LMFDB - Embedded newform 1008.2.df.d.689.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(689,1008)] 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("1008.689"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.1
Root			$1.68124 + 0.416458i$ of defining polynomial
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.d.929.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71501 - 0.242362i) q^{3} +0.699656 q^{5} +(0.461278 - 2.60523i) q^{7} +(2.88252 + 0.831308i) q^{9} +0.265217i q^{11} +(-1.13823 - 0.657156i) q^{13} +(-1.19992 - 0.169570i) q^{15} +(1.86392 - 3.22840i) q^{17} +(0.382449 - 0.220807i) q^{19} +(-1.42251 + 4.35620i) q^{21} +4.96463i q^{23} -4.51048 q^{25} +(-4.74208 - 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} +(4.85521 - 2.80316i) q^{31} +(0.0642786 - 0.454850i) q^{33} +(0.322736 - 1.82276i) q^{35} +(-0.351124 - 0.608164i) q^{37} +(1.79280 + 1.40289i) q^{39} +(5.39354 - 9.34189i) q^{41} +(-3.73131 - 6.46283i) q^{43} +(2.01677 + 0.581630i) q^{45} +(3.50285 - 6.06712i) q^{47} +(-6.57445 - 2.40347i) q^{49} +(-3.97908 + 5.08500i) q^{51} +(-8.51919 - 4.91856i) q^{53} +0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} +(6.73182 + 11.6598i) q^{59} +(-4.89484 - 2.82604i) q^{61} +(3.49539 - 7.12617i) q^{63} +(-0.796368 - 0.459783i) q^{65} +(-2.97060 - 5.14523i) q^{67} +(1.20324 - 8.51439i) q^{69} -13.4323i q^{71} +(-6.66182 - 3.84620i) q^{73} +(7.73552 + 1.09317i) q^{75} +(0.690951 + 0.122339i) q^{77} +(0.698360 - 1.20959i) q^{79} +(7.61785 + 4.79253i) q^{81} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(0.506930 - 0.204363i) q^{87} +(-5.59261 - 9.68668i) q^{89} +(-2.23708 + 2.66221i) q^{91} +(-9.00612 + 3.63073i) q^{93} +(0.267582 - 0.154489i) q^{95} +(9.18225 - 5.30138i) q^{97} +(-0.220477 + 0.764493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{7} + 3 q^{13} + 3 q^{15} - 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} - 27 q^{33} - 15 q^{35} + q^{37} + 3 q^{39} + 6 q^{41} + 2 q^{43} - 15 q^{45} + 18 q^{47} + 13 q^{49} - 15 q^{51}+ \cdots + 9 q^{99}+O(q^{100}) $ 16 * q + q^7 + 3 * q^13 + 3 * q^15 - 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 - 27 * q^33 - 15 * q^35 + q^37 + 3 * q^39 + 6 * q^41 + 2 * q^43 - 15 * q^45 + 18 * q^47 + 13 * q^49 - 15 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 9 * q^63 - 39 * q^65 + 7 * q^67 - 21 * q^69 + 15 * q^75 - 45 * q^77 + q^79 + 6 * q^85 + 3 * q^87 - 21 * q^89 - 9 * q^91 - 69 * q^93 - 6 * q^95 + 3 * q^97 + 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.71501	−	0.242362i	−0.990162	−	0.139928i
$3$	−1.71501	−	0.242362i	−0.990162	−	0.139928i
$4$		0			0
$5$	0.699656			0.312896			0.156448	−	0.987686i	$-0.449996\pi$
$5$	0.699656			0.312896			0.156448	+	0.987686i	$0.449996\pi$
$6$		0			0
$7$	0.461278	−	2.60523i	0.174347	−	0.984684i
$7$	0.461278	−	2.60523i	0.174347	−	0.984684i
$8$		0			0
$9$	2.88252	+	0.831308i	0.960840	+	0.277103i
$10$		0			0
$11$			0.265217i			0.0799659i	0.999200	+	0.0399829i	$0.0127304\pi$
$11$			0.265217i			0.0799659i	−0.999200	+	0.0399829i	$0.987270\pi$
$12$		0			0
$13$	−1.13823	−	0.657156i	−0.315688	−	0.182262i	0.333781	−	0.942651i	$-0.391675\pi$
$13$	−1.13823	−	0.657156i	−0.315688	−	0.182262i	−0.649469	+	0.760388i	$0.725009\pi$
$14$		0			0
$15$	−1.19992	−	0.169570i	−0.309817	−	0.0437829i
$16$		0			0
$17$	1.86392	−	3.22840i	0.452067	−	0.783003i	−0.546447	−	0.837493i	$-0.684020\pi$
$17$	1.86392	−	3.22840i	0.452067	−	0.783003i	0.998514	+	0.0544906i	$0.0173535\pi$
$18$		0			0
$19$	0.382449	−	0.220807i	0.0877398	−	0.0506566i	−0.455488	−	0.890242i	$-0.650535\pi$
$19$	0.382449	−	0.220807i	0.0877398	−	0.0506566i	0.543228	+	0.839585i	$0.317202\pi$
$20$		0			0
$21$	−1.42251	+	4.35620i	−0.310416	+	0.950601i
$22$		0			0
$23$			4.96463i			1.03520i	0.855624	+	0.517598i	$0.173174\pi$
$23$			4.96463i			1.03520i	−0.855624	+	0.517598i	$0.826826\pi$
$24$		0			0
$25$	−4.51048			−0.902096
$26$		0			0
$27$	−4.74208	−	2.12432i	−0.912613	−	0.408825i
$28$		0			0
$29$	−0.273287	+	0.157782i	−0.0507480	+	0.0292994i	−0.525159	−	0.851004i	$-0.675994\pi$
$29$	−0.273287	+	0.157782i	−0.0507480	+	0.0292994i	0.474411	+	0.880303i	$0.342661\pi$
$30$		0			0
$31$	4.85521	−	2.80316i	0.872022	−	0.503462i	0.00400255	−	0.999992i	$-0.498726\pi$
$31$	4.85521	−	2.80316i	0.872022	−	0.503462i	0.868020	+	0.496530i	$0.165393\pi$
$32$		0			0
$33$	0.0642786	−	0.454850i	0.0111895	−	0.0791792i
$34$		0			0
$35$	0.322736	−	1.82276i	0.0545523	−	0.308103i
$36$		0			0
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	0.835719	−	0.549157i	$-0.185051\pi$
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	−0.893444	+	0.449175i	$0.851718\pi$
$38$		0			0
$39$	1.79280	+	1.40289i	0.287078	+	0.224643i
$40$		0			0
$41$	5.39354	−	9.34189i	0.842330	−	1.45896i	−0.0455900	−	0.998960i	$-0.514517\pi$
$41$	5.39354	−	9.34189i	0.842330	−	1.45896i	0.887920	−	0.459998i	$-0.152150\pi$
$42$		0			0
$43$	−3.73131	−	6.46283i	−0.569020	−	0.985572i	−0.996663	−	0.0816240i	$-0.973989\pi$
$43$	−3.73131	−	6.46283i	−0.569020	−	0.985572i	0.427643	−	0.903948i	$-0.359344\pi$
$44$		0			0
$45$	2.01677	+	0.581630i	0.300643	+	0.0867042i
$46$		0			0
$47$	3.50285	−	6.06712i	0.510943	−	0.884980i	−0.488976	−	0.872297i	$-0.662630\pi$
$47$	3.50285	−	6.06712i	0.510943	−	0.884980i	0.999920	−	0.0126827i	$-0.00403713\pi$
$48$		0			0
$49$	−6.57445	−	2.40347i	−0.939207	−	0.343353i
$50$		0			0
$51$	−3.97908	+	5.08500i	−0.557183	+	0.712043i
$52$		0			0
$53$	−8.51919	−	4.91856i	−1.17020	−	0.675616i	−0.216474	−	0.976288i	$-0.569456\pi$
$53$	−8.51919	−	4.91856i	−1.17020	−	0.675616i	−0.953727	+	0.300672i	$0.902789\pi$
$54$		0			0
$55$			0.185561i			0.0250210i
$56$		0			0
$57$	−0.709419	+	0.285995i	−0.0939648	+	0.0378809i
$58$		0			0
$59$	6.73182	+	11.6598i	0.876408	+	1.51798i	0.855256	+	0.518206i	$0.173400\pi$
$59$	6.73182	+	11.6598i	0.876408	+	1.51798i	0.0211522	+	0.999776i	$0.493267\pi$
$60$		0			0
$61$	−4.89484	−	2.82604i	−0.626720	−	0.361837i	0.152761	−	0.988263i	$-0.451184\pi$
$61$	−4.89484	−	2.82604i	−0.626720	−	0.361837i	−0.779481	+	0.626426i	$0.784517\pi$
$62$		0			0
$63$	3.49539	−	7.12617i	0.440378	−	0.897812i
$64$		0			0
$65$	−0.796368	−	0.459783i	−0.0987773	−	0.0570291i
$66$		0			0
$67$	−2.97060	−	5.14523i	−0.362916	−	0.628590i	0.625523	−	0.780206i	$-0.284886\pi$
$67$	−2.97060	−	5.14523i	−0.362916	−	0.628590i	−0.988439	+	0.151616i	$0.951552\pi$
$68$		0			0
$69$	1.20324	−	8.51439i	0.144853	−	1.02501i
$70$		0			0
$71$		−	13.4323i		−	1.59412i	−0.603900	−	0.797060i	$-0.706387\pi$
$71$		−	13.4323i		−	1.59412i	0.603900	−	0.797060i	$-0.293613\pi$
$72$		0			0
$73$	−6.66182	−	3.84620i	−0.779707	−	0.450164i	0.0566194	−	0.998396i	$-0.481968\pi$
$73$	−6.66182	−	3.84620i	−0.779707	−	0.450164i	−0.836326	+	0.548232i	$0.815301\pi$
$74$		0			0
$75$	7.73552	+	1.09317i	0.893221	+	0.126229i
$76$		0			0
$77$	0.690951	+	0.122339i	0.0787412	+	0.0139418i
$78$		0			0
$79$	0.698360	−	1.20959i	0.0785716	−	0.136090i	−0.824062	−	0.566499i	$-0.808297\pi$
$79$	0.698360	−	1.20959i	0.0785716	−	0.136090i	0.902634	+	0.430409i	$0.141631\pi$
$80$		0			0
$81$	7.61785	+	4.79253i	0.846428	+	0.532503i
$82$		0			0
$83$	−3.72399	−	6.45014i	−0.408761	−	0.707995i	0.585990	−	0.810318i	$-0.300706\pi$
$83$	−3.72399	−	6.45014i	−0.408761	−	0.707995i	−0.994751	+	0.102323i	$0.967372\pi$
$84$		0			0
$85$	1.30410	−	2.25877i	0.141450	−	0.244998i
$86$		0			0
$87$	0.506930	−	0.204363i	0.0543486	−	0.0219101i
$88$		0			0
$89$	−5.59261	−	9.68668i	−0.592815	−	1.02679i	−0.993851	−	0.110724i	$-0.964683\pi$
$89$	−5.59261	−	9.68668i	−0.592815	−	1.02679i	0.401036	−	0.916062i	$-0.368650\pi$
$90$		0			0
$91$	−2.23708	+	2.66221i	−0.234510	+	0.279076i
$92$		0			0
$93$	−9.00612	+	3.63073i	−0.933892	+	0.376489i
$94$		0			0
$95$	0.267582	−	0.154489i	0.0274534	−	0.0158502i
$96$		0			0
$97$	9.18225	−	5.30138i	0.932316	−	0.538273i	0.0447729	−	0.998997i	$-0.485744\pi$
$97$	9.18225	−	5.30138i	0.932316	−	0.538273i	0.887543	+	0.460724i	$0.152410\pi$
$98$		0			0
$99$	−0.220477	+	0.764493i	−0.0221588	+	0.0768345i
$100$		0			0
$101$	17.5071			1.74203			0.871013	−	0.491260i	$-0.163463\pi$
$101$	17.5071			1.74203			0.871013	+	0.491260i	$0.163463\pi$
$102$		0			0
$103$			8.54219i			0.841687i	0.907133	+	0.420844i	$0.138266\pi$
$103$			8.54219i			0.841687i	−0.907133	+	0.420844i	$0.861734\pi$
$104$		0			0
$105$	−0.995265	+	3.04784i	−0.0971279	+	0.297439i
$106$		0			0
$107$	9.09489	−	5.25093i	0.879236	−	0.507627i	0.00882940	−	0.999961i	$-0.497189\pi$
$107$	9.09489	−	5.25093i	0.879236	−	0.507627i	0.870406	+	0.492334i	$0.163856\pi$
$108$		0			0
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	0.292268	+	0.956337i	$0.405590\pi$
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	−0.974346	+	0.225057i	$0.927743\pi$
$110$		0			0
$111$	0.454785	+	1.12811i	0.0431663	+	0.107075i
$112$		0			0
$113$	13.3783	+	7.72396i	1.25852	+	0.726609i	0.972788	−	0.231699i	$-0.0744284\pi$
$113$	13.3783	+	7.72396i	1.25852	+	0.726609i	0.285737	+	0.958308i	$0.407762\pi$
$114$		0			0
$115$			3.47353i			0.323908i
$116$		0			0
$117$	−2.73467	−	2.84048i	−0.252820	−	0.262603i
$118$		0			0
$119$	−7.55095	−	6.34513i	−0.692194	−	0.581657i
$120$		0			0
$121$	10.9297			0.993605
$122$		0			0
$123$	−11.5141	+	14.7142i	−1.03819	+	1.32674i
$124$		0			0
$125$	−6.65406			−0.595157
$126$		0			0
$127$	−21.8304			−1.93713			−0.968566	−	0.248758i	$-0.919978\pi$
$127$	−21.8304			−1.93713			−0.968566	+	0.248758i	$0.919978\pi$
$128$		0			0
$129$	4.83290	+	11.9881i	0.425513	+	1.05550i
$130$		0			0
$131$	−5.20922			−0.455132			−0.227566	−	0.973763i	$-0.573077\pi$
$131$	−5.20922			−0.455132			−0.227566	+	0.973763i	$0.573077\pi$
$132$		0			0
$133$	−0.398838	−	1.09822i	−0.0345836	−	0.0952278i
$134$		0			0
$135$	−3.31782	−	1.48629i	−0.285552	−	0.127920i
$136$		0			0
$137$			2.69725i			0.230442i	0.993340	+	0.115221i	$0.0367576\pi$
$137$			2.69725i			0.230442i	−0.993340	+	0.115221i	$0.963242\pi$
$138$		0			0
$139$	−10.1448	−	5.85710i	−0.860470	−	0.496793i	0.00369951	−	0.999993i	$-0.498822\pi$
$139$	−10.1448	−	5.85710i	−0.860470	−	0.496793i	−0.864170	+	0.503200i	$0.832156\pi$
$140$		0			0
$141$	−7.47787	+	9.55621i	−0.629750	+	0.804778i
$142$		0			0
$143$	0.174289	−	0.301877i	0.0145748	−	0.0252442i
$144$		0			0
$145$	−0.191206	+	0.110393i	−0.0158788	+	0.00916765i
$146$		0			0
$147$	10.6927	+	5.71537i	0.881922	+	0.471396i
$148$		0			0
$149$			18.8280i			1.54245i	0.636564	+	0.771224i	$0.280355\pi$
$149$			18.8280i			1.54245i	−0.636564	+	0.771224i	$0.719645\pi$
$150$		0			0
$151$	−10.0029			−0.814021			−0.407010	−	0.913424i	$-0.633429\pi$
$151$	−10.0029			−0.814021			−0.407010	+	0.913424i	$0.633429\pi$
$152$		0			0
$153$	8.05659	−	7.75645i	0.651336	−	0.627072i
$154$		0			0
$155$	3.39698	−	1.96125i	0.272852	−	0.157531i
$156$		0			0
$157$	−0.218293	+	0.126032i	−0.0174217	+	0.0100584i	−0.508686	−	0.860952i	$-0.669868\pi$
$157$	−0.218293	+	0.126032i	−0.0174217	+	0.0100584i	0.491264	+	0.871011i	$0.336535\pi$
$158$		0			0
$159$	13.4184	+	10.5001i	1.06415	+	0.832713i
$160$		0			0
$161$	12.9340	+	2.29007i	1.01934	+	0.180483i
$162$		0			0
$163$	−4.29780	−	7.44400i	−0.336629	−	0.583059i	0.647167	−	0.762348i	$-0.275954\pi$
$163$	−4.29780	−	7.44400i	−0.336629	−	0.583059i	−0.983796	+	0.179289i	$0.942620\pi$
$164$		0			0
$165$	0.0449729	−	0.318238i	0.00350114	−	0.0247748i
$166$		0			0
$167$	2.24437	−	3.88736i	0.173674	−	0.300813i	−0.766027	−	0.642808i	$-0.777769\pi$
$167$	2.24437	−	3.88736i	0.173674	−	0.300813i	0.939702	+	0.341995i	$0.111103\pi$
$168$		0			0
$169$	−5.63629	−	9.76234i	−0.433561	−	0.750949i
$170$		0			0
$171$	1.28598	−	0.318548i	0.0983410	−	0.0243599i
$172$		0			0
$173$	−3.56072	+	6.16736i	−0.270717	+	0.468895i	−0.969046	−	0.246882i	$-0.920594\pi$
$173$	−3.56072	+	6.16736i	−0.270717	+	0.468895i	0.698329	+	0.715777i	$0.253927\pi$
$174$		0			0
$175$	−2.08059	+	11.7508i	−0.157277	+	0.888280i
$176$		0			0
$177$	−8.71922	−	21.6283i	−0.655377	−	1.62568i
$178$		0			0
$179$	22.1270	+	12.7750i	1.65385	+	0.954848i	0.975470	+	0.220134i	$0.0706494\pi$
$179$	22.1270	+	12.7750i	1.65385	+	0.954848i	0.678376	+	0.734715i	$0.262684\pi$
$180$		0			0
$181$		−	0.943175i		−	0.0701057i	−0.999385	−	0.0350528i	$-0.988840\pi$
$181$		−	0.943175i		−	0.0701057i	0.999385	−	0.0350528i	$-0.0111599\pi$
$182$		0			0
$183$	7.70977	+	6.03301i	0.569923	+	0.445973i
$184$		0			0
$185$	−0.245666	−	0.425506i	−0.0180617	−	0.0312838i
$186$		0			0
$187$	0.856227	+	0.494343i	0.0626135	+	0.0361499i
$188$		0			0
$189$	−7.72175	+	11.3743i	−0.561675	+	0.827358i
$190$		0			0
$191$	2.57413	+	1.48617i	0.186258	+	0.107536i	0.590229	−	0.807236i	$-0.299037\pi$
$191$	2.57413	+	1.48617i	0.186258	+	0.107536i	−0.403972	+	0.914771i	$0.632371\pi$
$192$		0			0
$193$	9.25721	+	16.0340i	0.666348	+	1.15415i	0.978918	+	0.204254i	$0.0654769\pi$
$193$	9.25721	+	16.0340i	0.666348	+	1.15415i	−0.312570	+	0.949895i	$0.601190\pi$
$194$		0			0
$195$	1.25434	+	0.981542i	0.0898255	+	0.0702897i
$196$		0			0
$197$			14.1774i			1.01010i	0.863091	+	0.505048i	$0.168525\pi$
$197$			14.1774i			1.01010i	−0.863091	+	0.505048i	$0.831475\pi$
$198$		0			0
$199$	20.5293	+	11.8526i	1.45529	+	0.840209i	0.998774	−	0.0495081i	$-0.0157654\pi$
$199$	20.5293	+	11.8526i	1.45529	+	0.840209i	0.456512	+	0.889717i	$0.349099\pi$
$200$		0			0
$201$	3.84760	+	9.54408i	0.271389	+	0.673187i
$202$		0			0
$203$	0.284998	+	0.784756i	0.0200029	+	0.0550790i
$204$		0			0
$205$	3.77362	−	6.53611i	0.263561	−	0.456502i
$206$		0			0
$207$	−4.12714	+	14.3106i	−0.286856	+	0.994659i
$208$		0			0
$209$	0.0585617	+	0.101432i	0.00405080	+	0.00701619i
$210$		0			0
$211$	−3.04004	+	5.26550i	−0.209285	+	0.362492i	−0.951489	−	0.307681i	$-0.900447\pi$
$211$	−3.04004	+	5.26550i	−0.209285	+	0.362492i	0.742205	+	0.670173i	$0.233780\pi$
$212$		0			0
$213$	−3.25549	+	23.0365i	−0.223062	+	1.57844i
$214$		0			0
$215$	−2.61063	−	4.52175i	−0.178044	−	0.308381i
$216$		0			0
$217$	−5.06327	−	13.9420i	−0.343717	−	0.946444i
$218$		0			0
$219$	10.4929	+	8.21085i	0.709045	+	0.554838i
$220$		0			0
$221$	−4.24313	+	2.44977i	−0.285424	+	0.164790i
$222$		0			0
$223$	0.796137	−	0.459650i	0.0533133	−	0.0307804i	−0.473106	−	0.881005i	$-0.656867\pi$
$223$	0.796137	−	0.459650i	0.0533133	−	0.0307804i	0.526420	+	0.850225i	$0.323534\pi$
$224$		0			0
$225$	−13.0016	−	3.74960i	−0.866771	−	0.249973i
$226$		0			0
$227$	−10.0059			−0.664118			−0.332059	−	0.943259i	$-0.607743\pi$
$227$	−10.0059			−0.664118			−0.332059	+	0.943259i	$0.607743\pi$
$228$		0			0
$229$			2.75025i			0.181742i	0.995863	+	0.0908710i	$0.0289651\pi$
$229$			2.75025i			0.181742i	−0.995863	+	0.0908710i	$0.971035\pi$
$230$		0			0
$231$	−1.15534	−	0.377273i	−0.0760156	−	0.0248227i
$232$		0			0
$233$	5.55513	−	3.20725i	0.363928	−	0.210114i	−0.306874	−	0.951750i	$-0.599283\pi$
$233$	5.55513	−	3.20725i	0.363928	−	0.210114i	0.670803	+	0.741636i	$0.265950\pi$
$234$		0			0
$235$	2.45079	−	4.24489i	0.159872	−	0.276906i
$236$		0			0
$237$	−1.49085	+	1.90521i	−0.0968414	+	0.123757i
$238$		0			0
$239$	11.4288	+	6.59844i	0.739270	+	0.426818i	0.821804	−	0.569770i	$-0.192968\pi$
$239$	11.4288	+	6.59844i	0.739270	+	0.426818i	−0.0825337	+	0.996588i	$0.526301\pi$
$240$		0			0
$241$		−	2.54868i		−	0.164175i	−0.996625	−	0.0820874i	$-0.973841\pi$
$241$		−	2.54868i		−	0.164175i	0.996625	−	0.0820874i	$-0.0261587\pi$
$242$		0			0
$243$	−11.9032	−	10.0655i	−0.763589	−	0.645703i
$244$		0			0
$245$	−4.59985	−	1.68160i	−0.293874	−	0.107434i
$246$		0			0
$247$	−0.580418			−0.0369311
$248$		0			0
$249$	4.82341	+	11.9646i	0.305671	+	0.758227i
$250$		0			0
$251$	18.7893			1.18597			0.592986	−	0.805213i	$-0.297949\pi$
$251$	18.7893			1.18597			0.592986	+	0.805213i	$0.297949\pi$
$252$		0			0
$253$	−1.31670			−0.0827804
$254$		0			0
$255$	−2.78399	+	3.55775i	−0.174340	+	0.222795i
$256$		0			0
$257$	14.3945			0.897907			0.448953	−	0.893555i	$-0.351797\pi$
$257$	14.3945			0.897907			0.448953	+	0.893555i	$0.351797\pi$
$258$		0			0
$259$	−1.74637	+	0.634226i	−0.108514	+	0.0394089i
$260$		0			0
$261$	−0.918920	+	0.227625i	−0.0568797	+	0.0140896i
$262$		0			0
$263$			7.84976i			0.484037i	0.970272	+	0.242019i	$0.0778095\pi$
$263$			7.84976i			0.484037i	−0.970272	+	0.242019i	$0.922190\pi$
$264$		0			0
$265$	−5.96050	−	3.44130i	−0.366151	−	0.211397i
$266$		0			0
$267$	7.24369	+	17.9682i	0.443307	+	1.09964i
$268$		0			0
$269$	7.72267	−	13.3760i	0.470859	−	0.815552i	−0.528585	−	0.848880i	$-0.677277\pi$
$269$	7.72267	−	13.3760i	0.470859	−	0.815552i	0.999444	+	0.0333281i	$0.0106106\pi$
$270$		0			0
$271$	−10.9476	+	6.32057i	−0.665016	+	0.383947i	−0.794186	−	0.607675i	$-0.792102\pi$
$271$	−10.9476	+	6.32057i	−0.665016	+	0.383947i	0.129169	+	0.991623i	$0.458769\pi$
$272$		0			0
$273$	4.48184	−	4.02354i	0.271253	−	0.243516i
$274$		0			0
$275$		−	1.19626i		−	0.0721369i
$276$		0			0
$277$	−11.8906			−0.714439			−0.357219	−	0.934021i	$-0.616275\pi$
$277$	−11.8906			−0.714439			−0.357219	+	0.934021i	$0.616275\pi$
$278$		0			0
$279$	16.3255	−	4.04399i	0.977385	−	0.242107i
$280$		0			0
$281$	−2.75411	+	1.59009i	−0.164297	+	0.0948568i	−0.579894	−	0.814692i	$-0.696906\pi$
$281$	−2.75411	+	1.59009i	−0.164297	+	0.0948568i	0.415597	+	0.909549i	$0.363573\pi$
$282$		0			0
$283$	16.0195	−	9.24889i	0.952263	−	0.549789i	0.0584799	−	0.998289i	$-0.481375\pi$
$283$	16.0195	−	9.24889i	0.952263	−	0.549789i	0.893783	+	0.448499i	$0.148041\pi$
$284$		0			0
$285$	−0.496349	+	0.200098i	−0.0294012	+	0.0118528i
$286$		0			0
$287$	−21.8499	−	18.3606i	−1.28976	−	1.08379i
$288$		0			0
$289$	1.55161	+	2.68746i	0.0912711	+	0.158086i
$290$		0			0
$291$	−17.0325	+	6.86648i	−0.998463	+	0.402520i
$292$		0			0
$293$	1.42975	−	2.47639i	0.0835266	−	0.144672i	−0.821236	−	0.570589i	$-0.806715\pi$
$293$	1.42975	−	2.47639i	0.0835266	−	0.144672i	0.904762	+	0.425917i	$0.140048\pi$
$294$		0			0
$295$	4.70995	+	8.15788i	0.274224	+	0.474970i
$296$		0			0
$297$	0.563405	−	1.25768i	0.0326921	−	0.0729779i
$298$		0			0
$299$	3.26254	−	5.65088i	0.188677	−	0.326799i
$300$		0			0
$301$	−18.5583	+	6.73977i	−1.06968	+	0.388474i
$302$		0			0
$303$	−30.0249	−	4.24308i	−1.72489	−	0.243758i
$304$		0			0
$305$	−3.42470	−	1.97725i	−0.196098	−	0.113217i
$306$		0			0
$307$		−	21.6746i		−	1.23704i	−0.785771	−	0.618518i	$-0.787734\pi$
$307$		−	21.6746i		−	1.23704i	0.785771	−	0.618518i	$-0.212266\pi$
$308$		0			0
$309$	2.07031	−	14.6499i	0.117776	−	0.833406i
$310$		0			0
$311$	11.8462	+	20.5183i	0.671738	+	1.16348i	0.977411	+	0.211348i	$0.0677852\pi$
$311$	11.8462	+	20.5183i	0.671738	+	1.16348i	−0.305673	+	0.952136i	$0.598881\pi$
$312$		0			0
$313$	23.6283	+	13.6418i	1.33555	+	0.771081i	0.986144	−	0.165890i	$-0.0530496\pi$
$313$	23.6283	+	13.6418i	1.33555	+	0.771081i	0.349407	+	0.936971i	$0.386383\pi$
$314$		0			0
$315$	2.44557	−	4.98586i	0.137792	−	0.280922i
$316$		0			0
$317$	−21.2647	−	12.2772i	−1.19435	−	0.689556i	−0.235057	−	0.971982i	$-0.575528\pi$
$317$	−21.2647	−	12.2772i	−1.19435	−	0.689556i	−0.959289	+	0.282426i	$0.908861\pi$
$318$		0			0
$319$	−0.0418465	−	0.0724802i	−0.00234295	−	0.00405811i
$320$		0			0
$321$	−16.8705	+	6.80115i	−0.941617	+	0.379603i
$322$		0			0
$323$		−	1.64626i		−	0.0916006i
$324$		0			0
$325$	5.13396	+	2.96409i	0.284781	+	0.164418i
$326$		0			0
$327$	15.2021	−	19.4272i	0.840678	−	1.07433i
$328$		0			0
$329$	−14.1904	−	11.9244i	−0.782344	−	0.657411i
$330$		0			0
$331$	8.15579	−	14.1262i	0.448283	−	0.776449i	−0.549991	−	0.835170i	$-0.685369\pi$
$331$	8.15579	−	14.1262i	0.448283	−	0.776449i	0.998274	+	0.0587215i	$0.0187024\pi$
$332$		0			0
$333$	−0.506550	−	2.04494i	−0.0277588	−	0.112062i
$334$		0			0
$335$	−2.07840	−	3.59989i	−0.113555	−	0.196683i
$336$		0			0
$337$	13.6580	−	23.6563i	0.743998	−	1.28864i	−0.206663	−	0.978412i	$-0.566261\pi$
$337$	13.6580	−	23.6563i	0.743998	−	1.28864i	0.950661	−	0.310230i	$-0.100406\pi$
$338$		0			0
$339$	−21.0719	−	16.4891i	−1.14447	−	0.895564i
$340$		0			0
$341$	0.743445	+	1.28768i	0.0402598	+	0.0697320i
$342$		0			0
$343$	−9.29424	+	16.0193i	−0.501842	+	0.864960i
$344$		0			0
$345$	0.841854	−	5.95714i	0.0453239	−	0.320722i
$346$		0			0
$347$	5.37986	−	3.10606i	0.288806	−	0.166742i	−0.348597	−	0.937273i	$-0.613342\pi$
$347$	5.37986	−	3.10606i	0.288806	−	0.166742i	0.637403	+	0.770530i	$0.280009\pi$
$348$		0			0
$349$	−24.6529	+	14.2334i	−1.31964	+	0.761896i	−0.983671	−	0.179977i	$-0.942398\pi$
$349$	−24.6529	+	14.2334i	−1.31964	+	0.761896i	−0.335971	+	0.941872i	$0.609064\pi$
$350$		0			0
$351$	4.00155	+	5.53424i	0.213587	+	0.295396i
$352$		0			0
$353$	2.98691			0.158977			0.0794887	−	0.996836i	$-0.474671\pi$
$353$	2.98691			0.158977			0.0794887	+	0.996836i	$0.474671\pi$
$354$		0			0
$355$		−	9.39798i		−	0.498793i
$356$		0			0
$357$	11.4121	+	12.7120i	0.603994	+	0.672792i
$358$		0			0
$359$	−26.5977	+	15.3562i	−1.40377	+	0.810468i	−0.994777	−	0.102070i	$-0.967454\pi$
$359$	−26.5977	+	15.3562i	−1.40377	+	0.810468i	−0.408994	+	0.912537i	$0.634120\pi$
$360$		0			0
$361$	−9.40249	+	16.2856i	−0.494868	+	0.857136i
$362$		0			0
$363$	−18.7445	−	2.64894i	−0.983830	−	0.139033i
$364$		0			0
$365$	−4.66098	−	2.69102i	−0.243967	−	0.140854i
$366$		0			0
$367$		−	19.0384i		−	0.993794i	−0.867809	−	0.496897i	$-0.834473\pi$
$367$		−	19.0384i		−	0.993794i	0.867809	−	0.496897i	$-0.165527\pi$
$368$		0			0
$369$	23.3130	−	22.4445i	1.21363	−	1.16841i
$370$		0			0
$371$	−16.7437	+	19.9256i	−0.869289	+	1.03449i
$372$		0			0
$373$	4.11738			0.213190			0.106595	−	0.994303i	$-0.466005\pi$
$373$	4.11738			0.213190			0.106595	+	0.994303i	$0.466005\pi$
$374$		0			0
$375$	11.4118	+	1.61270i	0.589302	+	0.0832792i
$376$		0			0
$377$	0.414750			0.0213607
$378$		0			0
$379$	11.2436			0.577546			0.288773	−	0.957398i	$-0.406753\pi$
$379$	11.2436			0.577546			0.288773	+	0.957398i	$0.406753\pi$
$380$		0			0
$381$	37.4393	+	5.29086i	1.91807	+	0.271059i
$382$		0			0
$383$	−31.6093			−1.61516			−0.807580	−	0.589758i	$-0.799223\pi$
$383$	−31.6093			−1.61516			−0.807580	+	0.589758i	$0.799223\pi$
$384$		0			0
$385$	0.483428	+	0.0855949i	0.0246378	+	0.00436232i
$386$		0			0
$387$	−5.38299	−	21.7311i	−0.273633	−	1.10465i
$388$		0			0
$389$		−	21.2485i		−	1.07734i	−0.842516	−	0.538672i	$-0.818926\pi$
$389$		−	21.2485i		−	1.07734i	0.842516	−	0.538672i	$-0.181074\pi$
$390$		0			0
$391$	16.0278	+	9.25367i	0.810562	+	0.467978i
$392$		0			0
$393$	8.93387	+	1.26252i	0.450654	+	0.0636857i
$394$		0			0
$395$	0.488611	−	0.846300i	0.0245847	−	0.0425820i
$396$		0			0
$397$	20.6927	−	11.9469i	1.03854	−	0.599599i	0.119118	−	0.992880i	$-0.461993\pi$
$397$	20.6927	−	11.9469i	1.03854	−	0.599599i	0.919419	+	0.393281i	$0.128660\pi$
$398$		0			0
$399$	0.417843	+	1.98012i	0.0209183	+	0.0991301i
$400$		0			0
$401$			25.4174i			1.26928i	0.772806	+	0.634642i	$0.218853\pi$
$401$			25.4174i			1.26928i	−0.772806	+	0.634642i	$0.781147\pi$
$402$		0			0
$403$	−7.36845			−0.367049
$404$		0			0
$405$	5.32987	+	3.35312i	0.264844	+	0.166618i
$406$		0			0
$407$	0.161295	−	0.0931240i	0.00799512	−	0.00461598i
$408$		0			0
$409$	−19.3831	+	11.1908i	−0.958433	+	0.553351i	−0.895690	−	0.444678i	$-0.853318\pi$
$409$	−19.3831	+	11.1908i	−0.958433	+	0.553351i	−0.0627424	+	0.998030i	$0.519985\pi$
$410$		0			0
$411$	0.653713	−	4.62582i	0.0322453	−	0.228175i
$412$		0			0
$413$	33.4818	−	12.1595i	1.64753	−	0.598330i
$414$		0			0
$415$	−2.60551	−	4.51288i	−0.127900	−	0.221528i
$416$		0			0
$417$	15.9789	+	12.5037i	0.782489	+	0.612309i
$418$		0			0
$419$	7.04181	−	12.1968i	0.344015	−	0.595851i	−0.641159	−	0.767408i	$-0.721546\pi$
$419$	7.04181	−	12.1968i	0.344015	−	0.595851i	0.985174	+	0.171556i	$0.0548796\pi$
$420$		0			0
$421$	8.07639	+	13.9887i	0.393619	+	0.681768i	0.992924	−	0.118753i	$-0.0378896\pi$
$421$	8.07639	+	13.9887i	0.393619	+	0.681768i	−0.599305	+	0.800521i	$0.704556\pi$
$422$		0			0
$423$	15.1407	−	14.5766i	0.736165	−	0.708740i
$424$		0			0
$425$	−8.40717	+	14.5617i	−0.407808	+	0.706344i
$426$		0			0
$427$	−9.62036	+	11.4486i	−0.465562	+	0.554036i
$428$		0			0
$429$	−0.372071	+	0.475482i	−0.0179638	+	0.0229565i
$430$		0			0
$431$	−7.16179	−	4.13486i	−0.344971	−	0.199169i	0.317497	−	0.948259i	$-0.397158\pi$
$431$	−7.16179	−	4.13486i	−0.344971	−	0.199169i	−0.662468	+	0.749090i	$0.730491\pi$
$432$		0			0
$433$		−	4.35102i		−	0.209097i	−0.994520	−	0.104548i	$-0.966660\pi$
$433$		−	4.35102i		−	0.209097i	0.994520	−	0.104548i	$-0.0333397\pi$
$434$		0			0
$435$	0.354676	−	0.142984i	0.0170054	−	0.00685556i
$436$		0			0
$437$	1.09622	+	1.89872i	0.0524395	+	0.0908279i
$438$		0			0
$439$	18.0200	+	10.4039i	0.860048	+	0.496549i	0.864028	−	0.503443i	$-0.167934\pi$
$439$	18.0200	+	10.4039i	0.860048	+	0.496549i	−0.00398054	+	0.999992i	$0.501267\pi$
$440$		0			0
$441$	−16.9530	−	12.3934i	−0.807283	−	0.590164i
$442$		0			0
$443$	26.7927	+	15.4688i	1.27296	+	0.734945i	0.975544	−	0.219803i	$-0.0705414\pi$
$443$	26.7927	+	15.4688i	1.27296	+	0.734945i	0.297417	+	0.954748i	$0.403875\pi$
$444$		0			0
$445$	−3.91290	−	6.77734i	−0.185489	−	0.321277i
$446$		0			0
$447$	4.56320	−	32.2902i	0.215832	−	1.52727i
$448$		0			0
$449$		−	20.9215i		−	0.987346i	−0.869648	−	0.493673i	$-0.835654\pi$
$449$		−	20.9215i		−	0.987346i	0.869648	−	0.493673i	$-0.164346\pi$
$450$		0			0
$451$	2.47763	+	1.43046i	0.116667	+	0.0673577i
$452$		0			0
$453$	17.1550	+	2.42432i	0.806012	+	0.113904i
$454$		0			0
$455$	−1.56519	+	1.86263i	−0.0733771	+	0.0873216i
$456$		0			0
$457$	−1.15058	+	1.99286i	−0.0538217	+	0.0932218i	−0.891681	−	0.452664i	$-0.850474\pi$
$457$	−1.15058	+	1.99286i	−0.0538217	+	0.0932218i	0.837859	+	0.545886i	$0.183807\pi$
$458$		0			0
$459$	−15.6970	+	11.3498i	−0.732673	+	0.529762i
$460$		0			0
$461$	−8.92497	−	15.4585i	−0.415677	−	0.719974i	0.579822	−	0.814743i	$-0.303122\pi$
$461$	−8.92497	−	15.4585i	−0.415677	−	0.719974i	−0.995499	+	0.0947688i	$0.969789\pi$
$462$		0			0
$463$	6.24034	−	10.8086i	0.290013	−	0.502318i	−0.683799	−	0.729670i	$-0.739674\pi$
$463$	6.24034	−	10.8086i	0.290013	−	0.502318i	0.973813	+	0.227353i	$0.0730070\pi$
$464$		0			0
$465$	−6.30119	+	2.54026i	−0.292211	+	0.117802i
$466$		0			0
$467$	−2.42799	−	4.20541i	−0.112354	−	0.194603i	0.804365	−	0.594136i	$-0.202506\pi$
$467$	−2.42799	−	4.20541i	−0.112354	−	0.194603i	−0.916719	+	0.399533i	$0.869172\pi$
$468$		0			0
$469$	−14.7748	+	5.36571i	−0.682236	+	0.247766i
$470$		0			0
$471$	0.404920	−	0.163239i	0.0186577	−	0.00752168i
$472$		0			0
$473$	1.71405	−	0.989607i	0.0788121	−	0.0455022i
$474$		0			0
$475$	−1.72503	+	0.995945i	−0.0791497	+	0.0456971i
$476$		0			0
$477$	−20.4679	−	21.2599i	−0.937161	−	0.973425i
$478$		0			0
$479$	−8.81084			−0.402577			−0.201289	−	0.979532i	$-0.564513\pi$
$479$	−8.81084			−0.402577			−0.201289	+	0.979532i	$0.564513\pi$
$480$		0			0
$481$			0.922973i			0.0420839i
$482$		0			0
$483$	−21.6269	−	7.06221i	−0.984059	−	0.321342i
$484$		0			0
$485$	6.42441	−	3.70914i	0.291718	−	0.168423i
$486$		0			0
$487$	−4.66185	+	8.07456i	−0.211249	+	0.365893i	−0.952106	−	0.305770i	$-0.901086\pi$
$487$	−4.66185	+	8.07456i	−0.211249	+	0.365893i	0.740857	+	0.671663i	$0.234420\pi$
$488$		0			0
$489$	5.56662	+	13.8082i	0.251731	+	0.624427i
$490$		0			0
$491$	26.9192	+	15.5418i	1.21485	+	0.701391i	0.963811	−	0.266587i	$-0.0858960\pi$
$491$	26.9192	+	15.5418i	1.21485	+	0.701391i	0.251034	+	0.967978i	$0.419229\pi$
$492$		0			0
$493$			1.17637i			0.0529811i
$494$		0			0
$495$	−0.154258	+	0.534882i	−0.00693338	+	0.0240412i
$496$		0			0
$497$	−34.9942	−	6.19602i	−1.56971	−	0.277930i
$498$		0			0
$499$	22.3388			1.00002			0.500010	−	0.866020i	$-0.333330\pi$
$499$	22.3388			1.00002			0.500010	+	0.866020i	$0.333330\pi$
$500$		0			0
$501$	−4.79127	+	6.12291i	−0.214058	+	0.273552i
$502$		0			0
$503$	−12.2396			−0.545738			−0.272869	−	0.962051i	$-0.587973\pi$
$503$	−12.2396			−0.545738			−0.272869	+	0.962051i	$0.587973\pi$
$504$		0			0
$505$	12.2490			0.545072
$506$		0			0
$507$	7.30027	+	18.1085i	0.324216	+	0.804229i
$508$		0			0
$509$	−14.1099			−0.625411			−0.312706	−	0.949850i	$-0.601235\pi$
$509$	−14.1099			−0.625411			−0.312706	+	0.949850i	$0.601235\pi$
$510$		0			0
$511$	−13.0932	+	15.5814i	−0.579209	+	0.689281i
$512$		0			0
$513$	−2.28266	+	0.234640i	−0.100782	+	0.0103596i
$514$		0			0
$515$			5.97659i			0.263360i
$516$		0			0
$517$	1.60910	+	0.929015i	0.0707682	+	0.0408580i
$518$		0			0
$519$	7.60141	−	9.71409i	0.333665	−	0.426401i
$520$		0			0
$521$	−2.81632	+	4.87800i	−0.123385	+	0.213709i	−0.921101	−	0.389325i	$-0.872708\pi$
$521$	−2.81632	+	4.87800i	−0.123385	+	0.213709i	0.797715	+	0.603034i	$0.206042\pi$
$522$		0			0
$523$	33.2293	−	19.1849i	1.45302	−	0.838899i	0.454364	−	0.890816i	$-0.349867\pi$
$523$	33.2293	−	19.1849i	1.45302	−	0.838899i	0.998651	+	0.0519176i	$0.0165333\pi$
$524$		0			0
$525$	6.41619	−	19.6486i	0.280025	−	0.857533i
$526$		0			0
$527$		−	20.8995i		−	0.910395i
$528$		0			0
$529$	−1.64754			−0.0716321
$530$		0			0
$531$	9.71167	+	39.2060i	0.421451	+	1.70139i
$532$		0			0
$533$	−12.2782	+	7.08880i	−0.531826	+	0.307050i
$534$		0			0
$535$	6.36329	−	3.67385i	0.275109	−	0.158834i
$536$		0			0
$537$	−34.8518	−	27.2720i	−1.50396	−	1.17687i
$538$		0			0
$539$	0.637441	−	1.74365i	0.0274565	−	0.0751045i
$540$		0			0
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	0.788555	−	0.614965i	$-0.210830\pi$
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	−0.926852	+	0.375426i	$0.877496\pi$
$542$		0			0
$543$	−0.228590	+	1.61756i	−0.00980975	+	0.0694159i
$544$		0			0
$545$	−4.98232	+	8.62963i	−0.213419	+	0.369653i
$546$		0			0
$547$	6.52889	+	11.3084i	0.279155	+	0.483511i	0.971175	−	0.238368i	$-0.0766124\pi$
$547$	6.52889	+	11.3084i	0.279155	+	0.483511i	−0.692020	+	0.721878i	$0.743279\pi$
$548$		0			0
$549$	−11.7602	−	12.2152i	−0.501912	−	0.521333i
$550$		0			0
$551$	−0.0696787	+	0.120687i	−0.00296841	+	0.00514144i
$552$		0			0
$553$	−2.82913	−	2.37735i	−0.120307	−	0.101095i
$554$		0			0
$555$	0.318193	+	0.789287i	0.0135065	+	0.0335034i
$556$		0			0
$557$	25.5409	+	14.7460i	1.08220	+	0.624809i	0.931489	−	0.363769i	$-0.118510\pi$
$557$	25.5409	+	14.7460i	1.08220	+	0.624809i	0.150712	+	0.988578i	$0.451843\pi$
$558$		0			0
$559$			9.80822i			0.414844i
$560$		0			0
$561$	−1.34863	−	1.05532i	−0.0569391	−	0.0445557i
$562$		0			0
$563$	5.25934	+	9.10944i	0.221655	+	0.383917i	0.955311	−	0.295604i	$-0.0955209\pi$
$563$	5.25934	+	9.10944i	0.221655	+	0.383917i	−0.733656	+	0.679521i	$0.762188\pi$
$564$		0			0
$565$	9.36020	+	5.40411i	0.393787	+	0.227353i
$566$		0			0
$567$	15.9996	−	17.6356i	0.671919	−	0.740624i
$568$		0			0
$569$	−22.8054	−	13.1667i	−0.956053	−	0.551977i	−0.0610967	−	0.998132i	$-0.519460\pi$
$569$	−22.8054	−	13.1667i	−0.956053	−	0.551977i	−0.894956	+	0.446155i	$0.852793\pi$
$570$		0			0
$571$	−22.0295	−	38.1562i	−0.921906	−	1.59679i	−0.796463	−	0.604688i	$-0.793298\pi$
$571$	−22.0295	−	38.1562i	−0.921906	−	1.59679i	−0.125444	−	0.992101i	$-0.540035\pi$
$572$		0			0
$573$	−4.05447	−	3.17268i	−0.169378	−	0.132540i
$574$		0			0
$575$		−	22.3929i		−	0.933847i
$576$		0			0
$577$	12.1535	+	7.01684i	0.505957	+	0.292115i	0.731170	−	0.682195i	$-0.238974\pi$
$577$	12.1535	+	7.01684i	0.505957	+	0.292115i	−0.225213	+	0.974310i	$0.572308\pi$
$578$		0			0
$579$	−11.9902	−	29.7420i	−0.498295	−	1.23604i
$580$		0			0
$581$	−18.5219	+	6.72654i	−0.768418	+	0.279064i
$582$		0			0
$583$	1.30448	−	2.25943i	0.0540262	−	0.0935762i
$584$		0			0
$585$	−1.91332	−	1.98736i	−0.0791062	−	0.0821673i
$586$		0			0
$587$	1.52469	+	2.64085i	0.0629308	+	0.108999i	0.895774	−	0.444509i	$-0.146622\pi$
$587$	1.52469	+	2.64085i	0.0629308	+	0.108999i	−0.832843	+	0.553509i	$0.813289\pi$
$588$		0			0
$589$	1.23791	−	2.14413i	0.0510073	−	0.0883473i
$590$		0			0
$591$	3.43607	−	24.3144i	0.141341	−	1.00016i
$592$		0			0
$593$	−13.3041	−	23.0434i	−0.546334	−	0.946278i	−0.998522	−	0.0543552i	$-0.982690\pi$
$593$	−13.3041	−	23.0434i	−0.546334	−	0.946278i	0.452188	−	0.891923i	$-0.350644\pi$
$594$		0			0
$595$	−5.28306	−	4.43941i	−0.216585	−	0.181998i
$596$		0			0
$597$	−32.3354	−	25.3029i	−1.32340	−	1.03558i
$598$		0			0
$599$	3.86333	−	2.23050i	0.157852	−	0.0911356i	−0.418993	−	0.907989i	$-0.637617\pi$
$599$	3.86333	−	2.23050i	0.157852	−	0.0911356i	0.576845	+	0.816854i	$0.304284\pi$
$600$		0			0
$601$	−5.25019	+	3.03120i	−0.214160	+	0.123645i	−0.603243	−	0.797557i	$-0.706125\pi$
$601$	−5.25019	+	3.03120i	−0.214160	+	0.123645i	0.389083	+	0.921203i	$0.372792\pi$
$602$		0			0
$603$	−4.28554	−	17.3007i	−0.174521	−	0.704539i
$604$		0			0
$605$	7.64700			0.310895
$606$		0			0
$607$			45.3313i			1.83994i	0.391986	+	0.919971i	$0.371788\pi$
$607$			45.3313i			1.83994i	−0.391986	+	0.919971i	$0.628212\pi$
$608$		0			0
$609$	−0.298578	−	1.41494i	−0.0120990	−	0.0573361i
$610$		0			0
$611$	−7.97409	+	4.60384i	−0.322597	+	0.186251i
$612$		0			0
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	−0.305781	−	0.952102i	$-0.598917\pi$
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	0.977435	−	0.211237i	$-0.0677492\pi$
$614$		0			0
$615$	−8.05591	+	10.2949i	−0.324846	+	0.415131i
$616$		0			0
$617$	31.3001	+	18.0711i	1.26010	+	0.727516i	0.973093	−	0.230414i	$-0.0740079\pi$
$617$	31.3001	+	18.0711i	1.26010	+	0.727516i	0.287002	+	0.957930i	$0.407341\pi$
$618$		0			0
$619$			26.4462i			1.06296i	0.847069	+	0.531482i	$0.178365\pi$
$619$			26.4462i			1.06296i	−0.847069	+	0.531482i	$0.821635\pi$
$620$		0			0
$621$	10.5464	−	23.5426i	0.423214	−	0.944734i
$622$		0			0
$623$	−27.8158	+	10.1018i	−1.11442	+	0.404719i
$624$		0			0
$625$	17.8969			0.715874
$626$		0			0
$627$	−0.0758507	−	0.188150i	−0.00302918	−	0.00751398i
$628$		0			0
$629$	−2.61787			−0.104381
$630$		0			0
$631$	32.0484			1.27583			0.637914	−	0.770107i	$-0.279797\pi$
$631$	32.0484			1.27583			0.637914	+	0.770107i	$0.279797\pi$
$632$		0			0
$633$	6.48985	−	8.29359i	0.257949	−	0.329641i
$634$		0			0
$635$	−15.2737			−0.606120
$636$		0			0
$637$	5.90376	+	7.05613i	0.233916	+	0.279574i
$638$		0			0
$639$	11.1664	−	38.7189i	0.441735	−	1.53170i
$640$		0			0
$641$			24.4154i			0.964351i	0.876075	+	0.482176i	$0.160153\pi$
$641$			24.4154i			0.964351i	−0.876075	+	0.482176i	$0.839847\pi$
$642$		0			0
$643$	−31.9014	−	18.4183i	−1.25807	−	0.726346i	−0.285370	−	0.958418i	$-0.592116\pi$
$643$	−31.9014	−	18.4183i	−1.25807	−	0.726346i	−0.972699	+	0.232071i	$0.925450\pi$
$644$		0			0
$645$	3.38136	+	8.38757i	0.133141	+	0.330260i
$646$		0			0
$647$	13.2847	−	23.0098i	0.522276	−	0.904608i	−0.477389	−	0.878692i	$-0.658417\pi$
$647$	13.2847	−	23.0098i	0.522276	−	0.904608i	0.999664	−	0.0259155i	$-0.00825009\pi$
$648$		0			0
$649$	−3.09239	+	1.78539i	−0.121387	+	0.0700827i
$650$		0			0
$651$	5.30455	+	25.1378i	0.207902	+	0.985228i
$652$		0			0
$653$			30.3418i			1.18737i	0.804699	+	0.593683i	$0.202327\pi$
$653$			30.3418i			1.18737i	−0.804699	+	0.593683i	$0.797673\pi$
$654$		0			0
$655$	−3.64466			−0.142409
$656$		0			0
$657$	−16.0055	−	16.6248i	−0.624432	−	0.648595i
$658$		0			0
$659$	−40.9873	+	23.6640i	−1.59664	+	0.921820i	−0.604511	+	0.796597i	$0.706631\pi$
$659$	−40.9873	+	23.6640i	−1.59664	+	0.921820i	−0.992129	+	0.125223i	$0.960035\pi$
$660$		0			0
$661$	30.4187	−	17.5623i	1.18315	−	0.683092i	0.226409	−	0.974032i	$-0.427301\pi$
$661$	30.4187	−	17.5623i	1.18315	−	0.683092i	0.956741	+	0.290940i	$0.0939679\pi$
$662$		0			0
$663$	7.87075	−	3.17301i	0.305674	−	0.123229i
$664$		0			0
$665$	−0.279049	−	0.768376i	−0.0108211	−	0.0297963i
$666$		0			0
$667$	−0.783329	−	1.35677i	−0.0303306	−	0.0525342i
$668$		0			0
$669$	−1.47679	+	0.595351i	−0.0570958	+	0.0230176i
$670$		0			0
$671$	0.749513	−	1.29819i	0.0289346	−	0.0501162i
$672$		0			0
$673$	−2.54758	−	4.41254i	−0.0982020	−	0.170091i	0.812738	−	0.582629i	$-0.197976\pi$
$673$	−2.54758	−	4.41254i	−0.0982020	−	0.170091i	−0.910940	+	0.412538i	$0.864642\pi$
$674$		0			0
$675$	21.3890	+	9.58169i	0.823265	+	0.368800i
$676$		0			0
$677$	−8.42072	+	14.5851i	−0.323635	+	0.560551i	−0.981235	−	0.192815i	$-0.938238\pi$
$677$	−8.42072	+	14.5851i	−0.323635	+	0.560551i	0.657601	+	0.753367i	$0.271571\pi$
$678$		0			0
$679$	−9.57573	−	26.3673i	−0.367483	−	1.01188i
$680$		0			0
$681$	17.1603	+	2.42506i	0.657584	+	0.0929287i
$682$		0			0
$683$	15.7555	+	9.09645i	0.602868	+	0.348066i	0.770169	−	0.637840i	$-0.220172\pi$
$683$	15.7555	+	9.09645i	0.602868	+	0.348066i	−0.167301	+	0.985906i	$0.553505\pi$
$684$		0			0
$685$			1.88715i			0.0721042i
$686$		0			0
$687$	0.666559	−	4.71672i	0.0254308	−	0.179954i
$688$		0			0
$689$	6.46452	+	11.1969i	0.246279	+	0.426567i
$690$		0			0
$691$	3.05405	+	1.76326i	0.116182	+	0.0670775i	0.556965	−	0.830536i	$-0.311966\pi$
$691$	3.05405	+	1.76326i	0.116182	+	0.0670775i	−0.440783	+	0.897614i	$0.645299\pi$
$692$		0			0
$693$	1.88998	+	0.927037i	0.0717944	+	0.0352152i
$694$		0			0
$695$	−7.09786	−	4.09795i	−0.269237	−	0.155444i
$696$		0			0
$697$	−20.1063	−	34.8251i	−0.761579	−	1.31909i
$698$		0			0
$699$	−10.3044	+	4.15412i	−0.389749	+	0.157123i
$700$		0			0
$701$			13.3502i			0.504229i	0.967697	+	0.252114i	$0.0811259\pi$
$701$			13.3502i			0.504229i	−0.967697	+	0.252114i	$0.918874\pi$
$702$		0			0
$703$	−0.268574	−	0.155061i	−0.0101295	−	0.00584824i
$704$		0			0
$705$	−5.23193	+	6.68605i	−0.197046	+	0.251811i
$706$		0			0
$707$	8.07566	−	45.6101i	0.303716	−	1.71535i
$708$		0			0
$709$	21.1447	−	36.6237i	0.794107	−	1.37543i	−0.129298	−	0.991606i	$-0.541273\pi$
$709$	21.1447	−	36.6237i	0.794107	−	1.37543i	0.923405	−	0.383827i	$-0.125394\pi$
$710$		0			0
$711$	3.01858	−	2.90613i	0.113206	−	0.108988i
$712$		0			0
$713$	13.9166	+	24.1043i	0.521182	+	0.902715i
$714$		0			0
$715$	0.121942	−	0.211210i	0.00456038	−	0.00789881i
$716$		0			0
$717$	−18.0014	−	14.0863i	−0.672273	−	0.526063i
$718$		0			0
$719$	15.2035	+	26.3332i	0.566994	+	0.982062i	0.996861	+	0.0791697i	$0.0252269\pi$
$719$	15.2035	+	26.3332i	0.566994	+	0.982062i	−0.429868	+	0.902892i	$0.641440\pi$
$720$		0			0
$721$	22.2544	+	3.94032i	0.828796	+	0.146745i
$722$		0			0
$723$	−0.617704	+	4.37101i	−0.0229727	+	0.162560i
$724$		0			0
$725$	1.23265	−	0.711673i	0.0457796	−	0.0264309i
$726$		0			0
$727$	−11.3671	+	6.56280i	−0.421583	+	0.243401i	−0.695754	−	0.718280i	$-0.744930\pi$
$727$	−11.3671	+	6.56280i	−0.421583	+	0.243401i	0.274171	+	0.961681i	$0.411596\pi$
$728$		0			0
$729$	17.9746	+	20.1473i	0.665724	+	0.746198i
$730$		0			0
$731$	−27.8195			−1.02894
$732$		0			0
$733$			37.7588i			1.39465i	0.716753	+	0.697327i	$0.245628\pi$
$733$			37.7588i			1.39465i	−0.716753	+	0.697327i	$0.754372\pi$
$734$		0			0
$735$	7.48123	+	3.99879i	0.275949	+	0.147498i
$736$		0			0
$737$	1.36460	−	0.787853i	0.0502657	−	0.0290209i
$738$		0			0
$739$	13.1215	−	22.7271i	0.482683	−	0.836031i	−0.517119	−	0.855913i	$-0.672996\pi$
$739$	13.1215	−	22.7271i	0.482683	−	0.836031i	0.999802	+	0.0198820i	$0.00632906\pi$
$740$		0			0
$741$	0.995424	+	0.140672i	0.0365678	+	0.00516770i
$742$		0			0
$743$	8.78379	+	5.07132i	0.322246	+	0.186049i	0.652393	−	0.757881i	$-0.273765\pi$
$743$	8.78379	+	5.07132i	0.322246	+	0.186049i	−0.330147	+	0.943929i	$0.607098\pi$
$744$		0			0
$745$			13.1731i			0.482625i
$746$		0			0
$747$	−5.37242	−	21.6884i	−0.196567	−	0.793539i
$748$		0			0
$749$	−9.48462	−	26.1164i	−0.346561	−	0.954273i
$750$		0			0
$751$	−7.90737			−0.288544			−0.144272	−	0.989538i	$-0.546084\pi$
$751$	−7.90737			−0.288544			−0.144272	+	0.989538i	$0.546084\pi$
$752$		0			0
$753$	−32.2239	−	4.55383i	−1.17430	−	0.165951i
$754$		0			0
$755$	−6.99855			−0.254703
$756$		0			0
$757$	29.8903			1.08638			0.543191	−	0.839609i	$-0.317216\pi$
$757$	29.8903			1.08638			0.543191	+	0.839609i	$0.317216\pi$
$758$		0			0
$759$	2.25816	+	0.319119i	0.0819660	+	0.0115833i
$760$		0			0
$761$	−6.11374			−0.221623			−0.110811	−	0.993841i	$-0.535345\pi$
$761$	−6.11374			−0.221623			−0.110811	+	0.993841i	$0.535345\pi$
$762$		0			0
$763$	28.8484	+	24.2416i	1.04438	+	0.877604i
$764$		0			0
$765$	5.63684	−	5.42684i	0.203800	−	0.196208i
$766$		0			0
$767$		−	17.6954i		−	0.638944i
$768$		0			0
$769$	9.79863	+	5.65724i	0.353348	+	0.204005i	0.666159	−	0.745810i	$-0.267937\pi$
$769$	9.79863	+	5.65724i	0.353348	+	0.204005i	−0.312811	+	0.949815i	$0.601271\pi$
$770$		0			0
$771$	−24.6868	−	3.48870i	−0.889073	−	0.125642i
$772$		0			0
$773$	−19.2106	+	33.2737i	−0.690956	+	1.19677i	0.280569	+	0.959834i	$0.409477\pi$
$773$	−19.2106	+	33.2737i	−0.690956	+	1.19677i	−0.971525	+	0.236937i	$0.923856\pi$
$774$		0			0
$775$	−21.8994	+	12.6436i	−0.786648	+	0.454172i
$776$		0			0
$777$	3.14876	−	0.664448i	0.112961	−	0.0238369i
$778$		0			0
$779$		−	4.76373i		−	0.170678i
$780$		0			0
$781$	3.56247			0.127475
$782$		0			0
$783$	1.63112	−	0.167667i	0.0582916	−	0.00599193i
$784$		0			0
$785$	−0.152730	+	0.0881788i	−0.00545117	+	0.00314723i
$786$		0			0
$787$	−41.2747	+	23.8300i	−1.47129	+	0.849447i	−0.999480	−	0.0322557i	$-0.989731\pi$
$787$	−41.2747	+	23.8300i	−1.47129	+	0.849447i	−0.471806	+	0.881703i	$0.656398\pi$
$788$		0			0
$789$	1.90249	−	13.4624i	0.0677304	−	0.479275i
$790$		0			0
$791$	26.2938	−	31.2906i	0.934900	−	1.11257i
$792$		0			0
$793$	3.71430	+	6.43335i	0.131898	+	0.228455i
$794$		0			0
$795$	9.38828	+	7.34646i	0.332968	+	0.260552i
$796$		0			0
$797$	15.1359	−	26.2161i	0.536139	−	0.928621i	−0.462968	−	0.886375i	$-0.653215\pi$
$797$	15.1359	−	26.2161i	0.536139	−	0.928621i	0.999107	−	0.0422457i	$-0.0134512\pi$
$798$		0			0
$799$	−13.0581	−	22.6172i	−0.461961	−	0.800140i
$800$		0			0
$801$	−8.06819	−	32.5712i	−0.285075	−	1.15085i
$802$		0			0
$803$	1.02008	−	1.76683i	0.0359978	−	0.0623500i
$804$		0			0
$805$	9.04935	+	1.60226i	0.318948	+	0.0564723i
$806$		0			0
$807$	−16.4863	+	21.0684i	−0.580345	+	0.741642i
$808$		0			0
$809$	−0.219373	−	0.126655i	−0.00771273	−	0.00445295i	0.496139	−	0.868243i	$-0.334751\pi$
$809$	−0.219373	−	0.126655i	−0.00771273	−	0.00445295i	−0.503851	+	0.863790i	$0.668084\pi$
$810$		0			0
$811$			22.0629i			0.774735i	0.921925	+	0.387367i	$0.126615\pi$
$811$			22.0629i			0.774735i	−0.921925	+	0.387367i	$0.873385\pi$
$812$		0			0
$813$	20.3070	−	8.18657i	0.712199	−	0.287116i
$814$		0			0
$815$	−3.00698	−	5.20824i	−0.105330	−	0.182437i
$816$		0			0
$817$	−2.85407	−	1.64780i	−0.0998514	−	0.0576492i
$818$		0			0
$819$	−8.66156	+	5.81418i	−0.302659	+	0.203164i
$820$		0			0
$821$	24.2467	+	13.9988i	0.846214	+	0.488562i	0.859372	−	0.511352i	$-0.170855\pi$
$821$	24.2467	+	13.9988i	0.846214	+	0.488562i	−0.0131576	+	0.999913i	$0.504188\pi$
$822$		0			0
$823$	24.4771	+	42.3955i	0.853217	+	1.47782i	0.878289	+	0.478130i	$0.158685\pi$
$823$	24.4771	+	42.3955i	0.853217	+	1.47782i	−0.0250719	+	0.999686i	$0.507981\pi$
$824$		0			0
$825$	−0.289928	+	2.05159i	−0.0100940	+	0.0714272i
$826$		0			0
$827$			0.641658i			0.0223126i	0.999938	+	0.0111563i	$0.00355124\pi$
$827$			0.641658i			0.0223126i	−0.999938	+	0.0111563i	$0.996449\pi$
$828$		0			0
$829$	9.57180	+	5.52628i	0.332442	+	0.191936i	0.656925	−	0.753956i	$-0.271857\pi$
$829$	9.57180	+	5.52628i	0.332442	+	0.191936i	−0.324483	+	0.945892i	$0.605190\pi$
$830$		0			0
$831$	20.3926	+	2.88184i	0.707410	+	0.0999700i
$832$		0			0
$833$	−20.0136	+	16.7451i	−0.693430	+	0.580183i
$834$		0			0
$835$	1.57029	−	2.71981i	0.0543420	−	0.0941230i
$836$		0			0
$837$	−28.9786	+	2.97878i	−1.00165	+	0.102962i
$838$		0			0
$839$	−4.62330	−	8.00780i	−0.159614	−	0.276460i	0.775115	−	0.631820i	$-0.217692\pi$
$839$	−4.62330	−	8.00780i	−0.159614	−	0.276460i	−0.934730	+	0.355360i	$0.884358\pi$
$840$		0			0
$841$	−14.4502	+	25.0285i	−0.498283	+	0.863052i
$842$		0			0
$843$	5.10871	−	2.05952i	0.175953	−	0.0709338i
$844$		0			0
$845$	−3.94346	−	6.83028i	−0.135659	−	0.234969i
$846$		0			0
$847$	5.04161	−	28.4743i	0.173232	−	0.978388i
$848$		0			0
$849$	−29.7153	+	11.9794i	−1.01983	+	0.411132i
$850$		0			0
$851$	3.01931	−	1.74320i	0.103501	−	0.0597561i
$852$		0			0
$853$	34.3256	−	19.8179i	1.17529	−	0.678551i	0.220366	−	0.975417i	$-0.429275\pi$
$853$	34.3256	−	19.8179i	1.17529	−	0.678551i	0.954919	+	0.296866i	$0.0959414\pi$
$854$		0			0
$855$	0.899740	−	0.222874i	0.0307705	−	0.00762212i
$856$		0			0
$857$	−23.8520			−0.814770			−0.407385	−	0.913256i	$-0.633559\pi$
$857$	−23.8520			−0.814770			−0.407385	+	0.913256i	$0.633559\pi$
$858$		0			0
$859$		−	11.1138i		−	0.379197i	−0.981862	−	0.189598i	$-0.939281\pi$
$859$		−	11.1138i		−	0.379197i	0.981862	−	0.189598i	$-0.0607186\pi$
$860$		0			0
$861$	33.0228	+	36.7842i	1.12541	+	1.25360i
$862$		0			0
$863$	−38.7780	+	22.3885i	−1.32002	+	0.762113i	−0.983731	−	0.179646i	$-0.942505\pi$
$863$	−38.7780	+	22.3885i	−1.32002	+	0.762113i	−0.336287	+	0.941759i	$0.609171\pi$
$864$		0			0
$865$	−2.49128	+	4.31503i	−0.0847061	+	0.146715i
$866$		0			0
$867$	−2.00968	−	4.98508i	−0.0682525	−	0.169302i
$868$		0			0
$869$	0.320805	+	0.185217i	0.0108826	+	0.00628305i
$870$		0			0
$871$			7.80859i			0.264584i
$872$		0			0
$873$	30.8751	−	7.64804i	1.04496	−	0.258847i
$874$		0			0
$875$	−3.06937	+	17.3354i	−0.103764	+	0.586042i
$876$		0			0
$877$	3.68191			0.124329			0.0621647	−	0.998066i	$-0.480200\pi$
$877$	3.68191			0.124329			0.0621647	+	0.998066i	$0.480200\pi$
$878$		0			0
$879$	−3.05221	+	3.90052i	−0.102949	+	0.131561i
$880$		0			0
$881$	−17.3992			−0.586194			−0.293097	−	0.956083i	$-0.594686\pi$
$881$	−17.3992			−0.586194			−0.293097	+	0.956083i	$0.594686\pi$
$882$		0			0
$883$	2.02834			0.0682592			0.0341296	−	0.999417i	$-0.489134\pi$
$883$	2.02834			0.0682592			0.0341296	+	0.999417i	$0.489134\pi$
$884$		0			0
$885$	−6.10045	−	15.1324i	−0.205065	−	0.508669i
$886$		0			0
$887$	−46.3780			−1.55722			−0.778610	−	0.627508i	$-0.784075\pi$
$887$	−46.3780			−1.55722			−0.778610	+	0.627508i	$0.784075\pi$
$888$		0			0
$889$	−10.0699	+	56.8731i	−0.337732	+	1.90746i
$890$		0			0
$891$	−1.27106	+	2.02038i	−0.0425821	+	0.0676854i
$892$		0			0
$893$		−	3.09381i		−	0.103531i
$894$		0			0
$895$	15.4812	+	8.93810i	0.517481	+	0.298768i
$896$		0			0
$897$	−6.96484	+	8.90060i	−0.232549	+	0.297182i
$898$		0			0
$899$	−0.884576	+	1.53213i	−0.0295023	+	0.0510994i
$900$		0			0
$901$	−31.7582	+	18.3356i	−1.05802	+	0.610847i
$902$		0			0
$903$	33.4612	−	7.06094i	1.11352	−	0.234973i
$904$		0			0
$905$		−	0.659898i		−	0.0219357i
$906$		0			0
$907$	−16.0391			−0.532571			−0.266285	−	0.963894i	$-0.585796\pi$
$907$	−16.0391			−0.532571			−0.266285	+	0.963894i	$0.585796\pi$
$908$		0			0
$909$	50.4647	+	14.5538i	1.67381	+	0.482720i
$910$		0			0
$911$	−17.7833	+	10.2672i	−0.589187	+	0.340167i	−0.764776	−	0.644296i	$-0.777150\pi$
$911$	−17.7833	+	10.2672i	−0.589187	+	0.340167i	0.175589	+	0.984464i	$0.443817\pi$
$912$		0			0
$913$	1.71069	−	0.987665i	0.0566154	−	0.0326869i
$914$		0			0
$915$	5.39419	+	4.22103i	0.178326	+	0.139543i
$916$		0			0
$917$	−2.40290	+	13.5712i	−0.0793507	+	0.448161i
$918$		0			0
$919$	17.7069	+	30.6693i	0.584097	+	1.01169i	0.994987	+	0.100001i	$0.0318846\pi$
$919$	17.7069	+	30.6693i	0.584097	+	1.01169i	−0.410890	+	0.911685i	$0.634782\pi$
$920$		0			0
$921$	−5.25311	+	37.1722i	−0.173096	+	1.22486i
$922$		0			0
$923$	−8.82712	+	15.2890i	−0.290548	+	0.503244i
$924$		0			0
$925$	1.58374	+	2.74311i	0.0520730	+	0.0901930i
$926$		0			0
$927$	−7.10119	+	24.6230i	−0.233234	+	0.808727i
$928$		0			0
$929$	−19.8626	+	34.4030i	−0.651670	+	1.12873i	0.331048	+	0.943614i	$0.392598\pi$
$929$	−19.8626	+	34.4030i	−0.651670	+	1.12873i	−0.982718	+	0.185111i	$0.940735\pi$
$930$		0			0
$931$	−3.04509	+	0.532479i	−0.0997988	+	0.0174513i
$932$		0			0
$933$	−15.3435	−	38.0601i	−0.502325	−	1.24603i
$934$		0			0
$935$	0.599064	+	0.345870i	0.0195915	+	0.0113112i
$936$		0			0
$937$		−	23.2142i		−	0.758376i	−0.925320	−	0.379188i	$-0.876203\pi$
$937$		−	23.2142i		−	0.758376i	0.925320	−	0.379188i	$-0.123797\pi$
$938$		0			0
$939$	−37.2165	−	29.1225i	−1.21452	−	0.950376i
$940$		0			0
$941$	−17.9616	−	31.1104i	−0.585531	−	1.01417i	−0.994809	−	0.101760i	$-0.967553\pi$
$941$	−17.9616	−	31.1104i	−0.585531	−	1.01417i	0.409278	−	0.912410i	$-0.365781\pi$
$942$		0			0
$943$	46.3790	+	26.7769i	1.51031	+	0.871977i
$944$		0			0
$945$	−5.40257	+	7.95809i	−0.175745	+	0.258877i
$946$		0			0
$947$	26.7365	+	15.4363i	0.868818	+	0.501612i	0.866955	−	0.498386i	$-0.166074\pi$
$947$	26.7365	+	15.4363i	0.868818	+	0.501612i	0.00186277	+	0.999998i	$0.499407\pi$
$948$		0			0
$949$	5.05511	+	8.75571i	0.164096	+	0.284222i
$950$		0			0
$951$	33.4937	+	26.2093i	1.08611	+	0.849894i
$952$		0			0
$953$		−	30.4640i		−	0.986826i	−0.869795	−	0.493413i	$-0.835749\pi$
$953$		−	30.4640i		−	0.986826i	0.869795	−	0.493413i	$-0.164251\pi$
$954$		0			0
$955$	1.80100	+	1.03981i	0.0582791	+	0.0336475i
$956$		0			0
$957$	0.0542006	+	0.134446i	0.00175206	+	0.00434603i
$958$		0			0
$959$	7.02696	+	1.24418i	0.226912	+	0.0401768i
$960$		0			0
$961$	0.215406	−	0.373095i	0.00694859	−	0.0120353i
$962$		0			0
$963$	30.5813	−	7.57527i	0.985470	−	0.244110i
$964$		0			0
$965$	6.47686	+	11.2182i	0.208497	+	0.361128i
$966$		0			0
$967$	6.75865	−	11.7063i	0.217343	−	0.376450i	−0.736652	−	0.676272i	$-0.763594\pi$
$967$	6.75865	−	11.7063i	0.217343	−	0.376450i	0.953995	+	0.299823i	$0.0969275\pi$
$968$		0			0
$969$	−0.398993	+	2.82336i	−0.0128175	+	0.0906994i
$970$		0			0
$971$	16.6428	+	28.8261i	0.534092	+	0.925074i	0.999207	+	0.0398238i	$0.0126797\pi$
$971$	16.6428	+	28.8261i	0.534092	+	0.925074i	−0.465115	+	0.885250i	$0.653987\pi$
$972$		0			0
$973$	−19.9387	+	23.7278i	−0.639204	+	0.760677i
$974$		0			0
$975$	−8.08640	−	6.32773i	−0.258972	−	0.202649i
$976$		0			0
$977$	38.9127	−	22.4662i	1.24493	−	0.718758i	0.274833	−	0.961492i	$-0.411377\pi$
$977$	38.9127	−	22.4662i	1.24493	−	0.718758i	0.970093	+	0.242734i	$0.0780441\pi$
$978$		0			0
$979$	2.56907	−	1.48325i	0.0821079	−	0.0474050i
$980$		0			0
$981$	−30.7802	+	29.6335i	−0.982736	+	0.946125i
$982$		0			0
$983$	26.8949			0.857813			0.428907	−	0.903349i	$-0.358899\pi$
$983$	26.8949			0.857813			0.428907	+	0.903349i	$0.358899\pi$
$984$		0			0
$985$			9.91929i			0.316055i
$986$		0			0
$987$	21.4467	+	23.8896i	0.682657	+	0.760415i
$988$		0			0
$989$	32.0855	−	18.5246i	1.02026	−	0.589048i
$990$		0			0
$991$	−17.7201	+	30.6920i	−0.562896	+	0.974965i	0.434346	+	0.900746i	$0.356980\pi$
$991$	−17.7201	+	30.6920i	−0.562896	+	0.974965i	−0.997242	+	0.0742186i	$0.976354\pi$
$992$		0			0
$993$	−17.4109	+	22.2500i	−0.552520	+	0.706082i
$994$		0			0
$995$	14.3635	+	8.29275i	0.455352	+	0.262898i
$996$		0			0
$997$		−	32.4953i		−	1.02914i	−0.857449	−	0.514568i	$-0.827952\pi$
$997$		−	32.4953i		−	1.02914i	0.857449	−	0.514568i	$-0.172048\pi$
$998$		0			0
$999$	0.373122	+	3.62986i	0.0118050	+	0.114844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.d.689.1		16
3.2	odd	2		3024.2.df.d.17.4		16
4.3	odd	2		252.2.bm.a.185.8	yes	16
7.5	odd	6		1008.2.ca.d.257.3		16
9.2	odd	6		1008.2.ca.d.353.3		16
9.7	even	3		3024.2.ca.d.2033.4		16
12.11	even	2		756.2.bm.a.17.4		16
21.5	even	6		3024.2.ca.d.2609.4		16
28.3	even	6		1764.2.x.a.293.6		16
28.11	odd	6		1764.2.x.b.293.3		16
28.19	even	6		252.2.w.a.5.6	✓	16
28.23	odd	6		1764.2.w.b.509.3		16
28.27	even	2		1764.2.bm.a.1697.1		16
36.7	odd	6		756.2.w.a.521.4		16
36.11	even	6		252.2.w.a.101.6	yes	16
36.23	even	6		2268.2.t.b.1781.5		16
36.31	odd	6		2268.2.t.a.1781.4		16
63.47	even	6	inner	1008.2.df.d.929.1		16
63.61	odd	6		3024.2.df.d.1601.4		16
84.11	even	6		5292.2.x.b.881.5		16
84.23	even	6		5292.2.w.b.1097.5		16
84.47	odd	6		756.2.w.a.341.4		16
84.59	odd	6		5292.2.x.a.881.4		16
84.83	odd	2		5292.2.bm.a.2285.5		16
252.11	even	6		1764.2.x.a.1469.6		16
252.47	odd	6		252.2.bm.a.173.8	yes	16
252.79	odd	6		5292.2.bm.a.4625.5		16
252.83	odd	6		1764.2.w.b.1109.3		16
252.103	even	6		2268.2.t.b.2105.5		16
252.115	even	6		5292.2.x.b.4409.5		16
252.131	odd	6		2268.2.t.a.2105.4		16
252.151	odd	6		5292.2.x.a.4409.4		16
252.187	even	6		756.2.bm.a.89.4		16
252.191	even	6		1764.2.bm.a.1685.1		16
252.223	even	6		5292.2.w.b.521.5		16
252.227	odd	6		1764.2.x.b.1469.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.6	✓	16	28.19	even	6
252.2.w.a.101.6	yes	16	36.11	even	6
252.2.bm.a.173.8	yes	16	252.47	odd	6
252.2.bm.a.185.8	yes	16	4.3	odd	2
756.2.w.a.341.4		16	84.47	odd	6
756.2.w.a.521.4		16	36.7	odd	6
756.2.bm.a.17.4		16	12.11	even	2
756.2.bm.a.89.4		16	252.187	even	6
1008.2.ca.d.257.3		16	7.5	odd	6
1008.2.ca.d.353.3		16	9.2	odd	6
1008.2.df.d.689.1		16	1.1	even	1	trivial
1008.2.df.d.929.1		16	63.47	even	6	inner
1764.2.w.b.509.3		16	28.23	odd	6
1764.2.w.b.1109.3		16	252.83	odd	6
1764.2.x.a.293.6		16	28.3	even	6
1764.2.x.a.1469.6		16	252.11	even	6
1764.2.x.b.293.3		16	28.11	odd	6
1764.2.x.b.1469.3		16	252.227	odd	6
1764.2.bm.a.1685.1		16	252.191	even	6
1764.2.bm.a.1697.1		16	28.27	even	2
2268.2.t.a.1781.4		16	36.31	odd	6
2268.2.t.a.2105.4		16	252.131	odd	6
2268.2.t.b.1781.5		16	36.23	even	6
2268.2.t.b.2105.5		16	252.103	even	6
3024.2.ca.d.2033.4		16	9.7	even	3
3024.2.ca.d.2609.4		16	21.5	even	6
3024.2.df.d.17.4		16	3.2	odd	2
3024.2.df.d.1601.4		16	63.61	odd	6
5292.2.w.b.521.5		16	252.223	even	6
5292.2.w.b.1097.5		16	84.23	even	6
5292.2.x.a.881.4		16	84.59	odd	6
5292.2.x.a.4409.4		16	252.151	odd	6
5292.2.x.b.881.5		16	84.11	even	6
5292.2.x.b.4409.5		16	252.115	even	6
5292.2.bm.a.2285.5		16	84.83	odd	2
5292.2.bm.a.4625.5		16	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.71501 - 0.242362i) q^{3} +0.699656 q^{5} +(0.461278 - 2.60523i) q^{7} +(2.88252 + 0.831308i) q^{9} +0.265217i q^{11} +(-1.13823 - 0.657156i) q^{13} +(-1.19992 - 0.169570i) q^{15} +(1.86392 - 3.22840i) q^{17} +(0.382449 - 0.220807i) q^{19} +(-1.42251 + 4.35620i) q^{21} +4.96463i q^{23} -4.51048 q^{25} +(-4.74208 - 2.12432i) q^{27} +(-0.273287 + 0.157782i) q^{29} +(4.85521 - 2.80316i) q^{31} +(0.0642786 - 0.454850i) q^{33} +(0.322736 - 1.82276i) q^{35} +(-0.351124 - 0.608164i) q^{37} +(1.79280 + 1.40289i) q^{39} +(5.39354 - 9.34189i) q^{41} +(-3.73131 - 6.46283i) q^{43} +(2.01677 + 0.581630i) q^{45} +(3.50285 - 6.06712i) q^{47} +(-6.57445 - 2.40347i) q^{49} +(-3.97908 + 5.08500i) q^{51} +(-8.51919 - 4.91856i) q^{53} +0.185561i q^{55} +(-0.709419 + 0.285995i) q^{57} +(6.73182 + 11.6598i) q^{59} +(-4.89484 - 2.82604i) q^{61} +(3.49539 - 7.12617i) q^{63} +(-0.796368 - 0.459783i) q^{65} +(-2.97060 - 5.14523i) q^{67} +(1.20324 - 8.51439i) q^{69} -13.4323i q^{71} +(-6.66182 - 3.84620i) q^{73} +(7.73552 + 1.09317i) q^{75} +(0.690951 + 0.122339i) q^{77} +(0.698360 - 1.20959i) q^{79} +(7.61785 + 4.79253i) q^{81} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(0.506930 - 0.204363i) q^{87} +(-5.59261 - 9.68668i) q^{89} +(-2.23708 + 2.66221i) q^{91} +(-9.00612 + 3.63073i) q^{93} +(0.267582 - 0.154489i) q^{95} +(9.18225 - 5.30138i) q^{97} +(-0.220477 + 0.764493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{7} + 3 q^{13} + 3 q^{15} - 9 q^{17} + 16 q^{25} + 9 q^{27} + 6 q^{29} - 6 q^{31} - 27 q^{33} - 15 q^{35} + q^{37} + 3 q^{39} + 6 q^{41} + 2 q^{43} - 15 q^{45} + 18 q^{47} + 13 q^{49} - 15 q^{51}+ \cdots + 9 q^{99}+O(q^{100}) \) 16 * q + q^7 + 3 * q^13 + 3 * q^15 - 9 * q^17 + 16 * q^25 + 9 * q^27 + 6 * q^29 - 6 * q^31 - 27 * q^33 - 15 * q^35 + q^37 + 3 * q^39 + 6 * q^41 + 2 * q^43 - 15 * q^45 + 18 * q^47 + 13 * q^49 - 15 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 9 * q^63 - 39 * q^65 + 7 * q^67 - 21 * q^69 + 15 * q^75 - 45 * q^77 + q^79 + 6 * q^85 + 3 * q^87 - 21 * q^89 - 9 * q^91 - 69 * q^93 - 6 * q^95 + 3 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

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Database

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