LMFDB - Embedded newform 672.2.bi.c.17.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,2,Mod(17,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.24
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70874 - 0.283220i) q^{3} +(2.24840 - 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(2.83957 - 0.967897i) q^{9} +(-1.63808 + 2.83724i) q^{11} +0.912635 q^{13} +(3.47427 - 2.85492i) q^{15} +(-2.39448 + 4.14736i) q^{17} +(-2.66693 - 4.61926i) q^{19} +(4.54754 + 0.565618i) q^{21} +(-4.45569 + 2.57249i) q^{23} +(0.870190 - 1.50721i) q^{25} +(4.57796 - 2.45811i) q^{27} +1.35950 q^{29} +(-8.18469 - 4.72543i) q^{31} +(-1.99549 + 5.31204i) q^{33} +(6.67920 - 1.60340i) q^{35} +(1.59746 - 0.922292i) q^{37} +(1.55945 - 0.258476i) q^{39} -5.91833 q^{41} -8.00125i q^{43} +(5.12805 - 5.86230i) q^{45} +(3.29243 + 5.70266i) q^{47} +(5.87055 + 3.81269i) q^{49} +(-2.91692 + 7.76491i) q^{51} +(0.841712 - 1.45789i) q^{53} +8.50565i q^{55} +(-5.86535 - 7.13777i) q^{57} +(-1.50266 - 0.867561i) q^{59} +(-4.72347 - 8.18130i) q^{61} +(7.93074 - 0.321460i) q^{63} +(2.05197 - 1.18470i) q^{65} +(10.8634 + 6.27198i) q^{67} +(-6.88502 + 5.65766i) q^{69} +0.603989i q^{71} +(-1.29220 - 0.746053i) q^{73} +(1.06005 - 2.82189i) q^{75} +(-6.28759 + 5.96647i) q^{77} +(0.0625152 + 0.108280i) q^{79} +(7.12635 - 5.49683i) q^{81} +0.246431i q^{83} +12.4332i q^{85} +(2.32303 - 0.385038i) q^{87} +(-1.80671 - 3.12931i) q^{89} +(2.31516 + 0.685829i) q^{91} +(-15.3238 - 5.75646i) q^{93} +(-11.9926 - 6.92395i) q^{95} -5.10324i q^{97} +(-1.90529 + 9.64204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) $ 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.70874	−	0.283220i	0.986541	−	0.163517i
$3$	1.70874	−	0.283220i	0.986541	−	0.163517i
$4$		0			0
$5$	2.24840	−	1.29811i	1.00551	−	0.580533i	0.0956384	−	0.995416i	$-0.469511\pi$
$5$	2.24840	−	1.29811i	1.00551	−	0.580533i	0.909875	+	0.414883i	$0.136177\pi$
$6$		0			0
$7$	2.53678	+	0.751482i	0.958814	+	0.284033i
$7$	2.53678	+	0.751482i	0.958814	+	0.284033i
$8$		0			0
$9$	2.83957	−	0.967897i	0.946524	−	0.322632i
$10$		0			0
$11$	−1.63808	+	2.83724i	−0.493900	+	0.855460i	−0.999975	−	0.00702958i	$-0.997762\pi$
$11$	−1.63808	+	2.83724i	−0.493900	+	0.855460i	0.506075	+	0.862489i	$0.331096\pi$
$12$		0			0
$13$	0.912635			0.253119			0.126560	−	0.991959i	$-0.459606\pi$
$13$	0.912635			0.253119			0.126560	+	0.991959i	$0.459606\pi$
$14$		0			0
$15$	3.47427	−	2.85492i	0.897052	−	0.737138i
$16$		0			0
$17$	−2.39448	+	4.14736i	−0.580746	+	1.00588i	0.414645	+	0.909983i	$0.363906\pi$
$17$	−2.39448	+	4.14736i	−0.580746	+	1.00588i	−0.995391	+	0.0958985i	$0.969428\pi$
$18$		0			0
$19$	−2.66693	−	4.61926i	−0.611836	−	1.05973i	−0.990931	−	0.134373i	$-0.957098\pi$
$19$	−2.66693	−	4.61926i	−0.611836	−	1.05973i	0.379095	−	0.925358i	$-0.376235\pi$
$20$		0			0
$21$	4.54754	+	0.565618i	0.992354	+	0.123428i
$22$		0			0
$23$	−4.45569	+	2.57249i	−0.929075	+	0.536402i	−0.886519	−	0.462692i	$-0.846884\pi$
$23$	−4.45569	+	2.57249i	−0.929075	+	0.536402i	−0.0425563	+	0.999094i	$0.513550\pi$
$24$		0			0
$25$	0.870190	−	1.50721i	0.174038	−	0.301443i
$26$		0			0
$27$	4.57796	−	2.45811i	0.881029	−	0.473063i
$28$		0			0
$29$	1.35950			0.252453			0.126227	−	0.992001i	$-0.459713\pi$
$29$	1.35950			0.252453			0.126227	+	0.992001i	$0.459713\pi$
$30$		0			0
$31$	−8.18469	−	4.72543i	−1.47001	−	0.848713i	−0.470580	−	0.882357i	$-0.655955\pi$
$31$	−8.18469	−	4.72543i	−1.47001	−	0.848713i	−0.999434	+	0.0336443i	$0.989289\pi$
$32$		0			0
$33$	−1.99549	+	5.31204i	−0.347370	+	0.924707i
$34$		0			0
$35$	6.67920	−	1.60340i	1.12899	−	0.271024i
$36$		0			0
$37$	1.59746	−	0.922292i	0.262620	−	0.151624i	−0.362909	−	0.931825i	$-0.618216\pi$
$37$	1.59746	−	0.922292i	0.262620	−	0.151624i	0.625529	+	0.780201i	$0.284883\pi$
$38$		0			0
$39$	1.55945	−	0.258476i	0.249713	−	0.0413894i
$40$		0			0
$41$	−5.91833			−0.924288			−0.462144	−	0.886805i	$-0.652920\pi$
$41$	−5.91833			−0.924288			−0.462144	+	0.886805i	$0.652920\pi$
$42$		0			0
$43$		−	8.00125i		−	1.22018i	−0.792332	−	0.610090i	$-0.791133\pi$
$43$		−	8.00125i		−	1.22018i	0.792332	−	0.610090i	$-0.208867\pi$
$44$		0			0
$45$	5.12805	−	5.86230i	0.764444	−	0.873900i
$46$		0			0
$47$	3.29243	+	5.70266i	0.480250	+	0.831818i	0.999743	−	0.0226567i	$-0.00721246\pi$
$47$	3.29243	+	5.70266i	0.480250	+	0.831818i	−0.519493	+	0.854475i	$0.673879\pi$
$48$		0			0
$49$	5.87055	+	3.81269i	0.838650	+	0.544671i
$50$		0			0
$51$	−2.91692	+	7.76491i	−0.408451	+	1.08730i
$52$		0			0
$53$	0.841712	−	1.45789i	0.115618	−	0.200256i	−0.802409	−	0.596775i	$-0.796448\pi$
$53$	0.841712	−	1.45789i	0.115618	−	0.200256i	0.918027	+	0.396519i	$0.129782\pi$
$54$		0			0
$55$			8.50565i			1.14690i
$56$		0			0
$57$	−5.86535	−	7.13777i	−0.776885	−	0.945421i
$58$		0			0
$59$	−1.50266	−	0.867561i	−0.195630	−	0.112947i	0.398986	−	0.916957i	$-0.369362\pi$
$59$	−1.50266	−	0.867561i	−0.195630	−	0.112947i	−0.594615	+	0.804010i	$0.702696\pi$
$60$		0			0
$61$	−4.72347	−	8.18130i	−0.604779	−	1.04751i	−0.992086	−	0.125557i	$-0.959928\pi$
$61$	−4.72347	−	8.18130i	−0.604779	−	1.04751i	0.387308	−	0.921951i	$-0.373405\pi$
$62$		0			0
$63$	7.93074	−	0.321460i	0.999180	−	0.0405001i
$64$		0			0
$65$	2.05197	−	1.18470i	0.254515	−	0.146944i
$66$		0			0
$67$	10.8634	+	6.27198i	1.32717	+	0.766245i	0.984862	−	0.173341i	$-0.0554564\pi$
$67$	10.8634	+	6.27198i	1.32717	+	0.766245i	0.342313	+	0.939586i	$0.388790\pi$
$68$		0			0
$69$	−6.88502	+	5.65766i	−0.828860	+	0.681102i
$70$		0			0
$71$			0.603989i			0.0716803i	0.999358	+	0.0358401i	$0.0114107\pi$
$71$			0.603989i			0.0716803i	−0.999358	+	0.0358401i	$0.988589\pi$
$72$		0			0
$73$	−1.29220	−	0.746053i	−0.151241	−	0.0873189i	0.422470	−	0.906377i	$-0.361163\pi$
$73$	−1.29220	−	0.746053i	−0.151241	−	0.0873189i	−0.573711	+	0.819058i	$0.694497\pi$
$74$		0			0
$75$	1.06005	−	2.82189i	0.122404	−	0.325844i
$76$		0			0
$77$	−6.28759	+	5.96647i	−0.716537	+	0.679943i
$78$		0			0
$79$	0.0625152	+	0.108280i	0.00703351	+	0.0121824i	0.869521	−	0.493896i	$-0.164428\pi$
$79$	0.0625152	+	0.108280i	0.00703351	+	0.0121824i	−0.862487	+	0.506079i	$0.831094\pi$
$80$		0			0
$81$	7.12635	−	5.49683i	0.791817	−	0.610759i
$82$		0			0
$83$			0.246431i			0.0270493i	0.999909	+	0.0135247i	$0.00430516\pi$
$83$			0.246431i			0.0270493i	−0.999909	+	0.0135247i	$0.995695\pi$
$84$		0			0
$85$			12.4332i			1.34857i
$86$		0			0
$87$	2.32303	−	0.385038i	0.249055	−	0.0412804i
$88$		0			0
$89$	−1.80671	−	3.12931i	−0.191511	−	0.331706i	0.754241	−	0.656598i	$-0.228005\pi$
$89$	−1.80671	−	3.12931i	−0.191511	−	0.331706i	−0.945751	+	0.324892i	$0.894672\pi$
$90$		0			0
$91$	2.31516	+	0.685829i	0.242695	+	0.0718944i
$92$		0			0
$93$	−15.3238	−	5.75646i	−1.58901	−	0.596917i
$94$		0			0
$95$	−11.9926	−	6.92395i	−1.23042	−	0.710382i
$96$		0			0
$97$		−	5.10324i		−	0.518155i	−0.965857	−	0.259078i	$-0.916581\pi$
$97$		−	5.10324i		−	0.518155i	0.965857	−	0.259078i	$-0.0834185\pi$
$98$		0			0
$99$	−1.90529	+	9.64204i	−0.191489	+	0.969061i
$100$		0			0
$101$	−6.33114	−	3.65529i	−0.629972	−	0.363715i	0.150769	−	0.988569i	$-0.451825\pi$
$101$	−6.33114	−	3.65529i	−0.629972	−	0.363715i	−0.780741	+	0.624854i	$0.785158\pi$
$102$		0			0
$103$	−0.670566	+	0.387151i	−0.0660728	+	0.0381472i	−0.532672	−	0.846321i	$-0.678812\pi$
$103$	−0.670566	+	0.387151i	−0.0660728	+	0.0381472i	0.466600	+	0.884469i	$0.345479\pi$
$104$		0			0
$105$	10.9589	−	4.63148i	1.06948	−	0.451986i
$106$		0			0
$107$	−7.26435	−	12.5822i	−0.702271	−	1.21637i	−0.967667	−	0.252229i	$-0.918836\pi$
$107$	−7.26435	−	12.5822i	−0.702271	−	1.21637i	0.265397	−	0.964139i	$-0.414497\pi$
$108$		0			0
$109$	12.8015	+	7.39093i	1.22616	+	0.707923i	0.966224	−	0.257703i	$-0.0829658\pi$
$109$	12.8015	+	7.39093i	1.22616	+	0.707923i	0.259934	+	0.965626i	$0.416299\pi$
$110$		0			0
$111$	2.46842	−	2.02839i	0.234292	−	0.192526i
$112$		0			0
$113$			16.2708i			1.53063i	0.643657	+	0.765314i	$0.277416\pi$
$113$			16.2708i			1.53063i	−0.643657	+	0.765314i	$0.722584\pi$
$114$		0			0
$115$	−6.67877	+	11.5680i	−0.622798	+	1.07872i
$116$		0			0
$117$	2.59149	−	0.883337i	0.239584	−	0.0816646i
$118$		0			0
$119$	−9.19094	+	8.72154i	−0.842532	+	0.799503i
$120$		0			0
$121$	0.133385	+	0.231029i	0.0121259	+	0.0210026i
$122$		0			0
$123$	−10.1129	+	1.67619i	−0.911847	+	0.151137i
$124$		0			0
$125$			8.46270i			0.756927i
$126$		0			0
$127$	1.59996			0.141973			0.0709867	−	0.997477i	$-0.477385\pi$
$127$	1.59996			0.141973			0.0709867	+	0.997477i	$0.477385\pi$
$128$		0			0
$129$	−2.26611	−	13.6720i	−0.199520	−	1.20376i
$130$		0			0
$131$	7.96684	−	4.59965i	0.696066	−	0.401874i	−0.109815	−	0.993952i	$-0.535026\pi$
$131$	7.96684	−	4.59965i	0.696066	−	0.401874i	0.805880	+	0.592078i	$0.201692\pi$
$132$		0			0
$133$	−3.29414	−	13.7222i	−0.285638	−	1.18987i
$134$		0			0
$135$	7.10217	−	11.4695i	0.611257	−	0.987138i
$136$		0			0
$137$	−2.43936	−	1.40836i	−0.208408	−	0.120325i	0.392163	−	0.919896i	$-0.371727\pi$
$137$	−2.43936	−	1.40836i	−0.208408	−	0.120325i	−0.600571	+	0.799571i	$0.705060\pi$
$138$		0			0
$139$	2.80505			0.237921			0.118960	−	0.992899i	$-0.462044\pi$
$139$	2.80505			0.237921			0.118960	+	0.992899i	$0.462044\pi$
$140$		0			0
$141$	7.24101	+	8.81187i	0.609803	+	0.742093i
$142$		0			0
$143$	−1.49497	+	2.58936i	−0.125016	+	0.216533i
$144$		0			0
$145$	3.05670	−	1.76479i	0.253845	−	0.146558i
$146$		0			0
$147$	11.1111	+	4.85224i	0.916425	+	0.400206i
$148$		0			0
$149$	−8.67025	−	15.0173i	−0.710295	−	1.23027i	−0.964746	−	0.263181i	$-0.915228\pi$
$149$	−8.67025	−	15.0173i	−0.710295	−	1.23027i	0.254451	−	0.967086i	$-0.418105\pi$
$150$		0			0
$151$	6.41551	−	11.1120i	0.522087	−	0.904281i	−0.477583	−	0.878587i	$-0.658487\pi$
$151$	6.41551	−	11.1120i	0.522087	−	0.904281i	0.999670	−	0.0256942i	$-0.00817960\pi$
$152$		0			0
$153$	−2.78508	+	14.0943i	−0.225160	+	1.13946i
$154$		0			0
$155$	−24.5366			−1.97082
$156$		0			0
$157$	−8.55356	+	14.8152i	−0.682648	+	1.18238i	0.291521	+	0.956564i	$0.405839\pi$
$157$	−8.55356	+	14.8152i	−0.682648	+	1.18238i	−0.974170	+	0.225817i	$0.927495\pi$
$158$		0			0
$159$	1.02536	−	2.72954i	0.0813165	−	0.216466i
$160$		0			0
$161$	−13.2363	+	3.17749i	−1.04317	+	0.250421i
$162$		0			0
$163$	−21.6390	+	12.4933i	−1.69489	+	0.978547i	−0.744436	+	0.667694i	$0.767282\pi$
$163$	−21.6390	+	12.4933i	−1.69489	+	0.978547i	−0.950458	+	0.310853i	$0.899385\pi$
$164$		0			0
$165$	2.40897	+	14.5339i	0.187538	+	1.13146i
$166$		0			0
$167$	9.89286			0.765532			0.382766	−	0.923845i	$-0.374972\pi$
$167$	9.89286			0.765532			0.382766	+	0.923845i	$0.374972\pi$
$168$		0			0
$169$	−12.1671			−0.935931
$170$		0			0
$171$	−12.0439	−	10.5354i	−0.921021	−	0.805662i
$172$		0			0
$173$	13.3755	−	7.72235i	1.01692	−	0.587120i	0.103710	−	0.994608i	$-0.466929\pi$
$173$	13.3755	−	7.72235i	1.01692	−	0.587120i	0.913211	+	0.407488i	$0.133595\pi$
$174$		0			0
$175$	3.34013	−	3.16954i	0.252490	−	0.239595i
$176$		0			0
$177$	−2.81336	−	1.05685i	−0.211465	−	0.0794379i
$178$		0			0
$179$	−6.07462	+	10.5216i	−0.454038	+	0.786418i	−0.998632	−	0.0522822i	$-0.983350\pi$
$179$	−6.07462	+	10.5216i	−0.454038	+	0.786418i	0.544594	+	0.838700i	$0.316684\pi$
$180$		0			0
$181$	1.41922			0.105489			0.0527447	−	0.998608i	$-0.483203\pi$
$181$	1.41922			0.105489			0.0527447	+	0.998608i	$0.483203\pi$
$182$		0			0
$183$	−10.3883	−	12.6419i	−0.767924	−	0.934517i
$184$		0			0
$185$	2.39448	−	4.14736i	0.176045	−	0.304920i
$186$		0			0
$187$	−7.84469	−	13.5874i	−0.573661	−	0.993610i
$188$		0			0
$189$	13.4605	−	2.79543i	0.979109	−	0.203338i
$190$		0			0
$191$	3.62414	−	2.09240i	0.262234	−	0.151401i	−0.363119	−	0.931743i	$-0.618288\pi$
$191$	3.62414	−	2.09240i	0.262234	−	0.151401i	0.625353	+	0.780342i	$0.284955\pi$
$192$		0			0
$193$	−13.1905	+	22.8467i	−0.949476	+	1.64454i	−0.202946	+	0.979190i	$0.565051\pi$
$193$	−13.1905	+	22.8467i	−0.949476	+	1.64454i	−0.746531	+	0.665351i	$0.768282\pi$
$194$		0			0
$195$	3.17074	−	2.60550i	0.227061	−	0.186584i
$196$		0			0
$197$	−12.6908			−0.904184			−0.452092	−	0.891971i	$-0.649322\pi$
$197$	−12.6908			−0.904184			−0.452092	+	0.891971i	$0.649322\pi$
$198$		0			0
$199$	−0.939591	−	0.542473i	−0.0666058	−	0.0384549i	0.466327	−	0.884612i	$-0.345577\pi$
$199$	−0.939591	−	0.542473i	−0.0666058	−	0.0384549i	−0.532933	+	0.846157i	$0.678910\pi$
$200$		0			0
$201$	20.3390	+	7.64045i	1.43461	+	0.538916i
$202$		0			0
$203$	3.44876	+	1.02164i	0.242056	+	0.0717052i
$204$		0			0
$205$	−13.3067	+	7.68265i	−0.929384	+	0.536580i
$206$		0			0
$207$	−10.1623	+	11.6174i	−0.706332	+	0.807467i
$208$		0			0
$209$	17.4746			1.20874
$210$		0			0
$211$			7.89074i			0.543221i	0.962407	+	0.271610i	$0.0875562\pi$
$211$			7.89074i			0.543221i	−0.962407	+	0.271610i	$0.912444\pi$
$212$		0			0
$213$	0.171062	+	1.03206i	0.0117209	+	0.0707155i
$214$		0			0
$215$	−10.3865	−	17.9900i	−0.708355	−	1.22691i
$216$		0			0
$217$	−17.2117	−	18.1381i	−1.16841	−	1.23129i
$218$		0			0
$219$	−2.41933	−	0.908832i	−0.163483	−	0.0614132i
$220$		0			0
$221$	−2.18528	+	3.78502i	−0.146998	+	0.254608i
$222$		0			0
$223$			11.5392i			0.772720i	0.922348	+	0.386360i	$0.126268\pi$
$223$			11.5392i			0.772720i	−0.922348	+	0.386360i	$0.873732\pi$
$224$		0			0
$225$	1.01214	−	5.12210i	0.0674760	−	0.341473i
$226$		0			0
$227$	13.4825	+	7.78410i	0.894862	+	0.516649i	0.875530	−	0.483164i	$-0.160513\pi$
$227$	13.4825	+	7.78410i	0.894862	+	0.516649i	0.0193323	+	0.999813i	$0.493846\pi$
$228$		0			0
$229$	−1.78238	−	3.08717i	−0.117783	−	0.204006i	0.801106	−	0.598523i	$-0.204245\pi$
$229$	−1.78238	−	3.08717i	−0.117783	−	0.204006i	−0.918889	+	0.394517i	$0.870912\pi$
$230$		0			0
$231$	−9.05402	+	11.9759i	−0.595711	+	0.787957i
$232$		0			0
$233$	6.60666	−	3.81435i	0.432816	−	0.249887i	−0.267729	−	0.963494i	$-0.586273\pi$
$233$	6.60666	−	3.81435i	0.432816	−	0.249887i	0.700546	+	0.713607i	$0.252940\pi$
$234$		0			0
$235$	14.8054	+	8.54789i	0.965796	+	0.557603i
$236$		0			0
$237$	0.137489	+	0.167316i	0.00893087	+	0.0108683i
$238$		0			0
$239$			13.2745i			0.858658i	0.903148	+	0.429329i	$0.141250\pi$
$239$			13.2745i			0.858658i	−0.903148	+	0.429329i	$0.858750\pi$
$240$		0			0
$241$	9.92793	+	5.73189i	0.639514	+	0.369224i	0.784427	−	0.620221i	$-0.212957\pi$
$241$	9.92793	+	5.73189i	0.639514	+	0.369224i	−0.144913	+	0.989444i	$0.546290\pi$
$242$		0			0
$243$	10.6203	−	11.4110i	0.681290	−	0.732014i
$244$		0			0
$245$	18.1486	+	0.951816i	1.15947	+	0.0608093i
$246$		0			0
$247$	−2.43393	−	4.21570i	−0.154867	−	0.268238i
$248$		0			0
$249$	0.0697941	+	0.421086i	0.00442302	+	0.0266852i
$250$		0			0
$251$		−	1.44903i		−	0.0914619i	−0.998954	−	0.0457309i	$-0.985438\pi$
$251$		−	1.44903i		−	0.0914619i	0.998954	−	0.0457309i	$-0.0145617\pi$
$252$		0			0
$253$		−	16.8558i		−	1.05972i
$254$		0			0
$255$	3.52133	+	21.2451i	0.220514	+	1.33042i
$256$		0			0
$257$	−6.03418	−	10.4515i	−0.376402	−	0.651948i	0.614134	−	0.789202i	$-0.289506\pi$
$257$	−6.03418	−	10.4515i	−0.376402	−	0.651948i	−0.990536	+	0.137254i	$0.956172\pi$
$258$		0			0
$259$	4.74549	−	1.13920i	0.294870	−	0.0707862i
$260$		0			0
$261$	3.86041	−	1.31586i	0.238953	−	0.0814496i
$262$		0			0
$263$	21.7325	+	12.5473i	1.34008	+	0.773697i	0.986819	−	0.161827i	$-0.0517385\pi$
$263$	21.7325	+	12.5473i	1.34008	+	0.773697i	0.353264	+	0.935524i	$0.385072\pi$
$264$		0			0
$265$		−	4.37055i		−	0.268480i
$266$		0			0
$267$	−3.97347	−	4.83547i	−0.243172	−	0.295926i
$268$		0			0
$269$	−6.61826	−	3.82105i	−0.403522	−	0.232974i	0.284480	−	0.958682i	$-0.408179\pi$
$269$	−6.61826	−	3.82105i	−0.403522	−	0.232974i	−0.688003	+	0.725708i	$0.741512\pi$
$270$		0			0
$271$	9.27850	−	5.35694i	0.563629	−	0.325411i	−0.190972	−	0.981595i	$-0.561164\pi$
$271$	9.27850	−	5.35694i	0.563629	−	0.325411i	0.754601	+	0.656184i	$0.227831\pi$
$272$		0			0
$273$	4.15024	+	0.516203i	0.251184	+	0.0312420i
$274$		0			0
$275$	2.85088	+	4.93787i	0.171915	+	0.297765i
$276$		0			0
$277$	−3.08910	−	1.78349i	−0.185606	−	0.107160i	0.404318	−	0.914618i	$-0.367509\pi$
$277$	−3.08910	−	1.78349i	−0.185606	−	0.107160i	−0.589924	+	0.807459i	$0.700842\pi$
$278$		0			0
$279$	−27.8148	−	5.49627i	−1.66523	−	0.329053i
$280$		0			0
$281$			4.26336i			0.254331i	0.991882	+	0.127165i	$0.0405879\pi$
$281$			4.26336i			0.254331i	−0.991882	+	0.127165i	$0.959412\pi$
$282$		0			0
$283$	11.3202	−	19.6072i	0.672918	−	1.16553i	−0.304154	−	0.952623i	$-0.598374\pi$
$283$	11.3202	−	19.6072i	0.672918	−	1.16553i	0.977073	−	0.212906i	$-0.0682928\pi$
$284$		0			0
$285$	−22.4533	−	8.43466i	−1.33002	−	0.499626i
$286$		0			0
$287$	−15.0135	−	4.44752i	−0.886220	−	0.262529i
$288$		0			0
$289$	−2.96705	−	5.13907i	−0.174532	−	0.302298i
$290$		0			0
$291$	−1.44534	−	8.72009i	−0.0847272	−	0.511181i
$292$		0			0
$293$			5.96057i			0.348220i	0.984726	+	0.174110i	$0.0557049\pi$
$293$			5.96057i			0.348220i	−0.984726	+	0.174110i	$0.944295\pi$
$294$		0			0
$295$	−4.50477			−0.262278
$296$		0			0
$297$	−0.524829	+	17.0153i	−0.0304537	+	0.987330i
$298$		0			0
$299$	−4.06642	+	2.34775i	−0.235167	+	0.135774i
$300$		0			0
$301$	6.01280	−	20.2975i	0.346572	−	1.16993i
$302$		0			0
$303$	−11.8535	−	4.45282i	−0.680967	−	0.255808i
$304$		0			0
$305$	−21.2405	−	12.2632i	−1.21623	−	0.702189i
$306$		0			0
$307$	5.42113			0.309400			0.154700	−	0.987961i	$-0.450559\pi$
$307$	5.42113			0.309400			0.154700	+	0.987961i	$0.450559\pi$
$308$		0			0
$309$	−1.03617	+	0.851458i	−0.0589458	+	0.0484378i
$310$		0			0
$311$	12.1809	−	21.0979i	0.690714	−	1.19635i	−0.280890	−	0.959740i	$-0.590630\pi$
$311$	12.1809	−	21.0979i	0.690714	−	1.19635i	0.971604	−	0.236612i	$-0.0760370\pi$
$312$		0			0
$313$	14.1392	−	8.16327i	0.799195	−	0.461415i	−0.0439948	−	0.999032i	$-0.514009\pi$
$313$	14.1392	−	8.16327i	0.799195	−	0.461415i	0.843189	+	0.537617i	$0.180675\pi$
$314$		0			0
$315$	17.4142	−	11.0178i	0.981177	−	0.620780i
$316$		0			0
$317$	9.94185	+	17.2198i	0.558390	+	0.967160i	0.997631	+	0.0687904i	$0.0219140\pi$
$317$	9.94185	+	17.2198i	0.558390	+	0.967160i	−0.439241	+	0.898369i	$0.644753\pi$
$318$		0			0
$319$	−2.22697	+	3.85723i	−0.124687	+	0.215964i
$320$		0			0
$321$	−15.9764	−	19.4423i	−0.891716	−	1.08516i
$322$		0			0
$323$	25.5436			1.42128
$324$		0			0
$325$	0.794166	−	1.37554i	0.0440524	−	0.0763010i
$326$		0			0
$327$	23.9676	+	9.00354i	1.32541	+	0.497897i
$328$		0			0
$329$	4.06674	+	16.9406i	0.224207	+	0.933966i
$330$		0			0
$331$	1.90300	−	1.09870i	0.104599	−	0.0603900i	−0.446788	−	0.894640i	$-0.647432\pi$
$331$	1.90300	−	1.09870i	0.104599	−	0.0603900i	0.551387	+	0.834250i	$0.314099\pi$
$332$		0			0
$333$	3.64341	−	4.16509i	0.199658	−	0.228246i
$334$		0			0
$335$	32.5669			1.77932
$336$		0			0
$337$	29.4138			1.60227			0.801135	−	0.598484i	$-0.204230\pi$
$337$	29.4138			1.60227			0.801135	+	0.598484i	$0.204230\pi$
$338$		0			0
$339$	4.60822	+	27.8026i	0.250284	+	1.51003i
$340$		0			0
$341$	26.8144	−	15.4813i	1.45208	−	0.838358i
$342$		0			0
$343$	12.0271	+	14.0836i	0.649405	+	0.760443i
$344$		0			0
$345$	−8.13599	+	21.6582i	−0.438027	+	1.16604i
$346$		0			0
$347$	6.43016	−	11.1374i	0.345189	−	0.597885i	−0.640199	−	0.768209i	$-0.721148\pi$
$347$	6.43016	−	11.1374i	0.345189	−	0.597885i	0.985388	+	0.170324i	$0.0544815\pi$
$348$		0			0
$349$	30.0571			1.60892			0.804460	−	0.594006i	$-0.202455\pi$
$349$	30.0571			1.60892			0.804460	+	0.594006i	$0.202455\pi$
$350$		0			0
$351$	4.17801	−	2.24335i	0.223005	−	0.119741i
$352$		0			0
$353$	12.1069	−	20.9698i	0.644387	−	1.11611i	−0.340056	−	0.940405i	$-0.610446\pi$
$353$	12.1069	−	20.9698i	0.644387	−	1.11611i	0.984443	−	0.175705i	$-0.0562206\pi$
$354$		0			0
$355$	0.784045	+	1.35801i	0.0416128	+	0.0720755i
$356$		0			0
$357$	−13.2348	+	17.5059i	−0.700459	+	0.926510i
$358$		0			0
$359$	−3.16884	+	1.82953i	−0.167245	+	0.0965590i	−0.581286	−	0.813699i	$-0.697450\pi$
$359$	−3.16884	+	1.82953i	−0.167245	+	0.0965590i	0.414041	+	0.910258i	$0.364117\pi$
$360$		0			0
$361$	−4.72503	+	8.18398i	−0.248686	+	0.430736i
$362$		0			0
$363$	0.293351	+	0.356991i	0.0153970	+	0.0187372i
$364$		0			0
$365$	−3.87384			−0.202766
$366$		0			0
$367$	15.1950	+	8.77283i	0.793172	+	0.457938i	0.841078	−	0.540914i	$-0.181922\pi$
$367$	15.1950	+	8.77283i	0.793172	+	0.457938i	−0.0479063	+	0.998852i	$0.515255\pi$
$368$		0			0
$369$	−16.8055	+	5.72834i	−0.874861	+	0.298205i
$370$		0			0
$371$	3.23082	−	3.06582i	0.167736	−	0.159169i
$372$		0			0
$373$	3.25687	−	1.88036i	0.168635	−	0.0973612i	−0.413307	−	0.910592i	$-0.635626\pi$
$373$	3.25687	−	1.88036i	0.168635	−	0.0973612i	0.581942	+	0.813230i	$0.302293\pi$
$374$		0			0
$375$	2.39681	+	14.4605i	0.123771	+	0.746739i
$376$		0			0
$377$	1.24073			0.0639008
$378$		0			0
$379$			12.2799i			0.630774i	0.948963	+	0.315387i	$0.102134\pi$
$379$			12.2799i			0.630774i	−0.948963	+	0.315387i	$0.897866\pi$
$380$		0			0
$381$	2.73391	−	0.453140i	0.140062	−	0.0232151i
$382$		0			0
$383$	3.77515	+	6.53874i	0.192901	+	0.334114i	0.946210	−	0.323552i	$-0.104877\pi$
$383$	3.77515	+	6.53874i	0.192901	+	0.334114i	−0.753309	+	0.657666i	$0.771544\pi$
$384$		0			0
$385$	−6.39184	+	21.5770i	−0.325758	+	1.09967i
$386$		0			0
$387$	−7.74439	−	22.7201i	−0.393670	−	1.15493i
$388$		0			0
$389$	−18.2949	+	31.6877i	−0.927588	+	1.60663i	−0.140244	+	0.990117i	$0.544789\pi$
$389$	−18.2949	+	31.6877i	−0.927588	+	1.60663i	−0.787345	+	0.616513i	$0.788545\pi$
$390$		0			0
$391$		−	24.6391i		−	1.24605i
$392$		0			0
$393$	12.3105	−	10.1160i	0.620984	−	0.510283i
$394$		0			0
$395$	0.281118	+	0.162304i	0.0141446	+	0.00816638i
$396$		0			0
$397$	−3.83449	−	6.64152i	−0.192447	−	0.333329i	0.753613	−	0.657318i	$-0.228309\pi$
$397$	−3.83449	−	6.64152i	−0.192447	−	0.333329i	−0.946061	+	0.323989i	$0.894976\pi$
$398$		0			0
$399$	−9.51522	−	22.5147i	−0.476357	−	1.12714i
$400$		0			0
$401$	20.5062	−	11.8393i	1.02403	−	0.591224i	0.108761	−	0.994068i	$-0.465312\pi$
$401$	20.5062	−	11.8393i	1.02403	−	0.591224i	0.915269	+	0.402844i	$0.131978\pi$
$402$		0			0
$403$	−7.46964	−	4.31260i	−0.372089	−	0.214826i
$404$		0			0
$405$	8.88735	−	21.6099i	0.441616	−	1.07380i
$406$		0			0
$407$			6.04316i			0.299548i
$408$		0			0
$409$	13.5659	+	7.83230i	0.670793	+	0.387283i	0.796377	−	0.604800i	$-0.206747\pi$
$409$	13.5659	+	7.83230i	0.670793	+	0.387283i	−0.125584	+	0.992083i	$0.540080\pi$
$410$		0			0
$411$	−4.56710	−	1.71565i	−0.225278	−	0.0846267i
$412$		0			0
$413$	−3.15997	−	3.33004i	−0.155492	−	0.163860i
$414$		0			0
$415$	0.319895	+	0.554074i	0.0157030	+	0.0271984i
$416$		0			0
$417$	4.79309	−	0.794445i	0.234719	−	0.0389041i
$418$		0			0
$419$			35.4540i			1.73204i	0.500009	+	0.866020i	$0.333330\pi$
$419$			35.4540i			1.73204i	−0.500009	+	0.866020i	$0.666670\pi$
$420$		0			0
$421$		−	8.00460i		−	0.390120i	−0.980791	−	0.195060i	$-0.937510\pi$
$421$		−	8.00460i		−	0.390120i	0.980791	−	0.195060i	$-0.0624902\pi$
$422$		0			0
$423$	14.8687	+	13.0064i	0.722940	+	0.632392i
$424$		0			0
$425$	4.16730	+	7.21798i	0.202144	+	0.350123i
$426$		0			0
$427$	−5.83434	−	24.3038i	−0.282343	−	1.17614i
$428$		0			0
$429$	−1.82115	+	4.84795i	−0.0879261	+	0.234061i
$430$		0			0
$431$	−25.8583	−	14.9293i	−1.24555	−	0.719118i	−0.275331	−	0.961350i	$-0.588787\pi$
$431$	−25.8583	−	14.9293i	−1.24555	−	0.719118i	−0.970219	+	0.242231i	$0.922121\pi$
$432$		0			0
$433$		−	1.70747i		−	0.0820557i	−0.999158	−	0.0410278i	$-0.986937\pi$
$433$		−	1.70747i		−	0.0820557i	0.999158	−	0.0410278i	$-0.0130632\pi$
$434$		0			0
$435$	4.72328	−	3.88128i	0.226464	−	0.186093i
$436$		0			0
$437$	23.7660	+	13.7213i	1.13688	+	0.656379i
$438$		0			0
$439$	−14.3026	+	8.25762i	−0.682627	+	0.394115i	−0.800844	−	0.598873i	$-0.795615\pi$
$439$	−14.3026	+	8.25762i	−0.682627	+	0.394115i	0.118217	+	0.992988i	$0.462282\pi$
$440$		0			0
$441$	20.3602	+	5.14433i	0.969531	+	0.244968i
$442$		0			0
$443$	−7.12265	−	12.3368i	−0.338407	−	0.586138i	0.645726	−	0.763569i	$-0.276555\pi$
$443$	−7.12265	−	12.3368i	−0.338407	−	0.586138i	−0.984133	+	0.177431i	$0.943221\pi$
$444$		0			0
$445$	−8.12438	−	4.69062i	−0.385133	−	0.222356i
$446$		0			0
$447$	−19.0684	−	23.2051i	−0.901904	−	1.09756i
$448$		0			0
$449$		−	2.18010i		−	0.102885i	−0.998676	−	0.0514426i	$-0.983618\pi$
$449$		−	2.18010i		−	0.102885i	0.998676	−	0.0514426i	$-0.0163819\pi$
$450$		0			0
$451$	9.69470	−	16.7917i	0.456506	−	0.790691i
$452$		0			0
$453$	7.81529	−	20.8045i	0.367194	−	0.977480i
$454$		0			0
$455$	6.09568	−	1.46332i	0.285770	−	0.0686015i
$456$		0			0
$457$	−16.0855	−	27.8609i	−0.752447	−	1.30328i	−0.946633	−	0.322312i	$-0.895540\pi$
$457$	−16.0855	−	27.8609i	−0.752447	−	1.30328i	0.194186	−	0.980965i	$-0.437793\pi$
$458$		0			0
$459$	−0.767174	+	24.8723i	−0.0358086	+	1.16094i
$460$		0			0
$461$		−	13.9258i		−	0.648588i	−0.945956	−	0.324294i	$-0.894873\pi$
$461$		−	13.9258i		−	0.648588i	0.945956	−	0.324294i	$-0.105127\pi$
$462$		0			0
$463$	−15.5838			−0.724239			−0.362120	−	0.932132i	$-0.617947\pi$
$463$	−15.5838			−0.724239			−0.362120	+	0.932132i	$0.617947\pi$
$464$		0			0
$465$	−41.9266	+	6.94925i	−1.94430	+	0.322264i
$466$		0			0
$467$	16.6230	−	9.59729i	0.769220	−	0.444110i	−0.0633760	−	0.997990i	$-0.520187\pi$
$467$	16.6230	−	9.59729i	0.769220	−	0.444110i	0.832596	+	0.553880i	$0.186853\pi$
$468$		0			0
$469$	22.8448	+	24.0743i	1.05488	+	1.11165i
$470$		0			0
$471$	−10.4198	+	27.7378i	−0.480121	+	1.27809i
$472$		0			0
$473$	22.7015	+	13.1067i	1.04381	+	0.602647i
$474$		0			0
$475$	−9.28294			−0.425931
$476$		0			0
$477$	0.979016	−	4.95447i	0.0448261	−	0.226850i
$478$		0			0
$479$	3.02090	−	5.23235i	0.138028	−	0.239072i	−0.788722	−	0.614750i	$-0.789257\pi$
$479$	3.02090	−	5.23235i	0.138028	−	0.239072i	0.926750	+	0.375678i	$0.122590\pi$
$480$		0			0
$481$	1.45790	−	0.841716i	0.0664743	−	0.0383790i
$482$		0			0
$483$	−21.7174	+	9.17829i	−0.988178	+	0.417626i
$484$		0			0
$485$	−6.62457	−	11.4741i	−0.300806	−	0.521012i
$486$		0			0
$487$	−11.1385	+	19.2925i	−0.504735	+	0.874227i	0.495250	+	0.868751i	$0.335077\pi$
$487$	−11.1385	+	19.2925i	−0.504735	+	0.874227i	−0.999985	+	0.00547672i	$0.998257\pi$
$488$		0			0
$489$	−33.4370	+	27.4763i	−1.51207	+	1.24252i
$490$		0			0
$491$	4.63965			0.209384			0.104692	−	0.994505i	$-0.466614\pi$
$491$	4.63965			0.209384			0.104692	+	0.994505i	$0.466614\pi$
$492$		0			0
$493$	−3.25530	+	5.63834i	−0.146611	+	0.253938i
$494$		0			0
$495$	8.23260	+	24.1524i	0.370028	+	1.08557i
$496$		0			0
$497$	−0.453886	+	1.53219i	−0.0203596	+	0.0687281i
$498$		0			0
$499$	16.8940	−	9.75377i	0.756280	−	0.436639i	−0.0716782	−	0.997428i	$-0.522835\pi$
$499$	16.8940	−	9.75377i	0.756280	−	0.436639i	0.827959	+	0.560789i	$0.189502\pi$
$500$		0			0
$501$	16.9043	−	2.80185i	0.755229	−	0.125178i
$502$		0			0
$503$	−33.9146			−1.51218			−0.756090	−	0.654468i	$-0.772893\pi$
$503$	−33.9146			−1.51218			−0.756090	+	0.654468i	$0.772893\pi$
$504$		0			0
$505$	−18.9799			−0.844594
$506$		0			0
$507$	−20.7904	+	3.44596i	−0.923333	+	0.153041i
$508$		0			0
$509$	−20.9128	+	12.0740i	−0.926946	+	0.535172i	−0.885844	−	0.463983i	$-0.846420\pi$
$509$	−20.9128	+	12.0740i	−0.926946	+	0.535172i	−0.0411013	+	0.999155i	$0.513087\pi$
$510$		0			0
$511$	−2.71739	−	2.86364i	−0.120210	−	0.126680i
$512$		0			0
$513$	−23.5637	−	14.5912i	−1.04036	−	0.644216i
$514$		0			0
$515$	−1.00513	+	1.74094i	−0.0442914	+	0.0767150i
$516$		0			0
$517$	−21.5731			−0.948782
$518$		0			0
$519$	20.6681	−	16.9837i	0.907230	−	0.745501i
$520$		0			0
$521$	−2.98225	+	5.16541i	−0.130655	+	0.226301i	−0.923929	−	0.382564i	$-0.875041\pi$
$521$	−2.98225	+	5.16541i	−0.130655	+	0.226301i	0.793274	+	0.608864i	$0.208375\pi$
$522$		0			0
$523$	−6.49701	−	11.2532i	−0.284095	−	0.492066i	0.688295	−	0.725431i	$-0.258360\pi$
$523$	−6.49701	−	11.2532i	−0.284095	−	0.492066i	−0.972389	+	0.233365i	$0.925026\pi$
$524$		0			0
$525$	4.80973	−	6.36191i	0.209914	−	0.277656i
$526$		0			0
$527$	39.1961	−	22.6299i	1.70741	−	0.985774i
$528$		0			0
$529$	1.73544	−	3.00587i	0.0754539	−	0.130690i
$530$		0			0
$531$	−5.10662	−	1.00908i	−0.221609	−	0.0437905i
$532$		0			0
$533$	−5.40127			−0.233955
$534$		0			0
$535$	−32.6663	−	18.8599i	−1.41229	−	0.815383i
$536$		0			0
$537$	−7.40002	+	19.6990i	−0.319335	+	0.850076i
$538$		0			0
$539$	−20.4340	+	10.4107i	−0.880153	+	0.448418i
$540$		0			0
$541$	−18.7480	+	10.8242i	−0.806039	+	0.465367i	−0.845578	−	0.533851i	$-0.820744\pi$
$541$	−18.7480	+	10.8242i	−0.806039	+	0.465367i	0.0395397	+	0.999218i	$0.487411\pi$
$542$		0			0
$543$	2.42507	−	0.401950i	0.104070	−	0.0172493i
$544$		0			0
$545$	38.3770			1.64389
$546$		0			0
$547$			15.8930i			0.679536i	0.940509	+	0.339768i	$0.110349\pi$
$547$			15.8930i			0.679536i	−0.940509	+	0.339768i	$0.889651\pi$
$548$		0			0
$549$	−21.3313	−	18.6596i	−0.910398	−	0.796370i
$550$		0			0
$551$	−3.62570	−	6.27989i	−0.154460	−	0.267532i
$552$		0			0
$553$	0.0772175	+	0.321661i	0.00328362	+	0.0136784i
$554$		0			0
$555$	2.91692	−	7.76491i	0.123816	−	0.329602i
$556$		0			0
$557$	20.3420	−	35.2334i	0.861919	−	1.49289i	−0.00815471	−	0.999967i	$-0.502596\pi$
$557$	20.3420	−	35.2334i	0.861919	−	1.49289i	0.870074	−	0.492921i	$-0.164071\pi$
$558$		0			0
$559$		−	7.30223i		−	0.308851i
$560$		0			0
$561$	−17.2528	−	20.9956i	−0.728412	−	0.886433i
$562$		0			0
$563$	−38.8739	−	22.4439i	−1.63834	−	0.945896i	−0.981405	−	0.191950i	$-0.938519\pi$
$563$	−38.8739	−	22.4439i	−1.63834	−	0.945896i	−0.656936	−	0.753947i	$-0.728148\pi$
$564$		0			0
$565$	21.1213	+	36.5832i	0.888581	+	1.53907i
$566$		0			0
$567$	22.2088	−	8.58895i	0.932681	−	0.360702i
$568$		0			0
$569$	−12.8893	+	7.44164i	−0.540347	+	0.311970i	−0.745220	−	0.666819i	$-0.767655\pi$
$569$	−12.8893	+	7.44164i	−0.540347	+	0.311970i	0.204872	+	0.978789i	$0.434322\pi$
$570$		0			0
$571$	−6.27344	−	3.62197i	−0.262535	−	0.151575i	0.362955	−	0.931807i	$-0.381768\pi$
$571$	−6.27344	−	3.62197i	−0.262535	−	0.151575i	−0.625490	+	0.780232i	$0.715101\pi$
$572$		0			0
$573$	5.60010	−	4.60179i	0.233948	−	0.192243i
$574$		0			0
$575$			8.95423i			0.373417i
$576$		0			0
$577$	20.2309	+	11.6803i	0.842223	+	0.486258i	0.858019	−	0.513617i	$-0.171695\pi$
$577$	20.2309	+	11.6803i	0.842223	+	0.486258i	−0.0157961	+	0.999875i	$0.505028\pi$
$578$		0			0
$579$	−16.0686	+	42.7748i	−0.667786	+	1.77766i
$580$		0			0
$581$	−0.185188	+	0.625142i	−0.00768291	+	0.0259353i
$582$		0			0
$583$	2.75758	+	4.77627i	0.114207	+	0.197813i
$584$		0			0
$585$	4.68003	−	5.35014i	0.193496	−	0.221201i
$586$		0			0
$587$			8.33175i			0.343888i	0.985107	+	0.171944i	$0.0550048\pi$
$587$			8.33175i			0.343888i	−0.985107	+	0.171944i	$0.944995\pi$
$588$		0			0
$589$			50.4096i			2.07709i
$590$		0			0
$591$	−21.6853	+	3.59430i	−0.892014	+	0.147850i
$592$		0			0
$593$	−19.8845	−	34.4410i	−0.816560	−	1.41432i	−0.908202	−	0.418531i	$-0.862545\pi$
$593$	−19.8845	−	34.4410i	−0.816560	−	1.41432i	0.0916424	−	0.995792i	$-0.470788\pi$
$594$		0			0
$595$	−9.34332	+	31.5403i	−0.383039	+	1.29303i
$596$		0			0
$597$	−1.75915	−	0.660834i	−0.0719974	−	0.0270461i
$598$		0			0
$599$	12.0202	+	6.93989i	0.491134	+	0.283556i	0.725045	−	0.688702i	$-0.241819\pi$
$599$	12.0202	+	6.93989i	0.491134	+	0.283556i	−0.233911	+	0.972258i	$0.575152\pi$
$600$		0			0
$601$		−	17.2223i		−	0.702512i	−0.936279	−	0.351256i	$-0.885755\pi$
$601$		−	17.2223i		−	0.702512i	0.936279	−	0.351256i	$-0.114245\pi$
$602$		0			0
$603$	36.9180	+	7.29510i	1.50342	+	0.297080i
$604$		0			0
$605$	0.599803	+	0.346296i	0.0243855	+	0.0140790i
$606$		0			0
$607$	−7.37230	+	4.25640i	−0.299233	+	0.172762i	−0.642098	−	0.766622i	$-0.721936\pi$
$607$	−7.37230	+	4.25640i	−0.299233	+	0.172762i	0.342865	+	0.939385i	$0.388602\pi$
$608$		0			0
$609$	6.18239	+	0.768959i	0.250523	+	0.0311598i
$610$		0			0
$611$	3.00479	+	5.20445i	0.121561	+	0.210549i
$612$		0			0
$613$	−36.3973	−	21.0140i	−1.47007	−	0.848747i	−0.470637	−	0.882327i	$-0.655976\pi$
$613$	−36.3973	−	21.0140i	−1.47007	−	0.848747i	−0.999436	+	0.0335801i	$0.989309\pi$
$614$		0			0
$615$	−20.5619	+	16.8964i	−0.829134	+	0.681328i
$616$		0			0
$617$		−	16.0083i		−	0.644471i	−0.946660	−	0.322236i	$-0.895566\pi$
$617$		−	16.0083i		−	0.644471i	0.946660	−	0.322236i	$-0.104434\pi$
$618$		0			0
$619$	−10.1543	+	17.5878i	−0.408136	+	0.706913i	−0.994681	−	0.103004i	$-0.967155\pi$
$619$	−10.1543	+	17.5878i	−0.408136	+	0.706913i	0.586545	+	0.809917i	$0.300488\pi$
$620$		0			0
$621$	−14.0745	+	22.7293i	−0.564790	+	0.912096i
$622$		0			0
$623$	−2.23161	−	9.29609i	−0.0894075	−	0.372440i
$624$		0			0
$625$	15.3365	+	26.5636i	0.613460	+	1.06254i
$626$		0			0
$627$	29.8595	−	4.94915i	1.19247	−	0.197650i
$628$		0			0
$629$			8.83363i			0.352220i
$630$		0			0
$631$	28.0435			1.11639			0.558197	−	0.829708i	$-0.311493\pi$
$631$	28.0435			1.11639			0.558197	+	0.829708i	$0.311493\pi$
$632$		0			0
$633$	2.23481	+	13.4832i	0.0888259	+	0.535909i
$634$		0			0
$635$	3.59734	−	2.07693i	0.142756	−	0.0824203i
$636$		0			0
$637$	5.35767	+	3.47960i	0.212279	+	0.137867i
$638$		0			0
$639$	0.584599	+	1.71507i	0.0231264	+	0.0678471i
$640$		0			0
$641$	9.80778	+	5.66252i	0.387384	+	0.223656i	0.681026	−	0.732259i	$-0.261534\pi$
$641$	9.80778	+	5.66252i	0.387384	+	0.223656i	−0.293642	+	0.955915i	$0.594867\pi$
$642$		0			0
$643$	−32.8892			−1.29702			−0.648512	−	0.761204i	$-0.724608\pi$
$643$	−32.8892			−1.29702			−0.648512	+	0.761204i	$0.724608\pi$
$644$		0			0
$645$	−22.8430	−	27.7985i	−0.899441	−	1.09457i
$646$		0			0
$647$	13.6188	−	23.5884i	0.535409	−	0.927356i	−0.463734	−	0.885974i	$-0.653491\pi$
$647$	13.6188	−	23.5884i	0.535409	−	0.927356i	0.999143	−	0.0413818i	$-0.0131760\pi$
$648$		0			0
$649$	4.92296	−	2.84227i	0.193243	−	0.111569i
$650$		0			0
$651$	−34.5474	−	26.1185i	−1.35402	−	1.02366i
$652$		0			0
$653$	12.2895	+	21.2860i	0.480926	+	0.832987i	0.999760	−	0.0218870i	$-0.00696741\pi$
$653$	12.2895	+	21.2860i	0.480926	+	0.832987i	−0.518835	+	0.854874i	$0.673634\pi$
$654$		0			0
$655$	11.9417	−	20.6837i	0.466602	−	0.808179i
$656$		0			0
$657$	−4.39140	−	0.867753i	−0.171325	−	0.0338543i
$658$		0			0
$659$	−12.1725			−0.474172			−0.237086	−	0.971489i	$-0.576192\pi$
$659$	−12.1725			−0.474172			−0.237086	+	0.971489i	$0.576192\pi$
$660$		0			0
$661$	4.00322	−	6.93378i	0.155707	−	0.269693i	−0.777609	−	0.628748i	$-0.783568\pi$
$661$	4.00322	−	6.93378i	0.155707	−	0.269693i	0.933316	+	0.359055i	$0.116901\pi$
$662$		0			0
$663$	−2.66208	+	7.08653i	−0.103387	+	0.275218i
$664$		0			0
$665$	−25.2195	−	26.5768i	−0.977970	−	1.03060i
$666$		0			0
$667$	−6.05752	+	3.49731i	−0.234548	+	0.135416i
$668$		0			0
$669$	3.26812	+	19.7174i	0.126353	+	0.762319i
$670$		0			0
$671$	30.9497			1.19480
$672$		0			0
$673$	18.1260			0.698706			0.349353	−	0.936991i	$-0.386401\pi$
$673$	18.1260			0.698706			0.349353	+	0.936991i	$0.386401\pi$
$674$		0			0
$675$	0.278803	−	9.03898i	0.0107311	−	0.347910i
$676$		0			0
$677$	−39.1458	+	22.6008i	−1.50449	+	0.868620i	−0.504508	+	0.863407i	$0.668326\pi$
$677$	−39.1458	+	22.6008i	−1.50449	+	0.868620i	−0.999986	+	0.00521277i	$0.998341\pi$
$678$		0			0
$679$	3.83499	−	12.9458i	0.147173	−	0.496815i
$680$		0			0
$681$	25.2426	+	9.48249i	0.967298	+	0.363370i
$682$		0			0
$683$	6.38047	−	11.0513i	0.244142	−	0.422866i	−0.717748	−	0.696303i	$-0.754827\pi$
$683$	6.38047	−	11.0513i	0.244142	−	0.422866i	0.961890	+	0.273437i	$0.0881604\pi$
$684$		0			0
$685$	−7.31285			−0.279410
$686$		0			0
$687$	−3.91996	−	4.77036i	−0.149556	−	0.182000i
$688$		0			0
$689$	0.768176	−	1.33052i	0.0292652	−	0.0506888i
$690$		0			0
$691$	7.47003	+	12.9385i	0.284173	+	0.492203i	0.972408	−	0.233285i	$-0.0749475\pi$
$691$	7.47003	+	12.9385i	0.284173	+	0.492203i	−0.688235	+	0.725488i	$0.741614\pi$
$692$		0			0
$693$	−12.0791	+	23.0280i	−0.458848	+	0.874761i
$694$		0			0
$695$	6.30686	−	3.64127i	0.239233	−	0.138121i
$696$		0			0
$697$	14.1713	−	24.5454i	0.536776	−	0.929724i
$698$		0			0
$699$	10.2087	−	8.38887i	0.386130	−	0.317296i
$700$		0			0
$701$	−14.3141			−0.540636			−0.270318	−	0.962771i	$-0.587129\pi$
$701$	−14.3141			−0.540636			−0.270318	+	0.962771i	$0.587129\pi$
$702$		0			0
$703$	−8.52061	−	4.91938i	−0.321361	−	0.185538i
$704$		0			0
$705$	27.7194	+	10.4129i	1.04397	+	0.392173i
$706$		0			0
$707$	−13.3139	−	14.0304i	−0.500719	−	0.527668i
$708$		0			0
$709$	5.67964	−	3.27914i	0.213303	−	0.123151i	−0.389542	−	0.921009i	$-0.627367\pi$
$709$	5.67964	−	3.27914i	0.213303	−	0.123151i	0.602846	+	0.797858i	$0.294033\pi$
$710$		0			0
$711$	0.282320	+	0.246959i	0.0105878	+	0.00926170i
$712$		0			0
$713$	48.6246			1.82100
$714$		0			0
$715$			7.76255i			0.290303i
$716$		0			0
$717$	3.75961	+	22.6827i	0.140405	+	0.847100i
$718$		0			0
$719$	−19.5665	−	33.8902i	−0.729708	−	1.26389i	−0.957007	−	0.290066i	$-0.906323\pi$
$719$	−19.5665	−	33.8902i	−0.729708	−	1.26389i	0.227299	−	0.973825i	$-0.427010\pi$
$720$		0			0
$721$	−1.99202	+	0.478202i	−0.0741866	+	0.0178092i
$722$		0			0
$723$	18.5876	+	6.98252i	0.691281	+	0.259683i
$724$		0			0
$725$	1.18303	−	2.04906i	0.0439365	−	0.0761002i
$726$		0			0
$727$			34.4829i			1.27890i	0.768833	+	0.639450i	$0.220838\pi$
$727$			34.4829i			1.27890i	−0.768833	+	0.639450i	$0.779162\pi$
$728$		0			0
$729$	14.9154	−	22.5062i	0.552423	−	0.833564i
$730$		0			0
$731$	33.1841	+	19.1588i	1.22736	+	0.708615i
$732$		0			0
$733$	−9.89201	−	17.1335i	−0.365370	−	0.632839i	0.623466	−	0.781851i	$-0.285724\pi$
$733$	−9.89201	−	17.1335i	−0.365370	−	0.632839i	−0.988835	+	0.149012i	$0.952391\pi$
$734$		0			0
$735$	31.2808	−	3.51365i	1.15381	−	0.129603i
$736$		0			0
$737$	−35.5902	+	20.5480i	−1.31098	+	0.756896i
$738$		0			0
$739$	−6.03595	−	3.48486i	−0.222036	−	0.128193i	0.384857	−	0.922976i	$-0.374251\pi$
$739$	−6.03595	−	3.48486i	−0.222036	−	0.128193i	−0.606893	+	0.794784i	$0.707584\pi$
$740$		0			0
$741$	−5.35292	−	6.51418i	−0.196645	−	0.239305i
$742$		0			0
$743$			45.3956i			1.66540i	0.553723	+	0.832701i	$0.313207\pi$
$743$			45.3956i			1.66540i	−0.553723	+	0.832701i	$0.686793\pi$
$744$		0			0
$745$	−38.9883	−	22.5099i	−1.42842	−	0.824700i
$746$		0			0
$747$	0.238520	+	0.699759i	0.00872698	+	0.0256028i
$748$		0			0
$749$	−8.97277	−	37.3774i	−0.327858	−	1.36574i
$750$		0			0
$751$	10.3669	+	17.9560i	0.378293	+	0.655223i	0.990814	−	0.135231i	$-0.0431777\pi$
$751$	10.3669	+	17.9560i	0.378293	+	0.655223i	−0.612521	+	0.790455i	$0.709844\pi$
$752$		0			0
$753$	−0.410394	−	2.47601i	−0.0149556	−	0.0902309i
$754$		0			0
$755$		−	33.3122i		−	1.21236i
$756$		0			0
$757$		−	30.3555i		−	1.10329i	−0.834079	−	0.551645i	$-0.814000\pi$
$757$		−	30.3555i		−	1.10329i	0.834079	−	0.551645i	$-0.186000\pi$
$758$		0			0
$759$	−4.77390	−	28.8022i	−0.173282	−	1.04545i
$760$		0			0
$761$	−6.12394	−	10.6070i	−0.221993	−	0.384503i	0.733420	−	0.679775i	$-0.237923\pi$
$761$	−6.12394	−	10.6070i	−0.221993	−	0.384503i	−0.955413	+	0.295273i	$0.904589\pi$
$762$		0			0
$763$	26.9204	+	28.3693i	0.974585	+	1.02704i
$764$		0			0
$765$	12.0341	+	35.3050i	0.435092	+	1.27645i
$766$		0			0
$767$	−1.37138	−	0.791767i	−0.0495177	−	0.0285890i
$768$		0			0
$769$			19.0816i			0.688100i	0.938951	+	0.344050i	$0.111799\pi$
$769$			19.0816i			0.688100i	−0.938951	+	0.344050i	$0.888201\pi$
$770$		0			0
$771$	−13.2709	−	16.1499i	−0.477940	−	0.581624i
$772$		0			0
$773$	9.07434	+	5.23907i	0.326381	+	0.188436i	0.654233	−	0.756293i	$-0.272991\pi$
$773$	9.07434	+	5.23907i	0.326381	+	0.188436i	−0.327852	+	0.944729i	$0.606325\pi$
$774$		0			0
$775$	−14.2445	+	8.22405i	−0.511677	+	0.295417i
$776$		0			0
$777$	7.78616	−	3.29061i	0.279327	−	0.118050i
$778$		0			0
$779$	15.7838	+	27.3383i	0.565512	+	0.979496i
$780$		0			0
$781$	−1.71366	−	0.989382i	−0.0613196	−	0.0354029i
$782$		0			0
$783$	6.22375	−	3.34180i	0.222419	−	0.119426i
$784$		0			0
$785$			44.4139i			1.58520i
$786$		0			0
$787$	6.93206	−	12.0067i	0.247101	−	0.427992i	−0.715619	−	0.698491i	$-0.753855\pi$
$787$	6.93206	−	12.0067i	0.247101	−	0.427992i	0.962720	+	0.270499i	$0.0871887\pi$
$788$		0			0
$789$	40.6888	+	15.2849i	1.44856	+	0.544157i
$790$		0			0
$791$	−12.2272	+	41.2755i	−0.434750	+	1.46759i
$792$		0			0
$793$	−4.31081	−	7.46654i	−0.153081	−	0.265145i
$794$		0			0
$795$	−1.23783	−	7.46812i	−0.0439011	−	0.264867i
$796$		0			0
$797$		−	29.4639i		−	1.04366i	−0.853048	−	0.521832i	$-0.825249\pi$
$797$		−	29.4639i		−	1.04366i	0.853048	−	0.521832i	$-0.174751\pi$
$798$		0			0
$799$	−31.5346			−1.11561
$800$		0			0
$801$	−8.15912	−	7.13719i	−0.288288	−	0.252180i
$802$		0			0
$803$	4.23346	−	2.44419i	0.149396	−	0.0862536i
$804$		0			0
$805$	−25.6357	+	24.3265i	−0.903540	+	0.857395i
$806$		0			0
$807$	−12.3911	−	4.65476i	−0.436186	−	0.163855i
$808$		0			0
$809$	−42.7554	−	24.6848i	−1.50320	−	0.867873i	−0.999993	−	0.00370713i	$-0.998820\pi$
$809$	−42.7554	−	24.6848i	−1.50320	−	0.867873i	−0.503207	−	0.864166i	$-0.667847\pi$
$810$		0			0
$811$	−0.180195			−0.00632751			−0.00316376	−	0.999995i	$-0.501007\pi$
$811$	−0.180195			−0.00632751			−0.00316376	+	0.999995i	$0.501007\pi$
$812$		0			0
$813$	14.3373	−	11.7815i	0.502832	−	0.413194i
$814$		0			0
$815$	−32.4353	+	56.1796i	−1.13616	+	1.96788i
$816$		0			0
$817$	−36.9598	+	21.3388i	−1.29306	+	0.746549i
$818$		0			0
$819$	7.23787	−	0.293375i	0.252912	−	0.0102514i
$820$		0			0
$821$	−11.4858	−	19.8940i	−0.400857	−	0.694304i	0.592973	−	0.805223i	$-0.297954\pi$
$821$	−11.4858	−	19.8940i	−0.400857	−	0.694304i	−0.993830	+	0.110918i	$0.964621\pi$
$822$		0			0
$823$	22.0638	−	38.2157i	0.769097	−	1.33212i	−0.168956	−	0.985624i	$-0.554040\pi$
$823$	22.0638	−	38.2157i	0.769097	−	1.33212i	0.938053	−	0.346492i	$-0.112627\pi$
$824$		0			0
$825$	6.26992	+	7.63011i	0.218290	+	0.265646i
$826$		0			0
$827$	−19.7749			−0.687641			−0.343821	−	0.939035i	$-0.611721\pi$
$827$	−19.7749			−0.687641			−0.343821	+	0.939035i	$0.611721\pi$
$828$		0			0
$829$	13.8197	−	23.9365i	0.479979	−	0.831349i	−0.519757	−	0.854314i	$-0.673977\pi$
$829$	13.8197	−	23.9365i	0.479979	−	0.831349i	0.999736	+	0.0229656i	$0.00731081\pi$
$830$		0			0
$831$	−5.78358	−	2.17263i	−0.200630	−	0.0753676i
$832$		0			0
$833$	−29.8695	+	15.2179i	−1.03492	+	0.527267i
$834$		0			0
$835$	22.2431	−	12.8420i	0.769753	−	0.444417i
$836$		0			0
$837$	−49.0848	−	1.51400i	−1.69662	−	0.0523313i
$838$		0			0
$839$	28.3920			0.980200			0.490100	−	0.871666i	$-0.336960\pi$
$839$	28.3920			0.980200			0.490100	+	0.871666i	$0.336960\pi$
$840$		0			0
$841$	−27.1518			−0.936267
$842$		0			0
$843$	1.20747	+	7.28496i	0.0415874	+	0.250907i
$844$		0			0
$845$	−27.3565	+	15.7943i	−0.941091	+	0.543339i
$846$		0			0
$847$	0.164754	+	0.686307i	0.00566101	+	0.0235818i
$848$		0			0
$849$	13.7902	−	36.7097i	0.473277	−	1.25987i
$850$		0			0
$851$	−4.74518	+	8.21889i	−0.162663	+	0.281740i
$852$		0			0
$853$	30.7041			1.05129			0.525645	−	0.850704i	$-0.323824\pi$
$853$	30.7041			1.05129			0.525645	+	0.850704i	$0.323824\pi$
$854$		0			0
$855$	−40.7556	−	8.05342i	−1.39381	−	0.275421i
$856$		0			0
$857$	11.5192	−	19.9518i	0.393487	−	0.681539i	−0.599420	−	0.800435i	$-0.704602\pi$
$857$	11.5192	−	19.9518i	0.393487	−	0.681539i	0.992907	+	0.118895i	$0.0379353\pi$
$858$		0			0
$859$	26.3268	+	45.5994i	0.898260	+	1.55583i	0.829717	+	0.558184i	$0.188502\pi$
$859$	26.3268	+	45.5994i	0.898260	+	1.55583i	0.0685424	+	0.997648i	$0.478165\pi$
$860$		0			0
$861$	−26.9138	−	3.34751i	−0.917220	−	0.114083i
$862$		0			0
$863$	−22.4451	+	12.9587i	−0.764040	+	0.441119i	−0.830744	−	0.556654i	$-0.812085\pi$
$863$	−22.4451	+	12.9587i	−0.764040	+	0.441119i	0.0667045	+	0.997773i	$0.478752\pi$
$864$		0			0
$865$	20.0490	−	34.7258i	0.681685	−	1.18071i
$866$		0			0
$867$	−6.52539	−	7.94100i	−0.221614	−	0.269691i
$868$		0			0
$869$	−0.409620			−0.0138954
$870$		0			0
$871$	9.91432	+	5.72403i	0.335934	+	0.193951i
$872$		0			0
$873$	−4.93941	−	14.4910i	−0.167174	−	0.490446i
$874$		0			0
$875$	−6.35957	+	21.4681i	−0.214993	+	0.725753i
$876$		0			0
$877$	39.8660	−	23.0166i	1.34618	−	0.777216i	0.358472	−	0.933540i	$-0.383298\pi$
$877$	39.8660	−	23.0166i	1.34618	−	0.777216i	0.987706	+	0.156324i	$0.0499644\pi$
$878$		0			0
$879$	1.68815	+	10.1851i	0.0569400	+	0.343533i
$880$		0			0
$881$	−25.6170			−0.863060			−0.431530	−	0.902099i	$-0.642026\pi$
$881$	−25.6170			−0.863060			−0.431530	+	0.902099i	$0.642026\pi$
$882$		0			0
$883$		−	54.2412i		−	1.82536i	−0.408674	−	0.912680i	$-0.634009\pi$
$883$		−	54.2412i		−	1.82536i	0.408674	−	0.912680i	$-0.365991\pi$
$884$		0			0
$885$	−7.69747	+	1.27584i	−0.258748	+	0.0428869i
$886$		0			0
$887$	−17.2509	−	29.8794i	−0.579228	−	1.00325i	−0.995568	−	0.0940438i	$-0.970021\pi$
$887$	−17.2509	−	29.8794i	−0.579228	−	1.00325i	0.416340	−	0.909209i	$-0.363313\pi$
$888$		0			0
$889$	4.05875	+	1.20234i	0.136126	+	0.0403252i
$890$		0			0
$891$	3.92229	+	29.2234i	0.131402	+	0.979021i
$892$		0			0
$893$	17.5614	−	30.4172i	0.587669	−	1.01787i
$894$		0			0
$895$			31.5422i			1.05434i
$896$		0			0
$897$	−6.28352	+	5.16338i	−0.209800	+	0.172400i
$898$		0			0
$899$	−11.1271	−	6.42424i	−0.371110	−	0.214260i
$900$		0			0
$901$	4.03092	+	6.98176i	0.134289	+	0.232596i
$902$		0			0
$903$	4.52565	−	36.3860i	0.150604	−	1.21085i
$904$		0			0
$905$	3.19096	−	1.84230i	0.106071	−	0.0612402i
$906$		0			0
$907$	−11.9718	−	6.91190i	−0.397516	−	0.229506i	0.287896	−	0.957662i	$-0.407044\pi$
$907$	−11.9718	−	6.91190i	−0.397516	−	0.229506i	−0.685412	+	0.728156i	$0.740378\pi$
$908$		0			0
$909$	−21.5157	−	4.25156i	−0.713630	−	0.141015i
$910$		0			0
$911$			22.6663i			0.750969i	0.926829	+	0.375484i	$0.122524\pi$
$911$			22.6663i			0.750969i	−0.926829	+	0.375484i	$0.877476\pi$
$912$		0			0
$913$	−0.699183	−	0.403674i	−0.0231396	−	0.0133596i
$914$		0			0
$915$	−39.7676	−	14.9389i	−1.31468	−	0.493864i
$916$		0			0
$917$	23.6667	−	5.68140i	0.781543	−	0.187616i
$918$		0			0
$919$	6.58509	+	11.4057i	0.217222	+	0.376240i	0.953958	−	0.299941i	$-0.0969670\pi$
$919$	6.58509	+	11.4057i	0.217222	+	0.376240i	−0.736736	+	0.676181i	$0.763634\pi$
$920$		0			0
$921$	9.26329	−	1.53537i	0.305236	−	0.0505922i
$922$		0			0
$923$			0.551221i			0.0181437i
$924$		0			0
$925$		−	3.21028i		−	0.105553i
$926$		0			0
$927$	−1.52940	+	1.74838i	−0.0502320	+	0.0574245i
$928$		0			0
$929$	27.9226	+	48.3634i	0.916111	+	1.58675i	0.805267	+	0.592912i	$0.202022\pi$
$929$	27.9226	+	48.3634i	0.916111	+	1.58675i	0.110844	+	0.993838i	$0.464645\pi$
$930$		0			0
$931$	1.95547	−	37.2858i	0.0640881	−	1.22199i
$932$		0			0
$933$	14.8386	−	39.5006i	0.485793	−	1.29319i
$934$		0			0
$935$	−35.2760	−	20.3666i	−1.15365	−	0.666058i
$936$		0			0
$937$			32.0973i			1.04857i	0.851541	+	0.524287i	$0.175668\pi$
$937$			32.0973i			1.04857i	−0.851541	+	0.524287i	$0.824332\pi$
$938$		0			0
$939$	21.8482	−	17.9534i	0.712989	−	0.585887i
$940$		0			0
$941$	24.3540	+	14.0608i	0.793919	+	0.458370i	0.841341	−	0.540505i	$-0.181767\pi$
$941$	24.3540	+	14.0608i	0.793919	+	0.458370i	−0.0474212	+	0.998875i	$0.515100\pi$
$942$		0			0
$943$	26.3702	−	15.2249i	0.858733	−	0.495790i
$944$		0			0
$945$	26.6358	−	23.7585i	0.866462	−	0.772864i
$946$		0			0
$947$	10.9973	+	19.0479i	0.357365	+	0.618974i	0.987520	−	0.157495i	$-0.0503420\pi$
$947$	10.9973	+	19.0479i	0.357365	+	0.618974i	−0.630155	+	0.776469i	$0.717009\pi$
$948$		0			0
$949$	−1.17931	−	0.680874i	−0.0382820	−	0.0221021i
$950$		0			0
$951$	21.8650	+	26.6084i	0.709021	+	0.862836i
$952$		0			0
$953$			48.0977i			1.55804i	0.627001	+	0.779018i	$0.284282\pi$
$953$			48.0977i			1.55804i	−0.627001	+	0.779018i	$0.715718\pi$
$954$		0			0
$955$	5.43234	−	9.40909i	0.175786	−	0.304471i
$956$		0			0
$957$	−2.71287	+	7.22173i	−0.0876947	+	0.233445i
$958$		0			0
$959$	−5.12976	−	5.40584i	−0.165649	−	0.174564i
$960$		0			0
$961$	29.1595	+	50.5057i	0.940628	+	1.62921i
$962$		0			0
$963$	−32.8059	−	28.6970i	−1.05716	−	0.924747i
$964$		0			0
$965$			68.4912i			2.20481i
$966$		0			0
$967$	−11.0279			−0.354635			−0.177317	−	0.984154i	$-0.556742\pi$
$967$	−11.0279			−0.354635			−0.177317	+	0.984154i	$0.556742\pi$
$968$		0			0
$969$	43.6473	−	7.23446i	1.40215	−	0.232404i
$970$		0			0
$971$	2.36459	−	1.36519i	0.0758832	−	0.0438112i	−0.461578	−	0.887099i	$-0.652717\pi$
$971$	2.36459	−	1.36519i	0.0758832	−	0.0438112i	0.537461	+	0.843288i	$0.319383\pi$
$972$		0			0
$973$	7.11580	+	2.10794i	0.228122	+	0.0675775i
$974$		0			0
$975$	0.967443	−	2.57535i	0.0309830	−	0.0824773i
$976$		0			0
$977$	21.7078	+	12.5330i	0.694494	+	0.400967i	0.805294	−	0.592876i	$-0.202008\pi$
$977$	21.7078	+	12.5330i	0.694494	+	0.400967i	−0.110799	+	0.993843i	$0.535341\pi$
$978$		0			0
$979$	11.8381			0.378348
$980$		0			0
$981$	43.5044	+	8.59658i	1.38899	+	0.274468i
$982$		0			0
$983$	12.9850	−	22.4907i	0.414157	−	0.717342i	−0.581182	−	0.813773i	$-0.697410\pi$
$983$	12.9850	−	22.4907i	0.414157	−	0.717342i	0.995340	+	0.0964318i	$0.0307430\pi$
$984$		0			0
$985$	−28.5340	+	16.4741i	−0.909169	+	0.524909i
$986$		0			0
$987$	11.7469	+	27.7953i	0.373909	+	0.884734i
$988$		0			0
$989$	20.5832	+	35.6511i	0.654507	+	1.13364i
$990$		0			0
$991$	9.31944	−	16.1417i	0.296042	−	0.512759i	−0.679185	−	0.733967i	$-0.737667\pi$
$991$	9.31944	−	16.1417i	0.296042	−	0.512759i	0.975227	+	0.221208i	$0.0709999\pi$
$992$		0			0
$993$	2.94056	−	2.41636i	0.0933159	−	0.0766808i
$994$		0			0
$995$	−2.81676			−0.0892974
$996$		0			0
$997$	12.6672	−	21.9402i	0.401173	−	0.694853i	−0.592694	−	0.805427i	$-0.701936\pi$
$997$	12.6672	−	21.9402i	0.401173	−	0.694853i	0.993868	+	0.110575i	$0.0352691\pi$
$998$		0			0
$999$	5.04600	−	8.14894i	0.159648	−	0.257821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.17.24		48
3.2	odd	2	inner	672.2.bi.c.17.9		48
4.3	odd	2		168.2.ba.c.101.17	yes	48
7.5	odd	6	inner	672.2.bi.c.593.16		48
8.3	odd	2		168.2.ba.c.101.23	yes	48
8.5	even	2	inner	672.2.bi.c.17.1		48
12.11	even	2		168.2.ba.c.101.8	yes	48
21.5	even	6	inner	672.2.bi.c.593.1		48
24.5	odd	2	inner	672.2.bi.c.17.16		48
24.11	even	2		168.2.ba.c.101.2	yes	48
28.19	even	6		168.2.ba.c.5.2	✓	48
56.5	odd	6	inner	672.2.bi.c.593.9		48
56.19	even	6		168.2.ba.c.5.8	yes	48
84.47	odd	6		168.2.ba.c.5.23	yes	48
168.5	even	6	inner	672.2.bi.c.593.24		48
168.131	odd	6		168.2.ba.c.5.17	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.2	✓	48	28.19	even	6
168.2.ba.c.5.8	yes	48	56.19	even	6
168.2.ba.c.5.17	yes	48	168.131	odd	6
168.2.ba.c.5.23	yes	48	84.47	odd	6
168.2.ba.c.101.2	yes	48	24.11	even	2
168.2.ba.c.101.8	yes	48	12.11	even	2
168.2.ba.c.101.17	yes	48	4.3	odd	2
168.2.ba.c.101.23	yes	48	8.3	odd	2
672.2.bi.c.17.1		48	8.5	even	2	inner
672.2.bi.c.17.9		48	3.2	odd	2	inner
672.2.bi.c.17.16		48	24.5	odd	2	inner
672.2.bi.c.17.24		48	1.1	even	1	trivial
672.2.bi.c.593.1		48	21.5	even	6	inner
672.2.bi.c.593.9		48	56.5	odd	6	inner
672.2.bi.c.593.16		48	7.5	odd	6	inner
672.2.bi.c.593.24		48	168.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70874 - 0.283220i) q^{3} +(2.24840 - 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(2.83957 - 0.967897i) q^{9} +(-1.63808 + 2.83724i) q^{11} +0.912635 q^{13} +(3.47427 - 2.85492i) q^{15} +(-2.39448 + 4.14736i) q^{17} +(-2.66693 - 4.61926i) q^{19} +(4.54754 + 0.565618i) q^{21} +(-4.45569 + 2.57249i) q^{23} +(0.870190 - 1.50721i) q^{25} +(4.57796 - 2.45811i) q^{27} +1.35950 q^{29} +(-8.18469 - 4.72543i) q^{31} +(-1.99549 + 5.31204i) q^{33} +(6.67920 - 1.60340i) q^{35} +(1.59746 - 0.922292i) q^{37} +(1.55945 - 0.258476i) q^{39} -5.91833 q^{41} -8.00125i q^{43} +(5.12805 - 5.86230i) q^{45} +(3.29243 + 5.70266i) q^{47} +(5.87055 + 3.81269i) q^{49} +(-2.91692 + 7.76491i) q^{51} +(0.841712 - 1.45789i) q^{53} +8.50565i q^{55} +(-5.86535 - 7.13777i) q^{57} +(-1.50266 - 0.867561i) q^{59} +(-4.72347 - 8.18130i) q^{61} +(7.93074 - 0.321460i) q^{63} +(2.05197 - 1.18470i) q^{65} +(10.8634 + 6.27198i) q^{67} +(-6.88502 + 5.65766i) q^{69} +0.603989i q^{71} +(-1.29220 - 0.746053i) q^{73} +(1.06005 - 2.82189i) q^{75} +(-6.28759 + 5.96647i) q^{77} +(0.0625152 + 0.108280i) q^{79} +(7.12635 - 5.49683i) q^{81} +0.246431i q^{83} +12.4332i q^{85} +(2.32303 - 0.385038i) q^{87} +(-1.80671 - 3.12931i) q^{89} +(2.31516 + 0.685829i) q^{91} +(-15.3238 - 5.75646i) q^{93} +(-11.9926 - 6.92395i) q^{95} -5.10324i q^{97} +(-1.90529 + 9.64204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more