LMFDB - Embedded newform 891.2.f.e.163.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.9
Character	$\chi$	$=$	891.163
Dual form			891.2.f.e.82.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.803965 - 2.47435i) q^{2} +(-3.85802 - 2.80301i) q^{4} +(-0.634128 - 1.95164i) q^{5} +(-2.58046 - 1.87481i) q^{7} +(-5.82773 + 4.23409i) q^{8} +O(q^{10})$	\(q+(0.803965 - 2.47435i) q^{2} +(-3.85802 - 2.80301i) q^{4} +(-0.634128 - 1.95164i) q^{5} +(-2.58046 - 1.87481i) q^{7} +(-5.82773 + 4.23409i) q^{8} -5.33887 q^{10} +(-0.530779 + 3.27388i) q^{11} +(-0.430725 + 1.32563i) q^{13} +(-6.71355 + 4.87768i) q^{14} +(2.84408 + 8.75317i) q^{16} +(0.417491 + 1.28491i) q^{17} +(2.15510 - 1.56577i) q^{19} +(-3.02401 + 9.30694i) q^{20} +(7.67399 + 3.94542i) q^{22} +1.62134 q^{23} +(0.638288 - 0.463743i) q^{25} +(2.93380 + 2.13153i) q^{26} +(4.70033 + 14.4661i) q^{28} +(-7.44518 - 5.40924i) q^{29} +(2.19884 - 6.76734i) q^{31} +9.53801 q^{32} +3.51496 q^{34} +(-2.02263 + 6.22501i) q^{35} +(0.606109 + 0.440364i) q^{37} +(-2.14165 - 6.59131i) q^{38} +(11.9590 + 8.68870i) q^{40} +(-4.88811 + 3.55142i) q^{41} -7.09299 q^{43} +(11.2245 - 11.1429i) q^{44} +(1.30350 - 4.01177i) q^{46} +(-4.63580 + 3.36810i) q^{47} +(0.980730 + 3.01838i) q^{49} +(-0.634302 - 1.95218i) q^{50} +(5.37751 - 3.90699i) q^{52} +(-0.146386 + 0.450530i) q^{53} +(6.72603 - 1.04016i) q^{55} +22.9764 q^{56} +(-19.3700 + 14.0731i) q^{58} +(-1.24947 - 0.907796i) q^{59} +(2.90164 + 8.93034i) q^{61} +(-14.9770 - 10.8814i) q^{62} +(1.98007 - 6.09404i) q^{64} +2.86030 q^{65} +7.39729 q^{67} +(1.99092 - 6.12742i) q^{68} +(13.7767 + 10.0094i) q^{70} +(-0.485314 - 1.49364i) q^{71} +(-7.78114 - 5.65333i) q^{73} +(1.57691 - 1.14569i) q^{74} -12.7033 q^{76} +(7.50757 - 7.45300i) q^{77} +(0.714495 - 2.19899i) q^{79} +(15.2796 - 11.1013i) q^{80} +(4.85759 + 14.9501i) q^{82} +(2.35615 + 7.25149i) q^{83} +(2.24294 - 1.62959i) q^{85} +(-5.70252 + 17.5506i) q^{86} +(-10.7687 - 21.3266i) q^{88} -14.6343 q^{89} +(3.59679 - 2.61322i) q^{91} +(-6.25516 - 4.54464i) q^{92} +(4.60685 + 14.1784i) q^{94} +(-4.42245 - 3.21310i) q^{95} +(2.14060 - 6.58808i) q^{97} +8.25699 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) $ 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8	$ 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28} - 23 q^{29} - 3 q^{31} + 18 q^{32} - 8 q^{34} - 9 q^{35} - 21 q^{37} - q^{38} + 25 q^{40} + 10 q^{41} + 8 q^{43} - 19 q^{44} - 9 q^{46} - 34 q^{47} - q^{49} + 27 q^{52} - 2 q^{53} + 9 q^{55} + 114 q^{56} - q^{58} - 16 q^{59} + 3 q^{61} - 92 q^{62} + 13 q^{64} + 84 q^{65} - 10 q^{67} - 23 q^{68} + 46 q^{70} + 24 q^{71} - 20 q^{73} + 68 q^{74} - 16 q^{76} - 26 q^{77} - 19 q^{79} + 28 q^{80} + 47 q^{82} + 7 q^{83} - 25 q^{85} - 77 q^{86} - 18 q^{88} + 28 q^{89} + 10 q^{91} + 50 q^{92} + 63 q^{94} - 77 q^{95} + 33 q^{97} + 164 q^{98}+O(q^{100}) $ 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.803965	−	2.47435i	0.568489	−	1.74963i	−0.0888603	−	0.996044i	$-0.528322\pi$
$2$	0.803965	−	2.47435i	0.568489	−	1.74963i	0.657349	−	0.753586i	$-0.271678\pi$
$3$		0			0
$3$		0			0
$4$	−3.85802	−	2.80301i	−1.92901	−	1.40151i
$5$	−0.634128	−	1.95164i	−0.283590	−	0.872802i	−0.986818	−	0.161836i	$-0.948258\pi$
$5$	−0.634128	−	1.95164i	−0.283590	−	0.872802i	0.703227	−	0.710965i	$-0.251742\pi$
$6$		0			0
$7$	−2.58046	−	1.87481i	−0.975323	−	0.708613i	−0.0186641	−	0.999826i	$-0.505941\pi$
$7$	−2.58046	−	1.87481i	−0.975323	−	0.708613i	−0.956658	+	0.291213i	$0.905941\pi$
$8$	−5.82773	+	4.23409i	−2.06041	+	1.49698i
$9$		0			0
$10$	−5.33887			−1.68830
$11$	−0.530779	+	3.27388i	−0.160036	+	0.987111i
$11$	−0.530779	+	3.27388i	−0.160036	+	0.987111i
$12$		0			0
$13$	−0.430725	+	1.32563i	−0.119462	+	0.367665i	−0.992851	−	0.119357i	$-0.961917\pi$
$13$	−0.430725	+	1.32563i	−0.119462	+	0.367665i	0.873390	+	0.487022i	$0.161917\pi$
$14$	−6.71355	+	4.87768i	−1.79427	+	1.30361i
$15$		0			0
$16$	2.84408	+	8.75317i	0.711019	+	2.18829i
$17$	0.417491	+	1.28491i	0.101257	+	0.311636i	0.988834	−	0.149024i	$-0.0476130\pi$
$17$	0.417491	+	1.28491i	0.101257	+	0.311636i	−0.887577	+	0.460659i	$0.847613\pi$
$18$		0			0
$19$	2.15510	−	1.56577i	0.494415	−	0.359213i	−0.312465	−	0.949929i	$-0.601155\pi$
$19$	2.15510	−	1.56577i	0.494415	−	0.359213i	0.806880	+	0.590716i	$0.201155\pi$
$20$	−3.02401	+	9.30694i	−0.676189	+	2.08110i
$21$		0			0
$22$	7.67399	+	3.94542i	1.63610	+	0.841166i
$23$	1.62134			0.338073			0.169037	−	0.985610i	$-0.445934\pi$
$23$	1.62134			0.338073			0.169037	+	0.985610i	$0.445934\pi$
$24$		0			0
$25$	0.638288	−	0.463743i	0.127658	−	0.0927487i
$26$	2.93380	+	2.13153i	0.575365	+	0.418027i
$27$		0			0
$28$	4.70033	+	14.4661i	0.888279	+	2.73384i
$29$	−7.44518	−	5.40924i	−1.38254	−	1.00447i	−0.996638	−	0.0819292i	$-0.973892\pi$
$29$	−7.44518	−	5.40924i	−1.38254	−	1.00447i	−0.385897	−	0.922542i	$-0.626108\pi$
$30$		0			0
$31$	2.19884	−	6.76734i	0.394924	−	1.21545i	−0.534097	−	0.845423i	$-0.679348\pi$
$31$	2.19884	−	6.76734i	0.394924	−	1.21545i	0.929021	−	0.370028i	$-0.120652\pi$
$32$	9.53801			1.68610
$33$		0			0
$34$	3.51496			0.602810
$35$	−2.02263	+	6.22501i	−0.341887	+	1.05222i
$36$		0			0
$37$	0.606109	+	0.440364i	0.0996438	+	0.0723954i	0.636491	−	0.771284i	$-0.280385\pi$
$37$	0.606109	+	0.440364i	0.0996438	+	0.0723954i	−0.536848	+	0.843679i	$0.680385\pi$
$38$	−2.14165	−	6.59131i	−0.347421	−	1.06925i
$39$		0			0
$40$	11.9590	+	8.68870i	1.89088	+	1.37380i
$41$	−4.88811	+	3.55142i	−0.763395	+	0.554639i	−0.899950	−	0.435994i	$-0.856397\pi$
$41$	−4.88811	+	3.55142i	−0.763395	+	0.554639i	0.136555	+	0.990633i	$0.456397\pi$
$42$		0			0
$43$	−7.09299			−1.08167			−0.540836	−	0.841128i	$-0.681892\pi$
$43$	−7.09299			−1.08167			−0.540836	+	0.841128i	$0.681892\pi$
$44$	11.2245	−	11.1429i	1.69215	−	1.67985i
$45$		0			0
$46$	1.30350	−	4.01177i	0.192191	−	0.591503i
$47$	−4.63580	+	3.36810i	−0.676200	+	0.491288i	−0.872095	−	0.489337i	$-0.837239\pi$
$47$	−4.63580	+	3.36810i	−0.676200	+	0.491288i	0.195895	+	0.980625i	$0.437239\pi$
$48$		0			0
$49$	0.980730	+	3.01838i	0.140104	+	0.431196i
$50$	−0.634302	−	1.95218i	−0.0897039	−	0.276080i
$51$		0			0
$52$	5.37751	−	3.90699i	0.745727	−	0.541802i
$53$	−0.146386	+	0.450530i	−0.0201077	+	0.0618850i	−0.960607	−	0.277911i	$-0.910358\pi$
$53$	−0.146386	+	0.450530i	−0.0201077	+	0.0618850i	0.940499	+	0.339796i	$0.110358\pi$
$54$		0			0
$55$	6.72603	−	1.04016i	0.906937	−	0.140256i
$56$	22.9764			3.07035
$57$		0			0
$58$	−19.3700	+	14.0731i	−2.54341	+	1.84789i
$59$	−1.24947	−	0.907796i	−0.162668	−	0.118185i	0.503473	−	0.864011i	$-0.332055\pi$
$59$	−1.24947	−	0.907796i	−0.162668	−	0.118185i	−0.666141	+	0.745826i	$0.732055\pi$
$60$		0			0
$61$	2.90164	+	8.93034i	0.371518	+	1.14341i	0.945798	+	0.324755i	$0.105282\pi$
$61$	2.90164	+	8.93034i	0.371518	+	1.14341i	−0.574281	+	0.818659i	$0.694718\pi$
$62$	−14.9770	−	10.8814i	−1.90208	−	1.38194i
$63$		0			0
$64$	1.98007	−	6.09404i	0.247509	−	0.761754i
$65$	2.86030			0.354777
$66$		0			0
$67$	7.39729			0.903723			0.451861	−	0.892088i	$-0.350760\pi$
$67$	7.39729			0.903723			0.451861	+	0.892088i	$0.350760\pi$
$68$	1.99092	−	6.12742i	0.241435	−	0.743059i
$69$		0			0
$70$	13.7767	+	10.0094i	1.64664	+	1.19635i
$71$	−0.485314	−	1.49364i	−0.0575962	−	0.177263i	0.918119	−	0.396304i	$-0.129707\pi$
$71$	−0.485314	−	1.49364i	−0.0575962	−	0.177263i	−0.975716	+	0.219041i	$0.929707\pi$
$72$		0			0
$73$	−7.78114	−	5.65333i	−0.910713	−	0.661672i	0.0304819	−	0.999535i	$-0.490296\pi$
$73$	−7.78114	−	5.65333i	−0.910713	−	0.661672i	−0.941195	+	0.337863i	$0.890296\pi$
$74$	1.57691	−	1.14569i	0.183312	−	0.133184i
$75$		0			0
$76$	−12.7033			−1.45717
$77$	7.50757	−	7.45300i	0.855567	−	0.849348i
$78$		0			0
$79$	0.714495	−	2.19899i	0.0803869	−	0.247406i	−0.902784	−	0.430095i	$-0.858480\pi$
$79$	0.714495	−	2.19899i	0.0803869	−	0.247406i	0.983171	+	0.182689i	$0.0584802\pi$
$80$	15.2796	−	11.1013i	1.70831	−	1.24116i
$81$		0			0
$82$	4.85759	+	14.9501i	0.536431	+	1.65097i
$83$	2.35615	+	7.25149i	0.258621	+	0.795955i	0.993095	+	0.117317i	$0.0374294\pi$
$83$	2.35615	+	7.25149i	0.258621	+	0.795955i	−0.734473	+	0.678638i	$0.762571\pi$
$84$		0			0
$85$	2.24294	−	1.62959i	0.243281	−	0.176754i
$86$	−5.70252	+	17.5506i	−0.614919	+	1.89252i
$87$		0			0
$88$	−10.7687	−	21.3266i	−1.14794	−	2.27343i
$89$	−14.6343			−1.55124			−0.775619	−	0.631202i	$-0.782562\pi$
$89$	−14.6343			−1.55124			−0.775619	+	0.631202i	$0.782562\pi$
$90$		0			0
$91$	3.59679	−	2.61322i	0.377046	−	0.273940i
$92$	−6.25516	−	4.54464i	−0.652146	−	0.473812i
$93$		0			0
$94$	4.60685	+	14.1784i	0.475160	+	1.46239i
$95$	−4.42245	−	3.21310i	−0.453733	−	0.329657i
$96$		0			0
$97$	2.14060	−	6.58808i	0.217345	−	0.668918i	−0.781634	−	0.623737i	$-0.785614\pi$
$97$	2.14060	−	6.58808i	0.217345	−	0.668918i	0.998979	−	0.0451811i	$-0.0143865\pi$
$98$	8.25699			0.834082
$99$		0			0
$100$	−3.76240			−0.376240
$101$	−0.430165	+	1.32391i	−0.0428030	+	0.131734i	−0.970174	−	0.242408i	$-0.922063\pi$
$101$	−0.430165	+	1.32391i	−0.0428030	+	0.131734i	0.927371	+	0.374142i	$0.122063\pi$
$102$		0			0
$103$	−8.98367	−	6.52702i	−0.885187	−	0.643126i	0.0494316	−	0.998778i	$-0.484259\pi$
$103$	−8.98367	−	6.52702i	−0.885187	−	0.643126i	−0.934619	+	0.355651i	$0.884259\pi$
$104$	−3.10271	−	9.54916i	−0.304246	−	0.936373i
$105$		0			0
$106$	0.997080	+	0.724421i	0.0968449	+	0.0703620i
$107$	9.39767	−	6.82781i	0.908507	−	0.660069i	−0.0321295	−	0.999484i	$-0.510229\pi$
$107$	9.39767	−	6.82781i	0.908507	−	0.660069i	0.940637	+	0.339414i	$0.110229\pi$
$108$		0			0
$109$	−8.56778			−0.820645			−0.410322	−	0.911941i	$-0.634584\pi$
$109$	−8.56778			−0.820645			−0.410322	+	0.911941i	$0.634584\pi$
$110$	2.83376	−	17.4788i	0.270188	−	1.66654i
$111$		0			0
$112$	9.07154	−	27.9193i	0.857180	−	2.63813i
$113$	−11.1854	+	8.12666i	−1.05223	+	0.764491i	−0.972636	−	0.232336i	$-0.925363\pi$
$113$	−11.1854	+	8.12666i	−1.05223	+	0.764491i	−0.0795965	+	0.996827i	$0.525363\pi$
$114$		0			0
$115$	−1.02814	−	3.16428i	−0.0958744	−	0.295071i
$116$	13.5615	+	41.7379i	1.25915	+	3.87526i
$117$		0			0
$118$	−3.25074	+	2.36180i	−0.299255	+	0.217421i
$119$	1.33164	−	4.09837i	0.122071	−	0.375697i
$120$		0			0
$121$	−10.4365	−	3.47541i	−0.948777	−	0.315947i
$122$	24.4296			2.21175
$123$		0			0
$124$	−27.4521	+	19.9451i	−2.46527	+	1.79113i
$125$	−9.61066	−	6.98255i	−0.859603	−	0.624538i
$126$		0			0
$127$	−3.34643	−	10.2992i	−0.296947	−	0.913910i	−0.982560	−	0.185944i	$-0.940466\pi$
$127$	−3.34643	−	10.2992i	−0.296947	−	0.913910i	0.685613	−	0.727966i	$-0.259534\pi$
$128$	1.94595	+	1.41382i	0.171999	+	0.124965i
$129$		0			0
$130$	2.29958	−	7.07738i	0.201687	−	0.620728i
$131$	5.90263			0.515715			0.257857	−	0.966183i	$-0.416984\pi$
$131$	5.90263			0.515715			0.257857	+	0.966183i	$0.416984\pi$
$132$		0			0
$133$	−8.49670			−0.736757
$134$	5.94716	−	18.3035i	0.513757	−	1.58118i
$135$		0			0
$136$	−7.87344	−	5.72039i	−0.675142	−	0.490519i
$137$	−0.363812	−	1.11970i	−0.0310826	−	0.0956623i	0.934312	−	0.356457i	$-0.116015\pi$
$137$	−0.363812	−	1.11970i	−0.0310826	−	0.0956623i	−0.965394	+	0.260795i	$0.916015\pi$
$138$		0			0
$139$	−2.21011	−	1.60574i	−0.187459	−	0.136197i	0.490098	−	0.871667i	$-0.336961\pi$
$139$	−2.21011	−	1.60574i	−0.187459	−	0.136197i	−0.677557	+	0.735471i	$0.736961\pi$
$140$	25.2521	−	18.3467i	2.13419	−	1.55058i
$141$		0			0
$142$	−4.08598			−0.342887
$143$	−4.11134	−	2.11376i	−0.343808	−	0.176761i
$144$		0			0
$145$	−5.83572	+	17.9605i	−0.484630	+	1.49154i
$146$	−20.2441	+	14.7082i	−1.67541	+	1.21726i
$147$		0			0
$148$	−1.10403	−	3.39787i	−0.0907510	−	0.279303i
$149$	−1.38478	−	4.26190i	−0.113445	−	0.349149i	0.878174	−	0.478341i	$-0.158762\pi$
$149$	−1.38478	−	4.26190i	−0.113445	−	0.349149i	−0.991620	+	0.129192i	$0.958762\pi$
$150$		0			0
$151$	18.2104	−	13.2306i	1.48194	−	1.07669i	0.505016	−	0.863110i	$-0.331487\pi$
$151$	18.2104	−	13.2306i	1.48194	−	1.07669i	0.976925	−	0.213583i	$-0.0685133\pi$
$152$	−5.92973	+	18.2498i	−0.480964	+	1.48026i
$153$		0			0
$154$	−12.4055	−	24.5683i	−0.999664	−	1.97977i
$155$	−14.6018			−1.17284
$156$		0			0
$157$	13.8219	−	10.0422i	1.10311	−	0.801455i	0.121544	−	0.992586i	$-0.461216\pi$
$157$	13.8219	−	10.0422i	1.10311	−	0.801455i	0.981564	+	0.191131i	$0.0612156\pi$
$158$	−4.86664	−	3.53582i	−0.387169	−	0.281295i
$159$		0			0
$160$	−6.04831	−	18.6148i	−0.478161	−	1.47163i
$161$	−4.18381	−	3.03972i	−0.329730	−	0.239563i
$162$		0			0
$163$	5.85270	−	18.0128i	0.458419	−	1.41087i	−0.408655	−	0.912689i	$-0.634002\pi$
$163$	5.85270	−	18.0128i	0.458419	−	1.41087i	0.867074	−	0.498179i	$-0.165998\pi$
$164$	28.8131			2.24993
$165$		0			0
$166$	19.8370			1.53965
$167$	1.53637	−	4.72848i	0.118888	−	0.365900i	−0.873850	−	0.486196i	$-0.838384\pi$
$167$	1.53637	−	4.72848i	0.118888	−	0.365900i	0.992738	+	0.120295i	$0.0383842\pi$
$168$		0			0
$169$	8.94544	+	6.49924i	0.688111	+	0.499942i
$170$	−2.22893	−	6.85995i	−0.170951	−	0.526134i
$171$		0			0
$172$	27.3649	+	19.8818i	2.08655	+	1.51597i
$173$	11.5152	−	8.36630i	0.875486	−	0.636078i	−0.0565670	−	0.998399i	$-0.518015\pi$
$173$	11.5152	−	8.36630i	0.875486	−	0.636078i	0.932054	+	0.362321i	$0.118015\pi$
$174$		0			0
$175$	−2.51651			−0.190230
$176$	−30.1664	+	4.66516i	−2.27388	+	0.351650i
$177$		0			0
$178$	−11.7655	+	36.2105i	−0.881862	+	2.71409i
$179$	−6.36958	+	4.62777i	−0.476085	+	0.345896i	−0.799808	−	0.600256i	$-0.795065\pi$
$179$	−6.36958	+	4.62777i	−0.476085	+	0.345896i	0.323723	+	0.946152i	$0.395065\pi$
$180$		0			0
$181$	−4.43645	−	13.6540i	−0.329759	−	1.01489i	−0.969246	−	0.246092i	$-0.920853\pi$
$181$	−4.43645	−	13.6540i	−0.329759	−	1.01489i	0.639488	−	0.768801i	$-0.279147\pi$
$182$	−3.57433	−	11.0006i	−0.264947	−	0.815422i
$183$		0			0
$184$	−9.44874	+	6.86491i	−0.696571	+	0.506088i
$185$	0.475084	−	1.46216i	0.0349288	−	0.107500i
$186$		0			0
$187$	−4.42822	+	0.684814i	−0.323824	+	0.0500786i
$188$	27.3258			1.99294
$189$		0			0
$190$	−11.5058	+	8.35947i	−0.834720	+	0.606459i
$191$	−10.0948	−	7.33430i	−0.730434	−	0.530691i	0.159267	−	0.987236i	$-0.449087\pi$
$191$	−10.0948	−	7.33430i	−0.730434	−	0.530691i	−0.889701	+	0.456545i	$0.849087\pi$
$192$		0			0
$193$	−1.74259	−	5.36315i	−0.125435	−	0.386048i	0.868545	−	0.495610i	$-0.165055\pi$
$193$	−1.74259	−	5.36315i	−0.125435	−	0.386048i	−0.993980	+	0.109561i	$0.965055\pi$
$194$	−14.5803	−	10.5932i	−1.04680	−	0.760546i
$195$		0			0
$196$	4.67687	−	14.3939i	0.334062	−	1.02814i
$197$	1.45201			0.103451			0.0517257	−	0.998661i	$-0.483528\pi$
$197$	1.45201			0.103451			0.0517257	+	0.998661i	$0.483528\pi$
$198$		0			0
$199$	26.2193			1.85864			0.929319	−	0.369278i	$-0.120395\pi$
$199$	26.2193			1.85864			0.929319	+	0.369278i	$0.120395\pi$
$200$	−1.75624	+	5.40514i	−0.124185	+	0.382201i
$201$		0			0
$202$	2.92998	+	2.12876i	0.206153	+	0.149779i
$203$	9.07068	+	27.9167i	0.636637	+	1.95937i
$204$		0			0
$205$	10.0308	+	7.28780i	0.700581	+	0.509002i
$206$	−23.3727	+	16.9812i	−1.62845	+	1.18314i
$207$		0			0
$208$	−12.8285			−0.889497
$209$	3.98227	+	7.88663i	0.275459	+	0.545529i
$210$		0			0
$211$	−1.97600	+	6.08151i	−0.136034	+	0.418669i	−0.995749	−	0.0921042i	$-0.970641\pi$
$211$	−1.97600	+	6.08151i	−0.136034	+	0.418669i	0.859716	+	0.510773i	$0.170641\pi$
$212$	1.82760	−	1.32783i	0.125520	−	0.0911957i
$213$		0			0
$214$	−9.33899	−	28.7425i	−0.638400	−	1.96479i
$215$	4.49786	+	13.8430i	0.306752	+	0.944085i
$216$		0			0
$217$	−18.3615	+	13.3404i	−1.24646	+	0.905608i
$218$	−6.88820	+	21.1997i	−0.466528	+	1.43582i
$219$		0			0
$220$	−28.8647	−	14.8402i	−1.94606	−	1.00052i
$221$	−1.88314			−0.126674
$222$		0			0
$223$	13.8717	−	10.0784i	0.928919	−	0.674899i	−0.0168086	−	0.999859i	$-0.505351\pi$
$223$	13.8717	−	10.0784i	0.928919	−	0.674899i	0.945728	+	0.324959i	$0.105351\pi$
$224$	−24.6125	−	17.8820i	−1.64449	−	1.19479i
$225$		0			0
$226$	11.1155	+	34.2101i	0.739394	+	2.27562i
$227$	4.39674	+	3.19442i	0.291822	+	0.212021i	0.724057	−	0.689740i	$-0.242275\pi$
$227$	4.39674	+	3.19442i	0.291822	+	0.212021i	−0.432235	+	0.901761i	$0.642275\pi$
$228$		0			0
$229$	−4.47837	+	13.7830i	−0.295939	+	0.910807i	0.686965	+	0.726690i	$0.258942\pi$
$229$	−4.47837	+	13.7830i	−0.295939	+	0.910807i	−0.982904	+	0.184116i	$0.941058\pi$
$230$	−8.65613			−0.570768
$231$		0			0
$232$	66.2917			4.35227
$233$	−0.347544	+	1.06963i	−0.0227684	+	0.0700739i	−0.961795	−	0.273770i	$-0.911729\pi$
$233$	−0.347544	+	1.06963i	−0.0227684	+	0.0700739i	0.939027	+	0.343844i	$0.111729\pi$
$234$		0			0
$235$	9.51303	+	6.91162i	0.620561	+	0.450864i
$236$	2.27593	+	7.00459i	0.148150	+	0.455960i
$237$		0			0
$238$	−9.07021	−	6.58989i	−0.587934	−	0.427159i
$239$	−17.7904	+	12.9255i	−1.15077	+	0.836081i	−0.988583	−	0.150679i	$-0.951854\pi$
$239$	−17.7904	+	12.9255i	−1.15077	+	0.836081i	−0.162185	+	0.986760i	$0.551854\pi$
$240$		0			0
$241$	−11.1626			−0.719045			−0.359522	−	0.933136i	$-0.617060\pi$
$241$	−11.1626			−0.719045			−0.359522	+	0.933136i	$0.617060\pi$
$242$	−16.9900	+	23.0296i	−1.09216	+	1.48040i
$243$		0			0
$244$	13.8373	−	42.5868i	0.885841	−	2.72634i
$245$	5.26889	−	3.82807i	0.336617	−	0.244566i
$246$		0			0
$247$	1.14739	+	3.53130i	0.0730066	+	0.224691i
$248$	15.8393	+	48.7484i	1.00580	+	3.09552i
$249$		0			0
$250$	−25.0039	+	18.1664i	−1.58139	+	1.14894i
$251$	4.12725	−	12.7024i	0.260510	−	0.801767i	−0.732184	−	0.681107i	$-0.761499\pi$
$251$	4.12725	−	12.7024i	0.260510	−	0.801767i	0.992694	−	0.120660i	$-0.0385012\pi$
$252$		0			0
$253$	−0.860575	+	5.30808i	−0.0541039	+	0.333716i
$254$	−28.1743			−1.76781
$255$		0			0
$256$	15.4305	−	11.2109i	0.964409	−	0.700684i
$257$	−10.1064	−	7.34273i	−0.630420	−	0.458027i	0.226126	−	0.974098i	$-0.427394\pi$
$257$	−10.1064	−	7.34273i	−0.630420	−	0.458027i	−0.856546	+	0.516071i	$0.827394\pi$
$258$		0			0
$259$	−0.738440	−	2.27269i	−0.0458844	−	0.141218i
$260$	−11.0351	−	8.01746i	−0.684367	−	0.497222i
$261$		0			0
$262$	4.74551	−	14.6052i	0.293178	−	0.902310i
$263$	−5.32035			−0.328067			−0.164033	−	0.986455i	$-0.552450\pi$
$263$	−5.32035			−0.328067			−0.164033	+	0.986455i	$0.552450\pi$
$264$		0			0
$265$	0.972101			0.0597157
$266$	−6.83105	+	21.0238i	−0.418839	+	1.28905i
$267$		0			0
$268$	−28.5389	−	20.7347i	−1.74329	−	1.26657i
$269$	2.64157	+	8.12991i	0.161059	+	0.495690i	0.998724	−	0.0504948i	$-0.0160798\pi$
$269$	2.64157	+	8.12991i	0.161059	+	0.495690i	−0.837665	+	0.546184i	$0.816080\pi$
$270$		0			0
$271$	6.05238	+	4.39731i	0.367656	+	0.267117i	0.756238	−	0.654296i	$-0.227035\pi$
$271$	6.05238	+	4.39731i	0.367656	+	0.267117i	−0.388582	+	0.921414i	$0.627035\pi$
$272$	−10.0596	+	7.30875i	−0.609955	+	0.443158i
$273$		0			0
$274$	−3.06302			−0.185044
$275$	1.17945	+	2.33582i	0.0711234	+	0.140855i
$276$		0			0
$277$	3.95120	−	12.1606i	0.237405	−	0.730657i	−0.759388	−	0.650637i	$-0.774502\pi$
$277$	3.95120	−	12.1606i	0.237405	−	0.730657i	0.996793	−	0.0800194i	$-0.0254982\pi$
$278$	−5.75000	+	4.17762i	−0.344862	+	0.250557i
$279$		0			0
$280$	−14.5700	−	44.8417i	−0.870721	−	2.67980i
$281$	6.42591	+	19.7769i	0.383338	+	1.17979i	0.937679	+	0.347502i	$0.112970\pi$
$281$	6.42591	+	19.7769i	0.383338	+	1.17979i	−0.554342	+	0.832289i	$0.687030\pi$
$282$		0			0
$283$	−10.1490	+	7.37369i	−0.603296	+	0.438320i	−0.847047	−	0.531518i	$-0.821622\pi$
$283$	−10.1490	+	7.37369i	−0.603296	+	0.438320i	0.243751	+	0.969838i	$0.421622\pi$
$284$	−2.31435	+	7.12285i	−0.137332	+	0.422663i
$285$		0			0
$286$	−8.53556	+	8.47352i	−0.504718	+	0.501049i
$287$	19.2718			1.13758
$288$		0			0
$289$	12.2766	−	8.91947i	0.722153	−	0.524675i
$290$	39.7488	+	28.8792i	2.33413	+	1.69585i
$291$		0			0
$292$	14.1734	+	43.6213i	0.829436	+	2.55274i
$293$	−12.9510	−	9.40943i	−0.756604	−	0.549705i	0.141263	−	0.989972i	$-0.454884\pi$
$293$	−12.9510	−	9.40943i	−0.756604	−	0.549705i	−0.897867	+	0.440267i	$0.854884\pi$
$294$		0			0
$295$	−0.979369	+	3.01419i	−0.0570211	+	0.175493i
$296$	−5.39679			−0.313682
$297$		0			0
$298$	−11.6588			−0.675374
$299$	−0.698352	+	2.14931i	−0.0403867	+	0.124298i
$300$		0			0
$301$	18.3032	+	13.2980i	1.05498	+	0.766487i
$302$	−18.0967	−	55.6959i	−1.04135	−	3.20494i
$303$		0			0
$304$	19.8348	+	14.4108i	1.13760	+	0.826517i
$305$	15.5888	−	11.3260i	0.892614	−	0.648522i
$306$		0			0
$307$	−22.5571			−1.28740			−0.643702	−	0.765276i	$-0.722602\pi$
$307$	−22.5571			−1.28740			−0.643702	+	0.765276i	$0.722602\pi$
$308$	−49.8552	+	7.70998i	−2.84076	+	0.439317i
$309$		0			0
$310$	−11.7393	+	36.1300i	−0.666749	+	2.05204i
$311$	23.2510	−	16.8928i	1.31844	−	0.957903i	0.318490	−	0.947926i	$-0.396824\pi$
$311$	23.2510	−	16.8928i	1.31844	−	0.957903i	0.999950	−	0.00997719i	$-0.00317589\pi$
$312$		0			0
$313$	−7.64901	−	23.5412i	−0.432348	−	1.33063i	−0.895780	−	0.444497i	$-0.853382\pi$
$313$	−7.64901	−	23.5412i	−0.432348	−	1.33063i	0.463432	−	0.886132i	$-0.346618\pi$
$314$	−13.7356	−	42.2738i	−0.775144	−	2.38565i
$315$		0			0
$316$	−8.92032	+	6.48099i	−0.501807	+	0.364584i
$317$	8.16612	−	25.1327i	0.458655	−	1.41160i	−0.408134	−	0.912922i	$-0.633821\pi$
$317$	8.16612	−	25.1327i	0.458655	−	1.41160i	0.866790	−	0.498674i	$-0.166179\pi$
$318$		0			0
$319$	21.6609	−	21.5035i	1.21278	−	1.20396i
$320$	−13.1490			−0.735052
$321$		0			0
$322$	−10.8850	+	7.90839i	−0.606595	+	0.440717i
$323$	2.91161	+	2.11541i	0.162006	+	0.117705i
$324$		0			0
$325$	0.339828	+	1.04588i	0.0188502	+	0.0580151i
$326$	−39.8645	−	28.9633i	−2.20789	−	1.60413i
$327$		0			0
$328$	13.4495	−	41.3935i	0.742627	−	2.28557i
$329$	18.2771			1.00765
$330$		0			0
$331$	−26.1233			−1.43587			−0.717934	−	0.696111i	$-0.754912\pi$
$331$	−26.1233			−1.43587			−0.717934	+	0.696111i	$0.754912\pi$
$332$	11.2360	−	34.5807i	0.616653	−	1.89786i
$333$		0			0
$334$	−10.4647	−	7.60306i	−0.572604	−	0.416021i
$335$	−4.69083	−	14.4369i	−0.256287	−	0.788771i
$336$		0			0
$337$	−1.23753	−	0.899118i	−0.0674126	−	0.0489781i	0.553569	−	0.832804i	$-0.313266\pi$
$337$	−1.23753	−	0.899118i	−0.0674126	−	0.0489781i	−0.620981	+	0.783825i	$0.713266\pi$
$338$	23.2732	−	16.9090i	1.26590	−	0.919728i
$339$		0			0
$340$	−13.2210			−0.717012
$341$	20.9884	+	10.7907i	1.13658	+	0.584350i
$342$		0			0
$343$	−3.77138	+	11.6071i	−0.203635	+	0.626725i
$344$	41.3361	−	30.0324i	2.22869	−	1.61924i
$345$		0			0
$346$	−11.4433	−	35.2189i	−0.615197	−	1.89338i
$347$	−5.59552	−	17.2212i	−0.300383	−	0.924484i	−0.981360	−	0.192179i	$-0.938444\pi$
$347$	−5.59552	−	17.2212i	−0.300383	−	0.924484i	0.680977	−	0.732305i	$-0.261556\pi$
$348$		0			0
$349$	−10.0344	+	7.29041i	−0.537128	+	0.390247i	−0.823017	−	0.568016i	$-0.807711\pi$
$349$	−10.0344	+	7.29041i	−0.537128	+	0.390247i	0.285889	+	0.958263i	$0.407711\pi$
$350$	−2.02319	+	6.22673i	−0.108144	+	0.332833i
$351$		0			0
$352$	−5.06258	+	31.2263i	−0.269836	+	1.66437i
$353$	26.5886			1.41517			0.707585	−	0.706628i	$-0.249784\pi$
$353$	26.5886			1.41517			0.707585	+	0.706628i	$0.249784\pi$
$354$		0			0
$355$	−2.60731	+	1.89432i	−0.138382	+	0.100540i
$356$	56.4595	+	41.0203i	2.99235	+	2.17407i
$357$		0			0
$358$	6.32981	+	19.4811i	0.334541	+	1.02961i
$359$	21.8909	+	15.9047i	1.15536	+	0.839417i	0.989184	−	0.146679i	$-0.0468586\pi$
$359$	21.8909	+	15.9047i	1.15536	+	0.839417i	0.166174	+	0.986096i	$0.446859\pi$
$360$		0			0
$361$	−3.67850	+	11.3213i	−0.193605	+	0.595856i
$362$	−37.3515			−1.96315
$363$		0			0
$364$	−21.2013			−1.11125
$365$	−6.09905	+	18.7709i	−0.319239	+	0.982516i
$366$		0			0
$367$	8.13873	+	5.91314i	0.424838	+	0.308663i	0.779582	−	0.626301i	$-0.215432\pi$
$367$	8.13873	+	5.91314i	0.424838	+	0.308663i	−0.354743	+	0.934964i	$0.615432\pi$
$368$	4.61122	+	14.1919i	0.240377	+	0.739803i
$369$		0			0
$370$	−3.23594	−	2.35105i	−0.168228	−	0.122225i
$371$	1.22240	−	0.888128i	0.0634640	−	0.0461093i
$372$		0			0
$373$	−21.4066			−1.10839			−0.554195	−	0.832387i	$-0.686974\pi$
$373$	−21.4066			−1.10839			−0.554195	+	0.832387i	$0.686974\pi$
$374$	−1.86567	+	11.5075i	−0.0964713	+	0.595041i
$375$		0			0
$376$	12.7553	−	39.2568i	0.657805	−	2.02451i
$377$	10.3775	−	7.53969i	0.534468	−	0.388314i
$378$		0			0
$379$	5.03684	+	15.5018i	0.258725	+	0.796274i	0.993073	+	0.117501i	$0.0374882\pi$
$379$	5.03684	+	15.5018i	0.258725	+	0.796274i	−0.734348	+	0.678774i	$0.762512\pi$
$380$	8.05552	+	24.7923i	0.413240	+	1.27182i
$381$		0			0
$382$	−26.2635	+	19.0815i	−1.34376	+	0.976296i
$383$	4.92963	−	15.1718i	0.251892	−	0.775245i	−0.742534	−	0.669809i	$-0.766376\pi$
$383$	4.92963	−	15.1718i	0.251892	−	0.775245i	0.994426	−	0.105436i	$-0.0336239\pi$
$384$		0			0
$385$	−19.3064	−	9.92595i	−0.983943	−	0.505873i
$386$	−14.6713			−0.746750
$387$		0			0
$388$	−26.7249	+	19.4168i	−1.35675	+	0.985739i
$389$	19.7466	+	14.3468i	1.00119	+	0.727410i	0.962344	−	0.271836i	$-0.0876307\pi$
$389$	19.7466	+	14.3468i	1.00119	+	0.727410i	0.0388496	+	0.999245i	$0.487631\pi$
$390$		0			0
$391$	0.676897	+	2.08327i	0.0342321	+	0.105356i
$392$	−18.4955	−	13.4378i	−0.934164	−	0.678710i
$393$		0			0
$394$	1.16736	−	3.59278i	0.0588110	−	0.181002i
$395$	−4.74472			−0.238733
$396$		0			0
$397$	0.870040			0.0436661			0.0218330	−	0.999762i	$-0.493050\pi$
$397$	0.870040			0.0436661			0.0218330	+	0.999762i	$0.493050\pi$
$398$	21.0794	−	64.8758i	1.05662	−	3.25193i
$399$		0			0
$400$	5.87456	+	4.26812i	0.293728	+	0.213406i
$401$	10.8964	+	33.5357i	0.544140	+	1.67469i	0.723026	+	0.690821i	$0.242751\pi$
$401$	10.8964	+	33.5357i	0.544140	+	1.67469i	−0.178886	+	0.983870i	$0.557249\pi$
$402$		0			0
$403$	8.02393	+	5.82972i	0.399700	+	0.290399i
$404$	5.37052	−	3.90191i	0.267194	−	0.194127i
$405$		0			0
$406$	76.3681			3.79009
$407$	−1.76341	+	1.75059i	−0.0874089	+	0.0867736i
$408$		0			0
$409$	2.08479	−	6.41632i	0.103086	−	0.317266i	−0.886190	−	0.463321i	$-0.846658\pi$
$409$	2.08479	−	6.41632i	0.103086	−	0.317266i	0.989276	+	0.146055i	$0.0466576\pi$
$410$	26.0970	−	18.9606i	1.28884	−	0.936396i
$411$		0			0
$412$	16.3638	+	50.3627i	0.806188	+	2.48119i
$413$	1.52227	+	4.68507i	0.0749060	+	0.230537i
$414$		0			0
$415$	12.6582	−	9.19674i	0.621368	−	0.451450i
$416$	−4.10825	+	12.6439i	−0.201424	+	0.619919i
$417$		0			0
$418$	22.7159	−	3.51296i	1.11107	−	0.171824i
$419$	−0.959337			−0.0468667			−0.0234333	−	0.999725i	$-0.507460\pi$
$419$	−0.959337			−0.0468667			−0.0234333	+	0.999725i	$0.507460\pi$
$420$		0			0
$421$	5.85105	−	4.25103i	0.285163	−	0.207183i	−0.436004	−	0.899945i	$-0.643606\pi$
$421$	5.85105	−	4.25103i	0.285163	−	0.207183i	0.721166	+	0.692762i	$0.243606\pi$
$422$	13.4592	+	9.77865i	0.655182	+	0.476017i
$423$		0			0
$424$	−1.05449	−	3.24538i	−0.0512104	−	0.157610i
$425$	0.862347	+	0.626531i	0.0418300	+	0.0303912i
$426$		0			0
$427$	9.25516	−	28.4845i	0.447889	−	1.37846i
$428$	−55.3948			−2.67761
$429$		0			0
$430$	37.8686			1.82618
$431$	5.84066	−	17.9757i	0.281335	−	0.865859i	−0.706139	−	0.708074i	$-0.749565\pi$
$431$	5.84066	−	17.9757i	0.281335	−	0.865859i	0.987473	−	0.157786i	$-0.0504355\pi$
$432$		0			0
$433$	−13.3772	−	9.71907i	−0.642865	−	0.467069i	0.217968	−	0.975956i	$-0.430057\pi$
$433$	−13.3772	−	9.71907i	−0.642865	−	0.467069i	−0.860833	+	0.508887i	$0.830057\pi$
$434$	18.2469	+	56.1581i	0.875879	+	2.69568i
$435$		0			0
$436$	33.0546	+	24.0156i	1.58303	+	1.15014i
$437$	3.49416	−	2.53866i	0.167148	−	0.121440i
$438$		0			0
$439$	17.3201			0.826646			0.413323	−	0.910585i	$-0.364368\pi$
$439$	17.3201			0.826646			0.413323	+	0.910585i	$0.364368\pi$
$440$	−34.7933	+	34.5404i	−1.65871	+	1.64665i
$441$		0			0
$442$	−1.51398	+	4.65955i	−0.0720126	+	0.221632i
$443$	19.5207	−	14.1826i	0.927454	−	0.673835i	−0.0179138	−	0.999840i	$-0.505702\pi$
$443$	19.5207	−	14.1826i	0.927454	−	0.673835i	0.945368	+	0.326004i	$0.105702\pi$
$444$		0			0
$445$	9.28004	+	28.5610i	0.439916	+	1.35392i
$446$	−13.7851	−	42.4262i	−0.652744	−	2.00894i
$447$		0			0
$448$	−16.5347	+	12.0132i	−0.781190	+	0.567568i
$449$	−1.85589	+	5.71185i	−0.0875850	+	0.269559i	−0.985250	−	0.171119i	$-0.945262\pi$
$449$	−1.85589	+	5.71185i	−0.0875850	+	0.269559i	0.897665	+	0.440678i	$0.145262\pi$
$450$		0			0
$451$	−9.03241	−	17.8881i	−0.425320	−	0.842318i
$452$	65.9325			3.10120
$453$		0			0
$454$	11.4389	−	8.31088i	0.536856	−	0.390049i
$455$	−7.38089	−	5.36253i	−0.346022	−	0.251399i
$456$		0			0
$457$	10.0716	+	30.9971i	0.471129	+	1.44998i	0.851108	+	0.524990i	$0.175931\pi$
$457$	10.0716	+	30.9971i	0.471129	+	1.44998i	−0.379980	+	0.924995i	$0.624069\pi$
$458$	30.5035	+	22.1621i	1.42534	+	1.03557i
$459$		0			0
$460$	−4.90295	+	15.0897i	−0.228601	+	0.703563i
$461$	−5.89362			−0.274493			−0.137247	−	0.990537i	$-0.543825\pi$
$461$	−5.89362			−0.274493			−0.137247	+	0.990537i	$0.543825\pi$
$462$		0			0
$463$	−38.7985			−1.80312			−0.901558	−	0.432657i	$-0.857576\pi$
$463$	−38.7985			−1.80312			−0.901558	+	0.432657i	$0.857576\pi$
$464$	26.1733	−	80.5532i	1.21507	−	3.73959i
$465$		0			0
$466$	2.36723	+	1.71989i	0.109660	+	0.0796725i
$467$	−8.38637	−	25.8106i	−0.388075	−	1.19437i	−0.934225	−	0.356684i	$-0.883907\pi$
$467$	−8.38637	−	25.8106i	−0.388075	−	1.19437i	0.546150	−	0.837687i	$-0.316093\pi$
$468$		0			0
$469$	−19.0884	−	13.8685i	−0.881421	−	0.640390i
$470$	24.7499	−	17.9819i	1.14163	−	0.829441i
$471$		0			0
$472$	11.1253			0.512083
$473$	3.76481	−	23.2216i	0.173106	−	1.06773i
$474$		0			0
$475$	0.649459	−	1.99883i	0.0297992	−	0.0917126i
$476$	−16.6253	+	12.0790i	−0.762018	+	0.553639i
$477$		0			0
$478$	17.6793	+	54.4114i	0.808634	+	2.48872i
$479$	−3.16461	−	9.73965i	−0.144595	−	0.445016i	0.852364	−	0.522949i	$-0.175168\pi$
$479$	−3.16461	−	9.73965i	−0.144595	−	0.445016i	−0.996959	+	0.0779326i	$0.975168\pi$
$480$		0			0
$481$	−0.844828	+	0.613804i	−0.0385208	+	0.0279870i
$482$	−8.97432	+	27.6201i	−0.408769	+	1.25806i
$483$		0			0
$484$	30.5227	+	42.6620i	1.38740	+	1.93918i
$485$	−14.2150			−0.645470
$486$		0			0
$487$	19.8547	−	14.4253i	0.899704	−	0.653673i	−0.0386861	−	0.999251i	$-0.512317\pi$
$487$	19.8547	−	14.4253i	0.899704	−	0.653673i	0.938390	+	0.345578i	$0.112317\pi$
$488$	−54.7219	−	39.7578i	−2.47714	−	1.79975i
$489$		0			0
$490$	−5.23599	−	16.1147i	−0.236538	−	0.727988i
$491$	33.4428	+	24.2976i	1.50925	+	1.09654i	0.966507	+	0.256639i	$0.0826151\pi$
$491$	33.4428	+	24.2976i	1.50925	+	1.09654i	0.542745	+	0.839897i	$0.317385\pi$
$492$		0			0
$493$	3.84207	−	11.8247i	0.173038	−	0.532557i
$494$	9.66013			0.434630
$495$		0			0
$496$	65.4894			2.94056
$497$	−1.54797	+	4.76417i	−0.0694360	+	0.213702i
$498$		0			0
$499$	31.9812	+	23.2357i	1.43167	+	1.04017i	0.989702	+	0.143144i	$0.0457211\pi$
$499$	31.9812	+	23.2357i	1.43167	+	1.04017i	0.441972	+	0.897029i	$0.354279\pi$
$500$	17.5059	+	53.8776i	0.782887	+	2.40948i
$501$		0			0
$502$	−28.1120	−	20.4245i	−1.25470	−	0.911592i
$503$	−11.6394	+	8.45651i	−0.518975	+	0.377057i	−0.816218	−	0.577745i	$-0.803933\pi$
$503$	−11.6394	+	8.45651i	−0.518975	+	0.377057i	0.297243	+	0.954802i	$0.403933\pi$
$504$		0			0
$505$	2.85658			0.127116
$506$	12.4422	+	6.39687i	0.553122	+	0.284376i
$507$		0			0
$508$	−15.9583	+	49.1147i	−0.708036	+	2.17911i
$509$	−2.20138	+	1.59940i	−0.0975746	+	0.0708921i	−0.635503	−	0.772099i	$-0.719207\pi$
$509$	−2.20138	+	1.59940i	−0.0975746	+	0.0708921i	0.537928	+	0.842991i	$0.319207\pi$
$510$		0			0
$511$	9.47998	+	29.1764i	0.419370	+	1.29069i
$512$	−13.8476	−	42.6186i	−0.611984	−	1.88349i
$513$		0			0
$514$	−26.2937	+	19.1035i	−1.15976	+	0.842618i
$515$	−7.04162	+	21.6719i	−0.310291	+	0.954977i
$516$		0			0
$517$	−8.56617	−	16.9648i	−0.376740	−	0.746109i
$518$	−6.21710			−0.273164
$519$		0			0
$520$	−16.6691	+	12.1108i	−0.730986	+	0.531093i
$521$	−7.70787	−	5.60010i	−0.337688	−	0.245345i	0.405998	−	0.913874i	$-0.366924\pi$
$521$	−7.70787	−	5.60010i	−0.337688	−	0.245345i	−0.743686	+	0.668529i	$0.766924\pi$
$522$		0			0
$523$	2.02097	+	6.21991i	0.0883709	+	0.271978i	0.985469	−	0.169853i	$-0.0543292\pi$
$523$	2.02097	+	6.21991i	0.0883709	+	0.271978i	−0.897099	+	0.441831i	$0.854329\pi$
$524$	−22.7724	−	16.5451i	−0.994818	−	0.722777i
$525$		0			0
$526$	−4.27737	+	13.1644i	−0.186502	+	0.573995i
$527$	9.61340			0.418766
$528$		0			0
$529$	−20.3712			−0.885706
$530$	0.781536	−	2.40532i	0.0339477	−	0.104480i
$531$		0			0
$532$	32.7804	+	23.8164i	1.42121	+	1.03257i
$533$	−2.60246	−	8.00953i	−0.112725	−	0.346931i
$534$		0			0
$535$	−19.2848	−	14.0112i	−0.833754	−	0.605758i
$536$	−43.1094	+	31.3208i	−1.86204	+	1.35285i
$537$		0			0
$538$	22.2400			0.958834
$539$	−10.4023	+	1.60870i	−0.448061	+	0.0692915i
$540$		0			0
$541$	−2.21102	+	6.80483i	−0.0950594	+	0.292563i	−0.987269	−	0.159059i	$-0.949154\pi$
$541$	−2.21102	+	6.80483i	−0.0950594	+	0.292563i	0.892210	+	0.451621i	$0.149154\pi$
$542$	15.7464	−	11.4404i	0.676365	−	0.491408i
$543$		0			0
$544$	3.98204	+	12.2554i	0.170728	+	0.525448i
$545$	5.43307	+	16.7213i	0.232727	+	0.716260i
$546$		0			0
$547$	7.42533	−	5.39482i	0.317484	−	0.230666i	−0.417617	−	0.908623i	$-0.637135\pi$
$547$	7.42533	−	5.39482i	0.317484	−	0.230666i	0.735101	+	0.677957i	$0.237135\pi$
$548$	−1.73494	+	5.33959i	−0.0741128	+	0.228096i
$549$		0			0
$550$	6.72788	−	1.04045i	0.286878	−	0.0443649i
$551$	−24.5148			−1.04437
$552$		0			0
$553$	−5.96642	+	4.33486i	−0.253718	+	0.184337i
$554$	−26.9128	−	19.5533i	−1.14342	−	0.830741i
$555$		0			0
$556$	4.02573	+	12.3899i	0.170729	+	0.525449i
$557$	4.26551	+	3.09907i	0.180735	+	0.131312i	0.674475	−	0.738298i	$-0.264370\pi$
$557$	4.26551	+	3.09907i	0.180735	+	0.131312i	−0.493739	+	0.869610i	$0.664370\pi$
$558$		0			0
$559$	3.05513	−	9.40271i	0.129218	−	0.397692i
$560$	−60.2411			−2.54565
$561$		0			0
$562$	54.1012			2.28212
$563$	10.7237	−	33.0041i	0.451949	−	1.39096i	−0.422731	−	0.906255i	$-0.638929\pi$
$563$	10.7237	−	33.0041i	0.451949	−	1.39096i	0.874680	−	0.484701i	$-0.161071\pi$
$564$		0			0
$565$	22.9533	+	16.6765i	0.965653	+	0.701588i
$566$	10.0856	+	31.0404i	0.423931	+	1.30473i
$567$		0			0
$568$	9.15251	+	6.64969i	0.384031	+	0.279015i
$569$	−17.7171	+	12.8722i	−0.742739	+	0.539632i	−0.893568	−	0.448928i	$-0.851806\pi$
$569$	−17.7171	+	12.8722i	−0.742739	+	0.539632i	0.150829	+	0.988560i	$0.451806\pi$
$570$		0			0
$571$	30.9369			1.29467			0.647335	−	0.762206i	$-0.275884\pi$
$571$	30.9369			1.29467			0.647335	+	0.762206i	$0.275884\pi$
$572$	9.93674	+	19.6791i	0.415476	+	0.822823i
$573$		0			0
$574$	15.4939	−	47.6853i	0.646703	−	1.99035i
$575$	1.03488	−	0.751887i	0.0431576	−	0.0313558i
$576$		0			0
$577$	5.47213	+	16.8415i	0.227808	+	0.701120i	0.997994	+	0.0633014i	$0.0201630\pi$
$577$	5.47213	+	16.8415i	0.227808	+	0.701120i	−0.770187	+	0.637818i	$0.779837\pi$
$578$	−12.1999	−	37.5476i	−0.507451	−	1.56177i
$579$		0			0
$580$	72.8578	−	52.9343i	3.02526	−	2.19798i
$581$	7.51524	−	23.1295i	0.311785	−	0.959575i
$582$		0			0
$583$	−1.39728	−	0.718382i	−0.0578695	−	0.0297523i
$584$	69.2831			2.86695
$585$		0			0
$586$	−33.6944	+	24.4804i	−1.39190	+	1.01128i
$587$	−3.42864	−	2.49105i	−0.141515	−	0.102817i	0.514775	−	0.857325i	$-0.327875\pi$
$587$	−3.42864	−	2.49105i	−0.141515	−	0.102817i	−0.656290	+	0.754508i	$0.727875\pi$
$588$		0			0
$589$	−5.85740	−	18.0272i	−0.241350	−	0.742799i
$590$	6.67078	+	4.84660i	0.274632	+	0.199532i
$591$		0			0
$592$	−2.13076	+	6.55781i	−0.0875738	+	0.269524i
$593$	−47.0032			−1.93019			−0.965095	−	0.261898i	$-0.915652\pi$
$593$	−47.0032			−1.93019			−0.965095	+	0.261898i	$0.915652\pi$
$594$		0			0
$595$	−8.84299			−0.362527
$596$	−6.60368	+	20.3240i	−0.270497	+	0.832505i
$597$		0			0
$598$	4.75669	+	3.45593i	0.194515	+	0.141324i
$599$	0.608483	+	1.87272i	0.0248620	+	0.0765172i	0.962718	−	0.270508i	$-0.0871917\pi$
$599$	0.608483	+	1.87272i	0.0248620	+	0.0765172i	−0.937856	+	0.347025i	$0.887192\pi$
$600$		0			0
$601$	−26.3530	−	19.1466i	−1.07496	−	0.781005i	−0.0981640	−	0.995170i	$-0.531297\pi$
$601$	−26.3530	−	19.1466i	−1.07496	−	0.781005i	−0.976797	+	0.214165i	$0.931297\pi$
$602$	47.6192	−	34.5973i	1.94081	−	1.41008i
$603$		0			0
$604$	−107.342			−4.36767
$605$	−0.164667	+	22.5723i	−0.00669466	+	0.917694i
$606$		0			0
$607$	1.60982	−	4.95452i	0.0653406	−	0.201098i	−0.913056	−	0.407834i	$-0.866284\pi$
$607$	1.60982	−	4.95452i	0.0653406	−	0.201098i	0.978397	+	0.206736i	$0.0662842\pi$
$608$	20.5554	−	14.9344i	0.833632	−	0.605669i
$609$		0			0
$610$	−15.4915	−	47.6779i	−0.627232	−	1.93042i
$611$	−2.46812	−	7.59609i	−0.0998495	−	0.307305i
$612$		0			0
$613$	16.1287	−	11.7182i	0.651430	−	0.473292i	−0.212328	−	0.977199i	$-0.568104\pi$
$613$	16.1287	−	11.7182i	0.651430	−	0.473292i	0.863758	+	0.503907i	$0.168104\pi$
$614$	−18.1352	+	55.8143i	−0.731875	+	2.25248i
$615$		0			0
$616$	−12.1954	+	75.2218i	−0.491366	+	3.03077i
$617$	18.0901			0.728282			0.364141	−	0.931344i	$-0.381363\pi$
$617$	18.0901			0.728282			0.364141	+	0.931344i	$0.381363\pi$
$618$		0			0
$619$	−7.18654	+	5.22132i	−0.288851	+	0.209863i	−0.722769	−	0.691090i	$-0.757131\pi$
$619$	−7.18654	+	5.22132i	−0.288851	+	0.209863i	0.433918	+	0.900953i	$0.357131\pi$
$620$	56.3340	+	40.9290i	2.26243	+	1.64375i
$621$		0			0
$622$	−23.1058	−	71.1122i	−0.926457	−	2.85134i
$623$	37.7634	+	27.4367i	1.51296	+	1.09923i
$624$		0			0
$625$	−6.31405	+	19.4326i	−0.252562	+	0.777306i
$626$	−64.3988			−2.57389
$627$		0			0
$628$	−81.4735			−3.25115
$629$	−0.312781	+	0.962642i	−0.0124714	+	0.0383831i
$630$		0			0
$631$	−5.66972	−	4.11929i	−0.225708	−	0.163986i	0.469184	−	0.883100i	$-0.344548\pi$
$631$	−5.66972	−	4.11929i	−0.225708	−	0.163986i	−0.694892	+	0.719114i	$0.744548\pi$
$632$	5.14684	+	15.8403i	0.204730	+	0.630095i
$633$		0			0
$634$	−55.6219	−	40.4117i	−2.20903	−	1.60495i
$635$	−17.9784	+	13.0621i	−0.713450	+	0.518352i
$636$		0			0
$637$	−4.42369			−0.175273
$638$	−35.7926	−	70.8848i	−1.41704	−	2.80636i
$639$		0			0
$640$	1.52529	−	4.69435i	0.0602922	−	0.185560i
$641$	−6.35136	+	4.61453i	−0.250864	+	0.182263i	−0.706109	−	0.708103i	$-0.749551\pi$
$641$	−6.35136	+	4.61453i	−0.250864	+	0.182263i	0.455246	+	0.890366i	$0.349551\pi$
$642$		0			0
$643$	−1.70773	−	5.25586i	−0.0673464	−	0.207271i	0.911720	−	0.410812i	$-0.134755\pi$
$643$	−1.70773	−	5.25586i	−0.0673464	−	0.207271i	−0.979066	+	0.203541i	$0.934755\pi$
$644$	7.62084	+	23.4545i	0.300303	+	0.924239i
$645$		0			0
$646$	7.57510	−	5.50363i	0.298038	−	0.216538i
$647$	−1.80883	+	5.56701i	−0.0711125	+	0.218862i	−0.980296	−	0.197534i	$-0.936707\pi$
$647$	−1.80883	+	5.56701i	−0.0711125	+	0.218862i	0.909184	+	0.416395i	$0.136707\pi$
$648$		0			0
$649$	3.63521	−	3.60879i	0.142694	−	0.141657i
$650$	2.86109			0.112221
$651$		0			0
$652$	−73.0698	+	53.0883i	−2.86163	+	2.07910i
$653$	2.86049	+	2.07827i	0.111940	+	0.0813288i	0.642347	−	0.766414i	$-0.277961\pi$
$653$	2.86049	+	2.07827i	0.111940	+	0.0813288i	−0.530407	+	0.847743i	$0.677961\pi$
$654$		0			0
$655$	−3.74302	−	11.5198i	−0.146252	−	0.450117i
$656$	−44.9884	−	32.6860i	−1.75650	−	1.27617i
$657$		0			0
$658$	14.6941	−	45.2239i	0.572836	−	1.76301i
$659$	2.23371			0.0870131			0.0435066	−	0.999053i	$-0.486147\pi$
$659$	2.23371			0.0870131			0.0435066	+	0.999053i	$0.486147\pi$
$660$		0			0
$661$	−11.6018			−0.451258			−0.225629	−	0.974213i	$-0.572444\pi$
$661$	−11.6018			−0.451258			−0.225629	+	0.974213i	$0.572444\pi$
$662$	−21.0023	+	64.6383i	−0.816276	+	2.51224i
$663$		0			0
$664$	−44.4345	−	32.2836i	−1.72439	−	1.25285i
$665$	5.38799	+	16.5825i	0.208937	+	0.643043i
$666$		0			0
$667$	−12.0712	−	8.77023i	−0.467398	−	0.339585i
$668$	−19.1813	+	13.9361i	−0.742148	+	0.539202i
$669$		0			0
$670$	−39.4931			−1.52575
$671$	−30.7770	+	4.75959i	−1.18813	+	0.183742i
$672$		0			0
$673$	−14.1154	+	43.4428i	−0.544109	+	1.67460i	0.178989	+	0.983851i	$0.442717\pi$
$673$	−14.1154	+	43.4428i	−0.544109	+	1.67460i	−0.723098	+	0.690745i	$0.757283\pi$
$674$	−3.21966	+	2.33922i	−0.124017	+	0.0901035i
$675$		0			0
$676$	−16.2942	−	50.1484i	−0.626700	−	1.92878i
$677$	−8.06710	−	24.8280i	−0.310044	−	0.954216i	−0.977747	−	0.209789i	$-0.932722\pi$
$677$	−8.06710	−	24.8280i	−0.310044	−	0.954216i	0.667703	−	0.744428i	$-0.267278\pi$
$678$		0			0
$679$	−17.8752	+	12.9871i	−0.685986	+	0.498398i
$680$	−6.17140	+	18.9936i	−0.236662	+	0.728372i
$681$		0			0
$682$	43.5739	−	43.2572i	1.66853	−	1.65640i
$683$	−24.9486			−0.954631			−0.477315	−	0.878732i	$-0.658390\pi$
$683$	−24.9486			−0.954631			−0.477315	+	0.878732i	$0.658390\pi$
$684$		0			0
$685$	−1.95455	+	1.42006i	−0.0746795	+	0.0542579i
$686$	25.6880	+	18.6634i	0.980772	+	0.712573i
$687$		0			0
$688$	−20.1730	−	62.0862i	−0.769089	−	2.36701i
$689$	−0.534186	−	0.388109i	−0.0203509	−	0.0147858i
$690$		0			0
$691$	6.38351	−	19.6464i	0.242840	−	0.747385i	−0.753144	−	0.657856i	$-0.771464\pi$
$691$	6.38351	−	19.6464i	0.242840	−	0.747385i	0.995984	−	0.0895295i	$-0.0285363\pi$
$692$	−67.8768			−2.58029
$693$		0			0
$694$	−47.1100			−1.78827
$695$	−1.73234	+	5.33158i	−0.0657113	+	0.202238i
$696$		0			0
$697$	−6.60399	−	4.79808i	−0.250144	−	0.181740i
$698$	9.97173	+	30.6898i	0.377435	+	1.16163i
$699$		0			0
$700$	9.70873	+	7.05381i	0.366956	+	0.266609i
$701$	−14.4600	+	10.5058i	−0.546148	+	0.396800i	−0.826363	−	0.563138i	$-0.809594\pi$
$701$	−14.4600	+	10.5058i	−0.546148	+	0.396800i	0.280215	+	0.959937i	$0.409594\pi$
$702$		0			0
$703$	1.99574			0.0752708
$704$	18.9001	+	9.71710i	0.712326	+	0.366227i
$705$		0			0
$706$	21.3763	−	65.7896i	0.804509	−	2.47603i
$707$	3.59211	−	2.60982i	0.135095	−	0.0981525i
$708$		0			0
$709$	15.5111	+	47.7382i	0.582530	+	1.79284i	0.608969	+	0.793194i	$0.291583\pi$
$709$	15.5111	+	47.7382i	0.582530	+	1.79284i	−0.0264390	+	0.999650i	$0.508417\pi$
$710$	2.59103	+	7.97437i	0.0972396	+	0.299273i
$711$		0			0
$712$	85.2850	−	61.9632i	3.19619	−	2.32217i
$713$	3.56508	−	10.9722i	0.133513	−	0.410911i
$714$		0			0
$715$	−1.51819	+	9.36427i	−0.0567770	+	0.350204i
$716$	37.5457			1.40315
$717$		0			0
$718$	56.9533	−	41.3790i	2.12548	−	1.54425i
$719$	16.9117	+	12.2871i	0.630701	+	0.458231i	0.856643	−	0.515909i	$-0.172546\pi$
$719$	16.9117	+	12.2871i	0.630701	+	0.458231i	−0.225942	+	0.974141i	$0.572546\pi$
$720$		0			0
$721$	10.9451	+	33.6854i	0.407615	+	1.25451i
$722$	25.0554	+	18.2038i	0.932464	+	0.677475i
$723$		0			0
$724$	−21.1564	+	65.1128i	−0.786272	+	2.41990i
$725$	−7.26067			−0.269654
$726$		0			0
$727$	−17.5420			−0.650596			−0.325298	−	0.945611i	$-0.605465\pi$
$727$	−17.5420			−0.650596			−0.325298	+	0.945611i	$0.605465\pi$
$728$	−9.89649	+	30.4583i	−0.366788	+	1.12886i
$729$		0			0
$730$	41.5425	+	30.1824i	1.53756	+	1.11710i
$731$	−2.96126	−	9.11383i	−0.109526	−	0.337087i
$732$		0			0
$733$	8.32284	+	6.04689i	0.307411	+	0.223347i	0.730785	−	0.682608i	$-0.239154\pi$
$733$	8.32284	+	6.04689i	0.307411	+	0.223347i	−0.423374	+	0.905955i	$0.639154\pi$
$734$	21.1744	−	15.3841i	0.781562	−	0.567838i
$735$		0			0
$736$	15.4644			0.570024
$737$	−3.92633	+	24.2178i	−0.144628	+	0.892075i
$738$		0			0
$739$	−15.4883	+	47.6682i	−0.569748	+	1.75350i	0.0836567	+	0.996495i	$0.473340\pi$
$739$	−15.4883	+	47.6682i	−0.569748	+	1.75350i	−0.653405	+	0.757009i	$0.726660\pi$
$740$	−5.93133	+	4.30936i	−0.218040	+	0.158415i
$741$		0			0
$742$	−1.21477	−	3.73868i	−0.0445956	−	0.137251i
$743$	−0.630744	−	1.94123i	−0.0231398	−	0.0712169i	0.938820	−	0.344409i	$-0.111921\pi$
$743$	−0.630744	−	1.94123i	−0.0231398	−	0.0712169i	−0.961960	+	0.273192i	$0.911921\pi$
$744$		0			0
$745$	−7.43959	+	5.40518i	−0.272566	+	0.198031i
$746$	−17.2101	+	52.9673i	−0.630108	+	1.93927i
$747$		0			0
$748$	19.0037	+	9.77034i	0.694844	+	0.357239i
$749$	−37.0512			−1.35382
$750$		0			0
$751$	27.2802	−	19.8202i	0.995469	−	0.723250i	0.0343569	−	0.999410i	$-0.489062\pi$
$751$	27.2802	−	19.8202i	0.995469	−	0.723250i	0.961112	+	0.276159i	$0.0890617\pi$
$752$	−42.6661	−	30.9988i	−1.55587	−	1.13041i
$753$		0			0
$754$	−10.3127	−	31.7392i	−0.375566	−	1.15587i
$755$	−37.3692	−	27.1503i	−1.36000	−	0.988101i
$756$		0			0
$757$	−8.85943	+	27.2665i	−0.322001	+	0.991019i	0.650775	+	0.759271i	$0.274444\pi$
$757$	−8.85943	+	27.2665i	−0.322001	+	0.991019i	−0.972776	+	0.231748i	$0.925556\pi$
$758$	42.4063			1.54027
$759$		0			0
$760$	39.3774			1.42837
$761$	9.52787	−	29.3238i	0.345385	−	1.06299i	−0.615992	−	0.787752i	$-0.711245\pi$
$761$	9.52787	−	29.3238i	0.345385	−	1.06299i	0.961377	−	0.275234i	$-0.0887552\pi$
$762$		0			0
$763$	22.1088	+	16.0630i	0.800393	+	0.581520i
$764$	18.3877	+	56.5917i	0.665245	+	2.04741i
$765$		0			0
$766$	−33.5772	−	24.3953i	−1.21319	−	0.881437i
$767$	1.74158	−	1.26534i	0.0628850	−	0.0456886i
$768$		0			0
$769$	−30.6147			−1.10399			−0.551997	−	0.833846i	$-0.686134\pi$
$769$	−30.6147			−1.10399			−0.551997	+	0.833846i	$0.686134\pi$
$770$	−40.0819	+	39.7906i	−1.44445	+	1.43395i
$771$		0			0
$772$	−8.31003	+	25.5756i	−0.299085	+	0.920488i
$773$	41.9276	−	30.4622i	1.50803	−	1.09565i	0.540991	−	0.841028i	$-0.318049\pi$
$773$	41.9276	−	30.4622i	1.50803	−	1.09565i	0.967041	−	0.254621i	$-0.0819506\pi$
$774$		0			0
$775$	−1.73482	−	5.33921i	−0.0623164	−	0.191790i
$776$	15.4197	+	47.4571i	0.553536	+	1.70361i
$777$		0			0
$778$	51.3745	−	37.3258i	1.84187	−	1.33819i
$779$	−4.97367	+	15.3074i	−0.178200	+	0.548443i
$780$		0			0
$781$	5.14760	−	0.796065i	0.184196	−	0.0284854i
$782$	5.69895			0.203794
$783$		0			0
$784$	−23.6311	+	17.1690i	−0.843967	+	0.613178i
$785$	−28.3637	−	20.6074i	−1.01234	−	0.735510i
$786$		0			0
$787$	15.8180	+	48.6828i	0.563850	+	1.73535i	0.671343	+	0.741147i	$0.265718\pi$
$787$	15.8180	+	48.6828i	0.563850	+	1.73535i	−0.107493	+	0.994206i	$0.534282\pi$
$788$	−5.60187	−	4.07000i	−0.199558	−	0.144988i
$789$		0			0
$790$	−3.81459	+	11.7401i	−0.135717	+	0.417694i
$791$	44.0994			1.56799
$792$		0			0
$793$	−13.0882			−0.464775
$794$	0.699482	−	2.15278i	0.0248237	−	0.0763994i
$795$		0			0
$796$	−101.155	−	73.4931i	−3.58533	−	2.60489i
$797$	−4.26127	−	13.1148i	−0.150942	−	0.464551i	0.846785	−	0.531935i	$-0.178535\pi$
$797$	−4.26127	−	13.1148i	−0.150942	−	0.464551i	−0.997727	+	0.0673835i	$0.978535\pi$
$798$		0			0
$799$	−6.26310	−	4.55041i	−0.221573	−	0.160982i
$800$	6.08800	−	4.42319i	0.215243	−	0.156383i
$801$		0			0
$802$	91.7393			3.23943
$803$	22.6384	−	22.4738i	0.798891	−	0.793084i
$804$		0			0
$805$	−3.27937	+	10.0929i	−0.115583	+	0.355727i
$806$	20.8757	−	15.1671i	0.735316	−	0.534239i
$807$		0			0
$808$	−3.09868	−	9.53676i	−0.109011	−	0.335502i
$809$	3.05410	+	9.39956i	0.107377	+	0.330471i	0.990281	−	0.139082i	$-0.0444151\pi$
$809$	3.05410	+	9.39956i	0.107377	+	0.330471i	−0.882904	+	0.469553i	$0.844415\pi$
$810$		0			0
$811$	16.0323	−	11.6482i	0.562972	−	0.409023i	−0.269574	−	0.962980i	$-0.586883\pi$
$811$	16.0323	−	11.6482i	0.562972	−	0.409023i	0.832545	+	0.553957i	$0.186883\pi$
$812$	43.2560	−	133.128i	1.51799	−	4.67188i
$813$		0			0
$814$	2.91386	+	5.77071i	0.102131	+	0.202263i
$815$	−38.8659			−1.36141
$816$		0			0
$817$	−15.2861	+	11.1060i	−0.534794	+	0.388551i
$818$	−14.2001	−	10.3170i	−0.496496	−	0.360725i
$819$		0			0
$820$	−18.2712	−	56.2329i	−0.638057	−	1.96374i
$821$	−7.43153	−	5.39932i	−0.259362	−	0.188438i	0.450504	−	0.892775i	$-0.351244\pi$
$821$	−7.43153	−	5.39932i	−0.259362	−	0.188438i	−0.709866	+	0.704337i	$0.751244\pi$
$822$		0			0
$823$	3.48575	−	10.7280i	0.121505	−	0.373955i	−0.871743	−	0.489964i	$-0.837010\pi$
$823$	3.48575	−	10.7280i	0.121505	−	0.373955i	0.993248	+	0.116008i	$0.0370100\pi$
$824$	79.9904			2.78660
$825$		0			0
$826$	12.8163			0.445938
$827$	−5.47962	+	16.8645i	−0.190545	+	0.586437i	−1.00000		0.000745205i	$-0.999763\pi$
$827$	−5.47962	+	16.8645i	−0.190545	+	0.586437i	0.809455	+	0.587182i	$0.199763\pi$
$828$		0			0
$829$	32.1439	+	23.3539i	1.11640	+	0.811115i	0.983660	−	0.180035i	$-0.0576210\pi$
$829$	32.1439	+	23.3539i	1.11640	+	0.811115i	0.132744	+	0.991150i	$0.457621\pi$
$830$	−12.5792	−	38.7148i	−0.436630	−	1.34381i
$831$		0			0
$832$	7.22559	+	5.24970i	0.250502	+	0.182001i
$833$	−3.46888	+	2.52029i	−0.120190	+	0.0873229i
$834$		0			0
$835$	−10.2026			−0.353074
$836$	6.74266	−	41.5891i	0.233200	−	1.43839i
$837$		0			0
$838$	−0.771274	+	2.37374i	−0.0266432	+	0.0819993i
$839$	10.1921	−	7.40500i	0.351871	−	0.255649i	−0.397783	−	0.917480i	$-0.630220\pi$
$839$	10.1921	−	7.40500i	0.351871	−	0.255649i	0.749653	+	0.661831i	$0.230220\pi$
$840$		0			0
$841$	17.2093	+	52.9649i	0.593426	+	1.82638i
$842$	−5.81451	−	17.8952i	−0.200381	−	0.616710i
$843$		0			0
$844$	24.6700	−	17.9238i	0.849177	−	0.616963i
$845$	7.01166	−	21.5797i	0.241208	−	0.742363i
$846$		0			0
$847$	20.4153	+	28.5348i	0.701480	+	0.980466i
$848$	−4.35990			−0.149720
$849$		0			0
$850$	2.24356	−	1.63004i	0.0769533	−	0.0559098i
$851$	0.982711	+	0.713981i	0.0336869	+	0.0244750i
$852$		0			0
$853$	1.06878	+	3.28937i	0.0365944	+	0.112626i	0.967685	−	0.252162i	$-0.0811415\pi$
$853$	1.06878	+	3.28937i	0.0365944	+	0.112626i	−0.931091	+	0.364788i	$0.881142\pi$
$854$	−63.0397	−	45.8010i	−2.15717	−	1.56728i
$855$		0			0
$856$	−25.8575	+	79.5813i	−0.883792	+	2.72003i
$857$	−50.6641			−1.73065			−0.865327	−	0.501209i	$-0.832889\pi$
$857$	−50.6641			−1.73065			−0.865327	+	0.501209i	$0.832889\pi$
$858$		0			0
$859$	31.8788			1.08769			0.543846	−	0.839185i	$-0.316968\pi$
$859$	31.8788			1.08769			0.543846	+	0.839185i	$0.316968\pi$
$860$	21.4493	−	66.0141i	0.731414	−	2.25106i
$861$		0			0
$862$	−39.7825	−	28.9037i	−1.35500	−	0.984463i
$863$	−5.68134	−	17.4854i	−0.193395	−	0.595209i	−0.999992	−	0.00410640i	$-0.998693\pi$
$863$	−5.68134	−	17.4854i	−0.193395	−	0.595209i	0.806596	−	0.591102i	$-0.201307\pi$
$864$		0			0
$865$	−23.6302	−	17.1683i	−0.803450	−	0.583740i
$866$	−34.8032	+	25.2860i	−1.18266	+	0.859253i
$867$		0			0
$868$	108.233			3.67365
$869$	6.81998	+	3.50635i	0.231352	+	0.118945i
$870$		0			0
$871$	−3.18619	+	9.80610i	−0.107960	+	0.332267i
$872$	49.9307	−	36.2768i	1.69087	−	1.22849i
$873$		0			0
$874$	−3.47234	−	10.6868i	−0.117454	−	0.361485i
$875$	11.7089	+	36.0364i	0.395834	+	1.21825i
$876$		0			0
$877$	5.33020	−	3.87262i	0.179988	−	0.130769i	−0.494143	−	0.869381i	$-0.664518\pi$
$877$	5.33020	−	3.87262i	0.179988	−	0.130769i	0.674131	+	0.738611i	$0.264518\pi$
$878$	13.9248	−	42.8561i	0.469939	−	1.44632i
$879$		0			0
$880$	28.2341	+	55.9157i	0.951770	+	1.88492i
$881$	57.1119			1.92415			0.962074	−	0.272788i	$-0.0879458\pi$
$881$	57.1119			1.92415			0.962074	+	0.272788i	$0.0879458\pi$
$882$		0			0
$883$	35.9401	−	26.1120i	1.20948	−	0.878740i	0.214298	−	0.976768i	$-0.431254\pi$
$883$	35.9401	−	26.1120i	1.20948	−	0.878740i	0.995184	+	0.0980282i	$0.0312535\pi$
$884$	7.26518	+	5.27846i	0.244355	+	0.177534i
$885$		0			0
$886$	−19.3988	−	59.7033i	−0.651714	−	2.00577i
$887$	−26.2648	−	19.0825i	−0.881887	−	0.640728i	0.0518633	−	0.998654i	$-0.483484\pi$
$887$	−26.2648	−	19.0825i	−0.881887	−	0.640728i	−0.933750	+	0.357926i	$0.883484\pi$
$888$		0			0
$889$	−10.6738	+	32.8507i	−0.357989	+	1.10178i
$890$	78.1309			2.61895
$891$		0			0
$892$	−81.7672			−2.73777
$893$	−4.71693	+	14.5172i	−0.157846	+	0.485801i
$894$		0			0
$895$	13.0709	+	9.49656i	0.436912	+	0.317435i
$896$	−2.37081	−	7.29660i	−0.0792031	−	0.243762i
$897$		0			0
$898$	12.6410	+	9.18426i	0.421837	+	0.306483i
$899$	−52.9770	+	38.4900i	−1.76688	+	1.28371i
$900$		0			0
$901$	−0.640004			−0.0213216
$902$	−51.5232	+	7.96794i	−1.71553	+	0.265303i
$903$		0			0
$904$	30.7764	−	94.7199i	1.02361	−	3.15034i
$905$	−23.8345	+	17.3168i	−0.792284	+	0.575628i
$906$		0			0
$907$	−7.92238	−	24.3826i	−0.263058	−	0.809610i	−0.992134	−	0.125178i	$-0.960050\pi$
$907$	−7.92238	−	24.3826i	−0.263058	−	0.809610i	0.729076	−	0.684433i	$-0.239950\pi$
$908$	−8.00870	−	24.6482i	−0.265778	−	0.817981i
$909$		0			0
$910$	−19.2028	+	13.9516i	−0.636565	+	0.462492i
$911$	−3.43203	+	10.5627i	−0.113708	+	0.349958i	−0.991675	−	0.128763i	$-0.958899\pi$
$911$	−3.43203	+	10.5627i	−0.113708	+	0.349958i	0.877967	+	0.478721i	$0.158899\pi$
$912$		0			0
$913$	−24.9911	+	3.86481i	−0.827085	+	0.127907i
$914$	84.7950			2.80477
$915$		0			0
$916$	55.9116	−	40.6221i	1.84737	−	1.34219i
$917$	−15.2315	−	11.0663i	−0.502988	−	0.365442i
$918$		0			0
$919$	−6.38466	−	19.6500i	−0.210611	−	0.648193i	−0.999436	−	0.0335757i	$-0.989310\pi$
$919$	−6.38466	−	19.6500i	−0.210611	−	0.648193i	0.788826	−	0.614617i	$-0.210690\pi$
$920$	19.3896	+	14.0874i	0.639256	+	0.464446i
$921$		0			0
$922$	−4.73827	+	14.5829i	−0.156047	+	0.480262i
$923$	2.18906			0.0720539
$924$		0			0
$925$	0.591088			0.0194349
$926$	−31.1926	+	96.0010i	−1.02505	+	3.15479i
$927$		0			0
$928$	−71.0122	−	51.5934i	−2.33109	−	1.69364i
$929$	3.57386	+	10.9992i	0.117255	+	0.360872i	0.992411	−	0.122968i	$-0.0392414\pi$
$929$	3.57386	+	10.9992i	0.117255	+	0.360872i	−0.875156	+	0.483841i	$0.839241\pi$
$930$		0			0
$931$	6.83967	+	4.96931i	0.224161	+	0.162863i
$932$	4.33902	−	3.15249i	0.142129	−	0.103263i
$933$		0			0
$934$	−70.6068			−2.31032
$935$	4.14457	+	8.20805i	0.135542	+	0.268432i
$936$		0			0
$937$	4.26759	−	13.1343i	0.139416	−	0.429078i	−0.856835	−	0.515591i	$-0.827572\pi$
$937$	4.26759	−	13.1343i	0.139416	−	0.429078i	0.996251	+	0.0865129i	$0.0275724\pi$
$938$	−49.6621	+	36.0816i	−1.62152	+	1.17811i
$939$		0			0
$940$	−17.3281	−	53.3303i	−0.565179	−	1.73944i
$941$	6.49026	+	19.9750i	0.211576	+	0.651165i	0.999379	+	0.0352374i	$0.0112187\pi$
$941$	6.49026	+	19.9750i	0.211576	+	0.651165i	−0.787803	+	0.615928i	$0.788781\pi$
$942$		0			0
$943$	−7.92530	+	5.75807i	−0.258083	+	0.187509i
$944$	4.39249	−	13.5187i	0.142963	−	0.439996i
$945$		0			0
$946$	−54.4316	−	27.9848i	−1.76972	−	0.909865i
$947$	44.0625			1.43184			0.715919	−	0.698184i	$-0.246008\pi$
$947$	44.0625			1.43184			0.715919	+	0.698184i	$0.246008\pi$
$948$		0			0
$949$	10.8458	−	7.87991i	0.352069	−	0.255793i
$950$	−4.42366	−	3.21398i	−0.143523	−	0.104275i
$951$		0			0
$952$	9.59244	+	29.5225i	0.310893	+	0.956829i
$953$	16.0558	+	11.6652i	0.520098	+	0.377873i	0.816641	−	0.577146i	$-0.195834\pi$
$953$	16.0558	+	11.6652i	0.520098	+	0.377873i	−0.296543	+	0.955020i	$0.595834\pi$
$954$		0			0
$955$	−7.91255	+	24.3523i	−0.256044	+	0.788023i
$956$	104.866			3.39161
$957$		0			0
$958$	−26.6436			−0.860814
$959$	−1.16042	+	3.57142i	−0.0374721	+	0.115327i
$960$		0			0
$961$	−15.8825	−	11.5393i	−0.512339	−	0.372236i
$962$	0.839553	+	2.58388i	0.0270683	+	0.0833076i
$963$		0			0
$964$	43.0654	+	31.2888i	1.38704	+	1.00775i
$965$	−9.36194	+	6.80185i	−0.301371	+	0.218959i
$966$		0			0
$967$	43.4997			1.39885			0.699427	−	0.714704i	$-0.253438\pi$
$967$	43.4997			1.39885			0.699427	+	0.714704i	$0.253438\pi$
$968$	75.5366	−	23.9355i	2.42784	−	0.769318i
$969$		0			0
$970$	−11.4284	+	35.1729i	−0.366943	+	1.12933i
$971$	−3.61387	+	2.62563i	−0.115975	+	0.0842604i	−0.644261	−	0.764806i	$-0.722835\pi$
$971$	−3.61387	+	2.62563i	−0.115975	+	0.0842604i	0.528286	+	0.849066i	$0.322835\pi$
$972$		0			0
$973$	2.69264	+	8.28708i	0.0863219	+	0.265672i
$974$	−19.7308	−	60.7250i	−0.632214	−	1.94575i
$975$		0			0
$976$	−69.9163	+	50.7972i	−2.23797	+	1.62598i
$977$	−14.2291	+	43.7928i	−0.455230	+	1.40106i	0.415634	+	0.909532i	$0.363560\pi$
$977$	−14.2291	+	43.7928i	−0.455230	+	1.40106i	−0.870864	+	0.491523i	$0.836440\pi$
$978$		0			0
$979$	7.76761	−	47.9111i	0.248254	−	1.53124i
$980$	−31.0576			−0.992098
$981$		0			0
$982$	87.0077	−	63.2148i	2.77653	−	2.01726i
$983$	−44.9928	−	32.6892i	−1.43505	−	1.04262i	−0.989049	−	0.147591i	$-0.952848\pi$
$983$	−44.9928	−	32.6892i	−1.43505	−	1.04262i	−0.446000	−	0.895033i	$-0.647152\pi$
$984$		0			0
$985$	−0.920759	−	2.83380i	−0.0293378	−	0.0902925i
$986$	−26.1695	−	19.0133i	−0.833407	−	0.605505i
$987$		0			0
$988$	5.47163	−	16.8399i	0.174076	−	0.535750i
$989$	−11.5002			−0.365684
$990$		0			0
$991$	−54.8380			−1.74199			−0.870993	−	0.491295i	$-0.836524\pi$
$991$	−54.8380			−1.74199			−0.870993	+	0.491295i	$0.836524\pi$
$992$	20.9726	−	64.5470i	0.665880	−	2.04937i
$993$		0			0
$994$	10.5437	+	7.66045i	0.334426	+	0.242975i
$995$	−16.6264	−	51.1708i	−0.527092	−	1.62222i
$996$		0			0
$997$	−39.1492	−	28.4436i	−1.23987	−	0.900816i	−0.242278	−	0.970207i	$-0.577895\pi$
$997$	−39.1492	−	28.4436i	−1.23987	−	0.900816i	−0.997590	+	0.0693904i	$0.977895\pi$
$998$	83.2050	−	60.4520i	2.63381	−	1.91357i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.e.163.9		36
3.2	odd	2		891.2.f.f.163.1		36
9.2	odd	6		99.2.m.b.31.9	yes	72
9.4	even	3		297.2.n.b.262.9		72
9.5	odd	6		99.2.m.b.97.1	yes	72
9.7	even	3		297.2.n.b.64.1		72
11.4	even	5		9801.2.a.cp.1.18		18
11.5	even	5	inner	891.2.f.e.82.9		36
11.7	odd	10		9801.2.a.cn.1.1		18
33.5	odd	10		891.2.f.f.82.1		36
33.26	odd	10		9801.2.a.cm.1.1		18
33.29	even	10		9801.2.a.co.1.18		18
99.5	odd	30		99.2.m.b.16.9	✓	72
99.16	even	15		297.2.n.b.280.9		72
99.29	even	30		1089.2.e.o.364.1		36
99.38	odd	30		99.2.m.b.49.1	yes	72
99.49	even	15		297.2.n.b.181.1		72
99.59	odd	30		1089.2.e.p.727.18		36
99.92	odd	30		1089.2.e.p.364.18		36
99.95	even	30		1089.2.e.o.727.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.9	✓	72	99.5	odd	30
99.2.m.b.31.9	yes	72	9.2	odd	6
99.2.m.b.49.1	yes	72	99.38	odd	30
99.2.m.b.97.1	yes	72	9.5	odd	6
297.2.n.b.64.1		72	9.7	even	3
297.2.n.b.181.1		72	99.49	even	15
297.2.n.b.262.9		72	9.4	even	3
297.2.n.b.280.9		72	99.16	even	15
891.2.f.e.82.9		36	11.5	even	5	inner
891.2.f.e.163.9		36	1.1	even	1	trivial
891.2.f.f.82.1		36	33.5	odd	10
891.2.f.f.163.1		36	3.2	odd	2
1089.2.e.o.364.1		36	99.29	even	30
1089.2.e.o.727.1		36	99.95	even	30
1089.2.e.p.364.18		36	99.92	odd	30
1089.2.e.p.727.18		36	99.59	odd	30
9801.2.a.cm.1.1		18	33.26	odd	10
9801.2.a.cn.1.1		18	11.7	odd	10
9801.2.a.co.1.18		18	33.29	even	10
9801.2.a.cp.1.18		18	11.4	even	5

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.803965 - 2.47435i) q^{2} +(-3.85802 - 2.80301i) q^{4} +(-0.634128 - 1.95164i) q^{5} +(-2.58046 - 1.87481i) q^{7} +(-5.82773 + 4.23409i) q^{8} +O(q^{10})\)	\(q+(0.803965 - 2.47435i) q^{2} +(-3.85802 - 2.80301i) q^{4} +(-0.634128 - 1.95164i) q^{5} +(-2.58046 - 1.87481i) q^{7} +(-5.82773 + 4.23409i) q^{8} -5.33887 q^{10} +(-0.530779 + 3.27388i) q^{11} +(-0.430725 + 1.32563i) q^{13} +(-6.71355 + 4.87768i) q^{14} +(2.84408 + 8.75317i) q^{16} +(0.417491 + 1.28491i) q^{17} +(2.15510 - 1.56577i) q^{19} +(-3.02401 + 9.30694i) q^{20} +(7.67399 + 3.94542i) q^{22} +1.62134 q^{23} +(0.638288 - 0.463743i) q^{25} +(2.93380 + 2.13153i) q^{26} +(4.70033 + 14.4661i) q^{28} +(-7.44518 - 5.40924i) q^{29} +(2.19884 - 6.76734i) q^{31} +9.53801 q^{32} +3.51496 q^{34} +(-2.02263 + 6.22501i) q^{35} +(0.606109 + 0.440364i) q^{37} +(-2.14165 - 6.59131i) q^{38} +(11.9590 + 8.68870i) q^{40} +(-4.88811 + 3.55142i) q^{41} -7.09299 q^{43} +(11.2245 - 11.1429i) q^{44} +(1.30350 - 4.01177i) q^{46} +(-4.63580 + 3.36810i) q^{47} +(0.980730 + 3.01838i) q^{49} +(-0.634302 - 1.95218i) q^{50} +(5.37751 - 3.90699i) q^{52} +(-0.146386 + 0.450530i) q^{53} +(6.72603 - 1.04016i) q^{55} +22.9764 q^{56} +(-19.3700 + 14.0731i) q^{58} +(-1.24947 - 0.907796i) q^{59} +(2.90164 + 8.93034i) q^{61} +(-14.9770 - 10.8814i) q^{62} +(1.98007 - 6.09404i) q^{64} +2.86030 q^{65} +7.39729 q^{67} +(1.99092 - 6.12742i) q^{68} +(13.7767 + 10.0094i) q^{70} +(-0.485314 - 1.49364i) q^{71} +(-7.78114 - 5.65333i) q^{73} +(1.57691 - 1.14569i) q^{74} -12.7033 q^{76} +(7.50757 - 7.45300i) q^{77} +(0.714495 - 2.19899i) q^{79} +(15.2796 - 11.1013i) q^{80} +(4.85759 + 14.9501i) q^{82} +(2.35615 + 7.25149i) q^{83} +(2.24294 - 1.62959i) q^{85} +(-5.70252 + 17.5506i) q^{86} +(-10.7687 - 21.3266i) q^{88} -14.6343 q^{89} +(3.59679 - 2.61322i) q^{91} +(-6.25516 - 4.54464i) q^{92} +(4.60685 + 14.1784i) q^{94} +(-4.42245 - 3.21310i) q^{95} +(2.14060 - 6.58808i) q^{97} +8.25699 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) \) 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8	\( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28} - 23 q^{29} - 3 q^{31} + 18 q^{32} - 8 q^{34} - 9 q^{35} - 21 q^{37} - q^{38} + 25 q^{40} + 10 q^{41} + 8 q^{43} - 19 q^{44} - 9 q^{46} - 34 q^{47} - q^{49} + 27 q^{52} - 2 q^{53} + 9 q^{55} + 114 q^{56} - q^{58} - 16 q^{59} + 3 q^{61} - 92 q^{62} + 13 q^{64} + 84 q^{65} - 10 q^{67} - 23 q^{68} + 46 q^{70} + 24 q^{71} - 20 q^{73} + 68 q^{74} - 16 q^{76} - 26 q^{77} - 19 q^{79} + 28 q^{80} + 47 q^{82} + 7 q^{83} - 25 q^{85} - 77 q^{86} - 18 q^{88} + 28 q^{89} + 10 q^{91} + 50 q^{92} + 63 q^{94} - 77 q^{95} + 33 q^{97} + 164 q^{98}+O(q^{100}) \) 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

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