LMFDB - Embedded newform 280.2.bg.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(9,280)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("280.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bg (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	280.9
Dual form			280.2.bg.a.249.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.277116 + 0.159993i) q^{3} +(-2.00685 - 0.986173i) q^{5} +(-1.50695 - 2.17465i) q^{7} +(-1.44880 + 2.50940i) q^{9} +O(q^{10})$	\(q+(-0.277116 + 0.159993i) q^{3} +(-2.00685 - 0.986173i) q^{5} +(-1.50695 - 2.17465i) q^{7} +(-1.44880 + 2.50940i) q^{9} +(-2.08301 - 3.60788i) q^{11} -2.89761i q^{13} +(0.713913 - 0.0477982i) q^{15} +(-3.72628 + 2.15137i) q^{17} +(0.979442 - 1.69644i) q^{19} +(0.765529 + 0.361529i) q^{21} +(-2.23229 - 1.28881i) q^{23} +(3.05492 + 3.95821i) q^{25} -1.88715i q^{27} +5.96541 q^{29} +(-4.71509 - 8.16678i) q^{31} +(1.15447 + 0.666536i) q^{33} +(0.879645 + 5.85032i) q^{35} +(5.48144 + 3.16471i) q^{37} +(0.463598 + 0.802975i) q^{39} -7.19271 q^{41} +4.73966i q^{43} +(5.38224 - 3.60723i) q^{45} +(3.84122 + 2.21773i) q^{47} +(-2.45821 + 6.55418i) q^{49} +(0.688409 - 1.19236i) q^{51} +(-6.37373 + 3.67988i) q^{53} +(0.622303 + 9.29471i) q^{55} +0.626816i q^{57} +(-1.61034 - 2.78920i) q^{59} +(5.94998 - 10.3057i) q^{61} +(7.64035 - 0.630900i) q^{63} +(-2.85754 + 5.81508i) q^{65} +(10.1172 - 5.84119i) q^{67} +0.824804 q^{69} +7.58808 q^{71} +(8.57951 - 4.95338i) q^{73} +(-1.47986 - 0.608118i) q^{75} +(-4.70689 + 9.96672i) q^{77} +(-6.41634 + 11.1134i) q^{79} +(-4.04448 - 7.00525i) q^{81} +5.75180i q^{83} +(9.59972 - 0.642724i) q^{85} +(-1.65311 + 0.954424i) q^{87} +(-1.50907 + 2.61379i) q^{89} +(-6.30129 + 4.36655i) q^{91} +(2.61326 + 1.50877i) q^{93} +(-3.63859 + 2.43861i) q^{95} +0.414281i q^{97} +12.0715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 14 q^{9}+O(q^{10}) $ 24 * q + 14 * q^9	$ 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) $ 24 * q + 14 * q^9 - 2 * q^11 + 12 * q^15 - 10 * q^19 - 10 * q^21 - 2 * q^25 + 12 * q^29 + 4 * q^31 - 28 * q^35 + 20 * q^39 + 24 * q^41 - 8 * q^45 - 30 * q^49 - 12 * q^55 - 48 * q^59 - 18 * q^61 - 26 * q^65 - 60 * q^69 + 16 * q^71 - 14 * q^75 - 44 * q^79 + 12 * q^81 - 44 * q^85 + 30 * q^89 + 44 * q^91 - 26 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.277116	+	0.159993i	−0.159993	+	0.0923721i	−0.577859	−	0.816137i	$-0.696112\pi$
$3$	−0.277116	+	0.159993i	−0.159993	+	0.0923721i	0.417866	+	0.908509i	$0.362778\pi$
$4$		0			0
$5$	−2.00685	−	0.986173i	−0.897492	−	0.441030i
$5$	−2.00685	−	0.986173i	−0.897492	−	0.441030i
$6$		0			0
$7$	−1.50695	−	2.17465i	−0.569573	−	0.821941i
$7$	−1.50695	−	2.17465i	−0.569573	−	0.821941i
$8$		0			0
$9$	−1.44880	+	2.50940i	−0.482935	+	0.836468i
$10$		0			0
$11$	−2.08301	−	3.60788i	−0.628052	−	1.08782i	−0.987942	−	0.154823i	$-0.950519\pi$
$11$	−2.08301	−	3.60788i	−0.628052	−	1.08782i	0.359890	−	0.932995i	$-0.382814\pi$
$12$		0			0
$13$		−	2.89761i		−	0.803652i	−0.915716	−	0.401826i	$-0.868376\pi$
$13$		−	2.89761i		−	0.803652i	0.915716	−	0.401826i	$-0.131624\pi$
$14$		0			0
$15$	0.713913	−	0.0477982i	0.184332	−	0.0123414i
$16$		0			0
$17$	−3.72628	+	2.15137i	−0.903756	+	0.521784i	−0.878417	−	0.477895i	$-0.841400\pi$
$17$	−3.72628	+	2.15137i	−0.903756	+	0.521784i	−0.0253388	+	0.999679i	$0.508066\pi$
$18$		0			0
$19$	0.979442	−	1.69644i	0.224700	−	0.389191i	−0.731530	−	0.681810i	$-0.761193\pi$
$19$	0.979442	−	1.69644i	0.224700	−	0.389191i	0.956229	+	0.292619i	$0.0945266\pi$
$20$		0			0
$21$	0.765529	+	0.361529i	0.167052	+	0.0788922i
$22$		0			0
$23$	−2.23229	−	1.28881i	−0.465464	−	0.268736i	0.248875	−	0.968536i	$-0.419939\pi$
$23$	−2.23229	−	1.28881i	−0.465464	−	0.268736i	−0.714339	+	0.699800i	$0.753272\pi$
$24$		0			0
$25$	3.05492	+	3.95821i	0.610985	+	0.791642i
$26$		0			0
$27$		−	1.88715i		−	0.363183i
$28$		0			0
$29$	5.96541			1.10775			0.553874	−	0.832600i	$-0.313149\pi$
$29$	5.96541			1.10775			0.553874	+	0.832600i	$0.313149\pi$
$30$		0			0
$31$	−4.71509	−	8.16678i	−0.846856	−	1.46680i	−0.884000	−	0.467487i	$-0.845160\pi$
$31$	−4.71509	−	8.16678i	−0.846856	−	1.46680i	0.0371445	−	0.999310i	$-0.488174\pi$
$32$		0			0
$33$	1.15447	+	0.666536i	0.200968	+	0.116029i
$34$		0			0
$35$	0.879645	+	5.85032i	0.148687	+	0.988884i
$36$		0			0
$37$	5.48144	+	3.16471i	0.901143	+	0.520275i	0.877571	−	0.479447i	$-0.159163\pi$
$37$	5.48144	+	3.16471i	0.901143	+	0.520275i	0.0235722	+	0.999722i	$0.492496\pi$
$38$		0			0
$39$	0.463598	+	0.802975i	0.0742350	+	0.128579i
$40$		0			0
$41$	−7.19271			−1.12331			−0.561656	−	0.827371i	$-0.689836\pi$
$41$	−7.19271			−1.12331			−0.561656	+	0.827371i	$0.689836\pi$
$42$		0			0
$43$			4.73966i			0.722792i	0.932412	+	0.361396i	$0.117700\pi$
$43$			4.73966i			0.722792i	−0.932412	+	0.361396i	$0.882300\pi$
$44$		0			0
$45$	5.38224	−	3.60723i	0.802338	−	0.537734i
$46$		0			0
$47$	3.84122	+	2.21773i	0.560300	+	0.323489i	0.753266	−	0.657716i	$-0.228477\pi$
$47$	3.84122	+	2.21773i	0.560300	+	0.323489i	−0.192966	+	0.981205i	$0.561811\pi$
$48$		0			0
$49$	−2.45821	+	6.55418i	−0.351172	+	0.936311i
$50$		0			0
$51$	0.688409	−	1.19236i	0.0963965	−	0.166964i
$52$		0			0
$53$	−6.37373	+	3.67988i	−0.875500	+	0.505470i	−0.869172	−	0.494510i	$-0.835348\pi$
$53$	−6.37373	+	3.67988i	−0.875500	+	0.505470i	−0.00632781	+	0.999980i	$0.502014\pi$
$54$		0			0
$55$	0.622303	+	9.29471i	0.0839113	+	1.25330i
$56$		0			0
$57$			0.626816i			0.0830239i
$58$		0			0
$59$	−1.61034	−	2.78920i	−0.209649	−	0.363122i	0.741955	−	0.670450i	$-0.233899\pi$
$59$	−1.61034	−	2.78920i	−0.209649	−	0.363122i	−0.951604	+	0.307327i	$0.900565\pi$
$60$		0			0
$61$	5.94998	−	10.3057i	0.761817	−	1.31951i	−0.180096	−	0.983649i	$-0.557641\pi$
$61$	5.94998	−	10.3057i	0.761817	−	1.31951i	0.941913	−	0.335857i	$-0.109026\pi$
$62$		0			0
$63$	7.64035	−	0.630900i	0.962593	−	0.0794859i
$64$		0			0
$65$	−2.85754	+	5.81508i	−0.354435	+	0.721272i
$66$		0			0
$67$	10.1172	−	5.84119i	1.23602	−	0.713614i	0.267739	−	0.963492i	$-0.413724\pi$
$67$	10.1172	−	5.84119i	1.23602	−	0.713614i	0.968278	+	0.249877i	$0.0803902\pi$
$68$		0			0
$69$	0.824804			0.0992947
$70$		0			0
$71$	7.58808			0.900539			0.450270	−	0.892893i	$-0.351328\pi$
$71$	7.58808			0.900539			0.450270	+	0.892893i	$0.351328\pi$
$72$		0			0
$73$	8.57951	−	4.95338i	1.00416	−	0.579749i	0.0946803	−	0.995508i	$-0.469817\pi$
$73$	8.57951	−	4.95338i	1.00416	−	0.579749i	0.909475	+	0.415758i	$0.136484\pi$
$74$		0			0
$75$	−1.47986	−	0.608118i	−0.170879	−	0.0702194i
$76$		0			0
$77$	−4.70689	+	9.96672i	−0.536400	+	1.13581i
$78$		0			0
$79$	−6.41634	+	11.1134i	−0.721895	+	1.25036i	0.238345	+	0.971181i	$0.423395\pi$
$79$	−6.41634	+	11.1134i	−0.721895	+	1.25036i	−0.960239	+	0.279178i	$0.909938\pi$
$80$		0			0
$81$	−4.04448	−	7.00525i	−0.449387	−	0.778361i
$82$		0			0
$83$			5.75180i			0.631342i	0.948869	+	0.315671i	$0.102230\pi$
$83$			5.75180i			0.631342i	−0.948869	+	0.315671i	$0.897770\pi$
$84$		0			0
$85$	9.59972	−	0.642724i	1.04124	−	0.0697132i
$86$		0			0
$87$	−1.65311	+	0.954424i	−0.177232	+	0.102325i
$88$		0			0
$89$	−1.50907	+	2.61379i	−0.159961	+	0.277061i	−0.934855	−	0.355031i	$-0.884470\pi$
$89$	−1.50907	+	2.61379i	−0.159961	+	0.277061i	0.774893	+	0.632092i	$0.217804\pi$
$90$		0			0
$91$	−6.30129	+	4.36655i	−0.660554	+	0.457739i
$92$		0			0
$93$	2.61326	+	1.50877i	0.270982	+	0.156452i
$94$		0			0
$95$	−3.63859	+	2.43861i	−0.373311	+	0.250197i
$96$		0			0
$97$			0.414281i			0.0420639i	0.999779	+	0.0210320i	$0.00669517\pi$
$97$			0.414281i			0.0420639i	−0.999779	+	0.0210320i	$0.993305\pi$
$98$		0			0
$99$	12.0715			1.21323
$100$		0			0
$101$	−7.99935	−	13.8553i	−0.795965	−	1.37865i	−0.922224	−	0.386655i	$-0.873630\pi$
$101$	−7.99935	−	13.8553i	−0.795965	−	1.37865i	0.126259	−	0.991997i	$-0.459703\pi$
$102$		0			0
$103$	−2.24596	−	1.29670i	−0.221301	−	0.127768i	0.385252	−	0.922812i	$-0.374115\pi$
$103$	−2.24596	−	1.29670i	−0.221301	−	0.127768i	−0.606552	+	0.795043i	$0.707448\pi$
$104$		0			0
$105$	−1.17977	−	1.48048i	−0.115134	−	0.144480i
$106$		0			0
$107$	−17.0917	−	9.86787i	−1.65231	−	0.953963i	−0.976118	−	0.217239i	$-0.930295\pi$
$107$	−17.0917	−	9.86787i	−1.65231	−	0.953963i	−0.676194	−	0.736724i	$-0.736372\pi$
$108$		0			0
$109$	−4.69235	−	8.12738i	−0.449445	−	0.778462i	0.548905	−	0.835885i	$-0.315045\pi$
$109$	−4.69235	−	8.12738i	−0.449445	−	0.778462i	−0.998350	+	0.0574228i	$0.981712\pi$
$110$		0			0
$111$	−2.02533			−0.192236
$112$		0			0
$113$		−	2.61401i		−	0.245906i	−0.992413	−	0.122953i	$-0.960764\pi$
$113$		−	2.61401i		−	0.245906i	0.992413	−	0.122953i	$-0.0392364\pi$
$114$		0			0
$115$	3.20888	+	4.78788i	0.299230	+	0.446472i
$116$		0			0
$117$	7.27127	+	4.19807i	0.672229	+	0.388112i
$118$		0			0
$119$	10.2938	+	4.86135i	0.943630	+	0.445639i
$120$		0			0
$121$	−3.17788	+	5.50426i	−0.288899	+	0.500387i
$122$		0			0
$123$	1.99322	−	1.15078i	0.179722	−	0.103763i
$124$		0			0
$125$	−2.22730	−	10.9562i	−0.199216	−	0.979956i
$126$		0			0
$127$		−	20.3587i		−	1.80655i	−0.429067	−	0.903273i	$-0.641157\pi$
$127$		−	20.3587i		−	1.80655i	0.429067	−	0.903273i	$-0.358843\pi$
$128$		0			0
$129$	−0.758314	−	1.31344i	−0.0667658	−	0.115642i
$130$		0			0
$131$	1.82538	−	3.16165i	0.159484	−	0.276234i	−0.775199	−	0.631717i	$-0.782350\pi$
$131$	1.82538	−	3.16165i	0.159484	−	0.276234i	0.934683	+	0.355483i	$0.115684\pi$
$132$		0			0
$133$	−5.16514	+	0.426511i	−0.447875	+	0.0369832i
$134$		0			0
$135$	−1.86106	+	3.78724i	−0.160175	+	0.325954i
$136$		0			0
$137$	−9.24192	+	5.33582i	−0.789590	+	0.455870i	−0.839818	−	0.542868i	$-0.817339\pi$
$137$	−9.24192	+	5.33582i	−0.789590	+	0.455870i	0.0502281	+	0.998738i	$0.484005\pi$
$138$		0			0
$139$	−12.0047			−1.01823			−0.509113	−	0.860699i	$-0.670027\pi$
$139$	−12.0047			−1.01823			−0.509113	+	0.860699i	$0.670027\pi$
$140$		0			0
$141$	−1.41929			−0.119526
$142$		0			0
$143$	−10.4542	+	6.03576i	−0.874227	+	0.504735i
$144$		0			0
$145$	−11.9717	−	5.88293i	−0.994196	−	0.488550i
$146$		0			0
$147$	−0.367414	−	2.20957i	−0.0303038	−	0.182242i
$148$		0			0
$149$	6.71251	−	11.6264i	0.549910	−	0.952472i	−0.448370	−	0.893848i	$-0.647995\pi$
$149$	6.71251	−	11.6264i	0.549910	−	0.952472i	0.998280	−	0.0586242i	$-0.0186714\pi$
$150$		0			0
$151$	3.28727	+	5.69371i	0.267514	+	0.463348i	0.968219	−	0.250103i	$-0.0804645\pi$
$151$	3.28727	+	5.69371i	0.267514	+	0.463348i	−0.700705	+	0.713451i	$0.747131\pi$
$152$		0			0
$153$		−	12.4676i		−	1.00795i
$154$		0			0
$155$	1.40864	+	21.0394i	0.113145	+	1.68993i
$156$		0			0
$157$	−2.55523	+	1.47526i	−0.203930	+	0.117739i	−0.598487	−	0.801132i	$-0.704231\pi$
$157$	−2.55523	+	1.47526i	−0.203930	+	0.117739i	0.394558	+	0.918871i	$0.370898\pi$
$158$		0			0
$159$	1.17751	−	2.03951i	0.0933827	−	0.161744i
$160$		0			0
$161$	0.561229	+	6.79662i	0.0442311	+	0.535648i
$162$		0			0
$163$	−4.62597	−	2.67080i	−0.362334	−	0.209194i	0.307770	−	0.951461i	$-0.400417\pi$
$163$	−4.62597	−	2.67080i	−0.362334	−	0.209194i	−0.670104	+	0.742267i	$0.733751\pi$
$164$		0			0
$165$	−1.65954	−	2.47615i	−0.129195	−	0.192768i
$166$		0			0
$167$		−	1.56009i		−	0.120724i	−0.998177	−	0.0603618i	$-0.980775\pi$
$167$		−	1.56009i		−	0.120724i	0.998177	−	0.0603618i	$-0.0192254\pi$
$168$		0			0
$169$	4.60386			0.354143
$170$		0			0
$171$	2.83804	+	4.91563i	0.217030	+	0.375908i
$172$		0			0
$173$	−13.6101	−	7.85781i	−1.03476	−	0.597418i	−0.116414	−	0.993201i	$-0.537140\pi$
$173$	−13.6101	−	7.85781i	−1.03476	−	0.597418i	−0.918344	+	0.395783i	$0.870473\pi$
$174$		0			0
$175$	4.00411	−	12.6082i	0.302682	−	0.953092i
$176$		0			0
$177$	0.892504	+	0.515288i	0.0670847	+	0.0387314i
$178$		0			0
$179$	5.53583	+	9.58834i	0.413767	+	0.716666i	0.995298	−	0.0968583i	$-0.0308794\pi$
$179$	5.53583	+	9.58834i	0.413767	+	0.716666i	−0.581531	+	0.813524i	$0.697546\pi$
$180$		0			0
$181$	14.8950			1.10713			0.553567	−	0.832805i	$-0.313266\pi$
$181$	14.8950			1.10713			0.553567	+	0.832805i	$0.313266\pi$
$182$		0			0
$183$			3.80783i			0.281483i
$184$		0			0
$185$	−7.87949	−	11.7568i	−0.579312	−	0.864374i
$186$		0			0
$187$	15.5238	+	8.96266i	1.13521	+	0.655414i
$188$		0			0
$189$	−4.10390	+	2.84385i	−0.298515	+	0.206859i
$190$		0			0
$191$	0.506772	−	0.877755i	0.0366688	−	0.0635121i	−0.847109	−	0.531420i	$-0.821659\pi$
$191$	0.506772	−	0.877755i	0.0366688	−	0.0635121i	0.883777	+	0.467908i	$0.154992\pi$
$192$		0			0
$193$	6.53206	−	3.77129i	0.470188	−	0.271463i	−0.246131	−	0.969237i	$-0.579159\pi$
$193$	6.53206	−	3.77129i	0.470188	−	0.271463i	0.716318	+	0.697774i	$0.245826\pi$
$194$		0			0
$195$	−0.138500	−	2.06864i	−0.00991822	−	0.148138i
$196$		0			0
$197$		−	9.26180i		−	0.659876i	−0.944003	−	0.329938i	$-0.892972\pi$
$197$		−	9.26180i		−	0.659876i	0.944003	−	0.329938i	$-0.107028\pi$
$198$		0			0
$199$	−8.04961	−	13.9423i	−0.570622	−	0.988346i	−0.996502	−	0.0835668i	$-0.973369\pi$
$199$	−8.04961	−	13.9423i	−0.570622	−	0.988346i	0.425880	−	0.904780i	$-0.359965\pi$
$200$		0			0
$201$	−1.86910	+	3.23738i	−0.131836	+	0.228347i
$202$		0			0
$203$	−8.98957	−	12.9727i	−0.630944	−	0.910503i
$204$		0			0
$205$	14.4347	+	7.09326i	1.00816	+	0.495415i
$206$		0			0
$207$	6.46829	−	3.73447i	0.449577	−	0.259564i
$208$		0			0
$209$	−8.16076			−0.564492
$210$		0			0
$211$	3.20349			0.220537			0.110269	−	0.993902i	$-0.464829\pi$
$211$	3.20349			0.220537			0.110269	+	0.993902i	$0.464829\pi$
$212$		0			0
$213$	−2.10278	+	1.21404i	−0.144080	+	0.0831847i
$214$		0			0
$215$	4.67413	−	9.51181i	0.318773	−	0.648700i
$216$		0			0
$217$	−10.6545	+	22.5606i	−0.723273	+	1.53151i
$218$		0			0
$219$	−1.58501	+	2.74533i	−0.107105	+	0.185512i
$220$		0			0
$221$	6.23382	+	10.7973i	0.419332	+	0.726305i
$222$		0			0
$223$			18.7564i			1.25602i	0.778206	+	0.628010i	$0.216130\pi$
$223$			18.7564i			1.25602i	−0.778206	+	0.628010i	$0.783870\pi$
$224$		0			0
$225$	−14.3587	+	1.93136i	−0.957249	+	0.128757i
$226$		0			0
$227$	−5.85380	+	3.37969i	−0.388530	+	0.224318i	−0.681523	−	0.731797i	$-0.738682\pi$
$227$	−5.85380	+	3.37969i	−0.388530	+	0.224318i	0.292993	+	0.956115i	$0.405349\pi$
$228$		0			0
$229$	0.0815770	−	0.141295i	0.00539076	−	0.00933707i	−0.863317	−	0.504661i	$-0.831617\pi$
$229$	0.0815770	−	0.141295i	0.00539076	−	0.00933707i	0.868708	+	0.495324i	$0.164951\pi$
$230$		0			0
$231$	−0.290251	−	3.51501i	−0.0190971	−	0.231271i
$232$		0			0
$233$	23.6872	+	13.6758i	1.55180	+	0.895931i	0.997996	+	0.0632829i	$0.0201571\pi$
$233$	23.6872	+	13.6758i	1.55180	+	0.895931i	0.553802	+	0.832648i	$0.313176\pi$
$234$		0			0
$235$	−5.52171	−	8.23877i	−0.360196	−	0.537438i
$236$		0			0
$237$		−	4.10628i		−	0.266732i
$238$		0			0
$239$	−19.3226			−1.24988			−0.624938	−	0.780674i	$-0.714876\pi$
$239$	−19.3226			−1.24988			−0.624938	+	0.780674i	$0.714876\pi$
$240$		0			0
$241$	12.1760	+	21.0894i	0.784323	+	1.35849i	0.929403	+	0.369067i	$0.120323\pi$
$241$	12.1760	+	21.0894i	0.784323	+	1.35849i	−0.145080	+	0.989420i	$0.546344\pi$
$242$		0			0
$243$	7.14455	+	4.12491i	0.458323	+	0.264613i
$244$		0			0
$245$	11.3968	−	10.7291i	0.728116	−	0.685454i
$246$		0			0
$247$	−4.91563	−	2.83804i	−0.312774	−	0.180580i
$248$		0			0
$249$	−0.920248	−	1.59392i	−0.0583184	−	0.101010i
$250$		0			0
$251$	−8.53106			−0.538476			−0.269238	−	0.963074i	$-0.586772\pi$
$251$	−8.53106			−0.538476			−0.269238	+	0.963074i	$0.586772\pi$
$252$		0			0
$253$			10.7384i			0.675120i
$254$		0			0
$255$	−2.55741	+	1.71400i	−0.160151	+	0.107335i
$256$		0			0
$257$	18.9948	+	10.9666i	1.18486	+	0.684080i	0.957134	−	0.289645i	$-0.0935371\pi$
$257$	18.9948	+	10.9666i	1.18486	+	0.684080i	0.227728	+	0.973725i	$0.426870\pi$
$258$		0			0
$259$	−1.37811	−	16.6893i	−0.0856318	−	1.03702i
$260$		0			0
$261$	−8.64271	+	14.9696i	−0.534970	+	0.926596i
$262$		0			0
$263$	9.39051	−	5.42162i	0.579044	−	0.334311i	−0.181709	−	0.983352i	$-0.558163\pi$
$263$	9.39051	−	5.42162i	0.579044	−	0.334311i	0.760753	+	0.649041i	$0.224830\pi$
$264$		0			0
$265$	16.4202	−	1.09937i	1.00868	−	0.0675336i
$266$		0			0
$267$		−	0.965765i		−	0.0591039i
$268$		0			0
$269$	9.58343	+	16.5990i	0.584312	+	1.01206i	0.994961	+	0.100265i	$0.0319690\pi$
$269$	9.58343	+	16.5990i	0.584312	+	1.01206i	−0.410649	+	0.911794i	$0.634698\pi$
$270$		0			0
$271$	−5.95683	+	10.3175i	−0.361851	+	0.626745i	−0.988266	−	0.152745i	$-0.951189\pi$
$271$	−5.95683	+	10.3175i	−0.361851	+	0.626745i	0.626414	+	0.779490i	$0.284522\pi$
$272$		0			0
$273$	1.04757	−	2.21820i	0.0634019	−	0.134252i
$274$		0			0
$275$	7.91732	−	19.2668i	0.477433	−	1.16183i
$276$		0			0
$277$	8.13327	−	4.69574i	0.488681	−	0.282140i	−0.235346	−	0.971912i	$-0.575622\pi$
$277$	8.13327	−	4.69574i	0.488681	−	0.282140i	0.724027	+	0.689772i	$0.242289\pi$
$278$		0			0
$279$	27.3250			1.63590
$280$		0			0
$281$	1.15248			0.0687513			0.0343756	−	0.999409i	$-0.489056\pi$
$281$	1.15248			0.0687513			0.0343756	+	0.999409i	$0.489056\pi$
$282$		0			0
$283$	18.2525	−	10.5381i	1.08500	−	0.626424i	0.152758	−	0.988264i	$-0.451185\pi$
$283$	18.2525	−	10.5381i	1.08500	−	0.626424i	0.932240	+	0.361840i	$0.117851\pi$
$284$		0			0
$285$	0.618150	−	1.25793i	0.0366160	−	0.0745133i
$286$		0			0
$287$	10.8390	+	15.6416i	0.639809	+	0.923296i
$288$		0			0
$289$	0.756773	−	1.31077i	0.0445161	−	0.0771041i
$290$		0			0
$291$	−0.0662822	−	0.114804i	−0.00388553	−	0.00672994i
$292$		0			0
$293$			9.92590i			0.579877i	0.957045	+	0.289939i	$0.0936349\pi$
$293$			9.92590i			0.579877i	−0.957045	+	0.289939i	$0.906365\pi$
$294$		0			0
$295$	0.481092	+	7.18558i	0.0280102	+	0.418361i
$296$		0			0
$297$	−6.80863	+	3.93097i	−0.395077	+	0.228098i
$298$		0			0
$299$	−3.73447	+	6.46829i	−0.215970	+	0.374071i
$300$		0			0
$301$	10.3071	−	7.14243i	0.594092	−	0.411683i
$302$		0			0
$303$	4.43350	+	2.55968i	0.254698	+	0.147050i
$304$		0			0
$305$	−22.1039	+	14.8143i	−1.26567	+	0.848262i
$306$		0			0
$307$			2.94680i			0.168183i	0.996458	+	0.0840915i	$0.0267988\pi$
$307$			2.94680i			0.168183i	−0.996458	+	0.0840915i	$0.973201\pi$
$308$		0			0
$309$	0.829856			0.0472088
$310$		0			0
$311$	10.5413	+	18.2580i	0.597740	+	1.03532i	0.993154	+	0.116812i	$0.0372676\pi$
$311$	10.5413	+	18.2580i	0.597740	+	1.03532i	−0.395414	+	0.918503i	$0.629399\pi$
$312$		0			0
$313$	−11.0686	−	6.39048i	−0.625637	−	0.361211i	0.153424	−	0.988160i	$-0.450970\pi$
$313$	−11.0686	−	6.39048i	−0.625637	−	0.361211i	−0.779060	+	0.626949i	$0.784303\pi$
$314$		0			0
$315$	−15.9552	−	6.26858i	−0.898976	−	0.353195i
$316$		0			0
$317$	−6.15548	−	3.55387i	−0.345726	−	0.199605i	0.317075	−	0.948400i	$-0.397299\pi$
$317$	−6.15548	−	3.55387i	−0.345726	−	0.199605i	−0.662801	+	0.748795i	$0.730633\pi$
$318$		0			0
$319$	−12.4260	−	21.5225i	−0.695724	−	1.20503i
$320$		0			0
$321$	6.31517			0.352478
$322$		0			0
$323$			8.42857i			0.468978i
$324$		0			0
$325$	11.4693	−	8.85197i	0.636205	−	0.491019i
$326$		0			0
$327$	2.60065	+	1.50149i	0.143816	+	0.0830324i
$328$		0			0
$329$	−0.965739	−	11.6953i	−0.0532429	−	0.644784i
$330$		0			0
$331$	2.70602	−	4.68696i	0.148736	−	0.257619i	−0.782024	−	0.623248i	$-0.785813\pi$
$331$	2.70602	−	4.68696i	0.148736	−	0.257619i	0.930761	+	0.365629i	$0.119146\pi$
$332$		0			0
$333$	−15.8831	+	9.17009i	−0.870387	+	0.502518i
$334$		0			0
$335$	−26.0642	+	1.74506i	−1.42404	+	0.0953429i
$336$		0			0
$337$		−	16.9764i		−	0.924765i	−0.886681	−	0.462382i	$-0.846995\pi$
$337$		−	16.9764i		−	0.924765i	0.886681	−	0.462382i	$-0.153005\pi$
$338$		0			0
$339$	0.418224	+	0.724385i	0.0227148	+	0.0393432i
$340$		0			0
$341$	−19.6432	+	34.0230i	−1.06374	+	1.84245i
$342$		0			0
$343$	17.9574	−	4.53107i	0.969610	−	0.244655i
$344$		0			0
$345$	−1.65526	−	0.813400i	−0.0891163	−	0.0437920i
$346$		0			0
$347$	13.7424	−	7.93415i	0.737728	−	0.425928i	−0.0835145	−	0.996507i	$-0.526615\pi$
$347$	13.7424	−	7.93415i	0.737728	−	0.425928i	0.821243	+	0.570579i	$0.193281\pi$
$348$		0			0
$349$	−19.1130			−1.02309			−0.511547	−	0.859255i	$-0.670927\pi$
$349$	−19.1130			−1.02309			−0.511547	+	0.859255i	$0.670927\pi$
$350$		0			0
$351$	−5.46823			−0.291873
$352$		0			0
$353$	22.6110	−	13.0545i	1.20346	−	0.694820i	0.242140	−	0.970241i	$-0.422151\pi$
$353$	22.6110	−	13.0545i	1.20346	−	0.694820i	0.961324	+	0.275422i	$0.0888174\pi$
$354$		0			0
$355$	−15.2282	−	7.48316i	−0.808227	−	0.397165i
$356$		0			0
$357$	−3.63036	+	0.299776i	−0.192139	+	0.0158658i
$358$		0			0
$359$	11.5067	−	19.9301i	0.607298	−	1.05187i	−0.384386	−	0.923173i	$-0.625587\pi$
$359$	11.5067	−	19.9301i	0.607298	−	1.05187i	0.991684	−	0.128699i	$-0.0410800\pi$
$360$		0			0
$361$	7.58139	+	13.1313i	0.399020	+	0.691123i
$362$		0			0
$363$		−	2.03376i		−	0.106745i
$364$		0			0
$365$	−22.1027	+	1.47983i	−1.15691	+	0.0774578i
$366$		0			0
$367$	−28.2865	+	16.3312i	−1.47654	+	0.852482i	−0.999649	−	0.0264790i	$-0.991570\pi$
$367$	−28.2865	+	16.3312i	−1.47654	+	0.852482i	−0.476893	+	0.878961i	$0.658237\pi$
$368$		0			0
$369$	10.4208	−	18.0494i	0.542487	−	0.939614i
$370$		0			0
$371$	17.6073	+	8.31525i	0.914128	+	0.431707i
$372$		0			0
$373$	−20.9128	−	12.0740i	−1.08282	−	0.625169i	−0.151168	−	0.988508i	$-0.548303\pi$
$373$	−20.9128	−	12.0740i	−1.08282	−	0.625169i	−0.931657	+	0.363339i	$0.881637\pi$
$374$		0			0
$375$	2.37014	+	2.67980i	0.122394	+	0.138384i
$376$		0			0
$377$		−	17.2854i		−	0.890244i
$378$		0			0
$379$	−30.6614			−1.57497			−0.787484	−	0.616335i	$-0.788617\pi$
$379$	−30.6614			−1.57497			−0.787484	+	0.616335i	$0.788617\pi$
$380$		0			0
$381$	3.25726	+	5.64174i	0.166874	+	0.289035i
$382$		0			0
$383$	−27.6910	−	15.9874i	−1.41494	−	0.816919i	−0.419096	−	0.907942i	$-0.637653\pi$
$383$	−27.6910	−	15.9874i	−1.41494	−	0.816919i	−0.995849	+	0.0910234i	$0.970986\pi$
$384$		0			0
$385$	19.2750	−	15.3599i	0.982343	−	0.782815i
$386$		0			0
$387$	−11.8937	−	6.86684i	−0.604592	−	0.349061i
$388$		0			0
$389$	6.72442	+	11.6470i	0.340942	+	0.590528i	0.984608	−	0.174778i	$-0.0559208\pi$
$389$	6.72442	+	11.6470i	0.340942	+	0.590528i	−0.643666	+	0.765306i	$0.722587\pi$
$390$		0			0
$391$	11.0908			0.560887
$392$		0			0
$393$			1.16819i			0.0589275i
$394$		0			0
$395$	23.8364	−	15.9754i	1.19934	−	0.803810i
$396$		0			0
$397$	10.3921	+	5.99988i	0.521564	+	0.301125i	0.737574	−	0.675266i	$-0.235971\pi$
$397$	10.3921	+	5.99988i	0.521564	+	0.301125i	−0.216010	+	0.976391i	$0.569304\pi$
$398$		0			0
$399$	1.36311	−	0.944581i	0.0682407	−	0.0472882i
$400$		0			0
$401$	16.4468	−	28.4867i	0.821315	−	1.42256i	−0.0833891	−	0.996517i	$-0.526574\pi$
$401$	16.4468	−	28.4867i	0.821315	−	1.42256i	0.904704	−	0.426041i	$-0.140092\pi$
$402$		0			0
$403$	−23.6641	+	13.6625i	−1.17879	+	0.680577i
$404$		0			0
$405$	1.20829	+	18.0471i	0.0600406	+	0.896766i
$406$		0			0
$407$		−	26.3685i		−	1.30704i
$408$		0			0
$409$	10.2012	+	17.6690i	0.504416	+	0.873674i	0.999987	+	0.00510650i	$0.00162546\pi$
$409$	10.2012	+	17.6690i	0.504416	+	0.873674i	−0.495571	+	0.868567i	$0.665041\pi$
$410$		0			0
$411$	1.70739	−	2.95729i	0.0842194	−	0.145872i
$412$		0			0
$413$	−3.63882	+	7.70511i	−0.179055	+	0.379144i
$414$		0			0
$415$	5.67227	−	11.5430i	0.278441	−	0.566624i
$416$		0			0
$417$	3.32670	−	1.92067i	0.162909	−	0.0940557i
$418$		0			0
$419$	28.0820			1.37190			0.685949	−	0.727650i	$-0.259387\pi$
$419$	28.0820			1.37190			0.685949	+	0.727650i	$0.259387\pi$
$420$		0			0
$421$	−14.4438			−0.703949			−0.351974	−	0.936010i	$-0.614490\pi$
$421$	−14.4438			−0.703949			−0.351974	+	0.936010i	$0.614490\pi$
$422$		0			0
$423$	−11.1304	+	6.42612i	−0.541177	+	0.312449i
$424$		0			0
$425$	−19.8991	−	8.17714i	−0.965247	−	0.396649i
$426$		0			0
$427$	−31.3776	+	2.59100i	−1.51847	+	0.125387i
$428$		0			0
$429$	1.93136	−	3.34521i	0.0932469	−	0.161508i
$430$		0			0
$431$	6.67280	+	11.5576i	0.321417	+	0.556711i	0.980781	−	0.195113i	$-0.0625074\pi$
$431$	6.67280	+	11.5576i	0.321417	+	0.556711i	−0.659363	+	0.751824i	$0.729174\pi$
$432$		0			0
$433$		−	2.96912i		−	0.142687i	−0.997452	−	0.0713434i	$-0.977271\pi$
$433$		−	2.96912i		−	0.142687i	0.997452	−	0.0713434i	$-0.0227286\pi$
$434$		0			0
$435$	4.25878	−	0.285135i	0.204193	−	0.0136712i
$436$		0			0
$437$	−4.37279	+	2.52463i	−0.209179	+	0.120770i
$438$		0			0
$439$	−14.2690	+	24.7146i	−0.681023	+	1.17957i	0.293647	+	0.955914i	$0.405131\pi$
$439$	−14.2690	+	24.7146i	−0.681023	+	1.17957i	−0.974669	+	0.223652i	$0.928202\pi$
$440$		0			0
$441$	−12.8856	−	15.6644i	−0.613600	−	0.745921i
$442$		0			0
$443$	−6.02118	−	3.47633i	−0.286075	−	0.165165i	0.350096	−	0.936714i	$-0.386149\pi$
$443$	−6.02118	−	3.47633i	−0.286075	−	0.165165i	−0.636170	+	0.771549i	$0.719482\pi$
$444$		0			0
$445$	5.60614	−	3.75729i	0.265756	−	0.178113i
$446$		0			0
$447$			4.29582i			0.203185i
$448$		0			0
$449$	−5.33832			−0.251931			−0.125965	−	0.992035i	$-0.540203\pi$
$449$	−5.33832			−0.251931			−0.125965	+	0.992035i	$0.540203\pi$
$450$		0			0
$451$	14.9825	+	25.9505i	0.705499	+	1.22196i
$452$		0			0
$453$	−1.82191	−	1.05188i	−0.0856008	−	0.0494216i
$454$		0			0
$455$	16.9519	−	2.54887i	0.794719	−	0.119493i
$456$		0			0
$457$	−4.14044	−	2.39048i	−0.193681	−	0.111822i	0.400023	−	0.916505i	$-0.369002\pi$
$457$	−4.14044	−	2.39048i	−0.193681	−	0.111822i	−0.593705	+	0.804683i	$0.702335\pi$
$458$		0			0
$459$	4.05996	+	7.03206i	0.189503	+	0.328229i
$460$		0			0
$461$	−1.39398			−0.0649242			−0.0324621	−	0.999473i	$-0.510335\pi$
$461$	−1.39398			−0.0649242			−0.0324621	+	0.999473i	$0.510335\pi$
$462$		0			0
$463$		−	27.4620i		−	1.27627i	−0.769925	−	0.638135i	$-0.779706\pi$
$463$		−	27.4620i		−	1.27627i	0.769925	−	0.638135i	$-0.220294\pi$
$464$		0			0
$465$	−3.75652	−	5.60500i	−0.174205	−	0.259925i
$466$		0			0
$467$	33.9868	+	19.6223i	1.57272	+	0.908012i	0.995834	+	0.0911889i	$0.0290667\pi$
$467$	33.9868	+	19.6223i	1.57272	+	0.908012i	0.576889	+	0.816823i	$0.304267\pi$
$468$		0			0
$469$	−27.9487	−	13.1991i	−1.29055	−	0.609476i
$470$		0			0
$471$	0.472064	−	0.817639i	0.0217516	−	0.0376748i
$472$		0			0
$473$	17.1002	−	9.87278i	0.786266	−	0.453951i
$474$		0			0
$475$	9.70701	−	1.30567i	0.445388	−	0.0599081i
$476$		0			0
$477$		−	21.3257i		−	0.976436i
$478$		0			0
$479$	−4.64068	−	8.03789i	−0.212038	−	0.367260i	0.740314	−	0.672261i	$-0.234677\pi$
$479$	−4.64068	−	8.03789i	−0.212038	−	0.367260i	−0.952352	+	0.305000i	$0.901343\pi$
$480$		0			0
$481$	9.17009	−	15.8831i	0.418120	−	0.724205i
$482$		0			0
$483$	−1.24294	−	1.79366i	−0.0565556	−	0.0816144i
$484$		0			0
$485$	0.408553	−	0.831402i	0.0185515	−	0.0377520i
$486$		0			0
$487$	−10.3578	+	5.98006i	−0.469356	+	0.270983i	−0.715970	−	0.698131i	$-0.754015\pi$
$487$	−10.3578	+	5.98006i	−0.469356	+	0.270983i	0.246614	+	0.969114i	$0.420682\pi$
$488$		0			0
$489$	1.70924			0.0772946
$490$		0			0
$491$	−38.6956			−1.74631			−0.873153	−	0.487446i	$-0.837928\pi$
$491$	−38.6956			−1.74631			−0.873153	+	0.487446i	$0.837928\pi$
$492$		0			0
$493$	−22.2288	+	12.8338i	−1.00113	+	0.578005i
$494$		0			0
$495$	−24.2258	−	11.9046i	−1.08887	−	0.535072i
$496$		0			0
$497$	−11.4348	−	16.5014i	−0.512923	−	0.740190i
$498$		0			0
$499$	−14.1441	+	24.4983i	−0.633177	+	1.09669i	0.353722	+	0.935351i	$0.384916\pi$
$499$	−14.1441	+	24.4983i	−0.633177	+	1.09669i	−0.986898	+	0.161344i	$0.948417\pi$
$500$		0			0
$501$	0.249604	+	0.432327i	0.0111515	+	0.0193149i
$502$		0			0
$503$		−	8.88492i		−	0.396159i	−0.980186	−	0.198079i	$-0.936530\pi$
$503$		−	8.88492i		−	0.396159i	0.980186	−	0.198079i	$-0.0634704\pi$
$504$		0			0
$505$	2.38982	+	35.6943i	0.106345	+	1.58837i
$506$		0			0
$507$	−1.27581	+	0.736587i	−0.0566605	+	0.0327130i
$508$		0			0
$509$	1.08158	−	1.87336i	0.0479404	−	0.0830352i	−0.841059	−	0.540943i	$-0.818068\pi$
$509$	1.08158	−	1.87336i	0.0479404	−	0.0830352i	0.889000	+	0.457908i	$0.151401\pi$
$510$		0			0
$511$	−23.7008	−	11.1929i	−1.04846	−	0.495146i
$512$		0			0
$513$	−3.20145	−	1.84836i	−0.141348	−	0.0816070i
$514$		0			0
$515$	3.22853	+	4.81720i	0.142266	+	0.212271i
$516$		0			0
$517$		−	18.4783i		−	0.812673i
$518$		0			0
$519$	5.02878			0.220739
$520$		0			0
$521$	−14.8513	−	25.7232i	−0.650646	−	1.12695i	−0.982966	−	0.183786i	$-0.941165\pi$
$521$	−14.8513	−	25.7232i	−0.650646	−	1.12695i	0.332320	−	0.943167i	$-0.392169\pi$
$522$		0			0
$523$	10.3578	+	5.98006i	0.452914	+	0.261490i	0.709060	−	0.705148i	$-0.249120\pi$
$523$	10.3578	+	5.98006i	0.452914	+	0.261490i	−0.256146	+	0.966638i	$0.582453\pi$
$524$		0			0
$525$	0.907624	+	4.13457i	0.0396120	+	0.180448i
$526$		0			0
$527$	35.1395	+	20.2878i	1.53070	+	0.883750i
$528$		0			0
$529$	−8.17793	−	14.1646i	−0.355562	−	0.615852i
$530$		0			0
$531$	9.33229			0.404987
$532$		0			0
$533$			20.8417i			0.902752i
$534$		0			0
$535$	24.5690	+	36.6587i	1.06221	+	1.58489i
$536$		0			0
$537$	−3.06814	−	1.77139i	−0.132400	−	0.0764411i
$538$		0			0
$539$	28.7672	−	4.78351i	1.23909	−	0.206040i
$540$		0			0
$541$	−5.48408	+	9.49871i	−0.235779	+	0.408381i	−0.959499	−	0.281713i	$-0.909098\pi$
$541$	−5.48408	+	9.49871i	−0.235779	+	0.408381i	0.723720	+	0.690094i	$0.242431\pi$
$542$		0			0
$543$	−4.12764	+	2.38309i	−0.177134	+	0.102268i
$544$		0			0
$545$	1.40184	+	20.9379i	0.0600484	+	0.896883i
$546$		0			0
$547$			30.4206i			1.30069i	0.759638	+	0.650346i	$0.225376\pi$
$547$			30.4206i			1.30069i	−0.759638	+	0.650346i	$0.774624\pi$
$548$		0			0
$549$	17.2407	+	29.8618i	0.735816	+	1.27447i
$550$		0			0
$551$	5.84277	−	10.1200i	0.248910	−	0.431126i
$552$		0			0
$553$	33.8369	−	2.79408i	1.43889	−	0.118816i
$554$		0			0
$555$	4.06454	+	1.99732i	0.172530	+	0.0847817i
$556$		0			0
$557$	33.0596	−	19.0870i	1.40078	−	0.808742i	0.406309	−	0.913736i	$-0.366816\pi$
$557$	33.0596	−	19.0870i	1.40078	−	0.808742i	0.994473	+	0.104994i	$0.0334824\pi$
$558$		0			0
$559$	13.7337			0.580873
$560$		0			0
$561$	−5.73586			−0.242168
$562$		0			0
$563$	16.3320	−	9.42926i	0.688310	−	0.397396i	−0.114669	−	0.993404i	$-0.536581\pi$
$563$	16.3320	−	9.42926i	0.688310	−	0.397396i	0.802979	+	0.596008i	$0.203247\pi$
$564$		0			0
$565$	−2.57787	+	5.24594i	−0.108452	+	0.220698i
$566$		0			0
$567$	−9.13913	+	19.3519i	−0.383808	+	0.812703i
$568$		0			0
$569$	21.7747	−	37.7149i	0.912844	−	1.58109i	0.102816	−	0.994700i	$-0.467215\pi$
$569$	21.7747	−	37.7149i	0.912844	−	1.58109i	0.810028	−	0.586392i	$-0.199452\pi$
$570$		0			0
$571$	−7.21437	−	12.4957i	−0.301912	−	0.522927i	0.674657	−	0.738131i	$-0.264292\pi$
$571$	−7.21437	−	12.4957i	−0.301912	−	0.522927i	−0.976569	+	0.215205i	$0.930958\pi$
$572$		0			0
$573$			0.324320i			0.0135487i
$574$		0			0
$575$	−1.71808	−	12.7731i	−0.0716488	−	0.532674i
$576$		0			0
$577$	−29.8841	+	17.2536i	−1.24409	+	0.718276i	−0.969925	−	0.243406i	$-0.921735\pi$
$577$	−29.8841	+	17.2536i	−1.24409	+	0.718276i	−0.274167	+	0.961682i	$0.588402\pi$
$578$		0			0
$579$	−1.20676	+	2.09017i	−0.0501512	+	0.0868645i
$580$		0			0
$581$	12.5081	−	8.66767i	0.518925	−	0.359595i
$582$		0			0
$583$	26.5531	+	15.3305i	1.09972	+	0.634923i
$584$		0			0
$585$	−10.4523	−	15.5956i	−0.432151	−	0.644800i
$586$		0			0
$587$		−	9.37071i		−	0.386771i	−0.981123	−	0.193385i	$-0.938053\pi$
$587$		−	9.37071i		−	0.386771i	0.981123	−	0.193385i	$-0.0619468\pi$
$588$		0			0
$589$	−18.4726			−0.761152
$590$		0			0
$591$	1.48182	+	2.56660i	0.0609541	+	0.105576i
$592$		0			0
$593$	35.4505	+	20.4674i	1.45578	+	0.840494i	0.998800	−	0.0489841i	$-0.0155984\pi$
$593$	35.4505	+	20.4674i	1.45578	+	0.840494i	0.456978	+	0.889478i	$0.348932\pi$
$594$		0			0
$595$	−15.8640	−	19.9075i	−0.650360	−	0.816127i
$596$		0			0
$597$	4.46136	+	2.57577i	0.182591	+	0.105419i
$598$		0			0
$599$	17.8224	+	30.8693i	0.728203	+	1.26128i	0.957642	+	0.287961i	$0.0929773\pi$
$599$	17.8224	+	30.8693i	0.728203	+	1.26128i	−0.229440	+	0.973323i	$0.573689\pi$
$600$		0			0
$601$	15.3323			0.625417			0.312708	−	0.949849i	$-0.398764\pi$
$601$	15.3323			0.625417			0.312708	+	0.949849i	$0.398764\pi$
$602$		0			0
$603$			33.8509i			1.37852i
$604$		0			0
$605$	11.8057	−	7.91229i	0.479970	−	0.321680i
$606$		0			0
$607$	19.4036	+	11.2026i	0.787566	+	0.454701i	0.839105	−	0.543969i	$-0.183079\pi$
$607$	19.4036	+	11.2026i	0.787566	+	0.454701i	−0.0515389	+	0.998671i	$0.516413\pi$
$608$		0			0
$609$	4.56670	+	2.15667i	0.185052	+	0.0873927i
$610$		0			0
$611$	6.42612	−	11.1304i	0.259973	−	0.450286i
$612$		0			0
$613$	−24.4159	+	14.0965i	−0.986148	+	0.569353i	−0.904121	−	0.427277i	$-0.859473\pi$
$613$	−24.4159	+	14.0965i	−0.986148	+	0.569353i	−0.0820275	+	0.996630i	$0.526140\pi$
$614$		0			0
$615$	−5.13497	+	0.343798i	−0.207062	+	0.0138633i
$616$		0			0
$617$		−	31.0381i		−	1.24955i	−0.780807	−	0.624773i	$-0.785192\pi$
$617$		−	31.0381i		−	1.24955i	0.780807	−	0.624773i	$-0.214808\pi$
$618$		0			0
$619$	−15.0231	−	26.0208i	−0.603829	−	1.04586i	−0.992235	−	0.124374i	$-0.960308\pi$
$619$	−15.0231	−	26.0208i	−0.603829	−	1.04586i	0.388406	−	0.921488i	$-0.373026\pi$
$620$		0			0
$621$	−2.43219	+	4.21267i	−0.0976002	+	0.169049i
$622$		0			0
$623$	7.95818	−	0.657145i	0.318838	−	0.0263279i
$624$		0			0
$625$	−6.33488	+	24.1841i	−0.253395	+	0.967363i
$626$		0			0
$627$	2.26148	−	1.30567i	0.0903148	−	0.0521433i
$628$		0			0
$629$	−27.2338			−1.08588
$630$		0			0
$631$	26.4263			1.05201			0.526007	−	0.850480i	$-0.323688\pi$
$631$	26.4263			1.05201			0.526007	+	0.850480i	$0.323688\pi$
$632$		0			0
$633$	−0.887739	+	0.512537i	−0.0352845	+	0.0203715i
$634$		0			0
$635$	−20.0772	+	40.8570i	−0.796741	+	1.62136i
$636$		0			0
$637$	18.9914	+	7.12292i	0.752468	+	0.282220i
$638$		0			0
$639$	−10.9936	+	19.0415i	−0.434902	+	0.753272i
$640$		0			0
$641$	−3.50488	−	6.07064i	−0.138435	−	0.239776i	0.788470	−	0.615074i	$-0.210874\pi$
$641$	−3.50488	−	6.07064i	−0.138435	−	0.239776i	−0.926904	+	0.375298i	$0.877540\pi$
$642$		0			0
$643$		−	32.0207i		−	1.26277i	−0.775469	−	0.631386i	$-0.782486\pi$
$643$		−	32.0207i		−	1.26277i	0.775469	−	0.631386i	$-0.217514\pi$
$644$		0			0
$645$	0.226547	+	3.38371i	0.00892028	+	0.133233i
$646$		0			0
$647$	−23.8513	+	13.7706i	−0.937692	+	0.541377i	−0.889236	−	0.457449i	$-0.848763\pi$
$647$	−23.8513	+	13.7706i	−0.937692	+	0.541377i	−0.0484560	+	0.998825i	$0.515430\pi$
$648$		0			0
$649$	−6.70873	+	11.6199i	−0.263341	+	0.456119i
$650$		0			0
$651$	−0.657011	−	7.95655i	−0.0257503	−	0.311842i
$652$		0			0
$653$	10.2012	+	5.88965i	0.399203	+	0.230480i	0.686140	−	0.727470i	$-0.259304\pi$
$653$	10.2012	+	5.88965i	0.399203	+	0.230480i	−0.286937	+	0.957949i	$0.592637\pi$
$654$		0			0
$655$	−6.78119	+	4.54482i	−0.264963	+	0.177581i
$656$		0			0
$657$			28.7059i			1.11992i
$658$		0			0
$659$	7.11635			0.277214			0.138607	−	0.990347i	$-0.455738\pi$
$659$	7.11635			0.277214			0.138607	+	0.990347i	$0.455738\pi$
$660$		0			0
$661$	−14.9523	−	25.8982i	−0.581579	−	1.00732i	−0.995292	−	0.0969168i	$-0.969102\pi$
$661$	−14.9523	−	25.8982i	−0.581579	−	1.00732i	0.413714	−	0.910407i	$-0.364231\pi$
$662$		0			0
$663$	−3.45499	−	1.99474i	−0.134181	−	0.0774692i
$664$		0			0
$665$	10.7863	+	4.23778i	0.418275	+	0.164334i
$666$		0			0
$667$	−13.3165	−	7.68828i	−0.515617	−	0.297692i
$668$		0			0
$669$	−3.00089	−	5.19770i	−0.116021	−	0.200955i
$670$		0			0
$671$	−49.5756			−1.91384
$672$		0			0
$673$			10.8573i			0.418520i	0.977860	+	0.209260i	$0.0671054\pi$
$673$			10.8573i			0.418520i	−0.977860	+	0.209260i	$0.932895\pi$
$674$		0			0
$675$	7.46976	−	5.76511i	0.287511	−	0.221899i
$676$		0			0
$677$	18.4549	+	10.6549i	0.709279	+	0.409503i	0.810794	−	0.585332i	$-0.199036\pi$
$677$	18.4549	+	10.6549i	0.709279	+	0.409503i	−0.101515	+	0.994834i	$0.532369\pi$
$678$		0			0
$679$	0.900917	−	0.624301i	0.0345740	−	0.0239585i
$680$		0			0
$681$	1.08145	−	1.87313i	0.0414414	−	0.0717787i
$682$		0			0
$683$	15.3777	−	8.87831i	0.588411	−	0.339719i	−0.176058	−	0.984380i	$-0.556335\pi$
$683$	15.3777	−	8.87831i	0.588411	−	0.339719i	0.764469	+	0.644661i	$0.223001\pi$
$684$		0			0
$685$	23.8092	−	1.59408i	0.909704	−	0.0609068i
$686$		0			0
$687$			0.0522070i			0.00199182i
$688$		0			0
$689$	10.6628	+	18.4686i	0.406222	+	0.703597i
$690$		0			0
$691$	9.78672	−	16.9511i	0.372304	−	0.644850i	−0.617615	−	0.786480i	$-0.711901\pi$
$691$	9.78672	−	16.9511i	0.372304	−	0.644850i	0.989920	+	0.141630i	$0.0452345\pi$
$692$		0			0
$693$	−18.1912	−	26.2513i	−0.691025	−	0.997205i
$694$		0			0
$695$	24.0917	+	11.8387i	0.913851	+	0.449069i
$696$		0			0
$697$	26.8020	−	15.4742i	1.01520	−	0.586126i
$698$		0			0
$699$	−8.75213			−0.331036
$700$		0			0
$701$	−4.10176			−0.154921			−0.0774607	−	0.996995i	$-0.524681\pi$
$701$	−4.10176			−0.154921			−0.0774607	+	0.996995i	$0.524681\pi$
$702$		0			0
$703$	10.7375	−	6.19930i	0.404973	−	0.233811i
$704$		0			0
$705$	2.84830	+	1.39966i	0.107273	+	0.0527144i
$706$		0			0
$707$	−18.0758	+	38.2750i	−0.679810	+	1.43948i
$708$		0			0
$709$	6.87393	−	11.9060i	0.258156	−	0.447139i	−0.707592	−	0.706621i	$-0.750219\pi$
$709$	6.87393	−	11.9060i	0.258156	−	0.447139i	0.965748	+	0.259482i	$0.0835519\pi$
$710$		0			0
$711$	−18.5920	−	32.2024i	−0.697256	−	1.20768i
$712$		0			0
$713$			24.3075i			0.910321i
$714$		0			0
$715$	26.9324	−	1.80319i	1.00722	−	0.0674355i
$716$		0			0
$717$	5.35461	−	3.09149i	0.199972	−	0.115454i
$718$		0			0
$719$	7.59297	−	13.1514i	0.283170	−	0.490465i	−0.688994	−	0.724767i	$-0.741947\pi$
$719$	7.59297	−	13.1514i	0.283170	−	0.490465i	0.972164	+	0.234302i	$0.0752806\pi$
$720$		0			0
$721$	0.564666	+	6.83824i	0.0210293	+	0.254669i
$722$		0			0
$723$	−6.74832	−	3.89614i	−0.250973	−	0.144899i
$724$		0			0
$725$	18.2239	+	23.6123i	0.676817	+	0.876941i
$726$		0			0
$727$			2.68973i			0.0997565i	0.998755	+	0.0498783i	$0.0158833\pi$
$727$			2.68973i			0.0997565i	−0.998755	+	0.0498783i	$0.984117\pi$
$728$		0			0
$729$	21.6271			0.801002
$730$		0			0
$731$	−10.1968	−	17.6613i	−0.377141	−	0.653227i
$732$		0			0
$733$	−28.4602	−	16.4315i	−1.05120	−	0.606911i	−0.128216	−	0.991746i	$-0.540925\pi$
$733$	−28.4602	−	16.4315i	−1.05120	−	0.606911i	−0.922985	+	0.384835i	$0.874258\pi$
$734$		0			0
$735$	−1.44167	+	4.79661i	−0.0531767	+	0.176926i
$736$		0			0
$737$	−42.1486	−	24.3345i	−1.55257	−	0.896374i
$738$		0			0
$739$	13.5981	+	23.5527i	0.500216	+	0.866399i	1.00000		0.000248947i	$7.92422e-5\pi$
$739$	13.5981	+	23.5527i	0.500216	+	0.866399i	−0.499784	+	0.866150i	$0.666587\pi$
$740$		0			0
$741$	1.81627			0.0667223
$742$		0			0
$743$		−	23.8026i		−	0.873233i	−0.899648	−	0.436617i	$-0.856177\pi$
$743$		−	23.8026i		−	0.873233i	0.899648	−	0.436617i	$-0.143823\pi$
$744$		0			0
$745$	−24.9367	+	16.7128i	−0.913609	+	0.612310i
$746$		0			0
$747$	−14.4336	−	8.33323i	−0.528097	−	0.304897i
$748$		0			0
$749$	4.29709	+	52.0387i	0.157012	+	1.90145i
$750$		0			0
$751$	12.7271	−	22.0441i	0.464420	−	0.804399i	−0.534755	−	0.845007i	$-0.679596\pi$
$751$	12.7271	−	22.0441i	0.464420	−	0.804399i	0.999175	+	0.0406078i	$0.0129294\pi$
$752$		0			0
$753$	2.36410	−	1.36491i	0.0861524	−	0.0497401i
$754$		0			0
$755$	−0.982075	−	14.6683i	−0.0357414	−	0.533833i
$756$		0			0
$757$		−	21.9982i		−	0.799537i	−0.916616	−	0.399769i	$-0.869091\pi$
$757$		−	21.9982i		−	0.799537i	0.916616	−	0.399769i	$-0.130909\pi$
$758$		0			0
$759$	−1.71808	−	2.97580i	−0.0623623	−	0.108015i
$760$		0			0
$761$	−2.38991	+	4.13945i	−0.0866343	+	0.150055i	−0.906086	−	0.423093i	$-0.860945\pi$
$761$	−2.38991	+	4.13945i	−0.0866343	+	0.150055i	0.819452	+	0.573148i	$0.194278\pi$
$762$		0			0
$763$	−10.6031	+	22.4518i	−0.383858	+	0.812809i
$764$		0			0
$765$	−12.2953	+	25.0207i	−0.444536	+	0.904627i
$766$		0			0
$767$	−8.08200	+	4.66614i	−0.291824	+	0.168485i
$768$		0			0
$769$	−0.775623			−0.0279697			−0.0139848	−	0.999902i	$-0.504452\pi$
$769$	−0.775623			−0.0279697			−0.0139848	+	0.999902i	$0.504452\pi$
$770$		0			0
$771$	−7.01835			−0.252760
$772$		0			0
$773$	−1.95332	+	1.12775i	−0.0702560	+	0.0405623i	−0.534716	−	0.845032i	$-0.679582\pi$
$773$	−1.95332	+	1.12775i	−0.0702560	+	0.0405623i	0.464461	+	0.885594i	$0.346248\pi$
$774$		0			0
$775$	17.9216	−	43.6122i	0.643763	−	1.56660i
$776$		0			0
$777$	3.05207	+	4.40438i	0.109492	+	0.158006i
$778$		0			0
$779$	−7.04484	+	12.2020i	−0.252408	+	0.437183i
$780$		0			0
$781$	−15.8061	−	27.3769i	−0.565585	−	0.979623i
$782$		0			0
$783$		−	11.2576i		−	0.402315i
$784$		0			0
$785$	6.58284	−	0.440736i	0.234952	−	0.0157306i
$786$		0			0
$787$	38.1429	−	22.0218i	1.35965	−	0.784993i	0.370072	−	0.929003i	$-0.379333\pi$
$787$	38.1429	−	22.0218i	1.35965	−	0.784993i	0.989576	+	0.144010i	$0.0459997\pi$
$788$		0			0
$789$	−1.73484	+	3.00484i	−0.0617620	+	0.106975i
$790$		0			0
$791$	−5.68456	+	3.93918i	−0.202120	+	0.140061i
$792$		0			0
$793$	−29.8618	−	17.2407i	−1.06042	−	0.612236i
$794$		0			0
$795$	−4.37440	+	2.93176i	−0.155144	+	0.103979i
$796$		0			0
$797$		−	1.05089i		−	0.0372245i	−0.999827	−	0.0186122i	$-0.994075\pi$
$797$		−	1.05089i		−	0.0372245i	0.999827	−	0.0186122i	$-0.00592480\pi$
$798$		0			0
$799$	−19.0846			−0.675166
$800$		0			0
$801$	−4.37270	−	7.57374i	−0.154502	−	0.267605i
$802$		0			0
$803$	−35.7424	−	20.6359i	−1.26132	−	0.728226i
$804$		0			0
$805$	5.57634	−	14.1933i	0.196540	−	0.500247i
$806$		0			0
$807$	−5.31145	−	3.06657i	−0.186972	−	0.107948i
$808$		0			0
$809$	7.27506	+	12.6008i	0.255777	+	0.443019i	0.965106	−	0.261858i	$-0.0843353\pi$
$809$	7.27506	+	12.6008i	0.255777	+	0.443019i	−0.709329	+	0.704878i	$0.751002\pi$
$810$		0			0
$811$	13.0148			0.457010			0.228505	−	0.973543i	$-0.426616\pi$
$811$	13.0148			0.457010			0.228505	+	0.973543i	$0.426616\pi$
$812$		0			0
$813$		−	3.81221i		−	0.133700i
$814$		0			0
$815$	6.64977	+	9.92192i	0.232931	+	0.347550i
$816$		0			0
$817$	8.04057	+	4.64223i	0.281304	+	0.162411i
$818$		0			0
$819$	−1.82810	−	22.1387i	−0.0638790	−	0.773590i
$820$		0			0
$821$	1.75766	−	3.04435i	0.0613427	−	0.106249i	−0.833723	−	0.552183i	$-0.813795\pi$
$821$	1.75766	−	3.04435i	0.0613427	−	0.106249i	0.895066	+	0.445934i	$0.147128\pi$
$822$		0			0
$823$	−35.7049	+	20.6142i	−1.24459	+	0.718567i	−0.970026	−	0.243001i	$-0.921868\pi$
$823$	−35.7049	+	20.6142i	−1.24459	+	0.718567i	−0.274568	+	0.961568i	$0.588535\pi$
$824$		0			0
$825$	0.888540	+	6.60587i	0.0309350	+	0.229987i
$826$		0			0
$827$		−	6.21314i		−	0.216052i	−0.994148	−	0.108026i	$-0.965547\pi$
$827$		−	6.21314i		−	0.216052i	0.994148	−	0.108026i	$-0.0344530\pi$
$828$		0			0
$829$	−3.76940	−	6.52879i	−0.130917	−	0.226754i	0.793114	−	0.609074i	$-0.208459\pi$
$829$	−3.76940	−	6.52879i	−0.130917	−	0.226754i	−0.924030	+	0.382320i	$0.875125\pi$
$830$		0			0
$831$	−1.50257	+	2.60254i	−0.0521237	+	0.0902809i
$832$		0			0
$833$	−4.94048	−	29.7112i	−0.171177	−	1.02943i
$834$		0			0
$835$	−1.53852	+	3.13088i	−0.0532427	+	0.108348i
$836$		0			0
$837$	−15.4120	+	8.89811i	−0.532716	+	0.307564i
$838$		0			0
$839$	−16.2861			−0.562259			−0.281129	−	0.959670i	$-0.590709\pi$
$839$	−16.2861			−0.562259			−0.281129	+	0.959670i	$0.590709\pi$
$840$		0			0
$841$	6.58608			0.227106
$842$		0			0
$843$	−0.319371	+	0.184389i	−0.0109997	+	0.00635070i
$844$		0			0
$845$	−9.23928	−	4.54021i	−0.317841	−	0.156188i
$846$		0			0
$847$	16.7587	−	1.38385i	0.575837	−	0.0475496i
$848$		0			0
$849$	−3.37204	+	5.84055i	−0.115728	+	0.200447i
$850$		0			0
$851$	−8.15743	−	14.1291i	−0.279633	−	0.484339i
$852$		0			0
$853$			30.0261i			1.02808i	0.857768	+	0.514038i	$0.171851\pi$
$853$			30.0261i			1.02808i	−0.857768	+	0.514038i	$0.828149\pi$
$854$		0			0
$855$	−0.847868	−	12.6638i	−0.0289965	−	0.433091i
$856$		0			0
$857$	19.2379	−	11.1070i	0.657153	−	0.379407i	−0.134038	−	0.990976i	$-0.542795\pi$
$857$	19.2379	−	11.1070i	0.657153	−	0.379407i	0.791191	+	0.611569i	$0.209461\pi$
$858$		0			0
$859$	12.7242	−	22.0390i	0.434146	−	0.751962i	−0.563080	−	0.826402i	$-0.690384\pi$
$859$	12.7242	−	22.0390i	0.434146	−	0.751962i	0.997225	+	0.0744403i	$0.0237170\pi$
$860$		0			0
$861$	−5.50623	−	2.60038i	−0.187652	−	0.0886206i
$862$		0			0
$863$	7.41308	+	4.27994i	0.252344	+	0.145691i	0.620837	−	0.783940i	$-0.286793\pi$
$863$	7.41308	+	4.27994i	0.252344	+	0.145691i	−0.368493	+	0.929630i	$0.620126\pi$
$864$		0			0
$865$	19.5644	+	29.1914i	0.665208	+	0.992538i
$866$		0			0
$867$			0.484314i			0.0164482i
$868$		0			0
$869$	53.4613			1.81355
$870$		0			0
$871$	−16.9255	−	29.3158i	−0.573498	−	0.993327i
$872$		0			0
$873$	−1.03960	−	0.600213i	−0.0351851	−	0.0203141i
$874$		0			0
$875$	−20.4696	+	21.3541i	−0.691997	+	0.721900i
$876$		0			0
$877$	−36.9702	−	21.3447i	−1.24839	−	0.720760i	−0.277604	−	0.960695i	$-0.589540\pi$
$877$	−36.9702	−	21.3447i	−1.24839	−	0.720760i	−0.970789	+	0.239935i	$0.922874\pi$
$878$		0			0
$879$	−1.58808	−	2.75063i	−0.0535645	−	0.0927764i
$880$		0			0
$881$	−20.0315			−0.674879			−0.337439	−	0.941347i	$-0.609561\pi$
$881$	−20.0315			−0.674879			−0.337439	+	0.941347i	$0.609561\pi$
$882$		0			0
$883$			13.5719i			0.456730i	0.973576	+	0.228365i	$0.0733380\pi$
$883$			13.5719i			0.456730i	−0.973576	+	0.228365i	$0.926662\pi$
$884$		0			0
$885$	−1.28296	−	1.91427i	−0.0431263	−	0.0643475i
$886$		0			0
$887$	−25.2508	−	14.5786i	−0.847839	−	0.489500i	0.0120824	−	0.999927i	$-0.496154\pi$
$887$	−25.2508	−	14.5786i	−0.847839	−	0.489500i	−0.859921	+	0.510427i	$0.829487\pi$
$888$		0			0
$889$	−44.2731	+	30.6796i	−1.48487	+	1.02896i
$890$		0			0
$891$	−16.8494	+	29.1840i	−0.564477	+	0.977702i
$892$		0			0
$893$	7.52451	−	4.34428i	0.251798	−	0.145376i
$894$		0			0
$895$	−1.65384	−	24.7017i	−0.0552816	−	0.825686i
$896$		0			0
$897$		−	2.38996i		−	0.0797984i
$898$		0			0
$899$	−28.1274	−	48.7182i	−0.938103	−	1.62484i
$900$		0			0
$901$	15.8335	−	27.4245i	0.527492	−	0.913643i
$902$		0			0
$903$	−1.71353	+	3.62835i	−0.0570226	+	0.120744i
$904$		0			0
$905$	−29.8920	−	14.6890i	−0.993644	−	0.488279i
$906$		0			0
$907$	−41.5469	+	23.9871i	−1.37954	+	0.796479i	−0.992104	−	0.125416i	$-0.959973\pi$
$907$	−41.5469	+	23.9871i	−1.37954	+	0.796479i	−0.387439	+	0.921896i	$0.626640\pi$
$908$		0			0
$909$	46.3580			1.53760
$910$		0			0
$911$	42.2832			1.40091			0.700453	−	0.713699i	$-0.252981\pi$
$911$	42.2832			1.40091			0.700453	+	0.713699i	$0.252981\pi$
$912$		0			0
$913$	20.7518	−	11.9811i	0.686785	−	0.396516i
$914$		0			0
$915$	3.75518	−	7.64175i	0.124142	−	0.252629i
$916$		0			0
$917$	−9.62622	+	0.794883i	−0.317886	+	0.0262494i
$918$		0			0
$919$	−18.9821	+	32.8780i	−0.626162	+	1.08454i	0.362153	+	0.932119i	$0.382042\pi$
$919$	−18.9821	+	32.8780i	−0.626162	+	1.08454i	−0.988315	+	0.152426i	$0.951292\pi$
$920$		0			0
$921$	−0.471468	−	0.816607i	−0.0155354	−	0.0269081i
$922$		0			0
$923$		−	21.9873i		−	0.723720i
$924$		0			0
$925$	4.21878	+	31.3646i	0.138713	+	1.03126i
$926$		0			0
$927$	6.50791	−	3.75734i	0.213748	−	0.123407i
$928$		0			0
$929$	−1.26381	+	2.18899i	−0.0414643	+	0.0718183i	−0.886013	−	0.463661i	$-0.846536\pi$
$929$	−1.26381	+	2.18899i	−0.0414643	+	0.0718183i	0.844548	+	0.535479i	$0.179869\pi$
$930$		0			0
$931$	8.71112	+	10.5896i	0.285495	+	0.347062i
$932$		0			0
$933$	−5.84231	−	3.37306i	−0.191268	−	0.110429i
$934$		0			0
$935$	−22.3152	−	33.2959i	−0.729786	−	1.08889i
$936$		0			0
$937$		−	1.05740i		−	0.0345438i	−0.999851	−	0.0172719i	$-0.994502\pi$
$937$		−	1.05740i		−	0.0345438i	0.999851	−	0.0172719i	$-0.00549809\pi$
$938$		0			0
$939$	4.08973			0.133463
$940$		0			0
$941$	5.33792	+	9.24555i	0.174011	+	0.301396i	0.939819	−	0.341674i	$-0.110994\pi$
$941$	5.33792	+	9.24555i	0.174011	+	0.301396i	−0.765807	+	0.643070i	$0.777660\pi$
$942$		0			0
$943$	16.0562	+	9.27004i	0.522861	+	0.301874i
$944$		0			0
$945$	11.0405	−	1.66003i	0.359146	−	0.0540006i
$946$		0			0
$947$	25.3370	+	14.6283i	0.823341	+	0.475356i	0.851567	−	0.524245i	$-0.175653\pi$
$947$	25.3370	+	14.6283i	0.823341	+	0.475356i	−0.0282263	+	0.999602i	$0.508986\pi$
$948$		0			0
$949$	−14.3530	−	24.8601i	−0.465917	−	0.806992i
$950$		0			0
$951$	2.27438			0.0737517
$952$		0			0
$953$			6.31630i			0.204605i	0.994753	+	0.102302i	$0.0326209\pi$
$953$			6.31630i			0.204605i	−0.994753	+	0.102302i	$0.967379\pi$
$954$		0			0
$955$	−1.88264	+	1.26176i	−0.0609207	+	0.0408296i
$956$		0			0
$957$	6.88691	+	3.97616i	0.222622	+	0.128531i
$958$		0			0
$959$	25.5306	+	12.0571i	0.824428	+	0.389345i
$960$		0			0
$961$	−28.9642	+	50.1674i	−0.934329	+	1.61830i
$962$		0			0
$963$	49.5249	−	28.5932i	1.59592	−	0.921404i
$964$		0			0
$965$	−16.8280	+	1.12668i	−0.541713	+	0.0362690i
$966$		0			0
$967$		−	54.2185i		−	1.74355i	−0.489906	−	0.871775i	$-0.662969\pi$
$967$		−	54.2185i		−	1.74355i	0.489906	−	0.871775i	$-0.337031\pi$
$968$		0			0
$969$	−1.34851	−	2.33569i	−0.0433205	−	0.0750333i
$970$		0			0
$971$	7.20395	−	12.4776i	0.231186	−	0.400426i	−0.726971	−	0.686668i	$-0.759073\pi$
$971$	7.20395	−	12.4776i	0.231186	−	0.400426i	0.958157	+	0.286242i	$0.0924061\pi$
$972$		0			0
$973$	18.0905	+	26.1061i	0.579955	+	0.836922i
$974$		0			0
$975$	−1.76209	+	4.28804i	−0.0564320	+	0.137327i
$976$		0			0
$977$	−21.0650	+	12.1619i	−0.673929	+	0.389093i	−0.797564	−	0.603235i	$-0.793878\pi$
$977$	−21.0650	+	12.1619i	−0.673929	+	0.389093i	0.123635	+	0.992328i	$0.460545\pi$
$978$		0			0
$979$	12.5737			0.401856
$980$		0			0
$981$	27.1932			0.868211
$982$		0			0
$983$	−19.2591	+	11.1192i	−0.614270	+	0.354649i	−0.774635	−	0.632409i	$-0.782066\pi$
$983$	−19.2591	+	11.1192i	−0.614270	+	0.354649i	0.160365	+	0.987058i	$0.448733\pi$
$984$		0			0
$985$	−9.13374	+	18.5871i	−0.291025	+	0.592234i
$986$		0			0
$987$	2.13879	+	3.08645i	0.0680786	+	0.0982429i
$988$		0			0
$989$	6.10853	−	10.5803i	0.194240	−	0.336433i
$990$		0			0
$991$	6.13274	+	10.6222i	0.194813	+	0.337426i	0.946839	−	0.321707i	$-0.104257\pi$
$991$	6.13274	+	10.6222i	0.194813	+	0.337426i	−0.752026	+	0.659133i	$0.770923\pi$
$992$		0			0
$993$			1.73178i			0.0549563i
$994$		0			0
$995$	2.40483	+	35.9186i	0.0762383	+	1.13869i
$996$		0			0
$997$	−4.18103	+	2.41392i	−0.132414	+	0.0764495i	−0.564744	−	0.825266i	$-0.691025\pi$
$997$	−4.18103	+	2.41392i	−0.132414	+	0.0764495i	0.432330	+	0.901716i	$0.357692\pi$
$998$		0			0
$999$	5.97230	−	10.3443i	0.188955	−	0.327280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bg.a.9.6	✓	24
4.3	odd	2		560.2.bw.f.289.7		24
5.2	odd	4		1400.2.q.n.401.4		12
5.3	odd	4		1400.2.q.o.401.3		12
5.4	even	2	inner	280.2.bg.a.9.7	yes	24
7.2	even	3		1960.2.g.f.1569.6		12
7.4	even	3	inner	280.2.bg.a.249.7	yes	24
7.5	odd	6		1960.2.g.e.1569.7		12
20.19	odd	2		560.2.bw.f.289.6		24
28.11	odd	6		560.2.bw.f.529.6		24
35.2	odd	12		9800.2.a.cx.1.3		6
35.4	even	6	inner	280.2.bg.a.249.6	yes	24
35.9	even	6		1960.2.g.f.1569.7		12
35.12	even	12		9800.2.a.cw.1.4		6
35.18	odd	12		1400.2.q.o.1201.3		12
35.19	odd	6		1960.2.g.e.1569.6		12
35.23	odd	12		9800.2.a.cv.1.4		6
35.32	odd	12		1400.2.q.n.1201.4		12
35.33	even	12		9800.2.a.cy.1.3		6
140.39	odd	6		560.2.bw.f.529.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bg.a.9.6	✓	24	1.1	even	1	trivial
280.2.bg.a.9.7	yes	24	5.4	even	2	inner
280.2.bg.a.249.6	yes	24	35.4	even	6	inner
280.2.bg.a.249.7	yes	24	7.4	even	3	inner
560.2.bw.f.289.6		24	20.19	odd	2
560.2.bw.f.289.7		24	4.3	odd	2
560.2.bw.f.529.6		24	28.11	odd	6
560.2.bw.f.529.7		24	140.39	odd	6
1400.2.q.n.401.4		12	5.2	odd	4
1400.2.q.n.1201.4		12	35.32	odd	12
1400.2.q.o.401.3		12	5.3	odd	4
1400.2.q.o.1201.3		12	35.18	odd	12
1960.2.g.e.1569.6		12	35.19	odd	6
1960.2.g.e.1569.7		12	7.5	odd	6
1960.2.g.f.1569.6		12	7.2	even	3
1960.2.g.f.1569.7		12	35.9	even	6
9800.2.a.cv.1.4		6	35.23	odd	12
9800.2.a.cw.1.4		6	35.12	even	12
9800.2.a.cx.1.3		6	35.2	odd	12
9800.2.a.cy.1.3		6	35.33	even	12

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.277116 + 0.159993i) q^{3} +(-2.00685 - 0.986173i) q^{5} +(-1.50695 - 2.17465i) q^{7} +(-1.44880 + 2.50940i) q^{9} +O(q^{10})\)	\(q+(-0.277116 + 0.159993i) q^{3} +(-2.00685 - 0.986173i) q^{5} +(-1.50695 - 2.17465i) q^{7} +(-1.44880 + 2.50940i) q^{9} +(-2.08301 - 3.60788i) q^{11} -2.89761i q^{13} +(0.713913 - 0.0477982i) q^{15} +(-3.72628 + 2.15137i) q^{17} +(0.979442 - 1.69644i) q^{19} +(0.765529 + 0.361529i) q^{21} +(-2.23229 - 1.28881i) q^{23} +(3.05492 + 3.95821i) q^{25} -1.88715i q^{27} +5.96541 q^{29} +(-4.71509 - 8.16678i) q^{31} +(1.15447 + 0.666536i) q^{33} +(0.879645 + 5.85032i) q^{35} +(5.48144 + 3.16471i) q^{37} +(0.463598 + 0.802975i) q^{39} -7.19271 q^{41} +4.73966i q^{43} +(5.38224 - 3.60723i) q^{45} +(3.84122 + 2.21773i) q^{47} +(-2.45821 + 6.55418i) q^{49} +(0.688409 - 1.19236i) q^{51} +(-6.37373 + 3.67988i) q^{53} +(0.622303 + 9.29471i) q^{55} +0.626816i q^{57} +(-1.61034 - 2.78920i) q^{59} +(5.94998 - 10.3057i) q^{61} +(7.64035 - 0.630900i) q^{63} +(-2.85754 + 5.81508i) q^{65} +(10.1172 - 5.84119i) q^{67} +0.824804 q^{69} +7.58808 q^{71} +(8.57951 - 4.95338i) q^{73} +(-1.47986 - 0.608118i) q^{75} +(-4.70689 + 9.96672i) q^{77} +(-6.41634 + 11.1134i) q^{79} +(-4.04448 - 7.00525i) q^{81} +5.75180i q^{83} +(9.59972 - 0.642724i) q^{85} +(-1.65311 + 0.954424i) q^{87} +(-1.50907 + 2.61379i) q^{89} +(-6.30129 + 4.36655i) q^{91} +(2.61326 + 1.50877i) q^{93} +(-3.63859 + 2.43861i) q^{95} +0.414281i q^{97} +12.0715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{9}+O(q^{10}) \) 24 * q + 14 * q^9	\( 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) \) 24 * q + 14 * q^9 - 2 * q^11 + 12 * q^15 - 10 * q^19 - 10 * q^21 - 2 * q^25 + 12 * q^29 + 4 * q^31 - 28 * q^35 + 20 * q^39 + 24 * q^41 - 8 * q^45 - 30 * q^49 - 12 * q^55 - 48 * q^59 - 18 * q^61 - 26 * q^65 - 60 * q^69 + 16 * q^71 - 14 * q^75 - 44 * q^79 + 12 * q^81 - 44 * q^85 + 30 * q^89 + 44 * q^91 - 26 * q^95 - 44 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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