LMFDB - Embedded newform 936.2.s.f.529.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(529,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

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

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

Newform invariants

comment:select newform

sage:traces = [40,0,-3,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

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

Embedding invariants

Embedding label			529.11
Character	$\chi$	$=$	936.529
Dual form			936.2.s.f.913.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0896694 - 1.72973i) q^{3} +(-1.74688 - 3.02568i) q^{5} -3.26004 q^{7} +(-2.98392 - 0.310207i) q^{9} +(-2.07747 - 3.59829i) q^{11} +(3.60353 - 0.120733i) q^{13} +(-5.39024 + 2.75031i) q^{15} +(0.552555 + 0.957054i) q^{17} +(2.87832 + 4.98540i) q^{19} +(-0.292326 + 5.63898i) q^{21} +0.808173 q^{23} +(-3.60315 + 6.24083i) q^{25} +(-0.804141 + 5.13355i) q^{27} +(-0.545617 - 0.945036i) q^{29} +(0.736669 + 1.27595i) q^{31} +(-6.41035 + 3.27081i) q^{33} +(5.69488 + 9.86383i) q^{35} +(3.26057 - 5.64747i) q^{37} +(0.114291 - 6.24395i) q^{39} -6.64738 q^{41} -11.2959 q^{43} +(4.27395 + 9.57027i) q^{45} +(0.872054 - 1.51044i) q^{47} +3.62786 q^{49} +(1.70499 - 0.869952i) q^{51} +7.33676 q^{53} +(-7.25818 + 12.5715i) q^{55} +(8.88149 - 4.53168i) q^{57} +(-1.70455 + 2.95236i) q^{59} +13.0798 q^{61} +(9.72769 + 1.01129i) q^{63} +(-6.66022 - 10.6922i) q^{65} -9.98057 q^{67} +(0.0724685 - 1.39792i) q^{69} +(-7.73554 - 13.3984i) q^{71} -1.48179 q^{73} +(10.4719 + 6.79208i) q^{75} +(6.77265 + 11.7306i) q^{77} +(-6.20956 + 10.7553i) q^{79} +(8.80754 + 1.85127i) q^{81} +(1.53846 - 2.66470i) q^{83} +(1.93049 - 3.34371i) q^{85} +(-1.68358 + 0.859028i) q^{87} +(-3.25125 + 5.63133i) q^{89} +(-11.7476 + 0.393595i) q^{91} +(2.27310 - 1.15982i) q^{93} +(10.0561 - 17.4178i) q^{95} -7.51478 q^{97} +(5.08280 + 11.3815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) $ 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0896694	−	1.72973i	0.0517707	−	0.998659i
$3$	0.0896694	−	1.72973i	0.0517707	−	0.998659i
$4$		0			0
$5$	−1.74688	−	3.02568i	−0.781226	−	1.35312i	−0.931228	−	0.364438i	$-0.881261\pi$
$5$	−1.74688	−	3.02568i	−0.781226	−	1.35312i	0.150001	−	0.988686i	$-0.452072\pi$
$6$		0			0
$7$	−3.26004			−1.23218			−0.616090	−	0.787676i	$-0.711284\pi$
$7$	−3.26004			−1.23218			−0.616090	+	0.787676i	$0.711284\pi$
$8$		0			0
$9$	−2.98392	−	0.310207i	−0.994640	−	0.103402i
$10$		0			0
$11$	−2.07747	−	3.59829i	−0.626382	−	1.08493i	−0.988272	−	0.152705i	$-0.951202\pi$
$11$	−2.07747	−	3.59829i	−0.626382	−	1.08493i	0.361890	−	0.932221i	$-0.382132\pi$
$12$		0			0
$13$	3.60353	−	0.120733i	0.999439	−	0.0334854i
$13$	3.60353	−	0.120733i	0.999439	−	0.0334854i
$14$		0			0
$15$	−5.39024	+	2.75031i	−1.39175	+	0.710127i
$16$		0			0
$17$	0.552555	+	0.957054i	0.134014	+	0.232120i	0.925221	−	0.379430i	$-0.123880\pi$
$17$	0.552555	+	0.957054i	0.134014	+	0.232120i	−0.791206	+	0.611550i	$0.790547\pi$
$18$		0			0
$19$	2.87832	+	4.98540i	0.660333	+	1.14373i	0.980528	+	0.196378i	$0.0629181\pi$
$19$	2.87832	+	4.98540i	0.660333	+	1.14373i	−0.320195	+	0.947351i	$0.603749\pi$
$20$		0			0
$21$	−0.292326	+	5.63898i	−0.0637907	+	1.23053i
$22$		0			0
$23$	0.808173			0.168516			0.0842579	−	0.996444i	$-0.473148\pi$
$23$	0.808173			0.168516			0.0842579	+	0.996444i	$0.473148\pi$
$24$		0			0
$25$	−3.60315	+	6.24083i	−0.720629	+	1.24817i
$26$		0			0
$27$	−0.804141	+	5.13355i	−0.154757	+	0.987953i
$28$		0			0
$29$	−0.545617	−	0.945036i	−0.101318	−	0.175489i	0.810910	−	0.585171i	$-0.198973\pi$
$29$	−0.545617	−	0.945036i	−0.101318	−	0.175489i	−0.912228	+	0.409683i	$0.865639\pi$
$30$		0			0
$31$	0.736669	+	1.27595i	0.132310	+	0.229167i	0.924567	−	0.381021i	$-0.124427\pi$
$31$	0.736669	+	1.27595i	0.132310	+	0.229167i	−0.792257	+	0.610188i	$0.791094\pi$
$32$		0			0
$33$	−6.41035	+	3.27081i	−1.11590	+	0.569375i
$34$		0			0
$35$	5.69488	+	9.86383i	0.962611	+	1.66729i
$36$		0			0
$37$	3.26057	−	5.64747i	0.536035	−	0.928439i	−0.463078	−	0.886318i	$-0.653255\pi$
$37$	3.26057	−	5.64747i	0.536035	−	0.928439i	0.999112	−	0.0421215i	$-0.0134117\pi$
$38$		0			0
$39$	0.114291	−	6.24395i	0.0183012	−	0.999833i
$40$		0			0
$41$	−6.64738			−1.03815			−0.519073	−	0.854730i	$-0.673723\pi$
$41$	−6.64738			−1.03815			−0.519073	+	0.854730i	$0.673723\pi$
$42$		0			0
$43$	−11.2959			−1.72261			−0.861307	−	0.508084i	$-0.830354\pi$
$43$	−11.2959			−1.72261			−0.861307	+	0.508084i	$0.830354\pi$
$44$		0			0
$45$	4.27395	+	9.57027i	0.637122	+	1.42665i
$46$		0			0
$47$	0.872054	−	1.51044i	0.127202	−	0.220321i	−0.795389	−	0.606099i	$-0.792734\pi$
$47$	0.872054	−	1.51044i	0.127202	−	0.220321i	0.922592	+	0.385778i	$0.126067\pi$
$48$		0			0
$49$	3.62786			0.518266
$50$		0			0
$51$	1.70499	−	0.869952i	0.238746	−	0.121818i
$52$		0			0
$53$	7.33676			1.00778			0.503891	−	0.863767i	$-0.331901\pi$
$53$	7.33676			1.00778			0.503891	+	0.863767i	$0.331901\pi$
$54$		0			0
$55$	−7.25818	+	12.5715i	−0.978692	+	1.69514i
$56$		0			0
$57$	8.88149	−	4.53168i	1.17638	−	0.600236i
$58$		0			0
$59$	−1.70455	+	2.95236i	−0.221913	+	0.384365i	−0.955389	−	0.295351i	$-0.904564\pi$
$59$	−1.70455	+	2.95236i	−0.221913	+	0.384365i	0.733476	+	0.679716i	$0.237897\pi$
$60$		0			0
$61$	13.0798			1.67470			0.837350	−	0.546667i	$-0.184103\pi$
$61$	13.0798			1.67470			0.837350	+	0.546667i	$0.184103\pi$
$62$		0			0
$63$	9.72769	+	1.01129i	1.22557	+	0.127410i
$64$		0			0
$65$	−6.66022	−	10.6922i	−0.826098	−	1.32621i
$66$		0			0
$67$	−9.98057			−1.21932			−0.609660	−	0.792663i	$-0.708694\pi$
$67$	−9.98057			−1.21932			−0.609660	+	0.792663i	$0.708694\pi$
$68$		0			0
$69$	0.0724685	−	1.39792i	0.00872418	−	0.168290i
$70$		0			0
$71$	−7.73554	−	13.3984i	−0.918040	−	1.59009i	−0.802388	−	0.596802i	$-0.796438\pi$
$71$	−7.73554	−	13.3984i	−0.918040	−	1.59009i	−0.115652	−	0.993290i	$-0.536896\pi$
$72$		0			0
$73$	−1.48179			−0.173430			−0.0867152	−	0.996233i	$-0.527637\pi$
$73$	−1.48179			−0.173430			−0.0867152	+	0.996233i	$0.527637\pi$
$74$		0			0
$75$	10.4719	+	6.79208i	1.20919	+	0.784281i
$76$		0			0
$77$	6.77265	+	11.7306i	0.771815	+	1.33682i
$78$		0			0
$79$	−6.20956	+	10.7553i	−0.698630	+	1.21006i	0.270312	+	0.962773i	$0.412873\pi$
$79$	−6.20956	+	10.7553i	−0.698630	+	1.21006i	−0.968942	+	0.247290i	$0.920460\pi$
$80$		0			0
$81$	8.80754	+	1.85127i	0.978616	+	0.205696i
$82$		0			0
$83$	1.53846	−	2.66470i	0.168868	−	0.292488i	−0.769154	−	0.639063i	$-0.779322\pi$
$83$	1.53846	−	2.66470i	0.168868	−	0.292488i	0.938022	+	0.346575i	$0.112655\pi$
$84$		0			0
$85$	1.93049	−	3.34371i	0.209391	−	0.362676i
$86$		0			0
$87$	−1.68358	+	0.859028i	−0.180499	+	0.0920975i
$88$		0			0
$89$	−3.25125	+	5.63133i	−0.344632	+	0.596920i	−0.985287	−	0.170909i	$-0.945330\pi$
$89$	−3.25125	+	5.63133i	−0.344632	+	0.596920i	0.640655	+	0.767829i	$0.278663\pi$
$90$		0			0
$91$	−11.7476	+	0.393595i	−1.23149	+	0.0412600i
$92$		0			0
$93$	2.27310	−	1.15982i	0.235710	−	0.120268i
$94$		0			0
$95$	10.0561	−	17.4178i	1.03174	−	1.78702i
$96$		0			0
$97$	−7.51478			−0.763011			−0.381505	−	0.924367i	$-0.624594\pi$
$97$	−7.51478			−0.763011			−0.381505	+	0.924367i	$0.624594\pi$
$98$		0			0
$99$	5.08280	+	11.3815i	0.510840	+	1.14388i
$100$		0			0
$101$	−2.90712	−	5.03528i	−0.289269	−	0.501029i	0.684366	−	0.729138i	$-0.260079\pi$
$101$	−2.90712	−	5.03528i	−0.289269	−	0.501029i	−0.973635	+	0.228110i	$0.926746\pi$
$102$		0			0
$103$	−7.91522	−	13.7096i	−0.779910	−	1.35084i	−0.931993	−	0.362475i	$-0.881932\pi$
$103$	−7.91522	−	13.7096i	−0.779910	−	1.35084i	0.152084	−	0.988368i	$-0.451402\pi$
$104$		0			0
$105$	17.5724	−	8.96612i	1.71489	−	0.875003i
$106$		0			0
$107$	−6.39874	+	11.0829i	−0.618589	+	1.07143i	0.371154	+	0.928571i	$0.378962\pi$
$107$	−6.39874	+	11.0829i	−0.618589	+	1.07143i	−0.989743	+	0.142857i	$0.954371\pi$
$108$		0			0
$109$	−15.7657			−1.51008			−0.755040	−	0.655678i	$-0.772383\pi$
$109$	−15.7657			−1.51008			−0.755040	+	0.655678i	$0.772383\pi$
$110$		0			0
$111$	−9.47622	−	6.14631i	−0.899443	−	0.583382i
$112$		0			0
$113$	8.87881	−	15.3785i	0.835248	−	1.44669i	−0.0585804	−	0.998283i	$-0.518657\pi$
$113$	8.87881	−	15.3785i	0.835248	−	1.44669i	0.893828	−	0.448409i	$-0.148009\pi$
$114$		0			0
$115$	−1.41178	−	2.44527i	−0.131649	−	0.228023i
$116$		0			0
$117$	−10.7901	−	0.757584i	−0.997544	−	0.0700386i
$118$		0			0
$119$	−1.80135	−	3.12003i	−0.165130	−	0.286013i
$120$		0			0
$121$	−3.13180	+	5.42443i	−0.284709	+	0.493130i
$122$		0			0
$123$	−0.596067	+	11.4982i	−0.0537455	+	1.03675i
$124$		0			0
$125$	7.70824			0.689446
$126$		0			0
$127$	−10.5669	+	18.3024i	−0.937662	+	1.62408i	−0.167845	+	0.985813i	$0.553681\pi$
$127$	−10.5669	+	18.3024i	−0.937662	+	1.62408i	−0.769817	+	0.638265i	$0.779652\pi$
$128$		0			0
$129$	−1.01290	+	19.5389i	−0.0891809	+	1.72030i
$130$		0			0
$131$	−0.909216	−	1.57481i	−0.0794385	−	0.137592i	0.823569	−	0.567216i	$-0.191979\pi$
$131$	−0.909216	−	1.57481i	−0.0794385	−	0.137592i	−0.903008	+	0.429624i	$0.858646\pi$
$132$		0			0
$133$	−9.38345	−	16.2526i	−0.813648	−	1.40928i
$134$		0			0
$135$	16.9372	−	6.53460i	1.45772	−	0.562409i
$136$		0			0
$137$	−2.14499			−0.183259			−0.0916295	−	0.995793i	$-0.529208\pi$
$137$	−2.14499			−0.183259			−0.0916295	+	0.995793i	$0.529208\pi$
$138$		0			0
$139$	4.38582	−	7.59646i	0.372000	−	0.644323i	−0.617873	−	0.786278i	$-0.712005\pi$
$139$	4.38582	−	7.59646i	0.372000	−	0.644323i	0.989873	+	0.141955i	$0.0453387\pi$
$140$		0			0
$141$	−2.53446	−	1.64386i	−0.213440	−	0.138438i
$142$		0			0
$143$	−7.92067	−	12.7157i	−0.662360	−	1.06334i
$144$		0			0
$145$	−1.90625	+	3.30172i	−0.158305	+	0.274193i
$146$		0			0
$147$	0.325308	−	6.27521i	0.0268310	−	0.517571i
$148$		0			0
$149$	−4.09119	+	7.08615i	−0.335163	+	0.580520i	−0.983516	−	0.180820i	$-0.942125\pi$
$149$	−4.09119	+	7.08615i	−0.335163	+	0.580520i	0.648353	+	0.761340i	$0.275458\pi$
$150$		0			0
$151$	6.19162	−	10.7242i	0.503867	−	0.872724i	−0.496123	−	0.868252i	$-0.665243\pi$
$151$	6.19162	−	10.7242i	0.503867	−	0.872724i	0.999990	−	0.00447118i	$-0.00142323\pi$
$152$		0			0
$153$	−1.35189	−	3.02718i	−0.109294	−	0.244733i
$154$		0			0
$155$	2.57374	−	4.45784i	0.206728	−	0.358063i
$156$		0			0
$157$	10.5834	+	18.3309i	0.844644	+	1.46297i	0.885930	+	0.463819i	$0.153521\pi$
$157$	10.5834	+	18.3309i	0.844644	+	1.46297i	−0.0412855	+	0.999147i	$0.513145\pi$
$158$		0			0
$159$	0.657883	−	12.6906i	0.0521735	−	1.00643i
$160$		0			0
$161$	−2.63468			−0.207642
$162$		0			0
$163$	−1.14969	−	1.99132i	−0.0900504	−	0.155972i	0.817482	−	0.575955i	$-0.195369\pi$
$163$	−1.14969	−	1.99132i	−0.0900504	−	0.155972i	−0.907532	+	0.419983i	$0.862036\pi$
$164$		0			0
$165$	21.0945	+	13.6820i	1.64220	+	1.06514i
$166$		0			0
$167$	2.86707			0.221860			0.110930	−	0.993828i	$-0.464617\pi$
$167$	2.86707			0.221860			0.110930	+	0.993828i	$0.464617\pi$
$168$		0			0
$169$	12.9708	−	0.870132i	0.997757	−	0.0669332i
$170$		0			0
$171$	−7.04217	−	15.7689i	−0.538529	−	1.20588i
$172$		0			0
$173$	9.71181			0.738375			0.369188	−	0.929355i	$-0.379636\pi$
$173$	9.71181			0.738375			0.369188	+	0.929355i	$0.379636\pi$
$174$		0			0
$175$	11.7464	−	20.3454i	0.887944	−	1.53796i
$176$		0			0
$177$	4.95394	+	3.21314i	0.372361	+	0.241515i
$178$		0			0
$179$	−7.20045	+	12.4715i	−0.538187	+	0.932167i	0.460815	+	0.887496i	$0.347557\pi$
$179$	−7.20045	+	12.4715i	−0.538187	+	0.932167i	−0.999002	+	0.0446705i	$0.985776\pi$
$180$		0			0
$181$	−10.1986			−0.758056			−0.379028	−	0.925385i	$-0.623742\pi$
$181$	−10.1986			−0.758056			−0.379028	+	0.925385i	$0.623742\pi$
$182$		0			0
$183$	1.17286	−	22.6246i	0.0867004	−	1.67245i
$184$		0			0
$185$	−22.7832			−1.67506
$186$		0			0
$187$	2.29584	−	3.97651i	0.167888	−	0.290791i
$188$		0			0
$189$	2.62153	−	16.7356i	0.190688	−	1.21733i
$190$		0			0
$191$	17.0121			1.23095			0.615475	−	0.788157i	$-0.288964\pi$
$191$	17.0121			1.23095			0.615475	+	0.788157i	$0.288964\pi$
$192$		0			0
$193$	17.7222			1.27567			0.637837	−	0.770171i	$-0.279829\pi$
$193$	17.7222			1.27567			0.637837	+	0.770171i	$0.279829\pi$
$194$		0			0
$195$	−19.0918	+	10.5616i	−1.36719	+	0.756332i
$196$		0			0
$197$	10.3626	−	17.9486i	0.738306	−	1.27878i	−0.214952	−	0.976625i	$-0.568959\pi$
$197$	10.3626	−	17.9486i	0.738306	−	1.27878i	0.953258	−	0.302159i	$-0.0977073\pi$
$198$		0			0
$199$	3.07376	+	5.32390i	0.217893	+	0.377402i	0.954164	−	0.299286i	$-0.0967483\pi$
$199$	3.07376	+	5.32390i	0.217893	+	0.377402i	−0.736271	+	0.676687i	$0.763415\pi$
$200$		0			0
$201$	−0.894952	+	17.2637i	−0.0631251	+	1.21769i
$202$		0			0
$203$	1.77873	+	3.08085i	0.124843	+	0.216234i
$204$		0			0
$205$	11.6121	+	20.1128i	0.811027	+	1.40474i
$206$		0			0
$207$	−2.41152	−	0.250701i	−0.167612	−	0.0174250i
$208$		0			0
$209$	11.9593	−	20.7141i	0.827241	−	1.43282i
$210$		0			0
$211$	−2.34876			−0.161696			−0.0808478	−	0.996726i	$-0.525763\pi$
$211$	−2.34876			−0.161696			−0.0808478	+	0.996726i	$0.525763\pi$
$212$		0			0
$213$	−23.8692	+	12.1790i	−1.63549	+	0.834489i
$214$		0			0
$215$	19.7326	+	34.1779i	1.34575	+	2.33091i
$216$		0			0
$217$	−2.40157	−	4.15964i	−0.163029	−	0.282375i
$218$		0			0
$219$	−0.132871	+	2.56309i	−0.00897861	+	0.173198i
$220$		0			0
$221$	2.10670	+	3.38206i	0.141712	+	0.227502i
$222$		0			0
$223$	−8.52301	−	14.7623i	−0.570743	−	0.988556i	−0.996490	−	0.0837137i	$-0.973322\pi$
$223$	−8.52301	−	14.7623i	−0.570743	−	0.988556i	0.425747	−	0.904842i	$-0.360011\pi$
$224$		0			0
$225$	12.6874	−	17.5044i	0.845830	−	1.16696i
$226$		0			0
$227$	−8.62994			−0.572789			−0.286395	−	0.958112i	$-0.592457\pi$
$227$	−8.62994			−0.572789			−0.286395	+	0.958112i	$0.592457\pi$
$228$		0			0
$229$	−10.9992	−	19.0511i	−0.726845	−	1.25893i	−0.958210	−	0.286066i	$-0.907652\pi$
$229$	−10.9992	−	19.0511i	−0.726845	−	1.25893i	0.231365	−	0.972867i	$-0.425681\pi$
$230$		0			0
$231$	20.8980	−	10.6630i	1.37499	−	0.701572i
$232$		0			0
$233$	−8.82556			−0.578181			−0.289091	−	0.957302i	$-0.593353\pi$
$233$	−8.82556			−0.578181			−0.289091	+	0.957302i	$0.593353\pi$
$234$		0			0
$235$	−6.09348			−0.397495
$236$		0			0
$237$	18.0469	+	11.7053i	1.17227	+	0.760339i
$238$		0			0
$239$	−6.84824	−	11.8615i	−0.442976	−	0.767256i	0.554933	−	0.831895i	$-0.312744\pi$
$239$	−6.84824	−	11.8615i	−0.442976	−	0.767256i	−0.997909	+	0.0646387i	$0.979411\pi$
$240$		0			0
$241$	−10.7757			−0.694126			−0.347063	−	0.937842i	$-0.612821\pi$
$241$	−10.7757			−0.694126			−0.347063	+	0.937842i	$0.612821\pi$
$242$		0			0
$243$	3.99196	−	15.0687i	0.256084	−	0.966654i
$244$		0			0
$245$	−6.33742	−	10.9767i	−0.404883	−	0.701278i
$246$		0			0
$247$	10.9740	+	17.6175i	0.698261	+	1.12098i
$248$		0			0
$249$	−4.47125	−	2.90006i	−0.283354	−	0.183784i
$250$		0			0
$251$	−9.80361	−	16.9804i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$251$	−9.80361	−	16.9804i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$252$		0			0
$253$	−1.67896	−	2.90804i	−0.105555	−	0.182827i
$254$		0			0
$255$	−5.61060	−	3.63905i	−0.351349	−	0.227886i
$256$		0			0
$257$	−27.6851			−1.72695			−0.863476	−	0.504390i	$-0.831717\pi$
$257$	−27.6851			−1.72695			−0.863476	+	0.504390i	$0.831717\pi$
$258$		0			0
$259$	−10.6296	+	18.4110i	−0.660491	+	1.14400i
$260$		0			0
$261$	1.33492	+	2.98916i	0.0826294	+	0.185025i
$262$		0			0
$263$	11.8244	+	20.4805i	0.729123	+	1.26288i	0.957254	+	0.289248i	$0.0934053\pi$
$263$	11.8244	+	20.4805i	0.729123	+	1.26288i	−0.228131	+	0.973630i	$0.573261\pi$
$264$		0			0
$265$	−12.8164	−	22.1987i	−0.787306	−	1.36365i
$266$		0			0
$267$	9.44913	+	6.12874i	0.578277	+	0.375073i
$268$		0			0
$269$	−1.35958	−	2.35487i	−0.0828952	−	0.143579i	0.821597	−	0.570068i	$-0.193083\pi$
$269$	−1.35958	−	2.35487i	−0.0828952	−	0.143579i	−0.904492	+	0.426490i	$0.859750\pi$
$270$		0			0
$271$	0.815695	−	1.41283i	0.0495500	−	0.0858231i	−0.840187	−	0.542297i	$-0.817555\pi$
$271$	0.815695	−	1.41283i	0.0495500	−	0.0858231i	0.889737	+	0.456474i	$0.150888\pi$
$272$		0			0
$273$	−0.372592	+	20.3555i	−0.0225503	+	1.23197i
$274$		0			0
$275$	29.9418			1.80556
$276$		0			0
$277$	−8.71041			−0.523358			−0.261679	−	0.965155i	$-0.584276\pi$
$277$	−8.71041			−0.523358			−0.261679	+	0.965155i	$0.584276\pi$
$278$		0			0
$279$	−1.80235	−	4.03585i	−0.107904	−	0.241620i
$280$		0			0
$281$	−1.45902	+	2.52709i	−0.0870377	+	0.150754i	−0.906258	−	0.422726i	$-0.861073\pi$
$281$	−1.45902	+	2.52709i	−0.0870377	+	0.150754i	0.819220	+	0.573479i	$0.194407\pi$
$282$		0			0
$283$	27.6959			1.64635			0.823175	−	0.567787i	$-0.192200\pi$
$283$	27.6959			1.64635			0.823175	+	0.567787i	$0.192200\pi$
$284$		0			0
$285$	−29.2263	−	18.9562i	−1.73121	−	1.12287i
$286$		0			0
$287$	21.6707			1.27918
$288$		0			0
$289$	7.88937	−	13.6648i	0.464080	−	0.803811i
$290$		0			0
$291$	−0.673846	+	12.9985i	−0.0395016	+	0.761987i
$292$		0			0
$293$	6.05326	−	10.4846i	0.353635	−	0.612514i	−0.633248	−	0.773949i	$-0.718279\pi$
$293$	6.05326	−	10.4846i	0.353635	−	0.612514i	0.986883	+	0.161435i	$0.0516121\pi$
$294$		0			0
$295$	11.9105			0.693458
$296$		0			0
$297$	20.1426	−	7.77129i	1.16879	−	0.450936i
$298$		0			0
$299$	2.91228	−	0.0975734i	0.168421	−	0.00564282i
$300$		0			0
$301$	36.8252			2.12257
$302$		0			0
$303$	−8.97034	+	4.57701i	−0.515333	+	0.262943i
$304$		0			0
$305$	−22.8488	−	39.5753i	−1.30832	−	2.26608i
$306$		0			0
$307$	21.6976			1.23835			0.619173	−	0.785255i	$-0.287468\pi$
$307$	21.6976			1.23835			0.619173	+	0.785255i	$0.287468\pi$
$308$		0			0
$309$	−24.4236	+	12.4618i	−1.38941	+	0.708930i
$310$		0			0
$311$	−13.6794	−	23.6934i	−0.775686	−	1.34353i	−0.934408	−	0.356205i	$-0.884071\pi$
$311$	−13.6794	−	23.6934i	−0.775686	−	1.34353i	0.158722	−	0.987323i	$-0.449263\pi$
$312$		0			0
$313$	−5.73787	+	9.93828i	−0.324323	+	0.561745i	−0.981375	−	0.192101i	$-0.938470\pi$
$313$	−5.73787	+	9.93828i	−0.324323	+	0.561745i	0.657052	+	0.753845i	$0.271803\pi$
$314$		0			0
$315$	−13.9332	−	31.1995i	−0.785049	−	1.75789i
$316$		0			0
$317$	16.5421	−	28.6517i	0.929096	−	1.60924i	0.144259	−	0.989540i	$-0.453920\pi$
$317$	16.5421	−	28.6517i	0.929096	−	1.60924i	0.784837	−	0.619702i	$-0.212747\pi$
$318$		0			0
$319$	−2.26701	+	3.92658i	−0.126928	+	0.219846i
$320$		0			0
$321$	18.5967	+	12.0619i	1.03797	+	0.673228i
$322$		0			0
$323$	−3.18087	+	5.50942i	−0.176988	+	0.306552i
$324$		0			0
$325$	−12.2306	+	22.9240i	−0.678430	+	1.27160i
$326$		0			0
$327$	−1.41370	+	27.2704i	−0.0781779	+	1.50806i
$328$		0			0
$329$	−2.84293	+	4.92410i	−0.156736	+	0.271474i
$330$		0			0
$331$	5.16863			0.284094			0.142047	−	0.989860i	$-0.454632\pi$
$331$	5.16863			0.284094			0.142047	+	0.989860i	$0.454632\pi$
$332$		0			0
$333$	−11.4812	+	15.8402i	−0.629164	+	0.868035i
$334$		0			0
$335$	17.4348	+	30.1980i	0.952566	+	1.64989i
$336$		0			0
$337$	6.63334	+	11.4893i	0.361341	+	0.625862i	0.988182	−	0.153286i	$-0.0489856\pi$
$337$	6.63334	+	11.4893i	0.361341	+	0.625862i	−0.626841	+	0.779148i	$0.715652\pi$
$338$		0			0
$339$	−25.8045	−	16.7369i	−1.40151	−	0.909024i
$340$		0			0
$341$	3.06082	−	5.30150i	0.165753	−	0.287092i
$342$		0			0
$343$	10.9933			0.593583
$344$		0			0
$345$	−4.35625	+	2.22273i	−0.234533	+	0.119668i
$346$		0			0
$347$	−2.80449	+	4.85752i	−0.150553	+	0.260765i	−0.931431	−	0.363918i	$-0.881439\pi$
$347$	−2.80449	+	4.85752i	−0.150553	+	0.260765i	0.780878	+	0.624684i	$0.214772\pi$
$348$		0			0
$349$	−12.3179	−	21.3351i	−0.659360	−	1.14204i	−0.980782	−	0.195108i	$-0.937494\pi$
$349$	−12.3179	−	21.3351i	−0.659360	−	1.14204i	0.321422	−	0.946936i	$-0.395839\pi$
$350$		0			0
$351$	−2.27795	+	18.5960i	−0.121588	+	0.992581i
$352$		0			0
$353$	9.92300	+	17.1871i	0.528148	+	0.914780i	0.999461	+	0.0328137i	$0.0104468\pi$
$353$	9.92300	+	17.1871i	0.528148	+	0.914780i	−0.471313	+	0.881966i	$0.656220\pi$
$354$		0			0
$355$	−27.0261	+	46.8105i	−1.43439	+	2.48444i
$356$		0			0
$357$	−5.55834	+	2.83608i	−0.294178	+	0.150101i
$358$		0			0
$359$	11.8976			0.627930			0.313965	−	0.949435i	$-0.398343\pi$
$359$	11.8976			0.627930			0.313965	+	0.949435i	$0.398343\pi$
$360$		0			0
$361$	−7.06949	+	12.2447i	−0.372079	+	0.644459i
$362$		0			0
$363$	9.10196	+	5.90356i	0.477729	+	0.309857i
$364$		0			0
$365$	2.58850	+	4.48342i	0.135488	+	0.234673i
$366$		0			0
$367$	0.264953	+	0.458912i	0.0138304	+	0.0239550i	0.872858	−	0.487975i	$-0.162264\pi$
$367$	0.264953	+	0.458912i	0.0138304	+	0.0239550i	−0.859027	+	0.511930i	$0.828931\pi$
$368$		0			0
$369$	19.8352	+	2.06207i	1.03258	+	0.107347i
$370$		0			0
$371$	−23.9181			−1.24177
$372$		0			0
$373$	−7.43275	+	12.8739i	−0.384853	+	0.666585i	−0.991749	−	0.128196i	$-0.959081\pi$
$373$	−7.43275	+	12.8739i	−0.384853	+	0.666585i	0.606896	+	0.794781i	$0.292415\pi$
$374$		0			0
$375$	0.691193	−	13.3332i	0.0356931	−	0.688521i
$376$		0			0
$377$	−2.08024	−	3.33959i	−0.107138	−	0.171998i
$378$		0			0
$379$	2.35909	−	4.08607i	0.121178	−	0.209887i	−0.799054	−	0.601259i	$-0.794666\pi$
$379$	2.35909	−	4.08607i	0.121178	−	0.209887i	0.920233	+	0.391372i	$0.127999\pi$
$380$		0			0
$381$	30.7107	+	19.9191i	1.57336	+	1.02048i
$382$		0			0
$383$	0.211063	−	0.365573i	0.0107848	−	0.0186799i	−0.860583	−	0.509311i	$-0.829900\pi$
$383$	0.211063	−	0.365573i	0.0107848	−	0.0186799i	0.871367	+	0.490631i	$0.163234\pi$
$384$		0			0
$385$	23.6619	−	40.9837i	1.20592	−	2.08872i
$386$		0			0
$387$	33.7062	+	3.50409i	1.71338	+	0.178123i
$388$		0			0
$389$	−15.4956	+	26.8392i	−0.785658	+	1.36080i	0.142947	+	0.989730i	$0.454342\pi$
$389$	−15.4956	+	26.8392i	−0.785658	+	1.36080i	−0.928605	+	0.371069i	$0.878991\pi$
$390$		0			0
$391$	0.446561	+	0.773465i	0.0225835	+	0.0391158i
$392$		0			0
$393$	−2.80552	+	1.43148i	−0.141520	+	0.0722088i
$394$		0			0
$395$	43.3893			2.18315
$396$		0			0
$397$	9.90767	+	17.1606i	0.497252	+	0.861266i	0.999995	−	0.00317030i	$-0.00100914\pi$
$397$	9.90767	+	17.1606i	0.497252	+	0.861266i	−0.502743	+	0.864436i	$0.667676\pi$
$398$		0			0
$399$	−28.9540	+	14.7735i	−1.44951	+	0.739598i
$400$		0			0
$401$	−28.8904			−1.44272			−0.721358	−	0.692562i	$-0.756482\pi$
$401$	−28.8904			−1.44272			−0.721358	+	0.692562i	$0.756482\pi$
$402$		0			0
$403$	2.80866	+	4.50898i	0.139909	+	0.224608i
$404$		0			0
$405$	−9.78434	−	29.8827i	−0.486188	−	1.48488i
$406$		0			0
$407$	−27.0950			−1.34305
$408$		0			0
$409$	−2.23746	+	3.87539i	−0.110635	+	0.191626i	−0.916027	−	0.401118i	$-0.868622\pi$
$409$	−2.23746	+	3.87539i	−0.110635	+	0.191626i	0.805391	+	0.592743i	$0.201955\pi$
$410$		0			0
$411$	−0.192340	+	3.71025i	−0.00948744	+	0.183013i
$412$		0			0
$413$	5.55690	−	9.62483i	0.273437	−	0.473607i
$414$		0			0
$415$	−10.7500			−0.527697
$416$		0			0
$417$	−12.7465	−	8.26745i	−0.624201	−	0.404859i
$418$		0			0
$419$	−23.0891			−1.12798			−0.563988	−	0.825783i	$-0.690734\pi$
$419$	−23.0891			−1.12798			−0.563988	+	0.825783i	$0.690734\pi$
$420$		0			0
$421$	3.41595	−	5.91660i	0.166483	−	0.288357i	−0.770698	−	0.637201i	$-0.780092\pi$
$421$	3.41595	−	5.91660i	0.166483	−	0.288357i	0.937181	+	0.348843i	$0.113426\pi$
$422$		0			0
$423$	−3.07069	+	4.23652i	−0.149302	+	0.205987i
$424$		0			0
$425$	−7.96375			−0.386299
$426$		0			0
$427$	−42.6408			−2.06353
$428$		0			0
$429$	−22.7050	+	12.5604i	−1.09621	+	0.606422i
$430$		0			0
$431$	2.34407	−	4.06004i	0.112910	−	0.195565i	−0.804033	−	0.594585i	$-0.797316\pi$
$431$	2.34407	−	4.06004i	0.112910	−	0.195565i	0.916942	+	0.399020i	$0.130650\pi$
$432$		0			0
$433$	−8.67081	−	15.0183i	−0.416692	−	0.721732i	0.578912	−	0.815390i	$-0.303477\pi$
$433$	−8.67081	−	15.0183i	−0.416692	−	0.721732i	−0.995604	+	0.0936576i	$0.970144\pi$
$434$		0			0
$435$	5.54015	+	3.59336i	0.265630	+	0.172288i
$436$		0			0
$437$	2.32618	+	4.02907i	0.111277	+	0.192737i
$438$		0			0
$439$	−17.3274	−	30.0119i	−0.826990	−	1.43239i	−0.900389	−	0.435086i	$-0.856718\pi$
$439$	−17.3274	−	30.0119i	−0.826990	−	1.43239i	0.0733984	−	0.997303i	$-0.476616\pi$
$440$		0			0
$441$	−10.8252	−	1.12539i	−0.515487	−	0.0535900i
$442$		0			0
$443$	6.02528	−	10.4361i	0.286270	−	0.495834i	−0.686647	−	0.726991i	$-0.740918\pi$
$443$	6.02528	−	10.4361i	0.286270	−	0.495834i	0.972916	+	0.231158i	$0.0742513\pi$
$444$		0			0
$445$	22.7181			1.07694
$446$		0			0
$447$	11.8903	+	7.71206i	0.562390	+	0.364768i
$448$		0			0
$449$	−7.96171	−	13.7901i	−0.375737	−	0.650795i	0.614700	−	0.788761i	$-0.289277\pi$
$449$	−7.96171	−	13.7901i	−0.375737	−	0.650795i	−0.990437	+	0.137966i	$0.955944\pi$
$450$		0			0
$451$	13.8098	+	23.9192i	0.650276	+	1.12631i
$452$		0			0
$453$	−17.9948	−	11.6715i	−0.845468	−	0.548373i
$454$		0			0
$455$	21.7126	+	34.8570i	1.01790	+	1.63412i
$456$		0			0
$457$	11.8870	+	20.5889i	0.556051	+	0.963108i	0.997821	+	0.0659801i	$0.0210174\pi$
$457$	11.8870	+	20.5889i	0.556051	+	0.963108i	−0.441770	+	0.897128i	$0.645649\pi$
$458$		0			0
$459$	−5.35742	+	2.06697i	−0.250063	+	0.0964777i
$460$		0			0
$461$	−18.6163			−0.867046			−0.433523	−	0.901142i	$-0.642730\pi$
$461$	−18.6163			−0.867046			−0.433523	+	0.901142i	$0.642730\pi$
$462$		0			0
$463$	−5.18777	−	8.98549i	−0.241096	−	0.417591i	0.719931	−	0.694046i	$-0.244174\pi$
$463$	−5.18777	−	8.98549i	−0.241096	−	0.417591i	−0.961027	+	0.276455i	$0.910840\pi$
$464$		0			0
$465$	−7.48007	−	4.85160i	−0.346880	−	0.224988i
$466$		0			0
$467$	−10.1207			−0.468328			−0.234164	−	0.972197i	$-0.575235\pi$
$467$	−10.1207			−0.468328			−0.234164	+	0.972197i	$0.575235\pi$
$468$		0			0
$469$	32.5371			1.50242
$470$		0			0
$471$	32.6565	−	16.6626i	1.50473	−	0.767773i
$472$		0			0
$473$	23.4670	+	40.6461i	1.07901	+	1.86891i
$474$		0			0
$475$	−41.4841			−1.90342
$476$		0			0
$477$	−21.8923	−	2.27592i	−1.00238	−	0.104207i
$478$		0			0
$479$	1.97866	+	3.42713i	0.0904071	+	0.156590i	0.907682	−	0.419658i	$-0.137850\pi$
$479$	1.97866	+	3.42713i	0.0904071	+	0.156590i	−0.817275	+	0.576247i	$0.804517\pi$
$480$		0			0
$481$	11.0677	−	20.7445i	0.504645	−	0.945868i
$482$		0			0
$483$	−0.236250	+	4.55728i	−0.0107497	+	0.207363i
$484$		0			0
$485$	13.1274	+	22.7373i	0.596084	+	1.03245i
$486$		0			0
$487$	11.2053	+	19.4081i	0.507760	+	0.879466i	0.999960	+	0.00898379i	$0.00285967\pi$
$487$	11.2053	+	19.4081i	0.507760	+	0.879466i	−0.492200	+	0.870482i	$0.663807\pi$
$488$		0			0
$489$	−3.54753	+	1.81008i	−0.160425	+	0.0818549i
$490$		0			0
$491$	−2.20639			−0.0995730			−0.0497865	−	0.998760i	$-0.515854\pi$
$491$	−2.20639			−0.0995730			−0.0497865	+	0.998760i	$0.515854\pi$
$492$		0			0
$493$	0.602967	−	1.04437i	0.0271563	−	0.0470360i
$494$		0			0
$495$	25.5576	−	35.2609i	1.14873	−	1.58486i
$496$		0			0
$497$	25.2182	+	43.6792i	1.13119	+	1.95928i
$498$		0			0
$499$	−7.64022	−	13.2332i	−0.342023	−	0.592401i	0.642785	−	0.766046i	$-0.277779\pi$
$499$	−7.64022	−	13.2332i	−0.342023	−	0.592401i	−0.984808	+	0.173645i	$0.944445\pi$
$500$		0			0
$501$	0.257088	−	4.95925i	0.0114859	−	0.221563i
$502$		0			0
$503$	3.34762	+	5.79824i	0.149263	+	0.258531i	0.930955	−	0.365133i	$-0.118977\pi$
$503$	3.34762	+	5.79824i	0.149263	+	0.258531i	−0.781692	+	0.623664i	$0.785643\pi$
$504$		0			0
$505$	−10.1567	+	17.5920i	−0.451969	+	0.782834i
$506$		0			0
$507$	−0.342003	−	22.5141i	−0.0151889	−	0.999885i
$508$		0			0
$509$	−33.3335			−1.47748			−0.738741	−	0.673989i	$-0.764580\pi$
$509$	−33.3335			−1.47748			−0.738741	+	0.673989i	$0.764580\pi$
$510$		0			0
$511$	4.83069			0.213697
$512$		0			0
$513$	−27.9074	+	10.7671i	−1.23214	+	0.475377i
$514$		0			0
$515$	−27.6538	+	47.8978i	−1.21857	+	2.11063i
$516$		0			0
$517$	−7.24668			−0.318709
$518$		0			0
$519$	0.870852	−	16.7988i	0.0382262	−	0.737385i
$520$		0			0
$521$	−38.5782			−1.69014			−0.845072	−	0.534653i	$-0.820442\pi$
$521$	−38.5782			−1.69014			−0.845072	+	0.534653i	$0.820442\pi$
$522$		0			0
$523$	13.8573	−	24.0015i	0.605936	−	1.04951i	−0.385967	−	0.922513i	$-0.626132\pi$
$523$	13.8573	−	24.0015i	0.605936	−	1.04951i	0.991903	−	0.126999i	$-0.0405346\pi$
$524$		0			0
$525$	−34.1387	−	22.1424i	−1.48993	−	0.966375i
$526$		0			0
$527$	−0.814101	+	1.41006i	−0.0354628	+	0.0614233i
$528$		0			0
$529$	−22.3469			−0.971602
$530$		0			0
$531$	6.00208	−	8.28085i	0.260468	−	0.359358i
$532$		0			0
$533$	−23.9540	+	0.802560i	−1.03756	+	0.0347627i
$534$		0			0
$535$	44.7112			1.93303
$536$		0			0
$537$	20.9267	+	13.5731i	0.903054	+	0.585724i
$538$		0			0
$539$	−7.53678	−	13.0541i	−0.324632	−	0.562280i
$540$		0			0
$541$	−20.7927			−0.893948			−0.446974	−	0.894547i	$-0.647498\pi$
$541$	−20.7927			−0.893948			−0.446974	+	0.894547i	$0.647498\pi$
$542$		0			0
$543$	−0.914502	+	17.6408i	−0.0392451	+	0.757039i
$544$		0			0
$545$	27.5407	+	47.7019i	1.17971	+	2.04333i
$546$		0			0
$547$	17.6044	−	30.4917i	0.752709	−	1.30373i	−0.193797	−	0.981042i	$-0.562080\pi$
$547$	17.6044	−	30.4917i	0.752709	−	1.30373i	0.946505	−	0.322688i	$-0.104586\pi$
$548$		0			0
$549$	−39.0292	−	4.05746i	−1.66572	−	0.173168i
$550$		0			0
$551$	3.14092	−	5.44024i	0.133808	−	0.231762i
$552$		0			0
$553$	20.2434	−	35.0626i	0.860837	−	1.49101i
$554$		0			0
$555$	−2.04296	+	39.4088i	−0.0867188	+	1.67281i
$556$		0			0
$557$	−15.1215	+	26.1912i	−0.640720	+	1.10976i	0.344553	+	0.938767i	$0.388031\pi$
$557$	−15.1215	+	26.1912i	−0.640720	+	1.10976i	−0.985272	+	0.170992i	$0.945303\pi$
$558$		0			0
$559$	−40.7053	+	1.36380i	−1.72165	+	0.0576824i
$560$		0			0
$561$	−6.67241	−	4.32775i	−0.281710	−	0.182718i
$562$		0			0
$563$	−2.75421	+	4.77044i	−0.116076	+	0.201050i	−0.918209	−	0.396095i	$-0.870365\pi$
$563$	−2.75421	+	4.77044i	−0.116076	+	0.201050i	0.802133	+	0.597145i	$0.203698\pi$
$564$		0			0
$565$	−62.0407			−2.61007
$566$		0			0
$567$	−28.7129	−	6.03521i	−1.20583	−	0.253455i
$568$		0			0
$569$	19.7441	+	34.1979i	0.827717	+	1.43365i	0.899825	+	0.436252i	$0.143694\pi$
$569$	19.7441	+	34.1979i	0.827717	+	1.43365i	−0.0721073	+	0.997397i	$0.522972\pi$
$570$		0			0
$571$	12.3460	+	21.3840i	0.516665	+	0.894891i	0.999813	+	0.0193515i	$0.00616017\pi$
$571$	12.3460	+	21.3840i	0.516665	+	0.894891i	−0.483147	+	0.875539i	$0.660507\pi$
$572$		0			0
$573$	1.52546	−	29.4262i	0.0637271	−	1.22930i
$574$		0			0
$575$	−2.91197	+	5.04368i	−0.121437	+	0.210336i
$576$		0			0
$577$	31.8513			1.32599			0.662994	−	0.748625i	$-0.269286\pi$
$577$	31.8513			1.32599			0.662994	+	0.748625i	$0.269286\pi$
$578$		0			0
$579$	1.58914	−	30.6547i	0.0660425	−	1.27396i
$580$		0			0
$581$	−5.01545	+	8.68701i	−0.208076	+	0.360398i
$582$		0			0
$583$	−15.2419	−	26.3998i	−0.631256	−	1.09337i
$584$		0			0
$585$	16.5567	+	33.9707i	0.684537	+	1.40452i
$586$		0			0
$587$	15.5979	+	27.0163i	0.643793	+	1.11508i	0.984579	+	0.174941i	$0.0559734\pi$
$587$	15.5979	+	27.0163i	0.643793	+	1.11508i	−0.340786	+	0.940141i	$0.610693\pi$
$588$		0			0
$589$	−4.24074	+	7.34518i	−0.174737	+	0.302653i
$590$		0			0
$591$	−30.1170	−	19.5340i	−1.23885	−	0.803519i
$592$		0			0
$593$	−39.8104			−1.63482			−0.817409	−	0.576058i	$-0.804590\pi$
$593$	−39.8104			−1.63482			−0.817409	+	0.576058i	$0.804590\pi$
$594$		0			0
$595$	−6.29348	+	10.9006i	−0.258007	+	0.446882i
$596$		0			0
$597$	9.48453	−	4.83937i	0.388176	−	0.198062i
$598$		0			0
$599$	2.77344	+	4.80375i	0.113320	+	0.196276i	0.917107	−	0.398641i	$-0.130518\pi$
$599$	2.77344	+	4.80375i	0.113320	+	0.196276i	−0.803787	+	0.594917i	$0.797185\pi$
$600$		0			0
$601$	−15.9890	−	27.6937i	−0.652203	−	1.12965i	−0.982587	−	0.185803i	$-0.940511\pi$
$601$	−15.9890	−	27.6937i	−0.652203	−	1.12965i	0.330384	−	0.943847i	$-0.392822\pi$
$602$		0			0
$603$	29.7812	+	3.09605i	1.21278	+	0.126081i
$604$		0			0
$605$	21.8834			0.889688
$606$		0			0
$607$	14.2496	−	24.6810i	0.578372	−	1.00177i	−0.417295	−	0.908771i	$-0.637022\pi$
$607$	14.2496	−	24.6810i	0.578372	−	1.00177i	0.995666	−	0.0929978i	$-0.0296450\pi$
$608$		0			0
$609$	5.48854	−	2.80046i	0.222407	−	0.113481i
$610$		0			0
$611$	2.96011	−	5.54821i	0.119753	−	0.224456i
$612$		0			0
$613$	13.3338	−	23.0949i	0.538549	−	0.932793i	−0.460434	−	0.887694i	$-0.652306\pi$
$613$	13.3338	−	23.0949i	0.538549	−	0.932793i	0.998982	−	0.0450995i	$-0.0143605\pi$
$614$		0			0
$615$	35.8310	−	18.2823i	1.44484	−	0.737215i
$616$		0			0
$617$	1.52340	−	2.63861i	0.0613299	−	0.106226i	−0.833730	−	0.552172i	$-0.813799\pi$
$617$	1.52340	−	2.63861i	0.0613299	−	0.106226i	0.895060	+	0.445946i	$0.147133\pi$
$618$		0			0
$619$	3.60192	−	6.23871i	0.144774	−	0.250755i	−0.784515	−	0.620110i	$-0.787088\pi$
$619$	3.60192	−	6.23871i	0.144774	−	0.250755i	0.929288	+	0.369355i	$0.120421\pi$
$620$		0			0
$621$	−0.649885	+	4.14880i	−0.0260790	+	0.166486i
$622$		0			0
$623$	10.5992	−	18.3584i	0.424648	−	0.735512i
$624$		0			0
$625$	4.55040	+	7.88153i	0.182016	+	0.315261i
$626$		0			0
$627$	−34.7574	−	22.5437i	−1.38808	−	0.900310i
$628$		0			0
$629$	7.20658			0.287345
$630$		0			0
$631$	3.16229	+	5.47725i	0.125889	+	0.218046i	0.922080	−	0.386999i	$-0.126488\pi$
$631$	3.16229	+	5.47725i	0.125889	+	0.218046i	−0.796191	+	0.605045i	$0.793155\pi$
$632$		0			0
$633$	−0.210612	+	4.06272i	−0.00837109	+	0.161479i
$634$		0			0
$635$	73.8363			2.93011
$636$		0			0
$637$	13.0731	−	0.438003i	0.517975	−	0.0173543i
$638$		0			0
$639$	18.9260	+	42.3792i	0.748700	+	1.67650i
$640$		0			0
$641$	−34.7861			−1.37397			−0.686985	−	0.726672i	$-0.741066\pi$
$641$	−34.7861			−1.37397			−0.686985	+	0.726672i	$0.741066\pi$
$642$		0			0
$643$	7.43293	−	12.8742i	0.293126	−	0.507709i	−0.681421	−	0.731891i	$-0.738638\pi$
$643$	7.43293	−	12.8742i	0.293126	−	0.507709i	0.974547	+	0.224182i	$0.0719711\pi$
$644$		0			0
$645$	60.8878	−	31.0673i	2.39746	−	1.22327i
$646$		0			0
$647$	16.6248	−	28.7950i	0.653587	−	1.13205i	−0.328658	−	0.944449i	$-0.606597\pi$
$647$	16.6248	−	28.7950i	0.653587	−	1.13205i	0.982246	−	0.187598i	$-0.0600702\pi$
$648$		0			0
$649$	14.1646			0.556010
$650$		0			0
$651$	−7.41040	+	3.78107i	−0.290436	+	0.148192i
$652$		0			0
$653$	8.26905			0.323593			0.161796	−	0.986824i	$-0.448271\pi$
$653$	8.26905			0.323593			0.161796	+	0.986824i	$0.448271\pi$
$654$		0			0
$655$	−3.17657	+	5.50199i	−0.124119	+	0.214980i
$656$		0			0
$657$	4.42154	+	0.459662i	0.172501	+	0.0179331i
$658$		0			0
$659$	−17.8429			−0.695062			−0.347531	−	0.937669i	$-0.612980\pi$
$659$	−17.8429			−0.695062			−0.347531	+	0.937669i	$0.612980\pi$
$660$		0			0
$661$	30.9102			1.20227			0.601134	−	0.799148i	$-0.294716\pi$
$661$	30.9102			1.20227			0.601134	+	0.799148i	$0.294716\pi$
$662$		0			0
$663$	6.03895	−	3.34075i	0.234533	−	0.129744i
$664$		0			0
$665$	−32.7834	+	56.7826i	−1.27129	+	2.20193i
$666$		0			0
$667$	−0.440953	−	0.763753i	−0.0170738	−	0.0295726i
$668$		0			0
$669$	−26.2990	+	13.4188i	−1.01678	+	0.518800i
$670$		0			0
$671$	−27.1730	−	47.0650i	−1.04900	−	1.81693i
$672$		0			0
$673$	5.95868	+	10.3207i	0.229690	+	0.397835i	0.957716	−	0.287714i	$-0.0928954\pi$
$673$	5.95868	+	10.3207i	0.229690	+	0.397835i	−0.728026	+	0.685549i	$0.759562\pi$
$674$		0			0
$675$	−29.1402	−	23.5154i	−1.12161	−	0.905110i
$676$		0			0
$677$	7.28262	−	12.6139i	0.279894	−	0.484790i	−0.691464	−	0.722411i	$-0.743034\pi$
$677$	7.28262	−	12.6139i	0.279894	−	0.484790i	0.971358	+	0.237620i	$0.0763674\pi$
$678$		0			0
$679$	24.4985			0.940166
$680$		0			0
$681$	−0.773842	+	14.9275i	−0.0296537	+	0.572021i
$682$		0			0
$683$	20.2410	+	35.0584i	0.774500	+	1.34147i	0.935075	+	0.354449i	$0.115332\pi$
$683$	20.2410	+	35.0584i	0.774500	+	1.34147i	−0.160576	+	0.987024i	$0.551335\pi$
$684$		0			0
$685$	3.74703	+	6.49005i	0.143167	+	0.247972i
$686$		0			0
$687$	−33.9395	+	17.3173i	−1.29487	+	0.660695i
$688$		0			0
$689$	26.4382	−	0.885791i	1.00722	−	0.0337459i
$690$		0			0
$691$	17.9488	+	31.0883i	0.682805	+	1.18265i	0.974121	+	0.226026i	$0.0725736\pi$
$691$	17.9488	+	31.0883i	0.682805	+	1.18265i	−0.291316	+	0.956627i	$0.594093\pi$
$692$		0			0
$693$	−16.5701	−	37.1040i	−0.629447	−	1.40946i
$694$		0			0
$695$	−30.6459			−1.16247
$696$		0			0
$697$	−3.67305	−	6.36190i	−0.139127	−	0.240974i
$698$		0			0
$699$	−0.791383	+	15.2658i	−0.0299328	+	0.577406i
$700$		0			0
$701$	47.7682			1.80418			0.902090	−	0.431549i	$-0.142033\pi$
$701$	47.7682			1.80418			0.902090	+	0.431549i	$0.142033\pi$
$702$		0			0
$703$	37.5399			1.41584
$704$		0			0
$705$	−0.546399	+	10.5401i	−0.0205786	+	0.396962i
$706$		0			0
$707$	9.47732	+	16.4152i	0.356431	+	0.617357i
$708$		0			0
$709$	23.4567			0.880936			0.440468	−	0.897768i	$-0.354812\pi$
$709$	23.4567			0.880936			0.440468	+	0.897768i	$0.354812\pi$
$710$		0			0
$711$	21.8652	−	30.1666i	0.820009	−	1.13134i
$712$		0			0
$713$	0.595356	+	1.03119i	0.0222963	+	0.0386183i
$714$		0			0
$715$	−24.6372	+	46.1782i	−0.921381	+	1.72697i
$716$		0			0
$717$	−21.1312	+	10.7820i	−0.789160	+	0.402660i
$718$		0			0
$719$	−20.1360	−	34.8766i	−0.750947	−	1.30068i	−0.947364	−	0.320158i	$-0.896264\pi$
$719$	−20.1360	−	34.8766i	−0.750947	−	1.30068i	0.196417	−	0.980520i	$-0.437069\pi$
$720$		0			0
$721$	25.8039	+	44.6937i	0.960988	+	1.66448i
$722$		0			0
$723$	−0.966254	+	18.6391i	−0.0359354	+	0.693195i
$724$		0			0
$725$	7.86375			0.292052
$726$		0			0
$727$	18.7386	−	32.4562i	0.694976	−	1.20373i	−0.275213	−	0.961383i	$-0.588748\pi$
$727$	18.7386	−	32.4562i	0.694976	−	1.20373i	0.970189	−	0.242350i	$-0.0779183\pi$
$728$		0			0
$729$	−25.7067	−	8.25620i	−0.952101	−	0.305785i
$730$		0			0
$731$	−6.24163	−	10.8108i	−0.230855	−	0.399853i
$732$		0			0
$733$	4.76007	+	8.24469i	0.175817	+	0.304524i	0.940444	−	0.339949i	$-0.110410\pi$
$733$	4.76007	+	8.24469i	0.175817	+	0.304524i	−0.764627	+	0.644474i	$0.777077\pi$
$734$		0			0
$735$	−19.5550	+	9.97773i	−0.721298	+	0.368034i
$736$		0			0
$737$	20.7344	+	35.9130i	0.763761	+	1.32287i
$738$		0			0
$739$	−5.50057	+	9.52726i	−0.202342	+	0.350466i	−0.949282	−	0.314424i	$-0.898188\pi$
$739$	−5.50057	+	9.52726i	−0.202342	+	0.350466i	0.746941	+	0.664891i	$0.231522\pi$
$740$		0			0
$741$	31.4576	−	17.4023i	1.15562	−	0.639291i
$742$		0			0
$743$	10.0202			0.367606			0.183803	−	0.982963i	$-0.441159\pi$
$743$	10.0202			0.367606			0.183803	+	0.982963i	$0.441159\pi$
$744$		0			0
$745$	28.5872			1.04735
$746$		0			0
$747$	−5.41726	+	7.47399i	−0.198207	+	0.273459i
$748$		0			0
$749$	20.8601	−	36.1308i	0.762213	−	1.32019i
$750$		0			0
$751$	−13.8520			−0.505467			−0.252734	−	0.967536i	$-0.581330\pi$
$751$	−13.8520			−0.505467			−0.252734	+	0.967536i	$0.581330\pi$
$752$		0			0
$753$	−30.2505	+	15.4350i	−1.10239	+	0.562481i
$754$		0			0
$755$	−43.2640			−1.57454
$756$		0			0
$757$	5.21869	−	9.03903i	0.189676	−	0.328529i	−0.755466	−	0.655188i	$-0.772589\pi$
$757$	5.21869	−	9.03903i	0.189676	−	0.328529i	0.945142	+	0.326659i	$0.105923\pi$
$758$		0			0
$759$	−5.18067	+	2.64338i	−0.188047	+	0.0959486i
$760$		0			0
$761$	13.5198	−	23.4170i	0.490093	−	0.848866i	−0.509842	−	0.860268i	$-0.670296\pi$
$761$	13.5198	−	23.4170i	0.490093	−	0.848866i	0.999935	+	0.0114020i	$0.00362946\pi$
$762$		0			0
$763$	51.3968			1.86069
$764$		0			0
$765$	−6.79767	+	9.37850i	−0.245770	+	0.339080i
$766$		0			0
$767$	−5.78594	+	10.8447i	−0.208918	+	0.391580i
$768$		0			0
$769$	−40.1404			−1.44750			−0.723750	−	0.690062i	$-0.757583\pi$
$769$	−40.1404			−1.44750			−0.723750	+	0.690062i	$0.757583\pi$
$770$		0			0
$771$	−2.48251	+	47.8878i	−0.0894054	+	1.72464i
$772$		0			0
$773$	−11.8314	−	20.4926i	−0.425546	−	0.737067i	0.570925	−	0.821002i	$-0.306585\pi$
$773$	−11.8314	−	20.4926i	−0.425546	−	0.737067i	−0.996471	+	0.0839349i	$0.973251\pi$
$774$		0			0
$775$	−10.6173			−0.381385
$776$		0			0
$777$	30.8929	+	20.0372i	1.10828	+	0.718831i
$778$		0			0
$779$	−19.1333	−	33.1399i	−0.685522	−	1.18736i
$780$		0			0
$781$	−32.1408	+	55.6695i	−1.15009	+	1.99201i
$782$		0			0
$783$	5.29014	−	2.04101i	0.189054	−	0.0729397i
$784$		0			0
$785$	36.9756	−	64.0437i	1.31972	−	2.28582i
$786$		0			0
$787$	10.1504	−	17.5811i	0.361824	−	0.626698i	−0.626437	−	0.779472i	$-0.715487\pi$
$787$	10.1504	−	17.5811i	0.361824	−	0.626698i	0.988261	+	0.152774i	$0.0488206\pi$
$788$		0			0
$789$	36.4859	−	18.6165i	1.29893	−	0.662766i
$790$		0			0
$791$	−28.9453	+	50.1347i	−1.02918	+	1.78258i
$792$		0			0
$793$	47.1336	−	1.57917i	1.67376	−	0.0560780i
$794$		0			0
$795$	−39.5469	+	20.1784i	−1.40258	+	0.715653i
$796$		0			0
$797$	4.07456	−	7.05735i	0.144328	−	0.249984i	−0.784794	−	0.619757i	$-0.787231\pi$
$797$	4.07456	−	7.05735i	0.144328	−	0.249984i	0.929122	+	0.369773i	$0.120565\pi$
$798$		0			0
$799$	1.92743			0.0681877
$800$		0			0
$801$	11.4483	−	15.7949i	0.404507	−	0.558084i
$802$		0			0
$803$	3.07838	+	5.33191i	0.108634	+	0.188159i
$804$		0			0
$805$	4.60245	+	7.97168i	0.162215	+	0.280965i
$806$		0			0
$807$	−4.19519	+	2.14055i	−0.147678	+	0.0753509i
$808$		0			0
$809$	5.64102	−	9.77053i	0.198328	−	0.343513i	−0.749659	−	0.661825i	$-0.769782\pi$
$809$	5.64102	−	9.77053i	0.198328	−	0.343513i	0.947986	+	0.318311i	$0.103116\pi$
$810$		0			0
$811$	12.5271			0.439884			0.219942	−	0.975513i	$-0.429413\pi$
$811$	12.5271			0.439884			0.219942	+	0.975513i	$0.429413\pi$
$812$		0			0
$813$	−2.37066	−	1.53762i	−0.0831427	−	0.0539266i
$814$		0			0
$815$	−4.01672	+	6.95716i	−0.140699	+	0.243699i
$816$		0			0
$817$	−32.5134	−	56.3148i	−1.13750	−	1.97021i
$818$		0			0
$819$	35.1761	+	2.46975i	1.22915	+	0.0863001i
$820$		0			0
$821$	12.0938	+	20.9470i	0.422076	+	0.731057i	0.996142	−	0.0877518i	$-0.0279683\pi$
$821$	12.0938	+	20.9470i	0.422076	+	0.731057i	−0.574067	+	0.818809i	$0.694635\pi$
$822$		0			0
$823$	−1.31155	+	2.27167i	−0.0457177	+	0.0791855i	−0.887979	−	0.459884i	$-0.847891\pi$
$823$	−1.31155	+	2.27167i	−0.0457177	+	0.0791855i	0.842261	+	0.539070i	$0.181224\pi$
$824$		0			0
$825$	2.68486	−	51.7911i	0.0934749	−	1.80314i
$826$		0			0
$827$	47.9894			1.66875			0.834377	−	0.551195i	$-0.185828\pi$
$827$	47.9894			1.66875			0.834377	+	0.551195i	$0.185828\pi$
$828$		0			0
$829$	−0.761001	+	1.31809i	−0.0264306	+	0.0457792i	−0.878938	−	0.476936i	$-0.841747\pi$
$829$	−0.761001	+	1.31809i	−0.0264306	+	0.0457792i	0.852508	+	0.522715i	$0.175081\pi$
$830$		0			0
$831$	−0.781058	+	15.0666i	−0.0270946	+	0.522656i
$832$		0			0
$833$	2.00459	+	3.47206i	0.0694550	+	0.120300i
$834$		0			0
$835$	−5.00841	−	8.67482i	−0.173323	−	0.300205i
$836$		0			0
$837$	−7.14253	+	2.75569i	−0.246882	+	0.0952505i
$838$		0			0
$839$	−47.7459			−1.64837			−0.824185	−	0.566320i	$-0.808366\pi$
$839$	−47.7459			−1.64837			−0.824185	+	0.566320i	$0.808366\pi$
$840$		0			0
$841$	13.9046	−	24.0835i	0.479469	−	0.830465i
$842$		0			0
$843$	4.24035	+	2.75031i	0.146045	+	0.0947256i
$844$		0			0
$845$	−25.2912	−	37.7256i	−0.870043	−	1.29780i
$846$		0			0
$847$	10.2098	−	17.6839i	0.350812	−	0.607625i
$848$		0			0
$849$	2.48348	−	47.9064i	0.0852327	−	1.64414i
$850$		0			0
$851$	2.63511	−	4.56414i	0.0903303	−	0.156457i
$852$		0			0
$853$	−24.6570	+	42.7072i	−0.844241	+	1.46227i	0.0420383	+	0.999116i	$0.486615\pi$
$853$	−24.6570	+	42.7072i	−0.844241	+	1.46227i	−0.886279	+	0.463152i	$0.846718\pi$
$854$		0			0
$855$	−35.4098	+	48.8537i	−1.21099	+	1.67076i
$856$		0			0
$857$	9.82724	−	17.0213i	0.335692	−	0.581436i	−0.647925	−	0.761704i	$-0.724363\pi$
$857$	9.82724	−	17.0213i	0.335692	−	0.581436i	0.983618	+	0.180268i	$0.0576965\pi$
$858$		0			0
$859$	−1.87497	−	3.24755i	−0.0639732	−	0.110805i	0.832265	−	0.554378i	$-0.187044\pi$
$859$	−1.87497	−	3.24755i	−0.0639732	−	0.110805i	−0.896238	+	0.443573i	$0.853711\pi$
$860$		0			0
$861$	1.94320	−	37.4845i	0.0662241	−	1.27747i
$862$		0			0
$863$	−24.8648			−0.846407			−0.423203	−	0.906035i	$-0.639094\pi$
$863$	−24.8648			−0.846407			−0.423203	+	0.906035i	$0.639094\pi$
$864$		0			0
$865$	−16.9653	−	29.3848i	−0.576838	−	0.999113i
$866$		0			0
$867$	−22.9289	−	14.8718i	−0.778707	−	0.505072i
$868$		0			0
$869$	51.6008			1.75044
$870$		0			0
$871$	−35.9653	+	1.20499i	−1.21864	+	0.0408294i
$872$		0			0
$873$	22.4235	+	2.33114i	0.758921	+	0.0788972i
$874$		0			0
$875$	−25.1292			−0.849521
$876$		0			0
$877$	1.22672	−	2.12474i	0.0414233	−	0.0717472i	−0.844570	−	0.535444i	$-0.820144\pi$
$877$	1.22672	−	2.12474i	0.0414233	−	0.0717472i	0.885994	+	0.463697i	$0.153477\pi$
$878$		0			0
$879$	−17.5926	−	11.4106i	−0.593385	−	0.384871i
$880$		0			0
$881$	13.2745	−	22.9922i	0.447230	−	0.774625i	−0.550974	−	0.834522i	$-0.685744\pi$
$881$	13.2745	−	22.9922i	0.447230	−	0.774625i	0.998205	+	0.0598968i	$0.0190772\pi$
$882$		0			0
$883$	8.86518			0.298337			0.149169	−	0.988812i	$-0.452340\pi$
$883$	8.86518			0.298337			0.149169	+	0.988812i	$0.452340\pi$
$884$		0			0
$885$	1.06801	−	20.6020i	0.0359008	−	0.692528i
$886$		0			0
$887$	−23.2991			−0.782306			−0.391153	−	0.920326i	$-0.627924\pi$
$887$	−23.2991			−0.782306			−0.391153	+	0.920326i	$0.627924\pi$
$888$		0			0
$889$	34.4486	−	59.6667i	1.15537	−	2.00116i
$890$		0			0
$891$	−11.6360	−	35.5381i	−0.389822	−	1.19057i
$892$		0			0
$893$	10.0402			0.335983
$894$		0			0
$895$	50.3131			1.68178
$896$		0			0
$897$	0.0923667	−	5.04620i	0.00308404	−	0.168488i
$898$		0			0
$899$	0.803878	−	1.39236i	0.0268108	−	0.0464377i
$900$		0			0
$901$	4.05397	+	7.02168i	0.135057	+	0.233926i
$902$		0			0
$903$	3.30210	−	63.6976i	0.109887	−	2.11972i
$904$		0			0
$905$	17.8157	+	30.8577i	0.592213	+	1.02574i
$906$		0			0
$907$	6.34404	+	10.9882i	0.210650	+	0.364857i	0.951918	−	0.306352i	$-0.0991085\pi$
$907$	6.34404	+	10.9882i	0.210650	+	0.364857i	−0.741268	+	0.671209i	$0.765775\pi$
$908$		0			0
$909$	7.11263	+	15.9267i	0.235911	+	0.528254i
$910$		0			0
$911$	0.714408	−	1.23739i	0.0236694	−	0.0409966i	−0.853948	−	0.520358i	$-0.825798\pi$
$911$	0.714408	−	1.23739i	0.0236694	−	0.0409966i	0.877617	+	0.479362i	$0.159132\pi$
$912$		0			0
$913$	−12.7845			−0.423104
$914$		0			0
$915$	−70.5034	+	35.9736i	−2.33077	+	1.18925i
$916$		0			0
$917$	2.96408	+	5.13394i	0.0978825	+	0.169538i
$918$		0			0
$919$	−16.1627	−	27.9946i	−0.533158	−	0.923456i	−0.999250	−	0.0387201i	$-0.987672\pi$
$919$	−16.1627	−	27.9946i	−0.533158	−	0.923456i	0.466092	−	0.884736i	$-0.345661\pi$
$920$		0			0
$921$	1.94561	−	37.5309i	0.0641100	−	1.23669i
$922$		0			0
$923$	−29.4929	−	47.3474i	−0.970770	−	1.55846i
$924$		0			0
$925$	23.4966	+	40.6974i	0.772564	+	1.33812i
$926$		0			0
$927$	19.3656	+	43.3636i	0.636048	+	1.42425i
$928$		0			0
$929$	15.0290			0.493085			0.246542	−	0.969132i	$-0.420706\pi$
$929$	15.0290			0.493085			0.246542	+	0.969132i	$0.420706\pi$
$930$		0			0
$931$	10.4422	+	18.0863i	0.342228	+	0.592756i
$932$		0			0
$933$	−42.2097	+	21.5370i	−1.38188	+	0.705091i
$934$		0			0
$935$	−16.0422			−0.524635
$936$		0			0
$937$	3.69756			0.120794			0.0603970	−	0.998174i	$-0.480763\pi$
$937$	3.69756			0.120794			0.0603970	+	0.998174i	$0.480763\pi$
$938$		0			0
$939$	16.6760	+	10.8161i	0.544201	+	0.352970i
$940$		0			0
$941$	−1.16379	−	2.01574i	−0.0379384	−	0.0657112i	0.846433	−	0.532496i	$-0.178746\pi$
$941$	−1.16379	−	2.01574i	−0.0379384	−	0.0657112i	−0.884371	+	0.466784i	$0.845412\pi$
$942$		0			0
$943$	−5.37224			−0.174944
$944$		0			0
$945$	−55.2160	+	21.3031i	−1.79618	+	0.692989i
$946$		0			0
$947$	−19.3378	−	33.4940i	−0.628393	−	1.08841i	−0.987874	−	0.155257i	$-0.950380\pi$
$947$	−19.3378	−	33.4940i	−0.628393	−	1.08841i	0.359481	−	0.933152i	$-0.382954\pi$
$948$		0			0
$949$	−5.33967	+	0.178901i	−0.173333	+	0.00580738i
$950$		0			0
$951$	−48.0764	−	31.1825i	−1.55898	−	1.01116i
$952$		0			0
$953$	−18.4777	−	32.0043i	−0.598550	−	1.03672i	−0.993035	−	0.117817i	$-0.962410\pi$
$953$	−18.4777	−	32.0043i	−0.598550	−	1.03672i	0.394485	−	0.918902i	$-0.370923\pi$
$954$		0			0
$955$	−29.7180	−	51.4730i	−0.961650	−	1.66563i
$956$		0			0
$957$	6.58863	+	4.27340i	0.212980	+	0.138140i
$958$		0			0
$959$	6.99275			0.225808
$960$		0			0
$961$	14.4146	−	24.9669i	0.464988	−	0.805383i
$962$		0			0
$963$	22.5313	−	31.0857i	0.726062	−	1.00172i
$964$		0			0
$965$	−30.9585	−	53.6218i	−0.996591	−	1.72615i
$966$		0			0
$967$	−21.6462	−	37.4923i	−0.696094	−	1.20567i	−0.969810	−	0.243860i	$-0.921586\pi$
$967$	−21.6462	−	37.4923i	−0.696094	−	1.20567i	0.273716	−	0.961811i	$-0.411747\pi$
$968$		0			0
$969$	9.24458	+	5.99606i	0.296979	+	0.192621i
$970$		0			0
$971$	24.4287	+	42.3117i	0.783954	+	1.35785i	0.929622	+	0.368515i	$0.120134\pi$
$971$	24.4287	+	42.3117i	0.783954	+	1.35785i	−0.145668	+	0.989334i	$0.546533\pi$
$972$		0			0
$973$	−14.2979	+	24.7648i	−0.458371	+	0.793922i
$974$		0			0
$975$	38.5557	+	23.2111i	1.23477	+	0.743352i
$976$		0			0
$977$	−33.9666			−1.08669			−0.543345	−	0.839510i	$-0.682842\pi$
$977$	−33.9666			−1.08669			−0.543345	+	0.839510i	$0.682842\pi$
$978$		0			0
$979$	27.0175			0.863485
$980$		0			0
$981$	47.0436	+	4.89064i	1.50199	+	0.156146i
$982$		0			0
$983$	17.3063	−	29.9754i	0.551985	−	0.956067i	−0.446146	−	0.894960i	$-0.647204\pi$
$983$	17.3063	−	29.9754i	0.551985	−	0.956067i	0.998131	−	0.0611065i	$-0.0194629\pi$
$984$		0			0
$985$	−72.4088			−2.30714
$986$		0			0
$987$	8.26243	+	5.35904i	0.262996	+	0.170580i
$988$		0			0
$989$	−9.12908			−0.290288
$990$		0			0
$991$	9.40338	−	16.2871i	0.298708	−	0.517378i	−0.677132	−	0.735861i	$-0.736778\pi$
$991$	9.40338	−	16.2871i	0.298708	−	0.517378i	0.975841	+	0.218483i	$0.0701109\pi$
$992$		0			0
$993$	0.463468	−	8.94033i	0.0147077	−	0.283713i
$994$		0			0
$995$	10.7389	−	18.6004i	0.340447	−	0.589672i
$996$		0			0
$997$	7.20534			0.228196			0.114098	−	0.993470i	$-0.463602\pi$
$997$	7.20534			0.228196			0.114098	+	0.993470i	$0.463602\pi$
$998$		0			0
$999$	26.3696	+	21.2797i	0.834299	+	0.673259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.s.f.529.11	yes	40
3.2	odd	2		2808.2.s.f.1153.18		40
9.4	even	3		936.2.r.f.841.17	yes	40
9.5	odd	6		2808.2.r.f.2089.18		40
13.3	even	3		936.2.r.f.601.17	✓	40
39.29	odd	6		2808.2.r.f.289.18		40
117.68	odd	6		2808.2.s.f.1225.18		40
117.94	even	3	inner	936.2.s.f.913.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.r.f.601.17	✓	40	13.3	even	3
936.2.r.f.841.17	yes	40	9.4	even	3
936.2.s.f.529.11	yes	40	1.1	even	1	trivial
936.2.s.f.913.11	yes	40	117.94	even	3	inner
2808.2.r.f.289.18		40	39.29	odd	6
2808.2.r.f.2089.18		40	9.5	odd	6
2808.2.s.f.1153.18		40	3.2	odd	2
2808.2.s.f.1225.18		40	117.68	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.0896694 - 1.72973i) q^{3} +(-1.74688 - 3.02568i) q^{5} -3.26004 q^{7} +(-2.98392 - 0.310207i) q^{9} +(-2.07747 - 3.59829i) q^{11} +(3.60353 - 0.120733i) q^{13} +(-5.39024 + 2.75031i) q^{15} +(0.552555 + 0.957054i) q^{17} +(2.87832 + 4.98540i) q^{19} +(-0.292326 + 5.63898i) q^{21} +0.808173 q^{23} +(-3.60315 + 6.24083i) q^{25} +(-0.804141 + 5.13355i) q^{27} +(-0.545617 - 0.945036i) q^{29} +(0.736669 + 1.27595i) q^{31} +(-6.41035 + 3.27081i) q^{33} +(5.69488 + 9.86383i) q^{35} +(3.26057 - 5.64747i) q^{37} +(0.114291 - 6.24395i) q^{39} -6.64738 q^{41} -11.2959 q^{43} +(4.27395 + 9.57027i) q^{45} +(0.872054 - 1.51044i) q^{47} +3.62786 q^{49} +(1.70499 - 0.869952i) q^{51} +7.33676 q^{53} +(-7.25818 + 12.5715i) q^{55} +(8.88149 - 4.53168i) q^{57} +(-1.70455 + 2.95236i) q^{59} +13.0798 q^{61} +(9.72769 + 1.01129i) q^{63} +(-6.66022 - 10.6922i) q^{65} -9.98057 q^{67} +(0.0724685 - 1.39792i) q^{69} +(-7.73554 - 13.3984i) q^{71} -1.48179 q^{73} +(10.4719 + 6.79208i) q^{75} +(6.77265 + 11.7306i) q^{77} +(-6.20956 + 10.7553i) q^{79} +(8.80754 + 1.85127i) q^{81} +(1.53846 - 2.66470i) q^{83} +(1.93049 - 3.34371i) q^{85} +(-1.68358 + 0.859028i) q^{87} +(-3.25125 + 5.63133i) q^{89} +(-11.7476 + 0.393595i) q^{91} +(2.27310 - 1.15982i) q^{93} +(10.0561 - 17.4178i) q^{95} -7.51478 q^{97} +(5.08280 + 11.3815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{3} + q^{5} - 14 q^{7} - 9 q^{9} - 3 q^{13} + 2 q^{15} - q^{17} + 2 q^{19} - 30 q^{21} + 2 q^{23} - 23 q^{25} - 3 q^{27} + 12 q^{29} + 8 q^{31} - 5 q^{33} - 12 q^{35} + 18 q^{37} - 6 q^{39}+ \cdots + 28 q^{99}+O(q^{100}) \) 40 * q - 3 * q^3 + q^5 - 14 * q^7 - 9 * q^9 - 3 * q^13 + 2 * q^15 - q^17 + 2 * q^19 - 30 * q^21 + 2 * q^23 - 23 * q^25 - 3 * q^27 + 12 * q^29 + 8 * q^31 - 5 * q^33 - 12 * q^35 + 18 * q^37 - 6 * q^39 + 6 * q^41 - 16 * q^43 - 3 * q^45 + 4 * q^47 + 46 * q^49 - 37 * q^51 - 40 * q^53 - 14 * q^55 + 7 * q^57 - 4 * q^59 + 6 * q^61 - 8 * q^63 + 7 * q^65 - 54 * q^67 + 19 * q^69 + q^71 - 12 * q^73 - 28 * q^75 - 4 * q^77 + 13 * q^79 - 13 * q^81 - 15 * q^83 + 5 * q^85 + 37 * q^87 + 12 * q^89 - 57 * q^91 - 22 * q^93 + q^95 - 70 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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