LMFDB - Embedded newform 756.2.ck.a.605.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			605.20
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37168 + 1.05759i) q^{3} +(-0.403931 - 2.29081i) q^{5} +(2.60966 - 0.435529i) q^{7} +(0.762996 + 2.90135i) q^{9} +O(q^{10})$	\(q+(1.37168 + 1.05759i) q^{3} +(-0.403931 - 2.29081i) q^{5} +(2.60966 - 0.435529i) q^{7} +(0.762996 + 2.90135i) q^{9} +(1.79103 + 0.315807i) q^{11} +(-2.58138 - 3.07637i) q^{13} +(1.86868 - 3.56944i) q^{15} +1.25468 q^{17} -5.76919i q^{19} +(4.04022 + 2.16255i) q^{21} +(5.50076 + 6.55555i) q^{23} +(-0.386172 + 0.140555i) q^{25} +(-2.02186 + 4.78666i) q^{27} +(-4.11192 + 4.90039i) q^{29} +(2.63669 - 7.24423i) q^{31} +(2.12272 + 2.32737i) q^{33} +(-2.05183 - 5.80230i) q^{35} +(2.04970 - 3.55019i) q^{37} +(-0.287275 - 6.94984i) q^{39} +(-1.98773 + 1.66790i) q^{41} +(-4.77434 + 1.73772i) q^{43} +(6.33824 - 2.91982i) q^{45} +(5.64657 - 2.05518i) q^{47} +(6.62063 - 2.27316i) q^{49} +(1.72101 + 1.32694i) q^{51} +(-2.91534 - 1.68317i) q^{53} -4.23047i q^{55} +(6.10145 - 7.91347i) q^{57} +(-7.51642 + 6.30702i) q^{59} +(3.74706 + 10.2950i) q^{61} +(3.25478 + 7.23923i) q^{63} +(-6.00468 + 7.15609i) q^{65} +(1.64220 + 9.31340i) q^{67} +(0.612165 + 14.8097i) q^{69} +(4.63046 - 2.67340i) q^{71} +(-7.35335 + 4.24546i) q^{73} +(-0.678353 - 0.215616i) q^{75} +(4.81152 + 0.0441033i) q^{77} +(0.709479 - 4.02366i) q^{79} +(-7.83567 + 4.42744i) q^{81} +(-7.74206 - 6.49636i) q^{83} +(-0.506802 - 2.87422i) q^{85} +(-10.8228 + 2.37302i) q^{87} +6.53549 q^{89} +(-8.07638 - 6.90402i) q^{91} +(11.2781 - 7.14821i) q^{93} +(-13.2161 + 2.33036i) q^{95} +(3.30745 + 9.08716i) q^{97} +(0.450282 + 5.43737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.37168	+	1.05759i	0.791938	+	0.610601i
$3$	1.37168	+	1.05759i	0.791938	+	0.610601i
$4$		0			0
$5$	−0.403931	−	2.29081i	−0.180643	−	1.02448i	−0.931426	−	0.363931i	$-0.881435\pi$
$5$	−0.403931	−	2.29081i	−0.180643	−	1.02448i	0.750783	−	0.660549i	$-0.229677\pi$
$6$		0			0
$7$	2.60966	−	0.435529i	0.986358	−	0.164614i
$7$	2.60966	−	0.435529i	0.986358	−	0.164614i
$8$		0			0
$9$	0.762996	+	2.90135i	0.254332	+	0.967117i
$10$		0			0
$11$	1.79103	+	0.315807i	0.540016	+	0.0952194i	0.437002	−	0.899460i	$-0.356040\pi$
$11$	1.79103	+	0.315807i	0.540016	+	0.0952194i	0.103014	+	0.994680i	$0.467151\pi$
$12$		0			0
$13$	−2.58138	−	3.07637i	−0.715947	−	0.853233i	0.278283	−	0.960499i	$-0.410235\pi$
$13$	−2.58138	−	3.07637i	−0.715947	−	0.853233i	−0.994230	+	0.107267i	$0.965790\pi$
$14$		0			0
$15$	1.86868	−	3.56944i	0.482490	−	0.921626i
$16$		0			0
$17$	1.25468			0.304304			0.152152	−	0.988357i	$-0.451380\pi$
$17$	1.25468			0.304304			0.152152	+	0.988357i	$0.451380\pi$
$18$		0			0
$19$		−	5.76919i		−	1.32354i	−0.749706	−	0.661772i	$-0.769805\pi$
$19$		−	5.76919i		−	1.32354i	0.749706	−	0.661772i	$-0.230195\pi$
$20$		0			0
$21$	4.04022	+	2.16255i	0.881648	+	0.471907i
$22$		0			0
$23$	5.50076	+	6.55555i	1.14699	+	1.36693i	0.919473	+	0.393152i	$0.128616\pi$
$23$	5.50076	+	6.55555i	1.14699	+	1.36693i	0.227515	+	0.973775i	$0.426940\pi$
$24$		0			0
$25$	−0.386172	+	0.140555i	−0.0772343	+	0.0281110i
$26$		0			0
$27$	−2.02186	+	4.78666i	−0.389108	+	0.921192i
$28$		0			0
$29$	−4.11192	+	4.90039i	−0.763564	+	0.909980i	−0.998068	−	0.0621353i	$-0.980209\pi$
$29$	−4.11192	+	4.90039i	−0.763564	+	0.909980i	0.234504	+	0.972115i	$0.424653\pi$
$30$		0			0
$31$	2.63669	−	7.24423i	0.473563	−	1.30110i	−0.441308	−	0.897356i	$-0.645485\pi$
$31$	2.63669	−	7.24423i	0.473563	−	1.30110i	0.914871	−	0.403747i	$-0.132292\pi$
$32$		0			0
$33$	2.12272	+	2.32737i	0.369518	+	0.405142i
$34$		0			0
$35$	−2.05183	−	5.80230i	−0.346823	−	0.980767i
$36$		0			0
$37$	2.04970	−	3.55019i	0.336969	−	0.583648i	−0.646892	−	0.762582i	$-0.723931\pi$
$37$	2.04970	−	3.55019i	0.336969	−	0.583648i	0.983861	+	0.178934i	$0.0572648\pi$
$38$		0			0
$39$	−0.287275	−	6.94984i	−0.0460009	−	1.11287i
$40$		0			0
$41$	−1.98773	+	1.66790i	−0.310431	+	0.260482i	−0.784670	−	0.619914i	$-0.787168\pi$
$41$	−1.98773	+	1.66790i	−0.310431	+	0.260482i	0.474239	+	0.880396i	$0.342723\pi$
$42$		0			0
$43$	−4.77434	+	1.73772i	−0.728079	+	0.264999i	−0.679352	−	0.733813i	$-0.737739\pi$
$43$	−4.77434	+	1.73772i	−0.728079	+	0.264999i	−0.0487278	+	0.998812i	$0.515517\pi$
$44$		0			0
$45$	6.33824	−	2.91982i	0.944848	−	0.435261i
$46$		0			0
$47$	5.64657	−	2.05518i	0.823637	−	0.299779i	0.104392	−	0.994536i	$-0.466710\pi$
$47$	5.64657	−	2.05518i	0.823637	−	0.299779i	0.719245	+	0.694757i	$0.244488\pi$
$48$		0			0
$49$	6.62063	−	2.27316i	0.945804	−	0.324737i
$50$		0			0
$51$	1.72101	+	1.32694i	0.240990	+	0.185808i
$52$		0			0
$53$	−2.91534	−	1.68317i	−0.400453	−	0.231202i	0.286226	−	0.958162i	$-0.407599\pi$
$53$	−2.91534	−	1.68317i	−0.400453	−	0.231202i	−0.686679	+	0.726960i	$0.740932\pi$
$54$		0			0
$55$		−	4.23047i		−	0.570436i
$56$		0			0
$57$	6.10145	−	7.91347i	0.808157	−	1.04816i
$58$		0			0
$59$	−7.51642	+	6.30702i	−0.978554	+	0.821104i	−0.983871	−	0.178882i	$-0.942752\pi$
$59$	−7.51642	+	6.30702i	−0.978554	+	0.821104i	0.00531667	+	0.999986i	$0.498308\pi$
$60$		0			0
$61$	3.74706	+	10.2950i	0.479762	+	1.31814i	0.909696	+	0.415275i	$0.136315\pi$
$61$	3.74706	+	10.2950i	0.479762	+	1.31814i	−0.429934	+	0.902860i	$0.641463\pi$
$62$		0			0
$63$	3.25478	+	7.23923i	0.410064	+	0.912057i
$64$		0			0
$65$	−6.00468	+	7.15609i	−0.744788	+	0.887604i
$66$		0			0
$67$	1.64220	+	9.31340i	0.200627	+	1.13781i	0.904174	+	0.427164i	$0.140487\pi$
$67$	1.64220	+	9.31340i	0.200627	+	1.13781i	−0.703547	+	0.710649i	$0.748402\pi$
$68$		0			0
$69$	0.612165	+	14.8097i	0.0736960	+	1.78287i
$70$		0			0
$71$	4.63046	−	2.67340i	0.549534	−	0.317274i	−0.199400	−	0.979918i	$-0.563899\pi$
$71$	4.63046	−	2.67340i	0.549534	−	0.317274i	0.748934	+	0.662644i	$0.230566\pi$
$72$		0			0
$73$	−7.35335	+	4.24546i	−0.860644	+	0.496893i	−0.864228	−	0.503100i	$-0.832193\pi$
$73$	−7.35335	+	4.24546i	−0.860644	+	0.496893i	0.00358383	+	0.999994i	$0.498859\pi$
$74$		0			0
$75$	−0.678353	−	0.215616i	−0.0783294	−	0.0248972i
$76$		0			0
$77$	4.81152	+	0.0441033i	0.548324	+	0.00502604i
$78$		0			0
$79$	0.709479	−	4.02366i	0.0798227	−	0.452697i	−0.918532	−	0.395348i	$-0.870624\pi$
$79$	0.709479	−	4.02366i	0.0798227	−	0.452697i	0.998354	−	0.0573491i	$-0.0182648\pi$
$80$		0			0
$81$	−7.83567	+	4.42744i	−0.870631	+	0.491938i
$82$		0			0
$83$	−7.74206	−	6.49636i	−0.849802	−	0.713068i	0.109944	−	0.993938i	$-0.464933\pi$
$83$	−7.74206	−	6.49636i	−0.849802	−	0.713068i	−0.959746	+	0.280869i	$0.909377\pi$
$84$		0			0
$85$	−0.506802	−	2.87422i	−0.0549704	−	0.311753i
$86$		0			0
$87$	−10.8228	+	2.37302i	−1.16033	+	0.254415i
$88$		0			0
$89$	6.53549			0.692760			0.346380	−	0.938094i	$-0.387411\pi$
$89$	6.53549			0.692760			0.346380	+	0.938094i	$0.387411\pi$
$90$		0			0
$91$	−8.07638	−	6.90402i	−0.846634	−	0.723738i
$92$		0			0
$93$	11.2781	−	7.14821i	1.16949	−	0.741235i
$94$		0			0
$95$	−13.2161	+	2.33036i	−1.35594	+	0.239089i
$96$		0			0
$97$	3.30745	+	9.08716i	0.335821	+	0.922661i	0.986566	+	0.163364i	$0.0522346\pi$
$97$	3.30745	+	9.08716i	0.335821	+	0.922661i	−0.650745	+	0.759297i	$0.725543\pi$
$98$		0			0
$99$	0.450282	+	5.43737i	0.0452551	+	0.546476i
$100$		0			0
$101$	1.10030	+	0.923260i	0.109484	+	0.0918678i	0.695886	−	0.718152i	$-0.255012\pi$
$101$	1.10030	+	0.923260i	0.109484	+	0.0918678i	−0.586402	+	0.810020i	$0.699456\pi$
$102$		0			0
$103$	1.55330	−	0.273888i	0.153051	−	0.0269870i	−0.0965976	−	0.995324i	$-0.530796\pi$
$103$	1.55330	−	0.273888i	0.153051	−	0.0269870i	0.249649	+	0.968336i	$0.419685\pi$
$104$		0			0
$105$	3.32201	−	10.1289i	0.324195	−	0.988478i
$106$		0			0
$107$	−13.8232	+	7.98083i	−1.33634	+	0.771536i	−0.986263	−	0.165184i	$-0.947178\pi$
$107$	−13.8232	+	7.98083i	−1.33634	+	0.771536i	−0.350078	+	0.936721i	$0.613845\pi$
$108$		0			0
$109$	3.77704	−	6.54202i	0.361774	−	0.626612i	−0.626479	−	0.779439i	$-0.715504\pi$
$109$	3.77704	−	6.54202i	0.361774	−	0.626612i	0.988253	+	0.152827i	$0.0488378\pi$
$110$		0			0
$111$	6.56619	−	2.70196i	0.623235	−	0.256459i
$112$		0			0
$113$	−2.00364	+	5.50496i	−0.188487	+	0.517863i	−0.997558	−	0.0698478i	$-0.977749\pi$
$113$	−2.00364	+	5.50496i	−0.188487	+	0.517863i	0.809071	+	0.587711i	$0.199971\pi$
$114$		0			0
$115$	12.7956	−	15.2492i	1.19319	−	1.42199i
$116$		0			0
$117$	6.95605	−	9.83676i	0.643087	−	0.909409i
$118$		0			0
$119$	3.27427	−	0.546447i	0.300152	−	0.0500927i
$120$		0			0
$121$	−7.22856	−	2.63098i	−0.657142	−	0.239180i
$122$		0			0
$123$	−4.49048	+	0.185616i	−0.404893	+	0.0167364i
$124$		0			0
$125$	−5.33739	−	9.24464i	−0.477391	−	0.826866i
$126$		0			0
$127$	−3.42823	+	5.93786i	−0.304206	+	0.526900i	−0.977084	−	0.212853i	$-0.931724\pi$
$127$	−3.42823	+	5.93786i	−0.304206	+	0.526900i	0.672878	+	0.739753i	$0.265058\pi$
$128$		0			0
$129$	−8.38664	−	2.66572i	−0.738403	−	0.234703i
$130$		0			0
$131$	−10.3553	+	8.68914i	−0.904748	+	0.759174i	−0.971113	−	0.238622i	$-0.923304\pi$
$131$	−10.3553	+	8.68914i	−0.904748	+	0.759174i	0.0663648	+	0.997795i	$0.478860\pi$
$132$		0			0
$133$	−2.51265	−	15.0556i	−0.217874	−	1.30549i
$134$		0			0
$135$	11.7820	+	2.69822i	1.01403	+	0.232226i
$136$		0			0
$137$	−7.18160	−	19.7313i	−0.613566	−	1.68576i	−0.722207	−	0.691677i	$-0.756872\pi$
$137$	−7.18160	−	19.7313i	−0.613566	−	1.68576i	0.108642	−	0.994081i	$-0.465350\pi$
$138$		0			0
$139$	−20.1849	+	3.55915i	−1.71206	+	0.301883i	−0.941882	−	0.335944i	$-0.890945\pi$
$139$	−20.1849	+	3.55915i	−1.71206	+	0.301883i	−0.770180	+	0.637826i	$0.779834\pi$
$140$		0			0
$141$	9.91882	+	3.15272i	0.835315	+	0.265507i
$142$		0			0
$143$	−3.65180	−	6.32510i	−0.305379	−	0.528931i
$144$		0			0
$145$	12.8868	+	7.44019i	1.07019	+	0.617874i
$146$		0			0
$147$	11.4854	+	3.88389i	0.947303	+	0.320337i
$148$		0			0
$149$	−2.36927	+	6.50950i	−0.194098	+	0.533279i	−0.998118	−	0.0613227i	$-0.980468\pi$
$149$	−2.36927	+	6.50950i	−0.194098	+	0.533279i	0.804020	+	0.594602i	$0.202690\pi$
$150$		0			0
$151$	0.184744	−	1.04774i	0.0150343	−	0.0852635i	−0.976367	−	0.216117i	$-0.930661\pi$
$151$	0.184744	−	1.04774i	0.0150343	−	0.0852635i	0.991402	+	0.130854i	$0.0417718\pi$
$152$		0			0
$153$	0.957312	+	3.64025i	0.0773941	+	0.294297i
$154$		0			0
$155$	−17.6602	−	3.11397i	−1.41850	−	0.250120i
$156$		0			0
$157$	−4.42188	−	5.26979i	−0.352904	−	0.420575i	0.560164	−	0.828382i	$-0.310738\pi$
$157$	−4.42188	−	5.26979i	−0.352904	−	0.420575i	−0.913068	+	0.407807i	$0.866294\pi$
$158$		0			0
$159$	−2.21880	−	5.39201i	−0.175962	−	0.427614i
$160$		0			0
$161$	17.2102	+	14.7120i	1.35636	+	1.15947i
$162$		0			0
$163$	−11.1280	−	19.2742i	−0.871609	−	1.50967i	−0.860331	−	0.509735i	$-0.829743\pi$
$163$	−11.1280	−	19.2742i	−0.871609	−	1.50967i	−0.0112777	−	0.999936i	$-0.503590\pi$
$164$		0			0
$165$	4.47411	−	5.80284i	0.348309	−	0.451750i
$166$		0			0
$167$	0.764681	+	0.278321i	0.0591728	+	0.0215371i	0.371437	−	0.928458i	$-0.378865\pi$
$167$	0.764681	+	0.278321i	0.0591728	+	0.0215371i	−0.312264	+	0.949995i	$0.601087\pi$
$168$		0			0
$169$	−0.543105	+	3.08010i	−0.0417773	+	0.236931i
$170$		0			0
$171$	16.7384	−	4.40187i	1.28002	−	0.336619i
$172$		0			0
$173$	6.59740	+	5.53588i	0.501591	+	0.420885i	0.858159	−	0.513384i	$-0.171609\pi$
$173$	6.59740	+	5.53588i	0.501591	+	0.420885i	−0.356567	+	0.934270i	$0.616053\pi$
$174$		0			0
$175$	−0.946560	+	0.534989i	−0.0715532	+	0.0404414i
$176$		0			0
$177$	−16.9804	+	0.701891i	−1.27632	+	0.0527574i
$178$		0			0
$179$			21.6297i			1.61668i	0.588716	+	0.808340i	$0.299634\pi$
$179$			21.6297i			1.61668i	−0.588716	+	0.808340i	$0.700366\pi$
$180$		0			0
$181$	6.59068	+	3.80513i	0.489882	+	0.282833i	0.724525	−	0.689248i	$-0.242059\pi$
$181$	6.59068	+	3.80513i	0.489882	+	0.282833i	−0.234644	+	0.972081i	$0.575392\pi$
$182$		0			0
$183$	−5.74812	+	18.0842i	−0.424913	+	1.33682i
$184$		0			0
$185$	−8.96074	−	3.26144i	−0.658807	−	0.239786i
$186$		0			0
$187$	2.24716	+	0.396235i	0.164329	+	0.0289756i
$188$		0			0
$189$	−3.19165	+	13.3721i	−0.232158	+	0.972678i
$190$		0			0
$191$	−11.3970	−	2.00960i	−0.824660	−	0.145410i	−0.254635	−	0.967037i	$-0.581955\pi$
$191$	−11.3970	−	2.00960i	−0.824660	−	0.145410i	−0.570025	+	0.821628i	$0.693066\pi$
$192$		0			0
$193$	−10.6308	−	3.86929i	−0.765220	−	0.278517i	−0.0702244	−	0.997531i	$-0.522372\pi$
$193$	−10.6308	−	3.86929i	−0.765220	−	0.278517i	−0.694996	+	0.719014i	$0.744594\pi$
$194$		0			0
$195$	−15.8047	+	3.46535i	−1.13180	+	0.248159i
$196$		0			0
$197$	−3.98585	−	2.30123i	−0.283980	−	0.163956i	0.351244	−	0.936284i	$-0.385759\pi$
$197$	−3.98585	−	2.30123i	−0.283980	−	0.163956i	−0.635224	+	0.772328i	$0.719092\pi$
$198$		0			0
$199$		−	23.8528i		−	1.69088i	−0.534070	−	0.845440i	$-0.679338\pi$
$199$		−	23.8528i		−	1.69088i	0.534070	−	0.845440i	$-0.320662\pi$
$200$		0			0
$201$	−7.59721	+	14.5118i	−0.535866	+	1.02358i
$202$		0			0
$203$	−8.59644	+	14.5792i	−0.603351	+	1.02326i
$204$		0			0
$205$	4.62374	+	3.87978i	0.322936	+	0.270976i
$206$		0			0
$207$	−14.8229	+	20.9615i	−1.03026	+	1.45692i
$208$		0			0
$209$	1.82195	−	10.3328i	0.126027	−	0.714735i
$210$		0			0
$211$	7.50376	+	2.73115i	0.516580	+	0.188020i	0.587136	−	0.809488i	$-0.300255\pi$
$211$	7.50376	+	2.73115i	0.516580	+	0.188020i	−0.0705562	+	0.997508i	$0.522477\pi$
$212$		0			0
$213$	9.17886	+	1.23010i	0.628925	+	0.0842852i
$214$		0			0
$215$	5.90927	+	10.2352i	0.403009	+	0.698032i
$216$		0			0
$217$	3.72578	−	20.0533i	0.252922	−	1.36131i
$218$		0			0
$219$	−14.5764	−	1.95345i	−0.984980	−	0.132002i
$220$		0			0
$221$	−3.23880	−	3.85985i	−0.217865	−	0.259642i
$222$		0			0
$223$	−6.24957	−	1.10197i	−0.418502	−	0.0737932i	−0.0395680	−	0.999217i	$-0.512598\pi$
$223$	−6.24957	−	1.10197i	−0.418502	−	0.0737932i	−0.378934	+	0.925424i	$0.623709\pi$
$224$		0			0
$225$	−0.702447	−	1.01318i	−0.0468298	−	0.0675451i
$226$		0			0
$227$	0.624196	−	3.53999i	0.0414293	−	0.234957i	−0.957061	−	0.289887i	$-0.906382\pi$
$227$	0.624196	−	3.53999i	0.0414293	−	0.234957i	0.998490	+	0.0549295i	$0.0174934\pi$
$228$		0			0
$229$	−8.36647	+	22.9867i	−0.552872	+	1.51900i	0.276900	+	0.960899i	$0.410693\pi$
$229$	−8.36647	+	22.9867i	−0.552872	+	1.51900i	−0.829771	+	0.558104i	$0.811529\pi$
$230$		0			0
$231$	6.55321	+	5.14912i	0.431170	+	0.338788i
$232$		0			0
$233$	20.9694	+	12.1067i	1.37375	+	0.793136i	0.991398	−	0.130880i	$-0.0417804\pi$
$233$	20.9694	+	12.1067i	1.37375	+	0.793136i	0.382353	+	0.924016i	$0.375114\pi$
$234$		0			0
$235$	−6.98885	−	12.1050i	−0.455902	−	0.789646i
$236$		0			0
$237$	5.22857	−	4.76882i	0.339632	−	0.309768i
$238$		0			0
$239$	2.42563	−	0.427703i	0.156901	−	0.0276658i	−0.0946460	−	0.995511i	$-0.530172\pi$
$239$	2.42563	−	0.427703i	0.156901	−	0.0276658i	0.251547	+	0.967845i	$0.419061\pi$
$240$		0			0
$241$	2.20492	+	6.05798i	0.142032	+	0.390229i	0.990229	−	0.139452i	$-0.0445340\pi$
$241$	2.20492	+	6.05798i	0.142032	+	0.390229i	−0.848197	+	0.529681i	$0.822312\pi$
$242$		0			0
$243$	−15.4304	−	2.21394i	−0.989863	−	0.142024i
$244$		0			0
$245$	−7.88165	−	14.2484i	−0.503540	−	0.910296i
$246$		0			0
$247$	−17.7482	+	14.8925i	−1.12929	+	0.947587i
$248$		0			0
$249$	−3.74911	−	17.0989i	−0.237590	−	1.08360i
$250$		0			0
$251$	5.67332	−	9.82648i	0.358097	−	0.620242i	−0.629546	−	0.776963i	$-0.716759\pi$
$251$	5.67332	−	9.82648i	0.358097	−	0.620242i	0.987643	+	0.156721i	$0.0500924\pi$
$252$		0			0
$253$	7.78174	+	13.4784i	0.489234	+	0.847378i
$254$		0			0
$255$	2.34458	−	4.47849i	0.146824	−	0.280454i
$256$		0			0
$257$	19.1682	+	6.97665i	1.19568	+	0.435191i	0.861714	−	0.507395i	$-0.169391\pi$
$257$	19.1682	+	6.97665i	1.19568	+	0.435191i	0.333964	+	0.942586i	$0.391614\pi$
$258$		0			0
$259$	3.80282	−	10.1575i	0.236296	−	0.631156i
$260$		0			0
$261$	−17.3551	−	8.19113i	−1.07426	−	0.507018i
$262$		0			0
$263$	−18.9725	+	22.6105i	−1.16989	+	1.39422i	−0.267362	+	0.963596i	$0.586152\pi$
$263$	−18.9725	+	22.6105i	−1.16989	+	1.39422i	−0.902530	+	0.430627i	$0.858293\pi$
$264$		0			0
$265$	−2.67823	+	7.35837i	−0.164522	+	0.452021i
$266$		0			0
$267$	8.96458	+	6.91188i	0.548623	+	0.423000i
$268$		0			0
$269$	14.8916	−	25.7929i	0.907954	−	1.57262i	0.0910522	−	0.995846i	$-0.470977\pi$
$269$	14.8916	−	25.7929i	0.907954	−	1.57262i	0.816902	−	0.576777i	$-0.195690\pi$
$270$		0			0
$271$	−22.2490	+	12.8455i	−1.35153	+	0.780307i	−0.988464	−	0.151455i	$-0.951604\pi$
$271$	−22.2490	+	12.8455i	−1.35153	+	0.780307i	−0.363068	+	0.931763i	$0.618271\pi$
$272$		0			0
$273$	−3.77655	−	18.0116i	−0.228567	−	1.09011i
$274$		0			0
$275$	−0.736033	+	0.129783i	−0.0443845	+	0.00782618i
$276$		0			0
$277$	13.8688	+	11.6373i	0.833294	+	0.699216i	0.956045	−	0.293221i	$-0.0947272\pi$
$277$	13.8688	+	11.6373i	0.833294	+	0.699216i	−0.122751	+	0.992437i	$0.539172\pi$
$278$		0			0
$279$	23.0298	+	2.12263i	1.37876	+	0.127078i
$280$		0			0
$281$	3.92202	+	10.7757i	0.233968	+	0.642822i	1.00000		1.93050e-5i	$6.14496e-6\pi$
$281$	3.92202	+	10.7757i	0.233968	+	0.642822i	−0.766032	+	0.642802i	$0.777772\pi$
$282$		0			0
$283$	8.31293	−	1.46579i	0.494152	−	0.0871324i	0.0789820	−	0.996876i	$-0.474833\pi$
$283$	8.31293	−	1.46579i	0.494152	−	0.0871324i	0.415170	+	0.909744i	$0.363722\pi$
$284$		0			0
$285$	−20.5928	−	10.7808i	−1.21981	−	0.638597i
$286$		0			0
$287$	−4.46087	+	5.21836i	−0.263317	+	0.308030i
$288$		0			0
$289$	−15.4258			−0.907399
$290$		0			0
$291$	−5.07375	+	15.9626i	−0.297428	+	0.935743i
$292$		0			0
$293$	3.30387	+	18.7372i	0.193014	+	1.09464i	0.915218	+	0.402958i	$0.132018\pi$
$293$	3.30387	+	18.7372i	0.193014	+	1.09464i	−0.722204	+	0.691680i	$0.756871\pi$
$294$		0			0
$295$	17.4843	+	14.6711i	1.01797	+	0.854182i
$296$		0			0
$297$	−5.13288	+	7.93453i	−0.297840	+	0.460408i
$298$		0			0
$299$	5.96775	−	33.8448i	0.345124	−	1.95729i
$300$		0			0
$301$	−11.7026	+	6.61420i	−0.674524	+	0.381236i
$302$		0			0
$303$	0.532821	+	2.43008i	0.0306098	+	0.139604i
$304$		0			0
$305$	22.0702	−	12.7422i	1.26374	−	0.729619i
$306$		0			0
$307$	23.5264	−	13.5830i	1.34272	−	0.775223i	0.355518	−	0.934669i	$-0.384304\pi$
$307$	23.5264	−	13.5830i	1.34272	−	0.775223i	0.987207	+	0.159447i	$0.0509710\pi$
$308$		0			0
$309$	2.42029	+	1.26707i	0.137685	+	0.0720811i
$310$		0			0
$311$	−4.24642	−	24.0826i	−0.240792	−	1.36560i	−0.830065	−	0.557666i	$-0.811697\pi$
$311$	−4.24642	−	24.0826i	−0.240792	−	1.36560i	0.589273	−	0.807934i	$-0.299414\pi$
$312$		0			0
$313$	−8.71127	+	10.3817i	−0.492390	+	0.586807i	−0.953824	−	0.300367i	$-0.902891\pi$
$313$	−8.71127	+	10.3817i	−0.492390	+	0.586807i	0.461434	+	0.887175i	$0.347335\pi$
$314$		0			0
$315$	15.2690	−	10.3802i	0.860309	−	0.584859i
$316$		0			0
$317$	6.46678	+	17.7673i	0.363210	+	0.997912i	0.977887	+	0.209133i	$0.0670643\pi$
$317$	6.46678	+	17.7673i	0.363210	+	0.997912i	−0.614677	+	0.788779i	$0.710714\pi$
$318$		0			0
$319$	−8.91215	+	7.47818i	−0.498984	+	0.418698i
$320$		0			0
$321$	−27.4015	−	3.67220i	−1.52940	−	0.204962i
$322$		0			0
$323$		−	7.23846i		−	0.402759i
$324$		0			0
$325$	1.42926	+	0.825182i	0.0792809	+	0.0457728i
$326$		0			0
$327$	12.0997	−	4.97897i	0.669113	−	0.275338i
$328$		0			0
$329$	13.8405	−	7.82257i	0.763053	−	0.431272i
$330$		0			0
$331$	17.0985	−	6.22336i	0.939820	−	0.342067i	0.173725	−	0.984794i	$-0.444420\pi$
$331$	17.0985	−	6.22336i	0.939820	−	0.342067i	0.766095	+	0.642728i	$0.222197\pi$
$332$		0			0
$333$	11.8643	+	3.23813i	0.650158	+	0.177448i
$334$		0			0
$335$	20.6719	−	7.52394i	1.12942	−	0.411077i
$336$		0			0
$337$	4.58257	−	3.84523i	0.249629	−	0.209463i	−0.509384	−	0.860539i	$-0.670127\pi$
$337$	4.58257	−	3.84523i	0.249629	−	0.209463i	0.759012	+	0.651076i	$0.225682\pi$
$338$		0			0
$339$	−8.57036	+	5.43199i	−0.465478	+	0.295025i
$340$		0			0
$341$	7.01016	−	12.1420i	0.379622	−	0.657524i
$342$		0			0
$343$	16.2876	−	8.81565i	0.879445	−	0.476000i
$344$		0			0
$345$	33.6788	−	7.38443i	1.81321	−	0.397565i
$346$		0			0
$347$	9.25708	−	25.4336i	0.496946	−	1.36535i	−0.397265	−	0.917704i	$-0.630041\pi$
$347$	9.25708	−	25.4336i	0.496946	−	1.36535i	0.894211	−	0.447645i	$-0.147737\pi$
$348$		0			0
$349$	10.3811	−	12.3717i	0.555686	−	0.662241i	−0.412942	−	0.910757i	$-0.635499\pi$
$349$	10.3811	−	12.3717i	0.555686	−	0.662241i	0.968628	+	0.248517i	$0.0799431\pi$
$350$		0			0
$351$	19.9447	−	6.13619i	1.06457	−	0.327526i
$352$		0			0
$353$	−14.7706	+	5.37608i	−0.786162	+	0.286140i	−0.703740	−	0.710458i	$-0.748488\pi$
$353$	−14.7706	+	5.37608i	−0.786162	+	0.286140i	−0.0824224	+	0.996597i	$0.526266\pi$
$354$		0			0
$355$	−7.99462	−	9.52762i	−0.424310	−	0.505673i
$356$		0			0
$357$	5.06917	+	2.71330i	0.268289	+	0.143603i
$358$		0			0
$359$		−	2.52187i		−	0.133099i	−0.997783	−	0.0665496i	$-0.978801\pi$
$359$		−	2.52187i		−	0.133099i	0.997783	−	0.0665496i	$-0.0211991\pi$
$360$		0			0
$361$	−14.2836			−0.751767
$362$		0			0
$363$	−7.13275	−	11.2537i	−0.374372	−	0.590668i
$364$		0			0
$365$	12.6958	+	15.1302i	0.664527	+	0.791952i
$366$		0			0
$367$	34.5407	+	6.09046i	1.80301	+	0.317920i	0.971402	−	0.237442i	$-0.0763088\pi$
$367$	34.5407	+	6.09046i	1.80301	+	0.317920i	0.831609	+	0.555361i	$0.187420\pi$
$368$		0			0
$369$	−6.35579	−	4.49449i	−0.330869	−	0.233974i
$370$		0			0
$371$	−8.34111	−	3.12279i	−0.433049	−	0.162127i
$372$		0			0
$373$	5.32884	+	30.2213i	0.275917	+	1.56480i	0.736035	+	0.676944i	$0.236696\pi$
$373$	5.32884	+	30.2213i	0.275917	+	1.56480i	−0.460118	+	0.887858i	$0.652193\pi$
$374$		0			0
$375$	2.45588	−	18.3254i	0.126821	−	0.946322i
$376$		0			0
$377$	25.6899			1.32310
$378$		0			0
$379$	25.4637			1.30798			0.653991	−	0.756502i	$-0.273093\pi$
$379$	25.4637			1.30798			0.653991	+	0.756502i	$0.273093\pi$
$380$		0			0
$381$	−10.9823	+	4.51916i	−0.562638	+	0.231524i
$382$		0			0
$383$	−1.77070	−	10.0421i	−0.0904786	−	0.513130i	−0.996039	−	0.0889131i	$-0.971661\pi$
$383$	−1.77070	−	10.0421i	−0.0904786	−	0.513130i	0.905561	−	0.424216i	$-0.139450\pi$
$384$		0			0
$385$	−1.84249	−	11.0401i	−0.0939020	−	0.562655i
$386$		0			0
$387$	−8.68452	−	12.5262i	−0.441459	−	0.636740i
$388$		0			0
$389$	−19.5100	−	3.44014i	−0.989196	−	0.174422i	−0.344438	−	0.938809i	$-0.611931\pi$
$389$	−19.5100	−	3.44014i	−0.989196	−	0.174422i	−0.644758	+	0.764387i	$0.723042\pi$
$390$		0			0
$391$	6.90167	+	8.22509i	0.349033	+	0.415961i
$392$		0			0
$393$	−23.3937	+	0.966991i	−1.18006	+	0.0487782i
$394$		0			0
$395$	−9.50400			−0.478198
$396$		0			0
$397$		−	6.94762i		−	0.348691i	−0.984685	−	0.174346i	$-0.944219\pi$
$397$		−	6.94762i		−	0.348691i	0.984685	−	0.174346i	$-0.0557810\pi$
$398$		0			0
$399$	12.4762	−	23.3088i	0.624590	−	1.16690i
$400$		0			0
$401$	21.7144	+	25.8782i	1.08436	+	1.29229i	0.953665	+	0.300872i	$0.0972776\pi$
$401$	21.7144	+	25.8782i	1.08436	+	1.29229i	0.130699	+	0.991422i	$0.458278\pi$
$402$		0			0
$403$	−29.0923	+	10.5887i	−1.44919	+	0.527462i
$404$		0			0
$405$	13.3075	+	16.1616i	0.661254	+	0.803078i
$406$		0			0
$407$	4.79226	−	5.71119i	0.237543	−	0.283093i
$408$		0			0
$409$	5.58263	−	15.3382i	0.276043	−	0.758423i	−0.721758	−	0.692146i	$-0.756666\pi$
$409$	5.58263	−	15.3382i	0.276043	−	0.758423i	0.997801	−	0.0662772i	$-0.0211122\pi$
$410$		0			0
$411$	11.0168	−	34.6602i	0.543420	−	1.70966i
$412$		0			0
$413$	−16.8684	+	19.7328i	−0.830039	+	0.970987i
$414$		0			0
$415$	−11.7546	+	20.3596i	−0.577013	+	0.999416i
$416$		0			0
$417$	−31.4513	−	16.4654i	−1.54018	−	0.806315i
$418$		0			0
$419$	−18.4928	+	15.5173i	−0.903431	+	0.758069i	−0.970858	−	0.239656i	$-0.922965\pi$
$419$	−18.4928	+	15.5173i	−0.903431	+	0.758069i	0.0674271	+	0.997724i	$0.478521\pi$
$420$		0			0
$421$	0.657830	−	0.239431i	0.0320607	−	0.0116691i	−0.325940	−	0.945390i	$-0.605681\pi$
$421$	0.657830	−	0.239431i	0.0320607	−	0.0116691i	0.358001	+	0.933721i	$0.383459\pi$
$422$		0			0
$423$	10.2711	+	14.8146i	0.499399	+	0.720310i
$424$		0			0
$425$	−0.484520	+	0.176351i	−0.0235027	+	0.00855427i
$426$		0			0
$427$	14.2623	+	25.2344i	0.690201	+	1.22118i
$428$		0			0
$429$	1.68029	−	12.5381i	0.0811252	−	0.605346i
$430$		0			0
$431$	14.9907	+	8.65486i	0.722074	+	0.416890i	0.815516	−	0.578735i	$-0.196453\pi$
$431$	14.9907	+	8.65486i	0.722074	+	0.416890i	−0.0934413	+	0.995625i	$0.529787\pi$
$432$		0			0
$433$			27.8478i			1.33828i	0.743136	+	0.669141i	$0.233338\pi$
$433$			27.8478i			1.33828i	−0.743136	+	0.669141i	$0.766662\pi$
$434$		0			0
$435$	9.80781	+	23.8345i	0.470249	+	1.14278i
$436$		0			0
$437$	37.8202	−	31.7349i	1.80919	−	1.51809i
$438$		0			0
$439$	2.94890	+	8.10204i	0.140743	+	0.386689i	0.989959	−	0.141358i	$-0.0451467\pi$
$439$	2.94890	+	8.10204i	0.140743	+	0.386689i	−0.849215	+	0.528047i	$0.822924\pi$
$440$		0			0
$441$	11.6468	+	17.4744i	0.554607	+	0.832112i
$442$		0			0
$443$	13.2210	−	15.7562i	0.628148	−	0.748598i	−0.354300	−	0.935132i	$-0.615281\pi$
$443$	13.2210	−	15.7562i	0.628148	−	0.748598i	0.982449	+	0.186534i	$0.0597253\pi$
$444$		0			0
$445$	−2.63989	−	14.9715i	−0.125143	−	0.709719i
$446$		0			0
$447$	−10.1343	+	6.42322i	−0.479335	+	0.303808i
$448$		0			0
$449$	0.162556	−	0.0938518i	0.00767150	−	0.00442914i	−0.496159	−	0.868231i	$-0.665257\pi$
$449$	0.162556	−	0.0938518i	0.00767150	−	0.00442914i	0.503831	+	0.863802i	$0.331923\pi$
$450$		0			0
$451$	−4.08682	+	2.35952i	−0.192441	+	0.111106i
$452$		0			0
$453$	1.36149	−	1.24177i	0.0639682	−	0.0583435i
$454$		0			0
$455$	−12.5535	+	21.2902i	−0.588516	+	0.998098i
$456$		0			0
$457$	0.844709	−	4.79058i	0.0395138	−	0.224094i	−0.958656	−	0.284568i	$-0.908150\pi$
$457$	0.844709	−	4.79058i	0.0395138	−	0.224094i	0.998170	+	0.0604736i	$0.0192611\pi$
$458$		0			0
$459$	−2.53678	+	6.00570i	−0.118407	+	0.280322i
$460$		0			0
$461$	−23.6098	−	19.8110i	−1.09962	−	0.922690i	−0.102220	−	0.994762i	$-0.532595\pi$
$461$	−23.6098	−	19.8110i	−1.09962	−	0.922690i	−0.997399	+	0.0720715i	$0.977039\pi$
$462$		0			0
$463$	−1.71296	−	9.71467i	−0.0796080	−	0.451479i	−0.998390	−	0.0567150i	$-0.981937\pi$
$463$	−1.71296	−	9.71467i	−0.0796080	−	0.451479i	0.918782	−	0.394764i	$-0.129174\pi$
$464$		0			0
$465$	−20.9308	−	22.9486i	−0.970640	−	1.06422i
$466$		0			0
$467$	3.30666			0.153014			0.0765070	−	0.997069i	$-0.475623\pi$
$467$	3.30666			0.153014			0.0765070	+	0.997069i	$0.475623\pi$
$468$		0			0
$469$	8.34184	+	23.5896i	0.385190	+	1.08926i
$470$		0			0
$471$	−0.492099	−	11.9050i	−0.0226747	−	0.548553i
$472$		0			0
$473$	−9.09977	+	1.60453i	−0.418408	+	0.0737766i
$474$		0			0
$475$	0.810888	+	2.22790i	0.0372061	+	0.102223i
$476$		0			0
$477$	2.65908	−	9.74268i	0.121751	−	0.446087i
$478$		0			0
$479$	−11.0256	−	9.25158i	−0.503773	−	0.422716i	0.355159	−	0.934806i	$-0.384427\pi$
$479$	−11.0256	−	9.25158i	−0.503773	−	0.422716i	−0.858932	+	0.512090i	$0.828871\pi$
$480$		0			0
$481$	−16.2128	+	2.85875i	−0.739239	+	0.130348i
$482$		0			0
$483$	8.04757	+	38.3815i	0.366177	+	1.74642i
$484$		0			0
$485$	19.4809	−	11.2473i	0.884584	−	0.510715i
$486$		0			0
$487$	16.1563	−	27.9836i	0.732113	−	1.26806i	−0.223866	−	0.974620i	$-0.571868\pi$
$487$	16.1563	−	27.9836i	0.732113	−	1.26806i	0.955979	−	0.293436i	$-0.0947989\pi$
$488$		0			0
$489$	5.12028	−	38.2068i	0.231547	−	1.72777i
$490$		0			0
$491$	−7.74489	+	21.2789i	−0.349522	+	0.960303i	0.632999	+	0.774152i	$0.281824\pi$
$491$	−7.74489	+	21.2789i	−0.349522	+	0.960303i	−0.982521	+	0.186151i	$0.940399\pi$
$492$		0			0
$493$	−5.15912	+	6.14840i	−0.232355	+	0.276910i
$494$		0			0
$495$	12.2741	−	3.22783i	0.551679	−	0.145080i
$496$		0			0
$497$	10.9196	−	8.99335i	0.489810	−	0.403407i
$498$		0			0
$499$	−17.2967	−	6.29549i	−0.774307	−	0.281825i	−0.0755104	−	0.997145i	$-0.524059\pi$
$499$	−17.2967	−	6.29549i	−0.774307	−	0.281825i	−0.698797	+	0.715320i	$0.746281\pi$
$500$		0			0
$501$	0.754545	+	1.19049i	0.0337106	+	0.0531871i
$502$		0			0
$503$	12.3813	+	21.4450i	0.552053	+	0.956184i	0.998126	+	0.0611879i	$0.0194889\pi$
$503$	12.3813	+	21.4450i	0.552053	+	0.956184i	−0.446073	+	0.894997i	$0.647178\pi$
$504$		0			0
$505$	1.67056	−	2.89350i	0.0743391	−	0.128759i
$506$		0			0
$507$	−4.00246	+	3.65052i	−0.177755	+	0.162125i
$508$		0			0
$509$	1.25802	−	1.05560i	0.0557608	−	0.0467888i	−0.614481	−	0.788931i	$-0.710635\pi$
$509$	1.25802	−	1.05560i	0.0557608	−	0.0467888i	0.670242	+	0.742143i	$0.266190\pi$
$510$		0			0
$511$	−17.3407	+	14.2818i	−0.767107	+	0.631789i
$512$		0			0
$513$	27.6151	+	11.6645i	1.21924	+	0.515001i
$514$		0			0
$515$	−1.25485	−	3.44768i	−0.0552953	−	0.151923i
$516$		0			0
$517$	10.7622	−	1.89767i	0.473322	−	0.0834594i
$518$		0			0
$519$	3.19480	+	14.5708i	0.140236	+	0.639587i
$520$		0			0
$521$	−7.46457	−	12.9290i	−0.327029	−	0.566430i	0.654892	−	0.755722i	$-0.272714\pi$
$521$	−7.46457	−	12.9290i	−0.327029	−	0.566430i	−0.981921	+	0.189292i	$0.939381\pi$
$522$		0			0
$523$	32.3259	+	18.6633i	1.41351	+	0.816091i	0.995717	−	0.0924512i	$-0.0294702\pi$
$523$	32.3259	+	18.6633i	1.41351	+	0.816091i	0.417794	+	0.908542i	$0.362804\pi$
$524$		0			0
$525$	−1.86418	−	0.267243i	−0.0813593	−	0.0116634i
$526$		0			0
$527$	3.30818	−	9.08916i	0.144107	−	0.395930i
$528$		0			0
$529$	−8.72298	+	49.4705i	−0.379260	+	2.15089i
$530$		0			0
$531$	−24.0339	−	16.9955i	−1.04298	−	0.737543i
$532$		0			0
$533$	10.2622	+	1.80950i	0.444504	+	0.0783781i
$534$		0			0
$535$	23.8662	+	28.4426i	1.03182	+	1.22968i
$536$		0			0
$537$	−22.8754	+	29.6690i	−0.987147	+	1.28031i
$538$		0			0
$539$	12.5756	−	1.98046i	0.541671	−	0.0853045i
$540$		0			0
$541$	−1.30807	−	2.26565i	−0.0562385	−	0.0974080i	0.836536	−	0.547913i	$-0.184577\pi$
$541$	−1.30807	−	2.26565i	−0.0562385	−	0.0974080i	−0.892774	+	0.450505i	$0.851244\pi$
$542$		0			0
$543$	5.01601	+	12.1897i	0.215258	+	0.523109i
$544$		0			0
$545$	−16.5122	−	6.00993i	−0.707303	−	0.257437i
$546$		0			0
$547$	0.140528	−	0.796974i	0.00600855	−	0.0340762i	−0.981656	−	0.190660i	$-0.938937\pi$
$547$	0.140528	−	0.796974i	0.00600855	−	0.0340762i	0.987665	+	0.156584i	$0.0500482\pi$
$548$		0			0
$549$	−27.0103	+	18.7266i	−1.15277	+	0.799230i
$550$		0			0
$551$	28.2713	+	23.7224i	1.20440	+	1.01061i
$552$		0			0
$553$	0.0990807	−	10.8094i	0.00421334	−	0.459661i
$554$		0			0
$555$	−8.84196	−	13.9505i	−0.375320	−	0.592164i
$556$		0			0
$557$		−	12.8849i		−	0.545952i	−0.962021	−	0.272976i	$-0.911992\pi$
$557$		−	12.8849i		−	0.545952i	0.962021	−	0.272976i	$-0.0880080\pi$
$558$		0			0
$559$	17.6703	+	10.2019i	0.747372	+	0.431496i
$560$		0			0
$561$	2.66333	+	2.92009i	0.112446	+	0.123286i
$562$		0			0
$563$	−29.0171	−	10.5614i	−1.22292	−	0.445108i	−0.351756	−	0.936092i	$-0.614415\pi$
$563$	−29.0171	−	10.5614i	−1.22292	−	0.445108i	−0.871169	+	0.490984i	$0.836638\pi$
$564$		0			0
$565$	13.4201	+	2.36633i	0.564590	+	0.0995524i
$566$		0			0
$567$	−18.5202	+	14.9668i	−0.777773	+	0.628545i
$568$		0			0
$569$	2.93023	+	0.516678i	0.122842	+	0.0216603i	0.234731	−	0.972060i	$-0.424579\pi$
$569$	2.93023	+	0.516678i	0.122842	+	0.0216603i	−0.111889	+	0.993721i	$0.535690\pi$
$570$		0			0
$571$	3.81131	+	1.38720i	0.159498	+	0.0580526i	0.420535	−	0.907276i	$-0.361842\pi$
$571$	3.81131	+	1.38720i	0.159498	+	0.0580526i	−0.261037	+	0.965329i	$0.584064\pi$
$572$		0			0
$573$	−13.5077	−	14.8099i	−0.564292	−	0.618694i
$574$		0			0
$575$	−3.04565	−	1.75841i	−0.127013	−	0.0733307i
$576$		0			0
$577$			3.81347i			0.158757i	0.996845	+	0.0793785i	$0.0252936\pi$
$577$			3.81347i			0.158757i	−0.996845	+	0.0793785i	$0.974706\pi$
$578$		0			0
$579$	−10.4899	−	16.5504i	−0.435944	−	0.687813i
$580$		0			0
$581$	−23.0335	−	13.5814i	−0.955590	−	0.563451i
$582$		0			0
$583$	−4.68991	−	3.93530i	−0.194236	−	0.162983i
$584$		0			0
$585$	−25.3439	−	11.9616i	−1.04784	−	0.494551i
$586$		0			0
$587$	3.89708	−	22.1014i	0.160850	−	0.912223i	−0.792392	−	0.610013i	$-0.791164\pi$
$587$	3.89708	−	22.1014i	0.160850	−	0.912223i	0.953241	−	0.302211i	$-0.0977246\pi$
$588$		0			0
$589$	−41.7934	−	15.2115i	−1.72207	−	0.626781i
$590$		0			0
$591$	−3.03354	−	7.37196i	−0.124783	−	0.303242i
$592$		0			0
$593$	−11.6564	−	20.1895i	−0.478672	−	0.829085i	0.521028	−	0.853539i	$-0.325549\pi$
$593$	−11.6564	−	20.1895i	−0.478672	−	0.829085i	−0.999701	+	0.0244543i	$0.992215\pi$
$594$		0			0
$595$	−2.57439	−	7.28000i	−0.105540	−	0.298451i
$596$		0			0
$597$	25.2265	−	32.7183i	1.03245	−	1.33907i
$598$		0			0
$599$	25.7163	+	30.6474i	1.05074	+	1.25222i	0.966742	+	0.255755i	$0.0823240\pi$
$599$	25.7163	+	30.6474i	1.05074	+	1.25222i	0.0839964	+	0.996466i	$0.473232\pi$
$600$		0			0
$601$	−7.62355	−	1.34424i	−0.310971	−	0.0548326i	0.0159848	−	0.999872i	$-0.494912\pi$
$601$	−7.62355	−	1.34424i	−0.310971	−	0.0548326i	−0.326956	+	0.945040i	$0.606023\pi$
$602$		0			0
$603$	−25.7684	+	11.8707i	−1.04937	+	0.483412i
$604$		0			0
$605$	−3.10723	+	17.6220i	−0.126327	+	0.716435i
$606$		0			0
$607$	8.96428	−	24.6291i	0.363849	−	0.999666i	−0.613807	−	0.789456i	$-0.710363\pi$
$607$	8.96428	−	24.6291i	0.363849	−	0.999666i	0.977656	−	0.210211i	$-0.0674149\pi$
$608$		0			0
$609$	−27.2104	+	10.9064i	−1.10262	+	0.441951i
$610$		0			0
$611$	−20.8985	−	12.0657i	−0.845462	−	0.488128i
$612$		0			0
$613$	−3.43863	−	5.95588i	−0.138885	−	0.240556i	0.788190	−	0.615432i	$-0.211018\pi$
$613$	−3.43863	−	5.95588i	−0.138885	−	0.240556i	−0.927075	+	0.374876i	$0.877685\pi$
$614$		0			0
$615$	2.23905	+	10.2118i	0.0902874	+	0.411781i
$616$		0			0
$617$	17.2432	−	3.04044i	0.694185	−	0.122404i	0.184587	−	0.982816i	$-0.440905\pi$
$617$	17.2432	−	3.04044i	0.694185	−	0.122404i	0.509598	+	0.860413i	$0.329794\pi$
$618$		0			0
$619$	−1.26081	−	3.46404i	−0.0506762	−	0.139232i	0.911772	−	0.410696i	$-0.134714\pi$
$619$	−1.26081	−	3.46404i	−0.0506762	−	0.139232i	−0.962448	+	0.271464i	$0.912492\pi$
$620$		0			0
$621$	−42.5010	+	13.0758i	−1.70550	+	0.524715i
$622$		0			0
$623$	17.0554	−	2.84639i	0.683310	−	0.114038i
$624$		0			0
$625$	−20.5958	+	17.2819i	−0.823832	+	0.691277i
$626$		0			0
$627$	13.4270	−	12.2464i	0.536224	−	0.489073i
$628$		0			0
$629$	2.57171	−	4.45434i	0.102541	−	0.177606i
$630$		0			0
$631$	−22.6990	−	39.3158i	−0.903633	−	1.56514i	−0.822742	−	0.568415i	$-0.807557\pi$
$631$	−22.6990	−	39.3158i	−0.903633	−	1.56514i	−0.0808913	−	0.996723i	$-0.525777\pi$
$632$		0			0
$633$	7.40430	+	11.6822i	0.294294	+	0.464325i
$634$		0			0
$635$	14.9873	+	5.45492i	0.594751	+	0.216472i
$636$		0			0
$637$	−24.0835	−	14.4996i	−0.954222	−	0.574496i
$638$		0			0
$639$	11.2895	+	11.3948i	0.446605	+	0.450771i
$640$		0			0
$641$	−2.73662	+	3.26137i	−0.108090	+	0.128817i	−0.817377	−	0.576103i	$-0.804573\pi$
$641$	−2.73662	+	3.26137i	−0.108090	+	0.128817i	0.709287	+	0.704920i	$0.249017\pi$
$642$		0			0
$643$	5.17807	−	14.2266i	0.204203	−	0.561044i	−0.794743	−	0.606946i	$-0.792394\pi$
$643$	5.17807	−	14.2266i	0.204203	−	0.561044i	0.998946	+	0.0459029i	$0.0146165\pi$
$644$		0			0
$645$	−2.71902	+	20.2889i	−0.107061	+	0.798876i
$646$		0			0
$647$	9.64047	−	16.6978i	0.379006	−	0.656458i	−0.611912	−	0.790926i	$-0.709599\pi$
$647$	9.64047	−	16.6978i	0.379006	−	0.656458i	0.990918	+	0.134468i	$0.0429326\pi$
$648$		0			0
$649$	−15.4539	+	8.92233i	−0.606620	+	0.350232i
$650$		0			0
$651$	26.3188	−	23.5663i	1.03152	−	0.923637i
$652$		0			0
$653$	3.06019	−	0.539594i	0.119755	−	0.0211160i	−0.113450	−	0.993544i	$-0.536190\pi$
$653$	3.06019	−	0.539594i	0.119755	−	0.0211160i	0.233204	+	0.972428i	$0.425079\pi$
$654$		0			0
$655$	24.0880	+	20.2122i	0.941195	+	0.789756i
$656$		0			0
$657$	−17.9281	−	18.0954i	−0.699443	−	0.705968i
$658$		0			0
$659$	−3.25069	−	8.93121i	−0.126629	−	0.347911i	0.860136	−	0.510064i	$-0.170378\pi$
$659$	−3.25069	−	8.93121i	−0.126629	−	0.347911i	−0.986766	+	0.162153i	$0.948156\pi$
$660$		0			0
$661$	17.2839	−	3.04761i	0.672265	−	0.118538i	0.172912	−	0.984937i	$-0.444682\pi$
$661$	17.2839	−	3.04761i	0.672265	−	0.118538i	0.499353	+	0.866399i	$0.333571\pi$
$662$		0			0
$663$	−0.360437	−	8.71980i	−0.0139982	−	0.338649i
$664$		0			0
$665$	−33.4746	+	11.8374i	−1.29809	+	0.459035i
$666$		0			0
$667$	−54.7434			−2.11967
$668$		0			0
$669$	−7.40696	−	8.12104i	−0.286370	−	0.313978i
$670$		0			0
$671$	3.45988	+	19.6219i	0.133567	+	0.757497i
$672$		0			0
$673$	7.62458	+	6.39778i	0.293906	+	0.246616i	0.777802	−	0.628509i	$-0.216334\pi$
$673$	7.62458	+	6.39778i	0.293906	+	0.246616i	−0.483896	+	0.875125i	$0.660779\pi$
$674$		0			0
$675$	0.107998	−	2.13265i	0.00415684	−	0.0820859i
$676$		0			0
$677$	0.187175	−	1.06152i	0.00719371	−	0.0407975i	−0.981000	−	0.194010i	$-0.937851\pi$
$677$	0.187175	−	1.06152i	0.00719371	−	0.0407975i	0.988193	+	0.153212i	$0.0489618\pi$
$678$		0			0
$679$	12.5890	+	22.2739i	0.483123	+	0.854793i
$680$		0			0
$681$	4.60006	−	4.19558i	0.176275	−	0.160775i
$682$		0			0
$683$	19.7773	−	11.4184i	0.756758	−	0.436914i	−0.0713727	−	0.997450i	$-0.522738\pi$
$683$	19.7773	−	11.4184i	0.756758	−	0.436914i	0.828130	+	0.560535i	$0.189405\pi$
$684$		0			0
$685$	−42.2997	+	24.4217i	−1.61619	+	0.933107i
$686$		0			0
$687$	−35.7866	+	22.6820i	−1.36535	+	0.865372i
$688$		0			0
$689$	2.34755	+	13.3136i	0.0894344	+	0.507208i
$690$		0			0
$691$	2.69196	−	3.20816i	0.102407	−	0.122044i	−0.712407	−	0.701767i	$-0.752395\pi$
$691$	2.69196	−	3.20816i	0.102407	−	0.122044i	0.814814	+	0.579723i	$0.196839\pi$
$692$		0			0
$693$	3.54321	+	13.9936i	0.134595	+	0.531571i
$694$		0			0
$695$	16.3066	+	44.8021i	0.618546	+	1.69944i
$696$		0			0
$697$	−2.49395	+	2.09267i	−0.0944652	+	0.0792657i
$698$		0			0
$699$	15.9593	+	38.7836i	0.603636	+	1.46693i
$700$		0			0
$701$		−	19.8279i		−	0.748890i	−0.927249	−	0.374445i	$-0.877833\pi$
$701$		−	19.8279i		−	0.748890i	0.927249	−	0.374445i	$-0.122167\pi$
$702$		0			0
$703$	−20.4817	−	11.8251i	−0.772483	−	0.445993i
$704$		0			0
$705$	3.21576	−	23.9956i	0.121113	−	0.903726i
$706$		0			0
$707$	3.27351	+	1.93018i	0.123113	+	0.0725919i
$708$		0			0
$709$	−36.3221	+	13.2202i	−1.36411	+	0.496494i	−0.917322	−	0.398147i	$-0.869653\pi$
$709$	−36.3221	+	13.2202i	−1.36411	+	0.496494i	−0.446785	+	0.894641i	$0.647431\pi$
$710$		0			0
$711$	12.2154	−	1.01159i	0.458112	−	0.0379374i
$712$		0			0
$713$	61.9937	−	22.5639i	2.32168	−	0.845024i
$714$		0			0
$715$	−13.0145	+	10.9205i	−0.486715	+	0.408402i
$716$		0			0
$717$	3.77951	+	1.97865i	0.141148	+	0.0738942i
$718$		0			0
$719$	13.9956	−	24.2411i	0.521949	−	0.904041i	−0.477725	−	0.878509i	$-0.658539\pi$
$719$	13.9956	−	24.2411i	0.521949	−	0.904041i	0.999674	−	0.0255322i	$-0.00812804\pi$
$720$		0			0
$721$	3.93429	−	1.39126i	0.146521	−	0.0518133i
$722$		0			0
$723$	−3.38243	+	10.6415i	−0.125794	+	0.395762i
$724$		0			0
$725$	0.899131	−	2.47034i	0.0333929	−	0.0917462i
$726$		0			0
$727$	−0.372280	+	0.443665i	−0.0138071	+	0.0164546i	−0.772904	−	0.634523i	$-0.781196\pi$
$727$	−0.372280	+	0.443665i	−0.0138071	+	0.0164546i	0.759097	+	0.650978i	$0.225641\pi$
$728$		0			0
$729$	−18.8241	−	19.3559i	−0.697190	−	0.716886i
$730$		0			0
$731$	−5.99024	+	2.18027i	−0.221557	+	0.0806402i
$732$		0			0
$733$	19.4025	+	23.1230i	0.716646	+	0.854066i	0.994300	−	0.106615i	$-0.0340013\pi$
$733$	19.4025	+	23.1230i	0.716646	+	0.854066i	−0.277654	+	0.960681i	$0.589557\pi$
$734$		0			0
$735$	4.25790	−	27.8798i	0.157055	−	1.02836i
$736$		0			0
$737$			17.1992i			0.633541i
$738$		0			0
$739$	−14.3822			−0.529058			−0.264529	−	0.964378i	$-0.585217\pi$
$739$	−14.3822			−0.529058			−0.264529	+	0.964378i	$0.585217\pi$
$740$		0			0
$741$	−40.0950	+	1.65735i	−1.47293	+	0.0608841i
$742$		0			0
$743$	−18.5207	−	22.0721i	−0.679459	−	0.809747i	0.310579	−	0.950547i	$-0.399477\pi$
$743$	−18.5207	−	22.0721i	−0.679459	−	0.809747i	−0.990038	+	0.140800i	$0.955033\pi$
$744$		0			0
$745$	15.8690	+	2.79814i	0.581396	+	0.102516i
$746$		0			0
$747$	12.9411	−	27.4191i	0.473489	−	1.00321i
$748$		0			0
$749$	−32.5980	+	26.8477i	−1.19110	+	0.980992i
$750$		0			0
$751$	−4.38064	−	24.8439i	−0.159852	−	0.906566i	−0.954215	−	0.299122i	$-0.903306\pi$
$751$	−4.38064	−	24.8439i	−0.159852	−	0.906566i	0.794363	−	0.607444i	$-0.207805\pi$
$752$		0			0
$753$	18.1744	−	7.47870i	0.662311	−	0.272539i
$754$		0			0
$755$	−2.47478			−0.0900666
$756$		0			0
$757$	34.3865			1.24980			0.624899	−	0.780706i	$-0.285140\pi$
$757$	34.3865			1.24980			0.624899	+	0.780706i	$0.285140\pi$
$758$		0			0
$759$	−3.58059	+	26.7179i	−0.129967	+	0.969798i
$760$		0			0
$761$	−0.659485	−	3.74012i	−0.0239063	−	0.135579i	0.970519	−	0.241026i	$-0.0774839\pi$
$761$	−0.659485	−	3.74012i	−0.0239063	−	0.135579i	−0.994425	+	0.105447i	$0.966373\pi$
$762$		0			0
$763$	7.00753	−	18.7174i	0.253690	−	0.677617i
$764$		0			0
$765$	7.95243	−	3.66343i	0.287521	−	0.132452i
$766$		0			0
$767$	38.8055	+	6.84246i	1.40119	+	0.247067i
$768$		0			0
$769$	9.13219	+	10.8833i	0.329315	+	0.392463i	0.905142	−	0.425109i	$-0.139764\pi$
$769$	9.13219	+	10.8833i	0.329315	+	0.392463i	−0.575827	+	0.817572i	$0.695320\pi$
$770$		0			0
$771$	18.9141	+	29.8418i	0.681175	+	1.07473i
$772$		0			0
$773$	−45.9757			−1.65363			−0.826816	−	0.562472i	$-0.809850\pi$
$773$	−45.9757			−1.65363			−0.826816	+	0.562472i	$0.809850\pi$
$774$		0			0
$775$			3.16812i			0.113802i
$776$		0			0
$777$	15.9587	−	9.91096i	0.572516	−	0.355554i
$778$		0			0
$779$	9.62244	+	11.4676i	0.344760	+	0.410869i
$780$		0			0
$781$	9.13757	−	3.32580i	0.326968	−	0.119007i
$782$		0			0
$783$	−15.1428	−	29.5902i	−0.541158	−	1.05747i
$784$		0			0
$785$	−10.2859	+	12.2583i	−0.367121	+	0.437518i
$786$		0			0
$787$	−14.9123	+	40.9713i	−0.531567	+	1.46047i	0.325639	+	0.945494i	$0.394420\pi$
$787$	−14.9123	+	40.9713i	−0.531567	+	1.46047i	−0.857206	+	0.514973i	$0.827802\pi$
$788$		0			0
$789$	−49.9368	+	10.9492i	−1.77780	+	0.389801i
$790$		0			0
$791$	−2.83125	+	15.2387i	−0.100668	+	0.541826i
$792$		0			0
$793$	21.9986	−	38.1026i	0.781192	−	1.35306i
$794$		0			0
$795$	−11.4558	+	7.26083i	−0.406296	+	0.257515i
$796$		0			0
$797$	−6.63961	+	5.57130i	−0.235187	+	0.197345i	−0.752763	−	0.658292i	$-0.771279\pi$
$797$	−6.63961	+	5.57130i	−0.235187	+	0.197345i	0.517575	+	0.855638i	$0.326835\pi$
$798$		0			0
$799$	7.08461	−	2.57859i	0.250636	−	0.0912239i
$800$		0			0
$801$	4.98655	+	18.9617i	0.176191	+	0.669980i
$802$		0			0
$803$	−14.5108	+	5.28151i	−0.512076	+	0.186380i
$804$		0			0
$805$	26.7506	−	45.3680i	0.942836	−	1.59901i
$806$		0			0
$807$	47.7048	−	19.6304i	1.67929	−	0.691022i
$808$		0			0
$809$	−15.5273	−	8.96468i	−0.545910	−	0.315181i	0.201561	−	0.979476i	$-0.435399\pi$
$809$	−15.5273	−	8.96468i	−0.545910	−	0.315181i	−0.747471	+	0.664295i	$0.768732\pi$
$810$		0			0
$811$			22.3098i			0.783403i	0.920092	+	0.391702i	$0.128113\pi$
$811$			22.3098i			0.783403i	−0.920092	+	0.391702i	$0.871887\pi$
$812$		0			0
$813$	−44.1038	−	5.91055i	−1.54679	−	0.207292i
$814$		0			0
$815$	−39.6585	+	33.2775i	−1.38918	+	1.16566i
$816$		0			0
$817$	10.0252	+	27.5441i	0.350738	+	0.963645i
$818$		0			0
$819$	13.8687	−	28.7001i	0.484613	−	1.00286i
$820$		0			0
$821$	−2.61055	+	3.11113i	−0.0911089	+	0.108579i	−0.809673	−	0.586882i	$-0.800355\pi$
$821$	−2.61055	+	3.11113i	−0.0911089	+	0.108579i	0.718564	+	0.695461i	$0.244800\pi$
$822$		0			0
$823$	0.745963	+	4.23057i	0.0260026	+	0.147468i	0.995045	−	0.0994266i	$-0.0317009\pi$
$823$	0.745963	+	4.23057i	0.0260026	+	0.147468i	−0.969042	+	0.246895i	$0.920590\pi$
$824$		0			0
$825$	−1.14686	−	0.600404i	−0.0399284	−	0.0209034i
$826$		0			0
$827$	45.9946	−	26.5550i	1.59939	−	0.923407i	0.607783	−	0.794103i	$-0.292059\pi$
$827$	45.9946	−	26.5550i	1.59939	−	0.923407i	0.991605	−	0.129304i	$-0.0412742\pi$
$828$		0			0
$829$	−2.99691	+	1.73026i	−0.104087	+	0.0600946i	−0.551140	−	0.834413i	$-0.685807\pi$
$829$	−2.99691	+	1.73026i	−0.104087	+	0.0600946i	0.447053	+	0.894508i	$0.352474\pi$
$830$		0			0
$831$	6.71597	+	30.6301i	0.232975	+	1.06255i
$832$		0			0
$833$	8.30674	−	2.85208i	0.287812	−	0.0988187i
$834$		0			0
$835$	0.328701	−	1.86416i	0.0113752	−	0.0645119i
$836$		0			0
$837$	29.3446	+	27.2678i	1.01430	+	0.942511i
$838$		0			0
$839$	−41.5584	−	34.8716i	−1.43475	−	1.20390i	−0.942835	−	0.333261i	$-0.891851\pi$
$839$	−41.5584	−	34.8716i	−1.43475	−	1.20390i	−0.491919	−	0.870641i	$-0.663705\pi$
$840$		0			0
$841$	−2.07018	−	11.7406i	−0.0713855	−	0.404847i
$842$		0			0
$843$	−6.01651	+	18.9286i	−0.207220	+	0.651936i
$844$		0			0
$845$	7.27530			0.250278
$846$		0			0
$847$	−20.0099	−	3.71772i	−0.687550	−	0.127742i
$848$		0			0
$849$	12.9529	+	6.78110i	0.444541	+	0.232727i
$850$		0			0
$851$	34.5484	−	6.09181i	1.18430	−	0.208825i
$852$		0			0
$853$	−5.73931	−	15.7686i	−0.196510	−	0.539907i	0.801827	−	0.597557i	$-0.203862\pi$
$853$	−5.73931	−	15.7686i	−0.196510	−	0.539907i	−0.998337	+	0.0576493i	$0.981639\pi$
$854$		0			0
$855$	−16.8450	−	36.5665i	−0.576087	−	1.25055i
$856$		0			0
$857$	0.0945700	+	0.0793536i	0.00323045	+	0.00271067i	0.644401	−	0.764687i	$-0.277107\pi$
$857$	0.0945700	+	0.0793536i	0.00323045	+	0.00271067i	−0.641171	+	0.767398i	$0.721551\pi$
$858$		0			0
$859$	−45.9497	+	8.10217i	−1.56778	+	0.276442i	−0.889004	−	0.457900i	$-0.848602\pi$
$859$	−45.9497	+	8.10217i	−1.56778	+	0.276442i	−0.678779	+	0.734342i	$0.737491\pi$
$860$		0			0
$861$	−11.6378	+	2.44013i	−0.396614	+	0.0831593i
$862$		0			0
$863$	−39.1384	+	22.5966i	−1.33229	+	0.769197i	−0.985650	−	0.168803i	$-0.946010\pi$
$863$	−39.1384	+	22.5966i	−1.33229	+	0.769197i	−0.346638	+	0.937999i	$0.612677\pi$
$864$		0			0
$865$	10.0167	−	17.3495i	0.340579	−	0.589900i
$866$		0			0
$867$	−21.1592	−	16.3142i	−0.718604	−	0.554059i
$868$		0			0
$869$	2.54140	−	6.98244i	0.0862110	−	0.236863i
$870$		0			0
$871$	24.4123	−	29.0935i	0.827180	−	0.985795i
$872$		0			0
$873$	−23.8415	+	16.5295i	−0.806911	+	0.559440i
$874$		0			0
$875$	−17.9551	−	21.8008i	−0.606992	−	0.737000i
$876$		0			0
$877$	4.00075	+	1.45615i	0.135096	+	0.0491708i	0.408683	−	0.912676i	$-0.365988\pi$
$877$	4.00075	+	1.45615i	0.135096	+	0.0491708i	−0.273587	+	0.961847i	$0.588210\pi$
$878$		0			0
$879$	−15.2845	+	29.1955i	−0.515532	+	0.984740i
$880$		0			0
$881$	12.9250	+	22.3868i	0.435455	+	0.754230i	0.997333	−	0.0729906i	$-0.0232543\pi$
$881$	12.9250	+	22.3868i	0.435455	+	0.754230i	−0.561878	+	0.827220i	$0.689921\pi$
$882$		0			0
$883$	19.4673	−	33.7184i	0.655128	−	1.13472i	−0.326733	−	0.945117i	$-0.605948\pi$
$883$	19.4673	−	33.7184i	0.655128	−	1.13472i	0.981862	−	0.189599i	$-0.0607187\pi$
$884$		0			0
$885$	8.46679	+	38.6152i	0.284608	+	1.29804i
$886$		0			0
$887$	24.8856	−	20.8815i	0.835577	−	0.701132i	−0.120987	−	0.992654i	$-0.538606\pi$
$887$	24.8856	−	20.8815i	0.835577	−	0.701132i	0.956564	+	0.291522i	$0.0941616\pi$
$888$		0			0
$889$	−6.36039	+	16.9889i	−0.213321	+	0.569789i
$890$		0			0
$891$	−15.4322	+	5.45512i	−0.516997	+	0.182753i
$892$		0			0
$893$	−11.8567	−	32.5761i	−0.396771	−	1.09012i
$894$		0			0
$895$	49.5495	−	8.73691i	1.65626	−	0.292043i
$896$		0			0
$897$	43.9798	−	40.1127i	1.46844	−	1.33932i
$898$		0			0
$899$	24.6577	+	42.7085i	0.822382	+	1.42441i
$900$		0			0
$901$	−3.65781	−	2.11184i	−0.121859	−	0.0703555i
$902$		0			0
$903$	−23.0473	−	3.30399i	−0.766965	−	0.109950i
$904$		0			0
$905$	6.05464	−	16.6350i	0.201263	−	0.552966i
$906$		0			0
$907$	2.15628	−	12.2289i	0.0715981	−	0.406053i	−0.927854	−	0.372944i	$-0.878348\pi$
$907$	2.15628	−	12.2289i	0.0715981	−	0.406053i	0.999452	−	0.0331084i	$-0.0105407\pi$
$908$		0			0
$909$	−1.83918	+	3.89679i	−0.0610017	+	0.129248i
$910$		0			0
$911$	−57.6566	−	10.1664i	−1.91025	−	0.336828i	−0.912812	−	0.408380i	$-0.866094\pi$
$911$	−57.6566	−	10.1664i	−1.91025	−	0.336828i	−0.997437	+	0.0715519i	$0.977205\pi$
$912$		0			0
$913$	−11.8147	−	14.0802i	−0.391009	−	0.465986i
$914$		0			0
$915$	43.7493	+	5.86305i	1.44631	+	0.193827i
$916$		0			0
$917$	−23.2395	+	27.1857i	−0.767434	+	0.897751i
$918$		0			0
$919$	−0.493059	−	0.854003i	−0.0162645	−	0.0281710i	0.857779	−	0.514019i	$-0.171844\pi$
$919$	−0.493059	−	0.854003i	−0.0162645	−	0.0281710i	−0.874043	+	0.485848i	$0.838511\pi$
$920$		0			0
$921$	46.6360	+	6.24990i	1.53671	+	0.205941i
$922$		0			0
$923$	−20.1774	−	7.34396i	−0.664146	−	0.241729i
$924$		0			0
$925$	−0.292540	+	1.65908i	−0.00961867	+	0.0545502i
$926$		0			0
$927$	1.97981	+	4.29769i	0.0650254	+	0.141155i
$928$		0			0
$929$	36.9620	+	31.0148i	1.21268	+	1.01756i	0.999175	+	0.0406216i	$0.0129338\pi$
$929$	36.9620	+	31.0148i	1.21268	+	1.01756i	0.213509	+	0.976941i	$0.431511\pi$
$930$		0			0
$931$	−13.1143	−	38.1957i	−0.429804	−	1.25181i
$932$		0			0
$933$	19.6449	−	37.5246i	0.643145	−	1.22850i
$934$		0			0
$935$		−	5.30787i		−	0.173586i
$936$		0			0
$937$	26.0904	+	15.0633i	0.852336	+	0.492096i	0.861438	−	0.507862i	$-0.169564\pi$
$937$	26.0904	+	15.0633i	0.852336	+	0.492096i	−0.00910235	+	0.999959i	$0.502897\pi$
$938$		0			0
$939$	−22.9286	+	5.02735i	−0.748248	+	0.164061i
$940$		0			0
$941$	−15.6099	−	5.68154i	−0.508868	−	0.185213i	0.0748102	−	0.997198i	$-0.476165\pi$
$941$	−15.6099	−	5.68154i	−0.508868	−	0.185213i	−0.583678	+	0.811985i	$0.698387\pi$
$942$		0			0
$943$	−21.8680	−	3.85592i	−0.712121	−	0.125566i
$944$		0			0
$945$	31.9221	+	1.91003i	1.03843	+	0.0621334i
$946$		0			0
$947$	27.5701	+	4.86135i	0.895908	+	0.157973i	0.602598	−	0.798045i	$-0.294132\pi$
$947$	27.5701	+	4.86135i	0.895908	+	0.157973i	0.293310	+	0.956018i	$0.405243\pi$
$948$		0			0
$949$	32.0424	+	11.6625i	1.04014	+	0.378580i
$950$		0			0
$951$	−9.92026	+	31.2102i	−0.321687	+	1.01206i
$952$		0			0
$953$	−18.0641	−	10.4293i	−0.585154	−	0.337839i	0.178025	−	0.984026i	$-0.443029\pi$
$953$	−18.0641	−	10.4293i	−0.585154	−	0.337839i	−0.763179	+	0.646187i	$0.776362\pi$
$954$		0			0
$955$			26.9201i			0.871114i
$956$		0			0
$957$	−20.1335	+	0.832227i	−0.650822	+	0.0269021i
$958$		0			0
$959$	−27.3351	−	48.3641i	−0.882695	−	1.56176i
$960$		0			0
$961$	−21.7794	−	18.2751i	−0.702562	−	0.589519i
$962$		0			0
$963$	−33.7023	−	34.0166i	−1.08604	−	1.09617i
$964$		0			0
$965$	−4.56969	+	25.9160i	−0.147103	+	0.834265i
$966$		0			0
$967$	−6.46715	−	2.35385i	−0.207970	−	0.0756948i	0.235935	−	0.971769i	$-0.424185\pi$
$967$	−6.46715	−	2.35385i	−0.207970	−	0.0756948i	−0.443904	+	0.896074i	$0.646407\pi$
$968$		0			0
$969$	7.65535	−	9.92883i	0.245925	−	0.318960i
$970$		0			0
$971$	12.3951	+	21.4689i	0.397777	+	0.688971i	0.993451	−	0.114256i	$-0.0364483\pi$
$971$	12.3951	+	21.4689i	0.397777	+	0.688971i	−0.595674	+	0.803226i	$0.703115\pi$
$972$		0			0
$973$	−51.1256	+	18.0793i	−1.63901	+	0.579594i
$974$		0			0
$975$	1.08777	+	2.64345i	0.0348366	+	0.0846583i
$976$		0			0
$977$	−4.09139	−	4.87593i	−0.130895	−	0.155995i	0.696616	−	0.717444i	$-0.254688\pi$
$977$	−4.09139	−	4.87593i	−0.130895	−	0.155995i	−0.827511	+	0.561450i	$0.810244\pi$
$978$		0			0
$979$	11.7053	+	2.06395i	0.374102	+	0.0659642i
$980$		0			0
$981$	21.8625	+	5.96697i	0.698017	+	0.190511i
$982$		0			0
$983$	0.123225	−	0.698844i	0.00393027	−	0.0222897i	−0.982780	−	0.184782i	$-0.940842\pi$
$983$	0.123225	−	0.698844i	0.00393027	−	0.0222897i	0.986710	+	0.162492i	$0.0519532\pi$
$984$		0			0
$985$	−3.66167	+	10.0604i	−0.116671	+	0.320550i
$986$		0			0
$987$	27.2578	+	3.90760i	0.867626	+	0.124380i
$988$		0			0
$989$	−37.6542	−	21.7396i	−1.19733	−	0.691281i
$990$		0			0
$991$	21.3130	+	36.9152i	0.677031	+	1.17265i	0.975871	+	0.218348i	$0.0700668\pi$
$991$	21.3130	+	36.9152i	0.677031	+	1.17265i	−0.298840	+	0.954303i	$0.596600\pi$
$992$		0			0
$993$	30.0354	+	9.54684i	0.953146	+	0.302960i
$994$		0			0
$995$	−54.6422	+	9.63489i	−1.73227	+	0.305446i
$996$		0			0
$997$	−1.19249	−	3.27633i	−0.0377664	−	0.103762i	0.919376	−	0.393380i	$-0.128694\pi$
$997$	−1.19249	−	3.27633i	−0.0377664	−	0.103762i	−0.957143	+	0.289617i	$0.906472\pi$
$998$		0			0
$999$	12.8493	+	16.9892i	0.406535	+	0.537515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.20	yes	144
7.5	odd	6		756.2.ca.a.173.22	✓	144
27.5	odd	18		756.2.ca.a.437.22	yes	144
189.5	even	18	inner	756.2.ck.a.5.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.22	✓	144	7.5	odd	6
756.2.ca.a.437.22	yes	144	27.5	odd	18
756.2.ck.a.5.20	yes	144	189.5	even	18	inner
756.2.ck.a.605.20	yes	144	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37168 + 1.05759i) q^{3} +(-0.403931 - 2.29081i) q^{5} +(2.60966 - 0.435529i) q^{7} +(0.762996 + 2.90135i) q^{9} +O(q^{10})\)	\(q+(1.37168 + 1.05759i) q^{3} +(-0.403931 - 2.29081i) q^{5} +(2.60966 - 0.435529i) q^{7} +(0.762996 + 2.90135i) q^{9} +(1.79103 + 0.315807i) q^{11} +(-2.58138 - 3.07637i) q^{13} +(1.86868 - 3.56944i) q^{15} +1.25468 q^{17} -5.76919i q^{19} +(4.04022 + 2.16255i) q^{21} +(5.50076 + 6.55555i) q^{23} +(-0.386172 + 0.140555i) q^{25} +(-2.02186 + 4.78666i) q^{27} +(-4.11192 + 4.90039i) q^{29} +(2.63669 - 7.24423i) q^{31} +(2.12272 + 2.32737i) q^{33} +(-2.05183 - 5.80230i) q^{35} +(2.04970 - 3.55019i) q^{37} +(-0.287275 - 6.94984i) q^{39} +(-1.98773 + 1.66790i) q^{41} +(-4.77434 + 1.73772i) q^{43} +(6.33824 - 2.91982i) q^{45} +(5.64657 - 2.05518i) q^{47} +(6.62063 - 2.27316i) q^{49} +(1.72101 + 1.32694i) q^{51} +(-2.91534 - 1.68317i) q^{53} -4.23047i q^{55} +(6.10145 - 7.91347i) q^{57} +(-7.51642 + 6.30702i) q^{59} +(3.74706 + 10.2950i) q^{61} +(3.25478 + 7.23923i) q^{63} +(-6.00468 + 7.15609i) q^{65} +(1.64220 + 9.31340i) q^{67} +(0.612165 + 14.8097i) q^{69} +(4.63046 - 2.67340i) q^{71} +(-7.35335 + 4.24546i) q^{73} +(-0.678353 - 0.215616i) q^{75} +(4.81152 + 0.0441033i) q^{77} +(0.709479 - 4.02366i) q^{79} +(-7.83567 + 4.42744i) q^{81} +(-7.74206 - 6.49636i) q^{83} +(-0.506802 - 2.87422i) q^{85} +(-10.8228 + 2.37302i) q^{87} +6.53549 q^{89} +(-8.07638 - 6.90402i) q^{91} +(11.2781 - 7.14821i) q^{93} +(-13.2161 + 2.33036i) q^{95} +(3.30745 + 9.08716i) q^{97} +(0.450282 + 5.43737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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