LMFDB - Embedded newform 2214.2.i.b.1639.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2214,2,Mod(901,2214)] 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("2214.901"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2214, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2214 = 2 \cdot 3^{3} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2214.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$17.6788790075$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 738)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1639.7
Character	$\chi$	$=$	2214.1639
Dual form			2214.2.i.b.901.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.714167 - 1.23697i) q^{5} +(-2.06322 - 1.19120i) q^{7} -1.00000 q^{8} -1.42833 q^{10} +(3.59438 + 2.07522i) q^{11} +(3.86282 - 2.23020i) q^{13} +(-2.06322 + 1.19120i) q^{14} +(-0.500000 + 0.866025i) q^{16} -8.04790i q^{17} +0.0146965i q^{19} +(-0.714167 + 1.23697i) q^{20} +(3.59438 - 2.07522i) q^{22} +(1.70954 + 2.96101i) q^{23} +(1.47993 - 2.56332i) q^{25} -4.46041i q^{26} +2.38240i q^{28} +(-3.69126 - 2.13115i) q^{29} +(3.83330 + 6.63947i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.96968 - 4.02395i) q^{34} +3.40286i q^{35} +1.09021 q^{37} +(0.0127276 + 0.00734827i) q^{38} +(0.714167 + 1.23697i) q^{40} +(-2.12147 - 6.04147i) q^{41} +(-4.92281 + 8.52655i) q^{43} -4.15044i q^{44} +3.41907 q^{46} +(-11.3345 - 6.54395i) q^{47} +(-0.662088 - 1.14677i) q^{49} +(-1.47993 - 2.56332i) q^{50} +(-3.86282 - 2.23020i) q^{52} -2.16886i q^{53} -5.92821i q^{55} +(2.06322 + 1.19120i) q^{56} +(-3.69126 + 2.13115i) q^{58} +(-6.49314 - 11.2464i) q^{59} +(-0.312896 + 0.541952i) q^{61} +7.66660 q^{62} +1.00000 q^{64} +(-5.51740 - 3.18547i) q^{65} +(-6.40189 + 3.69613i) q^{67} +(-6.96968 + 4.02395i) q^{68} +(2.94696 + 1.70143i) q^{70} -11.1353i q^{71} -2.91859 q^{73} +(0.545105 - 0.944150i) q^{74} +(0.0127276 - 0.00734827i) q^{76} +(-4.94400 - 8.56325i) q^{77} +(10.9430 + 6.31792i) q^{79} +1.42833 q^{80} +(-6.29280 - 1.18348i) q^{82} +(-7.00585 + 12.1345i) q^{83} +(-9.95504 + 5.74754i) q^{85} +(4.92281 + 8.52655i) q^{86} +(-3.59438 - 2.07522i) q^{88} +0.614362i q^{89} -10.6265 q^{91} +(1.70954 - 2.96101i) q^{92} +(-11.3345 + 6.54395i) q^{94} +(0.0181792 - 0.0104958i) q^{95} +(-3.71537 - 2.14507i) q^{97} -1.32418 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 4 * q^5 - 36 * q^8 - 8 * q^10 - 18 * q^16 - 4 * q^20 + 4 * q^23 - 26 * q^25 + 8 * q^31 + 18 * q^32 - 60 * q^37 + 4 * q^40 + 6 * q^41 + 6 * q^43 + 8 * q^46 + 38 * q^49 + 26 * q^50 - 22 * q^59 - 46 * q^61 + 16 * q^62 + 36 * q^64 + 64 * q^73 - 30 * q^74 + 2 * q^77 + 8 * q^80 + 12 * q^82 - 68 * q^83 - 6 * q^86 + 36 * q^91 + 4 * q^92 + 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2214\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.714167	−	1.23697i	−0.319385	−	0.553191i	0.660975	−	0.750408i	$-0.270143\pi$
$5$	−0.714167	−	1.23697i	−0.319385	−	0.553191i	−0.980360	+	0.197217i	$0.936810\pi$
$6$		0			0
$7$	−2.06322	−	1.19120i	−0.779823	−	0.450231i	0.0565445	−	0.998400i	$-0.481992\pi$
$7$	−2.06322	−	1.19120i	−0.779823	−	0.450231i	−0.836368	+	0.548169i	$0.815325\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.42833			−0.451679
$11$	3.59438	+	2.07522i	1.08375	+	0.625702i	0.931905	−	0.362703i	$-0.118146\pi$
$11$	3.59438	+	2.07522i	1.08375	+	0.625702i	0.151842	+	0.988405i	$0.451479\pi$
$12$		0			0
$13$	3.86282	−	2.23020i	1.07135	−	0.618547i	0.142803	−	0.989751i	$-0.454388\pi$
$13$	3.86282	−	2.23020i	1.07135	−	0.618547i	0.928551	+	0.371204i	$0.121055\pi$
$14$	−2.06322	+	1.19120i	−0.551418	+	0.318361i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	8.04790i		−	1.95190i	−0.217990	−	0.975951i	$-0.569950\pi$
$17$		−	8.04790i		−	1.95190i	0.217990	−	0.975951i	$-0.430050\pi$
$18$		0			0
$19$			0.0146965i			0.00337162i	0.999999	+	0.00168581i	$0.000536610\pi$
$19$			0.0146965i			0.00337162i	−0.999999	+	0.00168581i	$0.999463\pi$
$20$	−0.714167	+	1.23697i	−0.159693	+	0.276596i
$21$		0			0
$22$	3.59438	−	2.07522i	0.766325	−	0.442438i
$23$	1.70954	+	2.96101i	0.356463	+	0.617412i	0.987367	−	0.158449i	$-0.0506492\pi$
$23$	1.70954	+	2.96101i	0.356463	+	0.617412i	−0.630904	+	0.775861i	$0.717316\pi$
$24$		0			0
$25$	1.47993	−	2.56332i	0.295986	−	0.512663i
$26$		−	4.46041i		−	0.874758i
$27$		0			0
$28$			2.38240i			0.450231i
$29$	−3.69126	−	2.13115i	−0.685449	−	0.395744i	0.116456	−	0.993196i	$-0.462847\pi$
$29$	−3.69126	−	2.13115i	−0.685449	−	0.395744i	−0.801905	+	0.597452i	$0.796180\pi$
$30$		0			0
$31$	3.83330	+	6.63947i	0.688481	+	1.19248i	0.972329	+	0.233615i	$0.0750557\pi$
$31$	3.83330	+	6.63947i	0.688481	+	1.19248i	−0.283848	+	0.958869i	$0.591611\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−6.96968	−	4.02395i	−1.19529	−	0.690102i
$35$			3.40286i			0.575189i
$36$		0			0
$37$	1.09021			0.179230			0.0896148	−	0.995977i	$-0.471436\pi$
$37$	1.09021			0.179230			0.0896148	+	0.995977i	$0.471436\pi$
$38$	0.0127276	+	0.00734827i	0.00206468	+	0.00119205i
$39$		0			0
$40$	0.714167	+	1.23697i	0.112920	+	0.195583i
$41$	−2.12147	−	6.04147i	−0.331319	−	0.943519i
$41$	−2.12147	−	6.04147i	−0.331319	−	0.943519i
$42$		0			0
$43$	−4.92281	+	8.52655i	−0.750721	+	1.30029i	0.196752	+	0.980453i	$0.436960\pi$
$43$	−4.92281	+	8.52655i	−0.750721	+	1.30029i	−0.947474	+	0.319834i	$0.896373\pi$
$44$		−	4.15044i		−	0.625702i
$45$		0			0
$46$	3.41907			0.504115
$47$	−11.3345	−	6.54395i	−1.65330	−	0.954533i	−0.975702	−	0.219100i	$-0.929688\pi$
$47$	−11.3345	−	6.54395i	−1.65330	−	0.954533i	−0.677597	−	0.735433i	$-0.736979\pi$
$48$		0			0
$49$	−0.662088	−	1.14677i	−0.0945840	−	0.163824i
$50$	−1.47993	−	2.56332i	−0.209294	−	0.362508i
$51$		0			0
$52$	−3.86282	−	2.23020i	−0.535677	−	0.309273i
$53$		−	2.16886i		−	0.297915i	−0.988844	−	0.148958i	$-0.952408\pi$
$53$		−	2.16886i		−	0.297915i	0.988844	−	0.148958i	$-0.0475918\pi$
$54$		0			0
$55$		−	5.92821i		−	0.799360i
$56$	2.06322	+	1.19120i	0.275709	+	0.159181i
$57$		0			0
$58$	−3.69126	+	2.13115i	−0.484686	+	0.279833i
$59$	−6.49314	−	11.2464i	−0.845335	−	1.46416i	−0.885330	−	0.464963i	$-0.846068\pi$
$59$	−6.49314	−	11.2464i	−0.845335	−	1.46416i	0.0399952	−	0.999200i	$-0.487266\pi$
$60$		0			0
$61$	−0.312896	+	0.541952i	−0.0400622	+	0.0693898i	−0.885361	−	0.464904i	$-0.846089\pi$
$61$	−0.312896	+	0.541952i	−0.0400622	+	0.0693898i	0.845299	+	0.534293i	$0.179422\pi$
$62$	7.66660			0.973660
$63$		0			0
$64$	1.00000			0.125000
$65$	−5.51740	−	3.18547i	−0.684350	−	0.395110i
$66$		0			0
$67$	−6.40189	+	3.69613i	−0.782116	+	0.451555i	−0.837180	−	0.546928i	$-0.815797\pi$
$67$	−6.40189	+	3.69613i	−0.782116	+	0.451555i	0.0550639	+	0.998483i	$0.482464\pi$
$68$	−6.96968	+	4.02395i	−0.845198	+	0.487975i
$69$		0			0
$70$	2.94696	+	1.70143i	0.352230	+	0.203360i
$71$		−	11.1353i		−	1.32152i	−0.750597	−	0.660760i	$-0.770234\pi$
$71$		−	11.1353i		−	1.32152i	0.750597	−	0.660760i	$-0.229766\pi$
$72$		0			0
$73$	−2.91859			−0.341596			−0.170798	−	0.985306i	$-0.554635\pi$
$73$	−2.91859			−0.341596			−0.170798	+	0.985306i	$0.554635\pi$
$74$	0.545105	−	0.944150i	0.0633672	−	0.109755i
$75$		0			0
$76$	0.0127276	−	0.00734827i	0.00145995	−	0.000842904i
$77$	−4.94400	−	8.56325i	−0.563421	−	0.975873i
$78$		0			0
$79$	10.9430	+	6.31792i	1.23118	+	0.710821i	0.967276	−	0.253728i	$-0.0816568\pi$
$79$	10.9430	+	6.31792i	1.23118	+	0.710821i	0.263903	+	0.964549i	$0.414990\pi$
$80$	1.42833			0.159693
$81$		0			0
$82$	−6.29280	−	1.18348i	−0.694924	−	0.130694i
$83$	−7.00585	+	12.1345i	−0.768992	+	1.33193i	0.169118	+	0.985596i	$0.445908\pi$
$83$	−7.00585	+	12.1345i	−0.768992	+	1.33193i	−0.938110	+	0.346337i	$0.887425\pi$
$84$		0			0
$85$	−9.95504	+	5.74754i	−1.07978	+	0.623409i
$86$	4.92281	+	8.52655i	0.530840	+	0.919442i
$87$		0			0
$88$	−3.59438	−	2.07522i	−0.383162	−	0.221219i
$89$			0.614362i			0.0651223i	0.999470	+	0.0325611i	$0.0103664\pi$
$89$			0.614362i			0.0651223i	−0.999470	+	0.0325611i	$0.989634\pi$
$90$		0			0
$91$	−10.6265			−1.11396
$92$	1.70954	−	2.96101i	0.178232	−	0.308706i
$93$		0			0
$94$	−11.3345	+	6.54395i	−1.16906	+	0.674957i
$95$	0.0181792	−	0.0104958i	0.00186515	−	0.00107684i
$96$		0			0
$97$	−3.71537	−	2.14507i	−0.377239	−	0.217799i	0.299378	−	0.954135i	$-0.403221\pi$
$97$	−3.71537	−	2.14507i	−0.377239	−	0.217799i	−0.676616	+	0.736336i	$0.736554\pi$
$98$	−1.32418			−0.133762
$99$		0			0
$100$	−2.95986			−0.295986
$101$	−4.04648	−	2.33624i	−0.402640	−	0.232464i	0.284982	−	0.958533i	$-0.408012\pi$
$101$	−4.04648	−	2.33624i	−0.402640	−	0.232464i	−0.687622	+	0.726068i	$0.741346\pi$
$102$		0			0
$103$	0.551394	+	0.955042i	0.0543304	+	0.0941031i	0.891912	−	0.452210i	$-0.149364\pi$
$103$	0.551394	+	0.955042i	0.0543304	+	0.0941031i	−0.837581	+	0.546313i	$0.816031\pi$
$104$	−3.86282	+	2.23020i	−0.378781	+	0.218689i
$105$		0			0
$106$	−1.87829	−	1.08443i	−0.182435	−	0.105329i
$107$	6.55946			0.634127			0.317064	−	0.948404i	$-0.397303\pi$
$107$	6.55946			0.634127			0.317064	+	0.948404i	$0.397303\pi$
$108$		0			0
$109$		−	13.5227i		−	1.29524i	−0.761964	−	0.647619i	$-0.775765\pi$
$109$		−	13.5227i		−	1.29524i	0.761964	−	0.647619i	$-0.224235\pi$
$110$	−5.13398	−	2.96410i	−0.489506	−	0.282616i
$111$		0			0
$112$	2.06322	−	1.19120i	0.194956	−	0.112558i
$113$	9.29636	+	16.1018i	0.874528	+	1.51473i	0.857264	+	0.514876i	$0.172162\pi$
$113$	9.29636	+	16.1018i	0.874528	+	1.51473i	0.0172638	+	0.999851i	$0.494504\pi$
$114$		0			0
$115$	2.44179	−	4.22930i	0.227698	−	0.394385i
$116$			4.26230i			0.395744i
$117$		0			0
$118$	−12.9863			−1.19548
$119$	−9.58665	+	16.6046i	−0.878807	+	1.52214i
$120$		0			0
$121$	3.11306	+	5.39197i	0.283005	+	0.490179i
$122$	0.312896	+	0.541952i	0.0283283	+	0.0490660i
$123$		0			0
$124$	3.83330	−	6.63947i	0.344241	−	0.596242i
$125$	−11.3693			−1.01690
$126$		0			0
$127$	13.5119			1.19898			0.599492	−	0.800381i	$-0.295369\pi$
$127$	13.5119			1.19898			0.599492	+	0.800381i	$0.295369\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−5.51740	+	3.18547i	−0.483908	+	0.279385i
$131$	−5.80001	−	10.0459i	−0.506749	−	0.877715i	−0.999969	−	0.00781101i	$-0.997514\pi$
$131$	−5.80001	−	10.0459i	−0.506749	−	0.877715i	0.493220	−	0.869904i	$-0.335820\pi$
$132$		0			0
$133$	0.0175065	−	0.0303221i	0.00151801	−	0.00262926i
$134$			7.39227i			0.638595i
$135$		0			0
$136$			8.04790i			0.690102i
$137$	5.75151	+	3.32063i	0.491384	+	0.283701i	0.725149	−	0.688592i	$-0.241771\pi$
$137$	5.75151	+	3.32063i	0.491384	+	0.283701i	−0.233764	+	0.972293i	$0.575104\pi$
$138$		0			0
$139$	−6.59661	−	11.4257i	−0.559517	−	0.969113i	−0.997537	−	0.0701470i	$-0.977653\pi$
$139$	−6.59661	−	11.4257i	−0.559517	−	0.969113i	0.438019	−	0.898966i	$-0.355680\pi$
$140$	2.94696	−	1.70143i	0.249064	−	0.143797i
$141$		0			0
$142$	−9.64348	−	5.56767i	−0.809263	−	0.467228i
$143$	18.5126			1.54810
$144$		0			0
$145$			6.08798i			0.505580i
$146$	−1.45930	+	2.52758i	−0.120772	+	0.209184i
$147$		0			0
$148$	−0.545105	−	0.944150i	−0.0448074	−	0.0776087i
$149$	−9.45898	+	5.46114i	−0.774910	+	0.447394i	−0.834623	−	0.550821i	$-0.814315\pi$
$149$	−9.45898	+	5.46114i	−0.774910	+	0.447394i	0.0597135	+	0.998216i	$0.480981\pi$
$150$		0			0
$151$	−8.42334	−	4.86322i	−0.685482	−	0.395763i	0.116435	−	0.993198i	$-0.462853\pi$
$151$	−8.42334	−	4.86322i	−0.685482	−	0.395763i	−0.801917	+	0.597435i	$0.796187\pi$
$152$		−	0.0146965i		−	0.00119205i
$153$		0			0
$154$	−9.88799			−0.796797
$155$	5.47524	−	9.48339i	0.439782	−	0.761724i
$156$		0			0
$157$	−2.32471	+	1.34217i	−0.185532	+	0.107117i	−0.589889	−	0.807484i	$-0.700829\pi$
$157$	−2.32471	+	1.34217i	−0.185532	+	0.107117i	0.404357	+	0.914601i	$0.367495\pi$
$158$	10.9430	−	6.31792i	0.870575	−	0.502627i
$159$		0			0
$160$	0.714167	−	1.23697i	0.0564599	−	0.0977914i
$161$		−	8.14560i		−	0.641963i
$162$		0			0
$163$	20.8186			1.63064			0.815320	−	0.579011i	$-0.196561\pi$
$163$	20.8186			1.63064			0.815320	+	0.579011i	$0.196561\pi$
$164$	−4.17133	+	4.85799i	−0.325726	+	0.379345i
$165$		0			0
$166$	7.00585	+	12.1345i	0.543759	+	0.941819i
$167$	15.8135	−	9.12995i	1.22369	−	0.706496i	0.257985	−	0.966149i	$-0.416941\pi$
$167$	15.8135	−	9.12995i	1.22369	−	0.706496i	0.965702	+	0.259652i	$0.0836080\pi$
$168$		0			0
$169$	3.44761	−	5.97143i	0.265201	−	0.459341i
$170$			11.4951i			0.881633i
$171$		0			0
$172$	9.84562			0.750721
$173$	−8.69165	+	15.0544i	−0.660814	+	1.14456i	0.319589	+	0.947556i	$0.396455\pi$
$173$	−8.69165	+	15.0544i	−0.660814	+	1.14456i	−0.980402	+	0.197006i	$0.936878\pi$
$174$		0			0
$175$	−6.10684	+	3.52579i	−0.461634	+	0.266524i
$176$	−3.59438	+	2.07522i	−0.270937	+	0.156425i
$177$		0			0
$178$	0.532053	+	0.307181i	0.0398791	+	0.0230242i
$179$		−	21.4868i		−	1.60600i	−0.595981	−	0.802999i	$-0.703237\pi$
$179$		−	21.4868i		−	1.60600i	0.595981	−	0.802999i	$-0.296763\pi$
$180$		0			0
$181$			8.54851i			0.635406i	0.948190	+	0.317703i	$0.102911\pi$
$181$			8.54851i			0.635406i	−0.948190	+	0.317703i	$0.897089\pi$
$182$	−5.31323	+	9.20279i	−0.393843	+	0.682156i
$183$		0			0
$184$	−1.70954	−	2.96101i	−0.126029	−	0.218288i
$185$	−0.778593	−	1.34856i	−0.0572433	−	0.0991483i
$186$		0			0
$187$	16.7011	−	28.9272i	1.22131	−	2.11537i
$188$			13.0879i			0.954533i
$189$		0			0
$190$		−	0.0209916i		−	0.00152289i
$191$	0.759862	+	0.438706i	0.0549817	+	0.0317437i	0.527239	−	0.849717i	$-0.323227\pi$
$191$	0.759862	+	0.438706i	0.0549817	+	0.0317437i	−0.472257	+	0.881461i	$0.656561\pi$
$192$		0			0
$193$	2.59152	−	1.49621i	0.186542	−	0.107700i	−0.403821	−	0.914838i	$-0.632318\pi$
$193$	2.59152	−	1.49621i	0.186542	−	0.107700i	0.590363	+	0.807138i	$0.298985\pi$
$194$	−3.71537	+	2.14507i	−0.266748	+	0.154007i
$195$		0			0
$196$	−0.662088	+	1.14677i	−0.0472920	+	0.0819121i
$197$	16.3005			1.16136			0.580681	−	0.814131i	$-0.302786\pi$
$197$	16.3005			1.16136			0.580681	+	0.814131i	$0.302786\pi$
$198$		0			0
$199$			12.4760i			0.884399i	0.896917	+	0.442199i	$0.145802\pi$
$199$			12.4760i			0.884399i	−0.896917	+	0.442199i	$0.854198\pi$
$200$	−1.47993	+	2.56332i	−0.104647	+	0.181254i
$201$		0			0
$202$	−4.04648	+	2.33624i	−0.284709	+	0.164377i
$203$	5.07725	+	8.79405i	0.356353	+	0.617221i
$204$		0			0
$205$	−5.95805	+	6.93883i	−0.416128	+	0.484629i
$206$	1.10279			0.0768349
$207$		0			0
$208$			4.46041i			0.309273i
$209$	−0.0304985	+	0.0528250i	−0.00210963	+	0.00365398i
$210$		0			0
$211$	13.1514	−	7.59299i	0.905383	−	0.522723i	0.0264399	−	0.999650i	$-0.491583\pi$
$211$	13.1514	−	7.59299i	0.905383	−	0.522723i	0.878943	+	0.476928i	$0.158250\pi$
$212$	−1.87829	+	1.08443i	−0.129001	+	0.0744789i
$213$		0			0
$214$	3.27973	−	5.68066i	0.224198	−	0.388322i
$215$	14.0628			0.959077
$216$		0			0
$217$		−	18.2649i		−	1.23990i
$218$	−11.7110	−	6.76135i	−0.793169	−	0.457936i
$219$		0			0
$220$	−5.13398	+	2.96410i	−0.346133	+	0.199840i
$221$	−17.9484	−	31.0876i	−1.20734	−	2.09118i
$222$		0			0
$223$	2.46975	−	4.27774i	0.165387	−	0.286459i	−0.771406	−	0.636344i	$-0.780446\pi$
$223$	2.46975	−	4.27774i	0.165387	−	0.286459i	0.936793	+	0.349885i	$0.113779\pi$
$224$		−	2.38240i		−	0.159181i
$225$		0			0
$226$	18.5927			1.23677
$227$	7.96322	+	4.59757i	0.528538	+	0.305151i	0.740421	−	0.672144i	$-0.234626\pi$
$227$	7.96322	+	4.59757i	0.528538	+	0.305151i	−0.211883	+	0.977295i	$0.567960\pi$
$228$		0			0
$229$	12.4634	−	7.19575i	0.823605	−	0.475509i	−0.0280530	−	0.999606i	$-0.508931\pi$
$229$	12.4634	−	7.19575i	0.823605	−	0.475509i	0.851658	+	0.524098i	$0.175597\pi$
$230$	−2.44179	−	4.22930i	−0.161007	−	0.278872i
$231$		0			0
$232$	3.69126	+	2.13115i	0.242343	+	0.139917i
$233$		−	15.4149i		−	1.00986i	−0.863159	−	0.504932i	$-0.831518\pi$
$233$		−	15.4149i		−	1.00986i	0.863159	−	0.504932i	$-0.168482\pi$
$234$		0			0
$235$			18.6939i			1.21945i
$236$	−6.49314	+	11.2464i	−0.422667	+	0.732081i
$237$		0			0
$238$	9.58665	+	16.6046i	0.621410	+	1.07631i
$239$	−8.19166	+	4.72946i	−0.529875	+	0.305923i	−0.740965	−	0.671543i	$-0.765632\pi$
$239$	−8.19166	+	4.72946i	−0.529875	+	0.305923i	0.211091	+	0.977466i	$0.432298\pi$
$240$		0			0
$241$	−3.02525	+	5.23989i	−0.194874	+	0.337531i	−0.946859	−	0.321649i	$-0.895763\pi$
$241$	−3.02525	+	5.23989i	−0.194874	+	0.337531i	0.751985	+	0.659180i	$0.229096\pi$
$242$	6.22612			0.400230
$243$		0			0
$244$	0.625792			0.0400622
$245$	−0.945682	+	1.63797i	−0.0604174	+	0.104646i
$246$		0			0
$247$	0.0327762	+	0.0567701i	0.00208550	+	0.00361220i
$248$	−3.83330	−	6.63947i	−0.243415	−	0.421607i
$249$		0			0
$250$	−5.68467	+	9.84614i	−0.359530	+	0.622725i
$251$	−21.9727			−1.38690			−0.693451	−	0.720504i	$-0.743911\pi$
$251$	−21.9727			−1.38690			−0.693451	+	0.720504i	$0.743911\pi$
$252$		0			0
$253$			14.1906i			0.892158i
$254$	6.75594	−	11.7016i	0.423905	−	0.734225i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.4040	−	7.16143i	0.773738	−	0.446718i	−0.0604686	−	0.998170i	$-0.519260\pi$
$257$	12.4040	−	7.16143i	0.773738	−	0.446718i	0.834206	+	0.551452i	$0.185926\pi$
$258$		0			0
$259$	−2.24934	−	1.29866i	−0.139767	−	0.0806947i
$260$			6.37095i			0.395110i
$261$		0			0
$262$	−11.6000			−0.716652
$263$	11.3331	+	6.54315i	0.698827	+	0.403468i	0.806910	−	0.590674i	$-0.201138\pi$
$263$	11.3331	+	6.54315i	0.698827	+	0.403468i	−0.108083	+	0.994142i	$0.534471\pi$
$264$		0			0
$265$	−2.68282	+	1.54893i	−0.164804	+	0.0951498i
$266$	−0.0175065	−	0.0303221i	−0.00107339	−	0.00185917i
$267$		0			0
$268$	6.40189	+	3.69613i	0.391058	+	0.225777i
$269$	11.4157			0.696029			0.348015	−	0.937489i	$-0.386856\pi$
$269$	11.4157			0.696029			0.348015	+	0.937489i	$0.386856\pi$
$270$		0			0
$271$	−21.5113			−1.30672			−0.653359	−	0.757048i	$-0.726641\pi$
$271$	−21.5113			−1.30672			−0.653359	+	0.757048i	$0.726641\pi$
$272$	6.96968	+	4.02395i	0.422599	+	0.243988i
$273$		0			0
$274$	5.75151	−	3.32063i	0.347461	−	0.200607i
$275$	10.6389	−	6.14236i	0.641548	−	0.370398i
$276$		0			0
$277$	−13.3063	+	23.0471i	−0.799496	+	1.38477i	0.120449	+	0.992720i	$0.461567\pi$
$277$	−13.3063	+	23.0471i	−0.799496	+	1.38477i	−0.919945	+	0.392048i	$0.871767\pi$
$278$	−13.1932			−0.791277
$279$		0			0
$280$		−	3.40286i		−	0.203360i
$281$	−12.6222	−	7.28744i	−0.752978	−	0.434732i	0.0737909	−	0.997274i	$-0.476490\pi$
$281$	−12.6222	−	7.28744i	−0.752978	−	0.434732i	−0.826769	+	0.562542i	$0.809824\pi$
$282$		0			0
$283$	−13.4593	−	23.3123i	−0.800075	−	1.38577i	−0.919566	−	0.392935i	$-0.871460\pi$
$283$	−13.4593	−	23.3123i	−0.800075	−	1.38577i	0.119491	−	0.992835i	$-0.461874\pi$
$284$	−9.64348	+	5.56767i	−0.572235	+	0.330380i
$285$		0			0
$286$	9.25631	−	16.0324i	0.547337	−	0.948016i
$287$	−2.81953	+	14.9920i	−0.166432	+	0.884948i
$288$		0			0
$289$	−47.7687			−2.80992
$290$	5.27235	+	3.04399i	0.309603	+	0.178749i
$291$		0			0
$292$	1.45930	+	2.52758i	0.0853989	+	0.147915i
$293$	12.4103	−	7.16509i	0.725017	−	0.418589i	−0.0915794	−	0.995798i	$-0.529192\pi$
$293$	12.4103	−	7.16509i	0.725017	−	0.418589i	0.816596	+	0.577209i	$0.195858\pi$
$294$		0			0
$295$	−9.27437	+	16.0637i	−0.539975	+	0.935264i
$296$	−1.09021			−0.0633672
$297$		0			0
$298$			10.9223i			0.632711i
$299$	13.2073	+	7.62523i	0.763797	+	0.440978i
$300$		0			0
$301$	20.3137	−	11.7281i	1.17086	−	0.675996i
$302$	−8.42334	+	4.86322i	−0.484709	+	0.279847i
$303$		0			0
$304$	−0.0127276	−	0.00734827i	−0.000729976	−	0.000421452i
$305$	0.893840			0.0511811
$306$		0			0
$307$	−4.41645			−0.252060			−0.126030	−	0.992026i	$-0.540224\pi$
$307$	−4.41645			−0.252060			−0.126030	+	0.992026i	$0.540224\pi$
$308$	−4.94400	+	8.56325i	−0.281710	+	0.487937i
$309$		0			0
$310$	−5.47524	−	9.48339i	−0.310973	−	0.538620i
$311$	−4.72361	+	2.72718i	−0.267852	+	0.154644i	−0.627911	−	0.778285i	$-0.716090\pi$
$311$	−4.72361	+	2.72718i	−0.267852	+	0.154644i	0.360059	+	0.932929i	$0.382756\pi$
$312$		0			0
$313$	−4.98572	−	2.87851i	−0.281810	−	0.162703i	0.352433	−	0.935837i	$-0.385355\pi$
$313$	−4.98572	−	2.87851i	−0.281810	−	0.162703i	−0.634242	+	0.773134i	$0.718688\pi$
$314$			2.68435i			0.151486i
$315$		0			0
$316$		−	12.6358i		−	0.710821i
$317$	20.7570	+	11.9841i	1.16583	+	0.673091i	0.952694	−	0.303931i	$-0.0982994\pi$
$317$	20.7570	+	11.9841i	1.16583	+	0.673091i	0.213135	+	0.977023i	$0.431633\pi$
$318$		0			0
$319$	−8.84519	−	15.3203i	−0.495236	−	0.857774i
$320$	−0.714167	−	1.23697i	−0.0399232	−	0.0691489i
$321$		0			0
$322$	−7.05430	−	4.07280i	−0.393121	−	0.226968i
$323$	0.118276			0.00658106
$324$		0			0
$325$		−	13.2022i		−	0.732325i
$326$	10.4093	−	18.0294i	0.576518	−	0.998559i
$327$		0			0
$328$	2.12147	+	6.04147i	0.117139	+	0.333584i
$329$	15.5903	+	27.0032i	0.859521	+	1.48873i
$330$		0			0
$331$	16.5404	+	9.54960i	0.909142	+	0.524893i	0.880155	−	0.474686i	$-0.157439\pi$
$331$	16.5404	+	9.54960i	0.909142	+	0.524893i	0.0289870	+	0.999580i	$0.490772\pi$
$332$	14.0117			0.768992
$333$		0			0
$334$		−	18.2599i		−	0.999137i
$335$	9.14404	+	5.27932i	0.499592	+	0.288440i
$336$		0			0
$337$	14.4120	+	24.9623i	0.785070	+	1.35978i	0.928957	+	0.370187i	$0.120706\pi$
$337$	14.4120	+	24.9623i	0.785070	+	1.35978i	−0.143887	+	0.989594i	$0.545960\pi$
$338$	−3.44761	−	5.97143i	−0.187525	−	0.324803i
$339$		0			0
$340$	9.95504	+	5.74754i	0.539888	+	0.311704i
$341$			31.8197i			1.72314i
$342$		0			0
$343$			19.8315i			1.07080i
$344$	4.92281	−	8.52655i	0.265420	−	0.459721i
$345$		0			0
$346$	8.69165	+	15.0544i	0.467266	+	0.809328i
$347$	−19.9667	+	11.5278i	−1.07187	+	0.618844i	−0.928691	−	0.370853i	$-0.879065\pi$
$347$	−19.9667	+	11.5278i	−1.07187	+	0.618844i	−0.143177	+	0.989697i	$0.545732\pi$
$348$		0			0
$349$	7.42676	−	12.8635i	0.397545	−	0.688569i	−0.595877	−	0.803076i	$-0.703195\pi$
$349$	7.42676	−	12.8635i	0.397545	−	0.688569i	0.993422	+	0.114507i	$0.0365288\pi$
$350$			7.05157i			0.376922i
$351$		0			0
$352$			4.15044i			0.221219i
$353$	4.63803	−	8.03331i	0.246858	−	0.427570i	−0.715795	−	0.698311i	$-0.753935\pi$
$353$	4.63803	−	8.03331i	0.246858	−	0.427570i	0.962652	+	0.270741i	$0.0872687\pi$
$354$		0			0
$355$	−13.7741	+	7.95249i	−0.731054	+	0.422074i
$356$	0.532053	−	0.307181i	0.0281988	−	0.0162806i
$357$		0			0
$358$	−18.6081	−	10.7434i	−0.983469	−	0.567806i
$359$	12.5634			0.663070			0.331535	−	0.943443i	$-0.392433\pi$
$359$	12.5634			0.663070			0.331535	+	0.943443i	$0.392433\pi$
$360$		0			0
$361$	18.9998			0.999989
$362$	7.40323	+	4.27426i	0.389105	+	0.224650i
$363$		0			0
$364$	5.31323	+	9.20279i	0.278489	+	0.482357i
$365$	2.08436	+	3.61022i	0.109101	+	0.188968i
$366$		0			0
$367$	−3.14993	+	5.45583i	−0.164425	+	0.284792i	−0.936451	−	0.350799i	$-0.885910\pi$
$367$	−3.14993	+	5.45583i	−0.164425	+	0.284792i	0.772026	+	0.635591i	$0.219243\pi$
$368$	−3.41907			−0.178232
$369$		0			0
$370$	−1.55719			−0.0809542
$371$	−2.58354	+	4.47483i	−0.134131	+	0.232321i
$372$		0			0
$373$	3.63352	+	6.29343i	0.188136	+	0.325862i	0.944629	−	0.328141i	$-0.106422\pi$
$373$	3.63352	+	6.29343i	0.188136	+	0.325862i	−0.756493	+	0.654002i	$0.773089\pi$
$374$	−16.7011	−	28.9272i	−0.863595	−	1.49579i
$375$		0			0
$376$	11.3345	+	6.54395i	0.584530	+	0.337478i
$377$	−19.0116			−0.979146
$378$		0			0
$379$	12.4631			0.640184			0.320092	−	0.947386i	$-0.396286\pi$
$379$	12.4631			0.640184			0.320092	+	0.947386i	$0.396286\pi$
$380$	−0.0181792	−	0.0104958i	−0.000932574	−	0.000538422i
$381$		0			0
$382$	0.759862	−	0.438706i	0.0388779	−	0.0224462i
$383$	17.6944	−	10.2158i	0.904139	−	0.522005i	0.0255984	−	0.999672i	$-0.491851\pi$
$383$	17.6944	−	10.2158i	0.904139	−	0.522005i	0.878541	+	0.477667i	$0.158518\pi$
$384$		0			0
$385$	−7.06168	+	12.2312i	−0.359897	+	0.623359i
$386$		−	2.99243i		−	0.152311i
$387$		0			0
$388$			4.29014i			0.217799i
$389$	15.4480	−	26.7567i	0.783245	−	1.35662i	−0.146798	−	0.989167i	$-0.546897\pi$
$389$	15.4480	−	26.7567i	0.783245	−	1.35662i	0.930042	−	0.367453i	$-0.119770\pi$
$390$		0			0
$391$	23.8299	−	13.7582i	1.20513	−	0.695781i
$392$	0.662088	+	1.14677i	0.0334405	+	0.0579206i
$393$		0			0
$394$	8.15025	−	14.1166i	0.410604	−	0.711186i
$395$		−	18.0482i		−	0.908103i
$396$		0			0
$397$		−	20.5484i		−	1.03129i	−0.856801	−	0.515647i	$-0.827552\pi$
$397$		−	20.5484i		−	1.03129i	0.856801	−	0.515647i	$-0.172448\pi$
$398$	10.8045	+	6.23799i	0.541581	+	0.312682i
$399$		0			0
$400$	1.47993	+	2.56332i	0.0739965	+	0.128166i
$401$	−16.6549	−	28.8472i	−0.831708	−	1.44056i	−0.896682	−	0.442674i	$-0.854030\pi$
$401$	−16.6549	−	28.8472i	−0.831708	−	1.44056i	0.0649741	−	0.997887i	$-0.479304\pi$
$402$		0			0
$403$	29.6147	+	17.0981i	1.47522	+	0.851716i
$404$			4.67247i			0.232464i
$405$		0			0
$406$	10.1545			0.503959
$407$	3.91864	+	2.26243i	0.194240	+	0.112144i
$408$		0			0
$409$	8.59951	+	14.8948i	0.425219	+	0.736500i	0.996441	−	0.0842953i	$-0.0268639\pi$
$409$	8.59951	+	14.8948i	0.425219	+	0.736500i	−0.571222	+	0.820795i	$0.693531\pi$
$410$	3.03018	+	8.62924i	0.149650	+	0.426168i
$411$		0			0
$412$	0.551394	−	0.955042i	0.0271652	−	0.0470515i
$413$			30.9385i			1.52238i
$414$		0			0
$415$	20.0134			0.982419
$416$	3.86282	+	2.23020i	0.189391	+	0.109345i
$417$		0			0
$418$	0.0304985	+	0.0528250i	0.00149173	+	0.00258375i
$419$	−0.647062	−	1.12074i	−0.0316111	−	0.0547520i	0.849787	−	0.527126i	$-0.176730\pi$
$419$	−0.647062	−	1.12074i	−0.0316111	−	0.0547520i	−0.881398	+	0.472374i	$0.843397\pi$
$420$		0			0
$421$	16.9999	+	9.81488i	0.828523	+	0.478348i	0.853347	−	0.521344i	$-0.174569\pi$
$421$	16.9999	+	9.81488i	0.828523	+	0.478348i	−0.0248238	+	0.999692i	$0.507902\pi$
$422$		−	15.1860i		−	0.739242i
$423$		0			0
$424$			2.16886i			0.105329i
$425$	−20.6293	−	11.9103i	−1.00067	−	0.577736i
$426$		0			0
$427$	1.29115	−	0.745443i	0.0624829	−	0.0360745i
$428$	−3.27973	−	5.68066i	−0.158532	−	0.274585i
$429$		0			0
$430$	7.03141	−	12.1788i	0.339085	−	0.587312i
$431$	−0.0569818			−0.00274472			−0.00137236	−	0.999999i	$-0.500437\pi$
$431$	−0.0569818			−0.00274472			−0.00137236	+	0.999999i	$0.500437\pi$
$432$		0			0
$433$	14.1350			0.679283			0.339642	−	0.940555i	$-0.389694\pi$
$433$	14.1350			0.679283			0.339642	+	0.940555i	$0.389694\pi$
$434$	−15.8179	−	9.13245i	−0.759282	−	0.438372i
$435$		0			0
$436$	−11.7110	+	6.76135i	−0.560855	+	0.323810i
$437$	−0.0435165	+	0.0251243i	−0.00208168	+	0.00120186i
$438$		0			0
$439$	2.88979	+	1.66842i	0.137922	+	0.0796293i	0.567373	−	0.823461i	$-0.307960\pi$
$439$	2.88979	+	1.66842i	0.137922	+	0.0796293i	−0.429451	+	0.903090i	$0.641293\pi$
$440$			5.92821i			0.282616i
$441$		0			0
$442$	−35.8969			−1.70744
$443$	−12.8324	+	22.2263i	−0.609684	+	1.05600i	0.381608	+	0.924324i	$0.375370\pi$
$443$	−12.8324	+	22.2263i	−0.609684	+	1.05600i	−0.991292	+	0.131680i	$0.957963\pi$
$444$		0			0
$445$	0.759950	−	0.438757i	0.0360251	−	0.0207991i
$446$	−2.46975	−	4.27774i	−0.116946	−	0.202557i
$447$		0			0
$448$	−2.06322	−	1.19120i	−0.0974779	−	0.0562789i
$449$	36.0194			1.69986			0.849930	−	0.526895i	$-0.176644\pi$
$449$	36.0194			1.69986			0.849930	+	0.526895i	$0.176644\pi$
$450$		0			0
$451$	4.91197	−	26.1179i	0.231296	−	1.22984i
$452$	9.29636	−	16.1018i	0.437264	−	0.757364i
$453$		0			0
$454$	7.96322	−	4.59757i	0.373733	−	0.215775i
$455$	7.58907	+	13.1447i	0.355781	+	0.616231i
$456$		0			0
$457$	−9.97284	−	5.75782i	−0.466510	−	0.269340i	0.248268	−	0.968691i	$-0.420139\pi$
$457$	−9.97284	−	5.75782i	−0.466510	−	0.269340i	−0.714778	+	0.699352i	$0.753472\pi$
$458$		−	14.3915i		−	0.672471i
$459$		0			0
$460$	−4.88358			−0.227698
$461$	1.57003	−	2.71937i	0.0731236	−	0.126654i	−0.827145	−	0.561988i	$-0.810037\pi$
$461$	1.57003	−	2.71937i	0.0731236	−	0.126654i	0.900269	+	0.435335i	$0.143370\pi$
$462$		0			0
$463$	20.9825	−	12.1143i	0.975139	−	0.562997i	0.0743402	−	0.997233i	$-0.476315\pi$
$463$	20.9825	−	12.1143i	0.975139	−	0.562997i	0.900799	+	0.434236i	$0.142982\pi$
$464$	3.69126	−	2.13115i	0.171362	−	0.0989361i
$465$		0			0
$466$	−13.3497	−	7.70745i	−0.618413	−	0.357041i
$467$	18.9167			0.875358			0.437679	−	0.899131i	$-0.355801\pi$
$467$	18.9167			0.875358			0.437679	+	0.899131i	$0.355801\pi$
$468$		0			0
$469$	17.6113			0.813216
$470$	16.1894	+	9.34695i	0.746761	+	0.431142i
$471$		0			0
$472$	6.49314	+	11.2464i	0.298871	+	0.517660i
$473$	−35.3889	+	20.4318i	−1.62718	+	0.939455i
$474$		0			0
$475$	0.0376718	+	0.0217498i	0.00172850	+	0.000997952i
$476$	19.1733			0.878807
$477$		0			0
$478$			9.45892i			0.432641i
$479$	8.82523	+	5.09525i	0.403235	+	0.232808i	0.687879	−	0.725825i	$-0.258542\pi$
$479$	8.82523	+	5.09525i	0.403235	+	0.232808i	−0.284644	+	0.958633i	$0.591875\pi$
$480$		0			0
$481$	4.21129	−	2.43139i	0.192018	−	0.110862i
$482$	3.02525	+	5.23989i	0.137796	+	0.238670i
$483$		0			0
$484$	3.11306	−	5.39197i	0.141503	−	0.245090i
$485$			6.12775i			0.278247i
$486$		0			0
$487$	4.83348			0.219026			0.109513	−	0.993985i	$-0.465071\pi$
$487$	4.83348			0.219026			0.109513	+	0.993985i	$0.465071\pi$
$488$	0.312896	−	0.541952i	0.0141641	−	0.0245330i
$489$		0			0
$490$	0.945682	+	1.63797i	0.0427216	+	0.0739959i
$491$	−9.64383	−	16.7036i	−0.435220	−	0.753823i	0.562094	−	0.827074i	$-0.309996\pi$
$491$	−9.64383	−	16.7036i	−0.435220	−	0.753823i	−0.997314	+	0.0732505i	$0.976663\pi$
$492$		0			0
$493$	−17.1513	+	29.7069i	−0.772454	+	1.33793i
$494$	0.0655525			0.00294935
$495$		0			0
$496$	−7.66660			−0.344241
$497$	−13.2644	+	22.9746i	−0.594990	+	1.03055i
$498$		0			0
$499$	−15.3525	+	8.86378i	−0.687273	+	0.396797i	−0.802590	−	0.596531i	$-0.796545\pi$
$499$	−15.3525	+	8.86378i	−0.687273	+	0.396797i	0.115316	+	0.993329i	$0.463212\pi$
$500$	5.68467	+	9.84614i	0.254226	+	0.440333i
$501$		0			0
$502$	−10.9863	+	19.0289i	−0.490344	+	0.849301i
$503$			16.3294i			0.728093i	0.931381	+	0.364046i	$0.118605\pi$
$503$			16.3294i			0.728093i	−0.931381	+	0.364046i	$0.881395\pi$
$504$		0			0
$505$			6.67385i			0.296983i
$506$	12.2895	+	7.09532i	0.546333	+	0.315426i
$507$		0			0
$508$	−6.75594	−	11.7016i	−0.299746	−	0.519176i
$509$	−33.0122	+	19.0596i	−1.46324	+	0.844802i	−0.999160	−	0.0409912i	$-0.986948\pi$
$509$	−33.0122	+	19.0596i	−1.46324	+	0.844802i	−0.464080	+	0.885793i	$0.653615\pi$
$510$		0			0
$511$	6.02170	+	3.47663i	0.266384	+	0.153797i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		−	14.3229i		−	0.631754i
$515$	0.787575	−	1.36412i	0.0347047	−	0.0601103i
$516$		0			0
$517$	−27.1602	−	47.0429i	−1.19451	−	2.06894i
$518$	−2.24934	+	1.29866i	−0.0988304	+	0.0570598i
$519$		0			0
$520$	5.51740	+	3.18547i	0.241954	+	0.139692i
$521$		−	7.83296i		−	0.343168i	−0.985169	−	0.171584i	$-0.945111\pi$
$521$		−	7.83296i		−	0.343168i	0.985169	−	0.171584i	$-0.0548885\pi$
$522$		0			0
$523$	−12.0929			−0.528784			−0.264392	−	0.964415i	$-0.585171\pi$
$523$	−12.0929			−0.528784			−0.264392	+	0.964415i	$0.585171\pi$
$524$	−5.80001	+	10.0459i	−0.253375	+	0.438858i
$525$		0			0
$526$	11.3331	−	6.54315i	0.494145	−	0.285295i
$527$	53.4338	−	30.8500i	2.32761	−	1.34385i
$528$		0			0
$529$	5.65497	−	9.79469i	0.245868	−	0.425856i
$530$			3.09785i			0.134562i
$531$		0			0
$532$	−0.0350130			−0.00151801
$533$	−21.6686	−	18.6058i	−0.938571	−	0.805907i
$534$		0			0
$535$	−4.68455	−	8.11388i	−0.202531	−	0.350794i
$536$	6.40189	−	3.69613i	0.276520	−	0.159649i
$537$		0			0
$538$	5.70786	−	9.88631i	0.246083	−	0.426229i
$539$		−	5.49590i		−	0.236725i
$540$		0			0
$541$	−1.56971			−0.0674872			−0.0337436	−	0.999431i	$-0.510743\pi$
$541$	−1.56971			−0.0674872			−0.0337436	+	0.999431i	$0.510743\pi$
$542$	−10.7556	+	18.6293i	−0.461995	+	0.800198i
$543$		0			0
$544$	6.96968	−	4.02395i	0.298823	−	0.172525i
$545$	−16.7272	+	9.65746i	−0.716515	+	0.413680i
$546$		0			0
$547$	29.8157	+	17.2141i	1.27483	+	0.736022i	0.975893	−	0.218251i	$-0.0700352\pi$
$547$	29.8157	+	17.2141i	1.27483	+	0.736022i	0.298935	+	0.954273i	$0.403368\pi$
$548$		−	6.64127i		−	0.283701i
$549$		0			0
$550$		−	12.2847i		−	0.523822i
$551$	0.0313205	−	0.0542487i	0.00133430	−	0.00231107i
$552$		0			0
$553$	−15.0518	−	26.0705i	−0.640068	−	1.10863i
$554$	13.3063	+	23.0471i	0.565329	+	0.979179i
$555$		0			0
$556$	−6.59661	+	11.4257i	−0.279759	+	0.484556i
$557$			11.2004i			0.474574i	0.971440	+	0.237287i	$0.0762582\pi$
$557$			11.2004i			0.474574i	−0.971440	+	0.237287i	$0.923742\pi$
$558$		0			0
$559$			43.9154i			1.85743i
$560$	−2.94696	−	1.70143i	−0.124532	−	0.0718986i
$561$		0			0
$562$	−12.6222	+	7.28744i	−0.532436	+	0.307402i
$563$	−16.9275	+	9.77312i	−0.713411	+	0.411888i	−0.812323	−	0.583208i	$-0.801797\pi$
$563$	−16.9275	+	9.77312i	−0.713411	+	0.411888i	0.0989120	+	0.995096i	$0.468464\pi$
$564$		0			0
$565$	13.2783	−	22.9987i	0.558623	−	0.967563i
$566$	−26.9187			−1.13148
$567$		0			0
$568$			11.1353i			0.467228i
$569$	8.30154	−	14.3787i	0.348018	−	0.602786i	−0.637879	−	0.770137i	$-0.720188\pi$
$569$	8.30154	−	14.3787i	0.348018	−	0.602786i	0.985897	+	0.167351i	$0.0535213\pi$
$570$		0			0
$571$	−11.4782	+	6.62696i	−0.480349	+	0.277330i	−0.720562	−	0.693391i	$-0.756116\pi$
$571$	−11.4782	+	6.62696i	−0.480349	+	0.277330i	0.240213	+	0.970720i	$0.422783\pi$
$572$	−9.25631	−	16.0324i	−0.387026	−	0.670349i
$573$		0			0
$574$	11.5737	+	9.93777i	0.483075	+	0.414794i
$575$	10.1200			0.422033
$576$		0			0
$577$		−	24.7685i		−	1.03112i	−0.856852	−	0.515562i	$-0.827583\pi$
$577$		−	24.7685i		−	1.03112i	0.856852	−	0.515562i	$-0.172417\pi$
$578$	−23.8843	+	41.3689i	−0.993457	+	1.72072i
$579$		0			0
$580$	5.27235	−	3.04399i	0.218922	−	0.126395i
$581$	28.9092	−	16.6907i	1.19936	−	0.692448i
$582$		0			0
$583$	4.50085	−	7.79570i	0.186406	−	0.322865i
$584$	2.91859			0.120772
$585$		0			0
$586$		−	14.3302i		−	0.591974i
$587$	−1.86665	−	1.07771i	−0.0770450	−	0.0444820i	0.460983	−	0.887409i	$-0.347497\pi$
$587$	−1.86665	−	1.07771i	−0.0770450	−	0.0444820i	−0.538028	+	0.842927i	$0.680830\pi$
$588$		0			0
$589$	−0.0975772	+	0.0563362i	−0.00402060	+	0.00232129i
$590$	9.27437	+	16.0637i	0.381820	+	0.661332i
$591$		0			0
$592$	−0.545105	+	0.944150i	−0.0224037	+	0.0388043i
$593$		−	15.7753i		−	0.647813i	−0.946089	−	0.323906i	$-0.895004\pi$
$593$		−	15.7753i		−	0.647813i	0.946089	−	0.323906i	$-0.104996\pi$
$594$		0			0
$595$	27.3859			1.12271
$596$	9.45898	+	5.46114i	0.387455	+	0.223697i
$597$		0			0
$598$	13.2073	−	7.62523i	0.540086	−	0.311819i
$599$	4.87085	+	8.43655i	0.199017	+	0.344708i	0.948210	−	0.317644i	$-0.102892\pi$
$599$	4.87085	+	8.43655i	0.199017	+	0.344708i	−0.749193	+	0.662352i	$0.769558\pi$
$600$		0			0
$601$	6.71345	+	3.87601i	0.273847	+	0.158106i	0.630635	−	0.776080i	$-0.282795\pi$
$601$	6.71345	+	3.87601i	0.273847	+	0.158106i	−0.356787	+	0.934186i	$0.616128\pi$
$602$		−	23.4562i		−	0.956003i
$603$		0			0
$604$			9.72644i			0.395763i
$605$	4.44649	−	7.70154i	0.180775	−	0.313112i
$606$		0			0
$607$	−11.7573	−	20.3642i	−0.477212	−	0.826556i	0.522447	−	0.852672i	$-0.325019\pi$
$607$	−11.7573	−	20.3642i	−0.477212	−	0.826556i	−0.999659	+	0.0261160i	$0.991686\pi$
$608$	−0.0127276	+	0.00734827i	−0.000516171	+	0.000298012i
$609$		0			0
$610$	0.446920	−	0.774088i	0.0180953	−	0.0313419i
$611$	−58.3773			−2.36169
$612$		0			0
$613$	4.18208			0.168913			0.0844564	−	0.996427i	$-0.473085\pi$
$613$	4.18208			0.168913			0.0844564	+	0.996427i	$0.473085\pi$
$614$	−2.20823	+	3.82476i	−0.0891168	+	0.154355i
$615$		0			0
$616$	4.94400	+	8.56325i	0.199199	+	0.345023i
$617$	−5.28838	−	9.15975i	−0.212902	−	0.368758i	0.739719	−	0.672916i	$-0.234958\pi$
$617$	−5.28838	−	9.15975i	−0.212902	−	0.368758i	−0.952622	+	0.304158i	$0.901625\pi$
$618$		0			0
$619$	−3.11818	+	5.40084i	−0.125330	+	0.217078i	−0.921862	−	0.387518i	$-0.873332\pi$
$619$	−3.11818	+	5.40084i	−0.125330	+	0.217078i	0.796532	+	0.604597i	$0.206666\pi$
$620$	−10.9505			−0.439782
$621$		0			0
$622$			5.45436i			0.218700i
$623$	0.731828	−	1.26756i	0.0293201	−	0.0507839i
$624$		0			0
$625$	0.719956	+	1.24700i	0.0287983	+	0.0498800i
$626$	−4.98572	+	2.87851i	−0.199270	+	0.115048i
$627$		0			0
$628$	2.32471	+	1.34217i	0.0927662	+	0.0535586i
$629$		−	8.77391i		−	0.349839i
$630$		0			0
$631$	18.7111			0.744878			0.372439	−	0.928057i	$-0.378522\pi$
$631$	18.7111			0.744878			0.372439	+	0.928057i	$0.378522\pi$
$632$	−10.9430	−	6.31792i	−0.435287	−	0.251313i
$633$		0			0
$634$	20.7570	−	11.9841i	0.824365	−	0.475948i
$635$	−9.64973	−	16.7138i	−0.382938	−	0.663268i
$636$		0			0
$637$	−5.11506	−	2.95318i	−0.202666	−	0.117009i
$638$	−17.6904			−0.700369
$639$		0			0
$640$	−1.42833			−0.0564599
$641$	19.8200	+	11.4431i	0.782842	+	0.451974i	0.837437	−	0.546535i	$-0.184053\pi$
$641$	19.8200	+	11.4431i	0.782842	+	0.451974i	−0.0545946	+	0.998509i	$0.517387\pi$
$642$		0			0
$643$	40.9513	−	23.6432i	1.61496	−	0.932398i	0.626763	−	0.779210i	$-0.284379\pi$
$643$	40.9513	−	23.6432i	1.61496	−	0.932398i	0.988197	−	0.153188i	$-0.0489540\pi$
$644$	−7.05430	+	4.07280i	−0.277978	+	0.160491i
$645$		0			0
$646$	0.0591381	−	0.102430i	0.00232676	−	0.00403006i
$647$	6.75872			0.265713			0.132856	−	0.991135i	$-0.457585\pi$
$647$	6.75872			0.265713			0.132856	+	0.991135i	$0.457585\pi$
$648$		0			0
$649$		−	53.8987i		−	2.11571i
$650$	−11.4334	−	6.60109i	−0.448456	−	0.258916i
$651$		0			0
$652$	−10.4093	−	18.0294i	−0.407660	−	0.706088i
$653$	−6.16367	+	3.55859i	−0.241203	+	0.139259i	−0.615729	−	0.787958i	$-0.711139\pi$
$653$	−6.16367	+	3.55859i	−0.241203	+	0.139259i	0.374527	+	0.927216i	$0.377805\pi$
$654$		0			0
$655$	−8.28435	+	14.3489i	−0.323696	+	0.560659i
$656$	6.29280	+	1.18348i	0.245693	+	0.0462073i
$657$		0			0
$658$	31.1806			1.21555
$659$	10.8085	+	6.24028i	0.421039	+	0.243087i	0.695522	−	0.718505i	$-0.255173\pi$
$659$	10.8085	+	6.24028i	0.421039	+	0.243087i	−0.274483	+	0.961592i	$0.588507\pi$
$660$		0			0
$661$	−2.42439	−	4.19917i	−0.0942980	−	0.163329i	0.815017	−	0.579436i	$-0.196727\pi$
$661$	−2.42439	−	4.19917i	−0.0942980	−	0.163329i	−0.909315	+	0.416108i	$0.863394\pi$
$662$	16.5404	−	9.54960i	0.642860	−	0.371156i
$663$		0			0
$664$	7.00585	−	12.1345i	0.271880	−	0.470909i
$665$	−0.0500103			−0.00193931
$666$		0			0
$667$		−	14.5731i		−	0.564273i
$668$	−15.8135	−	9.12995i	−0.611844	−	0.353248i
$669$		0			0
$670$	9.14404	−	5.27932i	0.353265	−	0.203958i
$671$	−2.24934	+	1.29865i	−0.0868346	+	0.0501340i
$672$		0			0
$673$	−6.80282	−	3.92761i	−0.262230	−	0.151398i	0.363122	−	0.931742i	$-0.381711\pi$
$673$	−6.80282	−	3.92761i	−0.262230	−	0.151398i	−0.625351	+	0.780343i	$0.715044\pi$
$674$	28.8239			1.11026
$675$		0			0
$676$	−6.89522			−0.265201
$677$	−1.16112	+	2.01112i	−0.0446256	+	0.0772937i	−0.887475	−	0.460855i	$-0.847543\pi$
$677$	−1.16112	+	2.01112i	−0.0446256	+	0.0772937i	0.842850	+	0.538149i	$0.180876\pi$
$678$		0			0
$679$	5.11041	+	8.85149i	0.196120	+	0.339689i
$680$	9.95504	−	5.74754i	0.381758	−	0.220408i
$681$		0			0
$682$	27.5567	+	15.9099i	1.05520	+	0.609221i
$683$			7.17931i			0.274709i	0.990522	+	0.137354i	$0.0438599\pi$
$683$			7.17931i			0.274709i	−0.990522	+	0.137354i	$0.956140\pi$
$684$		0			0
$685$		−	9.48595i		−	0.362440i
$686$	17.1746	+	9.91575i	0.655729	+	0.378585i
$687$		0			0
$688$	−4.92281	−	8.52655i	−0.187680	−	0.325072i
$689$	−4.83699	−	8.37792i	−0.184275	−	0.319173i
$690$		0			0
$691$	−40.8938	−	23.6100i	−1.55567	−	0.898168i	−0.997663	−	0.0683333i	$-0.978232\pi$
$691$	−40.8938	−	23.6100i	−1.55567	−	0.898168i	−0.558010	−	0.829834i	$-0.688435\pi$
$692$	17.3833			0.660814
$693$		0			0
$694$			23.0556i			0.875177i
$695$	−9.42217	+	16.3197i	−0.357403	+	0.619040i
$696$		0			0
$697$	−48.6211	+	17.0734i	−1.84166	+	0.646702i
$698$	−7.42676	−	12.8635i	−0.281107	−	0.486892i
$699$		0			0
$700$	6.10684	+	3.52579i	0.230817	+	0.133262i
$701$	17.6566			0.666879			0.333439	−	0.942772i	$-0.391791\pi$
$701$	17.6566			0.666879			0.333439	+	0.942772i	$0.391791\pi$
$702$		0			0
$703$			0.0160223i			0.000604293i
$704$	3.59438	+	2.07522i	0.135468	+	0.0782127i
$705$		0			0
$706$	−4.63803	−	8.03331i	−0.174555	−	0.302338i
$707$	5.56585	+	9.64033i	0.209325	+	0.362562i
$708$		0			0
$709$	−29.8030	−	17.2068i	−1.11928	−	0.646214i	−0.178059	−	0.984020i	$-0.556982\pi$
$709$	−29.8030	−	17.2068i	−1.11928	−	0.646214i	−0.941216	+	0.337806i	$0.890315\pi$
$710$			15.9050i			0.596903i
$711$		0			0
$712$		−	0.614362i		−	0.0230242i
$713$	−13.1063	+	22.7009i	−0.490836	+	0.850154i
$714$		0			0
$715$	−13.2211	−	22.8996i	−0.494441	−	0.856398i
$716$	−18.6081	+	10.7434i	−0.695417	+	0.401499i
$717$		0			0
$718$	6.28169	−	10.8802i	0.234431	−	0.406046i
$719$			21.6311i			0.806705i	0.915045	+	0.403353i	$0.132155\pi$
$719$			21.6311i			0.806705i	−0.915045	+	0.403353i	$0.867845\pi$
$720$		0			0
$721$		−	2.62728i		−	0.0978450i
$722$	9.49989	−	16.4543i	0.353549	−	0.612365i
$723$		0			0
$724$	7.40323	−	4.27426i	0.275139	−	0.158851i
$725$	−10.9256	+	6.30790i	−0.405767	+	0.234270i
$726$		0			0
$727$	25.7779	+	14.8829i	0.956049	+	0.551975i	0.894955	−	0.446157i	$-0.147208\pi$
$727$	25.7779	+	14.8829i	0.956049	+	0.551975i	0.0610942	+	0.998132i	$0.480541\pi$
$728$	10.6265			0.393843
$729$		0			0
$730$	4.16873			0.154292
$731$	68.6208	+	39.6183i	2.53803	+	1.46533i
$732$		0			0
$733$	19.2444	+	33.3324i	0.710810	+	1.23116i	0.964554	+	0.263887i	$0.0850046\pi$
$733$	19.2444	+	33.3324i	0.710810	+	1.23116i	−0.253744	+	0.967271i	$0.581662\pi$
$734$	3.14993	+	5.45583i	0.116266	+	0.201378i
$735$		0			0
$736$	−1.70954	+	2.96101i	−0.0630144	+	0.109144i
$737$	−30.6811			−1.13015
$738$		0			0
$739$	−17.9498			−0.660294			−0.330147	−	0.943930i	$-0.607098\pi$
$739$	−17.9498			−0.660294			−0.330147	+	0.943930i	$0.607098\pi$
$740$	−0.778593	+	1.34856i	−0.0286216	+	0.0495741i
$741$		0			0
$742$	2.58354	+	4.47483i	0.0948448	+	0.164276i
$743$	8.81832	+	15.2738i	0.323513	+	0.560340i	0.981210	−	0.192942i	$-0.0618028\pi$
$743$	8.81832	+	15.2738i	0.323513	+	0.560340i	−0.657698	+	0.753282i	$0.728469\pi$
$744$		0			0
$745$	13.5106	+	7.80034i	0.494989	+	0.285782i
$746$	7.26703			0.266065
$747$		0			0
$748$	−33.4023			−1.22131
$749$	−13.5336	−	7.81363i	−0.494507	−	0.285504i
$750$		0			0
$751$	10.9998	−	6.35076i	0.401390	−	0.231743i	−0.285694	−	0.958321i	$-0.592224\pi$
$751$	10.9998	−	6.35076i	0.401390	−	0.231743i	0.687084	+	0.726578i	$0.258891\pi$
$752$	11.3345	−	6.54395i	0.413325	−	0.238633i
$753$		0			0
$754$	−9.50579	+	16.4645i	−0.346180	+	0.599602i
$755$			13.8926i			0.505604i
$756$		0			0
$757$			23.1460i			0.841255i	0.907233	+	0.420627i	$0.138190\pi$
$757$			23.1460i			0.841255i	−0.907233	+	0.420627i	$0.861810\pi$
$758$	6.23153	−	10.7933i	0.226339	−	0.392031i
$759$		0			0
$760$	−0.0181792	+	0.0104958i	−0.000659430	+	0.000380722i
$761$	4.25263	+	7.36577i	0.154158	+	0.267009i	0.932752	−	0.360519i	$-0.117400\pi$
$761$	4.25263	+	7.36577i	0.154158	+	0.267009i	−0.778594	+	0.627528i	$0.784067\pi$
$762$		0			0
$763$	−16.1082	+	27.9003i	−0.583157	+	1.01006i
$764$		−	0.877413i		−	0.0317437i
$765$		0			0
$766$		−	20.4317i		−	0.738227i
$767$	−50.1637	−	28.9620i	−1.81131	−	1.04576i
$768$		0			0
$769$	9.38633	+	16.2576i	0.338480	+	0.586264i	0.984147	−	0.177355i	$-0.0567540\pi$
$769$	9.38633	+	16.2576i	0.338480	+	0.586264i	−0.645667	+	0.763619i	$0.723421\pi$
$770$	7.06168	+	12.2312i	0.254485	+	0.440781i
$771$		0			0
$772$	−2.59152	−	1.49621i	−0.0932708	−	0.0538499i
$773$			27.7742i			0.998970i	0.866322	+	0.499485i	$0.166477\pi$
$773$			27.7742i			0.998970i	−0.866322	+	0.499485i	$0.833523\pi$
$774$		0			0
$775$	22.6921			0.815124
$776$	3.71537	+	2.14507i	0.133374	+	0.0770035i
$777$		0			0
$778$	−15.4480	−	26.7567i	−0.553838	−	0.959275i
$779$	0.0887886	−	0.0311783i	0.00318118	−	0.00111708i
$780$		0			0
$781$	23.1082	−	40.0246i	0.826878	−	1.43219i
$782$		−	27.5164i		−	0.983983i
$783$		0			0
$784$	1.32418			0.0472920
$785$	3.32047	+	1.91707i	0.118513	+	0.0684233i
$786$		0			0
$787$	−7.04430	−	12.2011i	−0.251102	−	0.434922i	0.712727	−	0.701441i	$-0.247460\pi$
$787$	−7.04430	−	12.2011i	−0.251102	−	0.434922i	−0.963830	+	0.266519i	$0.914126\pi$
$788$	−8.15025	−	14.1166i	−0.290341	−	0.502885i
$789$		0			0
$790$	−15.6302	−	9.02410i	−0.556097	−	0.321063i
$791$		−	44.2953i		−	1.57496i
$792$		0			0
$793$			2.79129i			0.0991215i
$794$	−17.7954	−	10.2742i	−0.631536	−	0.364617i
$795$		0			0
$796$	10.8045	−	6.23799i	0.382956	−	0.221100i
$797$	7.09250	+	12.2846i	0.251229	+	0.435142i	0.963865	−	0.266393i	$-0.0858318\pi$
$797$	7.09250	+	12.2846i	0.251229	+	0.435142i	−0.712635	+	0.701535i	$0.752498\pi$
$798$		0			0
$799$	−52.6650	+	91.2185i	−1.86315	+	3.22708i
$800$	2.95986			0.104647
$801$		0			0
$802$	−33.3099			−1.17621
$803$	−10.4905	−	6.05672i	−0.370203	−	0.213737i
$804$		0			0
$805$	−10.0759	+	5.81732i	−0.355128	+	0.205034i
$806$	29.6147	−	17.0981i	1.04313	−	0.602254i
$807$		0			0
$808$	4.04648	+	2.33624i	0.142355	+	0.0821885i
$809$		−	21.6209i		−	0.760149i	−0.924956	−	0.380074i	$-0.875898\pi$
$809$		−	21.6209i		−	0.760149i	0.924956	−	0.380074i	$-0.124102\pi$
$810$		0			0
$811$	13.4305			0.471609			0.235804	−	0.971801i	$-0.424228\pi$
$811$	13.4305			0.471609			0.235804	+	0.971801i	$0.424228\pi$
$812$	5.07725	−	8.79405i	0.178176	−	0.308611i
$813$		0			0
$814$	3.91864	−	2.26243i	0.137348	−	0.0792980i
$815$	−14.8680	−	25.7521i	−0.520802	−	0.902056i
$816$		0			0
$817$	−0.125311	−	0.0723482i	−0.00438407	−	0.00253114i
$818$	17.1990			0.601350
$819$		0			0
$820$	8.98823	+	1.69041i	0.313882	+	0.0590317i
$821$	−2.84720	+	4.93150i	−0.0993681	+	0.172111i	−0.911423	−	0.411470i	$-0.865015\pi$
$821$	−2.84720	+	4.93150i	−0.0993681	+	0.172111i	0.812055	+	0.583581i	$0.198349\pi$
$822$		0			0
$823$	0.522209	−	0.301498i	0.0182031	−	0.0105095i	−0.490871	−	0.871232i	$-0.663321\pi$
$823$	0.522209	−	0.301498i	0.0182031	−	0.0105095i	0.509074	+	0.860723i	$0.329988\pi$
$824$	−0.551394	−	0.955042i	−0.0192087	−	0.0332705i
$825$		0			0
$826$	26.7935	+	15.4693i	0.932266	+	0.538244i
$827$			27.1613i			0.944491i	0.881467	+	0.472245i	$0.156556\pi$
$827$			27.1613i			0.944491i	−0.881467	+	0.472245i	$0.843444\pi$
$828$		0			0
$829$	43.2145			1.50090			0.750451	−	0.660926i	$-0.229836\pi$
$829$	43.2145			1.50090			0.750451	+	0.660926i	$0.229836\pi$
$830$	10.0067	−	17.3321i	0.347337	−	0.601606i
$831$		0			0
$832$	3.86282	−	2.23020i	0.133919	−	0.0773184i
$833$	−9.22908	+	5.32841i	−0.319769	+	0.184619i
$834$		0			0
$835$	−22.5870	−	13.0406i	−0.781655	−	0.451289i
$836$	0.0609970			0.00210963
$837$		0			0
$838$	−1.29412			−0.0447048
$839$	25.8547	+	14.9272i	0.892604	+	0.515345i	0.874793	−	0.484496i	$-0.160997\pi$
$839$	25.8547	+	14.9272i	0.892604	+	0.515345i	0.0178107	+	0.999841i	$0.494330\pi$
$840$		0			0
$841$	−5.41641	−	9.38150i	−0.186773	−	0.323500i
$842$	16.9999	−	9.81488i	0.585854	−	0.338243i
$843$		0			0
$844$	−13.1514	−	7.59299i	−0.452691	−	0.261361i
$845$	−9.84868			−0.338805
$846$		0			0
$847$		−	14.8331i		−	0.509671i
$848$	1.87829	+	1.08443i	0.0645006	+	0.0372394i
$849$		0			0
$850$	−20.6293	+	11.9103i	−0.707579	+	0.408521i
$851$	1.86376	+	3.22812i	0.0638887	+	0.110659i
$852$		0			0
$853$	0.896369	−	1.55256i	0.0306911	−	0.0531585i	−0.850272	−	0.526344i	$-0.823563\pi$
$853$	0.896369	−	1.55256i	0.0306911	−	0.0531585i	0.880963	+	0.473185i	$0.156896\pi$
$854$		−	1.49089i		−	0.0510171i
$855$		0			0
$856$	−6.55946			−0.224198
$857$	3.67633	−	6.36759i	0.125581	−	0.217513i	−0.796379	−	0.604798i	$-0.793254\pi$
$857$	3.67633	−	6.36759i	0.125581	−	0.217513i	0.921960	+	0.387285i	$0.126587\pi$
$858$		0			0
$859$	−8.38450	−	14.5224i	−0.286076	−	0.495497i	0.686794	−	0.726852i	$-0.259017\pi$
$859$	−8.38450	−	14.5224i	−0.286076	−	0.495497i	−0.972869	+	0.231355i	$0.925684\pi$
$860$	−7.03141	−	12.1788i	−0.239769	−	0.415293i
$861$		0			0
$862$	−0.0284909	+	0.0493477i	−0.000970403	+	0.00168079i
$863$	53.1750			1.81010			0.905048	−	0.425309i	$-0.139834\pi$
$863$	53.1750			1.81010			0.905048	+	0.425309i	$0.139834\pi$
$864$		0			0
$865$	24.8291			0.844216
$866$	7.06749	−	12.2412i	0.240163	−	0.415974i
$867$		0			0
$868$	−15.8179	+	9.13245i	−0.536894	+	0.309976i
$869$	26.2221	+	45.4180i	0.889524	+	1.54070i
$870$		0			0
$871$	−16.4863	+	28.5550i	−0.558616	+	0.967551i
$872$			13.5227i			0.457936i
$873$		0			0
$874$			0.0502485i			0.00169968i
$875$	23.4574	+	13.5432i	0.793006	+	0.457842i
$876$		0			0
$877$	−1.84817	−	3.20112i	−0.0624083	−	0.108094i	0.833133	−	0.553073i	$-0.186545\pi$
$877$	−1.84817	−	3.20112i	−0.0624083	−	0.108094i	−0.895541	+	0.444978i	$0.853211\pi$
$878$	2.88979	−	1.66842i	0.0975256	−	0.0563064i
$879$		0			0
$880$	5.13398	+	2.96410i	0.173066	+	0.0999199i
$881$	−7.14596			−0.240753			−0.120377	−	0.992728i	$-0.538410\pi$
$881$	−7.14596			−0.240753			−0.120377	+	0.992728i	$0.538410\pi$
$882$		0			0
$883$			20.1401i			0.677769i	0.940828	+	0.338885i	$0.110050\pi$
$883$			20.1401i			0.677769i	−0.940828	+	0.338885i	$0.889950\pi$
$884$	−17.9484	+	31.0876i	−0.603671	+	1.04559i
$885$		0			0
$886$	12.8324	+	22.2263i	0.431112	+	0.746708i
$887$	19.3659	−	11.1809i	0.650244	−	0.375419i	−0.138305	−	0.990390i	$-0.544166\pi$
$887$	19.3659	−	11.1809i	0.650244	−	0.375419i	0.788550	+	0.614971i	$0.210832\pi$
$888$		0			0
$889$	−27.8779	−	16.0953i	−0.934996	−	0.539820i
$890$		−	0.877515i		−	0.0294144i
$891$		0			0
$892$	−4.93951			−0.165387
$893$	0.0961733	−	0.166577i	0.00321832	−	0.00557429i
$894$		0			0
$895$	−26.5786	+	15.3452i	−0.888424	+	0.512932i
$896$	−2.06322	+	1.19120i	−0.0689273	+	0.0397952i
$897$		0			0
$898$	18.0097	−	31.1937i	0.600992	−	1.04095i
$899$		−	32.6773i		−	1.08985i
$900$		0			0
$901$	−17.4547			−0.581502
$902$	−20.1628	−	17.3128i	−0.671346	−	0.576454i
$903$		0			0
$904$	−9.29636	−	16.1018i	−0.309192	−	0.535537i
$905$	10.5743	−	6.10506i	0.351501	−	0.202939i
$906$		0			0
$907$	12.4416	−	21.5495i	0.413118	−	0.715541i	−0.582111	−	0.813109i	$-0.697773\pi$
$907$	12.4416	−	21.5495i	0.413118	−	0.715541i	0.995229	+	0.0975686i	$0.0311065\pi$
$908$		−	9.19514i		−	0.305151i
$909$		0			0
$910$	15.1781			0.503151
$911$	20.6692	−	35.8001i	0.684802	−	1.18611i	−0.288697	−	0.957420i	$-0.593222\pi$
$911$	20.6692	−	35.8001i	0.684802	−	1.18611i	0.973499	−	0.228691i	$-0.0734446\pi$
$912$		0			0
$913$	−50.3634	+	29.0773i	−1.66679	+	0.962319i
$914$	−9.97284	+	5.75782i	−0.329872	+	0.190452i
$915$		0			0
$916$	−12.4634	−	7.19575i	−0.411803	−	0.237754i
$917$			27.6359i			0.912617i
$918$		0			0
$919$			5.81914i			0.191956i	0.995383	+	0.0959778i	$0.0305978\pi$
$919$			5.81914i			0.191956i	−0.995383	+	0.0959778i	$0.969402\pi$
$920$	−2.44179	+	4.22930i	−0.0805034	+	0.139436i
$921$		0			0
$922$	−1.57003	−	2.71937i	−0.0517062	−	0.0895578i
$923$	−24.8340	−	43.0138i	−0.817423	−	1.41582i
$924$		0			0
$925$	1.61344	−	2.79455i	0.0530495	−	0.0918844i
$926$		−	24.2285i		−	0.796198i
$927$		0			0
$928$		−	4.26230i		−	0.139917i
$929$	−50.7596	−	29.3061i	−1.66537	−	0.961500i	−0.970086	−	0.242763i	$-0.921946\pi$
$929$	−50.7596	−	29.3061i	−1.66537	−	0.961500i	−0.695282	−	0.718737i	$-0.744721\pi$
$930$		0			0
$931$	0.0168535	−	0.00973039i	0.000552352	−	0.000318901i
$932$	−13.3497	+	7.70745i	−0.437284	+	0.252466i
$933$		0			0
$934$	9.45833	−	16.3823i	0.309486	−	0.536045i
$935$	−47.7096			−1.56027
$936$		0			0
$937$			6.28736i			0.205399i	0.994712	+	0.102700i	$0.0327480\pi$
$937$			6.28736i			0.205399i	−0.994712	+	0.102700i	$0.967252\pi$
$938$	8.80567	−	15.2519i	0.287515	−	0.497991i
$939$		0			0
$940$	16.1894	−	9.34695i	0.528039	−	0.304864i
$941$	28.1013	+	48.6729i	0.916077	+	1.58669i	0.805317	+	0.592845i	$0.201995\pi$
$941$	28.1013	+	48.6729i	0.916077	+	1.58669i	0.110761	+	0.993847i	$0.464671\pi$
$942$		0			0
$943$	14.2621	−	16.6098i	0.464437	−	0.540890i
$944$	12.9863			0.422667
$945$		0			0
$946$			40.8636i			1.32859i
$947$	−11.6205	+	20.1273i	−0.377616	+	0.654051i	−0.990715	−	0.135956i	$-0.956589\pi$
$947$	−11.6205	+	20.1273i	−0.377616	+	0.654051i	0.613099	+	0.790006i	$0.289923\pi$
$948$		0			0
$949$	−11.2740	+	6.50906i	−0.365970	+	0.211293i
$950$	0.0376718	−	0.0217498i	0.00122224	−	0.000705658i
$951$		0			0
$952$	9.58665	−	16.6046i	0.310705	−	0.538157i
$953$	−19.6687			−0.637133			−0.318566	−	0.947901i	$-0.603201\pi$
$953$	−19.6687			−0.637133			−0.318566	+	0.947901i	$0.603201\pi$
$954$		0			0
$955$		−	1.25324i		−	0.0405538i
$956$	8.19166	+	4.72946i	0.264937	+	0.152962i
$957$		0			0
$958$	8.82523	−	5.09525i	0.285130	−	0.164620i
$959$	−7.91108	−	13.7024i	−0.255462	−	0.442473i
$960$		0			0
$961$	−13.8884	+	24.0554i	−0.448013	+	0.775982i
$962$		−	4.86278i		−	0.156782i
$963$		0			0
$964$	6.05050			0.194874
$965$	−3.70156	−	2.13709i	−0.119157	−	0.0687955i
$966$		0			0
$967$	29.7728	−	17.1894i	0.957430	−	0.552772i	0.0620486	−	0.998073i	$-0.480237\pi$
$967$	29.7728	−	17.1894i	0.957430	−	0.552772i	0.895381	+	0.445301i	$0.146903\pi$
$968$	−3.11306	−	5.39197i	−0.100057	−	0.173305i
$969$		0			0
$970$	5.30679	+	3.06388i	0.170391	+	0.0983751i
$971$			0.680693i			0.0218445i	0.999940	+	0.0109222i	$0.00347672\pi$
$971$			0.680693i			0.0218445i	−0.999940	+	0.0109222i	$0.996523\pi$
$972$		0			0
$973$			31.4315i			1.00765i
$974$	2.41674	−	4.18592i	0.0774373	−	0.134125i
$975$		0			0
$976$	−0.312896	−	0.541952i	−0.0100156	−	0.0173475i
$977$	−46.5672	+	26.8856i	−1.48982	+	0.860146i	−0.999932	−	0.0116420i	$-0.996294\pi$
$977$	−46.5672	+	26.8856i	−1.48982	+	0.860146i	−0.489884	+	0.871788i	$0.662961\pi$
$978$		0			0
$979$	−1.27494	+	2.20825i	−0.0407471	+	0.0705761i
$980$	1.89136			0.0604174
$981$		0			0
$982$	−19.2877			−0.615494
$983$	25.3232	−	43.8611i	0.807686	−	1.39895i	−0.106777	−	0.994283i	$-0.534053\pi$
$983$	25.3232	−	43.8611i	0.807686	−	1.39895i	0.914463	−	0.404669i	$-0.132613\pi$
$984$		0			0
$985$	−11.6413	−	20.1633i	−0.370922	−	0.642456i
$986$	17.1513	+	29.7069i	0.546207	+	0.946059i
$987$		0			0
$988$	0.0327762	−	0.0567701i	0.00104275	−	0.00180610i
$989$	−33.6629			−1.07042
$990$		0			0
$991$		−	19.0963i		−	0.606613i	−0.952893	−	0.303306i	$-0.901909\pi$
$991$		−	19.0963i		−	0.606613i	0.952893	−	0.303306i	$-0.0980906\pi$
$992$	−3.83330	+	6.63947i	−0.121707	+	0.210804i
$993$		0			0
$994$	13.2644	+	22.9746i	0.420721	+	0.728711i
$995$	15.4325	−	8.90993i	0.489242	−	0.282464i
$996$		0			0
$997$	−38.5931	−	22.2817i	−1.22226	−	0.705670i	−0.256857	−	0.966449i	$-0.582687\pi$
$997$	−38.5931	−	22.2817i	−1.22226	−	0.705670i	−0.965398	+	0.260780i	$0.916020\pi$
$998$			17.7276i			0.561156i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2214.2.i.b.1639.7		36
3.2	odd	2		738.2.i.b.655.2	yes	36
9.4	even	3	inner	2214.2.i.b.901.8		36
9.5	odd	6		738.2.i.b.409.17	yes	36
41.40	even	2	inner	2214.2.i.b.1639.8		36
123.122	odd	2		738.2.i.b.655.17	yes	36
369.40	even	6	inner	2214.2.i.b.901.7		36
369.122	odd	6		738.2.i.b.409.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.i.b.409.2	✓	36	369.122	odd	6
738.2.i.b.409.17	yes	36	9.5	odd	6
738.2.i.b.655.2	yes	36	3.2	odd	2
738.2.i.b.655.17	yes	36	123.122	odd	2
2214.2.i.b.901.7		36	369.40	even	6	inner
2214.2.i.b.901.8		36	9.4	even	3	inner
2214.2.i.b.1639.7		36	1.1	even	1	trivial
2214.2.i.b.1639.8		36	41.40	even	2	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:	\( N \)	\(=\)	\( 2214 = 2 \cdot 3^{3} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2214.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.714167 - 1.23697i) q^{5} +(-2.06322 - 1.19120i) q^{7} -1.00000 q^{8} -1.42833 q^{10} +(3.59438 + 2.07522i) q^{11} +(3.86282 - 2.23020i) q^{13} +(-2.06322 + 1.19120i) q^{14} +(-0.500000 + 0.866025i) q^{16} -8.04790i q^{17} +0.0146965i q^{19} +(-0.714167 + 1.23697i) q^{20} +(3.59438 - 2.07522i) q^{22} +(1.70954 + 2.96101i) q^{23} +(1.47993 - 2.56332i) q^{25} -4.46041i q^{26} +2.38240i q^{28} +(-3.69126 - 2.13115i) q^{29} +(3.83330 + 6.63947i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.96968 - 4.02395i) q^{34} +3.40286i q^{35} +1.09021 q^{37} +(0.0127276 + 0.00734827i) q^{38} +(0.714167 + 1.23697i) q^{40} +(-2.12147 - 6.04147i) q^{41} +(-4.92281 + 8.52655i) q^{43} -4.15044i q^{44} +3.41907 q^{46} +(-11.3345 - 6.54395i) q^{47} +(-0.662088 - 1.14677i) q^{49} +(-1.47993 - 2.56332i) q^{50} +(-3.86282 - 2.23020i) q^{52} -2.16886i q^{53} -5.92821i q^{55} +(2.06322 + 1.19120i) q^{56} +(-3.69126 + 2.13115i) q^{58} +(-6.49314 - 11.2464i) q^{59} +(-0.312896 + 0.541952i) q^{61} +7.66660 q^{62} +1.00000 q^{64} +(-5.51740 - 3.18547i) q^{65} +(-6.40189 + 3.69613i) q^{67} +(-6.96968 + 4.02395i) q^{68} +(2.94696 + 1.70143i) q^{70} -11.1353i q^{71} -2.91859 q^{73} +(0.545105 - 0.944150i) q^{74} +(0.0127276 - 0.00734827i) q^{76} +(-4.94400 - 8.56325i) q^{77} +(10.9430 + 6.31792i) q^{79} +1.42833 q^{80} +(-6.29280 - 1.18348i) q^{82} +(-7.00585 + 12.1345i) q^{83} +(-9.95504 + 5.74754i) q^{85} +(4.92281 + 8.52655i) q^{86} +(-3.59438 - 2.07522i) q^{88} +0.614362i q^{89} -10.6265 q^{91} +(1.70954 - 2.96101i) q^{92} +(-11.3345 + 6.54395i) q^{94} +(0.0181792 - 0.0104958i) q^{95} +(-3.71537 - 2.14507i) q^{97} -1.32418 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 4 * q^5 - 36 * q^8 - 8 * q^10 - 18 * q^16 - 4 * q^20 + 4 * q^23 - 26 * q^25 + 8 * q^31 + 18 * q^32 - 60 * q^37 + 4 * q^40 + 6 * q^41 + 6 * q^43 + 8 * q^46 + 38 * q^49 + 26 * q^50 - 22 * q^59 - 46 * q^61 + 16 * q^62 + 36 * q^64 + 64 * q^73 - 30 * q^74 + 2 * q^77 + 8 * q^80 + 12 * q^82 - 68 * q^83 - 6 * q^86 + 36 * q^91 + 4 * q^92 + 76 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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