LMFDB - Embedded newform 252.2.b.e.55.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(55,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.55"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.2312.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x + 4 $ x^4 - x^3 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.3
Root			$1.28078 - 0.599676i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.2.b.e.55.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.28078 - 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} -3.33513i q^{5} +(-1.56155 + 2.13578i) q^{7} +(0.719224 - 2.73546i) q^{8} +(-2.00000 - 4.27156i) q^{10} -0.936426i q^{11} +1.87285i q^{13} +(-0.719224 + 3.67188i) q^{14} +(-0.719224 - 3.93481i) q^{16} +5.20798i q^{17} +7.12311 q^{19} +(-5.12311 - 4.27156i) q^{20} +(-0.561553 - 1.19935i) q^{22} +0.936426i q^{23} -6.12311 q^{25} +(1.12311 + 2.39871i) q^{26} +(1.28078 + 5.13416i) q^{28} +2.00000 q^{29} +(-3.28078 - 4.60831i) q^{32} +(3.12311 + 6.67026i) q^{34} +(7.12311 + 5.20798i) q^{35} +1.12311 q^{37} +(9.12311 - 4.27156i) q^{38} +(-9.12311 - 2.39871i) q^{40} +1.46228i q^{41} +9.06897i q^{43} +(-1.43845 - 1.19935i) q^{44} +(0.561553 + 1.19935i) q^{46} -6.24621 q^{47} +(-2.12311 - 6.67026i) q^{49} +(-7.84233 + 3.67188i) q^{50} +(2.87689 + 2.39871i) q^{52} -12.2462 q^{53} -3.12311 q^{55} +(4.71922 + 5.80766i) q^{56} +(2.56155 - 1.19935i) q^{58} -4.00000 q^{59} +4.79741i q^{61} +(-6.96543 - 3.93481i) q^{64} +6.24621 q^{65} -10.9418i q^{67} +(8.00000 + 6.67026i) q^{68} +(12.2462 + 2.39871i) q^{70} +3.86098i q^{71} +6.67026i q^{73} +(1.43845 - 0.673500i) q^{74} +(9.12311 - 10.9418i) q^{76} +(2.00000 + 1.46228i) q^{77} -2.39871i q^{79} +(-13.1231 + 2.39871i) q^{80} +(0.876894 + 1.87285i) q^{82} +10.2462 q^{83} +17.3693 q^{85} +(5.43845 + 11.6153i) q^{86} +(-2.56155 - 0.673500i) q^{88} -1.46228i q^{89} +(-4.00000 - 2.92456i) q^{91} +(1.43845 + 1.19935i) q^{92} +(-8.00000 + 3.74571i) q^{94} -23.7565i q^{95} -10.4160i q^{97} +(-6.71922 - 7.26994i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} + 2 q^{7} + 7 q^{8} - 8 q^{10} - 7 q^{14} - 7 q^{16} + 12 q^{19} - 4 q^{20} + 6 q^{22} - 8 q^{25} - 12 q^{26} + q^{28} + 8 q^{29} - 9 q^{32} - 4 q^{34} + 12 q^{35} - 12 q^{37} + 20 q^{38}+ \cdots - 31 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 + 2 * q^7 + 7 * q^8 - 8 * q^10 - 7 * q^14 - 7 * q^16 + 12 * q^19 - 4 * q^20 + 6 * q^22 - 8 * q^25 - 12 * q^26 + q^28 + 8 * q^29 - 9 * q^32 - 4 * q^34 + 12 * q^35 - 12 * q^37 + 20 * q^38 - 20 * q^40 - 14 * q^44 - 6 * q^46 + 8 * q^47 + 8 * q^49 - 19 * q^50 + 28 * q^52 - 16 * q^53 + 4 * q^55 + 23 * q^56 + 2 * q^58 - 16 * q^59 + q^64 - 8 * q^65 + 32 * q^68 + 16 * q^70 + 14 * q^74 + 20 * q^76 + 8 * q^77 - 36 * q^80 + 20 * q^82 + 8 * q^83 + 20 * q^85 + 30 * q^86 - 2 * q^88 - 16 * q^91 + 14 * q^92 - 32 * q^94 - 31 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.28078	−	0.599676i	0.905646	−	0.424035i
$2$	1.28078	−	0.599676i	0.905646	−	0.424035i
$3$		0			0
$3$		0			0
$4$	1.28078	−	1.53610i	0.640388	−	0.768051i
$5$		−	3.33513i		−	1.49152i	−0.666217	−	0.745758i	$-0.732087\pi$
$5$		−	3.33513i		−	1.49152i	0.666217	−	0.745758i	$-0.267913\pi$
$6$		0			0
$7$	−1.56155	+	2.13578i	−0.590211	+	0.807249i
$7$	−1.56155	+	2.13578i	−0.590211	+	0.807249i
$8$	0.719224	−	2.73546i	0.254284	−	0.967130i
$9$		0			0
$10$	−2.00000	−	4.27156i	−0.632456	−	1.35079i
$11$		−	0.936426i		−	0.282343i	−0.989985	−	0.141172i	$-0.954913\pi$
$11$		−	0.936426i		−	0.282343i	0.989985	−	0.141172i	$-0.0450869\pi$
$12$		0			0
$13$			1.87285i			0.519436i	0.965685	+	0.259718i	$0.0836296\pi$
$13$			1.87285i			0.519436i	−0.965685	+	0.259718i	$0.916370\pi$
$14$	−0.719224	+	3.67188i	−0.192221	+	0.981352i
$15$		0			0
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$			5.20798i			1.26312i	0.775326	+	0.631561i	$0.217585\pi$
$17$			5.20798i			1.26312i	−0.775326	+	0.631561i	$0.782415\pi$
$18$		0			0
$19$	7.12311			1.63415			0.817076	−	0.576530i	$-0.195593\pi$
$19$	7.12311			1.63415			0.817076	+	0.576530i	$0.195593\pi$
$20$	−5.12311	−	4.27156i	−1.14556	−	0.955149i
$21$		0			0
$22$	−0.561553	−	1.19935i	−0.119723	−	0.255703i
$23$			0.936426i			0.195258i	0.995223	+	0.0976292i	$0.0311259\pi$
$23$			0.936426i			0.195258i	−0.995223	+	0.0976292i	$0.968874\pi$
$24$		0			0
$25$	−6.12311			−1.22462
$26$	1.12311	+	2.39871i	0.220259	+	0.470425i
$27$		0			0
$28$	1.28078	+	5.13416i	0.242044	+	0.970265i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−3.28078	−	4.60831i	−0.579965	−	0.814642i
$33$		0			0
$34$	3.12311	+	6.67026i	0.535608	+	1.14394i
$35$	7.12311	+	5.20798i	1.20402	+	0.880310i
$36$		0			0
$37$	1.12311			0.184637			0.0923187	−	0.995730i	$-0.470572\pi$
$37$	1.12311			0.184637			0.0923187	+	0.995730i	$0.470572\pi$
$38$	9.12311	−	4.27156i	1.47996	−	0.692938i
$39$		0			0
$40$	−9.12311	−	2.39871i	−1.44249	−	0.379269i
$41$			1.46228i			0.228370i	0.993460	+	0.114185i	$0.0364256\pi$
$41$			1.46228i			0.228370i	−0.993460	+	0.114185i	$0.963574\pi$
$42$		0			0
$43$			9.06897i			1.38300i	0.722374	+	0.691502i	$0.243051\pi$
$43$			9.06897i			1.38300i	−0.722374	+	0.691502i	$0.756949\pi$
$44$	−1.43845	−	1.19935i	−0.216854	−	0.180809i
$45$		0			0
$46$	0.561553	+	1.19935i	0.0827964	+	0.176835i
$47$	−6.24621			−0.911104			−0.455552	−	0.890209i	$-0.650558\pi$
$47$	−6.24621			−0.911104			−0.455552	+	0.890209i	$0.650558\pi$
$48$		0			0
$49$	−2.12311	−	6.67026i	−0.303301	−	0.952895i
$50$	−7.84233	+	3.67188i	−1.10907	+	0.519283i
$51$		0			0
$52$	2.87689	+	2.39871i	0.398953	+	0.332641i
$53$	−12.2462			−1.68215			−0.841073	−	0.540921i	$-0.818076\pi$
$53$	−12.2462			−1.68215			−0.841073	+	0.540921i	$0.818076\pi$
$54$		0			0
$55$	−3.12311			−0.421119
$56$	4.71922	+	5.80766i	0.630633	+	0.776081i
$57$		0			0
$58$	2.56155	−	1.19935i	0.336348	−	0.157483i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$			4.79741i			0.614246i	0.951670	+	0.307123i	$0.0993662\pi$
$61$			4.79741i			0.614246i	−0.951670	+	0.307123i	$0.900634\pi$
$62$		0			0
$63$		0			0
$64$	−6.96543	−	3.93481i	−0.870679	−	0.491851i
$65$	6.24621			0.774747
$66$		0			0
$67$		−	10.9418i		−	1.33676i	−0.743822	−	0.668378i	$-0.766989\pi$
$67$		−	10.9418i		−	1.33676i	0.743822	−	0.668378i	$-0.233011\pi$
$68$	8.00000	+	6.67026i	0.970143	+	0.808888i
$69$		0			0
$70$	12.2462	+	2.39871i	1.46370	+	0.286700i
$71$			3.86098i			0.458215i	0.973401	+	0.229107i	$0.0735807\pi$
$71$			3.86098i			0.458215i	−0.973401	+	0.229107i	$0.926419\pi$
$72$		0			0
$73$			6.67026i			0.780695i	0.920668	+	0.390348i	$0.127645\pi$
$73$			6.67026i			0.780695i	−0.920668	+	0.390348i	$0.872355\pi$
$74$	1.43845	−	0.673500i	0.167216	−	0.0782928i
$75$		0			0
$76$	9.12311	−	10.9418i	1.04649	−	1.25511i
$77$	2.00000	+	1.46228i	0.227921	+	0.166642i
$78$		0			0
$79$		−	2.39871i		−	0.269875i	−0.990854	−	0.134938i	$-0.956917\pi$
$79$		−	2.39871i		−	0.269875i	0.990854	−	0.134938i	$-0.0430834\pi$
$80$	−13.1231	+	2.39871i	−1.46721	+	0.268183i
$81$		0			0
$82$	0.876894	+	1.87285i	0.0968368	+	0.206822i
$83$	10.2462			1.12467			0.562334	−	0.826910i	$-0.309904\pi$
$83$	10.2462			1.12467			0.562334	+	0.826910i	$0.309904\pi$
$84$		0			0
$85$	17.3693			1.88397
$86$	5.43845	+	11.6153i	0.586443	+	1.25251i
$87$		0			0
$88$	−2.56155	−	0.673500i	−0.273062	−	0.0717953i
$89$		−	1.46228i		−	0.155001i	−0.996992	−	0.0775006i	$-0.975306\pi$
$89$		−	1.46228i		−	0.155001i	0.996992	−	0.0775006i	$-0.0246940\pi$
$90$		0			0
$91$	−4.00000	−	2.92456i	−0.419314	−	0.306577i
$92$	1.43845	+	1.19935i	0.149968	+	0.125041i
$93$		0			0
$94$	−8.00000	+	3.74571i	−0.825137	+	0.386340i
$95$		−	23.7565i		−	2.43737i
$96$		0			0
$97$		−	10.4160i		−	1.05758i	−0.848752	−	0.528791i	$-0.822646\pi$
$97$		−	10.4160i		−	1.05758i	0.848752	−	0.528791i	$-0.177354\pi$
$98$	−6.71922	−	7.26994i	−0.678744	−	0.734375i
$99$		0			0
$100$	−7.84233	+	9.40572i	−0.784233	+	0.940572i
$101$		−	13.7511i		−	1.36829i	−0.729348	−	0.684143i	$-0.760176\pi$
$101$		−	13.7511i		−	1.36829i	0.729348	−	0.684143i	$-0.239824\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	5.12311	+	1.34700i	0.502362	+	0.132084i
$105$		0			0
$106$	−15.6847	+	7.34376i	−1.52343	+	0.713289i
$107$			9.47954i			0.916422i	0.888843	+	0.458211i	$0.151510\pi$
$107$			9.47954i			0.916422i	−0.888843	+	0.458211i	$0.848490\pi$
$108$		0			0
$109$	−8.24621			−0.789844			−0.394922	−	0.918715i	$-0.629228\pi$
$109$	−8.24621			−0.789844			−0.394922	+	0.918715i	$0.629228\pi$
$110$	−4.00000	+	1.87285i	−0.381385	+	0.178570i
$111$		0			0
$112$	9.52699	+	4.60831i	0.900216	+	0.435444i
$113$	4.24621			0.399450			0.199725	−	0.979852i	$-0.435995\pi$
$113$	4.24621			0.399450			0.199725	+	0.979852i	$0.435995\pi$
$114$		0			0
$115$	3.12311			0.291231
$116$	2.56155	−	3.07221i	0.237834	−	0.285247i
$117$		0			0
$118$	−5.12311	+	2.39871i	−0.471620	+	0.220819i
$119$	−11.1231	−	8.13254i	−1.01965	−	0.745509i
$120$		0			0
$121$	10.1231			0.920282
$122$	2.87689	+	6.14441i	0.260462	+	0.556289i
$123$		0			0
$124$		0			0
$125$			3.74571i			0.335026i
$126$		0			0
$127$		−	9.89012i		−	0.877606i	−0.898583	−	0.438803i	$-0.855403\pi$
$127$		−	9.89012i		−	0.877606i	0.898583	−	0.438803i	$-0.144597\pi$
$128$	−11.2808	−	0.862603i	−0.997089	−	0.0762440i
$129$		0			0
$130$	8.00000	−	3.74571i	0.701646	−	0.328520i
$131$	−5.75379			−0.502711			−0.251355	−	0.967895i	$-0.580876\pi$
$131$	−5.75379			−0.502711			−0.251355	+	0.967895i	$0.580876\pi$
$132$		0			0
$133$	−11.1231	+	15.2134i	−0.964496	+	1.31917i
$134$	−6.56155	−	14.0140i	−0.566832	−	1.21063i
$135$		0			0
$136$	14.2462	+	3.74571i	1.22160	+	0.321192i
$137$	−0.246211			−0.0210352			−0.0105176	−	0.999945i	$-0.503348\pi$
$137$	−0.246211			−0.0210352			−0.0105176	+	0.999945i	$0.503348\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$	17.1231	−	4.27156i	1.44717	−	0.361013i
$141$		0			0
$142$	2.31534	+	4.94506i	0.194299	+	0.414980i
$143$	1.75379			0.146659
$144$		0			0
$145$		−	6.67026i		−	0.553935i
$146$	4.00000	+	8.54312i	0.331042	+	0.707033i
$147$		0			0
$148$	1.43845	−	1.72521i	0.118240	−	0.141811i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$		−	9.06897i		−	0.738022i	−0.929425	−	0.369011i	$-0.879696\pi$
$151$		−	9.06897i		−	0.738022i	0.929425	−	0.369011i	$-0.120304\pi$
$152$	5.12311	−	19.4849i	0.415539	−	1.58044i
$153$		0			0
$154$	3.43845	+	0.673500i	0.277078	+	0.0542722i
$155$		0			0
$156$		0			0
$157$		−	21.8836i		−	1.74650i	−0.487268	−	0.873252i	$-0.662007\pi$
$157$		−	21.8836i		−	1.74650i	0.487268	−	0.873252i	$-0.337993\pi$
$158$	−1.43845	−	3.07221i	−0.114437	−	0.244412i
$159$		0			0
$160$	−15.3693	+	10.9418i	−1.21505	+	0.865027i
$161$	−2.00000	−	1.46228i	−0.157622	−	0.115244i
$162$		0			0
$163$			15.7392i			1.23279i	0.787436	+	0.616396i	$0.211408\pi$
$163$			15.7392i			1.23279i	−0.787436	+	0.616396i	$0.788592\pi$
$164$	2.24621	+	1.87285i	0.175400	+	0.146245i
$165$		0			0
$166$	13.1231	−	6.14441i	1.01855	−	0.476899i
$167$	−14.2462			−1.10240			−0.551202	−	0.834372i	$-0.685831\pi$
$167$	−14.2462			−1.10240			−0.551202	+	0.834372i	$0.685831\pi$
$168$		0			0
$169$	9.49242			0.730186
$170$	22.2462	−	10.4160i	1.70621	−	0.798868i
$171$		0			0
$172$	13.9309	+	11.6153i	1.06222	+	0.885660i
$173$			16.6757i			1.26783i	0.773404	+	0.633913i	$0.218552\pi$
$173$			16.6757i			1.26783i	−0.773404	+	0.633913i	$0.781448\pi$
$174$		0			0
$175$	9.56155	−	13.0776i	0.722785	−	0.988574i
$176$	−3.68466	+	0.673500i	−0.277742	+	0.0507670i
$177$		0			0
$178$	−0.876894	−	1.87285i	−0.0657260	−	0.140376i
$179$			16.1498i			1.20709i	0.797328	+	0.603547i	$0.206246\pi$
$179$			16.1498i			1.20709i	−0.797328	+	0.603547i	$0.793754\pi$
$180$		0			0
$181$		−	1.87285i		−	0.139208i	−0.997575	−	0.0696040i	$-0.977826\pi$
$181$		−	1.87285i		−	0.139208i	0.997575	−	0.0696040i	$-0.0221736\pi$
$182$	−6.87689	−	1.34700i	−0.509749	−	0.0998463i
$183$		0			0
$184$	2.56155	+	0.673500i	0.188840	+	0.0496511i
$185$		−	3.74571i		−	0.275390i
$186$		0			0
$187$	4.87689			0.356634
$188$	−8.00000	+	9.59482i	−0.583460	+	0.699774i
$189$		0			0
$190$	−14.2462	−	30.4268i	−1.03353	−	2.20739i
$191$		−	2.80928i		−	0.203272i	−0.994822	−	0.101636i	$-0.967592\pi$
$191$		−	2.80928i		−	0.203272i	0.994822	−	0.101636i	$-0.0324078\pi$
$192$		0			0
$193$	−15.3693			−1.10631			−0.553154	−	0.833079i	$-0.686576\pi$
$193$	−15.3693			−1.10631			−0.553154	+	0.833079i	$0.686576\pi$
$194$	−6.24621	−	13.3405i	−0.448452	−	0.957794i
$195$		0			0
$196$	−12.9654	−	5.28181i	−0.926102	−	0.377272i
$197$	16.2462			1.15749			0.578747	−	0.815507i	$-0.303542\pi$
$197$	16.2462			1.15749			0.578747	+	0.815507i	$0.303542\pi$
$198$		0			0
$199$	−3.12311			−0.221391			−0.110696	−	0.993854i	$-0.535308\pi$
$199$	−3.12311			−0.221391			−0.110696	+	0.993854i	$0.535308\pi$
$200$	−4.40388	+	16.7495i	−0.311401	+	1.18437i
$201$		0			0
$202$	−8.24621	−	17.6121i	−0.580201	−	1.23918i
$203$	−3.12311	+	4.27156i	−0.219199	+	0.299805i
$204$		0			0
$205$	4.87689			0.340617
$206$	−10.2462	+	4.79741i	−0.713887	+	0.334251i
$207$		0			0
$208$	7.36932	−	1.34700i	0.510970	−	0.0933976i
$209$		−	6.67026i		−	0.461392i
$210$		0			0
$211$			12.8147i			0.882199i	0.897458	+	0.441099i	$0.145411\pi$
$211$			12.8147i			0.882199i	−0.897458	+	0.441099i	$0.854589\pi$
$212$	−15.6847	+	18.8114i	−1.07723	+	1.29197i
$213$		0			0
$214$	5.68466	+	12.1412i	0.388595	+	0.829954i
$215$	30.2462			2.06277
$216$		0			0
$217$		0			0
$218$	−10.5616	+	4.94506i	−0.715319	+	0.334922i
$219$		0			0
$220$	−4.00000	+	4.79741i	−0.269680	+	0.323441i
$221$	−9.75379			−0.656111
$222$		0			0
$223$	27.1231			1.81630			0.908149	−	0.418648i	$-0.137496\pi$
$223$	27.1231			1.81630			0.908149	+	0.418648i	$0.137496\pi$
$224$	14.9654	+	0.189103i	0.999920	+	0.0126350i
$225$		0			0
$226$	5.43845	−	2.54635i	0.361760	−	0.169381i
$227$	16.4924			1.09464			0.547320	−	0.836923i	$-0.315648\pi$
$227$	16.4924			1.09464			0.547320	+	0.836923i	$0.315648\pi$
$228$		0			0
$229$			5.61856i			0.371285i	0.982617	+	0.185642i	$0.0594366\pi$
$229$			5.61856i			0.371285i	−0.982617	+	0.185642i	$0.940563\pi$
$230$	4.00000	−	1.87285i	0.263752	−	0.123492i
$231$		0			0
$232$	1.43845	−	5.47091i	0.0944387	−	0.359183i
$233$	−22.4924			−1.47353			−0.736764	−	0.676150i	$-0.763647\pi$
$233$	−22.4924			−1.47353			−0.736764	+	0.676150i	$0.763647\pi$
$234$		0			0
$235$			20.8319i			1.35893i
$236$	−5.12311	+	6.14441i	−0.333486	+	0.399967i
$237$		0			0
$238$	−19.1231	−	3.74571i	−1.23957	−	0.242798i
$239$		−	16.1498i		−	1.04464i	−0.852748	−	0.522322i	$-0.825066\pi$
$239$		−	16.1498i		−	1.04464i	0.852748	−	0.522322i	$-0.174934\pi$
$240$		0			0
$241$			23.7565i			1.53029i	0.643858	+	0.765145i	$0.277333\pi$
$241$			23.7565i			1.53029i	−0.643858	+	0.765145i	$0.722667\pi$
$242$	12.9654	−	6.07059i	0.833450	−	0.390232i
$243$		0			0
$244$	7.36932	+	6.14441i	0.471772	+	0.393356i
$245$	−22.2462	+	7.08084i	−1.42126	+	0.452378i
$246$		0			0
$247$			13.3405i			0.848837i
$248$		0			0
$249$		0			0
$250$	2.24621	+	4.79741i	0.142063	+	0.303415i
$251$	5.75379			0.363176			0.181588	−	0.983375i	$-0.441876\pi$
$251$	5.75379			0.363176			0.181588	+	0.983375i	$0.441876\pi$
$252$		0			0
$253$	0.876894			0.0551299
$254$	−5.93087	−	12.6670i	−0.372136	−	0.794800i
$255$		0			0
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$		−	2.28343i		−	0.142436i	−0.997461	−	0.0712181i	$-0.977311\pi$
$257$		−	2.28343i		−	0.142436i	0.997461	−	0.0712181i	$-0.0226886\pi$
$258$		0			0
$259$	−1.75379	+	2.39871i	−0.108975	+	0.149048i
$260$	8.00000	−	9.59482i	0.496139	−	0.595046i
$261$		0			0
$262$	−7.36932	+	3.45041i	−0.455278	+	0.213167i
$263$			24.6929i			1.52263i	0.648382	+	0.761315i	$0.275446\pi$
$263$			24.6929i			1.52263i	−0.648382	+	0.761315i	$0.724554\pi$
$264$		0			0
$265$			40.8427i			2.50895i
$266$	−5.12311	+	26.1552i	−0.314118	+	1.60368i
$267$		0			0
$268$	−16.8078	−	14.0140i	−1.02670	−	0.856043i
$269$			10.8265i			0.660106i	0.943962	+	0.330053i	$0.107067\pi$
$269$			10.8265i			0.660106i	−0.943962	+	0.330053i	$0.892933\pi$
$270$		0			0
$271$	−28.4924			−1.73079			−0.865396	−	0.501089i	$-0.832933\pi$
$271$	−28.4924			−1.73079			−0.865396	+	0.501089i	$0.832933\pi$
$272$	20.4924	−	3.74571i	1.24254	−	0.227117i
$273$		0			0
$274$	−0.315342	+	0.147647i	−0.0190505	+	0.00891969i
$275$			5.73384i			0.345763i
$276$		0			0
$277$	−5.12311			−0.307818			−0.153909	−	0.988085i	$-0.549186\pi$
$277$	−5.12311			−0.307818			−0.153909	+	0.988085i	$0.549186\pi$
$278$	−15.3693	+	7.19612i	−0.921790	+	0.431594i
$279$		0			0
$280$	19.3693	−	15.7392i	1.15754	−	0.940599i
$281$	−16.2462			−0.969168			−0.484584	−	0.874745i	$-0.661029\pi$
$281$	−16.2462			−0.969168			−0.484584	+	0.874745i	$0.661029\pi$
$282$		0			0
$283$	8.87689			0.527677			0.263838	−	0.964567i	$-0.415011\pi$
$283$	8.87689			0.527677			0.263838	+	0.964567i	$0.415011\pi$
$284$	5.93087	+	4.94506i	0.351932	+	0.293435i
$285$		0			0
$286$	2.24621	−	1.05171i	0.132821	−	0.0621887i
$287$	−3.12311	−	2.28343i	−0.184351	−	0.134786i
$288$		0			0
$289$	−10.1231			−0.595477
$290$	−4.00000	−	8.54312i	−0.234888	−	0.501669i
$291$		0			0
$292$	10.2462	+	8.54312i	0.599614	+	0.499948i
$293$		−	13.7511i		−	0.803348i	−0.915783	−	0.401674i	$-0.868429\pi$
$293$		−	13.7511i		−	0.803348i	0.915783	−	0.401674i	$-0.131571\pi$
$294$		0			0
$295$			13.3405i			0.776716i
$296$	0.807764	−	3.07221i	0.0469503	−	0.178568i
$297$		0			0
$298$	12.8078	−	5.99676i	0.741934	−	0.347383i
$299$	−1.75379			−0.101424
$300$		0			0
$301$	−19.3693	−	14.1617i	−1.11643	−	0.816265i
$302$	−5.43845	−	11.6153i	−0.312947	−	0.668387i
$303$		0			0
$304$	−5.12311	−	28.0281i	−0.293830	−	1.60752i
$305$	16.0000			0.916157
$306$		0			0
$307$	19.6155			1.11952			0.559759	−	0.828656i	$-0.310894\pi$
$307$	19.6155			1.11952			0.559759	+	0.828656i	$0.310894\pi$
$308$	4.80776	−	1.19935i	0.273948	−	0.0683395i
$309$		0			0
$310$		0			0
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$		0			0
$313$		−	22.9354i		−	1.29638i	−0.761478	−	0.648191i	$-0.775526\pi$
$313$		−	22.9354i		−	1.29638i	0.761478	−	0.648191i	$-0.224474\pi$
$314$	−13.1231	−	28.0281i	−0.740580	−	1.58171i
$315$		0			0
$316$	−3.68466	−	3.07221i	−0.207278	−	0.172825i
$317$	14.4924			0.813976			0.406988	−	0.913434i	$-0.366579\pi$
$317$	14.4924			0.813976			0.406988	+	0.913434i	$0.366579\pi$
$318$		0			0
$319$		−	1.87285i		−	0.104860i
$320$	−13.1231	+	23.2306i	−0.733604	+	1.29863i
$321$		0			0
$322$	−3.43845	−	0.673500i	−0.191617	−	0.0375327i
$323$			37.0970i			2.06413i
$324$		0			0
$325$		−	11.4677i		−	0.636112i
$326$	9.43845	+	20.1584i	0.522747	+	1.11647i
$327$		0			0
$328$	4.00000	+	1.05171i	0.220863	+	0.0580707i
$329$	9.75379	−	13.3405i	0.537744	−	0.735487i
$330$		0			0
$331$		−	17.6121i		−	0.968048i	−0.875055	−	0.484024i	$-0.839175\pi$
$331$		−	17.6121i		−	0.968048i	0.875055	−	0.484024i	$-0.160825\pi$
$332$	13.1231	−	15.7392i	0.720224	−	0.863803i
$333$		0			0
$334$	−18.2462	+	8.54312i	−0.998388	+	0.467459i
$335$	−36.4924			−1.99379
$336$		0			0
$337$	8.24621			0.449200			0.224600	−	0.974451i	$-0.427892\pi$
$337$	8.24621			0.449200			0.224600	+	0.974451i	$0.427892\pi$
$338$	12.1577	−	5.69238i	0.661290	−	0.309625i
$339$		0			0
$340$	22.2462	−	26.6811i	1.20647	−	1.44698i
$341$		0			0
$342$		0			0
$343$	17.5616	+	5.88148i	0.948235	+	0.317570i
$344$	24.8078	+	6.52262i	1.33754	+	0.351676i
$345$		0			0
$346$	10.0000	+	21.3578i	0.537603	+	1.14820i
$347$		−	20.1261i		−	1.08042i	−0.841529	−	0.540212i	$-0.818344\pi$
$347$		−	20.1261i		−	1.08042i	0.841529	−	0.540212i	$-0.181656\pi$
$348$		0			0
$349$		−	21.8836i		−	1.17140i	−0.810526	−	0.585702i	$-0.800819\pi$
$349$		−	21.8836i		−	1.17140i	0.810526	−	0.585702i	$-0.199181\pi$
$350$	4.40388	−	22.4833i	0.235397	−	1.20178i
$351$		0			0
$352$	−4.31534	+	3.07221i	−0.230008	+	0.163749i
$353$			28.9645i			1.54162i	0.637063	+	0.770812i	$0.280149\pi$
$353$			28.9645i			1.54162i	−0.637063	+	0.770812i	$0.719851\pi$
$354$		0			0
$355$	12.8769			0.683435
$356$	−2.24621	−	1.87285i	−0.119049	−	0.0992610i
$357$		0			0
$358$	9.68466	+	20.6843i	0.511850	+	1.09320i
$359$		−	22.8201i		−	1.20440i	−0.798346	−	0.602199i	$-0.794292\pi$
$359$		−	22.8201i		−	1.20440i	0.798346	−	0.602199i	$-0.205708\pi$
$360$		0			0
$361$	31.7386			1.67045
$362$	−1.12311	−	2.39871i	−0.0590291	−	0.126073i
$363$		0			0
$364$	−9.61553	+	2.39871i	−0.503991	+	0.125726i
$365$	22.2462			1.16442
$366$		0			0
$367$	−33.3693			−1.74186			−0.870932	−	0.491403i	$-0.836484\pi$
$367$	−33.3693			−1.74186			−0.870932	+	0.491403i	$0.836484\pi$
$368$	3.68466	−	0.673500i	0.192076	−	0.0351086i
$369$		0			0
$370$	−2.24621	−	4.79741i	−0.116775	−	0.249406i
$371$	19.1231	−	26.1552i	0.992822	−	1.35791i
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$	6.24621	−	2.92456i	0.322984	−	0.151225i
$375$		0			0
$376$	−4.49242	+	17.0862i	−0.231679	+	0.881155i
$377$			3.74571i			0.192914i
$378$		0			0
$379$		−	25.1035i		−	1.28948i	−0.764402	−	0.644740i	$-0.776966\pi$
$379$		−	25.1035i		−	1.28948i	0.764402	−	0.644740i	$-0.223034\pi$
$380$	−36.4924	−	30.4268i	−1.87202	−	1.56086i
$381$		0			0
$382$	−1.68466	−	3.59806i	−0.0861946	−	0.184093i
$383$	9.75379			0.498395			0.249198	−	0.968453i	$-0.419833\pi$
$383$	9.75379			0.498395			0.249198	+	0.968453i	$0.419833\pi$
$384$		0			0
$385$	4.87689	−	6.67026i	0.248550	−	0.339948i
$386$	−19.6847	+	9.21662i	−1.00192	+	0.469113i
$387$		0			0
$388$	−16.0000	−	13.3405i	−0.812277	−	0.677263i
$389$	16.2462			0.823716			0.411858	−	0.911248i	$-0.364880\pi$
$389$	16.2462			0.823716			0.411858	+	0.911248i	$0.364880\pi$
$390$		0			0
$391$	−4.87689			−0.246635
$392$	−19.7732	+	1.01025i	−0.998697	+	0.0510253i
$393$		0			0
$394$	20.8078	−	9.74247i	1.04828	−	0.490819i
$395$	−8.00000			−0.402524
$396$		0			0
$397$			18.1379i			0.910317i	0.890410	+	0.455159i	$0.150417\pi$
$397$			18.1379i			0.910317i	−0.890410	+	0.455159i	$0.849583\pi$
$398$	−4.00000	+	1.87285i	−0.200502	+	0.0938776i
$399$		0			0
$400$	4.40388	+	24.0932i	0.220194	+	1.20466i
$401$	−8.24621			−0.411796			−0.205898	−	0.978573i	$-0.566012\pi$
$401$	−8.24621			−0.411796			−0.205898	+	0.978573i	$0.566012\pi$
$402$		0			0
$403$		0			0
$404$	−21.1231	−	17.6121i	−1.05091	−	0.876234i
$405$		0			0
$406$	−1.43845	+	7.34376i	−0.0713889	+	0.364465i
$407$		−	1.05171i		−	0.0521311i
$408$		0			0
$409$		−	0.821147i		−	0.0406031i	−0.999794	−	0.0203016i	$-0.993537\pi$
$409$		−	0.821147i		−	0.0406031i	0.999794	−	0.0203016i	$-0.00646263\pi$
$410$	6.24621	−	2.92456i	0.308478	−	0.144434i
$411$		0			0
$412$	−10.2462	+	12.2888i	−0.504795	+	0.605427i
$413$	6.24621	−	8.54312i	0.307356	−	0.420379i
$414$		0			0
$415$		−	34.1725i		−	1.67746i
$416$	8.63068	−	6.14441i	0.423154	−	0.301255i
$417$		0			0
$418$	−4.00000	−	8.54312i	−0.195646	−	0.417858i
$419$	16.4924			0.805708			0.402854	−	0.915264i	$-0.368018\pi$
$419$	16.4924			0.805708			0.402854	+	0.915264i	$0.368018\pi$
$420$		0			0
$421$	10.8769			0.530107			0.265054	−	0.964234i	$-0.414610\pi$
$421$	10.8769			0.530107			0.265054	+	0.964234i	$0.414610\pi$
$422$	7.68466	+	16.4127i	0.374083	+	0.798959i
$423$		0			0
$424$	−8.80776	+	33.4990i	−0.427743	+	1.62685i
$425$		−	31.8890i		−	1.54685i
$426$		0			0
$427$	−10.2462	−	7.49141i	−0.495849	−	0.362535i
$428$	14.5616	+	12.1412i	0.703859	+	0.586866i
$429$		0			0
$430$	38.7386	−	18.1379i	1.86814	−	0.874689i
$431$			4.68213i			0.225530i	0.993622	+	0.112765i	$0.0359708\pi$
$431$			4.68213i			0.225530i	−0.993622	+	0.112765i	$0.964029\pi$
$432$		0			0
$433$		−	13.3405i		−	0.641105i	−0.947231	−	0.320552i	$-0.896131\pi$
$433$		−	13.3405i		−	0.641105i	0.947231	−	0.320552i	$-0.103869\pi$
$434$		0			0
$435$		0			0
$436$	−10.5616	+	12.6670i	−0.505807	+	0.606641i
$437$			6.67026i			0.319082i
$438$		0			0
$439$	−6.63068			−0.316465			−0.158233	−	0.987402i	$-0.550580\pi$
$439$	−6.63068			−0.316465			−0.158233	+	0.987402i	$0.550580\pi$
$440$	−2.24621	+	8.54312i	−0.107084	+	0.407277i
$441$		0			0
$442$	−12.4924	+	5.84912i	−0.594204	+	0.278214i
$443$		−	18.8438i		−	0.895296i	−0.894210	−	0.447648i	$-0.852262\pi$
$443$		−	18.8438i		−	0.895296i	0.894210	−	0.447648i	$-0.147738\pi$
$444$		0			0
$445$	−4.87689			−0.231187
$446$	34.7386	−	16.2651i	1.64492	−	0.770174i
$447$		0			0
$448$	19.2808	−	8.73222i	0.910931	−	0.412559i
$449$	−11.7538			−0.554696			−0.277348	−	0.960770i	$-0.589455\pi$
$449$	−11.7538			−0.554696			−0.277348	+	0.960770i	$0.589455\pi$
$450$		0			0
$451$	1.36932			0.0644786
$452$	5.43845	−	6.52262i	0.255803	−	0.306798i
$453$		0			0
$454$	21.1231	−	9.89012i	0.991356	−	0.464166i
$455$	−9.75379	+	13.3405i	−0.457265	+	0.625414i
$456$		0			0
$457$	0.246211			0.0115173			0.00575864	−	0.999983i	$-0.498167\pi$
$457$	0.246211			0.0115173			0.00575864	+	0.999983i	$0.498167\pi$
$458$	3.36932	+	7.19612i	0.157438	+	0.336252i
$459$		0			0
$460$	4.00000	−	4.79741i	0.186501	−	0.223680i
$461$			6.25969i			0.291543i	0.989318	+	0.145771i	$0.0465664\pi$
$461$			6.25969i			0.291543i	−0.989318	+	0.145771i	$0.953434\pi$
$462$		0			0
$463$			39.2652i			1.82481i	0.409292	+	0.912404i	$0.365776\pi$
$463$			39.2652i			1.82481i	−0.409292	+	0.912404i	$0.634224\pi$
$464$	−1.43845	−	7.86962i	−0.0667782	−	0.365338i
$465$		0			0
$466$	−28.8078	+	13.4882i	−1.33449	+	0.624828i
$467$	−34.2462			−1.58473			−0.792363	−	0.610050i	$-0.791149\pi$
$467$	−34.2462			−1.58473			−0.792363	+	0.610050i	$0.791149\pi$
$468$		0			0
$469$	23.3693	+	17.0862i	1.07909	+	0.788969i
$470$	12.4924	+	26.6811i	0.576232	+	1.23071i
$471$		0			0
$472$	−2.87689	+	10.9418i	−0.132420	+	0.503638i
$473$	8.49242			0.390482
$474$		0			0
$475$	−43.6155			−2.00122
$476$	−26.7386	+	6.67026i	−1.22556	+	0.305731i
$477$		0			0
$478$	−9.68466	−	20.6843i	−0.442966	−	0.946077i
$479$	−12.4924			−0.570793			−0.285397	−	0.958409i	$-0.592125\pi$
$479$	−12.4924			−0.570793			−0.285397	+	0.958409i	$0.592125\pi$
$480$		0			0
$481$			2.10341i			0.0959073i
$482$	14.2462	+	30.4268i	0.648897	+	1.38590i
$483$		0			0
$484$	12.9654	−	15.5501i	0.589338	−	0.706824i
$485$	−34.7386			−1.57740
$486$		0			0
$487$		−	1.57756i		−	0.0714860i	−0.999361	−	0.0357430i	$-0.988620\pi$
$487$		−	1.57756i		−	0.0714860i	0.999361	−	0.0357430i	$-0.0113798\pi$
$488$	13.1231	+	3.45041i	0.594055	+	0.156193i
$489$		0			0
$490$	−24.2462	+	22.4095i	−1.09533	+	1.01236i
$491$		−	11.3524i		−	0.512326i	−0.966634	−	0.256163i	$-0.917542\pi$
$491$		−	11.3524i		−	0.512326i	0.966634	−	0.256163i	$-0.0824585\pi$
$492$		0			0
$493$			10.4160i			0.469112i
$494$	8.00000	+	17.0862i	0.359937	+	0.768746i
$495$		0			0
$496$		0			0
$497$	−8.24621	−	6.02913i	−0.369893	−	0.270444i
$498$		0			0
$499$		−	13.8664i		−	0.620744i	−0.950615	−	0.310372i	$-0.899546\pi$
$499$		−	13.8664i		−	0.620744i	0.950615	−	0.310372i	$-0.100454\pi$
$500$	5.75379	+	4.79741i	0.257317	+	0.214547i
$501$		0			0
$502$	7.36932	−	3.45041i	0.328909	−	0.153999i
$503$	26.7386			1.19222			0.596108	−	0.802904i	$-0.296713\pi$
$503$	26.7386			1.19222			0.596108	+	0.802904i	$0.296713\pi$
$504$		0			0
$505$	−45.8617			−2.04082
$506$	1.12311	−	0.525853i	0.0499281	−	0.0233770i
$507$		0			0
$508$	−15.1922	−	12.6670i	−0.674046	−	0.562008i
$509$			3.33513i			0.147827i	0.997265	+	0.0739136i	$0.0235489\pi$
$509$			3.33513i			0.147827i	−0.997265	+	0.0739136i	$0.976451\pi$
$510$		0			0
$511$	−14.2462	−	10.4160i	−0.630215	−	0.460775i
$512$	−15.7732	+	16.2236i	−0.697083	+	0.716990i
$513$		0			0
$514$	−1.36932	−	2.92456i	−0.0603980	−	0.128997i
$515$			26.6811i			1.17571i
$516$		0			0
$517$			5.84912i			0.257244i
$518$	−0.807764	+	4.12391i	−0.0354911	+	0.181194i
$519$		0			0
$520$	4.49242	−	17.0862i	0.197006	−	0.749281i
$521$		−	29.7856i		−	1.30493i	−0.757818	−	0.652466i	$-0.773734\pi$
$521$		−	29.7856i		−	1.30493i	0.757818	−	0.652466i	$-0.226266\pi$
$522$		0			0
$523$	32.4924			1.42079			0.710397	−	0.703801i	$-0.248515\pi$
$523$	32.4924			1.42079			0.710397	+	0.703801i	$0.248515\pi$
$524$	−7.36932	+	8.83841i	−0.321930	+	0.386108i
$525$		0			0
$526$	14.8078	+	31.6261i	0.645649	+	1.37896i
$527$		0			0
$528$		0			0
$529$	22.1231			0.961874
$530$	24.4924	+	52.3104i	1.06388	+	2.27222i
$531$		0			0
$532$	9.12311	+	36.5712i	0.395537	+	1.58556i
$533$	−2.73863			−0.118623
$534$		0			0
$535$	31.6155			1.36686
$536$	−29.9309	−	7.86962i	−1.29282	−	0.339916i
$537$		0			0
$538$	6.49242	+	13.8664i	0.279908	+	0.597822i
$539$	−6.24621	+	1.98813i	−0.269043	+	0.0856349i
$540$		0			0
$541$	2.87689			0.123687			0.0618437	−	0.998086i	$-0.480302\pi$
$541$	2.87689			0.123687			0.0618437	+	0.998086i	$0.480302\pi$
$542$	−36.4924	+	17.0862i	−1.56748	+	0.733917i
$543$		0			0
$544$	24.0000	−	17.0862i	1.02899	−	0.732566i
$545$			27.5022i			1.17806i
$546$		0			0
$547$		−	16.7909i		−	0.717929i	−0.933351	−	0.358964i	$-0.883130\pi$
$547$		−	16.7909i		−	0.717929i	0.933351	−	0.358964i	$-0.116870\pi$
$548$	−0.315342	+	0.378206i	−0.0134707	+	0.0161562i
$549$		0			0
$550$	3.43845	+	7.34376i	0.146616	+	0.313139i
$551$	14.2462			0.606909
$552$		0			0
$553$	5.12311	+	3.74571i	0.217857	+	0.159284i
$554$	−6.56155	+	3.07221i	−0.278774	+	0.130526i
$555$		0			0
$556$	−15.3693	+	18.4332i	−0.651804	+	0.781743i
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$		0			0
$559$	−16.9848			−0.718382
$560$	15.3693	−	31.7738i	0.649472	−	1.34269i
$561$		0			0
$562$	−20.8078	+	9.74247i	−0.877723	+	0.410961i
$563$	−2.24621			−0.0946665			−0.0473333	−	0.998879i	$-0.515072\pi$
$563$	−2.24621			−0.0946665			−0.0473333	+	0.998879i	$0.515072\pi$
$564$		0			0
$565$		−	14.1617i		−	0.595786i
$566$	11.3693	−	5.32326i	0.477888	−	0.223753i
$567$		0			0
$568$	10.5616	+	2.77691i	0.443153	+	0.116517i
$569$	30.9848			1.29895			0.649476	−	0.760382i	$-0.274988\pi$
$569$	30.9848			1.29895			0.649476	+	0.760382i	$0.274988\pi$
$570$		0			0
$571$		−	8.83841i		−	0.369876i	−0.982750	−	0.184938i	$-0.940792\pi$
$571$		−	8.83841i		−	0.369876i	0.982750	−	0.184938i	$-0.0592084\pi$
$572$	2.24621	−	2.69400i	0.0939188	−	0.112642i
$573$		0			0
$574$	−5.36932	−	1.05171i	−0.224111	−	0.0438973i
$575$		−	5.73384i		−	0.239118i
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−12.9654	+	6.07059i	−0.539291	+	0.252503i
$579$		0			0
$580$	−10.2462	−	8.54312i	−0.425451	−	0.354734i
$581$	−16.0000	+	21.8836i	−0.663792	+	0.907887i
$582$		0			0
$583$			11.4677i			0.474943i
$584$	18.2462	+	4.79741i	0.755034	+	0.198518i
$585$		0			0
$586$	−8.24621	−	17.6121i	−0.340648	−	0.727549i
$587$	21.7538			0.897875			0.448937	−	0.893563i	$-0.351803\pi$
$587$	21.7538			0.897875			0.448937	+	0.893563i	$0.351803\pi$
$588$		0			0
$589$		0			0
$590$	8.00000	+	17.0862i	0.329355	+	0.703429i
$591$		0			0
$592$	−0.807764	−	4.41921i	−0.0331989	−	0.181628i
$593$			26.0399i			1.06933i	0.845064	+	0.534666i	$0.179562\pi$
$593$			26.0399i			1.06933i	−0.845064	+	0.534666i	$0.820438\pi$
$594$		0			0
$595$	−27.1231	+	37.0970i	−1.11194	+	1.52083i
$596$	12.8078	−	15.3610i	0.524626	−	0.629212i
$597$		0			0
$598$	−2.24621	+	1.05171i	−0.0918544	+	0.0430074i
$599$			17.2015i			0.702835i	0.936219	+	0.351417i	$0.114300\pi$
$599$			17.2015i			0.702835i	−0.936219	+	0.351417i	$0.885700\pi$
$600$		0			0
$601$		−	17.0862i		−	0.696962i	−0.937316	−	0.348481i	$-0.886698\pi$
$601$		−	17.0862i		−	0.696962i	0.937316	−	0.348481i	$-0.113302\pi$
$602$	−33.3002	−	6.52262i	−1.35721	−	0.265842i
$603$		0			0
$604$	−13.9309	−	11.6153i	−0.566839	−	0.472621i
$605$		−	33.7619i		−	1.37262i
$606$		0			0
$607$	7.61553			0.309105			0.154552	−	0.987985i	$-0.450606\pi$
$607$	7.61553			0.309105			0.154552	+	0.987985i	$0.450606\pi$
$608$	−23.3693	−	32.8255i	−0.947751	−	1.33125i
$609$		0			0
$610$	20.4924	−	9.59482i	0.829714	−	0.388483i
$611$		−	11.6982i		−	0.473260i
$612$		0			0
$613$	8.73863			0.352950			0.176475	−	0.984305i	$-0.443531\pi$
$613$	8.73863			0.352950			0.176475	+	0.984305i	$0.443531\pi$
$614$	25.1231	−	11.7630i	1.01389	−	0.474715i
$615$		0			0
$616$	5.43845	−	4.41921i	0.219121	−	0.178055i
$617$	−32.2462			−1.29818			−0.649092	−	0.760710i	$-0.724851\pi$
$617$	−32.2462			−1.29818			−0.649092	+	0.760710i	$0.724851\pi$
$618$		0			0
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$		0			0
$621$		0			0
$622$	−10.2462	+	4.79741i	−0.410836	+	0.192359i
$623$	3.12311	+	2.28343i	0.125125	+	0.0914835i
$624$		0			0
$625$	−18.1231			−0.724924
$626$	−13.7538	−	29.3751i	−0.549712	−	1.17406i
$627$		0			0
$628$	−33.6155	−	28.0281i	−1.34141	−	1.11844i
$629$			5.84912i			0.233220i
$630$		0			0
$631$		−	40.3169i		−	1.60499i	−0.596659	−	0.802495i	$-0.703506\pi$
$631$		−	40.3169i		−	1.60499i	0.596659	−	0.802495i	$-0.296494\pi$
$632$	−6.56155	−	1.72521i	−0.261005	−	0.0686250i
$633$		0			0
$634$	18.5616	−	8.69076i	0.737173	−	0.345154i
$635$	−32.9848			−1.30896
$636$		0			0
$637$	12.4924	−	3.97626i	0.494968	−	0.157545i
$638$	−1.12311	−	2.39871i	−0.0444642	−	0.0949657i
$639$		0			0
$640$	−2.87689	+	37.6229i	−0.113719	+	1.48717i
$641$	42.4924			1.67835			0.839175	−	0.543862i	$-0.183038\pi$
$641$	42.4924			1.67835			0.839175	+	0.543862i	$0.183038\pi$
$642$		0			0
$643$	−11.6155			−0.458072			−0.229036	−	0.973418i	$-0.573557\pi$
$643$	−11.6155			−0.458072			−0.229036	+	0.973418i	$0.573557\pi$
$644$	−4.80776	+	1.19935i	−0.189452	+	0.0472611i
$645$		0			0
$646$	22.2462	+	47.5130i	0.875265	+	1.86937i
$647$	32.9848			1.29677			0.648384	−	0.761313i	$-0.275445\pi$
$647$	32.9848			1.29677			0.648384	+	0.761313i	$0.275445\pi$
$648$		0			0
$649$			3.74571i			0.147032i
$650$	−6.87689	−	14.6875i	−0.269734	−	0.576092i
$651$		0			0
$652$	24.1771	+	20.1584i	0.946848	+	0.789465i
$653$	−16.7386			−0.655033			−0.327517	−	0.944845i	$-0.606212\pi$
$653$	−16.7386			−0.655033			−0.327517	+	0.944845i	$0.606212\pi$
$654$		0			0
$655$			19.1896i			0.749801i
$656$	5.75379	−	1.05171i	0.224648	−	0.0410622i
$657$		0			0
$658$	4.49242	−	22.9354i	0.175133	−	0.894113i
$659$		−	26.7963i		−	1.04384i	−0.852995	−	0.521919i	$-0.825217\pi$
$659$		−	26.7963i		−	1.04384i	0.852995	−	0.521919i	$-0.174783\pi$
$660$		0			0
$661$			8.54312i			0.332289i	0.986101	+	0.166144i	$0.0531318\pi$
$661$			8.54312i			0.332289i	−0.986101	+	0.166144i	$0.946868\pi$
$662$	−10.5616	−	22.5571i	−0.410486	−	0.876708i
$663$		0			0
$664$	7.36932	−	28.0281i	0.285985	−	1.08770i
$665$	50.7386	+	37.0970i	1.96756	+	1.43856i
$666$		0			0
$667$			1.87285i			0.0725171i
$668$	−18.2462	+	21.8836i	−0.705967	+	0.846704i
$669$		0			0
$670$	−46.7386	+	21.8836i	−1.80567	+	0.845439i
$671$	4.49242			0.173428
$672$		0			0
$673$	−27.8617			−1.07399			−0.536996	−	0.843585i	$-0.680441\pi$
$673$	−27.8617			−1.07399			−0.536996	+	0.843585i	$0.680441\pi$
$674$	10.5616	−	4.94506i	0.406816	−	0.190477i
$675$		0			0
$676$	12.1577	−	14.5813i	0.467603	−	0.560821i
$677$		−	9.18425i		−	0.352979i	−0.984302	−	0.176490i	$-0.943526\pi$
$677$		−	9.18425i		−	0.352979i	0.984302	−	0.176490i	$-0.0564742\pi$
$678$		0			0
$679$	22.2462	+	16.2651i	0.853731	+	0.624197i
$680$	12.4924	−	47.5130i	0.479063	−	1.82204i
$681$		0			0
$682$		0			0
$683$		−	32.1843i		−	1.23150i	−0.787942	−	0.615750i	$-0.788853\pi$
$683$		−	32.1843i		−	1.23150i	0.787942	−	0.615750i	$-0.211147\pi$
$684$		0			0
$685$			0.821147i			0.0313744i
$686$	26.0194	−	2.99838i	0.993426	−	0.114479i
$687$		0			0
$688$	35.6847	−	6.52262i	1.36046	−	0.248672i
$689$		−	22.9354i		−	0.873767i
$690$		0			0
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	25.6155	+	21.3578i	0.973756	+	0.811901i
$693$		0			0
$694$	−12.0691	−	25.7770i	−0.458138	−	0.978481i
$695$			40.0216i			1.51811i
$696$		0			0
$697$	−7.61553			−0.288459
$698$	−13.1231	−	28.0281i	−0.496717	−	1.06088i
$699$		0			0
$700$	−7.84233	−	31.4370i	−0.296412	−	1.18821i
$701$	34.0000			1.28416			0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000			1.28416			0.642081	+	0.766637i	$0.278071\pi$
$702$		0			0
$703$	8.00000			0.301726
$704$	−3.68466	+	6.52262i	−0.138871	+	0.245830i
$705$		0			0
$706$	17.3693	+	37.0970i	0.653703	+	1.39616i
$707$	29.3693	+	21.4731i	1.10455	+	0.807578i
$708$		0			0
$709$	6.00000			0.225335			0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000			0.225335			0.112667	+	0.993633i	$0.464061\pi$
$710$	16.4924	−	7.72197i	0.618950	−	0.289800i
$711$		0			0
$712$	−4.00000	−	1.05171i	−0.149906	−	0.0394143i
$713$		0			0
$714$		0			0
$715$		−	5.84912i		−	0.218745i
$716$	24.8078	+	20.6843i	0.927110	+	0.773008i
$717$		0			0
$718$	−13.6847	−	29.2274i	−0.510707	−	1.09076i
$719$	−28.4924			−1.06259			−0.531294	−	0.847187i	$-0.678294\pi$
$719$	−28.4924			−1.06259			−0.531294	+	0.847187i	$0.678294\pi$
$720$		0			0
$721$	12.4924	−	17.0862i	0.465242	−	0.636325i
$722$	40.6501	−	19.0329i	1.51284	−	0.708332i
$723$		0			0
$724$	−2.87689	−	2.39871i	−0.106919	−	0.0891472i
$725$	−12.2462			−0.454813
$726$		0			0
$727$	32.9848			1.22334			0.611670	−	0.791113i	$-0.290498\pi$
$727$	32.9848			1.22334			0.611670	+	0.791113i	$0.290498\pi$
$728$	−10.8769	+	8.83841i	−0.403125	+	0.327573i
$729$		0			0
$730$	28.4924	−	13.3405i	1.05455	−	0.493755i
$731$	−47.2311			−1.74690
$732$		0			0
$733$			36.0453i			1.33136i	0.746235	+	0.665682i	$0.231859\pi$
$733$			36.0453i			1.33136i	−0.746235	+	0.665682i	$0.768141\pi$
$734$	−42.7386	+	20.0108i	−1.57751	+	0.738612i
$735$		0			0
$736$	4.31534	−	3.07221i	0.159066	−	0.113243i
$737$	−10.2462			−0.377424
$738$		0			0
$739$			36.5712i			1.34529i	0.739964	+	0.672646i	$0.234842\pi$
$739$			36.5712i			1.34529i	−0.739964	+	0.672646i	$0.765158\pi$
$740$	−5.75379	−	4.79741i	−0.211513	−	0.176356i
$741$		0			0
$742$	8.80776	−	44.9666i	0.323343	−	1.65078i
$743$			35.1089i			1.28802i	0.765017	+	0.644010i	$0.222731\pi$
$743$			35.1089i			1.28802i	−0.765017	+	0.644010i	$0.777269\pi$
$744$		0			0
$745$		−	33.3513i		−	1.22190i
$746$	−12.8078	+	5.99676i	−0.468926	+	0.219557i
$747$		0			0
$748$	6.24621	−	7.49141i	0.228384	−	0.273913i
$749$	−20.2462	−	14.8028i	−0.739780	−	0.540883i
$750$		0			0
$751$			28.8492i			1.05272i	0.850261	+	0.526361i	$0.176444\pi$
$751$			28.8492i			1.05272i	−0.850261	+	0.526361i	$0.823556\pi$
$752$	4.49242	+	24.5776i	0.163822	+	0.896254i
$753$		0			0
$754$	2.24621	+	4.79741i	0.0818022	+	0.174711i
$755$	−30.2462			−1.10077
$756$		0			0
$757$	−34.9848			−1.27155			−0.635773	−	0.771876i	$-0.719319\pi$
$757$	−34.9848			−1.27155			−0.635773	+	0.771876i	$0.719319\pi$
$758$	−15.0540	−	32.1520i	−0.546785	−	1.16781i
$759$		0			0
$760$	−64.9848	−	17.0862i	−2.35725	−	0.619783i
$761$			29.7856i			1.07973i	0.841752	+	0.539864i	$0.181524\pi$
$761$			29.7856i			1.07973i	−0.841752	+	0.539864i	$0.818476\pi$
$762$		0			0
$763$	12.8769	−	17.6121i	0.466175	−	0.637600i
$764$	−4.31534	−	3.59806i	−0.156124	−	0.130173i
$765$		0			0
$766$	12.4924	−	5.84912i	0.451370	−	0.211337i
$767$		−	7.49141i		−	0.270499i
$768$		0			0
$769$		−	32.5302i		−	1.17307i	−0.809925	−	0.586534i	$-0.800492\pi$
$769$		−	32.5302i		−	1.17307i	0.809925	−	0.586534i	$-0.199508\pi$
$770$	2.24621	−	11.4677i	0.0809478	−	0.413266i
$771$		0			0
$772$	−19.6847	+	23.6089i	−0.708466	+	0.849701i
$773$		−	3.33513i		−	0.119956i	−0.998200	−	0.0599782i	$-0.980897\pi$
$773$		−	3.33513i		−	0.119956i	0.998200	−	0.0599782i	$-0.0191031\pi$
$774$		0			0
$775$		0			0
$776$	−28.4924	−	7.49141i	−1.02282	−	0.268926i
$777$		0			0
$778$	20.8078	−	9.74247i	0.745994	−	0.349284i
$779$			10.4160i			0.373191i
$780$		0			0
$781$	3.61553			0.129374
$782$	−6.24621	+	2.92456i	−0.223364	+	0.104582i
$783$		0			0
$784$	−24.7192	+	13.1514i	−0.882829	+	0.469694i
$785$	−72.9848			−2.60494
$786$		0			0
$787$	−44.9848			−1.60354			−0.801768	−	0.597635i	$-0.796107\pi$
$787$	−44.9848			−1.60354			−0.801768	+	0.597635i	$0.796107\pi$
$788$	20.8078	−	24.9559i	0.741246	−	0.889015i
$789$		0			0
$790$	−10.2462	+	4.79741i	−0.364544	+	0.170684i
$791$	−6.63068	+	9.06897i	−0.235760	+	0.322455i
$792$		0			0
$793$	−8.98485			−0.319061
$794$	10.8769	+	23.2306i	0.386007	+	0.824425i
$795$		0			0
$796$	−4.00000	+	4.79741i	−0.141776	+	0.170040i
$797$		−	39.6110i		−	1.40309i	−0.712623	−	0.701547i	$-0.752493\pi$
$797$		−	39.6110i		−	1.40309i	0.712623	−	0.701547i	$-0.247507\pi$
$798$		0			0
$799$		−	32.5302i		−	1.15083i
$800$	20.0885	+	28.2172i	0.710237	+	0.997627i
$801$		0			0
$802$	−10.5616	+	4.94506i	−0.372941	+	0.174616i
$803$	6.24621			0.220424
$804$		0			0
$805$	−4.87689	+	6.67026i	−0.171888	+	0.235096i
$806$		0			0
$807$		0			0
$808$	−37.6155	−	9.89012i	−1.32331	−	0.347933i
$809$	−22.4924			−0.790791			−0.395396	−	0.918511i	$-0.629393\pi$
$809$	−22.4924			−0.790791			−0.395396	+	0.918511i	$0.629393\pi$
$810$		0			0
$811$	0.492423			0.0172913			0.00864565	−	0.999963i	$-0.497248\pi$
$811$	0.492423			0.0172913			0.00864565	+	0.999963i	$0.497248\pi$
$812$	2.56155	+	10.2683i	0.0898929	+	0.360347i
$813$		0			0
$814$	−0.630683	−	1.34700i	−0.0221054	−	0.0472123i
$815$	52.4924			1.83873
$816$		0			0
$817$			64.5992i			2.26004i
$818$	−0.492423	−	1.05171i	−0.0172171	−	0.0367720i
$819$		0			0
$820$	6.24621	−	7.49141i	0.218127	−	0.261611i
$821$	57.2311			1.99738			0.998689	−	0.0511922i	$-0.0163021\pi$
$821$	57.2311			1.99738			0.998689	+	0.0511922i	$0.0163021\pi$
$822$		0			0
$823$			13.0452i			0.454728i	0.973810	+	0.227364i	$0.0730108\pi$
$823$			13.0452i			0.454728i	−0.973810	+	0.227364i	$0.926989\pi$
$824$	−5.75379	+	21.8836i	−0.200443	+	0.762353i
$825$		0			0
$826$	2.87689	−	14.6875i	0.100100	−	0.511044i
$827$		−	55.9408i		−	1.94525i	−0.232373	−	0.972627i	$-0.574649\pi$
$827$		−	55.9408i		−	1.94525i	0.232373	−	0.972627i	$-0.425351\pi$
$828$		0			0
$829$			21.0625i			0.731531i	0.930707	+	0.365765i	$0.119193\pi$
$829$			21.0625i			0.731531i	−0.930707	+	0.365765i	$0.880807\pi$
$830$	−20.4924	−	43.7673i	−0.711302	−	1.51918i
$831$		0			0
$832$	7.36932	−	13.0452i	0.255485	−	0.452262i
$833$	34.7386	−	11.0571i	1.20362	−	0.383106i
$834$		0			0
$835$			47.5130i			1.64426i
$836$	−10.2462	−	8.54312i	−0.354373	−	0.295470i
$837$		0			0
$838$	21.1231	−	9.89012i	0.729686	−	0.341648i
$839$	42.7386			1.47550			0.737751	−	0.675073i	$-0.235888\pi$
$839$	42.7386			1.47550			0.737751	+	0.675073i	$0.235888\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	13.9309	−	6.52262i	0.480089	−	0.224784i
$843$		0			0
$844$	19.6847	+	16.4127i	0.677574	+	0.564950i
$845$		−	31.6585i		−	1.08908i
$846$		0			0
$847$	−15.8078	+	21.6207i	−0.543161	+	0.742897i
$848$	8.80776	+	48.1865i	0.302460	+	1.65473i
$849$		0			0
$850$	−19.1231	−	40.8427i	−0.655917	−	1.40089i
$851$			1.05171i			0.0360520i
$852$		0			0
$853$			50.2070i			1.71905i	0.511090	+	0.859527i	$0.329242\pi$
$853$			50.2070i			1.71905i	−0.511090	+	0.859527i	$0.670758\pi$
$854$	−17.6155	−	3.45041i	−0.602791	−	0.118071i
$855$		0			0
$856$	25.9309	+	6.81791i	0.886299	+	0.233031i
$857$			56.4667i			1.92887i	0.264329	+	0.964433i	$0.414850\pi$
$857$			56.4667i			1.92887i	−0.264329	+	0.964433i	$0.585150\pi$
$858$		0			0
$859$	−25.8617			−0.882391			−0.441196	−	0.897411i	$-0.645445\pi$
$859$	−25.8617			−0.882391			−0.441196	+	0.897411i	$0.645445\pi$
$860$	38.7386	−	46.4613i	1.32098	−	1.58432i
$861$		0			0
$862$	2.80776	+	5.99676i	0.0956328	+	0.204251i
$863$		−	8.65840i		−	0.294735i	−0.989082	−	0.147368i	$-0.952920\pi$
$863$		−	8.65840i		−	0.294735i	0.989082	−	0.147368i	$-0.0470800\pi$
$864$		0			0
$865$	55.6155			1.89098
$866$	−8.00000	−	17.0862i	−0.271851	−	0.580614i
$867$		0			0
$868$		0			0
$869$	−2.24621			−0.0761975
$870$		0			0
$871$	20.4924			0.694359
$872$	−5.93087	+	22.5571i	−0.200845	+	0.763881i
$873$		0			0
$874$	4.00000	+	8.54312i	0.135302	+	0.288975i
$875$	−8.00000	−	5.84912i	−0.270449	−	0.197736i
$876$		0			0
$877$	36.2462			1.22395			0.611974	−	0.790878i	$-0.290376\pi$
$877$	36.2462			1.22395			0.611974	+	0.790878i	$0.290376\pi$
$878$	−8.49242	+	3.97626i	−0.286605	+	0.134192i
$879$		0			0
$880$	2.24621	+	12.2888i	0.0757198	+	0.414256i
$881$		−	46.8719i		−	1.57915i	−0.613652	−	0.789577i	$-0.710300\pi$
$881$		−	46.8719i		−	1.57915i	0.613652	−	0.789577i	$-0.289700\pi$
$882$		0			0
$883$			18.6638i			0.628087i	0.949409	+	0.314043i	$0.101684\pi$
$883$			18.6638i			0.628087i	−0.949409	+	0.314043i	$0.898316\pi$
$884$	−12.4924	+	14.9828i	−0.420166	+	0.503927i
$885$		0			0
$886$	−11.3002	−	24.1347i	−0.379637	−	0.810821i
$887$	26.7386			0.897795			0.448898	−	0.893583i	$-0.351817\pi$
$887$	26.7386			0.897795			0.448898	+	0.893583i	$0.351817\pi$
$888$		0			0
$889$	21.1231	+	15.4439i	0.708446	+	0.517973i
$890$	−6.24621	+	2.92456i	−0.209373	+	0.0980314i
$891$		0			0
$892$	34.7386	−	41.6639i	1.16314	−	1.39501i
$893$	−44.4924			−1.48888
$894$		0			0
$895$	53.8617			1.80040
$896$	19.4579	−	22.7462i	0.650041	−	0.759899i
$897$		0			0
$898$	−15.0540	+	7.04847i	−0.502358	+	0.235210i
$899$		0			0
$900$		0			0
$901$		−	63.7781i		−	2.12476i
$902$	1.75379	−	0.821147i	0.0583948	−	0.0273412i
$903$		0			0
$904$	3.05398	−	11.6153i	0.101574	−	0.386320i
$905$	−6.24621			−0.207631
$906$		0			0
$907$		−	38.4440i		−	1.27651i	−0.769824	−	0.638256i	$-0.779656\pi$
$907$		−	38.4440i		−	1.27651i	0.769824	−	0.638256i	$-0.220344\pi$
$908$	21.1231	−	25.3341i	0.700995	−	0.840740i
$909$		0			0
$910$	−4.49242	+	22.9354i	−0.148922	+	0.760299i
$911$		−	5.73384i		−	0.189971i	−0.995479	−	0.0949853i	$-0.969720\pi$
$911$		−	5.73384i		−	0.189971i	0.995479	−	0.0949853i	$-0.0302804\pi$
$912$		0			0
$913$		−	9.59482i		−	0.317542i
$914$	0.315342	−	0.147647i	0.0104306	−	0.00488373i
$915$		0			0
$916$	8.63068	+	7.19612i	0.285166	+	0.237766i
$917$	8.98485	−	12.2888i	0.296706	−	0.405813i
$918$		0			0
$919$		−	9.06897i		−	0.299158i	−0.988750	−	0.149579i	$-0.952208\pi$
$919$		−	9.06897i		−	0.299158i	0.988750	−	0.149579i	$-0.0477918\pi$
$920$	2.24621	−	8.54312i	0.0740554	−	0.281658i
$921$		0			0
$922$	3.75379	+	8.01726i	0.123624	+	0.264035i
$923$	−7.23106			−0.238013
$924$		0			0
$925$	−6.87689			−0.226111
$926$	23.5464	+	50.2899i	0.773783	+	1.65263i
$927$		0			0
$928$	−6.56155	−	9.21662i	−0.215394	−	0.302550i
$929$			3.56569i			0.116987i	0.998288	+	0.0584933i	$0.0186296\pi$
$929$			3.56569i			0.116987i	−0.998288	+	0.0584933i	$0.981370\pi$
$930$		0			0
$931$	−15.1231	−	47.5130i	−0.495640	−	1.55718i
$932$	−28.8078	+	34.5507i	−0.943630	+	1.13174i
$933$		0			0
$934$	−43.8617	+	20.5366i	−1.43520	+	0.671980i
$935$		−	16.2651i		−	0.531925i
$936$		0			0
$937$			28.7845i			0.940348i	0.882574	+	0.470174i	$0.155809\pi$
$937$			28.7845i			0.940348i	−0.882574	+	0.470174i	$0.844191\pi$
$938$	40.1771	+	7.86962i	1.31183	+	0.256952i
$939$		0			0
$940$	32.0000	+	26.6811i	1.04372	+	0.870240i
$941$			53.7727i			1.75294i	0.481457	+	0.876470i	$0.340108\pi$
$941$			53.7727i			1.75294i	−0.481457	+	0.876470i	$0.659892\pi$
$942$		0			0
$943$	−1.36932			−0.0445911
$944$	2.87689	+	15.7392i	0.0936349	+	0.512268i
$945$		0			0
$946$	10.8769	−	5.09271i	0.353638	−	0.165578i
$947$			48.6800i			1.58189i	0.611889	+	0.790943i	$0.290410\pi$
$947$			48.6800i			1.58189i	−0.611889	+	0.790943i	$0.709590\pi$
$948$		0			0
$949$	−12.4924			−0.405521
$950$	−55.8617	+	26.1552i	−1.81239	+	0.848587i
$951$		0			0
$952$	−30.2462	+	24.5776i	−0.980285	+	0.796566i
$953$	21.2311			0.687741			0.343871	−	0.939017i	$-0.388262\pi$
$953$	21.2311			0.687741			0.343871	+	0.939017i	$0.388262\pi$
$954$		0			0
$955$	−9.36932			−0.303184
$956$	−24.8078	−	20.6843i	−0.802340	−	0.668978i
$957$		0			0
$958$	−16.0000	+	7.49141i	−0.516937	+	0.242037i
$959$	0.384472	−	0.525853i	0.0124152	−	0.0169807i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	1.26137	+	2.69400i	0.0406681	+	0.0868580i
$963$		0			0
$964$	36.4924	+	30.4268i	1.17534	+	0.979980i
$965$			51.2587i			1.65008i
$966$		0			0
$967$			8.83841i			0.284224i	0.989851	+	0.142112i	$0.0453893\pi$
$967$			8.83841i			0.284224i	−0.989851	+	0.142112i	$0.954611\pi$
$968$	7.28078	−	27.6913i	0.234013	−	0.890032i
$969$		0			0
$970$	−44.4924	+	20.8319i	−1.42857	+	0.668873i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$		0			0
$973$	18.7386	−	25.6294i	0.600733	−	0.821639i
$974$	−0.946025	−	2.02050i	−0.0303126	−	0.0647410i
$975$		0			0
$976$	18.8769	−	3.45041i	0.604235	−	0.110445i
$977$	11.2614			0.360283			0.180142	−	0.983641i	$-0.442344\pi$
$977$	11.2614			0.360283			0.180142	+	0.983641i	$0.442344\pi$
$978$		0			0
$979$	−1.36932			−0.0437636
$980$	−17.6155	+	43.2414i	−0.562707	+	1.38130i
$981$		0			0
$982$	−6.80776	−	14.5399i	−0.217244	−	0.463986i
$983$	−5.26137			−0.167812			−0.0839058	−	0.996474i	$-0.526739\pi$
$983$	−5.26137			−0.167812			−0.0839058	+	0.996474i	$0.526739\pi$
$984$		0			0
$985$		−	54.1833i		−	1.72642i
$986$	6.24621	+	13.3405i	0.198920	+	0.424849i
$987$		0			0
$988$	20.4924	+	17.0862i	0.651951	+	0.543586i
$989$	−8.49242			−0.270043
$990$		0			0
$991$			0.525853i			0.0167043i	0.999965	+	0.00835213i	$0.00265860\pi$
$991$			0.525853i			0.0167043i	−0.999965	+	0.00835213i	$0.997341\pi$
$992$		0			0
$993$		0			0
$994$	−14.1771	−	2.77691i	−0.449670	−	0.0880783i
$995$			10.4160i			0.330208i
$996$		0			0
$997$		−	19.7802i		−	0.626446i	−0.949680	−	0.313223i	$-0.898591\pi$
$997$		−	19.7802i		−	0.626446i	0.949680	−	0.313223i	$-0.101409\pi$
$998$	−8.31534	−	17.7597i	−0.263218	−	0.562175i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.b.e.55.3		4
3.2	odd	2		84.2.b.a.55.2	yes	4
4.3	odd	2		252.2.b.d.55.4		4
7.6	odd	2		252.2.b.d.55.3		4
8.3	odd	2		4032.2.b.j.3583.4		4
8.5	even	2		4032.2.b.n.3583.4		4
12.11	even	2		84.2.b.b.55.1	yes	4
21.2	odd	6		588.2.o.c.31.4		8
21.5	even	6		588.2.o.a.31.4		8
21.11	odd	6		588.2.o.c.19.2		8
21.17	even	6		588.2.o.a.19.2		8
21.20	even	2		84.2.b.b.55.2	yes	4
24.5	odd	2		1344.2.b.f.895.1		4
24.11	even	2		1344.2.b.e.895.1		4
28.27	even	2	inner	252.2.b.e.55.4		4
56.13	odd	2		4032.2.b.j.3583.1		4
56.27	even	2		4032.2.b.n.3583.1		4
84.11	even	6		588.2.o.a.19.4		8
84.23	even	6		588.2.o.a.31.2		8
84.47	odd	6		588.2.o.c.31.2		8
84.59	odd	6		588.2.o.c.19.4		8
84.83	odd	2		84.2.b.a.55.1	✓	4
168.83	odd	2		1344.2.b.f.895.4		4
168.125	even	2		1344.2.b.e.895.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.b.a.55.1	✓	4	84.83	odd	2
84.2.b.a.55.2	yes	4	3.2	odd	2
84.2.b.b.55.1	yes	4	12.11	even	2
84.2.b.b.55.2	yes	4	21.20	even	2
252.2.b.d.55.3		4	7.6	odd	2
252.2.b.d.55.4		4	4.3	odd	2
252.2.b.e.55.3		4	1.1	even	1	trivial
252.2.b.e.55.4		4	28.27	even	2	inner
588.2.o.a.19.2		8	21.17	even	6
588.2.o.a.19.4		8	84.11	even	6
588.2.o.a.31.2		8	84.23	even	6
588.2.o.a.31.4		8	21.5	even	6
588.2.o.c.19.2		8	21.11	odd	6
588.2.o.c.19.4		8	84.59	odd	6
588.2.o.c.31.2		8	84.47	odd	6
588.2.o.c.31.4		8	21.2	odd	6
1344.2.b.e.895.1		4	24.11	even	2
1344.2.b.e.895.4		4	168.125	even	2
1344.2.b.f.895.1		4	24.5	odd	2
1344.2.b.f.895.4		4	168.83	odd	2
4032.2.b.j.3583.1		4	56.13	odd	2
4032.2.b.j.3583.4		4	8.3	odd	2
4032.2.b.n.3583.1		4	56.27	even	2
4032.2.b.n.3583.4		4	8.5	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28078 - 0.599676i) q^{2} +(1.28078 - 1.53610i) q^{4} -3.33513i q^{5} +(-1.56155 + 2.13578i) q^{7} +(0.719224 - 2.73546i) q^{8} +(-2.00000 - 4.27156i) q^{10} -0.936426i q^{11} +1.87285i q^{13} +(-0.719224 + 3.67188i) q^{14} +(-0.719224 - 3.93481i) q^{16} +5.20798i q^{17} +7.12311 q^{19} +(-5.12311 - 4.27156i) q^{20} +(-0.561553 - 1.19935i) q^{22} +0.936426i q^{23} -6.12311 q^{25} +(1.12311 + 2.39871i) q^{26} +(1.28078 + 5.13416i) q^{28} +2.00000 q^{29} +(-3.28078 - 4.60831i) q^{32} +(3.12311 + 6.67026i) q^{34} +(7.12311 + 5.20798i) q^{35} +1.12311 q^{37} +(9.12311 - 4.27156i) q^{38} +(-9.12311 - 2.39871i) q^{40} +1.46228i q^{41} +9.06897i q^{43} +(-1.43845 - 1.19935i) q^{44} +(0.561553 + 1.19935i) q^{46} -6.24621 q^{47} +(-2.12311 - 6.67026i) q^{49} +(-7.84233 + 3.67188i) q^{50} +(2.87689 + 2.39871i) q^{52} -12.2462 q^{53} -3.12311 q^{55} +(4.71922 + 5.80766i) q^{56} +(2.56155 - 1.19935i) q^{58} -4.00000 q^{59} +4.79741i q^{61} +(-6.96543 - 3.93481i) q^{64} +6.24621 q^{65} -10.9418i q^{67} +(8.00000 + 6.67026i) q^{68} +(12.2462 + 2.39871i) q^{70} +3.86098i q^{71} +6.67026i q^{73} +(1.43845 - 0.673500i) q^{74} +(9.12311 - 10.9418i) q^{76} +(2.00000 + 1.46228i) q^{77} -2.39871i q^{79} +(-13.1231 + 2.39871i) q^{80} +(0.876894 + 1.87285i) q^{82} +10.2462 q^{83} +17.3693 q^{85} +(5.43845 + 11.6153i) q^{86} +(-2.56155 - 0.673500i) q^{88} -1.46228i q^{89} +(-4.00000 - 2.92456i) q^{91} +(1.43845 + 1.19935i) q^{92} +(-8.00000 + 3.74571i) q^{94} -23.7565i q^{95} -10.4160i q^{97} +(-6.71922 - 7.26994i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} + 2 q^{7} + 7 q^{8} - 8 q^{10} - 7 q^{14} - 7 q^{16} + 12 q^{19} - 4 q^{20} + 6 q^{22} - 8 q^{25} - 12 q^{26} + q^{28} + 8 q^{29} - 9 q^{32} - 4 q^{34} + 12 q^{35} - 12 q^{37} + 20 q^{38}+ \cdots - 31 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 + 2 * q^7 + 7 * q^8 - 8 * q^10 - 7 * q^14 - 7 * q^16 + 12 * q^19 - 4 * q^20 + 6 * q^22 - 8 * q^25 - 12 * q^26 + q^28 + 8 * q^29 - 9 * q^32 - 4 * q^34 + 12 * q^35 - 12 * q^37 + 20 * q^38 - 20 * q^40 - 14 * q^44 - 6 * q^46 + 8 * q^47 + 8 * q^49 - 19 * q^50 + 28 * q^52 - 16 * q^53 + 4 * q^55 + 23 * q^56 + 2 * q^58 - 16 * q^59 + q^64 - 8 * q^65 + 32 * q^68 + 16 * q^70 + 14 * q^74 + 20 * q^76 + 8 * q^77 - 36 * q^80 + 20 * q^82 + 8 * q^83 + 20 * q^85 + 30 * q^86 - 2 * q^88 - 16 * q^91 + 14 * q^92 - 32 * q^94 - 31 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more