LMFDB - Embedded newform 980.2.x.m.67.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.4
Character	$\chi$	$=$	980.67
Dual form			980.2.x.m.863.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24267 - 0.675113i) q^{2} +(0.402205 - 0.107770i) q^{3} +(1.08845 + 1.67788i) q^{4} +(2.22809 - 0.188711i) q^{5} +(-0.572564 - 0.137611i) q^{6} +(-0.219816 - 2.81987i) q^{8} +(-2.44792 + 1.41331i) q^{9} +(-2.89618 - 1.26971i) q^{10} +(0.725638 + 0.418947i) q^{11} +(0.618604 + 0.557549i) q^{12} +(1.16367 - 1.16367i) q^{13} +(0.875811 - 0.316023i) q^{15} +(-1.63057 + 3.65256i) q^{16} +(4.94841 - 1.32592i) q^{17} +(3.99610 - 0.103649i) q^{18} +(-2.91741 - 5.05309i) q^{19} +(2.74179 + 3.53307i) q^{20} +(-0.618890 - 1.01050i) q^{22} +(0.896861 - 3.34713i) q^{23} +(-0.392310 - 1.11048i) q^{24} +(4.92878 - 0.840930i) q^{25} +(-2.23166 + 0.660445i) q^{26} +(-1.71555 + 1.71555i) q^{27} -5.00172i q^{29} +(-1.30169 - 0.198560i) q^{30} +(7.03267 + 4.06031i) q^{31} +(4.49215 - 3.43810i) q^{32} +(0.337005 + 0.0903002i) q^{33} +(-7.04437 - 1.69305i) q^{34} +(-5.03579 - 2.56901i) q^{36} +(-0.190621 + 0.711408i) q^{37} +(0.213956 + 8.24889i) q^{38} +(0.342623 - 0.593441i) q^{39} +(-1.02191 - 6.24145i) q^{40} -0.0958388 q^{41} +(4.87975 + 4.87975i) q^{43} +(0.0868733 + 1.67354i) q^{44} +(-5.18749 + 3.61093i) q^{45} +(-3.37419 + 3.55389i) q^{46} +(5.28468 + 1.41603i) q^{47} +(-0.262186 + 1.64481i) q^{48} +(-6.69255 - 2.28248i) q^{50} +(1.84738 - 1.06658i) q^{51} +(3.21908 + 0.685908i) q^{52} +(3.43436 + 12.8172i) q^{53} +(3.29006 - 0.973671i) q^{54} +(1.69585 + 0.796517i) q^{55} +(-1.71797 - 1.71797i) q^{57} +(-3.37672 + 6.21547i) q^{58} +(4.46933 - 7.74111i) q^{59} +(1.48352 + 1.12553i) q^{60} +(-0.919379 - 1.59241i) q^{61} +(-5.99810 - 9.79346i) q^{62} +(-7.90336 + 1.23971i) q^{64} +(2.37316 - 2.81235i) q^{65} +(-0.357822 - 0.339730i) q^{66} +(0.138137 + 0.515535i) q^{67} +(7.61081 + 6.85965i) q^{68} -1.44289i q^{69} +13.6494i q^{71} +(4.52344 + 6.59216i) q^{72} +(-1.55074 - 5.78744i) q^{73} +(0.717160 - 0.755353i) q^{74} +(1.89175 - 0.869402i) q^{75} +(5.30306 - 10.3951i) q^{76} +(-0.826407 + 0.506141i) q^{78} +(-5.30723 - 9.19239i) q^{79} +(-2.94379 + 8.44595i) q^{80} +(3.73481 - 6.46888i) q^{81} +(0.119096 + 0.0647020i) q^{82} +(4.36830 + 4.36830i) q^{83} +(10.7753 - 3.88809i) q^{85} +(-2.76953 - 9.35829i) q^{86} +(-0.539037 - 2.01171i) q^{87} +(1.02187 - 2.13830i) q^{88} +(2.50474 - 1.44611i) q^{89} +(8.88411 - 0.985047i) q^{90} +(6.59227 - 2.13834i) q^{92} +(3.26615 + 0.875163i) q^{93} +(-5.61112 - 5.32740i) q^{94} +(-7.45382 - 10.7082i) q^{95} +(1.43624 - 1.86694i) q^{96} +(-4.24461 - 4.24461i) q^{97} -2.36841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.24267	−	0.675113i	−0.878699	−	0.477377i
$2$	−1.24267	−	0.675113i	−0.878699	−	0.477377i
$3$	0.402205	−	0.107770i	0.232213	−	0.0622213i	−0.140836	−	0.990033i	$-0.544979\pi$
$3$	0.402205	−	0.107770i	0.232213	−	0.0622213i	0.373049	+	0.927812i	$0.378312\pi$
$4$	1.08845	+	1.67788i	0.544223	+	0.838941i
$5$	2.22809	−	0.188711i	0.996432	−	0.0843941i
$5$	2.22809	−	0.188711i	0.996432	−	0.0843941i
$6$	−0.572564	−	0.137611i	−0.233748	−	0.0561793i
$7$		0			0
$7$		0			0
$8$	−0.219816	−	2.81987i	−0.0777167	−	0.996975i
$9$	−2.44792	+	1.41331i	−0.815974	+	0.471103i
$10$	−2.89618	−	1.26971i	−0.915852	−	0.401517i
$11$	0.725638	+	0.418947i	0.218788	+	0.126317i	0.605389	−	0.795930i	$-0.293018\pi$
$11$	0.725638	+	0.418947i	0.218788	+	0.126317i	−0.386601	+	0.922247i	$0.626351\pi$
$12$	0.618604	+	0.557549i	0.178575	+	0.160951i
$13$	1.16367	−	1.16367i	0.322743	−	0.322743i	−0.527075	−	0.849819i	$-0.676711\pi$
$13$	1.16367	−	1.16367i	0.322743	−	0.322743i	0.849819	+	0.527075i	$0.176711\pi$
$14$		0			0
$15$	0.875811	−	0.316023i	0.226133	−	0.0815967i
$16$	−1.63057	+	3.65256i	−0.407643	+	0.913141i
$17$	4.94841	−	1.32592i	1.20016	−	0.321583i	0.397269	−	0.917702i	$-0.369958\pi$
$17$	4.94841	−	1.32592i	1.20016	−	0.321583i	0.802896	+	0.596119i	$0.203291\pi$
$18$	3.99610	−	0.103649i	0.941889	−	0.0244303i
$19$	−2.91741	−	5.05309i	−0.669299	−	1.15926i	−0.978101	−	0.208133i	$-0.933261\pi$
$19$	−2.91741	−	5.05309i	−0.669299	−	1.15926i	0.308802	−	0.951126i	$-0.400072\pi$
$20$	2.74179	+	3.53307i	0.613083	+	0.790019i
$21$		0			0
$22$	−0.618890	−	1.01050i	−0.131948	−	0.215439i
$23$	0.896861	−	3.34713i	0.187008	−	0.697925i	−0.807183	−	0.590301i	$-0.799009\pi$
$23$	0.896861	−	3.34713i	0.187008	−	0.697925i	0.994192	−	0.107624i	$-0.0343242\pi$
$24$	−0.392310	−	1.11048i	−0.0800799	−	0.226675i
$25$	4.92878	−	0.840930i	0.985755	−	0.168186i
$26$	−2.23166	+	0.660445i	−0.437664	+	0.129524i
$27$	−1.71555	+	1.71555i	−0.330159	+	0.330159i
$28$		0			0
$29$		−	5.00172i		−	0.928795i	−0.885627	−	0.464398i	$-0.846271\pi$
$29$		−	5.00172i		−	0.928795i	0.885627	−	0.464398i	$-0.153729\pi$
$30$	−1.30169	−	0.198560i	−0.237655	−	0.0362519i
$31$	7.03267	+	4.06031i	1.26310	+	0.729254i	0.973674	−	0.227945i	$-0.0732008\pi$
$31$	7.03267	+	4.06031i	1.26310	+	0.729254i	0.289430	+	0.957199i	$0.406534\pi$
$32$	4.49215	−	3.43810i	0.794108	−	0.607776i
$33$	0.337005	+	0.0903002i	0.0586650	+	0.0157192i
$34$	−7.04437	−	1.69305i	−1.20810	−	0.290356i
$35$		0			0
$36$	−5.03579	−	2.56901i	−0.839299	−	0.428169i
$37$	−0.190621	+	0.711408i	−0.0313379	+	0.116955i	−0.979823	−	0.199867i	$-0.935949\pi$
$37$	−0.190621	+	0.711408i	−0.0313379	+	0.116955i	0.948485	+	0.316822i	$0.102616\pi$
$38$	0.213956	+	8.24889i	0.0347083	+	1.33815i
$39$	0.342623	−	0.593441i	0.0548637	−	0.0950266i
$40$	−1.02191	−	6.24145i	−0.161578	−	0.986860i
$41$	−0.0958388			−0.0149675			−0.00748375	−	0.999972i	$-0.502382\pi$
$41$	−0.0958388			−0.0149675			−0.00748375	+	0.999972i	$0.502382\pi$
$42$		0			0
$43$	4.87975	+	4.87975i	0.744155	+	0.744155i	0.973375	−	0.229220i	$-0.0736174\pi$
$43$	4.87975	+	4.87975i	0.744155	+	0.744155i	−0.229220	+	0.973375i	$0.573617\pi$
$44$	0.0868733	+	1.67354i	0.0130966	+	0.252295i
$45$	−5.18749	+	3.61093i	−0.773305	+	0.538286i
$46$	−3.37419	+	3.55389i	−0.497497	+	0.523992i
$47$	5.28468	+	1.41603i	0.770850	+	0.206549i	0.622747	−	0.782423i	$-0.286017\pi$
$47$	5.28468	+	1.41603i	0.770850	+	0.206549i	0.148103	+	0.988972i	$0.452683\pi$
$48$	−0.262186	+	1.64481i	−0.0378433	+	0.237407i
$49$		0			0
$50$	−6.69255	−	2.28248i	−0.946470	−	0.322792i
$51$	1.84738	−	1.06658i	0.258684	−	0.149352i
$52$	3.21908	+	0.685908i	0.446407	+	0.0951183i
$53$	3.43436	+	12.8172i	0.471745	+	1.76058i	0.633497	+	0.773745i	$0.281619\pi$
$53$	3.43436	+	12.8172i	0.471745	+	1.76058i	−0.161752	+	0.986832i	$0.551714\pi$
$54$	3.29006	−	0.973671i	0.447720	−	0.132500i
$55$	1.69585	+	0.796517i	0.228668	+	0.107402i
$56$		0			0
$57$	−1.71797	−	1.71797i	−0.227550	−	0.227550i
$58$	−3.37672	+	6.21547i	−0.443385	+	0.816131i
$59$	4.46933	−	7.74111i	0.581858	−	1.00781i	−0.413402	−	0.910549i	$-0.635659\pi$
$59$	4.46933	−	7.74111i	0.581858	−	1.00781i	0.995259	−	0.0972582i	$-0.0310073\pi$
$60$	1.48352	+	1.12553i	0.191522	+	0.145306i
$61$	−0.919379	−	1.59241i	−0.117714	−	0.203887i	0.801147	−	0.598467i	$-0.204223\pi$
$61$	−0.919379	−	1.59241i	−0.117714	−	0.203887i	−0.918862	+	0.394580i	$0.870890\pi$
$62$	−5.99810	−	9.79346i	−0.761759	−	1.24377i
$63$		0			0
$64$	−7.90336	+	1.23971i	−0.987920	+	0.154963i
$65$	2.37316	−	2.81235i	0.294354	−	0.348830i
$66$	−0.357822	−	0.339730i	−0.0440449	−	0.0418178i
$67$	0.138137	+	0.515535i	0.0168761	+	0.0629826i	0.973850	−	0.227190i	$-0.0729539\pi$
$67$	0.138137	+	0.515535i	0.0168761	+	0.0629826i	−0.956974	+	0.290173i	$0.906287\pi$
$68$	7.61081	+	6.85965i	0.922946	+	0.831855i
$69$		−	1.44289i		−	0.173703i
$70$		0			0
$71$			13.6494i			1.61989i	0.586505	+	0.809946i	$0.300503\pi$
$71$			13.6494i			1.61989i	−0.586505	+	0.809946i	$0.699497\pi$
$72$	4.52344	+	6.59216i	0.533093	+	0.776894i
$73$	−1.55074	−	5.78744i	−0.181500	−	0.677368i	−0.995353	−	0.0962967i	$-0.969300\pi$
$73$	−1.55074	−	5.78744i	−0.181500	−	0.677368i	0.813852	−	0.581072i	$-0.197366\pi$
$74$	0.717160	−	0.755353i	0.0833681	−	0.0878080i
$75$	1.89175	−	0.869402i	0.218440	−	0.100390i
$76$	5.30306	−	10.3951i	0.608303	−	1.19240i
$77$		0			0
$78$	−0.826407	+	0.506141i	−0.0935721	+	0.0573091i
$79$	−5.30723	−	9.19239i	−0.597110	−	1.03422i	−0.993245	−	0.116033i	$-0.962982\pi$
$79$	−5.30723	−	9.19239i	−0.597110	−	1.03422i	0.396136	−	0.918192i	$-0.370351\pi$
$80$	−2.94379	+	8.44595i	−0.329125	+	0.944286i
$81$	3.73481	−	6.46888i	0.414979	−	0.718764i
$82$	0.119096	+	0.0647020i	0.0131519	+	0.00714514i
$83$	4.36830	+	4.36830i	0.479483	+	0.479483i	0.904966	−	0.425483i	$-0.139896\pi$
$83$	4.36830	+	4.36830i	0.479483	+	0.479483i	−0.425483	+	0.904966i	$0.639896\pi$
$84$		0			0
$85$	10.7753	−	3.88809i	1.16874	−	0.421723i
$86$	−2.76953	−	9.35829i	−0.298646	−	1.00913i
$87$	−0.539037	−	2.01171i	−0.0577908	−	0.215678i
$88$	1.02187	−	2.13830i	0.108932	−	0.227943i
$89$	2.50474	−	1.44611i	0.265502	−	0.153288i	−0.361340	−	0.932434i	$-0.617681\pi$
$89$	2.50474	−	1.44611i	0.265502	−	0.153288i	0.626842	+	0.779147i	$0.284347\pi$
$90$	8.88411	−	0.985047i	0.936467	−	0.103833i
$91$		0			0
$92$	6.59227	−	2.13834i	0.687292	−	0.222937i
$93$	3.26615	+	0.875163i	0.338684	+	0.0907502i
$94$	−5.61112	−	5.32740i	−0.578743	−	0.549480i
$95$	−7.45382	−	10.7082i	−0.764746	−	1.09864i
$96$	1.43624	−	1.86694i	0.146586	−	0.190544i
$97$	−4.24461	−	4.24461i	−0.430975	−	0.430975i	0.457985	−	0.888960i	$-0.348571\pi$
$97$	−4.24461	−	4.24461i	−0.430975	−	0.430975i	−0.888960	+	0.457985i	$0.848571\pi$
$98$		0			0
$99$	−2.36841			−0.238034
$100$	6.77569	+	7.35460i	0.677569	+	0.735460i
$101$	0.859895	−	1.48938i	0.0855628	−	0.148199i	−0.820068	−	0.572266i	$-0.806065\pi$
$101$	0.859895	−	1.48938i	0.0855628	−	0.148199i	0.905631	+	0.424067i	$0.139398\pi$
$102$	−3.01574	+	0.0782209i	−0.298603	+	0.00774502i
$103$	4.06549	−	15.1726i	0.400584	−	1.49500i	−0.411472	−	0.911422i	$-0.634985\pi$
$103$	4.06549	−	15.1726i	0.400584	−	1.49500i	0.812057	−	0.583579i	$-0.198348\pi$
$104$	−3.53719	−	3.02560i	−0.346850	−	0.296685i
$105$		0			0
$106$	4.38529	−	18.2461i	0.425937	−	1.77222i
$107$	13.4365	+	3.60029i	1.29895	+	0.348053i	0.841054	−	0.540951i	$-0.181936\pi$
$107$	13.4365	+	3.60029i	1.29895	+	0.348053i	0.457899	+	0.889004i	$0.348602\pi$
$108$	−4.74579	−	1.01121i	−0.456663	−	0.0973038i
$109$	−9.23440	−	5.33148i	−0.884495	−	0.510664i	−0.0123573	−	0.999924i	$-0.503934\pi$
$109$	−9.23440	−	5.33148i	−0.884495	−	0.510664i	−0.872138	+	0.489260i	$0.837267\pi$
$110$	−1.56964	−	2.13469i	−0.149659	−	0.203535i
$111$			0.306675i			0.0291083i
$112$		0			0
$113$	−5.62032	+	5.62032i	−0.528715	+	0.528715i	−0.920189	−	0.391474i	$-0.871965\pi$
$113$	−5.62032	+	5.62032i	−0.528715	+	0.528715i	0.391474	+	0.920189i	$0.371965\pi$
$114$	0.975040	+	3.29468i	0.0913209	+	0.308575i
$115$	1.36665	−	7.62696i	0.127440	−	0.711217i
$116$	8.39229	−	5.44409i	0.779204	−	0.505472i
$117$	−1.20395	+	4.49319i	−0.111305	+	0.415395i
$118$	−10.7800	+	6.60233i	−0.992381	+	0.607793i
$119$		0			0
$120$	−1.08366	−	2.40021i	−0.0989242	−	0.219108i
$121$	−5.14897	−	8.91827i	−0.468088	−	0.810752i
$122$	0.0674252	+	2.59952i	0.00610439	+	0.235350i
$123$	−0.0385468	+	0.0103286i	−0.00347565	+	0.000931297i
$124$	0.841950	+	16.2194i	0.0756093	+	1.45655i
$125$	10.8231	−	2.80378i	0.968045	−	0.250778i
$126$		0			0
$127$	4.54633	−	4.54633i	0.403421	−	0.403421i	−0.476016	−	0.879437i	$-0.657919\pi$
$127$	4.54633	−	4.54633i	0.403421	−	0.403421i	0.879437	+	0.476016i	$0.157919\pi$
$128$	10.6582	+	3.79512i	0.942060	+	0.335444i
$129$	2.48855	+	1.43677i	0.219105	+	0.126500i
$130$	−4.84770	+	1.89267i	−0.425172	+	0.165998i
$131$	−11.9545	+	6.90194i	−1.04447	+	0.603025i	−0.921096	−	0.389335i	$-0.872705\pi$
$131$	−11.9545	+	6.90194i	−1.04447	+	0.603025i	−0.123374	+	0.992360i	$0.539371\pi$
$132$	0.215298	+	0.663741i	0.0187393	+	0.0577713i
$133$		0			0
$134$	0.176386	−	0.733896i	0.0152374	−	0.0633990i
$135$	−3.49867	+	4.14616i	−0.301117	+	0.356844i
$136$	−4.82667	−	13.6624i	−0.413884	−	1.17154i
$137$	−13.8922	+	3.72240i	−1.18689	+	0.318026i	−0.797656	−	0.603112i	$-0.793927\pi$
$137$	−13.8922	+	3.72240i	−1.18689	+	0.318026i	−0.389235	+	0.921139i	$0.627260\pi$
$138$	−0.974111	+	1.79303i	−0.0829218	+	0.152633i
$139$	−1.45615			−0.123509			−0.0617544	−	0.998091i	$-0.519670\pi$
$139$	−1.45615			−0.123509			−0.0617544	+	0.998091i	$0.519670\pi$
$140$		0			0
$141$	2.27813			0.191853
$142$	9.21492	−	16.9617i	0.773299	−	1.42340i
$143$	1.33192	−	0.356886i	0.111380	−	0.0298443i
$144$	−1.17068	−	11.2457i	−0.0975569	−	0.937142i
$145$	−0.943879	−	11.1443i	−0.0783849	−	0.925482i
$146$	−1.98012	+	8.23879i	−0.163876	+	0.681847i
$147$		0			0
$148$	−1.40114	+	0.454489i	−0.115173	+	0.0373588i
$149$	−10.0147	+	5.78197i	−0.820433	+	0.473677i	−0.850566	−	0.525869i	$-0.823740\pi$
$149$	−10.0147	+	5.78197i	−0.820433	+	0.473677i	0.0301327	+	0.999546i	$0.490407\pi$
$150$	−2.93776	−	0.196766i	−0.239867	−	0.0160659i
$151$	4.17078	+	2.40800i	0.339414	+	0.195961i	0.660013	−	0.751254i	$-0.270551\pi$
$151$	4.17078	+	2.40800i	0.339414	+	0.195961i	−0.320599	+	0.947215i	$0.603884\pi$
$152$	−13.6078	+	9.33746i	−1.10374	+	0.757368i
$153$	−10.2394	+	10.2394i	−0.827805	+	0.827805i
$154$		0			0
$155$	16.4356	+	7.71960i	1.32014	+	0.620053i
$156$	1.36865	−	0.0710467i	0.109580	−	0.00568829i
$157$	−4.12149	+	1.10435i	−0.328931	+	0.0881368i	−0.419505	−	0.907753i	$-0.637796\pi$
$157$	−4.12149	+	1.10435i	−0.328931	+	0.0881368i	0.0905743	+	0.995890i	$0.471130\pi$
$158$	0.389220	+	15.0061i	0.0309647	+	1.19382i
$159$	2.76263	+	4.78501i	0.219091	+	0.379476i
$160$	9.36012	−	8.50812i	0.739982	−	0.672626i
$161$		0			0
$162$	−9.00835	+	5.51725i	−0.707763	+	0.433476i
$163$	2.10452	−	7.85417i	0.164839	−	0.615186i	−0.833222	−	0.552938i	$-0.813506\pi$
$163$	2.10452	−	7.85417i	0.164839	−	0.615186i	0.998061	−	0.0622476i	$-0.0198268\pi$
$164$	−0.104315	−	0.160806i	−0.00814566	−	0.0125569i
$165$	0.767918	+	0.137600i	0.0597824	+	0.0107122i
$166$	−2.47925	−	8.37743i	−0.192427	−	0.650215i
$167$	5.50649	−	5.50649i	0.426105	−	0.426105i	−0.461194	−	0.887299i	$-0.652579\pi$
$167$	5.50649	−	5.50649i	0.426105	−	0.426105i	0.887299	+	0.461194i	$0.152579\pi$
$168$		0			0
$169$			10.2918i			0.791674i
$170$	−16.0150	−	2.44293i	−1.22829	−	0.187364i
$171$	14.2832	+	8.24639i	1.09226	+	0.630617i
$172$	−2.87630	+	13.4990i	−0.219316	+	1.02929i
$173$	−3.02430	−	0.810358i	−0.229933	−	0.0616104i	0.142013	−	0.989865i	$-0.454643\pi$
$173$	−3.02430	−	0.810358i	−0.229933	−	0.0616104i	−0.371946	+	0.928254i	$0.621309\pi$
$174$	−0.688290	+	2.86380i	−0.0521791	+	0.217104i
$175$		0			0
$176$	−2.71344	+	1.96732i	−0.204533	+	0.148292i
$177$	0.963323	−	3.59517i	0.0724078	−	0.270230i
$178$	−4.08885	+	0.106055i	−0.306472	+	0.00794914i
$179$	−8.05255	+	13.9474i	−0.601876	+	1.04248i	0.390661	+	0.920535i	$0.372246\pi$
$179$	−8.05255	+	13.9474i	−0.601876	+	1.04248i	−0.992537	+	0.121945i	$0.961087\pi$
$180$	−11.7050	−	4.77369i	−0.872440	−	0.355810i
$181$	3.83256			0.284872			0.142436	−	0.989804i	$-0.454507\pi$
$181$	3.83256			0.284872			0.142436	+	0.989804i	$0.454507\pi$
$182$		0			0
$183$	−0.541393	−	0.541393i	−0.0400209	−	0.0400209i
$184$	−9.63562	−	1.79328i	−0.710348	−	0.132202i
$185$	−0.290471	+	1.62105i	−0.0213558	+	0.119182i
$186$	−3.46791	−	3.29256i	−0.254279	−	0.241422i
$187$	4.14624	+	1.11098i	0.303203	+	0.0812431i
$188$	3.37616	+	10.4083i	0.246232	+	0.759106i
$189$		0			0
$190$	2.03337	+	18.3389i	0.147516	+	1.33044i
$191$	2.42531	−	1.40025i	0.175489	−	0.101319i	−0.409682	−	0.912228i	$-0.634360\pi$
$191$	2.42531	−	1.40025i	0.175489	−	0.101319i	0.585172	+	0.810909i	$0.301027\pi$
$192$	−3.04516	+	1.35036i	−0.219766	+	0.0974541i
$193$	−2.23839	−	8.35378i	−0.161123	−	0.601318i	−0.998503	−	0.0546973i	$-0.982581\pi$
$193$	−2.23839	−	8.35378i	−0.161123	−	0.601318i	0.837380	−	0.546621i	$-0.184086\pi$
$194$	2.40905	+	8.14024i	0.172960	+	0.584435i
$195$	0.651407	−	1.38690i	0.0466482	−	0.0993178i
$196$		0			0
$197$	−4.90073	−	4.90073i	−0.349162	−	0.349162i	0.510635	−	0.859798i	$-0.329410\pi$
$197$	−4.90073	−	4.90073i	−0.349162	−	0.349162i	−0.859798	+	0.510635i	$0.829410\pi$
$198$	2.94314	+	1.59894i	0.209160	+	0.113632i
$199$	−6.19859	+	10.7363i	−0.439406	+	0.761074i	−0.997644	−	0.0686071i	$-0.978145\pi$
$199$	−6.19859	+	10.7363i	−0.439406	+	0.761074i	0.558237	+	0.829681i	$0.311478\pi$
$200$	−3.45474	−	13.7137i	−0.244287	−	0.969703i
$201$	0.111119	+	0.192463i	0.00783771	+	0.0135753i
$202$	−2.07406	+	1.27028i	−0.145931	+	0.0893766i
$203$		0			0
$204$	3.80037	+	1.93876i	0.266079	+	0.135740i
$205$	−0.213538	+	0.0180858i	−0.0149141	+	0.00126317i
$206$	−15.2953	+	16.1098i	−1.06567	+	1.12243i
$207$	2.53508	+	9.46105i	0.176200	+	0.657589i
$208$	2.35293	+	6.14782i	0.163146	+	0.426274i
$209$		−	4.88896i		−	0.338176i
$210$		0			0
$211$		−	0.877438i		−	0.0604053i	−0.999544	−	0.0302027i	$-0.990385\pi$
$211$		−	0.877438i		−	0.0604053i	0.999544	−	0.0302027i	$-0.00961527\pi$
$212$	−17.7676	+	19.7133i	−1.22029	+	1.35391i
$213$	1.47101	+	5.48987i	0.100792	+	0.376160i
$214$	−14.2665	−	13.5451i	−0.975235	−	0.925924i
$215$	11.7934	+	9.95166i	0.804302	+	0.678698i
$216$	5.21475	+	4.46054i	0.354819	+	0.303501i
$217$		0			0
$218$	7.87594	+	12.8595i	0.533426	+	0.870957i
$219$	−1.24743	−	2.16061i	−0.0842934	−	0.146000i
$220$	0.509376	+	3.71240i	0.0343421	+	0.250290i
$221$	4.21537	−	7.30123i	0.283556	−	0.491134i
$222$	0.207040	−	0.381095i	0.0138956	−	0.0255774i
$223$	12.6059	+	12.6059i	0.844153	+	0.844153i	0.989396	−	0.145243i	$-0.0463963\pi$
$223$	12.6059	+	12.6059i	0.844153	+	0.844153i	−0.145243	+	0.989396i	$0.546396\pi$
$224$		0			0
$225$	−10.8768	+	9.02441i	−0.725118	+	0.601628i
$226$	10.7785	−	3.18984i	0.716978	−	0.212185i
$227$	2.71787	+	10.1432i	0.180392	+	0.673230i	0.995570	+	0.0940208i	$0.0299720\pi$
$227$	2.71787	+	10.1432i	0.180392	+	0.673230i	−0.815179	+	0.579210i	$0.803361\pi$
$228$	1.01263	−	4.75246i	0.0670632	−	0.314739i
$229$	−23.5981	+	13.6244i	−1.55941	+	0.900324i	−0.562094	+	0.827073i	$0.690004\pi$
$229$	−23.5981	+	13.6244i	−1.55941	+	0.900324i	−0.997314	+	0.0732513i	$0.976662\pi$
$230$	−6.84734	+	8.55513i	−0.451500	+	0.564109i
$231$		0			0
$232$	−14.1042	+	1.09946i	−0.925986	+	0.0721830i
$233$	12.6865	+	3.39933i	0.831118	+	0.222697i	0.649201	−	0.760617i	$-0.275103\pi$
$233$	12.6865	+	3.39933i	0.831118	+	0.222697i	0.181917	+	0.983314i	$0.441770\pi$
$234$	4.52951	−	4.77074i	0.296104	−	0.311873i
$235$	12.0420	+	2.15776i	0.785531	+	0.140756i
$236$	17.8533	−	0.926765i	1.16215	−	0.0603272i
$237$	−3.12526	−	3.12526i	−0.203007	−	0.203007i
$238$		0			0
$239$	−10.7078			−0.692631			−0.346315	−	0.938118i	$-0.612567\pi$
$239$	−10.7078			−0.692631			−0.346315	+	0.938118i	$0.612567\pi$
$240$	−0.273781	+	3.71425i	−0.0176725	+	0.239754i
$241$	6.28701	−	10.8894i	0.404982	−	0.701449i	−0.589337	−	0.807887i	$-0.700611\pi$
$241$	6.28701	−	10.8894i	0.404982	−	0.701449i	0.994319	+	0.106438i	$0.0339445\pi$
$242$	0.377614	+	14.5586i	0.0242739	+	0.935861i
$243$	2.68881	−	10.0348i	0.172487	−	0.643732i
$244$	1.67118	−	3.27586i	0.106987	−	0.209716i
$245$		0			0
$246$	0.0548738	+	0.0131884i	0.00349863	+	0.000840864i
$247$	−9.27501	−	2.48523i	−0.590155	−	0.158132i
$248$	9.90367	−	20.7237i	0.628884	−	1.31596i
$249$	2.22772	+	1.28618i	0.141176	+	0.0815080i
$250$	−15.3423	−	3.82262i	−0.970335	−	0.241764i
$251$		−	14.8357i		−	0.936420i	−0.883617	−	0.468210i	$-0.844899\pi$
$251$		−	14.8357i		−	0.936420i	0.883617	−	0.468210i	$-0.155101\pi$
$252$		0			0
$253$	2.05307	−	2.05307i	0.129075	−	0.129075i
$254$	−8.71886	+	2.58029i	−0.547070	+	0.161902i
$255$	3.91485	−	2.72506i	0.245157	−	0.170650i
$256$	−10.6825	−	11.9116i	−0.667654	−	0.744472i
$257$	−3.93031	+	14.6681i	−0.245166	+	0.914972i	0.728134	+	0.685435i	$0.240388\pi$
$257$	−3.93031	+	14.6681i	−0.245166	+	0.914972i	−0.973300	+	0.229537i	$0.926279\pi$
$258$	−2.12246	−	3.46547i	−0.132139	−	0.215751i
$259$		0			0
$260$	7.30185	+	0.920788i	0.452842	+	0.0571049i
$261$	7.06897	+	12.2438i	0.437558	+	0.757873i
$262$	19.5151	−	0.506173i	1.20564	−	0.0312715i
$263$	−11.3208	+	3.03340i	−0.698072	+	0.187048i	−0.590367	−	0.807135i	$-0.701017\pi$
$263$	−11.3208	+	3.03340i	−0.698072	+	0.187048i	−0.107705	+	0.994183i	$0.534350\pi$
$264$	0.180556	−	0.970160i	0.0111124	−	0.0597092i
$265$	10.0708	+	27.9098i	0.618645	+	1.71448i
$266$		0			0
$267$	0.851570	−	0.851570i	0.0521153	−	0.0521153i
$268$	−0.714651	+	0.792909i	−0.0436543	+	0.0484346i
$269$	−17.9195	−	10.3458i	−1.09257	−	0.630797i	−0.158313	−	0.987389i	$-0.550605\pi$
$269$	−17.9195	−	10.3458i	−1.09257	−	0.630797i	−0.934260	+	0.356592i	$0.883939\pi$
$270$	7.14680	−	2.79030i	0.434941	−	0.169812i
$271$	−18.2735	+	10.5502i	−1.11003	+	0.640878i	−0.938838	−	0.344359i	$-0.888096\pi$
$271$	−18.2735	+	10.5502i	−1.11003	+	0.640878i	−0.171195	+	0.985237i	$0.554763\pi$
$272$	−3.22573	+	20.2364i	−0.195588	+	1.22701i
$273$		0			0
$274$	19.7764	+	4.75309i	1.19474	+	0.287145i
$275$	3.92881	+	1.45469i	0.236916	+	0.0877209i
$276$	2.42099	−	1.57050i	0.145727	−	0.0945331i
$277$	3.15920	−	0.846505i	0.189818	−	0.0508616i	−0.162658	−	0.986683i	$-0.552007\pi$
$277$	3.15920	−	0.846505i	0.189818	−	0.0508616i	0.352476	+	0.935821i	$0.385340\pi$
$278$	1.80951	+	0.983064i	0.108527	+	0.0589603i
$279$	−22.9539			−1.37421
$280$		0			0
$281$	2.60091			0.155157			0.0775787	−	0.996986i	$-0.475281\pi$
$281$	2.60091			0.155157			0.0775787	+	0.996986i	$0.475281\pi$
$282$	−2.83095	−	1.53799i	−0.168581	−	0.0915861i
$283$	−26.7711	+	7.17330i	−1.59138	+	0.426409i	−0.942424	−	0.334419i	$-0.891460\pi$
$283$	−26.7711	+	7.17330i	−1.59138	+	0.426409i	−0.648954	+	0.760828i	$0.724793\pi$
$284$	−22.9022	+	14.8567i	−1.35899	+	0.881582i
$285$	−4.15199	−	3.50359i	−0.245942	−	0.207535i
$286$	−1.89607	−	0.455703i	−0.112117	−	0.0269463i
$287$		0			0
$288$	−6.13735	+	14.7650i	−0.361647	+	0.870036i
$289$	8.00623	−	4.62240i	0.470955	−	0.271906i
$290$	−6.35072	+	14.4859i	−0.372927	+	0.850639i
$291$	−2.16465	−	1.24976i	−0.126894	−	0.0732622i
$292$	8.02274	−	8.90127i	0.469495	−	0.520907i
$293$	−11.9223	+	11.9223i	−0.696506	+	0.696506i	−0.963655	−	0.267149i	$-0.913918\pi$
$293$	−11.9223	+	11.9223i	−0.696506	+	0.696506i	0.267149	+	0.963655i	$0.413918\pi$
$294$		0			0
$295$	8.49725	−	18.0913i	0.494729	−	1.05332i
$296$	2.04798	+	0.381149i	0.119037	+	0.0221538i
$297$	−1.96360	+	0.526145i	−0.113940	+	0.0305300i
$298$	16.3484	−	0.424037i	0.947036	−	0.0245638i
$299$	−2.85130	−	4.93859i	−0.164895	−	0.285606i
$300$	3.51782	+	2.22783i	0.203101	+	0.128624i
$301$		0			0
$302$	−3.55722	−	5.80810i	−0.204695	−	0.334218i
$303$	0.185342	−	0.691707i	0.0106476	−	0.0397376i
$304$	23.2138	−	2.41657i	1.33140	−	0.138600i
$305$	−2.34897	−	3.37454i	−0.134501	−	0.193226i
$306$	19.6369	−	5.81141i	1.12257	−	0.332216i
$307$	−13.0364	+	13.0364i	−0.744028	+	0.744028i	−0.973350	−	0.229323i	$-0.926349\pi$
$307$	−13.0364	+	13.0364i	−0.744028	+	0.744028i	0.229323	+	0.973350i	$0.426349\pi$
$308$		0			0
$309$		−	6.54063i		−	0.372083i
$310$	−15.2124	−	20.6888i	−0.864009	−	1.17505i
$311$	−10.1447	−	5.85707i	−0.575255	−	0.332124i	0.183990	−	0.982928i	$-0.441099\pi$
$311$	−10.1447	−	5.85707i	−0.575255	−	0.332124i	−0.759246	+	0.650804i	$0.774432\pi$
$312$	−1.74874	−	0.835706i	−0.0990031	−	0.0473126i
$313$	18.4473	+	4.94295i	1.04270	+	0.279392i	0.739234	−	0.673449i	$-0.235188\pi$
$313$	18.4473	+	4.94295i	1.04270	+	0.279392i	0.303471	+	0.952841i	$0.401855\pi$
$314$	5.86721	+	1.41013i	0.331106	+	0.0795783i
$315$		0			0
$316$	9.64711	−	18.9103i	0.542693	−	1.06379i
$317$	−0.747448	+	2.78952i	−0.0419809	+	0.156675i	−0.983734	−	0.179629i	$-0.942510\pi$
$317$	−0.747448	+	2.78952i	−0.0419809	+	0.156675i	0.941754	+	0.336304i	$0.109177\pi$
$318$	−0.202605	−	7.81126i	−0.0113615	−	0.438034i
$319$	2.09546	−	3.62944i	0.117323	−	0.203209i
$320$	−17.3755	+	4.25363i	−0.971318	+	0.237785i
$321$	5.79221			0.323290
$322$		0			0
$323$	−21.1365	−	21.1365i	−1.17607	−	1.17607i
$324$	14.9191	−	0.774453i	0.828841	−	0.0430252i
$325$	4.75689	−	6.71402i	0.263865	−	0.372427i
$326$	−7.91767	+	8.33933i	−0.438519	+	0.461873i
$327$	−4.28869	−	1.14915i	−0.237165	−	0.0635482i
$328$	0.0210669	+	0.270253i	0.00116323	+	0.0149222i
$329$		0			0
$330$	−0.861371	−	0.689423i	−0.0474169	−	0.0379515i
$331$	−30.1984	+	17.4351i	−1.65986	+	0.958318i	−0.687075	+	0.726586i	$0.741106\pi$
$331$	−30.1984	+	17.4351i	−1.65986	+	0.958318i	−0.972780	+	0.231732i	$0.925561\pi$
$332$	−2.57483	+	12.0841i	−0.141312	+	0.663203i
$333$	−0.538813	−	2.01088i	−0.0295268	−	0.110195i
$334$	−10.5602	+	3.12523i	−0.577831	+	0.171005i
$335$	0.405069	+	1.12259i	0.0221313	+	0.0613336i
$336$		0			0
$337$	15.8847	+	15.8847i	0.865292	+	0.865292i	0.991947	−	0.126655i	$-0.0404240\pi$
$337$	15.8847	+	15.8847i	0.865292	+	0.865292i	−0.126655	+	0.991947i	$0.540424\pi$
$338$	6.94810	−	12.7892i	0.377927	−	0.695642i
$339$	−1.65481	+	2.86622i	−0.0898771	+	0.155672i
$340$	18.2521	+	13.8477i	0.989857	+	0.750996i
$341$	3.40211	+	5.89263i	0.184235	+	0.319104i
$342$	−12.1820	−	19.8903i	−0.658726	−	1.07554i
$343$		0			0
$344$	12.6876	−	14.8329i	0.684071	−	0.799738i
$345$	−0.272288	−	3.21488i	−0.0146595	−	0.173083i
$346$	3.21111	+	3.04875i	0.172630	+	0.163902i
$347$	−6.21524	−	23.1956i	−0.333651	−	1.24520i	−0.905324	−	0.424722i	$-0.860372\pi$
$347$	−6.21524	−	23.1956i	−0.333651	−	1.24520i	0.571673	−	0.820482i	$-0.306295\pi$
$348$	2.78870	−	3.09408i	0.149490	−	0.165860i
$349$		−	20.0084i		−	1.07102i	−0.844528	−	0.535512i	$-0.820119\pi$
$349$		−	20.0084i		−	1.07102i	0.844528	−	0.535512i	$-0.179881\pi$
$350$		0			0
$351$			3.99267i			0.213113i
$352$	4.70006	−	0.612842i	0.250514	−	0.0326646i
$353$	6.06381	+	22.6305i	0.322744	+	1.20450i	0.916560	+	0.399897i	$0.130954\pi$
$353$	6.06381	+	22.6305i	0.322744	+	1.20450i	−0.593816	+	0.804601i	$0.702379\pi$
$354$	−3.62424	+	3.81725i	−0.192626	+	0.202885i
$355$	2.57580	+	30.4122i	0.136709	+	1.61411i
$356$	5.15268	+	2.62865i	0.273092	+	0.139318i
$357$		0			0
$358$	19.4227	−	11.8956i	1.02652	−	0.628704i
$359$	13.4523	+	23.3000i	0.709984	+	1.22973i	0.964862	+	0.262756i	$0.0846313\pi$
$359$	13.4523	+	23.3000i	0.709984	+	1.22973i	−0.254878	+	0.966973i	$0.582035\pi$
$360$	11.3227	+	13.8343i	0.596756	+	0.729132i
$361$	−7.52251	+	13.0294i	−0.395922	+	0.685756i
$362$	−4.76260	−	2.58741i	−0.250317	−	0.135991i
$363$	−3.03206	−	3.03206i	−0.159142	−	0.159142i
$364$		0			0
$365$	−4.54734	−	12.6023i	−0.238019	−	0.659634i
$366$	0.307270	+	1.03827i	0.0160613	+	0.0542714i
$367$	−7.09214	−	26.4682i	−0.370207	−	1.38163i	−0.860223	−	0.509917i	$-0.829676\pi$
$367$	−7.09214	−	26.4682i	−0.370207	−	1.38163i	0.490017	−	0.871713i	$-0.336991\pi$
$368$	10.7632	+	8.73358i	0.561071	+	0.455270i
$369$	0.234606	−	0.135450i	0.0122131	−	0.00705123i
$370$	1.45535	−	1.81833i	0.0756602	−	0.0945305i
$371$		0			0
$372$	2.08661	+	6.43278i	0.108186	+	0.333524i
$373$	−21.1806	−	5.67531i	−1.09669	−	0.293857i	−0.335272	−	0.942121i	$-0.608828\pi$
$373$	−21.1806	−	5.67531i	−1.09669	−	0.293857i	−0.761415	+	0.648265i	$0.775495\pi$
$374$	−4.40236	−	4.17976i	−0.227641	−	0.216130i
$375$	4.05092	−	2.29410i	0.209189	−	0.118467i
$376$	2.83135	−	15.2134i	0.146016	−	0.784570i
$377$	−5.82033	−	5.82033i	−0.299762	−	0.299762i
$378$		0			0
$379$	−20.4602			−1.05097			−0.525484	−	0.850803i	$-0.676116\pi$
$379$	−20.4602			−1.05097			−0.525484	+	0.850803i	$0.676116\pi$
$380$	9.85403	−	24.1619i	0.505501	−	1.23948i
$381$	1.33859	−	2.31851i	0.0685783	−	0.118781i
$382$	−3.95918	+	0.102691i	−0.202569	+	0.00525415i
$383$	1.88076	−	7.01910i	0.0961024	−	0.358659i	−0.901082	−	0.433649i	$-0.857226\pi$
$383$	1.88076	−	7.01910i	0.0961024	−	0.358659i	0.997184	+	0.0749899i	$0.0238925\pi$
$384$	4.69577	+	0.377776i	0.239630	+	0.0192783i
$385$		0			0
$386$	−2.85817	+	11.8921i	−0.145477	+	0.605294i
$387$	−18.8418	−	5.04866i	−0.957785	−	0.256638i
$388$	2.50193	−	11.7420i	0.127016	−	0.596109i
$389$	4.81003	+	2.77707i	0.243878	+	0.140803i	0.616958	−	0.786996i	$-0.288365\pi$
$389$	4.81003	+	2.77707i	0.243878	+	0.140803i	−0.373080	+	0.927799i	$0.621698\pi$
$390$	−1.74579	+	1.28368i	−0.0884018	+	0.0650016i
$391$		−	17.7521i		−	0.897764i
$392$		0			0
$393$	−4.06433	+	4.06433i	−0.205018	+	0.205018i
$394$	2.78143	+	9.39852i	0.140126	+	0.473491i
$395$	−13.5597	−	19.4799i	−0.682262	−	0.980142i
$396$	−2.57788	−	3.97391i	−0.129543	−	0.199696i
$397$	7.78865	−	29.0677i	0.390901	−	1.45886i	−0.437749	−	0.899097i	$-0.644224\pi$
$397$	7.78865	−	29.0677i	0.390901	−	1.45886i	0.828650	−	0.559766i	$-0.189109\pi$
$398$	14.9510	−	9.15687i	0.749425	−	0.458992i
$399$		0			0
$400$	−4.96518	+	19.3739i	−0.248259	+	0.968694i
$401$	2.31962	+	4.01770i	0.115836	+	0.200634i	0.918114	−	0.396317i	$-0.129712\pi$
$401$	2.31962	+	4.01770i	0.115836	+	0.200634i	−0.802277	+	0.596951i	$0.796379\pi$
$402$	−0.00814920	−	0.314185i	−0.000406445	−	0.0156701i
$403$	12.9085	−	3.45883i	0.643020	−	0.172297i
$404$	3.43496	−	0.178309i	0.170895	−	0.00887118i
$405$	7.10074	−	15.1180i	0.352839	−	0.751222i
$406$		0			0
$407$	−0.436364	+	0.436364i	−0.0216298	+	0.0216298i
$408$	−3.41371	−	4.97491i	−0.169004	−	0.246295i
$409$	30.0868	+	17.3706i	1.48770	+	0.858922i	0.999901	−	0.0140366i	$-0.00446813\pi$
$409$	30.0868	+	17.3706i	1.48770	+	0.858922i	0.487795	+	0.872958i	$0.337801\pi$
$410$	0.277566	+	0.121687i	0.0137080	+	0.00600970i
$411$	−5.18634	+	2.99434i	−0.255823	+	0.147700i
$412$	29.8829	−	9.69314i	1.47222	−	0.477547i
$413$		0			0
$414$	3.23702	−	13.4684i	0.159091	−	0.661936i
$415$	10.5573	+	8.90861i	0.518238	+	0.437307i
$416$	1.22657	−	9.22818i	0.0601374	−	0.452449i
$417$	−0.585669	+	0.156930i	−0.0286803	+	0.00768487i
$418$	−3.30060	+	6.07535i	−0.161437	+	0.297155i
$419$	28.1311			1.37429			0.687147	−	0.726518i	$-0.258863\pi$
$419$	28.1311			1.37429			0.687147	+	0.726518i	$0.258863\pi$
$420$		0			0
$421$	3.94616			0.192324			0.0961621	−	0.995366i	$-0.469343\pi$
$421$	3.94616			0.192324			0.0961621	+	0.995366i	$0.469343\pi$
$422$	−0.592370	+	1.09036i	−0.0288361	+	0.0530781i
$423$	−14.9378	+	4.00256i	−0.726299	+	0.194611i
$424$	35.3879	−	12.5019i	1.71859	−	0.607145i
$425$	23.2746	−	10.6964i	1.12898	−	0.518853i
$426$	1.87831	−	7.81518i	0.0910044	−	0.378647i
$427$		0			0
$428$	8.58400	+	26.4635i	0.414923	+	1.27916i
$429$	0.497241	−	0.287082i	0.0240070	−	0.0138605i
$430$	−7.93677	−	20.3285i	−0.382745	−	0.980326i
$431$	12.1350	+	7.00616i	0.584523	+	0.337475i	0.762929	−	0.646482i	$-0.223761\pi$
$431$	12.1350	+	7.00616i	0.584523	+	0.337475i	−0.178406	+	0.983957i	$0.557094\pi$
$432$	−3.46884	−	9.06351i	−0.166894	−	0.436069i
$433$	2.21951	−	2.21951i	0.106663	−	0.106663i	−0.651761	−	0.758424i	$-0.725970\pi$
$433$	2.21951	−	2.21951i	0.106663	−	0.106663i	0.758424	+	0.651761i	$0.225970\pi$
$434$		0			0
$435$	−1.58066	−	4.38056i	−0.0757866	−	0.210032i
$436$	−1.10554	−	21.2973i	−0.0529458	−	1.01995i
$437$	−19.5299	+	5.23301i	−0.934240	+	0.250329i
$438$	0.0914837	+	3.52707i	0.00437126	+	0.168530i
$439$	−12.5163	−	21.6788i	−0.597369	−	1.03467i	−0.993208	−	0.116354i	$-0.962879\pi$
$439$	−12.5163	−	21.6788i	−0.597369	−	1.03467i	0.395839	−	0.918320i	$-0.370454\pi$
$440$	1.87330	−	4.95716i	0.0893061	−	0.236323i
$441$		0			0
$442$	−10.1675	+	6.22715i	−0.483617	+	0.296196i
$443$	−1.13949	+	4.25262i	−0.0541386	+	0.202048i	−0.987698	−	0.156376i	$-0.950019\pi$
$443$	−1.13949	+	4.25262i	−0.0541386	+	0.202048i	0.933559	+	0.358424i	$0.116686\pi$
$444$	−0.514564	+	0.333799i	−0.0244201	+	0.0158414i
$445$	5.30789	−	3.69474i	0.251618	−	0.175148i
$446$	−7.15454	−	24.1753i	−0.338777	−	1.14474i
$447$	−3.40482	+	3.40482i	−0.161042	+	0.161042i
$448$		0			0
$449$			24.2255i			1.14327i	0.820507	+	0.571636i	$0.193691\pi$
$449$			24.2255i			1.14327i	−0.820507	+	0.571636i	$0.806309\pi$
$450$	19.6087	−	3.87130i	0.924363	−	0.182495i
$451$	−0.0695443	−	0.0401514i	−0.00327471	−	0.00189066i
$452$	−15.5476	−	3.31282i	−0.731299	−	0.155822i
$453$	1.93702	+	0.519023i	0.0910091	+	0.0243858i
$454$	3.47042	−	14.4395i	0.162875	−	0.677681i
$455$		0			0
$456$	−4.46681	+	5.22209i	−0.209178	+	0.244547i
$457$	−2.42378	+	9.04568i	−0.113380	+	0.423139i	−0.999161	−	0.0409647i	$-0.986957\pi$
$457$	−2.42378	+	9.04568i	−0.113380	+	0.423139i	0.885781	+	0.464104i	$0.153624\pi$
$458$	38.5226	−	0.999182i	1.80004	−	0.0466887i
$459$	−6.21457	+	10.7640i	−0.290071	+	0.502418i
$460$	14.2846	−	6.00845i	0.666025	−	0.280146i
$461$	−12.3582			−0.575580			−0.287790	−	0.957693i	$-0.592921\pi$
$461$	−12.3582			−0.575580			−0.287790	+	0.957693i	$0.592921\pi$
$462$		0			0
$463$	−29.6788	−	29.6788i	−1.37929	−	1.37929i	−0.845818	−	0.533471i	$-0.820887\pi$
$463$	−29.6788	−	29.6788i	−1.37929	−	1.37929i	−0.533471	−	0.845818i	$-0.679113\pi$
$464$	18.2691	+	8.15567i	0.848121	+	0.378617i
$465$	7.44244	+	1.33358i	0.345135	+	0.0618434i
$466$	−13.4701	−	12.7890i	−0.623992	−	0.592440i
$467$	34.9600	+	9.36749i	1.61775	+	0.433476i	0.950341	−	0.311212i	$-0.100735\pi$
$467$	34.9600	+	9.36749i	1.61775	+	0.433476i	0.667413	+	0.744687i	$0.267401\pi$
$468$	−8.84947	+	2.87051i	−0.409067	+	0.132689i
$469$		0			0
$470$	−13.5074	−	10.8111i	−0.623051	−	0.498677i
$471$	−1.53867	+	0.888349i	−0.0708980	+	0.0409330i
$472$	−22.8114	−	10.9013i	−1.04998	−	0.501774i
$473$	1.49657	+	5.58529i	0.0688125	+	0.256812i
$474$	1.77375	+	5.99356i	0.0814713	+	0.275293i
$475$	−18.6285	−	22.4522i	−0.854736	−	1.03018i
$476$		0			0
$477$	−26.5217	−	26.5217i	−1.21434	−	1.21434i
$478$	13.3062	+	7.22898i	0.608614	+	0.330646i
$479$	−15.9325	+	27.5959i	−0.727974	+	1.26089i	0.229764	+	0.973246i	$0.426205\pi$
$479$	−15.9325	+	27.5959i	−0.727974	+	1.26089i	−0.957738	+	0.287642i	$0.907129\pi$
$480$	2.84776	−	4.43075i	0.129982	−	0.202235i
$481$	0.606023	+	1.04966i	0.0276323	+	0.0478605i
$482$	−15.1643	+	9.28749i	−0.690713	+	0.423034i
$483$		0			0
$484$	9.35944	−	18.3464i	0.425429	−	0.833928i
$485$	−10.2584	−	8.65638i	−0.465810	−	0.393066i
$486$	−10.1159	+	10.6547i	−0.458867	+	0.483305i
$487$	2.58469	+	9.64618i	0.117123	+	0.437110i	0.999437	−	0.0335518i	$-0.0106819\pi$
$487$	2.58469	+	9.64618i	0.117123	+	0.437110i	−0.882314	+	0.470662i	$0.844015\pi$
$488$	−4.28830	+	2.94257i	−0.194122	+	0.133204i
$489$		−	3.38579i		−	0.153111i
$490$		0			0
$491$			16.3501i			0.737871i	0.929455	+	0.368936i	$0.120278\pi$
$491$			16.3501i			0.737871i	−0.929455	+	0.368936i	$0.879722\pi$
$492$	−0.0592862	−	0.0534349i	−0.00267283	−	0.00240903i
$493$	−6.63188	−	24.7505i	−0.298685	−	1.11471i
$494$	9.84794	+	9.35000i	0.443080	+	0.420676i
$495$	−5.27703	+	0.446944i	−0.237185	+	0.0200887i
$496$	−26.2978	+	19.0666i	−1.18081	+	0.856117i
$497$		0			0
$498$	−1.90000	−	3.10225i	−0.0851412	−	0.139015i
$499$	4.74809	+	8.22393i	0.212554	+	0.368154i	0.952513	−	0.304498i	$-0.0984886\pi$
$499$	4.74809	+	8.22393i	0.212554	+	0.368154i	−0.739959	+	0.672652i	$0.765155\pi$
$500$	16.4847	+	15.1081i	0.737220	+	0.675653i
$501$	1.62130	−	2.80817i	0.0724343	−	0.125460i
$502$	−10.0158	+	18.4358i	−0.447025	+	0.822831i
$503$	−9.76866	−	9.76866i	−0.435563	−	0.435563i	0.454953	−	0.890516i	$-0.349656\pi$
$503$	−9.76866	−	9.76866i	−0.435563	−	0.435563i	−0.890516	+	0.454953i	$0.849656\pi$
$504$		0			0
$505$	1.63486	−	3.48075i	0.0727504	−	0.154891i
$506$	−3.93733	+	1.16523i	−0.175036	+	0.0518007i
$507$	1.10915	+	4.13939i	0.0492589	+	0.183837i
$508$	12.5766	+	2.67977i	0.557998	+	0.118896i
$509$	17.0075	−	9.81931i	0.753846	−	0.435233i	−0.0732360	−	0.997315i	$-0.523333\pi$
$509$	17.0075	−	9.81931i	0.753846	−	0.435233i	0.827082	+	0.562082i	$0.189999\pi$
$510$	−6.70458	+	0.743386i	−0.296884	+	0.0329177i
$511$		0			0
$512$	5.23310	+	22.0140i	0.231273	+	0.972889i
$513$	13.6738	+	3.66389i	0.603714	+	0.161765i
$514$	14.7867	−	15.5742i	0.652214	−	0.686948i
$515$	6.19503	−	34.5731i	0.272986	−	1.52347i
$516$	0.297929	+	5.73933i	0.0131156	+	0.252660i
$517$	3.24152	+	3.24152i	0.142562	+	0.142562i
$518$		0			0
$519$	−1.30372			−0.0572269
$520$	−8.45214	−	6.07381i	−0.370651	−	0.266354i
$521$	−21.2862	+	36.8688i	−0.932565	+	1.61525i	−0.153645	+	0.988126i	$0.549101\pi$
$521$	−21.2862	+	36.8688i	−0.932565	+	1.61525i	−0.778920	+	0.627124i	$0.784232\pi$
$522$	−0.518422	−	19.9873i	−0.0226907	−	0.874822i
$523$	0.529969	−	1.97787i	0.0231739	−	0.0864862i	−0.953370	−	0.301803i	$-0.902412\pi$
$523$	0.529969	−	1.97787i	0.0231739	−	0.0864862i	0.976544	+	0.215316i	$0.0690783\pi$
$524$	−24.5925	−	12.5459i	−1.07433	−	0.548069i
$525$		0			0
$526$	16.1159	+	3.87332i	0.702687	+	0.168885i
$527$	40.1842	+	10.7673i	1.75045	+	0.469032i
$528$	−0.879339	+	1.08369i	−0.0382683	+	0.0471616i
$529$	9.51967	+	5.49618i	0.413899	+	0.238964i
$530$	6.32758	−	41.4815i	0.274853	−	1.80184i
$531$			25.2662i			1.09646i
$532$		0			0
$533$	−0.111524	+	0.111524i	−0.00483066	+	0.00483066i
$534$	−1.63312	+	0.483313i	−0.0706722	+	0.0209150i
$535$	30.6171	+	5.48617i	1.32369	+	0.237188i
$536$	1.42338	−	0.502852i	0.0614805	−	0.0217199i
$537$	−1.73565	+	6.47754i	−0.0748989	+	0.279527i
$538$	15.2834	+	24.9542i	0.658915	+	1.07585i
$539$		0			0
$540$	−10.7649	−	1.35749i	−0.463246	−	0.0584169i
$541$	−2.22119	−	3.84722i	−0.0954965	−	0.165405i	0.814319	−	0.580417i	$-0.197111\pi$
$541$	−2.22119	−	3.84722i	−0.0954965	−	0.165405i	−0.909816	+	0.415012i	$0.863777\pi$
$542$	29.8304	−	0.773727i	1.28133	−	0.0332344i
$543$	1.54147	−	0.413036i	0.0661509	−	0.0177251i
$544$	17.6704	−	22.9694i	0.757610	−	0.984804i
$545$	−21.5812	−	10.1364i	−0.924437	−	0.434196i
$546$		0			0
$547$	13.7530	−	13.7530i	0.588037	−	0.588037i	−0.349062	−	0.937099i	$-0.613500\pi$
$547$	13.7530	−	13.7530i	0.588037	−	0.588037i	0.937099	+	0.349062i	$0.113500\pi$
$548$	−21.3667	−	19.2578i	−0.912738	−	0.822654i
$549$	4.50114	+	2.59873i	0.192104	+	0.110911i
$550$	−3.90013	−	4.46008i	−0.166302	−	0.190179i
$551$	−25.2741	+	14.5920i	−1.07671	+	0.621642i
$552$	−4.06875	+	0.317170i	−0.173178	+	0.0134996i
$553$		0			0
$554$	−4.49732	−	1.08089i	−0.191073	−	0.0459227i
$555$	0.0578729	+	0.683299i	0.00245657	+	0.0290044i
$556$	−1.58494	−	2.44324i	−0.0672163	−	0.103617i
$557$	12.0723	−	3.23476i	0.511519	−	0.137061i	0.00617797	−	0.999981i	$-0.498033\pi$
$557$	12.0723	−	3.23476i	0.511519	−	0.137061i	0.505341	+	0.862920i	$0.331367\pi$
$558$	28.5241	+	15.4965i	1.20752	+	0.656018i
$559$	11.3568			0.480342
$560$		0			0
$561$	1.78737			0.0754628
$562$	−3.23207	−	1.75591i	−0.136337	−	0.0740685i
$563$	7.45322	−	1.99709i	0.314116	−	0.0841671i	−0.0983168	−	0.995155i	$-0.531346\pi$
$563$	7.45322	−	1.99709i	0.314116	−	0.0841671i	0.412433	+	0.910988i	$0.364679\pi$
$564$	2.47962	+	3.82243i	0.104411	+	0.160953i
$565$	−11.4620	+	13.5832i	−0.482208	+	0.571449i
$566$	38.1104	+	9.15950i	1.60190	+	0.385003i
$567$		0			0
$568$	38.4897	−	3.00037i	1.61499	−	0.125893i
$569$	22.8689	−	13.2033i	0.958712	−	0.553513i	0.0629358	−	0.998018i	$-0.479954\pi$
$569$	22.8689	−	13.2033i	0.958712	−	0.553513i	0.895776	+	0.444505i	$0.146620\pi$
$570$	2.79422	+	7.15685i	0.117037	+	0.299768i
$571$	4.41042	+	2.54636i	0.184570	+	0.106562i	0.589438	−	0.807813i	$-0.299349\pi$
$571$	4.41042	+	2.54636i	0.184570	+	0.106562i	−0.404868	+	0.914375i	$0.632682\pi$
$572$	2.04853	+	1.84635i	0.0856534	+	0.0771997i
$573$	0.824564	−	0.824564i	0.0344467	−	0.0344467i
$574$		0			0
$575$	1.60572	−	17.2515i	0.0669633	−	0.719435i
$576$	17.5947	−	14.2046i	0.733114	−	0.591858i
$577$	19.0781	−	5.11195i	0.794230	−	0.212813i	0.161181	−	0.986925i	$-0.448470\pi$
$577$	19.0781	−	5.11195i	0.794230	−	0.212813i	0.633049	+	0.774111i	$0.281803\pi$
$578$	−13.0697	+	0.338997i	−0.543629	+	0.0141004i
$579$	−1.80058	−	3.11870i	−0.0748295	−	0.129609i
$580$	17.6714	−	13.7137i	0.733766	−	0.569428i
$581$		0			0
$582$	1.84621	+	3.01442i	0.0765278	+	0.124952i
$583$	−2.87763	+	10.7395i	−0.119179	+	0.444783i
$584$	−15.9790	+	5.64506i	−0.661214	+	0.233594i
$585$	−1.83459	+	10.2384i	−0.0758508	+	0.423307i
$586$	22.8643	−	6.76654i	0.944515	−	0.279523i
$587$	8.18830	−	8.18830i	0.337967	−	0.337967i	−0.517635	−	0.855602i	$-0.673187\pi$
$587$	8.18830	−	8.18830i	0.337967	−	0.337967i	0.855602	+	0.517635i	$0.173187\pi$
$588$		0			0
$589$		−	47.3823i		−	1.95235i
$590$	−22.7729	+	16.7449i	−0.937547	+	0.689376i
$591$	−2.49925	−	1.44294i	−0.102805	−	0.0593547i
$592$	−2.28764	−	1.85626i	−0.0940215	−	0.0762918i
$593$	−6.09096	−	1.63207i	−0.250126	−	0.0670210i	0.131578	−	0.991306i	$-0.457996\pi$
$593$	−6.09096	−	1.63207i	−0.250126	−	0.0670210i	−0.381703	+	0.924285i	$0.624662\pi$
$594$	2.79531	+	0.671828i	0.114693	+	0.0275654i
$595$		0			0
$596$	−20.6019	−	10.5101i	−0.843886	−	0.430509i
$597$	−1.33605	+	4.98620i	−0.0546808	+	0.204072i
$598$	0.209108	+	8.06198i	0.00855106	+	0.329679i
$599$	12.5631	−	21.7600i	0.513315	−	0.889088i	−0.486566	−	0.873644i	$-0.661751\pi$
$599$	12.5631	−	21.7600i	0.513315	−	0.889088i	0.999881	−	0.0154439i	$-0.00491615\pi$
$600$	−2.86744	−	5.14338i	−0.117063	−	0.209978i
$601$	23.9702			0.977766			0.488883	−	0.872349i	$-0.337405\pi$
$601$	23.9702			0.977766			0.488883	+	0.872349i	$0.337405\pi$
$602$		0			0
$603$	−1.06676	−	1.06676i	−0.0434417	−	0.0434417i
$604$	0.499326	+	9.61906i	0.0203173	+	0.391394i
$605$	−13.1553	−	18.8991i	−0.534841	−	0.768356i
$606$	−0.697300	+	0.734435i	−0.0283259	+	0.0298344i
$607$	−1.98316	−	0.531386i	−0.0804940	−	0.0215683i	0.218347	−	0.975871i	$-0.429933\pi$
$607$	−1.98316	−	0.531386i	−0.0804940	−	0.0215683i	−0.298841	+	0.954303i	$0.596600\pi$
$608$	−30.4785	−	12.6689i	−1.23607	−	0.513793i
$609$		0			0
$610$	0.640788	+	5.77925i	0.0259447	+	0.233995i
$611$	7.79739	−	4.50183i	0.315449	−	0.182124i
$612$	−28.3255	−	6.03546i	−1.14499	−	0.243969i
$613$	9.48807	+	35.4100i	0.383220	+	1.43020i	0.840954	+	0.541106i	$0.181994\pi$
$613$	9.48807	+	35.4100i	0.383220	+	1.43020i	−0.457735	+	0.889089i	$0.651339\pi$
$614$	25.0010	−	7.39888i	1.00896	−	0.298595i
$615$	−0.0839366	+	0.0302872i	−0.00338465	+	0.00122130i
$616$		0			0
$617$	7.99905	+	7.99905i	0.322029	+	0.322029i	0.849545	−	0.527516i	$-0.176876\pi$
$617$	7.99905	+	7.99905i	0.322029	+	0.322029i	−0.527516	+	0.849545i	$0.676876\pi$
$618$	−4.41566	+	8.12783i	−0.177624	+	0.326949i
$619$	−13.8212	+	23.9391i	−0.555523	+	0.962194i	0.442340	+	0.896847i	$0.354148\pi$
$619$	−13.8212	+	23.9391i	−0.555523	+	0.962194i	−0.997863	+	0.0653461i	$0.979185\pi$
$620$	4.93672	+	35.9794i	0.198264	+	1.44497i
$621$	4.20357	+	7.28080i	0.168683	+	0.292168i
$622$	8.65236	+	14.1272i	0.346928	+	0.566450i
$623$		0			0
$624$	1.60891	+	2.21910i	0.0644079	+	0.0888352i
$625$	23.5857	−	8.28952i	0.943427	−	0.331581i
$626$	−19.5868	−	18.5965i	−0.782848	−	0.743264i
$627$	−0.526885	−	1.96636i	−0.0210417	−	0.0785289i
$628$	−6.33899	−	5.71335i	−0.252953	−	0.227988i
$629$			3.77309i			0.150443i
$630$		0			0
$631$			11.5488i			0.459750i	0.973220	+	0.229875i	$0.0738318\pi$
$631$			11.5488i			0.459750i	−0.973220	+	0.229875i	$0.926168\pi$
$632$	−24.7547	+	16.9863i	−0.984691	+	0.675680i
$633$	−0.0945618	−	0.352910i	−0.00375850	−	0.0140269i
$634$	2.81207	−	2.96183i	0.111681	−	0.117629i
$635$	9.27169	−	10.9876i	0.367936	−	0.436029i
$636$	−5.02171	+	9.84358i	−0.199124	+	0.390324i
$637$		0			0
$638$	−5.05423	+	3.09551i	−0.200099	+	0.122553i
$639$	−19.2909	−	33.4128i	−0.763135	−	1.32179i
$640$	24.4636	+	6.44455i	0.967009	+	0.254743i
$641$	8.55730	−	14.8217i	0.337993	−	0.585421i	−0.646062	−	0.763285i	$-0.723585\pi$
$641$	8.55730	−	14.8217i	0.337993	−	0.585421i	0.984055	+	0.177864i	$0.0569186\pi$
$642$	−7.19780	−	3.91040i	−0.284074	−	0.154331i
$643$	−18.4696	−	18.4696i	−0.728370	−	0.728370i	0.241925	−	0.970295i	$-0.422221\pi$
$643$	−18.4696	−	18.4696i	−0.728370	−	0.728370i	−0.970295	+	0.241925i	$0.922221\pi$
$644$		0			0
$645$	5.81585	+	2.73163i	0.228999	+	0.107558i
$646$	11.9961	+	40.5352i	0.471981	+	1.59484i
$647$	−8.66156	−	32.3254i	−0.340521	−	1.27084i	−0.897758	−	0.440489i	$-0.854805\pi$
$647$	−8.66156	−	32.3254i	−0.340521	−	1.27084i	0.557237	−	0.830353i	$-0.311861\pi$
$648$	−19.0624	−	9.10972i	−0.748841	−	0.357864i
$649$	6.48624	−	3.74483i	0.254607	−	0.146997i
$650$	−10.4440	+	5.13185i	−0.409646	+	0.201288i
$651$		0			0
$652$	15.4690	−	5.01770i	0.605813	−	0.196508i
$653$	−10.2716	−	2.75226i	−0.401958	−	0.107704i	0.0521757	−	0.998638i	$-0.483384\pi$
$653$	−10.2716	−	2.75226i	−0.401958	−	0.107704i	−0.454133	+	0.890934i	$0.650051\pi$
$654$	4.55361	+	4.32337i	0.178060	+	0.169057i
$655$	−25.3332	+	17.6341i	−0.989852	+	0.689021i
$656$	0.156272	−	0.350057i	0.00610141	−	0.0136674i
$657$	11.9755	+	11.9755i	0.467210	+	0.467210i
$658$		0			0
$659$	−21.6586			−0.843698			−0.421849	−	0.906666i	$-0.638619\pi$
$659$	−21.6586			−0.843698			−0.421849	+	0.906666i	$0.638619\pi$
$660$	0.604960	+	1.43825i	0.0235480	+	0.0559837i
$661$	11.2670	−	19.5150i	0.438236	−	0.759046i	−0.559318	−	0.828953i	$-0.688937\pi$
$661$	11.2670	−	19.5150i	0.438236	−	0.759046i	0.997554	+	0.0699068i	$0.0222702\pi$
$662$	49.2972	−	1.27865i	1.91599	−	0.0496961i
$663$	0.908584	−	3.39088i	0.0352865	−	0.131691i
$664$	11.3578	−	13.2783i	0.440769	−	0.515296i
$665$		0			0
$666$	−0.688004	+	2.86261i	−0.0266596	+	0.110924i
$667$	−16.7414	−	4.48584i	−0.648229	−	0.173693i
$668$	15.2328	+	3.24573i	0.589373	+	0.125581i
$669$	6.42869	+	3.71161i	0.248548	+	0.143499i
$670$	0.254509	−	1.66847i	0.00983253	−	0.0644587i
$671$		−	1.54069i		−	0.0594775i
$672$		0			0
$673$	−12.3425	+	12.3425i	−0.475769	+	0.475769i	−0.903776	−	0.428007i	$-0.859216\pi$
$673$	−12.3425	+	12.3425i	−0.475769	+	0.475769i	0.428007	+	0.903776i	$0.359216\pi$
$674$	−9.01541	−	30.4633i	−0.347261	−	1.17340i
$675$	−7.01292	+	9.89825i	−0.269928	+	0.380984i
$676$	−17.2683	+	11.2020i	−0.664167	+	0.430847i
$677$	−3.54145	+	13.2169i	−0.136109	+	0.507966i	0.863882	+	0.503695i	$0.168026\pi$
$677$	−3.54145	+	13.2169i	−0.136109	+	0.507966i	−0.999991	+	0.00427157i	$0.998640\pi$
$678$	3.99141	−	2.44457i	0.153289	−	0.0938833i
$679$		0			0
$680$	−13.3325	−	29.5303i	−0.511278	−	1.13243i
$681$	2.18628	+	3.78675i	0.0837785	+	0.145109i
$682$	−0.249503	−	9.61940i	−0.00955398	−	0.368346i
$683$	−2.13814	+	0.572913i	−0.0818137	+	0.0219219i	−0.299494	−	0.954098i	$-0.596818\pi$
$683$	−2.13814	+	0.572913i	−0.0818137	+	0.0219219i	0.217680	+	0.976020i	$0.430151\pi$
$684$	1.70998	+	32.9412i	0.0653826	+	1.25954i
$685$	−30.2506	+	10.9155i	−1.15582	+	0.417059i
$686$		0			0
$687$	−8.02297	+	8.02297i	−0.306095	+	0.306095i
$688$	−25.7804	+	9.86681i	−0.982868	+	0.376169i
$689$	18.9114	+	10.9185i	0.720467	+	0.415962i
$690$	−1.83204	+	4.17885i	−0.0697447	+	0.159086i
$691$	−19.0959	+	11.0250i	−0.726442	+	0.419411i	−0.817119	−	0.576469i	$-0.804430\pi$
$691$	−19.0959	+	11.0250i	−0.726442	+	0.419411i	0.0906771	+	0.995880i	$0.471097\pi$
$692$	−1.93210	−	5.95644i	−0.0734473	−	0.226430i
$693$		0			0
$694$	−7.93616	+	33.0204i	−0.301252	+	1.25344i
$695$	−3.24443	+	0.274791i	−0.123068	+	0.0104234i
$696$	−5.55428	+	1.96222i	−0.210535	+	0.0743778i
$697$	−0.474249	+	0.127075i	−0.0179635	+	0.00481330i
$698$	−13.5079	+	24.8638i	−0.511282	+	0.941107i
$699$	5.46890			0.206853
$700$		0			0
$701$	3.86536			0.145993			0.0729964	−	0.997332i	$-0.476744\pi$
$701$	3.86536			0.145993			0.0729964	+	0.997332i	$0.476744\pi$
$702$	2.69550	−	4.96156i	0.101735	−	0.187262i
$703$	4.15093	−	1.11224i	0.156555	−	0.0419489i
$704$	−6.25435	−	2.41151i	−0.235720	−	0.0908873i
$705$	5.07587	−	0.429908i	0.191168	−	0.0161913i
$706$	7.74281	−	32.2159i	0.291404	−	1.21246i
$707$		0			0
$708$	7.08080	−	2.29681i	0.266113	−	0.0863192i
$709$	−27.5158	+	15.8862i	−1.03338	+	0.596620i	−0.917950	−	0.396696i	$-0.870157\pi$
$709$	−27.5158	+	15.8862i	−1.03338	+	0.596620i	−0.115427	+	0.993316i	$0.536823\pi$
$710$	17.3308	−	39.5312i	0.650414	−	1.48358i
$711$	25.9834	+	15.0015i	0.974452	+	0.562600i
$712$	−4.62844	−	6.74517i	−0.173458	−	0.252786i
$713$	19.8977	−	19.8977i	0.745175	−	0.745175i
$714$		0			0
$715$	2.90028	−	1.04652i	0.108464	−	0.0391377i
$716$	−32.1669	+	1.66978i	−1.20213	+	0.0624027i
$717$	−4.30673	+	1.15398i	−0.160838	+	0.0430963i
$718$	−0.986561	−	38.0360i	−0.0368181	−	1.41949i
$719$	−5.63438	−	9.75903i	−0.210127	−	0.363950i	0.741627	−	0.670812i	$-0.234054\pi$
$719$	−5.63438	−	9.75903i	−0.210127	−	0.363950i	−0.951754	+	0.306862i	$0.900721\pi$
$720$	−4.73058	−	24.8355i	−0.176298	−	0.925565i
$721$		0			0
$722$	18.1443	−	11.1126i	0.675260	−	0.413569i
$723$	1.35511	−	5.05733i	0.0503970	−	0.188084i
$724$	4.17153	+	6.43058i	0.155034	+	0.238991i
$725$	−4.20610	−	24.6523i	−0.156210	−	0.915565i
$726$	1.72086	+	5.81483i	0.0638672	+	0.215809i
$727$	−21.9895	+	21.9895i	−0.815544	+	0.815544i	−0.985459	−	0.169915i	$-0.945651\pi$
$727$	−21.9895	+	21.9895i	−0.815544	+	0.815544i	0.169915	+	0.985459i	$0.445651\pi$
$728$		0			0
$729$			18.0830i			0.669742i
$730$	−2.85714	+	18.7304i	−0.105747	+	0.693244i
$731$	30.6172	+	17.6768i	1.13242	+	0.653801i
$732$	0.319117	−	1.49767i	0.0117949	−	0.0553555i
$733$	−39.0339	−	10.4591i	−1.44175	−	0.386316i	−0.548604	−	0.836082i	$-0.684841\pi$
$733$	−39.0339	−	10.4591i	−1.44175	−	0.386316i	−0.893146	+	0.449766i	$0.851507\pi$
$734$	−9.05587	+	37.6792i	−0.334258	+	1.39077i
$735$		0			0
$736$	−7.47894	−	18.1193i	−0.275677	−	0.667887i
$737$	−0.115744	+	0.431964i	−0.00426350	+	0.0159116i
$738$	−0.382981	+	0.00993359i	−0.0140977	+	0.000365660i
$739$	−15.6220	+	27.0581i	−0.574665	+	0.995349i	0.421413	+	0.906869i	$0.361534\pi$
$739$	−15.6220	+	27.0581i	−0.574665	+	0.995349i	−0.996078	+	0.0884798i	$0.971799\pi$
$740$	−3.03610	+	1.27705i	−0.111609	+	0.0469454i
$741$	−3.99829			−0.146881
$742$		0			0
$743$	13.4261	+	13.4261i	0.492557	+	0.492557i	0.909111	−	0.416554i	$-0.136762\pi$
$743$	13.4261	+	13.4261i	0.492557	+	0.492557i	−0.416554	+	0.909111i	$0.636762\pi$
$744$	1.74989	−	9.40251i	0.0641542	−	0.344713i
$745$	−21.2225	+	14.7726i	−0.777531	+	0.541227i
$746$	22.4889	+	21.3518i	0.823378	+	0.781745i
$747$	−16.8670	−	4.51950i	−0.617131	−	0.165360i
$748$	2.64886	+	8.16615i	0.0968520	+	0.298584i
$749$		0			0
$750$	−6.58273	+	0.115975i	−0.240367	+	0.00423480i
$751$	−29.3693	+	16.9564i	−1.07170	+	0.618748i	−0.928646	−	0.370967i	$-0.879026\pi$
$751$	−29.3693	+	16.9564i	−1.07170	+	0.618748i	−0.143056	+	0.989715i	$0.545693\pi$
$752$	−13.7892	+	16.9937i	−0.502840	+	0.619696i
$753$	−1.59885	−	5.96698i	−0.0582652	−	0.217449i
$754$	3.30336	+	11.1621i	0.120301	+	0.406501i
$755$	9.74730	+	4.57818i	0.354741	+	0.166617i
$756$		0			0
$757$	10.7202	+	10.7202i	0.389633	+	0.389633i	0.874556	−	0.484924i	$-0.161153\pi$
$757$	10.7202	+	10.7202i	0.389633	+	0.389633i	−0.484924	+	0.874556i	$0.661153\pi$
$758$	25.4252	+	13.8129i	0.923484	+	0.501708i
$759$	0.604493	−	1.04701i	0.0219417	−	0.0380041i
$760$	−28.5573	+	23.3727i	−1.03588	+	0.847815i
$761$	−12.2719	−	21.2555i	−0.444854	−	0.770510i	0.553188	−	0.833057i	$-0.313411\pi$
$761$	−12.2719	−	21.2555i	−0.444854	−	0.770510i	−0.998042	+	0.0625464i	$0.980078\pi$
$762$	−3.22869	+	1.97744i	−0.116963	+	0.0716351i
$763$		0			0
$764$	4.98927	+	2.54528i	0.180506	+	0.0920851i
$765$	−20.8820	+	24.7465i	−0.754990	+	0.894713i
$766$	−7.07584	+	7.45268i	−0.255661	+	0.269276i
$767$	−3.80726	−	14.2089i	−0.137472	−	0.513054i
$768$	−5.58025	−	3.63963i	−0.201360	−	0.131334i
$769$			38.3029i			1.38124i	0.723219	+	0.690619i	$0.242662\pi$
$769$			38.3029i			1.38124i	−0.723219	+	0.690619i	$0.757338\pi$
$770$		0			0
$771$			6.32315i			0.227723i
$772$	11.5803	−	12.8484i	0.416784	−	0.462423i
$773$	−0.371576	−	1.38674i	−0.0133647	−	0.0498776i	0.958922	−	0.283672i	$-0.0915525\pi$
$773$	−0.371576	−	1.38674i	−0.0133647	−	0.0498776i	−0.972286	+	0.233794i	$0.924886\pi$
$774$	20.0057	+	18.9942i	0.719091	+	0.682731i
$775$	38.0769	+	14.0984i	1.36776	+	0.506429i
$776$	−11.0362	+	12.9023i	−0.396178	+	0.463166i
$777$		0			0
$778$	−4.10243	−	6.69829i	−0.147079	−	0.240145i
$779$	0.279601	+	0.484282i	0.0100177	+	0.0173512i
$780$	3.03607	−	0.416578i	0.108709	−	0.0149159i
$781$	−5.71840	+	9.90456i	−0.204620	+	0.354413i
$782$	−11.9847	+	22.0600i	−0.428572	+	0.788864i
$783$	8.58072	+	8.58072i	0.306650	+	0.306650i
$784$		0			0
$785$	−8.97465	+	3.23836i	−0.320319	+	0.115582i
$786$	7.79449	−	2.30673i	0.278020	−	0.0822783i
$787$	−3.70435	−	13.8248i	−0.132046	−	0.492801i	0.867947	−	0.496657i	$-0.165439\pi$
$787$	−3.70435	−	13.8248i	−0.132046	−	0.492801i	−0.999993	+	0.00385583i	$0.998773\pi$
$788$	2.88867	−	13.5570i	0.102905	−	0.482949i
$789$	−4.22637	+	2.44010i	−0.150463	+	0.0868698i
$790$	3.69903	+	33.3614i	0.131605	+	1.18695i
$791$		0			0
$792$	0.520614	+	6.67861i	0.0184992	+	0.237314i
$793$	−2.92289	−	0.783185i	−0.103795	−	0.0278117i
$794$	−29.3027	+	30.8632i	−1.03991	+	1.09529i
$795$	7.05837	+	10.1401i	0.250335	+	0.359632i
$796$	−24.7610	+	1.28534i	−0.877631	+	0.0455578i
$797$	9.85742	+	9.85742i	0.349168	+	0.349168i	0.859800	−	0.510632i	$-0.170588\pi$
$797$	9.85742	+	9.85742i	0.349168	+	0.349168i	−0.510632	+	0.859800i	$0.670588\pi$
$798$		0			0
$799$	28.0283			0.991569
$800$	19.2496	−	20.7232i	0.680577	−	0.732677i
$801$	−4.08761	+	7.07995i	−0.144429	+	0.250158i
$802$	−0.170116	−	6.55867i	−0.00600699	−	0.231595i
$803$	1.29936	−	4.84926i	0.0458533	−	0.171127i
$804$	−0.201984	+	0.395930i	−0.00712342	+	0.0139634i
$805$		0			0
$806$	−18.3761	−	4.41654i	−0.647271	−	0.155566i
$807$	−8.32229	−	2.22995i	−0.292959	−	0.0784980i
$808$	−4.38889	−	2.09740i	−0.154400	−	0.0737864i
$809$	−30.8498	−	17.8112i	−1.08462	−	0.626207i	−0.152483	−	0.988306i	$-0.548727\pi$
$809$	−30.8498	−	17.8112i	−1.08462	−	0.626207i	−0.932140	+	0.362099i	$0.882060\pi$
$810$	−19.0302	+	13.9929i	−0.668655	+	0.491660i
$811$			11.1150i			0.390299i	0.980774	+	0.195149i	$0.0625192\pi$
$811$			11.1150i			0.390299i	−0.980774	+	0.195149i	$0.937481\pi$
$812$		0			0
$813$	−6.21267	+	6.21267i	−0.217888	+	0.217888i
$814$	0.836851	−	0.247661i	0.0293316	−	0.00868050i
$815$	3.20689	−	17.8969i	0.112332	−	0.626903i
$816$	0.883481	+	8.48680i	0.0309280	+	0.297098i
$817$	10.4216	−	38.8940i	0.364607	−	1.36073i
$818$	−25.6608	−	41.8979i	−0.897207	−	1.46493i
$819$		0			0
$820$	−0.262770	−	0.338605i	−0.00917632	−	0.0118246i
$821$	−6.79984	−	11.7777i	−0.237316	−	0.411043i	0.722627	−	0.691238i	$-0.242934\pi$
$821$	−6.79984	−	11.7777i	−0.237316	−	0.411043i	−0.959943	+	0.280195i	$0.909601\pi$
$822$	8.46641	−	0.219598i	0.295300	−	0.00765936i
$823$	−24.5214	+	6.57048i	−0.854761	+	0.229033i	−0.659487	−	0.751716i	$-0.729226\pi$
$823$	−24.5214	+	6.57048i	−0.854761	+	0.229033i	−0.195274	+	0.980749i	$0.562560\pi$
$824$	−43.6785	−	8.12897i	−1.52161	−	0.283186i
$825$	1.73696	+	0.161672i	0.0604731	+	0.00562869i
$826$		0			0
$827$	17.3478	−	17.3478i	0.603242	−	0.603242i	−0.337929	−	0.941172i	$-0.609726\pi$
$827$	17.3478	−	17.3478i	0.603242	−	0.603242i	0.941172	+	0.337929i	$0.109726\pi$
$828$	−13.1152	+	14.5514i	−0.455786	+	0.505696i
$829$	−16.3045	−	9.41343i	−0.566280	−	0.326942i	0.189382	−	0.981903i	$-0.439351\pi$
$829$	−16.3045	−	9.41343i	−0.566280	−	0.326942i	−0.755662	+	0.654962i	$0.772685\pi$
$830$	−7.10490	−	18.1978i	−0.246615	−	0.631655i
$831$	1.17942	−	0.680936i	0.0409135	−	0.0236214i
$832$	−7.75428	+	10.6395i	−0.268831	+	0.368858i
$833$		0			0
$834$	0.833737	+	0.200381i	0.0288700	+	0.00693864i
$835$	11.2298	−	13.3081i	0.388624	−	0.460546i
$836$	8.20309	−	5.32136i	0.283710	−	0.184043i
$837$	−19.0306	+	5.09924i	−0.657794	+	0.176255i
$838$	−34.9576	−	18.9917i	−1.20759	−	0.656056i
$839$	3.21211			0.110894			0.0554472	−	0.998462i	$-0.482342\pi$
$839$	3.21211			0.110894			0.0554472	+	0.998462i	$0.482342\pi$
$840$		0			0
$841$	3.98283			0.137339
$842$	−4.90377	−	2.66410i	−0.168995	−	0.0918111i
$843$	1.04610	−	0.280301i	0.0360295	−	0.00965408i
$844$	1.47224	−	0.955043i	0.0506765	−	0.0328739i
$845$	1.94217	+	22.9310i	0.0668126	+	0.788849i
$846$	21.2649	+	5.11082i	0.731101	+	0.175714i
$847$		0			0
$848$	−52.4156	−	8.35517i	−1.79996	−	0.286918i
$849$	−9.99440	+	5.77027i	−0.343007	+	0.198035i
$850$	−36.1439	−	2.42085i	−1.23972	−	0.0830346i
$851$	2.21021	+	1.27607i	0.0757652	+	0.0437430i
$852$	−7.61024	+	8.44360i	−0.260723	+	0.289273i
$853$	31.7184	−	31.7184i	1.08602	−	1.08602i	0.0900831	−	0.995934i	$-0.471287\pi$
$853$	31.7184	−	31.7184i	1.08602	−	1.08602i	0.995934	−	0.0900831i	$-0.0287133\pi$
$854$		0			0
$855$	33.3804	+	15.6783i	1.14158	+	0.536187i
$856$	7.19881	−	38.6805i	0.246050	−	1.32207i
$857$	35.4579	−	9.50091i	1.21122	−	0.324545i	0.403978	−	0.914769i	$-0.367627\pi$
$857$	35.4579	−	9.50091i	1.21122	−	0.324545i	0.807240	+	0.590224i	$0.200960\pi$
$858$	−0.811718	+	0.0210540i	−0.0277116	+	0.000718771i
$859$	−5.30651	−	9.19114i	−0.181056	−	0.313598i	0.761185	−	0.648535i	$-0.224618\pi$
$859$	−5.30651	−	9.19114i	−0.181056	−	0.313598i	−0.942240	+	0.334938i	$0.891285\pi$
$860$	−3.86126	+	30.6198i	−0.131668	+	1.04412i
$861$		0			0
$862$	−10.3498	−	16.8988i	−0.352517	−	0.575576i
$863$	5.67140	−	21.1660i	0.193057	−	0.720498i	−0.799705	−	0.600394i	$-0.795011\pi$
$863$	5.67140	−	21.1660i	0.193057	−	0.720498i	0.992761	−	0.120104i	$-0.0383228\pi$
$864$	−1.80828	+	13.6048i	−0.0615191	+	0.462844i
$865$	−6.89133	−	1.23483i	−0.234312	−	0.0419856i
$866$	−4.25653	+	1.25969i	−0.144643	+	0.0428061i
$867$	2.72198	−	2.72198i	0.0924434	−	0.0924434i
$868$		0			0
$869$		−	8.89379i		−	0.301701i
$870$	−0.993141	+	6.51070i	−0.0336706	+	0.220733i
$871$	0.760656	+	0.439165i	0.0257739	+	0.0148805i
$872$	−13.0042	+	27.2118i	−0.440379	+	0.921507i
$873$	16.3894	+	4.39154i	0.554698	+	0.148631i
$874$	27.8020	+	6.68197i	0.940417	+	0.226021i
$875$		0			0
$876$	2.26749	−	4.44474i	0.0766114	−	0.150174i
$877$	2.95602	−	11.0320i	0.0998175	−	0.372524i	−0.897888	−	0.440224i	$-0.854899\pi$
$877$	2.95602	−	11.0320i	0.0998175	−	0.372524i	0.997706	+	0.0676994i	$0.0215659\pi$
$878$	0.917916	+	35.3895i	0.0309782	+	1.19434i
$879$	−3.51032	+	6.08006i	−0.118400	+	0.205075i
$880$	−5.67453	+	4.89541i	−0.191288	+	0.165024i
$881$	−27.2610			−0.918447			−0.459224	−	0.888321i	$-0.651872\pi$
$881$	−27.2610			−0.918447			−0.459224	+	0.888321i	$0.651872\pi$
$882$		0			0
$883$	29.9932	+	29.9932i	1.00935	+	1.00935i	0.999956	+	0.00939636i	$0.00299100\pi$
$883$	29.9932	+	29.9932i	1.00935	+	1.00935i	0.00939636	+	0.999956i	$0.497009\pi$
$884$	16.8388	−	0.874102i	0.566350	−	0.0293992i
$885$	1.46792	−	8.19216i	0.0493437	−	0.275376i
$886$	4.28700	−	4.51531i	0.144024	−	0.151695i
$887$	21.8561	+	5.85632i	0.733855	+	0.196636i	0.606345	−	0.795201i	$-0.292635\pi$
$887$	21.8561	+	5.85632i	0.733855	+	0.196636i	0.127510	+	0.991837i	$0.459302\pi$
$888$	0.864784	−	0.0674121i	0.0290202	−	0.00226220i
$889$		0			0
$890$	−9.09032	+	1.00791i	−0.304708	+	0.0337852i
$891$	5.42024	−	3.12937i	0.181585	−	0.104838i
$892$	−7.43038	+	34.8720i	−0.248787	+	1.16760i
$893$	−8.26224	−	30.8351i	−0.276485	−	1.03186i
$894$	6.52969	−	1.93242i	0.218386	−	0.0646298i
$895$	−15.3098	+	32.5957i	−0.511749	+	1.08956i
$896$		0			0
$897$	−1.67904	−	1.67904i	−0.0560615	−	0.0560615i
$898$	16.3549	−	30.1042i	0.545772	−	1.00459i
$899$	20.3085	−	35.1754i	0.677327	−	1.17317i
$900$	−26.9807	−	8.42735i	−0.899355	−	0.280912i
$901$	33.9892	+	58.8710i	1.13234	+	1.96128i
$902$	0.0593137	+	0.0968451i	0.00197493	+	0.00322459i
$903$		0			0
$904$	17.0840	+	14.6131i	0.568206	+	0.486026i
$905$	8.53929	−	0.723246i	0.283856	−	0.0240415i
$906$	−2.05667	−	1.95268i	−0.0683284	−	0.0648734i
$907$	−1.07561	−	4.01423i	−0.0357151	−	0.133290i	0.945766	−	0.324847i	$-0.105313\pi$
$907$	−1.07561	−	4.01423i	−0.0357151	−	0.133290i	−0.981481	+	0.191557i	$0.938646\pi$
$908$	−14.0609	+	15.6006i	−0.466627	+	0.517725i
$909$			4.86119i			0.161235i
$910$		0			0
$911$			29.4464i			0.975603i	0.872955	+	0.487801i	$0.162201\pi$
$911$			29.4464i			0.975603i	−0.872955	+	0.487801i	$0.837799\pi$
$912$	9.07626	−	3.47371i	0.300545	−	0.115026i
$913$	1.33972	+	4.99989i	0.0443381	+	0.165472i
$914$	9.11881	−	9.60445i	0.301624	−	0.317687i
$915$	−1.30844	−	1.10411i	−0.0432557	−	0.0365006i
$916$	−48.5454	−	24.7655i	−1.60398	−	0.818274i
$917$		0			0
$918$	14.9895	−	9.18048i	0.494728	−	0.303001i
$919$	−4.57597	−	7.92582i	−0.150947	−	0.261449i	0.780629	−	0.624995i	$-0.214899\pi$
$919$	−4.57597	−	7.92582i	−0.150947	−	0.261449i	−0.931576	+	0.363547i	$0.881566\pi$
$920$	−21.8075	−	2.17724i	−0.718970	−	0.0717815i
$921$	−3.83837	+	6.64825i	−0.126479	+	0.219067i
$922$	15.3572	+	8.34320i	0.505762	+	0.274769i
$923$	15.8834	+	15.8834i	0.522809	+	0.522809i
$924$		0			0
$925$	−0.341285	+	3.66667i	−0.0112214	+	0.120559i
$926$	16.8443	+	56.9174i	0.553539	+	1.87042i
$927$	11.4916	+	42.8871i	0.377433	+	1.40860i
$928$	−17.1964	−	22.4685i	−0.564500	−	0.737564i
$929$	−26.0531	+	15.0417i	−0.854773	+	0.493504i	−0.862259	−	0.506468i	$-0.830951\pi$
$929$	−26.0531	+	15.0417i	−0.854773	+	0.493504i	0.00748525	+	0.999972i	$0.497617\pi$
$930$	−8.34815	−	6.68168i	−0.273747	−	0.219101i
$931$		0			0
$932$	8.10485	+	24.9864i	0.265483	+	0.818456i
$933$	−4.71148	−	1.26244i	−0.154247	−	0.0413303i
$934$	−37.1195	−	35.2426i	−1.21459	−	1.15317i
$935$	9.44786	+	1.69293i	0.308978	+	0.0553647i
$936$	12.9349	+	2.40730i	0.422789	+	0.0786850i
$937$	6.79581	+	6.79581i	0.222009	+	0.222009i	0.809344	−	0.587335i	$-0.199823\pi$
$937$	6.79581	+	6.79581i	0.222009	+	0.222009i	−0.587335	+	0.809344i	$0.699823\pi$
$938$		0			0
$939$	7.95230			0.259514
$940$	9.48656	+	22.5536i	0.309417	+	0.735617i
$941$	9.08044	−	15.7278i	0.296014	−	0.512711i	−0.679206	−	0.733947i	$-0.737676\pi$
$941$	9.08044	−	15.7278i	0.296014	−	0.512711i	0.975220	+	0.221236i	$0.0710092\pi$
$942$	2.51179	−	0.0651496i	0.0818384	−	0.00212269i
$943$	−0.0859540	+	0.320785i	−0.00279905	+	0.0104462i
$944$	20.9873	+	28.9470i	0.683080	+	0.942144i
$945$		0			0
$946$	1.91096	−	7.95101i	0.0621306	−	0.258510i
$947$	16.9897	+	4.55237i	0.552091	+	0.147932i	0.524070	−	0.851675i	$-0.324413\pi$
$947$	16.9897	+	4.55237i	0.552091	+	0.147932i	0.0280205	+	0.999607i	$0.491080\pi$
$948$	1.84214	−	8.64549i	0.0598300	−	0.280792i
$949$	−8.53920	−	4.93011i	−0.277194	−	0.160038i
$950$	7.99129	+	40.4770i	0.259272	+	1.31325i
$951$			1.20251i			0.0389940i
$952$		0			0
$953$	12.8804	−	12.8804i	0.417238	−	0.417238i	−0.467013	−	0.884251i	$-0.654670\pi$
$953$	12.8804	−	12.8804i	0.417238	−	0.417238i	0.884251	+	0.467013i	$0.154670\pi$
$954$	15.0525	+	50.8628i	0.487343	+	1.64674i
$955$	5.13957	−	3.57757i	0.166312	−	0.115768i
$956$	−11.6549	−	17.9664i	−0.376945	−	0.581076i
$957$	0.451656	−	1.68560i	0.0146000	−	0.0544878i
$958$	38.4291	−	23.5363i	1.24159	−	0.760423i
$959$		0			0
$960$	−6.53007	+	3.58339i	−0.210757	+	0.115653i
$961$	17.4723	+	30.2629i	0.563622	+	0.976222i
$962$	−0.0444444	−	1.71351i	−0.00143294	−	0.0552459i
$963$	−37.9798	+	10.1766i	−1.22388	+	0.327938i
$964$	25.1142	−	1.30368i	0.808875	−	0.0419887i
$965$	−6.56378	−	18.1906i	−0.211296	−	0.585575i
$966$		0			0
$967$	−21.8531	+	21.8531i	−0.702748	+	0.702748i	−0.965000	−	0.262251i	$-0.915535\pi$
$967$	−21.8531	+	21.8531i	−0.702748	+	0.702748i	0.262251	+	0.965000i	$0.415535\pi$
$968$	−24.0166	+	16.4798i	−0.771922	+	0.529681i
$969$	−10.7791	−	6.22331i	−0.346274	−	0.199922i
$970$	6.90374	+	17.6826i	0.221666	+	0.567753i
$971$	49.5916	−	28.6317i	1.59147	−	0.918836i	0.598416	−	0.801186i	$-0.295797\pi$
$971$	49.5916	−	28.6317i	1.59147	−	0.918836i	0.993055	−	0.117650i	$-0.0375362\pi$
$972$	19.7638	−	6.41081i	0.633925	−	0.205627i
$973$		0			0
$974$	3.30035	−	13.7319i	0.105750	−	0.440000i
$975$	1.18967	−	3.21306i	0.0381000	−	0.102900i
$976$	7.31550	−	0.761547i	0.234163	−	0.0243765i
$977$	23.4116	−	6.27313i	0.749004	−	0.200695i	0.135928	−	0.990719i	$-0.456598\pi$
$977$	23.4116	−	6.27313i	0.749004	−	0.200695i	0.613076	+	0.790024i	$0.289932\pi$
$978$	−2.28579	+	4.20741i	−0.0730914	+	0.134538i
$979$	2.42338			0.0774516
$980$		0			0
$981$	30.1401			0.962300
$982$	11.0382	−	20.3178i	0.352243	−	0.648366i
$983$	13.7291	−	3.67869i	0.437889	−	0.117332i	−0.0331380	−	0.999451i	$-0.510550\pi$
$983$	13.7291	−	3.67869i	0.437889	−	0.117332i	0.471027	+	0.882119i	$0.343883\pi$
$984$	0.0375985	+	0.106427i	0.00119860	+	0.00339276i
$985$	−11.8441	−	9.99445i	−0.377384	−	0.318450i
$986$	−8.46817	+	35.2339i	−0.269682	+	1.12208i
$987$		0			0
$988$	−5.92542	−	18.2674i	−0.188513	−	0.581164i
$989$	20.7096	−	11.9567i	0.658527	−	0.380201i
$990$	6.85933	+	3.00718i	0.218004	+	0.0955746i
$991$	−40.1223	−	23.1646i	−1.27453	−	0.735848i	−0.298689	−	0.954350i	$-0.596549\pi$
$991$	−40.1223	−	23.1646i	−1.27453	−	0.735848i	−0.975836	+	0.218503i	$0.929883\pi$
$992$	45.5516	−	5.93948i	1.44626	−	0.188579i
$993$	−10.2670	+	10.2670i	−0.325812	+	0.325812i
$994$		0			0
$995$	−11.7850	+	25.0911i	−0.373609	+	0.795442i
$996$	0.266702	+	5.13778i	0.00845079	+	0.162797i
$997$	−44.4512	+	11.9107i	−1.40778	+	0.377214i	−0.881133	−	0.472869i	$-0.843219\pi$
$997$	−44.4512	+	11.9107i	−1.40778	+	0.377214i	−0.526649	+	0.850083i	$0.676552\pi$
$998$	−0.348214	−	13.4251i	−0.0110225	−	0.424965i
$999$	−0.893438	−	1.54748i	−0.0282671	−	0.0489601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.67.4		72
4.3	odd	2	inner	980.2.x.m.67.18		72
5.3	odd	4	inner	980.2.x.m.263.6		72
7.2	even	3	inner	980.2.x.m.667.8		72
7.3	odd	6		980.2.k.k.687.15		36
7.4	even	3		980.2.k.j.687.15		36
7.5	odd	6		140.2.w.b.107.8	yes	72
7.6	odd	2		140.2.w.b.67.4	yes	72
20.3	even	4	inner	980.2.x.m.263.8		72
28.3	even	6		980.2.k.k.687.7		36
28.11	odd	6		980.2.k.j.687.7		36
28.19	even	6		140.2.w.b.107.6	yes	72
28.23	odd	6	inner	980.2.x.m.667.6		72
28.27	even	2		140.2.w.b.67.18	yes	72
35.3	even	12		980.2.k.k.883.7		36
35.12	even	12		700.2.be.e.443.1		72
35.13	even	4		140.2.w.b.123.6	yes	72
35.18	odd	12		980.2.k.j.883.7		36
35.19	odd	6		700.2.be.e.107.11		72
35.23	odd	12	inner	980.2.x.m.863.18		72
35.27	even	4		700.2.be.e.543.13		72
35.33	even	12		140.2.w.b.23.18	yes	72
35.34	odd	2		700.2.be.e.207.15		72
140.3	odd	12		980.2.k.k.883.15		36
140.19	even	6		700.2.be.e.107.13		72
140.23	even	12	inner	980.2.x.m.863.4		72
140.27	odd	4		700.2.be.e.543.11		72
140.47	odd	12		700.2.be.e.443.15		72
140.83	odd	4		140.2.w.b.123.8	yes	72
140.103	odd	12		140.2.w.b.23.4	✓	72
140.123	even	12		980.2.k.j.883.15		36
140.139	even	2		700.2.be.e.207.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.4	✓	72	140.103	odd	12
140.2.w.b.23.18	yes	72	35.33	even	12
140.2.w.b.67.4	yes	72	7.6	odd	2
140.2.w.b.67.18	yes	72	28.27	even	2
140.2.w.b.107.6	yes	72	28.19	even	6
140.2.w.b.107.8	yes	72	7.5	odd	6
140.2.w.b.123.6	yes	72	35.13	even	4
140.2.w.b.123.8	yes	72	140.83	odd	4
700.2.be.e.107.11		72	35.19	odd	6
700.2.be.e.107.13		72	140.19	even	6
700.2.be.e.207.1		72	140.139	even	2
700.2.be.e.207.15		72	35.34	odd	2
700.2.be.e.443.1		72	35.12	even	12
700.2.be.e.443.15		72	140.47	odd	12
700.2.be.e.543.11		72	140.27	odd	4
700.2.be.e.543.13		72	35.27	even	4
980.2.k.j.687.7		36	28.11	odd	6
980.2.k.j.687.15		36	7.4	even	3
980.2.k.j.883.7		36	35.18	odd	12
980.2.k.j.883.15		36	140.123	even	12
980.2.k.k.687.7		36	28.3	even	6
980.2.k.k.687.15		36	7.3	odd	6
980.2.k.k.883.7		36	35.3	even	12
980.2.k.k.883.15		36	140.3	odd	12
980.2.x.m.67.4		72	1.1	even	1	trivial
980.2.x.m.67.18		72	4.3	odd	2	inner
980.2.x.m.263.6		72	5.3	odd	4	inner
980.2.x.m.263.8		72	20.3	even	4	inner
980.2.x.m.667.6		72	28.23	odd	6	inner
980.2.x.m.667.8		72	7.2	even	3	inner
980.2.x.m.863.4		72	140.23	even	12	inner
980.2.x.m.863.18		72	35.23	odd	12	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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.24267 - 0.675113i) q^{2} +(0.402205 - 0.107770i) q^{3} +(1.08845 + 1.67788i) q^{4} +(2.22809 - 0.188711i) q^{5} +(-0.572564 - 0.137611i) q^{6} +(-0.219816 - 2.81987i) q^{8} +(-2.44792 + 1.41331i) q^{9} +(-2.89618 - 1.26971i) q^{10} +(0.725638 + 0.418947i) q^{11} +(0.618604 + 0.557549i) q^{12} +(1.16367 - 1.16367i) q^{13} +(0.875811 - 0.316023i) q^{15} +(-1.63057 + 3.65256i) q^{16} +(4.94841 - 1.32592i) q^{17} +(3.99610 - 0.103649i) q^{18} +(-2.91741 - 5.05309i) q^{19} +(2.74179 + 3.53307i) q^{20} +(-0.618890 - 1.01050i) q^{22} +(0.896861 - 3.34713i) q^{23} +(-0.392310 - 1.11048i) q^{24} +(4.92878 - 0.840930i) q^{25} +(-2.23166 + 0.660445i) q^{26} +(-1.71555 + 1.71555i) q^{27} -5.00172i q^{29} +(-1.30169 - 0.198560i) q^{30} +(7.03267 + 4.06031i) q^{31} +(4.49215 - 3.43810i) q^{32} +(0.337005 + 0.0903002i) q^{33} +(-7.04437 - 1.69305i) q^{34} +(-5.03579 - 2.56901i) q^{36} +(-0.190621 + 0.711408i) q^{37} +(0.213956 + 8.24889i) q^{38} +(0.342623 - 0.593441i) q^{39} +(-1.02191 - 6.24145i) q^{40} -0.0958388 q^{41} +(4.87975 + 4.87975i) q^{43} +(0.0868733 + 1.67354i) q^{44} +(-5.18749 + 3.61093i) q^{45} +(-3.37419 + 3.55389i) q^{46} +(5.28468 + 1.41603i) q^{47} +(-0.262186 + 1.64481i) q^{48} +(-6.69255 - 2.28248i) q^{50} +(1.84738 - 1.06658i) q^{51} +(3.21908 + 0.685908i) q^{52} +(3.43436 + 12.8172i) q^{53} +(3.29006 - 0.973671i) q^{54} +(1.69585 + 0.796517i) q^{55} +(-1.71797 - 1.71797i) q^{57} +(-3.37672 + 6.21547i) q^{58} +(4.46933 - 7.74111i) q^{59} +(1.48352 + 1.12553i) q^{60} +(-0.919379 - 1.59241i) q^{61} +(-5.99810 - 9.79346i) q^{62} +(-7.90336 + 1.23971i) q^{64} +(2.37316 - 2.81235i) q^{65} +(-0.357822 - 0.339730i) q^{66} +(0.138137 + 0.515535i) q^{67} +(7.61081 + 6.85965i) q^{68} -1.44289i q^{69} +13.6494i q^{71} +(4.52344 + 6.59216i) q^{72} +(-1.55074 - 5.78744i) q^{73} +(0.717160 - 0.755353i) q^{74} +(1.89175 - 0.869402i) q^{75} +(5.30306 - 10.3951i) q^{76} +(-0.826407 + 0.506141i) q^{78} +(-5.30723 - 9.19239i) q^{79} +(-2.94379 + 8.44595i) q^{80} +(3.73481 - 6.46888i) q^{81} +(0.119096 + 0.0647020i) q^{82} +(4.36830 + 4.36830i) q^{83} +(10.7753 - 3.88809i) q^{85} +(-2.76953 - 9.35829i) q^{86} +(-0.539037 - 2.01171i) q^{87} +(1.02187 - 2.13830i) q^{88} +(2.50474 - 1.44611i) q^{89} +(8.88411 - 0.985047i) q^{90} +(6.59227 - 2.13834i) q^{92} +(3.26615 + 0.875163i) q^{93} +(-5.61112 - 5.32740i) q^{94} +(-7.45382 - 10.7082i) q^{95} +(1.43624 - 1.86694i) q^{96} +(-4.24461 - 4.24461i) q^{97} -2.36841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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