LMFDB - Embedded newform 819.2.fm.f.370.2

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			370.2
Character	$\chi$	$=$	819.370
Dual form			819.2.fm.f.622.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385482 - 1.43864i) q^{2} +(-0.189037 + 0.109141i) q^{4} +(-1.07205 - 1.07205i) q^{5} +(-0.612570 - 2.57386i) q^{7} +(-1.87643 - 1.87643i) q^{8} +O(q^{10})$	\(q+(-0.385482 - 1.43864i) q^{2} +(-0.189037 + 0.109141i) q^{4} +(-1.07205 - 1.07205i) q^{5} +(-0.612570 - 2.57386i) q^{7} +(-1.87643 - 1.87643i) q^{8} +(-1.12904 + 1.95556i) q^{10} +(-1.68564 + 0.451666i) q^{11} +(-3.51131 + 0.818944i) q^{13} +(-3.46672 + 1.87345i) q^{14} +(-2.19446 + 3.80091i) q^{16} +(1.43508 + 2.48563i) q^{17} +(-0.389597 + 1.45400i) q^{19} +(0.319663 + 0.0856533i) q^{20} +(1.29957 + 2.25092i) q^{22} +(3.21155 + 1.85419i) q^{23} -2.70140i q^{25} +(2.53172 + 4.73583i) q^{26} +(0.396712 + 0.419699i) q^{28} +(1.65473 - 2.86608i) q^{29} +(-1.32380 - 1.32380i) q^{31} +(1.18757 + 0.318208i) q^{32} +(3.02273 - 3.02273i) q^{34} +(-2.10261 + 3.41602i) q^{35} +(-5.83082 + 1.56236i) q^{37} +2.24196 q^{38} +4.02327i q^{40} +(-3.10007 + 0.830662i) q^{41} +(3.29020 - 1.89960i) q^{43} +(0.269354 - 0.269354i) q^{44} +(1.42951 - 5.33502i) q^{46} +(-5.86346 + 5.86346i) q^{47} +(-6.24951 + 3.15334i) q^{49} +(-3.88635 + 1.04134i) q^{50} +(0.574389 - 0.538038i) q^{52} +1.37219 q^{53} +(2.29131 + 1.32289i) q^{55} +(-3.68022 + 5.97912i) q^{56} +(-4.76112 - 1.27574i) q^{58} +(0.967827 + 0.259328i) q^{59} +(0.0305081 - 0.0176138i) q^{61} +(-1.39417 + 2.41477i) q^{62} +6.94669i q^{64} +(4.64227 + 2.88636i) q^{65} +(-1.26183 - 4.70921i) q^{67} +(-0.542567 - 0.313251i) q^{68} +(5.72495 + 1.70808i) q^{70} +(-11.4087 - 3.05695i) q^{71} +(11.3351 - 11.3351i) q^{73} +(4.49535 + 7.78618i) q^{74} +(-0.0850419 - 0.317381i) q^{76} +(2.19510 + 4.06193i) q^{77} -3.53025 q^{79} +(6.42736 - 1.72221i) q^{80} +(2.39005 + 4.13968i) q^{82} +(-10.8414 - 10.8414i) q^{83} +(1.12625 - 4.20321i) q^{85} +(-4.00116 - 4.00116i) q^{86} +(4.01051 + 2.31547i) q^{88} +(2.02252 + 7.54814i) q^{89} +(4.25878 + 8.53597i) q^{91} -0.809469 q^{92} +(10.6957 + 6.17514i) q^{94} +(1.97643 - 1.14109i) q^{95} +(2.46851 - 9.21262i) q^{97} +(6.94560 + 7.77524i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 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} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+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 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * 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 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.957448	−	0.288607i	$-0.906808\pi$
$2$	−0.385482	−	1.43864i	−0.272577	−	1.01727i	0.684870	−	0.728665i	$-0.259859\pi$
$3$		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	$-0.360093\pi$
$5$	−1.07205	−	1.07205i	−0.479437	−	0.479437i	−0.904952	+	0.425515i	$0.860093\pi$
$6$		0			0
$7$	−0.612570	−	2.57386i	−0.231530	−	0.972828i
$7$	−0.612570	−	2.57386i	−0.231530	−	0.972828i
$8$	−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	−0.503822	−	0.863808i	$-0.668073\pi$
$11$	−1.68564	+	0.451666i	−0.508240	+	0.136182i	−0.00441837	+	0.999990i	$0.501406\pi$
$12$		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	$-0.0535079\pi$
$17$	1.43508	+	2.48563i	0.348058	+	0.602854i	−0.637847	+	0.770164i	$0.720175\pi$
$18$		0			0
$19$	−0.389597	+	1.45400i	−0.0893798	+	0.333570i	−0.996108	−	0.0881466i	$-0.971906\pi$
$19$	−0.389597	+	1.45400i	−0.0893798	+	0.333570i	0.906728	+	0.421717i	$0.138572\pi$
$20$	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	0.795946	−	0.605368i	$-0.206974\pi$
$23$	3.21155	+	1.85419i	0.669654	+	0.386625i	−0.126292	+	0.991993i	$0.540307\pi$
$24$		0			0
$25$		−	2.70140i		−	0.540281i
$26$	2.53172	+	4.73583i	0.496510	+	0.928772i
$27$		0			0
$28$	0.396712	+	0.419699i	0.0749714	+	0.0793157i
$29$	1.65473	−	2.86608i	0.307276	−	0.532217i	−0.670490	−	0.741919i	$-0.733916\pi$
$29$	1.65473	−	2.86608i	0.307276	−	0.532217i	0.977765	+	0.209702i	$0.0672493\pi$
$30$		0			0
$31$	−1.32380	−	1.32380i	−0.237761	−	0.237761i	0.578161	−	0.815922i	$-0.303770\pi$
$31$	−1.32380	−	1.32380i	−0.237761	−	0.237761i	−0.815922	+	0.578161i	$0.803770\pi$
$32$	1.18757	+	0.318208i	0.209934	+	0.0562517i
$33$		0			0
$34$	3.02273	−	3.02273i	0.518394	−	0.518394i
$35$	−2.10261	+	3.41602i	−0.355406	+	0.577413i
$36$		0			0
$37$	−5.83082	+	1.56236i	−0.958580	+	0.256851i	−0.703999	−	0.710201i	$-0.748604\pi$
$37$	−5.83082	+	1.56236i	−0.958580	+	0.256851i	−0.254581	+	0.967051i	$0.581938\pi$
$38$	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	$-0.663966\pi$
$41$	−3.10007	+	0.830662i	−0.484150	+	0.129728i	0.00848433	+	0.999964i	$0.497299\pi$
$42$		0			0
$43$	3.29020	−	1.89960i	0.501751	−	0.289686i	−0.227685	−	0.973735i	$-0.573116\pi$
$43$	3.29020	−	1.89960i	0.501751	−	0.289686i	0.729436	+	0.684049i	$0.239782\pi$
$44$	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	$-0.956735\pi$
$47$	−5.86346	+	5.86346i	−0.855273	+	0.855273i	0.135504	+	0.990777i	$0.456735\pi$
$48$		0			0
$49$	−6.24951	+	3.15334i	−0.892788	+	0.450477i
$50$	−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
$56$	−3.68022	+	5.97912i	−0.491791	+	0.798993i
$57$		0			0
$58$	−4.76112	−	1.27574i	−0.625166	−	0.167513i
$59$	0.967827	+	0.259328i	0.126000	+	0.0337617i	0.321268	−	0.946988i	$-0.395891\pi$
$59$	0.967827	+	0.259328i	0.126000	+	0.0337617i	−0.195268	+	0.980750i	$0.562558\pi$
$60$		0			0
$61$	0.0305081	−	0.0176138i	0.00390616	−	0.00225522i	−0.498046	−	0.867151i	$-0.665949\pi$
$61$	0.0305081	−	0.0176138i	0.00390616	−	0.00225522i	0.501952	+	0.864896i	$0.332615\pi$
$62$	−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	−0.999176	−	0.0405858i	$-0.987078\pi$
$67$	−1.26183	−	4.70921i	−0.154157	−	0.575322i	0.845019	−	0.534736i	$-0.179589\pi$
$68$	−0.542567	−	0.313251i	−0.0657959	−	0.0379873i
$69$		0			0
$70$	5.72495	+	1.70808i	0.684262	+	0.204154i
$71$	−11.4087	−	3.05695i	−1.35396	−	0.362793i	−0.492366	−	0.870388i	$-0.663868\pi$
$71$	−11.4087	−	3.05695i	−1.35396	−	0.362793i	−0.861595	+	0.507596i	$0.830534\pi$
$72$		0			0
$73$	11.3351	−	11.3351i	1.32667	−	1.32667i	0.418410	−	0.908258i	$-0.362587\pi$
$73$	11.3351	−	11.3351i	1.32667	−	1.32667i	0.908258	−	0.418410i	$-0.137413\pi$
$74$	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	−0.977066	−	0.212936i	$-0.931698\pi$
$83$	−10.8414	−	10.8414i	−1.19000	−	1.19000i	−0.212936	−	0.977066i	$-0.568302\pi$
$84$		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	0.986382	+	0.164473i	$0.0525922\pi$
$89$	2.02252	+	7.54814i	0.214386	+	0.800101i	−0.771995	+	0.635628i	$0.780741\pi$
$90$		0			0
$91$	4.25878	+	8.53597i	0.446441	+	0.894813i
$92$	−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	−0.719825	−	0.694156i	$-0.755778\pi$
$97$	2.46851	−	9.21262i	0.250640	−	0.935400i	0.970465	−	0.241244i	$-0.0775554\pi$
$98$	6.94560	+	7.77524i	0.701612	+	0.785418i
$99$		0			0
$100$	0.294833	+	0.510666i	0.0294833	+	0.0510666i
$101$	6.74473	−	11.6822i	0.671125	−	1.16242i	−0.306460	−	0.951883i	$-0.599145\pi$
$101$	6.74473	−	11.6822i	0.671125	−	1.16242i	0.977585	−	0.210540i	$-0.0675221\pi$
$102$		0			0
$103$	−8.93370			−0.880264			−0.440132	−	0.897933i	$-0.645068\pi$
$103$	−8.93370			−0.880264			−0.440132	+	0.897933i	$0.645068\pi$
$104$	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	−0.356750	−	0.934200i	$-0.616115\pi$
$107$	6.52366	−	11.2993i	0.630666	−	1.09235i	0.987416	−	0.158146i	$-0.0505516\pi$
$108$		0			0
$109$	−14.0320	+	14.0320i	−1.34402	+	1.34402i	−0.452007	+	0.892015i	$0.649292\pi$
$109$	−14.0320	+	14.0320i	−1.34402	+	1.34402i	−0.892015	+	0.452007i	$0.850708\pi$
$110$	1.01990	−	3.80632i	0.0972436	−	0.362918i
$111$		0			0
$112$	11.1273	+	3.31990i	1.05143	+	0.313701i
$113$	5.60312	+	9.70489i	0.527097	+	0.912959i	0.999501	+	0.0315769i	$0.0100529\pi$
$113$	5.60312	+	9.70489i	0.527097	+	0.912959i	−0.472404	+	0.881382i	$0.656614\pi$
$114$		0			0
$115$	−1.45516	−	5.43074i	−0.135695	−	0.506419i
$116$			0.722393i			0.0670725i
$117$		0			0
$118$		−	1.49232i		−	0.137379i
$119$	5.51858	−	5.21632i	0.505887	−	0.478179i
$120$		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	0.653926	−	0.756558i	$-0.273121\pi$
$127$	3.67035	+	2.11908i	0.325691	+	0.188038i	−0.328235	+	0.944596i	$0.606454\pi$
$128$	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
$133$	3.98104	+	0.112094i	0.345200	+	0.00971974i
$134$	−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	−0.211306	−	0.977420i	$-0.567772\pi$
$137$	5.38885	−	20.1115i	0.460400	−	1.71824i	0.671706	−	0.740818i	$-0.265562\pi$
$138$		0			0
$139$	−16.2490	+	9.38137i	−1.37822	+	0.795718i	−0.991946	−	0.126665i	$-0.959573\pi$
$139$	−16.2490	+	9.38137i	−1.37822	+	0.795718i	−0.386278	+	0.922382i	$0.626239\pi$
$140$	0.0246439	−	0.875236i	0.00208279	−	0.0739709i
$141$		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	0.329160	−	0.944274i	$-0.393235\pi$
$149$	1.73434	+	0.464716i	0.142083	+	0.0380710i	−0.187077	+	0.982345i	$0.559901\pi$
$150$		0			0
$151$	14.9709	+	14.9709i	1.21832	+	1.21832i	0.968221	+	0.250095i	$0.0804619\pi$
$151$	14.9709	+	14.9709i	1.21832	+	1.21832i	0.250095	+	0.968221i	$0.419538\pi$
$152$	3.45938	−	1.99727i	0.280593	−	0.162000i
$153$		0			0
$154$	4.99748	−	4.72376i	0.402708	−	0.380651i
$155$			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
$161$	2.80512	−	9.40190i	0.221075	−	0.740973i
$162$		0			0
$163$	3.90415	−	14.5705i	0.305797	−	1.14125i	−0.626460	−	0.779453i	$-0.715497\pi$
$163$	3.90415	−	14.5705i	0.305797	−	1.14125i	0.932257	−	0.361796i	$-0.117836\pi$
$164$	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	−0.998503	−	0.0547052i	$-0.982578\pi$
$167$	−2.08221	−	7.77093i	−0.161127	−	0.601333i	0.837376	−	0.546627i	$-0.184089\pi$
$168$		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	−0.898899	−	0.438155i	$-0.855632\pi$
$173$	−10.9025	−	18.8837i	−0.828903	−	1.43570i	0.0699960	−	0.997547i	$-0.477701\pi$
$174$		0			0
$175$	−6.95303	+	1.65480i	−0.525600	+	0.125091i
$176$	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	0.151303	−	0.988487i	$-0.451653\pi$
$179$	−8.41680	−	4.85944i	−0.629101	−	0.363212i	−0.780404	+	0.625276i	$0.784986\pi$
$180$		0			0
$181$	−13.6038			−1.01116			−0.505580	−	0.862779i	$-0.668722\pi$
$181$	−13.6038			−1.01116			−0.505580	+	0.862779i	$0.668722\pi$
$182$	10.6385	−	9.41731i	0.788579	−	0.698058i
$183$		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	0.850312	−	0.526280i	$-0.176413\pi$
$191$	−0.423116	−	0.732859i	−0.0306156	−	0.0530278i	−0.880927	+	0.473252i	$0.843080\pi$
$192$		0			0
$193$	−1.53179	+	0.410441i	−0.110260	+	0.0295442i	−0.313527	−	0.949579i	$-0.601511\pi$
$193$	−1.53179	+	0.410441i	−0.110260	+	0.0295442i	0.203267	+	0.979123i	$0.434844\pi$
$194$	−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	0.997198	−	0.0748081i	$-0.0238344\pi$
$197$	1.35016	+	5.03888i	0.0961951	+	0.359005i	−0.901003	+	0.433813i	$0.857168\pi$
$198$		0			0
$199$	0.678170	+	1.17462i	0.0480742	+	0.0832670i	0.889061	−	0.457788i	$-0.151358\pi$
$199$	0.678170	+	1.17462i	0.0480742	+	0.0832670i	−0.840987	+	0.541055i	$0.818025\pi$
$200$	−5.06899	+	5.06899i	−0.358432	+	0.358432i
$201$		0			0
$202$	−19.4065	−	5.19995i	−1.36543	−	0.365867i
$203$	−8.39052	−	2.50337i	−0.588899	−	0.175702i
$204$		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	−0.0223853	−	0.999749i	$-0.507126\pi$
$211$	12.4140	−	21.5017i	0.854616	−	1.48024i	0.877001	−	0.480488i	$-0.159541\pi$
$212$	−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
$217$	−2.59635	+	4.21819i	−0.176252	+	0.286349i
$218$	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	$-0.426506\pi$
$223$	13.6453	−	3.65626i	0.913760	−	0.244841i	0.684916	+	0.728622i	$0.259839\pi$
$224$	0.0915535	−	3.25156i	0.00611717	−	0.217254i
$225$		0			0
$226$	11.8019	−	11.8019i	0.785053	−	0.785053i
$227$	5.76681	−	21.5220i	0.382757	−	1.42847i	−0.458916	−	0.888480i	$-0.651762\pi$
$227$	5.76681	−	21.5220i	0.382757	−	1.42847i	0.841673	−	0.539988i	$-0.181571\pi$
$228$		0			0
$229$	−8.69387	+	8.69387i	−0.574507	+	0.574507i	−0.933385	−	0.358877i	$-0.883160\pi$
$229$	−8.69387	+	8.69387i	−0.574507	+	0.574507i	0.358877	+	0.933385i	$0.383160\pi$
$230$	−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	$0.342048\pi$
$233$			26.8466i			1.75878i	−0.476104	+	0.879389i	$0.657952\pi$
$234$		0			0
$235$	12.5719			0.820099
$236$	−0.211259	+	0.0566065i	−0.0137518	+	0.00368477i
$237$		0			0
$238$	−9.63172	−	5.92845i	−0.624332	−	0.384284i
$239$	−6.42765	+	6.42765i	−0.415770	+	0.415770i	−0.883743	−	0.467973i	$-0.844984\pi$
$239$	−6.42765	+	6.42765i	−0.415770	+	0.415770i	0.467973	+	0.883743i	$0.344984\pi$
$240$		0			0
$241$	21.5089	+	5.76329i	1.38551	+	0.371246i	0.873120	−	0.487506i	$-0.162093\pi$
$241$	21.5089	+	5.76329i	1.38551	+	0.371246i	0.512391	+	0.858752i	$0.328760\pi$
$242$	8.37746	+	8.37746i	0.538523	+	0.538523i
$243$		0			0
$244$	−0.00384478	+	0.00665935i	−0.000246137	+	0.000426321i
$245$	10.0804	+	3.31926i	0.644011	+	0.212060i
$246$		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	−0.712134	−	0.702044i	$-0.752271\pi$
$251$	−15.2735	−	26.4545i	−0.964055	−	1.66979i	−0.251921	−	0.967748i	$-0.581062\pi$
$252$		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	$-0.967070\pi$
$257$	−6.53903	+	11.3259i	−0.407894	+	0.706493i	0.586760	+	0.809761i	$0.300403\pi$
$258$		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	−0.688750	−	0.724999i	$-0.741840\pi$
$263$	4.59748	−	7.96308i	0.283493	−	0.491024i	0.972243	+	0.233975i	$0.0751734\pi$
$264$		0			0
$265$	−1.47106	−	1.47106i	−0.0903664	−	0.0903664i
$266$	−1.37336	−	5.77050i	−0.0842061	−	0.353812i
$267$		0			0
$268$	0.752500	+	0.752500i	0.0459662	+	0.0459662i
$269$	10.0654	−	5.81128i	0.613700	−	0.354320i	−0.160712	−	0.987001i	$-0.551379\pi$
$269$	10.0654	−	5.81128i	0.613700	−	0.354320i	0.774412	+	0.632681i	$0.218046\pi$
$270$		0			0
$271$	−5.43020	−	20.2658i	−0.329861	−	1.23106i	−0.909334	−	0.416067i	$-0.863408\pi$
$271$	−5.43020	−	20.2658i	−0.329861	−	1.23106i	0.579473	−	0.814991i	$-0.303258\pi$
$272$	−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	−0.850971	−	0.525213i	$-0.823986\pi$
$277$	−13.6743	+	7.89485i	−0.821608	+	0.474356i	0.0293625	+	0.999569i	$0.490652\pi$
$278$	19.7601	+	19.7601i	1.18513	+	1.18513i
$279$		0			0
$280$	10.3553	−	2.46453i	0.618849	−	0.147284i
$281$	6.16446	+	6.16446i	0.367741	+	0.367741i	0.866653	−	0.498912i	$-0.166267\pi$
$281$	6.16446	+	6.16446i	0.367741	+	0.367741i	−0.498912	+	0.866653i	$0.666267\pi$
$282$		0			0
$283$	2.66486	−	4.61567i	0.158410	−	0.274373i	−0.775886	−	0.630873i	$-0.782697\pi$
$283$	2.66486	−	4.61567i	0.158410	−	0.274373i	0.934295	+	0.356500i	$0.116030\pi$
$284$	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	$-0.199205\pi$
$293$	20.8745	+	5.59331i	1.21950	+	0.326764i	0.409018	+	0.912526i	$0.365871\pi$
$294$		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
$301$	−6.90479	−	7.30489i	−0.397985	−	0.421047i
$302$	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	$-0.705082\pi$
$307$	3.48509	−	3.48509i	0.198904	−	0.198904i	0.799530	+	0.600626i	$0.205082\pi$
$308$	−0.858277	−	0.528281i	−0.0489049	−	0.0301016i
$309$		0			0
$310$	4.08338	−	1.09414i	0.231920	−	0.0621429i
$311$	−16.5536			−0.938671			−0.469335	−	0.883020i	$-0.655506\pi$
$311$	−16.5536			−0.938671			−0.469335	+	0.883020i	$0.655506\pi$
$312$		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	−0.934684	−	0.355480i	$-0.884317\pi$
$317$	−10.3124	+	10.3124i	−0.579204	+	0.579204i	0.355480	+	0.934684i	$0.384317\pi$
$318$		0			0
$319$	−1.49477	+	5.57856i	−0.0836911	+	0.312339i
$320$	7.44722	−	7.44722i	0.416312	−	0.416312i
$321$		0			0
$322$	−14.6073	−	0.411294i	−0.814031	−	0.0229205i
$323$	−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
$329$	18.6835	+	11.4999i	1.03005	+	0.634012i
$330$		0			0
$331$	22.7352	+	6.09189i	1.24964	+	0.334840i	0.822198	−	0.569202i	$-0.192748\pi$
$331$	22.7352	+	6.09189i	1.24964	+	0.334840i	0.427444	+	0.904042i	$0.359414\pi$
$332$	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	$0.130181\pi$
$337$			14.6004i			0.795337i	−0.917529	+	0.397668i	$0.869819\pi$
$338$	−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
$343$	11.9445	+	14.1537i	0.644944	+	0.764230i
$344$	−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	0.998719	−	0.0506002i	$-0.0161134\pi$
$347$	8.48574	+	14.6977i	0.455538	+	0.789016i	−0.543181	+	0.839616i	$0.682780\pi$
$348$		0			0
$349$	0.728645	+	2.71934i	0.0390035	+	0.145563i	0.982682	−	0.185302i	$-0.0593263\pi$
$349$	0.728645	+	2.71934i	0.0390035	+	0.145563i	−0.943678	+	0.330865i	$0.892660\pi$
$350$	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	$-0.263827\pi$
$353$	30.6157	−	8.20345i	1.62951	−	0.436625i	0.953775	+	0.300521i	$0.0971605\pi$
$354$		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	0.282733	−	0.959199i	$-0.408759\pi$
$359$	−12.8172	−	12.8172i	−0.676466	−	0.676466i	−0.959199	+	0.282733i	$0.908759\pi$
$360$		0			0
$361$	14.4922	+	8.36705i	0.762745	+	0.440371i
$362$	5.24402	+	19.5709i	0.275619	+	1.02863i
$363$		0			0
$364$	−1.73669	−	1.14881i	−0.0910272	−	0.0602140i
$365$	−24.3036			−1.27211
$366$		0			0
$367$	3.51454	+	2.02912i	0.183457	+	0.105919i	0.588916	−	0.808194i	$-0.299555\pi$
$367$	3.51454	+	2.02912i	0.183457	+	0.105919i	−0.405459	+	0.914113i	$0.632888\pi$
$368$	−14.0952	+	8.13787i	−0.734764	+	0.424216i
$369$		0			0
$370$	3.52794	−	13.1665i	0.183409	−	0.684492i
$371$	−0.840561	−	3.53182i	−0.0436398	−	0.183363i
$372$		0			0
$373$	5.07453	+	8.78935i	0.262749	+	0.455095i	0.966972	−	0.254884i	$-0.0820374\pi$
$373$	5.07453	+	8.78935i	0.262749	+	0.455095i	−0.704222	+	0.709980i	$0.748704\pi$
$374$	−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	0.987500	−	0.157618i	$-0.0503815\pi$
$379$	1.04136	+	3.88639i	0.0534908	+	0.199630i	−0.934009	+	0.357249i	$0.883715\pi$
$380$	−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	$-0.907557\pi$
$383$	0.289889	−	1.08188i	0.0148126	−	0.0552815i	0.972937	+	0.231072i	$0.0742234\pi$
$384$		0			0
$385$	2.00134	−	6.70787i	0.101998	−	0.341865i
$386$	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	$0.0199107\pi$
$389$			2.46580i			0.125021i	−0.998044	+	0.0625106i	$0.980089\pi$
$390$		0			0
$391$			10.6436i			0.538271i
$392$	17.6438	+	5.80975i	0.891147	+	0.293437i
$393$		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	$-0.299480\pi$
$397$	13.8529	+	3.71187i	0.695257	+	0.186294i	0.106152	+	0.994350i	$0.466147\pi$
$398$	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	−0.490347	−	0.871527i	$-0.663130\pi$
$401$	−9.59670	+	2.57143i	−0.479236	+	0.128411i	0.0111107	+	0.999938i	$0.496463\pi$
$402$		0			0
$403$	5.73238	+	3.56415i	0.285550	+	0.177543i
$404$			2.94450i			0.146494i
$405$		0			0
$406$	−0.367051	+	13.0359i	−0.0182164	+	0.646963i
$407$	9.12300	−	5.26716i	0.452210	−	0.261084i
$408$		0			0
$409$	−9.20429	+	34.3509i	−0.455123	+	1.69854i	0.232603	+	0.972572i	$0.425276\pi$
$409$	−9.20429	+	34.3509i	−0.455123	+	1.69854i	−0.687726	+	0.725970i	$0.741391\pi$
$410$	1.87570	−	7.00022i	0.0926344	−	0.345716i
$411$		0			0
$412$	1.68880	−	0.975031i	0.0832013	−	0.0480363i
$413$	0.0746130	−	2.64991i	0.00367146	−	0.130393i
$414$		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	$-0.117775\pi$
$419$	22.2160	+	12.8264i	1.08532	+	0.626611i	0.152995	+	0.988227i	$0.451108\pi$
$420$		0			0
$421$	−9.66177	+	9.66177i	−0.470886	+	0.470886i	−0.902201	−	0.431315i	$-0.858050\pi$
$421$	−9.66177	+	9.66177i	−0.470886	+	0.470886i	0.431315	+	0.902201i	$0.358050\pi$
$422$	−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
$427$	−0.0640239	−	0.0677338i	−0.00309834	−	0.00327787i
$428$			2.84799i			0.137663i
$429$		0			0
$430$			8.57890i			0.413712i
$431$	1.68005	+	6.27002i	0.0809250	+	0.302016i	0.994511	−	0.104629i	$-0.0333654\pi$
$431$	1.68005	+	6.27002i	0.0809250	+	0.302016i	−0.913586	+	0.406645i	$0.866699\pi$
$432$		0			0
$433$	16.7283	+	28.9743i	0.803912	+	1.39242i	0.917023	+	0.398834i	$0.130585\pi$
$433$	16.7283	+	28.9743i	0.803912	+	1.39242i	−0.113111	+	0.993582i	$0.536082\pi$
$434$	7.06930	+	2.10918i	0.339337	+	0.101244i
$435$		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	$-0.678065\pi$
$439$	9.81984	−	17.0085i	0.468675	−	0.811769i	0.999359	+	0.0358007i	$0.0113981\pi$
$440$	−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
$448$	17.8798	−	4.25534i	0.844741	−	0.201046i
$449$	5.76005	−	21.4968i	0.271834	−	1.01450i	−0.686100	−	0.727507i	$-0.740679\pi$
$449$	5.76005	−	21.4968i	0.271834	−	1.01450i	0.957934	−	0.286990i	$-0.0926546\pi$
$450$		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
$455$	4.58538	−	13.7167i	0.214966	−	0.643047i
$456$		0			0
$457$	−2.56831	−	9.58507i	−0.120141	−	0.448371i	0.879479	−	0.475937i	$-0.157891\pi$
$457$	−2.56831	−	9.58507i	−0.120141	−	0.448371i	−0.999620	+	0.0275663i	$0.991224\pi$
$458$	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	0.291293	+	0.956634i	$0.405915\pi$
$461$	−9.43198	+	35.2006i	−0.439291	+	1.63946i	−0.730584	+	0.682823i	$0.760752\pi$
$462$		0			0
$463$	−5.57925	−	5.57925i	−0.259290	−	0.259290i	0.565476	−	0.824765i	$-0.308693\pi$
$463$	−5.57925	−	5.57925i	−0.259290	−	0.259290i	−0.824765	+	0.565476i	$0.808693\pi$
$464$	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	$-0.680952\pi$
$467$	−23.2676			−1.07670			−0.538349	+	0.842722i	$0.680952\pi$
$468$		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
$476$	−0.473904	+	1.58838i	−0.0217214	+	0.0728033i
$477$		0			0
$478$	11.7248	+	6.76932i	0.536280	+	0.309622i
$479$	9.64340	+	35.9897i	0.440618	+	1.64441i	0.727252	+	0.686370i	$0.240797\pi$
$479$	9.64340	+	35.9897i	0.440618	+	1.64441i	−0.286634	+	0.958040i	$0.592536\pi$
$480$		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	−0.820308	−	0.571922i	$-0.806198\pi$
$487$	−40.0906	−	10.7422i	−1.81668	−	0.486777i	−0.996369	+	0.0851447i	$0.972865\pi$
$488$	−0.0902975	−	0.0241951i	−0.00408757	−	0.00109526i
$489$		0			0
$490$	0.889421	−	15.7815i	0.0401799	−	0.712937i
$491$	−7.22040	−	4.16870i	−0.325852	−	0.188131i	0.328146	−	0.944627i	$-0.393576\pi$
$491$	−7.22040	−	4.16870i	−0.325852	−	0.188131i	−0.653998	+	0.756496i	$0.726910\pi$
$492$		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
$497$	−0.879533	+	31.2369i	−0.0394524	+	1.40117i
$498$		0			0
$499$	−6.61818	+	6.61818i	−0.296270	+	0.296270i	−0.839551	−	0.543281i	$-0.817182\pi$
$499$	−6.61818	+	6.61818i	−0.296270	+	0.296270i	0.543281	+	0.839551i	$0.317182\pi$
$500$	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	$-0.716616\pi$
$503$	−6.07077	+	3.50496i	−0.270682	+	0.156278i	0.358515	+	0.933524i	$0.383283\pi$
$504$		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	$-0.537641\pi$
$509$	6.23491	−	1.67064i	0.276357	−	0.0740498i	0.394336	+	0.918966i	$0.370975\pi$
$510$		0			0
$511$	−36.1184	−	22.2313i	−1.59778	−	0.983457i
$512$	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
$518$	17.2868	−	16.3400i	0.759539	−	0.717938i
$519$		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	−0.998530	−	0.0541990i	$-0.982739\pi$
$523$	−35.3268	−	20.3959i	−1.54473	−	0.891852i	−0.546203	−	0.837653i	$-0.683927\pi$
$524$	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
$539$	9.11018	−	8.13810i	0.392403	−	0.350533i
$540$		0			0
$541$	−14.4412	−	14.4412i	−0.620878	−	0.620878i	0.324878	−	0.945756i	$-0.394677\pi$
$541$	−14.4412	−	14.4412i	−0.620878	−	0.620878i	−0.945756	+	0.324878i	$0.894677\pi$
$542$	−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
$553$	2.16253	+	9.08637i	0.0919600	+	0.386392i
$554$	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	0.798420	−	0.602100i	$-0.205669\pi$
$557$	42.2673	−	11.3255i	1.79092	−	0.479876i	0.992503	+	0.122224i	$0.0390027\pi$
$558$		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	$-0.130806\pi$
$563$	2.66750	+	4.62024i	0.112422	+	0.194720i	−0.804325	+	0.594190i	$0.797473\pi$
$564$		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	0.129606	−	0.991566i	$-0.458629\pi$
$569$	−15.8463	−	9.14887i	−0.664312	−	0.383541i	−0.793918	+	0.608025i	$0.791962\pi$
$570$		0			0
$571$		−	33.5009i		−	1.40197i	−0.713176	−	0.700985i	$-0.752744\pi$
$571$		−	33.5009i		−	1.40197i	0.713176	−	0.700985i	$-0.247256\pi$
$572$	−0.725200	+	1.16637i	−0.0303221	+	0.0487684i
$573$		0			0
$574$	9.19089	−	8.68749i	0.383620	−	0.362609i
$575$	5.00891	−	8.67568i	0.208886	−	0.361801i
$576$		0			0
$577$	−8.55149	−	8.55149i	−0.356003	−	0.356003i	0.506334	−	0.862337i	$-0.331000\pi$
$577$	−8.55149	−	8.55149i	−0.356003	−	0.356003i	−0.862337	+	0.506334i	$0.831000\pi$
$578$	−12.6056	−	3.37767i	−0.524325	−	0.140493i
$579$		0			0
$580$	0.774444	−	0.774444i	0.0321570	−	0.0321570i
$581$	−21.2632	+	34.5455i	−0.882146	+	1.43319i
$582$		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	$-0.943399\pi$
$587$	−42.3546	+	11.3489i	−1.74816	+	0.468419i	−0.763929	+	0.645300i	$0.776732\pi$
$588$		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	0.232973	−	0.972483i	$-0.425155\pi$
$593$	29.3548	−	29.3548i	1.20546	−	1.20546i	0.972483	−	0.232973i	$-0.0748454\pi$
$594$		0			0
$595$	−11.5084	−	0.324040i	−0.471798	−	0.0132843i
$596$	−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	$-0.362438\pi$
$601$	−3.87707	−	2.23843i	−0.158149	−	0.0913074i	−0.576986	+	0.816754i	$0.695771\pi$
$602$	−7.84743	+	12.7494i	−0.319837	+	0.519627i
$603$		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	$-0.757449\pi$
$607$	−12.0061	+	6.93170i	−0.487311	+	0.281349i	0.236147	+	0.971717i	$0.424115\pi$
$608$	−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	0.999960	−	0.00893943i	$-0.00284555\pi$
$613$	3.20626	+	11.9659i	0.129500	+	0.483299i	−0.870461	+	0.492238i	$0.836179\pi$
$614$	−6.35722	−	3.67034i	−0.256557	−	0.148123i
$615$		0			0
$616$	3.50297	−	11.7409i	0.141139	−	0.473053i
$617$	−4.24013	−	1.13614i	−0.170701	−	0.0457392i	0.172456	−	0.985017i	$-0.444830\pi$
$617$	−4.24013	−	1.13614i	−0.170701	−	0.0457392i	−0.343157	+	0.939278i	$0.611496\pi$
$618$		0			0
$619$	3.42700	−	3.42700i	0.137743	−	0.137743i	−0.634873	−	0.772616i	$-0.718948\pi$
$619$	3.42700	−	3.42700i	0.137743	−	0.137743i	0.772616	+	0.634873i	$0.218948\pi$
$620$	−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	−0.639081	−	0.769139i	$-0.720685\pi$
$631$	7.50951	−	28.0259i	0.298949	−	1.11569i	0.938030	−	0.346554i	$-0.112648\pi$
$632$	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
$637$	19.3616	−	16.1904i	0.767135	−	0.641486i
$638$	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	−0.964332	−	0.264696i	$-0.914728\pi$
$641$	−30.8187	+	17.7932i	−1.21726	+	0.702788i	−0.252932	+	0.967484i	$0.581395\pi$
$642$		0			0
$643$	1.54772	−	5.77618i	0.0610362	−	0.227790i	−0.928669	−	0.370909i	$-0.879046\pi$
$643$	1.54772	−	5.77618i	0.0610362	−	0.227790i	0.989706	+	0.143118i	$0.0457129\pi$
$644$	0.495857	+	2.08346i	0.0195395	+	0.0820999i
$645$		0			0
$646$	3.21739	+	5.57269i	0.126587	+	0.219255i
$647$	8.50730	−	14.7351i	0.334456	−	0.579296i	−0.648924	−	0.760853i	$-0.724781\pi$
$647$	8.50730	−	14.7351i	0.334456	−	0.579296i	0.983380	+	0.181558i	$0.0581140\pi$
$648$		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	−0.944049	−	0.329805i	$-0.893017\pi$
$653$	−4.76337	+	8.25040i	−0.186405	+	0.322863i	0.757644	+	0.652668i	$0.226350\pi$
$654$		0			0
$655$	−7.79881	+	7.79881i	−0.304725	+	0.304725i
$656$	3.64571	−	13.6060i	0.142341	−	0.531223i
$657$		0			0
$658$	9.34211	−	31.3119i	0.364193	−	1.22066i
$659$	14.3837	+	24.9132i	0.560308	+	0.970482i	0.997469	+	0.0710991i	$0.0226507\pi$
$659$	14.3837	+	24.9132i	0.560308	+	0.970482i	−0.437161	+	0.899383i	$0.644016\pi$
$660$		0			0
$661$	5.58403	+	20.8399i	0.217193	+	0.810577i	0.985383	+	0.170354i	$0.0544912\pi$
$661$	5.58403	+	20.8399i	0.217193	+	0.810577i	−0.768189	+	0.640223i	$0.778842\pi$
$662$		−	35.0561i		−	1.36250i
$663$		0			0
$664$			40.6864i			1.57894i
$665$	−4.14772	−	4.38806i	−0.160842	−	0.170162i
$666$		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	0.891550	−	0.452923i	$-0.149619\pi$
$673$	24.5175	+	14.1552i	0.945082	+	0.545643i	0.0535322	+	0.998566i	$0.482952\pi$
$674$	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
$679$	−25.2241	−	0.710231i	−0.968013	−	0.0272562i
$680$	−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	0.734966	+	0.678104i	$0.237198\pi$
$683$	−6.28752	+	23.4653i	−0.240585	+	0.897876i	−0.975551	+	0.219772i	$0.929469\pi$
$684$		0			0
$685$	−27.3377	+	15.7834i	−1.04452	+	0.603053i
$686$	15.7577	−	22.6399i	0.601633	−	0.864395i
$687$		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	$-0.448062\pi$
$691$	20.9371	−	5.61007i	0.796483	−	0.213417i	0.634039	+	0.773301i	$0.281396\pi$
$692$	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
$700$	1.13378	−	1.07168i	0.0428527	−	0.0405056i
$701$			33.2903i			1.25736i	0.777665	+	0.628678i	$0.216404\pi$
$701$			33.2903i			1.25736i	−0.777665	+	0.628678i	$0.783596\pi$
$702$		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
$707$	−34.2000	−	10.2038i	−1.28622	−	0.383754i
$708$		0			0
$709$	0.389951	−	1.45532i	0.0146449	−	0.0546556i	−0.958217	−	0.286043i	$-0.907660\pi$
$709$	0.389951	−	1.45532i	0.0146449	−	0.0546556i	0.972862	+	0.231388i	$0.0743266\pi$
$710$	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	−0.993032	−	0.117841i	$-0.962403\pi$
$719$	−16.0502	−	27.7997i	−0.598570	−	1.03675i	0.394463	−	0.918912i	$-0.370931\pi$
$720$		0			0
$721$	5.47252	+	22.9941i	0.203807	+	0.856345i
$722$	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	$-0.715404\pi$
$727$	−33.7702			−1.25247			−0.626233	+	0.779636i	$0.715404\pi$
$728$	8.02586	−	24.0085i	0.297458	−	0.889813i
$729$		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	$-0.292468\pi$
$733$	−5.09323	−	5.09323i	−0.188123	−	0.188123i	−0.794884	+	0.606761i	$0.792468\pi$
$734$	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	0.171324	−	0.985215i	$-0.445196\pi$
$739$	22.0821	−	5.91687i	0.812302	−	0.217656i	0.640978	+	0.767559i	$0.278529\pi$
$740$	−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	0.997557	−	0.0698588i	$-0.0222549\pi$
$743$	2.69085	+	10.0424i	0.0987179	+	0.368420i	−0.898839	+	0.438279i	$0.855588\pi$
$744$		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
$749$	−33.0791	−	9.86937i	−1.20868	−	0.360619i
$750$		0			0
$751$	−35.7335	−	20.6307i	−1.30393	−	0.752827i	−0.322858	−	0.946448i	$-0.604643\pi$
$751$	−35.7335	−	20.6307i	−1.30393	−	0.752827i	−0.981076	+	0.193621i	$0.937977\pi$
$752$	−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	−0.637714	−	0.770273i	$-0.720120\pi$
$757$	9.58077	−	16.5944i	0.348219	−	0.603133i	0.985933	+	0.167140i	$0.0534532\pi$
$758$	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	$-0.317531\pi$
$761$	16.3307	+	4.37578i	0.591986	+	0.158622i	0.0496251	+	0.998768i	$0.484197\pi$
$762$		0			0
$763$	44.7120	+	27.5208i	1.61868	+	0.996320i
$764$	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	$-0.240628\pi$
$769$	47.1631	−	12.6373i	1.70074	−	0.455713i	0.973127	+	0.230271i	$0.0739613\pi$
$770$	−10.4217	−	0.293442i	−0.375571	−	0.0105749i
$771$		0			0
$772$	0.244769	−	0.244769i	0.00880943	−	0.00880943i
$773$	2.27204	−	8.47936i	0.0817195	−	0.304981i	−0.912953	−	0.408064i	$-0.866204\pi$
$773$	2.27204	−	8.47936i	0.0817195	−	0.304981i	0.994673	+	0.103083i	$0.0328707\pi$
$774$		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
$784$	1.72872	−	30.6737i	0.0617400	−	1.09549i
$785$	−20.9051	+	20.9051i	−0.746136	+	0.746136i
$786$		0			0
$787$	−21.5745	−	5.78087i	−0.769047	−	0.206066i	−0.147097	−	0.989122i	$-0.546993\pi$
$787$	−21.5745	−	5.78087i	−0.769047	−	0.206066i	−0.621951	+	0.783056i	$0.713660\pi$
$788$	−0.805178	−	0.805178i	−0.0286833	−	0.0286833i
$789$		0			0
$790$	3.98580	−	6.90360i	0.141808	−	0.245619i
$791$	21.5467	−	20.3666i	0.766113	−	0.724152i
$792$		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	0.999994	+	0.00343670i	$0.00109394\pi$
$797$	14.1995	+	24.5943i	0.502973	+	0.871175i	−0.497021	+	0.867739i	$0.665573\pi$
$798$		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	−0.423700	−	0.905803i	$-0.639269\pi$
$809$	16.2864	−	28.2088i	0.572598	−	0.991770i	0.996298	−	0.0859669i	$-0.0273979\pi$
$810$		0			0
$811$	23.2549	+	23.2549i	0.816589	+	0.816589i	0.985612	−	0.169023i	$-0.0540614\pi$
$811$	23.2549	+	23.2549i	0.816589	+	0.816589i	−0.169023	+	0.985612i	$0.554061\pi$
$812$	1.85934	−	0.442517i	0.0652500	−	0.0155293i
$813$		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	−0.999921	−	0.0125363i	$-0.996009\pi$
$821$	−4.01809	−	14.9957i	−0.140232	−	0.523354i	0.859689	−	0.510817i	$-0.170657\pi$
$822$		0			0
$823$	−7.93891	+	4.58353i	−0.276733	+	0.159772i	−0.631944	−	0.775014i	$-0.717743\pi$
$823$	−7.93891	+	4.58353i	−0.276733	+	0.159772i	0.355210	+	0.934786i	$0.384409\pi$
$824$	16.7635	+	16.7635i	0.583983	+	0.583983i
$825$		0			0
$826$	−3.84102	+	0.914151i	−0.133646	+	0.0318074i
$827$	−23.9115	−	23.9115i	−0.831483	−	0.831483i	0.156237	−	0.987720i	$-0.450064\pi$
$827$	−23.9115	−	23.9115i	−0.831483	−	0.831483i	−0.987720	+	0.156237i	$0.950064\pi$
$828$		0			0
$829$	0.903774	−	1.56538i	0.0313894	−	0.0543680i	−0.849904	−	0.526938i	$-0.823340\pi$
$829$	0.903774	−	1.56538i	0.0313894	−	0.0543680i	0.881293	+	0.472570i	$0.156673\pi$
$830$	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	$-0.316997\pi$
$839$	17.2364	+	4.61847i	0.595066	+	0.159447i	0.0512985	+	0.998683i	$0.483664\pi$
$840$		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
$847$	14.4570	+	15.2947i	0.496747	+	0.525531i
$848$	−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	$-0.639981\pi$
$853$	13.9934	−	13.9934i	0.479126	−	0.479126i	0.904852	+	0.425726i	$0.139981\pi$
$854$	−0.0727645	+	0.118218i	−0.00248995	+	0.00404532i
$855$		0			0
$856$	−33.4436	+	8.96118i	−1.14308	+	0.306287i
$857$	39.0639			1.33440			0.667199	−	0.744879i	$-0.267493\pi$
$857$	39.0639			1.33440			0.667199	+	0.744879i	$0.267493\pi$
$858$		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	−0.373635	−	0.927576i	$-0.621889\pi$
$863$	16.2731	−	16.2731i	0.553941	−	0.553941i	0.927576	+	0.373635i	$0.121889\pi$
$864$		0			0
$865$	−8.55627	+	31.9324i	−0.290922	+	1.08574i
$866$	35.2351	−	35.2351i	1.19734	−	1.19734i
$867$		0			0
$868$	0.0304308	−	1.08076i	0.00103289	−	0.0366835i
$869$	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
$875$	26.3082	+	16.1930i	0.889379	+	0.547424i
$876$		0			0
$877$	43.5370	+	11.6657i	1.47014	+	0.393923i	0.902980	−	0.429683i	$-0.141375\pi$
$877$	43.5370	+	11.6657i	1.47014	+	0.393923i	0.567162	+	0.823607i	$0.308041\pi$
$878$	−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	$-0.875041\pi$
$881$	−3.87806	+	6.71699i	−0.130655	+	0.226301i	0.793274	+	0.608865i	$0.208375\pi$
$882$		0			0
$883$		−	50.1556i		−	1.68787i	−0.536446	−	0.843935i	$-0.680234\pi$
$883$		−	50.1556i		−	1.68787i	0.536446	−	0.843935i	$-0.319766\pi$
$884$	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	$-0.196984\pi$
$887$	21.4271	+	12.3709i	0.719450	+	0.415375i	−0.0951001	+	0.995468i	$0.530317\pi$
$888$		0			0
$889$	3.20586	−	10.7451i	0.107521	−	0.360378i
$890$	−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	−0.123706	−	0.992319i	$-0.539478\pi$
$907$	−31.4697	−	18.1690i	−1.04493	−	0.603292i	−0.921226	+	0.389027i	$0.872811\pi$
$908$	1.25879	+	4.69786i	0.0417743	+	0.155904i
$909$		0			0
$910$	−21.5009	−	1.30919i	−0.712748	−	0.0433991i
$911$	−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
$917$	−18.7239	+	4.45623i	−0.618318	+	0.147158i
$918$		0			0
$919$	12.6196	+	21.8577i	0.416281	+	0.721020i	0.995562	−	0.0941078i	$-0.0299998\pi$
$919$	12.6196	+	21.8577i	0.416281	+	0.721020i	−0.579281	+	0.815128i	$0.696666\pi$
$920$	−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	$-0.905199\pi$
$929$	0.568291	−	2.12089i	0.0186450	−	0.0695842i	0.974622	+	0.223859i	$0.0718655\pi$
$930$		0			0
$931$	−2.15016	−	10.3153i	−0.0704685	−	0.338071i
$932$	−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	$0.834773\pi$
$938$	13.1969	+	13.9616i	0.430893	+	0.455861i
$939$		0			0
$940$	−2.37655	+	1.37210i	−0.0775146	+	0.0447531i
$941$	−26.4335	−	26.4335i	−0.861707	−	0.861707i	0.129829	−	0.991536i	$-0.458557\pi$
$941$	−26.4335	−	26.4335i	−0.861707	−	0.861707i	−0.991536	+	0.129829i	$0.958557\pi$
$942$		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	−0.642044	−	0.766667i	$-0.721914\pi$
$947$	−25.0722	+	6.71808i	−0.814738	+	0.218308i	−0.172693	+	0.984976i	$0.555247\pi$
$948$		0			0
$949$	−30.5182	+	49.0837i	−0.990662	+	1.59333i
$950$		−	6.05644i		−	0.196497i
$951$		0			0
$952$	−20.1433	−	0.567171i	−0.652848	−	0.0183821i
$953$	−24.6170	+	14.2126i	−0.797422	+	0.460392i	−0.842569	−	0.538589i	$-0.818958\pi$
$953$	−24.6170	+	14.2126i	−0.797422	+	0.460392i	0.0451471	+	0.998980i	$0.485624\pi$
$954$		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
$959$	−55.0651	−	1.55046i	−1.77815	−	0.0500669i
$960$		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	−0.942922	−	0.333014i	$-0.891935\pi$
$967$	−18.9661	+	18.9661i	−0.609908	+	0.609908i	0.333014	+	0.942922i	$0.391935\pi$
$968$	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	$-0.808270\pi$
$971$	−23.2259	+	13.4095i	−0.745355	+	0.430331i	0.0786584	+	0.996902i	$0.474936\pi$
$972$		0			0
$973$	34.1000	+	36.0759i	1.09320	+	1.15654i
$974$			61.8168i			1.98074i
$975$		0			0
$976$			0.154611i			0.00494899i
$977$	8.48807	+	31.6779i	0.271557	+	1.01347i	0.958113	+	0.286389i	$0.0924549\pi$
$977$	8.48807	+	31.6779i	0.271557	+	1.01347i	−0.686556	+	0.727077i	$0.740878\pi$
$978$		0			0
$979$	−6.81848	−	11.8099i	−0.217919	−	0.377448i
$980$	−2.26783	+	0.472714i	−0.0724432	+	0.0151003i
$981$		0			0
$982$	−3.21392	+	11.9945i	−0.102560	+	0.382760i
$983$	21.2566	−	21.2566i	0.677982	−	0.677982i	−0.281561	−	0.959543i	$-0.590852\pi$
$983$	21.2566	−	21.2566i	0.677982	−	0.677982i	0.959543	+	0.281561i	$0.0908523\pi$
$984$		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	−0.436573	−	0.899669i	$-0.643808\pi$
$991$	17.6556	−	30.5804i	0.560849	−	0.971420i	0.997423	−	0.0717510i	$-0.0228587\pi$
$992$	−1.15086	−	1.99334i	−0.0365397	−	0.0632886i
$993$		0			0
$994$	45.2778	−	10.7760i	1.43612	−	0.341793i
$995$	0.532226	−	1.98630i	0.0168727	−	0.0629698i
$996$		0			0
$997$	−4.50099	+	2.59865i	−0.142548	+	0.0822999i	−0.569578	−	0.821938i	$-0.692893\pi$
$997$	−4.50099	+	2.59865i	−0.142548	+	0.0822999i	0.427030	+	0.904237i	$0.359560\pi$
$998$	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.f.370.2		32
3.2	odd	2		273.2.by.c.97.7	yes	32
7.6	odd	2		819.2.fm.e.370.2		32
13.11	odd	12		819.2.fm.e.622.2		32
21.20	even	2		273.2.by.d.97.7	yes	32
39.11	even	12		273.2.by.d.76.7	yes	32
91.76	even	12	inner	819.2.fm.f.622.2		32
273.167	odd	12		273.2.by.c.76.7	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.7	✓	32	273.167	odd	12
273.2.by.c.97.7	yes	32	3.2	odd	2
273.2.by.d.76.7	yes	32	39.11	even	12
273.2.by.d.97.7	yes	32	21.20	even	2
819.2.fm.e.370.2		32	7.6	odd	2
819.2.fm.e.622.2		32	13.11	odd	12
819.2.fm.f.370.2		32	1.1	even	1	trivial
819.2.fm.f.622.2		32	91.76	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.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.385482 - 1.43864i) q^{2} +(-0.189037 + 0.109141i) q^{4} +(-1.07205 - 1.07205i) q^{5} +(-0.612570 - 2.57386i) q^{7} +(-1.87643 - 1.87643i) q^{8} +O(q^{10})\)	\(q+(-0.385482 - 1.43864i) q^{2} +(-0.189037 + 0.109141i) q^{4} +(-1.07205 - 1.07205i) q^{5} +(-0.612570 - 2.57386i) q^{7} +(-1.87643 - 1.87643i) q^{8} +(-1.12904 + 1.95556i) q^{10} +(-1.68564 + 0.451666i) q^{11} +(-3.51131 + 0.818944i) q^{13} +(-3.46672 + 1.87345i) q^{14} +(-2.19446 + 3.80091i) q^{16} +(1.43508 + 2.48563i) q^{17} +(-0.389597 + 1.45400i) q^{19} +(0.319663 + 0.0856533i) q^{20} +(1.29957 + 2.25092i) q^{22} +(3.21155 + 1.85419i) q^{23} -2.70140i q^{25} +(2.53172 + 4.73583i) q^{26} +(0.396712 + 0.419699i) q^{28} +(1.65473 - 2.86608i) q^{29} +(-1.32380 - 1.32380i) q^{31} +(1.18757 + 0.318208i) q^{32} +(3.02273 - 3.02273i) q^{34} +(-2.10261 + 3.41602i) q^{35} +(-5.83082 + 1.56236i) q^{37} +2.24196 q^{38} +4.02327i q^{40} +(-3.10007 + 0.830662i) q^{41} +(3.29020 - 1.89960i) q^{43} +(0.269354 - 0.269354i) q^{44} +(1.42951 - 5.33502i) q^{46} +(-5.86346 + 5.86346i) q^{47} +(-6.24951 + 3.15334i) q^{49} +(-3.88635 + 1.04134i) q^{50} +(0.574389 - 0.538038i) q^{52} +1.37219 q^{53} +(2.29131 + 1.32289i) q^{55} +(-3.68022 + 5.97912i) q^{56} +(-4.76112 - 1.27574i) q^{58} +(0.967827 + 0.259328i) q^{59} +(0.0305081 - 0.0176138i) q^{61} +(-1.39417 + 2.41477i) q^{62} +6.94669i q^{64} +(4.64227 + 2.88636i) q^{65} +(-1.26183 - 4.70921i) q^{67} +(-0.542567 - 0.313251i) q^{68} +(5.72495 + 1.70808i) q^{70} +(-11.4087 - 3.05695i) q^{71} +(11.3351 - 11.3351i) q^{73} +(4.49535 + 7.78618i) q^{74} +(-0.0850419 - 0.317381i) q^{76} +(2.19510 + 4.06193i) q^{77} -3.53025 q^{79} +(6.42736 - 1.72221i) q^{80} +(2.39005 + 4.13968i) q^{82} +(-10.8414 - 10.8414i) q^{83} +(1.12625 - 4.20321i) q^{85} +(-4.00116 - 4.00116i) q^{86} +(4.01051 + 2.31547i) q^{88} +(2.02252 + 7.54814i) q^{89} +(4.25878 + 8.53597i) q^{91} -0.809469 q^{92} +(10.6957 + 6.17514i) q^{94} +(1.97643 - 1.14109i) q^{95} +(2.46851 - 9.21262i) q^{97} +(6.94560 + 7.77524i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 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 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * 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 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

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