LMFDB - Embedded newform 980.2.s.e.19.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(19,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,6,6,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	980.19
Dual form			980.2.s.e.619.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.674125 - 1.24320i) q^{2} +(0.634715 - 0.366453i) q^{3} +(-1.09111 + 1.67615i) q^{4} +(0.661137 - 2.13609i) q^{5} +(-0.883452 - 0.542044i) q^{6} +(2.81934 + 0.226536i) q^{8} +(-1.23142 + 2.13289i) q^{9} +(-3.10129 + 0.618067i) q^{10} +(-2.33007 + 1.34527i) q^{11} +(-0.0783137 + 1.46372i) q^{12} -3.95118 q^{13} +(-0.363144 - 1.59809i) q^{15} +(-1.61896 - 3.65773i) q^{16} +(-0.709509 - 1.22891i) q^{17} +(3.48175 + 0.0930760i) q^{18} +(-1.61265 + 2.79319i) q^{19} +(2.85904 + 3.43888i) q^{20} +(3.24320 + 1.98987i) q^{22} +(-2.45620 + 4.25426i) q^{23} +(1.87249 - 0.889369i) q^{24} +(-4.12580 - 2.82450i) q^{25} +(2.66359 + 4.91212i) q^{26} +4.00375i q^{27} -5.17926 q^{29} +(-1.74194 + 1.52877i) q^{30} +(-3.81745 - 6.61201i) q^{31} +(-3.45592 + 4.47846i) q^{32} +(-0.985953 + 1.70772i) q^{33} +(-1.04948 + 1.71050i) q^{34} +(-2.23142 - 4.39127i) q^{36} +(-3.87963 - 2.23990i) q^{37} +(4.55962 + 0.121890i) q^{38} +(-2.50787 + 1.44792i) q^{39} +(2.34787 - 5.87261i) q^{40} -0.325509i q^{41} +9.28165 q^{43} +(0.287494 - 5.37338i) q^{44} +(3.74191 + 4.04057i) q^{45} +(6.94469 + 0.185649i) q^{46} +(-5.68610 - 3.28287i) q^{47} +(-2.36796 - 1.72834i) q^{48} +(-0.730128 + 7.03327i) q^{50} +(-0.900672 - 0.520003i) q^{51} +(4.31117 - 6.62277i) q^{52} +(1.39942 - 0.807955i) q^{53} +(4.97748 - 2.69903i) q^{54} +(1.33312 + 5.86665i) q^{55} +2.36383i q^{57} +(3.49147 + 6.43888i) q^{58} +(3.81745 + 6.61201i) q^{59} +(3.07486 + 1.13500i) q^{60} +(-12.3842 - 7.15003i) q^{61} +(-5.64664 + 9.20319i) q^{62} +(7.89736 + 1.27737i) q^{64} +(-2.61227 + 8.44009i) q^{65} +(2.78770 + 0.0745223i) q^{66} +(-1.51329 - 2.62109i) q^{67} +(2.83398 + 0.151627i) q^{68} +3.60032i q^{69} +15.4089i q^{71} +(-3.95498 + 5.73438i) q^{72} +(0.709509 + 1.22891i) q^{73} +(-0.169301 + 6.33314i) q^{74} +(-3.65375 - 0.280844i) q^{75} +(-2.92222 - 5.75071i) q^{76} +(3.49068 + 2.14171i) q^{78} +(10.5765 + 6.10637i) q^{79} +(-8.88360 + 1.03999i) q^{80} +(-2.22709 - 3.85743i) q^{81} +(-0.404674 + 0.219434i) q^{82} -5.26172i q^{83} +(-3.09414 + 0.703103i) q^{85} +(-6.25699 - 11.5390i) q^{86} +(-3.28735 + 1.89795i) q^{87} +(-6.87401 + 3.26492i) q^{88} +(-4.10930 - 2.37250i) q^{89} +(2.50073 - 7.37581i) q^{90} +(-4.45079 - 8.75882i) q^{92} +(-4.84598 - 2.79783i) q^{93} +(-0.248133 + 9.28205i) q^{94} +(4.90033 + 5.29144i) q^{95} +(-0.552378 + 4.10898i) q^{96} +8.35134 q^{97} -6.62638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} + 6 q^{5} + 4 q^{9} + 12 q^{10} + 18 q^{16} + 48 q^{24} - 26 q^{25} + 18 q^{26} - 26 q^{30} - 28 q^{36} - 42 q^{40} - 26 q^{44} - 36 q^{45} - 22 q^{46} + 36 q^{50} - 48 q^{54} + 4 q^{60}+ \cdots - 60 q^{96}+O(q^{100}) $ 32 * q + 6 * q^4 + 6 * q^5 + 4 * q^9 + 12 * q^10 + 18 * q^16 + 48 * q^24 - 26 * q^25 + 18 * q^26 - 26 * q^30 - 28 * q^36 - 42 * q^40 - 26 * q^44 - 36 * q^45 - 22 * q^46 + 36 * q^50 - 48 * q^54 + 4 * q^60 - 36 * q^61 + 36 * q^64 - 4 * q^65 + 24 * q^66 + 14 * q^74 - 72 * q^80 + 72 * q^81 + 20 * q^85 + 8 * q^86 + 108 * q^89 - 30 * q^94 - 60 * q^96

Character values

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

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.674125	−	1.24320i	−0.476679	−	0.879078i
$2$	−0.674125	−	1.24320i	−0.476679	−	0.879078i
$3$	0.634715	−	0.366453i	0.366453	−	0.211572i	−0.305455	−	0.952207i	$-0.598809\pi$
$3$	0.634715	−	0.366453i	0.366453	−	0.211572i	0.671908	+	0.740635i	$0.265475\pi$
$4$	−1.09111	+	1.67615i	−0.545555	+	0.838075i
$5$	0.661137	−	2.13609i	0.295670	−	0.955290i
$5$	0.661137	−	2.13609i	0.295670	−	0.955290i
$6$	−0.883452	−	0.542044i	−0.360668	−	0.221289i
$7$		0			0
$7$		0			0
$8$	2.81934	+	0.226536i	0.996787	+	0.0800926i
$9$	−1.23142	+	2.13289i	−0.410475	+	0.710964i
$10$	−3.10129	+	0.618067i	−0.980714	+	0.195450i
$11$	−2.33007	+	1.34527i	−0.702542	+	0.405613i	−0.808294	−	0.588780i	$-0.799609\pi$
$11$	−2.33007	+	1.34527i	−0.702542	+	0.405613i	0.105751	+	0.994393i	$0.466275\pi$
$12$	−0.0783137	+	1.46372i	−0.0226072	+	0.422539i
$13$	−3.95118			−1.09586			−0.547930	−	0.836524i	$-0.684584\pi$
$13$	−3.95118			−1.09586			−0.547930	+	0.836524i	$0.684584\pi$
$14$		0			0
$15$	−0.363144	−	1.59809i	−0.0937633	−	0.412624i
$16$	−1.61896	−	3.65773i	−0.404740	−	0.914432i
$17$	−0.709509	−	1.22891i	−0.172081	−	0.298053i	0.767066	−	0.641568i	$-0.221716\pi$
$17$	−0.709509	−	1.22891i	−0.172081	−	0.298053i	−0.939147	+	0.343515i	$0.888382\pi$
$18$	3.48175	+	0.0930760i	0.820657	+	0.0219382i
$19$	−1.61265	+	2.79319i	−0.369966	+	0.640801i	−0.989560	−	0.144122i	$-0.953964\pi$
$19$	−1.61265	+	2.79319i	−0.369966	+	0.640801i	0.619593	+	0.784923i	$0.287297\pi$
$20$	2.85904	+	3.43888i	0.639301	+	0.768957i
$21$		0			0
$22$	3.24320	+	1.98987i	0.691452	+	0.424242i
$23$	−2.45620	+	4.25426i	−0.512152	+	0.887074i	0.487748	+	0.872984i	$0.337818\pi$
$23$	−2.45620	+	4.25426i	−0.512152	+	0.887074i	−0.999901	+	0.0140897i	$0.995515\pi$
$24$	1.87249	−	0.889369i	0.382221	−	0.181542i
$25$	−4.12580	−	2.82450i	−0.825159	−	0.564900i
$26$	2.66359	+	4.91212i	0.522373	+	0.963345i
$27$			4.00375i			0.770522i
$28$		0			0
$29$	−5.17926			−0.961765			−0.480882	−	0.876785i	$-0.659684\pi$
$29$	−5.17926			−0.961765			−0.480882	+	0.876785i	$0.659684\pi$
$30$	−1.74194	+	1.52877i	−0.318033	+	0.279114i
$31$	−3.81745	−	6.61201i	−0.685634	−	1.18755i	−0.973237	−	0.229803i	$-0.926192\pi$
$31$	−3.81745	−	6.61201i	−0.685634	−	1.18755i	0.287603	−	0.957750i	$-0.407142\pi$
$32$	−3.45592	+	4.47846i	−0.610926	+	0.791688i
$33$	−0.985953	+	1.70772i	−0.171632	+	0.297276i
$34$	−1.04948	+	1.71050i	−0.179985	+	0.293349i
$35$		0			0
$36$	−2.23142	−	4.39127i	−0.371904	−	0.731878i
$37$	−3.87963	−	2.23990i	−0.637806	−	0.368238i	0.145963	−	0.989290i	$-0.453372\pi$
$37$	−3.87963	−	2.23990i	−0.637806	−	0.368238i	−0.783769	+	0.621052i	$0.786705\pi$
$38$	4.55962	+	0.121890i	0.739669	+	0.0197732i
$39$	−2.50787	+	1.44792i	−0.401581	+	0.231853i
$40$	2.34787	−	5.87261i	0.371231	−	0.928540i
$41$		−	0.325509i		−	0.0508359i	−0.999677	−	0.0254180i	$-0.991908\pi$
$41$		−	0.325509i		−	0.0508359i	0.999677	−	0.0254180i	$-0.00809166\pi$
$42$		0			0
$43$	9.28165			1.41544			0.707719	−	0.706494i	$-0.249724\pi$
$43$	9.28165			1.41544			0.707719	+	0.706494i	$0.249724\pi$
$44$	0.287494	−	5.37338i	0.0433413	−	0.810067i
$45$	3.74191	+	4.04057i	0.557812	+	0.602333i
$46$	6.94469	+	0.185649i	1.02394	+	0.0273725i
$47$	−5.68610	−	3.28287i	−0.829403	−	0.478856i	0.0242453	−	0.999706i	$-0.492282\pi$
$47$	−5.68610	−	3.28287i	−0.829403	−	0.478856i	−0.853648	+	0.520850i	$0.825615\pi$
$48$	−2.36796	−	1.72834i	−0.341786	−	0.249465i
$49$		0			0
$50$	−0.730128	+	7.03327i	−0.103256	+	0.994655i
$51$	−0.900672	−	0.520003i	−0.126119	−	0.0728150i
$52$	4.31117	−	6.62277i	0.597851	−	0.918412i
$53$	1.39942	−	0.807955i	0.192225	−	0.110981i	−0.400799	−	0.916166i	$-0.631267\pi$
$53$	1.39942	−	0.807955i	0.192225	−	0.110981i	0.593024	+	0.805185i	$0.297934\pi$
$54$	4.97748	−	2.69903i	0.677349	−	0.367292i
$55$	1.33312	+	5.86665i	0.179758	+	0.791059i
$56$		0			0
$57$			2.36383i			0.313097i
$58$	3.49147	+	6.43888i	0.458453	+	0.845466i
$59$	3.81745	+	6.61201i	0.496989	+	0.860811i	0.999994	−	0.00347297i	$-0.00110548\pi$
$59$	3.81745	+	6.61201i	0.496989	+	0.860811i	−0.503005	+	0.864284i	$0.667772\pi$
$60$	3.07486	+	1.13500i	0.396963	+	0.146528i
$61$	−12.3842	−	7.15003i	−1.58564	−	0.915467i	−0.994014	−	0.109252i	$-0.965154\pi$
$61$	−12.3842	−	7.15003i	−1.58564	−	0.915467i	−0.591622	−	0.806215i	$-0.701512\pi$
$62$	−5.64664	+	9.20319i	−0.717124	+	1.16881i
$63$		0			0
$64$	7.89736	+	1.27737i	0.987170	+	0.159671i
$65$	−2.61227	+	8.44009i	−0.324012	+	1.04686i
$66$	2.78770	+	0.0745223i	0.343142	+	0.00917306i
$67$	−1.51329	−	2.62109i	−0.184878	−	0.320218i	0.758658	−	0.651490i	$-0.225856\pi$
$67$	−1.51329	−	2.62109i	−0.184878	−	0.320218i	−0.943535	+	0.331272i	$0.892522\pi$
$68$	2.83398	+	0.151627i	0.343671	+	0.0183875i
$69$			3.60032i			0.433427i
$70$		0			0
$71$			15.4089i			1.82870i	0.404922	+	0.914351i	$0.367299\pi$
$71$			15.4089i			1.82870i	−0.404922	+	0.914351i	$0.632701\pi$
$72$	−3.95498	+	5.73438i	−0.466099	+	0.675803i
$73$	0.709509	+	1.22891i	0.0830418	+	0.143833i	0.904555	−	0.426357i	$-0.140203\pi$
$73$	0.709509	+	1.22891i	0.0830418	+	0.143833i	−0.821513	+	0.570189i	$0.806870\pi$
$74$	−0.169301	+	6.33314i	−0.0196808	+	0.736212i
$75$	−3.65375	−	0.280844i	−0.421899	−	0.0324291i
$76$	−2.92222	−	5.75071i	−0.335202	−	0.659652i
$77$		0			0
$78$	3.49068	+	2.14171i	0.395241	+	0.242501i
$79$	10.5765	+	6.10637i	1.18995	+	0.687021i	0.958296	−	0.285776i	$-0.0922515\pi$
$79$	10.5765	+	6.10637i	1.18995	+	0.687021i	0.231659	+	0.972797i	$0.425585\pi$
$80$	−8.88360	+	1.03999i	−0.993217	+	0.116274i
$81$	−2.22709	−	3.85743i	−0.247454	−	0.428604i
$82$	−0.404674	+	0.219434i	−0.0446887	+	0.0242324i
$83$		−	5.26172i		−	0.577549i	−0.957397	−	0.288774i	$-0.906752\pi$
$83$		−	5.26172i		−	0.577549i	0.957397	−	0.288774i	$-0.0932477\pi$
$84$		0			0
$85$	−3.09414	+	0.703103i	−0.335607	+	0.0762622i
$86$	−6.25699	−	11.5390i	−0.674709	−	1.24428i
$87$	−3.28735	+	1.89795i	−0.352441	+	0.203482i
$88$	−6.87401	+	3.26492i	−0.732772	+	0.348041i
$89$	−4.10930	−	2.37250i	−0.435585	−	0.251485i	0.266138	−	0.963935i	$-0.414252\pi$
$89$	−4.10930	−	2.37250i	−0.435585	−	0.251485i	−0.701723	+	0.712450i	$0.747586\pi$
$90$	2.50073	−	7.37581i	0.263601	−	0.777479i
$91$		0			0
$92$	−4.45079	−	8.75882i	−0.464027	−	0.913170i
$93$	−4.84598	−	2.79783i	−0.502505	−	0.290121i
$94$	−0.248133	+	9.28205i	−0.0255929	+	0.957370i
$95$	4.90033	+	5.29144i	0.502763	+	0.542891i
$96$	−0.552378	+	4.10898i	−0.0563768	+	0.419371i
$97$	8.35134			0.847950			0.423975	−	0.905674i	$-0.360634\pi$
$97$	8.35134			0.847950			0.423975	+	0.905674i	$0.360634\pi$
$98$		0			0
$99$		−	6.62638i		−	0.665976i
$100$	9.23599	−	3.83361i	0.923599	−	0.383361i
$101$	0.241927	−	0.139677i	0.0240727	−	0.0138984i	−0.487915	−	0.872891i	$-0.662243\pi$
$101$	0.241927	−	0.139677i	0.0240727	−	0.0138984i	0.511988	+	0.858993i	$0.328909\pi$
$102$	−0.0393039	+	1.47027i	−0.00389167	+	0.145578i
$103$	11.6053	+	6.70030i	1.14350	+	0.660200i	0.947295	−	0.320362i	$-0.103805\pi$
$103$	11.6053	+	6.70030i	1.14350	+	0.660200i	0.196206	+	0.980563i	$0.437138\pi$
$104$	−11.1397	−	0.895084i	−1.09234	−	0.0877703i
$105$		0			0
$106$	−1.94784	−	1.19510i	−0.189191	−	0.116078i
$107$	−2.71447	+	4.70160i	−0.262418	+	0.454521i	−0.966884	−	0.255217i	$-0.917853\pi$
$107$	−2.71447	+	4.70160i	−0.262418	+	0.454521i	0.704466	+	0.709738i	$0.251187\pi$
$108$	−6.71089	−	4.36853i	−0.645756	−	0.420362i
$109$	−4.45851	−	7.72237i	−0.427048	−	0.739669i	0.569561	−	0.821949i	$-0.307113\pi$
$109$	−4.45851	−	7.72237i	−0.427048	−	0.739669i	−0.996609	+	0.0822798i	$0.973780\pi$
$110$	6.39475	−	5.61220i	0.609716	−	0.535102i
$111$	−3.28327			−0.311634
$112$		0			0
$113$			1.05161i			0.0989268i	0.998776	+	0.0494634i	$0.0157511\pi$
$113$			1.05161i			0.0989268i	−0.998776	+	0.0494634i	$0.984249\pi$
$114$	2.93873	−	1.59352i	0.275237	−	0.149247i
$115$	7.46361	+	8.05931i	0.695985	+	0.751535i
$116$	5.65114	−	8.68122i	0.524695	−	0.806031i
$117$	4.86558	−	8.42743i	0.449823	−	0.779116i
$118$	5.64664	−	9.20319i	0.519815	−	0.847222i
$119$		0			0
$120$	−0.661802	−	4.58781i	−0.0604140	−	0.418808i
$121$	−1.88052	+	3.25715i	−0.170956	+	0.296105i
$122$	−0.540428	+	20.2161i	−0.0489280	+	1.83028i
$123$	−0.119284	−	0.206605i	−0.0107554	−	0.0186290i
$124$	15.2480	+	0.815817i	1.36931	+	0.0732626i
$125$	−8.76112	+	6.94570i	−0.783618	+	0.621243i
$126$		0			0
$127$	−1.71773			−0.152424			−0.0762121	−	0.997092i	$-0.524283\pi$
$127$	−1.71773			−0.152424			−0.0762121	+	0.997092i	$0.524283\pi$
$128$	−3.73579	−	10.6791i	−0.330200	−	0.943911i
$129$	5.89120	−	3.40128i	0.518691	−	0.299466i
$130$	12.2537	−	2.44209i	1.07472	−	0.214186i
$131$	−7.07173	+	12.2486i	−0.617860	+	1.07016i	0.372016	+	0.928226i	$0.378667\pi$
$131$	−7.07173	+	12.2486i	−0.617860	+	1.07016i	−0.989876	+	0.141938i	$0.954667\pi$
$132$	−1.78661	−	3.51591i	−0.155505	−	0.306021i
$133$		0			0
$134$	−2.23841	+	3.64827i	−0.193369	+	0.315163i
$135$	8.55239	+	2.64703i	0.736073	+	0.227820i
$136$	−1.72196	−	3.62543i	−0.147657	−	0.310878i
$137$	12.8787	−	7.43551i	1.10030	−	0.635259i	0.164000	−	0.986460i	$-0.447560\pi$
$137$	12.8787	−	7.43551i	1.10030	−	0.635259i	0.936300	+	0.351202i	$0.114227\pi$
$138$	4.47593	−	2.42707i	0.381016	−	0.206606i
$139$	7.06762			0.599468			0.299734	−	0.954023i	$-0.403102\pi$
$139$	7.06762			0.599468			0.299734	+	0.954023i	$0.403102\pi$
$140$		0			0
$141$	−4.81207			−0.405249
$142$	19.1564	−	10.3875i	1.60757	−	0.871703i
$143$	9.20652	−	5.31538i	0.769888	−	0.444495i
$144$	9.79516	+	1.05116i	0.816263	+	0.0875963i
$145$	−3.42420	+	11.0634i	−0.284365	+	0.918765i
$146$	1.04948	−	1.71050i	0.0868557	−	0.141562i
$147$		0			0
$148$	7.98751	−	4.05885i	0.656569	−	0.333636i
$149$	−4.39289	+	7.60870i	−0.359879	+	0.623329i	−0.987940	−	0.154835i	$-0.950515\pi$
$149$	−4.39289	+	7.60870i	−0.359879	+	0.623329i	0.628061	+	0.778164i	$0.283849\pi$
$150$	2.11394	+	4.73168i	0.172602	+	0.386340i
$151$	0.260095	−	0.150166i	0.0211663	−	0.0122204i	−0.489380	−	0.872071i	$-0.662777\pi$
$151$	0.260095	−	0.150166i	0.0211663	−	0.0122204i	0.510546	+	0.859851i	$0.329443\pi$
$152$	−5.17936	+	7.50962i	−0.420101	+	0.609110i
$153$	3.49483			0.282540
$154$		0			0
$155$	−16.6477	+	3.78298i	−1.33718	+	0.303856i
$156$	0.309431	−	5.78341i	0.0247743	−	0.463043i
$157$	−9.61742	−	16.6579i	−0.767553	−	1.32944i	−0.938886	−	0.344228i	$-0.888141\pi$
$157$	−9.61742	−	16.6579i	−0.767553	−	1.32944i	0.171333	−	0.985213i	$-0.445193\pi$
$158$	0.461544	−	17.2653i	0.0367185	−	1.37355i
$159$	0.592155	−	1.02564i	0.0469609	−	0.0813387i
$160$	7.28158	+	10.3430i	0.575659	+	0.817690i
$161$		0			0
$162$	−3.29424	+	5.36912i	−0.258820	+	0.421838i
$163$	5.35958	−	9.28306i	0.419795	−	0.727105i	−0.576124	−	0.817362i	$-0.695435\pi$
$163$	5.35958	−	9.28306i	0.419795	−	0.727105i	0.995919	+	0.0902569i	$0.0287688\pi$
$164$	0.545602	+	0.355166i	0.0426043	+	0.0277338i
$165$	2.99600	+	3.23512i	0.233238	+	0.251854i
$166$	−6.54139	+	3.54706i	−0.507710	+	0.275305i
$167$		−	13.2256i		−	1.02343i	−0.859155	−	0.511715i	$-0.829010\pi$
$167$		−	13.2256i		−	1.02343i	0.859155	−	0.511715i	$-0.170990\pi$
$168$		0			0
$169$	2.61180			0.200908
$170$	2.95994	+	3.37267i	0.227017	+	0.258672i
$171$	−3.97171	−	6.87920i	−0.303724	−	0.526065i
$172$	−10.1273	+	15.5574i	−0.772199	+	1.18624i
$173$	5.62704	−	9.74632i	0.427816	−	0.740999i	−0.568863	−	0.822432i	$-0.692616\pi$
$173$	5.62704	−	9.74632i	0.427816	−	0.740999i	0.996679	+	0.0814335i	$0.0259498\pi$
$174$	4.57563	+	2.80739i	0.346878	+	0.212828i
$175$		0			0
$176$	8.69290	+	6.34483i	0.655252	+	0.478259i
$177$	4.84598	+	2.79783i	0.364246	+	0.210298i
$178$	−0.179323	+	6.70806i	−0.0134409	+	0.502790i
$179$	−0.697992	+	0.402986i	−0.0521703	+	0.0301206i	−0.525858	−	0.850572i	$-0.676256\pi$
$179$	−0.697992	+	0.402986i	−0.0521703	+	0.0301206i	0.473688	+	0.880693i	$0.342922\pi$
$180$	−10.8554	+	1.86330i	−0.809117	+	0.138882i
$181$			0.0667108i			0.00495857i	0.999997	+	0.00247929i	$0.000789182\pi$
$181$			0.0667108i			0.00495857i	−0.999997	+	0.00247929i	$0.999211\pi$
$182$		0			0
$183$	−10.4806			−0.774747
$184$	−7.88860	+	11.4378i	−0.581555	+	0.843205i
$185$	−7.34961	+	6.80636i	−0.540354	+	0.500414i
$186$	−0.211471	+	7.91062i	−0.0155058	+	0.580035i
$187$	3.30641	+	1.90896i	0.241789	+	0.139597i
$188$	11.7067	−	5.94878i	0.853802	−	0.433860i
$189$		0			0
$190$	3.27491	−	9.65920i	0.237587	−	0.700752i
$191$	−15.1210	−	8.73010i	−1.09412	−	0.631688i	−0.159446	−	0.987207i	$-0.550971\pi$
$191$	−15.1210	−	8.73010i	−1.09412	−	0.631688i	−0.934669	+	0.355519i	$0.884304\pi$
$192$	5.48067	−	2.08325i	0.395533	−	0.150345i
$193$	−14.8928	+	8.59835i	−1.07201	+	0.618923i	−0.928729	−	0.370760i	$-0.879097\pi$
$193$	−14.8928	+	8.59835i	−1.07201	+	0.618923i	−0.143277	+	0.989683i	$0.545764\pi$
$194$	−5.62985	−	10.3824i	−0.404200	−	0.745414i
$195$	1.43485	+	6.31432i	0.102751	+	0.452178i
$196$		0			0
$197$		−	11.9392i		−	0.850635i	−0.905044	−	0.425318i	$-0.860162\pi$
$197$		−	11.9392i		−	0.850635i	0.905044	−	0.425318i	$-0.139838\pi$
$198$	−8.23793	+	4.46701i	−0.585445	+	0.317457i
$199$	−7.76016	−	13.4410i	−0.550103	−	0.952807i	−0.998267	−	0.0588552i	$-0.981255\pi$
$199$	−7.76016	−	13.4410i	−0.550103	−	0.952807i	0.448163	−	0.893952i	$-0.352078\pi$
$200$	−10.9922	−	8.89788i	−0.777264	−	0.629175i
$201$	−1.92101	−	1.10910i	−0.135498	−	0.0782297i
$202$	−0.336736	−	0.206605i	−0.0236927	−	0.0145367i
$203$		0			0
$204$	1.85433	−	0.942281i	0.129829	−	0.0659728i
$205$	−0.695318	−	0.215206i	−0.0485631	−	0.0150306i
$206$	0.506436	−	18.9445i	0.0352850	−	1.31993i
$207$	−6.04924	−	10.4776i	−0.420452	−	0.728243i
$208$	6.39679	+	14.4523i	0.443538	+	1.00209i
$209$		−	8.67775i		−	0.600253i
$210$		0			0
$211$		−	14.1636i		−	0.975063i	−0.873105	−	0.487531i	$-0.837897\pi$
$211$		−	14.1636i		−	0.975063i	0.873105	−	0.487531i	$-0.162103\pi$
$212$	−0.172666	+	3.22720i	−0.0118588	+	0.221645i
$213$	5.64664	+	9.78027i	0.386901	+	0.670133i
$214$	7.67494	+	0.205171i	0.524648	+	0.0140252i
$215$	6.13644	−	19.8265i	0.418502	−	1.35215i
$216$	−0.906994	+	11.2879i	−0.0617132	+	0.768047i
$217$		0			0
$218$	−6.59488	+	10.7487i	−0.446662	+	0.727993i
$219$	0.900672	+	0.520003i	0.0608618	+	0.0351385i
$220$	−11.2880	−	4.16665i	−0.761035	−	0.280916i
$221$	2.80340	+	4.85563i	0.188577	+	0.326625i
$222$	2.21334	+	4.08178i	0.148550	+	0.273951i
$223$		−	3.03443i		−	0.203201i	−0.994825	−	0.101600i	$-0.967604\pi$
$223$		−	3.03443i		−	0.203201i	0.994825	−	0.101600i	$-0.0323963\pi$
$224$		0			0
$225$	11.1050	−	5.32171i	0.740331	−	0.354780i
$226$	1.30736	−	0.708914i	0.0869643	−	0.0471563i
$227$	−12.7971	+	7.38839i	−0.849371	+	0.490385i	−0.860439	−	0.509554i	$-0.829810\pi$
$227$	−12.7971	+	7.38839i	−0.849371	+	0.490385i	0.0110676	+	0.999939i	$0.496477\pi$
$228$	−3.96214	−	2.57920i	−0.262399	−	0.170812i
$229$	5.56933	+	3.21545i	0.368031	+	0.212483i	0.672598	−	0.740008i	$-0.265178\pi$
$229$	5.56933	+	3.21545i	0.368031	+	0.212483i	−0.304567	+	0.952491i	$0.598512\pi$
$230$	4.98796	−	14.7118i	0.328896	−	0.970066i
$231$		0			0
$232$	−14.6021	−	1.17329i	−0.958675	−	0.0770303i
$233$	15.1300	+	8.73532i	0.991201	+	0.572270i	0.905633	−	0.424062i	$-0.139396\pi$
$233$	15.1300	+	8.73532i	0.991201	+	0.572270i	0.0855677	+	0.996332i	$0.472730\pi$
$234$	−13.7570	−	0.367760i	−0.899324	−	0.0240412i
$235$	−10.7718	+	9.97562i	−0.702676	+	0.650737i
$236$	−15.2480	−	0.815817i	−0.992559	−	0.0531052i
$237$	8.95079			0.581416
$238$		0			0
$239$		−	3.22490i		−	0.208601i	−0.994546	−	0.104301i	$-0.966740\pi$
$239$		−	3.22490i		−	0.208601i	0.994546	−	0.104301i	$-0.0332604\pi$
$240$	−5.25745	+	3.91552i	−0.339367	+	0.252745i
$241$	17.7424	−	10.2436i	1.14289	−	0.659848i	0.195745	−	0.980655i	$-0.437287\pi$
$241$	17.7424	−	10.2436i	1.14289	−	0.659848i	0.947145	+	0.320807i	$0.103954\pi$
$242$	5.31701	+	0.142137i	0.341790	+	0.00913692i
$243$	−13.2292	−	7.63787i	−0.848653	−	0.489970i
$244$	25.4971	−	12.9563i	1.63228	−	0.829444i
$245$		0			0
$246$	−0.176440	+	0.287572i	−0.0112494	+	0.0183349i
$247$	6.37185	−	11.0364i	0.405431	−	0.702227i
$248$	−9.26482	−	19.5063i	−0.588317	−	1.23865i
$249$	−1.92817	−	3.33969i	−0.122193	−	0.211644i
$250$	14.5410	+	6.20958i	0.919655	+	0.392728i
$251$	−15.1647			−0.957189			−0.478594	−	0.878036i	$-0.658854\pi$
$251$	−15.1647			−0.957189			−0.478594	+	0.878036i	$0.658854\pi$
$252$		0			0
$253$		−	13.2170i		−	0.830943i
$254$	1.15797	+	2.13549i	0.0726574	+	0.133993i
$255$	−1.70624	+	1.58013i	−0.106849	+	0.0989513i
$256$	−10.7579	+	11.8434i	−0.672372	+	0.740214i
$257$	−2.36577	+	4.09764i	−0.147573	+	0.255604i	−0.930330	−	0.366724i	$-0.880479\pi$
$257$	−2.36577	+	4.09764i	−0.147573	+	0.255604i	0.782757	+	0.622327i	$0.213813\pi$
$258$	−8.19989	−	5.03106i	−0.510503	−	0.313220i
$259$		0			0
$260$	−11.2966	−	13.5876i	−0.700584	−	0.842668i
$261$	6.37787	−	11.0468i	0.394780	−	0.683780i
$262$	19.9947	+	0.534510i	1.23528	+	0.0330221i
$263$	−2.35021	−	4.07068i	−0.144920	−	0.251009i	0.784423	−	0.620226i	$-0.212959\pi$
$263$	−2.35021	−	4.07068i	−0.144920	−	0.251009i	−0.929343	+	0.369217i	$0.879626\pi$
$264$	−3.16660	+	4.59129i	−0.194891	+	0.282574i
$265$	−0.800660	−	3.52346i	−0.0491842	−	0.216444i
$266$		0			0
$267$	−3.47764			−0.212828
$268$	6.04451	+	0.323401i	0.369227	+	0.0197549i
$269$	−21.2532	+	12.2706i	−1.29583	+	0.748149i	−0.979682	−	0.200559i	$-0.935724\pi$
$269$	−21.2532	+	12.2706i	−1.29583	+	0.748149i	−0.316151	+	0.948709i	$0.602391\pi$
$270$	−2.47459	−	12.4168i	−0.150599	−	0.755662i
$271$	−13.1957	+	22.8556i	−0.801582	+	1.38838i	0.116993	+	0.993133i	$0.462675\pi$
$271$	−13.1957	+	22.8556i	−0.801582	+	1.38838i	−0.918574	+	0.395248i	$0.870659\pi$
$272$	−3.34634	+	4.58474i	−0.202902	+	0.277991i
$273$		0			0
$274$	−17.9257	−	10.9984i	−1.08293	−	0.664435i
$275$	13.4131	+	1.03099i	0.808840	+	0.0621712i
$276$	−6.03468	−	3.92834i	−0.363245	−	0.236458i
$277$	20.8453	−	12.0350i	1.25247	−	0.723115i	0.280872	−	0.959745i	$-0.409376\pi$
$277$	20.8453	−	12.0350i	1.25247	−	0.723115i	0.971600	+	0.236630i	$0.0760429\pi$
$278$	−4.76446	−	8.78649i	−0.285753	−	0.526979i
$279$	18.8036			1.12574
$280$		0			0
$281$	−7.78577			−0.464460			−0.232230	−	0.972661i	$-0.574602\pi$
$281$	−7.78577			−0.464460			−0.232230	+	0.972661i	$0.574602\pi$
$282$	3.24394	+	5.98238i	0.193174	+	0.356245i
$283$	−6.88540	+	3.97529i	−0.409294	+	0.236306i	−0.690487	−	0.723345i	$-0.742604\pi$
$283$	−6.88540	+	3.97529i	−0.409294	+	0.236306i	0.281192	+	0.959651i	$0.409270\pi$
$284$	−25.8277	−	16.8128i	−1.53259	−	0.997657i
$285$	5.04937	+	1.56282i	0.299099	+	0.0925734i
$286$	−12.8145	−	7.86234i	−0.757734	−	0.464910i
$287$		0			0
$288$	−5.29637	−	12.8860i	−0.312091	−	0.759314i
$289$	7.49319	−	12.9786i	0.440776	−	0.763447i
$290$	16.0624	−	3.20113i	0.943216	−	0.187977i
$291$	5.30071	−	3.06037i	0.310733	−	0.179402i
$292$	−2.83398	−	0.151627i	−0.165846	−	0.00887333i
$293$	−2.11501			−0.123560			−0.0617801	−	0.998090i	$-0.519678\pi$
$293$	−2.11501			−0.123560			−0.0617801	+	0.998090i	$0.519678\pi$
$294$		0			0
$295$	16.6477	−	3.78298i	0.969269	−	0.220254i
$296$	−10.4306	−	7.19392i	−0.606264	−	0.418138i
$297$	−5.38611	−	9.32902i	−0.312534	−	0.541325i
$298$	12.4205	+	0.332032i	0.719501	+	0.0192341i
$299$	9.70487	−	16.8093i	0.561247	−	0.972108i
$300$	4.45738	−	5.81780i	0.257347	−	0.335891i
$301$		0			0
$302$	−0.362024	−	0.222121i	−0.0208321	−	0.0127816i
$303$	0.102370	−	0.177310i	0.00588100	−	0.0101862i
$304$	12.8275	+	1.37657i	0.735709	+	0.0789517i
$305$	−23.4608	+	21.7267i	−1.34336	+	1.24407i
$306$	−2.35595	−	4.34478i	−0.134681	−	0.248375i
$307$		−	18.6560i		−	1.06475i	−0.846508	−	0.532376i	$-0.821299\pi$
$307$		−	18.6560i		−	1.06475i	0.846508	−	0.532376i	$-0.178701\pi$
$308$		0			0
$309$	9.82137			0.558718
$310$	15.9257	+	18.1463i	0.904518	+	1.03064i
$311$	4.09153	+	7.08673i	0.232009	+	0.401852i	0.958399	−	0.285431i	$-0.0921367\pi$
$311$	4.09153	+	7.08673i	0.232009	+	0.401852i	−0.726390	+	0.687283i	$0.758803\pi$
$312$	−7.39855	+	3.51405i	−0.418860	+	0.198944i
$313$	−11.6871	+	20.2427i	−0.660597	+	1.14419i	0.319863	+	0.947464i	$0.396363\pi$
$313$	−11.6871	+	20.2427i	−0.660597	+	1.14419i	−0.980459	+	0.196723i	$0.936970\pi$
$314$	−14.2258	+	23.1859i	−0.802806	+	1.30846i
$315$		0			0
$316$	−21.7754	+	11.0652i	−1.22496	+	0.622464i
$317$	−22.6966	−	13.1039i	−1.27477	−	0.735988i	−0.298887	−	0.954288i	$-0.596615\pi$
$317$	−22.6966	−	13.1039i	−1.27477	−	0.735988i	−0.975882	+	0.218300i	$0.929949\pi$
$318$	−1.67427	−	0.0447574i	−0.0938883	−	0.00250987i
$319$	12.0680	−	6.96749i	0.675680	−	0.390104i
$320$	7.94981	−	16.0250i	0.444408	−	0.895824i
$321$			3.97890i			0.222081i
$322$		0			0
$323$	4.57675			0.254657
$324$	8.89563	+	0.475946i	0.494202	+	0.0264414i
$325$	16.3017	+	11.1601i	0.904258	+	0.619051i
$326$	−15.1538	−	0.405098i	−0.839289	−	0.0224363i
$327$	−5.65977	−	3.26767i	−0.312986	−	0.180702i
$328$	0.0737395	−	0.917720i	0.00407158	−	0.0506726i
$329$		0			0
$330$	2.00224	−	5.90552i	0.110220	−	0.325088i
$331$	−16.9060	−	9.76067i	−0.929237	−	0.536495i	−0.0426665	−	0.999089i	$-0.513585\pi$
$331$	−16.9060	−	9.76067i	−0.929237	−	0.536495i	−0.886570	+	0.462594i	$0.846919\pi$
$332$	8.81943	+	5.74111i	0.484029	+	0.315085i
$333$	9.55493	−	5.51654i	0.523607	−	0.302305i
$334$	−16.4422	+	8.91574i	−0.899675	+	0.487848i
$335$	−6.59940	+	1.49963i	−0.360564	+	0.0819333i
$336$		0			0
$337$			31.7520i			1.72964i	0.502082	+	0.864820i	$0.332567\pi$
$337$			31.7520i			1.72964i	−0.502082	+	0.864820i	$0.667433\pi$
$338$	−1.76068	−	3.24700i	−0.0957684	−	0.176614i
$339$	0.385364	+	0.667470i	0.0209301	+	0.0362520i
$340$	2.19754	−	5.95341i	0.119178	−	0.322869i
$341$	17.7898	+	10.2710i	0.963373	+	0.556204i
$342$	−5.87481	+	9.57508i	−0.317674	+	0.517761i
$343$		0			0
$344$	26.1681	+	2.10263i	1.41089	+	0.113366i
$345$	7.69062	+	2.38030i	0.414049	+	0.128151i
$346$	−15.9100	−	0.425314i	−0.855326	−	0.0228650i
$347$	−9.19210	−	15.9212i	−0.493458	−	0.854694i	0.506514	−	0.862232i	$-0.330934\pi$
$347$	−9.19210	−	15.9212i	−0.493458	−	0.854694i	−0.999972	+	0.00753782i	$0.997601\pi$
$348$	0.405607	−	7.58097i	0.0217428	−	0.406383i
$349$			2.37390i			0.127072i	0.997980	+	0.0635360i	$0.0202378\pi$
$349$			2.37390i			0.127072i	−0.997980	+	0.0635360i	$0.979762\pi$
$350$		0			0
$351$		−	15.8195i		−	0.844384i
$352$	2.02781	−	15.0843i	0.108082	−	0.803994i
$353$	1.07710	+	1.86560i	0.0573284	+	0.0992958i	0.893265	−	0.449530i	$-0.148408\pi$
$353$	1.07710	+	1.86560i	0.0573284	+	0.0992958i	−0.835937	+	0.548826i	$0.815075\pi$
$354$	0.211471	−	7.91062i	0.0112396	−	0.420445i
$355$	32.9149	+	10.1874i	1.74694	+	0.540692i
$356$	8.46037	−	4.29914i	0.448399	−	0.227854i
$357$		0			0
$358$	0.971527	+	0.596083i	0.0513468	+	0.0315039i
$359$	−4.40004	−	2.54037i	−0.232225	−	0.134075i	0.379373	−	0.925244i	$-0.376140\pi$
$359$	−4.40004	−	2.54037i	−0.232225	−	0.134075i	−0.611598	+	0.791168i	$0.709473\pi$
$360$	9.63439	+	12.2394i	0.507777	+	0.645075i
$361$	4.29874	+	7.44564i	0.226250	+	0.391876i
$362$	0.0829350	−	0.0449714i	0.00435897	−	0.00236364i
$363$			2.75648i			0.144678i
$364$		0			0
$365$	3.09414	−	0.703103i	0.161955	−	0.0368021i
$366$	7.06523	+	13.0295i	0.369306	+	0.681063i
$367$	−11.7306	+	6.77267i	−0.612333	+	0.353530i	−0.773878	−	0.633335i	$-0.781686\pi$
$367$	−11.7306	+	6.77267i	−0.612333	+	0.353530i	0.161545	+	0.986865i	$0.448352\pi$
$368$	19.5374	+	2.09663i	1.01846	+	0.109295i
$369$	0.694275	+	0.400840i	0.0361425	+	0.0208669i
$370$	13.4162	+	4.54872i	0.697478	+	0.236476i
$371$		0			0
$372$	9.97707	−	5.06985i	0.517287	−	0.262860i
$373$	6.17822	+	3.56700i	0.319896	+	0.184692i	0.651346	−	0.758781i	$-0.274205\pi$
$373$	6.17822	+	3.56700i	0.319896	+	0.184692i	−0.331450	+	0.943473i	$0.607538\pi$
$374$	0.144287	−	5.39742i	0.00746089	−	0.279094i
$375$	−3.01554	+	7.61907i	−0.155722	+	0.393447i
$376$	−15.2874	−	10.5436i	−0.788386	−	0.543747i
$377$	20.4642			1.05396
$378$		0			0
$379$			16.2436i			0.834379i	0.908820	+	0.417189i	$0.136985\pi$
$379$			16.2436i			0.834379i	−0.908820	+	0.417189i	$0.863015\pi$
$380$	−14.2160	+	2.44014i	−0.729268	+	0.125176i
$381$	−1.09027	+	0.629468i	−0.0558562	+	0.0322486i
$382$	−0.659856	+	24.6836i	−0.0337612	+	1.26292i
$383$	8.56254	+	4.94358i	0.437525	+	0.252605i	0.702547	−	0.711637i	$-0.252046\pi$
$383$	8.56254	+	4.94358i	0.437525	+	0.252605i	−0.265022	+	0.964242i	$0.585379\pi$
$384$	−6.28456	−	5.40921i	−0.320707	−	0.276038i
$385$		0			0
$386$	20.7291	+	12.7184i	1.05508	+	0.647349i
$387$	−11.4296	+	19.7967i	−0.581002	+	1.00632i
$388$	−9.11222	+	13.9981i	−0.462603	+	0.710645i
$389$	15.9811	+	27.6802i	0.810276	+	1.40344i	0.912671	+	0.408696i	$0.134016\pi$
$389$	15.9811	+	27.6802i	0.810276	+	1.40344i	−0.102395	+	0.994744i	$0.532650\pi$
$390$	6.88272	−	6.04045i	0.348520	−	0.305870i
$391$	6.97078			0.352527
$392$		0			0
$393$			10.3658i			0.522886i
$394$	−14.8429	+	8.04854i	−0.747774	+	0.405480i
$395$	20.0363	−	18.5554i	1.00814	−	0.933621i
$396$	11.1068	+	7.23011i	0.558138	+	0.363326i
$397$	8.73784	−	15.1344i	0.438539	−	0.759573i	−0.559038	−	0.829142i	$-0.688829\pi$
$397$	8.73784	−	15.1344i	0.438539	−	0.759573i	0.997577	+	0.0695697i	$0.0221626\pi$
$398$	−11.4786	+	18.7084i	−0.575369	+	0.937766i
$399$		0			0
$400$	−3.65177	+	19.6638i	−0.182588	+	0.983189i
$401$	8.67926	−	15.0329i	0.433422	−	0.750708i	−0.563744	−	0.825950i	$-0.690639\pi$
$401$	8.67926	−	15.0329i	0.433422	−	0.750708i	0.997165	+	0.0752415i	$0.0239728\pi$
$402$	−0.0838301	+	3.13588i	−0.00418106	+	0.156404i
$403$	15.0834	+	26.1252i	0.751358	+	1.30139i
$404$	−0.0298500	+	0.557909i	−0.00148509	+	0.0277570i
$405$	−9.71225	+	2.20698i	−0.482606	+	0.109666i
$406$		0			0
$407$	12.0531			0.597448
$408$	−2.42150	−	1.67010i	−0.119882	−	0.0826823i
$409$	−6.32187	+	3.64993i	−0.312596	+	0.180478i	−0.648088	−	0.761566i	$-0.724431\pi$
$409$	−6.32187	+	3.64993i	−0.312596	+	0.180478i	0.335491	+	0.942043i	$0.391098\pi$
$410$	0.201186	+	1.00950i	0.00993589	+	0.0498555i
$411$	5.44952	−	9.43885i	0.268805	−	0.465584i
$412$	−23.8933	+	12.1414i	−1.17714	+	0.598164i
$413$		0			0
$414$	−8.94784	+	14.5837i	−0.439762	+	0.716748i
$415$	−11.2395	−	3.47872i	−0.551727	−	0.170764i
$416$	13.6549	−	17.6952i	0.669489	−	0.867578i
$417$	4.48592	−	2.58995i	0.219677	−	0.126830i
$418$	−10.7882	+	5.84989i	−0.527669	+	0.286128i
$419$	−17.9278			−0.875831			−0.437915	−	0.899016i	$-0.644283\pi$
$419$	−17.9278			−0.875831			−0.437915	+	0.899016i	$0.644283\pi$
$420$		0			0
$421$	12.6334			0.615716			0.307858	−	0.951432i	$-0.400388\pi$
$421$	12.6334			0.615716			0.307858	+	0.951432i	$0.400388\pi$
$422$	−17.6082	+	9.54805i	−0.857156	+	0.464792i
$423$	14.0040	−	8.08522i	0.680898	−	0.393117i
$424$	4.12847	−	1.96088i	0.200496	−	0.0952288i
$425$	−0.543758	+	7.07422i	−0.0263761	+	0.343150i
$426$	8.35232	−	13.6130i	0.404671	−	0.659554i
$427$		0			0
$428$	−4.91881	−	9.67983i	−0.237759	−	0.467892i
$429$	3.89567	−	6.74750i	0.188085	−	0.325773i
$430$	−28.7851	+	5.73668i	−1.38814	+	0.276647i
$431$	28.2962	−	16.3368i	1.36298	−	0.786918i	0.372962	−	0.927847i	$-0.378342\pi$
$431$	28.2962	−	16.3368i	1.36298	−	0.786918i	0.990020	+	0.140929i	$0.0450090\pi$
$432$	14.6446	−	6.48191i	0.704590	−	0.311861i
$433$	−23.5884			−1.13359			−0.566794	−	0.823860i	$-0.691816\pi$
$433$	−23.5884			−1.13359			−0.566794	+	0.823860i	$0.691816\pi$
$434$		0			0
$435$	1.88082	+	8.27690i	0.0901783	+	0.396847i
$436$	17.8086	+	0.952818i	0.852877	+	0.0456317i
$437$	−7.92195	−	13.7212i	−0.378958	−	0.656375i
$438$	0.0393039	−	1.47027i	0.00187801	−	0.0702520i
$439$	9.19501	−	15.9262i	0.438854	−	0.760117i	−0.558748	−	0.829338i	$-0.688718\pi$
$439$	9.19501	−	15.9262i	0.438854	−	0.760117i	0.997601	+	0.0692207i	$0.0220513\pi$
$440$	2.42951	+	16.8421i	0.115822	+	0.802915i
$441$		0			0
$442$	4.14669	−	6.75849i	0.197238	−	0.321469i
$443$	−1.69217	+	2.93092i	−0.0803973	+	0.139252i	−0.903421	−	0.428755i	$-0.858952\pi$
$443$	−1.69217	+	2.93092i	−0.0803973	+	0.139252i	0.823023	+	0.568008i	$0.192286\pi$
$444$	3.58241	−	5.50326i	0.170014	−	0.261173i
$445$	−7.78470	+	7.20929i	−0.369030	+	0.341753i
$446$	−3.77242	+	2.04559i	−0.178629	+	0.0968614i
$447$			6.43914i			0.304561i
$448$		0			0
$449$	−11.9013			−0.561658			−0.280829	−	0.959758i	$-0.590609\pi$
$449$	−11.9013			−0.561658			−0.280829	+	0.959758i	$0.590609\pi$
$450$	−14.1021	−	10.2182i	−0.664779	−	0.481692i
$451$	0.437896	+	0.758458i	0.0206197	+	0.0357144i
$452$	−1.76265	−	1.14742i	−0.0829081	−	0.0539700i
$453$	0.110058	−	0.190625i	0.00517096	−	0.00895636i
$454$	17.8121	+	10.9287i	0.835963	+	0.512907i
$455$		0			0
$456$	−0.535494	+	6.66445i	−0.0250768	+	0.312092i
$457$	18.2475	+	10.5352i	0.853582	+	0.492816i	0.861858	−	0.507150i	$-0.169301\pi$
$457$	18.2475	+	10.5352i	0.853582	+	0.492816i	−0.00827601	+	0.999966i	$0.502634\pi$
$458$	0.243037	−	9.09142i	0.0113564	−	0.424814i
$459$	4.92023	−	2.84070i	0.229657	−	0.132592i
$460$	−21.6522	+	3.71653i	−1.00954	+	0.173284i
$461$		−	29.6708i		−	1.38191i	−0.722899	−	0.690954i	$-0.757191\pi$
$461$		−	29.6708i		−	1.38191i	0.722899	−	0.690954i	$-0.242809\pi$
$462$		0			0
$463$	−15.0481			−0.699342			−0.349671	−	0.936873i	$-0.613707\pi$
$463$	−15.0481			−0.699342			−0.349671	+	0.936873i	$0.613707\pi$
$464$	8.38501	+	18.9443i	0.389264	+	0.879468i
$465$	−9.18028	+	8.50172i	−0.425725	+	0.394258i
$466$	0.660251	−	24.6984i	0.0305855	−	1.14413i
$467$	−4.45656	−	2.57299i	−0.206225	−	0.119064i	0.393331	−	0.919397i	$-0.371323\pi$
$467$	−4.45656	−	2.57299i	−0.206225	−	0.119064i	−0.599556	+	0.800333i	$0.704656\pi$
$468$	8.81676	+	17.3507i	0.407555	+	0.802036i
$469$		0			0
$470$	19.6633	+	6.66674i	0.906999	+	0.307514i
$471$	−12.2086	−	7.04865i	−0.562544	−	0.324785i
$472$	9.26482	+	19.5063i	0.426448	+	0.897850i
$473$	−21.6269	+	12.4863i	−0.994405	+	0.574120i
$474$	−6.03395	−	11.1277i	−0.277149	−	0.511110i
$475$	14.5428	−	6.96919i	0.667270	−	0.319768i
$476$		0			0
$477$			3.97974i			0.182220i
$478$	−4.00921	+	2.17399i	−0.183377	+	0.0994358i
$479$	19.9783	+	34.6035i	0.912834	+	1.58107i	0.810042	+	0.586372i	$0.199444\pi$
$479$	19.9783	+	34.6035i	0.912834	+	1.58107i	0.102792	+	0.994703i	$0.467222\pi$
$480$	8.41196	+	3.89653i	0.383952	+	0.177851i
$481$	15.3291	+	8.85025i	0.698946	+	0.403537i
$482$	−24.6955	−	15.1520i	−1.12485	−	0.690153i
$483$		0			0
$484$	−3.40763	−	6.70594i	−0.154892	−	0.304816i
$485$	5.52138	−	17.8392i	0.250713	−	0.810038i
$486$	−0.577301	+	21.5955i	−0.0261869	+	0.979590i
$487$	6.11246	+	10.5871i	0.276982	+	0.479747i	0.970633	−	0.240564i	$-0.0773325\pi$
$487$	6.11246	+	10.5871i	0.276982	+	0.479747i	−0.693651	+	0.720311i	$0.743999\pi$
$488$	−33.2956	−	22.9638i	−1.50722	−	1.03952i
$489$		−	7.85613i		−	0.355266i
$490$		0			0
$491$			22.9515i			1.03579i	0.855445	+	0.517894i	$0.173284\pi$
$491$			22.9515i			1.03579i	−0.855445	+	0.517894i	$0.826716\pi$
$492$	0.476453	+	0.0254918i	0.0214802	+	0.00114926i
$493$	3.67473	+	6.36483i	0.165502	+	0.286657i
$494$	−18.0159	−	0.481610i	−0.810573	−	0.0216687i
$495$	−14.1546	−	4.38094i	−0.636200	−	0.196909i
$496$	−18.0047	+	24.6678i	−0.808433	+	1.10762i
$497$		0			0
$498$	−2.85209	+	4.64848i	−0.127805	+	0.208303i
$499$	3.64376	+	2.10372i	0.163117	+	0.0941756i	0.579336	−	0.815089i	$-0.303312\pi$
$499$	3.64376	+	2.10372i	0.163117	+	0.0941756i	−0.416219	+	0.909264i	$0.636645\pi$
$500$	−2.08270	−	22.2635i	−0.0931411	−	0.995653i
$501$	−4.84657	−	8.39451i	−0.216529	−	0.375039i
$502$	10.2229	+	18.8528i	0.456272	+	0.841443i
$503$			43.1904i			1.92576i	0.269924	+	0.962882i	$0.413001\pi$
$503$			43.1904i			1.92576i	−0.269924	+	0.962882i	$0.586999\pi$
$504$		0			0
$505$	−0.138416	−	0.609125i	−0.00615942	−	0.0271057i
$506$	−16.4314	+	8.90988i	−0.730463	+	0.396093i
$507$	1.65775	−	0.957101i	0.0736232	−	0.0425064i
$508$	1.87424	−	2.87918i	0.0831558	−	0.127743i
$509$	32.3532	+	18.6791i	1.43403	+	0.827937i	0.997425	−	0.0717169i	$-0.0228478\pi$
$509$	32.3532	+	18.6791i	1.43403	+	0.827937i	0.436604	+	0.899654i	$0.356181\pi$
$510$	3.11464	+	1.05600i	0.137919	+	0.0467606i
$511$		0			0
$512$	21.9760	+	5.39037i	0.971211	+	0.238223i
$513$	−11.1832	−	6.45664i	−0.493751	−	0.285067i
$514$	6.68903	+	0.178815i	0.295040	+	0.00788717i
$515$	21.9851	−	20.3601i	0.968781	−	0.897174i
$516$	−0.726880	+	13.5857i	−0.0319991	+	0.598077i
$517$	17.6653			0.776921
$518$		0			0
$519$		−	8.24817i		−	0.362055i
$520$	−9.27686	+	23.2037i	−0.406817	+	1.01755i
$521$	−13.9610	+	8.06040i	−0.611643	+	0.353132i	−0.773608	−	0.633664i	$-0.781550\pi$
$521$	−13.9610	+	8.06040i	−0.611643	+	0.353132i	0.161965	+	0.986796i	$0.448217\pi$
$522$	−18.0329	−	0.482065i	−0.789279	−	0.0210994i
$523$	−13.8279	−	7.98356i	−0.604653	−	0.349097i	0.166217	−	0.986089i	$-0.446845\pi$
$523$	−13.8279	−	7.98356i	−0.604653	−	0.349097i	−0.770870	+	0.636993i	$0.780178\pi$
$524$	−12.8145	−	25.2178i	−0.559802	−	1.10165i
$525$		0			0
$526$	−3.47635	+	5.66594i	−0.151576	+	0.247047i
$527$	−5.41703	+	9.38257i	−0.235969	+	0.408711i
$528$	7.84259	+	0.841618i	0.341305	+	0.0366267i
$529$	−0.565805	−	0.980002i	−0.0246002	−	0.0426088i
$530$	−3.84063	+	3.37064i	−0.166826	+	0.146411i
$531$	−18.8036			−0.816007
$532$		0			0
$533$			1.28614i			0.0557090i
$534$	2.34437	+	4.32342i	0.101451	+	0.187092i
$535$	8.24843	+	8.90677i	0.356611	+	0.385073i
$536$	−3.67271	−	7.73257i	−0.158637	−	0.333996i
$537$	−0.295350	+	0.511562i	−0.0127453	+	0.0220755i
$538$	29.5822	+	18.1502i	1.27538	+	0.782511i
$539$		0			0
$540$	−13.7684	+	11.4469i	−0.592498	+	0.492596i
$541$	7.31686	−	12.6732i	0.314576	−	0.544862i	−0.664771	−	0.747047i	$-0.731471\pi$
$541$	7.31686	−	12.6732i	0.314576	−	0.544862i	0.979347	+	0.202185i	$0.0648042\pi$
$542$	37.3098	+	0.997384i	1.60259	+	0.0428413i
$543$	0.0244463	+	0.0423423i	0.00104909	+	0.00181708i
$544$	7.95562	+	1.06949i	0.341094	+	0.0458540i
$545$	−19.4434	+	4.41826i	−0.832864	+	0.189257i
$546$		0			0
$547$	16.5936			0.709493			0.354747	−	0.934963i	$-0.384567\pi$
$547$	16.5936			0.709493			0.354747	+	0.934963i	$0.384567\pi$
$548$	−1.58902	+	29.6996i	−0.0678798	+	1.26870i
$549$	30.5005	−	17.6094i	1.30173	−	0.751553i
$550$	−7.76037	−	17.3702i	−0.330903	−	0.740669i
$551$	8.35232	−	14.4666i	0.355821	−	0.616300i
$552$	−0.815602	+	10.1505i	−0.0347143	+	0.432035i
$553$		0			0
$554$	−29.0143	−	17.8018i	−1.23270	−	0.756327i
$555$	−2.17069	+	7.01338i	−0.0921408	+	0.297701i
$556$	−7.71155	+	11.8464i	−0.327043	+	0.502399i
$557$	21.4562	−	12.3878i	0.909129	−	0.524886i	0.0289782	−	0.999580i	$-0.490775\pi$
$557$	21.4562	−	12.3878i	0.909129	−	0.524886i	0.880151	+	0.474694i	$0.157441\pi$
$558$	−12.6760	−	23.3767i	−0.536617	−	0.989615i
$559$	−36.6734			−1.55112
$560$		0			0
$561$	2.79817			0.118139
$562$	5.24859	+	9.67930i	0.221398	+	0.408296i
$563$	−20.7434	+	11.9762i	−0.874230	+	0.504737i	−0.868751	−	0.495248i	$-0.835077\pi$
$563$	−20.7434	+	11.9762i	−0.874230	+	0.504737i	−0.00547814	+	0.999985i	$0.501744\pi$
$564$	5.25049	−	8.06575i	0.221086	−	0.339629i
$565$	2.24633	+	0.695256i	0.0945038	+	0.0292496i
$566$	9.58371	+	5.88011i	0.402833	+	0.247159i
$567$		0			0
$568$	−3.49068	+	43.4430i	−0.146466	+	1.82283i
$569$	−4.58078	+	7.93415i	−0.192036	+	0.332617i	−0.945925	−	0.324385i	$-0.894843\pi$
$569$	−4.58078	+	7.93415i	−0.192036	+	0.332617i	0.753889	+	0.657002i	$0.228176\pi$
$570$	−1.46101	−	7.33093i	−0.0611949	−	0.307059i
$571$	−21.4132	+	12.3629i	−0.896114	+	0.517372i	−0.875938	−	0.482425i	$-0.839756\pi$
$571$	−21.4132	+	12.3629i	−0.896114	+	0.517372i	−0.0201768	+	0.999796i	$0.506423\pi$
$572$	−1.13594	+	21.2312i	−0.0474959	+	0.887720i
$573$	−12.7967			−0.534589
$574$		0			0
$575$	22.1499	−	10.6147i	0.923716	−	0.442662i
$576$	−12.4495	+	15.2712i	−0.518729	+	0.636301i
$577$	−4.75184	−	8.23042i	−0.197822	−	0.342637i	0.750000	−	0.661438i	$-0.230053\pi$
$577$	−4.75184	−	8.23042i	−0.197822	−	0.342637i	−0.947822	+	0.318801i	$0.896720\pi$
$578$	−21.1864	−	0.566366i	−0.881237	−	0.0235577i
$579$	−6.30178	+	10.9150i	−0.261893	+	0.453612i
$580$	−14.8077	−	17.8109i	−0.614857	−	0.739555i
$581$		0			0
$582$	−7.37801	−	4.52679i	−0.305828	−	0.187642i
$583$	−2.17383	+	3.76518i	−0.0900308	+	0.155938i
$584$	1.72196	+	3.62543i	0.0712551	+	0.150022i
$585$	−14.7850	−	15.9650i	−0.611283	−	0.660072i
$586$	1.42578	+	2.62939i	0.0588985	+	0.108619i
$587$			14.2100i			0.586508i	0.956035	+	0.293254i	$0.0947382\pi$
$587$			14.2100i			0.586508i	−0.956035	+	0.293254i	$0.905262\pi$
$588$		0			0
$589$	24.6248			1.01465
$590$	−15.9257	−	18.1463i	−0.655650	−	0.747072i
$591$	−4.37516	−	7.57801i	−0.179970	−	0.311717i
$592$	−1.91200	+	17.8169i	−0.0785828	+	0.732271i
$593$	−8.87854	+	15.3781i	−0.364598	+	0.631502i	−0.988712	−	0.149831i	$-0.952127\pi$
$593$	−8.87854	+	15.3781i	−0.364598	+	0.631502i	0.624114	+	0.781334i	$0.285460\pi$
$594$	−7.96695	+	12.9850i	−0.326888	+	0.532779i
$595$		0			0
$596$	−7.96020	−	15.6651i	−0.326063	−	0.641666i
$597$	−9.85098	−	5.68746i	−0.403174	−	0.232772i
$598$	−27.4397	−	0.733533i	−1.12209	−	0.0299964i
$599$	−18.1537	+	10.4811i	−0.741741	+	0.428244i	−0.822702	−	0.568473i	$-0.807534\pi$
$599$	−18.1537	+	10.4811i	−0.741741	+	0.428244i	0.0809612	+	0.996717i	$0.474201\pi$
$600$	−10.2375	−	1.61950i	−0.417946	−	0.0661159i
$601$			20.7196i			0.845169i	0.906324	+	0.422585i	$0.138877\pi$
$601$			20.7196i			0.845169i	−0.906324	+	0.422585i	$0.861123\pi$
$602$		0			0
$603$	7.45401			0.303551
$604$	−0.0320917	+	0.599807i	−0.00130579	+	0.0244058i
$605$	5.71430	+	6.17039i	0.232320	+	0.250862i
$606$	−0.289442	−	0.00773753i	−0.0117578	−	0.000314316i
$607$	−2.77584	−	1.60263i	−0.112668	−	0.0650487i	0.442607	−	0.896716i	$-0.354054\pi$
$607$	−2.77584	−	1.60263i	−0.112668	−	0.0650487i	−0.555275	+	0.831667i	$0.687387\pi$
$608$	−6.93600	−	16.8752i	−0.281292	−	0.684380i
$609$		0			0
$610$	42.8262	+	14.5200i	1.73398	+	0.587899i
$611$	22.4668	+	12.9712i	0.908909	+	0.524759i
$612$	−3.81324	+	5.85786i	−0.154141	+	0.236790i
$613$	−4.15308	+	2.39778i	−0.167741	+	0.0968454i	−0.581520	−	0.813532i	$-0.697542\pi$
$613$	−4.15308	+	2.39778i	−0.167741	+	0.0968454i	0.413779	+	0.910377i	$0.364209\pi$
$614$	−23.1932	+	12.5765i	−0.936000	+	0.507545i
$615$	−0.520191	+	0.118207i	−0.0209761	+	0.00476655i
$616$		0			0
$617$		−	8.95961i		−	0.360700i	−0.983602	−	0.180350i	$-0.942277\pi$
$617$		−	8.95961i		−	0.360700i	0.983602	−	0.180350i	$-0.0577231\pi$
$618$	−6.62084	−	12.2100i	−0.266329	−	0.491157i
$619$	−12.8347	−	22.2303i	−0.515868	−	0.893510i	−0.999830	−	0.0184212i	$-0.994136\pi$
$619$	−12.8347	−	22.2303i	−0.515868	−	0.893510i	0.483962	−	0.875089i	$-0.339197\pi$
$620$	11.8237	−	32.0318i	0.474850	−	1.28643i
$621$	−17.0330	−	9.83400i	−0.683510	−	0.394625i
$622$	6.05205	−	9.86394i	0.242665	−	0.395508i
$623$		0			0
$624$	9.35623	+	6.82898i	0.374549	+	0.273378i
$625$	9.04437	+	23.3066i	0.361775	+	0.932265i
$626$	33.0444	+	0.883361i	1.32072	+	0.0353062i
$627$	−3.17999	−	5.50790i	−0.126996	−	0.219964i
$628$	38.4147	+	2.05531i	1.53291	+	0.0820160i
$629$			6.35693i			0.253467i
$630$		0			0
$631$		−	1.75095i		−	0.0697043i	−0.999392	−	0.0348521i	$-0.988904\pi$
$631$		−	1.75095i		−	0.0697043i	0.999392	−	0.0348521i	$-0.0110960\pi$
$632$	28.4356	+	19.6119i	1.13111	+	0.780120i
$633$	−5.19029	−	8.98985i	−0.206296	−	0.357314i
$634$	−0.990445	+	37.0502i	−0.0393356	+	1.47145i
$635$	−1.13566	+	3.66924i	−0.0450672	+	0.145609i
$636$	1.07302	+	2.11163i	0.0425482	+	0.0837315i
$637$		0			0
$638$	−16.7974	−	10.3061i	−0.665014	−	0.408021i
$639$	−32.8655	−	18.9749i	−1.30014	−	0.750636i
$640$	−25.2815	+	0.919623i	−0.999339	+	0.0363513i
$641$	20.3887	+	35.3143i	0.805306	+	1.39483i	0.916084	+	0.400986i	$0.131332\pi$
$641$	20.3887	+	35.3143i	0.805306	+	1.39483i	−0.110778	+	0.993845i	$0.535334\pi$
$642$	4.94658	−	2.68228i	0.195226	−	0.105861i
$643$			35.0077i			1.38057i	0.723538	+	0.690285i	$0.242515\pi$
$643$			35.0077i			1.38057i	−0.723538	+	0.690285i	$0.757485\pi$
$644$		0			0
$645$	−3.37057	−	14.8329i	−0.132716	−	0.584043i
$646$	−3.08530	−	5.68983i	−0.121390	−	0.223863i
$647$	−20.9951	+	12.1215i	−0.825404	+	0.476547i	−0.852276	−	0.523092i	$-0.824779\pi$
$647$	−20.9951	+	12.1215i	−0.825404	+	0.476547i	0.0268724	+	0.999639i	$0.491445\pi$
$648$	−5.40508	−	11.3799i	−0.212331	−	0.447046i
$649$	−17.7898	−	10.2710i	−0.698312	−	0.403171i
$650$	2.88486	−	27.7897i	0.113154	−	1.09000i
$651$		0			0
$652$	9.71192	+	19.1123i	0.380348	+	0.748495i
$653$	−37.4046	−	21.5956i	−1.46376	−	0.845100i	−0.464574	−	0.885534i	$-0.653792\pi$
$653$	−37.4046	−	21.5956i	−1.46376	−	0.845100i	−0.999182	+	0.0404346i	$0.987126\pi$
$654$	−0.246984	+	9.23906i	−0.00965782	+	0.361276i
$655$	21.4888	+	23.2039i	0.839636	+	0.906651i
$656$	−1.19062	+	0.526985i	−0.0464860	+	0.0205753i
$657$	−3.49483			−0.136346
$658$		0			0
$659$		−	11.6398i		−	0.453422i	−0.973962	−	0.226711i	$-0.927203\pi$
$659$		−	11.6398i		−	0.453422i	0.973962	−	0.226711i	$-0.0727973\pi$
$660$	−8.69152	+	1.49187i	−0.338317	+	0.0580710i
$661$	−14.8021	+	8.54599i	−0.575735	+	0.332400i	−0.759436	−	0.650582i	$-0.774525\pi$
$661$	−14.8021	+	8.54599i	−0.575735	+	0.332400i	0.183702	+	0.982982i	$0.441192\pi$
$662$	−0.737751	+	27.5975i	−0.0286735	+	1.07261i
$663$	3.55871	+	2.05462i	0.138209	+	0.0797950i
$664$	1.19197	−	14.8346i	0.0462574	−	0.575693i
$665$		0			0
$666$	−13.2994	−	8.15989i	−0.515342	−	0.316189i
$667$	12.7213	−	22.0339i	0.492570	−	0.853157i
$668$	22.1682	+	14.4306i	0.857712	+	0.558338i
$669$	−1.11198	−	1.92600i	−0.0429915	−	0.0744634i
$670$	6.31316	+	7.19346i	0.243899	+	0.277907i
$671$	38.4748			1.48530
$672$		0			0
$673$			3.77972i			0.145697i	0.997343	+	0.0728487i	$0.0232090\pi$
$673$			3.77972i			0.145697i	−0.997343	+	0.0728487i	$0.976791\pi$
$674$	39.4742	−	21.4048i	1.52049	−	0.824482i
$675$	11.3086	−	16.5187i	0.435268	−	0.635803i
$676$	−2.84976	+	4.37777i	−0.109606	+	0.168376i
$677$	13.8872	−	24.0534i	0.533729	−	0.924446i	−0.465494	−	0.885051i	$-0.654123\pi$
$677$	13.8872	−	24.0534i	0.533729	−	0.924446i	0.999224	−	0.0393956i	$-0.0125432\pi$
$678$	0.570017	−	0.929044i	0.0218914	−	0.0356797i
$679$		0			0
$680$	−8.88272	+	1.28135i	−0.340637	+	0.0491376i
$681$	−5.41499	+	9.37904i	−0.207503	+	0.359405i
$682$	0.776321	−	29.0403i	0.0297269	−	1.11201i
$683$	5.58652	+	9.67614i	0.213762	+	0.370247i	0.952889	−	0.303319i	$-0.0980948\pi$
$683$	5.58652	+	9.67614i	0.213762	+	0.370247i	−0.739127	+	0.673567i	$0.764761\pi$
$684$	15.8641	+	0.848783i	0.606580	+	0.0324540i
$685$	−7.36837	−	32.4260i	−0.281531	−	1.23893i
$686$		0			0
$687$	4.71324			0.179821
$688$	−15.0266	−	33.9497i	−0.572884	−	1.29432i
$689$	−5.52935	+	3.19237i	−0.210652	+	0.121620i
$690$	−2.22524	−	11.1656i	−0.0847134	−	0.425068i
$691$	17.7057	−	30.6672i	0.673556	−	1.16663i	−0.303332	−	0.952885i	$-0.598099\pi$
$691$	17.7057	−	30.6672i	0.673556	−	1.16663i	0.976889	−	0.213749i	$-0.0685675\pi$
$692$	10.1966	+	20.0661i	0.387616	+	0.762797i
$693$		0			0
$694$	−13.5966	+	22.1605i	−0.516122	+	0.841202i
$695$	4.67267	−	15.0971i	0.177244	−	0.572666i
$696$	−9.69812	+	4.60627i	−0.367606	+	0.174600i
$697$	−0.400020	+	0.230952i	−0.0151518	+	0.00874791i
$698$	2.95124	−	1.60031i	0.111706	−	0.0605725i
$699$	12.8043			0.484304
$700$		0			0
$701$	2.24955			0.0849643			0.0424821	−	0.999097i	$-0.486473\pi$
$701$	2.24955			0.0849643			0.0424821	+	0.999097i	$0.486473\pi$
$702$	−19.6669	+	10.6643i	−0.742279	+	0.402500i
$703$	12.5129	−	7.22434i	0.471934	−	0.272471i
$704$	−20.1198	+	7.64771i	−0.758293	+	0.288234i
$705$	−3.18144	+	10.2790i	−0.119820	+	0.387131i
$706$	1.59321	−	2.59671i	0.0599614	−	0.0977283i
$707$		0			0
$708$	−9.97707	+	5.06985i	−0.374961	+	0.190537i
$709$	7.94601	−	13.7629i	0.298418	−	0.516876i	−0.677356	−	0.735656i	$-0.736874\pi$
$709$	7.94601	−	13.7629i	0.298418	−	0.516876i	0.975774	+	0.218780i	$0.0702076\pi$
$710$	−9.52375	−	47.7875i	−0.357420	−	1.79343i
$711$	−26.0485	+	15.0391i	−0.976893	+	0.564010i
$712$	−11.0480	−	7.61980i	−0.414043	−	0.285564i
$713$	37.5056			1.40460
$714$		0			0
$715$	−5.26739	−	23.1802i	−0.196989	−	0.866890i
$716$	0.0861211	−	1.60964i	0.00321850	−	0.0601551i
$717$	−1.18177	−	2.04689i	−0.0441341	−	0.0764425i
$718$	−0.192011	+	7.18267i	−0.00716579	+	0.268055i
$719$	−18.0142	+	31.2015i	−0.671817	+	1.16362i	0.305572	+	0.952169i	$0.401152\pi$
$719$	−18.0142	+	31.2015i	−0.671817	+	1.16362i	−0.977388	+	0.211452i	$0.932181\pi$
$720$	8.72131	−	20.2284i	0.325024	−	0.753869i
$721$		0			0
$722$	6.35856	−	10.3635i	0.236641	−	0.385690i
$723$	7.50758	−	13.0035i	0.279210	−	0.483606i
$724$	−0.111817	−	0.0727888i	−0.00415565	−	0.00270517i
$725$	21.3686	+	14.6288i	0.793609	+	0.543301i
$726$	3.42687	−	1.85822i	0.127183	−	0.0689648i
$727$		−	51.4779i		−	1.90921i	−0.297878	−	0.954604i	$-0.596279\pi$
$727$		−	51.4779i		−	1.90921i	0.297878	−	0.954604i	$-0.403721\pi$
$728$		0			0
$729$	2.16686			0.0802541
$730$	−2.95994	−	3.37267i	−0.109552	−	0.124828i
$731$	−6.58541	−	11.4063i	−0.243570	−	0.421876i
$732$	11.4355	−	17.5670i	0.422667	−	0.649296i
$733$	17.9717	−	31.1280i	0.663801	−	1.14974i	−0.315807	−	0.948823i	$-0.602275\pi$
$733$	17.9717	−	31.1280i	0.663801	−	1.14974i	0.979609	−	0.200914i	$-0.0643913\pi$
$734$	16.3277	+	10.0179i	0.602667	+	0.369768i
$735$		0			0
$736$	−10.5641	−	25.7024i	−0.389398	−	0.947401i
$737$	7.05214	+	4.07155i	0.259769	+	0.149978i
$738$	0.0302971	−	1.13334i	0.00111525	−	0.0417189i
$739$	−15.7903	+	9.11653i	−0.580855	+	0.335357i	−0.761473	−	0.648196i	$-0.775524\pi$
$739$	−15.7903	+	9.11653i	−0.580855	+	0.335357i	0.180618	+	0.983553i	$0.442190\pi$
$740$	−3.38925	−	19.7455i	−0.124591	−	0.725860i
$741$		−	9.33993i		−	0.343111i
$742$		0			0
$743$	−29.1171			−1.06820			−0.534102	−	0.845420i	$-0.679350\pi$
$743$	−29.1171			−1.06820			−0.534102	+	0.845420i	$0.679350\pi$
$744$	−13.0287	−	8.98582i	−0.477654	−	0.329436i
$745$	13.3486	+	14.4140i	0.489055	+	0.528088i
$746$	0.269608	−	10.0854i	0.00987105	−	0.369252i
$747$	11.2227	+	6.47941i	0.410616	+	0.237069i
$748$	−6.80736	+	3.45916i	−0.248902	+	0.126479i
$749$		0			0
$750$	11.5049	−	1.38728i	0.420100	−	0.0506564i
$751$	37.2703	+	21.5180i	1.36001	+	0.785203i	0.989625	−	0.143675i	$-0.0458921\pi$
$751$	37.2703	+	21.5180i	1.36001	+	0.785203i	0.370386	+	0.928878i	$0.379225\pi$
$752$	−2.80229	+	26.1130i	−0.102189	+	0.952245i
$753$	−9.62527	+	5.55715i	−0.350764	+	0.202514i
$754$	−13.7954	−	25.4411i	−0.502400	−	0.926512i
$755$	−0.148810	−	0.654869i	−0.00541576	−	0.0238331i
$756$		0			0
$757$		−	10.6531i		−	0.387193i	−0.981081	−	0.193597i	$-0.937985\pi$
$757$		−	10.6531i		−	0.387193i	0.981081	−	0.193597i	$-0.0620153\pi$
$758$	20.1941	−	10.9502i	0.733484	−	0.397730i
$759$	−4.84339	−	8.38899i	−0.175804	−	0.304501i
$760$	12.6170	+	16.0285i	0.457666	+	0.581414i
$761$	−12.3298	−	7.11864i	−0.446956	−	0.258050i	0.259588	−	0.965720i	$-0.416413\pi$
$761$	−12.3298	−	7.11864i	−0.446956	−	0.258050i	−0.706544	+	0.707669i	$0.749747\pi$
$762$	1.51754	+	0.931088i	0.0549745	+	0.0337297i
$763$		0			0
$764$	31.1316	−	15.8195i	1.12630	−	0.572331i
$765$	2.31056	−	7.46528i	0.0835385	−	0.269908i
$766$	0.373656	−	13.9776i	0.0135007	−	0.505030i
$767$	−15.0834	−	26.1252i	−0.544630	−	0.943327i
$768$	−2.48817	+	11.4595i	−0.0897842	+	0.413508i
$769$			35.5770i			1.28294i	0.767149	+	0.641469i	$0.221675\pi$
$769$			35.5770i			1.28294i	−0.767149	+	0.641469i	$0.778325\pi$
$770$		0			0
$771$			3.46777i			0.124889i
$772$	1.83753	−	34.3443i	0.0661342	−	1.23608i
$773$	5.94268	+	10.2930i	0.213743	+	0.370214i	0.952883	−	0.303338i	$-0.0981010\pi$
$773$	5.94268	+	10.2930i	0.213743	+	0.370214i	−0.739140	+	0.673552i	$0.764768\pi$
$774$	32.3164	+	0.863899i	1.16159	+	0.0310522i
$775$	−2.92564	+	38.0622i	−0.105092	+	1.36723i
$776$	23.5453	+	1.89188i	0.845226	+	0.0679145i
$777$		0			0
$778$	23.6388	−	38.5277i	0.847491	−	1.38129i
$779$	0.909207	+	0.524931i	0.0325757	+	0.0188076i
$780$	−12.1493	−	4.48460i	−0.435015	−	0.160574i
$781$	−20.7291	−	35.9038i	−0.741745	−	1.28474i
$782$	−4.69918	−	8.66609i	−0.168042	−	0.309899i
$783$		−	20.7365i		−	0.741061i
$784$		0			0
$785$	−41.9412	+	9.53058i	−1.49694	+	0.340161i
$786$	12.8868	−	6.98786i	0.459658	−	0.249249i
$787$	40.1645	−	23.1890i	1.43171	−	0.826597i	0.434457	−	0.900692i	$-0.356940\pi$
$787$	40.1645	−	23.1890i	1.43171	−	0.826597i	0.997251	+	0.0740951i	$0.0236068\pi$
$788$	20.0119	+	13.0270i	0.712896	+	0.464068i
$789$	−2.98342	−	1.72248i	−0.106213	−	0.0613219i
$790$	−36.5751	−	12.4006i	−1.30128	−	0.441194i
$791$		0			0
$792$	1.50111	−	18.6820i	0.0533398	−	0.663836i
$793$	48.9322	+	28.2510i	1.73763	+	1.00322i
$794$	−24.7055	−	0.660441i	−0.876766	−	0.0234382i
$795$	−1.79937	−	1.94299i	−0.0638171	−	0.0689107i
$796$	30.9963	+	1.65841i	1.09864	+	0.0587806i
$797$	−9.09251			−0.322073			−0.161037	−	0.986948i	$-0.551484\pi$
$797$	−9.09251			−0.322073			−0.161037	+	0.986948i	$0.551484\pi$
$798$		0			0
$799$			9.31691i			0.329609i
$800$	26.9078	−	8.71597i	0.951336	−	0.308156i
$801$	10.1206	−	5.84312i	0.357593	−	0.206457i
$802$	−24.5399	−	0.656013i	−0.866534	−	0.0231646i
$803$	−3.30641	−	1.90896i	−0.116681	−	0.0673656i
$804$	3.95505	−	2.00976i	0.139484	−	0.0708788i
$805$		0			0
$806$	22.3109	−	36.3634i	0.785867	−	1.28085i
$807$	−8.99316	+	15.5766i	−0.316574	+	0.548323i
$808$	0.713717	−	0.338991i	0.0251085	−	0.0119257i
$809$	−8.66128	−	15.0018i	−0.304515	−	0.527435i	0.672639	−	0.739971i	$-0.265161\pi$
$809$	−8.66128	−	15.0018i	−0.304515	−	0.527435i	−0.977153	+	0.212536i	$0.931828\pi$
$810$	9.29100	+	10.5865i	0.326452	+	0.371972i
$811$	16.4459			0.577493			0.288746	−	0.957406i	$-0.406762\pi$
$811$	16.4459			0.577493			0.288746	+	0.957406i	$0.406762\pi$
$812$		0			0
$813$			19.3424i			0.678368i
$814$	−8.12527	−	14.9844i	−0.284791	−	0.525203i
$815$	−16.2861	−	17.5859i	−0.570476	−	0.616009i
$816$	−0.443879	+	4.13628i	−0.0155389	+	0.144799i
$817$	−14.9680	+	25.9254i	−0.523664	+	0.907013i
$818$	8.79934	+	5.39886i	0.307662	+	0.188767i
$819$		0			0
$820$	1.11939	−	0.930643i	0.0390906	−	0.0324995i
$821$	−22.4527	+	38.8892i	−0.783603	+	1.35724i	0.146226	+	0.989251i	$0.453287\pi$
$821$	−22.4527	+	38.8892i	−0.783603	+	1.35724i	−0.929830	+	0.367990i	$0.880046\pi$
$822$	−15.4081	−	0.411897i	−0.537418	−	0.0143666i
$823$	−11.8546	−	20.5328i	−0.413226	−	0.715729i	0.582014	−	0.813179i	$-0.302265\pi$
$823$	−11.8546	−	20.5328i	−0.413226	−	0.715729i	−0.995240	+	0.0974497i	$0.968931\pi$
$824$	31.2013	+	21.5194i	1.08695	+	0.749665i
$825$	8.89130	−	4.26088i	0.309555	−	0.148345i
$826$		0			0
$827$	−8.20536			−0.285328			−0.142664	−	0.989771i	$-0.545567\pi$
$827$	−8.20536			−0.285328			−0.142664	+	0.989771i	$0.545567\pi$
$828$	24.1624	+	1.29277i	0.839702	+	0.0449268i
$829$	19.1548	−	11.0590i	0.665272	−	0.384095i	−0.129011	−	0.991643i	$-0.541180\pi$
$829$	19.1548	−	11.0590i	0.665272	−	0.384095i	0.794283	+	0.607548i	$0.207847\pi$
$830$	3.25210	+	16.3181i	0.112882	+	0.566410i
$831$	8.82054	−	15.2776i	0.305981	−	0.529975i
$832$	−31.2039	−	5.04710i	−1.08180	−	0.174977i
$833$		0			0
$834$	−6.24391	−	3.83096i	−0.216209	−	0.132655i
$835$	−28.2512	−	8.74396i	−0.977674	−	0.302597i
$836$	14.5452	+	9.46838i	0.503057	+	0.327471i
$837$	26.4729	−	15.2841i	0.915036	−	0.528296i
$838$	12.0856	+	22.2879i	0.417490	+	0.769923i
$839$	−3.64977			−0.126004			−0.0630020	−	0.998013i	$-0.520067\pi$
$839$	−3.64977			−0.126004			−0.0630020	+	0.998013i	$0.520067\pi$
$840$		0			0
$841$	−2.17525			−0.0750086
$842$	−8.51652	−	15.7059i	−0.293499	−	0.541262i
$843$	−4.94174	+	2.85312i	−0.170203	+	0.0982665i
$844$	23.7403	+	15.4541i	0.817176	+	0.531950i
$845$	1.72676	−	5.57905i	0.0594023	−	0.191925i
$846$	−19.4920	−	11.9594i	−0.670150	−	0.411172i
$847$		0			0
$848$	−5.22088	−	3.81065i	−0.179286	−	0.130858i
$849$	−2.91351	+	5.04634i	−0.0999913	+	0.173190i
$850$	9.16126	−	4.09291i	0.314229	−	0.140386i
$851$	19.0582	−	11.0033i	0.653308	−	0.377188i
$852$	−22.5543	−	1.20673i	−0.772697	−	0.0413419i
$853$	1.03474			0.0354290			0.0177145	−	0.999843i	$-0.494361\pi$
$853$	1.03474			0.0354290			0.0177145	+	0.999843i	$0.494361\pi$
$854$		0			0
$855$	−17.3205	+	3.93584i	−0.592347	+	0.134603i
$856$	−8.71810	+	12.6405i	−0.297979	+	0.432043i
$857$	−24.2563	−	42.0132i	−0.828581	−	1.43514i	−0.899152	−	0.437637i	$-0.855815\pi$
$857$	−24.2563	−	42.0132i	−0.828581	−	1.43514i	0.0705709	−	0.997507i	$-0.477518\pi$
$858$	−11.0147	−	0.294451i	−0.376035	−	0.0100524i
$859$	−12.4674	+	21.5941i	−0.425382	+	0.736783i	−0.996456	−	0.0841157i	$-0.973193\pi$
$859$	−12.4674	+	21.5941i	−0.425382	+	0.736783i	0.571074	+	0.820898i	$0.306527\pi$
$860$	26.5366	+	31.9184i	0.904891	+	1.08841i
$861$		0			0
$862$	−39.3852	−	24.1649i	−1.34147	−	0.823060i
$863$	−2.98354	+	5.16765i	−0.101561	+	0.175909i	−0.912328	−	0.409460i	$-0.865717\pi$
$863$	−2.98354	+	5.16765i	−0.101561	+	0.175909i	0.810767	+	0.585369i	$0.199050\pi$
$864$	−17.9307	−	13.8366i	−0.610013	−	0.470732i
$865$	−17.0988	−	18.4635i	−0.581377	−	0.627779i
$866$	15.9016	+	29.3252i	0.540357	+	0.996511i
$867$		−	10.9836i		−	0.373023i
$868$		0			0
$869$	−32.8588			−1.11466
$870$	9.02197	−	7.91791i	0.305873	−	0.268442i
$871$	5.97927	+	10.3564i	0.202600	+	0.350913i
$872$	−10.8207	−	22.7820i	−0.366434	−	0.771496i
$873$	−10.2840	+	17.8125i	−0.348062	+	0.602861i
$874$	−11.7179	+	19.0984i	−0.396363	+	0.646014i
$875$		0			0
$876$	−1.85433	+	0.942281i	−0.0626522	+	0.0318367i
$877$	−29.2974	−	16.9149i	−0.989304	−	0.571175i	−0.0842381	−	0.996446i	$-0.526846\pi$
$877$	−29.2974	−	16.9149i	−0.989304	−	0.571175i	−0.905066	+	0.425270i	$0.860179\pi$
$878$	−25.9981	−	0.694996i	−0.877394	−	0.0234550i
$879$	−1.34243	+	0.775051i	−0.0452789	+	0.0261418i
$880$	19.3004	−	14.3741i	0.650615	−	0.484549i
$881$			20.9239i			0.704944i	0.935822	+	0.352472i	$0.114659\pi$
$881$			20.9239i			0.704944i	−0.935822	+	0.352472i	$0.885341\pi$
$882$		0			0
$883$	−14.7876			−0.497642			−0.248821	−	0.968549i	$-0.580043\pi$
$883$	−14.7876			−0.497642			−0.248821	+	0.968549i	$0.580043\pi$
$884$	−11.1976	−	0.599107i	−0.376615	−	0.0201501i
$885$	9.18028	−	8.50172i	0.308592	−	0.285782i
$886$	4.78446	+	0.127901i	0.160737	+	0.00429691i
$887$	6.40786	+	3.69958i	0.215155	+	0.124220i	0.603705	−	0.797208i	$-0.293691\pi$
$887$	6.40786	+	3.69958i	0.215155	+	0.124220i	−0.388550	+	0.921428i	$0.627024\pi$
$888$	−9.25667	−	0.743780i	−0.310633	−	0.0249596i
$889$		0			0
$890$	14.2105	+	4.81800i	0.476336	+	0.161500i
$891$	10.3785	+	5.99206i	0.347694	+	0.200741i
$892$	5.08617	+	3.31090i	0.170297	+	0.110857i
$893$	18.3393	−	10.5882i	0.613702	−	0.354321i
$894$	8.00516	−	4.34079i	0.267733	−	0.145178i
$895$	0.399347	+	1.75740i	0.0133487	+	0.0587435i
$896$		0			0
$897$		−	14.2255i		−	0.474976i
$898$	8.02298	+	14.7958i	0.267730	+	0.493741i
$899$	19.7716	+	34.2453i	0.659418	+	1.14215i
$900$	−3.19675	+	24.4201i	−0.106558	+	0.814005i
$901$	−1.98580	−	1.14650i	−0.0661566	−	0.0381956i
$902$	0.647721	−	1.05569i	0.0215668	−	0.0351506i
$903$		0			0
$904$	−0.238227	+	2.96484i	−0.00792331	+	0.0986090i
$905$	0.142500	+	0.0441050i	0.00473687	+	0.00146610i
$906$	−0.311179	−	0.00831860i	−0.0103382	−	0.000276367i
$907$	−9.25608	−	16.0320i	−0.307343	−	0.532334i	0.670437	−	0.741966i	$-0.266107\pi$
$907$	−9.25608	−	16.0320i	−0.307343	−	0.532334i	−0.977780	+	0.209632i	$0.932773\pi$
$908$	1.57895	−	29.5113i	0.0523994	−	0.979368i
$909$			0.688006i			0.0228197i
$910$		0			0
$911$			10.8437i			0.359267i	0.983734	+	0.179634i	$0.0574912\pi$
$911$			10.8437i			0.359267i	−0.983734	+	0.179634i	$0.942509\pi$
$912$	8.64626	−	3.82695i	0.286306	−	0.126723i
$913$	7.07841	+	12.2602i	0.234261	+	0.405752i
$914$	0.796292	−	29.7874i	0.0263390	−	0.985279i
$915$	−6.92911	+	22.3875i	−0.229069	+	0.740109i
$916$	−11.4663	+	5.82661i	−0.378858	+	0.192517i
$917$		0			0
$918$	−6.84842	−	4.20187i	−0.226032	−	0.138682i
$919$	13.9555	+	8.05723i	0.460351	+	0.265784i	0.712192	−	0.701985i	$-0.247703\pi$
$919$	13.9555	+	8.05723i	0.460351	+	0.265784i	−0.251841	+	0.967769i	$0.581036\pi$
$920$	19.2167	+	24.4127i	0.633557	+	0.804864i
$921$	−6.83653	−	11.8412i	−0.225271	−	0.390181i
$922$	−36.8869	+	20.0019i	−1.21480	+	0.658726i
$923$		−	60.8834i		−	2.00400i
$924$		0			0
$925$	9.67993	+	20.1994i	0.318274	+	0.664152i
$926$	10.1443	+	18.7078i	0.333362	+	0.614776i
$927$	−28.5820	+	16.5018i	−0.938757	+	0.541991i
$928$	17.8991	−	23.1951i	0.587567	−	0.761417i
$929$	−42.7419	−	24.6770i	−1.40232	−	0.809627i	−0.407686	−	0.913122i	$-0.633664\pi$
$929$	−42.7419	−	24.6770i	−1.40232	−	0.809627i	−0.994630	+	0.103495i	$0.966998\pi$
$930$	16.7580	+	5.68173i	0.549517	+	0.186311i
$931$		0			0
$932$	−31.1502	+	15.8290i	−1.02036	+	0.518496i
$933$	5.19390	+	2.99870i	0.170041	+	0.0981731i
$934$	−0.194477	+	7.27493i	−0.00636349	+	0.238043i
$935$	6.26370	−	5.80072i	0.204845	−	0.189704i
$936$	15.6268	−	22.6576i	0.510779	−	0.740586i
$937$	31.3085			1.02280			0.511402	−	0.859342i	$-0.329126\pi$
$937$	31.3085			1.02280			0.511402	+	0.859342i	$0.329126\pi$
$938$		0			0
$939$			17.1311i			0.559054i
$940$	−4.96740	−	28.9397i	−0.162019	−	0.943908i
$941$	−37.9492	+	21.9100i	−1.23711	+	0.714245i	−0.968502	−	0.249005i	$-0.919896\pi$
$941$	−37.9492	+	21.9100i	−1.23711	+	0.714245i	−0.268606	+	0.963250i	$0.586563\pi$
$942$	−0.532766	+	19.9295i	−0.0173584	+	0.649338i
$943$	1.38480	+	0.799514i	0.0450952	+	0.0260358i
$944$	18.0047	−	24.6678i	0.586002	−	0.802867i
$945$		0			0
$946$	30.1022	+	18.4693i	0.978708	+	0.600488i
$947$	−7.31729	+	12.6739i	−0.237780	+	0.411847i	−0.960077	−	0.279736i	$-0.909753\pi$
$947$	−7.31729	+	12.6739i	−0.237780	+	0.411847i	0.722297	+	0.691583i	$0.243086\pi$
$948$	−9.76629	+	15.0029i	−0.317194	+	0.487270i
$949$	−2.80340	−	4.85563i	−0.0910021	−	0.157620i
$950$	−18.4678	−	13.3816i	−0.599174	−	0.434155i
$951$	−19.2078			−0.622857
$952$		0			0
$953$		−	28.2044i		−	0.913630i	−0.889562	−	0.456815i	$-0.848990\pi$
$953$		−	28.2044i		−	0.913630i	0.889562	−	0.456815i	$-0.151010\pi$
$954$	4.94763	−	2.68285i	0.160186	−	0.0868604i
$955$	−28.6454	+	26.5280i	−0.926942	+	0.858427i
$956$	5.40542	+	3.51872i	0.174824	+	0.113804i
$957$	5.10651	−	8.84473i	0.165070	−	0.285909i
$958$	29.5513	−	48.1643i	0.954759	−	1.55612i
$959$		0			0
$960$	−0.826540	−	13.0845i	−0.0266765	−	0.422301i
$961$	−13.6458	+	23.6352i	−0.440187	+	0.762427i
$962$	0.668938	−	25.0234i	0.0215674	−	0.806785i
$963$	−6.68534	−	11.5793i	−0.215432	−	0.373139i
$964$	−2.18913	+	40.9158i	−0.0705072	+	1.31781i
$965$	8.52071	+	37.4971i	0.274291	+	1.20707i
$966$		0			0
$967$	−8.88824			−0.285827			−0.142913	−	0.989735i	$-0.545647\pi$
$967$	−8.88824			−0.285827			−0.142913	+	0.989735i	$0.545647\pi$
$968$	−6.03968	+	8.75702i	−0.194123	+	0.281461i
$969$	2.90493	−	1.67716i	0.0933198	−	0.0538782i
$970$	−25.8999	+	5.16169i	−0.831596	+	0.165732i
$971$	−4.37105	+	7.57089i	−0.140274	+	0.242961i	−0.927600	−	0.373576i	$-0.878132\pi$
$971$	−4.37105	+	7.57089i	−0.140274	+	0.242961i	0.787326	+	0.616537i	$0.211465\pi$
$972$	27.2367	−	13.8403i	0.873618	−	0.443929i
$973$		0			0
$974$	9.04134	−	14.7360i	0.289703	−	0.472173i
$975$	14.4366	+	1.10967i	0.462342	+	0.0355377i
$976$	−6.10333	+	56.8737i	−0.195363	+	1.82048i
$977$	−36.3569	+	20.9907i	−1.16316	+	0.671551i	−0.952059	−	0.305914i	$-0.901038\pi$
$977$	−36.3569	+	20.9907i	−1.16316	+	0.671551i	−0.211100	+	0.977464i	$0.567705\pi$
$978$	−9.76676	+	5.29601i	−0.312307	+	0.169348i
$979$	12.7666			0.408022
$980$		0			0
$981$	21.9613			0.701170
$982$	28.5334	−	15.4722i	0.910539	−	0.493738i
$983$	9.53036	−	5.50236i	0.303971	−	0.175498i	−0.340254	−	0.940333i	$-0.610513\pi$
$983$	9.53036	−	5.50236i	0.303971	−	0.175498i	0.644226	+	0.764836i	$0.277180\pi$
$984$	−0.289497	−	0.609513i	−0.00922884	−	0.0194306i
$985$	−25.5033	−	7.89347i	−0.812603	−	0.251507i
$986$	5.43554	−	8.85913i	0.173103	−	0.282132i
$987$		0			0
$988$	11.5462	+	22.7221i	0.367334	+	0.722885i
$989$	−22.7975	+	39.4865i	−0.724920	+	1.25560i
$990$	4.09555	+	20.5503i	0.130165	+	0.653132i
$991$	−31.6799	+	18.2904i	−1.00634	+	0.581013i	−0.910119	−	0.414346i	$-0.864010\pi$
$991$	−31.6799	+	18.2904i	−1.00634	+	0.581013i	−0.0962255	+	0.995360i	$0.530677\pi$
$992$	42.8044	+	5.75429i	1.35904	+	0.182699i
$993$	−14.3073			−0.454028
$994$		0			0
$995$	−33.8418	+	7.69010i	−1.07286	+	0.243792i
$996$	7.70167	+	0.412065i	0.244037	+	0.0130568i
$997$	7.23204	+	12.5263i	0.229041	+	0.396711i	0.957524	−	0.288353i	$-0.0931076\pi$
$997$	7.23204	+	12.5263i	0.229041	+	0.396711i	−0.728483	+	0.685064i	$0.759774\pi$
$998$	0.159008	−	5.94811i	0.00503331	−	0.188284i
$999$	8.96801	−	15.5331i	0.283735	−	0.491444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.e.19.6		32
4.3	odd	2	inner	980.2.s.e.19.1		32
5.4	even	2	inner	980.2.s.e.19.11		32
7.2	even	3		980.2.c.d.979.12		32
7.3	odd	6	inner	980.2.s.e.619.16		32
7.4	even	3		140.2.s.b.59.16	yes	32
7.5	odd	6		980.2.c.d.979.11		32
7.6	odd	2		140.2.s.b.19.6	yes	32
20.19	odd	2	inner	980.2.s.e.19.16		32
28.3	even	6	inner	980.2.s.e.619.11		32
28.11	odd	6		140.2.s.b.59.11	yes	32
28.19	even	6		980.2.c.d.979.24		32
28.23	odd	6		980.2.c.d.979.23		32
28.27	even	2		140.2.s.b.19.1	✓	32
35.4	even	6		140.2.s.b.59.1	yes	32
35.9	even	6		980.2.c.d.979.21		32
35.13	even	4		700.2.p.e.551.3		32
35.18	odd	12		700.2.p.e.451.9		32
35.19	odd	6		980.2.c.d.979.22		32
35.24	odd	6	inner	980.2.s.e.619.1		32
35.27	even	4		700.2.p.e.551.14		32
35.32	odd	12		700.2.p.e.451.8		32
35.34	odd	2		140.2.s.b.19.11	yes	32
140.19	even	6		980.2.c.d.979.9		32
140.27	odd	4		700.2.p.e.551.8		32
140.39	odd	6		140.2.s.b.59.6	yes	32
140.59	even	6	inner	980.2.s.e.619.6		32
140.67	even	12		700.2.p.e.451.14		32
140.79	odd	6		980.2.c.d.979.10		32
140.83	odd	4		700.2.p.e.551.9		32
140.123	even	12		700.2.p.e.451.3		32
140.139	even	2		140.2.s.b.19.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.1	✓	32	28.27	even	2
140.2.s.b.19.6	yes	32	7.6	odd	2
140.2.s.b.19.11	yes	32	35.34	odd	2
140.2.s.b.19.16	yes	32	140.139	even	2
140.2.s.b.59.1	yes	32	35.4	even	6
140.2.s.b.59.6	yes	32	140.39	odd	6
140.2.s.b.59.11	yes	32	28.11	odd	6
140.2.s.b.59.16	yes	32	7.4	even	3
700.2.p.e.451.3		32	140.123	even	12
700.2.p.e.451.8		32	35.32	odd	12
700.2.p.e.451.9		32	35.18	odd	12
700.2.p.e.451.14		32	140.67	even	12
700.2.p.e.551.3		32	35.13	even	4
700.2.p.e.551.8		32	140.27	odd	4
700.2.p.e.551.9		32	140.83	odd	4
700.2.p.e.551.14		32	35.27	even	4
980.2.c.d.979.9		32	140.19	even	6
980.2.c.d.979.10		32	140.79	odd	6
980.2.c.d.979.11		32	7.5	odd	6
980.2.c.d.979.12		32	7.2	even	3
980.2.c.d.979.21		32	35.9	even	6
980.2.c.d.979.22		32	35.19	odd	6
980.2.c.d.979.23		32	28.23	odd	6
980.2.c.d.979.24		32	28.19	even	6
980.2.s.e.19.1		32	4.3	odd	2	inner
980.2.s.e.19.6		32	1.1	even	1	trivial
980.2.s.e.19.11		32	5.4	even	2	inner
980.2.s.e.19.16		32	20.19	odd	2	inner
980.2.s.e.619.1		32	35.24	odd	6	inner
980.2.s.e.619.6		32	140.59	even	6	inner
980.2.s.e.619.11		32	28.3	even	6	inner
980.2.s.e.619.16		32	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.674125 - 1.24320i) q^{2} +(0.634715 - 0.366453i) q^{3} +(-1.09111 + 1.67615i) q^{4} +(0.661137 - 2.13609i) q^{5} +(-0.883452 - 0.542044i) q^{6} +(2.81934 + 0.226536i) q^{8} +(-1.23142 + 2.13289i) q^{9} +(-3.10129 + 0.618067i) q^{10} +(-2.33007 + 1.34527i) q^{11} +(-0.0783137 + 1.46372i) q^{12} -3.95118 q^{13} +(-0.363144 - 1.59809i) q^{15} +(-1.61896 - 3.65773i) q^{16} +(-0.709509 - 1.22891i) q^{17} +(3.48175 + 0.0930760i) q^{18} +(-1.61265 + 2.79319i) q^{19} +(2.85904 + 3.43888i) q^{20} +(3.24320 + 1.98987i) q^{22} +(-2.45620 + 4.25426i) q^{23} +(1.87249 - 0.889369i) q^{24} +(-4.12580 - 2.82450i) q^{25} +(2.66359 + 4.91212i) q^{26} +4.00375i q^{27} -5.17926 q^{29} +(-1.74194 + 1.52877i) q^{30} +(-3.81745 - 6.61201i) q^{31} +(-3.45592 + 4.47846i) q^{32} +(-0.985953 + 1.70772i) q^{33} +(-1.04948 + 1.71050i) q^{34} +(-2.23142 - 4.39127i) q^{36} +(-3.87963 - 2.23990i) q^{37} +(4.55962 + 0.121890i) q^{38} +(-2.50787 + 1.44792i) q^{39} +(2.34787 - 5.87261i) q^{40} -0.325509i q^{41} +9.28165 q^{43} +(0.287494 - 5.37338i) q^{44} +(3.74191 + 4.04057i) q^{45} +(6.94469 + 0.185649i) q^{46} +(-5.68610 - 3.28287i) q^{47} +(-2.36796 - 1.72834i) q^{48} +(-0.730128 + 7.03327i) q^{50} +(-0.900672 - 0.520003i) q^{51} +(4.31117 - 6.62277i) q^{52} +(1.39942 - 0.807955i) q^{53} +(4.97748 - 2.69903i) q^{54} +(1.33312 + 5.86665i) q^{55} +2.36383i q^{57} +(3.49147 + 6.43888i) q^{58} +(3.81745 + 6.61201i) q^{59} +(3.07486 + 1.13500i) q^{60} +(-12.3842 - 7.15003i) q^{61} +(-5.64664 + 9.20319i) q^{62} +(7.89736 + 1.27737i) q^{64} +(-2.61227 + 8.44009i) q^{65} +(2.78770 + 0.0745223i) q^{66} +(-1.51329 - 2.62109i) q^{67} +(2.83398 + 0.151627i) q^{68} +3.60032i q^{69} +15.4089i q^{71} +(-3.95498 + 5.73438i) q^{72} +(0.709509 + 1.22891i) q^{73} +(-0.169301 + 6.33314i) q^{74} +(-3.65375 - 0.280844i) q^{75} +(-2.92222 - 5.75071i) q^{76} +(3.49068 + 2.14171i) q^{78} +(10.5765 + 6.10637i) q^{79} +(-8.88360 + 1.03999i) q^{80} +(-2.22709 - 3.85743i) q^{81} +(-0.404674 + 0.219434i) q^{82} -5.26172i q^{83} +(-3.09414 + 0.703103i) q^{85} +(-6.25699 - 11.5390i) q^{86} +(-3.28735 + 1.89795i) q^{87} +(-6.87401 + 3.26492i) q^{88} +(-4.10930 - 2.37250i) q^{89} +(2.50073 - 7.37581i) q^{90} +(-4.45079 - 8.75882i) q^{92} +(-4.84598 - 2.79783i) q^{93} +(-0.248133 + 9.28205i) q^{94} +(4.90033 + 5.29144i) q^{95} +(-0.552378 + 4.10898i) q^{96} +8.35134 q^{97} -6.62638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} + 6 q^{5} + 4 q^{9} + 12 q^{10} + 18 q^{16} + 48 q^{24} - 26 q^{25} + 18 q^{26} - 26 q^{30} - 28 q^{36} - 42 q^{40} - 26 q^{44} - 36 q^{45} - 22 q^{46} + 36 q^{50} - 48 q^{54} + 4 q^{60}+ \cdots - 60 q^{96}+O(q^{100}) \) 32 * q + 6 * q^4 + 6 * q^5 + 4 * q^9 + 12 * q^10 + 18 * q^16 + 48 * q^24 - 26 * q^25 + 18 * q^26 - 26 * q^30 - 28 * q^36 - 42 * q^40 - 26 * q^44 - 36 * q^45 - 22 * q^46 + 36 * q^50 - 48 * q^54 + 4 * q^60 - 36 * q^61 + 36 * q^64 - 4 * q^65 + 24 * q^66 + 14 * q^74 - 72 * q^80 + 72 * q^81 + 20 * q^85 + 8 * q^86 + 108 * q^89 - 30 * q^94 - 60 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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