LMFDB - Embedded newform 675.2.l.h.76.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			76.13
Character	$\chi$	$=$	675.76
Dual form			675.2.l.h.151.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26326 - 1.06000i) q^{2} +(-1.44261 - 0.958575i) q^{3} +(0.124928 - 0.708504i) q^{4} +(-2.83849 + 0.318243i) q^{6} +(0.215456 + 1.22191i) q^{7} +(1.05587 + 1.82882i) q^{8} +(1.16227 + 2.76571i) q^{9} +(3.30366 + 1.20243i) q^{11} +(-0.859377 + 0.902344i) q^{12} +(0.452936 + 0.380059i) q^{13} +(1.56741 + 1.31521i) q^{14} +(4.62449 + 1.68318i) q^{16} +(2.58056 - 4.46967i) q^{17} +(4.39990 + 2.26180i) q^{18} +(1.41748 + 2.45515i) q^{19} +(0.860474 - 1.96928i) q^{21} +(5.44797 - 1.98290i) q^{22} +(1.16257 - 6.59324i) q^{23} +(0.229849 - 3.65042i) q^{24} +0.975040 q^{26} +(0.974431 - 5.10397i) q^{27} +0.892646 q^{28} +(-7.21421 + 6.05345i) q^{29} +(0.196771 - 1.11595i) q^{31} +(3.65733 - 1.33116i) q^{32} +(-3.61329 - 4.90146i) q^{33} +(-1.47793 - 8.38176i) q^{34} +(2.10471 - 0.477957i) q^{36} +(-2.34734 + 4.06570i) q^{37} +(4.39311 + 1.59896i) q^{38} +(-0.289098 - 0.982452i) q^{39} +(4.43129 + 3.71830i) q^{41} +(-1.00044 - 3.39982i) q^{42} +(-2.03181 - 0.739520i) q^{43} +(1.26465 - 2.19044i) q^{44} +(-5.52022 - 9.56131i) q^{46} +(1.08312 + 6.14268i) q^{47} +(-5.05791 - 6.86110i) q^{48} +(5.13120 - 1.86760i) q^{49} +(-8.00727 + 3.97434i) q^{51} +(0.325858 - 0.273427i) q^{52} +8.21098 q^{53} +(-4.17926 - 7.48054i) q^{54} +(-2.00717 + 1.68421i) q^{56} +(0.308566 - 4.90059i) q^{57} +(-2.69677 + 15.2942i) q^{58} +(12.6981 - 4.62173i) q^{59} +(-1.38440 - 7.85133i) q^{61} +(-0.934331 - 1.61831i) q^{62} +(-3.12903 + 2.01608i) q^{63} +(-1.71215 + 2.96553i) q^{64} +(-9.76008 - 2.36173i) q^{66} +(-3.37266 - 2.83000i) q^{67} +(-2.84439 - 2.38673i) q^{68} +(-7.99725 + 8.39709i) q^{69} +(-3.43788 + 5.95458i) q^{71} +(-3.83078 + 5.04582i) q^{72} +(0.715668 + 1.23957i) q^{73} +(1.34436 + 7.62423i) q^{74} +(1.91656 - 0.697573i) q^{76} +(-0.757476 + 4.29586i) q^{77} +(-1.40661 - 0.934649i) q^{78} +(0.970806 - 0.814603i) q^{79} +(-6.29826 + 6.42899i) q^{81} +9.53928 q^{82} +(1.17090 - 0.982501i) q^{83} +(-1.28774 - 0.855668i) q^{84} +(-3.35061 + 1.21952i) q^{86} +(16.2100 - 1.81742i) q^{87} +(1.28920 + 7.31144i) q^{88} +(-6.52774 - 11.3064i) q^{89} +(-0.366811 + 0.635335i) q^{91} +(-4.52610 - 1.64736i) q^{92} +(-1.35358 + 1.42126i) q^{93} +(7.87952 + 6.61170i) q^{94} +(-6.55214 - 1.58548i) q^{96} +(-13.0234 - 4.74011i) q^{97} +(4.50238 - 7.79835i) q^{98} +(0.514163 + 10.5345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	1.26326	−	1.06000i	0.893261	−	0.749535i	−0.0756008	−	0.997138i	$-0.524087\pi$
$2$	1.26326	−	1.06000i	0.893261	−	0.749535i	0.968861	+	0.247604i	$0.0796430\pi$
$3$	−1.44261	−	0.958575i	−0.832893	−	0.553433i
$3$	−1.44261	−	0.958575i	−0.832893	−	0.553433i
$4$	0.124928	−	0.708504i	0.0624641	−	0.354252i
$5$		0			0
$5$		0			0
$6$	−2.83849	+	0.318243i	−1.15881	+	0.129922i
$7$	0.215456	+	1.22191i	0.0814348	+	0.461840i	0.998069	+	0.0621128i	$0.0197839\pi$
$7$	0.215456	+	1.22191i	0.0814348	+	0.461840i	−0.916634	+	0.399727i	$0.869105\pi$
$8$	1.05587	+	1.82882i	0.373307	+	0.646587i
$9$	1.16227	+	2.76571i	0.387423	+	0.921902i
$10$		0			0
$11$	3.30366	+	1.20243i	0.996092	+	0.362548i	0.788076	−	0.615578i	$-0.211077\pi$
$11$	3.30366	+	1.20243i	0.996092	+	0.362548i	0.208016	+	0.978125i	$0.433299\pi$
$12$	−0.859377	+	0.902344i	−0.248081	+	0.260484i
$13$	0.452936	+	0.380059i	0.125622	+	0.105409i	0.703434	−	0.710760i	$-0.251649\pi$
$13$	0.452936	+	0.380059i	0.125622	+	0.105409i	−0.577812	+	0.816170i	$0.696093\pi$
$14$	1.56741	+	1.31521i	0.418907	+	0.351505i
$15$		0			0
$16$	4.62449	+	1.68318i	1.15612	+	0.420794i
$17$	2.58056	−	4.46967i	0.625879	−	1.08405i	−0.362491	−	0.931987i	$-0.618074\pi$
$17$	2.58056	−	4.46967i	0.625879	−	1.08405i	0.988370	−	0.152067i	$-0.0485929\pi$
$18$	4.39990	+	2.26180i	1.03707	+	0.533112i
$19$	1.41748	+	2.45515i	0.325192	+	0.563250i	0.981551	−	0.191199i	$-0.0612376\pi$
$19$	1.41748	+	2.45515i	0.325192	+	0.563250i	−0.656359	+	0.754449i	$0.727904\pi$
$20$		0			0
$21$	0.860474	−	1.96928i	0.187771	−	0.429732i
$22$	5.44797	−	1.98290i	1.16151	−	0.422756i
$23$	1.16257	−	6.59324i	0.242412	−	1.37479i	−0.584016	−	0.811742i	$-0.698519\pi$
$23$	1.16257	−	6.59324i	0.242412	−	1.37479i	0.826427	−	0.563043i	$-0.190370\pi$
$24$	0.229849	−	3.65042i	0.0469177	−	0.745139i
$25$		0			0
$26$	0.975040			0.191221
$27$	0.974431	−	5.10397i	0.187529	−	0.982259i
$28$	0.892646			0.168694
$29$	−7.21421	+	6.05345i	−1.33965	+	1.12410i	−0.357929	+	0.933749i	$0.616517\pi$
$29$	−7.21421	+	6.05345i	−1.33965	+	1.12410i	−0.981717	+	0.190348i	$0.939038\pi$
$30$		0			0
$31$	0.196771	−	1.11595i	0.0353412	−	0.200430i	−0.962025	−	0.272962i	$-0.911997\pi$
$31$	0.196771	−	1.11595i	0.0353412	−	0.200430i	0.997366	+	0.0725319i	$0.0231079\pi$
$32$	3.65733	−	1.33116i	0.646531	−	0.235318i
$33$	−3.61329	−	4.90146i	−0.628992	−	0.853234i
$34$	−1.47793	−	8.38176i	−0.253463	−	1.43746i
$35$		0			0
$36$	2.10471	−	0.477957i	0.350785	−	0.0796595i
$37$	−2.34734	+	4.06570i	−0.385900	+	0.668398i	−0.991894	−	0.127072i	$-0.959442\pi$
$37$	−2.34734	+	4.06570i	−0.385900	+	0.668398i	0.605994	+	0.795469i	$0.292776\pi$
$38$	4.39311	+	1.59896i	0.712657	+	0.259386i
$39$	−0.289098	−	0.982452i	−0.0462927	−	0.157318i
$40$		0			0
$41$	4.43129	+	3.71830i	0.692052	+	0.580700i	0.919500	−	0.393090i	$-0.128594\pi$
$41$	4.43129	+	3.71830i	0.692052	+	0.580700i	−0.227448	+	0.973790i	$0.573038\pi$
$42$	−1.00044	−	3.39982i	−0.154371	−	0.524603i
$43$	−2.03181	−	0.739520i	−0.309849	−	0.112776i	0.182415	−	0.983222i	$-0.441608\pi$
$43$	−2.03181	−	0.739520i	−0.309849	−	0.112776i	−0.492264	+	0.870446i	$0.663831\pi$
$44$	1.26465	−	2.19044i	0.190653	−	0.330221i
$45$		0			0
$46$	−5.52022	−	9.56131i	−0.813913	−	1.40974i
$47$	1.08312	+	6.14268i	0.157989	+	0.896002i	0.956002	+	0.293361i	$0.0947739\pi$
$47$	1.08312	+	6.14268i	0.157989	+	0.896002i	−0.798012	+	0.602641i	$0.794115\pi$
$48$	−5.05791	−	6.86110i	−0.730046	−	0.990314i
$49$	5.13120	−	1.86760i	0.733029	−	0.266801i
$50$		0			0
$51$	−8.00727	+	3.97434i	−1.12124	+	0.556519i
$52$	0.325858	−	0.273427i	0.0451883	−	0.0379175i
$53$	8.21098			1.12787			0.563933	−	0.825821i	$-0.309288\pi$
$53$	8.21098			1.12787			0.563933	+	0.825821i	$0.309288\pi$
$54$	−4.17926	−	7.48054i	−0.568725	−	1.01797i
$55$		0			0
$56$	−2.00717	+	1.68421i	−0.268219	+	0.225063i
$57$	0.308566	−	4.90059i	0.0408706	−	0.649099i
$58$	−2.69677	+	15.2942i	−0.354104	+	2.00822i
$59$	12.6981	−	4.62173i	1.65315	−	0.601698i	0.663886	−	0.747833i	$-0.268906\pi$
$59$	12.6981	−	4.62173i	1.65315	−	0.601698i	0.989265	+	0.146136i	$0.0466836\pi$
$60$		0			0
$61$	−1.38440	−	7.85133i	−0.177254	−	1.00526i	−0.935509	−	0.353302i	$-0.885059\pi$
$61$	−1.38440	−	7.85133i	−0.177254	−	1.00526i	0.758255	−	0.651958i	$-0.226052\pi$
$62$	−0.934331	−	1.61831i	−0.118660	−	0.205525i
$63$	−3.12903	+	2.01608i	−0.394221	+	0.254002i
$64$	−1.71215	+	2.96553i	−0.214019	+	0.370691i
$65$		0			0
$66$	−9.76008	−	2.36173i	−1.20138	−	0.290709i
$67$	−3.37266	−	2.83000i	−0.412036	−	0.345739i	0.413088	−	0.910691i	$-0.364450\pi$
$67$	−3.37266	−	2.83000i	−0.412036	−	0.345739i	−0.825124	+	0.564952i	$0.808895\pi$
$68$	−2.84439	−	2.38673i	−0.344933	−	0.289433i
$69$	−7.99725	+	8.39709i	−0.962755	+	1.01089i
$70$		0			0
$71$	−3.43788	+	5.95458i	−0.408001	+	0.706679i	−0.994666	−	0.103151i	$-0.967107\pi$
$71$	−3.43788	+	5.95458i	−0.408001	+	0.706679i	0.586664	+	0.809830i	$0.300441\pi$
$72$	−3.83078	+	5.04582i	−0.451462	+	0.594655i
$73$	0.715668	+	1.23957i	0.0837626	+	0.145081i	0.904863	−	0.425702i	$-0.139973\pi$
$73$	0.715668	+	1.23957i	0.0837626	+	0.145081i	−0.821101	+	0.570783i	$0.806640\pi$
$74$	1.34436	+	7.62423i	0.156278	+	0.886298i
$75$		0			0
$76$	1.91656	−	0.697573i	0.219845	−	0.0800171i
$77$	−0.757476	+	4.29586i	−0.0863224	+	0.489559i
$78$	−1.40661	−	0.934649i	−0.159267	−	0.105828i
$79$	0.970806	−	0.814603i	0.109224	−	0.0916500i	−0.586540	−	0.809920i	$-0.699510\pi$
$79$	0.970806	−	0.814603i	0.109224	−	0.0916500i	0.695764	+	0.718270i	$0.255066\pi$
$80$		0			0
$81$	−6.29826	+	6.42899i	−0.699807	+	0.714332i
$82$	9.53928			1.05344
$83$	1.17090	−	0.982501i	0.128523	−	0.107844i	−0.576260	−	0.817266i	$-0.695489\pi$
$83$	1.17090	−	0.982501i	0.128523	−	0.107844i	0.704783	+	0.709423i	$0.251044\pi$
$84$	−1.28774	−	0.855668i	−0.140504	−	0.0933610i
$85$		0			0
$86$	−3.35061	+	1.21952i	−0.361305	+	0.131504i
$87$	16.2100	−	1.81742i	1.73789	−	0.194848i
$88$	1.28920	+	7.31144i	0.137430	+	0.779402i
$89$	−6.52774	−	11.3064i	−0.691939	−	1.19847i	−0.971202	−	0.238259i	$-0.923423\pi$
$89$	−6.52774	−	11.3064i	−0.691939	−	1.19847i	0.279262	−	0.960215i	$-0.409910\pi$
$90$		0			0
$91$	−0.366811	+	0.635335i	−0.0384522	+	0.0666012i
$92$	−4.52610	−	1.64736i	−0.471878	−	0.171750i
$93$	−1.35358	+	1.42126i	−0.140360	+	0.147378i
$94$	7.87952	+	6.61170i	0.812711	+	0.681945i
$95$		0			0
$96$	−6.55214	−	1.58548i	−0.668724	−	0.161817i
$97$	−13.0234	−	4.74011i	−1.32232	−	0.481286i	−0.418120	−	0.908392i	$-0.637311\pi$
$97$	−13.0234	−	4.74011i	−1.32232	−	0.481286i	−0.904202	+	0.427106i	$0.859533\pi$
$98$	4.50238	−	7.79835i	0.454809	−	0.787753i
$99$	0.514163	+	10.5345i	0.0516753	+	1.05876i
$100$		0			0
$101$	2.04974	+	11.6247i	0.203957	+	1.15670i	0.899072	+	0.437800i	$0.144242\pi$
$101$	2.04974	+	11.6247i	0.203957	+	1.15670i	−0.695115	+	0.718898i	$0.744647\pi$
$102$	−5.90246	+	13.5084i	−0.584431	+	1.33753i
$103$	2.30128	−	0.837596i	0.226751	−	0.0825308i	−0.226146	−	0.974093i	$-0.572613\pi$
$103$	2.30128	−	0.837596i	0.226751	−	0.0825308i	0.452897	+	0.891563i	$0.350390\pi$
$104$	−0.216818	+	1.22963i	−0.0212607	+	0.120576i
$105$		0			0
$106$	10.3726	−	8.70366i	1.00748	−	0.845374i
$107$	6.83945			0.661195			0.330597	−	0.943772i	$-0.392750\pi$
$107$	6.83945			0.661195			0.330597	+	0.943772i	$0.392750\pi$
$108$	−3.49445	−	1.32802i	−0.336253	−	0.127789i
$109$	−18.7944			−1.80018			−0.900088	−	0.435708i	$-0.856498\pi$
$109$	−18.7944			−1.80018			−0.900088	+	0.435708i	$0.856498\pi$
$110$		0			0
$111$	7.28358	−	3.61514i	0.691327	−	0.343134i
$112$	−1.06032	+	6.01338i	−0.100191	+	0.568211i
$113$	−12.9670	+	4.71959i	−1.21983	+	0.443982i	−0.870103	−	0.492870i	$-0.835948\pi$
$113$	−12.9670	+	4.71959i	−1.21983	+	0.443982i	−0.349727	+	0.936852i	$0.613726\pi$
$114$	−4.80484	−	6.51781i	−0.450014	−	0.610449i
$115$		0			0
$116$	3.38763	+	5.86754i	0.314533	+	0.544788i
$117$	−0.524697	+	1.69442i	−0.0485083	+	0.156649i
$118$	11.1420	−	19.2985i	1.02570	−	1.77657i
$119$	6.01754	+	2.19021i	0.551627	+	0.200776i
$120$		0			0
$121$	1.04185	+	0.874216i	0.0947136	+	0.0794742i
$122$	−10.0713	−	8.45081i	−0.911811	−	0.765101i
$123$	−2.82838	−	9.61179i	−0.255026	−	0.866666i
$124$	−0.766069	−	0.278826i	−0.0687950	−	0.0250393i
$125$		0			0
$126$	−1.81574	+	5.86362i	−0.161759	+	0.522372i
$127$	−4.27399	−	7.40277i	−0.379255	−	0.656890i	0.611699	−	0.791091i	$-0.290486\pi$
$127$	−4.27399	−	7.40277i	−0.379255	−	0.656890i	−0.990954	+	0.134201i	$0.957153\pi$
$128$	2.33227	+	13.2270i	0.206146	+	1.16911i
$129$	2.22224	+	3.01449i	0.195657	+	0.265411i
$130$		0			0
$131$	1.68189	−	9.53845i	0.146947	−	0.833379i	−0.818836	−	0.574028i	$-0.805380\pi$
$131$	1.68189	−	9.53845i	0.146947	−	0.833379i	0.965783	−	0.259351i	$-0.0835087\pi$
$132$	−3.92410	+	1.94770i	−0.341549	+	0.169525i
$133$	−2.69457	+	2.26101i	−0.233649	+	0.196055i
$134$	−7.26035			−0.627198
$135$		0			0
$136$	10.8990			0.934580
$137$	−11.3374	+	9.51323i	−0.968622	+	0.812770i	−0.982334	−	0.187136i	$-0.940080\pi$
$137$	−11.3374	+	9.51323i	−0.968622	+	0.812770i	0.0137123	+	0.999906i	$0.495635\pi$
$138$	−1.20168	+	19.0848i	−0.102294	+	1.62461i
$139$	0.474713	−	2.69223i	0.0402646	−	0.228352i	−0.958034	−	0.286653i	$-0.907457\pi$
$139$	0.474713	−	2.69223i	0.0402646	−	0.228352i	0.998299	+	0.0583011i	$0.0185684\pi$
$140$		0			0
$141$	4.32570	−	9.89977i	0.364289	−	0.833711i
$142$	1.96893	+	11.1664i	0.165229	+	0.937060i
$143$	1.03935	+	1.80021i	0.0869151	+	0.150541i
$144$	0.719730	+	14.7463i	0.0599775	+	1.22886i
$145$		0			0
$146$	2.21803	+	0.807296i	0.183565	+	0.0668123i
$147$	−9.19258	−	2.22441i	−0.758191	−	0.183466i
$148$	2.58732	+	2.17102i	0.212676	+	0.178456i
$149$	14.9253	+	12.5238i	1.22273	+	1.02599i	0.998677	+	0.0514162i	$0.0163735\pi$
$149$	14.9253	+	12.5238i	1.22273	+	1.02599i	0.224054	+	0.974577i	$0.428071\pi$
$150$		0			0
$151$	−12.9070	−	4.69775i	−1.05035	−	0.382297i	−0.241557	−	0.970387i	$-0.577658\pi$
$151$	−12.9070	−	4.69775i	−1.05035	−	0.382297i	−0.808796	+	0.588089i	$0.799880\pi$
$152$	−2.99336	+	5.18465i	−0.242793	+	0.420530i
$153$	15.3611	+	1.94213i	1.24187	+	0.157012i
$154$	3.59673	+	6.22972i	0.289833	+	0.502005i
$155$		0			0
$156$	−0.732187	+	0.0820907i	−0.0586219	+	0.00657252i
$157$	−11.1077	+	4.04287i	−0.886491	+	0.322656i	−0.744826	−	0.667258i	$-0.767468\pi$
$157$	−11.1077	+	4.04287i	−0.886491	+	0.322656i	−0.141665	+	0.989915i	$0.545245\pi$
$158$	0.362901	−	2.05811i	0.0288708	−	0.163735i
$159$	−11.8453	−	7.87084i	−0.939392	−	0.624198i
$160$		0			0
$161$	8.30684			0.654671
$162$	−1.14161	+	14.7977i	−0.0896932	+	1.16261i
$163$	−13.4522			−1.05366			−0.526828	−	0.849972i	$-0.676619\pi$
$163$	−13.4522			−1.05366			−0.526828	+	0.849972i	$0.676619\pi$
$164$	3.18802	−	2.67507i	0.248943	−	0.208888i
$165$		0			0
$166$	0.437699	−	2.48231i	0.0339720	−	0.192665i
$167$	−2.43207	+	0.885201i	−0.188199	+	0.0684989i	−0.434401	−	0.900720i	$-0.643040\pi$
$167$	−2.43207	+	0.885201i	−0.188199	+	0.0684989i	0.246201	+	0.969219i	$0.420818\pi$
$168$	4.51002	−	0.505650i	0.347955	−	0.0390117i
$169$	−2.19672	−	12.4582i	−0.168978	−	0.958324i
$170$		0			0
$171$	−5.14273	+	6.77388i	−0.393274	+	0.518011i
$172$	−0.777784	+	1.34716i	−0.0593055	+	0.102720i
$173$	−15.5458	−	5.65820i	−1.18192	−	0.430185i	−0.325042	−	0.945699i	$-0.605379\pi$
$173$	−15.5458	−	5.65820i	−1.18192	−	0.430185i	−0.856881	+	0.515515i	$0.827601\pi$
$174$	18.5510	−	19.4785i	1.40635	−	1.47666i
$175$		0			0
$176$	13.2539	+	11.1213i	0.999047	+	0.838300i
$177$	−22.7487	−	5.50470i	−1.70990	−	0.413759i
$178$	−20.2310	−	7.36349i	−1.51638	−	0.551917i
$179$	0.606831	−	1.05106i	0.0453567	−	0.0785601i	−0.842456	−	0.538765i	$-0.818891\pi$
$179$	0.606831	−	1.05106i	0.0453567	−	0.0785601i	0.887812	+	0.460205i	$0.152224\pi$
$180$		0			0
$181$	1.84215	+	3.19070i	0.136926	+	0.237163i	0.926332	−	0.376709i	$-0.122944\pi$
$181$	1.84215	+	3.19070i	0.136926	+	0.237163i	−0.789405	+	0.613872i	$0.789611\pi$
$182$	0.210078	+	1.19141i	0.0155720	+	0.0883135i
$183$	−5.52893	+	12.6535i	−0.408710	+	0.935373i
$184$	13.2854	−	4.83549i	0.979413	−	0.356477i
$185$		0			0
$186$	−0.203391	+	3.23022i	−0.0149134	+	0.236851i
$187$	13.8998	−	11.6633i	1.01645	−	0.852906i
$188$	4.48743			0.327279
$189$	6.44655	+	0.0909880i	0.468917	+	0.00661840i
$190$		0			0
$191$	2.91058	−	2.44226i	0.210602	−	0.176716i	−0.531385	−	0.847131i	$-0.678328\pi$
$191$	2.91058	−	2.44226i	0.210602	−	0.176716i	0.741987	+	0.670415i	$0.233884\pi$
$192$	5.31265	−	2.63689i	0.383407	−	0.190301i
$193$	1.57899	−	8.95492i	0.113658	−	0.644589i	−0.873747	−	0.486380i	$-0.838317\pi$
$193$	1.57899	−	8.95492i	0.113658	−	0.644589i	0.987406	−	0.158209i	$-0.0505719\pi$
$194$	−21.4764	+	7.81678i	−1.54192	+	0.561212i
$195$		0			0
$196$	−0.682172	−	3.86879i	−0.0487266	−	0.276342i
$197$	3.37091	+	5.83859i	0.240167	+	0.415982i	0.960762	−	0.277375i	$-0.0894643\pi$
$197$	3.37091	+	5.83859i	0.240167	+	0.415982i	−0.720594	+	0.693357i	$0.756131\pi$
$198$	11.8161	+	12.7628i	0.839736	+	0.907015i
$199$	5.30284	−	9.18479i	0.375909	−	0.651093i	−0.614554	−	0.788875i	$-0.710664\pi$
$199$	5.30284	−	9.18479i	0.375909	−	0.651093i	0.990463	+	0.137782i	$0.0439973\pi$
$200$		0			0
$201$	2.15268	+	7.31553i	0.151838	+	0.515998i
$202$	14.9115	+	12.5123i	1.04917	+	0.880360i
$203$	−8.95113	−	7.51089i	−0.628246	−	0.527161i
$204$	1.81550	+	6.16969i	0.127110	+	0.431965i
$205$		0			0
$206$	2.01926	−	3.49746i	0.140688	−	0.243680i
$207$	19.5862	−	4.44780i	1.36133	−	0.309144i
$208$	1.45489	+	2.51995i	0.100879	+	0.174727i
$209$	1.73072	+	9.81541i	0.119717	+	0.678946i
$210$		0			0
$211$	16.7832	−	6.10860i	1.15541	−	0.420534i	0.307952	−	0.951402i	$-0.400356\pi$
$211$	16.7832	−	6.10860i	1.15541	−	0.420534i	0.847454	+	0.530868i	$0.178134\pi$
$212$	1.02578	−	5.81751i	0.0704511	−	0.399548i
$213$	10.6674	−	5.29470i	0.730921	−	0.362787i
$214$	8.64002	−	7.24983i	0.590619	−	0.495588i
$215$		0			0
$216$	10.3631	−	3.60708i	0.705122	−	0.245430i
$217$	1.40598			0.0954443
$218$	−23.7422	+	19.9221i	−1.60803	+	1.34929i
$219$	0.155791	−	2.47425i	0.0105274	−	0.167194i
$220$		0			0
$221$	2.86757	−	1.04371i	0.192894	−	0.0702075i
$222$	5.36900	−	12.2875i	0.360344	−	0.824682i
$223$	−3.38789	−	19.2137i	−0.226870	−	1.28664i	−0.859078	−	0.511844i	$-0.828963\pi$
$223$	−3.38789	−	19.2137i	−0.226870	−	1.28664i	0.632209	−	0.774798i	$-0.282149\pi$
$224$	2.41456	+	4.18213i	0.161329	+	0.279431i
$225$		0			0
$226$	−11.3779	+	19.7071i	−0.756846	+	1.31090i
$227$	3.45732	+	1.25836i	0.229470	+	0.0835203i	0.454196	−	0.890902i	$-0.349927\pi$
$227$	3.45732	+	1.25836i	0.229470	+	0.0835203i	−0.224726	+	0.974422i	$0.572149\pi$
$228$	−3.43354	−	0.830843i	−0.227392	−	0.0550239i
$229$	3.32291	+	2.78825i	0.219584	+	0.184253i	0.745943	−	0.666009i	$-0.231999\pi$
$229$	3.32291	+	2.78825i	0.219584	+	0.184253i	−0.526360	+	0.850262i	$0.676443\pi$
$230$		0			0
$231$	5.21065	−	5.47117i	0.342835	−	0.359976i
$232$	−18.6880	−	6.80187i	−1.22693	−	0.446564i
$233$	−3.94398	+	6.83118i	−0.258379	+	0.447525i	−0.965808	−	0.259259i	$-0.916522\pi$
$233$	−3.94398	+	6.83118i	−0.258379	+	0.447525i	0.707429	+	0.706784i	$0.249855\pi$
$234$	1.13326	+	2.69667i	0.0740835	+	0.176287i
$235$		0			0
$236$	−1.68816	−	9.57403i	−0.109890	−	0.623216i
$237$	−2.18136	+	0.244567i	−0.141694	+	0.0158864i
$238$	9.92335	−	3.61180i	0.643235	−	0.234119i
$239$	4.95815	−	28.1191i	0.320716	−	1.81887i	−0.217493	−	0.976062i	$-0.569788\pi$
$239$	4.95815	−	28.1191i	0.320716	−	1.81887i	0.538210	−	0.842811i	$-0.319101\pi$
$240$		0			0
$241$	−10.0815	+	8.45937i	−0.649405	+	0.544916i	−0.906890	−	0.421367i	$-0.861551\pi$
$241$	−10.0815	+	8.45937i	−0.649405	+	0.544916i	0.257485	+	0.966282i	$0.417106\pi$
$242$	2.24280			0.144173
$243$	15.2486	−	3.23719i	0.978200	−	0.207666i
$244$	−5.73565			−0.367187
$245$		0			0
$246$	−13.7615	−	9.14411i	−0.877401	−	0.583007i
$247$	−0.291072	+	1.65075i	−0.0185205	+	0.105035i
$248$	2.24863	−	0.818435i	0.142788	−	0.0519707i
$249$	−2.63096	+	0.294975i	−0.166730	+	0.0186933i
$250$		0			0
$251$	−13.5512	−	23.4713i	−0.855341	−	1.48149i	−0.876328	−	0.481715i	$-0.840014\pi$
$251$	−13.5512	−	23.4713i	−0.855341	−	1.48149i	0.0209869	−	0.999780i	$-0.493319\pi$
$252$	1.03749	+	2.46880i	0.0653560	+	0.155520i
$253$	11.7687	−	20.3839i	0.739890	−	1.28153i
$254$	−13.2461	−	4.82119i	−0.831135	−	0.302509i
$255$		0			0
$256$	11.7205	+	9.83471i	0.732534	+	0.614669i
$257$	1.44970	+	1.21645i	0.0904300	+	0.0758798i	0.686882	−	0.726769i	$-0.258979\pi$
$257$	1.44970	+	1.21645i	0.0904300	+	0.0758798i	−0.596452	+	0.802649i	$0.703423\pi$
$258$	6.00263	+	1.45251i	0.373708	+	0.0904292i
$259$	−5.47368	−	1.99226i	−0.340118	−	0.123793i
$260$		0			0
$261$	−25.1269	−	12.9167i	−1.55532	−	0.799522i
$262$	−7.98612	−	13.8324i	−0.493384	−	0.854566i
$263$	3.65398	+	20.7228i	0.225314	+	1.27782i	0.862084	+	0.506766i	$0.169159\pi$
$263$	3.65398	+	20.7228i	0.225314	+	1.27782i	−0.636770	+	0.771054i	$0.719730\pi$
$264$	5.14874	−	11.7834i	0.316883	−	0.725217i
$265$		0			0
$266$	−1.00727	+	5.71250i	−0.0617596	+	0.350256i
$267$	−1.42100	+	22.5681i	−0.0869638	+	1.38114i
$268$	−2.42640	+	2.03599i	−0.148216	+	0.124368i
$269$	−1.06528			−0.0649512			−0.0324756	−	0.999473i	$-0.510339\pi$
$269$	−1.06528			−0.0649512			−0.0324756	+	0.999473i	$0.510339\pi$
$270$		0			0
$271$	−5.32687			−0.323585			−0.161792	−	0.986825i	$-0.551727\pi$
$271$	−5.32687			−0.323585			−0.161792	+	0.986825i	$0.551727\pi$
$272$	19.4571	−	16.3264i	1.17976	−	0.989934i
$273$	1.13818	−	0.564927i	0.0688859	−	0.0341909i
$274$	−4.23809	+	24.0354i	−0.256032	+	1.45203i
$275$		0			0
$276$	4.95029	+	6.71511i	0.297972	+	0.404202i
$277$	2.98294	+	16.9171i	0.179228	+	1.01645i	0.933150	+	0.359487i	$0.117048\pi$
$277$	2.98294	+	16.9171i	0.179228	+	1.01645i	−0.753923	+	0.656963i	$0.771841\pi$
$278$	−2.25408	−	3.90419i	−0.135191	−	0.234158i
$279$	3.31508	−	0.752817i	0.198468	−	0.0450700i
$280$		0			0
$281$	−11.6900	−	4.25480i	−0.697365	−	0.253820i	−0.0310798	−	0.999517i	$-0.509895\pi$
$281$	−11.6900	−	4.25480i	−0.697365	−	0.253820i	−0.666286	+	0.745697i	$0.732117\pi$
$282$	−5.02929	−	17.0912i	−0.299490	−	1.01777i
$283$	15.8689	+	13.3156i	0.943306	+	0.791528i	0.978158	−	0.207865i	$-0.0666514\pi$
$283$	15.8689	+	13.3156i	0.943306	+	0.791528i	−0.0348514	+	0.999393i	$0.511096\pi$
$284$	3.78936	+	3.17965i	0.224857	+	0.188677i
$285$		0			0
$286$	3.22120	+	1.17242i	0.190474	+	0.0693268i
$287$	−3.58868	+	6.21578i	−0.211833	+	0.366906i
$288$	7.93240	+	8.56794i	0.467421	+	0.504871i
$289$	−4.81863	−	8.34611i	−0.283449	−	0.490948i
$290$		0			0
$291$	14.2439	+	19.3220i	0.834993	+	1.13268i
$292$	0.967650	−	0.352196i	0.0566274	−	0.0206107i
$293$	1.08632	−	6.16081i	0.0634634	−	0.359919i	−0.936494	−	0.350684i	$-0.885949\pi$
$293$	1.08632	−	6.16081i	0.0634634	−	0.359919i	0.999957	−	0.00923499i	$-0.00293963\pi$
$294$	−13.9705	+	6.93414i	−0.814776	+	0.404407i
$295$		0			0
$296$	−9.91394			−0.576236
$297$	9.35638	−	15.6901i	0.542912	−	0.910432i
$298$	32.1299			1.86123
$299$	3.03239	−	2.54448i	0.175367	−	0.147151i
$300$		0			0
$301$	0.465862	−	2.64203i	0.0268518	−	0.152284i
$302$	−21.2845	+	7.74692i	−1.22478	+	0.445785i
$303$	8.18613	−	18.7348i	0.470281	−	1.07628i
$304$	2.42268	+	13.7397i	0.138950	+	0.788025i
$305$		0			0
$306$	21.4637	−	13.8294i	1.22700	−	0.790573i
$307$	9.12444	−	15.8040i	0.520759	−	0.901981i	−0.478949	−	0.877843i	$-0.658982\pi$
$307$	9.12444	−	15.8040i	0.520759	−	0.901981i	0.999709	−	0.0241389i	$-0.00768441\pi$
$308$	2.94900	+	1.07335i	0.168035	+	0.0611597i
$309$	−4.12275	−	0.997617i	−0.234535	−	0.0567525i
$310$		0			0
$311$	−3.62362	−	3.04058i	−0.205477	−	0.172416i	0.534242	−	0.845332i	$-0.320597\pi$
$311$	−3.62362	−	3.04058i	−0.205477	−	0.172416i	−0.739719	+	0.672916i	$0.765042\pi$
$312$	1.49148	−	1.56605i	0.0844385	−	0.0886602i
$313$	−32.5545	−	11.8489i	−1.84009	−	0.669737i	−0.989620	−	0.143711i	$-0.954096\pi$
$313$	−32.5545	−	11.8489i	−1.84009	−	0.669737i	−0.850469	−	0.526026i	$-0.823681\pi$
$314$	−9.74647	+	16.8814i	−0.550025	+	0.952672i
$315$		0			0
$316$	−0.455868	−	0.789587i	−0.0256446	−	0.0444177i
$317$	−0.179070	−	1.01556i	−0.0100576	−	0.0570395i	0.979366	−	0.202095i	$-0.0647750\pi$
$317$	−0.179070	−	1.01556i	−0.0100576	−	0.0570395i	−0.989424	+	0.145056i	$0.953664\pi$
$318$	−23.3068	+	2.61309i	−1.30698	+	0.146535i
$319$	−31.1122	+	11.3239i	−1.74195	+	0.634018i
$320$		0			0
$321$	−9.86669	−	6.55613i	−0.550705	−	0.365927i
$322$	10.4937	−	8.80527i	0.584792	−	0.490699i
$323$	14.6316			0.814124
$324$	3.76813	+	5.26550i	0.209341	+	0.292528i
$325$		0			0
$326$	−16.9936	+	14.2593i	−0.941189	+	0.789752i
$327$	27.1130	+	18.0158i	1.49936	+	0.996278i
$328$	−2.12123	+	12.0301i	−0.117125	+	0.664251i
$329$	−7.27246	+	2.64696i	−0.400943	+	0.145931i
$330$		0			0
$331$	2.20443	+	12.5020i	0.121167	+	0.687170i	0.983511	+	0.180848i	$0.0578842\pi$
$331$	2.20443	+	12.5020i	0.121167	+	0.687170i	−0.862344	+	0.506322i	$0.831005\pi$
$332$	−0.549827	−	0.952329i	−0.0301757	−	0.0522658i
$333$	−13.9728	−	1.76660i	−0.765703	−	0.0968090i
$334$	−2.13403	+	3.69624i	−0.116769	+	0.202249i
$335$		0			0
$336$	7.29390	−	7.65858i	0.397915	−	0.417810i
$337$	−7.11709	−	5.97195i	−0.387693	−	0.325313i	0.428021	−	0.903769i	$-0.359211\pi$
$337$	−7.11709	−	5.97195i	−0.387693	−	0.325313i	−0.815714	+	0.578456i	$0.803655\pi$
$338$	−15.9808	−	13.4095i	−0.869239	−	0.729378i
$339$	23.2304	+	5.62126i	1.26170	+	0.305305i
$340$		0			0
$341$	1.99192	−	3.45010i	0.107868	−	0.186833i
$342$	0.683719	+	14.0085i	0.0369713	+	0.757492i
$343$	7.73027	+	13.3892i	0.417395	+	0.722950i
$344$	−0.792885	−	4.49667i	−0.0427495	−	0.242444i
$345$		0			0
$346$	−25.6361	+	9.33077i	−1.37820	+	0.501625i
$347$	4.36400	−	24.7495i	0.234272	−	1.32862i	−0.609870	−	0.792502i	$-0.708778\pi$
$347$	4.36400	−	24.7495i	0.234272	−	1.32862i	0.844142	−	0.536120i	$-0.180111\pi$
$348$	0.737440	−	11.7119i	0.0395310	−	0.627823i
$349$	1.83471	−	1.53950i	0.0982096	−	0.0824076i	−0.592361	−	0.805673i	$-0.701804\pi$
$349$	1.83471	−	1.53950i	0.0982096	−	0.0824076i	0.690570	+	0.723265i	$0.257360\pi$
$350$		0			0
$351$	2.38116	−	1.94143i	0.127097	−	0.103626i
$352$	13.6832			0.729319
$353$	−9.80842	+	8.23024i	−0.522049	+	0.438051i	−0.865346	−	0.501176i	$-0.832901\pi$
$353$	−9.80842	+	8.23024i	−0.522049	+	0.438051i	0.343296	+	0.939227i	$0.388457\pi$
$354$	−34.5726	+	17.1598i	−1.83751	+	0.912034i
$355$		0			0
$356$	−8.82611	+	3.21244i	−0.467783	+	0.170259i
$357$	−6.58151	−	8.92789i	−0.348331	−	0.472514i
$358$	−0.347542	−	1.97101i	−0.0183682	−	0.104171i
$359$	−0.774475	−	1.34143i	−0.0408753	−	0.0707980i	0.844864	−	0.534981i	$-0.179681\pi$
$359$	−0.774475	−	1.34143i	−0.0408753	−	0.0707980i	−0.885739	+	0.464183i	$0.846348\pi$
$360$		0			0
$361$	5.48150	−	9.49423i	0.288500	−	0.499696i
$362$	5.70927	+	2.07800i	0.300073	+	0.109218i
$363$	−0.664986	−	2.25985i	−0.0349027	−	0.118611i
$364$	0.404312	+	0.339258i	0.0211917	+	0.0177819i
$365$		0			0
$366$	6.42824	+	21.8453i	0.336009	+	1.14187i
$367$	−4.65249	−	1.69337i	−0.242858	−	0.0883931i	0.217723	−	0.976011i	$-0.430137\pi$
$367$	−4.65249	−	1.69337i	−0.242858	−	0.0883931i	−0.460582	+	0.887617i	$0.652359\pi$
$368$	16.4739	−	28.5336i	0.858760	−	1.48742i
$369$	−5.13336	+	16.5773i	−0.267232	+	0.862980i
$370$		0			0
$371$	1.76911	+	10.0331i	0.0918474	+	0.520893i
$372$	0.837866	+	1.13657i	0.0434413	+	0.0589285i
$373$	−16.2628	+	5.91918i	−0.842057	+	0.306484i	−0.726798	−	0.686852i	$-0.758992\pi$
$373$	−16.2628	+	5.91918i	−0.842057	+	0.306484i	−0.115260	+	0.993335i	$0.536770\pi$
$374$	5.19594	−	29.4676i	0.268676	−	1.52374i
$375$		0			0
$376$	−10.0903	+	8.46673i	−0.520365	+	0.436638i
$377$	−5.56825			−0.286779
$378$	8.24012	−	6.71841i	0.423826	−	0.345558i
$379$	8.91774			0.458073			0.229037	−	0.973418i	$-0.426442\pi$
$379$	8.91774			0.458073			0.229037	+	0.973418i	$0.426442\pi$
$380$		0			0
$381$	−0.930389	+	14.7763i	−0.0476653	+	0.757012i
$382$	1.08801	−	6.17043i	0.0556676	−	0.315707i
$383$	23.1914	−	8.44098i	1.18502	−	0.431314i	0.327051	−	0.945007i	$-0.393945\pi$
$383$	23.1914	−	8.44098i	1.18502	−	0.431314i	0.857974	+	0.513693i	$0.171723\pi$
$384$	9.31447	−	21.3171i	0.475327	−	1.08783i
$385$		0			0
$386$	−7.49755	−	12.9861i	−0.381615	−	0.660977i
$387$	−0.316220	−	6.47892i	−0.0160744	−	0.329342i
$388$	−4.98537	+	8.63492i	−0.253094	+	0.438372i
$389$	6.71441	+	2.44385i	0.340434	+	0.123908i	0.506579	−	0.862193i	$-0.330910\pi$
$389$	6.71441	+	2.44385i	0.340434	+	0.123908i	−0.166145	+	0.986101i	$0.553132\pi$
$390$		0			0
$391$	−26.4695	−	22.2106i	−1.33862	−	1.12324i
$392$	8.83341	+	7.41211i	0.446155	+	0.374368i
$393$	−11.5696	+	12.1481i	−0.583611	+	0.612790i
$394$	10.4473	+	3.80249i	0.526325	+	0.191567i
$395$		0			0
$396$	7.52797	+	0.951772i	0.378295	+	0.0478284i
$397$	2.23966	+	3.87921i	0.112405	+	0.194692i	0.916740	−	0.399485i	$-0.130811\pi$
$397$	2.23966	+	3.87921i	0.112405	+	0.194692i	−0.804334	+	0.594177i	$0.797478\pi$
$398$	−3.03702	−	17.2238i	−0.152232	−	0.863352i
$399$	6.05458	−	0.678822i	0.303108	−	0.0339836i
$400$		0			0
$401$	0.799427	−	4.53377i	0.0399215	−	0.226406i	−0.958319	−	0.285700i	$-0.907774\pi$
$401$	0.799427	−	4.53377i	0.0399215	−	0.226406i	0.998241	+	0.0592942i	$0.0188850\pi$
$402$	10.4739	+	6.95959i	0.522390	+	0.347113i
$403$	0.513250	−	0.430668i	0.0255668	−	0.0214531i
$404$	8.49220			0.422503
$405$		0			0
$406$	−19.2692			−0.956313
$407$	−12.6435	+	10.6092i	−0.626717	+	0.525878i
$408$	−15.7230	−	10.4475i	−0.778406	−	0.517228i
$409$	2.13917	−	12.1318i	0.105775	−	0.599880i	−0.885133	−	0.465339i	$-0.845933\pi$
$409$	2.13917	−	12.1318i	0.105775	−	0.599880i	0.990908	−	0.134542i	$-0.0429563\pi$
$410$		0			0
$411$	25.4747	−	2.85615i	1.25657	−	0.140883i
$412$	−0.305945	−	1.73510i	−0.0150728	−	0.0854823i
$413$	8.38323	+	14.5202i	0.412512	+	0.714491i
$414$	20.0278	−	26.3801i	0.984312	−	1.29651i
$415$		0			0
$416$	2.16246	+	0.787071i	0.106023	+	0.0385893i
$417$	−3.26553	+	3.42880i	−0.159914	+	0.167909i
$418$	12.5907	+	10.5649i	0.615832	+	0.516744i
$419$	12.8029	+	10.7429i	0.625462	+	0.524825i	0.899515	−	0.436890i	$-0.143920\pi$
$419$	12.8029	+	10.7429i	0.625462	+	0.524825i	−0.274053	+	0.961715i	$0.588364\pi$
$420$		0			0
$421$	7.93497	+	2.88809i	0.386727	+	0.140757i	0.528064	−	0.849205i	$-0.322918\pi$
$421$	7.93497	+	2.88809i	0.386727	+	0.140757i	−0.141338	+	0.989961i	$0.545140\pi$
$422$	14.7265	−	25.5070i	0.716875	−	1.24166i
$423$	−15.7300	+	10.1350i	−0.764818	+	0.492783i
$424$	8.66975	+	15.0164i	0.421040	+	0.729263i
$425$		0			0
$426$	7.86338	−	17.9961i	0.380982	−	0.871914i
$427$	9.29536	−	3.38323i	0.449834	−	0.163726i
$428$	0.854441	−	4.84578i	0.0413010	−	0.234229i
$429$	0.226253	−	3.59331i	0.0109236	−	0.173487i
$430$		0			0
$431$	−11.6530			−0.561306			−0.280653	−	0.959809i	$-0.590551\pi$
$431$	−11.6530			−0.561306			−0.280653	+	0.959809i	$0.590551\pi$
$432$	13.0971	−	21.9631i	0.630136	−	1.05670i
$433$	10.8242			0.520178			0.260089	−	0.965585i	$-0.416248\pi$
$433$	10.8242			0.520178			0.260089	+	0.965585i	$0.416248\pi$
$434$	1.77612	−	1.49034i	0.0852567	−	0.0715388i
$435$		0			0
$436$	−2.34795	+	13.3159i	−0.112446	+	0.637716i
$437$	17.8353	−	6.49152i	0.853178	−	0.310531i
$438$	−2.42590	−	3.29076i	−0.115914	−	0.157239i
$439$	4.86673	+	27.6006i	0.232276	+	1.31731i	0.848274	+	0.529557i	$0.177642\pi$
$439$	4.86673	+	27.6006i	0.232276	+	1.31731i	−0.615998	+	0.787748i	$0.711247\pi$
$440$		0			0
$441$	11.1291	+	12.0207i	0.529956	+	0.572416i
$442$	2.51615	−	4.35811i	0.119681	−	0.207294i
$443$	26.3006	+	9.57265i	1.24958	+	0.454810i	0.880260	−	0.474491i	$-0.157368\pi$
$443$	26.3006	+	9.57265i	1.24958	+	0.454810i	0.369321	+	0.929302i	$0.379590\pi$
$444$	−1.65142	−	5.61208i	−0.0783728	−	0.266337i
$445$		0			0
$446$	−24.6463	−	20.6807i	−1.16704	−	0.979260i
$447$	−9.52645	−	32.3741i	−0.450586	−	1.53124i
$448$	−3.99251	−	1.45315i	−0.188628	−	0.0686551i
$449$	12.5470	−	21.7321i	0.592130	−	1.02560i	−0.401815	−	0.915721i	$-0.631621\pi$
$449$	12.5470	−	21.7321i	0.592130	−	1.02560i	0.993945	−	0.109878i	$-0.0350461\pi$
$450$		0			0
$451$	10.1685	+	17.6123i	0.478815	+	0.829333i
$452$	1.72391	+	9.77675i	0.0810857	+	0.459860i
$453$	14.1166	+	19.1493i	0.663256	+	0.899714i
$454$	5.70136	−	2.07512i	0.267578	−	0.0973904i
$455$		0			0
$456$	9.28813	−	4.61009i	0.434956	−	0.215887i
$457$	12.8412	−	10.7750i	0.600686	−	0.504036i	−0.290980	−	0.956729i	$-0.593981\pi$
$457$	12.8412	−	10.7750i	0.600686	−	0.504036i	0.891666	+	0.452694i	$0.149537\pi$
$458$	7.15325			0.334249
$459$	−20.2985	−	17.5265i	−0.947451	−	0.818067i
$460$		0			0
$461$	19.8382	−	16.6462i	0.923956	−	0.775291i	−0.0507663	−	0.998711i	$-0.516166\pi$
$461$	19.8382	−	16.6462i	0.923956	−	0.775291i	0.974722	+	0.223419i	$0.0717219\pi$
$462$	0.782959	−	12.4348i	0.0364265	−	0.578520i
$463$	−3.00727	+	17.0551i	−0.139760	+	0.792616i	0.831667	+	0.555275i	$0.187387\pi$
$463$	−3.00727	+	17.0551i	−0.139760	+	0.792616i	−0.971426	+	0.237341i	$0.923724\pi$
$464$	−43.5511	+	15.8513i	−2.02181	+	0.735878i
$465$		0			0
$466$	2.25878	+	12.8102i	0.104636	+	0.593420i
$467$	6.19652	+	10.7327i	0.286741	+	0.496649i	0.973030	−	0.230679i	$-0.0740949\pi$
$467$	6.19652	+	10.7327i	0.286741	+	0.496649i	−0.686289	+	0.727329i	$0.740762\pi$
$468$	1.13495	+	0.583431i	0.0524632	+	0.0269691i
$469$	2.73135	−	4.73083i	0.126122	−	0.218449i
$470$		0			0
$471$	19.8995	+	4.81526i	0.916921	+	0.221875i
$472$	21.8599	+	18.3426i	1.00618	+	0.844288i
$473$	−5.82321	−	4.88625i	−0.267751	−	0.224670i
$474$	−2.49638	+	2.62119i	−0.114663	+	0.120395i
$475$		0			0
$476$	2.30353	−	3.98983i	0.105582	−	0.182874i
$477$	9.54337	+	22.7092i	0.436961	+	1.03978i
$478$	−23.5429	−	40.7774i	−1.07682	−	1.86512i
$479$	−3.96462	−	22.4845i	−0.181148	−	1.02734i	−0.930805	−	0.365515i	$-0.880893\pi$
$479$	−3.96462	−	22.4845i	−0.181148	−	1.02734i	0.749657	−	0.661826i	$-0.230218\pi$
$480$		0			0
$481$	−2.60840	+	0.949380i	−0.118933	+	0.0432880i
$482$	−3.76860	+	21.3728i	−0.171655	+	0.973503i
$483$	−11.9836	−	7.96273i	−0.545271	−	0.362317i
$484$	0.749542	−	0.628940i	0.0340701	−	0.0285882i
$485$		0			0
$486$	15.8316	−	20.2530i	0.718134	−	0.918695i
$487$	−3.22215			−0.146009			−0.0730047	−	0.997332i	$-0.523259\pi$
$487$	−3.22215			−0.146009			−0.0730047	+	0.997332i	$0.523259\pi$
$488$	12.8970	−	10.8218i	0.583818	−	0.489881i
$489$	19.4063	+	12.8949i	0.877583	+	0.583128i
$490$		0			0
$491$	24.5814	−	8.94691i	1.10934	−	0.403768i	0.278591	−	0.960410i	$-0.410132\pi$
$491$	24.5814	−	8.94691i	1.10934	−	0.403768i	0.830753	+	0.556641i	$0.187910\pi$
$492$	−7.16333	+	0.803132i	−0.322948	+	0.0362080i
$493$	8.44015	+	47.8665i	0.380125	+	2.15580i
$494$	1.38210	+	2.39387i	0.0621836	+	0.107705i
$495$		0			0
$496$	2.78830	−	4.82948i	0.125198	−	0.216850i
$497$	−8.01669	−	2.91784i	−0.359598	−	0.130883i
$498$	−3.01091	+	3.16145i	−0.134922	+	0.141668i
$499$	−26.2418	−	22.0195i	−1.17474	−	0.985727i	−0.999999	−	0.00111367i	$-0.999646\pi$
$499$	−26.2418	−	22.0195i	−1.17474	−	0.985727i	−0.174745	−	0.984614i	$-0.555910\pi$
$500$		0			0
$501$	4.35707	+	1.05432i	0.194660	+	0.0471034i
$502$	−41.9983	−	15.2861i	−1.87447	−	0.682253i
$503$	7.93150	−	13.7378i	0.353648	−	0.612537i	−0.633237	−	0.773958i	$-0.718274\pi$
$503$	7.93150	−	13.7378i	0.353648	−	0.612537i	0.986886	+	0.161421i	$0.0516076\pi$
$504$	−6.99091	−	3.59373i	−0.311400	−	0.160077i
$505$		0			0
$506$	−6.74011	−	38.2250i	−0.299634	−	1.69931i
$507$	−8.77311	+	20.0781i	−0.389628	+	0.891700i
$508$	−5.77883	+	2.10332i	−0.256394	+	0.0933198i
$509$	2.38054	−	13.5007i	0.105516	−	0.598410i	−0.885497	−	0.464645i	$-0.846182\pi$
$509$	2.38054	−	13.5007i	0.105516	−	0.598410i	0.991013	−	0.133765i	$-0.0427068\pi$
$510$		0			0
$511$	−1.36046	+	1.14156i	−0.0601830	+	0.0504995i
$512$	−1.63110			−0.0720849
$513$	13.9122	−	4.84240i	0.614240	−	0.213797i
$514$	3.12079			0.137652
$515$		0			0
$516$	2.41340	−	1.19787i	0.106244	−	0.0527333i
$517$	−3.80791	+	21.5957i	−0.167472	+	0.949779i
$518$	−9.02649	+	3.28537i	−0.396601	+	0.144351i
$519$	17.0027	+	23.0644i	0.746337	+	1.01241i
$520$		0			0
$521$	13.9166	+	24.1042i	0.609697	+	1.05603i	0.991290	+	0.131696i	$0.0420422\pi$
$521$	13.9166	+	24.1042i	0.609697	+	1.05603i	−0.381593	+	0.924330i	$0.624625\pi$
$522$	−45.4335	+	10.3174i	−1.98857	+	0.451583i
$523$	−4.58572	+	7.94269i	−0.200519	+	0.347310i	−0.948696	−	0.316190i	$-0.897596\pi$
$523$	−4.58572	+	7.94269i	−0.200519	+	0.347310i	0.748177	+	0.663500i	$0.230930\pi$
$524$	−6.54791	−	2.38325i	−0.286047	−	0.104113i
$525$		0			0
$526$	26.5821	+	22.3050i	1.15903	+	0.972545i
$527$	−4.48012	−	3.75927i	−0.195157	−	0.163756i
$528$	−8.45959	−	28.7486i	−0.368156	−	1.25112i
$529$	−20.5063	−	7.46369i	−0.891579	−	0.324508i
$530$		0			0
$531$	27.5409	+	29.7475i	1.19518	+	1.29093i
$532$	1.26531	+	2.19158i	0.0548581	+	0.0950170i
$533$	0.593923	+	3.36830i	0.0257257	+	0.145897i
$534$	22.1271	+	30.0156i	0.957533	+	1.29890i
$535$		0			0
$536$	1.61447	−	9.15611i	0.0697345	−	0.395484i
$537$	−1.88294	+	0.934584i	−0.0812550	+	0.0403303i
$538$	−1.34572	+	1.12920i	−0.0580183	+	0.0486832i
$539$	19.1974			0.826892
$540$		0			0
$541$	25.6800			1.10407			0.552035	−	0.833821i	$-0.313852\pi$
$541$	25.6800			1.10407			0.552035	+	0.833821i	$0.313852\pi$
$542$	−6.72923	+	5.64650i	−0.289045	+	0.242538i
$543$	0.401012	−	6.36879i	0.0172091	−	0.273311i
$544$	3.48814	−	19.7822i	0.149553	−	0.848155i
$545$		0			0
$546$	0.838997	−	1.92013i	0.0359058	−	0.0821738i
$547$	6.83888	+	38.7852i	0.292409	+	1.65834i	0.677549	+	0.735477i	$0.263042\pi$
$547$	6.83888	+	38.7852i	0.292409	+	1.65834i	−0.385140	+	0.922858i	$0.625847\pi$
$548$	5.32379	+	9.22108i	0.227421	+	0.393905i
$549$	20.1054	−	12.9542i	0.858079	−	0.552872i
$550$		0			0
$551$	−25.0881	−	9.13133i	−1.06879	−	0.389008i
$552$	−23.8009	−	5.75930i	−1.01303	−	0.245132i
$553$	1.20454	+	1.01073i	0.0512222	+	0.0429806i
$554$	21.7004	+	18.2088i	0.921962	+	0.773618i
$555$		0			0
$556$	−1.84815	−	0.672672i	−0.0783790	−	0.0285276i
$557$	−2.06550	+	3.57754i	−0.0875178	+	0.151585i	−0.906461	−	0.422289i	$-0.861227\pi$
$557$	−2.06550	+	3.57754i	−0.0875178	+	0.151585i	0.818944	+	0.573874i	$0.194560\pi$
$558$	3.38982	−	4.46499i	0.143503	−	0.189018i
$559$	−0.639222	−	1.10716i	−0.0270362	−	0.0468281i
$560$		0			0
$561$	−31.2322	+	3.50167i	−1.31862	+	0.147840i
$562$	−19.2776	+	7.01647i	−0.813176	+	0.295972i
$563$	−3.02191	+	17.1381i	−0.127358	+	0.722286i	0.852521	+	0.522694i	$0.175073\pi$
$563$	−3.02191	+	17.1381i	−0.127358	+	0.722286i	−0.979879	+	0.199592i	$0.936038\pi$
$564$	−6.47362	−	4.30153i	−0.272589	−	0.181127i
$565$		0			0
$566$	34.1610			1.43590
$567$	−9.21266	−	6.31076i	−0.386895	−	0.265027i
$568$	−14.5199			−0.609239
$569$	3.52883	−	2.96104i	0.147936	−	0.124133i	−0.565816	−	0.824532i	$-0.691439\pi$
$569$	3.52883	−	2.96104i	0.147936	−	0.124133i	0.713752	+	0.700398i	$0.246994\pi$
$570$		0			0
$571$	−2.79686	+	15.8618i	−0.117045	+	0.663794i	0.868673	+	0.495386i	$0.164974\pi$
$571$	−2.79686	+	15.8618i	−0.117045	+	0.663794i	−0.985717	+	0.168407i	$0.946138\pi$
$572$	1.40530	−	0.511488i	0.0587586	−	0.0213864i
$573$	−6.53993	+	0.733238i	−0.273209	+	0.0306315i
$574$	2.05530	+	11.6562i	0.0857864	+	0.486519i
$575$		0			0
$576$	−10.1918	−	1.28856i	−0.424656	−	0.0536899i
$577$	−13.8423	+	23.9756i	−0.576262	+	0.998116i	0.419641	+	0.907690i	$0.362156\pi$
$577$	−13.8423	+	23.9756i	−0.576262	+	0.998116i	−0.995903	+	0.0904254i	$0.971177\pi$
$578$	−14.9341	−	5.43556i	−0.621176	−	0.226089i
$579$	−10.8618	+	11.4049i	−0.451403	+	0.473972i
$580$		0			0
$581$	1.45281	+	1.21905i	0.0602726	+	0.0505748i
$582$	38.4752	+	9.31017i	1.59485	+	0.385919i
$583$	27.1263	+	9.87317i	1.12346	+	0.408905i
$584$	−1.51131	+	2.61766i	−0.0625384	+	0.108320i
$585$		0			0
$586$	−5.15817	−	8.93422i	−0.213082	−	0.369069i
$587$	−2.96430	−	16.8114i	−0.122350	−	0.693880i	−0.982847	−	0.184424i	$-0.940958\pi$
$587$	−2.96430	−	16.8114i	−0.122350	−	0.693880i	0.860497	−	0.509455i	$-0.170153\pi$
$588$	−2.72441	+	6.23508i	−0.112353	+	0.257130i
$589$	3.01873	−	1.09873i	0.124385	−	0.0452723i
$590$		0			0
$591$	0.733801	−	11.6541i	0.0301845	−	0.479385i
$592$	−17.6985	+	14.8508i	−0.727405	+	0.610366i
$593$	7.85373			0.322514			0.161257	−	0.986912i	$-0.448445\pi$
$593$	7.85373			0.322514			0.161257	+	0.986912i	$0.448445\pi$
$594$	−4.81198	−	29.7385i	−0.197438	−	1.22018i
$595$		0			0
$596$	10.7378	−	9.01007i	0.439837	−	0.369067i
$597$	−16.4543	+	8.16694i	−0.673428	+	0.334251i
$598$	1.13355	−	6.42867i	0.0463543	−	0.262888i
$599$	−45.0491	+	16.3965i	−1.84066	+	0.669944i	−0.851253	+	0.524756i	$0.824157\pi$
$599$	−45.0491	+	16.3965i	−1.84066	+	0.669944i	−0.989404	+	0.145188i	$0.953621\pi$
$600$		0			0
$601$	4.31451	+	24.4688i	0.175993	+	0.998104i	0.936992	+	0.349351i	$0.113598\pi$
$601$	4.31451	+	24.4688i	0.175993	+	0.998104i	−0.760999	+	0.648753i	$0.775291\pi$
$602$	−2.21206	−	3.83139i	−0.0901567	−	0.156156i
$603$	3.90700	−	12.6170i	0.159105	−	0.513804i
$604$	−4.94082	+	8.55775i	−0.201039	+	0.348210i
$605$		0			0
$606$	−9.51765	−	32.3442i	−0.386628	−	1.31389i
$607$	−34.1399	−	28.6468i	−1.38570	−	1.16274i	−0.967049	−	0.254590i	$-0.918060\pi$
$607$	−34.1399	−	28.6468i	−1.38570	−	1.16274i	−0.418648	−	0.908148i	$-0.637496\pi$
$608$	8.45239	+	7.09240i	0.342790	+	0.287635i
$609$	5.71327	+	19.4156i	0.231513	+	0.786761i
$610$		0			0
$611$	−1.84400	+	3.19389i	−0.0746001	+	0.129211i
$612$	3.29504	−	10.6408i	0.133194	−	0.430128i
$613$	2.94457	+	5.10015i	0.118930	+	0.205993i	0.919344	−	0.393455i	$-0.128720\pi$
$613$	2.94457	+	5.10015i	0.118930	+	0.205993i	−0.800414	+	0.599448i	$0.795387\pi$
$614$	−5.22571	−	29.6365i	−0.210893	−	1.19603i
$615$		0			0
$616$	−8.65617	+	3.15059i	−0.348767	+	0.126941i
$617$	5.33141	−	30.2359i	0.214635	−	1.21725i	−0.666905	−	0.745143i	$-0.732381\pi$
$617$	5.33141	−	30.2359i	0.214635	−	1.21725i	0.881539	−	0.472110i	$-0.156508\pi$
$618$	−6.26559	+	3.10987i	−0.252039	+	0.125097i
$619$	−34.9350	+	29.3139i	−1.40416	+	1.17823i	−0.444938	+	0.895561i	$0.646774\pi$
$619$	−34.9350	+	29.3139i	−1.40416	+	1.17823i	−0.959219	+	0.282666i	$0.908781\pi$
$620$		0			0
$621$	−32.5188	−	12.3584i	−1.30494	−	0.495924i
$622$	−7.80060			−0.312776
$623$	12.4090	−	10.4124i	0.497155	−	0.417162i
$624$	0.316711	−	5.02994i	0.0126786	−	0.201359i
$625$		0			0
$626$	−53.6846	+	19.5396i	−2.14567	+	0.780960i
$627$	6.91204	−	15.8189i	0.276040	−	0.631745i
$628$	1.47672	+	8.37491i	0.0589277	+	0.334195i
$629$	12.1149	+	20.9836i	0.483053	+	0.836672i
$630$		0			0
$631$	−6.80759	+	11.7911i	−0.271006	+	0.469396i	−0.969120	−	0.246591i	$-0.920690\pi$
$631$	−6.80759	+	11.7911i	−0.271006	+	0.469396i	0.698114	+	0.715987i	$0.254023\pi$
$632$	2.51481	+	0.915317i	0.100034	+	0.0364094i
$633$	−30.0673	−	7.27564i	−1.19507	−	0.289181i
$634$	−1.30271	−	1.09310i	−0.0517371	−	0.0434126i
$635$		0			0
$636$	−7.05633	+	7.40913i	−0.279802	+	0.293791i
$637$	3.03391	+	1.10425i	0.120208	+	0.0437520i
$638$	−27.2995	+	47.2841i	−1.08080	+	1.87199i
$639$	−20.4644	−	2.58734i	−0.809558	−	0.102354i
$640$		0			0
$641$	1.38566	+	7.85848i	0.0547304	+	0.310391i	0.999867	−	0.0162827i	$-0.00518316\pi$
$641$	1.38566	+	7.85848i	0.0547304	+	0.310391i	−0.945137	+	0.326674i	$0.894072\pi$
$642$	−19.4137	+	2.17661i	−0.766198	+	0.0859039i
$643$	−14.1909	+	5.16505i	−0.559633	+	0.203690i	−0.606321	−	0.795220i	$-0.707355\pi$
$643$	−14.1909	+	5.16505i	−0.559633	+	0.203690i	0.0466885	+	0.998909i	$0.485133\pi$
$644$	1.03776	−	5.88543i	0.0408935	−	0.231918i
$645$		0			0
$646$	18.4835	−	15.5095i	0.727225	−	0.610214i
$647$	44.8366			1.76271			0.881355	−	0.472455i	$-0.156632\pi$
$647$	44.8366			1.76271			0.881355	+	0.472455i	$0.156632\pi$
$648$	−18.4077	−	4.73022i	−0.723121	−	0.185821i
$649$	47.5075			1.86483
$650$		0			0
$651$	−2.02829	−	1.34774i	−0.0794950	−	0.0528221i
$652$	−1.68056	+	9.53092i	−0.0658157	+	0.373260i
$653$	−17.5167	+	6.37556i	−0.685482	+	0.249495i	−0.661199	−	0.750210i	$-0.729952\pi$
$653$	−17.5167	+	6.37556i	−0.685482	+	0.249495i	−0.0242823	+	0.999705i	$0.507730\pi$
$654$	53.3477	−	5.98119i	2.08606	−	0.233883i
$655$		0			0
$656$	14.2339	+	24.6539i	0.555742	+	0.962573i
$657$	−2.59650	+	3.42005i	−0.101299	+	0.133429i
$658$	−6.38123	+	11.0526i	−0.248766	+	0.430876i
$659$	8.86949	+	3.22823i	0.345506	+	0.125754i	0.508944	−	0.860800i	$-0.330036\pi$
$659$	8.86949	+	3.22823i	0.345506	+	0.125754i	−0.163438	+	0.986554i	$0.552258\pi$
$660$		0			0
$661$	−21.0425	−	17.6567i	−0.818457	−	0.686767i	0.134153	−	0.990961i	$-0.457169\pi$
$661$	−21.0425	−	17.6567i	−0.818457	−	0.686767i	−0.952610	+	0.304194i	$0.901613\pi$
$662$	16.0369	+	13.4565i	0.623291	+	0.523003i
$663$	−5.13727	−	1.24311i	−0.199515	−	0.0482784i
$664$	3.03314	+	1.10397i	0.117709	+	0.0428425i
$665$		0			0
$666$	−19.5239	+	12.5795i	−0.756534	+	0.487446i
$667$	31.5248	+	54.6026i	1.22065	+	2.11422i
$668$	0.323334	+	1.83372i	0.0125102	+	0.0709486i
$669$	−13.5303	+	30.9654i	−0.523112	+	1.19719i
$670$		0			0
$671$	4.86712	−	27.6028i	0.187893	−	1.06559i
$672$	0.525616	−	8.34774i	0.0202761	−	0.322021i
$673$	20.4558	−	17.1645i	0.788514	−	0.661642i	−0.156863	−	0.987620i	$-0.550138\pi$
$673$	20.4558	−	17.1645i	0.788514	−	0.661642i	0.945377	+	0.325979i	$0.105694\pi$
$674$	−15.3210			−0.590144
$675$		0			0
$676$	−9.10112			−0.350043
$677$	−25.9121	+	21.7428i	−0.995883	+	0.835645i	−0.986409	−	0.164310i	$-0.947460\pi$
$677$	−25.9121	+	21.7428i	−0.995883	+	0.835645i	−0.00947415	+	0.999955i	$0.503016\pi$
$678$	35.3046	−	17.5232i	1.35587	−	0.672973i
$679$	2.98604	−	16.9347i	0.114594	−	0.649894i
$680$		0			0
$681$	−3.78134	−	5.12942i	−0.144901	−	0.196560i
$682$	−1.14080	−	6.46982i	−0.0436836	−	0.247742i
$683$	−8.68268	−	15.0388i	−0.332233	−	0.575445i	0.650716	−	0.759321i	$-0.274469\pi$
$683$	−8.68268	−	15.0388i	−0.332233	−	0.575445i	−0.982949	+	0.183876i	$0.941136\pi$
$684$	4.15684	+	4.48989i	0.158941	+	0.171675i
$685$		0			0
$686$	23.9579	+	8.71998i	0.914718	+	0.332930i
$687$	−2.12093	−	7.20762i	−0.0809183	−	0.274988i
$688$	−8.15137	−	6.83981i	−0.310768	−	0.260765i
$689$	3.71905	+	3.12066i	0.141685	+	0.118888i
$690$		0			0
$691$	−13.7800	−	5.01549i	−0.524214	−	0.190798i	0.0663389	−	0.997797i	$-0.478868\pi$
$691$	−13.7800	−	5.01549i	−0.524214	−	0.190798i	−0.590553	+	0.806999i	$0.701090\pi$
$692$	−5.95096	+	10.3074i	−0.226222	+	0.391827i
$693$	−12.7615	+	2.89799i	−0.484768	+	0.110085i
$694$	−20.7216	−	35.8909i	−0.786582	−	1.36240i
$695$		0			0
$696$	20.4394	+	27.7263i	0.774755	+	1.05096i
$697$	28.0548	−	10.2111i	1.06265	−	0.386773i
$698$	0.685839	−	3.88958i	0.0259594	−	0.147223i
$699$	12.2378	−	6.07415i	0.462877	−	0.229745i
$700$		0			0
$701$	−28.8893			−1.09113			−0.545567	−	0.838067i	$-0.683686\pi$
$701$	−28.8893			−1.09113			−0.545567	+	0.838067i	$0.683686\pi$
$702$	0.950109	−	4.97657i	0.0358596	−	0.187829i
$703$	−13.3092			−0.501966
$704$	−9.22221	+	7.73836i	−0.347575	+	0.291650i
$705$		0			0
$706$	−3.66652	+	20.7939i	−0.137991	+	0.782588i
$707$	−13.7627	+	5.00922i	−0.517600	+	0.188391i
$708$	−6.74206	+	15.4299i	−0.253382	+	0.579889i
$709$	0.360524	+	2.04463i	0.0135398	+	0.0767878i	0.990829	−	0.135122i	$-0.0431427\pi$
$709$	0.360524	+	2.04463i	0.0135398	+	0.0767878i	−0.977289	+	0.211910i	$0.932032\pi$
$710$		0			0
$711$	3.38129	+	1.73818i	0.126808	+	0.0651867i
$712$	13.7849	−	23.8762i	0.516612	−	0.894798i
$713$	−7.12893	−	2.59472i	−0.266981	−	0.0971730i
$714$	−17.7777	−	4.30184i	−0.665316	−	0.160992i
$715$		0			0
$716$	−0.668871	−	0.561249i	−0.0249969	−	0.0209749i
$717$	−34.1070	+	35.8122i	−1.27375	+	1.33743i
$718$	−2.40028	−	0.873632i	−0.0895778	−	0.0326037i
$719$	−9.24248	+	16.0084i	−0.344686	+	0.597014i	−0.985297	−	0.170852i	$-0.945348\pi$
$719$	−9.24248	+	16.0084i	−0.344686	+	0.597014i	0.640610	+	0.767866i	$0.278681\pi$
$720$		0			0
$721$	1.51929	+	2.63149i	0.0565814	+	0.0980019i
$722$	−3.13934	−	17.8041i	−0.116834	−	0.662600i
$723$	22.6526	−	2.53975i	0.842460	−	0.0944542i
$724$	2.49076	−	0.906563i	0.0925684	−	0.0336921i
$725$		0			0
$726$	−3.23549	−	2.14989i	−0.120080	−	0.0797899i
$727$	31.4598	−	26.3979i	1.16678	−	0.979045i	0.166804	−	0.985990i	$-0.446655\pi$
$727$	31.4598	−	26.3979i	1.16678	−	0.979045i	0.999976	+	0.00694522i	$0.00221075\pi$
$728$	−1.54922			−0.0574179
$729$	−25.1010	−	9.94693i	−0.929666	−	0.368405i
$730$		0			0
$731$	−8.54864	+	7.17316i	−0.316183	+	0.265309i
$732$	8.27432	+	5.49804i	0.305828	+	0.203214i
$733$	0.580566	−	3.29255i	0.0214437	−	0.121613i	−0.972207	−	0.234123i	$-0.924778\pi$
$733$	0.580566	−	3.29255i	0.0214437	−	0.121613i	0.993651	+	0.112510i	$0.0358891\pi$
$734$	−7.67229	+	2.79248i	−0.283189	+	0.103072i
$735$		0			0
$736$	−4.52477	−	25.6612i	−0.166785	−	0.945886i
$737$	−7.73924	−	13.4048i	−0.285078	−	0.493770i
$738$	11.0872	+	26.3829i	0.408126	+	0.971166i
$739$	−9.86291	+	17.0831i	−0.362813	+	0.628411i	−0.988423	−	0.151726i	$-0.951517\pi$
$739$	−9.86291	+	17.0831i	−0.362813	+	0.628411i	0.625610	+	0.780136i	$0.284850\pi$
$740$		0			0
$741$	2.00227	−	2.10238i	0.0735554	−	0.0772330i
$742$	12.8700	+	10.7992i	0.472471	+	0.396450i
$743$	−17.2023	−	14.4345i	−0.631092	−	0.529549i	0.270176	−	0.962811i	$-0.412918\pi$
$743$	−17.2023	−	14.4345i	−0.631092	−	0.529549i	−0.901268	+	0.433262i	$0.857362\pi$
$744$	−4.02844	−	0.974796i	−0.147690	−	0.0357378i
$745$		0			0
$746$	−14.2698	+	24.7161i	−0.522456	+	0.904921i
$747$	4.07821	+	2.09643i	0.149214	+	0.0767045i
$748$	−6.52702	−	11.3051i	−0.238652	−	0.413357i
$749$	1.47360	+	8.35721i	0.0538442	+	0.305366i
$750$		0			0
$751$	−23.9497	+	8.71699i	−0.873938	+	0.318088i	−0.739761	−	0.672870i	$-0.765061\pi$
$751$	−23.9497	+	8.71699i	−0.873938	+	0.318088i	−0.134177	+	0.990957i	$0.542839\pi$
$752$	−5.33034	+	30.2299i	−0.194378	+	1.10237i
$753$	−2.94990	+	46.8498i	−0.107500	+	1.70730i
$754$	−7.03415	+	5.90235i	−0.256169	+	0.214951i
$755$		0			0
$756$	0.869822	−	4.55604i	0.0316351	−	0.165701i
$757$	−43.0981			−1.56643			−0.783214	−	0.621753i	$-0.786421\pi$
$757$	−43.0981			−1.56643			−0.783214	+	0.621753i	$0.786421\pi$
$758$	11.2654	−	9.45282i	0.409179	−	0.343342i
$759$	−36.5172	+	18.1250i	−1.32549	+	0.657896i
$760$		0			0
$761$	−26.5013	+	9.64570i	−0.960673	+	0.349656i	−0.774297	−	0.632822i	$-0.781896\pi$
$761$	−26.5013	+	9.64570i	−0.960673	+	0.349656i	−0.186376	+	0.982479i	$0.559674\pi$
$762$	14.4876	+	19.6525i	0.524829	+	0.711935i
$763$	−4.04937	−	22.9651i	−0.146597	−	0.831393i
$764$	−1.36674	−	2.36726i	−0.0494469	−	0.0856445i
$765$		0			0
$766$	20.3493	−	35.2461i	0.735251	−	1.27349i
$767$	7.50796	+	2.73267i	0.271097	+	0.0986711i
$768$	−7.48092	−	25.4227i	−0.269945	−	0.917363i
$769$	−0.986304	−	0.827608i	−0.0355670	−	0.0298443i	0.624831	−	0.780760i	$-0.285168\pi$
$769$	−0.986304	−	0.827608i	−0.0355670	−	0.0298443i	−0.660398	+	0.750916i	$0.729612\pi$
$770$		0			0
$771$	−0.925308	−	3.14451i	−0.0333241	−	0.113247i
$772$	−6.14733	−	2.23745i	−0.221247	−	0.0805274i
$773$	2.44988	−	4.24332i	0.0881162	−	0.152622i	−0.818599	−	0.574366i	$-0.805249\pi$
$773$	2.44988	−	4.24332i	0.0881162	−	0.152622i	0.906715	+	0.421744i	$0.138582\pi$
$774$	−7.26714	−	7.84938i	−0.261212	−	0.282140i
$775$		0			0
$776$	−5.08217	−	28.8224i	−0.182439	−	1.03466i
$777$	5.98668	+	8.12099i	0.214771	+	0.291339i
$778$	11.0725	−	4.03007i	0.396970	−	0.144485i
$779$	−2.84770	+	16.1501i	−0.102029	+	0.578637i
$780$		0			0
$781$	−18.5176	+	15.5381i	−0.662612	+	0.555997i
$782$	−56.9812			−2.03764
$783$	23.8668	+	42.7198i	0.852931	+	1.52668i
$784$	26.8727			0.959739
$785$		0			0
$786$	−1.73847	+	27.6101i	−0.0620091	+	0.984818i
$787$	5.48979	−	31.1341i	0.195690	−	1.10981i	−0.715743	−	0.698363i	$-0.753912\pi$
$787$	5.48979	−	31.1341i	0.195690	−	1.10981i	0.911433	−	0.411448i	$-0.134977\pi$
$788$	4.55778	−	1.65890i	0.162364	−	0.0590958i
$789$	14.5930	−	33.3975i	0.519525	−	1.18898i
$790$		0			0
$791$	−8.56074	−	14.8276i	−0.304385	−	0.527210i
$792$	−18.7229	+	12.0634i	−0.665289	+	0.428655i
$793$	2.35692	−	4.08231i	0.0836967	−	0.144967i
$794$	6.94125	+	2.52641i	0.246336	+	0.0896589i
$795$		0			0
$796$	−5.84498	−	4.90452i	−0.207170	−	0.173836i
$797$	−19.8522	−	16.6580i	−0.703202	−	0.590057i	0.219480	−	0.975617i	$-0.429564\pi$
$797$	−19.8522	−	16.6580i	−0.703202	−	0.590057i	−0.922683	+	0.385560i	$0.874008\pi$
$798$	6.92896	−	7.27539i	0.245283	−	0.257546i
$799$	30.2508	+	11.0104i	1.07020	+	0.389520i
$800$		0			0
$801$	23.6831	−	31.1949i	0.836802	−	1.10222i
$802$	−3.79592	−	6.57473i	−0.134039	−	0.232162i
$803$	0.873820	+	4.95568i	0.0308364	+	0.174882i
$804$	5.45201	−	0.611264i	0.192278	−	0.0215576i
$805$		0			0
$806$	0.191860	−	1.08809i	0.00675797	−	0.0383264i
$807$	1.53679	+	1.02115i	0.0540974	+	0.0359461i
$808$	−19.0952	+	16.0228i	−0.671768	+	0.563680i
$809$	−16.8506			−0.592435			−0.296217	−	0.955121i	$-0.595725\pi$
$809$	−16.8506			−0.592435			−0.296217	+	0.955121i	$0.595725\pi$
$810$		0			0
$811$	−26.5505			−0.932313			−0.466156	−	0.884702i	$-0.654362\pi$
$811$	−26.5505			−0.932313			−0.466156	+	0.884702i	$0.654362\pi$
$812$	−6.43974	+	5.40358i	−0.225991	+	0.189629i
$813$	7.68462	+	5.10621i	0.269511	+	0.179082i
$814$	−4.72633	+	26.8044i	−0.165658	+	0.939493i
$815$		0			0
$816$	−43.7191	+	4.90166i	−1.53047	+	0.171592i
$817$	−1.06443	−	6.03666i	−0.0372396	−	0.211196i
$818$	−10.1574	−	17.5932i	−0.355146	−	0.615132i
$819$	−2.18348	−	0.276061i	−0.0762970	−	0.00964634i
$820$		0			0
$821$	43.6959	+	15.9040i	1.52500	+	0.555054i	0.962390	−	0.271670i	$-0.0875760\pi$
$821$	43.6959	+	15.9040i	1.52500	+	0.555054i	0.562608	+	0.826724i	$0.309798\pi$
$822$	29.1536	−	30.6113i	1.01685	−	1.06769i
$823$	−0.306870	−	0.257495i	−0.0106968	−	0.00897570i	0.637424	−	0.770514i	$-0.280000\pi$
$823$	−0.306870	−	0.257495i	−0.0106968	−	0.00897570i	−0.648120	+	0.761538i	$0.724445\pi$
$824$	3.96167	+	3.32424i	0.138011	+	0.115805i
$825$		0			0
$826$	25.9816	+	9.45654i	0.904017	+	0.329035i
$827$	0.550903	−	0.954191i	0.0191568	−	0.0331805i	−0.856288	−	0.516498i	$-0.827235\pi$
$827$	0.550903	−	0.954191i	0.0191568	−	0.0331805i	0.875445	+	0.483318i	$0.160569\pi$
$828$	−0.704416	−	14.4325i	−0.0244801	−	0.501565i
$829$	2.63061	+	4.55635i	0.0913648	+	0.158249i	0.908086	−	0.418784i	$-0.137544\pi$
$829$	2.63061	+	4.55635i	0.0913648	+	0.158249i	−0.816721	+	0.577033i	$0.804210\pi$
$830$		0			0
$831$	11.9131	−	27.2642i	0.413260	−	0.945785i
$832$	−1.90257	+	0.692479i	−0.0659597	+	0.0240074i
$833$	4.89382	−	27.7542i	0.169561	−	0.961627i
$834$	−0.490683	+	7.79295i	−0.0169910	+	0.269848i
$835$		0			0
$836$	7.17047			0.247996
$837$	−5.50401	−	2.09173i	−0.190246	−	0.0723006i
$838$	27.5609			0.952075
$839$	27.5648	−	23.1296i	0.951642	−	0.798523i	−0.0279310	−	0.999610i	$-0.508892\pi$
$839$	27.5648	−	23.1296i	0.951642	−	0.798523i	0.979573	+	0.201087i	$0.0644474\pi$
$840$		0			0
$841$	10.3649	−	58.7823i	0.357410	−	2.02698i
$842$	13.0853	−	4.76267i	0.450950	−	0.164132i
$843$	12.7856	+	17.3437i	0.440358	+	0.597350i
$844$	−2.23126	−	12.6541i	−0.0768033	−	0.435573i
$845$		0			0
$846$	−9.12791	+	29.4770i	−0.313824	+	1.01344i
$847$	−0.843742	+	1.46140i	−0.0289913	+	0.0502145i
$848$	37.9716	+	13.8205i	1.30395	+	0.474599i
$849$	−10.1287	−	34.4207i	−0.347616	−	1.18132i
$850$		0			0
$851$	24.0772	+	20.2032i	0.825357	+	0.692557i
$852$	−2.41865	−	8.21938i	−0.0828615	−	0.281591i
$853$	−0.376728	−	0.137118i	−0.0128989	−	0.00469483i	0.335563	−	0.942018i	$-0.391074\pi$
$853$	−0.376728	−	0.137118i	−0.0128989	−	0.00469483i	−0.348462	+	0.937323i	$0.613296\pi$
$854$	8.15623	−	14.1270i	0.279101	−	0.483416i
$855$		0			0
$856$	7.22159	+	12.5082i	0.246829	+	0.427520i
$857$	6.70198	+	38.0088i	0.228935	+	1.29836i	0.855018	+	0.518599i	$0.173546\pi$
$857$	6.70198	+	38.0088i	0.228935	+	1.29836i	−0.626083	+	0.779757i	$0.715343\pi$
$858$	−3.52310	−	4.77912i	−0.120277	−	0.163156i
$859$	−16.0641	+	5.84684i	−0.548099	+	0.199492i	−0.601202	−	0.799097i	$-0.705311\pi$
$859$	−16.0641	+	5.84684i	−0.548099	+	0.199492i	0.0531029	+	0.998589i	$0.483089\pi$
$860$		0			0
$861$	11.1354	−	5.52695i	0.379493	−	0.188358i
$862$	−14.7208	+	12.3522i	−0.501393	+	0.420719i
$863$	−23.2510			−0.791472			−0.395736	−	0.918364i	$-0.629511\pi$
$863$	−23.2510			−0.791472			−0.395736	+	0.918364i	$0.629511\pi$
$864$	−3.23038	−	19.9640i	−0.109900	−	0.679190i
$865$		0			0
$866$	13.6738	−	11.4737i	0.464654	−	0.389891i
$867$	−1.04895	+	16.6592i	−0.0356242	+	0.565777i
$868$	0.175647	−	0.996144i	0.00596185	−	0.0338113i
$869$	4.18672	−	1.52384i	0.142025	−	0.0516928i
$870$		0			0
$871$	−0.452035	−	2.56362i	−0.0153166	−	0.0868648i
$872$	−19.8445	−	34.3716i	−0.672019	−	1.16397i
$873$	−2.02688	−	41.5281i	−0.0685995	−	1.40551i
$874$	15.6496	−	27.1059i	0.529356	−	0.916872i
$875$		0			0
$876$	−1.73355	−	0.419482i	−0.0585712	−	0.0141730i
$877$	0.600510	+	0.503887i	0.0202778	+	0.0170151i	0.652870	−	0.757470i	$-0.273565\pi$
$877$	0.600510	+	0.503887i	0.0202778	+	0.0170151i	−0.632592	+	0.774485i	$0.718009\pi$
$878$	35.4047	+	29.7080i	1.19485	+	1.00260i
$879$	−7.47274	+	7.84636i	−0.252049	+	0.264651i
$880$		0			0
$881$	4.60962	−	7.98410i	0.155302	−	0.268991i	−0.777867	−	0.628429i	$-0.783698\pi$
$881$	4.60962	−	7.98410i	0.155302	−	0.268991i	0.933169	+	0.359438i	$0.117032\pi$
$882$	26.8009	+	3.38848i	0.902434	+	0.114096i
$883$	18.1599	+	31.4539i	0.611129	+	1.05851i	0.991050	+	0.133488i	$0.0426178\pi$
$883$	18.1599	+	31.4539i	0.611129	+	1.05851i	−0.379921	+	0.925019i	$0.624049\pi$
$884$	−0.381232	−	2.16207i	−0.0128222	−	0.0727183i
$885$		0			0
$886$	43.3716	−	15.7860i	1.45710	−	0.530340i
$887$	−5.82770	+	33.0505i	−0.195675	+	1.10973i	0.715779	+	0.698326i	$0.246072\pi$
$887$	−5.82770	+	33.0505i	−0.195675	+	1.10973i	−0.911454	+	0.411401i	$0.865040\pi$
$888$	14.3020	+	9.50326i	0.479943	+	0.318908i
$889$	8.12468	−	6.81741i	0.272493	−	0.228649i
$890$		0			0
$891$	−28.5378	+	13.6660i	−0.956051	+	0.457827i
$892$	−14.0362			−0.469967
$893$	−13.5459	+	11.3664i	−0.453296	+	0.380361i
$894$	−46.3510	−	30.7989i	−1.55021	−	1.03007i
$895$		0			0
$896$	−15.6597	+	5.69966i	−0.523154	+	0.190412i
$897$	−6.81363	+	0.763925i	−0.227501	+	0.0255067i
$898$	−7.18587	−	40.7531i	−0.239796	−	1.35995i
$899$	5.33576	+	9.24181i	0.177958	+	0.308232i
$900$		0			0
$901$	21.1890	−	36.7004i	0.705907	−	1.22267i
$902$	31.5146	+	11.4704i	1.04932	+	0.381921i
$903$	−3.20465	+	3.36487i	−0.106644	+	0.111976i
$904$	−22.3228	−	18.7310i	−0.742444	−	0.622985i
$905$		0			0
$906$	38.1313	+	9.22696i	1.26683	+	0.306545i
$907$	9.18415	+	3.34276i	0.304955	+	0.110994i	0.489965	−	0.871742i	$-0.337010\pi$
$907$	9.18415	+	3.34276i	0.304955	+	0.110994i	−0.185010	+	0.982737i	$0.559232\pi$
$908$	1.32347	−	2.29232i	0.0439209	−	0.0760732i
$909$	−29.7681	+	19.1800i	−0.987345	+	0.636160i
$910$		0			0
$911$	6.63575	+	37.6332i	0.219852	+	1.24684i	0.872285	+	0.488998i	$0.162637\pi$
$911$	6.63575	+	37.6332i	0.219852	+	1.24684i	−0.652433	+	0.757847i	$0.726252\pi$
$912$	9.67553	−	22.1434i	0.320389	−	0.733241i
$913$	5.04965	−	1.83792i	0.167119	−	0.0608264i
$914$	4.80022	−	27.2234i	0.158777	−	0.900470i
$915$		0			0
$916$	2.39061	−	2.00596i	0.0789880	−	0.0662788i
$917$	12.0175			0.396854
$918$	−44.2204	−	0.624136i	−1.45949	−	0.0205996i
$919$	15.3144			0.505176			0.252588	−	0.967574i	$-0.418718\pi$
$919$	15.3144			0.505176			0.252588	+	0.967574i	$0.418718\pi$
$920$		0			0
$921$	−28.3123	+	14.0526i	−0.932924	+	0.463049i
$922$	7.41579	−	42.0570i	0.244226	−	1.38507i
$923$	−3.82023	+	1.39045i	−0.125745	+	0.0457673i
$924$	−3.22538	−	4.37527i	−0.106107	−	0.143936i
$925$		0			0
$926$	14.2794	+	24.7327i	0.469252	+	0.812768i
$927$	4.99125	+	5.39114i	0.163934	+	0.177068i
$928$	−18.3267	+	31.7427i	−0.601603	+	1.04201i
$929$	−0.281736	−	0.102544i	−0.00924347	−	0.00336435i	0.337394	−	0.941363i	$-0.390454\pi$
$929$	−0.281736	−	0.102544i	−0.00924347	−	0.00336435i	−0.346638	+	0.937999i	$0.612677\pi$
$930$		0			0
$931$	11.8586	+	9.95056i	0.388651	+	0.326117i
$932$	4.34720	+	3.64773i	0.142397	+	0.119485i
$933$	2.31286	+	7.85990i	0.0757198	+	0.257321i
$934$	19.2045	+	6.98986i	0.628390	+	0.228715i
$935$		0			0
$936$	−3.65281	+	0.829512i	−0.119396	+	0.0271135i
$937$	−7.61820	−	13.1951i	−0.248876	−	0.431065i	0.714338	−	0.699800i	$-0.246728\pi$
$937$	−7.61820	−	13.1951i	−0.248876	−	0.431065i	−0.963214	+	0.268735i	$0.913394\pi$
$938$	−1.56429	−	8.87151i	−0.0510758	−	0.289665i
$939$	35.6055	+	48.2992i	1.16194	+	1.57619i
$940$		0			0
$941$	−1.63828	+	9.29115i	−0.0534064	+	0.302883i	−0.999797	−	0.0201414i	$-0.993588\pi$
$941$	−1.63828	+	9.29115i	−0.0534064	+	0.302883i	0.946391	+	0.323024i	$0.104699\pi$
$942$	30.2425	−	15.0106i	0.985353	−	0.489072i
$943$	29.6673	−	24.8938i	0.966100	−	0.810654i
$944$	66.5014			2.16444
$945$		0			0
$946$	−12.5357			−0.407570
$947$	43.2160	−	36.2626i	1.40433	−	1.17837i	0.445195	−	0.895433i	$-0.353134\pi$
$947$	43.2160	−	36.2626i	1.40433	−	1.17837i	0.959137	−	0.282941i	$-0.0913102\pi$
$948$	−0.0992362	+	1.57605i	−0.00322304	+	0.0511878i
$949$	−0.146959	+	0.833444i	−0.00477048	+	0.0270547i
$950$		0			0
$951$	−0.715159	+	1.63671i	−0.0231906	+	0.0530740i
$952$	2.34825	+	13.3176i	0.0761073	+	0.431626i
$953$	7.53769	+	13.0557i	0.244170	+	0.422915i	0.961898	−	0.273409i	$-0.0881512\pi$
$953$	7.53769	+	13.0557i	0.244170	+	0.422915i	−0.717728	+	0.696324i	$0.754818\pi$
$954$	36.1275	+	18.5716i	1.16967	+	0.601278i
$955$		0			0
$956$	−19.3031	−	7.02574i	−0.624306	−	0.227229i
$957$	55.7377	+	13.4873i	1.80174	+	0.435984i
$958$	−28.8419	−	24.2012i	−0.931840	−	0.781907i
$959$	−14.0671	−	11.8037i	−0.454249	−	0.381160i
$960$		0			0
$961$	27.9239	+	10.1635i	0.900770	+	0.327853i
$962$	−2.28875	+	3.96422i	−0.0737921	+	0.127812i
$963$	7.94928	+	18.9159i	0.256162	+	0.609557i
$964$	4.73403	+	8.19958i	0.152473	+	0.264091i
$965$		0			0
$966$	−23.5789	+	2.64360i	−0.758638	+	0.0850563i
$967$	8.26273	−	3.00739i	0.265711	−	0.0967110i	−0.205729	−	0.978609i	$-0.565957\pi$
$967$	8.26273	−	3.00739i	0.265711	−	0.0967110i	0.471440	+	0.881898i	$0.343734\pi$
$968$	−0.498727	+	2.82842i	−0.0160297	+	0.0909089i
$969$	−21.1077	−	14.0255i	−0.678079	−	0.450563i
$970$		0			0
$971$	−1.79910			−0.0577358			−0.0288679	−	0.999583i	$-0.509190\pi$
$971$	−1.79910			−0.0577358			−0.0288679	+	0.999583i	$0.509190\pi$
$972$	−0.388579	−	11.2081i	−0.0124637	−	0.359501i
$973$	3.39195			0.108741
$974$	−4.07041	+	3.41548i	−0.130424	+	0.109439i
$975$		0			0
$976$	6.81303	−	38.6386i	0.218080	−	1.23679i
$977$	11.9561	−	4.35167i	0.382510	−	0.139222i	−0.143606	−	0.989635i	$-0.545870\pi$
$977$	11.9561	−	4.35167i	0.382510	−	0.139222i	0.526116	+	0.850413i	$0.323648\pi$
$978$	38.1839	−	4.28107i	1.22099	−	0.136893i
$979$	−7.97027	−	45.2017i	−0.254731	−	1.44465i
$980$		0			0
$981$	−21.8441	−	51.9798i	−0.697430	−	1.65959i
$982$	21.5690	−	37.3586i	0.688295	−	1.19216i
$983$	−49.2740	−	17.9343i	−1.57160	−	0.572015i	−0.598242	−	0.801315i	$-0.704134\pi$
$983$	−49.2740	−	17.9343i	−1.57160	−	0.572015i	−0.973356	+	0.229301i	$0.926356\pi$
$984$	14.5919	−	15.3214i	0.465172	−	0.488429i
$985$		0			0
$986$	61.4007	+	51.5213i	1.95540	+	1.64077i
$987$	13.0287	+	3.15266i	0.414707	+	0.100350i
$988$	1.13320	+	0.412451i	0.0360519	+	0.0131218i
$989$	−7.23795	+	12.5365i	−0.230154	+	0.398638i
$990$		0			0
$991$	−7.43264	−	12.8737i	−0.236106	−	0.408947i	0.723488	−	0.690337i	$-0.242538\pi$
$991$	−7.43264	−	12.8737i	−0.236106	−	0.408947i	−0.959593	+	0.281390i	$0.909204\pi$
$992$	−0.765844	−	4.34332i	−0.0243156	−	0.137900i
$993$	8.80392	−	20.1486i	0.279384	−	0.639397i
$994$	−13.2201	+	4.81172i	−0.419316	+	0.152618i
$995$		0			0
$996$	−0.119690	+	1.90089i	−0.00379252	+	0.0602321i
$997$	17.3621	−	14.5685i	0.549864	−	0.461390i	−0.325031	−	0.945703i	$-0.605375\pi$
$997$	17.3621	−	14.5685i	0.549864	−	0.461390i	0.874895	+	0.484313i	$0.160930\pi$
$998$	−56.4909			−1.78819
$999$	18.4639	+	15.9425i	0.584172	+	0.504397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.h.76.13		96
5.2	odd	4		135.2.p.a.49.13	yes	96
5.3	odd	4		135.2.p.a.49.4	✓	96
5.4	even	2	inner	675.2.l.h.76.4		96
15.2	even	4		405.2.p.a.199.4		96
15.8	even	4		405.2.p.a.199.13		96
27.16	even	9	inner	675.2.l.h.151.13		96
135.38	even	36		405.2.p.a.289.4		96
135.43	odd	36		135.2.p.a.124.13	yes	96
135.92	even	36		405.2.p.a.289.13		96
135.97	odd	36		135.2.p.a.124.4	yes	96
135.124	even	18	inner	675.2.l.h.151.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.4	✓	96	5.3	odd	4
135.2.p.a.49.13	yes	96	5.2	odd	4
135.2.p.a.124.4	yes	96	135.97	odd	36
135.2.p.a.124.13	yes	96	135.43	odd	36
405.2.p.a.199.4		96	15.2	even	4
405.2.p.a.199.13		96	15.8	even	4
405.2.p.a.289.4		96	135.38	even	36
405.2.p.a.289.13		96	135.92	even	36
675.2.l.h.76.4		96	5.4	even	2	inner
675.2.l.h.76.13		96	1.1	even	1	trivial
675.2.l.h.151.4		96	135.124	even	18	inner
675.2.l.h.151.13		96	27.16	even	9	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26326 - 1.06000i) q^{2} +(-1.44261 - 0.958575i) q^{3} +(0.124928 - 0.708504i) q^{4} +(-2.83849 + 0.318243i) q^{6} +(0.215456 + 1.22191i) q^{7} +(1.05587 + 1.82882i) q^{8} +(1.16227 + 2.76571i) q^{9} +(3.30366 + 1.20243i) q^{11} +(-0.859377 + 0.902344i) q^{12} +(0.452936 + 0.380059i) q^{13} +(1.56741 + 1.31521i) q^{14} +(4.62449 + 1.68318i) q^{16} +(2.58056 - 4.46967i) q^{17} +(4.39990 + 2.26180i) q^{18} +(1.41748 + 2.45515i) q^{19} +(0.860474 - 1.96928i) q^{21} +(5.44797 - 1.98290i) q^{22} +(1.16257 - 6.59324i) q^{23} +(0.229849 - 3.65042i) q^{24} +0.975040 q^{26} +(0.974431 - 5.10397i) q^{27} +0.892646 q^{28} +(-7.21421 + 6.05345i) q^{29} +(0.196771 - 1.11595i) q^{31} +(3.65733 - 1.33116i) q^{32} +(-3.61329 - 4.90146i) q^{33} +(-1.47793 - 8.38176i) q^{34} +(2.10471 - 0.477957i) q^{36} +(-2.34734 + 4.06570i) q^{37} +(4.39311 + 1.59896i) q^{38} +(-0.289098 - 0.982452i) q^{39} +(4.43129 + 3.71830i) q^{41} +(-1.00044 - 3.39982i) q^{42} +(-2.03181 - 0.739520i) q^{43} +(1.26465 - 2.19044i) q^{44} +(-5.52022 - 9.56131i) q^{46} +(1.08312 + 6.14268i) q^{47} +(-5.05791 - 6.86110i) q^{48} +(5.13120 - 1.86760i) q^{49} +(-8.00727 + 3.97434i) q^{51} +(0.325858 - 0.273427i) q^{52} +8.21098 q^{53} +(-4.17926 - 7.48054i) q^{54} +(-2.00717 + 1.68421i) q^{56} +(0.308566 - 4.90059i) q^{57} +(-2.69677 + 15.2942i) q^{58} +(12.6981 - 4.62173i) q^{59} +(-1.38440 - 7.85133i) q^{61} +(-0.934331 - 1.61831i) q^{62} +(-3.12903 + 2.01608i) q^{63} +(-1.71215 + 2.96553i) q^{64} +(-9.76008 - 2.36173i) q^{66} +(-3.37266 - 2.83000i) q^{67} +(-2.84439 - 2.38673i) q^{68} +(-7.99725 + 8.39709i) q^{69} +(-3.43788 + 5.95458i) q^{71} +(-3.83078 + 5.04582i) q^{72} +(0.715668 + 1.23957i) q^{73} +(1.34436 + 7.62423i) q^{74} +(1.91656 - 0.697573i) q^{76} +(-0.757476 + 4.29586i) q^{77} +(-1.40661 - 0.934649i) q^{78} +(0.970806 - 0.814603i) q^{79} +(-6.29826 + 6.42899i) q^{81} +9.53928 q^{82} +(1.17090 - 0.982501i) q^{83} +(-1.28774 - 0.855668i) q^{84} +(-3.35061 + 1.21952i) q^{86} +(16.2100 - 1.81742i) q^{87} +(1.28920 + 7.31144i) q^{88} +(-6.52774 - 11.3064i) q^{89} +(-0.366811 + 0.635335i) q^{91} +(-4.52610 - 1.64736i) q^{92} +(-1.35358 + 1.42126i) q^{93} +(7.87952 + 6.61170i) q^{94} +(-6.55214 - 1.58548i) q^{96} +(-13.0234 - 4.74011i) q^{97} +(4.50238 - 7.79835i) q^{98} +(0.514163 + 10.5345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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