LMFDB - Embedded newform 720.2.q.f.241.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(241,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("720.241"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,2,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			241.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	720.241
Dual form			720.2.q.f.481.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 1.65831i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.18614 + 2.05446i) q^{7} +(-2.50000 + 1.65831i) q^{9} +(0.686141 - 1.18843i) q^{11} +(-2.37228 - 4.10891i) q^{13} +(1.18614 - 1.26217i) q^{15} -7.37228 q^{17} -3.37228 q^{19} +(4.00000 + 0.939764i) q^{21} +(-2.18614 - 3.78651i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.00000 + 3.31662i) q^{27} +(2.18614 - 3.78651i) q^{29} +(-3.37228 - 5.84096i) q^{31} +(-2.31386 - 0.543620i) q^{33} -2.37228 q^{35} -4.00000 q^{37} +(-5.62772 + 5.98844i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-5.68614 + 9.84868i) q^{43} +(-2.68614 - 1.33591i) q^{45} +(-0.813859 + 1.40965i) q^{47} +(0.686141 + 1.18843i) q^{49} +(3.68614 + 12.2255i) q^{51} +11.4891 q^{53} +1.37228 q^{55} +(1.68614 + 5.59230i) q^{57} +(-0.686141 - 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} +(-0.441578 - 7.10313i) q^{63} +(2.37228 - 4.10891i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(-5.18614 + 5.51856i) q^{69} +6.00000 q^{71} -14.1168 q^{73} +(1.68614 + 0.396143i) q^{75} +(1.62772 + 2.81929i) q^{77} +(1.00000 - 1.73205i) q^{79} +(3.50000 - 8.29156i) q^{81} +(0.813859 - 1.40965i) q^{83} +(-3.68614 - 6.38458i) q^{85} +(-7.37228 - 1.73205i) q^{87} -1.11684 q^{89} +11.2554 q^{91} +(-8.00000 + 8.51278i) q^{93} +(-1.68614 - 2.92048i) q^{95} +(1.31386 - 2.27567i) q^{97} +(0.255437 + 4.10891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5} + q^{7} - 10 q^{9} - 3 q^{11} + 2 q^{13} - q^{15} - 18 q^{17} - 2 q^{19} + 16 q^{21} - 3 q^{23} - 2 q^{25} + 16 q^{27} + 3 q^{29} - 2 q^{31} - 15 q^{33} + 2 q^{35} - 16 q^{37}+ \cdots + 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 + q^7 - 10 * q^9 - 3 * q^11 + 2 * q^13 - q^15 - 18 * q^17 - 2 * q^19 + 16 * q^21 - 3 * q^23 - 2 * q^25 + 16 * q^27 + 3 * q^29 - 2 * q^31 - 15 * q^33 + 2 * q^35 - 16 * q^37 - 34 * q^39 + 6 * q^41 - 17 * q^43 - 5 * q^45 - 9 * q^47 - 3 * q^49 + 9 * q^51 - 6 * q^55 + q^57 + 3 * q^59 - q^61 - 19 * q^63 - 2 * q^65 - 14 * q^67 - 15 * q^69 + 24 * q^71 - 22 * q^73 + q^75 + 18 * q^77 + 4 * q^79 + 14 * q^81 + 9 * q^83 - 9 * q^85 - 18 * q^87 + 30 * q^89 + 68 * q^91 - 32 * q^93 - q^95 + 11 * q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	1.65831i	−0.288675	−	0.957427i
$3$	−0.500000	−	1.65831i	−0.288675	−	0.957427i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−1.18614	+	2.05446i	−0.448319	+	0.776511i	−0.998277	−	0.0586811i	$-0.981310\pi$
$7$	−1.18614	+	2.05446i	−0.448319	+	0.776511i	0.549958	+	0.835192i	$0.314644\pi$
$8$		0			0
$9$	−2.50000	+	1.65831i	−0.833333	+	0.552771i
$10$		0			0
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	−0.743851	−	0.668346i	$-0.767003\pi$
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	0.950730	+	0.310021i	$0.100336\pi$
$12$		0			0
$13$	−2.37228	−	4.10891i	−0.657952	−	1.13961i	−0.981145	−	0.193274i	$-0.938089\pi$
$13$	−2.37228	−	4.10891i	−0.657952	−	1.13961i	0.323192	−	0.946333i	$-0.395244\pi$
$14$		0			0
$15$	1.18614	−	1.26217i	0.306260	−	0.325891i
$16$		0			0
$17$	−7.37228			−1.78804			−0.894020	−	0.448026i	$-0.852127\pi$
$17$	−7.37228			−1.78804			−0.894020	+	0.448026i	$0.852127\pi$
$18$		0			0
$19$	−3.37228			−0.773654			−0.386827	−	0.922152i	$-0.626429\pi$
$19$	−3.37228			−0.773654			−0.386827	+	0.922152i	$0.626429\pi$
$20$		0			0
$21$	4.00000	+	0.939764i	0.872872	+	0.205073i
$22$		0			0
$23$	−2.18614	−	3.78651i	−0.455842	−	0.789541i	0.542894	−	0.839801i	$-0.317328\pi$
$23$	−2.18614	−	3.78651i	−0.455842	−	0.789541i	−0.998736	+	0.0502598i	$0.983995\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	4.00000	+	3.31662i	0.769800	+	0.638285i
$28$		0			0
$29$	2.18614	−	3.78651i	0.405956	−	0.703137i	−0.588476	−	0.808515i	$-0.700272\pi$
$29$	2.18614	−	3.78651i	0.405956	−	0.703137i	0.994432	+	0.105378i	$0.0336052\pi$
$30$		0			0
$31$	−3.37228	−	5.84096i	−0.605680	−	1.04907i	−0.991944	−	0.126680i	$-0.959568\pi$
$31$	−3.37228	−	5.84096i	−0.605680	−	1.04907i	0.386264	−	0.922388i	$-0.373765\pi$
$32$		0			0
$33$	−2.31386	−	0.543620i	−0.402791	−	0.0946322i
$34$		0			0
$35$	−2.37228			−0.400989
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$	−5.62772	+	5.98844i	−0.901156	+	0.958918i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−5.68614	+	9.84868i	−0.867128	+	1.50191i	−0.00221007	+	0.999998i	$0.500703\pi$
$43$	−5.68614	+	9.84868i	−0.867128	+	1.50191i	−0.864918	+	0.501913i	$0.832630\pi$
$44$		0			0
$45$	−2.68614	−	1.33591i	−0.400426	−	0.199145i
$46$		0			0
$47$	−0.813859	+	1.40965i	−0.118714	+	0.205618i	−0.919258	−	0.393655i	$-0.871210\pi$
$47$	−0.813859	+	1.40965i	−0.118714	+	0.205618i	0.800545	+	0.599273i	$0.204544\pi$
$48$		0			0
$49$	0.686141	+	1.18843i	0.0980201	+	0.169776i
$50$		0			0
$51$	3.68614	+	12.2255i	0.516163	+	1.71192i
$52$		0			0
$53$	11.4891			1.57815			0.789076	−	0.614295i	$-0.210560\pi$
$53$	11.4891			1.57815			0.789076	+	0.614295i	$0.210560\pi$
$54$		0			0
$55$	1.37228			0.185038
$56$		0			0
$57$	1.68614	+	5.59230i	0.223335	+	0.740718i
$58$		0			0
$59$	−0.686141	−	1.18843i	−0.0893279	−	0.154720i	0.817899	−	0.575361i	$-0.195139\pi$
$59$	−0.686141	−	1.18843i	−0.0893279	−	0.154720i	−0.907227	+	0.420641i	$0.861805\pi$
$60$		0			0
$61$	−4.55842	+	7.89542i	−0.583646	+	1.01090i	0.411397	+	0.911456i	$0.365041\pi$
$61$	−4.55842	+	7.89542i	−0.583646	+	1.01090i	−0.995043	+	0.0994483i	$0.968292\pi$
$62$		0			0
$63$	−0.441578	−	7.10313i	−0.0556336	−	0.894910i
$64$		0			0
$65$	2.37228	−	4.10891i	0.294245	−	0.509648i
$66$		0			0
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	0.569066	−	0.822292i	$-0.307305\pi$
$67$	−3.50000	−	6.06218i	−0.427593	−	0.740613i	−0.996659	+	0.0816792i	$0.973972\pi$
$68$		0			0
$69$	−5.18614	+	5.51856i	−0.624338	+	0.664356i
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−14.1168			−1.65225			−0.826126	−	0.563486i	$-0.809460\pi$
$73$	−14.1168			−1.65225			−0.826126	+	0.563486i	$0.809460\pi$
$74$		0			0
$75$	1.68614	+	0.396143i	0.194699	+	0.0457427i
$76$		0			0
$77$	1.62772	+	2.81929i	0.185496	+	0.321288i
$78$		0			0
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	−0.804272	−	0.594261i	$-0.797445\pi$
$79$	1.00000	−	1.73205i	0.112509	−	0.194871i	0.916781	+	0.399390i	$0.130778\pi$
$80$		0			0
$81$	3.50000	−	8.29156i	0.388889	−	0.921285i
$82$		0			0
$83$	0.813859	−	1.40965i	0.0893327	−	0.154729i	−0.817897	−	0.575365i	$-0.804860\pi$
$83$	0.813859	−	1.40965i	0.0893327	−	0.154729i	0.907229	+	0.420637i	$0.138193\pi$
$84$		0			0
$85$	−3.68614	−	6.38458i	−0.399818	−	0.692505i
$86$		0			0
$87$	−7.37228	−	1.73205i	−0.790392	−	0.185695i
$88$		0			0
$89$	−1.11684			−0.118385			−0.0591926	−	0.998247i	$-0.518853\pi$
$89$	−1.11684			−0.118385			−0.0591926	+	0.998247i	$0.518853\pi$
$90$		0			0
$91$	11.2554			1.17989
$92$		0			0
$93$	−8.00000	+	8.51278i	−0.829561	+	0.882734i
$94$		0			0
$95$	−1.68614	−	2.92048i	−0.172994	−	0.299635i
$96$		0			0
$97$	1.31386	−	2.27567i	0.133402	−	0.231059i	−0.791584	−	0.611061i	$-0.790743\pi$
$97$	1.31386	−	2.27567i	0.133402	−	0.231059i	0.924986	+	0.380001i	$0.124076\pi$
$98$		0			0
$99$	0.255437	+	4.10891i	0.0256724	+	0.412961i
$100$		0			0
$101$	4.37228	−	7.57301i	0.435058	−	0.753543i	−0.562242	−	0.826973i	$-0.690061\pi$
$101$	4.37228	−	7.57301i	0.435058	−	0.753543i	0.997300	+	0.0734297i	$0.0233944\pi$
$102$		0			0
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$		0			0
$105$	1.18614	+	3.93398i	0.115755	+	0.383917i
$106$		0			0
$107$	14.4891			1.40072			0.700358	−	0.713791i	$-0.253024\pi$
$107$	14.4891			1.40072			0.700358	+	0.713791i	$0.253024\pi$
$108$		0			0
$109$	9.62772			0.922168			0.461084	−	0.887356i	$-0.347461\pi$
$109$	9.62772			0.922168			0.461084	+	0.887356i	$0.347461\pi$
$110$		0			0
$111$	2.00000	+	6.63325i	0.189832	+	0.629600i
$112$		0			0
$113$	−7.37228	−	12.7692i	−0.693526	−	1.20122i	−0.970675	−	0.240395i	$-0.922723\pi$
$113$	−7.37228	−	12.7692i	−0.693526	−	1.20122i	0.277149	−	0.960827i	$-0.410610\pi$
$114$		0			0
$115$	2.18614	−	3.78651i	0.203859	−	0.353094i
$116$		0			0
$117$	12.7446	+	6.33830i	1.17824	+	0.585976i
$118$		0			0
$119$	8.74456	−	15.1460i	0.801613	−	1.38843i
$120$		0			0
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$		0			0
$123$	3.55842	−	3.78651i	0.320852	−	0.341418i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−9.11684			−0.808989			−0.404495	−	0.914540i	$-0.632553\pi$
$127$	−9.11684			−0.808989			−0.404495	+	0.914540i	$0.632553\pi$
$128$		0			0
$129$	19.1753	+	4.50506i	1.68829	+	0.396648i
$130$		0			0
$131$	4.37228	+	7.57301i	0.382008	+	0.661657i	0.991349	−	0.131251i	$-0.0418993\pi$
$131$	4.37228	+	7.57301i	0.382008	+	0.661657i	−0.609341	+	0.792908i	$0.708566\pi$
$132$		0			0
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$		0			0
$135$	−0.872281	+	5.12241i	−0.0750740	+	0.440867i
$136$		0			0
$137$	0.941578	−	1.63086i	0.0804444	−	0.139334i	−0.822996	−	0.568046i	$-0.807699\pi$
$137$	0.941578	−	1.63086i	0.0804444	−	0.139334i	0.903441	+	0.428713i	$0.141033\pi$
$138$		0			0
$139$	9.05842	+	15.6896i	0.768325	+	1.33078i	0.938470	+	0.345359i	$0.112243\pi$
$139$	9.05842	+	15.6896i	0.768325	+	1.33078i	−0.170145	+	0.985419i	$0.554424\pi$
$140$		0			0
$141$	2.74456	+	0.644810i	0.231134	+	0.0543028i
$142$		0			0
$143$	−6.51087			−0.544467
$144$		0			0
$145$	4.37228			0.363098
$146$		0			0
$147$	1.62772	−	1.73205i	0.134252	−	0.142857i
$148$		0			0
$149$	−9.55842	−	16.5557i	−0.783056	−	1.35629i	−0.930153	−	0.367171i	$-0.880326\pi$
$149$	−9.55842	−	16.5557i	−0.783056	−	1.35629i	0.147097	−	0.989122i	$-0.453007\pi$
$150$		0			0
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$		0			0
$153$	18.4307	−	12.2255i	1.49003	−	0.988377i
$154$		0			0
$155$	3.37228	−	5.84096i	0.270868	−	0.469157i
$156$		0			0
$157$	−2.37228	−	4.10891i	−0.189329	−	0.327927i	0.755698	−	0.654920i	$-0.227298\pi$
$157$	−2.37228	−	4.10891i	−0.189329	−	0.327927i	−0.945027	+	0.326993i	$0.893964\pi$
$158$		0			0
$159$	−5.74456	−	19.0526i	−0.455573	−	1.51097i
$160$		0			0
$161$	10.3723			0.817450
$162$		0			0
$163$	−1.48913			−0.116637			−0.0583186	−	0.998298i	$-0.518574\pi$
$163$	−1.48913			−0.116637			−0.0583186	+	0.998298i	$0.518574\pi$
$164$		0			0
$165$	−0.686141	−	2.27567i	−0.0534160	−	0.177161i
$166$		0			0
$167$	3.81386	+	6.60580i	0.295125	+	0.511172i	0.975014	−	0.222143i	$-0.0713053\pi$
$167$	3.81386	+	6.60580i	0.295125	+	0.511172i	−0.679889	+	0.733315i	$0.737972\pi$
$168$		0			0
$169$	−4.75544	+	8.23666i	−0.365803	+	0.633589i
$170$		0			0
$171$	8.43070	−	5.59230i	0.644712	−	0.427654i
$172$		0			0
$173$	−4.62772	+	8.01544i	−0.351839	+	0.609403i	−0.986572	−	0.163329i	$-0.947777\pi$
$173$	−4.62772	+	8.01544i	−0.351839	+	0.609403i	0.634733	+	0.772732i	$0.281110\pi$
$174$		0			0
$175$	−1.18614	−	2.05446i	−0.0896638	−	0.155302i
$176$		0			0
$177$	−1.62772	+	1.73205i	−0.122347	+	0.130189i
$178$		0			0
$179$	3.25544			0.243323			0.121661	−	0.992572i	$-0.461178\pi$
$179$	3.25544			0.243323			0.121661	+	0.992572i	$0.461178\pi$
$180$		0			0
$181$	−7.86141			−0.584334			−0.292167	−	0.956367i	$-0.594376\pi$
$181$	−7.86141			−0.584334			−0.292167	+	0.956367i	$0.594376\pi$
$182$		0			0
$183$	15.3723	+	3.61158i	1.13635	+	0.266976i
$184$		0			0
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$		0			0
$187$	−5.05842	+	8.76144i	−0.369908	+	0.640700i
$188$		0			0
$189$	−11.5584	+	4.28384i	−0.840751	+	0.311604i
$190$		0			0
$191$	−2.74456	+	4.75372i	−0.198590	+	0.343967i	−0.948071	−	0.318058i	$-0.896969\pi$
$191$	−2.74456	+	4.75372i	−0.198590	+	0.343967i	0.749482	+	0.662025i	$0.230303\pi$
$192$		0			0
$193$	−1.94158	−	3.36291i	−0.139758	−	0.242068i	0.787647	−	0.616127i	$-0.211299\pi$
$193$	−1.94158	−	3.36291i	−0.139758	−	0.242068i	−0.927405	+	0.374059i	$0.877966\pi$
$194$		0			0
$195$	−8.00000	−	1.87953i	−0.572892	−	0.134596i
$196$		0			0
$197$	17.4891			1.24605			0.623024	−	0.782202i	$-0.285904\pi$
$197$	17.4891			1.24605			0.623024	+	0.782202i	$0.285904\pi$
$198$		0			0
$199$	9.48913			0.672666			0.336333	−	0.941743i	$-0.390813\pi$
$199$	9.48913			0.672666			0.336333	+	0.941743i	$0.390813\pi$
$200$		0			0
$201$	−8.30298	+	8.83518i	−0.585647	+	0.623186i
$202$		0			0
$203$	5.18614	+	8.98266i	0.363996	+	0.630459i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$		0			0
$207$	11.7446	+	5.84096i	0.816304	+	0.405975i
$208$		0			0
$209$	−2.31386	+	4.00772i	−0.160053	+	0.277220i
$210$		0			0
$211$	−3.62772	−	6.28339i	−0.249742	−	0.432567i	0.713712	−	0.700439i	$-0.247013\pi$
$211$	−3.62772	−	6.28339i	−0.249742	−	0.432567i	−0.963454	+	0.267873i	$0.913679\pi$
$212$		0			0
$213$	−3.00000	−	9.94987i	−0.205557	−	0.681754i
$214$		0			0
$215$	−11.3723			−0.775583
$216$		0			0
$217$	16.0000			1.08615
$218$		0			0
$219$	7.05842	+	23.4101i	0.476964	+	1.58191i
$220$		0			0
$221$	17.4891	+	30.2921i	1.17645	+	2.03766i
$222$		0			0
$223$	6.18614	−	10.7147i	0.414255	−	0.717510i	−0.581095	−	0.813836i	$-0.697376\pi$
$223$	6.18614	−	10.7147i	0.414255	−	0.717510i	0.995350	+	0.0963255i	$0.0307090\pi$
$224$		0			0
$225$	−0.186141	−	2.99422i	−0.0124094	−	0.199615i
$226$		0			0
$227$	0.941578	−	1.63086i	0.0624947	−	0.108244i	−0.833085	−	0.553145i	$-0.813428\pi$
$227$	0.941578	−	1.63086i	0.0624947	−	0.108244i	0.895580	+	0.444901i	$0.146761\pi$
$228$		0			0
$229$	−9.18614	−	15.9109i	−0.607037	−	1.05142i	−0.991726	−	0.128373i	$-0.959025\pi$
$229$	−9.18614	−	15.9109i	−0.607037	−	1.05142i	0.384689	−	0.923046i	$-0.374309\pi$
$230$		0			0
$231$	3.86141	−	4.10891i	0.254062	−	0.270347i
$232$		0			0
$233$	−10.1168			−0.662776			−0.331388	−	0.943494i	$-0.607517\pi$
$233$	−10.1168			−0.662776			−0.331388	+	0.943494i	$0.607517\pi$
$234$		0			0
$235$	−1.62772			−0.106181
$236$		0			0
$237$	−3.37228	−	0.792287i	−0.219053	−	0.0514646i
$238$		0			0
$239$	−7.37228	−	12.7692i	−0.476873	−	0.825969i	0.522776	−	0.852470i	$-0.324897\pi$
$239$	−7.37228	−	12.7692i	−0.476873	−	0.825969i	−0.999649	+	0.0265017i	$0.991563\pi$
$240$		0			0
$241$	−5.24456	+	9.08385i	−0.337832	+	0.585142i	−0.984025	−	0.178032i	$-0.943027\pi$
$241$	−5.24456	+	9.08385i	−0.337832	+	0.585142i	0.646193	+	0.763174i	$0.276360\pi$
$242$		0			0
$243$	−15.5000	−	1.65831i	−0.994325	−	0.106381i
$244$		0			0
$245$	−0.686141	+	1.18843i	−0.0438359	+	0.0759260i
$246$		0			0
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$		0			0
$249$	−2.74456	−	0.644810i	−0.173930	−	0.0408632i
$250$		0			0
$251$	−15.6060			−0.985040			−0.492520	−	0.870301i	$-0.663924\pi$
$251$	−15.6060			−0.985040			−0.492520	+	0.870301i	$0.663924\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$		0			0
$255$	−8.74456	+	9.30506i	−0.547606	+	0.582706i
$256$		0			0
$257$	0.686141	+	1.18843i	0.0428003	+	0.0741323i	0.886632	−	0.462476i	$-0.153039\pi$
$257$	0.686141	+	1.18843i	0.0428003	+	0.0741323i	−0.843832	+	0.536608i	$0.819705\pi$
$258$		0			0
$259$	4.74456	−	8.21782i	0.294813	−	0.510631i
$260$		0			0
$261$	0.813859	+	13.0916i	0.0503766	+	0.810348i
$262$		0			0
$263$	2.74456	−	4.75372i	0.169237	−	0.293127i	−0.768915	−	0.639351i	$-0.779203\pi$
$263$	2.74456	−	4.75372i	0.169237	−	0.293127i	0.938152	+	0.346224i	$0.112536\pi$
$264$		0			0
$265$	5.74456	+	9.94987i	0.352886	+	0.611216i
$266$		0			0
$267$	0.558422	+	1.85208i	0.0341749	+	0.113345i
$268$		0			0
$269$	4.37228			0.266583			0.133291	−	0.991077i	$-0.457445\pi$
$269$	4.37228			0.266583			0.133291	+	0.991077i	$0.457445\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$	−5.62772	−	18.6650i	−0.340605	−	1.12966i
$274$		0			0
$275$	0.686141	+	1.18843i	0.0413758	+	0.0716651i
$276$		0			0
$277$	−2.62772	+	4.55134i	−0.157884	+	0.273464i	−0.934106	−	0.356997i	$-0.883801\pi$
$277$	−2.62772	+	4.55134i	−0.157884	+	0.273464i	0.776221	+	0.630461i	$0.217134\pi$
$278$		0			0
$279$	18.1168	+	9.01011i	1.08463	+	0.539421i
$280$		0			0
$281$	−2.18614	+	3.78651i	−0.130414	+	0.225884i	−0.923836	−	0.382788i	$-0.874964\pi$
$281$	−2.18614	+	3.78651i	−0.130414	+	0.225884i	0.793422	+	0.608672i	$0.208297\pi$
$282$		0			0
$283$	−15.9307	−	27.5928i	−0.946982	−	1.64022i	−0.751733	−	0.659467i	$-0.770782\pi$
$283$	−15.9307	−	27.5928i	−0.946982	−	1.64022i	−0.195249	−	0.980754i	$-0.562551\pi$
$284$		0			0
$285$	−4.00000	+	4.25639i	−0.236940	+	0.252127i
$286$		0			0
$287$	−7.11684			−0.420094
$288$		0			0
$289$	37.3505			2.19709
$290$		0			0
$291$	−4.43070	−	1.04095i	−0.259732	−	0.0610218i
$292$		0			0
$293$	4.11684	+	7.13058i	0.240509	+	0.416573i	0.960859	−	0.277037i	$-0.0893524\pi$
$293$	4.11684	+	7.13058i	0.240509	+	0.416573i	−0.720351	+	0.693610i	$0.756019\pi$
$294$		0			0
$295$	0.686141	−	1.18843i	0.0399487	−	0.0691931i
$296$		0			0
$297$	6.68614	−	2.47805i	0.387969	−	0.143791i
$298$		0			0
$299$	−10.3723	+	17.9653i	−0.599845	+	1.03896i
$300$		0			0
$301$	−13.4891	−	23.3639i	−0.777500	−	1.34667i
$302$		0			0
$303$	−14.7446	−	3.46410i	−0.847053	−	0.199007i
$304$		0			0
$305$	−9.11684			−0.522029
$306$		0			0
$307$	33.2337			1.89675			0.948373	−	0.317156i	$-0.102728\pi$
$307$	33.2337			1.89675			0.948373	+	0.317156i	$0.102728\pi$
$308$		0			0
$309$	−18.9783	+	20.1947i	−1.07963	+	1.14884i
$310$		0			0
$311$	−4.62772	−	8.01544i	−0.262414	−	0.454514i	0.704469	−	0.709735i	$-0.251185\pi$
$311$	−4.62772	−	8.01544i	−0.262414	−	0.454514i	−0.966883	+	0.255221i	$0.917852\pi$
$312$		0			0
$313$	−4.68614	+	8.11663i	−0.264876	+	0.458779i	−0.967531	−	0.252752i	$-0.918664\pi$
$313$	−4.68614	+	8.11663i	−0.264876	+	0.458779i	0.702655	+	0.711531i	$0.251998\pi$
$314$		0			0
$315$	5.93070	−	3.93398i	0.334157	−	0.221655i
$316$		0			0
$317$	4.37228	−	7.57301i	0.245572	−	0.425343i	−0.716720	−	0.697361i	$-0.754358\pi$
$317$	4.37228	−	7.57301i	0.245572	−	0.425343i	0.962292	+	0.272018i	$0.0876910\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$		0			0
$321$	−7.24456	−	24.0275i	−0.404352	−	1.34108i
$322$		0			0
$323$	24.8614			1.38333
$324$		0			0
$325$	4.74456			0.263181
$326$		0			0
$327$	−4.81386	−	15.9658i	−0.266207	−	0.882909i
$328$		0			0
$329$	−1.93070	−	3.34408i	−0.106443	−	0.184365i
$330$		0			0
$331$	−9.11684	+	15.7908i	−0.501107	+	0.867943i	0.498892	+	0.866664i	$0.333740\pi$
$331$	−9.11684	+	15.7908i	−0.501107	+	0.867943i	−0.999999	+	0.00127880i	$0.999593\pi$
$332$		0			0
$333$	10.0000	−	6.63325i	0.547997	−	0.363500i
$334$		0			0
$335$	3.50000	−	6.06218i	0.191225	−	0.331212i
$336$		0			0
$337$	−1.68614	−	2.92048i	−0.0918499	−	0.159089i	0.816440	−	0.577431i	$-0.195945\pi$
$337$	−1.68614	−	2.92048i	−0.0918499	−	0.159089i	−0.908290	+	0.418342i	$0.862611\pi$
$338$		0			0
$339$	−17.4891	+	18.6101i	−0.949879	+	1.01076i
$340$		0			0
$341$	−9.25544			−0.501210
$342$		0			0
$343$	−19.8614			−1.07242
$344$		0			0
$345$	−7.37228	−	1.73205i	−0.396910	−	0.0932505i
$346$		0			0
$347$	−11.0584	−	19.1537i	−0.593647	−	1.02823i	−0.993736	−	0.111751i	$-0.964354\pi$
$347$	−11.0584	−	19.1537i	−0.593647	−	1.02823i	0.400089	−	0.916476i	$-0.368979\pi$
$348$		0			0
$349$	−0.441578	+	0.764836i	−0.0236371	+	0.0409407i	−0.877602	−	0.479390i	$-0.840858\pi$
$349$	−0.441578	+	0.764836i	−0.0236371	+	0.0409407i	0.853965	+	0.520331i	$0.174191\pi$
$350$		0			0
$351$	4.13859	−	24.3036i	0.220902	−	1.29723i
$352$		0			0
$353$	−15.1753	+	26.2843i	−0.807698	+	1.39897i	0.106757	+	0.994285i	$0.465953\pi$
$353$	−15.1753	+	26.2843i	−0.807698	+	1.39897i	−0.914455	+	0.404689i	$0.867380\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$		0			0
$357$	−29.4891	−	6.92820i	−1.56073	−	0.366679i
$358$		0			0
$359$	−5.48913			−0.289705			−0.144852	−	0.989453i	$-0.546271\pi$
$359$	−5.48913			−0.289705			−0.144852	+	0.989453i	$0.546271\pi$
$360$		0			0
$361$	−7.62772			−0.401459
$362$		0			0
$363$	10.8139	−	11.5070i	0.567580	−	0.603961i
$364$		0			0
$365$	−7.05842	−	12.2255i	−0.369455	−	0.639914i
$366$		0			0
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$		0			0
$369$	−8.05842	−	4.00772i	−0.419505	−	0.208634i
$370$		0			0
$371$	−13.6277	+	23.6039i	−0.707516	+	1.22545i
$372$		0			0
$373$	−3.74456	−	6.48577i	−0.193886	−	0.335821i	0.752649	−	0.658422i	$-0.228776\pi$
$373$	−3.74456	−	6.48577i	−0.193886	−	0.335821i	−0.946535	+	0.322602i	$0.895443\pi$
$374$		0			0
$375$	0.500000	+	1.65831i	0.0258199	+	0.0856349i
$376$		0			0
$377$	−20.7446			−1.06840
$378$		0			0
$379$	10.8614			0.557913			0.278956	−	0.960304i	$-0.410011\pi$
$379$	10.8614			0.557913			0.278956	+	0.960304i	$0.410011\pi$
$380$		0			0
$381$	4.55842	+	15.1186i	0.233535	+	0.774548i
$382$		0			0
$383$	11.4891	+	19.8997i	0.587067	+	1.01683i	0.994614	+	0.103646i	$0.0330508\pi$
$383$	11.4891	+	19.8997i	0.587067	+	1.01683i	−0.407547	+	0.913184i	$0.633616\pi$
$384$		0			0
$385$	−1.62772	+	2.81929i	−0.0829562	+	0.143684i
$386$		0			0
$387$	−2.11684	−	34.0511i	−0.107605	−	1.73092i
$388$		0			0
$389$	5.18614	−	8.98266i	0.262948	−	0.455439i	−0.704076	−	0.710124i	$-0.748639\pi$
$389$	5.18614	−	8.98266i	0.262948	−	0.455439i	0.967024	+	0.254686i	$0.0819720\pi$
$390$		0			0
$391$	16.1168	+	27.9152i	0.815064	+	1.41173i
$392$		0			0
$393$	10.3723	−	11.0371i	0.523212	−	0.556749i
$394$		0			0
$395$	2.00000			0.100631
$396$		0			0
$397$	11.2554			0.564894			0.282447	−	0.959283i	$-0.408854\pi$
$397$	11.2554			0.564894			0.282447	+	0.959283i	$0.408854\pi$
$398$		0			0
$399$	−13.4891	−	3.16915i	−0.675301	−	0.158656i
$400$		0			0
$401$	−8.05842	−	13.9576i	−0.402418	−	0.697009i	0.591599	−	0.806232i	$-0.298497\pi$
$401$	−8.05842	−	13.9576i	−0.402418	−	0.697009i	−0.994017	+	0.109223i	$0.965164\pi$
$402$		0			0
$403$	−16.0000	+	27.7128i	−0.797017	+	1.38047i
$404$		0			0
$405$	8.93070	−	1.11469i	0.443770	−	0.0553895i
$406$		0			0
$407$	−2.74456	+	4.75372i	−0.136043	+	0.235633i
$408$		0			0
$409$	5.43070	+	9.40625i	0.268531	+	0.465109i	0.968483	−	0.249081i	$-0.0801285\pi$
$409$	5.43070	+	9.40625i	0.268531	+	0.465109i	−0.699952	+	0.714190i	$0.746795\pi$
$410$		0			0
$411$	−3.17527	−	0.746000i	−0.156624	−	0.0367975i
$412$		0			0
$413$	3.25544			0.160190
$414$		0			0
$415$	1.62772			0.0799016
$416$		0			0
$417$	21.4891	−	22.8665i	1.05233	−	1.11978i
$418$		0			0
$419$	−15.8614	−	27.4728i	−0.774880	−	1.34213i	−0.934862	−	0.355012i	$-0.884477\pi$
$419$	−15.8614	−	27.4728i	−0.774880	−	1.34213i	0.159981	−	0.987120i	$-0.448857\pi$
$420$		0			0
$421$	19.2337	−	33.3137i	0.937393	−	1.62361i	0.167082	−	0.985943i	$-0.446566\pi$
$421$	19.2337	−	33.3137i	0.937393	−	1.62361i	0.770311	−	0.637669i	$-0.220101\pi$
$422$		0			0
$423$	−0.302985	−	4.87375i	−0.0147316	−	0.236970i
$424$		0			0
$425$	3.68614	−	6.38458i	0.178804	−	0.309698i
$426$		0			0
$427$	−10.8139	−	18.7302i	−0.523319	−	0.906416i
$428$		0			0
$429$	3.25544	+	10.7971i	0.157174	+	0.521287i
$430$		0			0
$431$	26.2337			1.26363			0.631816	−	0.775118i	$-0.282310\pi$
$431$	26.2337			1.26363			0.631816	+	0.775118i	$0.282310\pi$
$432$		0			0
$433$	0.627719			0.0301662			0.0150831	−	0.999886i	$-0.495199\pi$
$433$	0.627719			0.0301662			0.0150831	+	0.999886i	$0.495199\pi$
$434$		0			0
$435$	−2.18614	−	7.25061i	−0.104817	−	0.347640i
$436$		0			0
$437$	7.37228	+	12.7692i	0.352664	+	0.610832i
$438$		0			0
$439$	8.11684	−	14.0588i	0.387396	−	0.670989i	−0.604703	−	0.796451i	$-0.706708\pi$
$439$	8.11684	−	14.0588i	0.387396	−	0.670989i	0.992098	+	0.125462i	$0.0400414\pi$
$440$		0			0
$441$	−3.68614	−	1.83324i	−0.175531	−	0.0872972i
$442$		0			0
$443$	−13.2446	+	22.9403i	−0.629268	+	1.08992i	0.358431	+	0.933556i	$0.383312\pi$
$443$	−13.2446	+	22.9403i	−0.629268	+	1.08992i	−0.987699	+	0.156368i	$0.950021\pi$
$444$		0			0
$445$	−0.558422	−	0.967215i	−0.0264717	−	0.0458504i
$446$		0			0
$447$	−22.6753	+	24.1287i	−1.07250	+	1.14125i
$448$		0			0
$449$	−18.8614			−0.890125			−0.445062	−	0.895500i	$-0.646819\pi$
$449$	−18.8614			−0.890125			−0.445062	+	0.895500i	$0.646819\pi$
$450$		0			0
$451$	4.11684			0.193855
$452$		0			0
$453$	16.8614	+	3.96143i	0.792218	+	0.186124i
$454$		0			0
$455$	5.62772	+	9.74749i	0.263832	+	0.456970i
$456$		0			0
$457$	−15.0584	+	26.0820i	−0.704403	+	1.22006i	0.262503	+	0.964931i	$0.415452\pi$
$457$	−15.0584	+	26.0820i	−0.704403	+	1.22006i	−0.966906	+	0.255131i	$0.917881\pi$
$458$		0			0
$459$	−29.4891	−	24.4511i	−1.37643	−	1.14128i
$460$		0			0
$461$	−9.55842	+	16.5557i	−0.445180	+	0.771075i	−0.998065	−	0.0621833i	$-0.980194\pi$
$461$	−9.55842	+	16.5557i	−0.445180	+	0.771075i	0.552885	+	0.833258i	$0.313527\pi$
$462$		0			0
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	0.999190	−	0.0402476i	$-0.0128147\pi$
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	−0.534450	+	0.845200i	$0.679481\pi$
$464$		0			0
$465$	−11.3723	−	2.67181i	−0.527377	−	0.123902i
$466$		0			0
$467$	−25.8832			−1.19773			−0.598865	−	0.800850i	$-0.704381\pi$
$467$	−25.8832			−1.19773			−0.598865	+	0.800850i	$0.704381\pi$
$468$		0			0
$469$	16.6060			0.766792
$470$		0			0
$471$	−5.62772	+	5.98844i	−0.259312	+	0.275933i
$472$		0			0
$473$	7.80298	+	13.5152i	0.358782	+	0.621428i
$474$		0			0
$475$	1.68614	−	2.92048i	0.0773654	−	0.134001i
$476$		0			0
$477$	−28.7228	+	19.0526i	−1.31513	+	0.872357i
$478$		0			0
$479$	−11.7446	+	20.3422i	−0.536623	+	0.929458i	0.462460	+	0.886640i	$0.346967\pi$
$479$	−11.7446	+	20.3422i	−0.536623	+	0.929458i	−0.999083	+	0.0428178i	$0.986366\pi$
$480$		0			0
$481$	9.48913	+	16.4356i	0.432667	+	0.749401i
$482$		0			0
$483$	−5.18614	−	17.2005i	−0.235978	−	0.782649i
$484$		0			0
$485$	2.62772			0.119319
$486$		0			0
$487$	1.25544			0.0568893			0.0284446	−	0.999595i	$-0.490945\pi$
$487$	1.25544			0.0568893			0.0284446	+	0.999595i	$0.490945\pi$
$488$		0			0
$489$	0.744563	+	2.46943i	0.0336703	+	0.111672i
$490$		0			0
$491$	1.80298	+	3.12286i	0.0813676	+	0.140933i	0.903838	−	0.427876i	$-0.140738\pi$
$491$	1.80298	+	3.12286i	0.0813676	+	0.140933i	−0.822470	+	0.568808i	$0.807405\pi$
$492$		0			0
$493$	−16.1168	+	27.9152i	−0.725866	+	1.25724i
$494$		0			0
$495$	−3.43070	+	2.27567i	−0.154199	+	0.102284i
$496$		0			0
$497$	−7.11684	+	12.3267i	−0.319234	+	0.552930i
$498$		0			0
$499$	−1.05842	−	1.83324i	−0.0473815	−	0.0820671i	0.841362	−	0.540472i	$-0.181754\pi$
$499$	−1.05842	−	1.83324i	−0.0473815	−	0.0820671i	−0.888743	+	0.458405i	$0.848421\pi$
$500$		0			0
$501$	9.04755	−	9.62747i	0.404215	−	0.430124i
$502$		0			0
$503$	−21.8614			−0.974752			−0.487376	−	0.873192i	$-0.662046\pi$
$503$	−21.8614			−0.974752			−0.487376	+	0.873192i	$0.662046\pi$
$504$		0			0
$505$	8.74456			0.389128
$506$		0			0
$507$	16.0367	+	3.76767i	0.712214	+	0.167328i
$508$		0			0
$509$	−4.67527	−	8.09780i	−0.207228	−	0.358929i	0.743613	−	0.668611i	$-0.233111\pi$
$509$	−4.67527	−	8.09780i	−0.207228	−	0.358929i	−0.950840	+	0.309682i	$0.899777\pi$
$510$		0			0
$511$	16.7446	−	29.0024i	0.740736	−	1.28299i
$512$		0			0
$513$	−13.4891	−	11.1846i	−0.595559	−	0.493812i
$514$		0			0
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	1.11684	+	1.93443i	0.0491187	+	0.0850762i
$518$		0			0
$519$	15.6060	+	3.66648i	0.685026	+	0.160941i
$520$		0			0
$521$	−41.2337			−1.80648			−0.903240	−	0.429135i	$-0.858818\pi$
$521$	−41.2337			−1.80648			−0.903240	+	0.429135i	$0.858818\pi$
$522$		0			0
$523$	11.1168			0.486106			0.243053	−	0.970013i	$-0.421851\pi$
$523$	11.1168			0.486106			0.243053	+	0.970013i	$0.421851\pi$
$524$		0			0
$525$	−2.81386	+	2.99422i	−0.122807	+	0.130678i
$526$		0			0
$527$	24.8614	+	43.0612i	1.08298	+	1.87578i
$528$		0			0
$529$	1.94158	−	3.36291i	0.0844164	−	0.146214i
$530$		0			0
$531$	3.68614	+	1.83324i	0.159965	+	0.0795559i
$532$		0			0
$533$	7.11684	−	12.3267i	0.308265	−	0.533930i
$534$		0			0
$535$	7.24456	+	12.5480i	0.313210	+	0.542495i
$536$		0			0
$537$	−1.62772	−	5.39853i	−0.0702412	−	0.232964i
$538$		0			0
$539$	1.88316			0.0811133
$540$		0			0
$541$	21.6277			0.929848			0.464924	−	0.885351i	$-0.346082\pi$
$541$	21.6277			0.929848			0.464924	+	0.885351i	$0.346082\pi$
$542$		0			0
$543$	3.93070	+	13.0367i	0.168683	+	0.559457i
$544$		0			0
$545$	4.81386	+	8.33785i	0.206203	+	0.357154i
$546$		0			0
$547$	19.7337	−	34.1798i	0.843752	−	1.46142i	−0.0429494	−	0.999077i	$-0.513675\pi$
$547$	19.7337	−	34.1798i	0.843752	−	1.46142i	0.886701	−	0.462343i	$-0.152991\pi$
$548$		0			0
$549$	−1.69702	−	27.2978i	−0.0724269	−	1.16504i
$550$		0			0
$551$	−7.37228	+	12.7692i	−0.314070	+	0.543985i
$552$		0			0
$553$	2.37228	+	4.10891i	0.100880	+	0.174729i
$554$		0			0
$555$	−4.74456	+	5.04868i	−0.201395	+	0.214304i
$556$		0			0
$557$	−9.76631			−0.413812			−0.206906	−	0.978361i	$-0.566339\pi$
$557$	−9.76631			−0.413812			−0.206906	+	0.978361i	$0.566339\pi$
$558$		0			0
$559$	53.9565			2.28212
$560$		0			0
$561$	17.0584	+	4.00772i	0.720207	+	0.169206i
$562$		0			0
$563$	8.36141	+	14.4824i	0.352391	+	0.610360i	0.986668	−	0.162747i	$-0.0520353\pi$
$563$	8.36141	+	14.4824i	0.352391	+	0.610360i	−0.634277	+	0.773106i	$0.718702\pi$
$564$		0			0
$565$	7.37228	−	12.7692i	0.310154	−	0.537203i
$566$		0			0
$567$	12.8832	+	17.0256i	0.541042	+	0.715006i
$568$		0			0
$569$	−4.80298	+	8.31901i	−0.201352	+	0.348751i	−0.948964	−	0.315384i	$-0.897867\pi$
$569$	−4.80298	+	8.31901i	−0.201352	+	0.348751i	0.747613	+	0.664135i	$0.231200\pi$
$570$		0			0
$571$	−15.8030	−	27.3716i	−0.661334	−	1.14546i	−0.980265	−	0.197687i	$-0.936657\pi$
$571$	−15.8030	−	27.3716i	−0.661334	−	1.14546i	0.318931	−	0.947778i	$-0.396676\pi$
$572$		0			0
$573$	9.25544	+	2.17448i	0.386651	+	0.0908403i
$574$		0			0
$575$	4.37228			0.182337
$576$		0			0
$577$	−23.8832			−0.994269			−0.497134	−	0.867674i	$-0.665614\pi$
$577$	−23.8832			−0.994269			−0.497134	+	0.867674i	$0.665614\pi$
$578$		0			0
$579$	−4.60597	+	4.90120i	−0.191418	+	0.203687i
$580$		0			0
$581$	1.93070	+	3.34408i	0.0800991	+	0.138736i
$582$		0			0
$583$	7.88316	−	13.6540i	0.326487	−	0.565492i
$584$		0			0
$585$	0.883156	+	14.2063i	0.0365140	+	0.587357i
$586$		0			0
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	−0.440524	−	0.897741i	$-0.645207\pi$
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	0.997728	−	0.0673658i	$-0.0214594\pi$
$588$		0			0
$589$	11.3723	+	19.6974i	0.468587	+	0.811616i
$590$		0			0
$591$	−8.74456	−	29.0024i	−0.359703	−	1.19300i
$592$		0			0
$593$	37.7228			1.54909			0.774545	−	0.632519i	$-0.217979\pi$
$593$	37.7228			1.54909			0.774545	+	0.632519i	$0.217979\pi$
$594$		0			0
$595$	17.4891			0.716984
$596$		0			0
$597$	−4.74456	−	15.7359i	−0.194182	−	0.644029i
$598$		0			0
$599$	−19.1168	−	33.1113i	−0.781093	−	1.35289i	−0.931305	−	0.364239i	$-0.881329\pi$
$599$	−19.1168	−	33.1113i	−0.781093	−	1.35289i	0.150212	−	0.988654i	$-0.452004\pi$
$600$		0			0
$601$	−13.4307	+	23.2627i	−0.547850	+	0.948904i	0.450572	+	0.892740i	$0.351220\pi$
$601$	−13.4307	+	23.2627i	−0.547850	+	0.948904i	−0.998422	+	0.0561635i	$0.982113\pi$
$602$		0			0
$603$	18.8030	+	9.35135i	0.765717	+	0.380816i
$604$		0			0
$605$	−4.55842	+	7.89542i	−0.185326	+	0.320994i
$606$		0			0
$607$	0.441578	+	0.764836i	0.0179231	+	0.0310437i	0.874848	−	0.484398i	$-0.160961\pi$
$607$	0.441578	+	0.764836i	0.0179231	+	0.0310437i	−0.856925	+	0.515442i	$0.827628\pi$
$608$		0			0
$609$	12.3030	−	13.0916i	0.498542	−	0.530497i
$610$		0			0
$611$	7.72281			0.312432
$612$		0			0
$613$	−0.233688			−0.00943857			−0.00471928	−	0.999989i	$-0.501502\pi$
$613$	−0.233688			−0.00943857			−0.00471928	+	0.999989i	$0.501502\pi$
$614$		0			0
$615$	5.05842	+	1.18843i	0.203975	+	0.0479221i
$616$		0			0
$617$	11.0584	+	19.1537i	0.445195	+	0.771101i	0.998066	−	0.0621663i	$-0.0198009\pi$
$617$	11.0584	+	19.1537i	0.445195	+	0.771101i	−0.552870	+	0.833267i	$0.686468\pi$
$618$		0			0
$619$	−19.0584	+	33.0102i	−0.766023	+	1.32679i	0.173682	+	0.984802i	$0.444434\pi$
$619$	−19.0584	+	33.0102i	−0.766023	+	1.32679i	−0.939704	+	0.341988i	$0.888900\pi$
$620$		0			0
$621$	3.81386	−	22.3966i	0.153045	−	0.898746i
$622$		0			0
$623$	1.32473	−	2.29451i	0.0530743	−	0.0919275i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	7.80298	+	1.83324i	0.311621	+	0.0732126i
$628$		0			0
$629$	29.4891			1.17581
$630$		0			0
$631$	−33.7228			−1.34248			−0.671242	−	0.741238i	$-0.734239\pi$
$631$	−33.7228			−1.34248			−0.671242	+	0.741238i	$0.734239\pi$
$632$		0			0
$633$	−8.60597	+	9.15759i	−0.342057	+	0.363981i
$634$		0			0
$635$	−4.55842	−	7.89542i	−0.180895	−	0.313320i
$636$		0			0
$637$	3.25544	−	5.63858i	0.128985	−	0.223409i
$638$		0			0
$639$	−15.0000	+	9.94987i	−0.593391	+	0.393611i
$640$		0			0
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	−0.167247	−	0.985915i	$-0.553488\pi$
$641$	19.5000	−	33.7750i	0.770204	−	1.33403i	0.937451	−	0.348117i	$-0.113179\pi$
$642$		0			0
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	0.953858	−	0.300257i	$-0.0970725\pi$
$643$	5.50000	+	9.52628i	0.216899	+	0.375680i	−0.736959	+	0.675937i	$0.763739\pi$
$644$		0			0
$645$	5.68614	+	18.8588i	0.223892	+	0.742564i
$646$		0			0
$647$	−24.0951			−0.947276			−0.473638	−	0.880720i	$-0.657059\pi$
$647$	−24.0951			−0.947276			−0.473638	+	0.880720i	$0.657059\pi$
$648$		0			0
$649$	−1.88316			−0.0739203
$650$		0			0
$651$	−8.00000	−	26.5330i	−0.313545	−	1.03991i
$652$		0			0
$653$	18.8614	+	32.6689i	0.738104	+	1.27843i	0.953348	+	0.301873i	$0.0976119\pi$
$653$	18.8614	+	32.6689i	0.738104	+	1.27843i	−0.215244	+	0.976560i	$0.569055\pi$
$654$		0			0
$655$	−4.37228	+	7.57301i	−0.170839	+	0.295902i
$656$		0			0
$657$	35.2921	−	23.4101i	1.37688	−	0.913316i
$658$		0			0
$659$	−2.74456	+	4.75372i	−0.106913	+	0.185179i	−0.914518	−	0.404545i	$-0.867430\pi$
$659$	−2.74456	+	4.75372i	−0.106913	+	0.185179i	0.807605	+	0.589724i	$0.200763\pi$
$660$		0			0
$661$	−11.1168	−	19.2549i	−0.432395	−	0.748930i	0.564684	−	0.825307i	$-0.308998\pi$
$661$	−11.1168	−	19.2549i	−0.432395	−	0.748930i	−0.997079	+	0.0763770i	$0.975665\pi$
$662$		0			0
$663$	41.4891	−	44.1485i	1.61130	−	1.71458i
$664$		0			0
$665$	8.00000			0.310227
$666$		0			0
$667$	−19.1168			−0.740207
$668$		0			0
$669$	−20.8614	−	4.90120i	−0.806549	−	0.189491i
$670$		0			0
$671$	6.25544	+	10.8347i	0.241488	+	0.418270i
$672$		0			0
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	−0.753420	−	0.657539i	$-0.771597\pi$
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	0.946156	+	0.323711i	$0.104931\pi$
$674$		0			0
$675$	−4.87228	+	1.80579i	−0.187534	+	0.0695049i
$676$		0			0
$677$	21.8614	−	37.8651i	0.840202	−	1.45527i	−0.0495215	−	0.998773i	$-0.515770\pi$
$677$	21.8614	−	37.8651i	0.840202	−	1.45527i	0.889724	−	0.456500i	$-0.150897\pi$
$678$		0			0
$679$	3.11684	+	5.39853i	0.119613	+	0.207177i
$680$		0			0
$681$	−3.17527	−	0.746000i	−0.121676	−	0.0285868i
$682$		0			0
$683$	−33.0951			−1.26635			−0.633174	−	0.774009i	$-0.718248\pi$
$683$	−33.0951			−1.26635			−0.633174	+	0.774009i	$0.718248\pi$
$684$		0			0
$685$	1.88316			0.0719517
$686$		0			0
$687$	−21.7921	+	23.1889i	−0.831421	+	0.884713i
$688$		0			0
$689$	−27.2554	−	47.2078i	−1.03835	−	1.79847i
$690$		0			0
$691$	−0.883156	+	1.52967i	−0.0335968	+	0.0581914i	−0.882335	−	0.470622i	$-0.844030\pi$
$691$	−0.883156	+	1.52967i	−0.0335968	+	0.0581914i	0.848738	+	0.528813i	$0.177363\pi$
$692$		0			0
$693$	−8.74456	−	4.34896i	−0.332178	−	0.165203i
$694$		0			0
$695$	−9.05842	+	15.6896i	−0.343606	+	0.595142i
$696$		0			0
$697$	−11.0584	−	19.1537i	−0.418868	−	0.725500i
$698$		0			0
$699$	5.05842	+	16.7769i	0.191327	+	0.634560i
$700$		0			0
$701$	14.1386			0.534007			0.267004	−	0.963696i	$-0.413966\pi$
$701$	14.1386			0.534007			0.267004	+	0.963696i	$0.413966\pi$
$702$		0			0
$703$	13.4891			0.508752
$704$		0			0
$705$	0.813859	+	2.69927i	0.0306517	+	0.101660i
$706$		0			0
$707$	10.3723	+	17.9653i	0.390090	+	0.675655i
$708$		0			0
$709$	12.9307	−	22.3966i	0.485623	−	0.841123i	−0.514241	−	0.857646i	$-0.671926\pi$
$709$	12.9307	−	22.3966i	0.485623	−	0.841123i	0.999863	+	0.0165226i	$0.00525955\pi$
$710$		0			0
$711$	0.372281	+	5.98844i	0.0139616	+	0.224584i
$712$		0			0
$713$	−14.7446	+	25.5383i	−0.552188	+	0.956418i
$714$		0			0
$715$	−3.25544	−	5.63858i	−0.121746	−	0.210871i
$716$		0			0
$717$	−17.4891	+	18.6101i	−0.653143	+	0.695008i
$718$		0			0
$719$	38.2337			1.42588			0.712938	−	0.701227i	$-0.247364\pi$
$719$	38.2337			1.42588			0.712938	+	0.701227i	$0.247364\pi$
$720$		0			0
$721$	37.9565			1.41357
$722$		0			0
$723$	17.6861	+	4.15520i	0.657755	+	0.154534i
$724$		0			0
$725$	2.18614	+	3.78651i	0.0811912	+	0.140627i
$726$		0			0
$727$	0.441578	−	0.764836i	0.0163772	−	0.0283662i	−0.857721	−	0.514116i	$-0.828120\pi$
$727$	0.441578	−	0.764836i	0.0163772	−	0.0283662i	0.874098	+	0.485750i	$0.161453\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$		0			0
$731$	41.9198	−	72.6073i	1.55046	−	2.68548i
$732$		0			0
$733$	−17.1168	−	29.6472i	−0.632225	−	1.09505i	−0.987096	−	0.160131i	$-0.948808\pi$
$733$	−17.1168	−	29.6472i	−0.632225	−	1.09505i	0.354871	−	0.934915i	$-0.384525\pi$
$734$		0			0
$735$	2.31386	+	0.543620i	0.0853480	+	0.0200517i
$736$		0			0
$737$	−9.60597			−0.353840
$738$		0			0
$739$	23.8832			0.878556			0.439278	−	0.898351i	$-0.355234\pi$
$739$	23.8832			0.878556			0.439278	+	0.898351i	$0.355234\pi$
$740$		0			0
$741$	18.9783	−	20.1947i	0.697183	−	0.741871i
$742$		0			0
$743$	12.5584	+	21.7518i	0.460724	+	0.797997i	0.998997	−	0.0447732i	$-0.0142565\pi$
$743$	12.5584	+	21.7518i	0.460724	+	0.797997i	−0.538273	+	0.842770i	$0.680923\pi$
$744$		0			0
$745$	9.55842	−	16.5557i	0.350193	−	0.606553i
$746$		0			0
$747$	0.302985	+	4.87375i	0.0110856	+	0.178321i
$748$		0			0
$749$	−17.1861	+	29.7673i	−0.627968	+	1.08767i
$750$		0			0
$751$	−9.11684	−	15.7908i	−0.332678	−	0.576216i	0.650358	−	0.759628i	$-0.274619\pi$
$751$	−9.11684	−	15.7908i	−0.332678	−	0.576216i	−0.983036	+	0.183412i	$0.941286\pi$
$752$		0			0
$753$	7.80298	+	25.8796i	0.284357	+	0.943104i
$754$		0			0
$755$	−10.0000			−0.363937
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$	3.00000	+	9.94987i	0.108893	+	0.361158i
$760$		0			0
$761$	−6.04755	−	10.4747i	−0.219223	−	0.379706i	0.735347	−	0.677690i	$-0.237019\pi$
$761$	−6.04755	−	10.4747i	−0.219223	−	0.379706i	−0.954571	+	0.297984i	$0.903686\pi$
$762$		0			0
$763$	−11.4198	+	19.7797i	−0.413426	+	0.716074i
$764$		0			0
$765$	19.8030	+	9.84868i	0.715978	+	0.356080i
$766$		0			0
$767$	−3.25544	+	5.63858i	−0.117547	+	0.203597i
$768$		0			0
$769$	9.06930	+	15.7085i	0.327047	+	0.566462i	0.981925	−	0.189273i	$-0.0606131\pi$
$769$	9.06930	+	15.7085i	0.327047	+	0.566462i	−0.654877	+	0.755735i	$0.727280\pi$
$770$		0			0
$771$	1.62772	−	1.73205i	0.0586209	−	0.0623783i
$772$		0			0
$773$	14.7446			0.530325			0.265163	−	0.964204i	$-0.414574\pi$
$773$	14.7446			0.530325			0.265163	+	0.964204i	$0.414574\pi$
$774$		0			0
$775$	6.74456			0.242272
$776$		0			0
$777$	−16.0000	−	3.75906i	−0.573997	−	0.134855i
$778$		0			0
$779$	−5.05842	−	8.76144i	−0.181237	−	0.313911i
$780$		0			0
$781$	4.11684	−	7.13058i	0.147312	−	0.255152i
$782$		0			0
$783$	21.3030	−	7.89542i	0.761307	−	0.282159i
$784$		0			0
$785$	2.37228	−	4.10891i	0.0846704	−	0.146653i
$786$		0			0
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$		0			0
$789$	−9.25544	−	2.17448i	−0.329502	−	0.0774136i
$790$		0			0
$791$	34.9783			1.24368
$792$		0			0
$793$	43.2554			1.53605
$794$		0			0
$795$	13.6277	−	14.5012i	0.483325	−	0.514305i
$796$		0			0
$797$	−1.62772	−	2.81929i	−0.0576568	−	0.0998644i	0.835756	−	0.549100i	$-0.185030\pi$
$797$	−1.62772	−	2.81929i	−0.0576568	−	0.0998644i	−0.893413	+	0.449236i	$0.851696\pi$
$798$		0			0
$799$	6.00000	−	10.3923i	0.212265	−	0.367653i
$800$		0			0
$801$	2.79211	−	1.85208i	0.0986544	−	0.0654399i
$802$		0			0
$803$	−9.68614	+	16.7769i	−0.341816	+	0.592044i
$804$		0			0
$805$	5.18614	+	8.98266i	0.182787	+	0.316597i
$806$		0			0
$807$	−2.18614	−	7.25061i	−0.0769558	−	0.255234i
$808$		0			0
$809$	−12.3505			−0.434222			−0.217111	−	0.976147i	$-0.569663\pi$
$809$	−12.3505			−0.434222			−0.217111	+	0.976147i	$0.569663\pi$
$810$		0			0
$811$	−9.37228			−0.329105			−0.164553	−	0.986368i	$-0.552618\pi$
$811$	−9.37228			−0.329105			−0.164553	+	0.986368i	$0.552618\pi$
$812$		0			0
$813$	4.00000	+	13.2665i	0.140286	+	0.465276i
$814$		0			0
$815$	−0.744563	−	1.28962i	−0.0260809	−	0.0451734i
$816$		0			0
$817$	19.1753	−	33.2125i	0.670858	−	1.16196i
$818$		0			0
$819$	−28.1386	+	18.6650i	−0.983242	+	0.652209i
$820$		0			0
$821$	−25.4198	+	44.0284i	−0.887158	+	1.53660i	−0.0439382	+	0.999034i	$0.513990\pi$
$821$	−25.4198	+	44.0284i	−0.887158	+	1.53660i	−0.843220	+	0.537569i	$0.819343\pi$
$822$		0			0
$823$	19.0475	+	32.9913i	0.663956	+	1.15001i	0.979567	+	0.201117i	$0.0644570\pi$
$823$	19.0475	+	32.9913i	0.663956	+	1.15001i	−0.315612	+	0.948888i	$0.602210\pi$
$824$		0			0
$825$	1.62772	−	1.73205i	0.0566699	−	0.0603023i
$826$		0			0
$827$	−8.13859			−0.283007			−0.141503	−	0.989938i	$-0.545194\pi$
$827$	−8.13859			−0.283007			−0.141503	+	0.989938i	$0.545194\pi$
$828$		0			0
$829$	−32.8832			−1.14208			−0.571040	−	0.820923i	$-0.693460\pi$
$829$	−32.8832			−1.14208			−0.571040	+	0.820923i	$0.693460\pi$
$830$		0			0
$831$	8.86141	+	2.08191i	0.307399	+	0.0722206i
$832$		0			0
$833$	−5.05842	−	8.76144i	−0.175264	−	0.303566i
$834$		0			0
$835$	−3.81386	+	6.60580i	−0.131984	+	0.228603i
$836$		0			0
$837$	5.88316	−	34.5484i	0.203352	−	1.19417i
$838$		0			0
$839$	22.1168	−	38.3075i	0.763558	−	1.32252i	−0.177447	−	0.984130i	$-0.556784\pi$
$839$	22.1168	−	38.3075i	0.763558	−	1.32252i	0.941005	−	0.338391i	$-0.109883\pi$
$840$		0			0
$841$	4.94158	+	8.55906i	0.170399	+	0.295140i
$842$		0			0
$843$	7.37228	+	1.73205i	0.253915	+	0.0596550i
$844$		0			0
$845$	−9.51087			−0.327184
$846$		0			0
$847$	−21.6277			−0.743137
$848$		0			0
$849$	−37.7921	+	40.2145i	−1.29702	+	1.38016i
$850$		0			0
$851$	8.74456	+	15.1460i	0.299760	+	0.519199i
$852$		0			0
$853$	0.883156	−	1.52967i	0.0302387	−	0.0523749i	−0.850510	−	0.525959i	$-0.823707\pi$
$853$	0.883156	−	1.52967i	0.0302387	−	0.0523749i	0.880749	+	0.473584i	$0.157040\pi$
$854$		0			0
$855$	9.05842	+	4.50506i	0.309791	+	0.154070i
$856$		0			0
$857$	−11.7446	+	20.3422i	−0.401187	+	0.694876i	−0.993869	−	0.110560i	$-0.964735\pi$
$857$	−11.7446	+	20.3422i	−0.401187	+	0.694876i	0.592683	+	0.805436i	$0.298069\pi$
$858$		0			0
$859$	0.0584220	+	0.101190i	0.00199333	+	0.00345255i	0.867020	−	0.498273i	$-0.166032\pi$
$859$	0.0584220	+	0.101190i	0.00199333	+	0.00345255i	−0.865027	+	0.501725i	$0.832699\pi$
$860$		0			0
$861$	3.55842	+	11.8020i	0.121271	+	0.402209i
$862$		0			0
$863$	42.6060			1.45032			0.725162	−	0.688578i	$-0.241765\pi$
$863$	42.6060			1.45032			0.725162	+	0.688578i	$0.241765\pi$
$864$		0			0
$865$	−9.25544			−0.314694
$866$		0			0
$867$	−18.6753	−	61.9389i	−0.634245	−	2.10355i
$868$		0			0
$869$	−1.37228	−	2.37686i	−0.0465515	−	0.0806295i
$870$		0			0
$871$	−16.6060	+	28.7624i	−0.562672	+	0.974576i
$872$		0			0
$873$	0.489125	+	7.86797i	0.0165544	+	0.266290i
$874$		0			0
$875$	1.18614	−	2.05446i	0.0400989	−	0.0694533i
$876$		0			0
$877$	27.9783	+	48.4598i	0.944758	+	1.63637i	0.756234	+	0.654301i	$0.227037\pi$
$877$	27.9783	+	48.4598i	0.944758	+	1.63637i	0.188524	+	0.982069i	$0.439630\pi$
$878$		0			0
$879$	9.76631	−	10.3923i	0.329410	−	0.350524i
$880$		0			0
$881$	27.3505			0.921463			0.460731	−	0.887540i	$-0.347587\pi$
$881$	27.3505			0.921463			0.460731	+	0.887540i	$0.347587\pi$
$882$		0			0
$883$	−12.7228			−0.428157			−0.214078	−	0.976816i	$-0.568675\pi$
$883$	−12.7228			−0.428157			−0.214078	+	0.976816i	$0.568675\pi$
$884$		0			0
$885$	−2.31386	−	0.543620i	−0.0777795	−	0.0182736i
$886$		0			0
$887$	−18.8614	−	32.6689i	−0.633304	−	1.09691i	−0.986872	−	0.161506i	$-0.948365\pi$
$887$	−18.8614	−	32.6689i	−0.633304	−	1.09691i	0.353568	−	0.935409i	$-0.384968\pi$
$888$		0			0
$889$	10.8139	−	18.7302i	0.362685	−	0.628189i
$890$		0			0
$891$	−7.45245	−	9.84868i	−0.249667	−	0.329943i
$892$		0			0
$893$	2.74456	−	4.75372i	0.0918433	−	0.159077i
$894$		0			0
$895$	1.62772	+	2.81929i	0.0544086	+	0.0942385i
$896$		0			0
$897$	34.9783	+	8.21782i	1.16789	+	0.274385i
$898$		0			0
$899$	−29.4891			−0.983517
$900$		0			0
$901$	−84.7011			−2.82180
$902$		0			0
$903$	−32.0000	+	34.0511i	−1.06489	+	1.13315i
$904$		0			0
$905$	−3.93070	−	6.80818i	−0.130661	−	0.226311i
$906$		0			0
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	−0.918265	−	0.395966i	$-0.870410\pi$
$907$	−3.50000	+	6.06218i	−0.116216	+	0.201291i	0.802049	+	0.597258i	$0.203743\pi$
$908$		0			0
$909$	1.62772	+	26.1831i	0.0539880	+	0.868440i
$910$		0			0
$911$	−21.0000	+	36.3731i	−0.695761	+	1.20509i	0.274162	+	0.961683i	$0.411599\pi$
$911$	−21.0000	+	36.3731i	−0.695761	+	1.20509i	−0.969923	+	0.243410i	$0.921734\pi$
$912$		0			0
$913$	−1.11684	−	1.93443i	−0.0369621	−	0.0640203i
$914$		0			0
$915$	4.55842	+	15.1186i	0.150697	+	0.499805i
$916$		0			0
$917$	−20.7446			−0.685046
$918$		0			0
$919$	−42.4674			−1.40087			−0.700435	−	0.713716i	$-0.747011\pi$
$919$	−42.4674			−1.40087			−0.700435	+	0.713716i	$0.747011\pi$
$920$		0			0
$921$	−16.6168	−	55.1118i	−0.547544	−	1.81600i
$922$		0			0
$923$	−14.2337	−	24.6535i	−0.468508	−	0.811479i
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$		0			0
$927$	42.9783	+	21.3745i	1.41159	+	0.702031i
$928$		0			0
$929$	19.9783	−	34.6033i	0.655465	−	1.13530i	−0.326312	−	0.945262i	$-0.605806\pi$
$929$	19.9783	−	34.6033i	0.655465	−	1.13530i	0.981777	−	0.190037i	$-0.0608607\pi$
$930$		0			0
$931$	−2.31386	−	4.00772i	−0.0758337	−	0.131348i
$932$		0			0
$933$	−10.9783	+	11.6819i	−0.359412	+	0.382449i
$934$		0			0
$935$	−10.1168			−0.330856
$936$		0			0
$937$	−17.7228			−0.578979			−0.289490	−	0.957181i	$-0.593486\pi$
$937$	−17.7228			−0.578979			−0.289490	+	0.957181i	$0.593486\pi$
$938$		0			0
$939$	15.8030	+	3.71277i	0.515711	+	0.121162i
$940$		0			0
$941$	−18.8139	−	32.5866i	−0.613314	−	1.06229i	−0.990678	−	0.136226i	$-0.956503\pi$
$941$	−18.8139	−	32.5866i	−0.613314	−	1.06229i	0.377363	−	0.926065i	$-0.376831\pi$
$942$		0			0
$943$	6.55842	−	11.3595i	0.213572	−	0.369917i
$944$		0			0
$945$	−9.48913	−	7.86797i	−0.308681	−	0.255945i
$946$		0			0
$947$	11.3614	−	19.6785i	0.369196	−	0.639466i	−0.620244	−	0.784409i	$-0.712966\pi$
$947$	11.3614	−	19.6785i	0.369196	−	0.639466i	0.989440	+	0.144943i	$0.0462997\pi$
$948$		0			0
$949$	33.4891	+	58.0049i	1.08710	+	1.88292i
$950$		0			0
$951$	−14.7446	−	3.46410i	−0.478125	−	0.112331i
$952$		0			0
$953$	30.8614			0.999699			0.499850	−	0.866112i	$-0.333389\pi$
$953$	30.8614			0.999699			0.499850	+	0.866112i	$0.333389\pi$
$954$		0			0
$955$	−5.48913			−0.177624
$956$		0			0
$957$	−7.11684	+	7.57301i	−0.230055	+	0.244801i
$958$		0			0
$959$	2.23369	+	3.86886i	0.0721295	+	0.124932i
$960$		0			0
$961$	−7.24456	+	12.5480i	−0.233696	+	0.404773i
$962$		0			0
$963$	−36.2228	+	24.0275i	−1.16726	+	0.774275i
$964$		0			0
$965$	1.94158	−	3.36291i	0.0625016	−	0.108256i
$966$		0			0
$967$	9.44158	+	16.3533i	0.303621	+	0.525886i	0.976953	−	0.213453i	$-0.0684711\pi$
$967$	9.44158	+	16.3533i	0.303621	+	0.525886i	−0.673333	+	0.739340i	$0.735138\pi$
$968$		0			0
$969$	−12.4307	−	41.2280i	−0.399332	−	1.32443i
$970$		0			0
$971$	−22.9783			−0.737407			−0.368704	−	0.929547i	$-0.620198\pi$
$971$	−22.9783			−0.737407			−0.368704	+	0.929547i	$0.620198\pi$
$972$		0			0
$973$	−42.9783			−1.37782
$974$		0			0
$975$	−2.37228	−	7.86797i	−0.0759738	−	0.251977i
$976$		0			0
$977$	20.0584	+	34.7422i	0.641726	+	1.11150i	0.985047	+	0.172284i	$0.0551146\pi$
$977$	20.0584	+	34.7422i	0.641726	+	1.11150i	−0.343322	+	0.939218i	$0.611552\pi$
$978$		0			0
$979$	−0.766312	+	1.32729i	−0.0244914	+	0.0424204i
$980$		0			0
$981$	−24.0693	+	15.9658i	−0.768474	+	0.509748i
$982$		0			0
$983$	7.93070	−	13.7364i	0.252950	−	0.438123i	−0.711387	−	0.702801i	$-0.751932\pi$
$983$	7.93070	−	13.7364i	0.252950	−	0.438123i	0.964337	+	0.264678i	$0.0852658\pi$
$984$		0			0
$985$	8.74456	+	15.1460i	0.278625	+	0.482593i
$986$		0			0
$987$	−4.58017	+	4.87375i	−0.145788	+	0.155133i
$988$		0			0
$989$	49.7228			1.58109
$990$		0			0
$991$	18.2337			0.579212			0.289606	−	0.957146i	$-0.406476\pi$
$991$	18.2337			0.579212			0.289606	+	0.957146i	$0.406476\pi$
$992$		0			0
$993$	30.7446	+	7.22316i	0.975649	+	0.229220i
$994$		0			0
$995$	4.74456	+	8.21782i	0.150413	+	0.260523i
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$		0			0
$999$	−16.0000	−	13.2665i	−0.506218	−	0.419733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.f.241.1		4
3.2	odd	2		2160.2.q.f.721.1		4
4.3	odd	2		90.2.e.c.61.2	yes	4
9.2	odd	6		6480.2.a.bn.1.2		2
9.4	even	3	inner	720.2.q.f.481.2		4
9.5	odd	6		2160.2.q.f.1441.1		4
9.7	even	3		6480.2.a.be.1.2		2
12.11	even	2		270.2.e.c.181.2		4
20.3	even	4		450.2.j.g.349.1		8
20.7	even	4		450.2.j.g.349.4		8
20.19	odd	2		450.2.e.j.151.1		4
36.7	odd	6		810.2.a.i.1.1		2
36.11	even	6		810.2.a.k.1.1		2
36.23	even	6		270.2.e.c.91.2		4
36.31	odd	6		90.2.e.c.31.1	✓	4
60.23	odd	4		1350.2.j.f.1099.3		8
60.47	odd	4		1350.2.j.f.1099.2		8
60.59	even	2		1350.2.e.l.451.1		4
180.7	even	12		4050.2.c.v.649.1		4
180.23	odd	12		1350.2.j.f.199.2		8
180.43	even	12		4050.2.c.v.649.4		4
180.47	odd	12		4050.2.c.ba.649.3		4
180.59	even	6		1350.2.e.l.901.1		4
180.67	even	12		450.2.j.g.49.1		8
180.79	odd	6		4050.2.a.bw.1.2		2
180.83	odd	12		4050.2.c.ba.649.2		4
180.103	even	12		450.2.j.g.49.4		8
180.119	even	6		4050.2.a.bo.1.2		2
180.139	odd	6		450.2.e.j.301.2		4
180.167	odd	12		1350.2.j.f.199.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.e.c.31.1	✓	4	36.31	odd	6
90.2.e.c.61.2	yes	4	4.3	odd	2
270.2.e.c.91.2		4	36.23	even	6
270.2.e.c.181.2		4	12.11	even	2
450.2.e.j.151.1		4	20.19	odd	2
450.2.e.j.301.2		4	180.139	odd	6
450.2.j.g.49.1		8	180.67	even	12
450.2.j.g.49.4		8	180.103	even	12
450.2.j.g.349.1		8	20.3	even	4
450.2.j.g.349.4		8	20.7	even	4
720.2.q.f.241.1		4	1.1	even	1	trivial
720.2.q.f.481.2		4	9.4	even	3	inner
810.2.a.i.1.1		2	36.7	odd	6
810.2.a.k.1.1		2	36.11	even	6
1350.2.e.l.451.1		4	60.59	even	2
1350.2.e.l.901.1		4	180.59	even	6
1350.2.j.f.199.2		8	180.23	odd	12
1350.2.j.f.199.3		8	180.167	odd	12
1350.2.j.f.1099.2		8	60.47	odd	4
1350.2.j.f.1099.3		8	60.23	odd	4
2160.2.q.f.721.1		4	3.2	odd	2
2160.2.q.f.1441.1		4	9.5	odd	6
4050.2.a.bo.1.2		2	180.119	even	6
4050.2.a.bw.1.2		2	180.79	odd	6
4050.2.c.v.649.1		4	180.7	even	12
4050.2.c.v.649.4		4	180.43	even	12
4050.2.c.ba.649.2		4	180.83	odd	12
4050.2.c.ba.649.3		4	180.47	odd	12
6480.2.a.be.1.2		2	9.7	even	3
6480.2.a.bn.1.2		2	9.2	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.65831i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.18614 + 2.05446i) q^{7} +(-2.50000 + 1.65831i) q^{9} +(0.686141 - 1.18843i) q^{11} +(-2.37228 - 4.10891i) q^{13} +(1.18614 - 1.26217i) q^{15} -7.37228 q^{17} -3.37228 q^{19} +(4.00000 + 0.939764i) q^{21} +(-2.18614 - 3.78651i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.00000 + 3.31662i) q^{27} +(2.18614 - 3.78651i) q^{29} +(-3.37228 - 5.84096i) q^{31} +(-2.31386 - 0.543620i) q^{33} -2.37228 q^{35} -4.00000 q^{37} +(-5.62772 + 5.98844i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-5.68614 + 9.84868i) q^{43} +(-2.68614 - 1.33591i) q^{45} +(-0.813859 + 1.40965i) q^{47} +(0.686141 + 1.18843i) q^{49} +(3.68614 + 12.2255i) q^{51} +11.4891 q^{53} +1.37228 q^{55} +(1.68614 + 5.59230i) q^{57} +(-0.686141 - 1.18843i) q^{59} +(-4.55842 + 7.89542i) q^{61} +(-0.441578 - 7.10313i) q^{63} +(2.37228 - 4.10891i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(-5.18614 + 5.51856i) q^{69} +6.00000 q^{71} -14.1168 q^{73} +(1.68614 + 0.396143i) q^{75} +(1.62772 + 2.81929i) q^{77} +(1.00000 - 1.73205i) q^{79} +(3.50000 - 8.29156i) q^{81} +(0.813859 - 1.40965i) q^{83} +(-3.68614 - 6.38458i) q^{85} +(-7.37228 - 1.73205i) q^{87} -1.11684 q^{89} +11.2554 q^{91} +(-8.00000 + 8.51278i) q^{93} +(-1.68614 - 2.92048i) q^{95} +(1.31386 - 2.27567i) q^{97} +(0.255437 + 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5} + q^{7} - 10 q^{9} - 3 q^{11} + 2 q^{13} - q^{15} - 18 q^{17} - 2 q^{19} + 16 q^{21} - 3 q^{23} - 2 q^{25} + 16 q^{27} + 3 q^{29} - 2 q^{31} - 15 q^{33} + 2 q^{35} - 16 q^{37}+ \cdots + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 + q^7 - 10 * q^9 - 3 * q^11 + 2 * q^13 - q^15 - 18 * q^17 - 2 * q^19 + 16 * q^21 - 3 * q^23 - 2 * q^25 + 16 * q^27 + 3 * q^29 - 2 * q^31 - 15 * q^33 + 2 * q^35 - 16 * q^37 - 34 * q^39 + 6 * q^41 - 17 * q^43 - 5 * q^45 - 9 * q^47 - 3 * q^49 + 9 * q^51 - 6 * q^55 + q^57 + 3 * q^59 - q^61 - 19 * q^63 - 2 * q^65 - 14 * q^67 - 15 * q^69 + 24 * q^71 - 22 * q^73 + q^75 + 18 * q^77 + 4 * q^79 + 14 * q^81 + 9 * q^83 - 9 * q^85 - 18 * q^87 + 30 * q^89 + 68 * q^91 - 32 * q^93 - q^95 + 11 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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