LMFDB - Embedded newform 616.2.q.b.529.2

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			529.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	616.529
Dual form			616.2.q.b.177.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.207107 - 0.358719i) q^{3} +(-0.707107 - 1.22474i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.82843 q^{13} -0.585786 q^{15} +(1.00000 - 1.73205i) q^{17} +(1.29289 + 2.23936i) q^{19} +(0.414214 - 1.01461i) q^{21} +(-2.70711 - 4.68885i) q^{23} +(1.50000 - 2.59808i) q^{25} +2.41421 q^{27} +1.00000 q^{29} +(4.82843 - 8.36308i) q^{31} +(0.207107 + 0.358719i) q^{33} +(-2.29289 - 2.95680i) q^{35} +(4.53553 + 7.85578i) q^{37} +(0.378680 - 0.655892i) q^{39} +6.24264 q^{41} -8.00000 q^{43} +(2.00000 - 3.46410i) q^{45} +(-2.41421 - 4.18154i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-0.414214 - 0.717439i) q^{51} +(-1.29289 + 2.23936i) q^{53} +1.41421 q^{55} +1.07107 q^{57} +(-2.20711 + 3.82282i) q^{59} +(4.08579 + 7.07679i) q^{61} +(4.58579 + 5.91359i) q^{63} +(-1.29289 - 2.23936i) q^{65} +(-4.03553 + 6.98975i) q^{67} -2.24264 q^{69} -5.75736 q^{71} +(1.70711 - 2.95680i) q^{73} +(-0.621320 - 1.07616i) q^{75} +(-1.00000 + 2.44949i) q^{77} +(-4.03553 - 6.98975i) q^{79} +(-3.74264 + 6.48244i) q^{81} -10.4853 q^{83} -2.82843 q^{85} +(0.207107 - 0.358719i) q^{87} +(4.58579 + 7.94282i) q^{89} +(4.79289 - 0.655892i) q^{91} +(-2.00000 - 3.46410i) q^{93} +(1.82843 - 3.16693i) q^{95} -15.8284 q^{97} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	−0.800025	−	0.599966i	$-0.795181\pi$
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	0.919599	+	0.392859i	$0.128514\pi$
$4$		0			0
$5$	−0.707107	−	1.22474i	−0.316228	−	0.547723i	0.663470	−	0.748203i	$-0.269083\pi$
$5$	−0.707107	−	1.22474i	−0.316228	−	0.547723i	−0.979698	+	0.200480i	$0.935750\pi$
$6$		0			0
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$7$	2.62132	−	0.358719i	0.990766	−	0.135583i
$8$		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
$13$	1.82843			0.507114			0.253557	−	0.967320i	$-0.418399\pi$
$13$	1.82843			0.507114			0.253557	+	0.967320i	$0.418399\pi$
$14$		0			0
$15$	−0.585786			−0.151249
$16$		0			0
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		0			0
$19$	1.29289	+	2.23936i	0.296610	+	0.513744i	0.975358	−	0.220628i	$-0.0708105\pi$
$19$	1.29289	+	2.23936i	0.296610	+	0.513744i	−0.678748	+	0.734371i	$0.737477\pi$
$20$		0			0
$21$	0.414214	−	1.01461i	0.0903888	−	0.221406i
$22$		0			0
$23$	−2.70711	−	4.68885i	−0.564471	−	0.977692i	−0.997099	−	0.0761195i	$-0.975747\pi$
$23$	−2.70711	−	4.68885i	−0.564471	−	0.977692i	0.432628	−	0.901573i	$-0.357586\pi$
$24$		0			0
$25$	1.50000	−	2.59808i	0.300000	−	0.519615i
$26$		0			0
$27$	2.41421			0.464616
$28$		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
$31$	4.82843	−	8.36308i	0.867211	−	1.50205i	0.00237631	−	0.999997i	$-0.499244\pi$
$31$	4.82843	−	8.36308i	0.867211	−	1.50205i	0.864835	−	0.502057i	$-0.167423\pi$
$32$		0			0
$33$	0.207107	+	0.358719i	0.0360527	+	0.0624450i
$34$		0			0
$35$	−2.29289	−	2.95680i	−0.387570	−	0.499790i
$36$		0			0
$37$	4.53553	+	7.85578i	0.745637	+	1.29148i	0.949896	+	0.312565i	$0.101188\pi$
$37$	4.53553	+	7.85578i	0.745637	+	1.29148i	−0.204259	+	0.978917i	$0.565479\pi$
$38$		0			0
$39$	0.378680	−	0.655892i	0.0606373	−	0.105027i
$40$		0			0
$41$	6.24264			0.974937			0.487468	−	0.873141i	$-0.337920\pi$
$41$	6.24264			0.974937			0.487468	+	0.873141i	$0.337920\pi$
$42$		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
$47$	−2.41421	−	4.18154i	−0.352149	−	0.609940i	0.634477	−	0.772942i	$-0.281216\pi$
$47$	−2.41421	−	4.18154i	−0.352149	−	0.609940i	−0.986626	+	0.163002i	$0.947882\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$		0			0
$51$	−0.414214	−	0.717439i	−0.0580015	−	0.100462i
$52$		0			0
$53$	−1.29289	+	2.23936i	−0.177593	+	0.307599i	−0.941055	−	0.338252i	$-0.890164\pi$
$53$	−1.29289	+	2.23936i	−0.177593	+	0.307599i	0.763463	+	0.645852i	$0.223498\pi$
$54$		0			0
$55$	1.41421			0.190693
$56$		0			0
$57$	1.07107			0.141866
$58$		0			0
$59$	−2.20711	+	3.82282i	−0.287341	+	0.497689i	−0.973174	−	0.230070i	$-0.926105\pi$
$59$	−2.20711	+	3.82282i	−0.287341	+	0.497689i	0.685833	+	0.727759i	$0.259438\pi$
$60$		0			0
$61$	4.08579	+	7.07679i	0.523131	+	0.906090i	0.999638	+	0.0269190i	$0.00856962\pi$
$61$	4.08579	+	7.07679i	0.523131	+	0.906090i	−0.476506	+	0.879171i	$0.658097\pi$
$62$		0			0
$63$	4.58579	+	5.91359i	0.577755	+	0.745042i
$64$		0			0
$65$	−1.29289	−	2.23936i	−0.160364	−	0.277758i
$66$		0			0
$67$	−4.03553	+	6.98975i	−0.493019	+	0.853934i	−0.999968	−	0.00804237i	$-0.997440\pi$
$67$	−4.03553	+	6.98975i	−0.493019	+	0.853934i	0.506949	+	0.861976i	$0.330773\pi$
$68$		0			0
$69$	−2.24264			−0.269982
$70$		0			0
$71$	−5.75736			−0.683273			−0.341636	−	0.939832i	$-0.610981\pi$
$71$	−5.75736			−0.683273			−0.341636	+	0.939832i	$0.610981\pi$
$72$		0			0
$73$	1.70711	−	2.95680i	0.199802	−	0.346067i	−0.748662	−	0.662952i	$-0.769304\pi$
$73$	1.70711	−	2.95680i	0.199802	−	0.346067i	0.948464	+	0.316885i	$0.102637\pi$
$74$		0			0
$75$	−0.621320	−	1.07616i	−0.0717439	−	0.124264i
$76$		0			0
$77$	−1.00000	+	2.44949i	−0.113961	+	0.279145i
$78$		0			0
$79$	−4.03553	−	6.98975i	−0.454033	−	0.786408i	0.544599	−	0.838697i	$-0.316682\pi$
$79$	−4.03553	−	6.98975i	−0.454033	−	0.786408i	−0.998632	+	0.0522883i	$0.983349\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$	−10.4853			−1.15091			−0.575455	−	0.817834i	$-0.695175\pi$
$83$	−10.4853			−1.15091			−0.575455	+	0.817834i	$0.695175\pi$
$84$		0			0
$85$	−2.82843			−0.306786
$86$		0			0
$87$	0.207107	−	0.358719i	0.0222042	−	0.0384588i
$88$		0			0
$89$	4.58579	+	7.94282i	0.486092	+	0.841937i	0.999872	−	0.0159854i	$-0.00508851\pi$
$89$	4.58579	+	7.94282i	0.486092	+	0.841937i	−0.513780	+	0.857922i	$0.671755\pi$
$90$		0			0
$91$	4.79289	−	0.655892i	0.502432	−	0.0687562i
$92$		0			0
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$		0			0
$95$	1.82843	−	3.16693i	0.187593	−	0.324920i
$96$		0			0
$97$	−15.8284			−1.60713			−0.803567	−	0.595215i	$-0.797067\pi$
$97$	−15.8284			−1.60713			−0.803567	+	0.595215i	$0.797067\pi$
$98$		0			0
$99$	−2.82843			−0.284268
$100$		0			0
$101$	3.74264	−	6.48244i	0.372407	−	0.645027i	−0.617529	−	0.786548i	$-0.711866\pi$
$101$	3.74264	−	6.48244i	0.372407	−	0.645027i	0.989935	+	0.141521i	$0.0451993\pi$
$102$		0			0
$103$	7.94975	+	13.7694i	0.783312	+	1.35674i	0.930002	+	0.367554i	$0.119805\pi$
$103$	7.94975	+	13.7694i	0.783312	+	1.35674i	−0.146690	+	0.989182i	$0.546862\pi$
$104$		0			0
$105$	−1.53553	+	0.210133i	−0.149853	+	0.0205069i
$106$		0			0
$107$	−6.77817	−	11.7401i	−0.655271	−	1.13496i	−0.981826	−	0.189784i	$-0.939221\pi$
$107$	−6.77817	−	11.7401i	−0.655271	−	1.13496i	0.326555	−	0.945178i	$-0.394112\pi$
$108$		0			0
$109$	4.24264	−	7.34847i	0.406371	−	0.703856i	−0.588109	−	0.808782i	$-0.700127\pi$
$109$	4.24264	−	7.34847i	0.406371	−	0.703856i	0.994480	+	0.104926i	$0.0334606\pi$
$110$		0			0
$111$	3.75736			0.356633
$112$		0			0
$113$	−7.48528			−0.704156			−0.352078	−	0.935971i	$-0.614525\pi$
$113$	−7.48528			−0.704156			−0.352078	+	0.935971i	$0.614525\pi$
$114$		0			0
$115$	−3.82843	+	6.63103i	−0.357003	+	0.618347i
$116$		0			0
$117$	2.58579	+	4.47871i	0.239056	+	0.414057i
$118$		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
$123$	1.29289	−	2.23936i	0.116576	−	0.201916i
$124$		0			0
$125$	−11.3137			−1.01193
$126$		0			0
$127$	6.41421			0.569169			0.284585	−	0.958651i	$-0.408144\pi$
$127$	6.41421			0.569169			0.284585	+	0.958651i	$0.408144\pi$
$128$		0			0
$129$	−1.65685	+	2.86976i	−0.145878	+	0.252668i
$130$		0			0
$131$	2.46447	+	4.26858i	0.215321	+	0.372948i	0.953372	−	0.301798i	$-0.0975868\pi$
$131$	2.46447	+	4.26858i	0.215321	+	0.372948i	−0.738051	+	0.674745i	$0.764253\pi$
$132$		0			0
$133$	4.19239	+	5.40629i	0.363526	+	0.468784i
$134$		0			0
$135$	−1.70711	−	2.95680i	−0.146924	−	0.254480i
$136$		0			0
$137$	−8.50000	+	14.7224i	−0.726204	+	1.25782i	0.232273	+	0.972651i	$0.425384\pi$
$137$	−8.50000	+	14.7224i	−0.726204	+	1.25782i	−0.958477	+	0.285171i	$0.907949\pi$
$138$		0			0
$139$	−3.31371			−0.281065			−0.140533	−	0.990076i	$-0.544881\pi$
$139$	−3.31371			−0.281065			−0.140533	+	0.990076i	$0.544881\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$		0			0
$143$	−0.914214	+	1.58346i	−0.0764504	+	0.132416i
$144$		0			0
$145$	−0.707107	−	1.22474i	−0.0587220	−	0.101710i
$146$		0			0
$147$	0.721825	−	2.80821i	0.0595352	−	0.231617i
$148$		0			0
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	0.981797	+	0.189933i	$0.0608272\pi$
$149$	8.00000	+	13.8564i	0.655386	+	1.13516i	−0.326411	+	0.945228i	$0.605840\pi$
$150$		0			0
$151$	−2.79289	+	4.83743i	−0.227282	+	0.393665i	−0.957002	−	0.290082i	$-0.906317\pi$
$151$	−2.79289	+	4.83743i	−0.227282	+	0.393665i	0.729719	+	0.683747i	$0.239651\pi$
$152$		0			0
$153$	5.65685			0.457330
$154$		0			0
$155$	−13.6569			−1.09694
$156$		0			0
$157$	3.65685	−	6.33386i	0.291849	−	0.505497i	−0.682398	−	0.730981i	$-0.739063\pi$
$157$	3.65685	−	6.33386i	0.291849	−	0.505497i	0.974247	+	0.225484i	$0.0723963\pi$
$158$		0			0
$159$	0.535534	+	0.927572i	0.0424706	+	0.0735612i
$160$		0			0
$161$	−8.77817	−	11.3199i	−0.691817	−	0.892131i
$162$		0			0
$163$	−2.55025	−	4.41717i	−0.199751	−	0.345979i	0.748696	−	0.662913i	$-0.230680\pi$
$163$	−2.55025	−	4.41717i	−0.199751	−	0.345979i	−0.948448	+	0.316934i	$0.897347\pi$
$164$		0			0
$165$	0.292893	−	0.507306i	0.0228017	−	0.0394937i
$166$		0			0
$167$	−0.272078			−0.0210540			−0.0105270	−	0.999945i	$-0.503351\pi$
$167$	−0.272078			−0.0210540			−0.0105270	+	0.999945i	$0.503351\pi$
$168$		0			0
$169$	−9.65685			−0.742835
$170$		0			0
$171$	−3.65685	+	6.33386i	−0.279647	+	0.484362i
$172$		0			0
$173$	−1.08579	−	1.88064i	−0.0825508	−	0.142982i	0.821794	−	0.569785i	$-0.192973\pi$
$173$	−1.08579	−	1.88064i	−0.0825508	−	0.142982i	−0.904345	+	0.426802i	$0.859640\pi$
$174$		0			0
$175$	3.00000	−	7.34847i	0.226779	−	0.555492i
$176$		0			0
$177$	0.914214	+	1.58346i	0.0687165	+	0.119020i
$178$		0			0
$179$	−9.44975	+	16.3674i	−0.706307	+	1.22336i	0.259910	+	0.965633i	$0.416307\pi$
$179$	−9.44975	+	16.3674i	−0.706307	+	1.22336i	−0.966218	+	0.257727i	$0.917026\pi$
$180$		0			0
$181$	−13.3137			−0.989600			−0.494800	−	0.869007i	$-0.664759\pi$
$181$	−13.3137			−0.989600			−0.494800	+	0.869007i	$0.664759\pi$
$182$		0			0
$183$	3.38478			0.250210
$184$		0			0
$185$	6.41421	−	11.1097i	0.471582	−	0.816805i
$186$		0			0
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$		0			0
$189$	6.32843	−	0.866025i	0.460325	−	0.0629941i
$190$		0			0
$191$	3.24264	+	5.61642i	0.234629	+	0.406390i	0.959165	−	0.282848i	$-0.0912791\pi$
$191$	3.24264	+	5.61642i	0.234629	+	0.406390i	−0.724536	+	0.689237i	$0.757946\pi$
$192$		0			0
$193$	−11.6066	+	20.1032i	−0.835461	+	1.44706i	0.0581927	+	0.998305i	$0.481466\pi$
$193$	−11.6066	+	20.1032i	−0.835461	+	1.44706i	−0.893654	+	0.448756i	$0.851867\pi$
$194$		0			0
$195$	−1.07107			−0.0767008
$196$		0			0
$197$	−11.1421			−0.793844			−0.396922	−	0.917852i	$-0.629922\pi$
$197$	−11.1421			−0.793844			−0.396922	+	0.917852i	$0.629922\pi$
$198$		0			0
$199$	−12.0208	+	20.8207i	−0.852133	+	1.47594i	0.0271465	+	0.999631i	$0.491358\pi$
$199$	−12.0208	+	20.8207i	−0.852133	+	1.47594i	−0.879279	+	0.476306i	$0.841975\pi$
$200$		0			0
$201$	1.67157	+	2.89525i	0.117904	+	0.204215i
$202$		0			0
$203$	2.62132	−	0.358719i	0.183981	−	0.0251772i
$204$		0			0
$205$	−4.41421	−	7.64564i	−0.308302	−	0.533995i
$206$		0			0
$207$	7.65685	−	13.2621i	0.532188	−	0.921777i
$208$		0			0
$209$	−2.58579			−0.178863
$210$		0			0
$211$	−4.92893			−0.339322			−0.169661	−	0.985503i	$-0.554267\pi$
$211$	−4.92893			−0.339322			−0.169661	+	0.985503i	$0.554267\pi$
$212$		0			0
$213$	−1.19239	+	2.06528i	−0.0817011	+	0.141510i
$214$		0			0
$215$	5.65685	+	9.79796i	0.385794	+	0.668215i
$216$		0			0
$217$	9.65685	−	23.6544i	0.655550	−	1.60576i
$218$		0			0
$219$	−0.707107	−	1.22474i	−0.0477818	−	0.0827606i
$220$		0			0
$221$	1.82843	−	3.16693i	0.122993	−	0.213031i
$222$		0			0
$223$	19.5563			1.30959			0.654795	−	0.755807i	$-0.272755\pi$
$223$	19.5563			1.30959			0.654795	+	0.755807i	$0.272755\pi$
$224$		0			0
$225$	8.48528			0.565685
$226$		0			0
$227$	14.0711	−	24.3718i	0.933930	−	1.61761i	0.157398	−	0.987535i	$-0.449689\pi$
$227$	14.0711	−	24.3718i	0.933930	−	1.61761i	0.776532	−	0.630078i	$-0.216977\pi$
$228$		0			0
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		0			0
$231$	0.671573	+	0.866025i	0.0441863	+	0.0569803i
$232$		0			0
$233$	−10.1924	−	17.6537i	−0.667726	−	1.15653i	−0.978539	−	0.206064i	$-0.933935\pi$
$233$	−10.1924	−	17.6537i	−0.667726	−	1.15653i	0.310813	−	0.950471i	$-0.399399\pi$
$234$		0			0
$235$	−3.41421	+	5.91359i	−0.222719	+	0.385760i
$236$		0			0
$237$	−3.34315			−0.217161
$238$		0			0
$239$	−11.7279			−0.758616			−0.379308	−	0.925270i	$-0.623838\pi$
$239$	−11.7279			−0.758616			−0.379308	+	0.925270i	$0.623838\pi$
$240$		0			0
$241$	11.3640	−	19.6830i	0.732017	−	1.26789i	−0.224003	−	0.974589i	$-0.571912\pi$
$241$	11.3640	−	19.6830i	0.732017	−	1.26789i	0.956020	−	0.293302i	$-0.0947542\pi$
$242$		0			0
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$		0			0
$245$	−7.07107	−	6.92820i	−0.451754	−	0.442627i
$246$		0			0
$247$	2.36396	+	4.09450i	0.150415	+	0.260527i
$248$		0			0
$249$	−2.17157	+	3.76127i	−0.137618	+	0.238361i
$250$		0			0
$251$	0.485281			0.0306307			0.0153153	−	0.999883i	$-0.495125\pi$
$251$	0.485281			0.0306307			0.0153153	+	0.999883i	$0.495125\pi$
$252$		0			0
$253$	5.41421			0.340389
$254$		0			0
$255$	−0.585786	+	1.01461i	−0.0366834	+	0.0635375i
$256$		0			0
$257$	9.74264	+	16.8747i	0.607729	+	1.05262i	0.991614	+	0.129237i	$0.0412527\pi$
$257$	9.74264	+	16.8747i	0.607729	+	1.05262i	−0.383885	+	0.923381i	$0.625414\pi$
$258$		0			0
$259$	14.7071	+	18.9655i	0.913855	+	1.17846i
$260$		0			0
$261$	1.41421	+	2.44949i	0.0875376	+	0.151620i
$262$		0			0
$263$	11.5208	−	19.9546i	0.710404	−	1.23046i	−0.254302	−	0.967125i	$-0.581846\pi$
$263$	11.5208	−	19.9546i	0.710404	−	1.23046i	0.964706	−	0.263331i	$-0.0848210\pi$
$264$		0			0
$265$	3.65685			0.224639
$266$		0			0
$267$	3.79899			0.232494
$268$		0			0
$269$	6.82843	−	11.8272i	0.416337	−	0.721116i	−0.579231	−	0.815163i	$-0.696647\pi$
$269$	6.82843	−	11.8272i	0.416337	−	0.721116i	0.995568	+	0.0940473i	$0.0299805\pi$
$270$		0			0
$271$	0.0355339	+	0.0615465i	0.00215853	+	0.00373869i	0.867103	−	0.498129i	$-0.165980\pi$
$271$	0.0355339	+	0.0615465i	0.00215853	+	0.00373869i	−0.864944	+	0.501868i	$0.832646\pi$
$272$		0			0
$273$	0.757359	−	1.85514i	0.0458375	−	0.112278i
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	12.3995	−	21.4766i	0.745013	−	1.29040i	−0.205175	−	0.978725i	$-0.565776\pi$
$277$	12.3995	−	21.4766i	0.745013	−	1.29040i	0.950188	−	0.311676i	$-0.100890\pi$
$278$		0			0
$279$	27.3137			1.63523
$280$		0			0
$281$	−11.8995			−0.709864			−0.354932	−	0.934892i	$-0.615496\pi$
$281$	−11.8995			−0.709864			−0.354932	+	0.934892i	$0.615496\pi$
$282$		0			0
$283$	−13.7782	+	23.8645i	−0.819027	+	1.41860i	0.0873721	+	0.996176i	$0.472153\pi$
$283$	−13.7782	+	23.8645i	−0.819027	+	1.41860i	−0.906400	+	0.422421i	$0.861180\pi$
$284$		0			0
$285$	−0.757359	−	1.31178i	−0.0448621	−	0.0777034i
$286$		0			0
$287$	16.3640	−	2.23936i	0.965934	−	0.132185i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−3.27817	+	5.67796i	−0.192170	+	0.332848i
$292$		0			0
$293$	−13.1716			−0.769492			−0.384746	−	0.923023i	$-0.625711\pi$
$293$	−13.1716			−0.769492			−0.384746	+	0.923023i	$0.625711\pi$
$294$		0			0
$295$	6.24264			0.363461
$296$		0			0
$297$	−1.20711	+	2.09077i	−0.0700434	+	0.121319i
$298$		0			0
$299$	−4.94975	−	8.57321i	−0.286251	−	0.495802i
$300$		0			0
$301$	−20.9706	+	2.86976i	−1.20872	+	0.165410i
$302$		0			0
$303$	−1.55025	−	2.68512i	−0.0890597	−	0.154256i
$304$		0			0
$305$	5.77817	−	10.0081i	0.330857	−	0.573062i
$306$		0			0
$307$	8.58579			0.490017			0.245008	−	0.969521i	$-0.421209\pi$
$307$	8.58579			0.490017			0.245008	+	0.969521i	$0.421209\pi$
$308$		0			0
$309$	6.58579			0.374652
$310$		0			0
$311$	13.6066	−	23.5673i	0.771560	−	1.33638i	−0.165148	−	0.986269i	$-0.552810\pi$
$311$	13.6066	−	23.5673i	0.771560	−	1.33638i	0.936708	−	0.350112i	$-0.113856\pi$
$312$		0			0
$313$	4.67157	+	8.09140i	0.264053	+	0.457353i	0.967315	−	0.253578i	$-0.0816073\pi$
$313$	4.67157	+	8.09140i	0.264053	+	0.457353i	−0.703262	+	0.710931i	$0.748274\pi$
$314$		0			0
$315$	4.00000	−	9.79796i	0.225374	−	0.552052i
$316$		0			0
$317$	−10.4853	−	18.1610i	−0.588912	−	1.02003i	−0.994375	−	0.105914i	$-0.966223\pi$
$317$	−10.4853	−	18.1610i	−0.588912	−	1.02003i	0.405463	−	0.914111i	$-0.367110\pi$
$318$		0			0
$319$	−0.500000	+	0.866025i	−0.0279946	+	0.0484881i
$320$		0			0
$321$	−5.61522			−0.313411
$322$		0			0
$323$	5.17157			0.287754
$324$		0			0
$325$	2.74264	−	4.75039i	0.152134	−	0.263504i
$326$		0			0
$327$	−1.75736	−	3.04384i	−0.0971822	−	0.168324i
$328$		0			0
$329$	−7.82843	−	10.0951i	−0.431595	−	0.556563i
$330$		0			0
$331$	2.69239	+	4.66335i	0.147987	+	0.256321i	0.930483	−	0.366334i	$-0.119387\pi$
$331$	2.69239	+	4.66335i	0.147987	+	0.256321i	−0.782496	+	0.622655i	$0.786054\pi$
$332$		0			0
$333$	−12.8284	+	22.2195i	−0.702993	+	1.21762i
$334$		0			0
$335$	11.4142			0.623625
$336$		0			0
$337$	−2.24264			−0.122164			−0.0610822	−	0.998133i	$-0.519455\pi$
$337$	−2.24264			−0.122164			−0.0610822	+	0.998133i	$0.519455\pi$
$338$		0			0
$339$	−1.55025	+	2.68512i	−0.0841982	+	0.145835i
$340$		0			0
$341$	4.82843	+	8.36308i	0.261474	+	0.452886i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$		0			0
$345$	1.58579	+	2.74666i	0.0853759	+	0.147875i
$346$		0			0
$347$	4.29289	−	7.43551i	0.230455	−	0.399159i	−0.727487	−	0.686121i	$-0.759312\pi$
$347$	4.29289	−	7.43551i	0.230455	−	0.399159i	0.957942	+	0.286962i	$0.0926454\pi$
$348$		0			0
$349$	24.2843			1.29991			0.649954	−	0.759974i	$-0.274788\pi$
$349$	24.2843			1.29991			0.649954	+	0.759974i	$0.274788\pi$
$350$		0			0
$351$	4.41421			0.235613
$352$		0			0
$353$	1.34315	−	2.32640i	0.0714884	−	0.123822i	−0.828065	−	0.560632i	$-0.810558\pi$
$353$	1.34315	−	2.32640i	0.0714884	−	0.123822i	0.899554	+	0.436810i	$0.143892\pi$
$354$		0			0
$355$	4.07107	+	7.05130i	0.216070	+	0.374244i
$356$		0			0
$357$	−1.34315	−	1.73205i	−0.0710868	−	0.0916698i
$358$		0			0
$359$	−6.96447	−	12.0628i	−0.367570	−	0.636651i	0.621615	−	0.783323i	$-0.286477\pi$
$359$	−6.96447	−	12.0628i	−0.367570	−	0.636651i	−0.989185	+	0.146672i	$0.953144\pi$
$360$		0			0
$361$	6.15685	−	10.6640i	0.324045	−	0.561262i
$362$		0			0
$363$	−0.414214			−0.0217406
$364$		0			0
$365$	−4.82843			−0.252731
$366$		0			0
$367$	−4.12132	+	7.13834i	−0.215131	+	0.372618i	−0.953313	−	0.301984i	$-0.902351\pi$
$367$	−4.12132	+	7.13834i	−0.215131	+	0.372618i	0.738182	+	0.674602i	$0.235685\pi$
$368$		0			0
$369$	8.82843	+	15.2913i	0.459590	+	0.796032i
$370$		0			0
$371$	−2.58579	+	6.33386i	−0.134247	+	0.328837i
$372$		0			0
$373$	6.81371	+	11.8017i	0.352800	+	0.611068i	0.986739	−	0.162315i	$-0.0518961\pi$
$373$	6.81371	+	11.8017i	0.352800	+	0.611068i	−0.633939	+	0.773383i	$0.718563\pi$
$374$		0			0
$375$	−2.34315	+	4.05845i	−0.121000	+	0.209577i
$376$		0			0
$377$	1.82843			0.0941688
$378$		0			0
$379$	−7.38478			−0.379330			−0.189665	−	0.981849i	$-0.560740\pi$
$379$	−7.38478			−0.379330			−0.189665	+	0.981849i	$0.560740\pi$
$380$		0			0
$381$	1.32843	−	2.30090i	0.0680574	−	0.117879i
$382$		0			0
$383$	4.05025	+	7.01524i	0.206958	+	0.358462i	0.950755	−	0.309944i	$-0.100310\pi$
$383$	4.05025	+	7.01524i	0.206958	+	0.358462i	−0.743797	+	0.668406i	$0.766977\pi$
$384$		0			0
$385$	3.70711	−	0.507306i	0.188932	−	0.0258547i
$386$		0			0
$387$	−11.3137	−	19.5959i	−0.575108	−	0.996116i
$388$		0			0
$389$	−16.6066	+	28.7635i	−0.841988	+	1.45837i	0.0462232	+	0.998931i	$0.485281\pi$
$389$	−16.6066	+	28.7635i	−0.841988	+	1.45837i	−0.888211	+	0.459435i	$0.848052\pi$
$390$		0			0
$391$	−10.8284			−0.547617
$392$		0			0
$393$	2.04163			0.102987
$394$		0			0
$395$	−5.70711	+	9.88500i	−0.287156	+	0.497368i
$396$		0			0
$397$	−17.8284	−	30.8797i	−0.894783	−	1.54981i	−0.834073	−	0.551654i	$-0.813997\pi$
$397$	−17.8284	−	30.8797i	−0.894783	−	1.54981i	−0.0607103	−	0.998155i	$-0.519337\pi$
$398$		0			0
$399$	2.80761	−	0.384213i	0.140556	−	0.0192347i
$400$		0			0
$401$	12.5000	+	21.6506i	0.624220	+	1.08118i	0.988691	+	0.149966i	$0.0479165\pi$
$401$	12.5000	+	21.6506i	0.624220	+	1.08118i	−0.364471	+	0.931215i	$0.618750\pi$
$402$		0			0
$403$	8.82843	−	15.2913i	0.439775	−	0.761713i
$404$		0			0
$405$	10.5858			0.526012
$406$		0			0
$407$	−9.07107			−0.449636
$408$		0			0
$409$	16.9497	−	29.3578i	0.838111	−	1.45165i	−0.0533610	−	0.998575i	$-0.516993\pi$
$409$	16.9497	−	29.3578i	0.838111	−	1.45165i	0.891472	−	0.453076i	$-0.149673\pi$
$410$		0			0
$411$	3.52082	+	6.09823i	0.173669	+	0.300804i
$412$		0			0
$413$	−4.41421	+	10.8126i	−0.217209	+	0.532052i
$414$		0			0
$415$	7.41421	+	12.8418i	0.363949	+	0.630379i
$416$		0			0
$417$	−0.686292	+	1.18869i	−0.0336078	+	0.0582105i
$418$		0			0
$419$	−25.4558			−1.24360			−0.621800	−	0.783176i	$-0.713598\pi$
$419$	−25.4558			−1.24360			−0.621800	+	0.783176i	$0.713598\pi$
$420$		0			0
$421$	9.65685			0.470646			0.235323	−	0.971917i	$-0.424385\pi$
$421$	9.65685			0.470646			0.235323	+	0.971917i	$0.424385\pi$
$422$		0			0
$423$	6.82843	−	11.8272i	0.332009	−	0.575057i
$424$		0			0
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$	13.2487	+	17.0849i	0.641151	+	0.826795i
$428$		0			0
$429$	0.378680	+	0.655892i	0.0182828	+	0.0316668i
$430$		0			0
$431$	−3.86396	+	6.69258i	−0.186120	+	0.322370i	−0.943954	−	0.330078i	$-0.892925\pi$
$431$	−3.86396	+	6.69258i	−0.186120	+	0.322370i	0.757833	+	0.652449i	$0.226258\pi$
$432$		0			0
$433$	−13.4558			−0.646647			−0.323323	−	0.946289i	$-0.604800\pi$
$433$	−13.4558			−0.646647			−0.323323	+	0.946289i	$0.604800\pi$
$434$		0			0
$435$	−0.585786			−0.0280863
$436$		0			0
$437$	7.00000	−	12.1244i	0.334855	−	0.579987i
$438$		0			0
$439$	−0.964466	−	1.67050i	−0.0460315	−	0.0797288i	0.842092	−	0.539334i	$-0.181324\pi$
$439$	−0.964466	−	1.67050i	−0.0460315	−	0.0797288i	−0.888123	+	0.459606i	$0.847991\pi$
$440$		0			0
$441$	14.1421	+	13.8564i	0.673435	+	0.659829i
$442$		0			0
$443$	−2.65685	−	4.60181i	−0.126231	−	0.218638i	0.795982	−	0.605320i	$-0.206955\pi$
$443$	−2.65685	−	4.60181i	−0.126231	−	0.218638i	−0.922213	+	0.386681i	$0.873621\pi$
$444$		0			0
$445$	6.48528	−	11.2328i	0.307432	−	0.532488i
$446$		0			0
$447$	6.62742			0.313466
$448$		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
$451$	−3.12132	+	5.40629i	−0.146977	+	0.254572i
$452$		0			0
$453$	1.15685	+	2.00373i	0.0543538	+	0.0941435i
$454$		0			0
$455$	−4.19239	−	5.40629i	−0.196542	−	0.253451i
$456$		0			0
$457$	−14.6569	−	25.3864i	−0.685619	−	1.18753i	−0.973242	−	0.229783i	$-0.926198\pi$
$457$	−14.6569	−	25.3864i	−0.685619	−	1.18753i	0.287623	−	0.957744i	$-0.407135\pi$
$458$		0			0
$459$	2.41421	−	4.18154i	0.112686	−	0.195178i
$460$		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
$463$	−13.7990			−0.641293			−0.320647	−	0.947199i	$-0.603900\pi$
$463$	−13.7990			−0.641293			−0.320647	+	0.947199i	$0.603900\pi$
$464$		0			0
$465$	−2.82843	+	4.89898i	−0.131165	+	0.227185i
$466$		0			0
$467$	−17.9706	−	31.1259i	−0.831578	−	1.44034i	−0.896786	−	0.442464i	$-0.854104\pi$
$467$	−17.9706	−	31.1259i	−0.831578	−	1.44034i	0.0652076	−	0.997872i	$-0.479229\pi$
$468$		0			0
$469$	−8.07107	+	19.7700i	−0.372687	+	0.912894i
$470$		0			0
$471$	−1.51472	−	2.62357i	−0.0697946	−	0.120888i
$472$		0			0
$473$	4.00000	−	6.92820i	0.183920	−	0.318559i
$474$		0			0
$475$	7.75736			0.355932
$476$		0			0
$477$	−7.31371			−0.334872
$478$		0			0
$479$	−7.03553	+	12.1859i	−0.321462	+	0.556788i	−0.980790	−	0.195067i	$-0.937507\pi$
$479$	−7.03553	+	12.1859i	−0.321462	+	0.556788i	0.659328	+	0.751855i	$0.270841\pi$
$480$		0			0
$481$	8.29289	+	14.3637i	0.378123	+	0.654929i
$482$		0			0
$483$	−5.87868	+	0.804479i	−0.267489	+	0.0366051i
$484$		0			0
$485$	11.1924	+	19.3858i	0.508220	+	0.880263i
$486$		0			0
$487$	11.6569	−	20.1903i	0.528222	−	0.914908i	−0.471236	−	0.882007i	$-0.656192\pi$
$487$	11.6569	−	20.1903i	0.528222	−	0.914908i	0.999459	−	0.0329011i	$-0.0104746\pi$
$488$		0			0
$489$	−2.11270			−0.0955395
$490$		0			0
$491$	−0.828427			−0.0373864			−0.0186932	−	0.999825i	$-0.505951\pi$
$491$	−0.828427			−0.0373864			−0.0186932	+	0.999825i	$0.505951\pi$
$492$		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
$497$	−15.0919	+	2.06528i	−0.676963	+	0.0926403i
$498$		0			0
$499$	11.8995	+	20.6105i	0.532695	+	0.922654i	0.999271	+	0.0381732i	$0.0121539\pi$
$499$	11.8995	+	20.6105i	0.532695	+	0.922654i	−0.466577	+	0.884481i	$0.654513\pi$
$500$		0			0
$501$	−0.0563492	+	0.0975997i	−0.00251750	+	0.00436043i
$502$		0			0
$503$	−19.7279			−0.879625			−0.439812	−	0.898090i	$-0.644955\pi$
$503$	−19.7279			−0.879625			−0.439812	+	0.898090i	$0.644955\pi$
$504$		0			0
$505$	−10.5858			−0.471061
$506$		0			0
$507$	−2.00000	+	3.46410i	−0.0888231	+	0.153846i
$508$		0			0
$509$	−17.8284	−	30.8797i	−0.790231	−	1.36872i	−0.925824	−	0.377956i	$-0.876627\pi$
$509$	−17.8284	−	30.8797i	−0.790231	−	1.36872i	0.135593	−	0.990765i	$-0.456706\pi$
$510$		0			0
$511$	3.41421	−	8.36308i	0.151036	−	0.369961i
$512$		0			0
$513$	3.12132	+	5.40629i	0.137810	+	0.238693i
$514$		0			0
$515$	11.2426	−	19.4728i	0.495410	−	0.858075i
$516$		0			0
$517$	4.82843			0.212354
$518$		0			0
$519$	−0.899495			−0.0394834
$520$		0			0
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	−0.967002	−	0.254769i	$-0.918001\pi$
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	0.704137	+	0.710064i	$0.251334\pi$
$522$		0			0
$523$	6.53553	+	11.3199i	0.285779	+	0.494984i	0.972798	−	0.231656i	$-0.0744144\pi$
$523$	6.53553	+	11.3199i	0.285779	+	0.494984i	−0.687019	+	0.726640i	$0.741081\pi$
$524$		0			0
$525$	−2.01472	−	2.59808i	−0.0879295	−	0.113389i
$526$		0			0
$527$	−9.65685	−	16.7262i	−0.420659	−	0.728603i
$528$		0			0
$529$	−3.15685	+	5.46783i	−0.137255	+	0.237732i
$530$		0			0
$531$	−12.4853			−0.541815
$532$		0			0
$533$	11.4142			0.494404
$534$		0			0
$535$	−9.58579	+	16.6031i	−0.414430	+	0.717813i
$536$		0			0
$537$	3.91421	+	6.77962i	0.168911	+	0.292562i
$538$		0			0
$539$	−1.74264	+	6.77962i	−0.0750608	+	0.292019i
$540$		0			0
$541$	4.42893	+	7.67114i	0.190415	+	0.329808i	0.945388	−	0.325948i	$-0.105683\pi$
$541$	4.42893	+	7.67114i	0.190415	+	0.329808i	−0.754973	+	0.655756i	$0.772350\pi$
$542$		0			0
$543$	−2.75736	+	4.77589i	−0.118330	+	0.204953i
$544$		0			0
$545$	−12.0000			−0.514024
$546$		0			0
$547$	−43.6985			−1.86841			−0.934206	−	0.356734i	$-0.883890\pi$
$547$	−43.6985			−1.86841			−0.934206	+	0.356734i	$0.883890\pi$
$548$		0			0
$549$	−11.5563	+	20.0162i	−0.493213	+	0.854270i
$550$		0			0
$551$	1.29289	+	2.23936i	0.0550791	+	0.0953998i
$552$		0			0
$553$	−13.0858	−	16.8747i	−0.556464	−	0.717587i
$554$		0			0
$555$	−2.65685	−	4.60181i	−0.112777	−	0.195336i
$556$		0			0
$557$	9.41421	−	16.3059i	0.398893	−	0.690903i	−0.594697	−	0.803950i	$-0.702728\pi$
$557$	9.41421	−	16.3059i	0.398893	−	0.690903i	0.993590	+	0.113047i	$0.0360611\pi$
$558$		0			0
$559$	−14.6274			−0.618674
$560$		0			0
$561$	0.828427			0.0349762
$562$		0			0
$563$	−1.39340	+	2.41344i	−0.0587247	+	0.101714i	−0.893893	−	0.448280i	$-0.852037\pi$
$563$	−1.39340	+	2.41344i	−0.0587247	+	0.101714i	0.835168	+	0.549994i	$0.185370\pi$
$564$		0			0
$565$	5.29289	+	9.16756i	0.222674	+	0.385682i
$566$		0			0
$567$	−7.48528	+	18.3351i	−0.314352	+	0.770003i
$568$		0			0
$569$	6.48528	+	11.2328i	0.271877	+	0.470905i	0.969343	−	0.245713i	$-0.0790222\pi$
$569$	6.48528	+	11.2328i	0.271877	+	0.470905i	−0.697465	+	0.716618i	$0.745689\pi$
$570$		0			0
$571$	−3.70711	+	6.42090i	−0.155138	+	0.268706i	−0.933109	−	0.359593i	$-0.882915\pi$
$571$	−3.70711	+	6.42090i	−0.155138	+	0.268706i	0.777972	+	0.628300i	$0.216249\pi$
$572$		0			0
$573$	2.68629			0.112221
$574$		0			0
$575$	−16.2426			−0.677365
$576$		0			0
$577$	−7.98528	+	13.8309i	−0.332432	+	0.575788i	−0.982988	−	0.183669i	$-0.941202\pi$
$577$	−7.98528	+	13.8309i	−0.332432	+	0.575788i	0.650556	+	0.759458i	$0.274536\pi$
$578$		0			0
$579$	4.80761	+	8.32703i	0.199798	+	0.346059i
$580$		0			0
$581$	−27.4853	+	3.76127i	−1.14028	+	0.156044i
$582$		0			0
$583$	−1.29289	−	2.23936i	−0.0535462	−	0.0927447i
$584$		0			0
$585$	3.65685	−	6.33386i	0.151192	−	0.261873i
$586$		0			0
$587$	16.2132			0.669191			0.334595	−	0.942362i	$-0.391400\pi$
$587$	16.2132			0.669191			0.334595	+	0.942362i	$0.391400\pi$
$588$		0			0
$589$	24.9706			1.02889
$590$		0			0
$591$	−2.30761	+	3.99690i	−0.0949225	+	0.164411i
$592$		0			0
$593$	5.29289	+	9.16756i	0.217353	+	0.376467i	0.953998	−	0.299813i	$-0.0969244\pi$
$593$	5.29289	+	9.16756i	0.217353	+	0.376467i	−0.736645	+	0.676280i	$0.763591\pi$
$594$		0			0
$595$	−7.41421	+	1.01461i	−0.303953	+	0.0415950i
$596$		0			0
$597$	4.97918	+	8.62420i	0.203784	+	0.352965i
$598$		0			0
$599$	−22.4853	+	38.9456i	−0.918724	+	1.59128i	−0.117368	+	0.993089i	$0.537446\pi$
$599$	−22.4853	+	38.9456i	−0.918724	+	1.59128i	−0.801356	+	0.598188i	$0.795888\pi$
$600$		0			0
$601$	−23.6569			−0.964983			−0.482492	−	0.875901i	$-0.660268\pi$
$601$	−23.6569			−0.964983			−0.482492	+	0.875901i	$0.660268\pi$
$602$		0			0
$603$	−22.8284			−0.929645
$604$		0			0
$605$	−0.707107	+	1.22474i	−0.0287480	+	0.0497930i
$606$		0			0
$607$	−11.1421	−	19.2987i	−0.452245	−	0.783312i	0.546280	−	0.837603i	$-0.316044\pi$
$607$	−11.1421	−	19.2987i	−0.452245	−	0.783312i	−0.998525	+	0.0542908i	$0.982710\pi$
$608$		0			0
$609$	0.414214	−	1.01461i	0.0167848	−	0.0411141i
$610$		0			0
$611$	−4.41421	−	7.64564i	−0.178580	−	0.309310i
$612$		0			0
$613$	−14.3137	+	24.7921i	−0.578125	+	1.00134i	0.417569	+	0.908645i	$0.362882\pi$
$613$	−14.3137	+	24.7921i	−0.578125	+	1.00134i	−0.995694	+	0.0926971i	$0.970451\pi$
$614$		0			0
$615$	−3.65685			−0.147459
$616$		0			0
$617$	33.6274			1.35379			0.676894	−	0.736080i	$-0.263325\pi$
$617$	33.6274			1.35379			0.676894	+	0.736080i	$0.263325\pi$
$618$		0			0
$619$	−0.343146	+	0.594346i	−0.0137922	+	0.0238888i	−0.872839	−	0.488008i	$-0.837724\pi$
$619$	−0.343146	+	0.594346i	−0.0137922	+	0.0238888i	0.859047	+	0.511897i	$0.171057\pi$
$620$		0			0
$621$	−6.53553	−	11.3199i	−0.262262	−	0.454251i
$622$		0			0
$623$	14.8701	+	19.1757i	0.595756	+	0.768256i
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$		0			0
$627$	−0.535534	+	0.927572i	−0.0213872	+	0.0370437i
$628$		0			0
$629$	18.1421			0.723374
$630$		0			0
$631$	−4.38478			−0.174555			−0.0872776	−	0.996184i	$-0.527817\pi$
$631$	−4.38478			−0.174555			−0.0872776	+	0.996184i	$0.527817\pi$
$632$		0			0
$633$	−1.02082	+	1.76810i	−0.0405738	+	0.0702758i
$634$		0			0
$635$	−4.53553	−	7.85578i	−0.179987	−	0.311747i
$636$		0			0
$637$	12.3284	−	3.43861i	0.488470	−	0.136243i
$638$		0			0
$639$	−8.14214	−	14.1026i	−0.322098	−	0.557890i
$640$		0			0
$641$	−22.1274	+	38.3258i	−0.873980	+	1.51378i	−0.0161355	+	0.999870i	$0.505136\pi$
$641$	−22.1274	+	38.3258i	−0.873980	+	1.51378i	−0.857845	+	0.513909i	$0.828197\pi$
$642$		0			0
$643$	35.5858			1.40337			0.701683	−	0.712489i	$-0.252432\pi$
$643$	35.5858			1.40337			0.701683	+	0.712489i	$0.252432\pi$
$644$		0			0
$645$	4.68629			0.184523
$646$		0			0
$647$	6.53553	−	11.3199i	0.256938	−	0.445030i	−0.708482	−	0.705729i	$-0.750620\pi$
$647$	6.53553	−	11.3199i	0.256938	−	0.445030i	0.965420	+	0.260699i	$0.0839529\pi$
$648$		0			0
$649$	−2.20711	−	3.82282i	−0.0866365	−	0.150059i
$650$		0			0
$651$	−6.48528	−	8.36308i	−0.254178	−	0.327775i
$652$		0			0
$653$	24.5355	+	42.4968i	0.960150	+	1.66303i	0.722117	+	0.691771i	$0.243169\pi$
$653$	24.5355	+	42.4968i	0.960150	+	1.66303i	0.238032	+	0.971257i	$0.423498\pi$
$654$		0			0
$655$	3.48528	−	6.03668i	0.136181	−	0.235873i
$656$		0			0
$657$	9.65685			0.376750
$658$		0			0
$659$	31.3137			1.21981			0.609904	−	0.792475i	$-0.291208\pi$
$659$	31.3137			1.21981			0.609904	+	0.792475i	$0.291208\pi$
$660$		0			0
$661$	2.31371	−	4.00746i	0.0899928	−	0.155872i	−0.817515	−	0.575907i	$-0.804649\pi$
$661$	2.31371	−	4.00746i	0.0899928	−	0.155872i	0.907508	+	0.420035i	$0.137982\pi$
$662$		0			0
$663$	−0.757359	−	1.31178i	−0.0294134	−	0.0509455i
$664$		0			0
$665$	3.65685	−	8.95743i	0.141807	−	0.347354i
$666$		0			0
$667$	−2.70711	−	4.68885i	−0.104820	−	0.181553i
$668$		0			0
$669$	4.05025	−	7.01524i	0.156592	−	0.271225i
$670$		0			0
$671$	−8.17157			−0.315460
$672$		0			0
$673$	16.2426			0.626108			0.313054	−	0.949735i	$-0.398648\pi$
$673$	16.2426			0.626108			0.313054	+	0.949735i	$0.398648\pi$
$674$		0			0
$675$	3.62132	−	6.27231i	0.139385	−	0.241421i
$676$		0			0
$677$	−4.14214	−	7.17439i	−0.159195	−	0.275734i	0.775383	−	0.631491i	$-0.217557\pi$
$677$	−4.14214	−	7.17439i	−0.159195	−	0.275734i	−0.934579	+	0.355756i	$0.884223\pi$
$678$		0			0
$679$	−41.4914	+	5.67796i	−1.59229	+	0.217900i
$680$		0			0
$681$	−5.82843	−	10.0951i	−0.223346	−	0.386846i
$682$		0			0
$683$	−7.44975	+	12.9033i	−0.285057	+	0.493733i	−0.972623	−	0.232389i	$-0.925346\pi$
$683$	−7.44975	+	12.9033i	−0.285057	+	0.493733i	0.687566	+	0.726122i	$0.258679\pi$
$684$		0			0
$685$	24.0416			0.918583
$686$		0			0
$687$	1.65685			0.0632129
$688$		0			0
$689$	−2.36396	+	4.09450i	−0.0900597	+	0.155988i
$690$		0			0
$691$	−14.6924	−	25.4480i	−0.558925	−	0.968086i	−0.997587	−	0.0694339i	$-0.977881\pi$
$691$	−14.6924	−	25.4480i	−0.558925	−	0.968086i	0.438662	−	0.898652i	$-0.355453\pi$
$692$		0			0
$693$	−7.41421	+	1.01461i	−0.281643	+	0.0385419i
$694$		0			0
$695$	2.34315	+	4.05845i	0.0888806	+	0.153946i
$696$		0			0
$697$	6.24264	−	10.8126i	0.236457	−	0.409555i
$698$		0			0
$699$	−8.44365			−0.319368
$700$		0			0
$701$	42.4558			1.60354			0.801768	−	0.597636i	$-0.203893\pi$
$701$	42.4558			1.60354			0.801768	+	0.597636i	$0.203893\pi$
$702$		0			0
$703$	−11.7279	+	20.3134i	−0.442327	+	0.766133i
$704$		0			0
$705$	1.41421	+	2.44949i	0.0532624	+	0.0922531i
$706$		0			0
$707$	7.48528	−	18.3351i	0.281513	−	0.689563i
$708$		0			0
$709$	−9.46447	−	16.3929i	−0.355445	−	0.615650i	0.631749	−	0.775173i	$-0.282337\pi$
$709$	−9.46447	−	16.3929i	−0.355445	−	0.615650i	−0.987194	+	0.159524i	$0.949004\pi$
$710$		0			0
$711$	11.4142	−	19.7700i	0.428066	−	0.741433i
$712$		0			0
$713$	−52.2843			−1.95806
$714$		0			0
$715$	2.58579			0.0967029
$716$		0			0
$717$	−2.42893	+	4.20703i	−0.0907101	+	0.157115i
$718$		0			0
$719$	−14.4142	−	24.9662i	−0.537559	−	0.931080i	−0.999035	−	0.0439272i	$-0.986013\pi$
$719$	−14.4142	−	24.9662i	−0.537559	−	0.931080i	0.461475	−	0.887153i	$-0.347320\pi$
$720$		0			0
$721$	25.7782	+	33.2422i	0.960029	+	1.23800i
$722$		0			0
$723$	−4.70711	−	8.15295i	−0.175059	−	0.303211i
$724$		0			0
$725$	1.50000	−	2.59808i	0.0557086	−	0.0964901i
$726$		0			0
$727$	−13.7990			−0.511776			−0.255888	−	0.966706i	$-0.582368\pi$
$727$	−13.7990			−0.511776			−0.255888	+	0.966706i	$0.582368\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	−8.00000	+	13.8564i	−0.295891	+	0.512498i
$732$		0			0
$733$	−14.3284	−	24.8176i	−0.529233	−	0.916658i	−0.999419	−	0.0340904i	$-0.989147\pi$
$733$	−14.3284	−	24.8176i	−0.529233	−	0.916658i	0.470186	−	0.882567i	$-0.344187\pi$
$734$		0			0
$735$	−3.94975	+	1.10165i	−0.145689	+	0.0406350i
$736$		0			0
$737$	−4.03553	−	6.98975i	−0.148651	−	0.257471i
$738$		0			0
$739$	−18.2132	+	31.5462i	−0.669984	+	1.16045i	0.307925	+	0.951411i	$0.400366\pi$
$739$	−18.2132	+	31.5462i	−0.669984	+	1.16045i	−0.977908	+	0.209035i	$0.932968\pi$
$740$		0			0
$741$	1.95837			0.0719425
$742$		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
$747$	−14.8284	−	25.6836i	−0.542544	−	0.939713i
$748$		0			0
$749$	−21.9792	−	28.3432i	−0.803102	−	1.03564i
$750$		0			0
$751$	−5.65685	−	9.79796i	−0.206422	−	0.357533i	0.744163	−	0.667998i	$-0.232848\pi$
$751$	−5.65685	−	9.79796i	−0.206422	−	0.357533i	−0.950585	+	0.310465i	$0.899515\pi$
$752$		0			0
$753$	0.100505	−	0.174080i	0.00366261	−	0.00634382i
$754$		0			0
$755$	7.89949			0.287492
$756$		0			0
$757$	17.3137			0.629277			0.314639	−	0.949212i	$-0.398117\pi$
$757$	17.3137			0.629277			0.314639	+	0.949212i	$0.398117\pi$
$758$		0			0
$759$	1.12132	−	1.94218i	0.0407013	−	0.0704968i
$760$		0			0
$761$	13.9706	+	24.1977i	0.506433	+	0.877167i	0.999972	+	0.00744361i	$0.00236940\pi$
$761$	13.9706	+	24.1977i	0.506433	+	0.877167i	−0.493540	+	0.869723i	$0.664297\pi$
$762$		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
$767$	−4.03553	+	6.98975i	−0.145715	+	0.252385i
$768$		0			0
$769$	30.9706			1.11683			0.558414	−	0.829563i	$-0.311410\pi$
$769$	30.9706			1.11683			0.558414	+	0.829563i	$0.311410\pi$
$770$		0			0
$771$	8.07107			0.290672
$772$		0			0
$773$	−17.3137	+	29.9882i	−0.622731	+	1.07860i	0.366244	+	0.930519i	$0.380643\pi$
$773$	−17.3137	+	29.9882i	−0.622731	+	1.07860i	−0.988975	+	0.148083i	$0.952690\pi$
$774$		0			0
$775$	−14.4853	−	25.0892i	−0.520327	−	0.901232i
$776$		0			0
$777$	9.84924	−	1.34784i	0.353340	−	0.0483534i
$778$		0			0
$779$	8.07107	+	13.9795i	0.289176	+	0.500868i
$780$		0			0
$781$	2.87868	−	4.98602i	0.103007	−	0.178414i
$782$		0			0
$783$	2.41421			0.0862770
$784$		0			0
$785$	−10.3431			−0.369163
$786$		0			0
$787$	−2.80761	+	4.86293i	−0.100081	+	0.173345i	−0.911718	−	0.410817i	$-0.865243\pi$
$787$	−2.80761	+	4.86293i	−0.100081	+	0.173345i	0.811637	+	0.584162i	$0.198577\pi$
$788$		0			0
$789$	−4.77208	−	8.26548i	−0.169890	−	0.294259i
$790$		0			0
$791$	−19.6213	+	2.68512i	−0.697654	+	0.0954717i
$792$		0			0
$793$	7.47056	+	12.9394i	0.265287	+	0.459491i
$794$		0			0
$795$	0.757359	−	1.31178i	0.0268608	−	0.0465242i
$796$		0			0
$797$	9.31371			0.329908			0.164954	−	0.986301i	$-0.447252\pi$
$797$	9.31371			0.329908			0.164954	+	0.986301i	$0.447252\pi$
$798$		0			0
$799$	−9.65685			−0.341635
$800$		0			0
$801$	−12.9706	+	22.4657i	−0.458292	+	0.793786i
$802$		0			0
$803$	1.70711	+	2.95680i	0.0602425	+	0.104343i
$804$		0			0
$805$	−7.65685	+	18.7554i	−0.269869	+	0.661040i
$806$		0			0
$807$	−2.82843	−	4.89898i	−0.0995654	−	0.172452i
$808$		0			0
$809$	4.00000	−	6.92820i	0.140633	−	0.243583i	−0.787102	−	0.616822i	$-0.788420\pi$
$809$	4.00000	−	6.92820i	0.140633	−	0.243583i	0.927735	+	0.373240i	$0.121753\pi$
$810$		0			0
$811$	49.6569			1.74369			0.871844	−	0.489784i	$-0.162924\pi$
$811$	49.6569			1.74369			0.871844	+	0.489784i	$0.162924\pi$
$812$		0			0
$813$	0.0294373			0.00103241
$814$		0			0
$815$	−3.60660	+	6.24682i	−0.126334	+	0.218816i
$816$		0			0
$817$	−10.3431	−	17.9149i	−0.361861	−	0.626761i
$818$		0			0
$819$	8.38478	+	10.8126i	0.292988	+	0.377822i
$820$		0			0
$821$	11.0858	+	19.2011i	0.386897	+	0.670125i	0.992030	−	0.125999i	$-0.0402137\pi$
$821$	11.0858	+	19.2011i	0.386897	+	0.670125i	−0.605134	+	0.796124i	$0.706880\pi$
$822$		0			0
$823$	13.5858	−	23.5313i	0.473571	−	0.820249i	−0.525972	−	0.850502i	$-0.676298\pi$
$823$	13.5858	−	23.5313i	0.473571	−	0.820249i	0.999542	+	0.0302536i	$0.00963149\pi$
$824$		0			0
$825$	1.24264			0.0432632
$826$		0			0
$827$	32.5269			1.13107			0.565536	−	0.824724i	$-0.308669\pi$
$827$	32.5269			1.13107			0.565536	+	0.824724i	$0.308669\pi$
$828$		0			0
$829$	−18.7071	+	32.4017i	−0.649725	+	1.12536i	0.333464	+	0.942763i	$0.391782\pi$
$829$	−18.7071	+	32.4017i	−0.649725	+	1.12536i	−0.983189	+	0.182593i	$0.941551\pi$
$830$		0			0
$831$	−5.13604	−	8.89588i	−0.178167	−	0.308595i
$832$		0			0
$833$	3.48528	−	13.5592i	0.120758	−	0.469800i
$834$		0			0
$835$	0.192388	+	0.333226i	0.00665787	+	0.0115318i
$836$		0			0
$837$	11.6569	−	20.1903i	0.402920	−	0.697878i
$838$		0			0
$839$	26.4853			0.914373			0.457187	−	0.889371i	$-0.348857\pi$
$839$	26.4853			0.914373			0.457187	+	0.889371i	$0.348857\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	−2.46447	+	4.26858i	−0.0848807	+	0.147018i
$844$		0			0
$845$	6.82843	+	11.8272i	0.234905	+	0.406867i
$846$		0			0
$847$	−1.62132	−	2.09077i	−0.0557092	−	0.0718397i
$848$		0			0
$849$	5.70711	+	9.88500i	0.195867	+	0.339252i
$850$		0			0
$851$	24.5563	−	42.5328i	0.841781	−	1.45801i
$852$		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
$855$	10.3431			0.353728
$856$		0			0
$857$	24.1421	−	41.8154i	0.824680	−	1.42839i	−0.0774842	−	0.996994i	$-0.524689\pi$
$857$	24.1421	−	41.8154i	0.824680	−	1.42839i	0.902164	−	0.431393i	$-0.141978\pi$
$858$		0			0
$859$	6.20711	+	10.7510i	0.211784	+	0.366820i	0.952273	−	0.305248i	$-0.0987394\pi$
$859$	6.20711	+	10.7510i	0.211784	+	0.366820i	−0.740489	+	0.672068i	$0.765406\pi$
$860$		0			0
$861$	2.58579	−	6.33386i	0.0881234	−	0.215857i
$862$		0			0
$863$	13.1924	+	22.8499i	0.449074	+	0.777819i	0.998326	−	0.0578377i	$-0.0184206\pi$
$863$	13.1924	+	22.8499i	0.449074	+	0.777819i	−0.549252	+	0.835657i	$0.685087\pi$
$864$		0			0
$865$	−1.53553	+	2.65962i	−0.0522097	+	0.0904299i
$866$		0			0
$867$	5.38478			0.182877
$868$		0			0
$869$	8.07107			0.273792
$870$		0			0
$871$	−7.37868	+	12.7802i	−0.250017	+	0.433042i
$872$		0			0
$873$	−22.3848	−	38.7716i	−0.757610	−	1.31222i
$874$		0			0
$875$	−29.6569	+	4.05845i	−1.00258	+	0.137201i
$876$		0			0
$877$	−6.64214	−	11.5045i	−0.224289	−	0.388480i	0.731817	−	0.681501i	$-0.238673\pi$
$877$	−6.64214	−	11.5045i	−0.224289	−	0.388480i	−0.956106	+	0.293021i	$0.905339\pi$
$878$		0			0
$879$	−2.72792	+	4.72490i	−0.0920105	+	0.159367i
$880$		0			0
$881$	19.8284			0.668037			0.334018	−	0.942567i	$-0.391595\pi$
$881$	19.8284			0.668037			0.334018	+	0.942567i	$0.391595\pi$
$882$		0			0
$883$	39.6690			1.33497			0.667485	−	0.744623i	$-0.267371\pi$
$883$	39.6690			1.33497			0.667485	+	0.744623i	$0.267371\pi$
$884$		0			0
$885$	1.29289	−	2.23936i	0.0434601	−	0.0752752i
$886$		0			0
$887$	15.8640	+	27.4772i	0.532660	+	0.922594i	0.999273	+	0.0381321i	$0.0121408\pi$
$887$	15.8640	+	27.4772i	0.532660	+	0.922594i	−0.466613	+	0.884462i	$0.654526\pi$
$888$		0			0
$889$	16.8137	−	2.30090i	0.563914	−	0.0771698i
$890$		0			0
$891$	−3.74264	−	6.48244i	−0.125383	−	0.217170i
$892$		0			0
$893$	6.24264	−	10.8126i	0.208902	−	0.361829i
$894$		0			0
$895$	26.7279			0.893416
$896$		0			0
$897$	−4.10051			−0.136912
$898$		0			0
$899$	4.82843	−	8.36308i	0.161037	−	0.278924i
$900$		0			0
$901$	2.58579	+	4.47871i	0.0861450	+	0.149208i
$902$		0			0
$903$	−3.31371	+	8.11689i	−0.110273	+	0.270113i
$904$		0			0
$905$	9.41421	+	16.3059i	0.312939	+	0.542026i
$906$		0			0
$907$	6.31371	−	10.9357i	0.209643	−	0.363113i	−0.741959	−	0.670445i	$-0.766103\pi$
$907$	6.31371	−	10.9357i	0.209643	−	0.363113i	0.951602	+	0.307333i	$0.0994364\pi$
$908$		0			0
$909$	21.1716			0.702217
$910$		0			0
$911$	38.4853			1.27507			0.637537	−	0.770420i	$-0.279953\pi$
$911$	38.4853			1.27507			0.637537	+	0.770420i	$0.279953\pi$
$912$		0			0
$913$	5.24264	−	9.08052i	0.173506	−	0.300521i
$914$		0			0
$915$	−2.39340	−	4.14549i	−0.0791233	−	0.137046i
$916$		0			0
$917$	7.99138	+	10.3053i	0.263899	+	0.340310i
$918$		0			0
$919$	−2.72792	−	4.72490i	−0.0899858	−	0.155860i	0.817519	−	0.575902i	$-0.195349\pi$
$919$	−2.72792	−	4.72490i	−0.0899858	−	0.155860i	−0.907505	+	0.420041i	$0.862016\pi$
$920$		0			0
$921$	1.77817	−	3.07989i	0.0585928	−	0.101486i
$922$		0			0
$923$	−10.5269			−0.346498
$924$		0			0
$925$	27.2132			0.894765
$926$		0			0
$927$	−22.4853	+	38.9456i	−0.738514	+	1.27914i
$928$		0			0
$929$	20.7132	+	35.8763i	0.679578	+	1.17706i	0.975108	+	0.221730i	$0.0711705\pi$
$929$	20.7132	+	35.8763i	0.679578	+	1.17706i	−0.295530	+	0.955334i	$0.595496\pi$
$930$		0			0
$931$	12.9289	+	12.6677i	0.423729	+	0.415168i
$932$		0			0
$933$	−5.63604	−	9.76191i	−0.184516	−	0.319590i
$934$		0			0
$935$	1.41421	−	2.44949i	0.0462497	−	0.0801069i
$936$		0			0
$937$	−21.4142			−0.699572			−0.349786	−	0.936830i	$-0.613746\pi$
$937$	−21.4142			−0.699572			−0.349786	+	0.936830i	$0.613746\pi$
$938$		0			0
$939$	3.87006			0.126295
$940$		0			0
$941$	25.4706	−	44.1163i	0.830317	−	1.43815i	−0.0674707	−	0.997721i	$-0.521493\pi$
$941$	25.4706	−	44.1163i	0.830317	−	1.43815i	0.897787	−	0.440429i	$-0.145174\pi$
$942$		0			0
$943$	−16.8995	−	29.2708i	−0.550323	−	0.953188i
$944$		0			0
$945$	−5.53553	−	7.13834i	−0.180071	−	0.232210i
$946$		0			0
$947$	−0.100505	−	0.174080i	−0.00326598	−	0.00565684i	0.864388	−	0.502826i	$-0.167706\pi$
$947$	−0.100505	−	0.174080i	−0.00326598	−	0.00565684i	−0.867654	+	0.497169i	$0.834373\pi$
$948$		0			0
$949$	3.12132	−	5.40629i	0.101322	−	0.175495i
$950$		0			0
$951$	−8.68629			−0.281672
$952$		0			0
$953$	17.6152			0.570613			0.285307	−	0.958436i	$-0.407905\pi$
$953$	17.6152			0.570613			0.285307	+	0.958436i	$0.407905\pi$
$954$		0			0
$955$	4.58579	−	7.94282i	0.148393	−	0.257023i
$956$		0			0
$957$	0.207107	+	0.358719i	0.00669481	+	0.0115958i
$958$		0			0
$959$	−17.0000	+	41.6413i	−0.548959	+	1.34467i
$960$		0			0
$961$	−31.1274	−	53.9143i	−1.00411	−	1.73917i
$962$		0			0
$963$	19.1716	−	33.2061i	0.617795	−	1.07005i
$964$		0			0
$965$	32.8284			1.05678
$966$		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
$969$	1.07107	−	1.85514i	0.0344077	−	0.0595958i
$970$		0			0
$971$	−15.1066	−	26.1654i	−0.484794	−	0.839688i	0.515053	−	0.857158i	$-0.327772\pi$
$971$	−15.1066	−	26.1654i	−0.484794	−	0.839688i	−0.999847	+	0.0174704i	$0.994439\pi$
$972$		0			0
$973$	−8.68629	+	1.18869i	−0.278470	+	0.0381077i
$974$		0			0
$975$	−1.13604	−	1.96768i	−0.0363824	−	0.0630161i
$976$		0			0
$977$	−1.51472	+	2.62357i	−0.0484601	+	0.0839354i	−0.889238	−	0.457445i	$-0.848765\pi$
$977$	−1.51472	+	2.62357i	−0.0484601	+	0.0839354i	0.840778	+	0.541380i	$0.182098\pi$
$978$		0			0
$979$	−9.17157			−0.293125
$980$		0			0
$981$	24.0000			0.766261
$982$		0			0
$983$	14.7574	−	25.5605i	0.470687	−	0.815253i	−0.528751	−	0.848777i	$-0.677340\pi$
$983$	14.7574	−	25.5605i	0.470687	−	0.815253i	0.999438	+	0.0335236i	$0.0106729\pi$
$984$		0			0
$985$	7.87868	+	13.6463i	0.251036	+	0.434806i
$986$		0			0
$987$	−5.24264	+	0.717439i	−0.166875	+	0.0228363i
$988$		0			0
$989$	21.6569	+	37.5108i	0.688648	+	1.19277i
$990$		0			0
$991$	−0.0502525	+	0.0870399i	−0.00159632	+	0.00276491i	−0.866822	−	0.498617i	$-0.833841\pi$
$991$	−0.0502525	+	0.0870399i	−0.00159632	+	0.00276491i	0.865226	+	0.501382i	$0.167175\pi$
$992$		0			0
$993$	2.23045			0.0707811
$994$		0			0
$995$	34.0000			1.07787
$996$		0			0
$997$	−20.7279	+	35.9018i	−0.656460	+	1.13702i	0.325066	+	0.945691i	$0.394614\pi$
$997$	−20.7279	+	35.9018i	−0.656460	+	1.13702i	−0.981526	+	0.191330i	$0.938720\pi$
$998$		0			0
$999$	10.9497	+	18.9655i	0.346435	+	0.600042i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.b.177.2	✓	4	7.2	even	3	inner
616.2.q.b.529.2	yes	4	1.1	even	1	trivial
1232.2.q.h.177.1		4	28.23	odd	6
1232.2.q.h.529.1		4	4.3	odd	2
4312.2.a.m.1.2		2	7.3	odd	6
4312.2.a.u.1.1		2	7.4	even	3
8624.2.a.bg.1.2		2	28.11	odd	6
8624.2.a.cd.1.1		2	28.3	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)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{3} +(-0.707107 - 1.22474i) q^{5} +(2.62132 - 0.358719i) q^{7} +(1.41421 + 2.44949i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.82843 q^{13} -0.585786 q^{15} +(1.00000 - 1.73205i) q^{17} +(1.29289 + 2.23936i) q^{19} +(0.414214 - 1.01461i) q^{21} +(-2.70711 - 4.68885i) q^{23} +(1.50000 - 2.59808i) q^{25} +2.41421 q^{27} +1.00000 q^{29} +(4.82843 - 8.36308i) q^{31} +(0.207107 + 0.358719i) q^{33} +(-2.29289 - 2.95680i) q^{35} +(4.53553 + 7.85578i) q^{37} +(0.378680 - 0.655892i) q^{39} +6.24264 q^{41} -8.00000 q^{43} +(2.00000 - 3.46410i) q^{45} +(-2.41421 - 4.18154i) q^{47} +(6.74264 - 1.88064i) q^{49} +(-0.414214 - 0.717439i) q^{51} +(-1.29289 + 2.23936i) q^{53} +1.41421 q^{55} +1.07107 q^{57} +(-2.20711 + 3.82282i) q^{59} +(4.08579 + 7.07679i) q^{61} +(4.58579 + 5.91359i) q^{63} +(-1.29289 - 2.23936i) q^{65} +(-4.03553 + 6.98975i) q^{67} -2.24264 q^{69} -5.75736 q^{71} +(1.70711 - 2.95680i) q^{73} +(-0.621320 - 1.07616i) q^{75} +(-1.00000 + 2.44949i) q^{77} +(-4.03553 - 6.98975i) q^{79} +(-3.74264 + 6.48244i) q^{81} -10.4853 q^{83} -2.82843 q^{85} +(0.207107 - 0.358719i) q^{87} +(4.58579 + 7.94282i) q^{89} +(4.79289 - 0.655892i) q^{91} +(-2.00000 - 3.46410i) q^{93} +(1.82843 - 3.16693i) q^{95} -15.8284 q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{7} - 2 q^{11} - 4 q^{13} - 8 q^{15} + 4 q^{17} + 8 q^{19} - 4 q^{21} - 8 q^{23} + 6 q^{25} + 4 q^{27} + 4 q^{29} + 8 q^{31} - 2 q^{33} - 12 q^{35} + 4 q^{37} + 10 q^{39} + 8 q^{41}+ \cdots - 52 q^{97}+O(q^{100}) \) 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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