LMFDB - Embedded newform 1530.2.m.g.647.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1530,2,Mod(647,1530)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1530.647"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1530, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,16,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.3
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.g.953.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.73205 - 1.41421i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.22474 + 0.224745i) q^{10} +2.82843i q^{11} +(-2.44949 + 2.44949i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +6.89898i q^{19} +(-1.41421 + 1.73205i) q^{20} +(2.00000 + 2.00000i) q^{22} +(-1.73205 - 1.73205i) q^{23} +(1.00000 + 4.89898i) q^{25} +3.46410i q^{26} +(2.00000 - 2.00000i) q^{28} +2.82843 q^{29} -7.34847 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.00000i q^{34} +(-0.635674 - 6.29253i) q^{35} +(6.44949 + 6.44949i) q^{37} +(4.87832 + 4.87832i) q^{38} +(0.224745 + 2.22474i) q^{40} -0.635674i q^{41} +(3.44949 - 3.44949i) q^{43} +2.82843 q^{44} -2.44949 q^{46} +(-2.82843 + 2.82843i) q^{47} +1.00000i q^{49} +(4.17121 + 2.75699i) q^{50} +(2.44949 + 2.44949i) q^{52} +(5.51399 + 5.51399i) q^{53} +(4.00000 - 4.89898i) q^{55} -2.82843i q^{56} +(2.00000 - 2.00000i) q^{58} -4.87832 q^{59} +5.34847 q^{61} +(-5.19615 + 5.19615i) q^{62} +1.00000i q^{64} +(7.70674 - 0.778539i) q^{65} +(-1.44949 - 1.44949i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-4.89898 - 4.00000i) q^{70} +0.635674i q^{71} +(-3.34847 + 3.34847i) q^{73} +9.12096 q^{74} +6.89898 q^{76} +(-5.65685 + 5.65685i) q^{77} +6.44949i q^{79} +(1.73205 + 1.41421i) q^{80} +(-0.449490 - 0.449490i) q^{82} +(-2.82843 - 2.82843i) q^{83} +(2.22474 - 0.224745i) q^{85} -4.87832i q^{86} +(2.00000 - 2.00000i) q^{88} +12.4422 q^{89} -9.79796 q^{91} +(-1.73205 + 1.73205i) q^{92} +4.00000i q^{94} +(9.75663 - 11.9494i) q^{95} +(6.44949 + 6.44949i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{7} - 8 q^{10} - 8 q^{16} + 16 q^{22} + 8 q^{25} + 16 q^{28} + 32 q^{37} - 8 q^{40} + 8 q^{43} + 32 q^{55} + 16 q^{58} - 16 q^{61} + 8 q^{67} + 32 q^{73} + 16 q^{76} + 16 q^{82} + 8 q^{85} + 16 q^{88}+ \cdots + 32 q^{97}+O(q^{100}) $ 8 * q + 16 * q^7 - 8 * q^10 - 8 * q^16 + 16 * q^22 + 8 * q^25 + 16 * q^28 + 32 * q^37 - 8 * q^40 + 8 * q^43 + 32 * q^55 + 16 * q^58 - 16 * q^61 + 8 * q^67 + 32 * q^73 + 16 * q^76 + 16 * q^82 + 8 * q^85 + 16 * q^88 + 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−1.73205	−	1.41421i	−0.774597	−	0.632456i
$5$	−1.73205	−	1.41421i	−0.774597	−	0.632456i
$6$		0			0
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	0.975579	−	0.219650i	$-0.0704915\pi$
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	−0.219650	+	0.975579i	$0.570491\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−2.22474	+	0.224745i	−0.703526	+	0.0710706i
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$		0			0
$13$	−2.44949	+	2.44949i	−0.679366	+	0.679366i	−0.959857	−	0.280491i	$-0.909503\pi$
$13$	−2.44949	+	2.44949i	−0.679366	+	0.679366i	0.280491	+	0.959857i	$0.409503\pi$
$14$	2.82843			0.755929
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$		0			0
$19$			6.89898i			1.58273i	0.611341	+	0.791367i	$0.290630\pi$
$19$			6.89898i			1.58273i	−0.611341	+	0.791367i	$0.709370\pi$
$20$	−1.41421	+	1.73205i	−0.316228	+	0.387298i
$21$		0			0
$22$	2.00000	+	2.00000i	0.426401	+	0.426401i
$23$	−1.73205	−	1.73205i	−0.361158	−	0.361158i	0.503081	−	0.864239i	$-0.332200\pi$
$23$	−1.73205	−	1.73205i	−0.361158	−	0.361158i	−0.864239	+	0.503081i	$0.832200\pi$
$24$		0			0
$25$	1.00000	+	4.89898i	0.200000	+	0.979796i
$26$			3.46410i			0.679366i
$27$		0			0
$28$	2.00000	−	2.00000i	0.377964	−	0.377964i
$29$	2.82843			0.525226			0.262613	−	0.964901i	$-0.415416\pi$
$29$	2.82843			0.525226			0.262613	+	0.964901i	$0.415416\pi$
$30$		0			0
$31$	−7.34847			−1.31982			−0.659912	−	0.751343i	$-0.729406\pi$
$31$	−7.34847			−1.31982			−0.659912	+	0.751343i	$0.729406\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			1.00000i			0.171499i
$35$	−0.635674	−	6.29253i	−0.107449	−	1.06363i
$36$		0			0
$37$	6.44949	+	6.44949i	1.06029	+	1.06029i	0.998062	+	0.0622276i	$0.0198205\pi$
$37$	6.44949	+	6.44949i	1.06029	+	1.06029i	0.0622276	+	0.998062i	$0.480180\pi$
$38$	4.87832	+	4.87832i	0.791367	+	0.791367i
$39$		0			0
$40$	0.224745	+	2.22474i	0.0355353	+	0.351763i
$41$		−	0.635674i		−	0.0992757i	−0.998767	−	0.0496378i	$-0.984193\pi$
$41$		−	0.635674i		−	0.0992757i	0.998767	−	0.0496378i	$-0.0158067\pi$
$42$		0			0
$43$	3.44949	−	3.44949i	0.526042	−	0.526042i	−0.393348	−	0.919390i	$-0.628683\pi$
$43$	3.44949	−	3.44949i	0.526042	−	0.526042i	0.919390	+	0.393348i	$0.128683\pi$
$44$	2.82843			0.426401
$45$		0			0
$46$	−2.44949			−0.361158
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	−0.882632	−	0.470064i	$-0.844231\pi$
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	0.470064	+	0.882632i	$0.344231\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	4.17121	+	2.75699i	0.589898	+	0.389898i
$51$		0			0
$52$	2.44949	+	2.44949i	0.339683	+	0.339683i
$53$	5.51399	+	5.51399i	0.757405	+	0.757405i	0.975849	−	0.218445i	$-0.0700983\pi$
$53$	5.51399	+	5.51399i	0.757405	+	0.757405i	−0.218445	+	0.975849i	$0.570098\pi$
$54$		0			0
$55$	4.00000	−	4.89898i	0.539360	−	0.660578i
$56$		−	2.82843i		−	0.377964i
$57$		0			0
$58$	2.00000	−	2.00000i	0.262613	−	0.262613i
$59$	−4.87832			−0.635103			−0.317551	−	0.948241i	$-0.602861\pi$
$59$	−4.87832			−0.635103			−0.317551	+	0.948241i	$0.602861\pi$
$60$		0			0
$61$	5.34847			0.684801			0.342401	−	0.939554i	$-0.388760\pi$
$61$	5.34847			0.684801			0.342401	+	0.939554i	$0.388760\pi$
$62$	−5.19615	+	5.19615i	−0.659912	+	0.659912i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	7.70674	−	0.778539i	0.955904	−	0.0965659i
$66$		0			0
$67$	−1.44949	−	1.44949i	−0.177083	−	0.177083i	0.613000	−	0.790083i	$-0.289963\pi$
$67$	−1.44949	−	1.44949i	−0.177083	−	0.177083i	−0.790083	+	0.613000i	$0.789963\pi$
$68$	0.707107	+	0.707107i	0.0857493	+	0.0857493i
$69$		0			0
$70$	−4.89898	−	4.00000i	−0.585540	−	0.478091i
$71$			0.635674i			0.0754407i	0.999288	+	0.0377203i	$0.0120096\pi$
$71$			0.635674i			0.0754407i	−0.999288	+	0.0377203i	$0.987990\pi$
$72$		0			0
$73$	−3.34847	+	3.34847i	−0.391909	+	0.391909i	−0.875367	−	0.483459i	$-0.839380\pi$
$73$	−3.34847	+	3.34847i	−0.391909	+	0.391909i	0.483459	+	0.875367i	$0.339380\pi$
$74$	9.12096			1.06029
$75$		0			0
$76$	6.89898			0.791367
$77$	−5.65685	+	5.65685i	−0.644658	+	0.644658i
$78$		0			0
$79$			6.44949i			0.725624i	0.931862	+	0.362812i	$0.118183\pi$
$79$			6.44949i			0.725624i	−0.931862	+	0.362812i	$0.881817\pi$
$80$	1.73205	+	1.41421i	0.193649	+	0.158114i
$81$		0			0
$82$	−0.449490	−	0.449490i	−0.0496378	−	0.0496378i
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	0.534628	−	0.845088i	$-0.320452\pi$
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	−0.845088	+	0.534628i	$0.820452\pi$
$84$		0			0
$85$	2.22474	−	0.224745i	0.241307	−	0.0243770i
$86$		−	4.87832i		−	0.526042i
$87$		0			0
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	12.4422			1.31887			0.659435	−	0.751762i	$-0.270796\pi$
$89$	12.4422			1.31887			0.659435	+	0.751762i	$0.270796\pi$
$90$		0			0
$91$	−9.79796			−1.02711
$92$	−1.73205	+	1.73205i	−0.180579	+	0.180579i
$93$		0			0
$94$			4.00000i			0.412568i
$95$	9.75663	−	11.9494i	1.00101	−	1.22598i
$96$		0			0
$97$	6.44949	+	6.44949i	0.654846	+	0.654846i	0.954156	−	0.299310i	$-0.0967563\pi$
$97$	6.44949	+	6.44949i	0.654846	+	0.654846i	−0.299310	+	0.954156i	$0.596756\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		0			0
$100$	4.89898	−	1.00000i	0.489898	−	0.100000i
$101$		−	7.84961i		−	0.781065i	−0.920589	−	0.390533i	$-0.872291\pi$
$101$		−	7.84961i		−	0.781065i	0.920589	−	0.390533i	$-0.127709\pi$
$102$		0			0
$103$	−2.89898	+	2.89898i	−0.285645	+	0.285645i	−0.835355	−	0.549710i	$-0.814738\pi$
$103$	−2.89898	+	2.89898i	−0.285645	+	0.285645i	0.549710	+	0.835355i	$0.314738\pi$
$104$	3.46410			0.339683
$105$		0			0
$106$	7.79796			0.757405
$107$	1.27135	−	1.27135i	0.122906	−	0.122906i	−0.642978	−	0.765884i	$-0.722302\pi$
$107$	1.27135	−	1.27135i	0.122906	−	0.122906i	0.765884	+	0.642978i	$0.222302\pi$
$108$		0			0
$109$			13.3485i			1.27855i	0.768978	+	0.639276i	$0.220766\pi$
$109$			13.3485i			1.27855i	−0.768978	+	0.639276i	$0.779234\pi$
$110$	−0.635674	−	6.29253i	−0.0606092	−	0.599969i
$111$		0			0
$112$	−2.00000	−	2.00000i	−0.188982	−	0.188982i
$113$	−5.51399	−	5.51399i	−0.518713	−	0.518713i	0.398469	−	0.917182i	$-0.369542\pi$
$113$	−5.51399	−	5.51399i	−0.518713	−	0.518713i	−0.917182	+	0.398469i	$0.869542\pi$
$114$		0			0
$115$	0.550510	+	5.44949i	0.0513353	+	0.508168i
$116$		−	2.82843i		−	0.262613i
$117$		0			0
$118$	−3.44949	+	3.44949i	−0.317551	+	0.317551i
$119$	−2.82843			−0.259281
$120$		0			0
$121$	3.00000			0.272727
$122$	3.78194	−	3.78194i	0.342401	−	0.342401i
$123$		0			0
$124$			7.34847i			0.659912i
$125$	5.19615	−	9.89949i	0.464758	−	0.885438i
$126$		0			0
$127$	4.89898	+	4.89898i	0.434714	+	0.434714i	0.890228	−	0.455514i	$-0.150545\pi$
$127$	4.89898	+	4.89898i	0.434714	+	0.434714i	−0.455514	+	0.890228i	$0.650545\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	4.89898	−	6.00000i	0.429669	−	0.526235i
$131$			5.65685i			0.494242i	0.968985	+	0.247121i	$0.0794845\pi$
$131$			5.65685i			0.494242i	−0.968985	+	0.247121i	$0.920516\pi$
$132$		0			0
$133$	−13.7980	+	13.7980i	−1.19643	+	1.19643i
$134$	−2.04989			−0.177083
$135$		0			0
$136$	1.00000			0.0857493
$137$	2.68556	−	2.68556i	0.229443	−	0.229443i	−0.583017	−	0.812460i	$-0.698128\pi$
$137$	2.68556	−	2.68556i	0.229443	−	0.229443i	0.812460	+	0.583017i	$0.198128\pi$
$138$		0			0
$139$		−	5.79796i		−	0.491776i	−0.969298	−	0.245888i	$-0.920920\pi$
$139$		−	5.79796i		−	0.491776i	0.969298	−	0.245888i	$-0.0790796\pi$
$140$	−6.29253	+	0.635674i	−0.531816	+	0.0537243i
$141$		0			0
$142$	0.449490	+	0.449490i	0.0377203	+	0.0377203i
$143$	−6.92820	−	6.92820i	−0.579365	−	0.579365i
$144$		0			0
$145$	−4.89898	−	4.00000i	−0.406838	−	0.332182i
$146$			4.73545i			0.391909i
$147$		0			0
$148$	6.44949	−	6.44949i	0.530145	−	0.530145i
$149$	−11.9494			−0.978932			−0.489466	−	0.872022i	$-0.662808\pi$
$149$	−11.9494			−0.978932			−0.489466	+	0.872022i	$0.662808\pi$
$150$		0			0
$151$	−18.6969			−1.52154			−0.760768	−	0.649024i	$-0.775177\pi$
$151$	−18.6969			−1.52154			−0.760768	+	0.649024i	$0.775177\pi$
$152$	4.87832	−	4.87832i	0.395684	−	0.395684i
$153$		0			0
$154$			8.00000i			0.644658i
$155$	12.7279	+	10.3923i	1.02233	+	0.834730i
$156$		0			0
$157$	−13.3485	−	13.3485i	−1.06532	−	1.06532i	−0.997712	−	0.0676121i	$-0.978462\pi$
$157$	−13.3485	−	13.3485i	−1.06532	−	1.06532i	−0.0676121	−	0.997712i	$-0.521538\pi$
$158$	4.56048	+	4.56048i	0.362812	+	0.362812i
$159$		0			0
$160$	2.22474	−	0.224745i	0.175882	−	0.0177676i
$161$		−	6.92820i		−	0.546019i
$162$		0			0
$163$	15.7980	−	15.7980i	1.23739	−	1.23739i	0.276328	−	0.961063i	$-0.410882\pi$
$163$	15.7980	−	15.7980i	1.23739	−	1.23739i	0.961063	−	0.276328i	$-0.0891177\pi$
$164$	−0.635674			−0.0496378
$165$		0			0
$166$	−4.00000			−0.310460
$167$	−14.9528	+	14.9528i	−1.15708	+	1.15708i	−0.171981	+	0.985100i	$0.555017\pi$
$167$	−14.9528	+	14.9528i	−1.15708	+	1.15708i	−0.985100	+	0.171981i	$0.944983\pi$
$168$		0			0
$169$			1.00000i			0.0769231i
$170$	1.41421	−	1.73205i	0.108465	−	0.132842i
$171$		0			0
$172$	−3.44949	−	3.44949i	−0.263021	−	0.263021i
$173$	15.0956	+	15.0956i	1.14770	+	1.14770i	0.987004	+	0.160697i	$0.0513742\pi$
$173$	15.0956	+	15.0956i	1.14770	+	1.14770i	0.160697	+	0.987004i	$0.448626\pi$
$174$		0			0
$175$	−7.79796	+	11.7980i	−0.589470	+	0.891842i
$176$		−	2.82843i		−	0.213201i
$177$		0			0
$178$	8.79796	−	8.79796i	0.659435	−	0.659435i
$179$	−13.3636			−0.998842			−0.499421	−	0.866359i	$-0.666454\pi$
$179$	−13.3636			−0.998842			−0.499421	+	0.866359i	$0.666454\pi$
$180$		0			0
$181$	−25.3485			−1.88414			−0.942068	−	0.335421i	$-0.891122\pi$
$181$	−25.3485			−1.88414			−0.942068	+	0.335421i	$0.891122\pi$
$182$	−6.92820	+	6.92820i	−0.513553	+	0.513553i
$183$		0			0
$184$			2.44949i			0.180579i
$185$	−2.04989	−	20.2918i	−0.150711	−	1.49188i
$186$		0			0
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$	2.82843	+	2.82843i	0.206284	+	0.206284i
$189$		0			0
$190$	−1.55051	−	15.3485i	−0.112486	−	1.11349i
$191$		−	11.3137i		−	0.818631i	−0.912393	−	0.409316i	$-0.865768\pi$
$191$		−	11.3137i		−	0.818631i	0.912393	−	0.409316i	$-0.134232\pi$
$192$		0			0
$193$	−0.651531	+	0.651531i	−0.0468982	+	0.0468982i	−0.730167	−	0.683269i	$-0.760558\pi$
$193$	−0.651531	+	0.651531i	−0.0468982	+	0.0468982i	0.683269	+	0.730167i	$0.260558\pi$
$194$	9.12096			0.654846
$195$		0			0
$196$	1.00000			0.0714286
$197$	12.9029	−	12.9029i	0.919293	−	0.919293i	−0.0776848	−	0.996978i	$-0.524753\pi$
$197$	12.9029	−	12.9029i	0.919293	−	0.919293i	0.996978	+	0.0776848i	$0.0247528\pi$
$198$		0			0
$199$			18.4495i			1.30785i	0.756560	+	0.653925i	$0.226879\pi$
$199$			18.4495i			1.30785i	−0.756560	+	0.653925i	$0.773121\pi$
$200$	2.75699	−	4.17121i	0.194949	−	0.294949i
$201$		0			0
$202$	−5.55051	−	5.55051i	−0.390533	−	0.390533i
$203$	5.65685	+	5.65685i	0.397033	+	0.397033i
$204$		0			0
$205$	−0.898979	+	1.10102i	−0.0627875	+	0.0768986i
$206$			4.09978i			0.285645i
$207$		0			0
$208$	2.44949	−	2.44949i	0.169842	−	0.169842i
$209$	−19.5133			−1.34976
$210$		0			0
$211$	24.4949			1.68630			0.843149	−	0.537680i	$-0.180699\pi$
$211$	24.4949			1.68630			0.843149	+	0.537680i	$0.180699\pi$
$212$	5.51399	−	5.51399i	0.378702	−	0.378702i
$213$		0			0
$214$		−	1.79796i		−	0.122906i
$215$	−10.8530	+	1.09638i	−0.740169	+	0.0747722i
$216$		0			0
$217$	−14.6969	−	14.6969i	−0.997693	−	0.997693i
$218$	9.43879	+	9.43879i	0.639276	+	0.639276i
$219$		0			0
$220$	−4.89898	−	4.00000i	−0.330289	−	0.269680i
$221$		−	3.46410i		−	0.233021i
$222$		0			0
$223$	5.10102	−	5.10102i	0.341590	−	0.341590i	−0.515375	−	0.856965i	$-0.672347\pi$
$223$	5.10102	−	5.10102i	0.341590	−	0.341590i	0.856965	+	0.515375i	$0.172347\pi$
$224$	−2.82843			−0.188982
$225$		0			0
$226$	−7.79796			−0.518713
$227$	−11.9494	+	11.9494i	−0.793108	+	0.793108i	−0.981998	−	0.188890i	$-0.939511\pi$
$227$	−11.9494	+	11.9494i	−0.793108	+	0.793108i	0.188890	+	0.981998i	$0.439511\pi$
$228$		0			0
$229$		−	29.5959i		−	1.95575i	−0.209182	−	0.977877i	$-0.567080\pi$
$229$		−	29.5959i		−	1.95575i	0.209182	−	0.977877i	$-0.432920\pi$
$230$	4.24264	+	3.46410i	0.279751	+	0.228416i
$231$		0			0
$232$	−2.00000	−	2.00000i	−0.131306	−	0.131306i
$233$	−7.70674	−	7.70674i	−0.504885	−	0.504885i	0.408067	−	0.912952i	$-0.366203\pi$
$233$	−7.70674	−	7.70674i	−0.504885	−	0.504885i	−0.912952	+	0.408067i	$0.866203\pi$
$234$		0			0
$235$	8.89898	−	0.898979i	0.580505	−	0.0586430i
$236$			4.87832i			0.317551i
$237$		0			0
$238$	−2.00000	+	2.00000i	−0.129641	+	0.129641i
$239$	−26.7272			−1.72884			−0.864419	−	0.502772i	$-0.832314\pi$
$239$	−26.7272			−1.72884			−0.864419	+	0.502772i	$0.832314\pi$
$240$		0			0
$241$	−17.1010			−1.10157			−0.550787	−	0.834646i	$-0.685672\pi$
$241$	−17.1010			−1.10157			−0.550787	+	0.834646i	$0.685672\pi$
$242$	2.12132	−	2.12132i	0.136364	−	0.136364i
$243$		0			0
$244$		−	5.34847i		−	0.342401i
$245$	1.41421	−	1.73205i	0.0903508	−	0.110657i
$246$		0			0
$247$	−16.8990	−	16.8990i	−1.07526	−	1.07526i
$248$	5.19615	+	5.19615i	0.329956	+	0.329956i
$249$		0			0
$250$	−3.32577	−	10.6742i	−0.210340	−	0.675098i
$251$		−	15.9063i		−	1.00400i	−0.864869	−	0.501998i	$-0.832598\pi$
$251$		−	15.9063i		−	1.00400i	0.864869	−	0.501998i	$-0.167402\pi$
$252$		0			0
$253$	4.89898	−	4.89898i	0.307996	−	0.307996i
$254$	6.92820			0.434714
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.92820	+	6.92820i	−0.432169	+	0.432169i	−0.889366	−	0.457196i	$-0.848854\pi$
$257$	−6.92820	+	6.92820i	−0.432169	+	0.432169i	0.457196	+	0.889366i	$0.348854\pi$
$258$		0			0
$259$			25.7980i			1.60301i
$260$	−0.778539	−	7.70674i	−0.0482829	−	0.477952i
$261$		0			0
$262$	4.00000	+	4.00000i	0.247121	+	0.247121i
$263$	13.5065	+	13.5065i	0.832844	+	0.832844i	0.987905	−	0.155061i	$-0.0495574\pi$
$263$	13.5065	+	13.5065i	0.832844	+	0.832844i	−0.155061	+	0.987905i	$0.549557\pi$
$264$		0			0
$265$	−1.75255	−	17.3485i	−0.107658	−	1.06571i
$266$			19.5133i			1.19643i
$267$		0			0
$268$	−1.44949	+	1.44949i	−0.0885417	+	0.0885417i
$269$	5.37113			0.327483			0.163742	−	0.986503i	$-0.447644\pi$
$269$	5.37113			0.327483			0.163742	+	0.986503i	$0.447644\pi$
$270$		0			0
$271$	−11.1010			−0.674339			−0.337169	−	0.941444i	$-0.609470\pi$
$271$	−11.1010			−0.674339			−0.337169	+	0.941444i	$0.609470\pi$
$272$	0.707107	−	0.707107i	0.0428746	−	0.0428746i
$273$		0			0
$274$		−	3.79796i		−	0.229443i
$275$	−13.8564	+	2.82843i	−0.835573	+	0.170561i
$276$		0			0
$277$	18.0000	+	18.0000i	1.08152	+	1.08152i	0.996368	+	0.0851468i	$0.0271359\pi$
$277$	18.0000	+	18.0000i	1.08152	+	1.08152i	0.0851468	+	0.996368i	$0.472864\pi$
$278$	−4.09978	−	4.09978i	−0.245888	−	0.245888i
$279$		0			0
$280$	−4.00000	+	4.89898i	−0.239046	+	0.292770i
$281$		−	6.78534i		−	0.404779i	−0.979305	−	0.202390i	$-0.935129\pi$
$281$		−	6.78534i		−	0.404779i	0.979305	−	0.202390i	$-0.0648708\pi$
$282$		0			0
$283$	22.8990	−	22.8990i	1.36120	−	1.36120i	0.488816	−	0.872387i	$-0.337429\pi$
$283$	22.8990	−	22.8990i	1.36120	−	1.36120i	0.872387	−	0.488816i	$-0.162571\pi$
$284$	0.635674			0.0377203
$285$		0			0
$286$	−9.79796			−0.579365
$287$	1.27135	−	1.27135i	0.0750454	−	0.0750454i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	−6.29253	+	0.635674i	−0.369510	+	0.0373281i
$291$		0			0
$292$	3.34847	+	3.34847i	0.195954	+	0.195954i
$293$	20.9275	+	20.9275i	1.22260	+	1.22260i	0.966706	+	0.255890i	$0.0823686\pi$
$293$	20.9275	+	20.9275i	1.22260	+	1.22260i	0.255890	+	0.966706i	$0.417631\pi$
$294$		0			0
$295$	8.44949	+	6.89898i	0.491948	+	0.401674i
$296$		−	9.12096i		−	0.530145i
$297$		0			0
$298$	−8.44949	+	8.44949i	−0.489466	+	0.489466i
$299$	8.48528			0.490716
$300$		0			0
$301$	13.7980			0.795301
$302$	−13.2207	+	13.2207i	−0.760768	+	0.760768i
$303$		0			0
$304$		−	6.89898i		−	0.395684i
$305$	−9.26382	−	7.56388i	−0.530445	−	0.433106i
$306$		0			0
$307$	10.3485	+	10.3485i	0.590618	+	0.590618i	0.937798	−	0.347180i	$-0.112861\pi$
$307$	10.3485	+	10.3485i	0.590618	+	0.590618i	−0.347180	+	0.937798i	$0.612861\pi$
$308$	5.65685	+	5.65685i	0.322329	+	0.322329i
$309$		0			0
$310$	16.3485	−	1.65153i	0.928531	−	0.0938006i
$311$			24.5344i			1.39122i	0.718419	+	0.695610i	$0.244866\pi$
$311$			24.5344i			1.39122i	−0.718419	+	0.695610i	$0.755134\pi$
$312$		0			0
$313$	19.3485	−	19.3485i	1.09364	−	1.09364i	0.0985034	−	0.995137i	$-0.468594\pi$
$313$	19.3485	−	19.3485i	1.09364	−	1.09364i	0.995137	−	0.0985034i	$-0.0314055\pi$
$314$	−18.8776			−1.06532
$315$		0			0
$316$	6.44949			0.362812
$317$	−2.51059	+	2.51059i	−0.141009	+	0.141009i	−0.774087	−	0.633079i	$-0.781791\pi$
$317$	−2.51059	+	2.51059i	−0.141009	+	0.141009i	0.633079	+	0.774087i	$0.281791\pi$
$318$		0			0
$319$			8.00000i			0.447914i
$320$	1.41421	−	1.73205i	0.0790569	−	0.0968246i
$321$		0			0
$322$	−4.89898	−	4.89898i	−0.273009	−	0.273009i
$323$	−4.87832	−	4.87832i	−0.271437	−	0.271437i
$324$		0			0
$325$	−14.4495	−	9.55051i	−0.801513	−	0.529767i
$326$		−	22.3417i		−	1.23739i
$327$		0			0
$328$	−0.449490	+	0.449490i	−0.0248189	+	0.0248189i
$329$	−11.3137			−0.623745
$330$		0			0
$331$	0.696938			0.0383072			0.0191536	−	0.999817i	$-0.493903\pi$
$331$	0.696938			0.0383072			0.0191536	+	0.999817i	$0.493903\pi$
$332$	−2.82843	+	2.82843i	−0.155230	+	0.155230i
$333$		0			0
$334$			21.1464i			1.15708i
$335$	0.460702	+	4.56048i	0.0251708	+	0.249166i
$336$		0			0
$337$	12.2474	+	12.2474i	0.667161	+	0.667161i	0.957058	−	0.289897i	$-0.0936210\pi$
$337$	12.2474	+	12.2474i	0.667161	+	0.667161i	−0.289897	+	0.957058i	$0.593621\pi$
$338$	0.707107	+	0.707107i	0.0384615	+	0.0384615i
$339$		0			0
$340$	−0.224745	−	2.22474i	−0.0121885	−	0.120654i
$341$		−	20.7846i		−	1.12555i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	−4.87832			−0.263021
$345$		0			0
$346$	21.3485			1.14770
$347$	7.84961	−	7.84961i	0.421389	−	0.421389i	−0.464293	−	0.885682i	$-0.653691\pi$
$347$	7.84961	−	7.84961i	0.421389	−	0.421389i	0.885682	+	0.464293i	$0.153691\pi$
$348$		0			0
$349$		−	19.7980i		−	1.05976i	−0.848072	−	0.529880i	$-0.822237\pi$
$349$		−	19.7980i		−	1.05976i	0.848072	−	0.529880i	$-0.177763\pi$
$350$	2.82843	+	13.8564i	0.151186	+	0.740656i
$351$		0			0
$352$	−2.00000	−	2.00000i	−0.106600	−	0.106600i
$353$	−12.5851	−	12.5851i	−0.669835	−	0.669835i	0.287843	−	0.957678i	$-0.407062\pi$
$353$	−12.5851	−	12.5851i	−0.669835	−	0.669835i	−0.957678	+	0.287843i	$0.907062\pi$
$354$		0			0
$355$	0.898979	−	1.10102i	0.0477129	−	0.0584361i
$356$		−	12.4422i		−	0.659435i
$357$		0			0
$358$	−9.44949	+	9.44949i	−0.499421	+	0.499421i
$359$	−21.0703			−1.11205			−0.556025	−	0.831166i	$-0.687674\pi$
$359$	−21.0703			−1.11205			−0.556025	+	0.831166i	$0.687674\pi$
$360$		0			0
$361$	−28.5959			−1.50505
$362$	−17.9241	+	17.9241i	−0.942068	+	0.942068i
$363$		0			0
$364$			9.79796i			0.513553i
$365$	10.5352	−	1.06427i	0.551436	−	0.0557063i
$366$		0			0
$367$	3.79796	+	3.79796i	0.198252	+	0.198252i	0.799250	−	0.600998i	$-0.205230\pi$
$367$	3.79796	+	3.79796i	0.198252	+	0.198252i	−0.600998	+	0.799250i	$0.705230\pi$
$368$	1.73205	+	1.73205i	0.0902894	+	0.0902894i
$369$		0			0
$370$	−15.7980	−	12.8990i	−0.821297	−	0.670586i
$371$			22.0560i			1.14509i
$372$		0			0
$373$	18.2474	−	18.2474i	0.944817	−	0.944817i	−0.0537380	−	0.998555i	$-0.517114\pi$
$373$	18.2474	−	18.2474i	0.944817	−	0.944817i	0.998555	+	0.0537380i	$0.0171136\pi$
$374$	−2.82843			−0.146254
$375$		0			0
$376$	4.00000			0.206284
$377$	−6.92820	+	6.92820i	−0.356821	+	0.356821i
$378$		0			0
$379$		−	0.898979i		−	0.0461775i	−0.999733	−	0.0230887i	$-0.992650\pi$
$379$		−	0.898979i		−	0.0461775i	0.999733	−	0.0230887i	$-0.00735003\pi$
$380$	−11.9494	−	9.75663i	−0.612990	−	0.500505i
$381$		0			0
$382$	−8.00000	−	8.00000i	−0.409316	−	0.409316i
$383$	−8.83523	−	8.83523i	−0.451459	−	0.451459i	0.444380	−	0.895839i	$-0.353424\pi$
$383$	−8.83523	−	8.83523i	−0.451459	−	0.451459i	−0.895839	+	0.444380i	$0.853424\pi$
$384$		0			0
$385$	17.7980	−	1.79796i	0.907068	−	0.0916325i
$386$			0.921404i			0.0468982i
$387$		0			0
$388$	6.44949	−	6.44949i	0.327423	−	0.327423i
$389$	20.1489			1.02159			0.510796	−	0.859702i	$-0.329351\pi$
$389$	20.1489			1.02159			0.510796	+	0.859702i	$0.329351\pi$
$390$		0			0
$391$	2.44949			0.123876
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	18.2474i		−	0.919293i
$395$	9.12096	−	11.1708i	0.458925	−	0.562066i
$396$		0			0
$397$	−4.69694	−	4.69694i	−0.235733	−	0.235733i	0.579348	−	0.815080i	$-0.303307\pi$
$397$	−4.69694	−	4.69694i	−0.235733	−	0.235733i	−0.815080	+	0.579348i	$0.803307\pi$
$398$	13.0458	+	13.0458i	0.653925	+	0.653925i
$399$		0			0
$400$	−1.00000	−	4.89898i	−0.0500000	−	0.244949i
$401$			21.7060i			1.08395i	0.840396	+	0.541973i	$0.182323\pi$
$401$			21.7060i			1.08395i	−0.840396	+	0.541973i	$0.817677\pi$
$402$		0			0
$403$	18.0000	−	18.0000i	0.896644	−	0.896644i
$404$	−7.84961			−0.390533
$405$		0			0
$406$	8.00000			0.397033
$407$	−18.2419	+	18.2419i	−0.904218	+	0.904218i
$408$		0			0
$409$			20.0000i			0.988936i	0.869196	+	0.494468i	$0.164637\pi$
$409$			20.0000i			0.988936i	−0.869196	+	0.494468i	$0.835363\pi$
$410$	0.142865	+	1.41421i	0.00705558	+	0.0698430i
$411$		0			0
$412$	2.89898	+	2.89898i	0.142822	+	0.142822i
$413$	−9.75663	−	9.75663i	−0.480092	−	0.480092i
$414$		0			0
$415$	0.898979	+	8.89898i	0.0441292	+	0.436834i
$416$		−	3.46410i		−	0.169842i
$417$		0			0
$418$	−13.7980	+	13.7980i	−0.674880	+	0.674880i
$419$	25.4558			1.24360			0.621800	−	0.783176i	$-0.286402\pi$
$419$	25.4558			1.24360			0.621800	+	0.783176i	$0.286402\pi$
$420$		0			0
$421$	−25.1010			−1.22335			−0.611674	−	0.791110i	$-0.709504\pi$
$421$	−25.1010			−1.22335			−0.611674	+	0.791110i	$0.709504\pi$
$422$	17.3205	−	17.3205i	0.843149	−	0.843149i
$423$		0			0
$424$		−	7.79796i		−	0.378702i
$425$	−4.17121	−	2.75699i	−0.202333	−	0.133734i
$426$		0			0
$427$	10.6969	+	10.6969i	0.517661	+	0.517661i
$428$	−1.27135	−	1.27135i	−0.0614530	−	0.0614530i
$429$		0			0
$430$	−6.89898	+	8.44949i	−0.332698	+	0.407471i
$431$		−	15.7634i		−	0.759298i	−0.925131	−	0.379649i	$-0.876045\pi$
$431$		−	15.7634i		−	0.759298i	0.925131	−	0.379649i	$-0.123955\pi$
$432$		0			0
$433$	12.7980	−	12.7980i	0.615031	−	0.615031i	−0.329222	−	0.944253i	$-0.606786\pi$
$433$	12.7980	−	12.7980i	0.615031	−	0.615031i	0.944253	+	0.329222i	$0.106786\pi$
$434$	−20.7846			−0.997693
$435$		0			0
$436$	13.3485			0.639276
$437$	11.9494	−	11.9494i	0.571617	−	0.571617i
$438$		0			0
$439$		−	30.4495i		−	1.45327i	−0.687021	−	0.726637i	$-0.741082\pi$
$439$		−	30.4495i		−	1.45327i	0.687021	−	0.726637i	$-0.258918\pi$
$440$	−6.29253	+	0.635674i	−0.299985	+	0.0303046i
$441$		0			0
$442$	−2.44949	−	2.44949i	−0.116510	−	0.116510i
$443$	−3.32124	−	3.32124i	−0.157797	−	0.157797i	0.623793	−	0.781590i	$-0.285591\pi$
$443$	−3.32124	−	3.32124i	−0.157797	−	0.157797i	−0.781590	+	0.623793i	$0.785591\pi$
$444$		0			0
$445$	−21.5505	−	17.5959i	−1.02159	−	0.834127i
$446$		−	7.21393i		−	0.341590i
$447$		0			0
$448$	−2.00000	+	2.00000i	−0.0944911	+	0.0944911i
$449$	−14.7778			−0.697408			−0.348704	−	0.937233i	$-0.613378\pi$
$449$	−14.7778			−0.697408			−0.348704	+	0.937233i	$0.613378\pi$
$450$		0			0
$451$	1.79796			0.0846626
$452$	−5.51399	+	5.51399i	−0.259356	+	0.259356i
$453$		0			0
$454$			16.8990i			0.793108i
$455$	16.9706	+	13.8564i	0.795592	+	0.649598i
$456$		0			0
$457$	3.20204	+	3.20204i	0.149785	+	0.149785i	0.778022	−	0.628237i	$-0.216223\pi$
$457$	3.20204	+	3.20204i	0.149785	+	0.149785i	−0.628237	+	0.778022i	$0.716223\pi$
$458$	−20.9275	−	20.9275i	−0.977877	−	0.977877i
$459$		0			0
$460$	5.44949	−	0.550510i	0.254084	−	0.0256677i
$461$			8.83523i			0.411498i	0.978605	+	0.205749i	$0.0659630\pi$
$461$			8.83523i			0.411498i	−0.978605	+	0.205749i	$0.934037\pi$
$462$		0			0
$463$	−3.79796	+	3.79796i	−0.176506	+	0.176506i	−0.789831	−	0.613325i	$-0.789832\pi$
$463$	−3.79796	+	3.79796i	−0.176506	+	0.176506i	0.613325	+	0.789831i	$0.289832\pi$
$464$	−2.82843			−0.131306
$465$		0			0
$466$	−10.8990			−0.504885
$467$	−22.3417	+	22.3417i	−1.03385	+	1.03385i	−0.0344434	+	0.999407i	$0.510966\pi$
$467$	−22.3417	+	22.3417i	−1.03385	+	1.03385i	−0.999407	+	0.0344434i	$0.989034\pi$
$468$		0			0
$469$		−	5.79796i		−	0.267725i
$470$	5.65685	−	6.92820i	0.260931	−	0.319574i
$471$		0			0
$472$	3.44949	+	3.44949i	0.158776	+	0.158776i
$473$	9.75663	+	9.75663i	0.448610	+	0.448610i
$474$		0			0
$475$	−33.7980	+	6.89898i	−1.55076	+	0.316547i
$476$			2.82843i			0.129641i
$477$		0			0
$478$	−18.8990	+	18.8990i	−0.864419	+	0.864419i
$479$	−28.3485			−1.29528			−0.647638	−	0.761948i	$-0.724243\pi$
$479$	−28.3485			−1.29528			−0.647638	+	0.761948i	$0.724243\pi$
$480$		0			0
$481$	−31.5959			−1.44065
$482$	−12.0922	+	12.0922i	−0.550787	+	0.550787i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$	−2.04989	−	20.2918i	−0.0930806	−	0.921403i
$486$		0			0
$487$	−9.34847	−	9.34847i	−0.423620	−	0.423620i	0.462828	−	0.886448i	$-0.346835\pi$
$487$	−9.34847	−	9.34847i	−0.423620	−	0.423620i	−0.886448	+	0.462828i	$0.846835\pi$
$488$	−3.78194	−	3.78194i	−0.171200	−	0.171200i
$489$		0			0
$490$	−0.224745	−	2.22474i	−0.0101529	−	0.100504i
$491$			40.0908i			1.80927i	0.426185	+	0.904636i	$0.359857\pi$
$491$			40.0908i			1.80927i	−0.426185	+	0.904636i	$0.640143\pi$
$492$		0			0
$493$	−2.00000	+	2.00000i	−0.0900755	+	0.0900755i
$494$	−23.8988			−1.07526
$495$		0			0
$496$	7.34847			0.329956
$497$	−1.27135	+	1.27135i	−0.0570278	+	0.0570278i
$498$		0			0
$499$			30.2929i			1.35609i	0.735018	+	0.678047i	$0.237174\pi$
$499$			30.2929i			1.35609i	−0.735018	+	0.678047i	$0.762826\pi$
$500$	−9.89949	−	5.19615i	−0.442719	−	0.232379i
$501$		0			0
$502$	−11.2474	−	11.2474i	−0.501998	−	0.501998i
$503$	15.5885	+	15.5885i	0.695055	+	0.695055i	0.963340	−	0.268285i	$-0.0864568\pi$
$503$	15.5885	+	15.5885i	0.695055	+	0.695055i	−0.268285	+	0.963340i	$0.586457\pi$
$504$		0			0
$505$	−11.1010	+	13.5959i	−0.493989	+	0.605010i
$506$		−	6.92820i		−	0.307996i
$507$		0			0
$508$	4.89898	−	4.89898i	0.217357	−	0.217357i
$509$	−31.4626			−1.39456			−0.697279	−	0.716800i	$-0.745606\pi$
$509$	−31.4626			−1.39456			−0.697279	+	0.716800i	$0.745606\pi$
$510$		0			0
$511$	−13.3939			−0.592510
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			9.79796i			0.432169i
$515$	9.12096	−	0.921404i	0.401917	−	0.0406019i
$516$		0			0
$517$	−8.00000	−	8.00000i	−0.351840	−	0.351840i
$518$	18.2419	+	18.2419i	0.801504	+	0.801504i
$519$		0			0
$520$	−6.00000	−	4.89898i	−0.263117	−	0.214834i
$521$			22.9774i			1.00666i	0.864095	+	0.503328i	$0.167891\pi$
$521$			22.9774i			1.00666i	−0.864095	+	0.503328i	$0.832109\pi$
$522$		0			0
$523$	31.2474	−	31.2474i	1.36636	−	1.36636i	0.500782	−	0.865573i	$-0.333046\pi$
$523$	31.2474	−	31.2474i	1.36636	−	1.36636i	0.865573	−	0.500782i	$-0.166954\pi$
$524$	5.65685			0.247121
$525$		0			0
$526$	19.1010			0.832844
$527$	5.19615	−	5.19615i	0.226348	−	0.226348i
$528$		0			0
$529$		−	17.0000i		−	0.739130i
$530$	−13.5065	−	11.0280i	−0.586683	−	0.479025i
$531$		0			0
$532$	13.7980	+	13.7980i	0.598217	+	0.598217i
$533$	1.55708	+	1.55708i	0.0674445	+	0.0674445i
$534$		0			0
$535$	−4.00000	+	0.404082i	−0.172935	+	0.0174700i
$536$			2.04989i			0.0885417i
$537$		0			0
$538$	3.79796	−	3.79796i	0.163742	−	0.163742i
$539$	−2.82843			−0.121829
$540$		0			0
$541$	14.2474			0.612546			0.306273	−	0.951944i	$-0.400918\pi$
$541$	14.2474			0.612546			0.306273	+	0.951944i	$0.400918\pi$
$542$	−7.84961	+	7.84961i	−0.337169	+	0.337169i
$543$		0			0
$544$		−	1.00000i		−	0.0428746i
$545$	18.8776	−	23.1202i	0.808627	−	0.990362i
$546$		0			0
$547$	11.7980	+	11.7980i	0.504444	+	0.504444i	0.912816	−	0.408372i	$-0.133903\pi$
$547$	11.7980	+	11.7980i	0.504444	+	0.504444i	−0.408372	+	0.912816i	$0.633903\pi$
$548$	−2.68556	−	2.68556i	−0.114722	−	0.114722i
$549$		0			0
$550$	−7.79796	+	11.7980i	−0.332506	+	0.503067i
$551$			19.5133i			0.831293i
$552$		0			0
$553$	−12.8990	+	12.8990i	−0.548520	+	0.548520i
$554$	25.4558			1.08152
$555$		0			0
$556$	−5.79796			−0.245888
$557$	20.9275	−	20.9275i	0.886726	−	0.886726i	−0.107482	−	0.994207i	$-0.534279\pi$
$557$	20.9275	−	20.9275i	0.886726	−	0.886726i	0.994207	+	0.107482i	$0.0342787\pi$
$558$		0			0
$559$			16.8990i			0.714751i
$560$	0.635674	+	6.29253i	0.0268622	+	0.265908i
$561$		0			0
$562$	−4.79796	−	4.79796i	−0.202390	−	0.202390i
$563$	15.4135	+	15.4135i	0.649601	+	0.649601i	0.952897	−	0.303296i	$-0.0980870\pi$
$563$	15.4135	+	15.4135i	0.649601	+	0.649601i	−0.303296	+	0.952897i	$0.598087\pi$
$564$		0			0
$565$	1.75255	+	17.3485i	0.0737304	+	0.729856i
$566$		−	32.3840i		−	1.36120i
$567$		0			0
$568$	0.449490	−	0.449490i	0.0188602	−	0.0188602i
$569$	15.2706			0.640178			0.320089	−	0.947388i	$-0.396287\pi$
$569$	15.2706			0.640178			0.320089	+	0.947388i	$0.396287\pi$
$570$		0			0
$571$	12.8990			0.539805			0.269903	−	0.962888i	$-0.413008\pi$
$571$	12.8990			0.539805			0.269903	+	0.962888i	$0.413008\pi$
$572$	−6.92820	+	6.92820i	−0.289683	+	0.289683i
$573$		0			0
$574$		−	1.79796i		−	0.0750454i
$575$	6.75323	−	10.2173i	0.281629	−	0.426092i
$576$		0			0
$577$	16.1010	+	16.1010i	0.670294	+	0.670294i	0.957784	−	0.287490i	$-0.0928207\pi$
$577$	16.1010	+	16.1010i	0.670294	+	0.670294i	−0.287490	+	0.957784i	$0.592821\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$		0			0
$580$	−4.00000	+	4.89898i	−0.166091	+	0.203419i
$581$		−	11.3137i		−	0.469372i
$582$		0			0
$583$	−15.5959	+	15.5959i	−0.645917	+	0.645917i
$584$	4.73545			0.195954
$585$		0			0
$586$	29.5959			1.22260
$587$	−31.6055	+	31.6055i	−1.30450	+	1.30450i	−0.379173	+	0.925326i	$0.623792\pi$
$587$	−31.6055	+	31.6055i	−1.30450	+	1.30450i	−0.925326	+	0.379173i	$0.876208\pi$
$588$		0			0
$589$		−	50.6969i		−	2.08893i
$590$	10.8530	−	1.09638i	0.446811	−	0.0451371i
$591$		0			0
$592$	−6.44949	−	6.44949i	−0.265072	−	0.265072i
$593$	−18.5276	−	18.5276i	−0.760839	−	0.760839i	0.215635	−	0.976474i	$-0.430818\pi$
$593$	−18.5276	−	18.5276i	−0.760839	−	0.760839i	−0.976474	+	0.215635i	$0.930818\pi$
$594$		0			0
$595$	4.89898	+	4.00000i	0.200839	+	0.163984i
$596$			11.9494i			0.489466i
$597$		0			0
$598$	6.00000	−	6.00000i	0.245358	−	0.245358i
$599$	24.1845			0.988152			0.494076	−	0.869419i	$-0.335507\pi$
$599$	24.1845			0.988152			0.494076	+	0.869419i	$0.335507\pi$
$600$		0			0
$601$	13.1010			0.534402			0.267201	−	0.963641i	$-0.413901\pi$
$601$	13.1010			0.534402			0.267201	+	0.963641i	$0.413901\pi$
$602$	9.75663	−	9.75663i	0.397651	−	0.397651i
$603$		0			0
$604$			18.6969i			0.760768i
$605$	−5.19615	−	4.24264i	−0.211254	−	0.172488i
$606$		0			0
$607$	8.44949	+	8.44949i	0.342954	+	0.342954i	0.857477	−	0.514523i	$-0.172031\pi$
$607$	8.44949	+	8.44949i	0.342954	+	0.342954i	−0.514523	+	0.857477i	$0.672031\pi$
$608$	−4.87832	−	4.87832i	−0.197842	−	0.197842i
$609$		0			0
$610$	−11.8990	+	1.20204i	−0.481776	+	0.0486692i
$611$		−	13.8564i		−	0.560570i
$612$		0			0
$613$	−30.9444	+	30.9444i	−1.24983	+	1.24983i	−0.294038	+	0.955794i	$0.594999\pi$
$613$	−30.9444	+	30.9444i	−1.24983	+	1.24983i	−0.955794	+	0.294038i	$0.905001\pi$
$614$	14.6349			0.590618
$615$		0			0
$616$	8.00000			0.322329
$617$	23.1202	−	23.1202i	0.930785	−	0.930785i	−0.0669697	−	0.997755i	$-0.521333\pi$
$617$	23.1202	−	23.1202i	0.930785	−	0.930785i	0.997755	+	0.0669697i	$0.0213331\pi$
$618$		0			0
$619$			4.00000i			0.160774i	0.996764	+	0.0803868i	$0.0256155\pi$
$619$			4.00000i			0.160774i	−0.996764	+	0.0803868i	$0.974384\pi$
$620$	10.3923	−	12.7279i	0.417365	−	0.511166i
$621$		0			0
$622$	17.3485	+	17.3485i	0.695610	+	0.695610i
$623$	24.8844	+	24.8844i	0.996972	+	0.996972i
$624$		0			0
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$		−	27.3629i		−	1.09364i
$627$		0			0
$628$	−13.3485	+	13.3485i	−0.532662	+	0.532662i
$629$	−9.12096			−0.363676
$630$		0			0
$631$	40.4949			1.61208			0.806038	−	0.591864i	$-0.201608\pi$
$631$	40.4949			1.61208			0.806038	+	0.591864i	$0.201608\pi$
$632$	4.56048	−	4.56048i	0.181406	−	0.181406i
$633$		0			0
$634$			3.55051i			0.141009i
$635$	−1.55708	−	15.4135i	−0.0617908	−	0.611665i
$636$		0			0
$637$	−2.44949	−	2.44949i	−0.0970523	−	0.0970523i
$638$	5.65685	+	5.65685i	0.223957	+	0.223957i
$639$		0			0
$640$	−0.224745	−	2.22474i	−0.00888382	−	0.0879408i
$641$			17.3205i			0.684119i	0.939678	+	0.342059i	$0.111124\pi$
$641$			17.3205i			0.684119i	−0.939678	+	0.342059i	$0.888876\pi$
$642$		0			0
$643$	13.5959	−	13.5959i	0.536171	−	0.536171i	−0.386231	−	0.922402i	$-0.626223\pi$
$643$	13.5959	−	13.5959i	0.536171	−	0.536171i	0.922402	+	0.386231i	$0.126223\pi$
$644$	−6.92820			−0.273009
$645$		0			0
$646$	−6.89898			−0.271437
$647$	6.00680	−	6.00680i	0.236152	−	0.236152i	−0.579103	−	0.815254i	$-0.696597\pi$
$647$	6.00680	−	6.00680i	0.236152	−	0.236152i	0.815254	+	0.579103i	$0.196597\pi$
$648$		0			0
$649$		−	13.7980i		−	0.541617i
$650$	−16.9706	+	3.46410i	−0.665640	+	0.135873i
$651$		0			0
$652$	−15.7980	−	15.7980i	−0.618696	−	0.618696i
$653$	11.3458	+	11.3458i	0.443996	+	0.443996i	0.893353	−	0.449356i	$-0.148347\pi$
$653$	11.3458	+	11.3458i	0.443996	+	0.443996i	−0.449356	+	0.893353i	$0.648347\pi$
$654$		0			0
$655$	8.00000	−	9.79796i	0.312586	−	0.382838i
$656$			0.635674i			0.0248189i
$657$		0			0
$658$	−8.00000	+	8.00000i	−0.311872	+	0.311872i
$659$	21.2774			0.828851			0.414425	−	0.910083i	$-0.363983\pi$
$659$	21.2774			0.828851			0.414425	+	0.910083i	$0.363983\pi$
$660$		0			0
$661$	25.5959			0.995566			0.497783	−	0.867302i	$-0.334148\pi$
$661$	25.5959			0.995566			0.497783	+	0.867302i	$0.334148\pi$
$662$	0.492810	−	0.492810i	0.0191536	−	0.0191536i
$663$		0			0
$664$			4.00000i			0.155230i
$665$	43.4120	−	4.38551i	1.68345	−	0.170063i
$666$		0			0
$667$	−4.89898	−	4.89898i	−0.189689	−	0.189689i
$668$	14.9528	+	14.9528i	0.578541	+	0.578541i
$669$		0			0
$670$	3.55051	+	2.89898i	0.137168	+	0.111997i
$671$			15.1278i			0.584001i
$672$		0			0
$673$	26.4495	−	26.4495i	1.01955	−	1.01955i	0.0197479	−	0.999805i	$-0.493714\pi$
$673$	26.4495	−	26.4495i	1.01955	−	1.01955i	0.999805	−	0.0197479i	$-0.00628636\pi$
$674$	17.3205			0.667161
$675$		0			0
$676$	1.00000			0.0384615
$677$	26.4094	−	26.4094i	1.01499	−	1.01499i	0.0151081	−	0.999886i	$-0.495191\pi$
$677$	26.4094	−	26.4094i	1.01499	−	1.01499i	0.999886	−	0.0151081i	$-0.00480925\pi$
$678$		0			0
$679$			25.7980i			0.990035i
$680$	−1.73205	−	1.41421i	−0.0664211	−	0.0542326i
$681$		0			0
$682$	−14.6969	−	14.6969i	−0.562775	−	0.562775i
$683$	12.5851	+	12.5851i	0.481554	+	0.481554i	0.905628	−	0.424074i	$-0.139400\pi$
$683$	12.5851	+	12.5851i	0.481554	+	0.481554i	−0.424074	+	0.905628i	$0.639400\pi$
$684$		0			0
$685$	−8.44949	+	0.853572i	−0.322838	+	0.0326133i
$686$		−	16.9706i		−	0.647939i
$687$		0			0
$688$	−3.44949	+	3.44949i	−0.131511	+	0.131511i
$689$	−27.0129			−1.02911
$690$		0			0
$691$	−9.30306			−0.353905			−0.176953	−	0.984219i	$-0.556624\pi$
$691$	−9.30306			−0.353905			−0.176953	+	0.984219i	$0.556624\pi$
$692$	15.0956	−	15.0956i	0.573850	−	0.573850i
$693$		0			0
$694$		−	11.1010i		−	0.421389i
$695$	−8.19955	+	10.0424i	−0.311027	+	0.380928i
$696$		0			0
$697$	0.449490	+	0.449490i	0.0170256	+	0.0170256i
$698$	−13.9993	−	13.9993i	−0.529880	−	0.529880i
$699$		0			0
$700$	11.7980	+	7.79796i	0.445921	+	0.294735i
$701$		−	26.3772i		−	0.996255i	−0.867104	−	0.498127i	$-0.834021\pi$
$701$		−	26.3772i		−	0.996255i	0.867104	−	0.498127i	$-0.165979\pi$
$702$		0			0
$703$	−44.4949	+	44.4949i	−1.67816	+	1.67816i
$704$	−2.82843			−0.106600
$705$		0			0
$706$	−17.7980			−0.669835
$707$	15.6992	−	15.6992i	0.590430	−	0.590430i
$708$		0			0
$709$		−	35.5505i		−	1.33513i	−0.744553	−	0.667564i	$-0.767337\pi$
$709$		−	35.5505i		−	1.33513i	0.744553	−	0.667564i	$-0.232663\pi$
$710$	−0.142865	−	1.41421i	−0.00536161	−	0.0530745i
$711$		0			0
$712$	−8.79796	−	8.79796i	−0.329717	−	0.329717i
$713$	12.7279	+	12.7279i	0.476664	+	0.476664i
$714$		0			0
$715$	2.20204	+	21.7980i	0.0823517	+	0.815197i
$716$			13.3636i			0.499421i
$717$		0			0
$718$	−14.8990	+	14.8990i	−0.556025	+	0.556025i
$719$	47.8617			1.78494			0.892471	−	0.451105i	$-0.148970\pi$
$719$	47.8617			1.78494			0.892471	+	0.451105i	$0.148970\pi$
$720$		0			0
$721$	−11.5959			−0.431855
$722$	−20.2204	+	20.2204i	−0.752524	+	0.752524i
$723$		0			0
$724$			25.3485i			0.942068i
$725$	2.82843	+	13.8564i	0.105045	+	0.514614i
$726$		0			0
$727$	12.0000	+	12.0000i	0.445055	+	0.445055i	0.893707	−	0.448651i	$-0.148096\pi$
$727$	12.0000	+	12.0000i	0.445055	+	0.445055i	−0.448651	+	0.893707i	$0.648096\pi$
$728$	6.92820	+	6.92820i	0.256776	+	0.256776i
$729$		0			0
$730$	6.69694	−	8.20204i	0.247865	−	0.303571i
$731$			4.87832i			0.180431i
$732$		0			0
$733$	16.0454	−	16.0454i	0.592651	−	0.592651i	−0.345696	−	0.938347i	$-0.612357\pi$
$733$	16.0454	−	16.0454i	0.592651	−	0.592651i	0.938347	+	0.345696i	$0.112357\pi$
$734$	5.37113			0.198252
$735$		0			0
$736$	2.44949			0.0902894
$737$	4.09978	−	4.09978i	0.151017	−	0.151017i
$738$		0			0
$739$		−	44.0000i		−	1.61857i	−0.587419	−	0.809283i	$-0.699856\pi$
$739$		−	44.0000i		−	1.61857i	0.587419	−	0.809283i	$-0.300144\pi$
$740$	−20.2918	+	2.04989i	−0.745941	+	0.0753554i
$741$		0			0
$742$	15.5959	+	15.5959i	0.572544	+	0.572544i
$743$	−7.67463	−	7.67463i	−0.281555	−	0.281555i	0.552174	−	0.833729i	$-0.313798\pi$
$743$	−7.67463	−	7.67463i	−0.281555	−	0.281555i	−0.833729	+	0.552174i	$0.813798\pi$
$744$		0			0
$745$	20.6969	+	16.8990i	0.758277	+	0.619131i
$746$		−	25.8058i		−	0.944817i
$747$		0			0
$748$	−2.00000	+	2.00000i	−0.0731272	+	0.0731272i
$749$	5.08540			0.185816
$750$		0			0
$751$	−10.0454			−0.366562			−0.183281	−	0.983061i	$-0.558672\pi$
$751$	−10.0454			−0.366562			−0.183281	+	0.983061i	$0.558672\pi$
$752$	2.82843	−	2.82843i	0.103142	−	0.103142i
$753$		0			0
$754$			9.79796i			0.356821i
$755$	32.3840	+	26.4415i	1.17858	+	0.962303i
$756$		0			0
$757$	28.0454	+	28.0454i	1.01933	+	1.01933i	0.999810	+	0.0195182i	$0.00621322\pi$
$757$	28.0454	+	28.0454i	1.01933	+	1.01933i	0.0195182	+	0.999810i	$0.493787\pi$
$758$	−0.635674	−	0.635674i	−0.0230887	−	0.0230887i
$759$		0			0
$760$	−15.3485	+	1.55051i	−0.556747	+	0.0562429i
$761$			32.2412i			1.16874i	0.811487	+	0.584371i	$0.198659\pi$
$761$			32.2412i			1.16874i	−0.811487	+	0.584371i	$0.801341\pi$
$762$		0			0
$763$	−26.6969	+	26.6969i	−0.966494	+	0.966494i
$764$	−11.3137			−0.409316
$765$		0			0
$766$	−12.4949			−0.451459
$767$	11.9494	−	11.9494i	0.431467	−	0.431467i
$768$		0			0
$769$			6.00000i			0.216366i	0.994131	+	0.108183i	$0.0345032\pi$
$769$			6.00000i			0.216366i	−0.994131	+	0.108183i	$0.965497\pi$
$770$	11.3137	−	13.8564i	0.407718	−	0.499350i
$771$		0			0
$772$	0.651531	+	0.651531i	0.0234491	+	0.0234491i
$773$	31.6055	+	31.6055i	1.13677	+	1.13677i	0.989025	+	0.147746i	$0.0472017\pi$
$773$	31.6055	+	31.6055i	1.13677	+	1.13677i	0.147746	+	0.989025i	$0.452798\pi$
$774$		0			0
$775$	−7.34847	−	36.0000i	−0.263965	−	1.29316i
$776$		−	9.12096i		−	0.327423i
$777$		0			0
$778$	14.2474	−	14.2474i	0.510796	−	0.510796i
$779$	4.38551			0.157127
$780$		0			0
$781$	−1.79796			−0.0643360
$782$	1.73205	−	1.73205i	0.0619380	−	0.0619380i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	4.24264	+	41.9978i	0.151426	+	1.49897i
$786$		0			0
$787$	6.20204	+	6.20204i	0.221079	+	0.221079i	0.808953	−	0.587874i	$-0.200035\pi$
$787$	6.20204	+	6.20204i	0.221079	+	0.221079i	−0.587874	+	0.808953i	$0.700035\pi$
$788$	−12.9029	−	12.9029i	−0.459647	−	0.459647i
$789$		0			0
$790$	−1.44949	−	14.3485i	−0.0515705	−	0.510496i
$791$		−	22.0560i		−	0.784220i
$792$		0			0
$793$	−13.1010	+	13.1010i	−0.465231	+	0.465231i
$794$	−6.64247			−0.235733
$795$		0			0
$796$	18.4495			0.653925
$797$	7.99247	−	7.99247i	0.283108	−	0.283108i	−0.551239	−	0.834347i	$-0.685845\pi$
$797$	7.99247	−	7.99247i	0.283108	−	0.283108i	0.834347	+	0.551239i	$0.185845\pi$
$798$		0			0
$799$		−	4.00000i		−	0.141510i
$800$	−4.17121	−	2.75699i	−0.147474	−	0.0974745i
$801$		0			0
$802$	15.3485	+	15.3485i	0.541973	+	0.541973i
$803$	−9.47090	−	9.47090i	−0.334221	−	0.334221i
$804$		0			0
$805$	−9.79796	+	12.0000i	−0.345333	+	0.422944i
$806$		−	25.4558i		−	0.896644i
$807$		0			0
$808$	−5.55051	+	5.55051i	−0.195266	+	0.195266i
$809$	20.1489			0.708399			0.354199	−	0.935170i	$-0.384753\pi$
$809$	20.1489			0.708399			0.354199	+	0.935170i	$0.384753\pi$
$810$		0			0
$811$	−1.30306			−0.0457567			−0.0228783	−	0.999738i	$-0.507283\pi$
$811$	−1.30306			−0.0457567			−0.0228783	+	0.999738i	$0.507283\pi$
$812$	5.65685	−	5.65685i	0.198517	−	0.198517i
$813$		0			0
$814$			25.7980i			0.904218i
$815$	−49.7046	+	5.02118i	−1.74107	+	0.175884i
$816$		0			0
$817$	23.7980	+	23.7980i	0.832585	+	0.832585i
$818$	14.1421	+	14.1421i	0.494468	+	0.494468i
$819$		0			0
$820$	1.10102	+	0.898979i	0.0384493	+	0.0313937i
$821$		−	48.1475i		−	1.68036i	−0.542309	−	0.840179i	$-0.682450\pi$
$821$		−	48.1475i		−	1.68036i	0.542309	−	0.840179i	$-0.317550\pi$
$822$		0			0
$823$	−3.79796	+	3.79796i	−0.132389	+	0.132389i	−0.770196	−	0.637807i	$-0.779842\pi$
$823$	−3.79796	+	3.79796i	−0.132389	+	0.132389i	0.637807	+	0.770196i	$0.279842\pi$
$824$	4.09978			0.142822
$825$		0			0
$826$	−13.7980			−0.480092
$827$	6.57826	−	6.57826i	0.228748	−	0.228748i	−0.583421	−	0.812170i	$-0.698286\pi$
$827$	6.57826	−	6.57826i	0.228748	−	0.228748i	0.812170	+	0.583421i	$0.198286\pi$
$828$		0			0
$829$			6.89898i			0.239611i	0.992797	+	0.119806i	$0.0382272\pi$
$829$			6.89898i			0.239611i	−0.992797	+	0.119806i	$0.961773\pi$
$830$	6.92820	+	5.65685i	0.240481	+	0.196352i
$831$		0			0
$832$	−2.44949	−	2.44949i	−0.0849208	−	0.0849208i
$833$	−0.707107	−	0.707107i	−0.0244998	−	0.0244998i
$834$		0			0
$835$	47.0454	−	4.75255i	1.62807	−	0.164469i
$836$			19.5133i			0.674880i
$837$		0			0
$838$	18.0000	−	18.0000i	0.621800	−	0.621800i
$839$	−55.7114			−1.92337			−0.961685	−	0.274158i	$-0.911601\pi$
$839$	−55.7114			−1.92337			−0.961685	+	0.274158i	$0.911601\pi$
$840$		0			0
$841$	−21.0000			−0.724138
$842$	−17.7491	+	17.7491i	−0.611674	+	0.611674i
$843$		0			0
$844$		−	24.4949i		−	0.843149i
$845$	1.41421	−	1.73205i	0.0486504	−	0.0595844i
$846$		0			0
$847$	6.00000	+	6.00000i	0.206162	+	0.206162i
$848$	−5.51399	−	5.51399i	−0.189351	−	0.189351i
$849$		0			0
$850$	−4.89898	+	1.00000i	−0.168034	+	0.0342997i
$851$		−	22.3417i		−	0.765863i
$852$		0			0
$853$	8.24745	−	8.24745i	0.282387	−	0.282387i	−0.551673	−	0.834060i	$-0.686010\pi$
$853$	8.24745	−	8.24745i	0.282387	−	0.282387i	0.834060	+	0.551673i	$0.186010\pi$
$854$	15.1278			0.517661
$855$		0			0
$856$	−1.79796			−0.0614530
$857$	17.1134	−	17.1134i	0.584584	−	0.584584i	−0.351576	−	0.936159i	$-0.614354\pi$
$857$	17.1134	−	17.1134i	0.584584	−	0.584584i	0.936159	+	0.351576i	$0.114354\pi$
$858$		0			0
$859$		−	16.2929i		−	0.555905i	−0.960595	−	0.277953i	$-0.910344\pi$
$859$		−	16.2929i		−	0.555905i	0.960595	−	0.277953i	$-0.0896558\pi$
$860$	1.09638	+	10.8530i	0.0373861	+	0.370084i
$861$		0			0
$862$	−11.1464	−	11.1464i	−0.379649	−	0.379649i
$863$	−37.4052	−	37.4052i	−1.27329	−	1.27329i	−0.944352	−	0.328937i	$-0.893310\pi$
$863$	−37.4052	−	37.4052i	−1.27329	−	1.27329i	−0.328937	−	0.944352i	$-0.606690\pi$
$864$		0			0
$865$	−4.79796	−	47.4949i	−0.163135	−	1.61487i
$866$		−	18.0990i		−	0.615031i
$867$		0			0
$868$	−14.6969	+	14.6969i	−0.498847	+	0.498847i
$869$	−18.2419			−0.618814
$870$		0			0
$871$	7.10102			0.240609
$872$	9.43879	−	9.43879i	0.319638	−	0.319638i
$873$		0			0
$874$		−	16.8990i		−	0.571617i
$875$	30.1913	−	9.40669i	1.02065	−	0.318004i
$876$		0			0
$877$	7.34847	+	7.34847i	0.248140	+	0.248140i	0.820207	−	0.572067i	$-0.193858\pi$
$877$	7.34847	+	7.34847i	0.248140	+	0.248140i	−0.572067	+	0.820207i	$0.693858\pi$
$878$	−21.5310	−	21.5310i	−0.726637	−	0.726637i
$879$		0			0
$880$	−4.00000	+	4.89898i	−0.134840	+	0.165145i
$881$			11.3779i			0.383332i	0.981460	+	0.191666i	$0.0613890\pi$
$881$			11.3779i			0.383332i	−0.981460	+	0.191666i	$0.938611\pi$
$882$		0			0
$883$	−13.0454	+	13.0454i	−0.439013	+	0.439013i	−0.891680	−	0.452667i	$-0.850473\pi$
$883$	−13.0454	+	13.0454i	−0.439013	+	0.439013i	0.452667	+	0.891680i	$0.350473\pi$
$884$	−3.46410			−0.116510
$885$		0			0
$886$	−4.69694			−0.157797
$887$	0.810647	−	0.810647i	0.0272189	−	0.0272189i	−0.693366	−	0.720585i	$-0.743873\pi$
$887$	0.810647	−	0.810647i	0.0272189	−	0.0272189i	0.720585	+	0.693366i	$0.243873\pi$
$888$		0			0
$889$			19.5959i			0.657226i
$890$	−27.6807	+	2.79632i	−0.927859	+	0.0937328i
$891$		0			0
$892$	−5.10102	−	5.10102i	−0.170795	−	0.170795i
$893$	−19.5133	−	19.5133i	−0.652986	−	0.652986i
$894$		0			0
$895$	23.1464	+	18.8990i	0.773700	+	0.631723i
$896$			2.82843i			0.0944911i
$897$		0			0
$898$	−10.4495	+	10.4495i	−0.348704	+	0.348704i
$899$	−20.7846			−0.693206
$900$		0			0
$901$	−7.79796			−0.259788
$902$	1.27135	−	1.27135i	0.0423313	−	0.0423313i
$903$		0			0
$904$			7.79796i			0.259356i
$905$	43.9048	+	35.8481i	1.45945	+	1.19163i
$906$		0			0
$907$	12.8990	+	12.8990i	0.428304	+	0.428304i	0.888050	−	0.459747i	$-0.152060\pi$
$907$	12.8990	+	12.8990i	0.428304	+	0.428304i	−0.459747	+	0.888050i	$0.652060\pi$
$908$	11.9494	+	11.9494i	0.396554	+	0.396554i
$909$		0			0
$910$	21.7980	−	2.20204i	0.722595	−	0.0729969i
$911$			13.2207i			0.438022i	0.975722	+	0.219011i	$0.0702831\pi$
$911$			13.2207i			0.438022i	−0.975722	+	0.219011i	$0.929717\pi$
$912$		0			0
$913$	8.00000	−	8.00000i	0.264761	−	0.264761i
$914$	4.52837			0.149785
$915$		0			0
$916$	−29.5959			−0.977877
$917$	−11.3137	+	11.3137i	−0.373612	+	0.373612i
$918$		0			0
$919$			28.8990i			0.953289i	0.879096	+	0.476645i	$0.158147\pi$
$919$			28.8990i			0.953289i	−0.879096	+	0.476645i	$0.841853\pi$
$920$	3.46410	−	4.24264i	0.114208	−	0.139876i
$921$		0			0
$922$	6.24745	+	6.24745i	0.205749	+	0.205749i
$923$	−1.55708	−	1.55708i	−0.0512519	−	0.0512519i
$924$		0			0
$925$	−25.1464	+	38.0454i	−0.826809	+	1.25093i
$926$			5.37113i			0.176506i
$927$		0			0
$928$	−2.00000	+	2.00000i	−0.0656532	+	0.0656532i
$929$	26.3772			0.865409			0.432705	−	0.901536i	$-0.357559\pi$
$929$	26.3772			0.865409			0.432705	+	0.901536i	$0.357559\pi$
$930$		0			0
$931$	−6.89898			−0.226105
$932$	−7.70674	+	7.70674i	−0.252443	+	0.252443i
$933$		0			0
$934$			31.5959i			1.03385i
$935$	0.635674	+	6.29253i	0.0207888	+	0.205788i
$936$		0			0
$937$	16.7980	+	16.7980i	0.548765	+	0.548765i	0.926084	−	0.377318i	$-0.123154\pi$
$937$	16.7980	+	16.7980i	0.548765	+	0.548765i	−0.377318	+	0.926084i	$0.623154\pi$
$938$	−4.09978	−	4.09978i	−0.133862	−	0.133862i
$939$		0			0
$940$	−0.898979	−	8.89898i	−0.0293215	−	0.290253i
$941$		−	25.5201i		−	0.831930i	−0.909381	−	0.415965i	$-0.863444\pi$
$941$		−	25.5201i		−	0.831930i	0.909381	−	0.415965i	$-0.136556\pi$
$942$		0			0
$943$	−1.10102	+	1.10102i	−0.0358542	+	0.0358542i
$944$	4.87832			0.158776
$945$		0			0
$946$	13.7980			0.448610
$947$	8.77101	−	8.77101i	0.285020	−	0.285020i	−0.550087	−	0.835107i	$-0.685406\pi$
$947$	8.77101	−	8.77101i	0.285020	−	0.285020i	0.835107	+	0.550087i	$0.185406\pi$
$948$		0			0
$949$		−	16.4041i		−	0.532499i
$950$	−19.0205	+	28.7771i	−0.617105	+	0.933652i
$951$		0			0
$952$	2.00000	+	2.00000i	0.0648204	+	0.0648204i
$953$	−23.8988	−	23.8988i	−0.774157	−	0.774157i	0.204673	−	0.978830i	$-0.434387\pi$
$953$	−23.8988	−	23.8988i	−0.774157	−	0.774157i	−0.978830	+	0.204673i	$0.934387\pi$
$954$		0			0
$955$	−16.0000	+	19.5959i	−0.517748	+	0.634109i
$956$			26.7272i			0.864419i
$957$		0			0
$958$	−20.0454	+	20.0454i	−0.647638	+	0.647638i
$959$	10.7423			0.346885
$960$		0			0
$961$	23.0000			0.741935
$962$	−22.3417	+	22.3417i	−0.720325	+	0.720325i
$963$		0			0
$964$			17.1010i			0.550787i
$965$	2.04989	−	0.207081i	0.0659882	−	0.00666617i
$966$		0			0
$967$	7.59592	+	7.59592i	0.244268	+	0.244268i	0.818613	−	0.574345i	$-0.194743\pi$
$967$	7.59592	+	7.59592i	0.244268	+	0.244268i	−0.574345	+	0.818613i	$0.694743\pi$
$968$	−2.12132	−	2.12132i	−0.0681818	−	0.0681818i
$969$		0			0
$970$	−15.7980	−	12.8990i	−0.507242	−	0.414161i
$971$		−	56.7756i		−	1.82202i	−0.412388	−	0.911008i	$-0.635305\pi$
$971$		−	56.7756i		−	1.82202i	0.412388	−	0.911008i	$-0.364695\pi$
$972$		0			0
$973$	11.5959	−	11.5959i	0.371748	−	0.371748i
$974$	−13.2207			−0.423620
$975$		0			0
$976$	−5.34847			−0.171200
$977$	18.3848	−	18.3848i	0.588181	−	0.588181i	−0.348957	−	0.937139i	$-0.613464\pi$
$977$	18.3848	−	18.3848i	0.588181	−	0.588181i	0.937139	+	0.348957i	$0.113464\pi$
$978$		0			0
$979$			35.1918i			1.12474i
$980$	−1.73205	−	1.41421i	−0.0553283	−	0.0451754i
$981$		0			0
$982$	28.3485	+	28.3485i	0.904636	+	0.904636i
$983$	33.1947	+	33.1947i	1.05875	+	1.05875i	0.998163	+	0.0605832i	$0.0192960\pi$
$983$	33.1947	+	33.1947i	1.05875	+	1.05875i	0.0605832	+	0.998163i	$0.480704\pi$
$984$		0			0
$985$	−40.5959	+	4.10102i	−1.29349	+	0.130669i
$986$			2.82843i			0.0900755i
$987$		0			0
$988$	−16.8990	+	16.8990i	−0.537628	+	0.537628i
$989$	−11.9494			−0.379968
$990$		0			0
$991$	−55.3485			−1.75820			−0.879101	−	0.476635i	$-0.841856\pi$
$991$	−55.3485			−1.75820			−0.879101	+	0.476635i	$0.841856\pi$
$992$	5.19615	−	5.19615i	0.164978	−	0.164978i
$993$		0			0
$994$			1.79796i			0.0570278i
$995$	26.0915	−	31.9555i	0.827157	−	1.01306i
$996$		0			0
$997$	−22.8990	−	22.8990i	−0.725218	−	0.725218i	0.244445	−	0.969663i	$-0.421394\pi$
$997$	−22.8990	−	22.8990i	−0.725218	−	0.725218i	−0.969663	+	0.244445i	$0.921394\pi$
$998$	21.4203	+	21.4203i	0.678047	+	0.678047i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.g.647.3	yes	8
3.2	odd	2	inner	1530.2.m.g.647.2	✓	8
5.3	odd	4	inner	1530.2.m.g.953.2	yes	8
15.8	even	4	inner	1530.2.m.g.953.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.g.647.2	✓	8	3.2	odd	2	inner
1530.2.m.g.647.3	yes	8	1.1	even	1	trivial
1530.2.m.g.953.2	yes	8	5.3	odd	4	inner
1530.2.m.g.953.3	yes	8	15.8	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-1.73205 - 1.41421i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.22474 + 0.224745i) q^{10} +2.82843i q^{11} +(-2.44949 + 2.44949i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} +6.89898i q^{19} +(-1.41421 + 1.73205i) q^{20} +(2.00000 + 2.00000i) q^{22} +(-1.73205 - 1.73205i) q^{23} +(1.00000 + 4.89898i) q^{25} +3.46410i q^{26} +(2.00000 - 2.00000i) q^{28} +2.82843 q^{29} -7.34847 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.00000i q^{34} +(-0.635674 - 6.29253i) q^{35} +(6.44949 + 6.44949i) q^{37} +(4.87832 + 4.87832i) q^{38} +(0.224745 + 2.22474i) q^{40} -0.635674i q^{41} +(3.44949 - 3.44949i) q^{43} +2.82843 q^{44} -2.44949 q^{46} +(-2.82843 + 2.82843i) q^{47} +1.00000i q^{49} +(4.17121 + 2.75699i) q^{50} +(2.44949 + 2.44949i) q^{52} +(5.51399 + 5.51399i) q^{53} +(4.00000 - 4.89898i) q^{55} -2.82843i q^{56} +(2.00000 - 2.00000i) q^{58} -4.87832 q^{59} +5.34847 q^{61} +(-5.19615 + 5.19615i) q^{62} +1.00000i q^{64} +(7.70674 - 0.778539i) q^{65} +(-1.44949 - 1.44949i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-4.89898 - 4.00000i) q^{70} +0.635674i q^{71} +(-3.34847 + 3.34847i) q^{73} +9.12096 q^{74} +6.89898 q^{76} +(-5.65685 + 5.65685i) q^{77} +6.44949i q^{79} +(1.73205 + 1.41421i) q^{80} +(-0.449490 - 0.449490i) q^{82} +(-2.82843 - 2.82843i) q^{83} +(2.22474 - 0.224745i) q^{85} -4.87832i q^{86} +(2.00000 - 2.00000i) q^{88} +12.4422 q^{89} -9.79796 q^{91} +(-1.73205 + 1.73205i) q^{92} +4.00000i q^{94} +(9.75663 - 11.9494i) q^{95} +(6.44949 + 6.44949i) q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{7} - 8 q^{10} - 8 q^{16} + 16 q^{22} + 8 q^{25} + 16 q^{28} + 32 q^{37} - 8 q^{40} + 8 q^{43} + 32 q^{55} + 16 q^{58} - 16 q^{61} + 8 q^{67} + 32 q^{73} + 16 q^{76} + 16 q^{82} + 8 q^{85} + 16 q^{88}+ \cdots + 32 q^{97}+O(q^{100}) \) 8 * q + 16 * q^7 - 8 * q^10 - 8 * q^16 + 16 * q^22 + 8 * q^25 + 16 * q^28 + 32 * q^37 - 8 * q^40 + 8 * q^43 + 32 * q^55 + 16 * q^58 - 16 * q^61 + 8 * q^67 + 32 * q^73 + 16 * q^76 + 16 * q^82 + 8 * q^85 + 16 * q^88 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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