LMFDB - Embedded newform 819.2.fm.f.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.f.370.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385482 + 1.43864i) q^{2} +(-0.189037 - 0.109141i) q^{4} +(-1.07205 + 1.07205i) q^{5} +(-0.612570 + 2.57386i) q^{7} +(-1.87643 + 1.87643i) q^{8} +O(q^{10})$	\(q+(-0.385482 + 1.43864i) q^{2} +(-0.189037 - 0.109141i) q^{4} +(-1.07205 + 1.07205i) q^{5} +(-0.612570 + 2.57386i) q^{7} +(-1.87643 + 1.87643i) q^{8} +(-1.12904 - 1.95556i) q^{10} +(-1.68564 - 0.451666i) q^{11} +(-3.51131 - 0.818944i) q^{13} +(-3.46672 - 1.87345i) q^{14} +(-2.19446 - 3.80091i) q^{16} +(1.43508 - 2.48563i) q^{17} +(-0.389597 - 1.45400i) q^{19} +(0.319663 - 0.0856533i) q^{20} +(1.29957 - 2.25092i) q^{22} +(3.21155 - 1.85419i) q^{23} +2.70140i q^{25} +(2.53172 - 4.73583i) q^{26} +(0.396712 - 0.419699i) q^{28} +(1.65473 + 2.86608i) q^{29} +(-1.32380 + 1.32380i) q^{31} +(1.18757 - 0.318208i) q^{32} +(3.02273 + 3.02273i) q^{34} +(-2.10261 - 3.41602i) q^{35} +(-5.83082 - 1.56236i) q^{37} +2.24196 q^{38} -4.02327i q^{40} +(-3.10007 - 0.830662i) q^{41} +(3.29020 + 1.89960i) q^{43} +(0.269354 + 0.269354i) q^{44} +(1.42951 + 5.33502i) q^{46} +(-5.86346 - 5.86346i) q^{47} +(-6.24951 - 3.15334i) q^{49} +(-3.88635 - 1.04134i) q^{50} +(0.574389 + 0.538038i) q^{52} +1.37219 q^{53} +(2.29131 - 1.32289i) q^{55} +(-3.68022 - 5.97912i) q^{56} +(-4.76112 + 1.27574i) q^{58} +(0.967827 - 0.259328i) q^{59} +(0.0305081 + 0.0176138i) q^{61} +(-1.39417 - 2.41477i) q^{62} -6.94669i q^{64} +(4.64227 - 2.88636i) q^{65} +(-1.26183 + 4.70921i) q^{67} +(-0.542567 + 0.313251i) q^{68} +(5.72495 - 1.70808i) q^{70} +(-11.4087 + 3.05695i) q^{71} +(11.3351 + 11.3351i) q^{73} +(4.49535 - 7.78618i) q^{74} +(-0.0850419 + 0.317381i) q^{76} +(2.19510 - 4.06193i) q^{77} -3.53025 q^{79} +(6.42736 + 1.72221i) q^{80} +(2.39005 - 4.13968i) q^{82} +(-10.8414 + 10.8414i) q^{83} +(1.12625 + 4.20321i) q^{85} +(-4.00116 + 4.00116i) q^{86} +(4.01051 - 2.31547i) q^{88} +(2.02252 - 7.54814i) q^{89} +(4.25878 - 8.53597i) q^{91} -0.809469 q^{92} +(10.6957 - 6.17514i) q^{94} +(1.97643 + 1.14109i) q^{95} +(2.46851 + 9.21262i) q^{97} +(6.94560 - 7.77524i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

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

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	−0.904952	−	0.425515i	$-0.860093\pi$
$5$	−1.07205	+	1.07205i	−0.479437	+	0.479437i	0.425515	+	0.904952i	$0.360093\pi$
$6$		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	−0.00441837	−	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	−0.637847	−	0.770164i	$-0.720175\pi$
$17$	1.43508	−	2.48563i	0.348058	−	0.602854i	0.985904	+	0.167310i	$0.0535079\pi$
$18$		0			0
$19$	−0.389597	−	1.45400i	−0.0893798	−	0.333570i	0.906728	−	0.421717i	$-0.138572\pi$
$19$	−0.389597	−	1.45400i	−0.0893798	−	0.333570i	−0.996108	+	0.0881466i	$0.971906\pi$
$20$	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
$28$	0.396712	−	0.419699i	0.0749714	−	0.0793157i
$29$	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	−0.815922	−	0.578161i	$-0.803770\pi$
$31$	−1.32380	+	1.32380i	−0.237761	+	0.237761i	0.578161	+	0.815922i	$0.303770\pi$
$32$	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	−0.254581	−	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	0.00848433	−	0.999964i	$-0.497299\pi$
$41$	−3.10007	−	0.830662i	−0.484150	−	0.129728i	−0.492634	+	0.870236i	$0.663966\pi$
$42$		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	0.135504	−	0.990777i	$-0.456735\pi$
$47$	−5.86346	−	5.86346i	−0.855273	−	0.855273i	−0.990777	+	0.135504i	$0.956735\pi$
$48$		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	−0.195268	−	0.980750i	$-0.562558\pi$
$59$	0.967827	−	0.259328i	0.126000	−	0.0337617i	0.321268	+	0.946988i	$0.395891\pi$
$60$		0			0
$61$	0.0305081	+	0.0176138i	0.00390616	+	0.00225522i	0.501952	−	0.864896i	$-0.332615\pi$
$61$	0.0305081	+	0.0176138i	0.00390616	+	0.00225522i	−0.498046	+	0.867151i	$0.665949\pi$
$62$	−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
$70$	5.72495	−	1.70808i	0.684262	−	0.204154i
$71$	−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	$0.137413\pi$
$73$	11.3351	+	11.3351i	1.32667	+	1.32667i	0.418410	+	0.908258i	$0.362587\pi$
$74$	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	$0.568302\pi$
$83$	−10.8414	+	10.8414i	−1.19000	+	1.19000i	−0.977066	+	0.212936i	$0.931698\pi$
$84$		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	$-0.780741\pi$
$89$	2.02252	−	7.54814i	0.214386	−	0.800101i	0.986382	−	0.164473i	$-0.0525922\pi$
$90$		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	0.970465	+	0.241244i	$0.0775554\pi$
$97$	2.46851	+	9.21262i	0.250640	+	0.935400i	−0.719825	+	0.694156i	$0.755778\pi$
$98$	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	0.977585	+	0.210540i	$0.0675221\pi$
$101$	6.74473	+	11.6822i	0.671125	+	1.16242i	−0.306460	+	0.951883i	$0.599145\pi$
$102$		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	0.987416	+	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
$112$	11.1273	−	3.31990i	1.05143	−	0.313701i
$113$	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
$119$	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	−0.328235	−	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	$0.102942\pi$
$131$			7.27464i			0.635589i	−0.948160	+	0.317794i	$0.897058\pi$
$132$		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	0.671706	+	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	−0.386278	−	0.922382i	$-0.626239\pi$
$139$	−16.2490	−	9.38137i	−1.37822	−	0.795718i	−0.991946	+	0.126665i	$0.959573\pi$
$140$	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	−0.187077	−	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
$154$	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	$0.283836\pi$
$157$			19.5001i			1.55628i	−0.628093	+	0.778138i	$0.716164\pi$
$158$	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	0.932257	+	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	$0.184089\pi$
$167$	−2.08221	+	7.77093i	−0.161127	+	0.601333i	−0.998503	+	0.0547052i	$0.982578\pi$
$168$		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	$0.477701\pi$
$173$	−10.9025	+	18.8837i	−0.828903	+	1.43570i	−0.898899	+	0.438155i	$0.855632\pi$
$174$		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	−0.780404	−	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	$-0.668722\pi$
$181$	−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	−0.880927	−	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	−0.840987	−	0.541055i	$-0.818025\pi$
$199$	0.678170	−	1.17462i	0.0480742	−	0.0832670i	0.889061	+	0.457788i	$0.151358\pi$
$200$	−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	0.877001	+	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
$217$	−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	0.684916	−	0.728622i	$-0.259839\pi$
$223$	13.6453	+	3.65626i	0.913760	+	0.244841i	0.228844	+	0.973463i	$0.426506\pi$
$224$	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	0.841673	+	0.539988i	$0.181571\pi$
$227$	5.76681	+	21.5220i	0.382757	+	1.42847i	−0.458916	+	0.888480i	$0.651762\pi$
$228$		0			0
$229$	−8.69387	−	8.69387i	−0.574507	−	0.574507i	0.358877	−	0.933385i	$-0.383160\pi$
$229$	−8.69387	−	8.69387i	−0.574507	−	0.574507i	−0.933385	+	0.358877i	$0.883160\pi$
$230$	−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
$238$	−9.63172	+	5.92845i	−0.624332	+	0.384284i
$239$	−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	0.512391	−	0.858752i	$-0.328760\pi$
$241$	21.5089	−	5.76329i	1.38551	−	0.371246i	0.873120	+	0.487506i	$0.162093\pi$
$242$	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	−0.251921	+	0.967748i	$0.581062\pi$
$251$	−15.2735	+	26.4545i	−0.964055	+	1.66979i	−0.712134	+	0.702044i	$0.752271\pi$
$252$		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	0.586760	−	0.809761i	$-0.300403\pi$
$257$	−6.53903	−	11.3259i	−0.407894	−	0.706493i	−0.994654	+	0.103268i	$0.967070\pi$
$258$		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
$266$	−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	0.774412	−	0.632681i	$-0.218046\pi$
$269$	10.0654	+	5.81128i	0.613700	+	0.354320i	−0.160712	+	0.987001i	$0.551379\pi$
$270$		0			0
$271$	−5.43020	+	20.2658i	−0.329861	+	1.23106i	0.579473	+	0.814991i	$0.303258\pi$
$271$	−5.43020	+	20.2658i	−0.329861	+	1.23106i	−0.909334	+	0.416067i	$0.863408\pi$
$272$	−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
$280$	10.3553	+	2.46453i	0.618849	+	0.147284i
$281$	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	0.934295	−	0.356500i	$-0.116030\pi$
$283$	2.66486	+	4.61567i	0.158410	+	0.274373i	−0.775886	+	0.630873i	$0.782697\pi$
$284$	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	0.409018	−	0.912526i	$-0.365871\pi$
$293$	20.8745	−	5.59331i	1.21950	−	0.326764i	0.810483	+	0.585762i	$0.199205\pi$
$294$		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	0.799530	−	0.600626i	$-0.205082\pi$
$307$	3.48509	+	3.48509i	0.198904	+	0.198904i	−0.600626	+	0.799530i	$0.705082\pi$
$308$	−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	$0.202476\pi$
$313$			21.0200i			1.18812i	−0.804421	+	0.594060i	$0.797524\pi$
$314$	−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
$322$	−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	0.427444	−	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
$343$	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	−0.543181	−	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	−0.943678	−	0.330865i	$-0.892660\pi$
$349$	0.728645	−	2.71934i	0.0390035	−	0.145563i	0.982682	+	0.185302i	$0.0593263\pi$
$350$	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	0.953775	−	0.300521i	$-0.0971605\pi$
$353$	30.6157	+	8.20345i	1.62951	+	0.436625i	0.675733	+	0.737146i	$0.263827\pi$
$354$		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
$364$	−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	−0.405459	−	0.914113i	$-0.632888\pi$
$367$	3.51454	−	2.02912i	0.183457	−	0.105919i	0.588916	+	0.808194i	$0.299555\pi$
$368$	−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	−0.704222	−	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	0.972937	−	0.231072i	$-0.0742234\pi$
$383$	0.289889	+	1.08188i	0.0148126	+	0.0552815i	−0.958124	+	0.286354i	$0.907557\pi$
$384$		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	$-0.980089\pi$
$389$		−	2.46580i		−	0.125021i	0.998044	−	0.0625106i	$-0.0199107\pi$
$390$		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	0.106152	−	0.994350i	$-0.466147\pi$
$397$	13.8529	−	3.71187i	0.695257	−	0.186294i	0.589105	+	0.808056i	$0.299480\pi$
$398$	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
$406$	−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	−0.687726	−	0.725970i	$-0.741391\pi$
$409$	−9.20429	−	34.3509i	−0.455123	−	1.69854i	0.232603	−	0.972572i	$-0.425276\pi$
$410$	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	0.152995	−	0.988227i	$-0.451108\pi$
$419$	22.2160	−	12.8264i	1.08532	−	0.626611i	0.932327	+	0.361616i	$0.117775\pi$
$420$		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
$427$	−0.0640239	+	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	−0.913586	−	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	$-0.536082\pi$
$433$	16.7283	−	28.9743i	0.803912	−	1.39242i	0.917023	−	0.398834i	$-0.130585\pi$
$434$	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	0.999359	−	0.0358007i	$-0.0113981\pi$
$439$	9.81984	+	17.0085i	0.468675	+	0.811769i	−0.530684	+	0.847570i	$0.678065\pi$
$440$	−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	0.957934	+	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
$455$	4.58538	+	13.7167i	0.214966	+	0.643047i
$456$		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	$-0.760752\pi$
$461$	−9.43198	−	35.2006i	−0.439291	−	1.63946i	0.291293	−	0.956634i	$-0.405915\pi$
$462$		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	$-0.680952\pi$
$467$	−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	−0.286634	−	0.958040i	$-0.592536\pi$
$479$	9.64340	−	35.9897i	0.440618	−	1.64441i	0.727252	−	0.686370i	$-0.240797\pi$
$480$		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
$490$	0.889421	+	15.7815i	0.0401799	+	0.712937i
$491$	−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
$497$	−0.879533	−	31.2369i	−0.0394524	−	1.40117i
$498$		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	0.358515	−	0.933524i	$-0.383283\pi$
$503$	−6.07077	−	3.50496i	−0.270682	−	0.156278i	−0.629198	+	0.777245i	$0.716616\pi$
$504$		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	0.394336	−	0.918966i	$-0.370975\pi$
$509$	6.23491	+	1.67064i	0.276357	+	0.0740498i	−0.117978	+	0.993016i	$0.537641\pi$
$510$		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	$-0.906379\pi$
$521$		−	13.2340i		−	0.579793i	0.957058	−	0.289896i	$-0.0936208\pi$
$522$		0			0
$523$	−35.3268	+	20.3959i	−1.54473	+	0.891852i	−0.546203	+	0.837653i	$0.683927\pi$
$523$	−35.3268	+	20.3959i	−1.54473	+	0.891852i	−0.998530	+	0.0541990i	$0.982739\pi$
$524$	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	−0.945756	−	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
$553$	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	0.992503	−	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	−0.804325	−	0.594190i	$-0.797473\pi$
$563$	2.66750	−	4.62024i	0.112422	−	0.194720i	0.916746	+	0.399470i	$0.130806\pi$
$564$		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
$574$	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	−0.862337	−	0.506334i	$-0.831000\pi$
$577$	−8.55149	+	8.55149i	−0.356003	+	0.356003i	0.506334	+	0.862337i	$0.331000\pi$
$578$	−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	−0.763929	−	0.645300i	$-0.776732\pi$
$587$	−42.3546	−	11.3489i	−1.74816	−	0.468419i	−0.984232	+	0.176881i	$0.943399\pi$
$588$		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	$0.0748454\pi$
$593$	29.3548	+	29.3548i	1.20546	+	1.20546i	0.232973	+	0.972483i	$0.425155\pi$
$594$		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	−0.576986	−	0.816754i	$-0.695771\pi$
$601$	−3.87707	+	2.23843i	−0.158149	+	0.0913074i	0.418837	+	0.908062i	$0.362438\pi$
$602$	−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	0.236147	−	0.971717i	$-0.424115\pi$
$607$	−12.0061	−	6.93170i	−0.487311	−	0.281349i	−0.723458	+	0.690368i	$0.757449\pi$
$608$	−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
$616$	3.50297	+	11.7409i	0.141139	+	0.473053i
$617$	−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	0.772616	−	0.634873i	$-0.218948\pi$
$619$	3.42700	+	3.42700i	0.137743	+	0.137743i	−0.634873	+	0.772616i	$0.718948\pi$
$620$	−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
$637$	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	−0.252932	−	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	0.989706	−	0.143118i	$-0.0457129\pi$
$643$	1.54772	+	5.77618i	0.0610362	+	0.227790i	−0.928669	+	0.370909i	$0.879046\pi$
$644$	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	0.983380	−	0.181558i	$-0.0581140\pi$
$647$	8.50730	+	14.7351i	0.334456	+	0.579296i	−0.648924	+	0.760853i	$0.724781\pi$
$648$		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
$658$	9.34211	+	31.3119i	0.364193	+	1.22066i
$659$	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	$-0.778842\pi$
$661$	5.58403	−	20.8399i	0.217193	−	0.810577i	0.985383	−	0.170354i	$-0.0544912\pi$
$662$			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	0.0535322	−	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	$-0.876394\pi$
$677$		−	19.7036i		−	0.757270i	0.925546	−	0.378635i	$-0.123606\pi$
$678$		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	−0.975551	−	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
$686$	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	0.634039	−	0.773301i	$-0.281396\pi$
$691$	20.9371	+	5.61007i	0.796483	+	0.213417i	0.162444	+	0.986718i	$0.448062\pi$
$692$	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	$-0.783596\pi$
$701$		−	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
$707$	−34.2000	+	10.2038i	−1.28622	+	0.383754i
$708$		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	$0.370931\pi$
$719$	−16.0502	+	27.7997i	−0.598570	+	1.03675i	−0.993032	+	0.117841i	$0.962403\pi$
$720$		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	−0.794884	−	0.606761i	$-0.792468\pi$
$733$	−5.09323	+	5.09323i	−0.188123	+	0.188123i	0.606761	+	0.794884i	$0.292468\pi$
$734$	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
$749$	−33.0791	+	9.86937i	−1.20868	+	0.360619i
$750$		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	0.0496251	−	0.998768i	$-0.484197\pi$
$761$	16.3307	−	4.37578i	0.591986	−	0.158622i	0.542361	+	0.840146i	$0.317531\pi$
$762$		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	0.973127	−	0.230271i	$-0.0739613\pi$
$769$	47.1631	+	12.6373i	1.70074	+	0.455713i	0.727617	+	0.685984i	$0.240628\pi$
$770$	−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	0.994673	−	0.103083i	$-0.0328707\pi$
$773$	2.27204	+	8.47936i	0.0817195	+	0.304981i	−0.912953	+	0.408064i	$0.866204\pi$
$774$		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	−0.621951	−	0.783056i	$-0.713660\pi$
$787$	−21.5745	+	5.78087i	−0.769047	+	0.206066i	−0.147097	+	0.989122i	$0.546993\pi$
$788$	−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	−0.497021	−	0.867739i	$-0.665573\pi$
$797$	14.1995	−	24.5943i	0.502973	−	0.871175i	0.999994	−	0.00343670i	$-0.00109394\pi$
$798$		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	−0.169023	−	0.985612i	$-0.554061\pi$
$811$	23.2549	−	23.2549i	0.816589	−	0.816589i	0.985612	+	0.169023i	$0.0540614\pi$
$812$	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	0.859689	+	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
$826$	−3.84102	−	0.914151i	−0.133646	−	0.0318074i
$827$	−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	0.881293	−	0.472570i	$-0.156673\pi$
$829$	0.903774	+	1.56538i	0.0313894	+	0.0543680i	−0.849904	+	0.526938i	$0.823340\pi$
$830$	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	0.0512985	−	0.998683i	$-0.483664\pi$
$839$	17.2364	−	4.61847i	0.595066	−	0.159447i	0.543767	+	0.839236i	$0.316997\pi$
$840$		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	0.904852	−	0.425726i	$-0.139981\pi$
$853$	13.9934	+	13.9934i	0.479126	+	0.479126i	−0.425726	+	0.904852i	$0.639981\pi$
$854$	−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	$-0.839992\pi$
$859$		−	28.2404i		−	0.963549i	0.876295	−	0.481775i	$-0.160008\pi$
$860$	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
$868$	0.0304308	+	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	0.567162	−	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	0.793274	−	0.608865i	$-0.208375\pi$
$881$	−3.87806	−	6.71699i	−0.130655	−	0.226301i	−0.923929	+	0.382563i	$0.875041\pi$
$882$		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	−0.0951001	−	0.995468i	$-0.530317\pi$
$887$	21.4271	−	12.3709i	0.719450	−	0.415375i	0.814550	+	0.580093i	$0.196984\pi$
$888$		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	−0.921226	−	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
$910$	−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	−0.579281	−	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	0.974622	−	0.223859i	$-0.0718655\pi$
$929$	0.568291	+	2.12089i	0.0186450	+	0.0695842i	−0.955977	+	0.293443i	$0.905199\pi$
$930$		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	$-0.834773\pi$
$937$		−	30.3704i		−	0.992157i	0.868278	−	0.496079i	$-0.165227\pi$
$938$	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	−0.991536	−	0.129829i	$-0.958557\pi$
$941$	−26.4335	+	26.4335i	−0.861707	+	0.861707i	0.129829	+	0.991536i	$0.458557\pi$
$942$		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
$952$	−20.1433	+	0.567171i	−0.652848	+	0.0183821i
$953$	−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
$959$	−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	0.333014	−	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	0.0786584	−	0.996902i	$-0.474936\pi$
$971$	−23.2259	−	13.4095i	−0.745355	−	0.430331i	−0.824013	+	0.566571i	$0.808270\pi$
$972$		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	−0.686556	−	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
$980$	−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	0.959543	−	0.281561i	$-0.0908523\pi$
$983$	21.2566	+	21.2566i	0.677982	+	0.677982i	−0.281561	+	0.959543i	$0.590852\pi$
$984$		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
$994$	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	0.427030	−	0.904237i	$-0.359560\pi$
$997$	−4.50099	−	2.59865i	−0.142548	−	0.0822999i	−0.569578	+	0.821938i	$0.692893\pi$
$998$	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.622.2		32
3.2	odd	2		273.2.by.c.76.7	✓	32
7.6	odd	2		819.2.fm.e.622.2		32
13.6	odd	12		819.2.fm.e.370.2		32
21.20	even	2		273.2.by.d.76.7	yes	32
39.32	even	12		273.2.by.d.97.7	yes	32
91.6	even	12	inner	819.2.fm.f.370.2		32
273.188	odd	12		273.2.by.c.97.7	yes	32

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more