LMFDB - Embedded newform 1100.2.q.b.441.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(221,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [52] 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:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			441.5
Character	$\chi$	$=$	1100.441
Dual form			1100.2.q.b.661.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.183465 - 0.564647i) q^{3} +(-1.90569 + 1.16976i) q^{5} -0.847663 q^{7} +(2.14188 - 1.55617i) q^{9} +(0.809017 + 0.587785i) q^{11} +(-1.56806 + 1.13926i) q^{13} +(1.01013 + 0.861436i) q^{15} +(0.205397 - 0.632148i) q^{17} +(-1.12667 + 3.46753i) q^{19} +(0.155516 + 0.478630i) q^{21} +(-2.38568 - 1.73330i) q^{23} +(2.26335 - 4.45839i) q^{25} +(-2.71260 - 1.97082i) q^{27} +(2.84555 + 8.75770i) q^{29} +(-2.49271 + 7.67177i) q^{31} +(0.183465 - 0.564647i) q^{33} +(1.61539 - 0.991558i) q^{35} +(-3.87595 + 2.81604i) q^{37} +(0.930967 + 0.676387i) q^{39} +(-1.32264 + 0.960955i) q^{41} +8.78217 q^{43} +(-2.26144 + 5.47106i) q^{45} +(3.81393 + 11.7381i) q^{47} -6.28147 q^{49} -0.394624 q^{51} +(-0.582359 - 1.79232i) q^{53} +(-2.22930 - 0.173788i) q^{55} +2.16464 q^{57} +(-8.41365 + 6.11287i) q^{59} +(7.84307 + 5.69833i) q^{61} +(-1.81559 + 1.31911i) q^{63} +(1.65559 - 4.00534i) q^{65} +(-1.67960 + 5.16926i) q^{67} +(-0.541013 + 1.66507i) q^{69} +(1.87087 + 5.75794i) q^{71} +(-6.83518 - 4.96605i) q^{73} +(-2.93266 - 0.460033i) q^{75} +(-0.685773 - 0.498244i) q^{77} +(-1.46378 - 4.50505i) q^{79} +(1.83923 - 5.66057i) q^{81} +(-4.15712 + 12.7943i) q^{83} +(0.348034 + 1.44495i) q^{85} +(4.42295 - 3.21346i) q^{87} +(9.60280 + 6.97684i) q^{89} +(1.32919 - 0.965712i) q^{91} +4.78917 q^{93} +(-1.90908 - 7.92599i) q^{95} +(-2.30736 - 7.10133i) q^{97} +2.64751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	−0.183465	−	0.564647i	−0.105924	−	0.325999i	0.884023	−	0.467444i	$-0.154825\pi$
$3$	−0.183465	−	0.564647i	−0.105924	−	0.325999i	−0.989946	+	0.141445i	$0.954825\pi$
$4$		0			0
$5$	−1.90569	+	1.16976i	−0.852253	+	0.523130i
$5$	−1.90569	+	1.16976i	−0.852253	+	0.523130i
$6$		0			0
$7$	−0.847663			−0.320386			−0.160193	−	0.987086i	$-0.551212\pi$
$7$	−0.847663			−0.320386			−0.160193	+	0.987086i	$0.551212\pi$
$8$		0			0
$9$	2.14188	−	1.55617i	0.713961	−	0.518723i
$10$		0			0
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$12$		0			0
$13$	−1.56806	+	1.13926i	−0.434902	+	0.315975i	−0.783606	−	0.621258i	$-0.786622\pi$
$13$	−1.56806	+	1.13926i	−0.434902	+	0.315975i	0.348704	+	0.937233i	$0.386622\pi$
$14$		0			0
$15$	1.01013	+	0.861436i	0.260814	+	0.222422i
$16$		0			0
$17$	0.205397	−	0.632148i	0.0498162	−	0.153318i	−0.923054	−	0.384671i	$-0.874315\pi$
$17$	0.205397	−	0.632148i	0.0498162	−	0.153318i	0.972870	+	0.231352i	$0.0743150\pi$
$18$		0			0
$19$	−1.12667	+	3.46753i	−0.258476	+	0.795507i	0.734649	+	0.678447i	$0.237347\pi$
$19$	−1.12667	+	3.46753i	−0.258476	+	0.795507i	−0.993125	+	0.117059i	$0.962653\pi$
$20$		0			0
$21$	0.155516	+	0.478630i	0.0339365	+	0.104446i
$22$		0			0
$23$	−2.38568	−	1.73330i	−0.497448	−	0.361417i	0.310593	−	0.950543i	$-0.399472\pi$
$23$	−2.38568	−	1.73330i	−0.497448	−	0.361417i	−0.808041	+	0.589126i	$0.799472\pi$
$24$		0			0
$25$	2.26335	−	4.45839i	0.452669	−	0.891679i
$26$		0			0
$27$	−2.71260	−	1.97082i	−0.522040	−	0.379284i
$28$		0			0
$29$	2.84555	+	8.75770i	0.528405	+	1.62626i	0.757483	+	0.652855i	$0.226429\pi$
$29$	2.84555	+	8.75770i	0.528405	+	1.62626i	−0.229078	+	0.973408i	$0.573571\pi$
$30$		0			0
$31$	−2.49271	+	7.67177i	−0.447704	+	1.37789i	0.431787	+	0.901975i	$0.357883\pi$
$31$	−2.49271	+	7.67177i	−0.447704	+	1.37789i	−0.879491	+	0.475915i	$0.842117\pi$
$32$		0			0
$33$	0.183465	−	0.564647i	0.0319372	−	0.0982925i
$34$		0			0
$35$	1.61539	−	0.991558i	0.273050	−	0.167604i
$36$		0			0
$37$	−3.87595	+	2.81604i	−0.637202	+	0.462955i	−0.858888	−	0.512164i	$-0.828844\pi$
$37$	−3.87595	+	2.81604i	−0.637202	+	0.462955i	0.221686	+	0.975118i	$0.428844\pi$
$38$		0			0
$39$	0.930967	+	0.676387i	0.149074	+	0.108309i
$40$		0			0
$41$	−1.32264	+	0.960955i	−0.206562	+	0.150076i	−0.686257	−	0.727359i	$-0.740747\pi$
$41$	−1.32264	+	0.960955i	−0.206562	+	0.150076i	0.479695	+	0.877435i	$0.340747\pi$
$42$		0			0
$43$	8.78217			1.33927			0.669634	−	0.742691i	$-0.266451\pi$
$43$	8.78217			1.33927			0.669634	+	0.742691i	$0.266451\pi$
$44$		0			0
$45$	−2.26144	+	5.47106i	−0.337116	+	0.815578i
$46$		0			0
$47$	3.81393	+	11.7381i	0.556318	+	1.71217i	0.692436	+	0.721479i	$0.256537\pi$
$47$	3.81393	+	11.7381i	0.556318	+	1.71217i	−0.136118	+	0.990693i	$0.543463\pi$
$48$		0			0
$49$	−6.28147			−0.897353
$50$		0			0
$51$	−0.394624			−0.0552584
$52$		0			0
$53$	−0.582359	−	1.79232i	−0.0799932	−	0.246194i	0.903060	−	0.429514i	$-0.141315\pi$
$53$	−0.582359	−	1.79232i	−0.0799932	−	0.246194i	−0.983053	+	0.183321i	$0.941315\pi$
$54$		0			0
$55$	−2.22930	−	0.173788i	−0.300599	−	0.0234335i
$56$		0			0
$57$	2.16464			0.286713
$58$		0			0
$59$	−8.41365	+	6.11287i	−1.09536	+	0.795828i	−0.980297	−	0.197530i	$-0.936708\pi$
$59$	−8.41365	+	6.11287i	−1.09536	+	0.795828i	−0.115066	+	0.993358i	$0.536708\pi$
$60$		0			0
$61$	7.84307	+	5.69833i	1.00420	+	0.729596i	0.962985	−	0.269554i	$-0.0868764\pi$
$61$	7.84307	+	5.69833i	1.00420	+	0.729596i	0.0412175	+	0.999150i	$0.486876\pi$
$62$		0			0
$63$	−1.81559	+	1.31911i	−0.228743	+	0.166192i
$64$		0			0
$65$	1.65559	−	4.00534i	0.205351	−	0.496801i
$66$		0			0
$67$	−1.67960	+	5.16926i	−0.205195	+	0.631526i	0.794510	+	0.607251i	$0.207728\pi$
$67$	−1.67960	+	5.16926i	−0.205195	+	0.631526i	−0.999705	+	0.0242750i	$0.992272\pi$
$68$		0			0
$69$	−0.541013	+	1.66507i	−0.0651303	+	0.200450i
$70$		0			0
$71$	1.87087	+	5.75794i	0.222031	+	0.683342i	0.998579	+	0.0532841i	$0.0169689\pi$
$71$	1.87087	+	5.75794i	0.222031	+	0.683342i	−0.776548	+	0.630058i	$0.783031\pi$
$72$		0			0
$73$	−6.83518	−	4.96605i	−0.799997	−	0.581232i	0.110916	−	0.993830i	$-0.464621\pi$
$73$	−6.83518	−	4.96605i	−0.799997	−	0.581232i	−0.910913	+	0.412598i	$0.864621\pi$
$74$		0			0
$75$	−2.93266	−	0.460033i	−0.338635	−	0.0531200i
$76$		0			0
$77$	−0.685773	−	0.498244i	−0.0781511	−	0.0567801i
$78$		0			0
$79$	−1.46378	−	4.50505i	−0.164688	−	0.506858i	0.834325	−	0.551273i	$-0.185858\pi$
$79$	−1.46378	−	4.50505i	−0.164688	−	0.506858i	−0.999013	+	0.0444149i	$0.985858\pi$
$80$		0			0
$81$	1.83923	−	5.66057i	0.204359	−	0.628952i
$82$		0			0
$83$	−4.15712	+	12.7943i	−0.456303	+	1.40436i	0.413295	+	0.910597i	$0.364378\pi$
$83$	−4.15712	+	12.7943i	−0.456303	+	1.40436i	−0.869598	+	0.493760i	$0.835622\pi$
$84$		0			0
$85$	0.348034	+	1.44495i	0.0377496	+	0.156726i
$86$		0			0
$87$	4.42295	−	3.21346i	0.474190	−	0.344519i
$88$		0			0
$89$	9.60280	+	6.97684i	1.01789	+	0.739544i	0.965850	−	0.259101i	$-0.0834263\pi$
$89$	9.60280	+	6.97684i	1.01789	+	0.739544i	0.0520443	+	0.998645i	$0.483426\pi$
$90$		0			0
$91$	1.32919	−	0.965712i	0.139337	−	0.101234i
$92$		0			0
$93$	4.78917			0.496614
$94$		0			0
$95$	−1.90908	−	7.92599i	−0.195867	−	0.813189i
$96$		0			0
$97$	−2.30736	−	7.10133i	−0.234277	−	0.721031i	−0.997216	−	0.0745610i	$-0.976244\pi$
$97$	−2.30736	−	7.10133i	−0.234277	−	0.721031i	0.762939	−	0.646470i	$-0.223756\pi$
$98$		0			0
$99$	2.64751			0.266085
$100$		0			0
$101$	14.3183			1.42472			0.712360	−	0.701814i	$-0.247626\pi$
$101$	14.3183			1.42472			0.712360	+	0.701814i	$0.247626\pi$
$102$		0			0
$103$	−1.53880	−	4.73593i	−0.151622	−	0.466645i	0.846181	−	0.532896i	$-0.178896\pi$
$103$	−1.53880	−	4.73593i	−0.151622	−	0.466645i	−0.997803	+	0.0662511i	$0.978896\pi$
$104$		0			0
$105$	−0.856247	−	0.730207i	−0.0835612	−	0.0712609i
$106$		0			0
$107$	−17.6378			−1.70511			−0.852555	−	0.522637i	$-0.824948\pi$
$107$	−17.6378			−1.70511			−0.852555	+	0.522637i	$0.824948\pi$
$108$		0			0
$109$	10.1240	−	7.35553i	0.969706	−	0.704532i	0.0143213	−	0.999897i	$-0.495441\pi$
$109$	10.1240	−	7.35553i	0.969706	−	0.704532i	0.955384	+	0.295365i	$0.0954412\pi$
$110$		0			0
$111$	2.30117	+	1.67190i	0.218418	+	0.158690i
$112$		0			0
$113$	14.4694	−	10.5126i	1.36116	−	0.988943i	0.362793	−	0.931870i	$-0.381823\pi$
$113$	14.4694	−	10.5126i	1.36116	−	0.988943i	0.998370	−	0.0570732i	$-0.0181768\pi$
$114$		0			0
$115$	6.57391	+	0.512475i	0.613020	+	0.0477886i
$116$		0			0
$117$	−1.58572	+	4.88034i	−0.146600	+	0.451188i
$118$		0			0
$119$	−0.174108	+	0.535848i	−0.0159604	+	0.0491211i
$120$		0			0
$121$	0.309017	+	0.951057i	0.0280925	+	0.0864597i
$122$		0			0
$123$	0.785259	+	0.570524i	0.0708044	+	0.0514424i
$124$		0			0
$125$	0.901981	+	11.1439i	0.0806756	+	0.996740i
$126$		0			0
$127$	−8.61441	−	6.25874i	−0.764406	−	0.555373i	0.135853	−	0.990729i	$-0.456623\pi$
$127$	−8.61441	−	6.25874i	−0.764406	−	0.555373i	−0.900258	+	0.435356i	$0.856623\pi$
$128$		0			0
$129$	−1.61122	−	4.95883i	−0.141860	−	0.436600i
$130$		0			0
$131$	0.885503	−	2.72530i	0.0773668	−	0.238110i	−0.904892	−	0.425641i	$-0.860048\pi$
$131$	0.885503	−	2.72530i	0.0773668	−	0.238110i	0.982259	+	0.187531i	$0.0600485\pi$
$132$		0			0
$133$	0.955036	−	2.93930i	0.0828121	−	0.254869i
$134$		0			0
$135$	7.47477	+	0.582703i	0.643325	+	0.0501511i
$136$		0			0
$137$	−11.3275	+	8.22990i	−0.967772	+	0.703128i	−0.954943	−	0.296790i	$-0.904084\pi$
$137$	−11.3275	+	8.22990i	−0.967772	+	0.703128i	−0.0128296	+	0.999918i	$0.504084\pi$
$138$		0			0
$139$	−4.13859	−	3.00686i	−0.351031	−	0.255039i	0.398270	−	0.917268i	$-0.369611\pi$
$139$	−4.13859	−	3.00686i	−0.351031	−	0.255039i	−0.749301	+	0.662229i	$0.769611\pi$
$140$		0			0
$141$	5.92814	−	4.30705i	0.499239	−	0.362719i
$142$		0			0
$143$	−1.93823			−0.162083
$144$		0			0
$145$	−15.6671	−	13.3609i	−1.30108	−	1.10956i
$146$		0			0
$147$	1.15243	+	3.54681i	0.0950508	+	0.292536i
$148$		0			0
$149$	−10.6060			−0.868878			−0.434439	−	0.900701i	$-0.643053\pi$
$149$	−10.6060			−0.868878			−0.434439	+	0.900701i	$0.643053\pi$
$150$		0			0
$151$	3.19591			0.260080			0.130040	−	0.991509i	$-0.458489\pi$
$151$	3.19591			0.260080			0.130040	+	0.991509i	$0.458489\pi$
$152$		0			0
$153$	−0.543792	−	1.67362i	−0.0439630	−	0.135304i
$154$		0			0
$155$	−4.22375	−	17.5359i	−0.339260	−	1.40852i
$156$		0			0
$157$	−10.7982			−0.861790			−0.430895	−	0.902402i	$-0.641802\pi$
$157$	−10.7982			−0.861790			−0.430895	+	0.902402i	$0.641802\pi$
$158$		0			0
$159$	−0.905184	+	0.657655i	−0.0717858	+	0.0521554i
$160$		0			0
$161$	2.02225	+	1.46925i	0.159376	+	0.115793i
$162$		0			0
$163$	16.3343	−	11.8675i	1.27940	−	0.929537i	0.279863	−	0.960040i	$-0.409711\pi$
$163$	16.3343	−	11.8675i	1.27940	−	0.929537i	0.999535	+	0.0305032i	$0.00971097\pi$
$164$		0			0
$165$	0.310871	+	1.29065i	0.0242012	+	0.100477i
$166$		0			0
$167$	−0.387318	+	1.19204i	−0.0299716	+	0.0922431i	−0.964923	−	0.262532i	$-0.915443\pi$
$167$	−0.387318	+	1.19204i	−0.0299716	+	0.0922431i	0.934952	+	0.354775i	$0.115443\pi$
$168$		0			0
$169$	−2.85632	+	8.79086i	−0.219717	+	0.676220i
$170$		0			0
$171$	2.98287	+	9.18034i	0.228106	+	0.702038i
$172$		0			0
$173$	19.4515	+	14.1323i	1.47887	+	1.07446i	0.977919	+	0.208985i	$0.0670159\pi$
$173$	19.4515	+	14.1323i	1.47887	+	1.07446i	0.500950	+	0.865476i	$0.332984\pi$
$174$		0			0
$175$	−1.91855	+	3.77921i	−0.145029	+	0.285682i
$176$		0			0
$177$	4.99523	+	3.62924i	0.375464	+	0.272791i
$178$		0			0
$179$	0.546782	+	1.68282i	0.0408684	+	0.125780i	0.969409	−	0.245451i	$-0.0789359\pi$
$179$	0.546782	+	1.68282i	0.0408684	+	0.125780i	−0.928541	+	0.371231i	$0.878936\pi$
$180$		0			0
$181$	2.48932	−	7.66135i	0.185030	−	0.569464i	−0.814919	−	0.579575i	$-0.803219\pi$
$181$	2.48932	−	7.66135i	0.185030	−	0.569464i	0.999949	+	0.0101113i	$0.00321859\pi$
$182$		0			0
$183$	1.77861	−	5.47401i	0.131479	−	0.404651i
$184$		0			0
$185$	4.09230	−	9.90043i	0.300872	−	0.727894i
$186$		0			0
$187$	0.537737	−	0.390689i	0.0393232	−	0.0285700i
$188$		0			0
$189$	2.29937	+	1.67059i	0.167255	+	0.121518i
$190$		0			0
$191$	−18.2461	+	13.2565i	−1.32024	+	0.959209i	−0.320309	+	0.947313i	$0.603787\pi$
$191$	−18.2461	+	13.2565i	−1.32024	+	0.959209i	−0.999929	+	0.0118958i	$0.996213\pi$
$192$		0			0
$193$	−2.13266			−0.153512			−0.0767562	−	0.997050i	$-0.524456\pi$
$193$	−2.13266			−0.153512			−0.0767562	+	0.997050i	$0.524456\pi$
$194$		0			0
$195$	−2.56535	−	0.199984i	−0.183708	−	0.0143212i
$196$		0			0
$197$	−1.94231	−	5.97782i	−0.138384	−	0.425902i	0.857717	−	0.514122i	$-0.171882\pi$
$197$	−1.94231	−	5.97782i	−0.138384	−	0.425902i	−0.996101	+	0.0882198i	$0.971882\pi$
$198$		0			0
$199$	−14.9271			−1.05816			−0.529078	−	0.848573i	$-0.677462\pi$
$199$	−14.9271			−1.05816			−0.529078	+	0.848573i	$0.677462\pi$
$200$		0			0
$201$	3.22696			0.227612
$202$		0			0
$203$	−2.41206	−	7.42357i	−0.169294	−	0.521033i
$204$		0			0
$205$	1.39647	−	3.37845i	0.0975336	−	0.235961i
$206$		0			0
$207$	−7.80715			−0.542634
$208$		0			0
$209$	−2.94966	+	2.14305i	−0.204032	+	0.148238i
$210$		0			0
$211$	−15.9707	−	11.6034i	−1.09947	−	0.798812i	−0.118497	−	0.992954i	$-0.537808\pi$
$211$	−15.9707	−	11.6034i	−1.09947	−	0.798812i	−0.980973	+	0.194142i	$0.937808\pi$
$212$		0			0
$213$	2.90797	−	2.11276i	0.199251	−	0.144764i
$214$		0			0
$215$	−16.7361	+	10.2730i	−1.14139	+	0.700612i
$216$		0			0
$217$	2.11298	−	6.50307i	0.143438	−	0.441457i
$218$		0			0
$219$	−1.55005	+	4.77056i	−0.104743	+	0.322365i
$220$		0			0
$221$	0.398108	+	1.22525i	0.0267796	+	0.0824192i
$222$		0			0
$223$	−13.0755	−	9.49992i	−0.875601	−	0.636162i	0.0564827	−	0.998404i	$-0.482011\pi$
$223$	−13.0755	−	9.49992i	−0.875601	−	0.636162i	−0.932084	+	0.362242i	$0.882011\pi$
$224$		0			0
$225$	−2.09019	−	13.0715i	−0.139346	−	0.871434i
$226$		0			0
$227$	3.67114	+	2.66724i	0.243662	+	0.177031i	0.702913	−	0.711276i	$-0.251882\pi$
$227$	3.67114	+	2.66724i	0.243662	+	0.177031i	−0.459251	+	0.888306i	$0.651882\pi$
$228$		0			0
$229$	3.65550	+	11.2505i	0.241562	+	0.743453i	0.996183	+	0.0872910i	$0.0278210\pi$
$229$	3.65550	+	11.2505i	0.241562	+	0.743453i	−0.754620	+	0.656162i	$0.772179\pi$
$230$		0			0
$231$	−0.155516	+	0.478630i	−0.0102322	+	0.0314916i
$232$		0			0
$233$	6.94716	−	21.3812i	0.455124	−	1.40073i	−0.415866	−	0.909426i	$-0.636521\pi$
$233$	6.94716	−	21.3812i	0.455124	−	1.40073i	0.870990	−	0.491301i	$-0.163479\pi$
$234$		0			0
$235$	−20.9988	−	17.9078i	−1.36981	−	1.16818i
$236$		0			0
$237$	−2.27521	+	1.65304i	−0.147791	+	0.107376i
$238$		0			0
$239$	10.3481	+	7.51835i	0.669364	+	0.486322i	0.869812	−	0.493383i	$-0.164240\pi$
$239$	10.3481	+	7.51835i	0.669364	+	0.486322i	−0.200448	+	0.979704i	$0.564240\pi$
$240$		0			0
$241$	15.1442	−	11.0029i	0.975526	−	0.708761i	0.0188220	−	0.999823i	$-0.494008\pi$
$241$	15.1442	−	11.0029i	0.975526	−	0.708761i	0.956704	+	0.291061i	$0.0940084\pi$
$242$		0			0
$243$	−13.5925			−0.871961
$244$		0			0
$245$	11.9706	−	7.34778i	0.764771	−	0.469432i
$246$		0			0
$247$	−2.18375	−	6.72089i	−0.138949	−	0.427640i
$248$		0			0
$249$	7.98695			0.506153
$250$		0			0
$251$	22.3525			1.41088			0.705440	−	0.708769i	$-0.250749\pi$
$251$	22.3525			1.41088			0.705440	+	0.708769i	$0.250749\pi$
$252$		0			0
$253$	−0.911248	−	2.80453i	−0.0572897	−	0.176319i
$254$		0			0
$255$	0.752033	−	0.461613i	0.0470941	−	0.0289073i
$256$		0			0
$257$	−4.13475			−0.257919			−0.128959	−	0.991650i	$-0.541164\pi$
$257$	−4.13475			−0.257919			−0.128959	+	0.991650i	$0.541164\pi$
$258$		0			0
$259$	3.28550	−	2.38705i	0.204151	−	0.148324i
$260$		0			0
$261$	19.7233	+	14.3298i	1.22084	+	0.886993i
$262$		0			0
$263$	−0.312975	+	0.227390i	−0.0192989	+	0.0140215i	−0.597393	−	0.801949i	$-0.703797\pi$
$263$	−0.312975	+	0.227390i	−0.0192989	+	0.0140215i	0.578094	+	0.815970i	$0.303797\pi$
$264$		0			0
$265$	3.20637	+	2.73439i	0.196966	+	0.167972i
$266$		0			0
$267$	2.17768	−	6.70220i	0.133272	−	0.410168i
$268$		0			0
$269$	4.73914	−	14.5856i	0.288950	−	0.889298i	−0.696236	−	0.717813i	$-0.745143\pi$
$269$	4.73914	−	14.5856i	0.288950	−	0.889298i	0.985187	−	0.171485i	$-0.0548566\pi$
$270$		0			0
$271$	−3.99489	−	12.2950i	−0.242672	−	0.746869i	−0.996011	−	0.0892353i	$-0.971558\pi$
$271$	−3.99489	−	12.2950i	−0.242672	−	0.746869i	0.753338	−	0.657633i	$-0.228442\pi$
$272$		0			0
$273$	−0.789146	−	0.573348i	−0.0477613	−	0.0347006i
$274$		0			0
$275$	4.45166	−	2.27655i	0.268445	−	0.137281i
$276$		0			0
$277$	−8.86986	−	6.44433i	−0.532938	−	0.387202i	0.288518	−	0.957475i	$-0.406838\pi$
$277$	−8.86986	−	6.44433i	−0.532938	−	0.387202i	−0.821456	+	0.570272i	$0.806838\pi$
$278$		0			0
$279$	6.59948	+	20.3111i	0.395101	+	1.21600i
$280$		0			0
$281$	3.18797	−	9.81155i	0.190178	−	0.585308i	−0.809821	−	0.586677i	$-0.800436\pi$
$281$	3.18797	−	9.81155i	0.190178	−	0.585308i	0.999999	+	0.00136916i	$0.000435816\pi$
$282$		0			0
$283$	6.80463	−	20.9425i	0.404493	−	1.24490i	−0.516825	−	0.856091i	$-0.672886\pi$
$283$	6.80463	−	20.9425i	0.404493	−	1.24490i	0.921318	−	0.388810i	$-0.127114\pi$
$284$		0			0
$285$	−4.12514	+	2.53210i	−0.244352	+	0.149988i
$286$		0			0
$287$	1.12115	−	0.814566i	0.0661796	−	0.0480823i
$288$		0			0
$289$	13.3959	+	9.73267i	0.787992	+	0.572510i
$290$		0			0
$291$	−3.58643	+	2.60569i	−0.210240	+	0.152748i
$292$		0			0
$293$	28.5400			1.66733			0.833663	−	0.552273i	$-0.186239\pi$
$293$	28.5400			1.66733			0.833663	+	0.552273i	$0.186239\pi$
$294$		0			0
$295$	8.88328	−	21.4912i	0.517205	−	1.25126i
$296$		0			0
$297$	−1.03612	−	3.18885i	−0.0601219	−	0.185036i
$298$		0			0
$299$	5.71558			0.330540
$300$		0			0
$301$	−7.44432			−0.429083
$302$		0			0
$303$	−2.62690	−	8.08477i	−0.150911	−	0.464458i
$304$		0			0
$305$	−21.6122	−	1.68480i	−1.23751	−	0.0964712i
$306$		0			0
$307$	−15.0349			−0.858089			−0.429045	−	0.903283i	$-0.641150\pi$
$307$	−15.0349			−0.858089			−0.429045	+	0.903283i	$0.641150\pi$
$308$		0			0
$309$	−2.39181	+	1.73775i	−0.136065	+	0.0988573i
$310$		0			0
$311$	−4.44091	−	3.22651i	−0.251821	−	0.182958i	0.454713	−	0.890638i	$-0.349742\pi$
$311$	−4.44091	−	3.22651i	−0.251821	−	0.182958i	−0.706533	+	0.707680i	$0.749742\pi$
$312$		0			0
$313$	−10.9784	+	7.97625i	−0.620534	+	0.450844i	−0.853108	−	0.521734i	$-0.825285\pi$
$313$	−10.9784	+	7.97625i	−0.620534	+	0.450844i	0.232574	+	0.972579i	$0.425285\pi$
$314$		0			0
$315$	1.91694	−	4.63762i	0.108007	−	0.261300i
$316$		0			0
$317$	1.22977	−	3.78485i	0.0690709	−	0.212578i	−0.910563	−	0.413370i	$-0.864351\pi$
$317$	1.22977	−	3.78485i	0.0690709	−	0.212578i	0.979634	+	0.200792i	$0.0643515\pi$
$318$		0			0
$319$	−2.84555	+	8.75770i	−0.159320	+	0.490337i
$320$		0			0
$321$	3.23592	+	9.95913i	0.180611	+	0.555865i
$322$		0			0
$323$	1.96058	+	1.42444i	0.109090	+	0.0792582i
$324$		0			0
$325$	1.53022	+	9.56959i	0.0848813	+	0.530825i
$326$		0			0
$327$	−6.01069	−	4.36702i	−0.332392	−	0.241497i
$328$		0			0
$329$	−3.23292	−	9.94991i	−0.178237	−	0.548556i
$330$		0			0
$331$	−2.28262	+	7.02517i	−0.125464	+	0.386138i	−0.993985	−	0.109513i	$-0.965071\pi$
$331$	−2.28262	+	7.02517i	−0.125464	+	0.386138i	0.868521	+	0.495652i	$0.165071\pi$
$332$		0			0
$333$	−3.91960	+	12.0633i	−0.214793	+	0.661063i
$334$		0			0
$335$	−2.84598	−	11.8158i	−0.155492	−	0.645564i
$336$		0			0
$337$	26.5469	−	19.2875i	1.44610	−	1.05066i	0.459381	−	0.888239i	$-0.348071\pi$
$337$	26.5469	−	19.2875i	1.44610	−	1.05066i	0.986722	−	0.162416i	$-0.0519287\pi$
$338$		0			0
$339$	−8.59054	−	6.24139i	−0.466574	−	0.338986i
$340$		0			0
$341$	−6.52600	+	4.74142i	−0.353403	+	0.256762i
$342$		0			0
$343$	11.2582			0.607886
$344$		0			0
$345$	−0.916714	−	3.80596i	−0.0493542	−	0.204906i
$346$		0			0
$347$	10.4904	+	32.2862i	0.563155	+	1.73321i	0.673369	+	0.739306i	$0.264846\pi$
$347$	10.4904	+	32.2862i	0.563155	+	1.73321i	−0.110214	+	0.993908i	$0.535154\pi$
$348$		0			0
$349$	−6.94679			−0.371853			−0.185927	−	0.982564i	$-0.559529\pi$
$349$	−6.94679			−0.371853			−0.185927	+	0.982564i	$0.559529\pi$
$350$		0			0
$351$	6.49881			0.346881
$352$		0			0
$353$	−0.563159	−	1.73323i	−0.0299740	−	0.0922503i	0.934950	−	0.354779i	$-0.115444\pi$
$353$	−0.563159	−	1.73323i	−0.0299740	−	0.0922503i	−0.964924	+	0.262528i	$0.915444\pi$
$354$		0			0
$355$	−10.3007	−	8.78442i	−0.546704	−	0.466229i
$356$		0			0
$357$	0.334508			0.0177040
$358$		0			0
$359$	−21.0608	+	15.3016i	−1.11155	+	0.807586i	−0.982906	−	0.184106i	$-0.941061\pi$
$359$	−21.0608	+	15.3016i	−1.11155	+	0.807586i	−0.128640	+	0.991691i	$0.541061\pi$
$360$		0			0
$361$	4.61692	+	3.35439i	0.242996	+	0.176547i
$362$		0			0
$363$	0.480318	−	0.348971i	0.0252101	−	0.0183162i
$364$		0			0
$365$	18.8348	+	1.46829i	0.985860	+	0.0768536i
$366$		0			0
$367$	−6.13593	+	18.8845i	−0.320293	+	0.985761i	0.653228	+	0.757162i	$0.273414\pi$
$367$	−6.13593	+	18.8845i	−0.320293	+	0.985761i	−0.973521	+	0.228599i	$0.926586\pi$
$368$		0			0
$369$	−1.33753	+	4.11651i	−0.0696293	+	0.214297i
$370$		0			0
$371$	0.493644	+	1.51928i	0.0256287	+	0.0788771i
$372$		0			0
$373$	−11.0510	−	8.02906i	−0.572202	−	0.415729i	0.263703	−	0.964604i	$-0.415056\pi$
$373$	−11.0510	−	8.02906i	−0.572202	−	0.415729i	−0.835904	+	0.548875i	$0.815056\pi$
$374$		0			0
$375$	6.12689	−	2.55382i	0.316391	−	0.131878i
$376$		0			0
$377$	−14.4393	−	10.4908i	−0.743663	−	0.540303i
$378$		0			0
$379$	8.29221	+	25.5208i	0.425942	+	1.31091i	0.902089	+	0.431549i	$0.142033\pi$
$379$	8.29221	+	25.5208i	0.425942	+	1.31091i	−0.476147	+	0.879365i	$0.657967\pi$
$380$		0			0
$381$	−1.95354	+	6.01237i	−0.100083	+	0.308023i
$382$		0			0
$383$	6.77448	−	20.8497i	0.346160	−	1.06537i	−0.614801	−	0.788683i	$-0.710764\pi$
$383$	6.77448	−	20.8497i	0.346160	−	1.06537i	0.960960	−	0.276687i	$-0.0892365\pi$
$384$		0			0
$385$	1.88970	+	0.147313i	0.0963079	+	0.00750778i
$386$		0			0
$387$	18.8104	−	13.6665i	0.956186	−	0.694710i
$388$		0			0
$389$	−12.4524	−	9.04718i	−0.631361	−	0.458710i	0.225511	−	0.974241i	$-0.427595\pi$
$389$	−12.4524	−	9.04718i	−0.631361	−	0.458710i	−0.856871	+	0.515530i	$0.827595\pi$
$390$		0			0
$391$	−1.58571	+	1.15209i	−0.0801929	+	0.0582635i
$392$		0			0
$393$	−1.70129			−0.0858188
$394$		0			0
$395$	8.05933	+	6.87299i	0.405509	+	0.345818i
$396$		0			0
$397$	2.98165	+	9.17657i	0.149645	+	0.460559i	0.997579	−	0.0695424i	$-0.0221539\pi$
$397$	2.98165	+	9.17657i	0.149645	+	0.460559i	−0.847934	+	0.530101i	$0.822154\pi$
$398$		0			0
$399$	−1.83488			−0.0918590
$400$		0			0
$401$	27.5670			1.37663			0.688315	−	0.725412i	$-0.258351\pi$
$401$	27.5670			1.37663			0.688315	+	0.725412i	$0.258351\pi$
$402$		0			0
$403$	−4.83145	−	14.8697i	−0.240672	−	0.740711i
$404$		0			0
$405$	3.11647	+	12.9388i	0.154858	+	0.642932i
$406$		0			0
$407$	−4.79094			−0.237478
$408$		0			0
$409$	11.7961	−	8.57039i	0.583281	−	0.423779i	−0.256624	−	0.966511i	$-0.582610\pi$
$409$	11.7961	−	8.57039i	0.583281	−	0.423779i	0.839906	+	0.542733i	$0.182610\pi$
$410$		0			0
$411$	6.72519	+	4.88613i	0.331729	+	0.241015i
$412$		0			0
$413$	7.13193	−	5.18165i	0.350939	−	0.254972i
$414$		0			0
$415$	−7.04400	−	29.2449i	−0.345776	−	1.43557i
$416$		0			0
$417$	−0.938530	+	2.88850i	−0.0459600	+	0.141450i
$418$		0			0
$419$	−6.06601	+	18.6693i	−0.296344	+	0.912053i	0.686423	+	0.727203i	$0.259180\pi$
$419$	−6.06601	+	18.6693i	−0.296344	+	0.912053i	−0.982767	+	0.184850i	$0.940820\pi$
$420$		0			0
$421$	5.94307	+	18.2909i	0.289647	+	0.891443i	0.984967	+	0.172742i	$0.0552628\pi$
$421$	5.94307	+	18.2909i	0.289647	+	0.891443i	−0.695320	+	0.718701i	$0.744737\pi$
$422$		0			0
$423$	26.4354	+	19.2064i	1.28533	+	0.933849i
$424$		0			0
$425$	−2.35348	−	2.34651i	−0.114160	−	0.113823i
$426$		0			0
$427$	−6.64828	−	4.83026i	−0.321733	−	0.233753i
$428$		0			0
$429$	0.355598	+	1.09442i	0.0171684	+	0.0528390i
$430$		0			0
$431$	10.1382	−	31.2021i	0.488339	−	1.50295i	−0.338747	−	0.940878i	$-0.610003\pi$
$431$	10.1382	−	31.2021i	0.488339	−	1.50295i	0.827086	−	0.562076i	$-0.189997\pi$
$432$		0			0
$433$	−11.0483	+	34.0030i	−0.530945	+	1.63408i	0.221305	+	0.975205i	$0.428968\pi$
$433$	−11.0483	+	34.0030i	−0.530945	+	1.63408i	−0.752251	+	0.658877i	$0.771032\pi$
$434$		0			0
$435$	−4.66983	+	11.2976i	−0.223901	+	0.541681i
$436$		0			0
$437$	8.69814	−	6.31957i	0.416088	−	0.302306i
$438$		0			0
$439$	4.93542	+	3.58579i	0.235555	+	0.171141i	0.699301	−	0.714828i	$-0.253495\pi$
$439$	4.93542	+	3.58579i	0.235555	+	0.171141i	−0.463746	+	0.885968i	$0.653495\pi$
$440$		0			0
$441$	−13.4542	+	9.77503i	−0.640675	+	0.465478i
$442$		0			0
$443$	−0.708578			−0.0336655			−0.0168328	−	0.999858i	$-0.505358\pi$
$443$	−0.708578			−0.0336655			−0.0168328	+	0.999858i	$0.505358\pi$
$444$		0			0
$445$	−26.4612	−	2.06281i	−1.25438	−	0.0977865i
$446$		0			0
$447$	1.94583	+	5.98865i	0.0920346	+	0.283254i
$448$		0			0
$449$	−15.7174			−0.741752			−0.370876	−	0.928682i	$-0.620943\pi$
$449$	−15.7174			−0.741752			−0.370876	+	0.928682i	$0.620943\pi$
$450$		0			0
$451$	−1.63487			−0.0769832
$452$		0			0
$453$	−0.586339	−	1.80456i	−0.0275486	−	0.0847858i
$454$		0			0
$455$	−1.40338	+	3.39518i	−0.0657915	+	0.159168i
$456$		0			0
$457$	−37.4678			−1.75267			−0.876336	−	0.481701i	$-0.840019\pi$
$457$	−37.4678			−1.75267			−0.876336	+	0.481701i	$0.840019\pi$
$458$		0			0
$459$	−1.80301	+	1.30996i	−0.0841573	+	0.0611439i
$460$		0			0
$461$	−25.2682	−	18.3584i	−1.17686	−	0.855036i	−0.185043	−	0.982730i	$-0.559242\pi$
$461$	−25.2682	−	18.3584i	−1.17686	−	0.855036i	−0.991814	+	0.127694i	$0.959242\pi$
$462$		0			0
$463$	−14.2971	+	10.3875i	−0.664444	+	0.482747i	−0.868161	−	0.496283i	$-0.834698\pi$
$463$	−14.2971	+	10.3875i	−0.664444	+	0.482747i	0.203717	+	0.979030i	$0.434698\pi$
$464$		0			0
$465$	−9.12670	+	5.60216i	−0.423240	+	0.259794i
$466$		0			0
$467$	−4.46198	+	13.7326i	−0.206476	+	0.635467i	0.793174	+	0.608995i	$0.208427\pi$
$467$	−4.46198	+	13.7326i	−0.206476	+	0.635467i	−0.999650	+	0.0264716i	$0.991573\pi$
$468$		0			0
$469$	1.42373	−	4.38179i	0.0657417	−	0.202332i
$470$		0			0
$471$	1.98109	+	6.09717i	0.0912839	+	0.280943i
$472$		0			0
$473$	7.10492	+	5.16203i	0.326685	+	0.237350i
$474$		0			0
$475$	12.9096	+	12.8714i	0.592332	+	0.590579i
$476$		0			0
$477$	−4.03650	−	2.93269i	−0.184818	−	0.134278i
$478$		0			0
$479$	7.39461	+	22.7583i	0.337868	+	1.03985i	0.965292	+	0.261174i	$0.0841096\pi$
$479$	7.39461	+	22.7583i	0.337868	+	1.03985i	−0.627423	+	0.778678i	$0.715890\pi$
$480$		0			0
$481$	2.86952	−	8.83147i	0.130839	−	0.402680i
$482$		0			0
$483$	0.458596	−	1.41141i	0.0208668	−	0.0642216i
$484$		0			0
$485$	12.7040	+	10.8339i	0.576857	+	0.491943i
$486$		0			0
$487$	6.75979	−	4.91128i	0.306316	−	0.222551i	−0.423998	−	0.905663i	$-0.639374\pi$
$487$	6.75979	−	4.91128i	0.306316	−	0.222551i	0.730314	+	0.683112i	$0.239374\pi$
$488$		0			0
$489$	−9.69773	−	7.04582i	−0.438547	−	0.318623i
$490$		0			0
$491$	6.83580	−	4.96650i	0.308495	−	0.224135i	−0.422755	−	0.906244i	$-0.638937\pi$
$491$	6.83580	−	4.96650i	0.308495	−	0.224135i	0.731251	+	0.682109i	$0.238937\pi$
$492$		0			0
$493$	6.12063			0.275659
$494$		0			0
$495$	−5.04535	+	3.09694i	−0.226772	+	0.139197i
$496$		0			0
$497$	−1.58587	−	4.88079i	−0.0711358	−	0.218933i
$498$		0			0
$499$	20.6004			0.922202			0.461101	−	0.887348i	$-0.347455\pi$
$499$	20.6004			0.922202			0.461101	+	0.887348i	$0.347455\pi$
$500$		0			0
$501$	0.744143			0.0332459
$502$		0			0
$503$	7.87119	+	24.2250i	0.350959	+	1.08014i	0.958316	+	0.285711i	$0.0922299\pi$
$503$	7.87119	+	24.2250i	0.350959	+	1.08014i	−0.607357	+	0.794429i	$0.707770\pi$
$504$		0			0
$505$	−27.2862	+	16.7489i	−1.21422	+	0.745315i
$506$		0			0
$507$	5.48777			0.243720
$508$		0			0
$509$	−8.26940	+	6.00807i	−0.366535	+	0.266303i	−0.755773	−	0.654834i	$-0.772738\pi$
$509$	−8.26940	+	6.00807i	−0.366535	+	0.266303i	0.389238	+	0.921137i	$0.372738\pi$
$510$		0			0
$511$	5.79392	+	4.20953i	0.256308	+	0.186219i
$512$		0			0
$513$	9.89009	−	7.18557i	0.436658	−	0.317251i
$514$		0			0
$515$	8.47235	+	7.22521i	0.373336	+	0.318381i
$516$		0			0
$517$	−3.81393	+	11.7381i	−0.167736	+	0.516239i
$518$		0			0
$519$	4.41111	−	13.5760i	0.193626	−	0.595921i
$520$		0			0
$521$	3.42107	+	10.5290i	0.149880	+	0.461283i	0.997606	−	0.0691511i	$-0.0220291\pi$
$521$	3.42107	+	10.5290i	0.149880	+	0.461283i	−0.847726	+	0.530434i	$0.822029\pi$
$522$		0			0
$523$	−7.57263	−	5.50184i	−0.331128	−	0.240579i	0.409781	−	0.912184i	$-0.365605\pi$
$523$	−7.57263	−	5.50184i	−0.331128	−	0.240579i	−0.740909	+	0.671605i	$0.765605\pi$
$524$		0			0
$525$	2.48591	+	0.389953i	0.108494	+	0.0170189i
$526$		0			0
$527$	4.33770	+	3.15152i	0.188953	+	0.137282i
$528$		0			0
$529$	−4.42025	−	13.6041i	−0.192185	−	0.591484i
$530$		0			0
$531$	−8.50839	+	26.1861i	−0.369233	+	1.13638i
$532$		0			0
$533$	0.979203	−	3.01368i	0.0424140	−	0.130537i
$534$		0			0
$535$	33.6123	−	20.6319i	1.45318	−	0.891995i
$536$		0			0
$537$	0.849886	−	0.617478i	0.0366753	−	0.0266461i
$538$		0			0
$539$	−5.08181	−	3.69215i	−0.218889	−	0.159032i
$540$		0			0
$541$	17.0431	−	12.3825i	0.732739	−	0.532366i	−0.157689	−	0.987489i	$-0.550404\pi$
$541$	17.0431	−	12.3825i	0.732739	−	0.532366i	0.890429	+	0.455122i	$0.150404\pi$
$542$		0			0
$543$	−4.78266			−0.205244
$544$		0			0
$545$	−10.6891	+	25.8600i	−0.457872	+	1.10772i
$546$		0			0
$547$	8.21320	+	25.2776i	0.351171	+	1.08079i	0.958196	+	0.286111i	$0.0923627\pi$
$547$	8.21320	+	25.2776i	0.351171	+	1.08079i	−0.607025	+	0.794683i	$0.707637\pi$
$548$		0			0
$549$	25.6665			1.09542
$550$		0			0
$551$	−33.5736			−1.43028
$552$		0			0
$553$	1.24079	+	3.81876i	0.0527638	+	0.162390i
$554$		0			0
$555$	−6.34105	−	0.494322i	−0.269162	−	0.0209828i
$556$		0			0
$557$	−7.28426			−0.308644			−0.154322	−	0.988021i	$-0.549319\pi$
$557$	−7.28426			−0.308644			−0.154322	+	0.988021i	$0.549319\pi$
$558$		0			0
$559$	−13.7710	+	10.0052i	−0.582451	+	0.423175i
$560$		0			0
$561$	−0.319257	−	0.231954i	−0.0134791	−	0.00979311i
$562$		0			0
$563$	−16.0027	+	11.6266i	−0.674432	+	0.490003i	−0.871506	−	0.490385i	$-0.836856\pi$
$563$	−16.0027	+	11.6266i	−0.674432	+	0.490003i	0.197074	+	0.980389i	$0.436856\pi$
$564$		0			0
$565$	−15.2770	+	36.9594i	−0.642709	+	1.55490i
$566$		0			0
$567$	−1.55905	+	4.79825i	−0.0654738	+	0.201508i
$568$		0			0
$569$	−10.1315	+	31.1817i	−0.424736	+	1.30720i	0.478510	+	0.878082i	$0.341177\pi$
$569$	−10.1315	+	31.1817i	−0.424736	+	1.30720i	−0.903246	+	0.429122i	$0.858823\pi$
$570$		0			0
$571$	4.63043	+	14.2510i	0.193778	+	0.596386i	0.999989	+	0.00475824i	$0.00151460\pi$
$571$	4.63043	+	14.2510i	0.193778	+	0.596386i	−0.806211	+	0.591628i	$0.798485\pi$
$572$		0			0
$573$	10.8328	+	7.87047i	0.452546	+	0.328794i
$574$		0			0
$575$	−13.1273	+	6.71324i	−0.547448	+	0.279961i
$576$		0			0
$577$	−29.8213	−	21.6664i	−1.24148	−	0.901985i	−0.243780	−	0.969831i	$-0.578387\pi$
$577$	−29.8213	−	21.6664i	−1.24148	−	0.901985i	−0.997696	+	0.0678461i	$0.978387\pi$
$578$		0			0
$579$	0.391269	+	1.20420i	0.0162606	+	0.0500449i
$580$		0			0
$581$	3.52384	−	10.8453i	0.146193	−	0.449937i
$582$		0			0
$583$	0.582359	−	1.79232i	0.0241189	−	0.0742302i
$584$		0			0
$585$	−2.68691	−	11.1554i	−0.111090	−	0.461217i
$586$		0			0
$587$	0.787058	−	0.571831i	0.0324854	−	0.0236020i	−0.571424	−	0.820655i	$-0.693609\pi$
$587$	0.787058	−	0.571831i	0.0324854	−	0.0236020i	0.603909	+	0.797053i	$0.293609\pi$
$588$		0			0
$589$	−23.7937	−	17.2871i	−0.980401	−	0.712303i
$590$		0			0
$591$	−3.01902	+	2.19344i	−0.124186	+	0.0902262i
$592$		0			0
$593$	−14.1863			−0.582562			−0.291281	−	0.956638i	$-0.594081\pi$
$593$	−14.1863			−0.582562			−0.291281	+	0.956638i	$0.594081\pi$
$594$		0			0
$595$	−0.295015	−	1.22483i	−0.0120944	−	0.0502130i
$596$		0			0
$597$	2.73861	+	8.42857i	0.112084	+	0.344958i
$598$		0			0
$599$	17.0820			0.697953			0.348977	−	0.937131i	$-0.386529\pi$
$599$	17.0820			0.697953			0.348977	+	0.937131i	$0.386529\pi$
$600$		0			0
$601$	30.0302			1.22496			0.612478	−	0.790488i	$-0.290173\pi$
$601$	30.0302			1.22496			0.612478	+	0.790488i	$0.290173\pi$
$602$		0			0
$603$	4.44675	+	13.6857i	0.181086	+	0.557325i
$604$		0			0
$605$	−1.70140	−	1.45095i	−0.0691716	−	0.0589895i
$606$		0			0
$607$	29.8206			1.21038			0.605191	−	0.796080i	$-0.293097\pi$
$607$	29.8206			1.21038			0.605191	+	0.796080i	$0.293097\pi$
$608$		0			0
$609$	−3.74917	+	2.72393i	−0.151924	+	0.110379i
$610$		0			0
$611$	−19.3532	−	14.0609i	−0.782948	−	0.568845i
$612$		0			0
$613$	12.8274	−	9.31966i	0.518094	−	0.376418i	−0.297791	−	0.954631i	$-0.596250\pi$
$613$	12.8274	−	9.31966i	0.518094	−	0.376418i	0.815886	+	0.578213i	$0.196250\pi$
$614$		0			0
$615$	−2.16384	−	0.168684i	−0.0872543	−	0.00680200i
$616$		0			0
$617$	−5.26408	+	16.2012i	−0.211924	+	0.652235i	0.787434	+	0.616399i	$0.211409\pi$
$617$	−5.26408	+	16.2012i	−0.211924	+	0.652235i	−0.999358	+	0.0358356i	$0.988591\pi$
$618$		0			0
$619$	10.2548	−	31.5610i	0.412174	−	1.26854i	−0.502580	−	0.864531i	$-0.667616\pi$
$619$	10.2548	−	31.5610i	0.412174	−	1.26854i	0.914754	−	0.404011i	$-0.132384\pi$
$620$		0			0
$621$	3.05538	+	9.40348i	0.122608	+	0.377349i
$622$		0			0
$623$	−8.13993	−	5.91401i	−0.326119	−	0.236940i
$624$		0			0
$625$	−14.7545	−	20.1818i	−0.590181	−	0.807271i
$626$		0			0
$627$	1.75123	+	1.27234i	0.0699373	+	0.0508124i
$628$		0			0
$629$	0.984046	+	3.02858i	0.0392365	+	0.120757i
$630$		0			0
$631$	0.597601	−	1.83923i	0.0237901	−	0.0732184i	−0.938457	−	0.345397i	$-0.887744\pi$
$631$	0.597601	−	1.83923i	0.0237901	−	0.0732184i	0.962247	+	0.272179i	$0.0877442\pi$
$632$		0			0
$633$	−3.62177	+	11.1467i	−0.143952	+	0.443040i
$634$		0			0
$635$	23.7376	+	1.85049i	0.941999	+	0.0734345i
$636$		0			0
$637$	9.84974	−	7.15625i	0.390261	−	0.283541i
$638$		0			0
$639$	12.9675	+	9.42146i	0.512987	+	0.372707i
$640$		0			0
$641$	−0.280060	+	0.203475i	−0.0110617	+	0.00803679i	−0.593302	−	0.804980i	$-0.702176\pi$
$641$	−0.280060	+	0.203475i	−0.0110617	+	0.00803679i	0.582241	+	0.813016i	$0.302176\pi$
$642$		0			0
$643$	7.43954			0.293387			0.146693	−	0.989182i	$-0.453137\pi$
$643$	7.43954			0.293387			0.146693	+	0.989182i	$0.453137\pi$
$644$		0			0
$645$	8.87111	+	7.56528i	0.349300	+	0.297883i
$646$		0			0
$647$	−1.54909	−	4.76761i	−0.0609010	−	0.187434i	0.915977	−	0.401230i	$-0.131417\pi$
$647$	−1.54909	−	4.76761i	−0.0609010	−	0.187434i	−0.976878	+	0.213796i	$0.931417\pi$
$648$		0			0
$649$	−10.3998			−0.408229
$650$		0			0
$651$	−4.05960			−0.159108
$652$		0			0
$653$	11.4001	+	35.0860i	0.446122	+	1.37302i	0.881249	+	0.472653i	$0.156704\pi$
$653$	11.4001	+	35.0860i	0.446122	+	1.37302i	−0.435126	+	0.900369i	$0.643296\pi$
$654$		0			0
$655$	1.50043	+	6.22941i	0.0586268	+	0.243403i
$656$		0			0
$657$	−22.3682			−0.872665
$658$		0			0
$659$	20.2546	−	14.7159i	0.789009	−	0.573249i	−0.118660	−	0.992935i	$-0.537860\pi$
$659$	20.2546	−	14.7159i	0.789009	−	0.573249i	0.907669	+	0.419686i	$0.137860\pi$
$660$		0			0
$661$	−13.9719	−	10.1512i	−0.543443	−	0.394834i	0.281919	−	0.959438i	$-0.409029\pi$
$661$	−13.9719	−	10.1512i	−0.543443	−	0.394834i	−0.825362	+	0.564604i	$0.809029\pi$
$662$		0			0
$663$	0.618795	−	0.449581i	0.0240320	−	0.0174603i
$664$		0			0
$665$	1.61825	+	6.71856i	0.0627531	+	0.260535i
$666$		0			0
$667$	8.39112	−	25.8252i	0.324906	−	0.999957i
$668$		0			0
$669$	−2.96520	+	9.12596i	−0.114641	+	0.352830i
$670$		0			0
$671$	2.99579	+	9.22009i	0.115651	+	0.355937i
$672$		0			0
$673$	6.06468	+	4.40624i	0.233776	+	0.169848i	0.698506	−	0.715604i	$-0.253849\pi$
$673$	6.06468	+	4.40624i	0.233776	+	0.169848i	−0.464730	+	0.885453i	$0.653849\pi$
$674$		0			0
$675$	−14.9262	+	7.63319i	−0.574511	+	0.293802i
$676$		0			0
$677$	23.9470	+	17.3985i	0.920357	+	0.668678i	0.943613	−	0.331051i	$-0.107403\pi$
$677$	23.9470	+	17.3985i	0.920357	+	0.668678i	−0.0232559	+	0.999730i	$0.507403\pi$
$678$		0			0
$679$	1.95587	+	6.01953i	0.0750592	+	0.231009i
$680$		0			0
$681$	0.832523	−	2.56224i	0.0319024	−	0.0981854i
$682$		0			0
$683$	10.3902	−	31.9778i	0.397570	−	1.22360i	−0.529371	−	0.848390i	$-0.677572\pi$
$683$	10.3902	−	31.9778i	0.397570	−	1.22360i	0.926942	−	0.375206i	$-0.122428\pi$
$684$		0			0
$685$	11.9598	−	28.9341i	0.456959	−	1.10551i
$686$		0			0
$687$	5.68189	−	4.12814i	0.216778	−	0.157498i
$688$		0			0
$689$	2.95510	+	2.14700i	0.112580	+	0.0817944i
$690$		0			0
$691$	−23.2660	+	16.9038i	−0.885082	+	0.643050i	−0.934591	−	0.355724i	$-0.884234\pi$
$691$	−23.2660	+	16.9038i	−0.885082	+	0.643050i	0.0495089	+	0.998774i	$0.484234\pi$
$692$		0			0
$693$	−2.24420			−0.0852501
$694$		0			0
$695$	11.4042	+	0.889025i	0.432586	+	0.0337226i
$696$		0			0
$697$	0.335799	+	1.03348i	0.0127193	+	0.0391459i
$698$		0			0
$699$	−13.3474			−0.504844
$700$		0			0
$701$	8.70805			0.328898			0.164449	−	0.986386i	$-0.447415\pi$
$701$	8.70805			0.328898			0.164449	+	0.986386i	$0.447415\pi$
$702$		0			0
$703$	−5.39781	−	16.6127i	−0.203582	−	0.626561i
$704$		0			0
$705$	−6.25904	+	15.1424i	−0.235729	+	0.570295i
$706$		0			0
$707$	−12.1371			−0.456461
$708$		0			0
$709$	−27.5148	+	19.9907i	−1.03334	+	0.750767i	−0.968975	−	0.247160i	$-0.920503\pi$
$709$	−27.5148	+	19.9907i	−1.03334	+	0.750767i	−0.0643668	+	0.997926i	$0.520503\pi$
$710$		0			0
$711$	−10.1459	−	7.37141i	−0.380500	−	0.276449i
$712$		0			0
$713$	19.2443	−	13.9818i	0.720703	−	0.523621i
$714$		0			0
$715$	3.69368	−	2.26726i	0.138136	−	0.0847906i
$716$		0			0
$717$	2.34670	−	7.22239i	0.0876390	−	0.269725i
$718$		0			0
$719$	−4.31841	+	13.2907i	−0.161050	+	0.495659i	−0.998723	−	0.0505111i	$-0.983915\pi$
$719$	−4.31841	+	13.2907i	−0.161050	+	0.495659i	0.837674	+	0.546171i	$0.183915\pi$
$720$		0			0
$721$	1.30438	+	4.01447i	0.0485776	+	0.149507i
$722$		0			0
$723$	−8.99122	−	6.53250i	−0.334387	−	0.242946i
$724$		0			0
$725$	45.4857	+	7.13513i	1.68930	+	0.264992i
$726$		0			0
$727$	−5.43309	−	3.94737i	−0.201502	−	0.146400i	0.482458	−	0.875919i	$-0.339744\pi$
$727$	−5.43309	−	3.94737i	−0.201502	−	0.146400i	−0.683961	+	0.729519i	$0.739744\pi$
$728$		0			0
$729$	−3.02394	−	9.30672i	−0.111998	−	0.344693i
$730$		0			0
$731$	1.80383	−	5.55163i	0.0667172	−	0.205334i
$732$		0			0
$733$	−9.29774	+	28.6155i	−0.343420	+	1.05694i	0.619005	+	0.785387i	$0.287536\pi$
$733$	−9.29774	+	28.6155i	−0.343420	+	1.05694i	−0.962424	+	0.271550i	$0.912464\pi$
$734$		0			0
$735$	−6.34508	−	5.41108i	−0.234042	−	0.199591i
$736$		0			0
$737$	−4.39724	+	3.19478i	−0.161974	+	0.117681i
$738$		0			0
$739$	9.18838	+	6.67575i	0.338000	+	0.245571i	0.743818	−	0.668383i	$-0.233013\pi$
$739$	9.18838	+	6.67575i	0.338000	+	0.245571i	−0.405818	+	0.913954i	$0.633013\pi$
$740$		0			0
$741$	−3.39429	+	2.46609i	−0.124692	+	0.0905942i
$742$		0			0
$743$	−20.2060			−0.741286			−0.370643	−	0.928775i	$-0.620863\pi$
$743$	−20.2060			−0.741286			−0.370643	+	0.928775i	$0.620863\pi$
$744$		0			0
$745$	20.2118	−	12.4064i	0.740503	−	0.454536i
$746$		0			0
$747$	11.0060	+	33.8731i	0.402690	+	1.23935i
$748$		0			0
$749$	14.9509			0.546294
$750$		0			0
$751$	−11.7935			−0.430350			−0.215175	−	0.976575i	$-0.569032\pi$
$751$	−11.7935			−0.430350			−0.215175	+	0.976575i	$0.569032\pi$
$752$		0			0
$753$	−4.10091	−	12.6213i	−0.149445	−	0.459946i
$754$		0			0
$755$	−6.09044	+	3.73844i	−0.221654	+	0.136056i
$756$		0			0
$757$	−30.8273			−1.12044			−0.560218	−	0.828345i	$-0.689283\pi$
$757$	−30.8273			−1.12044			−0.560218	+	0.828345i	$0.689283\pi$
$758$		0			0
$759$	−1.41639	+	1.02907i	−0.0514117	+	0.0373528i
$760$		0			0
$761$	−2.10223	−	1.52736i	−0.0762057	−	0.0553666i	0.549030	−	0.835803i	$-0.314997\pi$
$761$	−2.10223	−	1.52736i	−0.0762057	−	0.0553666i	−0.625236	+	0.780436i	$0.714997\pi$
$762$		0			0
$763$	−8.58176	+	6.23501i	−0.310680	+	0.225723i
$764$		0			0
$765$	2.99403	+	2.55331i	0.108249	+	0.0923150i
$766$		0			0
$767$	6.22895	−	19.1707i	0.224914	−	0.692215i
$768$		0			0
$769$	15.9748	−	49.1653i	0.576065	−	1.77294i	−0.0564606	−	0.998405i	$-0.517982\pi$
$769$	15.9748	−	49.1653i	0.576065	−	1.77294i	0.632525	−	0.774540i	$-0.282018\pi$
$770$		0			0
$771$	0.758582	+	2.33467i	0.0273197	+	0.0840812i
$772$		0			0
$773$	−3.77892	−	2.74555i	−0.135918	−	0.0987504i	0.517749	−	0.855533i	$-0.326770\pi$
$773$	−3.77892	−	2.74555i	−0.135918	−	0.0987504i	−0.653667	+	0.756782i	$0.726770\pi$
$774$		0			0
$775$	28.5619	+	28.4774i	1.02597	+	1.02294i
$776$		0			0
$777$	−1.95062	−	1.41721i	−0.0699780	−	0.0508420i
$778$		0			0
$779$	−1.84196	−	5.66898i	−0.0659952	−	0.203112i
$780$		0			0
$781$	−1.87087	+	5.75794i	−0.0669450	+	0.206035i
$782$		0			0
$783$	9.54100	−	29.3642i	0.340968	−	1.04939i
$784$		0			0
$785$	20.5781	−	12.6312i	0.734463	−	0.450828i
$786$		0			0
$787$	21.9067	−	15.9162i	0.780890	−	0.567350i	−0.124356	−	0.992238i	$-0.539686\pi$
$787$	21.9067	−	15.9162i	0.780890	−	0.567350i	0.905246	+	0.424888i	$0.139686\pi$
$788$		0			0
$789$	0.185815	+	0.135002i	0.00661519	+	0.00480622i
$790$		0			0
$791$	−12.2651	+	8.91114i	−0.436098	+	0.316844i
$792$		0			0
$793$	−18.7903			−0.667264
$794$		0			0
$795$	0.955710	−	2.31213i	0.0338955	−	0.0820029i
$796$		0			0
$797$	9.18763	+	28.2766i	0.325442	+	1.00161i	0.971240	+	0.238101i	$0.0765248\pi$
$797$	9.18763	+	28.2766i	0.325442	+	1.00161i	−0.645798	+	0.763508i	$0.723475\pi$
$798$		0			0
$799$	8.20356			0.290221
$800$		0			0
$801$	31.4252			1.11036
$802$		0			0
$803$	−2.61081	−	8.03523i	−0.0921333	−	0.283557i
$804$		0			0
$805$	−5.57245	−	0.434406i	−0.196403	−	0.0153108i
$806$		0			0
$807$	−9.10517			−0.320517
$808$		0			0
$809$	33.2025	−	24.1230i	1.16734	−	0.848120i	0.176649	−	0.984274i	$-0.443474\pi$
$809$	33.2025	−	24.1230i	1.16734	−	0.848120i	0.990688	+	0.136154i	$0.0434742\pi$
$810$		0			0
$811$	−16.9644	−	12.3254i	−0.595702	−	0.432803i	0.248649	−	0.968594i	$-0.420013\pi$
$811$	−16.9644	−	12.3254i	−0.595702	−	0.432803i	−0.844351	+	0.535791i	$0.820013\pi$
$812$		0			0
$813$	−6.20942	+	4.51141i	−0.217774	+	0.158222i
$814$		0			0
$815$	−17.2460	+	41.7230i	−0.604101	+	1.46149i
$816$		0			0
$817$	−9.89460	+	30.4525i	−0.346168	+	1.06540i
$818$		0			0
$819$	1.34416	−	4.13688i	0.0469686	−	0.144554i
$820$		0			0
$821$	−2.59355	−	7.98211i	−0.0905154	−	0.278578i	0.895544	−	0.444974i	$-0.146787\pi$
$821$	−2.59355	−	7.98211i	−0.0905154	−	0.278578i	−0.986059	+	0.166396i	$0.946787\pi$
$822$		0			0
$823$	11.6952	+	8.49705i	0.407668	+	0.296188i	0.772657	−	0.634823i	$-0.218927\pi$
$823$	11.6952	+	8.49705i	0.407668	+	0.296188i	−0.364989	+	0.931012i	$0.618927\pi$
$824$		0			0
$825$	−2.10217	−	2.09595i	−0.0731883	−	0.0729717i
$826$		0			0
$827$	43.1116	+	31.3224i	1.49914	+	1.08919i	0.970723	+	0.240200i	$0.0772132\pi$
$827$	43.1116	+	31.3224i	1.49914	+	1.08919i	0.528414	+	0.848987i	$0.322787\pi$
$828$		0			0
$829$	−8.10306	−	24.9387i	−0.281431	−	0.866155i	−0.987446	−	0.157958i	$-0.949509\pi$
$829$	−8.10306	−	24.9387i	−0.281431	−	0.866155i	0.706015	−	0.708197i	$-0.250491\pi$
$830$		0			0
$831$	−2.01146	+	6.19065i	−0.0697769	+	0.214751i
$832$		0			0
$833$	−1.29020	+	3.97082i	−0.0447027	+	0.137581i
$834$		0			0
$835$	−0.656288	−	2.72474i	−0.0227118	−	0.0942935i
$836$		0			0
$837$	21.8814	−	15.8978i	0.756332	−	0.549507i
$838$		0			0
$839$	−4.49620	−	3.26668i	−0.155226	−	0.112778i	0.507461	−	0.861675i	$-0.330584\pi$
$839$	−4.49620	−	3.26668i	−0.155226	−	0.112778i	−0.662687	+	0.748896i	$0.730584\pi$
$840$		0			0
$841$	−45.1386	+	32.7951i	−1.55650	+	1.13087i
$842$		0			0
$843$	−6.12494			−0.210954
$844$		0			0
$845$	−4.83987	−	20.0939i	−0.166497	−	0.691251i
$846$		0			0
$847$	−0.261942	−	0.806175i	−0.00900044	−	0.0277005i
$848$		0			0
$849$	−13.0735			−0.448682
$850$		0			0
$851$	14.1278			0.484295
$852$		0			0
$853$	16.4920	+	50.7570i	0.564674	+	1.73789i	0.668919	+	0.743335i	$0.266757\pi$
$853$	16.4920	+	50.7570i	0.564674	+	1.73789i	−0.104246	+	0.994552i	$0.533243\pi$
$854$		0			0
$855$	−16.4232	−	14.0057i	−0.561662	−	0.478985i
$856$		0			0
$857$	26.7477			0.913684			0.456842	−	0.889548i	$-0.348981\pi$
$857$	26.7477			0.913684			0.456842	+	0.889548i	$0.348981\pi$
$858$		0			0
$859$	23.5556	−	17.1141i	0.803706	−	0.583927i	−0.108293	−	0.994119i	$-0.534538\pi$
$859$	23.5556	−	17.1141i	0.803706	−	0.583927i	0.911999	+	0.410192i	$0.134538\pi$
$860$		0			0
$861$	−0.665635	−	0.483612i	−0.0226848	−	0.0164814i
$862$		0			0
$863$	−2.91476	+	2.11770i	−0.0992197	+	0.0720873i	−0.636289	−	0.771451i	$-0.719531\pi$
$863$	−2.91476	+	2.11770i	−0.0992197	+	0.0720873i	0.537069	+	0.843538i	$0.319531\pi$
$864$		0			0
$865$	−53.6000	−	4.17844i	−1.82245	−	0.142071i
$866$		0			0
$867$	3.03785	−	9.34954i	0.103171	−	0.317527i
$868$		0			0
$869$	1.46378	−	4.50505i	0.0496553	−	0.152823i
$870$		0			0
$871$	−3.25545	−	10.0192i	−0.110307	−	0.339489i
$872$		0			0
$873$	−15.9930	−	11.6196i	−0.541281	−	0.393263i
$874$		0			0
$875$	−0.764575	−	9.44626i	−0.0258474	−	0.319342i
$876$		0			0
$877$	−25.0044	−	18.1667i	−0.844338	−	0.613447i	0.0792412	−	0.996855i	$-0.474750\pi$
$877$	−25.0044	−	18.1667i	−0.844338	−	0.613447i	−0.923579	+	0.383408i	$0.874750\pi$
$878$		0			0
$879$	−5.23610	−	16.1151i	−0.176609	−	0.543547i
$880$		0			0
$881$	12.3374	−	37.9707i	0.415658	−	1.27926i	−0.496003	−	0.868321i	$-0.665199\pi$
$881$	12.3374	−	37.9707i	0.415658	−	1.27926i	0.911661	−	0.410943i	$-0.134801\pi$
$882$		0			0
$883$	−2.45187	+	7.54607i	−0.0825119	+	0.253946i	−0.983798	−	0.179278i	$-0.942624\pi$
$883$	−2.45187	+	7.54607i	−0.0825119	+	0.253946i	0.901287	+	0.433223i	$0.142624\pi$
$884$		0			0
$885$	−13.7647	−	1.07304i	−0.462695	−	0.0360699i
$886$		0			0
$887$	16.3210	−	11.8579i	0.548007	−	0.398150i	−0.279043	−	0.960279i	$-0.590017\pi$
$887$	16.3210	−	11.8579i	0.548007	−	0.398150i	0.827050	+	0.562128i	$0.190017\pi$
$888$		0			0
$889$	7.30212	+	5.30530i	0.244905	+	0.177934i
$890$		0			0
$891$	4.81517	−	3.49842i	0.161314	−	0.117202i
$892$		0			0
$893$	−44.9991			−1.50584
$894$		0			0
$895$	−3.01049	−	2.56734i	−0.100630	−	0.0858169i
$896$		0			0
$897$	−1.04861	−	3.22728i	−0.0350120	−	0.107756i
$898$		0			0
$899$	−74.2802			−2.47738
$900$		0			0
$901$	−1.25262			−0.0417310
$902$		0			0
$903$	1.36577	+	4.20341i	0.0454500	+	0.139881i
$904$		0			0
$905$	4.21801	+	17.5121i	0.140211	+	0.582122i
$906$		0			0
$907$	20.8718			0.693036			0.346518	−	0.938043i	$-0.387364\pi$
$907$	20.8718			0.693036			0.346518	+	0.938043i	$0.387364\pi$
$908$		0			0
$909$	30.6681	−	22.2816i	1.01720	−	0.739036i
$910$		0			0
$911$	12.2529	+	8.90222i	0.405955	+	0.294944i	0.771962	−	0.635668i	$-0.219275\pi$
$911$	12.2529	+	8.90222i	0.405955	+	0.294944i	−0.366007	+	0.930612i	$0.619275\pi$
$912$		0			0
$913$	−10.8835	+	7.90731i	−0.360191	+	0.261694i
$914$		0			0
$915$	3.01376	+	12.5123i	0.0996318	+	0.413645i
$916$		0			0
$917$	−0.750608	+	2.31013i	−0.0247873	+	0.0762873i
$918$		0			0
$919$	−1.06096	+	3.26529i	−0.0349977	+	0.107712i	−0.967029	−	0.254665i	$-0.918035\pi$
$919$	−1.06096	+	3.26529i	−0.0349977	+	0.107712i	0.932032	+	0.362377i	$0.118035\pi$
$920$		0			0
$921$	2.75838	+	8.48943i	0.0908919	+	0.279736i
$922$		0			0
$923$	−9.49346	−	6.89740i	−0.312481	−	0.227031i
$924$		0			0
$925$	3.78241	+	23.6542i	0.124365	+	0.777745i
$926$		0			0
$927$	−10.6658	−	7.74918i	−0.350312	−	0.254516i
$928$		0			0
$929$	1.75137	+	5.39016i	0.0574606	+	0.176845i	0.975667	−	0.219256i	$-0.0703629\pi$
$929$	1.75137	+	5.39016i	0.0574606	+	0.176845i	−0.918207	+	0.396101i	$0.870363\pi$
$930$		0			0
$931$	7.07714	−	21.7812i	0.231944	−	0.713850i
$932$		0			0
$933$	−1.00709	+	3.09950i	−0.0329706	+	0.101473i
$934$		0			0
$935$	−0.567753	+	1.37355i	−0.0185675	+	0.0449200i
$936$		0			0
$937$	10.6120	−	7.71009i	0.346680	−	0.251878i	−0.400795	−	0.916168i	$-0.631266\pi$
$937$	10.6120	−	7.71009i	0.346680	−	0.251878i	0.747475	+	0.664290i	$0.231266\pi$
$938$		0			0
$939$	6.51791	+	4.73554i	0.212704	+	0.154539i
$940$		0			0
$941$	−25.2700	+	18.3597i	−0.823778	+	0.598510i	−0.917792	−	0.397061i	$-0.870030\pi$
$941$	−25.2700	+	18.3597i	−0.823778	+	0.598510i	0.0940140	+	0.995571i	$0.470030\pi$
$942$		0			0
$943$	4.82102			0.156994
$944$		0			0
$945$	−6.33608	−	0.493935i	−0.206113	−	0.0160677i
$946$		0			0
$947$	10.8971	+	33.5379i	0.354109	+	1.08983i	0.956525	+	0.291652i	$0.0942048\pi$
$947$	10.8971	+	33.5379i	0.354109	+	1.08983i	−0.602416	+	0.798182i	$0.705795\pi$
$948$		0			0
$949$	16.3756			0.531575
$950$		0			0
$951$	−2.36273			−0.0766167
$952$		0			0
$953$	4.00131	+	12.3148i	0.129615	+	0.398915i	0.994714	−	0.102687i	$-0.0327441\pi$
$953$	4.00131	+	12.3148i	0.129615	+	0.398915i	−0.865098	+	0.501602i	$0.832744\pi$
$954$		0			0
$955$	19.2645	−	46.6063i	0.623385	−	1.50814i
$956$		0			0
$957$	5.46707			0.176725
$958$		0			0
$959$	9.60188	−	6.97618i	0.310061	−	0.225273i
$960$		0			0
$961$	−27.5630	−	20.0257i	−0.889127	−	0.645989i
$962$		0			0
$963$	−37.7781	+	27.4474i	−1.21738	+	0.884480i
$964$		0			0
$965$	4.06420	−	2.49469i	0.130831	−	0.0803070i
$966$		0			0
$967$	8.72742	−	26.8602i	0.280655	−	0.863767i	−0.707013	−	0.707201i	$-0.749958\pi$
$967$	8.72742	−	26.8602i	0.280655	−	0.863767i	0.987667	−	0.156566i	$-0.0500424\pi$
$968$		0			0
$969$	0.444611	−	1.36837i	0.0142830	−	0.0439584i
$970$		0			0
$971$	−8.18419	−	25.1883i	−0.262643	−	0.808332i	−0.992227	−	0.124441i	$-0.960286\pi$
$971$	−8.18419	−	25.1883i	−0.262643	−	0.808332i	0.729584	−	0.683891i	$-0.239714\pi$
$972$		0			0
$973$	3.50813	+	2.54881i	0.112465	+	0.0817110i
$974$		0			0
$975$	5.12270	−	2.61972i	0.164058	−	0.0838981i
$976$		0			0
$977$	−39.3814	−	28.6123i	−1.25992	−	0.915388i	−0.261169	−	0.965293i	$-0.584108\pi$
$977$	−39.3814	−	28.6123i	−1.25992	−	0.915388i	−0.998754	+	0.0499053i	$0.984108\pi$
$978$		0			0
$979$	3.66794	+	11.2888i	0.117228	+	0.360790i
$980$		0			0
$981$	10.2380	−	31.5094i	0.326875	−	1.00602i
$982$		0			0
$983$	3.02874	−	9.32151i	0.0966018	−	0.297310i	−0.891066	−	0.453874i	$-0.850042\pi$
$983$	3.02874	−	9.32151i	0.0966018	−	0.297310i	0.987668	+	0.156564i	$0.0500417\pi$
$984$		0			0
$985$	10.6940	+	9.11988i	0.340741	+	0.290583i
$986$		0			0
$987$	−5.02506	+	3.65092i	−0.159949	+	0.116210i
$988$		0			0
$989$	−20.9514	−	15.2221i	−0.666217	−	0.484035i
$990$		0			0
$991$	15.9914	−	11.6184i	0.507984	−	0.369072i	−0.304074	−	0.952648i	$-0.598347\pi$
$991$	15.9914	−	11.6184i	0.507984	−	0.369072i	0.812058	+	0.583576i	$0.198347\pi$
$992$		0			0
$993$	4.38552			0.139170
$994$		0			0
$995$	28.4466	−	17.4611i	0.901817	−	0.553554i
$996$		0			0
$997$	−0.326506	−	1.00488i	−0.0103405	−	0.0318249i	0.945753	−	0.324886i	$-0.105326\pi$
$997$	−0.326506	−	1.00488i	−0.0103405	−	0.0318249i	−0.956094	+	0.293061i	$0.905326\pi$
$998$		0			0
$999$	16.0638			0.508237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.441.5	✓	52
25.11	even	5	inner	1100.2.q.b.661.5	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.441.5	✓	52	1.1	even	1	trivial
1100.2.q.b.661.5	yes	52	25.11	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:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.183465 - 0.564647i) q^{3} +(-1.90569 + 1.16976i) q^{5} -0.847663 q^{7} +(2.14188 - 1.55617i) q^{9} +(0.809017 + 0.587785i) q^{11} +(-1.56806 + 1.13926i) q^{13} +(1.01013 + 0.861436i) q^{15} +(0.205397 - 0.632148i) q^{17} +(-1.12667 + 3.46753i) q^{19} +(0.155516 + 0.478630i) q^{21} +(-2.38568 - 1.73330i) q^{23} +(2.26335 - 4.45839i) q^{25} +(-2.71260 - 1.97082i) q^{27} +(2.84555 + 8.75770i) q^{29} +(-2.49271 + 7.67177i) q^{31} +(0.183465 - 0.564647i) q^{33} +(1.61539 - 0.991558i) q^{35} +(-3.87595 + 2.81604i) q^{37} +(0.930967 + 0.676387i) q^{39} +(-1.32264 + 0.960955i) q^{41} +8.78217 q^{43} +(-2.26144 + 5.47106i) q^{45} +(3.81393 + 11.7381i) q^{47} -6.28147 q^{49} -0.394624 q^{51} +(-0.582359 - 1.79232i) q^{53} +(-2.22930 - 0.173788i) q^{55} +2.16464 q^{57} +(-8.41365 + 6.11287i) q^{59} +(7.84307 + 5.69833i) q^{61} +(-1.81559 + 1.31911i) q^{63} +(1.65559 - 4.00534i) q^{65} +(-1.67960 + 5.16926i) q^{67} +(-0.541013 + 1.66507i) q^{69} +(1.87087 + 5.75794i) q^{71} +(-6.83518 - 4.96605i) q^{73} +(-2.93266 - 0.460033i) q^{75} +(-0.685773 - 0.498244i) q^{77} +(-1.46378 - 4.50505i) q^{79} +(1.83923 - 5.66057i) q^{81} +(-4.15712 + 12.7943i) q^{83} +(0.348034 + 1.44495i) q^{85} +(4.42295 - 3.21346i) q^{87} +(9.60280 + 6.97684i) q^{89} +(1.32919 - 0.965712i) q^{91} +4.78917 q^{93} +(-1.90908 - 7.92599i) q^{95} +(-2.30736 - 7.10133i) q^{97} +2.64751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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