LMFDB - Embedded newform 1100.2.q.b.221.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(221,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			221.7
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.287074 + 0.208571i) q^{3} +(1.90283 - 1.17441i) q^{5} -3.22759 q^{7} +(-0.888142 - 2.73342i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(-1.10504 - 3.40097i) q^{13} +(0.791201 + 0.0597318i) q^{15} +(-1.91122 + 1.38858i) q^{17} +(-5.96028 + 4.33039i) q^{19} +(-0.926558 - 0.673184i) q^{21} +(2.33680 - 7.19193i) q^{23} +(2.24150 - 4.46941i) q^{25} +(0.644108 - 1.98236i) q^{27} +(-5.12636 - 3.72452i) q^{29} +(-6.17586 + 4.48703i) q^{31} +(-0.287074 + 0.208571i) q^{33} +(-6.14155 + 3.79053i) q^{35} +(2.29508 + 7.06353i) q^{37} +(0.392116 - 1.20681i) q^{39} +(-2.50450 - 7.70805i) q^{41} -4.93377 q^{43} +(-4.90015 - 4.15818i) q^{45} +(10.3550 + 7.52338i) q^{47} +3.41735 q^{49} -0.838279 q^{51} +(2.61550 + 1.90027i) q^{53} +(0.528928 + 2.17261i) q^{55} -2.61424 q^{57} +(-4.07289 - 12.5351i) q^{59} +(3.70068 - 11.3895i) q^{61} +(2.86656 + 8.82236i) q^{63} +(-6.09685 - 5.17368i) q^{65} +(2.26355 - 1.64456i) q^{67} +(2.17087 - 1.57723i) q^{69} +(1.85297 + 1.34626i) q^{71} +(0.353466 - 1.08786i) q^{73} +(1.57567 - 0.815539i) q^{75} +(0.997381 - 3.06962i) q^{77} +(1.46702 + 1.06585i) q^{79} +(-6.37718 + 4.63330i) q^{81} +(5.88093 - 4.27274i) q^{83} +(-2.00595 + 4.88679i) q^{85} +(-0.694817 - 2.13843i) q^{87} +(-1.14668 + 3.52911i) q^{89} +(3.56662 + 10.9769i) q^{91} -2.70879 q^{93} +(-6.25570 + 15.2398i) q^{95} +(2.50040 + 1.81664i) q^{97} +2.87409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	0.287074	+	0.208571i	0.165742	+	0.120419i	0.667564	−	0.744552i	$-0.267337\pi$
$3$	0.287074	+	0.208571i	0.165742	+	0.120419i	−0.501822	+	0.864971i	$0.667337\pi$
$4$		0			0
$5$	1.90283	−	1.17441i	0.850970	−	0.525214i
$5$	1.90283	−	1.17441i	0.850970	−	0.525214i
$6$		0			0
$7$	−3.22759			−1.21992			−0.609958	−	0.792434i	$-0.708814\pi$
$7$	−3.22759			−1.21992			−0.609958	+	0.792434i	$0.708814\pi$
$8$		0			0
$9$	−0.888142	−	2.73342i	−0.296047	−	0.911140i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	−1.10504	−	3.40097i	−0.306483	−	0.943259i	−0.979119	−	0.203286i	$-0.934838\pi$
$13$	−1.10504	−	3.40097i	−0.306483	−	0.943259i	0.672636	−	0.739973i	$-0.265162\pi$
$14$		0			0
$15$	0.791201	+	0.0597318i	0.204287	+	0.0154227i
$16$		0			0
$17$	−1.91122	+	1.38858i	−0.463538	+	0.336780i	−0.794918	−	0.606717i	$-0.792486\pi$
$17$	−1.91122	+	1.38858i	−0.463538	+	0.336780i	0.331379	+	0.943498i	$0.392486\pi$
$18$		0			0
$19$	−5.96028	+	4.33039i	−1.36738	+	0.993461i	−0.369445	+	0.929253i	$0.620452\pi$
$19$	−5.96028	+	4.33039i	−1.36738	+	0.993461i	−0.997937	+	0.0642077i	$0.979548\pi$
$20$		0			0
$21$	−0.926558	−	0.673184i	−0.202192	−	0.146901i
$22$		0			0
$23$	2.33680	−	7.19193i	0.487256	−	1.49962i	−0.341430	−	0.939907i	$-0.610911\pi$
$23$	2.33680	−	7.19193i	0.487256	−	1.49962i	0.828686	−	0.559714i	$-0.189089\pi$
$24$		0			0
$25$	2.24150	−	4.46941i	0.448301	−	0.893883i
$26$		0			0
$27$	0.644108	−	1.98236i	0.123959	−	0.381506i
$28$		0			0
$29$	−5.12636	−	3.72452i	−0.951942	−	0.691626i	−0.000676541	−	1.00000i	$-0.500215\pi$
$29$	−5.12636	−	3.72452i	−0.951942	−	0.691626i	−0.951265	+	0.308373i	$0.900215\pi$
$30$		0			0
$31$	−6.17586	+	4.48703i	−1.10922	+	0.805894i	−0.982540	−	0.186050i	$-0.940431\pi$
$31$	−6.17586	+	4.48703i	−1.10922	+	0.805894i	−0.126677	+	0.991944i	$0.540431\pi$
$32$		0			0
$33$	−0.287074	+	0.208571i	−0.0499732	+	0.0363076i
$34$		0			0
$35$	−6.14155	+	3.79053i	−1.03811	+	0.640717i
$36$		0			0
$37$	2.29508	+	7.06353i	0.377309	+	1.16124i	0.941908	+	0.335872i	$0.109031\pi$
$37$	2.29508	+	7.06353i	0.377309	+	1.16124i	−0.564599	+	0.825365i	$0.690969\pi$
$38$		0			0
$39$	0.392116	−	1.20681i	0.0627889	−	0.193244i
$40$		0			0
$41$	−2.50450	−	7.70805i	−0.391137	−	1.20380i	−0.931930	−	0.362639i	$-0.881876\pi$
$41$	−2.50450	−	7.70805i	−0.391137	−	1.20380i	0.540793	−	0.841156i	$-0.318124\pi$
$42$		0			0
$43$	−4.93377			−0.752393			−0.376196	−	0.926540i	$-0.622768\pi$
$43$	−4.93377			−0.752393			−0.376196	+	0.926540i	$0.622768\pi$
$44$		0			0
$45$	−4.90015	−	4.15818i	−0.730471	−	0.619865i
$46$		0			0
$47$	10.3550	+	7.52338i	1.51044	+	1.09740i	0.965982	+	0.258609i	$0.0832641\pi$
$47$	10.3550	+	7.52338i	1.51044	+	1.09740i	0.544457	+	0.838789i	$0.316736\pi$
$48$		0			0
$49$	3.41735			0.488193
$50$		0			0
$51$	−0.838279			−0.117383
$52$		0			0
$53$	2.61550	+	1.90027i	0.359266	+	0.261022i	0.752746	−	0.658311i	$-0.228729\pi$
$53$	2.61550	+	1.90027i	0.359266	+	0.261022i	−0.393480	+	0.919333i	$0.628729\pi$
$54$		0			0
$55$	0.528928	+	2.17261i	0.0713207	+	0.292955i
$56$		0			0
$57$	−2.61424			−0.346264
$58$		0			0
$59$	−4.07289	−	12.5351i	−0.530245	−	1.63193i	−0.753704	−	0.657214i	$-0.771735\pi$
$59$	−4.07289	−	12.5351i	−0.530245	−	1.63193i	0.223459	−	0.974713i	$-0.428265\pi$
$60$		0			0
$61$	3.70068	−	11.3895i	0.473824	−	1.45828i	−0.373713	−	0.927544i	$-0.621915\pi$
$61$	3.70068	−	11.3895i	0.473824	−	1.45828i	0.847537	−	0.530736i	$-0.178085\pi$
$62$		0			0
$63$	2.86656	+	8.82236i	0.361153	+	1.11151i
$64$		0			0
$65$	−6.09685	−	5.17368i	−0.756221	−	0.641716i
$66$		0			0
$67$	2.26355	−	1.64456i	0.276536	−	0.200915i	−0.440869	−	0.897571i	$-0.645330\pi$
$67$	2.26355	−	1.64456i	0.276536	−	0.200915i	0.717405	+	0.696656i	$0.245330\pi$
$68$		0			0
$69$	2.17087	−	1.57723i	0.261342	−	0.189876i
$70$		0			0
$71$	1.85297	+	1.34626i	0.219907	+	0.159772i	0.692285	−	0.721624i	$-0.256604\pi$
$71$	1.85297	+	1.34626i	0.219907	+	0.159772i	−0.472378	+	0.881396i	$0.656604\pi$
$72$		0			0
$73$	0.353466	−	1.08786i	0.0413700	−	0.127324i	−0.928238	−	0.371986i	$-0.878677\pi$
$73$	0.353466	−	1.08786i	0.0413700	−	0.127324i	0.969608	+	0.244662i	$0.0786770\pi$
$74$		0			0
$75$	1.57567	−	0.815539i	0.181943	−	0.0941703i
$76$		0			0
$77$	0.997381	−	3.06962i	0.113662	−	0.349816i
$78$		0			0
$79$	1.46702	+	1.06585i	0.165052	+	0.119917i	0.667245	−	0.744838i	$-0.267473\pi$
$79$	1.46702	+	1.06585i	0.165052	+	0.119917i	−0.502193	+	0.864756i	$0.667473\pi$
$80$		0			0
$81$	−6.37718	+	4.63330i	−0.708576	+	0.514811i
$82$		0			0
$83$	5.88093	−	4.27274i	0.645516	−	0.468994i	−0.216225	−	0.976344i	$-0.569375\pi$
$83$	5.88093	−	4.27274i	0.645516	−	0.468994i	0.861741	+	0.507349i	$0.169375\pi$
$84$		0			0
$85$	−2.00595	+	4.88679i	−0.217576	+	0.530047i
$86$		0			0
$87$	−0.694817	−	2.13843i	−0.0744922	−	0.229263i
$88$		0			0
$89$	−1.14668	+	3.52911i	−0.121548	+	0.374085i	−0.993256	−	0.115940i	$-0.963012\pi$
$89$	−1.14668	+	3.52911i	−0.121548	+	0.374085i	0.871709	+	0.490024i	$0.163012\pi$
$90$		0			0
$91$	3.56662	+	10.9769i	0.373884	+	1.15070i
$92$		0			0
$93$	−2.70879			−0.280889
$94$		0			0
$95$	−6.25570	+	15.2398i	−0.641821	+	1.56357i
$96$		0			0
$97$	2.50040	+	1.81664i	0.253877	+	0.184452i	0.707443	−	0.706770i	$-0.249849\pi$
$97$	2.50040	+	1.81664i	0.253877	+	0.184452i	−0.453566	+	0.891222i	$0.649849\pi$
$98$		0			0
$99$	2.87409			0.288857
$100$		0			0
$101$	−3.03581			−0.302075			−0.151037	−	0.988528i	$-0.548261\pi$
$101$	−3.03581			−0.302075			−0.151037	+	0.988528i	$0.548261\pi$
$102$		0			0
$103$	−8.08187	−	5.87182i	−0.796330	−	0.578568i	0.113505	−	0.993537i	$-0.463792\pi$
$103$	−8.08187	−	5.87182i	−0.796330	−	0.578568i	−0.909835	+	0.414970i	$0.863792\pi$
$104$		0			0
$105$	−2.55368	−	0.192790i	−0.249213	−	0.0188144i
$106$		0			0
$107$	5.85006			0.565546			0.282773	−	0.959187i	$-0.408746\pi$
$107$	5.85006			0.565546			0.282773	+	0.959187i	$0.408746\pi$
$108$		0			0
$109$	1.09115	+	3.35821i	0.104513	+	0.321658i	0.989616	−	0.143738i	$-0.0459121\pi$
$109$	1.09115	+	3.35821i	0.104513	+	0.321658i	−0.885103	+	0.465395i	$0.845912\pi$
$110$		0			0
$111$	−0.814393	+	2.50644i	−0.0772988	+	0.237901i
$112$		0			0
$113$	−3.67954	−	11.3245i	−0.346142	−	1.06532i	−0.960970	−	0.276654i	$-0.910774\pi$
$113$	−3.67954	−	11.3245i	−0.346142	−	1.06532i	0.614827	−	0.788662i	$-0.289226\pi$
$114$		0			0
$115$	−3.99978	−	16.4294i	−0.372981	−	1.53205i
$116$		0			0
$117$	−8.31484	+	6.04108i	−0.768707	+	0.558498i
$118$		0			0
$119$	6.16863	−	4.48177i	0.565477	−	0.410843i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	0.888703	−	2.73515i	0.0801317	−	0.246620i
$124$		0			0
$125$	−0.983748	−	11.1370i	−0.0879891	−	0.996121i
$126$		0			0
$127$	−0.187014	+	0.575570i	−0.0165948	+	0.0510735i	−0.959011	−	0.283369i	$-0.908548\pi$
$127$	−0.187014	+	0.575570i	−0.0165948	+	0.0510735i	0.942416	+	0.334442i	$0.108548\pi$
$128$		0			0
$129$	−1.41636	−	1.02904i	−0.124703	−	0.0906022i
$130$		0			0
$131$	0.258573	−	0.187864i	0.0225916	−	0.0164138i	−0.576432	−	0.817145i	$-0.695555\pi$
$131$	0.258573	−	0.187864i	0.0225916	−	0.0164138i	0.599024	+	0.800731i	$0.295555\pi$
$132$		0			0
$133$	19.2373	−	13.9767i	1.66809	−	1.21194i
$134$		0			0
$135$	−1.10249	−	4.52854i	−0.0948869	−	0.389755i
$136$		0			0
$137$	−0.220119	−	0.677458i	−0.0188061	−	0.0578791i	0.941213	−	0.337813i	$-0.109687\pi$
$137$	−0.220119	−	0.677458i	−0.0188061	−	0.0578791i	−0.960019	+	0.279934i	$0.909687\pi$
$138$		0			0
$139$	6.93430	−	21.3416i	0.588160	−	1.81017i	0.00196741	−	0.999998i	$-0.499374\pi$
$139$	6.93430	−	21.3416i	0.588160	−	1.81017i	0.586192	−	0.810172i	$-0.300626\pi$
$140$		0			0
$141$	1.40350	+	4.31953i	0.118196	+	0.363770i
$142$		0			0
$143$	3.57599			0.299039
$144$		0			0
$145$	−14.1287	−	1.06665i	−1.17333	−	0.0885802i
$146$		0			0
$147$	0.981034	+	0.712763i	0.0809143	+	0.0587877i
$148$		0			0
$149$	8.78434			0.719641			0.359821	−	0.933021i	$-0.382838\pi$
$149$	8.78434			0.719641			0.359821	+	0.933021i	$0.382838\pi$
$150$		0			0
$151$	−23.3459			−1.89986			−0.949930	−	0.312463i	$-0.898846\pi$
$151$	−23.3459			−1.89986			−0.949930	+	0.312463i	$0.898846\pi$
$152$		0			0
$153$	5.49300	+	3.99090i	0.444083	+	0.322645i
$154$		0			0
$155$	−6.48197	+	15.7911i	−0.520644	+	1.26837i
$156$		0			0
$157$	−7.47850			−0.596849			−0.298425	−	0.954433i	$-0.596461\pi$
$157$	−7.47850			−0.596849			−0.298425	+	0.954433i	$0.596461\pi$
$158$		0			0
$159$	0.354499	+	1.09104i	0.0281136	+	0.0865248i
$160$		0			0
$161$	−7.54224	+	23.2126i	−0.594412	+	1.82941i
$162$		0			0
$163$	4.80965	+	14.8026i	0.376721	+	1.15943i	0.942310	+	0.334741i	$0.108649\pi$
$163$	4.80965	+	14.8026i	0.376721	+	1.15943i	−0.565589	+	0.824687i	$0.691351\pi$
$164$		0			0
$165$	−0.301303	+	0.734019i	−0.0234564	+	0.0571433i
$166$		0			0
$167$	6.14367	−	4.46364i	0.475412	−	0.345407i	−0.324135	−	0.946011i	$-0.605073\pi$
$167$	6.14367	−	4.46364i	0.475412	−	0.345407i	0.799547	+	0.600604i	$0.205073\pi$
$168$		0			0
$169$	0.171750	−	0.124784i	0.0132115	−	0.00959874i
$170$		0			0
$171$	17.1303	+	12.4459i	1.30999	+	0.951764i
$172$		0			0
$173$	−2.29806	+	7.07272i	−0.174719	+	0.537729i	−0.999621	−	0.0275473i	$-0.991230\pi$
$173$	−2.29806	+	7.07272i	−0.174719	+	0.537729i	0.824902	+	0.565276i	$0.191230\pi$
$174$		0			0
$175$	−7.23466	+	14.4254i	−0.546889	+	1.09046i
$176$		0			0
$177$	1.44524	−	4.44798i	0.108631	−	0.334331i
$178$		0			0
$179$	−1.13085	−	0.821608i	−0.0845234	−	0.0614099i	0.544721	−	0.838617i	$-0.316636\pi$
$179$	−1.13085	−	0.821608i	−0.0845234	−	0.0614099i	−0.629244	+	0.777207i	$0.716636\pi$
$180$		0			0
$181$	3.57267	−	2.59570i	0.265554	−	0.192937i	−0.447038	−	0.894515i	$-0.647521\pi$
$181$	3.57267	−	2.59570i	0.265554	−	0.192937i	0.712592	+	0.701579i	$0.247521\pi$
$182$		0			0
$183$	3.43790	−	2.49778i	0.254137	−	0.184641i
$184$		0			0
$185$	12.6626	+	10.7453i	0.930977	+	0.790010i
$186$		0			0
$187$	−0.730020	−	2.24677i	−0.0533843	−	0.164300i
$188$		0			0
$189$	−2.07892	+	6.39826i	−0.151219	+	0.465405i
$190$		0			0
$191$	0.648720	+	1.99656i	0.0469398	+	0.144466i	0.971779	−	0.235892i	$-0.0758010\pi$
$191$	0.648720	+	1.99656i	0.0469398	+	0.144466i	−0.924840	+	0.380357i	$0.875801\pi$
$192$		0			0
$193$	20.9332			1.50681			0.753403	−	0.657559i	$-0.228411\pi$
$193$	20.9332			1.50681			0.753403	+	0.657559i	$0.228411\pi$
$194$		0			0
$195$	−0.671165	−	2.75686i	−0.0480631	−	0.197423i
$196$		0			0
$197$	19.3668	+	14.0708i	1.37983	+	1.00250i	0.996896	+	0.0787236i	$0.0250845\pi$
$197$	19.3668	+	14.0708i	1.37983	+	1.00250i	0.382929	+	0.923778i	$0.374916\pi$
$198$		0			0
$199$	18.6766			1.32395			0.661973	−	0.749527i	$-0.269719\pi$
$199$	18.6766			1.32395			0.661973	+	0.749527i	$0.269719\pi$
$200$		0			0
$201$	0.992814			0.0700277
$202$		0			0
$203$	16.5458	+	12.0212i	1.16129	+	0.843726i
$204$		0			0
$205$	−13.8181	−	11.7258i	−0.965096	−	0.818963i
$206$		0			0
$207$	−21.7340			−1.51061
$208$		0			0
$209$	−2.27662	−	7.00672i	−0.157477	−	0.484665i
$210$		0			0
$211$	−1.52204	+	4.68436i	−0.104782	+	0.322485i	−0.989679	−	0.143301i	$-0.954228\pi$
$211$	−1.52204	+	4.68436i	−0.104782	+	0.322485i	0.884897	+	0.465786i	$0.154228\pi$
$212$		0			0
$213$	0.251148	+	0.772955i	0.0172084	+	0.0529620i
$214$		0			0
$215$	−9.38811	+	5.79429i	−0.640264	+	0.395167i
$216$		0			0
$217$	19.9332	−	14.4823i	1.35315	−	0.983122i
$218$		0			0
$219$	0.328367	−	0.238572i	0.0221890	−	0.0161212i
$220$		0			0
$221$	6.83449	+	4.96555i	0.459738	+	0.334019i
$222$		0			0
$223$	0.669743	−	2.06126i	0.0448493	−	0.138032i	−0.926124	−	0.377218i	$-0.876881\pi$
$223$	0.669743	−	2.06126i	0.0448493	−	0.138032i	0.970974	+	0.239186i	$0.0768807\pi$
$224$		0			0
$225$	−14.2076	−	2.15750i	−0.947170	−	0.143833i
$226$		0			0
$227$	−3.72776	+	11.4729i	−0.247420	+	0.761481i	0.747809	+	0.663914i	$0.231106\pi$
$227$	−3.72776	+	11.4729i	−0.247420	+	0.761481i	−0.995229	+	0.0975666i	$0.968894\pi$
$228$		0			0
$229$	−15.9954	−	11.6213i	−1.05701	−	0.767959i	−0.0834731	−	0.996510i	$-0.526601\pi$
$229$	−15.9954	−	11.6213i	−1.05701	−	0.767959i	−0.973532	+	0.228551i	$0.926601\pi$
$230$		0			0
$231$	0.926558	−	0.673184i	0.0609630	−	0.0442922i
$232$		0			0
$233$	−6.45082	+	4.68680i	−0.422607	+	0.307042i	−0.778686	−	0.627414i	$-0.784114\pi$
$233$	−6.45082	+	4.68680i	−0.422607	+	0.307042i	0.356079	+	0.934456i	$0.384114\pi$
$234$		0			0
$235$	28.5394	+	2.15458i	1.86171	+	0.140550i
$236$		0			0
$237$	0.198836	+	0.611955i	0.0129158	+	0.0397508i
$238$		0			0
$239$	−0.545643	+	1.67932i	−0.0352947	+	0.108626i	−0.967152	−	0.254200i	$-0.918188\pi$
$239$	−0.545643	+	1.67932i	−0.0352947	+	0.108626i	0.931857	+	0.362826i	$0.118188\pi$
$240$		0			0
$241$	2.46676	+	7.59190i	0.158898	+	0.489037i	0.998535	−	0.0541105i	$-0.0172323\pi$
$241$	2.46676	+	7.59190i	0.158898	+	0.489037i	−0.839637	+	0.543148i	$0.817232\pi$
$242$		0			0
$243$	−9.05023			−0.580573
$244$		0			0
$245$	6.50264	−	4.01339i	0.415438	−	0.256406i
$246$		0			0
$247$	21.3139	+	15.4854i	1.35617	+	0.985315i
$248$		0			0
$249$	2.57943			0.163465
$250$		0			0
$251$	−1.89717			−0.119748			−0.0598741	−	0.998206i	$-0.519070\pi$
$251$	−1.89717			−0.119748			−0.0598741	+	0.998206i	$0.519070\pi$
$252$		0			0
$253$	6.11782	+	4.44486i	0.384624	+	0.279446i
$254$		0			0
$255$	−1.59510	+	0.984487i	−0.0998890	+	0.0616509i
$256$		0			0
$257$	29.4152			1.83487			0.917436	−	0.397883i	$-0.130255\pi$
$257$	29.4152			1.83487			0.917436	+	0.397883i	$0.130255\pi$
$258$		0			0
$259$	−7.40758	−	22.7982i	−0.460285	−	1.41661i
$260$		0			0
$261$	−5.62774	+	17.3204i	−0.348348	+	1.07211i
$262$		0			0
$263$	3.53354	+	10.8751i	0.217887	+	0.670588i	0.998936	+	0.0461177i	$0.0146849\pi$
$263$	3.53354	+	10.8751i	0.217887	+	0.670588i	−0.781049	+	0.624470i	$0.785315\pi$
$264$		0			0
$265$	7.20854	+	0.544209i	0.442817	+	0.0334305i
$266$		0			0
$267$	−1.06525	+	0.773951i	−0.0651924	+	0.0473651i
$268$		0			0
$269$	−9.66366	+	7.02106i	−0.589204	+	0.428082i	−0.842031	−	0.539430i	$-0.818640\pi$
$269$	−9.66366	+	7.02106i	−0.589204	+	0.428082i	0.252827	+	0.967512i	$0.418640\pi$
$270$		0			0
$271$	7.22320	+	5.24796i	0.438778	+	0.318791i	0.785149	−	0.619306i	$-0.212586\pi$
$271$	7.22320	+	5.24796i	0.438778	+	0.318791i	−0.346371	+	0.938098i	$0.612586\pi$
$272$		0			0
$273$	−1.26559	+	3.89509i	−0.0765971	+	0.235742i
$274$		0			0
$275$	3.55800	+	3.51292i	0.214556	+	0.211837i
$276$		0			0
$277$	−4.79563	+	14.7594i	−0.288141	+	0.886808i	0.697298	+	0.716781i	$0.254385\pi$
$277$	−4.79563	+	14.7594i	−0.288141	+	0.886808i	−0.985439	+	0.170027i	$0.945615\pi$
$278$		0			0
$279$	17.7500	+	12.8961i	1.06266	+	0.772069i
$280$		0			0
$281$	20.7973	−	15.1102i	1.24067	−	0.901396i	0.243023	−	0.970021i	$-0.421861\pi$
$281$	20.7973	−	15.1102i	1.24067	−	0.901396i	0.997643	+	0.0686246i	$0.0218611\pi$
$282$		0			0
$283$	10.9683	−	7.96892i	0.651997	−	0.473703i	−0.211954	−	0.977280i	$-0.567983\pi$
$283$	10.9683	−	7.96892i	0.651997	−	0.473703i	0.863951	+	0.503576i	$0.167983\pi$
$284$		0			0
$285$	−4.97444	+	3.07020i	−0.294660	+	0.181863i
$286$		0			0
$287$	8.08350	+	24.8784i	0.477154	+	1.46853i
$288$		0			0
$289$	−3.52869	+	10.8602i	−0.207570	+	0.638836i
$290$		0			0
$291$	0.338899	+	1.04302i	0.0198666	+	0.0611431i
$292$		0			0
$293$	−32.9731			−1.92631			−0.963153	−	0.268953i	$-0.913322\pi$
$293$	−32.9731			−1.92631			−0.963153	+	0.268953i	$0.913322\pi$
$294$		0			0
$295$	−22.4714	−	19.0688i	−1.30833	−	1.11023i
$296$		0			0
$297$	1.68630	+	1.22517i	0.0978489	+	0.0710914i
$298$		0			0
$299$	−27.0418			−1.56387
$300$		0			0
$301$	15.9242			0.917855
$302$		0			0
$303$	−0.871503	−	0.633184i	−0.0500665	−	0.0363755i
$304$		0			0
$305$	−6.33427	−	26.0185i	−0.362699	−	1.48981i
$306$		0			0
$307$	4.76541			0.271976			0.135988	−	0.990710i	$-0.456579\pi$
$307$	4.76541			0.271976			0.135988	+	0.990710i	$0.456579\pi$
$308$		0			0
$309$	−1.09540	−	3.37129i	−0.0623151	−	0.191786i
$310$		0			0
$311$	−7.86724	+	24.2129i	−0.446110	+	1.37299i	0.435151	+	0.900358i	$0.356695\pi$
$311$	−7.86724	+	24.2129i	−0.446110	+	1.37299i	−0.881261	+	0.472629i	$0.843305\pi$
$312$		0			0
$313$	−3.65953	−	11.2629i	−0.206849	−	0.636616i	−0.999632	−	0.0271124i	$-0.991369\pi$
$313$	−3.65953	−	11.2629i	−0.206849	−	0.636616i	0.792783	−	0.609504i	$-0.208631\pi$
$314$		0			0
$315$	15.8157	+	13.4209i	0.891112	+	0.756182i
$316$		0			0
$317$	−4.61057	+	3.34977i	−0.258955	+	0.188142i	−0.709686	−	0.704518i	$-0.751163\pi$
$317$	−4.61057	+	3.34977i	−0.258955	+	0.188142i	0.450731	+	0.892660i	$0.351163\pi$
$318$		0			0
$319$	5.12636	−	3.72452i	0.287021	−	0.208533i
$320$		0			0
$321$	1.67940	+	1.22016i	0.0937349	+	0.0681024i
$322$		0			0
$323$	5.37828	−	16.5526i	0.299256	−	0.921014i
$324$		0			0
$325$	−17.6773	−	2.68439i	−0.980560	−	0.148903i
$326$		0			0
$327$	−0.387186	+	1.19164i	−0.0214114	+	0.0658976i
$328$		0			0
$329$	−33.4219	−	24.2824i	−1.84261	−	1.33873i
$330$		0			0
$331$	−21.7598	+	15.8094i	−1.19603	+	0.868964i	−0.993888	−	0.110393i	$-0.964789\pi$
$331$	−21.7598	+	15.8094i	−1.19603	+	0.868964i	−0.202138	+	0.979357i	$0.564789\pi$
$332$		0			0
$333$	17.2692	−	12.5468i	0.946348	−	0.687562i
$334$		0			0
$335$	2.37574	−	5.78766i	0.129801	−	0.316214i
$336$		0			0
$337$	−7.36614	−	22.6706i	−0.401259	−	1.23495i	−0.923979	−	0.382444i	$-0.875083\pi$
$337$	−7.36614	−	22.6706i	−0.401259	−	1.23495i	0.522720	−	0.852505i	$-0.324917\pi$
$338$		0			0
$339$	1.30566	−	4.01841i	0.0709137	−	0.218250i
$340$		0			0
$341$	−2.35897	−	7.26016i	−0.127745	−	0.393160i
$342$		0			0
$343$	11.5633			0.624361
$344$		0			0
$345$	2.27847	−	5.55068i	0.122668	−	0.298839i
$346$		0			0
$347$	−2.76849	−	2.01142i	−0.148620	−	0.107979i	0.510990	−	0.859586i	$-0.329279\pi$
$347$	−2.76849	−	2.01142i	−0.148620	−	0.107979i	−0.659611	+	0.751608i	$0.729279\pi$
$348$		0			0
$349$	31.6305			1.69314			0.846572	−	0.532274i	$-0.178662\pi$
$349$	31.6305			1.69314			0.846572	+	0.532274i	$0.178662\pi$
$350$		0			0
$351$	−7.45372			−0.397850
$352$		0			0
$353$	5.62585	+	4.08742i	0.299434	+	0.217551i	0.727349	−	0.686267i	$-0.240752\pi$
$353$	5.62585	+	4.08742i	0.299434	+	0.217551i	−0.427916	+	0.903819i	$0.640752\pi$
$354$		0			0
$355$	5.10696	+	0.385550i	0.271049	+	0.0204629i
$356$		0			0
$357$	2.70562			0.143197
$358$		0			0
$359$	3.25254	+	10.0103i	0.171662	+	0.528323i	0.999465	−	0.0326965i	$-0.0104095\pi$
$359$	3.25254	+	10.0103i	0.171662	+	0.528323i	−0.827803	+	0.561019i	$0.810409\pi$
$360$		0			0
$361$	10.9013	−	33.5506i	0.573750	−	1.76582i
$362$		0			0
$363$	−0.109653	−	0.337476i	−0.00575526	−	0.0177129i
$364$		0			0
$365$	−0.605009	−	2.48512i	−0.0316676	−	0.130077i
$366$		0			0
$367$	20.7497	−	15.0756i	1.08313	−	0.786939i	0.104902	−	0.994483i	$-0.466547\pi$
$367$	20.7497	−	15.0756i	1.08313	−	0.786939i	0.978226	+	0.207544i	$0.0665470\pi$
$368$		0			0
$369$	−18.8450	+	13.6917i	−0.981030	+	0.712760i
$370$		0			0
$371$	−8.44176	−	6.13330i	−0.438274	−	0.318425i
$372$		0			0
$373$	6.64661	−	20.4562i	0.344148	−	1.05918i	−0.617890	−	0.786265i	$-0.712012\pi$
$373$	6.64661	−	20.4562i	0.344148	−	1.05918i	0.962038	−	0.272915i	$-0.0879877\pi$
$374$		0			0
$375$	2.04045	−	3.40232i	0.105368	−	0.175695i
$376$		0			0
$377$	−7.00213	+	21.5504i	−0.360628	+	1.10990i
$378$		0			0
$379$	0.777008	+	0.564529i	0.0399122	+	0.0289979i	0.607563	−	0.794272i	$-0.292147\pi$
$379$	0.777008	+	0.564529i	0.0399122	+	0.0289979i	−0.567650	+	0.823270i	$0.692147\pi$
$380$		0			0
$381$	−0.173734	+	0.126225i	−0.00890067	+	0.00646672i
$382$		0			0
$383$	−5.34421	+	3.88279i	−0.273076	+	0.198401i	−0.715892	−	0.698211i	$-0.753980\pi$
$383$	−5.34421	+	3.88279i	−0.273076	+	0.198401i	0.442816	+	0.896613i	$0.353980\pi$
$384$		0			0
$385$	−1.70716	−	7.01230i	−0.0870052	−	0.357380i
$386$		0			0
$387$	4.38189	+	13.4861i	0.222744	+	0.685535i
$388$		0			0
$389$	9.69665	−	29.8432i	0.491640	−	1.51311i	−0.330489	−	0.943810i	$-0.607214\pi$
$389$	9.69665	−	29.8432i	0.491640	−	1.51311i	0.822129	−	0.569301i	$-0.192786\pi$
$390$		0			0
$391$	5.52044	+	16.9902i	0.279181	+	0.859230i
$392$		0			0
$393$	0.113413			0.00572092
$394$		0			0
$395$	4.04323	+	0.305243i	0.203437	+	0.0153585i
$396$		0			0
$397$	−29.4061	−	21.3648i	−1.47585	−	1.07227i	−0.978864	−	0.204512i	$-0.934439\pi$
$397$	−29.4061	−	21.3648i	−1.47585	−	1.07227i	−0.496988	−	0.867757i	$-0.665561\pi$
$398$		0			0
$399$	8.43769			0.422413
$400$		0			0
$401$	−21.2701			−1.06218			−0.531090	−	0.847316i	$-0.678217\pi$
$401$	−21.2701			−1.06218			−0.531090	+	0.847316i	$0.678217\pi$
$402$		0			0
$403$	22.0848	+	16.0456i	1.10012	+	0.799286i
$404$		0			0
$405$	−6.69327	+	16.3058i	−0.332591	+	0.810242i
$406$		0			0
$407$	−7.42704			−0.368144
$408$		0			0
$409$	−4.54582	−	13.9906i	−0.224776	−	0.691790i	−0.998314	−	0.0580401i	$-0.981515\pi$
$409$	−4.54582	−	13.9906i	−0.224776	−	0.691790i	0.773538	−	0.633750i	$-0.218485\pi$
$410$		0			0
$411$	0.0781078	−	0.240391i	0.00385277	−	0.0118576i
$412$		0			0
$413$	13.1456	+	40.4581i	0.646854	+	1.99081i
$414$		0			0
$415$	6.17242	−	15.0369i	0.302992	−	0.738134i
$416$		0			0
$417$	6.44190	−	4.68032i	0.315461	−	0.229196i
$418$		0			0
$419$	12.3824	−	8.99633i	0.604919	−	0.439499i	−0.242702	−	0.970101i	$-0.578034\pi$
$419$	12.3824	−	8.99633i	0.604919	−	0.439499i	0.847621	+	0.530601i	$0.178034\pi$
$420$		0			0
$421$	−18.8516	−	13.6965i	−0.918770	−	0.667526i	0.0244474	−	0.999701i	$-0.492217\pi$
$421$	−18.8516	−	13.6965i	−0.918770	−	0.667526i	−0.943218	+	0.332176i	$0.892217\pi$
$422$		0			0
$423$	11.3678	−	34.9865i	0.552722	−	1.70110i
$424$		0			0
$425$	1.92214	+	11.6545i	0.0932376	+	0.565328i
$426$		0			0
$427$	−11.9443	+	36.7608i	−0.578025	+	1.77898i
$428$		0			0
$429$	1.02657	+	0.745849i	0.0495634	+	0.0360100i
$430$		0			0
$431$	−26.5141	+	19.2636i	−1.27714	+	0.927896i	−0.999463	−	0.0327786i	$-0.989564\pi$
$431$	−26.5141	+	19.2636i	−1.27714	+	0.927896i	−0.277677	+	0.960675i	$0.589564\pi$
$432$		0			0
$433$	20.7074	−	15.0448i	0.995134	−	0.723007i	0.0340949	−	0.999419i	$-0.489145\pi$
$433$	20.7074	−	15.0448i	0.995134	−	0.723007i	0.961039	+	0.276411i	$0.0891452\pi$
$434$		0			0
$435$	−3.83351	−	3.25305i	−0.183803	−	0.155972i
$436$		0			0
$437$	17.2159	+	52.9852i	0.823549	+	2.53462i
$438$		0			0
$439$	−1.41214	+	4.34612i	−0.0673977	+	0.207429i	−0.979083	−	0.203460i	$-0.934781\pi$
$439$	−1.41214	+	4.34612i	−0.0673977	+	0.207429i	0.911686	+	0.410889i	$0.134781\pi$
$440$		0			0
$441$	−3.03509	−	9.34106i	−0.144528	−	0.444812i
$442$		0			0
$443$	−32.6572			−1.55159			−0.775795	−	0.630985i	$-0.782651\pi$
$443$	−32.6572			−1.55159			−0.775795	+	0.630985i	$0.782651\pi$
$444$		0			0
$445$	1.96271	+	8.06196i	0.0930412	+	0.382174i
$446$		0			0
$447$	2.52176	+	1.83216i	0.119275	+	0.0866584i
$448$		0			0
$449$	−1.59337			−0.0751955			−0.0375978	−	0.999293i	$-0.511971\pi$
$449$	−1.59337			−0.0751955			−0.0375978	+	0.999293i	$0.511971\pi$
$450$		0			0
$451$	8.10472			0.381636
$452$		0			0
$453$	−6.70199	−	4.86928i	−0.314887	−	0.228779i
$454$		0			0
$455$	19.6781	+	16.6985i	0.922526	+	0.782839i
$456$		0			0
$457$	31.3578			1.46685			0.733427	−	0.679768i	$-0.237919\pi$
$457$	31.3578			1.46685			0.733427	+	0.679768i	$0.237919\pi$
$458$		0			0
$459$	1.52164	+	4.68312i	0.0710240	+	0.218589i
$460$		0			0
$461$	−6.44913	+	19.8484i	−0.300366	+	0.924431i	0.681000	+	0.732283i	$0.261545\pi$
$461$	−6.44913	+	19.8484i	−0.300366	+	0.924431i	−0.981366	+	0.192148i	$0.938455\pi$
$462$		0			0
$463$	−7.10291	−	21.8605i	−0.330100	−	1.01594i	−0.969085	−	0.246725i	$-0.920645\pi$
$463$	−7.10291	−	21.8605i	−0.330100	−	1.01594i	0.638985	−	0.769219i	$-0.279355\pi$
$464$		0			0
$465$	−5.15437	+	3.18125i	−0.239028	+	0.147527i
$466$		0			0
$467$	−29.1148	+	21.1532i	−1.34727	+	0.978852i	−0.348131	+	0.937446i	$0.613184\pi$
$467$	−29.1148	+	21.1532i	−1.34727	+	0.978852i	−0.999142	+	0.0414057i	$0.986816\pi$
$468$		0			0
$469$	−7.30581	+	5.30798i	−0.337351	+	0.245100i
$470$		0			0
$471$	−2.14688	−	1.55980i	−0.0989231	−	0.0718718i
$472$		0			0
$473$	1.52462	−	4.69229i	0.0701020	−	0.215752i
$474$		0			0
$475$	5.99434	+	36.3455i	0.275039	+	1.66765i
$476$		0			0
$477$	2.87130	−	8.83696i	0.131468	−	0.404616i
$478$		0			0
$479$	−22.9764	−	16.6934i	−1.04982	−	0.762739i	−0.0776421	−	0.996981i	$-0.524739\pi$
$479$	−22.9764	−	16.6934i	−1.04982	−	0.762739i	−0.972178	+	0.234242i	$0.924739\pi$
$480$		0			0
$481$	21.4867	−	15.6110i	0.979709	−	0.711800i
$482$		0			0
$483$	−7.00667	+	5.09064i	−0.318815	+	0.231632i
$484$		0			0
$485$	6.89131	+	0.520260i	0.312918	+	0.0236238i
$486$		0			0
$487$	−10.9049	−	33.5619i	−0.494149	−	1.52083i	−0.818279	−	0.574822i	$-0.805071\pi$
$487$	−10.9049	−	33.5619i	−0.494149	−	1.52083i	0.324130	−	0.946013i	$-0.394929\pi$
$488$		0			0
$489$	−1.70667	+	5.25260i	−0.0771784	+	0.237531i
$490$		0			0
$491$	−12.4359	−	38.2737i	−0.561224	−	1.72727i	−0.678914	−	0.734218i	$-0.737549\pi$
$491$	−12.4359	−	38.2737i	−0.561224	−	1.72727i	0.117690	−	0.993050i	$-0.462451\pi$
$492$		0			0
$493$	14.9694			0.674188
$494$		0			0
$495$	5.46889	−	3.37537i	0.245808	−	0.151711i
$496$		0			0
$497$	−5.98064	−	4.34519i	−0.268269	−	0.194908i
$498$		0			0
$499$	12.6231			0.565088			0.282544	−	0.959254i	$-0.408822\pi$
$499$	12.6231			0.565088			0.282544	+	0.959254i	$0.408822\pi$
$500$		0			0
$501$	2.69468			0.120389
$502$		0			0
$503$	−19.7710	−	14.3645i	−0.881547	−	0.640481i	0.0521133	−	0.998641i	$-0.483404\pi$
$503$	−19.7710	−	14.3645i	−0.881547	−	0.640481i	−0.933660	+	0.358160i	$0.883404\pi$
$504$		0			0
$505$	−5.77663	+	3.56530i	−0.257056	+	0.158654i
$506$		0			0
$507$	0.0753313			0.00334558
$508$		0			0
$509$	10.1673	+	31.2916i	0.450656	+	1.38698i	0.876160	+	0.482020i	$0.160097\pi$
$509$	10.1673	+	31.2916i	0.450656	+	1.38698i	−0.425505	+	0.904956i	$0.639903\pi$
$510$		0			0
$511$	−1.14084	+	3.51116i	−0.0504679	+	0.155324i
$512$		0			0
$513$	4.74534	+	14.6047i	0.209512	+	0.644812i
$514$		0			0
$515$	−22.2743	−	1.68160i	−0.981525	−	0.0741002i
$516$		0			0
$517$	−10.3550	+	7.52338i	−0.455414	+	0.330878i
$518$		0			0
$519$	−2.13488	+	1.55108i	−0.0937109	+	0.0680850i
$520$		0			0
$521$	−25.1884	−	18.3004i	−1.10352	−	0.801757i	−0.121892	−	0.992543i	$-0.538896\pi$
$521$	−25.1884	−	18.3004i	−1.10352	−	0.801757i	−0.981632	+	0.190786i	$0.938896\pi$
$522$		0			0
$523$	7.07659	−	21.7795i	0.309438	−	0.952351i	−0.668546	−	0.743670i	$-0.733083\pi$
$523$	7.07659	−	21.7795i	0.309438	−	0.952351i	0.977984	−	0.208680i	$-0.0669168\pi$
$524$		0			0
$525$	−5.08562	+	2.63223i	−0.221955	+	0.114880i
$526$		0			0
$527$	5.57281	−	17.1514i	0.242756	−	0.747125i
$528$		0			0
$529$	−27.6558	−	20.0931i	−1.20243	−	0.873615i
$530$		0			0
$531$	−30.6463	+	22.2658i	−1.32994	+	0.966255i
$532$		0			0
$533$	−23.4473	+	17.0354i	−1.01561	+	0.737886i
$534$		0			0
$535$	11.1316	−	6.87039i	0.481263	−	0.297033i
$536$		0			0
$537$	−0.153273	−	0.471725i	−0.00661420	−	0.0203564i
$538$		0			0
$539$	−1.05602	+	3.25010i	−0.0454860	+	0.139992i
$540$		0			0
$541$	6.26225	+	19.2732i	0.269235	+	0.828621i	0.990687	+	0.136156i	$0.0434750\pi$
$541$	6.26225	+	19.2732i	0.269235	+	0.828621i	−0.721452	+	0.692464i	$0.756525\pi$
$542$		0			0
$543$	1.56701			0.0672468
$544$		0			0
$545$	6.02019	+	5.10863i	0.257877	+	0.218830i
$546$		0			0
$547$	−25.2374	−	18.3361i	−1.07908	−	0.783994i	−0.101554	−	0.994830i	$-0.532381\pi$
$547$	−25.2374	−	18.3361i	−1.07908	−	0.783994i	−0.977521	+	0.210836i	$0.932381\pi$
$548$		0			0
$549$	−34.4191			−1.46897
$550$		0			0
$551$	46.6832			1.98877
$552$		0			0
$553$	−4.73493	−	3.44013i	−0.201350	−	0.146289i
$554$		0			0
$555$	1.39395	+	5.72576i	0.0591700	+	0.243045i
$556$		0			0
$557$	16.5366			0.700679			0.350340	−	0.936623i	$-0.386066\pi$
$557$	16.5366			0.700679			0.350340	+	0.936623i	$0.386066\pi$
$558$		0			0
$559$	5.45202	+	16.7796i	0.230596	+	0.709701i
$560$		0			0
$561$	0.259042	−	0.797251i	0.0109368	−	0.0336599i
$562$		0			0
$563$	0.239693	+	0.737700i	0.0101019	+	0.0310903i	0.955980	−	0.293431i	$-0.0947969\pi$
$563$	0.239693	+	0.737700i	0.0101019	+	0.0310903i	−0.945879	+	0.324521i	$0.894797\pi$
$564$		0			0
$565$	−20.3011	−	17.2272i	−0.854075	−	0.724753i
$566$		0			0
$567$	20.5830	−	14.9544i	0.864403	−	0.628025i
$568$		0			0
$569$	1.69396	−	1.23074i	0.0710147	−	0.0515952i	−0.551712	−	0.834035i	$-0.686025\pi$
$569$	1.69396	−	1.23074i	0.0710147	−	0.0515952i	0.622726	+	0.782440i	$0.286025\pi$
$570$		0			0
$571$	−1.13174	−	0.822260i	−0.0473620	−	0.0344105i	0.563852	−	0.825876i	$-0.309319\pi$
$571$	−1.13174	−	0.822260i	−0.0473620	−	0.0344105i	−0.611214	+	0.791465i	$0.709319\pi$
$572$		0			0
$573$	−0.230194	+	0.708464i	−0.00961649	+	0.0295965i
$574$		0			0
$575$	−26.9058	−	26.5649i	−1.12205	−	1.10783i
$576$		0			0
$577$	9.01348	−	27.7406i	0.375236	−	1.15486i	−0.568083	−	0.822971i	$-0.692315\pi$
$577$	9.01348	−	27.7406i	0.375236	−	1.15486i	0.943319	−	0.331887i	$-0.107685\pi$
$578$		0			0
$579$	6.00938	+	4.36607i	0.249741	+	0.181448i
$580$		0			0
$581$	−18.9812	+	13.7907i	−0.787474	+	0.572134i
$582$		0			0
$583$	−2.61550	+	1.90027i	−0.108323	+	0.0787011i
$584$		0			0
$585$	−8.72697	+	21.2602i	−0.360816	+	0.879001i
$586$		0			0
$587$	−8.01441	−	24.6658i	−0.330790	−	1.01807i	−0.968759	−	0.248005i	$-0.920225\pi$
$587$	−8.01441	−	24.6658i	−0.330790	−	1.01807i	0.637969	−	0.770062i	$-0.279775\pi$
$588$		0			0
$589$	17.3792	−	53.4878i	0.716099	−	2.20393i
$590$		0			0
$591$	2.62493	+	8.07871i	0.107975	+	0.332314i
$592$		0			0
$593$	−6.52272			−0.267856			−0.133928	−	0.990991i	$-0.542759\pi$
$593$	−6.52272			−0.267856			−0.133928	+	0.990991i	$0.542759\pi$
$594$		0			0
$595$	6.47438	−	15.7726i	0.265424	−	0.646612i
$596$		0			0
$597$	5.36156	+	3.89540i	0.219434	+	0.159428i
$598$		0			0
$599$	16.4214			0.670960			0.335480	−	0.942047i	$-0.391102\pi$
$599$	16.4214			0.670960			0.335480	+	0.942047i	$0.391102\pi$
$600$		0			0
$601$	−8.76354			−0.357472			−0.178736	−	0.983897i	$-0.557201\pi$
$601$	−8.76354			−0.357472			−0.178736	+	0.983897i	$0.557201\pi$
$602$		0			0
$603$	−6.50563	−	4.72662i	−0.264930	−	0.192483i
$604$		0			0
$605$	−2.22972	−	0.168333i	−0.0906511	−	0.00684371i
$606$		0			0
$607$	−14.0617			−0.570745			−0.285373	−	0.958417i	$-0.592117\pi$
$607$	−14.0617			−0.570745			−0.285373	+	0.958417i	$0.592117\pi$
$608$		0			0
$609$	2.24259	+	6.90197i	0.0908742	+	0.279682i
$610$		0			0
$611$	14.1440	−	43.5308i	0.572206	−	1.76107i
$612$		0			0
$613$	4.48949	+	13.8172i	0.181329	+	0.558072i	0.999866	−	0.0163813i	$-0.00521458\pi$
$613$	4.48949	+	13.8172i	0.181329	+	0.558072i	−0.818537	+	0.574454i	$0.805215\pi$
$614$		0			0
$615$	−1.52115	−	6.24822i	−0.0613385	−	0.251952i
$616$		0			0
$617$	19.8190	−	14.3994i	0.797883	−	0.579696i	−0.112409	−	0.993662i	$-0.535857\pi$
$617$	19.8190	−	14.3994i	0.797883	−	0.579696i	0.910292	+	0.413966i	$0.135857\pi$
$618$		0			0
$619$	−24.8073	+	18.0236i	−0.997091	+	0.724429i	−0.961462	−	0.274936i	$-0.911343\pi$
$619$	−24.8073	+	18.0236i	−0.997091	+	0.724429i	−0.0356282	+	0.999365i	$0.511343\pi$
$620$		0			0
$621$	−12.7519	−	9.26476i	−0.511714	−	0.371782i
$622$		0			0
$623$	3.70101	−	11.3905i	0.148278	−	0.456352i
$624$		0			0
$625$	−14.9513	−	20.0364i	−0.598053	−	0.801457i
$626$		0			0
$627$	0.807844	−	2.48629i	0.0322622	−	0.0992927i
$628$		0			0
$629$	−14.1947	−	10.3130i	−0.565979	−	0.411208i
$630$		0			0
$631$	1.99325	−	1.44818i	0.0793502	−	0.0576513i	−0.547403	−	0.836869i	$-0.684383\pi$
$631$	1.99325	−	1.44818i	0.0793502	−	0.0576513i	0.626753	+	0.779218i	$0.284383\pi$
$632$		0			0
$633$	−1.41396	+	1.02730i	−0.0562000	+	0.0408317i
$634$		0			0
$635$	0.320102	+	1.31484i	0.0127029	+	0.0521779i
$636$		0			0
$637$	−3.77632	−	11.6223i	−0.149623	−	0.460493i
$638$		0			0
$639$	2.03420	−	6.26062i	0.0804717	−	0.247666i
$640$		0			0
$641$	−9.57837	−	29.4792i	−0.378323	−	1.16436i	−0.941209	−	0.337824i	$-0.890309\pi$
$641$	−9.57837	−	29.4792i	−0.378323	−	1.16436i	0.562886	−	0.826534i	$-0.309691\pi$
$642$		0			0
$643$	−6.62377			−0.261216			−0.130608	−	0.991434i	$-0.541693\pi$
$643$	−6.62377			−0.261216			−0.130608	+	0.991434i	$0.541693\pi$
$644$		0			0
$645$	−3.90361	−	0.294703i	−0.153704	−	0.0116039i
$646$		0			0
$647$	−27.7697	−	20.1758i	−1.09174	−	0.793194i	−0.112046	−	0.993703i	$-0.535740\pi$
$647$	−27.7697	−	20.1758i	−1.09174	−	0.793194i	−0.979692	+	0.200509i	$0.935740\pi$
$648$		0			0
$649$	13.1802			0.517366
$650$		0			0
$651$	8.74289			0.342661
$652$		0			0
$653$	34.8841	+	25.3448i	1.36512	+	0.991817i	0.998101	+	0.0616029i	$0.0196212\pi$
$653$	34.8841	+	25.3448i	1.36512	+	0.991817i	0.367018	+	0.930214i	$0.380379\pi$
$654$		0			0
$655$	0.271389	−	0.661145i	0.0106041	−	0.0258331i
$656$		0			0
$657$	−3.28749			−0.128257
$658$		0			0
$659$	6.25805	+	19.2603i	0.243779	+	0.750274i	0.995835	+	0.0911751i	$0.0290623\pi$
$659$	6.25805	+	19.2603i	0.243779	+	0.750274i	−0.752056	+	0.659099i	$0.770938\pi$
$660$		0			0
$661$	−11.0739	+	34.0821i	−0.430726	+	1.32564i	0.466677	+	0.884428i	$0.345451\pi$
$661$	−11.0739	+	34.0821i	−0.430726	+	1.32564i	−0.897403	+	0.441212i	$0.854549\pi$
$662$		0			0
$663$	0.926333	+	2.85096i	0.0359758	+	0.110722i
$664$		0			0
$665$	20.1909	−	49.1879i	0.782968	−	1.90743i
$666$		0			0
$667$	−38.7658	+	28.1650i	−1.50102	+	1.09055i
$668$		0			0
$669$	0.622185	−	0.452044i	0.0240551	−	0.0174770i
$670$		0			0
$671$	9.68852	+	7.03912i	0.374021	+	0.271742i
$672$		0			0
$673$	−2.42253	+	7.45577i	−0.0933816	+	0.287399i	−0.986829	−	0.161770i	$-0.948280\pi$
$673$	−2.42253	+	7.45577i	−0.0933816	+	0.287399i	0.893447	+	0.449169i	$0.148280\pi$
$674$		0			0
$675$	−7.41622	−	7.32226i	−0.285451	−	0.281834i
$676$		0			0
$677$	3.24348	−	9.98240i	0.124657	−	0.383655i	−0.869181	−	0.494493i	$-0.835354\pi$
$677$	3.24348	−	9.98240i	0.124657	−	0.383655i	0.993838	+	0.110838i	$0.0353536\pi$
$678$		0			0
$679$	−8.07026	−	5.86339i	−0.309708	−	0.225016i
$680$		0			0
$681$	−3.46305	+	2.51606i	−0.132705	+	0.0964155i
$682$		0			0
$683$	3.25963	−	2.36826i	0.124726	−	0.0906190i	−0.523673	−	0.851919i	$-0.675439\pi$
$683$	3.25963	−	2.36826i	0.124726	−	0.0906190i	0.648399	+	0.761300i	$0.275439\pi$
$684$		0			0
$685$	−1.21446	−	1.03057i	−0.0464023	−	0.0393762i
$686$		0			0
$687$	−2.16798	−	6.67236i	−0.0827137	−	0.254567i
$688$		0			0
$689$	3.57252	−	10.9951i	0.136102	−	0.418880i
$690$		0			0
$691$	−1.84774	−	5.68675i	−0.0702912	−	0.216334i	0.909740	−	0.415179i	$-0.136281\pi$
$691$	−1.84774	−	5.68675i	−0.0702912	−	0.216334i	−0.980031	+	0.198845i	$0.936281\pi$
$692$		0			0
$693$	−9.27638			−0.352381
$694$		0			0
$695$	−11.8691	−	48.7531i	−0.450220	−	1.84931i
$696$		0			0
$697$	15.4899	+	11.2541i	0.586721	+	0.426278i
$698$		0			0
$699$	−2.82940			−0.107018
$700$		0			0
$701$	6.26754			0.236722			0.118361	−	0.992971i	$-0.462236\pi$
$701$	6.26754			0.236722			0.118361	+	0.992971i	$0.462236\pi$
$702$		0			0
$703$	−44.2672	−	32.1620i	−1.66957	−	1.21301i
$704$		0			0
$705$	7.74354	+	6.57104i	0.291639	+	0.247480i
$706$		0			0
$707$	9.79836			0.368505
$708$		0			0
$709$	10.2271	+	31.4757i	0.384086	+	1.18210i	0.937141	+	0.348951i	$0.113462\pi$
$709$	10.2271	+	31.4757i	0.384086	+	1.18210i	−0.553055	+	0.833145i	$0.686538\pi$
$710$		0			0
$711$	1.61049	−	4.95659i	0.0603983	−	0.185887i
$712$		0			0
$713$	17.8386	+	54.9016i	0.668062	+	2.05608i
$714$		0			0
$715$	6.80449	−	4.19969i	0.254474	−	0.157060i
$716$		0			0
$717$	−0.506897	+	0.368282i	−0.0189304	+	0.0137538i
$718$		0			0
$719$	−6.71572	+	4.87925i	−0.250454	+	0.181965i	−0.705928	−	0.708284i	$-0.749470\pi$
$719$	−6.71572	+	4.87925i	−0.250454	+	0.181965i	0.455474	+	0.890249i	$0.349470\pi$
$720$		0			0
$721$	26.0850	+	18.9518i	0.971455	+	0.705804i
$722$		0			0
$723$	−0.875312	+	2.69393i	−0.0325532	+	0.100188i
$724$		0			0
$725$	−28.1372	+	14.5633i	−1.04499	+	0.540868i
$726$		0			0
$727$	9.34142	−	28.7499i	0.346454	−	1.06628i	−0.614347	−	0.789036i	$-0.710580\pi$
$727$	9.34142	−	28.7499i	0.346454	−	1.06628i	0.960801	−	0.277240i	$-0.0894196\pi$
$728$		0			0
$729$	16.5335	+	12.0123i	0.612351	+	0.444899i
$730$		0			0
$731$	9.42950	−	6.85093i	0.348763	−	0.253391i
$732$		0			0
$733$	11.5369	−	8.38201i	0.426123	−	0.309597i	−0.353974	−	0.935255i	$-0.615170\pi$
$733$	11.5369	−	8.38201i	0.426123	−	0.309597i	0.780097	+	0.625659i	$0.215170\pi$
$734$		0			0
$735$	2.70382	+	0.204125i	0.0997317	+	0.00752925i
$736$		0			0
$737$	0.864598	+	2.66096i	0.0318479	+	0.0980177i
$738$		0			0
$739$	4.55991	−	14.0340i	0.167739	−	0.516248i	−0.831489	−	0.555542i	$-0.812511\pi$
$739$	4.55991	−	14.0340i	0.167739	−	0.516248i	0.999228	+	0.0392940i	$0.0125109\pi$
$740$		0			0
$741$	2.88884	+	8.89094i	0.106124	+	0.326617i
$742$		0			0
$743$	15.0111			0.550704			0.275352	−	0.961343i	$-0.411206\pi$
$743$	15.0111			0.550704			0.275352	+	0.961343i	$0.411206\pi$
$744$		0			0
$745$	16.7151	−	10.3165i	0.612393	−	0.377966i
$746$		0			0
$747$	−16.9023	−	12.2802i	−0.618422	−	0.449310i
$748$		0			0
$749$	−18.8816			−0.689919
$750$		0			0
$751$	−2.18048			−0.0795667			−0.0397834	−	0.999208i	$-0.512667\pi$
$751$	−2.18048			−0.0795667			−0.0397834	+	0.999208i	$0.512667\pi$
$752$		0			0
$753$	−0.544628	−	0.395695i	−0.0198474	−	0.0144199i
$754$		0			0
$755$	−44.4232	+	27.4177i	−1.61672	+	0.997833i
$756$		0			0
$757$	−43.3212			−1.57454			−0.787269	−	0.616610i	$-0.788505\pi$
$757$	−43.3212			−1.57454			−0.787269	+	0.616610i	$0.788505\pi$
$758$		0			0
$759$	0.829197	+	2.55201i	0.0300979	+	0.0926319i
$760$		0			0
$761$	6.92553	−	21.3146i	0.251050	−	0.772653i	−0.743532	−	0.668700i	$-0.766851\pi$
$761$	6.92553	−	21.3146i	0.251050	−	0.772653i	0.994582	−	0.103953i	$-0.0331491\pi$
$762$		0			0
$763$	−3.52178	−	10.8389i	−0.127497	−	0.392395i
$764$		0			0
$765$	15.1392	+	1.14293i	0.547359	+	0.0413229i
$766$		0			0
$767$	−38.1307	+	27.7035i	−1.37682	+	1.00032i
$768$		0			0
$769$	−22.5985	+	16.4187i	−0.814922	+	0.592075i	−0.915253	−	0.402879i	$-0.868010\pi$
$769$	−22.5985	+	16.4187i	−0.814922	+	0.592075i	0.100332	+	0.994954i	$0.468010\pi$
$770$		0			0
$771$	8.44435	+	6.13518i	0.304116	+	0.220953i
$772$		0			0
$773$	−2.73160	+	8.40699i	−0.0982487	+	0.302379i	−0.988087	−	0.153898i	$-0.950817\pi$
$773$	−2.73160	+	8.40699i	−0.0982487	+	0.302379i	0.889838	+	0.456277i	$0.150817\pi$
$774$		0			0
$775$	6.21116	+	37.6602i	0.223112	+	1.35279i
$776$		0			0
$777$	2.62853	−	8.08978i	0.0942980	−	0.290219i
$778$		0			0
$779$	48.3064	+	35.0966i	1.73076	+	1.25747i
$780$		0			0
$781$	−1.85297	+	1.34626i	−0.0663046	+	0.0481731i
$782$		0			0
$783$	−10.6853	+	7.76331i	−0.381861	+	0.277438i
$784$		0			0
$785$	−14.2303	+	8.78285i	−0.507901	+	0.313473i
$786$		0			0
$787$	−6.03821	−	18.5837i	−0.215239	−	0.662438i	−0.999137	−	0.0415474i	$-0.986771\pi$
$787$	−6.03821	−	18.5837i	−0.215239	−	0.662438i	0.783897	−	0.620890i	$-0.213229\pi$
$788$		0			0
$789$	−1.25385	+	3.85895i	−0.0446382	+	0.137382i
$790$		0			0
$791$	11.8761	+	36.5507i	0.422264	+	1.29960i
$792$		0			0
$793$	−42.8249			−1.52076
$794$		0			0
$795$	1.95588	+	1.65972i	0.0693679	+	0.0588644i
$796$		0			0
$797$	25.7832	+	18.7326i	0.913287	+	0.663542i	0.941844	−	0.336050i	$-0.109091\pi$
$797$	25.7832	+	18.7326i	0.913287	+	0.663542i	−0.0285572	+	0.999592i	$0.509091\pi$
$798$		0			0
$799$	−30.2376			−1.06973
$800$		0			0
$801$	10.6649			0.376827
$802$		0			0
$803$	0.925385	+	0.672332i	0.0326561	+	0.0237261i
$804$		0			0
$805$	12.9097	+	53.0273i	0.455005	+	1.86897i
$806$		0			0
$807$	−4.23858			−0.149205
$808$		0			0
$809$	11.1778	+	34.4017i	0.392991	+	1.20950i	0.930515	+	0.366253i	$0.119360\pi$
$809$	11.1778	+	34.4017i	0.392991	+	1.20950i	−0.537525	+	0.843248i	$0.680640\pi$
$810$		0			0
$811$	9.04112	−	27.8257i	0.317477	−	0.977093i	−0.657246	−	0.753676i	$-0.728279\pi$
$811$	9.04112	−	27.8257i	0.317477	−	0.977093i	0.974723	−	0.223417i	$-0.0717212\pi$
$812$		0			0
$813$	0.979018	+	3.01311i	0.0343357	+	0.105674i
$814$		0			0
$815$	26.5363	+	22.5183i	0.929527	+	0.788780i
$816$		0			0
$817$	29.4066	−	21.3652i	1.02881	−	0.747472i
$818$		0			0
$819$	26.8369	−	19.4982i	0.937758	−	0.681321i
$820$		0			0
$821$	8.20242	+	5.95940i	0.286266	+	0.207985i	0.721646	−	0.692262i	$-0.243386\pi$
$821$	8.20242	+	5.95940i	0.286266	+	0.207985i	−0.435380	+	0.900247i	$0.643386\pi$
$822$		0			0
$823$	−5.65623	+	17.4081i	−0.197164	+	0.606808i	0.802781	+	0.596274i	$0.203353\pi$
$823$	−5.65623	+	17.4081i	−0.197164	+	0.606808i	−0.999945	+	0.0105336i	$0.996647\pi$
$824$		0			0
$825$	0.288715	+	1.75057i	0.0100518	+	0.0609469i
$826$		0			0
$827$	13.5392	−	41.6694i	0.470804	−	1.44899i	−0.380730	−	0.924686i	$-0.624327\pi$
$827$	13.5392	−	41.6694i	0.470804	−	1.44899i	0.851534	−	0.524300i	$-0.175673\pi$
$828$		0			0
$829$	30.9050	+	22.4538i	1.07338	+	0.779853i	0.976516	−	0.215445i	$-0.0691201\pi$
$829$	30.9050	+	22.4538i	1.07338	+	0.779853i	0.0968598	+	0.995298i	$0.469120\pi$
$830$		0			0
$831$	−4.45509	+	3.23682i	−0.154546	+	0.112284i
$832$		0			0
$833$	−6.53131	+	4.74527i	−0.226296	+	0.164414i
$834$		0			0
$835$	6.44819	−	15.7087i	0.223149	−	0.543624i
$836$		0			0
$837$	4.91698	+	15.1329i	0.169956	+	0.523070i
$838$		0			0
$839$	14.7195	−	45.3021i	0.508175	−	1.56400i	−0.287192	−	0.957873i	$-0.592722\pi$
$839$	14.7195	−	45.3021i	0.508175	−	1.56400i	0.795367	−	0.606129i	$-0.207278\pi$
$840$		0			0
$841$	3.44606	+	10.6059i	0.118829	+	0.365720i
$842$		0			0
$843$	9.12192			0.314176
$844$		0			0
$845$	0.180263	−	0.439147i	0.00620123	−	0.0151071i
$846$		0			0
$847$	2.61118	+	1.89713i	0.0897211	+	0.0651862i
$848$		0			0
$849$	4.81080			0.165106
$850$		0			0
$851$	56.1636			1.92526
$852$		0			0
$853$	−12.7189	−	9.24079i	−0.435485	−	0.316399i	0.348353	−	0.937363i	$-0.386741\pi$
$853$	−12.7189	−	9.24079i	−0.435485	−	0.316399i	−0.783838	+	0.620965i	$0.786741\pi$
$854$		0			0
$855$	47.2128	+	3.56433i	1.61464	+	0.121897i
$856$		0			0
$857$	19.3135			0.659737			0.329868	−	0.944027i	$-0.392996\pi$
$857$	19.3135			0.659737			0.329868	+	0.944027i	$0.392996\pi$
$858$		0			0
$859$	−4.19511	−	12.9112i	−0.143135	−	0.440526i	0.853631	−	0.520878i	$-0.174395\pi$
$859$	−4.19511	−	12.9112i	−0.143135	−	0.440526i	−0.996767	+	0.0803526i	$0.974395\pi$
$860$		0			0
$861$	−2.86837	+	8.82794i	−0.0977538	+	0.300855i
$862$		0			0
$863$	6.09709	+	18.7649i	0.207547	+	0.638765i	0.999599	+	0.0283113i	$0.00901298\pi$
$863$	6.09709	+	18.7649i	0.207547	+	0.638765i	−0.792052	+	0.610454i	$0.790987\pi$
$864$		0			0
$865$	3.93348	+	16.1570i	0.133742	+	0.549356i
$866$		0			0
$867$	−3.27812	+	2.38170i	−0.111331	+	0.0808867i
$868$		0			0
$869$	−1.46702	+	1.06585i	−0.0497651	+	0.0361565i
$870$		0			0
$871$	−8.09442	−	5.88094i	−0.274269	−	0.199268i
$872$		0			0
$873$	2.74494	−	8.44807i	0.0929022	−	0.285924i
$874$		0			0
$875$	3.17514	+	35.9456i	0.107339	+	1.21518i
$876$		0			0
$877$	−10.8802	+	33.4858i	−0.367398	+	1.13073i	0.581068	+	0.813855i	$0.302635\pi$
$877$	−10.8802	+	33.4858i	−0.367398	+	1.13073i	−0.948466	+	0.316879i	$0.897365\pi$
$878$		0			0
$879$	−9.46571	−	6.87724i	−0.319270	−	0.231963i
$880$		0			0
$881$	34.2782	−	24.9046i	1.15486	−	0.839056i	0.165741	−	0.986169i	$-0.446998\pi$
$881$	34.2782	−	24.9046i	1.15486	−	0.839056i	0.989120	+	0.147114i	$0.0469983\pi$
$882$		0			0
$883$	24.1360	−	17.5358i	0.812241	−	0.590128i	−0.102239	−	0.994760i	$-0.532600\pi$
$883$	24.1360	−	17.5358i	0.812241	−	0.590128i	0.914479	+	0.404632i	$0.132600\pi$
$884$		0			0
$885$	−2.47374	−	10.1610i	−0.0831537	−	0.341560i
$886$		0			0
$887$	−5.09476	−	15.6801i	−0.171065	−	0.526485i	0.828367	−	0.560186i	$-0.189270\pi$
$887$	−5.09476	−	15.6801i	−0.171065	−	0.526485i	−0.999432	+	0.0337014i	$0.989270\pi$
$888$		0			0
$889$	0.603605	−	1.85770i	0.0202442	−	0.0623054i
$890$		0			0
$891$	−2.43587	−	7.49683i	−0.0816046	−	0.251153i
$892$		0			0
$893$	−94.2981			−3.15557
$894$		0			0
$895$	−3.11671	−	0.235296i	−0.104180	−	0.00786509i
$896$		0			0
$897$	−7.76299	−	5.64015i	−0.259199	−	0.188319i
$898$		0			0
$899$	48.3717			1.61329
$900$		0			0
$901$	−7.63746			−0.254441
$902$		0			0
$903$	4.57142	+	3.32133i	0.152127	+	0.110527i
$904$		0			0
$905$	3.74975	−	9.13495i	0.124646	−	0.303656i
$906$		0			0
$907$	18.2596			0.606301			0.303150	−	0.952943i	$-0.401962\pi$
$907$	18.2596			0.606301			0.303150	+	0.952943i	$0.401962\pi$
$908$		0			0
$909$	2.69623	+	8.29814i	0.0894283	+	0.275232i
$910$		0			0
$911$	8.05762	−	24.7988i	0.266961	−	0.821621i	−0.724274	−	0.689512i	$-0.757825\pi$
$911$	8.05762	−	24.7988i	0.266961	−	0.821621i	0.991235	−	0.132109i	$-0.0421749\pi$
$912$		0			0
$913$	2.24631	+	6.91344i	0.0743421	+	0.228802i
$914$		0			0
$915$	3.60830	−	8.79037i	0.119287	−	0.290601i
$916$		0			0
$917$	−0.834569	+	0.606350i	−0.0275599	+	0.0200234i
$918$		0			0
$919$	15.0513	−	10.9354i	0.496496	−	0.360725i	−0.311181	−	0.950351i	$-0.600725\pi$
$919$	15.0513	−	10.9354i	0.496496	−	0.360725i	0.807677	+	0.589625i	$0.200725\pi$
$920$		0			0
$921$	1.36802	+	0.993928i	0.0450780	+	0.0327510i
$922$		0			0
$923$	2.53099	−	7.78958i	0.0833085	−	0.256397i
$924$		0			0
$925$	36.7143	+	5.57526i	1.20716	+	0.183314i
$926$		0			0
$927$	−8.87230	+	27.3061i	−0.291405	+	0.896851i
$928$		0			0
$929$	−3.33143	−	2.42043i	−0.109301	−	0.0794117i	0.531792	−	0.846875i	$-0.321519\pi$
$929$	−3.33143	−	2.42043i	−0.109301	−	0.0794117i	−0.641093	+	0.767463i	$0.721519\pi$
$930$		0			0
$931$	−20.3684	+	14.7985i	−0.667547	+	0.485001i
$932$		0			0
$933$	−7.30860	+	5.31001i	−0.239273	+	0.173842i
$934$		0			0
$935$	−4.02774	−	3.41787i	−0.131721	−	0.111776i
$936$		0			0
$937$	2.95862	+	9.10570i	0.0966540	+	0.297470i	0.987681	−	0.156480i	$-0.0500145\pi$
$937$	2.95862	+	9.10570i	0.0966540	+	0.297470i	−0.891027	+	0.453950i	$0.850015\pi$
$938$		0			0
$939$	1.29856	−	3.99656i	0.0423769	−	0.130423i
$940$		0			0
$941$	−7.84457	−	24.1431i	−0.255726	−	0.787043i	−0.993686	−	0.112198i	$-0.964211\pi$
$941$	−7.84457	−	24.1431i	−0.255726	−	0.787043i	0.737960	−	0.674844i	$-0.235789\pi$
$942$		0			0
$943$	−61.2883			−1.99582
$944$		0			0
$945$	3.55838	+	14.6163i	0.115754	+	0.475468i
$946$		0			0
$947$	−2.77562	−	2.01661i	−0.0901955	−	0.0655309i	0.541774	−	0.840524i	$-0.317753\pi$
$947$	−2.77562	−	2.01661i	−0.0901955	−	0.0655309i	−0.631969	+	0.774994i	$0.717753\pi$
$948$		0			0
$949$	−4.09036			−0.132779
$950$		0			0
$951$	−2.02224			−0.0655757
$952$		0			0
$953$	−21.7042	−	15.7690i	−0.703069	−	0.510809i	0.177861	−	0.984056i	$-0.443082\pi$
$953$	−21.7042	−	15.7690i	−0.703069	−	0.510809i	−0.880930	+	0.473246i	$0.843082\pi$
$954$		0			0
$955$	3.57919	+	3.03724i	0.115820	+	0.0982826i
$956$		0			0
$957$	2.24847			0.0726829
$958$		0			0
$959$	0.710456	+	2.18656i	0.0229418	+	0.0706076i
$960$		0			0
$961$	8.42833	−	25.9397i	0.271882	−	0.836766i
$962$		0			0
$963$	−5.19568	−	15.9907i	−0.167428	−	0.515292i
$964$		0			0
$965$	39.8323	−	24.5843i	1.28225	−	0.791395i
$966$		0			0
$967$	−37.6435	+	27.3496i	−1.21053	+	0.879504i	−0.995279	−	0.0970539i	$-0.969058\pi$
$967$	−37.6435	+	27.3496i	−1.21053	+	0.879504i	−0.215254	+	0.976558i	$0.569058\pi$
$968$		0			0
$969$	4.99637	−	3.63008i	0.160507	−	0.116615i
$970$		0			0
$971$	7.35266	+	5.34202i	0.235958	+	0.171434i	0.699481	−	0.714651i	$-0.253415\pi$
$971$	7.35266	+	5.34202i	0.235958	+	0.171434i	−0.463523	+	0.886085i	$0.653415\pi$
$972$		0			0
$973$	−22.3811	+	68.8820i	−0.717505	+	2.20825i
$974$		0			0
$975$	−4.51480	−	4.45760i	−0.144589	−	0.142757i
$976$		0			0
$977$	−3.52410	+	10.8461i	−0.112746	+	0.346996i	−0.991470	−	0.130333i	$-0.958395\pi$
$977$	−3.52410	+	10.8461i	−0.112746	+	0.346996i	0.878724	+	0.477330i	$0.158395\pi$
$978$		0			0
$979$	−3.00204	−	2.18111i	−0.0959456	−	0.0697086i
$980$		0			0
$981$	8.21029	−	5.96513i	0.262134	−	0.190452i
$982$		0			0
$983$	0.273660	−	0.198825i	0.00872839	−	0.00634155i	−0.583413	−	0.812176i	$-0.698283\pi$
$983$	0.273660	−	0.198825i	0.00872839	−	0.00634155i	0.592141	+	0.805834i	$0.298283\pi$
$984$		0			0
$985$	53.3765	+	4.02966i	1.70072	+	0.128396i
$986$		0			0
$987$	−4.52993	−	13.9417i	−0.144189	−	0.443769i
$988$		0			0
$989$	−11.5292	+	35.4833i	−0.366608	+	1.12830i
$990$		0			0
$991$	2.73870	+	8.42884i	0.0869976	+	0.267751i	0.985086	−	0.172065i	$-0.0550438\pi$
$991$	2.73870	+	8.42884i	0.0869976	+	0.267751i	−0.898088	+	0.439816i	$0.855044\pi$
$992$		0			0
$993$	−9.54406			−0.302872
$994$		0			0
$995$	35.5383	−	21.9340i	1.12664	−	0.695355i
$996$		0			0
$997$	44.4962	+	32.3284i	1.40921	+	1.02385i	0.993437	+	0.114383i	$0.0364891\pi$
$997$	44.4962	+	32.3284i	1.40921	+	1.02385i	0.415773	+	0.909468i	$0.363511\pi$
$998$		0			0
$999$	15.4808			0.489789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.7	✓	52
25.6	even	5	inner	1100.2.q.b.881.7	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.7	✓	52	1.1	even	1	trivial
1100.2.q.b.881.7	yes	52	25.6	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.287074 + 0.208571i) q^{3} +(1.90283 - 1.17441i) q^{5} -3.22759 q^{7} +(-0.888142 - 2.73342i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(-1.10504 - 3.40097i) q^{13} +(0.791201 + 0.0597318i) q^{15} +(-1.91122 + 1.38858i) q^{17} +(-5.96028 + 4.33039i) q^{19} +(-0.926558 - 0.673184i) q^{21} +(2.33680 - 7.19193i) q^{23} +(2.24150 - 4.46941i) q^{25} +(0.644108 - 1.98236i) q^{27} +(-5.12636 - 3.72452i) q^{29} +(-6.17586 + 4.48703i) q^{31} +(-0.287074 + 0.208571i) q^{33} +(-6.14155 + 3.79053i) q^{35} +(2.29508 + 7.06353i) q^{37} +(0.392116 - 1.20681i) q^{39} +(-2.50450 - 7.70805i) q^{41} -4.93377 q^{43} +(-4.90015 - 4.15818i) q^{45} +(10.3550 + 7.52338i) q^{47} +3.41735 q^{49} -0.838279 q^{51} +(2.61550 + 1.90027i) q^{53} +(0.528928 + 2.17261i) q^{55} -2.61424 q^{57} +(-4.07289 - 12.5351i) q^{59} +(3.70068 - 11.3895i) q^{61} +(2.86656 + 8.82236i) q^{63} +(-6.09685 - 5.17368i) q^{65} +(2.26355 - 1.64456i) q^{67} +(2.17087 - 1.57723i) q^{69} +(1.85297 + 1.34626i) q^{71} +(0.353466 - 1.08786i) q^{73} +(1.57567 - 0.815539i) q^{75} +(0.997381 - 3.06962i) q^{77} +(1.46702 + 1.06585i) q^{79} +(-6.37718 + 4.63330i) q^{81} +(5.88093 - 4.27274i) q^{83} +(-2.00595 + 4.88679i) q^{85} +(-0.694817 - 2.13843i) q^{87} +(-1.14668 + 3.52911i) q^{89} +(3.56662 + 10.9769i) q^{91} -2.70879 q^{93} +(-6.25570 + 15.2398i) q^{95} +(2.50040 + 1.81664i) q^{97} +2.87409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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