LMFDB - Embedded newform 976.2.bw.c.545.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [976,2,Mod(225,976)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("976.225"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(976, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 0, 28])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 976 = 2^{4} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	976.bw (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.79339923728$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			545.3
Character	$\chi$	$=$	976.545
Dual form			976.2.bw.c.625.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.246407 + 0.179025i) q^{3} +(-0.519162 + 0.576588i) q^{5} +(0.0513167 + 0.0228477i) q^{7} +(-0.898385 - 2.76494i) q^{9} +0.357306 q^{11} +(-2.36883 - 4.10294i) q^{13} +(-0.231149 + 0.0491322i) q^{15} +(-3.95384 - 0.840414i) q^{17} +(-2.65207 + 1.18078i) q^{19} +(0.00855448 + 0.0148168i) q^{21} +(-1.05067 - 3.23364i) q^{23} +(0.459718 + 4.37392i) q^{25} +(0.555983 - 1.71114i) q^{27} +(0.0456986 - 0.0791523i) q^{29} +(-0.561226 - 5.33971i) q^{31} +(0.0880425 + 0.0639667i) q^{33} +(-0.0398154 + 0.0177270i) q^{35} +(1.48315 - 1.07757i) q^{37} +(0.150832 - 1.43507i) q^{39} +(5.99975 - 4.35907i) q^{41} +(-6.36493 + 1.35291i) q^{43} +(2.06064 + 0.917457i) q^{45} +(4.89237 - 8.47384i) q^{47} +(-4.68180 - 5.19967i) q^{49} +(-0.823797 - 0.914919i) q^{51} +(1.26632 - 3.89734i) q^{53} +(-0.185500 + 0.206018i) q^{55} +(-0.864877 - 0.183835i) q^{57} +(-0.882408 + 8.39555i) q^{59} +(-7.78300 + 0.651866i) q^{61} +(0.0170704 - 0.162414i) q^{63} +(3.59551 + 0.764250i) q^{65} +(9.58869 - 10.6493i) q^{67} +(0.320009 - 0.984886i) q^{69} +(-6.75098 - 7.49772i) q^{71} +(1.20997 + 1.34380i) q^{73} +(-0.669764 + 1.16007i) q^{75} +(0.0183358 + 0.00816361i) q^{77} +(-10.7624 + 2.28762i) q^{79} +(-6.61267 + 4.80439i) q^{81} +(-1.43727 + 13.6747i) q^{83} +(2.53726 - 1.84342i) q^{85} +(0.0254307 - 0.0113225i) q^{87} +(9.19896 + 6.68343i) q^{89} +(-0.0278181 - 0.264672i) q^{91} +(0.817652 - 1.41621i) q^{93} +(0.696033 - 2.14217i) q^{95} +(-0.0409000 - 0.389138i) q^{97} +(-0.320998 - 0.987930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39}+ \cdots + 31 q^{99}+O(q^{100}) $ 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/976\mathbb{Z}\right)^\times$.

$n$	$245$	$367$	$673$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{15}\right)$

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
$3$	0.246407	+	0.179025i	0.142263	+	0.103360i	0.656640	−	0.754204i	$-0.271977\pi$
$3$	0.246407	+	0.179025i	0.142263	+	0.103360i	−0.514377	+	0.857564i	$0.671977\pi$
$4$		0			0
$5$	−0.519162	+	0.576588i	−0.232176	+	0.257858i	−0.847964	−	0.530054i	$-0.822171\pi$
$5$	−0.519162	+	0.576588i	−0.232176	+	0.257858i	0.615787	+	0.787913i	$0.288838\pi$
$6$		0			0
$7$	0.0513167	+	0.0228477i	0.0193959	+	0.00863561i	0.416412	−	0.909176i	$-0.363288\pi$
$7$	0.0513167	+	0.0228477i	0.0193959	+	0.00863561i	−0.397016	+	0.917812i	$0.629954\pi$
$8$		0			0
$9$	−0.898385	−	2.76494i	−0.299462	−	0.921648i
$10$		0			0
$11$	0.357306			0.107732			0.0538659	−	0.998548i	$-0.482846\pi$
$11$	0.357306			0.107732			0.0538659	+	0.998548i	$0.482846\pi$
$12$		0			0
$13$	−2.36883	−	4.10294i	−0.656996	−	1.13795i	−0.981389	−	0.192028i	$-0.938494\pi$
$13$	−2.36883	−	4.10294i	−0.656996	−	1.13795i	0.324393	−	0.945922i	$-0.394840\pi$
$14$		0			0
$15$	−0.231149	+	0.0491322i	−0.0596824	+	0.0126859i
$16$		0			0
$17$	−3.95384	−	0.840414i	−0.958947	−	0.203830i	−0.298254	−	0.954487i	$-0.596404\pi$
$17$	−3.95384	−	0.840414i	−0.958947	−	0.203830i	−0.660693	+	0.750656i	$0.729737\pi$
$18$		0			0
$19$	−2.65207	+	1.18078i	−0.608427	+	0.270889i	−0.687736	−	0.725961i	$-0.741395\pi$
$19$	−2.65207	+	1.18078i	−0.608427	+	0.270889i	0.0793089	+	0.996850i	$0.474729\pi$
$20$		0			0
$21$	0.00855448	+	0.0148168i	0.00186674	+	0.00323329i
$22$		0			0
$23$	−1.05067	−	3.23364i	−0.219080	−	0.674260i	−0.998839	−	0.0481793i	$-0.984658\pi$
$23$	−1.05067	−	3.23364i	−0.219080	−	0.674260i	0.779758	−	0.626081i	$-0.215342\pi$
$24$		0			0
$25$	0.459718	+	4.37392i	0.0919436	+	0.874785i
$26$		0			0
$27$	0.555983	−	1.71114i	0.106999	−	0.329309i
$28$		0			0
$29$	0.0456986	−	0.0791523i	0.00848602	−	0.0146982i	−0.861751	−	0.507331i	$-0.830632\pi$
$29$	0.0456986	−	0.0791523i	0.00848602	−	0.0146982i	0.870237	+	0.492633i	$0.163965\pi$
$30$		0			0
$31$	−0.561226	−	5.33971i	−0.100799	−	0.959040i	−0.921683	−	0.387945i	$-0.873185\pi$
$31$	−0.561226	−	5.33971i	−0.100799	−	0.959040i	0.820884	−	0.571096i	$-0.193481\pi$
$32$		0			0
$33$	0.0880425	+	0.0639667i	0.0153262	+	0.0111352i
$34$		0			0
$35$	−0.0398154	+	0.0177270i	−0.00673003	+	0.00299640i
$36$		0			0
$37$	1.48315	−	1.07757i	0.243829	−	0.177152i	−0.459159	−	0.888354i	$-0.651849\pi$
$37$	1.48315	−	1.07757i	0.243829	−	0.177152i	0.702987	+	0.711202i	$0.251849\pi$
$38$		0			0
$39$	0.150832	−	1.43507i	0.0241525	−	0.229795i
$40$		0			0
$41$	5.99975	−	4.35907i	0.937003	−	0.680772i	−0.0106944	−	0.999943i	$-0.503404\pi$
$41$	5.99975	−	4.35907i	0.937003	−	0.680772i	0.947697	+	0.319170i	$0.103404\pi$
$42$		0			0
$43$	−6.36493	+	1.35291i	−0.970643	+	0.206317i	−0.665836	−	0.746098i	$-0.731925\pi$
$43$	−6.36493	+	1.35291i	−0.970643	+	0.206317i	−0.304806	+	0.952414i	$0.598592\pi$
$44$		0			0
$45$	2.06064	+	0.917457i	0.307182	+	0.136766i
$46$		0			0
$47$	4.89237	−	8.47384i	0.713626	−	1.23604i	−0.249861	−	0.968282i	$-0.580385\pi$
$47$	4.89237	−	8.47384i	0.713626	−	1.23604i	0.963487	−	0.267755i	$-0.0862816\pi$
$48$		0			0
$49$	−4.68180	−	5.19967i	−0.668829	−	0.742810i
$50$		0			0
$51$	−0.823797	−	0.914919i	−0.115355	−	0.128114i
$52$		0			0
$53$	1.26632	−	3.89734i	0.173943	−	0.535341i	−0.825641	−	0.564196i	$-0.809186\pi$
$53$	1.26632	−	3.89734i	0.173943	−	0.535341i	0.999584	+	0.0288554i	$0.00918623\pi$
$54$		0			0
$55$	−0.185500	+	0.206018i	−0.0250128	+	0.0277795i
$56$		0			0
$57$	−0.864877	−	0.183835i	−0.114556	−	0.0243496i
$58$		0			0
$59$	−0.882408	+	8.39555i	−0.114880	+	1.09301i	0.773468	+	0.633835i	$0.218520\pi$
$59$	−0.882408	+	8.39555i	−0.114880	+	1.09301i	−0.888348	+	0.459172i	$0.848146\pi$
$60$		0			0
$61$	−7.78300	+	0.651866i	−0.996511	+	0.0834628i
$61$	−7.78300	+	0.651866i	−0.996511	+	0.0834628i
$62$		0			0
$63$	0.0170704	−	0.162414i	0.00215067	−	0.0204622i
$64$		0			0
$65$	3.59551	+	0.764250i	0.445969	+	0.0947936i
$66$		0			0
$67$	9.58869	−	10.6493i	1.17145	−	1.30102i	0.226418	−	0.974030i	$-0.427298\pi$
$67$	9.58869	−	10.6493i	1.17145	−	1.30102i	0.945027	−	0.326992i	$-0.106035\pi$
$68$		0			0
$69$	0.320009	−	0.984886i	0.0385246	−	0.118566i
$70$		0			0
$71$	−6.75098	−	7.49772i	−0.801194	−	0.889816i	0.194652	−	0.980872i	$-0.437642\pi$
$71$	−6.75098	−	7.49772i	−0.801194	−	0.889816i	−0.995846	+	0.0910567i	$0.970976\pi$
$72$		0			0
$73$	1.20997	+	1.34380i	0.141616	+	0.157280i	0.809780	−	0.586733i	$-0.199586\pi$
$73$	1.20997	+	1.34380i	0.141616	+	0.157280i	−0.668164	+	0.744014i	$0.732920\pi$
$74$		0			0
$75$	−0.669764	+	1.16007i	−0.0773377	+	0.133953i
$76$		0			0
$77$	0.0183358	+	0.00816361i	0.00208955	+	0.000930329i
$78$		0			0
$79$	−10.7624	+	2.28762i	−1.21086	+	0.257377i	−0.768731	−	0.639572i	$-0.779112\pi$
$79$	−10.7624	+	2.28762i	−1.21086	+	0.257377i	−0.442134	+	0.896949i	$0.645778\pi$
$80$		0			0
$81$	−6.61267	+	4.80439i	−0.734741	+	0.533821i
$82$		0			0
$83$	−1.43727	+	13.6747i	−0.157761	+	1.50099i	0.573675	+	0.819083i	$0.305517\pi$
$83$	−1.43727	+	13.6747i	−0.157761	+	1.50099i	−0.731436	+	0.681910i	$0.761150\pi$
$84$		0			0
$85$	2.53726	−	1.84342i	0.275204	−	0.199948i
$86$		0			0
$87$	0.0254307	−	0.0113225i	0.00272646	−	0.00121390i
$88$		0			0
$89$	9.19896	+	6.68343i	0.975087	+	0.708442i	0.956605	−	0.291387i	$-0.0941167\pi$
$89$	9.19896	+	6.68343i	0.975087	+	0.708442i	0.0184820	+	0.999829i	$0.494117\pi$
$90$		0			0
$91$	−0.0278181	−	0.264672i	−0.00291613	−	0.0277451i
$92$		0			0
$93$	0.817652	−	1.41621i	0.0847865	−	0.146855i
$94$		0			0
$95$	0.696033	−	2.14217i	0.0714115	−	0.219782i
$96$		0			0
$97$	−0.0409000	−	0.389138i	−0.00415277	−	0.0395109i	0.992249	−	0.124263i	$-0.0396567\pi$
$97$	−0.0409000	−	0.389138i	−0.00415277	−	0.0395109i	−0.996402	+	0.0847524i	$0.972990\pi$
$98$		0			0
$99$	−0.320998	−	0.987930i	−0.0322615	−	0.0992907i
$100$		0			0
$101$	−4.68632	−	8.11695i	−0.466307	−	0.807667i	0.532953	−	0.846145i	$-0.321082\pi$
$101$	−4.68632	−	8.11695i	−0.466307	−	0.807667i	−0.999259	+	0.0384783i	$0.987749\pi$
$102$		0			0
$103$	5.60665	−	2.49624i	0.552440	−	0.245962i	−0.111479	−	0.993767i	$-0.535559\pi$
$103$	5.60665	−	2.49624i	0.552440	−	0.245962i	0.663919	+	0.747805i	$0.268892\pi$
$104$		0			0
$105$	−0.0129844	−	0.00275991i	−0.00126714	−	0.000269340i
$106$		0			0
$107$	3.36397	−	0.715034i	0.325207	−	0.0691249i	−0.0424152	−	0.999100i	$-0.513505\pi$
$107$	3.36397	−	0.715034i	0.325207	−	0.0691249i	0.367622	+	0.929975i	$0.380172\pi$
$108$		0			0
$109$	8.66259	+	15.0040i	0.829726	+	1.43713i	0.898253	+	0.439478i	$0.144837\pi$
$109$	8.66259	+	15.0040i	0.829726	+	1.43713i	−0.0685276	+	0.997649i	$0.521830\pi$
$110$		0			0
$111$	0.558371			0.0529982
$112$		0			0
$113$	−5.50681	−	16.9482i	−0.518037	−	1.59435i	−0.777687	−	0.628652i	$-0.783607\pi$
$113$	−5.50681	−	16.9482i	−0.518037	−	1.59435i	0.259650	−	0.965703i	$-0.416393\pi$
$114$		0			0
$115$	2.40995	+	1.07298i	0.224729	+	0.100056i
$116$		0			0
$117$	−9.21627	+	10.2357i	−0.852045	+	0.946291i
$118$		0			0
$119$	−0.183696	−	0.133463i	−0.0168394	−	0.0122346i
$120$		0			0
$121$	−10.8723			−0.988394
$122$		0			0
$123$	2.25876			0.203666
$124$		0			0
$125$	−5.89911	−	4.28595i	−0.527632	−	0.383347i
$126$		0			0
$127$	−4.70375	+	5.22405i	−0.417391	+	0.463559i	−0.914771	−	0.403973i	$-0.867629\pi$
$127$	−4.70375	+	5.22405i	−0.417391	+	0.463559i	0.497380	+	0.867533i	$0.334295\pi$
$128$		0			0
$129$	−1.81057	−	0.806116i	−0.159411	−	0.0709746i
$130$		0			0
$131$	5.04928	+	15.5401i	0.441158	+	1.35774i	0.886643	+	0.462455i	$0.153031\pi$
$131$	5.04928	+	15.5401i	0.441158	+	1.35774i	−0.445485	+	0.895290i	$0.646969\pi$
$132$		0			0
$133$	−0.163074			−0.0141403
$134$		0			0
$135$	0.697978	+	1.20893i	0.0600723	+	0.104048i
$136$		0			0
$137$	13.3474	−	2.83707i	1.14034	−	0.242387i	0.401234	−	0.915975i	$-0.368581\pi$
$137$	13.3474	−	2.83707i	1.14034	−	0.242387i	0.739107	+	0.673588i	$0.235248\pi$
$138$		0			0
$139$	12.7699	+	2.71432i	1.08313	+	0.230226i	0.714700	−	0.699431i	$-0.246563\pi$
$139$	12.7699	+	2.71432i	1.08313	+	0.230226i	0.368427	+	0.929657i	$0.379896\pi$
$140$		0			0
$141$	2.72254	−	1.21215i	0.229279	−	0.102082i
$142$		0			0
$143$	−0.846398	−	1.46600i	−0.0707793	−	0.122593i
$144$		0			0
$145$	0.0219133	+	0.0674422i	0.00181980	+	0.00560077i
$146$		0			0
$147$	−0.222757	−	2.11939i	−0.0183727	−	0.174805i
$148$		0			0
$149$	3.73973	−	11.5097i	0.306371	−	0.942912i	−0.672791	−	0.739832i	$-0.734905\pi$
$149$	3.73973	−	11.5097i	0.306371	−	0.942912i	0.979162	−	0.203080i	$-0.0650952\pi$
$150$		0			0
$151$	2.99221	−	5.18267i	0.243503	−	0.421759i	−0.718207	−	0.695830i	$-0.755037\pi$
$151$	2.99221	−	5.18267i	0.243503	−	0.421759i	0.961710	+	0.274070i	$0.0883701\pi$
$152$		0			0
$153$	1.22837	+	11.6872i	0.0993078	+	0.944850i
$154$		0			0
$155$	3.37018	+	2.44858i	0.270699	+	0.196675i
$156$		0			0
$157$	−0.231733	+	0.103174i	−0.0184943	+	0.00823420i	−0.415963	−	0.909382i	$-0.636555\pi$
$157$	−0.231733	+	0.103174i	−0.0184943	+	0.00823420i	0.397469	+	0.917616i	$0.369889\pi$
$158$		0			0
$159$	1.00975	−	0.733627i	0.0800785	−	0.0581804i
$160$		0			0
$161$	0.0199640	−	0.189945i	0.00157339	−	0.0149698i
$162$		0			0
$163$	−17.5102	+	12.7219i	−1.37150	+	0.996456i	−0.373887	+	0.927474i	$0.621975\pi$
$163$	−17.5102	+	12.7219i	−1.37150	+	0.996456i	−0.997618	+	0.0689820i	$0.978025\pi$
$164$		0			0
$165$	−0.0825908	+	0.0175552i	−0.00642969	+	0.00136667i
$166$		0			0
$167$	−0.909760	−	0.405051i	−0.0703993	−	0.0313438i	0.371235	−	0.928539i	$-0.378934\pi$
$167$	−0.909760	−	0.405051i	−0.0703993	−	0.0313438i	−0.441634	+	0.897195i	$0.645601\pi$
$168$		0			0
$169$	−4.72274	+	8.18002i	−0.363287	+	0.629232i
$170$		0			0
$171$	5.64737	+	6.27204i	0.431865	+	0.479635i
$172$		0			0
$173$	12.4239	+	13.7981i	0.944568	+	1.04905i	0.998723	+	0.0505168i	$0.0160869\pi$
$173$	12.4239	+	13.7981i	0.944568	+	1.04905i	−0.0541549	+	0.998533i	$0.517246\pi$
$174$		0			0
$175$	−0.0763428	+	0.234959i	−0.00577097	+	0.0177612i
$176$		0			0
$177$	−1.72044	+	1.91075i	−0.129316	+	0.143621i
$178$		0			0
$179$	3.96583	+	0.842962i	0.296420	+	0.0630060i	0.353721	−	0.935351i	$-0.384916\pi$
$179$	3.96583	+	0.842962i	0.296420	+	0.0630060i	−0.0573013	+	0.998357i	$0.518250\pi$
$180$		0			0
$181$	−0.272709	+	2.59465i	−0.0202703	+	0.192859i	−0.999971	−	0.00760654i	$-0.997579\pi$
$181$	−0.272709	+	2.59465i	−0.0202703	+	0.192859i	0.979701	+	0.200465i	$0.0642454\pi$
$182$		0			0
$183$	−2.03448	−	1.23273i	−0.150393	−	0.0911258i
$184$		0			0
$185$	−0.148681	+	1.41460i	−0.0109312	+	0.104004i
$186$		0			0
$187$	−1.41273	−	0.300285i	−0.103309	−	0.0219590i
$188$		0			0
$189$	0.0676268	−	0.0751072i	0.00491912	−	0.00546324i
$190$		0			0
$191$	5.18256	−	15.9503i	0.374997	−	1.15412i	−0.568484	−	0.822694i	$-0.692470\pi$
$191$	5.18256	−	15.9503i	0.374997	−	1.15412i	0.943481	−	0.331427i	$-0.107530\pi$
$192$		0			0
$193$	10.5719	+	11.7413i	0.760982	+	0.845156i	0.991795	−	0.127842i	$-0.0408051\pi$
$193$	10.5719	+	11.7413i	0.760982	+	0.845156i	−0.230813	+	0.972998i	$0.574138\pi$
$194$		0			0
$195$	0.749139	+	0.832003i	0.0536470	+	0.0595810i
$196$		0			0
$197$	8.33958	−	14.4446i	0.594170	−	1.02913i	−0.399493	−	0.916736i	$-0.630814\pi$
$197$	8.33958	−	14.4446i	0.594170	−	1.02913i	0.993663	−	0.112397i	$-0.0358528\pi$
$198$		0			0
$199$	−21.6201	−	9.62587i	−1.53261	−	0.682360i	−0.544874	−	0.838518i	$-0.683422\pi$
$199$	−21.6201	−	9.62587i	−1.53261	−	0.682360i	−0.987732	+	0.156158i	$0.950089\pi$
$200$		0			0
$201$	4.26921	−	0.907450i	0.301127	−	0.0640066i
$202$		0			0
$203$	0.00415355	−	0.00301773i	0.000291522	−	0.000211803i
$204$		0			0
$205$	−0.601454	+	5.72245i	−0.0420073	+	0.399673i
$206$		0			0
$207$	−7.99692	+	5.81010i	−0.555824	+	0.403830i
$208$		0			0
$209$	−0.947601	+	0.421899i	−0.0655469	+	0.0291834i
$210$		0			0
$211$	17.6581	+	12.8294i	1.21564	+	0.883211i	0.995730	−	0.0923106i	$-0.0294253\pi$
$211$	17.6581	+	12.8294i	1.21564	+	0.883211i	0.219905	+	0.975521i	$0.429425\pi$
$212$		0			0
$213$	−0.321207	−	3.05608i	−0.0220088	−	0.209399i
$214$		0			0
$215$	2.52436	−	4.37232i	0.172160	−	0.298190i
$216$		0			0
$217$	0.0931997	−	0.286839i	0.00632681	−	0.0194719i
$218$		0			0
$219$	0.0575694	+	0.547736i	0.00389018	+	0.0370126i
$220$		0			0
$221$	5.91781	+	18.2132i	0.398075	+	1.22515i
$222$		0			0
$223$	12.3612	+	21.4103i	0.827769	+	1.43374i	0.899785	+	0.436334i	$0.143723\pi$
$223$	12.3612	+	21.4103i	0.827769	+	1.43374i	−0.0720161	+	0.997403i	$0.522943\pi$
$224$		0			0
$225$	11.6806	−	5.20056i	0.778710	−	0.346704i
$226$		0			0
$227$	−5.04428	−	1.07220i	−0.334801	−	0.0711641i	0.0374439	−	0.999299i	$-0.488078\pi$
$227$	−5.04428	−	1.07220i	−0.334801	−	0.0711641i	−0.372245	+	0.928135i	$0.621412\pi$
$228$		0			0
$229$	−15.2445	+	3.24032i	−1.00738	+	0.214126i	−0.681919	−	0.731428i	$-0.738854\pi$
$229$	−15.2445	+	3.24032i	−1.00738	+	0.214126i	−0.325465	+	0.945554i	$0.605521\pi$
$230$		0			0
$231$	0.00305657	+	0.00529413i	0.000201107	+	0.000348328i
$232$		0			0
$233$	−10.2382			−0.670730			−0.335365	−	0.942088i	$-0.608860\pi$
$233$	−10.2382			−0.670730			−0.335365	+	0.942088i	$0.608860\pi$
$234$		0			0
$235$	2.34598	+	7.22018i	0.153035	+	0.470993i
$236$		0			0
$237$	−3.06147	−	1.36305i	−0.198864	−	0.0885399i
$238$		0			0
$239$	10.7496	−	11.9386i	0.695333	−	0.772246i	−0.287293	−	0.957843i	$-0.592755\pi$
$239$	10.7496	−	11.9386i	0.695333	−	0.772246i	0.982626	+	0.185597i	$0.0594219\pi$
$240$		0			0
$241$	−0.486166	−	0.353220i	−0.0313167	−	0.0227529i	0.572017	−	0.820242i	$-0.306161\pi$
$241$	−0.486166	−	0.353220i	−0.0313167	−	0.0227529i	−0.603333	+	0.797489i	$0.706161\pi$
$242$		0			0
$243$	−7.88711			−0.505958
$244$		0			0
$245$	5.42868			0.346826
$246$		0			0
$247$	11.1270	+	8.08422i	0.707993	+	0.514387i
$248$		0			0
$249$	−2.80226	+	3.11223i	−0.177586	+	0.197230i
$250$		0			0
$251$	−16.9943	−	7.56635i	−1.07267	−	0.477584i	−0.207074	−	0.978325i	$-0.566394\pi$
$251$	−16.9943	−	7.56635i	−1.07267	−	0.477584i	−0.865597	+	0.500741i	$0.833061\pi$
$252$		0			0
$253$	−0.375411	−	1.15540i	−0.0236019	−	0.0726392i
$254$		0			0
$255$	0.955216			0.0598180
$256$		0			0
$257$	3.00738	+	5.20894i	0.187596	+	0.324925i	0.944448	−	0.328661i	$-0.106597\pi$
$257$	3.00738	+	5.20894i	0.187596	+	0.324925i	−0.756853	+	0.653586i	$0.773264\pi$
$258$		0			0
$259$	0.100730	−	0.0214109i	0.00625909	−	0.00133041i
$260$		0			0
$261$	−0.259907	−	0.0552449i	−0.0160878	−	0.00341957i
$262$		0			0
$263$	8.37686	−	3.72962i	0.516539	−	0.229978i	−0.131874	−	0.991266i	$-0.542100\pi$
$263$	8.37686	−	3.72962i	0.516539	−	0.229978i	0.648413	+	0.761288i	$0.275433\pi$
$264$		0			0
$265$	1.58973	+	2.75350i	0.0976565	+	0.169146i
$266$		0			0
$267$	1.07018	+	3.29369i	0.0654942	+	0.201570i
$268$		0			0
$269$	2.41995	+	23.0243i	0.147547	+	1.40382i	0.778330	+	0.627856i	$0.216067\pi$
$269$	2.41995	+	23.0243i	0.147547	+	1.40382i	−0.630783	+	0.775959i	$0.717266\pi$
$270$		0			0
$271$	2.74643	−	8.45264i	0.166834	−	0.513461i	−0.832333	−	0.554276i	$-0.812995\pi$
$271$	2.74643	−	8.45264i	0.166834	−	0.513461i	0.999167	+	0.0408146i	$0.0129953\pi$
$272$		0			0
$273$	0.0405283	−	0.0701970i	0.00245288	−	0.00424852i
$274$		0			0
$275$	0.164260	+	1.56283i	0.00990524	+	0.0942421i
$276$		0			0
$277$	1.70524	+	1.23893i	0.102458	+	0.0744402i	0.637835	−	0.770173i	$-0.279830\pi$
$277$	1.70524	+	1.23893i	0.102458	+	0.0744402i	−0.535377	+	0.844613i	$0.679830\pi$
$278$		0			0
$279$	−14.2598	+	6.34887i	−0.853712	+	0.380097i
$280$		0			0
$281$	−8.81948	+	6.40773i	−0.526126	+	0.382253i	−0.818907	−	0.573927i	$-0.805419\pi$
$281$	−8.81948	+	6.40773i	−0.526126	+	0.382253i	0.292780	+	0.956180i	$0.405419\pi$
$282$		0			0
$283$	−1.28047	+	12.1829i	−0.0761162	+	0.724197i	0.888202	+	0.459453i	$0.151954\pi$
$283$	−1.28047	+	12.1829i	−0.0761162	+	0.724197i	−0.964319	+	0.264745i	$0.914712\pi$
$284$		0			0
$285$	0.555009	−	0.403238i	0.0328759	−	0.0238857i
$286$		0			0
$287$	0.407482	−	0.0866130i	0.0240529	−	0.00511260i
$288$		0			0
$289$	−0.603735	−	0.268800i	−0.0355138	−	0.0158118i
$290$		0			0
$291$	0.0595873	−	0.103208i	0.00349307	−	0.00605018i
$292$		0			0
$293$	2.08473	+	2.31533i	0.121791	+	0.135263i	0.800957	−	0.598722i	$-0.204325\pi$
$293$	2.08473	+	2.31533i	0.121791	+	0.135263i	−0.679165	+	0.733985i	$0.737658\pi$
$294$		0			0
$295$	−4.38266	−	4.86744i	−0.255168	−	0.283393i
$296$		0			0
$297$	0.198656	−	0.611400i	0.0115272	−	0.0354770i
$298$		0			0
$299$	−10.7785	+	11.9708i	−0.623339	+	0.692289i
$300$		0			0
$301$	−0.357538	−	0.0759971i	−0.0206082	−	0.00438040i
$302$		0			0
$303$	0.298395	−	2.83904i	0.0171424	−	0.163099i
$304$		0			0
$305$	3.66478	−	4.82601i	0.209845	−	0.276337i
$306$		0			0
$307$	−0.0698649	+	0.664720i	−0.00398740	+	0.0379376i	−0.996335	−	0.0855407i	$-0.972738\pi$
$307$	−0.0698649	+	0.664720i	−0.00398740	+	0.0379376i	0.992347	+	0.123478i	$0.0394049\pi$
$308$		0			0
$309$	1.82841	+	0.388640i	0.104014	+	0.0221089i
$310$		0			0
$311$	12.5553	−	13.9441i	0.711947	−	0.790697i	−0.273283	−	0.961934i	$-0.588110\pi$
$311$	12.5553	−	13.9441i	0.711947	−	0.790697i	0.985230	+	0.171237i	$0.0547763\pi$
$312$		0			0
$313$	−1.36172	+	4.19095i	−0.0769690	+	0.236886i	−0.982137	−	0.188168i	$-0.939745\pi$
$313$	−1.36172	+	4.19095i	−0.0769690	+	0.236886i	0.905168	+	0.425054i	$0.139745\pi$
$314$		0			0
$315$	0.0847836	+	0.0941617i	0.00477702	+	0.00530541i
$316$		0			0
$317$	4.04105	+	4.48804i	0.226968	+	0.252073i	0.845863	−	0.533400i	$-0.179086\pi$
$317$	4.04105	+	4.48804i	0.226968	+	0.252073i	−0.618895	+	0.785474i	$0.712419\pi$
$318$		0			0
$319$	0.0163284	−	0.0282816i	0.000914214	−	0.00158346i
$320$		0			0
$321$	0.956914	+	0.426045i	0.0534097	+	0.0237795i
$322$		0			0
$323$	11.4782	−	2.43977i	0.638664	−	0.135752i
$324$		0			0
$325$	16.8569	−	12.2473i	0.935055	−	0.679357i
$326$		0			0
$327$	−0.551579	+	5.24792i	−0.0305024	+	0.290211i
$328$		0			0
$329$	0.444668	−	0.323070i	0.0245153	−	0.0178114i
$330$		0			0
$331$	−11.1012	+	4.94258i	−0.610179	+	0.271669i	−0.688474	−	0.725261i	$-0.741719\pi$
$331$	−11.1012	+	4.94258i	−0.610179	+	0.271669i	0.0782953	+	0.996930i	$0.475052\pi$
$332$		0			0
$333$	−4.31187	−	3.13275i	−0.236289	−	0.171674i
$334$		0			0
$335$	1.16219	+	11.0575i	0.0634970	+	0.604133i
$336$		0			0
$337$	16.4343	−	28.4651i	0.895234	−	1.55059i	0.0617193	−	0.998094i	$-0.480342\pi$
$337$	16.4343	−	28.4651i	0.895234	−	1.55059i	0.833515	−	0.552497i	$-0.186325\pi$
$338$		0			0
$339$	1.67724	−	5.16201i	0.0910952	−	0.280362i
$340$		0			0
$341$	−0.200529	−	1.90791i	−0.0108593	−	0.103319i
$342$		0			0
$343$	−0.242964	−	0.747765i	−0.0131188	−	0.0403755i
$344$		0			0
$345$	0.401737	+	0.695829i	0.0216288	+	0.0374622i
$346$		0			0
$347$	19.3240	−	8.60362i	1.03737	−	0.461866i	0.183864	−	0.982952i	$-0.441139\pi$
$347$	19.3240	−	8.60362i	1.03737	−	0.461866i	0.853505	+	0.521085i	$0.174473\pi$
$348$		0			0
$349$	−18.8538	−	4.00750i	−1.00922	−	0.214516i	−0.326501	−	0.945197i	$-0.605870\pi$
$349$	−18.8538	−	4.00750i	−1.00922	−	0.214516i	−0.682719	+	0.730681i	$0.739203\pi$
$350$		0			0
$351$	−8.33773	+	1.77224i	−0.445035	+	0.0945951i
$352$		0			0
$353$	−1.48031	−	2.56397i	−0.0787889	−	0.136466i	0.823939	−	0.566679i	$-0.191772\pi$
$353$	−1.48031	−	2.56397i	−0.0787889	−	0.136466i	−0.902728	+	0.430212i	$0.858439\pi$
$354$		0			0
$355$	7.82795			0.415464
$356$		0			0
$357$	−0.0213708	−	0.0657725i	−0.00113106	−	0.00348105i
$358$		0			0
$359$	31.0373	+	13.8187i	1.63809	+	0.729324i	0.999201	−	0.0399770i	$-0.0127285\pi$
$359$	31.0373	+	13.8187i	1.63809	+	0.729324i	0.638887	+	0.769301i	$0.279395\pi$
$360$		0			0
$361$	−7.07423	+	7.85673i	−0.372328	+	0.413512i
$362$		0			0
$363$	−2.67902	−	1.94642i	−0.140612	−	0.102161i
$364$		0			0
$365$	−1.40299			−0.0734358
$366$		0			0
$367$	0.121417			0.00633790			0.00316895	−	0.999995i	$-0.498991\pi$
$367$	0.121417			0.00633790			0.00316895	+	0.999995i	$0.498991\pi$
$368$		0			0
$369$	−17.4427	−	12.6728i	−0.908029	−	0.659722i
$370$		0			0
$371$	0.154029	−	0.171066i	0.00799677	−	0.00888131i
$372$		0			0
$373$	−0.701698	−	0.312416i	−0.0363326	−	0.0161763i	0.388490	−	0.921453i	$-0.372997\pi$
$373$	−0.701698	−	0.312416i	−0.0363326	−	0.0161763i	−0.424822	+	0.905277i	$0.639663\pi$
$374$		0			0
$375$	−0.686287	−	2.11217i	−0.0354397	−	0.109072i
$376$		0			0
$377$	−0.433009			−0.0223011
$378$		0			0
$379$	−8.04967	−	13.9424i	−0.413484	−	0.716175i	0.581784	−	0.813343i	$-0.302355\pi$
$379$	−8.04967	−	13.9424i	−0.413484	−	0.716175i	−0.995268	+	0.0971683i	$0.969021\pi$
$380$		0			0
$381$	−2.09427	+	0.445151i	−0.107293	+	0.0228058i
$382$		0			0
$383$	−16.5520	−	3.51824i	−0.845770	−	0.179774i	−0.235408	−	0.971897i	$-0.575643\pi$
$383$	−16.5520	−	3.51824i	−0.845770	−	0.179774i	−0.610362	+	0.792123i	$0.708976\pi$
$384$		0			0
$385$	−0.0142263	+	0.00633395i	−0.000725038	+	0.000322808i
$386$		0			0
$387$	9.45887	+	16.3832i	0.480821	+	0.832807i
$388$		0			0
$389$	−9.06792	−	27.9082i	−0.459762	−	1.41500i	−0.865452	−	0.500991i	$-0.832969\pi$
$389$	−9.06792	−	27.9082i	−0.459762	−	1.41500i	0.405690	−	0.914011i	$-0.367031\pi$
$390$		0			0
$391$	1.43659	+	13.6683i	0.0726517	+	0.691234i
$392$		0			0
$393$	−1.53789	+	4.73313i	−0.0775762	+	0.238755i
$394$		0			0
$395$	4.26842	−	7.39312i	0.214768	−	0.371988i
$396$		0			0
$397$	0.812155	+	7.72714i	0.0407609	+	0.387814i	0.995816	+	0.0913846i	$0.0291293\pi$
$397$	0.812155	+	7.72714i	0.0407609	+	0.387814i	−0.955055	+	0.296429i	$0.904204\pi$
$398$		0			0
$399$	−0.0401825	−	0.0291943i	−0.00201164	−	0.00146154i
$400$		0			0
$401$	10.8913	−	4.84912i	0.543885	−	0.242153i	−0.116355	−	0.993208i	$-0.537121\pi$
$401$	10.8913	−	4.84912i	0.543885	−	0.242153i	0.660240	+	0.751054i	$0.270454\pi$
$402$		0			0
$403$	−20.5790	+	14.9516i	−1.02512	+	0.744790i
$404$		0			0
$405$	0.662897	−	6.30704i	0.0329396	−	0.313400i
$406$		0			0
$407$	0.529938	−	0.385023i	0.0262681	−	0.0190849i
$408$		0			0
$409$	−23.8723	+	5.07422i	−1.18041	+	0.250904i	−0.756004	−	0.654567i	$-0.772851\pi$
$409$	−23.8723	+	5.07422i	−1.18041	+	0.250904i	−0.424407	+	0.905471i	$0.639517\pi$
$410$		0			0
$411$	3.79678	+	1.69044i	0.187282	+	0.0833831i
$412$		0			0
$413$	−0.237101	+	0.410671i	−0.0116670	+	0.0202078i
$414$		0			0
$415$	−7.13849	−	7.92810i	−0.350415	−	0.389175i
$416$		0			0
$417$	2.66065	+	2.95495i	0.130293	+	0.144705i
$418$		0			0
$419$	6.72086	−	20.6847i	0.328335	−	1.01051i	−0.641577	−	0.767059i	$-0.721719\pi$
$419$	6.72086	−	20.6847i	0.328335	−	1.01051i	0.969912	−	0.243454i	$-0.0782805\pi$
$420$		0			0
$421$	5.92290	−	6.57805i	0.288665	−	0.320595i	−0.581318	−	0.813676i	$-0.697463\pi$
$421$	5.92290	−	6.57805i	0.288665	−	0.320595i	0.869983	+	0.493082i	$0.164130\pi$
$422$		0			0
$423$	−27.8249	−	5.91437i	−1.35289	−	0.287566i
$424$		0			0
$425$	1.85826	−	17.6801i	0.0901387	−	0.857613i
$426$		0			0
$427$	−0.414292	−	0.144372i	−0.0200490	−	0.00698664i
$428$		0			0
$429$	0.0538932	−	0.512759i	0.00260199	−	0.0247563i
$430$		0			0
$431$	−6.97394	−	1.48236i	−0.335923	−	0.0714027i	0.0368620	−	0.999320i	$-0.488264\pi$
$431$	−6.97394	−	1.48236i	−0.335923	−	0.0714027i	−0.372785	+	0.927918i	$0.621597\pi$
$432$		0			0
$433$	12.8192	−	14.2372i	0.616054	−	0.684197i	−0.351695	−	0.936115i	$-0.614395\pi$
$433$	12.8192	−	14.2372i	0.616054	−	0.684197i	0.967749	+	0.251918i	$0.0810612\pi$
$434$		0			0
$435$	−0.00667425	+	0.0205412i	−0.000320006	+	0.000984877i
$436$		0			0
$437$	6.60467	+	7.33523i	0.315944	+	0.350891i
$438$		0			0
$439$	−24.5013	−	27.2114i	−1.16938	−	1.29873i	−0.946062	−	0.323987i	$-0.894977\pi$
$439$	−24.5013	−	27.2114i	−1.16938	−	1.29873i	−0.223321	−	0.974745i	$-0.571690\pi$
$440$		0			0
$441$	−10.1707	+	17.6162i	−0.484321	+	0.838868i
$442$		0			0
$443$	32.7390	+	14.5763i	1.55548	+	0.692543i	0.991118	−	0.132987i	$-0.0424569\pi$
$443$	32.7390	+	14.5763i	1.55548	+	0.692543i	0.564359	+	0.825530i	$0.309124\pi$
$444$		0			0
$445$	−8.62934	+	1.83422i	−0.409070	+	0.0869505i
$446$		0			0
$447$	2.98202	−	2.16656i	0.141045	−	0.102475i
$448$		0			0
$449$	−1.06647	+	10.1467i	−0.0503296	+	0.478855i	0.940106	+	0.340881i	$0.110725\pi$
$449$	−1.06647	+	10.1467i	−0.0503296	+	0.478855i	−0.990436	+	0.137973i	$0.955941\pi$
$450$		0			0
$451$	2.14374	−	1.55752i	0.100945	−	0.0733408i
$452$		0			0
$453$	1.66513	−	0.741363i	0.0782346	−	0.0348323i
$454$		0			0
$455$	0.167049	+	0.121368i	0.00783136	+	0.00568982i
$456$		0			0
$457$	−1.13997	−	10.8461i	−0.0533256	−	0.507359i	−0.988287	−	0.152609i	$-0.951233\pi$
$457$	−1.13997	−	10.8461i	−0.0533256	−	0.507359i	0.934961	−	0.354750i	$-0.115434\pi$
$458$		0			0
$459$	−3.63633	+	6.29831i	−0.169729	+	0.293980i
$460$		0			0
$461$	2.97286	−	9.14952i	0.138460	−	0.426135i	−0.857652	−	0.514230i	$-0.828078\pi$
$461$	2.97286	−	9.14952i	0.138460	−	0.426135i	0.996112	+	0.0880946i	$0.0280778\pi$
$462$		0			0
$463$	−2.59648	−	24.7039i	−0.120669	−	1.14809i	−0.872460	−	0.488686i	$-0.837476\pi$
$463$	−2.59648	−	24.7039i	−0.120669	−	1.14809i	0.751791	−	0.659402i	$-0.229190\pi$
$464$		0			0
$465$	0.392078	+	1.20669i	0.0181822	+	0.0559591i
$466$		0			0
$467$	−14.0947	−	24.4127i	−0.652224	−	1.12969i	−0.982582	−	0.185830i	$-0.940503\pi$
$467$	−14.0947	−	24.4127i	−0.652224	−	1.12969i	0.330358	−	0.943856i	$-0.392831\pi$
$468$		0			0
$469$	0.735373	−	0.327409i	0.0339564	−	0.0151183i
$470$		0			0
$471$	−0.0755713	−	0.0160632i	−0.00348214	−	0.000740152i
$472$		0			0
$473$	−2.27423	+	0.483402i	−0.104569	+	0.0222268i
$474$		0			0
$475$	−6.38384	−	11.0571i	−0.292911	−	0.507336i
$476$		0			0
$477$	−11.9136			−0.545485
$478$		0			0
$479$	−8.58133	−	26.4106i	−0.392091	−	1.20673i	−0.931204	−	0.364498i	$-0.881240\pi$
$479$	−8.58133	−	26.4106i	−0.392091	−	1.20673i	0.539113	−	0.842233i	$-0.318760\pi$
$480$		0			0
$481$	−7.93455	−	3.53269i	−0.361784	−	0.161077i
$482$		0			0
$483$	0.0389242	−	0.0432297i	0.00177111	−	0.00196702i
$484$		0			0
$485$	0.245606	+	0.178443i	0.0111524	+	0.00810269i
$486$		0			0
$487$	−0.123526			−0.00559750			−0.00279875	−	0.999996i	$-0.500891\pi$
$487$	−0.123526			−0.00559750			−0.00279875	+	0.999996i	$0.500891\pi$
$488$		0			0
$489$	−6.59217			−0.298108
$490$		0			0
$491$	−15.7011	−	11.4075i	−0.708579	−	0.514813i	0.174136	−	0.984722i	$-0.444287\pi$
$491$	−15.7011	−	11.4075i	−0.708579	−	0.514813i	−0.882715	+	0.469909i	$0.844287\pi$
$492$		0			0
$493$	−0.247206	+	0.274550i	−0.0111336	+	0.0123651i
$494$		0			0
$495$	0.736279	+	0.327813i	0.0330933	+	0.0147341i
$496$		0			0
$497$	−0.175133	−	0.539003i	−0.00785577	−	0.0241776i
$498$		0			0
$499$	1.38403			0.0619576			0.0309788	−	0.999520i	$-0.490138\pi$
$499$	1.38403			0.0619576			0.0309788	+	0.999520i	$0.490138\pi$
$500$		0			0
$501$	−0.151657	−	0.262677i	−0.00677552	−	0.0117355i
$502$		0			0
$503$	−2.65066	+	0.563414i	−0.118187	+	0.0251214i	−0.266625	−	0.963800i	$-0.585909\pi$
$503$	−2.65066	+	0.563414i	−0.118187	+	0.0251214i	0.148438	+	0.988922i	$0.452575\pi$
$504$		0			0
$505$	7.11310	+	1.51194i	0.316529	+	0.0672803i
$506$		0			0
$507$	−2.62814	+	1.17012i	−0.116720	+	0.0519670i
$508$		0			0
$509$	−4.03921	−	6.99611i	−0.179035	−	0.310097i	0.762515	−	0.646970i	$-0.223964\pi$
$509$	−4.03921	−	6.99611i	−0.179035	−	0.310097i	−0.941550	+	0.336873i	$0.890631\pi$
$510$		0			0
$511$	0.0313887	+	0.0966045i	0.00138855	+	0.00427353i
$512$		0			0
$513$	0.545970	+	5.19456i	0.0241052	+	0.229345i
$514$		0			0
$515$	−1.47146	+	4.52868i	−0.0648402	+	0.199558i
$516$		0			0
$517$	1.74807	−	3.02775i	0.0768802	−	0.133160i
$518$		0			0
$519$	0.591119	+	5.62412i	0.0259473	+	0.246872i
$520$		0			0
$521$	8.76525	+	6.36833i	0.384012	+	0.279001i	0.762998	−	0.646401i	$-0.223727\pi$
$521$	8.76525	+	6.36833i	0.384012	+	0.279001i	−0.378985	+	0.925403i	$0.623727\pi$
$522$		0			0
$523$	3.89454	−	1.73396i	0.170296	−	0.0758208i	−0.319818	−	0.947479i	$-0.603622\pi$
$523$	3.89454	−	1.73396i	0.170296	−	0.0758208i	0.490114	+	0.871658i	$0.336955\pi$
$524$		0			0
$525$	−0.0608749	+	0.0442282i	−0.00265680	+	0.00193028i
$526$		0			0
$527$	−2.26857	+	21.5840i	−0.0988205	+	0.940214i
$528$		0			0
$529$	9.25490	−	6.72408i	0.402387	−	0.292351i
$530$		0			0
$531$	24.0060	−	5.10262i	1.04177	−	0.221435i
$532$		0			0
$533$	−32.0974	−	14.2907i	−1.39029	−	0.618998i
$534$		0			0
$535$	−1.33417	+	2.31084i	−0.0576810	+	0.0999065i
$536$		0			0
$537$	0.826295	+	0.917693i	0.0356573	+	0.0396014i
$538$		0			0
$539$	−1.67284	−	1.85787i	−0.0720541	−	0.0800242i
$540$		0			0
$541$	−1.22930	+	3.78339i	−0.0528516	+	0.162660i	−0.973998	−	0.226555i	$-0.927254\pi$
$541$	−1.22930	+	3.78339i	−0.0528516	+	0.162660i	0.921147	+	0.389215i	$0.127254\pi$
$542$		0			0
$543$	−0.531704	+	0.590518i	−0.0228176	+	0.0253415i
$544$		0			0
$545$	−13.1484	−	2.79479i	−0.563218	−	0.119716i
$546$		0			0
$547$	2.22028	−	21.1245i	0.0949321	−	0.903219i	−0.838605	−	0.544739i	$-0.816629\pi$
$547$	2.22028	−	21.1245i	0.0949321	−	0.903219i	0.933538	−	0.358479i	$-0.116705\pi$
$548$		0			0
$549$	8.79450	+	20.9339i	0.375340	+	0.893438i
$550$		0			0
$551$	−0.0277347	+	0.263878i	−0.00118154	+	0.0112416i
$552$		0			0
$553$	−0.604558	−	0.128503i	−0.0257084	−	0.00546449i
$554$		0			0
$555$	−0.289885	+	0.321950i	−0.0123049	+	0.0136660i
$556$		0			0
$557$	10.6673	−	32.8306i	0.451989	−	1.39108i	−0.422645	−	0.906295i	$-0.638898\pi$
$557$	10.6673	−	32.8306i	0.451989	−	1.39108i	0.874634	−	0.484784i	$-0.161102\pi$
$558$		0			0
$559$	20.6284	+	22.9101i	0.872486	+	0.968994i
$560$		0			0
$561$	−0.294347	−	0.326906i	−0.0124274	−	0.0138020i
$562$		0			0
$563$	1.65368	−	2.86427i	0.0696945	−	0.120714i	−0.829072	−	0.559141i	$-0.811131\pi$
$563$	1.65368	−	2.86427i	0.0696945	−	0.120714i	0.898767	+	0.438427i	$0.144464\pi$
$564$		0			0
$565$	12.6311	+	5.62372i	0.531393	+	0.236592i
$566$		0			0
$567$	−0.449110	+	0.0954612i	−0.0188608	+	0.00400899i
$568$		0			0
$569$	26.6605	−	19.3700i	1.11767	−	0.812033i	0.133813	−	0.991007i	$-0.457278\pi$
$569$	26.6605	−	19.3700i	1.11767	−	0.812033i	0.983854	+	0.178974i	$0.0572778\pi$
$570$		0			0
$571$	−0.510448	+	4.85659i	−0.0213616	+	0.203242i	−0.999997	−	0.00236039i	$-0.999249\pi$
$571$	−0.510448	+	4.85659i	−0.0213616	+	0.203242i	0.978636	+	0.205602i	$0.0659153\pi$
$572$		0			0
$573$	4.13252	−	3.00245i	0.172638	−	0.125429i
$574$		0			0
$575$	13.6607	−	6.08212i	0.569689	−	0.253642i
$576$		0			0
$577$	−6.15702	−	4.47334i	−0.256320	−	0.186228i	0.452203	−	0.891915i	$-0.350638\pi$
$577$	−6.15702	−	4.47334i	−0.256320	−	0.186228i	−0.708523	+	0.705688i	$0.750638\pi$
$578$		0			0
$579$	0.503004	+	4.78576i	0.0209041	+	0.198890i
$580$		0			0
$581$	−0.386191	+	0.668902i	−0.0160219	+	0.0277507i
$582$		0			0
$583$	0.452464	−	1.39254i	0.0187392	−	0.0576732i
$584$		0			0
$585$	−1.11705	−	10.6280i	−0.0461842	−	0.439413i
$586$		0			0
$587$	−12.3725	−	38.0785i	−0.510666	−	1.57167i	−0.791032	−	0.611775i	$-0.790456\pi$
$587$	−12.3725	−	38.0785i	−0.510666	−	1.57167i	0.280366	−	0.959893i	$-0.409544\pi$
$588$		0			0
$589$	7.79343	+	13.4986i	0.321123	+	0.556201i
$590$		0			0
$591$	4.64087	−	2.06625i	0.190900	−	0.0849941i
$592$		0			0
$593$	−19.2116	−	4.08354i	−0.788924	−	0.167691i	−0.204207	−	0.978928i	$-0.565461\pi$
$593$	−19.2116	−	4.08354i	−0.788924	−	0.167691i	−0.584718	+	0.811237i	$0.698795\pi$
$594$		0			0
$595$	0.172322	−	0.0366281i	0.00706450	−	0.00150161i
$596$		0			0
$597$	−3.60406	−	6.24241i	−0.147504	−	0.255485i
$598$		0			0
$599$	−6.47096			−0.264396			−0.132198	−	0.991223i	$-0.542204\pi$
$599$	−6.47096			−0.264396			−0.132198	+	0.991223i	$0.542204\pi$
$600$		0			0
$601$	12.6153	+	38.8259i	0.514589	+	1.58374i	0.784028	+	0.620725i	$0.213162\pi$
$601$	12.6153	+	38.8259i	0.514589	+	1.58374i	−0.269439	+	0.963017i	$0.586838\pi$
$602$		0			0
$603$	−38.0591	−	16.9450i	−1.54989	−	0.690054i
$604$		0			0
$605$	5.64451	−	6.26886i	0.229482	−	0.254865i
$606$		0			0
$607$	26.9283	+	19.5645i	1.09298	+	0.794100i	0.979901	−	0.199486i	$-0.0639271\pi$
$607$	26.9283	+	19.5645i	1.09298	+	0.794100i	0.113084	+	0.993585i	$0.463927\pi$
$608$		0			0
$609$	0.00156371			6.33648e−5
$610$		0			0
$611$	−46.3568			−1.87540
$612$		0			0
$613$	10.2035	+	7.41328i	0.412116	+	0.299420i	0.774458	−	0.632626i	$-0.218023\pi$
$613$	10.2035	+	7.41328i	0.412116	+	0.299420i	−0.362342	+	0.932045i	$0.618023\pi$
$614$		0			0
$615$	−1.17266	+	1.30237i	−0.0472864	+	0.0525168i
$616$		0			0
$617$	31.1298	+	13.8599i	1.25324	+	0.557978i	0.922592	−	0.385776i	$-0.126066\pi$
$617$	31.1298	+	13.8599i	1.25324	+	0.557978i	0.330647	+	0.943754i	$0.392733\pi$
$618$		0			0
$619$	2.18227	+	6.71633i	0.0877128	+	0.269952i	0.985286	−	0.170913i	$-0.0546717\pi$
$619$	2.18227	+	6.71633i	0.0877128	+	0.269952i	−0.897573	+	0.440865i	$0.854672\pi$
$620$		0			0
$621$	−6.11736			−0.245481
$622$		0			0
$623$	0.319359	+	0.553147i	0.0127949	+	0.0221613i
$624$		0			0
$625$	−15.9757	+	3.39574i	−0.639029	+	0.135830i
$626$		0			0
$627$	−0.309026	−	0.0656854i	−0.0123413	−	0.00262322i
$628$		0			0
$629$	−6.76975	+	3.01408i	−0.269927	+	0.120179i
$630$		0			0
$631$	15.1558	+	26.2506i	0.603342	+	1.04502i	0.992311	+	0.123768i	$0.0394979\pi$
$631$	15.1558	+	26.2506i	0.603342	+	1.04502i	−0.388969	+	0.921251i	$0.627169\pi$
$632$		0			0
$633$	2.05430	+	6.32249i	0.0816512	+	0.251296i
$634$		0			0
$635$	−0.570113	−	5.42426i	−0.0226242	−	0.215255i
$636$		0			0
$637$	−10.2435	+	31.5263i	−0.405863	+	1.24912i
$638$		0			0
$639$	−14.6658	+	25.4019i	−0.580170	+	1.00488i
$640$		0			0
$641$	−3.82603	−	36.4023i	−0.151119	−	1.43780i	−0.762767	−	0.646673i	$-0.776160\pi$
$641$	−3.82603	−	36.4023i	−0.151119	−	1.43780i	0.611648	−	0.791130i	$-0.290507\pi$
$642$		0			0
$643$	−39.4652	−	28.6732i	−1.55636	−	1.13076i	−0.938919	−	0.344138i	$-0.888171\pi$
$643$	−39.4652	−	28.6732i	−1.55636	−	1.13076i	−0.617437	−	0.786620i	$-0.711829\pi$
$644$		0			0
$645$	1.40477	−	0.625446i	0.0553130	−	0.0246269i
$646$		0			0
$647$	35.8065	−	26.0150i	1.40770	−	1.02275i	0.414049	−	0.910255i	$-0.364114\pi$
$647$	35.8065	−	26.0150i	1.40770	−	1.02275i	0.993652	−	0.112499i	$-0.0358857\pi$
$648$		0			0
$649$	−0.315289	+	2.99978i	−0.0123762	+	0.117752i
$650$		0			0
$651$	0.0743164	−	0.0539940i	0.00291269	−	0.00211619i
$652$		0			0
$653$	−14.7927	+	3.14429i	−0.578884	+	0.123046i	−0.488043	−	0.872820i	$-0.662289\pi$
$653$	−14.7927	+	3.14429i	−0.578884	+	0.123046i	−0.0908413	+	0.995865i	$0.528956\pi$
$654$		0			0
$655$	−11.5816	−	5.15648i	−0.452532	−	0.201480i
$656$		0			0
$657$	2.62853	−	4.55274i	0.102549	−	0.177619i
$658$		0			0
$659$	1.04211	+	1.15738i	0.0405949	+	0.0450852i	0.763100	−	0.646280i	$-0.223676\pi$
$659$	1.04211	+	1.15738i	0.0405949	+	0.0450852i	−0.722505	+	0.691365i	$0.757010\pi$
$660$		0			0
$661$	−24.7463	−	27.4836i	−0.962521	−	1.06899i	−0.997575	−	0.0696025i	$-0.977827\pi$
$661$	−24.7463	−	27.4836i	−0.962521	−	1.06899i	0.0350538	−	0.999385i	$-0.488840\pi$
$662$		0			0
$663$	−1.80242	+	5.54728i	−0.0700002	+	0.215439i
$664$		0			0
$665$	0.0846617	−	0.0940264i	0.00328304	−	0.00364619i
$666$		0			0
$667$	−0.303964	−	0.0646096i	−0.0117695	−	0.00250169i
$668$		0			0
$669$	−0.787084	+	7.48860i	−0.0304304	+	0.289526i
$670$		0			0
$671$	−2.78091	+	0.232915i	−0.107356	+	0.00899160i
$672$		0			0
$673$	4.80346	−	45.7019i	0.185160	−	1.76168i	−0.369151	−	0.929369i	$-0.620352\pi$
$673$	4.80346	−	45.7019i	0.185160	−	1.76168i	0.554311	−	0.832309i	$-0.312982\pi$
$674$		0			0
$675$	7.73999	+	1.64519i	0.297912	+	0.0633232i
$676$		0			0
$677$	9.96991	−	11.0727i	0.383175	−	0.425559i	−0.520444	−	0.853896i	$-0.674234\pi$
$677$	9.96991	−	11.0727i	0.383175	−	0.425559i	0.903619	+	0.428337i	$0.140900\pi$
$678$		0			0
$679$	0.00679204	−	0.0209037i	0.000260654	−	0.000802212i
$680$		0			0
$681$	−1.05100	−	1.16725i	−0.0402742	−	0.0447291i
$682$		0			0
$683$	−7.58159	−	8.42020i	−0.290101	−	0.322190i	0.580423	−	0.814315i	$-0.302887\pi$
$683$	−7.58159	−	8.42020i	−0.290101	−	0.322190i	−0.870525	+	0.492125i	$0.836220\pi$
$684$		0			0
$685$	−5.29362	+	9.16882i	−0.202259	+	0.350323i
$686$		0			0
$687$	−4.33644	−	1.93071i	−0.165446	−	0.0736611i
$688$		0			0
$689$	−18.9902	+	4.03650i	−0.723471	+	0.153778i
$690$		0			0
$691$	4.46886	−	3.24681i	0.170003	−	0.123515i	−0.499530	−	0.866296i	$-0.666494\pi$
$691$	4.46886	−	3.24681i	0.170003	−	0.123515i	0.669534	+	0.742782i	$0.266494\pi$
$692$		0			0
$693$	0.00609935	−	0.0580314i	0.000231695	−	0.00220443i
$694$		0			0
$695$	−8.19469	+	5.95379i	−0.310842	+	0.225840i
$696$		0			0
$697$	−27.3854	+	12.1928i	−1.03730	+	0.461835i
$698$		0			0
$699$	−2.52277	−	1.83290i	−0.0954201	−	0.0693267i
$700$		0			0
$701$	2.61991	+	24.9268i	0.0989527	+	0.941472i	0.925536	+	0.378658i	$0.123614\pi$
$701$	2.61991	+	24.9268i	0.0989527	+	0.941472i	−0.826584	+	0.562814i	$0.809719\pi$
$702$		0			0
$703$	−2.66105	+	4.60907i	−0.100363	+	0.173834i
$704$		0			0
$705$	−0.714528	+	2.19909i	−0.0269107	+	0.0828225i
$706$		0			0
$707$	−0.0550333	−	0.523607i	−0.00206974	−	0.0196923i
$708$		0			0
$709$	−10.8415	−	33.3666i	−0.407159	−	1.25311i	−0.919079	−	0.394074i	$-0.871065\pi$
$709$	−10.8415	−	33.3666i	−0.407159	−	1.25311i	0.511919	−	0.859034i	$-0.328935\pi$
$710$		0			0
$711$	15.9939	+	27.7023i	0.599819	+	1.03892i
$712$		0			0
$713$	−16.6770	+	7.42509i	−0.624559	+	0.278072i
$714$		0			0
$715$	1.28470	+	0.273071i	0.0480450	+	0.0102123i
$716$		0			0
$717$	4.78608	−	1.01731i	0.178740	−	0.0379923i
$718$		0			0
$719$	23.9566	+	41.4940i	0.893430	+	1.54747i	0.835736	+	0.549132i	$0.185041\pi$
$719$	23.9566	+	41.4940i	0.893430	+	1.54747i	0.0576941	+	0.998334i	$0.481625\pi$
$720$		0			0
$721$	0.344748			0.0128391
$722$		0			0
$723$	−0.0565593	−	0.174072i	−0.00210346	−	0.00647379i
$724$		0			0
$725$	0.367215	+	0.163494i	0.0136380	+	0.00607203i
$726$		0			0
$727$	−20.7669	+	23.0640i	−0.770203	+	0.855397i	−0.992833	−	0.119506i	$-0.961869\pi$
$727$	−20.7669	+	23.0640i	−0.770203	+	0.855397i	0.222631	+	0.974903i	$0.428536\pi$
$728$		0			0
$729$	17.8946	+	13.0012i	0.662762	+	0.481525i
$730$		0			0
$731$	26.3029			0.972848
$732$		0			0
$733$	21.6320			0.798998			0.399499	−	0.916734i	$-0.369184\pi$
$733$	21.6320			0.798998			0.399499	+	0.916734i	$0.369184\pi$
$734$		0			0
$735$	1.33766	+	0.971870i	0.0493405	+	0.0358480i
$736$		0			0
$737$	3.42610	−	3.80506i	0.126202	−	0.140161i
$738$		0			0
$739$	−7.04269	−	3.13561i	−0.259070	−	0.115345i	0.273092	−	0.961988i	$-0.411954\pi$
$739$	−7.04269	−	3.13561i	−0.259070	−	0.115345i	−0.532162	+	0.846643i	$0.678620\pi$
$740$		0			0
$741$	1.29448	+	3.98401i	0.0475541	+	0.146356i
$742$		0			0
$743$	49.0283			1.79867			0.899337	−	0.437257i	$-0.144050\pi$
$743$	49.0283			1.79867			0.899337	+	0.437257i	$0.144050\pi$
$744$		0			0
$745$	4.69484	+	8.13169i	0.172005	+	0.297922i
$746$		0			0
$747$	39.1010	−	8.31117i	1.43063	−	0.304090i
$748$		0			0
$749$	0.188965	+	0.0401657i	0.00690462	+	0.00146762i
$750$		0			0
$751$	−25.0365	+	11.1470i	−0.913595	+	0.406759i	−0.809035	−	0.587760i	$-0.800010\pi$
$751$	−25.0365	+	11.1470i	−0.913595	+	0.406759i	−0.104560	+	0.994519i	$0.533343\pi$
$752$		0			0
$753$	−2.83294	−	4.90680i	−0.103238	−	0.178814i
$754$		0			0
$755$	1.43482	+	4.41592i	0.0522184	+	0.160712i
$756$		0			0
$757$	−2.71645	−	25.8453i	−0.0987312	−	0.939364i	−0.925991	−	0.377545i	$-0.876768\pi$
$757$	−2.71645	−	25.8453i	−0.0987312	−	0.939364i	0.827260	−	0.561819i	$-0.189898\pi$
$758$		0			0
$759$	0.114341	−	0.351906i	0.00415032	−	0.0127734i
$760$		0			0
$761$	−17.5038	+	30.3174i	−0.634511	+	1.09901i	0.352107	+	0.935960i	$0.385465\pi$
$761$	−17.5038	+	30.3174i	−0.634511	+	1.09901i	−0.986618	+	0.163046i	$0.947868\pi$
$762$		0			0
$763$	0.101728	+	0.967879i	0.00368281	+	0.0350396i
$764$		0			0
$765$	−7.37640	−	5.35927i	−0.266694	−	0.193765i
$766$		0			0
$767$	36.5367	−	16.2672i	1.31926	−	0.587374i
$768$		0			0
$769$	1.57602	−	1.14505i	0.0568329	−	0.0412915i	−0.559006	−	0.829164i	$-0.688817\pi$
$769$	1.57602	−	1.14505i	0.0568329	−	0.0412915i	0.615839	+	0.787872i	$0.288817\pi$
$770$		0			0
$771$	−0.191491	+	1.82192i	−0.00689638	+	0.0656147i
$772$		0			0
$773$	3.58999	−	2.60828i	0.129123	−	0.0938132i	−0.521349	−	0.853343i	$-0.674571\pi$
$773$	3.58999	−	2.60828i	0.129123	−	0.0938132i	0.650472	+	0.759530i	$0.274571\pi$
$774$		0			0
$775$	23.0975	−	4.90952i	0.829686	−	0.176355i
$776$		0			0
$777$	0.0286538	+	0.0127575i	0.00102795	+	0.000457672i
$778$		0			0
$779$	−10.7647	+	18.6449i	−0.385684	+	0.668024i
$780$		0			0
$781$	−2.41216	−	2.67898i	−0.0863140	−	0.0958614i
$782$		0			0
$783$	−0.110033	−	0.122204i	−0.00393226	−	0.00436722i
$784$		0			0
$785$	0.0608180	−	0.187179i	0.00217069	−	0.00668069i
$786$		0			0
$787$	25.5709	−	28.3994i	0.911504	−	1.01233i	−0.0883637	−	0.996088i	$-0.528164\pi$
$787$	25.5709	−	28.3994i	0.911504	−	1.01233i	0.999868	−	0.0162399i	$-0.00516955\pi$
$788$		0			0
$789$	2.73181	+	0.580664i	0.0972550	+	0.0206722i
$790$		0			0
$791$	0.104636	−	0.995545i	0.00372043	−	0.0353975i
$792$		0			0
$793$	21.1112	+	30.3890i	0.749680	+	1.07915i
$794$		0			0
$795$	−0.101224	+	0.963082i	−0.00359005	+	0.0341570i
$796$		0			0
$797$	45.5210	+	9.67579i	1.61244	+	0.342734i	0.923950	−	0.382514i	$-0.124942\pi$
$797$	45.5210	+	9.67579i	1.61244	+	0.342734i	0.688487	+	0.725248i	$0.258275\pi$
$798$		0			0
$799$	−26.4652	+	29.3926i	−0.936271	+	1.03983i
$800$		0			0
$801$	10.2151	−	31.4389i	0.360933	−	1.11084i
$802$		0			0
$803$	0.432328	+	0.480149i	0.0152565	+	0.0169441i
$804$		0			0
$805$	0.0991555	+	0.110123i	0.00349477	+	0.00388134i
$806$		0			0
$807$	−3.52563	+	6.10657i	−0.124108	+	0.214961i
$808$		0			0
$809$	−11.4343	−	5.09088i	−0.402009	−	0.178986i	0.195765	−	0.980651i	$-0.437281\pi$
$809$	−11.4343	−	5.09088i	−0.402009	−	0.178986i	−0.597773	+	0.801665i	$0.703948\pi$
$810$		0			0
$811$	37.9646	−	8.06963i	1.33312	−	0.283363i	0.514396	−	0.857553i	$-0.328016\pi$
$811$	37.9646	−	8.06963i	1.33312	−	0.283363i	0.818722	+	0.574190i	$0.194683\pi$
$812$		0			0
$813$	2.18997	−	1.59111i	0.0768057	−	0.0558026i
$814$		0			0
$815$	1.75534	−	16.7009i	0.0614867	−	0.585007i
$816$		0			0
$817$	15.2828	−	11.1036i	0.534676	−	0.388465i
$818$		0			0
$819$	−0.706811	+	0.314692i	−0.0246980	+	0.0109962i
$820$		0			0
$821$	22.8420	+	16.5957i	0.797191	+	0.579193i	0.910089	−	0.414413i	$-0.136013\pi$
$821$	22.8420	+	16.5957i	0.797191	+	0.579193i	−0.112898	+	0.993607i	$0.536013\pi$
$822$		0			0
$823$	4.37643	+	41.6390i	0.152553	+	1.45144i	0.756278	+	0.654251i	$0.227016\pi$
$823$	4.37643	+	41.6390i	0.152553	+	1.45144i	−0.603725	+	0.797193i	$0.706317\pi$
$824$		0			0
$825$	−0.239311	+	0.414498i	−0.00833172	+	0.0144310i
$826$		0			0
$827$	11.2645	−	34.6686i	0.391705	−	1.20554i	−0.539793	−	0.841798i	$-0.681497\pi$
$827$	11.2645	−	34.6686i	0.391705	−	1.20554i	0.931498	−	0.363747i	$-0.118503\pi$
$828$		0			0
$829$	0.852766	+	8.11352i	0.0296178	+	0.281794i	0.999300	+	0.0374230i	$0.0119149\pi$
$829$	0.852766	+	8.11352i	0.0296178	+	0.281794i	−0.969682	+	0.244371i	$0.921418\pi$
$830$		0			0
$831$	0.198384	+	0.610563i	0.00688186	+	0.0211802i
$832$		0			0
$833$	14.1412	+	24.4933i	0.489964	+	0.848643i
$834$		0			0
$835$	0.705861	−	0.314270i	0.0244273	−	0.0108757i
$836$		0			0
$837$	−9.44902	−	2.00845i	−0.326606	−	0.0694222i
$838$		0			0
$839$	−45.0833	+	9.58276i	−1.55645	+	0.330834i	−0.904179	−	0.427153i	$-0.859517\pi$
$839$	−45.0833	+	9.58276i	−1.55645	+	0.330834i	−0.652270	+	0.757986i	$0.726183\pi$
$840$		0			0
$841$	14.4958	+	25.1075i	0.499856	+	0.865776i
$842$		0			0
$843$	−3.32032			−0.114358
$844$		0			0
$845$	−2.26464	−	6.96983i	−0.0779058	−	0.239770i
$846$		0			0
$847$	−0.557932	−	0.248408i	−0.0191708	−	0.00853538i
$848$		0			0
$849$	−2.49656	+	2.77271i	−0.0856816	+	0.0951591i
$850$		0			0
$851$	−5.04278	−	3.66380i	−0.172864	−	0.125593i
$852$		0			0
$853$	−18.6777			−0.639511			−0.319755	−	0.947500i	$-0.603601\pi$
$853$	−18.6777			−0.639511			−0.319755	+	0.947500i	$0.603601\pi$
$854$		0			0
$855$	−6.54828			−0.223947
$856$		0			0
$857$	34.7107	+	25.2188i	1.18569	+	0.861458i	0.992803	−	0.119762i	$-0.0382132\pi$
$857$	34.7107	+	25.2188i	1.18569	+	0.861458i	0.192892	+	0.981220i	$0.438213\pi$
$858$		0			0
$859$	−22.7808	+	25.3007i	−0.777272	+	0.863248i	−0.993586	−	0.113076i	$-0.963930\pi$
$859$	−22.7808	+	25.3007i	−0.777272	+	0.863248i	0.216315	+	0.976324i	$0.430596\pi$
$860$		0			0
$861$	0.115912	+	0.0516074i	0.00395028	+	0.00175878i
$862$		0			0
$863$	5.86069	+	18.0373i	0.199500	+	0.613998i	0.999895	+	0.0145245i	$0.00462344\pi$
$863$	5.86069	+	18.0373i	0.199500	+	0.613998i	−0.800394	+	0.599474i	$0.795377\pi$
$864$		0			0
$865$	−14.4058			−0.489812
$866$		0			0
$867$	−0.100642	−	0.174318i	−0.00341800	−	0.00592015i
$868$		0			0
$869$	−3.84547	+	0.817379i	−0.130449	+	0.0277277i
$870$		0			0
$871$	−66.4075	−	14.1154i	−2.25013	−	0.478281i
$872$		0			0
$873$	−1.03920	+	0.462682i	−0.0351716	+	0.0156594i
$874$		0			0
$875$	−0.204799	−	0.354722i	−0.00692346	−	0.0119918i
$876$		0			0
$877$	5.88436	+	18.1102i	0.198701	+	0.611538i	0.999913	+	0.0131584i	$0.00418857\pi$
$877$	5.88436	+	18.1102i	0.198701	+	0.611538i	−0.801213	+	0.598380i	$0.795811\pi$
$878$		0			0
$879$	0.0991902	+	0.943731i	0.00334560	+	0.0318313i
$880$		0			0
$881$	7.62139	−	23.4562i	0.256771	−	0.790261i	−0.736704	−	0.676215i	$-0.763619\pi$
$881$	7.62139	−	23.4562i	0.256771	−	0.790261i	0.993476	−	0.114046i	$-0.0363810\pi$
$882$		0			0
$883$	0.968729	−	1.67789i	0.0326003	−	0.0564654i	−0.849265	−	0.527967i	$-0.822954\pi$
$883$	0.968729	−	1.67789i	0.0326003	−	0.0564654i	0.881865	+	0.471502i	$0.156288\pi$
$884$		0			0
$885$	−0.208524	−	1.98398i	−0.00700947	−	0.0666906i
$886$		0			0
$887$	−8.65390	−	6.28743i	−0.290570	−	0.211111i	0.432945	−	0.901420i	$-0.357475\pi$
$887$	−8.65390	−	6.28743i	−0.290570	−	0.211111i	−0.723514	+	0.690309i	$0.757475\pi$
$888$		0			0
$889$	−0.360739	+	0.160611i	−0.0120988	+	0.00538673i
$890$		0			0
$891$	−2.36275	+	1.71663i	−0.0791549	+	0.0575094i
$892$		0			0
$893$	−2.96920	+	28.2500i	−0.0993604	+	0.945351i
$894$		0			0
$895$	−2.54495	+	1.84901i	−0.0850683	+	0.0618057i
$896$		0			0
$897$	−4.79898	+	1.02005i	−0.160233	+	0.0340586i
$898$		0			0
$899$	−0.448298	−	0.199595i	−0.0149516	−	0.00665686i
$900$		0			0
$901$	−8.28221	+	14.3452i	−0.275920	+	0.477908i
$902$		0			0
$903$	−0.0744944	−	0.0827345i	−0.00247902	−	0.00275323i
$904$		0			0
$905$	−1.35446	−	1.50429i	−0.0450239	−	0.0500041i
$906$		0			0
$907$	10.2223	−	31.4610i	0.339426	−	1.04465i	−0.625074	−	0.780565i	$-0.714931\pi$
$907$	10.2223	−	31.4610i	0.339426	−	1.04465i	0.964500	−	0.264081i	$-0.0850688\pi$
$908$		0			0
$909$	−18.2328	+	20.2496i	−0.604743	+	0.671636i
$910$		0			0
$911$	31.3797	+	6.66997i	1.03966	+	0.220986i	0.695949	−	0.718091i	$-0.254984\pi$
$911$	31.3797	+	6.66997i	1.03966	+	0.220986i	0.343708	+	0.939077i	$0.388317\pi$
$912$		0			0
$913$	−0.513544	+	4.88605i	−0.0169958	+	0.161705i
$914$		0			0
$915$	1.76700	−	0.533074i	0.0584153	−	0.0176229i
$916$		0			0
$917$	−0.0959424	+	0.912831i	−0.00316830	+	0.0301443i
$918$		0			0
$919$	18.3673	+	3.90409i	0.605882	+	0.128784i	0.500630	−	0.865661i	$-0.333102\pi$
$919$	18.3673	+	3.90409i	0.605882	+	0.128784i	0.105252	+	0.994446i	$0.466435\pi$
$920$		0			0
$921$	−0.136217	+	0.151284i	−0.00448849	+	0.00498498i
$922$		0			0
$923$	−14.7707	+	45.4597i	−0.486185	+	1.49632i
$924$		0			0
$925$	5.39505	+	5.99181i	0.177388	+	0.197010i
$926$		0			0
$927$	−11.9389	−	13.2595i	−0.392125	−	0.435499i
$928$		0			0
$929$	−6.66171	+	11.5384i	−0.218564	+	0.378563i	−0.954369	−	0.298630i	$-0.903470\pi$
$929$	−6.66171	+	11.5384i	−0.218564	+	0.378563i	0.735805	+	0.677193i	$0.236804\pi$
$930$		0			0
$931$	18.5561	+	8.26172i	0.608153	+	0.270767i
$932$		0			0
$933$	5.59006	−	1.18820i	0.183010	−	0.0389000i
$934$		0			0
$935$	0.906576	−	0.658666i	0.0296482	−	0.0215407i
$936$		0			0
$937$	1.02112	−	9.71534i	0.0333586	−	0.317386i	−0.965100	−	0.261882i	$-0.915657\pi$
$937$	1.02112	−	9.71534i	0.0333586	−	0.317386i	0.998458	−	0.0555040i	$-0.0176765\pi$
$938$		0			0
$939$	−1.08582	+	0.788895i	−0.0354344	+	0.0257446i
$940$		0			0
$941$	−39.4254	+	17.5533i	−1.28523	+	0.572222i	−0.931709	−	0.363205i	$-0.881682\pi$
$941$	−39.4254	+	17.5533i	−1.28523	+	0.572222i	−0.353521	+	0.935426i	$0.615016\pi$
$942$		0			0
$943$	−20.3994	−	14.8210i	−0.664296	−	0.482640i
$944$		0			0
$945$	0.00819662	+	0.0779856i	0.000266636	+	0.00253687i
$946$		0			0
$947$	−2.67152	+	4.62721i	−0.0868128	+	0.150364i	−0.906162	−	0.422930i	$-0.861002\pi$
$947$	−2.67152	+	4.62721i	−0.0868128	+	0.150364i	0.819349	+	0.573294i	$0.194335\pi$
$948$		0			0
$949$	2.64734	−	8.14766i	0.0859361	−	0.264484i
$950$		0			0
$951$	0.192270	+	1.82933i	0.00623480	+	0.0593201i
$952$		0			0
$953$	−8.74449	−	26.9128i	−0.283262	−	0.871791i	−0.986914	−	0.161246i	$-0.948449\pi$
$953$	−8.74449	−	26.9128i	−0.283262	−	0.871791i	0.703652	−	0.710544i	$-0.251551\pi$
$954$		0			0
$955$	6.50615	+	11.2690i	0.210534	+	0.364656i
$956$		0			0
$957$	0.00908653	−	0.00404558i	0.000293726	−	0.000130775i
$958$		0			0
$959$	0.749763	+	0.159367i	0.0242111	+	0.00514623i
$960$		0			0
$961$	2.12505	−	0.451694i	0.0685501	−	0.0145708i
$962$		0			0
$963$	−4.99917	−	8.65881i	−0.161096	−	0.279026i
$964$		0			0
$965$	−12.2584			−0.394612
$966$		0			0
$967$	9.05061	+	27.8549i	0.291048	+	0.895753i	0.984520	+	0.175270i	$0.0560799\pi$
$967$	9.05061	+	27.8549i	0.291048	+	0.895753i	−0.693472	+	0.720483i	$0.743920\pi$
$968$		0			0
$969$	3.26509	+	1.45371i	0.104890	+	0.0466999i
$970$		0			0
$971$	−20.9928	+	23.3149i	−0.673691	+	0.748210i	−0.978959	−	0.204057i	$-0.934587\pi$
$971$	−20.9928	+	23.3149i	−0.673691	+	0.748210i	0.305268	+	0.952267i	$0.401254\pi$
$972$		0			0
$973$	0.593292	+	0.431052i	0.0190201	+	0.0138189i
$974$		0			0
$975$	6.34624			0.203242
$976$		0			0
$977$	18.8722			0.603775			0.301887	−	0.953344i	$-0.402383\pi$
$977$	18.8722			0.603775			0.301887	+	0.953344i	$0.402383\pi$
$978$		0			0
$979$	3.28684	+	2.38803i	0.105048	+	0.0763217i
$980$		0			0
$981$	33.7030	−	37.4310i	1.07605	−	1.19508i
$982$		0			0
$983$	20.4435	+	9.10203i	0.652046	+	0.290310i	0.705977	−	0.708235i	$-0.250508\pi$
$983$	20.4435	+	9.10203i	0.652046	+	0.290310i	−0.0539305	+	0.998545i	$0.517175\pi$
$984$		0			0
$985$	3.99898	+	12.3076i	0.127418	+	0.392152i
$986$		0			0
$987$	0.167407			0.00532862
$988$		0			0
$989$	11.0623	+	19.1604i	0.351760	+	0.609266i
$990$		0			0
$991$	−6.78121	+	1.44139i	−0.215412	+	0.0457873i	−0.314354	−	0.949306i	$-0.601788\pi$
$991$	−6.78121	+	1.44139i	−0.215412	+	0.0457873i	0.0989413	+	0.995093i	$0.468454\pi$
$992$		0			0
$993$	−3.62026	−	0.769511i	−0.114886	−	0.0244197i
$994$		0			0
$995$	16.7745	−	7.46848i	0.531787	−	0.236767i
$996$		0			0
$997$	−3.66171	−	6.34227i	−0.115968	−	0.200862i	0.802199	−	0.597057i	$-0.203664\pi$
$997$	−3.66171	−	6.34227i	−0.115968	−	0.200862i	−0.918166	+	0.396196i	$0.870330\pi$
$998$		0			0
$999$	−1.01927	−	3.13699i	−0.0322483	−	0.0992500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	976.2.bw.c.545.3		32
4.3	odd	2		61.2.i.a.57.2	yes	32
12.11	even	2		549.2.bl.b.118.3		32
61.15	even	15	inner	976.2.bw.c.625.3		32
244.15	odd	30		61.2.i.a.15.2	✓	32
244.147	odd	30		3721.2.a.j.1.11		16
244.219	odd	30		3721.2.a.l.1.6		16
732.503	even	30		549.2.bl.b.442.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.15.2	✓	32	244.15	odd	30
61.2.i.a.57.2	yes	32	4.3	odd	2
549.2.bl.b.118.3		32	12.11	even	2
549.2.bl.b.442.3		32	732.503	even	30
976.2.bw.c.545.3		32	1.1	even	1	trivial
976.2.bw.c.625.3		32	61.15	even	15	inner
3721.2.a.j.1.11		16	244.147	odd	30
3721.2.a.l.1.6		16	244.219	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 976 = 2^{4} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	976.bw (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.246407 + 0.179025i) q^{3} +(-0.519162 + 0.576588i) q^{5} +(0.0513167 + 0.0228477i) q^{7} +(-0.898385 - 2.76494i) q^{9} +0.357306 q^{11} +(-2.36883 - 4.10294i) q^{13} +(-0.231149 + 0.0491322i) q^{15} +(-3.95384 - 0.840414i) q^{17} +(-2.65207 + 1.18078i) q^{19} +(0.00855448 + 0.0148168i) q^{21} +(-1.05067 - 3.23364i) q^{23} +(0.459718 + 4.37392i) q^{25} +(0.555983 - 1.71114i) q^{27} +(0.0456986 - 0.0791523i) q^{29} +(-0.561226 - 5.33971i) q^{31} +(0.0880425 + 0.0639667i) q^{33} +(-0.0398154 + 0.0177270i) q^{35} +(1.48315 - 1.07757i) q^{37} +(0.150832 - 1.43507i) q^{39} +(5.99975 - 4.35907i) q^{41} +(-6.36493 + 1.35291i) q^{43} +(2.06064 + 0.917457i) q^{45} +(4.89237 - 8.47384i) q^{47} +(-4.68180 - 5.19967i) q^{49} +(-0.823797 - 0.914919i) q^{51} +(1.26632 - 3.89734i) q^{53} +(-0.185500 + 0.206018i) q^{55} +(-0.864877 - 0.183835i) q^{57} +(-0.882408 + 8.39555i) q^{59} +(-7.78300 + 0.651866i) q^{61} +(0.0170704 - 0.162414i) q^{63} +(3.59551 + 0.764250i) q^{65} +(9.58869 - 10.6493i) q^{67} +(0.320009 - 0.984886i) q^{69} +(-6.75098 - 7.49772i) q^{71} +(1.20997 + 1.34380i) q^{73} +(-0.669764 + 1.16007i) q^{75} +(0.0183358 + 0.00816361i) q^{77} +(-10.7624 + 2.28762i) q^{79} +(-6.61267 + 4.80439i) q^{81} +(-1.43727 + 13.6747i) q^{83} +(2.53726 - 1.84342i) q^{85} +(0.0254307 - 0.0113225i) q^{87} +(9.19896 + 6.68343i) q^{89} +(-0.0278181 - 0.264672i) q^{91} +(0.817652 - 1.41621i) q^{93} +(0.696033 - 2.14217i) q^{95} +(-0.0409000 - 0.389138i) q^{97} +(-0.320998 - 0.987930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 2 q^{5} - q^{7} - 2 q^{9} + 18 q^{11} - 2 q^{15} - 24 q^{17} - 9 q^{19} - 3 q^{21} + 2 q^{23} + 28 q^{25} - 35 q^{27} - 4 q^{29} + 11 q^{31} - 35 q^{33} + 58 q^{35} - 14 q^{37} - 17 q^{39}+ \cdots + 31 q^{99}+O(q^{100}) \) 32 * q + 4 * q^3 + 2 * q^5 - q^7 - 2 * q^9 + 18 * q^11 - 2 * q^15 - 24 * q^17 - 9 * q^19 - 3 * q^21 + 2 * q^23 + 28 * q^25 - 35 * q^27 - 4 * q^29 + 11 * q^31 - 35 * q^33 + 58 * q^35 - 14 * q^37 - 17 * q^39 + 11 * q^41 - 40 * q^43 + 12 * q^45 - 40 * q^47 + q^49 + 9 * q^51 + 17 * q^53 + 60 * q^55 - 38 * q^57 + 11 * q^59 - 55 * q^61 + 58 * q^63 + 59 * q^65 + 13 * q^67 - 32 * q^69 - 63 * q^71 - 46 * q^73 - q^75 - 31 * q^77 + 49 * q^79 + 48 * q^81 - 39 * q^83 + 21 * q^85 - 17 * q^87 + 32 * q^89 - 70 * q^91 + 67 * q^93 - 47 * q^95 + 37 * q^97 + 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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