LMFDB - Embedded newform 768.2.n.b.481.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(97,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("768.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.n (of order $8$, degree $4$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			481.3
Character	$\chi$	$=$	768.481
Dual form			768.2.n.b.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382683 - 0.923880i) q^{3} +(2.51374 + 1.04122i) q^{5} +(-2.01027 - 2.01027i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.382683 - 0.923880i) q^{3} +(2.51374 + 1.04122i) q^{5} +(-2.01027 - 2.01027i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(-1.32741 + 3.20465i) q^{11} +(5.55375 - 2.30044i) q^{13} -2.72085i q^{15} -4.16447i q^{17} +(4.49866 - 1.86340i) q^{19} +(-1.08795 + 2.62654i) q^{21} +(1.94282 - 1.94282i) q^{23} +(1.69919 + 1.69919i) q^{25} +(0.923880 + 0.382683i) q^{27} +(1.96103 + 4.73434i) q^{29} +2.87015 q^{31} +3.46869 q^{33} +(-2.96015 - 7.14642i) q^{35} +(-6.31049 - 2.61389i) q^{37} +(-4.25066 - 4.25066i) q^{39} +(0.756366 - 0.756366i) q^{41} +(1.53775 - 3.71245i) q^{43} +(-2.51374 + 1.04122i) q^{45} +1.08220i q^{47} +1.08236i q^{49} +(-3.84747 + 1.59367i) q^{51} +(2.90450 - 7.01208i) q^{53} +(-6.67351 + 6.67351i) q^{55} +(-3.44312 - 3.44312i) q^{57} +(10.3425 + 4.28402i) q^{59} +(2.97711 + 7.18739i) q^{61} +2.84295 q^{63} +16.3559 q^{65} +(-3.88805 - 9.38659i) q^{67} +(-2.53841 - 1.05145i) q^{69} +(1.88924 + 1.88924i) q^{71} +(-7.00727 + 7.00727i) q^{73} +(0.919594 - 2.22010i) q^{75} +(9.11066 - 3.77376i) q^{77} -11.0255i q^{79} -1.00000i q^{81} +(-2.30515 + 0.954824i) q^{83} +(4.33615 - 10.4684i) q^{85} +(3.62351 - 3.62351i) q^{87} +(7.65800 + 7.65800i) q^{89} +(-15.7890 - 6.54003i) q^{91} +(-1.09836 - 2.65168i) q^{93} +13.2487 q^{95} -11.3029 q^{97} +(-1.32741 - 3.20465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

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
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$		0			0
$5$	2.51374	+	1.04122i	1.12418	+	0.465649i	0.865798	−	0.500394i	$-0.166812\pi$
$5$	2.51374	+	1.04122i	1.12418	+	0.465649i	0.258379	+	0.966044i	$0.416812\pi$
$6$		0			0
$7$	−2.01027	−	2.01027i	−0.759810	−	0.759810i	0.216477	−	0.976288i	$-0.430543\pi$
$7$	−2.01027	−	2.01027i	−0.759810	−	0.759810i	−0.976288	+	0.216477i	$0.930543\pi$
$8$		0			0
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$		0			0
$11$	−1.32741	+	3.20465i	−0.400229	+	0.966238i	0.587381	+	0.809310i	$0.300159\pi$
$11$	−1.32741	+	3.20465i	−0.400229	+	0.966238i	−0.987610	+	0.156928i	$0.949841\pi$
$12$		0			0
$13$	5.55375	−	2.30044i	1.54033	−	0.638027i	0.558798	−	0.829304i	$-0.311263\pi$
$13$	5.55375	−	2.30044i	1.54033	−	0.638027i	0.981536	+	0.191277i	$0.0612628\pi$
$14$		0			0
$15$		−	2.72085i		−	0.702520i
$16$		0			0
$17$		−	4.16447i		−	1.01003i	−0.863110	−	0.505016i	$-0.831486\pi$
$17$		−	4.16447i		−	1.01003i	0.863110	−	0.505016i	$-0.168514\pi$
$18$		0			0
$19$	4.49866	−	1.86340i	1.03206	−	0.427494i	0.198606	−	0.980079i	$-0.436359\pi$
$19$	4.49866	−	1.86340i	1.03206	−	0.427494i	0.833456	+	0.552585i	$0.186359\pi$
$20$		0			0
$21$	−1.08795	+	2.62654i	−0.237410	+	0.573159i
$22$		0			0
$23$	1.94282	−	1.94282i	0.405106	−	0.405106i	−0.474922	−	0.880028i	$-0.657524\pi$
$23$	1.94282	−	1.94282i	0.405106	−	0.405106i	0.880028	+	0.474922i	$0.157524\pi$
$24$		0			0
$25$	1.69919	+	1.69919i	0.339838	+	0.339838i
$26$		0			0
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$		0			0
$29$	1.96103	+	4.73434i	0.364154	+	0.879145i	0.994683	+	0.102980i	$0.0328377\pi$
$29$	1.96103	+	4.73434i	0.364154	+	0.879145i	−0.630530	+	0.776165i	$0.717162\pi$
$30$		0			0
$31$	2.87015			0.515495			0.257747	−	0.966212i	$-0.417020\pi$
$31$	2.87015			0.515495			0.257747	+	0.966212i	$0.417020\pi$
$32$		0			0
$33$	3.46869			0.603821
$34$		0			0
$35$	−2.96015	−	7.14642i	−0.500356	−	1.20797i
$36$		0			0
$37$	−6.31049	−	2.61389i	−1.03744	−	0.429721i	−0.202046	−	0.979376i	$-0.564759\pi$
$37$	−6.31049	−	2.61389i	−1.03744	−	0.429721i	−0.835392	+	0.549655i	$0.814759\pi$
$38$		0			0
$39$	−4.25066	−	4.25066i	−0.680650	−	0.680650i
$40$		0			0
$41$	0.756366	−	0.756366i	0.118125	−	0.118125i	−0.645574	−	0.763698i	$-0.723382\pi$
$41$	0.756366	−	0.756366i	0.118125	−	0.118125i	0.763698	+	0.645574i	$0.223382\pi$
$42$		0			0
$43$	1.53775	−	3.71245i	0.234504	−	0.566143i	−0.762193	−	0.647350i	$-0.775877\pi$
$43$	1.53775	−	3.71245i	0.234504	−	0.566143i	0.996697	+	0.0812067i	$0.0258774\pi$
$44$		0			0
$45$	−2.51374	+	1.04122i	−0.374726	+	0.155216i
$46$		0			0
$47$			1.08220i			0.157855i	0.996880	+	0.0789273i	$0.0251495\pi$
$47$			1.08220i			0.157855i	−0.996880	+	0.0789273i	$0.974851\pi$
$48$		0			0
$49$			1.08236i			0.154623i
$50$		0			0
$51$	−3.84747	+	1.59367i	−0.538754	+	0.223159i
$52$		0			0
$53$	2.90450	−	7.01208i	0.398963	−	0.963183i	−0.588949	−	0.808170i	$-0.700458\pi$
$53$	2.90450	−	7.01208i	0.398963	−	0.963183i	0.987912	−	0.155013i	$-0.0495418\pi$
$54$		0			0
$55$	−6.67351	+	6.67351i	−0.899856	+	0.899856i
$56$		0			0
$57$	−3.44312	−	3.44312i	−0.456053	−	0.456053i
$58$		0			0
$59$	10.3425	+	4.28402i	1.34648	+	0.557732i	0.935311	−	0.353826i	$-0.115120\pi$
$59$	10.3425	+	4.28402i	1.34648	+	0.557732i	0.411172	+	0.911558i	$0.365120\pi$
$60$		0			0
$61$	2.97711	+	7.18739i	0.381180	+	0.920251i	0.991738	+	0.128279i	$0.0409454\pi$
$61$	2.97711	+	7.18739i	0.381180	+	0.920251i	−0.610558	+	0.791972i	$0.709055\pi$
$62$		0			0
$63$	2.84295			0.358178
$64$		0			0
$65$	16.3559			2.02870
$66$		0			0
$67$	−3.88805	−	9.38659i	−0.475001	−	1.14676i	−0.961926	−	0.273311i	$-0.911881\pi$
$67$	−3.88805	−	9.38659i	−0.475001	−	1.14676i	0.486924	−	0.873444i	$-0.338119\pi$
$68$		0			0
$69$	−2.53841	−	1.05145i	−0.305589	−	0.126579i
$70$		0			0
$71$	1.88924	+	1.88924i	0.224211	+	0.224211i	0.810269	−	0.586058i	$-0.199321\pi$
$71$	1.88924	+	1.88924i	0.224211	+	0.224211i	−0.586058	+	0.810269i	$0.699321\pi$
$72$		0			0
$73$	−7.00727	+	7.00727i	−0.820139	+	0.820139i	−0.986128	−	0.165989i	$-0.946918\pi$
$73$	−7.00727	+	7.00727i	−0.820139	+	0.820139i	0.165989	+	0.986128i	$0.446918\pi$
$74$		0			0
$75$	0.919594	−	2.22010i	0.106186	−	0.256355i
$76$		0			0
$77$	9.11066	−	3.77376i	1.03826	−	0.430060i
$78$		0			0
$79$		−	11.0255i		−	1.24047i	−0.784417	−	0.620234i	$-0.787038\pi$
$79$		−	11.0255i		−	1.24047i	0.784417	−	0.620234i	$-0.212962\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−2.30515	+	0.954824i	−0.253023	+	0.104806i	−0.505590	−	0.862774i	$-0.668725\pi$
$83$	−2.30515	+	0.954824i	−0.253023	+	0.104806i	0.252567	+	0.967579i	$0.418725\pi$
$84$		0			0
$85$	4.33615	−	10.4684i	0.470321	−	1.13546i
$86$		0			0
$87$	3.62351	−	3.62351i	0.388481	−	0.388481i
$88$		0			0
$89$	7.65800	+	7.65800i	0.811747	+	0.811747i	0.984896	−	0.173149i	$-0.0553943\pi$
$89$	7.65800	+	7.65800i	0.811747	+	0.811747i	−0.173149	+	0.984896i	$0.555394\pi$
$90$		0			0
$91$	−15.7890	−	6.54003i	−1.65514	−	0.685582i
$92$		0			0
$93$	−1.09836	−	2.65168i	−0.113895	−	0.274966i
$94$		0			0
$95$	13.2487			1.35928
$96$		0			0
$97$	−11.3029			−1.14764			−0.573819	−	0.818982i	$-0.694539\pi$
$97$	−11.3029			−1.14764			−0.573819	+	0.818982i	$0.694539\pi$
$98$		0			0
$99$	−1.32741	−	3.20465i	−0.133410	−	0.322079i
$100$		0			0
$101$	−3.56392	−	1.47622i	−0.354623	−	0.146890i	0.198258	−	0.980150i	$-0.436472\pi$
$101$	−3.56392	−	1.47622i	−0.354623	−	0.146890i	−0.552881	+	0.833260i	$0.686472\pi$
$102$		0			0
$103$	1.94329	+	1.94329i	0.191478	+	0.191478i	0.796335	−	0.604856i	$-0.206769\pi$
$103$	1.94329	+	1.94329i	0.191478	+	0.191478i	−0.604856	+	0.796335i	$0.706769\pi$
$104$		0			0
$105$	−5.46964	+	5.46964i	−0.533782	+	0.533782i
$106$		0			0
$107$	−5.35190	+	12.9206i	−0.517388	+	1.24908i	0.422114	+	0.906543i	$0.361288\pi$
$107$	−5.35190	+	12.9206i	−0.517388	+	1.24908i	−0.939502	+	0.342542i	$0.888712\pi$
$108$		0			0
$109$	−12.1425	+	5.02958i	−1.16304	+	0.481747i	−0.878886	−	0.477032i	$-0.841713\pi$
$109$	−12.1425	+	5.02958i	−1.16304	+	0.481747i	−0.284154	+	0.958779i	$0.591713\pi$
$110$		0			0
$111$			6.83043i			0.648315i
$112$		0			0
$113$		−	13.8394i		−	1.30190i	−0.759121	−	0.650950i	$-0.774371\pi$
$113$		−	13.8394i		−	1.30190i	0.759121	−	0.650950i	$-0.225629\pi$
$114$		0			0
$115$	6.90664	−	2.86082i	0.644048	−	0.266773i
$116$		0			0
$117$	−2.30044	+	5.55375i	−0.212676	+	0.513445i
$118$		0			0
$119$	−8.37171	+	8.37171i	−0.767433	+	0.767433i
$120$		0			0
$121$	−0.729588	−	0.729588i	−0.0663262	−	0.0663262i
$122$		0			0
$123$	−0.988240	−	0.409342i	−0.0891066	−	0.0369092i
$124$		0			0
$125$	−2.70404	−	6.52814i	−0.241857	−	0.583894i
$126$		0			0
$127$	5.47542			0.485865			0.242932	−	0.970043i	$-0.421891\pi$
$127$	5.47542			0.485865			0.242932	+	0.970043i	$0.421891\pi$
$128$		0			0
$129$	−4.01832			−0.353794
$130$		0			0
$131$	8.03254	+	19.3923i	0.701806	+	1.69431i	0.719525	+	0.694466i	$0.244359\pi$
$131$	8.03254	+	19.3923i	0.701806	+	1.69431i	−0.0177195	+	0.999843i	$0.505641\pi$
$132$		0			0
$133$	−12.7894	−	5.29756i	−1.10899	−	0.459357i
$134$		0			0
$135$	1.92393	+	1.92393i	0.165586	+	0.165586i
$136$		0			0
$137$	−3.73965	+	3.73965i	−0.319500	+	0.319500i	−0.848575	−	0.529075i	$-0.822539\pi$
$137$	−3.73965	+	3.73965i	−0.319500	+	0.319500i	0.529075	+	0.848575i	$0.322539\pi$
$138$		0			0
$139$	−4.05949	+	9.80047i	−0.344321	+	0.831265i	0.652947	+	0.757403i	$0.273532\pi$
$139$	−4.05949	+	9.80047i	−0.344321	+	0.831265i	−0.997268	+	0.0738616i	$0.976468\pi$
$140$		0			0
$141$	0.999819	−	0.414139i	0.0841999	−	0.0348768i
$142$		0			0
$143$			20.8515i			1.74369i
$144$		0			0
$145$			13.9427i			1.15788i
$146$		0			0
$147$	0.999970	−	0.414201i	0.0824761	−	0.0341627i
$148$		0			0
$149$	−4.32999	+	10.4535i	−0.354727	+	0.856386i	0.641297	+	0.767293i	$0.278397\pi$
$149$	−4.32999	+	10.4535i	−0.354727	+	0.856386i	−0.996023	+	0.0890929i	$0.971603\pi$
$150$		0			0
$151$	−12.1795	+	12.1795i	−0.991157	+	0.991157i	−0.999961	−	0.00880460i	$-0.997197\pi$
$151$	−12.1795	+	12.1795i	−0.991157	+	0.991157i	0.00880460	+	0.999961i	$0.497197\pi$
$152$		0			0
$153$	2.94473	+	2.94473i	0.238067	+	0.238067i
$154$		0			0
$155$	7.21481	+	2.98847i	0.579507	+	0.240040i
$156$		0			0
$157$	5.53996	+	13.3746i	0.442137	+	1.06741i	0.975198	+	0.221336i	$0.0710417\pi$
$157$	5.53996	+	13.3746i	0.442137	+	1.06741i	−0.533061	+	0.846077i	$0.678958\pi$
$158$		0			0
$159$	−7.58982			−0.601912
$160$		0			0
$161$	−7.81117			−0.615607
$162$		0			0
$163$	5.79233	+	13.9839i	0.453690	+	1.09530i	0.970908	+	0.239451i	$0.0769675\pi$
$163$	5.79233	+	13.9839i	0.453690	+	1.09530i	−0.517218	+	0.855854i	$0.673032\pi$
$164$		0			0
$165$	8.71936	+	3.61168i	0.678802	+	0.281169i
$166$		0			0
$167$	−4.07626	−	4.07626i	−0.315430	−	0.315430i	0.531579	−	0.847009i	$-0.321599\pi$
$167$	−4.07626	−	4.07626i	−0.315430	−	0.315430i	−0.847009	+	0.531579i	$0.821599\pi$
$168$		0			0
$169$	16.3598	−	16.3598i	1.25844	−	1.25844i
$170$		0			0
$171$	−1.86340	+	4.49866i	−0.142498	+	0.344021i
$172$		0			0
$173$	−4.29724	+	1.77998i	−0.326713	+	0.135329i	−0.540010	−	0.841658i	$-0.681580\pi$
$173$	−4.29724	+	1.77998i	−0.326713	+	0.135329i	0.213297	+	0.976987i	$0.431580\pi$
$174$		0			0
$175$		−	6.83165i		−	0.516424i
$176$		0			0
$177$		−	11.1947i		−	0.841443i
$178$		0			0
$179$	−0.273384	+	0.113240i	−0.0204337	+	0.00846392i	−0.392877	−	0.919591i	$-0.628520\pi$
$179$	−0.273384	+	0.113240i	−0.0204337	+	0.00846392i	0.372443	+	0.928055i	$0.378520\pi$
$180$		0			0
$181$	−4.00336	+	9.66497i	−0.297567	+	0.718391i	0.702411	+	0.711772i	$0.252107\pi$
$181$	−4.00336	+	9.66497i	−0.297567	+	0.718391i	−0.999978	+	0.00661937i	$0.997893\pi$
$182$		0			0
$183$	5.50099	−	5.50099i	0.406645	−	0.406645i
$184$		0			0
$185$	−13.1413	−	13.1413i	−0.966165	−	0.966165i
$186$		0			0
$187$	13.3457	+	5.52796i	0.975932	+	0.404244i
$188$		0			0
$189$	−1.08795	−	2.62654i	−0.0791367	−	0.191053i
$190$		0			0
$191$	−15.1625			−1.09712			−0.548561	−	0.836110i	$-0.684824\pi$
$191$	−15.1625			−1.09712			−0.548561	+	0.836110i	$0.684824\pi$
$192$		0			0
$193$	−18.3549			−1.32122			−0.660608	−	0.750731i	$-0.729701\pi$
$193$	−18.3549			−1.32122			−0.660608	+	0.750731i	$0.729701\pi$
$194$		0			0
$195$	−6.25915	−	15.1109i	−0.448227	−	1.08212i
$196$		0			0
$197$	6.65334	+	2.75590i	0.474031	+	0.196350i	0.606891	−	0.794785i	$-0.292416\pi$
$197$	6.65334	+	2.75590i	0.474031	+	0.196350i	−0.132861	+	0.991135i	$0.542416\pi$
$198$		0			0
$199$	0.849057	+	0.849057i	0.0601880	+	0.0601880i	0.736560	−	0.676372i	$-0.236449\pi$
$199$	0.849057	+	0.849057i	0.0601880	+	0.0601880i	−0.676372	+	0.736560i	$0.736449\pi$
$200$		0			0
$201$	−7.18419	+	7.18419i	−0.506734	+	0.506734i
$202$		0			0
$203$	5.57510	−	13.4595i	0.391295	−	0.944671i
$204$		0			0
$205$	2.68885	−	1.11376i	0.187797	−	0.0777883i
$206$		0			0
$207$			2.74756i			0.190969i
$208$		0			0
$209$			16.8901i			1.16831i
$210$		0			0
$211$	−7.40729	+	3.06820i	−0.509939	+	0.211224i	−0.622791	−	0.782388i	$-0.714001\pi$
$211$	−7.40729	+	3.06820i	−0.509939	+	0.211224i	0.112852	+	0.993612i	$0.464001\pi$
$212$		0			0
$213$	1.02245	−	2.46841i	0.0700570	−	0.169133i
$214$		0			0
$215$	7.73098	−	7.73098i	0.527248	−	0.527248i
$216$		0			0
$217$	−5.76978	−	5.76978i	−0.391678	−	0.391678i
$218$		0			0
$219$	9.15544	+	3.79231i	0.618667	+	0.256260i
$220$		0			0
$221$	−9.58012	−	23.1285i	−0.644429	−	1.55579i
$222$		0			0
$223$	−0.188370			−0.0126142			−0.00630710	−	0.999980i	$-0.502008\pi$
$223$	−0.188370			−0.0126142			−0.00630710	+	0.999980i	$0.502008\pi$
$224$		0			0
$225$	−2.40301			−0.160201
$226$		0			0
$227$	−0.106761	−	0.257744i	−0.00708599	−	0.0171071i	0.920297	−	0.391221i	$-0.127947\pi$
$227$	−0.106761	−	0.257744i	−0.00708599	−	0.0171071i	−0.927383	+	0.374113i	$0.877947\pi$
$228$		0			0
$229$	−2.03685	−	0.843689i	−0.134599	−	0.0557526i	0.314367	−	0.949301i	$-0.398208\pi$
$229$	−2.03685	−	0.843689i	−0.134599	−	0.0557526i	−0.448966	+	0.893549i	$0.648208\pi$
$230$		0			0
$231$	−6.97299	−	6.97299i	−0.458789	−	0.458789i
$232$		0			0
$233$	−4.32675	+	4.32675i	−0.283455	+	0.283455i	−0.834485	−	0.551030i	$-0.814235\pi$
$233$	−4.32675	+	4.32675i	−0.283455	+	0.283455i	0.551030	+	0.834485i	$0.314235\pi$
$234$		0			0
$235$	−1.12681	+	2.72036i	−0.0735049	+	0.177456i
$236$		0			0
$237$	−10.1863	+	4.21928i	−0.661668	+	0.274072i
$238$		0			0
$239$			8.26905i			0.534880i	0.963575	+	0.267440i	$0.0861777\pi$
$239$			8.26905i			0.534880i	−0.963575	+	0.267440i	$0.913822\pi$
$240$		0			0
$241$		−	22.7291i		−	1.46411i	−0.681244	−	0.732057i	$-0.738561\pi$
$241$		−	22.7291i		−	1.46411i	0.681244	−	0.732057i	$-0.261439\pi$
$242$		0			0
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$		0			0
$245$	−1.12698	+	2.72077i	−0.0720000	+	0.173823i
$246$		0			0
$247$	20.6978	−	20.6978i	1.31697	−	1.31697i
$248$		0			0
$249$	1.76429	+	1.76429i	0.111807	+	0.111807i
$250$		0			0
$251$	−12.3335	−	5.10871i	−0.778485	−	0.322459i	−0.0421812	−	0.999110i	$-0.513431\pi$
$251$	−12.3335	−	5.10871i	−0.778485	−	0.322459i	−0.736304	+	0.676651i	$0.763431\pi$
$252$		0			0
$253$	3.64714	+	8.80497i	0.229294	+	0.553564i
$254$		0			0
$255$	−11.3309			−0.709568
$256$		0			0
$257$	15.9974			0.997893			0.498947	−	0.866633i	$-0.333720\pi$
$257$	15.9974			0.997893			0.498947	+	0.866633i	$0.333720\pi$
$258$		0			0
$259$	7.43116	+	17.9404i	0.461750	+	1.11476i
$260$		0			0
$261$	−4.73434	−	1.96103i	−0.293048	−	0.121385i
$262$		0			0
$263$	4.44583	+	4.44583i	0.274141	+	0.274141i	0.830765	−	0.556623i	$-0.187903\pi$
$263$	4.44583	+	4.44583i	0.274141	+	0.274141i	−0.556623	+	0.830765i	$0.687903\pi$
$264$		0			0
$265$	14.6023	−	14.6023i	0.897011	−	0.897011i
$266$		0			0
$267$	4.14448	−	10.0057i	0.253638	−	0.612336i
$268$		0			0
$269$	11.1204	−	4.60621i	0.678021	−	0.280846i	−0.0169781	−	0.999856i	$-0.505405\pi$
$269$	11.1204	−	4.60621i	0.678021	−	0.280846i	0.695000	+	0.719010i	$0.255405\pi$
$270$		0			0
$271$		−	18.7073i		−	1.13638i	−0.822896	−	0.568192i	$-0.807643\pi$
$271$		−	18.7073i		−	1.13638i	0.822896	−	0.568192i	$-0.192357\pi$
$272$		0			0
$273$			17.0899i			1.03433i
$274$		0			0
$275$	−7.70082	+	3.18978i	−0.464377	+	0.192351i
$276$		0			0
$277$	4.13646	−	9.98630i	0.248536	−	0.600019i	−0.749544	−	0.661954i	$-0.769727\pi$
$277$	4.13646	−	9.98630i	0.248536	−	0.600019i	0.998080	+	0.0619354i	$0.0197273\pi$
$278$		0			0
$279$	−2.02950	+	2.02950i	−0.121503	+	0.121503i
$280$		0			0
$281$	−13.2105	−	13.2105i	−0.788071	−	0.788071i	0.193106	−	0.981178i	$-0.438144\pi$
$281$	−13.2105	−	13.2105i	−0.788071	−	0.788071i	−0.981178	+	0.193106i	$0.938144\pi$
$282$		0			0
$283$	−21.9884	−	9.10789i	−1.30707	−	0.541408i	−0.383045	−	0.923730i	$-0.625125\pi$
$283$	−21.9884	−	9.10789i	−1.30707	−	0.541408i	−0.924029	+	0.382321i	$0.875125\pi$
$284$		0			0
$285$	−5.07004	−	12.2402i	−0.300323	−	0.725044i
$286$		0			0
$287$	−3.04100			−0.179504
$288$		0			0
$289$	−0.342832			−0.0201666
$290$		0			0
$291$	4.32544	+	10.4425i	0.253562	+	0.612152i
$292$		0			0
$293$	18.8878	+	7.82359i	1.10344	+	0.457059i	0.858673	−	0.512524i	$-0.171289\pi$
$293$	18.8878	+	7.82359i	1.10344	+	0.457059i	0.244764	+	0.969583i	$0.421289\pi$
$294$		0			0
$295$	21.5378	+	21.5378i	1.25398	+	1.25398i
$296$		0			0
$297$	−2.45273	+	2.45273i	−0.142322	+	0.142322i
$298$		0			0
$299$	6.32060	−	15.2593i	0.365530	−	0.882466i
$300$		0			0
$301$	−10.5543	+	4.37173i	−0.608340	+	0.251983i
$302$		0			0
$303$			3.85756i			0.221611i
$304$		0			0
$305$			21.1670i			1.21202i
$306$		0			0
$307$	10.7709	−	4.46145i	0.614728	−	0.254629i	−0.0535206	−	0.998567i	$-0.517044\pi$
$307$	10.7709	−	4.46145i	0.614728	−	0.254629i	0.668249	+	0.743938i	$0.267044\pi$
$308$		0			0
$309$	1.05170	−	2.53903i	0.0598292	−	0.144440i
$310$		0			0
$311$	6.79085	−	6.79085i	0.385074	−	0.385074i	−0.487852	−	0.872926i	$-0.662220\pi$
$311$	6.79085	−	6.79085i	0.385074	−	0.385074i	0.872926	+	0.487852i	$0.162220\pi$
$312$		0			0
$313$	12.7080	+	12.7080i	0.718300	+	0.718300i	0.968257	−	0.249957i	$-0.0804166\pi$
$313$	12.7080	+	12.7080i	0.718300	+	0.718300i	−0.249957	+	0.968257i	$0.580417\pi$
$314$		0			0
$315$	7.14642	+	2.96015i	0.402655	+	0.166785i
$316$		0			0
$317$	6.89303	+	16.6412i	0.387151	+	0.934665i	0.990541	+	0.137219i	$0.0438163\pi$
$317$	6.89303	+	16.6412i	0.387151	+	0.934665i	−0.603390	+	0.797446i	$0.706184\pi$
$318$		0			0
$319$	−17.7750			−0.995208
$320$		0			0
$321$	13.9852			0.780577
$322$		0			0
$323$	−7.76010	−	18.7345i	−0.431783	−	1.04242i
$324$		0			0
$325$	13.3457	+	5.52799i	0.740289	+	0.306638i
$326$		0			0
$327$	9.29346	+	9.29346i	0.513930	+	0.513930i
$328$		0			0
$329$	2.17550	−	2.17550i	0.119939	−	0.119939i
$330$		0			0
$331$	0.259261	−	0.625913i	0.0142503	−	0.0344033i	−0.916594	−	0.399819i	$-0.869073\pi$
$331$	0.259261	−	0.625913i	0.0142503	−	0.0344033i	0.930845	+	0.365415i	$0.119073\pi$
$332$		0			0
$333$	6.31049	−	2.61389i	0.345813	−	0.143240i
$334$		0			0
$335$		−	27.6438i		−	1.51034i
$336$		0			0
$337$			24.3244i			1.32504i	0.749046	+	0.662518i	$0.230512\pi$
$337$			24.3244i			1.32504i	−0.749046	+	0.662518i	$0.769488\pi$
$338$		0			0
$339$	−12.7859	+	5.29611i	−0.694436	+	0.287645i
$340$		0			0
$341$	−3.80987	+	9.19783i	−0.206316	+	0.498091i
$342$		0			0
$343$	−11.8960	+	11.8960i	−0.642326	+	0.642326i
$344$		0			0
$345$	−5.28611	−	5.28611i	−0.284595	−	0.284595i
$346$		0			0
$347$	6.95491	+	2.88082i	0.373359	+	0.154650i	0.561469	−	0.827498i	$-0.310236\pi$
$347$	6.95491	+	2.88082i	0.373359	+	0.154650i	−0.188110	+	0.982148i	$0.560236\pi$
$348$		0			0
$349$	−11.9159	−	28.7676i	−0.637845	−	1.53989i	−0.829545	−	0.558440i	$-0.811400\pi$
$349$	−11.9159	−	28.7676i	−0.637845	−	1.53989i	0.191700	−	0.981454i	$-0.438600\pi$
$350$		0			0
$351$	6.01134			0.320862
$352$		0			0
$353$	−22.1334			−1.17804			−0.589021	−	0.808118i	$-0.700486\pi$
$353$	−22.1334			−1.17804			−0.589021	+	0.808118i	$0.700486\pi$
$354$		0			0
$355$	2.78193	+	6.71616i	0.147649	+	0.356457i
$356$		0			0
$357$	10.9382	+	4.53074i	0.578909	+	0.239792i
$358$		0			0
$359$	10.1669	+	10.1669i	0.536586	+	0.536586i	0.922524	−	0.385939i	$-0.126122\pi$
$359$	10.1669	+	10.1669i	0.536586	+	0.536586i	−0.385939	+	0.922524i	$0.626122\pi$
$360$		0			0
$361$	3.33060	−	3.33060i	0.175295	−	0.175295i
$362$		0			0
$363$	−0.394850	+	0.953252i	−0.0207243	+	0.0500328i
$364$		0			0
$365$	−24.9106	+	10.3183i	−1.30388	+	0.540084i
$366$		0			0
$367$			9.77761i			0.510387i	0.966890	+	0.255194i	$0.0821392\pi$
$367$			9.77761i			0.510387i	−0.966890	+	0.255194i	$0.917861\pi$
$368$		0			0
$369$			1.06966i			0.0556844i
$370$		0			0
$371$	−19.9350	+	8.25734i	−1.03497	+	0.428700i
$372$		0			0
$373$	2.04735	−	4.94275i	0.106008	−	0.255926i	−0.861971	−	0.506958i	$-0.830770\pi$
$373$	2.04735	−	4.94275i	0.106008	−	0.255926i	0.967979	+	0.251032i	$0.0807700\pi$
$374$		0			0
$375$	−4.99642	+	4.99642i	−0.258014	+	0.258014i
$376$		0			0
$377$	21.7821	+	21.7821i	1.12184	+	1.12184i
$378$		0			0
$379$	−29.0333	−	12.0260i	−1.49134	−	0.617733i	−0.519732	−	0.854329i	$-0.673968\pi$
$379$	−29.0333	−	12.0260i	−1.49134	−	0.617733i	−0.971608	+	0.236596i	$0.923968\pi$
$380$		0			0
$381$	−2.09535	−	5.05863i	−0.107348	−	0.259161i
$382$		0			0
$383$	−2.47568			−0.126501			−0.0632507	−	0.997998i	$-0.520147\pi$
$383$	−2.47568			−0.126501			−0.0632507	+	0.997998i	$0.520147\pi$
$384$		0			0
$385$	26.8311			1.36744
$386$		0			0
$387$	1.53775	+	3.71245i	0.0781680	+	0.188714i
$388$		0			0
$389$	9.49742	+	3.93396i	0.481538	+	0.199460i	0.610229	−	0.792225i	$-0.291077\pi$
$389$	9.49742	+	3.93396i	0.481538	+	0.199460i	−0.128691	+	0.991685i	$0.541077\pi$
$390$		0			0
$391$	−8.09081	−	8.09081i	−0.409170	−	0.409170i
$392$		0			0
$393$	14.8422	−	14.8422i	0.748689	−	0.748689i
$394$		0			0
$395$	11.4800	−	27.7153i	0.577623	−	1.39451i
$396$		0			0
$397$	13.8666	−	5.74373i	0.695944	−	0.288269i	−0.00653022	−	0.999979i	$-0.502079\pi$
$397$	13.8666	−	5.74373i	0.695944	−	0.288269i	0.702474	+	0.711709i	$0.252079\pi$
$398$		0			0
$399$			13.8432i			0.693027i
$400$		0			0
$401$		−	21.9112i		−	1.09419i	−0.837069	−	0.547097i	$-0.815733\pi$
$401$		−	21.9112i		−	1.09419i	0.837069	−	0.547097i	$-0.184267\pi$
$402$		0			0
$403$	15.9401	−	6.60262i	0.794034	−	0.328900i
$404$		0			0
$405$	1.04122	−	2.51374i	0.0517388	−	0.124909i
$406$		0			0
$407$	16.7532	−	16.7532i	0.830426	−	0.830426i
$408$		0			0
$409$	13.0005	+	13.0005i	0.642835	+	0.642835i	0.951251	−	0.308417i	$-0.0997991\pi$
$409$	13.0005	+	13.0005i	0.642835	+	0.642835i	−0.308417	+	0.951251i	$0.599799\pi$
$410$		0			0
$411$	4.88609	+	2.02388i	0.241013	+	0.0998308i
$412$		0			0
$413$	−12.1792	−	29.4033i	−0.599301	−	1.44684i
$414$		0			0
$415$	−6.78872			−0.333245
$416$		0			0
$417$	10.6080			0.519474
$418$		0			0
$419$	−7.98199	−	19.2702i	−0.389946	−	0.941412i	−0.989950	−	0.141416i	$-0.954835\pi$
$419$	−7.98199	−	19.2702i	−0.389946	−	0.941412i	0.600005	−	0.799997i	$-0.295165\pi$
$420$		0			0
$421$	5.11481	+	2.11863i	0.249281	+	0.103255i	0.503825	−	0.863806i	$-0.331926\pi$
$421$	5.11481	+	2.11863i	0.249281	+	0.103255i	−0.254545	+	0.967061i	$0.581926\pi$
$422$		0			0
$423$	−0.765228	−	0.765228i	−0.0372067	−	0.0372067i
$424$		0			0
$425$	7.07622	−	7.07622i	0.343247	−	0.343247i
$426$		0			0
$427$	8.46379	−	20.4334i	0.409591	−	0.988841i
$428$		0			0
$429$	19.2642	−	7.97951i	0.930086	−	0.385254i
$430$		0			0
$431$			5.20156i			0.250551i	0.992122	+	0.125275i	$0.0399814\pi$
$431$			5.20156i			0.250551i	−0.992122	+	0.125275i	$0.960019\pi$
$432$		0			0
$433$			6.44939i			0.309938i	0.987919	+	0.154969i	$0.0495278\pi$
$433$			6.44939i			0.309938i	−0.987919	+	0.154969i	$0.950472\pi$
$434$		0			0
$435$	12.8814	−	5.33566i	0.617617	−	0.255825i
$436$		0			0
$437$	5.11982	−	12.3603i	0.244914	−	0.591275i
$438$		0			0
$439$	20.5461	−	20.5461i	0.980610	−	0.980610i	−0.0192051	−	0.999816i	$-0.506114\pi$
$439$	20.5461	−	20.5461i	0.980610	−	0.980610i	0.999816	+	0.0192051i	$0.00611355\pi$
$440$		0			0
$441$	−0.765344	−	0.765344i	−0.0364450	−	0.0364450i
$442$		0			0
$443$	−16.1487	−	6.68902i	−0.767249	−	0.317805i	−0.0354912	−	0.999370i	$-0.511300\pi$
$443$	−16.1487	−	6.68902i	−0.767249	−	0.317805i	−0.731757	+	0.681565i	$0.761300\pi$
$444$		0			0
$445$	11.2765	+	27.2239i	0.534557	+	1.29054i
$446$		0			0
$447$	11.3148			0.535172
$448$		0			0
$449$	−0.794308			−0.0374857			−0.0187428	−	0.999824i	$-0.505966\pi$
$449$	−0.794308			−0.0374857			−0.0187428	+	0.999824i	$0.505966\pi$
$450$		0			0
$451$	1.41988	+	3.42790i	0.0668596	+	0.161413i
$452$		0			0
$453$	15.9133	+	6.59152i	0.747674	+	0.309697i
$454$		0			0
$455$	−32.8798	−	32.8798i	−1.54143	−	1.54143i
$456$		0			0
$457$	21.2796	−	21.2796i	0.995420	−	0.995420i	−0.00456968	−	0.999990i	$-0.501455\pi$
$457$	21.2796	−	21.2796i	0.995420	−	0.995420i	0.999990	+	0.00456968i	$0.00145458\pi$
$458$		0			0
$459$	1.59367	−	3.84747i	0.0743864	−	0.179585i
$460$		0			0
$461$	0.541763	−	0.224405i	0.0252324	−	0.0104516i	−0.370032	−	0.929019i	$-0.620653\pi$
$461$	0.541763	−	0.224405i	0.0252324	−	0.0104516i	0.395264	+	0.918568i	$0.370653\pi$
$462$		0			0
$463$			13.0365i			0.605859i	0.953013	+	0.302929i	$0.0979646\pi$
$463$			13.0365i			0.605859i	−0.953013	+	0.302929i	$0.902035\pi$
$464$		0			0
$465$		−	7.80925i		−	0.362145i
$466$		0			0
$467$	36.1793	−	14.9860i	1.67418	−	0.693467i	0.675156	−	0.737675i	$-0.264076\pi$
$467$	36.1793	−	14.9860i	1.67418	−	0.693467i	0.999022	+	0.0442081i	$0.0140765\pi$
$468$		0			0
$469$	−11.0535	+	26.6856i	−0.510405	+	1.23223i
$470$		0			0
$471$	10.2365	−	10.2365i	0.471674	−	0.471674i
$472$		0			0
$473$	9.85587	+	9.85587i	0.453174	+	0.453174i
$474$		0			0
$475$	10.8103	+	4.47779i	0.496012	+	0.205455i
$476$		0			0
$477$	2.90450	+	7.01208i	0.132988	+	0.321061i
$478$		0			0
$479$	−27.6976			−1.26554			−0.632768	−	0.774341i	$-0.718081\pi$
$479$	−27.6976			−1.26554			−0.632768	+	0.774341i	$0.718081\pi$
$480$		0			0
$481$	−41.0600			−1.87217
$482$		0			0
$483$	2.98921	+	7.21658i	0.136014	+	0.328366i
$484$		0			0
$485$	−28.4125	−	11.7689i	−1.29015	−	0.534396i
$486$		0			0
$487$	−22.8658	−	22.8658i	−1.03615	−	1.03615i	−0.999322	−	0.0368273i	$-0.988275\pi$
$487$	−22.8658	−	22.8658i	−1.03615	−	1.03615i	−0.0368273	−	0.999322i	$-0.511725\pi$
$488$		0			0
$489$	10.7028	−	10.7028i	0.483999	−	0.483999i
$490$		0			0
$491$	−10.1610	+	24.5308i	−0.458559	+	1.10706i	0.510423	+	0.859924i	$0.329489\pi$
$491$	−10.1610	+	24.5308i	−0.458559	+	1.10706i	−0.968981	+	0.247135i	$0.920511\pi$
$492$		0			0
$493$	19.7160	−	8.16665i	0.887965	−	0.367807i
$494$		0			0
$495$		−	9.43777i		−	0.424196i
$496$		0			0
$497$		−	7.59575i		−	0.340716i
$498$		0			0
$499$	−11.6135	+	4.81046i	−0.519890	+	0.215346i	−0.627169	−	0.778883i	$-0.715786\pi$
$499$	−11.6135	+	4.81046i	−0.519890	+	0.215346i	0.107278	+	0.994229i	$0.465786\pi$
$500$		0			0
$501$	−2.20606	+	5.32589i	−0.0985593	+	0.237943i
$502$		0			0
$503$	−12.9948	+	12.9948i	−0.579412	+	0.579412i	−0.934741	−	0.355330i	$-0.884369\pi$
$503$	−12.9948	+	12.9948i	−0.579412	+	0.579412i	0.355330	+	0.934741i	$0.384369\pi$
$504$		0			0
$505$	−7.42167	−	7.42167i	−0.330260	−	0.330260i
$506$		0			0
$507$	−21.3751	−	8.85384i	−0.949300	−	0.393213i
$508$		0			0
$509$	13.3636	+	32.2627i	0.592333	+	1.43002i	0.881244	+	0.472662i	$0.156707\pi$
$509$	13.3636	+	32.2627i	0.592333	+	1.43002i	−0.288911	+	0.957356i	$0.593293\pi$
$510$		0			0
$511$	28.1730			1.24630
$512$		0			0
$513$	4.86931			0.214985
$514$		0			0
$515$	2.86152	+	6.90832i	0.126094	+	0.304417i
$516$		0			0
$517$	−3.46806	−	1.43652i	−0.152525	−	0.0631780i
$518$		0			0
$519$	3.28896	+	3.28896i	0.144370	+	0.144370i
$520$		0			0
$521$	1.74966	−	1.74966i	0.0766541	−	0.0766541i	−0.667740	−	0.744394i	$-0.732738\pi$
$521$	1.74966	−	1.74966i	0.0766541	−	0.0766541i	0.744394	+	0.667740i	$0.232738\pi$
$522$		0			0
$523$	7.05117	−	17.0230i	0.308326	−	0.744366i	−0.691433	−	0.722440i	$-0.743020\pi$
$523$	7.05117	−	17.0230i	0.308326	−	0.744366i	0.999760	−	0.0219253i	$-0.00697960\pi$
$524$		0			0
$525$	−6.31162	+	2.61436i	−0.275462	+	0.114100i
$526$		0			0
$527$		−	11.9527i		−	0.520667i
$528$		0			0
$529$			15.4509i			0.671779i
$530$		0			0
$531$	−10.3425	+	4.28402i	−0.448828	+	0.185911i
$532$		0			0
$533$	2.46070	−	5.94064i	0.106585	−	0.257318i
$534$		0			0
$535$	−26.9065	+	26.9065i	−1.16327	+	1.16327i
$536$		0			0
$537$	0.209239	+	0.209239i	0.00902935	+	0.00902935i
$538$		0			0
$539$	−3.46858	−	1.43673i	−0.149402	−	0.0618845i
$540$		0			0
$541$	−7.86315	−	18.9833i	−0.338063	−	0.816157i	−0.997902	−	0.0647494i	$-0.979375\pi$
$541$	−7.86315	−	18.9833i	−0.338063	−	0.816157i	0.659838	−	0.751408i	$-0.270625\pi$
$542$		0			0
$543$	10.4613			0.448937
$544$		0			0
$545$	−35.7599			−1.53179
$546$		0			0
$547$	−0.832145	−	2.00898i	−0.0355799	−	0.0858976i	0.905091	−	0.425219i	$-0.139803\pi$
$547$	−0.832145	−	2.00898i	−0.0355799	−	0.0858976i	−0.940671	+	0.339321i	$0.889803\pi$
$548$		0			0
$549$	−7.18739	−	2.97711i	−0.306750	−	0.127060i
$550$		0			0
$551$	17.6440	+	17.6440i	0.751659	+	0.751659i
$552$		0			0
$553$	−22.1643	+	22.1643i	−0.942520	+	0.942520i
$554$		0			0
$555$	−7.11200	+	17.1699i	−0.301888	+	0.728821i
$556$		0			0
$557$	−27.8685	+	11.5435i	−1.18083	+	0.489115i	−0.884758	−	0.466051i	$-0.845676\pi$
$557$	−27.8685	+	11.5435i	−1.18083	+	0.489115i	−0.296070	+	0.955166i	$0.595676\pi$
$558$		0			0
$559$		−	24.1555i		−	1.02167i
$560$		0			0
$561$		−	14.4453i		−	0.609879i
$562$		0			0
$563$	−17.3847	+	7.20096i	−0.732676	+	0.303484i	−0.717651	−	0.696403i	$-0.754783\pi$
$563$	−17.3847	+	7.20096i	−0.732676	+	0.303484i	−0.0150247	+	0.999887i	$0.504783\pi$
$564$		0			0
$565$	14.4099	−	34.7886i	0.606229	−	1.46357i
$566$		0			0
$567$	−2.01027	+	2.01027i	−0.0844233	+	0.0844233i
$568$		0			0
$569$	−5.37251	−	5.37251i	−0.225227	−	0.225227i	0.585468	−	0.810695i	$-0.300911\pi$
$569$	−5.37251	−	5.37251i	−0.225227	−	0.225227i	−0.810695	+	0.585468i	$0.800911\pi$
$570$		0			0
$571$	37.6829	+	15.6087i	1.57698	+	0.653206i	0.987931	−	0.154893i	$-0.0495033\pi$
$571$	37.6829	+	15.6087i	1.57698	+	0.653206i	0.589047	+	0.808099i	$0.299503\pi$
$572$		0			0
$573$	5.80245	+	14.0084i	0.242401	+	0.585207i
$574$		0			0
$575$	6.60243			0.275340
$576$		0			0
$577$	28.6100			1.19105			0.595525	−	0.803337i	$-0.296944\pi$
$577$	28.6100			1.19105			0.595525	+	0.803337i	$0.296944\pi$
$578$		0			0
$579$	7.02413	+	16.9577i	0.291913	+	0.704740i
$580$		0			0
$581$	6.55342	+	2.71452i	0.271882	+	0.112617i
$582$		0			0
$583$	18.6158	+	18.6158i	0.770987	+	0.770987i
$584$		0			0
$585$	−11.5654	+	11.5654i	−0.478170	+	0.478170i
$586$		0			0
$587$	−14.0646	+	33.9550i	−0.580509	+	1.40147i	0.311844	+	0.950133i	$0.399053\pi$
$587$	−14.0646	+	33.9550i	−0.580509	+	1.40147i	−0.892353	+	0.451339i	$0.850947\pi$
$588$		0			0
$589$	12.9118	−	5.34826i	0.532023	−	0.220371i
$590$		0			0
$591$		−	7.20152i		−	0.296231i
$592$		0			0
$593$			28.6736i			1.17749i	0.808321	+	0.588743i	$0.200377\pi$
$593$			28.6736i			1.17749i	−0.808321	+	0.588743i	$0.799623\pi$
$594$		0			0
$595$	−29.7611	+	12.3274i	−1.22009	+	0.505376i
$596$		0			0
$597$	0.459506	−	1.10935i	0.0188063	−	0.0454025i
$598$		0			0
$599$	28.5413	−	28.5413i	1.16617	−	1.16617i	0.183067	−	0.983100i	$-0.441397\pi$
$599$	28.5413	−	28.5413i	1.16617	−	1.16617i	0.983100	−	0.183067i	$-0.0586027\pi$
$600$		0			0
$601$	−29.9824	−	29.9824i	−1.22301	−	1.22301i	−0.966558	−	0.256448i	$-0.917448\pi$
$601$	−29.9824	−	29.9824i	−1.22301	−	1.22301i	−0.256448	−	0.966558i	$-0.582552\pi$
$602$		0			0
$603$	9.38659	+	3.88805i	0.382252	+	0.158334i
$604$		0			0
$605$	−1.07433	−	2.59365i	−0.0436776	−	0.105447i
$606$		0			0
$607$	20.2791			0.823105			0.411552	−	0.911386i	$-0.364987\pi$
$607$	20.2791			0.823105			0.411552	+	0.911386i	$0.364987\pi$
$608$		0			0
$609$	−14.5684			−0.590343
$610$		0			0
$611$	2.48953	+	6.01025i	0.100715	+	0.243149i
$612$		0			0
$613$	22.4278	+	9.28988i	0.905849	+	0.375215i	0.786466	−	0.617633i	$-0.211908\pi$
$613$	22.4278	+	9.28988i	0.905849	+	0.375215i	0.119383	+	0.992848i	$0.461908\pi$
$614$		0			0
$615$	−2.05796	−	2.05796i	−0.0829848	−	0.0829848i
$616$		0			0
$617$	−28.6181	+	28.6181i	−1.15212	+	1.15212i	−0.165993	+	0.986127i	$0.553083\pi$
$617$	−28.6181	+	28.6181i	−1.15212	+	1.15212i	−0.986127	+	0.165993i	$0.946917\pi$
$618$		0			0
$619$	−0.706861	+	1.70651i	−0.0284111	+	0.0685905i	−0.937448	−	0.348124i	$-0.886819\pi$
$619$	−0.706861	+	1.70651i	−0.0284111	+	0.0685905i	0.909037	+	0.416715i	$0.136819\pi$
$620$		0			0
$621$	2.53841	−	1.05145i	0.101863	−	0.0421931i
$622$		0			0
$623$		−	30.7893i		−	1.23355i
$624$		0			0
$625$		−	31.2406i		−	1.24962i
$626$		0			0
$627$	15.6044	−	6.46357i	0.623181	−	0.258130i
$628$		0			0
$629$	−10.8855	+	26.2799i	−0.434032	+	1.04785i
$630$		0			0
$631$	−24.6361	+	24.6361i	−0.980748	+	0.980748i	−0.999818	−	0.0190703i	$-0.993929\pi$
$631$	−24.6361	+	24.6361i	−0.980748	+	0.980748i	0.0190703	+	0.999818i	$0.493929\pi$
$632$		0			0
$633$	5.66930	+	5.66930i	0.225334	+	0.225334i
$634$		0			0
$635$	13.7638	+	5.70114i	0.546198	+	0.226243i
$636$		0			0
$637$	2.48990	+	6.01116i	0.0986536	+	0.238171i
$638$		0			0
$639$	−2.67179			−0.105694
$640$		0			0
$641$	0.278463			0.0109986			0.00549931	−	0.999985i	$-0.498250\pi$
$641$	0.278463			0.0109986			0.00549931	+	0.999985i	$0.498250\pi$
$642$		0			0
$643$	−5.39050	−	13.0138i	−0.212581	−	0.513215i	0.781238	−	0.624234i	$-0.214589\pi$
$643$	−5.39050	−	13.0138i	−0.212581	−	0.513215i	−0.993818	+	0.111019i	$0.964589\pi$
$644$		0			0
$645$	−10.1010	−	4.18397i	−0.397727	−	0.164744i
$646$		0			0
$647$	−17.8303	−	17.8303i	−0.700980	−	0.700980i	0.263641	−	0.964621i	$-0.415077\pi$
$647$	−17.8303	−	17.8303i	−0.700980	−	0.700980i	−0.964621	+	0.263641i	$0.915077\pi$
$648$		0			0
$649$	−27.4575	+	27.4575i	−1.07780	+	1.07780i
$650$		0			0
$651$	−3.12258	+	7.53858i	−0.122384	+	0.295460i
$652$		0			0
$653$	−31.3223	+	12.9741i	−1.22574	+	0.507716i	−0.899229	−	0.437478i	$-0.855872\pi$
$653$	−31.3223	+	12.9741i	−1.22574	+	0.507716i	−0.326507	+	0.945195i	$0.605872\pi$
$654$		0			0
$655$			57.1107i			2.23150i
$656$		0			0
$657$		−	9.90978i		−	0.386617i
$658$		0			0
$659$	38.2358	−	15.8378i	1.48946	−	0.616953i	0.518258	−	0.855224i	$-0.326581\pi$
$659$	38.2358	−	15.8378i	1.48946	−	0.616953i	0.971199	+	0.238271i	$0.0765807\pi$
$660$		0			0
$661$	7.49776	−	18.1012i	0.291629	−	0.704055i	−0.708369	−	0.705842i	$-0.750569\pi$
$661$	7.49776	−	18.1012i	0.291629	−	0.704055i	0.999998	+	0.00178728i	$0.000568910\pi$
$662$		0			0
$663$	−17.7018	+	17.7018i	−0.687479	+	0.687479i
$664$		0			0
$665$	−26.6334	−	26.6334i	−1.03280	−	1.03280i
$666$		0			0
$667$	13.0079	+	5.38804i	0.503667	+	0.208626i
$668$		0			0
$669$	0.0720861	+	0.174031i	0.00278701	+	0.00672844i
$670$		0			0
$671$	−26.9849			−1.04174
$672$		0			0
$673$	18.3856			0.708711			0.354356	−	0.935111i	$-0.384700\pi$
$673$	18.3856			0.708711			0.354356	+	0.935111i	$0.384700\pi$
$674$		0			0
$675$	0.919594	+	2.22010i	0.0353952	+	0.0854515i
$676$		0			0
$677$	−34.2111	−	14.1707i	−1.31484	−	0.544624i	−0.388546	−	0.921429i	$-0.627023\pi$
$677$	−34.2111	−	14.1707i	−1.31484	−	0.544624i	−0.926293	+	0.376805i	$0.877023\pi$
$678$		0			0
$679$	22.7219	+	22.7219i	0.871986	+	0.871986i
$680$		0			0
$681$	−0.197269	+	0.197269i	−0.00755936	+	0.00755936i
$682$		0			0
$683$	9.51662	−	22.9752i	0.364143	−	0.879120i	−0.630542	−	0.776155i	$-0.717167\pi$
$683$	9.51662	−	22.9752i	0.364143	−	0.879120i	0.994685	−	0.102964i	$-0.0328328\pi$
$684$		0			0
$685$	−13.2943	+	5.50668i	−0.507949	+	0.210399i
$686$		0			0
$687$			2.20467i			0.0841133i
$688$		0			0
$689$		−	45.6250i		−	1.73817i
$690$		0			0
$691$	18.8902	−	7.82459i	0.718618	−	0.297661i	0.00675270	−	0.999977i	$-0.497851\pi$
$691$	18.8902	−	7.82459i	0.718618	−	0.297661i	0.711866	+	0.702316i	$0.247851\pi$
$692$		0			0
$693$	−3.77376	+	9.11066i	−0.143353	+	0.346085i
$694$		0			0
$695$	−20.4090	+	20.4090i	−0.774156	+	0.774156i
$696$		0			0
$697$	−3.14987	−	3.14987i	−0.119310	−	0.119310i
$698$		0			0
$699$	5.65317	+	2.34162i	0.213823	+	0.0885683i
$700$		0			0
$701$	5.48707	+	13.2470i	0.207244	+	0.500331i	0.992987	−	0.118222i	$-0.0377194\pi$
$701$	5.48707	+	13.2470i	0.207244	+	0.500331i	−0.785743	+	0.618552i	$0.787719\pi$
$702$		0			0
$703$	−33.2595			−1.25440
$704$		0			0
$705$	2.94449			0.110896
$706$		0			0
$707$	4.19683	+	10.1320i	0.157838	+	0.381055i
$708$		0			0
$709$	−3.85647	−	1.59740i	−0.144833	−	0.0599917i	0.309090	−	0.951033i	$-0.399976\pi$
$709$	−3.85647	−	1.59740i	−0.144833	−	0.0599917i	−0.453922	+	0.891041i	$0.649976\pi$
$710$		0			0
$711$	7.79622	+	7.79622i	0.292381	+	0.292381i
$712$		0			0
$713$	5.57619	−	5.57619i	0.208830	−	0.208830i
$714$		0			0
$715$	−21.7110	+	52.4151i	−0.811946	+	1.96021i
$716$		0			0
$717$	7.63960	−	3.16443i	0.285306	−	0.118178i
$718$		0			0
$719$		−	8.78550i		−	0.327644i	−0.986490	−	0.163822i	$-0.947618\pi$
$719$		−	8.78550i		−	0.327644i	0.986490	−	0.163822i	$-0.0523823\pi$
$720$		0			0
$721$		−	7.81307i		−	0.290974i
$722$		0			0
$723$	−20.9990	+	8.69807i	−0.780961	+	0.323485i
$724$		0			0
$725$	−4.71238	+	11.3767i	−0.175013	+	0.422520i
$726$		0			0
$727$	10.0533	−	10.0533i	0.372858	−	0.372858i	−0.495659	−	0.868517i	$-0.665073\pi$
$727$	10.0533	−	10.0533i	0.372858	−	0.372858i	0.868517	+	0.495659i	$0.165073\pi$
$728$		0			0
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$		0			0
$731$	−15.4604	−	6.40390i	−0.571823	−	0.236857i
$732$		0			0
$733$	−10.3759	−	25.0496i	−0.383242	−	0.925228i	−0.991334	−	0.131362i	$-0.958065\pi$
$733$	−10.3759	−	25.0496i	−0.383242	−	0.925228i	0.608093	−	0.793866i	$-0.291935\pi$
$734$		0			0
$735$	2.94494			0.108626
$736$		0			0
$737$	35.2418			1.29815
$738$		0			0
$739$	−12.3459	−	29.8057i	−0.454153	−	1.09642i	−0.970728	−	0.240180i	$-0.922793\pi$
$739$	−12.3459	−	29.8057i	−0.454153	−	1.09642i	0.516575	−	0.856242i	$-0.327207\pi$
$740$		0			0
$741$	−27.0429	−	11.2016i	−0.993447	−	0.411499i
$742$		0			0
$743$	−16.0222	−	16.0222i	−0.587799	−	0.587799i	0.349236	−	0.937035i	$-0.386441\pi$
$743$	−16.0222	−	16.0222i	−0.587799	−	0.587799i	−0.937035	+	0.349236i	$0.886441\pi$
$744$		0			0
$745$	−21.7689	+	21.7689i	−0.797551	+	0.797551i
$746$		0			0
$747$	0.954824	−	2.30515i	0.0349352	−	0.0843410i
$748$		0			0
$749$	36.7327	−	15.2152i	1.34218	−	0.555951i
$750$		0			0
$751$			26.5917i			0.970346i	0.874418	+	0.485173i	$0.161243\pi$
$751$			26.5917i			0.970346i	−0.874418	+	0.485173i	$0.838757\pi$
$752$		0			0
$753$			13.3497i			0.486491i
$754$		0			0
$755$	−43.2978	+	17.9345i	−1.57577	+	0.652704i
$756$		0			0
$757$	−5.33084	+	12.8698i	−0.193753	+	0.467760i	−0.990662	−	0.136338i	$-0.956467\pi$
$757$	−5.33084	+	12.8698i	−0.193753	+	0.467760i	0.796910	+	0.604098i	$0.206467\pi$
$758$		0			0
$759$	6.73903	−	6.73903i	0.244611	−	0.244611i
$760$		0			0
$761$	11.8263	+	11.8263i	0.428704	+	0.428704i	0.888187	−	0.459483i	$-0.151965\pi$
$761$	11.8263	+	11.8263i	0.428704	+	0.428704i	−0.459483	+	0.888187i	$0.651965\pi$
$762$		0			0
$763$	34.5205	+	14.2989i	1.24973	+	0.517653i
$764$		0			0
$765$	4.33615	+	10.4684i	0.156774	+	0.378485i
$766$		0			0
$767$	67.2950			2.42988
$768$		0			0
$769$	39.2000			1.41359			0.706795	−	0.707419i	$-0.250140\pi$
$769$	39.2000			1.41359			0.706795	+	0.707419i	$0.250140\pi$
$770$		0			0
$771$	−6.12196	−	14.7797i	−0.220477	−	0.532278i
$772$		0			0
$773$	−39.7946	−	16.4834i	−1.43131	−	0.592868i	−0.473636	−	0.880721i	$-0.657059\pi$
$773$	−39.7946	−	16.4834i	−1.43131	−	0.592868i	−0.957675	+	0.287852i	$0.907059\pi$
$774$		0			0
$775$	4.87693	+	4.87693i	0.175184	+	0.175184i
$776$		0			0
$777$	13.7310	−	13.7310i	0.492596	−	0.492596i
$778$		0			0
$779$	1.99321	−	4.81205i	0.0714143	−	0.172409i
$780$		0			0
$781$	−8.56214	+	3.54655i	−0.306377	+	0.126906i
$782$		0			0
$783$			5.12441i			0.183132i
$784$		0			0
$785$			39.3887i			1.40584i
$786$		0			0
$787$	3.18736	−	1.32025i	0.113617	−	0.0470618i	−0.325151	−	0.945662i	$-0.605415\pi$
$787$	3.18736	−	1.32025i	0.113617	−	0.0470618i	0.438768	+	0.898600i	$0.355415\pi$
$788$		0			0
$789$	2.40606	−	5.80875i	0.0856581	−	0.206797i
$790$		0			0
$791$	−27.8209	+	27.8209i	−0.989197	+	0.989197i
$792$		0			0
$793$	33.0683	+	33.0683i	1.17429	+	1.17429i
$794$		0			0
$795$	−19.0788	−	7.90269i	−0.676655	−	0.280280i
$796$		0			0
$797$	9.15542	+	22.1031i	0.324302	+	0.782934i	0.998994	+	0.0448349i	$0.0142762\pi$
$797$	9.15542	+	22.1031i	0.324302	+	0.782934i	−0.674693	+	0.738099i	$0.735724\pi$
$798$		0			0
$799$	4.50678			0.159438
$800$		0			0
$801$	−10.8300			−0.382661
$802$		0			0
$803$	−13.1543	−	31.7574i	−0.464206	−	1.12069i
$804$		0			0
$805$	−19.6352	−	8.13318i	−0.692051	−	0.286657i
$806$		0			0
$807$	−8.51117	−	8.51117i	−0.299607	−	0.299607i
$808$		0			0
$809$	−1.21564	+	1.21564i	−0.0427396	+	0.0427396i	−0.728154	−	0.685414i	$-0.759621\pi$
$809$	−1.21564	+	1.21564i	−0.0427396	+	0.0427396i	0.685414	+	0.728154i	$0.259621\pi$
$810$		0			0
$811$	−6.74157	+	16.2756i	−0.236728	+	0.571513i	−0.996941	−	0.0781619i	$-0.975095\pi$
$811$	−6.74157	+	16.2756i	−0.236728	+	0.571513i	0.760212	+	0.649675i	$0.225095\pi$
$812$		0			0
$813$	−17.2832	+	7.15896i	−0.606150	+	0.251076i
$814$		0			0
$815$			41.1830i			1.44258i
$816$		0			0
$817$		−	19.5665i		−	0.684544i
$818$		0			0
$819$	15.7890	−	6.54003i	0.551714	−	0.228527i
$820$		0			0
$821$	−2.00047	+	4.82956i	−0.0698169	+	0.168553i	−0.954936	−	0.296811i	$-0.904077\pi$
$821$	−2.00047	+	4.82956i	−0.0698169	+	0.168553i	0.885119	+	0.465364i	$0.154077\pi$
$822$		0			0
$823$	13.5268	−	13.5268i	0.471516	−	0.471516i	−0.430889	−	0.902405i	$-0.641800\pi$
$823$	13.5268	−	13.5268i	0.471516	−	0.471516i	0.902405	+	0.430889i	$0.141800\pi$
$824$		0			0
$825$	5.89395	+	5.89395i	0.205201	+	0.205201i
$826$		0			0
$827$	−22.3808	−	9.27041i	−0.778255	−	0.322364i	−0.0420440	−	0.999116i	$-0.513387\pi$
$827$	−22.3808	−	9.27041i	−0.778255	−	0.322364i	−0.736211	+	0.676752i	$0.763387\pi$
$828$		0			0
$829$	−1.75314	−	4.23245i	−0.0608890	−	0.146999i	0.890507	−	0.454970i	$-0.150350\pi$
$829$	−1.75314	−	4.23245i	−0.0608890	−	0.146999i	−0.951396	+	0.307971i	$0.900350\pi$
$830$		0			0
$831$	−10.8091			−0.374963
$832$		0			0
$833$	4.50746			0.156174
$834$		0			0
$835$	−6.00234	−	14.4909i	−0.207720	−	0.501479i
$836$		0			0
$837$	2.65168	+	1.09836i	0.0916553	+	0.0379649i
$838$		0			0
$839$	23.6794	+	23.6794i	0.817503	+	0.817503i	0.985746	−	0.168242i	$-0.0538091\pi$
$839$	23.6794	+	23.6794i	0.817503	+	0.817503i	−0.168242	+	0.985746i	$0.553809\pi$
$840$		0			0
$841$	1.93775	−	1.93775i	0.0668190	−	0.0668190i
$842$		0			0
$843$	−7.14946	+	17.2603i	−0.246241	+	0.594477i
$844$		0			0
$845$	58.1583	−	24.0900i	2.00071	−	0.828720i
$846$		0			0
$847$			2.93333i			0.100791i
$848$		0			0
$849$			23.8001i			0.816816i
$850$		0			0
$851$	−17.3385	+	7.18182i	−0.594354	+	0.246190i
$852$		0			0
$853$	−1.47996	+	3.57295i	−0.0506730	+	0.122335i	−0.947189	−	0.320676i	$-0.896090\pi$
$853$	−1.47996	+	3.57295i	−0.0506730	+	0.122335i	0.896516	+	0.443011i	$0.146090\pi$
$854$		0			0
$855$	−9.36821	+	9.36821i	−0.320386	+	0.320386i
$856$		0			0
$857$	−1.99585	−	1.99585i	−0.0681769	−	0.0681769i	0.672196	−	0.740373i	$-0.265351\pi$
$857$	−1.99585	−	1.99585i	−0.0681769	−	0.0681769i	−0.740373	+	0.672196i	$0.765351\pi$
$858$		0			0
$859$	28.4574	+	11.7874i	0.970953	+	0.402182i	0.811067	−	0.584954i	$-0.198887\pi$
$859$	28.4574	+	11.7874i	0.970953	+	0.402182i	0.159886	+	0.987135i	$0.448887\pi$
$860$		0			0
$861$	1.16374	+	2.80952i	0.0396601	+	0.0957480i
$862$		0			0
$863$	56.7230			1.93087			0.965436	−	0.260639i	$-0.0839333\pi$
$863$	56.7230			1.93087			0.965436	+	0.260639i	$0.0839333\pi$
$864$		0			0
$865$	−12.6555			−0.430299
$866$		0			0
$867$	0.131196	+	0.316736i	0.00445566	+	0.0107569i
$868$		0			0
$869$	35.3329	+	14.6354i	1.19859	+	0.496471i
$870$		0			0
$871$	−43.1866	−	43.1866i	−1.46332	−	1.46332i
$872$		0			0
$873$	7.99237	−	7.99237i	0.270501	−	0.270501i
$874$		0			0
$875$	−7.68746	+	18.5592i	−0.259883	+	0.627414i
$876$		0			0
$877$	−35.4309	+	14.6760i	−1.19642	+	0.495572i	−0.889839	−	0.456274i	$-0.849184\pi$
$877$	−35.4309	+	14.6760i	−1.19642	+	0.495572i	−0.306577	+	0.951846i	$0.599184\pi$
$878$		0			0
$879$		−	20.4440i		−	0.689560i
$880$		0			0
$881$		−	16.0453i		−	0.540579i	−0.962779	−	0.270290i	$-0.912881\pi$
$881$		−	16.0453i		−	0.540579i	0.962779	−	0.270290i	$-0.0871194\pi$
$882$		0			0
$883$	−3.76841	+	1.56093i	−0.126817	+	0.0525294i	−0.445190	−	0.895436i	$-0.646864\pi$
$883$	−3.76841	+	1.56093i	−0.126817	+	0.0525294i	0.318373	+	0.947966i	$0.396864\pi$
$884$		0			0
$885$	11.6562	−	28.1405i	0.391818	−	0.945931i
$886$		0			0
$887$	−41.9135	+	41.9135i	−1.40732	+	1.40732i	−0.633923	+	0.773396i	$0.718556\pi$
$887$	−41.9135	+	41.9135i	−1.40732	+	1.40732i	−0.773396	+	0.633923i	$0.781444\pi$
$888$		0			0
$889$	−11.0071	−	11.0071i	−0.369165	−	0.369165i
$890$		0			0
$891$	3.20465	+	1.32741i	0.107360	+	0.0444699i
$892$		0			0
$893$	2.01657	+	4.86843i	0.0674819	+	0.162916i
$894$		0			0
$895$	−0.805124			−0.0269123
$896$		0			0
$897$	−16.5165			−0.551470
$898$		0			0
$899$	5.62845	+	13.5883i	0.187719	+	0.453195i
$900$		0			0
$901$	−29.2016	−	12.0957i	−0.972846	−	0.402966i
$902$		0			0
$903$	8.07791	+	8.07791i	0.268816	+	0.268816i
$904$		0			0
$905$	−20.1268	+	20.1268i	−0.669037	+	0.669037i
$906$		0			0
$907$	−8.10967	+	19.5785i	−0.269277	+	0.650093i	−0.999450	−	0.0331702i	$-0.989440\pi$
$907$	−8.10967	+	19.5785i	−0.269277	+	0.650093i	0.730173	+	0.683263i	$0.239440\pi$
$908$		0			0
$909$	3.56392	−	1.47622i	0.118208	−	0.0489632i
$910$		0			0
$911$			32.2546i			1.06864i	0.845282	+	0.534321i	$0.179433\pi$
$911$			32.2546i			1.06864i	−0.845282	+	0.534321i	$0.820567\pi$
$912$		0			0
$913$		−	8.65464i		−	0.286427i
$914$		0			0
$915$	19.5558	−	8.10028i	0.646495	−	0.267787i
$916$		0			0
$917$	22.8361	−	55.1312i	0.754114	−	1.82059i
$918$		0			0
$919$	31.0572	−	31.0572i	1.02448	−	1.02448i	0.0247905	−	0.999693i	$-0.492108\pi$
$919$	31.0572	−	31.0572i	1.02448	−	1.02448i	0.999693	−	0.0247905i	$-0.00789188\pi$
$920$		0			0
$921$	−8.24369	−	8.24369i	−0.271639	−	0.271639i
$922$		0			0
$923$	14.8384	+	6.14628i	0.488413	+	0.202307i
$924$		0			0
$925$	−6.28122	−	15.1642i	−0.206525	−	0.498596i
$926$		0			0
$927$	−2.74823			−0.0902637
$928$		0			0
$929$	−32.4744			−1.06545			−0.532725	−	0.846288i	$-0.678832\pi$
$929$	−32.4744			−1.06545			−0.532725	+	0.846288i	$0.678832\pi$
$930$		0			0
$931$	2.01687	+	4.86916i	0.0661004	+	0.159580i
$932$		0			0
$933$	−8.87268	−	3.67518i	−0.290478	−	0.120320i
$934$		0			0
$935$	27.7917	+	27.7917i	0.908884	+	0.908884i
$936$		0			0
$937$	−29.6117	+	29.6117i	−0.967373	+	0.967373i	−0.999484	−	0.0321113i	$-0.989777\pi$
$937$	−29.6117	+	29.6117i	−0.967373	+	0.967373i	0.0321113	+	0.999484i	$0.489777\pi$
$938$		0			0
$939$	6.87753	−	16.6038i	0.224440	−	0.541845i
$940$		0			0
$941$	−7.86542	+	3.25796i	−0.256405	+	0.106207i	−0.507184	−	0.861838i	$-0.669313\pi$
$941$	−7.86542	+	3.25796i	−0.256405	+	0.106207i	0.250778	+	0.968045i	$0.419313\pi$
$942$		0			0
$943$		−	2.93896i		−	0.0957058i
$944$		0			0
$945$		−	7.73523i		−	0.251627i
$946$		0			0
$947$	48.5504	−	20.1102i	1.57767	−	0.653494i	0.589631	−	0.807672i	$-0.299273\pi$
$947$	48.5504	−	20.1102i	1.57767	−	0.653494i	0.988043	+	0.154178i	$0.0492730\pi$
$948$		0			0
$949$	−22.7968	+	55.0364i	−0.740017	+	1.78656i
$950$		0			0
$951$	12.7367	−	12.7367i	0.413014	−	0.413014i
$952$		0			0
$953$	−17.0094	−	17.0094i	−0.550988	−	0.550988i	0.375738	−	0.926726i	$-0.377389\pi$
$953$	−17.0094	−	17.0094i	−0.550988	−	0.550988i	−0.926726	+	0.375738i	$0.877389\pi$
$954$		0			0
$955$	−38.1146	−	15.7876i	−1.23336	−	0.510874i
$956$		0			0
$957$	6.80219	+	16.4219i	0.219884	+	0.530846i
$958$		0			0
$959$	15.0354			0.485518
$960$		0			0
$961$	−22.7622			−0.734265
$962$		0			0
$963$	−5.35190	−	12.9206i	−0.172463	−	0.416362i
$964$		0			0
$965$	−46.1394	−	19.1116i	−1.48528	−	0.615223i
$966$		0			0
$967$	−28.7386	−	28.7386i	−0.924170	−	0.924170i	0.0731512	−	0.997321i	$-0.476694\pi$
$967$	−28.7386	−	28.7386i	−0.924170	−	0.924170i	−0.997321	+	0.0731512i	$0.976694\pi$
$968$		0			0
$969$	−14.3388	+	14.3388i	−0.460628	+	0.460628i
$970$		0			0
$971$	−12.3179	+	29.7379i	−0.395299	+	0.954336i	0.593466	+	0.804859i	$0.297759\pi$
$971$	−12.3179	+	29.7379i	−0.395299	+	0.954336i	−0.988765	+	0.149477i	$0.952241\pi$
$972$		0			0
$973$	27.8622	−	11.5409i	0.893222	−	0.369985i
$974$		0			0
$975$		−	14.4453i		−	0.462621i
$976$		0			0
$977$			13.3790i			0.428032i	0.976830	+	0.214016i	$0.0686545\pi$
$977$			13.3790i			0.428032i	−0.976830	+	0.214016i	$0.931345\pi$
$978$		0			0
$979$	−34.7065	+	14.3759i	−1.10922	+	0.459456i
$980$		0			0
$981$	5.02958	−	12.1425i	0.160582	−	0.387680i
$982$		0			0
$983$	13.7710	−	13.7710i	0.439227	−	0.439227i	−0.452525	−	0.891752i	$-0.649477\pi$
$983$	13.7710	−	13.7710i	0.439227	−	0.439227i	0.891752	+	0.452525i	$0.149477\pi$
$984$		0			0
$985$	13.8552	+	13.8552i	0.441464	+	0.441464i
$986$		0			0
$987$	−2.84243	−	1.17737i	−0.0904757	−	0.0374763i
$988$		0			0
$989$	−4.22505	−	10.2002i	−0.134349	−	0.324347i
$990$		0			0
$991$	−8.30842			−0.263926			−0.131963	−	0.991255i	$-0.542128\pi$
$991$	−8.30842			−0.263926			−0.131963	+	0.991255i	$0.542128\pi$
$992$		0			0
$993$	−0.677483			−0.0214993
$994$		0			0
$995$	1.25025	+	3.01836i	0.0396355	+	0.0956885i
$996$		0			0
$997$	25.3066	+	10.4823i	0.801468	+	0.331979i	0.745544	−	0.666456i	$-0.232190\pi$
$997$	25.3066	+	10.4823i	0.801468	+	0.331979i	0.0559236	+	0.998435i	$0.482190\pi$
$998$		0			0
$999$	−4.82984	−	4.82984i	−0.152809	−	0.152809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.481.3		32
4.3	odd	2		768.2.n.a.481.7		32
8.3	odd	2		96.2.n.a.37.8	yes	32
8.5	even	2		384.2.n.a.241.6		32
24.5	odd	2		1152.2.v.c.1009.7		32
24.11	even	2		288.2.v.d.37.1		32
32.3	odd	8		96.2.n.a.13.8	✓	32
32.13	even	8	inner	768.2.n.b.289.3		32
32.19	odd	8		768.2.n.a.289.7		32
32.29	even	8		384.2.n.a.145.6		32
96.29	odd	8		1152.2.v.c.145.7		32
96.35	even	8		288.2.v.d.109.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.8	✓	32	32.3	odd	8
96.2.n.a.37.8	yes	32	8.3	odd	2
288.2.v.d.37.1		32	24.11	even	2
288.2.v.d.109.1		32	96.35	even	8
384.2.n.a.145.6		32	32.29	even	8
384.2.n.a.241.6		32	8.5	even	2
768.2.n.a.289.7		32	32.19	odd	8
768.2.n.a.481.7		32	4.3	odd	2
768.2.n.b.289.3		32	32.13	even	8	inner
768.2.n.b.481.3		32	1.1	even	1	trivial
1152.2.v.c.145.7		32	96.29	odd	8
1152.2.v.c.1009.7		32	24.5	odd	2

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 - 0.923880i) q^{3} +(2.51374 + 1.04122i) q^{5} +(-2.01027 - 2.01027i) q^{7} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.382683 - 0.923880i) q^{3} +(2.51374 + 1.04122i) q^{5} +(-2.01027 - 2.01027i) q^{7} +(-0.707107 + 0.707107i) q^{9} +(-1.32741 + 3.20465i) q^{11} +(5.55375 - 2.30044i) q^{13} -2.72085i q^{15} -4.16447i q^{17} +(4.49866 - 1.86340i) q^{19} +(-1.08795 + 2.62654i) q^{21} +(1.94282 - 1.94282i) q^{23} +(1.69919 + 1.69919i) q^{25} +(0.923880 + 0.382683i) q^{27} +(1.96103 + 4.73434i) q^{29} +2.87015 q^{31} +3.46869 q^{33} +(-2.96015 - 7.14642i) q^{35} +(-6.31049 - 2.61389i) q^{37} +(-4.25066 - 4.25066i) q^{39} +(0.756366 - 0.756366i) q^{41} +(1.53775 - 3.71245i) q^{43} +(-2.51374 + 1.04122i) q^{45} +1.08220i q^{47} +1.08236i q^{49} +(-3.84747 + 1.59367i) q^{51} +(2.90450 - 7.01208i) q^{53} +(-6.67351 + 6.67351i) q^{55} +(-3.44312 - 3.44312i) q^{57} +(10.3425 + 4.28402i) q^{59} +(2.97711 + 7.18739i) q^{61} +2.84295 q^{63} +16.3559 q^{65} +(-3.88805 - 9.38659i) q^{67} +(-2.53841 - 1.05145i) q^{69} +(1.88924 + 1.88924i) q^{71} +(-7.00727 + 7.00727i) q^{73} +(0.919594 - 2.22010i) q^{75} +(9.11066 - 3.77376i) q^{77} -11.0255i q^{79} -1.00000i q^{81} +(-2.30515 + 0.954824i) q^{83} +(4.33615 - 10.4684i) q^{85} +(3.62351 - 3.62351i) q^{87} +(7.65800 + 7.65800i) q^{89} +(-15.7890 - 6.54003i) q^{91} +(-1.09836 - 2.65168i) q^{93} +13.2487 q^{95} -11.3029 q^{97} +(-1.32741 - 3.20465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} - 48 q^{35} - 16 q^{43} + 16 q^{51} + 32 q^{53} - 32 q^{55} + 64 q^{59} + 32 q^{61} - 16 q^{63} + 16 q^{67} + 32 q^{69} - 64 q^{71} + 32 q^{75} + 32 q^{77} - 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 - 48 * q^35 - 16 * q^43 + 16 * q^51 + 32 * q^53 - 32 * q^55 + 64 * q^59 + 32 * q^61 - 16 * q^63 + 16 * q^67 + 32 * q^69 - 64 * q^71 + 32 * q^75 + 32 * q^77 - 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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