LMFDB - Embedded newform 616.2.q.b.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [616,2,Mod(177,616)] 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("616.177"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(616, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.91878476451$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	616.177
Dual form			616.2.q.b.529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20711 - 2.09077i) q^{3} +(0.707107 - 1.22474i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(-0.500000 - 0.866025i) q^{11} -3.82843 q^{13} -3.41421 q^{15} +(1.00000 + 1.73205i) q^{17} +(2.70711 - 4.68885i) q^{19} +(-2.41421 + 5.91359i) q^{21} +(-1.29289 + 2.23936i) q^{23} +(1.50000 + 2.59808i) q^{25} -0.414214 q^{27} +1.00000 q^{29} +(-0.828427 - 1.43488i) q^{31} +(-1.20711 + 2.09077i) q^{33} +(-3.70711 + 0.507306i) q^{35} +(-2.53553 + 4.39167i) q^{37} +(4.62132 + 8.00436i) q^{39} -2.24264 q^{41} -8.00000 q^{43} +(2.00000 + 3.46410i) q^{45} +(0.414214 - 0.717439i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(2.41421 - 4.18154i) q^{51} +(-2.70711 - 4.68885i) q^{53} -1.41421 q^{55} -13.0711 q^{57} +(-0.792893 - 1.37333i) q^{59} +(6.91421 - 11.9758i) q^{61} +(7.41421 - 1.01461i) q^{63} +(-2.70711 + 4.68885i) q^{65} +(3.03553 + 5.25770i) q^{67} +6.24264 q^{69} -14.2426 q^{71} +(0.292893 + 0.507306i) q^{73} +(3.62132 - 6.27231i) q^{75} +(-1.00000 + 2.44949i) q^{77} +(3.03553 - 5.25770i) q^{79} +(4.74264 + 8.21449i) q^{81} +6.48528 q^{83} +2.82843 q^{85} +(-1.20711 - 2.09077i) q^{87} +(7.41421 - 12.8418i) q^{89} +(6.20711 + 8.00436i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(-3.82843 - 6.63103i) q^{95} -10.1716 q^{97} +2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{7} - 2 q^{11} - 4 q^{13} - 8 q^{15} + 4 q^{17} + 8 q^{19} - 4 q^{21} - 8 q^{23} + 6 q^{25} + 4 q^{27} + 4 q^{29} + 8 q^{31} - 2 q^{33} - 12 q^{35} + 4 q^{37} + 10 q^{39} + 8 q^{41}+ \cdots - 52 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^7 - 2 * q^11 - 4 * q^13 - 8 * q^15 + 4 * q^17 + 8 * q^19 - 4 * q^21 - 8 * q^23 + 6 * q^25 + 4 * q^27 + 4 * q^29 + 8 * q^31 - 2 * q^33 - 12 * q^35 + 4 * q^37 + 10 * q^39 + 8 * q^41 - 32 * q^43 + 8 * q^45 - 4 * q^47 + 10 * q^49 + 4 * q^51 - 8 * q^53 - 24 * q^57 - 6 * q^59 + 22 * q^61 + 24 * q^63 - 8 * q^65 - 2 * q^67 + 8 * q^69 - 40 * q^71 + 4 * q^73 + 6 * q^75 - 4 * q^77 - 2 * q^79 + 2 * q^81 - 8 * q^83 - 2 * q^87 + 24 * q^89 + 22 * q^91 - 8 * q^93 - 4 * q^95 - 52 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	−0.969528	−	0.244981i	$-0.921218\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	0.272605	−	0.962126i	$-0.412115\pi$
$4$		0			0
$5$	0.707107	−	1.22474i	0.316228	−	0.547723i	−0.663470	−	0.748203i	$-0.730917\pi$
$5$	0.707107	−	1.22474i	0.316228	−	0.547723i	0.979698	+	0.200480i	$0.0642503\pi$
$6$		0			0
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$8$		0			0
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−3.82843			−1.06181			−0.530907	−	0.847430i	$-0.678149\pi$
$13$	−3.82843			−1.06181			−0.530907	+	0.847430i	$0.678149\pi$
$14$		0			0
$15$	−3.41421			−0.881546
$16$		0			0
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	2.70711	−	4.68885i	0.621053	−	1.07570i	−0.368237	−	0.929732i	$-0.620039\pi$
$19$	2.70711	−	4.68885i	0.621053	−	1.07570i	0.989290	−	0.145963i	$-0.0466281\pi$
$20$		0			0
$21$	−2.41421	+	5.91359i	−0.526825	+	1.29045i
$22$		0			0
$23$	−1.29289	+	2.23936i	−0.269587	+	0.466938i	−0.968755	−	0.248019i	$-0.920220\pi$
$23$	−1.29289	+	2.23936i	−0.269587	+	0.466938i	0.699168	+	0.714957i	$0.253554\pi$
$24$		0			0
$25$	1.50000	+	2.59808i	0.300000	+	0.519615i
$26$		0			0
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	−0.828427	−	1.43488i	−0.148790	−	0.257712i	0.781991	−	0.623290i	$-0.214204\pi$
$31$	−0.828427	−	1.43488i	−0.148790	−	0.257712i	−0.930780	+	0.365579i	$0.880871\pi$
$32$		0			0
$33$	−1.20711	+	2.09077i	−0.210130	+	0.363956i
$34$		0			0
$35$	−3.70711	+	0.507306i	−0.626615	+	0.0857504i
$36$		0			0
$37$	−2.53553	+	4.39167i	−0.416839	+	0.721987i	−0.995620	−	0.0934968i	$-0.970196\pi$
$37$	−2.53553	+	4.39167i	−0.416839	+	0.721987i	0.578780	+	0.815483i	$0.303529\pi$
$38$		0			0
$39$	4.62132	+	8.00436i	0.740003	+	1.28172i
$40$		0			0
$41$	−2.24264			−0.350242			−0.175121	−	0.984547i	$-0.556032\pi$
$41$	−2.24264			−0.350242			−0.175121	+	0.984547i	$0.556032\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$	2.00000	+	3.46410i	0.298142	+	0.516398i
$46$		0			0
$47$	0.414214	−	0.717439i	0.0604193	−	0.104649i	−0.834234	−	0.551411i	$-0.814090\pi$
$47$	0.414214	−	0.717439i	0.0604193	−	0.104649i	0.894653	+	0.446762i	$0.147423\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$		0			0
$51$	2.41421	−	4.18154i	0.338058	−	0.585533i
$52$		0			0
$53$	−2.70711	−	4.68885i	−0.371850	−	0.644063i	0.618000	−	0.786178i	$-0.287943\pi$
$53$	−2.70711	−	4.68885i	−0.371850	−	0.644063i	−0.989850	+	0.142115i	$0.954610\pi$
$54$		0			0
$55$	−1.41421			−0.190693
$56$		0			0
$57$	−13.0711			−1.73131
$58$		0			0
$59$	−0.792893	−	1.37333i	−0.103226	−	0.178793i	0.809786	−	0.586725i	$-0.199583\pi$
$59$	−0.792893	−	1.37333i	−0.103226	−	0.178793i	−0.913012	+	0.407933i	$0.866250\pi$
$60$		0			0
$61$	6.91421	−	11.9758i	0.885274	−	1.53334i	0.0398754	−	0.999205i	$-0.487304\pi$
$61$	6.91421	−	11.9758i	0.885274	−	1.53334i	0.845399	−	0.534135i	$-0.179363\pi$
$62$		0			0
$63$	7.41421	−	1.01461i	0.934103	−	0.127829i
$64$		0			0
$65$	−2.70711	+	4.68885i	−0.335775	+	0.581580i
$66$		0			0
$67$	3.03553	+	5.25770i	0.370849	+	0.642330i	0.989696	−	0.143181i	$-0.0457332\pi$
$67$	3.03553	+	5.25770i	0.370849	+	0.642330i	−0.618847	+	0.785512i	$0.712400\pi$
$68$		0			0
$69$	6.24264			0.751526
$70$		0			0
$71$	−14.2426			−1.69029			−0.845145	−	0.534537i	$-0.820486\pi$
$71$	−14.2426			−1.69029			−0.845145	+	0.534537i	$0.820486\pi$
$72$		0			0
$73$	0.292893	+	0.507306i	0.0342806	+	0.0593757i	0.882657	−	0.470018i	$-0.155753\pi$
$73$	0.292893	+	0.507306i	0.0342806	+	0.0593757i	−0.848376	+	0.529394i	$0.822419\pi$
$74$		0			0
$75$	3.62132	−	6.27231i	0.418154	−	0.724264i
$76$		0			0
$77$	−1.00000	+	2.44949i	−0.113961	+	0.279145i
$78$		0			0
$79$	3.03553	−	5.25770i	0.341524	−	0.591537i	−0.643192	−	0.765705i	$-0.722390\pi$
$79$	3.03553	−	5.25770i	0.341524	−	0.591537i	0.984716	+	0.174168i	$0.0557235\pi$
$80$		0			0
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$		0			0
$83$	6.48528			0.711852			0.355926	−	0.934514i	$-0.384165\pi$
$83$	6.48528			0.711852			0.355926	+	0.934514i	$0.384165\pi$
$84$		0			0
$85$	2.82843			0.306786
$86$		0			0
$87$	−1.20711	−	2.09077i	−0.129415	−	0.224154i
$88$		0			0
$89$	7.41421	−	12.8418i	0.785905	−	1.36123i	−0.142552	−	0.989787i	$-0.545531\pi$
$89$	7.41421	−	12.8418i	0.785905	−	1.36123i	0.928457	−	0.371440i	$-0.121136\pi$
$90$		0			0
$91$	6.20711	+	8.00436i	0.650682	+	0.839085i
$92$		0			0
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$		0			0
$95$	−3.82843	−	6.63103i	−0.392788	−	0.680329i
$96$		0			0
$97$	−10.1716			−1.03277			−0.516383	−	0.856358i	$-0.672722\pi$
$97$	−10.1716			−1.03277			−0.516383	+	0.856358i	$0.672722\pi$
$98$		0			0
$99$	2.82843			0.284268
$100$		0			0
$101$	−4.74264	−	8.21449i	−0.471910	−	0.817373i	0.527573	−	0.849510i	$-0.323102\pi$
$101$	−4.74264	−	8.21449i	−0.471910	−	0.817373i	−0.999483	+	0.0321369i	$0.989769\pi$
$102$		0			0
$103$	−1.94975	+	3.37706i	−0.192114	+	0.332752i	−0.945951	−	0.324310i	$-0.894868\pi$
$103$	−1.94975	+	3.37706i	−0.192114	+	0.332752i	0.753836	+	0.657062i	$0.228201\pi$
$104$		0			0
$105$	5.53553	+	7.13834i	0.540213	+	0.696630i
$106$		0			0
$107$	8.77817	−	15.2042i	0.848618	−	1.46985i	−0.0338234	−	0.999428i	$-0.510768\pi$
$107$	8.77817	−	15.2042i	0.848618	−	1.46985i	0.882442	−	0.470422i	$-0.155898\pi$
$108$		0			0
$109$	−4.24264	−	7.34847i	−0.406371	−	0.703856i	0.588109	−	0.808782i	$-0.299873\pi$
$109$	−4.24264	−	7.34847i	−0.406371	−	0.703856i	−0.994480	+	0.104926i	$0.966539\pi$
$110$		0			0
$111$	12.2426			1.16202
$112$		0			0
$113$	9.48528			0.892300			0.446150	−	0.894958i	$-0.352795\pi$
$113$	9.48528			0.892300			0.446150	+	0.894958i	$0.352795\pi$
$114$		0			0
$115$	1.82843	+	3.16693i	0.170502	+	0.295318i
$116$		0			0
$117$	5.41421	−	9.37769i	0.500544	−	0.866968i
$118$		0			0
$119$	2.00000	−	4.89898i	0.183340	−	0.449089i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	2.70711	+	4.68885i	0.244092	+	0.422779i
$124$		0			0
$125$	11.3137			1.01193
$126$		0			0
$127$	3.58579			0.318187			0.159094	−	0.987264i	$-0.449143\pi$
$127$	3.58579			0.318187			0.159094	+	0.987264i	$0.449143\pi$
$128$		0			0
$129$	9.65685	+	16.7262i	0.850239	+	1.47266i
$130$		0			0
$131$	9.53553	−	16.5160i	0.833123	−	1.44301i	−0.0624257	−	0.998050i	$-0.519884\pi$
$131$	9.53553	−	16.5160i	0.833123	−	1.44301i	0.895549	−	0.444963i	$-0.146783\pi$
$132$		0			0
$133$	−14.1924	+	1.94218i	−1.23064	+	0.168409i
$134$		0			0
$135$	−0.292893	+	0.507306i	−0.0252082	+	0.0436619i
$136$		0			0
$137$	−8.50000	−	14.7224i	−0.726204	−	1.25782i	−0.958477	−	0.285171i	$-0.907949\pi$
$137$	−8.50000	−	14.7224i	−0.726204	−	1.25782i	0.232273	−	0.972651i	$-0.425384\pi$
$138$		0			0
$139$	19.3137			1.63817			0.819084	−	0.573674i	$-0.194482\pi$
$139$	19.3137			1.63817			0.819084	+	0.573674i	$0.194482\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$		0			0
$143$	1.91421	+	3.31552i	0.160075	+	0.277257i
$144$		0			0
$145$	0.707107	−	1.22474i	0.0587220	−	0.101710i
$146$		0			0
$147$	16.2782	−	4.54026i	1.34260	−	0.374474i
$148$		0			0
$149$	8.00000	−	13.8564i	0.655386	−	1.13516i	−0.326411	−	0.945228i	$-0.605840\pi$
$149$	8.00000	−	13.8564i	0.655386	−	1.13516i	0.981797	−	0.189933i	$-0.0608272\pi$
$150$		0			0
$151$	−4.20711	−	7.28692i	−0.342369	−	0.593001i	0.642503	−	0.766283i	$-0.277896\pi$
$151$	−4.20711	−	7.28692i	−0.342369	−	0.593001i	−0.984872	+	0.173282i	$0.944563\pi$
$152$		0			0
$153$	−5.65685			−0.457330
$154$		0			0
$155$	−2.34315			−0.188206
$156$		0			0
$157$	−7.65685	−	13.2621i	−0.611083	−	1.05843i	−0.991058	−	0.133431i	$-0.957401\pi$
$157$	−7.65685	−	13.2621i	−0.611083	−	1.05843i	0.379975	−	0.924997i	$-0.375933\pi$
$158$		0			0
$159$	−6.53553	+	11.3199i	−0.518302	+	0.897725i
$160$		0			0
$161$	6.77817	−	0.927572i	0.534195	−	0.0731029i
$162$		0			0
$163$	−12.4497	+	21.5636i	−0.975139	+	1.68899i	−0.295665	+	0.955292i	$0.595541\pi$
$163$	−12.4497	+	21.5636i	−0.975139	+	1.68899i	−0.679474	+	0.733700i	$0.737792\pi$
$164$		0			0
$165$	1.70711	+	2.95680i	0.132898	+	0.230186i
$166$		0			0
$167$	−25.7279			−1.99089			−0.995443	−	0.0953565i	$-0.969601\pi$
$167$	−25.7279			−1.99089			−0.995443	+	0.0953565i	$0.969601\pi$
$168$		0			0
$169$	1.65685			0.127450
$170$		0			0
$171$	7.65685	+	13.2621i	0.585534	+	1.01418i
$172$		0			0
$173$	−3.91421	+	6.77962i	−0.297592	+	0.515445i	−0.975585	−	0.219624i	$-0.929517\pi$
$173$	−3.91421	+	6.77962i	−0.297592	+	0.515445i	0.677992	+	0.735069i	$0.262850\pi$
$174$		0			0
$175$	3.00000	−	7.34847i	0.226779	−	0.555492i
$176$		0			0
$177$	−1.91421	+	3.31552i	−0.143881	+	0.249209i
$178$		0			0
$179$	0.449747	+	0.778985i	0.0336157	+	0.0582241i	0.882344	−	0.470605i	$-0.155964\pi$
$179$	0.449747	+	0.778985i	0.0336157	+	0.0582241i	−0.848728	+	0.528829i	$0.822631\pi$
$180$		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
$183$	−33.3848			−2.46787
$184$		0			0
$185$	3.58579	+	6.21076i	0.263632	+	0.456624i
$186$		0			0
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$		0			0
$189$	0.671573	+	0.866025i	0.0488497	+	0.0629941i
$190$		0			0
$191$	−5.24264	+	9.08052i	−0.379344	+	0.657043i	−0.990967	−	0.134106i	$-0.957184\pi$
$191$	−5.24264	+	9.08052i	−0.379344	+	0.657043i	0.611623	+	0.791150i	$0.290517\pi$
$192$		0			0
$193$	9.60660	+	16.6391i	0.691498	+	1.19771i	0.971347	+	0.237666i	$0.0763824\pi$
$193$	9.60660	+	16.6391i	0.691498	+	1.19771i	−0.279849	+	0.960044i	$0.590284\pi$
$194$		0			0
$195$	13.0711			0.936039
$196$		0			0
$197$	17.1421			1.22133			0.610663	−	0.791890i	$-0.290903\pi$
$197$	17.1421			1.22133			0.610663	+	0.791890i	$0.290903\pi$
$198$		0			0
$199$	12.0208	+	20.8207i	0.852133	+	1.47594i	0.879279	+	0.476306i	$0.158025\pi$
$199$	12.0208	+	20.8207i	0.852133	+	1.47594i	−0.0271465	+	0.999631i	$0.508642\pi$
$200$		0			0
$201$	7.32843	−	12.6932i	0.516907	−	0.895310i
$202$		0			0
$203$	−1.62132	−	2.09077i	−0.113794	−	0.146743i
$204$		0			0
$205$	−1.58579	+	2.74666i	−0.110756	+	0.191835i
$206$		0			0
$207$	−3.65685	−	6.33386i	−0.254169	−	0.440234i
$208$		0			0
$209$	−5.41421			−0.374509
$210$		0			0
$211$	−19.0711			−1.31291			−0.656453	−	0.754367i	$-0.727944\pi$
$211$	−19.0711			−1.31291			−0.656453	+	0.754367i	$0.727944\pi$
$212$		0			0
$213$	17.1924	+	29.7781i	1.17800	+	2.04036i
$214$		0			0
$215$	−5.65685	+	9.79796i	−0.385794	+	0.668215i
$216$		0			0
$217$	−1.65685	+	4.05845i	−0.112475	+	0.275505i
$218$		0			0
$219$	0.707107	−	1.22474i	0.0477818	−	0.0827606i
$220$		0			0
$221$	−3.82843	−	6.63103i	−0.257528	−	0.446051i
$222$		0			0
$223$	−11.5563			−0.773870			−0.386935	−	0.922107i	$-0.626466\pi$
$223$	−11.5563			−0.773870			−0.386935	+	0.922107i	$0.626466\pi$
$224$		0			0
$225$	−8.48528			−0.565685
$226$		0			0
$227$	−0.0710678	−	0.123093i	−0.00471694	−	0.00816997i	0.863657	−	0.504079i	$-0.168168\pi$
$227$	−0.0710678	−	0.123093i	−0.00471694	−	0.00816997i	−0.868374	+	0.495909i	$0.834835\pi$
$228$		0			0
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$		0			0
$231$	6.32843	−	0.866025i	0.416380	−	0.0569803i
$232$		0			0
$233$	8.19239	−	14.1896i	0.536701	−	0.929594i	−0.462378	−	0.886683i	$-0.653004\pi$
$233$	8.19239	−	14.1896i	0.536701	−	0.929594i	0.999079	−	0.0429107i	$-0.0136631\pi$
$234$		0			0
$235$	−0.585786	−	1.01461i	−0.0382125	−	0.0661860i
$236$		0			0
$237$	−14.6569			−0.952065
$238$		0			0
$239$	13.7279			0.887985			0.443993	−	0.896030i	$-0.353562\pi$
$239$	13.7279			0.887985			0.443993	+	0.896030i	$0.353562\pi$
$240$		0			0
$241$	−1.36396	−	2.36245i	−0.0878605	−	0.152179i	0.818746	−	0.574156i	$-0.194670\pi$
$241$	−1.36396	−	2.36245i	−0.0878605	−	0.152179i	−0.906607	+	0.421977i	$0.861336\pi$
$242$		0			0
$243$	10.8284	−	18.7554i	0.694644	−	1.20316i
$244$		0			0
$245$	7.07107	+	6.92820i	0.451754	+	0.442627i
$246$		0			0
$247$	−10.3640	+	17.9509i	−0.659443	+	1.14219i
$248$		0			0
$249$	−7.82843	−	13.5592i	−0.496106	−	0.859282i
$250$		0			0
$251$	−16.4853			−1.04054			−0.520271	−	0.854001i	$-0.674169\pi$
$251$	−16.4853			−1.04054			−0.520271	+	0.854001i	$0.674169\pi$
$252$		0			0
$253$	2.58579			0.162567
$254$		0			0
$255$	−3.41421	−	5.91359i	−0.213806	−	0.370323i
$256$		0			0
$257$	1.25736	−	2.17781i	0.0784319	−	0.135848i	−0.824142	−	0.566384i	$-0.808342\pi$
$257$	1.25736	−	2.17781i	0.0784319	−	0.135848i	0.902574	+	0.430536i	$0.141675\pi$
$258$		0			0
$259$	13.2929	−	1.81909i	0.825980	−	0.113033i
$260$		0			0
$261$	−1.41421	+	2.44949i	−0.0875376	+	0.151620i
$262$		0			0
$263$	−12.5208	−	21.6867i	−0.772067	−	1.33726i	−0.936429	−	0.350858i	$-0.885890\pi$
$263$	−12.5208	−	21.6867i	−0.772067	−	1.33726i	0.164362	−	0.986400i	$-0.447443\pi$
$264$		0			0
$265$	−7.65685			−0.470357
$266$		0			0
$267$	−35.7990			−2.19086
$268$		0			0
$269$	1.17157	+	2.02922i	0.0714321	+	0.123724i	0.899529	−	0.436861i	$-0.143910\pi$
$269$	1.17157	+	2.02922i	0.0714321	+	0.123724i	−0.828097	+	0.560585i	$0.810576\pi$
$270$		0			0
$271$	−7.03553	+	12.1859i	−0.427378	+	0.740241i	−0.996639	−	0.0819160i	$-0.973896\pi$
$271$	−7.03553	+	12.1859i	−0.427378	+	0.740241i	0.569261	+	0.822157i	$0.307229\pi$
$272$		0			0
$273$	9.24264	−	22.6398i	0.559390	−	1.37022i
$274$		0			0
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	−7.39949	−	12.8163i	−0.444593	−	0.770057i	0.553431	−	0.832895i	$-0.313318\pi$
$277$	−7.39949	−	12.8163i	−0.444593	−	0.770057i	−0.998024	+	0.0628380i	$0.979985\pi$
$278$		0			0
$279$	4.68629			0.280561
$280$		0			0
$281$	7.89949			0.471244			0.235622	−	0.971845i	$-0.424287\pi$
$281$	7.89949			0.471244			0.235622	+	0.971845i	$0.424287\pi$
$282$		0			0
$283$	1.77817	+	3.07989i	0.105702	+	0.183080i	0.914025	−	0.405659i	$-0.132958\pi$
$283$	1.77817	+	3.07989i	0.105702	+	0.183080i	−0.808323	+	0.588739i	$0.799625\pi$
$284$		0			0
$285$	−9.24264	+	16.0087i	−0.547487	+	0.948275i
$286$		0			0
$287$	3.63604	+	4.68885i	0.214629	+	0.276774i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	12.2782	+	21.2664i	0.719759	+	1.24666i
$292$		0			0
$293$	−18.8284			−1.09997			−0.549984	−	0.835175i	$-0.685366\pi$
$293$	−18.8284			−1.09997			−0.549984	+	0.835175i	$0.685366\pi$
$294$		0			0
$295$	−2.24264			−0.130572
$296$		0			0
$297$	0.207107	+	0.358719i	0.0120176	+	0.0208150i
$298$		0			0
$299$	4.94975	−	8.57321i	0.286251	−	0.495802i
$300$		0			0
$301$	12.9706	+	16.7262i	0.747611	+	0.964080i
$302$		0			0
$303$	−11.4497	+	19.8315i	−0.657771	+	1.13929i
$304$		0			0
$305$	−9.77817	−	16.9363i	−0.559897	−	0.969769i
$306$		0			0
$307$	11.4142			0.651444			0.325722	−	0.945466i	$-0.394393\pi$
$307$	11.4142			0.651444			0.325722	+	0.945466i	$0.394393\pi$
$308$		0			0
$309$	9.41421			0.535556
$310$		0			0
$311$	−7.60660	−	13.1750i	−0.431331	−	0.747087i	0.565657	−	0.824640i	$-0.308622\pi$
$311$	−7.60660	−	13.1750i	−0.431331	−	0.747087i	−0.996988	+	0.0775535i	$0.975289\pi$
$312$		0			0
$313$	10.3284	−	17.8894i	0.583797	−	1.01117i	−0.411227	−	0.911533i	$-0.634900\pi$
$313$	10.3284	−	17.8894i	0.583797	−	1.01117i	0.995024	−	0.0996335i	$-0.0317670\pi$
$314$		0			0
$315$	4.00000	−	9.79796i	0.225374	−	0.552052i
$316$		0			0
$317$	6.48528	−	11.2328i	0.364250	−	0.630899i	−0.624406	−	0.781100i	$-0.714659\pi$
$317$	6.48528	−	11.2328i	0.364250	−	0.630899i	0.988655	+	0.150201i	$0.0479921\pi$
$318$		0			0
$319$	−0.500000	−	0.866025i	−0.0279946	−	0.0484881i
$320$		0			0
$321$	−42.3848			−2.36569
$322$		0			0
$323$	10.8284			0.602510
$324$		0			0
$325$	−5.74264	−	9.94655i	−0.318544	−	0.551735i
$326$		0			0
$327$	−10.2426	+	17.7408i	−0.566419	+	0.981067i
$328$		0			0
$329$	−2.17157	+	0.297173i	−0.119723	+	0.0163837i
$330$		0			0
$331$	−15.6924	+	27.1800i	−0.862532	+	1.49395i	0.00694571	+	0.999976i	$0.497789\pi$
$331$	−15.6924	+	27.1800i	−0.862532	+	1.49395i	−0.869477	+	0.493973i	$0.835544\pi$
$332$		0			0
$333$	−7.17157	−	12.4215i	−0.393000	−	0.680696i
$334$		0			0
$335$	8.58579			0.469092
$336$		0			0
$337$	6.24264			0.340058			0.170029	−	0.985439i	$-0.445614\pi$
$337$	6.24264			0.340058			0.170029	+	0.985439i	$0.445614\pi$
$338$		0			0
$339$	−11.4497	−	19.8315i	−0.621865	−	1.07710i
$340$		0			0
$341$	−0.828427	+	1.43488i	−0.0448618	+	0.0777030i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		0			0
$345$	4.41421	−	7.64564i	0.237653	−	0.411628i
$346$		0			0
$347$	5.70711	+	9.88500i	0.306374	+	0.530655i	0.977566	−	0.210628i	$-0.0675510\pi$
$347$	5.70711	+	9.88500i	0.306374	+	0.530655i	−0.671193	+	0.741283i	$0.734218\pi$
$348$		0			0
$349$	−32.2843			−1.72814			−0.864069	−	0.503374i	$-0.832092\pi$
$349$	−32.2843			−1.72814			−0.864069	+	0.503374i	$0.832092\pi$
$350$		0			0
$351$	1.58579			0.0846430
$352$		0			0
$353$	12.6569	+	21.9223i	0.673656	+	1.16681i	0.976860	+	0.213881i	$0.0686105\pi$
$353$	12.6569	+	21.9223i	0.673656	+	1.16681i	−0.303203	+	0.952926i	$0.598056\pi$
$354$		0			0
$355$	−10.0711	+	17.4436i	−0.534517	+	0.925810i
$356$		0			0
$357$	−12.6569	+	1.73205i	−0.669872	+	0.0916698i
$358$		0			0
$359$	−14.0355	+	24.3103i	−0.740767	+	1.28305i	0.211379	+	0.977404i	$0.432204\pi$
$359$	−14.0355	+	24.3103i	−0.740767	+	1.28305i	−0.952146	+	0.305642i	$0.901129\pi$
$360$		0			0
$361$	−5.15685	−	8.93193i	−0.271413	−	0.470102i
$362$		0			0
$363$	2.41421			0.126713
$364$		0			0
$365$	0.828427			0.0433619
$366$		0			0
$367$	0.121320	+	0.210133i	0.00633287	+	0.0109689i	0.869174	−	0.494506i	$-0.164651\pi$
$367$	0.121320	+	0.210133i	0.00633287	+	0.0109689i	−0.862842	+	0.505474i	$0.831318\pi$
$368$		0			0
$369$	3.17157	−	5.49333i	0.165105	−	0.285971i
$370$		0			0
$371$	−5.41421	+	13.2621i	−0.281092	+	0.688532i
$372$		0			0
$373$	−15.8137	+	27.3901i	−0.818803	+	1.41821i	0.0877621	+	0.996141i	$0.472028\pi$
$373$	−15.8137	+	27.3901i	−0.818803	+	1.41821i	−0.906565	+	0.422067i	$0.861305\pi$
$374$		0			0
$375$	−13.6569	−	23.6544i	−0.705237	−	1.22151i
$376$		0			0
$377$	−3.82843			−0.197174
$378$		0			0
$379$	29.3848			1.50939			0.754697	−	0.656073i	$-0.227784\pi$
$379$	29.3848			1.50939			0.754697	+	0.656073i	$0.227784\pi$
$380$		0			0
$381$	−4.32843	−	7.49706i	−0.221752	−	0.384086i
$382$		0			0
$383$	13.9497	−	24.1617i	0.712799	−	1.23460i	−0.251004	−	0.967986i	$-0.580761\pi$
$383$	13.9497	−	24.1617i	0.712799	−	1.23460i	0.963802	−	0.266618i	$-0.0859061\pi$
$384$		0			0
$385$	2.29289	+	2.95680i	0.116857	+	0.150692i
$386$		0			0
$387$	11.3137	−	19.5959i	0.575108	−	0.996116i
$388$		0			0
$389$	4.60660	+	7.97887i	0.233564	+	0.404545i	0.958854	−	0.283898i	$-0.0916278\pi$
$389$	4.60660	+	7.97887i	0.233564	+	0.404545i	−0.725290	+	0.688443i	$0.758295\pi$
$390$		0			0
$391$	−5.17157			−0.261538
$392$		0			0
$393$	−46.0416			−2.32249
$394$		0			0
$395$	−4.29289	−	7.43551i	−0.215999	−	0.374121i
$396$		0			0
$397$	−12.1716	+	21.0818i	−0.610874	+	1.05806i	0.380220	+	0.924896i	$0.375848\pi$
$397$	−12.1716	+	21.0818i	−0.610874	+	1.05806i	−0.991093	+	0.133168i	$0.957485\pi$
$398$		0			0
$399$	21.1924	+	27.3286i	1.06095	+	1.36814i
$400$		0			0
$401$	12.5000	−	21.6506i	0.624220	−	1.08118i	−0.364471	−	0.931215i	$-0.618750\pi$
$401$	12.5000	−	21.6506i	0.624220	−	1.08118i	0.988691	−	0.149966i	$-0.0479165\pi$
$402$		0			0
$403$	3.17157	+	5.49333i	0.157987	+	0.273642i
$404$		0			0
$405$	13.4142			0.666558
$406$		0			0
$407$	5.07107			0.251363
$408$		0			0
$409$	7.05025	+	12.2114i	0.348613	+	0.603815i	0.986003	−	0.166726i	$-0.0533196\pi$
$409$	7.05025	+	12.2114i	0.348613	+	0.603815i	−0.637391	+	0.770541i	$0.719986\pi$
$410$		0			0
$411$	−20.5208	+	35.5431i	−1.01222	+	1.75321i
$412$		0			0
$413$	−1.58579	+	3.88437i	−0.0780314	+	0.191137i
$414$		0			0
$415$	4.58579	−	7.94282i	0.225107	−	0.389897i
$416$		0			0
$417$	−23.3137	−	40.3805i	−1.14168	−	1.97744i
$418$		0			0
$419$	25.4558			1.24360			0.621800	−	0.783176i	$-0.286402\pi$
$419$	25.4558			1.24360			0.621800	+	0.783176i	$0.286402\pi$
$420$		0			0
$421$	−1.65685			−0.0807501			−0.0403751	−	0.999185i	$-0.512855\pi$
$421$	−1.65685			−0.0807501			−0.0403751	+	0.999185i	$0.512855\pi$
$422$		0			0
$423$	1.17157	+	2.02922i	0.0569638	+	0.0986642i
$424$		0			0
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$	−36.2487	+	4.96053i	−1.75420	+	0.240057i
$428$		0			0
$429$	4.62132	−	8.00436i	0.223119	−	0.386454i
$430$		0			0
$431$	8.86396	+	15.3528i	0.426962	+	0.739520i	0.996601	−	0.0823749i	$-0.0262505\pi$
$431$	8.86396	+	15.3528i	0.426962	+	0.739520i	−0.569639	+	0.821895i	$0.692917\pi$
$432$		0			0
$433$	37.4558			1.80001			0.900006	−	0.435876i	$-0.143562\pi$
$433$	37.4558			1.80001			0.900006	+	0.435876i	$0.143562\pi$
$434$		0			0
$435$	−3.41421			−0.163699
$436$		0			0
$437$	7.00000	+	12.1244i	0.334855	+	0.579987i
$438$		0			0
$439$	−8.03553	+	13.9180i	−0.383515	+	0.664268i	−0.991562	−	0.129633i	$-0.958620\pi$
$439$	−8.03553	+	13.9180i	−0.383515	+	0.664268i	0.608047	+	0.793901i	$0.291953\pi$
$440$		0			0
$441$	−14.1421	−	13.8564i	−0.673435	−	0.659829i
$442$		0			0
$443$	8.65685	−	14.9941i	0.411300	−	0.712392i	−0.583733	−	0.811946i	$-0.698408\pi$
$443$	8.65685	−	14.9941i	0.411300	−	0.712392i	0.995032	+	0.0995543i	$0.0317417\pi$
$444$		0			0
$445$	−10.4853	−	18.1610i	−0.497050	−	0.860916i
$446$		0			0
$447$	−38.6274			−1.82701
$448$		0			0
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$		0			0
$451$	1.12132	+	1.94218i	0.0528009	+	0.0914539i
$452$		0			0
$453$	−10.1569	+	17.5922i	−0.477211	+	0.826553i
$454$		0			0
$455$	14.1924	−	1.94218i	0.665349	−	0.0910510i
$456$		0			0
$457$	−3.34315	+	5.79050i	−0.156386	+	0.270868i	−0.933563	−	0.358414i	$-0.883318\pi$
$457$	−3.34315	+	5.79050i	−0.156386	+	0.270868i	0.777177	+	0.629282i	$0.216651\pi$
$458$		0			0
$459$	−0.414214	−	0.717439i	−0.0193338	−	0.0334872i
$460$		0			0
$461$	−13.0000			−0.605470			−0.302735	−	0.953075i	$-0.597900\pi$
$461$	−13.0000			−0.605470			−0.302735	+	0.953075i	$0.597900\pi$
$462$		0			0
$463$	25.7990			1.19898			0.599490	−	0.800382i	$-0.295370\pi$
$463$	25.7990			1.19898			0.599490	+	0.800382i	$0.295370\pi$
$464$		0			0
$465$	2.82843	+	4.89898i	0.131165	+	0.227185i
$466$		0			0
$467$	15.9706	−	27.6618i	0.739030	−	1.28004i	−0.213903	−	0.976855i	$-0.568618\pi$
$467$	15.9706	−	27.6618i	0.739030	−	1.28004i	0.952933	−	0.303182i	$-0.0980489\pi$
$468$		0			0
$469$	6.07107	−	14.8710i	0.280336	−	0.686680i
$470$		0			0
$471$	−18.4853	+	32.0174i	−0.851757	+	1.47529i
$472$		0			0
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$		0			0
$475$	16.2426			0.745263
$476$		0			0
$477$	15.3137			0.701167
$478$		0			0
$479$	0.0355339	+	0.0615465i	0.00162359	+	0.00281213i	0.866836	−	0.498593i	$-0.166150\pi$
$479$	0.0355339	+	0.0615465i	0.00162359	+	0.00281213i	−0.865212	+	0.501405i	$0.832817\pi$
$480$		0			0
$481$	9.70711	−	16.8132i	0.442606	−	0.766616i
$482$		0			0
$483$	−10.1213	−	13.0519i	−0.460536	−	0.593883i
$484$		0			0
$485$	−7.19239	+	12.4576i	−0.326590	+	0.565670i
$486$		0			0
$487$	0.343146	+	0.594346i	0.0155494	+	0.0269324i	0.873695	−	0.486473i	$-0.161717\pi$
$487$	0.343146	+	0.594346i	0.0155494	+	0.0269324i	−0.858146	+	0.513406i	$0.828384\pi$
$488$		0			0
$489$	60.1127			2.71839
$490$		0			0
$491$	4.82843			0.217904			0.108952	−	0.994047i	$-0.465251\pi$
$491$	4.82843			0.217904			0.108952	+	0.994047i	$0.465251\pi$
$492$		0			0
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$		0			0
$495$	2.00000	−	3.46410i	0.0898933	−	0.155700i
$496$		0			0
$497$	23.0919	+	29.7781i	1.03581	+	1.33573i
$498$		0			0
$499$	−7.89949	+	13.6823i	−0.353630	+	0.612505i	−0.986883	−	0.161440i	$-0.948386\pi$
$499$	−7.89949	+	13.6823i	−0.353630	+	0.612505i	0.633253	+	0.773945i	$0.281719\pi$
$500$		0			0
$501$	31.0563	+	53.7912i	1.38750	+	2.40321i
$502$		0			0
$503$	5.72792			0.255395			0.127698	−	0.991813i	$-0.459241\pi$
$503$	5.72792			0.255395			0.127698	+	0.991813i	$0.459241\pi$
$504$		0			0
$505$	−13.4142			−0.596925
$506$		0			0
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$		0			0
$509$	−12.1716	+	21.0818i	−0.539495	+	0.934434i	0.459436	+	0.888211i	$0.348052\pi$
$509$	−12.1716	+	21.0818i	−0.539495	+	0.934434i	−0.998931	+	0.0462225i	$0.985282\pi$
$510$		0			0
$511$	0.585786	−	1.43488i	0.0259137	−	0.0634753i
$512$		0			0
$513$	−1.12132	+	1.94218i	−0.0495075	+	0.0857495i
$514$		0			0
$515$	2.75736	+	4.77589i	0.121504	+	0.210451i
$516$		0			0
$517$	−0.828427			−0.0364342
$518$		0			0
$519$	18.8995			0.829596
$520$		0			0
$521$	−6.00000	−	10.3923i	−0.262865	−	0.455295i	0.704137	−	0.710064i	$-0.251334\pi$
$521$	−6.00000	−	10.3923i	−0.262865	−	0.455295i	−0.967002	+	0.254769i	$0.918001\pi$
$522$		0			0
$523$	−0.535534	+	0.927572i	−0.0234173	+	0.0405599i	−0.877497	−	0.479583i	$-0.840788\pi$
$523$	−0.535534	+	0.927572i	−0.0234173	+	0.0405599i	0.854079	+	0.520143i	$0.174121\pi$
$524$		0			0
$525$	−18.9853	+	2.59808i	−0.828586	+	0.113389i
$526$		0			0
$527$	1.65685	−	2.86976i	0.0721737	−	0.125009i
$528$		0			0
$529$	8.15685	+	14.1281i	0.354646	+	0.614265i
$530$		0			0
$531$	4.48528			0.194645
$532$		0			0
$533$	8.58579			0.371892
$534$		0			0
$535$	−12.4142	−	21.5020i	−0.536713	−	0.929615i
$536$		0			0
$537$	1.08579	−	1.88064i	0.0468551	−	0.0811555i
$538$		0			0
$539$	6.74264	−	1.88064i	0.290426	−	0.0810048i
$540$		0			0
$541$	18.5711	−	32.1660i	0.798433	−	1.38293i	−0.122204	−	0.992505i	$-0.538996\pi$
$541$	18.5711	−	32.1660i	0.798433	−	1.38293i	0.920637	−	0.390421i	$-0.127670\pi$
$542$		0			0
$543$	−11.2426	−	19.4728i	−0.482468	−	0.835659i
$544$		0			0
$545$	−12.0000			−0.514024
$546$		0			0
$547$	15.6985			0.671219			0.335609	−	0.942001i	$-0.391058\pi$
$547$	15.6985			0.671219			0.335609	+	0.942001i	$0.391058\pi$
$548$		0			0
$549$	19.5563	+	33.8726i	0.834645	+	1.44565i
$550$		0			0
$551$	2.70711	−	4.68885i	0.115327	−	0.199752i
$552$		0			0
$553$	−15.9142	+	2.17781i	−0.676741	+	0.0926099i
$554$		0			0
$555$	8.65685	−	14.9941i	0.367463	−	0.636465i
$556$		0			0
$557$	6.58579	+	11.4069i	0.279049	+	0.483327i	0.971149	−	0.238475i	$-0.0766476\pi$
$557$	6.58579	+	11.4069i	0.279049	+	0.483327i	−0.692100	+	0.721802i	$0.743314\pi$
$558$		0			0
$559$	30.6274			1.29540
$560$		0			0
$561$	−4.82843			−0.203856
$562$		0			0
$563$	−22.6066	−	39.1558i	−0.952755	−	1.65022i	−0.739425	−	0.673239i	$-0.764902\pi$
$563$	−22.6066	−	39.1558i	−0.952755	−	1.65022i	−0.213330	−	0.976980i	$-0.568431\pi$
$564$		0			0
$565$	6.70711	−	11.6170i	0.282170	−	0.488733i
$566$		0			0
$567$	9.48528	−	23.2341i	0.398344	−	0.975740i
$568$		0			0
$569$	−10.4853	+	18.1610i	−0.439566	+	0.761350i	−0.997656	−	0.0684300i	$-0.978201\pi$
$569$	−10.4853	+	18.1610i	−0.439566	+	0.761350i	0.558090	+	0.829780i	$0.311534\pi$
$570$		0			0
$571$	−2.29289	−	3.97141i	−0.0959546	−	0.166198i	0.814052	−	0.580792i	$-0.197257\pi$
$571$	−2.29289	−	3.97141i	−0.0959546	−	0.166198i	−0.910007	+	0.414594i	$0.863924\pi$
$572$		0			0
$573$	25.3137			1.05750
$574$		0			0
$575$	−7.75736			−0.323504
$576$		0			0
$577$	8.98528	+	15.5630i	0.374062	+	0.647895i	0.990186	−	0.139754i	$-0.0446313\pi$
$577$	8.98528	+	15.5630i	0.374062	+	0.647895i	−0.616124	+	0.787649i	$0.711298\pi$
$578$		0			0
$579$	23.1924	−	40.1704i	0.963843	−	1.66942i
$580$		0			0
$581$	−10.5147	−	13.5592i	−0.436224	−	0.562532i
$582$		0			0
$583$	−2.70711	+	4.68885i	−0.112117	+	0.194192i
$584$		0			0
$585$	−7.65685	−	13.2621i	−0.316572	−	0.548319i
$586$		0			0
$587$	−26.2132			−1.08193			−0.540967	−	0.841044i	$-0.681942\pi$
$587$	−26.2132			−1.08193			−0.540967	+	0.841044i	$0.681942\pi$
$588$		0			0
$589$	−8.97056			−0.369626
$590$		0			0
$591$	−20.6924	−	35.8403i	−0.851171	−	1.47427i
$592$		0			0
$593$	6.70711	−	11.6170i	0.275428	−	0.477055i	−0.694815	−	0.719188i	$-0.744514\pi$
$593$	6.70711	−	11.6170i	0.275428	−	0.477055i	0.970243	+	0.242133i	$0.0778471\pi$
$594$		0			0
$595$	−4.58579	−	5.91359i	−0.187999	−	0.242434i
$596$		0			0
$597$	29.0208	−	50.2655i	1.18774	−	2.05723i
$598$		0			0
$599$	−5.51472	−	9.55177i	−0.225325	−	0.390275i	0.731092	−	0.682279i	$-0.239011\pi$
$599$	−5.51472	−	9.55177i	−0.225325	−	0.390275i	−0.956417	+	0.292004i	$0.905678\pi$
$600$		0			0
$601$	−12.3431			−0.503487			−0.251744	−	0.967794i	$-0.581004\pi$
$601$	−12.3431			−0.503487			−0.251744	+	0.967794i	$0.581004\pi$
$602$		0			0
$603$	−17.1716			−0.699281
$604$		0			0
$605$	0.707107	+	1.22474i	0.0287480	+	0.0497930i
$606$		0			0
$607$	17.1421	−	29.6910i	0.695778	−	1.20512i	−0.274140	−	0.961690i	$-0.588393\pi$
$607$	17.1421	−	29.6910i	0.695778	−	1.20512i	0.969918	−	0.243433i	$-0.0782735\pi$
$608$		0			0
$609$	−2.41421	+	5.91359i	−0.0978289	+	0.239631i
$610$		0			0
$611$	−1.58579	+	2.74666i	−0.0641541	+	0.111118i
$612$		0			0
$613$	8.31371	+	14.3998i	0.335788	+	0.581601i	0.983636	−	0.180168i	$-0.0576643\pi$
$613$	8.31371	+	14.3998i	0.335788	+	0.581601i	−0.647848	+	0.761769i	$0.724331\pi$
$614$		0			0
$615$	7.65685			0.308754
$616$		0			0
$617$	−11.6274			−0.468102			−0.234051	−	0.972224i	$-0.575198\pi$
$617$	−11.6274			−0.468102			−0.234051	+	0.972224i	$0.575198\pi$
$618$		0			0
$619$	−11.6569	−	20.1903i	−0.468529	−	0.811515i	0.530824	−	0.847482i	$-0.321882\pi$
$619$	−11.6569	−	20.1903i	−0.468529	−	0.811515i	−0.999353	+	0.0359666i	$0.988549\pi$
$620$		0			0
$621$	0.535534	−	0.927572i	0.0214902	−	0.0372222i
$622$		0			0
$623$	−38.8701	+	5.31925i	−1.55730	+	0.213111i
$624$		0			0
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$		0			0
$627$	6.53553	+	11.3199i	0.261004	+	0.452072i
$628$		0			0
$629$	−10.1421			−0.404393
$630$		0			0
$631$	32.3848			1.28922			0.644609	−	0.764513i	$-0.277020\pi$
$631$	32.3848			1.28922			0.644609	+	0.764513i	$0.277020\pi$
$632$		0			0
$633$	23.0208	+	39.8732i	0.914995	+	1.58482i
$634$		0			0
$635$	2.53553	−	4.39167i	0.100620	−	0.174278i
$636$		0			0
$637$	6.67157	−	25.9553i	0.264337	−	1.02839i
$638$		0			0
$639$	20.1421	−	34.8872i	0.796811	−	1.38012i
$640$		0			0
$641$	23.1274	+	40.0579i	0.913478	+	1.58219i	0.809114	+	0.587651i	$0.199947\pi$
$641$	23.1274	+	40.0579i	0.913478	+	1.58219i	0.104364	+	0.994539i	$0.466719\pi$
$642$		0			0
$643$	38.4142			1.51491			0.757454	−	0.652888i	$-0.226443\pi$
$643$	38.4142			1.51491			0.757454	+	0.652888i	$0.226443\pi$
$644$		0			0
$645$	27.3137			1.07548
$646$		0			0
$647$	−0.535534	−	0.927572i	−0.0210540	−	0.0364666i	0.855306	−	0.518122i	$-0.173369\pi$
$647$	−0.535534	−	0.927572i	−0.0210540	−	0.0364666i	−0.876360	+	0.481656i	$0.840036\pi$
$648$		0			0
$649$	−0.792893	+	1.37333i	−0.0311238	+	0.0539080i
$650$		0			0
$651$	10.4853	−	1.43488i	0.410951	−	0.0562373i
$652$		0			0
$653$	17.4645	−	30.2493i	0.683437	−	1.18375i	−0.290488	−	0.956879i	$-0.593818\pi$
$653$	17.4645	−	30.2493i	0.683437	−	1.18375i	0.973925	−	0.226870i	$-0.0728491\pi$
$654$		0			0
$655$	−13.4853	−	23.3572i	−0.526914	−	0.912641i
$656$		0			0
$657$	−1.65685			−0.0646400
$658$		0			0
$659$	8.68629			0.338370			0.169185	−	0.985584i	$-0.445886\pi$
$659$	8.68629			0.338370			0.169185	+	0.985584i	$0.445886\pi$
$660$		0			0
$661$	−20.3137	−	35.1844i	−0.790112	−	1.36851i	−0.925897	−	0.377775i	$-0.876689\pi$
$661$	−20.3137	−	35.1844i	−0.790112	−	1.36851i	0.135786	−	0.990738i	$-0.456644\pi$
$662$		0			0
$663$	−9.24264	+	16.0087i	−0.358954	+	0.621727i
$664$		0			0
$665$	−7.65685	+	18.7554i	−0.296920	+	0.727303i
$666$		0			0
$667$	−1.29289	+	2.23936i	−0.0500610	+	0.0867082i
$668$		0			0
$669$	13.9497	+	24.1617i	0.539328	+	0.934144i
$670$		0			0
$671$	−13.8284			−0.533841
$672$		0			0
$673$	7.75736			0.299024			0.149512	−	0.988760i	$-0.452230\pi$
$673$	7.75736			0.299024			0.149512	+	0.988760i	$0.452230\pi$
$674$		0			0
$675$	−0.621320	−	1.07616i	−0.0239146	−	0.0414214i
$676$		0			0
$677$	24.1421	−	41.8154i	0.927858	−	1.60710i	0.140958	−	0.990016i	$-0.454982\pi$
$677$	24.1421	−	41.8154i	0.927858	−	1.60710i	0.786900	−	0.617081i	$-0.211685\pi$
$678$		0			0
$679$	16.4914	+	21.2664i	0.632881	+	0.816130i
$680$		0			0
$681$	−0.171573	+	0.297173i	−0.00657469	+	0.0113877i
$682$		0			0
$683$	2.44975	+	4.24309i	0.0937370	+	0.162357i	0.909081	−	0.416620i	$-0.136785\pi$
$683$	2.44975	+	4.24309i	0.0937370	+	0.162357i	−0.815344	+	0.578977i	$0.803452\pi$
$684$		0			0
$685$	−24.0416			−0.918583
$686$		0			0
$687$	−9.65685			−0.368432
$688$		0			0
$689$	10.3640	+	17.9509i	0.394835	+	0.683875i
$690$		0			0
$691$	3.69239	−	6.39540i	0.140465	−	0.243293i	−0.787207	−	0.616689i	$-0.788474\pi$
$691$	3.69239	−	6.39540i	0.140465	−	0.243293i	0.927672	+	0.373397i	$0.121807\pi$
$692$		0			0
$693$	−4.58579	−	5.91359i	−0.174200	−	0.224639i
$694$		0			0
$695$	13.6569	−	23.6544i	0.518034	−	0.897261i
$696$		0			0
$697$	−2.24264	−	3.88437i	−0.0849461	−	0.147131i
$698$		0			0
$699$	−39.5563			−1.49616
$700$		0			0
$701$	−8.45584			−0.319373			−0.159686	−	0.987168i	$-0.551048\pi$
$701$	−8.45584			−0.319373			−0.159686	+	0.987168i	$0.551048\pi$
$702$		0			0
$703$	13.7279	+	23.7775i	0.517758	+	0.896784i
$704$		0			0
$705$	−1.41421	+	2.44949i	−0.0532624	+	0.0922531i
$706$		0			0
$707$	−9.48528	+	23.2341i	−0.356731	+	0.873808i
$708$		0			0
$709$	−16.5355	+	28.6404i	−0.621005	+	1.07561i	0.368294	+	0.929709i	$0.379942\pi$
$709$	−16.5355	+	28.6404i	−0.621005	+	1.07561i	−0.989299	+	0.145903i	$0.953391\pi$
$710$		0			0
$711$	8.58579	+	14.8710i	0.321992	+	0.557707i
$712$		0			0
$713$	4.28427			0.160447
$714$		0			0
$715$	5.41421			0.202480
$716$		0			0
$717$	−16.5711	−	28.7019i	−0.618858	−	1.07189i
$718$		0			0
$719$	−11.5858	+	20.0672i	−0.432077	+	0.748379i	−0.997052	−	0.0767288i	$-0.975552\pi$
$719$	−11.5858	+	20.0672i	−0.432077	+	0.748379i	0.564975	+	0.825108i	$0.308886\pi$
$720$		0			0
$721$	10.2218	−	1.39882i	0.380681	−	0.0520950i
$722$		0			0
$723$	−3.29289	+	5.70346i	−0.122464	+	0.212114i
$724$		0			0
$725$	1.50000	+	2.59808i	0.0557086	+	0.0964901i
$726$		0			0
$727$	25.7990			0.956832			0.478416	−	0.878133i	$-0.341211\pi$
$727$	25.7990			0.956832			0.478416	+	0.878133i	$0.341211\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$		0			0
$733$	−8.67157	+	15.0196i	−0.320292	+	0.554762i	−0.980548	−	0.196279i	$-0.937114\pi$
$733$	−8.67157	+	15.0196i	−0.320292	+	0.554762i	0.660256	+	0.751040i	$0.270448\pi$
$734$		0			0
$735$	5.94975	−	23.1471i	0.219460	−	0.853792i
$736$		0			0
$737$	3.03553	−	5.25770i	0.111815	−	0.193670i
$738$		0			0
$739$	24.2132	+	41.9385i	0.890697	+	1.54273i	0.839041	+	0.544068i	$0.183117\pi$
$739$	24.2132	+	41.9385i	0.890697	+	1.54273i	0.0516557	+	0.998665i	$0.483550\pi$
$740$		0			0
$741$	50.0416			1.83833
$742$		0			0
$743$	34.0000			1.24734			0.623670	−	0.781688i	$-0.285641\pi$
$743$	34.0000			1.24734			0.623670	+	0.781688i	$0.285641\pi$
$744$		0			0
$745$	−11.3137	−	19.5959i	−0.414502	−	0.717939i
$746$		0			0
$747$	−9.17157	+	15.8856i	−0.335570	+	0.581225i
$748$		0			0
$749$	−46.0208	+	6.29780i	−1.68156	+	0.230117i
$750$		0			0
$751$	5.65685	−	9.79796i	0.206422	−	0.357533i	−0.744163	−	0.667998i	$-0.767152\pi$
$751$	5.65685	−	9.79796i	0.206422	−	0.357533i	0.950585	+	0.310465i	$0.100485\pi$
$752$		0			0
$753$	19.8995	+	34.4669i	0.725178	+	1.25604i
$754$		0			0
$755$	−11.8995			−0.433067
$756$		0			0
$757$	−5.31371			−0.193130			−0.0965650	−	0.995327i	$-0.530786\pi$
$757$	−5.31371			−0.193130			−0.0965650	+	0.995327i	$0.530786\pi$
$758$		0			0
$759$	−3.12132	−	5.40629i	−0.113297	−	0.196236i
$760$		0			0
$761$	−19.9706	+	34.5900i	−0.723932	+	1.25389i	0.235480	+	0.971879i	$0.424334\pi$
$761$	−19.9706	+	34.5900i	−0.723932	+	1.25389i	−0.959412	+	0.282008i	$0.908999\pi$
$762$		0			0
$763$	−8.48528	+	20.7846i	−0.307188	+	0.752453i
$764$		0			0
$765$	−4.00000	+	6.92820i	−0.144620	+	0.250490i
$766$		0			0
$767$	3.03553	+	5.25770i	0.109607	+	0.189845i
$768$		0			0
$769$	−2.97056			−0.107121			−0.0535606	−	0.998565i	$-0.517057\pi$
$769$	−2.97056			−0.107121			−0.0535606	+	0.998565i	$0.517057\pi$
$770$		0			0
$771$	−6.07107			−0.218644
$772$		0			0
$773$	5.31371	+	9.20361i	0.191121	+	0.331031i	0.945622	−	0.325268i	$-0.105454\pi$
$773$	5.31371	+	9.20361i	0.191121	+	0.331031i	−0.754501	+	0.656299i	$0.772121\pi$
$774$		0			0
$775$	2.48528	−	4.30463i	0.0892739	−	0.154627i
$776$		0			0
$777$	−19.8492	−	25.5965i	−0.712088	−	0.918271i
$778$		0			0
$779$	−6.07107	+	10.5154i	−0.217519	+	0.376753i
$780$		0			0
$781$	7.12132	+	12.3345i	0.254821	+	0.441363i
$782$		0			0
$783$	−0.414214			−0.0148028
$784$		0			0
$785$	−21.6569			−0.772966
$786$		0			0
$787$	−21.1924	−	36.7063i	−0.755427	−	1.30844i	−0.945162	−	0.326603i	$-0.894096\pi$
$787$	−21.1924	−	36.7063i	−0.755427	−	1.30844i	0.189735	−	0.981835i	$-0.439237\pi$
$788$		0			0
$789$	−30.2279	+	52.3563i	−1.07614	+	1.86393i
$790$		0			0
$791$	−15.3787	−	19.8315i	−0.546803	−	0.705129i
$792$		0			0
$793$	−26.4706	+	45.8484i	−0.939997	+	1.62812i
$794$		0			0
$795$	9.24264	+	16.0087i	0.327803	+	0.567771i
$796$		0			0
$797$	−13.3137			−0.471596			−0.235798	−	0.971802i	$-0.575770\pi$
$797$	−13.3137			−0.471596			−0.235798	+	0.971802i	$0.575770\pi$
$798$		0			0
$799$	1.65685			0.0586153
$800$		0			0
$801$	20.9706	+	36.3221i	0.740958	+	1.28338i
$802$		0			0
$803$	0.292893	−	0.507306i	0.0103360	−	0.0179024i
$804$		0			0
$805$	3.65685	−	8.95743i	0.128887	−	0.315708i
$806$		0			0
$807$	2.82843	−	4.89898i	0.0995654	−	0.172452i
$808$		0			0
$809$	4.00000	+	6.92820i	0.140633	+	0.243583i	0.927735	−	0.373240i	$-0.121753\pi$
$809$	4.00000	+	6.92820i	0.140633	+	0.243583i	−0.787102	+	0.616822i	$0.788420\pi$
$810$		0			0
$811$	38.3431			1.34641			0.673205	−	0.739456i	$-0.264917\pi$
$811$	38.3431			1.34641			0.673205	+	0.739456i	$0.264917\pi$
$812$		0			0
$813$	33.9706			1.19140
$814$		0			0
$815$	17.6066	+	30.4955i	0.616732	+	1.06821i
$816$		0			0
$817$	−21.6569	+	37.5108i	−0.757677	+	1.31234i
$818$		0			0
$819$	−28.3848	+	3.88437i	−0.991844	+	0.135731i
$820$		0			0
$821$	13.9142	−	24.1001i	0.485609	−	0.841100i	−0.514254	−	0.857638i	$-0.671931\pi$
$821$	13.9142	−	24.1001i	0.485609	−	0.841100i	0.999863	+	0.0165379i	$0.00526441\pi$
$822$		0			0
$823$	16.4142	+	28.4303i	0.572164	+	0.991016i	0.996343	+	0.0854384i	$0.0272291\pi$
$823$	16.4142	+	28.4303i	0.572164	+	0.991016i	−0.424180	+	0.905578i	$0.639438\pi$
$824$		0			0
$825$	−7.24264			−0.252156
$826$		0			0
$827$	−32.5269			−1.13107			−0.565536	−	0.824724i	$-0.691331\pi$
$827$	−32.5269			−1.13107			−0.565536	+	0.824724i	$0.691331\pi$
$828$		0			0
$829$	−17.2929	−	29.9522i	−0.600607	−	1.04028i	−0.992729	−	0.120369i	$-0.961592\pi$
$829$	−17.2929	−	29.9522i	−0.600607	−	1.04028i	0.392122	−	0.919913i	$-0.371741\pi$
$830$		0			0
$831$	−17.8640	+	30.9413i	−0.619694	+	1.07334i
$832$		0			0
$833$	−13.4853	+	3.76127i	−0.467237	+	0.130320i
$834$		0			0
$835$	−18.1924	+	31.5101i	−0.629574	+	1.09045i
$836$		0			0
$837$	0.343146	+	0.594346i	0.0118609	+	0.0205436i
$838$		0			0
$839$	9.51472			0.328485			0.164242	−	0.986420i	$-0.447482\pi$
$839$	9.51472			0.328485			0.164242	+	0.986420i	$0.447482\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	−9.53553	−	16.5160i	−0.328421	−	0.568842i
$844$		0			0
$845$	1.17157	−	2.02922i	0.0403033	−	0.0698074i
$846$		0			0
$847$	2.62132	−	0.358719i	0.0900696	−	0.0123257i
$848$		0			0
$849$	4.29289	−	7.43551i	0.147332	−	0.255186i
$850$		0			0
$851$	−6.55635	−	11.3559i	−0.224749	−	0.389276i
$852$		0			0
$853$	−50.0000			−1.71197			−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000			−1.71197			−0.855984	+	0.517003i	$0.827048\pi$
$854$		0			0
$855$	21.6569			0.740649
$856$		0			0
$857$	−4.14214	−	7.17439i	−0.141493	−	0.245072i	0.786566	−	0.617506i	$-0.211857\pi$
$857$	−4.14214	−	7.17439i	−0.141493	−	0.245072i	−0.928059	+	0.372433i	$0.878523\pi$
$858$		0			0
$859$	4.79289	−	8.30153i	0.163531	−	0.283245i	−0.772601	−	0.634891i	$-0.781045\pi$
$859$	4.79289	−	8.30153i	0.163531	−	0.283245i	0.936133	+	0.351647i	$0.114378\pi$
$860$		0			0
$861$	5.41421	−	13.2621i	0.184516	−	0.451970i
$862$		0			0
$863$	−5.19239	+	8.99348i	−0.176751	+	0.306142i	−0.940766	−	0.339057i	$-0.889892\pi$
$863$	−5.19239	+	8.99348i	−0.176751	+	0.306142i	0.764015	+	0.645199i	$0.223225\pi$
$864$		0			0
$865$	5.53553	+	9.58783i	0.188214	+	0.325996i
$866$		0			0
$867$	−31.3848			−1.06588
$868$		0			0
$869$	−6.07107			−0.205947
$870$		0			0
$871$	−11.6213	−	20.1287i	−0.393773	−	0.682036i
$872$		0			0
$873$	14.3848	−	24.9152i	0.486851	−	0.843251i
$874$		0			0
$875$	−18.3431	−	23.6544i	−0.620112	−	0.799664i
$876$		0			0
$877$	21.6421	−	37.4853i	0.730803	−	1.26579i	−0.225737	−	0.974188i	$-0.572479\pi$
$877$	21.6421	−	37.4853i	0.730803	−	1.26579i	0.956540	−	0.291600i	$-0.0941875\pi$
$878$		0			0
$879$	22.7279	+	39.3659i	0.766594	+	1.32778i
$880$		0			0
$881$	14.1716			0.477452			0.238726	−	0.971087i	$-0.423270\pi$
$881$	14.1716			0.477452			0.238726	+	0.971087i	$0.423270\pi$
$882$		0			0
$883$	−53.6690			−1.80611			−0.903054	−	0.429528i	$-0.858680\pi$
$883$	−53.6690			−1.80611			−0.903054	+	0.429528i	$0.858680\pi$
$884$		0			0
$885$	2.70711	+	4.68885i	0.0909984	+	0.157614i
$886$		0			0
$887$	3.13604	−	5.43178i	0.105298	−	0.182381i	−0.808562	−	0.588411i	$-0.799754\pi$
$887$	3.13604	−	5.43178i	0.105298	−	0.182381i	0.913860	+	0.406030i	$0.133087\pi$
$888$		0			0
$889$	−5.81371	−	7.49706i	−0.194986	−	0.251443i
$890$		0			0
$891$	4.74264	−	8.21449i	0.158884	−	0.275196i
$892$		0			0
$893$	−2.24264	−	3.88437i	−0.0750471	−	0.129985i
$894$		0			0
$895$	1.27208			0.0425209
$896$		0			0
$897$	−23.8995			−0.797981
$898$		0			0
$899$	−0.828427	−	1.43488i	−0.0276296	−	0.0478559i
$900$		0			0
$901$	5.41421	−	9.37769i	0.180374	−	0.312416i
$902$		0			0
$903$	19.3137	−	47.3087i	0.642720	−	1.57434i
$904$		0			0
$905$	6.58579	−	11.4069i	0.218919	−	0.379179i
$906$		0			0
$907$	−16.3137	−	28.2562i	−0.541688	−	0.938231i	−0.998807	−	0.0488255i	$-0.984452\pi$
$907$	−16.3137	−	28.2562i	−0.541688	−	0.938231i	0.457120	−	0.889405i	$-0.348881\pi$
$908$		0			0
$909$	26.8284			0.889843
$910$		0			0
$911$	21.5147			0.712814			0.356407	−	0.934331i	$-0.384002\pi$
$911$	21.5147			0.712814			0.356407	+	0.934331i	$0.384002\pi$
$912$		0			0
$913$	−3.24264	−	5.61642i	−0.107316	−	0.185876i
$914$		0			0
$915$	−23.6066	+	40.8878i	−0.780410	+	1.35171i
$916$		0			0
$917$	−49.9914	+	6.84116i	−1.65086	+	0.225915i
$918$		0			0
$919$	22.7279	−	39.3659i	0.749725	−	1.29856i	−0.198229	−	0.980156i	$-0.563519\pi$
$919$	22.7279	−	39.3659i	0.749725	−	1.29856i	0.947954	−	0.318406i	$-0.103148\pi$
$920$		0			0
$921$	−13.7782	−	23.8645i	−0.454006	−	0.786362i
$922$		0			0
$923$	54.5269			1.79478
$924$		0			0
$925$	−15.2132			−0.500207
$926$		0			0
$927$	−5.51472	−	9.55177i	−0.181127	−	0.313721i
$928$		0			0
$929$	−21.7132	+	37.6084i	−0.712387	+	1.23389i	0.251572	+	0.967839i	$0.419053\pi$
$929$	−21.7132	+	37.6084i	−0.712387	+	1.23389i	−0.963959	+	0.266052i	$0.914281\pi$
$930$		0			0
$931$	27.0711	+	26.5241i	0.887218	+	0.869293i
$932$		0			0
$933$	−18.3640	+	31.8073i	−0.601209	+	1.04132i
$934$		0			0
$935$	−1.41421	−	2.44949i	−0.0462497	−	0.0801069i
$936$		0			0
$937$	−18.5858			−0.607171			−0.303586	−	0.952804i	$-0.598184\pi$
$937$	−18.5858			−0.607171			−0.303586	+	0.952804i	$0.598184\pi$
$938$		0			0
$939$	−49.8701			−1.62745
$940$		0			0
$941$	−8.47056	−	14.6714i	−0.276132	−	0.478275i	0.694288	−	0.719698i	$-0.255720\pi$
$941$	−8.47056	−	14.6714i	−0.276132	−	0.478275i	−0.970420	+	0.241422i	$0.922386\pi$
$942$		0			0
$943$	2.89949	−	5.02207i	0.0944205	−	0.163541i
$944$		0			0
$945$	1.53553	−	0.210133i	0.0499509	−	0.00683563i
$946$		0			0
$947$	−19.8995	+	34.4669i	−0.646647	+	1.12002i	0.337272	+	0.941407i	$0.390496\pi$
$947$	−19.8995	+	34.4669i	−0.646647	+	1.12002i	−0.983919	+	0.178618i	$0.942837\pi$
$948$		0			0
$949$	−1.12132	−	1.94218i	−0.0363996	−	0.0630460i
$950$		0			0
$951$	−31.3137			−1.01542
$952$		0			0
$953$	54.3848			1.76170			0.880848	−	0.473399i	$-0.156973\pi$
$953$	54.3848			1.76170			0.880848	+	0.473399i	$0.156973\pi$
$954$		0			0
$955$	7.41421	+	12.8418i	0.239918	+	0.415551i
$956$		0			0
$957$	−1.20711	+	2.09077i	−0.0390202	+	0.0675850i
$958$		0			0
$959$	−17.0000	+	41.6413i	−0.548959	+	1.34467i
$960$		0			0
$961$	14.1274	−	24.4694i	0.455723	−	0.789336i
$962$		0			0
$963$	24.8284	+	43.0041i	0.800085	+	1.38579i
$964$		0			0
$965$	27.1716			0.874684
$966$		0			0
$967$	−29.6569			−0.953700			−0.476850	−	0.878985i	$-0.658222\pi$
$967$	−29.6569			−0.953700			−0.476850	+	0.878985i	$0.658222\pi$
$968$		0			0
$969$	−13.0711	−	22.6398i	−0.419903	−	0.727294i
$970$		0			0
$971$	6.10660	−	10.5769i	0.195970	−	0.339430i	−0.751248	−	0.660020i	$-0.770548\pi$
$971$	6.10660	−	10.5769i	0.195970	−	0.339430i	0.947218	+	0.320590i	$0.103881\pi$
$972$		0			0
$973$	−31.3137	−	40.3805i	−1.00387	−	1.29454i
$974$		0			0
$975$	−13.8640	+	24.0131i	−0.444002	+	0.769034i
$976$		0			0
$977$	−18.4853	−	32.0174i	−0.591397	−	1.02433i	−0.994045	−	0.108974i	$-0.965243\pi$
$977$	−18.4853	−	32.0174i	−0.591397	−	1.02433i	0.402648	−	0.915355i	$-0.368090\pi$
$978$		0			0
$979$	−14.8284			−0.473919
$980$		0			0
$981$	24.0000			0.766261
$982$		0			0
$983$	23.2426	+	40.2574i	0.741325	+	1.28401i	0.951892	+	0.306433i	$0.0991357\pi$
$983$	23.2426	+	40.2574i	0.741325	+	1.28401i	−0.210567	+	0.977579i	$0.567531\pi$
$984$		0			0
$985$	12.1213	−	20.9947i	0.386217	−	0.668948i
$986$		0			0
$987$	3.24264	+	4.18154i	0.103214	+	0.133100i
$988$		0			0
$989$	10.3431	−	17.9149i	0.328893	−	0.569659i
$990$		0			0
$991$	−9.94975	−	17.2335i	−0.316064	−	0.547439i	0.663599	−	0.748088i	$-0.269028\pi$
$991$	−9.94975	−	17.2335i	−0.316064	−	0.547439i	−0.979663	+	0.200649i	$0.935695\pi$
$992$		0			0
$993$	75.7696			2.40447
$994$		0			0
$995$	34.0000			1.07787
$996$		0			0
$997$	4.72792	+	8.18900i	0.149735	+	0.259348i	0.931129	−	0.364689i	$-0.118825\pi$
$997$	4.72792	+	8.18900i	0.149735	+	0.259348i	−0.781395	+	0.624037i	$0.785491\pi$
$998$		0			0
$999$	1.05025	−	1.81909i	0.0332285	−	0.0575535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.q.b.177.1	✓	4
4.3	odd	2		1232.2.q.h.177.2		4
7.2	even	3		4312.2.a.u.1.2		2
7.4	even	3	inner	616.2.q.b.529.1	yes	4
7.5	odd	6		4312.2.a.m.1.1		2
28.11	odd	6		1232.2.q.h.529.2		4
28.19	even	6		8624.2.a.cd.1.2		2
28.23	odd	6		8624.2.a.bg.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.b.177.1	✓	4	1.1	even	1	trivial
616.2.q.b.529.1	yes	4	7.4	even	3	inner
1232.2.q.h.177.2		4	4.3	odd	2
1232.2.q.h.529.2		4	28.11	odd	6
4312.2.a.m.1.1		2	7.5	odd	6
4312.2.a.u.1.2		2	7.2	even	3
8624.2.a.bg.1.1		2	28.23	odd	6
8624.2.a.cd.1.2		2	28.19	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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 - 2.09077i) q^{3} +(0.707107 - 1.22474i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(-0.500000 - 0.866025i) q^{11} -3.82843 q^{13} -3.41421 q^{15} +(1.00000 + 1.73205i) q^{17} +(2.70711 - 4.68885i) q^{19} +(-2.41421 + 5.91359i) q^{21} +(-1.29289 + 2.23936i) q^{23} +(1.50000 + 2.59808i) q^{25} -0.414214 q^{27} +1.00000 q^{29} +(-0.828427 - 1.43488i) q^{31} +(-1.20711 + 2.09077i) q^{33} +(-3.70711 + 0.507306i) q^{35} +(-2.53553 + 4.39167i) q^{37} +(4.62132 + 8.00436i) q^{39} -2.24264 q^{41} -8.00000 q^{43} +(2.00000 + 3.46410i) q^{45} +(0.414214 - 0.717439i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(2.41421 - 4.18154i) q^{51} +(-2.70711 - 4.68885i) q^{53} -1.41421 q^{55} -13.0711 q^{57} +(-0.792893 - 1.37333i) q^{59} +(6.91421 - 11.9758i) q^{61} +(7.41421 - 1.01461i) q^{63} +(-2.70711 + 4.68885i) q^{65} +(3.03553 + 5.25770i) q^{67} +6.24264 q^{69} -14.2426 q^{71} +(0.292893 + 0.507306i) q^{73} +(3.62132 - 6.27231i) q^{75} +(-1.00000 + 2.44949i) q^{77} +(3.03553 - 5.25770i) q^{79} +(4.74264 + 8.21449i) q^{81} +6.48528 q^{83} +2.82843 q^{85} +(-1.20711 - 2.09077i) q^{87} +(7.41421 - 12.8418i) q^{89} +(6.20711 + 8.00436i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(-3.82843 - 6.63103i) q^{95} -10.1716 q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{7} - 2 q^{11} - 4 q^{13} - 8 q^{15} + 4 q^{17} + 8 q^{19} - 4 q^{21} - 8 q^{23} + 6 q^{25} + 4 q^{27} + 4 q^{29} + 8 q^{31} - 2 q^{33} - 12 q^{35} + 4 q^{37} + 10 q^{39} + 8 q^{41}+ \cdots - 52 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^7 - 2 * q^11 - 4 * q^13 - 8 * q^15 + 4 * q^17 + 8 * q^19 - 4 * q^21 - 8 * q^23 + 6 * q^25 + 4 * q^27 + 4 * q^29 + 8 * q^31 - 2 * q^33 - 12 * q^35 + 4 * q^37 + 10 * q^39 + 8 * q^41 - 32 * q^43 + 8 * q^45 - 4 * q^47 + 10 * q^49 + 4 * q^51 - 8 * q^53 - 24 * q^57 - 6 * q^59 + 22 * q^61 + 24 * q^63 - 8 * q^65 - 2 * q^67 + 8 * q^69 - 40 * q^71 + 4 * q^73 + 6 * q^75 - 4 * q^77 - 2 * q^79 + 2 * q^81 - 8 * q^83 - 2 * q^87 + 24 * q^89 + 22 * q^91 - 8 * q^93 - 4 * q^95 - 52 * q^97

Introduction

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