LMFDB - Embedded newform 1352.2.o.d.361.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1352,2,Mod(361,1352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1352.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1352, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1352 = 2^{3} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1352.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,0,0,0,0,-6,0,0,0,0,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$10.7957743533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.1731891456.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$2.21837 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	1352.361
Dual form			1352.2.o.d.1161.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.780776 + 1.35234i) q^{3} +3.56155i q^{5} +(1.35234 + 0.780776i) q^{7} +(0.280776 - 0.486319i) q^{9} +(-2.70469 + 1.56155i) q^{11} +(-4.81645 + 2.78078i) q^{15} +(-3.34233 + 5.78908i) q^{17} +(2.70469 + 1.56155i) q^{19} +2.43845i q^{21} +(-4.00000 - 6.92820i) q^{23} -7.68466 q^{25} +5.56155 q^{27} +(1.00000 + 1.73205i) q^{29} +4.00000i q^{31} +(-4.22351 - 2.43845i) q^{33} +(-2.78078 + 4.81645i) q^{35} +(2.32498 - 1.34233i) q^{37} +(4.43674 - 2.56155i) q^{41} +(4.78078 - 8.28055i) q^{43} +(1.73205 + 1.00000i) q^{45} +12.6847i q^{47} +(-2.28078 - 3.95042i) q^{49} -10.4384 q^{51} -5.12311 q^{53} +(-5.56155 - 9.63289i) q^{55} +4.87689i q^{57} +(-2.70469 - 1.56155i) q^{59} +(-1.43845 + 2.49146i) q^{61} +(0.759413 - 0.438447i) q^{63} +(2.70469 - 1.56155i) q^{67} +(6.24621 - 10.8188i) q^{69} +(-4.05703 - 2.34233i) q^{71} +6.00000i q^{73} +(-6.00000 - 10.3923i) q^{75} -4.87689 q^{77} +8.00000 q^{79} +(3.50000 + 6.06218i) q^{81} -14.2462i q^{83} +(-20.6181 - 11.9039i) q^{85} +(-1.56155 + 2.70469i) q^{87} +(-8.66025 + 5.00000i) q^{89} +(-5.40938 + 3.12311i) q^{93} +(-5.56155 + 9.63289i) q^{95} +(-7.14143 - 4.12311i) q^{97} +1.75379i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 6 q^{9} - 2 q^{17} - 32 q^{23} - 12 q^{25} + 28 q^{27} + 8 q^{29} - 14 q^{35} + 30 q^{43} - 10 q^{49} - 100 q^{51} - 8 q^{53} - 28 q^{55} - 28 q^{61} - 16 q^{69} - 48 q^{75} - 72 q^{77}+ \cdots - 28 q^{95}+O(q^{100}) $ 8 * q - 2 * q^3 - 6 * q^9 - 2 * q^17 - 32 * q^23 - 12 * q^25 + 28 * q^27 + 8 * q^29 - 14 * q^35 + 30 * q^43 - 10 * q^49 - 100 * q^51 - 8 * q^53 - 28 * q^55 - 28 * q^61 - 16 * q^69 - 48 * q^75 - 72 * q^77 + 64 * q^79 + 28 * q^81 + 4 * q^87 - 28 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1185$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.780776	+	1.35234i	0.450781	+	0.780776i	0.998435	−	0.0559290i	$-0.0178120\pi$
$3$	0.780776	+	1.35234i	0.450781	+	0.780776i	−0.547653	+	0.836705i	$0.684479\pi$
$4$		0			0
$5$			3.56155i			1.59277i	0.604787	+	0.796387i	$0.293258\pi$
$5$			3.56155i			1.59277i	−0.604787	+	0.796387i	$0.706742\pi$
$6$		0			0
$7$	1.35234	+	0.780776i	0.511138	+	0.295106i	0.733301	−	0.679904i	$-0.237978\pi$
$7$	1.35234	+	0.780776i	0.511138	+	0.295106i	−0.222163	+	0.975009i	$0.571312\pi$
$8$		0			0
$9$	0.280776	−	0.486319i	0.0935921	−	0.162106i
$10$		0			0
$11$	−2.70469	+	1.56155i	−0.815494	+	0.470826i	−0.848860	−	0.528617i	$-0.822711\pi$
$11$	−2.70469	+	1.56155i	−0.815494	+	0.470826i	0.0333659	+	0.999443i	$0.489377\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−4.81645	+	2.78078i	−1.24360	+	0.717993i
$16$		0			0
$17$	−3.34233	+	5.78908i	−0.810634	+	1.40406i	0.101787	+	0.994806i	$0.467544\pi$
$17$	−3.34233	+	5.78908i	−0.810634	+	1.40406i	−0.912421	+	0.409253i	$0.865789\pi$
$18$		0			0
$19$	2.70469	+	1.56155i	0.620498	+	0.358245i	0.777063	−	0.629423i	$-0.216709\pi$
$19$	2.70469	+	1.56155i	0.620498	+	0.358245i	−0.156565	+	0.987668i	$0.550042\pi$
$20$		0			0
$21$			2.43845i			0.532113i
$22$		0			0
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$		0			0
$25$	−7.68466			−1.53693
$26$		0			0
$27$	5.56155			1.07032
$28$		0			0
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$		0			0
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$		0			0
$33$	−4.22351	−	2.43845i	−0.735219	−	0.424479i
$34$		0			0
$35$	−2.78078	+	4.81645i	−0.470037	+	0.814128i
$36$		0			0
$37$	2.32498	−	1.34233i	0.382225	−	0.220678i	−0.296561	−	0.955014i	$-0.595840\pi$
$37$	2.32498	−	1.34233i	0.382225	−	0.220678i	0.678786	+	0.734336i	$0.262506\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.43674	−	2.56155i	0.692902	−	0.400047i	−0.111796	−	0.993731i	$-0.535660\pi$
$41$	4.43674	−	2.56155i	0.692902	−	0.400047i	0.804698	+	0.593684i	$0.202327\pi$
$42$		0			0
$43$	4.78078	−	8.28055i	0.729062	−	1.26277i	−0.228219	−	0.973610i	$-0.573290\pi$
$43$	4.78078	−	8.28055i	0.729062	−	1.26277i	0.957280	−	0.289162i	$-0.0933766\pi$
$44$		0			0
$45$	1.73205	+	1.00000i	0.258199	+	0.149071i
$46$		0			0
$47$			12.6847i			1.85025i	0.379666	+	0.925124i	$0.376039\pi$
$47$			12.6847i			1.85025i	−0.379666	+	0.925124i	$0.623961\pi$
$48$		0			0
$49$	−2.28078	−	3.95042i	−0.325825	−	0.564346i
$50$		0			0
$51$	−10.4384			−1.46167
$52$		0			0
$53$	−5.12311			−0.703713			−0.351856	−	0.936054i	$-0.614449\pi$
$53$	−5.12311			−0.703713			−0.351856	+	0.936054i	$0.614449\pi$
$54$		0			0
$55$	−5.56155	−	9.63289i	−0.749920	−	1.29890i
$56$		0			0
$57$			4.87689i			0.645960i
$58$		0			0
$59$	−2.70469	−	1.56155i	−0.352120	−	0.203297i	0.313498	−	0.949589i	$-0.398499\pi$
$59$	−2.70469	−	1.56155i	−0.352120	−	0.203297i	−0.665619	+	0.746292i	$0.731832\pi$
$60$		0			0
$61$	−1.43845	+	2.49146i	−0.184174	+	0.318999i	−0.943298	−	0.331947i	$-0.892294\pi$
$61$	−1.43845	+	2.49146i	−0.184174	+	0.318999i	0.759124	+	0.650946i	$0.225628\pi$
$62$		0			0
$63$	0.759413	−	0.438447i	0.0956770	−	0.0552392i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.70469	−	1.56155i	0.330430	−	0.190774i	−0.325602	−	0.945507i	$-0.605567\pi$
$67$	2.70469	−	1.56155i	0.330430	−	0.190774i	0.656032	+	0.754733i	$0.272234\pi$
$68$		0			0
$69$	6.24621	−	10.8188i	0.751955	−	1.30243i
$70$		0			0
$71$	−4.05703	−	2.34233i	−0.481481	−	0.277983i	0.239552	−	0.970883i	$-0.422999\pi$
$71$	−4.05703	−	2.34233i	−0.481481	−	0.277983i	−0.721034	+	0.692900i	$0.756333\pi$
$72$		0			0
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$		0			0
$75$	−6.00000	−	10.3923i	−0.692820	−	1.20000i
$76$		0			0
$77$	−4.87689			−0.555774
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	3.50000	+	6.06218i	0.388889	+	0.673575i
$82$		0			0
$83$		−	14.2462i		−	1.56372i	−0.623451	−	0.781862i	$-0.714270\pi$
$83$		−	14.2462i		−	1.56372i	0.623451	−	0.781862i	$-0.285730\pi$
$84$		0			0
$85$	−20.6181	−	11.9039i	−2.23635	−	1.29116i
$86$		0			0
$87$	−1.56155	+	2.70469i	−0.167416	+	0.289973i
$88$		0			0
$89$	−8.66025	+	5.00000i	−0.917985	+	0.529999i	−0.882992	−	0.469389i	$-0.844474\pi$
$89$	−8.66025	+	5.00000i	−0.917985	+	0.529999i	−0.0349934	+	0.999388i	$0.511141\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−5.40938	+	3.12311i	−0.560926	+	0.323851i
$94$		0			0
$95$	−5.56155	+	9.63289i	−0.570603	+	0.988314i
$96$		0			0
$97$	−7.14143	−	4.12311i	−0.725102	−	0.418638i	0.0915255	−	0.995803i	$-0.470826\pi$
$97$	−7.14143	−	4.12311i	−0.725102	−	0.418638i	−0.816628	+	0.577165i	$0.804159\pi$
$98$		0			0
$99$			1.75379i			0.176262i
$100$		0			0
$101$	0.561553	+	0.972638i	0.0558766	+	0.0967811i	0.892611	−	0.450828i	$-0.148871\pi$
$101$	0.561553	+	0.972638i	0.0558766	+	0.0967811i	−0.836734	+	0.547609i	$0.815538\pi$
$102$		0			0
$103$	14.2462			1.40372			0.701860	−	0.712314i	$-0.252353\pi$
$103$	14.2462			1.40372			0.701860	+	0.712314i	$0.252353\pi$
$104$		0			0
$105$	−8.68466			−0.847536
$106$		0			0
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	0.753010	−	0.658009i	$-0.228601\pi$
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	−0.946357	+	0.323122i	$0.895268\pi$
$108$		0			0
$109$			17.8078i			1.70567i	0.522177	+	0.852837i	$0.325120\pi$
$109$			17.8078i			1.70567i	−0.522177	+	0.852837i	$0.674880\pi$
$110$		0			0
$111$	3.63058	+	2.09612i	0.344600	+	0.198955i
$112$		0			0
$113$	−7.24621	+	12.5508i	−0.681666	+	1.18068i	0.292806	+	0.956172i	$0.405411\pi$
$113$	−7.24621	+	12.5508i	−0.681666	+	1.18068i	−0.974472	+	0.224509i	$0.927922\pi$
$114$		0			0
$115$	24.6752	−	14.2462i	2.30097	−	1.32847i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.03996	+	5.21922i	−0.828692	+	0.478445i
$120$		0			0
$121$	−0.623106	+	1.07925i	−0.0566460	+	0.0981137i
$122$		0			0
$123$	6.92820	+	4.00000i	0.624695	+	0.360668i
$124$		0			0
$125$		−	9.56155i		−	0.855211i
$126$		0			0
$127$	3.12311	+	5.40938i	0.277131	+	0.480005i	0.970670	−	0.240414i	$-0.0772831\pi$
$127$	3.12311	+	5.40938i	0.277131	+	0.480005i	−0.693540	+	0.720418i	$0.743950\pi$
$128$		0			0
$129$	14.9309			1.31459
$130$		0			0
$131$	15.8078			1.38113			0.690565	−	0.723270i	$-0.257362\pi$
$131$	15.8078			1.38113			0.690565	+	0.723270i	$0.257362\pi$
$132$		0			0
$133$	2.43845	+	4.22351i	0.211440	+	0.366225i
$134$		0			0
$135$			19.8078i			1.70478i
$136$		0			0
$137$	4.43674	+	2.56155i	0.379056	+	0.218848i	0.677408	−	0.735608i	$-0.263103\pi$
$137$	4.43674	+	2.56155i	0.379056	+	0.218848i	−0.298351	+	0.954456i	$0.596437\pi$
$138$		0			0
$139$	2.34233	−	4.05703i	0.198674	−	0.344113i	−0.749425	−	0.662089i	$-0.769670\pi$
$139$	2.34233	−	4.05703i	0.198674	−	0.344113i	0.948099	+	0.317976i	$0.103003\pi$
$140$		0			0
$141$	−17.1540	+	9.90388i	−1.44463	+	0.834057i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−6.16879	+	3.56155i	−0.512290	+	0.295771i
$146$		0			0
$147$	3.56155	−	6.16879i	0.293752	−	0.508793i
$148$		0			0
$149$	0.213225	+	0.123106i	0.0174681	+	0.0100852i	0.508709	−	0.860939i	$-0.330123\pi$
$149$	0.213225	+	0.123106i	0.0174681	+	0.0100852i	−0.491241	+	0.871024i	$0.663456\pi$
$150$		0			0
$151$		−	6.43845i		−	0.523953i	−0.965074	−	0.261977i	$-0.915626\pi$
$151$		−	6.43845i		−	0.523953i	0.965074	−	0.261977i	$-0.0843744\pi$
$152$		0			0
$153$	1.87689	+	3.25088i	0.151738	+	0.262818i
$154$		0			0
$155$	−14.2462			−1.14428
$156$		0			0
$157$	10.4924			0.837386			0.418693	−	0.908128i	$-0.362488\pi$
$157$	10.4924			0.837386			0.418693	+	0.908128i	$0.362488\pi$
$158$		0			0
$159$	−4.00000	−	6.92820i	−0.317221	−	0.549442i
$160$		0			0
$161$		−	12.4924i		−	0.984541i
$162$		0			0
$163$	10.8188	+	6.24621i	0.847390	+	0.489241i	0.859769	−	0.510682i	$-0.170607\pi$
$163$	10.8188	+	6.24621i	0.847390	+	0.489241i	−0.0123792	+	0.999923i	$0.503941\pi$
$164$		0			0
$165$	8.68466	−	15.0423i	0.676100	−	1.17104i
$166$		0			0
$167$	1.94528	−	1.12311i	0.150530	−	0.0869085i	−0.422843	−	0.906203i	$-0.638968\pi$
$167$	1.94528	−	1.12311i	0.150530	−	0.0869085i	0.573373	+	0.819294i	$0.305635\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	1.51883	−	0.876894i	0.116147	−	0.0670578i
$172$		0			0
$173$	−6.56155	+	11.3649i	−0.498866	+	0.864061i	−0.999999	−	0.00130937i	$-0.999583\pi$
$173$	−6.56155	+	11.3649i	−0.498866	+	0.864061i	0.501134	+	0.865370i	$0.332917\pi$
$174$		0			0
$175$	−10.3923	−	6.00000i	−0.785584	−	0.453557i
$176$		0			0
$177$		−	4.87689i		−	0.366570i
$178$		0			0
$179$	−2.34233	−	4.05703i	−0.175074	−	0.303237i	0.765113	−	0.643896i	$-0.222683\pi$
$179$	−2.34233	−	4.05703i	−0.175074	−	0.303237i	−0.940187	+	0.340659i	$0.889350\pi$
$180$		0			0
$181$	14.8769			1.10579			0.552895	−	0.833251i	$-0.313523\pi$
$181$	14.8769			1.10579			0.552895	+	0.833251i	$0.313523\pi$
$182$		0			0
$183$	−4.49242			−0.332089
$184$		0			0
$185$	4.78078	+	8.28055i	0.351490	+	0.608798i
$186$		0			0
$187$		−	20.8769i		−	1.52667i
$188$		0			0
$189$	7.52113	+	4.34233i	0.547082	+	0.315858i
$190$		0			0
$191$	4.68466	−	8.11407i	0.338970	−	0.587113i	−0.645269	−	0.763955i	$-0.723255\pi$
$191$	4.68466	−	8.11407i	0.338970	−	0.587113i	0.984239	+	0.176842i	$0.0565882\pi$
$192$		0			0
$193$	−2.91791	+	1.68466i	−0.210036	+	0.121264i	−0.601328	−	0.799002i	$-0.705362\pi$
$193$	−2.91791	+	1.68466i	−0.210036	+	0.121264i	0.391292	+	0.920267i	$0.372028\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.7173	−	7.34233i	0.906069	−	0.523119i	0.0269049	−	0.999638i	$-0.491435\pi$
$197$	12.7173	−	7.34233i	0.906069	−	0.523119i	0.879164	+	0.476519i	$0.158102\pi$
$198$		0			0
$199$	−1.56155	+	2.70469i	−0.110696	+	0.191730i	−0.916051	−	0.401062i	$-0.868641\pi$
$199$	−1.56155	+	2.70469i	−0.110696	+	0.191730i	0.805355	+	0.592792i	$0.201975\pi$
$200$		0			0
$201$	4.22351	+	2.43845i	0.297904	+	0.171995i
$202$		0			0
$203$			3.12311i			0.219199i
$204$		0			0
$205$	9.12311	+	15.8017i	0.637185	+	1.10364i
$206$		0			0
$207$	−4.49242			−0.312245
$208$		0			0
$209$	−9.75379			−0.674684
$210$		0			0
$211$	−1.65767	−	2.87117i	−0.114119	−	0.197659i	0.803308	−	0.595563i	$-0.203071\pi$
$211$	−1.65767	−	2.87117i	−0.114119	−	0.197659i	−0.917427	+	0.397904i	$0.869738\pi$
$212$		0			0
$213$		−	7.31534i		−	0.501239i
$214$		0			0
$215$	29.4916	+	17.0270i	2.01131	+	1.16123i
$216$		0			0
$217$	−3.12311	+	5.40938i	−0.212010	+	0.367212i
$218$		0			0
$219$	−8.11407	+	4.68466i	−0.548298	+	0.316560i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−2.87117	+	1.65767i	−0.192268	+	0.111006i	−0.593044	−	0.805170i	$-0.702074\pi$
$223$	−2.87117	+	1.65767i	−0.192268	+	0.111006i	0.400776	+	0.916176i	$0.368741\pi$
$224$		0			0
$225$	−2.15767	+	3.73720i	−0.143845	+	0.249146i
$226$		0			0
$227$	6.92820	+	4.00000i	0.459841	+	0.265489i	0.711977	−	0.702202i	$-0.247800\pi$
$227$	6.92820	+	4.00000i	0.459841	+	0.265489i	−0.252136	+	0.967692i	$0.581133\pi$
$228$		0			0
$229$			13.8078i			0.912443i	0.889866	+	0.456221i	$0.150797\pi$
$229$			13.8078i			0.912443i	−0.889866	+	0.456221i	$0.849203\pi$
$230$		0			0
$231$	−3.80776	−	6.59524i	−0.250532	−	0.433935i
$232$		0			0
$233$	−13.8078			−0.904577			−0.452288	−	0.891872i	$-0.649392\pi$
$233$	−13.8078			−0.904577			−0.452288	+	0.891872i	$0.649392\pi$
$234$		0			0
$235$	−45.1771			−2.94703
$236$		0			0
$237$	6.24621	+	10.8188i	0.405735	+	0.702754i
$238$		0			0
$239$			1.56155i			0.101008i	0.998724	+	0.0505042i	$0.0160828\pi$
$239$			1.56155i			0.101008i	−0.998724	+	0.0505042i	$0.983917\pi$
$240$		0			0
$241$	−17.5337	−	10.1231i	−1.12945	−	0.652087i	−0.185651	−	0.982616i	$-0.559439\pi$
$241$	−17.5337	−	10.1231i	−1.12945	−	0.652087i	−0.943796	+	0.330529i	$0.892773\pi$
$242$		0			0
$243$	2.87689	−	4.98293i	0.184553	−	0.319655i
$244$		0			0
$245$	14.0696	−	8.12311i	0.898876	−	0.518966i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	19.2658	−	11.1231i	1.22092	−	0.704898i
$250$		0			0
$251$	2.87689	−	4.98293i	0.181588	−	0.314520i	−0.760833	−	0.648947i	$-0.775210\pi$
$251$	2.87689	−	4.98293i	0.181588	−	0.314520i	0.942421	+	0.334428i	$0.108543\pi$
$252$		0			0
$253$	21.6375	+	12.4924i	1.36034	+	0.785392i
$254$		0			0
$255$		−	37.1771i		−	2.32812i
$256$		0			0
$257$	7.78078	+	13.4767i	0.485351	+	0.840653i	0.999858	−	0.0168328i	$-0.00535831\pi$
$257$	7.78078	+	13.4767i	0.485351	+	0.840653i	−0.514507	+	0.857486i	$0.672025\pi$
$258$		0			0
$259$	4.19224			0.260493
$260$		0			0
$261$	1.12311			0.0695185
$262$		0			0
$263$	4.87689	+	8.44703i	0.300722	+	0.520866i	0.976300	−	0.216423i	$-0.0694390\pi$
$263$	4.87689	+	8.44703i	0.300722	+	0.520866i	−0.675578	+	0.737289i	$0.736106\pi$
$264$		0			0
$265$		−	18.2462i		−	1.12086i
$266$		0			0
$267$	−13.5234	−	7.80776i	−0.827621	−	0.477827i
$268$		0			0
$269$	6.56155	−	11.3649i	0.400065	−	0.692933i	−0.593668	−	0.804710i	$-0.702321\pi$
$269$	6.56155	−	11.3649i	0.400065	−	0.692933i	0.993733	+	0.111777i	$0.0356542\pi$
$270$		0			0
$271$	0.166481	−	0.0961180i	0.0101130	−	0.00583875i	−0.494935	−	0.868930i	$-0.664808\pi$
$271$	0.166481	−	0.0961180i	0.0101130	−	0.00583875i	0.505048	+	0.863091i	$0.331475\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	20.7846	−	12.0000i	1.25336	−	0.723627i
$276$		0			0
$277$	2.31534	−	4.01029i	0.139115	−	0.240955i	−0.788047	−	0.615616i	$-0.788907\pi$
$277$	2.31534	−	4.01029i	0.139115	−	0.240955i	0.927162	+	0.374661i	$0.122241\pi$
$278$		0			0
$279$	1.94528	+	1.12311i	0.116461	+	0.0672386i
$280$		0			0
$281$		−	10.0000i		−	0.596550i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$		−	10.0000i		−	0.596550i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$		0			0
$283$	12.2462	+	21.2111i	0.727962	+	1.26087i	0.957743	+	0.287624i	$0.0928655\pi$
$283$	12.2462	+	21.2111i	0.727962	+	1.26087i	−0.229782	+	0.973242i	$0.573801\pi$
$284$		0			0
$285$	−17.3693			−1.02887
$286$		0			0
$287$	8.00000			0.472225
$288$		0			0
$289$	−13.8423	−	23.9756i	−0.814255	−	1.41033i
$290$		0			0
$291$		−	12.8769i		−	0.754857i
$292$		0			0
$293$	16.9408	+	9.78078i	0.989692	+	0.571399i	0.905182	−	0.425024i	$-0.139734\pi$
$293$	16.9408	+	9.78078i	0.989692	+	0.571399i	0.0845099	+	0.996423i	$0.473068\pi$
$294$		0			0
$295$	5.56155	−	9.63289i	0.323806	−	0.560849i
$296$		0			0
$297$	−15.0423	+	8.68466i	−0.872841	+	0.503935i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	12.9305	−	7.46543i	0.745302	−	0.430301i
$302$		0			0
$303$	−0.876894	+	1.51883i	−0.0503763	+	0.0872543i
$304$		0			0
$305$	−8.87348	−	5.12311i	−0.508094	−	0.293348i
$306$		0			0
$307$		−	4.87689i		−	0.278339i	−0.990269	−	0.139170i	$-0.955557\pi$
$307$		−	4.87689i		−	0.278339i	0.990269	−	0.139170i	$-0.0444433\pi$
$308$		0			0
$309$	11.1231	+	19.2658i	0.632771	+	1.09599i
$310$		0			0
$311$	19.1231			1.08437			0.542186	−	0.840259i	$-0.317597\pi$
$311$	19.1231			1.08437			0.542186	+	0.840259i	$0.317597\pi$
$312$		0			0
$313$	6.19224			0.350006			0.175003	−	0.984568i	$-0.444007\pi$
$313$	6.19224			0.350006			0.175003	+	0.984568i	$0.444007\pi$
$314$		0			0
$315$	1.56155	+	2.70469i	0.0879835	+	0.152392i
$316$		0			0
$317$			4.24621i			0.238491i	0.992865	+	0.119245i	$0.0380476\pi$
$317$			4.24621i			0.238491i	−0.992865	+	0.119245i	$0.961952\pi$
$318$		0			0
$319$	−5.40938	−	3.12311i	−0.302867	−	0.174860i
$320$		0			0
$321$	3.12311	−	5.40938i	0.174315	−	0.301922i
$322$		0			0
$323$	−18.0799	+	10.4384i	−1.00599	+	0.580811i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−24.0822	+	13.9039i	−1.33175	+	0.768886i
$328$		0			0
$329$	−9.90388	+	17.1540i	−0.546019	+	0.945732i
$330$		0			0
$331$	−24.6752	−	14.2462i	−1.35627	−	0.783043i	−0.367151	−	0.930161i	$-0.619667\pi$
$331$	−24.6752	−	14.2462i	−1.35627	−	0.783043i	−0.989119	+	0.147119i	$0.953000\pi$
$332$		0			0
$333$		−	1.50758i		−	0.0826147i
$334$		0			0
$335$	5.56155	+	9.63289i	0.303860	+	0.526301i
$336$		0			0
$337$	33.8078			1.84163			0.920813	−	0.390004i	$-0.127526\pi$
$337$	33.8078			1.84163			0.920813	+	0.390004i	$0.127526\pi$
$338$		0			0
$339$	−22.6307			−1.22913
$340$		0			0
$341$	−6.24621	−	10.8188i	−0.338251	−	0.585868i
$342$		0			0
$343$		−	18.0540i		−	0.974823i
$344$		0			0
$345$	38.5316	+	22.2462i	2.07447	+	1.19770i
$346$		0			0
$347$	2.34233	−	4.05703i	0.125743	−	0.217793i	−0.796280	−	0.604928i	$-0.793202\pi$
$347$	2.34233	−	4.05703i	0.125743	−	0.217793i	0.922023	+	0.387135i	$0.126535\pi$
$348$		0			0
$349$	14.6626	−	8.46543i	0.784869	−	0.453144i	−0.0532841	−	0.998579i	$-0.516969\pi$
$349$	14.6626	−	8.46543i	0.784869	−	0.453144i	0.838153	+	0.545435i	$0.183636\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.3102	+	7.68466i	−0.708431	+	0.409013i	−0.810480	−	0.585766i	$-0.800794\pi$
$353$	−13.3102	+	7.68466i	−0.708431	+	0.409013i	0.102049	+	0.994779i	$0.467460\pi$
$354$		0			0
$355$	8.34233	−	14.4493i	0.442765	−	0.766891i
$356$		0			0
$357$	−14.1164	−	8.15009i	−0.747118	−	0.431349i
$358$		0			0
$359$			2.24621i			0.118550i	0.998242	+	0.0592752i	$0.0188790\pi$
$359$			2.24621i			0.118550i	−0.998242	+	0.0592752i	$0.981121\pi$
$360$		0			0
$361$	−4.62311	−	8.00745i	−0.243321	−	0.421445i
$362$		0			0
$363$	−1.94602			−0.102140
$364$		0			0
$365$	−21.3693			−1.11852
$366$		0			0
$367$	15.8078	+	27.3799i	0.825159	+	1.42922i	0.901798	+	0.432158i	$0.142248\pi$
$367$	15.8078	+	27.3799i	0.825159	+	1.42922i	−0.0766395	+	0.997059i	$0.524419\pi$
$368$		0			0
$369$		−	2.87689i		−	0.149765i
$370$		0			0
$371$	−6.92820	−	4.00000i	−0.359694	−	0.207670i
$372$		0			0
$373$	−14.8078	+	25.6478i	−0.766717	+	1.32799i	0.172617	+	0.984989i	$0.444778\pi$
$373$	−14.8078	+	25.6478i	−0.766717	+	1.32799i	−0.939334	+	0.343004i	$0.888556\pi$
$374$		0			0
$375$	12.9305	−	7.46543i	0.667729	−	0.385513i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	19.2658	−	11.1231i	0.989617	−	0.571356i	0.0844571	−	0.996427i	$-0.473084\pi$
$379$	19.2658	−	11.1231i	0.989617	−	0.571356i	0.905160	+	0.425072i	$0.139751\pi$
$380$		0			0
$381$	−4.87689	+	8.44703i	−0.249851	+	0.432754i
$382$		0			0
$383$	27.5463	+	15.9039i	1.40755	+	0.812650i	0.995152	−	0.0983524i	$-0.0313572\pi$
$383$	27.5463	+	15.9039i	1.40755	+	0.812650i	0.412400	+	0.911003i	$0.364691\pi$
$384$		0			0
$385$		−	17.3693i		−	0.885222i
$386$		0			0
$387$	−2.68466	−	4.64996i	−0.136469	−	0.236371i
$388$		0			0
$389$	28.7386			1.45711			0.728553	−	0.684989i	$-0.240193\pi$
$389$	28.7386			1.45711			0.728553	+	0.684989i	$0.240193\pi$
$390$		0			0
$391$	53.4773			2.70446
$392$		0			0
$393$	12.3423	+	21.3775i	0.622588	+	1.07835i
$394$		0			0
$395$			28.4924i			1.43361i
$396$		0			0
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	0.455905	−	0.890028i	$-0.349316\pi$
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	−0.542834	+	0.839840i	$0.682649\pi$
$398$		0			0
$399$	−3.80776	+	6.59524i	−0.190627	+	0.330175i
$400$		0			0
$401$	32.5760	−	18.8078i	1.62677	−	0.939215i	0.641719	−	0.766940i	$-0.278222\pi$
$401$	32.5760	−	18.8078i	1.62677	−	0.939215i	0.985049	−	0.172275i	$-0.0551118\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−21.5908	+	12.4654i	−1.07285	+	0.619412i
$406$		0			0
$407$	−4.19224	+	7.26117i	−0.207801	+	0.359923i
$408$		0			0
$409$	−18.2931	−	10.5616i	−0.904538	−	0.522235i	−0.0258682	−	0.999665i	$-0.508235\pi$
$409$	−18.2931	−	10.5616i	−0.904538	−	0.522235i	−0.878670	+	0.477430i	$0.841568\pi$
$410$		0			0
$411$			8.00000i			0.394611i
$412$		0			0
$413$	−2.43845	−	4.22351i	−0.119988	−	0.207826i
$414$		0			0
$415$	50.7386			2.49066
$416$		0			0
$417$	7.31534			0.358234
$418$		0			0
$419$	−13.4654	−	23.3228i	−0.657830	−	1.13939i	−0.981176	−	0.193114i	$-0.938141\pi$
$419$	−13.4654	−	23.3228i	−0.657830	−	1.13939i	0.323347	−	0.946281i	$-0.395192\pi$
$420$		0			0
$421$		−	18.6847i		−	0.910635i	−0.890329	−	0.455317i	$-0.849526\pi$
$421$		−	18.6847i		−	0.910635i	0.890329	−	0.455317i	$-0.150474\pi$
$422$		0			0
$423$	6.16879	+	3.56155i	0.299937	+	0.173169i
$424$		0			0
$425$	25.6847	−	44.4871i	1.24589	−	2.15794i
$426$		0			0
$427$	−3.89055	+	2.24621i	−0.188277	+	0.108702i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.5041	+	7.21922i	−0.602299	+	0.347738i	−0.769946	−	0.638109i	$-0.779717\pi$
$431$	−12.5041	+	7.21922i	−0.602299	+	0.347738i	0.167646	+	0.985847i	$0.446383\pi$
$432$		0			0
$433$	19.5885	−	33.9283i	0.941365	−	1.63049i	0.178495	−	0.983941i	$-0.442877\pi$
$433$	19.5885	−	33.9283i	0.941365	−	1.63049i	0.762870	−	0.646551i	$-0.223789\pi$
$434$		0			0
$435$	−9.63289	−	5.56155i	−0.461862	−	0.266656i
$436$		0			0
$437$		−	24.9848i		−	1.19519i
$438$		0			0
$439$	6.43845	+	11.1517i	0.307290	+	0.532242i	0.977769	−	0.209687i	$-0.0672444\pi$
$439$	6.43845	+	11.1517i	0.307290	+	0.532242i	−0.670478	+	0.741929i	$0.733911\pi$
$440$		0			0
$441$	−2.56155			−0.121979
$442$		0			0
$443$	0.192236			0.00913340			0.00456670	−	0.999990i	$-0.498546\pi$
$443$	0.192236			0.00913340			0.00456670	+	0.999990i	$0.498546\pi$
$444$		0			0
$445$	−17.8078	−	30.8440i	−0.844169	−	1.46214i
$446$		0			0
$447$			0.384472i			0.0181849i
$448$		0			0
$449$	−14.4961	−	8.36932i	−0.684112	−	0.394972i	0.117290	−	0.993098i	$-0.462579\pi$
$449$	−14.4961	−	8.36932i	−0.684112	−	0.394972i	−0.801403	+	0.598125i	$0.795913\pi$
$450$		0			0
$451$	−8.00000	+	13.8564i	−0.376705	+	0.652473i
$452$		0			0
$453$	8.70700	−	5.02699i	0.409090	−	0.236188i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−21.4243	+	12.3693i	−1.00219	+	0.578612i	−0.908894	−	0.417027i	$-0.863072\pi$
$457$	−21.4243	+	12.3693i	−1.00219	+	0.578612i	−0.0932915	+	0.995639i	$0.529739\pi$
$458$		0			0
$459$	−18.5885	+	32.1963i	−0.867639	+	1.50279i
$460$		0			0
$461$	12.2908	+	7.09612i	0.572441	+	0.330499i	0.758124	−	0.652111i	$-0.226116\pi$
$461$	12.2908	+	7.09612i	0.572441	+	0.330499i	−0.185682	+	0.982610i	$0.559450\pi$
$462$		0			0
$463$		−	21.7538i		−	1.01098i	−0.862831	−	0.505492i	$-0.831311\pi$
$463$		−	21.7538i		−	1.01098i	0.862831	−	0.505492i	$-0.168689\pi$
$464$		0			0
$465$	−11.1231	−	19.2658i	−0.515822	−	0.893429i
$466$		0			0
$467$	−7.50758			−0.347409			−0.173705	−	0.984798i	$-0.555574\pi$
$467$	−7.50758			−0.347409			−0.173705	+	0.984798i	$0.555574\pi$
$468$		0			0
$469$	4.87689			0.225194
$470$		0			0
$471$	8.19224	+	14.1894i	0.377478	+	0.653812i
$472$		0			0
$473$			29.8617i			1.37304i
$474$		0			0
$475$	−20.7846	−	12.0000i	−0.953663	−	0.550598i
$476$		0			0
$477$	−1.43845	+	2.49146i	−0.0658620	+	0.114076i
$478$		0			0
$479$	−27.5463	+	15.9039i	−1.25862	+	0.726667i	−0.972807	−	0.231617i	$-0.925598\pi$
$479$	−27.5463	+	15.9039i	−1.25862	+	0.726667i	−0.285817	+	0.958284i	$0.592265\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	16.8941	−	9.75379i	0.768706	−	0.443813i
$484$		0			0
$485$	14.6847	−	25.4346i	0.666796	−	1.15492i
$486$		0			0
$487$	−15.8017	−	9.12311i	−0.716043	−	0.413407i	0.0972518	−	0.995260i	$-0.468995\pi$
$487$	−15.8017	−	9.12311i	−0.716043	−	0.413407i	−0.813294	+	0.581852i	$0.802328\pi$
$488$		0			0
$489$			19.5076i			0.882163i
$490$		0			0
$491$	19.0270	+	32.9557i	0.858676	+	1.48727i	0.873192	+	0.487376i	$0.162046\pi$
$491$	19.0270	+	32.9557i	0.858676	+	1.48727i	−0.0145164	+	0.999895i	$0.504621\pi$
$492$		0			0
$493$	−13.3693			−0.602124
$494$		0			0
$495$	−6.24621			−0.280746
$496$		0			0
$497$	−3.65767	−	6.33527i	−0.164069	−	0.284176i
$498$		0			0
$499$		−	4.49242i		−	0.201108i	−0.994932	−	0.100554i	$-0.967938\pi$
$499$		−	4.49242i		−	0.201108i	0.994932	−	0.100554i	$-0.0320616\pi$
$500$		0			0
$501$	3.03765	+	1.75379i	0.135712	+	0.0783535i
$502$		0			0
$503$	−8.68466	+	15.0423i	−0.387230	+	0.670702i	−0.992076	−	0.125641i	$-0.959901\pi$
$503$	−8.68466	+	15.0423i	−0.387230	+	0.670702i	0.604846	+	0.796342i	$0.293235\pi$
$504$		0			0
$505$	−3.46410	+	2.00000i	−0.154150	+	0.0889988i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.5885	+	9.00000i	−0.690946	+	0.398918i	−0.803966	−	0.594675i	$-0.797281\pi$
$509$	−15.5885	+	9.00000i	−0.690946	+	0.398918i	0.113020	+	0.993593i	$0.463948\pi$
$510$		0			0
$511$	−4.68466	+	8.11407i	−0.207237	+	0.358945i
$512$		0			0
$513$	15.0423	+	8.68466i	0.664132	+	0.383437i
$514$		0			0
$515$			50.7386i			2.23581i
$516$		0			0
$517$	−19.8078	−	34.3081i	−0.871144	−	1.50887i
$518$		0			0
$519$	−20.4924			−0.899518
$520$		0			0
$521$	2.68466			0.117617			0.0588085	−	0.998269i	$-0.481270\pi$
$521$	2.68466			0.117617			0.0588085	+	0.998269i	$0.481270\pi$
$522$		0			0
$523$	−16.2462	−	28.1393i	−0.710397	−	1.23044i	−0.964708	−	0.263322i	$-0.915182\pi$
$523$	−16.2462	−	28.1393i	−0.710397	−	1.23044i	0.254311	−	0.967123i	$-0.418151\pi$
$524$		0			0
$525$		−	18.7386i		−	0.817821i
$526$		0			0
$527$	−23.1563	−	13.3693i	−1.00871	−	0.582377i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$		0			0
$531$	−1.51883	+	0.876894i	−0.0659114	+	0.0380540i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	12.3376	−	7.12311i	0.533400	−	0.307959i
$536$		0			0
$537$	3.65767	−	6.33527i	0.157840	−	0.273387i
$538$		0			0
$539$	12.3376	+	7.12311i	0.531417	+	0.306814i
$540$		0			0
$541$		−	6.68466i		−	0.287396i	−0.989622	−	0.143698i	$-0.954101\pi$
$541$		−	6.68466i		−	0.287396i	0.989622	−	0.143698i	$-0.0458994\pi$
$542$		0			0
$543$	11.6155	+	20.1187i	0.498470	+	0.863375i
$544$		0			0
$545$	−63.4233			−2.71676
$546$		0			0
$547$	−33.5616			−1.43499			−0.717494	−	0.696564i	$-0.754711\pi$
$547$	−33.5616			−1.43499			−0.717494	+	0.696564i	$0.754711\pi$
$548$		0			0
$549$	0.807764	+	1.39909i	0.0344745	+	0.0597116i
$550$		0			0
$551$			6.24621i			0.266098i
$552$		0			0
$553$	10.8188	+	6.24621i	0.460060	+	0.265616i
$554$		0			0
$555$	−7.46543	+	12.9305i	−0.316890	+	0.548870i
$556$		0			0
$557$	−2.75143	+	1.58854i	−0.116582	+	0.0673086i	−0.557157	−	0.830407i	$-0.688108\pi$
$557$	−2.75143	+	1.58854i	−0.116582	+	0.0673086i	0.440575	+	0.897716i	$0.354775\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	28.2328	−	16.3002i	1.19199	−	0.688194i
$562$		0			0
$563$	15.0270	−	26.0275i	0.633312	−	1.09693i	−0.353558	−	0.935413i	$-0.615028\pi$
$563$	15.0270	−	26.0275i	0.633312	−	1.09693i	0.986870	−	0.161516i	$-0.0516383\pi$
$564$		0			0
$565$	−44.7004	−	25.8078i	−1.88056	−	1.08574i
$566$		0			0
$567$			10.9309i			0.459053i
$568$		0			0
$569$	−14.6577	−	25.3878i	−0.614482	−	1.06431i	−0.990475	−	0.137691i	$-0.956032\pi$
$569$	−14.6577	−	25.3878i	−0.614482	−	1.06431i	0.375994	−	0.926622i	$-0.377301\pi$
$570$		0			0
$571$	−8.19224			−0.342834			−0.171417	−	0.985199i	$-0.554835\pi$
$571$	−8.19224			−0.342834			−0.171417	+	0.985199i	$0.554835\pi$
$572$		0			0
$573$	14.6307			0.611206
$574$		0			0
$575$	30.7386	+	53.2409i	1.28189	+	2.22030i
$576$		0			0
$577$		−	7.75379i		−	0.322794i	−0.986890	−	0.161397i	$-0.948400\pi$
$577$		−	7.75379i		−	0.322794i	0.986890	−	0.161397i	$-0.0516000\pi$
$578$		0			0
$579$	−4.55648	−	2.63068i	−0.189361	−	0.109327i
$580$		0			0
$581$	11.1231	−	19.2658i	0.461464	−	0.799279i
$582$		0			0
$583$	13.8564	−	8.00000i	0.573874	−	0.331326i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	35.4939	−	20.4924i	1.46499	−	0.845813i	0.465755	−	0.884913i	$-0.345783\pi$
$587$	35.4939	−	20.4924i	1.46499	−	0.845813i	0.999235	+	0.0391007i	$0.0124493\pi$
$588$		0			0
$589$	−6.24621	+	10.8188i	−0.257371	+	0.445779i
$590$		0			0
$591$	19.8587	+	11.4654i	0.816878	+	0.471625i
$592$		0			0
$593$		−	5.50758i		−	0.226169i	−0.993585	−	0.113085i	$-0.963927\pi$
$593$		−	5.50758i		−	0.226169i	0.993585	−	0.113085i	$-0.0360731\pi$
$594$		0			0
$595$	−18.5885	−	32.1963i	−0.762056	−	1.31992i
$596$		0			0
$597$	−4.87689			−0.199598
$598$		0			0
$599$	−1.36932			−0.0559488			−0.0279744	−	0.999609i	$-0.508906\pi$
$599$	−1.36932			−0.0559488			−0.0279744	+	0.999609i	$0.508906\pi$
$600$		0			0
$601$	5.58854	+	9.67964i	0.227961	+	0.394841i	0.957204	−	0.289415i	$-0.0934607\pi$
$601$	5.58854	+	9.67964i	0.227961	+	0.394841i	−0.729242	+	0.684255i	$0.760127\pi$
$602$		0			0
$603$		−	1.75379i		−	0.0714198i
$604$		0			0
$605$	−3.84381	−	2.21922i	−0.156273	−	0.0902243i
$606$		0			0
$607$	4.68466	−	8.11407i	0.190144	−	0.329340i	−0.755154	−	0.655548i	$-0.772438\pi$
$607$	4.68466	−	8.11407i	0.190144	−	0.329340i	0.945298	+	0.326208i	$0.105771\pi$
$608$		0			0
$609$	−4.22351	+	2.43845i	−0.171145	+	0.0988109i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	5.19615	−	3.00000i	0.209871	−	0.121169i	−0.391381	−	0.920229i	$-0.628002\pi$
$613$	5.19615	−	3.00000i	0.209871	−	0.121169i	0.601251	+	0.799060i	$0.294669\pi$
$614$		0			0
$615$	−14.2462	+	24.6752i	−0.574463	+	0.994999i
$616$		0			0
$617$	31.0572	+	17.9309i	1.25031	+	0.721870i	0.971172	−	0.238380i	$-0.0766163\pi$
$617$	31.0572	+	17.9309i	1.25031	+	0.721870i	0.279143	+	0.960250i	$0.409950\pi$
$618$		0			0
$619$			46.2462i			1.85879i	0.369084	+	0.929396i	$0.379672\pi$
$619$			46.2462i			1.85879i	−0.369084	+	0.929396i	$0.620328\pi$
$620$		0			0
$621$	−22.2462	−	38.5316i	−0.892710	−	1.54622i
$622$		0			0
$623$	−15.6155			−0.625623
$624$		0			0
$625$	−4.36932			−0.174773
$626$		0			0
$627$	−7.61553	−	13.1905i	−0.304135	−	0.526777i
$628$		0			0
$629$			17.9460i			0.715555i
$630$		0			0
$631$	−30.5840	−	17.6577i	−1.21753	−	0.702941i	−0.253140	−	0.967430i	$-0.581463\pi$
$631$	−30.5840	−	17.6577i	−1.21753	−	0.702941i	−0.964389	+	0.264489i	$0.914797\pi$
$632$		0			0
$633$	2.58854	−	4.48348i	0.102885	−	0.178202i
$634$		0			0
$635$	−19.2658	+	11.1231i	−0.764539	+	0.441407i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−2.27824	+	1.31534i	−0.0901257	+	0.0520341i
$640$		0			0
$641$	4.12311	−	7.14143i	0.162853	−	0.282069i	−0.773038	−	0.634360i	$-0.781264\pi$
$641$	4.12311	−	7.14143i	0.162853	−	0.282069i	0.935891	+	0.352290i	$0.114597\pi$
$642$		0			0
$643$	18.9328	+	10.9309i	0.746638	+	0.431071i	0.824478	−	0.565894i	$-0.191469\pi$
$643$	18.9328	+	10.9309i	0.746638	+	0.431071i	−0.0778401	+	0.996966i	$0.524802\pi$
$644$		0			0
$645$			53.1771i			2.09385i
$646$		0			0
$647$	−1.56155	−	2.70469i	−0.0613910	−	0.106332i	0.833696	−	0.552223i	$-0.186220\pi$
$647$	−1.56155	−	2.70469i	−0.0613910	−	0.106332i	−0.895087	+	0.445891i	$0.852887\pi$
$648$		0			0
$649$	9.75379			0.382870
$650$		0			0
$651$	−9.75379			−0.382281
$652$		0			0
$653$	6.56155	+	11.3649i	0.256773	+	0.444745i	0.965376	−	0.260864i	$-0.0840073\pi$
$653$	6.56155	+	11.3649i	0.256773	+	0.444745i	−0.708602	+	0.705608i	$0.750674\pi$
$654$		0			0
$655$			56.3002i			2.19983i
$656$		0			0
$657$	2.91791	+	1.68466i	0.113839	+	0.0657248i
$658$		0			0
$659$	8.24621	−	14.2829i	0.321227	−	0.556381i	−0.659515	−	0.751692i	$-0.729238\pi$
$659$	8.24621	−	14.2829i	0.321227	−	0.556381i	0.980741	+	0.195311i	$0.0625715\pi$
$660$		0			0
$661$	−7.56788	+	4.36932i	−0.294356	+	0.169947i	−0.639905	−	0.768454i	$-0.721026\pi$
$661$	−7.56788	+	4.36932i	−0.294356	+	0.169947i	0.345548	+	0.938401i	$0.387693\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.0423	+	8.68466i	−0.583314	+	0.336777i
$666$		0			0
$667$	8.00000	−	13.8564i	0.309761	−	0.536522i
$668$		0			0
$669$	−4.48348	−	2.58854i	−0.173341	−	0.100079i
$670$		0			0
$671$		−	8.98485i		−	0.346856i
$672$		0			0
$673$	17.1501	+	29.7048i	0.661088	+	1.14504i	0.980330	+	0.197364i	$0.0632381\pi$
$673$	17.1501	+	29.7048i	0.661088	+	1.14504i	−0.319243	+	0.947673i	$0.603429\pi$
$674$		0			0
$675$	−42.7386			−1.64501
$676$		0			0
$677$	23.3693			0.898156			0.449078	−	0.893493i	$-0.351753\pi$
$677$	23.3693			0.898156			0.449078	+	0.893493i	$0.351753\pi$
$678$		0			0
$679$	−6.43845	−	11.1517i	−0.247085	−	0.427964i
$680$		0			0
$681$			12.4924i			0.478711i
$682$		0			0
$683$	−20.7846	−	12.0000i	−0.795301	−	0.459167i	0.0465244	−	0.998917i	$-0.485185\pi$
$683$	−20.7846	−	12.0000i	−0.795301	−	0.459167i	−0.841825	+	0.539750i	$0.818519\pi$
$684$		0			0
$685$	−9.12311	+	15.8017i	−0.348576	+	0.603751i
$686$		0			0
$687$	−18.6729	+	10.7808i	−0.712414	+	0.411312i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−42.4221	+	24.4924i	−1.61381	+	0.931736i	−0.625338	+	0.780354i	$0.715039\pi$
$691$	−42.4221	+	24.4924i	−1.61381	+	0.931736i	−0.988475	+	0.151382i	$0.951628\pi$
$692$		0			0
$693$	−1.36932	+	2.37173i	−0.0520160	+	0.0900944i
$694$		0			0
$695$	14.4493	+	8.34233i	0.548095	+	0.316443i
$696$		0			0
$697$			34.2462i			1.29717i
$698$		0			0
$699$	−10.7808	−	18.6729i	−0.407766	−	0.706272i
$700$		0			0
$701$	−47.3693			−1.78911			−0.894557	−	0.446953i	$-0.852509\pi$
$701$	−47.3693			−1.78911			−0.894557	+	0.446953i	$0.852509\pi$
$702$		0			0
$703$	8.38447			0.316226
$704$		0			0
$705$	−35.2732	−	61.0950i	−1.32847	−	2.30097i
$706$		0			0
$707$			1.75379i			0.0659580i
$708$		0			0
$709$	21.4243	+	12.3693i	0.804606	+	0.464539i	0.845079	−	0.534641i	$-0.179553\pi$
$709$	21.4243	+	12.3693i	0.804606	+	0.464539i	−0.0404733	+	0.999181i	$0.512887\pi$
$710$		0			0
$711$	2.24621	−	3.89055i	0.0842395	−	0.145907i
$712$		0			0
$713$	27.7128	−	16.0000i	1.03785	−	0.599205i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.11176	+	1.21922i	−0.0788650	+	0.0455327i
$718$		0			0
$719$	−2.43845	+	4.22351i	−0.0909387	+	0.157511i	−0.907906	−	0.419173i	$-0.862320\pi$
$719$	−2.43845	+	4.22351i	−0.0909387	+	0.157511i	0.816968	+	0.576683i	$0.195653\pi$
$720$		0			0
$721$	19.2658	+	11.1231i	0.717495	+	0.414246i
$722$		0			0
$723$		−	31.6155i		−	1.17579i
$724$		0			0
$725$	−7.68466	−	13.3102i	−0.285401	−	0.494329i
$726$		0			0
$727$	−28.1080			−1.04247			−0.521233	−	0.853414i	$-0.674528\pi$
$727$	−28.1080			−1.04247			−0.521233	+	0.853414i	$0.674528\pi$
$728$		0			0
$729$	29.9848			1.11055
$730$		0			0
$731$	31.9579	+	55.3526i	1.18200	+	2.04729i
$732$		0			0
$733$		−	31.5616i		−	1.16575i	−0.812561	−	0.582876i	$-0.801927\pi$
$733$		−	31.5616i		−	1.16575i	0.812561	−	0.582876i	$-0.198073\pi$
$734$		0			0
$735$	21.9705	+	12.6847i	0.810393	+	0.467881i
$736$		0			0
$737$	−4.87689	+	8.44703i	−0.179643	+	0.311150i
$738$		0			0
$739$	−5.40938	+	3.12311i	−0.198987	+	0.114885i	−0.596183	−	0.802849i	$-0.703317\pi$
$739$	−5.40938	+	3.12311i	−0.198987	+	0.114885i	0.397196	+	0.917734i	$0.369983\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−38.0321	+	21.9579i	−1.39526	+	0.805556i	−0.993892	−	0.110360i	$-0.964800\pi$
$743$	−38.0321	+	21.9579i	−1.39526	+	0.805556i	−0.401372	+	0.915915i	$0.631466\pi$
$744$		0			0
$745$	−0.438447	+	0.759413i	−0.0160635	+	0.0278227i
$746$		0			0
$747$	−6.92820	−	4.00000i	−0.253490	−	0.146352i
$748$		0			0
$749$		−	6.24621i		−	0.228232i
$750$		0			0
$751$	−20.4924	−	35.4939i	−0.747779	−	1.29519i	−0.948885	−	0.315622i	$-0.897787\pi$
$751$	−20.4924	−	35.4939i	−0.747779	−	1.29519i	0.201106	−	0.979570i	$-0.435546\pi$
$752$		0			0
$753$	8.98485			0.327426
$754$		0			0
$755$	22.9309			0.834540
$756$		0			0
$757$	2.56155	+	4.43674i	0.0931012	+	0.161256i	0.908815	−	0.417200i	$-0.136989\pi$
$757$	2.56155	+	4.43674i	0.0931012	+	0.161256i	−0.815713	+	0.578456i	$0.803655\pi$
$758$		0			0
$759$			39.0152i			1.41616i
$760$		0			0
$761$	11.6979	+	6.75379i	0.424049	+	0.244825i	0.696808	−	0.717258i	$-0.254603\pi$
$761$	11.6979	+	6.75379i	0.424049	+	0.244825i	−0.272759	+	0.962082i	$0.587936\pi$
$762$		0			0
$763$	−13.9039	+	24.0822i	−0.503354	+	0.871835i
$764$		0			0
$765$	−11.5782	+	6.68466i	−0.418610	+	0.241684i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−37.9854	+	21.9309i	−1.36979	+	0.790847i	−0.990901	−	0.134595i	$-0.957027\pi$
$769$	−37.9854	+	21.9309i	−1.36979	+	0.790847i	−0.378887	+	0.925443i	$0.623693\pi$
$770$		0			0
$771$	−12.1501	+	21.0446i	−0.437575	+	0.757902i
$772$		0			0
$773$	−0.712669	−	0.411460i	−0.0256329	−	0.0147992i	0.487129	−	0.873330i	$-0.338044\pi$
$773$	−0.712669	−	0.411460i	−0.0256329	−	0.0147992i	−0.512762	+	0.858531i	$0.671378\pi$
$774$		0			0
$775$		−	30.7386i		−	1.10416i
$776$		0			0
$777$	3.27320	+	5.66935i	0.117425	+	0.203387i
$778$		0			0
$779$	16.0000			0.573259
$780$		0			0
$781$	14.6307			0.523527
$782$		0			0
$783$	5.56155	+	9.63289i	0.198754	+	0.344251i
$784$		0			0
$785$			37.3693i			1.33377i
$786$		0			0
$787$	−13.8564	−	8.00000i	−0.493928	−	0.285169i	0.232275	−	0.972650i	$-0.425383\pi$
$787$	−13.8564	−	8.00000i	−0.493928	−	0.285169i	−0.726202	+	0.687481i	$0.758716\pi$
$788$		0			0
$789$	−7.61553	+	13.1905i	−0.271120	+	0.469594i
$790$		0			0
$791$	−19.5987	+	11.3153i	−0.696851	+	0.402327i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	24.6752	−	14.2462i	0.875138	−	0.505261i
$796$		0			0
$797$	−23.2462	+	40.2636i	−0.823423	+	1.42621i	0.0796955	+	0.996819i	$0.474605\pi$
$797$	−23.2462	+	40.2636i	−0.823423	+	1.42621i	−0.903119	+	0.429391i	$0.858728\pi$
$798$		0			0
$799$	−73.4326	−	42.3963i	−2.59786	−	1.49987i
$800$		0			0
$801$			5.61553i			0.198415i
$802$		0			0
$803$	−9.36932	−	16.2281i	−0.330636	−	0.572678i
$804$		0			0
$805$	44.4924			1.56815
$806$		0			0
$807$	20.4924			0.721367
$808$		0			0
$809$	−7.58854	−	13.1437i	−0.266799	−	0.462109i	0.701234	−	0.712931i	$-0.252633\pi$
$809$	−7.58854	−	13.1437i	−0.266799	−	0.462109i	−0.968033	+	0.250822i	$0.919299\pi$
$810$		0			0
$811$			2.73863i			0.0961664i	0.998843	+	0.0480832i	$0.0153113\pi$
$811$			2.73863i			0.0961664i	−0.998843	+	0.0480832i	$0.984689\pi$
$812$		0			0
$813$	0.259969	+	0.150093i	0.00911752	+	0.00526400i
$814$		0			0
$815$	−22.2462	+	38.5316i	−0.779251	+	1.34970i
$816$		0			0
$817$	25.8610	−	14.9309i	0.904763	−	0.522365i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.9408	−	9.78078i	0.591238	−	0.341351i	−0.174349	−	0.984684i	$-0.555782\pi$
$821$	16.9408	−	9.78078i	0.591238	−	0.341351i	0.765587	+	0.643333i	$0.222449\pi$
$822$		0			0
$823$	15.8078	−	27.3799i	0.551024	−	0.954402i	−0.447177	−	0.894445i	$-0.647571\pi$
$823$	15.8078	−	27.3799i	0.551024	−	0.954402i	0.998201	−	0.0599561i	$-0.0190961\pi$
$824$		0			0
$825$	32.4563	+	18.7386i	1.12998	+	0.652395i
$826$		0			0
$827$		−	21.8617i		−	0.760207i	−0.924944	−	0.380104i	$-0.875888\pi$
$827$		−	21.8617i		−	0.760207i	0.924944	−	0.380104i	$-0.124112\pi$
$828$		0			0
$829$	−7.24621	−	12.5508i	−0.251671	−	0.435908i	0.712315	−	0.701860i	$-0.247647\pi$
$829$	−7.24621	−	12.5508i	−0.251671	−	0.435908i	−0.963986	+	0.265953i	$0.914314\pi$
$830$		0			0
$831$	7.23106			0.250843
$832$		0			0
$833$	30.4924			1.05650
$834$		0			0
$835$	4.00000	+	6.92820i	0.138426	+	0.239760i
$836$		0			0
$837$			22.2462i			0.768942i
$838$		0			0
$839$	33.5486	+	19.3693i	1.15823	+	0.668703i	0.950879	−	0.309564i	$-0.100183\pi$
$839$	33.5486	+	19.3693i	1.15823	+	0.668703i	0.207349	+	0.978267i	$0.433516\pi$
$840$		0			0
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$		0			0
$843$	13.5234	−	7.80776i	0.465772	−	0.268914i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.68531	+	0.973012i	−0.0579078	+	0.0334331i
$848$		0			0
$849$	−19.1231	+	33.1222i	−0.656303	+	1.13675i
$850$		0			0
$851$	−18.5999	−	10.7386i	−0.637595	−	0.368116i
$852$		0			0
$853$			17.3153i			0.592866i	0.955054	+	0.296433i	$0.0957971\pi$
$853$			17.3153i			0.592866i	−0.955054	+	0.296433i	$0.904203\pi$
$854$		0			0
$855$	3.12311	+	5.40938i	0.106808	+	0.184997i
$856$		0			0
$857$	8.73863			0.298506			0.149253	−	0.988799i	$-0.452313\pi$
$857$	8.73863			0.298506			0.149253	+	0.988799i	$0.452313\pi$
$858$		0			0
$859$	−52.9848			−1.80782			−0.903910	−	0.427723i	$-0.859316\pi$
$859$	−52.9848			−1.80782			−0.903910	+	0.427723i	$0.859316\pi$
$860$		0			0
$861$	6.24621	+	10.8188i	0.212870	+	0.368702i
$862$		0			0
$863$			4.30019i			0.146380i	0.997318	+	0.0731900i	$0.0233180\pi$
$863$			4.30019i			0.146380i	−0.997318	+	0.0731900i	$0.976682\pi$
$864$		0			0
$865$	−40.4768	−	23.3693i	−1.37625	−	0.794581i
$866$		0			0
$867$	21.6155	−	37.4392i	0.734102	−	1.27150i
$868$		0			0
$869$	−21.6375	+	12.4924i	−0.734002	+	0.423776i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−4.01029	+	2.31534i	−0.135728	+	0.0783624i
$874$		0			0
$875$	7.46543	−	12.9305i	0.252378	−	0.437131i
$876$		0			0
$877$	21.9237	+	12.6577i	0.740312	+	0.427419i	0.822183	−	0.569224i	$-0.192756\pi$
$877$	21.9237	+	12.6577i	0.740312	+	0.427419i	−0.0818709	+	0.996643i	$0.526090\pi$
$878$		0			0
$879$			30.5464i			1.03030i
$880$		0			0
$881$	−5.09612	−	8.82674i	−0.171693	−	0.297380i	0.767319	−	0.641265i	$-0.221590\pi$
$881$	−5.09612	−	8.82674i	−0.171693	−	0.297380i	−0.939012	+	0.343885i	$0.888257\pi$
$882$		0			0
$883$	−12.6847			−0.426873			−0.213436	−	0.976957i	$-0.568466\pi$
$883$	−12.6847			−0.426873			−0.213436	+	0.976957i	$0.568466\pi$
$884$		0			0
$885$	17.3693			0.583863
$886$		0			0
$887$	−26.7386	−	46.3127i	−0.897795	−	1.55503i	−0.830306	−	0.557307i	$-0.811835\pi$
$887$	−26.7386	−	46.3127i	−0.897795	−	1.55503i	−0.0674892	−	0.997720i	$-0.521499\pi$
$888$		0			0
$889$			9.75379i			0.327132i
$890$		0			0
$891$	−18.9328	−	10.9309i	−0.634273	−	0.366198i
$892$		0			0
$893$	−19.8078	+	34.3081i	−0.662842	+	1.14808i
$894$		0			0
$895$	14.4493	−	8.34233i	0.482988	−	0.278853i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.92820	+	4.00000i	−0.231069	+	0.133407i
$900$		0			0
$901$	17.1231	−	29.6581i	0.570453	−	0.988054i
$902$		0			0
$903$	20.1917	+	11.6577i	0.671937	+	0.387943i
$904$		0			0
$905$			52.9848i			1.76128i
$906$		0			0
$907$	−0.0961180	−	0.166481i	−0.00319154	−	0.00552792i	0.864425	−	0.502761i	$-0.167683\pi$
$907$	−0.0961180	−	0.166481i	−0.00319154	−	0.00552792i	−0.867617	+	0.497233i	$0.834349\pi$
$908$		0			0
$909$	0.630683			0.0209184
$910$		0			0
$911$	−9.36932			−0.310419			−0.155210	−	0.987882i	$-0.549605\pi$
$911$	−9.36932			−0.310419			−0.155210	+	0.987882i	$0.549605\pi$
$912$		0			0
$913$	22.2462	+	38.5316i	0.736242	+	1.27521i
$914$		0			0
$915$		−	16.0000i		−	0.528944i
$916$		0			0
$917$	21.3775	+	12.3423i	0.705949	+	0.407580i
$918$		0			0
$919$	20.4924	−	35.4939i	0.675983	−	1.17084i	−0.300198	−	0.953877i	$-0.597053\pi$
$919$	20.4924	−	35.4939i	0.675983	−	1.17084i	0.976181	−	0.216959i	$-0.0696139\pi$
$920$		0			0
$921$	6.59524	−	3.80776i	0.217321	−	0.125470i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−17.8667	+	10.3153i	−0.587453	+	0.339166i
$926$		0			0
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$		0			0
$929$	−41.4495	−	23.9309i	−1.35991	−	0.785146i	−0.370302	−	0.928912i	$-0.620746\pi$
$929$	−41.4495	−	23.9309i	−1.35991	−	0.785146i	−0.989612	+	0.143765i	$0.954079\pi$
$930$		0			0
$931$		−	14.2462i		−	0.466901i
$932$		0			0
$933$	14.9309	+	25.8610i	0.488815	+	0.846652i
$934$		0			0
$935$	74.3542			2.43164
$936$		0			0
$937$	12.7386			0.416153			0.208077	−	0.978113i	$-0.433280\pi$
$937$	12.7386			0.416153			0.208077	+	0.978113i	$0.433280\pi$
$938$		0			0
$939$	4.83475	+	8.37404i	0.157776	+	0.273276i
$940$		0			0
$941$		−	30.7926i		−	1.00381i	−0.864923	−	0.501905i	$-0.832633\pi$
$941$		−	30.7926i		−	1.00381i	0.864923	−	0.501905i	$-0.167367\pi$
$942$		0			0
$943$	−35.4939	−	20.4924i	−1.15584	−	0.667325i
$944$		0			0
$945$	−15.4654	+	26.7869i	−0.503091	+	0.871379i
$946$		0			0
$947$	15.0423	−	8.68466i	0.488808	−	0.282213i	−0.235272	−	0.971930i	$-0.575598\pi$
$947$	15.0423	−	8.68466i	0.488808	−	0.282213i	0.724080	+	0.689716i	$0.242265\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−5.74234	+	3.31534i	−0.186208	+	0.107507i
$952$		0			0
$953$	29.8348	−	51.6753i	0.966442	−	1.67393i	0.260754	−	0.965405i	$-0.416029\pi$
$953$	29.8348	−	51.6753i	0.966442	−	1.67393i	0.705689	−	0.708522i	$-0.250638\pi$
$954$		0			0
$955$	28.8987	+	16.6847i	0.935139	+	0.539903i
$956$		0			0
$957$		−	9.75379i		−	0.315295i
$958$		0			0
$959$	4.00000	+	6.92820i	0.129167	+	0.223723i
$960$		0			0
$961$	15.0000			0.483871
$962$		0			0
$963$	−2.24621			−0.0723831
$964$		0			0
$965$	−6.00000	−	10.3923i	−0.193147	−	0.334540i
$966$		0			0
$967$		−	1.56155i		−	0.0502162i	−0.999685	−	0.0251081i	$-0.992007\pi$
$967$		−	1.56155i		−	0.0502162i	0.999685	−	0.0251081i	$-0.00799299\pi$
$968$		0			0
$969$	−28.2328	−	16.3002i	−0.906967	−	0.523637i
$970$		0			0
$971$	9.65767	−	16.7276i	0.309929	−	0.536813i	−0.668417	−	0.743787i	$-0.733028\pi$
$971$	9.65767	−	16.7276i	0.309929	−	0.536813i	0.978347	+	0.206973i	$0.0663612\pi$
$972$		0			0
$973$	6.33527	−	3.65767i	0.203099	−	0.117260i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.6261	−	10.7538i	0.595902	−	0.344044i	−0.171526	−	0.985180i	$-0.554870\pi$
$977$	18.6261	−	10.7538i	0.595902	−	0.344044i	0.767428	+	0.641135i	$0.221536\pi$
$978$		0			0
$979$	15.6155	−	27.0469i	0.499074	−	0.864422i
$980$		0			0
$981$	8.66025	+	5.00000i	0.276501	+	0.159638i
$982$		0			0
$983$			10.9309i			0.348641i	0.984689	+	0.174320i	$0.0557728\pi$
$983$			10.9309i			0.348641i	−0.984689	+	0.174320i	$0.944227\pi$
$984$		0			0
$985$	26.1501	+	45.2933i	0.833211	+	1.44316i
$986$		0			0
$987$	−30.9309			−0.984540
$988$		0			0
$989$	−76.4924			−2.43232
$990$		0			0
$991$	−10.9309	−	18.9328i	−0.347231	−	0.601421i	0.638526	−	0.769600i	$-0.279545\pi$
$991$	−10.9309	−	18.9328i	−0.347231	−	0.601421i	−0.985756	+	0.168179i	$0.946211\pi$
$992$		0			0
$993$		−	44.4924i		−	1.41192i
$994$		0			0
$995$	−9.63289	−	5.56155i	−0.305383	−	0.176313i
$996$		0			0
$997$	8.12311	−	14.0696i	0.257261	−	0.445590i	−0.708246	−	0.705966i	$-0.750513\pi$
$997$	8.12311	−	14.0696i	0.257261	−	0.445590i	0.965507	+	0.260376i	$0.0838465\pi$
$998$		0			0
$999$	12.9305	−	7.46543i	0.409103	−	0.236196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1352.2.o.d.361.4		8
13.2	odd	12		104.2.a.b.1.1	✓	2
13.3	even	3		1352.2.f.c.337.2		4
13.4	even	6	inner	1352.2.o.d.1161.3		8
13.5	odd	4		1352.2.i.f.1329.2		4
13.6	odd	12		1352.2.i.f.529.2		4
13.7	odd	12		1352.2.i.d.529.2		4
13.8	odd	4		1352.2.i.d.1329.2		4
13.9	even	3	inner	1352.2.o.d.1161.4		8
13.10	even	6		1352.2.f.c.337.1		4
13.11	odd	12		1352.2.a.g.1.1		2
13.12	even	2	inner	1352.2.o.d.361.3		8
39.2	even	12		936.2.a.j.1.1		2
52.3	odd	6		2704.2.f.k.337.4		4
52.11	even	12		2704.2.a.p.1.2		2
52.15	even	12		208.2.a.e.1.2		2
52.23	odd	6		2704.2.f.k.337.3		4
65.2	even	12		2600.2.d.k.1249.3		4
65.28	even	12		2600.2.d.k.1249.2		4
65.54	odd	12		2600.2.a.p.1.2		2
91.41	even	12		5096.2.a.m.1.2		2
104.67	even	12		832.2.a.n.1.1		2
104.93	odd	12		832.2.a.k.1.2		2
156.119	odd	12		1872.2.a.u.1.1		2
208.67	even	12		3328.2.b.w.1665.3		4
208.93	odd	12		3328.2.b.y.1665.2		4
208.171	even	12		3328.2.b.w.1665.2		4
208.197	odd	12		3328.2.b.y.1665.3		4
260.119	even	12		5200.2.a.bw.1.1		2
312.197	even	12		7488.2.a.cu.1.2		2
312.275	odd	12		7488.2.a.cv.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.a.b.1.1	✓	2	13.2	odd	12
208.2.a.e.1.2		2	52.15	even	12
832.2.a.k.1.2		2	104.93	odd	12
832.2.a.n.1.1		2	104.67	even	12
936.2.a.j.1.1		2	39.2	even	12
1352.2.a.g.1.1		2	13.11	odd	12
1352.2.f.c.337.1		4	13.10	even	6
1352.2.f.c.337.2		4	13.3	even	3
1352.2.i.d.529.2		4	13.7	odd	12
1352.2.i.d.1329.2		4	13.8	odd	4
1352.2.i.f.529.2		4	13.6	odd	12
1352.2.i.f.1329.2		4	13.5	odd	4
1352.2.o.d.361.3		8	13.12	even	2	inner
1352.2.o.d.361.4		8	1.1	even	1	trivial
1352.2.o.d.1161.3		8	13.4	even	6	inner
1352.2.o.d.1161.4		8	13.9	even	3	inner
1872.2.a.u.1.1		2	156.119	odd	12
2600.2.a.p.1.2		2	65.54	odd	12
2600.2.d.k.1249.2		4	65.28	even	12
2600.2.d.k.1249.3		4	65.2	even	12
2704.2.a.p.1.2		2	52.11	even	12
2704.2.f.k.337.3		4	52.23	odd	6
2704.2.f.k.337.4		4	52.3	odd	6
3328.2.b.w.1665.2		4	208.171	even	12
3328.2.b.w.1665.3		4	208.67	even	12
3328.2.b.y.1665.2		4	208.93	odd	12
3328.2.b.y.1665.3		4	208.197	odd	12
5096.2.a.m.1.2		2	91.41	even	12
5200.2.a.bw.1.1		2	260.119	even	12
7488.2.a.cu.1.2		2	312.197	even	12
7488.2.a.cv.1.2		2	312.275	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1352.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.780776 + 1.35234i) q^{3} +3.56155i q^{5} +(1.35234 + 0.780776i) q^{7} +(0.280776 - 0.486319i) q^{9} +(-2.70469 + 1.56155i) q^{11} +(-4.81645 + 2.78078i) q^{15} +(-3.34233 + 5.78908i) q^{17} +(2.70469 + 1.56155i) q^{19} +2.43845i q^{21} +(-4.00000 - 6.92820i) q^{23} -7.68466 q^{25} +5.56155 q^{27} +(1.00000 + 1.73205i) q^{29} +4.00000i q^{31} +(-4.22351 - 2.43845i) q^{33} +(-2.78078 + 4.81645i) q^{35} +(2.32498 - 1.34233i) q^{37} +(4.43674 - 2.56155i) q^{41} +(4.78078 - 8.28055i) q^{43} +(1.73205 + 1.00000i) q^{45} +12.6847i q^{47} +(-2.28078 - 3.95042i) q^{49} -10.4384 q^{51} -5.12311 q^{53} +(-5.56155 - 9.63289i) q^{55} +4.87689i q^{57} +(-2.70469 - 1.56155i) q^{59} +(-1.43845 + 2.49146i) q^{61} +(0.759413 - 0.438447i) q^{63} +(2.70469 - 1.56155i) q^{67} +(6.24621 - 10.8188i) q^{69} +(-4.05703 - 2.34233i) q^{71} +6.00000i q^{73} +(-6.00000 - 10.3923i) q^{75} -4.87689 q^{77} +8.00000 q^{79} +(3.50000 + 6.06218i) q^{81} -14.2462i q^{83} +(-20.6181 - 11.9039i) q^{85} +(-1.56155 + 2.70469i) q^{87} +(-8.66025 + 5.00000i) q^{89} +(-5.40938 + 3.12311i) q^{93} +(-5.56155 + 9.63289i) q^{95} +(-7.14143 - 4.12311i) q^{97} +1.75379i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 6 q^{9} - 2 q^{17} - 32 q^{23} - 12 q^{25} + 28 q^{27} + 8 q^{29} - 14 q^{35} + 30 q^{43} - 10 q^{49} - 100 q^{51} - 8 q^{53} - 28 q^{55} - 28 q^{61} - 16 q^{69} - 48 q^{75} - 72 q^{77}+ \cdots - 28 q^{95}+O(q^{100}) \) 8 * q - 2 * q^3 - 6 * q^9 - 2 * q^17 - 32 * q^23 - 12 * q^25 + 28 * q^27 + 8 * q^29 - 14 * q^35 + 30 * q^43 - 10 * q^49 - 100 * q^51 - 8 * q^53 - 28 * q^55 - 28 * q^61 - 16 * q^69 - 48 * q^75 - 72 * q^77 + 64 * q^79 + 28 * q^81 + 4 * q^87 - 28 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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