LMFDB - Embedded newform 448.2.i.j.193.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,2,Mod(65,448)] 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("448.65"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.57729801055$
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			193.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	448.193
Dual form			448.2.i.j.65.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207107 + 0.358719i) q^{3} +(-0.914214 - 1.58346i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(1.41421 + 2.44949i) q^{9} +(-1.20711 + 2.09077i) q^{11} -2.82843 q^{13} +0.757359 q^{15} +(0.0857864 - 0.148586i) q^{17} +(3.20711 + 5.55487i) q^{19} +(-0.671573 - 0.866025i) q^{21} +(2.62132 + 4.54026i) q^{23} +(0.828427 - 1.43488i) q^{25} -2.41421 q^{27} +2.82843 q^{29} +(-2.79289 + 4.83743i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(4.79289 - 0.655892i) q^{35} +(4.32843 + 7.49706i) q^{37} +(0.585786 - 1.01461i) q^{39} -6.82843 q^{41} -9.65685 q^{43} +(2.58579 - 4.47871i) q^{45} +(-5.20711 - 9.01897i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(0.0355339 + 0.0615465i) q^{51} +(-0.500000 + 0.866025i) q^{53} +4.41421 q^{55} -2.65685 q^{57} +(5.44975 - 9.43924i) q^{59} +(4.32843 + 7.49706i) q^{61} +(-7.41421 + 1.01461i) q^{63} +(2.58579 + 4.47871i) q^{65} +(-1.37868 + 2.38794i) q^{67} -2.17157 q^{69} +13.6569 q^{71} +(7.32843 - 12.6932i) q^{73} +(0.343146 + 0.594346i) q^{75} +(-3.91421 - 5.04757i) q^{77} +(-3.03553 - 5.25770i) q^{79} +(-3.74264 + 6.48244i) q^{81} +7.31371 q^{83} -0.313708 q^{85} +(-0.585786 + 1.01461i) q^{87} +(4.50000 + 7.79423i) q^{89} +(2.82843 - 6.92820i) q^{91} +(-1.15685 - 2.00373i) q^{93} +(5.86396 - 10.1567i) q^{95} -1.17157 q^{97} -6.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{5} - 4 q^{7} - 2 q^{11} + 20 q^{15} + 6 q^{17} + 10 q^{19} - 14 q^{21} + 2 q^{23} - 8 q^{25} - 4 q^{27} - 14 q^{31} - 2 q^{33} + 22 q^{35} + 6 q^{37} + 8 q^{39} - 16 q^{41} - 16 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^5 - 4 * q^7 - 2 * q^11 + 20 * q^15 + 6 * q^17 + 10 * q^19 - 14 * q^21 + 2 * q^23 - 8 * q^25 - 4 * q^27 - 14 * q^31 - 2 * q^33 + 22 * q^35 + 6 * q^37 + 8 * q^39 - 16 * q^41 - 16 * q^43 + 16 * q^45 - 18 * q^47 - 20 * q^49 - 14 * q^51 - 2 * q^53 + 12 * q^55 + 12 * q^57 + 2 * q^59 + 6 * q^61 - 24 * q^63 + 16 * q^65 - 14 * q^67 - 20 * q^69 + 32 * q^71 + 18 * q^73 + 24 * q^75 - 10 * q^77 + 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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.207107	+	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
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$7$	−1.00000	+	2.44949i	−0.377964	+	0.925820i
$8$		0			0
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	−1.20711	+	2.09077i	−0.363956	+	0.630391i	−0.988608	−	0.150513i	$-0.951908\pi$
$11$	−1.20711	+	2.09077i	−0.363956	+	0.630391i	0.624652	+	0.780903i	$0.285241\pi$
$12$		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	−0.855435	−	0.517911i	$-0.826710\pi$
$17$	0.0857864	−	0.148586i	0.0208063	−	0.0360375i	0.876241	+	0.481873i	$0.160043\pi$
$18$		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
$21$	−0.671573	−	0.866025i	−0.146549	−	0.188982i
$22$		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	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$		0			0
$31$	−2.79289	+	4.83743i	−0.501618	+	0.868829i	0.498380	+	0.866959i	$0.333929\pi$
$31$	−2.79289	+	4.83743i	−0.501618	+	0.868829i	−0.999998	+	0.00186981i	$0.999405\pi$
$32$		0			0
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$		0			0
$35$	4.79289	−	0.655892i	0.810147	−	0.110866i
$36$		0			0
$37$	4.32843	+	7.49706i	0.711589	+	1.23251i	0.964260	+	0.264956i	$0.0853575\pi$
$37$	4.32843	+	7.49706i	0.711589	+	1.23251i	−0.252671	+	0.967552i	$0.581309\pi$
$38$		0			0
$39$	0.585786	−	1.01461i	0.0938009	−	0.162468i
$40$		0			0
$41$	−6.82843			−1.06642			−0.533211	−	0.845983i	$-0.679015\pi$
$41$	−6.82843			−1.06642			−0.533211	+	0.845983i	$0.679015\pi$
$42$		0			0
$43$	−9.65685			−1.47266			−0.736328	−	0.676625i	$-0.763442\pi$
$43$	−9.65685			−1.47266			−0.736328	+	0.676625i	$0.763442\pi$
$44$		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	$-0.892093\pi$
$47$	−5.20711	−	9.01897i	−0.759535	−	1.31555i	0.183554	−	0.983010i	$-0.441240\pi$
$48$		0			0
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		0			0
$51$	0.0355339	+	0.0615465i	0.00497574	+	0.00861824i
$52$		0			0
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	−0.898321	−	0.439340i	$-0.855212\pi$
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	0.829640	+	0.558298i	$0.188546\pi$
$54$		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
$63$	−7.41421	+	1.01461i	−0.934103	+	0.127829i
$64$		0			0
$65$	2.58579	+	4.47871i	0.320727	+	0.555516i
$66$		0			0
$67$	−1.37868	+	2.38794i	−0.168433	+	0.291734i	−0.937869	−	0.346990i	$-0.887204\pi$
$67$	−1.37868	+	2.38794i	−0.168433	+	0.291734i	0.769436	+	0.638723i	$0.220537\pi$
$68$		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	$-0.505209\pi$
$73$	7.32843	−	12.6932i	0.857728	−	1.48563i	0.874091	−	0.485762i	$-0.161458\pi$
$74$		0			0
$75$	0.343146	+	0.594346i	0.0396231	+	0.0686292i
$76$		0			0
$77$	−3.91421	−	5.04757i	−0.446066	−	0.575224i
$78$		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	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$		0			0
$91$	2.82843	−	6.92820i	0.296500	−	0.726273i
$92$		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	$-0.518943\pi$
$97$	−1.17157			−0.118955			−0.0594776	+	0.998230i	$0.518943\pi$
$98$		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	0.580841	−	0.814017i	$-0.302724\pi$
$103$	−4.20711	−	7.28692i	−0.414539	−	0.718002i	−0.995380	+	0.0960150i	$0.969390\pi$
$104$		0			0
$105$	−0.757359	+	1.85514i	−0.0739107	+	0.181044i
$106$		0			0
$107$	−6.44975	−	11.1713i	−0.623521	−	1.07997i	−0.988825	−	0.149081i	$-0.952368\pi$
$107$	−6.44975	−	11.1713i	−0.623521	−	1.07997i	0.365304	−	0.930888i	$-0.380965\pi$
$108$		0			0
$109$	−4.08579	+	7.07679i	−0.391347	+	0.677834i	−0.992628	−	0.121205i	$-0.961324\pi$
$109$	−4.08579	+	7.07679i	−0.391347	+	0.677834i	0.601280	+	0.799038i	$0.294658\pi$
$110$		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
$119$	0.278175	+	0.358719i	0.0255002	+	0.0328838i
$120$		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
$133$	−16.8137	+	2.30090i	−1.45793	+	0.199514i
$134$		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
$147$	2.79289	−	0.778985i	0.230354	−	0.0642496i
$148$		0			0
$149$	3.08579	+	5.34474i	0.252797	+	0.437858i	0.964295	−	0.264831i	$-0.0853160\pi$
$149$	3.08579	+	5.34474i	0.252797	+	0.437858i	−0.711497	+	0.702689i	$0.751983\pi$
$150$		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
$161$	−13.7426	+	1.88064i	−1.08307	+	0.148215i
$162$		0			0
$163$	3.37868	+	5.85204i	0.264639	+	0.458368i	0.967469	−	0.252990i	$-0.0814140\pi$
$163$	3.37868	+	5.85204i	0.264639	+	0.458368i	−0.702830	+	0.711358i	$0.748081\pi$
$164$		0			0
$165$	−0.914214	+	1.58346i	−0.0711714	+	0.123273i
$166$		0			0
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$		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
$175$	2.68629	+	3.46410i	0.203065	+	0.261861i
$176$		0			0
$177$	2.25736	+	3.90986i	0.169674	+	0.293883i
$178$		0			0
$179$	2.79289	−	4.83743i	0.208751	−	0.361567i	−0.742571	−	0.669768i	$-0.766394\pi$
$179$	2.79289	−	4.83743i	0.208751	−	0.361567i	0.951321	+	0.308201i	$0.0997270\pi$
$180$		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
$189$	2.41421	−	5.91359i	0.175608	−	0.430150i
$190$		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	$-0.265979\pi$
$197$	18.8284			1.34147			0.670735	+	0.741697i	$0.265979\pi$
$198$		0			0
$199$	−5.62132	+	9.73641i	−0.398485	+	0.690196i	−0.993539	−	0.113489i	$-0.963797\pi$
$199$	−5.62132	+	9.73641i	−0.398485	+	0.690196i	0.595054	+	0.803685i	$0.297131\pi$
$200$		0			0
$201$	−0.571068	−	0.989118i	−0.0402800	−	0.0697670i
$202$		0			0
$203$	−2.82843	+	6.92820i	−0.198517	+	0.486265i
$204$		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	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$		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
$217$	−9.05635	−	11.6786i	−0.614785	−	0.792795i
$218$		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	$-0.475002\pi$
$223$	2.34315			0.156909			0.0784543	+	0.996918i	$0.475002\pi$
$224$		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
$231$	2.62132	−	0.358719i	0.172470	−	0.0236020i
$232$		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	−0.982939	−	0.183929i	$-0.941118\pi$
$241$	−5.15685	+	8.93193i	−0.332182	+	0.575356i	0.650757	+	0.759286i	$0.274452\pi$
$242$		0			0
$243$	−5.17157	−	8.95743i	−0.331757	−	0.574619i
$244$		0			0
$245$	−3.18629	+	12.3960i	−0.203565	+	0.791954i
$246$		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	0.786992	−	0.616964i	$-0.211637\pi$
$257$	−2.25736	−	3.90986i	−0.140810	−	0.243890i	−0.927802	+	0.373073i	$0.878304\pi$
$258$		0			0
$259$	−22.6924	+	3.10538i	−1.41004	+	0.192959i
$260$		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	$0.203258\pi$
$271$	15.1066	+	26.1654i	0.917661	+	1.58943i	0.114702	+	0.993400i	$0.463409\pi$
$272$		0			0
$273$	1.89949	+	2.44949i	0.114963	+	0.148250i
$274$		0			0
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	5.15685	−	8.93193i	0.309845	−	0.536668i	−0.668483	−	0.743727i	$-0.733056\pi$
$277$	5.15685	−	8.93193i	0.309845	−	0.536668i	0.978328	+	0.207060i	$0.0663894\pi$
$278$		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
$287$	6.82843	−	16.7262i	0.403069	−	0.987314i
$288$		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
$301$	9.65685	−	23.6544i	0.556612	−	1.36341i
$302$		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	$-0.654843\pi$
$311$	9.37868	−	16.2443i	0.531816	−	0.921133i	0.999310	−	0.0371364i	$-0.0118236\pi$
$312$		0			0
$313$	14.6421	+	25.3609i	0.827622	+	1.43348i	0.899898	+	0.436099i	$0.143640\pi$
$313$	14.6421	+	25.3609i	0.827622	+	1.43348i	−0.0722760	+	0.997385i	$0.523026\pi$
$314$		0			0
$315$	8.38478	+	10.8126i	0.472429	+	0.609219i
$316$		0			0
$317$	−4.84315	−	8.38857i	−0.272018	−	0.471149i	0.697360	−	0.716721i	$-0.254358\pi$
$317$	−4.84315	−	8.38857i	−0.272018	−	0.471149i	−0.969379	+	0.245571i	$0.921024\pi$
$318$		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
$329$	27.2990	−	3.73578i	1.50504	−	0.205960i
$330$		0			0
$331$	14.2071	+	24.6074i	0.780893	+	1.35255i	0.931422	+	0.363941i	$0.118569\pi$
$331$	14.2071	+	24.6074i	0.780893	+	1.35255i	−0.150529	+	0.988606i	$0.548098\pi$
$332$		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
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		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	$-0.447150\pi$
$347$	17.4497	−	30.2238i	0.936752	−	1.62250i	0.771480	−	0.636253i	$-0.219517\pi$
$348$		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	−0.893473	−	0.449116i	$-0.851739\pi$
$353$	−1.08579	+	1.88064i	−0.0577906	+	0.100096i	0.835683	+	0.549212i	$0.185072\pi$
$354$		0			0
$355$	−12.4853	−	21.6251i	−0.662650	−	1.14774i
$356$		0			0
$357$	−0.186292	+	0.0254934i	−0.00985959	+	0.00134925i
$358$		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	−0.916375	−	0.400320i	$-0.868899\pi$
$367$	−2.13604	+	3.69973i	−0.111500	+	0.193124i	0.804875	+	0.593444i	$0.202232\pi$
$368$		0			0
$369$	−9.65685	−	16.7262i	−0.502716	−	0.870729i
$370$		0			0
$371$	−1.62132	−	2.09077i	−0.0841748	−	0.108547i
$372$		0			0
$373$	−4.15685	−	7.19988i	−0.215234	−	0.372796i	0.738111	−	0.674679i	$-0.235718\pi$
$373$	−4.15685	−	7.19988i	−0.215234	−	0.372796i	−0.953345	+	0.301883i	$0.902385\pi$
$374$		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	$-0.144905\pi$
$379$	34.9706			1.79632			0.898159	+	0.439672i	$0.144905\pi$
$380$		0			0
$381$	1.17157	−	2.02922i	0.0600215	−	0.103960i
$382$		0			0
$383$	5.62132	+	9.73641i	0.287236	+	0.497507i	0.973149	−	0.230176i	$-0.0739303\pi$
$383$	5.62132	+	9.73641i	0.287236	+	0.497507i	−0.685913	+	0.727684i	$0.740597\pi$
$384$		0			0
$385$	−4.41421	+	10.8126i	−0.224969	+	0.551060i
$386$		0			0
$387$	−13.6569	−	23.6544i	−0.694217	−	1.20242i
$388$		0			0
$389$	9.08579	−	15.7370i	0.460668	−	0.797900i	−0.538327	−	0.842736i	$-0.680943\pi$
$389$	9.08579	−	15.7370i	0.460668	−	0.797900i	0.998994	+	0.0448365i	$0.0142767\pi$
$390$		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
$399$	2.65685	−	6.50794i	0.133009	−	0.325804i
$400$		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	−0.987525	−	0.157461i	$-0.949669\pi$
$409$	−7.22792	+	12.5191i	−0.357398	+	0.619031i	0.630128	+	0.776492i	$0.283003\pi$
$410$		0			0
$411$	−2.30761	−	3.99690i	−0.113826	−	0.197153i
$412$		0			0
$413$	17.6716	+	22.7883i	0.869561	+	1.12134i
$414$		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	$-0.368412\pi$
$421$	16.4853			0.803443			0.401722	+	0.915762i	$0.368412\pi$
$422$		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
$427$	−22.6924	+	3.10538i	−1.09816	+	0.150280i
$428$		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	$-0.410765\pi$
$433$	11.5147			0.553362			0.276681	+	0.960962i	$0.410765\pi$
$434$		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	$-0.984459\pi$
$439$	−11.3492	−	19.6575i	−0.541670	−	0.938200i	0.457139	−	0.889395i	$-0.348874\pi$
$440$		0			0
$441$	4.92893	−	19.1757i	0.234711	−	0.913126i
$442$		0			0
$443$	−5.96447	−	10.3308i	−0.283380	−	0.490829i	0.688835	−	0.724918i	$-0.258123\pi$
$443$	−5.96447	−	10.3308i	−0.283380	−	0.490829i	−0.972215	+	0.234089i	$0.924789\pi$
$444$		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
$455$	−13.5563	+	1.85514i	−0.635531	+	0.0869705i
$456$		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
$469$	−4.47056	−	5.76500i	−0.206431	−	0.266203i
$470$		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	$-0.605735\pi$
$479$	14.3492	−	24.8536i	0.655634	−	1.13559i	0.981735	−	0.190256i	$-0.0609317\pi$
$480$		0			0
$481$	−12.2426	−	21.2049i	−0.558216	−	0.966859i
$482$		0			0
$483$	2.17157	−	5.31925i	0.0988100	−	0.242034i
$484$		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	$-0.526295\pi$
$491$	−3.65685			−0.165032			−0.0825158	+	0.996590i	$0.526295\pi$
$492$		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
$497$	−13.6569	+	33.4523i	−0.612594	+	1.50054i
$498$		0			0
$499$	−2.27817	−	3.94591i	−0.101985	−	0.176643i	0.810517	−	0.585715i	$-0.199186\pi$
$499$	−2.27817	−	3.94591i	−0.101985	−	0.176643i	−0.912502	+	0.409071i	$0.865853\pi$
$500$		0			0
$501$	−0.414214	+	0.717439i	−0.0185057	+	0.0320528i
$502$		0			0
$503$	−10.3431			−0.461178			−0.230589	−	0.973051i	$-0.574065\pi$
$503$	−10.3431			−0.461178			−0.230589	+	0.973051i	$0.574065\pi$
$504$		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
$511$	23.7635	+	30.6441i	1.05123	+	1.35562i
$512$		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	−0.932453	−	0.361293i	$-0.882336\pi$
$521$	−3.50000	+	6.06218i	−0.153338	+	0.265589i	0.779115	+	0.626881i	$0.215669\pi$
$522$		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
$525$	−1.79899	+	0.246186i	−0.0785144	+	0.0107444i
$526$		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
$539$	16.2782	−	4.54026i	0.701151	−	0.195563i
$540$		0			0
$541$	−12.9142	−	22.3681i	−0.555225	−	0.961679i	−0.997886	−	0.0649894i	$-0.979299\pi$
$541$	−12.9142	−	22.3681i	−0.555225	−	0.961679i	0.442661	−	0.896689i	$-0.354035\pi$
$542$		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	$-0.575356\pi$
$547$	−10.9706			−0.469067			−0.234534	+	0.972108i	$0.575356\pi$
$548$		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
$553$	15.9142	−	2.17781i	0.676741	−	0.0926099i
$554$		0			0
$555$	3.27817	+	5.67796i	0.139151	+	0.241016i
$556$		0			0
$557$	−0.0857864	+	0.148586i	−0.00363489	+	0.00629581i	−0.867837	−	0.496849i	$-0.834490\pi$
$557$	−0.0857864	+	0.148586i	−0.00363489	+	0.00629581i	0.864202	+	0.503145i	$0.167824\pi$
$558$		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
$567$	−12.1360	−	15.6500i	−0.509666	−	0.657238i
$568$		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	−0.991812	−	0.127710i	$-0.959237\pi$
$571$	−9.20711	+	15.9472i	−0.385305	+	0.667369i	0.606506	+	0.795079i	$0.292571\pi$
$572$		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	$0.468176\pi$
$577$	−19.5000	+	33.7750i	−0.811796	+	1.40607i	−0.911606	+	0.411065i	$0.865157\pi$
$578$		0			0
$579$	1.89340	+	3.27946i	0.0786869	+	0.136290i
$580$		0			0
$581$	−7.31371	+	17.9149i	−0.303424	+	0.743233i
$582$		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	0.804202	−	0.594356i	$-0.202593\pi$
$593$	−2.74264	−	4.75039i	−0.112627	−	0.195075i	−0.916829	+	0.399281i	$0.869260\pi$
$594$		0			0
$595$	0.313708	−	0.768426i	0.0128608	−	0.0315024i
$596$		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	$-0.320997\pi$
$601$	26.1421			1.06636			0.533180	+	0.846002i	$0.320997\pi$
$602$		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	$-0.911673\pi$
$607$	−17.6924	−	30.6441i	−0.718112	−	1.24381i	0.243635	−	0.969867i	$-0.421660\pi$
$608$		0			0
$609$	−1.89949	−	2.44949i	−0.0769714	−	0.0992583i
$610$		0			0
$611$	14.7279	+	25.5095i	0.595828	+	1.03200i
$612$		0			0
$613$	2.25736	−	3.90986i	0.0911739	−	0.157918i	−0.816831	−	0.576876i	$-0.804271\pi$
$613$	2.25736	−	3.90986i	0.0911739	−	0.157918i	0.908005	+	0.418959i	$0.137605\pi$
$614$		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
$623$	−23.5919	+	3.22848i	−0.945189	+	0.129346i
$624$		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
$637$	14.1421	+	13.8564i	0.560332	+	0.549011i
$638$		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	$0.351217\pi$
$647$	−13.9350	+	24.1362i	−0.547843	+	0.948891i	−0.998422	+	0.0561548i	$0.982116\pi$
$648$		0			0
$649$	13.1569	+	22.7883i	0.516452	+	0.894521i
$650$		0			0
$651$	6.06497	−	0.829972i	0.237705	−	0.0325292i
$652$		0			0
$653$	−19.4706	−	33.7240i	−0.761942	−	1.31972i	−0.941848	−	0.336038i	$-0.890913\pi$
$653$	−19.4706	−	33.7240i	−0.761942	−	1.31972i	0.179906	−	0.983684i	$-0.442421\pi$
$654$		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	$-0.735618\pi$
$659$	−34.6274			−1.34889			−0.674446	+	0.738324i	$0.735618\pi$
$660$		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
$665$	19.0147	+	24.5204i	0.737359	+	0.950860i
$666$		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
$679$	1.17157	−	2.86976i	0.0449608	−	0.110131i
$680$		0			0
$681$	−3.32843	−	5.76500i	−0.127546	−	0.220915i
$682$		0			0
$683$	−8.72183	+	15.1066i	−0.333731	+	0.578040i	−0.983240	−	0.182314i	$-0.941641\pi$
$683$	−8.72183	+	15.1066i	−0.333731	+	0.578040i	0.649509	+	0.760354i	$0.274975\pi$
$684$		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
$693$	6.82843	−	16.7262i	0.259390	−	0.635374i
$694$		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	$-0.585169\pi$
$701$	−14.0000			−0.528773			−0.264386	+	0.964417i	$0.585169\pi$
$702$		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
$707$	21.8640	+	28.1946i	0.822279	+	1.06037i
$708$		0			0
$709$	−18.2990	−	31.6948i	−0.687233	−	1.19032i	−0.972729	−	0.231943i	$-0.925492\pi$
$709$	−18.2990	−	31.6948i	−0.687233	−	1.19032i	0.285496	−	0.958380i	$-0.407842\pi$
$710$		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	$-0.970177\pi$
$719$	−15.5208	−	26.8828i	−0.578829	−	1.00256i	0.416785	−	0.909005i	$-0.363157\pi$
$720$		0			0
$721$	22.0563	−	3.01834i	0.821421	−	0.112409i
$722$		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	$-0.280234\pi$
$727$	34.3431			1.27372			0.636858	+	0.770981i	$0.280234\pi$
$728$		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
$735$	−3.78680	−	3.71029i	−0.139678	−	0.136856i
$736$		0			0
$737$	−3.32843	−	5.76500i	−0.122604	−	0.212357i
$738$		0			0
$739$	−3.34924	+	5.80106i	−0.123204	+	0.213395i	−0.921029	−	0.389493i	$-0.872650\pi$
$739$	−3.34924	+	5.80106i	−0.123204	+	0.213395i	0.797826	+	0.602888i	$0.205984\pi$
$740$		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
$749$	33.8137	−	4.62730i	1.23553	−	0.169078i
$750$		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	$-0.464396\pi$
$757$	6.14214			0.223240			0.111620	+	0.993751i	$0.464396\pi$
$758$		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	$0.109752\pi$
$761$	21.0563	+	36.4707i	0.763292	+	1.32206i	−0.177853	+	0.984057i	$0.556915\pi$
$762$		0			0
$763$	−13.2487	−	17.0849i	−0.479636	−	0.618514i
$764$		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	$-0.419614\pi$
$769$	13.8579			0.499727			0.249864	+	0.968281i	$0.419614\pi$
$770$		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
$777$	3.58579	−	8.78335i	0.128639	−	0.315101i
$778$		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
$791$	−18.1421	+	44.4390i	−0.645060	+	1.58007i
$792$		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
$805$	15.5416	+	20.0417i	0.547771	+	0.706376i
$806$		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
$819$	20.9706	−	2.86976i	0.732771	−	0.100277i
$820$		0			0
$821$	7.57107	+	13.1135i	0.264232	+	0.457663i	0.967362	−	0.253398i	$-0.0815482\pi$
$821$	7.57107	+	13.1135i	0.264232	+	0.457663i	−0.703130	+	0.711061i	$0.748215\pi$
$822$		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	$-0.757826\pi$
$827$	−41.6569			−1.44855			−0.724275	+	0.689511i	$0.757826\pi$
$828$		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
$833$	−1.15685	+	0.322666i	−0.0400826	+	0.0111797i
$834$		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	$-0.518218\pi$
$839$	−3.31371			−0.114402			−0.0572010	+	0.998363i	$0.518218\pi$
$840$		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
$847$	−13.5563	+	1.85514i	−0.465802	+	0.0637435i
$848$		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	−0.997118	−	0.0758709i	$-0.975826\pi$
$857$	−12.6716	+	21.9478i	−0.432853	+	0.749723i	0.564265	+	0.825594i	$0.309160\pi$
$858$		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
$861$	4.58579	+	5.91359i	0.156283	+	0.201535i
$862$		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
$875$	12.1716	−	29.8141i	0.411474	−	1.00790i
$876$		0			0
$877$	25.7132	+	44.5366i	0.868273	+	1.50389i	0.863760	+	0.503903i	$0.168103\pi$
$877$	25.7132	+	44.5366i	0.868273	+	1.50389i	0.00451320	+	0.999990i	$0.498563\pi$
$878$		0			0
$879$	5.92893	−	10.2692i	0.199978	−	0.346372i
$880$		0			0
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$		0			0
$883$	41.2548			1.38834			0.694168	−	0.719813i	$-0.255773\pi$
$883$	41.2548			1.38834			0.694168	+	0.719813i	$0.255773\pi$
$884$		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	$-0.991806\pi$
$887$	−15.5503	−	26.9338i	−0.522126	−	0.904349i	0.477542	−	0.878609i	$-0.341528\pi$
$888$		0			0
$889$	5.65685	−	13.8564i	0.189725	−	0.464729i
$890$		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
$903$	6.48528	+	8.36308i	0.215817	+	0.278306i
$904$		0			0
$905$	−8.51472	−	14.7479i	−0.283039	−	0.490238i
$906$		0			0
$907$	12.7635	−	22.1070i	0.423804	−	0.734049i	−0.572504	−	0.819902i	$-0.694028\pi$
$907$	12.7635	−	22.1070i	0.423804	−	0.734049i	0.996308	+	0.0858524i	$0.0273613\pi$
$908$		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
$917$	−20.2574	+	2.77216i	−0.668957	+	0.0915447i
$918$		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	0.979927	−	0.199358i	$-0.0638857\pi$
$929$	9.67157	+	16.7517i	0.317314	+	0.549604i	−0.662613	+	0.748962i	$0.730552\pi$
$930$		0			0
$931$	11.1777	−	43.4859i	0.366333	−	1.42519i
$932$		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	$-0.412448\pi$
$937$	16.6274			0.543194			0.271597	+	0.962411i	$0.412448\pi$
$938$		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
$945$	−11.5711	+	1.58346i	−0.376407	+	0.0515101i
$946$		0			0
$947$	−9.10660	−	15.7731i	−0.295925	−	0.512557i	0.679275	−	0.733884i	$-0.262294\pi$
$947$	−9.10660	−	15.7731i	−0.295925	−	0.512557i	−0.975200	+	0.221327i	$0.928961\pi$
$948$		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
$959$	−18.0650	−	23.2956i	−0.583348	−	0.752256i
$960$		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
$973$	15.3137	−	37.5108i	0.490935	−	1.20254i
$974$		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	−0.996699	−	0.0811848i	$-0.974130\pi$
$983$	−13.4203	+	23.2447i	−0.428041	+	0.741389i	0.568658	+	0.822574i	$0.307463\pi$
$984$		0			0
$985$	−17.2132	−	29.8141i	−0.548458	−	0.949958i
$986$		0			0
$987$	−4.31371	+	10.5664i	−0.137307	+	0.336332i
$988$		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	448.2.i.j.193.1		4
4.3	odd	2		448.2.i.g.193.2		4
7.2	even	3	inner	448.2.i.j.65.1		4
7.3	odd	6		3136.2.a.bx.1.1		2
7.4	even	3		3136.2.a.bd.1.2		2
8.3	odd	2		224.2.i.d.193.1	yes	4
8.5	even	2		224.2.i.a.193.2	yes	4
24.5	odd	2		2016.2.s.q.865.1		4
24.11	even	2		2016.2.s.s.865.1		4
28.3	even	6		3136.2.a.be.1.2		2
28.11	odd	6		3136.2.a.bw.1.1		2
28.23	odd	6		448.2.i.g.65.2		4
56.3	even	6		1568.2.a.u.1.1		2
56.5	odd	6		1568.2.i.x.961.1		4
56.11	odd	6		1568.2.a.l.1.2		2
56.13	odd	2		1568.2.i.x.1537.1		4
56.19	even	6		1568.2.i.o.961.2		4
56.27	even	2		1568.2.i.o.1537.2		4
56.37	even	6		224.2.i.a.65.2	✓	4
56.45	odd	6		1568.2.a.j.1.2		2
56.51	odd	6		224.2.i.d.65.1	yes	4
56.53	even	6		1568.2.a.w.1.1		2
168.107	even	6		2016.2.s.s.289.1		4
168.149	odd	6		2016.2.s.q.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.i.a.65.2	✓	4	56.37	even	6
224.2.i.a.193.2	yes	4	8.5	even	2
224.2.i.d.65.1	yes	4	56.51	odd	6
224.2.i.d.193.1	yes	4	8.3	odd	2
448.2.i.g.65.2		4	28.23	odd	6
448.2.i.g.193.2		4	4.3	odd	2
448.2.i.j.65.1		4	7.2	even	3	inner
448.2.i.j.193.1		4	1.1	even	1	trivial
1568.2.a.j.1.2		2	56.45	odd	6
1568.2.a.l.1.2		2	56.11	odd	6
1568.2.a.u.1.1		2	56.3	even	6
1568.2.a.w.1.1		2	56.53	even	6
1568.2.i.o.961.2		4	56.19	even	6
1568.2.i.o.1537.2		4	56.27	even	2
1568.2.i.x.961.1		4	56.5	odd	6
1568.2.i.x.1537.1		4	56.13	odd	2
2016.2.s.q.289.1		4	168.149	odd	6
2016.2.s.q.865.1		4	24.5	odd	2
2016.2.s.s.289.1		4	168.107	even	6
2016.2.s.s.865.1		4	24.11	even	2
3136.2.a.bd.1.2		2	7.4	even	3
3136.2.a.be.1.2		2	28.3	even	6
3136.2.a.bw.1.1		2	28.11	odd	6
3136.2.a.bx.1.1		2	7.3	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{3} +(-0.914214 - 1.58346i) q^{5} +(-1.00000 + 2.44949i) q^{7} +(1.41421 + 2.44949i) q^{9} +(-1.20711 + 2.09077i) q^{11} -2.82843 q^{13} +0.757359 q^{15} +(0.0857864 - 0.148586i) q^{17} +(3.20711 + 5.55487i) q^{19} +(-0.671573 - 0.866025i) q^{21} +(2.62132 + 4.54026i) q^{23} +(0.828427 - 1.43488i) q^{25} -2.41421 q^{27} +2.82843 q^{29} +(-2.79289 + 4.83743i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(4.79289 - 0.655892i) q^{35} +(4.32843 + 7.49706i) q^{37} +(0.585786 - 1.01461i) q^{39} -6.82843 q^{41} -9.65685 q^{43} +(2.58579 - 4.47871i) q^{45} +(-5.20711 - 9.01897i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(0.0355339 + 0.0615465i) q^{51} +(-0.500000 + 0.866025i) q^{53} +4.41421 q^{55} -2.65685 q^{57} +(5.44975 - 9.43924i) q^{59} +(4.32843 + 7.49706i) q^{61} +(-7.41421 + 1.01461i) q^{63} +(2.58579 + 4.47871i) q^{65} +(-1.37868 + 2.38794i) q^{67} -2.17157 q^{69} +13.6569 q^{71} +(7.32843 - 12.6932i) q^{73} +(0.343146 + 0.594346i) q^{75} +(-3.91421 - 5.04757i) q^{77} +(-3.03553 - 5.25770i) q^{79} +(-3.74264 + 6.48244i) q^{81} +7.31371 q^{83} -0.313708 q^{85} +(-0.585786 + 1.01461i) q^{87} +(4.50000 + 7.79423i) q^{89} +(2.82843 - 6.92820i) q^{91} +(-1.15685 - 2.00373i) q^{93} +(5.86396 - 10.1567i) q^{95} -1.17157 q^{97} -6.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{5} - 4 q^{7} - 2 q^{11} + 20 q^{15} + 6 q^{17} + 10 q^{19} - 14 q^{21} + 2 q^{23} - 8 q^{25} - 4 q^{27} - 14 q^{31} - 2 q^{33} + 22 q^{35} + 6 q^{37} + 8 q^{39} - 16 q^{41} - 16 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^5 - 4 * q^7 - 2 * q^11 + 20 * q^15 + 6 * q^17 + 10 * q^19 - 14 * q^21 + 2 * q^23 - 8 * q^25 - 4 * q^27 - 14 * q^31 - 2 * q^33 + 22 * q^35 + 6 * q^37 + 8 * q^39 - 16 * q^41 - 16 * q^43 + 16 * q^45 - 18 * q^47 - 20 * q^49 - 14 * q^51 - 2 * q^53 + 12 * q^55 + 12 * q^57 + 2 * q^59 + 6 * q^61 - 24 * q^63 + 16 * q^65 - 14 * q^67 - 20 * q^69 + 32 * q^71 + 18 * q^73 + 24 * q^75 - 10 * q^77 + 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

Introduction

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