LMFDB - Embedded newform 896.2.z.a.607.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(31,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

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

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

chi := DirichletCharacter("896.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			607.5
Character	$\chi$	$=$	896.607
Dual form			896.2.z.a.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.282507 + 1.05433i) q^{3} +(1.39922 - 0.374919i) q^{5} +(0.298614 + 2.62885i) q^{7} +(1.56627 + 0.904287i) q^{9} +(1.42219 - 5.30770i) q^{11} +(1.84531 - 1.84531i) q^{13} +1.58116i q^{15} +(5.69424 - 3.28757i) q^{17} +(-3.24453 + 0.869370i) q^{19} +(-2.85604 - 0.427830i) q^{21} +(0.256173 - 0.443704i) q^{23} +(-2.51288 + 1.45081i) q^{25} +(-3.71137 + 3.71137i) q^{27} +(2.30263 + 2.30263i) q^{29} +(3.79637 + 6.57551i) q^{31} +(5.19429 + 2.99893i) q^{33} +(1.40343 + 3.56637i) q^{35} +(-1.07603 - 4.01582i) q^{37} +(1.42426 + 2.46689i) q^{39} -0.453189 q^{41} +(3.40842 + 3.40842i) q^{43} +(2.53059 + 0.678070i) q^{45} +(1.71468 - 2.96992i) q^{47} +(-6.82166 + 1.57002i) q^{49} +(1.85753 + 6.93238i) q^{51} +(1.37226 + 0.367696i) q^{53} -7.95984i q^{55} -3.66642i q^{57} +(6.57560 + 1.76193i) q^{59} +(-1.30846 - 4.88324i) q^{61} +(-1.90952 + 4.38752i) q^{63} +(1.89015 - 3.27384i) q^{65} +(-6.19818 - 1.66080i) q^{67} +(0.395441 + 0.395441i) q^{69} -6.44865 q^{71} +(7.43995 + 12.8864i) q^{73} +(-0.819730 - 3.05927i) q^{75} +(14.3778 + 2.15377i) q^{77} +(3.33780 + 1.92708i) q^{79} +(-0.151668 - 0.262697i) q^{81} +(2.44051 + 2.44051i) q^{83} +(6.73491 - 6.73491i) q^{85} +(-3.07824 + 1.77722i) q^{87} +(3.81344 - 6.60506i) q^{89} +(5.40208 + 4.30001i) q^{91} +(-8.00527 + 2.14500i) q^{93} +(-4.21387 + 2.43288i) q^{95} -11.2152i q^{97} +(7.02722 - 7.02722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.282507	+	1.05433i	−0.163106	+	0.608719i	0.835169	+	0.549994i	$0.185370\pi$
$3$	−0.282507	+	1.05433i	−0.163106	+	0.608719i	−0.998274	+	0.0587246i	$0.981297\pi$
$4$		0			0
$5$	1.39922	−	0.374919i	0.625749	−	0.167669i	0.0680093	−	0.997685i	$-0.478335\pi$
$5$	1.39922	−	0.374919i	0.625749	−	0.167669i	0.557740	+	0.830016i	$0.311669\pi$
$6$		0			0
$7$	0.298614	+	2.62885i	0.112866	+	0.993610i
$7$	0.298614	+	2.62885i	0.112866	+	0.993610i
$8$		0			0
$9$	1.56627	+	0.904287i	0.522090	+	0.301429i
$10$		0			0
$11$	1.42219	−	5.30770i	0.428807	−	1.60033i	−0.326658	−	0.945143i	$-0.605923\pi$
$11$	1.42219	−	5.30770i	0.428807	−	1.60033i	0.755465	−	0.655189i	$-0.227411\pi$
$12$		0			0
$13$	1.84531	−	1.84531i	0.511798	−	0.511798i	−0.403279	−	0.915077i	$-0.632130\pi$
$13$	1.84531	−	1.84531i	0.511798	−	0.511798i	0.915077	+	0.403279i	$0.132130\pi$
$14$		0			0
$15$			1.58116i			0.408253i
$16$		0			0
$17$	5.69424	−	3.28757i	1.38106	−	0.797353i	0.388771	−	0.921334i	$-0.372900\pi$
$17$	5.69424	−	3.28757i	1.38106	−	0.797353i	0.992285	+	0.123982i	$0.0395664\pi$
$18$		0			0
$19$	−3.24453	+	0.869370i	−0.744347	+	0.199447i	−0.611009	−	0.791624i	$-0.709236\pi$
$19$	−3.24453	+	0.869370i	−0.744347	+	0.199447i	−0.133338	+	0.991071i	$0.542569\pi$
$20$		0			0
$21$	−2.85604	−	0.427830i	−0.623238	−	0.0933601i
$22$		0			0
$23$	0.256173	−	0.443704i	0.0534157	−	0.0925187i	−0.838081	−	0.545546i	$-0.816322\pi$
$23$	0.256173	−	0.443704i	0.0534157	−	0.0925187i	0.891497	+	0.453027i	$0.149656\pi$
$24$		0			0
$25$	−2.51288	+	1.45081i	−0.502576	+	0.290162i
$26$		0			0
$27$	−3.71137	+	3.71137i	−0.714254	+	0.714254i
$28$		0			0
$29$	2.30263	+	2.30263i	0.427587	+	0.427587i	0.887806	−	0.460219i	$-0.152229\pi$
$29$	2.30263	+	2.30263i	0.427587	+	0.427587i	−0.460219	+	0.887806i	$0.652229\pi$
$30$		0			0
$31$	3.79637	+	6.57551i	0.681848	+	1.18100i	0.974416	+	0.224751i	$0.0721568\pi$
$31$	3.79637	+	6.57551i	0.681848	+	1.18100i	−0.292568	+	0.956245i	$0.594510\pi$
$32$		0			0
$33$	5.19429	+	2.99893i	0.904211	+	0.522046i
$34$		0			0
$35$	1.40343	+	3.56637i	0.237223	+	0.602827i
$36$		0			0
$37$	−1.07603	−	4.01582i	−0.176899	−	0.660196i	−0.996220	−	0.0868615i	$-0.972316\pi$
$37$	−1.07603	−	4.01582i	−0.176899	−	0.660196i	0.819321	−	0.573334i	$-0.194350\pi$
$38$		0			0
$39$	1.42426	+	2.46689i	0.228064	+	0.395018i
$40$		0			0
$41$	−0.453189			−0.0707762			−0.0353881	−	0.999374i	$-0.511267\pi$
$41$	−0.453189			−0.0707762			−0.0353881	+	0.999374i	$0.511267\pi$
$42$		0			0
$43$	3.40842	+	3.40842i	0.519779	+	0.519779i	0.917504	−	0.397726i	$-0.130200\pi$
$43$	3.40842	+	3.40842i	0.519779	+	0.519779i	−0.397726	+	0.917504i	$0.630200\pi$
$44$		0			0
$45$	2.53059	+	0.678070i	0.377238	+	0.101081i
$46$		0			0
$47$	1.71468	−	2.96992i	0.250112	−	0.433207i	−0.713444	−	0.700712i	$-0.752866\pi$
$47$	1.71468	−	2.96992i	0.250112	−	0.433207i	0.963556	+	0.267505i	$0.0861992\pi$
$48$		0			0
$49$	−6.82166	+	1.57002i	−0.974523	+	0.224289i
$50$		0			0
$51$	1.85753	+	6.93238i	0.260106	+	0.970727i
$52$		0			0
$53$	1.37226	+	0.367696i	0.188495	+	0.0505070i	0.351831	−	0.936063i	$-0.385559\pi$
$53$	1.37226	+	0.367696i	0.188495	+	0.0505070i	−0.163337	+	0.986570i	$0.552226\pi$
$54$		0			0
$55$		−	7.95984i		−	1.07330i
$56$		0			0
$57$		−	3.66642i		−	0.485629i
$58$		0			0
$59$	6.57560	+	1.76193i	0.856070	+	0.229383i	0.660055	−	0.751218i	$-0.270533\pi$
$59$	6.57560	+	1.76193i	0.856070	+	0.229383i	0.196015	+	0.980601i	$0.437200\pi$
$60$		0			0
$61$	−1.30846	−	4.88324i	−0.167531	−	0.625235i	−0.997704	−	0.0677284i	$-0.978425\pi$
$61$	−1.30846	−	4.88324i	−0.167531	−	0.625235i	0.830173	−	0.557506i	$-0.188242\pi$
$62$		0			0
$63$	−1.90952	+	4.38752i	−0.240577	+	0.552775i
$64$		0			0
$65$	1.89015	−	3.27384i	0.234445	−	0.406070i
$66$		0			0
$67$	−6.19818	−	1.66080i	−0.757229	−	0.202899i	−0.140507	−	0.990080i	$-0.544873\pi$
$67$	−6.19818	−	1.66080i	−0.757229	−	0.202899i	−0.616722	+	0.787181i	$0.711540\pi$
$68$		0			0
$69$	0.395441	+	0.395441i	0.0476055	+	0.0476055i
$70$		0			0
$71$	−6.44865			−0.765314			−0.382657	−	0.923890i	$-0.624991\pi$
$71$	−6.44865			−0.765314			−0.382657	+	0.923890i	$0.624991\pi$
$72$		0			0
$73$	7.43995	+	12.8864i	0.870780	+	1.50823i	0.861191	+	0.508281i	$0.169719\pi$
$73$	7.43995	+	12.8864i	0.870780	+	1.50823i	0.00958835	+	0.999954i	$0.496948\pi$
$74$		0			0
$75$	−0.819730	−	3.05927i	−0.0946543	−	0.353255i
$76$		0			0
$77$	14.3778	+	2.15377i	1.63850	+	0.245445i
$78$		0			0
$79$	3.33780	+	1.92708i	0.375532	+	0.216813i	0.675873	−	0.737019i	$-0.263767\pi$
$79$	3.33780	+	1.92708i	0.375532	+	0.216813i	−0.300341	+	0.953832i	$0.597100\pi$
$80$		0			0
$81$	−0.151668	−	0.262697i	−0.0168520	−	0.0291886i
$82$		0			0
$83$	2.44051	+	2.44051i	0.267881	+	0.267881i	0.828246	−	0.560365i	$-0.189339\pi$
$83$	2.44051	+	2.44051i	0.267881	+	0.267881i	−0.560365	+	0.828246i	$0.689339\pi$
$84$		0			0
$85$	6.73491	−	6.73491i	0.730503	−	0.730503i
$86$		0			0
$87$	−3.07824	+	1.77722i	−0.330022	+	0.190538i
$88$		0			0
$89$	3.81344	−	6.60506i	0.404223	−	0.700135i	−0.590007	−	0.807398i	$-0.700875\pi$
$89$	3.81344	−	6.60506i	0.404223	−	0.700135i	0.994231	+	0.107262i	$0.0342085\pi$
$90$		0			0
$91$	5.40208	+	4.30001i	0.566292	+	0.450763i
$92$		0			0
$93$	−8.00527	+	2.14500i	−0.830107	+	0.222427i
$94$		0			0
$95$	−4.21387	+	2.43288i	−0.432334	+	0.249608i
$96$		0			0
$97$		−	11.2152i		−	1.13873i	−0.822085	−	0.569365i	$-0.807189\pi$
$97$		−	11.2152i		−	1.13873i	0.822085	−	0.569365i	$-0.192811\pi$
$98$		0			0
$99$	7.02722	−	7.02722i	0.706263	−	0.706263i
$100$		0			0
$101$	−5.03457	+	18.7893i	−0.500959	+	1.86960i	−0.00725520	+	0.999974i	$0.502309\pi$
$101$	−5.03457	+	18.7893i	−0.500959	+	1.86960i	−0.493704	+	0.869630i	$0.664357\pi$
$102$		0			0
$103$	−6.15035	−	3.55091i	−0.606012	−	0.349881i	0.165391	−	0.986228i	$-0.447111\pi$
$103$	−6.15035	−	3.55091i	−0.606012	−	0.349881i	−0.771403	+	0.636347i	$0.780445\pi$
$104$		0			0
$105$	−4.15662	+	0.472156i	−0.405645	+	0.0460777i
$106$		0			0
$107$	−11.5830	+	3.10366i	−1.11977	+	0.300042i	−0.770791	−	0.637088i	$-0.780139\pi$
$107$	−11.5830	+	3.10366i	−1.11977	+	0.300042i	−0.348981	+	0.937130i	$0.613472\pi$
$108$		0			0
$109$	−2.68591	+	10.0240i	−0.257264	+	0.960122i	0.709553	+	0.704652i	$0.248897\pi$
$109$	−2.68591	+	10.0240i	−0.257264	+	0.960122i	−0.966817	+	0.255470i	$0.917770\pi$
$110$		0			0
$111$	4.53799			0.430727
$112$		0			0
$113$	−13.4601			−1.26622			−0.633109	−	0.774062i	$-0.718222\pi$
$113$	−13.4601			−1.26622			−0.633109	+	0.774062i	$0.718222\pi$
$114$		0			0
$115$	0.192088	−	0.716883i	0.0179123	−	0.0668497i
$116$		0			0
$117$	4.55896	−	1.22157i	0.421476	−	0.112934i
$118$		0			0
$119$	10.3429	+	13.9876i	0.948132	+	1.28224i
$120$		0			0
$121$	−16.6227	−	9.59715i	−1.51116	−	0.872468i
$122$		0			0
$123$	0.128029	−	0.477811i	0.0115440	−	0.0430828i
$124$		0			0
$125$	−8.09362	+	8.09362i	−0.723916	+	0.723916i
$126$		0			0
$127$		−	13.7356i		−	1.21884i	−0.792849	−	0.609418i	$-0.791403\pi$
$127$		−	13.7356i		−	1.21884i	0.792849	−	0.609418i	$-0.208597\pi$
$128$		0			0
$129$	−4.55651	+	2.63070i	−0.401178	+	0.231620i
$130$		0			0
$131$	2.81460	−	0.754169i	0.245912	−	0.0658920i	−0.133757	−	0.991014i	$-0.542704\pi$
$131$	2.81460	−	0.754169i	0.245912	−	0.0658920i	0.379670	+	0.925122i	$0.376038\pi$
$132$		0			0
$133$	−3.25430	−	8.26977i	−0.282184	−	0.717080i
$134$		0			0
$135$	−3.80156	+	6.58449i	−0.327186	+	0.566703i
$136$		0			0
$137$	6.25695	−	3.61245i	0.534568	−	0.308633i	−0.208307	−	0.978064i	$-0.566795\pi$
$137$	6.25695	−	3.61245i	0.534568	−	0.308633i	0.742874	+	0.669431i	$0.233462\pi$
$138$		0			0
$139$	0.708981	−	0.708981i	0.0601350	−	0.0601350i	−0.676400	−	0.736535i	$-0.736461\pi$
$139$	0.708981	−	0.708981i	0.0601350	−	0.0601350i	0.736535	+	0.676400i	$0.236461\pi$
$140$		0			0
$141$	2.64687	+	2.64687i	0.222906	+	0.222906i
$142$		0			0
$143$	−7.16997	−	12.4188i	−0.599583	−	1.03851i
$144$		0			0
$145$	4.08518	+	2.35858i	0.339255	+	0.195869i
$146$		0			0
$147$	0.271845	−	7.63583i	0.0224214	−	0.629793i
$148$		0			0
$149$	−2.46397	−	9.19566i	−0.201856	−	0.753338i	−0.990385	−	0.138340i	$-0.955823\pi$
$149$	−2.46397	−	9.19566i	−0.201856	−	0.753338i	0.788529	−	0.614998i	$-0.210843\pi$
$150$		0			0
$151$	−3.55073	−	6.15004i	−0.288954	−	0.500483i	0.684606	−	0.728913i	$-0.259974\pi$
$151$	−3.55073	−	6.15004i	−0.288954	−	0.500483i	−0.973560	+	0.228430i	$0.926641\pi$
$152$		0			0
$153$	11.8916			0.961381
$154$		0			0
$155$	7.77723	+	7.77723i	0.624683	+	0.624683i
$156$		0			0
$157$	−8.47741	−	2.27152i	−0.676571	−	0.181287i	−0.0958582	−	0.995395i	$-0.530560\pi$
$157$	−8.47741	−	2.27152i	−0.676571	−	0.181287i	−0.580713	+	0.814108i	$0.697226\pi$
$158$		0			0
$159$	−0.775348	+	1.34294i	−0.0614891	+	0.106502i
$160$		0			0
$161$	1.24293	+	0.540942i	0.0979563	+	0.0426322i
$162$		0			0
$163$	−3.28686	−	12.2667i	−0.257447	−	0.960805i	−0.966713	−	0.255864i	$-0.917640\pi$
$163$	−3.28686	−	12.2667i	−0.257447	−	0.960805i	0.709266	−	0.704941i	$-0.249027\pi$
$164$		0			0
$165$	8.39231	+	2.24871i	0.653340	+	0.175062i
$166$		0			0
$167$		−	21.5280i		−	1.66588i	−0.553361	−	0.832942i	$-0.686655\pi$
$167$		−	21.5280i		−	1.66588i	0.553361	−	0.832942i	$-0.313345\pi$
$168$		0			0
$169$			6.18963i			0.476126i
$170$		0			0
$171$	−5.86798	−	1.57232i	−0.448736	−	0.120238i
$172$		0			0
$173$	−5.18431	−	19.3481i	−0.394156	−	1.47101i	−0.823213	−	0.567733i	$-0.807821\pi$
$173$	−5.18431	−	19.3481i	−0.394156	−	1.47101i	0.429057	−	0.903278i	$-0.358846\pi$
$174$		0			0
$175$	−4.56434	−	6.17274i	−0.345032	−	0.466615i
$176$		0			0
$177$	−3.71531	+	6.43510i	−0.279260	+	0.483692i
$178$		0			0
$179$	−6.57967	−	1.76302i	−0.491787	−	0.131774i	0.00439858	−	0.999990i	$-0.498600\pi$
$179$	−6.57967	−	1.76302i	−0.491787	−	0.131774i	−0.496186	+	0.868216i	$0.665267\pi$
$180$		0			0
$181$	6.32019	+	6.32019i	0.469776	+	0.469776i	0.901842	−	0.432066i	$-0.142215\pi$
$181$	6.32019	+	6.32019i	0.469776	+	0.469776i	−0.432066	+	0.901842i	$0.642215\pi$
$182$		0			0
$183$	5.51821			0.407917
$184$		0			0
$185$	−3.01121	−	5.21558i	−0.221389	−	0.383457i
$186$		0			0
$187$	−9.35112	−	34.8989i	−0.683822	−	2.55206i
$188$		0			0
$189$	−10.8649	−	8.64836i	−0.790305	−	0.629076i
$190$		0			0
$191$	−11.5374	−	6.66112i	−0.834817	−	0.481982i	0.0206820	−	0.999786i	$-0.493416\pi$
$191$	−11.5374	−	6.66112i	−0.834817	−	0.481982i	−0.855499	+	0.517804i	$0.826750\pi$
$192$		0			0
$193$	5.25772	+	9.10664i	0.378459	+	0.655511i	0.990838	−	0.135054i	$-0.0431207\pi$
$193$	5.25772	+	9.10664i	0.378459	+	0.655511i	−0.612379	+	0.790564i	$0.709787\pi$
$194$		0			0
$195$	2.91773	+	2.91773i	0.208943	+	0.208943i
$196$		0			0
$197$	−14.0642	+	14.0642i	−1.00203	+	1.00203i	−0.00203129	+	0.999998i	$0.500647\pi$
$197$	−14.0642	+	14.0642i	−1.00203	+	1.00203i	−0.999998	+	0.00203129i	$0.999353\pi$
$198$		0			0
$199$	20.9503	−	12.0957i	1.48513	−	0.857439i	0.485272	−	0.874363i	$-0.338721\pi$
$199$	20.9503	−	12.0957i	1.48513	−	0.857439i	0.999857	+	0.0169240i	$0.00538734\pi$
$200$		0			0
$201$	3.50206	−	6.06575i	0.247017	−	0.427845i
$202$		0			0
$203$	−5.36565	+	6.74085i	−0.376595	+	0.473115i
$204$		0			0
$205$	−0.634110	+	0.169909i	−0.0442882	+	0.0118670i
$206$		0			0
$207$	0.802472	−	0.463307i	0.0557757	−	0.0322021i
$208$		0			0
$209$			18.4574i			1.27673i
$210$		0			0
$211$	8.81296	−	8.81296i	0.606709	−	0.606709i	−0.335375	−	0.942085i	$-0.608863\pi$
$211$	8.81296	−	8.81296i	0.606709	−	0.606709i	0.942085	+	0.335375i	$0.108863\pi$
$212$		0			0
$213$	1.82179	−	6.79902i	0.124827	−	0.465861i
$214$		0			0
$215$	6.04700	+	3.49124i	0.412402	+	0.238101i
$216$		0			0
$217$	−16.1523	+	11.9436i	−1.09649	+	0.810785i
$218$		0			0
$219$	−15.6883	+	4.20368i	−1.06012	+	0.284058i
$220$		0			0
$221$	4.44106	−	16.5743i	0.298738	−	1.11490i
$222$		0			0
$223$	5.44902			0.364893			0.182447	−	0.983216i	$-0.441598\pi$
$223$	5.44902			0.364893			0.182447	+	0.983216i	$0.441598\pi$
$224$		0			0
$225$	−5.24780			−0.349853
$226$		0			0
$227$	0.389502	−	1.45364i	0.0258521	−	0.0964815i	−0.951794	−	0.306737i	$-0.900763\pi$
$227$	0.389502	−	1.45364i	0.0258521	−	0.0964815i	0.977647	+	0.210255i	$0.0674295\pi$
$228$		0			0
$229$	−4.77902	+	1.28054i	−0.315807	+	0.0846202i	−0.413241	−	0.910622i	$-0.635603\pi$
$229$	−4.77902	+	1.28054i	−0.315807	+	0.0846202i	0.0974340	+	0.995242i	$0.468937\pi$
$230$		0			0
$231$	−6.33263	+	14.5505i	−0.416656	+	0.957354i
$232$		0			0
$233$	−10.7652	−	6.21528i	−0.705251	−	0.407177i	0.104049	−	0.994572i	$-0.466820\pi$
$233$	−10.7652	−	6.21528i	−0.705251	−	0.407177i	−0.809300	+	0.587395i	$0.800153\pi$
$234$		0			0
$235$	1.28574	−	4.79843i	0.0838721	−	0.313015i
$236$		0			0
$237$	−2.97474	+	2.97474i	−0.193230	+	0.193230i
$238$		0			0
$239$			7.34038i			0.474810i	0.971411	+	0.237405i	$0.0762968\pi$
$239$			7.34038i			0.474810i	−0.971411	+	0.237405i	$0.923703\pi$
$240$		0			0
$241$	−8.98405	+	5.18694i	−0.578713	+	0.334120i	−0.760622	−	0.649195i	$-0.775106\pi$
$241$	−8.98405	+	5.18694i	−0.578713	+	0.334120i	0.181909	+	0.983315i	$0.441773\pi$
$242$		0			0
$243$	−14.8897	+	3.98968i	−0.955173	+	0.255938i
$244$		0			0
$245$	−8.95636	+	4.75438i	−0.572201	+	0.303746i
$246$		0			0
$247$	−4.38292	+	7.59144i	−0.278879	+	0.483032i
$248$		0			0
$249$	−3.26257	+	1.88365i	−0.206757	+	0.119371i
$250$		0			0
$251$	−0.401720	+	0.401720i	−0.0253563	+	0.0253563i	−0.719671	−	0.694315i	$-0.755707\pi$
$251$	−0.401720	+	0.401720i	−0.0253563	+	0.0253563i	0.694315	+	0.719671i	$0.255707\pi$
$252$		0			0
$253$	−1.99072	−	1.99072i	−0.125156	−	0.125156i
$254$		0			0
$255$	5.19817	+	9.00349i	0.325522	+	0.563820i
$256$		0			0
$257$	7.92211	+	4.57383i	0.494168	+	0.285308i	0.726302	−	0.687376i	$-0.241237\pi$
$257$	7.92211	+	4.57383i	0.494168	+	0.285308i	−0.232134	+	0.972684i	$0.574571\pi$
$258$		0			0
$259$	10.2356	−	4.02791i	0.636012	−	0.250282i
$260$		0			0
$261$	1.52430	+	5.68877i	0.0943519	+	0.352126i
$262$		0			0
$263$	2.29116	+	3.96841i	0.141279	+	0.244703i	0.927979	−	0.372634i	$-0.121545\pi$
$263$	2.29116	+	3.96841i	0.141279	+	0.244703i	−0.786699	+	0.617336i	$0.788212\pi$
$264$		0			0
$265$	2.05795			0.126419
$266$		0			0
$267$	5.88661	+	5.88661i	0.360254	+	0.360254i
$268$		0			0
$269$	9.22279	+	2.47124i	0.562323	+	0.150674i	0.528773	−	0.848763i	$-0.322652\pi$
$269$	9.22279	+	2.47124i	0.562323	+	0.150674i	0.0335497	+	0.999437i	$0.489319\pi$
$270$		0			0
$271$	−3.64178	+	6.30775i	−0.221223	+	0.383169i	−0.955179	−	0.296027i	$-0.904338\pi$
$271$	−3.64178	+	6.30775i	−0.221223	+	0.383169i	0.733957	+	0.679196i	$0.237671\pi$
$272$		0			0
$273$	−6.05976	+	4.48080i	−0.366754	+	0.271190i
$274$		0			0
$275$	4.12667	+	15.4009i	0.248848	+	0.928712i
$276$		0			0
$277$	−31.2724	−	8.37942i	−1.87898	−	0.503470i	−0.999627	−	0.0272931i	$-0.991311\pi$
$277$	−31.2724	−	8.37942i	−1.87898	−	0.503470i	−0.879349	−	0.476177i	$-0.842022\pi$
$278$		0			0
$279$			13.7320i			0.822115i
$280$		0			0
$281$		−	4.09880i		−	0.244514i	−0.992498	−	0.122257i	$-0.960987\pi$
$281$		−	4.09880i		−	0.244514i	0.992498	−	0.122257i	$-0.0390132\pi$
$282$		0			0
$283$	13.1954	+	3.53570i	0.784387	+	0.210176i	0.628718	−	0.777633i	$-0.283580\pi$
$283$	13.1954	+	3.53570i	0.784387	+	0.210176i	0.155669	+	0.987809i	$0.450247\pi$
$284$		0			0
$285$	−1.37461	−	5.13012i	−0.0814249	−	0.303882i
$286$		0			0
$287$	−0.135329	−	1.19136i	−0.00798819	−	0.0703239i
$288$		0			0
$289$	13.1162	−	22.7180i	0.771543	−	1.33635i
$290$		0			0
$291$	11.8245	+	3.16838i	0.693167	+	0.185733i
$292$		0			0
$293$	16.6941	+	16.6941i	0.975280	+	0.975280i	0.999702	−	0.0244213i	$-0.00777432\pi$
$293$	16.6941	+	16.6941i	0.975280	+	0.975280i	−0.0244213	+	0.999702i	$0.507774\pi$
$294$		0			0
$295$	9.86128			0.574146
$296$		0			0
$297$	14.4206	+	24.9771i	0.836766	+	1.44932i
$298$		0			0
$299$	−0.346054	−	1.29149i	−0.0200128	−	0.0746889i
$300$		0			0
$301$	−7.94240	+	9.97801i	−0.457792	+	0.575123i
$302$		0			0
$303$	−18.3878	−	10.6162i	−1.05635	−	0.609886i
$304$		0			0
$305$	−3.66164	−	6.34215i	−0.209665	−	0.363151i
$306$		0			0
$307$	−16.7590	−	16.7590i	−0.956484	−	0.956484i	0.0426074	−	0.999092i	$-0.486434\pi$
$307$	−16.7590	−	16.7590i	−0.956484	−	0.956484i	−0.999092	+	0.0426074i	$0.986434\pi$
$308$		0			0
$309$	5.48135	−	5.48135i	0.311823	−	0.311823i
$310$		0			0
$311$	18.6053	−	10.7418i	1.05501	−	0.609111i	0.130963	−	0.991387i	$-0.458193\pi$
$311$	18.6053	−	10.7418i	1.05501	−	0.609111i	0.924048	+	0.382277i	$0.124860\pi$
$312$		0			0
$313$	10.4249	−	18.0565i	0.589253	−	1.02062i	−0.405078	−	0.914282i	$-0.632756\pi$
$313$	10.4249	−	18.0565i	0.589253	−	1.02062i	0.994331	−	0.106334i	$-0.0339111\pi$
$314$		0			0
$315$	−1.02687	+	6.85501i	−0.0578576	+	0.386236i
$316$		0			0
$317$	−14.3981	+	3.85795i	−0.808676	+	0.216684i	−0.639390	−	0.768883i	$-0.720813\pi$
$317$	−14.3981	+	3.85795i	−0.808676	+	0.216684i	−0.169287	+	0.985567i	$0.554146\pi$
$318$		0			0
$319$	15.4964	−	8.94686i	0.867633	−	0.500928i
$320$		0			0
$321$		−	13.0891i		−	0.730565i
$322$		0			0
$323$	−15.6170	+	15.6170i	−0.868955	+	0.868955i
$324$		0			0
$325$	−1.95985	+	7.31425i	−0.108713	+	0.405722i
$326$		0			0
$327$	−9.80980	−	5.66369i	−0.542483	−	0.313203i
$328$		0			0
$329$	8.31948	+	3.62078i	0.458668	+	0.199620i
$330$		0			0
$331$	2.89002	−	0.774378i	0.158850	−	0.0425637i	−0.178518	−	0.983937i	$-0.557130\pi$
$331$	2.89002	−	0.774378i	0.158850	−	0.0425637i	0.337367	+	0.941373i	$0.390464\pi$
$332$		0			0
$333$	1.94609	−	7.26290i	0.106645	−	0.398005i
$334$		0			0
$335$	−9.29528			−0.507855
$336$		0			0
$337$	−20.5605			−1.12000			−0.560000	−	0.828493i	$-0.689199\pi$
$337$	−20.5605			−1.12000			−0.560000	+	0.828493i	$0.689199\pi$
$338$		0			0
$339$	3.80257	−	14.1914i	0.206527	−	0.770771i
$340$		0			0
$341$	40.3000	−	10.7983i	2.18237	−	0.584763i
$342$		0			0
$343$	−6.16439	−	17.4643i	−0.332846	−	0.942981i
$344$		0			0
$345$	0.701566	+	0.405049i	0.0377711	+	0.0218071i
$346$		0			0
$347$	−1.55085	+	5.78787i	−0.0832542	+	0.310709i	−0.994978	−	0.100095i	$-0.968085\pi$
$347$	−1.55085	+	5.78787i	−0.0832542	+	0.310709i	0.911724	+	0.410804i	$0.134752\pi$
$348$		0			0
$349$	−3.15549	+	3.15549i	−0.168909	+	0.168909i	−0.786500	−	0.617590i	$-0.788109\pi$
$349$	−3.15549	+	3.15549i	−0.168909	+	0.168909i	0.617590	+	0.786500i	$0.288109\pi$
$350$		0			0
$351$			13.6973i			0.731108i
$352$		0			0
$353$	6.03486	−	3.48423i	0.321203	−	0.185447i	−0.330726	−	0.943727i	$-0.607293\pi$
$353$	6.03486	−	3.48423i	0.321203	−	0.185447i	0.651929	+	0.758280i	$0.273960\pi$
$354$		0			0
$355$	−9.02307	+	2.41773i	−0.478895	+	0.128320i
$356$		0			0
$357$	−17.6695	+	6.95325i	−0.935168	+	0.368005i
$358$		0			0
$359$	−18.6187	+	32.2485i	−0.982656	+	1.70201i	−0.330735	+	0.943724i	$0.607297\pi$
$359$	−18.6187	+	32.2485i	−0.982656	+	1.70201i	−0.651921	+	0.758287i	$0.726037\pi$
$360$		0			0
$361$	−6.68329	+	3.85860i	−0.351752	+	0.203084i
$362$		0			0
$363$	14.8146	−	14.8146i	0.777566	−	0.777566i
$364$		0			0
$365$	15.2415	+	15.2415i	0.797774	+	0.797774i
$366$		0			0
$367$	13.0391	+	22.5844i	0.680637	+	1.17890i	0.974787	+	0.223138i	$0.0716300\pi$
$367$	13.0391	+	22.5844i	0.680637	+	1.17890i	−0.294150	+	0.955759i	$0.595037\pi$
$368$		0			0
$369$	−0.709816	−	0.409813i	−0.0369516	−	0.0213340i
$370$		0			0
$371$	−0.556840	+	3.71726i	−0.0289097	+	0.192991i
$372$		0			0
$373$	−9.46676	−	35.3304i	−0.490170	−	1.82934i	−0.555555	−	0.831480i	$-0.687494\pi$
$373$	−9.46676	−	35.3304i	−0.490170	−	1.82934i	0.0653850	−	0.997860i	$-0.479172\pi$
$374$		0			0
$375$	−6.24686	−	10.8199i	−0.322586	−	0.558736i
$376$		0			0
$377$	8.49813			0.437676
$378$		0			0
$379$	−0.261074	−	0.261074i	−0.0134105	−	0.0134105i	0.700370	−	0.713780i	$-0.253018\pi$
$379$	−0.261074	−	0.261074i	−0.0134105	−	0.0134105i	−0.713780	+	0.700370i	$0.753018\pi$
$380$		0			0
$381$	14.4819	+	3.88041i	0.741929	+	0.198799i
$382$		0			0
$383$	8.76848	−	15.1875i	0.448048	−	0.776043i	−0.550211	−	0.835026i	$-0.685453\pi$
$383$	8.76848	−	15.1875i	0.448048	−	0.776043i	0.998259	+	0.0589834i	$0.0187859\pi$
$384$		0			0
$385$	20.9252	−	2.37692i	1.06645	−	0.121139i
$386$		0			0
$387$	2.25632	+	8.42070i	0.114695	+	0.428048i
$388$		0			0
$389$	21.5199	+	5.76625i	1.09110	+	0.292361i	0.759137	−	0.650930i	$-0.225621\pi$
$389$	21.5199	+	5.76625i	1.09110	+	0.292361i	0.331967	+	0.943291i	$0.392288\pi$
$390$		0			0
$391$		−	3.36874i		−	0.170365i
$392$		0			0
$393$			3.18058i			0.160439i
$394$		0			0
$395$	5.39281	+	1.44500i	0.271342	+	0.0727058i
$396$		0			0
$397$	6.12529	+	22.8599i	0.307419	+	1.14730i	0.930843	+	0.365420i	$0.119075\pi$
$397$	6.12529	+	22.8599i	0.307419	+	1.14730i	−0.623424	+	0.781884i	$0.714259\pi$
$398$		0			0
$399$	9.63844	−	1.09484i	0.482526	−	0.0548108i
$400$		0			0
$401$	−3.87231	+	6.70703i	−0.193374	+	0.334933i	−0.946366	−	0.323096i	$-0.895276\pi$
$401$	−3.87231	+	6.70703i	−0.193374	+	0.334933i	0.752992	+	0.658029i	$0.228610\pi$
$402$		0			0
$403$	19.1394	+	5.12838i	0.953400	+	0.255463i
$404$		0			0
$405$	−0.310707	−	0.310707i	−0.0154392	−	0.0154392i
$406$		0			0
$407$	−22.8451			−1.13239
$408$		0			0
$409$	−15.9651	−	27.6524i	−0.789425	−	1.36732i	−0.926320	−	0.376739i	$-0.877045\pi$
$409$	−15.9651	−	27.6524i	−0.789425	−	1.36732i	0.136894	−	0.990586i	$-0.456288\pi$
$410$		0			0
$411$	2.04109	+	7.61745i	0.100680	+	0.375741i
$412$		0			0
$413$	−2.66827	+	17.8124i	−0.131297	+	0.876489i
$414$		0			0
$415$	4.32981	+	2.49981i	0.212542	+	0.122711i
$416$		0			0
$417$	0.547209	+	0.947793i	0.0267969	+	0.0464136i
$418$		0			0
$419$	6.96449	+	6.96449i	0.340238	+	0.340238i	0.856457	−	0.516219i	$-0.172661\pi$
$419$	6.96449	+	6.96449i	0.340238	+	0.340238i	−0.516219	+	0.856457i	$0.672661\pi$
$420$		0			0
$421$	−6.31935	+	6.31935i	−0.307986	+	0.307986i	−0.844128	−	0.536142i	$-0.819881\pi$
$421$	−6.31935	+	6.31935i	−0.307986	+	0.307986i	0.536142	+	0.844128i	$0.319881\pi$
$422$		0			0
$423$	5.37132	−	3.10113i	0.261162	−	0.150782i
$424$		0			0
$425$	−9.53929	+	16.5225i	−0.462724	+	0.801461i
$426$		0			0
$427$	12.4466	−	4.89795i	0.602331	−	0.237028i
$428$		0			0
$429$	15.1191	−	4.05114i	0.729955	−	0.195591i
$430$		0			0
$431$	−5.61569	+	3.24222i	−0.270498	+	0.156172i	−0.629114	−	0.777313i	$-0.716582\pi$
$431$	−5.61569	+	3.24222i	−0.270498	+	0.156172i	0.358616	+	0.933485i	$0.383249\pi$
$432$		0			0
$433$		−	17.1718i		−	0.825223i	−0.910907	−	0.412612i	$-0.864617\pi$
$433$		−	17.1718i		−	0.825223i	0.910907	−	0.412612i	$-0.135383\pi$
$434$		0			0
$435$	−3.64081	+	3.64081i	−0.174564	+	0.174564i
$436$		0			0
$437$	−0.445418	+	1.66232i	−0.0213072	+	0.0795196i
$438$		0			0
$439$	−27.1054	−	15.6493i	−1.29367	−	0.746900i	−0.314366	−	0.949302i	$-0.601792\pi$
$439$	−27.1054	−	15.6493i	−1.29367	−	0.746900i	−0.979302	+	0.202402i	$0.935125\pi$
$440$		0			0
$441$	−12.1043	−	3.70966i	−0.576396	−	0.176650i
$442$		0			0
$443$	−11.7094	+	3.13752i	−0.556330	+	0.149068i	−0.526020	−	0.850472i	$-0.676316\pi$
$443$	−11.7094	+	3.13752i	−0.556330	+	0.149068i	−0.0303104	+	0.999541i	$0.509650\pi$
$444$		0			0
$445$	2.85946	−	10.6717i	0.135552	−	0.505885i
$446$		0			0
$447$	10.3914			0.491495
$448$		0			0
$449$	33.4968			1.58081			0.790406	−	0.612583i	$-0.209869\pi$
$449$	33.4968			1.58081			0.790406	+	0.612583i	$0.209869\pi$
$450$		0			0
$451$	−0.644522	+	2.40539i	−0.0303494	+	0.113265i
$452$		0			0
$453$	7.48729	−	2.00621i	0.351783	−	0.0942601i
$454$		0			0
$455$	9.17085	+	3.99130i	0.429936	+	0.187115i
$456$		0			0
$457$	−2.60908	−	1.50635i	−0.122047	−	0.0704641i	0.437733	−	0.899105i	$-0.355781\pi$
$457$	−2.60908	−	1.50635i	−0.122047	−	0.0704641i	−0.559781	+	0.828641i	$0.689115\pi$
$458$		0			0
$459$	−8.93205	+	33.3349i	−0.416912	+	1.55594i
$460$		0			0
$461$	20.6763	−	20.6763i	0.962993	−	0.962993i	−0.0363467	−	0.999339i	$-0.511572\pi$
$461$	20.6763	−	20.6763i	0.962993	−	0.962993i	0.999339	+	0.0363467i	$0.0115721\pi$
$462$		0			0
$463$			11.6775i			0.542697i	0.962481	+	0.271349i	$0.0874696\pi$
$463$			11.6775i			0.542697i	−0.962481	+	0.271349i	$0.912530\pi$
$464$		0			0
$465$	−10.3969	+	6.00266i	−0.482145	+	0.278367i
$466$		0			0
$467$	9.80739	−	2.62788i	0.453832	−	0.121604i	−0.0246599	−	0.999696i	$-0.507850\pi$
$467$	9.80739	−	2.62788i	0.453832	−	0.121604i	0.478492	+	0.878092i	$0.341184\pi$
$468$		0			0
$469$	2.51512	−	16.7900i	0.116137	−	0.775290i
$470$		0			0
$471$	4.78986	−	8.29629i	0.220705	−	0.382273i
$472$		0			0
$473$	22.9383	−	13.2434i	1.05470	−	0.608933i
$474$		0			0
$475$	6.89183	−	6.89183i	0.316219	−	0.316219i
$476$		0			0
$477$	1.81683	+	1.81683i	0.0831870	+	0.0831870i
$478$		0			0
$479$	−5.72312	−	9.91273i	−0.261496	−	0.452924i	0.705144	−	0.709064i	$-0.250882\pi$
$479$	−5.72312	−	9.91273i	−0.261496	−	0.452924i	−0.966640	+	0.256140i	$0.917549\pi$
$480$		0			0
$481$	−9.39606	−	5.42482i	−0.428424	−	0.247350i
$482$		0			0
$483$	−0.921468	+	1.15764i	−0.0419283	+	0.0526743i
$484$		0			0
$485$	−4.20479	−	15.6925i	−0.190930	−	0.712560i
$486$		0			0
$487$	−4.85037	−	8.40108i	−0.219791	−	0.380689i	0.734953	−	0.678118i	$-0.237204\pi$
$487$	−4.85037	−	8.40108i	−0.219791	−	0.380689i	−0.954744	+	0.297429i	$0.903871\pi$
$488$		0			0
$489$	13.8618			0.626851
$490$		0			0
$491$	−11.4667	−	11.4667i	−0.517483	−	0.517483i	0.399326	−	0.916809i	$-0.369244\pi$
$491$	−11.4667	−	11.4667i	−0.517483	−	0.517483i	−0.916809	+	0.399326i	$0.869244\pi$
$492$		0			0
$493$	20.6817	+	5.54166i	0.931459	+	0.249584i
$494$		0			0
$495$	7.19798	−	12.4673i	0.323525	−	0.560362i
$496$		0			0
$497$	−1.92566	−	16.9525i	−0.0863776	−	0.760424i
$498$		0			0
$499$	4.93931	+	18.4338i	0.221114	+	0.825209i	0.983924	+	0.178586i	$0.0571524\pi$
$499$	4.93931	+	18.4338i	0.221114	+	0.825209i	−0.762810	+	0.646623i	$0.776181\pi$
$500$		0			0
$501$	22.6976	+	6.08181i	1.01405	+	0.271715i
$502$		0			0
$503$			22.4043i			0.998960i	0.866325	+	0.499480i	$0.166476\pi$
$503$			22.4043i			0.998960i	−0.866325	+	0.499480i	$0.833524\pi$
$504$		0			0
$505$			28.1779i			1.25390i
$506$		0			0
$507$	−6.52593	−	1.74862i	−0.289827	−	0.0776588i
$508$		0			0
$509$	3.91534	+	14.6122i	0.173544	+	0.647676i	0.996795	+	0.0799982i	$0.0254915\pi$
$509$	3.91534	+	14.6122i	0.173544	+	0.647676i	−0.823251	+	0.567678i	$0.807842\pi$
$510$		0			0
$511$	−31.6546	+	23.4065i	−1.40032	+	1.03544i
$512$		0			0
$513$	8.81512	−	15.2682i	0.389197	−	0.674109i
$514$		0			0
$515$	−9.93698	−	2.66261i	−0.437876	−	0.117328i
$516$		0			0
$517$	−13.3248	−	13.3248i	−0.586025	−	0.586025i
$518$		0			0
$519$	21.8639			0.959721
$520$		0			0
$521$	3.63800	+	6.30121i	0.159384	+	0.276061i	0.934647	−	0.355578i	$-0.115716\pi$
$521$	3.63800	+	6.30121i	0.159384	+	0.276061i	−0.775263	+	0.631639i	$0.782383\pi$
$522$		0			0
$523$	4.66897	+	17.4249i	0.204160	+	0.761936i	0.989704	+	0.143130i	$0.0457166\pi$
$523$	4.66897	+	17.4249i	0.204160	+	0.761936i	−0.785544	+	0.618806i	$0.787617\pi$
$524$		0			0
$525$	7.79758	−	3.06849i	0.340314	−	0.133920i
$526$		0			0
$527$	43.2349	+	24.9617i	1.88334	+	1.08735i
$528$		0			0
$529$	11.3688	+	19.6913i	0.494294	+	0.856141i
$530$		0			0
$531$	8.70588	+	8.70588i	0.377803	+	0.377803i
$532$		0			0
$533$	−0.836275	+	0.836275i	−0.0362231	+	0.0362231i
$534$		0			0
$535$	−15.0435	+	8.68540i	−0.650389	+	0.375502i
$536$		0			0
$537$	3.71761	−	6.43909i	0.160427	−	0.277867i
$538$		0			0
$539$	−1.36852	+	38.4402i	−0.0589463	+	1.65574i
$540$		0			0
$541$	2.61709	−	0.701247i	0.112518	−	0.0301490i	−0.202121	−	0.979361i	$-0.564783\pi$
$541$	2.61709	−	0.701247i	0.112518	−	0.0301490i	0.314638	+	0.949212i	$0.398117\pi$
$542$		0			0
$543$	−8.44907	+	4.87808i	−0.362585	+	0.209338i
$544$		0			0
$545$			15.0327i			0.643931i
$546$		0			0
$547$	−20.4366	+	20.4366i	−0.873807	+	0.873807i	−0.992885	−	0.119078i	$-0.962006\pi$
$547$	−20.4366	+	20.4366i	−0.873807	+	0.873807i	0.119078	+	0.992885i	$0.462006\pi$
$548$		0			0
$549$	2.36645	−	8.83170i	0.100998	−	0.376928i
$550$		0			0
$551$	−9.47278	−	5.46911i	−0.403554	−	0.232992i
$552$		0			0
$553$	−4.06928	+	9.35002i	−0.173043	+	0.397603i
$554$		0			0
$555$	6.34964	−	1.70138i	0.269527	−	0.0722196i
$556$		0			0
$557$	−1.22222	+	4.56137i	−0.0517869	+	0.193271i	−0.986973	−	0.160885i	$-0.948565\pi$
$557$	−1.22222	+	4.56137i	−0.0517869	+	0.193271i	0.935186	+	0.354156i	$0.115232\pi$
$558$		0			0
$559$	12.5792			0.532044
$560$		0			0
$561$	39.4367			1.66502
$562$		0			0
$563$	−1.89945	+	7.08884i	−0.0800522	+	0.298759i	−0.994331	−	0.106326i	$-0.966091\pi$
$563$	−1.89945	+	7.08884i	−0.0800522	+	0.298759i	0.914279	+	0.405085i	$0.132758\pi$
$564$		0			0
$565$	−18.8336	+	5.04645i	−0.792335	+	0.212306i
$566$		0			0
$567$	0.645300	−	0.477158i	0.0271001	−	0.0200387i
$568$		0			0
$569$	10.8006	+	6.23575i	0.452787	+	0.261416i	0.709006	−	0.705202i	$-0.249144\pi$
$569$	10.8006	+	6.23575i	0.452787	+	0.261416i	−0.256220	+	0.966619i	$0.582477\pi$
$570$		0			0
$571$	9.94080	−	37.0996i	0.416010	−	1.55257i	−0.366795	−	0.930302i	$-0.619545\pi$
$571$	9.94080	−	37.0996i	0.416010	−	1.55257i	0.782805	−	0.622267i	$-0.213788\pi$
$572$		0			0
$573$	10.2824	−	10.2824i	0.429555	−	0.429555i
$574$		0			0
$575$			1.48663i			0.0619969i
$576$		0			0
$577$	−16.4040	+	9.47084i	−0.682906	+	0.394276i	−0.800949	−	0.598732i	$-0.795671\pi$
$577$	−16.4040	+	9.47084i	−0.682906	+	0.394276i	0.118043	+	0.993009i	$0.462338\pi$
$578$		0			0
$579$	−11.0868	+	2.97069i	−0.460750	+	0.123458i
$580$		0			0
$581$	−5.68696	+	7.14450i	−0.235935	+	0.296404i
$582$		0			0
$583$	3.90324	−	6.76062i	0.161656	−	0.279996i
$584$		0			0
$585$	5.92098	−	3.41848i	0.244803	−	0.141337i
$586$		0			0
$587$	7.54134	−	7.54134i	0.311264	−	0.311264i	−0.534135	−	0.845399i	$-0.679363\pi$
$587$	7.54134	−	7.54134i	0.311264	−	0.311264i	0.845399	+	0.534135i	$0.179363\pi$
$588$		0			0
$589$	−18.0340	−	18.0340i	−0.743078	−	0.743078i
$590$		0			0
$591$	−10.8551	−	18.8015i	−0.446517	−	0.773391i
$592$		0			0
$593$	−10.2804	−	5.93539i	−0.422165	−	0.243737i	0.273838	−	0.961776i	$-0.411707\pi$
$593$	−10.2804	−	5.93539i	−0.422165	−	0.243737i	−0.696003	+	0.718039i	$0.745040\pi$
$594$		0			0
$595$	19.7162	+	15.6939i	0.808284	+	0.643387i
$596$		0			0
$597$	6.83423	+	25.5057i	0.279706	+	1.04388i
$598$		0			0
$599$	10.9170	+	18.9089i	0.446058	+	0.772595i	0.998125	−	0.0612043i	$-0.0194941\pi$
$599$	10.9170	+	18.9089i	0.446058	+	0.772595i	−0.552067	+	0.833800i	$0.686161\pi$
$600$		0			0
$601$	−37.4893			−1.52922			−0.764610	−	0.644493i	$-0.777068\pi$
$601$	−37.4893			−1.52922			−0.764610	+	0.644493i	$0.777068\pi$
$602$		0			0
$603$	−8.20620	−	8.20620i	−0.334182	−	0.334182i
$604$		0			0
$605$	−26.8570	−	7.19631i	−1.09189	−	0.292572i
$606$		0			0
$607$	2.33958	−	4.05227i	0.0949605	−	0.164476i	−0.814632	−	0.579979i	$-0.803061\pi$
$607$	2.33958	−	4.05227i	0.0949605	−	0.164476i	0.909592	+	0.415502i	$0.136394\pi$
$608$		0			0
$609$	−5.59125	−	7.56151i	−0.226569	−	0.306408i
$610$		0			0
$611$	−2.31630	−	8.64456i	−0.0937075	−	0.349721i
$612$		0			0
$613$	4.89703	+	1.31216i	0.197789	+	0.0529975i	0.356354	−	0.934351i	$-0.384020\pi$
$613$	4.89703	+	1.31216i	0.197789	+	0.0529975i	−0.158564	+	0.987349i	$0.550687\pi$
$614$		0			0
$615$		−	0.716563i		−	0.0288946i
$616$		0			0
$617$			16.4696i			0.663041i	0.943448	+	0.331520i	$0.107562\pi$
$617$			16.4696i			0.663041i	−0.943448	+	0.331520i	$0.892438\pi$
$618$		0			0
$619$	14.6852	+	3.93490i	0.590249	+	0.158157i	0.541567	−	0.840657i	$-0.317831\pi$
$619$	14.6852	+	3.93490i	0.590249	+	0.158157i	0.0486822	+	0.998814i	$0.484498\pi$
$620$		0			0
$621$	0.696000	+	2.59751i	0.0279295	+	0.104234i
$622$		0			0
$623$	18.5024	+	8.05257i	0.741285	+	0.322619i
$624$		0			0
$625$	−1.03623	+	1.79481i	−0.0414493	+	0.0717922i
$626$		0			0
$627$	−19.4602	−	5.21435i	−0.777167	−	0.208241i
$628$		0			0
$629$	−19.3295	−	19.3295i	−0.770717	−	0.770717i
$630$		0			0
$631$	6.82302			0.271620			0.135810	−	0.990735i	$-0.456636\pi$
$631$	6.82302			0.271620			0.135810	+	0.990735i	$0.456636\pi$
$632$		0			0
$633$	6.80206	+	11.7815i	0.270357	+	0.468273i
$634$		0			0
$635$	−5.14974	−	19.2191i	−0.204361	−	0.762686i
$636$		0			0
$637$	−9.69092	+	15.4853i	−0.383968	+	0.613549i
$638$		0			0
$639$	−10.1003	−	5.83143i	−0.399563	−	0.230688i
$640$		0			0
$641$	−16.5379	−	28.6446i	−0.653210	−	1.13139i	−0.982339	−	0.187108i	$-0.940089\pi$
$641$	−16.5379	−	28.6446i	−0.653210	−	1.13139i	0.329130	−	0.944285i	$-0.393245\pi$
$642$		0			0
$643$	−14.7445	−	14.7445i	−0.581464	−	0.581464i	0.353841	−	0.935306i	$-0.384875\pi$
$643$	−14.7445	−	14.7445i	−0.581464	−	0.581464i	−0.935306	+	0.353841i	$0.884875\pi$
$644$		0			0
$645$	−5.38925	+	5.38925i	−0.212201	+	0.212201i
$646$		0			0
$647$	−9.62533	+	5.55719i	−0.378411	+	0.218476i	−0.677127	−	0.735867i	$-0.736775\pi$
$647$	−9.62533	+	5.55719i	−0.378411	+	0.218476i	0.298716	+	0.954342i	$0.403442\pi$
$648$		0			0
$649$	18.7035	−	32.3955i	0.734178	−	1.27163i
$650$		0			0
$651$	−8.02937	−	20.4041i	−0.314696	−	0.799699i
$652$		0			0
$653$	−16.2451	+	4.35285i	−0.635718	+	0.170340i	−0.562263	−	0.826958i	$-0.690069\pi$
$653$	−16.2451	+	4.35285i	−0.635718	+	0.170340i	−0.0734551	+	0.997299i	$0.523403\pi$
$654$		0			0
$655$	3.65548	−	2.11049i	0.142831	−	0.0824638i
$656$		0			0
$657$			26.9114i			1.04991i
$658$		0			0
$659$	32.5839	−	32.5839i	1.26929	−	1.26929i	0.322834	−	0.946455i	$-0.395364\pi$
$659$	32.5839	−	32.5839i	1.26929	−	1.26929i	0.946455	−	0.322834i	$-0.104636\pi$
$660$		0			0
$661$	−4.53812	+	16.9365i	−0.176512	+	0.658753i	0.819777	+	0.572683i	$0.194097\pi$
$661$	−4.53812	+	16.9365i	−0.176512	+	0.658753i	−0.996289	+	0.0860697i	$0.972569\pi$
$662$		0			0
$663$	16.2201	+	9.36470i	0.629938	+	0.363695i
$664$		0			0
$665$	−7.65398	−	10.3511i	−0.296809	−	0.401399i
$666$		0			0
$667$	1.61155	−	0.431815i	0.0623996	−	0.0167199i
$668$		0			0
$669$	−1.53939	+	5.74507i	−0.0595162	+	0.222117i
$670$		0			0
$671$	−27.7796			−1.07242
$672$		0			0
$673$	11.0728			0.426827			0.213413	−	0.976962i	$-0.431542\pi$
$673$	11.0728			0.426827			0.213413	+	0.976962i	$0.431542\pi$
$674$		0			0
$675$	3.94173	−	14.7107i	0.151717	−	0.566217i
$676$		0			0
$677$	−5.69655	+	1.52639i	−0.218936	+	0.0586638i	−0.366620	−	0.930371i	$-0.619485\pi$
$677$	−5.69655	+	1.52639i	−0.218936	+	0.0586638i	0.147684	+	0.989035i	$0.452818\pi$
$678$		0			0
$679$	29.4830	−	3.34902i	1.13145	−	0.128523i
$680$		0			0
$681$	1.42258	+	0.821328i	0.0545135	+	0.0314734i
$682$		0			0
$683$	−0.824476	+	3.07699i	−0.0315477	+	0.117738i	−0.979904	−	0.199469i	$-0.936078\pi$
$683$	−0.824476	+	3.07699i	−0.0315477	+	0.117738i	0.948356	+	0.317207i	$0.102745\pi$
$684$		0			0
$685$	7.40047	−	7.40047i	0.282757	−	0.282757i
$686$		0			0
$687$		−	5.40044i		−	0.206040i
$688$		0			0
$689$	3.21077	−	1.85374i	0.122321	−	0.0706218i
$690$		0			0
$691$	−20.4319	+	5.47470i	−0.777265	+	0.208267i	−0.625578	−	0.780161i	$-0.715137\pi$
$691$	−20.4319	+	5.47470i	−0.777265	+	0.208267i	−0.151686	+	0.988429i	$0.548470\pi$
$692$		0			0
$693$	20.5719	+	16.3751i	0.781462	+	0.622037i
$694$		0			0
$695$	0.726208	−	1.25783i	0.0275466	−	0.0477122i
$696$		0			0
$697$	−2.58056	+	1.48989i	−0.0977458	+	0.0564336i
$698$		0			0
$699$	9.59422	−	9.59422i	0.362887	−	0.362887i
$700$		0			0
$701$	−19.0687	−	19.0687i	−0.720214	−	0.720214i	0.248435	−	0.968649i	$-0.420084\pi$
$701$	−19.0687	−	19.0687i	−0.720214	−	0.720214i	−0.968649	+	0.248435i	$0.920084\pi$
$702$		0			0
$703$	6.98246	+	12.0940i	0.263348	+	0.456133i
$704$		0			0
$705$	4.69591	+	2.71118i	0.176858	+	0.102109i
$706$		0			0
$707$	−50.8975	−	7.62437i	−1.91420	−	0.286744i
$708$		0			0
$709$	9.03837	+	33.7317i	0.339443	+	1.26682i	0.898971	+	0.438008i	$0.144316\pi$
$709$	9.03837	+	33.7317i	0.339443	+	1.26682i	−0.559528	+	0.828812i	$0.689018\pi$
$710$		0			0
$711$	3.48527	+	6.03666i	0.130708	+	0.226392i
$712$		0			0
$713$	3.89011			0.145686
$714$		0			0
$715$	−14.6884	−	14.6884i	−0.549315	−	0.549315i
$716$		0			0
$717$	−7.73920	−	2.07371i	−0.289026	−	0.0774442i
$718$		0			0
$719$	−25.7551	+	44.6092i	−0.960505	+	1.66364i	−0.239268	+	0.970953i	$0.576908\pi$
$719$	−25.7551	+	44.6092i	−0.960505	+	1.66364i	−0.721236	+	0.692689i	$0.756426\pi$
$720$		0			0
$721$	7.49820	−	17.2287i	0.279248	−	0.641629i
$722$		0			0
$723$	−2.93070	−	10.9375i	−0.108994	−	0.406771i
$724$		0			0
$725$	−9.12690	−	2.44555i	−0.338965	−	0.0908253i
$726$		0			0
$727$			10.3415i			0.383546i	0.981439	+	0.191773i	$0.0614237\pi$
$727$			10.3415i			0.383546i	−0.981439	+	0.191773i	$0.938576\pi$
$728$		0			0
$729$		−	17.7358i		−	0.656881i
$730$		0			0
$731$	30.6138	+	8.20293i	1.13229	+	0.303396i
$732$		0			0
$733$	−5.21156	−	19.4498i	−0.192493	−	0.718395i	−0.992901	−	0.118940i	$-0.962051\pi$
$733$	−5.21156	−	19.4498i	−0.192493	−	0.718395i	0.800408	−	0.599455i	$-0.204616\pi$
$734$		0			0
$735$	−2.48245	−	10.7861i	−0.0915666	−	0.397852i
$736$		0			0
$737$	−17.6300	+	30.5361i	−0.649411	+	1.12481i
$738$		0			0
$739$	29.5182	+	7.90938i	1.08584	+	0.290951i	0.756988	−	0.653429i	$-0.226670\pi$
$739$	29.5182	+	7.90938i	1.08584	+	0.290951i	0.328856	+	0.944380i	$0.393337\pi$
$740$		0			0
$741$	−6.76569	−	6.76569i	−0.248544	−	0.248544i
$742$		0			0
$743$	36.5659			1.34147			0.670735	−	0.741697i	$-0.265979\pi$
$743$	36.5659			1.34147			0.670735	+	0.741697i	$0.265979\pi$
$744$		0			0
$745$	−6.89526	−	11.9429i	−0.252623	−	0.437556i
$746$		0			0
$747$	1.61558	+	6.02943i	0.0591110	+	0.220605i
$748$		0			0
$749$	−11.6179	−	29.5232i	−0.424509	−	1.07875i
$750$		0			0
$751$	−30.5955	−	17.6643i	−1.11644	−	0.644580i	−0.175954	−	0.984398i	$-0.556301\pi$
$751$	−30.5955	−	17.6643i	−1.11644	−	0.644580i	−0.940491	+	0.339819i	$0.889634\pi$
$752$		0			0
$753$	−0.310057	−	0.537034i	−0.0112991	−	0.0195706i
$754$		0			0
$755$	−7.27401	−	7.27401i	−0.264728	−	0.264728i
$756$		0			0
$757$	1.06021	−	1.06021i	0.0385339	−	0.0385339i	−0.687577	−	0.726111i	$-0.741326\pi$
$757$	1.06021	−	1.06021i	0.0385339	−	0.0385339i	0.726111	+	0.687577i	$0.241326\pi$
$758$		0			0
$759$	2.66127	−	1.53649i	0.0965981	−	0.0557709i
$760$		0			0
$761$	−15.2003	+	26.3277i	−0.551010	+	0.954378i	0.447192	+	0.894438i	$0.352424\pi$
$761$	−15.2003	+	26.3277i	−0.551010	+	0.954378i	−0.998202	+	0.0599396i	$0.980909\pi$
$762$		0			0
$763$	−27.1535	−	4.06755i	−0.983023	−	0.147255i
$764$		0			0
$765$	16.6390	−	4.45840i	0.601584	−	0.161194i
$766$		0			0
$767$	15.3853	−	8.88274i	0.555533	−	0.320737i
$768$		0			0
$769$			38.0523i			1.37220i	0.727507	+	0.686101i	$0.240679\pi$
$769$			38.0523i			1.37220i	−0.727507	+	0.686101i	$0.759321\pi$
$770$		0			0
$771$	−7.06039	+	7.06039i	−0.254274	+	0.254274i
$772$		0			0
$773$	4.02680	−	15.0282i	0.144834	−	0.540528i	−0.854929	−	0.518746i	$-0.826399\pi$
$773$	4.02680	−	15.0282i	0.144834	−	0.540528i	0.999763	−	0.0217825i	$-0.00693413\pi$
$774$		0			0
$775$	−19.0796	−	11.0156i	−0.685361	−	0.395693i
$776$		0			0
$777$	1.35511	+	11.9297i	0.0486142	+	0.427975i
$778$		0			0
$779$	1.47039	−	0.393989i	0.0526820	−	0.0141161i
$780$		0			0
$781$	−9.17123	+	34.2275i	−0.328172	+	1.22476i
$782$		0			0
$783$	−17.0918			−0.610812
$784$		0			0
$785$	−12.7134			−0.453760
$786$		0			0
$787$	4.32518	−	16.1418i	0.154176	−	0.575393i	−0.844998	−	0.534769i	$-0.820399\pi$
$787$	4.32518	−	16.1418i	0.154176	−	0.575393i	0.999175	−	0.0406241i	$-0.0129346\pi$
$788$		0			0
$789$	−4.83129	+	1.29454i	−0.171998	+	0.0460868i
$790$		0			0
$791$	−4.01937	−	35.3845i	−0.142912	−	1.25813i
$792$		0			0
$793$	−11.4256	−	6.59659i	−0.405736	−	0.234252i
$794$		0			0
$795$	−0.581386	+	2.16976i	−0.0206196	+	0.0769535i
$796$		0			0
$797$	6.46029	−	6.46029i	0.228835	−	0.228835i	−0.583371	−	0.812206i	$-0.698267\pi$
$797$	6.46029	−	6.46029i	0.228835	−	0.228835i	0.812206	+	0.583371i	$0.198267\pi$
$798$		0			0
$799$		−	22.5486i		−	0.797710i
$800$		0			0
$801$	11.9457	−	6.89688i	0.422082	−	0.243689i
$802$		0			0
$803$	78.9780	−	21.1621i	2.78707	−	0.746794i
$804$		0			0
$805$	1.94194	+	0.290899i	0.0684442	+	0.0102528i
$806$		0			0
$807$	−5.21101	+	9.02573i	−0.183436	+	0.317721i
$808$		0			0
$809$	−24.9554	+	14.4080i	−0.877386	+	0.506559i	−0.869796	−	0.493412i	$-0.835750\pi$
$809$	−24.9554	+	14.4080i	−0.877386	+	0.506559i	−0.00759061	+	0.999971i	$0.502416\pi$
$810$		0			0
$811$	−32.3761	+	32.3761i	−1.13688	+	1.13688i	−0.147873	+	0.989006i	$0.547243\pi$
$811$	−32.3761	+	32.3761i	−1.13688	+	1.13688i	−0.989006	+	0.147873i	$0.952757\pi$
$812$		0			0
$813$	−5.62163	−	5.62163i	−0.197159	−	0.197159i
$814$		0			0
$815$	−9.19808	−	15.9315i	−0.322195	−	0.558058i
$816$		0			0
$817$	−14.0219	−	8.09555i	−0.490564	−	0.283227i
$818$		0			0
$819$	4.57268	+	11.6200i	0.159782	+	0.406036i
$820$		0			0
$821$	−7.00094	−	26.1279i	−0.244334	−	0.911869i	−0.973717	−	0.227762i	$-0.926859\pi$
$821$	−7.00094	−	26.1279i	−0.244334	−	0.911869i	0.729382	−	0.684106i	$-0.239808\pi$
$822$		0			0
$823$	12.1699	+	21.0790i	0.424218	+	0.734767i	0.996347	−	0.0853968i	$-0.0272158\pi$
$823$	12.1699	+	21.0790i	0.424218	+	0.734767i	−0.572129	+	0.820163i	$0.693882\pi$
$824$		0			0
$825$	−17.4035			−0.605913
$826$		0			0
$827$	−31.7583	−	31.7583i	−1.10435	−	1.10435i	−0.993880	−	0.110466i	$-0.964766\pi$
$827$	−31.7583	−	31.7583i	−1.10435	−	1.10435i	−0.110466	−	0.993880i	$-0.535234\pi$
$828$		0			0
$829$	−39.6910	−	10.6352i	−1.37853	−	0.369375i	−0.507941	−	0.861392i	$-0.669593\pi$
$829$	−39.6910	−	10.6352i	−1.37853	−	0.369375i	−0.870586	+	0.492017i	$0.836260\pi$
$830$		0			0
$831$	17.6694	−	30.6042i	0.612944	−	1.06165i
$832$		0			0
$833$	−33.6826	+	31.3668i	−1.16703	+	1.08679i
$834$		0			0
$835$	−8.07125	−	30.1223i	−0.279317	−	1.04243i
$836$		0			0
$837$	−38.4939	−	10.3144i	−1.33054	−	0.356518i
$838$		0			0
$839$			12.4384i			0.429423i	0.976678	+	0.214711i	$0.0688811\pi$
$839$			12.4384i			0.429423i	−0.976678	+	0.214711i	$0.931119\pi$
$840$		0			0
$841$		−	18.3958i		−	0.634339i
$842$		0			0
$843$	4.32149	+	1.15794i	0.148840	+	0.0398816i
$844$		0			0
$845$	2.32061	+	8.66065i	0.0798316	+	0.297935i
$846$		0			0
$847$	20.2656	−	46.5645i	0.696335	−	1.59997i
$848$		0			0
$849$	−7.45561	+	12.9135i	−0.255876	+	0.443190i
$850$		0			0
$851$	−2.05748	−	0.551301i	−0.0705297	−	0.0188984i
$852$		0			0
$853$	11.8456	+	11.8456i	0.405585	+	0.405585i	0.880196	−	0.474611i	$-0.157411\pi$
$853$	11.8456	+	11.8456i	0.405585	+	0.405585i	−0.474611	+	0.880196i	$0.657411\pi$
$854$		0			0
$855$	−8.80008			−0.300956
$856$		0			0
$857$	7.54656	+	13.0710i	0.257786	+	0.446498i	0.965648	−	0.259852i	$-0.0836738\pi$
$857$	7.54656	+	13.0710i	0.257786	+	0.446498i	−0.707863	+	0.706350i	$0.750340\pi$
$858$		0			0
$859$	11.8045	+	44.0551i	0.402765	+	1.50314i	0.808141	+	0.588990i	$0.200474\pi$
$859$	11.8045	+	44.0551i	0.402765	+	1.50314i	−0.405375	+	0.914150i	$0.632859\pi$
$860$		0			0
$861$	1.29432	+	0.193888i	0.0441104	+	0.00660767i
$862$		0			0
$863$	23.4497	+	13.5387i	0.798237	+	0.460862i	0.842854	−	0.538142i	$-0.180874\pi$
$863$	23.4497	+	13.5387i	0.798237	+	0.460862i	−0.0446175	+	0.999004i	$0.514207\pi$
$864$		0			0
$865$	−14.5080	−	25.1285i	−0.493286	−	0.854396i
$866$		0			0
$867$	20.2469	+	20.2469i	0.687619	+	0.687619i
$868$		0			0
$869$	14.9754	−	14.9754i	0.508004	−	0.508004i
$870$		0			0
$871$	−14.5023	+	8.37290i	−0.491391	+	0.283705i
$872$		0			0
$873$	10.1418	−	17.5660i	0.343246	−	0.594520i
$874$		0			0
$875$	−23.6938	−	18.8600i	−0.800995	−	0.637585i
$876$		0			0
$877$	8.80425	−	2.35909i	0.297298	−	0.0796609i	−0.107087	−	0.994250i	$-0.534152\pi$
$877$	8.80425	−	2.35909i	0.297298	−	0.0796609i	0.404385	+	0.914589i	$0.367486\pi$
$878$		0			0
$879$	−22.3173	+	12.8849i	−0.752745	+	0.434598i
$880$		0			0
$881$		−	0.723819i		−	0.0243861i	−0.999926	−	0.0121930i	$-0.996119\pi$
$881$		−	0.723819i		−	0.0243861i	0.999926	−	0.0121930i	$-0.00388126\pi$
$882$		0			0
$883$	−21.2381	+	21.2381i	−0.714718	+	0.714718i	−0.967518	−	0.252800i	$-0.918648\pi$
$883$	−21.2381	+	21.2381i	−0.714718	+	0.714718i	0.252800	+	0.967518i	$0.418648\pi$
$884$		0			0
$885$	−2.78588	+	10.3971i	−0.0936464	+	0.349493i
$886$		0			0
$887$	−17.5247	−	10.1179i	−0.588422	−	0.339726i	0.176051	−	0.984381i	$-0.443668\pi$
$887$	−17.5247	−	10.1179i	−0.588422	−	0.339726i	−0.764473	+	0.644655i	$0.777001\pi$
$888$		0			0
$889$	36.1088	−	4.10164i	1.21105	−	0.137565i
$890$		0			0
$891$	−1.61002	+	0.431403i	−0.0539377	+	0.0144526i
$892$		0			0
$893$	−2.98139	+	11.1267i	−0.0997683	+	0.372340i
$894$		0			0
$895$	−9.86738			−0.329830
$896$		0			0
$897$	1.45942			0.0487288
$898$		0			0
$899$	−6.39931	+	23.8825i	−0.213429	+	0.796528i
$900$		0			0
$901$	9.02281	−	2.41766i	0.300594	−	0.0805438i
$902$		0			0
$903$	−8.27634	−	11.1928i	−0.275419	−	0.372473i
$904$		0			0
$905$	11.2129	+	6.47376i	0.372729	+	0.215195i
$906$		0			0
$907$	3.46515	−	12.9321i	0.115058	−	0.429404i	−0.884233	−	0.467046i	$-0.845318\pi$
$907$	3.46515	−	12.9321i	0.115058	−	0.429404i	0.999291	+	0.0376423i	$0.0119848\pi$
$908$		0			0
$909$	−24.8764	+	24.8764i	−0.825099	+	0.825099i
$910$		0			0
$911$		−	34.5549i		−	1.14485i	−0.819955	−	0.572427i	$-0.806002\pi$
$911$		−	34.5549i		−	1.14485i	0.819955	−	0.572427i	$-0.193998\pi$
$912$		0			0
$913$	16.4244	−	9.48262i	0.543568	−	0.313829i
$914$		0			0
$915$	7.72117	−	2.06888i	0.255254	−	0.0683951i
$916$		0			0
$917$	2.82307	+	7.17393i	0.0932260	+	0.236904i
$918$		0			0
$919$	26.7589	−	46.3478i	0.882695	−	1.52887i	0.0343626	−	0.999409i	$-0.489060\pi$
$919$	26.7589	−	46.3478i	0.882695	−	1.52887i	0.848333	−	0.529464i	$-0.177607\pi$
$920$		0			0
$921$	22.4040	−	12.9350i	0.738238	−	0.426222i
$922$		0			0
$923$	−11.8998	+	11.8998i	−0.391686	+	0.391686i
$924$		0			0
$925$	8.53014	+	8.53014i	0.280469	+	0.280469i
$926$		0			0
$927$	−6.42208	−	11.1234i	−0.210929	−	0.365339i
$928$		0			0
$929$	−0.0427340	−	0.0246725i	−0.00140206	−	0.000809477i	0.499299	−	0.866430i	$-0.333591\pi$
$929$	−0.0427340	−	0.0246725i	−0.00140206	−	0.000809477i	−0.500701	+	0.865620i	$0.666924\pi$
$930$		0			0
$931$	20.7682	−	11.0245i	0.680649	−	0.361314i
$932$		0			0
$933$	6.06927	+	22.6508i	0.198699	+	0.741554i
$934$		0			0
$935$	−26.1685	−	45.3252i	−0.855802	−	1.48229i
$936$		0			0
$937$	−0.977039			−0.0319185			−0.0159592	−	0.999873i	$-0.505080\pi$
$937$	−0.977039			−0.0319185			−0.0159592	+	0.999873i	$0.505080\pi$
$938$		0			0
$939$	16.0925	+	16.0925i	0.525157	+	0.525157i
$940$		0			0
$941$	37.6344	+	10.0841i	1.22685	+	0.328733i	0.813351	−	0.581773i	$-0.197641\pi$
$941$	37.6344	+	10.0841i	1.22685	+	0.328733i	0.413496	+	0.910506i	$0.364307\pi$
$942$		0			0
$943$	−0.116095	+	0.201082i	−0.00378056	+	0.00654812i
$944$		0			0
$945$	−18.4448	−	8.02748i	−0.600010	−	0.261134i
$946$		0			0
$947$	−5.93312	−	22.1427i	−0.192801	−	0.719541i	−0.992825	−	0.119574i	$-0.961847\pi$
$947$	−5.93312	−	22.1427i	−0.192801	−	0.719541i	0.800025	−	0.599967i	$-0.204820\pi$
$948$		0			0
$949$	37.5084	+	10.0504i	1.21757	+	0.326248i
$950$		0			0
$951$		−	16.2702i		−	0.527599i
$952$		0			0
$953$		−	34.2308i		−	1.10884i	−0.832235	−	0.554422i	$-0.812939\pi$
$953$		−	34.2308i		−	1.10884i	0.832235	−	0.554422i	$-0.187061\pi$
$954$		0			0
$955$	−18.6407	−	4.99477i	−0.603200	−	0.161627i
$956$		0			0
$957$	5.05511	+	18.8659i	0.163408	+	0.609849i
$958$		0			0
$959$	11.3650	+	15.3698i	0.366995	+	0.496318i
$960$		0			0
$961$	−13.3248	+	23.0793i	−0.429834	+	0.744494i
$962$		0			0
$963$	−20.9487	−	5.61320i	−0.675064	−	0.180883i
$964$		0			0
$965$	10.7710	+	10.7710i	0.346729	+	0.346729i
$966$		0			0
$967$	−21.2761			−0.684193			−0.342096	−	0.939665i	$-0.611137\pi$
$967$	−21.2761			−0.684193			−0.342096	+	0.939665i	$0.611137\pi$
$968$		0			0
$969$	−12.0536	−	20.8775i	−0.387218	−	0.670680i
$970$		0			0
$971$	7.74616	+	28.9091i	0.248586	+	0.927736i	0.971547	+	0.236847i	$0.0761139\pi$
$971$	7.74616	+	28.9091i	0.248586	+	0.927736i	−0.722961	+	0.690889i	$0.757219\pi$
$972$		0			0
$973$	2.07551	+	1.65209i	0.0665379	+	0.0529635i
$974$		0			0
$975$	−7.15798	−	4.13266i	−0.229239	−	0.132351i
$976$		0			0
$977$	1.50722	+	2.61058i	0.0482201	+	0.0835197i	0.889128	−	0.457659i	$-0.151312\pi$
$977$	1.50722	+	2.61058i	0.0482201	+	0.0835197i	−0.840908	+	0.541178i	$0.817978\pi$
$978$		0			0
$979$	−29.6342	−	29.6342i	−0.947115	−	0.947115i
$980$		0			0
$981$	−13.2714	+	13.2714i	−0.423724	+	0.423724i
$982$		0			0
$983$	−35.2886	+	20.3739i	−1.12553	+	0.649826i	−0.942807	−	0.333339i	$-0.891825\pi$
$983$	−35.2886	+	20.3739i	−1.12553	+	0.649826i	−0.182724	+	0.983164i	$0.558491\pi$
$984$		0			0
$985$	−14.4059	+	24.9517i	−0.459010	+	0.795029i
$986$		0			0
$987$	−6.16781	+	7.74860i	−0.196324	+	0.246641i
$988$		0			0
$989$	2.38547	−	0.639186i	0.0758536	−	0.0203249i
$990$		0			0
$991$	21.1944	−	12.2366i	0.673262	−	0.388708i	−0.124049	−	0.992276i	$-0.539588\pi$
$991$	21.1944	−	12.2366i	0.673262	−	0.388708i	0.797312	+	0.603568i	$0.206255\pi$
$992$		0			0
$993$			3.26581i			0.103637i
$994$		0			0
$995$	24.7792	−	24.7792i	0.785552	−	0.785552i
$996$		0			0
$997$	11.1506	−	41.6146i	0.353143	−	1.31795i	−0.529662	−	0.848209i	$-0.677681\pi$
$997$	11.1506	−	41.6146i	0.353143	−	1.31795i	0.882805	−	0.469740i	$-0.155652\pi$
$998$		0			0
$999$	18.8978	+	10.9106i	0.597899	+	0.345197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.z.a.607.5		56
4.3	odd	2		896.2.z.b.607.10		56
7.3	odd	6	inner	896.2.z.a.479.5		56
8.3	odd	2		112.2.v.a.19.12	yes	56
8.5	even	2		448.2.z.a.47.10		56
16.3	odd	4		448.2.z.a.271.10		56
16.5	even	4		896.2.z.b.159.10		56
16.11	odd	4	inner	896.2.z.a.159.5		56
16.13	even	4		112.2.v.a.75.3	yes	56
28.3	even	6		896.2.z.b.479.10		56
56.3	even	6		112.2.v.a.3.3	✓	56
56.11	odd	6		784.2.w.f.227.3		56
56.19	even	6		784.2.j.a.195.14		56
56.27	even	2		784.2.w.f.19.12		56
56.45	odd	6		448.2.z.a.367.10		56
56.51	odd	6		784.2.j.a.195.13		56
112.3	even	12		448.2.z.a.143.10		56
112.13	odd	4		784.2.w.f.411.3		56
112.45	odd	12		112.2.v.a.59.12	yes	56
112.59	even	12	inner	896.2.z.a.31.5		56
112.61	odd	12		784.2.j.a.587.13		56
112.93	even	12		784.2.j.a.587.14		56
112.101	odd	12		896.2.z.b.31.10		56
112.109	even	12		784.2.w.f.619.12		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.3	✓	56	56.3	even	6
112.2.v.a.19.12	yes	56	8.3	odd	2
112.2.v.a.59.12	yes	56	112.45	odd	12
112.2.v.a.75.3	yes	56	16.13	even	4
448.2.z.a.47.10		56	8.5	even	2
448.2.z.a.143.10		56	112.3	even	12
448.2.z.a.271.10		56	16.3	odd	4
448.2.z.a.367.10		56	56.45	odd	6
784.2.j.a.195.13		56	56.51	odd	6
784.2.j.a.195.14		56	56.19	even	6
784.2.j.a.587.13		56	112.61	odd	12
784.2.j.a.587.14		56	112.93	even	12
784.2.w.f.19.12		56	56.27	even	2
784.2.w.f.227.3		56	56.11	odd	6
784.2.w.f.411.3		56	112.13	odd	4
784.2.w.f.619.12		56	112.109	even	12
896.2.z.a.31.5		56	112.59	even	12	inner
896.2.z.a.159.5		56	16.11	odd	4	inner
896.2.z.a.479.5		56	7.3	odd	6	inner
896.2.z.a.607.5		56	1.1	even	1	trivial
896.2.z.b.31.10		56	112.101	odd	12
896.2.z.b.159.10		56	16.5	even	4
896.2.z.b.479.10		56	28.3	even	6
896.2.z.b.607.10		56	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.282507 + 1.05433i) q^{3} +(1.39922 - 0.374919i) q^{5} +(0.298614 + 2.62885i) q^{7} +(1.56627 + 0.904287i) q^{9} +(1.42219 - 5.30770i) q^{11} +(1.84531 - 1.84531i) q^{13} +1.58116i q^{15} +(5.69424 - 3.28757i) q^{17} +(-3.24453 + 0.869370i) q^{19} +(-2.85604 - 0.427830i) q^{21} +(0.256173 - 0.443704i) q^{23} +(-2.51288 + 1.45081i) q^{25} +(-3.71137 + 3.71137i) q^{27} +(2.30263 + 2.30263i) q^{29} +(3.79637 + 6.57551i) q^{31} +(5.19429 + 2.99893i) q^{33} +(1.40343 + 3.56637i) q^{35} +(-1.07603 - 4.01582i) q^{37} +(1.42426 + 2.46689i) q^{39} -0.453189 q^{41} +(3.40842 + 3.40842i) q^{43} +(2.53059 + 0.678070i) q^{45} +(1.71468 - 2.96992i) q^{47} +(-6.82166 + 1.57002i) q^{49} +(1.85753 + 6.93238i) q^{51} +(1.37226 + 0.367696i) q^{53} -7.95984i q^{55} -3.66642i q^{57} +(6.57560 + 1.76193i) q^{59} +(-1.30846 - 4.88324i) q^{61} +(-1.90952 + 4.38752i) q^{63} +(1.89015 - 3.27384i) q^{65} +(-6.19818 - 1.66080i) q^{67} +(0.395441 + 0.395441i) q^{69} -6.44865 q^{71} +(7.43995 + 12.8864i) q^{73} +(-0.819730 - 3.05927i) q^{75} +(14.3778 + 2.15377i) q^{77} +(3.33780 + 1.92708i) q^{79} +(-0.151668 - 0.262697i) q^{81} +(2.44051 + 2.44051i) q^{83} +(6.73491 - 6.73491i) q^{85} +(-3.07824 + 1.77722i) q^{87} +(3.81344 - 6.60506i) q^{89} +(5.40208 + 4.30001i) q^{91} +(-8.00527 + 2.14500i) q^{93} +(-4.21387 + 2.43288i) q^{95} -11.2152i q^{97} +(7.02722 - 7.02722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 6 q^{5} + 8 q^{7} + 2 q^{11} - 12 q^{17} - 6 q^{19} + 10 q^{21} + 12 q^{23} + 24 q^{29} - 12 q^{33} - 2 q^{35} - 6 q^{37} + 4 q^{39} - 12 q^{45} - 8 q^{49} - 34 q^{51} - 6 q^{53} + 42 q^{59}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 6 * q^5 + 8 * q^7 + 2 * q^11 - 12 * q^17 - 6 * q^19 + 10 * q^21 + 12 * q^23 + 24 * q^29 - 12 * q^33 - 2 * q^35 - 6 * q^37 + 4 * q^39 - 12 * q^45 - 8 * q^49 - 34 * q^51 - 6 * q^53 + 42 * q^59 + 6 * q^61 - 4 * q^65 + 6 * q^67 + 80 * q^71 + 24 * q^75 - 10 * q^77 - 8 * q^81 + 28 * q^85 + 12 * q^87 + 16 * q^91 - 10 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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