LMFDB - Embedded newform 819.2.fm.e.622.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			622.2
Character	$\chi$	$=$	819.622
Dual form			819.2.fm.e.370.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385482 + 1.43864i) q^{2} +(-0.189037 - 0.109141i) q^{4} +(1.07205 - 1.07205i) q^{5} +(1.81743 + 1.92274i) q^{7} +(-1.87643 + 1.87643i) q^{8} +O(q^{10})$	\(q+(-0.385482 + 1.43864i) q^{2} +(-0.189037 - 0.109141i) q^{4} +(1.07205 - 1.07205i) q^{5} +(1.81743 + 1.92274i) q^{7} +(-1.87643 + 1.87643i) q^{8} +(1.12904 + 1.95556i) q^{10} +(-1.68564 - 0.451666i) q^{11} +(3.51131 + 0.818944i) q^{13} +(-3.46672 + 1.87345i) q^{14} +(-2.19446 - 3.80091i) q^{16} +(-1.43508 + 2.48563i) q^{17} +(0.389597 + 1.45400i) q^{19} +(-0.319663 + 0.0856533i) q^{20} +(1.29957 - 2.25092i) q^{22} +(3.21155 - 1.85419i) q^{23} +2.70140i q^{25} +(-2.53172 + 4.73583i) q^{26} +(-0.133713 - 0.561826i) q^{28} +(1.65473 + 2.86608i) q^{29} +(1.32380 - 1.32380i) q^{31} +(1.18757 - 0.318208i) q^{32} +(-3.02273 - 3.02273i) q^{34} +(4.00967 + 0.112899i) q^{35} +(-5.83082 - 1.56236i) q^{37} -2.24196 q^{38} +4.02327i q^{40} +(3.10007 + 0.830662i) q^{41} +(3.29020 + 1.89960i) q^{43} +(0.269354 + 0.269354i) q^{44} +(1.42951 + 5.33502i) q^{46} +(5.86346 + 5.86346i) q^{47} +(-0.393883 + 6.98891i) q^{49} +(-3.88635 - 1.04134i) q^{50} +(-0.574389 - 0.538038i) q^{52} +1.37219 q^{53} +(-2.29131 + 1.32289i) q^{55} +(-7.01818 - 0.197610i) q^{56} +(-4.76112 + 1.27574i) q^{58} +(-0.967827 + 0.259328i) q^{59} +(-0.0305081 - 0.0176138i) q^{61} +(1.39417 + 2.41477i) q^{62} -6.94669i q^{64} +(4.64227 - 2.88636i) q^{65} +(-1.26183 + 4.70921i) q^{67} +(0.542567 - 0.313251i) q^{68} +(-1.70808 + 5.72495i) q^{70} +(-11.4087 + 3.05695i) q^{71} +(-11.3351 - 11.3351i) q^{73} +(4.49535 - 7.78618i) q^{74} +(0.0850419 - 0.317381i) q^{76} +(-2.19510 - 4.06193i) q^{77} -3.53025 q^{79} +(-6.42736 - 1.72221i) q^{80} +(-2.39005 + 4.13968i) q^{82} +(10.8414 - 10.8414i) q^{83} +(1.12625 + 4.20321i) q^{85} +(-4.00116 + 4.00116i) q^{86} +(4.01051 - 2.31547i) q^{88} +(-2.02252 + 7.54814i) q^{89} +(4.80695 + 8.23973i) q^{91} -0.809469 q^{92} +(-10.6957 + 6.17514i) q^{94} +(1.97643 + 1.14109i) q^{95} +(-2.46851 - 9.21262i) q^{97} +(-9.90269 - 3.26076i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.385482	+	1.43864i	−0.272577	+	1.01727i	0.684870	+	0.728665i	$0.259859\pi$
$2$	−0.385482	+	1.43864i	−0.272577	+	1.01727i	−0.957448	+	0.288607i	$0.906808\pi$
$3$		0			0
$3$		0			0
$4$	−0.189037	−	0.109141i	−0.0945186	−	0.0545703i
$5$	1.07205	−	1.07205i	0.479437	−	0.479437i	−0.425515	−	0.904952i	$-0.639907\pi$
$5$	1.07205	−	1.07205i	0.479437	−	0.479437i	0.904952	+	0.425515i	$0.139907\pi$
$6$		0			0
$7$	1.81743	+	1.92274i	0.686925	+	0.726729i
$7$	1.81743	+	1.92274i	0.686925	+	0.726729i
$8$	−1.87643	+	1.87643i	−0.663418	+	0.663418i
$9$		0			0
$10$	1.12904	+	1.95556i	0.357034	+	0.618401i
$11$	−1.68564	−	0.451666i	−0.508240	−	0.136182i	−0.00441837	−	0.999990i	$-0.501406\pi$
$11$	−1.68564	−	0.451666i	−0.508240	−	0.136182i	−0.503822	+	0.863808i	$0.668073\pi$
$12$		0			0
$13$	3.51131	+	0.818944i	0.973863	+	0.227134i
$13$	3.51131	+	0.818944i	0.973863	+	0.227134i
$14$	−3.46672	+	1.87345i	−0.926521	+	0.500700i
$15$		0			0
$16$	−2.19446	−	3.80091i	−0.548614	−	0.950228i
$17$	−1.43508	+	2.48563i	−0.348058	+	0.602854i	−0.985904	−	0.167310i	$-0.946492\pi$
$17$	−1.43508	+	2.48563i	−0.348058	+	0.602854i	0.637847	+	0.770164i	$0.279825\pi$
$18$		0			0
$19$	0.389597	+	1.45400i	0.0893798	+	0.333570i	0.996108	−	0.0881466i	$-0.0280944\pi$
$19$	0.389597	+	1.45400i	0.0893798	+	0.333570i	−0.906728	+	0.421717i	$0.861428\pi$
$20$	−0.319663	+	0.0856533i	−0.0714787	+	0.0191527i
$21$		0			0
$22$	1.29957	−	2.25092i	0.277069	−	0.479898i
$23$	3.21155	−	1.85419i	0.669654	−	0.386625i	−0.126292	−	0.991993i	$-0.540307\pi$
$23$	3.21155	−	1.85419i	0.669654	−	0.386625i	0.795946	+	0.605368i	$0.206974\pi$
$24$		0			0
$25$			2.70140i			0.540281i
$26$	−2.53172	+	4.73583i	−0.496510	+	0.928772i
$27$		0			0
$28$	−0.133713	−	0.561826i	−0.0252693	−	0.106175i
$29$	1.65473	+	2.86608i	0.307276	+	0.532217i	0.977765	−	0.209702i	$-0.0672493\pi$
$29$	1.65473	+	2.86608i	0.307276	+	0.532217i	−0.670490	+	0.741919i	$0.733916\pi$
$30$		0			0
$31$	1.32380	−	1.32380i	0.237761	−	0.237761i	−0.578161	−	0.815922i	$-0.696230\pi$
$31$	1.32380	−	1.32380i	0.237761	−	0.237761i	0.815922	+	0.578161i	$0.196230\pi$
$32$	1.18757	−	0.318208i	0.209934	−	0.0562517i
$33$		0			0
$34$	−3.02273	−	3.02273i	−0.518394	−	0.518394i
$35$	4.00967	+	0.112899i	0.677757	+	0.0190835i
$36$		0			0
$37$	−5.83082	−	1.56236i	−0.958580	−	0.256851i	−0.254581	−	0.967051i	$-0.581938\pi$
$37$	−5.83082	−	1.56236i	−0.958580	−	0.256851i	−0.703999	+	0.710201i	$0.748604\pi$
$38$	−2.24196			−0.363694
$39$		0			0
$40$			4.02327i			0.636134i
$41$	3.10007	+	0.830662i	0.484150	+	0.129728i	0.492634	−	0.870236i	$-0.336034\pi$
$41$	3.10007	+	0.830662i	0.484150	+	0.129728i	−0.00848433	+	0.999964i	$0.502701\pi$
$42$		0			0
$43$	3.29020	+	1.89960i	0.501751	+	0.289686i	0.729436	−	0.684049i	$-0.239782\pi$
$43$	3.29020	+	1.89960i	0.501751	+	0.289686i	−0.227685	+	0.973735i	$0.573116\pi$
$44$	0.269354	+	0.269354i	0.0406066	+	0.0406066i
$45$		0			0
$46$	1.42951	+	5.33502i	0.210770	+	0.786605i
$47$	5.86346	+	5.86346i	0.855273	+	0.855273i	0.990777	−	0.135504i	$-0.0432652\pi$
$47$	5.86346	+	5.86346i	0.855273	+	0.855273i	−0.135504	+	0.990777i	$0.543265\pi$
$48$		0			0
$49$	−0.393883	+	6.98891i	−0.0562690	+	0.998416i
$50$	−3.88635	−	1.04134i	−0.549612	−	0.147268i
$51$		0			0
$52$	−0.574389	−	0.538038i	−0.0796534	−	0.0746125i
$53$	1.37219			0.188484			0.0942422	−	0.995549i	$-0.469957\pi$
$53$	1.37219			0.188484			0.0942422	+	0.995549i	$0.469957\pi$
$54$		0			0
$55$	−2.29131	+	1.32289i	−0.308960	+	0.178378i
$56$	−7.01818	−	0.197610i	−0.937843	−	0.0264067i
$57$		0			0
$58$	−4.76112	+	1.27574i	−0.625166	+	0.167513i
$59$	−0.967827	+	0.259328i	−0.126000	+	0.0337617i	−0.321268	−	0.946988i	$-0.604109\pi$
$59$	−0.967827	+	0.259328i	−0.126000	+	0.0337617i	0.195268	+	0.980750i	$0.437442\pi$
$60$		0			0
$61$	−0.0305081	−	0.0176138i	−0.00390616	−	0.00225522i	0.498046	−	0.867151i	$-0.334051\pi$
$61$	−0.0305081	−	0.0176138i	−0.00390616	−	0.00225522i	−0.501952	+	0.864896i	$0.667385\pi$
$62$	1.39417	+	2.41477i	0.177059	+	0.306676i
$63$		0			0
$64$		−	6.94669i		−	0.868336i
$65$	4.64227	−	2.88636i	0.575803	−	0.358009i
$66$		0			0
$67$	−1.26183	+	4.70921i	−0.154157	+	0.575322i	0.845019	+	0.534736i	$0.179589\pi$
$67$	−1.26183	+	4.70921i	−0.154157	+	0.575322i	−0.999176	+	0.0405858i	$0.987078\pi$
$68$	0.542567	−	0.313251i	0.0657959	−	0.0379873i
$69$		0			0
$70$	−1.70808	+	5.72495i	−0.204154	+	0.684262i
$71$	−11.4087	+	3.05695i	−1.35396	+	0.362793i	−0.861595	−	0.507596i	$-0.830534\pi$
$71$	−11.4087	+	3.05695i	−1.35396	+	0.362793i	−0.492366	+	0.870388i	$0.663868\pi$
$72$		0			0
$73$	−11.3351	−	11.3351i	−1.32667	−	1.32667i	−0.908258	−	0.418410i	$-0.862587\pi$
$73$	−11.3351	−	11.3351i	−1.32667	−	1.32667i	−0.418410	−	0.908258i	$-0.637413\pi$
$74$	4.49535	−	7.78618i	0.522574	−	0.905125i
$75$		0			0
$76$	0.0850419	−	0.317381i	0.00975497	−	0.0364061i
$77$	−2.19510	−	4.06193i	−0.250155	−	0.462900i
$78$		0			0
$79$	−3.53025			−0.397184			−0.198592	−	0.980082i	$-0.563637\pi$
$79$	−3.53025			−0.397184			−0.198592	+	0.980082i	$0.563637\pi$
$80$	−6.42736	−	1.72221i	−0.718600	−	0.192548i
$81$		0			0
$82$	−2.39005	+	4.13968i	−0.263937	+	0.457151i
$83$	10.8414	−	10.8414i	1.19000	−	1.19000i	0.212936	−	0.977066i	$-0.431698\pi$
$83$	10.8414	−	10.8414i	1.19000	−	1.19000i	0.977066	−	0.212936i	$-0.0683025\pi$
$84$		0			0
$85$	1.12625	+	4.20321i	0.122159	+	0.455902i
$86$	−4.00116	+	4.00116i	−0.431456	+	0.431456i
$87$		0			0
$88$	4.01051	−	2.31547i	0.427522	−	0.246830i
$89$	−2.02252	+	7.54814i	−0.214386	+	0.800101i	0.771995	+	0.635628i	$0.219259\pi$
$89$	−2.02252	+	7.54814i	−0.214386	+	0.800101i	−0.986382	+	0.164473i	$0.947408\pi$
$90$		0			0
$91$	4.80695	+	8.23973i	0.503906	+	0.863759i
$92$	−0.809469			−0.0843930
$93$		0			0
$94$	−10.6957	+	6.17514i	−1.10317	+	0.636918i
$95$	1.97643	+	1.14109i	0.202778	+	0.117074i
$96$		0			0
$97$	−2.46851	−	9.21262i	−0.250640	−	0.935400i	−0.970465	−	0.241244i	$-0.922445\pi$
$97$	−2.46851	−	9.21262i	−0.250640	−	0.935400i	0.719825	−	0.694156i	$-0.244222\pi$
$98$	−9.90269	−	3.26076i	−1.00032	−	0.329386i
$99$		0			0
$100$	0.294833	−	0.510666i	0.0294833	−	0.0510666i
$101$	−6.74473	−	11.6822i	−0.671125	−	1.16242i	−0.977585	−	0.210540i	$-0.932478\pi$
$101$	−6.74473	−	11.6822i	−0.671125	−	1.16242i	0.306460	−	0.951883i	$-0.400855\pi$
$102$		0			0
$103$	8.93370			0.880264			0.440132	−	0.897933i	$-0.354932\pi$
$103$	8.93370			0.880264			0.440132	+	0.897933i	$0.354932\pi$
$104$	−8.12543	+	5.05205i	−0.796764	+	0.495394i
$105$		0			0
$106$	−0.528954	+	1.97408i	−0.0513766	+	0.191740i
$107$	6.52366	+	11.2993i	0.630666	+	1.09235i	0.987416	+	0.158146i	$0.0505516\pi$
$107$	6.52366	+	11.2993i	0.630666	+	1.09235i	−0.356750	+	0.934200i	$0.616115\pi$
$108$		0			0
$109$	−14.0320	−	14.0320i	−1.34402	−	1.34402i	−0.892015	−	0.452007i	$-0.850708\pi$
$109$	−14.0320	−	14.0320i	−1.34402	−	1.34402i	−0.452007	−	0.892015i	$-0.649292\pi$
$110$	−1.01990	−	3.80632i	−0.0972436	−	0.362918i
$111$		0			0
$112$	3.31990	−	11.1273i	0.313701	−	1.05143i
$113$	5.60312	−	9.70489i	0.527097	−	0.912959i	−0.472404	−	0.881382i	$-0.656614\pi$
$113$	5.60312	−	9.70489i	0.527097	−	0.912959i	0.999501	−	0.0315769i	$-0.0100529\pi$
$114$		0			0
$115$	1.45516	−	5.43074i	0.135695	−	0.506419i
$116$		−	0.722393i		−	0.0670725i
$117$		0			0
$118$		−	1.49232i		−	0.137379i
$119$	−7.38739	+	1.75817i	−0.677201	+	0.161172i
$120$		0			0
$121$	−6.88890	−	3.97731i	−0.626263	−	0.361573i
$122$	0.0371003	−	0.0371003i	0.00335890	−	0.00335890i
$123$		0			0
$124$	−0.394727	+	0.105767i	−0.0354475	+	0.00949814i
$125$	8.25632	+	8.25632i	0.738467	+	0.738467i
$126$		0			0
$127$	3.67035	−	2.11908i	0.325691	−	0.188038i	−0.328235	−	0.944596i	$-0.606454\pi$
$127$	3.67035	−	2.11908i	0.325691	−	0.188038i	0.653926	+	0.756558i	$0.273121\pi$
$128$	12.3689	+	3.31424i	1.09327	+	0.292940i
$129$		0			0
$130$	2.36293	+	7.79120i	0.207242	+	0.683333i
$131$		−	7.27464i		−	0.635589i	−0.948160	−	0.317794i	$-0.897058\pi$
$131$		−	7.27464i		−	0.635589i	0.948160	−	0.317794i	$-0.102942\pi$
$132$		0			0
$133$	−2.08760	+	3.39164i	−0.181018	+	0.294092i
$134$	−6.28845	−	3.63064i	−0.543239	−	0.313639i
$135$		0			0
$136$	−1.97129	−	7.35694i	−0.169036	−	0.630852i
$137$	5.38885	+	20.1115i	0.460400	+	1.71824i	0.671706	+	0.740818i	$0.265562\pi$
$137$	5.38885	+	20.1115i	0.460400	+	1.71824i	−0.211306	+	0.977420i	$0.567772\pi$
$138$		0			0
$139$	16.2490	+	9.38137i	1.37822	+	0.795718i	0.991946	−	0.126665i	$-0.0404272\pi$
$139$	16.2490	+	9.38137i	1.37822	+	0.795718i	0.386278	+	0.922382i	$0.373761\pi$
$140$	−0.745654	−	0.458960i	−0.0630193	−	0.0387892i
$141$		0			0
$142$		−	17.5914i		−	1.47624i
$143$	−5.54893	−	2.96639i	−0.464025	−	0.248062i
$144$		0			0
$145$	4.84654	+	1.29863i	0.402484	+	0.107845i
$146$	20.6765	−	11.9376i	1.71120	−	0.987963i
$147$		0			0
$148$	0.931724	+	0.931724i	0.0765872	+	0.0765872i
$149$	1.73434	−	0.464716i	0.142083	−	0.0380710i	−0.187077	−	0.982345i	$-0.559901\pi$
$149$	1.73434	−	0.464716i	0.142083	−	0.0380710i	0.329160	+	0.944274i	$0.393235\pi$
$150$		0			0
$151$	14.9709	−	14.9709i	1.21832	−	1.21832i	0.250095	−	0.968221i	$-0.419538\pi$
$151$	14.9709	−	14.9709i	1.21832	−	1.21832i	0.968221	−	0.250095i	$-0.0804619\pi$
$152$	−3.45938	−	1.99727i	−0.280593	−	0.162000i
$153$		0			0
$154$	6.68982	−	1.59216i	0.539081	−	0.128300i
$155$		−	2.83836i		−	0.227983i
$156$		0			0
$157$		−	19.5001i		−	1.55628i	−0.628093	−	0.778138i	$-0.716164\pi$
$157$		−	19.5001i		−	1.55628i	0.628093	−	0.778138i	$-0.283836\pi$
$158$	1.36085	−	5.07876i	0.108263	−	0.404044i
$159$		0			0
$160$	0.931999	−	1.61427i	0.0736810	−	0.127619i
$161$	9.40190	+	2.80512i	0.740973	+	0.221075i
$162$		0			0
$163$	3.90415	+	14.5705i	0.305797	+	1.14125i	0.932257	+	0.361796i	$0.117836\pi$
$163$	3.90415	+	14.5705i	0.305797	+	1.14125i	−0.626460	+	0.779453i	$0.715497\pi$
$164$	−0.495370	−	0.495370i	−0.0386819	−	0.0386819i
$165$		0			0
$166$	11.4177	+	19.7761i	0.886188	+	1.53492i
$167$	2.08221	−	7.77093i	0.161127	−	0.601333i	−0.837376	−	0.546627i	$-0.815911\pi$
$167$	2.08221	−	7.77093i	0.161127	−	0.601333i	0.998503	−	0.0547052i	$-0.0174219\pi$
$168$		0			0
$169$	11.6587	+	5.75114i	0.896820	+	0.442396i
$170$	−6.48105			−0.497074
$171$		0			0
$172$	−0.414647	−	0.718190i	−0.0316166	−	0.0547615i
$173$	10.9025	−	18.8837i	0.828903	−	1.43570i	−0.0699960	−	0.997547i	$-0.522299\pi$
$173$	10.9025	−	18.8837i	0.828903	−	1.43570i	0.898899	−	0.438155i	$-0.144368\pi$
$174$		0			0
$175$	−5.19410	+	4.90962i	−0.392637	+	0.371132i
$176$	1.98232	+	7.39814i	0.149423	+	0.557656i
$177$		0			0
$178$	−10.0794	−	5.81935i	−0.755484	−	0.436179i
$179$	−8.41680	+	4.85944i	−0.629101	+	0.363212i	−0.780404	−	0.625276i	$-0.784986\pi$
$179$	−8.41680	+	4.85944i	−0.629101	+	0.363212i	0.151303	+	0.988487i	$0.451653\pi$
$180$		0			0
$181$	13.6038			1.01116			0.505580	−	0.862779i	$-0.331278\pi$
$181$	13.6038			1.01116			0.505580	+	0.862779i	$0.331278\pi$
$182$	−13.7070	+	3.73921i	−1.01603	+	0.277168i
$183$		0			0
$184$	−2.54699	+	9.50550i	−0.187767	+	0.700755i
$185$	−7.92588	+	4.57601i	−0.582722	+	0.336435i
$186$		0			0
$187$	3.54170	−	3.54170i	0.258995	−	0.258995i
$188$	−0.468470	−	1.74835i	−0.0341667	−	0.127512i
$189$		0			0
$190$	−2.40350	+	2.40350i	−0.174368	+	0.174368i
$191$	−0.423116	+	0.732859i	−0.0306156	+	0.0530278i	−0.880927	−	0.473252i	$-0.843080\pi$
$191$	−0.423116	+	0.732859i	−0.0306156	+	0.0530278i	0.850312	+	0.526280i	$0.176413\pi$
$192$		0			0
$193$	−1.53179	−	0.410441i	−0.110260	−	0.0295442i	0.203267	−	0.979123i	$-0.434844\pi$
$193$	−1.53179	−	0.410441i	−0.110260	−	0.0295442i	−0.313527	+	0.949579i	$0.601511\pi$
$194$	14.2052			1.01987
$195$		0			0
$196$	0.837233	−	1.27818i	0.0598024	−	0.0912982i
$197$	1.35016	−	5.03888i	0.0961951	−	0.359005i	−0.901003	−	0.433813i	$-0.857168\pi$
$197$	1.35016	−	5.03888i	0.0961951	−	0.359005i	0.997198	+	0.0748081i	$0.0238344\pi$
$198$		0			0
$199$	−0.678170	+	1.17462i	−0.0480742	+	0.0832670i	−0.889061	−	0.457788i	$-0.848642\pi$
$199$	−0.678170	+	1.17462i	−0.0480742	+	0.0832670i	0.840987	+	0.541055i	$0.181975\pi$
$200$	−5.06899	−	5.06899i	−0.358432	−	0.358432i
$201$		0			0
$202$	19.4065	−	5.19995i	1.36543	−	0.365867i
$203$	−2.50337	+	8.39052i	−0.175702	+	0.588899i
$204$		0			0
$205$	4.21396	−	2.43293i	0.294316	−	0.169923i
$206$	−3.44379	+	12.8524i	−0.239940	+	0.895468i
$207$		0			0
$208$	−4.59270	−	15.1433i	−0.318446	−	1.05000i
$209$		−	2.62689i		−	0.181706i
$210$		0			0
$211$	12.4140	+	21.5017i	0.854616	+	1.48024i	0.877001	+	0.480488i	$0.159541\pi$
$211$	12.4140	+	21.5017i	0.854616	+	1.48024i	−0.0223853	+	0.999749i	$0.507126\pi$
$212$	−0.259394	−	0.149761i	−0.0178153	−	0.0102857i
$213$		0			0
$214$	−18.7704	+	5.02951i	−1.28312	+	0.343810i
$215$	5.56375	−	1.49080i	0.379444	−	0.101672i
$216$		0			0
$217$	4.95123	+	0.139411i	0.336112	+	0.00946384i
$218$	25.5961	−	14.7779i	1.73358	−	1.00089i
$219$		0			0
$220$	0.577523			0.0389366
$221$	−7.07461	+	7.55258i	−0.475890	+	0.508042i
$222$		0			0
$223$	−13.6453	−	3.65626i	−0.913760	−	0.244841i	−0.228844	−	0.973463i	$-0.573494\pi$
$223$	−13.6453	−	3.65626i	−0.913760	−	0.244841i	−0.684916	+	0.728622i	$0.740161\pi$
$224$	2.77015	+	1.70507i	0.185089	+	0.113924i
$225$		0			0
$226$	11.8019	+	11.8019i	0.785053	+	0.785053i
$227$	−5.76681	−	21.5220i	−0.382757	−	1.42847i	−0.841673	−	0.539988i	$-0.818429\pi$
$227$	−5.76681	−	21.5220i	−0.382757	−	1.42847i	0.458916	−	0.888480i	$-0.348238\pi$
$228$		0			0
$229$	8.69387	+	8.69387i	0.574507	+	0.574507i	0.933385	−	0.358877i	$-0.116840\pi$
$229$	8.69387	+	8.69387i	0.574507	+	0.574507i	−0.358877	+	0.933385i	$0.616840\pi$
$230$	7.25194	+	4.18691i	0.478179	+	0.276077i
$231$		0			0
$232$	−8.48298	−	2.27301i	−0.556935	−	0.149230i
$233$		−	26.8466i		−	1.75878i	−0.476104	−	0.879389i	$-0.657952\pi$
$233$		−	26.8466i		−	1.75878i	0.476104	−	0.879389i	$-0.342048\pi$
$234$		0			0
$235$	12.5719			0.820099
$236$	0.211259	+	0.0566065i	0.0137518	+	0.00368477i
$237$		0			0
$238$	0.318328	−	11.3055i	0.0206341	−	0.732829i
$239$	−6.42765	−	6.42765i	−0.415770	−	0.415770i	0.467973	−	0.883743i	$-0.344984\pi$
$239$	−6.42765	−	6.42765i	−0.415770	−	0.415770i	−0.883743	+	0.467973i	$0.844984\pi$
$240$		0			0
$241$	−21.5089	+	5.76329i	−1.38551	+	0.371246i	−0.873120	−	0.487506i	$-0.837907\pi$
$241$	−21.5089	+	5.76329i	−1.38551	+	0.371246i	−0.512391	+	0.858752i	$0.671240\pi$
$242$	8.37746	−	8.37746i	0.538523	−	0.538523i
$243$		0			0
$244$	0.00384478	+	0.00665935i	0.000246137	+	0.000426321i
$245$	7.07022	+	7.91475i	0.451700	+	0.505655i
$246$		0			0
$247$	0.177256	+	5.42450i	0.0112785	+	0.345153i
$248$			4.96803i			0.315470i
$249$		0			0
$250$	−15.0605	+	8.69520i	−0.952511	+	0.549933i
$251$	15.2735	−	26.4545i	0.964055	−	1.66979i	0.251921	−	0.967748i	$-0.418938\pi$
$251$	15.2735	−	26.4545i	0.964055	−	1.66979i	0.712134	−	0.702044i	$-0.247729\pi$
$252$		0			0
$253$	−6.25099	+	1.67495i	−0.392996	+	0.105303i
$254$	1.63374	+	6.09718i	0.102510	+	0.382571i
$255$		0			0
$256$	−2.58931	+	4.48482i	−0.161832	+	0.280301i
$257$	6.53903	+	11.3259i	0.407894	+	0.706493i	0.994654	−	0.103268i	$-0.0329300\pi$
$257$	6.53903	+	11.3259i	0.407894	+	0.706493i	−0.586760	+	0.809761i	$0.699597\pi$
$258$		0			0
$259$	−7.59309	−	14.0506i	−0.471812	−	0.873065i
$260$	−1.19258	+	0.0389699i	−0.0739608	+	0.00241681i
$261$		0			0
$262$	10.4656	+	2.80425i	0.646566	+	0.173247i
$263$	4.59748	+	7.96308i	0.283493	+	0.491024i	0.972243	−	0.233975i	$-0.0751734\pi$
$263$	4.59748	+	7.96308i	0.283493	+	0.491024i	−0.688750	+	0.724999i	$0.741840\pi$
$264$		0			0
$265$	1.47106	−	1.47106i	0.0903664	−	0.0903664i
$266$	−4.07461	−	4.31072i	−0.249831	−	0.264307i
$267$		0			0
$268$	0.752500	−	0.752500i	0.0459662	−	0.0459662i
$269$	−10.0654	−	5.81128i	−0.613700	−	0.354320i	0.160712	−	0.987001i	$-0.448621\pi$
$269$	−10.0654	−	5.81128i	−0.613700	−	0.354320i	−0.774412	+	0.632681i	$0.781954\pi$
$270$		0			0
$271$	5.43020	−	20.2658i	0.329861	−	1.23106i	−0.579473	−	0.814991i	$-0.696742\pi$
$271$	5.43020	−	20.2658i	0.329861	−	1.23106i	0.909334	−	0.416067i	$-0.136592\pi$
$272$	12.5969			0.763798
$273$		0			0
$274$	−31.0104			−1.87341
$275$	1.22013	−	4.55360i	0.0735768	−	0.274592i
$276$		0			0
$277$	−13.6743	−	7.89485i	−0.821608	−	0.474356i	0.0293625	−	0.999569i	$-0.490652\pi$
$277$	−13.6743	−	7.89485i	−0.821608	−	0.474356i	−0.850971	+	0.525213i	$0.823986\pi$
$278$	−19.7601	+	19.7601i	−1.18513	+	1.18513i
$279$		0			0
$280$	−7.73571	+	7.31201i	−0.462297	+	0.436976i
$281$	6.16446	−	6.16446i	0.367741	−	0.367741i	−0.498912	−	0.866653i	$-0.666267\pi$
$281$	6.16446	−	6.16446i	0.367741	−	0.367741i	0.866653	+	0.498912i	$0.166267\pi$
$282$		0			0
$283$	−2.66486	−	4.61567i	−0.158410	−	0.274373i	0.775886	−	0.630873i	$-0.217303\pi$
$283$	−2.66486	−	4.61567i	−0.158410	−	0.274373i	−0.934295	+	0.356500i	$0.883970\pi$
$284$	2.49030	+	0.667274i	0.147772	+	0.0395954i
$285$		0			0
$286$	6.40658	−	6.83942i	0.378829	−	0.404423i
$287$	4.03702	+	7.47032i	0.238298	+	0.440959i
$288$		0			0
$289$	4.38109	+	7.58828i	0.257711	+	0.446369i
$290$	−3.73652	+	6.47183i	−0.219416	+	0.380039i
$291$		0			0
$292$	0.905632	+	3.37986i	0.0529981	+	0.197792i
$293$	−20.8745	+	5.59331i	−1.21950	+	0.326764i	−0.810483	−	0.585762i	$-0.800795\pi$
$293$	−20.8745	+	5.59331i	−1.21950	+	0.326764i	−0.409018	+	0.912526i	$0.634129\pi$
$294$		0			0
$295$	−0.759548	+	1.31558i	−0.0442226	+	0.0765958i
$296$	13.8728	−	8.00945i	0.806339	−	0.465540i
$297$		0			0
$298$			2.67424i			0.154914i
$299$	12.7952	−	3.88056i	0.739967	−	0.224418i
$300$		0			0
$301$	2.32728	+	9.77861i	0.134142	+	0.563630i
$302$	15.7667	+	27.3088i	0.907274	+	1.57144i
$303$		0			0
$304$	4.67156	−	4.67156i	0.267933	−	0.267933i
$305$	−0.0515893	+	0.0138233i	−0.00295399	+	0.000791520i
$306$		0			0
$307$	−3.48509	−	3.48509i	−0.198904	−	0.198904i	0.600626	−	0.799530i	$-0.294918\pi$
$307$	−3.48509	−	3.48509i	−0.198904	−	0.198904i	−0.799530	+	0.600626i	$0.794918\pi$
$308$	−0.0283660	+	1.00743i	−0.00161630	+	0.0574037i
$309$		0			0
$310$	4.08338	+	1.09414i	0.231920	+	0.0621429i
$311$	16.5536			0.938671			0.469335	−	0.883020i	$-0.344494\pi$
$311$	16.5536			0.938671			0.469335	+	0.883020i	$0.344494\pi$
$312$		0			0
$313$		−	21.0200i		−	1.18812i	−0.804421	−	0.594060i	$-0.797524\pi$
$313$		−	21.0200i		−	1.18812i	0.804421	−	0.594060i	$-0.202476\pi$
$314$	28.0536	+	7.51694i	1.58316	+	0.424205i
$315$		0			0
$316$	0.667349	+	0.385294i	0.0375413	+	0.0216745i
$317$	−10.3124	−	10.3124i	−0.579204	−	0.579204i	0.355480	−	0.934684i	$-0.384317\pi$
$317$	−10.3124	−	10.3124i	−0.579204	−	0.579204i	−0.934684	+	0.355480i	$0.884317\pi$
$318$		0			0
$319$	−1.49477	−	5.57856i	−0.0836911	−	0.312339i
$320$	−7.44722	−	7.44722i	−0.416312	−	0.416312i
$321$		0			0
$322$	−7.65982	+	12.4446i	−0.426865	+	0.693511i
$323$	−4.17320	−	1.11821i	−0.232203	−	0.0622187i
$324$		0			0
$325$	−2.21230	+	9.48548i	−0.122716	+	0.526160i
$326$	−22.4667			−1.24431
$327$		0			0
$328$	−7.37575	+	4.25839i	−0.407258	+	0.235130i
$329$	−0.617489	+	21.9304i	−0.0340433	+	1.20906i
$330$		0			0
$331$	22.7352	−	6.09189i	1.24964	−	0.334840i	0.427444	−	0.904042i	$-0.359414\pi$
$331$	22.7352	−	6.09189i	1.24964	−	0.334840i	0.822198	+	0.569202i	$0.192748\pi$
$332$	−3.23268	+	0.866193i	−0.177416	+	0.0475385i
$333$		0			0
$334$	10.3769	+	5.99111i	0.567799	+	0.327819i
$335$	3.69578	+	6.40128i	0.201922	+	0.349739i
$336$		0			0
$337$		−	14.6004i		−	0.795337i	−0.917529	−	0.397668i	$-0.869819\pi$
$337$		−	14.6004i		−	0.795337i	0.917529	−	0.397668i	$-0.130181\pi$
$338$	−12.7680	+	14.5556i	−0.694489	+	0.791723i
$339$		0			0
$340$	0.245839	−	0.917483i	0.0133325	−	0.0497575i
$341$	−2.82936	+	1.63353i	−0.153219	+	0.0884607i
$342$		0			0
$343$	−14.1537	+	11.9445i	−0.764230	+	0.644944i
$344$	−9.73830	+	2.60937i	−0.525054	+	0.140688i
$345$		0			0
$346$	22.9641	+	22.9641i	1.23456	+	1.23456i
$347$	8.48574	−	14.6977i	0.455538	−	0.789016i	−0.543181	−	0.839616i	$-0.682780\pi$
$347$	8.48574	−	14.6977i	0.455538	−	0.789016i	0.998719	+	0.0506002i	$0.0161134\pi$
$348$		0			0
$349$	−0.728645	+	2.71934i	−0.0390035	+	0.145563i	−0.982682	−	0.185302i	$-0.940674\pi$
$349$	−0.728645	+	2.71934i	−0.0390035	+	0.145563i	0.943678	+	0.330865i	$0.107340\pi$
$350$	−5.06093	−	9.36502i	−0.270518	−	0.500581i
$351$		0			0
$352$	−2.14553			−0.114357
$353$	−30.6157	−	8.20345i	−1.62951	−	0.436625i	−0.675733	−	0.737146i	$-0.736173\pi$
$353$	−30.6157	−	8.20345i	−1.62951	−	0.436625i	−0.953775	+	0.300521i	$0.902839\pi$
$354$		0			0
$355$	−8.95350	+	15.5079i	−0.475203	+	0.823075i
$356$	1.20614	−	1.20614i	0.0639253	−	0.0639253i
$357$		0			0
$358$	−3.74646	−	13.9820i	−0.198006	−	0.738970i
$359$	−12.8172	+	12.8172i	−0.676466	+	0.676466i	−0.959199	−	0.282733i	$-0.908759\pi$
$359$	−12.8172	+	12.8172i	−0.676466	+	0.676466i	0.282733	+	0.959199i	$0.408759\pi$
$360$		0			0
$361$	14.4922	−	8.36705i	0.762745	−	0.440371i
$362$	−5.24402	+	19.5709i	−0.275619	+	1.02863i
$363$		0			0
$364$	−0.00940337	−	2.08225i	−0.000492870	−	0.109140i
$365$	−24.3036			−1.27211
$366$		0			0
$367$	−3.51454	+	2.02912i	−0.183457	+	0.105919i	−0.588916	−	0.808194i	$-0.700445\pi$
$367$	−3.51454	+	2.02912i	−0.183457	+	0.105919i	0.405459	+	0.914113i	$0.367112\pi$
$368$	−14.0952	−	8.13787i	−0.734764	−	0.424216i
$369$		0			0
$370$	−3.52794	−	13.1665i	−0.183409	−	0.684492i
$371$	2.49386	+	2.63836i	0.129475	+	0.136977i
$372$		0			0
$373$	5.07453	−	8.78935i	0.262749	−	0.455095i	−0.704222	−	0.709980i	$-0.748704\pi$
$373$	5.07453	−	8.78935i	0.262749	−	0.455095i	0.966972	+	0.254884i	$0.0820374\pi$
$374$	3.72997	+	6.46050i	0.192872	+	0.334065i
$375$		0			0
$376$	−22.0047			−1.13481
$377$	3.46312	+	11.4188i	0.178360	+	0.588099i
$378$		0			0
$379$	1.04136	−	3.88639i	0.0534908	−	0.199630i	−0.934009	−	0.357249i	$-0.883715\pi$
$379$	1.04136	−	3.88639i	0.0534908	−	0.199630i	0.987500	+	0.157618i	$0.0503815\pi$
$380$	−0.249080	−	0.431418i	−0.0127775	−	0.0221313i
$381$		0			0
$382$	−0.891216	−	0.891216i	−0.0455986	−	0.0455986i
$383$	−0.289889	−	1.08188i	−0.0148126	−	0.0552815i	0.958124	−	0.286354i	$-0.0924433\pi$
$383$	−0.289889	−	1.08188i	−0.0148126	−	0.0552815i	−0.972937	+	0.231072i	$0.925777\pi$
$384$		0			0
$385$	−6.70787	−	2.00134i	−0.341865	−	0.101998i
$386$	1.18095	−	2.04547i	0.0601090	−	0.104112i
$387$		0			0
$388$	−0.538830	+	2.01094i	−0.0273550	+	0.102090i
$389$		−	2.46580i		−	0.125021i	−0.998044	−	0.0625106i	$-0.980089\pi$
$389$		−	2.46580i		−	0.125021i	0.998044	−	0.0625106i	$-0.0199107\pi$
$390$		0			0
$391$			10.6436i			0.538271i
$392$	−12.3751	−	13.8533i	−0.625037	−	0.699697i
$393$		0			0
$394$	6.72867	+	3.88480i	0.338985	+	0.195713i
$395$	−3.78462	+	3.78462i	−0.190425	+	0.190425i
$396$		0			0
$397$	−13.8529	+	3.71187i	−0.695257	+	0.186294i	−0.589105	−	0.808056i	$-0.700520\pi$
$397$	−13.8529	+	3.71187i	−0.695257	+	0.186294i	−0.106152	+	0.994350i	$0.533853\pi$
$398$	−1.42844	−	1.42844i	−0.0716012	−	0.0716012i
$399$		0			0
$400$	10.2678	−	5.92812i	0.513390	−	0.296406i
$401$	−9.59670	−	2.57143i	−0.479236	−	0.128411i	0.0111107	−	0.999938i	$-0.496463\pi$
$401$	−9.59670	−	2.57143i	−0.479236	−	0.128411i	−0.490347	+	0.871527i	$0.663130\pi$
$402$		0			0
$403$	5.73238	−	3.56415i	0.285550	−	0.177543i
$404$			2.94450i			0.146494i
$405$		0			0
$406$	−11.1059	−	6.83584i	−0.551178	−	0.339257i
$407$	9.12300	+	5.26716i	0.452210	+	0.261084i
$408$		0			0
$409$	9.20429	+	34.3509i	0.455123	+	1.69854i	0.687726	+	0.725970i	$0.258609\pi$
$409$	9.20429	+	34.3509i	0.455123	+	1.69854i	−0.232603	+	0.972572i	$0.574724\pi$
$410$	1.87570	+	7.00022i	0.0926344	+	0.345716i
$411$		0			0
$412$	−1.68880	−	0.975031i	−0.0832013	−	0.0480363i
$413$	−2.25758	−	1.38957i	−0.111088	−	0.0683763i
$414$		0			0
$415$		−	23.2452i		−	1.14106i
$416$	4.43051	−	0.144776i	0.217224	−	0.00709821i
$417$		0			0
$418$	3.77914	+	1.01262i	0.184844	+	0.0495288i
$419$	−22.2160	+	12.8264i	−1.08532	+	0.626611i	−0.932327	−	0.361616i	$-0.882225\pi$
$419$	−22.2160	+	12.8264i	−1.08532	+	0.626611i	−0.152995	+	0.988227i	$0.548892\pi$
$420$		0			0
$421$	−9.66177	−	9.66177i	−0.470886	−	0.470886i	0.431315	−	0.902201i	$-0.358050\pi$
$421$	−9.66177	−	9.66177i	−0.470886	−	0.470886i	−0.902201	+	0.431315i	$0.858050\pi$
$422$	−35.7186	+	9.57077i	−1.73875	+	0.465898i
$423$		0			0
$424$	−2.57481	+	2.57481i	−0.125044	+	0.125044i
$425$	−6.71469	−	3.87673i	−0.325710	−	0.188049i
$426$		0			0
$427$	−0.0215794	−	0.0906712i	−0.00104430	−	0.00438789i
$428$		−	2.84799i		−	0.137663i
$429$		0			0
$430$			8.57890i			0.413712i
$431$	1.68005	−	6.27002i	0.0809250	−	0.302016i	−0.913586	−	0.406645i	$-0.866699\pi$
$431$	1.68005	−	6.27002i	0.0809250	−	0.302016i	0.994511	+	0.104629i	$0.0333654\pi$
$432$		0			0
$433$	−16.7283	+	28.9743i	−0.803912	+	1.39242i	0.113111	+	0.993582i	$0.463918\pi$
$433$	−16.7283	+	28.9743i	−0.803912	+	1.39242i	−0.917023	+	0.398834i	$0.869415\pi$
$434$	−2.10918	+	7.06930i	−0.101244	+	0.339337i
$435$		0			0
$436$	1.12111	+	4.18403i	0.0536913	+	0.200379i
$437$	3.94720	+	3.94720i	0.188820	+	0.188820i
$438$		0			0
$439$	−9.81984	−	17.0085i	−0.468675	−	0.811769i	0.530684	−	0.847570i	$-0.321935\pi$
$439$	−9.81984	−	17.0085i	−0.468675	−	0.811769i	−0.999359	+	0.0358007i	$0.988602\pi$
$440$	1.81717	−	6.78178i	0.0866303	−	0.323309i
$441$		0			0
$442$	−8.13831	−	13.0892i	−0.387100	−	0.622590i
$443$	−16.3344			−0.776072			−0.388036	−	0.921644i	$-0.626846\pi$
$443$	−16.3344			−0.776072			−0.388036	+	0.921644i	$0.626846\pi$
$444$		0			0
$445$	5.92376	+	10.2603i	0.280813	+	0.486383i
$446$	10.5201	−	18.2213i	0.498140	−	0.862804i
$447$		0			0
$448$	13.3567	−	12.6251i	0.631045	−	0.596481i
$449$	5.76005	+	21.4968i	0.271834	+	1.01450i	0.957934	+	0.286990i	$0.0926546\pi$
$449$	5.76005	+	21.4968i	0.271834	+	1.01450i	−0.686100	+	0.727507i	$0.740679\pi$
$450$		0			0
$451$	−4.85043	−	2.80040i	−0.228398	−	0.131865i
$452$	−2.11840	+	1.22306i	−0.0996410	+	0.0575277i
$453$		0			0
$454$	33.1855			1.55747
$455$	13.9867	+	3.68012i	0.655709	+	0.172527i
$456$		0			0
$457$	−2.56831	+	9.58507i	−0.120141	+	0.448371i	−0.999620	−	0.0275663i	$-0.991224\pi$
$457$	−2.56831	+	9.58507i	−0.120141	+	0.448371i	0.879479	+	0.475937i	$0.157891\pi$
$458$	−15.8587	+	9.15602i	−0.741028	+	0.427833i
$459$		0			0
$460$	−0.867794	+	0.867794i	−0.0404611	+	0.0404611i
$461$	9.43198	+	35.2006i	0.439291	+	1.63946i	0.730584	+	0.682823i	$0.239248\pi$
$461$	9.43198	+	35.2006i	0.439291	+	1.63946i	−0.291293	+	0.956634i	$0.594085\pi$
$462$		0			0
$463$	−5.57925	+	5.57925i	−0.259290	+	0.259290i	−0.824765	−	0.565476i	$-0.808693\pi$
$463$	−5.57925	+	5.57925i	−0.259290	+	0.259290i	0.565476	+	0.824765i	$0.308693\pi$
$464$	7.26247	−	12.5790i	0.337152	−	0.583964i
$465$		0			0
$466$	38.6226	+	10.3489i	1.78916	+	0.479403i
$467$	23.2676			1.07670			0.538349	−	0.842722i	$-0.319048\pi$
$467$	23.2676			1.07670			0.538349	+	0.842722i	$0.319048\pi$
$468$		0			0
$469$	−11.3479	+	6.13250i	−0.523997	+	0.283173i
$470$	−4.84624	+	18.0864i	−0.223540	+	0.834264i
$471$		0			0
$472$	1.32945	−	2.30267i	0.0611928	−	0.105989i
$473$	−4.68812	−	4.68812i	−0.215560	−	0.215560i
$474$		0			0
$475$	−3.92783	+	1.05246i	−0.180221	+	0.0482902i
$476$	1.58838	+	0.473904i	0.0728033	+	0.0217214i
$477$		0			0
$478$	11.7248	−	6.76932i	0.536280	−	0.309622i
$479$	−9.64340	+	35.9897i	−0.440618	+	1.64441i	0.286634	+	0.958040i	$0.407464\pi$
$479$	−9.64340	+	35.9897i	−0.440618	+	1.64441i	−0.727252	+	0.686370i	$0.759203\pi$
$480$		0			0
$481$	−19.1943	−	10.2611i	−0.875187	−	0.467864i
$482$		−	33.1652i		−	1.51063i
$483$		0			0
$484$	0.868172	+	1.50372i	0.0394624	+	0.0683508i
$485$	−12.5228	−	7.23004i	−0.568631	−	0.328299i
$486$		0			0
$487$	−40.0906	+	10.7422i	−1.81668	+	0.486777i	−0.996369	−	0.0851447i	$-0.972865\pi$
$487$	−40.0906	+	10.7422i	−1.81668	+	0.486777i	−0.820308	+	0.571922i	$0.806198\pi$
$488$	0.0902975	−	0.0241951i	0.00408757	−	0.00109526i
$489$		0			0
$490$	−14.1119	+	7.12050i	−0.637511	+	0.321672i
$491$	−7.22040	+	4.16870i	−0.325852	+	0.188131i	−0.653998	−	0.756496i	$-0.726910\pi$
$491$	−7.22040	+	4.16870i	−0.325852	+	0.188131i	0.328146	+	0.944627i	$0.393576\pi$
$492$		0			0
$493$	−9.49867			−0.427799
$494$	−7.87223	−	1.83604i	−0.354189	−	0.0826074i
$495$		0			0
$496$	−7.93666	−	2.12662i	−0.356366	−	0.0954881i
$497$	−26.6122	−	16.3802i	−1.19372	−	0.734751i
$498$		0			0
$499$	−6.61818	−	6.61818i	−0.296270	−	0.296270i	0.543281	−	0.839551i	$-0.317182\pi$
$499$	−6.61818	−	6.61818i	−0.296270	−	0.296270i	−0.839551	+	0.543281i	$0.817182\pi$
$500$	−0.659651	−	2.46185i	−0.0295005	−	0.110097i
$501$		0			0
$502$	32.1708	+	32.1708i	1.43585	+	1.43585i
$503$	6.07077	+	3.50496i	0.270682	+	0.156278i	0.629198	−	0.777245i	$-0.283384\pi$
$503$	6.07077	+	3.50496i	0.270682	+	0.156278i	−0.358515	+	0.933524i	$0.616717\pi$
$504$		0			0
$505$	−19.7547	−	5.29324i	−0.879071	−	0.235546i
$506$		−	9.63859i		−	0.428487i
$507$		0			0
$508$	−0.925111			−0.0410452
$509$	−6.23491	−	1.67064i	−0.276357	−	0.0740498i	0.117978	−	0.993016i	$-0.462359\pi$
$509$	−6.23491	−	1.67064i	−0.276357	−	0.0740498i	−0.394336	+	0.918966i	$0.629025\pi$
$510$		0			0
$511$	1.19371	−	42.3951i	0.0528067	−	1.87545i
$512$	12.6554	+	12.6554i	0.559297	+	0.559297i
$513$		0			0
$514$	−18.8146	+	5.04136i	−0.829878	+	0.222365i
$515$	9.57741	−	9.57741i	0.422031	−	0.422031i
$516$		0			0
$517$	−7.23536	−	12.5320i	−0.318211	−	0.551157i
$518$	23.1408	−	5.50744i	1.01675	−	0.241983i
$519$		0			0
$520$	−3.29483	+	14.1270i	−0.144488	+	0.619508i
$521$			13.2340i			0.579793i	0.957058	+	0.289896i	$0.0936208\pi$
$521$			13.2340i			0.579793i	−0.957058	+	0.289896i	$0.906379\pi$
$522$		0			0
$523$	35.3268	−	20.3959i	1.54473	−	0.891852i	0.546203	−	0.837653i	$-0.316073\pi$
$523$	35.3268	−	20.3959i	1.54473	−	0.891852i	0.998530	−	0.0541990i	$-0.0172605\pi$
$524$	−0.793960	+	1.37518i	−0.0346843	+	0.0600749i
$525$		0			0
$526$	−13.2282	+	3.54450i	−0.576779	+	0.154547i
$527$	1.39072	+	5.19023i	0.0605806	+	0.226090i
$528$		0			0
$529$	−4.62397	+	8.00896i	−0.201042	+	0.348216i
$530$	1.54926	+	2.68339i	0.0672954	+	0.116559i
$531$		0			0
$532$	0.764799	−	0.413304i	0.0331583	−	0.0179190i
$533$	10.2051	+	5.45550i	0.442030	+	0.236304i
$534$		0			0
$535$	19.1072	+	5.11975i	0.826075	+	0.221346i
$536$	−6.46878	−	11.2042i	−0.279409	−	0.483950i
$537$		0			0
$538$	12.2404	−	12.2404i	0.527721	−	0.527721i
$539$	3.82060	−	11.6029i	0.164565	−	0.499772i
$540$		0			0
$541$	−14.4412	+	14.4412i	−0.620878	+	0.620878i	−0.945756	−	0.324878i	$-0.894677\pi$
$541$	−14.4412	+	14.4412i	−0.620878	+	0.620878i	0.324878	+	0.945756i	$0.394677\pi$
$542$	27.0619	+	15.6242i	1.16241	+	0.671117i
$543$		0			0
$544$	−0.913306	+	3.40851i	−0.0391577	+	0.146138i
$545$	−30.0861			−1.28875
$546$		0			0
$547$	3.47188			0.148447			0.0742234	−	0.997242i	$-0.476352\pi$
$547$	3.47188			0.148447			0.0742234	+	0.997242i	$0.476352\pi$
$548$	1.17629	−	4.38996i	0.0502484	−	0.187530i
$549$		0			0
$550$	6.08065	+	3.51066i	0.259280	+	0.149695i
$551$	−3.52259	+	3.52259i	−0.150067	+	0.150067i
$552$		0			0
$553$	−6.41599	−	6.78777i	−0.272836	−	0.288645i
$554$	16.6290	−	16.6290i	0.706500	−	0.706500i
$555$		0			0
$556$	−2.04778	−	3.54686i	−0.0868452	−	0.150420i
$557$	42.2673	+	11.3255i	1.79092	+	0.479876i	0.992503	−	0.122224i	$-0.0390027\pi$
$557$	42.2673	+	11.3255i	1.79092	+	0.479876i	0.798420	+	0.602100i	$0.205669\pi$
$558$		0			0
$559$	9.99727	+	9.36459i	0.422840	+	0.396080i
$560$	−8.36993	−	15.4881i	−0.353694	−	0.654494i
$561$		0			0
$562$	6.49215	+	11.2447i	0.273855	+	0.474330i
$563$	−2.66750	+	4.62024i	−0.112422	+	0.194720i	−0.916746	−	0.399470i	$-0.869194\pi$
$563$	−2.66750	+	4.62024i	−0.112422	+	0.194720i	0.804325	+	0.594190i	$0.202527\pi$
$564$		0			0
$565$	−4.39731	−	16.4110i	−0.184996	−	0.690416i
$566$	7.66755	−	2.05451i	0.322291	−	0.0863577i
$567$		0			0
$568$	15.6714	−	27.1437i	0.657559	−	1.13893i
$569$	−15.8463	+	9.14887i	−0.664312	+	0.383541i	−0.793918	−	0.608025i	$-0.791962\pi$
$569$	−15.8463	+	9.14887i	−0.664312	+	0.383541i	0.129606	+	0.991566i	$0.458629\pi$
$570$		0			0
$571$			33.5009i			1.40197i	0.713176	+	0.700985i	$0.247256\pi$
$571$			33.5009i			1.40197i	−0.713176	+	0.700985i	$0.752744\pi$
$572$	0.725200	+	1.16637i	0.0303221	+	0.0487684i
$573$		0			0
$574$	−12.3033	+	2.92814i	−0.513530	+	0.122218i
$575$	5.00891	+	8.67568i	0.208886	+	0.361801i
$576$		0			0
$577$	8.55149	−	8.55149i	0.356003	−	0.356003i	−0.506334	−	0.862337i	$-0.669000\pi$
$577$	8.55149	−	8.55149i	0.356003	−	0.356003i	0.862337	+	0.506334i	$0.169000\pi$
$578$	−12.6056	+	3.37767i	−0.524325	+	0.140493i
$579$		0			0
$580$	−0.774444	−	0.774444i	−0.0321570	−	0.0321570i
$581$	40.5489	+	1.14173i	1.68225	+	0.0473668i
$582$		0			0
$583$	−2.31302	−	0.619771i	−0.0957953	−	0.0256683i
$584$	42.5389			1.76027
$585$		0			0
$586$		−	32.1870i		−	1.32963i
$587$	42.3546	+	11.3489i	1.74816	+	0.468419i	0.984232	−	0.176881i	$-0.0566009\pi$
$587$	42.3546	+	11.3489i	1.74816	+	0.468419i	0.763929	+	0.645300i	$0.223268\pi$
$588$		0			0
$589$	2.44055	+	1.40905i	0.100561	+	0.0580589i
$590$	−1.59985	−	1.59985i	−0.0658647	−	0.0658647i
$591$		0			0
$592$	6.85708	+	25.5910i	0.281824	+	1.05178i
$593$	−29.3548	−	29.3548i	−1.20546	−	1.20546i	−0.972483	−	0.232973i	$-0.925155\pi$
$593$	−29.3548	−	29.3548i	−1.20546	−	1.20546i	−0.232973	−	0.972483i	$-0.574845\pi$
$594$		0			0
$595$	−6.03482	+	9.80453i	−0.247403	+	0.401947i
$596$	−0.378575	−	0.101439i	−0.0155070	−	0.00415510i
$597$		0			0
$598$	0.650389	+	19.9036i	0.0265964	+	0.813919i
$599$	17.3994			0.710920			0.355460	−	0.934691i	$-0.384324\pi$
$599$	17.3994			0.710920			0.355460	+	0.934691i	$0.384324\pi$
$600$		0			0
$601$	3.87707	−	2.23843i	0.158149	−	0.0913074i	−0.418837	−	0.908062i	$-0.637562\pi$
$601$	3.87707	−	2.23843i	0.158149	−	0.0913074i	0.576986	+	0.816754i	$0.304229\pi$
$602$	−14.9650	−	0.421368i	−0.609929	−	0.0171737i
$603$		0			0
$604$	−4.46400	+	1.19612i	−0.181638	+	0.0486696i
$605$	−11.6491	+	3.12138i	−0.473605	+	0.126902i
$606$		0			0
$607$	12.0061	+	6.93170i	0.487311	+	0.281349i	0.723458	−	0.690368i	$-0.242551\pi$
$607$	12.0061	+	6.93170i	0.487311	+	0.281349i	−0.236147	+	0.971717i	$0.575885\pi$
$608$	0.925346	+	1.60275i	0.0375277	+	0.0649999i
$609$		0			0
$610$		−	0.0795470i		−	0.00322077i
$611$	15.7866	+	25.3903i	0.638657	+	1.02718i
$612$		0			0
$613$	3.20626	−	11.9659i	0.129500	−	0.483299i	−0.870461	−	0.492238i	$-0.836179\pi$
$613$	3.20626	−	11.9659i	0.129500	−	0.483299i	0.999960	+	0.00893943i	$0.00284555\pi$
$614$	6.35722	−	3.67034i	0.256557	−	0.148123i
$615$		0			0
$616$	11.7409	+	3.50297i	0.473053	+	0.141139i
$617$	−4.24013	+	1.13614i	−0.170701	+	0.0457392i	−0.343157	−	0.939278i	$-0.611496\pi$
$617$	−4.24013	+	1.13614i	−0.170701	+	0.0457392i	0.172456	+	0.985017i	$0.444830\pi$
$618$		0			0
$619$	−3.42700	−	3.42700i	−0.137743	−	0.137743i	0.634873	−	0.772616i	$-0.281052\pi$
$619$	−3.42700	−	3.42700i	−0.137743	−	0.137743i	−0.772616	+	0.634873i	$0.781052\pi$
$620$	−0.309781	+	0.536556i	−0.0124411	+	0.0215486i
$621$		0			0
$622$	−6.38114	+	23.8147i	−0.255860	+	0.954883i
$623$	−18.1889	+	9.82944i	−0.728724	+	0.393808i
$624$		0			0
$625$	4.19541			0.167816
$626$	30.2402	+	8.10283i	1.20864	+	0.323854i
$627$		0			0
$628$	−2.12825	+	3.68624i	−0.0849265	+	0.147097i
$629$	12.2511	−	12.2511i	0.488485	−	0.488485i
$630$		0			0
$631$	7.50951	+	28.0259i	0.298949	+	1.11569i	0.938030	+	0.346554i	$0.112648\pi$
$631$	7.50951	+	28.0259i	0.298949	+	1.11569i	−0.639081	+	0.769139i	$0.720685\pi$
$632$	6.62427	−	6.62427i	0.263499	−	0.263499i
$633$		0			0
$634$	18.8111	−	10.8606i	0.747086	−	0.431330i
$635$	1.66305	−	6.20658i	0.0659961	−	0.246301i
$636$		0			0
$637$	−7.10658	+	24.2177i	−0.281573	+	0.959540i
$638$	8.60175			0.340546
$639$		0			0
$640$	16.8132	−	9.70709i	0.664599	−	0.383707i
$641$	−30.8187	−	17.7932i	−1.21726	−	0.702788i	−0.252932	−	0.967484i	$-0.581395\pi$
$641$	−30.8187	−	17.7932i	−1.21726	−	0.702788i	−0.964332	+	0.264696i	$0.914728\pi$
$642$		0			0
$643$	−1.54772	−	5.77618i	−0.0610362	−	0.227790i	0.928669	−	0.370909i	$-0.120954\pi$
$643$	−1.54772	−	5.77618i	−0.0610362	−	0.227790i	−0.989706	+	0.143118i	$0.954287\pi$
$644$	−1.47116	−	1.55640i	−0.0579716	−	0.0613308i
$645$		0			0
$646$	3.21739	−	5.57269i	0.126587	−	0.219255i
$647$	−8.50730	−	14.7351i	−0.334456	−	0.579296i	0.648924	−	0.760853i	$-0.275219\pi$
$647$	−8.50730	−	14.7351i	−0.334456	−	0.579296i	−0.983380	+	0.181558i	$0.941886\pi$
$648$		0			0
$649$	1.74854			0.0686361
$650$	−12.7934	−	6.83919i	−0.501798	−	0.268255i
$651$		0			0
$652$	0.852204	−	3.18047i	0.0333749	−	0.124557i
$653$	−4.76337	−	8.25040i	−0.186405	−	0.322863i	0.757644	−	0.652668i	$-0.226350\pi$
$653$	−4.76337	−	8.25040i	−0.186405	−	0.322863i	−0.944049	+	0.329805i	$0.893017\pi$
$654$		0			0
$655$	−7.79881	−	7.79881i	−0.304725	−	0.304725i
$656$	−3.64571	−	13.6060i	−0.142341	−	0.531223i
$657$		0			0
$658$	−31.3119	−	9.34211i	−1.22066	−	0.364193i
$659$	14.3837	−	24.9132i	0.560308	−	0.970482i	−0.437161	−	0.899383i	$-0.644016\pi$
$659$	14.3837	−	24.9132i	0.560308	−	0.970482i	0.997469	−	0.0710991i	$-0.0226507\pi$
$660$		0			0
$661$	−5.58403	+	20.8399i	−0.217193	+	0.810577i	0.768189	+	0.640223i	$0.221158\pi$
$661$	−5.58403	+	20.8399i	−0.217193	+	0.810577i	−0.985383	+	0.170354i	$0.945509\pi$
$662$			35.0561i			1.36250i
$663$		0			0
$664$			40.6864i			1.57894i
$665$	1.39800	+	5.87403i	0.0542121	+	0.227785i
$666$		0			0
$667$	10.6285	+	6.13636i	0.411537	+	0.237601i
$668$	−1.24174	+	1.24174i	−0.0480444	+	0.0480444i
$669$		0			0
$670$	−10.6338	+	2.84932i	−0.410819	+	0.110079i
$671$	0.0434701	+	0.0434701i	0.00167814	+	0.00167814i
$672$		0			0
$673$	24.5175	−	14.1552i	0.945082	−	0.545643i	0.0535322	−	0.998566i	$-0.482952\pi$
$673$	24.5175	−	14.1552i	0.945082	−	0.545643i	0.891550	+	0.452923i	$0.149619\pi$
$674$	21.0048	+	5.62821i	0.809074	+	0.216791i
$675$		0			0
$676$	−1.57624	−	2.35961i	−0.0606245	−	0.0907544i
$677$			19.7036i			0.757270i	0.925546	+	0.378635i	$0.123606\pi$
$677$			19.7036i			0.757270i	−0.925546	+	0.378635i	$0.876394\pi$
$678$		0			0
$679$	13.2271	−	21.4896i	0.507611	−	0.824696i
$680$	−10.0004	−	5.77371i	−0.383496	−	0.221412i
$681$		0			0
$682$	−1.25940	−	4.70013i	−0.0482248	−	0.179977i
$683$	−6.28752	−	23.4653i	−0.240585	−	0.897876i	−0.975551	−	0.219772i	$-0.929469\pi$
$683$	−6.28752	−	23.4653i	−0.240585	−	0.897876i	0.734966	−	0.678104i	$-0.237198\pi$
$684$		0			0
$685$	27.3377	+	15.7834i	1.04452	+	0.603053i
$686$	−11.7279	−	24.9665i	−0.447772	−	0.953227i
$687$		0			0
$688$		−	16.6744i		−	0.635704i
$689$	4.81818	+	1.12374i	0.183558	+	0.0428113i
$690$		0			0
$691$	−20.9371	−	5.61007i	−0.796483	−	0.213417i	−0.162444	−	0.986718i	$-0.551938\pi$
$691$	−20.9371	−	5.61007i	−0.796483	−	0.213417i	−0.634039	+	0.773301i	$0.718604\pi$
$692$	−4.12196	+	2.37982i	−0.156694	+	0.0904671i
$693$		0			0
$694$	17.8736	+	17.8736i	0.678474	+	0.678474i
$695$	27.4771	−	7.36248i	1.04227	−	0.279275i
$696$		0			0
$697$	−6.51357	+	6.51357i	−0.246719	+	0.246719i
$698$	−3.63127	−	2.09652i	−0.137446	−	0.0793543i
$699$		0			0
$700$	1.51772	−	0.361212i	0.0573643	−	0.0136525i
$701$		−	33.2903i		−	1.25736i	−0.777665	−	0.628678i	$-0.783596\pi$
$701$		−	33.2903i		−	1.25736i	0.777665	−	0.628678i	$-0.216404\pi$
$702$		0			0
$703$		−	9.08668i		−	0.342711i
$704$	−3.13758	+	11.7096i	−0.118252	+	0.441323i
$705$		0			0
$706$	23.6036	−	40.8827i	0.888334	−	1.53864i
$707$	10.2038	−	34.2000i	0.383754	−	1.28622i
$708$		0			0
$709$	0.389951	+	1.45532i	0.0146449	+	0.0546556i	0.972862	−	0.231388i	$-0.0743266\pi$
$709$	0.389951	+	1.45532i	0.0146449	+	0.0546556i	−0.958217	+	0.286043i	$0.907660\pi$
$710$	−18.8589	−	18.8589i	−0.707762	−	0.707762i
$711$		0			0
$712$	−10.3684	−	17.9587i	−0.388574	−	0.673030i
$713$	1.79687	−	6.70601i	0.0672933	−	0.251142i
$714$		0			0
$715$	−9.12887	+	2.76862i	−0.341400	+	0.103540i
$716$	2.12145			0.0792823
$717$		0			0
$718$	−13.4985	−	23.3801i	−0.503761	−	0.872539i
$719$	16.0502	−	27.7997i	0.598570	−	1.03675i	−0.394463	−	0.918912i	$-0.629069\pi$
$719$	16.0502	−	27.7997i	0.598570	−	1.03675i	0.993032	−	0.117841i	$-0.0375974\pi$
$720$		0			0
$721$	16.2364	+	17.1772i	0.604675	+	0.639713i
$722$	6.45070	+	24.0744i	0.240070	+	0.895955i
$723$		0			0
$724$	−2.57162	−	1.48473i	−0.0955735	−	0.0551794i
$725$	−7.74243	+	4.47009i	−0.287546	+	0.166015i
$726$		0			0
$727$	33.7702			1.25247			0.626233	−	0.779636i	$-0.284596\pi$
$727$	33.7702			1.25247			0.626233	+	0.779636i	$0.284596\pi$
$728$	−24.4812	−	6.44137i	−0.907334	−	0.238733i
$729$		0			0
$730$	9.36860	−	34.9641i	0.346748	−	1.29408i
$731$	−9.44341	+	5.45215i	−0.349277	+	0.201655i
$732$		0			0
$733$	5.09323	−	5.09323i	0.188123	−	0.188123i	−0.606761	−	0.794884i	$-0.707532\pi$
$733$	5.09323	−	5.09323i	0.188123	−	0.188123i	0.794884	+	0.606761i	$0.207532\pi$
$734$	−1.56438	−	5.83834i	−0.0577423	−	0.215497i
$735$		0			0
$736$	3.22391	−	3.22391i	0.118835	−	0.118835i
$737$	4.25399	−	7.36812i	0.156698	−	0.271408i
$738$		0			0
$739$	22.0821	+	5.91687i	0.812302	+	0.217656i	0.640978	−	0.767559i	$-0.278529\pi$
$739$	22.0821	+	5.91687i	0.812302	+	0.217656i	0.171324	+	0.985215i	$0.445196\pi$
$740$	1.99772			0.0734375
$741$		0			0
$742$	−4.75699	+	2.57072i	−0.174635	+	0.0943741i
$743$	2.69085	−	10.0424i	0.0987179	−	0.368420i	−0.898839	−	0.438279i	$-0.855588\pi$
$743$	2.69085	−	10.0424i	0.0987179	−	0.368420i	0.997557	+	0.0698588i	$0.0222549\pi$
$744$		0			0
$745$	1.36111	−	2.35751i	0.0498672	−	0.0863725i
$746$	10.6886	+	10.6886i	0.391336	+	0.391336i
$747$		0			0
$748$	−1.05606	+	0.282970i	−0.0386133	+	0.0103464i
$749$	−9.86937	+	33.0791i	−0.360619	+	1.20868i
$750$		0			0
$751$	−35.7335	+	20.6307i	−1.30393	+	0.752827i	−0.981076	−	0.193621i	$-0.937977\pi$
$751$	−35.7335	+	20.6307i	−1.30393	+	0.752827i	−0.322858	+	0.946448i	$0.604643\pi$
$752$	9.41938	−	35.1536i	0.343489	−	1.28192i
$753$		0			0
$754$	−17.7625	+	0.580426i	−0.646874	+	0.0211379i
$755$		−	32.0993i		−	1.16821i
$756$		0			0
$757$	9.58077	+	16.5944i	0.348219	+	0.603133i	0.985933	−	0.167140i	$-0.0534532\pi$
$757$	9.58077	+	16.5944i	0.348219	+	0.603133i	−0.637714	+	0.770273i	$0.720120\pi$
$758$	5.18969	+	2.99627i	0.188498	+	0.108829i
$759$		0			0
$760$	−5.84982	+	1.56745i	−0.212195	+	0.0568576i
$761$	−16.3307	+	4.37578i	−0.591986	+	0.158622i	−0.542361	−	0.840146i	$-0.682469\pi$
$761$	−16.3307	+	4.37578i	−0.591986	+	0.158622i	−0.0496251	+	0.998768i	$0.515803\pi$
$762$		0			0
$763$	1.47773	−	52.4821i	0.0534974	−	1.89998i
$764$	0.159969	−	0.0923584i	0.00578749	−	0.00334141i
$765$		0			0
$766$	1.66818			0.0602739
$767$	−3.61072	+	0.117987i	−0.130376	+	0.00426027i
$768$		0			0
$769$	−47.1631	−	12.6373i	−1.70074	−	0.455713i	−0.727617	−	0.685984i	$-0.759372\pi$
$769$	−47.1631	−	12.6373i	−1.70074	−	0.455713i	−0.973127	+	0.230271i	$0.926039\pi$
$770$	5.46497	−	8.87872i	0.196944	−	0.319967i
$771$		0			0
$772$	0.244769	+	0.244769i	0.00880943	+	0.00880943i
$773$	−2.27204	−	8.47936i	−0.0817195	−	0.304981i	0.912953	−	0.408064i	$-0.133796\pi$
$773$	−2.27204	−	8.47936i	−0.0817195	−	0.304981i	−0.994673	+	0.103083i	$0.967129\pi$
$774$		0			0
$775$	3.57611	+	3.57611i	0.128458	+	0.128458i
$776$	21.9188	+	12.6548i	0.786840	+	0.454282i
$777$		0			0
$778$	3.54740	+	0.950523i	0.127180	+	0.0340779i
$779$			4.83112i			0.173093i
$780$		0			0
$781$	20.6117			0.737543
$782$	−15.3123	−	4.10293i	−0.547568	−	0.146721i
$783$		0			0
$784$	27.4286	−	13.8398i	0.979593	−	0.494277i
$785$	−20.9051	−	20.9051i	−0.746136	−	0.746136i
$786$		0			0
$787$	21.5745	−	5.78087i	0.769047	−	0.206066i	0.147097	−	0.989122i	$-0.453007\pi$
$787$	21.5745	−	5.78087i	0.769047	−	0.206066i	0.621951	+	0.783056i	$0.286340\pi$
$788$	−0.805178	+	0.805178i	−0.0286833	+	0.0286833i
$789$		0			0
$790$	−3.98580	−	6.90360i	−0.141808	−	0.245619i
$791$	28.8433	−	6.86461i	1.02555	−	0.244077i
$792$		0			0
$793$	−0.0926987	−	0.0868322i	−0.00329183	−	0.00308350i
$794$		−	21.3602i		−	0.758045i
$795$		0			0
$796$	0.256399	−	0.148032i	0.00908781	−	0.00524685i
$797$	−14.1995	+	24.5943i	−0.502973	+	0.871175i	0.497021	+	0.867739i	$0.334427\pi$
$797$	−14.1995	+	24.5943i	−0.502973	+	0.871175i	−0.999994	+	0.00343670i	$0.998906\pi$
$798$		0			0
$799$	−22.9889	+	6.15986i	−0.813290	+	0.217920i
$800$	0.859607	+	3.20810i	0.0303917	+	0.113423i
$801$		0			0
$802$	7.39872	−	12.8150i	0.261258	−	0.452512i
$803$	13.9872	+	24.2265i	0.493597	+	0.854935i
$804$		0			0
$805$	13.0866	−	7.07209i	0.461241	−	0.249259i
$806$	2.91780	+	9.62076i	0.102775	+	0.338877i
$807$		0			0
$808$	34.5769	+	9.26484i	1.21641	+	0.325936i
$809$	16.2864	+	28.2088i	0.572598	+	0.991770i	0.996298	+	0.0859669i	$0.0273979\pi$
$809$	16.2864	+	28.2088i	0.572598	+	0.991770i	−0.423700	+	0.905803i	$0.639269\pi$
$810$		0			0
$811$	−23.2549	+	23.2549i	−0.816589	+	0.816589i	−0.985612	−	0.169023i	$-0.945939\pi$
$811$	−23.2549	+	23.2549i	−0.816589	+	0.816589i	0.169023	+	0.985612i	$0.445939\pi$
$812$	1.38898	−	1.31290i	0.0487435	−	0.0460738i
$813$		0			0
$814$	−11.0943	+	11.0943i	−0.388855	+	0.388855i
$815$	19.8058	+	11.4349i	0.693767	+	0.400547i
$816$		0			0
$817$	−1.48016	+	5.52403i	−0.0517842	+	0.193261i
$818$	−52.9666			−1.85194
$819$		0			0
$820$	−1.06213			−0.0370911
$821$	−4.01809	+	14.9957i	−0.140232	+	0.523354i	0.859689	+	0.510817i	$0.170657\pi$
$821$	−4.01809	+	14.9957i	−0.140232	+	0.523354i	−0.999921	+	0.0125363i	$0.996009\pi$
$822$		0			0
$823$	−7.93891	−	4.58353i	−0.276733	−	0.159772i	0.355210	−	0.934786i	$-0.384409\pi$
$823$	−7.93891	−	4.58353i	−0.276733	−	0.159772i	−0.631944	+	0.775014i	$0.717743\pi$
$824$	−16.7635	+	16.7635i	−0.583983	+	0.583983i
$825$		0			0
$826$	2.86935	−	2.71219i	0.0998374	−	0.0943692i
$827$	−23.9115	+	23.9115i	−0.831483	+	0.831483i	−0.987720	−	0.156237i	$-0.950064\pi$
$827$	−23.9115	+	23.9115i	−0.831483	+	0.831483i	0.156237	+	0.987720i	$0.450064\pi$
$828$		0			0
$829$	−0.903774	−	1.56538i	−0.0313894	−	0.0543680i	0.849904	−	0.526938i	$-0.176660\pi$
$829$	−0.903774	−	1.56538i	−0.0313894	−	0.0543680i	−0.881293	+	0.472570i	$0.843327\pi$
$830$	33.4415	+	8.96061i	1.16077	+	0.311027i
$831$		0			0
$832$	5.68895	−	24.3920i	0.197229	−	0.845641i
$833$	−16.8066	−	11.0087i	−0.582314	−	0.381428i
$834$		0			0
$835$	−6.09861	−	10.5631i	−0.211051	−	0.365551i
$836$	−0.286700	+	0.496579i	−0.00991573	+	0.0171746i
$837$		0			0
$838$	−9.88871	−	36.9052i	−0.341600	−	1.27487i
$839$	−17.2364	+	4.61847i	−0.595066	+	0.159447i	−0.543767	−	0.839236i	$-0.683003\pi$
$839$	−17.2364	+	4.61847i	−0.595066	+	0.159447i	−0.0512985	+	0.998683i	$0.516336\pi$
$840$		0			0
$841$	9.02374	−	15.6296i	0.311163	−	0.538951i
$842$	17.6243	−	10.1754i	0.607372	−	0.350666i
$843$		0			0
$844$		−	5.41949i		−	0.186547i
$845$	18.6642	−	6.33317i	0.642069	−	0.217868i
$846$		0			0
$847$	−4.87276	−	20.4741i	−0.167430	−	0.703497i
$848$	−3.01121	−	5.21556i	−0.103405	−	0.179103i
$849$		0			0
$850$	8.16561	−	8.16561i	0.280078	−	0.280078i
$851$	−21.6229	+	5.79383i	−0.741222	+	0.198610i
$852$		0			0
$853$	−13.9934	−	13.9934i	−0.479126	−	0.479126i	0.425726	−	0.904852i	$-0.360019\pi$
$853$	−13.9934	−	13.9934i	−0.479126	−	0.479126i	−0.904852	+	0.425726i	$0.860019\pi$
$854$	0.138762	+	0.00390709i	0.00474833	+	0.000133698i
$855$		0			0
$856$	−33.4436	−	8.96118i	−1.14308	−	0.306287i
$857$	−39.0639			−1.33440			−0.667199	−	0.744879i	$-0.732507\pi$
$857$	−39.0639			−1.33440			−0.667199	+	0.744879i	$0.732507\pi$
$858$		0			0
$859$			28.2404i			0.963549i	0.876295	+	0.481775i	$0.160008\pi$
$859$			28.2404i			0.963549i	−0.876295	+	0.481775i	$0.839992\pi$
$860$	−1.21446	−	0.325414i	−0.0414128	−	0.0110965i
$861$		0			0
$862$	8.37267	+	4.83396i	0.285174	+	0.164645i
$863$	16.2731	+	16.2731i	0.553941	+	0.553941i	0.927576	−	0.373635i	$-0.121889\pi$
$863$	16.2731	+	16.2731i	0.553941	+	0.553941i	−0.373635	+	0.927576i	$0.621889\pi$
$864$		0			0
$865$	−8.55627	−	31.9324i	−0.290922	−	1.08574i
$866$	−35.2351	−	35.2351i	−1.19734	−	1.19734i
$867$		0			0
$868$	−0.920752	−	0.566735i	−0.0312524	−	0.0192362i
$869$	5.95074	+	1.59449i	0.201865	+	0.0540895i
$870$		0			0
$871$	−8.28727	+	15.5022i	−0.280803	+	0.525271i
$872$	52.6601			1.78330
$873$		0			0
$874$	−7.20017	+	4.15702i	−0.243549	+	0.140613i
$875$	−0.869485	+	30.8801i	−0.0293939	+	1.04394i
$876$		0			0
$877$	43.5370	−	11.6657i	1.47014	−	0.393923i	0.567162	−	0.823607i	$-0.308041\pi$
$877$	43.5370	−	11.6657i	1.47014	−	0.393923i	0.902980	+	0.429683i	$0.141375\pi$
$878$	28.2544	−	7.57075i	0.953540	−	0.255500i
$879$		0			0
$880$	10.0564	+	5.80604i	0.339000	+	0.195722i
$881$	3.87806	+	6.71699i	0.130655	+	0.226301i	0.923929	−	0.382563i	$-0.124959\pi$
$881$	3.87806	+	6.71699i	0.130655	+	0.226301i	−0.793274	+	0.608865i	$0.791625\pi$
$882$		0			0
$883$			50.1556i			1.68787i	0.536446	+	0.843935i	$0.319766\pi$
$883$			50.1556i			1.68787i	−0.536446	+	0.843935i	$0.680234\pi$
$884$	2.16166	−	0.655591i	0.0727044	−	0.0220499i
$885$		0			0
$886$	6.29663	−	23.4993i	0.211539	−	0.789476i
$887$	−21.4271	+	12.3709i	−0.719450	+	0.415375i	−0.814550	−	0.580093i	$-0.803016\pi$
$887$	−21.4271	+	12.3709i	−0.719450	+	0.415375i	0.0951001	+	0.995468i	$0.469683\pi$
$888$		0			0
$889$	10.7451	+	3.20586i	0.360378	+	0.107521i
$890$	−17.0443	+	4.56701i	−0.571327	+	0.153087i
$891$		0			0
$892$	2.18043	+	2.18043i	0.0730062	+	0.0730062i
$893$	−6.24107	+	10.8098i	−0.208849	+	0.361738i
$894$		0			0
$895$	−3.81368	+	14.2328i	−0.127477	+	0.475751i
$896$	16.1072	+	29.8057i	0.538105	+	0.995737i
$897$		0			0
$898$	−33.1466			−1.10612
$899$	5.98463	+	1.60358i	0.199599	+	0.0534823i
$900$		0			0
$901$	−1.96920	+	3.41075i	−0.0656035	+	0.113629i
$902$	5.89852	−	5.89852i	0.196399	−	0.196399i
$903$		0			0
$904$	7.69668	+	28.7244i	0.255988	+	0.955359i
$905$	14.5840	−	14.5840i	0.484788	−	0.484788i
$906$		0			0
$907$	−31.4697	+	18.1690i	−1.04493	+	0.603292i	−0.921226	−	0.389027i	$-0.872811\pi$
$907$	−31.4697	+	18.1690i	−1.04493	+	0.603292i	−0.123706	+	0.992319i	$0.539478\pi$
$908$	−1.25879	+	4.69786i	−0.0417743	+	0.155904i
$909$		0			0
$910$	−10.6860	+	18.7033i	−0.354238	+	0.620007i
$911$	−17.4606			−0.578497			−0.289248	−	0.957254i	$-0.593405\pi$
$911$	−17.4606			−0.578497			−0.289248	+	0.957254i	$0.593405\pi$
$912$		0			0
$913$	−23.1715	+	13.3781i	−0.766864	+	0.442749i
$914$	−12.7994	−	7.38975i	−0.423367	−	0.244431i
$915$		0			0
$916$	−0.694610	−	2.59232i	−0.0229506	−	0.0856527i
$917$	13.9873	−	13.2212i	0.461900	−	0.436601i
$918$		0			0
$919$	12.6196	−	21.8577i	0.416281	−	0.721020i	−0.579281	−	0.815128i	$-0.696666\pi$
$919$	12.6196	−	21.8577i	0.416281	−	0.721020i	0.995562	+	0.0941078i	$0.0299998\pi$
$920$	7.45989	+	12.9209i	0.245945	+	0.425990i
$921$		0			0
$922$	−54.2769			−1.78751
$923$	−42.5629	+	1.39083i	−1.40098	+	0.0457796i
$924$		0			0
$925$	4.22057	−	15.7514i	0.138771	−	0.517902i
$926$	−5.87583	−	10.1772i	−0.193092	−	0.334444i
$927$		0			0
$928$	2.87711	+	2.87711i	0.0944457	+	0.0944457i
$929$	−0.568291	−	2.12089i	−0.0186450	−	0.0695842i	0.955977	−	0.293443i	$-0.0948012\pi$
$929$	−0.568291	−	2.12089i	−0.0186450	−	0.0695842i	−0.974622	+	0.223859i	$0.928134\pi$
$930$		0			0
$931$	−10.3153	+	2.15016i	−0.338071	+	0.0704685i
$932$	−2.93005	+	5.07500i	−0.0959771	+	0.166237i
$933$		0			0
$934$	−8.96927	+	33.4738i	−0.293483	+	1.09529i
$935$		−	7.59379i		−	0.248344i
$936$		0			0
$937$			30.3704i			0.992157i	0.868278	+	0.496079i	$0.165227\pi$
$937$			30.3704i			0.992157i	−0.868278	+	0.496079i	$0.834773\pi$
$938$	−4.44804	−	18.6895i	−0.145234	−	0.610234i
$939$		0			0
$940$	−2.37655	−	1.37210i	−0.0775146	−	0.0447531i
$941$	26.4335	−	26.4335i	0.861707	−	0.861707i	−0.129829	−	0.991536i	$-0.541443\pi$
$941$	26.4335	−	26.4335i	0.861707	−	0.861707i	0.991536	+	0.129829i	$0.0414429\pi$
$942$		0			0
$943$	11.4962	−	3.08041i	0.374369	−	0.100312i
$944$	3.10954	+	3.10954i	0.101207	+	0.101207i
$945$		0			0
$946$	8.55170	−	4.93733i	0.278040	−	0.160526i
$947$	−25.0722	−	6.71808i	−0.814738	−	0.218308i	−0.172693	−	0.984976i	$-0.555247\pi$
$947$	−25.0722	−	6.71808i	−0.814738	−	0.218308i	−0.642044	+	0.766667i	$0.721914\pi$
$948$		0			0
$949$	−30.5182	−	49.0837i	−0.990662	−	1.59333i
$950$		−	6.05644i		−	0.196497i
$951$		0			0
$952$	10.5628	−	17.1610i	0.342343	−	0.556192i
$953$	−24.6170	−	14.2126i	−0.797422	−	0.460392i	0.0451471	−	0.998980i	$-0.485624\pi$
$953$	−24.6170	−	14.2126i	−0.797422	−	0.460392i	−0.842569	+	0.538589i	$0.818958\pi$
$954$		0			0
$955$	0.332061	+	1.23927i	0.0107452	+	0.0401018i
$956$	0.513547	+	1.91658i	0.0166093	+	0.0619867i
$957$		0			0
$958$	−48.0588	−	27.7468i	−1.55271	−	0.896458i
$959$	−28.8753	+	46.9126i	−0.932432	+	1.51489i
$960$		0			0
$961$			27.4951i			0.886939i
$962$	22.1610	−	23.6583i	0.714501	−	0.762774i
$963$		0			0
$964$	4.69499	+	1.25802i	0.151216	+	0.0405181i
$965$	−2.08217	+	1.20214i	−0.0670275	+	0.0386983i
$966$		0			0
$967$	−18.9661	−	18.9661i	−0.609908	−	0.609908i	0.333014	−	0.942922i	$-0.391935\pi$
$967$	−18.9661	−	18.9661i	−0.609908	−	0.609908i	−0.942922	+	0.333014i	$0.891935\pi$
$968$	20.3897	−	5.46340i	0.655349	−	0.175600i
$969$		0			0
$970$	15.2287	−	15.2287i	0.488965	−	0.488965i
$971$	23.2259	+	13.4095i	0.745355	+	0.430331i	0.824013	−	0.566571i	$-0.191730\pi$
$971$	23.2259	+	13.4095i	0.745355	+	0.430331i	−0.0786584	+	0.996902i	$0.525064\pi$
$972$		0			0
$973$	11.4935	+	48.2927i	0.368465	+	1.54819i
$974$		−	61.8168i		−	1.98074i
$975$		0			0
$976$			0.154611i			0.00494899i
$977$	8.48807	−	31.6779i	0.271557	−	1.01347i	−0.686556	−	0.727077i	$-0.740878\pi$
$977$	8.48807	−	31.6779i	0.271557	−	1.01347i	0.958113	−	0.286389i	$-0.0924549\pi$
$978$		0			0
$979$	6.81848	−	11.8099i	0.217919	−	0.377448i
$980$	−0.472714	−	2.26783i	−0.0151003	−	0.0724432i
$981$		0			0
$982$	−3.21392	−	11.9945i	−0.102560	−	0.382760i
$983$	−21.2566	−	21.2566i	−0.677982	−	0.677982i	0.281561	−	0.959543i	$-0.409148\pi$
$983$	−21.2566	−	21.2566i	−0.677982	−	0.677982i	−0.959543	+	0.281561i	$0.909148\pi$
$984$		0			0
$985$	−3.95450	−	6.84939i	−0.126001	−	0.218240i
$986$	3.66157	−	13.6652i	0.116608	−	0.435188i
$987$		0			0
$988$	0.558526	−	1.04478i	0.0177691	−	0.0332388i
$989$	14.0889			0.448000
$990$		0			0
$991$	17.6556	+	30.5804i	0.560849	+	0.971420i	0.997423	+	0.0717510i	$0.0228587\pi$
$991$	17.6556	+	30.5804i	0.560849	+	0.971420i	−0.436573	+	0.899669i	$0.643808\pi$
$992$	1.15086	−	1.99334i	0.0365397	−	0.0632886i
$993$		0			0
$994$	33.8237	−	31.9711i	1.07282	−	1.01406i
$995$	0.532226	+	1.98630i	0.0168727	+	0.0629698i
$996$		0			0
$997$	4.50099	+	2.59865i	0.142548	+	0.0822999i	0.569578	−	0.821938i	$-0.307107\pi$
$997$	4.50099	+	2.59865i	0.142548	+	0.0822999i	−0.427030	+	0.904237i	$0.640440\pi$
$998$	12.0724	−	6.96998i	0.382144	−	0.220631i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.e.622.2		32
3.2	odd	2		273.2.by.d.76.7	yes	32
7.6	odd	2		819.2.fm.f.622.2		32
13.6	odd	12		819.2.fm.f.370.2		32
21.20	even	2		273.2.by.c.76.7	✓	32
39.32	even	12		273.2.by.c.97.7	yes	32
91.6	even	12	inner	819.2.fm.e.370.2		32
273.188	odd	12		273.2.by.d.97.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.7	✓	32	21.20	even	2
273.2.by.c.97.7	yes	32	39.32	even	12
273.2.by.d.76.7	yes	32	3.2	odd	2
273.2.by.d.97.7	yes	32	273.188	odd	12
819.2.fm.e.370.2		32	91.6	even	12	inner
819.2.fm.e.622.2		32	1.1	even	1	trivial
819.2.fm.f.370.2		32	13.6	odd	12
819.2.fm.f.622.2		32	7.6	odd	2

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

\(f(q)\)	\(=\)	\(q+(-0.385482 + 1.43864i) q^{2} +(-0.189037 - 0.109141i) q^{4} +(1.07205 - 1.07205i) q^{5} +(1.81743 + 1.92274i) q^{7} +(-1.87643 + 1.87643i) q^{8} +O(q^{10})\)	\(q+(-0.385482 + 1.43864i) q^{2} +(-0.189037 - 0.109141i) q^{4} +(1.07205 - 1.07205i) q^{5} +(1.81743 + 1.92274i) q^{7} +(-1.87643 + 1.87643i) q^{8} +(1.12904 + 1.95556i) q^{10} +(-1.68564 - 0.451666i) q^{11} +(3.51131 + 0.818944i) q^{13} +(-3.46672 + 1.87345i) q^{14} +(-2.19446 - 3.80091i) q^{16} +(-1.43508 + 2.48563i) q^{17} +(0.389597 + 1.45400i) q^{19} +(-0.319663 + 0.0856533i) q^{20} +(1.29957 - 2.25092i) q^{22} +(3.21155 - 1.85419i) q^{23} +2.70140i q^{25} +(-2.53172 + 4.73583i) q^{26} +(-0.133713 - 0.561826i) q^{28} +(1.65473 + 2.86608i) q^{29} +(1.32380 - 1.32380i) q^{31} +(1.18757 - 0.318208i) q^{32} +(-3.02273 - 3.02273i) q^{34} +(4.00967 + 0.112899i) q^{35} +(-5.83082 - 1.56236i) q^{37} -2.24196 q^{38} +4.02327i q^{40} +(3.10007 + 0.830662i) q^{41} +(3.29020 + 1.89960i) q^{43} +(0.269354 + 0.269354i) q^{44} +(1.42951 + 5.33502i) q^{46} +(5.86346 + 5.86346i) q^{47} +(-0.393883 + 6.98891i) q^{49} +(-3.88635 - 1.04134i) q^{50} +(-0.574389 - 0.538038i) q^{52} +1.37219 q^{53} +(-2.29131 + 1.32289i) q^{55} +(-7.01818 - 0.197610i) q^{56} +(-4.76112 + 1.27574i) q^{58} +(-0.967827 + 0.259328i) q^{59} +(-0.0305081 - 0.0176138i) q^{61} +(1.39417 + 2.41477i) q^{62} -6.94669i q^{64} +(4.64227 - 2.88636i) q^{65} +(-1.26183 + 4.70921i) q^{67} +(0.542567 - 0.313251i) q^{68} +(-1.70808 + 5.72495i) q^{70} +(-11.4087 + 3.05695i) q^{71} +(-11.3351 - 11.3351i) q^{73} +(4.49535 - 7.78618i) q^{74} +(0.0850419 - 0.317381i) q^{76} +(-2.19510 - 4.06193i) q^{77} -3.53025 q^{79} +(-6.42736 - 1.72221i) q^{80} +(-2.39005 + 4.13968i) q^{82} +(10.8414 - 10.8414i) q^{83} +(1.12625 + 4.20321i) q^{85} +(-4.00116 + 4.00116i) q^{86} +(4.01051 - 2.31547i) q^{88} +(-2.02252 + 7.54814i) q^{89} +(4.80695 + 8.23973i) q^{91} -0.809469 q^{92} +(-10.6957 + 6.17514i) q^{94} +(1.97643 + 1.14109i) q^{95} +(-2.46851 - 9.21262i) q^{97} +(-9.90269 - 3.26076i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

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