LMFDB - Embedded newform 819.2.gh.d.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("819.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.gh (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	819.19
Dual form			819.2.gh.d.388.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49615 + 0.400893i) q^{2} +(0.345704 + 0.199592i) q^{4} +(-0.481371 + 0.128983i) q^{5} +(-2.58563 - 0.560827i) q^{7} +(-1.75331 - 1.75331i) q^{8} +O(q^{10})$	\(q+(1.49615 + 0.400893i) q^{2} +(0.345704 + 0.199592i) q^{4} +(-0.481371 + 0.128983i) q^{5} +(-2.58563 - 0.560827i) q^{7} +(-1.75331 - 1.75331i) q^{8} -0.771912 q^{10} +(-1.32217 - 1.32217i) q^{11} +(-3.48498 + 0.924630i) q^{13} +(-3.64366 - 1.87564i) q^{14} +(-2.31951 - 4.01751i) q^{16} +(1.95881 - 3.39275i) q^{17} +(-2.70752 - 2.70752i) q^{19} +(-0.192156 - 0.0514880i) q^{20} +(-1.44812 - 2.50822i) q^{22} +(4.25685 - 2.45769i) q^{23} +(-4.11505 + 2.37582i) q^{25} +(-5.58473 - 0.0137152i) q^{26} +(-0.781926 - 0.709952i) q^{28} +(2.28804 - 3.96301i) q^{29} +(-1.12967 + 4.21599i) q^{31} +(-0.576239 - 2.15055i) q^{32} +(4.29080 - 4.29080i) q^{34} +(1.31698 - 0.0635363i) q^{35} +(0.0389735 - 0.145451i) q^{37} +(-2.96543 - 5.13628i) q^{38} +(1.07014 + 0.617844i) q^{40} +(-4.92590 + 1.31989i) q^{41} +(-5.06441 + 2.92394i) q^{43} +(-0.193185 - 0.720977i) q^{44} +(7.35416 - 1.97054i) q^{46} +(2.39236 + 8.92840i) q^{47} +(6.37095 + 2.90018i) q^{49} +(-7.10918 + 1.90490i) q^{50} +(-1.38932 - 0.375926i) q^{52} +(-6.56146 - 11.3648i) q^{53} +(0.806994 + 0.465918i) q^{55} +(3.55010 + 5.51670i) q^{56} +(5.01200 - 5.01200i) q^{58} +(0.986638 + 3.68218i) q^{59} -11.7615i q^{61} +(-3.38032 + 5.85488i) q^{62} +5.82948i q^{64} +(1.55830 - 0.894592i) q^{65} +(6.99516 - 6.99516i) q^{67} +(1.35433 - 0.781926i) q^{68} +(1.99588 + 0.432909i) q^{70} +(1.82020 + 0.487720i) q^{71} +(6.55409 + 1.75616i) q^{73} +(0.116621 - 0.201993i) q^{74} +(-0.395600 - 1.47640i) q^{76} +(2.67714 + 4.16016i) q^{77} +(2.22755 - 3.85822i) q^{79} +(1.63474 + 1.63474i) q^{80} -7.89902 q^{82} +(5.85648 + 5.85648i) q^{83} +(-0.505305 + 1.88582i) q^{85} +(-8.74931 + 2.34437i) q^{86} +4.63635i q^{88} +(-11.9450 - 3.20066i) q^{89} +(9.52941 - 0.436280i) q^{91} +1.96215 q^{92} +14.3173i q^{94} +(1.65254 + 0.954096i) q^{95} +(-2.09507 + 7.81890i) q^{97} +(8.36924 + 6.89317i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^7	$ 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) $ 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.49615	+	0.400893i	1.05794	+	0.283474i	0.745529	−	0.666473i	$-0.232197\pi$
$2$	1.49615	+	0.400893i	1.05794	+	0.283474i	0.312410	+	0.949947i	$0.398864\pi$
$3$		0			0
$3$		0			0
$4$	0.345704	+	0.199592i	0.172852	+	0.0997962i
$5$	−0.481371	+	0.128983i	−0.215276	+	0.0576829i	−0.364845	−	0.931068i	$-0.618878\pi$
$5$	−0.481371	+	0.128983i	−0.215276	+	0.0576829i	0.149569	+	0.988751i	$0.452211\pi$
$6$		0			0
$7$	−2.58563	−	0.560827i	−0.977276	−	0.211973i
$7$	−2.58563	−	0.560827i	−0.977276	−	0.211973i
$8$	−1.75331	−	1.75331i	−0.619888	−	0.619888i
$9$		0			0
$10$	−0.771912			−0.244100
$11$	−1.32217	−	1.32217i	−0.398650	−	0.398650i	0.479106	−	0.877757i	$-0.340961\pi$
$11$	−1.32217	−	1.32217i	−0.398650	−	0.398650i	−0.877757	+	0.479106i	$0.840961\pi$
$12$		0			0
$13$	−3.48498	+	0.924630i	−0.966559	+	0.256446i
$13$	−3.48498	+	0.924630i	−0.966559	+	0.256446i
$14$	−3.64366	−	1.87564i	−0.973809	−	0.501286i
$15$		0			0
$16$	−2.31951	−	4.01751i	−0.579878	−	1.00438i
$17$	1.95881	−	3.39275i	0.475080	−	0.822863i	−0.524512	−	0.851403i	$-0.675752\pi$
$17$	1.95881	−	3.39275i	0.475080	−	0.822863i	0.999593	+	0.0285396i	$0.00908567\pi$
$18$		0			0
$19$	−2.70752	−	2.70752i	−0.621147	−	0.621147i	0.324678	−	0.945825i	$-0.394744\pi$
$19$	−2.70752	−	2.70752i	−0.621147	−	0.621147i	−0.945825	+	0.324678i	$0.894744\pi$
$20$	−0.192156	−	0.0514880i	−0.0429674	−	0.0115131i
$21$		0			0
$22$	−1.44812	−	2.50822i	−0.308741	−	0.534755i
$23$	4.25685	−	2.45769i	0.887614	−	0.512464i	0.0144528	−	0.999896i	$-0.495399\pi$
$23$	4.25685	−	2.45769i	0.887614	−	0.512464i	0.873161	+	0.487431i	$0.162066\pi$
$24$		0			0
$25$	−4.11505	+	2.37582i	−0.823009	+	0.475165i
$26$	−5.58473	−	0.0137152i	−1.09526	−	0.00268977i
$27$		0			0
$28$	−0.781926	−	0.709952i	−0.147770	−	0.134168i
$29$	2.28804	−	3.96301i	0.424879	−	0.735912i	−0.571530	−	0.820581i	$-0.693650\pi$
$29$	2.28804	−	3.96301i	0.424879	−	0.735912i	0.996409	+	0.0846692i	$0.0269833\pi$
$30$		0			0
$31$	−1.12967	+	4.21599i	−0.202895	+	0.757214i	0.787186	+	0.616716i	$0.211537\pi$
$31$	−1.12967	+	4.21599i	−0.202895	+	0.757214i	−0.990081	+	0.140498i	$0.955130\pi$
$32$	−0.576239	−	2.15055i	−0.101866	−	0.380168i
$33$		0			0
$34$	4.29080	−	4.29080i	0.735866	−	0.735866i
$35$	1.31698	−	0.0635363i	0.222611	−	0.0107396i
$36$		0			0
$37$	0.0389735	−	0.145451i	0.00640721	−	0.0239120i	−0.962648	−	0.270755i	$-0.912727\pi$
$37$	0.0389735	−	0.145451i	0.00640721	−	0.0239120i	0.969055	+	0.246843i	$0.0793933\pi$
$38$	−2.96543	−	5.13628i	−0.481057	−	0.833214i
$39$		0			0
$40$	1.07014	+	0.617844i	0.169204	+	0.0976898i
$41$	−4.92590	+	1.31989i	−0.769296	+	0.206132i	−0.622060	−	0.782969i	$-0.713704\pi$
$41$	−4.92590	+	1.31989i	−0.769296	+	0.206132i	−0.147235	+	0.989101i	$0.547037\pi$
$42$		0			0
$43$	−5.06441	+	2.92394i	−0.772315	+	0.445896i	−0.833700	−	0.552218i	$-0.813782\pi$
$43$	−5.06441	+	2.92394i	−0.772315	+	0.445896i	0.0613847	+	0.998114i	$0.480448\pi$
$44$	−0.193185	−	0.720977i	−0.0291238	−	0.108691i
$45$		0			0
$46$	7.35416	−	1.97054i	1.08431	−	0.290541i
$47$	2.39236	+	8.92840i	0.348961	+	1.30234i	0.887916	+	0.460006i	$0.152153\pi$
$47$	2.39236	+	8.92840i	0.348961	+	1.30234i	−0.538955	+	0.842335i	$0.681181\pi$
$48$		0			0
$49$	6.37095	+	2.90018i	0.910135	+	0.414311i
$50$	−7.10918	+	1.90490i	−1.00539	+	0.269393i
$51$		0			0
$52$	−1.38932	−	0.375926i	−0.192664	−	0.0521316i
$53$	−6.56146	−	11.3648i	−0.901285	−	1.56107i	−0.825827	−	0.563923i	$-0.809291\pi$
$53$	−6.56146	−	11.3648i	−0.901285	−	1.56107i	−0.0754580	−	0.997149i	$-0.524042\pi$
$54$		0			0
$55$	0.806994	+	0.465918i	0.108815	+	0.0628244i
$56$	3.55010	+	5.51670i	0.474402	+	0.737200i
$57$		0			0
$58$	5.01200	−	5.01200i	0.658108	−	0.658108i
$59$	0.986638	+	3.68218i	0.128449	+	0.479380i	0.999939	−	0.0110341i	$-0.00351234\pi$
$59$	0.986638	+	3.68218i	0.128449	+	0.479380i	−0.871490	+	0.490414i	$0.836846\pi$
$60$		0			0
$61$		−	11.7615i		−	1.50590i	−0.658076	−	0.752951i	$-0.728630\pi$
$61$		−	11.7615i		−	1.50590i	0.658076	−	0.752951i	$-0.271370\pi$
$62$	−3.38032	+	5.85488i	−0.429301	+	0.743571i
$63$		0			0
$64$			5.82948i			0.728685i
$65$	1.55830	−	0.894592i	0.193284	−	0.110961i
$66$		0			0
$67$	6.99516	−	6.99516i	0.854594	−	0.854594i	−0.136101	−	0.990695i	$-0.543457\pi$
$67$	6.99516	−	6.99516i	0.854594	−	0.854594i	0.990695	+	0.136101i	$0.0434570\pi$
$68$	1.35433	−	0.781926i	0.164237	−	0.0948224i
$69$		0			0
$70$	1.99588	+	0.432909i	0.238553	+	0.0517425i
$71$	1.82020	+	0.487720i	0.216017	+	0.0578817i	0.365205	−	0.930927i	$-0.380999\pi$
$71$	1.82020	+	0.487720i	0.216017	+	0.0578817i	−0.149187	+	0.988809i	$0.547666\pi$
$72$		0			0
$73$	6.55409	+	1.75616i	0.767098	+	0.205543i	0.621089	−	0.783740i	$-0.286690\pi$
$73$	6.55409	+	1.75616i	0.767098	+	0.205543i	0.146009	+	0.989283i	$0.453357\pi$
$74$	0.116621	−	0.201993i	0.0135569	−	0.0234812i
$75$		0			0
$76$	−0.395600	−	1.47640i	−0.0453784	−	0.169355i
$77$	2.67714	+	4.16016i	0.305088	+	0.474094i
$78$		0			0
$79$	2.22755	−	3.85822i	0.250618	−	0.434084i	−0.713078	−	0.701085i	$-0.752699\pi$
$79$	2.22755	−	3.85822i	0.250618	−	0.434084i	0.963696	+	0.267001i	$0.0860327\pi$
$80$	1.63474	+	1.63474i	0.182769	+	0.182769i
$81$		0			0
$82$	−7.89902			−0.872301
$83$	5.85648	+	5.85648i	0.642832	+	0.642832i	0.951251	−	0.308418i	$-0.0997997\pi$
$83$	5.85648	+	5.85648i	0.642832	+	0.642832i	−0.308418	+	0.951251i	$0.599800\pi$
$84$		0			0
$85$	−0.505305	+	1.88582i	−0.0548080	+	0.204546i
$86$	−8.74931	+	2.34437i	−0.943462	+	0.252800i
$87$		0			0
$88$			4.63635i			0.494237i
$89$	−11.9450	−	3.20066i	−1.26617	−	0.339269i	−0.437607	−	0.899167i	$-0.644174\pi$
$89$	−11.9450	−	3.20066i	−1.26617	−	0.339269i	−0.828562	+	0.559898i	$0.810840\pi$
$90$		0			0
$91$	9.52941	−	0.436280i	0.998954	−	0.0457346i
$92$	1.96215			0.204568
$93$		0			0
$94$			14.3173i			1.47672i
$95$	1.65254	+	0.954096i	0.169547	+	0.0978882i
$96$		0			0
$97$	−2.09507	+	7.81890i	−0.212722	+	0.793889i	0.774234	+	0.632899i	$0.218135\pi$
$97$	−2.09507	+	7.81890i	−0.212722	+	0.793889i	−0.986956	+	0.160990i	$0.948531\pi$
$98$	8.36924	+	6.89317i	0.845421	+	0.696316i
$99$		0			0
$100$	−1.89678			−0.189678
$101$	7.13841			0.710298			0.355149	−	0.934810i	$-0.384430\pi$
$101$	7.13841			0.710298			0.355149	+	0.934810i	$0.384430\pi$
$102$		0			0
$103$	−6.77987	+	11.7431i	−0.668041	+	1.15708i	0.310410	+	0.950603i	$0.399534\pi$
$103$	−6.77987	+	11.7431i	−0.668041	+	1.15708i	−0.978451	+	0.206478i	$0.933800\pi$
$104$	7.73139	+	4.48907i	0.758126	+	0.440190i
$105$		0			0
$106$	−5.26088	−	19.6339i	−0.510982	−	1.90701i
$107$	−7.16684	−	12.4133i	−0.692844	−	1.20004i	−0.970902	−	0.239477i	$-0.923024\pi$
$107$	−7.16684	−	12.4133i	−0.692844	−	1.20004i	0.278058	−	0.960564i	$-0.410309\pi$
$108$		0			0
$109$	8.27315	+	2.21678i	0.792424	+	0.212329i	0.632255	−	0.774760i	$-0.282129\pi$
$109$	8.27315	+	2.21678i	0.792424	+	0.212329i	0.160169	+	0.987090i	$0.448796\pi$
$110$	1.02060	+	1.02060i	0.0973106	+	0.0973106i
$111$		0			0
$112$	3.74426	+	11.6886i	0.353800	+	1.10447i
$113$	−5.02934	−	8.71107i	−0.473120	−	0.819468i	0.526406	−	0.850233i	$-0.323539\pi$
$113$	−5.02934	−	8.71107i	−0.473120	−	0.819468i	−0.999527	+	0.0307647i	$0.990206\pi$
$114$		0			0
$115$	−1.73212	+	1.73212i	−0.161521	+	0.161521i
$116$	1.58197	−	0.913352i	0.146882	−	0.0848026i
$117$		0			0
$118$			5.90464i			0.543566i
$119$	−6.96749	+	7.67384i	−0.638709	+	0.703460i
$120$		0			0
$121$		−	7.50371i		−	0.682156i
$122$	4.71509	−	17.5970i	0.426884	−	1.59315i
$123$		0			0
$124$	−1.23201	+	1.23201i	−0.110638	+	0.110638i
$125$	3.43636	−	3.43636i	0.307358	−	0.307358i
$126$		0			0
$127$	−16.1635	−	9.33200i	−1.43428	−	0.828081i	−0.436835	−	0.899542i	$-0.643901\pi$
$127$	−16.1635	−	9.33200i	−1.43428	−	0.828081i	−0.997443	+	0.0714604i	$0.977234\pi$
$128$	−3.48947	+	13.0229i	−0.308429	+	1.15107i
$129$		0			0
$130$	2.69010	−	0.713733i	0.235937	−	0.0625985i
$131$	1.88052	+	1.08572i	0.164302	+	0.0948599i	0.579896	−	0.814690i	$-0.303093\pi$
$131$	1.88052	+	1.08572i	0.164302	+	0.0948599i	−0.415594	+	0.909550i	$0.636426\pi$
$132$		0			0
$133$	5.48218	+	8.51908i	0.475366	+	0.738698i
$134$	13.2701	−	7.66151i	1.14636	−	0.661854i
$135$		0			0
$136$	−9.38293	+	2.51415i	−0.804579	+	0.215586i
$137$	8.68418	−	2.32692i	0.741940	−	0.198802i	0.132000	−	0.991250i	$-0.457860\pi$
$137$	8.68418	−	2.32692i	0.741940	−	0.198802i	0.609940	+	0.792448i	$0.291193\pi$
$138$		0			0
$139$	−7.57721	+	4.37470i	−0.642690	+	0.371057i	−0.785650	−	0.618671i	$-0.787671\pi$
$139$	−7.57721	+	4.37470i	−0.642690	+	0.371057i	0.142960	+	0.989729i	$0.454338\pi$
$140$	0.467968	+	0.240895i	0.0395505	+	0.0203593i
$141$		0			0
$142$	2.52776	+	1.45941i	0.212125	+	0.122471i
$143$	5.83026	+	3.38522i	0.487551	+	0.283087i
$144$		0			0
$145$	−0.590237	+	2.20279i	−0.0490165	+	0.182932i
$146$	9.10188	+	5.25497i	0.753277	+	0.434905i
$147$		0			0
$148$	0.0425043	−	0.0425043i	0.00349383	−	0.00349383i
$149$	10.5464	−	10.5464i	0.863991	−	0.863991i	−0.127808	−	0.991799i	$-0.540794\pi$
$149$	10.5464	−	10.5464i	0.863991	−	0.863991i	0.991799	+	0.127808i	$0.0407942\pi$
$150$		0			0
$151$	−1.50664	+	5.62287i	−0.122609	+	0.457583i	−0.999743	−	0.0226626i	$-0.992786\pi$
$151$	−1.50664	+	5.62287i	−0.122609	+	0.457583i	0.877134	+	0.480245i	$0.159452\pi$
$152$			9.49422i			0.770083i
$153$		0			0
$154$	2.33763	+	7.29748i	0.188371	+	0.588047i
$155$		−	2.17516i		−	0.174713i
$156$		0			0
$157$	8.97361	−	5.18091i	0.716172	−	0.413482i	−0.0971703	−	0.995268i	$-0.530979\pi$
$157$	8.97361	−	5.18091i	0.716172	−	0.413482i	0.813342	+	0.581786i	$0.197646\pi$
$158$	4.87948	−	4.87948i	0.388190	−	0.388190i
$159$		0			0
$160$	0.554770	+	0.960889i	0.0438584	+	0.0759650i
$161$	−12.3850	+	3.96732i	−0.976072	+	0.312669i
$162$		0			0
$163$	6.45941	+	6.45941i	0.505940	+	0.505940i	0.913278	−	0.407338i	$-0.133543\pi$
$163$	6.45941	+	6.45941i	0.505940	+	0.505940i	−0.407338	+	0.913278i	$0.633543\pi$
$164$	−1.96634	−	0.526880i	−0.153546	−	0.0411424i
$165$		0			0
$166$	6.41436	+	11.1100i	0.497851	+	0.862304i
$167$	1.16987	+	4.36602i	0.0905275	+	0.337853i	0.996303	−	0.0859038i	$-0.0273778\pi$
$167$	1.16987	+	4.36602i	0.0905275	+	0.337853i	−0.905776	+	0.423757i	$0.860711\pi$
$168$		0			0
$169$	11.2901	−	6.44462i	0.868471	−	0.495740i
$170$	−1.51203	+	2.61891i	−0.115967	+	0.200861i
$171$		0			0
$172$	−2.33438			−0.177995
$173$	16.4696			1.25216			0.626081	−	0.779758i	$-0.284658\pi$
$173$	16.4696			1.25216			0.626081	+	0.779758i	$0.284658\pi$
$174$		0			0
$175$	11.9724	−	3.83517i	0.905029	−	0.289911i
$176$	−2.24505	+	8.37864i	−0.169227	+	0.631564i
$177$		0			0
$178$	−16.5884	−	9.57733i	−1.24336	−	0.717851i
$179$			5.18994i			0.387914i	0.981010	+	0.193957i	$0.0621322\pi$
$179$			5.18994i			0.387914i	−0.981010	+	0.193957i	$0.937868\pi$
$180$		0			0
$181$	−23.2601			−1.72891			−0.864454	−	0.502713i	$-0.832335\pi$
$181$	−23.2601			−1.72891			−0.864454	+	0.502713i	$0.832335\pi$
$182$	14.4323	+	3.16753i	1.06980	+	0.234793i
$183$		0			0
$184$	−11.7727	−	3.15447i	−0.867892	−	0.232551i
$185$			0.0750429i			0.00551726i
$186$		0			0
$187$	−7.07569	+	1.89593i	−0.517426	+	0.138644i
$188$	−0.954992	+	3.56408i	−0.0696500	+	0.259937i
$189$		0			0
$190$	2.08997	+	2.08997i	0.151622	+	0.151622i
$191$	−19.0528			−1.37861			−0.689305	−	0.724471i	$-0.742084\pi$
$191$	−19.0528			−1.37861			−0.689305	+	0.724471i	$0.742084\pi$
$192$		0			0
$193$	−2.42204	−	2.42204i	−0.174342	−	0.174342i	0.614542	−	0.788884i	$-0.289341\pi$
$193$	−2.42204	−	2.42204i	−0.174342	−	0.174342i	−0.788884	+	0.614542i	$0.789341\pi$
$194$	−6.26908	+	10.8584i	−0.450094	+	0.779585i
$195$		0			0
$196$	1.62361	+	2.27420i	0.115972	+	0.162443i
$197$	−2.33053	−	8.69765i	−0.166043	−	0.619682i	−0.997905	−	0.0646986i	$-0.979391\pi$
$197$	−2.33053	−	8.69765i	−0.166043	−	0.619682i	0.831862	−	0.554983i	$-0.187275\pi$
$198$		0			0
$199$	11.1179	−	19.2568i	0.788127	−	1.36508i	−0.138986	−	0.990294i	$-0.544384\pi$
$199$	11.1179	−	19.2568i	0.788127	−	1.36508i	0.927113	−	0.374782i	$-0.122282\pi$
$200$	11.3805	+	3.04939i	0.804722	+	0.215625i
$201$		0			0
$202$	10.6801	+	2.86173i	0.751452	+	0.201351i
$203$	−8.13859	+	8.96367i	−0.571217	+	0.629126i
$204$		0			0
$205$	2.20094	−	1.27071i	0.153720	−	0.0887504i
$206$	−14.8514	+	14.8514i	−1.03475	+	1.03475i
$207$		0			0
$208$	11.7981	+	11.8562i	0.818054	+	0.822082i
$209$			7.15961i			0.495241i
$210$		0			0
$211$	1.21409	−	2.10286i	0.0835813	−	0.144767i	−0.821204	−	0.570634i	$-0.806697\pi$
$211$	1.21409	−	2.10286i	0.0835813	−	0.144767i	0.904786	+	0.425867i	$0.140031\pi$
$212$		−	5.23847i		−	0.359779i
$213$		0			0
$214$	−5.74626	−	21.4453i	−0.392807	−	1.46597i
$215$	2.06072	−	2.06072i	0.140540	−	0.140540i
$216$		0			0
$217$	5.28535	−	10.2674i	0.358793	−	0.696998i
$218$	11.4892	+	6.63329i	0.778146	+	0.449263i
$219$		0			0
$220$	0.185987	+	0.322140i	0.0125393	+	0.0217186i
$221$	−3.68935	+	13.6348i	−0.248173	+	0.917178i
$222$		0			0
$223$	−0.632245	+	0.169409i	−0.0423382	+	0.0113445i	−0.279926	−	0.960022i	$-0.590310\pi$
$223$	−0.632245	+	0.169409i	−0.0423382	+	0.0113445i	0.237588	+	0.971366i	$0.423643\pi$
$224$	0.283852	+	5.88370i	0.0189657	+	0.393122i
$225$		0			0
$226$	−4.03245	−	15.0493i	−0.268235	−	1.00106i
$227$	1.79175	−	0.480097i	0.118922	−	0.0318652i	−0.198867	−	0.980026i	$-0.563726\pi$
$227$	1.79175	−	0.480097i	0.118922	−	0.0318652i	0.317789	+	0.948161i	$0.397059\pi$
$228$		0			0
$229$	3.91765	+	14.6209i	0.258885	+	0.966174i	0.965887	+	0.258962i	$0.0833805\pi$
$229$	3.91765	+	14.6209i	0.258885	+	0.966174i	−0.707002	+	0.707211i	$0.749953\pi$
$230$	−3.28591	+	1.89712i	−0.216667	+	0.125093i
$231$		0			0
$232$	−10.9600	+	2.93673i	−0.719560	+	0.192806i
$233$	−20.8054	−	12.0120i	−1.36300	−	0.786931i	−0.372982	−	0.927839i	$-0.621665\pi$
$233$	−20.8054	−	12.0120i	−1.36300	−	0.786931i	−0.990023	+	0.140907i	$0.954998\pi$
$234$		0			0
$235$	−2.30322	−	3.98930i	−0.150246	−	0.260233i
$236$	−0.393851	+	1.46987i	−0.0256375	+	0.0956805i
$237$		0			0
$238$	−13.5008	+	8.68802i	−0.875128	+	0.563161i
$239$	−2.03275	+	2.03275i	−0.131487	+	0.131487i	−0.769788	−	0.638300i	$-0.779638\pi$
$239$	−2.03275	+	2.03275i	−0.131487	+	0.131487i	0.638300	+	0.769788i	$0.279638\pi$
$240$		0			0
$241$	−5.78978	−	21.6078i	−0.372953	−	1.39188i	−0.856313	−	0.516457i	$-0.827251\pi$
$241$	−5.78978	−	21.6078i	−0.372953	−	1.39188i	0.483361	−	0.875421i	$-0.339416\pi$
$242$	3.00818	−	11.2267i	0.193373	−	0.721679i
$243$		0			0
$244$	2.34750	−	4.06599i	0.150283	−	0.260298i
$245$	−3.44086	−	0.574318i	−0.219829	−	0.0366919i
$246$		0			0
$247$	11.9391	+	6.93218i	0.759666	+	0.441084i
$248$	9.37258	−	5.41126i	0.595160	−	0.343616i
$249$		0			0
$250$	6.51893	−	3.76371i	0.412293	−	0.238038i
$251$	−10.2228	−	17.7064i	−0.645256	−	1.11762i	−0.984242	−	0.176825i	$-0.943417\pi$
$251$	−10.2228	−	17.7064i	−0.645256	−	1.11762i	0.338986	−	0.940791i	$-0.389916\pi$
$252$		0			0
$253$	−8.87779	−	2.37880i	−0.558142	−	0.149554i
$254$	−20.4419	−	20.4419i	−1.28264	−	1.28264i
$255$		0			0
$256$	−4.61208	+	7.98836i	−0.288255	+	0.499273i
$257$	2.38426	+	4.12966i	0.148726	+	0.257601i	0.930757	−	0.365639i	$-0.119149\pi$
$257$	2.38426	+	4.12966i	0.148726	+	0.257601i	−0.782031	+	0.623240i	$0.785816\pi$
$258$		0			0
$259$	−0.182344	+	0.354225i	−0.0113303	+	0.0220105i
$260$	0.717266	+	0.00176149i	0.0444830	+	0.000109243i
$261$		0			0
$262$	2.37829	+	2.37829i	0.146931	+	0.146931i
$263$	30.2896			1.86773			0.933867	−	0.357619i	$-0.116411\pi$
$263$	30.2896			1.86773			0.933867	+	0.357619i	$0.116411\pi$
$264$		0			0
$265$	4.62436	+	4.62436i	0.284072	+	0.284072i
$266$	4.78694	+	14.9436i	0.293506	+	0.916251i
$267$		0			0
$268$	3.81443	−	1.02207i	0.233004	−	0.0624332i
$269$	−9.92350	−	5.72934i	−0.605047	−	0.349324i	0.165978	−	0.986130i	$-0.446922\pi$
$269$	−9.92350	−	5.72934i	−0.605047	−	0.349324i	−0.771024	+	0.636806i	$0.780255\pi$
$270$		0			0
$271$	−28.5679	−	7.65475i	−1.73538	−	0.464993i	−0.753967	−	0.656912i	$-0.771862\pi$
$271$	−28.5679	−	7.65475i	−1.73538	−	0.464993i	−0.981411	+	0.191919i	$0.938529\pi$
$272$	−18.1739			−1.10195
$273$		0			0
$274$	13.9257			0.841282
$275$	8.58205	+	2.29955i	0.517517	+	0.138668i
$276$		0			0
$277$	26.8500	+	15.5019i	1.61326	+	0.931416i	0.988608	+	0.150514i	$0.0480928\pi$
$277$	26.8500	+	15.5019i	1.61326	+	0.931416i	0.624653	+	0.780903i	$0.285241\pi$
$278$	−13.0904	+	3.50757i	−0.785112	+	0.210370i
$279$		0			0
$280$	−2.42048	−	2.19768i	−0.144651	−	0.131336i
$281$	−18.5399	−	18.5399i	−1.10600	−	1.10600i	−0.993671	−	0.112327i	$-0.964169\pi$
$281$	−18.5399	−	18.5399i	−1.10600	−	1.10600i	−0.112327	−	0.993671i	$-0.535831\pi$
$282$		0			0
$283$	−3.11440			−0.185132			−0.0925658	−	0.995707i	$-0.529507\pi$
$283$	−3.11440			−0.185132			−0.0925658	+	0.995707i	$0.529507\pi$
$284$	0.531904	+	0.531904i	0.0315627	+	0.0315627i
$285$		0			0
$286$	7.36585	+	7.40212i	0.435552	+	0.437696i
$287$	13.4768	−	0.650170i	0.795508	−	0.0383783i
$288$		0			0
$289$	0.826155	+	1.43094i	0.0485974	+	0.0841731i
$290$	−1.76617	+	3.05909i	−0.103713	+	0.179636i
$291$		0			0
$292$	1.91526	+	1.91526i	0.112082	+	0.112082i
$293$	10.6395	+	2.85085i	0.621567	+	0.166548i	0.555840	−	0.831289i	$-0.312397\pi$
$293$	10.6395	+	2.85085i	0.621567	+	0.166548i	0.0657272	+	0.997838i	$0.479063\pi$
$294$		0			0
$295$	−0.949878	−	1.64524i	−0.0553040	−	0.0957894i
$296$	−0.323353	+	0.186688i	−0.0187945	+	0.0108510i
$297$		0			0
$298$	20.0069	−	11.5510i	1.15897	−	0.669131i
$299$	−12.5626	+	12.5010i	−0.726512	+	0.722952i
$300$		0			0
$301$	14.7345	−	4.71996i	0.849283	−	0.272054i
$302$	−4.50833	+	7.80866i	−0.259425	+	0.449338i
$303$		0			0
$304$	−4.59736	+	17.1576i	−0.263677	+	0.984055i
$305$	1.51703	+	5.66163i	0.0868649	+	0.324184i
$306$		0			0
$307$	−2.19463	+	2.19463i	−0.125254	+	0.125254i	−0.766955	−	0.641701i	$-0.778229\pi$
$307$	−2.19463	+	2.19463i	−0.125254	+	0.125254i	0.641701	+	0.766955i	$0.278229\pi$
$308$	0.0951619	+	1.97252i	0.00542235	+	0.112395i
$309$		0			0
$310$	0.872006	−	3.25437i	0.0495266	−	0.184836i
$311$	2.52308	+	4.37011i	0.143071	+	0.247806i	0.928652	−	0.370953i	$-0.120969\pi$
$311$	2.52308	+	4.37011i	0.143071	+	0.247806i	−0.785581	+	0.618759i	$0.787636\pi$
$312$		0			0
$313$	−18.6079	−	10.7433i	−1.05178	−	0.607245i	−0.128632	−	0.991692i	$-0.541059\pi$
$313$	−18.6079	−	10.7433i	−1.05178	−	0.607245i	−0.923147	+	0.384447i	$0.874392\pi$
$314$	15.5029	−	4.15398i	0.874877	−	0.234423i
$315$		0			0
$316$	1.54014	−	0.889202i	0.0866398	−	0.0500215i
$317$	−2.37875	−	8.87762i	−0.133604	−	0.498617i	0.866396	−	0.499358i	$-0.166431\pi$
$317$	−2.37875	−	8.87762i	−0.133604	−	0.498617i	−1.00000		0.000741159i	$0.999764\pi$
$318$		0			0
$319$	−8.26497	+	2.21459i	−0.462750	+	0.123993i
$320$	−0.751903	−	2.80614i	−0.0420327	−	0.156868i
$321$		0			0
$322$	−20.1203	+	0.970677i	−1.12126	+	0.0540937i
$323$	−14.4894	+	3.88243i	−0.806214	+	0.216024i
$324$		0			0
$325$	12.1441	−	12.0846i	0.673632	−	0.670332i
$326$	7.07473	+	12.2538i	0.391833	+	0.678674i
$327$		0			0
$328$	10.9508	+	6.32244i	0.604656	+	0.349098i
$329$	−1.17846	−	24.4272i	−0.0649707	−	1.34672i
$330$		0			0
$331$	−16.9208	+	16.9208i	−0.930052	+	0.930052i	−0.997709	−	0.0676566i	$-0.978448\pi$
$331$	−16.9208	+	16.9208i	−0.930052	+	0.930052i	0.0676566	+	0.997709i	$0.478448\pi$
$332$	0.855701	+	3.19352i	0.0469627	+	0.175267i
$333$		0			0
$334$			7.00123i			0.383090i
$335$	−2.46501	+	4.26952i	−0.134678	+	0.233269i
$336$		0			0
$337$			26.6085i			1.44946i	0.689035	+	0.724728i	$0.258035\pi$
$337$			26.6085i			1.44946i	−0.689035	+	0.724728i	$0.741965\pi$
$338$	19.4753	−	5.11601i	1.05932	−	0.278274i
$339$		0			0
$340$	−0.551082	+	0.551082i	−0.0298866	+	0.0298866i
$341$	7.06789	−	4.08065i	0.382748	−	0.220979i
$342$		0			0
$343$	−14.8464	−	11.0718i	−0.801630	−	0.597820i
$344$	14.0060	+	3.75290i	0.755154	+	0.202343i
$345$		0			0
$346$	24.6411	+	6.60255i	1.32471	+	0.354955i
$347$	10.2574	−	17.7664i	0.550648	−	0.953751i	−0.447580	−	0.894244i	$-0.647714\pi$
$347$	10.2574	−	17.7664i	0.550648	−	0.953751i	0.998228	−	0.0595067i	$-0.0189528\pi$
$348$		0			0
$349$	−2.23268	−	8.33248i	−0.119513	−	0.446027i	0.880072	−	0.474840i	$-0.157494\pi$
$349$	−2.23268	−	8.33248i	−0.119513	−	0.446027i	−0.999585	+	0.0288126i	$0.990827\pi$
$350$	19.4500	−	0.938343i	1.03965	−	0.0501565i
$351$		0			0
$352$	−2.08152	+	3.60529i	−0.110945	+	0.192163i
$353$	0.967089	+	0.967089i	0.0514729	+	0.0514729i	0.732375	−	0.680902i	$-0.238412\pi$
$353$	0.967089	+	0.967089i	0.0514729	+	0.0514729i	−0.680902	+	0.732375i	$0.738412\pi$
$354$		0			0
$355$	−0.939097			−0.0498421
$356$	−3.49061	−	3.49061i	−0.185002	−	0.185002i
$357$		0			0
$358$	−2.08061	+	7.76493i	−0.109963	+	0.410389i
$359$	29.5009	−	7.90474i	1.55700	−	0.417196i	0.625286	−	0.780395i	$-0.284982\pi$
$359$	29.5009	−	7.90474i	1.55700	−	0.417196i	0.931712	+	0.363199i	$0.118315\pi$
$360$		0			0
$361$		−	4.33871i		−	0.228353i
$362$	−34.8006	−	9.32479i	−1.82908	−	0.490100i
$363$		0			0
$364$	3.38143	+	1.75117i	0.177235	+	0.0917864i
$365$	−3.38146			−0.176994
$366$		0			0
$367$			5.02135i			0.262112i	0.991375	+	0.131056i	$0.0418368\pi$
$367$			5.02135i			0.262112i	−0.991375	+	0.131056i	$0.958163\pi$
$368$	−19.7476	−	11.4013i	−1.02942	−	0.594333i
$369$		0			0
$370$	−0.0300841	+	0.112276i	−0.00156400	+	0.00583693i
$371$	10.5918	+	33.0649i	0.549900	+	1.71665i
$372$		0			0
$373$	5.86321			0.303586			0.151793	−	0.988412i	$-0.451495\pi$
$373$	5.86321			0.303586			0.151793	+	0.988412i	$0.451495\pi$
$374$	−11.3464			−0.586707
$375$		0			0
$376$	11.4597	−	19.8488i	0.590988	−	1.02362i
$377$	−4.30946	+	15.9266i	−0.221949	+	0.820260i
$378$		0			0
$379$	−4.04123	−	15.0821i	−0.207584	−	0.774714i	−0.988646	−	0.150261i	$-0.951989\pi$
$379$	−4.04123	−	15.0821i	−0.207584	−	0.774714i	0.781062	−	0.624453i	$-0.214678\pi$
$380$	0.380861	+	0.659670i	0.0195377	+	0.0338404i
$381$		0			0
$382$	−28.5058	−	7.63811i	−1.45849	−	0.390800i
$383$	−23.1330	−	23.1330i	−1.18204	−	1.18204i	−0.979215	−	0.202826i	$-0.934987\pi$
$383$	−23.1330	−	23.1330i	−1.18204	−	1.18204i	−0.202826	−	0.979215i	$-0.565013\pi$
$384$		0			0
$385$	−1.82529	−	1.65727i	−0.0930252	−	0.0844625i
$386$	−2.65276	−	4.59472i	−0.135022	−	0.233865i
$387$		0			0
$388$	−2.28487	+	2.28487i	−0.115997	+	0.115997i
$389$	6.25191	−	3.60954i	0.316984	−	0.183011i	−0.333063	−	0.942904i	$-0.608082\pi$
$389$	6.25191	−	3.60954i	0.316984	−	0.183011i	0.650048	+	0.759894i	$0.274749\pi$
$390$		0			0
$391$		−	19.2566i		−	0.973847i
$392$	−6.08532	−	16.2551i	−0.307355	−	0.821008i
$393$		0			0
$394$		−	13.9473i		−	0.702654i
$395$	−0.574631	+	2.14455i	−0.0289128	+	0.107904i
$396$		0			0
$397$	16.1760	−	16.1760i	0.811849	−	0.811849i	−0.173062	−	0.984911i	$-0.555366\pi$
$397$	16.1760	−	16.1760i	0.811849	−	0.811849i	0.984911	+	0.173062i	$0.0553661\pi$
$398$	24.3540	−	24.3540i	1.22075	−	1.22075i
$399$		0			0
$400$	19.0898	+	11.0215i	0.954489	+	0.551075i
$401$	−6.62242	+	24.7152i	−0.330708	+	1.23422i	0.577740	+	0.816221i	$0.303935\pi$
$401$	−6.62242	+	24.7152i	−0.330708	+	1.23422i	−0.908448	+	0.417998i	$0.862732\pi$
$402$		0			0
$403$	0.0386479	−	15.7371i	0.00192519	−	0.783923i
$404$	2.46778	+	1.42477i	0.122776	+	0.0708850i
$405$		0			0
$406$	−15.7700	+	10.1483i	−0.782653	+	0.503652i
$407$	−0.243841	+	0.140782i	−0.0120868	+	0.00697830i
$408$		0			0
$409$	−2.26093	+	0.605814i	−0.111796	+	0.0299556i	−0.314283	−	0.949329i	$-0.601764\pi$
$409$	−2.26093	+	0.605814i	−0.111796	+	0.0299556i	0.202487	+	0.979285i	$0.435097\pi$
$410$	3.80236	−	1.01884i	0.187785	−	0.0503169i
$411$		0			0
$412$	−4.68766	+	2.70642i	−0.230944	+	0.133336i
$413$	−0.486012	−	10.0741i	−0.0239151	−	0.495714i
$414$		0			0
$415$	−3.57453	−	2.06375i	−0.175467	−	0.101306i
$416$	3.99665	+	6.96182i	0.195952	+	0.341331i
$417$		0			0
$418$	−2.87024	+	10.7119i	−0.140388	+	0.523935i
$419$	−11.7770	−	6.79945i	−0.575344	−	0.332175i	0.183937	−	0.982938i	$-0.441116\pi$
$419$	−11.7770	−	6.79945i	−0.575344	−	0.332175i	−0.759281	+	0.650763i	$0.774449\pi$
$420$		0			0
$421$	17.9357	−	17.9357i	0.874134	−	0.874134i	−0.118786	−	0.992920i	$-0.537900\pi$
$421$	17.9357	−	17.9357i	0.874134	−	0.874134i	0.992920	+	0.118786i	$0.0379002\pi$
$422$	2.65948	−	2.65948i	0.129462	−	0.129462i
$423$		0			0
$424$	−8.42170	+	31.4302i	−0.408994	+	1.52639i
$425$			18.6151i			0.902965i
$426$		0			0
$427$	−6.59615	+	30.4108i	−0.319210	+	1.47168i
$428$		−	5.72178i		−	0.276573i
$429$		0			0
$430$	3.90928	−	2.25702i	0.188522	−	0.108843i
$431$	−6.24073	+	6.24073i	−0.300605	+	0.300605i	−0.841251	−	0.540645i	$-0.818180\pi$
$431$	−6.24073	+	6.24073i	−0.300605	+	0.300605i	0.540645	+	0.841251i	$0.318180\pi$
$432$		0			0
$433$	10.8154	+	18.7328i	0.519753	+	0.900239i	0.999736	+	0.0229615i	$0.00730952\pi$
$433$	10.8154	+	18.7328i	0.519753	+	0.900239i	−0.479983	+	0.877278i	$0.659357\pi$
$434$	12.0238	−	13.2428i	0.577162	−	0.635673i
$435$		0			0
$436$	2.41761	+	2.41761i	0.115782	+	0.115782i
$437$	−18.1797	−	4.87124i	−0.869654	−	0.233023i
$438$		0			0
$439$	16.1671	+	28.0022i	0.771612	+	1.33647i	0.936679	+	0.350188i	$0.113882\pi$
$439$	16.1671	+	28.0022i	0.771612	+	1.33647i	−0.165068	+	0.986282i	$0.552784\pi$
$440$	−0.598011	−	2.23181i	−0.0285090	−	0.106397i
$441$		0			0
$442$	−10.9859	+	18.9207i	−0.522548	+	0.899968i
$443$	−0.185670	+	0.321591i	−0.00882147	+	0.0152792i	−0.870402	−	0.492341i	$-0.836141\pi$
$443$	−0.185670	+	0.321591i	−0.00882147	+	0.0152792i	0.861581	+	0.507620i	$0.169475\pi$
$444$		0			0
$445$	6.16281			0.292145
$446$	−1.01385			−0.0480071
$447$		0			0
$448$	3.26933	−	15.0729i	0.154461	−	0.712126i
$449$	−0.0242973	+	0.0906789i	−0.00114666	+	0.00427940i	−0.966497	−	0.256679i	$-0.917372\pi$
$449$	−0.0242973	+	0.0906789i	−0.00114666	+	0.00427940i	0.965350	+	0.260958i	$0.0840384\pi$
$450$		0			0
$451$	8.25801	+	4.76777i	0.388855	+	0.224505i
$452$		−	4.01527i		−	0.188862i
$453$		0			0
$454$	2.87319			0.134846
$455$	−4.53091	+	1.43914i	−0.212412	+	0.0674681i
$456$		0			0
$457$	−25.9289	−	6.94763i	−1.21290	−	0.324997i	−0.405003	−	0.914315i	$-0.632730\pi$
$457$	−25.9289	−	6.94763i	−1.21290	−	0.324997i	−0.807901	+	0.589319i	$0.799396\pi$
$458$			23.4456i			1.09554i
$459$		0			0
$460$	−0.944520	+	0.253083i	−0.0440385	+	0.0118001i
$461$	8.04498	−	30.0243i	0.374692	−	1.39837i	−0.479102	−	0.877759i	$-0.659038\pi$
$461$	8.04498	−	30.0243i	0.374692	−	1.39837i	0.853794	−	0.520610i	$-0.174296\pi$
$462$		0			0
$463$	−9.36086	−	9.36086i	−0.435036	−	0.435036i	0.455301	−	0.890337i	$-0.349531\pi$
$463$	−9.36086	−	9.36086i	−0.435036	−	0.435036i	−0.890337	+	0.455301i	$0.849531\pi$
$464$	−21.2286			−0.985511
$465$		0			0
$466$	−26.3125	−	26.3125i	−1.21890	−	1.21890i
$467$	−4.36513	+	7.56063i	−0.201994	+	0.349864i	−0.949171	−	0.314761i	$-0.898076\pi$
$467$	−4.36513	+	7.56063i	−0.201994	+	0.349864i	0.747177	+	0.664626i	$0.231409\pi$
$468$		0			0
$469$	−22.0099	+	14.1638i	−1.01632	+	0.654024i
$470$	−1.84669	−	6.89194i	−0.0851814	−	0.317901i
$471$		0			0
$472$	4.72612	−	8.18588i	0.217537	−	0.376786i
$473$	10.5620	+	2.83007i	0.485640	+	0.130127i
$474$		0			0
$475$	17.5741	+	4.70898i	0.806357	+	0.216063i
$476$	−3.94033	+	1.26222i	−0.180605	+	0.0578538i
$477$		0			0
$478$	−3.85621	+	2.22638i	−0.176379	+	0.101832i
$479$	10.6673	−	10.6673i	0.487401	−	0.487401i	−0.420084	−	0.907485i	$-0.638000\pi$
$479$	10.6673	−	10.6673i	0.487401	−	0.487401i	0.907485	+	0.420084i	$0.138000\pi$
$480$		0			0
$481$	−0.00133335	+	0.542930i	−6.07954e−5	+	0.0247555i
$482$		−	34.6496i		−	1.57824i
$483$		0			0
$484$	1.49768	−	2.59406i	0.0680766	−	0.117912i
$485$		−	4.03402i		−	0.183175i
$486$		0			0
$487$	−1.48935	−	5.55834i	−0.0674890	−	0.251872i	0.923936	−	0.382546i	$-0.124953\pi$
$487$	−1.48935	−	5.55834i	−0.0674890	−	0.251872i	−0.991425	+	0.130674i	$0.958286\pi$
$488$	−20.6215	+	20.6215i	−0.933491	+	0.933491i
$489$		0			0
$490$	−4.91781	−	2.23868i	−0.222164	−	0.101133i
$491$	−9.09449	−	5.25071i	−0.410428	−	0.236961i	0.280545	−	0.959841i	$-0.409485\pi$
$491$	−9.09449	−	5.25071i	−0.410428	−	0.236961i	−0.690974	+	0.722880i	$0.742818\pi$
$492$		0			0
$493$	−8.96367	−	15.5255i	−0.403703	−	0.699234i
$494$	15.0836	+	15.1579i	0.678644	+	0.681985i
$495$		0			0
$496$	19.5581	−	5.24057i	0.878183	−	0.235308i
$497$	−4.43282	−	2.28188i	−0.198839	−	0.102356i
$498$		0			0
$499$	7.26921	+	27.1291i	0.325414	+	1.21446i	0.913895	+	0.405952i	$0.133060\pi$
$499$	7.26921	+	27.1291i	0.325414	+	1.21446i	−0.588480	+	0.808512i	$0.700274\pi$
$500$	1.87384	−	0.502093i	0.0838005	−	0.0224543i
$501$		0			0
$502$	−8.19647	−	30.5897i	−0.365827	−	1.36528i
$503$	6.05090	−	3.49349i	0.269796	−	0.155767i	−0.358999	−	0.933338i	$-0.616882\pi$
$503$	6.05090	−	3.49349i	0.269796	−	0.155767i	0.628795	+	0.777571i	$0.283548\pi$
$504$		0			0
$505$	−3.43622	+	0.920733i	−0.152910	+	0.0409721i
$506$	−12.3289	−	7.11808i	−0.548085	−	0.316437i
$507$		0			0
$508$	−3.72519	−	6.45222i	−0.165279	−	0.286271i
$509$	7.37216	−	27.5133i	0.326765	−	1.21950i	−0.585760	−	0.810484i	$-0.699204\pi$
$509$	7.37216	−	27.5133i	0.326765	−	1.21950i	0.912525	−	0.409020i	$-0.134129\pi$
$510$		0			0
$511$	−15.9615	−	8.21649i	−0.706097	−	0.363476i
$512$	8.96398	−	8.96398i	0.396156	−	0.396156i
$513$		0			0
$514$	1.91166	+	7.13442i	0.0843198	+	0.314686i
$515$	1.74898	−	6.52727i	0.0770691	−	0.287626i
$516$		0			0
$517$	8.64178	−	14.9680i	0.380065	−	0.658292i
$518$	−0.414821	+	0.456874i	−0.0182262	+	0.0200739i
$519$		0			0
$520$	−4.30068	−	1.16369i	−0.188597	−	0.0510313i
$521$	19.6339	−	11.3356i	0.860176	−	0.496623i	−0.00389533	−	0.999992i	$-0.501240\pi$
$521$	19.6339	−	11.3356i	0.860176	−	0.496623i	0.864071	+	0.503370i	$0.167907\pi$
$522$		0			0
$523$	6.45318	−	3.72574i	0.282178	−	0.162915i	−0.352231	−	0.935913i	$-0.614577\pi$
$523$	6.45318	−	3.72574i	0.282178	−	0.162915i	0.634409	+	0.772998i	$0.281244\pi$
$524$	0.433403	+	0.750676i	0.0189333	+	0.0327934i
$525$		0			0
$526$	45.3178	+	12.1429i	1.97595	+	0.529454i
$527$	12.0910	+	12.0910i	0.526692	+	0.526692i
$528$		0			0
$529$	0.580504	−	1.00546i	0.0252393	−	0.0437158i
$530$	5.06487	+	8.77261i	0.220004	+	0.381058i
$531$		0			0
$532$	0.194870	+	4.03928i	0.00844870	+	0.175125i
$533$	15.9462	−	9.15441i	0.690707	−	0.396522i
$534$		0			0
$535$	5.05101	+	5.05101i	0.218374	+	0.218374i
$536$	−24.5293			−1.05951
$537$		0			0
$538$	−12.5502	−	12.5502i	−0.541078	−	0.541078i
$539$	−4.58896	−	12.2580i	−0.197660	−	0.527991i
$540$		0			0
$541$	−31.2751	+	8.38015i	−1.34462	+	0.360291i	−0.858147	−	0.513403i	$-0.828384\pi$
$541$	−31.2751	+	8.38015i	−1.34462	+	0.360291i	−0.486476	+	0.873694i	$0.661718\pi$
$542$	−39.6732	−	22.9053i	−1.70411	−	0.983869i
$543$		0			0
$544$	−8.42504	−	2.25748i	−0.361221	−	0.0967888i
$545$	−4.26838			−0.182837
$546$		0			0
$547$	6.51126			0.278401			0.139201	−	0.990264i	$-0.455547\pi$
$547$	6.51126			0.278401			0.139201	+	0.990264i	$0.455547\pi$
$548$	3.46659	+	0.928871i	0.148086	+	0.0396794i
$549$		0			0
$550$	11.9182	+	6.88097i	0.508193	+	0.293405i
$551$	−16.9248	+	4.53499i	−0.721022	+	0.193197i
$552$		0			0
$553$	−7.92340	+	8.72666i	−0.336937	+	0.371095i
$554$	33.9571	+	33.9571i	1.44270	+	1.44270i
$555$		0			0
$556$	−3.49263			−0.148120
$557$	19.9940	+	19.9940i	0.847173	+	0.847173i	0.989780	−	0.142606i	$-0.0455482\pi$
$557$	19.9940	+	19.9940i	0.847173	+	0.847173i	−0.142606	+	0.989780i	$0.545548\pi$
$558$		0			0
$559$	14.9458	−	14.8726i	0.632139	−	0.629042i
$560$	−3.31001	−	5.14362i	−0.139874	−	0.217358i
$561$		0			0
$562$	−20.3060	−	35.1710i	−0.856557	−	1.48360i
$563$	−16.8095	+	29.1149i	−0.708435	+	1.22705i	0.257002	+	0.966411i	$0.417265\pi$
$563$	−16.8095	+	29.1149i	−0.708435	+	1.22705i	−0.965437	+	0.260635i	$0.916068\pi$
$564$		0			0
$565$	3.54456	+	3.54456i	0.149121	+	0.149121i
$566$	−4.65961	−	1.24854i	−0.195858	−	0.0524800i
$567$		0			0
$568$	−2.33624	−	4.04648i	−0.0980264	−	0.169787i
$569$	−0.0609060	+	0.0351641i	−0.00255331	+	0.00147416i	−0.501276	−	0.865287i	$-0.667136\pi$
$569$	−0.0609060	+	0.0351641i	−0.00255331	+	0.00147416i	0.498723	+	0.866762i	$0.333803\pi$
$570$		0			0
$571$	−13.7331	+	7.92880i	−0.574712	+	0.331810i	−0.759029	−	0.651057i	$-0.774326\pi$
$571$	−13.7331	+	7.92880i	−0.574712	+	0.331810i	0.184317	+	0.982867i	$0.440993\pi$
$572$	1.33988	+	2.33396i	0.0560233	+	0.0975878i
$573$		0			0
$574$	20.4239	+	4.42998i	0.852478	+	0.184904i
$575$	−11.6781	+	20.2270i	−0.487010	+	0.843526i
$576$		0			0
$577$	1.91254	−	7.13771i	0.0796202	−	0.297147i	−0.914621	−	0.404312i	$-0.867511\pi$
$577$	1.91254	−	7.13771i	0.0796202	−	0.297147i	0.994241	+	0.107166i	$0.0341775\pi$
$578$	0.662399	+	2.47211i	0.0275522	+	0.102826i
$579$		0			0
$580$	−0.643708	+	0.643708i	−0.0267285	+	0.0267285i
$581$	−11.8582	−	18.4272i	−0.491962	−	0.764487i
$582$		0			0
$583$	−6.35082	+	23.7016i	−0.263024	+	0.981620i
$584$	−8.41224	−	14.5704i	−0.348101	−	0.602929i
$585$		0			0
$586$	14.7755	+	8.53061i	0.610368	+	0.352396i
$587$	−29.1856	+	7.82025i	−1.20462	+	0.322776i	−0.804648	−	0.593752i	$-0.797646\pi$
$587$	−29.1856	+	7.82025i	−1.20462	+	0.322776i	−0.399970	+	0.916528i	$0.630979\pi$
$588$		0			0
$589$	14.4735	−	8.35626i	0.596368	−	0.344314i
$590$	−0.761598	−	2.84232i	−0.0313545	−	0.117017i
$591$		0			0
$592$	−0.674751	+	0.180799i	−0.0277321	+	0.00743079i
$593$	9.20475	+	34.3526i	0.377994	+	1.41069i	0.848921	+	0.528520i	$0.177253\pi$
$593$	9.20475	+	34.3526i	0.377994	+	1.41069i	−0.470927	+	0.882172i	$0.656081\pi$
$594$		0			0
$595$	2.36415	−	4.59265i	0.0969208	−	0.188280i
$596$	5.75089	−	1.54095i	0.235566	−	0.0631196i
$597$		0			0
$598$	−23.8071	+	13.6672i	−0.973543	+	0.558892i
$599$	13.8227	+	23.9416i	0.564779	+	0.978225i	0.997070	+	0.0764915i	$0.0243718\pi$
$599$	13.8227	+	23.9416i	0.564779	+	0.978225i	−0.432292	+	0.901734i	$0.642295\pi$
$600$		0			0
$601$	−6.87190	−	3.96749i	−0.280311	−	0.161837i	0.353253	−	0.935528i	$-0.385075\pi$
$601$	−6.87190	−	3.96749i	−0.280311	−	0.161837i	−0.633564	+	0.773690i	$0.718409\pi$
$602$	23.9372	−	1.15482i	0.975609	−	0.0470671i
$603$		0			0
$604$	−1.64313	+	1.64313i	−0.0668582	+	0.0668582i
$605$	0.967851	+	3.61207i	0.0393487	+	0.146852i
$606$		0			0
$607$		−	18.5507i		−	0.752950i	−0.926427	−	0.376475i	$-0.877136\pi$
$607$		−	18.5507i		−	0.752950i	0.926427	−	0.376475i	$-0.122864\pi$
$608$	−4.26248	+	7.38284i	−0.172867	+	0.299414i
$609$		0			0
$610$			9.07883i			0.367591i
$611$	−16.5928	−	28.9032i	−0.671271	−	1.16930i
$612$		0			0
$613$	0.559180	−	0.559180i	0.0225851	−	0.0225851i	−0.695724	−	0.718309i	$-0.744916\pi$
$613$	0.559180	−	0.559180i	0.0225851	−	0.0225851i	0.718309	+	0.695724i	$0.244916\pi$
$614$	−4.16332	+	2.40369i	−0.168018	+	0.0970051i
$615$		0			0
$616$	2.60019	−	11.9879i	0.104765	−	0.483006i
$617$	19.9976	+	5.35834i	0.805074	+	0.215719i	0.637810	−	0.770193i	$-0.279840\pi$
$617$	19.9976	+	5.35834i	0.805074	+	0.215719i	0.167263	+	0.985912i	$0.446507\pi$
$618$		0			0
$619$	4.26865	+	1.14378i	0.171572	+	0.0459724i	0.343582	−	0.939123i	$-0.388360\pi$
$619$	4.26865	+	1.14378i	0.171572	+	0.0459724i	−0.172011	+	0.985095i	$0.555026\pi$
$620$	0.434146	−	0.751963i	0.0174357	−	0.0301995i
$621$		0			0
$622$	2.02297	+	7.54983i	0.0811138	+	0.302721i
$623$	29.0903	+	14.9748i	1.16548	+	0.599952i
$624$		0			0
$625$	10.6682	−	18.4778i	0.426727	−	0.739113i
$626$	−23.5333	−	23.5333i	−0.940580	−	0.940580i
$627$		0			0
$628$	4.13628			0.165056
$629$	−0.417138	−	0.417138i	−0.0166324	−	0.0166324i
$630$		0			0
$631$	−0.378204	+	1.41148i	−0.0150561	+	0.0561900i	−0.973045	−	0.230615i	$-0.925926\pi$
$631$	−0.378204	+	1.41148i	−0.0150561	+	0.0561900i	0.957989	+	0.286805i	$0.0925930\pi$
$632$	−10.6702	+	2.85908i	−0.424439	+	0.113728i
$633$		0			0
$634$		−	14.2359i		−	0.565379i
$635$	8.98431	+	2.40734i	0.356531	+	0.0955323i
$636$		0			0
$637$	−24.8842	−	4.21629i	−0.985948	−	0.167055i
$638$	−13.2535			−0.524710
$639$		0			0
$640$		−	6.71892i		−	0.265589i
$641$	−31.8488	−	18.3879i	−1.25795	−	0.726280i	−0.285277	−	0.958445i	$-0.592086\pi$
$641$	−31.8488	−	18.3879i	−1.25795	−	0.726280i	−0.972676	+	0.232165i	$0.925419\pi$
$642$		0			0
$643$	−1.34555	+	5.02165i	−0.0530632	+	0.198035i	−0.987369	−	0.158438i	$-0.949354\pi$
$643$	−1.34555	+	5.02165i	−0.0530632	+	0.198035i	0.934306	+	0.356473i	$0.116021\pi$
$644$	−5.07338	−	1.10042i	−0.199919	−	0.0433628i
$645$		0			0
$646$	−23.2348			−0.914162
$647$	−32.3694			−1.27257			−0.636286	−	0.771453i	$-0.719530\pi$
$647$	−32.3694			−1.27257			−0.636286	+	0.771453i	$0.719530\pi$
$648$		0			0
$649$	3.56398	−	6.17299i	0.139898	−	0.242311i
$650$	23.0140	−	13.2119i	0.902684	−	0.518213i
$651$		0			0
$652$	0.943796	+	3.52229i	0.0369619	+	0.137944i
$653$	13.5395	+	23.4511i	0.529843	+	0.917714i	0.999394	+	0.0348091i	$0.0110823\pi$
$653$	13.5395	+	23.4511i	0.529843	+	0.917714i	−0.469551	+	0.882905i	$0.655584\pi$
$654$		0			0
$655$	−1.04527	−	0.280079i	−0.0408420	−	0.0109436i
$656$	16.7283	+	16.7283i	0.653132	+	0.653132i
$657$		0			0
$658$	8.02953	−	37.0192i	0.313024	−	1.44316i
$659$	−7.42697	−	12.8639i	−0.289314	−	0.501106i	0.684332	−	0.729170i	$-0.260094\pi$
$659$	−7.42697	−	12.8639i	−0.289314	−	0.501106i	−0.973646	+	0.228064i	$0.926760\pi$
$660$		0			0
$661$	−5.56955	+	5.56955i	−0.216630	+	0.216630i	−0.807077	−	0.590446i	$-0.798952\pi$
$661$	−5.56955	+	5.56955i	−0.216630	+	0.216630i	0.590446	+	0.807077i	$0.298952\pi$
$662$	−32.0995	+	18.5327i	−1.24758	+	0.720293i
$663$		0			0
$664$		−	20.5364i		−	0.796968i
$665$	−3.73778	−	3.39373i	−0.144945	−	0.131603i
$666$		0			0
$667$		−	22.4932i		−	0.870941i
$668$	−0.466995	+	1.74285i	−0.0180686	+	0.0674329i
$669$		0			0
$670$	−5.39965	+	5.39965i	−0.208607	+	0.208607i
$671$	−15.5507	+	15.5507i	−0.600329	+	0.600329i
$672$		0			0
$673$	−23.9408	−	13.8222i	−0.922850	−	0.532808i	−0.0383067	−	0.999266i	$-0.512196\pi$
$673$	−23.9408	−	13.8222i	−0.922850	−	0.532808i	−0.884543	+	0.466458i	$0.845530\pi$
$674$	−10.6671	+	39.8103i	−0.410883	+	1.53344i
$675$		0			0
$676$	5.18934	+	0.0254885i	0.199590	+	0.000980327i
$677$	1.80840	+	1.04408i	0.0695025	+	0.0401273i	0.534349	−	0.845264i	$-0.320557\pi$
$677$	1.80840	+	1.04408i	0.0695025	+	0.0401273i	−0.464846	+	0.885392i	$0.653890\pi$
$678$		0			0
$679$	9.80212	−	19.0418i	0.376171	−	0.730757i
$680$	4.19239	−	2.42048i	0.160771	−	0.0928210i
$681$		0			0
$682$	12.2105	−	3.27180i	0.467566	−	0.125284i
$683$	−5.91048	+	1.58371i	−0.226158	+	0.0605989i	−0.370119	−	0.928985i	$-0.620683\pi$
$683$	−5.91048	+	1.58371i	−0.226158	+	0.0605989i	0.143960	+	0.989583i	$0.454016\pi$
$684$		0			0
$685$	−3.88018	+	2.24022i	−0.148254	+	0.0855945i
$686$	−17.7739	−	22.5169i	−0.678610	−	0.859698i
$687$		0			0
$688$	23.4939	+	13.5642i	0.895697	+	0.517131i
$689$	33.3747	+	33.5391i	1.27148	+	1.27774i
$690$		0			0
$691$	−11.5152	+	42.9755i	−0.438060	+	1.63486i	0.295575	+	0.955320i	$0.404489\pi$
$691$	−11.5152	+	42.9755i	−0.438060	+	1.63486i	−0.733635	+	0.679544i	$0.762178\pi$
$692$	5.69362	+	3.28721i	0.216439	+	0.124961i
$693$		0			0
$694$	22.4691	−	22.4691i	0.852916	−	0.852916i
$695$	3.08319	−	3.08319i	0.116952	−	0.116952i
$696$		0			0
$697$	−5.17082	+	19.2978i	−0.195859	+	0.730954i
$698$		−	13.3617i		−	0.505749i
$699$		0			0
$700$	4.90438	+	1.06377i	0.185368	+	0.0402066i
$701$		−	44.7626i		−	1.69066i	−0.534245	−	0.845329i	$-0.679404\pi$
$701$		−	44.7626i		−	1.69066i	0.534245	−	0.845329i	$-0.320596\pi$
$702$		0			0
$703$	−0.499333	+	0.288290i	−0.0188327	+	0.0108731i
$704$	7.70758	−	7.70758i	0.290490	−	0.290490i
$705$		0			0
$706$	1.05921	+	1.83461i	0.0398640	+	0.0690465i
$707$	−18.4573	−	4.00341i	−0.694157	−	0.150564i
$708$		0			0
$709$	13.0926	+	13.0926i	0.491703	+	0.491703i	0.908842	−	0.417140i	$-0.136967\pi$
$709$	13.0926	+	13.0926i	0.491703	+	0.491703i	−0.417140	+	0.908842i	$0.636967\pi$
$710$	−1.40503	−	0.376477i	−0.0527299	−	0.0141289i
$711$		0			0
$712$	15.3315	+	26.5550i	0.574574	+	0.995191i
$713$	5.55277	+	20.7232i	0.207953	+	0.776090i
$714$		0			0
$715$	−3.24316	−	0.877543i	−0.121287	−	0.0328182i
$716$	−1.03587	+	1.79418i	−0.0387123	+	0.0670517i
$717$		0			0
$718$	47.3068			1.76547
$719$	37.3979			1.39471			0.697354	−	0.716727i	$-0.254361\pi$
$719$	37.3979			1.39471			0.697354	+	0.716727i	$0.254361\pi$
$720$		0			0
$721$	24.1161	−	26.5609i	0.898129	−	0.989180i
$722$	1.73936	−	6.49136i	0.0647321	−	0.241584i
$723$		0			0
$724$	−8.04110	−	4.64253i	−0.298845	−	0.172538i
$725$			21.7439i			0.807550i
$726$		0			0
$727$	−27.5337			−1.02117			−0.510584	−	0.859828i	$-0.670571\pi$
$727$	−27.5337			−1.02117			−0.510584	+	0.859828i	$0.670571\pi$
$728$	−17.4729	−	15.9431i	−0.647589	−	0.590889i
$729$		0			0
$730$	−5.05918	−	1.35560i	−0.187249	−	0.0501732i
$731$			22.9097i			0.847346i
$732$		0			0
$733$	−9.16124	+	2.45475i	−0.338378	+	0.0906681i	−0.424007	−	0.905659i	$-0.639377\pi$
$733$	−9.16124	+	2.45475i	−0.338378	+	0.0906681i	0.0856288	+	0.996327i	$0.472710\pi$
$734$	−2.01302	+	7.51270i	−0.0743020	+	0.277299i
$735$		0			0
$736$	−7.73836	−	7.73836i	−0.285240	−	0.285240i
$737$	−18.4976			−0.681369
$738$		0			0
$739$	28.8936	+	28.8936i	1.06287	+	1.06287i	0.997886	+	0.0649823i	$0.0206991\pi$
$739$	28.8936	+	28.8936i	1.06287	+	1.06287i	0.0649823	+	0.997886i	$0.479301\pi$
$740$	−0.0149780	+	0.0259426i	−0.000550602	+	0.000953670i
$741$		0			0
$742$	2.59148	+	53.7163i	0.0951362	+	1.97199i
$743$	12.0328	+	44.9072i	0.441442	+	1.64748i	0.725163	+	0.688577i	$0.241764\pi$
$743$	12.0328	+	44.9072i	0.441442	+	1.64748i	−0.283721	+	0.958907i	$0.591569\pi$
$744$		0			0
$745$	−3.71641	+	6.43701i	−0.136159	+	0.235834i
$746$	8.77226	+	2.35052i	0.321175	+	0.0860586i
$747$		0			0
$748$	−2.82451	−	0.756824i	−0.103274	−	0.0276722i
$749$	11.5690	+	36.1156i	0.422724	+	1.31964i
$750$		0			0
$751$	−5.61614	+	3.24248i	−0.204936	+	0.118320i	−0.598956	−	0.800782i	$-0.704417\pi$
$751$	−5.61614	+	3.24248i	−0.204936	+	0.118320i	0.394020	+	0.919102i	$0.371084\pi$
$752$	30.3208	−	30.3208i	1.10569	−	1.10569i
$753$		0			0
$754$	−12.8325	+	22.1009i	−0.467330	+	0.804869i
$755$		−	2.90102i		−	0.105579i
$756$		0			0
$757$	−24.5681	+	42.5532i	−0.892943	+	1.54662i	−0.0566137	+	0.998396i	$0.518030\pi$
$757$	−24.5681	+	42.5532i	−0.892943	+	1.54662i	−0.836330	+	0.548227i	$0.815303\pi$
$758$		−	24.1852i		−	0.878444i
$759$		0			0
$760$	−1.22459	−	4.57024i	−0.0444206	−	0.165780i
$761$	26.7729	−	26.7729i	0.970518	−	0.970518i	−0.0290600	−	0.999578i	$-0.509251\pi$
$761$	26.7729	−	26.7729i	0.970518	−	0.970518i	0.999578	+	0.0290600i	$0.00925140\pi$
$762$		0			0
$763$	−20.1481	−	10.3716i	−0.729408	−	0.375476i
$764$	−6.58662	−	3.80279i	−0.238296	−	0.137580i
$765$		0			0
$766$	−25.3366	−	43.8843i	−0.915450	−	1.58561i
$767$	−6.84307	−	11.9201i	−0.247089	−	0.430408i
$768$		0			0
$769$	−28.1795	+	7.55069i	−1.01618	+	0.272285i	−0.728210	−	0.685355i	$-0.759647\pi$
$769$	−28.1795	+	7.55069i	−1.01618	+	0.272285i	−0.287971	+	0.957639i	$0.592981\pi$
$770$	−2.06652	−	3.21128i	−0.0744721	−	0.115726i
$771$		0			0
$772$	−0.353889	−	1.32073i	−0.0127367	−	0.0475342i
$773$	26.2056	−	7.02178i	0.942551	−	0.252556i	0.245352	−	0.969434i	$-0.421096\pi$
$773$	26.2056	−	7.02178i	0.942551	−	0.252556i	0.697198	+	0.716878i	$0.254430\pi$
$774$		0			0
$775$	−5.36779	−	20.0329i	−0.192817	−	0.719602i
$776$	17.3822	−	10.0356i	0.623986	−	0.360258i
$777$		0			0
$778$	10.8008	−	2.89408i	0.387229	−	0.103758i
$779$	16.9106	+	9.76332i	0.605884	+	0.349807i
$780$		0			0
$781$	−1.76176	−	3.05146i	−0.0630409	−	0.109190i
$782$	7.71982	−	28.8108i	0.276060	−	1.03027i
$783$		0			0
$784$	−3.12598	−	32.3223i	−0.111642	−	1.15437i
$785$	−3.65138	+	3.65138i	−0.130323	+	0.130323i
$786$		0			0
$787$	9.68235	+	36.1350i	0.345138	+	1.28807i	0.892451	+	0.451145i	$0.148984\pi$
$787$	9.68235	+	36.1350i	0.345138	+	1.28807i	−0.547312	+	0.836929i	$0.684349\pi$
$788$	0.930311	−	3.47197i	0.0331410	−	0.123684i
$789$		0			0
$790$	−1.71947	+	2.97821i	−0.0611760	+	0.105960i
$791$	8.11860	+	25.3442i	0.288664	+	0.901135i
$792$		0			0
$793$	10.8750	+	40.9885i	0.386183	+	1.45554i
$794$	30.6865	−	17.7169i	1.08902	−	0.628749i
$795$		0			0
$796$	7.68701	−	4.43810i	0.272459	−	0.157304i
$797$	25.2215	+	43.6849i	0.893391	+	1.54740i	0.835783	+	0.549060i	$0.185014\pi$
$797$	25.2215	+	43.6849i	0.893391	+	1.54740i	0.0576081	+	0.998339i	$0.481653\pi$
$798$		0			0
$799$	34.9780	+	9.37233i	1.23743	+	0.331569i
$800$	7.48059	+	7.48059i	0.264479	+	0.264479i
$801$		0			0
$802$	−19.8163	+	34.3228i	−0.699738	+	1.21198i
$803$	−6.34369	−	10.9876i	−0.223864	−	0.387744i
$804$		0			0
$805$	5.45005	−	3.50720i	0.192089	−	0.123613i
$806$	6.36673	−	23.5297i	0.224258	−	0.828797i
$807$		0			0
$808$	−12.5158	−	12.5158i	−0.440305	−	0.440305i
$809$	29.7053			1.04438			0.522192	−	0.852828i	$-0.325114\pi$
$809$	29.7053			1.04438			0.522192	+	0.852828i	$0.325114\pi$
$810$		0			0
$811$	34.9826	+	34.9826i	1.22840	+	1.22840i	0.964567	+	0.263837i	$0.0849882\pi$
$811$	34.9826	+	34.9826i	1.22840	+	1.22840i	0.263837	+	0.964567i	$0.415012\pi$
$812$	−4.60262	+	1.47438i	−0.161520	+	0.0517405i
$813$		0			0
$814$	−0.421262	+	0.112877i	−0.0147652	+	0.00395633i
$815$	−3.94252	−	2.27622i	−0.138101	−	0.0797324i
$816$		0			0
$817$	21.6286	+	5.79536i	0.756688	+	0.202754i
$818$	−3.62556			−0.126765
$819$		0			0
$820$	1.01450			0.0354278
$821$	−23.8258	−	6.38412i	−0.831528	−	0.222807i	−0.182148	−	0.983271i	$-0.558305\pi$
$821$	−23.8258	−	6.38412i	−0.831528	−	0.222807i	−0.649380	+	0.760464i	$0.724972\pi$
$822$		0			0
$823$	18.4697	+	10.6635i	0.643813	+	0.371706i	0.786082	−	0.618122i	$-0.212106\pi$
$823$	18.4697	+	10.6635i	0.643813	+	0.371706i	−0.142269	+	0.989828i	$0.545440\pi$
$824$	32.4764	−	8.70204i	1.13137	−	0.303150i
$825$		0			0
$826$	3.31148	−	15.2672i	0.115221	−	0.531214i
$827$	32.1618	+	32.1618i	1.11837	+	1.11837i	0.991980	+	0.126394i	$0.0403404\pi$
$827$	32.1618	+	32.1618i	1.11837	+	1.11837i	0.126394	+	0.991980i	$0.459660\pi$
$828$		0			0
$829$	3.83801			0.133300			0.0666498	−	0.997776i	$-0.478769\pi$
$829$	3.83801			0.133300			0.0666498	+	0.997776i	$0.478769\pi$
$830$	−4.52069	−	4.52069i	−0.156915	−	0.156915i
$831$		0			0
$832$	−5.39011	−	20.3156i	−0.186868	−	0.704316i
$833$	22.3190	−	15.9342i	0.773309	−	0.552086i
$834$		0			0
$835$	−1.12629	−	1.95078i	−0.0389767	−	0.0675096i
$836$	−1.42900	+	2.47511i	−0.0494232	+	0.0856034i
$837$		0			0
$838$	−14.8943	−	14.8943i	−0.514516	−	0.514516i
$839$	2.40437	+	0.644249i	0.0830081	+	0.0222420i	0.300084	−	0.953913i	$-0.402985\pi$
$839$	2.40437	+	0.644249i	0.0830081	+	0.0222420i	−0.217076	+	0.976155i	$0.569652\pi$
$840$		0			0
$841$	4.02972	+	6.97968i	0.138956	+	0.240679i
$842$	34.0249	−	19.6443i	1.17257	−	0.676986i
$843$		0			0
$844$	0.839431	−	0.484646i	0.0288944	−	0.0166822i
$845$	−4.60349	+	4.55849i	−0.158365	+	0.156817i
$846$		0			0
$847$	−4.20828	+	19.4018i	−0.144598	+	0.666654i
$848$	−30.4387	+	52.7214i	−1.04527	+	1.81046i
$849$		0			0
$850$	−7.46266	+	27.8510i	−0.255967	+	0.955282i
$851$	−0.191570	−	0.714948i	−0.00656693	−	0.0245081i
$852$		0			0
$853$	32.8081	−	32.8081i	1.12333	−	1.12333i	0.132088	−	0.991238i	$-0.457832\pi$
$853$	32.8081	−	32.8081i	1.12333	−	1.12333i	0.991238	−	0.132088i	$-0.0421683\pi$
$854$	−22.0603	+	42.8548i	−0.754888	+	1.46646i
$855$		0			0
$856$	−9.19871	+	34.3300i	−0.314405	+	1.17338i
$857$	2.87093	+	4.97259i	0.0980690	+	0.169861i	0.910885	−	0.412660i	$-0.135400\pi$
$857$	2.87093	+	4.97259i	0.0980690	+	0.169861i	−0.812816	+	0.582520i	$0.802067\pi$
$858$		0			0
$859$	24.6782	+	14.2480i	0.842010	+	0.486135i	0.857947	−	0.513738i	$-0.171740\pi$
$859$	24.6782	+	14.2480i	0.842010	+	0.486135i	−0.0159371	+	0.999873i	$0.505073\pi$
$860$	1.12370	−	0.301096i	0.0383180	−	0.0102673i
$861$		0			0
$862$	−11.8389	+	6.83521i	−0.403236	+	0.232808i
$863$	12.2968	+	45.8924i	0.418589	+	1.56220i	0.777536	+	0.628839i	$0.216469\pi$
$863$	12.2968	+	45.8924i	0.418589	+	1.56220i	−0.358946	+	0.933358i	$0.616864\pi$
$864$		0			0
$865$	−7.92800	+	2.12430i	−0.269560	+	0.0722284i
$866$	8.67160	+	32.3629i	0.294673	+	1.09973i
$867$		0			0
$868$	3.87647	−	2.49458i	0.131576	−	0.0846715i
$869$	−8.04644	+	2.15604i	−0.272957	+	0.0731386i
$870$		0			0
$871$	−17.9100	+	30.8459i	−0.606858	+	1.04517i
$872$	−10.6187	−	18.3921i	−0.359593	−	0.622834i
$873$		0			0
$874$	−25.2468	−	14.5762i	−0.853985	−	0.493049i
$875$	−10.8124	+	6.95795i	−0.365524	+	0.235222i
$876$		0			0
$877$	−4.95687	+	4.95687i	−0.167381	+	0.167381i	−0.785827	−	0.618446i	$-0.787763\pi$
$877$	−4.95687	+	4.95687i	−0.167381	+	0.167381i	0.618446	+	0.785827i	$0.287763\pi$
$878$	12.9625	+	48.3767i	0.437463	+	1.63264i
$879$		0			0
$880$		−	4.32281i		−	0.145722i
$881$	7.51305	−	13.0130i	0.253121	−	0.438419i	−0.711262	−	0.702927i	$-0.751876\pi$
$881$	7.51305	−	13.0130i	0.253121	−	0.438419i	0.964383	+	0.264508i	$0.0852096\pi$
$882$		0			0
$883$			31.3175i			1.05392i	0.849890	+	0.526960i	$0.176668\pi$
$883$			31.3175i			1.05392i	−0.849890	+	0.526960i	$0.823332\pi$
$884$	−3.99683	+	3.97725i	−0.134428	+	0.133769i
$885$		0			0
$886$	−0.406714	+	0.406714i	−0.0136638	+	0.0136638i
$887$	16.9729	−	9.79931i	0.569894	−	0.329029i	−0.187213	−	0.982319i	$-0.559945\pi$
$887$	16.9729	−	9.79931i	0.569894	−	0.329029i	0.757107	+	0.653291i	$0.226612\pi$
$888$		0			0
$889$	36.5592	+	33.1940i	1.22616	+	1.11329i
$890$	9.22050	+	2.47062i	0.309072	+	0.0828155i
$891$		0			0
$892$	−0.252382	−	0.0676257i	−0.00845039	−	0.00226428i
$893$	17.6964	−	30.6511i	0.592189	−	1.02570i
$894$		0			0
$895$	−0.669413	−	2.49828i	−0.0223760	−	0.0835084i
$896$	16.3261	−	31.7154i	0.545416	−	1.05954i
$897$		0			0
$898$	−0.0727050	+	0.125929i	−0.00242620	+	0.00420230i
$899$	14.1233	+	14.1233i	0.471037	+	0.471037i
$900$		0			0
$901$	−51.4105			−1.71273
$902$	10.4439	+	10.4439i	0.347743	+	0.347743i
$903$		0			0
$904$	−6.45521	+	24.0912i	−0.214697	+	0.801260i
$905$	11.1967	−	3.00015i	0.372192	−	0.0997284i
$906$		0			0
$907$			21.2974i			0.707170i	0.935402	+	0.353585i	$0.115037\pi$
$907$			21.2974i			0.707170i	−0.935402	+	0.353585i	$0.884963\pi$
$908$	0.715238	+	0.191648i	0.0237360	+	0.00636005i
$909$		0			0
$910$	−7.35587	+	0.336770i	−0.243845	+	0.0111638i
$911$	−16.5757			−0.549178			−0.274589	−	0.961562i	$-0.588542\pi$
$911$	−16.5757			−0.549178			−0.274589	+	0.961562i	$0.588542\pi$
$912$		0			0
$913$		−	15.4866i		−	0.512531i
$914$	−36.0084	−	20.7894i	−1.19105	−	0.687653i
$915$		0			0
$916$	−1.56387	+	5.83642i	−0.0516716	+	0.192841i
$917$	−4.25343	−	3.86192i	−0.140461	−	0.127532i
$918$		0			0
$919$	53.6703			1.77042			0.885210	−	0.465192i	$-0.154015\pi$
$919$	53.6703			1.77042			0.885210	+	0.465192i	$0.154015\pi$
$920$	6.07389			0.200250
$921$		0			0
$922$	24.0730	−	41.6957i	0.792802	−	1.37317i
$923$	−6.79430	−	0.0166857i	−0.223637	−	0.000549216i
$924$		0			0
$925$	0.185188	+	0.691132i	0.00608896	+	0.0227243i
$926$	−10.2526	−	17.7580i	−0.336920	−	0.583563i
$927$		0			0
$928$	−9.84112	−	2.63692i	−0.323051	−	0.0865612i
$929$	−33.6552	−	33.6552i	−1.10419	−	1.10419i	−0.993899	−	0.110293i	$-0.964821\pi$
$929$	−33.6552	−	33.6552i	−1.10419	−	1.10419i	−0.110293	−	0.993899i	$-0.535179\pi$
$930$		0			0
$931$	−9.39716	−	25.1017i	−0.307980	−	0.822676i
$932$	−4.79500	−	8.30518i	−0.157065	−	0.272045i
$933$		0			0
$934$	−9.56190	+	9.56190i	−0.312875	+	0.312875i
$935$	3.16149	−	1.82529i	0.103392	−	0.0596933i
$936$		0			0
$937$		−	32.4762i		−	1.06095i	−0.847701	−	0.530475i	$-0.822014\pi$
$937$		−	32.4762i		−	1.06095i	0.847701	−	0.530475i	$-0.177986\pi$
$938$	−38.6084	+	12.3676i	−1.26061	+	0.403816i
$939$		0			0
$940$		−	1.83882i		−	0.0599758i
$941$	2.07793	−	7.75495i	0.0677387	−	0.252804i	−0.923750	−	0.382996i	$-0.874892\pi$
$941$	2.07793	−	7.75495i	0.0677387	−	0.252804i	0.991489	+	0.130191i	$0.0415591\pi$
$942$		0			0
$943$	−17.7249	+	17.7249i	−0.577202	+	0.577202i
$944$	12.5047	−	12.5047i	0.406993	−	0.406993i
$945$		0			0
$946$	14.6678	+	8.46844i	0.476890	+	0.275333i
$947$	0.0658379	−	0.245710i	0.00213944	−	0.00798452i	−0.964848	−	0.262809i	$-0.915351\pi$
$947$	0.0658379	−	0.245710i	0.00213944	−	0.00798452i	0.966987	+	0.254825i	$0.0820177\pi$
$948$		0			0
$949$	−24.4647	−	0.0600812i	−0.794156	−	0.00195032i
$950$	24.4058	+	14.0907i	0.791828	+	0.457162i
$951$		0			0
$952$	25.6708	−	1.23845i	0.831994	−	0.0401385i
$953$	47.1992	−	27.2505i	1.52893	−	0.882729i	0.529525	−	0.848295i	$-0.322370\pi$
$953$	47.1992	−	27.2505i	1.52893	−	0.882729i	0.999407	−	0.0344345i	$-0.0109630\pi$
$954$		0			0
$955$	9.17145	−	2.45748i	0.296781	−	0.0795222i
$956$	−1.10845	+	0.297008i	−0.0358498	+	0.00960593i
$957$		0			0
$958$	20.2363	−	11.6834i	0.653805	−	0.377475i
$959$	−23.7591	+	1.14623i	−0.767220	+	0.0370136i
$960$		0			0
$961$	10.3484	+	5.97465i	0.333819	+	0.192731i
$962$	−0.219652	+	0.811771i	−0.00708185	+	0.0261725i
$963$		0			0
$964$	2.31119	−	8.62549i	0.0744385	−	0.277808i
$965$	1.47830	+	0.853498i	0.0475882	+	0.0274751i
$966$		0			0
$967$	36.3550	−	36.3550i	1.16910	−	1.16910i	0.186676	−	0.982422i	$-0.440229\pi$
$967$	36.3550	−	36.3550i	1.16910	−	1.16910i	0.982422	−	0.186676i	$-0.0597715\pi$
$968$	−13.1563	+	13.1563i	−0.422860	+	0.422860i
$969$		0			0
$970$	1.61721	−	6.03550i	0.0519254	−	0.193788i
$971$		−	35.0003i		−	1.12321i	−0.827404	−	0.561607i	$-0.810183\pi$
$971$		−	35.0003i		−	1.12321i	0.827404	−	0.561607i	$-0.189817\pi$
$972$		0			0
$973$	22.0453	−	7.06186i	0.706740	−	0.226393i
$974$		−	8.91318i		−	0.285597i
$975$		0			0
$976$	−47.2519	+	27.2809i	−1.51249	+	0.873239i
$977$	−26.3886	+	26.3886i	−0.844248	+	0.844248i	−0.989408	−	0.145160i	$-0.953630\pi$
$977$	−26.3886	+	26.3886i	−0.844248	+	0.844248i	0.145160	+	0.989408i	$0.453630\pi$
$978$		0			0
$979$	11.5616	+	20.0252i	0.369509	+	0.640008i
$980$	−1.07489	−	0.885314i	−0.0343361	−	0.0282803i
$981$		0			0
$982$	−11.5018	−	11.5018i	−0.367036	−	0.367036i
$983$	−35.2426	−	9.44322i	−1.12406	−	0.301192i	−0.351537	−	0.936174i	$-0.614341\pi$
$983$	−35.2426	−	9.44322i	−1.12406	−	0.301192i	−0.772527	+	0.634982i	$0.781007\pi$
$984$		0			0
$985$	2.24370	+	3.88620i	0.0714901	+	0.123825i
$986$	−7.18694	−	26.8220i	−0.228879	−	0.854187i
$987$		0			0
$988$	2.74378	+	4.77943i	0.0872913	+	0.152054i
$989$	−14.3723	+	24.8935i	−0.457012	+	0.791568i
$990$		0			0
$991$	−19.6643			−0.624658			−0.312329	−	0.949974i	$-0.601109\pi$
$991$	−19.6643			−0.624658			−0.312329	+	0.949974i	$0.601109\pi$
$992$	9.71767			0.308536
$993$		0			0
$994$	−5.71739	−	5.19112i	−0.181344	−	0.164652i
$995$	−2.86804	+	10.7037i	−0.0909230	+	0.339329i
$996$		0			0
$997$	32.5153	+	18.7727i	1.02977	+	0.594538i	0.916919	−	0.399074i	$-0.130668\pi$
$997$	32.5153	+	18.7727i	1.02977	+	0.594538i	0.112852	+	0.993612i	$0.464002\pi$
$998$			43.5033i			1.37707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.gh.d.19.8		40
3.2	odd	2		273.2.cg.b.19.3	yes	40
7.3	odd	6		819.2.et.d.136.3		40
13.11	odd	12		819.2.et.d.271.3		40
21.17	even	6		273.2.bt.b.136.8	✓	40
39.11	even	12		273.2.bt.b.271.8	yes	40
91.24	even	12	inner	819.2.gh.d.388.8		40
273.206	odd	12		273.2.cg.b.115.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.8	✓	40	21.17	even	6
273.2.bt.b.271.8	yes	40	39.11	even	12
273.2.cg.b.19.3	yes	40	3.2	odd	2
273.2.cg.b.115.3	yes	40	273.206	odd	12
819.2.et.d.136.3		40	7.3	odd	6
819.2.et.d.271.3		40	13.11	odd	12
819.2.gh.d.19.8		40	1.1	even	1	trivial
819.2.gh.d.388.8		40	91.24	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.gh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.49615 + 0.400893i) q^{2} +(0.345704 + 0.199592i) q^{4} +(-0.481371 + 0.128983i) q^{5} +(-2.58563 - 0.560827i) q^{7} +(-1.75331 - 1.75331i) q^{8} +O(q^{10})\)	\(q+(1.49615 + 0.400893i) q^{2} +(0.345704 + 0.199592i) q^{4} +(-0.481371 + 0.128983i) q^{5} +(-2.58563 - 0.560827i) q^{7} +(-1.75331 - 1.75331i) q^{8} -0.771912 q^{10} +(-1.32217 - 1.32217i) q^{11} +(-3.48498 + 0.924630i) q^{13} +(-3.64366 - 1.87564i) q^{14} +(-2.31951 - 4.01751i) q^{16} +(1.95881 - 3.39275i) q^{17} +(-2.70752 - 2.70752i) q^{19} +(-0.192156 - 0.0514880i) q^{20} +(-1.44812 - 2.50822i) q^{22} +(4.25685 - 2.45769i) q^{23} +(-4.11505 + 2.37582i) q^{25} +(-5.58473 - 0.0137152i) q^{26} +(-0.781926 - 0.709952i) q^{28} +(2.28804 - 3.96301i) q^{29} +(-1.12967 + 4.21599i) q^{31} +(-0.576239 - 2.15055i) q^{32} +(4.29080 - 4.29080i) q^{34} +(1.31698 - 0.0635363i) q^{35} +(0.0389735 - 0.145451i) q^{37} +(-2.96543 - 5.13628i) q^{38} +(1.07014 + 0.617844i) q^{40} +(-4.92590 + 1.31989i) q^{41} +(-5.06441 + 2.92394i) q^{43} +(-0.193185 - 0.720977i) q^{44} +(7.35416 - 1.97054i) q^{46} +(2.39236 + 8.92840i) q^{47} +(6.37095 + 2.90018i) q^{49} +(-7.10918 + 1.90490i) q^{50} +(-1.38932 - 0.375926i) q^{52} +(-6.56146 - 11.3648i) q^{53} +(0.806994 + 0.465918i) q^{55} +(3.55010 + 5.51670i) q^{56} +(5.01200 - 5.01200i) q^{58} +(0.986638 + 3.68218i) q^{59} -11.7615i q^{61} +(-3.38032 + 5.85488i) q^{62} +5.82948i q^{64} +(1.55830 - 0.894592i) q^{65} +(6.99516 - 6.99516i) q^{67} +(1.35433 - 0.781926i) q^{68} +(1.99588 + 0.432909i) q^{70} +(1.82020 + 0.487720i) q^{71} +(6.55409 + 1.75616i) q^{73} +(0.116621 - 0.201993i) q^{74} +(-0.395600 - 1.47640i) q^{76} +(2.67714 + 4.16016i) q^{77} +(2.22755 - 3.85822i) q^{79} +(1.63474 + 1.63474i) q^{80} -7.89902 q^{82} +(5.85648 + 5.85648i) q^{83} +(-0.505305 + 1.88582i) q^{85} +(-8.74931 + 2.34437i) q^{86} +4.63635i q^{88} +(-11.9450 - 3.20066i) q^{89} +(9.52941 - 0.436280i) q^{91} +1.96215 q^{92} +14.3173i q^{94} +(1.65254 + 0.954096i) q^{95} +(-2.09507 + 7.81890i) q^{97} +(8.36924 + 6.89317i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^7	\( 40 q - 8 q^{7} - 4 q^{11} + 18 q^{14} + 32 q^{16} - 4 q^{17} + 14 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} + 24 q^{25} + 32 q^{26} + 16 q^{28} - 8 q^{29} + 14 q^{31} + 26 q^{32} - 24 q^{34} - 26 q^{35} + 36 q^{37} + 8 q^{38} - 30 q^{40} + 2 q^{41} - 66 q^{43} + 32 q^{44} - 26 q^{46} + 4 q^{47} - 14 q^{49} + 20 q^{50} + 2 q^{52} + 8 q^{53} - 42 q^{55} - 46 q^{56} + 24 q^{58} - 14 q^{59} - 24 q^{62} - 28 q^{65} - 44 q^{67} + 18 q^{68} - 4 q^{70} + 6 q^{71} + 14 q^{73} + 20 q^{74} - 64 q^{76} - 24 q^{77} - 20 q^{80} + 48 q^{82} + 12 q^{83} + 2 q^{85} + 60 q^{86} + 2 q^{89} - 14 q^{91} - 236 q^{92} - 24 q^{95} - 62 q^{97} + 88 q^{98}+O(q^{100}) \) 40 * q - 8 * q^7 - 4 * q^11 + 18 * q^14 + 32 * q^16 - 4 * q^17 + 14 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 + 24 * q^25 + 32 * q^26 + 16 * q^28 - 8 * q^29 + 14 * q^31 + 26 * q^32 - 24 * q^34 - 26 * q^35 + 36 * q^37 + 8 * q^38 - 30 * q^40 + 2 * q^41 - 66 * q^43 + 32 * q^44 - 26 * q^46 + 4 * q^47 - 14 * q^49 + 20 * q^50 + 2 * q^52 + 8 * q^53 - 42 * q^55 - 46 * q^56 + 24 * q^58 - 14 * q^59 - 24 * q^62 - 28 * q^65 - 44 * q^67 + 18 * q^68 - 4 * q^70 + 6 * q^71 + 14 * q^73 + 20 * q^74 - 64 * q^76 - 24 * q^77 - 20 * q^80 + 48 * q^82 + 12 * q^83 + 2 * q^85 + 60 * q^86 + 2 * q^89 - 14 * q^91 - 236 * q^92 - 24 * q^95 - 62 * q^97 + 88 * q^98

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