LMFDB - Embedded newform 936.2.r.f.841.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(601,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.601"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.r (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.10
Character	$\chi$	$=$	936.841
Dual form			936.2.r.f.601.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.389445 + 1.68770i) q^{3} +(0.0819095 - 0.141871i) q^{5} +(0.591337 - 1.02423i) q^{7} +(-2.69666 - 1.31453i) q^{9} +2.29493 q^{11} +(-3.42118 - 1.13821i) q^{13} +(0.207537 + 0.193490i) q^{15} +(3.94208 + 6.82788i) q^{17} +(3.06904 + 5.31573i) q^{19} +(1.49829 + 1.39688i) q^{21} +(0.573384 + 0.993131i) q^{23} +(2.48658 + 4.30689i) q^{25} +(3.26874 - 4.03922i) q^{27} -1.56932 q^{29} +(-0.925310 + 1.60268i) q^{31} +(-0.893751 + 3.87316i) q^{33} +(-0.0968723 - 0.167788i) q^{35} +(-5.72598 + 9.91769i) q^{37} +(3.25333 - 5.33065i) q^{39} +(-2.95467 - 5.11764i) q^{41} +(0.743066 - 1.28703i) q^{43} +(-0.407378 + 0.274907i) q^{45} +(-4.66028 - 8.07184i) q^{47} +(2.80064 + 4.85085i) q^{49} +(-13.0586 + 3.99396i) q^{51} -2.44339 q^{53} +(0.187977 - 0.325586i) q^{55} +(-10.1666 + 3.10943i) q^{57} +12.4101 q^{59} +(-6.44679 + 11.1662i) q^{61} +(-2.94102 + 1.98466i) q^{63} +(-0.441707 + 0.392137i) q^{65} +(-6.07271 - 10.5182i) q^{67} +(-1.89941 + 0.580930i) q^{69} +(4.54262 + 7.86805i) q^{71} +7.68457 q^{73} +(-8.23712 + 2.51931i) q^{75} +(1.35708 - 2.35053i) q^{77} +(6.50531 + 11.2675i) q^{79} +(5.54400 + 7.08972i) q^{81} +(-0.0150208 - 0.0260167i) q^{83} +1.29157 q^{85} +(0.611164 - 2.64854i) q^{87} +(7.59038 - 13.1469i) q^{89} +(-3.18886 + 2.83099i) q^{91} +(-2.34449 - 2.18580i) q^{93} +1.00553 q^{95} +(-1.37072 + 2.37416i) q^{97} +(-6.18866 - 3.01677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + q^{5} + 7 q^{7} + 6 q^{9} + 11 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} - q^{23} - 23 q^{25} - 3 q^{27} - 24 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{35} + 18 q^{37} + 6 q^{39} - 3 q^{41} + 8 q^{43}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q + q^5 + 7 * q^7 + 6 * q^9 + 11 * q^15 - q^17 + 2 * q^19 - 30 * q^21 - q^23 - 23 * q^25 - 3 * q^27 - 24 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^35 + 18 * q^37 + 6 * q^39 - 3 * q^41 + 8 * q^43 + 24 * q^45 + 4 * q^47 - 23 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 + 8 * q^59 - 3 * q^61 + 10 * q^63 - 32 * q^65 + 27 * q^67 - 38 * q^69 + q^71 - 12 * q^73 + 32 * q^75 - 4 * q^77 + 13 * q^79 + 26 * q^81 - 15 * q^83 - 10 * q^85 + 25 * q^87 + 12 * q^89 - 57 * q^91 - 7 * q^93 - 2 * q^95 + 35 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.389445	+	1.68770i	−0.224846	+	0.974394i
$3$	−0.389445	+	1.68770i	−0.224846	+	0.974394i
$4$		0			0
$5$	0.0819095	−	0.141871i	0.0366311	−	0.0634469i	−0.847129	−	0.531388i	$-0.821671\pi$
$5$	0.0819095	−	0.141871i	0.0366311	−	0.0634469i	0.883760	+	0.467941i	$0.155004\pi$
$6$		0			0
$7$	0.591337	−	1.02423i	0.223504	−	0.387121i	−0.732365	−	0.680912i	$-0.761584\pi$
$7$	0.591337	−	1.02423i	0.223504	−	0.387121i	0.955870	+	0.293791i	$0.0949170\pi$
$8$		0			0
$9$	−2.69666	−	1.31453i	−0.898888	−	0.438178i
$10$		0			0
$11$	2.29493			0.691948			0.345974	−	0.938244i	$-0.387548\pi$
$11$	2.29493			0.691948			0.345974	+	0.938244i	$0.387548\pi$
$12$		0			0
$13$	−3.42118	−	1.13821i	−0.948864	−	0.315684i
$13$	−3.42118	−	1.13821i	−0.948864	−	0.315684i
$14$		0			0
$15$	0.207537	+	0.193490i	0.0535859	+	0.0499589i
$16$		0			0
$17$	3.94208	+	6.82788i	0.956094	+	1.65600i	0.731845	+	0.681471i	$0.238660\pi$
$17$	3.94208	+	6.82788i	0.956094	+	1.65600i	0.224249	+	0.974532i	$0.428007\pi$
$18$		0			0
$19$	3.06904	+	5.31573i	0.704085	+	1.21951i	0.967021	+	0.254698i	$0.0819760\pi$
$19$	3.06904	+	5.31573i	0.704085	+	1.21951i	−0.262935	+	0.964813i	$0.584691\pi$
$20$		0			0
$21$	1.49829	+	1.39688i	0.326954	+	0.304824i
$22$		0			0
$23$	0.573384	+	0.993131i	0.119559	+	0.207082i	0.919593	−	0.392873i	$-0.128519\pi$
$23$	0.573384	+	0.993131i	0.119559	+	0.207082i	−0.800034	+	0.599955i	$0.795185\pi$
$24$		0			0
$25$	2.48658	+	4.30689i	0.497316	+	0.861377i
$26$		0			0
$27$	3.26874	−	4.03922i	0.629070	−	0.777349i
$28$		0			0
$29$	−1.56932			−0.291415			−0.145708	−	0.989328i	$-0.546546\pi$
$29$	−1.56932			−0.291415			−0.145708	+	0.989328i	$0.546546\pi$
$30$		0			0
$31$	−0.925310	+	1.60268i	−0.166191	+	0.287851i	−0.937077	−	0.349122i	$-0.886480\pi$
$31$	−0.925310	+	1.60268i	−0.166191	+	0.287851i	0.770887	+	0.636972i	$0.219813\pi$
$32$		0			0
$33$	−0.893751	+	3.87316i	−0.155582	+	0.674231i
$34$		0			0
$35$	−0.0968723	−	0.167788i	−0.0163744	−	0.0283613i
$36$		0			0
$37$	−5.72598	+	9.91769i	−0.941346	+	1.63046i	−0.178438	+	0.983951i	$0.557105\pi$
$37$	−5.72598	+	9.91769i	−0.941346	+	1.63046i	−0.762907	+	0.646508i	$0.776229\pi$
$38$		0			0
$39$	3.25333	−	5.33065i	0.520949	−	0.853588i
$40$		0			0
$41$	−2.95467	−	5.11764i	−0.461442	−	0.799241i	0.537591	−	0.843206i	$-0.319334\pi$
$41$	−2.95467	−	5.11764i	−0.461442	−	0.799241i	−0.999033	+	0.0439645i	$0.986001\pi$
$42$		0			0
$43$	0.743066	−	1.28703i	0.113317	−	0.196270i	−0.803789	−	0.594914i	$-0.797186\pi$
$43$	0.743066	−	1.28703i	0.113317	−	0.196270i	0.917106	+	0.398644i	$0.130519\pi$
$44$		0			0
$45$	−0.407378	+	0.274907i	−0.0607283	+	0.0409807i
$46$		0			0
$47$	−4.66028	−	8.07184i	−0.679771	−	1.17740i	−0.975050	−	0.221987i	$-0.928746\pi$
$47$	−4.66028	−	8.07184i	−0.679771	−	1.17740i	0.295278	−	0.955411i	$-0.404588\pi$
$48$		0			0
$49$	2.80064	+	4.85085i	0.400092	+	0.692979i
$50$		0			0
$51$	−13.0586	+	3.99396i	−1.82857	+	0.559266i
$52$		0			0
$53$	−2.44339			−0.335626			−0.167813	−	0.985819i	$-0.553670\pi$
$53$	−2.44339			−0.335626			−0.167813	+	0.985819i	$0.553670\pi$
$54$		0			0
$55$	0.187977	−	0.325586i	0.0253468	−	0.0439020i
$56$		0			0
$57$	−10.1666	+	3.10943i	−1.34660	+	0.411854i
$58$		0			0
$59$	12.4101			1.61565			0.807826	−	0.589420i	$-0.200644\pi$
$59$	12.4101			1.61565			0.807826	+	0.589420i	$0.200644\pi$
$60$		0			0
$61$	−6.44679	+	11.1662i	−0.825427	+	1.42968i	0.0761655	+	0.997095i	$0.475732\pi$
$61$	−6.44679	+	11.1662i	−0.825427	+	1.42968i	−0.901592	+	0.432586i	$0.857601\pi$
$62$		0			0
$63$	−2.94102	+	1.98466i	−0.370533	+	0.250044i
$64$		0			0
$65$	−0.441707	+	0.392137i	−0.0547871	+	0.0486386i
$66$		0			0
$67$	−6.07271	−	10.5182i	−0.741899	−	1.28501i	−0.951630	−	0.307248i	$-0.900592\pi$
$67$	−6.07271	−	10.5182i	−0.741899	−	1.28501i	0.209731	−	0.977759i	$-0.432741\pi$
$68$		0			0
$69$	−1.89941	+	0.580930i	−0.228662	+	0.0699358i
$70$		0			0
$71$	4.54262	+	7.86805i	0.539110	+	0.933766i	0.998952	+	0.0457654i	$0.0145727\pi$
$71$	4.54262	+	7.86805i	0.539110	+	0.933766i	−0.459842	+	0.888001i	$0.652094\pi$
$72$		0			0
$73$	7.68457			0.899411			0.449705	−	0.893177i	$-0.351529\pi$
$73$	7.68457			0.899411			0.449705	+	0.893177i	$0.351529\pi$
$74$		0			0
$75$	−8.23712	+	2.51931i	−0.951141	+	0.290905i
$76$		0			0
$77$	1.35708	−	2.35053i	0.154654	−	0.267868i
$78$		0			0
$79$	6.50531	+	11.2675i	0.731904	+	1.26769i	0.956068	+	0.293144i	$0.0947014\pi$
$79$	6.50531	+	11.2675i	0.731904	+	1.26769i	−0.224164	+	0.974551i	$0.571965\pi$
$80$		0			0
$81$	5.54400	+	7.08972i	0.616000	+	0.787746i
$82$		0			0
$83$	−0.0150208	−	0.0260167i	−0.00164874	−	0.00285571i	0.865200	−	0.501427i	$-0.167191\pi$
$83$	−0.0150208	−	0.0260167i	−0.00164874	−	0.00285571i	−0.866849	+	0.498571i	$0.833858\pi$
$84$		0			0
$85$	1.29157			0.140091
$86$		0			0
$87$	0.611164	−	2.64854i	0.0655237	−	0.283953i
$88$		0			0
$89$	7.59038	−	13.1469i	0.804578	−	1.39357i	−0.111997	−	0.993709i	$-0.535725\pi$
$89$	7.59038	−	13.1469i	0.804578	−	1.39357i	0.916575	−	0.399862i	$-0.130942\pi$
$90$		0			0
$91$	−3.18886	+	2.83099i	−0.334283	+	0.296769i
$92$		0			0
$93$	−2.34449	−	2.18580i	−0.243113	−	0.226657i
$94$		0			0
$95$	1.00553			0.103166
$96$		0			0
$97$	−1.37072	+	2.37416i	−0.139176	+	0.241060i	−0.927185	−	0.374604i	$-0.877779\pi$
$97$	−1.37072	+	2.37416i	−0.139176	+	0.241060i	0.788009	+	0.615664i	$0.211112\pi$
$98$		0			0
$99$	−6.18866	−	3.01677i	−0.621984	−	0.303197i
$100$		0			0
$101$	−14.2372			−1.41665			−0.708326	−	0.705886i	$-0.750549\pi$
$101$	−14.2372			−1.41665			−0.708326	+	0.705886i	$0.750549\pi$
$102$		0			0
$103$	3.14211	−	5.44230i	0.309602	−	0.536246i	−0.668674	−	0.743556i	$-0.733138\pi$
$103$	3.14211	−	5.44230i	0.309602	−	0.536246i	0.978275	+	0.207310i	$0.0664710\pi$
$104$		0			0
$105$	0.320902	−	0.0981472i	0.0313168	−	0.00957819i
$106$		0			0
$107$	−5.10344	+	8.83941i	−0.493368	+	0.854538i	−0.999971	−	0.00764122i	$-0.997568\pi$
$107$	−5.10344	+	8.83941i	−0.493368	+	0.854538i	0.506603	+	0.862180i	$0.330901\pi$
$108$		0			0
$109$	−7.43590			−0.712230			−0.356115	−	0.934442i	$-0.615899\pi$
$109$	−7.43590			−0.712230			−0.356115	+	0.934442i	$0.615899\pi$
$110$		0			0
$111$	−14.5081	−	13.5261i	−1.37705	−	1.28384i
$112$		0			0
$113$	10.0453			0.944981			0.472491	−	0.881336i	$-0.343355\pi$
$113$	10.0453			0.944981			0.472491	+	0.881336i	$0.343355\pi$
$114$		0			0
$115$	0.187863			0.0175183
$116$		0			0
$117$	7.72955	+	7.56664i	0.714597	+	0.699536i
$118$		0			0
$119$	9.32438			0.854765
$120$		0			0
$121$	−5.73328			−0.521207
$122$		0			0
$123$	9.78773	−	2.99356i	0.882530	−	0.269920i
$124$		0			0
$125$	1.63379			0.146131
$126$		0			0
$127$	8.84715	−	15.3237i	0.785058	−	1.35976i	−0.143907	−	0.989591i	$-0.545967\pi$
$127$	8.84715	−	15.3237i	0.785058	−	1.35976i	0.928965	−	0.370169i	$-0.120700\pi$
$128$		0			0
$129$	1.88273	+	1.75530i	0.165766	+	0.154546i
$130$		0			0
$131$	1.77284	−	3.07065i	0.154894	−	0.268284i	−0.778126	−	0.628108i	$-0.783830\pi$
$131$	1.77284	−	3.07065i	0.154894	−	0.268284i	0.933020	+	0.359823i	$0.117163\pi$
$132$		0			0
$133$	7.25934			0.629465
$134$		0			0
$135$	−0.305309	−	0.794592i	−0.0262768	−	0.0683876i
$136$		0			0
$137$	0.337834	−	0.585145i	0.0288631	−	0.0499923i	−0.851233	−	0.524788i	$-0.824145\pi$
$137$	0.337834	−	0.585145i	0.0288631	−	0.0499923i	0.880096	+	0.474796i	$0.157478\pi$
$138$		0			0
$139$	1.29110			0.109510			0.0547550	−	0.998500i	$-0.482562\pi$
$139$	1.29110			0.109510			0.0547550	+	0.998500i	$0.482562\pi$
$140$		0			0
$141$	15.4378	−	4.72161i	1.30009	−	0.397631i
$142$		0			0
$143$	−7.85138	−	2.61213i	−0.656565	−	0.218437i
$144$		0			0
$145$	−0.128542	+	0.222642i	−0.0106749	+	0.0184894i
$146$		0			0
$147$	−9.27748	+	2.83750i	−0.765194	+	0.234033i
$148$		0			0
$149$	19.3867			1.58822			0.794111	−	0.607772i	$-0.207937\pi$
$149$	19.3867			1.58822			0.794111	+	0.607772i	$0.207937\pi$
$150$		0			0
$151$	2.65901	+	4.60555i	0.216387	+	0.374794i	0.953701	−	0.300757i	$-0.0972392\pi$
$151$	2.65901	+	4.60555i	0.216387	+	0.374794i	−0.737313	+	0.675551i	$0.763906\pi$
$152$		0			0
$153$	−1.65498	−	23.5945i	−0.133797	−	1.90750i
$154$		0			0
$155$	0.151583	+	0.262550i	0.0121755	+	0.0210885i
$156$		0			0
$157$	−6.44003	+	11.1545i	−0.513971	+	0.890223i	0.485898	+	0.874015i	$0.338493\pi$
$157$	−6.44003	+	11.1545i	−0.513971	+	0.890223i	−0.999869	+	0.0162076i	$0.994841\pi$
$158$		0			0
$159$	0.951568	−	4.12371i	0.0754643	−	0.327032i
$160$		0			0
$161$	1.35625			0.106888
$162$		0			0
$163$	9.15301	+	15.8535i	0.716919	+	1.24174i	0.962215	+	0.272292i	$0.0877817\pi$
$163$	9.15301	+	15.8535i	0.716919	+	1.24174i	−0.245295	+	0.969448i	$0.578885\pi$
$164$		0			0
$165$	0.476284	+	0.444047i	0.0370787	+	0.0345690i
$166$		0			0
$167$	−5.86630	−	10.1607i	−0.453948	−	0.786261i	0.544679	−	0.838645i	$-0.316652\pi$
$167$	−5.86630	−	10.1607i	−0.453948	−	0.786261i	−0.998627	+	0.0523833i	$0.983318\pi$
$168$		0			0
$169$	10.4089	+	7.78807i	0.800687	+	0.599083i
$170$		0			0
$171$	−1.28846	−	18.3691i	−0.0985307	−	1.40472i
$172$		0			0
$173$	5.55966	−	9.62962i	0.422693	−	0.732126i	−0.573509	−	0.819200i	$-0.694418\pi$
$173$	5.55966	−	9.62962i	0.422693	−	0.732126i	0.996202	+	0.0870733i	$0.0277514\pi$
$174$		0			0
$175$	5.88163			0.444610
$176$		0			0
$177$	−4.83304	+	20.9445i	−0.363274	+	1.57428i
$178$		0			0
$179$	9.27406	−	16.0631i	0.693176	−	1.20062i	−0.277616	−	0.960692i	$-0.589544\pi$
$179$	9.27406	−	16.0631i	0.693176	−	1.20062i	0.970792	−	0.239924i	$-0.0771224\pi$
$180$		0			0
$181$	−11.4050			−0.847725			−0.423863	−	0.905727i	$-0.639326\pi$
$181$	−11.4050			−0.847725			−0.423863	+	0.905727i	$0.639326\pi$
$182$		0			0
$183$	−16.3345	−	15.2289i	−1.20748	−	1.12575i
$184$		0			0
$185$	0.938025	+	1.62471i	0.0689650	+	0.119451i
$186$		0			0
$187$	9.04680	+	15.6695i	0.661568	+	1.14587i
$188$		0			0
$189$	−2.20415	−	5.73647i	−0.160328	−	0.417267i
$190$		0			0
$191$	7.68395	−	13.3090i	0.555991	−	0.963005i	−0.441835	−	0.897096i	$-0.645672\pi$
$191$	7.68395	−	13.3090i	0.555991	−	0.963005i	0.997826	−	0.0659081i	$-0.0209944\pi$
$192$		0			0
$193$	−6.76272	−	11.7134i	−0.486792	−	0.843148i	0.513093	−	0.858333i	$-0.328500\pi$
$193$	−6.76272	−	11.7134i	−0.486792	−	0.843148i	−0.999885	+	0.0151852i	$0.995166\pi$
$194$		0			0
$195$	−0.489789	−	0.898186i	−0.0350745	−	0.0643204i
$196$		0			0
$197$	6.58807	−	11.4109i	0.469380	−	0.812991i	−0.530007	−	0.847993i	$-0.677811\pi$
$197$	6.58807	−	11.4109i	0.469380	−	0.812991i	0.999387	+	0.0350026i	$0.0111439\pi$
$198$		0			0
$199$	−11.9218	−	20.6492i	−0.845117	−	1.46379i	−0.885520	−	0.464602i	$-0.846197\pi$
$199$	−11.9218	−	20.6492i	−0.845117	−	1.46379i	0.0404027	−	0.999183i	$-0.487136\pi$
$200$		0			0
$201$	20.1166	−	6.15263i	1.41892	−	0.433973i
$202$		0			0
$203$	−0.927997	+	1.60734i	−0.0651326	+	0.112813i
$204$		0			0
$205$	−0.968063			−0.0676125
$206$		0			0
$207$	−0.240721	−	3.43187i	−0.0167312	−	0.238532i
$208$		0			0
$209$	7.04323	+	12.1992i	0.487191	+	0.843839i
$210$		0			0
$211$	4.39612	+	7.61431i	0.302642	+	0.524191i	0.976733	−	0.214457i	$-0.0687981\pi$
$211$	4.39612	+	7.61431i	0.302642	+	0.524191i	−0.674092	+	0.738648i	$0.735465\pi$
$212$		0			0
$213$	−15.0480	+	4.60241i	−1.03107	+	0.315352i
$214$		0			0
$215$	−0.121728	−	0.210840i	−0.00830181	−	0.0143792i
$216$		0			0
$217$	1.09434	+	1.89545i	0.0742887	+	0.128672i
$218$		0			0
$219$	−2.99272	+	12.9692i	−0.202229	+	0.876381i
$220$		0			0
$221$	−5.71496	−	27.8463i	−0.384430	−	1.87315i
$222$		0			0
$223$	6.13562			0.410871			0.205436	−	0.978671i	$-0.434139\pi$
$223$	6.13562			0.410871			0.205436	+	0.978671i	$0.434139\pi$
$224$		0			0
$225$	−1.04393	−	14.8829i	−0.0695951	−	0.992195i
$226$		0			0
$227$	−3.65732	+	6.33467i	−0.242745	+	0.420447i	−0.961495	−	0.274822i	$-0.911381\pi$
$227$	−3.65732	+	6.33467i	−0.242745	+	0.420447i	0.718750	+	0.695268i	$0.244715\pi$
$228$		0			0
$229$	0.942882	−	1.63312i	0.0623074	−	0.107920i	−0.833189	−	0.552988i	$-0.813487\pi$
$229$	0.942882	−	1.63312i	0.0623074	−	0.107920i	0.895496	+	0.445069i	$0.146821\pi$
$230$		0			0
$231$	3.43848	+	3.20575i	0.226235	+	0.210923i
$232$		0			0
$233$	−1.27460			−0.0835016			−0.0417508	−	0.999128i	$-0.513294\pi$
$233$	−1.27460			−0.0835016			−0.0417508	+	0.999128i	$0.513294\pi$
$234$		0			0
$235$	−1.52688			−0.0996030
$236$		0			0
$237$	−21.5497	+	6.59092i	−1.39980	+	0.428126i
$238$		0			0
$239$	−9.08366	+	15.7334i	−0.587573	+	1.01771i	0.406976	+	0.913439i	$0.366583\pi$
$239$	−9.08366	+	15.7334i	−0.587573	+	1.01771i	−0.994549	+	0.104267i	$0.966750\pi$
$240$		0			0
$241$	6.86105	−	11.8837i	0.441959	−	0.765496i	−0.555876	−	0.831265i	$-0.687617\pi$
$241$	6.86105	−	11.8837i	0.441959	−	0.765496i	0.997835	+	0.0657698i	$0.0209503\pi$
$242$		0			0
$243$	−14.1244	+	6.59555i	−0.906081	+	0.423105i
$244$		0			0
$245$	0.917597			0.0586231
$246$		0			0
$247$	−4.44928	−	21.6793i	−0.283101	−	1.37942i
$248$		0			0
$249$	0.0497582	−	0.0152185i	0.00315330	−	0.000964430i
$250$		0			0
$251$	6.05088	+	10.4804i	0.381928	+	0.661519i	0.991338	−	0.131337i	$-0.0419269\pi$
$251$	6.05088	+	10.4804i	0.381928	+	0.661519i	−0.609410	+	0.792855i	$0.708594\pi$
$252$		0			0
$253$	1.31588	+	2.27917i	0.0827286	+	0.143290i
$254$		0			0
$255$	−0.502998	+	2.17979i	−0.0314989	+	0.136504i
$256$		0			0
$257$	−5.13545	−	8.89485i	−0.320340	−	0.554846i	0.660218	−	0.751074i	$-0.270464\pi$
$257$	−5.13545	−	8.89485i	−0.320340	−	0.554846i	−0.980558	+	0.196228i	$0.937131\pi$
$258$		0			0
$259$	6.77197	+	11.7294i	0.420790	+	0.728829i
$260$		0			0
$261$	4.23193	+	2.06292i	0.261950	+	0.127692i
$262$		0			0
$263$	30.8388			1.90160			0.950802	−	0.309800i	$-0.100262\pi$
$263$	30.8388			1.90160			0.950802	+	0.309800i	$0.100262\pi$
$264$		0			0
$265$	−0.200137	+	0.346648i	−0.0122943	+	0.0212944i
$266$		0			0
$267$	19.2320	+	17.9303i	1.17698	+	1.09732i
$268$		0			0
$269$	−3.97010	−	6.87641i	−0.242061	−	0.419262i	0.719240	−	0.694762i	$-0.244490\pi$
$269$	−3.97010	−	6.87641i	−0.242061	−	0.419262i	−0.961301	+	0.275500i	$0.911157\pi$
$270$		0			0
$271$	−1.39269	+	2.41221i	−0.0845997	+	0.146531i	−0.905221	−	0.424942i	$-0.860294\pi$
$271$	−1.39269	+	2.41221i	−0.0845997	+	0.146531i	0.820621	+	0.571473i	$0.193628\pi$
$272$		0			0
$273$	−3.53598	−	6.48436i	−0.214007	−	0.392451i
$274$		0			0
$275$	5.70654	+	9.88402i	0.344117	+	0.596029i
$276$		0			0
$277$	−7.48453	+	12.9636i	−0.449702	+	0.778907i	−0.998366	−	0.0571360i	$-0.981803\pi$
$277$	−7.48453	+	12.9636i	−0.449702	+	0.778907i	0.548664	+	0.836043i	$0.315136\pi$
$278$		0			0
$279$	4.60203	−	3.10555i	0.275517	−	0.185924i
$280$		0			0
$281$	−3.99438	−	6.91847i	−0.238285	−	0.412722i	0.721937	−	0.691958i	$-0.243252\pi$
$281$	−3.99438	−	6.91847i	−0.238285	−	0.412722i	−0.960222	+	0.279237i	$0.909919\pi$
$282$		0			0
$283$	−13.5539	−	23.4760i	−0.805694	−	1.39550i	−0.915822	−	0.401585i	$-0.868459\pi$
$283$	−13.5539	−	23.4760i	−0.805694	−	1.39550i	0.110128	−	0.993917i	$-0.464874\pi$
$284$		0			0
$285$	−0.391600	+	1.69704i	−0.0231964	+	0.100524i
$286$		0			0
$287$	−6.98883			−0.412537
$288$		0			0
$289$	−22.5799	+	39.1096i	−1.32823	+	2.30056i
$290$		0			0
$291$	−3.47305	−	3.23798i	−0.203594	−	0.189814i
$292$		0			0
$293$	4.12323			0.240882			0.120441	−	0.992721i	$-0.461569\pi$
$293$	4.12323			0.240882			0.120441	+	0.992721i	$0.461569\pi$
$294$		0			0
$295$	1.01650	−	1.76063i	0.0591831	−	0.102508i
$296$		0			0
$297$	7.50155	−	9.26974i	0.435284	−	0.537885i
$298$		0			0
$299$	−0.831254	−	4.05031i	−0.0480727	−	0.234236i
$300$		0			0
$301$	−0.878805	−	1.52214i	−0.0506535	−	0.0877344i
$302$		0			0
$303$	5.54460	−	24.0281i	0.318529	−	1.38038i
$304$		0			0
$305$	1.05611	+	1.82923i	0.0604725	+	0.104742i
$306$		0			0
$307$	−1.14030			−0.0650801			−0.0325401	−	0.999470i	$-0.510360\pi$
$307$	−1.14030			−0.0650801			−0.0325401	+	0.999470i	$0.510360\pi$
$308$		0			0
$309$	7.96129	+	7.42242i	0.452902	+	0.422247i
$310$		0			0
$311$	−4.33348	+	7.50580i	−0.245729	+	0.425615i	−0.962336	−	0.271862i	$-0.912361\pi$
$311$	−4.33348	+	7.50580i	−0.245729	+	0.425615i	0.716607	+	0.697477i	$0.245694\pi$
$312$		0			0
$313$	−15.7844	−	27.3395i	−0.892189	−	1.54532i	−0.837245	−	0.546828i	$-0.815835\pi$
$313$	−15.7844	−	27.3395i	−0.892189	−	1.54532i	−0.0549444	−	0.998489i	$-0.517498\pi$
$314$		0			0
$315$	0.0406693	+	0.579809i	0.00229146	+	0.0326685i
$316$		0			0
$317$	−14.7648	−	25.5734i	−0.829276	−	1.43635i	−0.898607	−	0.438754i	$-0.855420\pi$
$317$	−14.7648	−	25.5734i	−0.829276	−	1.43635i	0.0693313	−	0.997594i	$-0.477913\pi$
$318$		0			0
$319$	−3.60148			−0.201644
$320$		0			0
$321$	−12.9308	−	12.0555i	−0.721725	−	0.672875i
$322$		0			0
$323$	−24.1968	+	41.9100i	−1.34634	+	2.33193i
$324$		0			0
$325$	−3.60488	−	17.5649i	−0.199963	−	0.974325i
$326$		0			0
$327$	2.89588	−	12.5496i	0.160142	−	0.693993i
$328$		0			0
$329$	−11.0232			−0.607728
$330$		0			0
$331$	5.11550	−	8.86030i	0.281173	−	0.487006i	−0.690501	−	0.723332i	$-0.742610\pi$
$331$	5.11550	−	8.86030i	0.281173	−	0.487006i	0.971674	+	0.236325i	$0.0759432\pi$
$332$		0			0
$333$	28.4782	−	19.2177i	1.56060	−	1.05312i
$334$		0			0
$335$	−1.98965			−0.108706
$336$		0			0
$337$	5.89434	−	10.2093i	0.321085	−	0.556136i	−0.659627	−	0.751593i	$-0.729286\pi$
$337$	5.89434	−	10.2093i	0.321085	−	0.556136i	0.980712	+	0.195457i	$0.0626190\pi$
$338$		0			0
$339$	−3.91209	+	16.9534i	−0.212476	+	0.920784i
$340$		0			0
$341$	−2.12352	+	3.67805i	−0.114995	+	0.199178i
$342$		0			0
$343$	14.9032			0.804698
$344$		0			0
$345$	−0.0731622	+	0.317056i	−0.00393892	+	0.0170697i
$346$		0			0
$347$	−21.4732			−1.15274			−0.576371	−	0.817188i	$-0.695532\pi$
$347$	−21.4732			−1.15274			−0.576371	+	0.817188i	$0.695532\pi$
$348$		0			0
$349$	24.0763			1.28878			0.644388	−	0.764699i	$-0.277112\pi$
$349$	24.0763			1.28878			0.644388	+	0.764699i	$0.277112\pi$
$350$		0			0
$351$	−15.7805	+	10.0984i	−0.842299	+	0.539011i
$352$		0			0
$353$	−22.4765			−1.19631			−0.598153	−	0.801382i	$-0.704098\pi$
$353$	−22.4765			−1.19631			−0.598153	+	0.801382i	$0.704098\pi$
$354$		0			0
$355$	1.48834			0.0789927
$356$		0			0
$357$	−3.63134	+	15.7368i	−0.192191	+	0.832878i
$358$		0			0
$359$	10.8784			0.574142			0.287071	−	0.957909i	$-0.407319\pi$
$359$	10.8784			0.574142			0.287071	+	0.957909i	$0.407319\pi$
$360$		0			0
$361$	−9.33797	+	16.1738i	−0.491472	+	0.851255i
$362$		0			0
$363$	2.23280	−	9.67606i	0.117192	−	0.507861i
$364$		0			0
$365$	0.629439	−	1.09022i	0.0329464	−	0.0570648i
$366$		0			0
$367$	7.49630			0.391304			0.195652	−	0.980673i	$-0.437318\pi$
$367$	7.49630			0.391304			0.195652	+	0.980673i	$0.437318\pi$
$368$		0			0
$369$	1.24044	+	17.6846i	0.0645749	+	0.920622i
$370$		0			0
$371$	−1.44487	+	2.50259i	−0.0750138	+	0.129928i
$372$		0			0
$373$	−3.47232			−0.179790			−0.0898950	−	0.995951i	$-0.528653\pi$
$373$	−3.47232			−0.179790			−0.0898950	+	0.995951i	$0.528653\pi$
$374$		0			0
$375$	−0.636274	+	2.75736i	−0.0328570	+	0.142389i
$376$		0			0
$377$	5.36892	+	1.78622i	0.276514	+	0.0919952i
$378$		0			0
$379$	−3.64926	+	6.32070i	−0.187450	+	0.324673i	−0.944399	−	0.328801i	$-0.893356\pi$
$379$	−3.64926	+	6.32070i	−0.187450	+	0.324673i	0.756949	+	0.653473i	$0.226689\pi$
$380$		0			0
$381$	22.4164	+	20.8991i	1.14842	+	1.07069i
$382$		0			0
$383$	9.86819			0.504241			0.252121	−	0.967696i	$-0.418872\pi$
$383$	9.86819			0.504241			0.252121	+	0.967696i	$0.418872\pi$
$384$		0			0
$385$	−0.222315	−	0.385062i	−0.0113302	−	0.0196246i
$386$		0			0
$387$	−3.69564	+	2.49390i	−0.187860	+	0.126772i
$388$		0			0
$389$	−3.98393	−	6.90036i	−0.201993	−	0.349862i	0.747177	−	0.664625i	$-0.231409\pi$
$389$	−3.98393	−	6.90036i	−0.201993	−	0.349862i	−0.949171	+	0.314762i	$0.898075\pi$
$390$		0			0
$391$	−4.52065	+	7.82999i	−0.228619	+	0.395980i
$392$		0			0
$393$	4.49192	+	4.18788i	0.226587	+	0.211251i
$394$		0			0
$395$	2.13139			0.107242
$396$		0			0
$397$	0.689713	+	1.19462i	0.0346157	+	0.0599562i	0.882814	−	0.469722i	$-0.155646\pi$
$397$	0.689713	+	1.19462i	0.0346157	+	0.0599562i	−0.848199	+	0.529678i	$0.822313\pi$
$398$		0			0
$399$	−2.82712	+	12.2516i	−0.141533	+	0.613347i
$400$		0			0
$401$	8.16119	+	14.1356i	0.407550	+	0.705898i	0.994615	−	0.103642i	$-0.0330498\pi$
$401$	8.16119	+	14.1356i	0.407550	+	0.705898i	−0.587064	+	0.809540i	$0.699716\pi$
$402$		0			0
$403$	4.98985	−	4.42987i	0.248562	−	0.220667i
$404$		0			0
$405$	1.45994	−	0.205820i	0.0725448	−	0.0102273i
$406$		0			0
$407$	−13.1407	+	22.7604i	−0.651363	+	1.12819i
$408$		0			0
$409$	21.3753			1.05694			0.528471	−	0.848951i	$-0.322766\pi$
$409$	21.3753			1.05694			0.528471	+	0.848951i	$0.322766\pi$
$410$		0			0
$411$	0.855982	+	0.798044i	0.0422225	+	0.0393646i
$412$		0			0
$413$	7.33853	−	12.7107i	0.361106	−	0.625453i
$414$		0			0
$415$	−0.00492138			−0.000241581
$416$		0			0
$417$	−0.502815	+	2.17900i	−0.0246229	+	0.106706i
$418$		0			0
$419$	7.17856	+	12.4336i	0.350696	+	0.607423i	0.986372	−	0.164533i	$-0.0526118\pi$
$419$	7.17856	+	12.4336i	0.350696	+	0.607423i	−0.635676	+	0.771956i	$0.719278\pi$
$420$		0			0
$421$	11.9163	+	20.6396i	0.580765	+	1.00591i	0.995389	+	0.0959216i	$0.0305798\pi$
$421$	11.9163	+	20.6396i	0.580765	+	1.00591i	−0.414624	+	0.909993i	$0.636087\pi$
$422$		0			0
$423$	1.95650	+	27.8931i	0.0951281	+	1.35621i
$424$		0			0
$425$	−19.6046	+	33.9561i	−0.950962	+	1.64711i
$426$		0			0
$427$	7.62445	+	13.2059i	0.368973	+	0.639080i
$428$		0			0
$429$	7.46617	−	12.2335i	0.360470	−	0.590639i
$430$		0			0
$431$	8.70791	−	15.0825i	0.419445	−	0.726501i	−0.576438	−	0.817141i	$-0.695558\pi$
$431$	8.70791	−	15.0825i	0.419445	−	0.726501i	0.995884	+	0.0906400i	$0.0288913\pi$
$432$		0			0
$433$	−11.2829	−	19.5426i	−0.542222	−	0.939156i	−0.998776	−	0.0494604i	$-0.984250\pi$
$433$	−11.2829	−	19.5426i	−0.542222	−	0.939156i	0.456554	−	0.889696i	$-0.349084\pi$
$434$		0			0
$435$	−0.325692	−	0.303648i	−0.0156158	−	0.0145588i
$436$		0			0
$437$	−3.51947	+	6.09591i	−0.168359	+	0.291607i
$438$		0			0
$439$	7.91113			0.377578			0.188789	−	0.982018i	$-0.439544\pi$
$439$	7.91113			0.377578			0.188789	+	0.982018i	$0.439544\pi$
$440$		0			0
$441$	−1.17578	−	16.7627i	−0.0559894	−	0.798222i
$442$		0			0
$443$	15.4761	+	26.8054i	0.735292	+	1.27356i	0.954595	+	0.297906i	$0.0962881\pi$
$443$	15.4761	+	26.8054i	0.735292	+	1.27356i	−0.219304	+	0.975657i	$0.570379\pi$
$444$		0			0
$445$	−1.24345	−	2.15372i	−0.0589451	−	0.102096i
$446$		0			0
$447$	−7.55007	+	32.7190i	−0.357106	+	1.54755i
$448$		0			0
$449$	−8.11874	−	14.0621i	−0.383147	−	0.663631i	0.608363	−	0.793659i	$-0.291826\pi$
$449$	−8.11874	−	14.0621i	−0.383147	−	0.663631i	−0.991510	+	0.130028i	$0.958493\pi$
$450$		0			0
$451$	−6.78077	−	11.7446i	−0.319294	−	0.553034i
$452$		0			0
$453$	−8.80832	+	2.69401i	−0.413851	+	0.126576i
$454$		0			0
$455$	0.140439	+	0.684293i	0.00658388	+	0.0320802i
$456$		0			0
$457$	−18.1012			−0.846740			−0.423370	−	0.905957i	$-0.639153\pi$
$457$	−18.1012			−0.846740			−0.423370	+	0.905957i	$0.639153\pi$
$458$		0			0
$459$	40.4649	+	6.39566i	1.88874	+	0.298524i
$460$		0			0
$461$	2.62760	−	4.55114i	0.122380	−	0.211968i	−0.798326	−	0.602226i	$-0.794281\pi$
$461$	2.62760	−	4.55114i	0.122380	−	0.211968i	0.920706	+	0.390258i	$0.127614\pi$
$462$		0			0
$463$	−0.365876	+	0.633715i	−0.0170037	+	0.0294513i	−0.874402	−	0.485202i	$-0.838746\pi$
$463$	−0.365876	+	0.633715i	−0.0170037	+	0.0294513i	0.857398	+	0.514653i	$0.172079\pi$
$464$		0			0
$465$	−0.502140	+	0.153578i	−0.0232862	+	0.00712203i
$466$		0			0
$467$	−14.0792			−0.651509			−0.325755	−	0.945454i	$-0.605618\pi$
$467$	−14.0792			−0.651509			−0.325755	+	0.945454i	$0.605618\pi$
$468$		0			0
$469$	−14.3641			−0.663271
$470$		0			0
$471$	−16.3173	−	15.2129i	−0.751864	−	0.700973i
$472$		0			0
$473$	1.70529	−	2.95364i	0.0784092	−	0.135809i
$474$		0			0
$475$	−15.2628	+	26.4360i	−0.700306	+	1.21297i
$476$		0			0
$477$	6.58901	+	3.21192i	0.301690	+	0.147064i
$478$		0			0
$479$	11.6567			0.532608			0.266304	−	0.963889i	$-0.414197\pi$
$479$	11.6567			0.532608			0.266304	+	0.963889i	$0.414197\pi$
$480$		0			0
$481$	30.8781	−	27.4128i	1.40792	−	1.24992i
$482$		0			0
$483$	−0.528187	+	2.28895i	−0.0240333	+	0.104151i
$484$		0			0
$485$	0.224551	+	0.388933i	0.0101963	+	0.0176605i
$486$		0			0
$487$	11.8331	+	20.4956i	0.536211	+	0.928744i	0.999104	+	0.0423299i	$0.0134780\pi$
$487$	11.8331	+	20.4956i	0.536211	+	0.928744i	−0.462893	+	0.886414i	$0.653189\pi$
$488$		0			0
$489$	−30.3205	+	9.27347i	−1.37114	+	0.419361i
$490$		0			0
$491$	−11.8980	−	20.6079i	−0.536948	−	0.930021i	−0.999066	−	0.0432026i	$-0.986244\pi$
$491$	−11.8980	−	20.6079i	−0.536948	−	0.930021i	0.462119	−	0.886818i	$-0.347089\pi$
$492$		0			0
$493$	−6.18638	−	10.7151i	−0.278620	−	0.482585i
$494$		0			0
$495$	−0.934904	+	0.630893i	−0.0420208	+	0.0283565i
$496$		0			0
$497$	10.7449			0.481974
$498$		0			0
$499$	10.6364	−	18.4229i	0.476153	−	0.824720i	−0.523474	−	0.852042i	$-0.675364\pi$
$499$	10.6364	−	18.4229i	0.476153	−	0.824720i	0.999627	+	0.0273211i	$0.00869766\pi$
$500$		0			0
$501$	19.4329	−	5.94351i	0.868197	−	0.265536i
$502$		0			0
$503$	−5.15430	−	8.92750i	−0.229819	−	0.398058i	0.727936	−	0.685646i	$-0.240480\pi$
$503$	−5.15430	−	8.92750i	−0.229819	−	0.398058i	−0.957754	+	0.287588i	$0.907147\pi$
$504$		0			0
$505$	−1.16616	+	2.01985i	−0.0518934	+	0.0898821i
$506$		0			0
$507$	−17.1976	+	14.5341i	−0.763774	+	0.645483i
$508$		0			0
$509$	17.4759	+	30.2691i	0.774606	+	1.34166i	0.935016	+	0.354606i	$0.115385\pi$
$509$	17.4759	+	30.2691i	0.774606	+	1.34166i	−0.160410	+	0.987050i	$0.551282\pi$
$510$		0			0
$511$	4.54417	−	7.87073i	0.201022	−	0.348181i
$512$		0			0
$513$	31.5033	+	4.97923i	1.39090	+	0.219838i
$514$		0			0
$515$	−0.514738	−	0.891552i	−0.0226821	−	0.0392865i
$516$		0			0
$517$	−10.6950	−	18.5243i	−0.470367	−	0.814699i
$518$		0			0
$519$	14.0867	+	13.1333i	0.618339	+	0.576486i
$520$		0			0
$521$	16.5589			0.725460			0.362730	−	0.931894i	$-0.381845\pi$
$521$	16.5589			0.725460			0.362730	+	0.931894i	$0.381845\pi$
$522$		0			0
$523$	−8.46864	+	14.6681i	−0.370308	+	0.641392i	−0.989613	−	0.143759i	$-0.954081\pi$
$523$	−8.46864	+	14.6681i	−0.370308	+	0.641392i	0.619305	+	0.785151i	$0.287414\pi$
$524$		0			0
$525$	−2.29057	+	9.92643i	−0.0999689	+	0.433225i
$526$		0			0
$527$	−14.5906			−0.635575
$528$		0			0
$529$	10.8425	−	18.7797i	0.471411	−	0.816508i
$530$		0			0
$531$	−33.4658	−	16.3135i	−1.45229	−	0.707944i
$532$		0			0
$533$	4.28348	+	20.8714i	0.185538	+	0.904041i
$534$		0			0
$535$	0.836040	+	1.44806i	0.0361452	+	0.0626053i
$536$		0			0
$537$	23.4980	+	21.9076i	1.01401	+	0.945381i
$538$		0			0
$539$	6.42728	+	11.1324i	0.276843	+	0.479506i
$540$		0			0
$541$	−19.8748			−0.854484			−0.427242	−	0.904137i	$-0.640515\pi$
$541$	−19.8748			−0.854484			−0.427242	+	0.904137i	$0.640515\pi$
$542$		0			0
$543$	4.44162	−	19.2482i	0.190608	−	0.826018i
$544$		0			0
$545$	−0.609071	+	1.05494i	−0.0260897	+	0.0451888i
$546$		0			0
$547$	−10.1868	−	17.6440i	−0.435556	−	0.754405i	0.561785	−	0.827283i	$-0.310115\pi$
$547$	−10.1868	−	17.6440i	−0.435556	−	0.754405i	−0.997341	+	0.0728786i	$0.976781\pi$
$548$		0			0
$549$	32.0631	−	21.6369i	1.36842	−	0.923440i
$550$		0			0
$551$	−4.81630	−	8.34208i	−0.205181	−	0.355384i
$552$		0			0
$553$	15.3873			0.654335
$554$		0			0
$555$	−3.10733	+	0.950371i	−0.131899	+	0.0403410i
$556$		0			0
$557$	1.87658	−	3.25032i	0.0795131	−	0.137721i	−0.823527	−	0.567277i	$-0.807997\pi$
$557$	1.87658	−	3.25032i	0.0795131	−	0.137721i	0.903040	+	0.429557i	$0.141330\pi$
$558$		0			0
$559$	−4.00708	+	3.55739i	−0.169481	+	0.150461i
$560$		0			0
$561$	−29.9687	+	9.16587i	−1.26528	+	0.386983i
$562$		0			0
$563$	−36.5057			−1.53853			−0.769267	−	0.638928i	$-0.779378\pi$
$563$	−36.5057			−1.53853			−0.769267	+	0.638928i	$0.779378\pi$
$564$		0			0
$565$	0.822805	−	1.42514i	0.0346157	−	0.0599561i
$566$		0			0
$567$	10.5398	−	1.48589i	0.442632	−	0.0624017i
$568$		0			0
$569$	−6.77713			−0.284112			−0.142056	−	0.989859i	$-0.545371\pi$
$569$	−6.77713			−0.284112			−0.142056	+	0.989859i	$0.545371\pi$
$570$		0			0
$571$	6.78237	−	11.7474i	0.283834	−	0.491614i	−0.688492	−	0.725244i	$-0.741727\pi$
$571$	6.78237	−	11.7474i	0.283834	−	0.491614i	0.972326	+	0.233630i	$0.0750604\pi$
$572$		0			0
$573$	19.4691	+	18.1513i	0.813334	+	0.758283i
$574$		0			0
$575$	−2.85153	+	4.93900i	−0.118917	+	0.205971i
$576$		0			0
$577$	−16.9396			−0.705207			−0.352603	−	0.935773i	$-0.614704\pi$
$577$	−16.9396			−0.705207			−0.352603	+	0.935773i	$0.614704\pi$
$578$		0			0
$579$	22.4024	−	6.85173i	0.931012	−	0.284748i
$580$		0			0
$581$	−0.0355293			−0.00147401
$582$		0			0
$583$	−5.60742			−0.232236
$584$		0			0
$585$	1.70661	−	0.476823i	0.0705598	−	0.0197142i
$586$		0			0
$587$	14.0736			0.580880			0.290440	−	0.956893i	$-0.406198\pi$
$587$	14.0736			0.580880			0.290440	+	0.956893i	$0.406198\pi$
$588$		0			0
$589$	−11.3592			−0.468049
$590$		0			0
$591$	16.6924	+	15.5626i	0.686635	+	0.640160i
$592$		0			0
$593$	−7.05390			−0.289669			−0.144835	−	0.989456i	$-0.546265\pi$
$593$	−7.05390			−0.289669			−0.144835	+	0.989456i	$0.546265\pi$
$594$		0			0
$595$	0.763756	−	1.32286i	0.0313109	−	0.0542321i
$596$		0			0
$597$	39.4926	−	12.0787i	1.61633	−	0.494350i
$598$		0			0
$599$	−17.0464	+	29.5252i	−0.696497	+	1.20637i	0.273176	+	0.961964i	$0.411926\pi$
$599$	−17.0464	+	29.5252i	−0.696497	+	1.20637i	−0.969673	+	0.244405i	$0.921408\pi$
$600$		0			0
$601$	3.42399			0.139668			0.0698338	−	0.997559i	$-0.477753\pi$
$601$	3.42399			0.139668			0.0698338	+	0.997559i	$0.477753\pi$
$602$		0			0
$603$	2.54947	+	36.3469i	0.103822	+	1.48016i
$604$		0			0
$605$	−0.469610	+	0.813389i	−0.0190924	+	0.0330690i
$606$		0			0
$607$	−13.2226			−0.536689			−0.268344	−	0.963323i	$-0.586476\pi$
$607$	−13.2226			−0.536689			−0.268344	+	0.963323i	$0.586476\pi$
$608$		0			0
$609$	−2.35130	−	2.19215i	−0.0952795	−	0.0888304i
$610$		0			0
$611$	6.75616	+	32.9196i	0.273325	+	1.33178i
$612$		0			0
$613$	−18.3185	+	31.7287i	−0.739879	+	1.28151i	0.212670	+	0.977124i	$0.431784\pi$
$613$	−18.3185	+	31.7287i	−0.739879	+	1.28151i	−0.952549	+	0.304384i	$0.901549\pi$
$614$		0			0
$615$	0.377008	−	1.63380i	0.0152024	−	0.0658812i
$616$		0			0
$617$	12.0505			0.485135			0.242567	−	0.970135i	$-0.422010\pi$
$617$	12.0505			0.485135			0.242567	+	0.970135i	$0.422010\pi$
$618$		0			0
$619$	−7.09064	−	12.2814i	−0.284997	−	0.493629i	0.687611	−	0.726079i	$-0.258659\pi$
$619$	−7.09064	−	12.2814i	−0.284997	−	0.493629i	−0.972608	+	0.232450i	$0.925326\pi$
$620$		0			0
$621$	5.88572	+	0.930263i	0.236186	+	0.0373302i
$622$		0			0
$623$	−8.97694	−	15.5485i	−0.359654	−	0.622938i
$624$		0			0
$625$	−12.2991	+	21.3026i	−0.491963	+	0.852106i
$626$		0			0
$627$	−23.3316	+	7.13593i	−0.931775	+	0.284982i
$628$		0			0
$629$	−90.2891			−3.60006
$630$		0			0
$631$	0.0480189	+	0.0831713i	0.00191160	+	0.00331100i	0.866980	−	0.498344i	$-0.166058\pi$
$631$	0.0480189	+	0.0831713i	0.00191160	+	0.00331100i	−0.865068	+	0.501655i	$0.832725\pi$
$632$		0			0
$633$	−14.5627	+	4.45398i	−0.578816	+	0.177030i
$634$		0			0
$635$	−1.44933	−	2.51032i	−0.0575150	−	0.0996189i
$636$		0			0
$637$	−4.06018	−	19.7834i	−0.160870	−	0.783846i
$638$		0			0
$639$	−1.90710	−	27.1889i	−0.0754438	−	1.07558i
$640$		0			0
$641$	−20.6115	+	35.7002i	−0.814106	+	1.41007i	0.0958621	+	0.995395i	$0.469439\pi$
$641$	−20.6115	+	35.7002i	−0.814106	+	1.41007i	−0.909968	+	0.414678i	$0.863894\pi$
$642$		0			0
$643$	−25.4554			−1.00386			−0.501931	−	0.864908i	$-0.667377\pi$
$643$	−25.4554			−1.00386			−0.501931	+	0.864908i	$0.667377\pi$
$644$		0			0
$645$	0.403241	−	0.123331i	0.0158776	−	0.00485613i
$646$		0			0
$647$	0.857829	−	1.48580i	0.0337248	−	0.0584130i	−0.848670	−	0.528922i	$-0.822596\pi$
$647$	0.857829	−	1.48580i	0.0337248	−	0.0584130i	0.882395	+	0.470509i	$0.155930\pi$
$648$		0			0
$649$	28.4803			1.11795
$650$		0			0
$651$	−3.62514	+	1.10874i	−0.142081	+	0.0434551i
$652$		0			0
$653$	−6.34066	−	10.9824i	−0.248129	−	0.429773i	0.714877	−	0.699250i	$-0.246482\pi$
$653$	−6.34066	−	10.9824i	−0.248129	−	0.429773i	−0.963007	+	0.269477i	$0.913149\pi$
$654$		0			0
$655$	−0.290425	−	0.503032i	−0.0113479	−	0.0196551i
$656$		0			0
$657$	−20.7227	−	10.1016i	−0.808470	−	0.394102i
$658$		0			0
$659$	3.18418	−	5.51517i	0.124038	−	0.214840i	−0.797318	−	0.603559i	$-0.793749\pi$
$659$	3.18418	−	5.51517i	0.124038	−	0.214840i	0.921357	+	0.388718i	$0.127082\pi$
$660$		0			0
$661$	8.04701	+	13.9378i	0.312992	+	0.542119i	0.979009	−	0.203819i	$-0.0653353\pi$
$661$	8.04701	+	13.9378i	0.312992	+	0.542119i	−0.666016	+	0.745937i	$0.732002\pi$
$662$		0			0
$663$	49.2219	+	1.19948i	1.91162	+	0.0465841i
$664$		0			0
$665$	0.594609	−	1.02989i	0.0230580	−	0.0399376i
$666$		0			0
$667$	−0.899823	−	1.55854i	−0.0348413	−	0.0603469i
$668$		0			0
$669$	−2.38949	+	10.3551i	−0.0923830	+	0.400351i
$670$		0			0
$671$	−14.7950	+	25.6256i	−0.571153	+	0.989266i
$672$		0			0
$673$	8.43612			0.325188			0.162594	−	0.986693i	$-0.448014\pi$
$673$	8.43612			0.325188			0.162594	+	0.986693i	$0.448014\pi$
$674$		0			0
$675$	25.5245	+	4.03425i	0.982437	+	0.155278i
$676$		0			0
$677$	−1.55850	−	2.69939i	−0.0598978	−	0.103746i	0.834522	−	0.550975i	$-0.185744\pi$
$677$	−1.55850	−	2.69939i	−0.0598978	−	0.103746i	−0.894419	+	0.447229i	$0.852411\pi$
$678$		0			0
$679$	1.62112	+	2.80786i	0.0622128	+	0.107756i
$680$		0			0
$681$	−9.26670	−	8.63948i	−0.355101	−	0.331065i
$682$		0			0
$683$	3.44327	+	5.96391i	0.131753	+	0.228203i	0.924352	−	0.381540i	$-0.124606\pi$
$683$	3.44327	+	5.96391i	0.131753	+	0.228203i	−0.792599	+	0.609743i	$0.791273\pi$
$684$		0			0
$685$	−0.0553436	−	0.0958579i	−0.00211457	−	0.00366254i
$686$		0			0
$687$	2.38901	+	2.22731i	0.0911466	+	0.0849773i
$688$		0			0
$689$	8.35928	+	2.78111i	0.318463	+	0.105952i
$690$		0			0
$691$	27.0218			1.02796			0.513978	−	0.857803i	$-0.328171\pi$
$691$	27.0218			1.02796			0.513978	+	0.857803i	$0.328171\pi$
$692$		0			0
$693$	−6.74944	+	4.55466i	−0.256390	+	0.173017i
$694$		0			0
$695$	0.105754	−	0.183171i	0.00401147	−	0.00694807i
$696$		0			0
$697$	23.2951	−	40.3483i	0.882364	−	1.52830i
$698$		0			0
$699$	0.496386	−	2.15114i	0.0187750	−	0.0813635i
$700$		0			0
$701$	40.7031			1.53733			0.768667	−	0.639649i	$-0.220920\pi$
$701$	40.7031			1.53733			0.768667	+	0.639649i	$0.220920\pi$
$702$		0			0
$703$	−70.2930			−2.65115
$704$		0			0
$705$	0.594638	−	2.57692i	0.0223954	−	0.0970526i
$706$		0			0
$707$	−8.41896	+	14.5821i	−0.316628	+	0.548415i
$708$		0			0
$709$	11.4033	−	19.7511i	0.428259	−	0.741766i	−0.568460	−	0.822711i	$-0.692460\pi$
$709$	11.4033	−	19.7511i	0.428259	−	0.741766i	0.996719	+	0.0809449i	$0.0257938\pi$
$710$		0			0
$711$	−2.73108	−	38.9362i	−0.102424	−	1.46022i
$712$		0			0
$713$	−2.12223			−0.0794782
$714$		0			0
$715$	−1.01369	+	0.899929i	−0.0379098	+	0.0336554i
$716$		0			0
$717$	−23.0156	−	21.4578i	−0.859533	−	0.801355i
$718$		0			0
$719$	3.49446	+	6.05258i	0.130321	+	0.225723i	0.923800	−	0.382874i	$-0.125066\pi$
$719$	3.49446	+	6.05258i	0.130321	+	0.225723i	−0.793479	+	0.608598i	$0.791732\pi$
$720$		0			0
$721$	−3.71609	−	6.43646i	−0.138395	−	0.239706i
$722$		0			0
$723$	17.3841	+	16.2074i	0.646522	+	0.602761i
$724$		0			0
$725$	−3.90224	−	6.75888i	−0.144926	−	0.251019i
$726$		0			0
$727$	−13.2103	−	22.8809i	−0.489943	−	0.848606i	0.509990	−	0.860180i	$-0.329649\pi$
$727$	−13.2103	−	22.8809i	−0.489943	−	0.848606i	−0.999933	+	0.0115742i	$0.996316\pi$
$728$		0			0
$729$	−5.63063	−	26.4064i	−0.208542	−	0.978013i
$730$		0			0
$731$	11.7169			0.433365
$732$		0			0
$733$	−5.54271	+	9.60025i	−0.204725	+	0.354593i	−0.950045	−	0.312113i	$-0.898963\pi$
$733$	−5.54271	+	9.60025i	−0.204725	+	0.354593i	0.745320	+	0.666706i	$0.232297\pi$
$734$		0			0
$735$	−0.357354	+	1.54863i	−0.0131812	+	0.0571220i
$736$		0			0
$737$	−13.9365	−	24.1386i	−0.513356	−	0.889158i
$738$		0			0
$739$	4.41564	−	7.64811i	0.162432	−	0.281340i	−0.773308	−	0.634030i	$-0.781400\pi$
$739$	4.41564	−	7.64811i	0.162432	−	0.281340i	0.935740	+	0.352690i	$0.114733\pi$
$740$		0			0
$741$	38.3209	+	0.933838i	1.40775	+	0.0343054i
$742$		0			0
$743$	−20.2552	−	35.0831i	−0.743093	−	1.28707i	−0.951081	−	0.308943i	$-0.900025\pi$
$743$	−20.2552	−	35.0831i	−0.743093	−	1.28707i	0.207988	−	0.978131i	$-0.433308\pi$
$744$		0			0
$745$	1.58796	−	2.75042i	0.0581783	−	0.100768i
$746$		0			0
$747$	0.00630608	+	0.0899037i	0.000230727	+	0.00328941i
$748$		0			0
$749$	6.03570	+	10.4541i	0.220540	+	0.381986i
$750$		0			0
$751$	−20.8066	−	36.0382i	−0.759245	−	1.31505i	−0.943236	−	0.332123i	$-0.892235\pi$
$751$	−20.8066	−	36.0382i	−0.759245	−	1.31505i	0.183991	−	0.982928i	$-0.441098\pi$
$752$		0			0
$753$	−20.0443	+	6.13051i	−0.730455	+	0.223408i
$754$		0			0
$755$	0.871194			0.0317060
$756$		0			0
$757$	−1.58406	+	2.74368i	−0.0575738	+	0.0997207i	−0.893376	−	0.449310i	$-0.851670\pi$
$757$	−1.58406	+	2.74368i	−0.0575738	+	0.0997207i	0.835802	+	0.549031i	$0.185003\pi$
$758$		0			0
$759$	−4.35902	+	1.33320i	−0.158222	+	0.0483920i
$760$		0			0
$761$	1.87576			0.0679963			0.0339982	−	0.999422i	$-0.489176\pi$
$761$	1.87576			0.0679963			0.0339982	+	0.999422i	$0.489176\pi$
$762$		0			0
$763$	−4.39712	+	7.61604i	−0.159187	+	0.275719i
$764$		0			0
$765$	−3.48294	−	1.69782i	−0.125926	−	0.0613848i
$766$		0			0
$767$	−42.4571	−	14.1253i	−1.53304	−	0.510036i
$768$		0			0
$769$	2.21514	+	3.83674i	0.0798801	+	0.138356i	0.903198	−	0.429224i	$-0.141213\pi$
$769$	2.21514	+	3.83674i	0.0798801	+	0.138356i	−0.823318	+	0.567580i	$0.807880\pi$
$770$		0			0
$771$	17.0118	−	5.20303i	0.612666	−	0.187383i
$772$		0			0
$773$	−10.0735	−	17.4478i	−0.362319	−	0.627554i	0.626023	−	0.779804i	$-0.284681\pi$
$773$	−10.0735	−	17.4478i	−0.362319	−	0.627554i	−0.988342	+	0.152250i	$0.951348\pi$
$774$		0			0
$775$	−9.20344			−0.330597
$776$		0			0
$777$	−22.4330	+	6.86110i	−0.804780	+	0.246141i
$778$		0			0
$779$	18.1360	−	31.4125i	0.649789	−	1.12547i
$780$		0			0
$781$	10.4250	+	18.0567i	0.373036	+	0.646118i
$782$		0			0
$783$	−5.12970	+	6.33883i	−0.183321	+	0.226531i
$784$		0			0
$785$	1.05500	+	1.82731i	0.0376546	+	0.0652196i
$786$		0			0
$787$	29.5145			1.05208			0.526040	−	0.850460i	$-0.323676\pi$
$787$	29.5145			1.05208			0.526040	+	0.850460i	$0.323676\pi$
$788$		0			0
$789$	−12.0100	+	52.0467i	−0.427569	+	1.85291i
$790$		0			0
$791$	5.94015	−	10.2886i	0.211208	−	0.365822i
$792$		0			0
$793$	34.7651	−	30.8636i	1.23455	−	1.09600i
$794$		0			0
$795$	−0.507095	−	0.472772i	−0.0179848	−	0.0167675i
$796$		0			0
$797$	−13.8381			−0.490170			−0.245085	−	0.969502i	$-0.578816\pi$
$797$	−13.8381			−0.490170			−0.245085	+	0.969502i	$0.578816\pi$
$798$		0			0
$799$	36.7423	−	63.6396i	1.29985	−	2.25141i
$800$		0			0
$801$	−37.7508	+	25.4750i	−1.33386	+	0.900115i
$802$		0			0
$803$	17.6356			0.622346
$804$		0			0
$805$	0.111090	−	0.192414i	0.00391541	−	0.00678169i
$806$		0			0
$807$	13.1515	−	4.02235i	0.462953	−	0.141593i
$808$		0			0
$809$	11.0274	−	19.1000i	0.387702	−	0.671520i	−0.604438	−	0.796652i	$-0.706602\pi$
$809$	11.0274	−	19.1000i	0.387702	−	0.671520i	0.992140	+	0.125132i	$0.0399356\pi$
$810$		0			0
$811$	13.8289			0.485599			0.242799	−	0.970076i	$-0.421934\pi$
$811$	13.8289			0.485599			0.242799	+	0.970076i	$0.421934\pi$
$812$		0			0
$813$	−3.52870	−	3.28986i	−0.123757	−	0.115380i
$814$		0			0
$815$	2.99888			0.105046
$816$		0			0
$817$	9.12199			0.319138
$818$		0			0
$819$	12.3207	−	3.44237i	0.430521	−	0.120286i
$820$		0			0
$821$	45.3233			1.58179			0.790896	−	0.611950i	$-0.209615\pi$
$821$	45.3233			1.58179			0.790896	+	0.611950i	$0.209615\pi$
$822$		0			0
$823$	42.8013			1.49196			0.745980	−	0.665969i	$-0.231982\pi$
$823$	42.8013			1.49196			0.745980	+	0.665969i	$0.231982\pi$
$824$		0			0
$825$	−18.9036	+	5.78164i	−0.658140	+	0.201291i
$826$		0			0
$827$	−50.1954			−1.74546			−0.872732	−	0.488199i	$-0.837654\pi$
$827$	−50.1954			−1.74546			−0.872732	+	0.488199i	$0.837654\pi$
$828$		0			0
$829$	23.8288	−	41.2727i	0.827609	−	1.43346i	−0.0722999	−	0.997383i	$-0.523034\pi$
$829$	23.8288	−	41.2727i	0.827609	−	1.43346i	0.899909	−	0.436078i	$-0.143633\pi$
$830$		0			0
$831$	−18.9638	−	17.6803i	−0.657848	−	0.613321i
$832$		0			0
$833$	−22.0807	+	38.2449i	−0.765050	+	1.32511i
$834$		0			0
$835$	−1.92203			−0.0665144
$836$		0			0
$837$	3.44900	+	8.97630i	0.119215	+	0.310266i
$838$		0			0
$839$	20.6912	−	35.8382i	0.714340	−	1.23727i	−0.248874	−	0.968536i	$-0.580060\pi$
$839$	20.6912	−	35.8382i	0.714340	−	1.23727i	0.963214	−	0.268737i	$-0.0866062\pi$
$840$		0			0
$841$	−26.5372			−0.915077
$842$		0			0
$843$	13.2319	−	4.04695i	0.455731	−	0.139384i
$844$		0			0
$845$	1.95750	−	0.838813i	0.0673399	−	0.0288561i
$846$		0			0
$847$	−3.39030	+	5.87218i	−0.116492	+	0.201770i
$848$		0			0
$849$	44.8989	−	13.7323i	1.54093	−	0.471290i
$850$		0			0
$851$	−13.1328			−0.450185
$852$		0			0
$853$	16.3296	+	28.2836i	0.559113	+	0.968413i	0.997571	+	0.0696609i	$0.0221917\pi$
$853$	16.3296	+	28.2836i	0.559113	+	0.968413i	−0.438457	+	0.898752i	$0.644475\pi$
$854$		0			0
$855$	−2.71159	−	1.32181i	−0.0927343	−	0.0452049i
$856$		0			0
$857$	26.1956	+	45.3722i	0.894826	+	1.54988i	0.834020	+	0.551734i	$0.186034\pi$
$857$	26.1956	+	45.3722i	0.894826	+	1.54988i	0.0608053	+	0.998150i	$0.480633\pi$
$858$		0			0
$859$	17.0308	−	29.4983i	0.581085	−	1.00647i	−0.414266	−	0.910156i	$-0.635962\pi$
$859$	17.0308	−	29.4983i	0.581085	−	1.00647i	0.995351	−	0.0963126i	$-0.0307049\pi$
$860$		0			0
$861$	2.72177	−	11.7950i	0.0927576	−	0.401974i
$862$		0			0
$863$	53.1301			1.80857			0.904286	−	0.426928i	$-0.140404\pi$
$863$	53.1301			1.80857			0.904286	+	0.426928i	$0.140404\pi$
$864$		0			0
$865$	−0.910779	−	1.57752i	−0.0309674	−	0.0536371i
$866$		0			0
$867$	−57.2116	−	53.3392i	−1.94301	−	1.81149i
$868$		0			0
$869$	14.9292	+	25.8582i	0.506440	+	0.877179i
$870$		0			0
$871$	8.80380	+	42.8968i	0.298305	+	1.45350i
$872$		0			0
$873$	6.81730	−	4.60046i	0.230731	−	0.155702i
$874$		0			0
$875$	0.966123	−	1.67337i	0.0326609	−	0.0565704i
$876$		0			0
$877$	−24.0994			−0.813778			−0.406889	−	0.913478i	$-0.633386\pi$
$877$	−24.0994			−0.813778			−0.406889	+	0.913478i	$0.633386\pi$
$878$		0			0
$879$	−1.60577	+	6.95878i	−0.0541614	+	0.234714i
$880$		0			0
$881$	−11.0492	+	19.1378i	−0.372258	+	0.644770i	−0.989913	−	0.141680i	$-0.954750\pi$
$881$	−11.0492	+	19.1378i	−0.372258	+	0.644770i	0.617654	+	0.786450i	$0.288083\pi$
$882$		0			0
$883$	−39.3399			−1.32389			−0.661947	−	0.749551i	$-0.730270\pi$
$883$	−39.3399			−1.32389			−0.661947	+	0.749551i	$0.730270\pi$
$884$		0			0
$885$	2.57555	+	2.40122i	0.0865762	+	0.0807162i
$886$		0			0
$887$	−7.97956	−	13.8210i	−0.267927	−	0.464064i	0.700399	−	0.713751i	$-0.253005\pi$
$887$	−7.97956	−	13.8210i	−0.267927	−	0.464064i	−0.968326	+	0.249688i	$0.919672\pi$
$888$		0			0
$889$	−10.4633	−	18.1230i	−0.350928	−	0.607825i
$890$		0			0
$891$	12.7231	+	16.2704i	0.426240	+	0.545080i
$892$		0			0
$893$	28.6051	−	49.5455i	0.957234	−	1.65798i
$894$		0			0
$895$	−1.51927	−	2.63145i	−0.0507835	−	0.0879597i
$896$		0			0
$897$	7.15944	+	0.174468i	0.239047	+	0.00582531i
$898$		0			0
$899$	1.45211	−	2.51512i	0.0484305	−	0.0838841i
$900$		0			0
$901$	−9.63204	−	16.6832i	−0.320890	−	0.555797i
$902$		0			0
$903$	2.91115	−	0.890371i	0.0968772	−	0.0296297i
$904$		0			0
$905$	−0.934176	+	1.61804i	−0.0310531	+	0.0537855i
$906$		0			0
$907$	2.09929			0.0697056			0.0348528	−	0.999392i	$-0.488904\pi$
$907$	2.09929			0.0697056			0.0348528	+	0.999392i	$0.488904\pi$
$908$		0			0
$909$	38.3929	+	18.7152i	1.27341	+	0.620746i
$910$		0			0
$911$	13.9916	+	24.2342i	0.463563	+	0.802915i	0.999135	−	0.0415744i	$-0.0132374\pi$
$911$	13.9916	+	24.2342i	0.463563	+	0.802915i	−0.535572	+	0.844489i	$0.679904\pi$
$912$		0			0
$913$	−0.0344717	−	0.0597067i	−0.00114085	−	0.00197600i
$914$		0			0
$915$	−3.49849	+	1.07001i	−0.115657	+	0.0353733i
$916$		0			0
$917$	−2.09670	−	3.63158i	−0.0692390	−	0.119925i
$918$		0			0
$919$	11.9398	+	20.6803i	0.393857	+	0.682180i	0.992955	−	0.118496i	$-0.0378073\pi$
$919$	11.9398	+	20.6803i	0.393857	+	0.682180i	−0.599098	+	0.800676i	$0.704474\pi$
$920$		0			0
$921$	0.444083	−	1.92448i	0.0146330	−	0.0634137i
$922$		0			0
$923$	−6.58559	−	32.0885i	−0.216767	−	1.05621i
$924$		0			0
$925$	−56.9525			−1.87259
$926$		0			0
$927$	−15.6273	+	10.5456i	−0.513268	+	0.346364i
$928$		0			0
$929$	−28.5179	+	49.3944i	−0.935641	+	1.62058i	−0.162153	+	0.986766i	$0.551844\pi$
$929$	−28.5179	+	49.3944i	−0.935641	+	1.62058i	−0.773488	+	0.633811i	$0.781490\pi$
$930$		0			0
$931$	−17.1905	+	29.7749i	−0.563397	+	0.975832i
$932$		0			0
$933$	−10.9799	−	10.2367i	−0.359466	−	0.335135i
$934$		0			0
$935$	2.96408			0.0969357
$936$		0			0
$937$	10.0024			0.326765			0.163383	−	0.986563i	$-0.447759\pi$
$937$	10.0024			0.326765			0.163383	+	0.986563i	$0.447759\pi$
$938$		0			0
$939$	52.2880	−	15.9922i	1.70635	−	0.521885i
$940$		0			0
$941$	4.14330	−	7.17640i	0.135068	−	0.233944i	−0.790556	−	0.612390i	$-0.790208\pi$
$941$	4.14330	−	7.17640i	0.135068	−	0.233944i	0.925623	+	0.378446i	$0.123542\pi$
$942$		0			0
$943$	3.38832	−	5.86875i	0.110339	−	0.191113i
$944$		0			0
$945$	−0.994383	−	0.157166i	−0.0323473	−	0.00511262i
$946$		0			0
$947$	23.5580			0.765533			0.382766	−	0.923845i	$-0.374971\pi$
$947$	23.5580			0.765533			0.382766	+	0.923845i	$0.374971\pi$
$948$		0			0
$949$	−26.2903	−	8.74669i	−0.853419	−	0.283930i
$950$		0			0
$951$	48.9104	−	14.9592i	1.58603	−	0.485084i
$952$		0			0
$953$	−0.311414	−	0.539385i	−0.0100877	−	0.0174724i	0.860937	−	0.508711i	$-0.169878\pi$
$953$	−0.311414	−	0.539385i	−0.0100877	−	0.0174724i	−0.871025	+	0.491238i	$0.836544\pi$
$954$		0			0
$955$	−1.25878	−	2.18027i	−0.0407331	−	0.0705518i
$956$		0			0
$957$	1.40258	−	6.07823i	0.0453390	−	0.196481i
$958$		0			0
$959$	−0.399547	−	0.692036i	−0.0129020	−	0.0223470i
$960$		0			0
$961$	13.7876	+	23.8808i	0.444761	+	0.770349i
$962$		0			0
$963$	25.3820	−	17.1283i	0.817923	−	0.551951i
$964$		0			0
$965$	−2.21573			−0.0713268
$966$		0			0
$967$	6.51911	−	11.2914i	0.209641	−	0.363108i	−0.741961	−	0.670443i	$-0.766104\pi$
$967$	6.51911	−	11.2914i	0.209641	−	0.363108i	0.951601	+	0.307335i	$0.0994373\pi$
$968$		0			0
$969$	−61.3082	−	57.1585i	−1.96950	−	1.83620i
$970$		0			0
$971$	−19.1696	−	33.2028i	−0.615183	−	1.06553i	−0.990352	−	0.138572i	$-0.955749\pi$
$971$	−19.1696	−	33.2028i	−0.615183	−	1.06553i	0.375169	−	0.926956i	$-0.377585\pi$
$972$		0			0
$973$	0.763478	−	1.32238i	0.0244760	−	0.0423936i
$974$		0			0
$975$	31.0482	+	0.756611i	0.994337	+	0.0242309i
$976$		0			0
$977$	16.6020	+	28.7555i	0.531145	+	0.919971i	0.999339	+	0.0363451i	$0.0115715\pi$
$977$	16.6020	+	28.7555i	0.531145	+	0.919971i	−0.468194	+	0.883626i	$0.655095\pi$
$978$		0			0
$979$	17.4194	−	30.1713i	0.556727	−	0.964279i
$980$		0			0
$981$	20.0521	+	9.77475i	0.640215	+	0.312084i
$982$		0			0
$983$	−19.9244	−	34.5101i	−0.635491	−	1.10070i	−0.986411	−	0.164297i	$-0.947464\pi$
$983$	−19.9244	−	34.5101i	−0.635491	−	1.10070i	0.350920	−	0.936405i	$-0.385869\pi$
$984$		0			0
$985$	−1.07925	−	1.86932i	−0.0343878	−	0.0595614i
$986$		0			0
$987$	4.29293	−	18.6038i	0.136645	−	0.592166i
$988$		0			0
$989$	1.70425			0.0541920
$990$		0			0
$991$	6.71711	−	11.6344i	0.213376	−	0.369578i	−0.739393	−	0.673274i	$-0.764887\pi$
$991$	6.71711	−	11.6344i	0.213376	−	0.369578i	0.952769	+	0.303696i	$0.0982208\pi$
$992$		0			0
$993$	12.9613	+	12.0840i	0.411315	+	0.383475i
$994$		0			0
$995$	−3.90605			−0.123830
$996$		0			0
$997$	−13.7542	+	23.8230i	−0.435601	+	0.754483i	−0.997344	−	0.0728285i	$-0.976797\pi$
$997$	−13.7542	+	23.8230i	−0.435601	+	0.754483i	0.561744	+	0.827311i	$0.310131\pi$
$998$		0			0
$999$	21.3430	+	55.5469i	0.675262	+	1.75743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.r.f.841.10	yes	40
3.2	odd	2		2808.2.r.f.2089.11		40
9.2	odd	6		2808.2.s.f.1153.11		40
9.7	even	3		936.2.s.f.529.4	yes	40
13.3	even	3		936.2.s.f.913.4	yes	40
39.29	odd	6		2808.2.s.f.1225.11		40
117.16	even	3	inner	936.2.r.f.601.10	✓	40
117.29	odd	6		2808.2.r.f.289.11		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.10	✓	40	117.16	even	3	inner
936.2.r.f.841.10	yes	40	1.1	even	1	trivial
936.2.s.f.529.4	yes	40	9.7	even	3
936.2.s.f.913.4	yes	40	13.3	even	3
2808.2.r.f.289.11		40	117.29	odd	6
2808.2.r.f.2089.11		40	3.2	odd	2
2808.2.s.f.1153.11		40	9.2	odd	6
2808.2.s.f.1225.11		40	39.29	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.389445 + 1.68770i) q^{3} +(0.0819095 - 0.141871i) q^{5} +(0.591337 - 1.02423i) q^{7} +(-2.69666 - 1.31453i) q^{9} +2.29493 q^{11} +(-3.42118 - 1.13821i) q^{13} +(0.207537 + 0.193490i) q^{15} +(3.94208 + 6.82788i) q^{17} +(3.06904 + 5.31573i) q^{19} +(1.49829 + 1.39688i) q^{21} +(0.573384 + 0.993131i) q^{23} +(2.48658 + 4.30689i) q^{25} +(3.26874 - 4.03922i) q^{27} -1.56932 q^{29} +(-0.925310 + 1.60268i) q^{31} +(-0.893751 + 3.87316i) q^{33} +(-0.0968723 - 0.167788i) q^{35} +(-5.72598 + 9.91769i) q^{37} +(3.25333 - 5.33065i) q^{39} +(-2.95467 - 5.11764i) q^{41} +(0.743066 - 1.28703i) q^{43} +(-0.407378 + 0.274907i) q^{45} +(-4.66028 - 8.07184i) q^{47} +(2.80064 + 4.85085i) q^{49} +(-13.0586 + 3.99396i) q^{51} -2.44339 q^{53} +(0.187977 - 0.325586i) q^{55} +(-10.1666 + 3.10943i) q^{57} +12.4101 q^{59} +(-6.44679 + 11.1662i) q^{61} +(-2.94102 + 1.98466i) q^{63} +(-0.441707 + 0.392137i) q^{65} +(-6.07271 - 10.5182i) q^{67} +(-1.89941 + 0.580930i) q^{69} +(4.54262 + 7.86805i) q^{71} +7.68457 q^{73} +(-8.23712 + 2.51931i) q^{75} +(1.35708 - 2.35053i) q^{77} +(6.50531 + 11.2675i) q^{79} +(5.54400 + 7.08972i) q^{81} +(-0.0150208 - 0.0260167i) q^{83} +1.29157 q^{85} +(0.611164 - 2.64854i) q^{87} +(7.59038 - 13.1469i) q^{89} +(-3.18886 + 2.83099i) q^{91} +(-2.34449 - 2.18580i) q^{93} +1.00553 q^{95} +(-1.37072 + 2.37416i) q^{97} +(-6.18866 - 3.01677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + q^{5} + 7 q^{7} + 6 q^{9} + 11 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} - q^{23} - 23 q^{25} - 3 q^{27} - 24 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{35} + 18 q^{37} + 6 q^{39} - 3 q^{41} + 8 q^{43}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q + q^5 + 7 * q^7 + 6 * q^9 + 11 * q^15 - q^17 + 2 * q^19 - 30 * q^21 - q^23 - 23 * q^25 - 3 * q^27 - 24 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^35 + 18 * q^37 + 6 * q^39 - 3 * q^41 + 8 * q^43 + 24 * q^45 + 4 * q^47 - 23 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 + 8 * q^59 - 3 * q^61 + 10 * q^63 - 32 * q^65 + 27 * q^67 - 38 * q^69 + q^71 - 12 * q^73 + 32 * q^75 - 4 * q^77 + 13 * q^79 + 26 * q^81 - 15 * q^83 - 10 * q^85 + 25 * q^87 + 12 * q^89 - 57 * q^91 - 7 * q^93 - 2 * q^95 + 35 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more