LMFDB - Embedded newform 2214.2.i.b.901.7

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			901.7
Character	$\chi$	$=$	2214.901
Dual form			2214.2.i.b.1639.7

$q$-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 $\left(\mathbb{Z}/2214\mathbb{Z}\right)^\times$.

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

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	−0.980360	−	0.197217i	$-0.936810\pi$
$5$	−0.714167	+	1.23697i	−0.319385	+	0.553191i	0.660975	+	0.750408i	$0.270143\pi$
$6$		0			0
$7$	−2.06322	+	1.19120i	−0.779823	+	0.450231i	−0.836368	−	0.548169i	$-0.815325\pi$
$7$	−2.06322	+	1.19120i	−0.779823	+	0.450231i	0.0565445	+	0.998400i	$0.481992\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.42833			−0.451679
$11$	3.59438	−	2.07522i	1.08375	−	0.625702i	0.151842	−	0.988405i	$-0.451479\pi$
$11$	3.59438	−	2.07522i	1.08375	−	0.625702i	0.931905	+	0.362703i	$0.118146\pi$
$12$		0			0
$13$	3.86282	+	2.23020i	1.07135	+	0.618547i	0.928551	−	0.371204i	$-0.121055\pi$
$13$	3.86282	+	2.23020i	1.07135	+	0.618547i	0.142803	+	0.989751i	$0.454388\pi$
$14$	−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	$0.430050\pi$
$17$			8.04790i			1.95190i	−0.217990	+	0.975951i	$0.569950\pi$
$18$		0			0
$19$		−	0.0146965i		−	0.00337162i	−0.999999	−	0.00168581i	$-0.999463\pi$
$19$		−	0.0146965i		−	0.00337162i	0.999999	−	0.00168581i	$-0.000536610\pi$
$20$	−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	−0.630904	−	0.775861i	$-0.717316\pi$
$23$	1.70954	−	2.96101i	0.356463	−	0.617412i	0.987367	+	0.158449i	$0.0506492\pi$
$24$		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	−0.801905	−	0.597452i	$-0.796180\pi$
$29$	−3.69126	+	2.13115i	−0.685449	+	0.395744i	0.116456	+	0.993196i	$0.462847\pi$
$30$		0			0
$31$	3.83330	−	6.63947i	0.688481	−	1.19248i	−0.283848	−	0.958869i	$-0.591611\pi$
$31$	3.83330	−	6.63947i	0.688481	−	1.19248i	0.972329	−	0.233615i	$-0.0750557\pi$
$32$	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	−0.947474	−	0.319834i	$-0.896373\pi$
$43$	−4.92281	−	8.52655i	−0.750721	−	1.30029i	0.196752	−	0.980453i	$-0.436960\pi$
$44$			4.15044i			0.625702i
$45$		0			0
$46$	3.41907			0.504115
$47$	−11.3345	+	6.54395i	−1.65330	+	0.954533i	−0.677597	+	0.735433i	$0.736979\pi$
$47$	−11.3345	+	6.54395i	−1.65330	+	0.954533i	−0.975702	+	0.219100i	$0.929688\pi$
$48$		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	$0.0475918\pi$
$53$			2.16886i			0.297915i	−0.988844	+	0.148958i	$0.952408\pi$
$54$		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	0.0399952	+	0.999200i	$0.487266\pi$
$59$	−6.49314	+	11.2464i	−0.845335	+	1.46416i	−0.885330	+	0.464963i	$0.846068\pi$
$60$		0			0
$61$	−0.312896	−	0.541952i	−0.0400622	−	0.0693898i	0.845299	−	0.534293i	$-0.179422\pi$
$61$	−0.312896	−	0.541952i	−0.0400622	−	0.0693898i	−0.885361	+	0.464904i	$0.846089\pi$
$62$	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	0.0550639	−	0.998483i	$-0.482464\pi$
$67$	−6.40189	−	3.69613i	−0.782116	−	0.451555i	−0.837180	+	0.546928i	$0.815797\pi$
$68$	−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	$0.229766\pi$
$71$			11.1353i			1.32152i	−0.750597	+	0.660760i	$0.770234\pi$
$72$		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	0.263903	−	0.964549i	$-0.414990\pi$
$79$	10.9430	−	6.31792i	1.23118	−	0.710821i	0.967276	+	0.253728i	$0.0816568\pi$
$80$	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	−0.938110	−	0.346337i	$-0.887425\pi$
$83$	−7.00585	−	12.1345i	−0.768992	−	1.33193i	0.169118	−	0.985596i	$-0.445908\pi$
$84$		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	$-0.989634\pi$
$89$		−	0.614362i		−	0.0651223i	0.999470	−	0.0325611i	$-0.0103664\pi$
$90$		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	−0.676616	−	0.736336i	$-0.736554\pi$
$97$	−3.71537	+	2.14507i	−0.377239	+	0.217799i	0.299378	+	0.954135i	$0.403221\pi$
$98$	−1.32418			−0.133762
$99$		0			0
$100$	−2.95986			−0.295986
$101$	−4.04648	+	2.33624i	−0.402640	+	0.232464i	−0.687622	−	0.726068i	$-0.741346\pi$
$101$	−4.04648	+	2.33624i	−0.402640	+	0.232464i	0.284982	+	0.958533i	$0.408012\pi$
$102$		0			0
$103$	0.551394	−	0.955042i	0.0543304	−	0.0941031i	−0.837581	−	0.546313i	$-0.816031\pi$
$103$	0.551394	−	0.955042i	0.0543304	−	0.0941031i	0.891912	+	0.452210i	$0.149364\pi$
$104$	−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	$0.224235\pi$
$109$			13.5227i			1.29524i	−0.761964	+	0.647619i	$0.775765\pi$
$110$	−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	0.0172638	−	0.999851i	$-0.494504\pi$
$113$	9.29636	−	16.1018i	0.874528	−	1.51473i	0.857264	−	0.514876i	$-0.172162\pi$
$114$		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	0.493220	+	0.869904i	$0.335820\pi$
$131$	−5.80001	+	10.0459i	−0.506749	+	0.877715i	−0.999969	+	0.00781101i	$0.997514\pi$
$132$		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	−0.233764	−	0.972293i	$-0.575104\pi$
$137$	5.75151	−	3.32063i	0.491384	−	0.283701i	0.725149	+	0.688592i	$0.241771\pi$
$138$		0			0
$139$	−6.59661	+	11.4257i	−0.559517	+	0.969113i	0.438019	+	0.898966i	$0.355680\pi$
$139$	−6.59661	+	11.4257i	−0.559517	+	0.969113i	−0.997537	+	0.0701470i	$0.977653\pi$
$140$	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	0.0597135	−	0.998216i	$-0.480981\pi$
$149$	−9.45898	−	5.46114i	−0.774910	−	0.447394i	−0.834623	+	0.550821i	$0.814315\pi$
$150$		0			0
$151$	−8.42334	+	4.86322i	−0.685482	+	0.395763i	−0.801917	−	0.597435i	$-0.796187\pi$
$151$	−8.42334	+	4.86322i	−0.685482	+	0.395763i	0.116435	+	0.993198i	$0.462853\pi$
$152$			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	0.404357	−	0.914601i	$-0.367495\pi$
$157$	−2.32471	−	1.34217i	−0.185532	−	0.107117i	−0.589889	+	0.807484i	$0.700829\pi$
$158$	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	0.965702	−	0.259652i	$-0.0836080\pi$
$167$	15.8135	+	9.12995i	1.22369	+	0.706496i	0.257985	+	0.966149i	$0.416941\pi$
$168$		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	−0.980402	−	0.197006i	$-0.936878\pi$
$173$	−8.69165	−	15.0544i	−0.660814	−	1.14456i	0.319589	−	0.947556i	$-0.396455\pi$
$174$		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	$0.296763\pi$
$179$			21.4868i			1.60600i	−0.595981	+	0.802999i	$0.703237\pi$
$180$		0			0
$181$		−	8.54851i		−	0.635406i	−0.948190	−	0.317703i	$-0.897089\pi$
$181$		−	8.54851i		−	0.635406i	0.948190	−	0.317703i	$-0.102911\pi$
$182$	−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	−0.472257	−	0.881461i	$-0.656561\pi$
$191$	0.759862	−	0.438706i	0.0549817	−	0.0317437i	0.527239	+	0.849717i	$0.323227\pi$
$192$		0			0
$193$	2.59152	+	1.49621i	0.186542	+	0.107700i	0.590363	−	0.807138i	$-0.298985\pi$
$193$	2.59152	+	1.49621i	0.186542	+	0.107700i	−0.403821	+	0.914838i	$0.632318\pi$
$194$	−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	$-0.854198\pi$
$199$		−	12.4760i		−	0.884399i	0.896917	−	0.442199i	$-0.145802\pi$
$200$	−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	0.878943	−	0.476928i	$-0.158250\pi$
$211$	13.1514	+	7.59299i	0.905383	+	0.522723i	0.0264399	+	0.999650i	$0.491583\pi$
$212$	−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	0.936793	−	0.349885i	$-0.113779\pi$
$223$	2.46975	+	4.27774i	0.165387	+	0.286459i	−0.771406	+	0.636344i	$0.780446\pi$
$224$			2.38240i			0.159181i
$225$		0			0
$226$	18.5927			1.23677
$227$	7.96322	−	4.59757i	0.528538	−	0.305151i	−0.211883	−	0.977295i	$-0.567960\pi$
$227$	7.96322	−	4.59757i	0.528538	−	0.305151i	0.740421	+	0.672144i	$0.234626\pi$
$228$		0			0
$229$	12.4634	+	7.19575i	0.823605	+	0.475509i	0.851658	−	0.524098i	$-0.175597\pi$
$229$	12.4634	+	7.19575i	0.823605	+	0.475509i	−0.0280530	+	0.999606i	$0.508931\pi$
$230$	−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	$0.168482\pi$
$233$			15.4149i			1.00986i	−0.863159	+	0.504932i	$0.831518\pi$
$234$		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	0.211091	−	0.977466i	$-0.432298\pi$
$239$	−8.19166	−	4.72946i	−0.529875	−	0.305923i	−0.740965	+	0.671543i	$0.765632\pi$
$240$		0			0
$241$	−3.02525	−	5.23989i	−0.194874	−	0.337531i	0.751985	−	0.659180i	$-0.229096\pi$
$241$	−3.02525	−	5.23989i	−0.194874	−	0.337531i	−0.946859	+	0.321649i	$0.895763\pi$
$242$	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	0.834206	−	0.551452i	$-0.185926\pi$
$257$	12.4040	+	7.16143i	0.773738	+	0.446718i	−0.0604686	+	0.998170i	$0.519260\pi$
$258$		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	−0.108083	−	0.994142i	$-0.534471\pi$
$263$	11.3331	−	6.54315i	0.698827	−	0.403468i	0.806910	+	0.590674i	$0.201138\pi$
$264$		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	−0.919945	−	0.392048i	$-0.871767\pi$
$277$	−13.3063	−	23.0471i	−0.799496	−	1.38477i	0.120449	−	0.992720i	$-0.461567\pi$
$278$	−13.1932			−0.791277
$279$		0			0
$280$			3.40286i			0.203360i
$281$	−12.6222	+	7.28744i	−0.752978	+	0.434732i	−0.826769	−	0.562542i	$-0.809824\pi$
$281$	−12.6222	+	7.28744i	−0.752978	+	0.434732i	0.0737909	+	0.997274i	$0.476490\pi$
$282$		0			0
$283$	−13.4593	+	23.3123i	−0.800075	+	1.38577i	0.119491	+	0.992835i	$0.461874\pi$
$283$	−13.4593	+	23.3123i	−0.800075	+	1.38577i	−0.919566	+	0.392935i	$0.871460\pi$
$284$	−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	0.816596	−	0.577209i	$-0.195858\pi$
$293$	12.4103	+	7.16509i	0.725017	+	0.418589i	−0.0915794	+	0.995798i	$0.529192\pi$
$294$		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	0.360059	−	0.932929i	$-0.382756\pi$
$311$	−4.72361	−	2.72718i	−0.267852	−	0.154644i	−0.627911	+	0.778285i	$0.716090\pi$
$312$		0			0
$313$	−4.98572	+	2.87851i	−0.281810	+	0.162703i	−0.634242	−	0.773134i	$-0.718688\pi$
$313$	−4.98572	+	2.87851i	−0.281810	+	0.162703i	0.352433	+	0.935837i	$0.385355\pi$
$314$		−	2.68435i		−	0.151486i
$315$		0			0
$316$			12.6358i			0.710821i
$317$	20.7570	−	11.9841i	1.16583	−	0.673091i	0.213135	−	0.977023i	$-0.431633\pi$
$317$	20.7570	−	11.9841i	1.16583	−	0.673091i	0.952694	+	0.303931i	$0.0982994\pi$
$318$		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	0.0289870	−	0.999580i	$-0.490772\pi$
$331$	16.5404	−	9.54960i	0.909142	−	0.524893i	0.880155	+	0.474686i	$0.157439\pi$
$332$	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	−0.143887	−	0.989594i	$-0.545960\pi$
$337$	14.4120	−	24.9623i	0.785070	−	1.35978i	0.928957	−	0.370187i	$-0.120706\pi$
$338$	−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	−0.143177	−	0.989697i	$-0.545732\pi$
$347$	−19.9667	−	11.5278i	−1.07187	−	0.618844i	−0.928691	+	0.370853i	$0.879065\pi$
$348$		0			0
$349$	7.42676	+	12.8635i	0.397545	+	0.688569i	0.993422	−	0.114507i	$-0.0365288\pi$
$349$	7.42676	+	12.8635i	0.397545	+	0.688569i	−0.595877	+	0.803076i	$0.703195\pi$
$350$		−	7.05157i		−	0.376922i
$351$		0			0
$352$		−	4.15044i		−	0.221219i
$353$	4.63803	+	8.03331i	0.246858	+	0.427570i	0.962652	−	0.270741i	$-0.0872687\pi$
$353$	4.63803	+	8.03331i	0.246858	+	0.427570i	−0.715795	+	0.698311i	$0.753935\pi$
$354$		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	0.772026	−	0.635591i	$-0.219243\pi$
$367$	−3.14993	−	5.45583i	−0.164425	−	0.284792i	−0.936451	+	0.350799i	$0.885910\pi$
$368$	−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	−0.756493	−	0.654002i	$-0.773089\pi$
$373$	3.63352	−	6.29343i	0.188136	−	0.325862i	0.944629	+	0.328141i	$0.106422\pi$
$374$	−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	0.878541	−	0.477667i	$-0.158518\pi$
$383$	17.6944	+	10.2158i	0.904139	+	0.522005i	0.0255984	+	0.999672i	$0.491851\pi$
$384$		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	0.930042	+	0.367453i	$0.119770\pi$
$389$	15.4480	+	26.7567i	0.783245	+	1.35662i	−0.146798	+	0.989167i	$0.546897\pi$
$390$		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	$0.172448\pi$
$397$			20.5484i			1.03129i	−0.856801	+	0.515647i	$0.827552\pi$
$398$	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	0.0649741	+	0.997887i	$0.479304\pi$
$401$	−16.6549	+	28.8472i	−0.831708	+	1.44056i	−0.896682	+	0.442674i	$0.854030\pi$
$402$		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	−0.571222	−	0.820795i	$-0.693531\pi$
$409$	8.59951	−	14.8948i	0.425219	−	0.736500i	0.996441	+	0.0842953i	$0.0268639\pi$
$410$	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	−0.881398	−	0.472374i	$-0.843397\pi$
$419$	−0.647062	+	1.12074i	−0.0316111	+	0.0547520i	0.849787	+	0.527126i	$0.176730\pi$
$420$		0			0
$421$	16.9999	−	9.81488i	0.828523	−	0.478348i	−0.0248238	−	0.999692i	$-0.507902\pi$
$421$	16.9999	−	9.81488i	0.828523	−	0.478348i	0.853347	+	0.521344i	$0.174569\pi$
$422$			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	−0.429451	−	0.903090i	$-0.641293\pi$
$439$	2.88979	−	1.66842i	0.137922	−	0.0796293i	0.567373	+	0.823461i	$0.307960\pi$
$440$		−	5.92821i		−	0.282616i
$441$		0			0
$442$	−35.8969			−1.70744
$443$	−12.8324	−	22.2263i	−0.609684	−	1.05600i	−0.991292	−	0.131680i	$-0.957963\pi$
$443$	−12.8324	−	22.2263i	−0.609684	−	1.05600i	0.381608	−	0.924324i	$-0.375370\pi$
$444$		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	−0.714778	−	0.699352i	$-0.753472\pi$
$457$	−9.97284	+	5.75782i	−0.466510	+	0.269340i	0.248268	+	0.968691i	$0.420139\pi$
$458$			14.3915i			0.672471i
$459$		0			0
$460$	−4.88358			−0.227698
$461$	1.57003	+	2.71937i	0.0731236	+	0.126654i	0.900269	−	0.435335i	$-0.143370\pi$
$461$	1.57003	+	2.71937i	0.0731236	+	0.126654i	−0.827145	+	0.561988i	$0.810037\pi$
$462$		0			0
$463$	20.9825	+	12.1143i	0.975139	+	0.562997i	0.900799	−	0.434236i	$-0.142982\pi$
$463$	20.9825	+	12.1143i	0.975139	+	0.562997i	0.0743402	+	0.997233i	$0.476315\pi$
$464$	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	−0.284644	−	0.958633i	$-0.591875\pi$
$479$	8.82523	−	5.09525i	0.403235	−	0.232808i	0.687879	+	0.725825i	$0.258542\pi$
$480$		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	−0.997314	−	0.0732505i	$-0.976663\pi$
$491$	−9.64383	+	16.7036i	−0.435220	+	0.753823i	0.562094	+	0.827074i	$0.309996\pi$
$492$		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	0.115316	−	0.993329i	$-0.463212\pi$
$499$	−15.3525	−	8.86378i	−0.687273	−	0.396797i	−0.802590	+	0.596531i	$0.796545\pi$
$500$	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	$-0.881395\pi$
$503$		−	16.3294i		−	0.728093i	0.931381	−	0.364046i	$-0.118605\pi$
$504$		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	−0.464080	−	0.885793i	$-0.653615\pi$
$509$	−33.0122	−	19.0596i	−1.46324	−	0.844802i	−0.999160	+	0.0409912i	$0.986948\pi$
$510$		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	$0.0548885\pi$
$521$			7.83296i			0.343168i	−0.985169	+	0.171584i	$0.945111\pi$
$522$		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	0.298935	−	0.954273i	$-0.403368\pi$
$547$	29.8157	−	17.2141i	1.27483	−	0.736022i	0.975893	+	0.218251i	$0.0700352\pi$
$548$			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	$-0.923742\pi$
$557$		−	11.2004i		−	0.474574i	0.971440	−	0.237287i	$-0.0762582\pi$
$558$		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	0.0989120	−	0.995096i	$-0.468464\pi$
$563$	−16.9275	−	9.77312i	−0.713411	−	0.411888i	−0.812323	+	0.583208i	$0.801797\pi$
$564$		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	0.985897	−	0.167351i	$-0.0535213\pi$
$569$	8.30154	+	14.3787i	0.348018	+	0.602786i	−0.637879	+	0.770137i	$0.720188\pi$
$570$		0			0
$571$	−11.4782	−	6.62696i	−0.480349	−	0.277330i	0.240213	−	0.970720i	$-0.422783\pi$
$571$	−11.4782	−	6.62696i	−0.480349	−	0.277330i	−0.720562	+	0.693391i	$0.756116\pi$
$572$	−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	$0.172417\pi$
$577$			24.7685i			1.03112i	−0.856852	+	0.515562i	$0.827583\pi$
$578$	−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	−0.538028	−	0.842927i	$-0.680830\pi$
$587$	−1.86665	+	1.07771i	−0.0770450	+	0.0444820i	0.460983	+	0.887409i	$0.347497\pi$
$588$		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	$0.104996\pi$
$593$			15.7753i			0.647813i	−0.946089	+	0.323906i	$0.895004\pi$
$594$		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	−0.749193	−	0.662352i	$-0.769558\pi$
$599$	4.87085	−	8.43655i	0.199017	−	0.344708i	0.948210	+	0.317644i	$0.102892\pi$
$600$		0			0
$601$	6.71345	−	3.87601i	0.273847	−	0.158106i	−0.356787	−	0.934186i	$-0.616128\pi$
$601$	6.71345	−	3.87601i	0.273847	−	0.158106i	0.630635	+	0.776080i	$0.282795\pi$
$602$			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	−0.999659	−	0.0261160i	$-0.991686\pi$
$607$	−11.7573	+	20.3642i	−0.477212	+	0.826556i	0.522447	+	0.852672i	$0.325019\pi$
$608$	−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	−0.952622	−	0.304158i	$-0.901625\pi$
$617$	−5.28838	+	9.15975i	−0.212902	+	0.368758i	0.739719	+	0.672916i	$0.234958\pi$
$618$		0			0
$619$	−3.11818	−	5.40084i	−0.125330	−	0.217078i	0.796532	−	0.604597i	$-0.206666\pi$
$619$	−3.11818	−	5.40084i	−0.125330	−	0.217078i	−0.921862	+	0.387518i	$0.873332\pi$
$620$	−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	−0.0545946	−	0.998509i	$-0.517387\pi$
$641$	19.8200	−	11.4431i	0.782842	−	0.451974i	0.837437	+	0.546535i	$0.184053\pi$
$642$		0			0
$643$	40.9513	+	23.6432i	1.61496	+	0.932398i	0.988197	+	0.153188i	$0.0489540\pi$
$643$	40.9513	+	23.6432i	1.61496	+	0.932398i	0.626763	+	0.779210i	$0.284379\pi$
$644$	−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	0.374527	−	0.927216i	$-0.377805\pi$
$653$	−6.16367	−	3.55859i	−0.241203	−	0.139259i	−0.615729	+	0.787958i	$0.711139\pi$
$654$		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	−0.274483	−	0.961592i	$-0.588507\pi$
$659$	10.8085	−	6.24028i	0.421039	−	0.243087i	0.695522	+	0.718505i	$0.255173\pi$
$660$		0			0
$661$	−2.42439	+	4.19917i	−0.0942980	+	0.163329i	−0.909315	−	0.416108i	$-0.863394\pi$
$661$	−2.42439	+	4.19917i	−0.0942980	+	0.163329i	0.815017	+	0.579436i	$0.196727\pi$
$662$	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	−0.625351	−	0.780343i	$-0.715044\pi$
$673$	−6.80282	+	3.92761i	−0.262230	+	0.151398i	0.363122	+	0.931742i	$0.381711\pi$
$674$	28.8239			1.11026
$675$		0			0
$676$	−6.89522			−0.265201
$677$	−1.16112	−	2.01112i	−0.0446256	−	0.0772937i	0.842850	−	0.538149i	$-0.180876\pi$
$677$	−1.16112	−	2.01112i	−0.0446256	−	0.0772937i	−0.887475	+	0.460855i	$0.847543\pi$
$678$		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	$-0.956140\pi$
$683$		−	7.17931i		−	0.274709i	0.990522	−	0.137354i	$-0.0438599\pi$
$684$		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	−0.558010	+	0.829834i	$0.688435\pi$
$691$	−40.8938	+	23.6100i	−1.55567	+	0.898168i	−0.997663	+	0.0683333i	$0.978232\pi$
$692$	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	−0.941216	−	0.337806i	$-0.890315\pi$
$709$	−29.8030	+	17.2068i	−1.11928	+	0.646214i	−0.178059	+	0.984020i	$0.556982\pi$
$710$		−	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	$-0.867845\pi$
$719$		−	21.6311i		−	0.806705i	0.915045	−	0.403353i	$-0.132155\pi$
$720$		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	0.0610942	−	0.998132i	$-0.480541\pi$
$727$	25.7779	−	14.8829i	0.956049	−	0.551975i	0.894955	+	0.446157i	$0.147208\pi$
$728$	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	−0.253744	−	0.967271i	$-0.581662\pi$
$733$	19.2444	−	33.3324i	0.710810	−	1.23116i	0.964554	−	0.263887i	$-0.0850046\pi$
$734$	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	−0.657698	−	0.753282i	$-0.728469\pi$
$743$	8.81832	−	15.2738i	0.323513	−	0.560340i	0.981210	+	0.192942i	$0.0618028\pi$
$744$		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	0.687084	−	0.726578i	$-0.258891\pi$
$751$	10.9998	+	6.35076i	0.401390	+	0.231743i	−0.285694	+	0.958321i	$0.592224\pi$
$752$	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	$-0.861810\pi$
$757$		−	23.1460i		−	0.841255i	0.907233	−	0.420627i	$-0.138190\pi$
$758$	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	−0.778594	−	0.627528i	$-0.784067\pi$
$761$	4.25263	−	7.36577i	0.154158	−	0.267009i	0.932752	+	0.360519i	$0.117400\pi$
$762$		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	−0.645667	−	0.763619i	$-0.723421\pi$
$769$	9.38633	−	16.2576i	0.338480	−	0.586264i	0.984147	+	0.177355i	$0.0567540\pi$
$770$	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	$-0.833523\pi$
$773$		−	27.7742i		−	0.998970i	0.866322	−	0.499485i	$-0.166477\pi$
$774$		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	−0.963830	−	0.266519i	$-0.914126\pi$
$787$	−7.04430	+	12.2011i	−0.251102	+	0.434922i	0.712727	+	0.701441i	$0.247460\pi$
$788$	−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	−0.712635	−	0.701535i	$-0.752498\pi$
$797$	7.09250	−	12.2846i	0.251229	−	0.435142i	0.963865	+	0.266393i	$0.0858318\pi$
$798$		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	$0.124102\pi$
$809$			21.6209i			0.760149i	−0.924956	+	0.380074i	$0.875898\pi$
$810$		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	0.812055	−	0.583581i	$-0.198349\pi$
$821$	−2.84720	−	4.93150i	−0.0993681	−	0.172111i	−0.911423	+	0.411470i	$0.865015\pi$
$822$		0			0
$823$	0.522209	+	0.301498i	0.0182031	+	0.0105095i	0.509074	−	0.860723i	$-0.329988\pi$
$823$	0.522209	+	0.301498i	0.0182031	+	0.0105095i	−0.490871	+	0.871232i	$0.663321\pi$
$824$	−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	$-0.843444\pi$
$827$		−	27.1613i		−	0.944491i	0.881467	−	0.472245i	$-0.156556\pi$
$828$		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	0.0178107	−	0.999841i	$-0.494330\pi$
$839$	25.8547	−	14.9272i	0.892604	−	0.515345i	0.874793	+	0.484496i	$0.160997\pi$
$840$		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	0.880963	−	0.473185i	$-0.156896\pi$
$853$	0.896369	+	1.55256i	0.0306911	+	0.0531585i	−0.850272	+	0.526344i	$0.823563\pi$
$854$			1.49089i			0.0510171i
$855$		0			0
$856$	−6.55946			−0.224198
$857$	3.67633	+	6.36759i	0.125581	+	0.217513i	0.921960	−	0.387285i	$-0.126587\pi$
$857$	3.67633	+	6.36759i	0.125581	+	0.217513i	−0.796379	+	0.604798i	$0.793254\pi$
$858$		0			0
$859$	−8.38450	+	14.5224i	−0.286076	+	0.495497i	−0.972869	−	0.231355i	$-0.925684\pi$
$859$	−8.38450	+	14.5224i	−0.286076	+	0.495497i	0.686794	+	0.726852i	$0.259017\pi$
$860$	−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	−0.895541	−	0.444978i	$-0.853211\pi$
$877$	−1.84817	+	3.20112i	−0.0624083	+	0.108094i	0.833133	+	0.553073i	$0.186545\pi$
$878$	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	$-0.889950\pi$
$883$		−	20.1401i		−	0.677769i	0.940828	−	0.338885i	$-0.110050\pi$
$884$	−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	0.788550	−	0.614971i	$-0.210832\pi$
$887$	19.3659	+	11.1809i	0.650244	+	0.375419i	−0.138305	+	0.990390i	$0.544166\pi$
$888$		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	0.995229	−	0.0975686i	$-0.0311065\pi$
$907$	12.4416	+	21.5495i	0.413118	+	0.715541i	−0.582111	+	0.813109i	$0.697773\pi$
$908$			9.19514i			0.305151i
$909$		0			0
$910$	15.1781			0.503151
$911$	20.6692	+	35.8001i	0.684802	+	1.18611i	0.973499	+	0.228691i	$0.0734446\pi$
$911$	20.6692	+	35.8001i	0.684802	+	1.18611i	−0.288697	+	0.957420i	$0.593222\pi$
$912$		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	$-0.969402\pi$
$919$		−	5.81914i		−	0.191956i	0.995383	−	0.0959778i	$-0.0305978\pi$
$920$	−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	−0.695282	+	0.718737i	$0.744721\pi$
$929$	−50.7596	+	29.3061i	−1.66537	+	0.961500i	−0.970086	+	0.242763i	$0.921946\pi$
$930$		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	$-0.967252\pi$
$937$		−	6.28736i		−	0.205399i	0.994712	−	0.102700i	$-0.0327480\pi$
$938$	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	0.110761	−	0.993847i	$-0.464671\pi$
$941$	28.1013	−	48.6729i	0.916077	−	1.58669i	0.805317	−	0.592845i	$-0.201995\pi$
$942$		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	0.613099	−	0.790006i	$-0.289923\pi$
$947$	−11.6205	−	20.1273i	−0.377616	−	0.654051i	−0.990715	+	0.135956i	$0.956589\pi$
$948$		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	0.895381	−	0.445301i	$-0.146903\pi$
$967$	29.7728	+	17.1894i	0.957430	+	0.552772i	0.0620486	+	0.998073i	$0.480237\pi$
$968$	−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	$-0.996523\pi$
$971$		−	0.680693i		−	0.0218445i	0.999940	−	0.0109222i	$-0.00347672\pi$
$972$		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	−0.489884	−	0.871788i	$-0.662961\pi$
$977$	−46.5672	−	26.8856i	−1.48982	−	0.860146i	−0.999932	+	0.0116420i	$0.996294\pi$
$978$		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	0.914463	+	0.404669i	$0.132613\pi$
$983$	25.3232	+	43.8611i	0.807686	+	1.39895i	−0.106777	+	0.994283i	$0.534053\pi$
$984$		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	$0.0980906\pi$
$991$			19.0963i			0.606613i	−0.952893	+	0.303306i	$0.901909\pi$
$992$	−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	−0.965398	−	0.260780i	$-0.916020\pi$
$997$	−38.5931	+	22.2817i	−1.22226	+	0.705670i	−0.256857	+	0.966449i	$0.582687\pi$
$998$		−	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.901.7		36
3.2	odd	2		738.2.i.b.409.2	✓	36
9.2	odd	6		738.2.i.b.655.17	yes	36
9.7	even	3	inner	2214.2.i.b.1639.8		36
41.40	even	2	inner	2214.2.i.b.901.8		36
123.122	odd	2		738.2.i.b.409.17	yes	36
369.245	odd	6		738.2.i.b.655.2	yes	36
369.286	even	6	inner	2214.2.i.b.1639.7		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.i.b.409.2	✓	36	3.2	odd	2
738.2.i.b.409.17	yes	36	123.122	odd	2
738.2.i.b.655.2	yes	36	369.245	odd	6
738.2.i.b.655.17	yes	36	9.2	odd	6
2214.2.i.b.901.7		36	1.1	even	1	trivial
2214.2.i.b.901.8		36	41.40	even	2	inner
2214.2.i.b.1639.7		36	369.286	even	6	inner
2214.2.i.b.1639.8		36	9.7	even	3	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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