LMFDB - Embedded newform 693.2.m.k.64.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.53363286007$
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			64.5
Character	$\chi$	$=$	693.64
Dual form			693.2.m.k.379.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.123907 - 0.381345i) q^{2} +(1.48796 + 1.08107i) q^{4} +(-0.712476 - 2.19277i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(1.24541 - 0.904845i) q^{8} +O(q^{10})$	\(q+(0.123907 - 0.381345i) q^{2} +(1.48796 + 1.08107i) q^{4} +(-0.712476 - 2.19277i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(1.24541 - 0.904845i) q^{8} -0.924485 q^{10} +(-3.30642 - 0.259994i) q^{11} +(1.38796 - 4.27172i) q^{13} +(-0.324392 + 0.235684i) q^{14} +(0.945959 + 2.91136i) q^{16} +(-2.30765 - 7.10221i) q^{17} +(1.08998 - 0.791919i) q^{19} +(1.31040 - 4.03300i) q^{20} +(-0.508834 + 1.22867i) q^{22} +4.27146 q^{23} +(-0.255555 + 0.185671i) q^{25} +(-1.45702 - 1.05859i) q^{26} +(-0.568351 - 1.74920i) q^{28} +(0.910862 + 0.661780i) q^{29} +(-2.50687 + 7.71535i) q^{31} +4.30627 q^{32} -2.99433 q^{34} +(-0.712476 + 2.19277i) q^{35} +(-8.95237 - 6.50427i) q^{37} +(-0.166938 - 0.513784i) q^{38} +(-2.87145 - 2.08623i) q^{40} +(-0.939852 + 0.682843i) q^{41} +9.95451 q^{43} +(-4.63876 - 3.96132i) q^{44} +(0.529262 - 1.62890i) q^{46} +(10.3911 - 7.54956i) q^{47} +(0.309017 + 0.951057i) q^{49} +(0.0391400 + 0.120460i) q^{50} +(6.68326 - 4.85567i) q^{52} +(-3.62469 + 11.1556i) q^{53} +(1.78564 + 7.43547i) q^{55} -1.53941 q^{56} +(0.365228 - 0.265354i) q^{58} +(-0.848599 - 0.616543i) q^{59} +(-2.06929 - 6.36863i) q^{61} +(2.63160 + 1.91197i) q^{62} +(-1.35834 + 4.18055i) q^{64} -10.3558 q^{65} -2.46445 q^{67} +(4.24428 - 13.0626i) q^{68} +(0.747924 + 0.543398i) q^{70} +(-2.60280 - 8.01059i) q^{71} +(8.71874 + 6.33453i) q^{73} +(-3.58963 + 2.60802i) q^{74} +2.47797 q^{76} +(2.52213 + 2.15380i) q^{77} +(0.837891 - 2.57876i) q^{79} +(5.70999 - 4.14855i) q^{80} +(0.143945 + 0.443017i) q^{82} +(2.82105 + 8.68231i) q^{83} +(-13.9294 + 10.1203i) q^{85} +(1.23343 - 3.79610i) q^{86} +(-4.35311 + 2.66800i) q^{88} -5.28542 q^{89} +(-3.63374 + 2.64007i) q^{91} +(6.35577 + 4.61774i) q^{92} +(-1.59147 - 4.89803i) q^{94} +(-2.51309 - 1.82586i) q^{95} +(1.77561 - 5.46478i) q^{97} +0.400970 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) $ 32 * q - 10 * q^4 - 8 * q^7	$ 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) $ 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.123907	−	0.381345i	0.0876152	−	0.269652i	−0.897644	−	0.440722i	$-0.854722\pi$
$2$	0.123907	−	0.381345i	0.0876152	−	0.269652i	0.985259	+	0.171070i	$0.0547225\pi$
$3$		0			0
$3$		0			0
$4$	1.48796	+	1.08107i	0.743981	+	0.540534i
$5$	−0.712476	−	2.19277i	−0.318629	−	0.980639i	−0.974235	−	0.225536i	$-0.927587\pi$
$5$	−0.712476	−	2.19277i	−0.318629	−	0.980639i	0.655606	−	0.755103i	$-0.272413\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	1.24541	−	0.904845i	0.440320	−	0.319911i
$9$		0			0
$10$	−0.924485			−0.292348
$11$	−3.30642	−	0.259994i	−0.996923	−	0.0783910i
$11$	−3.30642	−	0.259994i	−0.996923	−	0.0783910i
$12$		0			0
$13$	1.38796	−	4.27172i	0.384952	−	1.18476i	−0.551563	−	0.834133i	$-0.685968\pi$
$13$	1.38796	−	4.27172i	0.384952	−	1.18476i	0.936515	−	0.350628i	$-0.114032\pi$
$14$	−0.324392	+	0.235684i	−0.0866973	+	0.0629893i
$15$		0			0
$16$	0.945959	+	2.91136i	0.236490	+	0.727840i
$17$	−2.30765	−	7.10221i	−0.559687	−	1.72254i	−0.683232	−	0.730201i	$-0.739426\pi$
$17$	−2.30765	−	7.10221i	−0.559687	−	1.72254i	0.123545	−	0.992339i	$-0.460574\pi$
$18$		0			0
$19$	1.08998	−	0.791919i	0.250059	−	0.181679i	−0.455694	−	0.890137i	$-0.650609\pi$
$19$	1.08998	−	0.791919i	0.250059	−	0.181679i	0.705753	+	0.708458i	$0.250609\pi$
$20$	1.31040	−	4.03300i	0.293015	−	0.901807i
$21$		0			0
$22$	−0.508834	+	1.22867i	−0.108484	+	0.261954i
$23$	4.27146			0.890661			0.445330	−	0.895366i	$-0.353086\pi$
$23$	4.27146			0.890661			0.445330	+	0.895366i	$0.353086\pi$
$24$		0			0
$25$	−0.255555	+	0.185671i	−0.0511109	+	0.0371342i
$26$	−1.45702	−	1.05859i	−0.285745	−	0.207606i
$27$		0			0
$28$	−0.568351	−	1.74920i	−0.107408	−	0.330569i
$29$	0.910862	+	0.661780i	0.169143	+	0.122889i	0.669136	−	0.743140i	$-0.266664\pi$
$29$	0.910862	+	0.661780i	0.169143	+	0.122889i	−0.499993	+	0.866029i	$0.666664\pi$
$30$		0			0
$31$	−2.50687	+	7.71535i	−0.450247	+	1.38572i	0.426378	+	0.904545i	$0.359789\pi$
$31$	−2.50687	+	7.71535i	−0.450247	+	1.38572i	−0.876625	+	0.481173i	$0.840211\pi$
$32$	4.30627			0.761249
$33$		0			0
$34$	−2.99433			−0.513523
$35$	−0.712476	+	2.19277i	−0.120430	+	0.370647i
$36$		0			0
$37$	−8.95237	−	6.50427i	−1.47176	−	1.06930i	−0.980099	−	0.198509i	$-0.936390\pi$
$37$	−8.95237	−	6.50427i	−1.47176	−	1.06930i	−0.491661	−	0.870787i	$-0.663610\pi$
$38$	−0.166938	−	0.513784i	−0.0270810	−	0.0833467i
$39$		0			0
$40$	−2.87145	−	2.08623i	−0.454016	−	0.329862i
$41$	−0.939852	+	0.682843i	−0.146780	+	0.106642i	−0.658752	−	0.752360i	$-0.728915\pi$
$41$	−0.939852	+	0.682843i	−0.146780	+	0.106642i	0.511972	+	0.859002i	$0.328915\pi$
$42$		0			0
$43$	9.95451			1.51805			0.759024	−	0.651063i	$-0.225676\pi$
$43$	9.95451			1.51805			0.759024	+	0.651063i	$0.225676\pi$
$44$	−4.63876	−	3.96132i	−0.699319	−	0.597192i
$45$		0			0
$46$	0.529262	−	1.62890i	0.0780354	−	0.240168i
$47$	10.3911	−	7.54956i	1.51569	−	1.10122i	0.552124	−	0.833762i	$-0.313818\pi$
$47$	10.3911	−	7.54956i	1.51569	−	1.10122i	0.963571	−	0.267454i	$-0.0861823\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.0391400	+	0.120460i	0.00553523	+	0.0170357i
$51$		0			0
$52$	6.68326	−	4.85567i	0.926801	−	0.673360i
$53$	−3.62469	+	11.1556i	−0.497889	+	1.53235i	0.314515	+	0.949252i	$0.398158\pi$
$53$	−3.62469	+	11.1556i	−0.497889	+	1.53235i	−0.812405	+	0.583094i	$0.801842\pi$
$54$		0			0
$55$	1.78564	+	7.43547i	0.240775	+	1.00260i
$56$	−1.53941			−0.205713
$57$		0			0
$58$	0.365228	−	0.265354i	0.0479568	−	0.0348427i
$59$	−0.848599	−	0.616543i	−0.110478	−	0.0802671i	0.531174	−	0.847263i	$-0.321751\pi$
$59$	−0.848599	−	0.616543i	−0.110478	−	0.0802671i	−0.641653	+	0.766995i	$0.721751\pi$
$60$		0			0
$61$	−2.06929	−	6.36863i	−0.264946	−	0.815419i	−0.991706	−	0.128528i	$-0.958975\pi$
$61$	−2.06929	−	6.36863i	−0.264946	−	0.815419i	0.726760	−	0.686891i	$-0.241025\pi$
$62$	2.63160	+	1.91197i	0.334213	+	0.242820i
$63$		0			0
$64$	−1.35834	+	4.18055i	−0.169793	+	0.522568i
$65$	−10.3558			−1.28448
$66$		0			0
$67$	−2.46445			−0.301080			−0.150540	−	0.988604i	$-0.548101\pi$
$67$	−2.46445			−0.301080			−0.150540	+	0.988604i	$0.548101\pi$
$68$	4.24428	−	13.0626i	0.514695	−	1.58407i
$69$		0			0
$70$	0.747924	+	0.543398i	0.0893940	+	0.0649485i
$71$	−2.60280	−	8.01059i	−0.308895	−	0.950682i	−0.978195	−	0.207689i	$-0.933406\pi$
$71$	−2.60280	−	8.01059i	−0.308895	−	0.950682i	0.669300	−	0.742993i	$-0.266594\pi$
$72$		0			0
$73$	8.71874	+	6.33453i	1.02045	+	0.741401i	0.966375	−	0.257136i	$-0.0827788\pi$
$73$	8.71874	+	6.33453i	1.02045	+	0.741401i	0.0540756	+	0.998537i	$0.482779\pi$
$74$	−3.58963	+	2.60802i	−0.417286	+	0.303176i
$75$		0			0
$76$	2.47797			0.284243
$77$	2.52213	+	2.15380i	0.287423	+	0.245449i
$78$		0			0
$79$	0.837891	−	2.57876i	0.0942702	−	0.290134i	−0.892793	−	0.450468i	$-0.851257\pi$
$79$	0.837891	−	2.57876i	0.0942702	−	0.290134i	0.987063	+	0.160334i	$0.0512572\pi$
$80$	5.70999	−	4.14855i	0.638396	−	0.463822i
$81$		0			0
$82$	0.143945	+	0.443017i	0.0158961	+	0.0489230i
$83$	2.82105	+	8.68231i	0.309651	+	0.953007i	0.977901	+	0.209070i	$0.0670437\pi$
$83$	2.82105	+	8.68231i	0.309651	+	0.953007i	−0.668250	+	0.743937i	$0.732956\pi$
$84$		0			0
$85$	−13.9294	+	10.1203i	−1.51086	+	1.09770i
$86$	1.23343	−	3.79610i	0.133004	−	0.409344i
$87$		0			0
$88$	−4.35311	+	2.66800i	−0.464043	+	0.284409i
$89$	−5.28542			−0.560253			−0.280126	−	0.959963i	$-0.590376\pi$
$89$	−5.28542			−0.560253			−0.280126	+	0.959963i	$0.590376\pi$
$90$		0			0
$91$	−3.63374	+	2.64007i	−0.380919	+	0.276754i
$92$	6.35577	+	4.61774i	0.662635	+	0.481433i
$93$		0			0
$94$	−1.59147	−	4.89803i	−0.164147	−	0.505193i
$95$	−2.51309	−	1.82586i	−0.257837	−	0.187330i
$96$		0			0
$97$	1.77561	−	5.46478i	0.180286	−	0.554864i	−0.819549	−	0.573009i	$-0.805776\pi$
$97$	1.77561	−	5.46478i	0.180286	−	0.554864i	0.999835	+	0.0181449i	$0.00577600\pi$
$98$	0.400970			0.0405041
$99$		0			0
$100$	−0.580979			−0.0580979
$101$	−2.95530	+	9.09549i	−0.294064	+	0.905035i	0.689470	+	0.724314i	$0.257843\pi$
$101$	−2.95530	+	9.09549i	−0.294064	+	0.905035i	−0.983534	+	0.180722i	$0.942157\pi$
$102$		0			0
$103$	0.653358	+	0.474692i	0.0643773	+	0.0467728i	0.619508	−	0.784990i	$-0.287332\pi$
$103$	0.653358	+	0.474692i	0.0643773	+	0.0467728i	−0.555131	+	0.831763i	$0.687332\pi$
$104$	−2.13665	−	6.57594i	−0.209516	−	0.644824i
$105$		0			0
$106$	3.80503	+	2.76452i	0.369577	+	0.268514i
$107$	−13.6302	+	9.90291i	−1.31768	+	0.957351i	−0.317722	+	0.948184i	$0.602918\pi$
$107$	−13.6302	+	9.90291i	−1.31768	+	0.957351i	−0.999958	+	0.00916669i	$0.997082\pi$
$108$		0			0
$109$	9.41870			0.902147			0.451074	−	0.892487i	$-0.351041\pi$
$109$	9.41870			0.902147			0.451074	+	0.892487i	$0.351041\pi$
$110$	3.05673	+	0.240360i	0.291448	+	0.0229174i
$111$		0			0
$112$	0.945959	−	2.91136i	0.0893847	−	0.275098i
$113$	−3.52035	+	2.55768i	−0.331166	+	0.240606i	−0.740925	−	0.671587i	$-0.765613\pi$
$113$	−3.52035	+	2.55768i	−0.331166	+	0.240606i	0.409759	+	0.912194i	$0.365613\pi$
$114$		0			0
$115$	−3.04331	−	9.36635i	−0.283790	−	0.873417i
$116$	0.639899	+	1.96941i	0.0594131	+	0.182855i
$117$		0			0
$118$	−0.340263	+	0.247215i	−0.0313237	+	0.0227580i
$119$	−2.30765	+	7.10221i	−0.211542	+	0.651059i
$120$		0			0
$121$	10.8648	+	1.71930i	0.987710	+	0.156300i
$122$	−2.68504			−0.243093
$123$		0			0
$124$	−12.0710	+	8.77006i	−1.08400	+	0.787575i
$125$	−8.73722	−	6.34796i	−0.781480	−	0.567779i
$126$		0			0
$127$	−1.96145	−	6.03673i	−0.174051	−	0.535673i	0.825538	−	0.564346i	$-0.190872\pi$
$127$	−1.96145	−	6.03673i	−0.174051	−	0.535673i	−0.999589	+	0.0286733i	$0.990872\pi$
$128$	8.39362	+	6.09832i	0.741898	+	0.539021i
$129$		0			0
$130$	−1.28315	+	3.94914i	−0.112540	+	0.346362i
$131$	15.2292			1.33058			0.665290	−	0.746585i	$-0.268308\pi$
$131$	15.2292			1.33058			0.665290	+	0.746585i	$0.268308\pi$
$132$		0			0
$133$	−1.34729			−0.116825
$134$	−0.305361	+	0.939805i	−0.0263792	+	0.0811868i
$135$		0			0
$136$	−9.30037	−	6.75712i	−0.797501	−	0.579418i
$137$	5.90200	+	18.1645i	0.504241	+	1.55190i	0.802042	+	0.597268i	$0.203747\pi$
$137$	5.90200	+	18.1645i	0.504241	+	1.55190i	−0.297801	+	0.954628i	$0.596253\pi$
$138$		0			0
$139$	3.18676	+	2.31532i	0.270297	+	0.196382i	0.714674	−	0.699457i	$-0.246575\pi$
$139$	3.18676	+	2.31532i	0.270297	+	0.196382i	−0.444377	+	0.895840i	$0.646575\pi$
$140$	−3.43068	+	2.49253i	−0.289945	+	0.210657i
$141$		0			0
$142$	−3.37730			−0.283417
$143$	−5.69981	+	13.7632i	−0.476642	+	1.15094i
$144$		0			0
$145$	0.802167	−	2.46882i	0.0666163	−	0.205024i
$146$	3.49595	−	2.53996i	0.289327	−	0.210208i
$147$		0			0
$148$	−6.28922	−	19.3562i	−0.516971	−	1.59107i
$149$	6.29823	+	19.3840i	0.515971	+	1.58800i	0.781508	+	0.623895i	$0.214451\pi$
$149$	6.29823	+	19.3840i	0.515971	+	1.58800i	−0.265537	+	0.964101i	$0.585549\pi$
$150$		0			0
$151$	3.97808	−	2.89024i	0.323732	−	0.235205i	−0.414035	−	0.910261i	$-0.635881\pi$
$151$	3.97808	−	2.89024i	0.323732	−	0.235205i	0.737766	+	0.675056i	$0.235881\pi$
$152$	0.640914	−	1.97253i	0.0519850	−	0.159993i
$153$		0			0
$154$	1.13385	−	0.694931i	0.0913683	−	0.0559992i
$155$	18.7041			1.50235
$156$		0			0
$157$	−1.81381	+	1.31781i	−0.144758	+	0.105173i	−0.657807	−	0.753186i	$-0.728516\pi$
$157$	−1.81381	+	1.31781i	−0.144758	+	0.105173i	0.513049	+	0.858359i	$0.328516\pi$
$158$	−0.879579	−	0.639052i	−0.0699756	−	0.0508402i
$159$		0			0
$160$	−3.06811	−	9.44268i	−0.242556	−	0.746510i
$161$	−3.45568	−	2.51070i	−0.272346	−	0.197871i
$162$		0			0
$163$	−3.03994	+	9.35597i	−0.238107	+	0.732816i	0.758588	+	0.651571i	$0.225890\pi$
$163$	−3.03994	+	9.35597i	−0.238107	+	0.732816i	−0.996694	+	0.0812454i	$0.974110\pi$
$164$	−2.13666			−0.166845
$165$		0			0
$166$	3.66050			0.284110
$167$	−2.67139	+	8.22170i	−0.206719	+	0.636214i	0.792920	+	0.609326i	$0.208560\pi$
$167$	−2.67139	+	8.22170i	−0.206719	+	0.636214i	−0.999638	+	0.0268885i	$0.991440\pi$
$168$		0			0
$169$	−5.80389	−	4.21677i	−0.446453	−	0.324367i
$170$	2.13339	+	6.56589i	0.163623	+	0.503581i
$171$		0			0
$172$	14.8119	+	10.7615i	1.12940	+	0.820557i
$173$	12.9178	−	9.38531i	0.982120	−	0.713552i	0.0239388	−	0.999713i	$-0.492379\pi$
$173$	12.9178	−	9.38531i	0.982120	−	0.713552i	0.958181	+	0.286161i	$0.0923793\pi$
$174$		0			0
$175$	0.315883			0.0238785
$176$	−2.37080	−	9.87212i	−0.178706	−	0.744139i
$177$		0			0
$178$	−0.654898	+	2.01557i	−0.0490867	+	0.151073i
$179$	−14.2192	+	10.3308i	−1.06279	+	0.772163i	−0.974603	−	0.223941i	$-0.928108\pi$
$179$	−14.2192	+	10.3308i	−1.06279	+	0.772163i	−0.0881881	+	0.996104i	$0.528108\pi$
$180$		0			0
$181$	6.41658	+	19.7482i	0.476941	+	1.46787i	0.843322	+	0.537409i	$0.180597\pi$
$181$	6.41658	+	19.7482i	0.476941	+	1.46787i	−0.366381	+	0.930465i	$0.619403\pi$
$182$	0.556532	+	1.71283i	0.0412529	+	0.126963i
$183$		0			0
$184$	5.31973	−	3.86501i	0.392175	−	0.284932i
$185$	−7.88407	+	24.2647i	−0.579648	+	1.78397i
$186$		0			0
$187$	5.78352	+	24.0829i	0.422933	+	1.76111i
$188$	23.6231			1.72289
$189$		0			0
$190$	−1.00767	+	0.732117i	−0.0731042	+	0.0531133i
$191$	8.49477	+	6.17181i	0.614660	+	0.446577i	0.851052	−	0.525081i	$-0.175965\pi$
$191$	8.49477	+	6.17181i	0.614660	+	0.446577i	−0.236392	+	0.971658i	$0.575965\pi$
$192$		0			0
$193$	−4.00178	−	12.3162i	−0.288054	−	0.886541i	−0.985466	−	0.169870i	$-0.945665\pi$
$193$	−4.00178	−	12.3162i	−0.288054	−	0.886541i	0.697412	−	0.716670i	$-0.254335\pi$
$194$	−1.86396	−	1.35424i	−0.133824	−	0.0972290i
$195$		0			0
$196$	−0.568351	+	1.74920i	−0.0405965	+	0.124943i
$197$	−0.664214			−0.0473233			−0.0236617	−	0.999720i	$-0.507532\pi$
$197$	−0.664214			−0.0473233			−0.0236617	+	0.999720i	$0.507532\pi$
$198$		0			0
$199$	13.3550			0.946710			0.473355	−	0.880872i	$-0.343043\pi$
$199$	13.3550			0.946710			0.473355	+	0.880872i	$0.343043\pi$
$200$	−0.150267	+	0.462474i	−0.0106255	+	0.0327019i
$201$		0			0
$202$	3.10234	+	2.25398i	0.218280	+	0.158590i
$203$	−0.347918	−	1.07078i	−0.0244191	−	0.0751542i
$204$		0			0
$205$	2.16694	+	1.57438i	0.151346	+	0.109959i
$206$	0.261977	−	0.190337i	0.0182528	−	0.0132614i
$207$		0			0
$208$	13.7495			0.953354
$209$	−3.80983	+	2.33503i	−0.263532	+	0.161517i
$210$		0			0
$211$	4.04178	−	12.4393i	0.278247	−	0.856358i	−0.710094	−	0.704106i	$-0.751348\pi$
$211$	4.04178	−	12.4393i	0.278247	−	0.856358i	0.988342	−	0.152251i	$-0.0486522\pi$
$212$	−17.4534	+	12.6807i	−1.19871	+	0.870911i
$213$		0			0
$214$	2.08756	+	6.42484i	0.142703	+	0.439193i
$215$	−7.09234	−	21.8280i	−0.483694	−	1.48866i
$216$		0			0
$217$	6.56307	−	4.76835i	0.445530	−	0.323697i
$218$	1.16704	−	3.59177i	0.0790418	−	0.243266i
$219$		0			0
$220$	−5.38129	+	12.9941i	−0.362807	+	0.876062i
$221$	−33.5416			−2.25625
$222$		0			0
$223$	−8.27567	+	6.01263i	−0.554180	+	0.402635i	−0.829324	−	0.558768i	$-0.811274\pi$
$223$	−8.27567	+	6.01263i	−0.554180	+	0.402635i	0.275144	+	0.961403i	$0.411274\pi$
$224$	−3.48385	−	2.53116i	−0.232774	−	0.169120i
$225$		0			0
$226$	0.539166	+	1.65938i	0.0358648	+	0.110380i
$227$	−2.41788	−	1.75669i	−0.160480	−	0.116596i	0.504647	−	0.863326i	$-0.331623\pi$
$227$	−2.41788	−	1.75669i	−0.160480	−	0.116596i	−0.665127	+	0.746730i	$0.731623\pi$
$228$		0			0
$229$	6.21177	−	19.1179i	0.410485	−	1.26334i	−0.505742	−	0.862685i	$-0.668781\pi$
$229$	6.21177	−	19.1179i	0.410485	−	1.26334i	0.916227	−	0.400659i	$-0.131219\pi$
$230$	−3.94890			−0.260383
$231$		0			0
$232$	1.73321			0.113791
$233$	1.44327	−	4.44193i	0.0945518	−	0.291001i	−0.892585	−	0.450880i	$-0.851110\pi$
$233$	1.44327	−	4.44193i	0.0945518	−	0.291001i	0.987137	+	0.159879i	$0.0511104\pi$
$234$		0			0
$235$	−23.9579	−	17.4064i	−1.56284	−	1.13547i
$236$	−0.596158	−	1.83479i	−0.0388066	−	0.119434i
$237$		0			0
$238$	2.42246	+	1.76002i	0.157025	+	0.114085i
$239$	18.4191	−	13.3823i	1.19143	−	0.865628i	0.198019	−	0.980198i	$-0.436549\pi$
$239$	18.4191	−	13.3823i	1.19143	−	0.865628i	0.993415	+	0.114570i	$0.0365491\pi$
$240$		0			0
$241$	−4.83714			−0.311587			−0.155794	−	0.987790i	$-0.549793\pi$
$241$	−4.83714			−0.311587			−0.155794	+	0.987790i	$0.549793\pi$
$242$	2.00187	−	3.93021i	0.128685	−	0.252643i
$243$		0			0
$244$	3.80589	−	11.7133i	0.243647	−	0.749869i
$245$	1.86529	−	1.35521i	0.119169	−	0.0865811i
$246$		0			0
$247$	−1.86999	−	5.75525i	−0.118985	−	0.366198i
$248$	3.85911	+	11.8771i	0.245054	+	0.754198i
$249$		0			0
$250$	−3.50336	+	2.54534i	−0.221572	+	0.160982i
$251$	4.96145	−	15.2698i	0.313164	−	0.963819i	−0.663340	−	0.748318i	$-0.730862\pi$
$251$	4.96145	−	15.2698i	0.313164	−	0.963819i	0.976504	−	0.215501i	$-0.0691384\pi$
$252$		0			0
$253$	−14.1232	−	1.11055i	−0.887920	−	0.0698198i
$254$	−2.54512			−0.159695
$255$		0			0
$256$	−3.74678	+	2.72220i	−0.234174	+	0.170137i
$257$	9.84920	+	7.15587i	0.614376	+	0.446371i	0.850953	−	0.525242i	$-0.176025\pi$
$257$	9.84920	+	7.15587i	0.614376	+	0.446371i	−0.236576	+	0.971613i	$0.576025\pi$
$258$		0			0
$259$	3.41950	+	10.5241i	0.212477	+	0.653938i
$260$	−15.4090	−	11.1953i	−0.955629	−	0.694305i
$261$		0			0
$262$	1.88700	−	5.80758i	0.116579	−	0.358793i
$263$	18.8786			1.16411			0.582053	−	0.813151i	$-0.302250\pi$
$263$	18.8786			1.16411			0.582053	+	0.813151i	$0.302250\pi$
$264$		0			0
$265$	27.0443			1.66132
$266$	−0.166938	+	0.513784i	−0.0102356	+	0.0315021i
$267$		0			0
$268$	−3.66701	−	2.66424i	−0.223998	−	0.162744i
$269$	0.219722	+	0.676236i	0.0133967	+	0.0412308i	0.957531	−	0.288329i	$-0.0930997\pi$
$269$	0.219722	+	0.676236i	0.0133967	+	0.0412308i	−0.944135	+	0.329560i	$0.893100\pi$
$270$		0			0
$271$	−11.9118	−	8.65441i	−0.723588	−	0.525718i	0.163940	−	0.986470i	$-0.447580\pi$
$271$	−11.9118	−	8.65441i	−0.723588	−	0.525718i	−0.887529	+	0.460753i	$0.847580\pi$
$272$	18.4942	−	13.4368i	1.12137	−	0.814726i
$273$		0			0
$274$	7.65823			0.462651
$275$	0.893244	−	0.547464i	0.0538646	−	0.0330133i
$276$		0			0
$277$	5.43342	−	16.7223i	0.326462	−	1.00475i	−0.644314	−	0.764761i	$-0.722857\pi$
$277$	5.43342	−	16.7223i	0.326462	−	1.00475i	0.970776	−	0.239987i	$-0.0771430\pi$
$278$	1.27779	−	0.928372i	0.0766370	−	0.0556801i
$279$		0			0
$280$	1.09679	+	3.37559i	0.0655460	+	0.201730i
$281$	−4.62684	−	14.2399i	−0.276014	−	0.849484i	−0.988949	−	0.148254i	$-0.952635\pi$
$281$	−4.62684	−	14.2399i	−0.276014	−	0.849484i	0.712935	−	0.701230i	$-0.247365\pi$
$282$		0			0
$283$	−14.1107	+	10.2520i	−0.838795	+	0.609421i	−0.922034	−	0.387109i	$-0.873474\pi$
$283$	−14.1107	+	10.2520i	−0.838795	+	0.609421i	0.0832385	+	0.996530i	$0.473474\pi$
$284$	4.78713	−	14.7333i	0.284064	−	0.874258i
$285$		0			0
$286$	4.54229	+	3.87895i	0.268591	+	0.229367i
$287$	1.16172			0.0685742
$288$		0			0
$289$	−31.3629	+	22.7865i	−1.84488	+	1.34038i
$290$	−0.842078	−	0.611805i	−0.0494485	−	0.0359264i
$291$		0			0
$292$	6.12509	+	18.8511i	0.358444	+	1.10318i
$293$	−21.0444	−	15.2897i	−1.22943	−	0.893231i	−0.232580	−	0.972577i	$-0.574717\pi$
$293$	−21.0444	−	15.2897i	−1.22943	−	0.893231i	−0.996847	+	0.0793461i	$0.974717\pi$
$294$		0			0
$295$	−0.747334	+	2.30006i	−0.0435115	+	0.133915i
$296$	−17.0347			−0.990124
$297$		0			0
$298$	8.17237			0.473413
$299$	5.92864	−	18.2465i	0.342862	−	1.05522i
$300$		0			0
$301$	−8.05337	−	5.85111i	−0.464188	−	0.337253i
$302$	−0.609271	−	1.87514i	−0.0350596	−	0.107902i
$303$		0			0
$304$	3.33664	+	2.42421i	0.191369	+	0.139038i
$305$	−12.4906	+	9.07498i	−0.715212	+	0.519632i
$306$		0			0
$307$	−23.5921			−1.34647			−0.673236	−	0.739428i	$-0.735096\pi$
$307$	−23.5921			−1.34647			−0.673236	+	0.739428i	$0.735096\pi$
$308$	1.42442	+	5.93137i	0.0811641	+	0.337971i
$309$		0			0
$310$	2.31756	−	7.13273i	0.131629	−	0.405112i
$311$	−3.68257	+	2.67555i	−0.208820	+	0.151716i	−0.687279	−	0.726393i	$-0.741195\pi$
$311$	−3.68257	+	2.67555i	−0.208820	+	0.151716i	0.478460	+	0.878109i	$0.341195\pi$
$312$		0			0
$313$	−4.05657	−	12.4848i	−0.229291	−	0.705684i	−0.997828	−	0.0658787i	$-0.979015\pi$
$313$	−4.05657	−	12.4848i	−0.229291	−	0.705684i	0.768537	−	0.639805i	$-0.220985\pi$
$314$	0.277798	+	0.854974i	0.0156770	+	0.0482490i
$315$		0			0
$316$	4.03457	−	2.93129i	0.226962	−	0.164898i
$317$	−2.76370	+	8.50580i	−0.155225	+	0.477733i	−0.998184	−	0.0602451i	$-0.980812\pi$
$317$	−2.76370	+	8.50580i	−0.155225	+	0.477733i	0.842959	+	0.537978i	$0.180812\pi$
$318$		0			0
$319$	−2.83963	−	2.42494i	−0.158989	−	0.135770i
$320$	10.1348			0.566552
$321$		0			0
$322$	−1.38563	+	1.00672i	−0.0772179	+	0.0561021i
$323$	−8.13967	−	5.91382i	−0.452904	−	0.329054i
$324$		0			0
$325$	0.438434	+	1.34936i	0.0243200	+	0.0748491i
$326$	3.19119	+	2.31853i	0.176744	+	0.128412i
$327$		0			0
$328$	−0.552637	+	1.70084i	−0.0305143	+	0.0939132i
$329$	−12.8441			−0.708117
$330$		0			0
$331$	25.9302			1.42525			0.712627	−	0.701543i	$-0.247505\pi$
$331$	25.9302			1.42525			0.712627	+	0.701543i	$0.247505\pi$
$332$	−5.18854	+	15.9687i	−0.284758	+	0.876396i
$333$		0			0
$334$	2.80430	+	2.03745i	0.153445	+	0.111484i
$335$	1.75586	+	5.40398i	0.0959328	+	0.295251i
$336$		0			0
$337$	12.7469	+	9.26115i	0.694367	+	0.504487i	0.878093	−	0.478490i	$-0.158816\pi$
$337$	12.7469	+	9.26115i	0.694367	+	0.504487i	−0.183726	+	0.982978i	$0.558816\pi$
$338$	−2.32719	+	1.69080i	−0.126582	+	0.0919674i
$339$		0			0
$340$	−31.6672			−1.71739
$341$	10.2947	−	24.8584i	0.557490	−	1.34616i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	12.3975	−	9.00728i	0.668426	−	0.485640i
$345$		0			0
$346$	−1.97845	−	6.08903i	−0.106362	−	0.327349i
$347$	−0.689010	−	2.12055i	−0.0369880	−	0.113837i	0.930858	−	0.365382i	$-0.119062\pi$
$347$	−0.689010	−	2.12055i	−0.0369880	−	0.113837i	−0.967846	+	0.251544i	$0.919062\pi$
$348$		0			0
$349$	−7.78134	+	5.65347i	−0.416525	+	0.302623i	−0.776238	−	0.630440i	$-0.782875\pi$
$349$	−7.78134	+	5.65347i	−0.416525	+	0.302623i	0.359713	+	0.933063i	$0.382875\pi$
$350$	0.0391400	−	0.120460i	0.00209212	−	0.00643888i
$351$		0			0
$352$	−14.2383	−	1.11960i	−0.758906	−	0.0596750i
$353$	9.98576			0.531488			0.265744	−	0.964044i	$-0.414382\pi$
$353$	9.98576			0.531488			0.265744	+	0.964044i	$0.414382\pi$
$354$		0			0
$355$	−15.7110	+	11.4147i	−0.833852	+	0.605829i
$356$	−7.86450	−	5.71389i	−0.416818	−	0.302836i
$357$		0			0
$358$	2.17777	+	6.70247i	0.115098	+	0.354237i
$359$	−8.28988	−	6.02295i	−0.437523	−	0.317879i	0.347127	−	0.937818i	$-0.387157\pi$
$359$	−8.28988	−	6.02295i	−0.437523	−	0.317879i	−0.784650	+	0.619939i	$0.787157\pi$
$360$		0			0
$361$	−5.31040	+	16.3437i	−0.279495	+	0.860196i
$362$	8.32595			0.437602
$363$		0			0
$364$	−8.26096			−0.432992
$365$	7.67832	−	23.6314i	0.401901	−	1.23693i
$366$		0			0
$367$	−2.98740	−	2.17047i	−0.155941	−	0.113298i	0.507079	−	0.861900i	$-0.330725\pi$
$367$	−2.98740	−	2.17047i	−0.155941	−	0.113298i	−0.663020	+	0.748602i	$0.730725\pi$
$368$	4.04063	+	12.4358i	0.210632	+	0.648259i
$369$		0			0
$370$	8.27632	+	6.01310i	0.430266	+	0.312606i
$371$	9.48956	−	6.89457i	0.492673	−	0.357948i
$372$		0			0
$373$	17.2657			0.893986			0.446993	−	0.894538i	$-0.352495\pi$
$373$	17.2657			0.893986			0.446993	+	0.894538i	$0.352495\pi$
$374$	9.90050	+	0.778506i	0.511943	+	0.0402556i
$375$		0			0
$376$	6.10999	−	18.8046i	0.315099	−	0.969774i
$377$	4.09118	−	2.97242i	0.210706	−	0.153087i
$378$		0			0
$379$	−1.60365	−	4.93553i	−0.0823740	−	0.253521i	0.901384	−	0.433020i	$-0.142552\pi$
$379$	−1.60365	−	4.93553i	−0.0823740	−	0.253521i	−0.983758	+	0.179499i	$0.942552\pi$
$380$	−1.76549	−	5.43363i	−0.0905679	−	0.278739i
$381$		0			0
$382$	3.40615	−	2.47471i	0.174274	−	0.126617i
$383$	5.44524	−	16.7587i	0.278239	−	0.856331i	−0.710105	−	0.704095i	$-0.751353\pi$
$383$	5.44524	−	16.7587i	0.278239	−	0.856331i	0.988344	−	0.152236i	$-0.0486473\pi$
$384$		0			0
$385$	2.92585	−	7.06499i	0.149115	−	0.360065i
$386$	−5.19258			−0.264295
$387$		0			0
$388$	8.54984	−	6.21183i	0.434053	−	0.315358i
$389$	8.59081	+	6.24159i	0.435571	+	0.316461i	0.783873	−	0.620922i	$-0.213241\pi$
$389$	8.59081	+	6.24159i	0.435571	+	0.316461i	−0.348302	+	0.937383i	$0.613241\pi$
$390$		0			0
$391$	−9.85703	−	30.3368i	−0.498492	−	1.53420i
$392$	1.24541	+	0.904845i	0.0629028	+	0.0457016i
$393$		0			0
$394$	−0.0823005	+	0.253295i	−0.00414624	+	0.0127608i
$395$	−6.25163			−0.314554
$396$		0			0
$397$	22.6262			1.13557			0.567787	−	0.823175i	$-0.307800\pi$
$397$	22.6262			1.13557			0.567787	+	0.823175i	$0.307800\pi$
$398$	1.65477	−	5.09286i	0.0829462	−	0.255282i
$399$		0			0
$400$	−0.782300	−	0.568374i	−0.0391150	−	0.0284187i
$401$	−1.42441	−	4.38389i	−0.0711318	−	0.218921i	0.909170	−	0.416424i	$-0.136717\pi$
$401$	−1.42441	−	4.38389i	−0.0711318	−	0.218921i	−0.980302	+	0.197503i	$0.936717\pi$
$402$		0			0
$403$	29.4784	+	21.4173i	1.46842	+	1.06687i
$404$	−14.2302	+	10.3389i	−0.707980	+	0.514378i
$405$		0			0
$406$	−0.451447			−0.0224049
$407$	27.9092	+	23.8334i	1.38341	+	1.18138i
$408$		0			0
$409$	6.50438	−	20.0184i	0.321621	−	0.989848i	−0.651322	−	0.758802i	$-0.725785\pi$
$409$	6.50438	−	20.0184i	0.321621	−	0.989848i	0.972943	−	0.231046i	$-0.0742149\pi$
$410$	0.868879	−	0.631278i	0.0429109	−	0.0311766i
$411$		0			0
$412$	0.458997	+	1.41265i	0.0226132	+	0.0695962i
$413$	0.324136	+	0.997588i	0.0159497	+	0.0490881i
$414$		0			0
$415$	17.0284	−	12.3719i	0.835892	−	0.607311i
$416$	5.97695	−	18.3952i	0.293044	−	0.901897i
$417$		0			0
$418$	0.418388	+	1.74219i	0.0204640	+	0.0852131i
$419$	−14.0827			−0.687984			−0.343992	−	0.938973i	$-0.611779\pi$
$419$	−14.0827			−0.687984			−0.343992	+	0.938973i	$0.611779\pi$
$420$		0			0
$421$	−22.3026	+	16.2038i	−1.08696	+	0.789725i	−0.978884	−	0.204417i	$-0.934470\pi$
$421$	−22.3026	+	16.2038i	−1.08696	+	0.789725i	−0.108080	+	0.994142i	$0.534470\pi$
$422$	−4.24287	−	3.08263i	−0.206540	−	0.150060i
$423$		0			0
$424$	5.57990	+	17.1732i	0.270984	+	0.834002i
$425$	1.90841	+	1.38654i	0.0925714	+	0.0672570i
$426$		0			0
$427$	−2.06929	+	6.36863i	−0.100140	+	0.308199i
$428$	−30.9869			−1.49781
$429$		0			0
$430$	−9.20279			−0.443798
$431$	10.6424	−	32.7540i	0.512627	−	1.57770i	−0.274931	−	0.961464i	$-0.588655\pi$
$431$	10.6424	−	32.7540i	0.512627	−	1.57770i	0.787558	−	0.616240i	$-0.211345\pi$
$432$		0			0
$433$	−13.0563	−	9.48594i	−0.627445	−	0.455865i	0.228069	−	0.973645i	$-0.426759\pi$
$433$	−13.0563	−	9.48594i	−0.627445	−	0.455865i	−0.855514	+	0.517780i	$0.826759\pi$
$434$	−1.00518	−	3.09363i	−0.0482502	−	0.148499i
$435$		0			0
$436$	14.0147	+	10.1823i	0.671181	+	0.487641i
$437$	4.65582	−	3.38265i	0.222718	−	0.161814i
$438$		0			0
$439$	19.3036			0.921309			0.460655	−	0.887580i	$-0.347615\pi$
$439$	19.3036			0.921309			0.460655	+	0.887580i	$0.347615\pi$
$440$	8.95180	+	7.64450i	0.426760	+	0.364437i
$441$		0			0
$442$	−4.15602	+	12.7909i	−0.197682	+	0.608402i
$443$	10.6233	−	7.71830i	0.504730	−	0.366708i	−0.306091	−	0.952002i	$-0.599021\pi$
$443$	10.6233	−	7.71830i	0.504730	−	0.366708i	0.810821	+	0.585295i	$0.199021\pi$
$444$		0			0
$445$	3.76573	+	11.5897i	0.178513	+	0.549406i
$446$	1.26748	+	3.90089i	0.0600168	+	0.184713i
$447$		0			0
$448$	3.55619	−	2.58372i	0.168014	−	0.122069i
$449$	3.94032	−	12.1270i	0.185955	−	0.572311i	−0.814008	−	0.580853i	$-0.802719\pi$
$449$	3.94032	−	12.1270i	0.185955	−	0.572311i	0.999964	+	0.00854221i	$0.00271910\pi$
$450$		0			0
$451$	3.28508	−	2.01341i	0.154688	−	0.0948077i
$452$	−8.00317			−0.376437
$453$		0			0
$454$	−0.969498	+	0.704382i	−0.0455008	+	0.0330583i
$455$	8.37802	+	6.08699i	0.392768	+	0.285362i
$456$		0			0
$457$	−2.84121	−	8.74436i	−0.132906	−	0.409044i	0.862352	−	0.506309i	$-0.168991\pi$
$457$	−2.84121	−	8.74436i	−0.132906	−	0.409044i	−0.995259	+	0.0972652i	$0.968991\pi$
$458$	−6.52083	−	4.73766i	−0.304698	−	0.221376i
$459$		0			0
$460$	5.59733	−	17.2268i	0.260977	−	0.803204i
$461$	−16.0714			−0.748521			−0.374260	−	0.927324i	$-0.622103\pi$
$461$	−16.0714			−0.748521			−0.374260	+	0.927324i	$0.622103\pi$
$462$		0			0
$463$	32.9203			1.52994			0.764968	−	0.644068i	$-0.222755\pi$
$463$	32.9203			1.52994			0.764968	+	0.644068i	$0.222755\pi$
$464$	−1.06504	+	3.27786i	−0.0494434	+	0.152171i
$465$		0			0
$466$	−1.51508	−	1.10077i	−0.0701847	−	0.0509921i
$467$	2.62969	+	8.09336i	0.121688	+	0.374516i	0.993283	−	0.115710i	$-0.0369143\pi$
$467$	2.62969	+	8.09336i	0.121688	+	0.374516i	−0.871595	+	0.490226i	$0.836914\pi$
$468$		0			0
$469$	1.99378	+	1.44857i	0.0920642	+	0.0668886i
$470$	−9.60639	+	6.97945i	−0.443110	+	0.321938i
$471$		0			0
$472$	−1.61473			−0.0743240
$473$	−32.9138	−	2.58811i	−1.51338	−	0.119001i
$474$		0			0
$475$	−0.131513	+	0.404757i	−0.00603425	+	0.0185715i
$476$	−11.1117	+	8.07310i	−0.509303	+	0.370030i
$477$		0			0
$478$	−2.82102	−	8.68220i	−0.129030	−	0.397115i
$479$	2.94258	+	9.05634i	0.134450	+	0.413795i	0.995504	−	0.0947188i	$-0.0301952\pi$
$479$	2.94258	+	9.05634i	0.134450	+	0.413795i	−0.861054	+	0.508513i	$0.830195\pi$
$480$		0			0
$481$	−40.2100	+	29.2143i	−1.83342	+	1.33206i
$482$	−0.599353	+	1.84462i	−0.0272998	+	0.0840201i
$483$		0			0
$484$	14.3078	+	14.3038i	0.650352	+	0.650175i
$485$	−13.2481			−0.601566
$486$		0			0
$487$	0.885370	−	0.643259i	0.0401199	−	0.0291488i	−0.567545	−	0.823343i	$-0.692107\pi$
$487$	0.885370	−	0.643259i	0.0401199	−	0.0291488i	0.607665	+	0.794194i	$0.292107\pi$
$488$	−8.33974	−	6.05918i	−0.377522	−	0.274286i
$489$		0			0
$490$	−0.285681	−	0.879237i	−0.0129058	−	0.0397199i
$491$	16.7211	+	12.1486i	0.754611	+	0.548257i	0.897253	−	0.441517i	$-0.145560\pi$
$491$	16.7211	+	12.1486i	0.754611	+	0.548257i	−0.142642	+	0.989774i	$0.545560\pi$
$492$		0			0
$493$	2.59815	−	7.99629i	0.117015	−	0.360135i
$494$	−2.42644			−0.109171
$495$		0			0
$496$	−24.8336			−1.11506
$497$	−2.60280	+	8.01059i	−0.116751	+	0.359324i
$498$		0			0
$499$	−19.2829	−	14.0099i	−0.863222	−	0.627167i	0.0655377	−	0.997850i	$-0.479124\pi$
$499$	−19.2829	−	14.0099i	−0.863222	−	0.627167i	−0.928760	+	0.370683i	$0.879124\pi$
$500$	−6.13808	−	18.8911i	−0.274503	−	0.844834i
$501$		0			0
$502$	−5.20830	−	3.78405i	−0.232458	−	0.168890i
$503$	12.2240	−	8.88123i	0.545039	−	0.395994i	−0.280914	−	0.959733i	$-0.590638\pi$
$503$	12.2240	−	8.88123i	0.545039	−	0.395994i	0.825953	+	0.563739i	$0.190638\pi$
$504$		0			0
$505$	22.0500			0.981210
$506$	−2.17347	+	5.24822i	−0.0966223	+	0.233312i
$507$		0			0
$508$	3.60755	−	11.1029i	0.160059	−	0.492611i
$509$	1.35615	−	0.985301i	0.0601103	−	0.0436727i	−0.557324	−	0.830295i	$-0.688172\pi$
$509$	1.35615	−	0.985301i	0.0601103	−	0.0436727i	0.617435	+	0.786622i	$0.288172\pi$
$510$		0			0
$511$	−3.33026	−	10.2495i	−0.147322	−	0.453411i
$512$	6.98600	+	21.5007i	0.308740	+	0.950206i
$513$		0			0
$514$	3.94924	−	2.86929i	0.174193	−	0.126559i
$515$	0.575392	−	1.77087i	0.0253548	−	0.0780340i
$516$		0			0
$517$	−36.3201	+	22.2604i	−1.59736	+	0.979011i
$518$	4.43703			0.194952
$519$		0			0
$520$	−12.8972	+	9.37039i	−0.565581	+	0.410919i
$521$	−29.1017	−	21.1436i	−1.27497	−	0.926319i	−0.275580	−	0.961278i	$-0.588870\pi$
$521$	−29.1017	−	21.1436i	−1.27497	−	0.926319i	−0.999389	+	0.0349596i	$0.988870\pi$
$522$		0			0
$523$	−4.93227	−	15.1800i	−0.215673	−	0.663774i	−0.999105	−	0.0422964i	$-0.986533\pi$
$523$	−4.93227	−	15.1800i	−0.215673	−	0.663774i	0.783432	−	0.621478i	$-0.213467\pi$
$524$	22.6605	+	16.4638i	0.989927	+	0.719224i
$525$		0			0
$526$	2.33919	−	7.19927i	0.101993	−	0.313903i
$527$	60.5811			2.63895
$528$		0			0
$529$	−4.75463			−0.206723
$530$	3.35097	−	10.3132i	0.145557	−	0.447978i
$531$		0			0
$532$	−2.00472	−	1.45651i	−0.0869157	−	0.0631479i
$533$	1.61243	+	4.96254i	0.0698420	+	0.214952i
$534$		0			0
$535$	31.4260	+	22.8323i	1.35867	+	0.987129i
$536$	−3.06925	+	2.22994i	−0.132571	+	0.0963188i
$537$		0			0
$538$	0.285104			0.0122917
$539$	−0.774471	−	3.22493i	−0.0333588	−	0.138908i
$540$		0			0
$541$	−2.37528	+	7.31035i	−0.102121	+	0.314296i	−0.989044	−	0.147621i	$-0.952838\pi$
$541$	−2.37528	+	7.31035i	−0.102121	+	0.314296i	0.886923	+	0.461917i	$0.152838\pi$
$542$	−4.77626	+	3.47016i	−0.205158	+	0.149056i
$543$		0			0
$544$	−9.93737	−	30.5841i	−0.426061	−	1.31128i
$545$	−6.71059	−	20.6531i	−0.287450	−	0.884681i
$546$		0			0
$547$	−12.3328	+	8.96030i	−0.527312	+	0.383115i	−0.819351	−	0.573292i	$-0.805666\pi$
$547$	−12.3328	+	8.96030i	−0.527312	+	0.383115i	0.292039	+	0.956406i	$0.405666\pi$
$548$	−10.8551	+	33.4085i	−0.463706	+	1.42714i
$549$		0			0
$550$	−0.0980941	−	0.408469i	−0.00418275	−	0.0174172i
$551$	1.51690			0.0646221
$552$		0			0
$553$	−2.19363	+	1.59376i	−0.0932826	+	0.0677738i
$554$	−5.70375	−	4.14401i	−0.242329	−	0.176062i
$555$		0			0
$556$	2.23876	+	6.89020i	0.0949447	+	0.292210i
$557$	−1.69483	−	1.23137i	−0.0718123	−	0.0521747i	0.551300	−	0.834307i	$-0.314132\pi$
$557$	−1.69483	−	1.23137i	−0.0718123	−	0.0521747i	−0.623112	+	0.782132i	$0.714132\pi$
$558$		0			0
$559$	13.8165	−	42.5228i	0.584376	−	1.79852i
$560$	−7.05793			−0.298252
$561$		0			0
$562$	−6.00363			−0.253248
$563$	−3.04944	+	9.38523i	−0.128519	+	0.395540i	−0.994526	−	0.104492i	$-0.966678\pi$
$563$	−3.04944	+	9.38523i	−0.128519	+	0.395540i	0.866007	+	0.500032i	$0.166678\pi$
$564$		0			0
$565$	8.11658	+	5.89704i	0.341467	+	0.248090i
$566$	2.16116	+	6.65135i	0.0908401	+	0.279577i
$567$		0			0
$568$	−10.4899	−	7.62135i	−0.440146	−	0.319785i
$569$	12.3543	−	8.97596i	0.517921	−	0.376292i	−0.297899	−	0.954597i	$-0.596286\pi$
$569$	12.3543	−	8.97596i	0.517921	−	0.376292i	0.815820	+	0.578306i	$0.196286\pi$
$570$		0			0
$571$	−20.5400			−0.859573			−0.429787	−	0.902930i	$-0.641411\pi$
$571$	−20.5400			−0.859573			−0.429787	+	0.902930i	$0.641411\pi$
$572$	−23.3601	+	14.3173i	−0.976734	+	0.598635i
$573$		0			0
$574$	0.143945	−	0.443017i	0.00600815	−	0.0184912i
$575$	−1.09159	+	0.793087i	−0.0455225	+	0.0330740i
$576$		0			0
$577$	13.6765	+	42.0920i	0.569362	+	1.75231i	0.654622	+	0.755956i	$0.272828\pi$
$577$	13.6765	+	42.0920i	0.569362	+	1.75231i	−0.0852608	+	0.996359i	$0.527172\pi$
$578$	4.80345	+	14.7835i	0.199797	+	0.614912i
$579$		0			0
$580$	3.86255	−	2.80631i	0.160384	−	0.116526i
$581$	2.82105	−	8.68231i	0.117037	−	0.360203i
$582$		0			0
$583$	14.8851	−	35.9428i	0.616479	−	1.48860i
$584$	16.5902			0.686507
$585$		0			0
$586$	−8.43818	+	6.13069i	−0.348578	+	0.253257i
$587$	2.88772	+	2.09805i	0.119189	+	0.0865959i	0.645783	−	0.763521i	$-0.276531\pi$
$587$	2.88772	+	2.09805i	0.119189	+	0.0865959i	−0.526594	+	0.850117i	$0.676531\pi$
$588$		0			0
$589$	3.37749	+	10.3948i	0.139167	+	0.428312i
$590$	0.784517	+	0.569985i	0.0322980	+	0.0234659i
$591$		0			0
$592$	10.4677	−	32.2164i	0.430221	−	1.32408i
$593$	−11.2563			−0.462240			−0.231120	−	0.972925i	$-0.574239\pi$
$593$	−11.2563			−0.462240			−0.231120	+	0.972925i	$0.574239\pi$
$594$		0			0
$595$	17.2177			0.705857
$596$	−11.5838	+	35.6514i	−0.474493	+	1.46034i
$597$		0			0
$598$	−6.22361	−	4.52171i	−0.254502	−	0.184907i
$599$	13.4813	+	41.4911i	0.550830	+	1.69528i	0.706708	+	0.707505i	$0.250179\pi$
$599$	13.4813	+	41.4911i	0.550830	+	1.69528i	−0.155878	+	0.987776i	$0.549821\pi$
$600$		0			0
$601$	14.3428	+	10.4206i	0.585054	+	0.425066i	0.840543	−	0.541746i	$-0.182236\pi$
$601$	14.3428	+	10.4206i	0.585054	+	0.425066i	−0.255489	+	0.966812i	$0.582236\pi$
$602$	−3.22916	+	2.34612i	−0.131611	+	0.0956208i
$603$		0			0
$604$	9.04378			0.367986
$605$	−3.97088	−	25.0490i	−0.161439	−	1.01839i
$606$		0			0
$607$	−2.21483	+	6.81655i	−0.0898972	+	0.276675i	−0.985890	−	0.167393i	$-0.946465\pi$
$607$	−2.21483	+	6.81655i	−0.0898972	+	0.276675i	0.895993	+	0.444068i	$0.146465\pi$
$608$	4.69376	−	3.41022i	0.190357	−	0.138303i
$609$		0			0
$610$	1.91303	+	5.88770i	0.0774563	+	0.238386i
$611$	−17.8271	−	54.8662i	−0.721208	−	2.21965i
$612$		0			0
$613$	10.0143	−	7.27582i	0.404474	−	0.293868i	−0.366887	−	0.930266i	$-0.619576\pi$
$613$	10.0143	−	7.27582i	0.404474	−	0.293868i	0.771361	+	0.636398i	$0.219576\pi$
$614$	−2.92321	+	8.99673i	−0.117971	+	0.363078i
$615$		0			0
$616$	5.08995	+	0.400238i	0.205080	+	0.0161260i
$617$	−6.11777			−0.246292			−0.123146	−	0.992389i	$-0.539298\pi$
$617$	−6.11777			−0.246292			−0.123146	+	0.992389i	$0.539298\pi$
$618$		0			0
$619$	−31.4088	+	22.8198i	−1.26243	+	0.917207i	−0.998874	−	0.0474378i	$-0.984894\pi$
$619$	−31.4088	+	22.8198i	−1.26243	+	0.917207i	−0.263553	+	0.964645i	$0.584894\pi$
$620$	27.8310	+	20.2204i	1.11772	+	0.812072i
$621$		0			0
$622$	0.564012	+	1.73585i	0.0226148	+	0.0696012i
$623$	4.27599	+	3.10669i	0.171314	+	0.124467i
$624$		0			0
$625$	−8.18266	+	25.1836i	−0.327306	+	1.00735i
$626$	−5.26366			−0.210378
$627$		0			0
$628$	−4.12353			−0.164547
$629$	−25.5358	+	78.5912i	−1.01818	+	3.13364i
$630$		0			0
$631$	7.85393	+	5.70621i	0.312660	+	0.227161i	0.733037	−	0.680189i	$-0.238102\pi$
$631$	7.85393	+	5.70621i	0.312660	+	0.227161i	−0.420377	+	0.907350i	$0.638102\pi$
$632$	−1.28986	−	3.96979i	−0.0513079	−	0.157910i
$633$		0			0
$634$	2.90120	+	2.10785i	0.115222	+	0.0837134i
$635$	−11.8397	+	8.60205i	−0.469844	+	0.341362i
$636$		0			0
$637$	4.49155			0.177962
$638$	−1.27659	+	0.782414i	−0.0505406	+	0.0309761i
$639$		0			0
$640$	7.39199	−	22.7502i	0.292194	−	0.899281i
$641$	−12.0125	+	8.72762i	−0.474467	+	0.344720i	−0.799179	−	0.601093i	$-0.794732\pi$
$641$	−12.0125	+	8.72762i	−0.474467	+	0.344720i	0.324713	+	0.945813i	$0.394732\pi$
$642$		0			0
$643$	−0.327423	−	1.00771i	−0.0129123	−	0.0397400i	0.944393	−	0.328820i	$-0.106651\pi$
$643$	−0.327423	−	1.00771i	−0.0129123	−	0.0397400i	−0.957305	+	0.289080i	$0.906651\pi$
$644$	−2.42769	−	7.47166i	−0.0956644	−	0.294425i
$645$		0			0
$646$	−3.26377	+	2.37126i	−0.128411	+	0.0932962i
$647$	3.88194	−	11.9474i	0.152615	−	0.469700i	−0.845297	−	0.534297i	$-0.820576\pi$
$647$	3.88194	−	11.9474i	0.152615	−	0.469700i	0.997911	+	0.0645974i	$0.0205763\pi$
$648$		0			0
$649$	2.64553	+	2.25918i	0.103846	+	0.0886806i
$650$	0.568898			0.0223140
$651$		0			0
$652$	−14.6378	+	10.6350i	−0.573259	+	0.416497i
$653$	23.9585	+	17.4069i	0.937568	+	0.681183i	0.947834	−	0.318764i	$-0.103268\pi$
$653$	23.9585	+	17.4069i	0.937568	+	0.681183i	−0.0102659	+	0.999947i	$0.503268\pi$
$654$		0			0
$655$	−10.8504	−	33.3942i	−0.423961	−	1.30482i
$656$	−2.87706	−	2.09031i	−0.112330	−	0.0816129i
$657$		0			0
$658$	−1.59147	+	4.89803i	−0.0620418	+	0.190945i
$659$	9.45208			0.368201			0.184100	−	0.982907i	$-0.441063\pi$
$659$	9.45208			0.368201			0.184100	+	0.982907i	$0.441063\pi$
$660$		0			0
$661$	−8.94284			−0.347836			−0.173918	−	0.984760i	$-0.555643\pi$
$661$	−8.94284			−0.347836			−0.173918	+	0.984760i	$0.555643\pi$
$662$	3.21292	−	9.88836i	0.124874	−	0.384322i
$663$		0			0
$664$	11.3695	+	8.26043i	0.441223	+	0.320567i
$665$	0.959913	+	2.95431i	0.0372238	+	0.114563i
$666$		0			0
$667$	3.89071	+	2.82677i	0.150649	+	0.109453i
$668$	−12.8632	+	9.34563i	−0.497690	+	0.361593i
$669$		0			0
$670$	2.27834			0.0880201
$671$	5.18614	+	21.5953i	0.200209	+	0.833679i
$672$		0			0
$673$	2.37389	−	7.30609i	0.0915068	−	0.281629i	−0.894821	−	0.446426i	$-0.852697\pi$
$673$	2.37389	−	7.30609i	0.0915068	−	0.281629i	0.986328	+	0.164797i	$0.0526968\pi$
$674$	5.11112	−	3.71345i	0.196873	−	0.143037i
$675$		0			0
$676$	−4.07735	−	12.5488i	−0.156821	−	0.482646i
$677$	10.8302	+	33.3320i	0.416240	+	1.28105i	0.911138	+	0.412102i	$0.135205\pi$
$677$	10.8302	+	33.3320i	0.416240	+	1.28105i	−0.494898	+	0.868951i	$0.664795\pi$
$678$		0			0
$679$	−4.64862	+	3.37742i	−0.178398	+	0.129613i
$680$	−8.19055	+	25.2079i	−0.314093	+	0.966679i
$681$		0			0
$682$	−8.20406	−	7.00596i	−0.314150	−	0.268272i
$683$	23.5098			0.899577			0.449789	−	0.893135i	$-0.351499\pi$
$683$	23.5098			0.899577			0.449789	+	0.893135i	$0.351499\pi$
$684$		0			0
$685$	35.6256	−	25.8835i	1.36118	−	0.988957i
$686$	−0.324392	−	0.235684i	−0.0123853	−	0.00899847i
$687$		0			0
$688$	9.41655	+	28.9812i	0.359003	+	1.10490i
$689$	42.6228	+	30.9673i	1.62380	+	1.17976i
$690$		0			0
$691$	−5.01981	+	15.4494i	−0.190963	+	0.587723i	−1.00000		3.45787e-5i	$-0.999989\pi$
$691$	−5.01981	+	15.4494i	−0.190963	+	0.587723i	0.809037	+	0.587757i	$0.199989\pi$
$692$	29.3673			1.11638
$693$		0			0
$694$	−0.894036			−0.0339371
$695$	2.80648	−	8.63745i	0.106456	−	0.327637i
$696$		0			0
$697$	7.01855	+	5.09927i	0.265846	+	0.193149i
$698$	1.19177	+	3.66788i	0.0451090	+	0.138831i
$699$		0			0
$700$	0.470022	+	0.341491i	0.0177652	+	0.0129071i
$701$	−18.2371	+	13.2501i	−0.688808	+	0.500448i	−0.876268	−	0.481824i	$-0.839974\pi$
$701$	−18.2371	+	13.2501i	−0.688808	+	0.500448i	0.187460	+	0.982272i	$0.439974\pi$
$702$		0			0
$703$	−14.9088			−0.562295
$704$	5.57816	−	13.4695i	0.210235	−	0.507650i
$705$		0			0
$706$	1.23730	−	3.80802i	0.0465664	−	0.143317i
$707$	7.73709	−	5.62132i	0.290983	−	0.211412i
$708$		0			0
$709$	7.45304	+	22.9381i	0.279905	+	0.861458i	0.987880	+	0.155221i	$0.0496089\pi$
$709$	7.45304	+	22.9381i	0.279905	+	0.861458i	−0.707975	+	0.706238i	$0.750391\pi$
$710$	2.40625	+	7.40567i	0.0903048	+	0.277930i
$711$		0			0
$712$	−6.58252	+	4.78248i	−0.246690	+	0.179231i
$713$	−10.7080	+	32.9558i	−0.401018	+	1.23421i
$714$		0			0
$715$	34.2406	+	2.69244i	1.28053	+	0.100692i
$716$	−32.3259			−1.20808
$717$		0			0
$718$	−3.32399	+	2.41502i	−0.124050	+	0.0901279i
$719$	26.0574	+	18.9318i	0.971776	+	0.706037i	0.955856	−	0.293837i	$-0.0949322\pi$
$719$	26.0574	+	18.9318i	0.971776	+	0.706037i	0.0159203	+	0.999873i	$0.494932\pi$
$720$		0			0
$721$	−0.249560	−	0.768068i	−0.00929412	−	0.0286044i
$722$	5.57461	+	4.05019i	0.207465	+	0.150732i
$723$		0			0
$724$	−11.8015	+	36.3214i	−0.438600	+	1.34987i
$725$	−0.355648			−0.0132084
$726$		0			0
$727$	7.29214			0.270450			0.135225	−	0.990815i	$-0.456824\pi$
$727$	7.29214			0.270450			0.135225	+	0.990815i	$0.456824\pi$
$728$	−2.13665	+	6.57594i	−0.0791896	+	0.243720i
$729$		0			0
$730$	−8.06034	−	5.85618i	−0.298326	−	0.216747i
$731$	−22.9715	−	70.6990i	−0.849632	−	2.61490i
$732$		0			0
$733$	−4.70741	−	3.42014i	−0.173872	−	0.126326i	0.497446	−	0.867495i	$-0.334271\pi$
$733$	−4.70741	−	3.42014i	−0.173872	−	0.126326i	−0.671318	+	0.741170i	$0.734271\pi$
$734$	−1.19786	+	0.870295i	−0.0442138	+	0.0321232i
$735$		0			0
$736$	18.3941			0.678014
$737$	8.14849	+	0.640740i	0.300154	+	0.0236020i
$738$		0			0
$739$	−4.36063	+	13.4206i	−0.160408	+	0.493686i	−0.998669	−	0.0515840i	$-0.983573\pi$
$739$	−4.36063	+	13.4206i	−0.160408	+	0.493686i	0.838260	+	0.545270i	$0.183573\pi$
$740$	−37.9629	+	27.5817i	−1.39555	+	1.01392i
$741$		0			0
$742$	−1.45339	−	4.47308i	−0.0533557	−	0.164212i
$743$	−0.704889	−	2.16943i	−0.0258599	−	0.0795885i	0.937294	−	0.348541i	$-0.113323\pi$
$743$	−0.704889	−	2.16943i	−0.0258599	−	0.0795885i	−0.963154	+	0.268952i	$0.913323\pi$
$744$		0			0
$745$	38.0173	−	27.6212i	1.39285	−	1.01196i
$746$	2.13934	−	6.58420i	0.0783267	−	0.241065i
$747$		0			0
$748$	−17.4296	+	42.0868i	−0.637288	+	1.53885i
$749$	16.8478			0.615607
$750$		0			0
$751$	20.6194	−	14.9809i	0.752412	−	0.546659i	−0.144161	−	0.989554i	$-0.546048\pi$
$751$	20.6194	−	14.9809i	0.752412	−	0.546659i	0.896574	+	0.442895i	$0.146048\pi$
$752$	31.8090	+	23.1106i	1.15996	+	0.842757i
$753$		0			0
$754$	−0.626592	−	1.92845i	−0.0228192	−	0.0702301i
$755$	−9.17194	−	6.66380i	−0.333801	−	0.242521i
$756$		0			0
$757$	7.77059	−	23.9154i	0.282427	−	0.869221i	−0.704731	−	0.709475i	$-0.748932\pi$
$757$	7.77059	−	23.9154i	0.282427	−	0.869221i	0.987158	−	0.159746i	$-0.0510677\pi$
$758$	−2.08084			−0.0755796
$759$		0			0
$760$	−4.78195			−0.173460
$761$	−8.79224	+	27.0597i	−0.318718	+	0.980914i	0.655478	+	0.755214i	$0.272467\pi$
$761$	−8.79224	+	27.0597i	−0.318718	+	0.980914i	−0.974197	+	0.225700i	$0.927533\pi$
$762$		0			0
$763$	−7.61988	−	5.53617i	−0.275858	−	0.200423i
$764$	5.96775	+	18.3668i	0.215906	+	0.664489i
$765$		0			0
$766$	−5.71616	−	4.15303i	−0.206533	−	0.150055i
$767$	−3.81152	+	2.76923i	−0.137626	+	0.0999912i
$768$		0			0
$769$	−45.0119			−1.62317			−0.811586	−	0.584233i	$-0.801395\pi$
$769$	−45.0119			−1.62317			−0.811586	+	0.584233i	$0.801395\pi$
$770$	−2.33167	−	1.99116i	−0.0840275	−	0.0717564i
$771$		0			0
$772$	7.36017	−	22.6523i	0.264898	−	0.815273i
$773$	24.9705	−	18.1422i	0.898128	−	0.652528i	−0.0398566	−	0.999205i	$-0.512690\pi$
$773$	24.9705	−	18.1422i	0.898128	−	0.652528i	0.937984	+	0.346677i	$0.112690\pi$
$774$		0			0
$775$	−0.791877	−	2.43715i	−0.0284451	−	0.0875449i
$776$	−2.73340	−	8.41255i	−0.0981235	−	0.301993i
$777$		0			0
$778$	3.44466	−	2.50269i	0.123497	−	0.0897258i
$779$	−0.483667	+	1.48857i	−0.0173292	+	0.0533337i
$780$		0			0
$781$	6.52324	+	27.1631i	0.233420	+	0.971971i
$782$	−12.7902			−0.457375
$783$		0			0
$784$	−2.47655	+	1.79932i	−0.0884483	+	0.0642614i
$785$	4.18196	+	3.03837i	0.149261	+	0.108444i
$786$		0			0
$787$	−11.0176	−	33.9085i	−0.392733	−	1.20871i	−0.930713	−	0.365751i	$-0.880812\pi$
$787$	−11.0176	−	33.9085i	−0.392733	−	1.20871i	0.537980	−	0.842958i	$-0.319188\pi$
$788$	−0.988326	−	0.718061i	−0.0352077	−	0.0255799i
$789$		0			0
$790$	−0.774618	+	2.38403i	−0.0275597	+	0.0848199i
$791$	4.35139			0.154718
$792$		0			0
$793$	−30.0771			−1.06807
$794$	2.80353	−	8.62838i	0.0994935	−	0.306210i
$795$		0			0
$796$	19.8717	+	14.4376i	0.704334	+	0.511729i
$797$	−13.7032	−	42.1740i	−0.485391	−	1.49388i	−0.831414	−	0.555653i	$-0.812468\pi$
$797$	−13.7032	−	42.1740i	−0.485391	−	1.49388i	0.346023	−	0.938226i	$-0.387532\pi$
$798$		0			0
$799$	−77.5975	−	56.3779i	−2.74520	−	1.99451i
$800$	−1.10049	+	0.799551i	−0.0389081	+	0.0282684i
$801$		0			0
$802$	−1.84827			−0.0652647
$803$	−27.1809	−	23.2114i	−0.959191	−	0.819114i
$804$		0			0
$805$	−3.04331	+	9.36635i	−0.107263	+	0.330120i
$806$	11.8199	−	8.58769i	0.416340	−	0.302488i
$807$		0			0
$808$	4.54944	+	14.0017i	0.160049	+	0.492579i
$809$	−1.98179	−	6.09932i	−0.0696760	−	0.214441i	0.910155	−	0.414267i	$-0.135962\pi$
$809$	−1.98179	−	6.09932i	−0.0696760	−	0.214441i	−0.979831	+	0.199827i	$0.935962\pi$
$810$		0			0
$811$	−27.9849	+	20.3322i	−0.982683	+	0.713961i	−0.958307	−	0.285742i	$-0.907760\pi$
$811$	−27.9849	+	20.3322i	−0.982683	+	0.713961i	−0.0243767	+	0.999703i	$0.507760\pi$
$812$	0.639899	−	1.96941i	0.0224561	−	0.0691126i
$813$		0			0
$814$	12.5469	−	7.68992i	0.439768	−	0.269532i
$815$	22.6814			0.794496
$816$		0			0
$817$	10.8502	−	7.88316i	0.379602	−	0.275797i
$818$	−6.82800	−	4.96083i	−0.238735	−	0.173451i
$819$		0			0
$820$	1.52232	+	4.68522i	0.0531618	+	0.163615i
$821$	−11.1679	−	8.11394i	−0.389762	−	0.283178i	0.375596	−	0.926783i	$-0.377438\pi$
$821$	−11.1679	−	8.11394i	−0.389762	−	0.283178i	−0.765358	+	0.643605i	$0.777438\pi$
$822$		0			0
$823$	−17.5513	+	54.0174i	−0.611801	+	1.88293i	−0.171168	+	0.985242i	$0.554754\pi$
$823$	−17.5513	+	54.0174i	−0.611801	+	1.88293i	−0.440633	+	0.897687i	$0.645246\pi$
$824$	1.24322			0.0433097
$825$		0			0
$826$	0.420588			0.0146341
$827$	−1.63590	+	5.03480i	−0.0568860	+	0.175077i	−0.975462	−	0.220167i	$-0.929340\pi$
$827$	−1.63590	+	5.03480i	−0.0568860	+	0.175077i	0.918576	+	0.395244i	$0.129340\pi$
$828$		0			0
$829$	−24.8059	−	18.0225i	−0.861544	−	0.625948i	0.0667606	−	0.997769i	$-0.478734\pi$
$829$	−24.8059	−	18.0225i	−0.861544	−	0.625948i	−0.928305	+	0.371821i	$0.878734\pi$
$830$	−2.60802	−	8.02666i	−0.0905257	−	0.278609i
$831$		0			0
$832$	15.9728	+	11.6049i	0.553757	+	0.402328i
$833$	6.04150	−	4.38941i	0.209326	−	0.152084i
$834$		0			0
$835$	19.9316			0.689763
$836$	−8.19321	−	0.644257i	−0.283368	−	0.0222821i
$837$		0			0
$838$	−1.74494	+	5.37036i	−0.0602778	+	0.185516i
$839$	−12.5166	+	9.09388i	−0.432123	+	0.313956i	−0.782497	−	0.622654i	$-0.786054\pi$
$839$	−12.5166	+	9.09388i	−0.432123	+	0.313956i	0.350374	+	0.936610i	$0.386054\pi$
$840$		0			0
$841$	−8.56978	−	26.3751i	−0.295510	−	0.909485i
$842$	3.41580	+	10.5128i	0.117716	+	0.362294i
$843$		0			0
$844$	19.4618	−	14.1398i	0.669901	−	0.486712i
$845$	−5.11130	+	15.7310i	−0.175834	+	0.541162i
$846$		0			0
$847$	−7.77924	−	7.77711i	−0.267298	−	0.267225i
$848$	−35.9069			−1.23305
$849$		0			0
$850$	0.765214	−	0.555961i	0.0262466	−	0.0190693i
$851$	−38.2397	−	27.7827i	−1.31084	−	0.952380i
$852$		0			0
$853$	−11.2368	−	34.5834i	−0.384741	−	1.18411i	−0.936668	−	0.350219i	$-0.886107\pi$
$853$	−11.2368	−	34.5834i	−0.384741	−	1.18411i	0.551927	−	0.833893i	$-0.313893\pi$
$854$	2.17225	+	1.57823i	0.0743327	+	0.0540059i
$855$		0			0
$856$	−8.01460	+	24.6664i	−0.273933	+	0.843080i
$857$	−17.0833			−0.583554			−0.291777	−	0.956486i	$-0.594246\pi$
$857$	−17.0833			−0.583554			−0.291777	+	0.956486i	$0.594246\pi$
$858$		0			0
$859$	21.3315			0.727822			0.363911	−	0.931434i	$-0.381441\pi$
$859$	21.3315			0.727822			0.363911	+	0.931434i	$0.381441\pi$
$860$	13.0444	−	40.1465i	0.444810	−	1.36899i
$861$		0			0
$862$	−11.1719	−	8.11687i	−0.380517	−	0.276462i
$863$	−4.61965	−	14.2178i	−0.157255	−	0.483980i	0.841128	−	0.540837i	$-0.181892\pi$
$863$	−4.61965	−	14.2178i	−0.157255	−	0.483980i	−0.998382	+	0.0568564i	$0.981892\pi$
$864$		0			0
$865$	−29.7835	−	21.6390i	−1.01267	−	0.735747i
$866$	−5.23518	+	3.80358i	−0.177899	+	0.129251i
$867$		0			0
$868$	14.9205			0.506435
$869$	−3.44088	+	8.30863i	−0.116724	+	0.281851i
$870$		0			0
$871$	−3.42057	+	10.5274i	−0.115901	+	0.356708i
$872$	11.7302	−	8.52246i	0.397233	−	0.288607i
$873$		0			0
$874$	−0.713071	−	2.19461i	−0.0241200	−	0.0742336i
$875$	3.33732	+	10.2712i	0.112822	+	0.347230i
$876$		0			0
$877$	−13.9555	+	10.1392i	−0.471242	+	0.342378i	−0.797925	−	0.602756i	$-0.794069\pi$
$877$	−13.9555	+	10.1392i	−0.471242	+	0.342378i	0.326683	+	0.945134i	$0.394069\pi$
$878$	2.39184	−	7.36132i	0.0807207	−	0.248433i
$879$		0			0
$880$	−19.9582	+	12.2323i	−0.672791	+	0.412350i
$881$	2.58251			0.0870069			0.0435035	−	0.999053i	$-0.486148\pi$
$881$	2.58251			0.0870069			0.0435035	+	0.999053i	$0.486148\pi$
$882$		0			0
$883$	−29.2922	+	21.2821i	−0.985762	+	0.716198i	−0.958989	−	0.283443i	$-0.908523\pi$
$883$	−29.2922	+	21.2821i	−0.985762	+	0.716198i	−0.0267732	+	0.999642i	$0.508523\pi$
$884$	−49.9086	−	36.2607i	−1.67861	−	1.21958i
$885$		0			0
$886$	−1.62704	−	5.00751i	−0.0546614	−	0.168230i
$887$	43.0200	+	31.2559i	1.44447	+	1.04947i	0.987084	+	0.160202i	$0.0512146\pi$
$887$	43.0200	+	31.2559i	1.44447	+	1.04947i	0.457387	+	0.889268i	$0.348785\pi$
$888$		0			0
$889$	−1.96145	+	6.03673i	−0.0657850	+	0.202465i
$890$	4.88629			0.163789
$891$		0			0
$892$	−18.8140			−0.629938
$893$	5.34745	−	16.4578i	0.178946	−	0.550738i
$894$		0			0
$895$	32.7840	+	23.8190i	1.09585	+	0.796180i
$896$	−3.20608	−	9.86729i	−0.107108	−	0.329643i
$897$		0			0
$898$	−4.13636	−	3.00524i	−0.138032	−	0.100286i
$899$	−7.38928	+	5.36862i	−0.246446	+	0.179054i
$900$		0			0
$901$	87.5943			2.91819
$902$	−0.360761	−	1.50222i	−0.0120120	−	0.0500186i
$903$		0			0
$904$	−2.06998	+	6.37073i	−0.0688464	+	0.211887i
$905$	38.7317	−	28.1402i	1.28749	−	0.935414i
$906$		0			0
$907$	15.1300	+	46.5653i	0.502382	+	1.54617i	0.805127	+	0.593102i	$0.202097\pi$
$907$	15.1300	+	46.5653i	0.502382	+	1.54617i	−0.302745	+	0.953072i	$0.597903\pi$
$908$	−1.69861	−	5.22779i	−0.0563704	−	0.173490i
$909$		0			0
$910$	3.35934	−	2.44070i	0.111361	−	0.0809084i
$911$	−0.308429	+	0.949246i	−0.0102187	+	0.0314499i	−0.956036	−	0.293250i	$-0.905263\pi$
$911$	−0.308429	+	0.949246i	−0.0102187	+	0.0314499i	0.945817	+	0.324700i	$0.105263\pi$
$912$		0			0
$913$	−7.07024	−	29.4408i	−0.233991	−	0.974348i
$914$	−3.68667			−0.121944
$915$		0			0
$916$	29.9106	−	21.7313i	0.988274	−	0.718023i
$917$	−12.3207	−	8.95149i	−0.406864	−	0.295604i
$918$		0			0
$919$	16.4871	+	50.7420i	0.543859	+	1.67382i	0.723688	+	0.690127i	$0.242445\pi$
$919$	16.4871	+	50.7420i	0.543859	+	1.67382i	−0.179830	+	0.983698i	$0.557555\pi$
$920$	−12.2653	−	8.91124i	−0.404374	−	0.293795i
$921$		0			0
$922$	−1.99136	+	6.12876i	−0.0655818	+	0.201840i
$923$	−37.8315			−1.24524
$924$		0			0
$925$	3.49547			0.114930
$926$	4.07904	−	12.5540i	0.134046	−	0.412550i
$927$		0			0
$928$	3.92242	+	2.84980i	0.128760	+	0.0935494i
$929$	−0.842763	−	2.59376i	−0.0276501	−	0.0850984i	0.936279	−	0.351257i	$-0.114246\pi$
$929$	−0.842763	−	2.59376i	−0.0276501	−	0.0850984i	−0.963929	+	0.266158i	$0.914246\pi$
$930$		0			0
$931$	1.08998	+	0.791919i	0.0357227	+	0.0259541i
$932$	6.94956	−	5.04915i	0.227641	−	0.165391i
$933$		0			0
$934$	3.41220			0.111651
$935$	48.6877	−	29.8404i	1.59226	−	0.975886i
$936$		0			0
$937$	3.91631	−	12.0532i	0.127940	−	0.393760i	−0.866485	−	0.499203i	$-0.833626\pi$
$937$	3.91631	−	12.0532i	0.127940	−	0.393760i	0.994425	+	0.105443i	$0.0336261\pi$
$938$	0.799446	−	0.580832i	0.0261028	−	0.0189648i
$939$		0			0
$940$	−16.8309	−	51.8002i	−0.548963	−	1.68954i
$941$	1.85489	+	5.70877i	0.0604677	+	0.186101i	0.976727	−	0.214484i	$-0.0688070\pi$
$941$	1.85489	+	5.70877i	0.0604677	+	0.186101i	−0.916260	+	0.400585i	$0.868807\pi$
$942$		0			0
$943$	−4.01454	+	2.91674i	−0.130731	+	0.0949820i
$944$	0.992241	−	3.05380i	0.0322947	−	0.0993928i
$945$		0			0
$946$	−5.06520	+	12.2308i	−0.164684	+	0.397658i
$947$	20.2935			0.659450			0.329725	−	0.944077i	$-0.393044\pi$
$947$	20.2935			0.659450			0.329725	+	0.944077i	$0.393044\pi$
$948$		0			0
$949$	39.1606	−	28.4519i	1.27121	−	0.923586i
$950$	0.138057	+	0.100304i	0.00447915	+	0.00325429i
$951$		0			0
$952$	3.55243	+	10.9332i	0.115135	+	0.354349i
$953$	−20.7822	−	15.0991i	−0.673201	−	0.489109i	0.197894	−	0.980223i	$-0.436590\pi$
$953$	−20.7822	−	15.0991i	−0.673201	−	0.489109i	−0.871095	+	0.491115i	$0.836590\pi$
$954$		0			0
$955$	7.48108	−	23.0244i	0.242082	−	0.745052i
$956$	41.8741			1.35431
$957$		0			0
$958$	3.81820			0.123360
$959$	5.90200	−	18.1645i	0.190585	−	0.586561i
$960$		0			0
$961$	−28.1628	−	20.4614i	−0.908476	−	0.660047i
$962$	6.15844	+	18.9537i	0.198556	+	0.611093i
$963$		0			0
$964$	−7.19748	−	5.22927i	−0.231815	−	0.168424i
$965$	−24.1555	+	17.5500i	−0.777594	+	0.564955i
$966$		0			0
$967$	−3.86788			−0.124383			−0.0621914	−	0.998064i	$-0.519809\pi$
$967$	−3.86788			−0.124383			−0.0621914	+	0.998064i	$0.519809\pi$
$968$	15.0869	−	7.68973i	0.484910	−	0.247157i
$969$		0			0
$970$	−1.64153	+	5.05210i	−0.0527063	+	0.162213i
$971$	−20.8901	+	15.1776i	−0.670397	+	0.487072i	−0.870158	−	0.492773i	$-0.835983\pi$
$971$	−20.8901	+	15.1776i	−0.670397	+	0.487072i	0.199761	+	0.979845i	$0.435983\pi$
$972$		0			0
$973$	−1.21723	−	3.74626i	−0.0390227	−	0.120100i
$974$	−0.135601	−	0.417336i	−0.00434492	−	0.0133723i
$975$		0			0
$976$	16.5839	−	12.0489i	0.530838	−	0.385676i
$977$	16.1377	−	49.6667i	0.516291	−	1.58898i	−0.264631	−	0.964350i	$-0.585250\pi$
$977$	16.1377	−	49.6667i	0.516291	−	1.58898i	0.780921	−	0.624630i	$-0.214750\pi$
$978$		0			0
$979$	17.4758	+	1.37417i	0.558529	+	0.0439188i
$980$	4.24055			0.135459
$981$		0			0
$982$	6.70465	−	4.87121i	0.213954	−	0.155447i
$983$	−26.2894	−	19.1004i	−0.838502	−	0.609208i	0.0834495	−	0.996512i	$-0.473406\pi$
$983$	−26.2894	−	19.1004i	−0.838502	−	0.609208i	−0.921952	+	0.387304i	$0.873406\pi$
$984$		0			0
$985$	0.473237	+	1.45647i	0.0150786	+	0.0464071i
$986$	−2.72742	−	1.98159i	−0.0868587	−	0.0631065i
$987$		0			0
$988$	3.43934	−	10.5852i	0.109420	−	0.336760i
$989$	42.5203			1.35207
$990$		0			0
$991$	1.37062			0.0435391			0.0217695	−	0.999763i	$-0.493070\pi$
$991$	1.37062			0.0435391			0.0217695	+	0.999763i	$0.493070\pi$
$992$	−10.7953	+	33.2244i	−0.342750	+	1.05488i
$993$		0			0
$994$	2.73230	+	1.98513i	0.0866632	+	0.0629645i
$995$	−9.51510	−	29.2845i	−0.301649	−	0.928380i
$996$		0			0
$997$	−6.99282	−	5.08058i	−0.221465	−	0.160904i	0.471521	−	0.881855i	$-0.343705\pi$
$997$	−6.99282	−	5.08058i	−0.221465	−	0.160904i	−0.692986	+	0.720951i	$0.743705\pi$
$998$	−7.73187	+	5.61753i	−0.244748	+	0.177820i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.k.64.5	yes	32
3.2	odd	2	inner	693.2.m.k.64.4	✓	32
11.4	even	5		7623.2.a.dc.1.9		16
11.5	even	5	inner	693.2.m.k.379.5	yes	32
11.7	odd	10		7623.2.a.db.1.8		16
33.5	odd	10	inner	693.2.m.k.379.4	yes	32
33.26	odd	10		7623.2.a.dc.1.8		16
33.29	even	10		7623.2.a.db.1.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.64.4	✓	32	3.2	odd	2	inner
693.2.m.k.64.5	yes	32	1.1	even	1	trivial
693.2.m.k.379.4	yes	32	33.5	odd	10	inner
693.2.m.k.379.5	yes	32	11.5	even	5	inner
7623.2.a.db.1.8		16	11.7	odd	10
7623.2.a.db.1.9		16	33.29	even	10
7623.2.a.dc.1.8		16	33.26	odd	10
7623.2.a.dc.1.9		16	11.4	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.123907 - 0.381345i) q^{2} +(1.48796 + 1.08107i) q^{4} +(-0.712476 - 2.19277i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(1.24541 - 0.904845i) q^{8} +O(q^{10})\)	\(q+(0.123907 - 0.381345i) q^{2} +(1.48796 + 1.08107i) q^{4} +(-0.712476 - 2.19277i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(1.24541 - 0.904845i) q^{8} -0.924485 q^{10} +(-3.30642 - 0.259994i) q^{11} +(1.38796 - 4.27172i) q^{13} +(-0.324392 + 0.235684i) q^{14} +(0.945959 + 2.91136i) q^{16} +(-2.30765 - 7.10221i) q^{17} +(1.08998 - 0.791919i) q^{19} +(1.31040 - 4.03300i) q^{20} +(-0.508834 + 1.22867i) q^{22} +4.27146 q^{23} +(-0.255555 + 0.185671i) q^{25} +(-1.45702 - 1.05859i) q^{26} +(-0.568351 - 1.74920i) q^{28} +(0.910862 + 0.661780i) q^{29} +(-2.50687 + 7.71535i) q^{31} +4.30627 q^{32} -2.99433 q^{34} +(-0.712476 + 2.19277i) q^{35} +(-8.95237 - 6.50427i) q^{37} +(-0.166938 - 0.513784i) q^{38} +(-2.87145 - 2.08623i) q^{40} +(-0.939852 + 0.682843i) q^{41} +9.95451 q^{43} +(-4.63876 - 3.96132i) q^{44} +(0.529262 - 1.62890i) q^{46} +(10.3911 - 7.54956i) q^{47} +(0.309017 + 0.951057i) q^{49} +(0.0391400 + 0.120460i) q^{50} +(6.68326 - 4.85567i) q^{52} +(-3.62469 + 11.1556i) q^{53} +(1.78564 + 7.43547i) q^{55} -1.53941 q^{56} +(0.365228 - 0.265354i) q^{58} +(-0.848599 - 0.616543i) q^{59} +(-2.06929 - 6.36863i) q^{61} +(2.63160 + 1.91197i) q^{62} +(-1.35834 + 4.18055i) q^{64} -10.3558 q^{65} -2.46445 q^{67} +(4.24428 - 13.0626i) q^{68} +(0.747924 + 0.543398i) q^{70} +(-2.60280 - 8.01059i) q^{71} +(8.71874 + 6.33453i) q^{73} +(-3.58963 + 2.60802i) q^{74} +2.47797 q^{76} +(2.52213 + 2.15380i) q^{77} +(0.837891 - 2.57876i) q^{79} +(5.70999 - 4.14855i) q^{80} +(0.143945 + 0.443017i) q^{82} +(2.82105 + 8.68231i) q^{83} +(-13.9294 + 10.1203i) q^{85} +(1.23343 - 3.79610i) q^{86} +(-4.35311 + 2.66800i) q^{88} -5.28542 q^{89} +(-3.63374 + 2.64007i) q^{91} +(6.35577 + 4.61774i) q^{92} +(-1.59147 - 4.89803i) q^{94} +(-2.51309 - 1.82586i) q^{95} +(1.77561 - 5.46478i) q^{97} +0.400970 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) 32 * q - 10 * q^4 - 8 * q^7	\( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

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