LMFDB - Embedded newform 672.2.bi.c.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(17,672)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			17.1
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70874 + 0.283220i) q^{3} +(-2.24840 + 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(2.83957 - 0.967897i) q^{9} +O(q^{10})$	\(q+(-1.70874 + 0.283220i) q^{3} +(-2.24840 + 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(2.83957 - 0.967897i) q^{9} +(1.63808 - 2.83724i) q^{11} -0.912635 q^{13} +(3.47427 - 2.85492i) q^{15} +(-2.39448 + 4.14736i) q^{17} +(2.66693 + 4.61926i) q^{19} +(-4.54754 - 0.565618i) q^{21} +(-4.45569 + 2.57249i) q^{23} +(0.870190 - 1.50721i) q^{25} +(-4.57796 + 2.45811i) q^{27} -1.35950 q^{29} +(-8.18469 - 4.72543i) q^{31} +(-1.99549 + 5.31204i) q^{33} +(-6.67920 + 1.60340i) q^{35} +(-1.59746 + 0.922292i) q^{37} +(1.55945 - 0.258476i) q^{39} -5.91833 q^{41} +8.00125i q^{43} +(-5.12805 + 5.86230i) q^{45} +(3.29243 + 5.70266i) q^{47} +(5.87055 + 3.81269i) q^{49} +(2.91692 - 7.76491i) q^{51} +(-0.841712 + 1.45789i) q^{53} +8.50565i q^{55} +(-5.86535 - 7.13777i) q^{57} +(1.50266 + 0.867561i) q^{59} +(4.72347 + 8.18130i) q^{61} +(7.93074 - 0.321460i) q^{63} +(2.05197 - 1.18470i) q^{65} +(-10.8634 - 6.27198i) q^{67} +(6.88502 - 5.65766i) q^{69} +0.603989i q^{71} +(-1.29220 - 0.746053i) q^{73} +(-1.06005 + 2.82189i) q^{75} +(6.28759 - 5.96647i) q^{77} +(0.0625152 + 0.108280i) q^{79} +(7.12635 - 5.49683i) q^{81} -0.246431i q^{83} -12.4332i q^{85} +(2.32303 - 0.385038i) q^{87} +(-1.80671 - 3.12931i) q^{89} +(-2.31516 - 0.685829i) q^{91} +(15.3238 + 5.75646i) q^{93} +(-11.9926 - 6.92395i) q^{95} -5.10324i q^{97} +(1.90529 - 9.64204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 4 * q^7 - 14 * q^9	$ 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

Display 100 coefficients 10 coefficients

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	−0.909875	−	0.414883i	$-0.863823\pi$
$5$	−2.24840	+	1.29811i	−1.00551	+	0.580533i	−0.0956384	+	0.995416i	$0.530489\pi$
$6$		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	−0.506075	−	0.862489i	$-0.668904\pi$
$11$	1.63808	−	2.83724i	0.493900	−	0.855460i	0.999975	+	0.00702958i	$0.00223760\pi$
$12$		0			0
$13$	−0.912635			−0.253119			−0.126560	−	0.991959i	$-0.540394\pi$
$13$	−0.912635			−0.253119			−0.126560	+	0.991959i	$0.540394\pi$
$14$		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	$0.0429019\pi$
$19$	2.66693	+	4.61926i	0.611836	+	1.05973i	−0.379095	+	0.925358i	$0.623765\pi$
$20$		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	$-0.540287\pi$
$29$	−1.35950			−0.252453			−0.126227	+	0.992001i	$0.540287\pi$
$30$		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	−0.625529	−	0.780201i	$-0.715117\pi$
$37$	−1.59746	+	0.922292i	−0.262620	+	0.151624i	0.362909	+	0.931825i	$0.381784\pi$
$38$		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	$0.208867\pi$
$43$			8.00125i			1.22018i	−0.792332	+	0.610090i	$0.791133\pi$
$44$		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	−0.918027	−	0.396519i	$-0.870218\pi$
$53$	−0.841712	+	1.45789i	−0.115618	+	0.200256i	0.802409	+	0.596775i	$0.203552\pi$
$54$		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	0.594615	−	0.804010i	$-0.297304\pi$
$59$	1.50266	+	0.867561i	0.195630	+	0.112947i	−0.398986	+	0.916957i	$0.630638\pi$
$60$		0			0
$61$	4.72347	+	8.18130i	0.604779	+	1.04751i	0.992086	+	0.125557i	$0.0400718\pi$
$61$	4.72347	+	8.18130i	0.604779	+	1.04751i	−0.387308	+	0.921951i	$0.626595\pi$
$62$		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	−0.342313	−	0.939586i	$-0.611210\pi$
$67$	−10.8634	−	6.27198i	−1.32717	−	0.766245i	−0.984862	+	0.173341i	$0.944544\pi$
$68$		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	$-0.995695\pi$
$83$		−	0.246431i		−	0.0270493i	0.999909	−	0.0135247i	$-0.00430516\pi$
$84$		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	0.780741	−	0.624854i	$-0.214842\pi$
$101$	6.33114	+	3.65529i	0.629972	+	0.363715i	−0.150769	+	0.988569i	$0.548175\pi$
$102$		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	$0.0811638\pi$
$107$	7.26435	+	12.5822i	0.702271	+	1.21637i	−0.265397	+	0.964139i	$0.585503\pi$
$108$		0			0
$109$	−12.8015	−	7.39093i	−1.22616	−	0.707923i	−0.259934	−	0.965626i	$-0.583701\pi$
$109$	−12.8015	−	7.39093i	−1.22616	−	0.707923i	−0.966224	+	0.257703i	$0.917034\pi$
$110$		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	−0.805880	−	0.592078i	$-0.798308\pi$
$131$	−7.96684	+	4.59965i	−0.696066	+	0.401874i	0.109815	+	0.993952i	$0.464974\pi$
$132$		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	$-0.537956\pi$
$139$	−2.80505			−0.237921			−0.118960	+	0.992899i	$0.537956\pi$
$140$		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	$0.0847718\pi$
$149$	8.67025	+	15.0173i	0.710295	+	1.23027i	−0.254451	+	0.967086i	$0.581895\pi$
$150$		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	$-0.594161\pi$
$157$	8.55356	−	14.8152i	0.682648	−	1.18238i	0.974170	−	0.225817i	$-0.0725052\pi$
$158$		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	$-0.232718\pi$
$163$	21.6390	−	12.4933i	1.69489	−	0.978547i	0.950458	−	0.310853i	$-0.100615\pi$
$164$		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	−0.913211	−	0.407488i	$-0.866405\pi$
$173$	−13.3755	+	7.72235i	−1.01692	+	0.587120i	−0.103710	+	0.994608i	$0.533071\pi$
$174$		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	−0.544594	−	0.838700i	$-0.683316\pi$
$179$	6.07462	−	10.5216i	0.454038	−	0.786418i	0.998632	+	0.0522822i	$0.0166495\pi$
$180$		0			0
$181$	−1.41922			−0.105489			−0.0527447	−	0.998608i	$-0.516797\pi$
$181$	−1.41922			−0.105489			−0.0527447	+	0.998608i	$0.516797\pi$
$182$		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	$-0.350678\pi$
$197$	12.6908			0.904184			0.452092	+	0.891971i	$0.350678\pi$
$198$		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	$-0.912444\pi$
$211$		−	7.89074i		−	0.543221i	0.962407	−	0.271610i	$-0.0875562\pi$
$212$		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	−0.0193323	−	0.999813i	$-0.506154\pi$
$227$	−13.4825	−	7.78410i	−0.894862	−	0.516649i	−0.875530	+	0.483164i	$0.839487\pi$
$228$		0			0
$229$	1.78238	+	3.08717i	0.117783	+	0.204006i	0.918889	−	0.394517i	$-0.129088\pi$
$229$	1.78238	+	3.08717i	0.117783	+	0.204006i	−0.801106	+	0.598523i	$0.795755\pi$
$230$		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	$0.0145617\pi$
$251$			1.44903i			0.0914619i	−0.998954	+	0.0457309i	$0.985438\pi$
$252$		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	0.688003	−	0.725708i	$-0.258488\pi$
$269$	6.61826	+	3.82105i	0.403522	+	0.232974i	−0.284480	+	0.958682i	$0.591821\pi$
$270$		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	0.589924	−	0.807459i	$-0.299158\pi$
$277$	3.08910	+	1.78349i	0.185606	+	0.107160i	−0.404318	+	0.914618i	$0.632491\pi$
$278$		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	$0.401626\pi$
$283$	−11.3202	+	19.6072i	−0.672918	+	1.16553i	−0.977073	+	0.212906i	$0.931707\pi$
$284$		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	$-0.944295\pi$
$293$		−	5.96057i		−	0.348220i	0.984726	−	0.174110i	$-0.0557049\pi$
$294$		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	$-0.549441\pi$
$307$	−5.42113			−0.309400			−0.154700	+	0.987961i	$0.549441\pi$
$308$		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	$-0.978086\pi$
$317$	−9.94185	−	17.2198i	−0.558390	−	0.967160i	0.439241	−	0.898369i	$-0.355247\pi$
$318$		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	−0.551387	−	0.834250i	$-0.685901\pi$
$331$	−1.90300	+	1.09870i	−0.104599	+	0.0603900i	0.446788	+	0.894640i	$0.352568\pi$
$332$		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	−0.985388	−	0.170324i	$-0.945518\pi$
$347$	−6.43016	+	11.1374i	−0.345189	+	0.597885i	0.640199	+	0.768209i	$0.278852\pi$
$348$		0			0
$349$	−30.0571			−1.60892			−0.804460	−	0.594006i	$-0.797545\pi$
$349$	−30.0571			−1.60892			−0.804460	+	0.594006i	$0.797545\pi$
$350$		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	−0.581942	−	0.813230i	$-0.697707\pi$
$373$	−3.25687	+	1.88036i	−0.168635	+	0.0973612i	0.413307	+	0.910592i	$0.364374\pi$
$374$		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	$-0.897866\pi$
$379$		−	12.2799i		−	0.630774i	0.948963	−	0.315387i	$-0.102134\pi$
$380$		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	$-0.455211\pi$
$389$	18.2949	−	31.6877i	0.927588	−	1.60663i	0.787345	−	0.616513i	$-0.211455\pi$
$390$		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	0.946061	−	0.323989i	$-0.105024\pi$
$397$	3.83449	+	6.64152i	0.192447	+	0.333329i	−0.753613	+	0.657318i	$0.771691\pi$
$398$		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	$-0.666670\pi$
$419$		−	35.4540i		−	1.73204i	0.500009	−	0.866020i	$-0.333330\pi$
$420$		0			0
$421$			8.00460i			0.390120i	0.980791	+	0.195060i	$0.0624902\pi$
$421$			8.00460i			0.390120i	−0.980791	+	0.195060i	$0.937510\pi$
$422$		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	0.984133	−	0.177431i	$-0.0567785\pi$
$443$	7.12265	+	12.3368i	0.338407	+	0.586138i	−0.645726	+	0.763569i	$0.723445\pi$
$444$		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	$0.105127\pi$
$461$			13.9258i			0.648588i	−0.945956	+	0.324294i	$0.894873\pi$
$462$		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	−0.832596	−	0.553880i	$-0.813147\pi$
$467$	−16.6230	+	9.59729i	−0.769220	+	0.444110i	0.0633760	+	0.997990i	$0.479813\pi$
$468$		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	$-0.533386\pi$
$491$	−4.63965			−0.209384			−0.104692	+	0.994505i	$0.533386\pi$
$492$		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	−0.827959	−	0.560789i	$-0.810498\pi$
$499$	−16.8940	+	9.75377i	−0.756280	+	0.436639i	0.0716782	+	0.997428i	$0.477165\pi$
$500$		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	0.0411013	−	0.999155i	$-0.486913\pi$
$509$	20.9128	−	12.0740i	0.926946	−	0.535172i	0.885844	+	0.463983i	$0.153580\pi$
$510$		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	0.972389	−	0.233365i	$-0.0749737\pi$
$523$	6.49701	+	11.2532i	0.284095	+	0.492066i	−0.688295	+	0.725431i	$0.741640\pi$
$524$		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	−0.0395397	−	0.999218i	$-0.512589\pi$
$541$	18.7480	−	10.8242i	0.806039	−	0.465367i	0.845578	+	0.533851i	$0.179256\pi$
$542$		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	$-0.889651\pi$
$547$		−	15.8930i		−	0.679536i	0.940509	−	0.339768i	$-0.110349\pi$
$548$		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	$0.497404\pi$
$557$	−20.3420	+	35.2334i	−0.861919	+	1.49289i	−0.870074	+	0.492921i	$0.835929\pi$
$558$		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	$0.0614810\pi$
$563$	38.8739	+	22.4439i	1.63834	+	0.945896i	0.656936	+	0.753947i	$0.271852\pi$
$564$		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	0.625490	−	0.780232i	$-0.284899\pi$
$571$	6.27344	+	3.62197i	0.262535	+	0.151575i	−0.362955	+	0.931807i	$0.618232\pi$
$572$		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	$-0.944995\pi$
$587$		−	8.33175i		−	0.343888i	0.985107	−	0.171944i	$-0.0550048\pi$
$588$		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	0.999436	−	0.0335801i	$-0.0106909\pi$
$613$	36.3973	+	21.0140i	1.47007	+	0.848747i	0.470637	+	0.882327i	$0.344024\pi$
$614$		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	−0.586545	−	0.809917i	$-0.699512\pi$
$619$	10.1543	−	17.5878i	0.408136	−	0.706913i	0.994681	+	0.103004i	$0.0328455\pi$
$620$		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	$-0.275392\pi$
$643$	32.8892			1.29702			0.648512	+	0.761204i	$0.275392\pi$
$644$		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	0.518835	−	0.854874i	$-0.326366\pi$
$653$	−12.2895	−	21.2860i	−0.480926	−	0.832987i	−0.999760	+	0.0218870i	$0.993033\pi$
$654$		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	$-0.423808\pi$
$659$	12.1725			0.474172			0.237086	+	0.971489i	$0.423808\pi$
$660$		0			0
$661$	−4.00322	+	6.93378i	−0.155707	+	0.269693i	−0.933316	−	0.359055i	$-0.883099\pi$
$661$	−4.00322	+	6.93378i	−0.155707	+	0.269693i	0.777609	+	0.628748i	$0.216432\pi$
$662$		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	$-0.331674\pi$
$677$	39.1458	−	22.6008i	1.50449	−	0.868620i	0.999986	−	0.00521277i	$-0.00165928\pi$
$678$		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	−0.961890	−	0.273437i	$-0.911840\pi$
$683$	−6.38047	+	11.0513i	−0.244142	+	0.422866i	0.717748	+	0.696303i	$0.245173\pi$
$684$		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	0.688235	−	0.725488i	$-0.258386\pi$
$691$	−7.47003	−	12.9385i	−0.284173	−	0.492203i	−0.972408	+	0.233285i	$0.925052\pi$
$692$		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	$-0.412871\pi$
$701$	14.3141			0.540636			0.270318	+	0.962771i	$0.412871\pi$
$702$		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	−0.602846	−	0.797858i	$-0.705967\pi$
$709$	−5.67964	+	3.27914i	−0.213303	+	0.123151i	0.389542	+	0.921009i	$0.372633\pi$
$710$		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	0.988835	−	0.149012i	$-0.0476093\pi$
$733$	9.89201	+	17.1335i	0.365370	+	0.632839i	−0.623466	+	0.781851i	$0.714276\pi$
$734$		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	0.606893	−	0.794784i	$-0.292416\pi$
$739$	6.03595	+	3.48486i	0.222036	+	0.128193i	−0.384857	+	0.922976i	$0.625749\pi$
$740$		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	$0.186000\pi$
$757$			30.3555i			1.10329i	−0.834079	+	0.551645i	$0.814000\pi$
$758$		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	0.327852	−	0.944729i	$-0.393675\pi$
$773$	−9.07434	−	5.23907i	−0.326381	−	0.188436i	−0.654233	+	0.756293i	$0.727009\pi$
$774$		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	−0.962720	−	0.270499i	$-0.912811\pi$
$787$	−6.93206	+	12.0067i	−0.247101	+	0.427992i	0.715619	+	0.698491i	$0.246145\pi$
$788$		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	$0.174751\pi$
$797$			29.4639i			1.04366i	−0.853048	+	0.521832i	$0.825249\pi$
$798$		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	$-0.498993\pi$
$811$	0.180195			0.00632751			0.00316376	+	0.999995i	$0.498993\pi$
$812$		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	0.993830	−	0.110918i	$-0.0353792\pi$
$821$	11.4858	+	19.8940i	0.400857	+	0.694304i	−0.592973	+	0.805223i	$0.702046\pi$
$822$		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	$-0.388279\pi$
$827$	19.7749			0.687641			0.343821	+	0.939035i	$0.388279\pi$
$828$		0			0
$829$	−13.8197	+	23.9365i	−0.479979	+	0.831349i	−0.999736	−	0.0229656i	$-0.992689\pi$
$829$	−13.8197	+	23.9365i	−0.479979	+	0.831349i	0.519757	+	0.854314i	$0.326023\pi$
$830$		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	$-0.676176\pi$
$853$	−30.7041			−1.05129			−0.525645	+	0.850704i	$0.676176\pi$
$854$		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	$-0.811498\pi$
$859$	−26.3268	−	45.5994i	−0.898260	−	1.55583i	−0.0685424	−	0.997648i	$-0.521835\pi$
$860$		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	−0.987706	−	0.156324i	$-0.950036\pi$
$877$	−39.8660	+	23.0166i	−1.34618	+	0.777216i	−0.358472	+	0.933540i	$0.616702\pi$
$878$		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	$0.365991\pi$
$883$			54.2412i			1.82536i	−0.408674	+	0.912680i	$0.634009\pi$
$884$		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	0.685412	−	0.728156i	$-0.259622\pi$
$907$	11.9718	+	6.91190i	0.397516	+	0.229506i	−0.287896	+	0.957662i	$0.592956\pi$
$908$		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	0.0474212	−	0.998875i	$-0.484900\pi$
$941$	−24.3540	−	14.0608i	−0.793919	−	0.458370i	−0.841341	+	0.540505i	$0.818233\pi$
$942$		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	0.630155	−	0.776469i	$-0.282991\pi$
$947$	−10.9973	−	19.0479i	−0.357365	−	0.618974i	−0.987520	+	0.157495i	$0.949658\pi$
$948$		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	−0.537461	−	0.843288i	$-0.680617\pi$
$971$	−2.36459	+	1.36519i	−0.0758832	+	0.0438112i	0.461578	+	0.887099i	$0.347283\pi$
$972$		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	−0.993868	−	0.110575i	$-0.964731\pi$
$997$	−12.6672	+	21.9402i	−0.401173	+	0.694853i	0.592694	+	0.805427i	$0.298064\pi$
$998$		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.17.1		48
3.2	odd	2	inner	672.2.bi.c.17.16		48
4.3	odd	2		168.2.ba.c.101.23	yes	48
7.5	odd	6	inner	672.2.bi.c.593.9		48
8.3	odd	2		168.2.ba.c.101.17	yes	48
8.5	even	2	inner	672.2.bi.c.17.24		48
12.11	even	2		168.2.ba.c.101.2	yes	48
21.5	even	6	inner	672.2.bi.c.593.24		48
24.5	odd	2	inner	672.2.bi.c.17.9		48
24.11	even	2		168.2.ba.c.101.8	yes	48
28.19	even	6		168.2.ba.c.5.8	yes	48
56.5	odd	6	inner	672.2.bi.c.593.16		48
56.19	even	6		168.2.ba.c.5.2	✓	48
84.47	odd	6		168.2.ba.c.5.17	yes	48
168.5	even	6	inner	672.2.bi.c.593.1		48
168.131	odd	6		168.2.ba.c.5.23	yes	48

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

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

\(f(q)\)	\(=\)	\(q+(-1.70874 + 0.283220i) q^{3} +(-2.24840 + 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(2.83957 - 0.967897i) q^{9} +O(q^{10})\)	\(q+(-1.70874 + 0.283220i) q^{3} +(-2.24840 + 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(2.83957 - 0.967897i) q^{9} +(1.63808 - 2.83724i) q^{11} -0.912635 q^{13} +(3.47427 - 2.85492i) q^{15} +(-2.39448 + 4.14736i) q^{17} +(2.66693 + 4.61926i) q^{19} +(-4.54754 - 0.565618i) q^{21} +(-4.45569 + 2.57249i) q^{23} +(0.870190 - 1.50721i) q^{25} +(-4.57796 + 2.45811i) q^{27} -1.35950 q^{29} +(-8.18469 - 4.72543i) q^{31} +(-1.99549 + 5.31204i) q^{33} +(-6.67920 + 1.60340i) q^{35} +(-1.59746 + 0.922292i) q^{37} +(1.55945 - 0.258476i) q^{39} -5.91833 q^{41} +8.00125i q^{43} +(-5.12805 + 5.86230i) q^{45} +(3.29243 + 5.70266i) q^{47} +(5.87055 + 3.81269i) q^{49} +(2.91692 - 7.76491i) q^{51} +(-0.841712 + 1.45789i) q^{53} +8.50565i q^{55} +(-5.86535 - 7.13777i) q^{57} +(1.50266 + 0.867561i) q^{59} +(4.72347 + 8.18130i) q^{61} +(7.93074 - 0.321460i) q^{63} +(2.05197 - 1.18470i) q^{65} +(-10.8634 - 6.27198i) q^{67} +(6.88502 - 5.65766i) q^{69} +0.603989i q^{71} +(-1.29220 - 0.746053i) q^{73} +(-1.06005 + 2.82189i) q^{75} +(6.28759 - 5.96647i) q^{77} +(0.0625152 + 0.108280i) q^{79} +(7.12635 - 5.49683i) q^{81} -0.246431i q^{83} -12.4332i q^{85} +(2.32303 - 0.385038i) q^{87} +(-1.80671 - 3.12931i) q^{89} +(-2.31516 - 0.685829i) q^{91} +(15.3238 + 5.75646i) q^{93} +(-11.9926 - 6.92395i) q^{95} -5.10324i q^{97} +(1.90529 - 9.64204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 4 * q^7 - 14 * q^9	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 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

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