LMFDB - Embedded newform 768.2.n.b.97.6

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			97.6
Character	$\chi$	$=$	768.97
Dual form			768.2.n.b.673.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 - 0.382683i) q^{3} +(0.00259461 - 0.00626394i) q^{5} +(2.41880 + 2.41880i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(0.923880 - 0.382683i) q^{3} +(0.00259461 - 0.00626394i) q^{5} +(2.41880 + 2.41880i) q^{7} +(0.707107 - 0.707107i) q^{9} +(1.29952 + 0.538278i) q^{11} +(0.559497 + 1.35074i) q^{13} -0.00678004i q^{15} +5.82199i q^{17} +(-2.67819 - 6.46573i) q^{19} +(3.16031 + 1.30904i) q^{21} +(-0.178878 + 0.178878i) q^{23} +(3.53550 + 3.53550i) q^{25} +(0.382683 - 0.923880i) q^{27} +(-5.72901 + 2.37303i) q^{29} +6.19719 q^{31} +1.40659 q^{33} +(0.0214270 - 0.00887537i) q^{35} +(2.02932 - 4.89922i) q^{37} +(1.03381 + 1.03381i) q^{39} +(-3.36712 + 3.36712i) q^{41} +(9.37558 + 3.88349i) q^{43} +(-0.00259461 - 0.00626394i) q^{45} -12.5050i q^{47} +4.70117i q^{49} +(2.22798 + 5.37882i) q^{51} +(8.36811 + 3.46618i) q^{53} +(0.00674348 - 0.00674348i) q^{55} +(-4.94866 - 4.94866i) q^{57} +(1.59507 - 3.85084i) q^{59} +(-7.27395 + 3.01297i) q^{61} +3.42070 q^{63} +0.00991266 q^{65} +(-4.38775 + 1.81747i) q^{67} +(-0.0968082 + 0.233716i) q^{69} +(-5.95188 - 5.95188i) q^{71} +(7.85539 - 7.85539i) q^{73} +(4.61936 + 1.91340i) q^{75} +(1.84128 + 4.44525i) q^{77} +1.42456i q^{79} -1.00000i q^{81} +(-3.03596 - 7.32946i) q^{83} +(0.0364686 + 0.0151058i) q^{85} +(-4.38479 + 4.38479i) q^{87} +(-9.96127 - 9.96127i) q^{89} +(-1.91387 + 4.62049i) q^{91} +(5.72545 - 2.37156i) q^{93} -0.0474498 q^{95} -1.24058 q^{97} +(1.29952 - 0.538278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

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
$3$	0.923880	−	0.382683i	0.533402	−	0.220942i
$3$	0.923880	−	0.382683i	0.533402	−	0.220942i
$4$		0			0
$5$	0.00259461	−	0.00626394i	0.00116034	−	0.00280132i	−0.923298	−	0.384084i	$-0.874517\pi$
$5$	0.00259461	−	0.00626394i	0.00116034	−	0.00280132i	0.924459	+	0.381282i	$0.124517\pi$
$6$		0			0
$7$	2.41880	+	2.41880i	0.914220	+	0.914220i	0.996601	−	0.0823812i	$-0.0262525\pi$
$7$	2.41880	+	2.41880i	0.914220	+	0.914220i	−0.0823812	+	0.996601i	$0.526253\pi$
$8$		0			0
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$		0			0
$11$	1.29952	+	0.538278i	0.391819	+	0.162297i	0.569890	−	0.821721i	$-0.306986\pi$
$11$	1.29952	+	0.538278i	0.391819	+	0.162297i	−0.178071	+	0.984018i	$0.556986\pi$
$12$		0			0
$13$	0.559497	+	1.35074i	0.155176	+	0.374629i	0.982280	−	0.187421i	$-0.0600128\pi$
$13$	0.559497	+	1.35074i	0.155176	+	0.374629i	−0.827103	+	0.562050i	$0.810013\pi$
$14$		0			0
$15$		−	0.00678004i		−	0.00175060i
$16$		0			0
$17$			5.82199i			1.41204i	0.708192	+	0.706020i	$0.249511\pi$
$17$			5.82199i			1.41204i	−0.708192	+	0.706020i	$0.750489\pi$
$18$		0			0
$19$	−2.67819	−	6.46573i	−0.614420	−	1.48334i	−0.858099	−	0.513484i	$-0.828354\pi$
$19$	−2.67819	−	6.46573i	−0.614420	−	1.48334i	0.243679	−	0.969856i	$-0.421646\pi$
$20$		0			0
$21$	3.16031	+	1.30904i	0.689637	+	0.285657i
$22$		0			0
$23$	−0.178878	+	0.178878i	−0.0372987	+	0.0372987i	−0.725510	−	0.688211i	$-0.758396\pi$
$23$	−0.178878	+	0.178878i	−0.0372987	+	0.0372987i	0.688211	+	0.725510i	$0.258396\pi$
$24$		0			0
$25$	3.53550	+	3.53550i	0.707100	+	0.707100i
$26$		0			0
$27$	0.382683	−	0.923880i	0.0736475	−	0.177801i
$28$		0			0
$29$	−5.72901	+	2.37303i	−1.06385	+	0.440661i	−0.844817	−	0.535056i	$-0.820290\pi$
$29$	−5.72901	+	2.37303i	−1.06385	+	0.440661i	−0.219034	+	0.975717i	$0.570290\pi$
$30$		0			0
$31$	6.19719			1.11305			0.556524	−	0.830832i	$-0.312135\pi$
$31$	6.19719			1.11305			0.556524	+	0.830832i	$0.312135\pi$
$32$		0			0
$33$	1.40659			0.244855
$34$		0			0
$35$	0.0214270	−	0.00887537i	0.00362183	−	0.00150021i
$36$		0			0
$37$	2.02932	−	4.89922i	0.333619	−	0.805427i	−0.664680	−	0.747128i	$-0.731432\pi$
$37$	2.02932	−	4.89922i	0.333619	−	0.805427i	0.998299	−	0.0582992i	$-0.0185677\pi$
$38$		0			0
$39$	1.03381	+	1.03381i	0.165543	+	0.165543i
$40$		0			0
$41$	−3.36712	+	3.36712i	−0.525856	+	0.525856i	−0.919334	−	0.393478i	$-0.871272\pi$
$41$	−3.36712	+	3.36712i	−0.525856	+	0.525856i	0.393478	+	0.919334i	$0.371272\pi$
$42$		0			0
$43$	9.37558	+	3.88349i	1.42976	+	0.592227i	0.957293	−	0.289120i	$-0.0933625\pi$
$43$	9.37558	+	3.88349i	1.42976	+	0.592227i	0.472470	+	0.881347i	$0.343363\pi$
$44$		0			0
$45$	−0.00259461	−	0.00626394i	−0.000386782	−	0.000933773i
$46$		0			0
$47$		−	12.5050i		−	1.82405i	−0.410137	−	0.912024i	$-0.634519\pi$
$47$		−	12.5050i		−	1.82405i	0.410137	−	0.912024i	$-0.365481\pi$
$48$		0			0
$49$			4.70117i			0.671595i
$50$		0			0
$51$	2.22798	+	5.37882i	0.311979	+	0.753185i
$52$		0			0
$53$	8.36811	+	3.46618i	1.14945	+	0.476117i	0.874348	−	0.485299i	$-0.161289\pi$
$53$	8.36811	+	3.46618i	1.14945	+	0.476117i	0.275100	+	0.961416i	$0.411289\pi$
$54$		0			0
$55$	0.00674348	−	0.00674348i	0.000909291	−	0.000909291i
$56$		0			0
$57$	−4.94866	−	4.94866i	−0.655465	−	0.655465i
$58$		0			0
$59$	1.59507	−	3.85084i	0.207661	−	0.501337i	−0.785393	−	0.618997i	$-0.787539\pi$
$59$	1.59507	−	3.85084i	0.207661	−	0.501337i	0.993054	+	0.117660i	$0.0375392\pi$
$60$		0			0
$61$	−7.27395	+	3.01297i	−0.931333	+	0.385771i	−0.796184	−	0.605054i	$-0.793151\pi$
$61$	−7.27395	+	3.01297i	−0.931333	+	0.385771i	−0.135149	+	0.990825i	$0.543151\pi$
$62$		0			0
$63$	3.42070			0.430967
$64$		0			0
$65$	0.00991266			0.00122951
$66$		0			0
$67$	−4.38775	+	1.81747i	−0.536049	+	0.222039i	−0.634250	−	0.773128i	$-0.718691\pi$
$67$	−4.38775	+	1.81747i	−0.536049	+	0.222039i	0.0982011	+	0.995167i	$0.468691\pi$
$68$		0			0
$69$	−0.0968082	+	0.233716i	−0.0116543	+	0.0281361i
$70$		0			0
$71$	−5.95188	−	5.95188i	−0.706358	−	0.706358i	0.259409	−	0.965768i	$-0.416472\pi$
$71$	−5.95188	−	5.95188i	−0.706358	−	0.706358i	−0.965768	+	0.259409i	$0.916472\pi$
$72$		0			0
$73$	7.85539	−	7.85539i	0.919404	−	0.919404i	−0.0775823	−	0.996986i	$-0.524720\pi$
$73$	7.85539	−	7.85539i	0.919404	−	0.919404i	0.996986	+	0.0775823i	$0.0247201\pi$
$74$		0			0
$75$	4.61936	+	1.91340i	0.533397	+	0.220940i
$76$		0			0
$77$	1.84128	+	4.44525i	0.209834	+	0.506584i
$78$		0			0
$79$			1.42456i			0.160276i	0.996784	+	0.0801378i	$0.0255360\pi$
$79$			1.42456i			0.160276i	−0.996784	+	0.0801378i	$0.974464\pi$
$80$		0			0
$81$		−	1.00000i		−	0.111111i
$82$		0			0
$83$	−3.03596	−	7.32946i	−0.333240	−	0.804513i	−0.998331	−	0.0577507i	$-0.981607\pi$
$83$	−3.03596	−	7.32946i	−0.333240	−	0.804513i	0.665091	−	0.746763i	$-0.268393\pi$
$84$		0			0
$85$	0.0364686	+	0.0151058i	0.00395557	+	0.00163845i
$86$		0			0
$87$	−4.38479	+	4.38479i	−0.470099	+	0.470099i
$88$		0			0
$89$	−9.96127	−	9.96127i	−1.05589	−	1.05589i	−0.998343	−	0.0575498i	$-0.981671\pi$
$89$	−9.96127	−	9.96127i	−1.05589	−	1.05589i	−0.0575498	−	0.998343i	$-0.518329\pi$
$90$		0			0
$91$	−1.91387	+	4.62049i	−0.200628	+	0.484359i
$92$		0			0
$93$	5.72545	−	2.37156i	0.593702	−	0.245919i
$94$		0			0
$95$	−0.0474498			−0.00486825
$96$		0			0
$97$	−1.24058			−0.125961			−0.0629807	−	0.998015i	$-0.520061\pi$
$97$	−1.24058			−0.125961			−0.0629807	+	0.998015i	$0.520061\pi$
$98$		0			0
$99$	1.29952	−	0.538278i	0.130606	−	0.0540989i
$100$		0			0
$101$	−6.15953	+	14.8704i	−0.612896	+	1.47966i	0.246908	+	0.969039i	$0.420585\pi$
$101$	−6.15953	+	14.8704i	−0.612896	+	1.47966i	−0.859804	+	0.510624i	$0.829415\pi$
$102$		0			0
$103$	5.60558	+	5.60558i	0.552334	+	0.552334i	0.927114	−	0.374779i	$-0.122282\pi$
$103$	5.60558	+	5.60558i	0.552334	+	0.552334i	−0.374779	+	0.927114i	$0.622282\pi$
$104$		0			0
$105$	0.0163995	−	0.0163995i	0.00160043	−	0.00160043i
$106$		0			0
$107$	−5.46375	−	2.26316i	−0.528201	−	0.218788i	0.102614	−	0.994721i	$-0.467279\pi$
$107$	−5.46375	−	2.26316i	−0.528201	−	0.218788i	−0.630815	+	0.775933i	$0.717279\pi$
$108$		0			0
$109$	0.982918	+	2.37297i	0.0941464	+	0.227290i	0.963936	−	0.266132i	$-0.0857458\pi$
$109$	0.982918	+	2.37297i	0.0941464	+	0.227290i	−0.869790	+	0.493422i	$0.835746\pi$
$110$		0			0
$111$		−	5.30288i		−	0.503327i
$112$		0			0
$113$			4.42809i			0.416560i	0.978069	+	0.208280i	$0.0667865\pi$
$113$			4.42809i			0.416560i	−0.978069	+	0.208280i	$0.933213\pi$
$114$		0			0
$115$	0.000656364		0.00158460i	6.12062e−5		0.000147765i
$116$		0			0
$117$	1.35074	+	0.559497i	0.124876	+	0.0517255i
$118$		0			0
$119$	−14.0822	+	14.0822i	−1.29091	+	1.29091i
$120$		0			0
$121$	−6.37917	−	6.37917i	−0.579925	−	0.579925i
$122$		0			0
$123$	−1.82227	+	4.39936i	−0.164309	+	0.396677i
$124$		0			0
$125$	0.0626391	−	0.0259460i	0.00560261	−	0.00232068i
$126$		0			0
$127$	−14.5930			−1.29492			−0.647458	−	0.762101i	$-0.724168\pi$
$127$	−14.5930			−1.29492			−0.647458	+	0.762101i	$0.724168\pi$
$128$		0			0
$129$	10.1481			0.893487
$130$		0			0
$131$	−8.62727	+	3.57353i	−0.753768	+	0.312221i	−0.726278	−	0.687401i	$-0.758752\pi$
$131$	−8.62727	+	3.57353i	−0.753768	+	0.312221i	−0.0274902	+	0.999622i	$0.508752\pi$
$132$		0			0
$133$	9.16129	−	22.1173i	0.794384	−	1.91781i
$134$		0			0
$135$	−0.00479421	−	0.00479421i	−0.000412620	−	0.000412620i
$136$		0			0
$137$	−0.109126	+	0.109126i	−0.00932323	+	0.00932323i	−0.711753	−	0.702430i	$-0.752098\pi$
$137$	−0.109126	+	0.109126i	−0.00932323	+	0.00932323i	0.702430	+	0.711753i	$0.252098\pi$
$138$		0			0
$139$	5.80724	+	2.40544i	0.492564	+	0.204027i	0.615118	−	0.788435i	$-0.289108\pi$
$139$	5.80724	+	2.40544i	0.492564	+	0.204027i	−0.122554	+	0.992462i	$0.539108\pi$
$140$		0			0
$141$	−4.78547	−	11.5532i	−0.403009	−	0.972951i
$142$		0			0
$143$			2.05648i			0.171971i
$144$		0			0
$145$			0.0420433i			0.00349150i
$146$		0			0
$147$	1.79906	+	4.34331i	0.148384	+	0.358230i
$148$		0			0
$149$	−15.4722	−	6.40879i	−1.26753	−	0.525028i	−0.355318	−	0.934745i	$-0.615627\pi$
$149$	−15.4722	−	6.40879i	−1.26753	−	0.525028i	−0.912213	+	0.409717i	$0.865627\pi$
$150$		0			0
$151$	9.38822	−	9.38822i	0.764003	−	0.764003i	−0.213041	−	0.977043i	$-0.568337\pi$
$151$	9.38822	−	9.38822i	0.764003	−	0.764003i	0.977043	+	0.213041i	$0.0683367\pi$
$152$		0			0
$153$	4.11677	+	4.11677i	0.332821	+	0.332821i
$154$		0			0
$155$	0.0160793	−	0.0388188i	0.00129152	−	0.00311800i
$156$		0			0
$157$	0.959615	−	0.397486i	0.0765856	−	0.0317228i	−0.344062	−	0.938947i	$-0.611803\pi$
$157$	0.959615	−	0.397486i	0.0765856	−	0.0317228i	0.420647	+	0.907224i	$0.361803\pi$
$158$		0			0
$159$	9.05757			0.718312
$160$		0			0
$161$	−0.865341			−0.0681984
$162$		0			0
$163$	−7.39543	+	3.06329i	−0.579255	+	0.239935i	−0.653020	−	0.757340i	$-0.726498\pi$
$163$	−7.39543	+	3.06329i	−0.579255	+	0.239935i	0.0737655	+	0.997276i	$0.476498\pi$
$164$		0			0
$165$	0.00364954	−	0.00881078i	0.000284117	−	0.000685918i
$166$		0			0
$167$	−0.697073	−	0.697073i	−0.0539412	−	0.0539412i	0.679622	−	0.733563i	$-0.262144\pi$
$167$	−0.697073	−	0.697073i	−0.0539412	−	0.0539412i	−0.733563	+	0.679622i	$0.762144\pi$
$168$		0			0
$169$	7.68091	−	7.68091i	0.590840	−	0.590840i
$170$		0			0
$171$	−6.46573	−	2.67819i	−0.494447	−	0.204807i
$172$		0			0
$173$	−6.61178	−	15.9623i	−0.502685	−	1.21359i	−0.948016	−	0.318222i	$-0.896914\pi$
$173$	−6.61178	−	15.9623i	−0.502685	−	1.21359i	0.445331	−	0.895366i	$-0.353086\pi$
$174$		0			0
$175$			17.1033i			1.29289i
$176$		0			0
$177$		−	4.16812i		−	0.313295i
$178$		0			0
$179$	1.14101	+	2.75465i	0.0852832	+	0.205892i	0.960768	−	0.277354i	$-0.0894576\pi$
$179$	1.14101	+	2.75465i	0.0852832	+	0.205892i	−0.875484	+	0.483246i	$0.839458\pi$
$180$		0			0
$181$	6.23325	+	2.58190i	0.463314	+	0.191911i	0.602115	−	0.798409i	$-0.294325\pi$
$181$	6.23325	+	2.58190i	0.463314	+	0.191911i	−0.138801	+	0.990320i	$0.544325\pi$
$182$		0			0
$183$	−5.56724	+	5.56724i	−0.411542	+	0.411542i
$184$		0			0
$185$	−0.0254231	−	0.0254231i	−0.00186915	−	0.00186915i
$186$		0			0
$187$	−3.13385	+	7.56577i	−0.229170	+	0.553264i
$188$		0			0
$189$	3.16031	−	1.30904i	0.229879	−	0.0952189i
$190$		0			0
$191$	5.12197			0.370613			0.185306	−	0.982681i	$-0.440672\pi$
$191$	5.12197			0.370613			0.185306	+	0.982681i	$0.440672\pi$
$192$		0			0
$193$	−20.7951			−1.49686			−0.748431	−	0.663213i	$-0.769192\pi$
$193$	−20.7951			−1.49686			−0.748431	+	0.663213i	$0.769192\pi$
$194$		0			0
$195$	0.00915810	−	0.00379341i	0.000655825	−	0.000271652i
$196$		0			0
$197$	3.47339	−	8.38550i	0.247469	−	0.597442i	−0.750519	−	0.660849i	$-0.770196\pi$
$197$	3.47339	−	8.38550i	0.247469	−	0.597442i	0.997988	+	0.0634065i	$0.0201965\pi$
$198$		0			0
$199$	−9.79652	−	9.79652i	−0.694457	−	0.694457i	0.268753	−	0.963209i	$-0.413389\pi$
$199$	−9.79652	−	9.79652i	−0.694457	−	0.694457i	−0.963209	+	0.268753i	$0.913389\pi$
$200$		0			0
$201$	−3.35824	+	3.35824i	−0.236872	+	0.236872i
$202$		0			0
$203$	−19.5972	−	8.11743i	−1.37545	−	0.569732i
$204$		0			0
$205$	0.0123551	+	0.0298278i	0.000862917	+	0.00208326i
$206$		0			0
$207$			0.252972i			0.0175828i
$208$		0			0
$209$		−	9.84394i		−	0.680919i
$210$		0			0
$211$	−2.59646	−	6.26841i	−0.178748	−	0.431535i	0.808957	−	0.587868i	$-0.200033\pi$
$211$	−2.59646	−	6.26841i	−0.178748	−	0.431535i	−0.987704	+	0.156333i	$0.950033\pi$
$212$		0			0
$213$	−7.77651	−	3.22114i	−0.532838	−	0.220709i
$214$		0			0
$215$	0.0486519	−	0.0486519i	0.00331804	−	0.00331804i
$216$		0			0
$217$	14.9897	+	14.9897i	1.01757	+	1.01757i
$218$		0			0
$219$	4.25131	−	10.2636i	0.287277	−	0.693547i
$220$		0			0
$221$	−7.86402	+	3.25738i	−0.528991	+	0.219115i
$222$		0			0
$223$	−14.6051			−0.978032			−0.489016	−	0.872275i	$-0.662644\pi$
$223$	−14.6051			−0.978032			−0.489016	+	0.872275i	$0.662644\pi$
$224$		0			0
$225$	4.99995			0.333330
$226$		0			0
$227$	−3.75119	+	1.55379i	−0.248975	+	0.103129i	−0.503681	−	0.863890i	$-0.668021\pi$
$227$	−3.75119	+	1.55379i	−0.248975	+	0.103129i	0.254706	+	0.967019i	$0.418021\pi$
$228$		0			0
$229$	−2.06540	+	4.98631i	−0.136485	+	0.329505i	−0.977314	−	0.211797i	$-0.932068\pi$
$229$	−2.06540	+	4.98631i	−0.136485	+	0.329505i	0.840828	+	0.541302i	$0.182068\pi$
$230$		0			0
$231$	3.40225	+	3.40225i	0.223852	+	0.223852i
$232$		0			0
$233$	−20.5003	+	20.5003i	−1.34302	+	1.34302i	−0.449987	+	0.893035i	$0.648572\pi$
$233$	−20.5003	+	20.5003i	−1.34302	+	1.34302i	−0.893035	+	0.449987i	$0.851428\pi$
$234$		0			0
$235$	−0.0783308	−	0.0324457i	−0.00510974	−	0.00211652i
$236$		0			0
$237$	0.545156	+	1.31612i	0.0354117	+	0.0854913i
$238$		0			0
$239$			2.23671i			0.144680i	0.997380	+	0.0723402i	$0.0230467\pi$
$239$			2.23671i			0.144680i	−0.997380	+	0.0723402i	$0.976953\pi$
$240$		0			0
$241$		−	19.6755i		−	1.26741i	−0.773575	−	0.633704i	$-0.781534\pi$
$241$		−	19.6755i		−	1.26741i	0.773575	−	0.633704i	$-0.218466\pi$
$242$		0			0
$243$	−0.382683	−	0.923880i	−0.0245492	−	0.0592669i
$244$		0			0
$245$	0.0294478	+	0.0121977i	0.00188135	+	0.000779282i
$246$		0			0
$247$	7.23511	−	7.23511i	0.460359	−	0.460359i
$248$		0			0
$249$	−5.60973	−	5.60973i	−0.355502	−	0.355502i
$250$		0			0
$251$	2.41942	−	5.84100i	0.152712	−	0.368680i	−0.828946	−	0.559329i	$-0.811059\pi$
$251$	2.41942	−	5.84100i	0.152712	−	0.368680i	0.981658	+	0.190648i	$0.0610590\pi$
$252$		0			0
$253$	−0.328742	+	0.136169i	−0.0206678	+	0.00856088i
$254$		0			0
$255$	0.0394733			0.00247191
$256$		0			0
$257$	9.46013			0.590106			0.295053	−	0.955481i	$-0.404663\pi$
$257$	9.46013			0.590106			0.295053	+	0.955481i	$0.404663\pi$
$258$		0			0
$259$	16.7588	−	6.94170i	1.04134	−	0.431336i
$260$		0			0
$261$	−2.37303	+	5.72901i	−0.146887	+	0.354617i
$262$		0			0
$263$	7.01762	+	7.01762i	0.432725	+	0.432725i	0.889554	−	0.456829i	$-0.151015\pi$
$263$	7.01762	+	7.01762i	0.432725	+	0.432725i	−0.456829	+	0.889554i	$0.651015\pi$
$264$		0			0
$265$	0.0434239	−	0.0434239i	0.00266751	−	0.00266751i
$266$		0			0
$267$	−13.0150	−	5.39100i	−0.796507	−	0.329924i
$268$		0			0
$269$	−0.579856	−	1.39990i	−0.0353545	−	0.0853532i	0.905216	−	0.424952i	$-0.139709\pi$
$269$	−0.579856	−	1.39990i	−0.0353545	−	0.0853532i	−0.940571	+	0.339598i	$0.889709\pi$
$270$		0			0
$271$			2.19594i			0.133394i	0.997773	+	0.0666969i	$0.0212460\pi$
$271$			2.19594i			0.133394i	−0.997773	+	0.0666969i	$0.978754\pi$
$272$		0			0
$273$			5.00118i			0.302685i
$274$		0			0
$275$	2.69136	+	6.49753i	0.162295	+	0.391816i
$276$		0			0
$277$	−24.0612	−	9.96649i	−1.44570	−	0.598829i	−0.484527	−	0.874776i	$-0.661008\pi$
$277$	−24.0612	−	9.96649i	−1.44570	−	0.598829i	−0.961173	+	0.275948i	$0.911008\pi$
$278$		0			0
$279$	4.38207	−	4.38207i	0.262348	−	0.262348i
$280$		0			0
$281$	18.0180	+	18.0180i	1.07487	+	1.07487i	0.996961	+	0.0779048i	$0.0248230\pi$
$281$	18.0180	+	18.0180i	1.07487	+	1.07487i	0.0779048	+	0.996961i	$0.475177\pi$
$282$		0			0
$283$	−1.15856	+	2.79702i	−0.0688695	+	0.166266i	−0.954566	−	0.297998i	$-0.903681\pi$
$283$	−1.15856	+	2.79702i	−0.0688695	+	0.166266i	0.885697	+	0.464264i	$0.153681\pi$
$284$		0			0
$285$	−0.0438379	+	0.0181583i	−0.00259673	+	0.00107560i
$286$		0			0
$287$	−16.2888			−0.961496
$288$		0			0
$289$	−16.8955			−0.993855
$290$		0			0
$291$	−1.14614	+	0.474748i	−0.0671881	+	0.0278302i
$292$		0			0
$293$	−3.52001	+	8.49805i	−0.205641	+	0.496461i	−0.992728	−	0.120381i	$-0.961588\pi$
$293$	−3.52001	+	8.49805i	−0.205641	+	0.496461i	0.787087	+	0.616842i	$0.211588\pi$
$294$		0			0
$295$	−0.0199829	−	0.0199829i	−0.00116345	−	0.00116345i
$296$		0			0
$297$	0.994607	−	0.994607i	0.0577130	−	0.0577130i
$298$		0			0
$299$	−0.341700	−	0.141537i	−0.0197610	−	0.00818529i
$300$		0			0
$301$	13.2843	+	32.0710i	0.765692	+	1.84854i
$302$		0			0
$303$			16.0956i			0.924670i
$304$		0			0
$305$			0.0533810i			0.00305659i
$306$		0			0
$307$	−1.41754	−	3.42224i	−0.0809032	−	0.195318i	0.878252	−	0.478198i	$-0.158710\pi$
$307$	−1.41754	−	3.42224i	−0.0809032	−	0.195318i	−0.959155	+	0.282881i	$0.908710\pi$
$308$		0			0
$309$	7.32405	+	3.03372i	0.416650	+	0.172582i
$310$		0			0
$311$	22.4396	−	22.4396i	1.27243	−	1.27243i	0.327622	−	0.944809i	$-0.393753\pi$
$311$	22.4396	−	22.4396i	1.27243	−	1.27243i	0.944809	−	0.327622i	$-0.106247\pi$
$312$		0			0
$313$	−2.24961	−	2.24961i	−0.127155	−	0.127155i	0.640665	−	0.767821i	$-0.278659\pi$
$313$	−2.24961	−	2.24961i	−0.127155	−	0.127155i	−0.767821	+	0.640665i	$0.778659\pi$
$314$		0			0
$315$	0.00887537	−	0.0214270i	0.000500071	−	0.00120728i
$316$		0			0
$317$	31.4340	−	13.0204i	1.76551	−	0.731298i	0.769852	−	0.638223i	$-0.220330\pi$
$317$	31.4340	−	13.0204i	1.76551	−	0.731298i	0.995659	−	0.0930756i	$-0.0296698\pi$
$318$		0			0
$319$	−8.72230			−0.488355
$320$		0			0
$321$	−5.91392			−0.330083
$322$		0			0
$323$	37.6434	−	15.5924i	2.09453	−	0.867585i
$324$		0			0
$325$	−2.79746	+	6.75366i	−0.155175	+	0.374626i
$326$		0			0
$327$	1.81620	+	1.81620i	0.100436	+	0.100436i
$328$		0			0
$329$	30.2472	−	30.2472i	1.66758	−	1.66758i
$330$		0			0
$331$	24.6043	+	10.1914i	1.35237	+	0.560172i	0.936952	−	0.349457i	$-0.113634\pi$
$331$	24.6043	+	10.1914i	1.35237	+	0.560172i	0.415422	+	0.909629i	$0.363634\pi$
$332$		0			0
$333$	−2.02932	−	4.89922i	−0.111206	−	0.268476i
$334$		0			0
$335$			0.0322002i			0.00175929i
$336$		0			0
$337$		−	20.1009i		−	1.09497i	−0.836817	−	0.547483i	$-0.815586\pi$
$337$		−	20.1009i		−	1.09497i	0.836817	−	0.547483i	$-0.184414\pi$
$338$		0			0
$339$	1.69456	+	4.09103i	0.0920358	+	0.222194i
$340$		0			0
$341$	8.05335	+	3.33581i	0.436113	+	0.180644i
$342$		0			0
$343$	5.56041	−	5.56041i	0.300234	−	0.300234i
$344$		0			0
$345$	0.00121280	+	0.00121280i	6.52950e−5	+	6.52950e-5i
$346$		0			0
$347$	−5.23707	+	12.6434i	−0.281141	+	0.678734i	−0.999863	−	0.0165638i	$-0.994727\pi$
$347$	−5.23707	+	12.6434i	−0.281141	+	0.678734i	0.718722	+	0.695297i	$0.244727\pi$
$348$		0			0
$349$	16.5877	−	6.87085i	0.887920	−	0.367788i	0.108357	−	0.994112i	$-0.465441\pi$
$349$	16.5877	−	6.87085i	0.887920	−	0.367788i	0.779563	+	0.626324i	$0.215441\pi$
$350$		0			0
$351$	1.46203			0.0780377
$352$		0			0
$353$	10.8817			0.579174			0.289587	−	0.957152i	$-0.406482\pi$
$353$	10.8817			0.579174			0.289587	+	0.957152i	$0.406482\pi$
$354$		0			0
$355$	−0.0527250	+	0.0218394i	−0.00279835	+	0.00115912i
$356$		0			0
$357$	−7.62124	+	18.3993i	−0.403359	+	0.973794i
$358$		0			0
$359$	−5.54201	−	5.54201i	−0.292496	−	0.292496i	0.545570	−	0.838066i	$-0.316313\pi$
$359$	−5.54201	−	5.54201i	−0.292496	−	0.292496i	−0.838066	+	0.545570i	$0.816313\pi$
$360$		0			0
$361$	−21.1979	+	21.1979i	−1.11568	+	1.11568i
$362$		0			0
$363$	−8.33479	−	3.45238i	−0.437463	−	0.181203i
$364$		0			0
$365$	−0.0288240	−	0.0695874i	−0.00150872	−	0.00364237i
$366$		0			0
$367$		−	2.99994i		−	0.156596i	−0.996930	−	0.0782979i	$-0.975051\pi$
$367$		−	2.99994i		−	0.156596i	0.996930	−	0.0782979i	$-0.0249485\pi$
$368$		0			0
$369$			4.76183i			0.247891i
$370$		0			0
$371$	11.8568	+	28.6248i	0.615572	+	1.48612i
$372$		0			0
$373$	15.3503	+	6.35832i	0.794811	+	0.329221i	0.742876	−	0.669429i	$-0.233461\pi$
$373$	15.3503	+	6.35832i	0.794811	+	0.329221i	0.0519347	+	0.998650i	$0.483461\pi$
$374$		0			0
$375$	0.0479419	−	0.0479419i	0.00247571	−	0.00247571i
$376$		0			0
$377$	−6.41072	−	6.41072i	−0.330169	−	0.330169i
$378$		0			0
$379$	−2.50517	+	6.04801i	−0.128682	+	0.310665i	−0.975069	−	0.221903i	$-0.928773\pi$
$379$	−2.50517	+	6.04801i	−0.128682	+	0.310665i	0.846387	+	0.532568i	$0.178773\pi$
$380$		0			0
$381$	−13.4821	+	5.58448i	−0.690711	+	0.286102i
$382$		0			0
$383$	32.1450			1.64253			0.821266	−	0.570545i	$-0.193268\pi$
$383$	32.1450			1.64253			0.821266	+	0.570545i	$0.193268\pi$
$384$		0			0
$385$	0.0326222			0.00166258
$386$		0			0
$387$	9.37558	−	3.88349i	0.476588	−	0.197409i
$388$		0			0
$389$	−2.48310	+	5.99473i	−0.125898	+	0.303945i	−0.974244	−	0.225498i	$-0.927599\pi$
$389$	−2.48310	+	5.99473i	−0.125898	+	0.303945i	0.848346	+	0.529443i	$0.177599\pi$
$390$		0			0
$391$	−1.04143	−	1.04143i	−0.0526672	−	0.0526672i
$392$		0			0
$393$	−6.60303	+	6.60303i	−0.333079	+	0.333079i
$394$		0			0
$395$	0.00892336	+	0.00369618i	0.000448983	+	0.000185975i
$396$		0			0
$397$	9.62118	+	23.2276i	0.482873	+	1.16576i	0.958238	+	0.285970i	$0.0923159\pi$
$397$	9.62118	+	23.2276i	0.482873	+	1.16576i	−0.475365	+	0.879788i	$0.657684\pi$
$398$		0			0
$399$		−	23.9396i		−	1.19848i
$400$		0			0
$401$			4.48158i			0.223800i	0.993719	+	0.111900i	$0.0356936\pi$
$401$			4.48158i			0.223800i	−0.993719	+	0.111900i	$0.964306\pi$
$402$		0			0
$403$	3.46730	+	8.37081i	0.172719	+	0.416980i
$404$		0			0
$405$	−0.00626394	−	0.00259461i	−0.000311258	−	0.000128927i
$406$		0			0
$407$	5.27428	−	5.27428i	0.261437	−	0.261437i
$408$		0			0
$409$	22.1171	+	22.1171i	1.09362	+	1.09362i	0.995139	+	0.0984792i	$0.0313978\pi$
$409$	22.1171	+	22.1171i	1.09362	+	1.09362i	0.0984792	+	0.995139i	$0.468602\pi$
$410$		0			0
$411$	−0.0590584	+	0.142579i	−0.00291313	+	0.00703293i
$412$		0			0
$413$	13.1726	−	5.45626i	0.648180	−	0.268485i
$414$		0			0
$415$	−0.0537885			−0.00264037
$416$		0			0
$417$	6.28571			0.307813
$418$		0			0
$419$	−8.59414	+	3.55981i	−0.419851	+	0.173908i	−0.582599	−	0.812760i	$-0.697964\pi$
$419$	−8.59414	+	3.55981i	−0.419851	+	0.173908i	0.162748	+	0.986668i	$0.447964\pi$
$420$		0			0
$421$	−7.82429	+	18.8895i	−0.381333	+	0.920619i	0.610376	+	0.792112i	$0.291018\pi$
$421$	−7.82429	+	18.8895i	−0.381333	+	0.920619i	−0.991709	+	0.128507i	$0.958982\pi$
$422$		0			0
$423$	−8.84240	−	8.84240i	−0.429932	−	0.429932i
$424$		0			0
$425$	−20.5836	+	20.5836i	−0.998453	+	0.998453i
$426$		0			0
$427$	−24.8820	−	10.3064i	−1.20412	−	0.498764i
$428$		0			0
$429$	0.786981	+	1.89994i	0.0379958	+	0.0917300i
$430$		0			0
$431$			17.2386i			0.830353i	0.909741	+	0.415177i	$0.136280\pi$
$431$			17.2386i			0.830353i	−0.909741	+	0.415177i	$0.863720\pi$
$432$		0			0
$433$			20.8456i			1.00177i	0.865513	+	0.500887i	$0.166993\pi$
$433$			20.8456i			1.00177i	−0.865513	+	0.500887i	$0.833007\pi$
$434$		0			0
$435$	0.0160893	+	0.0388429i	0.000771421	+	0.00186238i
$436$		0			0
$437$	1.63565	+	0.677508i	0.0782437	+	0.0324096i
$438$		0			0
$439$	11.5583	−	11.5583i	0.551648	−	0.551648i	−0.375269	−	0.926916i	$-0.622450\pi$
$439$	11.5583	−	11.5583i	0.551648	−	0.551648i	0.926916	+	0.375269i	$0.122450\pi$
$440$		0			0
$441$	3.32423	+	3.32423i	0.158297	+	0.158297i
$442$		0			0
$443$	7.86432	−	18.9861i	0.373645	−	0.902059i	−0.619481	−	0.785011i	$-0.712657\pi$
$443$	7.86432	−	18.9861i	0.373645	−	0.902059i	0.993126	−	0.117047i	$-0.0373429\pi$
$444$		0			0
$445$	−0.0882424	+	0.0365512i	−0.00418309	+	0.00173269i
$446$		0			0
$447$	−16.7470			−0.792105
$448$		0			0
$449$	−2.11825			−0.0999665			−0.0499832	−	0.998750i	$-0.515917\pi$
$449$	−2.11825			−0.0999665			−0.0499832	+	0.998750i	$0.515917\pi$
$450$		0			0
$451$	−6.18808	+	2.56319i	−0.291385	+	0.120696i
$452$		0			0
$453$	5.08087	−	12.2663i	0.238720	−	0.576321i
$454$		0			0
$455$	0.0239767	+	0.0239767i	0.00112405	+	0.00112405i
$456$		0			0
$457$	7.54089	−	7.54089i	0.352748	−	0.352748i	−0.508383	−	0.861131i	$-0.669757\pi$
$457$	7.54089	−	7.54089i	0.352748	−	0.352748i	0.861131	+	0.508383i	$0.169757\pi$
$458$		0			0
$459$	5.37882	+	2.22798i	0.251062	+	0.103993i
$460$		0			0
$461$	1.56851	+	3.78672i	0.0730529	+	0.176365i	0.956188	−	0.292754i	$-0.0945716\pi$
$461$	1.56851	+	3.78672i	0.0730529	+	0.176365i	−0.883135	+	0.469119i	$0.844572\pi$
$462$		0			0
$463$		−	8.35374i		−	0.388231i	−0.980979	−	0.194116i	$-0.937816\pi$
$463$		−	8.35374i		−	0.388231i	0.980979	−	0.194116i	$-0.0621837\pi$
$464$		0			0
$465$		−	0.0420172i		−	0.00194850i
$466$		0			0
$467$	11.8505	+	28.6097i	0.548377	+	1.32390i	0.918685	+	0.394990i	$0.129252\pi$
$467$	11.8505	+	28.6097i	0.548377	+	1.32390i	−0.370308	+	0.928909i	$0.620748\pi$
$468$		0			0
$469$	−15.0092	−	6.21700i	−0.693059	−	0.287075i
$470$		0			0
$471$	0.734458	−	0.734458i	0.0338420	−	0.0338420i
$472$		0			0
$473$	10.0933	+	10.0933i	0.464092	+	0.464092i
$474$		0			0
$475$	13.3908	−	32.3283i	0.614414	−	1.48333i
$476$		0			0
$477$	8.36811	−	3.46618i	0.383149	−	0.158706i
$478$		0			0
$479$	4.36086			0.199253			0.0996264	−	0.995025i	$-0.468235\pi$
$479$	4.36086			0.199253			0.0996264	+	0.995025i	$0.468235\pi$
$480$		0			0
$481$	7.75299			0.353506
$482$		0			0
$483$	−0.799470	+	0.331151i	−0.0363772	+	0.0150679i
$484$		0			0
$485$	−0.00321881	+	0.00777090i	−0.000146159	+	0.000352858i
$486$		0			0
$487$	−7.91861	−	7.91861i	−0.358827	−	0.358827i	0.504554	−	0.863380i	$-0.331657\pi$
$487$	−7.91861	−	7.91861i	−0.358827	−	0.358827i	−0.863380	+	0.504554i	$0.831657\pi$
$488$		0			0
$489$	−5.66022	+	5.66022i	−0.255964	+	0.255964i
$490$		0			0
$491$	37.8921	+	15.6954i	1.71005	+	0.708324i	0.999991	+	0.00417652i	$0.00132943\pi$
$491$	37.8921	+	15.6954i	1.71005	+	0.708324i	0.710054	+	0.704147i	$0.248671\pi$
$492$		0			0
$493$	−13.8158	−	33.3542i	−0.622231	−	1.50220i
$494$		0			0
$495$		−	0.00953672i		−	0.000428644i
$496$		0			0
$497$		−	28.7928i		−	1.29153i
$498$		0			0
$499$	−9.18191	−	22.1671i	−0.411039	−	0.992336i	−0.984859	−	0.173355i	$-0.944539\pi$
$499$	−9.18191	−	22.1671i	−0.411039	−	0.992336i	0.573821	−	0.818981i	$-0.305461\pi$
$500$		0			0
$501$	−0.910770	−	0.377253i	−0.0406902	−	0.0168544i
$502$		0			0
$503$	−16.5963	+	16.5963i	−0.739995	+	0.739995i	−0.972577	−	0.232582i	$-0.925283\pi$
$503$	−16.5963	+	16.5963i	−0.739995	+	0.739995i	0.232582	+	0.972577i	$0.425283\pi$
$504$		0			0
$505$	0.0771659	+	0.0771659i	0.00343384	+	0.00343384i
$506$		0			0
$507$	4.15688	−	10.0356i	0.184614	−	0.445697i
$508$		0			0
$509$	−5.26058	+	2.17900i	−0.233171	+	0.0965826i	−0.496210	−	0.868203i	$-0.665275\pi$
$509$	−5.26058	+	2.17900i	−0.233171	+	0.0965826i	0.263039	+	0.964785i	$0.415275\pi$
$510$		0			0
$511$	38.0012			1.68107
$512$		0			0
$513$	−6.99846			−0.308989
$514$		0			0
$515$	0.0496573	−	0.0205687i	0.00218816	−	0.000906367i
$516$		0			0
$517$	6.73118	−	16.2505i	0.296037	−	0.714697i
$518$		0			0
$519$	−12.2170	−	12.2170i	−0.536266	−	0.536266i
$520$		0			0
$521$	13.8290	−	13.8290i	0.605861	−	0.605861i	−0.336001	−	0.941862i	$-0.609074\pi$
$521$	13.8290	−	13.8290i	0.605861	−	0.605861i	0.941862	+	0.336001i	$0.109074\pi$
$522$		0			0
$523$	−20.8657	−	8.64286i	−0.912393	−	0.377926i	−0.123421	−	0.992354i	$-0.539387\pi$
$523$	−20.8657	−	8.64286i	−0.912393	−	0.377926i	−0.788972	+	0.614429i	$0.789387\pi$
$524$		0			0
$525$	6.54516	+	15.8014i	0.285654	+	0.689630i
$526$		0			0
$527$			36.0799i			1.57167i
$528$		0			0
$529$			22.9360i			0.997218i
$530$		0			0
$531$	−1.59507	−	3.85084i	−0.0692202	−	0.167112i
$532$		0			0
$533$	−6.43201	−	2.66423i	−0.278601	−	0.115400i
$534$		0			0
$535$	−0.0283526	+	0.0283526i	−0.00122579	+	0.00122579i
$536$		0			0
$537$	2.10832	+	2.10832i	0.0909805	+	0.0909805i
$538$		0			0
$539$	−2.53053	+	6.10925i	−0.108998	+	0.263144i
$540$		0			0
$541$	−24.5863	+	10.1840i	−1.05705	+	0.437843i	−0.842402	−	0.538849i	$-0.818859\pi$
$541$	−24.5863	+	10.1840i	−1.05705	+	0.437843i	−0.214645	+	0.976692i	$0.568859\pi$
$542$		0			0
$543$	6.74682			0.289534
$544$		0			0
$545$	0.0174145			0.000745953
$546$		0			0
$547$	9.15022	−	3.79015i	0.391235	−	0.162055i	−0.178389	−	0.983960i	$-0.557089\pi$
$547$	9.15022	−	3.79015i	0.391235	−	0.162055i	0.569625	+	0.821905i	$0.307089\pi$
$548$		0			0
$549$	−3.01297	+	7.27395i	−0.128590	+	0.310444i
$550$		0			0
$551$	30.6868	+	30.6868i	1.30730	+	1.30730i
$552$		0			0
$553$	−3.44572	+	3.44572i	−0.146527	+	0.146527i
$554$		0			0
$555$	−0.0332169	−	0.0137589i	−0.00140998	−	0.000584033i
$556$		0			0
$557$	2.57099	+	6.20693i	0.108936	+	0.262996i	0.968942	−	0.247289i	$-0.0795398\pi$
$557$	2.57099	+	6.20693i	0.108936	+	0.262996i	−0.860005	+	0.510285i	$0.829540\pi$
$558$		0			0
$559$			14.8368i			0.627530i
$560$		0			0
$561$			8.18913i			0.345746i
$562$		0			0
$563$	−16.2626	−	39.2615i	−0.685388	−	1.65467i	−0.753872	−	0.657021i	$-0.771816\pi$
$563$	−16.2626	−	39.2615i	−0.685388	−	1.65467i	0.0684842	−	0.997652i	$-0.478184\pi$
$564$		0			0
$565$	0.0277373	+	0.0114892i	0.00116692	+	0.000483353i
$566$		0			0
$567$	2.41880	−	2.41880i	0.101580	−	0.101580i
$568$		0			0
$569$	−23.1230	−	23.1230i	−0.969368	−	0.969368i	0.0301764	−	0.999545i	$-0.490393\pi$
$569$	−23.1230	−	23.1230i	−0.969368	−	0.969368i	−0.999545	+	0.0301764i	$0.990393\pi$
$570$		0			0
$571$	−3.47053	+	8.37861i	−0.145237	+	0.350634i	−0.979711	−	0.200413i	$-0.935772\pi$
$571$	−3.47053	+	8.37861i	−0.145237	+	0.350634i	0.834474	+	0.551047i	$0.185772\pi$
$572$		0			0
$573$	4.73208	−	1.96009i	0.197686	−	0.0818841i
$574$		0			0
$575$	−1.26485			−0.0527478
$576$		0			0
$577$	18.7910			0.782278			0.391139	−	0.920332i	$-0.372081\pi$
$577$	18.7910			0.782278			0.391139	+	0.920332i	$0.372081\pi$
$578$		0			0
$579$	−19.2121	+	7.95793i	−0.798429	+	0.330720i
$580$		0			0
$581$	10.3851	−	25.0719i	0.430847	−	1.04016i
$582$		0			0
$583$	9.00873	+	9.00873i	0.373104	+	0.373104i
$584$		0			0
$585$	0.00700931	−	0.00700931i	0.000289799	−	0.000289799i
$586$		0			0
$587$	−28.1601	−	11.6643i	−1.16229	−	0.481436i	−0.283653	−	0.958927i	$-0.591547\pi$
$587$	−28.1601	−	11.6643i	−1.16229	−	0.481436i	−0.878637	+	0.477490i	$0.841547\pi$
$588$		0			0
$589$	−16.5973	−	40.0693i	−0.683878	−	1.65103i
$590$		0			0
$591$		−	9.07640i		−	0.373353i
$592$		0			0
$593$		−	12.2535i		−	0.503189i	−0.967833	−	0.251594i	$-0.919045\pi$
$593$		−	12.2535i		−	0.503189i	0.967833	−	0.251594i	$-0.0809549\pi$
$594$		0			0
$595$	0.0516723	+	0.124748i	0.00211836	+	0.00511417i
$596$		0			0
$597$	−12.7998	−	5.30184i	−0.523859	−	0.216990i
$598$		0			0
$599$	−8.63937	+	8.63937i	−0.352995	+	0.352995i	−0.861223	−	0.508228i	$-0.830301\pi$
$599$	−8.63937	+	8.63937i	−0.352995	+	0.352995i	0.508228	+	0.861223i	$0.330301\pi$
$600$		0			0
$601$	−14.3695	−	14.3695i	−0.586143	−	0.586143i	0.350441	−	0.936585i	$-0.386032\pi$
$601$	−14.3695	−	14.3695i	−0.586143	−	0.586143i	−0.936585	+	0.350441i	$0.886032\pi$
$602$		0			0
$603$	−1.81747	+	4.38775i	−0.0740130	+	0.178683i
$604$		0			0
$605$	−0.0565102	+	0.0234073i	−0.00229747	+	0.000951642i
$606$		0			0
$607$	−21.4916			−0.872319			−0.436159	−	0.899869i	$-0.643662\pi$
$607$	−21.4916			−0.872319			−0.436159	+	0.899869i	$0.643662\pi$
$608$		0			0
$609$	−21.2119			−0.859548
$610$		0			0
$611$	16.8911	−	6.99653i	0.683341	−	0.283049i
$612$		0			0
$613$	−12.3921	+	29.9172i	−0.500513	+	1.20834i	0.448693	+	0.893686i	$0.351890\pi$
$613$	−12.3921	+	29.9172i	−0.500513	+	1.20834i	−0.949205	+	0.314658i	$0.898110\pi$
$614$		0			0
$615$	0.0228292	+	0.0228292i	0.000920563	+	0.000920563i
$616$		0			0
$617$	17.5651	−	17.5651i	0.707143	−	0.707143i	−0.258790	−	0.965933i	$-0.583324\pi$
$617$	17.5651	−	17.5651i	0.707143	−	0.707143i	0.965933	+	0.258790i	$0.0833239\pi$
$618$		0			0
$619$	−16.3569	−	6.77526i	−0.657440	−	0.272321i	0.0289208	−	0.999582i	$-0.490793\pi$
$619$	−16.3569	−	6.77526i	−0.657440	−	0.272321i	−0.686361	+	0.727261i	$0.740793\pi$
$620$		0			0
$621$	0.0968082	+	0.233716i	0.00388478	+	0.00937869i
$622$		0			0
$623$		−	48.1886i		−	1.93064i
$624$		0			0
$625$			24.9993i			0.999972i
$626$		0			0
$627$	−3.76711	−	9.09461i	−0.150444	−	0.363204i
$628$		0			0
$629$	28.5232	+	11.8147i	1.13729	+	0.471083i
$630$		0			0
$631$	−23.6874	+	23.6874i	−0.942982	+	0.942982i	−0.998460	−	0.0554784i	$-0.982332\pi$
$631$	−23.6874	+	23.6874i	−0.942982	+	0.942982i	0.0554784	+	0.998460i	$0.482332\pi$
$632$		0			0
$633$	−4.79763	−	4.79763i	−0.190689	−	0.190689i
$634$		0			0
$635$	−0.0378630	+	0.0914094i	−0.00150255	+	0.00362747i
$636$		0			0
$637$	−6.35007	+	2.63029i	−0.251599	+	0.104216i
$638$		0			0
$639$	−8.41723			−0.332981
$640$		0			0
$641$	6.79529			0.268398			0.134199	−	0.990954i	$-0.457154\pi$
$641$	6.79529			0.268398			0.134199	+	0.990954i	$0.457154\pi$
$642$		0			0
$643$	−18.4729	+	7.65173i	−0.728500	+	0.301755i	−0.715935	−	0.698166i	$-0.754000\pi$
$643$	−18.4729	+	7.65173i	−0.728500	+	0.301755i	−0.0125646	+	0.999921i	$0.504000\pi$
$644$		0			0
$645$	0.0263302	−	0.0635668i	0.00103675	−	0.00250294i
$646$		0			0
$647$	5.34732	+	5.34732i	0.210225	+	0.210225i	0.804363	−	0.594138i	$-0.202507\pi$
$647$	5.34732	+	5.34732i	0.210225	+	0.210225i	−0.594138	+	0.804363i	$0.702507\pi$
$648$		0			0
$649$	4.14565	−	4.14565i	0.162731	−	0.162731i
$650$		0			0
$651$	19.5850	+	8.11239i	0.767598	+	0.317950i
$652$		0			0
$653$	1.51225	+	3.65091i	0.0591791	+	0.142871i	0.950703	−	0.310102i	$-0.100363\pi$
$653$	1.51225	+	3.65091i	0.0591791	+	0.142871i	−0.891524	+	0.452973i	$0.850363\pi$
$654$		0			0
$655$			0.0633126i			0.00247383i
$656$		0			0
$657$		−	11.1092i		−	0.433411i
$658$		0			0
$659$	−7.07771	−	17.0871i	−0.275708	−	0.665619i	0.723999	−	0.689801i	$-0.242302\pi$
$659$	−7.07771	−	17.0871i	−0.275708	−	0.665619i	−0.999708	+	0.0241818i	$0.992302\pi$
$660$		0			0
$661$	−15.2261	−	6.30685i	−0.592226	−	0.245308i	0.0663821	−	0.997794i	$-0.478854\pi$
$661$	−15.2261	−	6.30685i	−0.592226	−	0.245308i	−0.658608	+	0.752486i	$0.728854\pi$
$662$		0			0
$663$	−6.01886	+	6.01886i	−0.233753	+	0.233753i
$664$		0			0
$665$	−0.114772	−	0.114772i	−0.00445065	−	0.00445065i
$666$		0			0
$667$	0.600311	−	1.44928i	0.0232441	−	0.0561163i
$668$		0			0
$669$	−13.4934	+	5.58914i	−0.521684	+	0.216089i
$670$		0			0
$671$	−11.0744			−0.427524
$672$		0			0
$673$	5.46222			0.210553			0.105276	−	0.994443i	$-0.466427\pi$
$673$	5.46222			0.210553			0.105276	+	0.994443i	$0.466427\pi$
$674$		0			0
$675$	4.61936	−	1.91340i	0.177799	−	0.0736468i
$676$		0			0
$677$	4.02477	−	9.71665i	0.154684	−	0.373441i	−0.827472	−	0.561507i	$-0.810222\pi$
$677$	4.02477	−	9.71665i	0.154684	−	0.373441i	0.982156	+	0.188066i	$0.0602218\pi$
$678$		0			0
$679$	−3.00070	−	3.00070i	−0.115156	−	0.115156i
$680$		0			0
$681$	−2.87104	+	2.87104i	−0.110018	+	0.110018i
$682$		0			0
$683$	39.7212	+	16.4530i	1.51989	+	0.629558i	0.977569	−	0.210615i	$-0.0675466\pi$
$683$	39.7212	+	16.4530i	1.51989	+	0.629558i	0.542319	+	0.840173i	$0.317547\pi$
$684$		0			0
$685$	0.000400418	0	0.000966695i	1.52992e−5	0	3.69355e-5i
$686$		0			0
$687$			5.39714i			0.205914i
$688$		0			0
$689$			13.2425i			0.504499i
$690$		0			0
$691$	7.36888	+	17.7900i	0.280325	+	0.676765i	0.999843	−	0.0177088i	$-0.00563718\pi$
$691$	7.36888	+	17.7900i	0.280325	+	0.676765i	−0.719518	+	0.694474i	$0.755637\pi$
$692$		0			0
$693$	4.44525	+	1.84128i	0.168861	+	0.0699446i
$694$		0			0
$695$	0.0301350	−	0.0301350i	0.00114309	−	0.00114309i
$696$		0			0
$697$	−19.6033	−	19.6033i	−0.742529	−	0.742529i
$698$		0			0
$699$	−11.0947	+	26.7850i	−0.419640	+	1.01310i
$700$		0			0
$701$	−0.759834	+	0.314734i	−0.0286985	+	0.0118873i	−0.396987	−	0.917824i	$-0.629944\pi$
$701$	−0.759834	+	0.314734i	−0.0286985	+	0.0118873i	0.368288	+	0.929712i	$0.379944\pi$
$702$		0			0
$703$	−37.1120			−1.39970
$704$		0			0
$705$	−0.0847847			−0.00319318
$706$		0			0
$707$	−50.8672	+	21.0699i	−1.91306	+	0.792415i
$708$		0			0
$709$	18.3991	−	44.4194i	0.690994	−	1.66821i	−0.0517745	−	0.998659i	$-0.516488\pi$
$709$	18.3991	−	44.4194i	0.690994	−	1.66821i	0.742768	−	0.669548i	$-0.233512\pi$
$710$		0			0
$711$	1.00732	+	1.00732i	0.0377773	+	0.0377773i
$712$		0			0
$713$	−1.10854	+	1.10854i	−0.0415152	+	0.0415152i
$714$		0			0
$715$	0.0128817	+	0.00533576i	0.000481747	+	0.000199546i
$716$		0			0
$717$	0.855950	+	2.06645i	0.0319660	+	0.0771729i
$718$		0			0
$719$		−	0.494401i		−	0.0184380i	−0.999958	−	0.00921901i	$-0.997065\pi$
$719$		−	0.494401i		−	0.0184380i	0.999958	−	0.00921901i	$-0.00293455\pi$
$720$		0			0
$721$			27.1175i			1.00991i
$722$		0			0
$723$	−7.52948	−	18.1778i	−0.280024	−	0.676039i
$724$		0			0
$725$	−28.6448	−	11.8651i	−1.06384	−	0.440657i
$726$		0			0
$727$	−13.9621	+	13.9621i	−0.517826	+	0.517826i	−0.916913	−	0.399087i	$-0.869327\pi$
$727$	−13.9621	+	13.9621i	−0.517826	+	0.517826i	0.399087	+	0.916913i	$0.369327\pi$
$728$		0			0
$729$	−0.707107	−	0.707107i	−0.0261891	−	0.0261891i
$730$		0			0
$731$	−22.6097	+	54.5845i	−0.836248	+	2.01888i
$732$		0			0
$733$	−21.0117	+	8.70335i	−0.776087	+	0.321466i	−0.735335	−	0.677704i	$-0.762975\pi$
$733$	−21.0117	+	8.70335i	−0.776087	+	0.321466i	−0.0407515	+	0.999169i	$0.512975\pi$
$734$		0			0
$735$	0.0318741			0.00117569
$736$		0			0
$737$	−6.68026			−0.246071
$738$		0			0
$739$	−23.9176	+	9.90698i	−0.879822	+	0.364434i	−0.776428	−	0.630206i	$-0.782970\pi$
$739$	−23.9176	+	9.90698i	−0.879822	+	0.364434i	−0.103394	+	0.994640i	$0.532970\pi$
$740$		0			0
$741$	3.91561	−	9.45312i	0.143844	−	0.347269i
$742$		0			0
$743$	−22.7644	−	22.7644i	−0.835144	−	0.835144i	0.153071	−	0.988215i	$-0.451084\pi$
$743$	−22.7644	−	22.7644i	−0.835144	−	0.835144i	−0.988215	+	0.153071i	$0.951084\pi$
$744$		0			0
$745$	−0.0802886	+	0.0802886i	−0.00294155	+	0.00294155i
$746$		0			0
$747$	−7.32946	−	3.03596i	−0.268171	−	0.111080i
$748$		0			0
$749$	−7.74158	−	18.6898i	−0.282871	−	0.682912i
$750$		0			0
$751$		−	31.4436i		−	1.14739i	−0.819068	−	0.573697i	$-0.805509\pi$
$751$		−	31.4436i		−	1.14739i	0.819068	−	0.573697i	$-0.194491\pi$
$752$		0			0
$753$		−	6.32225i		−	0.230396i
$754$		0			0
$755$	−0.0344485	−	0.0831660i	−0.00125371	−	0.00302672i
$756$		0			0
$757$	23.6692	+	9.80412i	0.860273	+	0.356337i	0.768814	−	0.639472i	$-0.220847\pi$
$757$	23.6692	+	9.80412i	0.860273	+	0.356337i	0.0914586	+	0.995809i	$0.470847\pi$
$758$		0			0
$759$	−0.251608	+	0.251608i	−0.00913279	+	0.00913279i
$760$		0			0
$761$	−5.35154	−	5.35154i	−0.193993	−	0.193993i	0.603426	−	0.797419i	$-0.293802\pi$
$761$	−5.35154	−	5.35154i	−0.193993	−	0.193993i	−0.797419	+	0.603426i	$0.793802\pi$
$762$		0			0
$763$	−3.36226	+	8.11722i	−0.121722	+	0.293863i
$764$		0			0
$765$	0.0364686	−	0.0151058i	0.00131852	−	0.000546151i
$766$		0			0
$767$	6.09394			0.220040
$768$		0			0
$769$	16.9993			0.613011			0.306505	−	0.951869i	$-0.400840\pi$
$769$	16.9993			0.613011			0.306505	+	0.951869i	$0.400840\pi$
$770$		0			0
$771$	8.74002	−	3.62023i	0.314764	−	0.130380i
$772$		0			0
$773$	16.2444	−	39.2174i	0.584269	−	1.41055i	−0.304640	−	0.952467i	$-0.598536\pi$
$773$	16.2444	−	39.2174i	0.584269	−	1.41055i	0.888910	−	0.458083i	$-0.151464\pi$
$774$		0			0
$775$	21.9102	+	21.9102i	0.787036	+	0.787036i
$776$		0			0
$777$	12.8266	−	12.8266i	0.460151	−	0.460151i
$778$		0			0
$779$	30.7887	+	12.7531i	1.10312	+	0.456927i
$780$		0			0
$781$	−4.53081	−	10.9383i	−0.162125	−	0.391405i
$782$		0			0
$783$			6.20104i			0.221607i
$784$		0			0
$785$		−	0.00704229i		−	0.000251350i
$786$		0			0
$787$	1.91880	+	4.63239i	0.0683978	+	0.165127i	0.954382	−	0.298589i	$-0.0965159\pi$
$787$	1.91880	+	4.63239i	0.0683978	+	0.165127i	−0.885984	+	0.463716i	$0.846516\pi$
$788$		0			0
$789$	9.16896	+	3.79791i	0.326424	+	0.135209i
$790$		0			0
$791$	−10.7107	+	10.7107i	−0.380827	+	0.380827i
$792$		0			0
$793$	−8.13949	−	8.13949i	−0.289042	−	0.289042i
$794$		0			0
$795$	0.0235009	−	0.0567361i	0.000833490	−	0.00201222i
$796$		0			0
$797$	8.85578	−	3.66818i	0.313688	−	0.129934i	−0.220285	−	0.975436i	$-0.570699\pi$
$797$	8.85578	−	3.66818i	0.313688	−	0.129934i	0.533972	+	0.845502i	$0.320699\pi$
$798$		0			0
$799$	72.8042			2.57563
$800$		0			0
$801$	−14.0874			−0.497752
$802$		0			0
$803$	14.4366	−	5.97983i	0.509456	−	0.211024i
$804$		0			0
$805$	−0.00224522	+	0.00542044i	−7.91336e−5	+	0.000191045i
$806$		0			0
$807$	−1.07143	−	1.07143i	−0.0377163	−	0.0377163i
$808$		0			0
$809$	13.2208	−	13.2208i	0.464819	−	0.464819i	−0.435412	−	0.900231i	$-0.643397\pi$
$809$	13.2208	−	13.2208i	0.464819	−	0.464819i	0.900231	+	0.435412i	$0.143397\pi$
$810$		0			0
$811$	−9.46797	−	3.92176i	−0.332465	−	0.137712i	0.210205	−	0.977657i	$-0.432587\pi$
$811$	−9.46797	−	3.92176i	−0.332465	−	0.137712i	−0.542671	+	0.839946i	$0.682587\pi$
$812$		0			0
$813$	0.840349	+	2.02878i	0.0294723	+	0.0711525i
$814$		0			0
$815$			0.0542726i			0.00190109i
$816$		0			0
$817$		−	71.0207i		−	2.48470i
$818$		0			0
$819$	1.91387	+	4.62049i	0.0668760	+	0.161453i
$820$		0			0
$821$	47.1649	+	19.5363i	1.64607	+	0.681823i	0.996889	−	0.0788144i	$-0.0251134\pi$
$821$	47.1649	+	19.5363i	1.64607	+	0.681823i	0.649177	+	0.760637i	$0.275113\pi$
$822$		0			0
$823$	−17.1355	+	17.1355i	−0.597306	+	0.597306i	−0.939595	−	0.342289i	$-0.888798\pi$
$823$	−17.1355	+	17.1355i	−0.597306	+	0.597306i	0.342289	+	0.939595i	$0.388798\pi$
$824$		0			0
$825$	4.97299	+	4.97299i	0.173137	+	0.173137i
$826$		0			0
$827$	7.74891	−	18.7075i	0.269456	−	0.650524i	−0.730002	−	0.683445i	$-0.760481\pi$
$827$	7.74891	−	18.7075i	0.269456	−	0.650524i	0.999458	+	0.0329210i	$0.0104810\pi$
$828$		0			0
$829$	−2.18250	+	0.904020i	−0.0758013	+	0.0313979i	−0.420262	−	0.907403i	$-0.638062\pi$
$829$	−2.18250	+	0.904020i	−0.0758013	+	0.0313979i	0.344461	+	0.938801i	$0.388062\pi$
$830$		0			0
$831$	−26.0437			−0.903446
$832$		0			0
$833$	−27.3701			−0.948319
$834$		0			0
$835$	−0.00617506	+	0.00255779i	−0.000213697	+	8.85161e-5i
$836$		0			0
$837$	2.37156	−	5.72545i	0.0819731	−	0.197901i
$838$		0			0
$839$	−19.2057	−	19.2057i	−0.663056	−	0.663056i	0.293043	−	0.956099i	$-0.405332\pi$
$839$	−19.2057	−	19.2057i	−0.663056	−	0.663056i	−0.956099	+	0.293043i	$0.905332\pi$
$840$		0			0
$841$	6.68416	−	6.68416i	0.230488	−	0.230488i
$842$		0			0
$843$	23.5417	+	9.75129i	0.810819	+	0.335852i
$844$		0			0
$845$	−0.0281838	−	0.0680418i	−0.000969553	−	0.00234071i
$846$		0			0
$847$		−	30.8599i		−	1.06036i
$848$		0			0
$849$			3.02747i			0.103903i
$850$		0			0
$851$	0.513362	+	1.23937i	0.0175978	+	0.0424849i
$852$		0			0
$853$	35.6393	+	14.7623i	1.22026	+	0.505450i	0.897494	−	0.441027i	$-0.145386\pi$
$853$	35.6393	+	14.7623i	1.22026	+	0.505450i	0.322771	+	0.946477i	$0.395386\pi$
$854$		0			0
$855$	−0.0335521	+	0.0335521i	−0.00114746	+	0.00114746i
$856$		0			0
$857$	8.16918	+	8.16918i	0.279054	+	0.279054i	0.832731	−	0.553677i	$-0.186776\pi$
$857$	8.16918	+	8.16918i	0.279054	+	0.279054i	−0.553677	+	0.832731i	$0.686776\pi$
$858$		0			0
$859$	2.26963	−	5.47938i	0.0774389	−	0.186954i	−0.880419	−	0.474197i	$-0.842739\pi$
$859$	2.26963	−	5.47938i	0.0774389	−	0.186954i	0.957858	+	0.287243i	$0.0927386\pi$
$860$		0			0
$861$	−15.0489	+	6.23344i	−0.512864	+	0.212435i
$862$		0			0
$863$	−40.5672			−1.38092			−0.690462	−	0.723369i	$-0.742593\pi$
$863$	−40.5672			−1.38092			−0.690462	+	0.723369i	$0.742593\pi$
$864$		0			0
$865$	−0.117142			−0.00398294
$866$		0			0
$867$	−15.6094	+	6.46564i	−0.530125	+	0.219585i
$868$		0			0
$869$	−0.766809	+	1.85124i	−0.0260122	+	0.0627991i
$870$		0			0
$871$	−4.90987	−	4.90987i	−0.166364	−	0.166364i
$872$		0			0
$873$	−0.877220	+	0.877220i	−0.0296894	+	0.0296894i
$874$		0			0
$875$	0.214269	+	0.0887533i	0.00724363	+	0.00300041i
$876$		0			0
$877$	−0.389401	−	0.940098i	−0.0131491	−	0.0317449i	0.917169	−	0.398499i	$-0.130469\pi$
$877$	−0.389401	−	0.940098i	−0.0131491	−	0.0317449i	−0.930318	+	0.366755i	$0.880469\pi$
$878$		0			0
$879$			9.19822i			0.310248i
$880$		0			0
$881$			19.7730i			0.666169i	0.942897	+	0.333085i	$0.108090\pi$
$881$			19.7730i			0.666169i	−0.942897	+	0.333085i	$0.891910\pi$
$882$		0			0
$883$	1.09620	+	2.64647i	0.0368902	+	0.0890608i	0.941251	−	0.337708i	$-0.109652\pi$
$883$	1.09620	+	2.64647i	0.0368902	+	0.0890608i	−0.904361	+	0.426769i	$0.859652\pi$
$884$		0			0
$885$	−0.0261089	−	0.0108147i	−0.000877641	−	0.000363531i
$886$		0			0
$887$	24.5575	−	24.5575i	0.824561	−	0.824561i	−0.162198	−	0.986758i	$-0.551858\pi$
$887$	24.5575	−	24.5575i	0.824561	−	0.824561i	0.986758	+	0.162198i	$0.0518582\pi$
$888$		0			0
$889$	−35.2974	−	35.2974i	−1.18384	−	1.18384i
$890$		0			0
$891$	0.538278	−	1.29952i	0.0180330	−	0.0435355i
$892$		0			0
$893$	−80.8542	+	33.4909i	−2.70568	+	1.12073i
$894$		0			0
$895$	0.0202154			0.000675727
$896$		0			0
$897$	−0.369854			−0.0123491
$898$		0			0
$899$	−35.5037	+	14.7061i	−1.18412	+	0.490477i
$900$		0			0
$901$	−20.1801	+	48.7190i	−0.672296	+	1.62307i
$902$		0			0
$903$	24.5461	+	24.5461i	0.816843	+	0.816843i
$904$		0			0
$905$	0.0323457	−	0.0323457i	0.00107521	−	0.00107521i
$906$		0			0
$907$	20.3745	+	8.43938i	0.676523	+	0.280225i	0.694373	−	0.719616i	$-0.255682\pi$
$907$	20.3745	+	8.43938i	0.676523	+	0.280225i	−0.0178494	+	0.999841i	$0.505682\pi$
$908$		0			0
$909$	6.15953	+	14.8704i	0.204299	+	0.493221i
$910$		0			0
$911$			15.6069i			0.517081i	0.966000	+	0.258540i	$0.0832415\pi$
$911$			15.6069i			0.517081i	−0.966000	+	0.258540i	$0.916758\pi$
$912$		0			0
$913$		−	11.1590i		−	0.369308i
$914$		0			0
$915$	0.0204280	+	0.0493176i	0.000675330	+	0.00163039i
$916$		0			0
$917$	−29.5113	−	12.2240i	−0.974548	−	0.403671i
$918$		0			0
$919$	−37.7928	+	37.7928i	−1.24667	+	1.24667i	−0.289489	+	0.957181i	$0.593485\pi$
$919$	−37.7928	+	37.7928i	−1.24667	+	1.24667i	−0.957181	+	0.289489i	$0.906515\pi$
$920$		0			0
$921$	−2.61927	−	2.61927i	−0.0863078	−	0.0863078i
$922$		0			0
$923$	4.70941	−	11.3695i	0.155012	−	0.374233i
$924$		0			0
$925$	24.4959	−	10.1465i	0.805420	−	0.333616i
$926$		0			0
$927$	7.92749			0.260373
$928$		0			0
$929$	8.36281			0.274375			0.137187	−	0.990545i	$-0.456194\pi$
$929$	8.36281			0.274375			0.137187	+	0.990545i	$0.456194\pi$
$930$		0			0
$931$	30.3965	−	12.5906i	0.996204	−	0.412641i
$932$		0			0
$933$	12.1442	−	29.3187i	0.397583	−	0.959851i
$934$		0			0
$935$	0.0392605	+	0.0392605i	0.00128395	+	0.00128395i
$936$		0			0
$937$	−37.8809	+	37.8809i	−1.23752	+	1.23752i	−0.276502	+	0.961013i	$0.589175\pi$
$937$	−37.8809	+	37.8809i	−1.23752	+	1.23752i	−0.961013	+	0.276502i	$0.910825\pi$
$938$		0			0
$939$	−2.93926	−	1.21748i	−0.0959190	−	0.0397310i
$940$		0			0
$941$	19.7558	+	47.6947i	0.644020	+	1.55480i	0.821211	+	0.570625i	$0.193299\pi$
$941$	19.7558	+	47.6947i	0.644020	+	1.55480i	−0.177191	+	0.984176i	$0.556701\pi$
$942$		0			0
$943$		−	1.20461i		−	0.0392275i
$944$		0			0
$945$		−	0.0231925i		−	0.000754451i
$946$		0			0
$947$	2.05678	+	4.96550i	0.0668363	+	0.161357i	0.953768	−	0.300543i	$-0.0971679\pi$
$947$	2.05678	+	4.96550i	0.0668363	+	0.161357i	−0.886932	+	0.461900i	$0.847168\pi$
$948$		0			0
$949$	15.0057	+	6.21556i	0.487105	+	0.201766i
$950$		0			0
$951$	24.0586	−	24.0586i	0.780152	−	0.780152i
$952$		0			0
$953$	−4.72605	−	4.72605i	−0.153092	−	0.153092i	0.626406	−	0.779497i	$-0.284525\pi$
$953$	−4.72605	−	4.72605i	−0.153092	−	0.153092i	−0.779497	+	0.626406i	$0.784525\pi$
$954$		0			0
$955$	0.0132895	−	0.0320837i	0.000430038	−	0.00103820i
$956$		0			0
$957$	−8.05835	+	3.33788i	−0.260490	+	0.107898i
$958$		0			0
$959$	−0.527906			−0.0170470
$960$		0			0
$961$	7.40512			0.238875
$962$		0			0
$963$	−5.46375	+	2.26316i	−0.176067	+	0.0729293i
$964$		0			0
$965$	−0.0539551	+	0.130259i	−0.00173688	+	0.00419319i
$966$		0			0
$967$	−29.3805	−	29.3805i	−0.944812	−	0.944812i	0.0537426	−	0.998555i	$-0.482885\pi$
$967$	−29.3805	−	29.3805i	−0.944812	−	0.944812i	−0.998555	+	0.0537426i	$0.982885\pi$
$968$		0			0
$969$	28.8110	−	28.8110i	0.925543	−	0.925543i
$970$		0			0
$971$	−22.4822	−	9.31244i	−0.721489	−	0.298850i	−0.00843940	−	0.999964i	$-0.502686\pi$
$971$	−22.4822	−	9.31244i	−0.721489	−	0.298850i	−0.713049	+	0.701114i	$0.752686\pi$
$972$		0			0
$973$	8.22827	+	19.8648i	0.263786	+	0.636836i
$974$		0			0
$975$			7.31011i			0.234111i
$976$		0			0
$977$			30.9704i			0.990831i	0.868656	+	0.495415i	$0.164984\pi$
$977$			30.9704i			0.990831i	−0.868656	+	0.495415i	$0.835016\pi$
$978$		0			0
$979$	−7.58291	−	18.3068i	−0.242351	−	0.585087i
$980$		0			0
$981$	2.37297	+	0.982918i	0.0757632	+	0.0313821i
$982$		0			0
$983$	−8.78738	+	8.78738i	−0.280274	+	0.280274i	−0.833218	−	0.552944i	$-0.813504\pi$
$983$	−8.78738	+	8.78738i	−0.280274	+	0.280274i	0.552944	+	0.833218i	$0.313504\pi$
$984$		0			0
$985$	−0.0435142	−	0.0435142i	−0.00138648	−	0.00138648i
$986$		0			0
$987$	16.3696	−	39.5198i	0.521052	−	1.25793i
$988$		0			0
$989$	−2.37176	+	0.982415i	−0.0754176	+	0.0312390i
$990$		0			0
$991$	43.3371			1.37665			0.688324	−	0.725403i	$-0.258347\pi$
$991$	43.3371			1.37665			0.688324	+	0.725403i	$0.258347\pi$
$992$		0			0
$993$	26.6315			0.845125
$994$		0			0
$995$	−0.0867829	+	0.0359467i	−0.00275120	+	0.00113959i
$996$		0			0
$997$	−4.40977	+	10.6461i	−0.139659	+	0.337166i	−0.978198	−	0.207675i	$-0.933410\pi$
$997$	−4.40977	+	10.6461i	−0.139659	+	0.337166i	0.838539	+	0.544842i	$0.183410\pi$
$998$		0			0
$999$	−3.74970	−	3.74970i	−0.118635	−	0.118635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.97.6		32
4.3	odd	2		768.2.n.a.97.2		32
8.3	odd	2		96.2.n.a.85.7	yes	32
8.5	even	2		384.2.n.a.49.3		32
24.5	odd	2		1152.2.v.c.433.5		32
24.11	even	2		288.2.v.d.181.2		32
32.3	odd	8		768.2.n.a.673.2		32
32.13	even	8		384.2.n.a.337.3		32
32.19	odd	8		96.2.n.a.61.7	✓	32
32.29	even	8	inner	768.2.n.b.673.6		32
96.77	odd	8		1152.2.v.c.721.5		32
96.83	even	8		288.2.v.d.253.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.7	✓	32	32.19	odd	8
96.2.n.a.85.7	yes	32	8.3	odd	2
288.2.v.d.181.2		32	24.11	even	2
288.2.v.d.253.2		32	96.83	even	8
384.2.n.a.49.3		32	8.5	even	2
384.2.n.a.337.3		32	32.13	even	8
768.2.n.a.97.2		32	4.3	odd	2
768.2.n.a.673.2		32	32.3	odd	8
768.2.n.b.97.6		32	1.1	even	1	trivial
768.2.n.b.673.6		32	32.29	even	8	inner
1152.2.v.c.433.5		32	24.5	odd	2
1152.2.v.c.721.5		32	96.77	odd	8

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)

\(f(q)\)	\(=\)	\(q+(0.923880 - 0.382683i) q^{3} +(0.00259461 - 0.00626394i) q^{5} +(2.41880 + 2.41880i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.923880 - 0.382683i) q^{3} +(0.00259461 - 0.00626394i) q^{5} +(2.41880 + 2.41880i) q^{7} +(0.707107 - 0.707107i) q^{9} +(1.29952 + 0.538278i) q^{11} +(0.559497 + 1.35074i) q^{13} -0.00678004i q^{15} +5.82199i q^{17} +(-2.67819 - 6.46573i) q^{19} +(3.16031 + 1.30904i) q^{21} +(-0.178878 + 0.178878i) q^{23} +(3.53550 + 3.53550i) q^{25} +(0.382683 - 0.923880i) q^{27} +(-5.72901 + 2.37303i) q^{29} +6.19719 q^{31} +1.40659 q^{33} +(0.0214270 - 0.00887537i) q^{35} +(2.02932 - 4.89922i) q^{37} +(1.03381 + 1.03381i) q^{39} +(-3.36712 + 3.36712i) q^{41} +(9.37558 + 3.88349i) q^{43} +(-0.00259461 - 0.00626394i) q^{45} -12.5050i q^{47} +4.70117i q^{49} +(2.22798 + 5.37882i) q^{51} +(8.36811 + 3.46618i) q^{53} +(0.00674348 - 0.00674348i) q^{55} +(-4.94866 - 4.94866i) q^{57} +(1.59507 - 3.85084i) q^{59} +(-7.27395 + 3.01297i) q^{61} +3.42070 q^{63} +0.00991266 q^{65} +(-4.38775 + 1.81747i) q^{67} +(-0.0968082 + 0.233716i) q^{69} +(-5.95188 - 5.95188i) q^{71} +(7.85539 - 7.85539i) q^{73} +(4.61936 + 1.91340i) q^{75} +(1.84128 + 4.44525i) q^{77} +1.42456i q^{79} -1.00000i q^{81} +(-3.03596 - 7.32946i) q^{83} +(0.0364686 + 0.0151058i) q^{85} +(-4.38479 + 4.38479i) q^{87} +(-9.96127 - 9.96127i) q^{89} +(-1.91387 + 4.62049i) q^{91} +(5.72545 - 2.37156i) q^{93} -0.0474498 q^{95} -1.24058 q^{97} +(1.29952 - 0.538278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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