LMFDB - Embedded newform 572.2.bg.a.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.2
Character	$\chi$	$=$	572.81
Dual form			572.2.bg.a.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59692 + 0.551993i) q^{3} +(1.71674 - 1.24728i) q^{5} +(-1.20270 - 0.255642i) q^{7} +(3.69867 - 1.64675i) q^{9} +O(q^{10})$	\(q+(-2.59692 + 0.551993i) q^{3} +(1.71674 - 1.24728i) q^{5} +(-1.20270 - 0.255642i) q^{7} +(3.69867 - 1.64675i) q^{9} +(2.14611 + 2.52868i) q^{11} +(-3.44761 + 1.05544i) q^{13} +(-3.76974 + 4.18672i) q^{15} +(-0.623261 - 5.92993i) q^{17} +(0.391593 + 0.434908i) q^{19} +3.26444 q^{21} +(-4.08829 - 7.08112i) q^{23} +(-0.153613 + 0.472771i) q^{25} +(-2.25249 + 1.63653i) q^{27} +(7.02874 - 7.80620i) q^{29} +(0.860931 + 0.625503i) q^{31} +(-6.96909 - 5.38214i) q^{33} +(-2.38358 + 1.06124i) q^{35} +(7.22297 - 8.02192i) q^{37} +(8.37059 - 4.64396i) q^{39} +(6.35069 - 1.34988i) q^{41} +(3.62268 - 6.27466i) q^{43} +(4.29568 - 7.44033i) q^{45} +(-3.05245 + 9.39447i) q^{47} +(-5.01368 - 2.23223i) q^{49} +(4.89184 + 15.0555i) q^{51} +(-5.31589 - 3.86222i) q^{53} +(6.83828 + 1.66427i) q^{55} +(-1.25700 - 0.913265i) q^{57} +(-9.56452 - 2.03300i) q^{59} +(-0.460871 - 4.38489i) q^{61} +(-4.86938 + 1.03502i) q^{63} +(-4.60221 + 6.11206i) q^{65} +(-3.58294 - 6.20584i) q^{67} +(14.5257 + 16.1324i) q^{69} +(-0.763579 - 7.26497i) q^{71} +(2.04795 + 6.30294i) q^{73} +(0.137954 - 1.31254i) q^{75} +(-1.93469 - 3.58988i) q^{77} +(-4.52358 - 3.28657i) q^{79} +(-3.18114 + 3.53301i) q^{81} +(8.13441 - 5.91000i) q^{83} +(-8.46627 - 9.40275i) q^{85} +(-13.9441 + 24.1519i) q^{87} +(4.51751 + 7.82455i) q^{89} +(4.41627 - 0.388026i) q^{91} +(-2.58104 - 1.14915i) q^{93} +(1.21471 + 0.258196i) q^{95} +(-1.65210 + 0.735564i) q^{97} +(12.1019 + 5.81863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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
$3$	−2.59692	+	0.551993i	−1.49933	+	0.318693i	−0.883218	−	0.468963i	$-0.844628\pi$
$3$	−2.59692	+	0.551993i	−1.49933	+	0.318693i	−0.616115	+	0.787656i	$0.711295\pi$
$4$		0			0
$5$	1.71674	−	1.24728i	0.767748	−	0.557802i	−0.133529	−	0.991045i	$-0.542631\pi$
$5$	1.71674	−	1.24728i	0.767748	−	0.557802i	0.901277	+	0.433243i	$0.142631\pi$
$6$		0			0
$7$	−1.20270	−	0.255642i	−0.454579	−	0.0966237i	−0.0250685	−	0.999686i	$-0.507980\pi$
$7$	−1.20270	−	0.255642i	−0.454579	−	0.0966237i	−0.429510	+	0.903062i	$0.641314\pi$
$8$		0			0
$9$	3.69867	−	1.64675i	1.23289	−	0.548918i
$10$		0			0
$11$	2.14611	+	2.52868i	0.647077	+	0.762425i
$11$	2.14611	+	2.52868i	0.647077	+	0.762425i
$12$		0			0
$13$	−3.44761	+	1.05544i	−0.956196	+	0.292727i
$13$	−3.44761	+	1.05544i	−0.956196	+	0.292727i
$14$		0			0
$15$	−3.76974	+	4.18672i	−0.973343	+	1.08101i
$16$		0			0
$17$	−0.623261	−	5.92993i	−0.151163	−	1.43822i	−0.762571	−	0.646904i	$-0.776063\pi$
$17$	−0.623261	−	5.92993i	−0.151163	−	1.43822i	0.611409	−	0.791315i	$-0.290603\pi$
$18$		0			0
$19$	0.391593	+	0.434908i	0.0898375	+	0.0997747i	0.786387	−	0.617734i	$-0.211949\pi$
$19$	0.391593	+	0.434908i	0.0898375	+	0.0997747i	−0.696550	+	0.717509i	$0.745282\pi$
$20$		0			0
$21$	3.26444			0.712358
$22$		0			0
$23$	−4.08829	−	7.08112i	−0.852467	−	1.47652i	−0.878975	−	0.476868i	$-0.841772\pi$
$23$	−4.08829	−	7.08112i	−0.852467	−	1.47652i	0.0265079	−	0.999649i	$-0.491561\pi$
$24$		0			0
$25$	−0.153613	+	0.472771i	−0.0307225	+	0.0945542i
$26$		0			0
$27$	−2.25249	+	1.63653i	−0.433492	+	0.314950i
$28$		0			0
$29$	7.02874	−	7.80620i	1.30520	−	1.44958i	0.488446	−	0.872594i	$-0.337564\pi$
$29$	7.02874	−	7.80620i	1.30520	−	1.44958i	0.816757	−	0.576981i	$-0.195770\pi$
$30$		0			0
$31$	0.860931	+	0.625503i	0.154628	+	0.112344i	0.662409	−	0.749142i	$-0.269534\pi$
$31$	0.860931	+	0.625503i	0.154628	+	0.112344i	−0.507781	+	0.861486i	$0.669534\pi$
$32$		0			0
$33$	−6.96909	−	5.38214i	−1.21316	−	0.936910i
$34$		0			0
$35$	−2.38358	+	1.06124i	−0.402899	+	0.179382i
$36$		0			0
$37$	7.22297	−	8.02192i	1.18745	−	1.31880i	0.251002	−	0.967987i	$-0.419240\pi$
$37$	7.22297	−	8.02192i	1.18745	−	1.31880i	0.936447	−	0.350809i	$-0.114093\pi$
$38$		0			0
$39$	8.37059	−	4.64396i	1.34037	−	0.743628i
$40$		0			0
$41$	6.35069	−	1.34988i	0.991810	−	0.210816i	0.316695	−	0.948528i	$-0.397427\pi$
$41$	6.35069	−	1.34988i	0.991810	−	0.210816i	0.675116	+	0.737712i	$0.264094\pi$
$42$		0			0
$43$	3.62268	−	6.27466i	0.552453	−	0.956877i	−0.445644	−	0.895211i	$-0.647025\pi$
$43$	3.62268	−	6.27466i	0.552453	−	0.956877i	0.998097	−	0.0616667i	$-0.0196416\pi$
$44$		0			0
$45$	4.29568	−	7.44033i	0.640362	−	1.10914i
$46$		0			0
$47$	−3.05245	+	9.39447i	−0.445245	+	1.37032i	0.436969	+	0.899477i	$0.356052\pi$
$47$	−3.05245	+	9.39447i	−0.445245	+	1.37032i	−0.882214	+	0.470848i	$0.843948\pi$
$48$		0			0
$49$	−5.01368	−	2.23223i	−0.716240	−	0.318891i
$50$		0			0
$51$	4.89184	+	15.0555i	0.684994	+	2.10820i
$52$		0			0
$53$	−5.31589	−	3.86222i	−0.730193	−	0.530516i	0.159431	−	0.987209i	$-0.449034\pi$
$53$	−5.31589	−	3.86222i	−0.730193	−	0.530516i	−0.889625	+	0.456693i	$0.849034\pi$
$54$		0			0
$55$	6.83828	+	1.66427i	0.922074	+	0.224410i
$56$		0			0
$57$	−1.25700	−	0.913265i	−0.166494	−	0.120965i
$58$		0			0
$59$	−9.56452	−	2.03300i	−1.24519	−	0.264674i	−0.462241	−	0.886754i	$-0.652954\pi$
$59$	−9.56452	−	2.03300i	−1.24519	−	0.264674i	−0.782954	+	0.622080i	$0.786288\pi$
$60$		0			0
$61$	−0.460871	−	4.38489i	−0.0590084	−	0.561428i	−0.983587	−	0.180436i	$-0.942249\pi$
$61$	−0.460871	−	4.38489i	−0.0590084	−	0.561428i	0.924578	−	0.380992i	$-0.124417\pi$
$62$		0			0
$63$	−4.86938	+	1.03502i	−0.613484	+	0.130400i
$64$		0			0
$65$	−4.60221	+	6.11206i	−0.570834	+	0.758108i
$66$		0			0
$67$	−3.58294	−	6.20584i	−0.437726	−	0.758164i	0.559788	−	0.828636i	$-0.310883\pi$
$67$	−3.58294	−	6.20584i	−0.437726	−	0.758164i	−0.997514	+	0.0704721i	$0.977549\pi$
$68$		0			0
$69$	14.5257	+	16.1324i	1.74869	+	1.94211i
$70$		0			0
$71$	−0.763579	−	7.26497i	−0.0906202	−	0.862193i	−0.941541	−	0.336899i	$-0.890622\pi$
$71$	−0.763579	−	7.26497i	−0.0906202	−	0.862193i	0.850921	−	0.525294i	$-0.176045\pi$
$72$		0			0
$73$	2.04795	+	6.30294i	0.239694	+	0.737703i	0.996464	+	0.0840214i	$0.0267764\pi$
$73$	2.04795	+	6.30294i	0.239694	+	0.737703i	−0.756770	+	0.653682i	$0.773224\pi$
$74$		0			0
$75$	0.137954	−	1.31254i	0.0159295	−	0.151559i
$76$		0			0
$77$	−1.93469	−	3.58988i	−0.220479	−	0.409105i
$78$		0			0
$79$	−4.52358	−	3.28657i	−0.508942	−	0.369768i	0.303480	−	0.952838i	$-0.401851\pi$
$79$	−4.52358	−	3.28657i	−0.508942	−	0.369768i	−0.812422	+	0.583070i	$0.801851\pi$
$80$		0			0
$81$	−3.18114	+	3.53301i	−0.353460	+	0.392557i
$82$		0			0
$83$	8.13441	−	5.91000i	0.892868	−	0.648707i	−0.0437562	−	0.999042i	$-0.513932\pi$
$83$	8.13441	−	5.91000i	0.892868	−	0.648707i	0.936624	+	0.350336i	$0.113932\pi$
$84$		0			0
$85$	−8.46627	−	9.40275i	−0.918296	−	1.01987i
$86$		0			0
$87$	−13.9441	+	24.1519i	−1.49497	+	2.58936i
$88$		0			0
$89$	4.51751	+	7.82455i	0.478855	+	0.829401i	0.999706	−	0.0242466i	$-0.00771868\pi$
$89$	4.51751	+	7.82455i	0.478855	+	0.829401i	−0.520851	+	0.853648i	$0.674385\pi$
$90$		0			0
$91$	4.41627	−	0.388026i	0.462951	−	0.0406762i
$92$		0			0
$93$	−2.58104	−	1.14915i	−0.267642	−	0.119162i
$94$		0			0
$95$	1.21471	+	0.258196i	0.124627	+	0.0264903i
$96$		0			0
$97$	−1.65210	+	0.735564i	−0.167746	+	0.0746852i	−0.488892	−	0.872345i	$-0.662599\pi$
$97$	−1.65210	+	0.735564i	−0.167746	+	0.0746852i	0.321146	+	0.947030i	$0.395932\pi$
$98$		0			0
$99$	12.1019	+	5.81863i	1.21628	+	0.584794i
$100$		0			0
$101$	−1.45692	+	13.8616i	−0.144969	+	1.37928i	0.644082	+	0.764956i	$0.277240\pi$
$101$	−1.45692	+	13.8616i	−0.144969	+	1.37928i	−0.789051	+	0.614328i	$0.789427\pi$
$102$		0			0
$103$	−0.717930	−	2.20956i	−0.0707397	−	0.217714i	0.909436	−	0.415843i	$-0.136514\pi$
$103$	−0.717930	−	2.20956i	−0.0707397	−	0.217714i	−0.980176	+	0.198129i	$0.936514\pi$
$104$		0			0
$105$	5.60418	−	4.07167i	0.546912	−	0.397355i
$106$		0			0
$107$	9.69613	−	2.06098i	0.937361	−	0.199242i	0.286189	−	0.958173i	$-0.407611\pi$
$107$	9.69613	−	2.06098i	0.937361	−	0.199242i	0.651171	+	0.758931i	$0.274278\pi$
$108$		0			0
$109$	−13.6494			−1.30737			−0.653687	−	0.756765i	$-0.726778\pi$
$109$	−13.6494			−1.30737			−0.653687	+	0.756765i	$0.726778\pi$
$110$		0			0
$111$	−14.3294	+	24.8193i	−1.36009	+	2.35575i
$112$		0			0
$113$	7.96090	+	8.84148i	0.748899	+	0.831737i	0.990337	−	0.138680i	$-0.0442858\pi$
$113$	7.96090	+	8.84148i	0.748899	+	0.831737i	−0.241438	+	0.970416i	$0.577619\pi$
$114$		0			0
$115$	−15.8507	−	7.05718i	−1.47808	−	0.658085i
$116$		0			0
$117$	−11.0135	+	9.58110i	−1.01820	+	0.885773i
$118$		0			0
$119$	−0.766343	+	7.29127i	−0.0702506	+	0.668389i
$120$		0			0
$121$	−1.78842	+	10.8536i	−0.162584	+	0.986695i
$122$		0			0
$123$	−15.7471	+	7.01106i	−1.41987	+	0.632166i
$124$		0			0
$125$	3.60464	+	11.0939i	0.322409	+	0.992273i
$126$		0			0
$127$	3.23857	+	1.44190i	0.287377	+	0.127948i	0.545362	−	0.838200i	$-0.316392\pi$
$127$	3.23857	+	1.44190i	0.287377	+	0.127948i	−0.257986	+	0.966149i	$0.583059\pi$
$128$		0			0
$129$	−5.94424	+	18.2945i	−0.523361	+	1.61074i
$130$		0			0
$131$	12.7295			1.11218			0.556090	−	0.831122i	$-0.312301\pi$
$131$	12.7295			1.11218			0.556090	+	0.831122i	$0.312301\pi$
$132$		0			0
$133$	−0.359788	−	0.623172i	−0.0311976	−	0.0540359i
$134$		0			0
$135$	−1.82572	+	5.61898i	−0.157133	+	0.483605i
$136$		0			0
$137$	0.647883	+	6.16419i	0.0553524	+	0.526643i	0.986705	+	0.162523i	$0.0519633\pi$
$137$	0.647883	+	6.16419i	0.0553524	+	0.526643i	−0.931352	+	0.364119i	$0.881370\pi$
$138$		0			0
$139$	1.57503	+	0.334782i	0.133592	+	0.0283958i	0.274222	−	0.961666i	$-0.411580\pi$
$139$	1.57503	+	0.334782i	0.133592	+	0.0283958i	−0.140630	+	0.990062i	$0.544913\pi$
$140$		0			0
$141$	2.74129	−	26.0816i	0.230858	−	2.19647i
$142$		0			0
$143$	−10.0678	−	6.45281i	−0.841914	−	0.539611i
$144$		0			0
$145$	2.32995	−	22.1680i	0.193492	−	1.84095i
$146$		0			0
$147$	14.2523	+	3.02942i	1.17551	+	0.249863i
$148$		0			0
$149$	0.112054	+	1.06612i	0.00917978	+	0.0873398i	0.998153	−	0.0607577i	$-0.0193517\pi$
$149$	0.112054	+	1.06612i	0.00917978	+	0.0873398i	−0.988973	+	0.148098i	$0.952685\pi$
$150$		0			0
$151$	1.86320	−	5.73435i	0.151625	−	0.466655i	−0.846178	−	0.532900i	$-0.821102\pi$
$151$	1.86320	−	5.73435i	0.151625	−	0.466655i	0.997803	+	0.0662457i	$0.0211021\pi$
$152$		0			0
$153$	−12.0704	−	20.9065i	−0.975831	−	1.69019i
$154$		0			0
$155$	2.25817			0.181381
$156$		0			0
$157$	3.04670	−	9.37678i	0.243153	−	0.748349i	−0.752781	−	0.658270i	$-0.771288\pi$
$157$	3.04670	−	9.37678i	0.243153	−	0.748349i	0.995935	−	0.0900781i	$-0.0287117\pi$
$158$		0			0
$159$	15.9369	+	7.09555i	1.26387	+	0.562713i
$160$		0			0
$161$	3.10676	+	9.56162i	0.244847	+	0.753561i
$162$		0			0
$163$	7.27988	−	3.24121i	0.570204	−	0.253871i	−0.101320	−	0.994854i	$-0.532307\pi$
$163$	7.27988	−	3.24121i	0.570204	−	0.253871i	0.671524	+	0.740983i	$0.265640\pi$
$164$		0			0
$165$	−18.6771	−	0.547294i	−1.45401	−	0.0426068i
$166$		0			0
$167$	−0.516038	+	4.90978i	−0.0399322	+	0.379930i	0.956244	+	0.292569i	$0.0945100\pi$
$167$	−0.516038	+	4.90978i	−0.0399322	+	0.379930i	−0.996177	+	0.0873610i	$0.972157\pi$
$168$		0			0
$169$	10.7721	−	7.27751i	0.828622	−	0.559809i
$170$		0			0
$171$	2.16456	+	0.963723i	0.165528	+	0.0736978i
$172$		0			0
$173$	−4.18728	−	4.65045i	−0.318353	−	0.353567i	0.562635	−	0.826705i	$-0.309788\pi$
$173$	−4.18728	−	4.65045i	−0.318353	−	0.353567i	−0.880988	+	0.473139i	$0.843121\pi$
$174$		0			0
$175$	0.305610	−	0.529333i	0.0231020	−	0.0400138i
$176$		0			0
$177$	25.9605			1.95131
$178$		0			0
$179$	3.61700	−	0.768817i	0.270347	−	0.0574640i	−0.0707433	−	0.997495i	$-0.522537\pi$
$179$	3.61700	−	0.768817i	0.270347	−	0.0574640i	0.341090	+	0.940031i	$0.389204\pi$
$180$		0			0
$181$	−7.56873	+	5.49901i	−0.562579	+	0.408738i	−0.832402	−	0.554172i	$-0.813035\pi$
$181$	−7.56873	+	5.49901i	−0.562579	+	0.408738i	0.269823	+	0.962910i	$0.413035\pi$
$182$		0			0
$183$	3.61727	+	11.1328i	0.267397	+	0.822962i
$184$		0			0
$185$	2.39434	−	22.7806i	0.176035	−	1.67486i
$186$		0			0
$187$	13.6573	−	14.3023i	0.998720	−	1.04589i
$188$		0			0
$189$	3.12744	−	1.39242i	0.227488	−	0.101284i
$190$		0			0
$191$	−15.1934	−	3.22946i	−1.09936	−	0.233676i	−0.377702	−	0.925927i	$-0.623286\pi$
$191$	−15.1934	−	3.22946i	−1.09936	−	0.233676i	−0.721656	+	0.692252i	$0.756619\pi$
$192$		0			0
$193$	−2.86257	−	1.27450i	−0.206052	−	0.0917404i	0.301116	−	0.953588i	$-0.402641\pi$
$193$	−2.86257	−	1.27450i	−0.206052	−	0.0917404i	−0.507168	+	0.861847i	$0.669308\pi$
$194$		0			0
$195$	8.57777	−	18.4129i	0.614267	−	1.31858i
$196$		0			0
$197$	2.19957	+	3.80976i	0.156713	+	0.271434i	0.933681	−	0.358105i	$-0.116577\pi$
$197$	2.19957	+	3.80976i	0.156713	+	0.271434i	−0.776969	+	0.629539i	$0.783244\pi$
$198$		0			0
$199$	6.08219	−	10.5347i	0.431155	−	0.746782i	−0.565818	−	0.824530i	$-0.691440\pi$
$199$	6.08219	−	10.5347i	0.431155	−	0.746782i	0.996973	+	0.0777478i	$0.0247729\pi$
$200$		0			0
$201$	12.7302	+	14.1383i	0.897919	+	0.997240i
$202$		0			0
$203$	−10.4491	+	7.59169i	−0.733381	+	0.532832i
$204$		0			0
$205$	9.21877	−	10.2385i	0.643867	−	0.715087i
$206$		0			0
$207$	−26.7821	−	19.4583i	−1.86148	−	1.35245i
$208$		0			0
$209$	−0.259340	+	1.92357i	−0.0179390	+	0.133056i
$210$		0			0
$211$	0.0394705	−	0.375537i	0.00271726	−	0.0258530i	−0.993079	−	0.117446i	$-0.962529\pi$
$211$	0.0394705	−	0.375537i	0.00271726	−	0.0258530i	0.995797	+	0.0915931i	$0.0291959\pi$
$212$		0			0
$213$	5.99317	+	18.4451i	0.410645	+	1.26384i
$214$		0			0
$215$	−1.60709	−	15.2904i	−0.109603	−	1.04280i
$216$		0			0
$217$	−0.875538	−	0.972384i	−0.0594354	−	0.0660097i
$218$		0			0
$219$	−8.79754	−	15.2378i	−0.594482	−	1.02967i
$220$		0			0
$221$	8.40746	+	19.7863i	0.565547	+	1.33097i
$222$		0			0
$223$	−21.2287	+	4.51229i	−1.42158	+	0.302165i	−0.853621	−	0.520894i	$-0.825599\pi$
$223$	−21.2287	+	4.51229i	−1.42158	+	0.302165i	−0.567955	+	0.823060i	$0.692265\pi$
$224$		0			0
$225$	0.210375	+	2.00159i	0.0140250	+	0.133439i
$226$		0			0
$227$	4.04523	+	0.859841i	0.268492	+	0.0570697i	0.340190	−	0.940357i	$-0.389509\pi$
$227$	4.04523	+	0.859841i	0.268492	+	0.0570697i	−0.0716984	+	0.997426i	$0.522842\pi$
$228$		0			0
$229$	0.330399	+	0.240049i	0.0218334	+	0.0158629i	0.598648	−	0.801012i	$-0.295705\pi$
$229$	0.330399	+	0.240049i	0.0218334	+	0.0158629i	−0.576815	+	0.816875i	$0.695705\pi$
$230$		0			0
$231$	7.00584	+	8.25470i	0.460950	+	0.543120i
$232$		0			0
$233$	−18.0264	−	13.0969i	−1.18095	−	0.858008i	−0.188669	−	0.982041i	$-0.560417\pi$
$233$	−18.0264	−	13.0969i	−1.18095	−	0.858008i	−0.992278	+	0.124033i	$0.960417\pi$
$234$		0			0
$235$	6.47731	+	19.9351i	0.422533	+	1.30042i
$236$		0			0
$237$	13.5615	+	6.03799i	0.880917	+	0.392209i
$238$		0			0
$239$	−3.98741	+	12.2720i	−0.257924	+	0.793809i	0.735315	+	0.677725i	$0.237034\pi$
$239$	−3.98741	+	12.2720i	−0.257924	+	0.793809i	−0.993239	+	0.116084i	$0.962966\pi$
$240$		0			0
$241$	−6.52348	+	11.2990i	−0.420214	+	0.727833i	−0.995960	−	0.0897960i	$-0.971379\pi$
$241$	−6.52348	+	11.2990i	−0.420214	+	0.727833i	0.575746	+	0.817629i	$0.304712\pi$
$242$		0			0
$243$	10.4873	−	18.1646i	0.672762	−	1.16526i
$244$		0			0
$245$	−11.3914	+	2.42132i	−0.727770	+	0.154692i
$246$		0			0
$247$	−1.80908	−	1.08609i	−0.115109	−	0.0691063i
$248$		0			0
$249$	−17.8622	+	19.8379i	−1.13197	+	1.25718i
$250$		0			0
$251$	−11.4790	+	5.11079i	−0.724550	+	0.322590i	−0.735663	−	0.677348i	$-0.763129\pi$
$251$	−11.4790	+	5.11079i	−0.724550	+	0.322590i	0.0111132	+	0.999938i	$0.496462\pi$
$252$		0			0
$253$	9.13196	−	25.5348i	0.574122	−	1.60536i
$254$		0			0
$255$	27.1765	+	19.7449i	1.70186	+	1.23647i
$256$		0			0
$257$	−14.0858	+	15.6438i	−0.878646	+	0.975835i	−0.999859	−	0.0167913i	$-0.994655\pi$
$257$	−14.0858	+	15.6438i	−0.878646	+	0.975835i	0.121213	+	0.992627i	$0.461322\pi$
$258$		0			0
$259$	−10.7378	+	7.80148i	−0.667216	+	0.484761i
$260$		0			0
$261$	13.1421	−	40.4472i	0.813474	−	2.50362i
$262$		0			0
$263$	7.32789	+	12.6923i	0.451857	+	0.782640i	0.998501	−	0.0547252i	$-0.0174283\pi$
$263$	7.32789	+	12.6923i	0.451857	+	0.782640i	−0.546644	+	0.837365i	$0.684095\pi$
$264$		0			0
$265$	−13.9433			−0.856527
$266$		0			0
$267$	−16.0507	−	17.8261i	−0.982287	−	1.09094i
$268$		0			0
$269$	1.41721	+	13.4838i	0.0864085	+	0.822122i	0.948799	+	0.315879i	$0.102299\pi$
$269$	1.41721	+	13.4838i	0.0864085	+	0.822122i	−0.862391	+	0.506243i	$0.831034\pi$
$270$		0			0
$271$	15.7454	−	17.4870i	0.956464	−	1.06226i	−0.0415418	−	0.999137i	$-0.513227\pi$
$271$	15.7454	−	17.4870i	0.956464	−	1.06226i	0.998006	−	0.0631240i	$-0.0201064\pi$
$272$		0			0
$273$	−11.2545	+	3.44542i	−0.681154	+	0.208526i
$274$		0			0
$275$	−1.52516	+	0.626182i	−0.0919703	+	0.0377602i
$276$		0			0
$277$	19.5049	−	8.68412i	1.17193	−	0.521778i	0.273923	−	0.961752i	$-0.411679\pi$
$277$	19.5049	−	8.68412i	1.17193	−	0.521778i	0.898011	+	0.439973i	$0.145012\pi$
$278$		0			0
$279$	4.21435	+	0.895787i	0.252306	+	0.0536294i
$280$		0			0
$281$	19.8345	−	14.4106i	1.18322	−	0.859663i	0.190693	−	0.981650i	$-0.438926\pi$
$281$	19.8345	−	14.4106i	1.18322	−	0.859663i	0.992532	+	0.121986i	$0.0389265\pi$
$282$		0			0
$283$	−5.79360	+	1.23147i	−0.344394	+	0.0732032i	−0.376862	−	0.926270i	$-0.622997\pi$
$283$	−5.79360	+	1.23147i	−0.344394	+	0.0732032i	0.0324676	+	0.999473i	$0.489663\pi$
$284$		0			0
$285$	−3.29704			−0.195300
$286$		0			0
$287$	−7.98307			−0.471226
$288$		0			0
$289$	−18.1471	+	3.85728i	−1.06748	+	0.226899i
$290$		0			0
$291$	3.88436	−	2.82215i	0.227705	−	0.165437i
$292$		0			0
$293$	−18.2539	−	3.87998i	−1.06640	−	0.226671i	−0.358897	−	0.933377i	$-0.616847\pi$
$293$	−18.2539	−	3.87998i	−1.06640	−	0.226671i	−0.707507	+	0.706706i	$0.750180\pi$
$294$		0			0
$295$	−18.9555	+	8.43953i	−1.10363	+	0.491368i
$296$		0			0
$297$	−8.97234	−	2.18365i	−0.520628	−	0.126708i
$298$		0			0
$299$	21.5686	+	20.0980i	1.24734	+	1.16230i
$300$		0			0
$301$	−5.96107	+	6.62044i	−0.343590	+	0.381596i
$302$		0			0
$303$	−3.86802	−	36.8018i	−0.222212	−	2.11421i
$304$		0			0
$305$	−6.26039	−	6.95287i	−0.358469	−	0.398120i
$306$		0			0
$307$	−6.09839			−0.348054			−0.174027	−	0.984741i	$-0.555678\pi$
$307$	−6.09839			−0.348054			−0.174027	+	0.984741i	$0.555678\pi$
$308$		0			0
$309$	3.08407	+	5.34176i	0.175446	+	0.303882i
$310$		0			0
$311$	6.05051	−	18.6216i	0.343093	−	1.05593i	−0.619504	−	0.784994i	$-0.712666\pi$
$311$	6.05051	−	18.6216i	0.343093	−	1.05593i	0.962597	−	0.270938i	$-0.0873339\pi$
$312$		0			0
$313$	−10.0089	+	7.27191i	−0.565738	+	0.411033i	−0.833554	−	0.552437i	$-0.813698\pi$
$313$	−10.0089	+	7.27191i	−0.565738	+	0.411033i	0.267817	+	0.963470i	$0.413698\pi$
$314$		0			0
$315$	−7.06848	+	7.85034i	−0.398264	+	0.442317i
$316$		0			0
$317$	17.7447	+	12.8923i	0.996643	+	0.724104i	0.961366	−	0.275274i	$-0.0887685\pi$
$317$	17.7447	+	12.8923i	0.996643	+	0.724104i	0.0352775	+	0.999378i	$0.488768\pi$
$318$		0			0
$319$	34.8238	+	1.02044i	1.94976	+	0.0571336i
$320$		0			0
$321$	−24.0425	+	10.7044i	−1.34192	+	0.597461i
$322$		0			0
$323$	2.33491	−	2.59318i	0.129918	−	0.144288i
$324$		0			0
$325$	0.0306147	−	1.79206i	0.00169820	−	0.0994057i
$326$		0			0
$327$	35.4464	−	7.53436i	1.96019	−	0.416651i
$328$		0			0
$329$	6.07281	−	10.5184i	0.334805	−	0.579899i
$330$		0			0
$331$	7.44135	−	12.8888i	0.409014	−	0.708433i	−0.585766	−	0.810480i	$-0.699206\pi$
$331$	7.44135	−	12.8888i	0.409014	−	0.708433i	0.994780	+	0.102048i	$0.0325394\pi$
$332$		0			0
$333$	13.5053	−	41.5649i	0.740083	−	2.27774i
$334$		0			0
$335$	−13.8914	−	6.18485i	−0.758969	−	0.337915i
$336$		0			0
$337$	6.16638	+	18.9782i	0.335904	+	1.03381i	0.966275	+	0.257512i	$0.0829028\pi$
$337$	6.16638	+	18.9782i	0.335904	+	1.03381i	−0.630371	+	0.776294i	$0.717097\pi$
$338$		0			0
$339$	−25.5543	−	18.5663i	−1.38792	−	1.00838i
$340$		0			0
$341$	0.265957	+	3.51941i	0.0144024	+	0.190587i
$342$		0			0
$343$	12.4225	+	9.02549i	0.670753	+	0.487330i
$344$		0			0
$345$	45.0585	+	9.57748i	2.42587	+	0.515634i
$346$		0			0
$347$	2.62899	+	25.0131i	0.141131	+	1.34277i	0.804264	+	0.594273i	$0.202560\pi$
$347$	2.62899	+	25.0131i	0.141131	+	1.34277i	−0.663132	+	0.748502i	$0.730773\pi$
$348$		0			0
$349$	32.2339	−	6.85153i	1.72544	−	0.366754i	0.764741	−	0.644337i	$-0.222867\pi$
$349$	32.2339	−	6.85153i	1.72544	−	0.366754i	0.960702	+	0.277583i	$0.0895335\pi$
$350$		0			0
$351$	6.03845	−	8.01949i	0.322309	−	0.428049i
$352$		0			0
$353$	0.750940	+	1.30067i	0.0399685	+	0.0692275i	0.885318	−	0.464987i	$-0.153941\pi$
$353$	0.750940	+	1.30067i	0.0399685	+	0.0692275i	−0.845349	+	0.534214i	$0.820608\pi$
$354$		0			0
$355$	−10.3723	−	11.5196i	−0.550506	−	0.611399i
$356$		0			0
$357$	−2.03459	−	19.3579i	−0.107682	−	1.02453i
$358$		0			0
$359$	4.52585	+	13.9291i	0.238865	+	0.735152i	0.996585	+	0.0825717i	$0.0263134\pi$
$359$	4.52585	+	13.9291i	0.238865	+	0.735152i	−0.757720	+	0.652580i	$0.773687\pi$
$360$		0			0
$361$	1.95024	−	18.5553i	0.102644	−	0.976595i
$362$		0			0
$363$	−1.34674	−	29.1733i	−0.0706855	−	1.53120i
$364$		0			0
$365$	11.3773	+	8.26611i	0.595517	+	0.432668i
$366$		0			0
$367$	−22.1449	+	24.5944i	−1.15595	+	1.28381i	−0.203518	+	0.979071i	$0.565237\pi$
$367$	−22.1449	+	24.5944i	−1.15595	+	1.28381i	−0.952434	+	0.304744i	$0.901429\pi$
$368$		0			0
$369$	21.2662	−	15.4508i	1.10707	−	0.804335i
$370$		0			0
$371$	5.40608	+	6.00406i	0.280670	+	0.311715i
$372$		0			0
$373$	6.42372	−	11.1262i	0.332608	−	0.576094i	−0.650415	−	0.759579i	$-0.725405\pi$
$373$	6.42372	−	11.1262i	0.332608	−	0.576094i	0.983022	+	0.183486i	$0.0587381\pi$
$374$		0			0
$375$	−15.4848	−	26.8204i	−0.799629	−	1.38500i
$376$		0			0
$377$	−15.9934	+	34.3312i	−0.823701	+	1.76815i
$378$		0			0
$379$	−6.47045	−	2.88083i	−0.332365	−	0.147978i	0.233768	−	0.972292i	$-0.424894\pi$
$379$	−6.47045	−	2.88083i	−0.332365	−	0.147978i	−0.566133	+	0.824314i	$0.691561\pi$
$380$		0			0
$381$	−9.20624	−	1.95685i	−0.471650	−	0.100252i
$382$		0			0
$383$	−15.5983	+	6.94481i	−0.797036	+	0.354863i	−0.764513	−	0.644608i	$-0.777021\pi$
$383$	−15.5983	+	6.94481i	−0.797036	+	0.354863i	−0.0325223	+	0.999471i	$0.510354\pi$
$384$		0			0
$385$	−7.79896	−	3.74977i	−0.397472	−	0.191106i
$386$		0			0
$387$	3.06627	−	29.1736i	0.155867	−	1.48298i
$388$		0			0
$389$	−0.188163	−	0.579107i	−0.00954026	−	0.0293619i	0.946173	−	0.323661i	$-0.104914\pi$
$389$	−0.188163	−	0.579107i	−0.00954026	−	0.0293619i	−0.955713	+	0.294299i	$0.904914\pi$
$390$		0			0
$391$	−39.4425	+	28.6566i	−1.99469	+	1.44923i
$392$		0			0
$393$	−33.0574	+	7.02658i	−1.66753	+	0.354444i
$394$		0			0
$395$	−11.8651			−0.596997
$396$		0			0
$397$	3.69260	−	6.39577i	0.185326	−	0.320994i	−0.758360	−	0.651836i	$-0.773999\pi$
$397$	3.69260	−	6.39577i	0.185326	−	0.320994i	0.943686	+	0.330841i	$0.107333\pi$
$398$		0			0
$399$	1.27833	+	1.41973i	0.0639965	+	0.0710753i
$400$		0			0
$401$	−21.3699	−	9.51449i	−1.06716	−	0.475131i	−0.203433	−	0.979089i	$-0.565210\pi$
$401$	−21.3699	−	9.51449i	−1.06716	−	0.475131i	−0.863728	+	0.503958i	$0.831877\pi$
$402$		0			0
$403$	−3.62834	−	1.24783i	−0.180740	−	0.0621588i
$404$		0			0
$405$	−1.05451	+	10.0330i	−0.0523992	+	0.498546i
$406$		0			0
$407$	35.7861	+	1.04864i	1.77385	+	0.0519790i
$408$		0			0
$409$	14.8865	−	6.62789i	0.736089	−	0.327728i	−0.00422325	−	0.999991i	$-0.501344\pi$
$409$	14.8865	−	6.62789i	0.736089	−	0.327728i	0.740312	+	0.672263i	$0.234678\pi$
$410$		0			0
$411$	−5.08509	−	15.6503i	−0.250829	−	0.771973i
$412$		0			0
$413$	10.9835	+	4.89019i	0.540465	+	0.240631i
$414$		0			0
$415$	6.59321	−	20.2918i	0.323648	−	0.996087i
$416$		0			0
$417$	−4.27502			−0.209348
$418$		0			0
$419$	2.57924	+	4.46738i	0.126004	+	0.218246i	0.922125	−	0.386892i	$-0.126451\pi$
$419$	2.57924	+	4.46738i	0.126004	+	0.218246i	−0.796121	+	0.605138i	$0.793118\pi$
$420$		0			0
$421$	11.9241	−	36.6985i	0.581143	−	1.78857i	−0.0330936	−	0.999452i	$-0.510536\pi$
$421$	11.9241	−	36.6985i	0.581143	−	1.78857i	0.614237	−	0.789122i	$-0.289464\pi$
$422$		0			0
$423$	4.18038	+	39.7737i	0.203257	+	1.93386i
$424$		0			0
$425$	2.89924	+	0.616252i	0.140634	+	0.0298926i
$426$		0			0
$427$	−0.566673	+	5.39154i	−0.0274232	+	0.260915i
$428$		0			0
$429$	29.7073	+	11.2001i	1.43428	+	0.540745i
$430$		0			0
$431$	3.63217	−	34.5578i	0.174955	−	1.66459i	−0.456912	−	0.889512i	$-0.651044\pi$
$431$	3.63217	−	34.5578i	0.174955	−	1.66459i	0.631867	−	0.775077i	$-0.282289\pi$
$432$		0			0
$433$	−33.2275	−	7.06272i	−1.59681	−	0.339413i	−0.678293	−	0.734791i	$-0.737280\pi$
$433$	−33.2275	−	7.06272i	−1.59681	−	0.339413i	−0.918518	+	0.395378i	$0.870613\pi$
$434$		0			0
$435$	6.18588	+	58.8547i	0.296590	+	2.82187i
$436$		0			0
$437$	1.47869	−	4.55094i	0.0707354	−	0.217701i
$438$		0			0
$439$	−13.8051	−	23.9111i	−0.658880	−	1.14121i	−0.980906	−	0.194483i	$-0.937697\pi$
$439$	−13.8051	−	23.9111i	−0.658880	−	1.14121i	0.322026	−	0.946731i	$-0.395636\pi$
$440$		0			0
$441$	−22.2199			−1.05809
$442$		0			0
$443$	−6.24562	+	19.2220i	−0.296738	+	0.913266i	0.685894	+	0.727702i	$0.259411\pi$
$443$	−6.24562	+	19.2220i	−0.296738	+	0.913266i	−0.982632	+	0.185565i	$0.940589\pi$
$444$		0			0
$445$	17.5148	+	7.79809i	0.830281	+	0.369665i
$446$		0			0
$447$	−0.879484	−	2.70677i	−0.0415982	−	0.128026i
$448$		0			0
$449$	−2.57872	+	1.14812i	−0.121697	+	0.0541832i	−0.466682	−	0.884425i	$-0.654551\pi$
$449$	−2.57872	+	1.14812i	−0.121697	+	0.0541832i	0.344985	+	0.938608i	$0.387884\pi$
$450$		0			0
$451$	17.0427	+	13.1618i	0.802509	+	0.619767i
$452$		0			0
$453$	−1.67327	+	15.9201i	−0.0786172	+	0.747993i
$454$		0			0
$455$	7.09759	−	6.17447i	0.332740	−	0.289464i
$456$		0			0
$457$	38.6910	+	17.2263i	1.80989	+	0.805814i	0.960629	+	0.277836i	$0.0896172\pi$
$457$	38.6910	+	17.2263i	1.80989	+	0.805814i	0.849258	+	0.527977i	$0.177049\pi$
$458$		0			0
$459$	11.1084	+	12.3371i	0.518495	+	0.575847i
$460$		0			0
$461$	−1.70373	+	2.95094i	−0.0793505	+	0.137439i	−0.902970	−	0.429704i	$-0.858618\pi$
$461$	−1.70373	+	2.95094i	−0.0793505	+	0.137439i	0.823619	+	0.567143i	$0.191951\pi$
$462$		0			0
$463$	0.0893967			0.00415462			0.00207731	−	0.999998i	$-0.499339\pi$
$463$	0.0893967			0.00415462			0.00207731	+	0.999998i	$0.499339\pi$
$464$		0			0
$465$	−5.86429	+	1.24649i	−0.271950	+	0.0578048i
$466$		0			0
$467$	22.0537	−	16.0229i	1.02052	−	0.741452i	0.0541320	−	0.998534i	$-0.482761\pi$
$467$	22.0537	−	16.0229i	1.02052	−	0.741452i	0.966390	+	0.257081i	$0.0827608\pi$
$468$		0			0
$469$	2.72274	+	8.37973i	0.125724	+	0.386940i
$470$		0			0
$471$	−2.73613	+	26.0325i	−0.126074	+	1.19952i
$472$		0			0
$473$	23.6413	−	4.30553i	1.08703	−	0.197969i
$474$		0			0
$475$	−0.265765	+	0.118326i	−0.0121942	+	0.00542919i
$476$		0			0
$477$	−26.0218	−	5.53111i	−1.19146	−	0.253252i
$478$		0			0
$479$	3.69508	+	1.64515i	0.168832	+	0.0751690i	0.489413	−	0.872052i	$-0.337211\pi$
$479$	3.69508	+	1.64515i	0.168832	+	0.0751690i	−0.320580	+	0.947221i	$0.603878\pi$
$480$		0			0
$481$	−16.4353	+	35.2799i	−0.749387	+	1.60863i
$482$		0			0
$483$	−13.3460	−	23.1159i	−0.607262	−	1.05181i
$484$		0			0
$485$	−1.91877	+	3.32341i	−0.0871269	+	0.150908i
$486$		0			0
$487$	−17.3802	−	19.3026i	−0.787570	−	0.874685i	0.207044	−	0.978332i	$-0.433616\pi$
$487$	−17.3802	−	19.3026i	−0.787570	−	0.874685i	−0.994614	+	0.103646i	$0.966949\pi$
$488$		0			0
$489$	−17.1161	+	12.4356i	−0.774019	+	0.562357i
$490$		0			0
$491$	18.4940	−	20.5397i	0.834624	−	0.926944i	−0.163599	−	0.986527i	$-0.552310\pi$
$491$	18.4940	−	20.5397i	0.834624	−	0.926944i	0.998223	+	0.0595827i	$0.0189770\pi$
$492$		0			0
$493$	−50.6710	−	36.8146i	−2.28211	−	1.65805i
$494$		0			0
$495$	28.0332	−	5.10539i	1.26000	−	0.229470i
$496$		0			0
$497$	−0.938875	+	8.93280i	−0.0421143	+	0.400691i
$498$		0			0
$499$	11.9609	+	36.8120i	0.535445	+	1.64793i	0.742685	+	0.669641i	$0.233552\pi$
$499$	11.9609	+	36.8120i	0.535445	+	1.64793i	−0.207240	+	0.978290i	$0.566448\pi$
$500$		0			0
$501$	−1.37005	−	13.0352i	−0.0612093	−	0.582368i
$502$		0			0
$503$	−8.97195	−	9.96436i	−0.400040	−	0.444289i	0.509146	−	0.860680i	$-0.329961\pi$
$503$	−8.97195	−	9.96436i	−0.400040	−	0.444289i	−0.909186	+	0.416391i	$0.863295\pi$
$504$		0			0
$505$	14.7882	+	25.6140i	0.658068	+	1.13981i
$506$		0			0
$507$	−23.9571	+	24.8452i	−1.06397	+	1.10342i
$508$		0			0
$509$	33.7092	−	7.16511i	1.49413	−	0.317588i	0.612859	−	0.790192i	$-0.290019\pi$
$509$	33.7092	−	7.16511i	1.49413	−	0.317588i	0.881275	+	0.472604i	$0.156686\pi$
$510$		0			0
$511$	−0.851775	−	8.10410i	−0.0376803	−	0.358504i
$512$		0			0
$513$	−1.59380	−	0.338772i	−0.0703678	−	0.0149571i
$514$		0			0
$515$	−3.98844	−	2.89777i	−0.175752	−	0.127691i
$516$		0			0
$517$	−30.3065	+	12.4429i	−1.33288	+	0.547239i
$518$		0			0
$519$	13.4411	+	9.76550i	0.589997	+	0.428658i
$520$		0			0
$521$	−5.53319	−	17.0294i	−0.242414	−	0.746072i	−0.996051	−	0.0887820i	$-0.971703\pi$
$521$	−5.53319	−	17.0294i	−0.242414	−	0.746072i	0.753638	−	0.657290i	$-0.228297\pi$
$522$		0			0
$523$	5.88437	+	2.61989i	0.257306	+	0.114560i	0.531336	−	0.847161i	$-0.321690\pi$
$523$	5.88437	+	2.61989i	0.257306	+	0.114560i	−0.274030	+	0.961721i	$0.588357\pi$
$524$		0			0
$525$	−0.501458	+	1.54333i	−0.0218854	+	0.0673565i
$526$		0			0
$527$	3.17260	−	5.49511i	0.138201	−	0.239371i
$528$		0			0
$529$	−21.9282	+	37.9808i	−0.953400	+	1.65134i
$530$		0			0
$531$	−38.7239	+	8.23101i	−1.68047	+	0.357195i
$532$		0			0
$533$	−20.4700	+	11.3566i	−0.886654	+	0.491911i
$534$		0			0
$535$	14.0751	−	15.6320i	0.608519	−	0.675829i
$536$		0			0
$537$	−8.96868	+	3.99311i	−0.387027	+	0.172316i
$538$		0			0
$539$	−5.11531	−	17.4686i	−0.220332	−	0.752426i
$540$		0			0
$541$	2.19106	+	1.59190i	0.0942011	+	0.0684411i	0.633889	−	0.773424i	$-0.281458\pi$
$541$	2.19106	+	1.59190i	0.0942011	+	0.0684411i	−0.539688	+	0.841865i	$0.681458\pi$
$542$		0			0
$543$	16.6200	−	18.4584i	0.713232	−	0.792125i
$544$		0			0
$545$	−23.4324	+	17.0246i	−1.00373	+	0.729255i
$546$		0			0
$547$	−5.11504	+	15.7425i	−0.218703	+	0.673099i	0.780167	+	0.625572i	$0.215134\pi$
$547$	−5.11504	+	15.7425i	−0.218703	+	0.673099i	−0.998870	+	0.0475277i	$0.984866\pi$
$548$		0			0
$549$	−8.92545	−	15.4593i	−0.380929	−	0.659788i
$550$		0			0
$551$	6.14738			0.261887
$552$		0			0
$553$	4.60033	+	5.10918i	0.195626	+	0.217265i
$554$		0			0
$555$	6.35682	+	60.4811i	0.269832	+	2.56728i
$556$		0			0
$557$	−6.78111	+	7.53119i	−0.287325	+	0.319107i	−0.869477	−	0.493973i	$-0.835544\pi$
$557$	−6.78111	+	7.53119i	−0.287325	+	0.319107i	0.582152	+	0.813080i	$0.302211\pi$
$558$		0			0
$559$	−5.86706	+	25.4561i	−0.248150	+	1.07668i
$560$		0			0
$561$	−27.5722	+	44.6807i	−1.16410	+	1.88642i
$562$		0			0
$563$	2.95743	−	1.31673i	0.124641	−	0.0554937i	−0.343469	−	0.939164i	$-0.611602\pi$
$563$	2.95743	−	1.31673i	0.124641	−	0.0554937i	0.468110	+	0.883670i	$0.344935\pi$
$564$		0			0
$565$	24.6946	+	5.24900i	1.03891	+	0.220827i
$566$		0			0
$567$	4.72915	−	3.43593i	0.198606	−	0.144295i
$568$		0			0
$569$	−16.4623	+	3.49917i	−0.690136	+	0.146693i	−0.539613	−	0.841913i	$-0.681429\pi$
$569$	−16.4623	+	3.49917i	−0.690136	+	0.146693i	−0.150524	+	0.988606i	$0.548096\pi$
$570$		0			0
$571$	26.0789			1.09137			0.545683	−	0.837992i	$-0.316270\pi$
$571$	26.0789			1.09137			0.545683	+	0.837992i	$0.316270\pi$
$572$		0			0
$573$	41.2388			1.72278
$574$		0			0
$575$	3.97576	−	0.845074i	0.165801	−	0.0352420i
$576$		0			0
$577$	−16.8144	+	12.2164i	−0.699994	+	0.508575i	−0.879930	−	0.475103i	$-0.842411\pi$
$577$	−16.8144	+	12.2164i	−0.699994	+	0.508575i	0.179936	+	0.983678i	$0.442411\pi$
$578$		0			0
$579$	8.13739	+	1.72965i	0.338178	+	0.0718820i
$580$		0			0
$581$	−11.2941	+	5.02847i	−0.468559	+	0.208616i
$582$		0			0
$583$	−1.64217	−	21.7309i	−0.0680119	−	0.900002i
$584$		0			0
$585$	−6.95700	+	30.1852i	−0.287636	+	1.24801i
$586$		0			0
$587$	−5.02361	+	5.57929i	−0.207347	+	0.230282i	−0.837844	−	0.545910i	$-0.816184\pi$
$587$	−5.02361	+	5.57929i	−0.207347	+	0.230282i	0.630498	+	0.776191i	$0.282851\pi$
$588$		0			0
$589$	0.0650982	+	0.619368i	0.00268232	+	0.0255206i
$590$		0			0
$591$	−7.81506	−	8.67951i	−0.321469	−	0.357027i
$592$		0			0
$593$	31.3321			1.28666			0.643328	−	0.765591i	$-0.277553\pi$
$593$	31.3321			1.28666			0.643328	+	0.765591i	$0.277553\pi$
$594$		0			0
$595$	7.77866	+	13.4730i	0.318894	+	0.552341i
$596$		0			0
$597$	−9.97991	+	30.7150i	−0.408451	+	1.25708i
$598$		0			0
$599$	−5.16956	+	3.75591i	−0.211223	+	0.153462i	−0.688367	−	0.725363i	$-0.741672\pi$
$599$	−5.16956	+	3.75591i	−0.211223	+	0.153462i	0.477144	+	0.878825i	$0.341672\pi$
$600$		0			0
$601$	−20.6519	+	22.9363i	−0.842409	+	0.935590i	−0.998640	−	0.0521309i	$-0.983399\pi$
$601$	−20.6519	+	22.9363i	−0.842409	+	0.935590i	0.156232	+	0.987720i	$0.450065\pi$
$602$		0			0
$603$	−23.4716	−	17.0531i	−0.955838	−	0.694457i
$604$		0			0
$605$	10.4673	+	20.8635i	0.425557	+	0.848223i
$606$		0			0
$607$	26.1946	−	11.6626i	1.06321	−	0.473370i	0.200824	−	0.979627i	$-0.435638\pi$
$607$	26.1946	−	11.6626i	1.06321	−	0.473370i	0.862382	+	0.506257i	$0.168971\pi$
$608$		0			0
$609$	22.9449	−	25.4828i	0.929772	−	1.03262i
$610$		0			0
$611$	0.608348	−	35.6102i	0.0246111	−	1.44063i
$612$		0			0
$613$	−20.0418	+	4.26001i	−0.809479	+	0.172060i	−0.594017	−	0.804452i	$-0.702459\pi$
$613$	−20.0418	+	4.26001i	−0.809479	+	0.172060i	−0.215462	+	0.976512i	$0.569126\pi$
$614$		0			0
$615$	−18.2889	+	31.6772i	−0.737478	+	1.27735i
$616$		0			0
$617$	−3.54271	+	6.13616i	−0.142624	+	0.247033i	−0.928484	−	0.371372i	$-0.878887\pi$
$617$	−3.54271	+	6.13616i	−0.142624	+	0.247033i	0.785860	+	0.618405i	$0.212221\pi$
$618$		0			0
$619$	3.47677	−	10.7004i	0.139743	−	0.430086i	−0.856554	−	0.516057i	$-0.827399\pi$
$619$	3.47677	−	10.7004i	0.139743	−	0.430086i	0.996298	+	0.0859713i	$0.0273993\pi$
$620$		0			0
$621$	20.7973	+	9.25955i	0.834566	+	0.371573i
$622$		0			0
$623$	−3.43293	−	10.5655i	−0.137537	−	0.423297i
$624$		0			0
$625$	18.0147	+	13.0884i	0.720588	+	0.523538i
$626$		0			0
$627$	−0.388311	−	5.13852i	−0.0155076	−	0.205213i
$628$		0			0
$629$	−52.0712	−	37.8320i	−2.07622	−	1.50846i
$630$		0			0
$631$	19.2340	+	4.08832i	0.765695	+	0.162753i	0.574172	−	0.818735i	$-0.305324\pi$
$631$	19.2340	+	4.08832i	0.765695	+	0.162753i	0.191523	+	0.981488i	$0.438657\pi$
$632$		0			0
$633$	0.104792	+	0.997027i	0.00416510	+	0.0396283i
$634$		0			0
$635$	7.35824	−	1.56404i	0.292003	−	0.0620671i
$636$		0			0
$637$	19.6412	+	2.40423i	0.778214	+	0.0952592i
$638$		0			0
$639$	−14.7878	−	25.6133i	−0.584998	−	1.01325i
$640$		0			0
$641$	8.74904	+	9.71679i	0.345566	+	0.383790i	0.890725	−	0.454543i	$-0.150197\pi$
$641$	8.74904	+	9.71679i	0.345566	+	0.383790i	−0.545159	+	0.838333i	$0.683531\pi$
$642$		0			0
$643$	4.55420	+	43.3304i	0.179600	+	1.70878i	0.598808	+	0.800892i	$0.295641\pi$
$643$	4.55420	+	43.3304i	0.179600	+	1.70878i	−0.419208	+	0.907890i	$0.637692\pi$
$644$		0			0
$645$	12.6137	+	38.8210i	0.496664	+	1.52858i
$646$		0			0
$647$	1.40504	−	13.3680i	0.0552377	−	0.525552i	−0.931559	−	0.363590i	$-0.881551\pi$
$647$	1.40504	−	13.3680i	0.0552377	−	0.525552i	0.986797	−	0.161962i	$-0.0517823\pi$
$648$		0			0
$649$	−15.3857	−	28.5486i	−0.603942	−	1.12063i
$650$		0			0
$651$	2.81045	+	2.04191i	0.110150	+	0.0800289i
$652$		0			0
$653$	−13.4159	+	14.8999i	−0.525006	+	0.583078i	−0.946074	−	0.323951i	$-0.894989\pi$
$653$	−13.4159	+	14.8999i	−0.525006	+	0.583078i	0.421068	+	0.907029i	$0.361655\pi$
$654$		0			0
$655$	21.8532	−	15.8772i	0.853873	−	0.620375i
$656$		0			0
$657$	17.9541	+	19.9400i	0.700455	+	0.777934i
$658$		0			0
$659$	2.88371	−	4.99474i	0.112334	−	0.194567i	−0.804377	−	0.594119i	$-0.797501\pi$
$659$	2.88371	−	4.99474i	0.112334	−	0.194567i	0.916711	+	0.399552i	$0.130834\pi$
$660$		0			0
$661$	21.5396	+	37.3078i	0.837795	+	1.45110i	0.891734	+	0.452559i	$0.149489\pi$
$661$	21.5396	+	37.3078i	0.837795	+	1.45110i	−0.0539392	+	0.998544i	$0.517178\pi$
$662$		0			0
$663$	−32.7554	−	46.7426i	−1.27211	−	1.81533i
$664$		0			0
$665$	−1.39493	−	0.621064i	−0.0540932	−	0.0240838i
$666$		0			0
$667$	−84.0122	−	17.8573i	−3.25297	−	0.691439i
$668$		0			0
$669$	52.6384	−	23.4361i	2.03512	−	0.906093i
$670$		0			0
$671$	10.0989	−	10.5759i	0.389864	−	0.408276i
$672$		0			0
$673$	2.93531	−	27.9276i	0.113148	−	1.07653i	−0.779695	−	0.626160i	$-0.784626\pi$
$673$	2.93531	−	27.9276i	0.113148	−	1.07653i	0.892842	−	0.450369i	$-0.148708\pi$
$674$		0			0
$675$	−0.427693	−	1.31630i	−0.0164619	−	0.0506645i
$676$		0			0
$677$	−4.01752	+	2.91890i	−0.154406	+	0.112182i	−0.662306	−	0.749234i	$-0.730422\pi$
$677$	−4.01752	+	2.91890i	−0.154406	+	0.112182i	0.507900	+	0.861416i	$0.330422\pi$
$678$		0			0
$679$	2.17503	−	0.462317i	0.0834700	−	0.0177421i
$680$		0			0
$681$	−10.9798			−0.420746
$682$		0			0
$683$	−22.7482	+	39.4010i	−0.870434	+	1.50764i	−0.00888649	+	0.999961i	$0.502829\pi$
$683$	−22.7482	+	39.4010i	−0.870434	+	1.50764i	−0.861548	+	0.507676i	$0.830505\pi$
$684$		0			0
$685$	8.80074	+	9.77421i	0.336259	+	0.373453i
$686$		0			0
$687$	−0.990527	−	0.441011i	−0.0377910	−	0.0168256i
$688$		0			0
$689$	22.4035	+	7.70483i	0.853504	+	0.293531i
$690$		0			0
$691$	0.986926	−	9.38998i	0.0375444	−	0.357211i	−0.959580	−	0.281435i	$-0.909190\pi$
$691$	0.986926	−	9.38998i	0.0375444	−	0.357211i	0.997125	−	0.0757767i	$-0.0241436\pi$
$692$		0			0
$693$	−13.0674	−	10.0918i	−0.496391	−	0.383357i
$694$		0			0
$695$	3.12147	−	1.38977i	0.118404	−	0.0527170i
$696$		0			0
$697$	−11.9628	−	36.8178i	−0.453124	−	1.39457i
$698$		0			0
$699$	54.0425	+	24.0613i	2.04407	+	0.910081i
$700$		0			0
$701$	−8.06407	+	24.8187i	−0.304576	+	0.937388i	0.675259	+	0.737580i	$0.264032\pi$
$701$	−8.06407	+	24.8187i	−0.304576	+	0.937388i	−0.979835	+	0.199808i	$0.935968\pi$
$702$		0			0
$703$	6.31726			0.238260
$704$		0			0
$705$	−27.8251	−	48.1945i	−1.04795	−	1.81511i
$706$		0			0
$707$	5.29586	−	16.2990i	0.199171	−	0.612986i
$708$		0			0
$709$	−2.55398	−	24.2995i	−0.0959168	−	0.912588i	−0.931627	−	0.363417i	$-0.881610\pi$
$709$	−2.55398	−	24.2995i	−0.0959168	−	0.912588i	0.835710	−	0.549171i	$-0.185056\pi$
$710$		0			0
$711$	−22.1434	−	4.70672i	−0.830442	−	0.176516i
$712$		0			0
$713$	0.909529	−	8.65359i	0.0340621	−	0.324080i
$714$		0			0
$715$	−25.3323	+	1.47965i	−0.947374	+	0.0553358i
$716$		0			0
$717$	3.58095	−	34.0704i	0.133733	−	1.27238i
$718$		0			0
$719$	14.4804	+	3.07791i	0.540029	+	0.114787i	0.469848	−	0.882747i	$-0.344309\pi$
$719$	14.4804	+	3.07791i	0.540029	+	0.114787i	0.0701816	+	0.997534i	$0.477642\pi$
$720$		0			0
$721$	0.298598	+	2.84097i	0.0111204	+	0.105803i
$722$		0			0
$723$	10.7040	−	32.9435i	0.398086	−	1.22518i
$724$		0			0
$725$	2.61084	+	4.52211i	0.0969643	+	0.167947i
$726$		0			0
$727$	8.63791			0.320362			0.160181	−	0.987088i	$-0.448792\pi$
$727$	8.63791			0.320362			0.160181	+	0.987088i	$0.448792\pi$
$728$		0			0
$729$	−12.8007	+	39.3965i	−0.474100	+	1.45913i
$730$		0			0
$731$	−39.4662	−	17.5715i	−1.45971	−	0.649905i
$732$		0			0
$733$	−11.9037	−	36.6358i	−0.439673	−	1.35317i	−0.888222	−	0.459415i	$-0.848059\pi$
$733$	−11.9037	−	36.6358i	−0.439673	−	1.35317i	0.448549	−	0.893758i	$-0.351941\pi$
$734$		0			0
$735$	28.2460	−	12.5759i	1.04187	−	0.463870i
$736$		0			0
$737$	8.00318	−	22.3785i	0.294801	−	0.824324i
$738$		0			0
$739$	−0.107197	+	1.01991i	−0.00394332	+	0.0375182i	−0.996317	−	0.0857508i	$-0.972671\pi$
$739$	−0.107197	+	1.01991i	−0.00394332	+	0.0375182i	0.992373	+	0.123269i	$0.0393378\pi$
$740$		0			0
$741$	5.29755	+	1.82189i	0.194610	+	0.0669289i
$742$		0			0
$743$	−12.2452	−	5.45192i	−0.449233	−	0.200012i	0.169634	−	0.985507i	$-0.445741\pi$
$743$	−12.2452	−	5.45192i	−0.449233	−	0.200012i	−0.618867	+	0.785496i	$0.712408\pi$
$744$		0			0
$745$	1.52212	+	1.69048i	0.0557660	+	0.0619345i
$746$		0			0
$747$	20.3542	−	35.2545i	0.744721	−	1.28990i
$748$		0			0
$749$	−12.1884			−0.445356
$750$		0			0
$751$	7.63798	−	1.62350i	0.278714	−	0.0592425i	−0.0664338	−	0.997791i	$-0.521162\pi$
$751$	7.63798	−	1.62350i	0.278714	−	0.0592425i	0.345148	+	0.938548i	$0.387829\pi$
$752$		0			0
$753$	26.9890	−	19.6087i	0.983534	−	0.714579i
$754$		0			0
$755$	−3.95372	−	12.1683i	−0.143891	−	0.442850i
$756$		0			0
$757$	−0.499279	+	4.75032i	−0.0181466	+	0.172653i	−0.999841	−	0.0178072i	$-0.994331\pi$
$757$	−0.499279	+	4.75032i	−0.0181466	+	0.172653i	0.981695	+	0.190461i	$0.0609981\pi$
$758$		0			0
$759$	−9.61995	+	71.3527i	−0.349182	+	2.58994i
$760$		0			0
$761$	−1.29465	+	0.576414i	−0.0469309	+	0.0208950i	−0.430068	−	0.902797i	$-0.641510\pi$
$761$	−1.29465	+	0.576414i	−0.0469309	+	0.0208950i	0.383137	+	0.923692i	$0.374844\pi$
$762$		0			0
$763$	16.4161	+	3.48936i	0.594304	+	0.126323i
$764$		0			0
$765$	−46.7979	−	20.8358i	−1.69198	−	0.753320i
$766$		0			0
$767$	35.1205	−	3.08579i	1.26813	−	0.111421i
$768$		0			0
$769$	0.269919	+	0.467514i	0.00973354	+	0.0168590i	0.870851	−	0.491547i	$-0.163568\pi$
$769$	0.269919	+	0.467514i	0.00973354	+	0.0168590i	−0.861118	+	0.508406i	$0.830235\pi$
$770$		0			0
$771$	27.9444	−	48.4010i	1.00639	−	1.74312i
$772$		0			0
$773$	25.2285	+	28.0191i	0.907406	+	1.00778i	0.999927	+	0.0120659i	$0.00384078\pi$
$773$	25.2285	+	28.0191i	0.907406	+	1.00778i	−0.0925211	+	0.995711i	$0.529493\pi$
$774$		0			0
$775$	−0.427969	+	0.310938i	−0.0153731	+	0.0111692i
$776$		0			0
$777$	23.5789	−	26.1870i	0.845889	−	0.939455i
$778$		0			0
$779$	3.07395	+	2.23336i	0.110136	+	0.0800184i
$780$		0			0
$781$	16.7320	−	17.5223i	0.598720	−	0.626996i
$782$		0			0
$783$	−3.05707	+	29.0861i	−0.109251	+	1.03945i
$784$		0			0
$785$	−6.46511	−	19.8976i	−0.230750	−	0.710174i
$786$		0			0
$787$	−1.51640	−	14.4276i	−0.0540537	−	0.514287i	−0.987730	−	0.156169i	$-0.950085\pi$
$787$	−1.51640	−	14.4276i	−0.0540537	−	0.514287i	0.933677	−	0.358117i	$-0.116581\pi$
$788$		0			0
$789$	−26.0360	−	28.9159i	−0.926907	−	1.02943i
$790$		0			0
$791$	−7.31434	−	12.6688i	−0.260068	−	0.450451i
$792$		0			0
$793$	6.21690	+	14.6310i	0.220769	+	0.519562i
$794$		0			0
$795$	36.2095	−	7.69657i	1.28422	−	0.272969i
$796$		0			0
$797$	−1.73269	−	16.4854i	−0.0613750	−	0.583944i	−0.981385	−	0.192050i	$-0.938487\pi$
$797$	−1.73269	−	16.4854i	−0.0613750	−	0.583944i	0.920010	−	0.391894i	$-0.128180\pi$
$798$		0			0
$799$	57.6110	+	12.2456i	2.03813	+	0.433218i
$800$		0			0
$801$	29.5939	+	21.5012i	1.04565	+	0.759708i
$802$		0			0
$803$	−11.5430	+	18.7054i	−0.407343	+	0.660099i
$804$		0			0
$805$	17.2595	+	12.5398i	0.608318	+	0.441969i
$806$		0			0
$807$	−11.1233	−	34.2341i	−0.391560	−	1.20510i
$808$		0			0
$809$	5.33417	+	2.37493i	0.187539	+	0.0834979i	0.498358	−	0.866971i	$-0.333937\pi$
$809$	5.33417	+	2.37493i	0.187539	+	0.0834979i	−0.310819	+	0.950469i	$0.600603\pi$
$810$		0			0
$811$	−13.6257	+	41.9357i	−0.478464	+	1.47256i	0.362765	+	0.931881i	$0.381833\pi$
$811$	−13.6257	+	41.9357i	−0.478464	+	1.47256i	−0.841229	+	0.540680i	$0.818167\pi$
$812$		0			0
$813$	−31.2368	+	54.1038i	−1.09552	+	1.89750i
$814$		0			0
$815$	8.45493	−	14.6444i	0.296163	−	0.512970i
$816$		0			0
$817$	4.14751	−	0.881581i	0.145103	−	0.0308426i
$818$		0			0
$819$	15.6953	−	8.70769i	0.548439	−	0.304271i
$820$		0			0
$821$	6.21586	−	6.90341i	0.216935	−	0.240931i	−0.624848	−	0.780746i	$-0.714839\pi$
$821$	6.21586	−	6.90341i	0.216935	−	0.240931i	0.841783	+	0.539815i	$0.181506\pi$
$822$		0			0
$823$	−19.1922	+	8.54492i	−0.668998	+	0.297857i	−0.712989	−	0.701175i	$-0.752659\pi$
$823$	−19.1922	+	8.54492i	−0.668998	+	0.297857i	0.0439914	+	0.999032i	$0.485993\pi$
$824$		0			0
$825$	3.61506	−	2.46802i	0.125860	−	0.0859254i
$826$		0			0
$827$	−43.5940	−	31.6729i	−1.51591	−	1.10137i	−0.963468	−	0.267824i	$-0.913695\pi$
$827$	−43.5940	−	31.6729i	−1.51591	−	1.10137i	−0.552444	−	0.833550i	$-0.686305\pi$
$828$		0			0
$829$	−14.0167	+	15.5671i	−0.486818	+	0.540667i	−0.935640	−	0.352954i	$-0.885177\pi$
$829$	−14.0167	+	15.5671i	−0.486818	+	0.540667i	0.448822	+	0.893621i	$0.351844\pi$
$830$		0			0
$831$	−45.8590	+	33.3185i	−1.59083	+	1.15581i
$832$		0			0
$833$	−10.1122	+	31.1220i	−0.350366	+	1.07831i
$834$		0			0
$835$	5.23797	+	9.07244i	0.181268	+	0.313965i
$836$		0			0
$837$	−2.96289			−0.102412
$838$		0			0
$839$	−12.8688	−	14.2922i	−0.444280	−	0.493423i	0.478858	−	0.877893i	$-0.341051\pi$
$839$	−12.8688	−	14.2922i	−0.444280	−	0.493423i	−0.923138	+	0.384470i	$0.874384\pi$
$840$		0			0
$841$	−8.50234	−	80.8943i	−0.293184	−	2.78946i
$842$		0			0
$843$	−43.5540	+	48.3716i	−1.50008	+	1.66601i
$844$		0			0
$845$	9.41572	−	25.9294i	0.323911	−	0.891999i
$846$		0			0
$847$	4.92559	−	12.5965i	0.169245	−	0.432821i
$848$		0			0
$849$	14.3658	−	6.39606i	0.493032	−	0.219512i
$850$		0			0
$851$	−86.3338	−	18.3508i	−2.95948	−	0.629058i
$852$		0			0
$853$	20.4831	−	14.8818i	0.701328	−	0.509545i	−0.179036	−	0.983842i	$-0.557298\pi$
$853$	20.4831	−	14.8818i	0.701328	−	0.509545i	0.880364	+	0.474298i	$0.157298\pi$
$854$		0			0
$855$	4.91801	−	1.04536i	0.168192	−	0.0357504i
$856$		0			0
$857$	50.9279			1.73967			0.869833	−	0.493347i	$-0.164227\pi$
$857$	50.9279			1.73967			0.869833	+	0.493347i	$0.164227\pi$
$858$		0			0
$859$	12.9443			0.441654			0.220827	−	0.975313i	$-0.429124\pi$
$859$	12.9443			0.441654			0.220827	+	0.975313i	$0.429124\pi$
$860$		0			0
$861$	20.7314	−	4.40659i	0.706524	−	0.150176i
$862$		0			0
$863$	41.8883	−	30.4337i	1.42590	−	1.03597i	0.435133	−	0.900366i	$-0.356701\pi$
$863$	41.8883	−	30.4337i	1.42590	−	1.03597i	0.990763	−	0.135607i	$-0.0432985\pi$
$864$		0			0
$865$	−12.9889	−	2.76087i	−0.441635	−	0.0938725i
$866$		0			0
$867$	44.9974	−	20.0341i	1.52819	−	0.680395i
$868$		0			0
$869$	−1.39742	−	18.4920i	−0.0474041	−	0.627299i
$870$		0			0
$871$	18.9025	+	17.6138i	0.640487	+	0.596819i
$872$		0			0
$873$	−4.89929	+	5.44122i	−0.165816	+	0.184157i
$874$		0			0
$875$	−1.49923	−	14.2642i	−0.0506832	−	0.482218i
$876$		0			0
$877$	−19.3094	−	21.4453i	−0.652033	−	0.724156i	0.322955	−	0.946414i	$-0.395324\pi$
$877$	−19.3094	−	21.4453i	−0.652033	−	0.724156i	−0.974988	+	0.222258i	$0.928657\pi$
$878$		0			0
$879$	49.5456			1.67113
$880$		0			0
$881$	−18.5883	−	32.1958i	−0.626255	−	1.08471i	−0.988297	−	0.152543i	$-0.951254\pi$
$881$	−18.5883	−	32.1958i	−0.626255	−	1.08471i	0.362042	−	0.932162i	$-0.382080\pi$
$882$		0			0
$883$	−3.18245	+	9.79457i	−0.107098	+	0.329614i	−0.990217	−	0.139535i	$-0.955439\pi$
$883$	−3.18245	+	9.79457i	−0.107098	+	0.329614i	0.883119	+	0.469149i	$0.155439\pi$
$884$		0			0
$885$	44.5674	−	32.3801i	1.49812	−	1.08844i
$886$		0			0
$887$	18.9728	−	21.0714i	0.637044	−	0.707509i	−0.335023	−	0.942210i	$-0.608744\pi$
$887$	18.9728	−	21.0714i	0.637044	−	0.707509i	0.972068	+	0.234700i	$0.0754109\pi$
$888$		0			0
$889$	−3.52642	−	2.56210i	−0.118272	−	0.0859300i
$890$		0			0
$891$	−15.7609	−	0.461841i	−0.528011	−	0.0154722i
$892$		0			0
$893$	−5.28104	+	2.35127i	−0.176723	+	0.0786823i
$894$		0			0
$895$	5.25050	−	5.83127i	0.175505	−	0.194918i
$896$		0			0
$897$	−67.1058	−	40.2873i	−2.24060	−	1.34515i
$898$		0			0
$899$	10.9341	−	2.32411i	0.364671	−	0.0775133i
$900$		0			0
$901$	−19.5895	+	33.9300i	−0.652621	+	1.13037i
$902$		0			0
$903$	11.8260	−	20.4832i	0.393545	−	0.681639i
$904$		0			0
$905$	−6.13471	+	18.8807i	−0.203925	+	0.627616i
$906$		0			0
$907$	−10.6267	−	4.73133i	−0.352855	−	0.157101i	0.222652	−	0.974898i	$-0.428529\pi$
$907$	−10.6267	−	4.73133i	−0.352855	−	0.157101i	−0.575507	+	0.817797i	$0.695195\pi$
$908$		0			0
$909$	17.4381	+	53.6688i	0.578384	+	1.78008i
$910$		0			0
$911$	33.8136	+	24.5670i	1.12029	+	0.813941i	0.984253	−	0.176763i	$-0.0565625\pi$
$911$	33.8136	+	24.5670i	1.12029	+	0.813941i	0.136040	+	0.990703i	$0.456563\pi$
$912$		0			0
$913$	32.4018	+	7.88581i	1.07234	+	0.260982i
$914$		0			0
$915$	20.0957	+	14.6004i	0.664343	+	0.482673i
$916$		0			0
$917$	−15.3098	−	3.25419i	−0.505573	−	0.107463i
$918$		0			0
$919$	4.77329	+	45.4148i	0.157456	+	1.49810i	0.732945	+	0.680287i	$0.238145\pi$
$919$	4.77329	+	45.4148i	0.157456	+	1.49810i	−0.575489	+	0.817809i	$0.695188\pi$
$920$		0			0
$921$	15.8371	−	3.36627i	0.521849	−	0.110922i
$922$		0			0
$923$	10.3003	+	24.2409i	0.339038	+	0.797899i
$924$		0			0
$925$	2.68299	+	4.64708i	0.0882163	+	0.152795i
$926$		0			0
$927$	−6.29399	−	6.99018i	−0.206722	−	0.229588i
$928$		0			0
$929$	0.568238	+	5.40642i	0.0186433	+	0.177379i	0.999881	−	0.0154225i	$-0.00490932\pi$
$929$	0.568238	+	5.40642i	0.0186433	+	0.177379i	−0.981238	+	0.192802i	$0.938243\pi$
$930$		0			0
$931$	−0.992504	−	3.05461i	−0.0325280	−	0.100111i
$932$		0			0
$933$	−5.43374	+	51.6986i	−0.177893	+	1.69254i
$934$		0			0
$935$	5.60696	−	41.5878i	0.183367	−	1.36007i
$936$		0			0
$937$	−15.5526	−	11.2996i	−0.508081	−	0.369142i	0.304014	−	0.952667i	$-0.401673\pi$
$937$	−15.5526	−	11.2996i	−0.508081	−	0.369142i	−0.812095	+	0.583525i	$0.801673\pi$
$938$		0			0
$939$	21.9784	−	24.4094i	0.717236	−	0.796572i
$940$		0			0
$941$	0.901886	−	0.655259i	0.0294007	−	0.0213608i	−0.572988	−	0.819564i	$-0.694216\pi$
$941$	0.901886	−	0.655259i	0.0294007	−	0.0213608i	0.602389	+	0.798203i	$0.294216\pi$
$942$		0			0
$943$	−35.5221	−	39.4513i	−1.15676	−	1.28471i
$944$		0			0
$945$	3.63224	−	6.29122i	0.118157	−	0.204654i
$946$		0			0
$947$	15.3431	+	26.5751i	0.498585	+	0.863574i	0.999999	−	0.00163348i	$-0.000519954\pi$
$947$	15.3431	+	26.5751i	0.498585	+	0.863574i	−0.501414	+	0.865208i	$0.667187\pi$
$948$		0			0
$949$	−13.7129	−	19.5686i	−0.445140	−	0.635224i
$950$		0			0
$951$	−53.1981	−	23.6853i	−1.72507	−	0.768050i
$952$		0			0
$953$	40.0166	+	8.50579i	1.29626	+	0.275529i	0.803850	−	0.594832i	$-0.202781\pi$
$953$	40.0166	+	8.50579i	1.29626	+	0.275529i	0.492414	+	0.870361i	$0.336115\pi$
$954$		0			0
$955$	−30.1112	+	13.4064i	−0.974375	+	0.433820i
$956$		0			0
$957$	−90.9980	+	16.5725i	−2.94155	+	0.535713i
$958$		0			0
$959$	0.796618	−	7.57931i	0.0257241	−	0.244749i
$960$		0			0
$961$	−9.22958	−	28.4057i	−0.297728	−	0.916314i
$962$		0			0
$963$	32.4689	−	23.5900i	1.04629	−	0.760178i
$964$		0			0
$965$	−6.50394	+	1.38246i	−0.209369	+	0.0445028i
$966$		0			0
$967$	−5.55774			−0.178725			−0.0893625	−	0.995999i	$-0.528483\pi$
$967$	−5.55774			−0.178725			−0.0893625	+	0.995999i	$0.528483\pi$
$968$		0			0
$969$	−4.63216	+	8.02313i	−0.148806	+	0.257740i
$970$		0			0
$971$	1.80299	+	2.00242i	0.0578607	+	0.0642608i	0.771380	−	0.636374i	$-0.219567\pi$
$971$	1.80299	+	2.00242i	0.0578607	+	0.0642608i	−0.713520	+	0.700635i	$0.752900\pi$
$972$		0			0
$973$	−1.80870	−	0.805286i	−0.0579843	−	0.0258163i
$974$		0			0
$975$	0.909701	+	4.67074i	0.0291337	+	0.149583i
$976$		0			0
$977$	−5.48152	+	52.1532i	−0.175369	+	1.66853i	0.453681	+	0.891164i	$0.350111\pi$
$977$	−5.48152	+	52.1532i	−0.175369	+	1.66853i	−0.629050	+	0.777365i	$0.716556\pi$
$978$		0			0
$979$	−10.0907	+	28.2157i	−0.322500	+	0.901777i
$980$		0			0
$981$	−50.4845	+	22.4772i	−1.61185	+	0.717641i
$982$		0			0
$983$	16.2372	+	49.9728i	0.517885	+	1.59389i	0.777971	+	0.628301i	$0.216249\pi$
$983$	16.2372	+	49.9728i	0.517885	+	1.59389i	−0.260086	+	0.965586i	$0.583751\pi$
$984$		0			0
$985$	8.52792	+	3.79688i	0.271722	+	0.120979i
$986$		0			0
$987$	−9.96452	+	30.6676i	−0.317174	+	0.976162i
$988$		0			0
$989$	−59.2422			−1.88379
$990$		0			0
$991$	0.872229	+	1.51074i	0.0277073	+	0.0479904i	0.879547	−	0.475813i	$-0.157846\pi$
$991$	0.872229	+	1.51074i	0.0277073	+	0.0479904i	−0.851839	+	0.523803i	$0.824513\pi$
$992$		0			0
$993$	−12.2101	+	37.5788i	−0.387475	+	1.19253i
$994$		0			0
$995$	−2.69818	−	25.6714i	−0.0855380	−	0.813840i
$996$		0			0
$997$	4.27043	+	0.907709i	0.135246	+	0.0287474i	0.275037	−	0.961434i	$-0.411310\pi$
$997$	4.27043	+	0.907709i	0.135246	+	0.0287474i	−0.139791	+	0.990181i	$0.544643\pi$
$998$		0			0
$999$	−3.14155	+	29.8899i	−0.0993943	+	0.945674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.81.2	✓	112
11.3	even	5	inner	572.2.bg.a.289.13	yes	112
13.9	even	3	inner	572.2.bg.a.477.13	yes	112
143.113	even	15	inner	572.2.bg.a.113.2	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.81.2	✓	112	1.1	even	1	trivial
572.2.bg.a.113.2	yes	112	143.113	even	15	inner
572.2.bg.a.289.13	yes	112	11.3	even	5	inner
572.2.bg.a.477.13	yes	112	13.9	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59692 + 0.551993i) q^{3} +(1.71674 - 1.24728i) q^{5} +(-1.20270 - 0.255642i) q^{7} +(3.69867 - 1.64675i) q^{9} +O(q^{10})\)	\(q+(-2.59692 + 0.551993i) q^{3} +(1.71674 - 1.24728i) q^{5} +(-1.20270 - 0.255642i) q^{7} +(3.69867 - 1.64675i) q^{9} +(2.14611 + 2.52868i) q^{11} +(-3.44761 + 1.05544i) q^{13} +(-3.76974 + 4.18672i) q^{15} +(-0.623261 - 5.92993i) q^{17} +(0.391593 + 0.434908i) q^{19} +3.26444 q^{21} +(-4.08829 - 7.08112i) q^{23} +(-0.153613 + 0.472771i) q^{25} +(-2.25249 + 1.63653i) q^{27} +(7.02874 - 7.80620i) q^{29} +(0.860931 + 0.625503i) q^{31} +(-6.96909 - 5.38214i) q^{33} +(-2.38358 + 1.06124i) q^{35} +(7.22297 - 8.02192i) q^{37} +(8.37059 - 4.64396i) q^{39} +(6.35069 - 1.34988i) q^{41} +(3.62268 - 6.27466i) q^{43} +(4.29568 - 7.44033i) q^{45} +(-3.05245 + 9.39447i) q^{47} +(-5.01368 - 2.23223i) q^{49} +(4.89184 + 15.0555i) q^{51} +(-5.31589 - 3.86222i) q^{53} +(6.83828 + 1.66427i) q^{55} +(-1.25700 - 0.913265i) q^{57} +(-9.56452 - 2.03300i) q^{59} +(-0.460871 - 4.38489i) q^{61} +(-4.86938 + 1.03502i) q^{63} +(-4.60221 + 6.11206i) q^{65} +(-3.58294 - 6.20584i) q^{67} +(14.5257 + 16.1324i) q^{69} +(-0.763579 - 7.26497i) q^{71} +(2.04795 + 6.30294i) q^{73} +(0.137954 - 1.31254i) q^{75} +(-1.93469 - 3.58988i) q^{77} +(-4.52358 - 3.28657i) q^{79} +(-3.18114 + 3.53301i) q^{81} +(8.13441 - 5.91000i) q^{83} +(-8.46627 - 9.40275i) q^{85} +(-13.9441 + 24.1519i) q^{87} +(4.51751 + 7.82455i) q^{89} +(4.41627 - 0.388026i) q^{91} +(-2.58104 - 1.14915i) q^{93} +(1.21471 + 0.258196i) q^{95} +(-1.65210 + 0.735564i) q^{97} +(12.1019 + 5.81863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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