LMFDB - Embedded newform 980.2.k.l.687.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(687,980)]

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

lf = mfeigenbasis(mf)

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")

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

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			687.3
Character	$\chi$	$=$	980.687
Dual form			980.2.k.l.883.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25629 - 0.649412i) q^{2} +(-2.28163 - 2.28163i) q^{3} +(1.15653 + 1.63170i) q^{4} +(-0.0430826 + 2.23565i) q^{5} +(1.38467 + 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +7.41170i q^{9} +O(q^{10})$	\(q+(-1.25629 - 0.649412i) q^{2} +(-2.28163 - 2.28163i) q^{3} +(1.15653 + 1.63170i) q^{4} +(-0.0430826 + 2.23565i) q^{5} +(1.38467 + 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +7.41170i q^{9} +(1.50599 - 2.78065i) q^{10} +1.40679i q^{11} +(1.08417 - 6.36171i) q^{12} +(0.699298 - 0.699298i) q^{13} +(5.19924 - 5.00264i) q^{15} +(-1.32489 + 3.77421i) q^{16} +(3.26865 + 3.26865i) q^{17} +(4.81325 - 9.31125i) q^{18} -2.80674 q^{19} +(-3.69774 + 2.51529i) q^{20} +(0.913587 - 1.76734i) q^{22} +(-1.48618 - 1.48618i) q^{23} +(-5.49341 + 7.28808i) q^{24} +(-4.99629 - 0.192635i) q^{25} +(-1.33265 + 0.424388i) q^{26} +(10.0659 - 10.0659i) q^{27} -4.85706i q^{29} +(-9.78053 + 2.90832i) q^{30} -3.67738i q^{31} +(4.11547 - 3.88110i) q^{32} +(3.20978 - 3.20978i) q^{33} +(-1.98367 - 6.22907i) q^{34} +(-12.0937 + 8.57184i) q^{36} +(-5.85431 - 5.85431i) q^{37} +(3.52608 + 1.82273i) q^{38} -3.19108 q^{39} +(6.27890 - 0.758579i) q^{40} -3.53368 q^{41} +(-2.49869 - 2.49869i) q^{43} +(-2.29546 + 1.62699i) q^{44} +(-16.5700 - 0.319315i) q^{45} +(0.901930 + 2.83222i) q^{46} +(-1.86901 + 1.86901i) q^{47} +(11.6343 - 5.58845i) q^{48} +(6.15168 + 3.48666i) q^{50} -14.9157i q^{51} +(1.94980 + 0.332288i) q^{52} +(-0.696542 + 0.696542i) q^{53} +(-19.1826 + 6.10876i) q^{54} +(-3.14510 - 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(-3.15424 + 6.10187i) q^{58} +7.06573 q^{59} +(14.1759 + 2.69791i) q^{60} -2.19831 q^{61} +(-2.38814 + 4.61985i) q^{62} +(-7.69065 + 2.20315i) q^{64} +(1.53326 + 1.59351i) q^{65} +(-6.11688 + 1.94794i) q^{66} +(2.25963 - 2.25963i) q^{67} +(-1.55317 + 9.11374i) q^{68} +6.78184i q^{69} +12.1891i q^{71} +(20.7598 - 2.91492i) q^{72} +(-4.68856 + 4.68856i) q^{73} +(3.55285 + 11.1566i) q^{74} +(10.9602 + 11.8392i) q^{75} +(-3.24607 - 4.57976i) q^{76} +(4.00892 + 2.07233i) q^{78} -0.599288 q^{79} +(-8.38074 - 3.12460i) q^{80} -23.6982 q^{81} +(4.43932 + 2.29482i) q^{82} +(-4.53764 - 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(1.51640 + 4.76176i) q^{86} +(-11.0820 + 11.0820i) q^{87} +(3.94035 - 0.553271i) q^{88} +0.463673i q^{89} +(20.6093 + 11.1619i) q^{90} +(0.706194 - 4.14381i) q^{92} +(-8.39043 + 8.39043i) q^{93} +(3.56178 - 1.13426i) q^{94} +(0.120922 - 6.27490i) q^{95} +(-18.2452 - 0.534737i) q^{96} +(-8.00558 - 8.00558i) q^{97} -10.4267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 8 q^{6}+O(q^{10}) $ 36 * q + 8 * q^6	$ 36 q + 8 q^{6} + 16 q^{10} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} + 28 q^{18} - 20 q^{20} + 4 q^{22} - 20 q^{25} + 32 q^{26} - 4 q^{30} + 20 q^{37} + 36 q^{40} - 20 q^{45} + 16 q^{46} + 24 q^{48} + 40 q^{50} - 16 q^{52} - 44 q^{53} - 16 q^{57} - 4 q^{58} + 40 q^{60} + 64 q^{61} - 40 q^{62} + 4 q^{65} - 32 q^{66} - 80 q^{68} + 80 q^{72} - 52 q^{73} - 8 q^{76} - 76 q^{78} + 20 q^{80} - 36 q^{81} - 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} + 16 q^{90} - 56 q^{92} + 32 q^{93} - 120 q^{96} - 20 q^{97}+O(q^{100}) $ 36 * q + 8 * q^6 + 16 * q^10 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 + 28 * q^18 - 20 * q^20 + 4 * q^22 - 20 * q^25 + 32 * q^26 - 4 * q^30 + 20 * q^37 + 36 * q^40 - 20 * q^45 + 16 * q^46 + 24 * q^48 + 40 * q^50 - 16 * q^52 - 44 * q^53 - 16 * q^57 - 4 * q^58 + 40 * q^60 + 64 * q^61 - 40 * q^62 + 4 * q^65 - 32 * q^66 - 80 * q^68 + 80 * q^72 - 52 * q^73 - 8 * q^76 - 76 * q^78 + 20 * q^80 - 36 * q^81 - 56 * q^82 - 20 * q^85 + 56 * q^86 - 40 * q^88 + 16 * q^90 - 56 * q^92 + 32 * q^93 - 120 * q^96 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.25629	−	0.649412i	−0.888331	−	0.459204i
$2$	−1.25629	−	0.649412i	−0.888331	−	0.459204i
$3$	−2.28163	−	2.28163i	−1.31730	−	1.31730i	−0.915904	−	0.401398i	$-0.868524\pi$
$3$	−2.28163	−	2.28163i	−1.31730	−	1.31730i	−0.401398	−	0.915904i	$-0.631476\pi$
$4$	1.15653	+	1.63170i	0.578263	+	0.815850i
$5$	−0.0430826	+	2.23565i	−0.0192671	+	0.999814i
$5$	−0.0430826	+	2.23565i	−0.0192671	+	0.999814i
$6$	1.38467	+	4.34811i	0.565290	+	1.77511i
$7$		0			0
$7$		0			0
$8$	−0.393286	−	2.80095i	−0.139048	−	0.990286i
$9$			7.41170i			2.47057i
$10$	1.50599	−	2.78065i	0.476234	−	0.879318i
$11$			1.40679i			0.424163i	0.977252	+	0.212082i	$0.0680243\pi$
$11$			1.40679i			0.424163i	−0.977252	+	0.212082i	$0.931976\pi$
$12$	1.08417	−	6.36171i	0.312973	−	1.83647i
$13$	0.699298	−	0.699298i	0.193950	−	0.193950i	−0.603450	−	0.797401i	$-0.706208\pi$
$13$	0.699298	−	0.699298i	0.193950	−	0.193950i	0.797401	+	0.603450i	$0.206208\pi$
$14$		0			0
$15$	5.19924	−	5.00264i	1.34244	−	1.29168i
$16$	−1.32489	+	3.77421i	−0.331223	+	0.943553i
$17$	3.26865	+	3.26865i	0.792764	+	0.792764i	0.981943	−	0.189179i	$-0.0605826\pi$
$17$	3.26865	+	3.26865i	0.792764	+	0.792764i	−0.189179	+	0.981943i	$0.560583\pi$
$18$	4.81325	−	9.31125i	1.13449	−	2.19468i
$19$	−2.80674			−0.643910			−0.321955	−	0.946755i	$-0.604340\pi$
$19$	−2.80674			−0.643910			−0.321955	+	0.946755i	$0.604340\pi$
$20$	−3.69774	+	2.51529i	−0.826840	+	0.562437i
$21$		0			0
$22$	0.913587	−	1.76734i	0.194777	−	0.376797i
$23$	−1.48618	−	1.48618i	−0.309890	−	0.309890i	0.534977	−	0.844867i	$-0.320320\pi$
$23$	−1.48618	−	1.48618i	−0.309890	−	0.309890i	−0.844867	+	0.534977i	$0.820320\pi$
$24$	−5.49341	+	7.28808i	−1.12134	+	1.48767i
$25$	−4.99629	−	0.192635i	−0.999258	−	0.0385271i
$26$	−1.33265	+	0.424388i	−0.261355	+	0.0832293i
$27$	10.0659	−	10.0659i	1.93718	−	1.93718i
$28$		0			0
$29$		−	4.85706i		−	0.901933i	−0.892541	−	0.450967i	$-0.851079\pi$
$29$		−	4.85706i		−	0.901933i	0.892541	−	0.450967i	$-0.148921\pi$
$30$	−9.78053	+	2.90832i	−1.78567	+	0.530983i
$31$		−	3.67738i		−	0.660477i	−0.943898	−	0.330238i	$-0.892871\pi$
$31$		−	3.67738i		−	0.660477i	0.943898	−	0.330238i	$-0.107129\pi$
$32$	4.11547	−	3.88110i	0.727518	−	0.686088i
$33$	3.20978	−	3.20978i	0.558751	−	0.558751i
$34$	−1.98367	−	6.22907i	−0.340196	−	1.06828i
$35$		0			0
$36$	−12.0937	+	8.57184i	−2.01561	+	1.42864i
$37$	−5.85431	−	5.85431i	−0.962443	−	0.962443i	0.0368766	−	0.999320i	$-0.488259\pi$
$37$	−5.85431	−	5.85431i	−0.962443	−	0.962443i	−0.999320	+	0.0368766i	$0.988259\pi$
$38$	3.52608	+	1.82273i	0.572005	+	0.295686i
$39$	−3.19108			−0.510982
$40$	6.27890	−	0.758579i	0.992781	−	0.119942i
$41$	−3.53368			−0.551868			−0.275934	−	0.961177i	$-0.588987\pi$
$41$	−3.53368			−0.551868			−0.275934	+	0.961177i	$0.588987\pi$
$42$		0			0
$43$	−2.49869	−	2.49869i	−0.381046	−	0.381046i	0.490433	−	0.871479i	$-0.336839\pi$
$43$	−2.49869	−	2.49869i	−0.381046	−	0.381046i	−0.871479	+	0.490433i	$0.836839\pi$
$44$	−2.29546	+	1.62699i	−0.346054	+	0.245278i
$45$	−16.5700	−	0.319315i	−2.47011	−	0.0476007i
$46$	0.901930	+	2.83222i	0.132982	+	0.417588i
$47$	−1.86901	+	1.86901i	−0.272624	+	0.272624i	−0.830156	−	0.557532i	$-0.811748\pi$
$47$	−1.86901	+	1.86901i	−0.272624	+	0.272624i	0.557532	+	0.830156i	$0.311748\pi$
$48$	11.6343	−	5.58845i	1.67926	−	0.806623i
$49$		0			0
$50$	6.15168	+	3.48666i	0.869980	+	0.493088i
$51$		−	14.9157i		−	2.08862i
$52$	1.94980	+	0.332288i	0.270389	+	0.0460800i
$53$	−0.696542	+	0.696542i	−0.0956775	+	0.0956775i	−0.753325	−	0.657648i	$-0.771551\pi$
$53$	−0.696542	+	0.696542i	−0.0956775	+	0.0956775i	0.657648	+	0.753325i	$0.271551\pi$
$54$	−19.1826	+	6.10876i	−2.61042	+	0.831297i
$55$	−3.14510	−	0.0606082i	−0.424085	−	0.00817240i
$56$		0			0
$57$	6.40395	+	6.40395i	0.848224	+	0.848224i
$58$	−3.15424	+	6.10187i	−0.414171	+	0.801215i
$59$	7.06573			0.919879			0.459940	−	0.887950i	$-0.347871\pi$
$59$	7.06573			0.919879			0.459940	+	0.887950i	$0.347871\pi$
$60$	14.1759	+	2.69791i	1.83010	+	0.348299i
$61$	−2.19831			−0.281465			−0.140732	−	0.990048i	$-0.544946\pi$
$61$	−2.19831			−0.281465			−0.140732	+	0.990048i	$0.544946\pi$
$62$	−2.38814	+	4.61985i	−0.303294	+	0.586722i
$63$		0			0
$64$	−7.69065	+	2.20315i	−0.961331	+	0.275394i
$65$	1.53326	+	1.59351i	0.190177	+	0.197651i
$66$	−6.11688	+	1.94794i	−0.752936	+	0.239775i
$67$	2.25963	−	2.25963i	0.276057	−	0.276057i	−0.555476	−	0.831533i	$-0.687464\pi$
$67$	2.25963	−	2.25963i	0.276057	−	0.276057i	0.831533	+	0.555476i	$0.187464\pi$
$68$	−1.55317	+	9.11374i	−0.188350	+	1.10520i
$69$			6.78184i			0.816438i
$70$		0			0
$71$			12.1891i			1.44658i	0.690546	+	0.723289i	$0.257370\pi$
$71$			12.1891i			1.44658i	−0.690546	+	0.723289i	$0.742630\pi$
$72$	20.7598	−	2.91492i	2.44657	−	0.343527i
$73$	−4.68856	+	4.68856i	−0.548754	+	0.548754i	−0.926080	−	0.377326i	$-0.876843\pi$
$73$	−4.68856	+	4.68856i	−0.548754	+	0.548754i	0.377326	+	0.926080i	$0.376843\pi$
$74$	3.55285	+	11.1566i	0.413010	+	1.29693i
$75$	10.9602	+	11.8392i	1.26557	+	1.36708i
$76$	−3.24607	−	4.57976i	−0.372350	−	0.525334i
$77$		0			0
$78$	4.00892	+	2.07233i	0.453921	+	0.234645i
$79$	−0.599288			−0.0674252			−0.0337126	−	0.999432i	$-0.510733\pi$
$79$	−0.599288			−0.0674252			−0.0337126	+	0.999432i	$0.510733\pi$
$80$	−8.38074	−	3.12460i	−0.936996	−	0.349341i
$81$	−23.6982			−2.63314
$82$	4.43932	+	2.29482i	0.490241	+	0.253420i
$83$	−4.53764	−	4.53764i	−0.498071	−	0.498071i	0.412766	−	0.910837i	$-0.364563\pi$
$83$	−4.53764	−	4.53764i	−0.498071	−	0.498071i	−0.910837	+	0.412766i	$0.864563\pi$
$84$		0			0
$85$	−7.44839	+	7.16674i	−0.807891	+	0.777342i
$86$	1.51640	+	4.76176i	0.163517	+	0.513473i
$87$	−11.0820	+	11.0820i	−1.18812	+	1.18812i
$88$	3.94035	−	0.553271i	0.420043	−	0.0589789i
$89$			0.463673i			0.0491493i	0.999698	+	0.0245746i	$0.00782314\pi$
$89$			0.463673i			0.0491493i	−0.999698	+	0.0245746i	$0.992177\pi$
$90$	20.6093	+	11.1619i	2.17242	+	1.17657i
$91$		0			0
$92$	0.706194	−	4.14381i	0.0736258	−	0.432022i
$93$	−8.39043	+	8.39043i	−0.870047	+	0.870047i
$94$	3.56178	−	1.13426i	0.367370	−	0.116990i
$95$	0.120922	−	6.27490i	0.0124063	−	0.643791i
$96$	−18.2452	−	0.534737i	−1.86215	−	0.0545763i
$97$	−8.00558	−	8.00558i	−0.812843	−	0.812843i	0.172216	−	0.985059i	$-0.444907\pi$
$97$	−8.00558	−	8.00558i	−0.812843	−	0.812843i	−0.985059	+	0.172216i	$0.944907\pi$
$98$		0			0
$99$	−10.4267			−1.04792
$100$	−5.46402	−	8.37523i	−0.546402	−	0.837523i
$101$	6.03099			0.600106			0.300053	−	0.953923i	$-0.402996\pi$
$101$	6.03099			0.600106			0.300053	+	0.953923i	$0.402996\pi$
$102$	−9.68645	+	18.7385i	−0.959102	+	1.85538i
$103$	−9.95088	−	9.95088i	−0.980489	−	0.980489i	0.0193242	−	0.999813i	$-0.493849\pi$
$103$	−9.95088	−	9.95088i	−0.980489	−	0.980489i	−0.999813	+	0.0193242i	$0.993849\pi$
$104$	−2.23372	−	1.68367i	−0.219035	−	0.165098i
$105$		0			0
$106$	1.32740	−	0.422716i	0.128929	−	0.0410578i
$107$	−14.1841	+	14.1841i	−1.37123	+	1.37123i	−0.512603	+	0.858626i	$0.671319\pi$
$107$	−14.1841	+	14.1841i	−1.37123	+	1.37123i	−0.858626	+	0.512603i	$0.828681\pi$
$108$	28.0660	+	4.78304i	2.70065	+	0.460249i
$109$		−	1.01514i		−	0.0972330i	−0.998818	−	0.0486165i	$-0.984519\pi$
$109$		−	1.01514i		−	0.0972330i	0.998818	−	0.0486165i	$-0.0154812\pi$
$110$	3.91179	+	2.11861i	0.372975	+	0.202001i
$111$			26.7148i			2.53566i
$112$		0			0
$113$	7.39345	−	7.39345i	0.695518	−	0.695518i	−0.267923	−	0.963440i	$-0.586337\pi$
$113$	7.39345	−	7.39345i	0.695518	−	0.695518i	0.963440	+	0.267923i	$0.0863372\pi$
$114$	−3.88641	−	12.2040i	−0.363996	−	1.14301i
$115$	3.38662	−	3.25856i	0.315803	−	0.303862i
$116$	7.92527	−	5.61732i	0.735842	−	0.521555i
$117$	5.18299	+	5.18299i	0.479167	+	0.479167i
$118$	−8.87660	−	4.58857i	−0.817157	−	0.422412i
$119$		0			0
$120$	−16.0569	−	12.5953i	−1.46579	−	1.14979i
$121$	9.02094			0.820086
$122$	2.76172	+	1.42761i	0.250034	+	0.129250i
$123$	8.06256	+	8.06256i	0.726977	+	0.726977i
$124$	6.00038	−	4.25299i	0.538850	−	0.381930i
$125$	0.645919	−	11.1617i	0.0577727	−	0.998330i
$126$		0			0
$127$	−8.87092	+	8.87092i	−0.787167	+	0.787167i	−0.981029	−	0.193862i	$-0.937899\pi$
$127$	−8.87092	+	8.87092i	−0.787167	+	0.787167i	0.193862	+	0.981029i	$0.437899\pi$
$128$	11.0924	+	2.22661i	0.980442	+	0.196806i
$129$			11.4022i			1.00391i
$130$	−0.891370	−	2.99763i	−0.0781783	−	0.262910i
$131$		−	13.1487i		−	1.14881i	−0.818572	−	0.574404i	$-0.805234\pi$
$131$		−	13.1487i		−	1.14881i	0.818572	−	0.574404i	$-0.194766\pi$
$132$	8.94960	+	1.52520i	0.778962	+	0.132752i
$133$		0			0
$134$	−4.30618	+	1.37132i	−0.371997	+	0.118464i
$135$	22.0702	+	22.9375i	1.89950	+	1.97415i
$136$	7.86981	−	10.4408i	0.674831	−	0.895295i
$137$	4.94200	+	4.94200i	0.422224	+	0.422224i	0.885969	−	0.463745i	$-0.153495\pi$
$137$	4.94200	+	4.94200i	0.422224	+	0.422224i	−0.463745	+	0.885969i	$0.653495\pi$
$138$	4.40421	−	8.51996i	0.374912	−	0.725267i
$139$	−21.2377			−1.80136			−0.900679	−	0.434485i	$-0.856931\pi$
$139$	−21.2377			−1.80136			−0.900679	+	0.434485i	$0.856931\pi$
$140$		0			0
$141$	8.52881			0.718255
$142$	7.91574	−	15.3130i	0.664274	−	1.28504i
$143$	0.983765	+	0.983765i	0.0822666	+	0.0822666i
$144$	−27.9733	−	9.81970i	−2.33111	−	0.818308i
$145$	10.8587	+	0.209255i	0.901766	+	0.0173777i
$146$	8.93499	−	2.84538i	0.739465	−	0.235485i
$147$		0			0
$148$	2.78181	−	16.3232i	0.228664	−	1.34176i
$149$		−	6.64454i		−	0.544342i	−0.962249	−	0.272171i	$-0.912258\pi$
$149$		−	6.64454i		−	0.544342i	0.962249	−	0.272171i	$-0.0877416\pi$
$150$	−6.08062	−	21.9912i	−0.496480	−	1.79557i
$151$		−	20.3868i		−	1.65906i	−0.558464	−	0.829529i	$-0.688609\pi$
$151$		−	20.3868i		−	1.65906i	0.558464	−	0.829529i	$-0.311391\pi$
$152$	1.10385	+	7.86154i	0.0895342	+	0.637655i
$153$	−24.2263	+	24.2263i	−1.95858	+	1.95858i
$154$		0			0
$155$	8.22134	+	0.158431i	0.660354	+	0.0127255i
$156$	−3.69057	−	5.20689i	−0.295482	−	0.416885i
$157$	−12.5648	−	12.5648i	−1.00278	−	1.00278i	−0.999996	−	0.00278769i	$-0.999113\pi$
$157$	−12.5648	−	12.5648i	−1.00278	−	1.00278i	−0.00278769	−	0.999996i	$-0.500887\pi$
$158$	0.752879	+	0.389185i	0.0598959	+	0.0309619i
$159$	3.17851			0.252072
$160$	8.49949	+	9.36796i	0.671944	+	0.740602i
$161$		0			0
$162$	29.7719	+	15.3899i	2.33910	+	1.20915i
$163$	−12.2953	−	12.2953i	−0.963042	−	0.963042i	0.0362991	−	0.999341i	$-0.488443\pi$
$163$	−12.2953	−	12.2953i	−0.963042	−	0.963042i	−0.999341	+	0.0362991i	$0.988443\pi$
$164$	−4.08680	−	5.76591i	−0.319125	−	0.450242i
$165$	7.03767	+	7.31424i	0.547882	+	0.569413i
$166$	2.75379	+	8.64739i	0.213736	+	0.671168i
$167$	−6.88960	+	6.88960i	−0.533133	+	0.533133i	−0.921503	−	0.388370i	$-0.873038\pi$
$167$	−6.88960	+	6.88960i	−0.533133	+	0.533133i	0.388370	+	0.921503i	$0.373038\pi$
$168$		0			0
$169$			12.0220i			0.924767i
$170$	14.0115	−	4.16643i	1.07463	−	0.319551i
$171$		−	20.8027i		−	1.59082i
$172$	1.18731	−	6.96691i	0.0905315	−	0.531222i
$173$	17.4943	−	17.4943i	1.33007	−	1.33007i	0.424767	−	0.905303i	$-0.360356\pi$
$173$	17.4943	−	17.4943i	1.33007	−	1.33007i	0.905303	−	0.424767i	$-0.139644\pi$
$174$	21.1190	−	6.72543i	1.60103	−	0.509854i
$175$		0			0
$176$	−5.30952	−	1.86384i	−0.400220	−	0.140493i
$177$	−16.1214	−	16.1214i	−1.21176	−	1.21176i
$178$	0.301115	−	0.582508i	0.0225695	−	0.0436608i
$179$	−20.5554			−1.53638			−0.768192	−	0.640219i	$-0.778844\pi$
$179$	−20.5554			−1.53638			−0.768192	+	0.640219i	$0.778844\pi$
$180$	−18.6426	−	27.4066i	−1.38954	−	2.04276i
$181$	7.85989			0.584221			0.292110	−	0.956385i	$-0.405643\pi$
$181$	7.85989			0.584221			0.292110	+	0.956385i	$0.405643\pi$
$182$		0			0
$183$	5.01574	+	5.01574i	0.370774	+	0.370774i
$184$	−3.57823	+	4.74722i	−0.263790	+	0.349969i
$185$	13.3404	−	12.8360i	0.980808	−	0.943721i
$186$	15.9897	−	5.09196i	1.17242	−	0.373361i
$187$	−4.59830	+	4.59830i	−0.336261	+	0.336261i
$188$	−5.21123	−	0.888105i	−0.380068	−	0.0647717i
$189$		0			0
$190$	−4.22691	+	7.80456i	−0.306652	+	0.566202i
$191$			8.67251i			0.627520i	0.949502	+	0.313760i	$0.101589\pi$
$191$			8.67251i			0.627520i	−0.949502	+	0.313760i	$0.898411\pi$
$192$	22.5740	+	12.5205i	1.62914	+	0.903587i
$193$	−3.75160	+	3.75160i	−0.270046	+	0.270046i	−0.829119	−	0.559073i	$-0.811157\pi$
$193$	−3.75160	+	3.75160i	−0.270046	+	0.270046i	0.559073	+	0.829119i	$0.311157\pi$
$194$	4.85840	+	15.2562i	0.348813	+	1.09533i
$195$	0.137480	−	7.13415i	0.00984515	−	0.510887i
$196$		0			0
$197$	−12.3437	−	12.3437i	−0.879452	−	0.879452i	0.114026	−	0.993478i	$-0.463625\pi$
$197$	−12.3437	−	12.3437i	−0.879452	−	0.879452i	−0.993478	+	0.114026i	$0.963625\pi$
$198$	13.0990	+	6.77124i	0.930903	+	0.481211i
$199$	−4.29882			−0.304735			−0.152368	−	0.988324i	$-0.548690\pi$
$199$	−4.29882			−0.304735			−0.152368	+	0.988324i	$0.548690\pi$
$200$	1.42541	+	14.0701i	0.100792	+	0.994908i
$201$	−10.3113			−0.727302
$202$	−7.57667	−	3.91660i	−0.533092	−	0.275571i
$203$		0			0
$204$	24.3380	−	17.2504i	1.70400	−	1.20777i
$205$	0.152240	−	7.90008i	0.0106329	−	0.551766i
$206$	6.03896	+	18.9634i	0.420754	+	1.32124i
$207$	11.0151	−	11.0151i	0.765605	−	0.765605i
$208$	1.71280	+	3.56579i	0.118762	+	0.247243i
$209$		−	3.94849i		−	0.273123i
$210$		0			0
$211$		−	19.5494i		−	1.34583i	−0.739718	−	0.672917i	$-0.765041\pi$
$211$		−	19.5494i		−	1.34583i	0.739718	−	0.672917i	$-0.234959\pi$
$212$	−1.94212	−	0.330978i	−0.133385	−	0.0227317i
$213$	27.8110	−	27.8110i	1.90558	−	1.90558i
$214$	27.0307	−	8.60801i	1.84778	−	0.588431i
$215$	5.69385	−	5.47855i	0.388317	−	0.373634i
$216$	−32.1528	−	24.2353i	−2.18772	−	1.64900i
$217$		0			0
$218$	−0.659246	+	1.27531i	−0.0446498	+	0.0863751i
$219$	21.3951			1.44575
$220$	−3.53849	−	5.20195i	−0.238565	−	0.350715i
$221$	4.57152			0.307514
$222$	17.3489	−	33.5615i	1.16438	−	2.25250i
$223$	9.54503	+	9.54503i	0.639183	+	0.639183i	0.950354	−	0.311171i	$-0.100721\pi$
$223$	9.54503	+	9.54503i	0.639183	+	0.639183i	−0.311171	+	0.950354i	$0.600721\pi$
$224$		0			0
$225$	1.42776	−	37.0310i	0.0951838	−	2.46873i
$226$	−14.0897	+	4.48692i	−0.937234	+	0.298465i
$227$	−13.0467	+	13.0467i	−0.865938	+	0.865938i	−0.992020	−	0.126082i	$-0.959760\pi$
$227$	−13.0467	+	13.0467i	−0.865938	+	0.865938i	0.126082	+	0.992020i	$0.459760\pi$
$228$	−3.04299	+	17.8557i	−0.201527	+	1.18252i
$229$			15.6173i			1.03202i	0.856583	+	0.516010i	$0.172583\pi$
$229$			15.6173i			1.03202i	−0.856583	+	0.516010i	$0.827417\pi$
$230$	−6.37072	+	1.89438i	−0.420073	+	0.124912i
$231$		0			0
$232$	−13.6044	+	1.91021i	−0.893172	+	0.125412i
$233$	2.70319	−	2.70319i	0.177092	−	0.177092i	−0.612995	−	0.790087i	$-0.710035\pi$
$233$	2.70319	−	2.70319i	0.177092	−	0.177092i	0.790087	+	0.612995i	$0.210035\pi$
$234$	−3.14544	−	9.87723i	−0.205624	−	0.645695i
$235$	−4.09794	−	4.25899i	−0.267320	−	0.277826i
$236$	8.17170	+	11.5291i	0.531932	+	0.750484i
$237$	1.36736	+	1.36736i	0.0888193	+	0.0888193i
$238$		0			0
$239$	15.4752			1.00101			0.500505	−	0.865734i	$-0.333148\pi$
$239$	15.4752			1.00101			0.500505	+	0.865734i	$0.333148\pi$
$240$	11.9926	+	26.2510i	0.774119	+	1.69449i
$241$	−28.7620			−1.85272			−0.926361	−	0.376636i	$-0.877081\pi$
$241$	−28.7620			−1.85272			−0.926361	+	0.376636i	$0.877081\pi$
$242$	−11.3329	−	5.85831i	−0.728507	−	0.376587i
$243$	23.8730	+	23.8730i	1.53146	+	1.53146i
$244$	−2.54241	−	3.58699i	−0.162761	−	0.229633i
$245$		0			0
$246$	−4.89298	−	15.3648i	−0.311965	−	0.979626i
$247$	−1.96275	+	1.96275i	−0.124887	+	0.124887i
$248$	−10.3002	+	1.44626i	−0.654061	+	0.0918378i
$249$			20.7065i			1.31222i
$250$	−8.05999	+	13.6028i	−0.509758	+	0.860318i
$251$		−	26.0285i		−	1.64291i	−0.570277	−	0.821453i	$-0.693164\pi$
$251$		−	26.0285i		−	1.64291i	0.570277	−	0.821453i	$-0.306836\pi$
$252$		0			0
$253$	2.09075	−	2.09075i	0.131444	−	0.131444i
$254$	16.9053	−	5.38356i	1.06073	−	0.337795i
$255$	33.3464	+	0.642608i	2.08823	+	0.0402417i
$256$	−12.4893	−	10.0008i	−0.780583	−	0.625052i
$257$	−16.3200	−	16.3200i	−1.01801	−	1.01801i	−0.999835	−	0.0181764i	$-0.994214\pi$
$257$	−16.3200	−	16.3200i	−1.01801	−	1.01801i	−0.0181764	−	0.999835i	$-0.505786\pi$
$258$	7.40472	−	14.3244i	0.460998	−	0.891801i
$259$		0			0
$260$	−0.826882	+	4.34476i	−0.0512811	+	0.269451i
$261$	35.9991			2.22829
$262$	−8.53894	+	16.5186i	−0.527538	+	1.02052i
$263$	8.02566	+	8.02566i	0.494883	+	0.494883i	0.909841	−	0.414958i	$-0.136204\pi$
$263$	8.02566	+	8.02566i	0.494883	+	0.494883i	−0.414958	+	0.909841i	$0.636204\pi$
$264$	−10.2528	−	7.72807i	−0.631016	−	0.475630i
$265$	−1.52722	−	1.58724i	−0.0938163	−	0.0975031i
$266$		0			0
$267$	1.05793	−	1.05793i	0.0647444	−	0.0647444i
$268$	6.30035	+	1.07371i	0.384855	+	0.0655875i
$269$			27.2178i			1.65950i	0.558136	+	0.829749i	$0.311517\pi$
$269$			27.2178i			1.65950i	−0.558136	+	0.829749i	$0.688483\pi$
$270$	−12.8306	−	43.1488i	−0.780847	−	2.62595i
$271$			0.155837i			0.00946643i	0.999989	+	0.00473321i	$0.00150663\pi$
$271$			0.155837i			0.00946643i	−0.999989	+	0.00473321i	$0.998493\pi$
$272$	−16.6672	+	8.00597i	−1.01060	+	0.485433i
$273$		0			0
$274$	−2.99919	−	9.41799i	−0.181188	−	0.568961i
$275$	0.270998	−	7.02873i	0.0163418	−	0.423848i
$276$	−11.0659	+	7.84339i	−0.666091	+	0.472116i
$277$	−14.8018	−	14.8018i	−0.889353	−	0.889353i	0.105108	−	0.994461i	$-0.466481\pi$
$277$	−14.8018	−	14.8018i	−0.889353	−	0.889353i	−0.994461	+	0.105108i	$0.966481\pi$
$278$	26.6807	+	13.7920i	1.60020	+	0.827191i
$279$	27.2556			1.63175
$280$		0			0
$281$	−2.56355			−0.152929			−0.0764644	−	0.997072i	$-0.524363\pi$
$281$	−2.56355			−0.152929			−0.0764644	+	0.997072i	$0.524363\pi$
$282$	−10.7147	−	5.53871i	−0.638048	−	0.329826i
$283$	14.5487	+	14.5487i	0.864828	+	0.864828i	0.991894	−	0.127066i	$-0.0405561\pi$
$283$	14.5487	+	14.5487i	0.864828	+	0.864828i	−0.127066	+	0.991894i	$0.540556\pi$
$284$	−19.8889	+	14.0970i	−1.18019	+	0.836503i
$285$	−14.5929	+	14.0411i	−0.864410	+	0.831724i
$286$	−0.597025	−	1.87476i	−0.0353028	−	0.110857i
$287$		0			0
$288$	28.7656	+	30.5026i	1.69503	+	1.79738i
$289$			4.36814i			0.256949i
$290$	−13.5058	−	7.31466i	−0.793087	−	0.429532i
$291$			36.5316i			2.14152i
$292$	−13.0728	−	2.22788i	−0.765025	−	0.130377i
$293$	−4.71102	+	4.71102i	−0.275221	+	0.275221i	−0.831198	−	0.555977i	$-0.812344\pi$
$293$	−4.71102	+	4.71102i	−0.275221	+	0.275221i	0.555977	+	0.831198i	$0.312344\pi$
$294$		0			0
$295$	−0.304410	+	15.7965i	−0.0177234	+	0.919708i
$296$	−14.0952	+	18.7001i	−0.819268	+	1.08692i
$297$	14.1606	+	14.1606i	0.821681	+	0.821681i
$298$	−4.31505	+	8.34746i	−0.249964	+	0.483556i
$299$	−2.07857			−0.120207
$300$	−6.64232	+	31.5761i	−0.383495	+	1.82305i
$301$		0			0
$302$	−13.2395	+	25.6118i	−0.761846	+	1.47379i
$303$	−13.7605	−	13.7605i	−0.790520	−	0.790520i
$304$	3.71862	−	10.5932i	0.213278	−	0.607563i
$305$	0.0947089	−	4.91466i	0.00542302	−	0.281413i
$306$	46.1680	−	14.7024i	2.63925	−	0.840478i
$307$	16.8508	−	16.8508i	0.961723	−	0.961723i	−0.0375706	−	0.999294i	$-0.511962\pi$
$307$	16.8508	−	16.8508i	0.961723	−	0.961723i	0.999294	+	0.0375706i	$0.0119619\pi$
$308$		0			0
$309$			45.4085i			2.58320i
$310$	−10.2255	−	5.53808i	−0.580769	−	0.314542i
$311$			18.1620i			1.02987i	0.857229	+	0.514936i	$0.172184\pi$
$311$			18.1620i			1.02987i	−0.857229	+	0.514936i	$0.827816\pi$
$312$	1.25501	+	8.93806i	0.0710509	+	0.506018i
$313$	1.10904	−	1.10904i	0.0626869	−	0.0626869i	−0.675068	−	0.737755i	$-0.735886\pi$
$313$	1.10904	−	1.10904i	0.0626869	−	0.0626869i	0.737755	+	0.675068i	$0.235886\pi$
$314$	7.62532	+	23.9449i	0.430322	+	1.35129i
$315$		0			0
$316$	−0.693093	−	0.977859i	−0.0389895	−	0.0550088i
$317$	20.8879	+	20.8879i	1.17318	+	1.17318i	0.981447	+	0.191733i	$0.0614107\pi$
$317$	20.8879	+	20.8879i	1.17318	+	1.17318i	0.191733	+	0.981447i	$0.438589\pi$
$318$	−3.99313	−	2.06416i	−0.223923	−	0.115753i
$319$	6.83286			0.382567
$320$	−4.59415	−	17.2885i	−0.256821	−	0.966459i
$321$	64.7258			3.61264
$322$		0			0
$323$	−9.17425	−	9.17425i	−0.510469	−	0.510469i
$324$	−27.4077	−	38.6684i	−1.52265	−	2.14825i
$325$	−3.62860	+	3.35918i	−0.201279	+	0.186334i
$326$	7.46173	+	23.4312i	0.413267	+	1.29773i
$327$	−2.31618	+	2.31618i	−0.128085	+	0.128085i
$328$	1.38975	+	9.89766i	0.0767360	+	0.546507i
$329$		0			0
$330$	−4.09139	−	13.7592i	−0.225224	−	0.757416i
$331$		−	12.6325i		−	0.694343i	−0.937802	−	0.347172i	$-0.887142\pi$
$331$		−	12.6325i		−	0.694343i	0.937802	−	0.347172i	$-0.112858\pi$
$332$	2.15617	−	12.6520i	0.118335	−	0.694367i
$333$	43.3904	−	43.3904i	2.37778	−	2.37778i
$334$	13.1295	−	4.18114i	0.718416	−	0.228782i
$335$	4.95439	+	5.14909i	0.270687	+	0.281325i
$336$		0			0
$337$	4.10542	+	4.10542i	0.223636	+	0.223636i	0.810028	−	0.586391i	$-0.199452\pi$
$337$	4.10542	+	4.10542i	0.223636	+	0.223636i	−0.586391	+	0.810028i	$0.699452\pi$
$338$	7.80721	−	15.1031i	0.424656	−	0.821499i
$339$	−33.7383			−1.83241
$340$	−20.3082	−	3.86500i	−1.10137	−	0.209609i
$341$	5.17330			0.280150
$342$	−13.5095	+	26.1342i	−0.730513	+	1.41318i
$343$		0			0
$344$	−6.01600	+	7.98140i	−0.324361	+	0.430328i
$345$	−15.1619	−	0.292179i	−0.816287	−	0.0157304i
$346$	−33.3390	+	10.6169i	−1.79232	+	0.570769i
$347$	−10.4434	+	10.4434i	−0.560631	+	0.560631i	−0.929487	−	0.368855i	$-0.879750\pi$
$347$	−10.4434	+	10.4434i	−0.560631	+	0.560631i	0.368855	+	0.929487i	$0.379750\pi$
$348$	−30.8992	−	5.26589i	−1.65637	−	0.282281i
$349$			5.05181i			0.270417i	0.990817	+	0.135209i	$0.0431705\pi$
$349$			5.05181i			0.270417i	−0.990817	+	0.135209i	$0.956830\pi$
$350$		0			0
$351$		−	14.0781i		−	0.751434i
$352$	5.45989	+	5.78960i	0.291013	+	0.308587i
$353$	−7.68947	+	7.68947i	−0.409269	+	0.409269i	−0.881484	−	0.472215i	$-0.843455\pi$
$353$	−7.68947	+	7.68947i	−0.409269	+	0.409269i	0.472215	+	0.881484i	$0.343455\pi$
$354$	9.78371	+	30.7226i	0.519998	+	1.63289i
$355$	−27.2506	−	0.525137i	−1.44631	−	0.0278714i
$356$	−0.756576	+	0.536251i	−0.0400984	+	0.0284212i
$357$		0			0
$358$	25.8236	+	13.3489i	1.36482	+	0.705514i
$359$	−4.98657			−0.263181			−0.131591	−	0.991304i	$-0.542008\pi$
$359$	−4.98657			−0.263181			−0.131591	+	0.991304i	$0.542008\pi$
$360$	5.62237	+	46.5373i	0.296325	+	2.45273i
$361$	−11.1222			−0.585379
$362$	−9.87429	−	5.10431i	−0.518981	−	0.268276i
$363$	−20.5825	−	20.5825i	−1.08030	−	1.08030i
$364$		0			0
$365$	−10.2800	−	10.6840i	−0.538079	−	0.559225i
$366$	−3.04394	−	9.55851i	−0.159109	−	0.499631i
$367$	11.2675	−	11.2675i	0.588160	−	0.588160i	−0.348973	−	0.937133i	$-0.613469\pi$
$367$	11.2675	−	11.2675i	0.588160	−	0.588160i	0.937133	+	0.348973i	$0.113469\pi$
$368$	7.57819	−	3.64013i	0.395041	−	0.189755i
$369$		−	26.1906i		−	1.36343i
$370$	−25.0953	+	7.46228i	−1.30464	+	0.387946i
$371$		0			0
$372$	−23.3944	−	3.98691i	−1.21294	−	0.206712i
$373$	−0.416629	+	0.416629i	−0.0215722	+	0.0215722i	−0.717811	−	0.696238i	$-0.754856\pi$
$373$	−0.416629	+	0.416629i	−0.0215722	+	0.0215722i	0.696238	+	0.717811i	$0.254856\pi$
$374$	8.76300	−	2.79061i	0.453124	−	0.144299i
$375$	−26.9406	+	23.9931i	−1.39121	+	1.23900i
$376$	5.97007	+	4.49996i	0.307883	+	0.232068i
$377$	−3.39653	−	3.39653i	−0.174930	−	0.174930i
$378$		0			0
$379$	23.7583			1.22038			0.610191	−	0.792254i	$-0.291093\pi$
$379$	23.7583			1.22038			0.610191	+	0.792254i	$0.291093\pi$
$380$	10.3786	−	7.05978i	0.532411	−	0.362159i
$381$	40.4804			2.07387
$382$	5.63203	−	10.8952i	0.288160	−	0.557446i
$383$	−3.03775	−	3.03775i	−0.155222	−	0.155222i	0.625224	−	0.780446i	$-0.285008\pi$
$383$	−3.03775	−	3.03775i	−0.155222	−	0.155222i	−0.780446	+	0.625224i	$0.785008\pi$
$384$	−20.2286	−	30.3892i	−1.03229	−	1.55079i
$385$		0			0
$386$	7.14943	−	2.27676i	0.363896	−	0.115884i
$387$	18.5195	−	18.5195i	0.941401	−	0.941401i
$388$	3.80404	−	22.3214i	0.193121	−	1.13320i
$389$		−	25.1901i		−	1.27719i	−0.769544	−	0.638593i	$-0.779517\pi$
$389$		−	25.1901i		−	1.27719i	0.769544	−	0.638593i	$-0.220483\pi$
$390$	−4.80572	+	8.87328i	−0.243347	+	0.449316i
$391$		−	9.71561i		−	0.491340i
$392$		0			0
$393$	−30.0006	+	30.0006i	−1.51333	+	1.51333i
$394$	7.49111	+	23.5234i	0.377396	+	1.18509i
$395$	0.0258189	−	1.33980i	0.00129909	−	0.0674127i
$396$	−12.0588	−	17.0133i	−0.605976	−	0.854949i
$397$	2.73642	+	2.73642i	0.137337	+	0.137337i	0.772433	−	0.635096i	$-0.219040\pi$
$397$	2.73642	+	2.73642i	0.137337	+	0.137337i	−0.635096	+	0.772433i	$0.719040\pi$
$398$	5.40057	+	2.79171i	0.270706	+	0.139936i
$399$		0			0
$400$	7.34658	−	18.6018i	0.367329	−	0.930091i
$401$	−5.48728			−0.274022			−0.137011	−	0.990570i	$-0.543750\pi$
$401$	−5.48728			−0.274022			−0.137011	+	0.990570i	$0.543750\pi$
$402$	12.9540	+	6.69627i	0.646085	+	0.333980i
$403$	−2.57158	−	2.57158i	−0.128100	−	0.128100i
$404$	6.97500	+	9.84076i	0.347019	+	0.489596i
$405$	1.02098	−	52.9811i	0.0507330	−	2.63265i
$406$		0			0
$407$	8.23579	−	8.23579i	0.408233	−	0.408233i
$408$	−41.7782	+	5.86615i	−2.06833	+	0.290418i
$409$		−	16.9930i		−	0.840250i	−0.907466	−	0.420125i	$-0.861986\pi$
$409$		−	16.9930i		−	0.840250i	0.907466	−	0.420125i	$-0.138014\pi$
$410$	−5.32167	+	9.82592i	−0.262818	+	0.485268i
$411$		−	22.5517i		−	1.11239i
$412$	4.72839	−	27.7453i	0.232951	−	1.36691i
$413$		0			0
$414$	−20.9916	+	6.68484i	−1.03168	+	0.328542i
$415$	10.3401	−	9.94910i	0.507575	−	0.488382i
$416$	0.163891	−	5.59198i	0.00803544	−	0.274169i
$417$	48.4567	+	48.4567i	2.37293	+	2.37293i
$418$	−2.56420	+	4.96045i	−0.125419	+	0.242624i
$419$	−3.87556			−0.189334			−0.0946668	−	0.995509i	$-0.530179\pi$
$419$	−3.87556			−0.189334			−0.0946668	+	0.995509i	$0.530179\pi$
$420$		0			0
$421$	20.7160			1.00964			0.504818	−	0.863226i	$-0.331560\pi$
$421$	20.7160			1.00964			0.504818	+	0.863226i	$0.331560\pi$
$422$	−12.6956	+	24.5597i	−0.618012	+	1.19555i
$423$	−13.8526	−	13.8526i	−0.673535	−	0.673535i
$424$	2.22492	+	1.67704i	0.108052	+	0.0814443i
$425$	−15.7015	−	16.9608i	−0.761632	−	0.822718i
$426$	−52.9995	+	16.8779i	−2.56783	+	0.817735i
$427$		0			0
$428$	−39.5485	−	6.73991i	−1.91165	−	0.325786i
$429$		−	4.48918i		−	0.216740i
$430$	−10.7110	+	3.18499i	−0.516529	+	0.153594i
$431$		−	9.76894i		−	0.470553i	−0.971928	−	0.235277i	$-0.924400\pi$
$431$		−	9.76894i		−	0.470553i	0.971928	−	0.235277i	$-0.0755996\pi$
$432$	24.6546	+	51.3270i	1.18619	+	2.46947i
$433$	−7.00877	+	7.00877i	−0.336820	+	0.336820i	−0.855169	−	0.518349i	$-0.826547\pi$
$433$	−7.00877	+	7.00877i	−0.336820	+	0.336820i	0.518349	+	0.855169i	$0.326547\pi$
$434$		0			0
$435$	−24.2981	−	25.2530i	−1.16501	−	1.21079i
$436$	1.65641	−	1.17404i	0.0793276	−	0.0562263i
$437$	4.17133	+	4.17133i	0.199542	+	0.199542i
$438$	−26.8785	−	13.8943i	−1.28430	−	0.663894i
$439$	4.42580			0.211232			0.105616	−	0.994407i	$-0.466319\pi$
$439$	4.42580			0.211232			0.105616	+	0.994407i	$0.466319\pi$
$440$	1.06716	+	8.83309i	0.0508750	+	0.421101i
$441$		0			0
$442$	−5.74315	−	2.96880i	−0.273174	−	0.141211i
$443$	3.11256	+	3.11256i	0.147882	+	0.147882i	0.777171	−	0.629289i	$-0.216654\pi$
$443$	3.11256	+	3.11256i	0.147882	+	0.147882i	−0.629289	+	0.777171i	$0.716654\pi$
$444$	−43.5905	+	30.8964i	−2.06872	+	1.46628i
$445$	−1.03661	−	0.0199762i	−0.0491402	−	0.000946965i
$446$	−5.79266	−	18.1900i	−0.274291	−	0.861321i
$447$	−15.1604	+	15.1604i	−0.717062	+	0.717062i
$448$		0			0
$449$		−	21.8355i		−	1.03048i	−0.857046	−	0.515240i	$-0.827703\pi$
$449$		−	21.8355i		−	1.03048i	0.857046	−	0.515240i	$-0.172297\pi$
$450$	−25.8421	+	45.5945i	−1.21821	+	2.14934i
$451$		−	4.97115i		−	0.234082i
$452$	20.6146	+	3.51317i	0.969631	+	0.165246i
$453$	−46.5153	+	46.5153i	−2.18548	+	2.18548i
$454$	24.8631	−	7.91772i	1.16688	−	0.371597i
$455$		0			0
$456$	15.4186	−	20.4557i	0.722041	−	0.957928i
$457$	−15.5775	−	15.5775i	−0.728683	−	0.728683i	0.241674	−	0.970357i	$-0.422304\pi$
$457$	−15.5775	−	15.5775i	−0.728683	−	0.728683i	−0.970357	+	0.241674i	$0.922304\pi$
$458$	10.1421	−	19.6198i	0.473908	−	0.916775i
$459$	65.8037			3.07146
$460$	9.23370	+	1.75733i	0.430524	+	0.0819360i
$461$	19.7670			0.920641			0.460321	−	0.887753i	$-0.347734\pi$
$461$	19.7670			0.920641			0.460321	+	0.887753i	$0.347734\pi$
$462$		0			0
$463$	14.5239	+	14.5239i	0.674983	+	0.674983i	0.958861	−	0.283877i	$-0.0916209\pi$
$463$	14.5239	+	14.5239i	0.674983	+	0.674983i	−0.283877	+	0.958861i	$0.591621\pi$
$464$	18.3316	+	6.43507i	0.851022	+	0.298741i
$465$	−18.3966	−	19.1196i	−0.853123	−	0.886649i
$466$	−5.15147	+	1.64050i	−0.238637	+	0.0759949i
$467$	−19.9348	+	19.9348i	−0.922473	+	0.922473i	−0.997204	−	0.0747303i	$-0.976190\pi$
$467$	−19.9348	+	19.9348i	−0.922473	+	0.922473i	0.0747303	+	0.997204i	$0.476190\pi$
$468$	−2.46282	+	14.4513i	−0.113844	+	0.668014i
$469$		0			0
$470$	2.38236	+	8.01178i	0.109890	+	0.369556i
$471$			57.3367i			2.64194i
$472$	−2.77885	−	19.7908i	−0.127907	−	0.910943i
$473$	3.51513	−	3.51513i	0.161626	−	0.161626i
$474$	−0.829817	−	2.60577i	−0.0381148	−	0.119687i
$475$	14.0233	+	0.540678i	0.643432	+	0.0248080i
$476$		0			0
$477$	−5.16257	−	5.16257i	−0.236378	−	0.236378i
$478$	−19.4414	−	10.0498i	−0.889228	−	0.459668i
$479$	1.41875			0.0648244			0.0324122	−	0.999475i	$-0.489681\pi$
$479$	1.41875			0.0648244			0.0324122	+	0.999475i	$0.489681\pi$
$480$	1.98154	−	40.7670i	0.0904444	−	1.86075i
$481$	−8.18782			−0.373332
$482$	36.1334	+	18.6784i	1.64583	+	0.850777i
$483$		0			0
$484$	10.4330	+	14.7195i	0.474225	+	0.669067i
$485$	18.2426	−	17.5528i	0.828353	−	0.797031i
$486$	−14.4880	−	45.4949i	−0.657189	−	2.06369i
$487$	−23.8013	+	23.8013i	−1.07854	+	1.07854i	−0.0818995	+	0.996641i	$0.526099\pi$
$487$	−23.8013	+	23.8013i	−1.07854	+	1.07854i	−0.996641	+	0.0818995i	$0.973901\pi$
$488$	0.864566	+	6.15736i	0.0391370	+	0.278731i
$489$			56.1067i			2.53723i
$490$		0			0
$491$		−	3.16673i		−	0.142913i	−0.997444	−	0.0714563i	$-0.977235\pi$
$491$		−	3.16673i		−	0.142913i	0.997444	−	0.0714563i	$-0.0227647\pi$
$492$	−3.83111	+	22.4803i	−0.172720	+	1.01349i
$493$	15.8760	−	15.8760i	0.715020	−	0.715020i
$494$	3.74041	−	1.19115i	0.168289	−	0.0535922i
$495$	0.449210	−	23.3105i	0.0201905	−	1.04773i
$496$	13.8792	+	4.87213i	0.623195	+	0.218765i
$497$		0			0
$498$	13.4470	−	26.0133i	0.602576	−	1.16568i
$499$	7.44903			0.333464			0.166732	−	0.986002i	$-0.446678\pi$
$499$	7.44903			0.333464			0.166732	+	0.986002i	$0.446678\pi$
$500$	18.9595	−	11.8548i	0.847895	−	0.530164i
$501$	31.4391			1.40459
$502$	−16.9032	+	32.6994i	−0.754429	+	1.45944i
$503$	19.3043	+	19.3043i	0.860736	+	0.860736i	0.991424	−	0.130687i	$-0.0417184\pi$
$503$	19.3043	+	19.3043i	0.860736	+	0.860736i	−0.130687	+	0.991424i	$0.541718\pi$
$504$		0			0
$505$	−0.259830	+	13.4832i	−0.0115623	+	0.599994i
$506$	−3.98434	+	1.26883i	−0.177125	+	0.0564062i
$507$	27.4297	−	27.4297i	1.21820	−	1.21820i
$508$	−24.7341	−	4.21523i	−1.09740	−	0.187020i
$509$		−	11.3832i		−	0.504553i	−0.967655	−	0.252276i	$-0.918821\pi$
$509$		−	11.3832i		−	0.504553i	0.967655	−	0.252276i	$-0.0811792\pi$
$510$	−41.4754	−	22.4629i	−1.83656	−	0.994672i
$511$		0			0
$512$	9.19554	+	20.6747i	0.406390	+	0.913700i
$513$	−28.2523	+	28.2523i	−1.24737	+	1.24737i
$514$	9.90421	+	31.1010i	0.436856	+	1.37181i
$515$	22.6754	−	21.8180i	0.999198	−	0.961416i
$516$	−18.6049	+	13.1869i	−0.819037	+	0.580522i
$517$	−2.62931	−	2.62931i	−0.115637	−	0.115637i
$518$		0			0
$519$	−79.8313			−3.50421
$520$	3.86035	−	4.92129i	0.169287	−	0.215813i
$521$	1.23560			0.0541325			0.0270662	−	0.999634i	$-0.491383\pi$
$521$	1.23560			0.0541325			0.0270662	+	0.999634i	$0.491383\pi$
$522$	−45.2253	−	23.3783i	−1.97946	−	1.02324i
$523$	−4.46402	−	4.46402i	−0.195198	−	0.195198i	0.602740	−	0.797938i	$-0.294076\pi$
$523$	−4.46402	−	4.46402i	−0.195198	−	0.195198i	−0.797938	+	0.602740i	$0.794076\pi$
$524$	21.4548	−	15.2068i	0.937256	−	0.664314i
$525$		0			0
$526$	−4.87059	−	15.2945i	−0.212368	−	0.666872i
$527$	12.0201	−	12.0201i	0.523602	−	0.523602i
$528$	7.86178	+	16.3670i	0.342140	+	0.712282i
$529$		−	18.5825i		−	0.807936i
$530$	0.887857	+	2.98582i	0.0385661	+	0.129696i
$531$			52.3691i			2.27262i
$532$		0			0
$533$	−2.47109	+	2.47109i	−0.107035	+	0.107035i
$534$	−2.01610	+	0.642035i	−0.0872454	+	0.0277836i
$535$	−31.0996	−	32.3218i	−1.34455	−	1.39739i
$536$	−7.21778	−	5.44042i	−0.311761	−	0.234991i
$537$	46.8999	+	46.8999i	2.02388	+	2.02388i
$538$	17.6756	−	34.1934i	0.762048	−	1.47418i
$539$		0			0
$540$	−11.9024	+	62.5398i	−0.512197	+	2.69128i
$541$	−32.2710			−1.38744			−0.693719	−	0.720246i	$-0.744029\pi$
$541$	−32.2710			−1.38744			−0.693719	+	0.720246i	$0.744029\pi$
$542$	0.101203	−	0.195776i	0.00434702	−	0.00840932i
$543$	−17.9334	−	17.9334i	−0.769595	−	0.769595i
$544$	26.1380	+	0.766059i	1.12066	+	0.0328445i
$545$	2.26951	+	0.0437350i	0.0972150	+	0.00187340i
$546$		0			0
$547$	−17.6256	+	17.6256i	−0.753617	+	0.753617i	−0.975152	−	0.221536i	$-0.928893\pi$
$547$	−17.6256	+	17.6256i	−0.753617	+	0.753617i	0.221536	+	0.975152i	$0.428893\pi$
$548$	−2.34831	+	13.7794i	−0.100315	+	0.588628i
$549$		−	16.2932i		−	0.695378i
$550$	−4.90500	+	8.65413i	−0.209150	+	0.369013i
$551$			13.6325i			0.580764i
$552$	18.9956	−	2.66721i	0.808507	−	0.113524i
$553$		0			0
$554$	8.98286	+	28.2078i	0.381645	+	1.19843i
$555$	−59.7250	−	1.15094i	−2.53519	−	0.0488548i
$556$	−24.5620	−	34.6536i	−1.04166	−	1.46964i
$557$	4.37875	+	4.37875i	0.185534	+	0.185534i	0.793762	−	0.608228i	$-0.208120\pi$
$557$	4.37875	+	4.37875i	0.185534	+	0.185534i	−0.608228	+	0.793762i	$0.708120\pi$
$558$	−34.2410	−	17.7002i	−1.44954	−	0.749307i
$559$	−3.49465			−0.147808
$560$		0			0
$561$	20.9833			0.885915
$562$	3.22057	+	1.66480i	0.135851	+	0.0702255i
$563$	3.63223	+	3.63223i	0.153080	+	0.153080i	0.779492	−	0.626412i	$-0.215477\pi$
$563$	3.63223	+	3.63223i	0.153080	+	0.153080i	−0.626412	+	0.779492i	$0.715477\pi$
$564$	9.86379	+	13.9165i	0.415341	+	0.585989i
$565$	16.2107	+	16.8477i	0.681988	+	0.708789i
$566$	−8.82925	−	27.7254i	−0.371121	−	1.16539i
$567$		0			0
$568$	34.1410	−	4.79380i	1.43253	−	0.201143i
$569$			34.6567i			1.45288i	0.687227	+	0.726442i	$0.258828\pi$
$569$			34.6567i			1.45288i	−0.687227	+	0.726442i	$0.741172\pi$
$570$	27.4514	−	8.16289i	1.14981	−	0.341906i
$571$		−	33.3982i		−	1.39767i	−0.715282	−	0.698836i	$-0.753702\pi$
$571$		−	33.3982i		−	1.39767i	0.715282	−	0.698836i	$-0.246298\pi$
$572$	−0.467459	+	2.74296i	−0.0195454	+	0.114689i
$573$	19.7875	−	19.7875i	0.826634	−	0.826634i
$574$		0			0
$575$	7.13910	+	7.71168i	0.297721	+	0.321599i
$576$	−16.3291	−	57.0008i	−0.680379	−	2.37503i
$577$	24.3607	+	24.3607i	1.01415	+	1.01415i	0.999898	+	0.0142510i	$0.00453637\pi$
$577$	24.3607	+	24.3607i	1.01415	+	1.01415i	0.0142510	+	0.999898i	$0.495464\pi$
$578$	2.83672	−	5.48765i	0.117992	−	0.228256i
$579$	17.1196			0.711464
$580$	12.2169	+	17.9602i	0.507281	+	0.745755i
$581$		0			0
$582$	23.7241	−	45.8942i	0.983394	−	1.90238i
$583$	−0.979889	−	0.979889i	−0.0405829	−	0.0405829i
$584$	14.9764	+	11.2885i	0.619726	+	0.467120i
$585$	−11.8107	+	11.3641i	−0.488311	+	0.469846i
$586$	8.97779	−	2.85901i	0.370869	−	0.118105i
$587$	−23.3690	+	23.3690i	−0.964544	+	0.964544i	−0.999393	−	0.0348489i	$-0.988905\pi$
$587$	−23.3690	+	23.3690i	−0.964544	+	0.964544i	0.0348489	+	0.999393i	$0.488905\pi$
$588$		0			0
$589$			10.3214i			0.425288i
$590$	10.6409	−	19.6473i	0.438078	−	0.808867i
$591$			56.3276i			2.31701i
$592$	29.8517	−	14.3391i	1.22690	−	0.589333i
$593$	4.58805	−	4.58805i	0.188409	−	0.188409i	−0.606599	−	0.795008i	$-0.707467\pi$
$593$	4.58805	−	4.58805i	0.188409	−	0.188409i	0.795008	+	0.606599i	$0.207467\pi$
$594$	−8.59374	−	26.9859i	−0.352606	−	1.10724i
$595$		0			0
$596$	10.8419	−	7.68459i	0.444101	−	0.314773i
$597$	9.80834	+	9.80834i	0.401429	+	0.401429i
$598$	2.61128	+	1.34985i	0.106783	+	0.0551994i
$599$	−17.5172			−0.715733			−0.357867	−	0.933773i	$-0.616496\pi$
$599$	−17.5172			−0.715733			−0.357867	+	0.933773i	$0.616496\pi$
$600$	28.8506	−	35.3551i	1.17782	−	1.44337i
$601$	−2.55297			−0.104138			−0.0520689	−	0.998643i	$-0.516582\pi$
$601$	−2.55297			−0.104138			−0.0520689	+	0.998643i	$0.516582\pi$
$602$		0			0
$603$	16.7477	+	16.7477i	0.682018	+	0.682018i
$604$	33.2652	−	23.5779i	1.35354	−	0.959372i
$605$	−0.388645	+	20.1677i	−0.0158007	+	0.819933i
$606$	8.35093	+	26.2234i	0.339233	+	1.06525i
$607$	15.6500	−	15.6500i	0.635214	−	0.635214i	−0.314157	−	0.949371i	$-0.601722\pi$
$607$	15.6500	−	15.6500i	0.635214	−	0.635214i	0.949371	+	0.314157i	$0.101722\pi$
$608$	−11.5510	+	10.8932i	−0.468457	+	0.441779i
$609$		0			0
$610$	−3.31062	+	6.11273i	−0.134043	+	0.247497i
$611$			2.61399i			0.105751i
$612$	−67.5483	−	11.5117i	−2.73048	−	0.465332i
$613$	5.70344	−	5.70344i	0.230360	−	0.230360i	−0.582483	−	0.812843i	$-0.697919\pi$
$613$	5.70344	−	5.70344i	0.230360	−	0.230360i	0.812843	+	0.582483i	$0.197919\pi$
$614$	−32.1125	+	10.2263i	−1.29596	+	0.412701i
$615$	−18.3724	+	17.6777i	−0.740849	+	0.712835i
$616$		0			0
$617$	−20.7105	−	20.7105i	−0.833772	−	0.833772i	0.154258	−	0.988031i	$-0.450701\pi$
$617$	−20.7105	−	20.7105i	−0.833772	−	0.833772i	−0.988031	+	0.154258i	$0.950701\pi$
$618$	29.4889	−	57.0462i	1.18622	−	2.29474i
$619$	30.5003			1.22591			0.612956	−	0.790117i	$-0.289980\pi$
$619$	30.5003			1.22591			0.612956	+	0.790117i	$0.289980\pi$
$620$	9.24969	+	13.5980i	0.371477	+	0.546109i
$621$	−29.9195			−1.20063
$622$	11.7946	−	22.8167i	0.472921	−	0.914866i
$623$		0			0
$624$	4.22784	−	12.0438i	0.169249	−	0.482138i
$625$	24.9258	+	1.92492i	0.997031	+	0.0769970i
$626$	−2.11351	+	0.673054i	−0.0844728	+	0.0269006i
$627$	−9.00902	+	9.00902i	−0.359786	+	0.359786i
$628$	5.97048	−	35.0336i	0.238248	−	1.39799i
$629$		−	38.2714i		−	1.52598i
$630$		0			0
$631$			24.2931i			0.967092i	0.875319	+	0.483546i	$0.160651\pi$
$631$			24.2931i			0.967092i	−0.875319	+	0.483546i	$0.839349\pi$
$632$	0.235692	+	1.67858i	0.00937532	+	0.0667702i
$633$	−44.6045	+	44.6045i	−1.77287	+	1.77287i
$634$	−12.6764	−	39.8061i	−0.503443	−	1.58090i
$635$	−19.4501	−	20.2145i	−0.771854	−	0.802187i
$636$	3.67603	+	5.18637i	0.145764	+	0.205653i
$637$		0			0
$638$	−8.58406	−	4.43735i	−0.339846	−	0.175676i
$639$	−90.3419			−3.57387
$640$	−5.45582	+	24.7029i	−0.215660	+	0.976468i
$641$	22.4171			0.885424			0.442712	−	0.896664i	$-0.354016\pi$
$641$	22.4171			0.885424			0.442712	+	0.896664i	$0.354016\pi$
$642$	−81.3144	−	42.0338i	−3.20922	−	1.65894i
$643$	−3.56268	−	3.56268i	−0.140498	−	0.140498i	0.633359	−	0.773858i	$-0.281675\pi$
$643$	−3.56268	−	3.56268i	−0.140498	−	0.140498i	−0.773858	+	0.633359i	$0.781675\pi$
$644$		0			0
$645$	−25.4913	−	0.491236i	−1.00372	−	0.0193424i
$646$	5.56764	+	17.4834i	0.219056	+	0.687875i
$647$	−11.7294	+	11.7294i	−0.461132	+	0.461132i	−0.899026	−	0.437895i	$-0.855724\pi$
$647$	−11.7294	+	11.7294i	−0.461132	+	0.461132i	0.437895	+	0.899026i	$0.355724\pi$
$648$	9.32019	+	66.3776i	0.366132	+	2.60756i
$649$			9.94000i			0.390179i
$650$	6.74007	−	1.86365i	0.264367	−	0.0730983i
$651$		0			0
$652$	5.84240	−	34.2821i	0.228806	−	1.34259i
$653$	−8.87321	+	8.87321i	−0.347235	+	0.347235i	−0.859079	−	0.511843i	$-0.828963\pi$
$653$	−8.87321	+	8.87321i	−0.347235	+	0.347235i	0.511843	+	0.859079i	$0.328963\pi$
$654$	4.41395	−	1.40564i	0.172599	−	0.0549648i
$655$	29.3960	+	0.566481i	1.14860	+	0.0221342i
$656$	4.68174	−	13.3368i	0.182791	−	0.520716i
$657$	−34.7502	−	34.7502i	−1.35573	−	1.35573i
$658$		0			0
$659$	33.3787			1.30025			0.650126	−	0.759827i	$-0.274716\pi$
$659$	33.3787			1.30025			0.650126	+	0.759827i	$0.274716\pi$
$660$	−3.79539	+	19.9425i	−0.147736	+	0.776260i
$661$	6.95780			0.270627			0.135313	−	0.990803i	$-0.456796\pi$
$661$	6.95780			0.270627			0.135313	+	0.990803i	$0.456796\pi$
$662$	−8.20368	+	15.8700i	−0.318845	+	0.616806i
$663$	−10.4305	−	10.4305i	−0.405088	−	0.405088i
$664$	−10.9251	+	14.4943i	−0.423977	+	0.562488i
$665$		0			0
$666$	−82.6892	+	26.3327i	−3.20414	+	1.02037i
$667$	−7.21847	+	7.21847i	−0.279500	+	0.279500i
$668$	−19.2098	−	3.27375i	−0.743248	−	0.126665i
$669$		−	43.5565i		−	1.68399i
$670$	−2.88026	−	9.68619i	−0.111274	−	0.374210i
$671$		−	3.09256i		−	0.119387i
$672$		0			0
$673$	−5.34897	+	5.34897i	−0.206188	+	0.206188i	−0.802645	−	0.596457i	$-0.796575\pi$
$673$	−5.34897	+	5.34897i	−0.206188	+	0.206188i	0.596457	+	0.802645i	$0.296575\pi$
$674$	−2.49149	−	7.82371i	−0.0959684	−	0.301358i
$675$	−52.2311	+	48.3530i	−2.01038	+	1.86111i
$676$	−19.6162	+	13.9037i	−0.754471	+	0.534759i
$677$	−21.2244	−	21.2244i	−0.815721	−	0.815721i	0.169764	−	0.985485i	$-0.445700\pi$
$677$	−21.2244	−	21.2244i	−0.815721	−	0.815721i	−0.985485	+	0.169764i	$0.945700\pi$
$678$	42.3851	+	21.9101i	1.62779	+	0.841451i
$679$		0			0
$680$	23.0030	+	18.0440i	0.882127	+	0.691955i
$681$	59.5354			2.28140
$682$	−6.49917	−	3.35961i	−0.248866	−	0.128646i
$683$	13.4673	+	13.4673i	0.515313	+	0.515313i	0.916150	−	0.400837i	$-0.131281\pi$
$683$	13.4673	+	13.4673i	0.515313	+	0.515313i	−0.400837	+	0.916150i	$0.631281\pi$
$684$	33.9438	−	24.0589i	1.29787	−	0.919916i
$685$	−11.2615	+	10.8357i	−0.430281	+	0.414010i
$686$		0			0
$687$	35.6329	−	35.6329i	1.35948	−	1.35948i
$688$	12.7411	−	6.12009i	0.485749	−	0.233326i
$689$			0.974181i			0.0371133i
$690$	18.8579	+	10.2134i	0.717909	+	0.388816i
$691$			28.2561i			1.07491i	0.843291	+	0.537457i	$0.180615\pi$
$691$			28.2561i			1.07491i	−0.843291	+	0.537457i	$0.819385\pi$
$692$	48.7782	+	8.31284i	1.85427	+	0.316007i
$693$		0			0
$694$	19.9020	−	6.33786i	0.755470	−	0.240582i
$695$	0.914975	−	47.4801i	0.0347070	−	1.80102i
$696$	35.3986	+	26.6818i	1.34178	+	1.01137i
$697$	−11.5504	−	11.5504i	−0.437501	−	0.437501i
$698$	3.28071	−	6.34654i	0.124177	−	0.240220i
$699$	−12.3354			−0.466567
$700$		0			0
$701$	−26.0149			−0.982568			−0.491284	−	0.871000i	$-0.663472\pi$
$701$	−26.0149			−0.982568			−0.491284	+	0.871000i	$0.663472\pi$
$702$	−9.14250	+	17.6862i	−0.345061	+	0.667522i
$703$	16.4315	+	16.4315i	0.619727	+	0.619727i
$704$	−3.09937	−	10.8191i	−0.116812	−	0.407762i
$705$	−0.367443	+	19.0675i	−0.0138387	+	0.718122i
$706$	14.6538	−	4.66656i	0.551504	−	0.175628i
$707$		0			0
$708$	7.66046	−	44.9501i	0.287898	−	1.68933i
$709$			17.6058i			0.661200i	0.943771	+	0.330600i	$0.107251\pi$
$709$			17.6058i			0.661200i	−0.943771	+	0.330600i	$0.892749\pi$
$710$	33.8936	+	18.3566i	1.27200	+	0.688910i
$711$		−	4.44175i		−	0.166579i
$712$	1.29873	−	0.182356i	0.0486718	−	0.00683409i
$713$	−5.46525	+	5.46525i	−0.204675	+	0.204675i
$714$		0			0
$715$	−2.24174	+	2.15697i	−0.0838363	+	0.0806663i
$716$	−23.7729	−	33.5403i	−0.888435	−	1.25346i
$717$	−35.3088	−	35.3088i	−1.31863	−	1.31863i
$718$	6.26458	+	3.23834i	0.233792	+	0.120854i
$719$	23.1731			0.864212			0.432106	−	0.901823i	$-0.357771\pi$
$719$	23.1731			0.864212			0.432106	+	0.901823i	$0.357771\pi$
$720$	23.1586	−	62.1156i	0.863070	−	2.31491i
$721$		0			0
$722$	13.9727	+	7.22290i	0.520011	+	0.268809i
$723$	65.6243	+	65.6243i	2.44059	+	2.44059i
$724$	9.09017	+	12.8250i	0.337834	+	0.476637i
$725$	−0.935642	+	24.2673i	−0.0347489	+	0.901264i
$726$	12.4910	+	39.2241i	0.463586	+	1.45574i
$727$	15.3777	−	15.3777i	0.570326	−	0.570326i	−0.361893	−	0.932220i	$-0.617869\pi$
$727$	15.3777	−	15.3777i	0.570326	−	0.570326i	0.932220	+	0.361893i	$0.117869\pi$
$728$		0			0
$729$		−	37.8443i		−	1.40164i
$730$	5.97633	+	20.0981i	0.221194	+	0.743865i
$731$		−	16.3347i		−	0.604160i
$732$	−2.38335	+	13.9850i	−0.0880910	+	0.516901i
$733$	29.5375	−	29.5375i	1.09099	−	1.09099i	0.0955709	−	0.995423i	$-0.469532\pi$
$733$	29.5375	−	29.5375i	1.09099	−	1.09099i	0.995423	−	0.0955709i	$-0.0304677\pi$
$734$	−21.4725	+	6.83800i	−0.792566	+	0.252395i
$735$		0			0
$736$	−11.8844	−	0.348310i	−0.438063	−	0.0128389i
$737$	3.17882	+	3.17882i	0.117093	+	0.117093i
$738$	−17.0085	+	32.9030i	−0.626091	+	1.21117i
$739$	−28.9475			−1.06485			−0.532426	−	0.846476i	$-0.678720\pi$
$739$	−28.9475			−1.06485			−0.532426	+	0.846476i	$0.678720\pi$
$740$	36.3731	+	6.92241i	1.33710	+	0.254473i
$741$	8.95654			0.329027
$742$		0			0
$743$	−23.4115	−	23.4115i	−0.858885	−	0.858885i	0.132322	−	0.991207i	$-0.457757\pi$
$743$	−23.4115	−	23.4115i	−0.858885	−	0.858885i	−0.991207	+	0.132322i	$0.957757\pi$
$744$	26.8010	+	20.2013i	0.982574	+	0.740617i
$745$	14.8549	+	0.286264i	0.544241	+	0.0104879i
$746$	0.793971	−	0.252843i	0.0290694	−	0.00925723i
$747$	33.6316	−	33.6316i	1.23052	−	1.23052i
$748$	−12.8211	−	2.18499i	−0.468786	−	0.0798912i
$749$		0			0
$750$	49.4266	−	12.6467i	1.80480	−	0.461793i
$751$			44.0147i			1.60612i	0.595899	+	0.803059i	$0.296796\pi$
$751$			44.0147i			1.60612i	−0.595899	+	0.803059i	$0.703204\pi$
$752$	−4.57781	−	9.53029i	−0.166936	−	0.347534i
$753$	−59.3875	+	59.3875i	−2.16420	+	2.16420i
$754$	2.06128	+	6.47277i	0.0750673	+	0.235725i
$755$	45.5779	+	0.878318i	1.65875	+	0.0319653i
$756$		0			0
$757$	24.7062	+	24.7062i	0.897961	+	0.897961i	0.995256	−	0.0972943i	$-0.0310188\pi$
$757$	24.7062	+	24.7062i	0.897961	+	0.897961i	−0.0972943	+	0.995256i	$0.531019\pi$
$758$	−29.8473	−	15.4289i	−1.08410	−	0.560405i
$759$	−9.54063			−0.346303
$760$	−17.6232	+	2.12913i	−0.639262	+	0.0772318i
$761$	4.49696			0.163015			0.0815073	−	0.996673i	$-0.474027\pi$
$761$	4.49696			0.163015			0.0815073	+	0.996673i	$0.474027\pi$
$762$	−50.8551	−	26.2885i	−1.84229	−	0.952331i
$763$		0			0
$764$	−14.1509	+	10.0300i	−0.511963	+	0.362872i
$765$	−53.1178	−	55.2052i	−1.92048	−	1.99595i
$766$	1.84354	+	5.78904i	0.0666098	+	0.209167i
$767$	4.94105	−	4.94105i	0.178411	−	0.178411i
$768$	5.67783	+	51.3143i	0.204881	+	1.85165i
$769$			14.9079i			0.537593i	0.963197	+	0.268797i	$0.0866259\pi$
$769$			14.9079i			0.537593i	−0.963197	+	0.268797i	$0.913374\pi$
$770$		0			0
$771$			74.4723i			2.68206i
$772$	−10.4603	−	1.78266i	−0.376475	−	0.0641593i
$773$	−19.5855	+	19.5855i	−0.704443	+	0.704443i	−0.965361	−	0.260918i	$-0.915975\pi$
$773$	−19.5855	+	19.5855i	−0.704443	+	0.704443i	0.260918	+	0.965361i	$0.415975\pi$
$774$	−35.2927	+	11.2391i	−1.26857	+	0.403981i
$775$	−0.708394	+	18.3732i	−0.0254462	+	0.659987i
$776$	−19.2747	+	25.5717i	−0.691923	+	0.917971i
$777$		0			0
$778$	−16.3587	+	31.6460i	−0.586489	+	1.13456i
$779$	9.91812			0.355354
$780$	11.7998	−	8.02651i	0.422500	−	0.287395i
$781$	−17.1475			−0.613585
$782$	−6.30944	+	12.2056i	−0.225625	+	0.436472i
$783$	−48.8906	−	48.8906i	−1.74721	−	1.74721i
$784$		0			0
$785$	28.6320	−	27.5493i	1.02192	−	0.983277i
$786$	57.1721	−	18.2067i	2.03926	−	0.649410i
$787$	−3.97509	+	3.97509i	−0.141697	+	0.141697i	−0.774397	−	0.632700i	$-0.781947\pi$
$787$	−3.97509	+	3.97509i	−0.141697	+	0.141697i	0.632700	+	0.774397i	$0.281947\pi$
$788$	5.86539	−	34.4170i	0.208946	−	1.22606i
$789$		−	36.6232i		−	1.30382i
$790$	−0.902519	+	1.66641i	−0.0321102	+	0.0592882i
$791$		0			0
$792$	4.10068	+	29.2047i	0.145711	+	1.03774i
$793$	−1.53727	+	1.53727i	−0.0545902	+	0.0545902i
$794$	−1.66067	−	5.21481i	−0.0589350	−	0.185067i
$795$	−0.136938	+	7.10604i	−0.00485670	+	0.252025i
$796$	−4.97170	−	7.01439i	−0.176217	−	0.248618i
$797$	10.9874	+	10.9874i	0.389195	+	0.389195i	0.874400	−	0.485205i	$-0.161255\pi$
$797$	10.9874	+	10.9874i	0.389195	+	0.389195i	−0.485205	+	0.874400i	$0.661255\pi$
$798$		0			0
$799$	−12.2183			−0.432252
$800$	−21.3097	+	18.5983i	−0.753411	+	0.657550i
$801$	−3.43661			−0.121427
$802$	6.89362	+	3.56351i	0.243422	+	0.125832i
$803$	−6.59582	−	6.59582i	−0.232761	−	0.232761i
$804$	−11.9253	−	16.8249i	−0.420572	−	0.593369i
$805$		0			0
$806$	1.56063	+	4.90067i	0.0549710	+	0.172619i
$807$	62.1011	−	62.1011i	2.18606	−	2.18606i
$808$	−2.37190	−	16.8925i	−0.0834433	−	0.594276i
$809$			16.6619i			0.585802i	0.956143	+	0.292901i	$0.0946207\pi$
$809$			16.6619i			0.585802i	−0.956143	+	0.292901i	$0.905379\pi$
$810$	−35.6892	+	65.8965i	−1.25399	+	2.31537i
$811$			30.5372i			1.07231i	0.844120	+	0.536154i	$0.180123\pi$
$811$			30.5372i			1.07231i	−0.844120	+	0.536154i	$0.819877\pi$
$812$		0			0
$813$	0.355563	−	0.355563i	0.0124701	−	0.0124701i
$814$	−15.6950	+	4.99811i	−0.550108	+	0.175184i
$815$	28.0177	−	26.9583i	0.981418	−	0.944308i
$816$	56.2951	+	19.7617i	1.97072	+	0.691798i
$817$	7.01317	+	7.01317i	0.245360	+	0.245360i
$818$	−11.0355	+	21.3481i	−0.385846	+	0.746420i
$819$		0			0
$820$	13.0666	−	8.88825i	0.456307	−	0.310391i
$821$	−18.4845			−0.645114			−0.322557	−	0.946550i	$-0.604542\pi$
$821$	−18.4845			−0.645114			−0.322557	+	0.946550i	$0.604542\pi$
$822$	−14.6453	+	28.3314i	−0.510815	+	0.988173i
$823$	30.2574	+	30.2574i	1.05471	+	1.05471i	0.998414	+	0.0562914i	$0.0179276\pi$
$823$	30.2574	+	30.2574i	1.05471	+	1.05471i	0.0562914	+	0.998414i	$0.482072\pi$
$824$	−23.9584	+	31.7855i	−0.834630	+	1.10730i
$825$	−16.6553	+	15.4187i	−0.579863	+	0.536809i
$826$		0			0
$827$	22.7990	−	22.7990i	0.792801	−	0.792801i	−0.189148	−	0.981949i	$-0.560573\pi$
$827$	22.7990	−	22.7990i	0.792801	−	0.792801i	0.981949	+	0.189148i	$0.0605726\pi$
$828$	30.7127	+	5.23410i	1.06734	+	0.181898i
$829$		−	33.4892i		−	1.16313i	−0.813501	−	0.581563i	$-0.802441\pi$
$829$		−	33.4892i		−	1.16313i	0.813501	−	0.581563i	$-0.197559\pi$
$830$	−19.4512	+	5.78397i	−0.675161	+	0.200764i
$831$			67.5445i			2.34309i
$832$	−3.83740	+	6.91871i	−0.133038	+	0.239863i
$833$		0			0
$834$	−29.4072	−	92.3440i	−1.01829	−	3.19761i
$835$	−15.1059	−	15.6996i	−0.522762	−	0.543306i
$836$	6.44276	−	4.56654i	0.222828	−	0.157937i
$837$	−37.0161	−	37.0161i	−1.27946	−	1.27946i
$838$	4.86883	+	2.51684i	0.168191	+	0.0869428i
$839$	6.43773			0.222255			0.111127	−	0.993806i	$-0.464554\pi$
$839$	6.43773			0.222255			0.111127	+	0.993806i	$0.464554\pi$
$840$		0			0
$841$	5.40897			0.186516
$842$	−26.0253	−	13.4532i	−0.896890	−	0.463629i
$843$	5.84909	+	5.84909i	0.201453	+	0.201453i
$844$	31.8987	−	22.6094i	1.09800	−	0.778247i
$845$	−26.8769	−	0.517937i	−0.924595	−	0.0178176i
$846$	8.40681	+	26.3989i	0.289032	+	0.907612i
$847$		0			0
$848$	−1.70605	−	3.55174i	−0.0585862	−	0.121967i
$849$		−	66.3894i		−	2.27848i
$850$	8.71104	+	31.5044i	0.298786	+	1.08059i
$851$			17.4011i			0.596504i
$852$	77.5434	+	13.2151i	2.65659	+	0.452740i
$853$	−10.0581	+	10.0581i	−0.344383	+	0.344383i	−0.858012	−	0.513629i	$-0.828301\pi$
$853$	−10.0581	+	10.0581i	−0.344383	+	0.344383i	0.513629	+	0.858012i	$0.328301\pi$
$854$		0			0
$855$	46.5077	+	0.896235i	1.59053	+	0.0306506i
$856$	45.3074	+	34.1506i	1.54857	+	1.16724i
$857$	0.368344	+	0.368344i	0.0125824	+	0.0125824i	0.713370	−	0.700788i	$-0.247168\pi$
$857$	0.368344	+	0.368344i	0.0125824	+	0.0125824i	−0.700788	+	0.713370i	$0.747168\pi$
$858$	−2.91533	+	5.63971i	−0.0995278	+	0.192537i
$859$	4.00947			0.136801			0.0684006	−	0.997658i	$-0.478210\pi$
$859$	4.00947			0.136801			0.0684006	+	0.997658i	$0.478210\pi$
$860$	15.5244	+	2.95457i	0.529379	+	0.100750i
$861$		0			0
$862$	−6.34407	+	12.2726i	−0.216080	+	0.418007i
$863$	10.4856	+	10.4856i	0.356934	+	0.356934i	0.862682	−	0.505747i	$-0.168783\pi$
$863$	10.4856	+	10.4856i	0.356934	+	0.356934i	−0.505747	+	0.862682i	$0.668783\pi$
$864$	2.35910	−	80.4926i	0.0802582	−	2.73841i
$865$	38.3576	+	39.8650i	1.30420	+	1.35545i
$866$	13.3566	−	4.25346i	0.453877	−	0.144539i
$867$	9.96649	−	9.96649i	0.338480	−	0.338480i
$868$		0			0
$869$		−	0.843073i		−	0.0285993i
$870$	14.1259	+	47.5046i	0.478912	+	1.61056i
$871$		−	3.16030i		−	0.107083i
$872$	−2.84336	+	0.399241i	−0.0962884	+	0.0135200i
$873$	59.3350	−	59.3350i	2.00818	−	2.00818i
$874$	−2.53148	−	7.94930i	−0.0856287	−	0.268889i
$875$		0			0
$876$	24.7440	+	34.9104i	0.836024	+	1.17951i
$877$	−21.9287	−	21.9287i	−0.740479	−	0.740479i	0.232191	−	0.972670i	$-0.425411\pi$
$877$	−21.9287	−	21.9287i	−0.740479	−	0.740479i	−0.972670	+	0.232191i	$0.925411\pi$
$878$	−5.56008	−	2.87417i	−0.187644	−	0.0969984i
$879$	21.4976			0.725097
$880$	4.39566	−	11.7900i	0.148178	−	0.397439i
$881$	−26.6186			−0.896802			−0.448401	−	0.893833i	$-0.648006\pi$
$881$	−26.6186			−0.896802			−0.448401	+	0.893833i	$0.648006\pi$
$882$		0			0
$883$	−20.2772	−	20.2772i	−0.682383	−	0.682383i	0.278154	−	0.960537i	$-0.410278\pi$
$883$	−20.2772	−	20.2772i	−0.682383	−	0.682383i	−0.960537	+	0.278154i	$0.910278\pi$
$884$	5.28708	+	7.45935i	0.177824	+	0.250885i
$885$	36.7364	−	35.3473i	1.23488	−	1.18819i
$886$	−1.88894	−	5.93161i	−0.0634602	−	0.199276i
$887$	30.2167	−	30.2167i	1.01458	−	1.01458i	0.0146841	−	0.999892i	$-0.495326\pi$
$887$	30.2167	−	30.2167i	1.01458	−	1.01458i	0.999892	−	0.0146841i	$-0.00467426\pi$
$888$	74.8268	−	10.5066i	2.51102	−	0.352577i
$889$		0			0
$890$	1.28931	+	0.698285i	0.0432179	+	0.0234066i
$891$		−	33.3385i		−	1.11688i
$892$	−4.53555	+	26.6137i	−0.151861	+	0.891093i
$893$	5.24583	−	5.24583i	0.175545	−	0.175545i
$894$	28.8912	−	9.20050i	0.966267	−	0.307711i
$895$	0.885581	−	45.9548i	0.0296017	−	1.53610i
$896$		0			0
$897$	4.74253	+	4.74253i	0.158348	+	0.158348i
$898$	−14.1802	+	27.4317i	−0.473201	+	0.915408i
$899$	−17.8613			−0.595706
$900$	62.0747	−	40.4977i	2.06916	−	1.34992i
$901$	−4.55351			−0.151699
$902$	−3.22832	+	6.24520i	−0.107491	+	0.207942i
$903$		0			0
$904$	−23.6164	−	17.8010i	−0.785471	−	0.592051i
$905$	−0.338624	+	17.5720i	−0.0112563	+	0.584112i
$906$	88.6443	−	28.2291i	2.94501	−	0.937848i
$907$	−0.867234	+	0.867234i	−0.0287960	+	0.0287960i	−0.721358	−	0.692562i	$-0.756482\pi$
$907$	−0.867234	+	0.867234i	−0.0287960	+	0.0287960i	0.692562	+	0.721358i	$0.256482\pi$
$908$	−36.3771	−	6.19943i	−1.20722	−	0.205735i
$909$			44.6999i			1.48260i
$910$		0			0
$911$		−	13.4236i		−	0.444743i	−0.974962	−	0.222372i	$-0.928620\pi$
$911$		−	13.4236i		−	0.444743i	0.974962	−	0.222372i	$-0.0713799\pi$
$912$	−32.6544	+	15.6853i	−1.08130	+	0.519393i
$913$	6.38351	−	6.38351i	0.211263	−	0.211263i
$914$	9.45361	+	29.6860i	0.312698	+	0.981926i
$915$	−11.4295	+	10.9974i	−0.377849	+	0.363562i
$916$	−25.4827	+	18.0618i	−0.841974	+	0.596779i
$917$		0			0
$918$	−82.6686	−	42.7338i	−2.72847	−	1.41042i
$919$	26.2486			0.865862			0.432931	−	0.901427i	$-0.357479\pi$
$919$	26.2486			0.865862			0.432931	+	0.901427i	$0.357479\pi$
$920$	−10.4590	−	8.20420i	−0.344822	−	0.270484i
$921$	−76.8945			−2.53376
$922$	−24.8331	−	12.8369i	−0.817834	−	0.422762i
$923$	8.52380	+	8.52380i	0.280564	+	0.280564i
$924$		0			0
$925$	28.1221	+	30.3776i	0.924649	+	0.998809i
$926$	−8.81423	−	27.6782i	−0.289653	−	0.909563i
$927$	73.7530	−	73.7530i	2.42236	−	2.42236i
$928$	−18.8507	−	19.9891i	−0.618806	−	0.656173i
$929$		−	19.9084i		−	0.653175i	−0.945167	−	0.326587i	$-0.894101\pi$
$929$		−	19.9084i		−	0.653175i	0.945167	−	0.326587i	$-0.105899\pi$
$930$	10.6950	+	35.9667i	0.350702	+	1.17940i
$931$		0			0
$932$	7.53711	+	1.28448i	0.246886	+	0.0420747i
$933$	41.4390	−	41.4390i	1.35665	−	1.35665i
$934$	37.9898	−	12.0980i	1.24307	−	0.395858i
$935$	−10.0821	−	10.4783i	−0.329720	−	0.342678i
$936$	12.4789	−	16.5557i	0.407885	−	0.541140i
$937$	3.76752	+	3.76752i	0.123080	+	0.123080i	0.765964	−	0.642884i	$-0.222262\pi$
$937$	3.76752	+	3.76752i	0.123080	+	0.123080i	−0.642884	+	0.765964i	$0.722262\pi$
$938$		0			0
$939$	−5.06087			−0.165155
$940$	2.21001	−	11.6122i	0.0720825	−	0.378750i
$941$	−4.83923			−0.157754			−0.0788772	−	0.996884i	$-0.525134\pi$
$941$	−4.83923			−0.157754			−0.0788772	+	0.996884i	$0.525134\pi$
$942$	37.2352	−	72.0316i	1.21319	−	2.34691i
$943$	5.25169	+	5.25169i	0.171019	+	0.171019i
$944$	−9.36132	+	26.6675i	−0.304685	+	0.867954i
$945$		0			0
$946$	−6.69879	+	2.13325i	−0.217797	+	0.0693580i
$947$	−21.9318	+	21.9318i	−0.712689	+	0.712689i	−0.967097	−	0.254408i	$-0.918119\pi$
$947$	−21.9318	+	21.9318i	−0.712689	+	0.712689i	0.254408	+	0.967097i	$0.418119\pi$
$948$	−0.649731	+	3.81250i	−0.0211023	+	0.123824i
$949$			6.55739i			0.212862i
$950$	−17.2662	−	9.78614i	−0.560189	−	0.317504i
$951$		−	95.3170i		−	3.09086i
$952$		0			0
$953$	22.3422	−	22.3422i	0.723734	−	0.723734i	−0.245630	−	0.969364i	$-0.578995\pi$
$953$	22.3422	−	22.3422i	0.723734	−	0.723734i	0.969364	+	0.245630i	$0.0789947\pi$
$954$	3.13304	+	9.83831i	0.101436	+	0.318527i
$955$	−19.3887	−	0.373634i	−0.627404	−	0.0120905i
$956$	17.8975	+	25.2509i	0.578847	+	0.816674i
$957$	−15.5901	−	15.5901i	−0.503956	−	0.503956i
$958$	−1.78236	−	0.921354i	−0.0575855	−	0.0297676i
$959$		0			0
$960$	−28.9640	+	49.9283i	−0.934808	+	1.61143i
$961$	17.4769			0.563770
$962$	10.2863	+	5.31727i	0.331643	+	0.171436i
$963$	−105.128	−	105.128i	−3.38771	−	3.38771i
$964$	−33.2640	−	46.9309i	−1.07136	−	1.51154i
$965$	−8.22565	−	8.54890i	−0.264793	−	0.275199i
$966$		0			0
$967$	8.85634	−	8.85634i	0.284801	−	0.284801i	−0.550219	−	0.835020i	$-0.685456\pi$
$967$	8.85634	−	8.85634i	0.284801	−	0.284801i	0.835020	+	0.550219i	$0.185456\pi$
$968$	−3.54781	−	25.2672i	−0.114031	−	0.812119i
$969$			41.8646i			1.34488i
$970$	−34.3170	+	10.2044i	−1.10185	+	0.327644i
$971$			9.45772i			0.303513i	0.988418	+	0.151756i	$0.0484929\pi$
$971$			9.45772i			0.303513i	−0.988418	+	0.151756i	$0.951507\pi$
$972$	−11.3438	+	66.5634i	−0.363854	+	2.13502i
$973$		0			0
$974$	45.3582	−	14.4445i	1.45337	−	0.462831i
$975$	15.9436	+	0.614715i	0.510603	+	0.0196866i
$976$	2.91252	−	8.29689i	0.0932276	−	0.265577i
$977$	−43.6781	−	43.6781i	−1.39739	−	1.39739i	−0.807451	−	0.589935i	$-0.799153\pi$
$977$	−43.6781	−	43.6781i	−1.39739	−	1.39739i	−0.589935	−	0.807451i	$-0.700847\pi$
$978$	36.4364	−	70.4863i	1.16511	−	2.25390i
$979$	−0.652291			−0.0208473
$980$		0			0
$981$	7.52393			0.240221
$982$	−2.05652	+	3.97833i	−0.0656260	+	0.126954i
$983$	−41.9474	−	41.9474i	−1.33791	−	1.33791i	−0.898079	−	0.439835i	$-0.855037\pi$
$983$	−41.9474	−	41.9474i	−1.33791	−	1.33791i	−0.439835	−	0.898079i	$-0.644963\pi$
$984$	19.4119	−	25.7537i	0.618830	−	0.820999i
$985$	28.1280	−	27.0644i	0.896233	−	0.862344i
$986$	−30.2550	+	9.63480i	−0.963515	+	0.306834i
$987$		0			0
$988$	−5.47258	−	0.932645i	−0.174106	−	0.0296714i
$989$			7.42701i			0.236165i
$990$	−15.7025	+	28.9930i	−0.499057	+	0.921459i
$991$		−	17.3438i		−	0.550944i	−0.961309	−	0.275472i	$-0.911166\pi$
$991$		−	17.3438i		−	0.550944i	0.961309	−	0.275472i	$-0.0888341\pi$
$992$	−14.2723	−	15.1341i	−0.453145	−	0.480509i
$993$	−28.8227	+	28.8227i	−0.914660	+	0.914660i
$994$		0			0
$995$	0.185204	−	9.61068i	0.00587137	−	0.304679i
$996$	−33.7867	+	23.9476i	−1.07057	+	0.758808i
$997$	−10.9093	−	10.9093i	−0.345501	−	0.345501i	0.512929	−	0.858431i	$-0.328560\pi$
$997$	−10.9093	−	10.9093i	−0.345501	−	0.345501i	−0.858431	+	0.512929i	$0.828560\pi$
$998$	−9.35813	−	4.83749i	−0.296227	−	0.153128i
$999$	−117.858			−3.72886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.k.l.687.3		36
4.3	odd	2	inner	980.2.k.l.687.6		36
5.3	odd	4	inner	980.2.k.l.883.6		36
7.2	even	3		980.2.x.l.67.10		72
7.3	odd	6		980.2.x.k.667.16		72
7.4	even	3		980.2.x.l.667.16		72
7.5	odd	6		980.2.x.k.67.10		72
7.6	odd	2		140.2.k.a.127.3	yes	36
20.3	even	4	inner	980.2.k.l.883.3		36
28.3	even	6		980.2.x.k.667.18		72
28.11	odd	6		980.2.x.l.667.18		72
28.19	even	6		980.2.x.k.67.7		72
28.23	odd	6		980.2.x.l.67.7		72
28.27	even	2		140.2.k.a.127.6	yes	36
35.3	even	12		980.2.x.k.863.7		72
35.13	even	4		140.2.k.a.43.6	yes	36
35.18	odd	12		980.2.x.l.863.7		72
35.23	odd	12		980.2.x.l.263.18		72
35.27	even	4		700.2.k.b.43.13		36
35.33	even	12		980.2.x.k.263.18		72
35.34	odd	2		700.2.k.b.407.16		36
140.3	odd	12		980.2.x.k.863.10		72
140.23	even	12		980.2.x.l.263.16		72
140.27	odd	4		700.2.k.b.43.16		36
140.83	odd	4		140.2.k.a.43.3	✓	36
140.103	odd	12		980.2.x.k.263.16		72
140.123	even	12		980.2.x.l.863.10		72
140.139	even	2		700.2.k.b.407.13		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.k.a.43.3	✓	36	140.83	odd	4
140.2.k.a.43.6	yes	36	35.13	even	4
140.2.k.a.127.3	yes	36	7.6	odd	2
140.2.k.a.127.6	yes	36	28.27	even	2
700.2.k.b.43.13		36	35.27	even	4
700.2.k.b.43.16		36	140.27	odd	4
700.2.k.b.407.13		36	140.139	even	2
700.2.k.b.407.16		36	35.34	odd	2
980.2.k.l.687.3		36	1.1	even	1	trivial
980.2.k.l.687.6		36	4.3	odd	2	inner
980.2.k.l.883.3		36	20.3	even	4	inner
980.2.k.l.883.6		36	5.3	odd	4	inner
980.2.x.k.67.7		72	28.19	even	6
980.2.x.k.67.10		72	7.5	odd	6
980.2.x.k.263.16		72	140.103	odd	12
980.2.x.k.263.18		72	35.33	even	12
980.2.x.k.667.16		72	7.3	odd	6
980.2.x.k.667.18		72	28.3	even	6
980.2.x.k.863.7		72	35.3	even	12
980.2.x.k.863.10		72	140.3	odd	12
980.2.x.l.67.7		72	28.23	odd	6
980.2.x.l.67.10		72	7.2	even	3
980.2.x.l.263.16		72	140.23	even	12
980.2.x.l.263.18		72	35.23	odd	12
980.2.x.l.667.16		72	7.4	even	3
980.2.x.l.667.18		72	28.11	odd	6
980.2.x.l.863.7		72	35.18	odd	12
980.2.x.l.863.10		72	140.123	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.25629 - 0.649412i) q^{2} +(-2.28163 - 2.28163i) q^{3} +(1.15653 + 1.63170i) q^{4} +(-0.0430826 + 2.23565i) q^{5} +(1.38467 + 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +7.41170i q^{9} +O(q^{10})\)	\(q+(-1.25629 - 0.649412i) q^{2} +(-2.28163 - 2.28163i) q^{3} +(1.15653 + 1.63170i) q^{4} +(-0.0430826 + 2.23565i) q^{5} +(1.38467 + 4.34811i) q^{6} +(-0.393286 - 2.80095i) q^{8} +7.41170i q^{9} +(1.50599 - 2.78065i) q^{10} +1.40679i q^{11} +(1.08417 - 6.36171i) q^{12} +(0.699298 - 0.699298i) q^{13} +(5.19924 - 5.00264i) q^{15} +(-1.32489 + 3.77421i) q^{16} +(3.26865 + 3.26865i) q^{17} +(4.81325 - 9.31125i) q^{18} -2.80674 q^{19} +(-3.69774 + 2.51529i) q^{20} +(0.913587 - 1.76734i) q^{22} +(-1.48618 - 1.48618i) q^{23} +(-5.49341 + 7.28808i) q^{24} +(-4.99629 - 0.192635i) q^{25} +(-1.33265 + 0.424388i) q^{26} +(10.0659 - 10.0659i) q^{27} -4.85706i q^{29} +(-9.78053 + 2.90832i) q^{30} -3.67738i q^{31} +(4.11547 - 3.88110i) q^{32} +(3.20978 - 3.20978i) q^{33} +(-1.98367 - 6.22907i) q^{34} +(-12.0937 + 8.57184i) q^{36} +(-5.85431 - 5.85431i) q^{37} +(3.52608 + 1.82273i) q^{38} -3.19108 q^{39} +(6.27890 - 0.758579i) q^{40} -3.53368 q^{41} +(-2.49869 - 2.49869i) q^{43} +(-2.29546 + 1.62699i) q^{44} +(-16.5700 - 0.319315i) q^{45} +(0.901930 + 2.83222i) q^{46} +(-1.86901 + 1.86901i) q^{47} +(11.6343 - 5.58845i) q^{48} +(6.15168 + 3.48666i) q^{50} -14.9157i q^{51} +(1.94980 + 0.332288i) q^{52} +(-0.696542 + 0.696542i) q^{53} +(-19.1826 + 6.10876i) q^{54} +(-3.14510 - 0.0606082i) q^{55} +(6.40395 + 6.40395i) q^{57} +(-3.15424 + 6.10187i) q^{58} +7.06573 q^{59} +(14.1759 + 2.69791i) q^{60} -2.19831 q^{61} +(-2.38814 + 4.61985i) q^{62} +(-7.69065 + 2.20315i) q^{64} +(1.53326 + 1.59351i) q^{65} +(-6.11688 + 1.94794i) q^{66} +(2.25963 - 2.25963i) q^{67} +(-1.55317 + 9.11374i) q^{68} +6.78184i q^{69} +12.1891i q^{71} +(20.7598 - 2.91492i) q^{72} +(-4.68856 + 4.68856i) q^{73} +(3.55285 + 11.1566i) q^{74} +(10.9602 + 11.8392i) q^{75} +(-3.24607 - 4.57976i) q^{76} +(4.00892 + 2.07233i) q^{78} -0.599288 q^{79} +(-8.38074 - 3.12460i) q^{80} -23.6982 q^{81} +(4.43932 + 2.29482i) q^{82} +(-4.53764 - 4.53764i) q^{83} +(-7.44839 + 7.16674i) q^{85} +(1.51640 + 4.76176i) q^{86} +(-11.0820 + 11.0820i) q^{87} +(3.94035 - 0.553271i) q^{88} +0.463673i q^{89} +(20.6093 + 11.1619i) q^{90} +(0.706194 - 4.14381i) q^{92} +(-8.39043 + 8.39043i) q^{93} +(3.56178 - 1.13426i) q^{94} +(0.120922 - 6.27490i) q^{95} +(-18.2452 - 0.534737i) q^{96} +(-8.00558 - 8.00558i) q^{97} -10.4267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 8 q^{6}+O(q^{10}) \) 36 * q + 8 * q^6	\( 36 q + 8 q^{6} + 16 q^{10} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} + 28 q^{18} - 20 q^{20} + 4 q^{22} - 20 q^{25} + 32 q^{26} - 4 q^{30} + 20 q^{37} + 36 q^{40} - 20 q^{45} + 16 q^{46} + 24 q^{48} + 40 q^{50} - 16 q^{52} - 44 q^{53} - 16 q^{57} - 4 q^{58} + 40 q^{60} + 64 q^{61} - 40 q^{62} + 4 q^{65} - 32 q^{66} - 80 q^{68} + 80 q^{72} - 52 q^{73} - 8 q^{76} - 76 q^{78} + 20 q^{80} - 36 q^{81} - 56 q^{82} - 20 q^{85} + 56 q^{86} - 40 q^{88} + 16 q^{90} - 56 q^{92} + 32 q^{93} - 120 q^{96} - 20 q^{97}+O(q^{100}) \) 36 * q + 8 * q^6 + 16 * q^10 + 16 * q^12 + 4 * q^13 - 8 * q^16 + 20 * q^17 + 28 * q^18 - 20 * q^20 + 4 * q^22 - 20 * q^25 + 32 * q^26 - 4 * q^30 + 20 * q^37 + 36 * q^40 - 20 * q^45 + 16 * q^46 + 24 * q^48 + 40 * q^50 - 16 * q^52 - 44 * q^53 - 16 * q^57 - 4 * q^58 + 40 * q^60 + 64 * q^61 - 40 * q^62 + 4 * q^65 - 32 * q^66 - 80 * q^68 + 80 * q^72 - 52 * q^73 - 8 * q^76 - 76 * q^78 + 20 * q^80 - 36 * q^81 - 56 * q^82 - 20 * q^85 + 56 * q^86 - 40 * q^88 + 16 * q^90 - 56 * q^92 + 32 * q^93 - 120 * q^96 - 20 * q^97

Introduction

L-functions

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