LMFDB - Embedded newform 1824.2.q.i.577.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1824,2,Mod(577,1824)] 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("1824.577"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1824, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1824 = 2^{5} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1824.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,0,0,-4,0,-2,0,8,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$14.5647133287$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1824.577
Dual form			1824.2.q.i.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(-1.41421 - 2.44949i) q^{5} +1.82843 q^{7} +(-0.500000 + 0.866025i) q^{9} +4.82843 q^{11} +(1.91421 - 3.31552i) q^{13} +(-1.41421 + 2.44949i) q^{15} +(2.41421 + 4.18154i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-0.914214 - 1.58346i) q^{21} +(3.00000 - 5.19615i) q^{23} +(-1.50000 + 2.59808i) q^{25} +1.00000 q^{27} +(-0.414214 + 0.717439i) q^{29} +5.82843 q^{31} +(-2.41421 - 4.18154i) q^{33} +(-2.58579 - 4.47871i) q^{35} +11.8284 q^{37} -3.82843 q^{39} +(5.65685 + 9.79796i) q^{41} +(0.500000 + 0.866025i) q^{43} +2.82843 q^{45} +(-3.82843 + 6.63103i) q^{47} -3.65685 q^{49} +(2.41421 - 4.18154i) q^{51} +(-5.82843 + 10.0951i) q^{53} +(-6.82843 - 11.8272i) q^{55} +(0.500000 + 4.33013i) q^{57} +(-6.82843 - 11.8272i) q^{59} +(2.08579 - 3.61269i) q^{61} +(-0.914214 + 1.58346i) q^{63} -10.8284 q^{65} +(6.50000 - 11.2583i) q^{67} -6.00000 q^{69} +(-7.07107 - 12.2474i) q^{71} +(-2.50000 - 4.33013i) q^{73} +3.00000 q^{75} +8.82843 q^{77} +(-2.91421 - 5.04757i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.828427 q^{83} +(6.82843 - 11.8272i) q^{85} +0.828427 q^{87} +(-4.00000 + 6.92820i) q^{89} +(3.50000 - 6.06218i) q^{91} +(-2.91421 - 5.04757i) q^{93} +(1.41421 + 12.2474i) q^{95} +(-8.65685 - 14.9941i) q^{97} +(-2.41421 + 4.18154i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 4 q^{7} - 2 q^{9} + 8 q^{11} + 2 q^{13} + 4 q^{17} - 16 q^{19} + 2 q^{21} + 12 q^{23} - 6 q^{25} + 4 q^{27} + 4 q^{29} + 12 q^{31} - 4 q^{33} - 16 q^{35} + 36 q^{37} - 4 q^{39} + 2 q^{43}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 4 * q^7 - 2 * q^9 + 8 * q^11 + 2 * q^13 + 4 * q^17 - 16 * q^19 + 2 * q^21 + 12 * q^23 - 6 * q^25 + 4 * q^27 + 4 * q^29 + 12 * q^31 - 4 * q^33 - 16 * q^35 + 36 * q^37 - 4 * q^39 + 2 * q^43 - 4 * q^47 + 8 * q^49 + 4 * q^51 - 12 * q^53 - 16 * q^55 + 2 * q^57 - 16 * q^59 + 14 * q^61 + 2 * q^63 - 32 * q^65 + 26 * q^67 - 24 * q^69 - 10 * q^73 + 12 * q^75 + 24 * q^77 - 6 * q^79 - 2 * q^81 + 8 * q^83 + 16 * q^85 - 8 * q^87 - 16 * q^89 + 14 * q^91 - 6 * q^93 - 12 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1824\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$799$	$1217$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	−1.41421	−	2.44949i	−0.632456	−	1.09545i	−0.987048	−	0.160424i	$-0.948714\pi$
$5$	−1.41421	−	2.44949i	−0.632456	−	1.09545i	0.354593	−	0.935021i	$-0.384620\pi$
$6$		0			0
$7$	1.82843			0.691080			0.345540	−	0.938404i	$-0.387696\pi$
$7$	1.82843			0.691080			0.345540	+	0.938404i	$0.387696\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	4.82843			1.45583			0.727913	−	0.685670i	$-0.240491\pi$
$11$	4.82843			1.45583			0.727913	+	0.685670i	$0.240491\pi$
$12$		0			0
$13$	1.91421	−	3.31552i	0.530907	−	0.919558i	−0.468442	−	0.883494i	$-0.655185\pi$
$13$	1.91421	−	3.31552i	0.530907	−	0.919558i	0.999349	−	0.0360643i	$-0.0114821\pi$
$14$		0			0
$15$	−1.41421	+	2.44949i	−0.365148	+	0.632456i
$16$		0			0
$17$	2.41421	+	4.18154i	0.585533	+	1.01417i	0.994809	+	0.101762i	$0.0324480\pi$
$17$	2.41421	+	4.18154i	0.585533	+	1.01417i	−0.409276	+	0.912411i	$0.634219\pi$
$18$		0			0
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$		0			0
$21$	−0.914214	−	1.58346i	−0.199498	−	0.345540i
$22$		0			0
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.414214	+	0.717439i	−0.0769175	+	0.133225i	−0.901919	−	0.431906i	$-0.857841\pi$
$29$	−0.414214	+	0.717439i	−0.0769175	+	0.133225i	0.825001	+	0.565131i	$0.191174\pi$
$30$		0			0
$31$	5.82843			1.04682			0.523408	−	0.852082i	$-0.324660\pi$
$31$	5.82843			1.04682			0.523408	+	0.852082i	$0.324660\pi$
$32$		0			0
$33$	−2.41421	−	4.18154i	−0.420261	−	0.727913i
$34$		0			0
$35$	−2.58579	−	4.47871i	−0.437078	−	0.757041i
$36$		0			0
$37$	11.8284			1.94458			0.972291	−	0.233775i	$-0.0751079\pi$
$37$	11.8284			1.94458			0.972291	+	0.233775i	$0.0751079\pi$
$38$		0			0
$39$	−3.82843			−0.613039
$40$		0			0
$41$	5.65685	+	9.79796i	0.883452	+	1.53018i	0.847477	+	0.530831i	$0.178120\pi$
$41$	5.65685	+	9.79796i	0.883452	+	1.53018i	0.0359748	+	0.999353i	$0.488546\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$		0			0
$45$	2.82843			0.421637
$46$		0			0
$47$	−3.82843	+	6.63103i	−0.558433	+	0.967235i	0.439194	+	0.898392i	$0.355264\pi$
$47$	−3.82843	+	6.63103i	−0.558433	+	0.967235i	−0.997628	+	0.0688429i	$0.978069\pi$
$48$		0			0
$49$	−3.65685			−0.522408
$50$		0			0
$51$	2.41421	−	4.18154i	0.338058	−	0.585533i
$52$		0			0
$53$	−5.82843	+	10.0951i	−0.800596	+	1.38667i	0.118628	+	0.992939i	$0.462150\pi$
$53$	−5.82843	+	10.0951i	−0.800596	+	1.38667i	−0.919224	+	0.393734i	$0.871183\pi$
$54$		0			0
$55$	−6.82843	−	11.8272i	−0.920745	−	1.59478i
$56$		0			0
$57$	0.500000	+	4.33013i	0.0662266	+	0.573539i
$58$		0			0
$59$	−6.82843	−	11.8272i	−0.888985	−	1.53977i	−0.841076	−	0.540916i	$-0.818078\pi$
$59$	−6.82843	−	11.8272i	−0.888985	−	1.53977i	−0.0479091	−	0.998852i	$-0.515256\pi$
$60$		0			0
$61$	2.08579	−	3.61269i	0.267058	−	0.462557i	−0.701043	−	0.713119i	$-0.747282\pi$
$61$	2.08579	−	3.61269i	0.267058	−	0.462557i	0.968101	+	0.250562i	$0.0806153\pi$
$62$		0			0
$63$	−0.914214	+	1.58346i	−0.115180	+	0.199498i
$64$		0			0
$65$	−10.8284			−1.34310
$66$		0			0
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	−0.129307	−	0.991605i	$-0.541275\pi$
$67$	6.50000	−	11.2583i	0.794101	−	1.37542i	0.923408	−	0.383819i	$-0.125391\pi$
$68$		0			0
$69$	−6.00000			−0.722315
$70$		0			0
$71$	−7.07107	−	12.2474i	−0.839181	−	1.45350i	−0.890580	−	0.454827i	$-0.849701\pi$
$71$	−7.07107	−	12.2474i	−0.839181	−	1.45350i	0.0513987	−	0.998678i	$-0.483632\pi$
$72$		0			0
$73$	−2.50000	−	4.33013i	−0.292603	−	0.506803i	0.681822	−	0.731519i	$-0.261188\pi$
$73$	−2.50000	−	4.33013i	−0.292603	−	0.506803i	−0.974424	+	0.224716i	$0.927855\pi$
$74$		0			0
$75$	3.00000			0.346410
$76$		0			0
$77$	8.82843			1.00609
$78$		0			0
$79$	−2.91421	−	5.04757i	−0.327875	−	0.567896i	0.654215	−	0.756308i	$-0.272999\pi$
$79$	−2.91421	−	5.04757i	−0.327875	−	0.567896i	−0.982090	+	0.188413i	$0.939666\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−0.828427			−0.0909317			−0.0454658	−	0.998966i	$-0.514477\pi$
$83$	−0.828427			−0.0909317			−0.0454658	+	0.998966i	$0.514477\pi$
$84$		0			0
$85$	6.82843	−	11.8272i	0.740647	−	1.28284i
$86$		0			0
$87$	0.828427			0.0888167
$88$		0			0
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	−0.996326	−	0.0856373i	$-0.972707\pi$
$89$	−4.00000	+	6.92820i	−0.423999	+	0.734388i	0.572327	+	0.820025i	$0.306041\pi$
$90$		0			0
$91$	3.50000	−	6.06218i	0.366900	−	0.635489i
$92$		0			0
$93$	−2.91421	−	5.04757i	−0.302190	−	0.523408i
$94$		0			0
$95$	1.41421	+	12.2474i	0.145095	+	1.25656i
$96$		0			0
$97$	−8.65685	−	14.9941i	−0.878970	−	1.52242i	−0.852472	−	0.522772i	$-0.824898\pi$
$97$	−8.65685	−	14.9941i	−0.878970	−	1.52242i	−0.0264981	−	0.999649i	$-0.508436\pi$
$98$		0			0
$99$	−2.41421	+	4.18154i	−0.242638	+	0.420261i
$100$		0			0
$101$	7.41421	−	12.8418i	0.737742	−	1.27781i	−0.215768	−	0.976445i	$-0.569226\pi$
$101$	7.41421	−	12.8418i	0.737742	−	1.27781i	0.953510	−	0.301362i	$-0.0974412\pi$
$102$		0			0
$103$	3.48528			0.343415			0.171707	−	0.985148i	$-0.445072\pi$
$103$	3.48528			0.343415			0.171707	+	0.985148i	$0.445072\pi$
$104$		0			0
$105$	−2.58579	+	4.47871i	−0.252347	+	0.437078i
$106$		0			0
$107$	−6.82843			−0.660129			−0.330064	−	0.943958i	$-0.607070\pi$
$107$	−6.82843			−0.660129			−0.330064	+	0.943958i	$0.607070\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	−5.91421	−	10.2437i	−0.561352	−	0.972291i
$112$		0			0
$113$	−6.34315			−0.596713			−0.298356	−	0.954455i	$-0.596438\pi$
$113$	−6.34315			−0.596713			−0.298356	+	0.954455i	$0.596438\pi$
$114$		0			0
$115$	−16.9706			−1.58251
$116$		0			0
$117$	1.91421	+	3.31552i	0.176969	+	0.306519i
$118$		0			0
$119$	4.41421	+	7.64564i	0.404650	+	0.700875i
$120$		0			0
$121$	12.3137			1.11943
$122$		0			0
$123$	5.65685	−	9.79796i	0.510061	−	0.883452i
$124$		0			0
$125$	−5.65685			−0.505964
$126$		0			0
$127$	2.82843	−	4.89898i	0.250982	−	0.434714i	−0.712814	−	0.701353i	$-0.752580\pi$
$127$	2.82843	−	4.89898i	0.250982	−	0.434714i	0.963797	+	0.266639i	$0.0859131\pi$
$128$		0			0
$129$	0.500000	−	0.866025i	0.0440225	−	0.0762493i
$130$		0			0
$131$	0.242641	+	0.420266i	0.0211996	+	0.0367188i	0.876431	−	0.481528i	$-0.159918\pi$
$131$	0.242641	+	0.420266i	0.0211996	+	0.0367188i	−0.855231	+	0.518247i	$0.826585\pi$
$132$		0			0
$133$	−7.31371	−	3.16693i	−0.634179	−	0.274608i
$134$		0			0
$135$	−1.41421	−	2.44949i	−0.121716	−	0.210819i
$136$		0			0
$137$	−7.41421	+	12.8418i	−0.633439	+	1.09715i	0.353405	+	0.935471i	$0.385024\pi$
$137$	−7.41421	+	12.8418i	−0.633439	+	1.09715i	−0.986844	+	0.161678i	$0.948309\pi$
$138$		0			0
$139$	−8.98528	+	15.5630i	−0.762122	+	1.32003i	0.179633	+	0.983734i	$0.442509\pi$
$139$	−8.98528	+	15.5630i	−0.762122	+	1.32003i	−0.941755	+	0.336300i	$0.890824\pi$
$140$		0			0
$141$	7.65685			0.644823
$142$		0			0
$143$	9.24264	−	16.0087i	0.772908	−	1.33872i
$144$		0			0
$145$	2.34315			0.194588
$146$		0			0
$147$	1.82843	+	3.16693i	0.150806	+	0.261204i
$148$		0			0
$149$	0.757359	+	1.31178i	0.0620453	+	0.107466i	0.895380	−	0.445304i	$-0.146904\pi$
$149$	0.757359	+	1.31178i	0.0620453	+	0.107466i	−0.833334	+	0.552769i	$0.813571\pi$
$150$		0			0
$151$	5.65685			0.460348			0.230174	−	0.973149i	$-0.426070\pi$
$151$	5.65685			0.460348			0.230174	+	0.973149i	$0.426070\pi$
$152$		0			0
$153$	−4.82843			−0.390355
$154$		0			0
$155$	−8.24264	−	14.2767i	−0.662065	−	1.14673i
$156$		0			0
$157$	11.3995	+	19.7445i	0.909779	+	1.57578i	0.814371	+	0.580345i	$0.197082\pi$
$157$	11.3995	+	19.7445i	0.909779	+	1.57578i	0.0954078	+	0.995438i	$0.469584\pi$
$158$		0			0
$159$	11.6569			0.924449
$160$		0			0
$161$	5.48528	−	9.50079i	0.432301	−	0.748767i
$162$		0			0
$163$	−3.34315			−0.261855			−0.130928	−	0.991392i	$-0.541796\pi$
$163$	−3.34315			−0.261855			−0.130928	+	0.991392i	$0.541796\pi$
$164$		0			0
$165$	−6.82843	+	11.8272i	−0.531592	+	0.920745i
$166$		0			0
$167$	−2.82843	+	4.89898i	−0.218870	+	0.379094i	−0.954463	−	0.298330i	$-0.903570\pi$
$167$	−2.82843	+	4.89898i	−0.218870	+	0.379094i	0.735593	+	0.677424i	$0.236904\pi$
$168$		0			0
$169$	−0.828427	−	1.43488i	−0.0637252	−	0.110375i
$170$		0			0
$171$	3.50000	−	2.59808i	0.267652	−	0.198680i
$172$		0			0
$173$	−2.75736	−	4.77589i	−0.209638	−	0.363104i	0.741962	−	0.670441i	$-0.233895\pi$
$173$	−2.75736	−	4.77589i	−0.209638	−	0.363104i	−0.951601	+	0.307338i	$0.900562\pi$
$174$		0			0
$175$	−2.74264	+	4.75039i	−0.207324	+	0.359096i
$176$		0			0
$177$	−6.82843	+	11.8272i	−0.513256	+	0.888985i
$178$		0			0
$179$	13.3137			0.995113			0.497557	−	0.867431i	$-0.334231\pi$
$179$	13.3137			0.995113			0.497557	+	0.867431i	$0.334231\pi$
$180$		0			0
$181$	−2.65685	+	4.60181i	−0.197482	+	0.342050i	−0.947711	−	0.319128i	$-0.896610\pi$
$181$	−2.65685	+	4.60181i	−0.197482	+	0.342050i	0.750229	+	0.661178i	$0.229943\pi$
$182$		0			0
$183$	−4.17157			−0.308372
$184$		0			0
$185$	−16.7279	−	28.9736i	−1.22986	−	2.13018i
$186$		0			0
$187$	11.6569	+	20.1903i	0.852434	+	1.47646i
$188$		0			0
$189$	1.82843			0.132999
$190$		0			0
$191$	16.4853			1.19283			0.596417	−	0.802675i	$-0.296591\pi$
$191$	16.4853			1.19283			0.596417	+	0.802675i	$0.296591\pi$
$192$		0			0
$193$	8.98528	+	15.5630i	0.646775	+	1.12025i	0.983889	+	0.178783i	$0.0572159\pi$
$193$	8.98528	+	15.5630i	0.646775	+	1.12025i	−0.337114	+	0.941464i	$0.609451\pi$
$194$		0			0
$195$	5.41421	+	9.37769i	0.387720	+	0.671551i
$196$		0			0
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$	3.08579	−	5.34474i	0.218746	−	0.378878i	−0.735679	−	0.677330i	$-0.763137\pi$
$199$	3.08579	−	5.34474i	0.218746	−	0.378878i	0.954425	+	0.298452i	$0.0964702\pi$
$200$		0			0
$201$	−13.0000			−0.916949
$202$		0			0
$203$	−0.757359	+	1.31178i	−0.0531562	+	0.0920692i
$204$		0			0
$205$	16.0000	−	27.7128i	1.11749	−	1.93555i
$206$		0			0
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$		0			0
$209$	−19.3137	−	8.36308i	−1.33596	−	0.578486i
$210$		0			0
$211$	−0.156854	−	0.271680i	−0.0107983	−	0.0187032i	0.860576	−	0.509322i	$-0.170104\pi$
$211$	−0.156854	−	0.271680i	−0.0107983	−	0.0187032i	−0.871374	+	0.490619i	$0.836771\pi$
$212$		0			0
$213$	−7.07107	+	12.2474i	−0.484502	+	0.839181i
$214$		0			0
$215$	1.41421	−	2.44949i	0.0964486	−	0.167054i
$216$		0			0
$217$	10.6569			0.723434
$218$		0			0
$219$	−2.50000	+	4.33013i	−0.168934	+	0.292603i
$220$		0			0
$221$	18.4853			1.24345
$222$		0			0
$223$	−8.91421	−	15.4399i	−0.596940	−	1.03393i	−0.993270	−	0.115822i	$-0.963050\pi$
$223$	−8.91421	−	15.4399i	−0.596940	−	1.03393i	0.396330	−	0.918108i	$-0.370284\pi$
$224$		0			0
$225$	−1.50000	−	2.59808i	−0.100000	−	0.173205i
$226$		0			0
$227$	0.485281			0.0322093			0.0161046	−	0.999870i	$-0.494874\pi$
$227$	0.485281			0.0322093			0.0161046	+	0.999870i	$0.494874\pi$
$228$		0			0
$229$	19.4853			1.28762			0.643812	−	0.765184i	$-0.277352\pi$
$229$	19.4853			1.28762			0.643812	+	0.765184i	$0.277352\pi$
$230$		0			0
$231$	−4.41421	−	7.64564i	−0.290434	−	0.503046i
$232$		0			0
$233$	8.24264	+	14.2767i	0.539993	+	0.935296i	0.998904	+	0.0468133i	$0.0149066\pi$
$233$	8.24264	+	14.2767i	0.539993	+	0.935296i	−0.458910	+	0.888483i	$0.651760\pi$
$234$		0			0
$235$	21.6569			1.41274
$236$		0			0
$237$	−2.91421	+	5.04757i	−0.189299	+	0.327875i
$238$		0			0
$239$	12.4853			0.807606			0.403803	−	0.914846i	$-0.367688\pi$
$239$	12.4853			0.807606			0.403803	+	0.914846i	$0.367688\pi$
$240$		0			0
$241$	−4.15685	+	7.19988i	−0.267767	+	0.463785i	−0.968285	−	0.249849i	$-0.919619\pi$
$241$	−4.15685	+	7.19988i	−0.267767	+	0.463785i	0.700518	+	0.713635i	$0.252952\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	5.17157	+	8.95743i	0.330400	+	0.572269i
$246$		0			0
$247$	−13.3995	+	9.94655i	−0.852589	+	0.632884i
$248$		0			0
$249$	0.414214	+	0.717439i	0.0262497	+	0.0454658i
$250$		0			0
$251$	−7.00000	+	12.1244i	−0.441836	+	0.765283i	−0.997826	−	0.0659066i	$-0.979006\pi$
$251$	−7.00000	+	12.1244i	−0.441836	+	0.765283i	0.555990	+	0.831189i	$0.312339\pi$
$252$		0			0
$253$	14.4853	−	25.0892i	0.910682	−	1.57735i
$254$		0			0
$255$	−13.6569			−0.855225
$256$		0			0
$257$	6.65685	−	11.5300i	0.415243	−	0.719222i	−0.580211	−	0.814466i	$-0.697030\pi$
$257$	6.65685	−	11.5300i	0.415243	−	0.719222i	0.995454	+	0.0952441i	$0.0303632\pi$
$258$		0			0
$259$	21.6274			1.34386
$260$		0			0
$261$	−0.414214	−	0.717439i	−0.0256392	−	0.0444084i
$262$		0			0
$263$	7.07107	+	12.2474i	0.436021	+	0.755210i	0.997378	−	0.0723633i	$-0.0230541\pi$
$263$	7.07107	+	12.2474i	0.436021	+	0.755210i	−0.561358	+	0.827573i	$0.689721\pi$
$264$		0			0
$265$	32.9706			2.02537
$266$		0			0
$267$	8.00000			0.489592
$268$		0			0
$269$	−4.82843	−	8.36308i	−0.294394	−	0.509906i	0.680449	−	0.732795i	$-0.261785\pi$
$269$	−4.82843	−	8.36308i	−0.294394	−	0.509906i	−0.974844	+	0.222889i	$0.928451\pi$
$270$		0			0
$271$	−1.65685	−	2.86976i	−0.100647	−	0.174325i	0.811305	−	0.584624i	$-0.198758\pi$
$271$	−1.65685	−	2.86976i	−0.100647	−	0.174325i	−0.911951	+	0.410298i	$0.865425\pi$
$272$		0			0
$273$	−7.00000			−0.423659
$274$		0			0
$275$	−7.24264	+	12.5446i	−0.436748	+	0.756469i
$276$		0			0
$277$	−16.6274			−0.999045			−0.499522	−	0.866301i	$-0.666491\pi$
$277$	−16.6274			−0.999045			−0.499522	+	0.866301i	$0.666491\pi$
$278$		0			0
$279$	−2.91421	+	5.04757i	−0.174469	+	0.302190i
$280$		0			0
$281$	−13.8995	+	24.0746i	−0.829174	+	1.43617i	0.0695124	+	0.997581i	$0.477856\pi$
$281$	−13.8995	+	24.0746i	−0.829174	+	1.43617i	−0.898687	+	0.438591i	$0.855478\pi$
$282$		0			0
$283$	4.82843	+	8.36308i	0.287020	+	0.497134i	0.973097	−	0.230395i	$-0.0740020\pi$
$283$	4.82843	+	8.36308i	0.287020	+	0.497134i	−0.686077	+	0.727529i	$0.740669\pi$
$284$		0			0
$285$	9.89949	−	7.34847i	0.586395	−	0.435286i
$286$		0			0
$287$	10.3431	+	17.9149i	0.610537	+	1.05748i
$288$		0			0
$289$	−3.15685	+	5.46783i	−0.185697	+	0.321637i
$290$		0			0
$291$	−8.65685	+	14.9941i	−0.507474	+	0.878970i
$292$		0			0
$293$	1.31371			0.0767477			0.0383738	−	0.999263i	$-0.487782\pi$
$293$	1.31371			0.0767477			0.0383738	+	0.999263i	$0.487782\pi$
$294$		0			0
$295$	−19.3137	+	33.4523i	−1.12449	+	1.94767i
$296$		0			0
$297$	4.82843			0.280174
$298$		0			0
$299$	−11.4853	−	19.8931i	−0.664211	−	1.15045i
$300$		0			0
$301$	0.914214	+	1.58346i	0.0526944	+	0.0912694i
$302$		0			0
$303$	−14.8284			−0.851871
$304$		0			0
$305$	−11.7990			−0.675608
$306$		0			0
$307$	−12.1421	−	21.0308i	−0.692988	−	1.20029i	−0.970854	−	0.239671i	$-0.922960\pi$
$307$	−12.1421	−	21.0308i	−0.692988	−	1.20029i	0.277866	−	0.960620i	$-0.410373\pi$
$308$		0			0
$309$	−1.74264	−	3.01834i	−0.0991354	−	0.171707i
$310$		0			0
$311$	−3.31371			−0.187903			−0.0939516	−	0.995577i	$-0.529950\pi$
$311$	−3.31371			−0.187903			−0.0939516	+	0.995577i	$0.529950\pi$
$312$		0			0
$313$	−5.34315	+	9.25460i	−0.302012	+	0.523101i	−0.976592	−	0.215102i	$-0.930992\pi$
$313$	−5.34315	+	9.25460i	−0.302012	+	0.523101i	0.674579	+	0.738202i	$0.264325\pi$
$314$		0			0
$315$	5.17157			0.291385
$316$		0			0
$317$	0.242641	−	0.420266i	0.0136281	−	0.0236045i	−0.859131	−	0.511756i	$-0.828995\pi$
$317$	0.242641	−	0.420266i	0.0136281	−	0.0236045i	0.872759	+	0.488151i	$0.162329\pi$
$318$		0			0
$319$	−2.00000	+	3.46410i	−0.111979	+	0.193952i
$320$		0			0
$321$	3.41421	+	5.91359i	0.190563	+	0.330064i
$322$		0			0
$323$	−2.41421	−	20.9077i	−0.134330	−	1.16334i
$324$		0			0
$325$	5.74264	+	9.94655i	0.318544	+	0.551735i
$326$		0			0
$327$	−1.00000	+	1.73205i	−0.0553001	+	0.0957826i
$328$		0			0
$329$	−7.00000	+	12.1244i	−0.385922	+	0.668437i
$330$		0			0
$331$	−12.3137			−0.676823			−0.338411	−	0.940998i	$-0.609890\pi$
$331$	−12.3137			−0.676823			−0.338411	+	0.940998i	$0.609890\pi$
$332$		0			0
$333$	−5.91421	+	10.2437i	−0.324097	+	0.561352i
$334$		0			0
$335$	−36.7696			−2.00894
$336$		0			0
$337$	−11.6716	−	20.2158i	−0.635791	−	1.10122i	−0.986347	−	0.164681i	$-0.947341\pi$
$337$	−11.6716	−	20.2158i	−0.635791	−	1.10122i	0.350556	−	0.936542i	$-0.385993\pi$
$338$		0			0
$339$	3.17157	+	5.49333i	0.172256	+	0.298356i
$340$		0			0
$341$	28.1421			1.52398
$342$		0			0
$343$	−19.4853			−1.05211
$344$		0			0
$345$	8.48528	+	14.6969i	0.456832	+	0.791257i
$346$		0			0
$347$	7.07107	+	12.2474i	0.379595	+	0.657477i	0.991003	−	0.133838i	$-0.0427301\pi$
$347$	7.07107	+	12.2474i	0.379595	+	0.657477i	−0.611408	+	0.791315i	$0.709397\pi$
$348$		0			0
$349$	−16.4558			−0.880861			−0.440431	−	0.897787i	$-0.645174\pi$
$349$	−16.4558			−0.880861			−0.440431	+	0.897787i	$0.645174\pi$
$350$		0			0
$351$	1.91421	−	3.31552i	0.102173	−	0.176969i
$352$		0			0
$353$	16.4853			0.877423			0.438711	−	0.898628i	$-0.355435\pi$
$353$	16.4853			0.877423			0.438711	+	0.898628i	$0.355435\pi$
$354$		0			0
$355$	−20.0000	+	34.6410i	−1.06149	+	1.83855i
$356$		0			0
$357$	4.41421	−	7.64564i	0.233625	−	0.404650i
$358$		0			0
$359$	−4.48528	−	7.76874i	−0.236724	−	0.410018i	0.723048	−	0.690798i	$-0.242740\pi$
$359$	−4.48528	−	7.76874i	−0.236724	−	0.410018i	−0.959772	+	0.280779i	$0.909407\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$		0			0
$363$	−6.15685	−	10.6640i	−0.323151	−	0.559714i
$364$		0			0
$365$	−7.07107	+	12.2474i	−0.370117	+	0.641061i
$366$		0			0
$367$	8.22792	−	14.2512i	0.429494	−	0.743905i	−0.567334	−	0.823488i	$-0.692025\pi$
$367$	8.22792	−	14.2512i	0.429494	−	0.743905i	0.996828	+	0.0795821i	$0.0253586\pi$
$368$		0			0
$369$	−11.3137			−0.588968
$370$		0			0
$371$	−10.6569	+	18.4582i	−0.553276	+	0.958303i
$372$		0			0
$373$	25.3137			1.31069			0.655347	−	0.755328i	$-0.272522\pi$
$373$	25.3137			1.31069			0.655347	+	0.755328i	$0.272522\pi$
$374$		0			0
$375$	2.82843	+	4.89898i	0.146059	+	0.252982i
$376$		0			0
$377$	1.58579	+	2.74666i	0.0816722	+	0.141460i
$378$		0			0
$379$	12.6569			0.650139			0.325069	−	0.945690i	$-0.394612\pi$
$379$	12.6569			0.650139			0.325069	+	0.945690i	$0.394612\pi$
$380$		0			0
$381$	−5.65685			−0.289809
$382$		0			0
$383$	15.7279	+	27.2416i	0.803659	+	1.39198i	0.917192	+	0.398444i	$0.130450\pi$
$383$	15.7279	+	27.2416i	0.803659	+	1.39198i	−0.113533	+	0.993534i	$0.536217\pi$
$384$		0			0
$385$	−12.4853	−	21.6251i	−0.636309	−	1.10212i
$386$		0			0
$387$	−1.00000			−0.0508329
$388$		0			0
$389$	6.65685	−	11.5300i	0.337516	−	0.584595i	−0.646449	−	0.762957i	$-0.723747\pi$
$389$	6.65685	−	11.5300i	0.337516	−	0.584595i	0.983965	+	0.178363i	$0.0570800\pi$
$390$		0			0
$391$	28.9706			1.46510
$392$		0			0
$393$	0.242641	−	0.420266i	0.0122396	−	0.0211996i
$394$		0			0
$395$	−8.24264	+	14.2767i	−0.414732	+	0.718337i
$396$		0			0
$397$	−15.2279	−	26.3755i	−0.764268	−	1.32375i	−0.940633	−	0.339425i	$-0.889767\pi$
$397$	−15.2279	−	26.3755i	−0.764268	−	1.32375i	0.176365	−	0.984325i	$-0.443566\pi$
$398$		0			0
$399$	0.914214	+	7.91732i	0.0457679	+	0.396362i
$400$		0			0
$401$	6.82843	+	11.8272i	0.340995	+	0.590621i	0.984618	−	0.174722i	$-0.0559026\pi$
$401$	6.82843	+	11.8272i	0.340995	+	0.590621i	−0.643622	+	0.765343i	$0.722569\pi$
$402$		0			0
$403$	11.1569	−	19.3242i	0.555762	−	0.962609i
$404$		0			0
$405$	−1.41421	+	2.44949i	−0.0702728	+	0.121716i
$406$		0			0
$407$	57.1127			2.83097
$408$		0			0
$409$	−4.31371	+	7.47156i	−0.213299	+	0.369445i	−0.952745	−	0.303771i	$-0.901754\pi$
$409$	−4.31371	+	7.47156i	−0.213299	+	0.369445i	0.739446	+	0.673216i	$0.235088\pi$
$410$		0			0
$411$	14.8284			0.731432
$412$		0			0
$413$	−12.4853	−	21.6251i	−0.614361	−	1.06410i
$414$		0			0
$415$	1.17157	+	2.02922i	0.0575103	+	0.0996107i
$416$		0			0
$417$	17.9706			0.880022
$418$		0			0
$419$	−0.142136			−0.00694378			−0.00347189	−	0.999994i	$-0.501105\pi$
$419$	−0.142136			−0.00694378			−0.00347189	+	0.999994i	$0.501105\pi$
$420$		0			0
$421$	−0.656854	−	1.13770i	−0.0320131	−	0.0554483i	0.849575	−	0.527468i	$-0.176858\pi$
$421$	−0.656854	−	1.13770i	−0.0320131	−	0.0554483i	−0.881588	+	0.472020i	$0.843525\pi$
$422$		0			0
$423$	−3.82843	−	6.63103i	−0.186144	−	0.322412i
$424$		0			0
$425$	−14.4853			−0.702639
$426$		0			0
$427$	3.81371	−	6.60554i	0.184558	−	0.319664i
$428$		0			0
$429$	−18.4853			−0.892478
$430$		0			0
$431$	2.31371	−	4.00746i	0.111447	−	0.193033i	−0.804907	−	0.593401i	$-0.797785\pi$
$431$	2.31371	−	4.00746i	0.111447	−	0.193033i	0.916354	+	0.400369i	$0.131118\pi$
$432$		0			0
$433$	−1.15685	+	2.00373i	−0.0555949	+	0.0962931i	−0.892483	−	0.451080i	$-0.851039\pi$
$433$	−1.15685	+	2.00373i	−0.0555949	+	0.0962931i	0.836889	+	0.547373i	$0.184372\pi$
$434$		0			0
$435$	−1.17157	−	2.02922i	−0.0561726	−	0.0972938i
$436$		0			0
$437$	−21.0000	+	15.5885i	−1.00457	+	0.745697i
$438$		0			0
$439$	6.57107	+	11.3814i	0.313620	+	0.543206i	0.979143	−	0.203171i	$-0.0651249\pi$
$439$	6.57107	+	11.3814i	0.313620	+	0.543206i	−0.665523	+	0.746377i	$0.731792\pi$
$440$		0			0
$441$	1.82843	−	3.16693i	0.0870680	−	0.150806i
$442$		0			0
$443$	−15.2426	+	26.4010i	−0.724200	+	1.25435i	0.235103	+	0.971970i	$0.424457\pi$
$443$	−15.2426	+	26.4010i	−0.724200	+	1.25435i	−0.959303	+	0.282380i	$0.908876\pi$
$444$		0			0
$445$	22.6274			1.07264
$446$		0			0
$447$	0.757359	−	1.31178i	0.0358219	−	0.0620453i
$448$		0			0
$449$	31.4558			1.48449			0.742247	−	0.670127i	$-0.233760\pi$
$449$	31.4558			1.48449			0.742247	+	0.670127i	$0.233760\pi$
$450$		0			0
$451$	27.3137	+	47.3087i	1.28615	+	2.22768i
$452$		0			0
$453$	−2.82843	−	4.89898i	−0.132891	−	0.230174i
$454$		0			0
$455$	−19.7990			−0.928191
$456$		0			0
$457$	32.3137			1.51157			0.755786	−	0.654819i	$-0.227255\pi$
$457$	32.3137			1.51157			0.755786	+	0.654819i	$0.227255\pi$
$458$		0			0
$459$	2.41421	+	4.18154i	0.112686	+	0.195178i
$460$		0			0
$461$	−14.0000	−	24.2487i	−0.652045	−	1.12938i	−0.982626	−	0.185597i	$-0.940578\pi$
$461$	−14.0000	−	24.2487i	−0.652045	−	1.12938i	0.330581	−	0.943778i	$-0.392755\pi$
$462$		0			0
$463$	−5.82843			−0.270870			−0.135435	−	0.990786i	$-0.543243\pi$
$463$	−5.82843			−0.270870			−0.135435	+	0.990786i	$0.543243\pi$
$464$		0			0
$465$	−8.24264	+	14.2767i	−0.382243	+	0.662065i
$466$		0			0
$467$	−26.6274			−1.23217			−0.616085	−	0.787680i	$-0.711282\pi$
$467$	−26.6274			−1.23217			−0.616085	+	0.787680i	$0.711282\pi$
$468$		0			0
$469$	11.8848	−	20.5850i	0.548788	−	0.950529i
$470$		0			0
$471$	11.3995	−	19.7445i	0.525261	−	0.909779i
$472$		0			0
$473$	2.41421	+	4.18154i	0.111006	+	0.192267i
$474$		0			0
$475$	10.5000	−	7.79423i	0.481773	−	0.357624i
$476$		0			0
$477$	−5.82843	−	10.0951i	−0.266865	−	0.462224i
$478$		0			0
$479$	−2.92893	+	5.07306i	−0.133826	+	0.231794i	−0.925148	−	0.379605i	$-0.876060\pi$
$479$	−2.92893	+	5.07306i	−0.133826	+	0.231794i	0.791322	+	0.611399i	$0.209393\pi$
$480$		0			0
$481$	22.6421	−	39.2173i	1.03239	−	1.78816i
$482$		0			0
$483$	−10.9706			−0.499178
$484$		0			0
$485$	−24.4853	+	42.4098i	−1.11182	+	1.92573i
$486$		0			0
$487$	−18.3431			−0.831207			−0.415604	−	0.909546i	$-0.636430\pi$
$487$	−18.3431			−0.831207			−0.415604	+	0.909546i	$0.636430\pi$
$488$		0			0
$489$	1.67157	+	2.89525i	0.0755911	+	0.130928i
$490$		0			0
$491$	12.7279	+	22.0454i	0.574403	+	0.994895i	0.996106	+	0.0881614i	$0.0280991\pi$
$491$	12.7279	+	22.0454i	0.574403	+	0.994895i	−0.421703	+	0.906734i	$0.638568\pi$
$492$		0			0
$493$	−4.00000			−0.180151
$494$		0			0
$495$	13.6569			0.613830
$496$		0			0
$497$	−12.9289	−	22.3936i	−0.579942	−	1.00449i
$498$		0			0
$499$	2.32843	+	4.03295i	0.104235	+	0.180540i	0.913425	−	0.407006i	$-0.133427\pi$
$499$	2.32843	+	4.03295i	0.104235	+	0.180540i	−0.809191	+	0.587546i	$0.800094\pi$
$500$		0			0
$501$	5.65685			0.252730
$502$		0			0
$503$	3.58579	−	6.21076i	0.159882	−	0.276924i	−0.774944	−	0.632030i	$-0.782222\pi$
$503$	3.58579	−	6.21076i	0.159882	−	0.276924i	0.934826	+	0.355106i	$0.115555\pi$
$504$		0			0
$505$	−41.9411			−1.86636
$506$		0			0
$507$	−0.828427	+	1.43488i	−0.0367917	+	0.0637252i
$508$		0			0
$509$	−4.31371	+	7.47156i	−0.191202	+	0.331171i	−0.945649	−	0.325190i	$-0.894572\pi$
$509$	−4.31371	+	7.47156i	−0.191202	+	0.331171i	0.754447	+	0.656361i	$0.227905\pi$
$510$		0			0
$511$	−4.57107	−	7.91732i	−0.202212	−	0.350242i
$512$		0			0
$513$	−4.00000	−	1.73205i	−0.176604	−	0.0764719i
$514$		0			0
$515$	−4.92893	−	8.53716i	−0.217195	−	0.376192i
$516$		0			0
$517$	−18.4853	+	32.0174i	−0.812982	+	1.40813i
$518$		0			0
$519$	−2.75736	+	4.77589i	−0.121035	+	0.209638i
$520$		0			0
$521$	−10.4853			−0.459369			−0.229684	−	0.973265i	$-0.573769\pi$
$521$	−10.4853			−0.459369			−0.229684	+	0.973265i	$0.573769\pi$
$522$		0			0
$523$	−4.15685	+	7.19988i	−0.181767	+	0.314829i	−0.942482	−	0.334256i	$-0.891515\pi$
$523$	−4.15685	+	7.19988i	−0.181767	+	0.314829i	0.760716	+	0.649085i	$0.224848\pi$
$524$		0			0
$525$	5.48528			0.239397
$526$		0			0
$527$	14.0711	+	24.3718i	0.612945	+	1.06165i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	13.6569			0.592657
$532$		0			0
$533$	43.3137			1.87612
$534$		0			0
$535$	9.65685	+	16.7262i	0.417502	+	0.723135i
$536$		0			0
$537$	−6.65685	−	11.5300i	−0.287264	−	0.497557i
$538$		0			0
$539$	−17.6569			−0.760535
$540$		0			0
$541$	−15.3995	+	26.6727i	−0.662076	+	1.14675i	0.317993	+	0.948093i	$0.396991\pi$
$541$	−15.3995	+	26.6727i	−0.662076	+	1.14675i	−0.980069	+	0.198656i	$0.936342\pi$
$542$		0			0
$543$	5.31371			0.228033
$544$		0			0
$545$	−2.82843	+	4.89898i	−0.121157	+	0.209849i
$546$		0			0
$547$	17.8137	−	30.8542i	0.761659	−	1.31923i	−0.180336	−	0.983605i	$-0.557718\pi$
$547$	17.8137	−	30.8542i	0.761659	−	1.31923i	0.941995	−	0.335627i	$-0.108948\pi$
$548$		0			0
$549$	2.08579	+	3.61269i	0.0890192	+	0.154186i
$550$		0			0
$551$	2.89949	−	2.15232i	0.123523	−	0.0916918i
$552$		0			0
$553$	−5.32843	−	9.22911i	−0.226588	−	0.392462i
$554$		0			0
$555$	−16.7279	+	28.9736i	−0.710061	+	1.22986i
$556$		0			0
$557$	−7.07107	+	12.2474i	−0.299611	+	0.518941i	−0.976047	−	0.217560i	$-0.930190\pi$
$557$	−7.07107	+	12.2474i	−0.299611	+	0.518941i	0.676436	+	0.736501i	$0.263523\pi$
$558$		0			0
$559$	3.82843			0.161925
$560$		0			0
$561$	11.6569	−	20.1903i	0.492153	−	0.852434i
$562$		0			0
$563$	−38.1421			−1.60750			−0.803750	−	0.594968i	$-0.797165\pi$
$563$	−38.1421			−1.60750			−0.803750	+	0.594968i	$0.797165\pi$
$564$		0			0
$565$	8.97056	+	15.5375i	0.377394	+	0.653666i
$566$		0			0
$567$	−0.914214	−	1.58346i	−0.0383934	−	0.0664993i
$568$		0			0
$569$	29.6569			1.24328			0.621640	−	0.783303i	$-0.286467\pi$
$569$	29.6569			1.24328			0.621640	+	0.783303i	$0.286467\pi$
$570$		0			0
$571$	29.2843			1.22551			0.612754	−	0.790273i	$-0.290062\pi$
$571$	29.2843			1.22551			0.612754	+	0.790273i	$0.290062\pi$
$572$		0			0
$573$	−8.24264	−	14.2767i	−0.344341	−	0.596417i
$574$		0			0
$575$	9.00000	+	15.5885i	0.375326	+	0.650084i
$576$		0			0
$577$	10.2843			0.428140			0.214070	−	0.976818i	$-0.431328\pi$
$577$	10.2843			0.428140			0.214070	+	0.976818i	$0.431328\pi$
$578$		0			0
$579$	8.98528	−	15.5630i	0.373416	−	0.646775i
$580$		0			0
$581$	−1.51472			−0.0628411
$582$		0			0
$583$	−28.1421	+	48.7436i	−1.16553	+	2.01875i
$584$		0			0
$585$	5.41421	−	9.37769i	0.223850	−	0.387720i
$586$		0			0
$587$	−12.0000	−	20.7846i	−0.495293	−	0.857873i	0.504692	−	0.863299i	$-0.331606\pi$
$587$	−12.0000	−	20.7846i	−0.495293	−	0.857873i	−0.999985	+	0.00542667i	$0.998273\pi$
$588$		0			0
$589$	−23.3137	−	10.0951i	−0.960625	−	0.415963i
$590$		0			0
$591$	8.00000	+	13.8564i	0.329076	+	0.569976i
$592$		0			0
$593$	−9.31371	+	16.1318i	−0.382468	+	0.662454i	−0.991414	−	0.130757i	$-0.958259\pi$
$593$	−9.31371	+	16.1318i	−0.382468	+	0.662454i	0.608946	+	0.793211i	$0.291593\pi$
$594$		0			0
$595$	12.4853	−	21.6251i	0.511847	−	0.886544i
$596$		0			0
$597$	−6.17157			−0.252586
$598$		0			0
$599$	10.8995	−	18.8785i	0.445341	−	0.771354i	−0.552735	−	0.833357i	$-0.686416\pi$
$599$	10.8995	−	18.8785i	0.445341	−	0.771354i	0.998076	+	0.0620036i	$0.0197490\pi$
$600$		0			0
$601$	−0.313708			−0.0127964			−0.00639822	−	0.999980i	$-0.502037\pi$
$601$	−0.313708			−0.0127964			−0.00639822	+	0.999980i	$0.502037\pi$
$602$		0			0
$603$	6.50000	+	11.2583i	0.264700	+	0.458475i
$604$		0			0
$605$	−17.4142	−	30.1623i	−0.707988	−	1.22627i
$606$		0			0
$607$	10.5147			0.426779			0.213390	−	0.976967i	$-0.431550\pi$
$607$	10.5147			0.426779			0.213390	+	0.976967i	$0.431550\pi$
$608$		0			0
$609$	1.51472			0.0613795
$610$		0			0
$611$	14.6569	+	25.3864i	0.592953	+	1.02702i
$612$		0			0
$613$	−2.51472	−	4.35562i	−0.101569	−	0.175922i	0.810763	−	0.585375i	$-0.199053\pi$
$613$	−2.51472	−	4.35562i	−0.101569	−	0.175922i	−0.912331	+	0.409453i	$0.865719\pi$
$614$		0			0
$615$	−32.0000			−1.29036
$616$		0			0
$617$	−10.8995	+	18.8785i	−0.438797	+	0.760019i	−0.997597	−	0.0692836i	$-0.977929\pi$
$617$	−10.8995	+	18.8785i	−0.438797	+	0.760019i	0.558800	+	0.829303i	$0.311262\pi$
$618$		0			0
$619$	15.3431			0.616693			0.308347	−	0.951274i	$-0.400224\pi$
$619$	15.3431			0.616693			0.308347	+	0.951274i	$0.400224\pi$
$620$		0			0
$621$	3.00000	−	5.19615i	0.120386	−	0.208514i
$622$		0			0
$623$	−7.31371	+	12.6677i	−0.293018	+	0.507521i
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$		0			0
$627$	2.41421	+	20.9077i	0.0964144	+	0.834973i
$628$		0			0
$629$	28.5563	+	49.4610i	1.13862	+	1.97214i
$630$		0			0
$631$	−14.2279	+	24.6435i	−0.566405	+	0.981042i	0.430513	+	0.902584i	$0.358333\pi$
$631$	−14.2279	+	24.6435i	−0.566405	+	0.981042i	−0.996917	+	0.0784572i	$0.975001\pi$
$632$		0			0
$633$	−0.156854	+	0.271680i	−0.00623440	+	0.0107983i
$634$		0			0
$635$	−16.0000			−0.634941
$636$		0			0
$637$	−7.00000	+	12.1244i	−0.277350	+	0.480384i
$638$		0			0
$639$	14.1421			0.559454
$640$		0			0
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$		0			0
$643$	−18.9853	−	32.8835i	−0.748706	−	1.29680i	−0.948443	−	0.316948i	$-0.897342\pi$
$643$	−18.9853	−	32.8835i	−0.748706	−	1.29680i	0.199737	−	0.979850i	$-0.435991\pi$
$644$		0			0
$645$	−2.82843			−0.111369
$646$		0			0
$647$	39.4558			1.55117			0.775585	−	0.631244i	$-0.217455\pi$
$647$	39.4558			1.55117			0.775585	+	0.631244i	$0.217455\pi$
$648$		0			0
$649$	−32.9706	−	57.1067i	−1.29421	−	2.24163i
$650$		0			0
$651$	−5.32843	−	9.22911i	−0.208838	−	0.361717i
$652$		0			0
$653$	−34.1421			−1.33609			−0.668043	−	0.744123i	$-0.732868\pi$
$653$	−34.1421			−1.33609			−0.668043	+	0.744123i	$0.732868\pi$
$654$		0			0
$655$	0.686292	−	1.18869i	0.0268156	−	0.0464460i
$656$		0			0
$657$	5.00000			0.195069
$658$		0			0
$659$	24.8995	−	43.1272i	0.969947	−	1.68000i	0.274254	−	0.961657i	$-0.411569\pi$
$659$	24.8995	−	43.1272i	0.969947	−	1.68000i	0.695693	−	0.718339i	$-0.255098\pi$
$660$		0			0
$661$	0.656854	−	1.13770i	0.0255487	−	0.0442516i	−0.852968	−	0.521963i	$-0.825200\pi$
$661$	0.656854	−	1.13770i	0.0255487	−	0.0442516i	0.878517	+	0.477711i	$0.158533\pi$
$662$		0			0
$663$	−9.24264	−	16.0087i	−0.358954	−	0.621727i
$664$		0			0
$665$	2.58579	+	22.3936i	0.100272	+	0.868385i
$666$		0			0
$667$	2.48528	+	4.30463i	0.0962305	+	0.166676i
$668$		0			0
$669$	−8.91421	+	15.4399i	−0.344643	+	0.596940i
$670$		0			0
$671$	10.0711	−	17.4436i	0.388789	−	0.673403i
$672$		0			0
$673$	33.6274			1.29624			0.648121	−	0.761538i	$-0.275555\pi$
$673$	33.6274			1.29624			0.648121	+	0.761538i	$0.275555\pi$
$674$		0			0
$675$	−1.50000	+	2.59808i	−0.0577350	+	0.100000i
$676$		0			0
$677$	−31.6569			−1.21667			−0.608336	−	0.793680i	$-0.708163\pi$
$677$	−31.6569			−1.21667			−0.608336	+	0.793680i	$0.708163\pi$
$678$		0			0
$679$	−15.8284	−	27.4156i	−0.607439	−	1.05212i
$680$		0			0
$681$	−0.242641	−	0.420266i	−0.00929801	−	0.0161046i
$682$		0			0
$683$	19.7990			0.757587			0.378794	−	0.925481i	$-0.376339\pi$
$683$	19.7990			0.757587			0.378794	+	0.925481i	$0.376339\pi$
$684$		0			0
$685$	41.9411			1.60249
$686$		0			0
$687$	−9.74264	−	16.8747i	−0.371705	−	0.643812i
$688$		0			0
$689$	22.3137	+	38.6485i	0.850085	+	1.47239i
$690$		0			0
$691$	12.6863			0.482609			0.241305	−	0.970449i	$-0.422425\pi$
$691$	12.6863			0.482609			0.241305	+	0.970449i	$0.422425\pi$
$692$		0			0
$693$	−4.41421	+	7.64564i	−0.167682	+	0.290434i
$694$		0			0
$695$	50.8284			1.92803
$696$		0			0
$697$	−27.3137	+	47.3087i	−1.03458	+	1.79195i
$698$		0			0
$699$	8.24264	−	14.2767i	0.311765	−	0.539993i
$700$		0			0
$701$	19.4142	+	33.6264i	0.733265	+	1.27005i	0.955481	+	0.295054i	$0.0953377\pi$
$701$	19.4142	+	33.6264i	0.733265	+	1.27005i	−0.222216	+	0.974998i	$0.571329\pi$
$702$		0			0
$703$	−47.3137	−	20.4874i	−1.78447	−	0.772698i
$704$		0			0
$705$	−10.8284	−	18.7554i	−0.407822	−	0.706369i
$706$		0			0
$707$	13.5563	−	23.4803i	0.509839	−	0.883067i
$708$		0			0
$709$	−14.5711	+	25.2378i	−0.547228	+	0.947827i	0.451235	+	0.892405i	$0.350984\pi$
$709$	−14.5711	+	25.2378i	−0.547228	+	0.947827i	−0.998463	+	0.0554215i	$0.982350\pi$
$710$		0			0
$711$	5.82843			0.218583
$712$		0			0
$713$	17.4853	−	30.2854i	0.654829	−	1.13420i
$714$		0			0
$715$	−52.2843			−1.95532
$716$		0			0
$717$	−6.24264	−	10.8126i	−0.233136	−	0.403803i
$718$		0			0
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	6.37258			0.237327
$722$		0			0
$723$	8.31371			0.309190
$724$		0			0
$725$	−1.24264	−	2.15232i	−0.0461505	−	0.0799350i
$726$		0			0
$727$	−0.571068	−	0.989118i	−0.0211797	−	0.0366844i	0.855241	−	0.518230i	$-0.173409\pi$
$727$	−0.571068	−	0.989118i	−0.0211797	−	0.0366844i	−0.876421	+	0.481546i	$0.840076\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.41421	+	4.18154i	−0.0892929	+	0.154660i
$732$		0			0
$733$	−3.65685			−0.135069			−0.0675345	−	0.997717i	$-0.521513\pi$
$733$	−3.65685			−0.135069			−0.0675345	+	0.997717i	$0.521513\pi$
$734$		0			0
$735$	5.17157	−	8.95743i	0.190756	−	0.330400i
$736$		0			0
$737$	31.3848	−	54.3600i	1.15607	−	2.00238i
$738$		0			0
$739$	14.6421	+	25.3609i	0.538620	+	0.932917i	0.998979	+	0.0451838i	$0.0143873\pi$
$739$	14.6421	+	25.3609i	0.538620	+	0.932917i	−0.460359	+	0.887733i	$0.652279\pi$
$740$		0			0
$741$	15.3137	+	6.63103i	0.562563	+	0.243597i
$742$		0			0
$743$	9.58579	+	16.6031i	0.351668	+	0.609108i	0.986542	−	0.163509i	$-0.0522811\pi$
$743$	9.58579	+	16.6031i	0.351668	+	0.609108i	−0.634874	+	0.772616i	$0.718948\pi$
$744$		0			0
$745$	2.14214	−	3.71029i	0.0784818	−	0.135934i
$746$		0			0
$747$	0.414214	−	0.717439i	0.0151553	−	0.0262497i
$748$		0			0
$749$	−12.4853			−0.456202
$750$		0			0
$751$	7.57107	−	13.1135i	0.276272	−	0.478517i	−0.694183	−	0.719798i	$-0.744234\pi$
$751$	7.57107	−	13.1135i	0.276272	−	0.478517i	0.970455	+	0.241281i	$0.0775675\pi$
$752$		0			0
$753$	14.0000			0.510188
$754$		0			0
$755$	−8.00000	−	13.8564i	−0.291150	−	0.504286i
$756$		0			0
$757$	4.25736	+	7.37396i	0.154736	+	0.268011i	0.932963	−	0.359972i	$-0.117214\pi$
$757$	4.25736	+	7.37396i	0.154736	+	0.268011i	−0.778227	+	0.627984i	$0.783881\pi$
$758$		0			0
$759$	−28.9706			−1.05156
$760$		0			0
$761$	14.3431			0.519939			0.259969	−	0.965617i	$-0.416288\pi$
$761$	14.3431			0.519939			0.259969	+	0.965617i	$0.416288\pi$
$762$		0			0
$763$	−1.82843	−	3.16693i	−0.0661935	−	0.114651i
$764$		0			0
$765$	6.82843	+	11.8272i	0.246882	+	0.427613i
$766$		0			0
$767$	−52.2843			−1.88788
$768$		0			0
$769$	21.4706	−	37.1881i	0.774248	−	1.34104i	−0.160968	−	0.986960i	$-0.551461\pi$
$769$	21.4706	−	37.1881i	0.774248	−	1.34104i	0.935216	−	0.354078i	$-0.115205\pi$
$770$		0			0
$771$	−13.3137			−0.479481
$772$		0			0
$773$	−17.8284	+	30.8797i	−0.641244	+	1.11067i	0.343911	+	0.939002i	$0.388248\pi$
$773$	−17.8284	+	30.8797i	−0.641244	+	1.11067i	−0.985155	+	0.171665i	$0.945085\pi$
$774$		0			0
$775$	−8.74264	+	15.1427i	−0.314045	+	0.543942i
$776$		0			0
$777$	−10.8137	−	18.7299i	−0.387940	−	0.671931i
$778$		0			0
$779$	−5.65685	−	48.9898i	−0.202678	−	1.75524i
$780$		0			0
$781$	−34.1421	−	59.1359i	−1.22170	−	2.11605i
$782$		0			0
$783$	−0.414214	+	0.717439i	−0.0148028	+	0.0256392i
$784$		0			0
$785$	32.2426	−	55.8459i	1.15079	−	1.99323i
$786$		0			0
$787$	−52.2548			−1.86268			−0.931342	−	0.364146i	$-0.881361\pi$
$787$	−52.2548			−1.86268			−0.931342	+	0.364146i	$0.881361\pi$
$788$		0			0
$789$	7.07107	−	12.2474i	0.251737	−	0.436021i
$790$		0			0
$791$	−11.5980			−0.412377
$792$		0			0
$793$	−7.98528	−	13.8309i	−0.283566	−	0.491150i
$794$		0			0
$795$	−16.4853	−	28.5533i	−0.584673	−	1.01268i
$796$		0			0
$797$	1.85786			0.0658089			0.0329045	−	0.999459i	$-0.489524\pi$
$797$	1.85786			0.0658089			0.0329045	+	0.999459i	$0.489524\pi$
$798$		0			0
$799$	−36.9706			−1.30792
$800$		0			0
$801$	−4.00000	−	6.92820i	−0.141333	−	0.244796i
$802$		0			0
$803$	−12.0711	−	20.9077i	−0.425979	−	0.737817i
$804$		0			0
$805$	−31.0294			−1.09364
$806$		0			0
$807$	−4.82843	+	8.36308i	−0.169969	+	0.294394i
$808$		0			0
$809$	5.45584			0.191817			0.0959086	−	0.995390i	$-0.469424\pi$
$809$	5.45584			0.191817			0.0959086	+	0.995390i	$0.469424\pi$
$810$		0			0
$811$	4.34315	−	7.52255i	0.152508	−	0.264152i	−0.779641	−	0.626227i	$-0.784598\pi$
$811$	4.34315	−	7.52255i	0.152508	−	0.264152i	0.932149	+	0.362075i	$0.117932\pi$
$812$		0			0
$813$	−1.65685	+	2.86976i	−0.0581084	+	0.100647i
$814$		0			0
$815$	4.72792	+	8.18900i	0.165612	+	0.286848i
$816$		0			0
$817$	−0.500000	−	4.33013i	−0.0174928	−	0.151492i
$818$		0			0
$819$	3.50000	+	6.06218i	0.122300	+	0.211830i
$820$		0			0
$821$	2.75736	−	4.77589i	0.0962325	−	0.166680i	−0.813890	−	0.581019i	$-0.802654\pi$
$821$	2.75736	−	4.77589i	0.0962325	−	0.166680i	0.910122	+	0.414340i	$0.135987\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$		0			0
$825$	14.4853			0.504313
$826$		0			0
$827$	7.58579	−	13.1390i	0.263784	−	0.456887i	−0.703461	−	0.710734i	$-0.748363\pi$
$827$	7.58579	−	13.1390i	0.263784	−	0.456887i	0.967244	+	0.253848i	$0.0816962\pi$
$828$		0			0
$829$	−24.7990			−0.861305			−0.430652	−	0.902518i	$-0.641716\pi$
$829$	−24.7990			−0.861305			−0.430652	+	0.902518i	$0.641716\pi$
$830$		0			0
$831$	8.31371	+	14.3998i	0.288399	+	0.499522i
$832$		0			0
$833$	−8.82843	−	15.2913i	−0.305887	−	0.529812i
$834$		0			0
$835$	16.0000			0.553703
$836$		0			0
$837$	5.82843			0.201460
$838$		0			0
$839$	−6.92893	−	12.0013i	−0.239213	−	0.414330i	0.721275	−	0.692648i	$-0.243556\pi$
$839$	−6.92893	−	12.0013i	−0.239213	−	0.414330i	−0.960489	+	0.278319i	$0.910223\pi$
$840$		0			0
$841$	14.1569	+	24.5204i	0.488167	+	0.845531i
$842$		0			0
$843$	27.7990			0.957448
$844$		0			0
$845$	−2.34315	+	4.05845i	−0.0806067	+	0.139615i
$846$		0			0
$847$	22.5147			0.773615
$848$		0			0
$849$	4.82843	−	8.36308i	0.165711	−	0.287020i
$850$		0			0
$851$	35.4853	−	61.4623i	1.21642	−	2.10690i
$852$		0			0
$853$	26.0858	+	45.1819i	0.893160	+	1.54700i	0.836065	+	0.548630i	$0.184851\pi$
$853$	26.0858	+	45.1819i	0.893160	+	1.54700i	0.0570953	+	0.998369i	$0.481816\pi$
$854$		0			0
$855$	−11.3137	−	4.89898i	−0.386921	−	0.167542i
$856$		0			0
$857$	−10.6569	−	18.4582i	−0.364031	−	0.630521i	0.624589	−	0.780954i	$-0.285267\pi$
$857$	−10.6569	−	18.4582i	−0.364031	−	0.630521i	−0.988620	+	0.150433i	$0.951933\pi$
$858$		0			0
$859$	−10.8137	+	18.7299i	−0.368959	+	0.639056i	−0.989403	−	0.145195i	$-0.953619\pi$
$859$	−10.8137	+	18.7299i	−0.368959	+	0.639056i	0.620444	+	0.784251i	$0.286952\pi$
$860$		0			0
$861$	10.3431	−	17.9149i	0.352493	−	0.610537i
$862$		0			0
$863$	−50.0000			−1.70202			−0.851010	−	0.525150i	$-0.824009\pi$
$863$	−50.0000			−1.70202			−0.851010	+	0.525150i	$0.824009\pi$
$864$		0			0
$865$	−7.79899	+	13.5082i	−0.265174	+	0.459294i
$866$		0			0
$867$	6.31371			0.214425
$868$		0			0
$869$	−14.0711	−	24.3718i	−0.477328	−	0.826757i
$870$		0			0
$871$	−24.8848	−	43.1017i	−0.843188	−	1.46045i
$872$		0			0
$873$	17.3137			0.585980
$874$		0			0
$875$	−10.3431			−0.349662
$876$		0			0
$877$	8.57107	+	14.8455i	0.289424	+	0.501298i	0.973672	−	0.227952i	$-0.0732028\pi$
$877$	8.57107	+	14.8455i	0.289424	+	0.501298i	−0.684248	+	0.729249i	$0.739869\pi$
$878$		0			0
$879$	−0.656854	−	1.13770i	−0.0221551	−	0.0383738i
$880$		0			0
$881$	−12.4853			−0.420640			−0.210320	−	0.977633i	$-0.567451\pi$
$881$	−12.4853			−0.420640			−0.210320	+	0.977633i	$0.567451\pi$
$882$		0			0
$883$	−6.67157	+	11.5555i	−0.224516	+	0.388874i	−0.956174	−	0.292798i	$-0.905414\pi$
$883$	−6.67157	+	11.5555i	−0.224516	+	0.388874i	0.731658	+	0.681672i	$0.238747\pi$
$884$		0			0
$885$	38.6274			1.29845
$886$		0			0
$887$	−3.31371	+	5.73951i	−0.111263	+	0.192714i	−0.916280	−	0.400539i	$-0.868823\pi$
$887$	−3.31371	+	5.73951i	−0.111263	+	0.192714i	0.805016	+	0.593252i	$0.202156\pi$
$888$		0			0
$889$	5.17157	−	8.95743i	0.173449	−	0.300422i
$890$		0			0
$891$	−2.41421	−	4.18154i	−0.0808792	−	0.140087i
$892$		0			0
$893$	26.7990	−	19.8931i	0.896794	−	0.665697i
$894$		0			0
$895$	−18.8284	−	32.6118i	−0.629365	−	1.09009i
$896$		0			0
$897$	−11.4853	+	19.8931i	−0.383482	+	0.664211i
$898$		0			0
$899$	−2.41421	+	4.18154i	−0.0805185	+	0.139462i
$900$		0			0
$901$	−56.2843			−1.87510
$902$		0			0
$903$	0.914214	−	1.58346i	0.0304231	−	0.0526944i
$904$		0			0
$905$	15.0294			0.499595
$906$		0			0
$907$	2.48528	+	4.30463i	0.0825224	+	0.142933i	0.904333	−	0.426828i	$-0.140369\pi$
$907$	2.48528	+	4.30463i	0.0825224	+	0.142933i	−0.821810	+	0.569761i	$0.807036\pi$
$908$		0			0
$909$	7.41421	+	12.8418i	0.245914	+	0.425935i
$910$		0			0
$911$	−11.3137			−0.374840			−0.187420	−	0.982280i	$-0.560013\pi$
$911$	−11.3137			−0.374840			−0.187420	+	0.982280i	$0.560013\pi$
$912$		0			0
$913$	−4.00000			−0.132381
$914$		0			0
$915$	5.89949	+	10.2182i	0.195031	+	0.337804i
$916$		0			0
$917$	0.443651	+	0.768426i	0.0146506	+	0.0253757i
$918$		0			0
$919$	38.4558			1.26854			0.634271	−	0.773111i	$-0.281301\pi$
$919$	38.4558			1.26854			0.634271	+	0.773111i	$0.281301\pi$
$920$		0			0
$921$	−12.1421	+	21.0308i	−0.400097	+	0.692988i
$922$		0			0
$923$	−54.1421			−1.78211
$924$		0			0
$925$	−17.7426	+	30.7312i	−0.583374	+	1.01043i
$926$		0			0
$927$	−1.74264	+	3.01834i	−0.0572358	+	0.0991354i
$928$		0			0
$929$	11.0711	+	19.1757i	0.363230	+	0.629133i	0.988490	−	0.151283i	$-0.0483406\pi$
$929$	11.0711	+	19.1757i	0.363230	+	0.629133i	−0.625260	+	0.780416i	$0.715007\pi$
$930$		0			0
$931$	14.6274	+	6.33386i	0.479394	+	0.207584i
$932$		0			0
$933$	1.65685	+	2.86976i	0.0542430	+	0.0939516i
$934$		0			0
$935$	32.9706	−	57.1067i	1.07825	−	1.86759i
$936$		0			0
$937$	−27.9853	+	48.4719i	−0.914239	+	1.58351i	−0.106228	+	0.994342i	$0.533877\pi$
$937$	−27.9853	+	48.4719i	−0.914239	+	1.58351i	−0.808011	+	0.589167i	$0.799456\pi$
$938$		0			0
$939$	10.6863			0.348734
$940$		0			0
$941$	19.3137	−	33.4523i	0.629609	−	1.09051i	−0.358021	−	0.933713i	$-0.616548\pi$
$941$	19.3137	−	33.4523i	0.629609	−	1.09051i	0.987630	−	0.156801i	$-0.0501182\pi$
$942$		0			0
$943$	67.8823			2.21055
$944$		0			0
$945$	−2.58579	−	4.47871i	−0.0841156	−	0.145693i
$946$		0			0
$947$	22.7279	+	39.3659i	0.738558	+	1.27922i	0.953145	+	0.302515i	$0.0978264\pi$
$947$	22.7279	+	39.3659i	0.738558	+	1.27922i	−0.214586	+	0.976705i	$0.568840\pi$
$948$		0			0
$949$	−19.1421			−0.621380
$950$		0			0
$951$	−0.485281			−0.0157363
$952$		0			0
$953$	24.8995	+	43.1272i	0.806574	+	1.39703i	0.915223	+	0.402947i	$0.132014\pi$
$953$	24.8995	+	43.1272i	0.806574	+	1.39703i	−0.108650	+	0.994080i	$0.534653\pi$
$954$		0			0
$955$	−23.3137	−	40.3805i	−0.754414	−	1.30668i
$956$		0			0
$957$	4.00000			0.129302
$958$		0			0
$959$	−13.5563	+	23.4803i	−0.437757	+	0.758218i
$960$		0			0
$961$	2.97056			0.0958246
$962$		0			0
$963$	3.41421	−	5.91359i	0.110021	−	0.190563i
$964$		0			0
$965$	25.4142	−	44.0187i	0.818112	−	1.41701i
$966$		0			0
$967$	−8.88478	−	15.3889i	−0.285715	−	0.494873i	0.687067	−	0.726594i	$-0.258898\pi$
$967$	−8.88478	−	15.3889i	−0.285715	−	0.494873i	−0.972782	+	0.231721i	$0.925564\pi$
$968$		0			0
$969$	−16.8995	+	12.5446i	−0.542890	+	0.402991i
$970$		0			0
$971$	24.7990	+	42.9531i	0.795837	+	1.37843i	0.922306	+	0.386460i	$0.126302\pi$
$971$	24.7990	+	42.9531i	0.795837	+	1.37843i	−0.126469	+	0.991971i	$0.540364\pi$
$972$		0			0
$973$	−16.4289	+	28.4557i	−0.526687	+	0.912249i
$974$		0			0
$975$	5.74264	−	9.94655i	0.183912	−	0.318544i
$976$		0			0
$977$	16.3431			0.522864			0.261432	−	0.965222i	$-0.415805\pi$
$977$	16.3431			0.522864			0.261432	+	0.965222i	$0.415805\pi$
$978$		0			0
$979$	−19.3137	+	33.4523i	−0.617269	+	1.06914i
$980$		0			0
$981$	2.00000			0.0638551
$982$		0			0
$983$	−21.7279	−	37.6339i	−0.693013	−	1.20033i	−0.970846	−	0.239704i	$-0.922949\pi$
$983$	−21.7279	−	37.6339i	−0.693013	−	1.20033i	0.277833	−	0.960629i	$-0.410384\pi$
$984$		0			0
$985$	22.6274	+	39.1918i	0.720969	+	1.24876i
$986$		0			0
$987$	14.0000			0.445625
$988$		0			0
$989$	6.00000			0.190789
$990$		0			0
$991$	25.8848	+	44.8337i	0.822257	+	1.42419i	0.903998	+	0.427537i	$0.140619\pi$
$991$	25.8848	+	44.8337i	0.822257	+	1.42419i	−0.0817407	+	0.996654i	$0.526048\pi$
$992$		0			0
$993$	6.15685	+	10.6640i	0.195382	+	0.338411i
$994$		0			0
$995$	−17.4558			−0.553387
$996$		0			0
$997$	−25.9142	+	44.8847i	−0.820711	+	1.42151i	0.0844419	+	0.996428i	$0.473089\pi$
$997$	−25.9142	+	44.8847i	−0.820711	+	1.42151i	−0.905153	+	0.425085i	$0.860244\pi$
$998$		0			0
$999$	11.8284			0.374235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1824.2.q.i.577.1	✓	4
4.3	odd	2		1824.2.q.j.577.1	yes	4
19.11	even	3	inner	1824.2.q.i.961.1	yes	4
76.11	odd	6		1824.2.q.j.961.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1824.2.q.i.577.1	✓	4	1.1	even	1	trivial
1824.2.q.i.961.1	yes	4	19.11	even	3	inner
1824.2.q.j.577.1	yes	4	4.3	odd	2
1824.2.q.j.961.1	yes	4	76.11	odd	6

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:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-1.41421 - 2.44949i) q^{5} +1.82843 q^{7} +(-0.500000 + 0.866025i) q^{9} +4.82843 q^{11} +(1.91421 - 3.31552i) q^{13} +(-1.41421 + 2.44949i) q^{15} +(2.41421 + 4.18154i) q^{17} +(-4.00000 - 1.73205i) q^{19} +(-0.914214 - 1.58346i) q^{21} +(3.00000 - 5.19615i) q^{23} +(-1.50000 + 2.59808i) q^{25} +1.00000 q^{27} +(-0.414214 + 0.717439i) q^{29} +5.82843 q^{31} +(-2.41421 - 4.18154i) q^{33} +(-2.58579 - 4.47871i) q^{35} +11.8284 q^{37} -3.82843 q^{39} +(5.65685 + 9.79796i) q^{41} +(0.500000 + 0.866025i) q^{43} +2.82843 q^{45} +(-3.82843 + 6.63103i) q^{47} -3.65685 q^{49} +(2.41421 - 4.18154i) q^{51} +(-5.82843 + 10.0951i) q^{53} +(-6.82843 - 11.8272i) q^{55} +(0.500000 + 4.33013i) q^{57} +(-6.82843 - 11.8272i) q^{59} +(2.08579 - 3.61269i) q^{61} +(-0.914214 + 1.58346i) q^{63} -10.8284 q^{65} +(6.50000 - 11.2583i) q^{67} -6.00000 q^{69} +(-7.07107 - 12.2474i) q^{71} +(-2.50000 - 4.33013i) q^{73} +3.00000 q^{75} +8.82843 q^{77} +(-2.91421 - 5.04757i) q^{79} +(-0.500000 - 0.866025i) q^{81} -0.828427 q^{83} +(6.82843 - 11.8272i) q^{85} +0.828427 q^{87} +(-4.00000 + 6.92820i) q^{89} +(3.50000 - 6.06218i) q^{91} +(-2.91421 - 5.04757i) q^{93} +(1.41421 + 12.2474i) q^{95} +(-8.65685 - 14.9941i) q^{97} +(-2.41421 + 4.18154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 4 q^{7} - 2 q^{9} + 8 q^{11} + 2 q^{13} + 4 q^{17} - 16 q^{19} + 2 q^{21} + 12 q^{23} - 6 q^{25} + 4 q^{27} + 4 q^{29} + 12 q^{31} - 4 q^{33} - 16 q^{35} + 36 q^{37} - 4 q^{39} + 2 q^{43}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 4 * q^7 - 2 * q^9 + 8 * q^11 + 2 * q^13 + 4 * q^17 - 16 * q^19 + 2 * q^21 + 12 * q^23 - 6 * q^25 + 4 * q^27 + 4 * q^29 + 12 * q^31 - 4 * q^33 - 16 * q^35 + 36 * q^37 - 4 * q^39 + 2 * q^43 - 4 * q^47 + 8 * q^49 + 4 * q^51 - 12 * q^53 - 16 * q^55 + 2 * q^57 - 16 * q^59 + 14 * q^61 + 2 * q^63 - 32 * q^65 + 26 * q^67 - 24 * q^69 - 10 * q^73 + 12 * q^75 + 24 * q^77 - 6 * q^79 - 2 * q^81 + 8 * q^83 + 16 * q^85 - 8 * q^87 - 16 * q^89 + 14 * q^91 - 6 * q^93 - 12 * q^97 - 4 * q^99

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