LMFDB - Embedded newform 819.2.gh.c.19.1

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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	819.19
Dual form			819.2.gh.c.388.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.45222 - 0.657070i) q^{2} +(3.84958 + 2.22256i) q^{4} +(2.20549 - 0.590961i) q^{5} +(2.58986 + 0.540936i) q^{7} +(-4.38935 - 4.38935i) q^{8} +O(q^{10})$	\(q+(-2.45222 - 0.657070i) q^{2} +(3.84958 + 2.22256i) q^{4} +(2.20549 - 0.590961i) q^{5} +(2.58986 + 0.540936i) q^{7} +(-4.38935 - 4.38935i) q^{8} -5.79666 q^{10} +(1.22725 + 1.22725i) q^{11} +(1.05331 - 3.44826i) q^{13} +(-5.99548 - 3.02821i) q^{14} +(3.43442 + 5.94858i) q^{16} +(3.75960 - 6.51182i) q^{17} +(-4.24907 - 4.24907i) q^{19} +(9.80368 + 2.62689i) q^{20} +(-2.20310 - 3.81588i) q^{22} +(-0.0187715 + 0.0108378i) q^{23} +(0.184846 - 0.106721i) q^{25} +(-4.84871 + 7.76380i) q^{26} +(8.76763 + 7.83850i) q^{28} +(-0.432921 + 0.749842i) q^{29} +(1.55740 - 5.81230i) q^{31} +(-1.30008 - 4.85196i) q^{32} +(-13.4981 + 13.4981i) q^{34} +(6.03160 - 0.337475i) q^{35} +(-2.43056 + 9.07099i) q^{37} +(7.62770 + 13.2116i) q^{38} +(-12.2746 - 7.08675i) q^{40} +(-2.45125 + 0.656811i) q^{41} +(1.71095 - 0.987815i) q^{43} +(1.99677 + 7.45205i) q^{44} +(0.0531531 - 0.0142423i) q^{46} +(-1.50594 - 5.62025i) q^{47} +(6.41478 + 2.80190i) q^{49} +(-0.523405 + 0.140246i) q^{50} +(11.7188 - 10.9333i) q^{52} +(6.87167 + 11.9021i) q^{53} +(3.43196 + 1.98144i) q^{55} +(-8.99345 - 13.7422i) q^{56} +(1.55432 - 1.55432i) q^{58} +(-1.50298 - 5.60919i) q^{59} +3.60438i q^{61} +(-7.63818 + 13.2297i) q^{62} -0.985368i q^{64} +(0.285288 - 8.22760i) q^{65} +(-0.794679 + 0.794679i) q^{67} +(28.9458 - 16.7119i) q^{68} +(-15.0125 - 3.13562i) q^{70} +(-12.5434 - 3.36098i) q^{71} +(9.58115 + 2.56726i) q^{73} +(11.9205 - 20.6470i) q^{74} +(-6.91334 - 25.8009i) q^{76} +(2.51455 + 3.84228i) q^{77} +(2.16727 - 3.75382i) q^{79} +(11.0900 + 11.0900i) q^{80} +6.44258 q^{82} +(-8.64819 - 8.64819i) q^{83} +(4.44355 - 16.5836i) q^{85} +(-4.84468 + 1.29813i) q^{86} -10.7737i q^{88} +(-2.34321 - 0.627860i) q^{89} +(4.59323 - 8.36076i) q^{91} -0.0963502 q^{92} +14.7716i q^{94} +(-11.8823 - 6.86026i) q^{95} +(1.99188 - 7.43379i) q^{97} +(-13.8894 - 11.0858i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7}+O(q^{10}) $ 36 * q + 4 * q^7	$ 36 q + 4 q^{7} - 4 q^{11} - 42 q^{14} + 12 q^{16} + 4 q^{17} - 24 q^{19} + 14 q^{20} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 28 q^{26} - 12 q^{28} - 8 q^{29} - 6 q^{31} - 46 q^{32} + 24 q^{34} + 10 q^{35} - 20 q^{37} - 8 q^{38} - 30 q^{40} + 34 q^{41} + 30 q^{43} + 32 q^{44} - 26 q^{46} - 4 q^{47} + 20 q^{50} + 98 q^{52} + 8 q^{53} + 30 q^{55} + 10 q^{56} - 96 q^{58} + 14 q^{59} - 48 q^{62} - 28 q^{65} + 62 q^{67} + 54 q^{68} - 148 q^{70} - 42 q^{71} - 52 q^{73} + 20 q^{74} - 12 q^{76} + 24 q^{77} - 76 q^{80} + 48 q^{82} - 60 q^{83} + 2 q^{85} - 12 q^{86} - 50 q^{89} + 40 q^{91} + 100 q^{92} - 24 q^{95} - 36 q^{97} - 16 q^{98}+O(q^{100}) $ 36 * q + 4 * q^7 - 4 * q^11 - 42 * q^14 + 12 * q^16 + 4 * q^17 - 24 * q^19 + 14 * q^20 + 4 * q^22 + 12 * q^23 - 24 * q^25 + 28 * q^26 - 12 * q^28 - 8 * q^29 - 6 * q^31 - 46 * q^32 + 24 * q^34 + 10 * q^35 - 20 * q^37 - 8 * q^38 - 30 * q^40 + 34 * q^41 + 30 * q^43 + 32 * q^44 - 26 * q^46 - 4 * q^47 + 20 * q^50 + 98 * q^52 + 8 * q^53 + 30 * q^55 + 10 * q^56 - 96 * q^58 + 14 * q^59 - 48 * q^62 - 28 * q^65 + 62 * q^67 + 54 * q^68 - 148 * q^70 - 42 * q^71 - 52 * q^73 + 20 * q^74 - 12 * q^76 + 24 * q^77 - 76 * q^80 + 48 * q^82 - 60 * q^83 + 2 * q^85 - 12 * q^86 - 50 * q^89 + 40 * q^91 + 100 * q^92 - 24 * q^95 - 36 * q^97 - 16 * 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 $

$2$	−2.45222	−	0.657070i	−1.73398	−	0.464619i	−0.752886	−	0.658150i	$-0.771339\pi$
$2$	−2.45222	−	0.657070i	−1.73398	−	0.464619i	−0.981094	+	0.193532i	$0.938006\pi$
$3$		0			0
$3$		0			0
$4$	3.84958	+	2.22256i	1.92479	+	1.11128i
$5$	2.20549	−	0.590961i	0.986327	−	0.264286i	0.270620	−	0.962686i	$-0.412771\pi$
$5$	2.20549	−	0.590961i	0.986327	−	0.264286i	0.715707	+	0.698401i	$0.246105\pi$
$6$		0			0
$7$	2.58986	+	0.540936i	0.978876	+	0.204455i
$7$	2.58986	+	0.540936i	0.978876	+	0.204455i
$8$	−4.38935	−	4.38935i	−1.55187	−	1.55187i
$9$		0			0
$10$	−5.79666			−1.83306
$11$	1.22725	+	1.22725i	0.370030	+	0.370030i	0.867488	−	0.497458i	$-0.165733\pi$
$11$	1.22725	+	1.22725i	0.370030	+	0.370030i	−0.497458	+	0.867488i	$0.665733\pi$
$12$		0			0
$13$	1.05331	−	3.44826i	0.292137	−	0.956377i
$13$	1.05331	−	3.44826i	0.292137	−	0.956377i
$14$	−5.99548	−	3.02821i	−1.60236	−	0.809324i
$15$		0			0
$16$	3.43442	+	5.94858i	0.858604	+	1.48715i
$17$	3.75960	−	6.51182i	0.911837	−	1.57935i	0.100370	−	0.994950i	$-0.467997\pi$
$17$	3.75960	−	6.51182i	0.911837	−	1.57935i	0.811467	−	0.584398i	$-0.198669\pi$
$18$		0			0
$19$	−4.24907	−	4.24907i	−0.974803	−	0.974803i	0.0248877	−	0.999690i	$-0.492077\pi$
$19$	−4.24907	−	4.24907i	−0.974803	−	0.974803i	−0.999690	+	0.0248877i	$0.992077\pi$
$20$	9.80368	+	2.62689i	2.19217	+	0.587390i
$21$		0			0
$22$	−2.20310	−	3.81588i	−0.469703	−	0.813549i
$23$	−0.0187715	+	0.0108378i	−0.00391414	+	0.00225983i	−0.501956	−	0.864893i	$-0.667386\pi$
$23$	−0.0187715	+	0.0108378i	−0.00391414	+	0.00225983i	0.498042	+	0.867153i	$0.334053\pi$
$24$		0			0
$25$	0.184846	−	0.106721i	0.0369691	−	0.0213441i
$26$	−4.84871	+	7.76380i	−0.950909	+	1.52261i
$27$		0			0
$28$	8.76763	+	7.83850i	1.65693	+	1.48134i
$29$	−0.432921	+	0.749842i	−0.0803915	+	0.139242i	−0.903418	−	0.428761i	$-0.858950\pi$
$29$	−0.432921	+	0.749842i	−0.0803915	+	0.139242i	0.823027	+	0.568003i	$0.192284\pi$
$30$		0			0
$31$	1.55740	−	5.81230i	0.279718	−	1.04392i	−0.672896	−	0.739737i	$-0.734950\pi$
$31$	1.55740	−	5.81230i	0.279718	−	1.04392i	0.952614	−	0.304183i	$-0.0983835\pi$
$32$	−1.30008	−	4.85196i	−0.229823	−	0.857713i
$33$		0			0
$34$	−13.4981	+	13.4981i	−2.31490	+	2.31490i
$35$	6.03160	−	0.337475i	1.01953	−	0.0570438i
$36$		0			0
$37$	−2.43056	+	9.07099i	−0.399582	+	1.49126i	0.414251	+	0.910163i	$0.364044\pi$
$37$	−2.43056	+	9.07099i	−0.399582	+	1.49126i	−0.813833	+	0.581099i	$0.802623\pi$
$38$	7.62770	+	13.2116i	1.23738	+	2.14320i
$39$		0			0
$40$	−12.2746	−	7.08675i	−1.94079	−	1.12051i
$41$	−2.45125	+	0.656811i	−0.382822	+	0.102577i	−0.445097	−	0.895482i	$-0.646831\pi$
$41$	−2.45125	+	0.656811i	−0.382822	+	0.102577i	0.0622757	+	0.998059i	$0.480164\pi$
$42$		0			0
$43$	1.71095	−	0.987815i	0.260917	−	0.150640i	−0.363836	−	0.931463i	$-0.618533\pi$
$43$	1.71095	−	0.987815i	0.260917	−	0.150640i	0.624753	+	0.780823i	$0.285200\pi$
$44$	1.99677	+	7.45205i	0.301025	+	1.12344i
$45$		0			0
$46$	0.0531531	−	0.0142423i	0.00783699	−	0.00209992i
$47$	−1.50594	−	5.62025i	−0.219664	−	0.819798i	−0.984472	−	0.175540i	$-0.943833\pi$
$47$	−1.50594	−	5.62025i	−0.219664	−	0.819798i	0.764808	−	0.644258i	$-0.222834\pi$
$48$		0			0
$49$	6.41478	+	2.80190i	0.916397	+	0.400271i
$50$	−0.523405	+	0.140246i	−0.0740206	+	0.0198338i
$51$		0			0
$52$	11.7188	−	10.9333i	1.62510	−	1.51618i
$53$	6.87167	+	11.9021i	0.943897	+	1.63488i	0.757945	+	0.652319i	$0.226204\pi$
$53$	6.87167	+	11.9021i	0.943897	+	1.63488i	0.185952	+	0.982559i	$0.440463\pi$
$54$		0			0
$55$	3.43196	+	1.98144i	0.462765	+	0.267177i
$56$	−8.99345	−	13.7422i	−1.20180	−	1.83637i
$57$		0			0
$58$	1.55432	−	1.55432i	0.204092	−	0.204092i
$59$	−1.50298	−	5.60919i	−0.195671	−	0.730254i	−0.992092	−	0.125512i	$-0.959943\pi$
$59$	−1.50298	−	5.60919i	−0.195671	−	0.730254i	0.796421	−	0.604742i	$-0.206724\pi$
$60$		0			0
$61$			3.60438i			0.461494i	0.973014	+	0.230747i	$0.0741170\pi$
$61$			3.60438i			0.461494i	−0.973014	+	0.230747i	$0.925883\pi$
$62$	−7.63818	+	13.2297i	−0.970050	+	1.68018i
$63$		0			0
$64$		−	0.985368i		−	0.123171i
$65$	0.285288	−	8.22760i	0.0353857	−	1.02051i
$66$		0			0
$67$	−0.794679	+	0.794679i	−0.0970854	+	0.0970854i	−0.753981	−	0.656896i	$-0.771869\pi$
$67$	−0.794679	+	0.794679i	−0.0970854	+	0.0970854i	0.656896	+	0.753981i	$0.271869\pi$
$68$	28.9458	−	16.7119i	3.51019	−	2.02661i
$69$		0			0
$70$	−15.0125	−	3.13562i	−1.79434	−	0.374778i
$71$	−12.5434	−	3.36098i	−1.48862	−	0.398875i	−0.579350	−	0.815079i	$-0.696694\pi$
$71$	−12.5434	−	3.36098i	−1.48862	−	0.398875i	−0.909272	+	0.416203i	$0.863360\pi$
$72$		0			0
$73$	9.58115	+	2.56726i	1.12139	+	0.300475i	0.771445	−	0.636296i	$-0.219534\pi$
$73$	9.58115	+	2.56726i	1.12139	+	0.300475i	0.349943	+	0.936771i	$0.386201\pi$
$74$	11.9205	−	20.6470i	1.38574	−	2.40016i
$75$		0			0
$76$	−6.91334	−	25.8009i	−0.793014	−	2.95957i
$77$	2.51455	+	3.84228i	0.286560	+	0.437868i
$78$		0			0
$79$	2.16727	−	3.75382i	0.243837	−	0.422338i	−0.717967	−	0.696077i	$-0.754927\pi$
$79$	2.16727	−	3.75382i	0.243837	−	0.422338i	0.961804	+	0.273739i	$0.0882606\pi$
$80$	11.0900	+	11.0900i	1.23990	+	1.23990i
$81$		0			0
$82$	6.44258			0.711464
$83$	−8.64819	−	8.64819i	−0.949263	−	0.949263i	0.0495109	−	0.998774i	$-0.484234\pi$
$83$	−8.64819	−	8.64819i	−0.949263	−	0.949263i	−0.998774	+	0.0495109i	$0.984234\pi$
$84$		0			0
$85$	4.44355	−	16.5836i	0.481971	−	1.79874i
$86$	−4.84468	+	1.29813i	−0.522415	+	0.139981i
$87$		0			0
$88$		−	10.7737i		−	1.14848i
$89$	−2.34321	−	0.627860i	−0.248379	−	0.0665530i	0.132481	−	0.991186i	$-0.457706\pi$
$89$	−2.34321	−	0.627860i	−0.248379	−	0.0665530i	−0.380861	+	0.924632i	$0.624372\pi$
$90$		0			0
$91$	4.59323	−	8.36076i	0.481501	−	0.876446i
$92$	−0.0963502			−0.0100452
$93$		0			0
$94$			14.7716i			1.52357i
$95$	−11.8823	−	6.86026i	−1.21910	−	0.703848i
$96$		0			0
$97$	1.99188	−	7.43379i	0.202245	−	0.754787i	−0.788027	−	0.615641i	$-0.788897\pi$
$97$	1.99188	−	7.43379i	0.202245	−	0.754787i	0.990272	−	0.139147i	$-0.0444360\pi$
$98$	−13.8894	−	11.0858i	−1.40304	−	1.11984i
$99$		0			0
$100$	0.948771			0.0948771
$101$	4.46176			0.443961			0.221981	−	0.975051i	$-0.428748\pi$
$101$	4.46176			0.443961			0.221981	+	0.975051i	$0.428748\pi$
$102$		0			0
$103$	−4.23657	+	7.33795i	−0.417441	+	0.723030i	−0.995681	−	0.0928371i	$-0.970406\pi$
$103$	−4.23657	+	7.33795i	−0.417441	+	0.723030i	0.578240	+	0.815867i	$0.303740\pi$
$104$	−19.7590	+	10.5123i	−1.93753	+	1.03081i
$105$		0			0
$106$	−9.03034	−	33.7017i	−0.877104	−	3.27340i
$107$	5.06882	+	8.77945i	0.490021	+	0.848741i	0.999934	−	0.0114847i	$-0.00365576\pi$
$107$	5.06882	+	8.77945i	0.490021	+	0.848741i	−0.509913	+	0.860226i	$0.670322\pi$
$108$		0			0
$109$	3.92728	+	1.05231i	0.376165	+	0.100793i	0.441948	−	0.897041i	$-0.354288\pi$
$109$	3.92728	+	1.05231i	0.376165	+	0.100793i	−0.0657825	+	0.997834i	$0.520954\pi$
$110$	−7.11396	−	7.11396i	−0.678290	−	0.678290i
$111$		0			0
$112$	5.67686	+	17.2638i	0.536413	+	1.63128i
$113$	2.30418	+	3.99096i	0.216759	+	0.375438i	0.953815	−	0.300394i	$-0.0971180\pi$
$113$	2.30418	+	3.99096i	0.216759	+	0.375438i	−0.737056	+	0.675831i	$0.763785\pi$
$114$		0			0
$115$	−0.0349958	+	0.0349958i	−0.00326338	+	0.00326338i
$116$	−3.33314	+	1.92439i	−0.309474	+	0.178675i
$117$		0			0
$118$			14.7425i			1.35716i
$119$	13.2593	−	14.8310i	1.21548	−	1.35956i
$120$		0			0
$121$		−	7.98770i		−	0.726155i
$122$	2.36833	−	8.83874i	0.214419	−	0.800222i
$123$		0			0
$124$	18.9135	−	18.9135i	1.69849	−	1.69849i
$125$	−7.72806	+	7.72806i	−0.691219	+	0.691219i
$126$		0			0
$127$	2.76191	+	1.59459i	0.245080	+	0.141497i	0.617509	−	0.786564i	$-0.288142\pi$
$127$	2.76191	+	1.59459i	0.245080	+	0.141497i	−0.372430	+	0.928060i	$0.621475\pi$
$128$	−3.24761	+	12.1202i	−0.287051	+	1.07129i
$129$		0			0
$130$	−6.10570	+	19.9884i	−0.535505	+	1.75310i
$131$	7.19475	+	4.15389i	0.628608	+	0.362927i	0.780213	−	0.625514i	$-0.215111\pi$
$131$	7.19475	+	4.15389i	0.628608	+	0.362927i	−0.151605	+	0.988441i	$0.548444\pi$
$132$		0			0
$133$	−8.70602	−	13.3030i	−0.754908	−	1.15351i
$134$	2.47088	−	1.42657i	0.213452	−	0.123237i
$135$		0			0
$136$	−45.0848	+	12.0804i	−3.86599	+	1.03589i
$137$	4.84610	−	1.29851i	0.414031	−	0.110939i	−0.0457898	−	0.998951i	$-0.514580\pi$
$137$	4.84610	−	1.29851i	0.414031	−	0.110939i	0.459820	+	0.888012i	$0.347914\pi$
$138$		0			0
$139$	−2.35400	+	1.35908i	−0.199663	+	0.115276i	−0.596498	−	0.802614i	$-0.703442\pi$
$139$	−2.35400	+	1.35908i	−0.199663	+	0.115276i	0.396835	+	0.917890i	$0.370108\pi$
$140$	23.9692	+	12.1064i	2.02577	+	1.02318i
$141$		0			0
$142$	28.5506	+	16.4837i	2.39592	+	1.38328i
$143$	5.52457	−	2.93921i	0.461988	−	0.245789i
$144$		0			0
$145$	−0.511679	+	1.90961i	−0.0424926	+	0.158585i
$146$	−21.8082	−	12.5910i	−1.80486	−	1.04204i
$147$		0			0
$148$	−29.5175	+	29.5175i	−2.42632	+	2.42632i
$149$	15.9474	−	15.9474i	1.30647	−	1.30647i	0.382518	−	0.923948i	$-0.375057\pi$
$149$	15.9474	−	15.9474i	1.30647	−	1.30647i	0.923948	−	0.382518i	$-0.124943\pi$
$150$		0			0
$151$	−5.41469	+	20.2079i	−0.440641	+	1.64450i	0.286553	+	0.958064i	$0.407490\pi$
$151$	−5.41469	+	20.2079i	−0.440641	+	1.64450i	−0.727195	+	0.686431i	$0.759176\pi$
$152$			37.3013i			3.02553i
$153$		0			0
$154$	−3.64158	−	11.0743i	−0.293447	−	0.892396i
$155$		−	13.7394i		−	1.10357i
$156$		0			0
$157$	5.68992	−	3.28508i	0.454105	−	0.262178i	−0.255457	−	0.966820i	$-0.582226\pi$
$157$	5.68992	−	3.28508i	0.454105	−	0.262178i	0.709563	+	0.704643i	$0.248893\pi$
$158$	−7.78114	+	7.78114i	−0.619034	+	0.619034i
$159$		0			0
$160$	−5.73463	−	9.93267i	−0.453362	−	0.785246i
$161$	−0.0544782	+	0.0179141i	−0.00429349	+	0.00141183i
$162$		0			0
$163$	17.1549	+	17.1549i	1.34368	+	1.34368i	0.892367	+	0.451310i	$0.149043\pi$
$163$	17.1549	+	17.1549i	1.34368	+	1.34368i	0.451310	+	0.892367i	$0.350957\pi$
$164$	−10.8961	−	2.91960i	−0.850843	−	0.227983i
$165$		0			0
$166$	15.5248	+	26.8897i	1.20496	+	2.08705i
$167$	−1.98472	−	7.40707i	−0.153582	−	0.573176i	−0.999223	−	0.0394232i	$-0.987448\pi$
$167$	−1.98472	−	7.40707i	−0.153582	−	0.573176i	0.845641	−	0.533753i	$-0.179219\pi$
$168$		0			0
$169$	−10.7811	−	7.26421i	−0.829312	−	0.558785i
$170$	−21.7931	+	37.7468i	−1.67146	+	2.89505i
$171$		0			0
$172$	8.78191			0.669614
$173$	−0.223665			−0.0170049			−0.00850246	−	0.999964i	$-0.502706\pi$
$173$	−0.223665			−0.0170049			−0.00850246	+	0.999964i	$0.502706\pi$
$174$		0			0
$175$	0.536454	−	0.176402i	0.0405521	−	0.0133348i
$176$	−3.08552	+	11.5153i	−0.232580	+	0.867999i
$177$		0			0
$178$	5.33351	+	3.07930i	0.399763	+	0.230803i
$179$			10.8654i			0.812115i	0.913848	+	0.406058i	$0.133097\pi$
$179$			10.8654i			0.812115i	−0.913848	+	0.406058i	$0.866903\pi$
$180$		0			0
$181$	−0.436016			−0.0324088			−0.0162044	−	0.999869i	$-0.505158\pi$
$181$	−0.436016			−0.0324088			−0.0162044	+	0.999869i	$0.505158\pi$
$182$	−16.7572	+	17.4843i	−1.24213	+	1.29603i
$183$		0			0
$184$	0.129966	+	0.0348242i	0.00958119	+	0.00256727i
$185$			21.4424i			1.57648i
$186$		0			0
$187$	12.6056	−	3.37767i	0.921815	−	0.246999i
$188$	6.69409	−	24.9827i	0.488216	−	1.82205i
$189$		0			0
$190$	24.6304	+	24.6304i	1.78688	+	1.78688i
$191$	8.84445			0.639962			0.319981	−	0.947424i	$-0.396323\pi$
$191$	8.84445			0.639962			0.319981	+	0.947424i	$0.396323\pi$
$192$		0			0
$193$	−6.37156	−	6.37156i	−0.458635	−	0.458635i	0.439572	−	0.898207i	$-0.355130\pi$
$193$	−6.37156	−	6.37156i	−0.458635	−	0.458635i	−0.898207	+	0.439572i	$0.855130\pi$
$194$	−9.76905	+	16.9205i	−0.701377	+	1.21482i
$195$		0			0
$196$	18.4668	+	25.0434i	1.31906	+	1.78881i
$197$	3.23591	+	12.0766i	0.230549	+	0.860421i	0.980105	+	0.198480i	$0.0636005\pi$
$197$	3.23591	+	12.0766i	0.230549	+	0.860421i	−0.749556	+	0.661941i	$0.769733\pi$
$198$		0			0
$199$	−4.17254	+	7.22706i	−0.295784	+	0.512313i	−0.975167	−	0.221471i	$-0.928914\pi$
$199$	−4.17254	+	7.22706i	−0.295784	+	0.512313i	0.679383	+	0.733784i	$0.262247\pi$
$200$	−1.27979	−	0.342918i	−0.0904945	−	0.0242479i
$201$		0			0
$202$	−10.9412	−	2.93169i	−0.769820	−	0.206273i
$203$	−1.52682	+	1.70781i	−0.107162	+	0.119864i
$204$		0			0
$205$	−5.01808	+	2.89719i	−0.350478	+	0.202348i
$206$	15.2105	−	15.2105i	1.05977	−	1.05977i
$207$		0			0
$208$	24.1298	−	5.57706i	1.67310	−	0.386699i
$209$		−	10.4294i		−	0.721413i
$210$		0			0
$211$	−0.0517275	+	0.0895946i	−0.00356106	+	0.00616794i	−0.867800	−	0.496913i	$-0.834467\pi$
$211$	−0.0517275	+	0.0895946i	−0.00356106	+	0.00616794i	0.864239	+	0.503081i	$0.167800\pi$
$212$			61.0908i			4.19573i
$213$		0			0
$214$	−6.66114	−	24.8597i	−0.455346	−	1.69937i
$215$	3.18972	−	3.18972i	0.217537	−	0.217537i
$216$		0			0
$217$	7.17754	−	14.2106i	0.487243	−	0.964679i
$218$	−8.93911	−	5.16100i	−0.605433	−	0.349547i
$219$		0			0
$220$	8.80774	+	15.2554i	0.593817	+	1.02852i
$221$	−18.4944	−	19.8231i	−1.24407	−	1.33345i
$222$		0			0
$223$	−25.3112	+	6.78211i	−1.69496	+	0.454163i	−0.971663	−	0.236372i	$-0.924041\pi$
$223$	−25.3112	+	6.78211i	−1.69496	+	0.454163i	−0.723298	+	0.690536i	$0.757375\pi$
$224$	−0.742426	−	13.2692i	−0.0496054	−	0.886583i
$225$		0			0
$226$	−3.02802	−	11.3007i	−0.201421	−	0.751712i
$227$	−13.1489	+	3.52323i	−0.872722	+	0.233845i	−0.667265	−	0.744821i	$-0.732535\pi$
$227$	−13.1489	+	3.52323i	−0.872722	+	0.233845i	−0.205458	+	0.978666i	$0.565868\pi$
$228$		0			0
$229$	−6.29210	−	23.4824i	−0.415794	−	1.55176i	−0.783241	−	0.621719i	$-0.786435\pi$
$229$	−6.29210	−	23.4824i	−0.415794	−	1.55176i	0.367447	−	0.930044i	$-0.380232\pi$
$230$	0.108812	−	0.0628227i	0.00717486	−	0.00414241i
$231$		0			0
$232$	5.19156	−	1.39107i	0.340843	−	0.0913285i
$233$	−8.29904	−	4.79145i	−0.543688	−	0.313899i	0.202884	−	0.979203i	$-0.434969\pi$
$233$	−8.29904	−	4.79145i	−0.543688	−	0.313899i	−0.746572	+	0.665304i	$0.768302\pi$
$234$		0			0
$235$	−6.64269	−	11.5055i	−0.433321	−	0.750535i
$236$	6.68091	−	24.9335i	0.434890	−	1.62303i
$237$		0			0
$238$	−42.2598	+	27.6566i	−2.73929	+	1.79271i
$239$	−5.64222	+	5.64222i	−0.364965	+	0.364965i	−0.865637	−	0.500672i	$-0.833086\pi$
$239$	−5.64222	+	5.64222i	−0.364965	+	0.364965i	0.500672	+	0.865637i	$0.333086\pi$
$240$		0			0
$241$	6.56799	+	24.5121i	0.423081	+	1.57896i	0.768078	+	0.640357i	$0.221213\pi$
$241$	6.56799	+	24.5121i	0.423081	+	1.57896i	−0.344997	+	0.938604i	$0.612120\pi$
$242$	−5.24848	+	19.5876i	−0.337385	+	1.25914i
$243$		0			0
$244$	−8.01095	+	13.8754i	−0.512849	+	0.888280i
$245$	15.8036	+	2.38869i	1.00965	+	0.152608i
$246$		0			0
$247$	−19.1275	+	10.1763i	−1.21705	+	0.647503i
$248$	−32.3482	+	18.6762i	−2.05411	+	1.18594i
$249$		0			0
$250$	24.0288	−	13.8730i	1.51971	−	0.877407i
$251$	5.75368	+	9.96567i	0.363169	+	0.629027i	0.988481	−	0.151348i	$-0.0483614\pi$
$251$	5.75368	+	9.96567i	0.363169	+	0.629027i	−0.625311	+	0.780375i	$0.715028\pi$
$252$		0			0
$253$	−0.0363381	−	0.00973676i	−0.00228456	−	0.000612145i
$254$	−5.72504	−	5.72504i	−0.359221	−	0.359221i
$255$		0			0
$256$	14.9423	−	25.8809i	0.933896	−	1.61756i
$257$	13.6912	+	23.7139i	0.854036	+	1.47923i	0.877536	+	0.479511i	$0.159186\pi$
$257$	13.6912	+	23.7139i	0.854036	+	1.47923i	−0.0234997	+	0.999724i	$0.507481\pi$
$258$		0			0
$259$	−11.2017	+	22.1778i	−0.696037	+	1.37806i
$260$	19.3846	−	31.0388i	1.20218	−	1.92494i
$261$		0			0
$262$	−14.9137	−	14.9137i	−0.921372	−	0.921372i
$263$	20.2715			1.25000			0.624998	−	0.780627i	$-0.285100\pi$
$263$	20.2715			1.25000			0.624998	+	0.780627i	$0.285100\pi$
$264$		0			0
$265$	22.1891	+	22.1891i	1.36307	+	1.36307i
$266$	12.6081	+	38.3423i	0.773052	+	2.35091i
$267$		0			0
$268$	−4.82540	+	1.29296i	−0.294758	+	0.0789803i
$269$	−1.57225	−	0.907738i	−0.0958617	−	0.0553458i	0.451303	−	0.892371i	$-0.350959\pi$
$269$	−1.57225	−	0.907738i	−0.0958617	−	0.0553458i	−0.547164	+	0.837025i	$0.684293\pi$
$270$		0			0
$271$	−21.2681	−	5.69876i	−1.29194	−	0.346175i	−0.453545	−	0.891234i	$-0.649841\pi$
$271$	−21.2681	−	5.69876i	−1.29194	−	0.346175i	−0.838398	+	0.545059i	$0.816507\pi$
$272$	51.6481			3.13163
$273$		0			0
$274$	−12.7369			−0.769466
$275$	0.357825	+	0.0958790i	0.0215777	+	0.00578172i
$276$		0			0
$277$	17.5808	+	10.1503i	1.05633	+	0.609873i	0.924415	−	0.381388i	$-0.124554\pi$
$277$	17.5808	+	10.1503i	1.05633	+	0.609873i	0.131916	+	0.991261i	$0.457887\pi$
$278$	6.66553	−	1.78602i	0.399772	−	0.107119i
$279$		0			0
$280$	−27.9561	−	24.9935i	−1.67070	−	1.49365i
$281$	14.1904	+	14.1904i	0.846529	+	0.846529i	0.989698	−	0.143169i	$-0.0457293\pi$
$281$	14.1904	+	14.1904i	0.846529	+	0.846529i	−0.143169	+	0.989698i	$0.545729\pi$
$282$		0			0
$283$	6.80207			0.404341			0.202171	−	0.979350i	$-0.435200\pi$
$283$	6.80207			0.404341			0.202171	+	0.979350i	$0.435200\pi$
$284$	−40.8167	−	40.8167i	−2.42203	−	2.42203i
$285$		0			0
$286$	−15.4787	+	3.57755i	−0.915276	+	0.211545i
$287$	−6.70370	+	0.375080i	−0.395707	+	0.0221403i
$288$		0			0
$289$	−19.7692	−	34.2413i	−1.16289	−	2.01419i
$290$	2.50950	−	4.34658i	0.147363	−	0.255240i
$291$		0			0
$292$	31.1775	+	31.1775i	1.82453	+	1.82453i
$293$	20.5482	+	5.50587i	1.20044	+	0.321656i	0.803004	−	0.595974i	$-0.203234\pi$
$293$	20.5482	+	5.50587i	1.20044	+	0.321656i	0.397435	+	0.917630i	$0.369901\pi$
$294$		0			0
$295$	−6.62962	−	11.4828i	−0.385991	−	0.668557i
$296$	50.4843	−	29.1471i	2.93434	−	1.69414i
$297$		0			0
$298$	−49.5852	+	28.6280i	−2.87239	+	1.65838i
$299$	0.0175991	+	0.0761448i	0.00101778	+	0.00440357i
$300$		0			0
$301$	4.96546	−	1.63279i	0.286204	−	0.0941127i
$302$	26.5560	−	45.9964i	1.52813	−	2.64679i
$303$		0			0
$304$	10.6829	−	39.8690i	0.612704	−	2.28664i
$305$	2.13005	+	7.94945i	0.121966	+	0.455184i
$306$		0			0
$307$	17.4862	−	17.4862i	0.997992	−	0.997992i	−0.00200593	−	0.999998i	$-0.500639\pi$
$307$	17.4862	−	17.4862i	0.997992	−	0.997992i	0.999998	+	0.00200593i	$0.000638508\pi$
$308$	1.14028	+	20.3799i	0.0649736	+	1.16125i
$309$		0			0
$310$	−9.02773	+	33.6919i	−0.512740	+	1.91357i
$311$	1.90903	+	3.30654i	0.108251	+	0.187497i	0.915062	−	0.403314i	$-0.132142\pi$
$311$	1.90903	+	3.30654i	0.108251	+	0.187497i	−0.806811	+	0.590810i	$0.798808\pi$
$312$		0			0
$313$	−11.1229	−	6.42180i	−0.628702	−	0.362981i	0.151547	−	0.988450i	$-0.451575\pi$
$313$	−11.1229	−	6.42180i	−0.628702	−	0.362981i	−0.780249	+	0.625469i	$0.784908\pi$
$314$	−16.1115	+	4.31705i	−0.909223	+	0.243625i
$315$		0			0
$316$	16.6862	−	9.63376i	0.938670	−	0.541941i
$317$	−2.44740	−	9.13383i	−0.137460	−	0.513007i	−0.999976	−	0.00697710i	$-0.997779\pi$
$317$	−2.44740	−	9.13383i	−0.137460	−	0.513007i	0.862516	−	0.506030i	$-0.168888\pi$
$318$		0			0
$319$	−1.45155	+	0.388941i	−0.0812712	+	0.0217765i
$320$	−0.582314	−	2.17322i	−0.0325523	−	0.121487i
$321$		0			0
$322$	0.145363	−	0.00813326i	0.00810078	−	0.000453249i
$323$	−43.6439	+	11.6944i	−2.42841	+	0.650692i
$324$		0			0
$325$	−0.173301	−	0.749807i	−0.00961299	−	0.0415918i
$326$	−30.7956	−	53.3396i	−1.70561	−	2.95421i
$327$		0			0
$328$	13.6424	+	7.87643i	0.753275	+	0.434903i
$329$	−0.859987	−	15.3703i	−0.0474126	−	0.847392i
$330$		0			0
$331$	11.1115	−	11.1115i	0.610743	−	0.610743i	−0.332397	−	0.943140i	$-0.607857\pi$
$331$	11.1115	−	11.1115i	0.610743	−	0.610743i	0.943140	+	0.332397i	$0.107857\pi$
$332$	−14.0708	−	52.5131i	−0.772237	−	2.88203i
$333$		0			0
$334$			19.4678i			1.06523i
$335$	−1.28304	+	2.22228i	−0.0700997	+	0.121416i
$336$		0			0
$337$		−	1.41323i		−	0.0769835i	−0.999259	−	0.0384917i	$-0.987745\pi$
$337$		−	1.41323i		−	0.0769835i	0.999259	−	0.0384917i	$-0.0122553\pi$
$338$	21.6644	+	24.8973i	1.17839	+	1.35424i
$339$		0			0
$340$	53.9638	−	53.9638i	2.92660	−	2.92660i
$341$	9.04449	−	5.22184i	0.489786	−	0.282778i
$342$		0			0
$343$	15.0977	+	10.7265i	0.815201	+	0.579177i
$344$	−11.8458	−	3.17407i	−0.638683	−	0.171135i
$345$		0			0
$346$	0.548475	+	0.146963i	0.0294862	+	0.00790081i
$347$	2.75091	−	4.76472i	0.147677	−	0.255784i	−0.782692	−	0.622410i	$-0.786154\pi$
$347$	2.75091	−	4.76472i	0.147677	−	0.255784i	0.930368	+	0.366626i	$0.119487\pi$
$348$		0			0
$349$	−3.51381	−	13.1137i	−0.188090	−	0.701960i	−0.993948	−	0.109852i	$-0.964962\pi$
$349$	−3.51381	−	13.1137i	−0.188090	−	0.701960i	0.805858	−	0.592109i	$-0.201704\pi$
$350$	−1.43141	+	0.0800892i	−0.0765121	+	0.00428095i
$351$		0			0
$352$	4.35905	−	7.55010i	0.232338	−	0.402421i
$353$	5.48924	+	5.48924i	0.292163	+	0.292163i	0.837934	−	0.545771i	$-0.183763\pi$
$353$	5.48924	+	5.48924i	0.292163	+	0.292163i	−0.545771	+	0.837934i	$0.683763\pi$
$354$		0			0
$355$	−29.6505			−1.57369
$356$	−7.62491	−	7.62491i	−0.404120	−	0.404120i
$357$		0			0
$358$	7.13930	−	26.6442i	0.377324	−	1.40819i
$359$	−22.0147	+	5.89881i	−1.16189	+	0.311327i	−0.787720	−	0.616033i	$-0.788739\pi$
$359$	−22.0147	+	5.89881i	−1.16189	+	0.311327i	−0.374169	+	0.927360i	$0.622072\pi$
$360$		0			0
$361$			17.1091i			0.900480i
$362$	1.06921	+	0.286493i	0.0561962	+	0.0150577i
$363$		0			0
$364$	36.2643	−	21.9767i	1.90077	−	1.15189i
$365$	22.6483			1.18547
$366$		0			0
$367$			21.2751i			1.11055i	0.831666	+	0.555276i	$0.187388\pi$
$367$			21.2751i			1.11055i	−0.831666	+	0.555276i	$0.812612\pi$
$368$	−0.128939	−	0.0744427i	−0.00672139	−	0.00388059i
$369$		0			0
$370$	14.0891	−	52.5814i	0.732460	−	2.73358i
$371$	11.3584	+	34.5419i	0.589700	+	1.79333i
$372$		0			0
$373$	16.6520			0.862207			0.431104	−	0.902302i	$-0.358124\pi$
$373$	16.6520			0.862207			0.431104	+	0.902302i	$0.358124\pi$
$374$	−33.1311			−1.71317
$375$		0			0
$376$	−18.0591	+	31.2793i	−0.931329	+	1.61311i
$377$	2.12965	+	2.28265i	0.109683	+	0.117562i
$378$		0			0
$379$	−4.72716	−	17.6420i	−0.242818	−	0.906209i	−0.974468	−	0.224528i	$-0.927916\pi$
$379$	−4.72716	−	17.6420i	−0.242818	−	0.906209i	0.731649	−	0.681681i	$-0.238751\pi$
$380$	−30.4947	−	52.8183i	−1.56434	−	2.70952i
$381$		0			0
$382$	−21.6885	−	5.81142i	−1.10968	−	0.297338i
$383$	−18.8703	−	18.8703i	−0.964225	−	0.964225i	0.0351564	−	0.999382i	$-0.488807\pi$
$383$	−18.8703	−	18.8703i	−0.964225	−	0.964225i	−0.999382	+	0.0351564i	$0.988807\pi$
$384$		0			0
$385$	7.81646	+	6.98813i	0.398364	+	0.356148i
$386$	11.4379	+	19.8110i	0.582174	+	1.00835i
$387$		0			0
$388$	24.1899	−	24.1899i	1.22806	−	1.22806i
$389$	−0.958138	+	0.553181i	−0.0485795	+	0.0280474i	−0.524093	−	0.851661i	$-0.675596\pi$
$389$	−0.958138	+	0.553181i	−0.0485795	+	0.0280474i	0.475514	+	0.879708i	$0.342262\pi$
$390$		0			0
$391$			0.162983i			0.00824238i
$392$	−15.8582	−	40.4552i	−0.800959	−	2.04330i
$393$		0			0
$394$		−	31.7406i		−	1.59907i
$395$	2.56154	−	9.55980i	0.128885	−	0.481006i
$396$		0			0
$397$	−10.0331	+	10.0331i	−0.503548	+	0.503548i	−0.912539	−	0.408990i	$-0.865881\pi$
$397$	−10.0331	+	10.0331i	−0.503548	+	0.503548i	0.408990	+	0.912539i	$0.365881\pi$
$398$	14.9807	−	14.9807i	0.750913	−	0.750913i
$399$		0			0
$400$	1.26967	+	0.733046i	0.0634837	+	0.0366523i
$401$	0.590311	−	2.20307i	0.0294787	−	0.110016i	−0.949619	−	0.313407i	$-0.898530\pi$
$401$	0.590311	−	2.20307i	0.0294787	−	0.110016i	0.979098	+	0.203391i	$0.0651962\pi$
$402$		0			0
$403$	−18.4019	−	11.4925i	−0.916665	−	0.572483i
$404$	17.1759	+	9.91652i	0.854533	+	0.493365i
$405$		0			0
$406$	4.86625	−	3.18468i	0.241508	−	0.158053i
$407$	−14.1153	+	8.14948i	−0.699670	+	0.403955i
$408$		0			0
$409$	19.0509	−	5.10468i	0.942008	−	0.252410i	0.245041	−	0.969513i	$-0.421199\pi$
$409$	19.0509	−	5.10468i	0.942008	−	0.252410i	0.696968	+	0.717102i	$0.254532\pi$
$410$	14.2091	−	3.80731i	0.701736	−	0.188030i
$411$		0			0
$412$	−32.6180	+	18.8320i	−1.60698	+	0.927788i
$413$	−0.858294	−	15.3400i	−0.0422339	−	0.754834i
$414$		0			0
$415$	−24.1843	−	13.9628i	−1.18716	−	0.685407i
$416$	−18.1002	−	0.627617i	−0.887436	−	0.0307715i
$417$		0			0
$418$	−6.85281	+	25.5751i	−0.335182	+	1.25092i
$419$	−11.9093	−	6.87586i	−0.581809	−	0.335908i	0.180043	−	0.983659i	$-0.442376\pi$
$419$	−11.9093	−	6.87586i	−0.581809	−	0.335908i	−0.761852	+	0.647751i	$0.775710\pi$
$420$		0			0
$421$	−18.9223	+	18.9223i	−0.922215	+	0.922215i	−0.997186	−	0.0749709i	$-0.976114\pi$
$421$	−18.9223	+	18.9223i	−0.922215	+	0.922215i	0.0749709	+	0.997186i	$0.476114\pi$
$422$	0.185717	−	0.185717i	0.00904056	−	0.00904056i
$423$		0			0
$424$	22.0802	−	82.4046i	1.07231	−	4.00192i
$425$		−	1.60491i		−	0.0778495i
$426$		0			0
$427$	−1.94974	+	9.33486i	−0.0943545	+	0.451745i
$428$			45.0630i			2.17820i
$429$		0			0
$430$	−9.91777	+	5.72603i	−0.478277	+	0.276134i
$431$	−20.1127	+	20.1127i	−0.968793	+	0.968793i	−0.999528	−	0.0307350i	$-0.990215\pi$
$431$	−20.1127	+	20.1127i	−0.968793	+	0.968793i	0.0307350	+	0.999528i	$0.490215\pi$
$432$		0			0
$433$	12.8931	+	22.3315i	0.619602	+	1.07318i	0.989558	+	0.144132i	$0.0460391\pi$
$433$	12.8931	+	22.3315i	0.619602	+	1.07318i	−0.369957	+	0.929049i	$0.620628\pi$
$434$	−26.9383	+	30.1314i	−1.29308	+	1.44635i
$435$		0			0
$436$	12.7796	+	12.7796i	0.612030	+	0.612030i
$437$	0.125812	+	0.0337112i	0.00601840	+	0.00161262i
$438$		0			0
$439$	−1.23875	−	2.14557i	−0.0591222	−	0.102403i	0.834949	−	0.550327i	$-0.185497\pi$
$439$	−1.23875	−	2.14557i	−0.0591222	−	0.102403i	−0.894072	+	0.447924i	$0.852164\pi$
$440$	−6.36682	−	23.7613i	−0.303526	−	1.13277i
$441$		0			0
$442$	32.3273	+	60.7627i	1.53765	+	2.89019i
$443$	11.6371	−	20.1560i	0.552894	−	0.957641i	−0.445170	−	0.895446i	$-0.646857\pi$
$443$	11.6371	−	20.1560i	0.552894	−	0.957641i	0.998064	−	0.0621947i	$-0.0198100\pi$
$444$		0			0
$445$	−5.53897			−0.262572
$446$	66.5248			3.15004
$447$		0			0
$448$	0.533021	−	2.55197i	0.0251829	−	0.120569i
$449$	2.13306	−	7.96070i	0.100665	−	0.375688i	−0.897152	−	0.441722i	$-0.854368\pi$
$449$	2.13306	−	7.96070i	0.100665	−	0.375688i	0.997817	+	0.0660335i	$0.0210344\pi$
$450$		0			0
$451$	−3.81438	−	2.20223i	−0.179612	−	0.103699i
$452$			20.4847i			0.963520i
$453$		0			0
$454$	34.5590			1.62193
$455$	5.18946	−	21.1540i	0.243286	−	0.991716i
$456$		0			0
$457$	5.33153	+	1.42858i	0.249399	+	0.0668261i	0.381352	−	0.924430i	$-0.375458\pi$
$457$	5.33153	+	1.42858i	0.249399	+	0.0668261i	−0.131954	+	0.991256i	$0.542125\pi$
$458$			61.7184i			2.88391i
$459$		0			0
$460$	−0.212500	+	0.0569391i	−0.00990785	+	0.00265480i
$461$	−8.89222	+	33.1862i	−0.414152	+	1.54564i	0.372377	+	0.928082i	$0.378543\pi$
$461$	−8.89222	+	33.1862i	−0.414152	+	1.54564i	−0.786529	+	0.617554i	$0.788124\pi$
$462$		0			0
$463$	10.3935	+	10.3935i	0.483025	+	0.483025i	0.906096	−	0.423072i	$-0.139048\pi$
$463$	10.3935	+	10.3935i	0.483025	+	0.483025i	−0.423072	+	0.906096i	$0.639048\pi$
$464$	−5.94733			−0.276098
$465$		0			0
$466$	17.2027	+	17.2027i	0.796902	+	0.796902i
$467$	−10.6589	+	18.4618i	−0.493237	+	0.854311i	−0.999970	−	0.00779214i	$-0.997520\pi$
$467$	−10.6589	+	18.4618i	−0.493237	+	0.854311i	0.506733	+	0.862103i	$0.330853\pi$
$468$		0			0
$469$	−2.48798	+	1.62824i	−0.114884	+	0.0751850i
$470$	8.72943	+	32.5787i	0.402658	+	1.50274i
$471$		0			0
$472$	−18.0236	+	31.2178i	−0.829603	+	1.43691i
$473$	3.31206	+	0.887464i	0.152289	+	0.0408056i
$474$		0			0
$475$	−1.23888	−	0.331958i	−0.0568439	−	0.0152313i
$476$	84.0057	−	27.6236i	3.85039	−	1.26613i
$477$		0			0
$478$	17.5433	−	10.1286i	0.802411	−	0.463272i
$479$	−10.5215	+	10.5215i	−0.480740	+	0.480740i	−0.905368	−	0.424628i	$-0.860405\pi$
$479$	−10.5215	+	10.5215i	−0.480740	+	0.480740i	0.424628	+	0.905368i	$0.360405\pi$
$480$		0			0
$481$	28.7190	+	17.9358i	1.30947	+	0.817803i
$482$		−	64.4246i		−	2.93446i
$483$		0			0
$484$	17.7531	−	30.7493i	0.806961	−	1.39770i
$485$		−	17.5723i		−	0.797918i
$486$		0			0
$487$	3.73572	+	13.9419i	0.169281	+	0.631767i	0.997455	+	0.0712956i	$0.0227134\pi$
$487$	3.73572	+	13.9419i	0.169281	+	0.631767i	−0.828174	+	0.560471i	$0.810620\pi$
$488$	15.8209	−	15.8209i	0.716178	−	0.716178i
$489$		0			0
$490$	−37.1843	−	16.2416i	−1.67981	−	0.733723i
$491$	−0.458913	−	0.264954i	−0.0207105	−	0.0119572i	0.489609	−	0.871942i	$-0.337140\pi$
$491$	−0.458913	−	0.264954i	−0.0207105	−	0.0119572i	−0.510319	+	0.859985i	$0.670473\pi$
$492$		0			0
$493$	3.25522	+	5.63821i	0.146608	+	0.253932i
$494$	53.5914	−	12.3864i	2.41119	−	0.557291i
$495$		0			0
$496$	39.9237	−	10.6975i	1.79263	−	0.480333i
$497$	−30.6675	−	15.4896i	−1.37562	−	0.694805i
$498$		0			0
$499$	6.57425	+	24.5354i	0.294304	+	1.09836i	0.941769	+	0.336261i	$0.109163\pi$
$499$	6.57425	+	24.5354i	0.294304	+	1.09836i	−0.647465	+	0.762095i	$0.724171\pi$
$500$	−46.9259	+	12.5738i	−2.09859	+	0.562316i
$501$		0			0
$502$	−7.56114	−	28.2186i	−0.337470	−	1.25946i
$503$	18.0905	−	10.4445i	0.806615	−	0.465699i	−0.0391641	−	0.999233i	$-0.512470\pi$
$503$	18.0905	−	10.4445i	0.806615	−	0.465699i	0.845779	+	0.533533i	$0.179136\pi$
$504$		0			0
$505$	9.84038	−	2.63672i	0.437891	−	0.117333i
$506$	0.0827112	+	0.0477533i	0.00367696	+	0.00212289i
$507$		0			0
$508$	7.08813	+	12.2770i	0.314485	+	0.544704i
$509$	2.99323	−	11.1709i	0.132673	−	0.495142i	−0.867324	−	0.497744i	$-0.834162\pi$
$509$	2.99323	−	11.1709i	0.132673	−	0.495142i	0.999997	+	0.00260275i	$0.000828483\pi$
$510$		0			0
$511$	23.4251	+	11.8316i	1.03627	+	0.523401i
$512$	−35.9022	+	35.9022i	−1.58667	+	1.58667i
$513$		0			0
$514$	−17.9922	−	67.1479i	−0.793602	−	2.96176i
$515$	−5.00729	+	18.6875i	−0.220647	+	0.823468i
$516$		0			0
$517$	5.04930	−	8.74564i	0.222068	−	0.384633i
$518$	42.0413	−	47.0246i	1.84719	−	2.06614i
$519$		0			0
$520$	−37.3660	+	34.8616i	−1.63861	+	1.52878i
$521$	−24.8573	+	14.3514i	−1.08902	+	0.628746i	−0.933315	−	0.359058i	$-0.883098\pi$
$521$	−24.8573	+	14.3514i	−1.08902	+	0.628746i	−0.155705	+	0.987804i	$0.549765\pi$
$522$		0			0
$523$	−1.33141	+	0.768693i	−0.0582187	+	0.0336126i	−0.528827	−	0.848730i	$-0.677368\pi$
$523$	−1.33141	+	0.768693i	−0.0582187	+	0.0336126i	0.470608	+	0.882342i	$0.344035\pi$
$524$	18.4645	+	31.9815i	0.806627	+	1.39712i
$525$		0			0
$526$	−49.7102	−	13.3198i	−2.16747	−	0.580771i
$527$	−31.9935	−	31.9935i	−1.39366	−	1.39366i
$528$		0			0
$529$	−11.4998	+	19.9182i	−0.499990	+	0.866008i
$530$	−39.8327	−	68.9923i	−1.73022	−	2.99684i
$531$		0			0
$532$	−3.94795	−	70.5606i	−0.171165	−	3.05919i
$533$	−0.317078	+	9.14440i	−0.0137342	+	0.396088i
$534$		0			0
$535$	16.3676	+	16.3676i	0.707631	+	0.707631i
$536$	6.97624			0.301328
$537$		0			0
$538$	3.25905	+	3.25905i	0.140508	+	0.140508i
$539$	4.43391	+	11.3112i	0.190982	+	0.487207i
$540$		0			0
$541$	−38.2161	+	10.2400i	−1.64304	+	0.440251i	−0.957652	−	0.287927i	$-0.907034\pi$
$541$	−38.2161	+	10.2400i	−1.64304	+	0.440251i	−0.685388	+	0.728178i	$0.740367\pi$
$542$	48.4094	+	27.9492i	2.07936	+	1.20052i
$543$		0			0
$544$	−36.4828	−	9.77555i	−1.56419	−	0.419123i
$545$	9.28347			0.397660
$546$		0			0
$547$	23.5304			1.00609			0.503043	−	0.864261i	$-0.332214\pi$
$547$	23.5304			1.00609			0.503043	+	0.864261i	$0.332214\pi$
$548$	21.5415	+	5.77203i	0.920207	+	0.246569i
$549$		0			0
$550$	−0.814467	−	0.470232i	−0.0347290	−	0.0200508i
$551$	5.02564	−	1.34662i	0.214099	−	0.0573678i
$552$		0			0
$553$	7.64350	−	8.54952i	0.325035	−	0.363563i
$554$	−36.4426	−	36.4426i	−1.54830	−	1.54830i
$555$		0			0
$556$	−12.0825			−0.512414
$557$	13.1965	+	13.1965i	0.559152	+	0.559152i	0.929066	−	0.369914i	$-0.120613\pi$
$557$	13.1965	+	13.1965i	0.559152	+	0.559152i	−0.369914	+	0.929066i	$0.620613\pi$
$558$		0			0
$559$	−1.60409	−	6.94028i	−0.0678456	−	0.293542i
$560$	22.7225	+	34.7204i	0.960202	+	1.46721i
$561$		0			0
$562$	−25.4739	−	44.1221i	−1.07455	−	1.86118i
$563$	−5.01839	+	8.69210i	−0.211500	+	0.366328i	−0.952184	−	0.305525i	$-0.901168\pi$
$563$	−5.01839	+	8.69210i	−0.211500	+	0.366328i	0.740684	+	0.671853i	$0.234501\pi$
$564$		0			0
$565$	7.44036	+	7.44036i	0.313018	+	0.313018i
$566$	−16.6802	−	4.46944i	−0.701119	−	0.187864i
$567$		0			0
$568$	40.3046	+	69.8097i	1.69114	+	2.92915i
$569$	−9.90569	+	5.71905i	−0.415268	+	0.239755i	−0.693051	−	0.720889i	$-0.743734\pi$
$569$	−9.90569	+	5.71905i	−0.415268	+	0.239755i	0.277783	+	0.960644i	$0.410401\pi$
$570$		0			0
$571$	−37.6951	+	21.7633i	−1.57749	+	0.910765i	−0.582284	+	0.812986i	$0.697841\pi$
$571$	−37.6951	+	21.7633i	−1.57749	+	0.910765i	−0.995208	+	0.0977796i	$0.968826\pi$
$572$	27.7999	+	0.963949i	1.16237	+	0.0403047i
$573$		0			0
$574$	16.6854	+	3.48502i	0.696435	+	0.145462i
$575$	−0.00231322	+	0.00400662i	−9.64681e−5	+	0.000167088i
$576$		0			0
$577$	0.354101	−	1.32152i	0.0147414	−	0.0550158i	−0.958163	−	0.286222i	$-0.907601\pi$
$577$	0.354101	−	1.32152i	0.0147414	−	0.0550158i	0.972905	+	0.231206i	$0.0742672\pi$
$578$	25.9795	+	96.9568i	1.08060	+	4.03287i
$579$		0			0
$580$	−6.21398	+	6.21398i	−0.258021	+	0.258021i
$581$	−17.7195	−	27.0758i	−0.735129	−	1.12329i
$582$		0			0
$583$	−6.17359	+	23.0401i	−0.255684	+	0.954225i
$584$	−30.7864	−	53.3236i	−1.27395	−	2.20655i
$585$		0			0
$586$	−46.7709	−	27.0032i	−1.93209	−	1.11549i
$587$	20.9489	−	5.61323i	0.864652	−	0.231683i	0.200878	−	0.979616i	$-0.435620\pi$
$587$	20.9489	−	5.61323i	0.864652	−	0.231683i	0.663774	+	0.747933i	$0.268954\pi$
$588$		0			0
$589$	−31.3144	+	18.0794i	−1.29029	+	0.744947i
$590$	8.71225	+	32.5145i	0.358678	+	1.33860i
$591$		0			0
$592$	−62.3071	+	16.6951i	−2.56081	+	0.686166i
$593$	1.09310	+	4.07949i	0.0448881	+	0.167525i	0.984731	−	0.174082i	$-0.0556957\pi$
$593$	1.09310	+	4.07949i	0.0448881	+	0.167525i	−0.939843	+	0.341606i	$0.889029\pi$
$594$		0			0
$595$	20.4788	−	40.5455i	0.839550	−	1.66220i
$596$	96.8352	−	25.9469i	3.96652	−	1.06283i
$597$		0			0
$598$	0.00687554	−	0.198288i	0.000281162	−	0.00810858i
$599$	−9.66178	−	16.7347i	−0.394770	−	0.683761i	0.598302	−	0.801271i	$-0.295842\pi$
$599$	−9.66178	−	16.7347i	−0.394770	−	0.683761i	−0.993072	+	0.117510i	$0.962509\pi$
$600$		0			0
$601$	−6.96892	−	4.02351i	−0.284268	−	0.164122i	0.351086	−	0.936343i	$-0.385813\pi$
$601$	−6.96892	−	4.02351i	−0.284268	−	0.164122i	−0.635354	+	0.772221i	$0.719146\pi$
$602$	−13.2493	+	0.741312i	−0.539999	+	0.0302136i
$603$		0			0
$604$	−65.7576	+	65.7576i	−2.67564	+	2.67564i
$605$	−4.72042	−	17.6168i	−0.191912	−	0.716226i
$606$		0			0
$607$		−	44.9749i		−	1.82547i	−0.408547	−	0.912737i	$-0.633964\pi$
$607$		−	44.9749i		−	1.82547i	0.408547	−	0.912737i	$-0.366036\pi$
$608$	−15.0922	+	26.1404i	−0.612068	+	1.06013i
$609$		0			0
$610$		−	20.8934i		−	0.845948i
$611$	−20.9663	−	0.726999i	−0.848207	−	0.0294112i
$612$		0			0
$613$	−3.82525	+	3.82525i	−0.154500	+	0.154500i	−0.780125	−	0.625624i	$-0.784844\pi$
$613$	−3.82525	+	3.82525i	−0.154500	+	0.154500i	0.625624	+	0.780125i	$0.284844\pi$
$614$	−54.3697	+	31.3904i	−2.19418	+	1.26681i
$615$		0			0
$616$	5.82787	−	27.9023i	0.234811	−	1.12422i
$617$	−21.1557	−	5.66866i	−0.851697	−	0.228212i	−0.193540	−	0.981092i	$-0.561997\pi$
$617$	−21.1557	−	5.66866i	−0.851697	−	0.228212i	−0.658157	+	0.752881i	$0.728664\pi$
$618$		0			0
$619$	−6.45170	−	1.72873i	−0.259316	−	0.0694834i	0.126819	−	0.991926i	$-0.459523\pi$
$619$	−6.45170	−	1.72873i	−0.259316	−	0.0694834i	−0.386135	+	0.922442i	$0.626190\pi$
$620$	30.5365	−	52.8909i	1.22638	−	2.12415i
$621$		0			0
$622$	−2.50873	−	9.36272i	−0.100591	−	0.375411i
$623$	−5.72895	−	2.89360i	−0.229526	−	0.115929i
$624$		0			0
$625$	−13.0108	+	22.5354i	−0.520433	+	0.901416i
$626$	23.0562	+	23.0562i	0.921510	+	0.921510i
$627$		0			0
$628$	29.2051			1.16541
$629$	49.9307	+	49.9307i	1.99087	+	1.99087i
$630$		0			0
$631$	−5.79046	+	21.6103i	−0.230515	+	0.860293i	0.749605	+	0.661886i	$0.230244\pi$
$631$	−5.79046	+	21.6103i	−0.230515	+	0.860293i	−0.980120	+	0.198407i	$0.936423\pi$
$632$	−25.9897	+	6.96392i	−1.03382	+	0.277010i
$633$		0			0
$634$			24.0063i			0.953411i
$635$	7.03371	+	1.88468i	0.279124	+	0.0747911i
$636$		0			0
$637$	16.4185	−	19.1686i	0.650523	−	0.759486i
$638$	3.81508			0.151040
$639$		0			0
$640$			28.6504i			1.13250i
$641$	−1.91511	−	1.10569i	−0.0756424	−	0.0436722i	0.461702	−	0.887035i	$-0.347239\pi$
$641$	−1.91511	−	1.10569i	−0.0756424	−	0.0436722i	−0.537344	+	0.843363i	$0.680572\pi$
$642$		0			0
$643$	−1.55263	+	5.79449i	−0.0612297	+	0.228512i	−0.989759	−	0.142746i	$-0.954407\pi$
$643$	−1.55263	+	5.79449i	−0.0612297	+	0.228512i	0.928530	+	0.371258i	$0.121074\pi$
$644$	−0.249534	−	0.0521193i	−0.00983301	−	0.00205379i
$645$		0			0
$646$	114.709			4.51315
$647$	−1.55351			−0.0610747			−0.0305373	−	0.999534i	$-0.509722\pi$
$647$	−1.55351			−0.0610747			−0.0305373	+	0.999534i	$0.509722\pi$
$648$		0			0
$649$	5.03936	−	8.72842i	0.197812	−	0.342621i
$650$	−0.0677042	+	1.95256i	−0.00265558	+	0.0765857i
$651$		0			0
$652$	27.9115	+	104.167i	1.09310	+	4.07950i
$653$	10.9877	+	19.0312i	0.429981	+	0.744749i	0.996871	−	0.0790445i	$-0.0251869\pi$
$653$	10.9877	+	19.0312i	0.429981	+	0.744749i	−0.566890	+	0.823793i	$0.691854\pi$
$654$		0			0
$655$	18.3228	+	4.90957i	0.715930	+	0.191833i
$656$	−12.3257	−	12.3257i	−0.481239	−	0.481239i
$657$		0			0
$658$	−7.99048	+	38.2564i	−0.311501	+	1.49139i
$659$	−13.5876	−	23.5344i	−0.529298	−	0.916771i	−0.999416	−	0.0341676i	$-0.989122\pi$
$659$	−13.5876	−	23.5344i	−0.529298	−	0.916771i	0.470118	−	0.882604i	$-0.344211\pi$
$660$		0			0
$661$	7.66117	−	7.66117i	0.297985	−	0.297985i	−0.542239	−	0.840224i	$-0.682423\pi$
$661$	7.66117	−	7.66117i	0.297985	−	0.297985i	0.840224	+	0.542239i	$0.182423\pi$
$662$	−34.5488	+	19.9468i	−1.34278	+	0.775254i
$663$		0			0
$664$			75.9199i			2.94626i
$665$	−27.0626	−	24.1947i	−1.04944	−	0.938231i
$666$		0			0
$667$		−	0.0187676i		−	0.000726684i
$668$	8.82230	−	32.9253i	0.341345	−	1.27392i
$669$		0			0
$670$	4.60648	−	4.60648i	0.177964	−	0.177964i
$671$	−4.42349	+	4.42349i	−0.170767	+	0.170767i
$672$		0			0
$673$	−33.8958	−	19.5698i	−1.30659	−	0.754359i	−0.325063	−	0.945692i	$-0.605386\pi$
$673$	−33.8958	−	19.5698i	−1.30659	−	0.754359i	−0.981525	+	0.191333i	$0.938719\pi$
$674$	−0.928590	+	3.46555i	−0.0357680	+	0.133488i
$675$		0			0
$676$	−25.3575	−	51.9257i	−0.975288	−	1.99714i
$677$	−13.3692	−	7.71873i	−0.513822	−	0.296655i	0.220582	−	0.975369i	$-0.429204\pi$
$677$	−13.3692	−	7.71873i	−0.513822	−	0.296655i	−0.734403	+	0.678714i	$0.762538\pi$
$678$		0			0
$679$	9.17990	−	18.1750i	0.352292	−	0.697494i
$680$	−92.2953	+	53.2867i	−3.53936	+	2.04345i
$681$		0			0
$682$	−25.6102	+	6.86223i	−0.980664	+	0.262768i
$683$	−45.0831	+	12.0800i	−1.72506	+	0.462227i	−0.979034	−	0.203695i	$-0.934705\pi$
$683$	−45.0831	+	12.0800i	−1.72506	+	0.462227i	−0.746021	+	0.665922i	$0.768038\pi$
$684$		0			0
$685$	9.92069	−	5.72771i	0.379050	−	0.218845i
$686$	−29.9749	−	36.2240i	−1.14445	−	1.38304i
$687$		0			0
$688$	11.7522	+	6.78514i	0.448049	+	0.258681i
$689$	48.2796	−	11.1587i	1.83931	−	0.425114i
$690$		0			0
$691$	−1.25695	+	4.69099i	−0.0478165	+	0.178454i	−0.985704	−	0.168486i	$-0.946112\pi$
$691$	−1.25695	+	4.69099i	−0.0478165	+	0.178454i	0.937888	+	0.346939i	$0.112779\pi$
$692$	−0.861017	−	0.497108i	−0.0327310	−	0.0188972i
$693$		0			0
$694$	−9.87660	+	9.87660i	−0.374910	+	0.374910i
$695$	−4.38857	+	4.38857i	−0.166468	+	0.166468i
$696$		0			0
$697$	−4.93870	+	18.4315i	−0.187067	+	0.698142i
$698$			34.4665i			1.30458i
$699$		0			0
$700$	2.45719	+	0.513224i	0.0928730	+	0.0193981i
$701$		−	34.8788i		−	1.31735i	−0.752426	−	0.658677i	$-0.771116\pi$
$701$		−	34.8788i		−	1.31735i	0.752426	−	0.658677i	$-0.228884\pi$
$702$		0			0
$703$	48.8709	−	28.2156i	1.84320	−	1.06417i
$704$	1.20930	−	1.20930i	0.0455770	−	0.0455770i
$705$		0			0
$706$	−9.85401	−	17.0676i	−0.370861	−	0.642349i
$707$	11.5553	+	2.41352i	0.434583	+	0.0907699i
$708$		0			0
$709$	−31.3560	−	31.3560i	−1.17760	−	1.17760i	−0.980354	−	0.197246i	$-0.936800\pi$
$709$	−31.3560	−	31.3560i	−1.17760	−	1.17760i	−0.197246	−	0.980354i	$-0.563200\pi$
$710$	72.7095	+	19.4825i	2.72874	+	0.731164i
$711$		0			0
$712$	7.52925	+	13.0410i	0.282171	+	0.488734i
$713$	0.0337575	+	0.125985i	0.00126423	+	0.00471816i
$714$		0			0
$715$	10.4475	−	9.74722i	0.390713	−	0.364525i
$716$	−24.1489	+	41.8271i	−0.902487	+	1.56315i
$717$		0			0
$718$	57.8607			2.15934
$719$	23.4461			0.874394			0.437197	−	0.899366i	$-0.355971\pi$
$719$	23.4461			0.874394			0.437197	+	0.899366i	$0.355971\pi$
$720$		0			0
$721$	−14.9415	+	16.7126i	−0.556450	+	0.622409i
$722$	11.2419	−	41.9553i	0.418380	−	1.56141i
$723$		0			0
$724$	−1.67848	−	0.969071i	−0.0623802	−	0.0360152i
$725$			0.184807i			0.00686355i
$726$		0			0
$727$	4.34538			0.161161			0.0805806	−	0.996748i	$-0.474323\pi$
$727$	4.34538			0.161161			0.0805806	+	0.996748i	$0.474323\pi$
$728$	−56.8596	+	16.5370i	−2.10736	+	0.612902i
$729$		0			0
$730$	−55.5386	−	14.8815i	−2.05558	−	0.550790i
$731$		−	14.8552i		−	0.549438i
$732$		0			0
$733$	42.9792	−	11.5162i	1.58747	−	0.425362i	0.646245	−	0.763130i	$-0.276339\pi$
$733$	42.9792	−	11.5162i	1.58747	−	0.425362i	0.941229	+	0.337768i	$0.109672\pi$
$734$	13.9792	−	52.1713i	0.515984	−	1.92568i
$735$		0			0
$736$	0.0769888	+	0.0769888i	0.00283784	+	0.00283784i
$737$	−1.95054			−0.0718491
$738$		0			0
$739$	20.6855	+	20.6855i	0.760929	+	0.760929i	0.976490	−	0.215561i	$-0.0691581\pi$
$739$	20.6855	+	20.6855i	0.760929	+	0.760929i	−0.215561	+	0.976490i	$0.569158\pi$
$740$	−47.6570	+	82.5443i	−1.75190	+	3.03439i
$741$		0			0
$742$	−5.15689	−	92.1676i	−0.189315	−	3.38358i
$743$	2.66460	+	9.94444i	0.0977548	+	0.364826i	0.997423	−	0.0717489i	$-0.0228580\pi$
$743$	2.66460	+	9.94444i	0.0977548	+	0.364826i	−0.899668	+	0.436575i	$0.856191\pi$
$744$		0			0
$745$	25.7477	−	44.5963i	0.943323	−	1.63388i
$746$	−40.8343	−	10.9415i	−1.49505	−	0.400598i
$747$		0			0
$748$	56.0335	+	15.0141i	2.04879	+	0.548971i
$749$	8.37842	+	25.4795i	0.306141	+	0.931000i
$750$		0			0
$751$	−18.5810	+	10.7278i	−0.678031	+	0.391462i	−0.799113	−	0.601181i	$-0.794697\pi$
$751$	−18.5810	+	10.7278i	−0.678031	+	0.391462i	0.121081	+	0.992643i	$0.461364\pi$
$752$	28.2605	−	28.2605i	1.03055	−	1.03055i
$753$		0			0
$754$	−3.72251	−	6.99688i	−0.135566	−	0.254811i
$755$			47.7683i			1.73847i
$756$		0			0
$757$	−18.9933	+	32.8973i	−0.690322	+	1.19567i	0.281410	+	0.959588i	$0.409198\pi$
$757$	−18.9933	+	32.8973i	−0.690322	+	1.19567i	−0.971732	+	0.236085i	$0.924136\pi$
$758$			46.3682i			1.68417i
$759$		0			0
$760$	22.0436	+	82.2677i	0.799604	+	2.98416i
$761$	−11.9557	+	11.9557i	−0.433393	+	0.433393i	−0.889781	−	0.456388i	$-0.849143\pi$
$761$	−11.9557	+	11.9557i	−0.433393	+	0.433393i	0.456388	+	0.889781i	$0.349143\pi$
$762$		0			0
$763$	9.60188	+	4.84975i	0.347611	+	0.175573i
$764$	34.0475	+	19.6573i	1.23179	+	0.711177i
$765$		0			0
$766$	33.8749	+	58.6731i	1.22395	+	2.11995i
$767$	−20.9251	−	0.725568i	−0.755561	−	0.0261987i
$768$		0			0
$769$	−35.8744	+	9.61252i	−1.29366	+	0.346636i	−0.839051	−	0.544052i	$-0.816889\pi$
$769$	−35.8744	+	9.61252i	−1.29366	+	0.346636i	−0.454614	+	0.890689i	$0.650223\pi$
$770$	−14.5760	−	22.2724i	−0.525282	−	0.802641i
$771$		0			0
$772$	−10.3667	−	38.6890i	−0.373106	−	1.39245i
$773$	−11.3980	+	3.05409i	−0.409958	+	0.109848i	−0.457903	−	0.889002i	$-0.651399\pi$
$773$	−11.3980	+	3.05409i	−0.409958	+	0.109848i	0.0479452	+	0.998850i	$0.484733\pi$
$774$		0			0
$775$	−0.332414	−	1.24059i	−0.0119407	−	0.0445631i
$776$	−41.3726	+	23.8865i	−1.48519	+	0.857474i
$777$		0			0
$778$	2.71304	−	0.726958i	0.0972673	−	0.0260627i
$779$	13.2064	+	7.62470i	0.473167	+	0.273183i
$780$		0			0
$781$	−11.2691	−	19.5186i	−0.403240	−	0.698431i
$782$	0.107091	−	0.399669i	0.00382956	−	0.0142921i
$783$		0			0
$784$	5.36368	+	47.7817i	0.191560	+	1.70649i
$785$	10.6077	−	10.6077i	0.378607	−	0.378607i
$786$		0			0
$787$	−1.05985	−	3.95541i	−0.0377795	−	0.140995i	0.944460	−	0.328626i	$-0.106586\pi$
$787$	−1.05985	−	3.95541i	−0.0377795	−	0.140995i	−0.982240	+	0.187631i	$0.939919\pi$
$788$	−14.3840	+	53.6818i	−0.512409	+	1.91234i
$789$		0			0
$790$	−12.5629	+	21.7596i	−0.446968	+	0.774172i
$791$	3.80866	+	11.5825i	0.135420	+	0.411825i
$792$		0			0
$793$	12.4289	+	3.79655i	0.441362	+	0.134819i
$794$	31.1959	−	18.0110i	1.10710	−	0.639185i
$795$		0			0
$796$	−32.1251	+	18.5475i	−1.13864	+	0.657397i
$797$	−1.02216	−	1.77043i	−0.0362067	−	0.0627119i	0.847354	−	0.531028i	$-0.178194\pi$
$797$	−1.02216	−	1.77043i	−0.0362067	−	0.0627119i	−0.883561	+	0.468316i	$0.844861\pi$
$798$		0			0
$799$	−42.2598	−	11.3235i	−1.49504	−	0.400596i
$800$	−0.758117	−	0.758117i	−0.0268035	−	0.0268035i
$801$		0			0
$802$	−2.89514	+	5.01454i	−0.102231	+	0.177069i
$803$	8.60781	+	14.9092i	0.303763	+	0.526133i
$804$		0			0
$805$	−0.109565	+	0.0717039i	−0.00386166	+	0.00252723i
$806$	37.5742	+	40.2735i	1.32349	+	1.41857i
$807$		0			0
$808$	−19.5842	−	19.5842i	−0.688970	−	0.688970i
$809$	27.1722			0.955322			0.477661	−	0.878544i	$-0.341485\pi$
$809$	27.1722			0.955322			0.477661	+	0.878544i	$0.341485\pi$
$810$		0			0
$811$	18.4741	+	18.4741i	0.648712	+	0.648712i	0.952682	−	0.303970i	$-0.0983122\pi$
$811$	18.4741	+	18.4741i	0.648712	+	0.648712i	−0.303970	+	0.952682i	$0.598312\pi$
$812$	−9.67333	+	3.18088i	−0.339467	+	0.111627i
$813$		0			0
$814$	39.9686	−	10.7096i	1.40090	−	0.375370i
$815$	47.9730	+	27.6972i	1.68042	+	0.970191i
$816$		0			0
$817$	−11.4672	−	3.07263i	−0.401187	−	0.107498i
$818$	−50.0712			−1.75070
$819$		0			0
$820$	−25.7567			−0.899462
$821$	1.59604	+	0.427657i	0.0557021	+	0.0149253i	0.286562	−	0.958062i	$-0.407487\pi$
$821$	1.59604	+	0.427657i	0.0557021	+	0.0149253i	−0.230860	+	0.972987i	$0.574154\pi$
$822$		0			0
$823$	−22.8653	−	13.2013i	−0.797033	−	0.460167i	0.0453998	−	0.998969i	$-0.485544\pi$
$823$	−22.8653	−	13.2013i	−0.797033	−	0.460167i	−0.842433	+	0.538802i	$0.818877\pi$
$824$	50.8046	−	13.6131i	1.76986	−	0.474233i
$825$		0			0
$826$	−7.97476	+	38.1811i	−0.277477	+	1.32849i
$827$	−21.2610	−	21.2610i	−0.739319	−	0.739319i	0.233127	−	0.972446i	$-0.425104\pi$
$827$	−21.2610	−	21.2610i	−0.739319	−	0.739319i	−0.972446	+	0.233127i	$0.925104\pi$
$828$		0			0
$829$	−28.6228			−0.994111			−0.497056	−	0.867719i	$-0.665586\pi$
$829$	−28.6228			−0.994111			−0.497056	+	0.867719i	$0.665586\pi$
$830$	50.1306	+	50.1306i	1.74006	+	1.74006i
$831$		0			0
$832$	−3.39781	−	1.03790i	−0.117798	−	0.0359828i
$833$	42.3625	−	31.2378i	1.46777	−	1.08233i
$834$		0			0
$835$	−8.75457	−	15.1634i	−0.302964	−	0.524750i
$836$	23.1798	−	40.1487i	0.801692	−	1.38857i
$837$		0			0
$838$	24.6864	+	24.6864i	0.852776	+	0.852776i
$839$	2.96674	+	0.794936i	0.102423	+	0.0274442i	0.309667	−	0.950845i	$-0.399783\pi$
$839$	2.96674	+	0.794936i	0.102423	+	0.0274442i	−0.207243	+	0.978289i	$0.566449\pi$
$840$		0			0
$841$	14.1252	+	24.4655i	0.487074	+	0.843638i
$842$	58.8348	−	33.9683i	2.02758	−	1.17062i
$843$		0			0
$844$	−0.398258	+	0.229935i	−0.0137086	+	0.00791467i
$845$	−28.0704	−	9.64999i	−0.965652	−	0.331970i
$846$		0			0
$847$	4.32084	−	20.6871i	0.148466	−	0.710816i
$848$	−47.2004	+	81.7534i	−1.62087	+	2.80742i
$849$		0			0
$850$	−1.05454	+	3.93559i	−0.0361703	+	0.134989i
$851$	−0.0526837	−	0.196618i	−0.00180597	−	0.00673999i
$852$		0			0
$853$	−15.7683	+	15.7683i	−0.539896	+	0.539896i	−0.923498	−	0.383603i	$-0.874683\pi$
$853$	−15.7683	+	15.7683i	−0.539896	+	0.539896i	0.383603	+	0.923498i	$0.374683\pi$
$854$	10.9148	−	21.6100i	0.373498	−	0.739479i
$855$		0			0
$856$	16.2873	−	60.7849i	0.556687	−	2.07758i
$857$	−8.97423	−	15.5438i	−0.306554	−	0.530967i	0.671052	−	0.741410i	$-0.265843\pi$
$857$	−8.97423	−	15.5438i	−0.306554	−	0.530967i	−0.977606	+	0.210443i	$0.932509\pi$
$858$		0			0
$859$	−49.1470	−	28.3750i	−1.67687	−	0.968144i	−0.963635	−	0.267223i	$-0.913894\pi$
$859$	−49.1470	−	28.3750i	−1.67687	−	0.968144i	−0.713239	−	0.700921i	$-0.752773\pi$
$860$	19.3685	−	5.18976i	0.660459	−	0.176969i
$861$		0			0
$862$	62.5361	−	36.1052i	2.12999	−	1.22975i
$863$	2.21271	+	8.25794i	0.0753215	+	0.281104i	0.993306	−	0.115513i	$-0.0368511\pi$
$863$	2.21271	+	8.25794i	0.0753215	+	0.281104i	−0.917985	+	0.396616i	$0.870184\pi$
$864$		0			0
$865$	−0.493292	+	0.132177i	−0.0167724	+	0.00449416i
$866$	−16.9433	−	63.2333i	−0.575757	−	2.14875i
$867$		0			0
$868$	59.2145	−	38.7524i	2.00987	−	1.31534i
$869$	7.26667	−	1.94710i	0.246505	−	0.0660508i
$870$		0			0
$871$	1.90322	+	3.57731i	0.0644880	+	0.121212i
$872$	−12.6192	−	21.8572i	−0.427341	−	0.740177i
$873$		0			0
$874$	−0.286368	−	0.165334i	−0.00968653	−	0.00559252i
$875$	−24.1950	+	15.8342i	−0.817941	+	0.535295i
$876$		0			0
$877$	19.6573	−	19.6573i	0.663781	−	0.663781i	−0.292488	−	0.956269i	$-0.594483\pi$
$877$	19.6573	−	19.6573i	0.663781	−	0.663781i	0.956269	+	0.292488i	$0.0944831\pi$
$878$	1.62789	+	6.07536i	0.0549386	+	0.205034i
$879$		0			0
$880$			27.2204i			0.917598i
$881$	−7.37078	+	12.7666i	−0.248328	+	0.430116i	−0.963062	−	0.269280i	$-0.913214\pi$
$881$	−7.37078	+	12.7666i	−0.248328	+	0.430116i	0.714734	+	0.699396i	$0.246548\pi$
$882$		0			0
$883$		−	16.7260i		−	0.562876i	−0.959579	−	0.281438i	$-0.909189\pi$
$883$		−	16.7260i		−	0.562876i	0.959579	−	0.281438i	$-0.0908114\pi$
$884$	−27.1379	−	117.416i	−0.912748	−	3.94911i
$885$		0			0
$886$	−41.7806	+	41.7806i	−1.40365	+	1.40365i
$887$	−15.9425	+	9.20441i	−0.535297	+	0.309054i	−0.743171	−	0.669102i	$-0.766679\pi$
$887$	−15.9425	+	9.20441i	−0.535297	+	0.309054i	0.207874	+	0.978156i	$0.433346\pi$
$888$		0			0
$889$	6.29039	+	5.62378i	0.210973	+	0.188615i
$890$	13.5828	+	3.63949i	0.455295	+	0.121996i
$891$		0			0
$892$	−112.511	−	30.1473i	−3.76715	−	1.00940i
$893$	−17.4820	+	30.2797i	−0.585012	+	1.01327i
$894$		0			0
$895$	6.42100	+	23.9635i	0.214630	+	0.801011i
$896$	−14.9671	+	29.6330i	−0.500017	+	0.989970i
$897$		0			0
$898$	−10.4615	+	18.1198i	−0.349104	+	0.604665i
$899$	3.68408	+	3.68408i	0.122871	+	0.122871i
$900$		0			0
$901$	103.339			3.44272
$902$	7.90667	+	7.90667i	0.263263	+	0.263263i
$903$		0			0
$904$	7.40386	−	27.6316i	0.246249	−	0.919012i
$905$	−0.961631	+	0.257668i	−0.0319657	+	0.00856518i
$906$		0			0
$907$		−	28.8547i		−	0.958105i	−0.877786	−	0.479053i	$-0.840980\pi$
$907$		−	28.8547i		−	0.958105i	0.877786	−	0.479053i	$-0.159020\pi$
$908$	−58.4483	−	15.6612i	−1.93968	−	0.519735i
$909$		0			0
$910$	−26.6254	+	48.4644i	−0.882622	+	1.60658i
$911$	13.0437			0.432159			0.216079	−	0.976376i	$-0.430673\pi$
$911$	13.0437			0.432159			0.216079	+	0.976376i	$0.430673\pi$
$912$		0			0
$913$		−	21.2270i		−	0.702512i
$914$	−12.1354	−	7.00638i	−0.401403	−	0.231750i
$915$		0			0
$916$	27.9691	−	104.382i	0.924126	−	3.44888i
$917$	16.3864	+	14.6499i	0.541127	+	0.483782i
$918$		0			0
$919$	6.81332			0.224751			0.112375	−	0.993666i	$-0.464154\pi$
$919$	6.81332			0.224751			0.112375	+	0.993666i	$0.464154\pi$
$920$	0.307218			0.0101287
$921$		0			0
$922$	43.6113	−	75.5370i	1.43626	−	2.48768i
$923$	−24.8016	+	39.7126i	−0.816356	+	1.30716i
$924$		0			0
$925$	0.518783	+	1.93612i	0.0170575	+	0.0636593i
$926$	−18.6578	−	32.3163i	−0.613133	−	1.06198i
$927$		0			0
$928$	4.20103	+	1.12566i	0.137906	+	0.0369517i
$929$	−3.62723	−	3.62723i	−0.119006	−	0.119006i	0.645096	−	0.764102i	$-0.276817\pi$
$929$	−3.62723	−	3.62723i	−0.119006	−	0.119006i	−0.764102	+	0.645096i	$0.776817\pi$
$930$		0			0
$931$	−15.3514	−	39.1623i	−0.503120	−	1.28349i
$932$	−21.2986	−	36.8902i	−0.697658	−	1.20838i
$933$		0			0
$934$	38.2687	−	38.2687i	1.25219	−	1.25219i
$935$	25.8056	−	14.8989i	0.843932	−	0.487245i
$936$		0			0
$937$		−	49.7519i		−	1.62532i	−0.582736	−	0.812662i	$-0.698018\pi$
$937$		−	49.7519i		−	1.62532i	0.582736	−	0.812662i	$-0.301982\pi$
$938$	7.17093	−	2.35802i	0.234139	−	0.0769921i
$939$		0			0
$940$		−	59.0551i		−	1.92616i
$941$	14.9061	−	55.6304i	0.485926	−	1.81350i	−0.0899311	−	0.995948i	$-0.528665\pi$
$941$	14.9061	−	55.6304i	0.485926	−	1.81350i	0.575857	−	0.817551i	$-0.304669\pi$
$942$		0			0
$943$	0.0388954	−	0.0388954i	0.00126661	−	0.00126661i
$944$	28.2049	−	28.2049i	0.917991	−	0.917991i
$945$		0			0
$946$	−7.53877	−	4.35251i	−0.245107	−	0.141512i
$947$	4.20655	−	15.6990i	0.136694	−	0.510151i	−0.863291	−	0.504707i	$-0.831601\pi$
$947$	4.20655	−	15.6990i	0.136694	−	0.510151i	0.999985	−	0.00544363i	$-0.00173277\pi$
$948$		0			0
$949$	18.9445	−	30.3342i	0.614966	−	0.984690i
$950$	2.81989	+	1.62807i	0.0914895	+	0.0528215i
$951$		0			0
$952$	−123.298	+	6.89869i	−3.99612	+	0.223588i
$953$	−8.84363	+	5.10587i	−0.286473	+	0.165395i	−0.636350	−	0.771400i	$-0.719557\pi$
$953$	−8.84363	+	5.10587i	−0.286473	+	0.165395i	0.349877	+	0.936796i	$0.386223\pi$
$954$		0			0
$955$	19.5064	−	5.22672i	0.631212	−	0.169133i
$956$	−34.2603	+	9.18003i	−1.10806	+	0.296903i
$957$		0			0
$958$	32.7144	−	18.8877i	1.05695	−	0.610233i
$959$	13.2532	−	0.741530i	0.427967	−	0.0239453i
$960$		0			0
$961$	−4.51058	−	2.60419i	−0.145503	−	0.0840060i
$962$	−58.6402	−	62.8530i	−1.89064	−	2.02646i
$963$		0			0
$964$	−29.1955	+	108.959i	−0.940323	+	3.50933i
$965$	−17.8178	−	10.2871i	−0.573575	−	0.331154i
$966$		0			0
$967$	13.8579	−	13.8579i	0.445641	−	0.445641i	−0.448261	−	0.893903i	$-0.647957\pi$
$967$	13.8579	−	13.8579i	0.445641	−	0.445641i	0.893903	+	0.448261i	$0.147957\pi$
$968$	−35.0608	+	35.0608i	−1.12690	+	1.12690i
$969$		0			0
$970$	−11.5462	+	43.0912i	−0.370727	+	1.38357i
$971$			5.48046i			0.175876i	0.996126	+	0.0879381i	$0.0280278\pi$
$971$			5.48046i			0.175876i	−0.996126	+	0.0879381i	$0.971972\pi$
$972$		0			0
$973$	−6.83170	+	2.24647i	−0.219014	+	0.0720186i
$974$		−	36.6432i		−	1.17412i
$975$		0			0
$976$	−21.4410	+	12.3790i	−0.686309	+	0.396241i
$977$	−15.5007	+	15.5007i	−0.495912	+	0.495912i	−0.910163	−	0.414251i	$-0.864044\pi$
$977$	−15.5007	+	15.5007i	−0.495912	+	0.495912i	0.414251	+	0.910163i	$0.364044\pi$
$978$		0			0
$979$	−2.10516	−	3.64625i	−0.0672813	−	0.116535i
$980$	55.5282	+	44.3198i	1.77378	+	1.41575i
$981$		0			0
$982$	0.951263	+	0.951263i	0.0303560	+	0.0303560i
$983$	0.0940093	+	0.0251897i	0.00299843	+	0.000803427i	0.260318	−	0.965523i	$-0.416173\pi$
$983$	0.0940093	+	0.0251897i	0.00299843	+	0.000803427i	−0.257320	+	0.966326i	$0.582839\pi$
$984$		0			0
$985$	14.2736	+	24.7225i	0.454794	+	0.787726i
$986$	−4.27782	−	15.9650i	−0.136234	−	0.508431i
$987$		0			0
$988$	−96.2504	−	3.33744i	−3.06213	−	0.106178i
$989$	−0.0214114	+	0.0370856i	−0.000680843	+	0.00117925i
$990$		0			0
$991$	9.43469			0.299703			0.149851	−	0.988709i	$-0.452120\pi$
$991$	9.43469			0.299703			0.149851	+	0.988709i	$0.452120\pi$
$992$	−30.2258			−0.959669
$993$		0			0
$994$	65.0256	+	58.1346i	2.06249	+	1.84392i
$995$	−4.93162	+	18.4051i	−0.156343	+	0.583479i
$996$		0			0
$997$	33.3314	+	19.2439i	1.05562	+	0.609461i	0.924217	−	0.381869i	$-0.124719\pi$
$997$	33.3314	+	19.2439i	1.05562	+	0.609461i	0.131400	+	0.991329i	$0.458053\pi$
$998$		−	64.4860i		−	2.04127i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.c.19.1		36
3.2	odd	2		273.2.cg.a.19.9	yes	36
7.3	odd	6		819.2.et.c.136.9		36
13.11	odd	12		819.2.et.c.271.9		36
21.17	even	6		273.2.bt.a.136.1	✓	36
39.11	even	12		273.2.bt.a.271.1	yes	36
91.24	even	12	inner	819.2.gh.c.388.1		36
273.206	odd	12		273.2.cg.a.115.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.1	✓	36	21.17	even	6
273.2.bt.a.271.1	yes	36	39.11	even	12
273.2.cg.a.19.9	yes	36	3.2	odd	2
273.2.cg.a.115.9	yes	36	273.206	odd	12
819.2.et.c.136.9		36	7.3	odd	6
819.2.et.c.271.9		36	13.11	odd	12
819.2.gh.c.19.1		36	1.1	even	1	trivial
819.2.gh.c.388.1		36	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)

\(f(q)\)	\(=\)	\(q+(-2.45222 - 0.657070i) q^{2} +(3.84958 + 2.22256i) q^{4} +(2.20549 - 0.590961i) q^{5} +(2.58986 + 0.540936i) q^{7} +(-4.38935 - 4.38935i) q^{8} +O(q^{10})\)	\(q+(-2.45222 - 0.657070i) q^{2} +(3.84958 + 2.22256i) q^{4} +(2.20549 - 0.590961i) q^{5} +(2.58986 + 0.540936i) q^{7} +(-4.38935 - 4.38935i) q^{8} -5.79666 q^{10} +(1.22725 + 1.22725i) q^{11} +(1.05331 - 3.44826i) q^{13} +(-5.99548 - 3.02821i) q^{14} +(3.43442 + 5.94858i) q^{16} +(3.75960 - 6.51182i) q^{17} +(-4.24907 - 4.24907i) q^{19} +(9.80368 + 2.62689i) q^{20} +(-2.20310 - 3.81588i) q^{22} +(-0.0187715 + 0.0108378i) q^{23} +(0.184846 - 0.106721i) q^{25} +(-4.84871 + 7.76380i) q^{26} +(8.76763 + 7.83850i) q^{28} +(-0.432921 + 0.749842i) q^{29} +(1.55740 - 5.81230i) q^{31} +(-1.30008 - 4.85196i) q^{32} +(-13.4981 + 13.4981i) q^{34} +(6.03160 - 0.337475i) q^{35} +(-2.43056 + 9.07099i) q^{37} +(7.62770 + 13.2116i) q^{38} +(-12.2746 - 7.08675i) q^{40} +(-2.45125 + 0.656811i) q^{41} +(1.71095 - 0.987815i) q^{43} +(1.99677 + 7.45205i) q^{44} +(0.0531531 - 0.0142423i) q^{46} +(-1.50594 - 5.62025i) q^{47} +(6.41478 + 2.80190i) q^{49} +(-0.523405 + 0.140246i) q^{50} +(11.7188 - 10.9333i) q^{52} +(6.87167 + 11.9021i) q^{53} +(3.43196 + 1.98144i) q^{55} +(-8.99345 - 13.7422i) q^{56} +(1.55432 - 1.55432i) q^{58} +(-1.50298 - 5.60919i) q^{59} +3.60438i q^{61} +(-7.63818 + 13.2297i) q^{62} -0.985368i q^{64} +(0.285288 - 8.22760i) q^{65} +(-0.794679 + 0.794679i) q^{67} +(28.9458 - 16.7119i) q^{68} +(-15.0125 - 3.13562i) q^{70} +(-12.5434 - 3.36098i) q^{71} +(9.58115 + 2.56726i) q^{73} +(11.9205 - 20.6470i) q^{74} +(-6.91334 - 25.8009i) q^{76} +(2.51455 + 3.84228i) q^{77} +(2.16727 - 3.75382i) q^{79} +(11.0900 + 11.0900i) q^{80} +6.44258 q^{82} +(-8.64819 - 8.64819i) q^{83} +(4.44355 - 16.5836i) q^{85} +(-4.84468 + 1.29813i) q^{86} -10.7737i q^{88} +(-2.34321 - 0.627860i) q^{89} +(4.59323 - 8.36076i) q^{91} -0.0963502 q^{92} +14.7716i q^{94} +(-11.8823 - 6.86026i) q^{95} +(1.99188 - 7.43379i) q^{97} +(-13.8894 - 11.0858i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7}+O(q^{10}) \) 36 * q + 4 * q^7	\( 36 q + 4 q^{7} - 4 q^{11} - 42 q^{14} + 12 q^{16} + 4 q^{17} - 24 q^{19} + 14 q^{20} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 28 q^{26} - 12 q^{28} - 8 q^{29} - 6 q^{31} - 46 q^{32} + 24 q^{34} + 10 q^{35} - 20 q^{37} - 8 q^{38} - 30 q^{40} + 34 q^{41} + 30 q^{43} + 32 q^{44} - 26 q^{46} - 4 q^{47} + 20 q^{50} + 98 q^{52} + 8 q^{53} + 30 q^{55} + 10 q^{56} - 96 q^{58} + 14 q^{59} - 48 q^{62} - 28 q^{65} + 62 q^{67} + 54 q^{68} - 148 q^{70} - 42 q^{71} - 52 q^{73} + 20 q^{74} - 12 q^{76} + 24 q^{77} - 76 q^{80} + 48 q^{82} - 60 q^{83} + 2 q^{85} - 12 q^{86} - 50 q^{89} + 40 q^{91} + 100 q^{92} - 24 q^{95} - 36 q^{97} - 16 q^{98}+O(q^{100}) \) 36 * q + 4 * q^7 - 4 * q^11 - 42 * q^14 + 12 * q^16 + 4 * q^17 - 24 * q^19 + 14 * q^20 + 4 * q^22 + 12 * q^23 - 24 * q^25 + 28 * q^26 - 12 * q^28 - 8 * q^29 - 6 * q^31 - 46 * q^32 + 24 * q^34 + 10 * q^35 - 20 * q^37 - 8 * q^38 - 30 * q^40 + 34 * q^41 + 30 * q^43 + 32 * q^44 - 26 * q^46 - 4 * q^47 + 20 * q^50 + 98 * q^52 + 8 * q^53 + 30 * q^55 + 10 * q^56 - 96 * q^58 + 14 * q^59 - 48 * q^62 - 28 * q^65 + 62 * q^67 + 54 * q^68 - 148 * q^70 - 42 * q^71 - 52 * q^73 + 20 * q^74 - 12 * q^76 + 24 * q^77 - 76 * q^80 + 48 * q^82 - 60 * q^83 + 2 * q^85 - 12 * q^86 - 50 * q^89 + 40 * q^91 + 100 * q^92 - 24 * q^95 - 36 * q^97 - 16 * q^98

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