LMFDB - Embedded newform 936.2.s.f.529.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(529,936)] 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, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.529"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [40,0,-3,0,1] 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			529.4
Character	$\chi$	$=$	936.529
Dual form			936.2.s.f.913.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26687 + 1.18112i) q^{3} +(0.0819095 + 0.141871i) q^{5} -1.18267 q^{7} +(0.209912 - 2.99265i) q^{9} +(-1.14747 - 1.98747i) q^{11} +(2.69631 - 2.39372i) q^{13} +(-0.271336 - 0.0829876i) q^{15} +(3.94208 + 6.82788i) q^{17} +(3.06904 + 5.31573i) q^{19} +(1.49829 - 1.39688i) q^{21} -1.14677 q^{23} +(2.48658 - 4.30689i) q^{25} +(3.26874 + 4.03922i) q^{27} +(0.784660 + 1.35907i) q^{29} +(-0.925310 - 1.60268i) q^{31} +(3.80113 + 1.16257i) q^{33} +(-0.0968723 - 0.167788i) q^{35} +(-5.72598 + 9.91769i) q^{37} +(-0.588603 + 6.21720i) q^{39} +5.90934 q^{41} -1.48613 q^{43} +(0.441765 - 0.215346i) q^{45} +(-4.66028 + 8.07184i) q^{47} -5.60128 q^{49} +(-13.0586 - 3.99396i) q^{51} -2.44339 q^{53} +(0.187977 - 0.325586i) q^{55} +(-10.1666 - 3.10943i) q^{57} +(-6.20503 + 10.7474i) q^{59} +12.8936 q^{61} +(-0.248258 + 3.53933i) q^{63} +(0.560454 + 0.186461i) q^{65} +12.1454 q^{67} +(1.45280 - 1.35447i) q^{69} +(4.54262 + 7.86805i) q^{71} +7.68457 q^{73} +(1.93678 + 8.39321i) q^{75} +(1.35708 + 2.35053i) q^{77} +(6.50531 - 11.2675i) q^{79} +(-8.91187 - 1.25639i) q^{81} +(-0.0150208 + 0.0260167i) q^{83} +(-0.645787 + 1.11854i) q^{85} +(-2.59929 - 0.794987i) q^{87} +(7.59038 - 13.1469i) q^{89} +(-3.18886 + 2.83099i) q^{91} +(3.06521 + 0.937488i) q^{93} +(-0.502767 + 0.870818i) q^{95} +2.74145 q^{97} +(-6.18866 + 3.01677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Character values

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

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

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
$3$	−1.26687	+	1.18112i	−0.731427	+	0.681920i
$3$	−1.26687	+	1.18112i	−0.731427	+	0.681920i
$4$		0			0
$5$	0.0819095	+	0.141871i	0.0366311	+	0.0634469i	0.883760	−	0.467941i	$-0.155004\pi$
$5$	0.0819095	+	0.141871i	0.0366311	+	0.0634469i	−0.847129	+	0.531388i	$0.821671\pi$
$6$		0			0
$7$	−1.18267			−0.447009			−0.223504	−	0.974703i	$-0.571750\pi$
$7$	−1.18267			−0.447009			−0.223504	+	0.974703i	$0.571750\pi$
$8$		0			0
$9$	0.209912	−	2.99265i	0.0699707	−	0.997549i
$10$		0			0
$11$	−1.14747	−	1.98747i	−0.345974	−	0.599245i	0.639556	−	0.768744i	$-0.279118\pi$
$11$	−1.14747	−	1.98747i	−0.345974	−	0.599245i	−0.985530	+	0.169500i	$0.945785\pi$
$12$		0			0
$13$	2.69631	−	2.39372i	0.747823	−	0.663899i
$13$	2.69631	−	2.39372i	0.747823	−	0.663899i
$14$		0			0
$15$	−0.271336	−	0.0829876i	−0.0700586	−	0.0214273i
$16$		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
$23$	−1.14677			−0.239118			−0.119559	−	0.992827i	$-0.538148\pi$
$23$	−1.14677			−0.239118			−0.119559	+	0.992827i	$0.538148\pi$
$24$		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
$29$	0.784660	+	1.35907i	0.145708	+	0.252373i	0.929637	−	0.368477i	$-0.120121\pi$
$29$	0.784660	+	1.35907i	0.145708	+	0.252373i	−0.783929	+	0.620850i	$0.786787\pi$
$30$		0			0
$31$	−0.925310	−	1.60268i	−0.166191	−	0.287851i	0.770887	−	0.636972i	$-0.219813\pi$
$31$	−0.925310	−	1.60268i	−0.166191	−	0.287851i	−0.937077	+	0.349122i	$0.886480\pi$
$32$		0			0
$33$	3.80113	+	1.16257i	0.661692	+	0.202377i
$34$		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
$39$	−0.588603	+	6.21720i	−0.0942519	+	0.995548i
$40$		0			0
$41$	5.90934			0.922884			0.461442	−	0.887170i	$-0.347332\pi$
$41$	5.90934			0.922884			0.461442	+	0.887170i	$0.347332\pi$
$42$		0			0
$43$	−1.48613			−0.226633			−0.113317	−	0.993559i	$-0.536147\pi$
$43$	−1.48613			−0.226633			−0.113317	+	0.993559i	$0.536147\pi$
$44$		0			0
$45$	0.441765	−	0.215346i	0.0658545	−	0.0321019i
$46$		0			0
$47$	−4.66028	+	8.07184i	−0.679771	+	1.17740i	0.295278	+	0.955411i	$0.404588\pi$
$47$	−4.66028	+	8.07184i	−0.679771	+	1.17740i	−0.975050	+	0.221987i	$0.928746\pi$
$48$		0			0
$49$	−5.60128			−0.800183
$50$		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
$59$	−6.20503	+	10.7474i	−0.807826	+	1.39920i	0.106540	+	0.994308i	$0.466023\pi$
$59$	−6.20503	+	10.7474i	−0.807826	+	1.39920i	−0.914366	+	0.404888i	$0.867310\pi$
$60$		0			0
$61$	12.8936			1.65085			0.825427	−	0.564509i	$-0.190934\pi$
$61$	12.8936			1.65085			0.825427	+	0.564509i	$0.190934\pi$
$62$		0			0
$63$	−0.248258	+	3.53933i	−0.0312775	+	0.445913i
$64$		0			0
$65$	0.560454	+	0.186461i	0.0695158	+	0.0231277i
$66$		0			0
$67$	12.1454			1.48380			0.741899	−	0.670512i	$-0.233925\pi$
$67$	12.1454			1.48380			0.741899	+	0.670512i	$0.233925\pi$
$68$		0			0
$69$	1.45280	−	1.35447i	0.174897	−	0.163059i
$70$		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
$75$	1.93678	+	8.39321i	0.223640	+	0.969164i
$76$		0			0
$77$	1.35708	+	2.35053i	0.154654	+	0.267868i
$78$		0			0
$79$	6.50531	−	11.2675i	0.731904	−	1.26769i	−0.224164	−	0.974551i	$-0.571965\pi$
$79$	6.50531	−	11.2675i	0.731904	−	1.26769i	0.956068	−	0.293144i	$-0.0947014\pi$
$80$		0			0
$81$	−8.91187	−	1.25639i	−0.990208	−	0.139598i
$82$		0			0
$83$	−0.0150208	+	0.0260167i	−0.00164874	+	0.00285571i	−0.866849	−	0.498571i	$-0.833858\pi$
$83$	−0.0150208	+	0.0260167i	−0.00164874	+	0.00285571i	0.865200	+	0.501427i	$0.167191\pi$
$84$		0			0
$85$	−0.645787	+	1.11854i	−0.0700455	+	0.121322i
$86$		0			0
$87$	−2.59929	−	0.794987i	−0.278673	−	0.0852315i
$88$		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
$93$	3.06521	+	0.937488i	0.317847	+	0.0972130i
$94$		0			0
$95$	−0.502767	+	0.870818i	−0.0515828	+	0.0893440i
$96$		0			0
$97$	2.74145			0.278352			0.139176	−	0.990268i	$-0.455555\pi$
$97$	2.74145			0.278352			0.139176	+	0.990268i	$0.455555\pi$
$98$		0			0
$99$	−6.18866	+	3.01677i	−0.621984	+	0.303197i
$100$		0			0
$101$	7.11858	+	12.3297i	0.708326	+	1.22686i	0.965478	+	0.260485i	$0.0838825\pi$
$101$	7.11858	+	12.3297i	0.708326	+	1.22686i	−0.257152	+	0.966371i	$0.582784\pi$
$102$		0			0
$103$	3.14211	+	5.44230i	0.309602	+	0.536246i	0.978275	−	0.207310i	$-0.0664710\pi$
$103$	3.14211	+	5.44230i	0.309602	+	0.536246i	−0.668674	+	0.743556i	$0.733138\pi$
$104$		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
$111$	−4.45992	−	19.3275i	−0.423317	−	1.83448i
$112$		0			0
$113$	−5.02265	+	8.69948i	−0.472491	+	0.818378i	−0.999504	−	0.0314788i	$-0.989978\pi$
$113$	−5.02265	+	8.69948i	−0.472491	+	0.818378i	0.527014	+	0.849857i	$0.323312\pi$
$114$		0			0
$115$	−0.0939313	−	0.162694i	−0.00875914	−	0.0151713i
$116$		0			0
$117$	−6.59757	−	8.57158i	−0.609946	−	0.792443i
$118$		0			0
$119$	−4.66219	−	8.07515i	−0.427382	−	0.740248i
$120$		0			0
$121$	2.86664	−	4.96517i	0.260604	−	0.451379i
$122$		0			0
$123$	−7.48636	+	6.97964i	−0.675022	+	0.629333i
$124$		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	0.933020	−	0.359823i	$-0.117163\pi$
$131$	1.77284	+	3.07065i	0.154894	+	0.268284i	−0.778126	+	0.628108i	$0.783830\pi$
$132$		0			0
$133$	−3.62967	−	6.28677i	−0.314732	−	0.545132i
$134$		0			0
$135$	−0.305309	+	0.794592i	−0.0262768	+	0.0683876i
$136$		0			0
$137$	−0.675667			−0.0577262			−0.0288631	−	0.999583i	$-0.509189\pi$
$137$	−0.675667			−0.0577262			−0.0288631	+	0.999583i	$0.509189\pi$
$138$		0			0
$139$	−0.645552	+	1.11813i	−0.0547550	+	0.0948385i	−0.892104	−	0.451831i	$-0.850771\pi$
$139$	−0.645552	+	1.11813i	−0.0547550	+	0.0948385i	0.837349	+	0.546669i	$0.184104\pi$
$140$		0			0
$141$	−3.62985	−	15.7303i	−0.305688	−	1.32473i
$142$		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
$147$	7.09609	−	6.61578i	0.585275	−	0.545661i
$148$		0			0
$149$	−9.69336	+	16.7894i	−0.794111	+	1.37544i	0.129291	+	0.991607i	$0.458730\pi$
$149$	−9.69336	+	16.7894i	−0.794111	+	1.37544i	−0.923402	+	0.383834i	$0.874603\pi$
$150$		0			0
$151$	2.65901	−	4.60555i	0.216387	−	0.374794i	−0.737313	−	0.675551i	$-0.763906\pi$
$151$	2.65901	−	4.60555i	0.216387	−	0.374794i	0.953701	+	0.300757i	$0.0972392\pi$
$152$		0			0
$153$	21.2609	−	10.3640i	1.71884	−	0.837879i
$154$		0			0
$155$	0.151583	−	0.262550i	0.0121755	−	0.0210885i
$156$		0			0
$157$	−6.44003	−	11.1545i	−0.513971	−	0.890223i	−0.999869	−	0.0162076i	$-0.994841\pi$
$157$	−6.44003	−	11.1545i	−0.513971	−	0.890223i	0.485898	−	0.874015i	$-0.338493\pi$
$158$		0			0
$159$	3.09546	−	2.88594i	0.245486	−	0.228870i
$160$		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
$165$	0.146414	+	0.634497i	0.0113983	+	0.0493956i
$166$		0			0
$167$	11.7326			0.907897			0.453948	−	0.891028i	$-0.350015\pi$
$167$	11.7326			0.907897			0.453948	+	0.891028i	$0.350015\pi$
$168$		0			0
$169$	1.54020	−	12.9084i	0.118477	−	0.992957i
$170$		0			0
$171$	16.5523	−	8.06871i	1.26579	−	0.617029i
$172$		0			0
$173$	−11.1193			−0.845387			−0.422693	−	0.906273i	$-0.638915\pi$
$173$	−11.1193			−0.845387			−0.422693	+	0.906273i	$0.638915\pi$
$174$		0			0
$175$	−2.94082	+	5.09364i	−0.222305	+	0.385043i
$176$		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
$185$	−1.87605			−0.137930
$186$		0			0
$187$	9.04680	−	15.6695i	0.661568	−	1.14587i
$188$		0			0
$189$	−3.86586	−	4.77708i	−0.281200	−	0.347482i
$190$		0			0
$191$	−15.3679			−1.11198			−0.555991	−	0.831188i	$-0.687661\pi$
$191$	−15.3679			−1.11198			−0.555991	+	0.831188i	$0.687661\pi$
$192$		0			0
$193$	13.5254			0.973583			0.486792	−	0.873518i	$-0.338167\pi$
$193$	13.5254			0.973583			0.486792	+	0.873518i	$0.338167\pi$
$194$		0			0
$195$	−0.930255	+	0.425742i	−0.0666170	+	0.0304880i
$196$		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
$201$	−15.3866	+	14.3452i	−1.08529	+	1.01183i
$202$		0			0
$203$	−0.927997	−	1.60734i	−0.0651326	−	0.112813i
$204$		0			0
$205$	0.484032	+	0.838367i	0.0338062	+	0.0585541i
$206$		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
$211$	−8.79225			−0.605283			−0.302642	−	0.953104i	$-0.597869\pi$
$211$	−8.79225			−0.605283			−0.302642	+	0.953104i	$0.597869\pi$
$212$		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
$219$	−9.73534	+	9.07640i	−0.657853	+	0.613326i
$220$		0			0
$221$	26.9731	+	8.97386i	1.81441	+	0.603647i
$222$		0			0
$223$	−3.06781	−	5.31360i	−0.205436	−	0.355825i	0.744836	−	0.667248i	$-0.232528\pi$
$223$	−3.06781	−	5.31360i	−0.205436	−	0.355825i	−0.950271	+	0.311423i	$0.899194\pi$
$224$		0			0
$225$	−12.3670	−	8.34553i	−0.824468	−	0.556369i
$226$		0			0
$227$	7.31465			0.485490			0.242745	−	0.970090i	$-0.421952\pi$
$227$	7.31465			0.485490			0.242745	+	0.970090i	$0.421952\pi$
$228$		0			0
$229$	0.942882	+	1.63312i	0.0623074	+	0.107920i	0.895496	−	0.445069i	$-0.146821\pi$
$229$	0.942882	+	1.63312i	0.0623074	+	0.107920i	−0.833189	+	0.552988i	$0.813487\pi$
$230$		0			0
$231$	−4.49550	−	1.37494i	−0.295782	−	0.0904644i
$232$		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
$237$	5.06692	+	21.9580i	0.329132	+	1.42633i
$238$		0			0
$239$	−9.08366	−	15.7334i	−0.587573	−	1.01771i	−0.994549	−	0.104267i	$-0.966750\pi$
$239$	−9.08366	−	15.7334i	−0.587573	−	1.01771i	0.406976	−	0.913439i	$-0.366583\pi$
$240$		0			0
$241$	−13.7221			−0.883918			−0.441959	−	0.897035i	$-0.645716\pi$
$241$	−13.7221			−0.883918			−0.441959	+	0.897035i	$0.645716\pi$
$242$		0			0
$243$	12.7741	−	8.93432i	0.819460	−	0.573137i
$244$		0			0
$245$	−0.458798	−	0.794662i	−0.0293116	−	0.0507691i
$246$		0			0
$247$	20.9994	+	6.98645i	1.33616	+	0.444537i
$248$		0			0
$249$	−0.0116995	−	0.0507011i	−0.000741428	−	0.00321305i
$250$		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
$257$	10.2709			0.640681			0.320340	−	0.947303i	$-0.396203\pi$
$257$	10.2709			0.640681			0.320340	+	0.947303i	$0.396203\pi$
$258$		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
$263$	−15.4194	−	26.7072i	−0.950802	−	1.64684i	−0.743696	−	0.668518i	$-0.766929\pi$
$263$	−15.4194	−	26.7072i	−0.950802	−	1.64684i	−0.207106	−	0.978319i	$-0.566404\pi$
$264$		0			0
$265$	−0.200137	−	0.346648i	−0.0122943	−	0.0212944i
$266$		0			0
$267$	5.91207	+	25.6206i	0.361813	+	1.56795i
$268$		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
$273$	0.696125	−	7.35292i	0.0421314	−	0.445019i
$274$		0			0
$275$	−11.4131			−0.688234
$276$		0			0
$277$	14.9691			0.899404			0.449702	−	0.893179i	$-0.351530\pi$
$277$	14.9691			0.899404			0.449702	+	0.893179i	$0.351530\pi$
$278$		0			0
$279$	−4.99050	+	2.43270i	−0.298774	+	0.145642i
$280$		0			0
$281$	−3.99438	+	6.91847i	−0.238285	+	0.412722i	−0.960222	−	0.279237i	$-0.909919\pi$
$281$	−3.99438	+	6.91847i	−0.238285	+	0.412722i	0.721937	+	0.691958i	$0.243252\pi$
$282$		0			0
$283$	27.1077			1.61139			0.805694	−	0.592332i	$-0.201793\pi$
$283$	27.1077			1.61139			0.805694	+	0.592332i	$0.201793\pi$
$284$		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
$293$	−2.06161	+	3.57082i	−0.120441	+	0.208610i	−0.919942	−	0.392055i	$-0.871764\pi$
$293$	−2.06161	+	3.57082i	−0.120441	+	0.208610i	0.799501	+	0.600665i	$0.205097\pi$
$294$		0			0
$295$	−2.03301			−0.118366
$296$		0			0
$297$	4.27706	−	11.1314i	0.248180	−	0.645910i
$298$		0			0
$299$	−3.09205	+	2.74504i	−0.178818	+	0.158750i
$300$		0			0
$301$	1.75761			0.101307
$302$		0			0
$303$	−23.5812	−	7.21227i	−1.35471	−	0.414334i
$304$		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
$309$	−10.4086	−	3.18347i	−0.592127	−	0.181101i
$310$		0			0
$311$	−4.33348	−	7.50580i	−0.245729	−	0.425615i	0.716607	−	0.697477i	$-0.245694\pi$
$311$	−4.33348	−	7.50580i	−0.245729	−	0.425615i	−0.962336	+	0.271862i	$0.912361\pi$
$312$		0			0
$313$	−15.7844	+	27.3395i	−0.892189	+	1.54532i	−0.0549444	+	0.998489i	$0.517498\pi$
$313$	−15.7844	+	27.3395i	−0.892189	+	1.54532i	−0.837245	+	0.546828i	$0.815835\pi$
$314$		0			0
$315$	−0.522464	+	0.254684i	−0.0294375	+	0.0143498i
$316$		0			0
$317$	−14.7648	+	25.5734i	−0.829276	+	1.43635i	0.0693313	+	0.997594i	$0.477913\pi$
$317$	−14.7648	+	25.5734i	−0.829276	+	1.43635i	−0.898607	+	0.438754i	$0.855420\pi$
$318$		0			0
$319$	1.80074	−	3.11898i	0.100822	−	0.174629i
$320$		0			0
$321$	−3.97502	−	17.2261i	−0.221864	−	0.961470i
$322$		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
$327$	9.42031	−	8.78269i	0.520944	−	0.485684i
$328$		0			0
$329$	5.51159	−	9.54635i	0.303864	−	0.526307i
$330$		0			0
$331$	−10.2310			−0.562346			−0.281173	−	0.959657i	$-0.590724\pi$
$331$	−10.2310			−0.562346			−0.281173	+	0.959657i	$0.590724\pi$
$332$		0			0
$333$	28.4782	+	19.2177i	1.56060	+	1.05312i
$334$		0			0
$335$	0.994825	+	1.72309i	0.0543531	+	0.0941423i
$336$		0			0
$337$	5.89434	+	10.2093i	0.321085	+	0.556136i	0.980712	−	0.195457i	$-0.0626190\pi$
$337$	5.89434	+	10.2093i	0.321085	+	0.556136i	−0.659627	+	0.751593i	$0.729286\pi$
$338$		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
$345$	0.311159	+	0.0951675i	0.0167523	+	0.00512365i
$346$		0			0
$347$	10.7366	−	18.5963i	0.576371	−	0.998304i	−0.419520	−	0.907746i	$-0.637802\pi$
$347$	10.7366	−	18.5963i	0.576371	−	0.998304i	0.995891	−	0.0905577i	$-0.0288650\pi$
$348$		0			0
$349$	−12.0382	−	20.8507i	−0.644388	−	1.11611i	−0.984442	−	0.175707i	$-0.943779\pi$
$349$	−12.0382	−	20.8507i	−0.644388	−	1.11611i	0.340054	−	0.940406i	$-0.389555\pi$
$350$		0			0
$351$	18.4823	+	3.06655i	0.986513	+	0.163680i
$352$		0			0
$353$	11.2383	+	19.4653i	0.598153	+	1.03603i	0.993094	+	0.117325i	$0.0374318\pi$
$353$	11.2383	+	19.4653i	0.598153	+	1.03603i	−0.394941	+	0.918707i	$0.629235\pi$
$354$		0			0
$355$	−0.744168	+	1.28894i	−0.0394964	+	0.0684097i
$356$		0			0
$357$	15.4441	+	4.72355i	0.817389	+	0.249997i
$358$		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
$367$	−3.74815	−	6.49199i	−0.195652	−	0.338879i	0.751462	−	0.659776i	$-0.229349\pi$
$367$	−3.74815	−	6.49199i	−0.195652	−	0.338879i	−0.947114	+	0.320897i	$0.896016\pi$
$368$		0			0
$369$	1.24044	−	17.6846i	0.0645749	−	0.920622i
$370$		0			0
$371$	2.88974			0.150028
$372$		0			0
$373$	1.73616	−	3.00712i	0.0898950	−	0.155703i	−0.817572	−	0.575827i	$-0.804680\pi$
$373$	1.73616	−	3.00712i	0.0898950	−	0.155703i	0.907467	+	0.420124i	$0.138014\pi$
$374$		0			0
$375$	−2.06980	+	1.92971i	−0.106884	+	0.0996496i
$376$		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
$381$	6.89097	+	29.8627i	0.353035	+	1.52991i
$382$		0			0
$383$	−4.93410	+	8.54611i	−0.252121	+	0.436686i	−0.964109	−	0.265505i	$-0.914461\pi$
$383$	−4.93410	+	8.54611i	−0.252121	+	0.436686i	0.711989	+	0.702191i	$0.247795\pi$
$384$		0			0
$385$	−0.222315	+	0.385062i	−0.0113302	+	0.0196246i
$386$		0			0
$387$	−0.311957	+	4.44747i	−0.0158577	+	0.226078i
$388$		0			0
$389$	−3.98393	+	6.90036i	−0.201993	+	0.349862i	−0.949171	−	0.314762i	$-0.898075\pi$
$389$	−3.98393	+	6.90036i	−0.201993	+	0.349862i	0.747177	+	0.664625i	$0.231409\pi$
$390$		0			0
$391$	−4.52065	−	7.82999i	−0.228619	−	0.395980i
$392$		0			0
$393$	−5.87277	−	1.79617i	−0.296242	−	0.0906050i
$394$		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
$399$	12.0237	+	3.67744i	0.601940	+	0.184102i
$400$		0			0
$401$	−16.3224			−0.815101			−0.407550	−	0.913183i	$-0.633617\pi$
$401$	−16.3224			−0.815101			−0.407550	+	0.913183i	$0.633617\pi$
$402$		0			0
$403$	−6.33130	−	2.10640i	−0.315385	−	0.104927i
$404$		0			0
$405$	−0.551722	−	1.36725i	−0.0274153	−	0.0679392i
$406$		0			0
$407$	26.2815			1.30273
$408$		0			0
$409$	−10.6877	+	18.5116i	−0.528471	+	0.915338i	0.470978	+	0.882145i	$0.343901\pi$
$409$	−10.6877	+	18.5116i	−0.528471	+	0.915338i	−0.999449	+	0.0331934i	$0.989432\pi$
$410$		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
$419$	−14.3571			−0.701391			−0.350696	−	0.936489i	$-0.614055\pi$
$419$	−14.3571			−0.701391			−0.350696	+	0.936489i	$0.614055\pi$
$420$		0			0
$421$	11.9163	−	20.6396i	0.580765	−	1.00591i	−0.414624	−	0.909993i	$-0.636087\pi$
$421$	11.9163	−	20.6396i	0.580765	−	1.00591i	0.995389	−	0.0959216i	$-0.0305798\pi$
$422$		0			0
$423$	23.1779	+	15.6409i	1.12695	+	0.760489i
$424$		0			0
$425$	39.2092			1.90192
$426$		0			0
$427$	−15.2489			−0.737946
$428$		0			0
$429$	13.0319	−	5.96420i	0.629186	−	0.287954i
$430$		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
$435$	−0.100120	−	0.433882i	−0.00480041	−	0.0208030i
$436$		0			0
$437$	−3.51947	−	6.09591i	−0.168359	−	0.291607i
$438$		0			0
$439$	−3.95556	−	6.85124i	−0.188789	−	0.326992i	0.756058	−	0.654505i	$-0.227123\pi$
$439$	−3.95556	−	6.85124i	−0.188789	−	0.326992i	−0.944847	+	0.327513i	$0.893789\pi$
$440$		0			0
$441$	−1.17578	+	16.7627i	−0.0559894	+	0.798222i
$442$		0			0
$443$	15.4761	−	26.8054i	0.735292	−	1.27356i	−0.219304	−	0.975657i	$-0.570379\pi$
$443$	15.4761	−	26.8054i	0.735292	−	1.27356i	0.954595	−	0.297906i	$-0.0962881\pi$
$444$		0			0
$445$	2.48690			0.117890
$446$		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
$453$	2.07108	+	8.97523i	0.0973079	+	0.421693i
$454$		0			0
$455$	−0.662835	−	0.220523i	−0.0310742	−	0.0103383i
$456$		0			0
$457$	9.05061	+	15.6761i	0.423370	+	0.733298i	0.996267	−	0.0863294i	$-0.0275137\pi$
$457$	9.05061	+	15.6761i	0.423370	+	0.733298i	−0.572897	+	0.819628i	$0.694180\pi$
$458$		0			0
$459$	−14.6937	+	38.2415i	−0.685842	+	1.78496i
$460$		0			0
$461$	−5.25520			−0.244759			−0.122380	−	0.992483i	$-0.539053\pi$
$461$	−5.25520			−0.244759			−0.122380	+	0.992483i	$0.539053\pi$
$462$		0			0
$463$	−0.365876	−	0.633715i	−0.0170037	−	0.0294513i	0.857398	−	0.514653i	$-0.172079\pi$
$463$	−0.365876	−	0.633715i	−0.0170037	−	0.0294513i	−0.874402	+	0.485202i	$0.838746\pi$
$464$		0			0
$465$	0.118067	+	0.511655i	0.00547522	+	0.0237274i
$466$		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
$471$	21.3334	+	6.52479i	0.982993	+	0.300646i
$472$		0			0
$473$	1.70529	+	2.95364i	0.0784092	+	0.135809i
$474$		0			0
$475$	30.5256			1.40061
$476$		0			0
$477$	−0.512898	+	7.31221i	−0.0234840	+	0.334803i
$478$		0			0
$479$	−5.82835	−	10.0950i	−0.266304	−	0.461252i	0.701600	−	0.712571i	$-0.252469\pi$
$479$	−5.82835	−	10.0950i	−0.266304	−	0.461252i	−0.967904	+	0.251318i	$0.919136\pi$
$480$		0			0
$481$	8.30115	+	40.4476i	0.378500	+	1.84425i
$482$		0			0
$483$	−1.71819	+	1.60190i	−0.0781806	+	0.0728889i
$484$		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
$491$	23.7959			1.07390			0.536948	−	0.843616i	$-0.319577\pi$
$491$	23.7959			1.07390			0.536948	+	0.843616i	$0.319577\pi$
$492$		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
$497$	−5.37244	−	9.30534i	−0.240987	−	0.417402i
$498$		0			0
$499$	10.6364	+	18.4229i	0.476153	+	0.824720i	0.999627	−	0.0273211i	$-0.00869766\pi$
$499$	10.6364	+	18.4229i	0.476153	+	0.824720i	−0.523474	+	0.852042i	$0.675364\pi$
$500$		0			0
$501$	−14.8637	+	13.8576i	−0.664060	+	0.619113i
$502$		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
$507$	13.2952	+	18.1725i	0.590460	+	0.807067i
$508$		0			0
$509$	−34.9518			−1.54921			−0.774606	−	0.632445i	$-0.782052\pi$
$509$	−34.9518			−1.54921			−0.774606	+	0.632445i	$0.782052\pi$
$510$		0			0
$511$	−9.08834			−0.402044
$512$		0			0
$513$	−11.4395	+	29.7723i	−0.505067	+	1.31448i
$514$		0			0
$515$	−0.514738	+	0.891552i	−0.0226821	+	0.0392865i
$516$		0			0
$517$	21.3901			0.940733
$518$		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
$527$	7.29529	−	12.6358i	0.317788	−	0.550424i
$528$		0			0
$529$	−21.6849			−0.942823
$530$		0			0
$531$	30.8608	+	20.8255i	1.33924	+	0.903749i
$532$		0			0
$533$	15.9334	−	14.1453i	0.690154	−	0.612702i
$534$		0			0
$535$	−1.67208			−0.0722904
$536$		0			0
$537$	7.22348	+	31.3037i	0.311716	+	1.35085i
$538$		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
$543$	14.4486	−	13.4706i	0.620049	−	0.578081i
$544$		0			0
$545$	−0.609071	−	1.05494i	−0.0260897	−	0.0451888i
$546$		0			0
$547$	−10.1868	+	17.6440i	−0.435556	+	0.754405i	−0.997341	−	0.0728786i	$-0.976781\pi$
$547$	−10.1868	+	17.6440i	−0.435556	+	0.754405i	0.561785	+	0.827283i	$0.310115\pi$
$548$		0			0
$549$	2.70652	−	38.5859i	0.115511	−	1.64681i
$550$		0			0
$551$	−4.81630	+	8.34208i	−0.205181	+	0.355384i
$552$		0			0
$553$	−7.69366	+	13.3258i	−0.327168	+	0.566671i
$554$		0			0
$555$	2.37671	−	2.21584i	0.100886	−	0.0940572i
$556$		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
$561$	7.04647	+	30.5366i	0.297502	+	1.28926i
$562$		0			0
$563$	18.2529	−	31.6149i	0.769267	−	1.33241i	−0.168694	−	0.985668i	$-0.553955\pi$
$563$	18.2529	−	31.6149i	0.769267	−	1.33241i	0.937961	−	0.346741i	$-0.112712\pi$
$564$		0			0
$565$	−1.64561			−0.0692314
$566$		0			0
$567$	10.5398	+	1.48589i	0.442632	+	0.0624017i
$568$		0			0
$569$	3.38857	+	5.86917i	0.142056	+	0.246048i	0.928271	−	0.371905i	$-0.121295\pi$
$569$	3.38857	+	5.86917i	0.142056	+	0.246048i	−0.786215	+	0.617953i	$0.787962\pi$
$570$		0			0
$571$	6.78237	+	11.7474i	0.283834	+	0.491614i	0.972326	−	0.233630i	$-0.0750604\pi$
$571$	6.78237	+	11.7474i	0.283834	+	0.491614i	−0.688492	+	0.725244i	$0.741727\pi$
$572$		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
$579$	−17.1350	+	15.9752i	−0.712105	+	0.663906i
$580$		0			0
$581$	0.0177647	−	0.0307693i	0.000737003	−	0.00127653i
$582$		0			0
$583$	2.80371	+	4.85617i	0.116118	+	0.201122i
$584$		0			0
$585$	0.675659	−	1.63810i	0.0279351	−	0.0677272i
$586$		0			0
$587$	−7.03680	−	12.1881i	−0.290440	−	0.503057i	0.683474	−	0.729975i	$-0.260468\pi$
$587$	−7.03680	−	12.1881i	−0.290440	−	0.503057i	−0.973914	+	0.226918i	$0.927135\pi$
$588$		0			0
$589$	5.67962	−	9.83739i	0.234025	−	0.405343i
$590$		0			0
$591$	5.13139	+	22.2374i	0.211077	+	0.914723i
$592$		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	−0.969673	−	0.244405i	$-0.921408\pi$
$599$	−17.0464	−	29.5252i	−0.696497	−	1.20637i	0.273176	−	0.961964i	$-0.411926\pi$
$600$		0			0
$601$	−1.71200	−	2.96527i	−0.0698338	−	0.120956i	0.828994	−	0.559257i	$-0.188914\pi$
$601$	−1.71200	−	2.96527i	−0.0698338	−	0.120956i	−0.898828	+	0.438301i	$0.855580\pi$
$602$		0			0
$603$	2.54947	−	36.3469i	0.103822	−	1.48016i
$604$		0			0
$605$	0.939221			0.0381848
$606$		0			0
$607$	6.61130	−	11.4511i	0.268344	−	0.464786i	−0.700090	−	0.714055i	$-0.746857\pi$
$607$	6.61130	−	11.4511i	0.268344	−	0.464786i	0.968434	+	0.249269i	$0.0801902\pi$
$608$		0			0
$609$	3.07411	+	0.940210i	0.124569	+	0.0380992i
$610$		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
$615$	−1.60342	−	0.490402i	−0.0646560	−	0.0197749i
$616$		0			0
$617$	−6.02525	+	10.4360i	−0.242567	+	0.420139i	−0.961445	−	0.274998i	$-0.911323\pi$
$617$	−6.02525	+	10.4360i	−0.242567	+	0.420139i	0.718877	+	0.695137i	$0.244656\pi$
$618$		0			0
$619$	−7.09064	+	12.2814i	−0.284997	+	0.493629i	−0.972608	−	0.232450i	$-0.925326\pi$
$619$	−7.09064	+	12.2814i	−0.284997	+	0.493629i	0.687611	+	0.726079i	$0.258659\pi$
$620$		0			0
$621$	−3.74849	−	4.63205i	−0.150422	−	0.185878i
$622$		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
$627$	5.48591	+	23.7737i	0.219086	+	0.949431i
$628$		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
$633$	11.1386	−	10.3847i	0.442721	−	0.412755i
$634$		0			0
$635$	2.89866			0.115030
$636$		0			0
$637$	−15.1028	+	13.4079i	−0.598395	+	0.531240i
$638$		0			0
$639$	24.4999	−	11.9429i	0.969199	−	0.472453i
$640$		0			0
$641$	41.2230			1.62821			0.814106	−	0.580716i	$-0.197227\pi$
$641$	41.2230			1.62821			0.814106	+	0.580716i	$0.197227\pi$
$642$		0			0
$643$	12.7277	−	22.0450i	0.501931	−	0.869369i	−0.498067	−	0.867139i	$-0.665957\pi$
$643$	12.7277	−	22.0450i	0.501931	−	0.869369i	0.999998	−	0.00223082i	$-0.000710091\pi$
$644$		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
$653$	12.6813			0.496259			0.248129	−	0.968727i	$-0.420184\pi$
$653$	12.6813			0.496259			0.248129	+	0.968727i	$0.420184\pi$
$654$		0			0
$655$	−0.290425	+	0.503032i	−0.0113479	+	0.0196551i
$656$		0			0
$657$	1.61308	−	22.9972i	0.0629324	−	0.897206i
$658$		0			0
$659$	−6.36837			−0.248076			−0.124038	−	0.992277i	$-0.539585\pi$
$659$	−6.36837			−0.248076			−0.124038	+	0.992277i	$0.539585\pi$
$660$		0			0
$661$	−16.0940			−0.625985			−0.312992	−	0.949756i	$-0.601331\pi$
$661$	−16.0940			−0.625985			−0.312992	+	0.949756i	$0.601331\pi$
$662$		0			0
$663$	−44.7706	+	20.4898i	−1.73875	+	0.795756i
$664$		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
$669$	10.1625	+	3.10818i	0.392905	+	0.120169i
$670$		0			0
$671$	−14.7950	−	25.6256i	−0.571153	−	0.989266i
$672$		0			0
$673$	−4.21806	−	7.30589i	−0.162594	−	0.281621i	0.773204	−	0.634157i	$-0.218653\pi$
$673$	−4.21806	−	7.30589i	−0.162594	−	0.281621i	−0.935798	+	0.352536i	$0.885319\pi$
$674$		0			0
$675$	25.5245	−	4.03425i	0.982437	−	0.155278i
$676$		0			0
$677$	−1.55850	+	2.69939i	−0.0598978	+	0.103746i	−0.894419	−	0.447229i	$-0.852411\pi$
$677$	−1.55850	+	2.69939i	−0.0598978	+	0.103746i	0.834522	+	0.550975i	$0.185744\pi$
$678$		0			0
$679$	−3.24224			−0.124426
$680$		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
$687$	−3.12342	−	0.955291i	−0.119166	−	0.0364466i
$688$		0			0
$689$	−6.58815	+	5.84880i	−0.250989	+	0.222821i
$690$		0			0
$691$	−13.5109	−	23.4015i	−0.513978	−	0.890236i	−0.999869	−	0.0162163i	$-0.994838\pi$
$691$	−13.5109	−	23.4015i	−0.513978	−	0.890236i	0.485891	−	0.874020i	$-0.338495\pi$
$692$		0			0
$693$	7.31917	−	3.56785i	0.278032	−	0.135532i
$694$		0			0
$695$	−0.211507			−0.00802294
$696$		0			0
$697$	23.2951	+	40.3483i	0.882364	+	1.52830i
$698$		0			0
$699$	1.61475	−	1.50545i	0.0610753	−	0.0569414i
$700$		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
$705$	1.93436	−	1.80343i	0.0728523	−	0.0679213i
$706$		0			0
$707$	−8.41896	−	14.5821i	−0.316628	−	0.548415i
$708$		0			0
$709$	−22.8066			−0.856518			−0.428259	−	0.903656i	$-0.640873\pi$
$709$	−22.8066			−0.856518			−0.428259	+	0.903656i	$0.640873\pi$
$710$		0			0
$711$	−32.3542	−	21.8333i	−1.21338	−	0.818812i
$712$		0			0
$713$	1.06112	+	1.83791i	0.0397391	+	0.0688302i
$714$		0			0
$715$	−0.272516	−	1.32784i	−0.0101915	−	0.0496586i
$716$		0			0
$717$	30.0908	+	9.20321i	1.12376	+	0.343700i
$718$		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
$725$	7.80448			0.289851
$726$		0			0
$727$	−13.2103	+	22.8809i	−0.489943	+	0.848606i	−0.999933	−	0.0115742i	$-0.996316\pi$
$727$	−13.2103	+	22.8809i	−0.489943	+	0.848606i	0.509990	+	0.860180i	$0.329649\pi$
$728$		0			0
$729$	−5.63063	+	26.4064i	−0.208542	+	0.978013i
$730$		0			0
$731$	−5.85845	−	10.1471i	−0.216683	−	0.375305i
$732$		0			0
$733$	−5.54271	−	9.60025i	−0.204725	−	0.354593i	0.745320	−	0.666706i	$-0.232297\pi$
$733$	−5.54271	−	9.60025i	−0.204725	−	0.354593i	−0.950045	+	0.312113i	$0.898963\pi$
$734$		0			0
$735$	1.51983	+	0.464837i	0.0560597	+	0.0171458i
$736$		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
$741$	−34.8554	+	15.9520i	−1.28044	+	0.586010i
$742$		0			0
$743$	40.5105			1.48619			0.743093	−	0.669189i	$-0.233358\pi$
$743$	40.5105			1.48619			0.743093	+	0.669189i	$0.233358\pi$
$744$		0			0
$745$	−3.17592			−0.116357
$746$		0			0
$747$	0.0747059	+	0.0504131i	0.00273334	+	0.00184452i
$748$		0			0
$749$	6.03570	−	10.4541i	0.220540	−	0.381986i
$750$		0			0
$751$	41.6133			1.51849			0.759245	−	0.650805i	$-0.225568\pi$
$751$	41.6133			1.51849			0.759245	+	0.650805i	$0.225568\pi$
$752$		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
$761$	−0.937881	+	1.62446i	−0.0339982	+	0.0588866i	−0.882524	−	0.470268i	$-0.844157\pi$
$761$	−0.937881	+	1.62446i	−0.0339982	+	0.0588866i	0.848526	+	0.529154i	$0.177491\pi$
$762$		0			0
$763$	8.79425			0.318373
$764$		0			0
$765$	3.21183	+	2.16741i	0.116124	+	0.0783628i
$766$		0			0
$767$	8.99564	+	43.8316i	0.324814	+	1.58267i
$768$		0			0
$769$	−4.43029			−0.159760			−0.0798801	−	0.996804i	$-0.525454\pi$
$769$	−4.43029			−0.159760			−0.0798801	+	0.996804i	$0.525454\pi$
$770$		0			0
$771$	−13.0119	+	12.1312i	−0.468611	+	0.436893i
$772$		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
$777$	5.27463	+	22.8581i	0.189226	+	0.820030i
$778$		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
$783$	−2.92474	+	7.61187i	−0.104522	+	0.272026i
$784$		0			0
$785$	1.05500	−	1.82731i	0.0376546	−	0.0652196i
$786$		0			0
$787$	−14.7573	+	25.5603i	−0.526040	+	0.911128i	0.473500	+	0.880794i	$0.342990\pi$
$787$	−14.7573	+	25.5603i	−0.526040	+	0.911128i	−0.999540	+	0.0303338i	$0.990343\pi$
$788$		0			0
$789$	51.0788	+	15.6223i	1.81845	+	0.556170i
$790$		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
$795$	0.662980	+	0.202771i	0.0235135	+	0.00719155i
$796$		0			0
$797$	6.91905	−	11.9841i	0.245085	−	0.424500i	−0.717070	−	0.697001i	$-0.754517\pi$
$797$	6.91905	−	11.9841i	0.245085	−	0.424500i	0.962156	+	0.272501i	$0.0878507\pi$
$798$		0			0
$799$	−73.4847			−2.59970
$800$		0			0
$801$	−37.7508	−	25.4750i	−1.33386	−	0.900115i
$802$		0			0
$803$	−8.81778	−	15.2729i	−0.311173	−	0.538967i
$804$		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
$813$	−1.08475	−	4.70088i	−0.0380439	−	0.164867i
$814$		0			0
$815$	−1.49944	+	2.59710i	−0.0525230	+	0.0909726i
$816$		0			0
$817$	−4.56099	−	7.89987i	−0.159569	−	0.276382i
$818$		0			0
$819$	7.80278	+	10.1374i	0.272651	+	0.354229i
$820$		0			0
$821$	−22.6616	−	39.2511i	−0.790896	−	1.36987i	−0.925412	−	0.378961i	$-0.876281\pi$
$821$	−22.6616	−	39.2511i	−0.790896	−	1.36987i	0.134516	−	0.990911i	$-0.457052\pi$
$822$		0			0
$823$	−21.4007	+	37.0670i	−0.745980	+	1.29207i	0.203756	+	0.979022i	$0.434685\pi$
$823$	−21.4007	+	37.0670i	−0.745980	+	1.29207i	−0.949736	+	0.313053i	$0.898648\pi$
$824$		0			0
$825$	14.4589	−	13.4802i	0.503393	−	0.469321i
$826$		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
$835$	0.961013	+	1.66452i	0.0332572	+	0.0576032i
$836$		0			0
$837$	3.44900	−	8.97630i	0.119215	−	0.310266i
$838$		0			0
$839$	−41.3824			−1.42868			−0.714340	−	0.699799i	$-0.753273\pi$
$839$	−41.3824			−1.42868			−0.714340	+	0.699799i	$0.753273\pi$
$840$		0			0
$841$	13.2686	−	22.9819i	0.457539	−	0.792480i
$842$		0			0
$843$	−3.11119	−	13.4826i	−0.107155	−	0.464367i
$844$		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
$849$	−34.3419	+	32.0175i	−1.17861	+	1.09884i
$850$		0			0
$851$	6.56638	−	11.3733i	0.225092	−	0.389872i
$852$		0			0
$853$	16.3296	−	28.2836i	0.559113	−	0.968413i	−0.438457	−	0.898752i	$-0.644475\pi$
$853$	16.3296	−	28.2836i	0.559113	−	0.968413i	0.997571	−	0.0696609i	$-0.0221917\pi$
$854$		0			0
$855$	2.50051	+	1.68740i	0.0855157	+	0.0577078i
$856$		0			0
$857$	26.1956	−	45.3722i	0.894826	−	1.54988i	0.0608053	−	0.998150i	$-0.480633\pi$
$857$	26.1956	−	45.3722i	0.894826	−	1.54988i	0.834020	−	0.551734i	$-0.186034\pi$
$858$		0			0
$859$	17.0308	+	29.4983i	0.581085	+	1.00647i	0.995351	+	0.0963126i	$0.0307049\pi$
$859$	17.0308	+	29.4983i	0.581085	+	1.00647i	−0.414266	+	0.910156i	$0.635962\pi$
$860$		0			0
$861$	8.85392	−	8.25464i	0.301741	−	0.281317i
$862$		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
$867$	−17.5873	−	76.2163i	−0.597296	−	2.58844i
$868$		0			0
$869$	−29.8585			−1.01288
$870$		0			0
$871$	32.7478	−	29.0727i	1.10962	−	0.985092i
$872$		0			0
$873$	0.575463	−	8.20418i	0.0194765	−	0.277669i
$874$		0			0
$875$	−1.93225			−0.0653219
$876$		0			0
$877$	12.0497	−	20.8707i	0.406889	−	0.704753i	−0.587650	−	0.809115i	$-0.699947\pi$
$877$	12.0497	−	20.8707i	0.406889	−	0.704753i	0.994539	+	0.104362i	$0.0332802\pi$
$878$		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
$887$	15.9591			0.535855			0.267927	−	0.963439i	$-0.413661\pi$
$887$	15.9591			0.535855			0.267927	+	0.963439i	$0.413661\pi$
$888$		0			0
$889$	−10.4633	+	18.1230i	−0.350928	+	0.607825i
$890$		0			0
$891$	7.72905	+	19.1537i	0.258933	+	0.641675i
$892$		0			0
$893$	−57.2102			−1.91447
$894$		0			0
$895$	3.03854			0.101567
$896$		0			0
$897$	0.674991	−	7.12969i	0.0225373	−	0.238053i
$898$		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
$903$	−2.22666	+	2.07595i	−0.0740987	+	0.0690832i
$904$		0			0
$905$	−0.934176	−	1.61804i	−0.0310531	−	0.0537855i
$906$		0			0
$907$	−1.04964	−	1.81803i	−0.0348528	−	0.0603669i	0.848073	−	0.529880i	$-0.177763\pi$
$907$	−1.04964	−	1.81803i	−0.0348528	−	0.0603669i	−0.882926	+	0.469513i	$0.844430\pi$
$908$		0			0
$909$	38.3929	−	18.7152i	1.27341	−	0.620746i
$910$		0			0
$911$	13.9916	−	24.2342i	0.463563	−	0.802915i	−0.535572	−	0.844489i	$-0.679904\pi$
$911$	13.9916	−	24.2342i	0.463563	−	0.802915i	0.999135	+	0.0415744i	$0.0132374\pi$
$912$		0			0
$913$	0.0689433			0.00228169
$914$		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
$921$	1.44461	−	1.34683i	0.0476014	−	0.0443794i
$922$		0			0
$923$	31.0823	+	10.3410i	1.02308	+	0.340377i
$924$		0			0
$925$	28.4762	+	49.3223i	0.936293	+	1.62171i
$926$		0			0
$927$	16.9464	−	8.26083i	0.556594	−	0.271321i
$928$		0			0
$929$	57.0357			1.87128			0.935641	−	0.352954i	$-0.114823\pi$
$929$	57.0357			1.87128			0.935641	+	0.352954i	$0.114823\pi$
$930$		0			0
$931$	−17.1905	−	29.7749i	−0.563397	−	0.975832i
$932$		0			0
$933$	14.3552	+	4.39051i	0.469968	+	0.143739i
$934$		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
$939$	−12.2944	−	53.2788i	−0.401211	−	1.73869i
$940$		0			0
$941$	4.14330	+	7.17640i	0.135068	+	0.233944i	0.925623	−	0.378446i	$-0.123542\pi$
$941$	4.14330	+	7.17640i	0.135068	+	0.233944i	−0.790556	+	0.612390i	$0.790208\pi$
$942$		0			0
$943$	−6.77665			−0.220678
$944$		0			0
$945$	0.361081	−	0.939744i	0.0117460	−	0.0305699i
$946$		0			0
$947$	−11.7790	−	20.4018i	−0.382766	−	0.662971i	0.608690	−	0.793408i	$-0.291695\pi$
$947$	−11.7790	−	20.4018i	−0.382766	−	0.662971i	−0.991457	+	0.130437i	$0.958362\pi$
$948$		0			0
$949$	20.7200	−	18.3947i	0.672600	−	0.597118i
$950$		0			0
$951$	−11.5002	−	49.8372i	−0.372919	−	1.61608i
$952$		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
$959$	0.799094			0.0258041
$960$		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
$965$	1.10786	+	1.91888i	0.0356634	+	0.0617708i
$966$		0			0
$967$	6.51911	+	11.2914i	0.209641	+	0.363108i	0.951601	−	0.307335i	$-0.0994373\pi$
$967$	6.51911	+	11.2914i	0.209641	+	0.363108i	−0.741961	+	0.670443i	$0.766104\pi$
$968$		0			0
$969$	−18.8466	−	81.6737i	−0.605441	−	2.62374i
$970$		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
$975$	25.3132	+	17.9946i	0.810670	+	0.576289i
$976$		0			0
$977$	−33.2040			−1.06229			−0.531145	−	0.847281i	$-0.678238\pi$
$977$	−33.2040			−1.06229			−0.531145	+	0.847281i	$0.678238\pi$
$978$		0			0
$979$	−34.8388			−1.11345
$980$		0			0
$981$	−1.56089	+	22.2530i	−0.0498352	+	0.710484i
$982$		0			0
$983$	−19.9244	+	34.5101i	−0.635491	+	1.10070i	0.350920	+	0.936405i	$0.385869\pi$
$983$	−19.9244	+	34.5101i	−0.635491	+	1.10070i	−0.986411	+	0.164297i	$0.947464\pi$
$984$		0			0
$985$	2.15850			0.0687756
$986$		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
$995$	1.95303	−	3.38274i	0.0619151	−	0.107240i
$996$		0			0
$997$	27.5085			0.871202			0.435601	−	0.900140i	$-0.356536\pi$
$997$	27.5085			0.871202			0.435601	+	0.900140i	$0.356536\pi$
$998$		0			0
$999$	−58.7765	+	9.28988i	−1.85961	+	0.293919i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.10	✓	40	13.3	even	3
936.2.r.f.841.10	yes	40	9.4	even	3
936.2.s.f.529.4	yes	40	1.1	even	1	trivial
936.2.s.f.913.4	yes	40	117.94	even	3	inner
2808.2.r.f.289.11		40	39.29	odd	6
2808.2.r.f.2089.11		40	9.5	odd	6
2808.2.s.f.1153.11		40	3.2	odd	2
2808.2.s.f.1225.11		40	117.68	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.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26687 + 1.18112i) q^{3} +(0.0819095 + 0.141871i) q^{5} -1.18267 q^{7} +(0.209912 - 2.99265i) q^{9} +(-1.14747 - 1.98747i) q^{11} +(2.69631 - 2.39372i) q^{13} +(-0.271336 - 0.0829876i) q^{15} +(3.94208 + 6.82788i) q^{17} +(3.06904 + 5.31573i) q^{19} +(1.49829 - 1.39688i) q^{21} -1.14677 q^{23} +(2.48658 - 4.30689i) q^{25} +(3.26874 + 4.03922i) q^{27} +(0.784660 + 1.35907i) q^{29} +(-0.925310 - 1.60268i) q^{31} +(3.80113 + 1.16257i) q^{33} +(-0.0968723 - 0.167788i) q^{35} +(-5.72598 + 9.91769i) q^{37} +(-0.588603 + 6.21720i) q^{39} +5.90934 q^{41} -1.48613 q^{43} +(0.441765 - 0.215346i) q^{45} +(-4.66028 + 8.07184i) q^{47} -5.60128 q^{49} +(-13.0586 - 3.99396i) q^{51} -2.44339 q^{53} +(0.187977 - 0.325586i) q^{55} +(-10.1666 - 3.10943i) q^{57} +(-6.20503 + 10.7474i) q^{59} +12.8936 q^{61} +(-0.248258 + 3.53933i) q^{63} +(0.560454 + 0.186461i) q^{65} +12.1454 q^{67} +(1.45280 - 1.35447i) q^{69} +(4.54262 + 7.86805i) q^{71} +7.68457 q^{73} +(1.93678 + 8.39321i) q^{75} +(1.35708 + 2.35053i) q^{77} +(6.50531 - 11.2675i) q^{79} +(-8.91187 - 1.25639i) q^{81} +(-0.0150208 + 0.0260167i) q^{83} +(-0.645787 + 1.11854i) q^{85} +(-2.59929 - 0.794987i) q^{87} +(7.59038 - 13.1469i) q^{89} +(-3.18886 + 2.83099i) q^{91} +(3.06521 + 0.937488i) q^{93} +(-0.502767 + 0.870818i) q^{95} +2.74145 q^{97} +(-6.18866 + 3.01677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more