LMFDB - Embedded newform 448.2.z.a.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(47,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("448.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.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:	$3.57729801055$
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			47.10
Character	$\chi$	$=$	448.47
Dual form			448.2.z.a.143.10

$q$-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 $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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	$-0.814630\pi$
$3$	0.282507	−	1.05433i	0.163106	−	0.608719i	0.998274	−	0.0587246i	$-0.0187034\pi$
$4$		0			0
$5$	−1.39922	+	0.374919i	−0.625749	+	0.167669i	−0.557740	−	0.830016i	$-0.688331\pi$
$5$	−1.39922	+	0.374919i	−0.625749	+	0.167669i	−0.0680093	+	0.997685i	$0.521665\pi$
$6$		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	$0.394077\pi$
$11$	−1.42219	+	5.30770i	−0.428807	+	1.60033i	−0.755465	+	0.655189i	$0.772589\pi$
$12$		0			0
$13$	−1.84531	+	1.84531i	−0.511798	+	0.511798i	−0.915077	−	0.403279i	$-0.867870\pi$
$13$	−1.84531	+	1.84531i	−0.511798	+	0.511798i	0.403279	+	0.915077i	$0.367870\pi$
$14$		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	0.133338	−	0.991071i	$-0.457431\pi$
$19$	3.24453	−	0.869370i	0.744347	−	0.199447i	0.611009	+	0.791624i	$0.290764\pi$
$20$		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	0.460219	−	0.887806i	$-0.347771\pi$
$29$	−2.30263	−	2.30263i	−0.427587	−	0.427587i	−0.887806	+	0.460219i	$0.847771\pi$
$30$		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	$0.0276838\pi$
$37$	1.07603	+	4.01582i	0.176899	+	0.660196i	−0.819321	+	0.573334i	$0.805650\pi$
$38$		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	0.397726	−	0.917504i	$-0.369800\pi$
$43$	−3.40842	−	3.40842i	−0.519779	−	0.519779i	−0.917504	+	0.397726i	$0.869800\pi$
$44$		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	0.163337	−	0.986570i	$-0.447774\pi$
$53$	−1.37226	−	0.367696i	−0.188495	−	0.0505070i	−0.351831	+	0.936063i	$0.614441\pi$
$54$		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	−0.196015	−	0.980601i	$-0.562800\pi$
$59$	−6.57560	−	1.76193i	−0.856070	−	0.229383i	−0.660055	+	0.751218i	$0.729467\pi$
$60$		0			0
$61$	1.30846	+	4.88324i	0.167531	+	0.625235i	0.997704	+	0.0677284i	$0.0215751\pi$
$61$	1.30846	+	4.88324i	0.167531	+	0.625235i	−0.830173	+	0.557506i	$0.811758\pi$
$62$		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	0.616722	−	0.787181i	$-0.288460\pi$
$67$	6.19818	+	1.66080i	0.757229	+	0.202899i	0.140507	+	0.990080i	$0.455127\pi$
$68$		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	0.560365	−	0.828246i	$-0.310661\pi$
$83$	−2.44051	−	2.44051i	−0.267881	−	0.267881i	−0.828246	+	0.560365i	$0.810661\pi$
$84$		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	$-0.497691\pi$
$101$	5.03457	−	18.7893i	0.500959	−	1.86960i	0.493704	−	0.869630i	$-0.335643\pi$
$102$		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	0.348981	−	0.937130i	$-0.386528\pi$
$107$	11.5830	−	3.10366i	1.11977	−	0.300042i	0.770791	+	0.637088i	$0.219861\pi$
$108$		0			0
$109$	2.68591	−	10.0240i	0.257264	−	0.960122i	−0.709553	−	0.704652i	$-0.751103\pi$
$109$	2.68591	−	10.0240i	0.257264	−	0.960122i	0.966817	−	0.255470i	$-0.0822302\pi$
$110$		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	−0.379670	−	0.925122i	$-0.623962\pi$
$131$	−2.81460	+	0.754169i	−0.245912	+	0.0658920i	0.133757	+	0.991014i	$0.457296\pi$
$132$		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	−0.736535	−	0.676400i	$-0.763539\pi$
$139$	−0.708981	+	0.708981i	−0.0601350	+	0.0601350i	0.676400	+	0.736535i	$0.263539\pi$
$140$		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	$0.0441766\pi$
$149$	2.46397	+	9.19566i	0.201856	+	0.753338i	−0.788529	+	0.614998i	$0.789157\pi$
$150$		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	0.580713	−	0.814108i	$-0.302774\pi$
$157$	8.47741	+	2.27152i	0.676571	+	0.181287i	0.0958582	+	0.995395i	$0.469440\pi$
$158$		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	$0.0823600\pi$
$163$	3.28686	+	12.2667i	0.257447	+	0.960805i	−0.709266	+	0.704941i	$0.750973\pi$
$164$		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	$0.192179\pi$
$173$	5.18431	+	19.3481i	0.394156	+	1.47101i	−0.429057	+	0.903278i	$0.641154\pi$
$174$		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	0.496186	−	0.868216i	$-0.334733\pi$
$179$	6.57967	+	1.76302i	0.491787	+	0.131774i	−0.00439858	+	0.999990i	$0.501400\pi$
$180$		0			0
$181$	−6.32019	−	6.32019i	−0.469776	−	0.469776i	0.432066	−	0.901842i	$-0.357785\pi$
$181$	−6.32019	−	6.32019i	−0.469776	−	0.469776i	−0.901842	+	0.432066i	$0.857785\pi$
$182$		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	$-0.499353\pi$
$197$	14.0642	−	14.0642i	1.00203	−	1.00203i	0.999998	−	0.00203129i	$-0.000646580\pi$
$198$		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	−0.942085	−	0.335375i	$-0.891137\pi$
$211$	−8.81296	+	8.81296i	−0.606709	+	0.606709i	0.335375	+	0.942085i	$0.391137\pi$
$212$		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	−0.977647	−	0.210255i	$-0.932570\pi$
$227$	−0.389502	+	1.45364i	−0.0258521	+	0.0964815i	0.951794	+	0.306737i	$0.0992371\pi$
$228$		0			0
$229$	4.77902	−	1.28054i	0.315807	−	0.0846202i	−0.0974340	−	0.995242i	$-0.531063\pi$
$229$	4.77902	−	1.28054i	0.315807	−	0.0846202i	0.413241	+	0.910622i	$0.364397\pi$
$230$		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	−0.694315	−	0.719671i	$-0.744293\pi$
$251$	0.401720	−	0.401720i	0.0253563	−	0.0253563i	0.719671	+	0.694315i	$0.244293\pi$
$252$		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	−0.0335497	−	0.999437i	$-0.510681\pi$
$269$	−9.22279	−	2.47124i	−0.562323	−	0.150674i	−0.528773	+	0.848763i	$0.677348\pi$
$270$		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	$0.00868875\pi$
$277$	31.2724	+	8.37942i	1.87898	+	0.503470i	0.879349	+	0.476177i	$0.157978\pi$
$278$		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	−0.155669	−	0.987809i	$-0.549753\pi$
$283$	−13.1954	−	3.53570i	−0.784387	−	0.210176i	−0.628718	+	0.777633i	$0.716420\pi$
$284$		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	0.0244213	−	0.999702i	$-0.492226\pi$
$293$	−16.6941	−	16.6941i	−0.975280	−	0.975280i	−0.999702	+	0.0244213i	$0.992226\pi$
$294$		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	0.999092	−	0.0426074i	$-0.0135665\pi$
$307$	16.7590	+	16.7590i	0.956484	+	0.956484i	−0.0426074	+	0.999092i	$0.513566\pi$
$308$		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	0.169287	−	0.985567i	$-0.445854\pi$
$317$	14.3981	−	3.85795i	0.808676	−	0.216684i	0.639390	+	0.768883i	$0.279187\pi$
$318$		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	−0.337367	−	0.941373i	$-0.609536\pi$
$331$	−2.89002	+	0.774378i	−0.158850	+	0.0425637i	0.178518	+	0.983937i	$0.442870\pi$
$332$		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	−0.911724	−	0.410804i	$-0.865248\pi$
$347$	1.55085	−	5.78787i	0.0832542	−	0.310709i	0.994978	+	0.100095i	$0.0319147\pi$
$348$		0			0
$349$	3.15549	−	3.15549i	0.168909	−	0.168909i	−0.617590	−	0.786500i	$-0.711891\pi$
$349$	3.15549	−	3.15549i	0.168909	−	0.168909i	0.786500	+	0.617590i	$0.211891\pi$
$350$		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	$0.312506\pi$
$373$	9.46676	+	35.3304i	0.490170	+	1.82934i	−0.0653850	+	0.997860i	$0.520828\pi$
$374$		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	0.713780	−	0.700370i	$-0.246982\pi$
$379$	0.261074	+	0.261074i	0.0134105	+	0.0134105i	−0.700370	+	0.713780i	$0.746982\pi$
$380$		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	−0.331967	−	0.943291i	$-0.607712\pi$
$389$	−21.5199	−	5.76625i	−1.09110	−	0.292361i	−0.759137	+	0.650930i	$0.774379\pi$
$390$		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	$-0.880925\pi$
$397$	−6.12529	−	22.8599i	−0.307419	−	1.14730i	0.623424	−	0.781884i	$-0.285741\pi$
$398$		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	0.516219	−	0.856457i	$-0.327339\pi$
$419$	−6.96449	−	6.96449i	−0.340238	−	0.340238i	−0.856457	+	0.516219i	$0.827339\pi$
$420$		0			0
$421$	6.31935	−	6.31935i	0.307986	−	0.307986i	−0.536142	−	0.844128i	$-0.680119\pi$
$421$	6.31935	−	6.31935i	0.307986	−	0.307986i	0.844128	+	0.536142i	$0.180119\pi$
$422$		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	0.0303104	−	0.999541i	$-0.490350\pi$
$443$	11.7094	−	3.13752i	0.556330	−	0.149068i	0.526020	+	0.850472i	$0.323684\pi$
$444$		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	−0.999339	−	0.0363467i	$-0.988428\pi$
$461$	−20.6763	+	20.6763i	−0.962993	+	0.962993i	0.0363467	+	0.999339i	$0.488428\pi$
$462$		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	−0.478492	−	0.878092i	$-0.658816\pi$
$467$	−9.80739	+	2.62788i	−0.453832	+	0.121604i	0.0246599	+	0.999696i	$0.492150\pi$
$468$		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	0.916809	−	0.399326i	$-0.130756\pi$
$491$	11.4667	+	11.4667i	0.517483	+	0.517483i	−0.399326	+	0.916809i	$0.630756\pi$
$492$		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	$-0.942848\pi$
$499$	−4.93931	−	18.4338i	−0.221114	−	0.825209i	0.762810	−	0.646623i	$-0.223819\pi$
$500$		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	$-0.974509\pi$
$509$	−3.91534	−	14.6122i	−0.173544	−	0.647676i	0.823251	−	0.567678i	$-0.192158\pi$
$510$		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	$-0.954283\pi$
$523$	−4.66897	−	17.4249i	−0.204160	−	0.761936i	0.785544	−	0.618806i	$-0.212383\pi$
$524$		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	−0.314638	−	0.949212i	$-0.601883\pi$
$541$	−2.61709	+	0.701247i	−0.112518	+	0.0301490i	0.202121	+	0.979361i	$0.435217\pi$
$542$		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	−0.119078	−	0.992885i	$-0.537994\pi$
$547$	20.4366	−	20.4366i	0.873807	−	0.873807i	0.992885	+	0.119078i	$0.0379937\pi$
$548$		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	−0.935186	−	0.354156i	$-0.884768\pi$
$557$	1.22222	−	4.56137i	0.0517869	−	0.193271i	0.986973	+	0.160885i	$0.0514348\pi$
$558$		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	−0.914279	−	0.405085i	$-0.867242\pi$
$563$	1.89945	−	7.08884i	0.0800522	−	0.298759i	0.994331	+	0.106326i	$0.0339087\pi$
$564$		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	$0.380455\pi$
$571$	−9.94080	+	37.0996i	−0.416010	+	1.55257i	−0.782805	+	0.622267i	$0.786212\pi$
$572$		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	−0.845399	−	0.534135i	$-0.820637\pi$
$587$	−7.54134	+	7.54134i	−0.311264	+	0.311264i	0.534135	+	0.845399i	$0.320637\pi$
$588$		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	0.158564	−	0.987349i	$-0.449313\pi$
$613$	−4.89703	−	1.31216i	−0.197789	−	0.0529975i	−0.356354	+	0.934351i	$0.615980\pi$
$614$		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	−0.0486822	−	0.998814i	$-0.515502\pi$
$619$	−14.6852	−	3.93490i	−0.590249	−	0.158157i	−0.541567	+	0.840657i	$0.682169\pi$
$620$		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	0.935306	−	0.353841i	$-0.115125\pi$
$643$	14.7445	+	14.7445i	0.581464	+	0.581464i	−0.353841	+	0.935306i	$0.615125\pi$
$644$		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	0.0734551	−	0.997299i	$-0.476597\pi$
$653$	16.2451	−	4.35285i	0.635718	−	0.170340i	0.562263	+	0.826958i	$0.309931\pi$
$654$		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	$0.604636\pi$
$659$	−32.5839	+	32.5839i	−1.26929	+	1.26929i	−0.946455	+	0.322834i	$0.895364\pi$
$660$		0			0
$661$	4.53812	−	16.9365i	0.176512	−	0.658753i	−0.819777	−	0.572683i	$-0.805903\pi$
$661$	4.53812	−	16.9365i	0.176512	−	0.658753i	0.996289	−	0.0860697i	$-0.0274308\pi$
$662$		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	−0.147684	−	0.989035i	$-0.547182\pi$
$677$	5.69655	−	1.52639i	0.218936	−	0.0586638i	0.366620	+	0.930371i	$0.380515\pi$
$678$		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	−0.948356	−	0.317207i	$-0.897255\pi$
$683$	0.824476	−	3.07699i	0.0315477	−	0.117738i	0.979904	+	0.199469i	$0.0639218\pi$
$684$		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	0.151686	−	0.988429i	$-0.451530\pi$
$691$	20.4319	−	5.47470i	0.777265	−	0.208267i	0.625578	+	0.780161i	$0.284863\pi$
$692$		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	0.968649	−	0.248435i	$-0.0799162\pi$
$701$	19.0687	+	19.0687i	0.720214	+	0.720214i	−0.248435	+	0.968649i	$0.579916\pi$
$702$		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	$-0.855684\pi$
$709$	−9.03837	−	33.7317i	−0.339443	−	1.26682i	0.559528	−	0.828812i	$-0.310982\pi$
$710$		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	$0.0379495\pi$
$733$	5.21156	+	19.4498i	0.192493	+	0.718395i	−0.800408	+	0.599455i	$0.795384\pi$
$734$		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	−0.328856	−	0.944380i	$-0.606663\pi$
$739$	−29.5182	−	7.90938i	−1.08584	−	0.290951i	−0.756988	+	0.653429i	$0.773330\pi$
$740$		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	−0.726111	−	0.687577i	$-0.758674\pi$
$757$	−1.06021	+	1.06021i	−0.0385339	+	0.0385339i	0.687577	+	0.726111i	$0.258674\pi$
$758$		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	$0.173601\pi$
$773$	−4.02680	+	15.0282i	−0.144834	+	0.540528i	−0.999763	+	0.0217825i	$0.993066\pi$
$774$		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	$0.179601\pi$
$787$	−4.32518	+	16.1418i	−0.154176	+	0.575393i	−0.999175	+	0.0406241i	$0.987065\pi$
$788$		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	−0.812206	−	0.583371i	$-0.801733\pi$
$797$	−6.46029	+	6.46029i	−0.228835	+	0.228835i	0.583371	+	0.812206i	$0.301733\pi$
$798$		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	$-0.452757\pi$
$811$	32.3761	−	32.3761i	1.13688	−	1.13688i	0.989006	−	0.147873i	$-0.0472427\pi$
$812$		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	$0.0731409\pi$
$821$	7.00094	+	26.1279i	0.244334	+	0.911869i	−0.729382	+	0.684106i	$0.760192\pi$
$822$		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	$0.0352344\pi$
$827$	31.7583	+	31.7583i	1.10435	+	1.10435i	0.110466	+	0.993880i	$0.464766\pi$
$828$		0			0
$829$	39.6910	+	10.6352i	1.37853	+	0.369375i	0.870586	−	0.492017i	$-0.163740\pi$
$829$	39.6910	+	10.6352i	1.37853	+	0.369375i	0.507941	+	0.861392i	$0.330407\pi$
$830$		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	0.474611	−	0.880196i	$-0.342589\pi$
$853$	−11.8456	−	11.8456i	−0.405585	−	0.405585i	−0.880196	+	0.474611i	$0.842589\pi$
$854$		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	$-0.799526\pi$
$859$	−11.8045	−	44.0551i	−0.402765	−	1.50314i	0.405375	−	0.914150i	$-0.367141\pi$
$860$		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	−0.404385	−	0.914589i	$-0.632514\pi$
$877$	−8.80425	+	2.35909i	−0.297298	+	0.0796609i	0.107087	+	0.994250i	$0.465848\pi$
$878$		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	−0.252800	−	0.967518i	$-0.581352\pi$
$883$	21.2381	−	21.2381i	0.714718	−	0.714718i	0.967518	+	0.252800i	$0.0813516\pi$
$884$		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	−0.999291	−	0.0376423i	$-0.988015\pi$
$907$	−3.46515	+	12.9321i	−0.115058	+	0.429404i	0.884233	+	0.467046i	$0.154682\pi$
$908$		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	−0.413496	−	0.910506i	$-0.635693\pi$
$941$	−37.6344	−	10.0841i	−1.22685	−	0.328733i	−0.813351	+	0.581773i	$0.802359\pi$
$942$		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	$0.0381530\pi$
$947$	5.93312	+	22.1427i	0.192801	+	0.719541i	−0.800025	+	0.599967i	$0.795180\pi$
$948$		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	$-0.923886\pi$
$971$	−7.74616	−	28.9091i	−0.248586	−	0.927736i	0.722961	−	0.690889i	$-0.242781\pi$
$972$		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	$0.322319\pi$
$997$	−11.1506	+	41.6146i	−0.353143	+	1.31795i	−0.882805	+	0.469740i	$0.844348\pi$
$998$		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	448.2.z.a.47.10		56
4.3	odd	2		112.2.v.a.19.12	yes	56
7.3	odd	6	inner	448.2.z.a.367.10		56
8.3	odd	2		896.2.z.b.607.10		56
8.5	even	2		896.2.z.a.607.5		56
16.3	odd	4		896.2.z.a.159.5		56
16.5	even	4		112.2.v.a.75.3	yes	56
16.11	odd	4	inner	448.2.z.a.271.10		56
16.13	even	4		896.2.z.b.159.10		56
28.3	even	6		112.2.v.a.3.3	✓	56
28.11	odd	6		784.2.w.f.227.3		56
28.19	even	6		784.2.j.a.195.14		56
28.23	odd	6		784.2.j.a.195.13		56
28.27	even	2		784.2.w.f.19.12		56
56.3	even	6		896.2.z.b.479.10		56
56.45	odd	6		896.2.z.a.479.5		56
112.3	even	12		896.2.z.a.31.5		56
112.5	odd	12		784.2.j.a.587.13		56
112.37	even	12		784.2.j.a.587.14		56
112.45	odd	12		896.2.z.b.31.10		56
112.53	even	12		784.2.w.f.619.12		56
112.59	even	12	inner	448.2.z.a.143.10		56
112.69	odd	4		784.2.w.f.411.3		56
112.101	odd	12		112.2.v.a.59.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.3	✓	56	28.3	even	6
112.2.v.a.19.12	yes	56	4.3	odd	2
112.2.v.a.59.12	yes	56	112.101	odd	12
112.2.v.a.75.3	yes	56	16.5	even	4
448.2.z.a.47.10		56	1.1	even	1	trivial
448.2.z.a.143.10		56	112.59	even	12	inner
448.2.z.a.271.10		56	16.11	odd	4	inner
448.2.z.a.367.10		56	7.3	odd	6	inner
784.2.j.a.195.13		56	28.23	odd	6
784.2.j.a.195.14		56	28.19	even	6
784.2.j.a.587.13		56	112.5	odd	12
784.2.j.a.587.14		56	112.37	even	12
784.2.w.f.19.12		56	28.27	even	2
784.2.w.f.227.3		56	28.11	odd	6
784.2.w.f.411.3		56	112.69	odd	4
784.2.w.f.619.12		56	112.53	even	12
896.2.z.a.31.5		56	112.3	even	12
896.2.z.a.159.5		56	16.3	odd	4
896.2.z.a.479.5		56	56.45	odd	6
896.2.z.a.607.5		56	8.5	even	2
896.2.z.b.31.10		56	112.45	odd	12
896.2.z.b.159.10		56	16.13	even	4
896.2.z.b.479.10		56	56.3	even	6
896.2.z.b.607.10		56	8.3	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.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

Fields

Representations

Groups

Database

Properties

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