176i	$-0.270031\pi$
$60$		0			0
$61$		−	13.0938i		−	1.67648i	−0.545299	−	0.838242i	$-0.683584\pi$
$61$		−	13.0938i		−	1.67648i	0.545299	−	0.838242i	$-0.316416\pi$
$62$	−6.62060	+	11.4672i	−0.840818	+	1.45634i
$63$		0			0
$64$		−	12.9174i		−	1.61468i
$65$	−0.968415	−	12.8167i	−0.120117	−	1.58971i
$66$		0			0
$67$	−6.52131	+	6.52131i	−0.796704	+	0.796704i	−0.982574	−	0.185870i	$-0.940490\pi$
$67$	−6.52131	+	6.52131i	−0.796704	+	0.796704i	0.185870	+	0.982574i	$0.440490\pi$
$68$	−6.42832	+	3.71139i	−0.779548	+	0.450072i
$69$		0			0
$70$	−17.8742	−	10.9404i	−2.13638	−	1.30763i
$71$	12.8101	+	3.43246i	1.52028	+	0.407358i	0.919834	−	0.392307i	$-0.128323\pi$
$71$	12.8101	+	3.43246i	1.52028	+	0.407358i	0.600446	+	0.799665i	$0.294990\pi$
$72$		0			0
$73$	4.73040	+	1.26751i	0.553652	+	0.148351i	0.524788	−	0.851233i	$-0.324145\pi$
$73$	4.73040	+	1.26751i	0.553652	+	0.148351i	0.0288635	+	0.999583i	$0.490811\pi$
$74$	11.6541	−	20.1856i	1.35477	−	2.34653i
$75$		0			0
$76$	3.39417	+	12.6672i	0.389338	+	1.45303i
$77$	2.13887	+	8.88845i	0.243746	+	1.01293i
$78$		0			0
$79$	−4.45795	+	7.72140i	−0.501559	+	0.868725i	0.498440	+	0.866924i	$0.333907\pi$
$79$	−4.45795	+	7.72140i	−0.501559	+	0.868725i	−0.999998	+	0.00180087i	$0.999427\pi$
$80$	3.14587	+	3.14587i	0.351719	+	0.351719i
$81$		0			0
$82$	4.75082			0.524641
$83$	−0.573646	−	0.573646i	−0.0629659	−	0.0629659i	0.674923	−	0.737889i	$-0.264177\pi$
$83$	−0.573646	−	0.573646i	−0.0629659	−	0.0629659i	−0.737889	+	0.674923i	$0.764177\pi$
$84$		0			0
$85$	2.33184	−	8.70254i	0.252923	−	0.943923i
$86$	8.02106	−	2.14924i	0.864933	−	0.231758i
$87$		0			0
$88$			7.19408i			0.766891i
$89$	8.03851	+	2.15391i	0.852081	+	0.228314i	0.658323	−	0.752735i	$-0.271266\pi$
$89$	8.03851	+	2.15391i	0.852081	+	0.228314i	0.193757	+	0.981050i	$0.437933\pi$
$90$		0			0
$91$	−6.40150	+	7.07254i	−0.671060	+	0.741403i
$92$	−8.96637			−0.934809
$93$		0			0
$94$		−	15.0700i		−	1.55436i
$95$	−13.7849	−	7.95872i	−1.41430	−	0.816547i
$96$		0			0
$97$	4.06679	−	15.1775i	0.412920	−	1.54104i	−0.376045	−	0.926602i	$-0.622716\pi$
$97$	4.06679	−	15.1775i	0.412920	−	1.54104i	0.788965	−	0.614438i	$-0.210617\pi$
$98$	3.24975	+	15.2103i	0.328274	+	1.53647i
$99$		0			0
$100$	22.6388			2.26388
$101$	−2.94757			−0.293294			−0.146647	−	0.989189i	$-0.546848\pi$
$101$	−2.94757			−0.293294			−0.146647	+	0.989189i	$0.546848\pi$
$102$		0			0
$103$	7.76476	−	13.4490i	0.765085	−	1.32517i	−0.175117	−	0.984548i	$-0.556030\pi$
$103$	7.76476	−	13.4490i	0.765085	−	1.32517i	0.940202	−	0.340618i	$-0.110636\pi$
$104$	−6.19968	+	4.23247i	−0.607929	+	0.415028i
$105$		0			0
$106$	2.92593	+	10.9197i	0.284191	+	1.06062i
$107$	−2.00547	−	3.47358i	−0.193877	−	0.335804i	0.752655	−	0.658415i	$-0.228773\pi$
$107$	−2.00547	−	3.47358i	−0.193877	−	0.335804i	−0.946532	+	0.322611i	$0.895439\pi$
$108$		0			0
$109$	3.62714	+	0.971889i	0.347417	+	0.0930901i	0.428308	−	0.903633i	$-0.359110\pi$
$109$	3.62714	+	0.971889i	0.347417	+	0.0930901i	−0.0808909	+	0.996723i	$0.525777\pi$
$110$	−19.3534	−	19.3534i	−1.84528	−	1.84528i
$111$		0			0
$112$	0.0846998	−	3.30082i	0.00800338	−	0.311898i
$113$	4.05082	+	7.01622i	0.381069	+	0.660031i	0.991215	−	0.132258i	$-0.0422227\pi$
$113$	4.05082	+	7.01622i	0.381069	+	0.660031i	−0.610146	+	0.792289i	$0.708889\pi$
$114$		0			0
$115$	7.69551	−	7.69551i	0.717610	−	0.717610i
$116$	5.74660	−	3.31780i	0.533558	−	0.308050i
$117$		0			0
$118$		−	18.8923i		−	1.73918i
$119$	−5.87470	+	3.19370i	−0.538533	+	0.292766i
$120$		0			0
$121$			0.939896i			0.0854451i
$122$	7.52995	−	28.1022i	0.681730	−	2.54425i
$123$		0			0
$124$	−12.3762	+	12.3762i	−1.11141	+	1.11141i
$125$	−6.82639	+	6.82639i	−0.610571	+	0.610571i
$126$		0			0
$127$	−9.30669	−	5.37322i	−0.825835	−	0.476796i	0.0265893	−	0.999646i	$-0.491535\pi$
$127$	−9.30669	−	5.37322i	−0.825835	−	0.476796i	−0.852425	+	0.522850i	$0.824869\pi$
$128$	3.83773	−	14.3226i	0.339210	−	1.26595i
$129$		0			0
$130$	5.29218	−	28.0644i	0.464155	−	2.46141i
$131$	14.4464	+	8.34065i	1.26219	+	0.728726i	0.973498	−	0.228696i	$-0.0734463\pi$
$131$	14.4464	+	8.34065i	1.26219	+	0.728726i	0.288692	+	0.957422i	$0.406780\pi$
$132$		0			0
$133$	2.76386	+	11.4857i	0.239657	+	0.995938i
$134$	−17.7465	+	10.2459i	−1.53306	+	0.885114i
$135$		0			0
$136$	−5.08254	+	1.36186i	−0.435824	+	0.116779i
$137$	13.0012	−	3.48367i	1.11077	−	0.297630i	0.343627	−	0.939106i	$-0.388344\pi$
$137$	13.0012	−	3.48367i	1.11077	−	0.297630i	0.767143	+	0.641476i	$0.221678\pi$
$138$		0			0
$139$	−13.5614	+	7.82969i	−1.15026	+	0.664106i	−0.948952	−	0.315421i	$-0.897854\pi$
$139$	−13.5614	+	7.82969i	−1.15026	+	0.664106i	−0.201313	+	0.979527i	$0.564521\pi$
$140$	−19.0786	−	20.0835i	−1.61244	−	1.69737i
$141$		0			0
$142$	25.5195	+	14.7337i	2.14155	+	1.23642i
$143$	−10.2895	+	7.02456i	−0.860453	+	0.587423i
$144$		0			0
$145$	−2.08455	+	7.77964i	−0.173112	+	0.646064i
$146$	9.42360	+	5.44072i	0.779903	+	0.450277i
$147$		0			0
$148$	21.7856	−	21.7856i	1.79076	−	1.79076i
$149$	−6.27597	+	6.27597i	−0.514148	+	0.514148i	−0.915795	−	0.401647i	$-0.868438\pi$
$149$	−6.27597	+	6.27597i	−0.514148	+	0.514148i	0.401647	+	0.915795i	$0.368438\pi$
$150$		0			0
$151$	−4.29176	+	16.0171i	−0.349259	+	1.30345i	0.538299	+	0.842754i	$0.319067\pi$
$151$	−4.29176	+	16.0171i	−0.349259	+	1.30345i	−0.887558	+	0.460697i	$0.847600\pi$
$152$			9.29624i			0.754025i
$153$		0			0
$154$	−0.521074	+	20.3066i	−0.0419893	+	1.63636i
$155$		−	21.2440i		−	1.70636i
$156$		0			0
$157$	−14.4182	+	8.32436i	−1.15070	+	0.664356i	−0.949058	−	0.315103i	$-0.897961\pi$
$157$	−14.4182	+	8.32436i	−1.15070	+	0.664356i	−0.201642	+	0.979459i	$0.564628\pi$
$158$	−14.0082	+	14.0082i	−1.11443	+	1.11443i
$159$		0			0
$160$	12.3645	+	21.4160i	0.977502	+	1.69308i
$161$	−8.07454	−	0.207195i	−0.636363	−	0.0163292i
$162$		0			0
$163$	−1.81122	−	1.81122i	−0.141866	−	0.141866i	0.632607	−	0.774473i	$-0.281985\pi$
$163$	−1.81122	−	1.81122i	−0.141866	−	0.141866i	−0.774473	+	0.632607i	$0.781985\pi$
$164$	6.06577	+	1.62532i	0.473657	+	0.126916i
$165$		0			0
$166$	−0.901283	−	1.56107i	−0.0699531	−	0.121162i
$167$	0.167384	+	0.624684i	0.0129525	+	0.0483395i	0.972100	−	0.234568i	$-0.0753676\pi$
$167$	0.167384	+	0.624684i	0.0129525	+	0.0483395i	−0.959147	+	0.282908i	$0.908701\pi$
$168$		0			0
$169$	−12.1072	−	4.73453i	−0.931323	−	0.364194i
$170$	10.0093	−	17.3366i	0.767679	−	1.32966i
$171$		0			0
$172$	10.9764			0.836945
$173$	0.904451			0.0687641			0.0343821	−	0.999409i	$-0.489054\pi$
$173$	0.904451			0.0687641			0.0343821	+	0.999409i	$0.489054\pi$
$174$		0			0
$175$	20.3870	+	0.523136i	1.54111	+	0.0395454i
$176$	1.11612	−	4.16543i	0.0841310	−	0.313981i
$177$		0			0
$178$	16.0138	+	9.24557i	1.20029	+	0.692985i
$179$			21.2755i			1.59021i	0.606474	+	0.795103i	$0.292584\pi$
$179$			21.2755i			1.59021i	−0.606474	+	0.795103i	$0.707416\pi$
$180$		0			0
$181$	−19.9161			−1.48035			−0.740176	−	0.672413i	$-0.765258\pi$
$181$	−19.9161			−1.48035			−0.740176	+	0.672413i	$0.765258\pi$
$182$	−17.8063	+	11.4979i	−1.31989	+	0.852281i
$183$		0			0
$184$	−6.13946	−	1.64506i	−0.452607	−	0.121276i
$185$			37.3955i			2.74937i
$186$		0			0
$187$	−8.43540	+	2.26026i	−0.616858	+	0.165287i
$188$	5.15566	−	19.2412i	0.376015	−	1.40331i
$189$		0			0
$190$	−25.0086	−	25.0086i	−1.81432	−	1.81432i
$191$	9.12189			0.660037			0.330018	−	0.943974i	$-0.392945\pi$
$191$	9.12189			0.660037			0.330018	+	0.943974i	$0.392945\pi$
$192$		0			0
$193$	11.2754	+	11.2754i	0.811619	+	0.811619i	0.984877	−	0.173257i	$-0.0554292\pi$
$193$	11.2754	+	11.2754i	0.811619	+	0.811619i	−0.173257	+	0.984877i	$0.555429\pi$
$194$	17.4565	−	30.2356i	1.25331	−	2.17079i
$195$		0			0
$196$	−1.05441	+	20.5320i	−0.0753147	+	1.46657i
$197$	−6.25761	−	23.3537i	−0.445836	−	1.66388i	−0.713719	−	0.700432i	$-0.752991\pi$
$197$	−6.25761	−	23.3537i	−0.445836	−	1.66388i	0.267883	−	0.963451i	$-0.413676\pi$
$198$		0			0
$199$	5.79667	−	10.0401i	0.410915	−	0.711726i	−0.584075	−	0.811700i	$-0.698543\pi$
$199$	5.79667	−	10.0401i	0.410915	−	0.711726i	0.994990	+	0.0999741i	$0.0318760\pi$
$200$	15.5012	+	4.15354i	1.09610	+	0.293700i
$201$		0			0
$202$	−6.32615	−	1.69509i	−0.445106	−	0.119266i
$203$	5.25169	−	2.85501i	0.368596	−	0.200382i
$204$		0			0
$205$	−6.60097	+	3.81107i	−0.461032	+	0.266177i
$206$	24.3992	−	24.3992i	1.69997	−	1.69997i
$207$		0			0
$208$	4.24631	−	1.48879i	0.294429	−	0.103229i
$209$			15.4288i			1.06723i
$210$		0			0
$211$	0.178987	−	0.310015i	0.0123220	−	0.0213423i	−0.859799	−	0.510633i	$-0.829411\pi$
$211$	0.178987	−	0.310015i	0.0123220	−	0.0213423i	0.872121	+	0.489291i	$0.162744\pi$
$212$			14.9431i			1.02630i
$213$		0			0
$214$	−2.30662	−	8.60841i	−0.157677	−	0.588459i
$215$	−9.42067	+	9.42067i	−0.642484	+	0.642484i
$216$		0			0
$217$	−11.4312	+	10.8592i	−0.775998	+	0.737169i
$218$	7.22575	+	4.17179i	0.489390	+	0.282549i
$219$		0			0
$220$	−18.0890	−	31.3312i	−1.21956	−	2.11235i
$221$	−6.91061	−	5.93966i	−0.464858	−	0.399545i
$222$		0			0
$223$	5.47574	−	1.46722i	0.366683	−	0.0982523i	−0.0707726	−	0.997492i	$-0.522546\pi$
$223$	5.47574	−	1.46722i	0.366683	−	0.0982523i	0.437455	+	0.899240i	$0.355880\pi$
$224$	5.20340	−	17.6003i	0.347667	−	1.17597i
$225$		0			0
$226$	4.65909	+	17.3880i	0.309918	+	1.15663i
$227$	−10.3200	+	2.76523i	−0.684961	+	0.183535i	−0.584485	−	0.811405i	$-0.698703\pi$
$227$	−10.3200	+	2.76523i	−0.684961	+	0.183535i	−0.100476	+	0.994939i	$0.532037\pi$
$228$		0			0
$229$	−7.29728	−	27.2338i	−0.482218	−	1.79966i	−0.592275	−	0.805736i	$-0.701770\pi$
$229$	−7.29728	−	27.2338i	−0.482218	−	1.79966i	0.110058	−	0.993925i	$-0.464896\pi$
$230$	20.9418	−	12.0908i	1.38086	−	0.797242i
$231$		0			0
$232$	4.54354	−	1.21744i	0.298298	−	0.0799286i
$233$	−1.17324	−	0.677369i	−0.0768614	−	0.0443759i	0.461077	−	0.887360i	$-0.347463\pi$
$233$	−1.17324	−	0.677369i	−0.0768614	−	0.0443759i	−0.537938	+	0.842984i	$0.680797\pi$
$234$		0			0
$235$	12.0891	+	20.9389i	0.788604	+	1.36590i
$236$	6.46330	−	24.1213i	0.420725	−	1.57017i
$237$		0			0
$238$	−14.4451	+	3.47598i	−0.936334	+	0.225314i
$239$	−7.36460	+	7.36460i	−0.476376	+	0.476376i	−0.903971	−	0.427594i	$-0.859361\pi$
$239$	−7.36460	+	7.36460i	−0.476376	+	0.476376i	0.427594	+	0.903971i	$0.359361\pi$
$240$		0			0
$241$	1.34404	+	5.01601i	0.0865770	+	0.323110i	0.995608	−	0.0936184i	$-0.0298434\pi$
$241$	1.34404	+	5.01601i	0.0865770	+	0.323110i	−0.909031	+	0.416728i	$0.863177\pi$
$242$	−0.540515	+	2.01723i	−0.0347456	+	0.129672i
$243$		0			0
$244$	19.2282	−	33.3043i	1.23096	−	2.13209i
$245$	−16.7169	−	18.5268i	−1.06800	−	1.18363i
$246$		0			0
$247$	−13.2962	+	9.07719i	−0.846017	+	0.577568i
$248$	−10.7449	+	6.20355i	−0.682300	+	0.393926i
$249$		0			0
$250$	−18.5767	+	10.7253i	−1.17489	+	0.678326i
$251$	4.58523	+	7.94186i	0.289417	+	0.501285i	0.973671	−	0.227959i	$-0.0732051\pi$
$251$	4.58523	+	7.94186i	0.289417	+	0.501285i	−0.684253	+	0.729244i	$0.739872\pi$
$252$		0			0
$253$	−10.1896	−	2.73029i	−0.640613	−	0.171652i
$254$	−16.8842	−	16.8842i	−1.05941	−	1.05941i
$255$		0			0
$256$	3.55585	−	6.15891i	0.222241	−	0.384932i
$257$	−1.89888	−	3.28895i	−0.118449	−	0.205159i	0.800704	−	0.599060i	$-0.204459\pi$
$257$	−1.89888	−	3.28895i	−0.118449	−	0.205159i	−0.919153	+	0.393901i	$0.871125\pi$
$258$		0			0
$259$	20.1221	−	19.1153i	1.25033	−	1.18776i
$260$	16.3582	−	34.0217i	1.01449	−	2.10993i
$261$		0			0
$262$	26.2088	+	26.2088i	1.61918	+	1.61918i
$263$	21.6207			1.33319			0.666594	−	0.745421i	$-0.267751\pi$
$263$	21.6207			1.33319			0.666594	+	0.745421i	$0.267751\pi$
$264$		0			0
$265$	−12.8251	−	12.8251i	−0.787840	−	0.787840i
$266$	−0.673335	+	26.2404i	−0.0412848	+	1.60890i
$267$		0			0
$268$	−26.1637	+	7.01053i	−1.59820	+	0.428236i
$269$	14.7786	+	8.53242i	0.901066	+	0.520231i	0.877546	−	0.479493i	$-0.159179\pi$
$269$	14.7786	+	8.53242i	0.901066	+	0.520231i	0.0235200	+	0.999723i	$0.492513\pi$
$270$		0			0
$271$	−9.29983	−	2.49188i	−0.564925	−	0.151371i	−0.0349568	−	0.999389i	$-0.511129\pi$
$271$	−9.29983	−	2.49188i	−0.564925	−	0.151371i	−0.529968	+	0.848018i	$0.677796\pi$
$272$	3.15412			0.191246
$273$		0			0
$274$	29.9070			1.80675
$275$	25.7272	+	6.89357i	1.55141	+	0.415698i
$276$		0			0
$277$	−6.00440	−	3.46664i	−0.360769	−	0.208290i	0.308649	−	0.951176i	$-0.400123\pi$
$277$	−6.00440	−	3.46664i	−0.360769	−	0.208290i	−0.669418	+	0.742886i	$0.733457\pi$
$278$	−33.6086	+	9.00539i	−2.01571	+	0.540108i
$279$		0			0
$280$	−9.37880	−	17.2520i	−0.560490	−	1.03100i
$281$	−15.5652	−	15.5652i	−0.928544	−	0.928544i	0.0690682	−	0.997612i	$-0.477997\pi$
$281$	−15.5652	−	15.5652i	−0.928544	−	0.928544i	−0.997612	+	0.0690682i	$0.977997\pi$
$282$		0			0
$283$	24.1017			1.43270			0.716349	−	0.697742i	$-0.245812\pi$
$283$	24.1017			1.43270			0.716349	+	0.697742i	$0.245812\pi$
$284$	27.5422	+	27.5422i	1.63433	+	1.63433i
$285$		0			0
$286$	−26.1233	+	9.15901i	−1.54470	+	0.541583i
$287$	5.42488	+	1.60382i	0.320221	+	0.0946708i
$288$		0			0
$289$	5.30630	+	9.19079i	0.312135	+	0.540635i
$290$	−8.94783	+	15.4981i	−0.525435	+	0.910080i
$291$		0			0
$292$	10.1705	+	10.1705i	0.595186	+	0.595186i
$293$	−12.3864	−	3.31893i	−0.723622	−	0.193894i	−0.121835	−	0.992550i	$-0.538878\pi$
$293$	−12.3864	−	3.31893i	−0.723622	−	0.193894i	−0.601787	+	0.798656i	$0.705545\pi$
$294$		0			0
$295$	15.1553	+	26.2497i	0.882373	+	1.52831i
$296$	18.9140	−	10.9200i	1.09936	−	0.634713i
$297$		0			0
$298$	−17.0788	+	9.86048i	−0.989351	+	0.571202i
$299$	−3.64190	−	10.3874i	−0.210617	−	0.600721i
$300$		0			0
$301$	9.88467	+	0.253643i	0.569743	+	0.0146197i
$302$	−18.4222	+	31.9082i	−1.06008	+	1.83611i
$303$		0			0
$304$	1.44226	−	5.38260i	0.0827195	−	0.308713i
$305$	12.0809	+	45.0867i	0.691753	+	2.58166i
$306$		0			0
$307$	15.4570	−	15.4570i	0.882178	−	0.882178i	−0.111577	−	0.993756i	$-0.535590\pi$
$307$	15.4570	−	15.4570i	0.882178	−	0.882178i	0.993756	+	0.111577i	$0.0355903\pi$
$308$	−7.61246	+	25.7489i	−0.433760	+	1.46718i
$309$		0			0
$310$	12.2170	−	45.5944i	0.693878	−	2.58959i
$311$	−1.62070	−	2.80714i	−0.0919017	−	0.159178i	0.816410	−	0.577473i	$-0.195961\pi$
$311$	−1.62070	−	2.80714i	−0.0919017	−	0.159178i	−0.908311	+	0.418295i	$0.862628\pi$
$312$		0			0
$313$	24.9122	+	14.3831i	1.40812	+	0.812978i	0.995207	−	0.0977925i	$-0.0311781\pi$
$313$	24.9122	+	14.3831i	1.40812	+	0.812978i	0.412913	+	0.910771i	$0.364511\pi$
$314$	−35.7319	+	9.57435i	−2.01647	+	0.540312i
$315$		0			0
$316$	−22.6778	+	13.0930i	−1.27573	+	0.736541i
$317$	0.144647	+	0.539831i	0.00812420	+	0.0303199i	0.969869	−	0.243627i	$-0.0783373\pi$
$317$	0.144647	+	0.539831i	0.00812420	+	0.0303199i	−0.961745	+	0.273947i	$0.911671\pi$
$318$		0			0
$319$	7.54083	−	2.02056i	0.422206	−	0.113130i
$320$	11.9182	+	44.4795i	0.666250	+	2.48648i
$321$		0			0
$322$	−17.2106	−	5.08819i	−0.959112	−	0.283554i
$323$	−10.9003	+	2.92073i	−0.606509	+	0.162513i
$324$		0			0
$325$	9.19526	+	26.2267i	0.510061	+	1.45480i
$326$	−2.84570	−	4.92890i	−0.157609	−	0.272986i
$327$		0			0
$328$	3.85516	+	2.22578i	0.212866	+	0.122898i
$329$	5.08748	−	17.2082i	0.280482	−	0.948720i
$330$		0			0
$331$	−0.504043	+	0.504043i	−0.0277047	+	0.0277047i	−0.720823	−	0.693119i	$-0.756236\pi$
$331$	−0.504043	+	0.504043i	−0.0277047	+	0.0277047i	0.693119	+	0.720823i	$0.256236\pi$
$332$	−0.616681	−	2.30148i	−0.0338448	−	0.126310i
$333$		0			0
$334$			1.43697i			0.0786277i
$335$	16.4384	−	28.4722i	0.898127	−	1.55560i
$336$		0			0
$337$			1.28970i			0.0702542i	0.999383	+	0.0351271i	$0.0111836\pi$
$337$			1.28970i			0.0702542i	−0.999383	+	0.0351271i	$0.988816\pi$
$338$	−23.2621	−	17.1240i	−1.26529	−	0.931421i
$339$		0			0
$340$	18.7108	−	18.7108i	1.01474	−	1.01474i
$341$	−17.8331	+	10.2959i	−0.965716	+	0.557556i
$342$		0			0
$343$	−1.42398	+	18.4654i	−0.0768879	+	0.997040i
$344$	7.51579	+	2.01385i	0.405224	+	0.108580i
$345$		0			0
$346$	1.94116	+	0.520131i	0.104357	+	0.0279624i
$347$	7.23774	−	12.5361i	0.388542	−	0.672975i	−0.603711	−	0.797203i	$-0.706312\pi$
$347$	7.23774	−	12.5361i	0.388542	−	0.672975i	0.992254	+	0.124228i	$0.0396453\pi$
$348$		0			0
$349$	1.55296	+	5.79571i	0.0831278	+	0.310237i	0.994953	−	0.100341i	$-0.0319934\pi$
$349$	1.55296	+	5.79571i	0.0831278	+	0.310237i	−0.911825	+	0.410578i	$0.865327\pi$
$350$	43.4543	+	12.8469i	2.32273	+	0.686698i
$351$		0			0
$352$	11.9850	−	20.7586i	0.638802	−	1.10644i
$353$	12.4611	+	12.4611i	0.663240	+	0.663240i	0.956142	−	0.292902i	$-0.0946211\pi$
$353$	12.4611	+	12.4611i	0.663240	+	0.663240i	−0.292902	+	0.956142i	$0.594621\pi$
$354$		0			0
$355$	−47.2770			−2.50920
$356$	17.2831	+	17.2831i	0.916003	+	0.916003i
$357$		0			0
$358$	−12.2351	+	45.6621i	−0.646646	+	2.41332i
$359$	6.88215	−	1.84407i	0.363226	−	0.0973262i	−0.0725899	−	0.997362i	$-0.523126\pi$
$359$	6.88215	−	1.84407i	0.363226	−	0.0973262i	0.435816	+	0.900036i	$0.356460\pi$
$360$		0			0
$361$			0.937248i			0.0493288i
$362$	−42.7445	−	11.4533i	−2.24660	−	0.601974i
$363$		0			0
$364$	−26.6684	+	8.58853i	−1.39780	+	0.450161i
$365$	−17.4580			−0.913794
$366$		0			0
$367$		−	2.38011i		−	0.124241i	−0.998069	−	0.0621203i	$-0.980214\pi$
$367$		−	2.38011i		−	0.124241i	0.998069	−	0.0621203i	$-0.0197862\pi$
$368$	3.29958	+	1.90501i	0.172002	+	0.0993056i
$369$		0			0
$370$	−21.5054	+	80.2592i	−1.11801	+	4.17248i
$371$	−0.345305	+	13.4568i	−0.0179273	+	0.698642i
$372$		0			0
$373$	0.909346			0.0470841			0.0235421	−	0.999723i	$-0.492506\pi$
$373$	0.909346			0.0470841			0.0235421	+	0.999723i	$0.492506\pi$
$374$	−19.4041			−1.00336
$375$		0			0
$376$	7.06037	−	12.2289i	0.364111	−	0.630658i
$377$	6.17775	+	5.30976i	0.318170	+	0.273467i
$378$		0			0
$379$	−7.19570	−	26.8547i	−0.369618	−	1.37943i	−0.861051	−	0.508519i	$-0.830193\pi$
$379$	−7.19570	−	26.8547i	−0.369618	−	1.37943i	0.491432	−	0.870916i	$-0.336474\pi$
$380$	−23.3748	−	40.4864i	−1.19910	−	2.07691i
$381$		0			0
$382$	19.5776	+	5.24581i	1.00168	+	0.268399i
$383$	−8.57505	−	8.57505i	−0.438165	−	0.438165i	0.453229	−	0.891394i	$-0.350272\pi$
$383$	−8.57505	−	8.57505i	−0.438165	−	0.438165i	−0.891394	+	0.453229i	$0.850272\pi$
$384$		0			0
$385$	−15.5658	−	28.6328i	−0.793309	−	1.45926i
$386$	17.7153	+	30.6838i	0.901684	+	1.56176i
$387$		0			0
$388$	32.6322	−	32.6322i	1.65665	−	1.65665i
$389$	−25.6348	+	14.8003i	−1.29974	+	0.750403i	−0.980358	−	0.197225i	$-0.936807\pi$
$389$	−25.6348	+	14.8003i	−1.29974	+	0.750403i	−0.319377	+	0.947628i	$0.603474\pi$
$390$		0			0
$391$		−	7.71567i		−	0.390198i
$392$	−4.48899	+	13.8652i	−0.226728	+	0.700300i
$393$		0			0
$394$		−	53.7210i		−	2.70642i
$395$	8.22625	−	30.7008i	0.413908	−	1.54472i
$396$		0			0
$397$	2.67697	−	2.67697i	0.134353	−	0.134353i	−0.636732	−	0.771085i	$-0.719714\pi$
$397$	2.67697	−	2.67697i	0.134353	−	0.134353i	0.771085	+	0.636732i	$0.219714\pi$
$398$	18.2148	−	18.2148i	0.913027	−	0.913027i
$399$		0			0
$400$	−8.33094	−	4.80987i	−0.416547	−	0.240494i
$401$	0.682164	−	2.54587i	0.0340656	−	0.127135i	−0.946799	−	0.321825i	$-0.895704\pi$
$401$	0.682164	−	2.54587i	0.0340656	−	0.127135i	0.980865	+	0.194691i	$0.0623703\pi$
$402$		0			0
$403$	−19.3645	−	9.31076i	−0.964613	−	0.463802i
$404$	−7.49721	−	4.32851i	−0.373000	−	0.215352i
$405$		0			0
$406$	12.9132	−	3.10735i	0.640870	−	0.154215i
$407$	31.3913	−	18.1238i	1.55601	−	0.898363i
$408$		0			0
$409$	−15.3494	+	4.11286i	−0.758978	+	0.203368i	−0.617497	−	0.786573i	$-0.711853\pi$
$409$	−15.3494	+	4.11286i	−0.758978	+	0.203368i	−0.141481	+	0.989941i	$0.545187\pi$
$410$	−16.3589	+	4.38334i	−0.807906	+	0.216478i
$411$		0			0
$412$	39.4997	−	22.8052i	1.94601	−	1.12353i
$413$	6.37783	−	21.5728i	0.313832	−	1.06153i
$414$		0			0
$415$	2.50455	+	1.44600i	0.122944	+	0.0709816i
$416$	24.9404	−	1.88447i	1.22280	−	0.0923936i
$417$		0			0
$418$	−8.87281	+	33.1138i	−0.433983	+	1.61965i
$419$	−34.6920	−	20.0294i	−1.69481	−	0.978501i	−0.950528	−	0.310640i	$-0.899457\pi$
$419$	−34.6920	−	20.0294i	−1.69481	−	0.978501i	−0.744286	−	0.667861i	$-0.767210\pi$
$420$		0			0
$421$	5.73237	−	5.73237i	0.279379	−	0.279379i	−0.553482	−	0.832861i	$-0.686701\pi$
$421$	5.73237	−	5.73237i	0.279379	−	0.279379i	0.832861	+	0.553482i	$0.186701\pi$
$422$	0.562430	−	0.562430i	0.0273787	−	0.0273787i
$423$		0			0
$424$	−2.74162	+	10.2319i	−0.133145	+	0.496903i
$425$			19.4809i			0.944964i
$426$		0			0
$427$	18.0853	−	29.5474i	0.875209	−	1.42990i
$428$		−	11.7802i		−	0.569417i
$429$		0			0
$430$	−25.6365	+	14.8013i	−1.23630	+	0.713780i
$431$	6.52548	−	6.52548i	0.314321	−	0.314321i	−0.532260	−	0.846581i	$-0.678657\pi$
$431$	6.52548	−	6.52548i	0.314321	−	0.314321i	0.846581	+	0.532260i	$0.178657\pi$
$432$		0			0
$433$	5.04205	+	8.73309i	0.242306	+	0.419686i	0.961371	−	0.275257i	$-0.0887630\pi$
$433$	5.04205	+	8.73309i	0.242306	+	0.419686i	−0.719065	+	0.694943i	$0.755430\pi$
$434$	−30.7788	+	16.7324i	−1.47743	+	0.803183i
$435$		0			0
$436$	7.79849	+	7.79849i	0.373480	+	0.373480i
$437$	−13.1670	−	3.52810i	−0.629865	−	0.168772i
$438$		0			0
$439$	2.19526	+	3.80230i	0.104774	+	0.181474i	0.913646	−	0.406511i	$-0.133255\pi$
$439$	2.19526	+	3.80230i	0.104774	+	0.181474i	−0.808872	+	0.587985i	$0.799921\pi$
$440$	−6.63761	−	24.7719i	−0.316436	−	1.18095i
$441$		0			0
$442$	−11.4160	−	16.7220i	−0.543002	−	0.795385i
$443$	−5.48205	+	9.49519i	−0.260460	+	0.451130i	−0.966364	−	0.257177i	$-0.917208\pi$
$443$	−5.48205	+	9.49519i	−0.260460	+	0.451130i	0.705904	+	0.708307i	$0.250541\pi$
$444$		0			0
$445$	−29.6669			−1.40635
$446$	12.5960			0.596436
$447$		0			0
$448$	17.8417	−	29.1494i	0.842943	−	1.37718i
$449$	5.37942	−	20.0763i	0.253871	−	0.947459i	−0.714844	−	0.699283i	$-0.753503\pi$
$449$	5.37942	−	20.0763i	0.253871	−	0.947459i	0.968715	−	0.248175i	$-0.0798308\pi$
$450$		0			0
$451$	6.39835	+	3.69409i	0.301286	+	0.173948i
$452$			23.7946i			1.11920i
$453$		0			0
$454$	−23.7392			−1.11414
$455$	15.5173	−	30.2597i	0.727462	−	1.41860i
$456$		0			0
$457$	−37.5976	−	10.0743i	−1.75874	−	0.471254i	−0.772286	−	0.635275i	$-0.780887\pi$
$457$	−37.5976	−	10.0743i	−1.75874	−	0.471254i	−0.986457	+	0.164021i	$0.947553\pi$
$458$		−	62.6465i		−	2.92728i
$459$		0			0
$460$	30.8746	−	8.27282i	1.43953	−	0.385722i
$461$	−3.90240	+	14.5639i	−0.181753	+	0.678311i	0.813550	+	0.581496i	$0.197532\pi$
$461$	−3.90240	+	14.5639i	−0.181753	+	0.678311i	−0.995302	+	0.0968151i	$0.969134\pi$
$462$		0			0
$463$	4.92292	+	4.92292i	0.228787	+	0.228787i	0.812186	−	0.583399i	$-0.198277\pi$
$463$	4.92292	+	4.92292i	0.228787	+	0.228787i	−0.583399	+	0.812186i	$0.698277\pi$
$464$	−2.81962			−0.130898
$465$		0			0
$466$	−2.12849	−	2.12849i	−0.0986006	−	0.0986006i
$467$	−8.08617	+	14.0057i	−0.374183	+	0.648105i	−0.990204	−	0.139625i	$-0.955410\pi$
$467$	−8.08617	+	14.0057i	−0.374183	+	0.648105i	0.616021	+	0.787730i	$0.288744\pi$
$468$		0			0
$469$	−23.7233	+	5.70865i	−1.09544	+	0.263601i
$470$	13.9044	+	51.8918i	0.641361	+	2.39359i
$471$		0			0
$472$	8.85111	−	15.3306i	0.407405	−	0.705646i
$473$	12.4738	+	3.34236i	0.573548	+	0.153682i
$474$		0			0
$475$	33.2448	+	8.90793i	1.52538	+	0.408724i
$476$	−19.6324	−	0.503772i	−0.899849	−	0.0230903i
$477$		0			0
$478$	−20.0413	+	11.5709i	−0.916669	+	0.529239i
$479$	20.7958	−	20.7958i	0.950184	−	0.950184i	−0.0486324	−	0.998817i	$-0.515486\pi$
$479$	20.7958	−	20.7958i	0.950184	−	0.950184i	0.998817	+	0.0486324i	$0.0154863\pi$
$480$		0			0
$481$	34.0870	+	16.3896i	1.55423	+	0.747301i
$482$			11.5384i			0.525561i
$483$		0			0
$484$	−1.38024	+	2.39065i	−0.0627382	+	0.108666i
$485$			56.0140i			2.54346i
$486$		0			0
$487$	4.64339	+	17.3294i	0.210412	+	0.785268i	0.987731	+	0.156162i	$0.0499122\pi$
$487$	4.64339	+	17.3294i	0.210412	+	0.785268i	−0.777319	+	0.629106i	$0.783421\pi$
$488$	19.2763	−	19.2763i	0.872598	−	0.872598i
$489$		0			0
$490$	−25.2239	−	49.3763i	−1.13950	−	2.23059i
$491$	1.73849	+	1.00372i	0.0784569	+	0.0452971i	0.538715	−	0.842488i	$-0.318910\pi$
$491$	1.73849	+	1.00372i	0.0784569	+	0.0452971i	−0.460258	+	0.887785i	$0.652243\pi$
$492$		0			0
$493$	2.85501	+	4.94502i	0.128583	+	0.222712i
$494$	−33.7568	+	11.8353i	−1.51879	+	0.532497i
$495$		0			0
$496$	7.18382	−	1.92490i	0.322563	−	0.0864305i
$497$	24.1663	+	25.4392i	1.08401	+	1.14111i
$498$		0			0
$499$	4.41437	+	16.4747i	0.197615	+	0.737507i	0.991575	+	0.129537i	$0.0413492\pi$
$499$	4.41437	+	16.4747i	0.197615	+	0.737507i	−0.793960	+	0.607970i	$0.791984\pi$
$500$	−27.3877	+	7.33850i	−1.22481	+	0.328188i
$501$		0			0
$502$	5.27375	+	19.6819i	0.235379	+	0.878446i
$503$	−13.6715	+	7.89323i	−0.609581	+	0.351942i	−0.772801	−	0.634648i	$-0.781145\pi$
$503$	−13.6715	+	7.89323i	−0.609581	+	0.351942i	0.163221	+	0.986590i	$0.447812\pi$
$504$		0			0
$505$	10.1496	−	2.71957i	0.451650	−	0.121019i
$506$	−20.2990	−	11.7196i	−0.902401	−	0.521001i
$507$		0			0
$508$	−15.7812	−	27.3338i	−0.700177	−	1.21274i
$509$	4.05672	−	15.1399i	0.179811	−	0.671064i	−0.815871	−	0.578234i	$-0.803742\pi$
$509$	4.05672	−	15.1399i	0.179811	−	0.671064i	0.995682	−	0.0928301i	$-0.0295914\pi$
$510$		0			0
$511$	8.92392	+	9.39397i	0.394771	+	0.415565i
$512$	−9.79620	+	9.79620i	−0.432935	+	0.432935i
$513$		0			0
$514$	−2.18401	−	8.15084i	−0.0963326	−	0.359518i
$515$	−14.3283	+	53.4740i	−0.631380	+	2.35634i
$516$		0			0
$517$	11.7180	−	20.2961i	0.515356	−	0.892624i
$518$	54.1794	−	29.4539i	2.38051	−	1.29413i
$519$		0			0
$520$	17.4427	−	20.2941i	0.764915	−	0.889955i
$521$	−14.0981	+	8.13957i	−0.617651	+	0.356601i	−0.775954	−	0.630790i	$-0.782731\pi$
$521$	−14.0981	+	8.13957i	−0.617651	+	0.356601i	0.158303	+	0.987391i	$0.449398\pi$
$522$		0			0
$523$	−14.9531	+	8.63317i	−0.653853	+	0.377502i	−0.789931	−	0.613196i	$-0.789884\pi$
$523$	−14.9531	+	8.63317i	−0.653853	+	0.377502i	0.136078	+	0.990698i	$0.456550\pi$
$524$	24.4965	+	42.4293i	1.07014	+	1.85353i
$525$		0			0
$526$	46.4029	+	12.4336i	2.02326	+	0.542132i
$527$	−10.6498	−	10.6498i	−0.463914	−	0.463914i
$528$		0			0
$529$	−6.83992	+	11.8471i	−0.297388	+	0.515090i
$530$	−20.1501	−	34.9011i	−0.875266	−	1.51601i
$531$		0			0
$532$	−9.83688	+	33.2729i	−0.426483	+	1.44256i
$533$	0.580842	+	7.68727i	0.0251591	+	0.332973i
$534$		0			0
$535$	10.1105	+	10.1105i	0.437115	+	0.437115i
$536$	−19.2010			−0.829358
$537$		0			0
$538$	26.8114	+	26.8114i	1.15592	+	1.15592i
$539$	−7.45030	+	23.0119i	−0.320907	+	0.991193i
$540$		0			0
$541$	5.38179	−	1.44205i	0.231381	−	0.0619984i	−0.141265	−	0.989972i	$-0.545117\pi$
$541$	5.38179	−	1.44205i	0.231381	−	0.0619984i	0.372647	+	0.927973i	$0.378450\pi$
$542$	−18.5265	−	10.6963i	−0.795782	−	0.459445i
$543$		0			0
$544$	16.9345	+	4.53759i	0.726061	+	0.194548i
$545$	−13.3863			−0.573407
$546$		0			0
$547$	1.45857			0.0623640			0.0311820	−	0.999514i	$-0.490073\pi$
$547$	1.45857			0.0623640			0.0311820	+	0.999514i	$0.490073\pi$
$548$	38.1847	+	10.2316i	1.63117	+	0.437071i
$549$		0			0
$550$	51.2520	+	29.5903i	2.18539	+	1.26174i
$551$	9.74433	−	2.61098i	0.415122	−	0.111232i
$552$		0			0
$553$	−20.7247	+	11.2667i	−0.881305	+	0.479109i
$554$	−10.8932	−	10.8932i	−0.462808	−	0.462808i
$555$		0			0
$556$	−45.9917			−1.95048
$557$	−25.3584	−	25.3584i	−1.07447	−	1.07447i	−0.996994	−	0.0774745i	$-0.975314\pi$
$557$	−25.3584	−	25.3584i	−1.07447	−	1.07447i	−0.0774745	−	0.996994i	$-0.524686\pi$
$558$		0			0
$559$	4.45833	+	12.7161i	0.188567	+	0.537832i
$560$	2.75385	+	11.4441i	0.116371	+	0.483602i
$561$		0			0
$562$	−24.4553	−	42.3578i	−1.03158	−	1.78675i
$563$	10.2234	−	17.7074i	0.430865	−	0.746280i	−0.566083	−	0.824348i	$-0.691542\pi$
$563$	10.2234	−	17.7074i	0.430865	−	0.746280i	0.996948	+	0.0780682i	$0.0248752\pi$
$564$		0			0
$565$	−20.4220	−	20.4220i	−0.859160	−	0.859160i
$566$	51.7278	+	13.8604i	2.17428	+	0.582597i
$567$		0			0
$568$	13.8056	+	23.9119i	0.579268	+	1.00332i
$569$	−2.54333	+	1.46839i	−0.106622	+	0.0615583i	−0.552363	−	0.833604i	$-0.686274\pi$
$569$	−2.54333	+	1.46839i	−0.106622	+	0.0615583i	0.445741	+	0.895162i	$0.352940\pi$
$570$		0			0
$571$	20.2914	−	11.7152i	0.849168	−	0.490268i	−0.0112018	−	0.999937i	$-0.503566\pi$
$571$	20.2914	−	11.7152i	0.849168	−	0.490268i	0.860370	+	0.509670i	$0.170232\pi$
$572$	−36.4872	+	2.75693i	−1.52561	+	0.115273i
$573$		0			0
$574$	10.7207	+	6.56191i	0.447474	+	0.273889i
$575$	−11.7660	+	20.3793i	−0.490677	+	0.849878i
$576$		0			0
$577$	−1.49434	+	5.57694i	−0.0622101	+	0.232171i	−0.990030	−	0.140858i	$-0.955014\pi$
$577$	−1.49434	+	5.57694i	−0.0622101	+	0.232171i	0.927820	+	0.373029i	$0.121681\pi$
$578$	6.10310	+	22.7771i	0.253855	+	0.947401i
$579$		0			0
$580$	−16.7265	+	16.7265i	−0.694531	+	0.694531i
$581$	−0.502161	−	2.08682i	−0.0208331	−	0.0865759i
$582$		0			0
$583$	−4.55022	+	16.9816i	−0.188451	+	0.703308i
$584$	5.09799	+	8.82998i	0.210956	+	0.365387i
$585$		0			0
$586$	−24.6754	−	14.2464i	−1.01933	−	0.588512i
$587$	−1.45889	+	0.390908i	−0.0602147	+	0.0161345i	−0.288801	−	0.957389i	$-0.593256\pi$
$587$	−1.45889	+	0.390908i	−0.0602147	+	0.0161345i	0.228586	+	0.973524i	$0.426590\pi$
$588$		0			0
$589$	−23.0441	+	13.3045i	−0.949514	+	0.548202i
$590$	17.4310	+	65.0532i	0.717621	+	2.67820i
$591$		0			0
$592$	−12.6456	+	3.38837i	−0.519729	+	0.139261i
$593$	−3.93254	−	14.6764i	−0.161490	−	0.602689i	−0.998462	−	0.0554430i	$-0.982343\pi$
$593$	−3.93254	−	14.6764i	−0.161490	−	0.602689i	0.836972	−	0.547246i	$-0.184324\pi$
$594$		0			0
$595$	17.2821	−	16.4174i	0.708498	−	0.673047i
$596$	−25.1794	+	6.74679i	−1.03139	+	0.276359i
$597$		0			0
$598$	−1.84274	−	24.3882i	−0.0753554	−	0.997307i
$599$	−21.2625	−	36.8277i	−0.868761	−	1.50474i	−0.863264	−	0.504753i	$-0.831584\pi$
$599$	−21.2625	−	36.8277i	−0.868761	−	1.50474i	−0.00549669	−	0.999985i	$-0.501750\pi$
$600$		0			0
$601$	7.41322	+	4.28002i	0.302391	+	0.174586i	0.643517	−	0.765432i	$-0.277475\pi$
$601$	7.41322	+	4.28002i	0.302391	+	0.174586i	−0.341125	+	0.940018i	$0.610808\pi$
$602$	21.0689	+	6.22885i	0.858704	+	0.253869i
$603$		0			0
$604$	−34.4373	+	34.4373i	−1.40123	+	1.40123i
$605$	−0.867194	−	3.23641i	−0.0352565	−	0.131579i
$606$		0			0
$607$		−	2.24372i		−	0.0910697i	−0.998963	−	0.0455349i	$-0.985501\pi$
$607$		−	2.24372i		−	0.0910697i	0.998963	−	0.0455349i	$-0.0144992\pi$
$608$	15.4871	−	26.8244i	0.628084	−	1.08787i
$609$		0			0
$610$			103.714i			4.19925i
$611$	24.3847	−	1.84248i	0.986501	−	0.0745390i
$612$		0			0
$613$	10.5452	−	10.5452i	0.425918	−	0.425918i	−0.461317	−	0.887235i	$-0.652623\pi$
$613$	10.5452	−	10.5452i	0.425918	−	0.425918i	0.887235	+	0.461317i	$0.152623\pi$
$614$	42.0633	−	24.2852i	1.69754	−	0.980073i
$615$		0			0
$616$	−9.93657	+	16.2342i	−0.400356	+	0.654093i
$617$	42.8048	+	11.4695i	1.72326	+	0.461745i	0.978612	−	0.205716i	$-0.0659522\pi$
$617$	42.8048	+	11.4695i	1.72326	+	0.461745i	0.744645	+	0.667461i	$0.232619\pi$
$618$		0			0
$619$	19.0455	+	5.10322i	0.765503	+	0.205116i	0.620384	−	0.784298i	$-0.286977\pi$
$619$	19.0455	+	5.10322i	0.765503	+	0.205116i	0.145119	+	0.989414i	$0.453643\pi$
$620$	31.1969	−	54.0346i	1.25290	−	2.17008i
$621$		0			0
$622$	−1.86407	−	6.95680i	−0.0747423	−	0.278942i
$623$	15.1647	+	15.9634i	0.607560	+	0.639562i
$624$		0			0
$625$	−2.06281	+	3.57289i	−0.0825123	+	0.142916i
$626$	45.1958	+	45.1958i	1.80639	+	1.80639i
$627$		0			0
$628$	−48.8974			−1.95122
$629$	18.7467	+	18.7467i	0.747481	+	0.747481i
$630$		0			0
$631$	−4.48791	+	16.7491i	−0.178661	+	0.666772i	0.817238	+	0.576300i	$0.195504\pi$
$631$	−4.48791	+	16.7491i	−0.178661	+	0.666772i	−0.995899	+	0.0904714i	$0.971163\pi$
$632$	−17.9302	+	4.80437i	−0.713223	+	0.191108i
$633$		0			0
$634$			1.24178i			0.0493175i
$635$	37.0040	+	9.91520i	1.46846	+	0.393473i
$636$		0			0
$637$	−24.2143	+	7.11803i	−0.959407	+	0.282027i
$638$	17.3463			0.686748
$639$		0			0
$640$			52.8589i			2.08943i
$641$	−38.3533	−	22.1433i	−1.51486	−	0.874607i	−0.999848	−	0.0174256i	$-0.994453\pi$
$641$	−38.3533	−	22.1433i	−1.51486	−	0.874607i	−0.515015	−	0.857181i	$-0.672214\pi$
$642$		0			0
$643$	−4.58915	+	17.1270i	−0.180979	+	0.675421i	0.814477	+	0.580196i	$0.197024\pi$
$643$	−4.58915	+	17.1270i	−0.180979	+	0.675421i	−0.995456	+	0.0952256i	$0.969643\pi$
$644$	−20.2335	−	12.3845i	−0.797312	−	0.488018i
$645$		0			0
$646$	−25.0742			−0.986529
$647$	8.74076			0.343635			0.171817	−	0.985129i	$-0.445036\pi$
$647$	8.74076			0.343635			0.171817	+	0.985129i	$0.445036\pi$
$648$		0			0
$649$	14.6900	−	25.4439i	0.576635	−	0.998760i
$650$	4.65265	+	61.5765i	0.182492	+	2.41523i
$651$		0			0
$652$	−1.94710	−	7.26668i	−0.0762544	−	0.284585i
$653$	−7.63256	−	13.2200i	−0.298685	−	0.517338i	0.677150	−	0.735845i	$-0.263215\pi$
$653$	−7.63256	−	13.2200i	−0.298685	−	0.517338i	−0.975835	+	0.218507i	$0.929881\pi$
$654$		0			0
$655$	−57.4399	−	15.3910i	−2.24436	−	0.601376i
$656$	−1.88685	−	1.88685i	−0.0736692	−	0.0736692i
$657$		0			0
$658$	20.8150	−	34.0071i	0.811453	−	1.32573i
$659$	16.9799	+	29.4100i	0.661443	+	1.14565i	0.980237	+	0.197829i	$0.0633889\pi$
$659$	16.9799	+	29.4100i	0.661443	+	1.14565i	−0.318794	+	0.947824i	$0.603278\pi$
$660$		0			0
$661$	−19.2329	+	19.2329i	−0.748072	+	0.748072i	−0.974117	−	0.226045i	$-0.927420\pi$
$661$	−19.2329	+	19.2329i	−0.748072	+	0.748072i	0.226045	+	0.974117i	$0.427420\pi$
$662$	−1.37165	+	0.791925i	−0.0533109	+	0.0307790i
$663$		0			0
$664$		−	1.68902i		−	0.0655466i
$665$	−20.1143	−	36.9996i	−0.779999	−	1.43478i
$666$		0			0
$667$			6.89743i			0.267070i
$668$	−0.491607	+	1.83470i	−0.0190208	+	0.0709867i
$669$		0			0
$670$	51.6544	−	51.6544i	1.99558	−	1.99558i
$671$	31.9926	−	31.9926i	1.23506	−	1.23506i
$672$		0			0
$673$	10.6058	+	6.12329i	0.408825	+	0.236035i	0.690285	−	0.723538i	$-0.257485\pi$
$673$	10.6058	+	6.12329i	0.408825	+	0.236035i	−0.281460	+	0.959573i	$0.590819\pi$
$674$	−0.741678	+	2.76798i	−0.0285684	+	0.106619i
$675$		0			0
$676$	−23.8423	−	29.8218i	−0.917010	−	1.14699i
$677$	−16.0226	−	9.25064i	−0.615798	−	0.355531i	0.159433	−	0.987209i	$-0.449033\pi$
$677$	−16.0226	−	9.25064i	−0.615798	−	0.355531i	−0.775231	+	0.631678i	$0.782367\pi$
$678$		0			0
$679$	30.1405	−	28.6324i	1.15669	−	1.09881i
$680$	16.2446	−	9.37880i	0.622950	−	0.359660i
$681$		0			0
$682$	−44.1948	+	11.8420i	−1.69231	+	0.453453i
$683$	−12.6237	+	3.38250i	−0.483031	+	0.129428i	−0.492113	−	0.870531i	$-0.663775\pi$
$683$	−12.6237	+	3.38250i	−0.483031	+	0.129428i	0.00908284	+	0.999959i	$0.497109\pi$
$684$		0			0
$685$	−41.5539	+	23.9912i	−1.58769	+	0.916655i
$686$	−13.6753	+	38.8121i	−0.522125	+	1.48185i
$687$		0			0
$688$	−4.03927	−	2.33207i	−0.153996	−	0.0889094i
$689$	−17.3114	+	6.06949i	−0.659512	+	0.231229i
$690$		0			0
$691$	6.01271	−	22.4398i	0.228734	−	0.853648i	−0.752139	−	0.659004i	$-0.770978\pi$
$691$	6.01271	−	22.4398i	0.228734	−	0.853648i	0.980874	−	0.194644i	$-0.0623553\pi$
$692$	2.30049	+	1.32819i	0.0874515	+	0.0504902i
$693$		0			0
$694$	22.7431	−	22.7431i	0.863317	−	0.863317i
$695$	39.4730	−	39.4730i	1.49730	−	1.49730i
$696$		0			0
$697$	−1.39860	+	5.21966i	−0.0529759	+	0.197709i
$698$			13.3320i			0.504623i
$699$		0			0
$700$	51.0866	+	31.2690i	1.93089	+	1.18186i
$701$		−	4.81650i		−	0.181917i	−0.995855	−	0.0909584i	$-0.971007\pi$
$701$		−	4.81650i		−	0.181917i	0.995855	−	0.0909584i	$-0.0289930\pi$
$702$		0			0
$703$	40.5641	−	23.4197i	1.52990	−	0.883290i
$704$	31.5617	−	31.5617i	1.18953	−	1.18953i
$705$		0			0
$706$	19.5783	+	33.9106i	0.736839	+	1.27624i
$707$	−6.65148	−	4.07123i	−0.250155	−	0.153114i
$708$		0			0
$709$	−4.63907	−	4.63907i	−0.174224	−	0.174224i	0.614608	−	0.788832i	$-0.289314\pi$
$709$	−4.63907	−	4.63907i	−0.174224	−	0.174224i	−0.788832	+	0.614608i	$0.789314\pi$
$710$	−101.467	−	27.1880i	−3.80799	−	1.02035i
$711$		0			0
$712$	8.66317	+	15.0050i	0.324666	+	0.562338i
$713$	−4.70873	−	17.5732i	−0.176343	−	0.658122i
$714$		0			0
$715$	28.9495	−	33.6818i	1.08265	−	1.25963i
$716$	−31.2432	+	54.1148i	−1.16761	+	2.02236i
$717$		0			0
$718$	15.8312			0.590813
$719$	11.0944			0.413753			0.206876	−	0.978367i	$-0.433670\pi$
$719$	11.0944			0.413753			0.206876	+	0.978367i	$0.433670\pi$
$720$		0			0
$721$	36.0979	−	19.6241i	1.34436	−	0.730840i
$722$	−0.538992	+	2.01155i	−0.0200592	+	0.0748620i
$723$		0			0
$724$	−50.6570	−	29.2469i	−1.88265	−	1.08695i
$725$		−	17.4150i		−	0.646776i
$726$		0			0
$727$	3.05345			0.113246			0.0566230	−	0.998396i	$-0.481967\pi$
$727$	3.05345			0.113246			0.0566230	+	0.998396i	$0.481967\pi$
$728$	−19.8362	+	0.987883i	−0.735177	+	0.0366134i
$729$		0			0
$730$	−37.4689	−	10.0397i	−1.38678	−	0.371588i
$731$			9.44535i			0.349349i
$732$		0			0
$733$	−16.4195	+	4.39960i	−0.606469	+	0.162503i	−0.548969	−	0.835843i	$-0.684980\pi$
$733$	−16.4195	+	4.39960i	−0.606469	+	0.162503i	−0.0574997	+	0.998346i	$0.518313\pi$
$734$	1.36875	−	5.10825i	0.0505215	−	0.188549i
$735$		0			0
$736$	14.9749	+	14.9749i	0.551982	+	0.551982i
$737$	−31.8676			−1.17386
$738$		0			0
$739$	−38.0804	−	38.0804i	−1.40081	−	1.40081i	−0.797523	−	0.603288i	$-0.793857\pi$
$739$	−38.0804	−	38.0804i	−1.40081	−	1.40081i	−0.603288	−	0.797523i	$-0.706143\pi$
$740$	−54.9154	+	95.1162i	−2.01873	+	3.49654i
$741$		0			0
$742$	−8.47984	+	28.6828i	−0.311305	+	1.05298i
$743$	0.571152	+	2.13157i	0.0209535	+	0.0781997i	0.975611	−	0.219507i	$-0.0704449\pi$
$743$	0.571152	+	2.13157i	0.0209535	+	0.0781997i	−0.954657	+	0.297707i	$0.903778\pi$
$744$		0			0
$745$	15.8200	−	27.4010i	0.579600	−	1.00390i
$746$	1.95166	+	0.522946i	0.0714555	+	0.0191464i
$747$		0			0
$748$	−24.7748	−	6.63840i	−0.905858	−	0.242724i
$749$	0.272216	−	10.6085i	0.00994656	−	0.387625i
$750$		0			0
$751$	−2.18913	+	1.26390i	−0.0798826	+	0.0461202i	−0.539409	−	0.842044i	$-0.681352\pi$
$751$	−2.18913	+	1.26390i	−0.0798826	+	0.0461202i	0.459527	+	0.888164i	$0.348019\pi$
$752$	−5.98527	+	5.98527i	−0.218260	+	0.218260i
$753$		0			0
$754$	10.2053	+	14.9487i	0.371655	+	0.544398i
$755$		−	59.1126i		−	2.15133i
$756$		0			0
$757$	−4.00640	+	6.93928i	−0.145615	+	0.252213i	−0.929602	−	0.368564i	$-0.879849\pi$
$757$	−4.00640	+	6.93928i	−0.145615	+	0.252213i	0.783987	+	0.620777i	$0.213183\pi$
$758$		−	61.7745i		−	2.24375i
$759$		0			0
$760$	−8.57717	−	32.0104i	−0.311127	−	1.16114i
$761$	−2.70358	+	2.70358i	−0.0980047	+	0.0980047i	−0.754409	−	0.656404i	$-0.772077\pi$
$761$	−2.70358	+	2.70358i	−0.0980047	+	0.0980047i	0.656404	+	0.754409i	$0.272077\pi$
$762$		0			0
$763$	6.84261	+	7.20303i	0.247719	+	0.260767i
$764$	23.2017	+	13.3955i	0.839409	+	0.484633i
$765$		0			0
$766$	−13.4727	−	23.3354i	−0.486787	−	0.843140i
$767$	30.5695	−	2.30980i	1.10380	−	0.0834020i
$768$		0			0
$769$	11.5757	−	3.10171i	0.417431	−	0.111850i	−0.0439891	−	0.999032i	$-0.514007\pi$
$769$	11.5757	−	3.10171i	0.417431	−	0.111850i	0.461420	+	0.887182i	$0.347340\pi$
$770$	−16.9417	−	70.4042i	−0.610535	−	2.53719i
$771$		0			0
$772$	12.1212	+	45.2371i	0.436253	+	1.62812i
$773$	−51.8808	+	13.9014i	−1.86602	+	0.500000i	−1.00000		2.85353e-6i	$-0.999999\pi$
$773$	−51.8808	+	13.9014i	−1.86602	+	0.500000i	−0.866024	+	0.500002i	$0.833332\pi$
$774$		0			0
$775$	11.8888	+	44.3698i	0.427060	+	1.59381i
$776$	28.3310	−	16.3569i	1.01702	−	0.587178i
$777$		0			0
$778$	−63.5294	+	17.0227i	−2.27764	+	0.610292i
$779$	8.26799	+	4.77353i	0.296232	+	0.171029i
$780$		0			0
$781$	22.9129	+	39.6863i	0.819887	+	1.42009i
$782$	4.43713	−	16.5596i	0.158671	−	0.592169i
$783$		0			0
$784$	4.75028	−	7.33164i	0.169653	−	0.261844i
$785$	41.9669	−	41.9669i	1.49786	−	1.49786i
$786$		0			0
$787$	−10.6814	−	39.8636i	−0.380752	−	1.42098i	−0.844756	−	0.535152i	$-0.820255\pi$
$787$	−10.6814	−	39.8636i	−0.380752	−	1.42098i	0.464004	−	0.885833i	$-0.346412\pi$
$788$	18.3786	−	68.5900i	0.654712	−	2.44342i
$789$		0			0
$790$	35.3108	−	61.1601i	1.25630	−	2.17598i
$791$	−0.549844	+	21.4279i	−0.0195502	+	0.761887i
$792$		0			0
$793$	46.3926	+	8.74836i	1.64745	+	0.310663i
$794$	7.28485	−	4.20591i	0.258530	−	0.149262i
$795$		0			0
$796$	29.4879	−	17.0249i	1.04517	−	0.603430i
$797$	−13.8424	−	23.9757i	−0.490322	−	0.849263i	0.509616	−	0.860402i	$-0.329788\pi$
$797$	−13.8424	−	23.9757i	−0.490322	−	0.849263i	−0.999938	+	0.0111392i	$0.996454\pi$
$798$		0			0
$799$	16.5573	+	4.43650i	0.585754	+	0.156952i
$800$	−37.8094	−	37.8094i	−1.33676	−	1.33676i
$801$		0			0
$802$	2.92816	−	5.07172i	0.103397	−	0.179089i
$803$	8.46106	+	14.6550i	0.298584	+	0.517163i
$804$		0			0
$805$	27.9948	−	6.73652i	0.986689	−	0.237431i
$806$	−36.2061	−	31.1191i	−1.27531	−	1.09612i
$807$		0			0
$808$	−4.33934	−	4.33934i	−0.152657	−	0.152657i
$809$	25.3210			0.890240			0.445120	−	0.895471i	$-0.353161\pi$
$809$	25.3210			0.890240			0.445120	+	0.895471i	$0.353161\pi$
$810$		0			0
$811$	−1.33822	−	1.33822i	−0.0469912	−	0.0469912i	0.683221	−	0.730212i	$-0.260579\pi$
$811$	−1.33822	−	1.33822i	−0.0469912	−	0.0469912i	−0.730212	+	0.683221i	$0.760579\pi$
$812$	17.5504	+	0.450347i	0.615898	+	0.0158041i
$813$		0			0
$814$	77.7955	−	20.8452i	2.72673	−	0.730625i
$815$	7.90785	+	4.56560i	0.277000	+	0.159926i
$816$		0			0
$817$	16.1188	+	4.31902i	0.563925	+	0.151103i
$818$	−35.3085			−1.23453
$819$		0			0
$820$	−22.3863			−0.781764
$821$	−46.2258	−	12.3862i	−1.61329	−	0.432280i	−0.664270	−	0.747493i	$-0.731257\pi$
$821$	−46.2258	−	12.3862i	−1.61329	−	0.432280i	−0.949021	+	0.315213i	$0.897924\pi$
$822$		0			0
$823$	28.2402	+	16.3045i	0.984392	+	0.568339i	0.903593	−	0.428392i	$-0.140920\pi$
$823$	28.2402	+	16.3045i	0.984392	+	0.568339i	0.0807984	+	0.996730i	$0.474253\pi$
$824$	31.2303	−	8.36814i	1.08796	−	0.291518i
$825$		0			0
$826$	26.0943	−	42.6323i	0.907938	−	1.48337i
$827$	−11.0465	−	11.0465i	−0.384123	−	0.384123i	0.488462	−	0.872585i	$-0.337558\pi$
$827$	−11.0465	−	11.0465i	−0.384123	−	0.384123i	−0.872585	+	0.488462i	$0.837558\pi$
$828$		0			0
$829$	11.7037			0.406486			0.203243	−	0.979128i	$-0.434852\pi$
$829$	11.7037			0.406486			0.203243	+	0.979128i	$0.434852\pi$
$830$	4.54377	+	4.54377i	0.157717	+	0.157717i
$831$		0			0
$832$	45.7678	+	8.63054i	1.58671	+	0.299210i
$833$	−17.6680	−	0.907329i	−0.612161	−	0.0314371i
$834$		0			0
$835$	−1.15273	−	1.99658i	−0.0398918	−	0.0690947i
$836$	−22.6573	+	39.2436i	−0.783619	+	1.35727i
$837$		0			0
$838$	−62.9383	−	62.9383i	−2.17417	−	2.17417i
$839$	−3.51868	−	0.942826i	−0.121478	−	0.0325500i	0.197568	−	0.980289i	$-0.436696\pi$
$839$	−3.51868	−	0.942826i	−0.121478	−	0.0325500i	−0.319046	+	0.947739i	$0.603362\pi$
$840$		0			0
$841$	11.9478	+	20.6941i	0.411992	+	0.713591i
$842$	15.5995	−	9.00639i	0.537595	−	0.310381i
$843$		0			0
$844$	0.910516	−	0.525687i	0.0313413	−	0.0180949i
$845$	46.0579	+	5.13205i	1.58444	+	0.176548i
$846$		0			0
$847$	−1.29820	+	2.12097i	−0.0446067	+	0.0728774i
$848$	3.17484	−	5.49898i	0.109024	−	0.188836i
$849$		0			0
$850$	−11.2031	+	41.8105i	−0.384263	+	1.43409i
$851$	8.28871	+	30.9339i	0.284133	+	1.06040i
$852$		0			0
$853$	19.8017	−	19.8017i	0.677999	−	0.677999i	−0.281548	−	0.959547i	$-0.590848\pi$
$853$	19.8017	−	19.8017i	0.677999	−	0.677999i	0.959547	+	0.281548i	$0.0908479\pi$
$854$	55.8073	−	53.0149i	1.90968	−	1.81413i
$855$		0			0
$856$	2.16132	−	8.06614i	0.0738722	−	0.275695i
$857$	0.00868032	+	0.0150348i	0.000296514	+	0.000513578i	0.866174	−	0.499743i	$-0.166572\pi$
$857$	0.00868032	+	0.0150348i	0.000296514	+	0.000513578i	−0.865877	+	0.500257i	$0.833239\pi$
$858$		0			0
$859$	−24.0350	−	13.8766i	−0.820065	−	0.473465i	0.0303739	−	0.999539i	$-0.490330\pi$
$859$	−24.0350	−	13.8766i	−0.820065	−	0.473465i	−0.850439	+	0.526074i	$0.823664\pi$
$860$	−37.7960	+	10.1274i	−1.28883	+	0.345341i
$861$		0			0
$862$	17.7578	−	10.2525i	0.604834	−	0.349201i
$863$	−13.4199	−	50.0837i	−0.456818	−	1.70487i	−0.682687	−	0.730711i	$-0.739189\pi$
$863$	−13.4199	−	50.0837i	−0.456818	−	1.70487i	0.225869	−	0.974158i	$-0.427478\pi$
$864$		0			0
$865$	−3.11436	+	0.834491i	−0.105891	+	0.0283735i
$866$	5.79916	+	21.6428i	0.197064	+	0.735452i
$867$		0			0
$868$	−45.0222	+	10.8339i	−1.52815	+	0.367726i
$869$	−29.7584	+	7.97374i	−1.00948	+	0.270490i
$870$		0			0
$871$	−18.7486	−	27.4628i	−0.635272	−	0.930541i
$872$	3.90900	+	6.77058i	0.132375	+	0.229281i
$873$		0			0
$874$	−26.2305	−	15.1442i	−0.887261	−	0.512260i
$875$	−24.8332	+	5.97571i	−0.839514	+	0.202016i
$876$		0			0
$877$	8.75967	−	8.75967i	0.295793	−	0.295793i	−0.543570	−	0.839364i	$-0.682928\pi$
$877$	8.75967	−	8.75967i	0.295793	−	0.295793i	0.839364	+	0.543570i	$0.182928\pi$
$878$	2.52490	+	9.42305i	0.0852112	+	0.318013i
$879$		0			0
$880$			15.3729i			0.518221i
$881$	2.60937	−	4.51956i	0.0879118	−	0.152268i	−0.818716	−	0.574198i	$-0.805314\pi$
$881$	2.60937	−	4.51956i	0.0879118	−	0.152268i	0.906628	+	0.421930i	$0.138647\pi$
$882$		0			0
$883$		−	32.1849i		−	1.08311i	−0.840666	−	0.541554i	$-0.817836\pi$
$883$		−	32.1849i		−	1.08311i	0.840666	−	0.541554i	$-0.182164\pi$
$884$	−8.85489	−	25.2559i	−0.297822	−	0.849448i
$885$		0			0
$886$	−17.2262	+	17.2262i	−0.578726	+	0.578726i
$887$	32.1333	−	18.5521i	1.07893	−	0.622920i	0.148322	−	0.988939i	$-0.452613\pi$
$887$	32.1333	−	18.5521i	1.07893	−	0.622920i	0.930607	+	0.366019i	$0.119279\pi$
$888$		0			0
$889$	−13.5799	−	24.9798i	−0.455455	−	0.837794i
$890$	−63.6719	−	17.0608i	−2.13429	−	0.571881i
$891$		0			0
$892$	16.0823	+	4.30924i	0.538475	+	0.144284i
$893$	15.1421	−	26.2268i	0.506710	−	0.877648i
$894$		0			0
$895$	−19.6298	−	73.2596i	−0.656153	−	2.44880i
$896$	28.4428	−	27.0196i	0.950207	−	0.902662i
$897$		0			0
$898$	23.0909	−	39.9947i	0.770554	−	1.33464i
$899$	9.52042	+	9.52042i	0.317524	+	0.317524i
$900$		0			0
$901$	−12.8587			−0.428386
$902$	11.6079	+	11.6079i	0.386501	+	0.386501i
$903$		0			0
$904$	−4.36560	+	16.2926i	−0.145198	+	0.541885i
$905$	68.5786	−	18.3756i	2.27963	−	0.610825i
$906$		0			0
$907$		−	39.5545i		−	1.31338i	−0.754159	−	0.656692i	$-0.771955\pi$
$907$		−	39.5545i		−	1.31338i	0.754159	−	0.656692i	$-0.228045\pi$
$908$	−30.3098	−	8.12150i	−1.00587	−	0.269521i
$909$		0			0
$910$	50.7054	−	56.0206i	1.68087	−	1.85706i
$911$	−28.2821			−0.937026			−0.468513	−	0.883457i	$-0.655210\pi$
$911$	−28.2821			−0.937026			−0.468513	+	0.883457i	$0.655210\pi$
$912$		0			0
$913$		−	2.80324i		−	0.0927735i
$914$	−74.8995	−	43.2433i	−2.47746	−	1.43036i
$915$		0			0
$916$	21.4322	−	79.9859i	0.708138	−	2.64281i
$917$	21.0796	+	38.7751i	0.696108	+	1.28047i
$918$		0			0
$919$	−39.6459			−1.30780			−0.653898	−	0.756582i	$-0.726868\pi$
$919$	−39.6459			−1.30780			−0.653898	+	0.756582i	$0.726868\pi$
$920$	22.6583			0.747022
$921$		0			0
$922$	−16.7509	+	29.0133i	−0.551660	+	0.955504i
$923$	−20.7204	+	43.0943i	−0.682021	+	1.41846i
$924$		0			0
$925$	−20.9278	−	78.1034i	−0.688100	−	2.56803i
$926$	7.73463	+	13.3968i	0.254176	+	0.440245i
$927$		0			0
$928$	−15.1386	−	4.05638i	−0.496950	−	0.133157i
$929$	−40.4827	−	40.4827i	−1.32819	−	1.32819i	−0.906945	−	0.421249i	$-0.861592\pi$
$929$	−40.4827	−	40.4827i	−1.32819	−	1.32819i	−0.421249	−	0.906945i	$-0.638408\pi$
$930$		0			0
$931$	−9.62734	+	29.7362i	−0.315523	+	0.974563i
$932$	−1.98944	−	3.44581i	−0.0651662	−	0.112871i
$933$		0			0
$934$	−25.4091	+	25.4091i	−0.831412	+	0.831412i
$935$	26.9608	−	15.5658i	0.881713	−	0.509057i
$936$		0			0
$937$		−	9.81862i		−	0.320760i	−0.987055	−	0.160380i	$-0.948728\pi$
$937$		−	9.81862i		−	0.320760i	0.987055	−	0.160380i	$-0.0512720\pi$
$938$	−54.1985	−	1.39075i	−1.76965	−	0.0454095i
$939$		0			0
$940$			71.0114i			2.31614i
$941$	−1.03365	+	3.85765i	−0.0336962	+	0.125756i	−0.980725	−	0.195392i	$-0.937402\pi$
$941$	−1.03365	+	3.85765i	−0.0336962	+	0.125756i	0.947029	+	0.321148i	$0.104069\pi$
$942$		0			0
$943$	−4.61566	+	4.61566i	−0.150307	+	0.150307i
$944$	−7.50332	+	7.50332i	−0.244212	+	0.244212i
$945$		0			0
$946$	24.8496	+	14.3469i	0.807929	+	0.466458i
$947$	−14.1448	+	52.7892i	−0.459645	+	1.71542i	0.214416	+	0.976742i	$0.431215\pi$
$947$	−14.1448	+	52.7892i	−0.459645	+	1.71542i	−0.674061	+	0.738676i	$0.735452\pi$
$948$		0			0
$949$	−7.65145	+	15.9135i	−0.248377	+	0.516573i
$950$	66.2282	+	38.2369i	2.14873	+	1.24057i
$951$		0			0
$952$	−13.3503	−	3.94690i	−0.432685	−	0.127920i
$953$	−24.4083	+	14.0921i	−0.790662	+	0.456489i	−0.840195	−	0.542284i	$-0.817560\pi$
$953$	−24.4083	+	14.0921i	−0.790662	+	0.456489i	0.0495337	+	0.998772i	$0.484226\pi$
$954$		0			0
$955$	−31.4101	+	8.41631i	−1.01641	+	0.272345i
$956$	−29.5470	+	7.91709i	−0.955617	+	0.256057i
$957$		0			0
$958$	56.5918	−	32.6733i	1.82840	−	1.05563i
$959$	34.1503	+	10.0963i	1.10277	+	0.326025i
$960$		0			0
$961$	−3.90866	−	2.25667i	−0.126086	−	0.0727957i
$962$	63.7331	+	54.7785i	2.05484	+	1.76613i
$963$		0			0
$964$	−3.94745	+	14.7321i	−0.127139	+	0.474488i
$965$	−49.2286	−	28.4221i	−1.58472	−	0.914940i
$966$		0			0
$967$	36.2386	−	36.2386i	1.16536	−	1.16536i	0.182070	−	0.983286i	$-0.441720\pi$
$967$	36.2386	−	36.2386i	1.16536	−	1.16536i	0.983286	−	0.182070i	$-0.0582797\pi$
$968$	−1.38369	+	1.38369i	−0.0444736	+	0.0444736i
$969$		0			0
$970$	−32.2125	+	120.219i	−1.03428	+	3.85999i
$971$			52.8645i			1.69650i	0.529594	+	0.848251i	$0.322344\pi$
$971$			52.8645i			1.69650i	−0.529594	+	0.848251i	$0.677656\pi$
$972$		0			0
$973$	−41.4172	−	1.06278i	−1.32777	−	0.0340710i
$974$			39.8631i			1.27729i
$975$		0			0
$976$	−14.1518	+	8.17052i	−0.452987	+	0.261532i
$977$	9.63697	−	9.63697i	0.308314	−	0.308314i	−0.535941	−	0.844255i	$-0.680043\pi$
$977$	9.63697	−	9.63697i	0.308314	−	0.308314i	0.844255	+	0.535941i	$0.180043\pi$
$978$		0			0
$979$	14.3781	+	24.9036i	0.459527	+	0.795924i
$980$	−15.3131	−	71.6722i	−0.489160	−	2.28948i
$981$		0			0
$982$	3.15397	+	3.15397i	0.100647	+	0.100647i
$983$	37.1166	+	9.94536i	1.18384	+	0.317208i	0.796447	−	0.604708i	$-0.206710\pi$
$983$	37.1166	+	9.94536i	1.18384	+	0.317208i	0.387389	+	0.921916i	$0.373377\pi$
$984$		0			0
$985$	43.0946	+	74.6420i	1.37311	+	2.37829i
$986$	3.28371	+	12.2550i	0.104575	+	0.390278i
$987$		0			0
$988$	−47.1491	+	3.56253i	−1.50001	+	0.113339i
$989$	−5.70477	+	9.88095i	−0.181401	+	0.314196i
$990$		0			0
$991$	8.44874			0.268383			0.134192	−	0.990955i	$-0.457156\pi$
$991$	8.44874			0.268383			0.134192	+	0.990955i	$0.457156\pi$
$992$	41.3393			1.31252
$993$		0			0
$994$	37.2368	+	68.4959i	1.18108	+	2.17256i
$995$	−10.6966	+	39.9202i	−0.339105	+	1.26556i
$996$		0			0
$997$	45.9688	+	26.5401i	1.45585	+	0.840534i	0.998803	−	0.0489103i	$-0.0155748\pi$
$997$	45.9688	+	26.5401i	1.45585	+	0.840534i	0.457044	+	0.889444i	$0.348908\pi$
$998$			37.8970i			1.19961i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.19.9		40
3.2	odd	2		273.2.cg.b.19.2	yes	40
7.3	odd	6		819.2.et.d.136.2		40
13.11	odd	12		819.2.et.d.271.2		40
21.17	even	6		273.2.bt.b.136.9	✓	40
39.11	even	12		273.2.bt.b.271.9	yes	40
91.24	even	12	inner	819.2.gh.d.388.9		40
273.206	odd	12		273.2.cg.b.115.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.9	✓	40	21.17	even	6
273.2.bt.b.271.9	yes	40	39.11	even	12
273.2.cg.b.19.2	yes	40	3.2	odd	2
273.2.cg.b.115.2	yes	40	273.206	odd	12
819.2.et.d.136.2		40	7.3	odd	6
819.2.et.d.271.2		40	13.11	odd	12
819.2.gh.d.19.9		40	1.1	even	1	trivial
819.2.gh.d.388.9		40	91.24	even	12	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.gh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14623 + 0.575080i) q^{2} +(2.54352 + 1.46850i) q^{4} +(-3.44337 + 0.922649i) q^{5} +(2.25660 + 1.38122i) q^{7} +(1.47218 + 1.47218i) q^{8} +O(q^{10})\)	\(q+(2.14623 + 0.575080i) q^{2} +(2.54352 + 1.46850i) q^{4} +(-3.44337 + 0.922649i) q^{5} +(2.25660 + 1.38122i) q^{7} +(1.47218 + 1.47218i) q^{8} -7.92086 q^{10} +(2.44335 + 2.44335i) q^{11} +(-0.668132 + 3.54311i) q^{13} +(4.04887 + 4.26213i) q^{14} +(-0.624002 - 1.08080i) q^{16} +(-1.26366 + 2.18873i) q^{17} +(3.15731 + 3.15731i) q^{19} +(-10.1132 - 2.70983i) q^{20} +(3.83886 + 6.64910i) q^{22} +(-2.64388 + 1.52645i) q^{23} +(6.67542 - 3.85405i) q^{25} +(-3.47153 + 7.22008i) q^{26} +(3.71139 + 6.82698i) q^{28} +(1.12965 - 1.95662i) q^{29} +(-1.54238 + 5.75625i) q^{31} +(-1.79541 - 6.70056i) q^{32} +(-3.97081 + 3.97081i) q^{34} +(-9.04470 - 2.67399i) q^{35} +(2.71503 - 10.1326i) q^{37} +(4.96060 + 8.59202i) q^{38} +(-6.42756 - 3.71095i) q^{40} +(2.06529 - 0.553392i) q^{41} +(3.23658 - 1.86864i) q^{43} +(2.62665 + 9.80278i) q^{44} +(-6.55221 + 1.75566i) q^{46} +(-1.75541 - 6.55128i) q^{47} +(3.18448 + 6.23370i) q^{49} +(16.5433 - 4.43278i) q^{50} +(-6.90247 + 8.03082i) q^{52} +(2.54393 + 4.40622i) q^{53} +(-10.6677 - 6.15901i) q^{55} +(1.28872 + 5.35551i) q^{56} +(3.54971 - 3.54971i) q^{58} +(-2.20064 - 8.21290i) q^{59} -13.0938i q^{61} +(-6.62060 + 11.4672i) q^{62} -12.9174i q^{64} +(-0.968415 - 12.8167i) q^{65} +(-6.52131 + 6.52131i) q^{67} +(-6.42832 + 3.71139i) q^{68} +(-17.8742 - 10.9404i) q^{70} +(12.8101 + 3.43246i) q^{71} +(4.73040 + 1.26751i) q^{73} +(11.6541 - 20.1856i) q^{74} +(3.39417 + 12.6672i) q^{76} +(2.13887 + 8.88845i) q^{77} +(-4.45795 + 7.72140i) q^{79} +(3.14587 + 3.14587i) q^{80} +4.75082 q^{82} +(-0.573646 - 0.573646i) q^{83} +(2.33184 - 8.70254i) q^{85} +(8.02106 - 2.14924i) q^{86} +7.19408i q^{88} +(8.03851 + 2.15391i) q^{89} +(-6.40150 + 7.07254i) q^{91} -8.96637 q^{92} -15.0700i q^{94} +(-13.7849 - 7.95872i) q^{95} +(4.06679 - 15.1775i) q^{97} +(3.24975 + 15.2103i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^7	\( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

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