LMFDB - Embedded newform 440.2.y.c.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [440,2,Mod(81,440)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("440.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(440, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-1,0,3,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 5 x^{10} + 4 x^{9} + 28 x^{8} - 81 x^{7} + 335 x^{6} - 235 x^{5} + 782 x^{4} + \cdots + 1 $ x^12 - x^11 + 5x^10 + 4x^9 + 28x^8 - 81x^7 + 335x^6 - 235x^5 + 782x^4 - 302x^3 + 711x^2 - 43x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$0.830630 + 2.55642i$ of defining polynomial
Character	$\chi$	$=$	440.361
Dual form			440.2.y.c.401.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36560 + 0.992167i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(0.156923 + 0.114011i) q^{7} +(-0.0465816 + 0.143363i) q^{9} +(-3.15191 + 1.03221i) q^{11} +(-0.153004 + 0.470899i) q^{13} +(1.36560 + 0.992167i) q^{15} +(-1.53931 - 4.73750i) q^{17} +(-5.87486 + 4.26833i) q^{19} -0.327411 q^{21} -2.41321 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.64347 - 5.05807i) q^{27} +(-1.70416 - 1.23814i) q^{29} +(-2.02898 + 6.24455i) q^{31} +(3.28013 - 4.53680i) q^{33} +(0.0599391 - 0.184474i) q^{35} +(-5.89647 - 4.28404i) q^{37} +(-0.258268 - 0.794866i) q^{39} +(-0.896909 + 0.651642i) q^{41} -5.46058 q^{43} +0.150741 q^{45} +(4.45214 - 3.23467i) q^{47} +(-2.15149 - 6.62161i) q^{49} +(6.80247 + 4.94228i) q^{51} +(-2.08269 + 6.40987i) q^{53} +(1.95568 + 2.67868i) q^{55} +(3.78781 - 11.6577i) q^{57} +(6.25768 + 4.54647i) q^{59} +(4.05549 + 12.4815i) q^{61} +(-0.0236547 + 0.0171861i) q^{63} +0.495133 q^{65} +4.49499 q^{67} +(3.29548 - 2.39430i) q^{69} +(0.117359 + 0.361193i) q^{71} +(11.8289 + 8.59419i) q^{73} +(0.521613 - 1.60536i) q^{75} +(-0.612289 - 0.197376i) q^{77} +(0.511049 - 1.57285i) q^{79} +(6.89691 + 5.01090i) q^{81} +(-2.68236 - 8.25544i) q^{83} +(-4.02996 + 2.92794i) q^{85} +3.55564 q^{87} +1.83811 q^{89} +(-0.0776975 + 0.0564505i) q^{91} +(-3.42486 - 10.5406i) q^{93} +(5.87486 + 4.26833i) q^{95} +(-3.97873 + 12.2453i) q^{97} +(-0.00115966 - 0.499950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} + 3 q^{5} - q^{7} - 10 q^{9} + 4 q^{11} + 18 q^{13} + q^{15} + 3 q^{17} + 4 q^{19} - 28 q^{21} - 18 q^{23} - 3 q^{25} + 23 q^{27} + 15 q^{29} - 8 q^{31} + 4 q^{33} + 6 q^{35} + 6 q^{37}+ \cdots + 79 q^{99}+O(q^{100}) $ 12 * q - q^3 + 3 * q^5 - q^7 - 10 * q^9 + 4 * q^11 + 18 * q^13 + q^15 + 3 * q^17 + 4 * q^19 - 28 * q^21 - 18 * q^23 - 3 * q^25 + 23 * q^27 + 15 * q^29 - 8 * q^31 + 4 * q^33 + 6 * q^35 + 6 * q^37 - 33 * q^39 + 2 * q^41 - 36 * q^43 - 10 * q^45 - 16 * q^47 - 16 * q^49 - 10 * q^51 + 19 * q^53 + 6 * q^55 + 62 * q^57 + 46 * q^59 + 18 * q^61 - 7 * q^63 + 2 * q^65 - 44 * q^67 - q^69 - 6 * q^71 + 25 * q^73 + 4 * q^75 + 10 * q^77 + 19 * q^79 + 30 * q^81 - 3 * q^85 + 6 * q^87 - 50 * q^89 - 46 * q^91 - 37 * q^93 - 4 * q^95 - 31 * q^97 + 79 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−1.36560	+	0.992167i	−0.788430	+	0.572828i	−0.907497	−	0.420058i	$-0.862010\pi$
$3$	−1.36560	+	0.992167i	−0.788430	+	0.572828i	0.119067	+	0.992886i	$0.462010\pi$
$4$		0			0
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	0.156923	+	0.114011i	0.0593111	+	0.0430921i	0.617046	−	0.786927i	$-0.288329\pi$
$7$	0.156923	+	0.114011i	0.0593111	+	0.0430921i	−0.557735	+	0.830019i	$0.688329\pi$
$8$		0			0
$9$	−0.0465816	+	0.143363i	−0.0155272	+	0.0477878i
$10$		0			0
$11$	−3.15191	+	1.03221i	−0.950337	+	0.311222i
$11$	−3.15191	+	1.03221i	−0.950337	+	0.311222i
$12$		0			0
$13$	−0.153004	+	0.470899i	−0.0424358	+	0.130604i	−0.970030	−	0.242986i	$-0.921873\pi$
$13$	−0.153004	+	0.470899i	−0.0424358	+	0.130604i	0.927594	+	0.373590i	$0.121873\pi$
$14$		0			0
$15$	1.36560	+	0.992167i	0.352596	+	0.256176i
$16$		0			0
$17$	−1.53931	−	4.73750i	−0.373337	−	1.14901i	−0.944594	−	0.328242i	$-0.893544\pi$
$17$	−1.53931	−	4.73750i	−0.373337	−	1.14901i	0.571257	−	0.820771i	$-0.306456\pi$
$18$		0			0
$19$	−5.87486	+	4.26833i	−1.34778	+	0.979223i	−0.348666	+	0.937247i	$0.613365\pi$
$19$	−5.87486	+	4.26833i	−1.34778	+	0.979223i	−0.999119	+	0.0419758i	$0.986635\pi$
$20$		0			0
$21$	−0.327411			−0.0714470
$22$		0			0
$23$	−2.41321			−0.503189			−0.251594	−	0.967833i	$-0.580955\pi$
$23$	−2.41321			−0.503189			−0.251594	+	0.967833i	$0.580955\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−1.64347	−	5.05807i	−0.316285	−	0.973426i
$28$		0			0
$29$	−1.70416	−	1.23814i	−0.316454	−	0.229917i	0.418207	−	0.908352i	$-0.362659\pi$
$29$	−1.70416	−	1.23814i	−0.316454	−	0.229917i	−0.734661	+	0.678434i	$0.762659\pi$
$30$		0			0
$31$	−2.02898	+	6.24455i	−0.364415	+	1.12155i	0.585931	+	0.810361i	$0.300729\pi$
$31$	−2.02898	+	6.24455i	−0.364415	+	1.12155i	−0.950346	+	0.311194i	$0.899271\pi$
$32$		0			0
$33$	3.28013	−	4.53680i	0.570997	−	0.789756i
$34$		0			0
$35$	0.0599391	−	0.184474i	0.0101316	−	0.0311817i
$36$		0			0
$37$	−5.89647	−	4.28404i	−0.969374	−	0.704291i	−0.0140649	−	0.999901i	$-0.504477\pi$
$37$	−5.89647	−	4.28404i	−0.969374	−	0.704291i	−0.955309	+	0.295610i	$0.904477\pi$
$38$		0			0
$39$	−0.258268	−	0.794866i	−0.0413559	−	0.127280i
$40$		0			0
$41$	−0.896909	+	0.651642i	−0.140074	+	0.101769i	−0.655615	−	0.755095i	$-0.727591\pi$
$41$	−0.896909	+	0.651642i	−0.140074	+	0.101769i	0.515542	+	0.856864i	$0.327591\pi$
$42$		0			0
$43$	−5.46058			−0.832731			−0.416365	−	0.909197i	$-0.636696\pi$
$43$	−5.46058			−0.832731			−0.416365	+	0.909197i	$0.636696\pi$
$44$		0			0
$45$	0.150741			0.0224712
$46$		0			0
$47$	4.45214	−	3.23467i	0.649412	−	0.471825i	−0.213659	−	0.976908i	$-0.568538\pi$
$47$	4.45214	−	3.23467i	0.649412	−	0.471825i	0.863071	+	0.505083i	$0.168538\pi$
$48$		0			0
$49$	−2.15149	−	6.62161i	−0.307356	−	0.945945i
$50$		0			0
$51$	6.80247	+	4.94228i	0.952536	+	0.692058i
$52$		0			0
$53$	−2.08269	+	6.40987i	−0.286080	+	0.880463i	0.699993	+	0.714149i	$0.253186\pi$
$53$	−2.08269	+	6.40987i	−0.286080	+	0.880463i	−0.986073	+	0.166313i	$0.946814\pi$
$54$		0			0
$55$	1.95568	+	2.67868i	0.263704	+	0.361193i
$56$		0			0
$57$	3.78781	−	11.6577i	0.501707	−	1.54410i
$58$		0			0
$59$	6.25768	+	4.54647i	0.814681	+	0.591900i	0.915184	−	0.403037i	$-0.132045\pi$
$59$	6.25768	+	4.54647i	0.814681	+	0.591900i	−0.100503	+	0.994937i	$0.532045\pi$
$60$		0			0
$61$	4.05549	+	12.4815i	0.519252	+	1.59809i	0.775409	+	0.631459i	$0.217544\pi$
$61$	4.05549	+	12.4815i	0.519252	+	1.59809i	−0.256157	+	0.966635i	$0.582456\pi$
$62$		0			0
$63$	−0.0236547	+	0.0171861i	−0.00298021	+	0.00216525i
$64$		0			0
$65$	0.495133			0.0614136
$66$		0			0
$67$	4.49499			0.549151			0.274575	−	0.961566i	$-0.411463\pi$
$67$	4.49499			0.549151			0.274575	+	0.961566i	$0.411463\pi$
$68$		0			0
$69$	3.29548	−	2.39430i	0.396729	−	0.288240i
$70$		0			0
$71$	0.117359	+	0.361193i	0.0139279	+	0.0428657i	0.957779	−	0.287506i	$-0.0928260\pi$
$71$	0.117359	+	0.361193i	0.0139279	+	0.0428657i	−0.943851	+	0.330371i	$0.892826\pi$
$72$		0			0
$73$	11.8289	+	8.59419i	1.38447	+	1.00587i	0.996447	+	0.0842222i	$0.0268406\pi$
$73$	11.8289	+	8.59419i	1.38447	+	1.00587i	0.388019	+	0.921651i	$0.373159\pi$
$74$		0			0
$75$	0.521613	−	1.60536i	0.0602307	−	0.185371i
$76$		0			0
$77$	−0.612289	−	0.197376i	−0.0697768	−	0.0224931i
$78$		0			0
$79$	0.511049	−	1.57285i	0.0574975	−	0.176959i	−0.918183	−	0.396156i	$-0.870344\pi$
$79$	0.511049	−	1.57285i	0.0574975	−	0.176959i	0.975681	+	0.219197i	$0.0703438\pi$
$80$		0			0
$81$	6.89691	+	5.01090i	0.766324	+	0.556767i
$82$		0			0
$83$	−2.68236	−	8.25544i	−0.294427	−	0.906152i	−0.983413	−	0.181378i	$-0.941944\pi$
$83$	−2.68236	−	8.25544i	−0.294427	−	0.906152i	0.688987	−	0.724774i	$-0.258056\pi$
$84$		0			0
$85$	−4.02996	+	2.92794i	−0.437111	+	0.317579i
$86$		0			0
$87$	3.55564			0.381205
$88$		0			0
$89$	1.83811			0.194840			0.0974198	−	0.995243i	$-0.468941\pi$
$89$	1.83811			0.194840			0.0974198	+	0.995243i	$0.468941\pi$
$90$		0			0
$91$	−0.0776975	+	0.0564505i	−0.00814491	+	0.00591762i
$92$		0			0
$93$	−3.42486	−	10.5406i	−0.355142	−	1.09301i
$94$		0			0
$95$	5.87486	+	4.26833i	0.602748	+	0.437922i
$96$		0			0
$97$	−3.97873	+	12.2453i	−0.403979	+	1.24332i	0.517765	+	0.855523i	$0.326764\pi$
$97$	−3.97873	+	12.2453i	−0.403979	+	1.24332i	−0.921745	+	0.387798i	$0.873236\pi$
$98$		0			0
$99$	−0.00115966	−	0.499950i	−0.000116550	−	0.0502469i
$100$		0			0
$101$	−0.308644	+	0.949908i	−0.0307112	+	0.0945194i	−0.965237	−	0.261376i	$-0.915824\pi$
$101$	−0.308644	+	0.949908i	−0.0307112	+	0.0945194i	0.934526	+	0.355895i	$0.115824\pi$
$102$		0			0
$103$	7.44256	+	5.40733i	0.733337	+	0.532800i	0.890617	−	0.454754i	$-0.150273\pi$
$103$	7.44256	+	5.40733i	0.733337	+	0.532800i	−0.157280	+	0.987554i	$0.550273\pi$
$104$		0			0
$105$	0.101176	+	0.311387i	0.00987373	+	0.0303882i
$106$		0			0
$107$	−2.30547	+	1.67502i	−0.222879	+	0.161931i	−0.693621	−	0.720340i	$-0.743986\pi$
$107$	−2.30547	+	1.67502i	−0.222879	+	0.161931i	0.470743	+	0.882270i	$0.343986\pi$
$108$		0			0
$109$	1.23155			0.117962			0.0589808	−	0.998259i	$-0.481215\pi$
$109$	1.23155			0.117962			0.0589808	+	0.998259i	$0.481215\pi$
$110$		0			0
$111$	12.3027			1.16772
$112$		0			0
$113$	7.78030	−	5.65272i	0.731909	−	0.531763i	−0.158258	−	0.987398i	$-0.550588\pi$
$113$	7.78030	−	5.65272i	0.731909	−	0.531763i	0.890167	+	0.455635i	$0.150588\pi$
$114$		0			0
$115$	0.745722	+	2.29510i	0.0695389	+	0.214019i
$116$		0			0
$117$	−0.0603825	−	0.0438704i	−0.00558236	−	0.00405582i
$118$		0			0
$119$	0.298575	−	0.918919i	0.0273703	−	0.0842371i
$120$		0			0
$121$	8.86910	−	6.50685i	0.806282	−	0.591532i
$122$		0			0
$123$	0.578281	−	1.77977i	0.0521418	−	0.160476i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	−5.27298	−	16.2286i	−0.467902	−	1.44005i	−0.855296	−	0.518139i	$-0.826625\pi$
$127$	−5.27298	−	16.2286i	−0.467902	−	1.44005i	0.387395	−	0.921914i	$-0.373375\pi$
$128$		0			0
$129$	7.45697	−	5.41781i	0.656550	−	0.477011i
$130$		0			0
$131$	−10.8561			−0.948506			−0.474253	−	0.880389i	$-0.657282\pi$
$131$	−10.8561			−0.948506			−0.474253	+	0.880389i	$0.657282\pi$
$132$		0			0
$133$	−1.40853			−0.122135
$134$		0			0
$135$	−4.30265	+	3.12606i	−0.370313	+	0.269048i
$136$		0			0
$137$	−2.96917	−	9.13817i	−0.253673	−	0.780727i	−0.994088	−	0.108576i	$-0.965371\pi$
$137$	−2.96917	−	9.13817i	−0.253673	−	0.780727i	0.740415	−	0.672150i	$-0.234629\pi$
$138$		0			0
$139$	−12.5873	−	9.14522i	−1.06764	−	0.775687i	−0.0921548	−	0.995745i	$-0.529375\pi$
$139$	−12.5873	−	9.14522i	−1.06764	−	0.775687i	−0.975487	+	0.220058i	$0.929375\pi$
$140$		0			0
$141$	−2.87051	+	8.83454i	−0.241741	+	0.744002i
$142$		0			0
$143$	−0.00380907	−	1.64216i	−0.000318530	−	0.137325i
$144$		0			0
$145$	−0.650930	+	2.00336i	−0.0540568	+	0.166370i
$146$		0			0
$147$	9.50782	+	6.90784i	0.784192	+	0.569749i
$148$		0			0
$149$	−1.87338	−	5.76568i	−0.153474	−	0.472343i	0.844530	−	0.535509i	$-0.179880\pi$
$149$	−1.87338	−	5.76568i	−0.153474	−	0.472343i	−0.998003	+	0.0631661i	$0.979880\pi$
$150$		0			0
$151$	−14.1108	+	10.2521i	−1.14832	+	0.834303i	−0.988256	−	0.152804i	$-0.951170\pi$
$151$	−14.1108	+	10.2521i	−1.14832	+	0.834303i	−0.160063	+	0.987107i	$0.551170\pi$
$152$		0			0
$153$	0.750887			0.0607057
$154$		0			0
$155$	6.56591			0.527387
$156$		0			0
$157$	−15.4447	+	11.2213i	−1.23262	+	0.895554i	−0.997084	−	0.0763106i	$-0.975686\pi$
$157$	−15.4447	+	11.2213i	−1.23262	+	0.895554i	−0.235540	+	0.971865i	$0.575686\pi$
$158$		0			0
$159$	−3.51553	−	10.8197i	−0.278800	−	0.858057i
$160$		0			0
$161$	−0.378687	−	0.275132i	−0.0298447	−	0.0216834i
$162$		0			0
$163$	−0.0312105	+	0.0960562i	−0.00244460	+	0.00752370i	−0.952271	−	0.305253i	$-0.901259\pi$
$163$	−0.0312105	+	0.0960562i	−0.00244460	+	0.00752370i	0.949827	+	0.312776i	$0.101259\pi$
$164$		0			0
$165$	−5.32837	−	1.71764i	−0.414813	−	0.133718i
$166$		0			0
$167$	3.47433	−	10.6929i	0.268852	−	0.827441i	−0.721929	−	0.691967i	$-0.756744\pi$
$167$	3.47433	−	10.6929i	0.268852	−	0.827441i	0.990781	−	0.135474i	$-0.0432557\pi$
$168$		0			0
$169$	10.3189	+	7.49711i	0.793760	+	0.576701i
$170$		0			0
$171$	−0.338262	−	1.04106i	−0.0258676	−	0.0796122i
$172$		0			0
$173$	−6.56139	+	4.76713i	−0.498853	+	0.362438i	−0.808579	−	0.588388i	$-0.799763\pi$
$173$	−6.56139	+	4.76713i	−0.498853	+	0.362438i	0.309725	+	0.950826i	$0.399763\pi$
$174$		0			0
$175$	−0.193967			−0.0146625
$176$		0			0
$177$	−13.0563			−0.981375
$178$		0			0
$179$	17.2144	−	12.5070i	1.28667	−	0.934817i	0.286933	−	0.957951i	$-0.407364\pi$
$179$	17.2144	−	12.5070i	1.28667	−	0.934817i	0.999732	+	0.0231333i	$0.00736420\pi$
$180$		0			0
$181$	2.66422	+	8.19962i	0.198030	+	0.609473i	0.999928	+	0.0120121i	$0.00382367\pi$
$181$	2.66422	+	8.19962i	0.198030	+	0.609473i	−0.801898	+	0.597461i	$0.796176\pi$
$182$		0			0
$183$	−17.9219	−	13.0210i	−1.32483	−	0.962543i
$184$		0			0
$185$	−2.25225	+	6.93172i	−0.165589	+	0.509630i
$186$		0			0
$187$	9.74185	+	13.3433i	0.712394	+	0.975759i
$188$		0			0
$189$	0.318778	−	0.981099i	0.0231877	−	0.0713644i
$190$		0			0
$191$	16.2969	+	11.8404i	1.17920	+	0.856742i	0.992082	−	0.125594i	$-0.0400837\pi$
$191$	16.2969	+	11.8404i	1.17920	+	0.856742i	0.187123	+	0.982337i	$0.440084\pi$
$192$		0			0
$193$	3.00173	+	9.23838i	0.216069	+	0.664993i	0.999076	+	0.0429799i	$0.0136851\pi$
$193$	3.00173	+	9.23838i	0.216069	+	0.664993i	−0.783006	+	0.622014i	$0.786315\pi$
$194$		0			0
$195$	−0.676153	+	0.491254i	−0.0484203	+	0.0351794i
$196$		0			0
$197$	−14.4934			−1.03261			−0.516304	−	0.856405i	$-0.672693\pi$
$197$	−14.4934			−1.03261			−0.516304	+	0.856405i	$0.672693\pi$
$198$		0			0
$199$	−20.8055			−1.47486			−0.737431	−	0.675423i	$-0.763961\pi$
$199$	−20.8055			−1.47486			−0.737431	+	0.675423i	$0.763961\pi$
$200$		0			0
$201$	−6.13836	+	4.45978i	−0.432967	+	0.314569i
$202$		0			0
$203$	−0.126259	−	0.388585i	−0.00886164	−	0.0272733i
$204$		0			0
$205$	0.896909	+	0.651642i	0.0626428	+	0.0455127i
$206$		0			0
$207$	0.112411	−	0.345965i	0.00781310	−	0.0240463i
$208$		0			0
$209$	14.1112	−	19.5175i	0.976094	−	1.35005i
$210$		0			0
$211$	2.64897	−	8.15269i	0.182363	−	0.561254i	−0.817530	−	0.575885i	$-0.804657\pi$
$211$	2.64897	−	8.15269i	0.182363	−	0.561254i	0.999893	+	0.0146312i	$0.00465742\pi$
$212$		0			0
$213$	−0.518629	−	0.376806i	−0.0355359	−	0.0258183i
$214$		0			0
$215$	1.68741	+	5.19332i	0.115081	+	0.354182i
$216$		0			0
$217$	−1.03034	+	0.748585i	−0.0699440	+	0.0508173i
$218$		0			0
$219$	−24.6804			−1.66775
$220$		0			0
$221$	2.46641			0.165908
$222$		0			0
$223$	−0.281479	+	0.204506i	−0.0188492	+	0.0136948i	−0.597170	−	0.802115i	$-0.703708\pi$
$223$	−0.281479	+	0.204506i	−0.0188492	+	0.0136948i	0.578321	+	0.815809i	$0.303708\pi$
$224$		0			0
$225$	−0.0465816	−	0.143363i	−0.00310544	−	0.00955756i
$226$		0			0
$227$	12.2437	+	8.89555i	0.812642	+	0.590419i	0.914595	−	0.404370i	$-0.132509\pi$
$227$	12.2437	+	8.89555i	0.812642	+	0.590419i	−0.101954	+	0.994789i	$0.532509\pi$
$228$		0			0
$229$	−8.28103	+	25.4864i	−0.547226	+	1.68419i	0.168413	+	0.985717i	$0.446136\pi$
$229$	−8.28103	+	25.4864i	−0.547226	+	1.68419i	−0.715639	+	0.698471i	$0.753864\pi$
$230$		0			0
$231$	1.03197	−	0.337956i	0.0678987	−	0.0222359i
$232$		0			0
$233$	0.260273	−	0.801038i	0.0170510	−	0.0524777i	−0.942169	−	0.335138i	$-0.891217\pi$
$233$	0.260273	−	0.801038i	0.0170510	−	0.0524777i	0.959220	+	0.282661i	$0.0912170\pi$
$234$		0			0
$235$	−4.45214	−	3.23467i	−0.290426	−	0.211007i
$236$		0			0
$237$	0.862638	+	2.65493i	0.0560343	+	0.172456i
$238$		0			0
$239$	−4.71378	+	3.42476i	−0.304909	+	0.221529i	−0.729709	−	0.683758i	$-0.760344\pi$
$239$	−4.71378	+	3.42476i	−0.304909	+	0.221529i	0.424800	+	0.905287i	$0.360344\pi$
$240$		0			0
$241$	−26.5420			−1.70972			−0.854860	−	0.518860i	$-0.826357\pi$
$241$	−26.5420			−1.70972			−0.854860	+	0.518860i	$0.826357\pi$
$242$		0			0
$243$	1.56504			0.100397
$244$		0			0
$245$	−5.63268	+	4.09238i	−0.359859	+	0.261453i
$246$		0			0
$247$	−1.11108	−	3.41954i	−0.0706960	−	0.217580i
$248$		0			0
$249$	11.8538	+	8.61229i	0.751204	+	0.545782i
$250$		0			0
$251$	6.60804	−	20.3374i	0.417096	−	1.28369i	−0.493268	−	0.869878i	$-0.664198\pi$
$251$	6.60804	−	20.3374i	0.417096	−	1.28369i	0.910363	−	0.413810i	$-0.135802\pi$
$252$		0			0
$253$	7.60622	−	2.49093i	0.478199	−	0.156603i
$254$		0			0
$255$	2.59831	−	7.99678i	0.162713	−	0.500778i
$256$		0			0
$257$	−17.0089	−	12.3577i	−1.06099	−	0.770853i	−0.0867176	−	0.996233i	$-0.527638\pi$
$257$	−17.0089	−	12.3577i	−1.06099	−	0.770853i	−0.974271	+	0.225380i	$0.927638\pi$
$258$		0			0
$259$	−0.436862	−	1.34452i	−0.0271453	−	0.0835446i
$260$		0			0
$261$	0.256887	−	0.186639i	0.0159009	−	0.0115527i
$262$		0			0
$263$	−1.64662			−0.101535			−0.0507675	−	0.998710i	$-0.516167\pi$
$263$	−1.64662			−0.101535			−0.0507675	+	0.998710i	$0.516167\pi$
$264$		0			0
$265$	6.73973			0.414018
$266$		0			0
$267$	−2.51013	+	1.82371i	−0.153617	+	0.111610i
$268$		0			0
$269$	4.99210	+	15.3641i	0.304374	+	0.936766i	0.979910	+	0.199439i	$0.0639121\pi$
$269$	4.99210	+	15.3641i	0.304374	+	0.936766i	−0.675537	+	0.737326i	$0.736088\pi$
$270$		0			0
$271$	−3.96493	−	2.88069i	−0.240853	−	0.174990i	0.460810	−	0.887499i	$-0.347559\pi$
$271$	−3.96493	−	2.88069i	−0.240853	−	0.174990i	−0.701663	+	0.712509i	$0.747559\pi$
$272$		0			0
$273$	0.0500954	−	0.154178i	0.00303191	−	0.00933126i
$274$		0			0
$275$	1.94323	−	2.68772i	0.117181	−	0.162076i
$276$		0			0
$277$	4.49420	−	13.8317i	0.270030	−	0.831067i	−0.720462	−	0.693495i	$-0.756070\pi$
$277$	4.49420	−	13.8317i	0.270030	−	0.831067i	0.990492	−	0.137572i	$-0.0439300\pi$
$278$		0			0
$279$	−0.800727	−	0.581762i	−0.0479383	−	0.0348292i
$280$		0			0
$281$	−1.07048	−	3.29459i	−0.0638593	−	0.196539i	0.914036	−	0.405632i	$-0.132949\pi$
$281$	−1.07048	−	3.29459i	−0.0638593	−	0.196539i	−0.977896	+	0.209094i	$0.932949\pi$
$282$		0			0
$283$	−1.17736	+	0.855401i	−0.0699867	+	0.0508483i	−0.622228	−	0.782836i	$-0.713773\pi$
$283$	−1.17736	+	0.855401i	−0.0699867	+	0.0508483i	0.552242	+	0.833684i	$0.313773\pi$
$284$		0			0
$285$	−12.2576			−0.726078
$286$		0			0
$287$	−0.215039			−0.0126934
$288$		0			0
$289$	−6.32117	+	4.59260i	−0.371833	+	0.270153i
$290$		0			0
$291$	−6.71600	−	20.6697i	−0.393699	−	1.21168i
$292$		0			0
$293$	−25.7750	−	18.7266i	−1.50579	−	1.09402i	−0.968001	−	0.250945i	$-0.919259\pi$
$293$	−25.7750	−	18.7266i	−1.50579	−	1.09402i	−0.537791	−	0.843078i	$-0.680741\pi$
$294$		0			0
$295$	2.39022	−	7.35635i	0.139164	−	0.428303i
$296$		0			0
$297$	10.4010	+	14.2462i	0.603530	+	0.826648i
$298$		0			0
$299$	0.369231	−	1.13638i	0.0213532	−	0.0657184i
$300$		0			0
$301$	−0.856888	−	0.622566i	−0.0493902	−	0.0358841i
$302$		0			0
$303$	−0.520983	−	1.60342i	−0.0299297	−	0.0921141i
$304$		0			0
$305$	10.6174	−	7.71400i	0.607951	−	0.441702i
$306$		0			0
$307$	16.1632			0.922480			0.461240	−	0.887275i	$-0.347405\pi$
$307$	16.1632			0.922480			0.461240	+	0.887275i	$0.347405\pi$
$308$		0			0
$309$	−15.5285			−0.883387
$310$		0			0
$311$	−18.2265	+	13.2423i	−1.03353	+	0.750904i	−0.969012	−	0.247012i	$-0.920551\pi$
$311$	−18.2265	+	13.2423i	−1.03353	+	0.750904i	−0.0645188	+	0.997916i	$0.520551\pi$
$312$		0			0
$313$	5.42223	+	16.6879i	0.306483	+	0.943256i	0.979120	+	0.203284i	$0.0651614\pi$
$313$	5.42223	+	16.6879i	0.306483	+	0.943256i	−0.672637	+	0.739972i	$0.734839\pi$
$314$		0			0
$315$	0.0236547	+	0.0171861i	0.00133279	+	0.000968329i
$316$		0			0
$317$	−8.70276	+	26.7843i	−0.488796	+	1.50436i	0.337611	+	0.941286i	$0.390381\pi$
$317$	−8.70276	+	26.7843i	−0.488796	+	1.50436i	−0.826407	+	0.563073i	$0.809619\pi$
$318$		0			0
$319$	6.64938	+	2.14347i	0.372294	+	0.120012i
$320$		0			0
$321$	1.48645	−	4.57483i	0.0829657	−	0.255342i
$322$		0			0
$323$	29.2644	+	21.2619i	1.62832	+	1.18304i
$324$		0			0
$325$	−0.153004	−	0.470899i	−0.00848716	−	0.0261208i
$326$		0			0
$327$	−1.68181	+	1.22191i	−0.0930044	+	0.0675716i
$328$		0			0
$329$	1.06743			0.0588493
$330$		0			0
$331$	0.970270			0.0533309			0.0266654	−	0.999644i	$-0.491511\pi$
$331$	0.970270			0.0533309			0.0266654	+	0.999644i	$0.491511\pi$
$332$		0			0
$333$	0.888841	−	0.645780i	0.0487082	−	0.0353886i
$334$		0			0
$335$	−1.38903	−	4.27499i	−0.0758908	−	0.233568i
$336$		0			0
$337$	−4.49317	−	3.26448i	−0.244759	−	0.177827i	0.458642	−	0.888621i	$-0.348336\pi$
$337$	−4.49317	−	3.26448i	−0.244759	−	0.177827i	−0.703401	+	0.710794i	$0.748336\pi$
$338$		0			0
$339$	−5.01634	+	15.4387i	−0.272450	+	0.838515i
$340$		0			0
$341$	−0.0505117	−	21.7766i	−0.00273536	−	1.17927i
$342$		0			0
$343$	0.836892	−	2.57569i	0.0451879	−	0.139074i
$344$		0			0
$345$	−3.29548	−	2.39430i	−0.177423	−	0.128905i
$346$		0			0
$347$	−5.14885	−	15.8465i	−0.276405	−	0.850687i	−0.988844	−	0.148953i	$-0.952410\pi$
$347$	−5.14885	−	15.8465i	−0.276405	−	0.850687i	0.712439	−	0.701734i	$-0.247590\pi$
$348$		0			0
$349$	26.7848	−	19.4603i	1.43376	−	1.04169i	0.444455	−	0.895801i	$-0.353397\pi$
$349$	26.7848	−	19.4603i	1.43376	−	1.04169i	0.989302	−	0.145884i	$-0.0466025\pi$
$350$		0			0
$351$	2.63330			0.140555
$352$		0			0
$353$	−6.70224			−0.356724			−0.178362	−	0.983965i	$-0.557080\pi$
$353$	−6.70224			−0.356724			−0.178362	+	0.983965i	$0.557080\pi$
$354$		0			0
$355$	0.307249	−	0.223230i	0.0163071	−	0.0118478i
$356$		0			0
$357$	0.503987	+	1.55111i	0.0266738	+	0.0820935i
$358$		0			0
$359$	−19.4646	−	14.1419i	−1.02730	−	0.746379i	−0.0595355	−	0.998226i	$-0.518962\pi$
$359$	−19.4646	−	14.1419i	−1.02730	−	0.746379i	−0.967767	+	0.251847i	$0.918962\pi$
$360$		0			0
$361$	10.4240	−	32.0816i	0.548629	−	1.68851i
$362$		0			0
$363$	−5.65576	+	17.6854i	−0.296850	+	0.928242i
$364$		0			0
$365$	4.51823	−	13.9057i	0.236495	−	0.727857i
$366$		0			0
$367$	6.71791	+	4.88085i	0.350672	+	0.254778i	0.749151	−	0.662399i	$-0.230462\pi$
$367$	6.71791	+	4.88085i	0.350672	+	0.254778i	−0.398479	+	0.917177i	$0.630462\pi$
$368$		0			0
$369$	−0.0516422	−	0.158938i	−0.00268839	−	0.00827400i
$370$		0			0
$371$	−1.05762	+	0.768403i	−0.0549087	+	0.0398935i
$372$		0			0
$373$	−16.0339			−0.830202			−0.415101	−	0.909775i	$-0.636254\pi$
$373$	−16.0339			−0.830202			−0.415101	+	0.909775i	$0.636254\pi$
$374$		0			0
$375$	−1.68797			−0.0871666
$376$		0			0
$377$	0.843784	−	0.613045i	0.0434571	−	0.0315734i
$378$		0			0
$379$	8.11474	+	24.9746i	0.416826	+	1.28286i	0.910607	+	0.413273i	$0.135614\pi$
$379$	8.11474	+	24.9746i	0.416826	+	1.28286i	−0.493781	+	0.869586i	$0.664386\pi$
$380$		0			0
$381$	23.3022	+	16.9301i	1.19381	+	0.867354i
$382$		0			0
$383$	−4.21474	+	12.9716i	−0.215363	+	0.662819i	0.783765	+	0.621058i	$0.213297\pi$
$383$	−4.21474	+	12.9716i	−0.215363	+	0.662819i	−0.999128	+	0.0417612i	$0.986703\pi$
$384$		0			0
$385$	0.00149219	+	0.643314i	7.60492e−5	+	0.0327863i
$386$		0			0
$387$	0.254362	−	0.782847i	0.0129300	−	0.0397944i
$388$		0			0
$389$	25.6125	+	18.6086i	1.29861	+	0.943493i	0.999941	−	0.0108655i	$-0.00345865\pi$
$389$	25.6125	+	18.6086i	1.29861	+	0.943493i	0.298665	+	0.954358i	$0.403459\pi$
$390$		0			0
$391$	3.71467	+	11.4326i	0.187859	+	0.578170i
$392$		0			0
$393$	14.8252	−	10.7711i	0.747830	−	0.543331i
$394$		0			0
$395$	−1.65379			−0.0832111
$396$		0			0
$397$	33.2898			1.67077			0.835383	−	0.549668i	$-0.185246\pi$
$397$	33.2898			1.67077			0.835383	+	0.549668i	$0.185246\pi$
$398$		0			0
$399$	1.92349	−	1.39750i	0.0962952	−	0.0699625i
$400$		0			0
$401$	−7.13851	−	21.9701i	−0.356480	−	1.09713i	−0.955146	−	0.296135i	$-0.904302\pi$
$401$	−7.13851	−	21.9701i	−0.356480	−	1.09713i	0.598666	−	0.800999i	$-0.295698\pi$
$402$		0			0
$403$	−2.63011	−	1.91089i	−0.131015	−	0.0951881i
$404$		0			0
$405$	2.63439	−	8.10781i	0.130904	−	0.402880i
$406$		0			0
$407$	23.0072	+	7.41653i	1.14042	+	0.367624i
$408$		0			0
$409$	−9.54290	+	29.3700i	−0.471866	+	1.45225i	0.378272	+	0.925695i	$0.376519\pi$
$409$	−9.54290	+	29.3700i	−0.471866	+	1.45225i	−0.850138	+	0.526560i	$0.823481\pi$
$410$		0			0
$411$	13.1213	+	9.53318i	0.647226	+	0.470237i
$412$		0			0
$413$	0.463624	+	1.42689i	0.0228134	+	0.0702125i
$414$		0			0
$415$	−7.02250	+	5.10214i	−0.344721	+	0.250454i
$416$		0			0
$417$	26.2628			1.28610
$418$		0			0
$419$	11.9155			0.582109			0.291054	−	0.956707i	$-0.405994\pi$
$419$	11.9155			0.582109			0.291054	+	0.956707i	$0.405994\pi$
$420$		0			0
$421$	3.69312	−	2.68321i	0.179992	−	0.130772i	−0.494141	−	0.869382i	$-0.664517\pi$
$421$	3.69312	−	2.68321i	0.179992	−	0.130772i	0.674133	+	0.738610i	$0.264517\pi$
$422$		0			0
$423$	0.256345	+	0.788950i	0.0124639	+	0.0383601i
$424$		0			0
$425$	4.02996	+	2.92794i	0.195482	+	0.142026i
$426$		0			0
$427$	−0.786631	+	2.42100i	−0.0380677	+	0.117160i
$428$		0			0
$429$	1.63450	+	2.23876i	0.0789145	+	0.108088i
$430$		0			0
$431$	−2.34293	+	7.21080i	−0.112855	+	0.347332i	−0.991494	−	0.130155i	$-0.958452\pi$
$431$	−2.34293	+	7.21080i	−0.112855	+	0.347332i	0.878639	+	0.477487i	$0.158452\pi$
$432$		0			0
$433$	8.56060	+	6.21964i	0.411396	+	0.298897i	0.774167	−	0.632982i	$-0.218169\pi$
$433$	8.56060	+	6.21964i	0.411396	+	0.298897i	−0.362771	+	0.931878i	$0.618169\pi$
$434$		0			0
$435$	−1.09875	−	3.38162i	−0.0526812	−	0.162136i
$436$		0			0
$437$	14.1772	−	10.3004i	0.678190	−	0.492734i
$438$		0			0
$439$	7.04399			0.336191			0.168096	−	0.985771i	$-0.446238\pi$
$439$	7.04399			0.336191			0.168096	+	0.985771i	$0.446238\pi$
$440$		0			0
$441$	1.04952			0.0499770
$442$		0			0
$443$	−0.942081	+	0.684462i	−0.0447596	+	0.0325198i	−0.609940	−	0.792448i	$-0.708807\pi$
$443$	−0.942081	+	0.684462i	−0.0447596	+	0.0325198i	0.565181	+	0.824967i	$0.308807\pi$
$444$		0			0
$445$	−0.568008	−	1.74815i	−0.0269262	−	0.0828702i
$446$		0			0
$447$	8.27881	+	6.01491i	0.391574	+	0.284495i
$448$		0			0
$449$	3.82127	−	11.7607i	0.180337	−	0.555020i	−0.819500	−	0.573079i	$-0.805749\pi$
$449$	3.82127	−	11.7607i	0.180337	−	0.555020i	0.999837	+	0.0180590i	$0.00574867\pi$
$450$		0			0
$451$	2.15435	−	2.97971i	0.101444	−	0.140309i
$452$		0			0
$453$	9.09791	−	28.0005i	0.427457	−	1.31558i
$454$		0			0
$455$	0.0776975	+	0.0564505i	0.00364251	+	0.00264644i
$456$		0			0
$457$	−11.1379	−	34.2789i	−0.521008	−	1.60350i	−0.772077	−	0.635529i	$-0.780782\pi$
$457$	−11.1379	−	34.2789i	−0.521008	−	1.60350i	0.251069	−	0.967969i	$-0.419218\pi$
$458$		0			0
$459$	−21.4328	+	15.5719i	−1.00040	+	0.726832i
$460$		0			0
$461$	−13.6603			−0.636222			−0.318111	−	0.948053i	$-0.603049\pi$
$461$	−13.6603			−0.636222			−0.318111	+	0.948053i	$0.603049\pi$
$462$		0			0
$463$	29.3515			1.36408			0.682041	−	0.731314i	$-0.261093\pi$
$463$	29.3515			1.36408			0.682041	+	0.731314i	$0.261093\pi$
$464$		0			0
$465$	−8.96641	+	6.51448i	−0.415807	+	0.302102i
$466$		0			0
$467$	7.46213	+	22.9661i	0.345306	+	1.06274i	0.961420	+	0.275085i	$0.0887062\pi$
$467$	7.46213	+	22.9661i	0.345306	+	1.06274i	−0.616114	+	0.787657i	$0.711294\pi$
$468$		0			0
$469$	0.705366	+	0.512478i	0.0325708	+	0.0236640i
$470$		0			0
$471$	9.95798	−	30.6475i	0.458839	−	1.41216i
$472$		0			0
$473$	17.2113	−	5.63645i	0.791375	−	0.259164i
$474$		0			0
$475$	2.24400	−	6.90631i	0.102962	−	0.316883i
$476$		0			0
$477$	−0.821925	−	0.597163i	−0.0376333	−	0.0273422i
$478$		0			0
$479$	12.4419	+	38.2923i	0.568486	+	1.74962i	0.657361	+	0.753576i	$0.271673\pi$
$479$	12.4419	+	38.2923i	0.568486	+	1.74962i	−0.0888751	+	0.996043i	$0.528327\pi$
$480$		0			0
$481$	2.91953	−	2.12117i	0.133119	−	0.0967168i
$482$		0			0
$483$	0.790111			0.0359513
$484$		0			0
$485$	12.8755			0.584644
$486$		0			0
$487$	−34.1376	+	24.8024i	−1.54692	+	1.12390i	−0.601122	+	0.799157i	$0.705279\pi$
$487$	−34.1376	+	24.8024i	−1.54692	+	1.12390i	−0.945801	+	0.324748i	$0.894721\pi$
$488$		0			0
$489$	−0.0526826	−	0.162140i	−0.00238239	−	0.00733224i
$490$		0			0
$491$	−29.3536	−	21.3267i	−1.32471	−	0.962459i	−0.999861	−	0.0166935i	$-0.994686\pi$
$491$	−29.3536	−	21.3267i	−1.32471	−	0.962459i	−0.324850	−	0.945765i	$-0.605314\pi$
$492$		0			0
$493$	−3.24248	+	9.97933i	−0.146034	+	0.449447i
$494$		0			0
$495$	−0.475123	+	0.155596i	−0.0213552	+	0.00699352i
$496$		0			0
$497$	−0.0227637	+	0.0700595i	−0.00102109	+	0.00314260i
$498$		0			0
$499$	−12.6811	−	9.21339i	−0.567686	−	0.412448i	0.266578	−	0.963813i	$-0.414107\pi$
$499$	−12.6811	−	9.21339i	−0.567686	−	0.412448i	−0.834264	+	0.551366i	$0.814107\pi$
$500$		0			0
$501$	5.86458	+	18.0493i	0.262010	+	0.806385i
$502$		0			0
$503$	−20.7825	+	15.0994i	−0.926645	+	0.673247i	−0.945169	−	0.326582i	$-0.894103\pi$
$503$	−20.7825	+	15.0994i	−0.926645	+	0.673247i	0.0185243	+	0.999828i	$0.494103\pi$
$504$		0			0
$505$	0.998793			0.0444457
$506$		0			0
$507$	−21.5299			−0.956174
$508$		0			0
$509$	17.6391	−	12.8156i	0.781840	−	0.568040i	−0.123690	−	0.992321i	$-0.539473\pi$
$509$	17.6391	−	12.8156i	0.781840	−	0.568040i	0.905531	+	0.424281i	$0.139473\pi$
$510$		0			0
$511$	0.876387	+	2.69724i	0.0387691	+	0.119319i
$512$		0			0
$513$	31.2447	+	22.7006i	1.37949	+	1.00226i
$514$		0			0
$515$	2.84280	−	8.74925i	0.125269	−	0.385538i
$516$		0			0
$517$	−10.6939	+	14.7909i	−0.470318	+	0.650505i
$518$		0			0
$519$	4.23045	−	13.0200i	0.185696	−	0.571514i
$520$		0			0
$521$	−32.2357	−	23.4206i	−1.41227	−	1.02608i	−0.992987	−	0.118221i	$-0.962281\pi$
$521$	−32.2357	−	23.4206i	−1.41227	−	1.02608i	−0.419285	−	0.907855i	$-0.637719\pi$
$522$		0			0
$523$	−3.54130	−	10.8990i	−0.154850	−	0.476580i	0.843295	−	0.537450i	$-0.180612\pi$
$523$	−3.54130	−	10.8990i	−0.154850	−	0.476580i	−0.998146	+	0.0608703i	$0.980612\pi$
$524$		0			0
$525$	0.264881	−	0.192448i	0.0115604	−	0.00839910i
$526$		0			0
$527$	32.7068			1.42473
$528$		0			0
$529$	−17.1764			−0.746801
$530$		0			0
$531$	−0.943290	+	0.685340i	−0.0409353	+	0.0297412i
$532$		0			0
$533$	−0.169627	−	0.522058i	−0.00734735	−	0.0226128i
$534$		0			0
$535$	2.30547	+	1.67502i	0.0996743	+	0.0724176i
$536$		0			0
$537$	−11.0990	+	34.1591i	−0.478956	+	1.47408i
$538$		0			0
$539$	13.6162	+	18.6500i	0.586491	+	0.803311i
$540$		0			0
$541$	13.4647	−	41.4402i	0.578894	−	1.78165i	−0.0436242	−	0.999048i	$-0.513890\pi$
$541$	13.4647	−	41.4402i	0.578894	−	1.78165i	0.622518	−	0.782605i	$-0.286110\pi$
$542$		0			0
$543$	−11.7736	−	8.55406i	−0.505256	−	0.367090i
$544$		0			0
$545$	−0.380571	−	1.17128i	−0.0163019	−	0.0501720i
$546$		0			0
$547$	−4.12614	+	2.99782i	−0.176421	+	0.128177i	−0.672491	−	0.740105i	$-0.734776\pi$
$547$	−4.12614	+	2.99782i	−0.176421	+	0.128177i	0.496070	+	0.868282i	$0.334776\pi$
$548$		0			0
$549$	−1.97830			−0.0844319
$550$		0			0
$551$	15.2965			0.651652
$552$		0			0
$553$	0.259517	−	0.188550i	0.0110358	−	0.00801796i
$554$		0			0
$555$	−3.80174	−	11.7006i	−0.161375	−	0.496661i
$556$		0			0
$557$	3.67172	+	2.66766i	0.155576	+	0.113032i	0.662850	−	0.748752i	$-0.269347\pi$
$557$	3.67172	+	2.66766i	0.155576	+	0.113032i	−0.507274	+	0.861785i	$0.669347\pi$
$558$		0			0
$559$	0.835493	−	2.57138i	0.0353376	−	0.108758i
$560$		0			0
$561$	−26.5422	−	8.55608i	−1.12061	−	0.361238i
$562$		0			0
$563$	−9.10085	+	28.0095i	−0.383555	+	1.18046i	0.553968	+	0.832538i	$0.313113\pi$
$563$	−9.10085	+	28.0095i	−0.383555	+	1.18046i	−0.937523	+	0.347923i	$0.886887\pi$
$564$		0			0
$565$	−7.78030	−	5.65272i	−0.327319	−	0.237812i
$566$		0			0
$567$	0.510984	+	1.57265i	0.0214593	+	0.0660449i
$568$		0			0
$569$	−8.62331	+	6.26520i	−0.361508	+	0.262651i	−0.753681	−	0.657241i	$-0.771724\pi$
$569$	−8.62331	+	6.26520i	−0.361508	+	0.262651i	0.392173	+	0.919892i	$0.371724\pi$
$570$		0			0
$571$	−35.1373			−1.47045			−0.735224	−	0.677824i	$-0.762923\pi$
$571$	−35.1373			−1.47045			−0.735224	+	0.677824i	$0.762923\pi$
$572$		0			0
$573$	−34.0028			−1.42049
$574$		0			0
$575$	1.95233	−	1.41845i	0.0814176	−	0.0591534i
$576$		0			0
$577$	10.7247	+	33.0072i	0.446474	+	1.37411i	0.880859	+	0.473379i	$0.156966\pi$
$577$	10.7247	+	33.0072i	0.446474	+	1.37411i	−0.434385	+	0.900727i	$0.643034\pi$
$578$		0			0
$579$	−13.2652	−	9.63772i	−0.551282	−	0.400530i
$580$		0			0
$581$	0.520288	−	1.60128i	0.0215852	−	0.0664324i
$582$		0			0
$583$	−0.0518489	−	22.3531i	−0.00214736	−	0.925771i
$584$		0			0
$585$	−0.0230641	+	0.0709839i	−0.000953581	+	0.00293482i
$586$		0			0
$587$	−22.9900	−	16.7032i	−0.948897	−	0.689414i	0.00164868	−	0.999999i	$-0.499475\pi$
$587$	−22.9900	−	16.7032i	−0.948897	−	0.689414i	−0.950546	+	0.310585i	$0.899475\pi$
$588$		0			0
$589$	−14.7339	−	45.3462i	−0.607099	−	1.86846i
$590$		0			0
$591$	19.7921	−	14.3798i	0.814139	−	0.591507i
$592$		0			0
$593$	−19.6141			−0.805456			−0.402728	−	0.915320i	$-0.631938\pi$
$593$	−19.6141			−0.805456			−0.402728	+	0.915320i	$0.631938\pi$
$594$		0			0
$595$	−0.966208			−0.0396107
$596$		0			0
$597$	28.4120	−	20.6425i	1.16282	−	0.844842i
$598$		0			0
$599$	−5.12839	−	15.7836i	−0.209540	−	0.644899i	−0.999496	−	0.0317355i	$-0.989897\pi$
$599$	−5.12839	−	15.7836i	−0.209540	−	0.644899i	0.789956	−	0.613164i	$-0.210103\pi$
$600$		0			0
$601$	8.74776	+	6.35562i	0.356829	+	0.259251i	0.751728	−	0.659473i	$-0.229221\pi$
$601$	8.74776	+	6.35562i	0.356829	+	0.259251i	−0.394899	+	0.918724i	$0.629221\pi$
$602$		0			0
$603$	−0.209384	+	0.644417i	−0.00852677	+	0.0262427i
$604$		0			0
$605$	−8.92909	−	6.42428i	−0.363019	−	0.261184i
$606$		0			0
$607$	−4.19437	+	12.9089i	−0.170244	+	0.523958i	−0.999384	−	0.0350828i	$-0.988831\pi$
$607$	−4.19437	+	12.9089i	−0.170244	+	0.523958i	0.829140	+	0.559041i	$0.188831\pi$
$608$		0			0
$609$	0.557961	+	0.405382i	0.0226097	+	0.0164269i
$610$		0			0
$611$	0.842006	+	2.59143i	0.0340639	+	0.104838i
$612$		0			0
$613$	10.1395	−	7.36678i	0.409531	−	0.297541i	−0.363881	−	0.931445i	$-0.618549\pi$
$613$	10.1395	−	7.36678i	0.409531	−	0.297541i	0.773412	+	0.633904i	$0.218549\pi$
$614$		0			0
$615$	−1.87136			−0.0754604
$616$		0			0
$617$	−46.5587			−1.87438			−0.937191	−	0.348816i	$-0.886584\pi$
$617$	−46.5587			−1.87438			−0.937191	+	0.348816i	$0.886584\pi$
$618$		0			0
$619$	17.0977	−	12.4222i	0.687214	−	0.499290i	−0.188529	−	0.982068i	$-0.560372\pi$
$619$	17.0977	−	12.4222i	0.687214	−	0.499290i	0.875743	+	0.482777i	$0.160372\pi$
$620$		0			0
$621$	3.96603	+	12.2062i	0.159151	+	0.489817i
$622$		0			0
$623$	0.288441	+	0.209565i	0.0115562	+	0.00839604i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	0.0942981	+	40.6538i	0.00376590	+	1.62356i
$628$		0			0
$629$	−11.2191	+	34.5290i	−0.447337	+	1.37676i
$630$		0			0
$631$	−9.44545	−	6.86252i	−0.376017	−	0.273193i	0.383684	−	0.923464i	$-0.374655\pi$
$631$	−9.44545	−	6.86252i	−0.376017	−	0.273193i	−0.759702	+	0.650272i	$0.774655\pi$
$632$		0			0
$633$	4.47139	+	13.7615i	0.177722	+	0.546972i
$634$		0			0
$635$	−13.8049	+	10.0298i	−0.547829	+	0.398021i
$636$		0			0
$637$	3.44730			0.136587
$638$		0			0
$639$	−0.0572486			−0.00226472
$640$		0			0
$641$	−6.92457	+	5.03099i	−0.273504	+	0.198712i	−0.716079	−	0.698019i	$-0.754065\pi$
$641$	−6.92457	+	5.03099i	−0.273504	+	0.198712i	0.442575	+	0.896731i	$0.354065\pi$
$642$		0			0
$643$	−10.8370	−	33.3527i	−0.427368	−	1.31530i	−0.900709	−	0.434424i	$-0.856952\pi$
$643$	−10.8370	−	33.3527i	−0.427368	−	1.31530i	0.473341	−	0.880879i	$-0.343048\pi$
$644$		0			0
$645$	−7.45697	−	5.41781i	−0.293618	−	0.213326i
$646$		0			0
$647$	−7.75719	+	23.8742i	−0.304967	+	0.938590i	0.674723	+	0.738071i	$0.264263\pi$
$647$	−7.75719	+	23.8742i	−0.304967	+	0.938590i	−0.979690	+	0.200520i	$0.935737\pi$
$648$		0			0
$649$	−24.4166	−	7.87085i	−0.958434	−	0.308958i
$650$		0			0
$651$	0.664310	−	2.04454i	0.0260364	−	0.0801317i
$652$		0			0
$653$	−38.4217	−	27.9150i	−1.50356	−	1.09240i	−0.968938	−	0.247303i	$-0.920456\pi$
$653$	−38.4217	−	27.9150i	−1.50356	−	1.09240i	−0.534618	−	0.845094i	$-0.679544\pi$
$654$		0			0
$655$	3.35473	+	10.3248i	0.131080	+	0.403424i
$656$		0			0
$657$	−1.78310	+	1.29550i	−0.0695653	+	0.0505422i
$658$		0			0
$659$	41.5603			1.61896			0.809479	−	0.587148i	$-0.199749\pi$
$659$	41.5603			1.61896			0.809479	+	0.587148i	$0.199749\pi$
$660$		0			0
$661$	38.3584			1.49197			0.745985	−	0.665963i	$-0.231979\pi$
$661$	38.3584			1.49197			0.745985	+	0.665963i	$0.231979\pi$
$662$		0			0
$663$	−3.36812	+	2.44709i	−0.130807	+	0.0950369i
$664$		0			0
$665$	0.435261	+	1.33960i	0.0168787	+	0.0519473i
$666$		0			0
$667$	4.11249	+	2.98790i	0.159236	+	0.115692i
$668$		0			0
$669$	0.181483	−	0.558548i	0.00701655	−	0.0215947i
$670$		0			0
$671$	−25.6661	−	35.1545i	−0.990827	−	1.35713i
$672$		0			0
$673$	−8.97885	+	27.6341i	−0.346109	+	1.06521i	0.614878	+	0.788622i	$0.289205\pi$
$673$	−8.97885	+	27.6341i	−0.346109	+	1.06521i	−0.960987	+	0.276593i	$0.910795\pi$
$674$		0			0
$675$	4.30265	+	3.12606i	0.165609	+	0.120322i
$676$		0			0
$677$	12.0547	+	37.1006i	0.463300	+	1.42589i	0.861108	+	0.508422i	$0.169771\pi$
$677$	12.0547	+	37.1006i	0.463300	+	1.42589i	−0.397808	+	0.917469i	$0.630229\pi$
$678$		0			0
$679$	−2.02045	+	1.46794i	−0.0775377	+	0.0563345i
$680$		0			0
$681$	−25.5458			−0.978919
$682$		0			0
$683$	−27.9569			−1.06974			−0.534871	−	0.844934i	$-0.679640\pi$
$683$	−27.9569			−1.06974			−0.534871	+	0.844934i	$0.679640\pi$
$684$		0			0
$685$	−7.77339	+	5.64770i	−0.297006	+	0.215788i
$686$		0			0
$687$	−13.9782	−	43.0204i	−0.533300	−	1.64133i
$688$		0			0
$689$	−2.69974	−	1.96148i	−0.102852	−	0.0747263i
$690$		0			0
$691$	9.14055	−	28.1317i	0.347723	−	1.07018i	−0.612387	−	0.790558i	$-0.709790\pi$
$691$	9.14055	−	28.1317i	0.347723	−	1.07018i	0.960110	−	0.279623i	$-0.0902095\pi$
$692$		0			0
$693$	0.0568178	−	0.0785857i	0.00215833	−	0.00298522i
$694$		0			0
$695$	−4.80792	+	14.7973i	−0.182375	+	0.561292i
$696$		0			0
$697$	4.46777	+	3.24603i	0.169229	+	0.122952i
$698$		0			0
$699$	0.439334	+	1.35213i	0.0166171	+	0.0511423i
$700$		0			0
$701$	−10.2512	+	7.44794i	−0.387183	+	0.281305i	−0.764300	−	0.644861i	$-0.776915\pi$
$701$	−10.2512	+	7.44794i	−0.387183	+	0.281305i	0.377117	+	0.926166i	$0.376915\pi$
$702$		0			0
$703$	52.9266			1.99617
$704$		0			0
$705$	9.28918			0.349851
$706$		0			0
$707$	−0.156733	+	0.113873i	−0.00589455	+	0.00428264i
$708$		0			0
$709$	−4.83073	−	14.8675i	−0.181422	−	0.558359i	0.818447	−	0.574583i	$-0.194836\pi$
$709$	−4.83073	−	14.8675i	−0.181422	−	0.558359i	−0.999868	+	0.0162237i	$0.994836\pi$
$710$		0			0
$711$	0.201683	+	0.146531i	0.00756371	+	0.00549535i
$712$		0			0
$713$	4.89635	−	15.0694i	0.183370	−	0.564354i
$714$		0			0
$715$	−1.56061	+	0.511079i	−0.0583637	+	0.0191133i
$716$		0			0
$717$	3.03920	−	9.35370i	0.113501	−	0.349321i
$718$		0			0
$719$	34.2785	+	24.9048i	1.27837	+	0.928791i	0.999503	−	0.0315382i	$-0.0100406\pi$
$719$	34.2785	+	24.9048i	1.27837	+	0.928791i	0.278869	+	0.960329i	$0.410041\pi$
$720$		0			0
$721$	0.551410	+	1.69706i	0.0205356	+	0.0632020i
$722$		0			0
$723$	36.2457	−	26.3341i	1.34799	−	0.979374i
$724$		0			0
$725$	2.10646			0.0782318
$726$		0			0
$727$	−22.6871			−0.841417			−0.420709	−	0.907196i	$-0.638219\pi$
$727$	−22.6871			−0.841417			−0.420709	+	0.907196i	$0.638219\pi$
$728$		0			0
$729$	−22.8280	+	16.5855i	−0.845480	+	0.614277i
$730$		0			0
$731$	8.40551	+	25.8695i	0.310889	+	0.956819i
$732$		0			0
$733$	10.1434	+	7.36960i	0.374655	+	0.272202i	0.759138	−	0.650929i	$-0.225621\pi$
$733$	10.1434	+	7.36960i	0.374655	+	0.272202i	−0.384484	+	0.923132i	$0.625621\pi$
$734$		0			0
$735$	3.63167	−	11.1771i	0.133956	−	0.412274i
$736$		0			0
$737$	−14.1678	+	4.63976i	−0.521878	+	0.170908i
$738$		0			0
$739$	4.49672	−	13.8395i	0.165415	−	0.509094i	−0.833652	−	0.552290i	$-0.813754\pi$
$739$	4.49672	−	13.8395i	0.165415	−	0.509094i	0.999067	+	0.0431962i	$0.0137541\pi$
$740$		0			0
$741$	4.91004	+	3.56735i	0.180375	+	0.131050i
$742$		0			0
$743$	1.02694	+	3.16061i	0.0376749	+	0.115951i	0.968125	−	0.250467i	$-0.0805840\pi$
$743$	1.02694	+	3.16061i	0.0376749	+	0.115951i	−0.930450	+	0.366418i	$0.880584\pi$
$744$		0			0
$745$	−4.90458	+	3.56339i	−0.179690	+	0.130552i
$746$		0			0
$747$	1.30848			0.0478746
$748$		0			0
$749$	−0.552752			−0.0201971
$750$		0			0
$751$	−18.0760	+	13.1330i	−0.659604	+	0.479230i	−0.866529	−	0.499126i	$-0.833654\pi$
$751$	−18.0760	+	13.1330i	−0.659604	+	0.479230i	0.206925	+	0.978357i	$0.433654\pi$
$752$		0			0
$753$	11.1542	+	34.3291i	0.406482	+	1.25102i
$754$		0			0
$755$	14.1108	+	10.2521i	0.513544	+	0.373112i
$756$		0			0
$757$	−7.59258	+	23.3676i	−0.275957	+	0.849309i	0.713007	+	0.701156i	$0.247333\pi$
$757$	−7.59258	+	23.3676i	−0.275957	+	0.849309i	−0.988965	+	0.148152i	$0.952667\pi$
$758$		0			0
$759$	−7.91563	+	10.9483i	−0.287319	+	0.397396i
$760$		0			0
$761$	−13.7261	+	42.2446i	−0.497571	+	1.53136i	0.315341	+	0.948978i	$0.397881\pi$
$761$	−13.7261	+	42.2446i	−0.497571	+	1.53136i	−0.812912	+	0.582387i	$0.802119\pi$
$762$		0			0
$763$	0.193259	+	0.140411i	0.00699643	+	0.00508321i
$764$		0			0
$765$	−0.232037	−	0.714136i	−0.00838931	−	0.0258197i
$766$		0			0
$767$	−3.09838	+	2.25111i	−0.111876	+	0.0812827i
$768$		0			0
$769$	−7.95061			−0.286706			−0.143353	−	0.989672i	$-0.545788\pi$
$769$	−7.95061			−0.286706			−0.143353	+	0.989672i	$0.545788\pi$
$770$		0			0
$771$	35.4883			1.27808
$772$		0			0
$773$	30.0107	−	21.8040i	1.07941	−	0.784237i	0.101830	−	0.994802i	$-0.467530\pi$
$773$	30.0107	−	21.8040i	1.07941	−	0.784237i	0.977580	+	0.210565i	$0.0675303\pi$
$774$		0			0
$775$	−2.02898	−	6.24455i	−0.0728831	−	0.224311i
$776$		0			0
$777$	1.93057	+	1.40264i	0.0692588	+	0.0503195i
$778$		0			0
$779$	2.48778	−	7.65661i	0.0891341	−	0.274327i
$780$		0			0
$781$	−0.742731	−	1.01731i	−0.0265770	−	0.0364022i
$782$		0			0
$783$	−3.46189	+	10.6546i	−0.123718	+	0.380764i
$784$		0			0
$785$	15.4447	+	11.2213i	0.551246	+	0.400504i
$786$		0			0
$787$	−12.2724	−	37.7705i	−0.437464	−	1.34637i	−0.890541	−	0.454903i	$-0.849674\pi$
$787$	−12.2724	−	37.7705i	−0.437464	−	1.34637i	0.453077	−	0.891471i	$-0.350326\pi$
$788$		0			0
$789$	2.24863	−	1.63372i	0.0800532	−	0.0581621i
$790$		0			0
$791$	1.86537			0.0663251
$792$		0			0
$793$	−6.49804			−0.230752
$794$		0			0
$795$	−9.20378	+	6.68694i	−0.326424	+	0.237161i
$796$		0			0
$797$	5.88136	+	18.1010i	0.208329	+	0.641169i	0.999560	+	0.0296529i	$0.00944019\pi$
$797$	5.88136	+	18.1010i	0.208329	+	0.641169i	−0.791232	+	0.611516i	$0.790560\pi$
$798$		0			0
$799$	−22.1775	−	16.1129i	−0.784583	−	0.570033i
$800$		0			0
$801$	−0.0856222	+	0.263518i	−0.00302531	+	0.00931095i
$802$		0			0
$803$	−46.1546	−	14.8783i	−1.62876	−	0.525042i
$804$		0			0
$805$	−0.144645	+	0.445173i	−0.00509808	+	0.0156903i
$806$		0			0
$807$	−22.0610	−	16.0282i	−0.776583	−	0.564220i
$808$		0			0
$809$	−8.89608	−	27.3793i	−0.312770	−	0.962606i	−0.976663	−	0.214778i	$-0.931097\pi$
$809$	−8.89608	−	27.3793i	−0.312770	−	0.962606i	0.663893	−	0.747827i	$-0.268903\pi$
$810$		0			0
$811$	−24.2405	+	17.6118i	−0.851200	+	0.618433i	−0.925477	−	0.378805i	$-0.876335\pi$
$811$	−24.2405	+	17.6118i	−0.851200	+	0.618433i	0.0742765	+	0.997238i	$0.476335\pi$
$812$		0			0
$813$	8.27264			0.290134
$814$		0			0
$815$	0.100999			0.00353786
$816$		0			0
$817$	32.0801	−	23.3076i	1.12234	−	0.815429i
$818$		0			0
$819$	−0.00447366	−	0.0137685i	−0.000156322	−	0.000481111i
$820$		0			0
$821$	11.7372	+	8.52757i	0.409631	+	0.297614i	0.773452	−	0.633854i	$-0.218528\pi$
$821$	11.7372	+	8.52757i	0.409631	+	0.297614i	−0.363821	+	0.931469i	$0.618528\pi$
$822$		0			0
$823$	1.81513	−	5.58640i	0.0632715	−	0.194730i	−0.914424	−	0.404758i	$-0.867356\pi$
$823$	1.81513	−	5.58640i	0.0632715	−	0.194730i	0.977695	+	0.210029i	$0.0673557\pi$
$824$		0			0
$825$	0.0129856	+	5.59836i	0.000452102	+	0.194910i
$826$		0			0
$827$	−8.03378	+	24.7254i	−0.279362	+	0.859787i	0.708670	+	0.705540i	$0.249295\pi$
$827$	−8.03378	+	24.7254i	−0.279362	+	0.859787i	−0.988032	+	0.154248i	$0.950705\pi$
$828$		0			0
$829$	−30.8232	−	22.3943i	−1.07053	−	0.777788i	−0.0945250	−	0.995522i	$-0.530133\pi$
$829$	−30.8232	−	22.3943i	−1.07053	−	0.777788i	−0.976008	+	0.217735i	$0.930133\pi$
$830$		0			0
$831$	7.58609	+	23.3476i	0.263159	+	0.809919i
$832$		0			0
$833$	−28.0581	+	20.3854i	−0.972155	+	0.706312i
$834$		0			0
$835$	−11.2432			−0.389086
$836$		0			0
$837$	34.9200			1.20701
$838$		0			0
$839$	41.3771	−	30.0622i	1.42849	−	1.03786i	0.438200	−	0.898877i	$-0.355616\pi$
$839$	41.3771	−	30.0622i	1.42849	−	1.03786i	0.990295	−	0.138985i	$-0.0443839\pi$
$840$		0			0
$841$	−7.59034	−	23.3607i	−0.261736	−	0.805540i
$842$		0			0
$843$	4.73062	+	3.43700i	0.162931	+	0.118377i
$844$		0			0
$845$	3.94146	−	12.1306i	0.135590	−	0.417305i
$846$		0			0
$847$	2.13361	−	0.00989806i	0.0733118	−	0.000340101i
$848$		0			0
$849$	0.759101	−	2.33627i	0.0260523	−	0.0801806i
$850$		0			0
$851$	14.2294	+	10.3383i	0.487778	+	0.354391i
$852$		0			0
$853$	−5.02832	−	15.4756i	−0.172166	−	0.529873i	0.827326	−	0.561721i	$-0.189861\pi$
$853$	−5.02832	−	15.4756i	−0.172166	−	0.529873i	−0.999493	+	0.0318481i	$0.989861\pi$
$854$		0			0
$855$	−0.885583	+	0.643413i	−0.0302863	+	0.0220043i
$856$		0			0
$857$	14.0851			0.481139			0.240569	−	0.970632i	$-0.422666\pi$
$857$	14.0851			0.481139			0.240569	+	0.970632i	$0.422666\pi$
$858$		0			0
$859$	15.4255			0.526312			0.263156	−	0.964753i	$-0.415237\pi$
$859$	15.4255			0.526312			0.263156	+	0.964753i	$0.415237\pi$
$860$		0			0
$861$	0.293658	−	0.213355i	0.0100078	−	0.00727112i
$862$		0			0
$863$	−0.0212865	−	0.0655130i	−0.000724600	−	0.00223009i	0.950694	−	0.310132i	$-0.100373\pi$
$863$	−0.0212865	−	0.0655130i	−0.000724600	−	0.00223009i	−0.951418	+	0.307902i	$0.900373\pi$
$864$		0			0
$865$	6.56139	+	4.76713i	0.223094	+	0.162087i
$866$		0			0
$867$	4.07557	−	12.5433i	0.138413	−	0.425993i
$868$		0			0
$869$	0.0127226	+	5.48498i	0.000431586	+	0.186065i
$870$		0			0
$871$	−0.687754	+	2.11669i	−0.0233036	+	0.0717212i
$872$		0			0
$873$	−1.57019	−	1.14081i	−0.0531429	−	0.0386105i
$874$		0			0
$875$	0.0599391	+	0.184474i	0.00202631	+	0.00623634i
$876$		0			0
$877$	29.8224	−	21.6672i	1.00703	−	0.731650i	0.0434461	−	0.999056i	$-0.486166\pi$
$877$	29.8224	−	21.6672i	1.00703	−	0.731650i	0.963584	+	0.267405i	$0.0861663\pi$
$878$		0			0
$879$	53.7783			1.81390
$880$		0			0
$881$	10.5610			0.355810			0.177905	−	0.984048i	$-0.443068\pi$
$881$	10.5610			0.355810			0.177905	+	0.984048i	$0.443068\pi$
$882$		0			0
$883$	18.8202	−	13.6736i	0.633349	−	0.460155i	−0.224210	−	0.974541i	$-0.571980\pi$
$883$	18.8202	−	13.6736i	0.633349	−	0.460155i	0.857559	+	0.514386i	$0.171980\pi$
$884$		0			0
$885$	4.03463	+	12.4173i	0.135623	+	0.417404i
$886$		0			0
$887$	−31.9236	−	23.1938i	−1.07189	−	0.778773i	−0.0956377	−	0.995416i	$-0.530489\pi$
$887$	−31.9236	−	23.1938i	−1.07189	−	0.778773i	−0.976251	+	0.216644i	$0.930489\pi$
$888$		0			0
$889$	1.02278	−	3.14781i	0.0343031	−	0.105574i
$890$		0			0
$891$	−26.9108	−	8.67487i	−0.901544	−	0.290619i
$892$		0			0
$893$	−12.3490	+	38.0065i	−0.413245	+	1.27184i
$894$		0			0
$895$	−17.2144	−	12.5070i	−0.575414	−	0.418063i
$896$		0			0
$897$	0.623253	+	1.91818i	0.0208098	+	0.0640460i
$898$		0			0
$899$	11.1894	−	8.12954i	0.373186	−	0.271135i
$900$		0			0
$901$	33.5727			1.11847
$902$		0			0
$903$	1.78786			0.0594961
$904$		0			0
$905$	6.97501	−	5.06764i	0.231857	−	0.168454i
$906$		0			0
$907$	−7.84754	−	24.1522i	−0.260573	−	0.801962i	−0.992680	−	0.120772i	$-0.961463\pi$
$907$	−7.84754	−	24.1522i	−0.260573	−	0.801962i	0.732107	−	0.681190i	$-0.238537\pi$
$908$		0			0
$909$	−0.121805	−	0.0884964i	−0.00404001	−	0.00293524i
$910$		0			0
$911$	0.149208	−	0.459214i	0.00494348	−	0.0152145i	−0.948554	−	0.316614i	$-0.897454\pi$
$911$	0.149208	−	0.459214i	0.00494348	−	0.0152145i	0.953498	+	0.301400i	$0.0974539\pi$
$912$		0			0
$913$	16.9759	+	23.2517i	0.561819	+	0.769518i
$914$		0			0
$915$	−6.84557	+	21.0685i	−0.226307	+	0.696503i
$916$		0			0
$917$	−1.70357	−	1.23772i	−0.0562570	−	0.0408731i
$918$		0			0
$919$	9.35566	+	28.7938i	0.308615	+	0.949819i	0.978303	+	0.207177i	$0.0664276\pi$
$919$	9.35566	+	28.7938i	0.308615	+	0.949819i	−0.669689	+	0.742642i	$0.733572\pi$
$920$		0			0
$921$	−22.0724	+	16.0366i	−0.727311	+	0.528422i
$922$		0			0
$923$	−0.188042			−0.00618948
$924$		0			0
$925$	7.28844			0.239642
$926$		0			0
$927$	−1.12190	+	0.815108i	−0.0368480	+	0.0267716i
$928$		0			0
$929$	2.96132	+	9.11400i	0.0971576	+	0.299020i	0.987810	−	0.155664i	$-0.0497519\pi$
$929$	2.96132	+	9.11400i	0.0971576	+	0.299020i	−0.890652	+	0.454685i	$0.849752\pi$
$930$		0			0
$931$	40.9030	+	29.7177i	1.34054	+	0.973960i
$932$		0			0
$933$	11.7515	−	36.1675i	0.384728	−	1.18407i
$934$		0			0
$935$	9.67984	−	13.3884i	0.316565	−	0.437846i
$936$		0			0
$937$	7.02631	−	21.6247i	0.229539	−	0.706450i	−0.768260	−	0.640138i	$-0.778877\pi$
$937$	7.02631	−	21.6247i	0.229539	−	0.706450i	0.997799	−	0.0663112i	$-0.0211230\pi$
$938$		0			0
$939$	−23.9618	−	17.4093i	−0.781963	−	0.568130i
$940$		0			0
$941$	18.3704	+	56.5384i	0.598859	+	1.84310i	0.534493	+	0.845173i	$0.320503\pi$
$941$	18.3704	+	56.5384i	0.598859	+	1.84310i	0.0643664	+	0.997926i	$0.479497\pi$
$942$		0			0
$943$	2.16443	−	1.57255i	0.0704834	−	0.0512092i
$944$		0			0
$945$	−1.03159			−0.0335576
$946$		0			0
$947$	−21.0694			−0.684662			−0.342331	−	0.939579i	$-0.611216\pi$
$947$	−21.0694			−0.684662			−0.342331	+	0.939579i	$0.611216\pi$
$948$		0			0
$949$	−5.85687	+	4.25526i	−0.190122	+	0.138132i
$950$		0			0
$951$	−14.6900	−	45.2113i	−0.476357	−	1.46608i
$952$		0			0
$953$	5.17248	+	3.75803i	0.167553	+	0.121735i	0.668402	−	0.743800i	$-0.266979\pi$
$953$	5.17248	+	3.75803i	0.167553	+	0.121735i	−0.500849	+	0.865535i	$0.666979\pi$
$954$		0			0
$955$	6.22487	−	19.1582i	0.201432	−	0.619945i
$956$		0			0
$957$	−11.2071	+	3.67016i	−0.362273	+	0.118639i
$958$		0			0
$959$	0.575921	−	1.77250i	0.0185975	−	0.0572371i
$960$		0			0
$961$	−9.79816	−	7.11878i	−0.316070	−	0.229638i
$962$		0			0
$963$	−0.132745	−	0.408546i	−0.00427763	−	0.0131652i
$964$		0			0
$965$	7.85864	−	5.70964i	0.252979	−	0.183800i
$966$		0			0
$967$	48.1138			1.54724			0.773618	−	0.633652i	$-0.218445\pi$
$967$	48.1138			1.54724			0.773618	+	0.633652i	$0.218445\pi$
$968$		0			0
$969$	−61.0589			−1.96149
$970$		0			0
$971$	23.1580	−	16.8253i	0.743176	−	0.539949i	−0.150528	−	0.988606i	$-0.548097\pi$
$971$	23.1580	−	16.8253i	0.743176	−	0.539949i	0.893704	+	0.448657i	$0.148097\pi$
$972$		0			0
$973$	−0.932578	−	2.87018i	−0.0298971	−	0.0920138i
$974$		0			0
$975$	0.676153	+	0.491254i	0.0216542	+	0.0157327i
$976$		0			0
$977$	−1.02272	+	3.14760i	−0.0327196	+	0.100701i	−0.966083	−	0.258233i	$-0.916860\pi$
$977$	−1.02272	+	3.14760i	−0.0327196	+	0.100701i	0.933363	+	0.358934i	$0.116860\pi$
$978$		0			0
$979$	−5.79357	+	1.89731i	−0.185163	+	0.0606384i
$980$		0			0
$981$	−0.0573678	+	0.176560i	−0.00183161	+	0.00563712i
$982$		0			0
$983$	−9.29131	−	6.75053i	−0.296347	−	0.215309i	0.429669	−	0.902986i	$-0.358630\pi$
$983$	−9.29131	−	6.75053i	−0.296347	−	0.215309i	−0.726016	+	0.687678i	$0.758630\pi$
$984$		0			0
$985$	4.47869	+	13.7840i	0.142703	+	0.439195i
$986$		0			0
$987$	−1.45768	+	1.05907i	−0.0463985	+	0.0337105i
$988$		0			0
$989$	13.1775			0.419021
$990$		0			0
$991$	28.8261			0.915693			0.457846	−	0.889031i	$-0.348621\pi$
$991$	28.8261			0.915693			0.457846	+	0.889031i	$0.348621\pi$
$992$		0			0
$993$	−1.32500	+	0.962670i	−0.0420476	+	0.0305494i
$994$		0			0
$995$	6.42925	+	19.7872i	0.203821	+	0.627296i
$996$		0			0
$997$	−20.4417	−	14.8518i	−0.647397	−	0.470361i	0.214987	−	0.976617i	$-0.431029\pi$
$997$	−20.4417	−	14.8518i	−0.647397	−	0.470361i	−0.862383	+	0.506256i	$0.831029\pi$
$998$		0			0
$999$	−11.9783	+	36.8654i	−0.378977	+	1.16637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.c.361.1	✓	12
4.3	odd	2		880.2.bo.i.801.3		12
11.4	even	5		4840.2.a.bb.1.5		6
11.5	even	5	inner	440.2.y.c.401.1	yes	12
11.7	odd	10		4840.2.a.ba.1.5		6
44.7	even	10		9680.2.a.dd.1.2		6
44.15	odd	10		9680.2.a.dc.1.2		6
44.27	odd	10		880.2.bo.i.401.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.c.361.1	✓	12	1.1	even	1	trivial
440.2.y.c.401.1	yes	12	11.5	even	5	inner
880.2.bo.i.401.3		12	44.27	odd	10
880.2.bo.i.801.3		12	4.3	odd	2
4840.2.a.ba.1.5		6	11.7	odd	10
4840.2.a.bb.1.5		6	11.4	even	5
9680.2.a.dc.1.2		6	44.15	odd	10
9680.2.a.dd.1.2		6	44.7	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36560 + 0.992167i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(0.156923 + 0.114011i) q^{7} +(-0.0465816 + 0.143363i) q^{9} +(-3.15191 + 1.03221i) q^{11} +(-0.153004 + 0.470899i) q^{13} +(1.36560 + 0.992167i) q^{15} +(-1.53931 - 4.73750i) q^{17} +(-5.87486 + 4.26833i) q^{19} -0.327411 q^{21} -2.41321 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.64347 - 5.05807i) q^{27} +(-1.70416 - 1.23814i) q^{29} +(-2.02898 + 6.24455i) q^{31} +(3.28013 - 4.53680i) q^{33} +(0.0599391 - 0.184474i) q^{35} +(-5.89647 - 4.28404i) q^{37} +(-0.258268 - 0.794866i) q^{39} +(-0.896909 + 0.651642i) q^{41} -5.46058 q^{43} +0.150741 q^{45} +(4.45214 - 3.23467i) q^{47} +(-2.15149 - 6.62161i) q^{49} +(6.80247 + 4.94228i) q^{51} +(-2.08269 + 6.40987i) q^{53} +(1.95568 + 2.67868i) q^{55} +(3.78781 - 11.6577i) q^{57} +(6.25768 + 4.54647i) q^{59} +(4.05549 + 12.4815i) q^{61} +(-0.0236547 + 0.0171861i) q^{63} +0.495133 q^{65} +4.49499 q^{67} +(3.29548 - 2.39430i) q^{69} +(0.117359 + 0.361193i) q^{71} +(11.8289 + 8.59419i) q^{73} +(0.521613 - 1.60536i) q^{75} +(-0.612289 - 0.197376i) q^{77} +(0.511049 - 1.57285i) q^{79} +(6.89691 + 5.01090i) q^{81} +(-2.68236 - 8.25544i) q^{83} +(-4.02996 + 2.92794i) q^{85} +3.55564 q^{87} +1.83811 q^{89} +(-0.0776975 + 0.0564505i) q^{91} +(-3.42486 - 10.5406i) q^{93} +(5.87486 + 4.26833i) q^{95} +(-3.97873 + 12.2453i) q^{97} +(-0.00115966 - 0.499950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} + 3 q^{5} - q^{7} - 10 q^{9} + 4 q^{11} + 18 q^{13} + q^{15} + 3 q^{17} + 4 q^{19} - 28 q^{21} - 18 q^{23} - 3 q^{25} + 23 q^{27} + 15 q^{29} - 8 q^{31} + 4 q^{33} + 6 q^{35} + 6 q^{37}+ \cdots + 79 q^{99}+O(q^{100}) \) 12 * q - q^3 + 3 * q^5 - q^7 - 10 * q^9 + 4 * q^11 + 18 * q^13 + q^15 + 3 * q^17 + 4 * q^19 - 28 * q^21 - 18 * q^23 - 3 * q^25 + 23 * q^27 + 15 * q^29 - 8 * q^31 + 4 * q^33 + 6 * q^35 + 6 * q^37 - 33 * q^39 + 2 * q^41 - 36 * q^43 - 10 * q^45 - 16 * q^47 - 16 * q^49 - 10 * q^51 + 19 * q^53 + 6 * q^55 + 62 * q^57 + 46 * q^59 + 18 * q^61 - 7 * q^63 + 2 * q^65 - 44 * q^67 - q^69 - 6 * q^71 + 25 * q^73 + 4 * q^75 + 10 * q^77 + 19 * q^79 + 30 * q^81 - 3 * q^85 + 6 * q^87 - 50 * q^89 - 46 * q^91 - 37 * q^93 - 4 * q^95 - 31 * q^97 + 79 * q^99

Introduction

L-functions

Modular forms

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Database

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