LMFDB - Embedded newform 1380.2.t.a.1057.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(1057,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1380.1057");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.3
Character	$\chi$	$=$	1380.1057
Dual form			1380.2.t.a.1333.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-1.62167 + 1.53954i) q^{5} +(2.42328 - 2.42328i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.62167 + 1.53954i) q^{5} +(2.42328 - 2.42328i) q^{7} -1.00000i q^{9} -4.29399i q^{11} +(-2.97472 + 2.97472i) q^{13} +(0.0580751 - 2.23531i) q^{15} +(-5.55993 + 5.55993i) q^{17} +3.90921 q^{19} +3.42704i q^{21} +(3.00108 + 3.74079i) q^{23} +(0.259632 - 4.99325i) q^{25} +(0.707107 + 0.707107i) q^{27} +6.44894i q^{29} -7.44378 q^{31} +(3.03631 + 3.03631i) q^{33} +(-0.199026 + 7.66051i) q^{35} +(-1.45878 + 1.45878i) q^{37} -4.20688i q^{39} -4.04416 q^{41} +(3.37770 + 3.37770i) q^{43} +(1.53954 + 1.62167i) q^{45} +(-7.41315 - 7.41315i) q^{47} -4.74461i q^{49} -7.86293i q^{51} +(0.484238 + 0.484238i) q^{53} +(6.61077 + 6.96344i) q^{55} +(-2.76423 + 2.76423i) q^{57} +15.1559i q^{59} -12.1499i q^{61} +(-2.42328 - 2.42328i) q^{63} +(0.244315 - 9.40370i) q^{65} +(-1.35595 + 1.35595i) q^{67} +(-4.76722 - 0.523058i) q^{69} -14.1317 q^{71} +(-8.24680 + 8.24680i) q^{73} +(3.34718 + 3.71435i) q^{75} +(-10.4056 - 10.4056i) q^{77} -7.52299 q^{79} -1.00000 q^{81} +(-3.22090 - 3.22090i) q^{83} +(0.456640 - 17.5761i) q^{85} +(-4.56009 - 4.56009i) q^{87} -7.86653 q^{89} +14.4172i q^{91} +(5.26355 - 5.26355i) q^{93} +(-6.33945 + 6.01839i) q^{95} +(-4.32463 + 4.32463i) q^{97} -4.29399 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) $ 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−1.62167	+	1.53954i	−0.725233	+	0.688503i
$5$	−1.62167	+	1.53954i	−0.725233	+	0.688503i
$6$		0			0
$7$	2.42328	−	2.42328i	0.915915	−	0.915915i	−0.0808141	−	0.996729i	$-0.525752\pi$
$7$	2.42328	−	2.42328i	0.915915	−	0.915915i	0.996729	+	0.0808141i	$0.0257520\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	4.29399i		−	1.29469i	−0.762198	−	0.647344i	$-0.775880\pi$
$11$		−	4.29399i		−	1.29469i	0.762198	−	0.647344i	$-0.224120\pi$
$12$		0			0
$13$	−2.97472	+	2.97472i	−0.825038	+	0.825038i	−0.986826	−	0.161788i	$-0.948274\pi$
$13$	−2.97472	+	2.97472i	−0.825038	+	0.825038i	0.161788	+	0.986826i	$0.448274\pi$
$14$		0			0
$15$	0.0580751	−	2.23531i	0.0149949	−	0.577156i
$16$		0			0
$17$	−5.55993	+	5.55993i	−1.34848	+	1.34848i	−0.461168	+	0.887313i	$0.652570\pi$
$17$	−5.55993	+	5.55993i	−1.34848	+	1.34848i	−0.887313	+	0.461168i	$0.847430\pi$
$18$		0			0
$19$	3.90921			0.896834			0.448417	−	0.893824i	$-0.351988\pi$
$19$	3.90921			0.896834			0.448417	+	0.893824i	$0.351988\pi$
$20$		0			0
$21$			3.42704i			0.747842i
$22$		0			0
$23$	3.00108	+	3.74079i	0.625768	+	0.780009i
$23$	3.00108	+	3.74079i	0.625768	+	0.780009i
$24$		0			0
$25$	0.259632	−	4.99325i	0.0519264	−	0.998651i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			6.44894i			1.19754i	0.800921	+	0.598769i	$0.204343\pi$
$29$			6.44894i			1.19754i	−0.800921	+	0.598769i	$0.795657\pi$
$30$		0			0
$31$	−7.44378			−1.33694			−0.668471	−	0.743738i	$-0.733051\pi$
$31$	−7.44378			−1.33694			−0.668471	+	0.743738i	$0.733051\pi$
$32$		0			0
$33$	3.03631	+	3.03631i	0.528554	+	0.528554i
$34$		0			0
$35$	−0.199026	+	7.66051i	−0.0336415	+	1.29486i
$36$		0			0
$37$	−1.45878	+	1.45878i	−0.239822	+	0.239822i	−0.816777	−	0.576954i	$-0.804241\pi$
$37$	−1.45878	+	1.45878i	−0.239822	+	0.239822i	0.576954	+	0.816777i	$0.304241\pi$
$38$		0			0
$39$		−	4.20688i		−	0.673640i
$40$		0			0
$41$	−4.04416			−0.631592			−0.315796	−	0.948827i	$-0.602272\pi$
$41$	−4.04416			−0.631592			−0.315796	+	0.948827i	$0.602272\pi$
$42$		0			0
$43$	3.37770	+	3.37770i	0.515094	+	0.515094i	0.916083	−	0.400989i	$-0.131333\pi$
$43$	3.37770	+	3.37770i	0.515094	+	0.515094i	−0.400989	+	0.916083i	$0.631333\pi$
$44$		0			0
$45$	1.53954	+	1.62167i	0.229501	+	0.241744i
$46$		0			0
$47$	−7.41315	−	7.41315i	−1.08132	−	1.08132i	−0.996387	−	0.0849330i	$-0.972932\pi$
$47$	−7.41315	−	7.41315i	−1.08132	−	1.08132i	−0.0849330	−	0.996387i	$-0.527068\pi$
$48$		0			0
$49$		−	4.74461i		−	0.677801i
$50$		0			0
$51$		−	7.86293i		−	1.10103i
$52$		0			0
$53$	0.484238	+	0.484238i	0.0665152	+	0.0665152i	0.739582	−	0.673067i	$-0.235023\pi$
$53$	0.484238	+	0.484238i	0.0665152	+	0.0665152i	−0.673067	+	0.739582i	$0.735023\pi$
$54$		0			0
$55$	6.61077	+	6.96344i	0.891397	+	0.938950i
$56$		0			0
$57$	−2.76423	+	2.76423i	−0.366131	+	0.366131i
$58$		0			0
$59$			15.1559i			1.97313i	0.163357	+	0.986567i	$0.447768\pi$
$59$			15.1559i			1.97313i	−0.163357	+	0.986567i	$0.552232\pi$
$60$		0			0
$61$		−	12.1499i		−	1.55563i	−0.628494	−	0.777815i	$-0.716328\pi$
$61$		−	12.1499i		−	1.55563i	0.628494	−	0.777815i	$-0.283672\pi$
$62$		0			0
$63$	−2.42328	−	2.42328i	−0.305305	−	0.305305i
$64$		0			0
$65$	0.244315	−	9.40370i	0.0303036	−	1.16639i
$66$		0			0
$67$	−1.35595	+	1.35595i	−0.165655	+	0.165655i	−0.785067	−	0.619411i	$-0.787371\pi$
$67$	−1.35595	+	1.35595i	−0.165655	+	0.165655i	0.619411	+	0.785067i	$0.287371\pi$
$68$		0			0
$69$	−4.76722	−	0.523058i	−0.573906	−	0.0629688i
$70$		0			0
$71$	−14.1317			−1.67712			−0.838560	−	0.544809i	$-0.816602\pi$
$71$	−14.1317			−1.67712			−0.838560	+	0.544809i	$0.816602\pi$
$72$		0			0
$73$	−8.24680	+	8.24680i	−0.965214	+	0.965214i	−0.999415	−	0.0342006i	$-0.989111\pi$
$73$	−8.24680	+	8.24680i	−0.965214	+	0.965214i	0.0342006	+	0.999415i	$0.489111\pi$
$74$		0			0
$75$	3.34718	+	3.71435i	0.386499	+	0.428896i
$76$		0			0
$77$	−10.4056	−	10.4056i	−1.18582	−	1.18582i
$78$		0			0
$79$	−7.52299			−0.846403			−0.423201	−	0.906036i	$-0.639094\pi$
$79$	−7.52299			−0.846403			−0.423201	+	0.906036i	$0.639094\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−3.22090	−	3.22090i	−0.353540	−	0.353540i	0.507885	−	0.861425i	$-0.330427\pi$
$83$	−3.22090	−	3.22090i	−0.353540	−	0.353540i	−0.861425	+	0.507885i	$0.830427\pi$
$84$		0			0
$85$	0.456640	−	17.5761i	0.0495296	−	1.90640i
$86$		0			0
$87$	−4.56009	−	4.56009i	−0.488893	−	0.488893i
$88$		0			0
$89$	−7.86653			−0.833850			−0.416925	−	0.908941i	$-0.636892\pi$
$89$	−7.86653			−0.833850			−0.416925	+	0.908941i	$0.636892\pi$
$90$		0			0
$91$			14.4172i			1.51133i
$92$		0			0
$93$	5.26355	−	5.26355i	0.545804	−	0.545804i
$94$		0			0
$95$	−6.33945	+	6.01839i	−0.650414	+	0.617473i
$96$		0			0
$97$	−4.32463	+	4.32463i	−0.439099	+	0.439099i	−0.891709	−	0.452610i	$-0.850493\pi$
$97$	−4.32463	+	4.32463i	−0.439099	+	0.439099i	0.452610	+	0.891709i	$0.350493\pi$
$98$		0			0
$99$	−4.29399			−0.431563
$100$		0			0
$101$	−8.38025			−0.833866			−0.416933	−	0.908937i	$-0.636895\pi$
$101$	−8.38025			−0.833866			−0.416933	+	0.908937i	$0.636895\pi$
$102$		0			0
$103$	0.329316	+	0.329316i	0.0324485	+	0.0324485i	0.723145	−	0.690696i	$-0.242696\pi$
$103$	0.329316	+	0.329316i	0.0324485	+	0.0324485i	−0.690696	+	0.723145i	$0.742696\pi$
$104$		0			0
$105$	−5.27607	−	5.55753i	−0.514891	−	0.542360i
$106$		0			0
$107$	−4.62917	+	4.62917i	−0.447519	+	0.447519i	−0.894529	−	0.447010i	$-0.852489\pi$
$107$	−4.62917	+	4.62917i	−0.447519	+	0.447519i	0.447010	+	0.894529i	$0.352489\pi$
$108$		0			0
$109$	19.3838			1.85664			0.928318	−	0.371788i	$-0.121255\pi$
$109$	19.3838			1.85664			0.928318	+	0.371788i	$0.121255\pi$
$110$		0			0
$111$		−	2.06303i		−	0.195814i
$112$		0			0
$113$	7.60107	+	7.60107i	0.715048	+	0.715048i	0.967587	−	0.252538i	$-0.0812654\pi$
$113$	7.60107	+	7.60107i	0.715048	+	0.715048i	−0.252538	+	0.967587i	$0.581265\pi$
$114$		0			0
$115$	−10.6259	−	1.44606i	−0.990867	−	0.134845i
$116$		0			0
$117$	2.97472	+	2.97472i	0.275013	+	0.275013i
$118$		0			0
$119$			26.9466i			2.47019i
$120$		0			0
$121$	−7.43838			−0.676216
$122$		0			0
$123$	2.85965	−	2.85965i	0.257846	−	0.257846i
$124$		0			0
$125$	7.26628	+	8.49713i	0.649916	+	0.760006i
$126$		0			0
$127$	4.71025	+	4.71025i	0.417967	+	0.417967i	0.884502	−	0.466536i	$-0.154498\pi$
$127$	4.71025	+	4.71025i	0.417967	+	0.417967i	−0.466536	+	0.884502i	$0.654498\pi$
$128$		0			0
$129$	−4.77678			−0.420572
$130$		0			0
$131$	3.75315			0.327914			0.163957	−	0.986467i	$-0.447574\pi$
$131$	3.75315			0.327914			0.163957	+	0.986467i	$0.447574\pi$
$132$		0			0
$133$	9.47312	−	9.47312i	0.821424	−	0.821424i
$134$		0			0
$135$	−2.23531	−	0.0580751i	−0.192385	−	0.00499831i
$136$		0			0
$137$	13.5311	−	13.5311i	1.15604	−	1.15604i	0.170724	−	0.985319i	$-0.445389\pi$
$137$	13.5311	−	13.5311i	1.15604	−	1.15604i	0.985319	−	0.170724i	$-0.0546106\pi$
$138$		0			0
$139$		−	13.4756i		−	1.14299i	−0.820606	−	0.571494i	$-0.806364\pi$
$139$		−	13.4756i		−	1.14299i	0.820606	−	0.571494i	$-0.193636\pi$
$140$		0			0
$141$	10.4838			0.882894
$142$		0			0
$143$	12.7734	+	12.7734i	1.06817	+	1.06817i
$144$		0			0
$145$	−9.92841	−	10.4581i	−0.824509	−	0.868495i
$146$		0			0
$147$	3.35494	+	3.35494i	0.276711	+	0.276711i
$148$		0			0
$149$	−1.23720			−0.101355			−0.0506777	−	0.998715i	$-0.516138\pi$
$149$	−1.23720			−0.101355			−0.0506777	+	0.998715i	$0.516138\pi$
$150$		0			0
$151$	−5.50269			−0.447802			−0.223901	−	0.974612i	$-0.571879\pi$
$151$	−5.50269			−0.447802			−0.223901	+	0.974612i	$0.571879\pi$
$152$		0			0
$153$	5.55993	+	5.55993i	0.449494	+	0.449494i
$154$		0			0
$155$	12.0714	−	11.4600i	0.969595	−	0.920489i
$156$		0			0
$157$	−5.05369	+	5.05369i	−0.403329	+	0.403329i	−0.879404	−	0.476076i	$-0.842059\pi$
$157$	−5.05369	+	5.05369i	−0.403329	+	0.403329i	0.476076	+	0.879404i	$0.342059\pi$
$158$		0			0
$159$	−0.684816			−0.0543095
$160$		0			0
$161$	16.3375	+	1.79254i	1.28757	+	0.141272i
$162$		0			0
$163$	0.132281	−	0.132281i	0.0103611	−	0.0103611i	−0.701907	−	0.712268i	$-0.747668\pi$
$163$	0.132281	−	0.132281i	0.0103611	−	0.0103611i	0.712268	+	0.701907i	$0.247668\pi$
$164$		0			0
$165$	−9.59842	−	0.249374i	−0.747236	−	0.0194137i
$166$		0			0
$167$	9.14511	+	9.14511i	0.707670	+	0.707670i	0.966045	−	0.258375i	$-0.0831870\pi$
$167$	9.14511	+	9.14511i	0.707670	+	0.707670i	−0.258375	+	0.966045i	$0.583187\pi$
$168$		0			0
$169$		−	4.69787i		−	0.361374i
$170$		0			0
$171$		−	3.90921i		−	0.298945i
$172$		0			0
$173$	−10.4998	+	10.4998i	−0.798283	+	0.798283i	−0.982825	−	0.184541i	$-0.940920\pi$
$173$	−10.4998	+	10.4998i	−0.798283	+	0.798283i	0.184541	+	0.982825i	$0.440920\pi$
$174$		0			0
$175$	−11.4709	−	12.7292i	−0.867119	−	0.962240i
$176$		0			0
$177$	−10.7169	−	10.7169i	−0.805529	−	0.805529i
$178$		0			0
$179$		−	18.6034i		−	1.39048i	−0.718777	−	0.695241i	$-0.755298\pi$
$179$		−	18.6034i		−	1.39048i	0.718777	−	0.695241i	$-0.244702\pi$
$180$		0			0
$181$			8.62136i			0.640820i	0.947279	+	0.320410i	$0.103821\pi$
$181$			8.62136i			0.640820i	−0.947279	+	0.320410i	$0.896179\pi$
$182$		0			0
$183$	8.59125	+	8.59125i	0.635083	+	0.635083i
$184$		0			0
$185$	0.119811	−	4.61152i	0.00880866	−	0.339046i
$186$		0			0
$187$	23.8743	+	23.8743i	1.74586	+	1.74586i
$188$		0			0
$189$	3.42704			0.249281
$190$		0			0
$191$		−	7.09143i		−	0.513118i	−0.966529	−	0.256559i	$-0.917411\pi$
$191$		−	7.09143i		−	0.513118i	0.966529	−	0.256559i	$-0.0825888\pi$
$192$		0			0
$193$	−2.02699	+	2.02699i	−0.145906	+	0.145906i	−0.776286	−	0.630381i	$-0.782899\pi$
$193$	−2.02699	+	2.02699i	−0.145906	+	0.145906i	0.630381	+	0.776286i	$0.282899\pi$
$194$		0			0
$195$	6.47667	+	6.82218i	0.463804	+	0.488546i
$196$		0			0
$197$	17.1838	+	17.1838i	1.22429	+	1.22429i	0.966091	+	0.258203i	$0.0831302\pi$
$197$	17.1838	+	17.1838i	1.22429	+	1.22429i	0.258203	+	0.966091i	$0.416870\pi$
$198$		0			0
$199$	−24.2591			−1.71968			−0.859839	−	0.510565i	$-0.829436\pi$
$199$	−24.2591			−1.71968			−0.859839	+	0.510565i	$0.829436\pi$
$200$		0			0
$201$		−	1.91760i		−	0.135257i
$202$		0			0
$203$	15.6276	+	15.6276i	1.09684	+	1.09684i
$204$		0			0
$205$	6.55830	−	6.22615i	0.458051	−	0.434853i
$206$		0			0
$207$	3.74079	−	3.00108i	0.260003	−	0.208589i
$208$		0			0
$209$		−	16.7861i		−	1.16112i
$210$		0			0
$211$	20.0827			1.38255			0.691277	−	0.722590i	$-0.257049\pi$
$211$	20.0827			1.38255			0.691277	+	0.722590i	$0.257049\pi$
$212$		0			0
$213$	9.99260	−	9.99260i	0.684681	−	0.684681i
$214$		0			0
$215$	−10.6776	−	0.277412i	−0.728207	−	0.0189194i
$216$		0			0
$217$	−18.0384	+	18.0384i	−1.22453	+	1.22453i
$218$		0			0
$219$		−	11.6627i		−	0.788094i
$220$		0			0
$221$		−	33.0784i		−	2.22510i
$222$		0			0
$223$	9.02181	−	9.02181i	0.604145	−	0.604145i	−0.337265	−	0.941410i	$-0.609502\pi$
$223$	9.02181	−	9.02181i	0.604145	−	0.604145i	0.941410	+	0.337265i	$0.109502\pi$
$224$		0			0
$225$	−4.99325	−	0.259632i	−0.332884	−	0.0173088i
$226$		0			0
$227$	−8.48763	+	8.48763i	−0.563343	+	0.563343i	−0.930256	−	0.366912i	$-0.880415\pi$
$227$	−8.48763	+	8.48763i	−0.563343	+	0.563343i	0.366912	+	0.930256i	$0.380415\pi$
$228$		0			0
$229$	−16.8119			−1.11096			−0.555480	−	0.831530i	$-0.687466\pi$
$229$	−16.8119			−1.11096			−0.555480	+	0.831530i	$0.687466\pi$
$230$		0			0
$231$	14.7157			0.968221
$232$		0			0
$233$	−13.3998	+	13.3998i	−0.877849	+	0.877849i	−0.993312	−	0.115463i	$-0.963165\pi$
$233$	−13.3998	+	13.3998i	−0.877849	+	0.877849i	0.115463	+	0.993312i	$0.463165\pi$
$234$		0			0
$235$	23.4345	+	0.608847i	1.52870	+	0.0397168i
$236$		0			0
$237$	5.31956	−	5.31956i	0.345542	−	0.345542i
$238$		0			0
$239$			0.795147i			0.0514338i	0.999669	+	0.0257169i	$0.00818685\pi$
$239$			0.795147i			0.0514338i	−0.999669	+	0.0257169i	$0.991813\pi$
$240$		0			0
$241$		−	23.1419i		−	1.49070i	−0.666674	−	0.745350i	$-0.732282\pi$
$241$		−	23.1419i		−	1.49070i	0.666674	−	0.745350i	$-0.267718\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	7.30451	+	7.69419i	0.466668	+	0.491564i
$246$		0			0
$247$	−11.6288	+	11.6288i	−0.739922	+	0.739922i
$248$		0			0
$249$	4.55504			0.288664
$250$		0			0
$251$			4.99742i			0.315435i	0.987484	+	0.157717i	$0.0504135\pi$
$251$			4.99742i			0.315435i	−0.987484	+	0.157717i	$0.949587\pi$
$252$		0			0
$253$	16.0629	−	12.8866i	1.00987	−	0.810174i
$254$		0			0
$255$	12.1053	+	12.7511i	0.758063	+	0.798504i
$256$		0			0
$257$	9.31312	+	9.31312i	0.580937	+	0.580937i	0.935161	−	0.354224i	$-0.115255\pi$
$257$	9.31312	+	9.31312i	0.580937	+	0.580937i	−0.354224	+	0.935161i	$0.615255\pi$
$258$		0			0
$259$			7.07009i			0.439314i
$260$		0			0
$261$	6.44894			0.399180
$262$		0			0
$263$	−2.98627	−	2.98627i	−0.184141	−	0.184141i	0.609016	−	0.793158i	$-0.291564\pi$
$263$	−2.98627	−	2.98627i	−0.184141	−	0.184141i	−0.793158	+	0.609016i	$0.791564\pi$
$264$		0			0
$265$	−1.53078	−	0.0397708i	−0.0940350	−	0.00244310i
$266$		0			0
$267$	5.56247	−	5.56247i	0.340418	−	0.340418i
$268$		0			0
$269$			6.65419i			0.405713i	0.979208	+	0.202857i	$0.0650225\pi$
$269$			6.65419i			0.405713i	−0.979208	+	0.202857i	$0.934978\pi$
$270$		0			0
$271$	3.10057			0.188346			0.0941731	−	0.995556i	$-0.469979\pi$
$271$	3.10057			0.188346			0.0941731	+	0.995556i	$0.469979\pi$
$272$		0			0
$273$	−10.1945	−	10.1945i	−0.616997	−	0.616997i
$274$		0			0
$275$	−21.4410	−	1.11486i	−1.29294	−	0.0672285i
$276$		0			0
$277$	−14.2733	−	14.2733i	−0.857599	−	0.857599i	0.133456	−	0.991055i	$-0.457393\pi$
$277$	−14.2733	−	14.2733i	−0.857599	−	0.857599i	−0.991055	+	0.133456i	$0.957393\pi$
$278$		0			0
$279$			7.44378i			0.445647i
$280$		0			0
$281$		−	5.58516i		−	0.333183i	−0.986026	−	0.166591i	$-0.946724\pi$
$281$		−	5.58516i		−	0.333183i	0.986026	−	0.166591i	$-0.0532760\pi$
$282$		0			0
$283$	15.5902	+	15.5902i	0.926739	+	0.926739i	0.997494	−	0.0707550i	$-0.0225408\pi$
$283$	15.5902	+	15.5902i	0.926739	+	0.926739i	−0.0707550	+	0.997494i	$0.522541\pi$
$284$		0			0
$285$	0.227028	−	8.73831i	0.0134480	−	0.517613i
$286$		0			0
$287$	−9.80015	+	9.80015i	−0.578485	+	0.578485i
$288$		0			0
$289$		−	44.8256i		−	2.63680i
$290$		0			0
$291$		−	6.11595i		−	0.358523i
$292$		0			0
$293$	−7.83471	−	7.83471i	−0.457708	−	0.457708i	0.440194	−	0.897903i	$-0.354910\pi$
$293$	−7.83471	−	7.83471i	−0.457708	−	0.457708i	−0.897903	+	0.440194i	$0.854910\pi$
$294$		0			0
$295$	−23.3332	−	24.5779i	−1.35851	−	1.43098i
$296$		0			0
$297$	3.03631	−	3.03631i	0.176185	−	0.176185i
$298$		0			0
$299$	−20.0551	−	2.20044i	−1.15982	−	0.127255i
$300$		0			0
$301$	16.3702			0.943564
$302$		0			0
$303$	5.92573	−	5.92573i	0.340424	−	0.340424i
$304$		0			0
$305$	18.7052	+	19.7031i	1.07106	+	1.12819i
$306$		0			0
$307$	12.4715	+	12.4715i	0.711788	+	0.711788i	0.966909	−	0.255121i	$-0.0821154\pi$
$307$	12.4715	+	12.4715i	0.711788	+	0.711788i	−0.255121	+	0.966909i	$0.582115\pi$
$308$		0			0
$309$	−0.465723			−0.0264941
$310$		0			0
$311$	6.97357			0.395435			0.197717	−	0.980259i	$-0.436647\pi$
$311$	6.97357			0.395435			0.197717	+	0.980259i	$0.436647\pi$
$312$		0			0
$313$	−3.65841	−	3.65841i	−0.206786	−	0.206786i	0.596114	−	0.802900i	$-0.296711\pi$
$313$	−3.65841	−	3.65841i	−0.206786	−	0.206786i	−0.802900	+	0.596114i	$0.796711\pi$
$314$		0			0
$315$	7.66051	+	0.199026i	0.431621	+	0.0112138i
$316$		0			0
$317$	12.0363	+	12.0363i	0.676024	+	0.676024i	0.959098	−	0.283074i	$-0.0913542\pi$
$317$	12.0363	+	12.0363i	0.676024	+	0.676024i	−0.283074	+	0.959098i	$0.591354\pi$
$318$		0			0
$319$	27.6917			1.55044
$320$		0			0
$321$		−	6.54664i		−	0.365398i
$322$		0			0
$323$	−21.7349	+	21.7349i	−1.20936	+	1.20936i
$324$		0			0
$325$	14.0812	+	15.6258i	0.781083	+	0.866766i
$326$		0			0
$327$	−13.7064	+	13.7064i	−0.757968	+	0.757968i
$328$		0			0
$329$	−35.9283			−1.98079
$330$		0			0
$331$	32.5843			1.79100			0.895499	−	0.445064i	$-0.146819\pi$
$331$	32.5843			1.79100			0.895499	+	0.445064i	$0.146819\pi$
$332$		0			0
$333$	1.45878	+	1.45878i	0.0799408	+	0.0799408i
$334$		0			0
$335$	0.111365	−	4.28643i	0.00608450	−	0.234193i
$336$		0			0
$337$	5.03755	−	5.03755i	0.274413	−	0.274413i	−0.556461	−	0.830874i	$-0.687841\pi$
$337$	5.03755	−	5.03755i	0.274413	−	0.274413i	0.830874	+	0.556461i	$0.187841\pi$
$338$		0			0
$339$	−10.7495			−0.583835
$340$		0			0
$341$			31.9635i			1.73092i
$342$		0			0
$343$	5.46546	+	5.46546i	0.295107	+	0.295107i
$344$		0			0
$345$	8.53613	−	6.49110i	0.459570	−	0.349469i
$346$		0			0
$347$	−5.38983	−	5.38983i	−0.289341	−	0.289341i	0.547479	−	0.836820i	$-0.315588\pi$
$347$	−5.38983	−	5.38983i	−0.289341	−	0.289341i	−0.836820	+	0.547479i	$0.815588\pi$
$348$		0			0
$349$			29.7785i			1.59400i	0.603976	+	0.797002i	$0.293582\pi$
$349$			29.7785i			1.59400i	−0.603976	+	0.797002i	$0.706418\pi$
$350$		0			0
$351$	−4.20688			−0.224547
$352$		0			0
$353$	16.8433	−	16.8433i	0.896476	−	0.896476i	−0.0986466	−	0.995123i	$-0.531451\pi$
$353$	16.8433	−	16.8433i	0.896476	−	0.896476i	0.995123	+	0.0986466i	$0.0314513\pi$
$354$		0			0
$355$	22.9169	−	21.7563i	1.21630	−	1.15470i
$356$		0			0
$357$	−19.0541	−	19.0541i	−1.00845	−	1.00845i
$358$		0			0
$359$	3.87689			0.204615			0.102307	−	0.994753i	$-0.467378\pi$
$359$	3.87689			0.204615			0.102307	+	0.994753i	$0.467378\pi$
$360$		0			0
$361$	−3.71808			−0.195688
$362$		0			0
$363$	5.25973	−	5.25973i	0.276064	−	0.276064i
$364$		0			0
$365$	0.677314	−	26.0699i	0.0354522	−	1.36456i
$366$		0			0
$367$	10.3782	−	10.3782i	0.541738	−	0.541738i	−0.382300	−	0.924038i	$-0.624868\pi$
$367$	10.3782	−	10.3782i	0.541738	−	0.541738i	0.924038	+	0.382300i	$0.124868\pi$
$368$		0			0
$369$			4.04416i			0.210531i
$370$		0			0
$371$	2.34689			0.121845
$372$		0			0
$373$	18.9119	+	18.9119i	0.979222	+	0.979222i	0.999788	−	0.0205660i	$-0.00654683\pi$
$373$	18.9119	+	18.9119i	0.979222	+	0.979222i	−0.0205660	+	0.999788i	$0.506547\pi$
$374$		0			0
$375$	−11.1464	−	0.870343i	−0.575598	−	0.0449443i
$376$		0			0
$377$	−19.1838	−	19.1838i	−0.988015	−	0.988015i
$378$		0			0
$379$	23.0884			1.18597			0.592985	−	0.805213i	$-0.297949\pi$
$379$	23.0884			1.18597			0.592985	+	0.805213i	$0.297949\pi$
$380$		0			0
$381$	−6.66129			−0.341268
$382$		0			0
$383$	−15.2739	−	15.2739i	−0.780459	−	0.780459i	0.199449	−	0.979908i	$-0.436085\pi$
$383$	−15.2739	−	15.2739i	−0.780459	−	0.780459i	−0.979908	+	0.199449i	$0.936085\pi$
$384$		0			0
$385$	32.8942	+	0.854615i	1.67644	+	0.0435552i
$386$		0			0
$387$	3.37770	−	3.37770i	0.171698	−	0.171698i
$388$		0			0
$389$	−7.72655			−0.391751			−0.195876	−	0.980629i	$-0.562755\pi$
$389$	−7.72655			−0.391751			−0.195876	+	0.980629i	$0.562755\pi$
$390$		0			0
$391$	−37.4843	−	4.11277i	−1.89566	−	0.207991i
$392$		0			0
$393$	−2.65388	+	2.65388i	−0.133870	+	0.133870i
$394$		0			0
$395$	12.1998	−	11.5819i	0.613839	−	0.582751i
$396$		0			0
$397$	−25.7465	−	25.7465i	−1.29218	−	1.29218i	−0.933436	−	0.358745i	$-0.883205\pi$
$397$	−25.7465	−	25.7465i	−1.29218	−	1.29218i	−0.358745	−	0.933436i	$-0.616795\pi$
$398$		0			0
$399$			13.3970i			0.670690i
$400$		0			0
$401$		−	4.30417i		−	0.214940i	−0.994208	−	0.107470i	$-0.965725\pi$
$401$		−	4.30417i		−	0.214940i	0.994208	−	0.107470i	$-0.0342750\pi$
$402$		0			0
$403$	22.1431	−	22.1431i	1.10303	−	1.10303i
$404$		0			0
$405$	1.62167	−	1.53954i	0.0805815	−	0.0765004i
$406$		0			0
$407$	6.26400	+	6.26400i	0.310495	+	0.310495i
$408$		0			0
$409$		−	10.1730i		−	0.503022i	−0.967854	−	0.251511i	$-0.919073\pi$
$409$		−	10.1730i		−	0.503022i	0.967854	−	0.251511i	$-0.0809274\pi$
$410$		0			0
$411$			19.1359i			0.943905i
$412$		0			0
$413$	36.7271	+	36.7271i	1.80722	+	1.80722i
$414$		0			0
$415$	10.1819	+	0.264534i	0.499812	+	0.0129855i
$416$		0			0
$417$	9.52871	+	9.52871i	0.466623	+	0.466623i
$418$		0			0
$419$	−0.763920			−0.0373199			−0.0186600	−	0.999826i	$-0.505940\pi$
$419$	−0.763920			−0.0373199			−0.0186600	+	0.999826i	$0.505940\pi$
$420$		0			0
$421$			2.69690i			0.131439i	0.997838	+	0.0657194i	$0.0209342\pi$
$421$			2.69690i			0.131439i	−0.997838	+	0.0657194i	$0.979066\pi$
$422$		0			0
$423$	−7.41315	+	7.41315i	−0.360440	+	0.360440i
$424$		0			0
$425$	26.3186	+	29.2057i	1.27664	+	1.41668i
$426$		0			0
$427$	−29.4425	−	29.4425i	−1.42482	−	1.42482i
$428$		0			0
$429$	−18.0643			−0.872154
$430$		0			0
$431$		−	12.1006i		−	0.582868i	−0.956591	−	0.291434i	$-0.905868\pi$
$431$		−	12.1006i		−	0.582868i	0.956591	−	0.291434i	$-0.0941323\pi$
$432$		0			0
$433$	16.5487	+	16.5487i	0.795281	+	0.795281i	0.982347	−	0.187066i	$-0.0598980\pi$
$433$	16.5487	+	16.5487i	0.795281	+	0.795281i	−0.187066	+	0.982347i	$0.559898\pi$
$434$		0			0
$435$	14.4154	+	0.374523i	0.691166	+	0.0179570i
$436$		0			0
$437$	11.7318	+	14.6235i	0.561210	+	0.699539i
$438$		0			0
$439$			26.7012i			1.27438i	0.770706	+	0.637190i	$0.219904\pi$
$439$			26.7012i			1.27438i	−0.770706	+	0.637190i	$0.780096\pi$
$440$		0			0
$441$	−4.74461			−0.225934
$442$		0			0
$443$	8.58880	−	8.58880i	0.408066	−	0.408066i	−0.472998	−	0.881064i	$-0.656828\pi$
$443$	8.58880	−	8.58880i	0.408066	−	0.408066i	0.881064	+	0.472998i	$0.156828\pi$
$444$		0			0
$445$	12.7569	−	12.1108i	0.604736	−	0.574109i
$446$		0			0
$447$	0.874832	−	0.874832i	0.0413781	−	0.0413781i
$448$		0			0
$449$		−	5.02794i		−	0.237283i	−0.992937	−	0.118642i	$-0.962146\pi$
$449$		−	5.02794i		−	0.237283i	0.992937	−	0.118642i	$-0.0378540\pi$
$450$		0			0
$451$			17.3656i			0.817714i
$452$		0			0
$453$	3.89099	−	3.89099i	0.182815	−	0.182815i
$454$		0			0
$455$	−22.1958	−	23.3799i	−1.04055	−	1.09607i
$456$		0			0
$457$	−22.2129	+	22.2129i	−1.03907	+	1.03907i	−0.0398684	+	0.999205i	$0.512694\pi$
$457$	−22.2129	+	22.2129i	−1.03907	+	1.03907i	−0.999205	+	0.0398684i	$0.987306\pi$
$458$		0			0
$459$	−7.86293			−0.367010
$460$		0			0
$461$	−3.08115			−0.143503			−0.0717517	−	0.997423i	$-0.522859\pi$
$461$	−3.08115			−0.143503			−0.0717517	+	0.997423i	$0.522859\pi$
$462$		0			0
$463$	−12.8994	+	12.8994i	−0.599486	+	0.599486i	−0.940176	−	0.340690i	$-0.889339\pi$
$463$	−12.8994	+	12.8994i	−0.599486	+	0.599486i	0.340690	+	0.940176i	$0.389339\pi$
$464$		0			0
$465$	−0.432298	+	16.6392i	−0.0200473	+	0.771623i
$466$		0			0
$467$	21.6873	−	21.6873i	1.00357	−	1.00357i	0.00357715	−	0.999994i	$-0.498861\pi$
$467$	21.6873	−	21.6873i	1.00357	−	1.00357i	0.999994	−	0.00357715i	$-0.00113865\pi$
$468$		0			0
$469$			6.57169i			0.303452i
$470$		0			0
$471$		−	7.14700i		−	0.329316i
$472$		0			0
$473$	14.5038	−	14.5038i	0.666885	−	0.666885i
$474$		0			0
$475$	1.01496	−	19.5197i	0.0465694	−	0.895624i
$476$		0			0
$477$	0.484238	−	0.484238i	0.0221717	−	0.0221717i
$478$		0			0
$479$	18.8616			0.861807			0.430903	−	0.902398i	$-0.358195\pi$
$479$	18.8616			0.861807			0.430903	+	0.902398i	$0.358195\pi$
$480$		0			0
$481$		−	8.67893i		−	0.395725i
$482$		0			0
$483$	−12.8198	+	10.2848i	−0.583323	+	0.467975i
$484$		0			0
$485$	0.355184	−	13.6711i	0.0161281	−	0.620771i
$486$		0			0
$487$	10.9118	+	10.9118i	0.494460	+	0.494460i	0.909708	−	0.415248i	$-0.136305\pi$
$487$	10.9118	+	10.9118i	0.494460	+	0.494460i	−0.415248	+	0.909708i	$0.636305\pi$
$488$		0			0
$489$			0.187074i			0.00845976i
$490$		0			0
$491$	−12.8654			−0.580605			−0.290303	−	0.956935i	$-0.593756\pi$
$491$	−12.8654			−0.580605			−0.290303	+	0.956935i	$0.593756\pi$
$492$		0			0
$493$	−35.8557	−	35.8557i	−1.61486	−	1.61486i
$494$		0			0
$495$	6.96344	−	6.61077i	0.312983	−	0.297132i
$496$		0			0
$497$	−34.2450	+	34.2450i	−1.53610	+	1.53610i
$498$		0			0
$499$			16.6623i			0.745908i	0.927850	+	0.372954i	$0.121655\pi$
$499$			16.6623i			0.745908i	−0.927850	+	0.372954i	$0.878345\pi$
$500$		0			0
$501$	−12.9331			−0.577810
$502$		0			0
$503$	2.18468	+	2.18468i	0.0974102	+	0.0974102i	0.754133	−	0.656722i	$-0.228058\pi$
$503$	2.18468	+	2.18468i	0.0974102	+	0.0974102i	−0.656722	+	0.754133i	$0.728058\pi$
$504$		0			0
$505$	13.5900	−	12.9017i	0.604747	−	0.574119i
$506$		0			0
$507$	3.32189	+	3.32189i	0.147530	+	0.147530i
$508$		0			0
$509$			23.5788i			1.04511i	0.852605	+	0.522557i	$0.175022\pi$
$509$			23.5788i			1.04511i	−0.852605	+	0.522557i	$0.824978\pi$
$510$		0			0
$511$			39.9686i			1.76811i
$512$		0			0
$513$	2.76423	+	2.76423i	0.122044	+	0.122044i
$514$		0			0
$515$	−1.04104	−	0.0270469i	−0.0458736	−	0.00119183i
$516$		0			0
$517$	−31.8320	+	31.8320i	−1.39997	+	1.39997i
$518$		0			0
$519$		−	14.8489i		−	0.651796i
$520$		0			0
$521$		−	40.5459i		−	1.77635i	−0.459509	−	0.888173i	$-0.651975\pi$
$521$		−	40.5459i		−	1.77635i	0.459509	−	0.888173i	$-0.348025\pi$
$522$		0			0
$523$	−16.7767	−	16.7767i	−0.733592	−	0.733592i	0.237737	−	0.971329i	$-0.423594\pi$
$523$	−16.7767	−	16.7767i	−0.733592	−	0.733592i	−0.971329	+	0.237737i	$0.923594\pi$
$524$		0			0
$525$	17.1121	+	0.889770i	0.746833	+	0.0388327i
$526$		0			0
$527$	41.3869	−	41.3869i	1.80284	−	1.80284i
$528$		0			0
$529$	−4.98707	+	22.4528i	−0.216829	+	0.976210i
$530$		0			0
$531$	15.1559			0.657711
$532$		0			0
$533$	12.0302	−	12.0302i	0.521087	−	0.521087i
$534$		0			0
$535$	0.380197	−	14.6338i	0.0164373	−	0.632674i
$536$		0			0
$537$	13.1546	+	13.1546i	0.567662	+	0.567662i
$538$		0			0
$539$	−20.3733			−0.877540
$540$		0			0
$541$	−5.07553			−0.218214			−0.109107	−	0.994030i	$-0.534799\pi$
$541$	−5.07553			−0.218214			−0.109107	+	0.994030i	$0.534799\pi$
$542$		0			0
$543$	−6.09622	−	6.09622i	−0.261614	−	0.261614i
$544$		0			0
$545$	−31.4342	+	29.8422i	−1.34649	+	1.27830i
$546$		0			0
$547$	10.0257	+	10.0257i	0.428667	+	0.428667i	0.888174	−	0.459507i	$-0.151974\pi$
$547$	10.0257	+	10.0257i	0.428667	+	0.428667i	−0.459507	+	0.888174i	$0.651974\pi$
$548$		0			0
$549$	−12.1499			−0.518543
$550$		0			0
$551$			25.2103i			1.07399i
$552$		0			0
$553$	−18.2303	+	18.2303i	−0.775233	+	0.775233i
$554$		0			0
$555$	3.17612	+	3.34556i	0.134819	+	0.142011i
$556$		0			0
$557$	−14.2312	+	14.2312i	−0.602996	+	0.602996i	−0.941106	−	0.338110i	$-0.890212\pi$
$557$	−14.2312	+	14.2312i	−0.602996	+	0.602996i	0.338110	+	0.941106i	$0.390212\pi$
$558$		0			0
$559$	−20.0954			−0.849943
$560$		0			0
$561$	−33.7634			−1.42549
$562$		0			0
$563$	−4.04643	−	4.04643i	−0.170537	−	0.170537i	0.616678	−	0.787215i	$-0.288478\pi$
$563$	−4.04643	−	4.04643i	−0.170537	−	0.170537i	−0.787215	+	0.616678i	$0.788478\pi$
$564$		0			0
$565$	−24.0286	−	0.624280i	−1.01089	−	0.0262637i
$566$		0			0
$567$	−2.42328	+	2.42328i	−0.101768	+	0.101768i
$568$		0			0
$569$	0.676811			0.0283734			0.0141867	−	0.999899i	$-0.495484\pi$
$569$	0.676811			0.0283734			0.0141867	+	0.999899i	$0.495484\pi$
$570$		0			0
$571$			23.5218i			0.984357i	0.870494	+	0.492178i	$0.163799\pi$
$571$			23.5218i			0.984357i	−0.870494	+	0.492178i	$0.836201\pi$
$572$		0			0
$573$	5.01440	+	5.01440i	0.209480	+	0.209480i
$574$		0			0
$575$	19.4579	−	14.0139i	0.811451	−	0.584421i
$576$		0			0
$577$	−11.6048	−	11.6048i	−0.483113	−	0.483113i	0.423011	−	0.906124i	$-0.360973\pi$
$577$	−11.6048	−	11.6048i	−0.483113	−	0.483113i	−0.906124	+	0.423011i	$0.860973\pi$
$578$		0			0
$579$		−	2.86659i		−	0.119132i
$580$		0			0
$581$	−15.6103			−0.647624
$582$		0			0
$583$	2.07932	−	2.07932i	0.0861164	−	0.0861164i
$584$		0			0
$585$	−9.40370	−	0.244315i	−0.388795	−	0.0101012i
$586$		0			0
$587$	9.63593	+	9.63593i	0.397717	+	0.397717i	0.877427	−	0.479710i	$-0.159258\pi$
$587$	9.63593	+	9.63593i	0.397717	+	0.397717i	−0.479710	+	0.877427i	$0.659258\pi$
$588$		0			0
$589$	−29.0993			−1.19902
$590$		0			0
$591$	−24.3015			−0.999631
$592$		0			0
$593$	16.4629	−	16.4629i	0.676049	−	0.676049i	−0.283055	−	0.959104i	$-0.591348\pi$
$593$	16.4629	−	16.4629i	0.676049	−	0.676049i	0.959104	+	0.283055i	$0.0913478\pi$
$594$		0			0
$595$	−41.4853	−	43.6985i	−1.70073	−	1.79146i
$596$		0			0
$597$	17.1537	−	17.1537i	0.702056	−	0.702056i
$598$		0			0
$599$		−	23.9384i		−	0.978097i	−0.872257	−	0.489048i	$-0.837344\pi$
$599$		−	23.9384i		−	0.978097i	0.872257	−	0.489048i	$-0.162656\pi$
$600$		0			0
$601$	−3.29617			−0.134454			−0.0672269	−	0.997738i	$-0.521415\pi$
$601$	−3.29617			−0.134454			−0.0672269	+	0.997738i	$0.521415\pi$
$602$		0			0
$603$	1.35595	+	1.35595i	0.0552184	+	0.0552184i
$604$		0			0
$605$	12.0626	−	11.4517i	0.490414	−	0.465577i
$606$		0			0
$607$	−2.10815	−	2.10815i	−0.0855670	−	0.0855670i	0.663028	−	0.748595i	$-0.269271\pi$
$607$	−2.10815	−	2.10815i	−0.0855670	−	0.0855670i	−0.748595	+	0.663028i	$0.769271\pi$
$608$		0			0
$609$	−22.1008			−0.895569
$610$		0			0
$611$	44.1041			1.78426
$612$		0			0
$613$	−18.3502	−	18.3502i	−0.741157	−	0.741157i	0.231644	−	0.972801i	$-0.425590\pi$
$613$	−18.3502	−	18.3502i	−0.741157	−	0.741157i	−0.972801	+	0.231644i	$0.925590\pi$
$614$		0			0
$615$	−0.234865	+	9.03997i	−0.00947068	+	0.364527i
$616$		0			0
$617$	31.6621	−	31.6621i	1.27467	−	1.27467i	0.331061	−	0.943610i	$-0.392594\pi$
$617$	31.6621	−	31.6621i	1.27467	−	1.27467i	0.943610	−	0.331061i	$-0.107406\pi$
$618$		0			0
$619$	2.85168			0.114619			0.0573093	−	0.998356i	$-0.481748\pi$
$619$	2.85168			0.114619			0.0573093	+	0.998356i	$0.481748\pi$
$620$		0			0
$621$	−0.523058	+	4.76722i	−0.0209896	+	0.191302i
$622$		0			0
$623$	−19.0628	+	19.0628i	−0.763736	+	0.763736i
$624$		0			0
$625$	−24.8652	−	2.59282i	−0.994607	−	0.103713i
$626$		0			0
$627$	11.8696	+	11.8696i	0.474025	+	0.474025i
$628$		0			0
$629$		−	16.2215i		−	0.646792i
$630$		0			0
$631$		−	8.75077i		−	0.348362i	−0.984714	−	0.174181i	$-0.944272\pi$
$631$		−	8.75077i		−	0.348362i	0.984714	−	0.174181i	$-0.0557279\pi$
$632$		0			0
$633$	−14.2006	+	14.2006i	−0.564425	+	0.564425i
$634$		0			0
$635$	−14.8901	−	0.386855i	−0.590895	−	0.0153519i
$636$		0			0
$637$	14.1139	+	14.1139i	0.559211	+	0.559211i
$638$		0			0
$639$			14.1317i			0.559040i
$640$		0			0
$641$			24.3110i			0.960228i	0.877206	+	0.480114i	$0.159405\pi$
$641$			24.3110i			0.960228i	−0.877206	+	0.480114i	$0.840595\pi$
$642$		0			0
$643$	−1.56365	−	1.56365i	−0.0616643	−	0.0616643i	0.675602	−	0.737266i	$-0.263884\pi$
$643$	−1.56365	−	1.56365i	−0.0616643	−	0.0616643i	−0.737266	+	0.675602i	$0.763884\pi$
$644$		0			0
$645$	7.74637	−	7.35405i	0.305013	−	0.289565i
$646$		0			0
$647$	−31.7988	−	31.7988i	−1.25014	−	1.25014i	−0.955657	−	0.294483i	$-0.904853\pi$
$647$	−31.7988	−	31.7988i	−1.25014	−	1.25014i	−0.294483	−	0.955657i	$-0.595147\pi$
$648$		0			0
$649$	65.0795			2.55459
$650$		0			0
$651$		−	25.5101i		−	0.999821i
$652$		0			0
$653$	10.8488	−	10.8488i	0.424546	−	0.424546i	−0.462220	−	0.886765i	$-0.652947\pi$
$653$	10.8488	−	10.8488i	0.424546	−	0.424546i	0.886765	+	0.462220i	$0.152947\pi$
$654$		0			0
$655$	−6.08637	+	5.77813i	−0.237814	+	0.225770i
$656$		0			0
$657$	8.24680	+	8.24680i	0.321738	+	0.321738i
$658$		0			0
$659$	−38.4656			−1.49841			−0.749203	−	0.662341i	$-0.769563\pi$
$659$	−38.4656			−1.49841			−0.749203	+	0.662341i	$0.769563\pi$
$660$		0			0
$661$		−	25.7565i		−	1.00181i	−0.865502	−	0.500905i	$-0.833001\pi$
$661$		−	25.7565i		−	1.00181i	0.865502	−	0.500905i	$-0.166999\pi$
$662$		0			0
$663$	23.3900	+	23.3900i	0.908391	+	0.908391i
$664$		0			0
$665$	−0.778033	+	29.9465i	−0.0301708	+	1.16128i
$666$		0			0
$667$	−24.1242	+	19.3538i	−0.934091	+	0.749381i
$668$		0			0
$669$			12.7588i			0.493282i
$670$		0			0
$671$	−52.1714			−2.01405
$672$		0			0
$673$	−30.2159	+	30.2159i	−1.16474	+	1.16474i	−0.181312	+	0.983426i	$0.558034\pi$
$673$	−30.2159	+	30.2159i	−1.16474	+	1.16474i	−0.983426	+	0.181312i	$0.941966\pi$
$674$		0			0
$675$	3.71435	−	3.34718i	0.142965	−	0.128833i
$676$		0			0
$677$	−0.437662	+	0.437662i	−0.0168207	+	0.0168207i	−0.715467	−	0.698646i	$-0.753786\pi$
$677$	−0.437662	+	0.437662i	−0.0168207	+	0.0168207i	0.698646	+	0.715467i	$0.253786\pi$
$678$		0			0
$679$			20.9596i			0.804355i
$680$		0			0
$681$		−	12.0033i		−	0.459968i
$682$		0			0
$683$	−4.39542	+	4.39542i	−0.168186	+	0.168186i	−0.786182	−	0.617996i	$-0.787945\pi$
$683$	−4.39542	+	4.39542i	−0.168186	+	0.168186i	0.617996	+	0.786182i	$0.287945\pi$
$684$		0			0
$685$	−1.11132	+	42.7748i	−0.0424614	+	1.63434i
$686$		0			0
$687$	11.8878	−	11.8878i	0.453548	−	0.453548i
$688$		0			0
$689$	−2.88094			−0.109755
$690$		0			0
$691$	6.66838			0.253677			0.126839	−	0.991923i	$-0.459517\pi$
$691$	6.66838			0.253677			0.126839	+	0.991923i	$0.459517\pi$
$692$		0			0
$693$	−10.4056	+	10.4056i	−0.395275	+	0.395275i
$694$		0			0
$695$	20.7463	+	21.8530i	0.786951	+	0.828933i
$696$		0			0
$697$	22.4853	−	22.4853i	0.851690	−	0.851690i
$698$		0			0
$699$		−	18.9502i		−	0.716761i
$700$		0			0
$701$		−	14.9673i		−	0.565309i	−0.959222	−	0.282654i	$-0.908785\pi$
$701$		−	14.9673i		−	0.565309i	0.959222	−	0.282654i	$-0.0912150\pi$
$702$		0			0
$703$	−5.70269	+	5.70269i	−0.215081	+	0.215081i
$704$		0			0
$705$	−17.0012	+	16.1402i	−0.640304	+	0.607875i
$706$		0			0
$707$	−20.3077	+	20.3077i	−0.763750	+	0.763750i
$708$		0			0
$709$	16.4512			0.617838			0.308919	−	0.951088i	$-0.400033\pi$
$709$	16.4512			0.617838			0.308919	+	0.951088i	$0.400033\pi$
$710$		0			0
$711$			7.52299i			0.282134i
$712$		0			0
$713$	−22.3394	−	27.8456i	−0.836615	−	1.04283i
$714$		0			0
$715$	−40.3794	−	1.04909i	−1.51011	−	0.0392337i
$716$		0			0
$717$	−0.562254	−	0.562254i	−0.0209978	−	0.0209978i
$718$		0			0
$719$			13.5756i			0.506286i	0.967429	+	0.253143i	$0.0814642\pi$
$719$			13.5756i			0.506286i	−0.967429	+	0.253143i	$0.918536\pi$
$720$		0			0
$721$	1.59605			0.0594401
$722$		0			0
$723$	16.3638	+	16.3638i	0.608576	+	0.608576i
$724$		0			0
$725$	32.2012	+	1.67435i	1.19592	+	0.0621839i
$726$		0			0
$727$	1.54345	−	1.54345i	0.0572435	−	0.0572435i	−0.677906	−	0.735149i	$-0.737112\pi$
$727$	1.54345	−	1.54345i	0.0572435	−	0.0572435i	0.735149	+	0.677906i	$0.237112\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−37.5595			−1.38919
$732$		0			0
$733$	−9.44932	−	9.44932i	−0.349019	−	0.349019i	0.510725	−	0.859744i	$-0.329377\pi$
$733$	−9.44932	−	9.44932i	−0.349019	−	0.349019i	−0.859744	+	0.510725i	$0.829377\pi$
$734$		0			0
$735$	−10.6057	−	0.275544i	−0.391197	−	0.0101636i
$736$		0			0
$737$	5.82242	+	5.82242i	0.214472	+	0.214472i
$738$		0			0
$739$		−	39.5398i		−	1.45450i	−0.686374	−	0.727248i	$-0.740799\pi$
$739$		−	39.5398i		−	1.45450i	0.686374	−	0.727248i	$-0.259201\pi$
$740$		0			0
$741$		−	16.4456i		−	0.604144i
$742$		0			0
$743$	13.1890	+	13.1890i	0.483858	+	0.483858i	0.906361	−	0.422503i	$-0.138848\pi$
$743$	13.1890	+	13.1890i	0.483858	+	0.483858i	−0.422503	+	0.906361i	$0.638848\pi$
$744$		0			0
$745$	2.00633	−	1.90472i	0.0735062	−	0.0697835i
$746$		0			0
$747$	−3.22090	+	3.22090i	−0.117847	+	0.117847i
$748$		0			0
$749$			22.4356i			0.819779i
$750$		0			0
$751$			37.2467i			1.35915i	0.733606	+	0.679576i	$0.237836\pi$
$751$			37.2467i			1.35915i	−0.733606	+	0.679576i	$0.762164\pi$
$752$		0			0
$753$	−3.53371	−	3.53371i	−0.128776	−	0.128776i
$754$		0			0
$755$	8.92355	−	8.47161i	0.324761	−	0.308313i
$756$		0			0
$757$	−10.5183	+	10.5183i	−0.382296	+	0.382296i	−0.871929	−	0.489633i	$-0.837131\pi$
$757$	−10.5183	+	10.5183i	−0.382296	+	0.382296i	0.489633	+	0.871929i	$0.337131\pi$
$758$		0			0
$759$	−2.24601	+	20.4704i	−0.0815249	+	0.743029i
$760$		0			0
$761$	52.6037			1.90688			0.953441	−	0.301579i	$-0.0975136\pi$
$761$	52.6037			1.90688			0.953441	+	0.301579i	$0.0975136\pi$
$762$		0			0
$763$	46.9725	−	46.9725i	1.70052	−	1.70052i
$764$		0			0
$765$	−17.5761	−	0.456640i	−0.635466	−	0.0165099i
$766$		0			0
$767$	−45.0846	−	45.0846i	−1.62791	−	1.62791i
$768$		0			0
$769$	24.2044			0.872833			0.436417	−	0.899745i	$-0.356247\pi$
$769$	24.2044			0.872833			0.436417	+	0.899745i	$0.356247\pi$
$770$		0			0
$771$	−13.1707			−0.474333
$772$		0			0
$773$	−3.19000	−	3.19000i	−0.114736	−	0.114736i	0.647408	−	0.762144i	$-0.275853\pi$
$773$	−3.19000	−	3.19000i	−0.114736	−	0.114736i	−0.762144	+	0.647408i	$0.775853\pi$
$774$		0			0
$775$	−1.93264	+	37.1687i	−0.0694226	+	1.33514i
$776$		0			0
$777$	−4.99931	−	4.99931i	−0.179349	−	0.179349i
$778$		0			0
$779$	−15.8095			−0.566433
$780$		0			0
$781$			60.6813i			2.17135i
$782$		0			0
$783$	−4.56009	+	4.56009i	−0.162964	+	0.162964i
$784$		0			0
$785$	0.415063	−	15.9758i	0.0148142	−	0.570200i
$786$		0			0
$787$	22.6154	−	22.6154i	0.806151	−	0.806151i	−0.177898	−	0.984049i	$-0.556930\pi$
$787$	22.6154	−	22.6154i	0.806151	−	0.806151i	0.984049	+	0.177898i	$0.0569297\pi$
$788$		0			0
$789$	4.22323			0.150351
$790$		0			0
$791$	36.8391			1.30985
$792$		0			0
$793$	36.1424	+	36.1424i	1.28345	+	1.28345i
$794$		0			0
$795$	1.11055	−	1.05430i	0.0393870	−	0.0373922i
$796$		0			0
$797$	3.37906	−	3.37906i	0.119693	−	0.119693i	−0.644723	−	0.764416i	$-0.723027\pi$
$797$	3.37906	−	3.37906i	0.119693	−	0.119693i	0.764416	+	0.644723i	$0.223027\pi$
$798$		0			0
$799$	82.4332			2.91628
$800$		0			0
$801$			7.86653i			0.277950i
$802$		0			0
$803$	35.4117	+	35.4117i	1.24965	+	1.24965i
$804$		0			0
$805$	−29.2537	+	22.2453i	−1.03106	+	0.784043i
$806$		0			0
$807$	−4.70522	−	4.70522i	−0.165632	−	0.165632i
$808$		0			0
$809$		−	47.1962i		−	1.65933i	−0.558261	−	0.829665i	$-0.688531\pi$
$809$		−	47.1962i		−	1.65933i	0.558261	−	0.829665i	$-0.311469\pi$
$810$		0			0
$811$	−3.16242			−0.111048			−0.0555238	−	0.998457i	$-0.517683\pi$
$811$	−3.16242			−0.111048			−0.0555238	+	0.998457i	$0.517683\pi$
$812$		0			0
$813$	−2.19243	+	2.19243i	−0.0768920	+	0.0768920i
$814$		0			0
$815$	−0.0108643	+	0.418168i	−0.000380561	+	0.0146478i
$816$		0			0
$817$	13.2041	+	13.2041i	0.461954	+	0.461954i
$818$		0			0
$819$	14.4172			0.503776
$820$		0			0
$821$	−22.8676			−0.798085			−0.399043	−	0.916932i	$-0.630657\pi$
$821$	−22.8676			−0.798085			−0.399043	+	0.916932i	$0.630657\pi$
$822$		0			0
$823$	−23.2903	+	23.2903i	−0.811847	+	0.811847i	−0.984911	−	0.173064i	$-0.944633\pi$
$823$	−23.2903	+	23.2903i	−0.811847	+	0.811847i	0.173064	+	0.984911i	$0.444633\pi$
$824$		0			0
$825$	15.9494	−	14.3728i	0.555287	−	0.500395i
$826$		0			0
$827$	3.50826	−	3.50826i	0.121994	−	0.121994i	−0.643474	−	0.765468i	$-0.722507\pi$
$827$	3.50826	−	3.50826i	0.121994	−	0.121994i	0.765468	+	0.643474i	$0.222507\pi$
$828$		0			0
$829$		−	4.58447i		−	0.159225i	−0.996826	−	0.0796126i	$-0.974632\pi$
$829$		−	4.58447i		−	0.159225i	0.996826	−	0.0796126i	$-0.0253683\pi$
$830$		0			0
$831$	20.1855			0.700227
$832$		0			0
$833$	26.3797	+	26.3797i	0.914002	+	0.914002i
$834$		0			0
$835$	−28.9096	−	0.751093i	−1.00046	−	0.0259926i
$836$		0			0
$837$	−5.26355	−	5.26355i	−0.181935	−	0.181935i
$838$		0			0
$839$	0.796335			0.0274925			0.0137463	−	0.999906i	$-0.495624\pi$
$839$	0.796335			0.0274925			0.0137463	+	0.999906i	$0.495624\pi$
$840$		0			0
$841$	−12.5889			−0.434099
$842$		0			0
$843$	3.94930	+	3.94930i	0.136021	+	0.136021i
$844$		0			0
$845$	7.23255	+	7.61839i	0.248807	+	0.262081i
$846$		0			0
$847$	−18.0253	+	18.0253i	−0.619356	+	0.619356i
$848$		0			0
$849$	−22.0478			−0.756679
$850$		0			0
$851$	−9.83493	−	1.07908i	−0.337137	−	0.0369905i
$852$		0			0
$853$	1.75847	−	1.75847i	0.0602089	−	0.0602089i	−0.676361	−	0.736570i	$-0.736444\pi$
$853$	1.75847	−	1.75847i	0.0602089	−	0.0602089i	0.736570	+	0.676361i	$0.236444\pi$
$854$		0			0
$855$	6.01839	+	6.33945i	0.205824	+	0.216805i
$856$		0			0
$857$	0.0724985	+	0.0724985i	0.00247650	+	0.00247650i	0.708344	−	0.705867i	$-0.249443\pi$
$857$	0.0724985	+	0.0724985i	0.00247650	+	0.00247650i	−0.705867	+	0.708344i	$0.749443\pi$
$858$		0			0
$859$			45.5671i			1.55473i	0.629050	+	0.777365i	$0.283444\pi$
$859$			45.5671i			1.55473i	−0.629050	+	0.777365i	$0.716556\pi$
$860$		0			0
$861$		−	13.8595i		−	0.472331i
$862$		0			0
$863$	−33.9486	+	33.9486i	−1.15562	+	1.15562i	−0.170217	+	0.985407i	$0.554447\pi$
$863$	−33.9486	+	33.9486i	−1.15562	+	1.15562i	−0.985407	+	0.170217i	$0.945553\pi$
$864$		0			0
$865$	0.862353	−	33.1920i	0.0293209	−	1.12856i
$866$		0			0
$867$	31.6965	+	31.6965i	1.07647	+	1.07647i
$868$		0			0
$869$			32.3037i			1.09583i
$870$		0			0
$871$		−	8.06711i		−	0.273344i
$872$		0			0
$873$	4.32463	+	4.32463i	0.146366	+	0.146366i
$874$		0			0
$875$	38.1992	+	2.98270i	1.29137	+	0.100834i
$876$		0			0
$877$	−32.7483	−	32.7483i	−1.10583	−	1.10583i	−0.993692	−	0.112140i	$-0.964229\pi$
$877$	−32.7483	−	32.7483i	−1.10583	−	1.10583i	−0.112140	−	0.993692i	$-0.535771\pi$
$878$		0			0
$879$	11.0799			0.373717
$880$		0			0
$881$		−	1.99317i		−	0.0671517i	−0.999436	−	0.0335759i	$-0.989310\pi$
$881$		−	1.99317i		−	0.0671517i	0.999436	−	0.0335759i	$-0.0106895\pi$
$882$		0			0
$883$	−34.5670	+	34.5670i	−1.16327	+	1.16327i	−0.179519	+	0.983754i	$0.557454\pi$
$883$	−34.5670	+	34.5670i	−1.16327	+	1.16327i	−0.983754	+	0.179519i	$0.942546\pi$
$884$		0			0
$885$	33.8783	+	0.880182i	1.13881	+	0.0295870i
$886$		0			0
$887$	5.83938	+	5.83938i	0.196067	+	0.196067i	0.798312	−	0.602244i	$-0.205727\pi$
$887$	5.83938	+	5.83938i	0.196067	+	0.196067i	−0.602244	+	0.798312i	$0.705727\pi$
$888$		0			0
$889$	22.8285			0.765644
$890$		0			0
$891$			4.29399i			0.143854i
$892$		0			0
$893$	−28.9796	−	28.9796i	−0.969764	−	0.969764i
$894$		0			0
$895$	28.6406	+	30.1685i	0.957351	+	1.00842i
$896$		0			0
$897$	15.7371	−	12.6252i	0.525446	−	0.421543i
$898$		0			0
$899$		−	48.0045i		−	1.60104i
$900$		0			0
$901$	−5.38466			−0.179389
$902$		0			0
$903$	−11.5755	+	11.5755i	−0.385208	+	0.385208i
$904$		0			0
$905$	−13.2729	−	13.9810i	−0.441207	−	0.464744i
$906$		0			0
$907$	−19.9819	+	19.9819i	−0.663489	+	0.663489i	−0.956201	−	0.292712i	$-0.905442\pi$
$907$	−19.9819	+	19.9819i	−0.663489	+	0.663489i	0.292712	+	0.956201i	$0.405442\pi$
$908$		0			0
$909$			8.38025i			0.277955i
$910$		0			0
$911$		−	46.9352i		−	1.55503i	−0.628862	−	0.777517i	$-0.716479\pi$
$911$		−	46.9352i		−	1.55503i	0.628862	−	0.777517i	$-0.283521\pi$
$912$		0			0
$913$	−13.8305	+	13.8305i	−0.457723	+	0.457723i
$914$		0			0
$915$	−27.1587	−	0.705604i	−0.897840	−	0.0233266i
$916$		0			0
$917$	9.09495	−	9.09495i	0.300342	−	0.300342i
$918$		0			0
$919$	−30.7173			−1.01327			−0.506634	−	0.862161i	$-0.669111\pi$
$919$	−30.7173			−1.01327			−0.506634	+	0.862161i	$0.669111\pi$
$920$		0			0
$921$	−17.6374			−0.581172
$922$		0			0
$923$	42.0377	−	42.0377i	1.38369	−	1.38369i
$924$		0			0
$925$	6.90533	+	7.66282i	0.227046	+	0.251952i
$926$		0			0
$927$	0.329316	−	0.329316i	0.0108162	−	0.0108162i
$928$		0			0
$929$			13.8148i			0.453250i	0.973982	+	0.226625i	$0.0727692\pi$
$929$			13.8148i			0.453250i	−0.973982	+	0.226625i	$0.927231\pi$
$930$		0			0
$931$		−	18.5477i		−	0.607875i
$932$		0			0
$933$	−4.93106	+	4.93106i	−0.161436	+	0.161436i
$934$		0			0
$935$	−75.4717	−	1.96081i	−2.46819	−	0.0641254i
$936$		0			0
$937$	−17.6846	+	17.6846i	−0.577730	+	0.577730i	−0.934277	−	0.356548i	$-0.883954\pi$
$937$	−17.6846	+	17.6846i	−0.577730	+	0.577730i	0.356548	+	0.934277i	$0.383954\pi$
$938$		0			0
$939$	5.17378			0.168840
$940$		0			0
$941$		−	28.1623i		−	0.918064i	−0.888420	−	0.459032i	$-0.848196\pi$
$941$		−	28.1623i		−	0.918064i	0.888420	−	0.459032i	$-0.151804\pi$
$942$		0			0
$943$	−12.1368	−	15.1284i	−0.395230	−	0.492648i
$944$		0			0
$945$	−5.55753	+	5.27607i	−0.180787	+	0.171630i
$946$		0			0
$947$	−43.3171	−	43.3171i	−1.40762	−	1.40762i	−0.772033	−	0.635583i	$-0.780760\pi$
$947$	−43.3171	−	43.3171i	−1.40762	−	1.40762i	−0.635583	−	0.772033i	$-0.719240\pi$
$948$		0			0
$949$		−	49.0637i		−	1.59268i
$950$		0			0
$951$	−17.0219			−0.551971
$952$		0			0
$953$	−36.1667	−	36.1667i	−1.17155	−	1.17155i	−0.981839	−	0.189716i	$-0.939243\pi$
$953$	−36.1667	−	36.1667i	−1.17155	−	1.17155i	−0.189716	−	0.981839i	$-0.560757\pi$
$954$		0			0
$955$	10.9175	+	11.5000i	0.353283	+	0.372130i
$956$		0			0
$957$	−19.5810	+	19.5810i	−0.632964	+	0.632964i
$958$		0			0
$959$		−	65.5795i		−	2.11767i
$960$		0			0
$961$	24.4098			0.787414
$962$		0			0
$963$	4.62917	+	4.62917i	0.149173	+	0.149173i
$964$		0			0
$965$	0.166478	−	6.40774i	0.00535911	−	0.206272i
$966$		0			0
$967$	−27.8045	−	27.8045i	−0.894133	−	0.894133i	0.100776	−	0.994909i	$-0.467868\pi$
$967$	−27.8045	−	27.8045i	−0.894133	−	0.894133i	−0.994909	+	0.100776i	$0.967868\pi$
$968$		0			0
$969$		−	30.7378i		−	0.987441i
$970$		0			0
$971$		−	20.9889i		−	0.673567i	−0.941582	−	0.336784i	$-0.890661\pi$
$971$		−	20.9889i		−	0.673567i	0.941582	−	0.336784i	$-0.109339\pi$
$972$		0			0
$973$	−32.6553	−	32.6553i	−1.04688	−	1.04688i
$974$		0			0
$975$	−21.0060	−	1.09224i	−0.672732	−	0.0349797i
$976$		0			0
$977$	−12.7848	+	12.7848i	−0.409022	+	0.409022i	−0.881397	−	0.472376i	$-0.843397\pi$
$977$	−12.7848	+	12.7848i	−0.409022	+	0.409022i	0.472376	+	0.881397i	$0.343397\pi$
$978$		0			0
$979$			33.7788i			1.07958i
$980$		0			0
$981$		−	19.3838i		−	0.618878i
$982$		0			0
$983$	22.2420	+	22.2420i	0.709411	+	0.709411i	0.966411	−	0.257000i	$-0.0827342\pi$
$983$	22.2420	+	22.2420i	0.709411	+	0.709411i	−0.257000	+	0.966411i	$0.582734\pi$
$984$		0			0
$985$	−54.3215	−	1.41131i	−1.73083	−	0.0449682i
$986$		0			0
$987$	25.4052	−	25.4052i	0.808656	−	0.808656i
$988$		0			0
$989$	−2.49853	+	22.7720i	−0.0794487	+	0.724107i
$990$		0			0
$991$	−37.8734			−1.20309			−0.601543	−	0.798840i	$-0.705447\pi$
$991$	−37.8734			−1.20309			−0.601543	+	0.798840i	$0.705447\pi$
$992$		0			0
$993$	−23.0406	+	23.0406i	−0.731172	+	0.731172i
$994$		0			0
$995$	39.3402	−	37.3478i	1.24717	−	1.18400i
$996$		0			0
$997$	24.5475	+	24.5475i	0.777428	+	0.777428i	0.979393	−	0.201965i	$-0.0647328\pi$
$997$	24.5475	+	24.5475i	0.777428	+	0.777428i	−0.201965	+	0.979393i	$0.564733\pi$
$998$		0			0
$999$	−2.06303			−0.0652714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.t.a.1057.3	✓	48
5.3	odd	4	inner	1380.2.t.a.1333.4	yes	48
23.22	odd	2	inner	1380.2.t.a.1057.4	yes	48
115.68	even	4	inner	1380.2.t.a.1333.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.t.a.1057.3	✓	48	1.1	even	1	trivial
1380.2.t.a.1057.4	yes	48	23.22	odd	2	inner
1380.2.t.a.1333.3	yes	48	115.68	even	4	inner
1380.2.t.a.1333.4	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.62167 + 1.53954i) q^{5} +(2.42328 - 2.42328i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-1.62167 + 1.53954i) q^{5} +(2.42328 - 2.42328i) q^{7} -1.00000i q^{9} -4.29399i q^{11} +(-2.97472 + 2.97472i) q^{13} +(0.0580751 - 2.23531i) q^{15} +(-5.55993 + 5.55993i) q^{17} +3.90921 q^{19} +3.42704i q^{21} +(3.00108 + 3.74079i) q^{23} +(0.259632 - 4.99325i) q^{25} +(0.707107 + 0.707107i) q^{27} +6.44894i q^{29} -7.44378 q^{31} +(3.03631 + 3.03631i) q^{33} +(-0.199026 + 7.66051i) q^{35} +(-1.45878 + 1.45878i) q^{37} -4.20688i q^{39} -4.04416 q^{41} +(3.37770 + 3.37770i) q^{43} +(1.53954 + 1.62167i) q^{45} +(-7.41315 - 7.41315i) q^{47} -4.74461i q^{49} -7.86293i q^{51} +(0.484238 + 0.484238i) q^{53} +(6.61077 + 6.96344i) q^{55} +(-2.76423 + 2.76423i) q^{57} +15.1559i q^{59} -12.1499i q^{61} +(-2.42328 - 2.42328i) q^{63} +(0.244315 - 9.40370i) q^{65} +(-1.35595 + 1.35595i) q^{67} +(-4.76722 - 0.523058i) q^{69} -14.1317 q^{71} +(-8.24680 + 8.24680i) q^{73} +(3.34718 + 3.71435i) q^{75} +(-10.4056 - 10.4056i) q^{77} -7.52299 q^{79} -1.00000 q^{81} +(-3.22090 - 3.22090i) q^{83} +(0.456640 - 17.5761i) q^{85} +(-4.56009 - 4.56009i) q^{87} -7.86653 q^{89} +14.4172i q^{91} +(5.26355 - 5.26355i) q^{93} +(-6.33945 + 6.01839i) q^{95} +(-4.32463 + 4.32463i) q^{97} -4.29399 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) \) 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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