LMFDB - Embedded newform 1568.2.i.x.1537.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1568,2,Mod(961,1568)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1568, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1568.961"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2,0,2,0,0,0,0,0,2,0,0,0,20,0,-6,0,10,0,0,0,2,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(25)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5205430369$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1537.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1568.1537
Dual form			1568.2.i.x.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207107 + 0.358719i) q^{3} +(-0.914214 - 1.58346i) q^{5} +(1.41421 + 2.44949i) q^{9} +(1.20711 - 2.09077i) q^{11} -2.82843 q^{13} +0.757359 q^{15} +(-0.0857864 + 0.148586i) q^{17} +(3.20711 + 5.55487i) q^{19} +(2.62132 + 4.54026i) q^{23} +(0.828427 - 1.43488i) q^{25} -2.41421 q^{27} -2.82843 q^{29} +(2.79289 - 4.83743i) q^{31} +(0.500000 + 0.866025i) q^{33} +(-4.32843 - 7.49706i) q^{37} +(0.585786 - 1.01461i) q^{39} +6.82843 q^{41} +9.65685 q^{43} +(2.58579 - 4.47871i) q^{45} +(5.20711 + 9.01897i) q^{47} +(-0.0355339 - 0.0615465i) q^{51} +(0.500000 - 0.866025i) q^{53} -4.41421 q^{55} -2.65685 q^{57} +(5.44975 - 9.43924i) q^{59} +(4.32843 + 7.49706i) q^{61} +(2.58579 + 4.47871i) q^{65} +(1.37868 - 2.38794i) q^{67} -2.17157 q^{69} +13.6569 q^{71} +(-7.32843 + 12.6932i) q^{73} +(0.343146 + 0.594346i) q^{75} +(-3.03553 - 5.25770i) q^{79} +(-3.74264 + 6.48244i) q^{81} +7.31371 q^{83} +0.313708 q^{85} +(0.585786 - 1.01461i) q^{87} +(-4.50000 - 7.79423i) q^{89} +(1.15685 + 2.00373i) q^{93} +(5.86396 - 10.1567i) q^{95} +1.17157 q^{97} +6.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{5} + 2 q^{11} + 20 q^{15} - 6 q^{17} + 10 q^{19} + 2 q^{23} - 8 q^{25} - 4 q^{27} + 14 q^{31} + 2 q^{33} - 6 q^{37} + 8 q^{39} + 16 q^{41} + 16 q^{43} + 16 q^{45} + 18 q^{47} + 14 q^{51}+ \cdots + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^5 + 2 * q^11 + 20 * q^15 - 6 * q^17 + 10 * q^19 + 2 * q^23 - 8 * q^25 - 4 * q^27 + 14 * q^31 + 2 * q^33 - 6 * q^37 + 8 * q^39 + 16 * q^41 + 16 * q^43 + 16 * q^45 + 18 * q^47 + 14 * q^51 + 2 * q^53 - 12 * q^55 + 12 * q^57 + 2 * q^59 + 6 * q^61 + 16 * q^65 + 14 * q^67 - 20 * q^69 + 32 * q^71 - 18 * q^73 + 24 * q^75 + 2 * q^79 + 2 * q^81 - 16 * q^83 - 44 * q^85 + 8 * q^87 - 18 * q^89 - 18 * q^93 - 2 * q^95 + 16 * q^97 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	−0.919599	−	0.392859i	$-0.871486\pi$
$3$	−0.207107	+	0.358719i	−0.119573	+	0.207107i	0.800025	+	0.599966i	$0.204819\pi$
$4$		0			0
$5$	−0.914214	−	1.58346i	−0.408849	−	0.708147i	0.585912	−	0.810374i	$-0.300736\pi$
$5$	−0.914214	−	1.58346i	−0.408849	−	0.708147i	−0.994761	+	0.102228i	$0.967403\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	1.20711	−	2.09077i	0.363956	−	0.630391i	−0.624652	−	0.780903i	$-0.714759\pi$
$11$	1.20711	−	2.09077i	0.363956	−	0.630391i	0.988608	+	0.150513i	$0.0480924\pi$
$12$		0			0
$13$	−2.82843			−0.784465			−0.392232	−	0.919866i	$-0.628297\pi$
$13$	−2.82843			−0.784465			−0.392232	+	0.919866i	$0.628297\pi$
$14$		0			0
$15$	0.757359			0.195549
$16$		0			0
$17$	−0.0857864	+	0.148586i	−0.0208063	+	0.0360375i	−0.876241	−	0.481873i	$-0.839957\pi$
$17$	−0.0857864	+	0.148586i	−0.0208063	+	0.0360375i	0.855435	+	0.517911i	$0.173290\pi$
$18$		0			0
$19$	3.20711	+	5.55487i	0.735761	+	1.27438i	0.954389	+	0.298567i	$0.0965085\pi$
$19$	3.20711	+	5.55487i	0.735761	+	1.27438i	−0.218628	+	0.975808i	$0.570158\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.62132	+	4.54026i	0.546583	+	0.946710i	0.998505	+	0.0546524i	$0.0174051\pi$
$23$	2.62132	+	4.54026i	0.546583	+	0.946710i	−0.451922	+	0.892057i	$0.649262\pi$
$24$		0			0
$25$	0.828427	−	1.43488i	0.165685	−	0.286976i
$26$		0			0
$27$	−2.41421			−0.464616
$28$		0			0
$29$	−2.82843			−0.525226			−0.262613	−	0.964901i	$-0.584584\pi$
$29$	−2.82843			−0.525226			−0.262613	+	0.964901i	$0.584584\pi$
$30$		0			0
$31$	2.79289	−	4.83743i	0.501618	−	0.868829i	−0.498380	−	0.866959i	$-0.666071\pi$
$31$	2.79289	−	4.83743i	0.501618	−	0.868829i	0.999998	−	0.00186981i	$-0.000595180\pi$
$32$		0			0
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.32843	−	7.49706i	−0.711589	−	1.23251i	−0.964260	−	0.264956i	$-0.914642\pi$
$37$	−4.32843	−	7.49706i	−0.711589	−	1.23251i	0.252671	−	0.967552i	$-0.418691\pi$
$38$		0			0
$39$	0.585786	−	1.01461i	0.0938009	−	0.162468i
$40$		0			0
$41$	6.82843			1.06642			0.533211	−	0.845983i	$-0.320985\pi$
$41$	6.82843			1.06642			0.533211	+	0.845983i	$0.320985\pi$
$42$		0			0
$43$	9.65685			1.47266			0.736328	−	0.676625i	$-0.236558\pi$
$43$	9.65685			1.47266			0.736328	+	0.676625i	$0.236558\pi$
$44$		0			0
$45$	2.58579	−	4.47871i	0.385466	−	0.667647i
$46$		0			0
$47$	5.20711	+	9.01897i	0.759535	+	1.31555i	0.943088	+	0.332543i	$0.107907\pi$
$47$	5.20711	+	9.01897i	0.759535	+	1.31555i	−0.183554	+	0.983010i	$0.558760\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.0355339	−	0.0615465i	−0.00497574	−	0.00861824i
$52$		0			0
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$		0			0
$55$	−4.41421			−0.595212
$56$		0			0
$57$	−2.65685			−0.351909
$58$		0			0
$59$	5.44975	−	9.43924i	0.709497	−	1.22888i	−0.255547	−	0.966797i	$-0.582256\pi$
$59$	5.44975	−	9.43924i	0.709497	−	1.22888i	0.965044	−	0.262088i	$-0.0844110\pi$
$60$		0			0
$61$	4.32843	+	7.49706i	0.554198	+	0.959900i	0.997965	+	0.0637575i	$0.0203084\pi$
$61$	4.32843	+	7.49706i	0.554198	+	0.959900i	−0.443767	+	0.896142i	$0.646358\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.58579	+	4.47871i	0.320727	+	0.555516i
$66$		0			0
$67$	1.37868	−	2.38794i	0.168433	−	0.291734i	−0.769436	−	0.638723i	$-0.779463\pi$
$67$	1.37868	−	2.38794i	0.168433	−	0.291734i	0.937869	+	0.346990i	$0.112796\pi$
$68$		0			0
$69$	−2.17157			−0.261427
$70$		0			0
$71$	13.6569			1.62077			0.810385	−	0.585897i	$-0.199258\pi$
$71$	13.6569			1.62077			0.810385	+	0.585897i	$0.199258\pi$
$72$		0			0
$73$	−7.32843	+	12.6932i	−0.857728	+	1.48563i	0.0163639	+	0.999866i	$0.494791\pi$
$73$	−7.32843	+	12.6932i	−0.857728	+	1.48563i	−0.874091	+	0.485762i	$0.838542\pi$
$74$		0			0
$75$	0.343146	+	0.594346i	0.0396231	+	0.0686292i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.03553	−	5.25770i	−0.341524	−	0.591537i	0.643192	−	0.765705i	$-0.277610\pi$
$79$	−3.03553	−	5.25770i	−0.341524	−	0.591537i	−0.984716	+	0.174168i	$0.944276\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$	7.31371			0.802784			0.401392	−	0.915906i	$-0.368527\pi$
$83$	7.31371			0.802784			0.401392	+	0.915906i	$0.368527\pi$
$84$		0			0
$85$	0.313708			0.0340265
$86$		0			0
$87$	0.585786	−	1.01461i	0.0628029	−	0.108778i
$88$		0			0
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.15685	+	2.00373i	0.119960	+	0.207777i
$94$		0			0
$95$	5.86396	−	10.1567i	0.601630	−	1.04205i
$96$		0			0
$97$	1.17157			0.118955			0.0594776	−	0.998230i	$-0.481057\pi$
$97$	1.17157			0.118955			0.0594776	+	0.998230i	$0.481057\pi$
$98$		0			0
$99$	6.82843			0.686283
$100$		0			0
$101$	6.74264	−	11.6786i	0.670918	−	1.16206i	−0.306726	−	0.951798i	$-0.599234\pi$
$101$	6.74264	−	11.6786i	0.670918	−	1.16206i	0.977644	−	0.210266i	$-0.0674330\pi$
$102$		0			0
$103$	4.20711	+	7.28692i	0.414539	+	0.718002i	0.995380	−	0.0960150i	$-0.0306097\pi$
$103$	4.20711	+	7.28692i	0.414539	+	0.718002i	−0.580841	+	0.814017i	$0.697276\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.44975	+	11.1713i	0.623521	+	1.07997i	0.988825	+	0.149081i	$0.0476316\pi$
$107$	6.44975	+	11.1713i	0.623521	+	1.07997i	−0.365304	+	0.930888i	$0.619035\pi$
$108$		0			0
$109$	4.08579	−	7.07679i	0.391347	−	0.677834i	−0.601280	−	0.799038i	$-0.705342\pi$
$109$	4.08579	−	7.07679i	0.391347	−	0.677834i	0.992628	+	0.121205i	$0.0386758\pi$
$110$		0			0
$111$	3.58579			0.340348
$112$		0			0
$113$	18.1421			1.70667			0.853334	−	0.521364i	$-0.174577\pi$
$113$	18.1421			1.70667			0.853334	+	0.521364i	$0.174577\pi$
$114$		0			0
$115$	4.79289	−	8.30153i	0.446940	−	0.774122i
$116$		0			0
$117$	−4.00000	−	6.92820i	−0.369800	−	0.640513i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.58579	+	4.47871i	0.235071	+	0.407156i
$122$		0			0
$123$	−1.41421	+	2.44949i	−0.127515	+	0.220863i
$124$		0			0
$125$	−12.1716			−1.08866
$126$		0			0
$127$	−5.65685			−0.501965			−0.250982	−	0.967992i	$-0.580754\pi$
$127$	−5.65685			−0.501965			−0.250982	+	0.967992i	$0.580754\pi$
$128$		0			0
$129$	−2.00000	+	3.46410i	−0.176090	+	0.304997i
$130$		0			0
$131$	3.86396	+	6.69258i	0.337596	+	0.584733i	0.983980	−	0.178279i	$-0.0570530\pi$
$131$	3.86396	+	6.69258i	0.337596	+	0.584733i	−0.646384	+	0.763012i	$0.723720\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.20711	+	3.82282i	0.189958	+	0.329016i
$136$		0			0
$137$	−5.57107	+	9.64937i	−0.475968	+	0.824402i	−0.999621	−	0.0275304i	$-0.991236\pi$
$137$	−5.57107	+	9.64937i	−0.475968	+	0.824402i	0.523653	+	0.851932i	$0.324569\pi$
$138$		0			0
$139$	−15.3137			−1.29889			−0.649446	−	0.760408i	$-0.724999\pi$
$139$	−15.3137			−1.29889			−0.649446	+	0.760408i	$0.724999\pi$
$140$		0			0
$141$	−4.31371			−0.363280
$142$		0			0
$143$	−3.41421	+	5.91359i	−0.285511	+	0.494519i
$144$		0			0
$145$	2.58579	+	4.47871i	0.214738	+	0.371937i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.08579	−	5.34474i	−0.252797	−	0.437858i	0.711497	−	0.702689i	$-0.248017\pi$
$149$	−3.08579	−	5.34474i	−0.252797	−	0.437858i	−0.964295	+	0.264831i	$0.914684\pi$
$150$		0			0
$151$	−0.449747	+	0.778985i	−0.0365999	+	0.0633929i	−0.883745	−	0.467969i	$-0.844986\pi$
$151$	−0.449747	+	0.778985i	−0.0365999	+	0.0633929i	0.847145	+	0.531361i	$0.178319\pi$
$152$		0			0
$153$	−0.485281			−0.0392327
$154$		0			0
$155$	−10.2132			−0.820344
$156$		0			0
$157$	4.67157	−	8.09140i	0.372832	−	0.645764i	−0.617168	−	0.786831i	$-0.711720\pi$
$157$	4.67157	−	8.09140i	0.372832	−	0.645764i	0.990000	+	0.141067i	$0.0450534\pi$
$158$		0			0
$159$	0.207107	+	0.358719i	0.0164246	+	0.0284483i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.37868	−	5.85204i	−0.264639	−	0.458368i	0.702830	−	0.711358i	$-0.251919\pi$
$163$	−3.37868	−	5.85204i	−0.264639	−	0.458368i	−0.967469	+	0.252990i	$0.918586\pi$
$164$		0			0
$165$	0.914214	−	1.58346i	0.0711714	−	0.123273i
$166$		0			0
$167$	−2.00000			−0.154765			−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000			−0.154765			−0.0773823	+	0.997001i	$0.524656\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$	−9.07107	+	15.7116i	−0.693682	+	1.20149i
$172$		0			0
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	0.995754	−	0.0920525i	$-0.0293428\pi$
$173$	5.50000	+	9.52628i	0.418157	+	0.724270i	−0.577597	+	0.816322i	$0.696009\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.25736	+	3.90986i	0.169674	+	0.293883i
$178$		0			0
$179$	−2.79289	+	4.83743i	−0.208751	+	0.361567i	−0.951321	−	0.308201i	$-0.900273\pi$
$179$	−2.79289	+	4.83743i	−0.208751	+	0.361567i	0.742571	+	0.669768i	$0.233606\pi$
$180$		0			0
$181$	9.31371			0.692283			0.346141	−	0.938182i	$-0.387492\pi$
$181$	9.31371			0.692283			0.346141	+	0.938182i	$0.387492\pi$
$182$		0			0
$183$	−3.58579			−0.265069
$184$		0			0
$185$	−7.91421	+	13.7078i	−0.581865	+	1.00782i
$186$		0			0
$187$	0.207107	+	0.358719i	0.0151451	+	0.0262322i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.44975	+	7.70719i	0.321972	+	0.557673i	0.980895	−	0.194538i	$-0.0623208\pi$
$191$	4.44975	+	7.70719i	0.321972	+	0.557673i	−0.658923	+	0.752211i	$0.728987\pi$
$192$		0			0
$193$	4.57107	−	7.91732i	0.329033	−	0.569901i	−0.653288	−	0.757110i	$-0.726611\pi$
$193$	4.57107	−	7.91732i	0.329033	−	0.569901i	0.982320	+	0.187209i	$0.0599440\pi$
$194$		0			0
$195$	−2.14214			−0.153402
$196$		0			0
$197$	−18.8284			−1.34147			−0.670735	−	0.741697i	$-0.734021\pi$
$197$	−18.8284			−1.34147			−0.670735	+	0.741697i	$0.734021\pi$
$198$		0			0
$199$	5.62132	−	9.73641i	0.398485	−	0.690196i	−0.595054	−	0.803685i	$-0.702869\pi$
$199$	5.62132	−	9.73641i	0.398485	−	0.690196i	0.993539	+	0.113489i	$0.0362028\pi$
$200$		0			0
$201$	0.571068	+	0.989118i	0.0402800	+	0.0697670i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.24264	−	10.8126i	−0.436005	−	0.755183i
$206$		0			0
$207$	−7.41421	+	12.8418i	−0.515323	+	0.892566i
$208$		0			0
$209$	15.4853			1.07114
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$		0			0
$213$	−2.82843	+	4.89898i	−0.193801	+	0.335673i
$214$		0			0
$215$	−8.82843	−	15.2913i	−0.602094	−	1.04286i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.03553	−	5.25770i	−0.205122	−	0.355282i
$220$		0			0
$221$	0.242641	−	0.420266i	0.0163218	−	0.0282702i
$222$		0			0
$223$	−2.34315			−0.156909			−0.0784543	−	0.996918i	$-0.524998\pi$
$223$	−2.34315			−0.156909			−0.0784543	+	0.996918i	$0.524998\pi$
$224$		0			0
$225$	4.68629			0.312419
$226$		0			0
$227$	−8.03553	+	13.9180i	−0.533337	+	0.923767i	0.465905	+	0.884835i	$0.345729\pi$
$227$	−8.03553	+	13.9180i	−0.533337	+	0.923767i	−0.999242	+	0.0389321i	$0.987604\pi$
$228$		0			0
$229$	−2.08579	−	3.61269i	−0.137833	−	0.238733i	0.788843	−	0.614594i	$-0.210680\pi$
$229$	−2.08579	−	3.61269i	−0.137833	−	0.238733i	−0.926676	+	0.375861i	$0.877347\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.08579	−	1.88064i	−0.0711322	−	0.123205i	0.828266	−	0.560336i	$-0.189328\pi$
$233$	−1.08579	−	1.88064i	−0.0711322	−	0.123205i	−0.899398	+	0.437131i	$0.855995\pi$
$234$		0			0
$235$	9.52082	−	16.4905i	0.621070	−	1.07572i
$236$		0			0
$237$	2.51472			0.163349
$238$		0			0
$239$	1.31371			0.0849767			0.0424884	−	0.999097i	$-0.486471\pi$
$239$	1.31371			0.0849767			0.0424884	+	0.999097i	$0.486471\pi$
$240$		0			0
$241$	5.15685	−	8.93193i	0.332182	−	0.575356i	−0.650757	−	0.759286i	$-0.725548\pi$
$241$	5.15685	−	8.93193i	0.332182	−	0.575356i	0.982939	+	0.183929i	$0.0588818\pi$
$242$		0			0
$243$	−5.17157	−	8.95743i	−0.331757	−	0.574619i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.07107	−	15.7116i	−0.577178	−	0.999702i
$248$		0			0
$249$	−1.51472	+	2.62357i	−0.0959914	+	0.166262i
$250$		0			0
$251$	30.9706			1.95484			0.977422	−	0.211295i	$-0.0677681\pi$
$251$	30.9706			1.95484			0.977422	+	0.211295i	$0.0677681\pi$
$252$		0			0
$253$	12.6569			0.795730
$254$		0			0
$255$	−0.0649712	+	0.112533i	−0.00406865	+	0.00704711i
$256$		0			0
$257$	2.25736	+	3.90986i	0.140810	+	0.243890i	0.927802	−	0.373073i	$-0.121696\pi$
$257$	2.25736	+	3.90986i	0.140810	+	0.243890i	−0.786992	+	0.616964i	$0.788363\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−4.00000	−	6.92820i	−0.247594	−	0.428845i
$262$		0			0
$263$	−5.44975	+	9.43924i	−0.336046	+	0.582048i	−0.983685	−	0.179899i	$-0.942423\pi$
$263$	−5.44975	+	9.43924i	−0.336046	+	0.582048i	0.647639	+	0.761947i	$0.275756\pi$
$264$		0			0
$265$	−1.82843			−0.112319
$266$		0			0
$267$	3.72792			0.228145
$268$		0			0
$269$	6.32843	−	10.9612i	0.385851	−	0.668314i	−0.606036	−	0.795437i	$-0.707241\pi$
$269$	6.32843	−	10.9612i	0.385851	−	0.668314i	0.991887	+	0.127124i	$0.0405745\pi$
$270$		0			0
$271$	−15.1066	−	26.1654i	−0.917661	−	1.58943i	−0.802958	−	0.596035i	$-0.796742\pi$
$271$	−15.1066	−	26.1654i	−0.917661	−	1.58943i	−0.114702	−	0.993400i	$-0.536591\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$		0			0
$277$	−5.15685	+	8.93193i	−0.309845	+	0.536668i	−0.978328	−	0.207060i	$-0.933611\pi$
$277$	−5.15685	+	8.93193i	−0.309845	+	0.536668i	0.668483	+	0.743727i	$0.266944\pi$
$278$		0			0
$279$	15.7990			0.945861
$280$		0			0
$281$	−12.4853			−0.744809			−0.372405	−	0.928070i	$-0.621467\pi$
$281$	−12.4853			−0.744809			−0.372405	+	0.928070i	$0.621467\pi$
$282$		0			0
$283$	2.79289	−	4.83743i	0.166020	−	0.287556i	−0.770997	−	0.636839i	$-0.780242\pi$
$283$	2.79289	−	4.83743i	0.166020	−	0.287556i	0.937017	+	0.349283i	$0.113575\pi$
$284$		0			0
$285$	2.42893	+	4.20703i	0.143878	+	0.249203i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.48528	+	14.6969i	0.499134	+	0.864526i
$290$		0			0
$291$	−0.242641	+	0.420266i	−0.0142238	+	0.0246364i
$292$		0			0
$293$	−28.6274			−1.67243			−0.836216	−	0.548401i	$-0.815237\pi$
$293$	−28.6274			−1.67243			−0.836216	+	0.548401i	$0.815237\pi$
$294$		0			0
$295$	−19.9289			−1.16031
$296$		0			0
$297$	−2.91421	+	5.04757i	−0.169100	+	0.292889i
$298$		0			0
$299$	−7.41421	−	12.8418i	−0.428775	−	0.742660i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	2.79289	+	4.83743i	0.160448	+	0.277903i
$304$		0			0
$305$	7.91421	−	13.7078i	0.453167	−	0.784907i
$306$		0			0
$307$	−14.3431			−0.818607			−0.409303	−	0.912398i	$-0.634228\pi$
$307$	−14.3431			−0.818607			−0.409303	+	0.912398i	$0.634228\pi$
$308$		0			0
$309$	−3.48528			−0.198271
$310$		0			0
$311$	−9.37868	+	16.2443i	−0.531816	+	0.921133i	0.467494	+	0.883996i	$0.345157\pi$
$311$	−9.37868	+	16.2443i	−0.531816	+	0.921133i	−0.999310	+	0.0371364i	$0.988176\pi$
$312$		0			0
$313$	−14.6421	−	25.3609i	−0.827622	−	1.43348i	−0.899898	−	0.436099i	$-0.856360\pi$
$313$	−14.6421	−	25.3609i	−0.827622	−	1.43348i	0.0722760	−	0.997385i	$-0.476974\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.84315	+	8.38857i	0.272018	+	0.471149i	0.969379	−	0.245571i	$-0.0789756\pi$
$317$	4.84315	+	8.38857i	0.272018	+	0.471149i	−0.697360	+	0.716721i	$0.745642\pi$
$318$		0			0
$319$	−3.41421	+	5.91359i	−0.191159	+	0.331098i
$320$		0			0
$321$	−5.34315			−0.298225
$322$		0			0
$323$	−1.10051			−0.0612337
$324$		0			0
$325$	−2.34315	+	4.05845i	−0.129974	+	0.225122i
$326$		0			0
$327$	1.69239	+	2.93130i	0.0935893	+	0.162101i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−14.2071	−	24.6074i	−0.780893	−	1.35255i	−0.931422	−	0.363941i	$-0.881431\pi$
$331$	−14.2071	−	24.6074i	−0.780893	−	1.35255i	0.150529	−	0.988606i	$-0.451902\pi$
$332$		0			0
$333$	12.2426	−	21.2049i	0.670893	−	1.16202i
$334$		0			0
$335$	−5.04163			−0.275454
$336$		0			0
$337$	9.17157			0.499607			0.249804	−	0.968296i	$-0.419634\pi$
$337$	9.17157			0.499607			0.249804	+	0.968296i	$0.419634\pi$
$338$		0			0
$339$	−3.75736	+	6.50794i	−0.204072	+	0.353463i
$340$		0			0
$341$	−6.74264	−	11.6786i	−0.365134	−	0.632431i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.98528	+	3.43861i	0.106884	+	0.185128i
$346$		0			0
$347$	−17.4497	+	30.2238i	−0.936752	+	1.62250i	−0.165271	+	0.986248i	$0.552850\pi$
$347$	−17.4497	+	30.2238i	−0.936752	+	1.62250i	−0.771480	+	0.636253i	$0.780483\pi$
$348$		0			0
$349$	−5.17157			−0.276828			−0.138414	−	0.990374i	$-0.544200\pi$
$349$	−5.17157			−0.276828			−0.138414	+	0.990374i	$0.544200\pi$
$350$		0			0
$351$	6.82843			0.364474
$352$		0			0
$353$	1.08579	−	1.88064i	0.0577906	−	0.100096i	−0.835683	−	0.549212i	$-0.814928\pi$
$353$	1.08579	−	1.88064i	0.0577906	−	0.100096i	0.893473	+	0.449116i	$0.148261\pi$
$354$		0			0
$355$	−12.4853	−	21.6251i	−0.662650	−	1.14774i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.69239	−	9.85951i	−0.300433	−	0.520365i	0.675801	−	0.737084i	$-0.263798\pi$
$359$	−5.69239	−	9.85951i	−0.300433	−	0.520365i	−0.976234	+	0.216719i	$0.930464\pi$
$360$		0			0
$361$	−11.0711	+	19.1757i	−0.582688	+	1.00924i
$362$		0			0
$363$	−2.14214			−0.112433
$364$		0			0
$365$	26.7990			1.40272
$366$		0			0
$367$	2.13604	−	3.69973i	0.111500	−	0.193124i	−0.804875	−	0.593444i	$-0.797768\pi$
$367$	2.13604	−	3.69973i	0.111500	−	0.193124i	0.916375	+	0.400320i	$0.131101\pi$
$368$		0			0
$369$	9.65685	+	16.7262i	0.502716	+	0.870729i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.15685	+	7.19988i	0.215234	+	0.372796i	0.953345	−	0.301883i	$-0.0976153\pi$
$373$	4.15685	+	7.19988i	0.215234	+	0.372796i	−0.738111	+	0.674679i	$0.764282\pi$
$374$		0			0
$375$	2.52082	−	4.36618i	0.130174	−	0.225469i
$376$		0			0
$377$	8.00000			0.412021
$378$		0			0
$379$	−34.9706			−1.79632			−0.898159	−	0.439672i	$-0.855095\pi$
$379$	−34.9706			−1.79632			−0.898159	+	0.439672i	$0.855095\pi$
$380$		0			0
$381$	1.17157	−	2.02922i	0.0600215	−	0.103960i
$382$		0			0
$383$	−5.62132	−	9.73641i	−0.287236	−	0.497507i	0.685913	−	0.727684i	$-0.259403\pi$
$383$	−5.62132	−	9.73641i	−0.287236	−	0.497507i	−0.973149	+	0.230176i	$0.926070\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	13.6569	+	23.6544i	0.694217	+	1.20242i
$388$		0			0
$389$	−9.08579	+	15.7370i	−0.460668	+	0.797900i	−0.998994	−	0.0448365i	$-0.985723\pi$
$389$	−9.08579	+	15.7370i	−0.460668	+	0.797900i	0.538327	+	0.842736i	$0.319057\pi$
$390$		0			0
$391$	−0.899495			−0.0454894
$392$		0			0
$393$	−3.20101			−0.161470
$394$		0			0
$395$	−5.55025	+	9.61332i	−0.279264	+	0.483699i
$396$		0			0
$397$	−2.08579	−	3.61269i	−0.104683	−	0.181316i	0.808926	−	0.587911i	$-0.200049\pi$
$397$	−2.08579	−	3.61269i	−0.104683	−	0.181316i	−0.913608	+	0.406595i	$0.866716\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.91421	−	6.77962i	−0.195466	−	0.338558i	0.751587	−	0.659634i	$-0.229289\pi$
$401$	−3.91421	−	6.77962i	−0.195466	−	0.338558i	−0.947053	+	0.321076i	$0.895955\pi$
$402$		0			0
$403$	−7.89949	+	13.6823i	−0.393502	+	0.681565i
$404$		0			0
$405$	13.6863			0.680077
$406$		0			0
$407$	−20.8995			−1.03595
$408$		0			0
$409$	7.22792	−	12.5191i	0.357398	−	0.619031i	−0.630128	−	0.776492i	$-0.716997\pi$
$409$	7.22792	−	12.5191i	0.357398	−	0.619031i	0.987525	+	0.157461i	$0.0503307\pi$
$410$		0			0
$411$	−2.30761	−	3.99690i	−0.113826	−	0.197153i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.68629	−	11.5810i	−0.328217	−	0.568489i
$416$		0			0
$417$	3.17157	−	5.49333i	0.155313	−	0.269009i
$418$		0			0
$419$	−9.65685			−0.471768			−0.235884	−	0.971781i	$-0.575799\pi$
$419$	−9.65685			−0.471768			−0.235884	+	0.971781i	$0.575799\pi$
$420$		0			0
$421$	−16.4853			−0.803443			−0.401722	−	0.915762i	$-0.631588\pi$
$421$	−16.4853			−0.803443			−0.401722	+	0.915762i	$0.631588\pi$
$422$		0			0
$423$	−14.7279	+	25.5095i	−0.716096	+	1.24031i
$424$		0			0
$425$	0.142136	+	0.246186i	0.00689459	+	0.0119418i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.41421	−	2.44949i	−0.0682789	−	0.118262i
$430$		0			0
$431$	6.37868	−	11.0482i	0.307250	−	0.532173i	−0.670510	−	0.741901i	$-0.733924\pi$
$431$	6.37868	−	11.0482i	0.307250	−	0.532173i	0.977760	+	0.209728i	$0.0672578\pi$
$432$		0			0
$433$	−11.5147			−0.553362			−0.276681	−	0.960962i	$-0.589235\pi$
$433$	−11.5147			−0.553362			−0.276681	+	0.960962i	$0.589235\pi$
$434$		0			0
$435$	−2.14214			−0.102708
$436$		0			0
$437$	−16.8137	+	29.1222i	−0.804309	+	1.39310i
$438$		0			0
$439$	11.3492	+	19.6575i	0.541670	+	0.938200i	0.998808	+	0.0488041i	$0.0155410\pi$
$439$	11.3492	+	19.6575i	0.541670	+	0.938200i	−0.457139	+	0.889395i	$0.651126\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.96447	+	10.3308i	0.283380	+	0.490829i	0.972215	−	0.234089i	$-0.0752108\pi$
$443$	5.96447	+	10.3308i	0.283380	+	0.490829i	−0.688835	+	0.724918i	$0.741877\pi$
$444$		0			0
$445$	−8.22792	+	14.2512i	−0.390041	+	0.675571i
$446$		0			0
$447$	2.55635			0.120911
$448$		0			0
$449$	1.17157			0.0552899			0.0276450	−	0.999618i	$-0.491199\pi$
$449$	1.17157			0.0552899			0.0276450	+	0.999618i	$0.491199\pi$
$450$		0			0
$451$	8.24264	−	14.2767i	0.388131	−	0.672262i
$452$		0			0
$453$	−0.186292	−	0.322666i	−0.00875274	−	0.0151602i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.64214	−	16.7007i	−0.451040	−	0.781224i	0.547411	−	0.836864i	$-0.315614\pi$
$457$	−9.64214	−	16.7007i	−0.451040	−	0.781224i	−0.998451	+	0.0556397i	$0.982280\pi$
$458$		0			0
$459$	0.207107	−	0.358719i	0.00966692	−	0.0167436i
$460$		0			0
$461$	25.4558			1.18560			0.592798	−	0.805351i	$-0.298023\pi$
$461$	25.4558			1.18560			0.592798	+	0.805351i	$0.298023\pi$
$462$		0			0
$463$	−11.3137			−0.525793			−0.262896	−	0.964824i	$-0.584678\pi$
$463$	−11.3137			−0.525793			−0.262896	+	0.964824i	$0.584678\pi$
$464$		0			0
$465$	2.11522	−	3.66367i	0.0980911	−	0.169899i
$466$		0			0
$467$	−6.27817	−	10.8741i	−0.290519	−	0.503194i	0.683413	−	0.730032i	$-0.260495\pi$
$467$	−6.27817	−	10.8741i	−0.290519	−	0.503194i	−0.973933	+	0.226837i	$0.927161\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.93503	+	3.35157i	0.0891614	+	0.154432i
$472$		0			0
$473$	11.6569	−	20.1903i	0.535983	−	0.928349i
$474$		0			0
$475$	10.6274			0.487619
$476$		0			0
$477$	2.82843			0.129505
$478$		0			0
$479$	−14.3492	+	24.8536i	−0.655634	+	1.13559i	0.326101	+	0.945335i	$0.394265\pi$
$479$	−14.3492	+	24.8536i	−0.655634	+	1.13559i	−0.981735	+	0.190256i	$0.939068\pi$
$480$		0			0
$481$	12.2426	+	21.2049i	0.558216	+	0.966859i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.07107	−	1.85514i	−0.0486347	−	0.0842377i
$486$		0			0
$487$	5.86396	−	10.1567i	0.265721	−	0.460243i	−0.702031	−	0.712146i	$-0.747723\pi$
$487$	5.86396	−	10.1567i	0.265721	−	0.460243i	0.967752	+	0.251903i	$0.0810565\pi$
$488$		0			0
$489$	2.79899			0.126575
$490$		0			0
$491$	3.65685			0.165032			0.0825158	−	0.996590i	$-0.473705\pi$
$491$	3.65685			0.165032			0.0825158	+	0.996590i	$0.473705\pi$
$492$		0			0
$493$	0.242641	−	0.420266i	0.0109280	−	0.0189278i
$494$		0			0
$495$	−6.24264	−	10.8126i	−0.280586	−	0.485989i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.27817	+	3.94591i	0.101985	+	0.176643i	0.912502	−	0.409071i	$-0.134147\pi$
$499$	2.27817	+	3.94591i	0.101985	+	0.176643i	−0.810517	+	0.585715i	$0.800814\pi$
$500$		0			0
$501$	0.414214	−	0.717439i	0.0185057	−	0.0320528i
$502$		0			0
$503$	10.3431			0.461178			0.230589	−	0.973051i	$-0.425935\pi$
$503$	10.3431			0.461178			0.230589	+	0.973051i	$0.425935\pi$
$504$		0			0
$505$	−24.6569			−1.09722
$506$		0			0
$507$	1.03553	−	1.79360i	0.0459897	−	0.0796565i
$508$		0			0
$509$	20.7426	+	35.9273i	0.919401	+	1.59245i	0.800326	+	0.599565i	$0.204660\pi$
$509$	20.7426	+	35.9273i	0.919401	+	1.59245i	0.119075	+	0.992885i	$0.462007\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−7.74264	−	13.4106i	−0.341846	−	0.592095i
$514$		0			0
$515$	7.69239	−	13.3236i	0.338967	−	0.587108i
$516$		0			0
$517$	25.1421			1.10575
$518$		0			0
$519$	−4.55635			−0.200002
$520$		0			0
$521$	3.50000	−	6.06218i	0.153338	−	0.265589i	−0.779115	−	0.626881i	$-0.784331\pi$
$521$	3.50000	−	6.06218i	0.153338	−	0.265589i	0.932453	+	0.361293i	$0.117664\pi$
$522$		0			0
$523$	8.86396	+	15.3528i	0.387594	+	0.671332i	0.992125	−	0.125249i	$-0.0399729\pi$
$523$	8.86396	+	15.3528i	0.387594	+	0.671332i	−0.604531	+	0.796581i	$0.706640\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.479185	+	0.829972i	0.0208736	+	0.0361542i
$528$		0			0
$529$	−2.24264	+	3.88437i	−0.0975061	+	0.168886i
$530$		0			0
$531$	30.8284			1.33784
$532$		0			0
$533$	−19.3137			−0.836570
$534$		0			0
$535$	11.7929	−	20.4259i	0.509851	−	0.883088i
$536$		0			0
$537$	−1.15685	−	2.00373i	−0.0499219	−	0.0864673i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	12.9142	+	22.3681i	0.555225	+	0.961679i	0.997886	+	0.0649894i	$0.0207013\pi$
$541$	12.9142	+	22.3681i	0.555225	+	0.961679i	−0.442661	+	0.896689i	$0.645965\pi$
$542$		0			0
$543$	−1.92893	+	3.34101i	−0.0827784	+	0.143376i
$544$		0			0
$545$	−14.9411			−0.640007
$546$		0			0
$547$	10.9706			0.469067			0.234534	−	0.972108i	$-0.424644\pi$
$547$	10.9706			0.469067			0.234534	+	0.972108i	$0.424644\pi$
$548$		0			0
$549$	−12.2426	+	21.2049i	−0.522503	+	0.905002i
$550$		0			0
$551$	−9.07107	−	15.7116i	−0.386440	−	0.669335i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−3.27817	−	5.67796i	−0.139151	−	0.241016i
$556$		0			0
$557$	0.0857864	−	0.148586i	0.00363489	−	0.00629581i	−0.864202	−	0.503145i	$-0.832176\pi$
$557$	0.0857864	−	0.148586i	0.00363489	−	0.00629581i	0.867837	+	0.496849i	$0.165510\pi$
$558$		0			0
$559$	−27.3137			−1.15525
$560$		0			0
$561$	−0.171573			−0.00724381
$562$		0			0
$563$	−7.03553	+	12.1859i	−0.296512	+	0.513575i	−0.975336	−	0.220727i	$-0.929157\pi$
$563$	−7.03553	+	12.1859i	−0.296512	+	0.513575i	0.678823	+	0.734302i	$0.262490\pi$
$564$		0			0
$565$	−16.5858	−	28.7274i	−0.697769	−	1.20857i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.3284	−	31.7458i	−0.768368	−	1.33085i	−0.938448	−	0.345422i	$-0.887736\pi$
$569$	−18.3284	−	31.7458i	−0.768368	−	1.33085i	0.170080	−	0.985430i	$-0.445597\pi$
$570$		0			0
$571$	9.20711	−	15.9472i	0.385305	−	0.667369i	−0.606506	−	0.795079i	$-0.707429\pi$
$571$	9.20711	−	15.9472i	0.385305	−	0.667369i	0.991812	+	0.127710i	$0.0407628\pi$
$572$		0			0
$573$	−3.68629			−0.153997
$574$		0			0
$575$	8.68629			0.362243
$576$		0			0
$577$	19.5000	−	33.7750i	0.811796	−	1.40607i	−0.0998105	−	0.995006i	$-0.531824\pi$
$577$	19.5000	−	33.7750i	0.811796	−	1.40607i	0.911606	−	0.411065i	$-0.134843\pi$
$578$		0			0
$579$	1.89340	+	3.27946i	0.0786869	+	0.136290i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.20711	−	2.09077i	−0.0499933	−	0.0865909i
$584$		0			0
$585$	−7.31371	+	12.6677i	−0.302385	+	0.523746i
$586$		0			0
$587$	−28.9706			−1.19574			−0.597872	−	0.801592i	$-0.703987\pi$
$587$	−28.9706			−1.19574			−0.597872	+	0.801592i	$0.703987\pi$
$588$		0			0
$589$	35.8284			1.47628
$590$		0			0
$591$	3.89949	−	6.75412i	0.160404	−	0.277828i
$592$		0			0
$593$	2.74264	+	4.75039i	0.112627	+	0.195075i	0.916829	−	0.399281i	$-0.130740\pi$
$593$	2.74264	+	4.75039i	0.112627	+	0.195075i	−0.804202	+	0.594356i	$0.797407\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.32843	+	4.03295i	0.0952962	+	0.165058i
$598$		0			0
$599$	−17.9350	+	31.0644i	−0.732805	+	1.26926i	0.222874	+	0.974847i	$0.428456\pi$
$599$	−17.9350	+	31.0644i	−0.732805	+	1.26926i	−0.955680	+	0.294409i	$0.904877\pi$
$600$		0			0
$601$	−26.1421			−1.06636			−0.533180	−	0.846002i	$-0.679003\pi$
$601$	−26.1421			−1.06636			−0.533180	+	0.846002i	$0.679003\pi$
$602$		0			0
$603$	7.79899			0.317599
$604$		0			0
$605$	4.72792	−	8.18900i	0.192217	−	0.332930i
$606$		0			0
$607$	17.6924	+	30.6441i	0.718112	+	1.24381i	0.961747	+	0.273939i	$0.0883267\pi$
$607$	17.6924	+	30.6441i	0.718112	+	1.24381i	−0.243635	+	0.969867i	$0.578340\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−14.7279	−	25.5095i	−0.595828	−	1.03200i
$612$		0			0
$613$	−2.25736	+	3.90986i	−0.0911739	+	0.157918i	−0.908005	−	0.418959i	$-0.862395\pi$
$613$	−2.25736	+	3.90986i	−0.0911739	+	0.157918i	0.816831	+	0.576876i	$0.195729\pi$
$614$		0			0
$615$	5.17157			0.208538
$616$		0			0
$617$	19.1127			0.769448			0.384724	−	0.923032i	$-0.374297\pi$
$617$	19.1127			0.769448			0.384724	+	0.923032i	$0.374297\pi$
$618$		0			0
$619$	8.96447	−	15.5269i	0.360312	−	0.624079i	−0.627700	−	0.778455i	$-0.716003\pi$
$619$	8.96447	−	15.5269i	0.360312	−	0.624079i	0.988012	+	0.154376i	$0.0493368\pi$
$620$		0			0
$621$	−6.32843	−	10.9612i	−0.253951	−	0.439856i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$		0			0
$627$	−3.20711	+	5.55487i	−0.128080	+	0.221840i
$628$		0			0
$629$	1.48528			0.0592220
$630$		0			0
$631$	29.6569			1.18062			0.590310	−	0.807176i	$-0.299005\pi$
$631$	29.6569			1.18062			0.590310	+	0.807176i	$0.299005\pi$
$632$		0			0
$633$	2.48528	−	4.30463i	0.0987811	−	0.171094i
$634$		0			0
$635$	5.17157	+	8.95743i	0.205228	+	0.355465i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	19.3137	+	33.4523i	0.764038	+	1.32335i
$640$		0			0
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	−0.647895	−	0.761730i	$-0.724350\pi$
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	0.983625	+	0.180229i	$0.0576838\pi$
$642$		0			0
$643$	−11.0294			−0.434959			−0.217479	−	0.976065i	$-0.569783\pi$
$643$	−11.0294			−0.434959			−0.217479	+	0.976065i	$0.569783\pi$
$644$		0			0
$645$	7.31371			0.287977
$646$		0			0
$647$	13.9350	−	24.1362i	0.547843	−	0.948891i	−0.450580	−	0.892736i	$-0.648783\pi$
$647$	13.9350	−	24.1362i	0.547843	−	0.948891i	0.998422	−	0.0561548i	$-0.0178840\pi$
$648$		0			0
$649$	−13.1569	−	22.7883i	−0.516452	−	0.894521i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	19.4706	+	33.7240i	0.761942	+	1.31972i	0.941848	+	0.336038i	$0.109087\pi$
$653$	19.4706	+	33.7240i	0.761942	+	1.31972i	−0.179906	+	0.983684i	$0.557579\pi$
$654$		0			0
$655$	7.06497	−	12.2369i	0.276051	−	0.478135i
$656$		0			0
$657$	−41.4558			−1.61735
$658$		0			0
$659$	34.6274			1.34889			0.674446	−	0.738324i	$-0.264382\pi$
$659$	34.6274			1.34889			0.674446	+	0.738324i	$0.264382\pi$
$660$		0			0
$661$	−15.3284	+	26.5496i	−0.596207	+	1.03266i	0.397169	+	0.917746i	$0.369993\pi$
$661$	−15.3284	+	26.5496i	−0.596207	+	1.03266i	−0.993375	+	0.114915i	$0.963341\pi$
$662$		0			0
$663$	0.100505	+	0.174080i	0.00390329	+	0.00676070i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.41421	−	12.8418i	−0.287079	−	0.497236i
$668$		0			0
$669$	0.485281	−	0.840532i	0.0187621	−	0.0324968i
$670$		0			0
$671$	20.8995			0.806816
$672$		0			0
$673$	−2.14214			−0.0825733			−0.0412866	−	0.999147i	$-0.513146\pi$
$673$	−2.14214			−0.0825733			−0.0412866	+	0.999147i	$0.513146\pi$
$674$		0			0
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$		0			0
$677$	−9.39949	−	16.2804i	−0.361252	−	0.625707i	0.626915	−	0.779087i	$-0.284317\pi$
$677$	−9.39949	−	16.2804i	−0.361252	−	0.625707i	−0.988167	+	0.153381i	$0.950984\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.32843	−	5.76500i	−0.127546	−	0.220915i
$682$		0			0
$683$	8.72183	−	15.1066i	0.333731	−	0.578040i	−0.649509	−	0.760354i	$-0.725025\pi$
$683$	8.72183	−	15.1066i	0.333731	−	0.578040i	0.983240	+	0.182314i	$0.0583588\pi$
$684$		0			0
$685$	20.3726			0.778396
$686$		0			0
$687$	1.72792			0.0659243
$688$		0			0
$689$	−1.41421	+	2.44949i	−0.0538772	+	0.0933181i
$690$		0			0
$691$	13.5208	+	23.4187i	0.514356	+	0.890891i	0.999861	+	0.0166570i	$0.00530235\pi$
$691$	13.5208	+	23.4187i	0.514356	+	0.890891i	−0.485505	+	0.874234i	$0.661364\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	14.0000	+	24.2487i	0.531050	+	0.919806i
$696$		0			0
$697$	−0.585786	+	1.01461i	−0.0221882	+	0.0384312i
$698$		0			0
$699$	0.899495			0.0340220
$700$		0			0
$701$	14.0000			0.528773			0.264386	−	0.964417i	$-0.414831\pi$
$701$	14.0000			0.528773			0.264386	+	0.964417i	$0.414831\pi$
$702$		0			0
$703$	27.7635	−	48.0877i	1.04712	−	1.81366i
$704$		0			0
$705$	3.94365	+	6.83060i	0.148526	+	0.257255i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	18.2990	+	31.6948i	0.687233	+	1.19032i	0.972729	+	0.231943i	$0.0745082\pi$
$709$	18.2990	+	31.6948i	0.687233	+	1.19032i	−0.285496	+	0.958380i	$0.592158\pi$
$710$		0			0
$711$	8.58579	−	14.8710i	0.321992	−	0.557707i
$712$		0			0
$713$	29.2843			1.09670
$714$		0			0
$715$	12.4853			0.466923
$716$		0			0
$717$	−0.272078	+	0.471253i	−0.0101609	+	0.0175993i
$718$		0			0
$719$	15.5208	+	26.8828i	0.578829	+	1.00256i	0.995614	+	0.0935558i	$0.0298234\pi$
$719$	15.5208	+	26.8828i	0.578829	+	1.00256i	−0.416785	+	0.909005i	$0.636843\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.13604	+	3.69973i	0.0794401	+	0.137594i
$724$		0			0
$725$	−2.34315	+	4.05845i	−0.0870222	+	0.150727i
$726$		0			0
$727$	−34.3431			−1.27372			−0.636858	−	0.770981i	$-0.719766\pi$
$727$	−34.3431			−1.27372			−0.636858	+	0.770981i	$0.719766\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	−0.828427	+	1.43488i	−0.0306405	+	0.0530709i
$732$		0			0
$733$	11.8431	+	20.5129i	0.437437	+	0.757662i	0.997491	−	0.0707935i	$-0.0225531\pi$
$733$	11.8431	+	20.5129i	0.437437	+	0.757662i	−0.560054	+	0.828456i	$0.689220\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.32843	−	5.76500i	−0.122604	−	0.212357i
$738$		0			0
$739$	3.34924	−	5.80106i	0.123204	−	0.213395i	−0.797826	−	0.602888i	$-0.794016\pi$
$739$	3.34924	−	5.80106i	0.123204	−	0.213395i	0.921029	+	0.389493i	$0.127350\pi$
$740$		0			0
$741$	7.51472			0.276060
$742$		0			0
$743$	26.3431			0.966436			0.483218	−	0.875500i	$-0.339468\pi$
$743$	26.3431			0.966436			0.483218	+	0.875500i	$0.339468\pi$
$744$		0			0
$745$	−5.64214	+	9.77247i	−0.206712	+	0.358035i
$746$		0			0
$747$	10.3431	+	17.9149i	0.378436	+	0.655470i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.8640	−	18.8169i	−0.396432	−	0.686640i	0.596851	−	0.802352i	$-0.296418\pi$
$751$	−10.8640	−	18.8169i	−0.396432	−	0.686640i	−0.993283	+	0.115712i	$0.963085\pi$
$752$		0			0
$753$	−6.41421	+	11.1097i	−0.233747	+	0.404862i
$754$		0			0
$755$	1.64466			0.0598553
$756$		0			0
$757$	−6.14214			−0.223240			−0.111620	−	0.993751i	$-0.535604\pi$
$757$	−6.14214			−0.223240			−0.111620	+	0.993751i	$0.535604\pi$
$758$		0			0
$759$	−2.62132	+	4.54026i	−0.0951479	+	0.164801i
$760$		0			0
$761$	−21.0563	−	36.4707i	−0.763292	−	1.32206i	−0.941145	−	0.338004i	$-0.890248\pi$
$761$	−21.0563	−	36.4707i	−0.763292	−	1.32206i	0.177853	−	0.984057i	$-0.443085\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.443651	+	0.768426i	0.0160402	+	0.0277825i
$766$		0			0
$767$	−15.4142	+	26.6982i	−0.556575	+	0.964016i
$768$		0			0
$769$	−13.8579			−0.499727			−0.249864	−	0.968281i	$-0.580386\pi$
$769$	−13.8579			−0.499727			−0.249864	+	0.968281i	$0.580386\pi$
$770$		0			0
$771$	−1.87006			−0.0673485
$772$		0			0
$773$	−4.57107	+	7.91732i	−0.164410	+	0.284766i	−0.936446	−	0.350813i	$-0.885905\pi$
$773$	−4.57107	+	7.91732i	−0.164410	+	0.284766i	0.772036	+	0.635579i	$0.219239\pi$
$774$		0			0
$775$	−4.62742	−	8.01492i	−0.166222	−	0.287904i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	21.8995	+	37.9310i	0.784631	+	1.35902i
$780$		0			0
$781$	16.4853	−	28.5533i	0.589890	−	1.02172i
$782$		0			0
$783$	6.82843			0.244028
$784$		0			0
$785$	−17.0833			−0.609728
$786$		0			0
$787$	23.1066	−	40.0218i	0.823661	−	1.42662i	−0.0792766	−	0.996853i	$-0.525261\pi$
$787$	23.1066	−	40.0218i	0.823661	−	1.42662i	0.902938	−	0.429771i	$-0.141406\pi$
$788$		0			0
$789$	−2.25736	−	3.90986i	−0.0803641	−	0.139195i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−12.2426	−	21.2049i	−0.434749	−	0.753007i
$794$		0			0
$795$	0.378680	−	0.655892i	0.0134304	−	0.0232621i
$796$		0			0
$797$	−47.1127			−1.66882			−0.834409	−	0.551146i	$-0.814191\pi$
$797$	−47.1127			−1.66882			−0.834409	+	0.551146i	$0.814191\pi$
$798$		0			0
$799$	−1.78680			−0.0632123
$800$		0			0
$801$	12.7279	−	22.0454i	0.449719	−	0.778936i
$802$		0			0
$803$	17.6924	+	30.6441i	0.624351	+	1.08141i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.62132	+	4.54026i	0.0922748	+	0.159825i
$808$		0			0
$809$	8.98528	−	15.5630i	0.315906	−	0.547165i	−0.663724	−	0.747978i	$-0.731025\pi$
$809$	8.98528	−	15.5630i	0.315906	−	0.547165i	0.979630	+	0.200813i	$0.0643584\pi$
$810$		0			0
$811$	17.6569			0.620016			0.310008	−	0.950734i	$-0.399668\pi$
$811$	17.6569			0.620016			0.310008	+	0.950734i	$0.399668\pi$
$812$		0			0
$813$	12.5147			0.438910
$814$		0			0
$815$	−6.17767	+	10.7000i	−0.216394	+	0.374806i
$816$		0			0
$817$	30.9706	+	53.6426i	1.08352	+	1.87672i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.57107	−	13.1135i	−0.264232	−	0.457663i	0.703130	−	0.711061i	$-0.251785\pi$
$821$	−7.57107	−	13.1135i	−0.264232	−	0.457663i	−0.967362	+	0.253398i	$0.918452\pi$
$822$		0			0
$823$	24.0061	−	41.5798i	0.836800	−	1.44938i	−0.0557566	−	0.998444i	$-0.517757\pi$
$823$	24.0061	−	41.5798i	0.836800	−	1.44938i	0.892556	−	0.450936i	$-0.148910\pi$
$824$		0			0
$825$	1.65685			0.0576843
$826$		0			0
$827$	41.6569			1.44855			0.724275	−	0.689511i	$-0.242174\pi$
$827$	41.6569			1.44855			0.724275	+	0.689511i	$0.242174\pi$
$828$		0			0
$829$	0.600505	−	1.04011i	0.0208564	−	0.0361243i	−0.855409	−	0.517953i	$-0.826694\pi$
$829$	0.600505	−	1.04011i	0.0208564	−	0.0361243i	0.876265	+	0.481829i	$0.160027\pi$
$830$		0			0
$831$	−2.13604	−	3.69973i	−0.0740984	−	0.128342i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.82843	+	3.16693i	0.0632753	+	0.109596i
$836$		0			0
$837$	−6.74264	+	11.6786i	−0.233060	+	0.403671i
$838$		0			0
$839$	3.31371			0.114402			0.0572010	−	0.998363i	$-0.481782\pi$
$839$	3.31371			0.114402			0.0572010	+	0.998363i	$0.481782\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$		0			0
$843$	2.58579	−	4.47871i	0.0890592	−	0.154255i
$844$		0			0
$845$	4.57107	+	7.91732i	0.157250	+	0.272364i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.15685	+	2.00373i	0.0397031	+	0.0687678i
$850$		0			0
$851$	22.6924	−	39.3044i	0.777885	−	1.34734i
$852$		0			0
$853$	40.4853			1.38619			0.693095	−	0.720846i	$-0.256247\pi$
$853$	40.4853			1.38619			0.693095	+	0.720846i	$0.256247\pi$
$854$		0			0
$855$	33.1716			1.13444
$856$		0			0
$857$	12.6716	−	21.9478i	0.432853	−	0.749723i	−0.564265	−	0.825594i	$-0.690840\pi$
$857$	12.6716	−	21.9478i	0.432853	−	0.749723i	0.997118	+	0.0758709i	$0.0241737\pi$
$858$		0			0
$859$	2.72183	+	4.71434i	0.0928675	+	0.160851i	0.908717	−	0.417414i	$-0.137063\pi$
$859$	2.72183	+	4.71434i	0.0928675	+	0.160851i	−0.815849	+	0.578265i	$0.803730\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.6924	−	28.9121i	−0.568216	−	0.984178i	−0.996743	−	0.0806492i	$-0.974301\pi$
$863$	−16.6924	−	28.9121i	−0.568216	−	0.984178i	0.428527	−	0.903529i	$-0.359033\pi$
$864$		0			0
$865$	10.0563	−	17.4181i	0.341926	−	0.592233i
$866$		0			0
$867$	−7.02944			−0.238732
$868$		0			0
$869$	−14.6569			−0.497200
$870$		0			0
$871$	−3.89949	+	6.75412i	−0.132129	+	0.228855i
$872$		0			0
$873$	1.65685	+	2.86976i	0.0560760	+	0.0971265i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−25.7132	−	44.5366i	−0.868273	−	1.50389i	−0.863760	−	0.503903i	$-0.831897\pi$
$877$	−25.7132	−	44.5366i	−0.868273	−	1.50389i	−0.00451320	−	0.999990i	$-0.501437\pi$
$878$		0			0
$879$	5.92893	−	10.2692i	0.199978	−	0.346372i
$880$		0			0
$881$	26.0000			0.875962			0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000			0.875962			0.437981	+	0.898984i	$0.355694\pi$
$882$		0			0
$883$	−41.2548			−1.38834			−0.694168	−	0.719813i	$-0.744227\pi$
$883$	−41.2548			−1.38834			−0.694168	+	0.719813i	$0.744227\pi$
$884$		0			0
$885$	4.12742	−	7.14890i	0.138742	−	0.240308i
$886$		0			0
$887$	15.5503	+	26.9338i	0.522126	+	0.904349i	0.999669	+	0.0257406i	$0.00819441\pi$
$887$	15.5503	+	26.9338i	0.522126	+	0.904349i	−0.477542	+	0.878609i	$0.658472\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	9.03553	+	15.6500i	0.302702	+	0.524295i
$892$		0			0
$893$	−33.3995	+	57.8496i	−1.11767	+	1.93586i
$894$		0			0
$895$	10.2132			0.341390
$896$		0			0
$897$	6.14214			0.205080
$898$		0			0
$899$	−7.89949	+	13.6823i	−0.263463	+	0.456331i
$900$		0			0
$901$	0.0857864	+	0.148586i	0.00285796	+	0.00495013i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.51472	−	14.7479i	−0.283039	−	0.490238i
$906$		0			0
$907$	−12.7635	+	22.1070i	−0.423804	+	0.734049i	−0.996308	−	0.0858524i	$-0.972639\pi$
$907$	−12.7635	+	22.1070i	−0.423804	+	0.734049i	0.572504	+	0.819902i	$0.305972\pi$
$908$		0			0
$909$	38.1421			1.26509
$910$		0			0
$911$	8.00000			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$912$		0			0
$913$	8.82843	−	15.2913i	0.292178	−	0.506068i
$914$		0			0
$915$	3.27817	+	5.67796i	0.108373	+	0.187708i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	3.27817	+	5.67796i	0.108137	+	0.187299i	0.915016	−	0.403419i	$-0.132178\pi$
$919$	3.27817	+	5.67796i	0.108137	+	0.187299i	−0.806879	+	0.590717i	$0.798845\pi$
$920$		0			0
$921$	2.97056	−	5.14517i	0.0978834	−	0.169539i
$922$		0			0
$923$	−38.6274			−1.27144
$924$		0			0
$925$	−14.3431			−0.471600
$926$		0			0
$927$	−11.8995	+	20.6105i	−0.390831	+	0.676939i
$928$		0			0
$929$	−9.67157	−	16.7517i	−0.317314	−	0.549604i	0.662613	−	0.748962i	$-0.269448\pi$
$929$	−9.67157	−	16.7517i	−0.317314	−	0.549604i	−0.979927	+	0.199358i	$0.936114\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−3.88478	−	6.72863i	−0.127182	−	0.220285i
$934$		0			0
$935$	0.378680	−	0.655892i	0.0123841	−	0.0214500i
$936$		0			0
$937$	−16.6274			−0.543194			−0.271597	−	0.962411i	$-0.587552\pi$
$937$	−16.6274			−0.543194			−0.271597	+	0.962411i	$0.587552\pi$
$938$		0			0
$939$	12.1299			0.395846
$940$		0			0
$941$	−19.1274	+	33.1297i	−0.623536	+	1.08000i	0.365286	+	0.930895i	$0.380971\pi$
$941$	−19.1274	+	33.1297i	−0.623536	+	1.08000i	−0.988822	+	0.149101i	$0.952362\pi$
$942$		0			0
$943$	17.8995	+	31.0028i	0.582888	+	1.00959i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.10660	+	15.7731i	0.295925	+	0.512557i	0.975200	−	0.221327i	$-0.0710389\pi$
$947$	9.10660	+	15.7731i	0.295925	+	0.512557i	−0.679275	+	0.733884i	$0.737706\pi$
$948$		0			0
$949$	20.7279	−	35.9018i	0.672857	−	1.16542i
$950$		0			0
$951$	−4.01219			−0.130104
$952$		0			0
$953$	−27.1127			−0.878266			−0.439133	−	0.898422i	$-0.644714\pi$
$953$	−27.1127			−0.878266			−0.439133	+	0.898422i	$0.644714\pi$
$954$		0			0
$955$	8.13604	−	14.0920i	0.263276	−	0.456007i
$956$		0			0
$957$	−1.41421	−	2.44949i	−0.0457150	−	0.0791808i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.100505	−	0.174080i	−0.00324210	−	0.00561548i
$962$		0			0
$963$	−18.2426	+	31.5972i	−0.587861	+	1.01820i
$964$		0			0
$965$	−16.7157			−0.538098
$966$		0			0
$967$	−18.3431			−0.589876			−0.294938	−	0.955516i	$-0.595299\pi$
$967$	−18.3431			−0.589876			−0.294938	+	0.955516i	$0.595299\pi$
$968$		0			0
$969$	0.227922	−	0.394773i	0.00732191	−	0.0126819i
$970$		0			0
$971$	−17.7929	−	30.8182i	−0.571001	−	0.989003i	−0.996463	−	0.0840268i	$-0.973222\pi$
$971$	−17.7929	−	30.8182i	−0.571001	−	0.989003i	0.425462	−	0.904976i	$-0.360111\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.970563	−	1.68106i	−0.0310829	−	0.0538371i
$976$		0			0
$977$	17.2574	−	29.8906i	0.552112	−	0.956286i	−0.446010	−	0.895028i	$-0.647155\pi$
$977$	17.2574	−	29.8906i	0.552112	−	0.956286i	0.998122	−	0.0612578i	$-0.0195112\pi$
$978$		0			0
$979$	−21.7279			−0.694427
$980$		0			0
$981$	23.1127			0.737932
$982$		0			0
$983$	13.4203	−	23.2447i	0.428041	−	0.741389i	−0.568658	−	0.822574i	$-0.692537\pi$
$983$	13.4203	−	23.2447i	0.428041	−	0.741389i	0.996699	+	0.0811848i	$0.0258704\pi$
$984$		0			0
$985$	17.2132	+	29.8141i	0.548458	+	0.949958i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	25.3137	+	43.8446i	0.804929	+	1.39418i
$990$		0			0
$991$	22.3492	−	38.7100i	0.709947	−	1.22966i	−0.254929	−	0.966960i	$-0.582052\pi$
$991$	22.3492	−	38.7100i	0.709947	−	1.22966i	0.964876	−	0.262705i	$-0.0846145\pi$
$992$		0			0
$993$	11.7696			0.373495
$994$		0			0
$995$	−20.5563			−0.651680
$996$		0			0
$997$	−22.6421	+	39.2173i	−0.717084	+	1.24203i	0.245067	+	0.969506i	$0.421190\pi$
$997$	−22.6421	+	39.2173i	−0.717084	+	1.24203i	−0.962150	+	0.272519i	$0.912143\pi$
$998$		0			0
$999$	10.4497	+	18.0995i	0.330615	+	0.572643i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.i.x.1537.1		4
4.3	odd	2		1568.2.i.o.1537.2		4
7.2	even	3	inner	1568.2.i.x.961.1		4
7.3	odd	6		1568.2.a.w.1.1		2
7.4	even	3		1568.2.a.j.1.2		2
7.5	odd	6		224.2.i.a.65.2	✓	4
7.6	odd	2		224.2.i.a.193.2	yes	4
21.5	even	6		2016.2.s.q.289.1		4
21.20	even	2		2016.2.s.q.865.1		4
28.3	even	6		1568.2.a.l.1.2		2
28.11	odd	6		1568.2.a.u.1.1		2
28.19	even	6		224.2.i.d.65.1	yes	4
28.23	odd	6		1568.2.i.o.961.2		4
28.27	even	2		224.2.i.d.193.1	yes	4
56.3	even	6		3136.2.a.bw.1.1		2
56.5	odd	6		448.2.i.j.65.1		4
56.11	odd	6		3136.2.a.be.1.2		2
56.13	odd	2		448.2.i.j.193.1		4
56.19	even	6		448.2.i.g.65.2		4
56.27	even	2		448.2.i.g.193.2		4
56.45	odd	6		3136.2.a.bd.1.2		2
56.53	even	6		3136.2.a.bx.1.1		2
84.47	odd	6		2016.2.s.s.289.1		4
84.83	odd	2		2016.2.s.s.865.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.i.a.65.2	✓	4	7.5	odd	6
224.2.i.a.193.2	yes	4	7.6	odd	2
224.2.i.d.65.1	yes	4	28.19	even	6
224.2.i.d.193.1	yes	4	28.27	even	2
448.2.i.g.65.2		4	56.19	even	6
448.2.i.g.193.2		4	56.27	even	2
448.2.i.j.65.1		4	56.5	odd	6
448.2.i.j.193.1		4	56.13	odd	2
1568.2.a.j.1.2		2	7.4	even	3
1568.2.a.l.1.2		2	28.3	even	6
1568.2.a.u.1.1		2	28.11	odd	6
1568.2.a.w.1.1		2	7.3	odd	6
1568.2.i.o.961.2		4	28.23	odd	6
1568.2.i.o.1537.2		4	4.3	odd	2
1568.2.i.x.961.1		4	7.2	even	3	inner
1568.2.i.x.1537.1		4	1.1	even	1	trivial
2016.2.s.q.289.1		4	21.5	even	6
2016.2.s.q.865.1		4	21.20	even	2
2016.2.s.s.289.1		4	84.47	odd	6
2016.2.s.s.865.1		4	84.83	odd	2
3136.2.a.bd.1.2		2	56.45	odd	6
3136.2.a.be.1.2		2	56.11	odd	6
3136.2.a.bw.1.1		2	56.3	even	6
3136.2.a.bx.1.1		2	56.53	even	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:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{3} +(-0.914214 - 1.58346i) q^{5} +(1.41421 + 2.44949i) q^{9} +(1.20711 - 2.09077i) q^{11} -2.82843 q^{13} +0.757359 q^{15} +(-0.0857864 + 0.148586i) q^{17} +(3.20711 + 5.55487i) q^{19} +(2.62132 + 4.54026i) q^{23} +(0.828427 - 1.43488i) q^{25} -2.41421 q^{27} -2.82843 q^{29} +(2.79289 - 4.83743i) q^{31} +(0.500000 + 0.866025i) q^{33} +(-4.32843 - 7.49706i) q^{37} +(0.585786 - 1.01461i) q^{39} +6.82843 q^{41} +9.65685 q^{43} +(2.58579 - 4.47871i) q^{45} +(5.20711 + 9.01897i) q^{47} +(-0.0355339 - 0.0615465i) q^{51} +(0.500000 - 0.866025i) q^{53} -4.41421 q^{55} -2.65685 q^{57} +(5.44975 - 9.43924i) q^{59} +(4.32843 + 7.49706i) q^{61} +(2.58579 + 4.47871i) q^{65} +(1.37868 - 2.38794i) q^{67} -2.17157 q^{69} +13.6569 q^{71} +(-7.32843 + 12.6932i) q^{73} +(0.343146 + 0.594346i) q^{75} +(-3.03553 - 5.25770i) q^{79} +(-3.74264 + 6.48244i) q^{81} +7.31371 q^{83} +0.313708 q^{85} +(0.585786 - 1.01461i) q^{87} +(-4.50000 - 7.79423i) q^{89} +(1.15685 + 2.00373i) q^{93} +(5.86396 - 10.1567i) q^{95} +1.17157 q^{97} +6.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{5} + 2 q^{11} + 20 q^{15} - 6 q^{17} + 10 q^{19} + 2 q^{23} - 8 q^{25} - 4 q^{27} + 14 q^{31} + 2 q^{33} - 6 q^{37} + 8 q^{39} + 16 q^{41} + 16 q^{43} + 16 q^{45} + 18 q^{47} + 14 q^{51}+ \cdots + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^5 + 2 * q^11 + 20 * q^15 - 6 * q^17 + 10 * q^19 + 2 * q^23 - 8 * q^25 - 4 * q^27 + 14 * q^31 + 2 * q^33 - 6 * q^37 + 8 * q^39 + 16 * q^41 + 16 * q^43 + 16 * q^45 + 18 * q^47 + 14 * q^51 + 2 * q^53 - 12 * q^55 + 12 * q^57 + 2 * q^59 + 6 * q^61 + 16 * q^65 + 14 * q^67 - 20 * q^69 + 32 * q^71 - 18 * q^73 + 24 * q^75 + 2 * q^79 + 2 * q^81 - 16 * q^83 - 44 * q^85 + 8 * q^87 - 18 * q^89 - 18 * q^93 - 2 * q^95 + 16 * q^97 + 16 * q^99

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