LMFDB - Embedded newform 820.2.u.b.201.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			201.5
Character	$\chi$	$=$	820.201
Dual form			820.2.u.b.461.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.0908517 q^{3} +(-0.309017 + 0.951057i) q^{5} +(-1.97649 - 1.43601i) q^{7} -2.99175 q^{9} +(0.753623 + 2.31941i) q^{11} +(4.00936 - 2.91297i) q^{13} +(-0.0280747 + 0.0864051i) q^{15} +(-2.34902 - 7.22953i) q^{17} +(0.0424476 + 0.0308400i) q^{19} +(-0.179568 - 0.130464i) q^{21} +(7.24674 - 5.26506i) q^{23} +(-0.809017 - 0.587785i) q^{25} -0.544361 q^{27} +(0.740816 - 2.28000i) q^{29} +(-2.43787 - 7.50298i) q^{31} +(0.0684679 + 0.210723i) q^{33} +(1.97649 - 1.43601i) q^{35} +(-2.18718 + 6.73145i) q^{37} +(0.364257 - 0.264648i) q^{39} +(-4.35499 - 4.69405i) q^{41} +(-0.252980 + 0.183801i) q^{43} +(0.924500 - 2.84532i) q^{45} +(6.04201 - 4.38978i) q^{47} +(-0.318710 - 0.980890i) q^{49} +(-0.213412 - 0.656815i) q^{51} +(-3.80300 + 11.7044i) q^{53} -2.43877 q^{55} +(0.00385644 + 0.00280187i) q^{57} +(6.95361 - 5.05210i) q^{59} +(-5.37950 - 3.90844i) q^{61} +(5.91316 + 4.29616i) q^{63} +(1.53144 + 4.71328i) q^{65} +(-2.08821 + 6.42685i) q^{67} +(0.658379 - 0.478340i) q^{69} +(0.546614 + 1.68230i) q^{71} -5.06288 q^{73} +(-0.0735006 - 0.0534013i) q^{75} +(1.84116 - 5.66650i) q^{77} -4.21972 q^{79} +8.92578 q^{81} +7.09058 q^{83} +7.60158 q^{85} +(0.0673045 - 0.207142i) q^{87} +(-4.25422 - 3.09087i) q^{89} -12.1075 q^{91} +(-0.221484 - 0.681659i) q^{93} +(-0.0424476 + 0.0308400i) q^{95} +(2.55392 - 7.86017i) q^{97} +(-2.25465 - 6.93909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	0.0908517			0.0524533			0.0262266	−	0.999656i	$-0.491651\pi$
$3$	0.0908517			0.0524533			0.0262266	+	0.999656i	$0.491651\pi$
$4$		0			0
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	−1.97649	−	1.43601i	−0.747044	−	0.542759i	0.147865	−	0.989007i	$-0.452760\pi$
$7$	−1.97649	−	1.43601i	−0.747044	−	0.542759i	−0.894909	+	0.446248i	$0.852760\pi$
$8$		0			0
$9$	−2.99175			−0.997249
$10$		0			0
$11$	0.753623	+	2.31941i	0.227226	+	0.699329i	0.998058	+	0.0622909i	$0.0198406\pi$
$11$	0.753623	+	2.31941i	0.227226	+	0.699329i	−0.770832	+	0.637038i	$0.780159\pi$
$12$		0			0
$13$	4.00936	−	2.91297i	1.11200	−	0.807913i	0.129019	−	0.991642i	$-0.458817\pi$
$13$	4.00936	−	2.91297i	1.11200	−	0.807913i	0.982977	+	0.183730i	$0.0588171\pi$
$14$		0			0
$15$	−0.0280747	+	0.0864051i	−0.00724886	+	0.0223097i
$16$		0			0
$17$	−2.34902	−	7.22953i	−0.569720	−	1.75342i	−0.653492	−	0.756934i	$-0.726696\pi$
$17$	−2.34902	−	7.22953i	−0.569720	−	1.75342i	0.0837712	−	0.996485i	$-0.473304\pi$
$18$		0			0
$19$	0.0424476	+	0.0308400i	0.00973814	+	0.00707518i	0.592644	−	0.805465i	$-0.298084\pi$
$19$	0.0424476	+	0.0308400i	0.00973814	+	0.00707518i	−0.582906	+	0.812540i	$0.698084\pi$
$20$		0			0
$21$	−0.179568	−	0.130464i	−0.0391849	−	0.0284695i
$22$		0			0
$23$	7.24674	−	5.26506i	1.51105	−	1.09784i	0.545341	−	0.838214i	$-0.316400\pi$
$23$	7.24674	−	5.26506i	1.51105	−	1.09784i	0.965709	−	0.259628i	$-0.0835998\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	−0.544361			−0.104762
$28$		0			0
$29$	0.740816	−	2.28000i	0.137566	−	0.423385i	−0.858414	−	0.512957i	$-0.828550\pi$
$29$	0.740816	−	2.28000i	0.137566	−	0.423385i	0.995980	+	0.0895721i	$0.0285499\pi$
$30$		0			0
$31$	−2.43787	−	7.50298i	−0.437854	−	1.34758i	−0.890134	−	0.455700i	$-0.849389\pi$
$31$	−2.43787	−	7.50298i	−0.437854	−	1.34758i	0.452280	−	0.891876i	$-0.350611\pi$
$32$		0			0
$33$	0.0684679	+	0.210723i	0.0119187	+	0.0366821i
$34$		0			0
$35$	1.97649	−	1.43601i	0.334088	−	0.242729i
$36$		0			0
$37$	−2.18718	+	6.73145i	−0.359570	+	1.10664i	0.593742	+	0.804656i	$0.297650\pi$
$37$	−2.18718	+	6.73145i	−0.359570	+	1.10664i	−0.953312	+	0.301988i	$0.902350\pi$
$38$		0			0
$39$	0.364257	−	0.264648i	0.0583278	−	0.0423777i
$40$		0			0
$41$	−4.35499	−	4.69405i	−0.680135	−	0.733087i
$41$	−4.35499	−	4.69405i	−0.680135	−	0.733087i
$42$		0			0
$43$	−0.252980	+	0.183801i	−0.0385791	+	0.0280294i	−0.606908	−	0.794772i	$-0.707590\pi$
$43$	−0.252980	+	0.183801i	−0.0385791	+	0.0280294i	0.568329	+	0.822802i	$0.307590\pi$
$44$		0			0
$45$	0.924500	−	2.84532i	0.137816	−	0.424155i
$46$		0			0
$47$	6.04201	−	4.38978i	0.881318	−	0.640315i	−0.0522816	−	0.998632i	$-0.516649\pi$
$47$	6.04201	−	4.38978i	0.881318	−	0.640315i	0.933600	+	0.358317i	$0.116649\pi$
$48$		0			0
$49$	−0.318710	−	0.980890i	−0.0455301	−	0.140127i
$50$		0			0
$51$	−0.213412	−	0.656815i	−0.0298837	−	0.0919726i
$52$		0			0
$53$	−3.80300	+	11.7044i	−0.522382	+	1.60773i	0.247055	+	0.969002i	$0.420537\pi$
$53$	−3.80300	+	11.7044i	−0.522382	+	1.60773i	−0.769436	+	0.638724i	$0.779463\pi$
$54$		0			0
$55$	−2.43877			−0.328844
$56$		0			0
$57$	0.00385644	+	0.00280187i	0.000510798	+	0.000371116i
$58$		0			0
$59$	6.95361	−	5.05210i	0.905283	−	0.657727i	−0.0345341	−	0.999404i	$-0.510995\pi$
$59$	6.95361	−	5.05210i	0.905283	−	0.657727i	0.939818	+	0.341677i	$0.110995\pi$
$60$		0			0
$61$	−5.37950	−	3.90844i	−0.688775	−	0.500424i	0.187482	−	0.982268i	$-0.439967\pi$
$61$	−5.37950	−	3.90844i	−0.688775	−	0.500424i	−0.876257	+	0.481844i	$0.839967\pi$
$62$		0			0
$63$	5.91316	+	4.29616i	0.744988	+	0.541266i
$64$		0			0
$65$	1.53144	+	4.71328i	0.189952	+	0.584611i
$66$		0			0
$67$	−2.08821	+	6.42685i	−0.255115	+	0.785164i	0.738692	+	0.674044i	$0.235444\pi$
$67$	−2.08821	+	6.42685i	−0.255115	+	0.785164i	−0.993807	+	0.111121i	$0.964556\pi$
$68$		0			0
$69$	0.658379	−	0.478340i	0.0792595	−	0.0575854i
$70$		0			0
$71$	0.546614	+	1.68230i	0.0648711	+	0.199653i	0.978238	−	0.207484i	$-0.0665274\pi$
$71$	0.546614	+	1.68230i	0.0648711	+	0.199653i	−0.913367	+	0.407136i	$0.866527\pi$
$72$		0			0
$73$	−5.06288			−0.592566			−0.296283	−	0.955100i	$-0.595747\pi$
$73$	−5.06288			−0.592566			−0.296283	+	0.955100i	$0.595747\pi$
$74$		0			0
$75$	−0.0735006	−	0.0534013i	−0.00848712	−	0.00616625i
$76$		0			0
$77$	1.84116	−	5.66650i	0.209820	−	0.645758i
$78$		0			0
$79$	−4.21972			−0.474756			−0.237378	−	0.971417i	$-0.576288\pi$
$79$	−4.21972			−0.474756			−0.237378	+	0.971417i	$0.576288\pi$
$80$		0			0
$81$	8.92578			0.991754
$82$		0			0
$83$	7.09058			0.778292			0.389146	−	0.921176i	$-0.372770\pi$
$83$	7.09058			0.778292			0.389146	+	0.921176i	$0.372770\pi$
$84$		0			0
$85$	7.60158			0.824507
$86$		0			0
$87$	0.0673045	−	0.207142i	0.00721580	−	0.0222079i
$88$		0			0
$89$	−4.25422	−	3.09087i	−0.450946	−	0.327631i	0.339023	−	0.940778i	$-0.389903\pi$
$89$	−4.25422	−	3.09087i	−0.450946	−	0.327631i	−0.789969	+	0.613147i	$0.789903\pi$
$90$		0			0
$91$	−12.1075			−1.26921
$92$		0			0
$93$	−0.221484	−	0.681659i	−0.0229669	−	0.0706848i
$94$		0			0
$95$	−0.0424476	+	0.0308400i	−0.00435503	+	0.00316411i
$96$		0			0
$97$	2.55392	−	7.86017i	0.259312	−	0.798079i	−0.733638	−	0.679541i	$-0.762179\pi$
$97$	2.55392	−	7.86017i	0.259312	−	0.798079i	0.992949	−	0.118538i	$-0.0378209\pi$
$98$		0			0
$99$	−2.25465	−	6.93909i	−0.226601	−	0.697405i
$100$		0			0
$101$	−13.0728	−	9.49791i	−1.30079	−	0.945078i	−0.300825	−	0.953679i	$-0.597262\pi$
$101$	−13.0728	−	9.49791i	−1.30079	−	0.945078i	−0.999963	+	0.00860153i	$0.997262\pi$
$102$		0			0
$103$	7.10825	+	5.16445i	0.700397	+	0.508868i	0.880062	−	0.474860i	$-0.157501\pi$
$103$	7.10825	+	5.16445i	0.700397	+	0.508868i	−0.179664	+	0.983728i	$0.557501\pi$
$104$		0			0
$105$	0.179568	−	0.130464i	0.0175240	−	0.0127319i
$106$		0			0
$107$	−1.93535	−	1.40611i	−0.187097	−	0.135934i	0.490294	−	0.871557i	$-0.336889\pi$
$107$	−1.93535	−	1.40611i	−0.187097	−	0.135934i	−0.677391	+	0.735623i	$0.736889\pi$
$108$		0			0
$109$	−5.51693			−0.528426			−0.264213	−	0.964464i	$-0.585112\pi$
$109$	−5.51693			−0.528426			−0.264213	+	0.964464i	$0.585112\pi$
$110$		0			0
$111$	−0.198709	+	0.611564i	−0.0188606	+	0.0580471i
$112$		0			0
$113$	−4.32616	−	13.3145i	−0.406970	−	1.25253i	−0.919239	−	0.393701i	$-0.871195\pi$
$113$	−4.32616	−	13.3145i	−0.406970	−	1.25253i	0.512268	−	0.858826i	$-0.328805\pi$
$114$		0			0
$115$	2.76801	+	8.51905i	0.258118	+	0.794406i
$116$		0			0
$117$	−11.9950	+	8.71487i	−1.10894	+	0.805690i
$118$		0			0
$119$	−5.73883	+	17.6623i	−0.526078	+	1.61910i
$120$		0			0
$121$	4.08746	−	2.96972i	0.371587	−	0.269974i
$122$		0			0
$123$	−0.395658	−	0.426463i	−0.0356753	−	0.0384528i
$124$		0			0
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	−1.75620	+	5.40502i	−0.155837	+	0.479618i	−0.998245	−	0.0592233i	$-0.981138\pi$
$127$	−1.75620	+	5.40502i	−0.155837	+	0.479618i	0.842408	+	0.538841i	$0.181138\pi$
$128$		0			0
$129$	−0.0229837	+	0.0166986i	−0.00202360	+	0.00147023i
$130$		0			0
$131$	4.09004	+	12.5878i	0.357348	+	1.09980i	0.954635	+	0.297777i	$0.0962452\pi$
$131$	4.09004	+	12.5878i	0.357348	+	1.09980i	−0.597287	+	0.802027i	$0.703755\pi$
$132$		0			0
$133$	−0.0396109	−	0.121910i	−0.00343470	−	0.0105709i
$134$		0			0
$135$	0.168217	−	0.517718i	0.0144778	−	0.0445580i
$136$		0			0
$137$	7.26460			0.620656			0.310328	−	0.950629i	$-0.399561\pi$
$137$	7.26460			0.620656			0.310328	+	0.950629i	$0.399561\pi$
$138$		0			0
$139$	14.9123	+	10.8344i	1.26484	+	0.918963i	0.998985	−	0.0450494i	$-0.0143445\pi$
$139$	14.9123	+	10.8344i	1.26484	+	0.918963i	0.265859	+	0.964012i	$0.414345\pi$
$140$		0			0
$141$	0.548927	−	0.398819i	0.0462280	−	0.0335866i
$142$		0			0
$143$	9.77792	+	7.10408i	0.817671	+	0.594073i
$144$		0			0
$145$	1.93948	+	1.40912i	0.161065	+	0.117021i
$146$		0			0
$147$	−0.0289554	−	0.0891156i	−0.00238820	−	0.00735013i
$148$		0			0
$149$	−4.22383	+	12.9996i	−0.346030	+	1.06497i	0.615000	+	0.788527i	$0.289156\pi$
$149$	−4.22383	+	12.9996i	−0.346030	+	1.06497i	−0.961030	+	0.276444i	$0.910844\pi$
$150$		0			0
$151$	−15.1338	+	10.9954i	−1.23157	+	0.894791i	−0.997007	−	0.0773092i	$-0.975367\pi$
$151$	−15.1338	+	10.9954i	−1.23157	+	0.894791i	−0.234567	+	0.972100i	$0.575367\pi$
$152$		0			0
$153$	7.02766	+	21.6289i	0.568153	+	1.74859i
$154$		0			0
$155$	7.88910			0.633668
$156$		0			0
$157$	1.41906	+	1.03101i	0.113254	+	0.0822835i	0.642970	−	0.765891i	$-0.277702\pi$
$157$	1.41906	+	1.03101i	0.113254	+	0.0822835i	−0.529717	+	0.848175i	$0.677702\pi$
$158$		0			0
$159$	−0.345509	+	1.06337i	−0.0274006	+	0.0843305i
$160$		0			0
$161$	−21.8838			−1.72468
$162$		0			0
$163$	17.1031			1.33962			0.669808	−	0.742534i	$-0.266376\pi$
$163$	17.1031			1.33962			0.669808	+	0.742534i	$0.266376\pi$
$164$		0			0
$165$	−0.221567			−0.0172490
$166$		0			0
$167$	−16.3624			−1.26616			−0.633079	−	0.774087i	$-0.718209\pi$
$167$	−16.3624			−1.26616			−0.633079	+	0.774087i	$0.718209\pi$
$168$		0			0
$169$	3.57235	−	10.9946i	0.274796	−	0.845735i
$170$		0			0
$171$	−0.126992	−	0.0922654i	−0.00971135	−	0.00705571i
$172$		0			0
$173$	5.19141			0.394696			0.197348	−	0.980334i	$-0.436767\pi$
$173$	5.19141			0.394696			0.197348	+	0.980334i	$0.436767\pi$
$174$		0			0
$175$	0.754953	+	2.32351i	0.0570691	+	0.175641i
$176$		0			0
$177$	0.631748	−	0.458992i	0.0474851	−	0.0344999i
$178$		0			0
$179$	6.94665	−	21.3796i	0.519217	−	1.59798i	−0.256259	−	0.966608i	$-0.582490\pi$
$179$	6.94665	−	21.3796i	0.519217	−	1.59798i	0.775476	−	0.631377i	$-0.217510\pi$
$180$		0			0
$181$	1.08979	+	3.35403i	0.0810036	+	0.249303i	0.983354	−	0.181700i	$-0.0581598\pi$
$181$	1.08979	+	3.35403i	0.0810036	+	0.249303i	−0.902351	+	0.431003i	$0.858160\pi$
$182$		0			0
$183$	−0.488737	−	0.355088i	−0.0361285	−	0.0262489i
$184$		0			0
$185$	−5.72611	−	4.16026i	−0.420992	−	0.305869i
$186$		0			0
$187$	14.9980	−	10.8967i	1.09676	−	0.796844i
$188$		0			0
$189$	1.07592	+	0.781705i	0.0782620	+	0.0568606i
$190$		0			0
$191$	26.4584			1.91446			0.957230	−	0.289328i	$-0.0934318\pi$
$191$	26.4584			1.91446			0.957230	+	0.289328i	$0.0934318\pi$
$192$		0			0
$193$	−5.82774	+	17.9360i	−0.419490	+	1.29106i	0.488682	+	0.872462i	$0.337478\pi$
$193$	−5.82774	+	17.9360i	−0.419490	+	1.29106i	−0.908172	+	0.418596i	$0.862522\pi$
$194$		0			0
$195$	0.139134	+	0.428210i	0.00996358	+	0.0306648i
$196$		0			0
$197$	0.218495	+	0.672459i	0.0155671	+	0.0479107i	0.958538	−	0.284964i	$-0.0919815\pi$
$197$	0.218495	+	0.672459i	0.0155671	+	0.0479107i	−0.942971	+	0.332874i	$0.891982\pi$
$198$		0			0
$199$	−3.39156	+	2.46411i	−0.240421	+	0.174676i	−0.701471	−	0.712698i	$-0.747473\pi$
$199$	−3.39156	+	2.46411i	−0.240421	+	0.174676i	0.461050	+	0.887374i	$0.347473\pi$
$200$		0			0
$201$	−0.189717	+	0.583890i	−0.0133816	+	0.0411844i
$202$		0			0
$203$	−4.73831	+	3.44258i	−0.332564	+	0.241622i
$204$		0			0
$205$	5.81007	−	2.69130i	0.405793	−	0.187968i
$206$		0			0
$207$	−21.6804	+	15.7517i	−1.50689	+	1.09482i
$208$		0			0
$209$	−0.0395411	+	0.121695i	−0.00273512	+	0.00841783i
$210$		0			0
$211$	−7.33009	+	5.32563i	−0.504625	+	0.366631i	−0.810781	−	0.585350i	$-0.800957\pi$
$211$	−7.33009	+	5.32563i	−0.504625	+	0.366631i	0.306156	+	0.951981i	$0.400957\pi$
$212$		0			0
$213$	0.0496608	+	0.152840i	0.00340270	+	0.0104724i
$214$		0			0
$215$	−0.0966298	−	0.297396i	−0.00659010	−	0.0202822i
$216$		0			0
$217$	−5.95590	+	18.3304i	−0.404313	+	1.24435i
$218$		0			0
$219$	−0.459972			−0.0310820
$220$		0			0
$221$	−30.4775	−	22.1432i	−2.05014	−	1.48951i
$222$		0			0
$223$	−0.566487	+	0.411577i	−0.0379348	+	0.0275612i	−0.606591	−	0.795014i	$-0.707463\pi$
$223$	−0.566487	+	0.411577i	−0.0379348	+	0.0275612i	0.568656	+	0.822575i	$0.307463\pi$
$224$		0			0
$225$	2.42037	+	1.75850i	0.161358	+	0.117234i
$226$		0			0
$227$	−14.3588	−	10.4323i	−0.953026	−	0.692414i	−0.00150538	−	0.999999i	$-0.500479\pi$
$227$	−14.3588	−	10.4323i	−0.953026	−	0.692414i	−0.951521	+	0.307585i	$0.900479\pi$
$228$		0			0
$229$	7.79167	+	23.9803i	0.514888	+	1.58466i	0.783486	+	0.621410i	$0.213440\pi$
$229$	7.79167	+	23.9803i	0.514888	+	1.58466i	−0.268598	+	0.963252i	$0.586560\pi$
$230$		0			0
$231$	0.167272	−	0.514812i	0.0110057	−	0.0338721i
$232$		0			0
$233$	16.4152	−	11.9263i	1.07539	−	0.781318i	0.0985188	−	0.995135i	$-0.468590\pi$
$233$	16.4152	−	11.9263i	1.07539	−	0.781318i	0.976874	+	0.213817i	$0.0685895\pi$
$234$		0			0
$235$	2.30784	+	7.10281i	0.150547	+	0.463336i
$236$		0			0
$237$	−0.383369			−0.0249025
$238$		0			0
$239$	−11.4115	−	8.29093i	−0.738148	−	0.536296i	0.153983	−	0.988074i	$-0.450790\pi$
$239$	−11.4115	−	8.29093i	−0.738148	−	0.536296i	−0.892130	+	0.451778i	$0.850790\pi$
$240$		0			0
$241$	−6.16830	+	18.9841i	−0.397335	+	1.22287i	0.529793	+	0.848127i	$0.322269\pi$
$241$	−6.16830	+	18.9841i	−0.397335	+	1.22287i	−0.927128	+	0.374744i	$0.877731\pi$
$242$		0			0
$243$	2.44400			0.156783
$244$		0			0
$245$	1.03137			0.0658917
$246$		0			0
$247$	0.260024			0.0165449
$248$		0			0
$249$	0.644191			0.0408240
$250$		0			0
$251$	−0.996253	+	3.06615i	−0.0628829	+	0.193534i	−0.977562	−	0.210646i	$-0.932443\pi$
$251$	−0.996253	+	3.06615i	−0.0628829	+	0.193534i	0.914679	+	0.404180i	$0.132443\pi$
$252$		0			0
$253$	17.6732	+	12.8403i	1.11110	+	0.807263i
$254$		0			0
$255$	0.690617			0.0432481
$256$		0			0
$257$	−6.35849	−	19.5694i	−0.396632	−	1.22071i	−0.927684	−	0.373367i	$-0.878203\pi$
$257$	−6.35849	−	19.5694i	−0.396632	−	1.22071i	0.531052	−	0.847339i	$-0.321797\pi$
$258$		0			0
$259$	13.9893	−	10.1638i	0.869255	−	0.631551i
$260$		0			0
$261$	−2.21633	+	6.82118i	−0.137188	+	0.422220i
$262$		0			0
$263$	5.02859	+	15.4764i	0.310076	+	0.954316i	0.977734	+	0.209848i	$0.0672968\pi$
$263$	5.02859	+	15.4764i	0.310076	+	0.954316i	−0.667658	+	0.744468i	$0.732703\pi$
$264$		0			0
$265$	−9.95637	−	7.23373i	−0.611615	−	0.444364i
$266$		0			0
$267$	−0.386503	−	0.280811i	−0.0236536	−	0.0171853i
$268$		0			0
$269$	−5.40228	+	3.92499i	−0.329383	+	0.239311i	−0.740169	−	0.672421i	$-0.765254\pi$
$269$	−5.40228	+	3.92499i	−0.329383	+	0.239311i	0.410786	+	0.911732i	$0.365254\pi$
$270$		0			0
$271$	−8.85226	−	6.43154i	−0.537736	−	0.390688i	0.285507	−	0.958377i	$-0.407838\pi$
$271$	−8.85226	−	6.43154i	−0.537736	−	0.390688i	−0.823244	+	0.567688i	$0.807838\pi$
$272$		0			0
$273$	−1.09999			−0.0665743
$274$		0			0
$275$	0.753623	−	2.31941i	0.0454452	−	0.139866i
$276$		0			0
$277$	−4.40584	−	13.5598i	−0.264721	−	0.814729i	−0.991757	−	0.128129i	$-0.959103\pi$
$277$	−4.40584	−	13.5598i	−0.264721	−	0.814729i	0.727036	−	0.686599i	$-0.240897\pi$
$278$		0			0
$279$	7.29348	+	22.4470i	0.436649	+	1.34387i
$280$		0			0
$281$	8.61872	−	6.26187i	0.514150	−	0.373552i	−0.300246	−	0.953862i	$-0.597069\pi$
$281$	8.61872	−	6.26187i	0.514150	−	0.373552i	0.814395	+	0.580310i	$0.197069\pi$
$282$		0			0
$283$	6.03974	−	18.5884i	0.359025	−	1.10497i	−0.594613	−	0.804012i	$-0.702695\pi$
$283$	6.03974	−	18.5884i	0.359025	−	1.10497i	0.953639	−	0.300954i	$-0.0973052\pi$
$284$		0			0
$285$	−0.00385644	+	0.00280187i	−0.000228436	+	0.000165968i
$286$		0			0
$287$	1.86691	+	15.5315i	0.110200	+	0.916797i
$288$		0			0
$289$	−32.9950	+	23.9722i	−1.94088	+	1.41013i
$290$		0			0
$291$	0.232028	−	0.714110i	0.0136017	−	0.0418619i
$292$		0			0
$293$	2.72113	−	1.97702i	0.158970	−	0.115499i	−0.505456	−	0.862852i	$-0.668676\pi$
$293$	2.72113	−	1.97702i	0.158970	−	0.115499i	0.664427	+	0.747354i	$0.268676\pi$
$294$		0			0
$295$	2.65604	+	8.17446i	0.154641	+	0.475936i
$296$		0			0
$297$	−0.410242	−	1.26260i	−0.0238047	−	0.0732633i
$298$		0			0
$299$	13.7178	−	42.2191i	0.793321	−	2.44159i
$300$		0			0
$301$	0.763952			0.0440335
$302$		0			0
$303$	−1.18768	−	0.862902i	−0.0682306	−	0.0495724i
$304$		0			0
$305$	5.37950	−	3.90844i	0.308029	−	0.223796i
$306$		0			0
$307$	14.7090	+	10.6867i	0.839485	+	0.609921i	0.922227	−	0.386650i	$-0.126368\pi$
$307$	14.7090	+	10.6867i	0.839485	+	0.609921i	−0.0827419	+	0.996571i	$0.526368\pi$
$308$		0			0
$309$	0.645797	+	0.469199i	0.0367381	+	0.0266918i
$310$		0			0
$311$	−5.96492	−	18.3581i	−0.338239	−	1.04099i	−0.965104	−	0.261866i	$-0.915662\pi$
$311$	−5.96492	−	18.3581i	−0.338239	−	1.04099i	0.626865	−	0.779128i	$-0.284338\pi$
$312$		0			0
$313$	−1.51096	+	4.65027i	−0.0854047	+	0.262849i	−0.984634	−	0.174628i	$-0.944128\pi$
$313$	−1.51096	+	4.65027i	−0.0854047	+	0.262849i	0.899230	+	0.437477i	$0.144128\pi$
$314$		0			0
$315$	−5.91316	+	4.29616i	−0.333169	+	0.242061i
$316$		0			0
$317$	−6.52217	−	20.0732i	−0.366321	−	1.12742i	−0.949149	−	0.314826i	$-0.898054\pi$
$317$	−6.52217	−	20.0732i	−0.366321	−	1.12742i	0.582828	−	0.812596i	$-0.301946\pi$
$318$		0			0
$319$	5.84655			0.327344
$320$		0			0
$321$	−0.175830	−	0.127748i	−0.00981387	−	0.00713019i
$322$		0			0
$323$	0.123248	−	0.379320i	0.00685773	−	0.0211059i
$324$		0			0
$325$	−4.95584			−0.274901
$326$		0			0
$327$	−0.501223			−0.0277177
$328$		0			0
$329$	−18.2457			−1.00592
$330$		0			0
$331$	14.4580			0.794683			0.397341	−	0.917671i	$-0.369933\pi$
$331$	14.4580			0.794683			0.397341	+	0.917671i	$0.369933\pi$
$332$		0			0
$333$	6.54349	−	20.1388i	0.358581	−	1.10360i
$334$		0			0
$335$	−5.46700	−	3.97201i	−0.298694	−	0.217014i
$336$		0			0
$337$	17.6855			0.963389			0.481694	−	0.876339i	$-0.340022\pi$
$337$	17.6855			0.963389			0.481694	+	0.876339i	$0.340022\pi$
$338$		0			0
$339$	−0.393039	−	1.20965i	−0.0213469	−	0.0656991i
$340$		0			0
$341$	15.5653	−	11.3088i	0.842907	−	0.612408i
$342$		0			0
$343$	−6.06330	+	18.6609i	−0.327388	+	1.00760i
$344$		0			0
$345$	0.251478	+	0.773971i	0.0135391	+	0.0416692i
$346$		0			0
$347$	22.0668	+	16.0324i	1.18461	+	0.860667i	0.992684	−	0.120743i	$-0.0385278\pi$
$347$	22.0668	+	16.0324i	1.18461	+	0.860667i	0.191922	+	0.981410i	$0.438528\pi$
$348$		0			0
$349$	−22.7639	−	16.5389i	−1.21852	−	0.885309i	−0.222547	−	0.974922i	$-0.571437\pi$
$349$	−22.7639	−	16.5389i	−1.21852	−	0.885309i	−0.995977	+	0.0896127i	$0.971437\pi$
$350$		0			0
$351$	−2.18254	+	1.58571i	−0.116495	+	0.0846387i
$352$		0			0
$353$	21.0360	+	15.2836i	1.11963	+	0.813462i	0.984154	−	0.177318i	$-0.0567423\pi$
$353$	21.0360	+	15.2836i	1.11963	+	0.813462i	0.135480	+	0.990780i	$0.456742\pi$
$354$		0			0
$355$	−1.76888			−0.0938823
$356$		0			0
$357$	−0.521383	+	1.60465i	−0.0275945	+	0.0849272i
$358$		0			0
$359$	−1.32026	−	4.06333i	−0.0696805	−	0.214455i	0.910152	−	0.414274i	$-0.135964\pi$
$359$	−1.32026	−	4.06333i	−0.0696805	−	0.214455i	−0.979833	+	0.199819i	$0.935964\pi$
$360$		0			0
$361$	−5.87047	−	18.0675i	−0.308972	−	0.950919i
$362$		0			0
$363$	0.371353	−	0.269804i	0.0194910	−	0.0141610i
$364$		0			0
$365$	1.56452	−	4.81509i	0.0818906	−	0.252033i
$366$		0			0
$367$	−1.51147	+	1.09815i	−0.0788982	+	0.0573229i	−0.626535	−	0.779393i	$-0.715528\pi$
$367$	−1.51147	+	1.09815i	−0.0788982	+	0.0573229i	0.547637	+	0.836716i	$0.315528\pi$
$368$		0			0
$369$	13.0290	+	14.0434i	0.678263	+	0.731070i
$370$		0			0
$371$	24.3242	−	17.6726i	1.26285	−	0.917514i
$372$		0			0
$373$	7.78644	−	23.9642i	0.403167	−	1.24082i	−0.519250	−	0.854623i	$-0.673789\pi$
$373$	7.78644	−	23.9642i	0.403167	−	1.24082i	0.922416	−	0.386197i	$-0.126211\pi$
$374$		0			0
$375$	0.0735006	−	0.0534013i	0.00379555	−	0.00275763i
$376$		0			0
$377$	−3.67137	−	11.2993i	−0.189085	−	0.581944i
$378$		0			0
$379$	5.85405	+	18.0169i	0.300702	+	0.925467i	0.981246	+	0.192759i	$0.0617436\pi$
$379$	5.85405	+	18.0169i	0.300702	+	0.925467i	−0.680544	+	0.732707i	$0.738256\pi$
$380$		0			0
$381$	−0.159553	+	0.491055i	−0.00817417	+	0.0251575i
$382$		0			0
$383$	29.9723			1.53151			0.765757	−	0.643130i	$-0.222364\pi$
$383$	29.9723			1.53151			0.765757	+	0.643130i	$0.222364\pi$
$384$		0			0
$385$	4.82022	+	3.50209i	0.245661	+	0.178483i
$386$		0			0
$387$	0.756853	−	0.549886i	0.0384730	−	0.0279523i
$388$		0			0
$389$	5.09971	+	3.70516i	0.258566	+	0.187859i	0.709514	−	0.704691i	$-0.248914\pi$
$389$	5.09971	+	3.70516i	0.258566	+	0.187859i	−0.450949	+	0.892550i	$0.648914\pi$
$390$		0			0
$391$	−55.0867	−	40.0228i	−2.78585	−	2.02404i
$392$		0			0
$393$	0.371587	+	1.14363i	0.0187441	+	0.0576883i
$394$		0			0
$395$	1.30397	−	4.01320i	0.0656097	−	0.201926i
$396$		0			0
$397$	19.9482	−	14.4932i	1.00117	−	0.727392i	0.0388306	−	0.999246i	$-0.487637\pi$
$397$	19.9482	−	14.4932i	1.00117	−	0.727392i	0.962339	+	0.271854i	$0.0876367\pi$
$398$		0			0
$399$	−0.00359872	−	0.0110757i	−0.000180161	−	0.000554480i
$400$		0			0
$401$	6.80044			0.339598			0.169799	−	0.985479i	$-0.445688\pi$
$401$	6.80044			0.339598			0.169799	+	0.985479i	$0.445688\pi$
$402$		0			0
$403$	−31.6303	−	22.9807i	−1.57562	−	1.14475i
$404$		0			0
$405$	−2.75822	+	8.48892i	−0.137057	+	0.421818i
$406$		0			0
$407$	−17.2613			−0.855611
$408$		0			0
$409$	−32.8589			−1.62477			−0.812384	−	0.583123i	$-0.801830\pi$
$409$	−32.8589			−1.62477			−0.812384	+	0.583123i	$0.801830\pi$
$410$		0			0
$411$	0.660001			0.0325555
$412$		0			0
$413$	−20.9986			−1.03327
$414$		0			0
$415$	−2.19111	+	6.74354i	−0.107557	+	0.331027i
$416$		0			0
$417$	1.35481	+	0.984325i	0.0663452	+	0.0482026i
$418$		0			0
$419$	−12.3371			−0.602705			−0.301352	−	0.953513i	$-0.597438\pi$
$419$	−12.3371			−0.602705			−0.301352	+	0.953513i	$0.597438\pi$
$420$		0			0
$421$	2.23903	+	6.89102i	0.109124	+	0.335848i	0.990676	−	0.136238i	$-0.0435012\pi$
$421$	2.23903	+	6.89102i	0.109124	+	0.335848i	−0.881553	+	0.472086i	$0.843501\pi$
$422$		0			0
$423$	−18.0762	+	13.1331i	−0.878894	+	0.638554i
$424$		0			0
$425$	−2.34902	+	7.22953i	−0.113944	+	0.350684i
$426$		0			0
$427$	5.02001	+	15.4500i	0.242935	+	0.747677i
$428$		0			0
$429$	0.888341	+	0.645418i	0.0428895	+	0.0311611i
$430$		0			0
$431$	2.60803	+	1.89484i	0.125624	+	0.0912713i	0.648823	−	0.760939i	$-0.275262\pi$
$431$	2.60803	+	1.89484i	0.125624	+	0.0912713i	−0.523199	+	0.852211i	$0.675262\pi$
$432$		0			0
$433$	14.6931	−	10.6752i	0.706108	−	0.513017i	−0.175808	−	0.984424i	$-0.556254\pi$
$433$	14.6931	−	10.6752i	0.706108	−	0.513017i	0.881916	+	0.471407i	$0.156254\pi$
$434$		0			0
$435$	0.176205	+	0.128021i	0.00844840	+	0.00613812i
$436$		0			0
$437$	0.469981			0.0224822
$438$		0			0
$439$	10.0872	−	31.0451i	0.481434	−	1.48170i	−0.355645	−	0.934621i	$-0.615739\pi$
$439$	10.0872	−	31.0451i	0.481434	−	1.48170i	0.837079	−	0.547082i	$-0.184261\pi$
$440$		0			0
$441$	0.953501	+	2.93457i	0.0454048	+	0.139742i
$442$		0			0
$443$	−10.8398	−	33.3616i	−0.515016	−	1.58506i	−0.783253	−	0.621703i	$-0.786441\pi$
$443$	−10.8398	−	33.3616i	−0.515016	−	1.58506i	0.268237	−	0.963353i	$-0.413559\pi$
$444$		0			0
$445$	4.25422	−	3.09087i	0.201669	−	0.146521i
$446$		0			0
$447$	−0.383743	+	1.18104i	−0.0181504	+	0.0558612i
$448$		0			0
$449$	15.4759	−	11.2439i	0.730351	−	0.530631i	−0.159324	−	0.987226i	$-0.550931\pi$
$449$	15.4759	−	11.2439i	0.730351	−	0.530631i	0.889674	+	0.456596i	$0.150931\pi$
$450$		0			0
$451$	7.60542	−	13.6385i	0.358125	−	0.642214i
$452$		0			0
$453$	−1.37494	+	0.998949i	−0.0646001	+	0.0469347i
$454$		0			0
$455$	3.74143	−	11.5149i	0.175401	−	0.539828i
$456$		0			0
$457$	−0.744554	+	0.540950i	−0.0348288	+	0.0253046i	−0.605063	−	0.796177i	$-0.706852\pi$
$457$	−0.744554	+	0.540950i	−0.0348288	+	0.0253046i	0.570235	+	0.821482i	$0.306852\pi$
$458$		0			0
$459$	1.27871	+	3.93547i	0.0596852	+	0.183692i
$460$		0			0
$461$	12.3396	+	37.9775i	0.574715	+	1.76879i	0.637149	+	0.770740i	$0.280113\pi$
$461$	12.3396	+	37.9775i	0.574715	+	1.76879i	−0.0624349	+	0.998049i	$0.519887\pi$
$462$		0			0
$463$	−4.70502	+	14.4806i	−0.218661	+	0.672969i	0.780212	+	0.625515i	$0.215111\pi$
$463$	−4.70502	+	14.4806i	−0.218661	+	0.672969i	−0.998873	+	0.0474546i	$0.984889\pi$
$464$		0			0
$465$	0.716739			0.0332380
$466$		0			0
$467$	−14.9364	−	10.8519i	−0.691173	−	0.502167i	0.185872	−	0.982574i	$-0.440489\pi$
$467$	−14.9364	−	10.8519i	−0.691173	−	0.502167i	−0.877046	+	0.480407i	$0.840489\pi$
$468$		0			0
$469$	13.3563	−	9.70393i	0.616737	−	0.448086i
$470$		0			0
$471$	0.128924	+	0.0936690i	0.00594052	+	0.00431604i
$472$		0			0
$473$	−0.616962	−	0.448249i	−0.0283679	−	0.0206105i
$474$		0			0
$475$	−0.0162135	−	0.0499001i	−0.000743928	−	0.00228957i
$476$		0			0
$477$	11.3776	−	35.0166i	0.520944	−	1.60330i
$478$		0			0
$479$	11.2342	−	8.16213i	0.513304	−	0.372937i	−0.300771	−	0.953696i	$-0.597244\pi$
$479$	11.2342	−	8.16213i	0.513304	−	0.372937i	0.814076	+	0.580759i	$0.197244\pi$
$480$		0			0
$481$	10.8393	+	33.3600i	0.494230	+	1.52108i
$482$		0			0
$483$	−1.98818			−0.0904653
$484$		0			0
$485$	6.68626	+	4.85785i	0.303607	+	0.220584i
$486$		0			0
$487$	9.46081	−	29.1174i	0.428710	−	1.31943i	−0.470687	−	0.882300i	$-0.655994\pi$
$487$	9.46081	−	29.1174i	0.428710	−	1.31943i	0.899397	−	0.437133i	$-0.144006\pi$
$488$		0			0
$489$	1.55384			0.0702673
$490$		0			0
$491$	4.33328			0.195558			0.0977791	−	0.995208i	$-0.468826\pi$
$491$	4.33328			0.195558			0.0977791	+	0.995208i	$0.468826\pi$
$492$		0			0
$493$	−18.2235			−0.820746
$494$		0			0
$495$	7.29619			0.327939
$496$		0			0
$497$	1.33542	−	4.11000i	0.0599018	−	0.184359i
$498$		0			0
$499$	−16.8161	−	12.2176i	−0.752790	−	0.546934i	0.143900	−	0.989592i	$-0.454036\pi$
$499$	−16.8161	−	12.2176i	−0.752790	−	0.546934i	−0.896690	+	0.442658i	$0.854036\pi$
$500$		0			0
$501$	−1.48655			−0.0664141
$502$		0			0
$503$	−3.39018	−	10.4339i	−0.151161	−	0.465224i	0.846591	−	0.532244i	$-0.178651\pi$
$503$	−3.39018	−	10.4339i	−0.151161	−	0.465224i	−0.997752	+	0.0670195i	$0.978651\pi$
$504$		0			0
$505$	13.0728	−	9.49791i	0.581730	−	0.422652i
$506$		0			0
$507$	0.324554	−	0.998874i	0.0144139	−	0.0443616i
$508$		0			0
$509$	−5.41347	−	16.6610i	−0.239948	−	0.738484i	−0.996426	−	0.0844653i	$-0.973082\pi$
$509$	−5.41347	−	16.6610i	−0.239948	−	0.738484i	0.756478	−	0.654019i	$-0.226918\pi$
$510$		0			0
$511$	10.0067	+	7.27033i	0.442673	+	0.321620i
$512$		0			0
$513$	−0.0231068	−	0.0167881i	−0.00102019	−	0.000741211i
$514$		0			0
$515$	−7.10825	+	5.16445i	−0.313227	+	0.227573i
$516$		0			0
$517$	14.7351	+	10.7057i	0.648049	+	0.470835i
$518$		0			0
$519$	0.471649			0.0207031
$520$		0			0
$521$	0.976544	−	3.00549i	0.0427832	−	0.131673i	−0.927383	−	0.374112i	$-0.877947\pi$
$521$	0.976544	−	3.00549i	0.0427832	−	0.131673i	0.970167	+	0.242439i	$0.0779475\pi$
$522$		0			0
$523$	3.44468	+	10.6016i	0.150625	+	0.463578i	0.997691	−	0.0679102i	$-0.0216332\pi$
$523$	3.44468	+	10.6016i	0.150625	+	0.463578i	−0.847066	+	0.531488i	$0.821633\pi$
$524$		0			0
$525$	0.0685888	+	0.211095i	0.00299346	+	0.00921292i
$526$		0			0
$527$	−48.5165	+	35.2493i	−2.11341	+	1.53548i
$528$		0			0
$529$	17.6869	−	54.4348i	0.768998	−	2.36673i
$530$		0			0
$531$	−20.8034	+	15.1146i	−0.902793	+	0.655917i
$532$		0			0
$533$	−31.1343	−	6.13419i	−1.34858	−	0.265701i
$534$		0			0
$535$	1.93535	−	1.40611i	0.0836725	−	0.0607916i
$536$		0			0
$537$	0.631115	−	1.94237i	0.0272346	−	0.0838195i
$538$		0			0
$539$	2.03490	−	1.47844i	0.0876494	−	0.0636810i
$540$		0			0
$541$	12.5530	+	38.6343i	0.539697	+	1.66102i	0.733275	+	0.679933i	$0.237991\pi$
$541$	12.5530	+	38.6343i	0.539697	+	1.66102i	−0.193577	+	0.981085i	$0.562009\pi$
$542$		0			0
$543$	0.0990095	+	0.304720i	0.00424890	+	0.0130768i
$544$		0			0
$545$	1.70483	−	5.24691i	0.0730267	−	0.224753i
$546$		0			0
$547$	1.87759			0.0802800			0.0401400	−	0.999194i	$-0.487220\pi$
$547$	1.87759			0.0802800			0.0401400	+	0.999194i	$0.487220\pi$
$548$		0			0
$549$	16.0941	+	11.6931i	0.686880	+	0.499047i
$550$		0			0
$551$	0.101761	−	0.0739337i	0.00433516	−	0.00314968i
$552$		0			0
$553$	8.34025	+	6.05955i	0.354663	+	0.257678i
$554$		0			0
$555$	−0.520227	−	0.377967i	−0.0220824	−	0.0160438i
$556$		0			0
$557$	−2.55647	−	7.86800i	−0.108321	−	0.333378i	0.882175	−	0.470923i	$-0.156079\pi$
$557$	−2.55647	−	7.86800i	−0.108321	−	0.333378i	−0.990496	+	0.137545i	$0.956079\pi$
$558$		0			0
$559$	−0.478882	+	1.47385i	−0.0202546	+	0.0623371i
$560$		0			0
$561$	1.36259	−	0.989982i	0.0575287	−	0.0417971i
$562$		0			0
$563$	0.778728	+	2.39668i	0.0328195	+	0.101008i	0.966124	−	0.258077i	$-0.0830888\pi$
$563$	0.778728	+	2.39668i	0.0328195	+	0.101008i	−0.933305	+	0.359085i	$0.883089\pi$
$564$		0			0
$565$	13.9997			0.588973
$566$		0			0
$567$	−17.6417	−	12.8175i	−0.740883	−	0.538283i
$568$		0			0
$569$	−12.1461	+	37.3820i	−0.509193	+	1.56713i	0.284413	+	0.958702i	$0.408201\pi$
$569$	−12.1461	+	37.3820i	−0.509193	+	1.56713i	−0.793606	+	0.608432i	$0.791799\pi$
$570$		0			0
$571$	−17.3551			−0.726288			−0.363144	−	0.931733i	$-0.618297\pi$
$571$	−17.3551			−0.726288			−0.363144	+	0.931733i	$0.618297\pi$
$572$		0			0
$573$	2.40379			0.100420
$574$		0			0
$575$	−8.95746			−0.373552
$576$		0			0
$577$	20.6882			0.861262			0.430631	−	0.902528i	$-0.358291\pi$
$577$	20.6882			0.861262			0.430631	+	0.902528i	$0.358291\pi$
$578$		0			0
$579$	−0.529461	+	1.62951i	−0.0220036	+	0.0677202i
$580$		0			0
$581$	−14.0145	−	10.1821i	−0.581418	−	0.422425i
$582$		0			0
$583$	−30.0134			−1.24303
$584$		0			0
$585$	−4.58168	−	14.1010i	−0.189429	−	0.583003i
$586$		0			0
$587$	−23.7983	+	17.2905i	−0.982260	+	0.713654i	−0.958213	−	0.286057i	$-0.907655\pi$
$587$	−23.7983	+	17.2905i	−0.982260	+	0.713654i	−0.0240474	+	0.999711i	$0.507655\pi$
$588$		0			0
$589$	0.127910	−	0.393667i	0.00527045	−	0.0162208i
$590$		0			0
$591$	0.0198507	+	0.0610941i	0.000816547	+	0.00251307i
$592$		0			0
$593$	−3.55177	−	2.58051i	−0.145854	−	0.105969i	0.512465	−	0.858708i	$-0.328732\pi$
$593$	−3.55177	−	2.58051i	−0.145854	−	0.105969i	−0.658319	+	0.752739i	$0.728732\pi$
$594$		0			0
$595$	−15.0245	−	10.9159i	−0.615943	−	0.447509i
$596$		0			0
$597$	−0.308129	+	0.223869i	−0.0126109	+	0.00916235i
$598$		0			0
$599$	29.9661	+	21.7716i	1.22438	+	0.889565i	0.996456	−	0.0841133i	$-0.0268058\pi$
$599$	29.9661	+	21.7716i	1.22438	+	0.889565i	0.227925	+	0.973679i	$0.426806\pi$
$600$		0			0
$601$	2.19056			0.0893547			0.0446773	−	0.999001i	$-0.485774\pi$
$601$	2.19056			0.0893547			0.0446773	+	0.999001i	$0.485774\pi$
$602$		0			0
$603$	6.24739	−	19.2275i	0.254413	−	0.783004i
$604$		0			0
$605$	1.56127	+	4.80510i	0.0634747	+	0.195355i
$606$		0			0
$607$	13.9397	+	42.9020i	0.565795	+	1.74134i	0.665577	+	0.746329i	$0.268185\pi$
$607$	13.9397	+	42.9020i	0.565795	+	1.74134i	−0.0997821	+	0.995009i	$0.531815\pi$
$608$		0			0
$609$	−0.430484	+	0.312765i	−0.0174441	+	0.0126739i
$610$		0			0
$611$	11.4373	−	35.2004i	0.462704	−	1.42406i
$612$		0			0
$613$	−29.4377	+	21.3877i	−1.18898	+	0.863842i	−0.993156	−	0.116797i	$-0.962737\pi$
$613$	−29.4377	+	21.3877i	−1.18898	+	0.863842i	−0.195821	+	0.980640i	$0.562737\pi$
$614$		0			0
$615$	0.527855	−	0.244509i	0.0212852	−	0.00985955i
$616$		0			0
$617$	20.0362	−	14.5571i	0.806627	−	0.586049i	−0.106224	−	0.994342i	$-0.533876\pi$
$617$	20.0362	−	14.5571i	0.806627	−	0.586049i	0.912851	+	0.408294i	$0.133876\pi$
$618$		0			0
$619$	−2.11778	+	6.51785i	−0.0851207	+	0.261974i	−0.984553	−	0.175085i	$-0.943980\pi$
$619$	−2.11778	+	6.51785i	−0.0851207	+	0.261974i	0.899433	+	0.437059i	$0.143980\pi$
$620$		0			0
$621$	−3.94484	+	2.86609i	−0.158301	+	0.115012i
$622$		0			0
$623$	3.96992	+	12.2182i	0.159051	+	0.489510i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	−0.00359238	+	0.0110562i	−0.000143466	+	0.000441543i
$628$		0			0
$629$	53.8029			2.14526
$630$		0			0
$631$	34.8603	+	25.3275i	1.38777	+	1.00827i	0.996106	+	0.0881630i	$0.0280996\pi$
$631$	34.8603	+	25.3275i	1.38777	+	1.00827i	0.391662	+	0.920109i	$0.371900\pi$
$632$		0			0
$633$	−0.665952	+	0.483842i	−0.0264692	+	0.0192310i
$634$		0			0
$635$	−4.59778	−	3.34048i	−0.182457	−	0.132563i
$636$		0			0
$637$	−4.13513	−	3.00435i	−0.163840	−	0.119037i
$638$		0			0
$639$	−1.63533	−	5.03303i	−0.0646926	−	0.199103i
$640$		0			0
$641$	−0.460958	+	1.41868i	−0.0182068	+	0.0560346i	−0.959747	−	0.280866i	$-0.909378\pi$
$641$	−0.460958	+	1.41868i	−0.0182068	+	0.0560346i	0.941540	+	0.336900i	$0.109378\pi$
$642$		0			0
$643$	33.7031	−	24.4868i	1.32912	−	0.965664i	0.329353	−	0.944207i	$-0.393169\pi$
$643$	33.7031	−	24.4868i	1.32912	−	0.965664i	0.999770	−	0.0214570i	$-0.00683051\pi$
$644$		0			0
$645$	−0.00877899	−	0.0270190i	−0.000345672	−	0.00106387i
$646$		0			0
$647$	17.3329			0.681428			0.340714	−	0.940167i	$-0.389331\pi$
$647$	17.3329			0.681428			0.340714	+	0.940167i	$0.389331\pi$
$648$		0			0
$649$	16.9583	+	12.3209i	0.665671	+	0.483639i
$650$		0			0
$651$	−0.541104	+	1.66535i	−0.0212075	+	0.0652701i
$652$		0			0
$653$	9.82237			0.384379			0.192190	−	0.981358i	$-0.438441\pi$
$653$	9.82237			0.384379			0.192190	+	0.981358i	$0.438441\pi$
$654$		0			0
$655$	−13.2356			−0.517159
$656$		0			0
$657$	15.1469			0.590935
$658$		0			0
$659$	−27.6114			−1.07559			−0.537794	−	0.843076i	$-0.680742\pi$
$659$	−27.6114			−1.07559			−0.537794	+	0.843076i	$0.680742\pi$
$660$		0			0
$661$	−3.48879	+	10.7374i	−0.135698	+	0.417636i	−0.995698	−	0.0926581i	$-0.970464\pi$
$661$	−3.48879	+	10.7374i	−0.135698	+	0.417636i	0.860000	+	0.510295i	$0.170464\pi$
$662$		0			0
$663$	−2.76893	−	2.01175i	−0.107536	−	0.0781297i
$664$		0			0
$665$	0.128184			0.00497075
$666$		0			0
$667$	−6.63584	−	20.4230i	−0.256941	−	0.790782i
$668$		0			0
$669$	−0.0514664	+	0.0373925i	−0.00198980	+	0.00144568i
$670$		0			0
$671$	5.01116	−	15.4228i	0.193454	−	0.595389i
$672$		0			0
$673$	3.16813	+	9.75051i	0.122123	+	0.375855i	0.993366	−	0.114997i	$-0.0366858\pi$
$673$	3.16813	+	9.75051i	0.122123	+	0.375855i	−0.871243	+	0.490851i	$0.836686\pi$
$674$		0			0
$675$	0.440397	+	0.319967i	0.0169509	+	0.0123155i
$676$		0			0
$677$	14.6696	+	10.6581i	0.563798	+	0.409623i	0.832847	−	0.553503i	$-0.186709\pi$
$677$	14.6696	+	10.6581i	0.563798	+	0.409623i	−0.269049	+	0.963126i	$0.586709\pi$
$678$		0			0
$679$	−16.3351	+	11.8681i	−0.626882	+	0.455456i
$680$		0			0
$681$	−1.30452	−	0.947790i	−0.0499893	−	0.0363194i
$682$		0			0
$683$	−9.72263			−0.372026			−0.186013	−	0.982547i	$-0.559557\pi$
$683$	−9.72263			−0.372026			−0.186013	+	0.982547i	$0.559557\pi$
$684$		0			0
$685$	−2.24488	+	6.90904i	−0.0857726	+	0.263981i
$686$		0			0
$687$	0.707887	+	2.17865i	0.0270076	+	0.0831207i
$688$		0			0
$689$	18.8470	+	58.0052i	0.718015	+	2.20982i
$690$		0			0
$691$	41.1148	−	29.8717i	1.56408	−	1.13637i	0.631522	−	0.775358i	$-0.282430\pi$
$691$	41.1148	−	29.8717i	1.56408	−	1.13637i	0.932560	−	0.361015i	$-0.117570\pi$
$692$		0			0
$693$	−5.50828	+	16.9527i	−0.209242	+	0.643981i
$694$		0			0
$695$	−14.9123	+	10.8344i	−0.565655	+	0.410973i
$696$		0			0
$697$	−23.7058	+	42.5109i	−0.897923	+	1.61022i
$698$		0			0
$699$	1.49135	−	1.08353i	0.0564079	−	0.0409827i
$700$		0			0
$701$	0.476152	−	1.46545i	0.0179840	−	0.0553491i	−0.941662	−	0.336561i	$-0.890736\pi$
$701$	0.476152	−	1.46545i	0.0179840	−	0.0553491i	0.959646	+	0.281212i	$0.0907363\pi$
$702$		0			0
$703$	−0.300438	+	0.218281i	−0.0113312	+	0.00823263i
$704$		0			0
$705$	0.209672	+	0.645303i	0.00789669	+	0.0243035i
$706$		0			0
$707$	12.1991	+	37.5451i	0.458796	+	1.41203i
$708$		0			0
$709$	−5.50237	+	16.9346i	−0.206646	+	0.635991i	0.792996	+	0.609227i	$0.208520\pi$
$709$	−5.50237	+	16.9346i	−0.206646	+	0.635991i	−0.999642	+	0.0267638i	$0.991480\pi$
$710$		0			0
$711$	12.6243			0.473450
$712$		0			0
$713$	−57.1703	−	41.5366i	−2.14104	−	1.55556i
$714$		0			0
$715$	−9.77792	+	7.10408i	−0.365674	+	0.265677i
$716$		0			0
$717$	−1.03675	−	0.753245i	−0.0387183	−	0.0281305i
$718$		0			0
$719$	20.5101	+	14.9014i	0.764897	+	0.555730i	0.900408	−	0.435045i	$-0.143268\pi$
$719$	20.5101	+	14.9014i	0.764897	+	0.555730i	−0.135511	+	0.990776i	$0.543268\pi$
$720$		0			0
$721$	−6.63323	−	20.4150i	−0.247034	−	0.760294i
$722$		0			0
$723$	−0.560400	+	1.72473i	−0.0208415	+	0.0641436i
$724$		0			0
$725$	−1.93948	+	1.40912i	−0.0720306	+	0.0523333i
$726$		0			0
$727$	1.71149	+	5.26744i	0.0634758	+	0.195359i	0.977765	−	0.209704i	$-0.0672499\pi$
$727$	1.71149	+	5.26744i	0.0634758	+	0.195359i	−0.914289	+	0.405062i	$0.867250\pi$
$728$		0			0
$729$	−26.5553			−0.983530
$730$		0			0
$731$	1.92305	+	1.39718i	0.0711265	+	0.0516765i
$732$		0			0
$733$	−6.63146	+	20.4095i	−0.244938	+	0.753843i	0.750708	+	0.660634i	$0.229712\pi$
$733$	−6.63146	+	20.4095i	−0.244938	+	0.753843i	−0.995647	+	0.0932090i	$0.970288\pi$
$734$		0			0
$735$	0.0937016			0.00345624
$736$		0			0
$737$	−16.4802			−0.607057
$738$		0			0
$739$	−45.7876			−1.68432			−0.842162	−	0.539224i	$-0.818718\pi$
$739$	−45.7876			−1.68432			−0.842162	+	0.539224i	$0.818718\pi$
$740$		0			0
$741$	0.0236236			0.000867834
$742$		0			0
$743$	2.75772	−	8.48738i	0.101171	−	0.311372i	−0.887642	−	0.460534i	$-0.847658\pi$
$743$	2.75772	−	8.48738i	0.101171	−	0.311372i	0.988813	+	0.149163i	$0.0476578\pi$
$744$		0			0
$745$	−11.0581	−	8.03421i	−0.405139	−	0.294351i
$746$		0			0
$747$	−21.2132			−0.776150
$748$		0			0
$749$	1.80602	+	5.55834i	0.0659904	+	0.203097i
$750$		0			0
$751$	−31.4486	+	22.8487i	−1.14757	+	0.833762i	−0.988157	−	0.153449i	$-0.950962\pi$
$751$	−31.4486	+	22.8487i	−1.14757	+	0.833762i	−0.159418	+	0.987211i	$0.550962\pi$
$752$		0			0
$753$	−0.0905113	+	0.278565i	−0.00329841	+	0.0101515i
$754$		0			0
$755$	−5.78061	−	17.7909i	−0.210378	−	0.647477i
$756$		0			0
$757$	25.1631	+	18.2820i	0.914567	+	0.664472i	0.942166	−	0.335147i	$-0.108786\pi$
$757$	25.1631	+	18.2820i	0.914567	+	0.664472i	−0.0275987	+	0.999619i	$0.508786\pi$
$758$		0			0
$759$	1.60564	+	1.16656i	0.0582809	+	0.0423436i
$760$		0			0
$761$	25.3336	−	18.4059i	0.918341	−	0.667214i	−0.0247696	−	0.999693i	$-0.507885\pi$
$761$	25.3336	−	18.4059i	0.918341	−	0.667214i	0.943111	+	0.332479i	$0.107885\pi$
$762$		0			0
$763$	10.9042	+	7.92234i	0.394758	+	0.286808i
$764$		0			0
$765$	−22.7420			−0.822238
$766$		0			0
$767$	13.1629	−	40.5113i	0.475286	−	1.46278i
$768$		0			0
$769$	4.30585	+	13.2520i	0.155273	+	0.477881i	0.998188	−	0.0601652i	$-0.0191627\pi$
$769$	4.30585	+	13.2520i	0.155273	+	0.477881i	−0.842916	+	0.538046i	$0.819163\pi$
$770$		0			0
$771$	−0.577680	−	1.77792i	−0.0208046	−	0.0640301i
$772$		0			0
$773$	1.14601	−	0.832627i	0.0412192	−	0.0299475i	−0.566985	−	0.823728i	$-0.691890\pi$
$773$	1.14601	−	0.832627i	0.0412192	−	0.0299475i	0.608204	+	0.793781i	$0.291890\pi$
$774$		0			0
$775$	−2.43787	+	7.50298i	−0.0875708	+	0.269515i
$776$		0			0
$777$	1.27096	−	0.923403i	0.0455953	−	0.0331269i
$778$		0			0
$779$	−0.0400943	−	0.333559i	−0.00143653	−	0.0119510i
$780$		0			0
$781$	−3.49002	+	2.53564i	−0.124883	+	0.0907325i
$782$		0			0
$783$	−0.403271	+	1.24114i	−0.0144117	+	0.0443548i
$784$		0			0
$785$	−1.41906	+	1.03101i	−0.0506485	+	0.0367983i
$786$		0			0
$787$	9.88675	+	30.4283i	0.352425	+	1.08465i	0.957488	+	0.288474i	$0.0931479\pi$
$787$	9.88675	+	30.4283i	0.352425	+	1.08465i	−0.605063	+	0.796178i	$0.706852\pi$
$788$		0			0
$789$	0.456856	+	1.40606i	0.0162645	+	0.0500570i
$790$		0			0
$791$	−10.5691	+	32.5285i	−0.375795	+	1.15658i
$792$		0			0
$793$	−32.9535			−1.17021
$794$		0			0
$795$	−0.904554	−	0.657197i	−0.0320812	−	0.0233084i
$796$		0			0
$797$	14.2213	−	10.3324i	0.503744	−	0.365991i	−0.306701	−	0.951806i	$-0.599225\pi$
$797$	14.2213	−	10.3324i	0.503744	−	0.365991i	0.810445	+	0.585814i	$0.199225\pi$
$798$		0			0
$799$	−45.9288	−	33.3693i	−1.62485	−	1.18052i
$800$		0			0
$801$	12.7275	+	9.24709i	0.449705	+	0.326730i
$802$		0			0
$803$	−3.81550	−	11.7429i	−0.134646	−	0.414398i
$804$		0			0
$805$	6.76246	−	20.8127i	0.238345	−	0.733552i
$806$		0			0
$807$	−0.490807	+	0.356592i	−0.0172772	+	0.0125526i
$808$		0			0
$809$	−5.34648	−	16.4548i	−0.187972	−	0.578520i	0.812015	−	0.583637i	$-0.198371\pi$
$809$	−5.34648	−	16.4548i	−0.187972	−	0.578520i	−0.999987	+	0.00511771i	$0.998371\pi$
$810$		0			0
$811$	19.9396			0.700174			0.350087	−	0.936717i	$-0.386152\pi$
$811$	19.9396			0.700174			0.350087	+	0.936717i	$0.386152\pi$
$812$		0			0
$813$	−0.804243	−	0.584317i	−0.0282060	−	0.0204929i
$814$		0			0
$815$	−5.28514	+	16.2660i	−0.185130	+	0.569773i
$816$		0			0
$817$	−0.0164068			−0.000574002
$818$		0			0
$819$	36.2226			1.26572
$820$		0			0
$821$	−0.477205			−0.0166546			−0.00832728	−	0.999965i	$-0.502651\pi$
$821$	−0.477205			−0.0166546			−0.00832728	+	0.999965i	$0.502651\pi$
$822$		0			0
$823$	19.9504			0.695426			0.347713	−	0.937601i	$-0.386958\pi$
$823$	19.9504			0.695426			0.347713	+	0.937601i	$0.386958\pi$
$824$		0			0
$825$	0.0684679	−	0.210723i	0.00238375	−	0.00733642i
$826$		0			0
$827$	−10.6145	−	7.71187i	−0.369102	−	0.268168i	0.387737	−	0.921770i	$-0.373257\pi$
$827$	−10.6145	−	7.71187i	−0.369102	−	0.268168i	−0.756838	+	0.653602i	$0.773257\pi$
$828$		0			0
$829$	−49.7985			−1.72957			−0.864786	−	0.502140i	$-0.832546\pi$
$829$	−49.7985			−1.72957			−0.864786	+	0.502140i	$0.832546\pi$
$830$		0			0
$831$	−0.400278	−	1.23193i	−0.0138855	−	0.0427352i
$832$		0			0
$833$	−6.34272	+	4.60825i	−0.219762	+	0.159667i
$834$		0			0
$835$	5.05625	−	15.5615i	0.174979	−	0.538529i
$836$		0			0
$837$	1.32708	+	4.08433i	0.0458706	+	0.141175i
$838$		0			0
$839$	42.2118	+	30.6687i	1.45731	+	1.05880i	0.984052	+	0.177880i	$0.0569237\pi$
$839$	42.2118	+	30.6687i	1.45731	+	1.05880i	0.473262	+	0.880922i	$0.343076\pi$
$840$		0			0
$841$	18.8119	+	13.6677i	0.648686	+	0.471298i
$842$		0			0
$843$	0.783026	−	0.568901i	0.0269688	−	0.0195940i
$844$		0			0
$845$	9.35253	+	6.79501i	0.321737	+	0.233755i
$846$		0			0
$847$	−12.3434			−0.424123
$848$		0			0
$849$	0.548721	−	1.68879i	0.0188320	−	0.0579591i
$850$		0			0
$851$	19.5916	+	60.2967i	0.671591	+	2.06694i
$852$		0			0
$853$	7.67956	+	23.6353i	0.262943	+	0.809256i	0.992160	+	0.124973i	$0.0398846\pi$
$853$	7.67956	+	23.6353i	0.262943	+	0.809256i	−0.729217	+	0.684283i	$0.760115\pi$
$854$		0			0
$855$	0.126992	−	0.0922654i	0.00434305	−	0.00315541i
$856$		0			0
$857$	5.52165	−	16.9939i	0.188616	−	0.580500i	−0.811376	−	0.584525i	$-0.801281\pi$
$857$	5.52165	−	16.9939i	0.188616	−	0.580500i	0.999992	+	0.00402460i	$0.00128107\pi$
$858$		0			0
$859$	12.3840	−	8.99753i	0.422538	−	0.306992i	−0.356120	−	0.934440i	$-0.615901\pi$
$859$	12.3840	−	8.99753i	0.422538	−	0.306992i	0.778658	+	0.627448i	$0.215901\pi$
$860$		0			0
$861$	0.169612	+	1.41107i	0.00578038	+	0.0480890i
$862$		0			0
$863$	1.92789	−	1.40069i	0.0656262	−	0.0476802i	−0.554489	−	0.832191i	$-0.687086\pi$
$863$	1.92789	−	1.40069i	0.0656262	−	0.0476802i	0.620115	+	0.784511i	$0.287086\pi$
$864$		0			0
$865$	−1.60423	+	4.93732i	−0.0545456	+	0.167874i
$866$		0			0
$867$	−2.99765	+	2.17792i	−0.101805	+	0.0739660i
$868$		0			0
$869$	−3.18008	−	9.78728i	−0.107877	−	0.332011i
$870$		0			0
$871$	10.3488	+	31.8504i	0.350657	+	1.07921i
$872$		0			0
$873$	−7.64069	+	23.5156i	−0.258598	+	0.795883i
$874$		0			0
$875$	−2.44308			−0.0825911
$876$		0			0
$877$	4.63719	+	3.36912i	0.156587	+	0.113767i	0.663320	−	0.748336i	$-0.269147\pi$
$877$	4.63719	+	3.36912i	0.156587	+	0.113767i	−0.506733	+	0.862103i	$0.669147\pi$
$878$		0			0
$879$	0.247219	−	0.179615i	0.00833851	−	0.00605828i
$880$		0			0
$881$	15.0138	+	10.9081i	0.505827	+	0.367505i	0.811238	−	0.584716i	$-0.198794\pi$
$881$	15.0138	+	10.9081i	0.505827	+	0.367505i	−0.305411	+	0.952221i	$0.598794\pi$
$882$		0			0
$883$	−43.5183	−	31.6179i	−1.46451	−	1.06403i	−0.982160	−	0.188046i	$-0.939785\pi$
$883$	−43.5183	−	31.6179i	−1.46451	−	1.06403i	−0.482347	−	0.875980i	$-0.660215\pi$
$884$		0			0
$885$	0.241306	+	0.742664i	0.00811142	+	0.0249644i
$886$		0			0
$887$	−9.49530	+	29.2235i	−0.318821	+	0.981230i	0.655332	+	0.755341i	$0.272529\pi$
$887$	−9.49530	+	29.2235i	−0.318821	+	0.981230i	−0.974153	+	0.225889i	$0.927471\pi$
$888$		0			0
$889$	11.2327	−	8.16106i	0.376734	−	0.273713i
$890$		0			0
$891$	6.72667	+	20.7026i	0.225352	+	0.693562i
$892$		0			0
$893$	0.391850			0.0131127
$894$		0			0
$895$	18.1866	+	13.2133i	0.607910	+	0.441672i
$896$		0			0
$897$	1.24629	−	3.83568i	0.0416123	−	0.128070i
$898$		0			0
$899$	−18.9128			−0.630777
$900$		0			0
$901$	93.5507			3.11663
$902$		0			0
$903$	0.0694064			0.00230970
$904$		0			0
$905$	−3.52664			−0.117229
$906$		0			0
$907$	−6.75293	+	20.7834i	−0.224227	+	0.690101i	0.774142	+	0.633012i	$0.218182\pi$
$907$	−6.75293	+	20.7834i	−0.224227	+	0.690101i	−0.998369	+	0.0570887i	$0.981818\pi$
$908$		0			0
$909$	39.1104	+	28.4153i	1.29721	+	0.942478i
$910$		0			0
$911$	−10.6105			−0.351543			−0.175772	−	0.984431i	$-0.556242\pi$
$911$	−10.6105			−0.351543			−0.175772	+	0.984431i	$0.556242\pi$
$912$		0			0
$913$	5.34362	+	16.4460i	0.176848	+	0.544282i
$914$		0			0
$915$	0.488737	−	0.355088i	0.0161572	−	0.0117389i
$916$		0			0
$917$	9.99228	−	30.7531i	0.329974	−	1.01556i
$918$		0			0
$919$	−11.9576	−	36.8018i	−0.394446	−	1.21398i	−0.929392	−	0.369094i	$-0.879668\pi$
$919$	−11.9576	−	36.8018i	−0.394446	−	1.21398i	0.534946	−	0.844886i	$-0.320332\pi$
$920$		0			0
$921$	1.33633	+	0.970904i	0.0440337	+	0.0319924i
$922$		0			0
$923$	7.09207	+	5.15269i	0.233438	+	0.169603i
$924$		0			0
$925$	5.72611	−	4.16026i	0.188273	−	0.136789i
$926$		0			0
$927$	−21.2661	−	15.4507i	−0.698470	−	0.507468i
$928$		0			0
$929$	−37.3282			−1.22470			−0.612349	−	0.790587i	$-0.709775\pi$
$929$	−37.3282			−1.22470			−0.612349	+	0.790587i	$0.709775\pi$
$930$		0			0
$931$	0.0167221	−	0.0514654i	0.000548046	−	0.00168671i
$932$		0			0
$933$	−0.541923	−	1.66787i	−0.0177418	−	0.0546035i
$934$		0			0
$935$	5.72872	+	17.6312i	0.187349	+	0.576602i
$936$		0			0
$937$	39.3414	−	28.5832i	1.28523	−	0.933773i	0.285531	−	0.958369i	$-0.407830\pi$
$937$	39.3414	−	28.5832i	1.28523	−	0.933773i	0.999697	+	0.0245963i	$0.00783005\pi$
$938$		0			0
$939$	−0.137274	+	0.422485i	−0.00447975	+	0.0137873i
$940$		0			0
$941$	−8.56692	+	6.22423i	−0.279273	+	0.202904i	−0.718600	−	0.695423i	$-0.755217\pi$
$941$	−8.56692	+	6.22423i	−0.279273	+	0.202904i	0.439327	+	0.898327i	$0.355217\pi$
$942$		0			0
$943$	−56.2739	−	11.0873i	−1.83253	−	0.361051i
$944$		0			0
$945$	−1.07592	+	0.781705i	−0.0349998	+	0.0254289i
$946$		0			0
$947$	7.17551	−	22.0840i	0.233173	−	0.717632i	−0.764186	−	0.644996i	$-0.776859\pi$
$947$	7.17551	−	22.0840i	0.233173	−	0.717632i	0.997359	−	0.0726359i	$-0.0231411\pi$
$948$		0			0
$949$	−20.2989	+	14.7480i	−0.658931	+	0.478741i
$950$		0			0
$951$	−0.592550	−	1.82368i	−0.0192148	−	0.0591370i
$952$		0			0
$953$	5.76601	+	17.7460i	0.186779	+	0.574848i	0.999974	−	0.00714332i	$-0.00227381\pi$
$953$	5.76601	+	17.7460i	0.186779	+	0.574848i	−0.813195	+	0.581991i	$0.802274\pi$
$954$		0			0
$955$	−8.17608	+	25.1634i	−0.264572	+	0.814268i
$956$		0			0
$957$	0.531169			0.0171703
$958$		0			0
$959$	−14.3584	−	10.4320i	−0.463657	−	0.336867i
$960$		0			0
$961$	−25.2721	+	18.3612i	−0.815227	+	0.592297i
$962$		0			0
$963$	5.79007	+	4.20674i	0.186583	+	0.135560i
$964$		0			0
$965$	−15.2572	−	11.0850i	−0.491148	−	0.356840i
$966$		0			0
$967$	−2.08674	−	6.42231i	−0.0671049	−	0.206528i	0.911881	−	0.410454i	$-0.134630\pi$
$967$	−2.08674	−	6.42231i	−0.0671049	−	0.206528i	−0.978986	+	0.203926i	$0.934630\pi$
$968$		0			0
$969$	0.0111973	−	0.0344619i	0.000359710	−	0.00110707i
$970$		0			0
$971$	12.8576	−	9.34161i	0.412621	−	0.299786i	−0.362041	−	0.932162i	$-0.617920\pi$
$971$	12.8576	−	9.34161i	0.412621	−	0.299786i	0.774662	+	0.632376i	$0.217920\pi$
$972$		0			0
$973$	−13.9157	−	42.8282i	−0.446118	−	1.37301i
$974$		0			0
$975$	−0.450247			−0.0144194
$976$		0			0
$977$	32.2304	+	23.4167i	1.03114	+	0.749168i	0.968537	−	0.248871i	$-0.0800594\pi$
$977$	32.2304	+	23.4167i	1.03114	+	0.749168i	0.0626042	+	0.998038i	$0.480059\pi$
$978$		0			0
$979$	3.96292	−	12.1966i	0.126656	−	0.389806i
$980$		0			0
$981$	16.5053			0.526972
$982$		0			0
$983$	−55.9667			−1.78506			−0.892530	−	0.450987i	$-0.851072\pi$
$983$	−55.9667			−1.78506			−0.892530	+	0.450987i	$0.851072\pi$
$984$		0			0
$985$	−0.707065			−0.0225290
$986$		0			0
$987$	−1.65766			−0.0527638
$988$		0			0
$989$	−0.865558	+	2.66391i	−0.0275232	+	0.0847076i
$990$		0			0
$991$	3.84651	+	2.79465i	0.122188	+	0.0887750i	0.647201	−	0.762319i	$-0.275939\pi$
$991$	3.84651	+	2.79465i	0.122188	+	0.0887750i	−0.525013	+	0.851094i	$0.675939\pi$
$992$		0			0
$993$	1.31353			0.0416837
$994$		0			0
$995$	−1.29546	−	3.98702i	−0.0410689	−	0.126397i
$996$		0			0
$997$	25.9288	−	18.8384i	0.821174	−	0.596617i	−0.0958749	−	0.995393i	$-0.530565\pi$
$997$	25.9288	−	18.8384i	0.821174	−	0.596617i	0.917048	+	0.398776i	$0.130565\pi$
$998$		0			0
$999$	1.19061	−	3.66433i	0.0376694	−	0.115934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.b.201.5	✓	32
41.10	even	5	inner	820.2.u.b.461.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.b.201.5	✓	32	1.1	even	1	trivial
820.2.u.b.461.5	yes	32	41.10	even	5	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.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.0908517 q^{3} +(-0.309017 + 0.951057i) q^{5} +(-1.97649 - 1.43601i) q^{7} -2.99175 q^{9} +(0.753623 + 2.31941i) q^{11} +(4.00936 - 2.91297i) q^{13} +(-0.0280747 + 0.0864051i) q^{15} +(-2.34902 - 7.22953i) q^{17} +(0.0424476 + 0.0308400i) q^{19} +(-0.179568 - 0.130464i) q^{21} +(7.24674 - 5.26506i) q^{23} +(-0.809017 - 0.587785i) q^{25} -0.544361 q^{27} +(0.740816 - 2.28000i) q^{29} +(-2.43787 - 7.50298i) q^{31} +(0.0684679 + 0.210723i) q^{33} +(1.97649 - 1.43601i) q^{35} +(-2.18718 + 6.73145i) q^{37} +(0.364257 - 0.264648i) q^{39} +(-4.35499 - 4.69405i) q^{41} +(-0.252980 + 0.183801i) q^{43} +(0.924500 - 2.84532i) q^{45} +(6.04201 - 4.38978i) q^{47} +(-0.318710 - 0.980890i) q^{49} +(-0.213412 - 0.656815i) q^{51} +(-3.80300 + 11.7044i) q^{53} -2.43877 q^{55} +(0.00385644 + 0.00280187i) q^{57} +(6.95361 - 5.05210i) q^{59} +(-5.37950 - 3.90844i) q^{61} +(5.91316 + 4.29616i) q^{63} +(1.53144 + 4.71328i) q^{65} +(-2.08821 + 6.42685i) q^{67} +(0.658379 - 0.478340i) q^{69} +(0.546614 + 1.68230i) q^{71} -5.06288 q^{73} +(-0.0735006 - 0.0534013i) q^{75} +(1.84116 - 5.66650i) q^{77} -4.21972 q^{79} +8.92578 q^{81} +7.09058 q^{83} +7.60158 q^{85} +(0.0673045 - 0.207142i) q^{87} +(-4.25422 - 3.09087i) q^{89} -12.1075 q^{91} +(-0.221484 - 0.681659i) q^{93} +(-0.0424476 + 0.0308400i) q^{95} +(2.55392 - 7.86017i) q^{97} +(-2.25465 - 6.93909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 8 q^{5} - 5 q^{7} + 46 q^{9} + q^{11} + q^{13} - 2 q^{15} + 7 q^{17} - 13 q^{19} - 6 q^{21} + 4 q^{23} - 8 q^{25} - 28 q^{27} + 3 q^{29} - q^{31} + 14 q^{33} + 5 q^{35} - 25 q^{37} + 26 q^{41}+ \cdots + 30 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 8 * q^5 - 5 * q^7 + 46 * q^9 + q^11 + q^13 - 2 * q^15 + 7 * q^17 - 13 * q^19 - 6 * q^21 + 4 * q^23 - 8 * q^25 - 28 * q^27 + 3 * q^29 - q^31 + 14 * q^33 + 5 * q^35 - 25 * q^37 + 26 * q^41 + 8 * q^43 + 19 * q^45 + q^47 - 15 * q^49 + 29 * q^51 - 33 * q^53 + 4 * q^55 - 29 * q^57 + 20 * q^59 - 24 * q^61 - 66 * q^63 - q^65 - 48 * q^67 - 16 * q^69 + 5 * q^71 + 4 * q^73 - 3 * q^75 - 16 * q^77 - 102 * q^79 + 200 * q^81 - 110 * q^83 + 8 * q^85 + 25 * q^87 - 34 * q^89 - 10 * q^91 - 18 * q^93 + 13 * q^95 - 36 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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