LMFDB - Embedded newform 1740.2.bc.c.853.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1740,2,Mod(853,1740)] 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("1740.853"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1740.bc (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.8939699517$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			853.7
Character	$\chi$	$=$	1740.853
Dual form			1740.2.bc.c.1177.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{3} +(0.0712321 - 2.23493i) q^{5} +(-0.799559 + 0.799559i) q^{7} -1.00000 q^{9} +(-0.319721 - 0.319721i) q^{11} +(1.26826 - 1.26826i) q^{13} +(2.23493 + 0.0712321i) q^{15} -3.94993 q^{17} +(2.75925 - 2.75925i) q^{19} +(-0.799559 - 0.799559i) q^{21} +(0.270640 + 0.270640i) q^{23} +(-4.98985 - 0.318398i) q^{25} -1.00000i q^{27} +(0.120713 + 5.38381i) q^{29} +(-3.45071 - 3.45071i) q^{31} +(0.319721 - 0.319721i) q^{33} +(1.73001 + 1.84391i) q^{35} -9.42147i q^{37} +(1.26826 + 1.26826i) q^{39} +(-5.22978 + 5.22978i) q^{41} -9.82527i q^{43} +(-0.0712321 + 2.23493i) q^{45} -5.91081i q^{47} +5.72141i q^{49} -3.94993i q^{51} +(-3.04710 - 3.04710i) q^{53} +(-0.737329 + 0.691780i) q^{55} +(2.75925 + 2.75925i) q^{57} -3.40967i q^{59} +(-8.02776 - 8.02776i) q^{61} +(0.799559 - 0.799559i) q^{63} +(-2.74415 - 2.92483i) q^{65} +(-2.10897 - 2.10897i) q^{67} +(-0.270640 + 0.270640i) q^{69} -4.89291i q^{71} +1.74581 q^{73} +(0.318398 - 4.98985i) q^{75} +0.511271 q^{77} +(2.41919 - 2.41919i) q^{79} +1.00000 q^{81} +(-1.43981 - 1.43981i) q^{83} +(-0.281362 + 8.82784i) q^{85} +(-5.38381 + 0.120713i) q^{87} +(-6.19743 + 6.19743i) q^{89} +2.02810i q^{91} +(3.45071 - 3.45071i) q^{93} +(-5.97019 - 6.36329i) q^{95} +3.50657i q^{97} +(0.319721 + 0.319721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 30 q^{9} + 4 q^{11} - 6 q^{13} - 6 q^{15} + 8 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{33} - 16 q^{35} - 6 q^{39} - 10 q^{41} - 6 q^{53} + 4 q^{55} + 8 q^{57} + 30 q^{61} - 2 q^{65} + 4 q^{67} + 12 q^{73}+ \cdots - 4 q^{99}+O(q^{100}) $ 30 * q - 30 * q^9 + 4 * q^11 - 6 * q^13 - 6 * q^15 + 8 * q^19 - 6 * q^25 + 4 * q^29 - 4 * q^33 - 16 * q^35 - 6 * q^39 - 10 * q^41 - 6 * q^53 + 4 * q^55 + 8 * q^57 + 30 * q^61 - 2 * q^65 + 4 * q^67 + 12 * q^73 + 8 * q^75 - 4 * q^77 - 4 * q^79 + 30 * q^81 - 28 * q^83 + 20 * q^85 + 10 * q^87 + 10 * q^89 + 20 * q^95 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1740\mathbb{Z}\right)^\times$.

$n$	$581$	$697$	$871$	$901$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$		0			0
$5$	0.0712321	−	2.23493i	0.0318559	−	0.999492i
$5$	0.0712321	−	2.23493i	0.0318559	−	0.999492i
$6$		0			0
$7$	−0.799559	+	0.799559i	−0.302205	+	0.302205i	−0.841876	−	0.539671i	$-0.818549\pi$
$7$	−0.799559	+	0.799559i	−0.302205	+	0.302205i	0.539671	+	0.841876i	$0.318549\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	−0.319721	−	0.319721i	−0.0963994	−	0.0963994i	0.657262	−	0.753662i	$-0.271714\pi$
$11$	−0.319721	−	0.319721i	−0.0963994	−	0.0963994i	−0.753662	+	0.657262i	$0.771714\pi$
$12$		0			0
$13$	1.26826	−	1.26826i	0.351753	−	0.351753i	−0.509008	−	0.860762i	$-0.669988\pi$
$13$	1.26826	−	1.26826i	0.351753	−	0.351753i	0.860762	+	0.509008i	$0.169988\pi$
$14$		0			0
$15$	2.23493	+	0.0712321i	0.577057	+	0.0183920i
$16$		0			0
$17$	−3.94993			−0.957999			−0.479000	−	0.877815i	$-0.659001\pi$
$17$	−3.94993			−0.957999			−0.479000	+	0.877815i	$0.659001\pi$
$18$		0			0
$19$	2.75925	−	2.75925i	0.633015	−	0.633015i	−0.315808	−	0.948823i	$-0.602275\pi$
$19$	2.75925	−	2.75925i	0.633015	−	0.633015i	0.948823	+	0.315808i	$0.102275\pi$
$20$		0			0
$21$	−0.799559	−	0.799559i	−0.174478	−	0.174478i
$22$		0			0
$23$	0.270640	+	0.270640i	0.0564324	+	0.0564324i	0.734760	−	0.678327i	$-0.237295\pi$
$23$	0.270640	+	0.270640i	0.0564324	+	0.0564324i	−0.678327	+	0.734760i	$0.737295\pi$
$24$		0			0
$25$	−4.98985	−	0.318398i	−0.997970	−	0.0636796i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	0.120713	+	5.38381i	0.0224158	+	0.999749i
$29$	0.120713	+	5.38381i	0.0224158	+	0.999749i
$30$		0			0
$31$	−3.45071	−	3.45071i	−0.619765	−	0.619765i	0.325706	−	0.945471i	$-0.394398\pi$
$31$	−3.45071	−	3.45071i	−0.619765	−	0.619765i	−0.945471	+	0.325706i	$0.894398\pi$
$32$		0			0
$33$	0.319721	−	0.319721i	0.0556562	−	0.0556562i
$34$		0			0
$35$	1.73001	+	1.84391i	0.292424	+	0.311678i
$36$		0			0
$37$		−	9.42147i		−	1.54888i	−0.632647	−	0.774440i	$-0.718032\pi$
$37$		−	9.42147i		−	1.54888i	0.632647	−	0.774440i	$-0.281968\pi$
$38$		0			0
$39$	1.26826	+	1.26826i	0.203085	+	0.203085i
$40$		0			0
$41$	−5.22978	+	5.22978i	−0.816754	+	0.816754i	−0.985636	−	0.168882i	$-0.945984\pi$
$41$	−5.22978	+	5.22978i	−0.816754	+	0.816754i	0.168882	+	0.985636i	$0.445984\pi$
$42$		0			0
$43$		−	9.82527i		−	1.49834i	−0.662378	−	0.749170i	$-0.730453\pi$
$43$		−	9.82527i		−	1.49834i	0.662378	−	0.749170i	$-0.269547\pi$
$44$		0			0
$45$	−0.0712321	+	2.23493i	−0.0106186	+	0.333164i
$46$		0			0
$47$		−	5.91081i		−	0.862180i	−0.902309	−	0.431090i	$-0.858129\pi$
$47$		−	5.91081i		−	0.862180i	0.902309	−	0.431090i	$-0.141871\pi$
$48$		0			0
$49$			5.72141i			0.817345i
$50$		0			0
$51$		−	3.94993i		−	0.553101i
$52$		0			0
$53$	−3.04710	−	3.04710i	−0.418551	−	0.418551i	0.466153	−	0.884704i	$-0.345640\pi$
$53$	−3.04710	−	3.04710i	−0.418551	−	0.418551i	−0.884704	+	0.466153i	$0.845640\pi$
$54$		0			0
$55$	−0.737329	+	0.691780i	−0.0994214	+	0.0932796i
$56$		0			0
$57$	2.75925	+	2.75925i	0.365472	+	0.365472i
$58$		0			0
$59$		−	3.40967i		−	0.443901i	−0.975058	−	0.221950i	$-0.928758\pi$
$59$		−	3.40967i		−	0.443901i	0.975058	−	0.221950i	$-0.0712423\pi$
$60$		0			0
$61$	−8.02776	−	8.02776i	−1.02785	−	1.02785i	−0.999601	−	0.0282480i	$-0.991007\pi$
$61$	−8.02776	−	8.02776i	−1.02785	−	1.02785i	−0.0282480	−	0.999601i	$-0.508993\pi$
$62$		0			0
$63$	0.799559	−	0.799559i	0.100735	−	0.100735i
$64$		0			0
$65$	−2.74415	−	2.92483i	−0.340369	−	0.362780i
$66$		0			0
$67$	−2.10897	−	2.10897i	−0.257652	−	0.257652i	0.566446	−	0.824099i	$-0.308318\pi$
$67$	−2.10897	−	2.10897i	−0.257652	−	0.257652i	−0.824099	+	0.566446i	$0.808318\pi$
$68$		0			0
$69$	−0.270640	+	0.270640i	−0.0325813	+	0.0325813i
$70$		0			0
$71$		−	4.89291i		−	0.580681i	−0.956923	−	0.290341i	$-0.906231\pi$
$71$		−	4.89291i		−	0.580681i	0.956923	−	0.290341i	$-0.0937686\pi$
$72$		0			0
$73$	1.74581			0.204331			0.102166	−	0.994767i	$-0.467423\pi$
$73$	1.74581			0.204331			0.102166	+	0.994767i	$0.467423\pi$
$74$		0			0
$75$	0.318398	−	4.98985i	0.0367654	−	0.576178i
$76$		0			0
$77$	0.511271			0.0582647
$78$		0			0
$79$	2.41919	−	2.41919i	0.272180	−	0.272180i	−0.557797	−	0.829977i	$-0.688353\pi$
$79$	2.41919	−	2.41919i	0.272180	−	0.272180i	0.829977	+	0.557797i	$0.188353\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−1.43981	−	1.43981i	−0.158040	−	0.158040i	0.623658	−	0.781698i	$-0.285646\pi$
$83$	−1.43981	−	1.43981i	−0.158040	−	0.158040i	−0.781698	+	0.623658i	$0.785646\pi$
$84$		0			0
$85$	−0.281362	+	8.82784i	−0.0305180	+	0.957513i
$86$		0			0
$87$	−5.38381	+	0.120713i	−0.577205	+	0.0129418i
$88$		0			0
$89$	−6.19743	+	6.19743i	−0.656926	+	0.656926i	−0.954651	−	0.297726i	$-0.903772\pi$
$89$	−6.19743	+	6.19743i	−0.656926	+	0.656926i	0.297726	+	0.954651i	$0.403772\pi$
$90$		0			0
$91$			2.02810i			0.212603i
$92$		0			0
$93$	3.45071	−	3.45071i	0.357822	−	0.357822i
$94$		0			0
$95$	−5.97019	−	6.36329i	−0.612529	−	0.652859i
$96$		0			0
$97$			3.50657i			0.356038i	0.984027	+	0.178019i	$0.0569689\pi$
$97$			3.50657i			0.356038i	−0.984027	+	0.178019i	$0.943031\pi$
$98$		0			0
$99$	0.319721	+	0.319721i	0.0321331	+	0.0321331i
$100$		0			0
$101$	0.515252	+	0.515252i	0.0512695	+	0.0512695i	0.732277	−	0.681007i	$-0.238458\pi$
$101$	0.515252	+	0.515252i	0.0512695	+	0.0512695i	−0.681007	+	0.732277i	$0.738458\pi$
$102$		0			0
$103$	−4.50575	−	4.50575i	−0.443964	−	0.443964i	0.449378	−	0.893342i	$-0.351646\pi$
$103$	−4.50575	−	4.50575i	−0.443964	−	0.443964i	−0.893342	+	0.449378i	$0.851646\pi$
$104$		0			0
$105$	−1.84391	+	1.73001i	−0.179948	+	0.168831i
$106$		0			0
$107$	−2.33805	+	2.33805i	−0.226028	+	0.226028i	−0.811031	−	0.585003i	$-0.801093\pi$
$107$	−2.33805	+	2.33805i	−0.226028	+	0.226028i	0.585003	+	0.811031i	$0.301093\pi$
$108$		0			0
$109$	1.65077			0.158115			0.0790573	−	0.996870i	$-0.474809\pi$
$109$	1.65077			0.158115			0.0790573	+	0.996870i	$0.474809\pi$
$110$		0			0
$111$	9.42147			0.894247
$112$		0			0
$113$	−0.735489			−0.0691890			−0.0345945	−	0.999401i	$-0.511014\pi$
$113$	−0.735489			−0.0691890			−0.0345945	+	0.999401i	$0.511014\pi$
$114$		0			0
$115$	0.624141	−	0.585585i	0.0582015	−	0.0546061i
$116$		0			0
$117$	−1.26826	+	1.26826i	−0.117251	+	0.117251i
$118$		0			0
$119$	3.15820	−	3.15820i	0.289512	−	0.289512i
$120$		0			0
$121$		−	10.7956i		−	0.981414i
$122$		0			0
$123$	−5.22978	−	5.22978i	−0.471553	−	0.471553i
$124$		0			0
$125$	−1.06704	+	11.1293i	−0.0954385	+	0.995435i
$126$		0			0
$127$	9.87429			0.876202			0.438101	−	0.898926i	$-0.355651\pi$
$127$	9.87429			0.876202			0.438101	+	0.898926i	$0.355651\pi$
$128$		0			0
$129$	9.82527			0.865067
$130$		0			0
$131$	8.11330	−	8.11330i	0.708863	−	0.708863i	−0.257433	−	0.966296i	$-0.582877\pi$
$131$	8.11330	−	8.11330i	0.708863	−	0.708863i	0.966296	+	0.257433i	$0.0828768\pi$
$132$		0			0
$133$			4.41236i			0.382601i
$134$		0			0
$135$	−2.23493	−	0.0712321i	−0.192352	−	0.00613068i
$136$		0			0
$137$	−5.15227			−0.440188			−0.220094	−	0.975479i	$-0.570636\pi$
$137$	−5.15227			−0.440188			−0.220094	+	0.975479i	$0.570636\pi$
$138$		0			0
$139$		−	2.85059i		−	0.241784i	−0.992666	−	0.120892i	$-0.961425\pi$
$139$		−	2.85059i		−	0.241784i	0.992666	−	0.120892i	$-0.0385754\pi$
$140$		0			0
$141$	5.91081			0.497780
$142$		0			0
$143$	−0.810981			−0.0678176
$144$		0			0
$145$	12.0411	+	0.113715i	0.999955	+	0.00944352i
$146$		0			0
$147$	−5.72141			−0.471894
$148$		0			0
$149$	−9.66746			−0.791989			−0.395995	−	0.918253i	$-0.629600\pi$
$149$	−9.66746			−0.791989			−0.395995	+	0.918253i	$0.629600\pi$
$150$		0			0
$151$		−	1.40564i		−	0.114390i	−0.998363	−	0.0571948i	$-0.981784\pi$
$151$		−	1.40564i		−	0.114390i	0.998363	−	0.0571948i	$-0.0182156\pi$
$152$		0			0
$153$	3.94993			0.319333
$154$		0			0
$155$	−7.95790	+	7.46630i	−0.639194	+	0.599707i
$156$		0			0
$157$		−	23.2145i		−	1.85272i	−0.376640	−	0.926360i	$-0.622921\pi$
$157$		−	23.2145i		−	1.85272i	0.376640	−	0.926360i	$-0.377079\pi$
$158$		0			0
$159$	3.04710	−	3.04710i	0.241651	−	0.241651i
$160$		0			0
$161$	−0.432786			−0.0341083
$162$		0			0
$163$	21.7935			1.70700			0.853500	−	0.521093i	$-0.174475\pi$
$163$	21.7935			1.70700			0.853500	+	0.521093i	$0.174475\pi$
$164$		0			0
$165$	−0.691780	−	0.737329i	−0.0538550	−	0.0574010i
$166$		0			0
$167$	−9.52550	−	9.52550i	−0.737106	−	0.737106i	0.234911	−	0.972017i	$-0.424520\pi$
$167$	−9.52550	−	9.52550i	−0.737106	−	0.737106i	−0.972017	+	0.234911i	$0.924520\pi$
$168$		0			0
$169$			9.78301i			0.752539i
$170$		0			0
$171$	−2.75925	+	2.75925i	−0.211005	+	0.211005i
$172$		0			0
$173$	−5.60109	+	5.60109i	−0.425843	+	0.425843i	−0.887210	−	0.461366i	$-0.847359\pi$
$173$	−5.60109	+	5.60109i	−0.425843	+	0.425843i	0.461366	+	0.887210i	$0.347359\pi$
$174$		0			0
$175$	4.24426	−	3.73510i	0.320836	−	0.282347i
$176$		0			0
$177$	3.40967			0.256286
$178$		0			0
$179$	−12.3759			−0.925018			−0.462509	−	0.886615i	$-0.653051\pi$
$179$	−12.3759			−0.925018			−0.462509	+	0.886615i	$0.653051\pi$
$180$		0			0
$181$	10.9683			0.815265			0.407632	−	0.913146i	$-0.366355\pi$
$181$	10.9683			0.815265			0.407632	+	0.913146i	$0.366355\pi$
$182$		0			0
$183$	8.02776	−	8.02776i	0.593429	−	0.593429i
$184$		0			0
$185$	−21.0564	−	0.671111i	−1.54809	−	0.0493411i
$186$		0			0
$187$	1.26287	+	1.26287i	0.0923506	+	0.0923506i
$188$		0			0
$189$	0.799559	+	0.799559i	0.0581593	+	0.0581593i
$190$		0			0
$191$	12.7044	+	12.7044i	0.919255	+	0.919255i	0.996975	−	0.0777199i	$-0.0247640\pi$
$191$	12.7044	+	12.7044i	0.919255	+	0.919255i	−0.0777199	+	0.996975i	$0.524764\pi$
$192$		0			0
$193$		−	12.2342i		−	0.880634i	−0.897842	−	0.440317i	$-0.854866\pi$
$193$		−	12.2342i		−	0.880634i	0.897842	−	0.440317i	$-0.145134\pi$
$194$		0			0
$195$	2.92483	−	2.74415i	0.209451	−	0.196512i
$196$		0			0
$197$	13.2932	−	13.2932i	0.947103	−	0.947103i	−0.0515662	−	0.998670i	$-0.516421\pi$
$197$	13.2932	−	13.2932i	0.947103	−	0.947103i	0.998670	+	0.0515662i	$0.0164213\pi$
$198$		0			0
$199$			21.4311i			1.51921i	0.650384	+	0.759605i	$0.274608\pi$
$199$			21.4311i			1.51921i	−0.650384	+	0.759605i	$0.725392\pi$
$200$		0			0
$201$	2.10897	−	2.10897i	0.148755	−	0.148755i
$202$		0			0
$203$	−4.40119	−	4.20816i	−0.308903	−	0.295355i
$204$		0			0
$205$	11.3157	+	12.0607i	0.790321	+	0.842358i
$206$		0			0
$207$	−0.270640	−	0.270640i	−0.0188108	−	0.0188108i
$208$		0			0
$209$	−1.76438			−0.122045
$210$		0			0
$211$	−3.60647	+	3.60647i	−0.248280	+	0.248280i	−0.820264	−	0.571985i	$-0.806174\pi$
$211$	−3.60647	+	3.60647i	−0.248280	+	0.248280i	0.571985	+	0.820264i	$0.306174\pi$
$212$		0			0
$213$	4.89291			0.335256
$214$		0			0
$215$	−21.9588	−	0.699875i	−1.49758	−	0.0477310i
$216$		0			0
$217$	5.51808			0.374592
$218$		0			0
$219$			1.74581i			0.117971i
$220$		0			0
$221$	−5.00956	+	5.00956i	−0.336979	+	0.336979i
$222$		0			0
$223$	−2.56999	−	2.56999i	−0.172099	−	0.172099i	0.615802	−	0.787901i	$-0.288832\pi$
$223$	−2.56999	−	2.56999i	−0.172099	−	0.172099i	−0.787901	+	0.615802i	$0.788832\pi$
$224$		0			0
$225$	4.98985	+	0.318398i	0.332657	+	0.0212265i
$226$		0			0
$227$	8.34642	−	8.34642i	0.553972	−	0.553972i	−0.373613	−	0.927585i	$-0.621881\pi$
$227$	8.34642	−	8.34642i	0.553972	−	0.553972i	0.927585	+	0.373613i	$0.121881\pi$
$228$		0			0
$229$	19.8418	+	19.8418i	1.31118	+	1.31118i	0.920544	+	0.390639i	$0.127746\pi$
$229$	19.8418	+	19.8418i	1.31118	+	1.31118i	0.390639	+	0.920544i	$0.372254\pi$
$230$		0			0
$231$			0.511271i			0.0336391i
$232$		0			0
$233$	−11.9222	−	11.9222i	−0.781048	−	0.781048i	0.198960	−	0.980008i	$-0.436244\pi$
$233$	−11.9222	−	11.9222i	−0.781048	−	0.781048i	−0.980008	+	0.198960i	$0.936244\pi$
$234$		0			0
$235$	−13.2103	−	0.421039i	−0.861742	−	0.0274656i
$236$		0			0
$237$	2.41919	+	2.41919i	0.157143	+	0.157143i
$238$		0			0
$239$		−	21.6273i		−	1.39895i	−0.714656	−	0.699476i	$-0.753417\pi$
$239$		−	21.6273i		−	1.39895i	0.714656	−	0.699476i	$-0.246583\pi$
$240$		0			0
$241$		−	3.86423i		−	0.248917i	−0.992225	−	0.124459i	$-0.960281\pi$
$241$		−	3.86423i		−	0.248917i	0.992225	−	0.124459i	$-0.0397194\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	12.7870	+	0.407548i	0.816930	+	0.0260373i
$246$		0			0
$247$		−	6.99892i		−	0.445331i
$248$		0			0
$249$	1.43981	−	1.43981i	0.0912443	−	0.0912443i
$250$		0			0
$251$	8.33678	+	8.33678i	0.526213	+	0.526213i	0.919441	−	0.393228i	$-0.128642\pi$
$251$	8.33678	+	8.33678i	0.526213	+	0.526213i	−0.393228	+	0.919441i	$0.628642\pi$
$252$		0			0
$253$		−	0.173059i		−	0.0108801i
$254$		0			0
$255$	−8.82784	−	0.281362i	−0.552820	−	0.0176196i
$256$		0			0
$257$	−10.2879	+	10.2879i	−0.641743	+	0.641743i	−0.950984	−	0.309241i	$-0.899925\pi$
$257$	−10.2879	+	10.2879i	−0.641743	+	0.641743i	0.309241	+	0.950984i	$0.399925\pi$
$258$		0			0
$259$	7.53302	+	7.53302i	0.468079	+	0.468079i
$260$		0			0
$261$	−0.120713	−	5.38381i	−0.00747193	−	0.333250i
$262$		0			0
$263$			19.5161i			1.20341i	0.798717	+	0.601707i	$0.205513\pi$
$263$			19.5161i			1.20341i	−0.798717	+	0.601707i	$0.794487\pi$
$264$		0			0
$265$	−7.02711	+	6.59301i	−0.431672	+	0.405005i
$266$		0			0
$267$	−6.19743	−	6.19743i	−0.379276	−	0.379276i
$268$		0			0
$269$	17.7621	+	17.7621i	1.08297	+	1.08297i	0.996231	+	0.0867438i	$0.0276461\pi$
$269$	17.7621	+	17.7621i	1.08297	+	1.08297i	0.0867438	+	0.996231i	$0.472354\pi$
$270$		0			0
$271$	−2.04007	+	2.04007i	−0.123926	+	0.123926i	−0.766350	−	0.642424i	$-0.777929\pi$
$271$	−2.04007	+	2.04007i	−0.123926	+	0.123926i	0.642424	+	0.766350i	$0.277929\pi$
$272$		0			0
$273$	−2.02810			−0.122746
$274$		0			0
$275$	1.49356	+	1.69716i	0.0900651	+	0.102342i
$276$		0			0
$277$	−5.33891	+	5.33891i	−0.320784	+	0.320784i	−0.849068	−	0.528284i	$-0.822836\pi$
$277$	−5.33891	+	5.33891i	−0.320784	+	0.320784i	0.528284	+	0.849068i	$0.322836\pi$
$278$		0			0
$279$	3.45071	+	3.45071i	0.206588	+	0.206588i
$280$		0			0
$281$	−7.25552			−0.432828			−0.216414	−	0.976302i	$-0.569436\pi$
$281$	−7.25552			−0.432828			−0.216414	+	0.976302i	$0.569436\pi$
$282$		0			0
$283$	−18.8306	+	18.8306i	−1.11936	+	1.11936i	−0.127528	+	0.991835i	$0.540704\pi$
$283$	−18.8306	+	18.8306i	−1.11936	+	1.11936i	−0.991835	+	0.127528i	$0.959296\pi$
$284$		0			0
$285$	6.36329	−	5.97019i	0.376929	−	0.353644i
$286$		0			0
$287$		−	8.36303i		−	0.493654i
$288$		0			0
$289$	−1.39803			−0.0822372
$290$		0			0
$291$	−3.50657			−0.205559
$292$		0			0
$293$			18.3897i			1.07434i	0.843475	+	0.537169i	$0.180506\pi$
$293$			18.3897i			1.07434i	−0.843475	+	0.537169i	$0.819494\pi$
$294$		0			0
$295$	−7.62038	−	0.242878i	−0.443675	−	0.0141409i
$296$		0			0
$297$	−0.319721	+	0.319721i	−0.0185521	+	0.0185521i
$298$		0			0
$299$	0.686487			0.0397006
$300$		0			0
$301$	7.85588	+	7.85588i	0.452806	+	0.452806i
$302$		0			0
$303$	−0.515252	+	0.515252i	−0.0296005	+	0.0296005i
$304$		0			0
$305$	−18.5133	+	17.3697i	−1.06007	+	0.994584i
$306$		0			0
$307$	4.10807			0.234460			0.117230	−	0.993105i	$-0.462599\pi$
$307$	4.10807			0.234460			0.117230	+	0.993105i	$0.462599\pi$
$308$		0			0
$309$	4.50575	−	4.50575i	0.256323	−	0.256323i
$310$		0			0
$311$	13.8583	+	13.8583i	0.785830	+	0.785830i	0.980808	−	0.194977i	$-0.0624633\pi$
$311$	13.8583	+	13.8583i	0.785830	+	0.785830i	−0.194977	+	0.980808i	$0.562463\pi$
$312$		0			0
$313$	−5.08029	−	5.08029i	−0.287155	−	0.287155i	0.548799	−	0.835954i	$-0.315085\pi$
$313$	−5.08029	−	5.08029i	−0.287155	−	0.287155i	−0.835954	+	0.548799i	$0.815085\pi$
$314$		0			0
$315$	−1.73001	−	1.84391i	−0.0974748	−	0.103893i
$316$		0			0
$317$			24.1177i			1.35459i	0.735713	+	0.677293i	$0.236847\pi$
$317$			24.1177i			1.35459i	−0.735713	+	0.677293i	$0.763153\pi$
$318$		0			0
$319$	1.68272	−	1.75991i	0.0942143	−	0.0985360i
$320$		0			0
$321$	−2.33805	−	2.33805i	−0.130497	−	0.130497i
$322$		0			0
$323$	−10.8989	+	10.8989i	−0.606428	+	0.606428i
$324$		0			0
$325$	−6.73227	+	5.92464i	−0.373439	+	0.328640i
$326$		0			0
$327$			1.65077i			0.0912875i
$328$		0			0
$329$	4.72604	+	4.72604i	0.260555	+	0.260555i
$330$		0			0
$331$	6.36032	−	6.36032i	0.349595	−	0.349595i	−0.510364	−	0.859959i	$-0.670489\pi$
$331$	6.36032	−	6.36032i	0.349595	−	0.349595i	0.859959	+	0.510364i	$0.170489\pi$
$332$		0			0
$333$			9.42147i			0.516294i
$334$		0			0
$335$	−4.86364	+	4.56319i	−0.265729	+	0.249314i
$336$		0			0
$337$			5.20906i			0.283755i	0.989884	+	0.141878i	$0.0453140\pi$
$337$			5.20906i			0.283755i	−0.989884	+	0.141878i	$0.954686\pi$
$338$		0			0
$339$		−	0.735489i		−	0.0399463i
$340$		0			0
$341$			2.20652i			0.119490i
$342$		0			0
$343$	−10.1715	−	10.1715i	−0.549210	−	0.549210i
$344$		0			0
$345$	0.585585	+	0.624141i	0.0315268	+	0.0336026i
$346$		0			0
$347$	−20.9481	−	20.9481i	−1.12455	−	1.12455i	−0.991048	−	0.133507i	$-0.957376\pi$
$347$	−20.9481	−	20.9481i	−1.12455	−	1.12455i	−0.133507	−	0.991048i	$-0.542624\pi$
$348$		0			0
$349$			34.4900i			1.84621i	0.384554	+	0.923103i	$0.374355\pi$
$349$			34.4900i			1.84621i	−0.384554	+	0.923103i	$0.625645\pi$
$350$		0			0
$351$	−1.26826	−	1.26826i	−0.0676950	−	0.0676950i
$352$		0			0
$353$	−8.64312	+	8.64312i	−0.460027	+	0.460027i	−0.898664	−	0.438637i	$-0.855461\pi$
$353$	−8.64312	+	8.64312i	−0.460027	+	0.460027i	0.438637	+	0.898664i	$0.355461\pi$
$354$		0			0
$355$	−10.9353	−	0.348532i	−0.580386	−	0.0184981i
$356$		0			0
$357$	3.15820	+	3.15820i	0.167150	+	0.167150i
$358$		0			0
$359$	0.355513	−	0.355513i	0.0187633	−	0.0187633i	−0.697663	−	0.716426i	$-0.745777\pi$
$359$	0.355513	−	0.355513i	0.0187633	−	0.0187633i	0.716426	+	0.697663i	$0.245777\pi$
$360$		0			0
$361$			3.77308i			0.198583i
$362$		0			0
$363$	10.7956			0.566620
$364$		0			0
$365$	0.124358	−	3.90176i	0.00650917	−	0.204228i
$366$		0			0
$367$	15.6397			0.816387			0.408194	−	0.912895i	$-0.366159\pi$
$367$	15.6397			0.816387			0.408194	+	0.912895i	$0.366159\pi$
$368$		0			0
$369$	5.22978	−	5.22978i	0.272251	−	0.272251i
$370$		0			0
$371$	4.87267			0.252976
$372$		0			0
$373$	2.88049	+	2.88049i	0.149146	+	0.149146i	0.777737	−	0.628590i	$-0.216368\pi$
$373$	2.88049	+	2.88049i	0.149146	+	0.149146i	−0.628590	+	0.777737i	$0.716368\pi$
$374$		0			0
$375$	−11.1293	−	1.06704i	−0.574715	−	0.0551015i
$376$		0			0
$377$	6.98119	+	6.67500i	0.359550	+	0.343780i
$378$		0			0
$379$	−4.09126	+	4.09126i	−0.210154	+	0.210154i	−0.804333	−	0.594179i	$-0.797477\pi$
$379$	−4.09126	+	4.09126i	−0.210154	+	0.210154i	0.594179	+	0.804333i	$0.297477\pi$
$380$		0			0
$381$			9.87429i			0.505875i
$382$		0			0
$383$	−7.10435	+	7.10435i	−0.363015	+	0.363015i	−0.864922	−	0.501907i	$-0.832632\pi$
$383$	−7.10435	+	7.10435i	−0.363015	+	0.363015i	0.501907	+	0.864922i	$0.332632\pi$
$384$		0			0
$385$	0.0364189	−	1.14266i	0.00185608	−	0.0582351i
$386$		0			0
$387$			9.82527i			0.499447i
$388$		0			0
$389$	−9.43244	−	9.43244i	−0.478244	−	0.478244i	0.426326	−	0.904570i	$-0.359808\pi$
$389$	−9.43244	−	9.43244i	−0.478244	−	0.478244i	−0.904570	+	0.426326i	$0.859808\pi$
$390$		0			0
$391$	−1.06901	−	1.06901i	−0.0540622	−	0.0540622i
$392$		0			0
$393$	8.11330	+	8.11330i	0.409262	+	0.409262i
$394$		0			0
$395$	−5.23440	−	5.57905i	−0.263371	−	0.280713i
$396$		0			0
$397$	24.3576	−	24.3576i	1.22247	−	1.22247i	0.255723	−	0.966750i	$-0.417686\pi$
$397$	24.3576	−	24.3576i	1.22247	−	1.22247i	0.966750	−	0.255723i	$-0.0823136\pi$
$398$		0			0
$399$	−4.41236			−0.220895
$400$		0			0
$401$	18.5161			0.924648			0.462324	−	0.886711i	$-0.347016\pi$
$401$	18.5161			0.924648			0.462324	+	0.886711i	$0.347016\pi$
$402$		0			0
$403$	−8.75282			−0.436009
$404$		0			0
$405$	0.0712321	−	2.23493i	0.00353955	−	0.111055i
$406$		0			0
$407$	−3.01224	+	3.01224i	−0.149311	+	0.149311i
$408$		0			0
$409$	10.7794	−	10.7794i	0.533005	−	0.533005i	−0.388460	−	0.921465i	$-0.626993\pi$
$409$	10.7794	−	10.7794i	0.533005	−	0.533005i	0.921465	+	0.388460i	$0.126993\pi$
$410$		0			0
$411$		−	5.15227i		−	0.254143i
$412$		0			0
$413$	2.72623	+	2.72623i	0.134149	+	0.134149i
$414$		0			0
$415$	−3.32044	+	3.11532i	−0.162994	+	0.152925i
$416$		0			0
$417$	2.85059			0.139594
$418$		0			0
$419$	−21.3335			−1.04221			−0.521104	−	0.853493i	$-0.674480\pi$
$419$	−21.3335			−1.04221			−0.521104	+	0.853493i	$0.674480\pi$
$420$		0			0
$421$	−0.402781	+	0.402781i	−0.0196304	+	0.0196304i	−0.716854	−	0.697223i	$-0.754419\pi$
$421$	−0.402781	+	0.402781i	−0.0196304	+	0.0196304i	0.697223	+	0.716854i	$0.254419\pi$
$422$		0			0
$423$			5.91081i			0.287393i
$424$		0			0
$425$	19.7096	+	1.25765i	0.956055	+	0.0610050i
$426$		0			0
$427$	12.8373			0.621242
$428$		0			0
$429$		−	0.810981i		−	0.0391545i
$430$		0			0
$431$	15.2992			0.736937			0.368469	−	0.929640i	$-0.379882\pi$
$431$	15.2992			0.736937			0.368469	+	0.929640i	$0.379882\pi$
$432$		0			0
$433$	9.89453			0.475501			0.237750	−	0.971326i	$-0.423590\pi$
$433$	9.89453			0.475501			0.237750	+	0.971326i	$0.423590\pi$
$434$		0			0
$435$	−0.113715	+	12.0411i	−0.00545222	+	0.577325i
$436$		0			0
$437$	1.49353			0.0714452
$438$		0			0
$439$	−13.6250			−0.650286			−0.325143	−	0.945665i	$-0.605412\pi$
$439$	−13.6250			−0.650286			−0.325143	+	0.945665i	$0.605412\pi$
$440$		0			0
$441$		−	5.72141i		−	0.272448i
$442$		0			0
$443$	−39.8001			−1.89096			−0.945481	−	0.325677i	$-0.894408\pi$
$443$	−39.8001			−1.89096			−0.945481	+	0.325677i	$0.894408\pi$
$444$		0			0
$445$	13.4094	+	14.2923i	0.635665	+	0.677519i
$446$		0			0
$447$		−	9.66746i		−	0.457255i
$448$		0			0
$449$	−11.0115	+	11.0115i	−0.519666	+	0.519666i	−0.917470	−	0.397804i	$-0.869772\pi$
$449$	−11.0115	+	11.0115i	−0.519666	+	0.519666i	0.397804	+	0.917470i	$0.369772\pi$
$450$		0			0
$451$	3.34414			0.157469
$452$		0			0
$453$	1.40564			0.0660429
$454$		0			0
$455$	4.53268	+	0.144466i	0.212495	+	0.00677267i
$456$		0			0
$457$	11.4146	+	11.4146i	0.533952	+	0.533952i	0.921746	−	0.387794i	$-0.126763\pi$
$457$	11.4146	+	11.4146i	0.533952	+	0.533952i	−0.387794	+	0.921746i	$0.626763\pi$
$458$		0			0
$459$			3.94993i			0.184367i
$460$		0			0
$461$	3.25059	−	3.25059i	0.151395	−	0.151395i	−0.627346	−	0.778741i	$-0.715859\pi$
$461$	3.25059	−	3.25059i	0.151395	−	0.151395i	0.778741	+	0.627346i	$0.215859\pi$
$462$		0			0
$463$	−5.96400	+	5.96400i	−0.277171	+	0.277171i	−0.831978	−	0.554808i	$-0.812792\pi$
$463$	−5.96400	+	5.96400i	−0.277171	+	0.277171i	0.554808	+	0.831978i	$0.312792\pi$
$464$		0			0
$465$	−7.46630	−	7.95790i	−0.346241	−	0.369039i
$466$		0			0
$467$	20.5942			0.952987			0.476494	−	0.879178i	$-0.341908\pi$
$467$	20.5942			0.952987			0.476494	+	0.879178i	$0.341908\pi$
$468$		0			0
$469$	3.37250			0.155727
$470$		0			0
$471$	23.2145			1.06967
$472$		0			0
$473$	−3.14134	+	3.14134i	−0.144439	+	0.144439i
$474$		0			0
$475$	−14.6468	+	12.8897i	−0.672041	+	0.591421i
$476$		0			0
$477$	3.04710	+	3.04710i	0.139517	+	0.139517i
$478$		0			0
$479$	17.8014	+	17.8014i	0.813367	+	0.813367i	0.985137	−	0.171770i	$-0.0549485\pi$
$479$	17.8014	+	17.8014i	0.813367	+	0.813367i	−0.171770	+	0.985137i	$0.554949\pi$
$480$		0			0
$481$	−11.9489	−	11.9489i	−0.544824	−	0.544824i
$482$		0			0
$483$		−	0.432786i		−	0.0196924i
$484$		0			0
$485$	7.83695	+	0.249780i	0.355858	+	0.0113419i
$486$		0			0
$487$	27.9540	−	27.9540i	1.26672	−	1.26672i	0.318942	−	0.947774i	$-0.396672\pi$
$487$	27.9540	−	27.9540i	1.26672	−	1.26672i	0.947774	−	0.318942i	$-0.103328\pi$
$488$		0			0
$489$			21.7935i			0.985537i
$490$		0			0
$491$	13.7674	−	13.7674i	0.621316	−	0.621316i	−0.324552	−	0.945868i	$-0.605213\pi$
$491$	13.7674	−	13.7674i	0.621316	−	0.621316i	0.945868	+	0.324552i	$0.105213\pi$
$492$		0			0
$493$	−0.476807	−	21.2657i	−0.0214743	−	0.957759i
$494$		0			0
$495$	0.737329	−	0.691780i	0.0331405	−	0.0310932i
$496$		0			0
$497$	3.91216	+	3.91216i	0.175485	+	0.175485i
$498$		0			0
$499$	23.1909			1.03817			0.519083	−	0.854724i	$-0.326274\pi$
$499$	23.1909			1.03817			0.519083	+	0.854724i	$0.326274\pi$
$500$		0			0
$501$	9.52550	−	9.52550i	0.425568	−	0.425568i
$502$		0			0
$503$	23.4763			1.04676			0.523378	−	0.852101i	$-0.324672\pi$
$503$	23.4763			1.04676			0.523378	+	0.852101i	$0.324672\pi$
$504$		0			0
$505$	1.18826	−	1.11485i	0.0528767	−	0.0496102i
$506$		0			0
$507$	−9.78301			−0.434479
$508$		0			0
$509$			34.0902i			1.51102i	0.655137	+	0.755510i	$0.272611\pi$
$509$			34.0902i			1.51102i	−0.655137	+	0.755510i	$0.727389\pi$
$510$		0			0
$511$	−1.39588	+	1.39588i	−0.0617499	+	0.0617499i
$512$		0			0
$513$	−2.75925	−	2.75925i	−0.121824	−	0.121824i
$514$		0			0
$515$	−10.3910	+	9.74909i	−0.457882	+	0.429596i
$516$		0			0
$517$	−1.88981	+	1.88981i	−0.0831136	+	0.0831136i
$518$		0			0
$519$	−5.60109	−	5.60109i	−0.245861	−	0.245861i
$520$		0			0
$521$		−	28.1656i		−	1.23396i	−0.786979	−	0.616979i	$-0.788356\pi$
$521$		−	28.1656i		−	1.23396i	0.786979	−	0.616979i	$-0.211644\pi$
$522$		0			0
$523$	−8.34491	−	8.34491i	−0.364897	−	0.364897i	0.500715	−	0.865612i	$-0.333070\pi$
$523$	−8.34491	−	8.34491i	−0.364897	−	0.364897i	−0.865612	+	0.500715i	$0.833070\pi$
$524$		0			0
$525$	3.73510	+	4.24426i	0.163013	+	0.185235i
$526$		0			0
$527$	13.6301	+	13.6301i	0.593735	+	0.593735i
$528$		0			0
$529$		−	22.8535i		−	0.993631i
$530$		0			0
$531$			3.40967i			0.147967i
$532$		0			0
$533$			13.2655i			0.574592i
$534$		0			0
$535$	5.05885	+	5.39194i	0.218713	+	0.233114i
$536$		0			0
$537$		−	12.3759i		−	0.534060i
$538$		0			0
$539$	1.82925	−	1.82925i	0.0787915	−	0.0787915i
$540$		0			0
$541$	15.0381	+	15.0381i	0.646539	+	0.646539i	0.952155	−	0.305616i	$-0.0988622\pi$
$541$	15.0381	+	15.0381i	0.646539	+	0.646539i	−0.305616	+	0.952155i	$0.598862\pi$
$542$		0			0
$543$			10.9683i			0.470693i
$544$		0			0
$545$	0.117587	−	3.68935i	0.00503689	−	0.158034i
$546$		0			0
$547$	−3.03930	+	3.03930i	−0.129951	+	0.129951i	−0.769091	−	0.639140i	$-0.779291\pi$
$547$	−3.03930	+	3.03930i	−0.129951	+	0.129951i	0.639140	+	0.769091i	$0.279291\pi$
$548$		0			0
$549$	8.02776	+	8.02776i	0.342616	+	0.342616i
$550$		0			0
$551$	15.1884	+	14.5222i	0.647046	+	0.618667i
$552$		0			0
$553$			3.86857i			0.164508i
$554$		0			0
$555$	0.671111	−	21.0564i	0.0284871	−	0.893793i
$556$		0			0
$557$	−10.2427	−	10.2427i	−0.433998	−	0.433998i	0.455988	−	0.889986i	$-0.349286\pi$
$557$	−10.2427	−	10.2427i	−0.433998	−	0.433998i	−0.889986	+	0.455988i	$0.849286\pi$
$558$		0			0
$559$	−12.4610	−	12.4610i	−0.527046	−	0.527046i
$560$		0			0
$561$	−1.26287	+	1.26287i	−0.0533186	+	0.0533186i
$562$		0			0
$563$	−9.62449			−0.405624			−0.202812	−	0.979218i	$-0.565008\pi$
$563$	−9.62449			−0.405624			−0.202812	+	0.979218i	$0.565008\pi$
$564$		0			0
$565$	−0.0523904	+	1.64377i	−0.00220408	+	0.0691538i
$566$		0			0
$567$	−0.799559	+	0.799559i	−0.0335783	+	0.0335783i
$568$		0			0
$569$	17.2953	+	17.2953i	0.725056	+	0.725056i	0.969631	−	0.244574i	$-0.0786482\pi$
$569$	17.2953	+	17.2953i	0.725056	+	0.725056i	−0.244574	+	0.969631i	$0.578648\pi$
$570$		0			0
$571$	13.6134			0.569704			0.284852	−	0.958571i	$-0.408055\pi$
$571$	13.6134			0.569704			0.284852	+	0.958571i	$0.408055\pi$
$572$		0			0
$573$	−12.7044	+	12.7044i	−0.530732	+	0.530732i
$574$		0			0
$575$	−1.26428	−	1.43663i	−0.0527243	−	0.0599115i
$576$		0			0
$577$			2.34439i			0.0975983i	0.998809	+	0.0487992i	$0.0155394\pi$
$577$			2.34439i			0.0975983i	−0.998809	+	0.0487992i	$0.984461\pi$
$578$		0			0
$579$	12.2342			0.508434
$580$		0			0
$581$	2.30243			0.0955208
$582$		0			0
$583$			1.94844i			0.0806962i
$584$		0			0
$585$	2.74415	+	2.92483i	0.113456	+	0.120927i
$586$		0			0
$587$	5.57123	−	5.57123i	0.229949	−	0.229949i	−0.582722	−	0.812671i	$-0.698012\pi$
$587$	5.57123	−	5.57123i	0.229949	−	0.229949i	0.812671	+	0.582722i	$0.198012\pi$
$588$		0			0
$589$	−19.0427			−0.784642
$590$		0			0
$591$	13.2932	+	13.2932i	0.546810	+	0.546810i
$592$		0			0
$593$	12.1678	−	12.1678i	0.499671	−	0.499671i	−0.411665	−	0.911335i	$-0.635053\pi$
$593$	12.1678	−	12.1678i	0.499671	−	0.499671i	0.911335	+	0.411665i	$0.135053\pi$
$594$		0			0
$595$	−6.83341	−	7.28334i	−0.280142	−	0.298588i
$596$		0			0
$597$	−21.4311			−0.877117
$598$		0			0
$599$	31.6977	−	31.6977i	1.29513	−	1.29513i	0.363563	−	0.931570i	$-0.381560\pi$
$599$	31.6977	−	31.6977i	1.29513	−	1.29513i	0.931570	−	0.363563i	$-0.118440\pi$
$600$		0			0
$601$	−32.4464	−	32.4464i	−1.32351	−	1.32351i	−0.910910	−	0.412605i	$-0.864619\pi$
$601$	−32.4464	−	32.4464i	−1.32351	−	1.32351i	−0.412605	−	0.910910i	$-0.635381\pi$
$602$		0			0
$603$	2.10897	+	2.10897i	0.0858840	+	0.0858840i
$604$		0			0
$605$	−24.1273	−	0.768990i	−0.980916	−	0.0312639i
$606$		0			0
$607$		−	17.9409i		−	0.728199i	−0.931360	−	0.364100i	$-0.881377\pi$
$607$		−	17.9409i		−	0.728199i	0.931360	−	0.364100i	$-0.118623\pi$
$608$		0			0
$609$	4.20816	−	4.40119i	0.170523	−	0.178345i
$610$		0			0
$611$	−7.49647	−	7.49647i	−0.303275	−	0.303275i
$612$		0			0
$613$	−13.6298	+	13.6298i	−0.550503	+	0.550503i	−0.926586	−	0.376083i	$-0.877271\pi$
$613$	−13.6298	+	13.6298i	−0.550503	+	0.550503i	0.376083	+	0.926586i	$0.377271\pi$
$614$		0			0
$615$	−12.0607	+	11.3157i	−0.486336	+	0.456292i
$616$		0			0
$617$		−	21.0513i		−	0.847493i	−0.905781	−	0.423747i	$-0.860715\pi$
$617$		−	21.0513i		−	0.847493i	0.905781	−	0.423747i	$-0.139285\pi$
$618$		0			0
$619$	27.5175	+	27.5175i	1.10602	+	1.10602i	0.993668	+	0.112355i	$0.0358393\pi$
$619$	27.5175	+	27.5175i	1.10602	+	1.10602i	0.112355	+	0.993668i	$0.464161\pi$
$620$		0			0
$621$	0.270640	−	0.270640i	0.0108604	−	0.0108604i
$622$		0			0
$623$		−	9.91041i		−	0.397052i
$624$		0			0
$625$	24.7972	+	3.17752i	0.991890	+	0.127101i
$626$		0			0
$627$		−	1.76438i		−	0.0704625i
$628$		0			0
$629$			37.2142i			1.48383i
$630$		0			0
$631$		−	0.557679i		−	0.0222008i	−0.999938	−	0.0111004i	$-0.996467\pi$
$631$		−	0.557679i		−	0.0222008i	0.999938	−	0.0111004i	$-0.00353345\pi$
$632$		0			0
$633$	−3.60647	−	3.60647i	−0.143344	−	0.143344i
$634$		0			0
$635$	0.703366	−	22.0684i	0.0279122	−	0.875757i
$636$		0			0
$637$	7.25626	+	7.25626i	0.287504	+	0.287504i
$638$		0			0
$639$			4.89291i			0.193560i
$640$		0			0
$641$	−22.2190	−	22.2190i	−0.877598	−	0.877598i	0.115687	−	0.993286i	$-0.463093\pi$
$641$	−22.2190	−	22.2190i	−0.877598	−	0.877598i	−0.993286	+	0.115687i	$0.963093\pi$
$642$		0			0
$643$	−2.34708	+	2.34708i	−0.0925597	+	0.0925597i	−0.751871	−	0.659311i	$-0.770848\pi$
$643$	−2.34708	+	2.34708i	−0.0925597	+	0.0925597i	0.659311	+	0.751871i	$0.270848\pi$
$644$		0			0
$645$	0.699875	−	21.9588i	0.0275575	−	0.864628i
$646$		0			0
$647$	−19.1106	−	19.1106i	−0.751315	−	0.751315i	0.223410	−	0.974725i	$-0.428281\pi$
$647$	−19.1106	−	19.1106i	−0.751315	−	0.751315i	−0.974725	+	0.223410i	$0.928281\pi$
$648$		0			0
$649$	−1.09014	+	1.09014i	−0.0427918	+	0.0427918i
$650$		0			0
$651$			5.51808i			0.216271i
$652$		0			0
$653$	6.37219			0.249363			0.124682	−	0.992197i	$-0.460209\pi$
$653$	6.37219			0.249363			0.124682	+	0.992197i	$0.460209\pi$
$654$		0			0
$655$	−17.5548	−	18.7106i	−0.685921	−	0.731084i
$656$		0			0
$657$	−1.74581			−0.0681105
$658$		0			0
$659$	24.5536	−	24.5536i	0.956473	−	0.956473i	−0.0426185	−	0.999091i	$-0.513570\pi$
$659$	24.5536	−	24.5536i	0.956473	−	0.956473i	0.999091	+	0.0426185i	$0.0135700\pi$
$660$		0			0
$661$	−13.1422			−0.511173			−0.255587	−	0.966786i	$-0.582269\pi$
$661$	−13.1422			−0.511173			−0.255587	+	0.966786i	$0.582269\pi$
$662$		0			0
$663$	−5.00956	−	5.00956i	−0.194555	−	0.194555i
$664$		0			0
$665$	9.86134	+	0.314302i	0.382406	+	0.0121881i
$666$		0			0
$667$	−1.42441	+	1.48975i	−0.0551533	+	0.0576832i
$668$		0			0
$669$	2.56999	−	2.56999i	0.0993615	−	0.0993615i
$670$		0			0
$671$			5.13328i			0.198168i
$672$		0			0
$673$	12.2134	−	12.2134i	0.470793	−	0.470793i	−0.431378	−	0.902171i	$-0.641973\pi$
$673$	12.2134	−	12.2134i	0.470793	−	0.470793i	0.902171	+	0.431378i	$0.141973\pi$
$674$		0			0
$675$	−0.318398	+	4.98985i	−0.0122551	+	0.192059i
$676$		0			0
$677$			9.75729i			0.375003i	0.982264	+	0.187502i	$0.0600390\pi$
$677$			9.75729i			0.375003i	−0.982264	+	0.187502i	$0.939961\pi$
$678$		0			0
$679$	−2.80371	−	2.80371i	−0.107596	−	0.107596i
$680$		0			0
$681$	8.34642	+	8.34642i	0.319836	+	0.319836i
$682$		0			0
$683$	−4.92297	−	4.92297i	−0.188372	−	0.188372i	0.606620	−	0.794992i	$-0.292525\pi$
$683$	−4.92297	−	4.92297i	−0.188372	−	0.188372i	−0.794992	+	0.606620i	$0.792525\pi$
$684$		0			0
$685$	−0.367007	+	11.5150i	−0.0140226	+	0.439965i
$686$		0			0
$687$	−19.8418	+	19.8418i	−0.757012	+	0.757012i
$688$		0			0
$689$	−7.72906			−0.294454
$690$		0			0
$691$	−27.5673			−1.04871			−0.524355	−	0.851500i	$-0.675693\pi$
$691$	−27.5673			−1.04871			−0.524355	+	0.851500i	$0.675693\pi$
$692$		0			0
$693$	−0.511271			−0.0194216
$694$		0			0
$695$	−6.37087	−	0.203053i	−0.241661	−	0.00770224i
$696$		0			0
$697$	20.6573	−	20.6573i	0.782450	−	0.782450i
$698$		0			0
$699$	11.9222	−	11.9222i	0.450938	−	0.450938i
$700$		0			0
$701$			24.0535i			0.908490i	0.890877	+	0.454245i	$0.150091\pi$
$701$			24.0535i			0.908490i	−0.890877	+	0.454245i	$0.849909\pi$
$702$		0			0
$703$	−25.9962	−	25.9962i	−0.980465	−	0.980465i
$704$		0			0
$705$	0.421039	−	13.2103i	0.0158572	−	0.497527i
$706$		0			0
$707$	−0.823949			−0.0309878
$708$		0			0
$709$	−10.5712			−0.397010			−0.198505	−	0.980100i	$-0.563609\pi$
$709$	−10.5712			−0.397010			−0.198505	+	0.980100i	$0.563609\pi$
$710$		0			0
$711$	−2.41919	+	2.41919i	−0.0907267	+	0.0907267i
$712$		0			0
$713$		−	1.86780i		−	0.0699497i
$714$		0			0
$715$	−0.0577678	+	1.81249i	−0.00216039	+	0.0677832i
$716$		0			0
$717$	21.6273			0.807685
$718$		0			0
$719$		−	22.5309i		−	0.840260i	−0.907464	−	0.420130i	$-0.861984\pi$
$719$		−	22.5309i		−	0.840260i	0.907464	−	0.420130i	$-0.138016\pi$
$720$		0			0
$721$	7.20522			0.268336
$722$		0			0
$723$	3.86423			0.143712
$724$		0			0
$725$	1.11185	−	26.9029i	0.0412933	−	0.999147i
$726$		0			0
$727$	−46.0258			−1.70700			−0.853502	−	0.521090i	$-0.825525\pi$
$727$	−46.0258			−1.70700			−0.853502	+	0.521090i	$0.825525\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$			38.8092i			1.43541i
$732$		0			0
$733$	−14.4383			−0.533290			−0.266645	−	0.963795i	$-0.585915\pi$
$733$	−14.4383			−0.533290			−0.266645	+	0.963795i	$0.585915\pi$
$734$		0			0
$735$	−0.407548	+	12.7870i	−0.0150326	+	0.471655i
$736$		0			0
$737$			1.34856i			0.0496750i
$738$		0			0
$739$	−18.0856	+	18.0856i	−0.665290	+	0.665290i	−0.956622	−	0.291332i	$-0.905902\pi$
$739$	−18.0856	+	18.0856i	−0.665290	+	0.665290i	0.291332	+	0.956622i	$0.405902\pi$
$740$		0			0
$741$	6.99892			0.257112
$742$		0			0
$743$	27.5892			1.01215			0.506074	−	0.862490i	$-0.331096\pi$
$743$	27.5892			1.01215			0.506074	+	0.862490i	$0.331096\pi$
$744$		0			0
$745$	−0.688633	+	21.6061i	−0.0252296	+	0.791588i
$746$		0			0
$747$	1.43981	+	1.43981i	0.0526799	+	0.0526799i
$748$		0			0
$749$		−	3.73882i		−	0.136614i
$750$		0			0
$751$	−9.86541	+	9.86541i	−0.359994	+	0.359994i	−0.863811	−	0.503817i	$-0.831929\pi$
$751$	−9.86541	+	9.86541i	−0.359994	+	0.359994i	0.503817	+	0.863811i	$0.331929\pi$
$752$		0			0
$753$	−8.33678	+	8.33678i	−0.303809	+	0.303809i
$754$		0			0
$755$	−3.14152	−	0.100127i	−0.114332	−	0.00364399i
$756$		0			0
$757$	41.1678			1.49627			0.748135	−	0.663547i	$-0.230950\pi$
$757$	41.1678			1.49627			0.748135	+	0.663547i	$0.230950\pi$
$758$		0			0
$759$	0.173059			0.00628163
$760$		0			0
$761$	−16.6734			−0.604410			−0.302205	−	0.953243i	$-0.597723\pi$
$761$	−16.6734			−0.604410			−0.302205	+	0.953243i	$0.597723\pi$
$762$		0			0
$763$	−1.31988	+	1.31988i	−0.0477830	+	0.0477830i
$764$		0			0
$765$	0.281362	−	8.82784i	0.0101727	−	0.319171i
$766$		0			0
$767$	−4.32436	−	4.32436i	−0.156144	−	0.156144i
$768$		0			0
$769$	14.6466	+	14.6466i	0.528171	+	0.528171i	0.920027	−	0.391856i	$-0.128167\pi$
$769$	14.6466	+	14.6466i	0.528171	+	0.528171i	−0.391856	+	0.920027i	$0.628167\pi$
$770$		0			0
$771$	−10.2879	−	10.2879i	−0.370510	−	0.370510i
$772$		0			0
$773$			29.5846i			1.06408i	0.846718	+	0.532041i	$0.178575\pi$
$773$			29.5846i			1.06408i	−0.846718	+	0.532041i	$0.821425\pi$
$774$		0			0
$775$	16.1198	+	18.3172i	0.579041	+	0.657974i
$776$		0			0
$777$	−7.53302	+	7.53302i	−0.270246	+	0.270246i
$778$		0			0
$779$			28.8605i			1.03404i
$780$		0			0
$781$	−1.56436	+	1.56436i	−0.0559773	+	0.0559773i
$782$		0			0
$783$	5.38381	−	0.120713i	0.192402	−	0.00431392i
$784$		0			0
$785$	−51.8829	−	1.65362i	−1.85178	−	0.0590201i
$786$		0			0
$787$	−13.3986	−	13.3986i	−0.477609	−	0.477609i	0.426757	−	0.904366i	$-0.359656\pi$
$787$	−13.3986	−	13.3986i	−0.477609	−	0.477609i	−0.904366	+	0.426757i	$0.859656\pi$
$788$		0			0
$789$	−19.5161			−0.694792
$790$		0			0
$791$	0.588066	−	0.588066i	0.0209092	−	0.0209092i
$792$		0			0
$793$	−20.3626			−0.723099
$794$		0			0
$795$	−6.59301	−	7.02711i	−0.233830	−	0.249226i
$796$		0			0
$797$	−36.0176			−1.27581			−0.637905	−	0.770115i	$-0.720199\pi$
$797$	−36.0176			−1.27581			−0.637905	+	0.770115i	$0.720199\pi$
$798$		0			0
$799$			23.3473i			0.825968i
$800$		0			0
$801$	6.19743	−	6.19743i	0.218975	−	0.218975i
$802$		0			0
$803$	−0.558171	−	0.558171i	−0.0196974	−	0.0196974i
$804$		0			0
$805$	−0.0308282	+	0.967247i	−0.00108655	+	0.0340910i
$806$		0			0
$807$	−17.7621	+	17.7621i	−0.625256	+	0.625256i
$808$		0			0
$809$	3.79355	+	3.79355i	0.133374	+	0.133374i	0.770642	−	0.637268i	$-0.219936\pi$
$809$	3.79355	+	3.79355i	0.133374	+	0.133374i	−0.637268	+	0.770642i	$0.719936\pi$
$810$		0			0
$811$		−	32.2348i		−	1.13192i	−0.824433	−	0.565959i	$-0.808506\pi$
$811$		−	32.2348i		−	1.13192i	0.824433	−	0.565959i	$-0.191494\pi$
$812$		0			0
$813$	−2.04007	−	2.04007i	−0.0715485	−	0.0715485i
$814$		0			0
$815$	1.55240	−	48.7071i	0.0543781	−	1.70613i
$816$		0			0
$817$	−27.1104	−	27.1104i	−0.948473	−	0.948473i
$818$		0			0
$819$		−	2.02810i		−	0.0708677i
$820$		0			0
$821$		−	29.9060i		−	1.04373i	−0.853029	−	0.521863i	$-0.825237\pi$
$821$		−	29.9060i		−	1.04373i	0.853029	−	0.521863i	$-0.174763\pi$
$822$		0			0
$823$		−	54.0680i		−	1.88469i	−0.334642	−	0.942345i	$-0.608616\pi$
$823$		−	54.0680i		−	1.88469i	0.334642	−	0.942345i	$-0.391384\pi$
$824$		0			0
$825$	−1.69716	+	1.49356i	−0.0590874	+	0.0519991i
$826$		0			0
$827$			10.6012i			0.368641i	0.982866	+	0.184321i	$0.0590085\pi$
$827$			10.6012i			0.368641i	−0.982866	+	0.184321i	$0.940991\pi$
$828$		0			0
$829$	8.11064	−	8.11064i	0.281694	−	0.281694i	−0.552090	−	0.833784i	$-0.686170\pi$
$829$	8.11064	−	8.11064i	0.281694	−	0.281694i	0.833784	+	0.552090i	$0.186170\pi$
$830$		0			0
$831$	−5.33891	−	5.33891i	−0.185205	−	0.185205i
$832$		0			0
$833$		−	22.5992i		−	0.783016i
$834$		0			0
$835$	−21.9674	+	20.6103i	−0.760213	+	0.713250i
$836$		0			0
$837$	−3.45071	+	3.45071i	−0.119274	+	0.119274i
$838$		0			0
$839$	31.1036	+	31.1036i	1.07381	+	1.07381i	0.997049	+	0.0767646i	$0.0244590\pi$
$839$	31.1036	+	31.1036i	1.07381	+	1.07381i	0.0767646	+	0.997049i	$0.475541\pi$
$840$		0			0
$841$	−28.9709	+	1.29979i	−0.998995	+	0.0448203i
$842$		0			0
$843$		−	7.25552i		−	0.249893i
$844$		0			0
$845$	21.8644	+	0.696864i	0.752157	+	0.0239728i
$846$		0			0
$847$	8.63168	+	8.63168i	0.296588	+	0.296588i
$848$		0			0
$849$	−18.8306	−	18.8306i	−0.646264	−	0.646264i
$850$		0			0
$851$	2.54983	−	2.54983i	0.0874071	−	0.0874071i
$852$		0			0
$853$	−41.3002			−1.41409			−0.707046	−	0.707167i	$-0.749973\pi$
$853$	−41.3002			−1.41409			−0.707046	+	0.707167i	$0.749973\pi$
$854$		0			0
$855$	5.97019	+	6.36329i	0.204176	+	0.217620i
$856$		0			0
$857$	−17.7684	+	17.7684i	−0.606956	+	0.606956i	−0.942149	−	0.335193i	$-0.891198\pi$
$857$	−17.7684	+	17.7684i	−0.606956	+	0.606956i	0.335193	+	0.942149i	$0.391198\pi$
$858$		0			0
$859$	9.41771	+	9.41771i	0.321328	+	0.321328i	0.849277	−	0.527948i	$-0.177039\pi$
$859$	9.41771	+	9.41771i	0.321328	+	0.321328i	−0.527948	+	0.849277i	$0.677039\pi$
$860$		0			0
$861$	8.36303			0.285011
$862$		0			0
$863$	29.5635	−	29.5635i	1.00635	−	1.00635i	0.00637359	−	0.999980i	$-0.497971\pi$
$863$	29.5635	−	29.5635i	1.00635	−	1.00635i	0.999980	−	0.00637359i	$-0.00202879\pi$
$864$		0			0
$865$	12.1191	+	12.9170i	0.412062	+	0.439193i
$866$		0			0
$867$		−	1.39803i		−	0.0474796i
$868$		0			0
$869$	−1.54693			−0.0524760
$870$		0			0
$871$	−5.34947			−0.181260
$872$		0			0
$873$		−	3.50657i		−	0.118679i
$874$		0			0
$875$	−8.04537	−	9.75169i	−0.271983	−	0.329667i
$876$		0			0
$877$	23.5657	−	23.5657i	0.795756	−	0.795756i	−0.186667	−	0.982423i	$-0.559769\pi$
$877$	23.5657	−	23.5657i	0.795756	−	0.795756i	0.982423	+	0.186667i	$0.0597686\pi$
$878$		0			0
$879$	−18.3897			−0.620269
$880$		0			0
$881$	−33.1762	−	33.1762i	−1.11773	−	1.11773i	−0.992073	−	0.125661i	$-0.959895\pi$
$881$	−33.1762	−	33.1762i	−1.11773	−	1.11773i	−0.125661	−	0.992073i	$-0.540105\pi$
$882$		0			0
$883$	4.98092	−	4.98092i	0.167621	−	0.167621i	−0.618312	−	0.785933i	$-0.712183\pi$
$883$	4.98092	−	4.98092i	0.167621	−	0.167621i	0.785933	+	0.618312i	$0.212183\pi$
$884$		0			0
$885$	0.242878	−	7.62038i	0.00816424	−	0.256156i
$886$		0			0
$887$	−0.354658			−0.0119082			−0.00595412	−	0.999982i	$-0.501895\pi$
$887$	−0.354658			−0.0119082			−0.00595412	+	0.999982i	$0.501895\pi$
$888$		0			0
$889$	−7.89507	+	7.89507i	−0.264792	+	0.264792i
$890$		0			0
$891$	−0.319721	−	0.319721i	−0.0107110	−	0.0107110i
$892$		0			0
$893$	−16.3094	−	16.3094i	−0.545773	−	0.545773i
$894$		0			0
$895$	−0.881561	+	27.6593i	−0.0294673	+	0.924549i
$896$		0			0
$897$			0.686487i			0.0229211i
$898$		0			0
$899$	18.1614	−	18.9945i	0.605717	−	0.633502i
$900$		0			0
$901$	12.0358	+	12.0358i	0.400972	+	0.400972i
$902$		0			0
$903$	−7.85588	+	7.85588i	−0.261427	+	0.261427i
$904$		0			0
$905$	0.781292	−	24.5133i	0.0259710	−	0.814851i
$906$		0			0
$907$		−	36.9971i		−	1.22847i	−0.789124	−	0.614234i	$-0.789465\pi$
$907$		−	36.9971i		−	1.22847i	0.789124	−	0.614234i	$-0.210535\pi$
$908$		0			0
$909$	−0.515252	−	0.515252i	−0.0170898	−	0.0170898i
$910$		0			0
$911$	26.4234	−	26.4234i	0.875446	−	0.875446i	−0.117614	−	0.993059i	$-0.537524\pi$
$911$	26.4234	−	26.4234i	0.875446	−	0.875446i	0.993059	+	0.117614i	$0.0375244\pi$
$912$		0			0
$913$			0.920675i			0.0304699i
$914$		0			0
$915$	−17.3697	−	18.5133i	−0.574223	−	0.612032i
$916$		0			0
$917$			12.9741i			0.428443i
$918$		0			0
$919$		−	18.3476i		−	0.605232i	−0.953112	−	0.302616i	$-0.902140\pi$
$919$		−	18.3476i		−	0.605232i	0.953112	−	0.302616i	$-0.0978600\pi$
$920$		0			0
$921$			4.10807i			0.135366i
$922$		0			0
$923$	−6.20550	−	6.20550i	−0.204257	−	0.204257i
$924$		0			0
$925$	−2.99978	+	47.0118i	−0.0986320	+	1.54574i
$926$		0			0
$927$	4.50575	+	4.50575i	0.147988	+	0.147988i
$928$		0			0
$929$		−	54.9661i		−	1.80338i	−0.432384	−	0.901690i	$-0.642327\pi$
$929$		−	54.9661i		−	1.80338i	0.432384	−	0.901690i	$-0.357673\pi$
$930$		0			0
$931$	15.7868	+	15.7868i	0.517392	+	0.517392i
$932$		0			0
$933$	−13.8583	+	13.8583i	−0.453699	+	0.453699i
$934$		0			0
$935$	2.91240	−	2.73248i	0.0952456	−	0.0893618i
$936$		0			0
$937$	21.8749	+	21.8749i	0.714621	+	0.714621i	0.967498	−	0.252877i	$-0.0813769\pi$
$937$	21.8749	+	21.8749i	0.714621	+	0.714621i	−0.252877	+	0.967498i	$0.581377\pi$
$938$		0			0
$939$	5.08029	−	5.08029i	0.165789	−	0.165789i
$940$		0			0
$941$		−	44.7740i		−	1.45959i	−0.683666	−	0.729795i	$-0.739616\pi$
$941$		−	44.7740i		−	1.45959i	0.683666	−	0.729795i	$-0.260384\pi$
$942$		0			0
$943$	−2.83078			−0.0921828
$944$		0			0
$945$	1.84391	−	1.73001i	0.0599825	−	0.0562771i
$946$		0			0
$947$	−7.60318			−0.247070			−0.123535	−	0.992340i	$-0.539423\pi$
$947$	−7.60318			−0.247070			−0.123535	+	0.992340i	$0.539423\pi$
$948$		0			0
$949$	2.21415	−	2.21415i	0.0718742	−	0.0718742i
$950$		0			0
$951$	−24.1177			−0.782071
$952$		0			0
$953$	12.5972	+	12.5972i	0.408063	+	0.408063i	0.881063	−	0.473000i	$-0.156829\pi$
$953$	12.5972	+	12.5972i	0.408063	+	0.408063i	−0.473000	+	0.881063i	$0.656829\pi$
$954$		0			0
$955$	29.2984	−	27.4884i	0.948073	−	0.889505i
$956$		0			0
$957$	1.75991	+	1.68272i	0.0568898	+	0.0543947i
$958$		0			0
$959$	4.11954	−	4.11954i	0.133027	−	0.133027i
$960$		0			0
$961$		−	7.18526i		−	0.231783i
$962$		0			0
$963$	2.33805	−	2.33805i	0.0753427	−	0.0753427i
$964$		0			0
$965$	−27.3425	−	0.871464i	−0.880187	−	0.0280534i
$966$		0			0
$967$			28.9276i			0.930248i	0.885246	+	0.465124i	$0.153990\pi$
$967$			28.9276i			0.930248i	−0.885246	+	0.465124i	$0.846010\pi$
$968$		0			0
$969$	−10.8989	−	10.8989i	−0.350122	−	0.350122i
$970$		0			0
$971$	23.2900	+	23.2900i	0.747412	+	0.747412i	0.973992	−	0.226581i	$-0.0727547\pi$
$971$	23.2900	+	23.2900i	0.747412	+	0.747412i	−0.226581	+	0.973992i	$0.572755\pi$
$972$		0			0
$973$	2.27921	+	2.27921i	0.0730681	+	0.0730681i
$974$		0			0
$975$	−5.92464	−	6.73227i	−0.189740	−	0.215605i
$976$		0			0
$977$	−15.6423	+	15.6423i	−0.500440	+	0.500440i	−0.911575	−	0.411134i	$-0.865133\pi$
$977$	−15.6423	+	15.6423i	−0.500440	+	0.500440i	0.411134	+	0.911575i	$0.365133\pi$
$978$		0			0
$979$	3.96289			0.126654
$980$		0			0
$981$	−1.65077			−0.0527049
$982$		0			0
$983$	58.8696			1.87765			0.938825	−	0.344394i	$-0.111916\pi$
$983$	58.8696			1.87765			0.938825	+	0.344394i	$0.111916\pi$
$984$		0			0
$985$	−28.7626	−	30.6564i	−0.916452	−	0.976794i
$986$		0			0
$987$	−4.72604	+	4.72604i	−0.150431	+	0.150431i
$988$		0			0
$989$	2.65912	−	2.65912i	0.0845550	−	0.0845550i
$990$		0			0
$991$		−	29.2034i		−	0.927676i	−0.885920	−	0.463838i	$-0.846472\pi$
$991$		−	29.2034i		−	0.927676i	0.885920	−	0.463838i	$-0.153528\pi$
$992$		0			0
$993$	6.36032	+	6.36032i	0.201839	+	0.201839i
$994$		0			0
$995$	47.8971	+	1.52658i	1.51844	+	0.0483959i
$996$		0			0
$997$	1.66761			0.0528137			0.0264069	−	0.999651i	$-0.491593\pi$
$997$	1.66761			0.0528137			0.0264069	+	0.999651i	$0.491593\pi$
$998$		0			0
$999$	−9.42147			−0.298082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1740.2.bc.c.853.7	yes	30
5.2	odd	4		1740.2.bb.c.157.9	yes	30
29.17	odd	4		1740.2.bb.c.133.9	✓	30
145.17	even	4	inner	1740.2.bc.c.1177.7	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1740.2.bb.c.133.9	✓	30	29.17	odd	4
1740.2.bb.c.157.9	yes	30	5.2	odd	4
1740.2.bc.c.853.7	yes	30	1.1	even	1	trivial
1740.2.bc.c.1177.7	yes	30	145.17	even	4	inner

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:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1740.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{3} +(0.0712321 - 2.23493i) q^{5} +(-0.799559 + 0.799559i) q^{7} -1.00000 q^{9} +(-0.319721 - 0.319721i) q^{11} +(1.26826 - 1.26826i) q^{13} +(2.23493 + 0.0712321i) q^{15} -3.94993 q^{17} +(2.75925 - 2.75925i) q^{19} +(-0.799559 - 0.799559i) q^{21} +(0.270640 + 0.270640i) q^{23} +(-4.98985 - 0.318398i) q^{25} -1.00000i q^{27} +(0.120713 + 5.38381i) q^{29} +(-3.45071 - 3.45071i) q^{31} +(0.319721 - 0.319721i) q^{33} +(1.73001 + 1.84391i) q^{35} -9.42147i q^{37} +(1.26826 + 1.26826i) q^{39} +(-5.22978 + 5.22978i) q^{41} -9.82527i q^{43} +(-0.0712321 + 2.23493i) q^{45} -5.91081i q^{47} +5.72141i q^{49} -3.94993i q^{51} +(-3.04710 - 3.04710i) q^{53} +(-0.737329 + 0.691780i) q^{55} +(2.75925 + 2.75925i) q^{57} -3.40967i q^{59} +(-8.02776 - 8.02776i) q^{61} +(0.799559 - 0.799559i) q^{63} +(-2.74415 - 2.92483i) q^{65} +(-2.10897 - 2.10897i) q^{67} +(-0.270640 + 0.270640i) q^{69} -4.89291i q^{71} +1.74581 q^{73} +(0.318398 - 4.98985i) q^{75} +0.511271 q^{77} +(2.41919 - 2.41919i) q^{79} +1.00000 q^{81} +(-1.43981 - 1.43981i) q^{83} +(-0.281362 + 8.82784i) q^{85} +(-5.38381 + 0.120713i) q^{87} +(-6.19743 + 6.19743i) q^{89} +2.02810i q^{91} +(3.45071 - 3.45071i) q^{93} +(-5.97019 - 6.36329i) q^{95} +3.50657i q^{97} +(0.319721 + 0.319721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 30 q^{9} + 4 q^{11} - 6 q^{13} - 6 q^{15} + 8 q^{19} - 6 q^{25} + 4 q^{29} - 4 q^{33} - 16 q^{35} - 6 q^{39} - 10 q^{41} - 6 q^{53} + 4 q^{55} + 8 q^{57} + 30 q^{61} - 2 q^{65} + 4 q^{67} + 12 q^{73}+ \cdots - 4 q^{99}+O(q^{100}) \) 30 * q - 30 * q^9 + 4 * q^11 - 6 * q^13 - 6 * q^15 + 8 * q^19 - 6 * q^25 + 4 * q^29 - 4 * q^33 - 16 * q^35 - 6 * q^39 - 10 * q^41 - 6 * q^53 + 4 * q^55 + 8 * q^57 + 30 * q^61 - 2 * q^65 + 4 * q^67 + 12 * q^73 + 8 * q^75 - 4 * q^77 - 4 * q^79 + 30 * q^81 - 28 * q^83 + 20 * q^85 + 10 * q^87 + 10 * q^89 + 20 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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