LMFDB - Embedded newform 980.2.k.j.883.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(687,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 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("980.687"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,-2,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			883.1
Character	$\chi$	$=$	980.883
Dual form			980.2.k.j.687.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38434 + 0.289136i) q^{2} +(0.881483 - 0.881483i) q^{3} +(1.83280 - 0.800525i) q^{4} +(1.71735 + 1.43203i) q^{5} +(-0.965404 + 1.47514i) q^{6} +(-2.30576 + 1.63813i) q^{8} +1.44598i q^{9} +(-2.79145 - 1.48587i) q^{10} -0.952199i q^{11} +(0.909933 - 2.32123i) q^{12} +(3.15680 + 3.15680i) q^{13} +(2.77612 - 0.251508i) q^{15} +(2.71832 - 2.93441i) q^{16} +(1.88053 - 1.88053i) q^{17} +(-0.418084 - 2.00173i) q^{18} -3.98095 q^{19} +(4.29394 + 1.24984i) q^{20} +(0.275315 + 1.31817i) q^{22} +(0.386810 - 0.386810i) q^{23} +(-0.588506 + 3.47647i) q^{24} +(0.898593 + 4.91859i) q^{25} +(-5.28284 - 3.45735i) q^{26} +(3.91905 + 3.91905i) q^{27} +7.23080i q^{29} +(-3.77038 + 1.15085i) q^{30} +3.94749i q^{31} +(-2.91464 + 4.84818i) q^{32} +(-0.839347 - 0.839347i) q^{33} +(-2.05957 + 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(0.735415 - 0.735415i) q^{37} +(5.51099 - 1.15104i) q^{38} +5.56534 q^{39} +(-6.30565 - 0.488671i) q^{40} -3.71449 q^{41} +(8.73324 - 8.73324i) q^{43} +(-0.762260 - 1.74519i) q^{44} +(-2.07068 + 2.48325i) q^{45} +(-0.423636 + 0.647317i) q^{46} +(-2.26785 - 2.26785i) q^{47} +(-0.190479 - 4.98278i) q^{48} +(-2.66610 - 6.54919i) q^{50} -3.31531i q^{51} +(8.31290 + 3.25869i) q^{52} +(-2.07846 - 2.07846i) q^{53} +(-6.55844 - 4.29217i) q^{54} +(1.36358 - 1.63526i) q^{55} +(-3.50914 + 3.50914i) q^{57} +(-2.09068 - 10.0099i) q^{58} -12.6017 q^{59} +(4.88674 - 2.68332i) q^{60} +6.02367 q^{61} +(-1.14136 - 5.46468i) q^{62} +(2.63307 - 7.55427i) q^{64} +(0.900712 + 9.94198i) q^{65} +(1.40463 + 0.919257i) q^{66} +(10.5349 + 10.5349i) q^{67} +(1.94122 - 4.95205i) q^{68} -0.681932i q^{69} +7.60710i q^{71} +(-2.36870 - 3.33408i) q^{72} +(-10.4081 - 10.4081i) q^{73} +(-0.805430 + 1.23070i) q^{74} +(5.12775 + 3.54356i) q^{75} +(-7.29629 + 3.18685i) q^{76} +(-7.70432 + 1.60914i) q^{78} +10.6973 q^{79} +(8.87046 - 1.14670i) q^{80} +2.57122 q^{81} +(5.14212 - 1.07399i) q^{82} +(5.72446 - 5.72446i) q^{83} +(5.92250 - 0.536560i) q^{85} +(-9.56469 + 14.6149i) q^{86} +(6.37382 + 6.37382i) q^{87} +(1.55982 + 2.19554i) q^{88} -2.11775i q^{89} +(2.14853 - 4.03637i) q^{90} +(0.399294 - 1.01860i) q^{92} +(3.47965 + 3.47965i) q^{93} +(3.79519 + 2.48376i) q^{94} +(-6.83669 - 5.70083i) q^{95} +(1.70439 + 6.84279i) q^{96} +(3.08588 - 3.08588i) q^{97} +1.37686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8} + 2 q^{10} + 10 q^{12} + 28 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{20} - 8 q^{22} + 16 q^{25} - 4 q^{26} + 32 q^{30} + 38 q^{32} - 64 q^{33} + 8 q^{36} + 4 q^{37}+ \cdots + 12 q^{97}+O(q^{100}) $ 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8 + 2 * q^10 + 10 * q^12 + 28 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^20 - 8 * q^22 + 16 * q^25 - 4 * q^26 + 32 * q^30 + 38 * q^32 - 64 * q^33 + 8 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^40 + 20 * q^41 - 12 * q^45 + 28 * q^46 - 6 * q^48 - 14 * q^50 + 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 - 20 * q^61 - 28 * q^62 - 4 * q^65 + 44 * q^66 - 12 * q^68 - 44 * q^72 - 12 * q^73 - 56 * q^76 + 32 * q^78 + 52 * q^80 + 52 * q^81 - 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 + 16 * q^90 + 22 * q^92 - 12 * q^93 - 48 * q^96 + 12 * q^97

Character values

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

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

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 $

$2$	−1.38434	+	0.289136i	−0.978877	+	0.204450i
$2$	−1.38434	+	0.289136i	−0.978877	+	0.204450i
$3$	0.881483	−	0.881483i	0.508924	−	0.508924i	−0.405272	−	0.914196i	$-0.632823\pi$
$3$	0.881483	−	0.881483i	0.508924	−	0.508924i	0.914196	+	0.405272i	$0.132823\pi$
$4$	1.83280	−	0.800525i	0.916400	−	0.400263i
$5$	1.71735	+	1.43203i	0.768023	+	0.640422i
$5$	1.71735	+	1.43203i	0.768023	+	0.640422i
$6$	−0.965404	+	1.47514i	−0.394125	+	0.602224i
$7$		0			0
$7$		0			0
$8$	−2.30576	+	1.63813i	−0.815210	+	0.579166i
$9$			1.44598i			0.481992i
$10$	−2.79145	−	1.48587i	−0.882734	−	0.469872i
$11$		−	0.952199i		−	0.287099i	−0.989643	−	0.143549i	$-0.954148\pi$
$11$		−	0.952199i		−	0.287099i	0.989643	−	0.143549i	$-0.0458516\pi$
$12$	0.909933	−	2.32123i	0.262675	−	0.670082i
$13$	3.15680	+	3.15680i	0.875540	+	0.875540i	0.993069	−	0.117529i	$-0.0374974\pi$
$13$	3.15680	+	3.15680i	0.875540	+	0.875540i	−0.117529	+	0.993069i	$0.537497\pi$
$14$		0			0
$15$	2.77612	−	0.251508i	0.716792	−	0.0649391i
$16$	2.71832	−	2.93441i	0.679580	−	0.733602i
$17$	1.88053	−	1.88053i	0.456095	−	0.456095i	−0.441276	−	0.897371i	$-0.645474\pi$
$17$	1.88053	−	1.88053i	0.456095	−	0.456095i	0.897371	+	0.441276i	$0.145474\pi$
$18$	−0.418084	−	2.00173i	−0.0985433	−	0.471811i
$19$	−3.98095			−0.913293			−0.456646	−	0.889648i	$-0.650950\pi$
$19$	−3.98095			−0.913293			−0.456646	+	0.889648i	$0.650950\pi$
$20$	4.29394	+	1.24984i	0.960154	+	0.279472i
$21$		0			0
$22$	0.275315	+	1.31817i	0.0586973	+	0.281034i
$23$	0.386810	−	0.386810i	0.0806554	−	0.0806554i	−0.665628	−	0.746284i	$-0.731836\pi$
$23$	0.386810	−	0.386810i	0.0806554	−	0.0806554i	0.746284	+	0.665628i	$0.231836\pi$
$24$	−0.588506	+	3.47647i	−0.120128	+	0.709631i
$25$	0.898593	+	4.91859i	0.179719	+	0.983718i
$26$	−5.28284	−	3.45735i	−1.03605	−	0.678042i
$27$	3.91905	+	3.91905i	0.754222	+	0.754222i
$28$		0			0
$29$			7.23080i			1.34273i	0.741129	+	0.671363i	$0.234291\pi$
$29$			7.23080i			1.34273i	−0.741129	+	0.671363i	$0.765709\pi$
$30$	−3.77038	+	1.15085i	−0.688374	+	0.210115i
$31$			3.94749i			0.708991i	0.935058	+	0.354495i	$0.115347\pi$
$31$			3.94749i			0.708991i	−0.935058	+	0.354495i	$0.884653\pi$
$32$	−2.91464	+	4.84818i	−0.515240	+	0.857046i
$33$	−0.839347	−	0.839347i	−0.146112	−	0.146112i
$34$	−2.05957	+	3.14702i	−0.353213	+	0.539710i
$35$		0			0
$36$	1.15754	+	2.65019i	0.192924	+	0.441698i
$37$	0.735415	−	0.735415i	0.120901	−	0.120901i	−0.644067	−	0.764969i	$-0.722754\pi$
$37$	0.735415	−	0.735415i	0.120901	−	0.120901i	0.764969	+	0.644067i	$0.222754\pi$
$38$	5.51099	−	1.15104i	0.894001	−	0.186723i
$39$	5.56534			0.891167
$40$	−6.30565	−	0.488671i	−0.997011	−	0.0772656i
$41$	−3.71449			−0.580106			−0.290053	−	0.957011i	$-0.593673\pi$
$41$	−3.71449			−0.580106			−0.290053	+	0.957011i	$0.593673\pi$
$42$		0			0
$43$	8.73324	−	8.73324i	1.33181	−	1.33181i	0.428052	−	0.903754i	$-0.359200\pi$
$43$	8.73324	−	8.73324i	1.33181	−	1.33181i	0.903754	−	0.428052i	$-0.140800\pi$
$44$	−0.762260	−	1.74519i	−0.114915	−	0.263097i
$45$	−2.07068	+	2.48325i	−0.308679	+	0.370181i
$46$	−0.423636	+	0.647317i	−0.0624617	+	0.0954417i
$47$	−2.26785	−	2.26785i	−0.330799	−	0.330799i	0.522091	−	0.852890i	$-0.325152\pi$
$47$	−2.26785	−	2.26785i	−0.330799	−	0.330799i	−0.852890	+	0.522091i	$0.825152\pi$
$48$	−0.190479	−	4.98278i	−0.0274933	−	0.719202i
$49$		0			0
$50$	−2.66610	−	6.54919i	−0.377044	−	0.926196i
$51$		−	3.31531i		−	0.464236i
$52$	8.31290	+	3.25869i	1.15279	+	0.451899i
$53$	−2.07846	−	2.07846i	−0.285498	−	0.285498i	0.549799	−	0.835297i	$-0.314704\pi$
$53$	−2.07846	−	2.07846i	−0.285498	−	0.285498i	−0.835297	+	0.549799i	$0.814704\pi$
$54$	−6.55844	−	4.29217i	−0.892491	−	0.584090i
$55$	1.36358	−	1.63526i	0.183864	−	0.220498i
$56$		0			0
$57$	−3.50914	+	3.50914i	−0.464797	+	0.464797i
$58$	−2.09068	−	10.0099i	−0.274520	−	1.31436i
$59$	−12.6017			−1.64060			−0.820300	−	0.571934i	$-0.806193\pi$
$59$	−12.6017			−1.64060			−0.820300	+	0.571934i	$0.806193\pi$
$60$	4.88674	−	2.68332i	0.630876	−	0.346415i
$61$	6.02367			0.771251			0.385626	−	0.922655i	$-0.373986\pi$
$61$	6.02367			0.771251			0.385626	+	0.922655i	$0.373986\pi$
$62$	−1.14136	−	5.46468i	−0.144953	−	0.694015i
$63$		0			0
$64$	2.63307	−	7.55427i	0.329134	−	0.944283i
$65$	0.900712	+	9.94198i	0.111720	+	1.23315i
$66$	1.40463	+	0.919257i	0.172898	+	0.113153i
$67$	10.5349	+	10.5349i	1.28705	+	1.28705i	0.936572	+	0.350475i	$0.113980\pi$
$67$	10.5349	+	10.5349i	1.28705	+	1.28705i	0.350475	+	0.936572i	$0.386020\pi$
$68$	1.94122	−	4.95205i	0.235408	−	0.600524i
$69$		−	0.681932i		−	0.0820949i
$70$		0			0
$71$			7.60710i			0.902797i	0.892322	+	0.451399i	$0.149075\pi$
$71$			7.60710i			0.902797i	−0.892322	+	0.451399i	$0.850925\pi$
$72$	−2.36870	−	3.33408i	−0.279154	−	0.392925i
$73$	−10.4081	−	10.4081i	−1.21818	−	1.21818i	−0.968269	−	0.249911i	$-0.919599\pi$
$73$	−10.4081	−	10.4081i	−1.21818	−	1.21818i	−0.249911	−	0.968269i	$-0.580401\pi$
$74$	−0.805430	+	1.23070i	−0.0936293	+	0.143066i
$75$	5.12775	+	3.54356i	0.592101	+	0.409175i
$76$	−7.29629	+	3.18685i	−0.836942	+	0.365557i
$77$		0			0
$78$	−7.70432	+	1.60914i	−0.872343	+	0.182199i
$79$	10.6973			1.20354			0.601769	−	0.798670i	$-0.294463\pi$
$79$	10.6973			1.20354			0.601769	+	0.798670i	$0.294463\pi$
$80$	8.87046	−	1.14670i	0.991748	−	0.128205i
$81$	2.57122			0.285691
$82$	5.14212	−	1.07399i	0.567853	−	0.118603i
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	−0.319309	−	0.947651i	$-0.603451\pi$
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	0.947651	+	0.319309i	$0.103451\pi$
$84$		0			0
$85$	5.92250	−	0.536560i	0.642386	−	0.0581981i
$86$	−9.56469	+	14.6149i	−1.03139	+	1.57596i
$87$	6.37382	+	6.37382i	0.683345	+	0.683345i
$88$	1.55982	+	2.19554i	0.166278	+	0.234046i
$89$		−	2.11775i		−	0.224481i	−0.993681	−	0.112241i	$-0.964197\pi$
$89$		−	2.11775i		−	0.224481i	0.993681	−	0.112241i	$-0.0358028\pi$
$90$	2.14853	−	4.03637i	0.226475	−	0.425471i
$91$		0			0
$92$	0.399294	−	1.01860i	0.0416293	−	0.106196i
$93$	3.47965	+	3.47965i	0.360823	+	0.360823i
$94$	3.79519	+	2.48376i	0.391444	+	0.256180i
$95$	−6.83669	−	5.70083i	−0.701430	−	0.584893i
$96$	1.70439	+	6.84279i	0.173953	+	0.698389i
$97$	3.08588	−	3.08588i	0.313324	−	0.313324i	−0.532872	−	0.846196i	$-0.678887\pi$
$97$	3.08588	−	3.08588i	0.313324	−	0.313324i	0.846196	+	0.532872i	$0.178887\pi$
$98$		0			0
$99$	1.37686			0.138379
$100$	5.58440	+	8.29545i	0.558440	+	0.829545i
$101$	1.43015			0.142305			0.0711525	−	0.997465i	$-0.477332\pi$
$101$	1.43015			0.142305			0.0711525	+	0.997465i	$0.477332\pi$
$102$	0.958575	+	4.58952i	0.0949130	+	0.454430i
$103$	7.19528	−	7.19528i	0.708972	−	0.708972i	−0.257347	−	0.966319i	$-0.582848\pi$
$103$	7.19528	−	7.19528i	0.708972	−	0.708972i	0.966319	+	0.257347i	$0.0828483\pi$
$104$	−12.4501	−	2.10758i	−1.22083	−	0.206666i
$105$		0			0
$106$	3.47825	+	2.27634i	0.337838	+	0.221097i
$107$	−0.0284436	−	0.0284436i	−0.00274975	−	0.00274975i	0.705731	−	0.708480i	$-0.250619\pi$
$107$	−0.0284436	−	0.0284436i	−0.00274975	−	0.00274975i	−0.708480	+	0.705731i	$0.750619\pi$
$108$	10.3201	+	4.04554i	0.993056	+	0.389282i
$109$			6.29292i			0.602752i	0.953505	+	0.301376i	$0.0974460\pi$
$109$			6.29292i			0.602752i	−0.953505	+	0.301376i	$0.902554\pi$
$110$	−1.41484	+	2.65802i	−0.134900	+	0.253432i
$111$		−	1.29651i		−	0.123059i
$112$		0			0
$113$	10.8513	+	10.8513i	1.02081	+	1.02081i	0.999779	+	0.0210265i	$0.00669344\pi$
$113$	10.8513	+	10.8513i	1.02081	+	1.02081i	0.0210265	+	0.999779i	$0.493307\pi$
$114$	3.84323	−	5.87246i	0.359951	−	0.550007i
$115$	1.21821	−	0.110366i	0.113599	−	0.0102917i
$116$	5.78844	+	13.2526i	0.537443	+	1.23047i
$117$	−4.56467	+	4.56467i	−0.422004	+	0.422004i
$118$	17.4450	−	3.64360i	1.60595	−	0.335420i
$119$		0			0
$120$	−5.98907	+	5.12756i	−0.546725	+	0.468080i
$121$	10.0933			0.917574
$122$	−8.33881	+	1.74166i	−0.754960	+	0.157682i
$123$	−3.27426	+	3.27426i	−0.295230	+	0.295230i
$124$	3.16007	+	7.23497i	0.283783	+	0.649720i
$125$	−5.50036	+	9.73376i	−0.491967	+	0.870614i
$126$		0			0
$127$	1.22418	+	1.22418i	0.108629	+	0.108629i	0.759332	−	0.650703i	$-0.225526\pi$
$127$	1.22418	+	1.22418i	0.108629	+	0.108629i	−0.650703	+	0.759332i	$0.725526\pi$
$128$	−1.46085	+	11.2190i	−0.129123	+	0.991629i
$129$		−	15.3964i		−	1.35558i
$130$	−4.12147	−	13.5027i	−0.361477	−	1.18426i
$131$			1.30460i			0.113984i	0.998375	+	0.0569918i	$0.0181509\pi$
$131$			1.30460i			0.113984i	−0.998375	+	0.0569918i	$0.981849\pi$
$132$	−2.21027	−	0.866437i	−0.192380	−	0.0754137i
$133$		0			0
$134$	−17.6300	−	11.5379i	−1.52300	−	0.996724i
$135$	1.11820	+	12.3426i	0.0962392	+	1.06228i
$136$	−1.25550	+	7.41660i	−0.107658	+	0.635968i
$137$	0.820169	−	0.820169i	0.0700718	−	0.0700718i	−0.671202	−	0.741274i	$-0.734222\pi$
$137$	0.820169	−	0.820169i	0.0700718	−	0.0700718i	0.741274	+	0.671202i	$0.234222\pi$
$138$	0.197171	+	0.944026i	0.0167843	+	0.0803608i
$139$	−17.4513			−1.48020			−0.740099	−	0.672498i	$-0.765221\pi$
$139$	−17.4513			−1.48020			−0.740099	+	0.672498i	$0.765221\pi$
$140$		0			0
$141$	−3.99813			−0.336704
$142$	−2.19949	−	10.5308i	−0.184577	−	0.883727i
$143$	3.00591	−	3.00591i	0.251367	−	0.251367i
$144$	4.24309	+	3.93063i	0.353590	+	0.327552i
$145$	−10.3547	+	12.4178i	−0.859911	+	1.03124i
$146$	17.4178	+	11.3990i	1.44151	+	0.943392i
$147$		0			0
$148$	0.759151	−	1.93659i	0.0624018	−	0.159186i
$149$		−	11.2109i		−	0.918434i	−0.888324	−	0.459217i	$-0.848130\pi$
$149$		−	11.2109i		−	0.918434i	0.888324	−	0.459217i	$-0.151870\pi$
$150$	−8.12312	−	3.42288i	−0.663250	−	0.279477i
$151$		−	15.0204i		−	1.22235i	−0.791497	−	0.611173i	$-0.790698\pi$
$151$		−	15.0204i		−	1.22235i	0.791497	−	0.611173i	$-0.209302\pi$
$152$	9.17912	−	6.52131i	0.744525	−	0.528948i
$153$	2.71920	+	2.71920i	0.219835	+	0.219835i
$154$		0			0
$155$	−5.65292	+	6.77924i	−0.454054	+	0.544521i
$156$	10.2002	−	4.45519i	0.816666	−	0.356701i
$157$	−5.32326	+	5.32326i	−0.424842	+	0.424842i	−0.886867	−	0.462025i	$-0.847123\pi$
$157$	−5.32326	+	5.32326i	−0.424842	+	0.424842i	0.462025	+	0.886867i	$0.347123\pi$
$158$	−14.8087	+	3.09297i	−1.17812	+	0.246063i
$159$	−3.66425			−0.290594
$160$	−11.9482	+	4.15220i	−0.944587	+	0.328260i
$161$		0			0
$162$	−3.55944	+	0.743432i	−0.279656	+	0.0584095i
$163$	4.70155	−	4.70155i	0.368254	−	0.368254i	−0.498586	−	0.866840i	$-0.666147\pi$
$163$	4.70155	−	4.70155i	0.368254	−	0.368254i	0.866840	+	0.498586i	$0.166147\pi$
$164$	−6.80792	+	2.97354i	−0.531610	+	0.232195i
$165$	−0.239486	−	2.64342i	−0.0186439	−	0.205790i
$166$	−6.26946	+	9.57976i	−0.486605	+	0.743533i
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	0.439276	−	0.898352i	$-0.355235\pi$
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	−0.898352	+	0.439276i	$0.855235\pi$
$168$		0			0
$169$			6.93083i			0.533141i
$170$	−8.04362	+	2.45519i	−0.616918	+	0.188304i
$171$		−	5.75636i		−	0.440200i
$172$	9.01511	−	22.9975i	0.687395	−	1.75354i
$173$	1.56525	+	1.56525i	0.119004	+	0.119004i	0.764101	−	0.645097i	$-0.223183\pi$
$173$	1.56525	+	1.56525i	0.119004	+	0.119004i	−0.645097	+	0.764101i	$0.723183\pi$
$174$	−10.6664	−	6.98064i	−0.808621	−	0.529201i
$175$		0			0
$176$	−2.79414	−	2.58838i	−0.210616	−	0.195106i
$177$	−11.1082	+	11.1082i	−0.834941	+	0.834941i
$178$	0.612319	+	2.93169i	0.0458952	+	0.219740i
$179$	−16.4699			−1.23101			−0.615507	−	0.788131i	$-0.711049\pi$
$179$	−16.4699			−1.23101			−0.615507	+	0.788131i	$0.711049\pi$
$180$	−1.80724	+	6.20894i	−0.134704	+	0.462787i
$181$	5.97636			0.444219			0.222110	−	0.975022i	$-0.428706\pi$
$181$	5.97636			0.444219			0.222110	+	0.975022i	$0.428706\pi$
$182$		0			0
$183$	5.30976	−	5.30976i	0.392508	−	0.392508i
$184$	−0.258247	+	1.52553i	−0.0190382	+	0.112464i
$185$	2.31610	−	0.209831i	0.170283	−	0.0154271i
$186$	−5.82311	−	3.81093i	−0.426971	−	0.279431i
$187$	−1.79064	−	1.79064i	−0.130944	−	0.130944i
$188$	−5.97198	−	2.34104i	−0.435551	−	0.170738i
$189$		0			0
$190$	11.1126	+	5.91516i	0.806195	+	0.429131i
$191$		−	8.04630i		−	0.582210i	−0.956691	−	0.291105i	$-0.905977\pi$
$191$		−	8.04630i		−	0.582210i	0.956691	−	0.291105i	$-0.0940229\pi$
$192$	−4.33795	−	8.97996i	−0.313065	−	0.648073i
$193$	−10.2952	−	10.2952i	−0.741065	−	0.741065i	0.231718	−	0.972783i	$-0.425565\pi$
$193$	−10.2952	−	10.2952i	−0.741065	−	0.741065i	−0.972783	+	0.231718i	$0.925565\pi$
$194$	−3.37967	+	5.16415i	−0.242647	+	0.370765i
$195$	9.55764	+	7.96972i	0.684437	+	0.570723i
$196$		0			0
$197$	16.4919	−	16.4919i	1.17500	−	1.17500i	0.194001	−	0.981001i	$-0.437854\pi$
$197$	16.4919	−	16.4919i	1.17500	−	1.17500i	0.981001	−	0.194001i	$-0.0621465\pi$
$198$	−1.90604	+	0.398099i	−0.135456	+	0.0282917i
$199$	−9.65586			−0.684486			−0.342243	−	0.939611i	$-0.611187\pi$
$199$	−9.65586			−0.684486			−0.342243	+	0.939611i	$0.611187\pi$
$200$	−10.1292	−	9.86908i	−0.716244	−	0.697850i
$201$	18.5727			1.31002
$202$	−1.97981	+	0.413507i	−0.139299	+	0.0290943i
$203$		0			0
$204$	−2.65399	−	6.07630i	−0.185816	−	0.425426i
$205$	−6.37909	−	5.31926i	−0.445535	−	0.371513i
$206$	−7.88031	+	12.0411i	−0.549047	+	0.838946i
$207$	0.559318	+	0.559318i	0.0388753	+	0.0388753i
$208$	17.8446	−	0.682152i	1.23730	−	0.0472987i
$209$			3.79066i			0.262205i
$210$		0			0
$211$		−	10.4344i		−	0.718333i	−0.933274	−	0.359166i	$-0.883061\pi$
$211$		−	10.4344i		−	0.718333i	0.933274	−	0.359166i	$-0.116939\pi$
$212$	−5.47326	−	2.14554i	−0.375905	−	0.147356i
$213$	6.70553	+	6.70553i	0.459455	+	0.459455i
$214$	0.0475997	+	0.0311516i	0.00325385	+	0.00212948i
$215$	27.5043	−	2.49180i	1.87578	−	0.169939i
$216$	−15.4563	−	2.61649i	−1.05167	−	0.178029i
$217$		0			0
$218$	−1.81951	−	8.71155i	−0.123233	−	0.590020i
$219$	−18.3492			−1.23992
$220$	1.19009	−	4.08868i	0.0802362	−	0.275659i
$221$	11.8729			0.798660
$222$	0.374868	+	1.79481i	0.0251595	+	0.120460i
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	−0.249973	−	0.968253i	$-0.580422\pi$
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	0.968253	+	0.249973i	$0.0804218\pi$
$224$		0			0
$225$	−7.11217	+	1.29934i	−0.474145	+	0.0866230i
$226$	−18.1594	−	11.8844i	−1.20795	−	0.790539i
$227$	−7.08686	−	7.08686i	−0.470371	−	0.470371i	0.431663	−	0.902035i	$-0.357927\pi$
$227$	−7.08686	−	7.08686i	−0.470371	−	0.470371i	−0.902035	+	0.431663i	$0.857927\pi$
$228$	−3.62240	+	9.24071i	−0.239899	+	0.611981i
$229$		−	17.0883i		−	1.12923i	−0.825355	−	0.564614i	$-0.809025\pi$
$229$		−	17.0883i		−	1.12923i	0.825355	−	0.564614i	$-0.190975\pi$
$230$	−1.65451	+	0.505012i	−0.109095	+	0.0332995i
$231$		0			0
$232$	−11.8450	−	16.6725i	−0.777661	−	1.09460i
$233$	−1.32616	−	1.32616i	−0.0868794	−	0.0868794i	0.662331	−	0.749211i	$-0.269567\pi$
$233$	−1.32616	−	1.32616i	−0.0868794	−	0.0868794i	−0.749211	+	0.662331i	$0.769567\pi$
$234$	4.99925	−	7.63887i	0.326811	−	0.499368i
$235$	−0.647071	−	7.14231i	−0.0422102	−	0.465913i
$236$	−23.0964	+	10.0880i	−1.50345	+	0.656671i
$237$	9.42947	−	9.42947i	0.612510	−	0.612510i
$238$		0			0
$239$	−15.2182			−0.984385			−0.492193	−	0.870486i	$-0.663804\pi$
$239$	−15.2182			−0.984385			−0.492193	+	0.870486i	$0.663804\pi$
$240$	6.80836	−	8.82995i	0.439478	−	0.569971i
$241$	13.1756			0.848715			0.424357	−	0.905495i	$-0.360500\pi$
$241$	13.1756			0.848715			0.424357	+	0.905495i	$0.360500\pi$
$242$	−13.9726	+	2.91834i	−0.898192	+	0.187598i
$243$	−9.49067	+	9.49067i	−0.608827	+	0.608827i
$244$	11.0402	−	4.82210i	0.706775	−	0.308703i
$245$		0			0
$246$	3.58599	−	5.47940i	0.228634	−	0.349354i
$247$	−12.5671	−	12.5671i	−0.799625	−	0.799625i
$248$	−6.46650	−	9.10198i	−0.410623	−	0.577976i
$249$		−	10.0920i		−	0.639556i
$250$	4.79999	−	15.0652i	0.303578	−	0.952807i
$251$			14.7048i			0.928161i	0.885793	+	0.464080i	$0.153615\pi$
$251$			14.7048i			0.928161i	−0.885793	+	0.464080i	$0.846385\pi$
$252$		0			0
$253$	−0.368320	−	0.368320i	−0.0231561	−	0.0231561i
$254$	−2.04864	−	1.34073i	−0.128543	−	0.0841249i
$255$	4.74761	−	5.69355i	0.297307	−	0.356544i
$256$	−1.22149	−	15.9533i	−0.0763433	−	0.997082i
$257$	−9.34659	+	9.34659i	−0.583025	+	0.583025i	−0.935733	−	0.352709i	$-0.885261\pi$
$257$	−9.34659	+	9.34659i	−0.583025	+	0.583025i	0.352709	+	0.935733i	$0.385261\pi$
$258$	4.45165	+	21.3139i	0.277148	+	1.32694i
$259$		0			0
$260$	9.60963	+	17.5006i	0.595964	+	1.08534i
$261$	−10.4556			−0.647183
$262$	−0.377207	−	1.80601i	−0.0233039	−	0.111576i
$263$	−7.47296	+	7.47296i	−0.460803	+	0.460803i	−0.898919	−	0.438116i	$-0.855646\pi$
$263$	−7.47296	+	7.47296i	−0.460803	+	0.460803i	0.438116	+	0.898919i	$0.355646\pi$
$264$	3.31029	+	0.560375i	0.203734	+	0.0344887i
$265$	−0.593033	−	6.54585i	−0.0364298	−	0.402108i
$266$		0			0
$267$	−1.86676	−	1.86676i	−0.114244	−	0.114244i
$268$	27.7419	+	10.8750i	1.69461	+	0.664294i
$269$			12.1965i			0.743635i	0.928306	+	0.371818i	$0.121265\pi$
$269$			12.1965i			0.743635i	−0.928306	+	0.371818i	$0.878735\pi$
$270$	−5.11665	−	16.7630i	−0.311389	−	1.02017i
$271$		−	6.58193i		−	0.399824i	−0.979814	−	0.199912i	$-0.935934\pi$
$271$		−	6.58193i		−	0.399824i	0.979814	−	0.199912i	$-0.0640656\pi$
$272$	−0.406362	−	10.6301i	−0.0246393	−	0.644546i
$273$		0			0
$274$	−0.898253	+	1.37253i	−0.0542655	+	0.0829178i
$275$	4.68348	−	0.855639i	0.282424	−	0.0515970i
$276$	−0.545904	−	1.24985i	−0.0328595	−	0.0752318i
$277$	−2.90395	+	2.90395i	−0.174481	+	0.174481i	−0.788945	−	0.614464i	$-0.789372\pi$
$277$	−2.90395	+	2.90395i	−0.174481	+	0.174481i	0.614464	+	0.788945i	$0.289372\pi$
$278$	24.1585	−	5.04579i	1.44893	−	0.302626i
$279$	−5.70799			−0.341728
$280$		0			0
$281$	−32.2773			−1.92550			−0.962752	−	0.270386i	$-0.912849\pi$
$281$	−32.2773			−1.92550			−0.962752	+	0.270386i	$0.912849\pi$
$282$	5.53478	−	1.15600i	0.329591	−	0.0688390i
$283$	−13.8084	+	13.8084i	−0.820825	+	0.820825i	−0.986226	−	0.165401i	$-0.947108\pi$
$283$	−13.8084	+	13.8084i	−0.820825	+	0.820825i	0.165401	+	0.986226i	$0.447108\pi$
$284$	6.08968	+	13.9423i	0.361356	+	0.827324i
$285$	−11.0516	+	1.00124i	−0.654641	+	0.0593084i
$286$	−3.29208	+	5.03032i	−0.194665	+	0.297449i
$287$		0			0
$288$	−7.01036	−	4.21450i	−0.413090	−	0.248342i
$289$			9.92721i			0.583954i
$290$	10.7440	−	20.1844i	0.630909	−	1.18527i
$291$		−	5.44030i		−	0.318916i
$292$	−27.4080	−	10.7441i	−1.60393	−	0.628749i
$293$	−12.6859	−	12.6859i	−0.741121	−	0.741121i	0.231673	−	0.972794i	$-0.425580\pi$
$293$	−12.6859	−	12.6859i	−0.741121	−	0.741121i	−0.972794	+	0.231673i	$0.925580\pi$
$294$		0			0
$295$	−21.6415	−	18.0460i	−1.26002	−	1.05068i
$296$	−0.490987	+	2.90039i	−0.0285380	+	0.168582i
$297$	3.73172	−	3.73172i	0.216536	−	0.216536i
$298$	3.24148	+	15.5197i	0.187774	+	0.899034i
$299$	2.44216			0.141234
$300$	12.2348	+	2.38974i	0.706379	+	0.137972i
$301$		0			0
$302$	4.34295	+	20.7934i	0.249909	+	1.19653i
$303$	1.26065	−	1.26065i	0.0724225	−	0.0724225i
$304$	−10.8215	+	11.6817i	−0.620655	+	0.669993i
$305$	10.3448	+	8.62606i	0.592339	+	0.493927i
$306$	−4.55052	−	2.97809i	−0.260136	−	0.170246i
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	0.362387	−	0.932028i	$-0.381962\pi$
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	−0.932028	+	0.362387i	$0.881962\pi$
$308$		0			0
$309$		−	12.6850i		−	0.721626i
$310$	5.86545	−	11.0192i	0.333135	−	0.625851i
$311$		−	13.9385i		−	0.790380i	−0.918599	−	0.395190i	$-0.870679\pi$
$311$		−	13.9385i		−	0.790380i	0.918599	−	0.395190i	$-0.129321\pi$
$312$	−12.8323	+	9.11674i	−0.726488	+	0.516134i
$313$	−3.47072	−	3.47072i	−0.196176	−	0.196176i	0.602182	−	0.798359i	$-0.294298\pi$
$313$	−3.47072	−	3.47072i	−0.196176	−	0.196176i	−0.798359	+	0.602182i	$0.794298\pi$
$314$	5.83006	−	8.90835i	0.329009	−	0.502727i
$315$		0			0
$316$	19.6060	−	8.56345i	1.10292	−	0.481732i
$317$	24.3266	−	24.3266i	1.36632	−	1.36632i	0.500688	−	0.865628i	$-0.333080\pi$
$317$	24.3266	−	24.3266i	1.36632	−	1.36632i	0.865628	−	0.500688i	$-0.166920\pi$
$318$	5.07257	−	1.05947i	0.284456	−	0.0594119i
$319$	6.88516			0.385495
$320$	15.3398	−	9.20271i	0.857522	−	0.514447i
$321$	−0.0501451			−0.00279883
$322$		0			0
$323$	−7.48630	+	7.48630i	−0.416549	+	0.416549i
$324$	4.71253	−	2.05833i	0.261807	−	0.114351i
$325$	−12.6903	+	18.3637i	−0.703934	+	1.01864i
$326$	−5.14916	+	7.86793i	−0.285186	+	0.435764i
$327$	5.54710	+	5.54710i	0.306755	+	0.306755i
$328$	8.56473	−	6.08482i	0.472908	−	0.335978i
$329$		0			0
$330$	1.09584	+	3.59015i	0.0603239	+	0.197631i
$331$			12.9558i			0.712118i	0.934464	+	0.356059i	$0.115880\pi$
$331$			12.9558i			0.712118i	−0.934464	+	0.356059i	$0.884120\pi$
$332$	5.90922	−	15.0744i	0.324311	−	0.827314i
$333$	1.06339	+	1.06339i	0.0582736	+	0.0582736i
$334$	9.92804	+	6.49739i	0.543238	+	0.355522i
$335$	3.00587	+	33.1785i	0.164228	+	1.81274i
$336$		0			0
$337$	7.43071	−	7.43071i	0.404776	−	0.404776i	−0.475136	−	0.879912i	$-0.657601\pi$
$337$	7.43071	−	7.43071i	0.404776	−	0.404776i	0.879912	+	0.475136i	$0.157601\pi$
$338$	−2.00395	−	9.59464i	−0.109001	−	0.521879i
$339$	19.1305			1.03903
$340$	10.4252	−	5.72452i	0.565388	−	0.310456i
$341$	3.75880			0.203550
$342$	1.66437	+	7.96877i	0.0899989	+	0.430902i
$343$		0			0
$344$	−5.83059	+	34.4429i	−0.314364	+	1.85704i
$345$	0.976545	−	1.17112i	0.0525754	−	0.0630508i
$346$	−2.61942	−	1.71427i	−0.140821	−	0.0921599i
$347$	−6.47913	−	6.47913i	−0.347818	−	0.347818i	0.511478	−	0.859296i	$-0.329098\pi$
$347$	−6.47913	−	6.47913i	−0.347818	−	0.347818i	−0.859296	+	0.511478i	$0.829098\pi$
$348$	16.7843	+	6.57954i	0.899735	+	0.352700i
$349$		−	19.9513i		−	1.06797i	−0.845495	−	0.533984i	$-0.820694\pi$
$349$		−	19.9513i		−	1.06797i	0.845495	−	0.533984i	$-0.179306\pi$
$350$		0			0
$351$			24.7434i			1.32070i
$352$	4.61644	+	2.77531i	0.246057	+	0.147925i
$353$	−1.75275	−	1.75275i	−0.0932896	−	0.0932896i	0.658922	−	0.752211i	$-0.271013\pi$
$353$	−1.75275	−	1.75275i	−0.0932896	−	0.0932896i	−0.752211	+	0.658922i	$0.771013\pi$
$354$	12.1657	−	18.5893i	0.646601	−	0.988008i
$355$	−10.8936	+	13.0641i	−0.578171	+	0.693369i
$356$	−1.69532	−	3.88142i	−0.0898516	−	0.205715i
$357$		0			0
$358$	22.7999	−	4.76203i	1.20501	−	0.251681i
$359$	−15.8929			−0.838796			−0.419398	−	0.907803i	$-0.637759\pi$
$359$	−15.8929			−0.838796			−0.419398	+	0.907803i	$0.637759\pi$
$360$	0.706607	−	9.11782i	0.0372414	−	0.480551i
$361$	−3.15203			−0.165896
$362$	−8.27332	+	1.72798i	−0.434836	+	0.0908206i
$363$	8.89708	−	8.89708i	0.466976	−	0.466976i
$364$		0			0
$365$	−2.96969	−	32.7792i	−0.155441	−	1.71574i
$366$	−5.81527	+	8.88576i	−0.303969	+	0.464466i
$367$	7.61243	+	7.61243i	0.397366	+	0.397366i	0.877303	−	0.479937i	$-0.159341\pi$
$367$	7.61243	+	7.61243i	0.397366	+	0.397366i	−0.479937	+	0.877303i	$0.659341\pi$
$368$	−0.0835854	−	2.18653i	−0.00435719	−	0.113981i
$369$		−	5.37107i		−	0.279607i
$370$	−3.14560	+	0.960146i	−0.163532	+	0.0499156i
$371$		0			0
$372$	9.16305	+	3.59195i	0.475082	+	0.186234i
$373$	−10.4404	−	10.4404i	−0.540581	−	0.540581i	0.383118	−	0.923699i	$-0.374850\pi$
$373$	−10.4404	−	10.4404i	−0.540581	−	0.540581i	−0.923699	+	0.383118i	$0.874850\pi$
$374$	2.99659	+	1.96112i	0.154950	+	0.101407i
$375$	3.73167	+	13.4286i	0.192703	+	0.693450i
$376$	8.94413	+	1.51409i	0.461259	+	0.0780831i
$377$	−22.8262	+	22.8262i	−1.17561	+	1.17561i
$378$		0			0
$379$	26.4563			1.35897			0.679483	−	0.733691i	$-0.262204\pi$
$379$	26.4563			1.35897			0.679483	+	0.733691i	$0.262204\pi$
$380$	−17.0940	−	4.97554i	−0.876902	−	0.255240i
$381$	2.15819			0.110567
$382$	2.32647	+	11.1388i	0.119033	+	0.569912i
$383$	−20.7755	+	20.7755i	−1.06158	+	1.06158i	−0.0636047	+	0.997975i	$0.520260\pi$
$383$	−20.7755	+	20.7755i	−1.06158	+	1.06158i	−0.997975	+	0.0636047i	$0.979740\pi$
$384$	8.60163	+	11.1771i	0.438950	+	0.570377i
$385$		0			0
$386$	17.2288	+	11.2754i	0.876922	+	0.573901i
$387$	12.6281	+	12.6281i	0.641920	+	0.641920i
$388$	3.18548	−	8.12614i	0.161718	−	0.412542i
$389$		−	9.35264i		−	0.474198i	−0.971486	−	0.237099i	$-0.923803\pi$
$389$		−	9.35264i		−	0.474198i	0.971486	−	0.237099i	$-0.0761965\pi$
$390$	−15.5354	−	8.26935i	−0.786664	−	0.418735i
$391$		−	1.45481i		−	0.0735731i
$392$		0			0
$393$	1.14998	+	1.14998i	0.0580090	+	0.0580090i
$394$	−18.0621	+	27.5989i	−0.909954	+	1.39041i
$395$	18.3710	+	15.3188i	0.924345	+	0.770773i
$396$	2.52351	−	1.10221i	0.126811	−	0.0553881i
$397$	12.5650	−	12.5650i	0.630620	−	0.630620i	−0.317603	−	0.948224i	$-0.602878\pi$
$397$	12.5650	−	12.5650i	0.630620	−	0.630620i	0.948224	+	0.317603i	$0.102878\pi$
$398$	13.3670	−	2.79186i	0.670028	−	0.139943i
$399$		0			0
$400$	16.8758	+	10.7335i	0.843790	+	0.536673i
$401$	6.15342			0.307287			0.153644	−	0.988126i	$-0.450899\pi$
$401$	6.15342			0.307287			0.153644	+	0.988126i	$0.450899\pi$
$402$	−25.7110	+	5.37004i	−1.28235	+	0.267833i
$403$	−12.4615	+	12.4615i	−0.620750	+	0.620750i
$404$	2.62118	−	1.14487i	0.130408	−	0.0569594i
$405$	4.41569	+	3.68206i	0.219417	+	0.182963i
$406$		0			0
$407$	−0.700261	−	0.700261i	−0.0347107	−	0.0347107i
$408$	5.43090	+	7.64431i	0.268870	+	0.378450i
$409$		−	6.54619i		−	0.323688i	−0.986816	−	0.161844i	$-0.948256\pi$
$409$		−	6.54619i		−	0.323688i	0.986816	−	0.161844i	$-0.0517442\pi$
$410$	10.3688	+	5.51924i	0.512080	+	0.272576i
$411$		−	1.44593i		−	0.0713224i
$412$	7.42751	−	18.9475i	0.365927	−	0.933478i
$413$		0			0
$414$	−0.936005	−	0.612568i	−0.0460022	−	0.0301061i
$415$	18.0285	−	1.63333i	0.884985	−	0.0801768i
$416$	−24.5057	+	6.10383i	−1.20149	+	0.299265i
$417$	−15.3830	+	15.3830i	−0.753309	+	0.753309i
$418$	−1.09602	−	5.24756i	−0.0536079	−	0.256667i
$419$	−17.7908			−0.869139			−0.434569	−	0.900638i	$-0.643099\pi$
$419$	−17.7908			−0.869139			−0.434569	+	0.900638i	$0.643099\pi$
$420$		0			0
$421$	−16.4678			−0.802591			−0.401295	−	0.915949i	$-0.631440\pi$
$421$	−16.4678			−0.802591			−0.401295	+	0.915949i	$0.631440\pi$
$422$	3.01695	+	14.4447i	0.146863	+	0.703159i
$423$	3.27925	−	3.27925i	0.159443	−	0.159443i
$424$	8.19721	+	1.38764i	0.398092	+	0.0673900i
$425$	10.9394	+	7.55973i	0.530638	+	0.366701i
$426$	−11.2215	−	7.34393i	−0.543686	−	0.355815i
$427$		0			0
$428$	−0.0749013	−	0.0293616i	−0.00362049	−	0.00141925i
$429$		−	5.29931i		−	0.255853i
$430$	−37.3548	+	11.4020i	−1.80141	+	0.549852i
$431$			15.1329i			0.728925i	0.931218	+	0.364463i	$0.118747\pi$
$431$			15.1329i			0.728925i	−0.931218	+	0.364463i	$0.881253\pi$
$432$	22.1533	−	0.846865i	1.06585	−	0.0407448i
$433$	5.45382	+	5.45382i	0.262094	+	0.262094i	0.825904	−	0.563811i	$-0.190665\pi$
$433$	5.45382	+	5.45382i	0.262094	+	0.262094i	−0.563811	+	0.825904i	$0.690665\pi$
$434$		0			0
$435$	1.81860	+	20.0736i	0.0871953	+	0.962454i
$436$	5.03764	+	11.5337i	0.241259	+	0.552363i
$437$	−1.53987	+	1.53987i	−0.0736620	+	0.0736620i
$438$	25.4015	−	5.30541i	1.21373	−	0.253502i
$439$	−25.7463			−1.22880			−0.614402	−	0.788993i	$-0.710603\pi$
$439$	−25.7463			−1.22880			−0.614402	+	0.788993i	$0.710603\pi$
$440$	−0.465312	+	6.00423i	−0.0221829	+	0.286241i
$441$		0			0
$442$	−16.4362	+	3.43289i	−0.781790	+	0.163286i
$443$	−12.2254	+	12.2254i	−0.580847	+	0.580847i	−0.935136	−	0.354289i	$-0.884723\pi$
$443$	−12.2254	+	12.2254i	−0.580847	+	0.580847i	0.354289	+	0.935136i	$0.384723\pi$
$444$	−1.03789	−	2.37625i	−0.0492561	−	0.112772i
$445$	3.03268	−	3.63693i	0.143763	−	0.172407i
$446$	−11.7474	+	17.9500i	−0.556255	+	0.849959i
$447$	−9.88223	−	9.88223i	−0.467413	−	0.467413i
$448$		0			0
$449$			11.0999i			0.523839i	0.965090	+	0.261919i	$0.0843555\pi$
$449$			11.0999i			0.523839i	−0.965090	+	0.261919i	$0.915645\pi$
$450$	9.46998	−	3.85512i	0.446419	−	0.181732i
$451$			3.53694i			0.166548i
$452$	28.5750	+	11.2015i	1.34406	+	0.526876i
$453$	−13.2403	−	13.2403i	−0.622082	−	0.622082i
$454$	11.8597	+	7.76157i	0.556603	+	0.364268i
$455$		0			0
$456$	2.34281	−	13.8397i	0.109712	−	0.648101i
$457$	−15.0173	+	15.0173i	−0.702480	+	0.702480i	−0.964942	−	0.262462i	$-0.915466\pi$
$457$	−15.0173	+	15.0173i	−0.702480	+	0.702480i	0.262462	+	0.964942i	$0.415466\pi$
$458$	4.94084	+	23.6561i	0.230870	+	1.10537i
$459$	14.7398			0.687994
$460$	2.14439	−	1.17749i	0.0999825	−	0.0549006i
$461$	8.61652			0.401311			0.200656	−	0.979662i	$-0.435693\pi$
$461$	8.61652			0.401311			0.200656	+	0.979662i	$0.435693\pi$
$462$		0			0
$463$	1.63340	−	1.63340i	0.0759103	−	0.0759103i	−0.668132	−	0.744043i	$-0.732906\pi$
$463$	1.63340	−	1.63340i	0.0759103	−	0.0759103i	0.744043	+	0.668132i	$0.232906\pi$
$464$	21.2181	+	19.6556i	0.985026	+	0.912488i
$465$	0.992826	+	10.9587i	0.0460412	+	0.508199i
$466$	2.21929	+	1.45241i	0.102807	+	0.0672818i
$467$	−18.0176	−	18.0176i	−0.833754	−	0.833754i	0.154274	−	0.988028i	$-0.450696\pi$
$467$	−18.0176	−	18.0176i	−0.833754	−	0.833754i	−0.988028	+	0.154274i	$0.950696\pi$
$468$	−4.71199	+	12.0203i	−0.217812	+	0.555637i
$469$		0			0
$470$	2.96086	+	9.70030i	0.136574	+	0.447441i
$471$			9.38472i			0.432425i
$472$	29.0565	−	20.6432i	1.33743	−	0.950179i
$473$	−8.31578	−	8.31578i	−0.382360	−	0.382360i
$474$	−10.3272	+	15.7800i	−0.474344	+	0.724800i
$475$	−3.57726	−	19.5807i	−0.164136	−	0.898423i
$476$		0			0
$477$	3.00540	−	3.00540i	0.137608	−	0.137608i
$478$	21.0672	−	4.40014i	0.963592	−	0.201258i
$479$	9.27849			0.423945			0.211972	−	0.977276i	$-0.432011\pi$
$479$	9.27849			0.423945			0.211972	+	0.977276i	$0.432011\pi$
$480$	−6.87203	+	14.1922i	−0.313664	+	0.647783i
$481$	4.64312			0.211708
$482$	−18.2395	+	3.80954i	−0.830787	+	0.173520i
$483$		0			0
$484$	18.4990	−	8.07996i	0.840865	−	0.367271i
$485$	9.71861	−	0.880476i	0.441300	−	0.0399803i
$486$	10.3942	−	15.8824i	0.471492	−	0.720441i
$487$	12.5929	+	12.5929i	0.570638	+	0.570638i	0.932307	−	0.361669i	$-0.117793\pi$
$487$	12.5929	+	12.5929i	0.570638	+	0.570638i	−0.361669	+	0.932307i	$0.617793\pi$
$488$	−13.8891	+	9.86754i	−0.628732	+	0.446683i
$489$		−	8.28866i		−	0.374826i
$490$		0			0
$491$		−	2.49970i		−	0.112810i	−0.998408	−	0.0564049i	$-0.982036\pi$
$491$		−	2.49970i		−	0.112810i	0.998408	−	0.0564049i	$-0.0179638\pi$
$492$	−3.37994	+	8.62219i	−0.152379	+	0.388719i
$493$	13.5977	+	13.5977i	0.612411	+	0.612411i
$494$	21.0307	+	13.7635i	0.946217	+	0.619251i
$495$	2.36455	+	1.97170i	0.106279	+	0.0886213i
$496$	11.5836	+	10.7305i	0.520117	+	0.481816i
$497$		0			0
$498$	2.91797	+	13.9708i	0.130757	+	0.626047i
$499$	−6.52398			−0.292053			−0.146027	−	0.989281i	$-0.546649\pi$
$499$	−6.52398			−0.292053			−0.146027	+	0.989281i	$0.546649\pi$
$500$	−2.28894	+	22.2432i	−0.102364	+	0.994747i
$501$	−10.4589			−0.467271
$502$	−4.25169	−	20.3565i	−0.189762	−	0.908555i
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	−0.953313	−	0.301985i	$-0.902351\pi$
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	0.301985	+	0.953313i	$0.402351\pi$
$504$		0			0
$505$	2.45607	+	2.04801i	0.109294	+	0.0911353i
$506$	0.616375	+	0.403386i	0.0274012	+	0.0179327i
$507$	6.10941	+	6.10941i	0.271328	+	0.271328i
$508$	3.22367	+	1.26369i	0.143027	+	0.0560673i
$509$		−	34.4631i		−	1.52755i	−0.645482	−	0.763775i	$-0.723344\pi$
$509$		−	34.4631i		−	1.52755i	0.645482	−	0.763775i	$-0.276656\pi$
$510$	−4.92611	+	9.25452i	−0.218132	+	0.409797i
$511$		0			0
$512$	6.30364	+	21.7316i	0.278584	+	0.960412i
$513$	−15.6016	−	15.6016i	−0.688825	−	0.688825i
$514$	10.2364	−	15.6413i	0.451510	−	0.689909i
$515$	22.6607	−	2.05299i	0.998549	−	0.0904654i
$516$	−12.3252	−	28.2185i	−0.542587	−	1.24225i
$517$	−2.15944	+	2.15944i	−0.0949721	+	0.0949721i
$518$		0			0
$519$	2.75949			0.121128
$520$	−18.3631	−	21.4483i	−0.805274	−	0.940572i
$521$	33.9051			1.48541			0.742705	−	0.669619i	$-0.233543\pi$
$521$	33.9051			1.48541			0.742705	+	0.669619i	$0.233543\pi$
$522$	14.4741	−	3.02308i	0.633513	−	0.132317i
$523$	13.0488	−	13.0488i	0.570583	−	0.570583i	−0.361708	−	0.932291i	$-0.617806\pi$
$523$	13.0488	−	13.0488i	0.570583	−	0.570583i	0.932291	+	0.361708i	$0.117806\pi$
$524$	1.04437	+	2.39107i	0.0456233	+	0.104455i
$525$		0			0
$526$	8.18443	−	12.5058i	0.356858	−	0.545280i
$527$	7.42338	+	7.42338i	0.323368	+	0.323368i
$528$	−4.74460	+	0.181374i	−0.206482	+	0.00789328i
$529$			22.7008i			0.986989i
$530$	2.71360	+	8.89022i	0.117871	+	0.386167i
$531$		−	18.2217i		−	0.790756i
$532$		0			0
$533$	−11.7259	−	11.7259i	−0.507906	−	0.507906i
$534$	3.12398	+	2.04449i	0.135188	+	0.0884737i
$535$	−0.00811564	−	0.0895797i	−0.000350870	−	0.00387287i
$536$	−41.5486	−	7.03346i	−1.79463	−	0.303799i
$537$	−14.5179	+	14.5179i	−0.626493	+	0.626493i
$538$	−3.52645	−	16.8842i	−0.152036	−	0.727928i
$539$		0			0
$540$	11.9300	+	21.7263i	0.513385	+	0.934953i
$541$	3.18298			0.136847			0.0684236	−	0.997656i	$-0.478203\pi$
$541$	3.18298			0.136847			0.0684236	+	0.997656i	$0.478203\pi$
$542$	1.90307	+	9.11163i	0.0817439	+	0.391378i
$543$	5.26806	−	5.26806i	0.226074	−	0.226074i
$544$	3.63609	+	14.5982i	0.155896	+	0.625893i
$545$	−9.01164	+	10.8072i	−0.386016	+	0.462928i
$546$		0			0
$547$	−15.6791	−	15.6791i	−0.670391	−	0.670391i	0.287415	−	0.957806i	$-0.407204\pi$
$547$	−15.6791	−	15.6791i	−0.670391	−	0.670391i	−0.957806	+	0.287415i	$0.907204\pi$
$548$	0.846640	−	2.15977i	0.0361667	−	0.0922609i
$549$			8.71008i			0.371737i
$550$	−6.23613	+	2.53866i	−0.265910	+	0.108249i
$551$		−	28.7854i		−	1.22630i
$552$	1.11709	+	1.57237i	0.0475466	+	0.0669246i
$553$		0			0
$554$	3.18042	−	4.85969i	0.135123	−	0.206469i
$555$	1.85664	−	2.22656i	0.0788099	−	0.0945124i
$556$	−31.9847	+	13.9702i	−1.35645	+	0.592468i
$557$	15.0928	−	15.0928i	0.639501	−	0.639501i	−0.310931	−	0.950432i	$-0.600641\pi$
$557$	15.0928	−	15.0928i	0.639501	−	0.639501i	0.950432	+	0.310931i	$0.100641\pi$
$558$	7.90180	−	1.65038i	0.334510	−	0.0698663i
$559$	55.1382			2.33210
$560$		0			0
$561$	−3.15683			−0.133282
$562$	44.6828	−	9.33253i	1.88483	−	0.393669i
$563$	9.62553	−	9.62553i	0.405668	−	0.405668i	−0.474557	−	0.880225i	$-0.657392\pi$
$563$	9.62553	−	9.62553i	0.405668	−	0.405668i	0.880225	+	0.474557i	$0.157392\pi$
$564$	−7.32778	+	3.20061i	−0.308555	+	0.134770i
$565$	3.09614	+	34.1749i	0.130255	+	1.43775i
$566$	15.1231	−	23.1081i	0.635669	−	0.971305i
$567$		0			0
$568$	−12.4614	−	17.5402i	−0.522869	−	0.735969i
$569$		−	23.4891i		−	0.984713i	−0.870394	−	0.492357i	$-0.836136\pi$
$569$		−	23.4891i		−	0.984713i	0.870394	−	0.492357i	$-0.163864\pi$
$570$	15.0097	−	4.58148i	0.628687	−	0.191897i
$571$		−	27.1159i		−	1.13476i	−0.823455	−	0.567382i	$-0.807956\pi$
$571$		−	27.1159i		−	1.13476i	0.823455	−	0.567382i	$-0.192044\pi$
$572$	3.10292	−	7.91553i	0.129740	−	0.330965i
$573$	−7.09267	−	7.09267i	−0.296301	−	0.296301i
$574$		0			0
$575$	2.25014	+	1.55497i	0.0938374	+	0.0648469i
$576$	10.9233	+	3.80736i	0.455137	+	0.158640i
$577$	−19.7304	+	19.7304i	−0.821388	+	0.821388i	−0.986307	−	0.164919i	$-0.947264\pi$
$577$	−19.7304	+	19.7304i	−0.821388	+	0.821388i	0.164919	+	0.986307i	$0.447264\pi$
$578$	−2.87031	−	13.7427i	−0.119389	−	0.571619i
$579$	−18.1501			−0.754292
$580$	−9.03732	+	31.0486i	−0.375254	+	1.28922i
$581$		0			0
$582$	1.57299	+	7.53124i	0.0652024	+	0.312180i
$583$	−1.97910	+	1.97910i	−0.0819661	+	0.0819661i
$584$	41.0485	+	6.94881i	1.69860	+	0.287544i
$585$	−14.3759	+	1.30241i	−0.594369	+	0.0538480i
$586$	21.2296	+	13.8937i	0.876988	+	0.573944i
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	0.998423	−	0.0561427i	$-0.0178802\pi$
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	−0.0561427	+	0.998423i	$0.517880\pi$
$588$		0			0
$589$		−	15.7148i		−	0.647516i
$590$	35.1770	+	18.7244i	1.44821	+	0.770872i
$591$		−	29.0747i		−	1.19597i
$592$	−0.158915	−	4.15710i	−0.00653138	−	0.170856i
$593$	−27.0033	−	27.0033i	−1.10889	−	1.10889i	−0.993296	−	0.115598i	$-0.963122\pi$
$593$	−27.0033	−	27.0033i	−1.10889	−	1.10889i	−0.115598	−	0.993296i	$-0.536878\pi$
$594$	−4.08700	+	6.24494i	−0.167691	+	0.256233i
$595$		0			0
$596$	−8.97462	−	20.5474i	−0.367615	−	0.841653i
$597$	−8.51148	+	8.51148i	−0.348352	+	0.348352i
$598$	−3.38079	+	0.706117i	−0.138251	+	0.0288753i
$599$	28.9601			1.18328			0.591640	−	0.806202i	$-0.298481\pi$
$599$	28.9601			1.18328			0.591640	+	0.806202i	$0.298481\pi$
$600$	−17.6282	+	0.229311i	−0.719667	+	0.00936158i
$601$	8.88262			0.362330			0.181165	−	0.983453i	$-0.442013\pi$
$601$	8.88262			0.362330			0.181165	+	0.983453i	$0.442013\pi$
$602$		0			0
$603$	−15.2333	+	15.2333i	−0.620347	+	0.620347i
$604$	−12.0242	−	27.5295i	−0.489260	−	1.12016i
$605$	17.3338	+	14.4539i	0.704718	+	0.587635i
$606$	−1.38067	+	2.10967i	−0.0560859	+	0.0856994i
$607$	32.4817	+	32.4817i	1.31839	+	1.31839i	0.915048	+	0.403344i	$0.132152\pi$
$607$	32.4817	+	32.4817i	1.31839	+	1.31839i	0.403344	+	0.915048i	$0.367848\pi$
$608$	11.6030	−	19.3004i	0.470565	−	0.782734i
$609$		0			0
$610$	−16.8148	−	8.95037i	−0.680810	−	0.362390i
$611$		−	14.3183i		−	0.579256i
$612$	7.16055	+	2.80697i	0.289448	+	0.113465i
$613$	0.163936	+	0.163936i	0.00662131	+	0.00662131i	0.710410	−	0.703788i	$-0.248510\pi$
$613$	0.163936	+	0.163936i	0.00662131	+	0.00662131i	−0.703788	+	0.710410i	$0.748510\pi$
$614$	16.7028	+	10.9311i	0.674071	+	0.441145i
$615$	−10.3119	+	0.934224i	−0.415815	+	0.0376716i
$616$		0			0
$617$	−27.1038	+	27.1038i	−1.09116	+	1.09116i	−0.0957517	+	0.995405i	$0.530525\pi$
$617$	−27.1038	+	27.1038i	−1.09116	+	1.09116i	−0.995405	+	0.0957517i	$0.969475\pi$
$618$	3.66770	+	17.5604i	0.147536	+	0.706383i
$619$	14.2994			0.574742			0.287371	−	0.957819i	$-0.407219\pi$
$619$	14.2994			0.574742			0.287371	+	0.957819i	$0.407219\pi$
$620$	−4.93373	+	16.9503i	−0.198143	+	0.680740i
$621$	3.03185			0.121664
$622$	4.03012	+	19.2957i	0.161593	+	0.773685i
$623$		0			0
$624$	15.1284	−	16.3310i	0.605619	−	0.653762i
$625$	−23.3851	+	8.83962i	−0.935402	+	0.353585i
$626$	5.80816	+	3.80115i	0.232141	+	0.151924i
$627$	3.34140	+	3.34140i	0.133443	+	0.133443i
$628$	−5.49507	+	14.0179i	−0.219277	+	0.559374i
$629$		−	2.76594i		−	0.110285i
$630$		0			0
$631$			30.7128i			1.22266i	0.791377	+	0.611328i	$0.209364\pi$
$631$			30.7128i			1.22266i	−0.791377	+	0.611328i	$0.790636\pi$
$632$	−24.6654	+	17.5235i	−0.981136	+	0.697049i
$633$	−9.19773	−	9.19773i	−0.365577	−	0.365577i
$634$	−26.6426	+	40.7099i	−1.05811	+	1.61680i
$635$	0.349288	+	3.85541i	0.0138611	+	0.152997i
$636$	−6.71584	+	2.93332i	−0.266300	+	0.116314i
$637$		0			0
$638$	−9.53141	+	1.99075i	−0.377352	+	0.0788144i
$639$	−10.9997			−0.435141
$640$	−18.5747	+	17.1750i	−0.734230	+	0.678901i
$641$	41.5504			1.64114			0.820572	−	0.571543i	$-0.193655\pi$
$641$	41.5504			1.64114			0.820572	+	0.571543i	$0.193655\pi$
$642$	0.0694179	−	0.0144987i	0.00273971	−	0.000572220i
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	−0.910090	−	0.414410i	$-0.863988\pi$
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	0.414410	+	0.910090i	$0.363988\pi$
$644$		0			0
$645$	22.0481	−	26.4410i	0.868142	−	1.04111i
$646$	8.19903	−	12.5281i	0.322587	−	0.492913i
$647$	−25.1918	−	25.1918i	−0.990392	−	0.990392i	0.00956185	−	0.999954i	$-0.496956\pi$
$647$	−25.1918	−	25.1918i	−0.990392	−	0.990392i	−0.999954	+	0.00956185i	$0.996956\pi$
$648$	−5.92862	+	4.21199i	−0.232898	+	0.165463i
$649$			11.9993i			0.471014i
$650$	12.2582	−	29.0909i	0.480805	−	1.14104i
$651$		0			0
$652$	4.85329	−	12.3807i	0.190070	−	0.484866i
$653$	9.30669	+	9.30669i	0.364199	+	0.364199i	0.865356	−	0.501157i	$-0.167092\pi$
$653$	9.30669	+	9.30669i	0.364199	+	0.364199i	−0.501157	+	0.865356i	$0.667092\pi$
$654$	−9.28294	−	6.07521i	−0.362992	−	0.237560i
$655$	−1.86822	+	2.24046i	−0.0729976	+	0.0875420i
$656$	−10.0972	+	10.8998i	−0.394228	+	0.425567i
$657$	15.0499	−	15.0499i	0.587153	−	0.587153i
$658$		0			0
$659$	10.3786			0.404294			0.202147	−	0.979355i	$-0.435208\pi$
$659$	10.3786			0.404294			0.202147	+	0.979355i	$0.435208\pi$
$660$	−2.55506	−	4.65315i	−0.0994554	−	0.181124i
$661$	−23.0565			−0.896793			−0.448397	−	0.893835i	$-0.648005\pi$
$661$	−23.0565			−0.896793			−0.448397	+	0.893835i	$0.648005\pi$
$662$	−3.74600	−	17.9353i	−0.145592	−	0.697076i
$663$	10.4658	−	10.4658i	0.406457	−	0.406457i
$664$	−3.82184	+	22.5767i	−0.148316	+	0.876144i
$665$		0			0
$666$	−1.77956	−	1.16463i	−0.0689567	−	0.0451286i
$667$	2.79694	+	2.79694i	0.108298	+	0.108298i
$668$	−15.6224	−	6.12406i	−0.604450	−	0.236947i
$669$		−	18.9099i		−	0.731100i
$670$	−13.7542	−	45.0613i	−0.531373	−	1.74087i
$671$		−	5.73573i		−	0.221425i
$672$		0			0
$673$	27.9624	+	27.9624i	1.07787	+	1.07787i	0.996700	+	0.0811716i	$0.0258662\pi$
$673$	27.9624	+	27.9624i	1.07787	+	1.07787i	0.0811716	+	0.996700i	$0.474134\pi$
$674$	−8.13815	+	12.4351i	−0.313470	+	0.478983i
$675$	−15.7546	+	22.7978i	−0.606394	+	0.877489i
$676$	5.54831	+	12.7028i	0.213396	+	0.488571i
$677$	24.2096	−	24.2096i	0.930450	−	0.930450i	−0.0672842	−	0.997734i	$-0.521433\pi$
$677$	24.2096	−	24.2096i	0.930450	−	0.930450i	0.997734	+	0.0672842i	$0.0214334\pi$
$678$	−26.4831	+	5.53131i	−1.01708	+	0.212429i
$679$		0			0
$680$	−12.7769	+	10.9390i	−0.489973	+	0.419492i
$681$	−12.4939			−0.478767
$682$	−5.20346	+	1.08680i	−0.199251	+	0.0416159i
$683$	1.36263	−	1.36263i	0.0521395	−	0.0521395i	−0.680556	−	0.732696i	$-0.738262\pi$
$683$	1.36263	−	1.36263i	0.0521395	−	0.0521395i	0.732696	+	0.680556i	$0.238262\pi$
$684$	−4.60812	−	10.5503i	−0.176196	−	0.403400i
$685$	2.58302	−	0.234014i	0.0986922	−	0.00894120i
$686$		0			0
$687$	−15.0630	−	15.0630i	−0.574691	−	0.574691i
$688$	−1.88716	−	49.3666i	−0.0719473	−	1.88208i
$689$		−	13.1226i		−	0.499930i
$690$	−1.01326	+	1.90358i	−0.0385741	+	0.0724680i
$691$		−	35.6585i		−	1.35651i	−0.734824	−	0.678257i	$-0.762735\pi$
$691$		−	35.6585i		−	1.35651i	0.734824	−	0.678257i	$-0.237265\pi$
$692$	4.12182	+	1.61577i	0.156688	+	0.0614225i
$693$		0			0
$694$	10.8427	+	7.09598i	0.411582	+	0.269360i
$695$	−29.9700	−	24.9907i	−1.13683	−	0.947952i
$696$	−25.1376	−	4.25537i	−0.952840	−	0.161299i
$697$	−6.98521	+	6.98521i	−0.264584	+	0.264584i
$698$	5.76863	+	27.6194i	0.218346	+	1.04541i
$699$	−2.33797			−0.0884301
$700$		0			0
$701$	33.6504			1.27096			0.635479	−	0.772119i	$-0.280803\pi$
$701$	33.6504			1.27096			0.635479	+	0.772119i	$0.280803\pi$
$702$	−7.15419	−	34.2532i	−0.270018	−	1.29281i
$703$	−2.92765	+	2.92765i	−0.110418	+	0.110418i
$704$	−7.19317	−	2.50720i	−0.271103	−	0.0944938i
$705$	−6.86620	−	5.72544i	−0.258596	−	0.215632i
$706$	2.93319	+	1.91962i	0.110392	+	0.0722460i
$707$		0			0
$708$	−11.4667	+	29.2514i	−0.430944	+	1.09934i
$709$		−	9.15581i		−	0.343854i	−0.985110	−	0.171927i	$-0.945001\pi$
$709$		−	9.15581i		−	0.343854i	0.985110	−	0.171927i	$-0.0549993\pi$
$710$	11.3031	−	21.2349i	0.424199	−	0.796930i
$711$			15.4680i			0.580096i
$712$	3.46915	+	4.88303i	0.130012	+	0.182999i
$713$	1.52693	+	1.52693i	0.0571839	+	0.0571839i
$714$		0			0
$715$	9.46674	−	0.857657i	0.354036	−	0.0320745i
$716$	−30.1860	+	13.1845i	−1.12810	+	0.492729i
$717$	−13.4146	+	13.4146i	−0.500978	+	0.500978i
$718$	22.0012	−	4.59521i	0.821078	−	0.171492i
$719$	−13.3464			−0.497738			−0.248869	−	0.968537i	$-0.580059\pi$
$719$	−13.3464			−0.497738			−0.248869	+	0.968537i	$0.580059\pi$
$720$	1.65811	+	12.8265i	0.0617939	+	0.478015i
$721$		0			0
$722$	4.36348	−	0.911364i	0.162392	−	0.0339175i
$723$	11.6141	−	11.6141i	0.431931	−	0.431931i
$724$	10.9535	−	4.78423i	0.407083	−	0.177804i
$725$	−35.5653	+	6.49754i	−1.32086	+	0.241313i
$726$	−9.74413	+	14.8891i	−0.361639	+	0.552585i
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	0.583602	−	0.812040i	$-0.301643\pi$
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	−0.812040	+	0.583602i	$0.801643\pi$
$728$		0			0
$729$			24.4454i			0.905384i
$730$	13.5887	+	44.5189i	0.502940	+	1.64772i
$731$		−	32.8462i		−	1.21486i
$732$	5.48113	−	13.9823i	0.202588	−	0.516801i
$733$	−7.26358	−	7.26358i	−0.268286	−	0.268286i	0.560123	−	0.828409i	$-0.310754\pi$
$733$	−7.26358	−	7.26358i	−0.268286	−	0.268286i	−0.828409	+	0.560123i	$0.810754\pi$
$734$	−12.7392	−	8.33717i	−0.470213	−	0.307731i
$735$		0			0
$736$	0.747914	+	3.00273i	0.0275685	+	0.110682i
$737$	10.0314	−	10.0314i	0.369510	−	0.369510i
$738$	1.55297	+	7.43539i	0.0571656	+	0.273701i
$739$	−43.7166			−1.60814			−0.804070	−	0.594535i	$-0.797336\pi$
$739$	−43.7166			−1.60814			−0.804070	+	0.594535i	$0.797336\pi$
$740$	4.07697	−	2.23868i	0.149873	−	0.0822954i
$741$	−22.1553			−0.813897
$742$		0			0
$743$	26.0186	−	26.0186i	0.954529	−	0.954529i	−0.0444813	−	0.999010i	$-0.514164\pi$
$743$	26.0186	−	26.0186i	0.954529	−	0.954529i	0.999010	+	0.0444813i	$0.0141635\pi$
$744$	−13.7233	−	2.32313i	−0.503122	−	0.0851699i
$745$	16.0543	−	19.2531i	0.588186	−	0.705378i
$746$	17.4717	+	11.4343i	0.639685	+	0.418641i
$747$	8.27744	+	8.27744i	0.302856	+	0.302856i
$748$	−4.71534	−	1.84843i	−0.172410	−	0.0675854i
$749$		0			0
$750$	−9.04860	−	17.5108i	−0.330408	−	0.639405i
$751$		−	8.43462i		−	0.307784i	−0.988088	−	0.153892i	$-0.950819\pi$
$751$		−	8.43462i		−	0.307784i	0.988088	−	0.153892i	$-0.0491807\pi$
$752$	−12.8195	+	0.490057i	−0.467479	+	0.0178705i
$753$	12.9620	+	12.9620i	0.472363	+	0.472363i
$754$	24.9994	−	38.1991i	0.910424	−	1.39113i
$755$	21.5097	−	25.7954i	0.782818	−	0.938790i
$756$		0			0
$757$	3.33081	−	3.33081i	0.121060	−	0.121060i	−0.643981	−	0.765041i	$-0.722718\pi$
$757$	3.33081	−	3.33081i	0.121060	−	0.121060i	0.765041	+	0.643981i	$0.222718\pi$
$758$	−36.6245	+	7.64945i	−1.33026	+	0.277841i
$759$	−0.649335			−0.0235694
$760$	25.1025	+	1.94537i	0.910563	+	0.0705661i
$761$	34.4634			1.24930			0.624649	−	0.780906i	$-0.285242\pi$
$761$	34.4634			1.24930			0.624649	+	0.780906i	$0.285242\pi$
$762$	−2.98767	+	0.624010i	−0.108232	+	0.0226055i
$763$		0			0
$764$	−6.44127	−	14.7473i	−0.233037	−	0.533537i
$765$	0.775853	+	8.56380i	0.0280510	+	0.309625i
$766$	22.7535	−	34.7674i	0.822116	−	1.25620i
$767$	−39.7811	−	39.7811i	−1.43641	−	1.43641i
$768$	−15.1393	−	12.9858i	−0.546292	−	0.468586i
$769$			18.7498i			0.676135i	0.941122	+	0.338067i	$0.109773\pi$
$769$			18.7498i			0.676135i	−0.941122	+	0.338067i	$0.890227\pi$
$770$		0			0
$771$			16.4777i			0.593431i
$772$	−27.1106	−	10.6275i	−0.975733	−	0.382492i
$773$	−31.4391	−	31.4391i	−1.13079	−	1.13079i	−0.990047	−	0.140739i	$-0.955052\pi$
$773$	−31.4391	−	31.4391i	−1.13079	−	1.13079i	−0.140739	−	0.990047i	$-0.544948\pi$
$774$	−21.1328	−	13.8303i	−0.759602	−	0.497121i
$775$	−19.4161	+	3.54719i	−0.697447	+	0.127419i
$776$	−2.06023	+	12.1704i	−0.0739581	+	0.436891i
$777$		0			0
$778$	2.70418	+	12.9472i	0.0969497	+	0.464181i
$779$	14.7872			0.529807
$780$	23.8972	+	6.95577i	0.855657	+	0.249057i
$781$	7.24348			0.259192
$782$	0.420639	+	2.01396i	0.0150420	+	0.0720190i
$783$	−28.3379	+	28.3379i	−1.01271	+	1.01271i
$784$		0			0
$785$	−16.7650	+	1.51885i	−0.598367	+	0.0542102i
$786$	−1.92447	−	1.25947i	−0.0686436	−	0.0449237i
$787$	0.763475	+	0.763475i	0.0272149	+	0.0272149i	0.720583	−	0.693368i	$-0.243874\pi$
$787$	0.763475	+	0.763475i	0.0272149	+	0.0272149i	−0.693368	+	0.720583i	$0.743874\pi$
$788$	17.0242	−	43.4287i	0.606463	−	1.54708i
$789$			13.1746i			0.469027i
$790$	−29.8610	−	15.8947i	−1.06240	−	0.565510i
$791$		0			0
$792$	−3.17471	+	2.25547i	−0.112808	+	0.0801447i
$793$	19.0155	+	19.0155i	0.675262	+	0.675262i
$794$	−13.7613	+	21.0273i	−0.488369	+	0.746230i
$795$	−6.29280	−	5.24730i	−0.223183	−	0.186103i
$796$	−17.6973	+	7.72976i	−0.627263	+	0.273974i
$797$	13.9414	−	13.9414i	0.493829	−	0.493829i	−0.415681	−	0.909510i	$-0.636457\pi$
$797$	13.9414	−	13.9414i	0.493829	−	0.493829i	0.909510	+	0.415681i	$0.136457\pi$
$798$		0			0
$799$	−8.52950			−0.301752
$800$	−26.4653	−	9.97936i	−0.935690	−	0.352824i
$801$	3.06222			0.108198
$802$	−8.51843	+	1.77917i	−0.300796	+	0.0628248i
$803$	−9.91062	+	9.91062i	−0.349738	+	0.349738i
$804$	34.0401	−	14.8679i	1.20050	−	0.524352i
$805$		0			0
$806$	13.6479	−	20.8540i	0.480726	−	0.734550i
$807$	10.7510	+	10.7510i	0.378454	+	0.378454i
$808$	−3.29758	+	2.34277i	−0.116008	+	0.0824182i
$809$		−	5.05111i		−	0.177587i	−0.996050	−	0.0887937i	$-0.971699\pi$
$809$		−	5.05111i		−	0.177587i	0.996050	−	0.0887937i	$-0.0283012\pi$
$810$	−7.17743	−	3.82049i	−0.252189	−	0.134238i
$811$			21.1629i			0.743131i	0.928407	+	0.371565i	$0.121179\pi$
$811$			21.1629i			0.743131i	−0.928407	+	0.371565i	$0.878821\pi$
$812$		0			0
$813$	−5.80185	−	5.80185i	−0.203480	−	0.203480i
$814$	1.17187	+	0.766930i	0.0410741	+	0.0268809i
$815$	14.8070	−	1.34146i	0.518665	−	0.0469894i
$816$	−9.72847	−	9.01206i	−0.340564	−	0.315485i
$817$	−34.7666	+	34.7666i	−1.21633	+	1.21633i
$818$	1.89274	+	9.06216i	0.0661781	+	0.316851i
$819$		0			0
$820$	−15.9498	−	4.64251i	−0.556991	−	0.162124i
$821$	42.7241			1.49108			0.745540	−	0.666461i	$-0.232192\pi$
$821$	42.7241			1.49108			0.745540	+	0.666461i	$0.232192\pi$
$822$	0.418070	+	2.00166i	0.0145819	+	0.0698159i
$823$	−3.37587	+	3.37587i	−0.117675	+	0.117675i	−0.763492	−	0.645817i	$-0.776517\pi$
$823$	−3.37587	+	3.37587i	−0.117675	+	0.117675i	0.645817	+	0.763492i	$0.276517\pi$
$824$	−4.80380	+	28.3774i	−0.167348	+	0.988574i
$825$	3.37417	−	4.88263i	0.117474	−	0.169992i
$826$		0			0
$827$	−6.21884	−	6.21884i	−0.216250	−	0.216250i	0.590666	−	0.806916i	$-0.298865\pi$
$827$	−6.21884	−	6.21884i	−0.216250	−	0.216250i	−0.806916	+	0.590666i	$0.798865\pi$
$828$	1.47287	+	0.577370i	0.0511856	+	0.0200650i
$829$		−	38.9224i		−	1.35183i	−0.736980	−	0.675915i	$-0.763749\pi$
$829$		−	38.9224i		−	1.35183i	0.736980	−	0.675915i	$-0.236251\pi$
$830$	−24.4853	+	7.47377i	−0.849899	+	0.259418i
$831$			5.11956i			0.177596i
$832$	32.1594	−	15.5353i	1.11493	−	0.538588i
$833$		0			0
$834$	16.8475	−	25.7431i	0.583383	−	0.891410i
$835$	−1.69271	−	18.6839i	−0.0585785	−	0.646585i
$836$	3.03452	+	6.94752i	0.104951	+	0.240285i
$837$	−15.4704	+	15.4704i	−0.534736	+	0.534736i
$838$	24.6286	−	5.14397i	0.850780	−	0.177695i
$839$	15.0742			0.520418			0.260209	−	0.965552i	$-0.416209\pi$
$839$	15.0742			0.520418			0.260209	+	0.965552i	$0.416209\pi$
$840$		0			0
$841$	−23.2844			−0.802910
$842$	22.7970	−	4.76143i	0.785638	−	0.164090i
$843$	−28.4519	+	28.4519i	−0.979936	+	0.979936i
$844$	−8.35299	−	19.1241i	−0.287522	−	0.658280i
$845$	−9.92514	+	11.9027i	−0.341435	+	0.409464i
$846$	−3.59146	+	5.48776i	−0.123477	+	0.188673i
$847$		0			0
$848$	−11.7489	+	0.449132i	−0.403461	+	0.0154233i
$849$			24.3438i			0.835476i
$850$	−17.3296	−	7.30227i	−0.594401	−	0.250466i
$851$		−	0.568931i		−	0.0195027i
$852$	17.6578	+	6.92195i	0.604948	+	0.237142i
$853$	14.0097	+	14.0097i	0.479684	+	0.479684i	0.905031	−	0.425346i	$-0.139848\pi$
$853$	14.0097	+	14.0097i	0.479684	+	0.479684i	−0.425346	+	0.905031i	$0.639848\pi$
$854$		0			0
$855$	8.24327	−	9.88570i	0.281914	−	0.338084i
$856$	0.112178	+	0.0189899i	0.00383418	+	0.000649060i
$857$	25.2063	−	25.2063i	0.861031	−	0.861031i	−0.130427	−	0.991458i	$-0.541635\pi$
$857$	25.2063	−	25.2063i	0.861031	−	0.861031i	0.991458	+	0.130427i	$0.0416349\pi$
$858$	1.53222	+	7.33605i	0.0523091	+	0.250449i
$859$	52.4008			1.78789			0.893947	−	0.448173i	$-0.147925\pi$
$859$	52.4008			1.78789			0.893947	+	0.448173i	$0.147925\pi$
$860$	48.4151	−	26.5848i	1.65094	−	0.906536i
$861$		0			0
$862$	−4.37546	−	20.9491i	−0.149029	−	0.713528i
$863$	−3.73158	+	3.73158i	−0.127024	+	0.127024i	−0.767761	−	0.640737i	$-0.778629\pi$
$863$	−3.73158	+	3.73158i	−0.127024	+	0.127024i	0.640737	+	0.767761i	$0.278629\pi$
$864$	−30.4229	+	7.57767i	−1.03501	+	0.257798i
$865$	0.446604	+	4.92958i	0.0151850	+	0.167611i
$866$	−9.12684	−	5.97305i	−0.310142	−	0.202972i
$867$	8.75067	+	8.75067i	0.297188	+	0.297188i
$868$		0			0
$869$		−	10.1859i		−	0.345535i
$870$	−8.32156	−	27.2629i	−0.282127	−	0.924297i
$871$			66.5135i			2.25372i
$872$	−10.3086	−	14.5100i	−0.349094	−	0.491370i
$873$	4.46212	+	4.46212i	0.151020	+	0.151020i
$874$	1.68647	−	2.57694i	0.0570458	−	0.0871662i
$875$		0			0
$876$	−33.6304	+	14.6890i	−1.13627	+	0.496295i
$877$	−7.89577	+	7.89577i	−0.266621	+	0.266621i	−0.827737	−	0.561116i	$-0.810372\pi$
$877$	−7.89577	+	7.89577i	−0.266621	+	0.266621i	0.561116	+	0.827737i	$0.310372\pi$
$878$	35.6417	−	7.44419i	1.20285	−	0.251229i
$879$	−22.3649			−0.754348
$880$	−1.09189	−	8.44644i	−0.0368076	−	0.284730i
$881$	−22.0701			−0.743561			−0.371781	−	0.928321i	$-0.621253\pi$
$881$	−22.0701			−0.743561			−0.371781	+	0.928321i	$0.621253\pi$
$882$		0			0
$883$	5.32169	−	5.32169i	0.179089	−	0.179089i	−0.611869	−	0.790959i	$-0.709582\pi$
$883$	5.32169	−	5.32169i	0.179089	−	0.179089i	0.790959	+	0.611869i	$0.209582\pi$
$884$	21.7607	−	9.50458i	0.731892	−	0.319674i
$885$	−34.9838	+	3.16942i	−1.17597	+	0.106539i
$886$	13.3893	−	20.4590i	0.449824	−	0.687332i
$887$	−3.58114	−	3.58114i	−0.120243	−	0.120243i	0.644425	−	0.764668i	$-0.277097\pi$
$887$	−3.58114	−	3.58114i	−0.120243	−	0.120243i	−0.764668	+	0.644425i	$0.777097\pi$
$888$	2.12385	+	2.98944i	0.0712718	+	0.100319i
$889$		0			0
$890$	−3.14670	+	5.91161i	−0.105478	+	0.198157i
$891$		−	2.44831i		−	0.0820216i
$892$	11.0724	−	28.2456i	0.370731	−	0.945732i
$893$	9.02818	+	9.02818i	0.302117	+	0.302117i
$894$	16.5377	+	10.8231i	0.553103	+	0.361978i
$895$	−28.2845	−	23.5853i	−0.945448	−	0.788369i
$896$		0			0
$897$	2.15273	−	2.15273i	0.0718774	−	0.0718774i
$898$	−3.20939	−	15.3661i	−0.107099	−	0.512774i
$899$	−28.5435			−0.951980
$900$	−11.9950	+	8.07491i	−0.399834	+	0.269164i
$901$	−7.81720			−0.260429
$902$	−1.02265	−	4.89633i	−0.0340507	−	0.163030i
$903$		0			0
$904$	−42.7964	−	7.24469i	−1.42339	−	0.240955i
$905$	10.2635	+	8.55831i	0.341171	+	0.284488i
$906$	22.1573	+	14.5008i	0.736126	+	0.481757i
$907$	2.39528	+	2.39528i	0.0795341	+	0.0795341i	0.745755	−	0.666221i	$-0.232089\pi$
$907$	2.39528	+	2.39528i	0.0795341	+	0.0795341i	−0.666221	+	0.745755i	$0.732089\pi$
$908$	−18.6620	−	7.31559i	−0.619321	−	0.242776i
$909$			2.06796i			0.0685899i
$910$		0			0
$911$		−	31.5983i		−	1.04690i	−0.852057	−	0.523449i	$-0.824645\pi$
$911$		−	31.5983i		−	1.04690i	0.852057	−	0.523449i	$-0.175355\pi$
$912$	0.758287	+	19.8362i	0.0251094	+	0.656842i
$913$	−5.45083	−	5.45083i	−0.180396	−	0.180396i
$914$	16.4470	−	25.1311i	0.544020	−	0.831264i
$915$	16.7224	−	1.51500i	0.552827	−	0.0500844i
$916$	−13.6796	−	31.3195i	−0.451988	−	1.03482i
$917$		0			0
$918$	−20.4049	+	4.26180i	−0.673462	+	0.140660i
$919$	46.2702			1.52631			0.763157	−	0.646213i	$-0.223648\pi$
$919$	46.2702			1.52631			0.763157	+	0.646213i	$0.223648\pi$
$920$	−2.62811	+	2.25006i	−0.0866461	+	0.0741824i
$921$	−17.5960			−0.579808
$922$	−11.9282	+	2.49135i	−0.392835	+	0.0820481i
$923$	−24.0141	+	24.0141i	−0.790435	+	0.790435i
$924$		0			0
$925$	4.27804	+	2.95637i	0.140661	+	0.0972047i
$926$	−1.78890	+	2.73345i	−0.0587870	+	0.0898268i
$927$	10.4042	+	10.4042i	0.341719	+	0.341719i
$928$	−35.0562	−	21.0751i	−1.15078	−	0.691826i
$929$			42.7925i			1.40397i	0.712189	+	0.701987i	$0.247704\pi$
$929$			42.7925i			1.40397i	−0.712189	+	0.701987i	$0.752296\pi$
$930$	−4.54297	−	14.8836i	−0.148970	−	0.488051i
$931$		0			0
$932$	−3.49220	−	1.36896i	−0.114391	−	0.0448418i
$933$	−12.2866	−	12.2866i	−0.402244	−	0.402244i
$934$	30.1520	+	19.7330i	0.986604	+	0.645682i
$935$	−0.510912	−	5.63940i	−0.0167086	−	0.184428i
$936$	3.04752	−	18.0025i	0.0996113	−	0.588432i
$937$	−18.9957	+	18.9957i	−0.620561	+	0.620561i	−0.945675	−	0.325114i	$-0.894597\pi$
$937$	−18.9957	+	18.9957i	−0.620561	+	0.620561i	0.325114	+	0.945675i	$0.394597\pi$
$938$		0			0
$939$	−6.11875			−0.199678
$940$	−6.90355	−	12.5724i	−0.225169	−	0.410067i
$941$	21.6808			0.706776			0.353388	−	0.935477i	$-0.385030\pi$
$941$	21.6808			0.706776			0.353388	+	0.935477i	$0.385030\pi$
$942$	−2.71346	−	12.9917i	−0.0884093	−	0.423291i
$943$	−1.43680	+	1.43680i	−0.0467887	+	0.0467887i
$944$	−34.2554	+	36.9785i	−1.11492	+	1.20355i
$945$		0			0
$946$	13.9163	+	9.10749i	0.452457	+	0.296110i
$947$	−10.8609	−	10.8609i	−0.352932	−	0.352932i	0.508268	−	0.861199i	$-0.330286\pi$
$947$	−10.8609	−	10.8609i	−0.352932	−	0.352932i	−0.861199	+	0.508268i	$0.830286\pi$
$948$	9.73381	−	24.8309i	0.316139	−	0.806469i
$949$		−	65.7129i		−	2.13313i
$950$	10.6136	+	26.0720i	0.344351	+	0.845888i
$951$		−	42.8869i		−	1.39070i
$952$		0			0
$953$	22.0087	+	22.0087i	0.712931	+	0.712931i	0.967147	−	0.254216i	$-0.0818174\pi$
$953$	22.0087	+	22.0087i	0.712931	+	0.712931i	−0.254216	+	0.967147i	$0.581817\pi$
$954$	−3.29153	+	5.02947i	−0.106567	+	0.162835i
$955$	11.5225	−	13.8183i	0.372860	−	0.447151i
$956$	−27.8920	+	12.1826i	−0.902091	+	0.394013i
$957$	6.06915	−	6.06915i	0.196188	−	0.196188i
$958$	−12.8446	+	2.68274i	−0.414990	+	0.0866755i
$959$		0			0
$960$	5.40976	−	21.6338i	0.174599	−	0.698228i
$961$	15.4173			0.497332
$962$	−6.42766	+	1.34249i	−0.207236	+	0.0432837i
$963$	0.0411288	−	0.0411288i	0.00132536	−	0.00132536i
$964$	24.1482	−	10.5474i	0.777763	−	0.339709i
$965$	−2.93747	−	32.4235i	−0.0945604	−	1.04375i
$966$		0			0
$967$	16.9281	+	16.9281i	0.544372	+	0.544372i	0.924807	−	0.380435i	$-0.124226\pi$
$967$	16.9281	+	16.9281i	0.544372	+	0.544372i	−0.380435	+	0.924807i	$0.624226\pi$
$968$	−23.2728	+	16.5342i	−0.748015	+	0.531428i
$969$			13.1981i			0.423983i
$970$	−13.1993	+	4.02888i	−0.423804	+	0.129360i
$971$			37.0888i			1.19024i	0.803638	+	0.595118i	$0.202895\pi$
$971$			37.0888i			1.19024i	−0.803638	+	0.595118i	$0.797105\pi$
$972$	−9.79698	+	24.9920i	−0.314238	+	0.801620i
$973$		0			0
$974$	−21.0739	−	13.7918i	−0.675251	−	0.441918i
$975$	5.00097	+	27.3736i	0.160159	+	0.876657i
$976$	16.3742	−	17.6759i	0.524127	−	0.565791i
$977$	16.5269	−	16.5269i	0.528744	−	0.528744i	−0.391454	−	0.920198i	$-0.628028\pi$
$977$	16.5269	−	16.5269i	0.528744	−	0.528744i	0.920198	+	0.391454i	$0.128028\pi$
$978$	2.39655	+	11.4743i	0.0766332	+	0.366909i
$979$	−2.01652			−0.0644484
$980$		0			0
$981$	−9.09942			−0.290522
$982$	0.722753	+	3.46044i	0.0230640	+	0.110427i
$983$	−14.0604	+	14.0604i	−0.448459	+	0.448459i	−0.894842	−	0.446383i	$-0.852712\pi$
$983$	−14.0604	+	14.0604i	−0.448459	+	0.448459i	0.446383	+	0.894842i	$0.352712\pi$
$984$	2.18600	−	12.9133i	0.0696872	−	0.411662i
$985$	51.9394	−	4.70554i	1.65493	−	0.149931i
$986$	−22.7555	−	14.8923i	−0.724682	−	0.474268i
$987$		0			0
$988$	−33.0932	−	12.9727i	−1.05284	−	0.412716i
$989$		−	6.75620i		−	0.214835i
$990$	−3.84343	−	2.04583i	−0.122152	−	0.0650207i
$991$			22.5584i			0.716592i	0.933608	+	0.358296i	$0.116642\pi$
$991$			22.5584i			0.716592i	−0.933608	+	0.358296i	$0.883358\pi$
$992$	−19.1382	−	11.5055i	−0.607638	−	0.365300i
$993$	11.4204	+	11.4204i	0.362414	+	0.362414i
$994$		0			0
$995$	−16.5825	−	13.8275i	−0.525701	−	0.438360i
$996$	−8.07893	−	18.4967i	−0.255991	−	0.586090i
$997$	−12.1793	+	12.1793i	−0.385722	+	0.385722i	−0.873158	−	0.487437i	$-0.837932\pi$
$997$	−12.1793	+	12.1793i	−0.385722	+	0.385722i	0.487437	+	0.873158i	$0.337932\pi$
$998$	9.03141	−	1.88632i	0.285884	−	0.0597103i
$999$	5.76426			0.182373

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.j.883.1		36
4.3	odd	2	inner	980.2.k.j.883.8		36
5.2	odd	4	inner	980.2.k.j.687.8		36
7.2	even	3		980.2.x.m.263.14		72
7.3	odd	6		140.2.w.b.23.11	yes	72
7.4	even	3		980.2.x.m.863.11		72
7.5	odd	6		140.2.w.b.123.14	yes	72
7.6	odd	2		980.2.k.k.883.1		36
20.7	even	4	inner	980.2.k.j.687.1		36
28.3	even	6		140.2.w.b.23.5	✓	72
28.11	odd	6		980.2.x.m.863.5		72
28.19	even	6		140.2.w.b.123.17	yes	72
28.23	odd	6		980.2.x.m.263.17		72
28.27	even	2		980.2.k.k.883.8		36
35.2	odd	12		980.2.x.m.67.5		72
35.3	even	12		700.2.be.e.107.2		72
35.12	even	12		140.2.w.b.67.5	yes	72
35.17	even	12		140.2.w.b.107.17	yes	72
35.19	odd	6		700.2.be.e.543.5		72
35.24	odd	6		700.2.be.e.443.8		72
35.27	even	4		980.2.k.k.687.8		36
35.32	odd	12		980.2.x.m.667.17		72
35.33	even	12		700.2.be.e.207.14		72
140.3	odd	12		700.2.be.e.107.5		72
140.19	even	6		700.2.be.e.543.2		72
140.27	odd	4		980.2.k.k.687.1		36
140.47	odd	12		140.2.w.b.67.11	yes	72
140.59	even	6		700.2.be.e.443.14		72
140.67	even	12		980.2.x.m.667.14		72
140.87	odd	12		140.2.w.b.107.14	yes	72
140.103	odd	12		700.2.be.e.207.8		72
140.107	even	12		980.2.x.m.67.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.5	✓	72	28.3	even	6
140.2.w.b.23.11	yes	72	7.3	odd	6
140.2.w.b.67.5	yes	72	35.12	even	12
140.2.w.b.67.11	yes	72	140.47	odd	12
140.2.w.b.107.14	yes	72	140.87	odd	12
140.2.w.b.107.17	yes	72	35.17	even	12
140.2.w.b.123.14	yes	72	7.5	odd	6
140.2.w.b.123.17	yes	72	28.19	even	6
700.2.be.e.107.2		72	35.3	even	12
700.2.be.e.107.5		72	140.3	odd	12
700.2.be.e.207.8		72	140.103	odd	12
700.2.be.e.207.14		72	35.33	even	12
700.2.be.e.443.8		72	35.24	odd	6
700.2.be.e.443.14		72	140.59	even	6
700.2.be.e.543.2		72	140.19	even	6
700.2.be.e.543.5		72	35.19	odd	6
980.2.k.j.687.1		36	20.7	even	4	inner
980.2.k.j.687.8		36	5.2	odd	4	inner
980.2.k.j.883.1		36	1.1	even	1	trivial
980.2.k.j.883.8		36	4.3	odd	2	inner
980.2.k.k.687.1		36	140.27	odd	4
980.2.k.k.687.8		36	35.27	even	4
980.2.k.k.883.1		36	7.6	odd	2
980.2.k.k.883.8		36	28.27	even	2
980.2.x.m.67.5		72	35.2	odd	12
980.2.x.m.67.11		72	140.107	even	12
980.2.x.m.263.14		72	7.2	even	3
980.2.x.m.263.17		72	28.23	odd	6
980.2.x.m.667.14		72	140.67	even	12
980.2.x.m.667.17		72	35.32	odd	12
980.2.x.m.863.5		72	28.11	odd	6
980.2.x.m.863.11		72	7.4	even	3

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38434 + 0.289136i) q^{2} +(0.881483 - 0.881483i) q^{3} +(1.83280 - 0.800525i) q^{4} +(1.71735 + 1.43203i) q^{5} +(-0.965404 + 1.47514i) q^{6} +(-2.30576 + 1.63813i) q^{8} +1.44598i q^{9} +(-2.79145 - 1.48587i) q^{10} -0.952199i q^{11} +(0.909933 - 2.32123i) q^{12} +(3.15680 + 3.15680i) q^{13} +(2.77612 - 0.251508i) q^{15} +(2.71832 - 2.93441i) q^{16} +(1.88053 - 1.88053i) q^{17} +(-0.418084 - 2.00173i) q^{18} -3.98095 q^{19} +(4.29394 + 1.24984i) q^{20} +(0.275315 + 1.31817i) q^{22} +(0.386810 - 0.386810i) q^{23} +(-0.588506 + 3.47647i) q^{24} +(0.898593 + 4.91859i) q^{25} +(-5.28284 - 3.45735i) q^{26} +(3.91905 + 3.91905i) q^{27} +7.23080i q^{29} +(-3.77038 + 1.15085i) q^{30} +3.94749i q^{31} +(-2.91464 + 4.84818i) q^{32} +(-0.839347 - 0.839347i) q^{33} +(-2.05957 + 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(0.735415 - 0.735415i) q^{37} +(5.51099 - 1.15104i) q^{38} +5.56534 q^{39} +(-6.30565 - 0.488671i) q^{40} -3.71449 q^{41} +(8.73324 - 8.73324i) q^{43} +(-0.762260 - 1.74519i) q^{44} +(-2.07068 + 2.48325i) q^{45} +(-0.423636 + 0.647317i) q^{46} +(-2.26785 - 2.26785i) q^{47} +(-0.190479 - 4.98278i) q^{48} +(-2.66610 - 6.54919i) q^{50} -3.31531i q^{51} +(8.31290 + 3.25869i) q^{52} +(-2.07846 - 2.07846i) q^{53} +(-6.55844 - 4.29217i) q^{54} +(1.36358 - 1.63526i) q^{55} +(-3.50914 + 3.50914i) q^{57} +(-2.09068 - 10.0099i) q^{58} -12.6017 q^{59} +(4.88674 - 2.68332i) q^{60} +6.02367 q^{61} +(-1.14136 - 5.46468i) q^{62} +(2.63307 - 7.55427i) q^{64} +(0.900712 + 9.94198i) q^{65} +(1.40463 + 0.919257i) q^{66} +(10.5349 + 10.5349i) q^{67} +(1.94122 - 4.95205i) q^{68} -0.681932i q^{69} +7.60710i q^{71} +(-2.36870 - 3.33408i) q^{72} +(-10.4081 - 10.4081i) q^{73} +(-0.805430 + 1.23070i) q^{74} +(5.12775 + 3.54356i) q^{75} +(-7.29629 + 3.18685i) q^{76} +(-7.70432 + 1.60914i) q^{78} +10.6973 q^{79} +(8.87046 - 1.14670i) q^{80} +2.57122 q^{81} +(5.14212 - 1.07399i) q^{82} +(5.72446 - 5.72446i) q^{83} +(5.92250 - 0.536560i) q^{85} +(-9.56469 + 14.6149i) q^{86} +(6.37382 + 6.37382i) q^{87} +(1.55982 + 2.19554i) q^{88} -2.11775i q^{89} +(2.14853 - 4.03637i) q^{90} +(0.399294 - 1.01860i) q^{92} +(3.47965 + 3.47965i) q^{93} +(3.79519 + 2.48376i) q^{94} +(-6.83669 - 5.70083i) q^{95} +(1.70439 + 6.84279i) q^{96} +(3.08588 - 3.08588i) q^{97} +1.37686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} - 8 q^{5} + 8 q^{6} - 2 q^{8} + 2 q^{10} + 10 q^{12} + 28 q^{16} + 4 q^{17} + 20 q^{18} + 28 q^{20} - 8 q^{22} + 16 q^{25} - 4 q^{26} + 32 q^{30} + 38 q^{32} - 64 q^{33} + 8 q^{36} + 4 q^{37}+ \cdots + 12 q^{97}+O(q^{100}) \) 36 * q - 2 * q^2 - 8 * q^5 + 8 * q^6 - 2 * q^8 + 2 * q^10 + 10 * q^12 + 28 * q^16 + 4 * q^17 + 20 * q^18 + 28 * q^20 - 8 * q^22 + 16 * q^25 - 4 * q^26 + 32 * q^30 + 38 * q^32 - 64 * q^33 + 8 * q^36 + 4 * q^37 + 12 * q^38 + 2 * q^40 + 20 * q^41 - 12 * q^45 + 28 * q^46 - 6 * q^48 - 14 * q^50 + 48 * q^52 + 24 * q^53 - 8 * q^57 - 30 * q^58 + 10 * q^60 - 20 * q^61 - 28 * q^62 - 4 * q^65 + 44 * q^66 - 12 * q^68 - 44 * q^72 - 12 * q^73 - 56 * q^76 + 32 * q^78 + 52 * q^80 + 52 * q^81 - 34 * q^82 + 8 * q^85 - 64 * q^86 - 16 * q^88 + 16 * q^90 + 22 * q^92 - 12 * q^93 - 48 * q^96 + 12 * q^97

Introduction

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