LMFDB - Embedded newform 820.2.bq.a.49.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(49,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 10, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	820.49
Dual form			820.2.bq.a.569.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52630 + 1.52630i) q^{3} +(2.01925 + 0.960543i) q^{5} +(-0.663644 + 4.19008i) q^{7} -1.65918i q^{9} +(0.501988 - 0.255776i) q^{11} +(-6.82894 + 1.08160i) q^{13} +(-4.54805 + 1.61590i) q^{15} +(5.72139 - 2.91520i) q^{17} +(-1.30618 + 8.24687i) q^{19} +(-5.38240 - 7.40824i) q^{21} +(3.64656 - 5.01906i) q^{23} +(3.15471 + 3.87915i) q^{25} +(-2.04650 - 2.04650i) q^{27} +(2.61830 - 5.13871i) q^{29} +(-0.662459 + 2.03884i) q^{31} +(-0.375794 + 1.15657i) q^{33} +(-5.36481 + 7.82335i) q^{35} +(-0.235334 + 0.0764648i) q^{37} +(8.77216 - 12.0738i) q^{39} +(-6.39744 + 0.269626i) q^{41} +(-5.54369 - 4.02773i) q^{43} +(1.59371 - 3.35029i) q^{45} +(0.604508 + 3.81672i) q^{47} +(-10.4590 - 3.39832i) q^{49} +(-4.28310 + 13.1820i) q^{51} +(-5.11328 - 2.60535i) q^{53} +(1.25932 - 0.0342931i) q^{55} +(-10.5936 - 14.5808i) q^{57} +(5.56649 + 4.04429i) q^{59} +(0.00839508 + 0.0115548i) q^{61} +(6.95209 + 1.10110i) q^{63} +(-14.8282 - 4.37547i) q^{65} +(-3.06934 + 6.02392i) q^{67} +(2.09485 + 13.2263i) q^{69} +(-7.94526 + 4.04831i) q^{71} +1.97734 q^{73} +(-10.7358 - 1.10570i) q^{75} +(0.738580 + 2.27311i) q^{77} +(2.64995 + 2.64995i) q^{79} +11.2247 q^{81} +3.01964i q^{83} +(14.3531 - 0.390855i) q^{85} +(3.84689 + 11.8395i) q^{87} +(-1.17725 - 0.186457i) q^{89} -29.3316i q^{91} +(-2.10077 - 4.12299i) q^{93} +(-10.5590 + 15.3978i) q^{95} +(-5.27287 + 10.3486i) q^{97} +(-0.424377 - 0.832887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.52630	+	1.52630i	−0.881209	+	0.881209i	−0.993658	−	0.112448i	$-0.964131\pi$
$3$	−1.52630	+	1.52630i	−0.881209	+	0.881209i	0.112448	+	0.993658i	$0.464131\pi$
$4$		0			0
$5$	2.01925	+	0.960543i	0.903035	+	0.429568i
$5$	2.01925	+	0.960543i	0.903035	+	0.429568i
$6$		0			0
$7$	−0.663644	+	4.19008i	−0.250834	+	1.58370i	0.464922	+	0.885352i	$0.346082\pi$
$7$	−0.663644	+	4.19008i	−0.250834	+	1.58370i	−0.715756	+	0.698350i	$0.753918\pi$
$8$		0			0
$9$		−	1.65918i		−	0.553059i
$10$		0			0
$11$	0.501988	−	0.255776i	0.151355	−	0.0771193i	−0.376672	−	0.926347i	$-0.622932\pi$
$11$	0.501988	−	0.255776i	0.151355	−	0.0771193i	0.528028	+	0.849227i	$0.322932\pi$
$12$		0			0
$13$	−6.82894	+	1.08160i	−1.89401	+	0.299981i	−0.991439	−	0.130569i	$-0.958320\pi$
$13$	−6.82894	+	1.08160i	−1.89401	+	0.299981i	−0.902567	+	0.430550i	$0.858320\pi$
$14$		0			0
$15$	−4.54805	+	1.61590i	−1.17430	+	0.417223i
$16$		0			0
$17$	5.72139	−	2.91520i	1.38764	−	0.707039i	0.408985	−	0.912541i	$-0.365883\pi$
$17$	5.72139	−	2.91520i	1.38764	−	0.707039i	0.978657	+	0.205502i	$0.0658828\pi$
$18$		0			0
$19$	−1.30618	+	8.24687i	−0.299657	+	1.89196i	0.134160	+	0.990960i	$0.457166\pi$
$19$	−1.30618	+	8.24687i	−0.299657	+	1.89196i	−0.433817	+	0.901001i	$0.642834\pi$
$20$		0			0
$21$	−5.38240	−	7.40824i	−1.17454	−	1.61661i
$22$		0			0
$23$	3.64656	−	5.01906i	0.760361	−	1.04655i	−0.236823	−	0.971553i	$-0.576106\pi$
$23$	3.64656	−	5.01906i	0.760361	−	1.04655i	0.997184	−	0.0749943i	$-0.0238938\pi$
$24$		0			0
$25$	3.15471	+	3.87915i	0.630943	+	0.775829i
$26$		0			0
$27$	−2.04650	−	2.04650i	−0.393848	−	0.393848i
$28$		0			0
$29$	2.61830	−	5.13871i	0.486207	−	0.954234i	−0.509394	−	0.860534i	$-0.670130\pi$
$29$	2.61830	−	5.13871i	0.486207	−	0.954234i	0.995600	−	0.0937008i	$-0.0298697\pi$
$30$		0			0
$31$	−0.662459	+	2.03884i	−0.118981	+	0.366186i	−0.992757	−	0.120143i	$-0.961665\pi$
$31$	−0.662459	+	2.03884i	−0.118981	+	0.366186i	0.873775	+	0.486330i	$0.161665\pi$
$32$		0			0
$33$	−0.375794	+	1.15657i	−0.0654173	+	0.201334i
$34$		0			0
$35$	−5.36481	+	7.82335i	−0.906819	+	1.32239i
$36$		0			0
$37$	−0.235334	+	0.0764648i	−0.0386887	+	0.0125707i	−0.328297	−	0.944574i	$-0.606475\pi$
$37$	−0.235334	+	0.0764648i	−0.0386887	+	0.0125707i	0.289609	+	0.957145i	$0.406475\pi$
$38$		0			0
$39$	8.77216	−	12.0738i	1.40467	−	1.93336i
$40$		0			0
$41$	−6.39744	+	0.269626i	−0.999113	+	0.0421085i
$41$	−6.39744	+	0.269626i	−0.999113	+	0.0421085i
$42$		0			0
$43$	−5.54369	−	4.02773i	−0.845405	−	0.614222i	0.0784706	−	0.996916i	$-0.474996\pi$
$43$	−5.54369	−	4.02773i	−0.845405	−	0.614222i	−0.923875	+	0.382694i	$0.874996\pi$
$44$		0			0
$45$	1.59371	−	3.35029i	0.237577	−	0.499432i
$46$		0			0
$47$	0.604508	+	3.81672i	0.0881766	+	0.556725i	0.991739	+	0.128269i	$0.0409422\pi$
$47$	0.604508	+	3.81672i	0.0881766	+	0.556725i	−0.903563	+	0.428456i	$0.859058\pi$
$48$		0			0
$49$	−10.4590	−	3.39832i	−1.49414	−	0.485475i
$50$		0			0
$51$	−4.28310	+	13.1820i	−0.599754	+	1.84585i
$52$		0			0
$53$	−5.11328	−	2.60535i	−0.702363	−	0.357872i	0.0660586	−	0.997816i	$-0.478958\pi$
$53$	−5.11328	−	2.60535i	−0.702363	−	0.357872i	−0.768422	+	0.639944i	$0.778958\pi$
$54$		0			0
$55$	1.25932	−	0.0342931i	0.169807	−	0.00462408i
$56$		0			0
$57$	−10.5936	−	14.5808i	−1.40315	−	1.93127i
$58$		0			0
$59$	5.56649	+	4.04429i	0.724695	+	0.526522i	0.887881	−	0.460073i	$-0.152177\pi$
$59$	5.56649	+	4.04429i	0.724695	+	0.526522i	−0.163185	+	0.986595i	$0.552177\pi$
$60$		0			0
$61$	0.00839508	+	0.0115548i	0.00107488	+	0.00147944i	0.809554	−	0.587045i	$-0.199709\pi$
$61$	0.00839508	+	0.0115548i	0.00107488	+	0.00147944i	−0.808479	+	0.588525i	$0.799709\pi$
$62$		0			0
$63$	6.95209	+	1.10110i	0.875881	+	0.138726i
$64$		0			0
$65$	−14.8282	−	4.37547i	−1.83922	−	0.542711i
$66$		0			0
$67$	−3.06934	+	6.02392i	−0.374979	+	0.735938i	−0.998964	−	0.0454978i	$-0.985513\pi$
$67$	−3.06934	+	6.02392i	−0.374979	+	0.735938i	0.623985	+	0.781436i	$0.285513\pi$
$68$		0			0
$69$	2.09485	+	13.2263i	0.252190	+	1.59226i
$70$		0			0
$71$	−7.94526	+	4.04831i	−0.942929	+	0.480446i	−0.856692	−	0.515828i	$-0.827484\pi$
$71$	−7.94526	+	4.04831i	−0.942929	+	0.480446i	−0.0862372	+	0.996275i	$0.527484\pi$
$72$		0			0
$73$	1.97734			0.231430			0.115715	−	0.993282i	$-0.463084\pi$
$73$	1.97734			0.231430			0.115715	+	0.993282i	$0.463084\pi$
$74$		0			0
$75$	−10.7358	−	1.10570i	−1.23966	−	0.127675i
$76$		0			0
$77$	0.738580	+	2.27311i	0.0841690	+	0.259045i
$78$		0			0
$79$	2.64995	+	2.64995i	0.298143	+	0.298143i	0.840286	−	0.542143i	$-0.182387\pi$
$79$	2.64995	+	2.64995i	0.298143	+	0.298143i	−0.542143	+	0.840286i	$0.682387\pi$
$80$		0			0
$81$	11.2247			1.24718
$82$		0			0
$83$			3.01964i			0.331448i	0.986172	+	0.165724i	$0.0529962\pi$
$83$			3.01964i			0.331448i	−0.986172	+	0.165724i	$0.947004\pi$
$84$		0			0
$85$	14.3531	−	0.390855i	1.55681	−	0.0423941i
$86$		0			0
$87$	3.84689	+	11.8395i	0.412430	+	1.26933i
$88$		0			0
$89$	−1.17725	−	0.186457i	−0.124788	−	0.0197644i	0.0937281	−	0.995598i	$-0.470122\pi$
$89$	−1.17725	−	0.186457i	−0.124788	−	0.0197644i	−0.218516	+	0.975833i	$0.570122\pi$
$90$		0			0
$91$		−	29.3316i		−	3.07479i
$92$		0			0
$93$	−2.10077	−	4.12299i	−0.217839	−	0.427534i
$94$		0			0
$95$	−10.5590	+	15.3978i	−1.08333	+	1.57978i
$96$		0			0
$97$	−5.27287	+	10.3486i	−0.535379	+	1.05074i	0.451948	+	0.892044i	$0.350729\pi$
$97$	−5.27287	+	10.3486i	−0.535379	+	1.05074i	−0.987327	+	0.158696i	$0.949271\pi$
$98$		0			0
$99$	−0.424377	−	0.832887i	−0.0426515	−	0.0837083i
$100$		0			0
$101$	2.04447	−	12.9083i	0.203432	−	1.28442i	−0.648680	−	0.761061i	$-0.724679\pi$
$101$	2.04447	−	12.9083i	0.203432	−	1.28442i	0.852112	−	0.523359i	$-0.175321\pi$
$102$		0			0
$103$	7.22048	−	5.24599i	0.711455	−	0.516903i	−0.172187	−	0.985064i	$-0.555083\pi$
$103$	7.22048	−	5.24599i	0.711455	−	0.516903i	0.883643	+	0.468162i	$0.155083\pi$
$104$		0			0
$105$	−3.75246	−	20.1291i	−0.366203	−	1.96440i
$106$		0			0
$107$	−2.36893	−	3.26055i	−0.229013	−	0.315210i	0.679010	−	0.734129i	$-0.262409\pi$
$107$	−2.36893	−	3.26055i	−0.229013	−	0.315210i	−0.908024	+	0.418919i	$0.862409\pi$
$108$		0			0
$109$	5.53818	−	5.53818i	0.530462	−	0.530462i	−0.390248	−	0.920710i	$-0.627611\pi$
$109$	5.53818	−	5.53818i	0.530462	−	0.530462i	0.920710	+	0.390248i	$0.127611\pi$
$110$		0			0
$111$	0.242483	−	0.475899i	0.0230154	−	0.0451703i
$112$		0			0
$113$	4.69002	+	1.52388i	0.441200	+	0.143355i	0.521189	−	0.853441i	$-0.325489\pi$
$113$	4.69002	+	1.52388i	0.441200	+	0.143355i	−0.0799892	+	0.996796i	$0.525489\pi$
$114$		0			0
$115$	12.1843	−	6.63205i	1.13620	−	0.618442i
$116$		0			0
$117$	1.79456	+	11.3304i	0.165907	+	1.04750i
$118$		0			0
$119$	8.41794	+	25.9078i	0.771671	+	2.37496i
$120$		0			0
$121$	−6.27907	+	8.64239i	−0.570824	+	0.785672i
$122$		0			0
$123$	9.35288	−	10.1759i	0.843321	−	0.917534i
$124$		0			0
$125$	2.64406	+	10.8632i	0.236492	+	0.971633i
$126$		0			0
$127$	15.0159	−	4.87896i	1.33244	−	0.432937i	0.445693	−	0.895186i	$-0.352957\pi$
$127$	15.0159	−	4.87896i	1.33244	−	0.432937i	0.886751	+	0.462248i	$0.152957\pi$
$128$		0			0
$129$	14.6088	−	2.31381i	1.28624	−	0.203720i
$130$		0			0
$131$	−0.0627219	−	0.0203796i	−0.00548004	−	0.00178057i	0.306276	−	0.951943i	$-0.400917\pi$
$131$	−0.0627219	−	0.0203796i	−0.00548004	−	0.00178057i	−0.311756	+	0.950162i	$0.600917\pi$
$132$		0			0
$133$	−33.6882	−	10.9460i	−2.92114	−	0.949135i
$134$		0			0
$135$	−2.16663	−	6.09813i	−0.186474	−	0.524843i
$136$		0			0
$137$	7.53598	+	7.53598i	0.643843	+	0.643843i	0.951498	−	0.307655i	$-0.0995444\pi$
$137$	7.53598	+	7.53598i	0.643843	+	0.643843i	−0.307655	+	0.951498i	$0.599544\pi$
$138$		0			0
$139$	−6.66371	+	4.84147i	−0.565208	+	0.410648i	−0.833361	−	0.552729i	$-0.813587\pi$
$139$	−6.66371	+	4.84147i	−0.565208	+	0.410648i	0.268153	+	0.963376i	$0.413587\pi$
$140$		0			0
$141$	−6.74811	−	4.90279i	−0.568293	−	0.412889i
$142$		0			0
$143$	−3.15140	+	2.28962i	−0.263533	+	0.191468i
$144$		0			0
$145$	10.2230	−	7.86133i	0.848970	−	0.652848i
$146$		0			0
$147$	21.1504	−	10.7767i	1.74445	−	0.888843i
$148$		0			0
$149$	8.10072	+	4.12752i	0.663637	+	0.338140i	0.753153	−	0.657846i	$-0.228532\pi$
$149$	8.10072	+	4.12752i	0.663637	+	0.338140i	−0.0895160	+	0.995985i	$0.528532\pi$
$150$		0			0
$151$	0.0804628	+	0.508022i	0.00654797	+	0.0413423i	0.990746	−	0.135729i	$-0.0433377\pi$
$151$	0.0804628	+	0.508022i	0.00654797	+	0.0413423i	−0.984198	+	0.177071i	$0.943338\pi$
$152$		0			0
$153$	−4.83683	−	9.49281i	−0.391034	−	0.767448i
$154$		0			0
$155$	−3.29606	+	3.48060i	−0.264746	+	0.279568i
$156$		0			0
$157$	−3.39185	+	21.4153i	−0.270699	+	1.70913i	0.359876	+	0.933000i	$0.382819\pi$
$157$	−3.39185	+	21.4153i	−0.270699	+	1.70913i	−0.630576	+	0.776128i	$0.717181\pi$
$158$		0			0
$159$	11.7809	−	3.82786i	0.934289	−	0.303569i
$160$		0			0
$161$	18.6103	+	18.6103i	1.46669	+	1.46669i
$162$		0			0
$163$		−	0.674798i		−	0.0528542i	−0.999651	−	0.0264271i	$-0.991587\pi$
$163$		−	0.674798i		−	0.0528542i	0.999651	−	0.0264271i	$-0.00841299\pi$
$164$		0			0
$165$	−1.86976	+	1.97444i	−0.145561	+	0.153710i
$166$		0			0
$167$	4.47481	−	4.47481i	0.346271	−	0.346271i	−0.512447	−	0.858719i	$-0.671261\pi$
$167$	4.47481	−	4.47481i	0.346271	−	0.346271i	0.858719	+	0.512447i	$0.171261\pi$
$168$		0			0
$169$	33.1008	−	10.7551i	2.54621	−	0.827315i
$170$		0			0
$171$	13.6830	+	2.16718i	1.04637	+	0.165728i
$172$		0			0
$173$	16.1962			1.23138			0.615689	−	0.787989i	$-0.288878\pi$
$173$	16.1962			1.23138			0.615689	+	0.787989i	$0.288878\pi$
$174$		0			0
$175$	−18.3475	+	10.6441i	−1.38694	+	0.804621i
$176$		0			0
$177$	−14.6689	+	2.32333i	−1.10258	+	0.174632i
$178$		0			0
$179$	11.2154	+	5.71455i	0.838282	+	0.427126i	0.819763	−	0.572703i	$-0.194105\pi$
$179$	11.2154	+	5.71455i	0.838282	+	0.427126i	0.0185185	+	0.999829i	$0.494105\pi$
$180$		0			0
$181$	11.4015	+	22.3767i	0.847468	+	1.66325i	0.743566	+	0.668662i	$0.233133\pi$
$181$	11.4015	+	22.3767i	0.847468	+	1.66325i	0.103902	+	0.994588i	$0.466867\pi$
$182$		0			0
$183$	−0.0304495	−	0.00482273i	−0.00225089	−	0.000356507i
$184$		0			0
$185$	−0.548646	−	0.0716476i	−0.0403373	−	0.00526763i
$186$		0			0
$187$	2.12643	−	2.92679i	0.155500	−	0.214028i
$188$		0			0
$189$	9.93313	−	7.21684i	0.722529	−	0.524948i
$190$		0			0
$191$	−1.15909	+	1.15909i	−0.0838689	+	0.0838689i	−0.747797	−	0.663928i	$-0.768888\pi$
$191$	−1.15909	+	1.15909i	−0.0838689	+	0.0838689i	0.663928	+	0.747797i	$0.268888\pi$
$192$		0			0
$193$	6.61389	+	3.36994i	0.476078	+	0.242574i	0.675528	−	0.737334i	$-0.263916\pi$
$193$	6.61389	+	3.36994i	0.476078	+	0.242574i	−0.199450	+	0.979908i	$0.563916\pi$
$194$		0			0
$195$	29.3106	−	15.9540i	2.09898	−	1.14249i
$196$		0			0
$197$	1.94602	−	5.98924i	0.138648	−	0.426715i	−0.857491	−	0.514498i	$-0.827978\pi$
$197$	1.94602	−	5.98924i	0.138648	−	0.426715i	0.996140	+	0.0877829i	$0.0279782\pi$
$198$		0			0
$199$	0.0632057	−	0.0100108i	0.00448054	−	0.000709647i	−0.154194	−	0.988041i	$-0.549278\pi$
$199$	0.0632057	−	0.0100108i	0.00448054	−	0.000709647i	0.158674	+	0.987331i	$0.449278\pi$
$200$		0			0
$201$	−4.50957	−	13.8790i	−0.318080	−	0.978951i
$202$		0			0
$203$	19.7940	+	14.3812i	1.38927	+	1.00936i
$204$		0			0
$205$	−13.1770	−	5.60058i	−0.920322	−	0.391161i
$206$		0			0
$207$	−8.32752	−	6.05030i	−0.578803	−	0.420525i
$208$		0			0
$209$	1.45366	+	4.47392i	0.100552	+	0.309467i
$210$		0			0
$211$	−14.7205	+	2.33150i	−1.01340	+	0.160507i	−0.640981	−	0.767557i	$-0.721472\pi$
$211$	−14.7205	+	2.33150i	−1.01340	+	0.160507i	−0.372421	+	0.928064i	$0.621472\pi$
$212$		0			0
$213$	5.94791	−	18.3058i	0.407544	−	1.25429i
$214$		0			0
$215$	−7.32527	−	13.4579i	−0.499579	−	0.917823i
$216$		0			0
$217$	−8.10327	−	4.12882i	−0.550085	−	0.280283i
$218$		0			0
$219$	−3.01801	+	3.01801i	−0.203938	+	0.203938i
$220$		0			0
$221$	−35.9180	+	26.0959i	−2.41610	+	1.75540i
$222$		0			0
$223$	−11.4172	+	15.7145i	−0.764554	+	1.05232i	0.232267	+	0.972652i	$0.425386\pi$
$223$	−11.4172	+	15.7145i	−0.764554	+	1.05232i	−0.996822	+	0.0796666i	$0.974614\pi$
$224$		0			0
$225$	6.43619	−	5.23423i	0.429080	−	0.348949i
$226$		0			0
$227$	−3.04035	−	0.481545i	−0.201795	−	0.0319612i	0.0547184	−	0.998502i	$-0.482574\pi$
$227$	−3.04035	−	0.481545i	−0.201795	−	0.0319612i	−0.256514	+	0.966541i	$0.582574\pi$
$228$		0			0
$229$	8.36984	+	16.4267i	0.553095	+	1.08551i	0.983166	+	0.182715i	$0.0584885\pi$
$229$	8.36984	+	16.4267i	0.553095	+	1.08551i	−0.430071	+	0.902795i	$0.641512\pi$
$230$		0			0
$231$	−4.59675	−	2.34216i	−0.302444	−	0.154103i
$232$		0			0
$233$	−6.07229	+	0.961756i	−0.397809	+	0.0630067i	−0.352134	−	0.935950i	$-0.614544\pi$
$233$	−6.07229	+	0.961756i	−0.397809	+	0.0630067i	−0.0456749	+	0.998956i	$0.514544\pi$
$234$		0			0
$235$	−2.44547	+	8.28755i	−0.159525	+	0.540620i
$236$		0			0
$237$	−8.08924			−0.525452
$238$		0			0
$239$	−2.53751	−	0.401902i	−0.164138	−	0.0259969i	0.0738246	−	0.997271i	$-0.476479\pi$
$239$	−2.53751	−	0.401902i	−0.164138	−	0.0259969i	−0.237962	+	0.971274i	$0.576479\pi$
$240$		0			0
$241$	12.0886	−	3.92781i	0.778693	−	0.253013i	0.107411	−	0.994215i	$-0.465744\pi$
$241$	12.0886	−	3.92781i	0.778693	−	0.253013i	0.671282	+	0.741202i	$0.265744\pi$
$242$		0			0
$243$	−10.9927	+	10.9927i	−0.705182	+	0.705182i
$244$		0			0
$245$	−17.8550	−	16.9083i	−1.14071	−	1.08023i
$246$		0			0
$247$		−	57.7301i		−	3.67328i
$248$		0			0
$249$	−4.60887	−	4.60887i	−0.292075	−	0.292075i
$250$		0			0
$251$	−26.8927	+	8.73798i	−1.69746	+	0.551537i	−0.988167	−	0.153382i	$-0.950983\pi$
$251$	−26.8927	+	8.73798i	−1.69746	+	0.551537i	−0.709288	+	0.704919i	$0.750983\pi$
$252$		0			0
$253$	0.546777	−	3.45221i	0.0343756	−	0.217039i
$254$		0			0
$255$	−21.3105	+	22.5036i	−1.33452	+	1.40923i
$256$		0			0
$257$	−11.0192	−	21.6265i	−0.687362	−	1.34902i	−0.925855	−	0.377879i	$-0.876654\pi$
$257$	−11.0192	−	21.6265i	−0.687362	−	1.34902i	0.238493	−	0.971144i	$-0.423346\pi$
$258$		0			0
$259$	−0.164215	−	1.03682i	−0.0102039	−	0.0644246i
$260$		0			0
$261$	−8.52603	−	4.34423i	−0.527748	−	0.268901i
$262$		0			0
$263$	13.8338	−	7.04870i	0.853032	−	0.434641i	0.0279194	−	0.999610i	$-0.491112\pi$
$263$	13.8338	−	7.04870i	0.853032	−	0.434641i	0.825112	+	0.564969i	$0.191112\pi$
$264$		0			0
$265$	−7.82243	−	10.1724i	−0.480528	−	0.624883i
$266$		0			0
$267$	2.08142	−	1.51224i	0.127381	−	0.0925475i
$268$		0			0
$269$	−13.4716	−	9.78771i	−0.821379	−	0.596767i	0.0957280	−	0.995408i	$-0.469482\pi$
$269$	−13.4716	−	9.78771i	−0.821379	−	0.596767i	−0.917107	+	0.398641i	$0.869482\pi$
$270$		0			0
$271$	14.7176	−	10.6930i	0.894031	−	0.649552i	−0.0428946	−	0.999080i	$-0.513658\pi$
$271$	14.7176	−	10.6930i	0.894031	−	0.649552i	0.936926	+	0.349528i	$0.113658\pi$
$272$		0			0
$273$	44.7688	+	44.7688i	2.70953	+	2.70953i
$274$		0			0
$275$	2.57582	+	1.14039i	0.155328	+	0.0687679i
$276$		0			0
$277$	−2.71399	−	0.881829i	−0.163068	−	0.0529840i	0.226345	−	0.974047i	$-0.427322\pi$
$277$	−2.71399	−	0.881829i	−0.163068	−	0.0529840i	−0.389413	+	0.921063i	$0.627322\pi$
$278$		0			0
$279$	3.38280	+	1.09914i	0.202523	+	0.0658036i
$280$		0			0
$281$	9.07960	−	1.43807i	0.541643	−	0.0857879i	0.120383	−	0.992728i	$-0.461588\pi$
$281$	9.07960	−	1.43807i	0.541643	−	0.0857879i	0.421261	+	0.906940i	$0.361588\pi$
$282$		0			0
$283$	−24.3086	+	7.89833i	−1.44499	+	0.469507i	−0.923450	−	0.383718i	$-0.874644\pi$
$283$	−24.3086	+	7.89833i	−1.44499	+	0.469507i	−0.521543	+	0.853225i	$0.674644\pi$
$284$		0			0
$285$	−7.38555	−	39.6178i	−0.437482	−	2.34676i
$286$		0			0
$287$	3.11587	−	26.9848i	0.183924	−	1.59286i
$288$		0			0
$289$	14.2436	−	19.6047i	0.837861	−	1.15322i
$290$		0			0
$291$	−7.74707	−	23.8430i	−0.454141	−	1.39770i
$292$		0			0
$293$	−2.98952	−	18.8751i	−0.174649	−	1.10269i	−0.906803	−	0.421554i	$-0.861485\pi$
$293$	−2.98952	−	18.8751i	−0.174649	−	1.10269i	0.732154	−	0.681139i	$-0.238515\pi$
$294$		0			0
$295$	7.35540	+	13.5133i	0.428248	+	0.786774i
$296$		0			0
$297$	−1.55076	−	0.503872i	−0.0899842	−	0.0292376i
$298$		0			0
$299$	−19.4735	+	38.2190i	−1.12618	+	2.21026i
$300$		0			0
$301$	20.5555	−	20.5555i	1.18480	−	1.18480i
$302$		0			0
$303$	16.5814	+	22.8223i	0.952576	+	1.31111i
$304$		0			0
$305$	0.00585282	+	0.0313959i	0.000335131	+	0.00179772i
$306$		0			0
$307$	6.08054	−	4.41777i	0.347035	−	0.252135i	−0.400589	−	0.916258i	$-0.631195\pi$
$307$	6.08054	−	4.41777i	0.347035	−	0.252135i	0.747624	+	0.664122i	$0.231195\pi$
$308$		0			0
$309$	−3.01367	+	19.0276i	−0.171442	+	1.08244i
$310$		0			0
$311$	2.20578	+	4.32909i	0.125078	+	0.245480i	0.945051	−	0.326922i	$-0.106012\pi$
$311$	2.20578	+	4.32909i	0.125078	+	0.245480i	−0.819973	+	0.572402i	$0.806012\pi$
$312$		0			0
$313$	−2.05746	+	4.03799i	−0.116295	+	0.228241i	−0.941815	−	0.336131i	$-0.890882\pi$
$313$	−2.05746	+	4.03799i	−0.116295	+	0.228241i	0.825521	+	0.564372i	$0.190882\pi$
$314$		0			0
$315$	12.9803	+	8.90118i	0.731359	+	0.501525i
$316$		0			0
$317$	10.2311	+	20.0797i	0.574636	+	1.12779i	0.977185	+	0.212389i	$0.0681243\pi$
$317$	10.2311	+	20.0797i	0.574636	+	1.12779i	−0.402549	+	0.915398i	$0.631876\pi$
$318$		0			0
$319$		−	3.24927i		−	0.181924i
$320$		0			0
$321$	8.59228	+	1.36088i	0.479574	+	0.0759571i
$322$		0			0
$323$	16.5681	+	50.9913i	0.921873	+	2.83723i
$324$		0			0
$325$	−25.7390	−	23.0783i	−1.42774	−	1.28015i
$326$		0			0
$327$			16.9058i			0.934895i
$328$		0			0
$329$	−16.3935			−0.903805
$330$		0			0
$331$	2.20626	+	2.20626i	0.121267	+	0.121267i	0.765136	−	0.643869i	$-0.222672\pi$
$331$	2.20626	+	2.20626i	0.121267	+	0.121267i	−0.643869	+	0.765136i	$0.722672\pi$
$332$		0			0
$333$	0.126869	+	0.390462i	0.00695236	+	0.0213972i
$334$		0			0
$335$	−11.9840	+	9.21554i	−0.654755	+	0.503499i
$336$		0			0
$337$	7.75879			0.422648			0.211324	−	0.977416i	$-0.432222\pi$
$337$	7.75879			0.422648			0.211324	+	0.977416i	$0.432222\pi$
$338$		0			0
$339$	−9.48427	+	4.83248i	−0.515115	+	0.262464i
$340$		0			0
$341$	0.188939	+	1.19291i	0.0102316	+	0.0645999i
$342$		0			0
$343$	7.69850	−	15.1092i	0.415680	−	0.815818i
$344$		0			0
$345$	−8.47446	+	28.7194i	−0.456249	+	1.54620i
$346$		0			0
$347$	19.8038	+	3.13662i	1.06313	+	0.168383i	0.663410	−	0.748256i	$-0.269109\pi$
$347$	19.8038	+	3.13662i	1.06313	+	0.168383i	0.399716	+	0.916639i	$0.369109\pi$
$348$		0			0
$349$	17.5116	+	24.1027i	0.937376	+	1.29019i	0.956912	+	0.290378i	$0.0937811\pi$
$349$	17.5116	+	24.1027i	0.937376	+	1.29019i	−0.0195361	+	0.999809i	$0.506219\pi$
$350$		0			0
$351$	16.1889	+	11.7619i	0.864098	+	0.627804i
$352$		0			0
$353$	16.2088	+	22.3096i	0.862709	+	1.18742i	0.980917	+	0.194429i	$0.0622853\pi$
$353$	16.2088	+	22.3096i	0.862709	+	1.18742i	−0.118207	+	0.992989i	$0.537715\pi$
$354$		0			0
$355$	−19.9320	+	0.542777i	−1.05788	+	0.0288076i
$356$		0			0
$357$	−52.3913	−	26.6947i	−2.77284	−	1.41283i
$358$		0			0
$359$	8.47141	−	26.0723i	0.447104	−	1.37604i	−0.433056	−	0.901367i	$-0.642565\pi$
$359$	8.47141	−	26.0723i	0.447104	−	1.37604i	0.880160	−	0.474677i	$-0.157435\pi$
$360$		0			0
$361$	−48.2346	−	15.6724i	−2.53866	−	0.824862i
$362$		0			0
$363$	−3.60714	−	22.7746i	−0.189326	−	1.19536i
$364$		0			0
$365$	3.99273	+	1.89932i	0.208989	+	0.0994148i
$366$		0			0
$367$	24.7816	+	18.0049i	1.29359	+	0.939846i	0.999871	−	0.0160472i	$-0.00510819\pi$
$367$	24.7816	+	18.0049i	1.29359	+	0.939846i	0.293715	+	0.955893i	$0.405108\pi$
$368$		0			0
$369$	0.447358	+	10.6145i	0.0232885	+	0.552569i
$370$		0			0
$371$	14.3100	−	19.6960i	0.742939	−	1.02257i
$372$		0			0
$373$	−25.4543	+	8.27061i	−1.31797	+	0.428236i	−0.881799	−	0.471625i	$-0.843667\pi$
$373$	−25.4543	+	8.27061i	−1.31797	+	0.428236i	−0.436176	+	0.899861i	$0.643667\pi$
$374$		0			0
$375$	−20.6161	−	12.5449i	−1.06461	−	0.647814i
$376$		0			0
$377$	−12.3222	+	37.9239i	−0.634626	+	1.95318i
$378$		0			0
$379$	1.27261	−	3.91668i	0.0653695	−	0.201187i	−0.913037	−	0.407877i	$-0.866269\pi$
$379$	1.27261	−	3.91668i	0.0653695	−	0.201187i	0.978406	+	0.206690i	$0.0662693\pi$
$380$		0			0
$381$	−15.4720	+	30.3655i	−0.792654	+	1.55567i
$382$		0			0
$383$	−22.6167	−	22.6167i	−1.15566	−	1.15566i	−0.985399	−	0.170261i	$-0.945539\pi$
$383$	−22.6167	−	22.6167i	−1.15566	−	1.15566i	−0.170261	−	0.985399i	$-0.554461\pi$
$384$		0			0
$385$	−0.692050	+	5.29942i	−0.0352701	+	0.270083i
$386$		0			0
$387$	−6.68271	+	9.19797i	−0.339701	+	0.467559i
$388$		0			0
$389$	−20.4365	−	28.1285i	−1.03617	−	1.42617i	−0.900210	−	0.435456i	$-0.856587\pi$
$389$	−20.4365	−	28.1285i	−1.03617	−	1.42617i	−0.135963	−	0.990714i	$-0.543413\pi$
$390$		0			0
$391$	6.23187	−	39.3465i	0.315159	−	1.98984i
$392$		0			0
$393$	0.126838	−	0.0646271i	0.00639812	−	0.00326000i
$394$		0			0
$395$	2.80551	+	7.89630i	0.141161	+	0.397306i
$396$		0			0
$397$	8.44293	−	1.33723i	0.423739	−	0.0671136i	0.0590764	−	0.998253i	$-0.481184\pi$
$397$	8.44293	−	1.33723i	0.423739	−	0.0671136i	0.364662	+	0.931140i	$0.381184\pi$
$398$		0			0
$399$	68.1251	−	34.7115i	3.41052	−	1.73775i
$400$		0			0
$401$			14.1447i			0.706353i	0.935557	+	0.353177i	$0.114899\pi$
$401$			14.1447i			0.706353i	−0.935557	+	0.353177i	$0.885101\pi$
$402$		0			0
$403$	2.31869	−	14.6396i	0.115502	−	0.729251i
$404$		0			0
$405$	22.6654	+	10.7818i	1.12625	+	0.535751i
$406$		0			0
$407$	−0.0985772	+	0.0985772i	−0.00488629	+	0.00488629i
$408$		0			0
$409$	10.0182			0.495368			0.247684	−	0.968841i	$-0.420330\pi$
$409$	10.0182			0.495368			0.247684	+	0.968841i	$0.420330\pi$
$410$		0			0
$411$	−23.0043			−1.13472
$412$		0			0
$413$	−20.6401	+	20.6401i	−1.01563	+	1.01563i
$414$		0			0
$415$	−2.90049	+	6.09740i	−0.142380	+	0.299309i
$416$		0			0
$417$	2.78128	−	17.5603i	0.136200	−	0.859933i
$418$		0			0
$419$		−	25.3066i		−	1.23631i	−0.786057	−	0.618154i	$-0.787881\pi$
$419$		−	25.3066i		−	1.23631i	0.786057	−	0.618154i	$-0.212119\pi$
$420$		0			0
$421$	14.5074	−	7.39191i	0.707050	−	0.360260i	−0.0632012	−	0.998001i	$-0.520131\pi$
$421$	14.5074	−	7.39191i	0.707050	−	0.360260i	0.770251	+	0.637741i	$0.220131\pi$
$422$		0			0
$423$	6.33261	−	1.00299i	0.307902	−	0.0487669i
$424$		0			0
$425$	29.3578	+	12.9975i	1.42406	+	0.630472i
$426$		0			0
$427$	−0.0539870	+	0.0275078i	−0.00261262	+	0.00133119i
$428$		0			0
$429$	1.31532	−	8.30463i	0.0635044	−	0.400951i
$430$		0			0
$431$	8.52308	+	11.7310i	0.410542	+	0.565063i	0.963351	−	0.268246i	$-0.0864438\pi$
$431$	8.52308	+	11.7310i	0.410542	+	0.565063i	−0.552808	+	0.833308i	$0.686444\pi$
$432$		0			0
$433$	−3.04889	+	4.19644i	−0.146520	+	0.201668i	−0.875969	−	0.482368i	$-0.839777\pi$
$433$	−3.04889	+	4.19644i	−0.146520	+	0.201668i	0.729448	+	0.684036i	$0.239777\pi$
$434$		0			0
$435$	−3.60454	+	27.6020i	−0.172825	+	1.32342i
$436$		0			0
$437$	36.6285	+	36.6285i	1.75218	+	1.75218i
$438$		0			0
$439$	−13.0782	+	25.6674i	−0.624187	+	1.22504i	0.334988	+	0.942222i	$0.391268\pi$
$439$	−13.0782	+	25.6674i	−0.624187	+	1.22504i	−0.959175	+	0.282813i	$0.908732\pi$
$440$		0			0
$441$	−5.63842	+	17.3533i	−0.268496	+	0.826347i
$442$		0			0
$443$	−10.5732	+	32.5408i	−0.502346	+	1.54606i	0.302842	+	0.953041i	$0.402065\pi$
$443$	−10.5732	+	32.5408i	−0.502346	+	1.54606i	−0.805188	+	0.593020i	$0.797935\pi$
$444$		0			0
$445$	−2.19805	−	1.50730i	−0.104198	−	0.0714528i
$446$		0			0
$447$	−18.6640	+	6.06429i	−0.882775	+	0.286831i
$448$		0			0
$449$	−11.1310	+	15.3206i	−0.525306	+	0.723022i	−0.986406	−	0.164326i	$-0.947455\pi$
$449$	−11.1310	+	15.3206i	−0.525306	+	0.723022i	0.461100	+	0.887348i	$0.347455\pi$
$450$		0			0
$451$	−3.14248	+	1.77166i	−0.147973	+	0.0834242i
$452$		0			0
$453$	−0.898204	−	0.652583i	−0.0422013	−	0.0306610i
$454$		0			0
$455$	28.1743	−	59.2277i	1.32083	−	2.77664i
$456$		0			0
$457$	1.58951	+	10.0358i	0.0743540	+	0.469453i	0.996568	+	0.0827738i	$0.0263779\pi$
$457$	1.58951	+	10.0358i	0.0743540	+	0.469453i	−0.922214	+	0.386679i	$0.873622\pi$
$458$		0			0
$459$	−17.6747	−	5.74287i	−0.824986	−	0.268054i
$460$		0			0
$461$	0.146379	−	0.450507i	0.00681753	−	0.0209822i	−0.947590	−	0.319489i	$-0.896489\pi$
$461$	0.146379	−	0.450507i	0.00681753	−	0.0209822i	0.954407	+	0.298507i	$0.0964887\pi$
$462$		0			0
$463$	18.4219	+	9.38645i	0.856140	+	0.436225i	0.826234	−	0.563327i	$-0.190479\pi$
$463$	18.4219	+	9.38645i	0.856140	+	0.436225i	0.0299066	+	0.999553i	$0.490479\pi$
$464$		0			0
$465$	−0.281660	−	10.3432i	−0.0130617	−	0.479655i
$466$		0			0
$467$	2.14840	+	2.95702i	0.0994160	+	0.136834i	0.855827	−	0.517262i	$-0.173049\pi$
$467$	2.14840	+	2.95702i	0.0994160	+	0.136834i	−0.756411	+	0.654097i	$0.773049\pi$
$468$		0			0
$469$	−23.2038	−	16.8585i	−1.07145	−	0.778454i
$470$		0			0
$471$	−27.5092	−	37.8631i	−1.26756	−	1.74464i
$472$		0			0
$473$	−3.81306	−	0.603929i	−0.175325	−	0.0277687i
$474$		0			0
$475$	−36.1114	+	20.9497i	−1.65691	+	0.961236i
$476$		0			0
$477$	−4.32273	+	8.48384i	−0.197924	+	0.388448i
$478$		0			0
$479$	−1.59007	−	10.0393i	−0.0726521	−	0.458707i	−0.997016	−	0.0771954i	$-0.975403\pi$
$479$	−1.59007	−	10.0393i	−0.0726521	−	0.458707i	0.924364	−	0.381512i	$-0.124597\pi$
$480$		0			0
$481$	1.52438	−	0.776710i	0.0695057	−	0.0354149i
$482$		0			0
$483$	−56.8097			−2.58493
$484$		0			0
$485$	−20.5875	+	15.8315i	−0.934830	+	0.718873i
$486$		0			0
$487$	−9.36954	−	28.8365i	−0.424574	−	1.30671i	−0.903401	−	0.428796i	$-0.858938\pi$
$487$	−9.36954	−	28.8365i	−0.424574	−	1.30671i	0.478827	−	0.877909i	$-0.341062\pi$
$488$		0			0
$489$	1.02994	+	1.02994i	0.0465756	+	0.0465756i
$490$		0			0
$491$	13.6970			0.618139			0.309070	−	0.951039i	$-0.399982\pi$
$491$	13.6970			0.618139			0.309070	+	0.951039i	$0.399982\pi$
$492$		0			0
$493$		−	37.0334i		−	1.66790i
$494$		0			0
$495$	−0.0568983	−	2.08944i	−0.00255739	−	0.0939133i
$496$		0			0
$497$	−11.6899	−	35.9779i	−0.524366	−	1.61383i
$498$		0			0
$499$	−26.5556	−	4.20599i	−1.18879	−	0.188286i	−0.469460	−	0.882954i	$-0.655551\pi$
$499$	−26.5556	−	4.20599i	−1.18879	−	0.188286i	−0.719331	+	0.694668i	$0.755551\pi$
$500$		0			0
$501$			13.6598i			0.610274i
$502$		0			0
$503$	3.20056	+	6.28146i	0.142706	+	0.280076i	0.951286	−	0.308310i	$-0.0997634\pi$
$503$	3.20056	+	6.28146i	0.142706	+	0.280076i	−0.808580	+	0.588386i	$0.799763\pi$
$504$		0			0
$505$	16.5272	−	24.1012i	0.735452	−	1.07249i
$506$		0			0
$507$	−34.1062	+	66.9372i	−1.51471	+	2.97278i
$508$		0			0
$509$	−0.480631	−	0.943291i	−0.0213036	−	0.0418106i	0.880109	−	0.474771i	$-0.157469\pi$
$509$	−0.480631	−	0.943291i	−0.0213036	−	0.0418106i	−0.901413	+	0.432960i	$0.857469\pi$
$510$		0			0
$511$	−1.31225	+	8.28520i	−0.0580504	+	0.366516i
$512$		0			0
$513$	19.5503	−	14.2041i	0.863165	−	0.627126i
$514$		0			0
$515$	19.6189	−	3.65736i	0.864514	−	0.161163i
$516$		0			0
$517$	1.27968	+	1.76133i	0.0562802	+	0.0774631i
$518$		0			0
$519$	−24.7203	+	24.7203i	−1.08510	+	1.08510i
$520$		0			0
$521$	−8.93107	+	17.5282i	−0.391277	+	0.767925i	−0.999669	−	0.0257116i	$-0.991815\pi$
$521$	−8.93107	+	17.5282i	−0.391277	+	0.767925i	0.608392	+	0.793637i	$0.291815\pi$
$522$		0			0
$523$	−8.82585	−	2.86769i	−0.385927	−	0.125395i	0.109626	−	0.993973i	$-0.465035\pi$
$523$	−8.82585	−	2.86769i	−0.385927	−	0.125395i	−0.495553	+	0.868577i	$0.665035\pi$
$524$		0			0
$525$	11.7577	−	44.2500i	0.513148	−	1.93123i
$526$		0			0
$527$	2.15343	+	13.5962i	0.0938047	+	0.592260i
$528$		0			0
$529$	−4.78618	−	14.7304i	−0.208095	−	0.640451i
$530$		0			0
$531$	6.71020	−	9.23580i	0.291198	−	0.400800i
$532$		0			0
$533$	43.3961	−	8.76072i	1.87969	−	0.379469i
$534$		0			0
$535$	−1.65155	−	8.85932i	−0.0714029	−	0.383022i
$536$		0			0
$537$	−25.8402	+	8.39600i	−1.11509	+	0.362314i
$538$		0			0
$539$	−6.11948	+	0.969231i	−0.263585	+	0.0417477i
$540$		0			0
$541$	15.0728	+	4.89744i	0.648029	+	0.210557i	0.614545	−	0.788882i	$-0.289340\pi$
$541$	15.0728	+	4.89744i	0.648029	+	0.210557i	0.0334841	+	0.999439i	$0.489340\pi$
$542$		0			0
$543$	−51.5557	−	16.7515i	−2.21247	−	0.718874i
$544$		0			0
$545$	16.5026	−	5.86329i	0.706895	−	0.251156i
$546$		0			0
$547$	−12.6634	−	12.6634i	−0.541447	−	0.541447i	0.382506	−	0.923953i	$-0.375061\pi$
$547$	−12.6634	−	12.6634i	−0.541447	−	0.541447i	−0.923953	+	0.382506i	$0.875061\pi$
$548$		0			0
$549$	0.0191715	−	0.0139289i	0.000818221	−	0.000594472i
$550$		0			0
$551$	38.9583	+	28.3049i	1.65968	+	1.20583i
$552$		0			0
$553$	−12.8621	+	9.34489i	−0.546954	+	0.397385i
$554$		0			0
$555$	0.946753	−	0.728042i	0.0401874	−	0.0309037i
$556$		0			0
$557$	7.15773	−	3.64705i	0.303283	−	0.154530i	−0.295726	−	0.955273i	$-0.595561\pi$
$557$	7.15773	−	3.64705i	0.303283	−	0.154530i	0.599009	+	0.800743i	$0.295561\pi$
$558$		0			0
$559$	42.2139	+	21.5090i	1.78546	+	0.909735i
$560$		0			0
$561$	1.22158	+	7.71273i	0.0515750	+	0.325632i
$562$		0			0
$563$	−10.2154	−	20.0488i	−0.430526	−	0.844955i	−0.999741	−	0.0227664i	$-0.992753\pi$
$563$	−10.2154	−	20.0488i	−0.430526	−	0.844955i	0.569215	−	0.822189i	$-0.307247\pi$
$564$		0			0
$565$	8.00656	+	7.58206i	0.336838	+	0.318980i
$566$		0			0
$567$	−7.44918	+	47.0323i	−0.312836	+	1.97517i
$568$		0			0
$569$	3.24221	−	1.05346i	0.135921	−	0.0441633i	−0.240267	−	0.970707i	$-0.577235\pi$
$569$	3.24221	−	1.05346i	0.135921	−	0.0441633i	0.376187	+	0.926544i	$0.377235\pi$
$570$		0			0
$571$	−22.5249	−	22.5249i	−0.942638	−	0.942638i	0.0558037	−	0.998442i	$-0.482228\pi$
$571$	−22.5249	−	22.5249i	−0.942638	−	0.942638i	−0.998442	+	0.0558037i	$0.982228\pi$
$572$		0			0
$573$		−	3.53824i		−	0.147812i
$574$		0			0
$575$	30.9735	−	1.68816i	1.29169	−	0.0704011i
$576$		0			0
$577$	15.6524	−	15.6524i	0.651619	−	0.651619i	−0.301764	−	0.953383i	$-0.597575\pi$
$577$	15.6524	−	15.6524i	0.651619	−	0.651619i	0.953383	+	0.301764i	$0.0975754\pi$
$578$		0			0
$579$	−15.2383	+	4.95123i	−0.633282	+	0.205766i
$580$		0			0
$581$	−12.6525	−	2.00396i	−0.524916	−	0.0831385i
$582$		0			0
$583$	−3.23319			−0.133905
$584$		0			0
$585$	−7.25969	+	24.6027i	−0.300151	+	1.01720i
$586$		0			0
$587$	3.35630	−	0.531585i	0.138529	−	0.0219409i	−0.0867847	−	0.996227i	$-0.527659\pi$
$587$	3.35630	−	0.531585i	0.138529	−	0.0219409i	0.225314	+	0.974286i	$0.427659\pi$
$588$		0			0
$589$	−15.9487	−	8.12629i	−0.657157	−	0.334838i
$590$		0			0
$591$	6.17116	+	12.1116i	0.253847	+	0.498204i
$592$		0			0
$593$	26.1384	+	4.13992i	1.07338	+	0.170006i	0.668013	−	0.744149i	$-0.267145\pi$
$593$	26.1384	+	4.13992i	1.07338	+	0.170006i	0.405364	+	0.914155i	$0.367145\pi$
$594$		0			0
$595$	−7.88762	+	60.3999i	−0.323361	+	2.47616i
$596$		0			0
$597$	−0.0811914	+	0.111750i	−0.00332294	+	0.00457364i
$598$		0			0
$599$	−27.6765	+	20.1081i	−1.13083	+	0.821596i	−0.985815	−	0.167833i	$-0.946323\pi$
$599$	−27.6765	+	20.1081i	−1.13083	+	0.821596i	−0.145015	+	0.989429i	$0.546323\pi$
$600$		0			0
$601$	17.8502	−	17.8502i	0.728125	−	0.728125i	−0.242121	−	0.970246i	$-0.577843\pi$
$601$	17.8502	−	17.8502i	0.728125	−	0.728125i	0.970246	+	0.242121i	$0.0778430\pi$
$602$		0			0
$603$	9.99475	+	5.09258i	0.407018	+	0.207386i
$604$		0			0
$605$	−20.9804	+	11.4198i	−0.852974	+	0.464281i
$606$		0			0
$607$	8.24295	−	25.3692i	0.334571	−	1.02970i	−0.632362	−	0.774673i	$-0.717914\pi$
$607$	8.24295	−	25.3692i	0.334571	−	1.02970i	0.966933	−	0.255031i	$-0.0820855\pi$
$608$		0			0
$609$	−52.1615	+	8.26158i	−2.11369	+	0.334776i
$610$		0			0
$611$	−8.25630	−	25.4103i	−0.334014	−	1.02799i
$612$		0			0
$613$	6.39929	+	4.64936i	0.258465	+	0.187786i	0.709470	−	0.704736i	$-0.248934\pi$
$613$	6.39929	+	4.64936i	0.258465	+	0.187786i	−0.451005	+	0.892521i	$0.648934\pi$
$614$		0			0
$615$	28.6602	−	11.5639i	1.15569	−	0.466301i
$616$		0			0
$617$	9.13950	+	6.64024i	0.367942	+	0.267326i	0.756357	−	0.654159i	$-0.226977\pi$
$617$	9.13950	+	6.64024i	0.367942	+	0.267326i	−0.388415	+	0.921485i	$0.626977\pi$
$618$		0			0
$619$	−0.0183810	−	0.0565710i	−0.000738796	−	0.00227378i	0.950686	−	0.310154i	$-0.100381\pi$
$619$	−0.0183810	−	0.0565710i	−0.000738796	−	0.00227378i	−0.951425	+	0.307880i	$0.900381\pi$
$620$		0			0
$621$	−17.7342	+	2.80882i	−0.711648	+	0.112714i
$622$		0			0
$623$	1.56254	−	4.80901i	0.0626020	−	0.192669i
$624$		0			0
$625$	−5.09556	+	24.4752i	−0.203822	+	0.979008i
$626$		0			0
$627$	−9.04726	−	4.60981i	−0.361313	−	0.184098i
$628$		0			0
$629$	−1.12353	+	1.12353i	−0.0447981	+	0.0447981i
$630$		0			0
$631$	8.92454	−	6.48406i	0.355280	−	0.258126i	−0.395801	−	0.918336i	$-0.629533\pi$
$631$	8.92454	−	6.48406i	0.355280	−	0.258126i	0.751081	+	0.660210i	$0.229533\pi$
$632$		0			0
$633$	18.9093	−	26.0265i	0.751579	−	1.03446i
$634$		0			0
$635$	35.0072	+	4.57158i	1.38922	+	0.181418i
$636$		0			0
$637$	75.0992	+	11.8945i	2.97554	+	0.471279i
$638$		0			0
$639$	6.71687	+	13.1826i	0.265715	+	0.521496i
$640$		0			0
$641$	−35.0821	−	17.8752i	−1.38566	−	0.706029i	−0.407369	−	0.913264i	$-0.633554\pi$
$641$	−35.0821	−	17.8752i	−1.38566	−	0.706029i	−0.978291	+	0.207234i	$0.933554\pi$
$642$		0			0
$643$	6.35391	−	1.00636i	0.250574	−	0.0396870i	−0.0298839	−	0.999553i	$-0.509514\pi$
$643$	6.35391	−	1.00636i	0.250574	−	0.0396870i	0.280458	+	0.959866i	$0.409514\pi$
$644$		0			0
$645$	31.7214	+	9.36026i	1.24903	+	0.368560i
$646$		0			0
$647$	6.00084			0.235918			0.117959	−	0.993018i	$-0.462365\pi$
$647$	6.00084			0.235918			0.117959	+	0.993018i	$0.462365\pi$
$648$		0			0
$649$	3.82874	+	0.606413i	0.150291	+	0.0238038i
$650$		0			0
$651$	18.6698	−	6.06619i	0.731728	−	0.237753i
$652$		0			0
$653$	2.83672	−	2.83672i	0.111009	−	0.111009i	−0.649420	−	0.760430i	$-0.724988\pi$
$653$	2.83672	−	2.83672i	0.111009	−	0.111009i	0.760430	+	0.649420i	$0.224988\pi$
$654$		0			0
$655$	−0.107076	−	0.101399i	−0.00418379	−	0.00396197i
$656$		0			0
$657$		−	3.28075i		−	0.127994i
$658$		0			0
$659$	26.7459	+	26.7459i	1.04187	+	1.04187i	0.999084	+	0.0427888i	$0.0136243\pi$
$659$	26.7459	+	26.7459i	1.04187	+	1.04187i	0.0427888	+	0.999084i	$0.486376\pi$
$660$		0			0
$661$	9.57587	−	3.11139i	0.372458	−	0.121019i	−0.116806	−	0.993155i	$-0.537265\pi$
$661$	9.57587	−	3.11139i	0.372458	−	0.121019i	0.489264	+	0.872136i	$0.337265\pi$
$662$		0			0
$663$	14.9914	−	94.6517i	0.582216	−	3.67597i
$664$		0			0
$665$	−57.5107	−	54.4616i	−2.23017	−	2.11193i
$666$		0			0
$667$	−16.2437	−	31.8801i	−0.628959	−	1.23440i
$668$		0			0
$669$	−6.55887	−	41.4111i	−0.253581	−	1.60105i
$670$		0			0
$671$	0.00716967	+	0.00365313i	0.000276782	+	0.000141028i
$672$		0			0
$673$	8.93358	−	4.55188i	0.344364	−	0.175462i	−0.273251	−	0.961943i	$-0.588099\pi$
$673$	8.93358	−	4.55188i	0.344364	−	0.175462i	0.617615	+	0.786481i	$0.288099\pi$
$674$		0			0
$675$	1.48255	−	14.3948i	0.0570633	−	0.554055i
$676$		0			0
$677$	27.6747	−	20.1068i	1.06362	−	0.772769i	0.0888693	−	0.996043i	$-0.471675\pi$
$677$	27.6747	−	20.1068i	1.06362	−	0.772769i	0.974756	+	0.223275i	$0.0716747\pi$
$678$		0			0
$679$	−39.8621	−	28.9615i	−1.52977	−	1.11144i
$680$		0			0
$681$	5.37547	−	3.90551i	0.205988	−	0.149659i
$682$		0			0
$683$	−35.0475	−	35.0475i	−1.34106	−	1.34106i	−0.895011	−	0.446044i	$-0.852832\pi$
$683$	−35.0475	−	35.0475i	−1.34106	−	1.34106i	−0.446044	−	0.895011i	$-0.647168\pi$
$684$		0			0
$685$	7.97837	+	22.4556i	0.304838	+	0.857986i
$686$		0			0
$687$	−37.8470	−	12.2972i	−1.44395	−	0.469169i
$688$		0			0
$689$	37.7362	+	12.2612i	1.43763	+	0.467116i
$690$		0			0
$691$	7.03385	−	1.11405i	0.267580	−	0.0423805i	−0.0212026	−	0.999775i	$-0.506749\pi$
$691$	7.03385	−	1.11405i	0.267580	−	0.0423805i	0.288783	+	0.957395i	$0.406749\pi$
$692$		0			0
$693$	3.77150	−	1.22544i	0.143268	−	0.0465504i
$694$		0			0
$695$	−18.1061	+	3.37534i	−0.686804	+	0.128034i
$696$		0			0
$697$	−35.8163	+	20.1924i	−1.35664	+	0.764843i
$698$		0			0
$699$	7.80020	−	10.7361i	0.295031	−	0.406075i
$700$		0			0
$701$	7.77351	+	23.9244i	0.293601	+	0.903612i	0.983688	+	0.179885i	$0.0575725\pi$
$701$	7.77351	+	23.9244i	0.293601	+	0.903612i	−0.690086	+	0.723727i	$0.742427\pi$
$702$		0			0
$703$	−0.323207	−	2.04065i	−0.0121900	−	0.0769645i
$704$		0			0
$705$	−8.91676	−	16.3818i	−0.335825	−	0.616974i
$706$		0			0
$707$	52.7299	+	17.1330i	1.98311	+	0.644352i
$708$		0			0
$709$	5.60096	−	10.9925i	0.210348	−	0.412832i	−0.761593	−	0.648056i	$-0.775582\pi$
$709$	5.60096	−	10.9925i	0.210348	−	0.412832i	0.971941	+	0.235224i	$0.0755823\pi$
$710$		0			0
$711$	4.39674	−	4.39674i	0.164891	−	0.164891i
$712$		0			0
$713$	7.81736	+	10.7597i	0.292763	+	0.402953i
$714$		0			0
$715$	−8.56273	+	1.59626i	−0.320228	+	0.0596969i
$716$		0			0
$717$	4.48642	−	3.25957i	0.167548	−	0.121731i
$718$		0			0
$719$	2.04558	−	12.9153i	0.0762874	−	0.481659i	−0.919734	−	0.392543i	$-0.871596\pi$
$719$	2.04558	−	12.9153i	0.0762874	−	0.481659i	0.996021	−	0.0891169i	$-0.0284045\pi$
$720$		0			0
$721$	17.1893	+	33.7359i	0.640163	+	1.25639i
$722$		0			0
$723$	−12.4557	+	24.4458i	−0.463234	+	0.909148i
$724$		0			0
$725$	28.1938	−	6.05438i	1.04709	−	0.224854i
$726$		0			0
$727$	16.2438	+	31.8802i	0.602448	+	1.18237i	0.967852	+	0.251522i	$0.0809310\pi$
$727$	16.2438	+	31.8802i	0.602448	+	1.18237i	−0.365403	+	0.930849i	$0.619069\pi$
$728$		0			0
$729$			0.117674i			0.00435828i
$730$		0			0
$731$	−43.4592	−	6.88327i	−1.60740	−	0.254587i
$732$		0			0
$733$	7.50676	+	23.1034i	0.277268	+	0.853344i	0.988610	+	0.150498i	$0.0480878\pi$
$733$	7.50676	+	23.1034i	0.277268	+	0.853344i	−0.711342	+	0.702846i	$0.751912\pi$
$734$		0			0
$735$	53.0593	−	1.44488i	1.95712	−	0.0532951i
$736$		0			0
$737$			3.80900i			0.140306i
$738$		0			0
$739$	−44.0374			−1.61994			−0.809971	−	0.586469i	$-0.800517\pi$
$739$	−44.0374			−1.61994			−0.809971	+	0.586469i	$0.800517\pi$
$740$		0			0
$741$	88.1134	+	88.1134i	3.23692	+	3.23692i
$742$		0			0
$743$	−10.9746	−	33.7764i	−0.402620	−	1.23914i	−0.922866	−	0.385121i	$-0.874160\pi$
$743$	−10.9746	−	33.7764i	−0.402620	−	1.23914i	0.520246	−	0.854016i	$-0.325840\pi$
$744$		0			0
$745$	12.3927	+	16.1156i	0.454033	+	0.590429i
$746$		0			0
$747$	5.01012			0.183311
$748$		0			0
$749$	15.2341	−	7.76217i	0.556642	−	0.283623i
$750$		0			0
$751$	−3.19177	−	20.1521i	−0.116470	−	0.735360i	−0.974935	−	0.222489i	$-0.928582\pi$
$751$	−3.19177	−	20.1521i	−0.116470	−	0.735360i	0.858466	−	0.512871i	$-0.171418\pi$
$752$		0			0
$753$	27.7096	−	54.3831i	1.00979	−	1.98183i
$754$		0			0
$755$	−0.325503	+	1.10311i	−0.0118463	+	0.0401463i
$756$		0			0
$757$	5.56149	+	0.880853i	0.202136	+	0.0320152i	0.256681	−	0.966496i	$-0.417371\pi$
$757$	5.56149	+	0.880853i	0.202136	+	0.0320152i	−0.0545454	+	0.998511i	$0.517371\pi$
$758$		0			0
$759$	4.43456	+	6.10365i	0.160964	+	0.221549i
$760$		0			0
$761$	4.19628	+	3.04878i	0.152115	+	0.110518i	0.661239	−	0.750175i	$-0.270031\pi$
$761$	4.19628	+	3.04878i	0.152115	+	0.110518i	−0.509124	+	0.860693i	$0.670031\pi$
$762$		0			0
$763$	19.5301	+	26.8808i	0.707036	+	0.973151i
$764$		0			0
$765$	−0.648497	−	23.8143i	−0.0234465	−	0.861008i
$766$		0			0
$767$	−42.3875	−	21.5975i	−1.53052	−	0.779841i
$768$		0			0
$769$	−7.16854	+	22.0625i	−0.258504	+	0.795594i	0.734615	+	0.678485i	$0.237363\pi$
$769$	−7.16854	+	22.0625i	−0.258504	+	0.795594i	−0.993119	+	0.117110i	$0.962637\pi$
$770$		0			0
$771$	49.8272	+	16.1898i	1.79448	+	0.583062i
$772$		0			0
$773$	0.735814	+	4.64575i	0.0264654	+	0.167096i	0.997381	−	0.0723258i	$-0.0230421\pi$
$773$	0.735814	+	4.64575i	0.0264654	+	0.167096i	−0.970916	+	0.239422i	$0.923042\pi$
$774$		0			0
$775$	−9.99882	+	3.86218i	−0.359168	+	0.138734i
$776$		0			0
$777$	1.83313	+	1.33185i	0.0657633	+	0.0477798i
$778$		0			0
$779$	6.13261	−	53.1110i	0.219724	−	1.90290i
$780$		0			0
$781$	−2.95297	+	4.06441i	−0.105665	+	0.145436i
$782$		0			0
$783$	−15.8747	+	5.15800i	−0.567315	+	0.184332i
$784$		0			0
$785$	−27.4193	+	39.9848i	−0.978637	+	1.42712i
$786$		0			0
$787$	−10.8266	+	33.3210i	−0.385928	+	1.18776i	0.549877	+	0.835246i	$0.314675\pi$
$787$	−10.8266	+	33.3210i	−0.385928	+	1.18776i	−0.935805	+	0.352518i	$0.885325\pi$
$788$		0			0
$789$	−10.3562	+	31.8730i	−0.368689	+	1.13471i
$790$		0			0
$791$	−9.49769	+	18.6403i	−0.337699	+	0.662771i
$792$		0			0
$793$	−0.0698271	−	0.0698271i	−0.00247963	−	0.00247963i
$794$		0			0
$795$	27.4654	+	3.58670i	0.974098	+	0.127207i
$796$		0			0
$797$	−19.3408	+	26.6204i	−0.685087	+	0.942941i	−0.999981	−	0.00618557i	$-0.998031\pi$
$797$	−19.3408	+	26.6204i	−0.685087	+	0.942941i	0.314894	+	0.949127i	$0.398031\pi$
$798$		0			0
$799$	14.5851	+	20.0747i	0.515984	+	0.710191i
$800$		0			0
$801$	−0.309366	+	1.95326i	−0.0109309	+	0.0690150i
$802$		0			0
$803$	0.992599	−	0.505754i	0.0350281	−	0.0178477i
$804$		0			0
$805$	19.7028	+	55.4547i	0.694431	+	1.95452i
$806$		0			0
$807$	35.5007	−	5.62276i	1.24968	−	0.197930i
$808$		0			0
$809$	−8.25584	+	4.20656i	−0.290260	+	0.147895i	−0.593058	−	0.805160i	$-0.702079\pi$
$809$	−8.25584	+	4.20656i	−0.290260	+	0.147895i	0.302798	+	0.953055i	$0.402079\pi$
$810$		0			0
$811$			12.3172i			0.432515i	0.976336	+	0.216258i	$0.0693851\pi$
$811$			12.3172i			0.432515i	−0.976336	+	0.216258i	$0.930615\pi$
$812$		0			0
$813$	−6.14281	+	38.7842i	−0.215438	+	1.36022i
$814$		0			0
$815$	0.648172	−	1.36258i	0.0227045	−	0.0477292i
$816$		0			0
$817$	40.4571	−	40.4571i	1.41542	−	1.41542i
$818$		0			0
$819$	−48.6663			−1.70054
$820$		0			0
$821$	−27.5922			−0.962975			−0.481487	−	0.876453i	$-0.659903\pi$
$821$	−27.5922			−0.962975			−0.481487	+	0.876453i	$0.659903\pi$
$822$		0			0
$823$	−3.17605	+	3.17605i	−0.110710	+	0.110710i	−0.760292	−	0.649582i	$-0.774944\pi$
$823$	−3.17605	+	3.17605i	−0.110710	+	0.110710i	0.649582	+	0.760292i	$0.274944\pi$
$824$		0			0
$825$	−5.67204	+	2.19090i	−0.197475	+	0.0762774i
$826$		0			0
$827$	4.57880	−	28.9094i	0.159221	−	1.00528i	−0.770614	−	0.637302i	$-0.780050\pi$
$827$	4.57880	−	28.9094i	0.159221	−	1.00528i	0.929835	−	0.367977i	$-0.119950\pi$
$828$		0			0
$829$		−	23.4237i		−	0.813538i	−0.913531	−	0.406769i	$-0.866655\pi$
$829$		−	23.4237i		−	0.813538i	0.913531	−	0.406769i	$-0.133345\pi$
$830$		0			0
$831$	5.48830	−	2.79643i	0.190387	−	0.0970069i
$832$		0			0
$833$	−69.7466	+	11.0468i	−2.41658	+	0.382748i
$834$		0			0
$835$	13.3340	−	4.73750i	0.461442	−	0.163948i
$836$		0			0
$837$	5.52819	−	2.81676i	0.191082	−	0.0973613i
$838$		0			0
$839$	6.26266	−	39.5409i	0.216211	−	1.36510i	−0.605793	−	0.795622i	$-0.707144\pi$
$839$	6.26266	−	39.5409i	0.216211	−	1.36510i	0.822004	−	0.569481i	$-0.192856\pi$
$840$		0			0
$841$	−2.50505	−	3.44791i	−0.0863811	−	0.118893i
$842$		0			0
$843$	−11.6633	+	16.0531i	−0.401704	+	0.552898i
$844$		0			0
$845$	77.1694	+	10.0775i	2.65471	+	0.346678i
$846$		0			0
$847$	−32.0453	−	32.0453i	−1.10109	−	1.10109i
$848$		0			0
$849$	25.0469	−	49.1573i	0.859608	−	1.68708i
$850$		0			0
$851$	−0.474380	+	1.45999i	−0.0162615	+	0.0500479i
$852$		0			0
$853$	8.40186	−	25.8583i	0.287674	−	0.885370i	−0.697910	−	0.716185i	$-0.745887\pi$
$853$	8.40186	−	25.8583i	0.287674	−	0.885370i	0.985584	−	0.169185i	$-0.0541134\pi$
$854$		0			0
$855$	25.5477	+	17.5192i	0.873714	+	0.599144i
$856$		0			0
$857$	30.5271	−	9.91885i	1.04278	−	0.338821i	0.262952	−	0.964809i	$-0.415304\pi$
$857$	30.5271	−	9.91885i	1.04278	−	0.338821i	0.779833	+	0.625988i	$0.215304\pi$
$858$		0			0
$859$	21.5284	−	29.6313i	0.734539	−	1.01101i	−0.264375	−	0.964420i	$-0.585166\pi$
$859$	21.5284	−	29.6313i	0.734539	−	1.01101i	0.998914	−	0.0465862i	$-0.0148342\pi$
$860$		0			0
$861$	36.4311	+	45.9426i	1.24157	+	1.56572i
$862$		0			0
$863$	−7.65194	−	5.55946i	−0.260475	−	0.189246i	0.449881	−	0.893088i	$-0.351466\pi$
$863$	−7.65194	−	5.55946i	−0.260475	−	0.189246i	−0.710357	+	0.703842i	$0.751466\pi$
$864$		0			0
$865$	32.7042	+	15.5572i	1.11198	+	0.528960i
$866$		0			0
$867$	8.18256	+	51.6626i	0.277894	+	1.75456i
$868$		0			0
$869$	2.00804	+	0.652451i	0.0681180	+	0.0221329i
$870$		0			0
$871$	14.4449	−	44.4567i	0.489446	−	1.50636i
$872$		0			0
$873$	17.1702	+	8.74863i	0.581122	+	0.296096i
$874$		0			0
$875$	−47.2724	+	3.86953i	−1.59810	+	0.130814i
$876$		0			0
$877$	−7.32773	−	10.0857i	−0.247440	−	0.340572i	0.667173	−	0.744903i	$-0.267504\pi$
$877$	−7.32773	−	10.0857i	−0.247440	−	0.340572i	−0.914613	+	0.404331i	$0.867504\pi$
$878$		0			0
$879$	33.3719	+	24.2461i	1.12561	+	0.817800i
$880$		0			0
$881$	20.8353	+	28.6774i	0.701961	+	0.966166i	0.999933	+	0.0115913i	$0.00368971\pi$
$881$	20.8353	+	28.6774i	0.701961	+	0.966166i	−0.297972	+	0.954575i	$0.596310\pi$
$882$		0			0
$883$	32.1629	+	5.09410i	1.08237	+	0.171430i	0.672045	−	0.740510i	$-0.265416\pi$
$883$	32.1629	+	5.09410i	1.08237	+	0.171430i	0.410323	+	0.911940i	$0.365416\pi$
$884$		0			0
$885$	−31.8519	−	9.39876i	−1.07069	−	0.315936i
$886$		0			0
$887$	5.61203	−	11.0142i	0.188434	−	0.369822i	−0.777391	−	0.629017i	$-0.783457\pi$
$887$	5.61203	−	11.0142i	0.188434	−	0.369822i	0.965825	+	0.259196i	$0.0834574\pi$
$888$		0			0
$889$	10.4780	+	66.1557i	0.351422	+	2.21879i
$890$		0			0
$891$	5.63465	−	2.87100i	0.188768	−	0.0961820i
$892$		0			0
$893$	−32.2655			−1.07973
$894$		0			0
$895$	17.1577	+	22.3120i	0.573518	+	0.745808i
$896$		0			0
$897$	−28.6111	−	88.0560i	−0.955298	−	2.94011i
$898$		0			0
$899$	8.74248	+	8.74248i	0.291578	+	0.291578i
$900$		0			0
$901$	−36.8502			−1.22766
$902$		0			0
$903$			62.7478i			2.08812i
$904$		0			0
$905$	1.52866	+	56.1358i	0.0508143	+	1.86602i
$906$		0			0
$907$	10.9576	+	33.7240i	0.363841	+	1.11979i	0.950704	+	0.310101i	$0.100363\pi$
$907$	10.9576	+	33.7240i	0.363841	+	1.11979i	−0.586863	+	0.809686i	$0.699637\pi$
$908$		0			0
$909$	−21.4171	−	3.39214i	−0.710360	−	0.112510i
$910$		0			0
$911$		−	22.8233i		−	0.756170i	−0.925771	−	0.378085i	$-0.876583\pi$
$911$		−	22.8233i		−	0.756170i	0.925771	−	0.378085i	$-0.123417\pi$
$912$		0			0
$913$	0.772350	+	1.51582i	0.0255611	+	0.0501664i
$914$		0			0
$915$	−0.0568527	−	0.0389864i	−0.00187949	−	0.00128885i
$916$		0			0
$917$	0.127017	−	0.249285i	0.00419448	−	0.00823212i
$918$		0			0
$919$	13.8908	+	27.2621i	0.458214	+	0.899295i	0.998334	+	0.0577070i	$0.0183789\pi$
$919$	13.8908	+	27.2621i	0.458214	+	0.899295i	−0.540120	+	0.841588i	$0.681621\pi$
$920$		0			0
$921$	−2.53788	+	16.0236i	−0.0836261	+	0.527994i
$922$		0			0
$923$	49.8790	−	36.2392i	1.64179	−	1.19283i
$924$		0			0
$925$	−1.03903	−	0.671672i	−0.0341631	−	0.0220844i
$926$		0			0
$927$	−8.70403	−	11.9801i	−0.285878	−	0.393477i
$928$		0			0
$929$	−24.5740	+	24.5740i	−0.806245	+	0.806245i	−0.984063	−	0.177818i	$-0.943096\pi$
$929$	−24.5740	+	24.5740i	−0.806245	+	0.806245i	0.177818	+	0.984063i	$0.443096\pi$
$930$		0			0
$931$	41.6868	−	81.8149i	1.36623	−	2.68137i
$932$		0			0
$933$	−9.97417	−	3.24080i	−0.326540	−	0.106099i
$934$		0			0
$935$	7.10510	−	3.86737i	0.232362	−	0.126477i
$936$		0			0
$937$	−2.75074	−	17.3675i	−0.0898627	−	0.567370i	−0.991003	−	0.133842i	$-0.957268\pi$
$937$	−2.75074	−	17.3675i	−0.0898627	−	0.567370i	0.901140	−	0.433528i	$-0.142732\pi$
$938$		0			0
$939$	−3.02289	−	9.30349i	−0.0986482	−	0.303608i
$940$		0			0
$941$	31.7577	−	43.7108i	1.03527	−	1.42493i	0.134358	−	0.990933i	$-0.457103\pi$
$941$	31.7577	−	43.7108i	1.03527	−	1.42493i	0.900914	−	0.433997i	$-0.142897\pi$
$942$		0			0
$943$	−21.9754	+	33.0924i	−0.715618	+	1.07764i
$944$		0			0
$945$	26.9895	−	5.03138i	0.877969	−	0.163671i
$946$		0			0
$947$	−10.2685	+	3.33643i	−0.333681	+	0.108419i	−0.471065	−	0.882098i	$-0.656130\pi$
$947$	−10.2685	+	3.33643i	−0.333681	+	0.108419i	0.137385	+	0.990518i	$0.456130\pi$
$948$		0			0
$949$	−13.5031	+	2.13868i	−0.438329	+	0.0694245i
$950$		0			0
$951$	−46.2633	−	15.0319i	−1.50019	−	0.487442i
$952$		0			0
$953$	−8.93935	−	2.90457i	−0.289574	−	0.0940883i	0.160628	−	0.987015i	$-0.448648\pi$
$953$	−8.93935	−	2.90457i	−0.289574	−	0.0940883i	−0.450202	+	0.892927i	$0.648648\pi$
$954$		0			0
$955$	−3.45385	+	1.22713i	−0.111764	+	0.0397091i
$956$		0			0
$957$	4.95936	+	4.95936i	0.160313	+	0.160313i
$958$		0			0
$959$	−36.5776	+	26.5752i	−1.18115	+	0.858157i
$960$		0			0
$961$	21.3615	+	15.5200i	0.689081	+	0.500647i
$962$		0			0
$963$	−5.40984	+	3.93048i	−0.174330	+	0.126658i
$964$		0			0
$965$	10.1181	+	13.1577i	0.325713	+	0.423560i
$966$		0			0
$967$	10.6180	−	5.41013i	0.341451	−	0.173978i	−0.274853	−	0.961486i	$-0.588629\pi$
$967$	10.6180	−	5.41013i	0.341451	−	0.173978i	0.616304	+	0.787508i	$0.288629\pi$
$968$		0			0
$969$	−103.116	−	52.5402i	−3.31256	−	1.68783i
$970$		0			0
$971$	8.38818	+	52.9609i	0.269190	+	1.69960i	0.637955	+	0.770074i	$0.279781\pi$
$971$	8.38818	+	52.9609i	0.269190	+	1.69960i	−0.368765	+	0.929522i	$0.620219\pi$
$972$		0			0
$973$	−15.8638	−	31.1345i	−0.508570	−	0.998126i
$974$		0			0
$975$	74.5098	−	4.06103i	2.38622	−	0.130057i
$976$		0			0
$977$	−1.01530	+	6.41032i	−0.0324822	+	0.205084i	−0.998592	−	0.0530469i	$-0.983107\pi$
$977$	−1.01530	+	6.41032i	−0.0324822	+	0.205084i	0.966110	+	0.258131i	$0.0831067\pi$
$978$		0			0
$979$	−0.638654	+	0.207511i	−0.0204115	+	0.00663209i
$980$		0			0
$981$	−9.18883	−	9.18883i	−0.293377	−	0.293377i
$982$		0			0
$983$		−	51.7443i		−	1.65039i	−0.564850	−	0.825193i	$-0.691066\pi$
$983$		−	51.7443i		−	1.65039i	0.564850	−	0.825193i	$-0.308934\pi$
$984$		0			0
$985$	9.68242	−	10.2245i	0.308507	−	0.325780i
$986$		0			0
$987$	25.0214	−	25.0214i	0.796441	−	0.796441i
$988$		0			0
$989$	−40.4308	+	13.1368i	−1.28563	+	0.417725i
$990$		0			0
$991$	−11.3931	−	1.80448i	−0.361913	−	0.0573213i	−0.0271697	−	0.999631i	$-0.508649\pi$
$991$	−11.3931	−	1.80448i	−0.361913	−	0.0573213i	−0.334743	+	0.942310i	$0.608649\pi$
$992$		0			0
$993$	−6.73483			−0.213723
$994$		0			0
$995$	0.137244	+	0.0404975i	0.00435092	+	0.00128386i
$996$		0			0
$997$	1.42388	−	0.225520i	0.0450947	−	0.00714230i	−0.133846	−	0.991002i	$-0.542733\pi$
$997$	1.42388	−	0.225520i	0.0450947	−	0.00714230i	0.178941	+	0.983860i	$0.442733\pi$
$998$		0			0
$999$	0.638096	+	0.325126i	0.0201885	+	0.0102865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bq.a.49.4	✓	176
5.4	even	2	inner	820.2.bq.a.49.19	yes	176
41.36	even	20	inner	820.2.bq.a.569.19	yes	176
205.159	even	20	inner	820.2.bq.a.569.4	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bq.a.49.4	✓	176	1.1	even	1	trivial
820.2.bq.a.49.19	yes	176	5.4	even	2	inner
820.2.bq.a.569.4	yes	176	205.159	even	20	inner
820.2.bq.a.569.19	yes	176	41.36	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52630 + 1.52630i) q^{3} +(2.01925 + 0.960543i) q^{5} +(-0.663644 + 4.19008i) q^{7} -1.65918i q^{9} +(0.501988 - 0.255776i) q^{11} +(-6.82894 + 1.08160i) q^{13} +(-4.54805 + 1.61590i) q^{15} +(5.72139 - 2.91520i) q^{17} +(-1.30618 + 8.24687i) q^{19} +(-5.38240 - 7.40824i) q^{21} +(3.64656 - 5.01906i) q^{23} +(3.15471 + 3.87915i) q^{25} +(-2.04650 - 2.04650i) q^{27} +(2.61830 - 5.13871i) q^{29} +(-0.662459 + 2.03884i) q^{31} +(-0.375794 + 1.15657i) q^{33} +(-5.36481 + 7.82335i) q^{35} +(-0.235334 + 0.0764648i) q^{37} +(8.77216 - 12.0738i) q^{39} +(-6.39744 + 0.269626i) q^{41} +(-5.54369 - 4.02773i) q^{43} +(1.59371 - 3.35029i) q^{45} +(0.604508 + 3.81672i) q^{47} +(-10.4590 - 3.39832i) q^{49} +(-4.28310 + 13.1820i) q^{51} +(-5.11328 - 2.60535i) q^{53} +(1.25932 - 0.0342931i) q^{55} +(-10.5936 - 14.5808i) q^{57} +(5.56649 + 4.04429i) q^{59} +(0.00839508 + 0.0115548i) q^{61} +(6.95209 + 1.10110i) q^{63} +(-14.8282 - 4.37547i) q^{65} +(-3.06934 + 6.02392i) q^{67} +(2.09485 + 13.2263i) q^{69} +(-7.94526 + 4.04831i) q^{71} +1.97734 q^{73} +(-10.7358 - 1.10570i) q^{75} +(0.738580 + 2.27311i) q^{77} +(2.64995 + 2.64995i) q^{79} +11.2247 q^{81} +3.01964i q^{83} +(14.3531 - 0.390855i) q^{85} +(3.84689 + 11.8395i) q^{87} +(-1.17725 - 0.186457i) q^{89} -29.3316i q^{91} +(-2.10077 - 4.12299i) q^{93} +(-10.5590 + 15.3978i) q^{95} +(-5.27287 + 10.3486i) q^{97} +(-0.424377 - 0.832887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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