LMFDB - Embedded newform 672.2.bi.c.17.9

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			17.9
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.609093 - 1.62142i) q^{3} +(-2.24840 + 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(-2.25801 + 1.97519i) q^{9} +O(q^{10})$	\(q+(-0.609093 - 1.62142i) q^{3} +(-2.24840 + 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(-2.25801 + 1.97519i) q^{9} +(1.63808 - 2.83724i) q^{11} +0.912635 q^{13} +(3.47427 + 2.85492i) q^{15} +(2.39448 - 4.14736i) q^{17} +(-2.66693 - 4.61926i) q^{19} +(-0.326671 - 4.57092i) q^{21} +(4.45569 - 2.57249i) q^{23} +(0.870190 - 1.50721i) q^{25} +(4.57796 + 2.45811i) q^{27} -1.35950 q^{29} +(-8.18469 - 4.72543i) q^{31} +(-5.59810 - 0.927874i) q^{33} +(-6.67920 + 1.60340i) q^{35} +(1.59746 - 0.922292i) q^{37} +(-0.555880 - 1.47977i) q^{39} +5.91833 q^{41} -8.00125i q^{43} +(2.51288 - 7.37217i) q^{45} +(-3.29243 - 5.70266i) q^{47} +(5.87055 + 3.81269i) q^{49} +(-8.18307 - 1.35633i) q^{51} +(-0.841712 + 1.45789i) q^{53} +8.50565i q^{55} +(-5.86535 + 7.13777i) q^{57} +(1.50266 + 0.867561i) q^{59} +(-4.72347 - 8.18130i) q^{61} +(-7.21241 + 3.31379i) q^{63} +(-2.05197 + 1.18470i) q^{65} +(10.8634 + 6.27198i) q^{67} +(-6.88502 - 5.65766i) q^{69} -0.603989i q^{71} +(-1.29220 - 0.746053i) q^{73} +(-2.97385 - 0.492910i) q^{75} +(6.28759 - 5.96647i) q^{77} +(0.0625152 + 0.108280i) q^{79} +(1.19722 - 8.92001i) q^{81} -0.246431i q^{83} +12.4332i q^{85} +(0.828064 + 2.20433i) q^{87} +(1.80671 + 3.12931i) q^{89} +(2.31516 + 0.685829i) q^{91} +(-2.67667 + 16.1491i) q^{93} +(11.9926 + 6.92395i) q^{95} -5.10324i q^{97} +(1.90529 + 9.64204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.609093	−	1.62142i	−0.351660	−	0.936128i
$3$	−0.609093	−	1.62142i	−0.351660	−	0.936128i
$4$		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
$9$	−2.25801	+	1.97519i	−0.752670	+	0.658398i
$10$		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	$-0.459606\pi$
$13$	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	$-0.636094\pi$
$17$	2.39448	−	4.14736i	0.580746	−	1.00588i	0.995391	−	0.0958985i	$-0.0305724\pi$
$18$		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
$21$	−0.326671	−	4.57092i	−0.0712854	−	0.997456i
$22$		0			0
$23$	4.45569	−	2.57249i	0.929075	−	0.536402i	0.0425563	−	0.999094i	$-0.486450\pi$
$23$	4.45569	−	2.57249i	0.929075	−	0.536402i	0.886519	+	0.462692i	$0.153116\pi$
$24$		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
$33$	−5.59810	−	0.927874i	−0.974504	−	0.161522i
$34$		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
$39$	−0.555880	−	1.47977i	−0.0890121	−	0.236952i
$40$		0			0
$41$	5.91833			0.924288			0.462144	−	0.886805i	$-0.347080\pi$
$41$	5.91833			0.924288			0.462144	+	0.886805i	$0.347080\pi$
$42$		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
$45$	2.51288	−	7.37217i	0.374598	−	1.09898i
$46$		0			0
$47$	−3.29243	−	5.70266i	−0.480250	−	0.831818i	0.519493	−	0.854475i	$-0.326121\pi$
$47$	−3.29243	−	5.70266i	−0.480250	−	0.831818i	−0.999743	+	0.0226567i	$0.992788\pi$
$48$		0			0
$49$	5.87055	+	3.81269i	0.838650	+	0.544671i
$50$		0			0
$51$	−8.18307	−	1.35633i	−1.14586	−	0.189924i
$52$		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	$-0.959928\pi$
$61$	−4.72347	−	8.18130i	−0.604779	−	1.04751i	0.387308	−	0.921951i	$-0.373405\pi$
$62$		0			0
$63$	−7.21241	+	3.31379i	−0.908678	+	0.417498i
$64$		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	$-0.988589\pi$
$71$		−	0.603989i		−	0.0716803i	0.999358	−	0.0358401i	$-0.0114107\pi$
$72$		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
$75$	−2.97385	−	0.492910i	−0.343391	−	0.0569164i
$76$		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
$81$	1.19722	−	8.92001i	0.133025	−	0.991113i
$82$		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
$87$	0.828064	+	2.20433i	0.0887778	+	0.236329i
$88$		0			0
$89$	1.80671	+	3.12931i	0.191511	+	0.331706i	0.945751	−	0.324892i	$-0.105328\pi$
$89$	1.80671	+	3.12931i	0.191511	+	0.331706i	−0.754241	+	0.656598i	$0.771995\pi$
$90$		0			0
$91$	2.31516	+	0.685829i	0.242695	+	0.0718944i
$92$		0			0
$93$	−2.67667	+	16.1491i	−0.277558	+	1.67458i
$94$		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
$105$	6.66805	+	9.85318i	0.650735	+	0.961572i
$106$		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	0.966224	−	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	$-0.722584\pi$
$113$		−	16.2708i		−	1.53063i	0.643657	−	0.765314i	$-0.277416\pi$
$114$		0			0
$115$	−6.67877	+	11.5680i	−0.622798	+	1.07872i
$116$		0			0
$117$	−2.06074	+	1.80263i	−0.190515	+	0.166653i
$118$		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
$123$	−3.60482	−	9.59610i	−0.325035	−	0.865251i
$124$		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
$129$	−12.9734	+	4.87351i	−1.14224	+	0.429089i
$130$		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
$135$	−13.4840	+	0.415906i	−1.16051	+	0.0357955i
$136$		0			0
$137$	2.43936	+	1.40836i	0.208408	+	0.120325i	0.600571	−	0.799571i	$-0.294940\pi$
$137$	2.43936	+	1.40836i	0.208408	+	0.120325i	−0.392163	+	0.919896i	$0.628273\pi$
$138$		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
$147$	2.60627	−	11.8409i	0.214961	−	0.976623i
$148$		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	$0.405839\pi$
$157$	−8.55356	+	14.8152i	−0.682648	+	1.18238i	−0.974170	+	0.225817i	$0.927495\pi$
$158$		0			0
$159$	2.87653	+	0.476779i	0.228124	+	0.0378110i
$160$		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
$165$	13.7912	−	5.18073i	1.07365	−	0.403320i
$166$		0			0
$167$	−9.89286			−0.765532			−0.382766	−	0.923845i	$-0.625028\pi$
$167$	−9.89286			−0.765532			−0.382766	+	0.923845i	$0.625028\pi$
$168$		0			0
$169$	−12.1671			−0.935931
$170$		0			0
$171$	15.1459	+	5.16263i	1.15823	+	0.394796i
$172$		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
$177$	0.491421	−	2.96487i	0.0369375	−	0.222853i
$178$		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	$-0.483203\pi$
$181$	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
$189$	9.76607	+	9.67594i	0.710377	+	0.703821i
$190$		0			0
$191$	−3.62414	+	2.09240i	−0.262234	+	0.151401i	−0.625353	−	0.780342i	$-0.715045\pi$
$191$	−3.62414	+	2.09240i	−0.262234	+	0.151401i	0.363119	+	0.931743i	$0.381712\pi$
$192$		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
$201$	3.55270	−	21.4344i	0.250588	−	1.51186i
$202$		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
$207$	−4.97982	+	14.6096i	−0.346121	+	1.01543i
$208$		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
$213$	−0.979320	+	0.367886i	−0.0671019	+	0.0252071i
$214$		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
$219$	−0.422594	+	2.54962i	−0.0285563	+	0.172287i
$220$		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	0.801106	−	0.598523i	$-0.204245\pi$
$229$	−1.78238	−	3.08717i	−0.117783	−	0.204006i	−0.918889	+	0.394517i	$0.870912\pi$
$230$		0			0
$231$	−13.5039	−	6.56069i	−0.888491	−	0.431662i
$232$		0			0
$233$	−6.60666	+	3.81435i	−0.432816	+	0.249887i	−0.700546	−	0.713607i	$-0.747060\pi$
$233$	−6.60666	+	3.81435i	−0.432816	+	0.249887i	0.267729	+	0.963494i	$0.413727\pi$
$234$		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	$-0.858750\pi$
$239$		−	13.2745i		−	0.858658i	0.903148	−	0.429329i	$-0.141250\pi$
$240$		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
$243$	−15.1923	+	3.49192i	−0.974588	+	0.224007i
$244$		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
$249$	−0.399568	+	0.150099i	−0.0253216	+	0.00951217i
$250$		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
$255$	20.1594	−	7.57298i	1.26243	−	0.474238i
$256$		0			0
$257$	6.03418	+	10.4515i	0.376402	+	0.651948i	0.990536	−	0.137254i	$-0.0438278\pi$
$257$	6.03418	+	10.4515i	0.376402	+	0.651948i	−0.614134	+	0.789202i	$0.710494\pi$
$258$		0			0
$259$	4.74549	−	1.13920i	0.294870	−	0.0707862i
$260$		0			0
$261$	3.06977	−	2.68528i	0.190014	−	0.166215i
$262$		0			0
$263$	−21.7325	−	12.5473i	−1.34008	−	0.773697i	−0.353264	−	0.935524i	$-0.614928\pi$
$263$	−21.7325	−	12.5473i	−1.34008	−	0.773697i	−0.986819	+	0.161827i	$0.948261\pi$
$264$		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
$273$	−0.298131	−	4.17158i	−0.0180437	−	0.252476i
$274$		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	$-0.959412\pi$
$281$		−	4.26336i		−	0.254331i	0.991882	−	0.127165i	$-0.0405879\pi$
$282$		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
$285$	3.92200	−	23.6624i	0.232319	−	1.40164i
$286$		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
$291$	−8.27449	+	3.10835i	−0.485059	+	0.182215i
$292$		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
$297$	14.4733	−	8.96219i	0.839826	−	0.520039i
$298$		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
$303$	2.07050	−	12.4919i	0.118947	−	0.717639i
$304$		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	$0.409370\pi$
$311$	−12.1809	+	21.0979i	−0.690714	+	1.19635i	−0.971604	+	0.236612i	$0.923963\pi$
$312$		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
$315$	11.9147	−	16.8132i	0.671316	−	0.947317i
$316$		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
$327$	4.18652	−	25.2583i	0.231515	−	1.39679i
$328$		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
$333$	−1.78537	+	5.23783i	−0.0978376	+	0.287031i
$334$		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
$339$	−26.3818	+	9.91044i	−1.43286	+	0.538261i
$340$		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
$345$	22.8245	+	3.78312i	1.22883	+	0.203676i
$346$		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	$-0.202455\pi$
$349$	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	$0.389554\pi$
$353$	−12.1069	+	20.9698i	−0.644387	+	1.11611i	−0.984443	+	0.175705i	$0.943779\pi$
$354$		0			0
$355$	0.784045	+	1.35801i	0.0416128	+	0.0720755i
$356$		0			0
$357$	−19.7394	−	9.59014i	−1.04472	−	0.507564i
$358$		0			0
$359$	3.16884	−	1.82953i	0.167245	−	0.0965590i	−0.414041	−	0.910258i	$-0.635883\pi$
$359$	3.16884	−	1.82953i	0.167245	−	0.0965590i	0.581286	+	0.813699i	$0.302550\pi$
$360$		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
$369$	−13.3636	+	11.6898i	−0.695684	+	0.608549i
$370$		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
$375$	−13.7216	+	5.15458i	−0.708581	+	0.266181i
$376$		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
$381$	−0.974524	−	2.59421i	−0.0499264	−	0.132905i
$382$		0			0
$383$	−3.77515	−	6.53874i	−0.192901	−	0.334114i	0.753309	−	0.657666i	$-0.228456\pi$
$383$	−3.77515	−	6.53874i	−0.192901	−	0.334114i	−0.946210	+	0.323552i	$0.895123\pi$
$384$		0			0
$385$	−6.39184	+	21.5770i	−0.325758	+	1.09967i
$386$		0			0
$387$	15.8040	+	18.0669i	0.803364	+	0.918393i
$388$		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	0.753613	−	0.657318i	$-0.228309\pi$
$397$	−3.83449	−	6.64152i	−0.192447	−	0.333329i	−0.946061	+	0.323989i	$0.894976\pi$
$398$		0			0
$399$	−20.2430	+	13.6993i	−1.01342	+	0.685822i
$400$		0			0
$401$	−20.5062	+	11.8393i	−1.02403	+	0.591224i	−0.915269	−	0.402844i	$-0.868022\pi$
$401$	−20.5062	+	11.8393i	−1.02403	+	0.591224i	−0.108761	+	0.994068i	$0.534688\pi$
$402$		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
$411$	0.797753	−	4.81305i	0.0393502	−	0.237410i
$412$		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
$417$	−1.70854	−	4.54816i	−0.0836674	−	0.222724i
$418$		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	$-0.937510\pi$
$421$		−	8.00460i		−	0.390120i	0.980791	−	0.195060i	$-0.0624902\pi$
$422$		0			0
$423$	18.6982	+	6.37347i	0.909137	+	0.309889i
$424$		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
$429$	−5.10902	−	0.846811i	−0.246666	−	0.0408844i
$430$		0			0
$431$	25.8583	+	14.9293i	1.24555	+	0.719118i	0.970219	−	0.242231i	$-0.0778793\pi$
$431$	25.8583	+	14.9293i	1.24555	+	0.719118i	0.275331	+	0.961350i	$0.411213\pi$
$432$		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
$441$	−20.7866	+	2.98637i	−0.989837	+	0.142208i
$442$		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	$0.0163819\pi$
$449$			2.18010i			0.102885i	−0.998676	+	0.0514426i	$0.983618\pi$
$450$		0			0
$451$	9.69470	−	16.7917i	0.456506	−	0.790691i
$452$		0			0
$453$	−21.9249	−	3.63400i	−1.03012	−	0.170740i
$454$		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
$459$	21.1565	−	13.1005i	0.987499	−	0.611481i
$460$		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
$465$	−14.9451	−	39.7841i	−0.693061	−	1.84494i
$466$		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
$471$	29.2316	+	4.84508i	1.34692	+	0.223249i
$472$		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	−0.926750	−	0.375678i	$-0.877410\pi$
$479$	−3.02090	+	5.23235i	−0.138028	+	0.239072i	0.788722	+	0.614750i	$0.210743\pi$
$480$		0			0
$481$	1.45790	−	0.841716i	0.0664743	−	0.0383790i
$482$		0			0
$483$	−13.2142	−	19.5262i	−0.601267	−	0.888474i
$484$		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
$495$	−16.8003	−	19.2058i	−0.755117	−	0.863238i
$496$		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
$501$	6.02567	+	16.0405i	0.269207	+	0.716636i
$502$		0			0
$503$	33.9146			1.51218			0.756090	−	0.654468i	$-0.227107\pi$
$503$	33.9146			1.51218			0.756090	+	0.654468i	$0.227107\pi$
$504$		0			0
$505$	−18.9799			−0.844594
$506$		0			0
$507$	7.41090	+	19.7280i	0.329130	+	0.876150i
$508$		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
$513$	−0.854465	−	27.7024i	−0.0377256	−	1.22309i
$514$		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	−0.793274	−	0.608864i	$-0.791625\pi$
$521$	2.98225	−	5.16541i	0.130655	−	0.226301i	0.923929	+	0.382564i	$0.124959\pi$
$522$		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
$525$	−7.17361	−	3.48520i	−0.313082	−	0.152107i
$526$		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
$537$	−20.7599	−	3.44091i	−0.895855	−	0.148486i
$538$		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
$543$	−0.864435	−	2.30115i	−0.0370965	−	0.0987516i
$544$		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
$549$	26.8253	+	9.14368i	1.14488	+	0.390243i
$550$		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
$555$	8.18307	+	1.35633i	0.347352	+	0.0575729i
$556$		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
$567$	9.74032	−	21.7285i	0.409055	−	0.912510i
$568$		0			0
$569$	12.8893	−	7.44164i	0.540347	−	0.311970i	−0.204872	−	0.978789i	$-0.565678\pi$
$569$	12.8893	−	7.44164i	0.540347	−	0.311970i	0.745220	+	0.666819i	$0.232345\pi$
$570$		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
$579$	45.0784	+	7.47165i	1.87339	+	0.310511i
$580$		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
$585$	2.29334	−	6.72810i	0.0948180	−	0.278173i
$586$		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
$591$	−7.72990	−	20.5772i	−0.317966	−	0.846432i
$592$		0			0
$593$	19.8845	+	34.4410i	0.816560	+	1.41432i	0.908202	+	0.418531i	$0.137455\pi$
$593$	19.8845	+	34.4410i	0.816560	+	1.41432i	−0.0916424	+	0.995792i	$0.529212\pi$
$594$		0			0
$595$	−9.34332	+	31.5403i	−0.383039	+	1.29303i
$596$		0			0
$597$	−0.307278	+	1.85389i	−0.0125761	+	0.0758746i
$598$		0			0
$599$	−12.0202	−	6.93989i	−0.491134	−	0.283556i	0.233911	−	0.972258i	$-0.424848\pi$
$599$	−12.0202	−	6.93989i	−0.491134	−	0.283556i	−0.725045	+	0.688702i	$0.758181\pi$
$600$		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
$609$	0.444110	+	6.21417i	0.0179962	+	0.251811i
$610$		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	$0.104434\pi$
$617$			16.0083i			0.644471i	−0.946660	+	0.322236i	$0.895566\pi$
$618$		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
$621$	26.7214	−	0.824208i	1.07229	−	0.0330743i
$622$		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
$627$	10.6437	+	28.3336i	0.425067	+	1.13154i
$628$		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
$633$	12.7942	−	4.80620i	0.508524	−	0.191029i
$634$		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
$639$	1.19299	+	1.36381i	0.0471941	+	0.0539516i
$640$		0			0
$641$	−9.80778	−	5.66252i	−0.387384	−	0.223656i	0.293642	−	0.955915i	$-0.405133\pi$
$641$	−9.80778	−	5.66252i	−0.387384	−	0.223656i	−0.681026	+	0.732259i	$0.738466\pi$
$642$		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	$0.346509\pi$
$647$	−13.6188	+	23.5884i	−0.535409	+	0.927356i	−0.999143	+	0.0413818i	$0.986824\pi$
$648$		0			0
$649$	4.92296	−	2.84227i	0.193243	−	0.111569i
$650$		0			0
$651$	−18.9259	+	38.9552i	−0.741763	+	1.52678i
$652$		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	−0.777609	−	0.628748i	$-0.783568\pi$
$661$	4.00322	−	6.93378i	0.155707	−	0.269693i	0.933316	+	0.359055i	$0.116901\pi$
$662$		0			0
$663$	−7.46816	−	1.23783i	−0.290039	−	0.0480734i
$664$		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
$669$	18.7098	−	7.02843i	0.723364	−	0.271735i
$670$		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
$675$	7.68858	−	4.76094i	0.295934	−	0.183249i
$676$		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
$681$	−4.40922	+	26.6020i	−0.168962	+	1.01939i
$682$		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	0.972408	−	0.233285i	$-0.0749475\pi$
$691$	7.47003	+	12.9385i	0.284173	+	0.492203i	−0.688235	+	0.725488i	$0.741614\pi$
$692$		0			0
$693$	−2.41250	+	25.8916i	−0.0916433	+	0.983539i
$694$		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
$705$	4.84186	−	29.2122i	0.182355	−	1.10020i
$706$		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
$711$	−0.355033	−	0.121017i	−0.0133148	−	0.00453848i
$712$		0			0
$713$	−48.6246			−1.82100
$714$		0			0
$715$			7.76255i			0.290303i
$716$		0			0
$717$	−21.5236	+	8.08543i	−0.803813	+	0.301956i
$718$		0			0
$719$	19.5665	+	33.8902i	0.729708	+	1.26389i	0.957007	+	0.290066i	$0.0936772\pi$
$719$	19.5665	+	33.8902i	0.729708	+	1.26389i	−0.227299	+	0.973825i	$0.572990\pi$
$720$		0			0
$721$	−1.99202	+	0.478202i	−0.0741866	+	0.0178092i
$722$		0			0
$723$	3.24677	−	19.5886i	0.120749	−	0.728508i
$724$		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
$735$	9.51092	+	30.0063i	0.350815	+	1.10680i
$736$		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	$-0.686793\pi$
$743$		−	45.3956i		−	1.66540i	0.553723	−	0.832701i	$-0.313207\pi$
$744$		0			0
$745$	−38.9883	−	22.5099i	−1.42842	−	0.824700i
$746$		0			0
$747$	0.486749	+	0.556443i	0.0178092	+	0.0203592i
$748$		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
$753$	2.34949	−	0.882594i	0.0856200	−	0.0321635i
$754$		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
$759$	−27.3303	+	10.2668i	−0.992029	+	0.372660i
$760$		0			0
$761$	6.12394	+	10.6070i	0.221993	+	0.384503i	0.955413	−	0.295273i	$-0.0954106\pi$
$761$	6.12394	+	10.6070i	0.221993	+	0.384503i	−0.733420	+	0.679775i	$0.762077\pi$
$762$		0			0
$763$	26.9204	+	28.3693i	0.974585	+	1.02704i
$764$		0			0
$765$	−24.5580	−	28.0743i	−0.887896	−	1.01503i
$766$		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
$777$	−4.73756	−	7.00056i	−0.169959	−	0.251144i
$778$		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
$789$	−7.10727	+	42.8800i	−0.253025	+	1.52657i
$790$		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
$795$	−7.08649	+	2.66207i	−0.251332	+	0.0944139i
$796$		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
$801$	−10.2606	−	3.49741i	−0.362539	−	0.123575i
$802$		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
$807$	2.16440	−	13.0584i	0.0761904	−	0.459676i
$808$		0			0
$809$	42.7554	+	24.6848i	1.50320	+	0.867873i	0.999993	+	0.00370713i	$0.00118002\pi$
$809$	42.7554	+	24.6848i	1.50320	+	0.867873i	0.503207	+	0.864166i	$0.332153\pi$
$810$		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
$819$	−6.58230	+	3.02428i	−0.230004	+	0.105677i
$820$		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	−0.519757	−	0.854314i	$-0.673977\pi$
$829$	13.8197	−	23.9365i	0.479979	−	0.831349i	0.999736	+	0.0229656i	$0.00731081\pi$
$830$		0			0
$831$	−1.01024	+	6.09504i	−0.0350449	+	0.211435i
$832$		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
$837$	−25.8536	−	41.7517i	−0.893630	−	1.44315i
$838$		0			0
$839$	−28.3920			−0.980200			−0.490100	−	0.871666i	$-0.663040\pi$
$839$	−28.3920			−0.980200			−0.490100	+	0.871666i	$0.663040\pi$
$840$		0			0
$841$	−27.1518			−0.936267
$842$		0			0
$843$	−6.91270	+	2.59678i	−0.238086	+	0.0894380i
$844$		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
$849$	−38.6866	−	6.41223i	−1.32772	−	0.220067i
$850$		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	−0.992907	−	0.118895i	$-0.962065\pi$
$857$	−11.5192	+	19.9518i	−0.393487	+	0.681539i	0.599420	+	0.800435i	$0.295398\pi$
$858$		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
$861$	−1.93334	−	27.0522i	−0.0658882	−	0.921936i
$862$		0			0
$863$	22.4451	−	12.9587i	0.764040	−	0.441119i	−0.0667045	−	0.997773i	$-0.521248\pi$
$863$	22.4451	−	12.9587i	0.764040	−	0.441119i	0.830744	+	0.556654i	$0.187915\pi$
$864$		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
$873$	10.0799	+	11.5232i	0.341152	+	0.390000i
$874$		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
$879$	−9.66459	+	3.63054i	−0.325979	+	0.122455i
$880$		0			0
$881$	25.6170			0.863060			0.431530	−	0.902099i	$-0.357974\pi$
$881$	25.6170			0.863060			0.431530	+	0.902099i	$0.357974\pi$
$882$		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
$885$	2.74382	+	7.30412i	0.0922326	+	0.245525i
$886$		0			0
$887$	17.2509	+	29.8794i	0.579228	+	1.00325i	0.995568	+	0.0940438i	$0.0299794\pi$
$887$	17.2509	+	29.8794i	0.579228	+	1.00325i	−0.416340	+	0.909209i	$0.636687\pi$
$888$		0			0
$889$	4.05875	+	1.20234i	0.136126	+	0.0403252i
$890$		0			0
$891$	−23.3471	−	18.0085i	−0.782156	−	0.603308i
$892$		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
$903$	−36.5731	+	2.61377i	−1.21708	+	0.0869810i
$904$		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	$-0.877476\pi$
$911$		−	22.6663i		−	0.750969i	0.926829	−	0.375484i	$-0.122524\pi$
$912$		0			0
$913$	−0.699183	−	0.403674i	−0.0231396	−	0.0133596i
$914$		0			0
$915$	6.94636	−	41.9092i	0.229640	−	1.38548i
$916$		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
$921$	−3.30198	−	8.78993i	−0.108804	−	0.289638i
$922$		0			0
$923$		−	0.551221i		−	0.0181437i
$924$		0			0
$925$		−	3.21028i		−	0.105553i
$926$		0			0
$927$	0.749446	−	2.19869i	0.0246150	−	0.0722144i
$928$		0			0
$929$	−27.9226	−	48.3634i	−0.916111	−	1.58675i	−0.805267	−	0.592912i	$-0.797978\pi$
$929$	−27.9226	−	48.3634i	−0.916111	−	1.58675i	−0.110844	−	0.993838i	$-0.535355\pi$
$930$		0			0
$931$	1.95547	−	37.2858i	0.0640881	−	1.22199i
$932$		0			0
$933$	41.6279	+	6.89973i	1.36283	+	0.225887i
$934$		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
$945$	−34.5185	−	9.07789i	−1.12289	−	0.295304i
$946$		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	$-0.715718\pi$
$953$		−	48.0977i		−	1.55804i	0.627001	−	0.779018i	$-0.284282\pi$
$954$		0			0
$955$	5.43234	−	9.40909i	0.175786	−	0.304471i
$956$		0			0
$957$	7.61063	+	1.26145i	0.246017	+	0.0407768i
$958$		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
$963$	−41.2553	−	14.0623i	−1.32943	−	0.453151i
$964$		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
$969$	15.5584	+	41.4169i	0.499809	+	1.33050i
$970$		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
$975$	−2.71404	−	0.449847i	−0.0869189	−	0.0144066i
$976$		0			0
$977$	−21.7078	−	12.5330i	−0.694494	−	0.400967i	0.110799	−	0.993843i	$-0.464659\pi$
$977$	−21.7078	−	12.5330i	−0.694494	−	0.400967i	−0.805294	+	0.592876i	$0.797992\pi$
$978$		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	−0.995340	−	0.0964318i	$-0.969257\pi$
$983$	−12.9850	+	22.4907i	−0.414157	+	0.717342i	0.581182	+	0.813773i	$0.302590\pi$
$984$		0			0
$985$	−28.5340	+	16.4741i	−0.909169	+	0.524909i
$986$		0			0
$987$	−24.9908	+	16.9123i	−0.795467	+	0.538325i
$988$		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
$999$	9.58019	−	0.295496i	0.303104	−	0.00934908i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.609093 - 1.62142i) q^{3} +(-2.24840 + 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(-2.25801 + 1.97519i) q^{9} +O(q^{10})\)	\(q+(-0.609093 - 1.62142i) q^{3} +(-2.24840 + 1.29811i) q^{5} +(2.53678 + 0.751482i) q^{7} +(-2.25801 + 1.97519i) q^{9} +(1.63808 - 2.83724i) q^{11} +0.912635 q^{13} +(3.47427 + 2.85492i) q^{15} +(2.39448 - 4.14736i) q^{17} +(-2.66693 - 4.61926i) q^{19} +(-0.326671 - 4.57092i) q^{21} +(4.45569 - 2.57249i) q^{23} +(0.870190 - 1.50721i) q^{25} +(4.57796 + 2.45811i) q^{27} -1.35950 q^{29} +(-8.18469 - 4.72543i) q^{31} +(-5.59810 - 0.927874i) q^{33} +(-6.67920 + 1.60340i) q^{35} +(1.59746 - 0.922292i) q^{37} +(-0.555880 - 1.47977i) q^{39} +5.91833 q^{41} -8.00125i q^{43} +(2.51288 - 7.37217i) q^{45} +(-3.29243 - 5.70266i) q^{47} +(5.87055 + 3.81269i) q^{49} +(-8.18307 - 1.35633i) q^{51} +(-0.841712 + 1.45789i) q^{53} +8.50565i q^{55} +(-5.86535 + 7.13777i) q^{57} +(1.50266 + 0.867561i) q^{59} +(-4.72347 - 8.18130i) q^{61} +(-7.21241 + 3.31379i) q^{63} +(-2.05197 + 1.18470i) q^{65} +(10.8634 + 6.27198i) q^{67} +(-6.88502 - 5.65766i) q^{69} -0.603989i q^{71} +(-1.29220 - 0.746053i) q^{73} +(-2.97385 - 0.492910i) q^{75} +(6.28759 - 5.96647i) q^{77} +(0.0625152 + 0.108280i) q^{79} +(1.19722 - 8.92001i) q^{81} -0.246431i q^{83} +12.4332i q^{85} +(0.828064 + 2.20433i) q^{87} +(1.80671 + 3.12931i) q^{89} +(2.31516 + 0.685829i) q^{91} +(-2.67667 + 16.1491i) q^{93} +(11.9926 + 6.92395i) q^{95} -5.10324i q^{97} +(1.90529 + 9.64204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 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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