LMFDB - Embedded newform 819.2.et.c.271.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (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			271.9
Character	$\chi$	$=$	819.271
Dual form			819.2.et.c.136.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79515 + 1.79515i) q^{2} +4.44512i q^{4} +(0.590961 + 2.20549i) q^{5} +(-2.51335 + 0.826467i) q^{7} +(-4.38935 + 4.38935i) q^{8} +O(q^{10})$	\(q+(1.79515 + 1.79515i) q^{2} +4.44512i q^{4} +(0.590961 + 2.20549i) q^{5} +(-2.51335 + 0.826467i) q^{7} +(-4.38935 + 4.38935i) q^{8} +(-2.89833 + 5.02005i) q^{10} +(0.449206 + 1.67646i) q^{11} +(-1.05331 - 3.44826i) q^{13} +(-5.99548 - 3.02821i) q^{14} -6.86883 q^{16} +7.51920 q^{17} +(-5.80433 - 1.55527i) q^{19} +(-9.80368 + 2.62689i) q^{20} +(-2.20310 + 3.81588i) q^{22} +0.0216755i q^{23} +(-0.184846 + 0.106721i) q^{25} +(4.29929 - 8.08100i) q^{26} +(-3.67374 - 11.1722i) q^{28} +(-0.432921 - 0.749842i) q^{29} +(5.81230 + 1.55740i) q^{31} +(-3.55188 - 3.55188i) q^{32} +(13.4981 + 13.4981i) q^{34} +(-3.30806 - 5.05478i) q^{35} +(-6.64042 + 6.64042i) q^{37} +(-7.62770 - 13.2116i) q^{38} +(-12.2746 - 7.08675i) q^{40} +(2.45125 + 0.656811i) q^{41} +(1.71095 + 0.987815i) q^{43} +(-7.45205 + 1.99677i) q^{44} +(-0.0389108 + 0.0389108i) q^{46} +(-5.62025 + 1.50594i) q^{47} +(5.63390 - 4.15441i) q^{49} +(-0.523405 - 0.140246i) q^{50} +(15.3279 - 4.68210i) q^{52} +(6.87167 + 11.9021i) q^{53} +(-3.43196 + 1.98144i) q^{55} +(7.40434 - 14.6596i) q^{56} +(0.568919 - 2.12324i) q^{58} +(4.10621 + 4.10621i) q^{59} +(3.12149 - 1.80219i) q^{61} +(7.63818 + 13.2297i) q^{62} +0.985368i q^{64} +(6.98266 - 4.36087i) q^{65} +(1.08555 - 0.290873i) q^{67} +33.4237i q^{68} +(3.13562 - 15.0125i) q^{70} +(-12.5434 + 3.36098i) q^{71} +(2.56726 - 9.58115i) q^{73} -23.8411 q^{74} +(6.91334 - 25.8009i) q^{76} +(-2.51455 - 3.84228i) q^{77} +(2.16727 - 3.75382i) q^{79} +(-4.05921 - 15.1492i) q^{80} +(3.22129 + 5.57944i) q^{82} +(8.64819 - 8.64819i) q^{83} +(4.44355 + 16.5836i) q^{85} +(1.29813 + 4.84468i) q^{86} +(-9.33028 - 5.38684i) q^{88} +(-1.71535 - 1.71535i) q^{89} +(5.49723 + 7.79618i) q^{91} -0.0963502 q^{92} +(-12.7926 - 7.38580i) q^{94} -13.7205i q^{95} +(-1.99188 - 7.43379i) q^{97} +(17.5715 + 2.65591i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.79515	+	1.79515i	1.26936	+	1.26936i	0.946418	+	0.322944i	$0.104672\pi$
$2$	1.79515	+	1.79515i	1.26936	+	1.26936i	0.322944	+	0.946418i	$0.395328\pi$
$3$		0			0
$3$		0			0
$4$			4.44512i			2.22256i
$5$	0.590961	+	2.20549i	0.264286	+	0.986327i	0.962686	+	0.270620i	$0.0872287\pi$
$5$	0.590961	+	2.20549i	0.264286	+	0.986327i	−0.698401	+	0.715707i	$0.746105\pi$
$6$		0			0
$7$	−2.51335	+	0.826467i	−0.949959	+	0.312375i
$7$	−2.51335	+	0.826467i	−0.949959	+	0.312375i
$8$	−4.38935	+	4.38935i	−1.55187	+	1.55187i
$9$		0			0
$10$	−2.89833	+	5.02005i	−0.916532	+	1.58748i
$11$	0.449206	+	1.67646i	0.135441	+	0.505471i	0.999996	+	0.00293308i	$0.000933629\pi$
$11$	0.449206	+	1.67646i	0.135441	+	0.505471i	−0.864555	+	0.502538i	$0.832400\pi$
$12$		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
$16$	−6.86883			−1.71721
$17$	7.51920			1.82367			0.911837	−	0.410552i	$-0.134664\pi$
$17$	7.51920			1.82367			0.911837	+	0.410552i	$0.134664\pi$
$18$		0			0
$19$	−5.80433	−	1.55527i	−1.33161	−	0.356803i	−0.478292	−	0.878201i	$-0.658744\pi$
$19$	−5.80433	−	1.55527i	−1.33161	−	0.356803i	−0.853313	+	0.521399i	$0.825411\pi$
$20$	−9.80368	+	2.62689i	−2.19217	+	0.587390i
$21$		0			0
$22$	−2.20310	+	3.81588i	−0.469703	+	0.813549i
$23$			0.0216755i			0.00451966i	0.999997	+	0.00225983i	$0.000719326\pi$
$23$			0.0216755i			0.00451966i	−0.999997	+	0.00225983i	$0.999281\pi$
$24$		0			0
$25$	−0.184846	+	0.106721i	−0.0369691	+	0.0213441i
$26$	4.29929	−	8.08100i	0.843161	−	1.58481i
$27$		0			0
$28$	−3.67374	−	11.1722i	−0.694272	−	2.11134i
$29$	−0.432921	−	0.749842i	−0.0803915	−	0.139242i	0.823027	−	0.568003i	$-0.192284\pi$
$29$	−0.432921	−	0.749842i	−0.0803915	−	0.139242i	−0.903418	+	0.428761i	$0.858950\pi$
$30$		0			0
$31$	5.81230	+	1.55740i	1.04392	+	0.279718i	0.739737	−	0.672896i	$-0.234950\pi$
$31$	5.81230	+	1.55740i	1.04392	+	0.279718i	0.304183	+	0.952614i	$0.401616\pi$
$32$	−3.55188	−	3.55188i	−0.627889	−	0.627889i
$33$		0			0
$34$	13.4981	+	13.4981i	2.31490	+	2.31490i
$35$	−3.30806	−	5.05478i	−0.559165	−	0.854414i
$36$		0			0
$37$	−6.64042	+	6.64042i	−1.09168	+	1.09168i	−0.0963296	+	0.995349i	$0.530710\pi$
$37$	−6.64042	+	6.64042i	−1.09168	+	1.09168i	−0.995349	+	0.0963296i	$0.969290\pi$
$38$	−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	$-0.353169\pi$
$41$	2.45125	+	0.656811i	0.382822	+	0.102577i	−0.0622757	+	0.998059i	$0.519836\pi$
$42$		0			0
$43$	1.71095	+	0.987815i	0.260917	+	0.150640i	0.624753	−	0.780823i	$-0.285200\pi$
$43$	1.71095	+	0.987815i	0.260917	+	0.150640i	−0.363836	+	0.931463i	$0.618533\pi$
$44$	−7.45205	+	1.99677i	−1.12344	+	0.301025i
$45$		0			0
$46$	−0.0389108	+	0.0389108i	−0.00573708	+	0.00573708i
$47$	−5.62025	+	1.50594i	−0.819798	+	0.219664i	−0.644258	−	0.764808i	$-0.722834\pi$
$47$	−5.62025	+	1.50594i	−0.819798	+	0.219664i	−0.175540	+	0.984472i	$0.556167\pi$
$48$		0			0
$49$	5.63390	−	4.15441i	0.804843	−	0.593487i
$50$	−0.523405	−	0.140246i	−0.0740206	−	0.0198338i
$51$		0			0
$52$	15.3279	−	4.68210i	2.12560	−	0.649291i
$53$	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
$56$	7.40434	−	14.6596i	0.989446	−	1.95898i
$57$		0			0
$58$	0.568919	−	2.12324i	0.0747028	−	0.278795i
$59$	4.10621	+	4.10621i	0.534583	+	0.534583i	0.921933	−	0.387350i	$-0.126609\pi$
$59$	4.10621	+	4.10621i	0.534583	+	0.534583i	−0.387350	+	0.921933i	$0.626609\pi$
$60$		0			0
$61$	3.12149	−	1.80219i	0.399666	−	0.230747i	−0.286674	−	0.958028i	$-0.592550\pi$
$61$	3.12149	−	1.80219i	0.399666	−	0.230747i	0.686340	+	0.727281i	$0.259216\pi$
$62$	7.63818	+	13.2297i	0.970050	+	1.68018i
$63$		0			0
$64$			0.985368i			0.123171i
$65$	6.98266	−	4.36087i	0.866093	−	0.540899i
$66$		0			0
$67$	1.08555	−	0.290873i	0.132621	−	0.0355357i	−0.191898	−	0.981415i	$-0.561464\pi$
$67$	1.08555	−	0.290873i	0.132621	−	0.0355357i	0.324519	+	0.945879i	$0.394798\pi$
$68$			33.4237i			4.05322i
$69$		0			0
$70$	3.13562	−	15.0125i	0.374778	−	1.79434i
$71$	−12.5434	+	3.36098i	−1.48862	+	0.398875i	−0.909272	−	0.416203i	$-0.863360\pi$
$71$	−12.5434	+	3.36098i	−1.48862	+	0.398875i	−0.579350	+	0.815079i	$0.696694\pi$
$72$		0			0
$73$	2.56726	−	9.58115i	0.300475	−	1.12139i	−0.636296	−	0.771445i	$-0.719534\pi$
$73$	2.56726	−	9.58115i	0.300475	−	1.12139i	0.936771	−	0.349943i	$-0.113799\pi$
$74$	−23.8411			−2.77147
$75$		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	$0.0882606\pi$
$80$	−4.05921	−	15.1492i	−0.453833	−	1.69373i
$81$		0			0
$82$	3.22129	+	5.57944i	0.355732	+	0.616146i
$83$	8.64819	−	8.64819i	0.949263	−	0.949263i	−0.0495109	−	0.998774i	$-0.515766\pi$
$83$	8.64819	−	8.64819i	0.949263	−	0.949263i	0.998774	+	0.0495109i	$0.0157663\pi$
$84$		0			0
$85$	4.44355	+	16.5836i	0.481971	+	1.79874i
$86$	1.29813	+	4.84468i	0.139981	+	0.522415i
$87$		0			0
$88$	−9.33028	−	5.38684i	−0.994611	−	0.574239i
$89$	−1.71535	−	1.71535i	−0.181826	−	0.181826i	0.610325	−	0.792151i	$-0.291039\pi$
$89$	−1.71535	−	1.71535i	−0.181826	−	0.181826i	−0.792151	+	0.610325i	$0.791039\pi$
$90$		0			0
$91$	5.49723	+	7.79618i	0.576266	+	0.817262i
$92$	−0.0963502			−0.0100452
$93$		0			0
$94$	−12.7926	−	7.38580i	−1.31945	−	0.761787i
$95$		−	13.7205i		−	1.40770i
$96$		0			0
$97$	−1.99188	−	7.43379i	−0.202245	−	0.754787i	−0.990272	−	0.139147i	$-0.955564\pi$
$97$	−1.99188	−	7.43379i	−0.202245	−	0.754787i	0.788027	−	0.615641i	$-0.211103\pi$
$98$	17.5715	+	2.65591i	1.77499	+	0.268288i
$99$		0			0
$100$	−0.474386	−	0.821660i	−0.0474386	−	0.0821660i
$101$	2.23088	−	3.86399i	0.221981	−	0.384482i	−0.733429	−	0.679766i	$-0.762081\pi$
$101$	2.23088	−	3.86399i	0.221981	−	0.384482i	0.955409	+	0.295285i	$0.0954145\pi$
$102$		0			0
$103$	4.23657	−	7.33795i	0.417441	−	0.723030i	−0.578240	−	0.815867i	$-0.696260\pi$
$103$	4.23657	−	7.33795i	0.417441	−	0.723030i	0.995681	+	0.0928371i	$0.0295936\pi$
$104$	19.7590	+	10.5123i	1.93753	+	1.03081i
$105$		0			0
$106$	−9.03034	+	33.7017i	−0.877104	+	3.27340i
$107$	−10.1376			−0.980042			−0.490021	−	0.871711i	$-0.663011\pi$
$107$	−10.1376			−0.980042			−0.490021	+	0.871711i	$0.663011\pi$
$108$		0			0
$109$	−1.05231	+	3.92728i	−0.100793	+	0.376165i	−0.997834	−	0.0657825i	$-0.979046\pi$
$109$	−1.05231	+	3.92728i	−0.100793	+	0.376165i	0.897041	+	0.441948i	$0.145712\pi$
$110$	−9.71785	−	2.60389i	−0.926561	−	0.248271i
$111$		0			0
$112$	17.2638	−	5.67686i	1.63128	−	0.536413i
$113$	2.30418	−	3.99096i	0.216759	−	0.375438i	−0.737056	−	0.675831i	$-0.763785\pi$
$113$	2.30418	−	3.99096i	0.216759	−	0.375438i	0.953815	+	0.300394i	$0.0971180\pi$
$114$		0			0
$115$	−0.0478052	+	0.0128094i	−0.00445786	+	0.00119448i
$116$	3.33314	−	1.92439i	0.309474	−	0.178675i
$117$		0			0
$118$			14.7425i			1.35716i
$119$	−18.8984	+	6.21437i	−1.73242	+	0.569671i
$120$		0			0
$121$	6.91755	−	3.99385i	0.628869	−	0.363077i
$122$	8.83874	+	2.36833i	0.800222	+	0.214419i
$123$		0			0
$124$	−6.92283	+	25.8364i	−0.621689	+	2.32017i
$125$	7.72806	+	7.72806i	0.691219	+	0.691219i
$126$		0			0
$127$	2.76191	−	1.59459i	0.245080	−	0.141497i	−0.372430	−	0.928060i	$-0.621475\pi$
$127$	2.76191	−	1.59459i	0.245080	−	0.141497i	0.617509	+	0.786564i	$0.288142\pi$
$128$	−8.87264	+	8.87264i	−0.784238	+	0.784238i
$129$		0			0
$130$	20.3633	+	4.70652i	1.78598	+	0.412789i
$131$	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
$133$	15.8737	−	0.888154i	1.37643	−	0.0770127i
$134$	2.47088	+	1.42657i	0.213452	+	0.123237i
$135$		0			0
$136$	−33.0044	+	33.0044i	−2.83010	+	2.83010i
$137$	−3.54760	+	3.54760i	−0.303092	+	0.303092i	−0.842222	−	0.539131i	$-0.818753\pi$
$137$	−3.54760	+	3.54760i	−0.303092	+	0.303092i	0.539131	+	0.842222i	$0.318753\pi$
$138$		0			0
$139$	2.35400	+	1.35908i	0.199663	+	0.115276i	0.596498	−	0.802614i	$-0.296558\pi$
$139$	2.35400	+	1.35908i	0.199663	+	0.115276i	−0.396835	+	0.917890i	$0.629892\pi$
$140$	22.4691	−	14.7047i	1.89899	−	1.24278i
$141$		0			0
$142$	−28.5506	−	16.4837i	−2.39592	−	1.38328i
$143$	5.30772	−	3.31481i	0.443854	−	0.277199i
$144$		0			0
$145$	1.39793	−	1.39793i	0.116092	−	0.116092i
$146$	21.8082	−	12.5910i	1.80486	−	1.04204i
$147$		0			0
$148$	−29.5175	−	29.5175i	−2.42632	−	2.42632i
$149$	5.83717	−	21.7846i	0.478200	−	1.78467i	−0.130704	−	0.991421i	$-0.541724\pi$
$149$	5.83717	−	21.7846i	0.478200	−	1.78467i	0.608904	−	0.793244i	$-0.291610\pi$
$150$		0			0
$151$	20.2079	+	5.41469i	1.64450	+	0.440641i	0.958064	−	0.286553i	$-0.0925096\pi$
$151$	20.2079	+	5.41469i	1.64450	+	0.440641i	0.686431	+	0.727195i	$0.259176\pi$
$152$	32.3038	−	18.6506i	2.62019	−	1.51277i
$153$		0			0
$154$	2.38347	−	11.4115i	0.192066	−	0.919561i
$155$			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	$0.248893\pi$
$158$	10.6292	−	2.84809i	0.845616	−	0.226582i
$159$		0			0
$160$	5.73463	−	9.93267i	0.453362	−	0.785246i
$161$	−0.0179141	−	0.0544782i	−0.00141183	−	0.00429349i
$162$		0			0
$163$	−23.4341	−	6.27914i	−1.83550	−	0.491820i	−0.837030	−	0.547158i	$-0.815710\pi$
$163$	−23.4341	−	6.27914i	−1.83550	−	0.491820i	−0.998468	+	0.0553377i	$0.982376\pi$
$164$	−2.91960	+	10.8961i	−0.227983	+	0.850843i
$165$		0			0
$166$	31.0496			2.40992
$167$	1.98472	−	7.40707i	0.153582	−	0.573176i	−0.845641	−	0.533753i	$-0.820781\pi$
$167$	1.98472	−	7.40707i	0.153582	−	0.573176i	0.999223	−	0.0394232i	$-0.0125520\pi$
$168$		0			0
$169$	−10.7811	+	7.26421i	−0.829312	+	0.558785i
$170$	−21.7931	+	37.7468i	−1.67146	+	2.89505i
$171$		0			0
$172$	−4.39095	+	7.60536i	−0.334807	+	0.579903i
$173$	−0.111832	−	0.193699i	−0.00850246	−	0.0147267i	0.861743	−	0.507345i	$-0.169373\pi$
$173$	−0.111832	−	0.193699i	−0.00850246	−	0.0147267i	−0.870245	+	0.492619i	$0.836040\pi$
$174$		0			0
$175$	0.376381	−	0.420996i	0.0284518	−	0.0318243i
$176$	−3.08552	−	11.5153i	−0.232580	−	0.867999i
$177$		0			0
$178$		−	6.15860i		−	0.461607i
$179$	9.40968	+	5.43268i	0.703312	+	0.406058i	0.808580	−	0.588386i	$-0.200237\pi$
$179$	9.40968	+	5.43268i	0.703312	+	0.406058i	−0.105268	+	0.994444i	$0.533570\pi$
$180$		0			0
$181$	0.436016			0.0324088			0.0162044	−	0.999869i	$-0.494842\pi$
$181$	0.436016			0.0324088			0.0162044	+	0.999869i	$0.494842\pi$
$182$	−4.12697	+	23.8637i	−0.305911	+	1.76889i
$183$		0			0
$184$	−0.0951414	−	0.0951414i	−0.00701391	−	0.00701391i
$185$	−18.5697	−	10.7212i	−1.36527	−	0.788238i
$186$		0			0
$187$	3.37767	+	12.6056i	0.246999	+	0.921815i
$188$	−6.69409	−	24.9827i	−0.488216	−	1.82205i
$189$		0			0
$190$	24.6304	−	24.6304i	1.78688	−	1.78688i
$191$	−4.42223	−	7.65952i	−0.319981	−	0.554223i	0.660503	−	0.750824i	$-0.270343\pi$
$191$	−4.42223	−	7.65952i	−0.319981	−	0.554223i	−0.980484	+	0.196600i	$0.937010\pi$
$192$		0			0
$193$	−2.33215	−	8.70371i	−0.167872	−	0.626507i	−0.997656	−	0.0684229i	$-0.978203\pi$
$193$	−2.33215	−	8.70371i	−0.167872	−	0.626507i	0.829784	−	0.558084i	$-0.188463\pi$
$194$	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	−0.749556	−	0.661941i	$-0.769733\pi$
$197$	3.23591	−	12.0766i	0.230549	−	0.860421i	0.980105	−	0.198480i	$-0.0636005\pi$
$198$		0			0
$199$	−8.34509			−0.591568			−0.295784	−	0.955255i	$-0.595581\pi$
$199$	−8.34509			−0.591568			−0.295784	+	0.955255i	$0.595581\pi$
$200$	0.342918	−	1.27979i	0.0242479	−	0.0904945i
$201$		0			0
$202$	10.9412	−	2.93169i	0.769820	−	0.206273i
$203$	1.70781	+	1.52682i	0.119864	+	0.107162i
$204$		0			0
$205$			5.79438i			0.404697i
$206$	20.7780	−	5.56744i	1.44767	−	0.387902i
$207$		0			0
$208$	7.23503	+	23.6856i	0.501659	+	1.64230i
$209$		−	10.4294i		−	0.721413i
$210$		0			0
$211$	−0.0517275	−	0.0895946i	−0.00356106	−	0.00616794i	0.864239	−	0.503081i	$-0.167800\pi$
$211$	−0.0517275	−	0.0895946i	−0.00356106	−	0.00616794i	−0.867800	+	0.496913i	$0.834467\pi$
$212$	−52.9062	+	30.5454i	−3.63361	+	2.09787i
$213$		0			0
$214$	−18.1986	−	18.1986i	−1.24403	−	1.24403i
$215$	−1.16752	+	4.35724i	−0.0796242	+	0.297162i
$216$		0			0
$217$	−15.8955	+	0.889374i	−1.07906	+	0.0603746i
$218$	−8.93911	+	5.16100i	−0.605433	+	0.349547i
$219$		0			0
$220$	−8.80774	−	15.2554i	−0.593817	−	1.02852i
$221$	−7.92008	−	25.9282i	−0.532762	−	1.74412i
$222$		0			0
$223$	25.3112	+	6.78211i	1.69496	+	0.454163i	0.971663	−	0.236372i	$-0.0759585\pi$
$223$	25.3112	+	6.78211i	1.69496	+	0.454163i	0.723298	+	0.690536i	$0.242625\pi$
$224$	11.8626	+	5.99162i	0.792606	+	0.400332i
$225$		0			0
$226$	11.3007	−	3.02802i	0.751712	−	0.201421i
$227$	−9.62565	+	9.62565i	−0.638877	+	0.638877i	−0.950278	−	0.311401i	$-0.899202\pi$
$227$	−9.62565	+	9.62565i	−0.638877	+	0.638877i	0.311401	+	0.950278i	$0.399202\pi$
$228$		0			0
$229$	−23.4824	+	6.29210i	−1.55176	+	0.415794i	−0.930044	−	0.367447i	$-0.880232\pi$
$229$	−23.4824	+	6.29210i	−1.55176	+	0.415794i	−0.621719	+	0.783241i	$0.713565\pi$
$230$	−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	0.746572	−	0.665304i	$-0.231698\pi$
$233$	8.29904	+	4.79145i	0.543688	+	0.313899i	−0.202884	+	0.979203i	$0.565031\pi$
$234$		0			0
$235$	−6.64269	−	11.5055i	−0.433321	−	0.750535i
$236$	−18.2526	+	18.2526i	−1.18814	+	1.18814i
$237$		0			0
$238$	−45.0812	−	22.7698i	−2.92218	−	1.47594i
$239$	−5.64222	−	5.64222i	−0.364965	−	0.364965i	0.500672	−	0.865637i	$-0.333086\pi$
$239$	−5.64222	−	5.64222i	−0.364965	−	0.364965i	−0.865637	+	0.500672i	$0.833086\pi$
$240$		0			0
$241$	−17.9441	−	17.9441i	−1.15588	−	1.15588i	−0.985353	−	0.170526i	$-0.945453\pi$
$241$	−17.9441	−	17.9441i	−1.15588	−	1.15588i	−0.170526	−	0.985353i	$-0.554547\pi$
$242$	19.5876	+	5.24848i	1.25914	+	0.337385i
$243$		0			0
$244$	8.01095	+	13.8754i	0.512849	+	0.888280i
$245$	12.4919	+	9.97045i	0.798081	+	0.636989i
$246$		0			0
$247$	0.750811	+	21.6531i	0.0477729	+	1.37775i
$248$	−32.3482	+	18.6762i	−2.05411	+	1.18594i
$249$		0			0
$250$			27.7460i			1.75481i
$251$	−5.75368	+	9.96567i	−0.363169	+	0.629027i	−0.988481	−	0.151348i	$-0.951639\pi$
$251$	−5.75368	+	9.96567i	−0.363169	+	0.629027i	0.625311	+	0.780375i	$0.284972\pi$
$252$		0			0
$253$	−0.0363381	+	0.00973676i	−0.00228456	+	0.000612145i
$254$	7.82055	+	2.09551i	0.490705	+	0.131484i
$255$		0			0
$256$	−29.8847			−1.86779
$257$	27.3825			1.70807			0.854036	−	0.520213i	$-0.174148\pi$
$257$	27.3825			1.70807			0.854036	+	0.520213i	$0.174148\pi$
$258$		0			0
$259$	11.2017	−	22.1778i	0.696037	−	1.37806i
$260$	19.3846	+	31.0388i	1.20218	+	1.92494i
$261$		0			0
$262$	5.45879	+	20.3725i	0.337245	+	1.25862i
$263$	−10.1358	+	17.5557i	−0.624998	+	1.08253i	0.363544	+	0.931577i	$0.381567\pi$
$263$	−10.1358	+	17.5557i	−0.624998	+	1.08253i	−0.988541	+	0.150951i	$0.951767\pi$
$264$		0			0
$265$	−22.1891	+	22.1891i	−1.36307	+	1.36307i
$266$	30.0901	+	26.9013i	1.84494	+	1.64943i
$267$		0			0
$268$	1.29296	+	4.82540i	0.0789803	+	0.294758i
$269$			1.81548i			0.110692i	0.998467	+	0.0553458i	$0.0176261\pi$
$269$			1.81548i			0.110692i	−0.998467	+	0.0553458i	$0.982374\pi$
$270$		0			0
$271$	−15.5693	−	15.5693i	−0.945768	−	0.945768i	0.0528356	−	0.998603i	$-0.483174\pi$
$271$	−15.5693	−	15.5693i	−0.945768	−	0.945768i	−0.998603	+	0.0528356i	$0.983174\pi$
$272$	−51.6481			−3.13163
$273$		0			0
$274$	−12.7369			−0.769466
$275$	−0.261946	−	0.261946i	−0.0157960	−	0.0157960i
$276$		0			0
$277$			20.3006i			1.21975i	0.792499	+	0.609873i	$0.208779\pi$
$277$			20.3006i			1.21975i	−0.792499	+	0.609873i	$0.791221\pi$
$278$	1.78602	+	6.66553i	0.107119	+	0.399772i
$279$		0			0
$280$	36.7074	+	7.66696i	2.19369	+	0.458188i
$281$	14.1904	−	14.1904i	0.846529	−	0.846529i	−0.143169	−	0.989698i	$-0.545729\pi$
$281$	14.1904	−	14.1904i	0.846529	−	0.846529i	0.989698	+	0.143169i	$0.0457293\pi$
$282$		0			0
$283$	3.40103	−	5.89076i	0.202171	−	0.350170i	−0.747057	−	0.664760i	$-0.768534\pi$
$283$	3.40103	−	5.89076i	0.202171	−	0.350170i	0.949228	+	0.314590i	$0.101867\pi$
$284$	−14.9400	−	55.7567i	−0.886523	−	3.30855i
$285$		0			0
$286$	15.4787	+	3.57755i	0.915276	+	0.211545i
$287$	−6.70370	+	0.375080i	−0.395707	+	0.0221403i
$288$		0			0
$289$	39.5384			2.32579
$290$	5.01900			0.294726
$291$		0			0
$292$	42.5893	+	11.4118i	2.49235	+	0.667823i
$293$	−20.5482	+	5.50587i	−1.20044	+	0.321656i	−0.803004	−	0.595974i	$-0.796766\pi$
$293$	−20.5482	+	5.50587i	−1.20044	+	0.321656i	−0.397435	+	0.917630i	$0.630099\pi$
$294$		0			0
$295$	−6.62962	+	11.4828i	−0.385991	+	0.668557i
$296$		−	58.2943i		−	3.38829i
$297$		0			0
$298$	49.5852	−	28.6280i	2.87239	−	1.65838i
$299$	0.0747429	−	0.0228311i	0.00432249	−	0.00132036i
$300$		0			0
$301$	−5.11661	−	1.06869i	−0.294917	−	0.0615982i
$302$	26.5560	+	45.9964i	1.52813	+	2.64679i
$303$		0			0
$304$	39.8690	+	10.6829i	2.28664	+	0.612704i
$305$	5.81940	+	5.81940i	0.333218	+	0.333218i
$306$		0			0
$307$	−17.4862	−	17.4862i	−0.997992	−	0.997992i	0.00200593	−	0.999998i	$-0.499361\pi$
$307$	−17.4862	−	17.4862i	−0.997992	−	0.997992i	−0.999998	+	0.00200593i	$0.999361\pi$
$308$	17.0794	−	11.1775i	0.973188	−	0.636895i
$309$		0			0
$310$	−24.6642	+	24.6642i	−1.40083	+	1.40083i
$311$	−1.90903	−	3.30654i	−0.108251	−	0.187497i	0.806811	−	0.590810i	$-0.201192\pi$
$311$	−1.90903	−	3.30654i	−0.108251	−	0.187497i	−0.915062	+	0.403314i	$0.867858\pi$
$312$		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
$317$	9.13383	−	2.44740i	0.513007	−	0.137460i	0.00697710	−	0.999976i	$-0.497779\pi$
$317$	9.13383	−	2.44740i	0.513007	−	0.137460i	0.506030	+	0.862516i	$0.331112\pi$
$318$		0			0
$319$	1.06261	−	1.06261i	0.0594946	−	0.0594946i
$320$	−2.17322	+	0.582314i	−0.121487	+	0.0325523i
$321$		0			0
$322$	0.0656381	−	0.129955i	0.00365787	−	0.00724211i
$323$	−43.6439	−	11.6944i	−2.42841	−	0.650692i
$324$		0			0
$325$	0.562701	+	0.524986i	0.0312131	+	0.0291210i
$326$	−30.7956	−	53.3396i	−1.70561	−	2.95421i
$327$		0			0
$328$	−13.6424	+	7.87643i	−0.753275	+	0.434903i
$329$	12.8811	−	8.42992i	0.710157	−	0.464756i
$330$		0			0
$331$	4.06709	−	15.1786i	0.223547	−	0.834290i	−0.759434	−	0.650585i	$-0.774524\pi$
$331$	4.06709	−	15.1786i	0.223547	−	0.834290i	0.982981	−	0.183706i	$-0.0588094\pi$
$332$	38.4422	+	38.4422i	2.10979	+	2.10979i
$333$		0			0
$334$	16.8596	−	9.73392i	0.922519	−	0.532617i
$335$	1.28304	+	2.22228i	0.0700997	+	0.121416i
$336$		0			0
$337$			1.41323i			0.0769835i	0.999259	+	0.0384917i	$0.0122553\pi$
$337$			1.41323i			0.0769835i	−0.999259	+	0.0384917i	$0.987745\pi$
$338$	−32.3939	−	6.31328i	−1.76200	−	0.343397i
$339$		0			0
$340$	−73.7159	+	19.7521i	−3.99780	+	1.07121i
$341$			10.4437i			0.565557i
$342$		0			0
$343$	−10.7265	+	15.0977i	−0.579177	+	0.815201i
$344$	−11.8458	+	3.17407i	−0.638683	+	0.171135i
$345$		0			0
$346$	0.146963	−	0.548475i	0.00790081	−	0.0294862i
$347$	−5.50183			−0.295353			−0.147677	−	0.989036i	$-0.547180\pi$
$347$	−5.50183			−0.295353			−0.147677	+	0.989036i	$0.547180\pi$
$348$		0			0
$349$	3.51381	−	13.1137i	0.188090	−	0.701960i	−0.805858	−	0.592109i	$-0.798296\pi$
$349$	3.51381	−	13.1137i	0.188090	−	0.701960i	0.993948	−	0.109852i	$-0.0350377\pi$
$350$	1.43141	−	0.0800892i	0.0765121	−	0.00428095i
$351$		0			0
$352$	4.35905	−	7.55010i	0.232338	−	0.402421i
$353$	−2.00920	−	7.49845i	−0.106939	−	0.399102i	0.891619	−	0.452787i	$-0.149570\pi$
$353$	−2.00920	−	7.49845i	−0.106939	−	0.399102i	−0.998558	+	0.0536846i	$0.982903\pi$
$354$		0			0
$355$	−14.8253	−	25.6781i	−0.786843	−	1.36285i
$356$	7.62491	−	7.62491i	0.404120	−	0.404120i
$357$		0			0
$358$	7.13930	+	26.6442i	0.377324	+	1.40819i
$359$	5.89881	+	22.0147i	0.311327	+	1.16189i	0.927360	+	0.374169i	$0.122072\pi$
$359$	5.89881	+	22.0147i	0.311327	+	1.16189i	−0.616033	+	0.787720i	$0.711261\pi$
$360$		0			0
$361$	14.8169	+	8.55456i	0.779839	+	0.450240i
$362$	0.782713	+	0.782713i	0.0411385	+	0.0411385i
$363$		0			0
$364$	−34.6550	+	24.4358i	−1.81641	+	1.28079i
$365$	22.6483			1.18547
$366$		0			0
$367$	−18.4248	−	10.6376i	−0.961767	−	0.555276i	−0.0650505	−	0.997882i	$-0.520721\pi$
$367$	−18.4248	−	10.6376i	−0.961767	−	0.555276i	−0.896716	+	0.442606i	$0.854054\pi$
$368$		−	0.148885i		−	0.00776119i
$369$		0			0
$370$	−14.0891	−	52.5814i	−0.732460	−	2.73358i
$371$	−27.1076	−	24.2350i	−1.40736	−	1.25822i
$372$		0			0
$373$	−8.32600	−	14.4210i	−0.431104	−	0.746694i	0.565865	−	0.824498i	$-0.308542\pi$
$373$	−8.32600	−	14.4210i	−0.431104	−	0.746694i	−0.996969	+	0.0778044i	$0.975209\pi$
$374$	−16.5656	+	28.6924i	−0.856584	+	1.48365i
$375$		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	0.731649	+	0.681681i	$0.238751\pi$
$379$	−4.72716	+	17.6420i	−0.242818	+	0.906209i	−0.974468	+	0.224528i	$0.927916\pi$
$380$	60.9893			3.12869
$381$		0			0
$382$	5.81142	−	21.6885i	0.297338	−	1.10968i
$383$	−25.7773	−	6.90700i	−1.31716	−	0.352931i	−0.469245	−	0.883068i	$-0.655474\pi$
$383$	−25.7773	−	6.90700i	−1.31716	−	0.352931i	−0.847912	+	0.530137i	$0.822140\pi$
$384$		0			0
$385$	6.98813	−	7.81646i	0.356148	−	0.398364i
$386$	11.4379	−	19.8110i	0.582174	−	1.00835i
$387$		0			0
$388$	33.0441	−	8.85414i	1.67756	−	0.449501i
$389$	0.958138	−	0.553181i	0.0485795	−	0.0280474i	−0.475514	−	0.879708i	$-0.657738\pi$
$389$	0.958138	−	0.553181i	0.0485795	−	0.0280474i	0.524093	+	0.851661i	$0.324404\pi$
$390$		0			0
$391$			0.162983i			0.00824238i
$392$	−6.49402	+	42.9643i	−0.327997	+	2.17003i
$393$		0			0
$394$	27.4882	−	15.8703i	1.38484	−	0.799535i
$395$	9.55980	+	2.56154i	0.481006	+	0.128885i
$396$		0			0
$397$	3.67238	−	13.7055i	0.184311	−	0.687860i	−0.810465	−	0.585787i	$-0.800786\pi$
$397$	3.67238	−	13.7055i	0.184311	−	0.687860i	0.994777	−	0.102073i	$-0.0325476\pi$
$398$	−14.9807	−	14.9807i	−0.750913	−	0.750913i
$399$		0			0
$400$	1.26967	−	0.733046i	0.0634837	−	0.0366523i
$401$	1.61276	−	1.61276i	0.0805374	−	0.0805374i	−0.665691	−	0.746228i	$-0.731863\pi$
$401$	1.61276	−	1.61276i	0.0805374	−	0.0805374i	0.746228	+	0.665691i	$0.231863\pi$
$402$		0			0
$403$	−0.751842	−	21.6828i	−0.0374519	−	1.08010i
$404$	17.1759	+	9.91652i	0.854533	+	0.493365i
$405$		0			0
$406$	0.324889	+	5.80664i	0.0161239	+	0.288179i
$407$	−14.1153	−	8.14948i	−0.699670	−	0.403955i
$408$		0			0
$409$	13.9463	−	13.9463i	0.689598	−	0.689598i	−0.272545	−	0.962143i	$-0.587865\pi$
$409$	13.9463	−	13.9463i	0.689598	−	0.689598i	0.962143	+	0.272545i	$0.0878654\pi$
$410$	−10.4018	+	10.4018i	−0.513707	+	0.513707i
$411$		0			0
$412$	32.6180	+	18.8320i	1.60698	+	0.927788i
$413$	−13.7140	−	6.92672i	−0.674823	−	0.340841i
$414$		0			0
$415$	24.1843	+	13.9628i	1.18716	+	0.685407i
$416$	−8.50658	+	15.9891i	−0.417069	+	0.783928i
$417$		0			0
$418$	18.7222	−	18.7222i	0.915735	−	0.915735i
$419$	11.9093	−	6.87586i	0.581809	−	0.335908i	−0.180043	−	0.983659i	$-0.557624\pi$
$419$	11.9093	−	6.87586i	0.581809	−	0.335908i	0.761852	+	0.647751i	$0.224290\pi$
$420$		0			0
$421$	−18.9223	−	18.9223i	−0.922215	−	0.922215i	0.0749709	−	0.997186i	$-0.476114\pi$
$421$	−18.9223	−	18.9223i	−0.922215	−	0.922215i	−0.997186	+	0.0749709i	$0.976114\pi$
$422$	0.0679771	−	0.253694i	0.00330907	−	0.0123496i
$423$		0			0
$424$	−82.4046	−	22.0802i	−4.00192	−	1.07231i
$425$	−1.38989	+	0.802454i	−0.0674196	+	0.0389247i
$426$		0			0
$427$	−6.35595	+	7.10935i	−0.307586	+	0.344046i
$428$		−	45.0630i		−	2.17820i
$429$		0			0
$430$	−9.91777	+	5.72603i	−0.478277	+	0.276134i
$431$	27.4744	−	7.36174i	1.32340	−	0.354603i	0.473147	−	0.880984i	$-0.343118\pi$
$431$	27.4744	−	7.36174i	1.32340	−	0.354603i	0.850249	+	0.526381i	$0.176451\pi$
$432$		0			0
$433$	−12.8931	+	22.3315i	−0.619602	+	1.07318i	0.369957	+	0.929049i	$0.379372\pi$
$433$	−12.8931	+	22.3315i	−0.619602	+	1.07318i	−0.989558	+	0.144132i	$0.953961\pi$
$434$	−30.1314	−	26.9383i	−1.44635	−	1.29308i
$435$		0			0
$436$	−17.4572	−	4.67765i	−0.836049	−	0.224019i
$437$	0.0337112	−	0.125812i	0.00161262	−	0.00601840i
$438$		0			0
$439$	−2.47750			−0.118244			−0.0591222	−	0.998251i	$-0.518830\pi$
$439$	−2.47750			−0.118244			−0.0591222	+	0.998251i	$0.518830\pi$
$440$	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
$445$	2.76948	−	4.79689i	0.131286	−	0.227394i
$446$	33.2624	+	57.6122i	1.57502	+	2.72802i
$447$		0			0
$448$	−0.814374	−	2.47658i	−0.0384756	−	0.117007i
$449$	2.13306	+	7.96070i	0.100665	+	0.375688i	0.997817	−	0.0660335i	$-0.0210344\pi$
$449$	2.13306	+	7.96070i	0.100665	+	0.375688i	−0.897152	+	0.441722i	$0.854368\pi$
$450$		0			0
$451$			4.40447i			0.207398i
$452$	17.7403	+	10.2424i	0.834433	+	0.481760i
$453$		0			0
$454$	−34.5590			−1.62193
$455$	−13.9458	+	16.7313i	−0.653789	+	0.784377i
$456$		0			0
$457$	−3.90295	−	3.90295i	−0.182572	−	0.182572i	0.609903	−	0.792476i	$-0.291208\pi$
$457$	−3.90295	−	3.90295i	−0.182572	−	0.182572i	−0.792476	+	0.609903i	$0.791208\pi$
$458$	−53.4497	−	30.8592i	−2.49754	−	1.44196i
$459$		0			0
$460$	−0.0569391	−	0.212500i	−0.00265480	−	0.00990785i
$461$	8.89222	+	33.1862i	0.414152	+	1.54564i	0.786529	+	0.617554i	$0.211876\pi$
$461$	8.89222	+	33.1862i	0.414152	+	1.54564i	−0.372377	+	0.928082i	$0.621457\pi$
$462$		0			0
$463$	10.3935	−	10.3935i	0.483025	−	0.483025i	−0.423072	−	0.906096i	$-0.639048\pi$
$463$	10.3935	−	10.3935i	0.483025	−	0.483025i	0.906096	+	0.423072i	$0.139048\pi$
$464$	2.97367	+	5.15054i	0.138049	+	0.239108i
$465$		0			0
$466$	6.29664	+	23.4994i	0.291686	+	1.08859i
$467$	10.6589	−	18.4618i	0.493237	−	0.854311i	−0.506733	−	0.862103i	$-0.669147\pi$
$467$	10.6589	−	18.4618i	0.493237	−	0.854311i	0.999970	+	0.00779214i	$0.00248034\pi$
$468$		0			0
$469$	−2.48798	+	1.62824i	−0.114884	+	0.0751850i
$470$	8.72943	−	32.5787i	0.402658	−	1.50274i
$471$		0			0
$472$	−36.0472			−1.65921
$473$	−0.887464	+	3.31206i	−0.0408056	+	0.152289i
$474$		0			0
$475$	1.23888	−	0.331958i	0.0568439	−	0.0152313i
$476$	−27.6236	−	84.0057i	−1.26613	−	3.85039i
$477$		0			0
$478$		−	20.2572i		−	0.926544i
$479$	−14.3726	+	3.85114i	−0.656703	+	0.175963i	−0.571758	−	0.820423i	$-0.693738\pi$
$479$	−14.3726	+	3.85114i	−0.656703	+	0.175963i	−0.0849452	+	0.996386i	$0.527072\pi$
$480$		0			0
$481$	29.8924	+	15.9035i	1.36298	+	0.725137i
$482$		−	64.4246i		−	2.93446i
$483$		0			0
$484$	17.7531	+	30.7493i	0.806961	+	1.39770i
$485$	15.2181	−	8.78616i	0.691017	−	0.398959i
$486$		0			0
$487$	10.2062	+	10.2062i	0.462486	+	0.462486i	0.899469	−	0.436984i	$-0.143953\pi$
$487$	10.2062	+	10.2062i	0.462486	+	0.462486i	−0.436984	+	0.899469i	$0.643953\pi$
$488$	−5.79085	+	21.6117i	−0.262139	+	0.978318i
$489$		0			0
$490$	4.52645	+	40.3233i	0.204484	+	1.82162i
$491$	−0.458913	+	0.264954i	−0.0207105	+	0.0119572i	−0.510319	−	0.859985i	$-0.670473\pi$
$491$	−0.458913	+	0.264954i	−0.0207105	+	0.0119572i	0.489609	+	0.871942i	$0.337140\pi$
$492$		0			0
$493$	−3.25522	−	5.63821i	−0.146608	−	0.253932i
$494$	−37.5226	+	40.2183i	−1.68822	+	1.80951i
$495$		0			0
$496$	−39.9237	−	10.6975i	−1.79263	−	0.480333i
$497$	28.7482	−	18.8140i	1.28953	−	0.843923i
$498$		0			0
$499$	−24.5354	+	6.57425i	−1.09836	+	0.294304i	−0.762095	−	0.647465i	$-0.775829\pi$
$499$	−24.5354	+	6.57425i	−1.09836	+	0.294304i	−0.336261	+	0.941769i	$0.609163\pi$
$500$	−34.3521	+	34.3521i	−1.53627	+	1.53627i
$501$		0			0
$502$	−28.2186	+	7.56114i	−1.25946	+	0.337470i
$503$	−18.0905	−	10.4445i	−0.806615	−	0.465699i	0.0391641	−	0.999233i	$-0.487530\pi$
$503$	−18.0905	−	10.4445i	−0.806615	−	0.465699i	−0.845779	+	0.533533i	$0.820864\pi$
$504$		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
$509$	−8.17767	+	8.17767i	−0.362469	+	0.362469i	−0.864721	−	0.502252i	$-0.832505\pi$
$509$	−8.17767	+	8.17767i	−0.362469	+	0.362469i	0.502252	+	0.864721i	$0.332505\pi$
$510$		0			0
$511$	1.46607	+	26.2026i	0.0648549	+	1.15913i
$512$	−35.9022	−	35.9022i	−1.58667	−	1.58667i
$513$		0			0
$514$	49.1556	+	49.1556i	2.16816	+	2.16816i
$515$	18.6875	+	5.00729i	0.823468	+	0.220647i
$516$		0			0
$517$	−5.04930	−	8.74564i	−0.222068	−	0.384633i
$518$	59.9211	−	19.7039i	2.63278	−	0.865739i
$519$		0			0
$520$	−11.5080	+	49.7907i	−0.504659	+	2.18347i
$521$	−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
$523$		−	1.53739i		−	0.0672252i	−0.999435	−	0.0336126i	$-0.989299\pi$
$523$		−	1.53739i		−	0.0672252i	0.999435	−	0.0336126i	$-0.0107012\pi$
$524$	−18.4645	+	31.9815i	−0.806627	+	1.39712i
$525$		0			0
$526$	−49.7102	+	13.3198i	−2.16747	+	0.580771i
$527$	43.7039	+	11.7104i	1.90377	+	0.510114i
$528$		0			0
$529$	22.9995			0.999980
$530$	−79.6655			−3.46045
$531$		0			0
$532$	3.94795	+	70.5606i	0.171165	+	3.05919i
$533$	−0.317078	−	9.14440i	−0.0137342	−	0.396088i
$534$		0			0
$535$	−5.99094	−	22.3585i	−0.259011	−	0.966642i
$536$	−3.48812	+	6.04160i	−0.150664	+	0.260958i
$537$		0			0
$538$	−3.25905	+	3.25905i	−0.140508	+	0.140508i
$539$	9.49547	+	7.57882i	0.408999	+	0.326443i
$540$		0			0
$541$	10.2400	+	38.2161i	0.440251	+	1.64304i	0.728178	+	0.685388i	$0.240367\pi$
$541$	10.2400	+	38.2161i	0.440251	+	1.64304i	−0.287927	+	0.957652i	$0.592966\pi$
$542$		−	55.8984i		−	2.40104i
$543$		0			0
$544$	−26.7073	−	26.7073i	−1.14507	−	1.14507i
$545$	−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	$0.332214\pi$
$548$	−15.7695	−	15.7695i	−0.673639	−	0.673639i
$549$		0			0
$550$		−	0.940465i		−	0.0401016i
$551$	1.34662	+	5.02564i	0.0573678	+	0.214099i
$552$		0			0
$553$	−2.34471	+	11.2259i	−0.0997071	+	0.477372i
$554$	−36.4426	+	36.4426i	−1.54830	+	1.54830i
$555$		0			0
$556$	−6.04127	+	10.4638i	−0.256207	+	0.443764i
$557$	4.83024	+	18.0267i	0.204664	+	0.763816i	0.989552	+	0.144178i	$0.0460538\pi$
$557$	4.83024	+	18.0267i	0.204664	+	0.763816i	−0.784888	+	0.619638i	$0.787280\pi$
$558$		0			0
$559$	1.60409	−	6.94028i	0.0678456	−	0.293542i
$560$	22.7225	+	34.7204i	0.960202	+	1.46721i
$561$		0			0
$562$	50.9478			2.14910
$563$	−10.0368			−0.423000			−0.211500	−	0.977378i	$-0.567835\pi$
$563$	−10.0368			−0.423000			−0.211500	+	0.977378i	$0.567835\pi$
$564$		0			0
$565$	10.1637	+	2.72336i	0.427591	+	0.114573i
$566$	16.6802	−	4.46944i	0.701119	−	0.187864i
$567$		0			0
$568$	40.3046	−	69.8097i	1.69114	−	2.92915i
$569$			11.4381i			0.479510i	0.970833	+	0.239755i	$0.0770672\pi$
$569$			11.4381i			0.479510i	−0.970833	+	0.239755i	$0.922933\pi$
$570$		0			0
$571$	37.6951	−	21.7633i	1.57749	−	0.910765i	0.582284	−	0.812986i	$-0.302159\pi$
$571$	37.6951	−	21.7633i	1.57749	−	0.910765i	0.995208	−	0.0977796i	$-0.0311740\pi$
$572$	14.7347	+	23.5934i	0.616090	+	0.986491i
$573$		0			0
$574$	−12.7075	−	11.3608i	−0.530400	−	0.474191i
$575$	−0.00231322	−	0.00400662i	−9.64681e−5	−	0.000167088i
$576$		0			0
$577$	1.32152	+	0.354101i	0.0550158	+	0.0147414i	0.286222	−	0.958163i	$-0.407601\pi$
$577$	1.32152	+	0.354101i	0.0550158	+	0.0147414i	−0.231206	+	0.972905i	$0.574267\pi$
$578$	70.9773	+	70.9773i	2.95227	+	2.95227i
$579$		0			0
$580$	6.21398	+	6.21398i	0.258021	+	0.258021i
$581$	−14.5885	+	28.8834i	−0.605234	+	1.19829i
$582$		0			0
$583$	−16.8666	+	16.8666i	−0.698541	+	0.698541i
$584$	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	$-0.564380\pi$
$587$	−20.9489	−	5.61323i	−0.864652	−	0.231683i	−0.663774	+	0.747933i	$0.731046\pi$
$588$		0			0
$589$	−31.3144	−	18.0794i	−1.29029	−	0.744947i
$590$	−32.5145	+	8.71225i	−1.33860	+	0.358678i
$591$		0			0
$592$	45.6120	−	45.6120i	1.87464	−	1.87464i
$593$	4.07949	−	1.09310i	0.167525	−	0.0448881i	−0.174082	−	0.984731i	$-0.555696\pi$
$593$	4.07949	−	1.09310i	0.167525	−	0.0448881i	0.341606	+	0.939843i	$0.389029\pi$
$594$		0			0
$595$	−24.8740	−	38.0079i	−1.01973	−	1.55817i
$596$	96.8352	+	25.9469i	3.96652	+	1.06283i
$597$		0			0
$598$	0.175160	+	0.0931894i	0.00716282	+	0.00381080i
$599$	−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	$-0.614187\pi$
$601$	6.96892	−	4.02351i	0.284268	−	0.164122i	0.635354	+	0.772221i	$0.280854\pi$
$602$	−7.26662	−	11.1035i	−0.296165	−	0.452546i
$603$		0			0
$604$	−24.0689	+	89.8265i	−0.979351	+	3.65499i
$605$	12.8964	+	12.8964i	0.524314	+	0.524314i
$606$		0			0
$607$	−38.9494	+	22.4875i	−1.58091	+	0.912737i	−0.586180	+	0.810180i	$0.699369\pi$
$607$	−38.9494	+	22.4875i	−1.58091	+	0.912737i	−0.994727	+	0.102557i	$0.967298\pi$
$608$	15.0922	+	26.1404i	0.612068	+	1.06013i
$609$		0			0
$610$			20.8934i			0.845948i
$611$	11.1128	+	17.7939i	0.449575	+	0.719864i
$612$		0			0
$613$	5.22539	−	1.40014i	0.211051	−	0.0565510i	−0.151744	−	0.988420i	$-0.548489\pi$
$613$	5.22539	−	1.40014i	0.211051	−	0.0565510i	0.362796	+	0.931869i	$0.381822\pi$
$614$		−	62.7808i		−	2.53363i
$615$		0			0
$616$	27.9023	+	5.82787i	1.12422	+	0.234811i
$617$	−21.1557	+	5.66866i	−0.851697	+	0.228212i	−0.658157	−	0.752881i	$-0.728664\pi$
$617$	−21.1557	+	5.66866i	−0.851697	+	0.228212i	−0.193540	+	0.981092i	$0.561997\pi$
$618$		0			0
$619$	−1.72873	+	6.45170i	−0.0694834	+	0.259316i	−0.991926	−	0.126819i	$-0.959523\pi$
$619$	−1.72873	+	6.45170i	−0.0694834	+	0.259316i	0.922442	+	0.386135i	$0.126190\pi$
$620$	−61.0731			−2.45275
$621$		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
$626$	−8.43914	−	31.4953i	−0.337296	−	1.25881i
$627$		0			0
$628$	14.6026	+	25.2924i	0.582706	+	1.00928i
$629$	−49.9307	+	49.9307i	−1.99087	+	1.99087i
$630$		0			0
$631$	−5.79046	−	21.6103i	−0.230515	−	0.860293i	−0.980120	−	0.198407i	$-0.936423\pi$
$631$	−5.79046	−	21.6103i	−0.230515	−	0.860293i	0.749605	−	0.661886i	$-0.230244\pi$
$632$	6.96392	+	25.9897i	0.277010	+	1.03382i
$633$		0			0
$634$	20.7900	+	12.0031i	0.825678	+	0.476705i
$635$	5.14903	+	5.14903i	0.204333	+	0.204333i
$636$		0			0
$637$	−20.2598	−	15.0513i	−0.802721	−	0.596354i
$638$	3.81508			0.151040
$639$		0			0
$640$	−24.8119	−	14.3252i	−0.980778	−	0.566252i
$641$		−	2.21138i		−	0.0873444i	−0.999046	−	0.0436722i	$-0.986094\pi$
$641$		−	2.21138i		−	0.0873444i	0.999046	−	0.0436722i	$-0.0139057\pi$
$642$		0			0
$643$	1.55263	+	5.79449i	0.0612297	+	0.228512i	0.989759	−	0.142746i	$-0.0455932\pi$
$643$	1.55263	+	5.79449i	0.0612297	+	0.228512i	−0.928530	+	0.371258i	$0.878926\pi$
$644$	0.242162	−	0.0796302i	0.00954253	−	0.00313787i
$645$		0			0
$646$	−57.3543	−	99.3405i	−2.25657	−	3.90850i
$647$	−0.776754	+	1.34538i	−0.0305373	+	0.0528922i	−0.880890	−	0.473321i	$-0.843055\pi$
$647$	−0.776754	+	1.34538i	−0.0305373	+	0.0528922i	0.850353	+	0.526213i	$0.176389\pi$
$648$		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
$653$	−21.9754			−0.859962			−0.429981	−	0.902838i	$-0.641480\pi$
$653$	−21.9754			−0.859962			−0.429981	+	0.902838i	$0.641480\pi$
$654$		0			0
$655$	−4.90957	+	18.3228i	−0.191833	+	0.715930i
$656$	−16.8373	−	4.51153i	−0.657384	−	0.176146i
$657$		0			0
$658$	38.2564	+	7.99048i	1.49139	+	0.311501i
$659$	−13.5876	+	23.5344i	−0.529298	+	0.916771i	0.470118	+	0.882604i	$0.344211\pi$
$659$	−13.5876	+	23.5344i	−0.529298	+	0.916771i	−0.999416	+	0.0341676i	$0.989122\pi$
$660$		0			0
$661$	10.4653	−	2.80418i	0.407055	−	0.109070i	−0.0494809	−	0.998775i	$-0.515757\pi$
$661$	10.4653	−	2.80418i	0.407055	−	0.109070i	0.456536	+	0.889705i	$0.349090\pi$
$662$	34.5488	−	19.9468i	1.34278	−	0.775254i
$663$		0			0
$664$			75.9199i			2.94626i
$665$	11.3396	+	34.4845i	0.439729	+	1.33725i
$666$		0			0
$667$	0.0162532	−	0.00938379i	0.000629327	−	0.000363342i
$668$	32.9253	+	8.82230i	1.27392	+	0.341345i
$669$		0			0
$670$	−1.68609	+	6.29257i	−0.0651393	+	0.243103i
$671$	4.42349	+	4.42349i	0.170767	+	0.170767i
$672$		0			0
$673$	−33.8958	+	19.5698i	−1.30659	+	0.754359i	−0.981525	−	0.191333i	$-0.938719\pi$
$673$	−33.8958	+	19.5698i	−1.30659	+	0.754359i	−0.325063	+	0.945692i	$0.605386\pi$
$674$	−2.53696	+	2.53696i	−0.0977199	+	0.0977199i
$675$		0			0
$676$	−32.2902	−	47.9231i	−1.24193	−	1.84320i
$677$	−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
$679$	11.1501	+	17.0375i	0.427901	+	0.653841i
$680$	−92.2953	−	53.2867i	−3.53936	−	2.04345i
$681$		0			0
$682$	−18.7479	+	18.7479i	−0.717896	+	0.717896i
$683$	33.0031	−	33.0031i	1.26283	−	1.26283i	0.313112	−	0.949716i	$-0.398628\pi$
$683$	33.0031	−	33.0031i	1.26283	−	1.26283i	0.949716	−	0.313112i	$-0.101372\pi$
$684$		0			0
$685$	−9.92069	−	5.72771i	−0.379050	−	0.218845i
$686$	−46.3584	+	7.84700i	−1.76997	+	0.299600i
$687$		0			0
$688$	−11.7522	−	6.78514i	−0.448049	−	0.258681i
$689$	33.8035	−	36.2320i	1.28781	−	1.38033i
$690$		0			0
$691$	3.43404	−	3.43404i	0.130637	−	0.130637i	−0.638765	−	0.769402i	$-0.720554\pi$
$691$	3.43404	−	3.43404i	0.130637	−	0.130637i	0.769402	+	0.638765i	$0.220554\pi$
$692$	0.861017	−	0.497108i	0.0327310	−	0.0188972i
$693$		0			0
$694$	−9.87660	−	9.87660i	−0.374910	−	0.374910i
$695$	−1.60633	+	5.99489i	−0.0609314	+	0.227399i
$696$		0			0
$697$	18.4315	+	4.93870i	0.698142	+	0.187067i
$698$	29.8489	−	17.2332i	1.12980	−	0.652288i
$699$		0			0
$700$	1.87137	+	1.67306i	0.0707313	+	0.0632357i
$701$			34.8788i			1.31735i	0.752426	+	0.658677i	$0.228884\pi$
$701$			34.8788i			1.31735i	−0.752426	+	0.658677i	$0.771116\pi$
$702$		0			0
$703$	48.8709	−	28.2156i	1.84320	−	1.06417i
$704$	−1.65193	+	0.442633i	−0.0622594	+	0.0166824i
$705$		0			0
$706$	9.85401	−	17.0676i	0.370861	−	0.642349i
$707$	−2.41352	+	11.5553i	−0.0907699	+	0.434583i
$708$		0			0
$709$	42.8331	+	11.4771i	1.60863	+	0.431032i	0.947635	−	0.319357i	$-0.103467\pi$
$709$	42.8331	+	11.4771i	1.60863	+	0.431032i	0.660997	+	0.750388i	$0.270134\pi$
$710$	19.4825	−	72.7095i	0.731164	−	2.72874i
$711$		0			0
$712$	15.0585			0.564341
$713$	−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
$718$	−28.9304	+	50.1088i	−1.07967	+	1.87005i
$719$	11.7231	+	20.3050i	0.437197	+	0.757247i	0.997472	−	0.0710594i	$-0.0226380\pi$
$719$	11.7231	+	20.3050i	0.437197	+	0.757247i	−0.560275	+	0.828306i	$0.689305\pi$
$720$		0			0
$721$	−4.58342	+	21.9443i	−0.170696	+	0.817247i
$722$	11.2419	+	41.9553i	0.418380	+	1.56141i
$723$		0			0
$724$			1.93814i			0.0720305i
$725$	0.160047	+	0.0924033i	0.00594400	+	0.00343177i
$726$		0			0
$727$	−4.34538			−0.161161			−0.0805806	−	0.996748i	$-0.525677\pi$
$727$	−4.34538			−0.161161			−0.0805806	+	0.996748i	$0.525677\pi$
$728$	−58.3494	−	10.0909i	−2.16257	−	0.373994i
$729$		0			0
$730$	40.6571	+	40.6571i	1.50479	+	1.50479i
$731$	12.8650	+	7.42758i	0.475827	+	0.274719i
$732$		0			0
$733$	11.5162	+	42.9792i	0.425362	+	1.58747i	0.763130	+	0.646245i	$0.223661\pi$
$733$	11.5162	+	42.9792i	0.425362	+	1.58747i	−0.337768	+	0.941229i	$0.609672\pi$
$734$	−13.9792	−	52.1713i	−0.515984	−	1.92568i
$735$		0			0
$736$	0.0769888	−	0.0769888i	0.00283784	−	0.00283784i
$737$	0.975271	+	1.68922i	0.0359246	+	0.0622232i
$738$		0			0
$739$	7.57142	+	28.2569i	0.278519	+	1.03945i	0.953446	+	0.301564i	$0.0975085\pi$
$739$	7.57142	+	28.2569i	0.278519	+	1.03945i	−0.674927	+	0.737885i	$0.735825\pi$
$740$	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	−0.899668	−	0.436575i	$-0.856191\pi$
$743$	2.66460	−	9.94444i	0.0977548	−	0.364826i	0.997423	+	0.0717489i	$0.0228580\pi$
$744$		0			0
$745$	51.4954			1.88665
$746$	10.9415	−	40.8343i	0.400598	−	1.49505i
$747$		0			0
$748$	−56.0335	+	15.0141i	−2.04879	+	0.548971i
$749$	25.4795	−	8.37842i	0.931000	−	0.306141i
$750$		0			0
$751$			21.4555i			0.782923i	0.920194	+	0.391462i	$0.128030\pi$
$751$			21.4555i			0.782923i	−0.920194	+	0.391462i	$0.871970\pi$
$752$	38.6046	−	10.3441i	1.40776	−	0.377209i
$753$		0			0
$754$	−7.92073	+	0.274648i	−0.288456	+	0.0100021i
$755$			47.7683i			1.73847i
$756$		0			0
$757$	−18.9933	−	32.8973i	−0.690322	−	1.19567i	−0.971732	−	0.236085i	$-0.924136\pi$
$757$	−18.9933	−	32.8973i	−0.690322	−	1.19567i	0.281410	−	0.959588i	$-0.409198\pi$
$758$	−40.1560	+	23.1841i	−1.45853	+	0.842084i
$759$		0			0
$760$	60.2242	+	60.2242i	2.18456	+	2.18456i
$761$	4.37608	−	16.3317i	0.158633	−	0.592025i	−0.840134	−	0.542379i	$-0.817524\pi$
$761$	4.37608	−	16.3317i	0.158633	−	0.592025i	0.998767	−	0.0496467i	$-0.0158095\pi$
$762$		0			0
$763$	−0.600936	−	10.7403i	−0.0217553	−	0.388827i
$764$	34.0475	−	19.6573i	1.23179	−	0.711177i
$765$		0			0
$766$	−33.8749	−	58.6731i	−1.22395	−	2.11995i
$767$	9.83418	−	18.4844i	0.355092	−	0.667434i
$768$		0			0
$769$	35.8744	+	9.61252i	1.29366	+	0.346636i	0.839051	−	0.544052i	$-0.183111\pi$
$769$	35.8744	+	9.61252i	1.29366	+	0.346636i	0.454614	+	0.890689i	$0.349777\pi$
$770$	26.5764	−	1.48698i	0.957748	−	0.0535872i
$771$		0			0
$772$	38.6890	−	10.3667i	1.39245	−	0.373106i
$773$	−8.34392	+	8.34392i	−0.300110	+	0.300110i	−0.841057	−	0.540947i	$-0.818066\pi$
$773$	−8.34392	+	8.34392i	−0.300110	+	0.300110i	0.540947	+	0.841057i	$0.318066\pi$
$774$		0			0
$775$	−1.24059	+	0.332414i	−0.0445631	+	0.0119407i
$776$	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
$782$	−0.292578	+	0.292578i	−0.0104626	+	0.0104626i
$783$		0			0
$784$	−38.6983	+	28.5359i	−1.38208	+	1.01914i
$785$	10.6077	+	10.6077i	0.378607	+	0.378607i
$786$		0			0
$787$	2.89556	+	2.89556i	0.103216	+	0.103216i	0.756829	−	0.653613i	$-0.226748\pi$
$787$	2.89556	+	2.89556i	0.103216	+	0.103216i	−0.653613	+	0.756829i	$0.726748\pi$
$788$	53.6818	+	14.3840i	1.91234	+	0.512409i
$789$		0			0
$790$	12.5629	+	21.7596i	0.446968	+	0.774172i
$791$	−2.49283	+	11.9350i	−0.0886348	+	0.424361i
$792$		0			0
$793$	−9.50234	−	8.86544i	−0.337438	−	0.314821i
$794$	31.1959	−	18.0110i	1.10710	−	0.639185i
$795$		0			0
$796$		−	37.0949i		−	1.31479i
$797$	1.02216	−	1.77043i	0.0362067	−	0.0627119i	−0.847354	−	0.531028i	$-0.821806\pi$
$797$	1.02216	−	1.77043i	0.0362067	−	0.0627119i	0.883561	+	0.468316i	$0.155139\pi$
$798$		0			0
$799$	−42.2598	+	11.3235i	−1.49504	+	0.400596i
$800$	1.03561	+	0.277490i	0.0366143	+	0.00981076i
$801$		0			0
$802$	5.79029			0.204462
$803$	17.2156			0.607526
$804$		0			0
$805$	0.109565	−	0.0717039i	0.00386166	−	0.00252723i
$806$	37.5742	−	40.2735i	1.32349	−	1.41857i
$807$		0			0
$808$	7.16832	+	26.7525i	0.252181	+	0.941150i
$809$	−13.5861	+	23.5318i	−0.477661	+	0.827333i	−0.999672	−	0.0256055i	$-0.991849\pi$
$809$	−13.5861	+	23.5318i	−0.477661	+	0.827333i	0.522011	+	0.852939i	$0.325182\pi$
$810$		0			0
$811$	−18.4741	+	18.4741i	−0.648712	+	0.648712i	−0.952682	−	0.303970i	$-0.901688\pi$
$811$	−18.4741	+	18.4741i	−0.648712	+	0.648712i	0.303970	+	0.952682i	$0.401688\pi$
$812$	−6.78691	+	7.59139i	−0.238174	+	0.266406i
$813$		0			0
$814$	−10.7096	−	39.9686i	−0.375370	−	1.40090i
$815$		−	55.3944i		−	1.94038i
$816$		0			0
$817$	−8.39458	−	8.39458i	−0.293689	−	0.293689i
$818$	50.0712			1.75070
$819$		0			0
$820$	−25.7567			−0.899462
$821$	−1.16838	−	1.16838i	−0.0407768	−	0.0407768i	0.686424	−	0.727201i	$-0.259179\pi$
$821$	−1.16838	−	1.16838i	−0.0407768	−	0.0407768i	−0.727201	+	0.686424i	$0.759179\pi$
$822$		0			0
$823$		−	26.4025i		−	0.920334i	−0.887832	−	0.460167i	$-0.847790\pi$
$823$		−	26.4025i		−	0.920334i	0.887832	−	0.460167i	$-0.152210\pi$
$824$	13.6131	+	50.8046i	0.474233	+	1.76986i
$825$		0			0
$826$	−12.1842	−	37.0532i	−0.423943	−	1.28925i
$827$	−21.2610	+	21.2610i	−0.739319	+	0.739319i	−0.972446	−	0.233127i	$-0.925104\pi$
$827$	−21.2610	+	21.2610i	−0.739319	+	0.739319i	0.233127	+	0.972446i	$0.425104\pi$
$828$		0			0
$829$	−14.3114	+	24.7881i	−0.497056	+	0.860926i	−0.999994	−	0.00339651i	$-0.998919\pi$
$829$	−14.3114	+	24.7881i	−0.497056	+	0.860926i	0.502939	+	0.864322i	$0.332252\pi$
$830$	18.3491	+	68.4797i	0.636906	+	2.37697i
$831$		0			0
$832$	3.39781	−	1.03790i	0.117798	−	0.0359828i
$833$	42.3625	−	31.2378i	1.46777	−	1.08233i
$834$		0			0
$835$	17.5091			0.605929
$836$	46.3597			1.60338
$837$		0			0
$838$	33.7222	+	9.03584i	1.16491	+	0.312138i
$839$	−2.96674	+	0.794936i	−0.102423	+	0.0274442i	−0.309667	−	0.950845i	$-0.600217\pi$
$839$	−2.96674	+	0.794936i	−0.102423	+	0.0274442i	0.207243	+	0.978289i	$0.433551\pi$
$840$		0			0
$841$	14.1252	−	24.4655i	0.487074	−	0.843638i
$842$		−	67.9366i		−	2.34125i
$843$		0			0
$844$	0.398258	−	0.229935i	0.0137086	−	0.00791467i
$845$	−22.3924	−	19.4847i	−0.770320	−	0.670295i
$846$		0			0
$847$	−14.0855	+	15.7551i	−0.483983	+	0.541352i
$848$	−47.2004	−	81.7534i	−1.62087	−	2.80742i
$849$		0			0
$850$	−3.93559	−	1.05454i	−0.134989	−	0.0361703i
$851$	−0.143935	−	0.143935i	−0.00493401	−	0.00493401i
$852$		0			0
$853$	15.7683	+	15.7683i	0.539896	+	0.539896i	0.923498	−	0.383603i	$-0.125317\pi$
$853$	15.7683	+	15.7683i	0.539896	+	0.539896i	−0.383603	+	0.923498i	$0.625317\pi$
$854$	−24.1722	+	1.35247i	−0.827157	+	0.0462804i
$855$		0			0
$856$	44.4976	−	44.4976i	1.52090	−	1.52090i
$857$	8.97423	+	15.5438i	0.306554	+	0.530967i	0.977606	−	0.210443i	$-0.0674907\pi$
$857$	8.97423	+	15.5438i	0.306554	+	0.530967i	−0.671052	+	0.741410i	$0.734157\pi$
$858$		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
$863$	−8.25794	+	2.21271i	−0.281104	+	0.0753215i	−0.396616	−	0.917985i	$-0.629816\pi$
$863$	−8.25794	+	2.21271i	−0.281104	+	0.0753215i	0.115513	+	0.993306i	$0.463149\pi$
$864$		0			0
$865$	0.361115	−	0.361115i	0.0122783	−	0.0122783i
$866$	−63.2333	+	16.9433i	−2.14875	+	0.575757i
$867$		0			0
$868$	−3.95337	−	70.6575i	−0.134186	−	2.39827i
$869$	7.26667	+	1.94710i	0.246505	+	0.0660508i
$870$		0			0
$871$	−2.14643	−	3.43689i	−0.0727290	−	0.116454i
$872$	−12.6192	−	21.8572i	−0.427341	−	0.740177i
$873$		0			0
$874$	0.286368	−	0.165334i	0.00968653	−	0.00559252i
$875$	−25.8104	−	13.0364i	−0.872549	−	0.440710i
$876$		0			0
$877$	7.19509	−	26.8524i	0.242961	−	0.906742i	−0.731437	−	0.681909i	$-0.761150\pi$
$877$	7.19509	−	26.8524i	0.242961	−	0.906742i	0.974397	−	0.224833i	$-0.0721835\pi$
$878$	−4.44747	−	4.44747i	−0.150095	−	0.150095i
$879$		0			0
$880$	23.5735	−	13.6102i	0.794664	−	0.458799i
$881$	7.37078	+	12.7666i	0.248328	+	0.430116i	0.963062	−	0.269280i	$-0.0867857\pi$
$881$	7.37078	+	12.7666i	0.248328	+	0.430116i	−0.714734	+	0.699396i	$0.753452\pi$
$882$		0			0
$883$			16.7260i			0.562876i	0.959579	+	0.281438i	$0.0908114\pi$
$883$			16.7260i			0.562876i	−0.959579	+	0.281438i	$0.909189\pi$
$884$	115.254	−	35.2057i	3.87641	−	1.18409i
$885$		0			0
$886$	57.0733	−	15.2927i	1.91742	−	0.513770i
$887$		−	18.4088i		−	0.618108i	−0.951045	−	0.309054i	$-0.899988\pi$
$887$		−	18.4088i		−	0.618108i	0.951045	−	0.309054i	$-0.100012\pi$
$888$		0			0
$889$	−5.62378	+	6.29039i	−0.188615	+	0.210973i
$890$	13.5828	−	3.63949i	0.455295	−	0.121996i
$891$		0			0
$892$	−30.1473	+	112.511i	−1.00940	+	3.76715i
$893$	34.9639			1.17002
$894$		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
$899$	−1.34847	−	5.03254i	−0.0449738	−	0.167845i
$900$		0			0
$901$	51.6695	+	89.4942i	1.72136	+	2.98148i
$902$	−7.90667	+	7.90667i	−0.263263	+	0.263263i
$903$		0			0
$904$	7.40386	+	27.6316i	0.246249	+	0.919012i
$905$	0.257668	+	0.961631i	0.00856518	+	0.0319657i
$906$		0			0
$907$	−24.9889	−	14.4274i	−0.829744	−	0.479053i	0.0240212	−	0.999711i	$-0.492353\pi$
$907$	−24.9889	−	14.4274i	−0.829744	−	0.479053i	−0.853765	+	0.520659i	$0.825686\pi$
$908$	−42.7872	−	42.7872i	−1.41994	−	1.41994i
$909$		0			0
$910$	−55.0700	+	5.00047i	−1.82555	+	0.165764i
$911$	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
$913$	18.3832	+	10.6135i	0.608393	+	0.351256i
$914$		−	14.0128i		−	0.463501i
$915$		0			0
$916$	−27.9691	−	104.382i	−0.924126	−	3.44888i
$917$	−21.5160	−	4.49398i	−0.710521	−	0.148404i
$918$		0			0
$919$	−3.40666	−	5.90051i	−0.112375	−	0.194640i	0.804352	−	0.594153i	$-0.202513\pi$
$919$	−3.40666	−	5.90051i	−0.112375	−	0.194640i	−0.916728	+	0.399513i	$0.869179\pi$
$920$	0.153609	−	0.266059i	0.00506434	−	0.00877169i
$921$		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
$926$	37.3156			1.22627
$927$		0			0
$928$	−1.12566	+	4.20103i	−0.0369517	+	0.137906i
$929$	−4.95489	−	1.32766i	−0.162565	−	0.0435590i	0.176619	−	0.984279i	$-0.443484\pi$
$929$	−4.95489	−	1.32766i	−0.162565	−	0.0435590i	−0.339183	+	0.940720i	$0.610151\pi$
$930$		0			0
$931$	−39.1623	+	15.3514i	−1.28349	+	0.503120i
$932$	−21.2986	+	36.8902i	−0.697658	+	1.20838i
$933$		0			0
$934$	52.2761	−	14.0073i	1.71053	−	0.458334i
$935$	−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	$-0.301982\pi$
$938$	−7.38922	−	1.54336i	−0.241267	−	0.0503925i
$939$		0			0
$940$	51.1432	−	29.5275i	1.66811	−	0.963082i
$941$	55.6304	+	14.9061i	1.81350	+	0.485926i	0.995948	−	0.0899311i	$-0.0286647\pi$
$941$	55.6304	+	14.9061i	1.81350	+	0.485926i	0.817551	+	0.575857i	$0.195331\pi$
$942$		0			0
$943$	−0.0142367	+	0.0531322i	−0.000463611	+	0.00173022i
$944$	−28.2049	−	28.2049i	−0.917991	−	0.917991i
$945$		0			0
$946$	−7.53877	+	4.35251i	−0.245107	+	0.141512i
$947$	11.4925	−	11.4925i	0.373456	−	0.373456i	−0.495278	−	0.868734i	$-0.664934\pi$
$947$	11.4925	−	11.4925i	0.373456	−	0.373456i	0.868734	+	0.495278i	$0.164934\pi$
$948$		0			0
$949$	−35.7425	+	1.23935i	−1.16025	+	0.0402311i
$950$	2.81989	+	1.62807i	0.0914895	+	0.0528215i
$951$		0			0
$952$	55.6747	−	110.229i	1.80443	−	3.57254i
$953$	−8.84363	−	5.10587i	−0.286473	−	0.165395i	0.349877	−	0.936796i	$-0.386223\pi$
$953$	−8.84363	−	5.10587i	−0.286473	−	0.165395i	−0.636350	+	0.771400i	$0.719557\pi$
$954$		0			0
$955$	14.2797	−	14.2797i	0.462079	−	0.462079i
$956$	25.0803	−	25.0803i	0.811155	−	0.811155i
$957$		0			0
$958$	−32.7144	−	18.8877i	−1.05695	−	0.610233i
$959$	5.98439	−	11.8483i	0.193246	−	0.382603i
$960$		0			0
$961$	4.51058	+	2.60419i	0.145503	+	0.0840060i
$962$	25.1121	+	82.2104i	0.809648	+	2.65057i
$963$		0			0
$964$	79.7635	−	79.7635i	2.56901	−	2.56901i
$965$	17.8178	−	10.2871i	0.573575	−	0.331154i
$966$		0			0
$967$	13.8579	+	13.8579i	0.445641	+	0.445641i	0.893903	−	0.448261i	$-0.147957\pi$
$967$	13.8579	+	13.8579i	0.445641	+	0.445641i	−0.448261	+	0.893903i	$0.647957\pi$
$968$	−12.8331	+	47.8940i	−0.412473	+	1.53937i
$969$		0			0
$970$	43.0912	+	11.5462i	1.38357	+	0.370727i
$971$	4.74622	−	2.74023i	0.152313	−	0.0879381i	−0.421906	−	0.906639i	$-0.638639\pi$
$971$	4.74622	−	2.74023i	0.152313	−	0.0879381i	0.574220	+	0.818701i	$0.305306\pi$
$972$		0			0
$973$	−7.03967	−	1.47035i	−0.225681	−	0.0471373i
$974$			36.6432i			1.17412i
$975$		0			0
$976$	−21.4410	+	12.3790i	−0.686309	+	0.396241i
$977$	21.1744	−	5.67366i	0.677428	−	0.181516i	0.0963296	−	0.995349i	$-0.469290\pi$
$977$	21.1744	−	5.67366i	0.677428	−	0.181516i	0.581099	+	0.813833i	$0.302623\pi$
$978$		0			0
$979$	2.10516	−	3.64625i	0.0672813	−	0.116535i
$980$	−44.3198	+	55.5282i	−1.41575	+	1.77378i
$981$		0			0
$982$	−1.29945	−	0.348186i	−0.0414671	−	0.0111111i
$983$	0.0251897	−	0.0940093i	0.000803427	−	0.00299843i	−0.965523	−	0.260318i	$-0.916173\pi$
$983$	0.0251897	−	0.0940093i	0.000803427	−	0.00299843i	0.966326	+	0.257320i	$0.0828393\pi$
$984$		0			0
$985$	28.5471			0.909588
$986$	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
$991$	−4.71735	+	8.17068i	−0.149851	+	0.259550i	−0.931172	−	0.364579i	$-0.881213\pi$
$991$	−4.71735	+	8.17068i	−0.149851	+	0.259550i	0.781321	+	0.624129i	$0.214546\pi$
$992$	−15.1129	−	26.1763i	−0.479835	−	0.831098i
$993$		0			0
$994$	85.3811	+	17.8333i	2.70813	+	0.565637i
$995$	−4.93162	−	18.4051i	−0.156343	−	0.583479i
$996$		0			0
$997$		−	38.4878i		−	1.21892i	−0.792816	−	0.609461i	$-0.791386\pi$
$997$		−	38.4878i		−	1.21892i	0.792816	−	0.609461i	$-0.208614\pi$
$998$	−55.8465	−	32.2430i	−1.76779	−	1.02063i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.1	✓	36	273.227	odd	12
273.2.bt.a.271.1	yes	36	3.2	odd	2
273.2.cg.a.19.9	yes	36	39.32	even	12
273.2.cg.a.115.9	yes	36	21.17	even	6
819.2.et.c.136.9		36	91.45	even	12	inner
819.2.et.c.271.9		36	1.1	even	1	trivial
819.2.gh.c.19.1		36	13.6	odd	12
819.2.gh.c.388.1		36	7.3	odd	6

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.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.79515 + 1.79515i) q^{2} +4.44512i q^{4} +(0.590961 + 2.20549i) q^{5} +(-2.51335 + 0.826467i) q^{7} +(-4.38935 + 4.38935i) q^{8} +O(q^{10})\)	\(q+(1.79515 + 1.79515i) q^{2} +4.44512i q^{4} +(0.590961 + 2.20549i) q^{5} +(-2.51335 + 0.826467i) q^{7} +(-4.38935 + 4.38935i) q^{8} +(-2.89833 + 5.02005i) q^{10} +(0.449206 + 1.67646i) q^{11} +(-1.05331 - 3.44826i) q^{13} +(-5.99548 - 3.02821i) q^{14} -6.86883 q^{16} +7.51920 q^{17} +(-5.80433 - 1.55527i) q^{19} +(-9.80368 + 2.62689i) q^{20} +(-2.20310 + 3.81588i) q^{22} +0.0216755i q^{23} +(-0.184846 + 0.106721i) q^{25} +(4.29929 - 8.08100i) q^{26} +(-3.67374 - 11.1722i) q^{28} +(-0.432921 - 0.749842i) q^{29} +(5.81230 + 1.55740i) q^{31} +(-3.55188 - 3.55188i) q^{32} +(13.4981 + 13.4981i) q^{34} +(-3.30806 - 5.05478i) q^{35} +(-6.64042 + 6.64042i) q^{37} +(-7.62770 - 13.2116i) q^{38} +(-12.2746 - 7.08675i) q^{40} +(2.45125 + 0.656811i) q^{41} +(1.71095 + 0.987815i) q^{43} +(-7.45205 + 1.99677i) q^{44} +(-0.0389108 + 0.0389108i) q^{46} +(-5.62025 + 1.50594i) q^{47} +(5.63390 - 4.15441i) q^{49} +(-0.523405 - 0.140246i) q^{50} +(15.3279 - 4.68210i) q^{52} +(6.87167 + 11.9021i) q^{53} +(-3.43196 + 1.98144i) q^{55} +(7.40434 - 14.6596i) q^{56} +(0.568919 - 2.12324i) q^{58} +(4.10621 + 4.10621i) q^{59} +(3.12149 - 1.80219i) q^{61} +(7.63818 + 13.2297i) q^{62} +0.985368i q^{64} +(6.98266 - 4.36087i) q^{65} +(1.08555 - 0.290873i) q^{67} +33.4237i q^{68} +(3.13562 - 15.0125i) q^{70} +(-12.5434 + 3.36098i) q^{71} +(2.56726 - 9.58115i) q^{73} -23.8411 q^{74} +(6.91334 - 25.8009i) q^{76} +(-2.51455 - 3.84228i) q^{77} +(2.16727 - 3.75382i) q^{79} +(-4.05921 - 15.1492i) q^{80} +(3.22129 + 5.57944i) q^{82} +(8.64819 - 8.64819i) q^{83} +(4.44355 + 16.5836i) q^{85} +(1.29813 + 4.84468i) q^{86} +(-9.33028 - 5.38684i) q^{88} +(-1.71535 - 1.71535i) q^{89} +(5.49723 + 7.79618i) q^{91} -0.0963502 q^{92} +(-12.7926 - 7.38580i) q^{94} -13.7205i q^{95} +(-1.99188 - 7.43379i) q^{97} +(17.5715 + 2.65591i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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