LMFDB - Embedded newform 832.2.w.i.257.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [832,2,Mod(257,832)] 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("832.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(832, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2,0,0,0,6,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.3
Root			$1.72124 + 0.193255i$ of defining polynomial
Character	$\chi$	$=$	832.257
Dual form			832.2.w.i.641.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.693255 + 1.20075i) q^{3} -3.44247i q^{5} +(2.74922 + 1.58726i) q^{7} +(0.538796 - 0.933222i) q^{9} +(2.74922 - 1.58726i) q^{11} +(-3.59476 - 0.278764i) q^{13} +(4.13356 - 2.38651i) q^{15} +(0.886509 - 1.53548i) q^{17} +(-5.54387 - 3.20075i) q^{19} +4.40150i q^{21} +(-0.693255 - 1.20075i) q^{23} -6.85061 q^{25} +5.65362 q^{27} +(2.55596 + 4.42706i) q^{29} -1.35218i q^{31} +(3.81181 + 2.20075i) q^{33} +(5.46410 - 9.46410i) q^{35} +(9.79308 - 5.65404i) q^{37} +(-2.15736 - 4.50967i) q^{39} +(-1.96410 + 1.13397i) q^{41} +(-2.13573 + 3.69919i) q^{43} +(-3.21259 - 1.85479i) q^{45} -1.57603i q^{47} +(1.53880 + 2.66527i) q^{49} +2.45831 q^{51} -3.73869 q^{53} +(-5.46410 - 9.46410i) q^{55} -8.87574i q^{57} +(11.7118 + 6.76178i) q^{59} +(-5.40657 + 9.36446i) q^{61} +(2.96254 - 1.71042i) q^{63} +(-0.959638 + 12.3749i) q^{65} +(0.882772 - 0.509669i) q^{67} +(0.961204 - 1.66485i) q^{69} +(11.5439 + 6.66485i) q^{71} -5.33055i q^{73} +(-4.74922 - 8.22589i) q^{75} +10.0776 q^{77} +11.1521 q^{79} +(2.30301 + 3.98893i) q^{81} +14.3490i q^{83} +(-5.28584 - 3.05178i) q^{85} +(-3.54387 + 6.13815i) q^{87} +(4.00567 - 2.31268i) q^{89} +(-9.44030 - 6.47220i) q^{91} +(1.62363 - 0.937403i) q^{93} +(-11.0185 + 19.0846i) q^{95} +(-10.2385 - 5.91117i) q^{97} -3.42084i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{19} - 2 q^{23} - 20 q^{25} - 28 q^{27} + 8 q^{29} + 6 q^{33} + 16 q^{35} + 24 q^{37} + 14 q^{39} + 12 q^{41} + 6 q^{43} - 30 q^{45} + 2 q^{49}+ \cdots + 30 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 + 6 * q^7 - 6 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^19 - 2 * q^23 - 20 * q^25 - 28 * q^27 + 8 * q^29 + 6 * q^33 + 16 * q^35 + 24 * q^37 + 14 * q^39 + 12 * q^41 + 6 * q^43 - 30 * q^45 + 2 * q^49 + 68 * q^51 - 20 * q^53 - 16 * q^55 + 18 * q^59 + 4 * q^61 - 36 * q^63 + 14 * q^65 - 42 * q^67 + 18 * q^69 + 54 * q^71 - 22 * q^75 + 60 * q^77 - 16 * q^79 - 20 * q^81 - 6 * q^85 + 10 * q^87 - 18 * q^89 - 46 * q^91 - 36 * q^93 - 16 * q^95 + 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.693255	+	1.20075i	0.400251	+	0.693255i	0.993756	−	0.111576i	$-0.0355897\pi$
$3$	0.693255	+	1.20075i	0.400251	+	0.693255i	−0.593505	+	0.804830i	$0.702256\pi$
$4$		0			0
$5$		−	3.44247i		−	1.53952i	−0.638333	−	0.769760i	$-0.720376\pi$
$5$		−	3.44247i		−	1.53952i	0.638333	−	0.769760i	$-0.279624\pi$
$6$		0			0
$7$	2.74922	+	1.58726i	1.03911	+	0.599928i	0.919580	−	0.392903i	$-0.128529\pi$
$7$	2.74922	+	1.58726i	1.03911	+	0.599928i	0.119526	+	0.992831i	$0.461862\pi$
$8$		0			0
$9$	0.538796	−	0.933222i	0.179599	−	0.311074i
$10$		0			0
$11$	2.74922	−	1.58726i	0.828920	−	0.478577i	−0.0245627	−	0.999698i	$-0.507819\pi$
$11$	2.74922	−	1.58726i	0.828920	−	0.478577i	0.853483	+	0.521121i	$0.174486\pi$
$12$		0			0
$13$	−3.59476	−	0.278764i	−0.997007	−	0.0773153i
$13$	−3.59476	−	0.278764i	−0.997007	−	0.0773153i
$14$		0			0
$15$	4.13356	−	2.38651i	1.06728	−	0.616194i
$16$		0			0
$17$	0.886509	−	1.53548i	0.215010	−	0.372408i	−0.738266	−	0.674510i	$-0.764355\pi$
$17$	0.886509	−	1.53548i	0.215010	−	0.372408i	0.953276	+	0.302102i	$0.0976882\pi$
$18$		0			0
$19$	−5.54387	−	3.20075i	−1.27185	−	0.734303i	−0.296514	−	0.955029i	$-0.595824\pi$
$19$	−5.54387	−	3.20075i	−1.27185	−	0.734303i	−0.975336	+	0.220726i	$0.929157\pi$
$20$		0			0
$21$			4.40150i			0.960487i
$22$		0			0
$23$	−0.693255	−	1.20075i	−0.144554	−	0.250374i	0.784653	−	0.619936i	$-0.212841\pi$
$23$	−0.693255	−	1.20075i	−0.144554	−	0.250374i	−0.929206	+	0.369561i	$0.879508\pi$
$24$		0			0
$25$	−6.85061			−1.37012
$26$		0			0
$27$	5.65362			1.08804
$28$		0			0
$29$	2.55596	+	4.42706i	0.474630	+	0.822084i	0.999578	−	0.0290507i	$-0.00924843\pi$
$29$	2.55596	+	4.42706i	0.474630	+	0.822084i	−0.524948	+	0.851135i	$0.675915\pi$
$30$		0			0
$31$		−	1.35218i		−	0.242858i	−0.992600	−	0.121429i	$-0.961252\pi$
$31$		−	1.35218i		−	0.242858i	0.992600	−	0.121429i	$-0.0387477\pi$
$32$		0			0
$33$	3.81181	+	2.20075i	0.663552	+	0.383102i
$34$		0			0
$35$	5.46410	−	9.46410i	0.923602	−	1.59973i
$36$		0			0
$37$	9.79308	−	5.65404i	1.60997	−	0.929518i	0.620598	−	0.784129i	$-0.286890\pi$
$37$	9.79308	−	5.65404i	1.60997	−	0.929518i	0.989374	−	0.145390i	$-0.0464436\pi$
$38$		0			0
$39$	−2.15736	−	4.50967i	−0.345453	−	0.722125i
$40$		0			0
$41$	−1.96410	+	1.13397i	−0.306741	+	0.177097i	−0.645467	−	0.763788i	$-0.723337\pi$
$41$	−1.96410	+	1.13397i	−0.306741	+	0.177097i	0.338726	+	0.940885i	$0.390004\pi$
$42$		0			0
$43$	−2.13573	+	3.69919i	−0.325695	+	0.564121i	−0.981653	−	0.190677i	$-0.938932\pi$
$43$	−2.13573	+	3.69919i	−0.325695	+	0.564121i	0.655958	+	0.754798i	$0.272265\pi$
$44$		0			0
$45$	−3.21259	−	1.85479i	−0.478905	−	0.276496i
$46$		0			0
$47$		−	1.57603i		−	0.229887i	−0.993372	−	0.114944i	$-0.963331\pi$
$47$		−	1.57603i		−	0.229887i	0.993372	−	0.114944i	$-0.0366687\pi$
$48$		0			0
$49$	1.53880	+	2.66527i	0.219828	+	0.380753i
$50$		0			0
$51$	2.45831			0.344232
$52$		0			0
$53$	−3.73869			−0.513548			−0.256774	−	0.966471i	$-0.582660\pi$
$53$	−3.73869			−0.513548			−0.256774	+	0.966471i	$0.582660\pi$
$54$		0			0
$55$	−5.46410	−	9.46410i	−0.736779	−	1.27614i
$56$		0			0
$57$		−	8.87574i		−	1.17562i
$58$		0			0
$59$	11.7118	+	6.76178i	1.52474	+	0.880309i	0.999570	+	0.0293119i	$0.00933161\pi$
$59$	11.7118	+	6.76178i	1.52474	+	0.880309i	0.525170	+	0.850997i	$0.324002\pi$
$60$		0			0
$61$	−5.40657	+	9.36446i	−0.692241	+	1.19900i	0.278861	+	0.960331i	$0.410043\pi$
$61$	−5.40657	+	9.36446i	−0.692241	+	1.19900i	−0.971102	+	0.238665i	$0.923290\pi$
$62$		0			0
$63$	2.96254	−	1.71042i	0.373244	−	0.215493i
$64$		0			0
$65$	−0.959638	+	12.3749i	−0.119028	+	1.53491i
$66$		0			0
$67$	0.882772	−	0.509669i	0.107848	−	0.0622659i	−0.445106	−	0.895478i	$-0.646834\pi$
$67$	0.882772	−	0.509669i	0.107848	−	0.0622659i	0.552954	+	0.833212i	$0.313501\pi$
$68$		0			0
$69$	0.961204	−	1.66485i	0.115715	−	0.200425i
$70$		0			0
$71$	11.5439	+	6.66485i	1.37000	+	0.790973i	0.990928	−	0.134393i	$-0.0429084\pi$
$71$	11.5439	+	6.66485i	1.37000	+	0.790973i	0.379077	+	0.925365i	$0.376242\pi$
$72$		0			0
$73$		−	5.33055i		−	0.623893i	−0.950100	−	0.311947i	$-0.899019\pi$
$73$		−	5.33055i		−	0.623893i	0.950100	−	0.311947i	$-0.100981\pi$
$74$		0			0
$75$	−4.74922	−	8.22589i	−0.548392	−	0.949843i
$76$		0			0
$77$	10.0776			1.14845
$78$		0			0
$79$	11.1521			1.25470			0.627352	−	0.778736i	$-0.284139\pi$
$79$	11.1521			1.25470			0.627352	+	0.778736i	$0.284139\pi$
$80$		0			0
$81$	2.30301	+	3.98893i	0.255890	+	0.443214i
$82$		0			0
$83$			14.3490i			1.57501i	0.616307	+	0.787506i	$0.288628\pi$
$83$			14.3490i			1.57501i	−0.616307	+	0.787506i	$0.711372\pi$
$84$		0			0
$85$	−5.28584	−	3.05178i	−0.573330	−	0.331012i
$86$		0			0
$87$	−3.54387	+	6.13815i	−0.379942	+	0.658079i
$88$		0			0
$89$	4.00567	−	2.31268i	0.424601	−	0.245143i	−0.272443	−	0.962172i	$-0.587832\pi$
$89$	4.00567	−	2.31268i	0.424601	−	0.245143i	0.697044	+	0.717029i	$0.254498\pi$
$90$		0			0
$91$	−9.44030	−	6.47220i	−0.989612	−	0.678471i
$92$		0			0
$93$	1.62363	−	0.937403i	0.168362	−	0.0972041i
$94$		0			0
$95$	−11.0185	+	19.0846i	−1.13047	+	1.95804i
$96$		0			0
$97$	−10.2385	−	5.91117i	−1.03956	−	0.600189i	−0.119849	−	0.992792i	$-0.538241\pi$
$97$	−10.2385	−	5.91117i	−1.03956	−	0.600189i	−0.919708	+	0.392603i	$0.871575\pi$
$98$		0			0
$99$		−	3.42084i		−	0.343808i
$100$		0			0
$101$	−3.16945	−	5.48965i	−0.315372	−	0.546241i	0.664144	−	0.747605i	$-0.268796\pi$
$101$	−3.16945	−	5.48965i	−0.315372	−	0.546241i	−0.979517	+	0.201363i	$0.935463\pi$
$102$		0			0
$103$	−6.88494			−0.678394			−0.339197	−	0.940715i	$-0.610155\pi$
$103$	−6.88494			−0.678394			−0.339197	+	0.940715i	$0.610155\pi$
$104$		0			0
$105$	15.1521			1.47869
$106$		0			0
$107$	−0.0797637	−	0.138155i	−0.00771104	−	0.0133559i	0.862144	−	0.506663i	$-0.169121\pi$
$107$	−0.0797637	−	0.138155i	−0.00771104	−	0.0133559i	−0.869855	+	0.493307i	$0.835788\pi$
$108$		0			0
$109$			10.9282i			1.04673i	0.852108	+	0.523366i	$0.175324\pi$
$109$			10.9282i			1.04673i	−0.852108	+	0.523366i	$0.824676\pi$
$110$		0			0
$111$	13.5782	+	7.83938i	1.28879	+	0.744081i
$112$		0			0
$113$	−5.99843	+	10.3896i	−0.564285	+	0.977371i	0.432831	+	0.901475i	$0.357515\pi$
$113$	−5.99843	+	10.3896i	−0.564285	+	0.977371i	−0.997116	+	0.0758954i	$0.975819\pi$
$114$		0			0
$115$	−4.13356	+	2.38651i	−0.385456	+	0.222543i
$116$		0			0
$117$	−2.19699	+	3.20451i	−0.203112	+	0.296257i
$118$		0			0
$119$	4.87441	−	2.81424i	0.446837	−	0.257981i
$120$		0			0
$121$	−0.461204	+	0.798828i	−0.0419276	+	0.0726208i
$122$		0			0
$123$	−2.72324	−	1.57227i	−0.245547	−	0.141766i
$124$		0			0
$125$			6.37067i			0.569810i
$126$		0			0
$127$	−6.26928	−	10.8587i	−0.556309	−	0.963555i	−0.997800	−	0.0662897i	$-0.978884\pi$
$127$	−6.26928	−	10.8587i	−0.556309	−	0.963555i	0.441492	−	0.897265i	$-0.354449\pi$
$128$		0			0
$129$	−5.92241			−0.521439
$130$		0			0
$131$	−9.33891			−0.815944			−0.407972	−	0.912994i	$-0.633764\pi$
$131$	−9.33891			−0.815944			−0.407972	+	0.912994i	$0.633764\pi$
$132$		0			0
$133$	−10.1609	−	17.5991i	−0.881058	−	1.52604i
$134$		0			0
$135$		−	19.4624i		−	1.67506i
$136$		0			0
$137$	−4.46254	−	2.57645i	−0.381260	−	0.220121i	0.297106	−	0.954844i	$-0.403978\pi$
$137$	−4.46254	−	2.57645i	−0.381260	−	0.220121i	−0.678366	+	0.734724i	$0.737312\pi$
$138$		0			0
$139$	−1.59983	+	2.77098i	−0.135696	+	0.235032i	−0.925863	−	0.377859i	$-0.876660\pi$
$139$	−1.59983	+	2.77098i	−0.135696	+	0.235032i	0.790167	+	0.612891i	$0.209994\pi$
$140$		0			0
$141$	1.89242	−	1.09259i	0.159370	−	0.0920125i
$142$		0			0
$143$	−10.3252	+	4.93944i	−0.863440	+	0.413057i
$144$		0			0
$145$	15.2400	−	8.79883i	1.26561	−	0.730703i
$146$		0			0
$147$	−2.13356	+	3.69543i	−0.175973	+	0.304794i
$148$		0			0
$149$	−6.59922	−	3.81006i	−0.540629	−	0.312133i	0.204705	−	0.978824i	$-0.434377\pi$
$149$	−6.59922	−	3.81006i	−0.540629	−	0.312133i	−0.745334	+	0.666691i	$0.767710\pi$
$150$		0			0
$151$			12.5042i			1.01758i	0.860891	+	0.508790i	$0.169907\pi$
$151$			12.5042i			1.01758i	−0.860891	+	0.508790i	$0.830093\pi$
$152$		0			0
$153$	−0.955296	−	1.65462i	−0.0772311	−	0.133768i
$154$		0			0
$155$	−4.65483			−0.373885
$156$		0			0
$157$	−1.80735			−0.144242			−0.0721211	−	0.997396i	$-0.522977\pi$
$157$	−1.80735			−0.144242			−0.0721211	+	0.997396i	$0.522977\pi$
$158$		0			0
$159$	−2.59186	−	4.48923i	−0.205548	−	0.356019i
$160$		0			0
$161$		−	4.40150i		−	0.346887i
$162$		0			0
$163$	10.1790	+	5.87684i	0.797280	+	0.460310i	0.842519	−	0.538667i	$-0.181072\pi$
$163$	10.1790	+	5.87684i	0.797280	+	0.460310i	−0.0452393	+	0.998976i	$0.514405\pi$
$164$		0			0
$165$	7.57603	−	13.1221i	0.589793	−	1.02155i
$166$		0			0
$167$	−14.7492	+	8.51546i	−1.14133	+	0.658946i	−0.946759	−	0.321942i	$-0.895664\pi$
$167$	−14.7492	+	8.51546i	−1.14133	+	0.658946i	−0.194569	+	0.980889i	$0.562331\pi$
$168$		0			0
$169$	12.8446	+	2.00418i	0.988045	+	0.154168i
$170$		0			0
$171$	−5.97403	+	3.44911i	−0.456845	+	0.263760i
$172$		0			0
$173$	7.66243	−	13.2717i	0.582563	−	1.00903i	−0.412611	−	0.910907i	$-0.635383\pi$
$173$	7.66243	−	13.2717i	0.582563	−	1.00903i	0.995174	−	0.0981221i	$-0.0312836\pi$
$174$		0			0
$175$	−18.8338	−	10.8737i	−1.42370	−	0.821975i
$176$		0			0
$177$			18.7505i			1.40938i
$178$		0			0
$179$	−0.637292	−	1.10382i	−0.0476334	−	0.0825035i	0.841226	−	0.540684i	$-0.181835\pi$
$179$	−0.637292	−	1.10382i	−0.0476334	−	0.0825035i	−0.888859	+	0.458181i	$0.848501\pi$
$180$		0			0
$181$	2.41650			0.179617			0.0898085	−	0.995959i	$-0.471375\pi$
$181$	2.41650			0.179617			0.0898085	+	0.995959i	$0.471375\pi$
$182$		0			0
$183$	−14.9925			−1.10828
$184$		0			0
$185$	−19.4639	−	33.7124i	−1.43101	−	2.47859i
$186$		0			0
$187$		−	5.62849i		−	0.411596i
$188$		0			0
$189$	15.5430	+	8.97377i	1.13059	+	0.652746i
$190$		0			0
$191$	3.35435	−	5.80990i	0.242712	−	0.420390i	−0.718774	−	0.695244i	$-0.755296\pi$
$191$	3.35435	−	5.80990i	0.242712	−	0.420390i	0.961486	+	0.274854i	$0.0886296\pi$
$192$		0			0
$193$	−4.64192	+	2.68001i	−0.334132	+	0.192911i	−0.657674	−	0.753302i	$-0.728460\pi$
$193$	−4.64192	+	2.68001i	−0.334132	+	0.192911i	0.323542	+	0.946214i	$0.395126\pi$
$194$		0			0
$195$	−15.5244	+	7.42664i	−1.11173	+	0.531833i
$196$		0			0
$197$	−7.46978	+	4.31268i	−0.532199	+	0.307266i	−0.741912	−	0.670498i	$-0.766081\pi$
$197$	−7.46978	+	4.31268i	−0.532199	+	0.307266i	0.209712	+	0.977763i	$0.432747\pi$
$198$		0			0
$199$	−5.43194	+	9.40840i	−0.385060	+	0.666944i	−0.991778	−	0.127974i	$-0.959153\pi$
$199$	−5.43194	+	9.40840i	−0.385060	+	0.666944i	0.606717	+	0.794918i	$0.292486\pi$
$200$		0			0
$201$	1.22397	+	0.706660i	0.0863323	+	0.0498440i
$202$		0			0
$203$			16.2279i			1.13898i
$204$		0			0
$205$	3.90368	+	6.76136i	0.272645	+	0.472234i
$206$		0			0
$207$	−1.49409			−0.103847
$208$		0			0
$209$	−20.3217			−1.40568
$210$		0			0
$211$	−5.41867	−	9.38541i	−0.373037	−	0.646118i	0.616994	−	0.786968i	$-0.288350\pi$
$211$	−5.41867	−	9.38541i	−0.373037	−	0.646118i	−0.990031	+	0.140849i	$0.955017\pi$
$212$		0			0
$213$			18.4818i			1.26635i
$214$		0			0
$215$	12.7343	+	7.35218i	0.868475	+	0.501414i
$216$		0			0
$217$	2.14626	−	3.71743i	0.145697	−	0.252355i
$218$		0			0
$219$	6.40067	−	3.69543i	0.432517	−	0.249714i
$220$		0			0
$221$	−3.61482	+	5.27255i	−0.243159	+	0.354670i
$222$		0			0
$223$	−6.27821	+	3.62473i	−0.420420	+	0.242730i	−0.695257	−	0.718761i	$-0.744709\pi$
$223$	−6.27821	+	3.62473i	−0.420420	+	0.242730i	0.274837	+	0.961491i	$0.411376\pi$
$224$		0			0
$225$	−3.69108	+	6.39314i	−0.246072	+	0.426210i
$226$		0			0
$227$	8.31254	+	4.79925i	0.551723	+	0.318537i	0.749817	−	0.661646i	$-0.230142\pi$
$227$	8.31254	+	4.79925i	0.551723	+	0.318537i	−0.198094	+	0.980183i	$0.563475\pi$
$228$		0			0
$229$		−	2.92820i		−	0.193501i	−0.995309	−	0.0967506i	$-0.969155\pi$
$229$		−	2.92820i		−	0.193501i	0.995309	−	0.0967506i	$-0.0308449\pi$
$230$		0			0
$231$	6.98634	+	12.1007i	0.459667	+	0.796167i
$232$		0			0
$233$	13.1521			0.861620			0.430810	−	0.902443i	$-0.358228\pi$
$233$	13.1521			0.861620			0.430810	+	0.902443i	$0.358228\pi$
$234$		0			0
$235$	−5.42543			−0.353916
$236$		0			0
$237$	7.73121	+	13.3909i	0.502196	+	0.869829i
$238$		0			0
$239$			9.02686i			0.583899i	0.956434	+	0.291949i	$0.0943039\pi$
$239$			9.02686i			0.583899i	−0.956434	+	0.291949i	$0.905696\pi$
$240$		0			0
$241$	14.5846	+	8.42042i	0.939477	+	0.542407i	0.889796	−	0.456358i	$-0.150846\pi$
$241$	14.5846	+	8.42042i	0.939477	+	0.542407i	0.0496804	+	0.998765i	$0.484180\pi$
$242$		0			0
$243$	5.28729	−	9.15785i	0.339180	−	0.587476i
$244$		0			0
$245$	9.17513	−	5.29726i	0.586177	−	0.338430i
$246$		0			0
$247$	19.0366	+	13.0514i	1.21127	+	0.830438i
$248$		0			0
$249$	−17.2296	+	9.94754i	−1.09188	+	0.630400i
$250$		0			0
$251$	−14.9604	+	25.9121i	−0.944290	+	1.63556i	−0.187123	+	0.982337i	$0.559916\pi$
$251$	−14.9604	+	25.9121i	−0.944290	+	1.63556i	−0.757167	+	0.653221i	$0.773417\pi$
$252$		0			0
$253$	−3.81181	−	2.20075i	−0.239647	−	0.138360i
$254$		0			0
$255$		−	8.46265i		−	0.529952i
$256$		0			0
$257$	2.07603	+	3.59578i	0.129499	+	0.224299i	0.923483	−	0.383640i	$-0.125330\pi$
$257$	2.07603	+	3.59578i	0.129499	+	0.224299i	−0.793984	+	0.607939i	$0.791996\pi$
$258$		0			0
$259$	35.8977			2.23058
$260$		0			0
$261$	5.50857			0.340972
$262$		0			0
$263$	4.90440	+	8.49467i	0.302418	+	0.523804i	0.976683	−	0.214686i	$-0.0688727\pi$
$263$	4.90440	+	8.49467i	0.302418	+	0.523804i	−0.674265	+	0.738490i	$0.735539\pi$
$264$		0			0
$265$			12.8703i			0.790617i
$266$		0			0
$267$	5.55390	+	3.20655i	0.339893	+	0.196238i
$268$		0			0
$269$	−3.45964	+	5.99227i	−0.210938	+	0.365355i	−0.952008	−	0.306072i	$-0.900985\pi$
$269$	−3.45964	+	5.99227i	−0.210938	+	0.365355i	0.741070	+	0.671427i	$0.234318\pi$
$270$		0			0
$271$	−11.0163	+	6.36028i	−0.669194	+	0.386359i	−0.795771	−	0.605597i	$-0.792934\pi$
$271$	−11.0163	+	6.36028i	−0.669194	+	0.386359i	0.126577	+	0.991957i	$0.459601\pi$
$272$		0			0
$273$	1.22698	−	15.8223i	0.0742603	−	0.957612i
$274$		0			0
$275$	−18.8338	+	10.8737i	−1.13572	+	0.655709i
$276$		0			0
$277$	−4.09766	+	7.09735i	−0.246204	+	0.426438i	−0.962470	−	0.271390i	$-0.912517\pi$
$277$	−4.09766	+	7.09735i	−0.246204	+	0.426438i	0.716265	+	0.697828i	$0.245850\pi$
$278$		0			0
$279$	−1.26188	−	0.728548i	−0.0755469	−	0.0436170i
$280$		0			0
$281$			8.00836i			0.477739i	0.971052	+	0.238869i	$0.0767768\pi$
$281$			8.00836i			0.477739i	−0.971052	+	0.238869i	$0.923223\pi$
$282$		0			0
$283$	−11.0163	−	19.0808i	−0.654853	−	1.13424i	−0.981931	−	0.189241i	$-0.939397\pi$
$283$	−11.0163	−	19.0808i	−0.654853	−	1.13424i	0.327078	−	0.944997i	$-0.393936\pi$
$284$		0			0
$285$	−30.5545			−1.80989
$286$		0			0
$287$	−7.19966			−0.424982
$288$		0			0
$289$	6.92820	+	12.0000i	0.407541	+	0.705882i
$290$		0			0
$291$		−	16.3918i		−	0.960904i
$292$		0			0
$293$	−6.97246	−	4.02555i	−0.407336	−	0.235175i	0.282309	−	0.959324i	$-0.408900\pi$
$293$	−6.97246	−	4.02555i	−0.407336	−	0.235175i	−0.689644	+	0.724148i	$0.742233\pi$
$294$		0			0
$295$	23.2772	−	40.3174i	1.35525	−	2.34737i
$296$		0			0
$297$	15.5430	−	8.97377i	0.901898	−	0.520711i
$298$		0			0
$299$	2.15736	+	4.50967i	0.124763	+	0.260801i
$300$		0			0
$301$	−11.7431	+	6.77991i	−0.676864	+	0.390788i
$302$		0			0
$303$	4.39448	−	7.61146i	0.252456	−	0.437267i
$304$		0			0
$305$	32.2369	+	18.6120i	1.84588	+	1.06572i
$306$		0			0
$307$			16.7281i			0.954722i	0.878707	+	0.477361i	$0.158407\pi$
$307$			16.7281i			0.954722i	−0.878707	+	0.477361i	$0.841593\pi$
$308$		0			0
$309$	−4.77302	−	8.26711i	−0.271528	−	0.470299i
$310$		0			0
$311$	3.79287			0.215074			0.107537	−	0.994201i	$-0.465704\pi$
$311$	3.79287			0.215074			0.107537	+	0.994201i	$0.465704\pi$
$312$		0			0
$313$	−26.6981			−1.50907			−0.754533	−	0.656263i	$-0.772136\pi$
$313$	−26.6981			−1.50907			−0.754533	+	0.656263i	$0.772136\pi$
$314$		0			0
$315$	−5.88808	−	10.1984i	−0.331755	−	0.574617i
$316$		0			0
$317$		−	18.6378i		−	1.04680i	−0.852086	−	0.523401i	$-0.824663\pi$
$317$		−	18.6378i		−	1.04680i	0.852086	−	0.523401i	$-0.175337\pi$
$318$		0			0
$319$	14.0538	+	8.11396i	0.786861	+	0.454295i
$320$		0			0
$321$	0.110593	−	0.191553i	0.00617270	−	0.0106914i
$322$		0			0
$323$	−9.82937	+	5.67499i	−0.546921	+	0.315765i
$324$		0			0
$325$	24.6263	+	1.90971i	1.36602	+	0.105931i
$326$		0			0
$327$	−13.1221	+	7.57603i	−0.725652	+	0.418955i
$328$		0			0
$329$	2.50157	−	4.33284i	0.137916	−	0.238877i
$330$		0			0
$331$	11.5179	+	6.64986i	0.633081	+	0.365509i	0.781944	−	0.623348i	$-0.214228\pi$
$331$	11.5179	+	6.64986i	0.633081	+	0.365509i	−0.148864	+	0.988858i	$0.547562\pi$
$332$		0			0
$333$		−	12.1855i		−	0.667761i
$334$		0			0
$335$	−1.75452	−	3.03892i	−0.0958597	−	0.166034i
$336$		0			0
$337$	−20.6174			−1.12310			−0.561550	−	0.827443i	$-0.689795\pi$
$337$	−20.6174			−1.12310			−0.561550	+	0.827443i	$0.689795\pi$
$338$		0			0
$339$	−16.6338			−0.903422
$340$		0			0
$341$	−2.14626	−	3.71743i	−0.116226	−	0.201310i
$342$		0			0
$343$		−	12.4518i		−	0.672332i
$344$		0			0
$345$	−5.73121	−	3.30892i	−0.308558	−	0.178146i
$346$		0			0
$347$	5.30675	−	9.19155i	0.284881	−	0.493428i	−0.687699	−	0.725996i	$-0.741379\pi$
$347$	5.30675	−	9.19155i	0.284881	−	0.493428i	0.972580	+	0.232567i	$0.0747126\pi$
$348$		0			0
$349$	−10.4164	+	6.01390i	−0.557576	+	0.321917i	−0.752172	−	0.658967i	$-0.770994\pi$
$349$	−10.4164	+	6.01390i	−0.557576	+	0.321917i	0.194596	+	0.980883i	$0.437660\pi$
$350$		0			0
$351$	−20.3234	−	1.57603i	−1.08478	−	0.0841221i
$352$		0			0
$353$	20.7265	−	11.9665i	1.10316	−	0.636910i	0.166112	−	0.986107i	$-0.446879\pi$
$353$	20.7265	−	11.9665i	1.10316	−	0.636910i	0.937049	+	0.349197i	$0.113545\pi$
$354$		0			0
$355$	22.9436	−	39.7394i	1.21772	−	2.10915i
$356$		0			0
$357$	6.75842	+	3.90197i	0.357693	+	0.206514i
$358$		0			0
$359$		−	0.104919i		−	0.00553740i	−0.999996	−	0.00276870i	$-0.999119\pi$
$359$		−	0.104919i		−	0.00553740i	0.999996	−	0.00276870i	$-0.000881306\pi$
$360$		0			0
$361$	10.9896	+	19.0346i	0.578401	+	1.00182i
$362$		0			0
$363$	−1.27893			−0.0671262
$364$		0			0
$365$	−18.3503			−0.960496
$366$		0			0
$367$	−6.07542	−	10.5229i	−0.317134	−	0.549293i	0.662754	−	0.748837i	$-0.269387\pi$
$367$	−6.07542	−	10.5229i	−0.317134	−	0.549293i	−0.979889	+	0.199544i	$0.936054\pi$
$368$		0			0
$369$			2.44393i			0.127226i
$370$		0			0
$371$	−10.2785	−	5.93427i	−0.533631	−	0.308092i
$372$		0			0
$373$	17.0602	−	29.5491i	0.883343	−	1.53000i	0.0357425	−	0.999361i	$-0.488620\pi$
$373$	17.0602	−	29.5491i	0.883343	−	1.53000i	0.847601	−	0.530634i	$-0.178046\pi$
$374$		0			0
$375$	−7.64960	+	4.41650i	−0.395024	+	0.228067i
$376$		0			0
$377$	−7.95396	−	16.6267i	−0.409650	−	0.856319i
$378$		0			0
$379$	28.2719	−	16.3228i	1.45223	−	0.838447i	0.453624	−	0.891193i	$-0.350131\pi$
$379$	28.2719	−	16.3228i	1.45223	−	0.838447i	0.998608	+	0.0527463i	$0.0167975\pi$
$380$		0			0
$381$	8.69242	−	15.0557i	0.445326	−	0.771327i
$382$		0			0
$383$	26.6743	+	15.4004i	1.36299	+	0.786924i	0.990021	−	0.140919i	$-0.0450056\pi$
$383$	26.6743	+	15.4004i	1.36299	+	0.786924i	0.372971	+	0.927843i	$0.378339\pi$
$384$		0			0
$385$		−	34.6918i		−	1.76806i
$386$		0			0
$387$	2.30144	+	3.98622i	0.116989	+	0.202631i
$388$		0			0
$389$	−1.41963			−0.0719782			−0.0359891	−	0.999352i	$-0.511458\pi$
$389$	−1.41963			−0.0719782			−0.0359891	+	0.999352i	$0.511458\pi$
$390$		0			0
$391$	−2.45831			−0.124322
$392$		0			0
$393$	−6.47424	−	11.2137i	−0.326582	−	0.565657i
$394$		0			0
$395$		−	38.3906i		−	1.93164i
$396$		0			0
$397$	18.0400	+	10.4154i	0.905402	+	0.522734i	0.878949	−	0.476916i	$-0.158245\pi$
$397$	18.0400	+	10.4154i	0.905402	+	0.522734i	0.0264531	+	0.999650i	$0.491579\pi$
$398$		0			0
$399$	14.0881	−	24.4013i	0.705288	−	1.22160i
$400$		0			0
$401$	7.26868	−	4.19657i	0.362980	−	0.209567i	−0.307407	−	0.951578i	$-0.599461\pi$
$401$	7.26868	−	4.19657i	0.362980	−	0.209567i	0.670387	+	0.742011i	$0.266128\pi$
$402$		0			0
$403$	−0.376938	+	4.86075i	−0.0187766	+	0.242131i
$404$		0			0
$405$	13.7318	−	7.92804i	0.682337	−	0.393948i
$406$		0			0
$407$	17.9489	−	31.0884i	0.889693	−	1.54099i
$408$		0			0
$409$	−4.71684	−	2.72327i	−0.233233	−	0.134657i	0.378830	−	0.925466i	$-0.376327\pi$
$409$	−4.71684	−	2.72327i	−0.233233	−	0.134657i	−0.612063	+	0.790809i	$0.709660\pi$
$410$		0			0
$411$		−	7.14453i		−	0.352414i
$412$		0			0
$413$	21.4654	+	37.1792i	1.05624	+	1.82947i
$414$		0			0
$415$	49.3962			2.42476
$416$		0			0
$417$	−4.43635			−0.217249
$418$		0			0
$419$	6.22602	+	10.7838i	0.304161	+	0.526822i	0.977074	−	0.212899i	$-0.0682906\pi$
$419$	6.22602	+	10.7838i	0.304161	+	0.526822i	−0.672913	+	0.739721i	$0.734957\pi$
$420$		0			0
$421$			18.7584i			0.914228i	0.889408	+	0.457114i	$0.151117\pi$
$421$			18.7584i			0.914228i	−0.889408	+	0.457114i	$0.848883\pi$
$422$		0			0
$423$	−1.47078	−	0.849157i	−0.0715119	−	0.0412874i
$424$		0			0
$425$	−6.07313	+	10.5190i	−0.294590	+	0.510245i
$426$		0			0
$427$	−29.7277	+	17.1633i	−1.43862	+	0.830590i
$428$		0			0
$429$	−13.0891	−	8.97377i	−0.631946	−	0.433258i
$430$		0			0
$431$	−14.9431	+	8.62739i	−0.719783	+	0.415567i	−0.814673	−	0.579921i	$-0.803083\pi$
$431$	−14.9431	+	8.62739i	−0.719783	+	0.415567i	0.0948900	+	0.995488i	$0.469750\pi$
$432$		0			0
$433$	8.96097	−	15.5209i	0.430637	−	0.745885i	−0.566292	−	0.824205i	$-0.691622\pi$
$433$	8.96097	−	15.5209i	0.430637	−	0.745885i	0.996928	+	0.0783203i	$0.0249557\pi$
$434$		0			0
$435$	21.1304	+	12.1997i	1.01313	+	0.584929i
$436$		0			0
$437$			8.87574i			0.424584i
$438$		0			0
$439$	−13.7550	−	23.8244i	−0.656491	−	1.13708i	−0.981518	−	0.191371i	$-0.938707\pi$
$439$	−13.7550	−	23.8244i	−0.656491	−	1.13708i	0.325027	−	0.945705i	$-0.394627\pi$
$440$		0			0
$441$	3.31639			0.157923
$442$		0			0
$443$	−0.223850			−0.0106354			−0.00531772	−	0.999986i	$-0.501693\pi$
$443$	−0.223850			−0.0106354			−0.00531772	+	0.999986i	$0.501693\pi$
$444$		0			0
$445$	−7.96133	−	13.7894i	−0.377403	−	0.653681i
$446$		0			0
$447$		−	10.5654i		−	0.499725i
$448$		0			0
$449$	−24.3636	−	14.0664i	−1.14979	−	0.663832i	−0.200955	−	0.979600i	$-0.564405\pi$
$449$	−24.3636	−	14.0664i	−1.14979	−	0.663832i	−0.948836	+	0.315768i	$0.897738\pi$
$450$		0			0
$451$	−3.59983	+	6.23508i	−0.169509	+	0.293599i
$452$		0			0
$453$	−15.0145	+	8.66861i	−0.705442	+	0.407287i
$454$		0			0
$455$	−22.2804	+	32.4980i	−1.04452	+	1.52353i
$456$		0			0
$457$	−7.22976	+	4.17410i	−0.338194	+	0.195256i	−0.659473	−	0.751728i	$-0.729221\pi$
$457$	−7.22976	+	4.17410i	−0.338194	+	0.195256i	0.321279	+	0.946985i	$0.395887\pi$
$458$		0			0
$459$	5.01198	−	8.68101i	0.233939	−	0.405195i
$460$		0			0
$461$	−10.5260	−	6.07717i	−0.490243	−	0.283042i	0.234432	−	0.972133i	$-0.424677\pi$
$461$	−10.5260	−	6.07717i	−0.490243	−	0.283042i	−0.724675	+	0.689090i	$0.758010\pi$
$462$		0			0
$463$			30.3490i			1.41044i	0.708989	+	0.705220i	$0.249152\pi$
$463$			30.3490i			1.41044i	−0.708989	+	0.705220i	$0.750848\pi$
$464$		0			0
$465$	−3.22698	−	5.58930i	−0.149648	−	0.259197i
$466$		0			0
$467$	35.7902			1.65617			0.828086	−	0.560602i	$-0.189430\pi$
$467$	35.7902			1.65617			0.828086	+	0.560602i	$0.189430\pi$
$468$		0			0
$469$	3.23591			0.149420
$470$		0			0
$471$	−1.25295	−	2.17018i	−0.0577331	−	0.0999966i
$472$		0			0
$473$			13.5598i			0.623481i
$474$		0			0
$475$	37.9789	+	21.9271i	1.74259	+	1.00608i
$476$		0			0
$477$	−2.01439	+	3.48903i	−0.0922326	+	0.159752i
$478$		0			0
$479$	14.7003	−	8.48720i	0.671672	−	0.387790i	−0.125038	−	0.992152i	$-0.539905\pi$
$479$	14.7003	−	8.48720i	0.671672	−	0.387790i	0.796710	+	0.604362i	$0.206572\pi$
$480$		0			0
$481$	−36.7799	+	17.5949i	−1.67702	+	0.802260i
$482$		0			0
$483$	5.28512	−	3.05136i	0.240481	−	0.138842i
$484$		0			0
$485$	−20.3490	+	35.2456i	−0.924003	+	1.60042i
$486$		0			0
$487$	7.19347	+	4.15315i	0.325967	+	0.188197i	0.654049	−	0.756452i	$-0.273069\pi$
$487$	7.19347	+	4.15315i	0.325967	+	0.188197i	−0.328082	+	0.944649i	$0.606402\pi$
$488$		0			0
$489$			16.2966i			0.736957i
$490$		0			0
$491$	19.5249	+	33.8181i	0.881146	+	1.52619i	0.850068	+	0.526673i	$0.176561\pi$
$491$	19.5249	+	33.8181i	0.881146	+	1.52619i	0.0310786	+	0.999517i	$0.490106\pi$
$492$		0			0
$493$	9.06354			0.408201
$494$		0			0
$495$	−11.7762			−0.529299
$496$		0			0
$497$	21.1577	+	36.6463i	0.949054	+	1.64381i
$498$		0			0
$499$		−	32.7546i		−	1.46630i	−0.680068	−	0.733149i	$-0.738050\pi$
$499$		−	32.7546i		−	1.46630i	0.680068	−	0.733149i	$-0.261950\pi$
$500$		0			0
$501$	−20.4499	−	11.8068i	−0.913635	−	0.527488i
$502$		0			0
$503$	−5.06827	+	8.77850i	−0.225983	+	0.391414i	−0.956614	−	0.291359i	$-0.905893\pi$
$503$	−5.06827	+	8.77850i	−0.225983	+	0.391414i	0.730631	+	0.682773i	$0.239226\pi$
$504$		0			0
$505$	−18.8980	+	10.9108i	−0.840949	+	0.485522i
$506$		0			0
$507$	6.49804	+	16.8126i	0.288588	+	0.746672i
$508$		0			0
$509$	35.9478	−	20.7545i	1.59336	−	0.919926i	0.600633	−	0.799525i	$-0.294915\pi$
$509$	35.9478	−	20.7545i	1.59336	−	0.919926i	0.992725	−	0.120401i	$-0.0384180\pi$
$510$		0			0
$511$	8.46097	−	14.6548i	0.374291	−	0.648291i
$512$		0			0
$513$	−31.3429	−	18.0958i	−1.38382	−	0.798951i
$514$		0			0
$515$			23.7012i			1.04440i
$516$		0			0
$517$	−2.50157	−	4.33284i	−0.110019	−	0.190558i
$518$		0			0
$519$	21.2480			0.932686
$520$		0			0
$521$	38.8591			1.70245			0.851223	−	0.524804i	$-0.175861\pi$
$521$	38.8591			1.70245			0.851223	+	0.524804i	$0.175861\pi$
$522$		0			0
$523$	−14.1701	−	24.5433i	−0.619613	−	1.07320i	−0.989556	−	0.144147i	$-0.953956\pi$
$523$	−14.1701	−	24.5433i	−0.619613	−	1.07320i	0.369943	−	0.929055i	$-0.379377\pi$
$524$		0			0
$525$		−	30.1530i		−	1.31598i
$526$		0			0
$527$	−2.07624	−	1.19872i	−0.0904424	−	0.0522169i
$528$		0			0
$529$	10.5388	−	18.2537i	0.458209	−	0.793640i
$530$		0			0
$531$	12.6205	−	7.28645i	0.547683	−	0.316205i
$532$		0			0
$533$	7.37658	−	3.52884i	0.319515	−	0.152851i
$534$		0			0
$535$	−0.475594	+	0.274584i	−0.0205617	+	0.0118713i
$536$		0			0
$537$	0.883611	−	1.53046i	0.0381306	−	0.0660442i
$538$		0			0
$539$	8.46097	+	4.88494i	0.364440	+	0.210409i
$540$		0			0
$541$		−	34.4879i		−	1.48275i	−0.671090	−	0.741376i	$-0.734174\pi$
$541$		−	34.4879i		−	1.48275i	0.671090	−	0.741376i	$-0.265826\pi$
$542$		0			0
$543$	1.67525	+	2.90162i	0.0718918	+	0.124520i
$544$		0			0
$545$	37.6200			1.61147
$546$		0			0
$547$	−27.7469			−1.18637			−0.593186	−	0.805065i	$-0.702130\pi$
$547$	−27.7469			−1.18637			−0.593186	+	0.805065i	$0.702130\pi$
$548$		0			0
$549$	5.82608	+	10.0911i	0.248651	+	0.430676i
$550$		0			0
$551$		−	32.7240i		−	1.39409i
$552$		0			0
$553$	30.6594	+	17.7012i	1.30377	+	0.752733i
$554$		0			0
$555$	26.9868	−	46.7426i	1.14553	−	1.98411i
$556$		0			0
$557$	−12.1511	+	7.01541i	−0.514857	+	0.297253i	−0.734828	−	0.678254i	$-0.762737\pi$
$557$	−12.1511	+	7.01541i	−0.514857	+	0.297253i	0.219971	+	0.975506i	$0.429404\pi$
$558$		0			0
$559$	8.70862	−	12.7023i	0.368335	−	0.537251i
$560$		0			0
$561$	6.75842	−	3.90197i	0.285341	−	0.164741i
$562$		0			0
$563$	−20.8268	+	36.0731i	−0.877745	+	1.52030i	−0.0239362	+	0.999713i	$0.507620\pi$
$563$	−20.8268	+	36.0731i	−0.877745	+	1.52030i	−0.853809	+	0.520586i	$0.825713\pi$
$564$		0			0
$565$	35.7659	+	20.6494i	1.50468	+	0.868728i
$566$		0			0
$567$			14.6219i			0.614062i
$568$		0			0
$569$	−18.0801	−	31.3157i	−0.757959	−	1.31282i	−0.943890	−	0.330260i	$-0.892864\pi$
$569$	−18.0801	−	31.3157i	−0.757959	−	1.31282i	0.185931	−	0.982563i	$-0.440470\pi$
$570$		0			0
$571$	−23.1786			−0.969994			−0.484997	−	0.874516i	$-0.661179\pi$
$571$	−23.1786			−0.969994			−0.484997	+	0.874516i	$0.661179\pi$
$572$		0			0
$573$	9.30167			0.388583
$574$		0			0
$575$	4.74922	+	8.22589i	0.198056	+	0.343043i
$576$		0			0
$577$			2.75597i			0.114733i	0.998353	+	0.0573663i	$0.0182703\pi$
$577$			2.75597i			0.114733i	−0.998353	+	0.0573663i	$0.981730\pi$
$578$		0			0
$579$	−6.43606	−	3.71586i	−0.267473	−	0.154426i
$580$		0			0
$581$	−22.7757	+	39.4486i	−0.944895	+	1.63661i
$582$		0			0
$583$	−10.2785	+	5.93427i	−0.425690	+	0.245772i
$584$		0			0
$585$	11.0314	+	7.56308i	0.456094	+	0.312695i
$586$		0			0
$587$	−13.9789	+	8.07070i	−0.576969	+	0.333113i	−0.759928	−	0.650007i	$-0.774766\pi$
$587$	−13.9789	+	8.07070i	−0.576969	+	0.333113i	0.182959	+	0.983121i	$0.441433\pi$
$588$		0			0
$589$	−4.32798	+	7.49628i	−0.178331	+	0.308879i
$590$		0			0
$591$	−10.3569	−	5.97957i	−0.426026	−	0.245966i
$592$		0			0
$593$		−	13.0028i		−	0.533961i	−0.963702	−	0.266981i	$-0.913974\pi$
$593$		−	13.0028i		−	0.533961i	0.963702	−	0.266981i	$-0.0860260\pi$
$594$		0			0
$595$	−9.68795	−	16.7800i	−0.397167	−	0.687914i
$596$		0			0
$597$	−15.0629			−0.616482
$598$		0			0
$599$	9.58930			0.391808			0.195904	−	0.980623i	$-0.437236\pi$
$599$	9.58930			0.391808			0.195904	+	0.980623i	$0.437236\pi$
$600$		0			0
$601$	10.4758	+	18.1446i	0.427317	+	0.740135i	0.996634	−	0.0819835i	$-0.0261255\pi$
$601$	10.4758	+	18.1446i	0.427317	+	0.740135i	−0.569317	+	0.822118i	$0.692792\pi$
$602$		0			0
$603$		−	1.09843i		−	0.0447315i
$604$		0			0
$605$	2.74994	+	1.58768i	0.111801	+	0.0645484i
$606$		0			0
$607$	−3.76772	+	6.52587i	−0.152927	+	0.264877i	−0.932302	−	0.361680i	$-0.882203\pi$
$607$	−3.76772	+	6.52587i	−0.152927	+	0.264877i	0.779375	+	0.626557i	$0.215537\pi$
$608$		0			0
$609$	−19.4857	+	11.2501i	−0.789601	+	0.455876i
$610$		0			0
$611$	−0.439340	+	5.66544i	−0.0177738	+	0.229199i
$612$		0			0
$613$	−6.77010	+	3.90872i	−0.273442	+	0.157872i	−0.630451	−	0.776229i	$-0.717130\pi$
$613$	−6.77010	+	3.90872i	−0.273442	+	0.157872i	0.357009	+	0.934101i	$0.383797\pi$
$614$		0			0
$615$	−5.41248	+	9.37469i	−0.218252	+	0.378024i
$616$		0			0
$617$	9.26409	+	5.34863i	0.372958	+	0.215328i	0.674750	−	0.738046i	$-0.264251\pi$
$617$	9.26409	+	5.34863i	0.372958	+	0.215328i	−0.301792	+	0.953374i	$0.597585\pi$
$618$		0			0
$619$		−	2.18518i		−	0.0878296i	−0.999035	−	0.0439148i	$-0.986017\pi$
$619$		−	2.18518i		−	0.0878296i	0.999035	−	0.0439148i	$-0.0139830\pi$
$620$		0			0
$621$	−3.91940	−	6.78860i	−0.157280	−	0.272417i
$622$		0			0
$623$	14.6833			0.588274
$624$		0			0
$625$	−12.3222			−0.492887
$626$		0			0
$627$	−14.0881	−	24.4013i	−0.562625	−	0.974496i
$628$		0			0
$629$		−	20.0494i		−	0.799423i
$630$		0			0
$631$	−11.3010	−	6.52466i	−0.449888	−	0.259743i	0.257895	−	0.966173i	$-0.416971\pi$
$631$	−11.3010	−	6.52466i	−0.449888	−	0.259743i	−0.707783	+	0.706430i	$0.750304\pi$
$632$		0			0
$633$	7.51304	−	13.0130i	0.298616	−	0.517219i
$634$		0			0
$635$	−37.3808	+	21.5818i	−1.48341	+	0.856448i
$636$		0			0
$637$	−4.78862	−	10.0100i	−0.189732	−	0.396610i
$638$		0			0
$639$	12.4396	−	7.18200i	0.492102	−	0.284115i
$640$		0			0
$641$	−1.43255	+	2.48124i	−0.0565821	+	0.0980032i	−0.892929	−	0.450197i	$-0.851354\pi$
$641$	−1.43255	+	2.48124i	−0.0565821	+	0.0980032i	0.836347	+	0.548201i	$0.184687\pi$
$642$		0			0
$643$	−29.4589	−	17.0081i	−1.16175	−	0.670734i	−0.210024	−	0.977696i	$-0.567354\pi$
$643$	−29.4589	−	17.0081i	−1.16175	−	0.670734i	−0.951722	+	0.306962i	$0.900687\pi$
$644$		0			0
$645$			20.3877i			0.802766i
$646$		0			0
$647$	4.58399	+	7.93971i	0.180215	+	0.312142i	0.941954	−	0.335742i	$-0.108987\pi$
$647$	4.58399	+	7.93971i	0.180215	+	0.312142i	−0.761738	+	0.647885i	$0.775654\pi$
$648$		0			0
$649$	42.9309			1.68518
$650$		0			0
$651$	5.95161			0.233262
$652$		0			0
$653$	6.46543	+	11.1985i	0.253012	+	0.438230i	0.964354	−	0.264617i	$-0.0852455\pi$
$653$	6.46543	+	11.1985i	0.253012	+	0.438230i	−0.711342	+	0.702846i	$0.751912\pi$
$654$		0			0
$655$			32.1489i			1.25616i
$656$		0			0
$657$	−4.97459	−	2.87208i	−0.194077	−	0.112050i
$658$		0			0
$659$	22.6056	−	39.1541i	0.880590	−	1.52523i	0.0299039	−	0.999553i	$-0.490480\pi$
$659$	22.6056	−	39.1541i	0.880590	−	1.52523i	0.850686	−	0.525674i	$-0.176187\pi$
$660$		0			0
$661$	−15.4709	+	8.93213i	−0.601748	+	0.347419i	−0.769729	−	0.638371i	$-0.779609\pi$
$661$	−15.4709	+	8.93213i	−0.601748	+	0.347419i	0.167981	+	0.985790i	$0.446275\pi$
$662$		0			0
$663$	−8.83702	−	0.685288i	−0.343201	−	0.0266144i
$664$		0			0
$665$	−60.5845	+	34.9785i	−2.34937	+	1.35641i
$666$		0			0
$667$	3.54387	−	6.13815i	0.137219	−	0.237670i
$668$		0			0
$669$	−8.70479	−	5.02571i	−0.336547	−	0.194305i
$670$		0			0
$671$			34.3266i			1.32516i
$672$		0			0
$673$	−15.9165	−	27.5682i	−0.613536	−	1.06268i	−0.990639	−	0.136504i	$-0.956413\pi$
$673$	−15.9165	−	27.5682i	−0.613536	−	1.06268i	0.377104	−	0.926171i	$-0.376920\pi$
$674$		0			0
$675$	−38.7307			−1.49075
$676$		0			0
$677$	−13.6123			−0.523162			−0.261581	−	0.965181i	$-0.584244\pi$
$677$	−13.6123			−0.523162			−0.261581	+	0.965181i	$0.584244\pi$
$678$		0			0
$679$	−18.7652	−	32.5022i	−0.720140	−	1.24732i
$680$		0			0
$681$			13.3084i			0.509979i
$682$		0			0
$683$	−7.62925	−	4.40475i	−0.291925	−	0.168543i	0.346885	−	0.937908i	$-0.387240\pi$
$683$	−7.62925	−	4.40475i	−0.291925	−	0.168543i	−0.638810	+	0.769365i	$0.720573\pi$
$684$		0			0
$685$	−8.86934	+	15.3622i	−0.338880	+	0.586958i
$686$		0			0
$687$	3.51605	−	2.02999i	0.134146	−	0.0774490i
$688$		0			0
$689$	13.4397	+	1.04221i	0.512011	+	0.0397051i
$690$		0			0
$691$	−17.3881	+	10.0390i	−0.661475	+	0.381903i	−0.792839	−	0.609431i	$-0.791398\pi$
$691$	−17.3881	+	10.0390i	−0.661475	+	0.381903i	0.131364	+	0.991334i	$0.458064\pi$
$692$		0			0
$693$	5.42977	−	9.40464i	0.206260	−	0.357253i
$694$		0			0
$695$	9.53903	+	5.50736i	0.361836	+	0.208906i
$696$		0			0
$697$			4.02112i			0.152311i
$698$		0			0
$699$	9.11772	+	15.7924i	0.344864	+	0.597322i
$700$		0			0
$701$	48.6918			1.83906			0.919532	−	0.393014i	$-0.128568\pi$
$701$	48.6918			1.83906			0.919532	+	0.393014i	$0.128568\pi$
$702$		0			0
$703$	−72.3887			−2.73019
$704$		0			0
$705$	−3.76120	−	6.51459i	−0.141655	−	0.245354i
$706$		0			0
$707$		−	20.1230i		−	0.756803i
$708$		0			0
$709$	1.47403	+	0.851030i	0.0553583	+	0.0319611i	0.527424	−	0.849602i	$-0.323158\pi$
$709$	1.47403	+	0.851030i	0.0553583	+	0.0319611i	−0.472065	+	0.881564i	$0.656491\pi$
$710$		0			0
$711$	6.00868	−	10.4073i	0.225343	−	0.390306i
$712$		0			0
$713$	−1.62363	+	0.937403i	−0.0608054	+	0.0351060i
$714$		0			0
$715$	17.0039	+	35.5444i	0.635909	+	1.32928i
$716$		0			0
$717$	−10.8390	+	6.25791i	−0.404791	+	0.233706i
$718$		0			0
$719$	−5.67742	+	9.83358i	−0.211732	+	0.366731i	−0.952257	−	0.305299i	$-0.901244\pi$
$719$	−5.67742	+	9.83358i	−0.211732	+	0.366731i	0.740525	+	0.672029i	$0.234577\pi$
$720$		0			0
$721$	−18.9282	−	10.9282i	−0.704923	−	0.406988i
$722$		0			0
$723$			23.3500i			0.868395i
$724$		0			0
$725$	−17.5099	−	30.3280i	−0.650302	−	1.12636i
$726$		0			0
$727$	14.9882			0.555881			0.277940	−	0.960598i	$-0.410348\pi$
$727$	14.9882			0.555881			0.277940	+	0.960598i	$0.410348\pi$
$728$		0			0
$729$	28.4798			1.05481
$730$		0			0
$731$	3.78668	+	6.55872i	0.140055	+	0.242583i
$732$		0			0
$733$		−	35.0688i		−	1.29529i	−0.761940	−	0.647647i	$-0.775753\pi$
$733$		−	35.0688i		−	1.29529i	0.761940	−	0.647647i	$-0.224247\pi$
$734$		0			0
$735$	12.7214	+	7.34470i	0.469236	+	0.270913i
$736$		0			0
$737$	1.61795	−	2.80238i	0.0595981	−	0.103227i
$738$		0			0
$739$	−27.8353	+	16.0707i	−1.02394	+	0.591170i	−0.915242	−	0.402905i	$-0.868001\pi$
$739$	−27.8353	+	16.0707i	−1.02394	+	0.591170i	−0.108695	+	0.994075i	$0.534667\pi$
$740$		0			0
$741$	−2.47424	+	31.9062i	−0.0908935	+	1.17210i
$742$		0			0
$743$	−17.2332	+	9.94958i	−0.632224	+	0.365015i	−0.781613	−	0.623764i	$-0.785603\pi$
$743$	−17.2332	+	9.94958i	−0.632224	+	0.365015i	0.149389	+	0.988778i	$0.452269\pi$
$744$		0			0
$745$	−13.1160	+	22.7176i	−0.480534	+	0.832310i
$746$		0			0
$747$	13.3909	+	7.73121i	0.489946	+	0.282870i
$748$		0			0
$749$		−	0.506423i		−	0.0185043i
$750$		0			0
$751$	−12.0608	−	20.8899i	−0.440105	−	0.762284i	0.557592	−	0.830115i	$-0.311725\pi$
$751$	−12.0608	−	20.8899i	−0.440105	−	0.762284i	−0.997697	+	0.0678313i	$0.978392\pi$
$752$		0			0
$753$	−41.4854			−1.51181
$754$		0			0
$755$	43.0455			1.56658
$756$		0			0
$757$	1.38205	+	2.39377i	0.0502313	+	0.0870031i	0.890048	−	0.455867i	$-0.150671\pi$
$757$	1.38205	+	2.39377i	0.0502313	+	0.0870031i	−0.839816	+	0.542870i	$0.817337\pi$
$758$		0			0
$759$		−	6.10273i		−	0.221515i
$760$		0			0
$761$	−3.86287	−	2.23023i	−0.140029	−	0.0808457i	0.428349	−	0.903613i	$-0.359095\pi$
$761$	−3.86287	−	2.23023i	−0.140029	−	0.0808457i	−0.568378	+	0.822768i	$0.692429\pi$
$762$		0			0
$763$	−17.3459	+	30.0440i	−0.627964	+	1.08767i
$764$		0			0
$765$	−5.69598	+	3.28858i	−0.205939	+	0.118899i
$766$		0			0
$767$	−40.2160	−	27.5718i	−1.45211	−	0.995560i
$768$		0			0
$769$	27.7369	−	16.0139i	1.00022	−	0.577476i	0.0919050	−	0.995768i	$-0.470704\pi$
$769$	27.7369	−	16.0139i	1.00022	−	0.577476i	0.908313	+	0.418292i	$0.137371\pi$
$770$		0			0
$771$	−2.87843	+	4.98559i	−0.103664	+	0.179552i
$772$		0			0
$773$	21.8277	+	12.6023i	0.785090	+	0.453272i	0.838231	−	0.545315i	$-0.183590\pi$
$773$	21.8277	+	12.6023i	0.785090	+	0.453272i	−0.0531414	+	0.998587i	$0.516923\pi$
$774$		0			0
$775$			9.26324i			0.332745i
$776$		0			0
$777$	24.8863	+	43.1043i	0.892790	+	1.54636i
$778$		0			0
$779$	14.5183			0.520172
$780$		0			0
$781$	42.3155			1.51417
$782$		0			0
$783$	14.4504	+	25.0289i	0.516417	+	0.894460i
$784$		0			0
$785$			6.22175i			0.222064i
$786$		0			0
$787$	33.0239	+	19.0664i	1.17717	+	0.679642i	0.955359	−	0.295446i	$-0.0954684\pi$
$787$	33.0239	+	19.0664i	1.17717	+	0.679642i	0.221816	+	0.975089i	$0.428802\pi$
$788$		0			0
$789$	−6.80000	+	11.7779i	−0.242086	+	0.419306i
$790$		0			0
$791$	−32.9820	+	19.0422i	−1.17270	+	0.677061i
$792$		0			0
$793$	22.0458	−	32.1558i	0.782869	−	1.14189i
$794$		0			0
$795$	−15.4541	+	8.92241i	−0.548099	+	0.316445i
$796$		0			0
$797$	−2.65663	+	4.60142i	−0.0941026	+	0.162991i	−0.909234	−	0.416286i	$-0.863332\pi$
$797$	−2.65663	+	4.60142i	−0.0941026	+	0.162991i	0.815131	+	0.579277i	$0.196665\pi$
$798$		0			0
$799$	−2.41996	−	1.39716i	−0.0856119	−	0.0494280i
$800$		0			0
$801$		−	4.98425i		−	0.176110i
$802$		0			0
$803$	−8.46097	−	14.6548i	−0.298581	−	0.517158i
$804$		0			0
$805$	−15.1521			−0.534040
$806$		0			0
$807$	−9.59364			−0.337712
$808$		0			0
$809$	8.58773	+	14.8744i	0.301929	+	0.522956i	0.976573	−	0.215188i	$-0.0690363\pi$
$809$	8.58773	+	14.8744i	0.301929	+	0.522956i	−0.674644	+	0.738143i	$0.735703\pi$
$810$		0			0
$811$			12.7281i			0.446943i	0.974710	+	0.223472i	$0.0717390\pi$
$811$			12.7281i			0.446943i	−0.974710	+	0.223472i	$0.928261\pi$
$812$		0			0
$813$	−15.2742	−	8.81859i	−0.535691	−	0.309281i
$814$		0			0
$815$	20.2309	−	35.0409i	0.708656	−	1.22743i
$816$		0			0
$817$	23.6804	−	13.6719i	0.828471	−	0.478318i
$818$		0			0
$819$	−11.1264	+	5.32270i	−0.388788	+	0.185990i
$820$		0			0
$821$	16.5302	−	9.54373i	0.576909	−	0.333078i	−0.182995	−	0.983114i	$-0.558579\pi$
$821$	16.5302	−	9.54373i	0.576909	−	0.333078i	0.759904	+	0.650035i	$0.225246\pi$
$822$		0			0
$823$	−22.4372	+	38.8623i	−0.782111	+	1.35466i	0.148600	+	0.988897i	$0.452523\pi$
$823$	−22.4372	+	38.8623i	−0.782111	+	1.35466i	−0.930710	+	0.365758i	$0.880810\pi$
$824$		0			0
$825$	−26.1133	−	15.0765i	−0.909147	−	0.524896i
$826$		0			0
$827$		−	29.7249i		−	1.03364i	−0.856095	−	0.516819i	$-0.827116\pi$
$827$		−	29.7249i		−	1.03364i	0.856095	−	0.516819i	$-0.172884\pi$
$828$		0			0
$829$	−23.4955	−	40.6954i	−0.816033	−	1.41341i	−0.908584	−	0.417703i	$-0.862835\pi$
$829$	−23.4955	−	40.6954i	−0.816033	−	1.41341i	0.0925509	−	0.995708i	$-0.470498\pi$
$830$		0			0
$831$	−11.3629			−0.394174
$832$		0			0
$833$	5.45663			0.189061
$834$		0			0
$835$	29.3142	+	50.7738i	1.01446	+	1.75710i
$836$		0			0
$837$		−	7.64469i		−	0.264239i
$838$		0			0
$839$	39.6444	+	22.8887i	1.36868	+	0.790206i	0.990759	−	0.135633i	$-0.0433070\pi$
$839$	39.6444	+	22.8887i	1.36868	+	0.790206i	0.377918	+	0.925839i	$0.376640\pi$
$840$		0			0
$841$	1.43411	−	2.48395i	0.0494521	−	0.0856536i
$842$		0			0
$843$	−9.61606	+	5.55183i	−0.331195	+	0.191215i
$844$		0			0
$845$	6.89933	−	44.2171i	0.237344	−	1.52111i
$846$		0			0
$847$	−2.53590	+	1.46410i	−0.0871345	+	0.0503071i
$848$		0			0
$849$	15.2742	−	26.4558i	0.524210	−	0.907959i
$850$		0			0
$851$	−13.5782	−	7.83938i	−0.465455	−	0.268730i
$852$		0			0
$853$			35.3624i			1.21079i	0.795927	+	0.605393i	$0.206984\pi$
$853$			35.3624i			1.21079i	−0.795927	+	0.605393i	$0.793016\pi$
$854$		0			0
$855$	11.8735	+	20.5654i	0.406063	+	0.703323i
$856$		0			0
$857$	−43.3068			−1.47933			−0.739666	−	0.672975i	$-0.765016\pi$
$857$	−43.3068			−1.47933			−0.739666	+	0.672975i	$0.765016\pi$
$858$		0			0
$859$	10.2009			0.348049			0.174025	−	0.984741i	$-0.444323\pi$
$859$	10.2009			0.348049			0.174025	+	0.984741i	$0.444323\pi$
$860$		0			0
$861$	−4.99119	−	8.64500i	−0.170099	−	0.294621i
$862$		0			0
$863$			4.26879i			0.145311i	0.997357	+	0.0726556i	$0.0231474\pi$
$863$			4.26879i			0.145311i	−0.997357	+	0.0726556i	$0.976853\pi$
$864$		0			0
$865$	−45.6875	−	26.3777i	−1.55342	−	0.896868i
$866$		0			0
$867$	−9.60602	+	16.6381i	−0.326237	+	0.565060i
$868$		0			0
$869$	30.6594	−	17.7012i	1.04005	−	0.600473i
$870$		0			0
$871$	−3.31543	+	1.58605i	−0.112339	+	0.0537413i
$872$		0			0
$873$	−11.0329	+	6.36984i	−0.373406	+	0.215586i
$874$		0			0
$875$	−10.1119	+	17.5144i	−0.341845	+	0.592094i
$876$		0			0
$877$	7.34659	+	4.24156i	0.248077	+	0.143227i	0.618883	−	0.785483i	$-0.287585\pi$
$877$	7.34659	+	4.24156i	0.248077	+	0.143227i	−0.370807	+	0.928710i	$0.620919\pi$
$878$		0			0
$879$		−	11.1629i		−	0.376516i
$880$		0			0
$881$	−25.5503	−	44.2544i	−0.860810	−	1.49097i	−0.871148	−	0.491021i	$-0.836624\pi$
$881$	−25.5503	−	44.2544i	−0.860810	−	1.49097i	0.0103376	−	0.999947i	$-0.496709\pi$
$882$		0			0
$883$	−21.5628			−0.725645			−0.362822	−	0.931858i	$-0.618187\pi$
$883$	−21.5628			−0.725645			−0.362822	+	0.931858i	$0.618187\pi$
$884$		0			0
$885$	64.5482			2.16977
$886$		0			0
$887$	3.53551	+	6.12367i	0.118711	+	0.205613i	0.919257	−	0.393658i	$-0.128791\pi$
$887$	3.53551	+	6.12367i	0.118711	+	0.205613i	−0.800546	+	0.599271i	$0.795457\pi$
$888$		0			0
$889$		−	39.8039i		−	1.33498i
$890$		0			0
$891$	12.6629	+	7.31095i	0.424224	+	0.244926i
$892$		0			0
$893$	−5.04447	+	8.73728i	−0.168807	+	0.292382i
$894$		0			0
$895$	−3.79988	+	2.19386i	−0.127016	+	0.0733326i
$896$		0			0
$897$	−3.91940	+	5.71680i	−0.130865	+	0.190878i
$898$		0			0
$899$	5.98616	−	3.45611i	0.199650	−	0.115268i
$900$		0			0
$901$	−3.31438	+	5.74067i	−0.110418	+	0.191250i
$902$		0			0
$903$	−16.2820	−	9.40041i	−0.541830	−	0.312826i
$904$		0			0
$905$		−	8.31873i		−	0.276524i
$906$		0			0
$907$	−20.2203	−	35.0226i	−0.671405	−	1.16291i	−0.977506	−	0.210908i	$-0.932358\pi$
$907$	−20.2203	−	35.0226i	−0.671405	−	1.16291i	0.306101	−	0.951999i	$-0.400975\pi$
$908$		0			0
$909$	−6.83076			−0.226562
$910$		0			0
$911$	5.91974			0.196130			0.0980649	−	0.995180i	$-0.468735\pi$
$911$	5.91974			0.196130			0.0980649	+	0.995180i	$0.468735\pi$
$912$		0			0
$913$	22.7757	+	39.4486i	0.753765	+	1.30556i
$914$		0			0
$915$			51.6113i			1.70622i
$916$		0			0
$917$	−25.6747	−	14.8233i	−0.847853	−	0.489508i
$918$		0			0
$919$	−25.2088	+	43.6630i	−0.831563	+	1.44031i	0.0652360	+	0.997870i	$0.479220\pi$
$919$	−25.2088	+	43.6630i	−0.831563	+	1.44031i	−0.896799	+	0.442439i	$0.854113\pi$
$920$		0			0
$921$	−20.0863	+	11.5968i	−0.661865	+	0.382128i
$922$		0			0
$923$	−39.6395	−	27.1766i	−1.30475	−	0.894527i
$924$		0			0
$925$	−67.0886	+	38.7336i	−2.20586	+	1.27355i
$926$		0			0
$927$	−3.70958	+	6.42518i	−0.121839	+	0.211031i
$928$		0			0
$929$	35.8923	+	20.7224i	1.17759	+	0.679881i	0.955455	−	0.295135i	$-0.0953648\pi$
$929$	35.8923	+	20.7224i	1.17759	+	0.679881i	0.222133	+	0.975016i	$0.428698\pi$
$930$		0			0
$931$		−	19.7012i		−	0.645681i
$932$		0			0
$933$	2.62942	+	4.55430i	0.0860835	+	0.149101i
$934$		0			0
$935$	−19.3759			−0.633660
$936$		0			0
$937$	5.67515			0.185399			0.0926995	−	0.995694i	$-0.470450\pi$
$937$	5.67515			0.185399			0.0926995	+	0.995694i	$0.470450\pi$
$938$		0			0
$939$	−18.5086	−	32.0578i	−0.604004	−	1.04617i
$940$		0			0
$941$		−	18.7044i		−	0.609744i	−0.952393	−	0.304872i	$-0.901386\pi$
$941$		−	18.7044i		−	0.609744i	0.952393	−	0.304872i	$-0.0986138\pi$
$942$		0			0
$943$	2.72324	+	1.57227i	0.0886811	+	0.0512000i
$944$		0			0
$945$	30.8919	−	53.5064i	1.00492	−	1.74056i
$946$		0			0
$947$	31.8550	−	18.3915i	1.03515	−	0.597643i	0.116693	−	0.993168i	$-0.462771\pi$
$947$	31.8550	−	18.3915i	1.03515	−	0.597643i	0.918455	+	0.395525i	$0.129437\pi$
$948$		0			0
$949$	−1.48597	+	19.1620i	−0.0482365	+	0.622026i
$950$		0			0
$951$	22.3794	−	12.9207i	0.725700	−	0.418983i
$952$		0			0
$953$	−9.16979	+	15.8825i	−0.297039	+	0.514486i	−0.975457	−	0.220190i	$-0.929332\pi$
$953$	−9.16979	+	15.8825i	−0.297039	+	0.514486i	0.678419	+	0.734676i	$0.262666\pi$
$954$		0			0
$955$	−20.0004	−	11.5472i	−0.647198	−	0.373660i
$956$		0			0
$957$			22.5002i			0.727327i
$958$		0			0
$959$	−8.17899	−	14.1664i	−0.264113	−	0.457458i
$960$		0			0
$961$	29.1716			0.941020
$962$		0			0
$963$	−0.171905			−0.00553957
$964$		0			0
$965$	9.22586	+	15.9797i	0.296991	+	0.514403i
$966$		0			0
$967$			17.0558i			0.548478i	0.961662	+	0.274239i	$0.0884260\pi$
$967$			17.0558i			0.548478i	−0.961662	+	0.274239i	$0.911574\pi$
$968$		0			0
$969$	−13.6285	−	7.86843i	−0.437811	−	0.252770i
$970$		0			0
$971$	−9.32268	+	16.1474i	−0.299179	+	0.518193i	−0.975948	−	0.218002i	$-0.930046\pi$
$971$	−9.32268	+	16.1474i	−0.299179	+	0.518193i	0.676769	+	0.736195i	$0.263379\pi$
$972$		0			0
$973$	−8.79655	+	5.07869i	−0.282004	+	0.162815i
$974$		0			0
$975$	14.7792	+	30.8940i	0.473313	+	0.989399i
$976$		0			0
$977$	−14.0081	+	8.08758i	−0.448159	+	0.258745i	−0.707052	−	0.707161i	$-0.749975\pi$
$977$	−14.0081	+	8.08758i	−0.448159	+	0.258745i	0.258893	+	0.965906i	$0.416642\pi$
$978$		0			0
$979$	7.34165	−	12.7161i	0.234640	−	0.406408i
$980$		0			0
$981$	10.1984	+	5.88808i	0.325611	+	0.187992i
$982$		0			0
$983$		−	55.0587i		−	1.75610i	−0.478568	−	0.878050i	$-0.658844\pi$
$983$		−	55.0587i		−	1.75610i	0.478568	−	0.878050i	$-0.341156\pi$
$984$		0			0
$985$	14.8463	+	25.7145i	0.473041	+	0.819332i
$986$		0			0
$987$	6.93689			0.220804
$988$		0			0
$989$	5.92241			0.188322
$990$		0			0
$991$	−18.5364	−	32.1060i	−0.588828	−	1.01988i	−0.994386	−	0.105811i	$-0.966256\pi$
$991$	−18.5364	−	32.1060i	−0.588828	−	1.01988i	0.405558	−	0.914069i	$-0.367077\pi$
$992$		0			0
$993$			18.4402i			0.585181i
$994$		0			0
$995$	32.3881	+	18.6993i	1.02677	+	0.592808i
$996$		0			0
$997$	24.3316	−	42.1436i	0.770591	−	1.33470i	−0.166649	−	0.986016i	$-0.553295\pi$
$997$	24.3316	−	42.1436i	0.770591	−	1.33470i	0.937240	−	0.348686i	$-0.113372\pi$
$998$		0			0
$999$	55.3664	−	31.9658i	1.75171	−	1.01135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.w.i.257.3		8
4.3	odd	2		832.2.w.g.257.2		8
8.3	odd	2		104.2.o.a.49.3	yes	8
8.5	even	2		208.2.w.c.49.2		8
13.4	even	6	inner	832.2.w.i.641.3		8
24.5	odd	2		1872.2.by.n.1297.1		8
24.11	even	2		936.2.bi.b.361.1		8
52.43	odd	6		832.2.w.g.641.2		8
104.3	odd	6		1352.2.f.f.337.4		8
104.11	even	12		1352.2.a.k.1.2		4
104.19	even	12		1352.2.i.l.529.3		8
104.29	even	6		2704.2.f.q.337.6		8
104.35	odd	6		1352.2.o.f.1161.3		8
104.37	odd	12		2704.2.a.bd.1.3		4
104.43	odd	6		104.2.o.a.17.3	✓	8
104.51	odd	2		1352.2.o.f.361.3		8
104.59	even	12		1352.2.i.k.529.3		8
104.67	even	12		1352.2.a.l.1.2		4
104.69	even	6		208.2.w.c.17.2		8
104.75	odd	6		1352.2.f.f.337.3		8
104.83	even	4		1352.2.i.l.1329.3		8
104.93	odd	12		2704.2.a.be.1.3		4
104.99	even	4		1352.2.i.k.1329.3		8
104.101	even	6		2704.2.f.q.337.5		8
312.173	odd	6		1872.2.by.n.433.4		8
312.251	even	6		936.2.bi.b.433.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.o.a.17.3	✓	8	104.43	odd	6
104.2.o.a.49.3	yes	8	8.3	odd	2
208.2.w.c.17.2		8	104.69	even	6
208.2.w.c.49.2		8	8.5	even	2
832.2.w.g.257.2		8	4.3	odd	2
832.2.w.g.641.2		8	52.43	odd	6
832.2.w.i.257.3		8	1.1	even	1	trivial
832.2.w.i.641.3		8	13.4	even	6	inner
936.2.bi.b.361.1		8	24.11	even	2
936.2.bi.b.433.4		8	312.251	even	6
1352.2.a.k.1.2		4	104.11	even	12
1352.2.a.l.1.2		4	104.67	even	12
1352.2.f.f.337.3		8	104.75	odd	6
1352.2.f.f.337.4		8	104.3	odd	6
1352.2.i.k.529.3		8	104.59	even	12
1352.2.i.k.1329.3		8	104.99	even	4
1352.2.i.l.529.3		8	104.19	even	12
1352.2.i.l.1329.3		8	104.83	even	4
1352.2.o.f.361.3		8	104.51	odd	2
1352.2.o.f.1161.3		8	104.35	odd	6
1872.2.by.n.433.4		8	312.173	odd	6
1872.2.by.n.1297.1		8	24.5	odd	2
2704.2.a.bd.1.3		4	104.37	odd	12
2704.2.a.be.1.3		4	104.93	odd	12
2704.2.f.q.337.5		8	104.101	even	6
2704.2.f.q.337.6		8	104.29	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:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.693255 + 1.20075i) q^{3} -3.44247i q^{5} +(2.74922 + 1.58726i) q^{7} +(0.538796 - 0.933222i) q^{9} +(2.74922 - 1.58726i) q^{11} +(-3.59476 - 0.278764i) q^{13} +(4.13356 - 2.38651i) q^{15} +(0.886509 - 1.53548i) q^{17} +(-5.54387 - 3.20075i) q^{19} +4.40150i q^{21} +(-0.693255 - 1.20075i) q^{23} -6.85061 q^{25} +5.65362 q^{27} +(2.55596 + 4.42706i) q^{29} -1.35218i q^{31} +(3.81181 + 2.20075i) q^{33} +(5.46410 - 9.46410i) q^{35} +(9.79308 - 5.65404i) q^{37} +(-2.15736 - 4.50967i) q^{39} +(-1.96410 + 1.13397i) q^{41} +(-2.13573 + 3.69919i) q^{43} +(-3.21259 - 1.85479i) q^{45} -1.57603i q^{47} +(1.53880 + 2.66527i) q^{49} +2.45831 q^{51} -3.73869 q^{53} +(-5.46410 - 9.46410i) q^{55} -8.87574i q^{57} +(11.7118 + 6.76178i) q^{59} +(-5.40657 + 9.36446i) q^{61} +(2.96254 - 1.71042i) q^{63} +(-0.959638 + 12.3749i) q^{65} +(0.882772 - 0.509669i) q^{67} +(0.961204 - 1.66485i) q^{69} +(11.5439 + 6.66485i) q^{71} -5.33055i q^{73} +(-4.74922 - 8.22589i) q^{75} +10.0776 q^{77} +11.1521 q^{79} +(2.30301 + 3.98893i) q^{81} +14.3490i q^{83} +(-5.28584 - 3.05178i) q^{85} +(-3.54387 + 6.13815i) q^{87} +(4.00567 - 2.31268i) q^{89} +(-9.44030 - 6.47220i) q^{91} +(1.62363 - 0.937403i) q^{93} +(-11.0185 + 19.0846i) q^{95} +(-10.2385 - 5.91117i) q^{97} -3.42084i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{19} - 2 q^{23} - 20 q^{25} - 28 q^{27} + 8 q^{29} + 6 q^{33} + 16 q^{35} + 24 q^{37} + 14 q^{39} + 12 q^{41} + 6 q^{43} - 30 q^{45} + 2 q^{49}+ \cdots + 30 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 + 6 * q^7 - 6 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^19 - 2 * q^23 - 20 * q^25 - 28 * q^27 + 8 * q^29 + 6 * q^33 + 16 * q^35 + 24 * q^37 + 14 * q^39 + 12 * q^41 + 6 * q^43 - 30 * q^45 + 2 * q^49 + 68 * q^51 - 20 * q^53 - 16 * q^55 + 18 * q^59 + 4 * q^61 - 36 * q^63 + 14 * q^65 - 42 * q^67 + 18 * q^69 + 54 * q^71 - 22 * q^75 + 60 * q^77 - 16 * q^79 - 20 * q^81 - 6 * q^85 + 10 * q^87 - 18 * q^89 - 46 * q^91 - 36 * q^93 - 16 * q^95 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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