LMFDB - Embedded newform 990.2.o.a.329.70

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.70
Character	$\chi$	$=$	990.329
Dual form			990.2.o.a.659.70

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(1.67359 + 0.446217i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.08392 + 0.810725i) q^{5} +(1.67248 - 0.450358i) q^{6} +(-1.06306 - 1.84128i) q^{7} -1.00000i q^{8} +(2.60178 + 1.49356i) q^{9} +(-1.39937 + 1.74407i) q^{10} +(2.70959 - 1.91262i) q^{11} +(1.22323 - 1.22626i) q^{12} +(2.63748 - 4.56825i) q^{13} +(-1.84128 - 1.06306i) q^{14} +(-3.84938 + 0.426938i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.850639i q^{17} +(2.99999 - 0.00742535i) q^{18} -2.62562i q^{19} +(-0.339852 + 2.21009i) q^{20} +(-0.957517 - 3.55589i) q^{21} +(1.39026 - 3.01117i) q^{22} +(1.13469 - 1.96534i) q^{23} +(0.446217 - 1.67359i) q^{24} +(3.68545 - 3.37897i) q^{25} -5.27496i q^{26} +(3.68785 + 3.66057i) q^{27} -2.12612 q^{28} +(4.51629 + 7.82244i) q^{29} +(-3.12019 + 2.29443i) q^{30} +(-3.51686 + 6.09138i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.38818 - 1.99188i) q^{33} +(0.425319 + 0.736675i) q^{34} +(3.70811 + 2.97523i) q^{35} +(2.59436 - 1.50643i) q^{36} +4.77143i q^{37} +(-1.31281 - 2.27385i) q^{38} +(6.45248 - 6.46847i) q^{39} +(0.810725 + 2.08392i) q^{40} +(4.60079 - 7.96881i) q^{41} +(-2.60718 - 2.60074i) q^{42} +(-4.38888 - 7.60176i) q^{43} +(-0.301586 - 3.30288i) q^{44} +(-6.63278 - 1.00314i) q^{45} -2.26938i q^{46} +(0.240394 + 0.416375i) q^{47} +(-0.450358 - 1.67248i) q^{48} +(1.23980 - 2.14739i) q^{49} +(1.50221 - 4.76900i) q^{50} +(-0.379569 + 1.42362i) q^{51} +(-2.63748 - 4.56825i) q^{52} -9.77771 q^{53} +(5.02406 + 1.32622i) q^{54} +(-4.09596 + 6.18249i) q^{55} +(-1.84128 + 1.06306i) q^{56} +(1.17160 - 4.39420i) q^{57} +(7.82244 + 4.51629i) q^{58} +(8.28833 + 4.78527i) q^{59} +(-1.55495 + 3.54713i) q^{60} +(5.31642 - 3.06944i) q^{61} +7.03372i q^{62} +(-0.0157872 - 6.37835i) q^{63} -1.00000 q^{64} +(-1.79270 + 11.6581i) q^{65} +(3.67036 - 4.41910i) q^{66} +(-2.27943 - 1.31603i) q^{67} +(0.736675 + 0.425319i) q^{68} +(2.77597 - 2.78285i) q^{69} +(4.69893 + 0.722567i) q^{70} +12.5151i q^{71} +(1.49356 - 2.60178i) q^{72} -6.05548 q^{73} +(2.38572 + 4.13218i) q^{74} +(7.67567 - 4.01049i) q^{75} +(-2.27385 - 1.31281i) q^{76} +(-6.40213 - 2.95587i) q^{77} +(2.35378 - 8.82810i) q^{78} +(-11.3092 + 6.52938i) q^{79} +(1.74407 + 1.39937i) q^{80} +(4.53853 + 7.77186i) q^{81} -9.20159i q^{82} +(-7.73026 + 4.46307i) q^{83} +(-3.55825 - 0.948713i) q^{84} +(-0.689634 - 1.77266i) q^{85} +(-7.60176 - 4.38888i) q^{86} +(4.06789 + 15.1068i) q^{87} +(-1.91262 - 2.70959i) q^{88} -8.26439i q^{89} +(-6.24572 + 2.44764i) q^{90} -11.2152 q^{91} +(-1.13469 - 1.96534i) q^{92} +(-8.60384 + 8.62516i) q^{93} +(0.416375 + 0.240394i) q^{94} +(2.12866 + 5.47158i) q^{95} +(-1.22626 - 1.22323i) q^{96} +(-10.8929 + 6.28902i) q^{97} -2.47959i q^{98} +(9.90638 - 0.929280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	1.67359	+	0.446217i	0.966245	+	0.257623i
$3$	1.67359	+	0.446217i	0.966245	+	0.257623i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.08392	+	0.810725i	−0.931958	+	0.362567i
$5$	−2.08392	+	0.810725i	−0.931958	+	0.362567i
$6$	1.67248	−	0.450358i	0.682786	−	0.183858i
$7$	−1.06306	−	1.84128i	−0.401800	−	0.695938i	0.592143	−	0.805833i	$-0.298282\pi$
$7$	−1.06306	−	1.84128i	−0.401800	−	0.695938i	−0.993943	+	0.109895i	$0.964949\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.60178	+	1.49356i	0.867260	+	0.497855i
$10$	−1.39937	+	1.74407i	−0.442518	+	0.551523i
$11$	2.70959	−	1.91262i	0.816972	−	0.576678i
$11$	2.70959	−	1.91262i	0.816972	−	0.576678i
$12$	1.22323	−	1.22626i	0.353116	−	0.353991i
$13$	2.63748	−	4.56825i	0.731505	−	1.26700i	−0.224734	−	0.974420i	$-0.572151\pi$
$13$	2.63748	−	4.56825i	0.731505	−	1.26700i	0.956240	−	0.292584i	$-0.0945152\pi$
$14$	−1.84128	−	1.06306i	−0.492102	−	0.284115i
$15$	−3.84938	+	0.426938i	−0.993906	+	0.110235i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			0.850639i			0.206310i	0.994665	+	0.103155i	$0.0328938\pi$
$17$			0.850639i			0.206310i	−0.994665	+	0.103155i	$0.967106\pi$
$18$	2.99999	−	0.00742535i	0.707105	−	0.00175017i
$19$		−	2.62562i		−	0.602358i	−0.953568	−	0.301179i	$-0.902620\pi$
$19$		−	2.62562i		−	0.602358i	0.953568	−	0.301179i	$-0.0973803\pi$
$20$	−0.339852	+	2.21009i	−0.0759931	+	0.494191i
$21$	−0.957517	−	3.55589i	−0.208947	−	0.775960i
$22$	1.39026	−	3.01117i	0.296405	−	0.641985i
$23$	1.13469	−	1.96534i	0.236600	−	0.409803i	−0.723137	−	0.690705i	$-0.757300\pi$
$23$	1.13469	−	1.96534i	0.236600	−	0.409803i	0.959736	+	0.280902i	$0.0906337\pi$
$24$	0.446217	−	1.67359i	0.0910836	−	0.341619i
$25$	3.68545	−	3.37897i	0.737090	−	0.675795i
$26$		−	5.27496i		−	1.03450i
$27$	3.68785	+	3.66057i	0.709727	+	0.704477i
$28$	−2.12612			−0.401800
$29$	4.51629	+	7.82244i	0.838653	+	1.45259i	0.891021	+	0.453962i	$0.149990\pi$
$29$	4.51629	+	7.82244i	0.838653	+	1.45259i	−0.0523679	+	0.998628i	$0.516677\pi$
$30$	−3.12019	+	2.29443i	−0.569666	+	0.418904i
$31$	−3.51686	+	6.09138i	−0.631646	+	1.09404i	0.355569	+	0.934650i	$0.384287\pi$
$31$	−3.51686	+	6.09138i	−0.631646	+	1.09404i	−0.987215	+	0.159393i	$0.949046\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	5.38818	−	1.99188i	0.937961	−	0.346741i
$34$	0.425319	+	0.736675i	0.0729417	+	0.126339i
$35$	3.70811	+	2.97523i	0.626785	+	0.502905i
$36$	2.59436	−	1.50643i	0.432393	−	0.251071i
$37$			4.77143i			0.784418i	0.919876	+	0.392209i	$0.128289\pi$
$37$			4.77143i			0.784418i	−0.919876	+	0.392209i	$0.871711\pi$
$38$	−1.31281	−	2.27385i	−0.212966	−	0.368868i
$39$	6.45248	−	6.46847i	1.03322	−	1.03578i
$40$	0.810725	+	2.08392i	0.128187	+	0.329497i
$41$	4.60079	−	7.96881i	0.718523	−	1.24452i	−0.243061	−	0.970011i	$-0.578152\pi$
$41$	4.60079	−	7.96881i	0.718523	−	1.24452i	0.961585	−	0.274508i	$-0.0885150\pi$
$42$	−2.60718	−	2.60074i	−0.402297	−	0.401302i
$43$	−4.38888	−	7.60176i	−0.669297	−	1.15926i	−0.978101	−	0.208131i	$-0.933262\pi$
$43$	−4.38888	−	7.60176i	−0.669297	−	1.15926i	0.308804	−	0.951126i	$-0.400071\pi$
$44$	−0.301586	−	3.30288i	−0.0454658	−	0.497929i
$45$	−6.63278	−	1.00314i	−0.988756	−	0.149539i
$46$		−	2.26938i		−	0.334602i
$47$	0.240394	+	0.416375i	0.0350651	+	0.0607345i	0.883025	−	0.469325i	$-0.155503\pi$
$47$	0.240394	+	0.416375i	0.0350651	+	0.0607345i	−0.847960	+	0.530060i	$0.822169\pi$
$48$	−0.450358	−	1.67248i	−0.0650036	−	0.241401i
$49$	1.23980	−	2.14739i	0.177114	−	0.306770i
$50$	1.50221	−	4.76900i	0.212444	−	0.674439i
$51$	−0.379569	+	1.42362i	−0.0531503	+	0.199346i
$52$	−2.63748	−	4.56825i	−0.365753	−	0.633502i
$53$	−9.77771			−1.34307			−0.671536	−	0.740972i	$-0.734365\pi$
$53$	−9.77771			−1.34307			−0.671536	+	0.740972i	$0.734365\pi$
$54$	5.02406	+	1.32622i	0.683687	+	0.180476i
$55$	−4.09596	+	6.18249i	−0.552299	+	0.833646i
$56$	−1.84128	+	1.06306i	−0.246051	+	0.142058i
$57$	1.17160	−	4.39420i	0.155182	−	0.582026i
$58$	7.82244	+	4.51629i	1.02714	+	0.593017i
$59$	8.28833	+	4.78527i	1.07905	+	0.622989i	0.930640	−	0.365937i	$-0.119251\pi$
$59$	8.28833	+	4.78527i	1.07905	+	0.622989i	0.148409	+	0.988926i	$0.452585\pi$
$60$	−1.55495	+	3.54713i	−0.200743	+	0.457932i
$61$	5.31642	−	3.06944i	0.680698	−	0.393001i	−0.119420	−	0.992844i	$-0.538103\pi$
$61$	5.31642	−	3.06944i	0.680698	−	0.393001i	0.800118	+	0.599843i	$0.204770\pi$
$62$			7.03372i			0.893283i
$63$	−0.0157872	−	6.37835i	−0.00198900	−	0.803597i
$64$	−1.00000			−0.125000
$65$	−1.79270	+	11.6581i	−0.222357	+	1.44601i
$66$	3.67036	−	4.41910i	0.451790	−	0.543954i
$67$	−2.27943	−	1.31603i	−0.278477	−	0.160779i	0.354257	−	0.935148i	$-0.384734\pi$
$67$	−2.27943	−	1.31603i	−0.278477	−	0.160779i	−0.632734	+	0.774369i	$0.718067\pi$
$68$	0.736675	+	0.425319i	0.0893349	+	0.0515776i
$69$	2.77597	−	2.78285i	0.334188	−	0.335016i
$70$	4.69893	+	0.722567i	0.561629	+	0.0863633i
$71$			12.5151i			1.48527i	0.669699	+	0.742633i	$0.266423\pi$
$71$			12.5151i			1.48527i	−0.669699	+	0.742633i	$0.733577\pi$
$72$	1.49356	−	2.60178i	0.176018	−	0.306623i
$73$	−6.05548			−0.708740			−0.354370	−	0.935105i	$-0.615305\pi$
$73$	−6.05548			−0.708740			−0.354370	+	0.935105i	$0.615305\pi$
$74$	2.38572	+	4.13218i	0.277334	+	0.480356i
$75$	7.67567	−	4.01049i	0.886310	−	0.463092i
$76$	−2.27385	−	1.31281i	−0.260829	−	0.150590i
$77$	−6.40213	−	2.95587i	−0.729591	−	0.336853i
$78$	2.35378	−	8.82810i	0.266513	−	0.999585i
$79$	−11.3092	+	6.52938i	−1.27239	+	0.734613i	−0.975437	−	0.220281i	$-0.929303\pi$
$79$	−11.3092	+	6.52938i	−1.27239	+	0.734613i	−0.296950	+	0.954893i	$0.595969\pi$
$80$	1.74407	+	1.39937i	0.194993	+	0.156454i
$81$	4.53853	+	7.77186i	0.504281	+	0.863540i
$82$		−	9.20159i		−	1.01615i
$83$	−7.73026	+	4.46307i	−0.848506	+	0.489885i	−0.860146	−	0.510047i	$-0.829628\pi$
$83$	−7.73026	+	4.46307i	−0.848506	+	0.489885i	0.0116406	+	0.999932i	$0.496295\pi$
$84$	−3.55825	−	0.948713i	−0.388237	−	0.103513i
$85$	−0.689634	−	1.77266i	−0.0748013	−	0.192272i
$86$	−7.60176	−	4.38888i	−0.819718	−	0.473265i
$87$	4.06789	+	15.1068i	0.436124	+	1.61961i
$88$	−1.91262	−	2.70959i	−0.203886	−	0.288843i
$89$		−	8.26439i		−	0.876024i	−0.898969	−	0.438012i	$-0.855683\pi$
$89$		−	8.26439i		−	0.876024i	0.898969	−	0.438012i	$-0.144317\pi$
$90$	−6.24572	+	2.44764i	−0.658357	+	0.258004i
$91$	−11.2152			−1.17567
$92$	−1.13469	−	1.96534i	−0.118300	−	0.204901i
$93$	−8.60384	+	8.62516i	−0.892177	+	0.894388i
$94$	0.416375	+	0.240394i	0.0429458	+	0.0247948i
$95$	2.12866	+	5.47158i	0.218396	+	0.561373i
$96$	−1.22626	−	1.22323i	−0.125155	−	0.124845i
$97$	−10.8929	+	6.28902i	−1.10601	+	0.638554i	−0.937792	−	0.347197i	$-0.887134\pi$
$97$	−10.8929	+	6.28902i	−1.10601	+	0.638554i	−0.168215	+	0.985750i	$0.553800\pi$
$98$		−	2.47959i		−	0.250477i
$99$	9.90638	−	0.929280i	0.995629	−	0.0933962i
$100$	−1.08355	−	4.88118i	−0.108355	−	0.488118i
$101$	−1.48058	−	2.56444i	−0.147323	−	0.255171i	0.782914	−	0.622130i	$-0.213732\pi$
$101$	−1.48058	−	2.56444i	−0.147323	−	0.255171i	−0.930237	+	0.366958i	$0.880399\pi$
$102$	0.383092	+	1.42267i	0.0379317	+	0.140866i
$103$	−1.15713	−	0.668067i	−0.114015	−	0.0658266i	0.441908	−	0.897060i	$-0.354302\pi$
$103$	−1.15713	−	0.668067i	−0.114015	−	0.0658266i	−0.555923	+	0.831234i	$0.687635\pi$
$104$	−4.56825	−	2.63748i	−0.447954	−	0.258626i
$105$	4.87824	+	6.63392i	0.476068	+	0.647404i
$106$	−8.46774	+	4.88885i	−0.822460	+	0.474847i
$107$			5.60586i			0.541939i	0.962588	+	0.270970i	$0.0873443\pi$
$107$			5.60586i			0.541939i	−0.962588	+	0.270970i	$0.912656\pi$
$108$	5.01407	−	1.36349i	0.482479	−	0.131202i
$109$			15.5011i			1.48474i	0.669991	+	0.742370i	$0.266298\pi$
$109$			15.5011i			1.48474i	−0.669991	+	0.742370i	$0.733702\pi$
$110$	−0.455958	+	7.40217i	−0.0434739	+	0.705769i
$111$	−2.12909	+	7.98540i	−0.202085	+	0.757941i
$112$	−1.06306	+	1.84128i	−0.100450	+	0.173984i
$113$	0.672865	−	1.16544i	0.0632978	−	0.109635i	−0.832640	−	0.553815i	$-0.813172\pi$
$113$	0.672865	−	1.16544i	0.0632978	−	0.109635i	0.895938	+	0.444180i	$0.146505\pi$
$114$	−1.18247	−	4.39129i	−0.110748	−	0.411282i
$115$	−0.771254	+	5.01554i	−0.0719198	+	0.467702i
$116$	9.03257			0.838653
$117$	13.6851	−	7.94634i	1.26519	−	0.734639i
$118$	9.57054			0.881040
$119$	1.56626	−	0.904282i	0.143579	−	0.0828954i
$120$	0.426938	+	3.84938i	0.0389739	+	0.351399i
$121$	3.68374	−	10.3648i	0.334886	−	0.942259i
$122$	3.06944	−	5.31642i	0.277894	−	0.481326i
$123$	11.2556	−	11.2835i	1.01489	−	1.01740i
$124$	3.51686	+	6.09138i	0.315823	+	0.547022i
$125$	−4.94076	+	10.0294i	−0.441915	+	0.897057i
$126$	−3.20285	−	5.51592i	−0.285333	−	0.491398i
$127$	−9.88138			−0.876831			−0.438415	−	0.898772i	$-0.644460\pi$
$127$	−9.88138			−0.876831			−0.438415	+	0.898772i	$0.644460\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−3.95313	−	14.6806i	−0.348054	−	1.29255i
$130$	4.27654	+	10.9926i	0.375078	+	0.964115i
$131$	1.52260	−	2.63722i	0.133030	−	0.230415i	−0.791813	−	0.610764i	$-0.790863\pi$
$131$	1.52260	−	2.63722i	0.133030	−	0.230415i	0.924843	+	0.380348i	$0.124196\pi$
$132$	0.969073	−	5.66223i	0.0843470	−	0.492834i
$133$	−4.83450	+	2.79120i	−0.419204	+	0.242028i
$134$	−2.63206			−0.227376
$135$	−10.6529	−	4.63850i	−0.916856	−	0.399218i
$136$	0.850639			0.0729417
$137$	7.14317	+	12.3723i	0.610282	+	1.05704i	0.991193	+	0.132428i	$0.0422773\pi$
$137$	7.14317	+	12.3723i	0.610282	+	1.05704i	−0.380910	+	0.924612i	$0.624389\pi$
$138$	1.01264	−	3.79801i	0.0862014	−	0.323308i
$139$	12.1121	+	6.99294i	1.02734	+	0.593133i	0.916221	−	0.400674i	$-0.131224\pi$
$139$	12.1121	+	6.99294i	1.02734	+	0.593133i	0.111116	+	0.993807i	$0.464557\pi$
$140$	4.43067	−	1.72370i	0.374460	−	0.145679i
$141$	0.216527	+	0.804108i	0.0182349	+	0.0677181i
$142$	6.25754	+	10.8384i	0.525121	+	0.909536i
$143$	−1.59085	−	17.4226i	−0.133034	−	1.45695i
$144$	−0.00742535	−	2.99999i	−0.000618780	−	0.249999i
$145$	−15.7534	−	12.6399i	−1.30825	−	1.04968i
$146$	−5.24420	+	3.02774i	−0.434013	+	0.250577i
$147$	3.03311	−	3.04063i	0.250167	−	0.250787i
$148$	4.13218	+	2.38572i	0.339663	+	0.196105i
$149$	0.223413	−	0.386962i	0.0183027	−	0.0317011i	−0.856729	−	0.515767i	$-0.827507\pi$
$149$	0.223413	−	0.386962i	0.0183027	−	0.0317011i	0.875032	+	0.484066i	$0.160840\pi$
$150$	4.64208	−	7.31103i	0.379024	−	0.596943i
$151$	−13.3077	+	7.68321i	−1.08297	+	0.625251i	−0.931695	−	0.363242i	$-0.881670\pi$
$151$	−13.3077	+	7.68321i	−1.08297	+	0.625251i	−0.151271	+	0.988492i	$0.548337\pi$
$152$	−2.62562			−0.212966
$153$	−1.27048	+	2.21318i	−0.102713	+	0.178925i
$154$	−7.02234	+	0.641209i	−0.565877	+	0.0516701i
$155$	2.39042	−	15.5451i	0.192003	−	1.24862i
$156$	−2.37562	−	8.82225i	−0.190202	−	0.706345i
$157$	−8.53958	−	4.93033i	−0.681532	−	0.393483i	0.118900	−	0.992906i	$-0.462063\pi$
$157$	−8.53958	−	4.93033i	−0.681532	−	0.393483i	−0.800432	+	0.599423i	$0.795397\pi$
$158$	−6.52938	+	11.3092i	−0.519449	+	0.899713i
$159$	−16.3638	−	4.36298i	−1.29774	−	0.346007i
$160$	2.21009	+	0.339852i	0.174723	+	0.0268676i
$161$	−4.82499			−0.380263
$162$	7.81641	+	4.46136i	0.614115	+	0.350518i
$163$		−	1.88442i		−	0.147599i	−0.997273	−	0.0737997i	$-0.976487\pi$
$163$		−	1.88442i		−	0.147599i	0.997273	−	0.0737997i	$-0.0235125\pi$
$164$	−4.60079	−	7.96881i	−0.359262	−	0.622259i
$165$	−9.61367	+	8.51924i	−0.748423	+	0.663222i
$166$	−4.46307	+	7.73026i	−0.346401	+	0.599984i
$167$	9.94407	+	5.74121i	0.769495	+	0.444268i	0.832695	−	0.553733i	$-0.186797\pi$
$167$	9.94407	+	5.74121i	0.769495	+	0.444268i	−0.0631993	+	0.998001i	$0.520130\pi$
$168$	−3.55589	+	0.957517i	−0.274343	+	0.0738740i
$169$	−7.41260	−	12.8390i	−0.570200	−	0.987616i
$170$	−1.48357	−	1.19035i	−0.113785	−	0.0912960i
$171$	3.92153	−	6.83129i	0.299887	−	0.522402i
$172$	−8.77775			−0.669297
$173$	2.69805	−	1.55772i	0.205129	−	0.118431i	−0.393917	−	0.919146i	$-0.628880\pi$
$173$	2.69805	−	1.55772i	0.205129	−	0.118431i	0.599046	+	0.800715i	$0.295547\pi$
$174$	11.0763	+	11.0489i	0.839690	+	0.837615i
$175$	−10.1395	−	3.19388i	−0.766474	−	0.241434i
$176$	−3.01117	−	1.39026i	−0.226976	−	0.104795i
$177$	11.7360	+	11.7070i	0.882129	+	0.879949i
$178$	−4.13220	−	7.15717i	−0.309721	−	0.536453i
$179$		−	4.95206i		−	0.370134i	−0.982726	−	0.185067i	$-0.940750\pi$
$179$		−	4.95206i		−	0.370134i	0.982726	−	0.185067i	$-0.0592503\pi$
$180$	−4.18513	+	5.24258i	−0.311941	+	0.390759i
$181$	23.5835			1.75295			0.876474	−	0.481450i	$-0.159890\pi$
$181$	23.5835			1.75295			0.876474	+	0.481450i	$0.159890\pi$
$182$	−9.71267	+	5.60761i	−0.719951	+	0.415664i
$183$	10.2671	−	2.76469i	0.758968	−	0.204372i
$184$	−1.96534	−	1.13469i	−0.144887	−	0.0836506i
$185$	−3.86832	−	9.94328i	−0.284405	−	0.731045i
$186$	−3.13856	+	11.7715i	−0.230131	+	0.863130i
$187$	1.62695	+	2.30488i	0.118974	+	0.168550i
$188$	0.480789			0.0350651
$189$	2.81971	−	10.6818i	0.205104	−	0.776984i
$190$	4.57926	+	3.67420i	0.332215	+	0.266555i
$191$	16.2865	−	9.40302i	1.17845	−	0.680379i	0.222795	−	0.974865i	$-0.428482\pi$
$191$	16.2865	−	9.40302i	1.17845	−	0.680379i	0.955656	+	0.294486i	$0.0951486\pi$
$192$	−1.67359	−	0.446217i	−0.120781	−	0.0322029i
$193$	6.10832	−	10.5799i	0.439686	−	0.761559i	−0.557979	−	0.829855i	$-0.688423\pi$
$193$	6.10832	−	10.5799i	0.439686	−	0.761559i	0.997665	+	0.0682963i	$0.0217563\pi$
$194$	−6.28902	+	10.8929i	−0.451526	+	0.782065i
$195$	−8.20230	+	18.7110i	−0.587379	+	1.33992i
$196$	−1.23980	−	2.14739i	−0.0885569	−	0.153385i
$197$			24.7685i			1.76468i	0.470610	+	0.882341i	$0.344034\pi$
$197$			24.7685i			1.76468i	−0.470610	+	0.882341i	$0.655966\pi$
$198$	8.11454	−	5.75797i	0.576675	−	0.409201i
$199$	−2.38733			−0.169233			−0.0846167	−	0.996414i	$-0.526967\pi$
$199$	−2.38733			−0.169233			−0.0846167	+	0.996414i	$0.526967\pi$
$200$	−3.37897	−	3.68545i	−0.238930	−	0.260601i
$201$	−3.22759	−	3.21961i	−0.227657	−	0.227094i
$202$	−2.56444	−	1.48058i	−0.180433	−	0.104173i
$203$	9.60219	−	16.6315i	0.673941	−	1.16730i
$204$	1.04310	+	1.04053i	0.0730319	+	0.0728513i
$205$	−3.12717	+	20.3363i	−0.218411	+	1.42035i
$206$	−1.33613			−0.0930928
$207$	5.88759	−	3.41866i	0.409216	−	0.237613i
$208$	−5.27496			−0.365753
$209$	−5.02182	−	7.11435i	−0.347367	−	0.492110i
$210$	7.54164	+	3.30602i	0.520423	+	0.228137i
$211$	−2.61561	−	1.51012i	−0.180066	−	0.103961i	0.407258	−	0.913313i	$-0.366485\pi$
$211$	−2.61561	−	1.51012i	−0.180066	−	0.103961i	−0.587324	+	0.809352i	$0.699818\pi$
$212$	−4.88885	+	8.46774i	−0.335768	+	0.581567i
$213$	−5.58444	+	20.9451i	−0.382639	+	1.43513i
$214$	2.80293	+	4.85482i	0.191604	+	0.331869i
$215$	15.3090	+	12.2833i	1.04407	+	0.837713i
$216$	3.66057	−	3.68785i	0.249070	−	0.250926i
$217$	14.9546			1.01518
$218$	7.75057	+	13.4244i	0.524935	+	0.909213i
$219$	−10.1344	−	2.70206i	−0.684817	−	0.182588i
$220$	3.30621	+	6.63845i	0.222905	+	0.447564i
$221$	3.88593	+	2.24354i	0.261396	+	0.150917i
$222$	2.14885	+	7.98011i	0.144221	+	0.535590i
$223$	11.1889	−	6.45990i	0.749263	−	0.432587i	−0.0761646	−	0.997095i	$-0.524267\pi$
$223$	11.1889	−	6.45990i	0.749263	−	0.432587i	0.825428	+	0.564508i	$0.190934\pi$
$224$			2.12612i			0.142058i
$225$	14.6354	−	3.28689i	0.975697	−	0.219126i
$226$		−	1.34573i		−	0.0895167i
$227$	−7.64871	+	4.41599i	−0.507663	+	0.293099i	−0.731872	−	0.681442i	$-0.761353\pi$
$227$	−7.64871	+	4.41599i	−0.507663	+	0.293099i	0.224210	+	0.974541i	$0.428020\pi$
$228$	−3.21969	−	3.21173i	−0.213229	−	0.212702i
$229$	6.62005	−	11.4663i	0.437465	−	0.757712i	−0.560028	−	0.828473i	$-0.689210\pi$
$229$	6.62005	−	11.4663i	0.437465	−	0.757712i	0.997493	+	0.0707620i	$0.0225431\pi$
$230$	1.83985	+	4.72922i	0.121316	+	0.311835i
$231$	−9.39556	−	7.80364i	−0.618183	−	0.513442i
$232$	7.82244	−	4.51629i	0.513568	−	0.296509i
$233$			8.87184i			0.581214i	0.956843	+	0.290607i	$0.0938572\pi$
$233$			8.87184i			0.581214i	−0.956843	+	0.290607i	$0.906143\pi$
$234$	7.87849	−	13.7243i	0.515033	−	0.897185i
$235$	−0.838528	−	0.672799i	−0.0546996	−	0.0438886i
$236$	8.28833	−	4.78527i	0.539524	−	0.311495i
$237$	−21.8405	+	5.88111i	−1.41869	+	0.382019i
$238$	0.904282	−	1.56626i	0.0586159	−	0.101526i
$239$	−7.75619	+	13.4341i	−0.501706	+	0.868980i	0.498292	+	0.867009i	$0.333961\pi$
$239$	−7.75619	+	13.4341i	−0.501706	+	0.868980i	−0.999998	+	0.00197116i	$0.999373\pi$
$240$	2.29443	+	3.12019i	0.148105	+	0.201408i
$241$	−19.0482	+	10.9975i	−1.22700	+	0.708410i	−0.966402	−	0.257036i	$-0.917254\pi$
$241$	−19.0482	+	10.9975i	−1.22700	+	0.708410i	−0.260601	+	0.965447i	$0.583921\pi$
$242$	−1.99221	−	10.8181i	−0.128064	−	0.695413i
$243$	4.12768	+	15.0320i	0.264791	+	0.964306i
$244$		−	6.13888i		−	0.393001i
$245$	−0.842694	+	5.48013i	−0.0538377	+	0.350112i
$246$	4.10590	−	15.3997i	0.261783	−	0.981846i
$247$	−11.9945	−	6.92502i	−0.763191	−	0.440628i
$248$	6.09138	+	3.51686i	0.386803	+	0.223321i
$249$	−14.9287	+	4.01995i	−0.946071	+	0.254754i
$250$	0.735873	+	11.1561i	0.0465407	+	0.705573i
$251$			18.6317i			1.17602i	0.808854	+	0.588010i	$0.200088\pi$
$251$			18.6317i			1.17602i	−0.808854	+	0.588010i	$0.799912\pi$
$252$	−5.53171	−	3.17551i	−0.348465	−	0.200038i
$253$	−0.684414	−	7.49551i	−0.0430288	−	0.471239i
$254$	−8.55753	+	4.94069i	−0.536947	+	0.310007i
$255$	−0.363170	−	3.27443i	−0.0227426	−	0.205053i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.81076	−	8.33248i	0.300087	−	0.519766i	−0.676068	−	0.736839i	$-0.736318\pi$
$257$	4.81076	−	8.33248i	0.300087	−	0.519766i	0.976155	+	0.217073i	$0.0696509\pi$
$258$	−10.7638	−	10.7372i	−0.670125	−	0.668468i
$259$	8.78553	−	5.07233i	0.545906	−	0.315179i
$260$	9.19989	+	7.38160i	0.570553	+	0.457787i
$261$	0.0670700	+	27.0976i	0.00415153	+	1.67730i
$262$		−	3.04520i		−	0.188133i
$263$	10.2301	−	5.90634i	0.630814	−	0.364201i	−0.150253	−	0.988648i	$-0.548009\pi$
$263$	10.2301	−	5.90634i	0.630814	−	0.364201i	0.781067	+	0.624447i	$0.214676\pi$
$264$	−1.99188	−	5.38818i	−0.122591	−	0.331619i
$265$	20.3760	−	7.92703i	1.25169	−	0.486954i
$266$	−2.79120	+	4.83450i	−0.171139	+	0.296422i
$267$	3.68771	−	13.8312i	0.225684	−	0.846454i
$268$	−2.27943	+	1.31603i	−0.139239	+	0.0803894i
$269$		−	3.72171i		−	0.226917i	−0.993543	−	0.113458i	$-0.963807\pi$
$269$		−	3.72171i		−	0.226917i	0.993543	−	0.113458i	$-0.0361928\pi$
$270$	−11.5449	+	1.30939i	−0.702602	+	0.0796871i
$271$			3.69288i			0.224326i	0.993690	+	0.112163i	$0.0357779\pi$
$271$			3.69288i			0.224326i	−0.993690	+	0.112163i	$0.964222\pi$
$272$	0.736675	−	0.425319i	0.0446675	−	0.0257888i
$273$	−18.7696	−	5.00442i	−1.13599	−	0.302881i
$274$	12.3723	+	7.14317i	0.747440	+	0.431535i
$275$	3.52335	−	16.2045i	0.212466	−	0.977168i
$276$	−1.02203	−	3.79549i	−0.0615193	−	0.228462i
$277$	−12.2738	−	21.2589i	−0.737462	−	1.27732i	−0.953635	−	0.300967i	$-0.902691\pi$
$277$	−12.2738	−	21.2589i	−0.737462	−	1.27732i	0.216172	−	0.976355i	$-0.430643\pi$
$278$	13.9859			0.838817
$279$	−18.2480	+	10.5958i	−1.09248	+	0.634352i
$280$	2.97523	−	3.70811i	0.177804	−	0.221602i
$281$	11.7870	+	20.4157i	0.703154	+	1.21790i	0.967354	+	0.253430i	$0.0815588\pi$
$281$	11.7870	+	20.4157i	0.703154	+	1.21790i	−0.264200	+	0.964468i	$0.585108\pi$
$282$	0.589572	+	0.588114i	0.0351085	+	0.0350217i
$283$	10.3652	−	17.9530i	0.616144	−	1.06719i	−0.374038	−	0.927413i	$-0.622027\pi$
$283$	10.3652	−	17.9530i	0.616144	−	1.06719i	0.990183	−	0.139780i	$-0.0446396\pi$
$284$	10.8384	+	6.25754i	0.643139	+	0.371317i
$285$	1.12098	+	10.1070i	0.0664009	+	0.598687i
$286$	−10.0890	−	14.2930i	−0.596576	−	0.845161i
$287$	−19.5637			−1.15481
$288$	−1.50643	−	2.59436i	−0.0887670	−	0.152874i
$289$	16.2764			0.957436
$290$	−19.9628	−	3.06973i	−1.17226	−	0.180261i
$291$	−21.0365	+	5.66462i	−1.23318	+	0.332066i
$292$	−3.02774	+	5.24420i	−0.177185	+	0.306893i
$293$	14.5464	+	8.39838i	0.849811	+	0.490639i	0.860587	−	0.509303i	$-0.170097\pi$
$293$	14.5464	+	8.39838i	0.849811	+	0.490639i	−0.0107762	+	0.999942i	$0.503430\pi$
$294$	1.10644	−	4.14981i	0.0645287	−	0.242022i
$295$	−21.1518	−	3.25256i	−1.23150	−	0.189372i
$296$	4.77143			0.277334
$297$	16.9938	+	2.86517i	0.986083	+	0.166254i
$298$		−	0.446825i		−	0.0258839i
$299$	−5.98545	−	10.3671i	−0.346148	−	0.599546i
$300$	0.364646	−	8.65257i	0.0210528	−	0.499557i
$301$	−9.33130	+	16.1623i	−0.537847	+	0.931578i
$302$	−7.68321	+	13.3077i	−0.442119	+	0.765773i
$303$	−1.33358	−	4.95247i	−0.0766123	−	0.284512i
$304$	−2.27385	+	1.31281i	−0.130414	+	0.0752948i
$305$	−8.59053	+	10.7066i	−0.491892	+	0.613059i
$306$	0.00631629	+	2.55191i	0.000361079	+	0.145883i
$307$	−5.35259			−0.305488			−0.152744	−	0.988266i	$-0.548811\pi$
$307$	−5.35259			−0.305488			−0.152744	+	0.988266i	$0.548811\pi$
$308$	−5.76092	+	4.06648i	−0.328259	+	0.231709i
$309$	−1.63845	−	1.63440i	−0.0932080	−	0.0929776i
$310$	−5.70241	−	14.6577i	−0.323875	−	0.832502i
$311$	−10.1324	−	5.84994i	−0.574555	−	0.331720i	0.184411	−	0.982849i	$-0.440962\pi$
$311$	−10.1324	−	5.84994i	−0.574555	−	0.331720i	−0.758967	+	0.651129i	$0.774295\pi$
$312$	−6.46847	−	6.45248i	−0.366205	−	0.365300i
$313$	22.0355	−	12.7222i	1.24552	−	0.719101i	0.275308	−	0.961356i	$-0.411220\pi$
$313$	22.0355	−	12.7222i	1.24552	−	0.719101i	0.970213	+	0.242255i	$0.0778870\pi$
$314$	−9.86065			−0.556469
$315$	5.20399	+	13.2792i	0.293212	+	0.748197i
$316$			13.0588i			0.734613i
$317$	6.34572	+	10.9911i	0.356411	+	0.617322i	0.987358	−	0.158504i	$-0.0506670\pi$
$317$	6.34572	+	10.9911i	0.356411	+	0.617322i	−0.630947	+	0.775826i	$0.717334\pi$
$318$	−16.3530	+	4.40347i	−0.917030	+	0.246934i
$319$	27.1987	+	12.5576i	1.52283	+	0.703092i
$320$	2.08392	−	0.810725i	0.116495	−	0.0453209i
$321$	−2.50143	+	9.38190i	−0.139616	+	0.523646i
$322$	−4.17857	+	2.41250i	−0.232862	+	0.134443i
$323$	2.23345			0.124273
$324$	8.99989	−	0.0445520i	0.499994	−	0.00247511i
$325$	−5.71570	−	25.7480i	−0.317050	−	1.42824i
$326$	−0.942211	−	1.63196i	−0.0521843	−	0.0903858i
$327$	−6.91687	+	25.9425i	−0.382504	+	1.43462i
$328$	−7.96881	−	4.60079i	−0.440004	−	0.254036i
$329$	0.511108	−	0.885265i	0.0281783	−	0.0488063i
$330$	−4.06606	+	12.1847i	−0.223829	+	0.670746i
$331$	−3.21813	−	5.57396i	−0.176884	−	0.306372i	0.763928	−	0.645302i	$-0.223268\pi$
$331$	−3.21813	−	5.57396i	−0.176884	−	0.306372i	−0.940812	+	0.338930i	$0.889935\pi$
$332$			8.92613i			0.489885i
$333$	−7.12644	+	12.4142i	−0.390527	+	0.680295i
$334$	11.4824			0.628290
$335$	5.81710	+	0.894511i	0.317822	+	0.0488723i
$336$	−2.60074	+	2.60718i	−0.141882	+	0.142233i
$337$	−8.23011	+	14.2550i	−0.448323	+	0.776517i	−0.998277	−	0.0586773i	$-0.981312\pi$
$337$	−8.23011	+	14.2550i	−0.448323	+	0.776517i	0.549955	+	0.835195i	$0.314645\pi$
$338$	−12.8390	−	7.41260i	−0.698350	−	0.403192i
$339$	1.64614	−	1.65021i	0.0894058	−	0.0896274i
$340$	−1.87999	−	0.289091i	−0.101957	−	0.0156782i
$341$	2.12127	+	23.2316i	0.114873	+	1.25806i
$342$	−0.0194962	−	7.87684i	−0.00105423	−	0.425930i
$343$	−20.1548			−1.08826
$344$	−7.60176	+	4.38888i	−0.409859	+	0.236632i
$345$	−3.52878	+	8.04980i	−0.189983	+	0.433387i
$346$	1.55772	−	2.69805i	0.0837436	−	0.145048i
$347$	−19.6808	−	11.3627i	−1.05652	−	0.609982i	−0.132052	−	0.991243i	$-0.542157\pi$
$347$	−19.6808	−	11.3627i	−1.05652	−	0.609982i	−0.924467	+	0.381261i	$0.875490\pi$
$348$	15.1168	+	4.03049i	0.810345	+	0.216057i
$349$	−22.0720	+	12.7433i	−1.18149	+	0.682131i	−0.956358	−	0.292198i	$-0.905613\pi$
$349$	−22.0720	+	12.7433i	−1.18149	+	0.682131i	−0.225128	+	0.974329i	$0.572280\pi$
$350$	−10.3780	+	2.30377i	−0.554727	+	0.123142i
$351$	26.4490	−	7.19235i	1.41174	−	0.383899i
$352$	−3.30288	+	0.301586i	−0.176044	+	0.0160746i
$353$	12.6341	+	21.8829i	0.672445	+	1.16471i	0.977209	+	0.212281i	$0.0680893\pi$
$353$	12.6341	+	21.8829i	0.672445	+	1.16471i	−0.304763	+	0.952428i	$0.598577\pi$
$354$	16.0171	+	4.27054i	0.851301	+	0.226976i
$355$	−10.1463	−	26.0804i	−0.538509	−	1.38421i
$356$	−7.15717	−	4.13220i	−0.379329	−	0.219006i
$357$	3.02478	−	0.814501i	0.160088	−	0.0431080i
$358$	−2.47603	−	4.28861i	−0.130862	−	0.226660i
$359$	−36.7591			−1.94007			−0.970036	−	0.242959i	$-0.921882\pi$
$359$	−36.7591			−1.94007			−0.970036	+	0.242959i	$0.921882\pi$
$360$	−1.00314	+	6.63278i	−0.0528702	+	0.349578i
$361$	12.1061			0.637164
$362$	20.4239	−	11.7917i	1.07346	−	0.619760i
$363$	10.7900	−	15.7027i	0.566330	−	0.824179i
$364$	−5.60761	+	9.71267i	−0.293919	+	0.509082i
$365$	12.6191	−	4.90933i	0.660515	−	0.256966i
$366$	7.50925	−	7.52786i	0.392515	−	0.393487i
$367$	−5.22004	+	3.01379i	−0.272484	+	0.157319i	−0.630016	−	0.776582i	$-0.716952\pi$
$367$	−5.22004	+	3.01379i	−0.272484	+	0.157319i	0.357532	+	0.933901i	$0.383618\pi$
$368$	−2.26938			−0.118300
$369$	23.8722	−	13.8615i	1.24274	−	0.721601i
$370$	−8.32171	−	6.67698i	−0.432625	−	0.347119i
$371$	10.3943	+	18.0035i	0.539646	+	0.934694i
$372$	3.16769	+	11.7637i	0.164237	+	0.609921i
$373$	13.5241	−	23.4245i	0.700253	−	1.21287i	−0.268125	−	0.963384i	$-0.586404\pi$
$373$	13.5241	−	23.4245i	0.700253	−	1.21287i	0.968378	−	0.249489i	$-0.0802626\pi$
$374$	2.56142	+	1.18261i	0.132448	+	0.0611513i
$375$	−12.7441	+	14.5804i	−0.658101	+	0.752929i
$376$	0.416375	−	0.240394i	0.0214729	−	0.0123974i
$377$	47.6464			2.45392
$378$	−2.89895	−	10.6605i	−0.149106	−	0.548319i
$379$	−19.7847			−1.01627			−0.508136	−	0.861277i	$-0.669665\pi$
$379$	−19.7847			−1.01627			−0.508136	+	0.861277i	$0.669665\pi$
$380$	5.80286	+	0.892321i	0.297680	+	0.0457751i
$381$	−16.5373	−	4.40924i	−0.847234	−	0.225892i
$382$	9.40302	−	16.2865i	0.481100	−	0.833290i
$383$	11.0614	−	19.1589i	0.565211	−	0.978975i	−0.431819	−	0.901960i	$-0.642128\pi$
$383$	11.0614	−	19.1589i	0.565211	−	0.978975i	0.997030	−	0.0770142i	$-0.0245387\pi$
$384$	−1.67248	+	0.450358i	−0.0853482	+	0.0229822i
$385$	15.7379	+	0.969424i	0.802079	+	0.0494064i
$386$		−	12.2166i		−	0.621810i
$387$	−0.0651779	−	26.3332i	−0.00331318	−	1.33859i
$388$			12.5780i			0.638554i
$389$	0.930800	−	0.537397i	0.0471934	−	0.0272471i	−0.476218	−	0.879327i	$-0.657993\pi$
$389$	0.930800	−	0.537397i	0.0471934	−	0.0272471i	0.523411	+	0.852080i	$0.324659\pi$
$390$	2.25208	+	20.3053i	0.114039	+	1.02820i
$391$	1.67180	+	0.965213i	0.0845465	+	0.0488129i
$392$	−2.14739	−	1.23980i	−0.108460	−	0.0626192i
$393$	3.72498	−	3.73421i	0.187900	−	0.188366i
$394$	12.3843	+	21.4502i	0.623910	+	1.08064i
$395$	18.2740	−	22.7754i	0.919463	−	1.14595i
$396$	4.14841	−	9.04382i	0.208466	−	0.454469i
$397$			12.7817i			0.641495i	0.947165	+	0.320748i	$0.103934\pi$
$397$			12.7817i			0.641495i	−0.947165	+	0.320748i	$0.896066\pi$
$398$	−2.06749	+	1.19367i	−0.103634	+	0.0598331i
$399$	−9.33642	+	2.51408i	−0.467406	+	0.125861i
$400$	−4.76900	−	1.50221i	−0.238450	−	0.0751103i
$401$	−5.33315	−	3.07909i	−0.266325	−	0.153763i	0.360892	−	0.932608i	$-0.382472\pi$
$401$	−5.33315	−	3.07909i	−0.266325	−	0.153763i	−0.627216	+	0.778845i	$0.715806\pi$
$402$	−4.40498	−	1.17447i	−0.219701	−	0.0585773i
$403$	18.5513	+	32.1318i	0.924105	+	1.60060i
$404$	−2.96116			−0.147323
$405$	−15.7588	−	12.5164i	−0.783060	−	0.621947i
$406$		−	19.2044i		−	0.953097i
$407$	9.12595	+	12.9286i	0.452357	+	0.640848i
$408$	1.42362	+	0.379569i	0.0704796	+	0.0187915i
$409$	23.0316	+	13.2973i	1.13884	+	0.657510i	0.946143	−	0.323749i	$-0.104943\pi$
$409$	23.0316	+	13.2973i	1.13884	+	0.657510i	0.192697	+	0.981258i	$0.438277\pi$
$410$	7.45996	+	19.1754i	0.368421	+	0.947004i
$411$	6.43397	+	23.8936i	0.317364	+	1.17858i
$412$	−1.15713	+	0.668067i	−0.0570075	+	0.0329133i
$413$		−	20.3482i		−	1.00127i
$414$	3.38947	−	5.90444i	0.166583	−	0.290187i
$415$	12.4909	−	15.5678i	0.613155	−	0.764193i
$416$	−4.56825	+	2.63748i	−0.223977	+	0.129313i
$417$	17.1503	+	17.1079i	0.839854	+	0.837778i
$418$	−7.90620	−	3.65030i	−0.386705	−	0.178542i
$419$	−0.137055	−	0.0791288i	−0.00669558	−	0.00386570i	0.496648	−	0.867952i	$-0.334564\pi$
$419$	−0.137055	−	0.0791288i	−0.00669558	−	0.00386570i	−0.503344	+	0.864086i	$0.667897\pi$
$420$	8.18426	−	0.907723i	0.399351	−	0.0442924i
$421$	−7.78571	−	13.4852i	−0.379452	−	0.657230i	0.611530	−	0.791221i	$-0.290554\pi$
$421$	−7.78571	−	13.4852i	−0.379452	−	0.657230i	−0.990983	+	0.133990i	$0.957221\pi$
$422$	−3.02025			−0.147023
$423$	0.00357003	+	1.44236i	0.000173581	+	0.0701300i
$424$			9.77771i			0.474847i
$425$	2.87429	+	3.13499i	0.139423	+	0.152069i
$426$	5.63626	+	20.9312i	0.273078	+	1.01412i
$427$	−11.3034	−	6.52601i	−0.547009	−	0.315816i
$428$	4.85482	+	2.80293i	0.234667	+	0.135485i
$429$	5.11182	−	29.8681i	0.246801	−	1.44204i
$430$	19.3996	+	2.98313i	0.935533	+	0.143859i
$431$	21.2474			1.02345			0.511726	−	0.859148i	$-0.329006\pi$
$431$	21.2474			1.02345			0.511726	+	0.859148i	$0.329006\pi$
$432$	1.32622	−	5.02406i	0.0638078	−	0.241720i
$433$			7.46083i			0.358544i	0.983800	+	0.179272i	$0.0573743\pi$
$433$			7.46083i			0.358544i	−0.983800	+	0.179272i	$0.942626\pi$
$434$	12.9510	−	7.47728i	0.621669	−	0.358921i
$435$	−20.7246	−	28.1834i	−0.993668	−	1.35129i
$436$	13.4244	+	7.75057i	0.642911	+	0.371185i
$437$	−5.16025	−	2.97927i	−0.246848	−	0.142518i
$438$	−10.1276	+	2.72713i	−0.483917	+	0.130307i
$439$	21.3969	−	12.3535i	1.02122	−	0.589601i	0.106762	−	0.994285i	$-0.465952\pi$
$439$	21.3969	−	12.3535i	1.02122	−	0.589601i	0.914457	+	0.404684i	$0.132618\pi$
$440$	6.18249	+	4.09596i	0.294739	+	0.195267i
$441$	6.43295	−	3.73532i	0.306331	−	0.177873i
$442$	4.48709			0.213429
$443$	−20.0786	−	34.7771i	−0.953962	−	1.65231i	−0.736726	−	0.676191i	$-0.763629\pi$
$443$	−20.0786	−	34.7771i	−0.953962	−	1.65231i	−0.217236	−	0.976119i	$-0.569704\pi$
$444$	5.85101	+	5.83655i	0.277677	+	0.276990i
$445$	6.70015	+	17.2223i	0.317618	+	0.816417i
$446$	6.45990	−	11.1889i	0.305885	−	0.529809i
$447$	0.546569	−	0.547923i	0.0258518	−	0.0259159i
$448$	1.06306	+	1.84128i	0.0502250	+	0.0869922i
$449$			38.9543i			1.83837i	0.393829	+	0.919184i	$0.371150\pi$
$449$			38.9543i			1.83837i	−0.393829	+	0.919184i	$0.628850\pi$
$450$	11.0312	−	10.1643i	0.520017	−	0.479148i
$451$	−2.77507	−	30.3918i	−0.130673	−	1.43109i
$452$	−0.672865	−	1.16544i	−0.0316489	−	0.0548175i
$453$	−25.7000	+	6.92039i	−1.20749	+	0.325148i
$454$	−4.41599	+	7.64871i	−0.207252	+	0.358972i
$455$	23.3716	−	9.09246i	1.09568	−	0.426261i
$456$	−4.39420	−	1.17160i	−0.205777	−	0.0548650i
$457$	6.52011	+	11.2932i	0.304998	+	0.528272i	0.977261	−	0.212041i	$-0.0680109\pi$
$457$	6.52011	+	11.2932i	0.304998	+	0.528272i	−0.672263	+	0.740312i	$0.734678\pi$
$458$		−	13.2401i		−	0.618669i
$459$	−3.11382	+	3.13703i	−0.145341	+	0.146424i
$460$	3.95796	+	3.17570i	0.184541	+	0.148068i
$461$	−17.6968	−	30.6517i	−0.824221	−	1.42759i	−0.902513	−	0.430662i	$-0.858280\pi$
$461$	−17.6968	−	30.6517i	−0.824221	−	1.42759i	0.0782919	−	0.996930i	$-0.475053\pi$
$462$	−12.0386	−	2.06037i	−0.560087	−	0.0958571i
$463$	−11.1320	−	6.42706i	−0.517348	−	0.298691i	0.218501	−	0.975837i	$-0.429883\pi$
$463$	−11.1320	−	6.42706i	−0.517348	−	0.298691i	−0.735849	+	0.677146i	$0.763217\pi$
$464$	4.51629	−	7.82244i	0.209663	−	0.363147i
$465$	10.9371	−	24.9495i	0.507195	−	1.15701i
$466$	4.43592	+	7.68324i	0.205490	+	0.355919i
$467$	−42.5434			−1.96867			−0.984337	−	0.176297i	$-0.943588\pi$
$467$	−42.5434			−1.96867			−0.984337	+	0.176297i	$0.943588\pi$
$468$	−0.0391684	−	15.8248i	−0.00181056	−	0.731503i
$469$			5.59609i			0.258404i
$470$	−1.06259	−	0.163397i	−0.0490134	−	0.00753693i
$471$	−12.0917	−	12.0618i	−0.557157	−	0.555780i
$472$	4.78527	−	8.28833i	0.220260	−	0.381501i
$473$	−26.4313	−	12.2034i	−1.21531	−	0.561111i
$474$	−15.9738	+	16.0134i	−0.733703	+	0.735521i
$475$	−8.87190	−	9.67659i	−0.407071	−	0.443992i
$476$		−	1.80856i		−	0.0828954i
$477$	−25.4395	−	14.6036i	−1.16479	−	0.668655i
$478$			15.5124i			0.709520i
$479$	−15.1857	−	26.3024i	−0.693854	−	1.20179i	−0.970566	−	0.240837i	$-0.922578\pi$
$479$	−15.1857	−	26.3024i	−0.693854	−	1.20179i	0.276712	−	0.960953i	$-0.410755\pi$
$480$	3.54713	+	1.55495i	0.161904	+	0.0709735i
$481$	21.7971	+	12.5846i	0.993862	+	0.573806i
$482$	−10.9975	+	19.0482i	−0.500922	+	0.867622i
$483$	−8.07504	−	2.15299i	−0.367427	−	0.0979646i
$484$	−7.13435	−	8.37264i	−0.324289	−	0.380575i
$485$	17.6013	−	21.9370i	0.799233	−	0.996107i
$486$	11.0907	+	10.9543i	0.503084	+	0.496897i
$487$		−	22.1449i		−	1.00348i	−0.865018	−	0.501740i	$-0.832693\pi$
$487$		−	22.1449i		−	1.00348i	0.865018	−	0.501740i	$-0.167307\pi$
$488$	−3.06944	−	5.31642i	−0.138947	−	0.240663i
$489$	0.840861	−	3.15374i	0.0380251	−	0.142617i
$490$	2.01027	+	5.16728i	0.0908147	+	0.233434i
$491$	−18.3433	+	31.7716i	−0.827823	+	1.43383i	0.0719195	+	0.997410i	$0.477088\pi$
$491$	−18.3433	+	31.7716i	−0.827823	+	1.43383i	−0.899743	+	0.436421i	$0.856246\pi$
$492$	−4.14401	−	15.3894i	−0.186826	−	0.693810i
$493$	−6.65407	+	3.84173i	−0.299684	+	0.173023i
$494$	−13.8500			−0.623143
$495$	−19.8907	+	9.96790i	−0.894022	+	0.448024i
$496$	7.03372			0.315823
$497$	23.0437	−	13.3043i	1.03365	−	0.596780i
$498$	−10.9187	+	10.9458i	−0.489278	+	0.490491i
$499$	−5.25554	+	9.10287i	−0.235270	+	0.407500i	−0.959351	−	0.282215i	$-0.908931\pi$
$499$	−5.25554	+	9.10287i	−0.235270	+	0.407500i	0.724081	+	0.689715i	$0.242264\pi$
$500$	6.21533	+	9.29353i	0.277958	+	0.415619i
$501$	14.0804	+	14.0456i	0.629067	+	0.627512i
$502$	9.31583	+	16.1355i	0.415786	+	0.720162i
$503$		−	10.7761i		−	0.480483i	−0.970713	−	0.240242i	$-0.922773\pi$
$503$		−	10.7761i		−	0.480483i	0.970713	−	0.240242i	$-0.0772267\pi$
$504$	−6.37835	+	0.0157872i	−0.284114	+	0.000703219i
$505$	5.16447	+	4.14375i	0.229816	+	0.184394i
$506$	−4.34048	−	6.14910i	−0.192958	−	0.273361i
$507$	−6.67665	−	24.7948i	−0.296520	−	1.10118i
$508$	−4.94069	+	8.55753i	−0.219208	+	0.379679i
$509$	12.7453	+	7.35852i	0.564927	+	0.326161i	0.755120	−	0.655586i	$-0.227578\pi$
$509$	12.7453	+	7.35852i	0.564927	+	0.326161i	−0.190194	+	0.981747i	$0.560912\pi$
$510$	−1.95173	−	2.65416i	−0.0864241	−	0.117528i
$511$	6.43735	+	11.1498i	0.284772	+	0.493239i
$512$			1.00000i			0.0441942i
$513$	9.61126	−	9.68289i	0.424347	−	0.427510i
$514$		−	9.62152i		−	0.424387i
$515$	2.95298	+	0.454087i	0.130124	+	0.0200095i
$516$	−14.6903	−	3.91678i	−0.646705	−	0.172427i
$517$	1.44774	+	0.668422i	0.0636715	+	0.0293971i
$518$	5.07233	−	8.78553i	0.222865	−	0.386014i
$519$	5.21050	−	1.40306i	0.228716	−	0.0615876i
$520$	11.6581	+	1.79270i	0.511243	+	0.0786152i
$521$			3.15671i			0.138298i	0.997606	+	0.0691490i	$0.0220284\pi$
$521$			3.15671i			0.138298i	−0.997606	+	0.0691490i	$0.977972\pi$
$522$	13.6069	+	23.4337i	0.595558	+	1.02567i
$523$	−10.3172			−0.451138			−0.225569	−	0.974227i	$-0.572424\pi$
$523$	−10.3172			−0.451138			−0.225569	+	0.974227i	$0.572424\pi$
$524$	−1.52260	−	2.63722i	−0.0665152	−	0.115208i
$525$	−15.5442	−	9.86964i	−0.678402	−	0.430746i
$526$	5.90634	−	10.2301i	0.257529	−	0.446053i
$527$	−5.18156	−	2.99158i	−0.225712	−	0.130315i
$528$	−4.41910	−	3.67036i	−0.192317	−	0.159732i
$529$	8.92495	+	15.4585i	0.388041	+	0.672107i
$530$	13.6826	−	17.0530i	0.594334	−	0.740735i
$531$	14.4173	+	24.8294i	0.625658	+	1.07750i
$532$			5.58240i			0.242028i
$533$	−24.2690	−	42.0352i	−1.05121	−	1.82074i
$534$	−3.72193	−	13.8220i	−0.161064	−	0.598136i
$535$	−4.54482	−	11.6822i	−0.196490	−	0.505064i
$536$	−1.31603	+	2.27943i	−0.0568439	+	0.0984565i
$537$	2.20969	−	8.28770i	0.0953553	−	0.357641i
$538$	−1.86085	−	3.22310i	−0.0802271	−	0.138957i
$539$	−0.747810	−	8.18981i	−0.0322105	−	0.352760i
$540$	−9.34351	+	6.90643i	−0.402081	+	0.297206i
$541$		−	34.7034i		−	1.49201i	−0.665938	−	0.746007i	$-0.731969\pi$
$541$		−	34.7034i		−	1.49201i	0.665938	−	0.746007i	$-0.268031\pi$
$542$	1.84644	+	3.19812i	0.0793113	+	0.137371i
$543$	39.4690	+	10.5234i	1.69378	+	0.451600i
$544$	0.425319	−	0.736675i	0.0182354	−	0.0315847i
$545$	−12.5672	−	32.3031i	−0.538318	−	1.38371i
$546$	−18.7572	+	5.05086i	−0.802734	+	0.216157i
$547$	22.1127	+	38.3004i	0.945473	+	1.63761i	0.754802	+	0.655953i	$0.227733\pi$
$547$	22.1127	+	38.3004i	0.945473	+	1.63761i	0.190671	+	0.981654i	$0.438934\pi$
$548$	14.2863			0.610282
$549$	18.4166	−	0.0455833i	0.786000	−	0.00194545i
$550$	−5.05094	−	15.7952i	−0.215373	−	0.673509i
$551$	20.5387	−	11.8580i	0.874980	−	0.505170i
$552$	−2.78285	−	2.77597i	−0.118446	−	0.118153i
$553$	24.0448	+	13.8823i	1.02249	+	0.590334i
$554$	−21.2589	−	12.2738i	−0.903203	−	0.521465i
$555$	−2.03711	−	18.3671i	−0.0864703	−	0.779638i
$556$	12.1121	−	6.99294i	0.513668	−	0.296567i
$557$		−	18.6694i		−	0.791049i	−0.918455	−	0.395525i	$-0.870563\pi$
$557$		−	18.6694i		−	0.791049i	0.918455	−	0.395525i	$-0.129437\pi$
$558$	−10.5053	+	18.3002i	−0.444725	+	0.774709i
$559$	−46.3023			−1.95838
$560$	0.722567	−	4.69893i	0.0305340	−	0.198566i
$561$	1.69437	+	4.58339i	0.0715362	+	0.193511i
$562$	20.4157	+	11.7870i	0.861184	+	0.497205i
$563$	31.0205	+	17.9097i	1.30736	+	0.754805i	0.981655	−	0.190667i	$-0.0610650\pi$
$563$	31.0205	+	17.9097i	1.30736	+	0.754805i	0.325705	+	0.945471i	$0.394398\pi$
$564$	0.804641	+	0.214536i	0.0338815	+	0.00903359i
$565$	−0.457349	+	2.97419i	−0.0192408	+	0.125125i
$566$		−	20.7303i		−	0.871360i
$567$	9.48541	−	16.6187i	0.398350	−	0.697918i
$568$	12.5151			0.525121
$569$	−1.31780	−	2.28250i	−0.0552451	−	0.0956873i	0.837080	−	0.547080i	$-0.184261\pi$
$569$	−1.31780	−	2.28250i	−0.0552451	−	0.0956873i	−0.892325	+	0.451393i	$0.850927\pi$
$570$	6.02430	+	8.19244i	0.252330	+	0.343143i
$571$	−23.4101	−	13.5158i	−0.979681	−	0.565619i	−0.0775075	−	0.996992i	$-0.524696\pi$
$571$	−23.4101	−	13.5158i	−0.979681	−	0.565619i	−0.902174	+	0.431372i	$0.858029\pi$
$572$	−15.8838	−	7.33357i	−0.664136	−	0.306632i
$573$	31.4527	−	8.46945i	1.31395	−	0.353816i
$574$	−16.9427	+	9.78186i	−0.707174	+	0.408287i
$575$	−2.45900	−	11.0773i	−0.102547	−	0.461954i
$576$	−2.60178	−	1.49356i	−0.108408	−	0.0622319i
$577$		−	35.3454i		−	1.47145i	−0.677282	−	0.735724i	$-0.736842\pi$
$577$		−	35.3454i		−	1.47145i	0.677282	−	0.735724i	$-0.263158\pi$
$578$	14.0958	−	8.13821i	0.586307	−	0.338505i
$579$	14.9437	−	14.9808i	0.621040	−	0.622579i
$580$	−18.8232	+	7.32293i	−0.781589	+	0.304068i
$581$	16.4355	+	9.48903i	0.681859	+	0.393671i
$582$	−15.3858	+	15.4240i	−0.637763	+	0.639343i
$583$	−26.4936	+	18.7011i	−1.09725	+	0.774519i
$584$			6.05548i			0.250577i
$585$	−22.0764	+	27.6544i	−0.912747	+	1.14337i
$586$	16.7968			0.693868
$587$	10.0601	+	17.4246i	0.415225	+	0.719190i	0.995452	−	0.0952644i	$-0.0303696\pi$
$587$	10.0601	+	17.4246i	0.415225	+	0.719190i	−0.580227	+	0.814455i	$0.697036\pi$
$588$	−1.11670	−	4.14706i	−0.0460521	−	0.171022i
$589$	15.9936	+	9.23393i	0.659006	+	0.380478i
$590$	−19.9442	+	7.75908i	−0.821092	+	0.319436i
$591$	−11.0521	+	41.4522i	−0.454624	+	1.70512i
$592$	4.13218	−	2.38572i	0.169832	−	0.0980523i
$593$		−	32.6723i		−	1.34169i	−0.741597	−	0.670846i	$-0.765931\pi$
$593$		−	32.6723i		−	1.34169i	0.741597	−	0.670846i	$-0.234069\pi$
$594$	16.1497	−	6.01562i	0.662630	−	0.246824i
$595$	−2.53084	+	3.15426i	−0.103754	+	0.129312i
$596$	−0.223413	−	0.386962i	−0.00915133	−	0.0158506i
$597$	−3.99541	−	1.06527i	−0.163521	−	0.0435985i
$598$	−10.3671	−	5.98545i	−0.423943	−	0.244763i
$599$	−31.6551	−	18.2761i	−1.29339	−	0.746740i	−0.314138	−	0.949377i	$-0.601715\pi$
$599$	−31.6551	−	18.2761i	−1.29339	−	0.746740i	−0.979254	+	0.202637i	$0.935049\pi$
$600$	−4.01049	−	7.67567i	−0.163728	−	0.313358i
$601$	27.9049	−	16.1109i	1.13827	−	0.657178i	0.192265	−	0.981343i	$-0.438417\pi$
$601$	27.9049	−	16.1109i	1.13827	−	0.657178i	0.946000	+	0.324165i	$0.105083\pi$
$602$			18.6626i			0.760630i
$603$	−3.96501	−	6.82851i	−0.161468	−	0.278078i
$604$			15.3664i			0.625251i
$605$	0.726412	+	24.5860i	0.0295329	+	0.999564i
$606$	−3.63115	−	3.62218i	−0.147506	−	0.147141i
$607$	5.61178	−	9.71989i	0.227775	−	0.394518i	−0.729373	−	0.684116i	$-0.760188\pi$
$607$	5.61178	−	9.71989i	0.227775	−	0.394518i	0.957148	+	0.289598i	$0.0935215\pi$
$608$	−1.31281	+	2.27385i	−0.0532415	+	0.0922169i
$609$	23.4913	−	23.5495i	0.951917	−	0.954276i
$610$	−2.08631	+	13.5675i	−0.0844721	+	0.549331i
$611$	2.53614			0.102601
$612$	1.28142	+	2.20686i	0.0517985	+	0.0892070i
$613$	−9.39642			−0.379518			−0.189759	−	0.981831i	$-0.560771\pi$
$613$	−9.39642			−0.379518			−0.189759	+	0.981831i	$0.560771\pi$
$614$	−4.63548	+	2.67629i	−0.187073	+	0.108006i
$615$	−14.3080	+	32.6392i	−0.576955	+	1.31614i
$616$	−2.95587	+	6.40213i	−0.119095	+	0.257949i
$617$	−6.58534	+	11.4061i	−0.265116	+	0.459194i	−0.967594	−	0.252511i	$-0.918743\pi$
$617$	−6.58534	+	11.4061i	−0.265116	+	0.459194i	0.702478	+	0.711705i	$0.252077\pi$
$618$	−2.23613	−	0.596205i	−0.0899505	−	0.0239829i
$619$	−21.9622	−	38.0397i	−0.882736	−	1.52894i	−0.848287	−	0.529538i	$-0.822365\pi$
$619$	−21.9622	−	38.0397i	−0.882736	−	1.52894i	−0.0344497	−	0.999406i	$-0.510968\pi$
$620$	−12.2673	−	9.84274i	−0.492666	−	0.395294i
$621$	11.3789	−	3.09428i	0.456618	−	0.124169i
$622$	−11.6999			−0.469122
$623$	−15.2170	+	8.78556i	−0.609658	+	0.351986i
$624$	−8.82810	−	2.35378i	−0.353407	−	0.0942265i
$625$	2.16507	−	24.9061i	0.0866028	−	0.996243i
$626$	12.7222	−	22.0355i	0.508482	−	0.880716i
$627$	−5.22991	−	14.1473i	−0.208862	−	0.564989i
$628$	−8.53958	+	4.93033i	−0.340766	+	0.196741i
$629$	−4.05876			−0.161834
$630$	11.1464	+	8.89811i	0.444082	+	0.354509i
$631$	4.05490			0.161423			0.0807114	−	0.996738i	$-0.474281\pi$
$631$	4.05490			0.161423			0.0807114	+	0.996738i	$0.474281\pi$
$632$	6.52938	+	11.3092i	0.259725	+	0.449856i
$633$	−3.70360	−	3.69445i	−0.147205	−	0.146841i
$634$	10.9911	+	6.34572i	0.436512	+	0.252021i
$635$	20.5920	−	8.01109i	0.817169	−	0.317910i
$636$	−11.9604	+	11.9900i	−0.474259	+	0.475435i
$637$	−6.53988	−	11.3274i	−0.259119	−	0.448808i
$638$	29.8335	−	2.72410i	1.18112	−	0.107848i
$639$	−18.6921	+	32.5615i	−0.739447	+	1.28811i
$640$	1.39937	−	1.74407i	0.0553148	−	0.0689404i
$641$	−13.9444	+	8.05080i	−0.550771	+	0.317988i	−0.749433	−	0.662080i	$-0.769674\pi$
$641$	−13.9444	+	8.05080i	−0.550771	+	0.317988i	0.198662	+	0.980068i	$0.436340\pi$
$642$	2.52465	+	9.37568i	0.0996398	+	0.370028i
$643$	21.5384	+	12.4352i	0.849392	+	0.490397i	0.860446	−	0.509542i	$-0.170185\pi$
$643$	21.5384	+	12.4352i	0.849392	+	0.490397i	−0.0110536	+	0.999939i	$0.503519\pi$
$644$	−2.41250	+	4.17857i	−0.0950657	+	0.164659i
$645$	20.1399	+	27.3883i	0.793009	+	1.07841i
$646$	1.93423	−	1.11673i	0.0761012	−	0.0439370i
$647$	17.1494			0.674214			0.337107	−	0.941466i	$-0.390552\pi$
$647$	17.1494			0.674214			0.337107	+	0.941466i	$0.390552\pi$
$648$	7.77186	−	4.53853i	0.305307	−	0.178290i
$649$	31.6104	−	2.88634i	1.24082	−	0.113299i
$650$	−17.8240	−	19.4406i	−0.699113	−	0.762523i
$651$	25.0277	+	6.67298i	0.980914	+	0.261535i
$652$	−1.63196	−	0.942211i	−0.0639124	−	0.0368998i
$653$	−13.1635	+	22.7999i	−0.515129	+	0.892230i	0.484717	+	0.874671i	$0.338923\pi$
$653$	−13.1635	+	22.7999i	−0.515129	+	0.892230i	−0.999846	+	0.0175584i	$0.994411\pi$
$654$	6.98106	+	25.9253i	0.272981	+	1.01376i
$655$	−1.03492	+	6.73018i	−0.0404376	+	0.262970i
$656$	−9.20159			−0.359262
$657$	−15.7550	−	9.04425i	−0.614662	−	0.352850i
$658$		−	1.02222i		−	0.0398501i
$659$	−4.99870	−	8.65801i	−0.194722	−	0.337268i	0.752088	−	0.659063i	$-0.229047\pi$
$659$	−4.99870	−	8.65801i	−0.194722	−	0.337268i	−0.946809	+	0.321795i	$0.895714\pi$
$660$	2.57105	+	12.5853i	0.100078	+	0.489882i
$661$	2.23982	−	3.87949i	0.0871191	−	0.150895i	−0.819173	−	0.573546i	$-0.805567\pi$
$661$	2.23982	−	3.87949i	0.0871191	−	0.150895i	0.906292	+	0.422652i	$0.138901\pi$
$662$	−5.57396	−	3.21813i	−0.216638	−	0.125076i
$663$	5.50233	+	5.48873i	0.213693	+	0.213165i
$664$	4.46307	+	7.73026i	0.173201	+	0.299992i
$665$	7.81181	−	9.73608i	0.302929	−	0.377549i
$666$	0.0354296	+	14.3143i	0.00137287	+	0.554666i
$667$	20.4984			0.793700
$668$	9.94407	−	5.74121i	0.384748	−	0.222134i
$669$	21.6081	−	5.81854i	0.835416	−	0.224958i
$670$	5.48501	−	2.13388i	0.211904	−	0.0824390i
$671$	8.53464	−	18.4852i	0.329476	−	0.713614i
$672$	−0.948713	+	3.55825i	−0.0365974	+	0.137263i
$673$	20.2918	+	35.1465i	0.782193	+	1.35480i	0.930662	+	0.365881i	$0.119232\pi$
$673$	20.2918	+	35.1465i	0.782193	+	1.35480i	−0.148469	+	0.988917i	$0.547435\pi$
$674$			16.4602i			0.634024i
$675$	25.9603	+	1.02969i	0.999214	+	0.0396326i
$676$	−14.8252			−0.570200
$677$	6.86534	−	3.96371i	0.263857	−	0.152338i	−0.362236	−	0.932086i	$-0.617987\pi$
$677$	6.86534	−	3.96371i	0.263857	−	0.152338i	0.626093	+	0.779749i	$0.284653\pi$
$678$	0.600488	−	2.25220i	0.0230616	−	0.0864951i
$679$	23.1597	+	13.3712i	0.888787	+	0.513141i
$680$	−1.77266	+	0.689634i	−0.0679785	+	0.0264463i
$681$	−14.7713	+	3.97755i	−0.566036	+	0.152420i
$682$	13.4528	+	19.0585i	0.515136	+	0.729787i
$683$	−40.4955			−1.54952			−0.774759	−	0.632257i	$-0.782129\pi$
$683$	−40.4955			−1.54952			−0.774759	+	0.632257i	$0.782129\pi$
$684$	−3.95530	−	6.81179i	−0.151235	−	0.260455i
$685$	−24.9164	−	19.9918i	−0.952005	−	0.763848i
$686$	−17.4546	+	10.0774i	−0.666418	+	0.384757i
$687$	16.1957	−	16.2358i	0.617903	−	0.619434i
$688$	−4.38888	+	7.60176i	−0.167324	+	0.289814i
$689$	−25.7885	+	44.6670i	−0.982464	+	1.70168i
$690$	0.968886	+	8.73572i	0.0368849	+	0.332563i
$691$	−12.8183	−	22.2019i	−0.487630	−	0.844600i	0.512269	−	0.858825i	$-0.328805\pi$
$691$	−12.8183	−	22.2019i	−0.487630	−	0.844600i	−0.999899	+	0.0142254i	$0.995472\pi$
$692$		−	3.11544i		−	0.118431i
$693$	−12.2422	−	17.2525i	−0.465041	−	0.655369i
$694$	−22.7254			−0.862644
$695$	−30.9100	−	4.75312i	−1.17248	−	0.180296i
$696$	15.1068	−	4.06789i	0.572620	−	0.154193i
$697$	6.77858	+	3.91361i	0.256757	+	0.148239i
$698$	−12.7433	+	22.0720i	−0.482339	+	0.835436i
$699$	−3.95877	+	14.8478i	−0.149734	+	0.561595i
$700$	−7.83572	+	7.18412i	−0.296163	+	0.271534i
$701$	13.3785			0.505300			0.252650	−	0.967558i	$-0.418698\pi$
$701$	13.3785			0.505300			0.252650	+	0.967558i	$0.418698\pi$
$702$	19.3094	−	19.4533i	0.728784	−	0.734216i
$703$	12.5280			0.472501
$704$	−2.70959	+	1.91262i	−0.102121	+	0.0720847i
$705$	−1.10314	−	1.50015i	−0.0415465	−	0.0564990i
$706$	21.8829	+	12.6341i	0.823574	+	0.475491i
$707$	−3.14790	+	5.45232i	−0.118389	+	0.205056i
$708$	16.0065	−	4.31017i	0.601561	−	0.161986i
$709$	16.3310	+	28.2862i	0.613325	+	1.06231i	0.990676	+	0.136239i	$0.0435016\pi$
$709$	16.3310	+	28.2862i	0.613325	+	1.06231i	−0.377351	+	0.926070i	$0.623165\pi$
$710$	−21.8272	−	17.5132i	−0.819158	−	0.657257i
$711$	−39.1762	+	0.0969659i	−1.46922	+	0.00363651i
$712$	−8.26439			−0.309721
$713$	7.98110	+	13.8237i	0.298895	+	0.517701i
$714$	2.21229	−	2.21777i	0.0827927	−	0.0829979i
$715$	17.4401	+	35.0175i	0.652224	+	1.30958i
$716$	−4.28861	−	2.47603i	−0.160273	−	0.0925336i
$717$	−18.9752	+	19.0222i	−0.708641	+	0.710397i
$718$	−31.8343	+	18.3796i	−1.18805	+	0.685919i
$719$		−	31.9199i		−	1.19041i	−0.803573	−	0.595206i	$-0.797071\pi$
$719$		−	31.9199i		−	1.19041i	0.803573	−	0.595206i	$-0.202929\pi$
$720$	2.44764	+	6.24572i	0.0912182	+	0.232764i
$721$			2.84079i			0.105796i
$722$	10.4842	−	6.05306i	0.390182	−	0.225272i
$723$	−36.7861	+	9.90561i	−1.36809	+	0.368394i
$724$	11.7917	−	20.4239i	0.438237	−	0.759048i
$725$	43.0763	+	13.5688i	1.59982	+	0.503932i
$726$	1.49309	−	18.9940i	0.0554136	−	0.704932i
$727$	−7.06137	+	4.07688i	−0.261892	+	0.151203i	−0.625197	−	0.780467i	$-0.714981\pi$
$727$	−7.06137	+	4.07688i	−0.261892	+	0.151203i	0.363306	+	0.931670i	$0.381648\pi$
$728$			11.2152i			0.415664i
$729$	0.200483	+	26.9993i	0.00742529	+	0.999972i
$730$	8.47382	−	10.5612i	0.313630	−	0.390886i
$731$	6.46635	−	3.73335i	0.239167	−	0.138083i
$732$	2.73927	−	10.2739i	0.101246	−	0.379736i
$733$	−25.0485	+	43.3853i	−0.925187	+	1.60247i	−0.133927	+	0.990991i	$0.542759\pi$
$733$	−25.0485	+	43.3853i	−0.925187	+	1.60247i	−0.791260	+	0.611480i	$0.790574\pi$
$734$	−3.01379	+	5.22004i	−0.111241	+	0.192675i
$735$	−3.85565	+	8.79544i	−0.142218	+	0.324425i
$736$	−1.96534	+	1.13469i	−0.0724435	+	0.0418253i
$737$	−8.69340	+	0.793793i	−0.320226	+	0.0292397i
$738$	13.7432	−	23.9405i	0.505893	−	0.881263i
$739$			16.7092i			0.614658i	0.951603	+	0.307329i	$0.0994352\pi$
$739$			16.7092i			0.614658i	−0.951603	+	0.307329i	$0.900565\pi$
$740$	−10.5453	−	1.62158i	−0.387653	−	0.0596104i
$741$	−16.9837	−	16.9418i	−0.623913	−	0.622371i
$742$	18.0035	+	10.3943i	0.660928	+	0.381587i
$743$	−7.12955	−	4.11625i	−0.261558	−	0.151010i	0.363487	−	0.931599i	$-0.381586\pi$
$743$	−7.12955	−	4.11625i	−0.261558	−	0.151010i	−0.625045	+	0.780589i	$0.714919\pi$
$744$	8.62516	+	8.60384i	0.316214	+	0.315432i
$745$	−0.151854	+	0.987524i	−0.00556351	+	0.0361801i
$746$		−	27.0482i		−	0.990307i
$747$	−26.7783	+	0.0662797i	−0.979767	+	0.00242505i
$748$	2.80956	−	0.256541i	0.102728	−	0.00938006i
$749$	10.3220	−	5.95938i	0.377156	−	0.217751i
$750$	−3.74649	+	18.9990i	−0.136803	+	0.693747i
$751$	−1.67986	+	2.90960i	−0.0612990	+	0.106173i	−0.895046	−	0.445973i	$-0.852858\pi$
$751$	−1.67986	+	2.90960i	−0.0612990	+	0.106173i	0.833747	+	0.552146i	$0.186191\pi$
$752$	0.240394	−	0.416375i	0.00876628	−	0.0151836i
$753$	−8.31376	+	31.1817i	−0.302970	+	1.13632i
$754$	41.2630	−	23.8232i	1.50271	−	0.867591i
$755$	21.5032	−	26.8001i	0.782583	−	0.975355i
$756$	−7.84083	−	7.78282i	−0.285168	−	0.283059i
$757$			7.65686i			0.278293i	0.990272	+	0.139147i	$0.0444359\pi$
$757$			7.65686i			0.278293i	−0.990272	+	0.139147i	$0.955564\pi$
$758$	−17.1340	+	9.89235i	−0.622337	+	0.359306i
$759$	2.19920	−	12.8498i	0.0798259	−	0.466418i
$760$	5.47158	−	2.12866i	0.198475	−	0.0772145i
$761$	8.27969	−	14.3408i	0.300139	−	0.519855i	−0.676029	−	0.736875i	$-0.736300\pi$
$761$	8.27969	−	14.3408i	0.300139	−	0.519855i	0.976167	+	0.217020i	$0.0696338\pi$
$762$	−16.5264	+	4.45016i	−0.598688	+	0.161212i
$763$	28.5419	−	16.4787i	1.03329	−	0.596568i
$764$		−	18.8060i		−	0.680379i
$765$	0.853310	−	5.64210i	0.0308515	−	0.203990i
$766$		−	22.1228i		−	0.799329i
$767$	43.7206	−	25.2421i	1.57866	−	0.911440i
$768$	−1.22323	+	1.22626i	−0.0441394	+	0.0442488i
$769$	−15.7217	−	9.07694i	−0.566940	−	0.327323i	0.188987	−	0.981980i	$-0.439480\pi$
$769$	−15.7217	−	9.07694i	−0.566940	−	0.327323i	−0.755926	+	0.654657i	$0.772813\pi$
$770$	14.1142	−	7.02942i	0.508639	−	0.253323i
$771$	11.7693	−	11.7985i	0.423862	−	0.424912i
$772$	−6.10832	−	10.5799i	−0.219843	−	0.380779i
$773$	−29.1490			−1.04842			−0.524209	−	0.851590i	$-0.675639\pi$
$773$	−29.1490			−1.04842			−0.524209	+	0.851590i	$0.675639\pi$
$774$	−13.2230	−	22.7726i	−0.475292	−	0.818544i
$775$	7.62140	+	34.3328i	0.273769	+	1.23327i
$776$	6.28902	+	10.8929i	0.225763	+	0.391033i
$777$	16.9667	−	4.56873i	0.608677	−	0.163902i
$778$	0.537397	−	0.930800i	0.0192666	−	0.0333708i
$779$	−20.9231	−	12.0799i	−0.749647	−	0.432809i
$780$	12.1030	+	16.4589i	0.433358	+	0.589323i
$781$	23.9366	+	33.9107i	0.856520	+	1.21342i
$782$	1.93043			0.0690319
$783$	−11.9792	+	45.3801i	−0.428101	+	1.62175i
$784$	−2.47959			−0.0885569
$785$	21.7929	+	3.35116i	0.777823	+	0.119608i
$786$	1.35882	−	5.09641i	0.0484676	−	0.181783i
$787$	8.70436	−	15.0764i	0.310277	−	0.537415i	−0.668145	−	0.744031i	$-0.732912\pi$
$787$	8.70436	−	15.0764i	0.310277	−	0.537415i	0.978422	+	0.206616i	$0.0662449\pi$
$788$	21.4502	+	12.3843i	0.764130	+	0.441171i
$789$	19.7564	−	5.31994i	0.703348	−	0.189395i
$790$	4.43804	−	28.8610i	0.157898	−	1.02683i
$791$	−2.86119			−0.101732
$792$	−0.929280	−	9.90638i	−0.0330205	−	0.352008i
$793$		−	32.3823i		−	1.14993i
$794$	6.39085	+	11.0693i	0.226803	+	0.392834i
$795$	37.6381	−	4.17447i	1.33489	−	0.148053i
$796$	−1.19367	+	2.06749i	−0.0423084	+	0.0732802i
$797$	14.9534	−	25.9001i	0.529677	−	0.917428i	−0.469723	−	0.882814i	$-0.655646\pi$
$797$	14.9534	−	25.9001i	0.529677	−	0.917428i	0.999401	−	0.0346145i	$-0.0110203\pi$
$798$	−6.82854	+	6.84547i	−0.241728	+	0.242327i
$799$	−0.354185	+	0.204489i	−0.0125302	+	0.00723429i
$800$	−4.88118	+	1.08355i	−0.172576	+	0.0383094i
$801$	12.3434	−	21.5021i	0.436133	−	0.759741i
$802$	−6.15819			−0.217453
$803$	−16.4079	+	11.5818i	−0.579020	+	0.408714i
$804$	−4.40206	+	1.18537i	−0.155249	+	0.0418048i
$805$	10.0549	−	3.91174i	0.354389	−	0.137871i
$806$	32.1318	+	18.5513i	1.13179	+	0.653441i
$807$	1.66069	−	6.22860i	0.0584591	−	0.219257i
$808$	−2.56444	+	1.48058i	−0.0902167	+	0.0520867i
$809$	−52.1806			−1.83457			−0.917286	−	0.398229i	$-0.869625\pi$
$809$	−52.1806			−1.83457			−0.917286	+	0.398229i	$0.869625\pi$
$810$	−19.9057	−	2.96016i	−0.699415	−	0.104010i
$811$		−	17.8096i		−	0.625381i	−0.949855	−	0.312690i	$-0.898770\pi$
$811$		−	17.8096i		−	0.625381i	0.949855	−	0.312690i	$-0.101230\pi$
$812$	−9.60219	−	16.6315i	−0.336971	−	0.583650i
$813$	−1.64782	+	6.18035i	−0.0577917	+	0.216754i
$814$	14.3676	+	6.63354i	0.503585	+	0.232505i
$815$	1.52775	+	3.92699i	0.0535147	+	0.137556i
$816$	1.42267	−	0.383092i	0.0498035	−	0.0134109i
$817$	−19.9593	+	11.5235i	−0.698288	+	0.403157i
$818$	26.5946			0.929859
$819$	−29.1796	−	16.7507i	−1.01962	−	0.585316i
$820$	16.0482	+	12.8764i	0.560428	+	0.449663i
$821$	−12.5414	−	21.7223i	−0.437697	−	0.758113i	0.559815	−	0.828618i	$-0.310872\pi$
$821$	−12.5414	−	21.7223i	−0.437697	−	0.758113i	−0.997511	+	0.0705051i	$0.977539\pi$
$822$	17.5188	+	17.4755i	0.611037	+	0.609527i
$823$	44.0111	+	25.4098i	1.53413	+	0.885730i	0.999165	+	0.0408549i	$0.0130081\pi$
$823$	44.0111	+	25.4098i	1.53413	+	0.885730i	0.534964	+	0.844875i	$0.320325\pi$
$824$	−0.668067	+	1.15713i	−0.0232732	+	0.0403104i
$825$	13.1274	−	25.5475i	0.457036	−	0.889448i
$826$	−10.1741	−	17.6220i	−0.354002	−	0.613149i
$827$		−	2.77453i		−	0.0964799i	−0.998836	−	0.0482399i	$-0.984639\pi$
$827$		−	2.77453i		−	0.0964799i	0.998836	−	0.0482399i	$-0.0153612\pi$
$828$	−0.0168510	−	6.80813i	−0.000585612	−	0.236599i
$829$	−1.73351			−0.0602072			−0.0301036	−	0.999547i	$-0.509584\pi$
$829$	−1.73351			−0.0602072			−0.0301036	+	0.999547i	$0.509584\pi$
$830$	3.03356	−	19.7276i	0.105296	−	0.684754i
$831$	−11.0552	−	41.0553i	−0.383501	−	1.42419i
$832$	−2.63748	+	4.56825i	−0.0914382	+	0.158376i
$833$	1.82665	+	1.05462i	0.0632898	+	0.0365404i
$834$	23.4066	+	6.24073i	0.810503	+	0.216099i
$835$	−25.3772	−	3.90232i	−0.878214	−	0.135045i
$836$	−8.67212	+	0.791850i	−0.299932	+	0.0273867i
$837$	−35.2675	+	9.59039i	−1.21902	+	0.331492i
$838$	−0.158258			−0.00546692
$839$	−2.50245	+	1.44479i	−0.0863942	+	0.0498797i	−0.542575	−	0.840008i	$-0.682550\pi$
$839$	−2.50245	+	1.44479i	−0.0863942	+	0.0498797i	0.456181	+	0.889887i	$0.349217\pi$
$840$	6.63392	−	4.87824i	0.228892	−	0.168315i
$841$	−26.2937	+	45.5420i	−0.906678	+	1.57041i
$842$	−13.4852	−	7.78571i	−0.464732	−	0.268313i
$843$	10.6167	+	39.4270i	0.365660	+	1.35794i
$844$	−2.61561	+	1.51012i	−0.0900330	+	0.0519806i
$845$	25.8562	+	20.7459i	0.889479	+	0.713680i
$846$	0.724272	+	1.24734i	0.0249010	+	0.0428843i
$847$	−23.0006	+	4.23568i	−0.790310	+	0.145540i
$848$	4.88885	+	8.46774i	0.167884	+	0.290783i
$849$	25.3579	−	25.4207i	0.870281	−	0.872437i
$850$	4.05670	+	1.27783i	0.139144	+	0.0438294i
$851$	9.37751	+	5.41411i	0.321457	+	0.185593i
$852$	15.3467	+	15.3088i	0.525770	+	0.524471i
$853$	8.03471	+	13.9165i	0.275103	+	0.476493i	0.970161	−	0.242461i	$-0.0779547\pi$
$853$	8.03471	+	13.9165i	0.275103	+	0.476493i	−0.695058	+	0.718954i	$0.744621\pi$
$854$	−13.0520			−0.446631
$855$	−2.63387	+	17.4151i	−0.0900763	+	0.595585i
$856$	5.60586			0.191604
$857$	24.2898	−	14.0237i	0.829723	−	0.479041i	−0.0240350	−	0.999711i	$-0.507651\pi$
$857$	24.2898	−	14.0237i	0.829723	−	0.479041i	0.853758	+	0.520670i	$0.174318\pi$
$858$	−10.5071	−	28.4224i	−0.358705	−	0.970325i
$859$	−18.2668	+	31.6391i	−0.623256	+	1.07951i	0.365620	+	0.930764i	$0.380857\pi$
$859$	−18.2668	+	31.6391i	−0.623256	+	1.07951i	−0.988875	+	0.148746i	$0.952476\pi$
$860$	18.2921	−	7.11634i	0.623757	−	0.242665i
$861$	−32.7416	−	8.72966i	−1.11583	−	0.297506i
$862$	18.4008	−	10.6237i	0.626734	−	0.361845i
$863$	−5.87019			−0.199823			−0.0999117	−	0.994996i	$-0.531856\pi$
$863$	−5.87019			−0.199823			−0.0999117	+	0.994996i	$0.531856\pi$
$864$	−1.36349	−	5.01407i	−0.0463868	−	0.170582i
$865$	−4.35964	+	5.43354i	−0.148232	+	0.184746i
$866$	3.73041	+	6.46127i	0.126765	+	0.219563i
$867$	27.2400	+	7.26281i	0.925118	+	0.246658i
$868$	7.47728	−	12.9510i	0.253795	−	0.439586i
$869$	−18.1551	+	39.3222i	−0.615869	+	1.33391i
$870$	−32.0397	−	14.0452i	−1.08625	−	0.476177i
$871$	−12.0239	+	6.94201i	−0.407415	+	0.235221i
$872$	15.5011			0.524935
$873$	−37.7340	+	0.0933965i	−1.27710	+	0.00316099i
$874$	−5.95854			−0.201551
$875$	23.7193	−	1.56456i	0.801857	−	0.0528917i
$876$	−7.40723	+	7.42559i	−0.250267	+	0.250887i
$877$	−3.79422	+	6.57178i	−0.128122	+	0.221913i	−0.922949	−	0.384923i	$-0.874228\pi$
$877$	−3.79422	+	6.57178i	−0.128122	+	0.221913i	0.794827	+	0.606836i	$0.207561\pi$
$878$	12.3535	−	21.3969i	0.416911	−	0.722111i
$879$	20.5972	+	20.5463i	0.694726	+	0.693008i
$880$	7.40217	+	0.455958i	0.249527	+	0.0153703i
$881$		−	15.9428i		−	0.537125i	−0.963262	−	0.268563i	$-0.913451\pi$
$881$		−	15.9428i		−	0.537125i	0.963262	−	0.268563i	$-0.0865486\pi$
$882$	3.70343	−	6.45136i	0.124701	−	0.217229i
$883$			21.6305i			0.727924i	0.931414	+	0.363962i	$0.118576\pi$
$883$			21.6305i			0.727924i	−0.931414	+	0.363962i	$0.881424\pi$
$884$	3.88593	−	2.24354i	0.130698	−	0.0754585i
$885$	−33.9479	−	14.8817i	−1.14115	−	0.500243i
$886$	−34.7771	−	20.0786i	−1.16836	−	0.674553i
$887$	−26.1744	−	15.1118i	−0.878852	−	0.507405i	−0.00857206	−	0.999963i	$-0.502729\pi$
$887$	−26.1744	−	15.1118i	−0.878852	−	0.507405i	−0.870280	+	0.492558i	$0.836062\pi$
$888$	7.98540	+	2.12909i	0.267973	+	0.0714477i
$889$	10.5045	+	18.1944i	0.352310	+	0.610220i
$890$	14.4137	+	11.5649i	0.483147	+	0.387656i
$891$	27.1622	+	12.3780i	0.909967	+	0.414680i
$892$		−	12.9198i		−	0.432587i
$893$	1.09324	−	0.631184i	0.0365840	−	0.0211218i
$894$	0.199381	−	0.747800i	0.00666829	−	0.0250102i
$895$	4.01476	+	10.3197i	0.134199	+	0.344950i
$896$	1.84128	+	1.06306i	0.0615128	+	0.0355144i
$897$	−5.39119	−	20.0211i	−0.180007	−	0.668484i
$898$	19.4772	+	33.7354i	0.649961	+	1.12577i
$899$	−63.5325			−2.11893
$900$	4.47119	−	14.3181i	0.149040	−	0.477271i
$901$		−	8.31730i		−	0.277089i
$902$	−17.5992	−	24.9325i	−0.585988	−	0.830162i
$903$	−22.8286	+	22.8852i	−0.759689	+	0.761571i
$904$	−1.16544	−	0.672865i	−0.0387618	−	0.0223792i
$905$	−49.1461	+	19.1197i	−1.63367	+	0.635561i
$906$	−18.7966	+	18.8432i	−0.624477	+	0.626024i
$907$	−2.13171	+	1.23075i	−0.0707824	+	0.0408662i	−0.534974	−	0.844869i	$-0.679678\pi$
$907$	−2.13171	+	1.23075i	−0.0707824	+	0.0408662i	0.464191	+	0.885735i	$0.346345\pi$
$908$			8.83197i			0.293099i
$909$	−0.0219877	−	8.88346i	−0.000729285	−	0.294646i
$910$	15.6942	−	19.5601i	0.520258	−	0.648412i
$911$	5.90049	−	3.40665i	0.195492	−	0.112867i	−0.399059	−	0.916925i	$-0.630663\pi$
$911$	5.90049	−	3.40665i	0.195492	−	0.112867i	0.594551	+	0.804058i	$0.297330\pi$
$912$	−4.39129	+	1.18247i	−0.145410	+	0.0391554i
$913$	−12.4097	+	26.8781i	−0.410700	+	0.889537i
$914$	11.2932	+	6.52011i	0.373545	+	0.215666i
$915$	−19.1545	+	14.0852i	−0.633227	+	0.465643i
$916$	−6.62005	−	11.4663i	−0.218732	−	0.378856i
$917$	−6.47448			−0.213806
$918$	−1.12813	+	4.27366i	−0.0372340	+	0.141052i
$919$		−	16.5804i		−	0.546939i	−0.961881	−	0.273469i	$-0.911829\pi$
$919$		−	16.5804i		−	0.546939i	0.961881	−	0.273469i	$-0.0881712\pi$
$920$	5.01554	+	0.771254i	0.165358	+	0.0254275i
$921$	−8.95802	−	2.38842i	−0.295177	−	0.0787010i
$922$	−30.6517	−	17.6968i	−1.00946	−	0.582812i
$923$	57.1720	+	33.0083i	1.88184	+	1.08648i
$924$	−11.4559	+	4.23498i	−0.376873	+	0.139320i
$925$	16.1225	+	17.5849i	0.530106	+	0.578187i
$926$	−12.8541			−0.422413
$927$	−2.01279	−	3.46641i	−0.0661086	−	0.113852i
$928$		−	9.03257i		−	0.296509i
$929$	25.1586	−	14.5253i	0.825427	−	0.476561i	−0.0268571	−	0.999639i	$-0.508550\pi$
$929$	25.1586	−	14.5253i	0.825427	−	0.476561i	0.852284	+	0.523079i	$0.175217\pi$
$930$	−3.00296	−	27.0754i	−0.0984709	−	0.887839i
$931$	−5.63823	−	3.25524i	−0.184786	−	0.106686i
$932$	7.68324	+	4.43592i	0.251673	+	0.145303i
$933$	−14.3471	−	14.3116i	−0.469703	−	0.468542i
$934$	−36.8437	+	21.2717i	−1.20556	+	0.696031i
$935$	−5.25906	−	3.48418i	−0.171990	−	0.113945i
$936$	−7.94634	−	13.6851i	−0.259734	−	0.447312i
$937$	8.96637			0.292919			0.146459	−	0.989217i	$-0.453212\pi$
$937$	8.96637			0.292919			0.146459	+	0.989217i	$0.453212\pi$
$938$	2.79805	+	4.84636i	0.0913595	+	0.158239i
$939$	42.5552	−	11.4591i	1.38874	−	0.373953i
$940$	−1.00193	+	0.389787i	−0.0326792	+	0.0127135i
$941$	−6.65048	+	11.5190i	−0.216800	+	0.375508i	−0.953828	−	0.300354i	$-0.902895\pi$
$941$	−6.65048	+	11.5190i	−0.216800	+	0.375508i	0.737028	+	0.675862i	$0.236228\pi$
$942$	−16.5027	−	4.39999i	−0.537686	−	0.143359i
$943$	−10.4410	−	18.0843i	−0.340005	−	0.588905i
$944$		−	9.57054i		−	0.311495i
$945$	2.78393	+	24.5460i	0.0905613	+	0.798480i
$946$	−28.9919	+	2.64725i	−0.942608	+	0.0860694i
$947$	−19.1895	−	33.2372i	−0.623575	−	1.08006i	−0.988815	−	0.149150i	$-0.952346\pi$
$947$	−19.1895	−	33.2372i	−0.623575	−	1.08006i	0.365240	−	0.930913i	$-0.380987\pi$
$948$	−5.82704	+	21.8550i	−0.189253	+	0.709816i
$949$	−15.9712	+	27.6629i	−0.518447	+	0.897977i
$950$	−12.5216	−	3.94422i	−0.406254	−	0.127967i
$951$	5.71569	+	21.2261i	0.185344	+	0.688304i
$952$	−0.904282	−	1.56626i	−0.0293080	−	0.0507629i
$953$			33.6003i			1.08842i	0.838949	+	0.544210i	$0.183170\pi$
$953$			33.6003i			1.08842i	−0.838949	+	0.544210i	$0.816830\pi$
$954$	−29.3330	+	0.0726029i	−0.949692	+	0.00235061i
$955$	−26.3165	+	32.7990i	−0.851583	+	1.06135i
$956$	7.75619	+	13.4341i	0.250853	+	0.434490i
$957$	39.9159	+	33.1528i	1.29030	+	1.07168i
$958$	−26.3024	−	15.1857i	−0.849794	−	0.490629i
$959$	15.1873	−	26.3051i	0.490423	−	0.849437i
$960$	3.84938	−	0.426938i	0.124238	−	0.0137794i
$961$	−9.23658	−	15.9982i	−0.297954	−	0.516072i
$962$	25.1691			0.811485
$963$	−8.37272	+	14.5852i	−0.269807	+	0.470002i
$964$			21.9950i			0.708410i
$965$	−4.15184	+	26.9999i	−0.133653	+	0.869156i
$966$	−8.06969	+	2.17297i	−0.259638	+	0.0699143i
$967$	17.0724	−	29.5702i	0.549011	−	0.950914i	−0.449332	−	0.893365i	$-0.648338\pi$
$967$	17.0724	−	29.5702i	0.549011	−	0.950914i	0.998343	−	0.0575493i	$-0.0183286\pi$
$968$	−10.3648	−	3.68374i	−0.333139	−	0.118400i
$969$	3.73788	+	0.996605i	0.120078	+	0.0320156i
$970$	4.27467	−	27.7986i	0.137251	−	0.892560i
$971$			0.123178i			0.00395297i	0.999998	+	0.00197648i	$0.000629135\pi$
$971$			0.123178i			0.00395297i	−0.999998	+	0.00197648i	$0.999371\pi$
$972$	15.0820	+	3.94134i	0.483754	+	0.126419i
$973$		−	29.7357i		−	0.953283i
$974$	−11.0724	−	19.1780i	−0.354784	−	0.614504i
$975$	1.92349	−	45.6420i	0.0616011	−	1.46171i
$976$	−5.31642	−	3.06944i	−0.170175	−	0.0982503i
$977$	4.64314	−	8.04215i	0.148547	−	0.257291i	−0.782144	−	0.623098i	$-0.785874\pi$
$977$	4.64314	−	8.04215i	0.148547	−	0.257291i	0.930691	+	0.365807i	$0.119207\pi$
$978$	−0.848664	−	3.15165i	−0.0271373	−	0.100779i
$979$	−15.8067	−	22.3931i	−0.505183	−	0.715687i
$980$	4.32458	+	3.46986i	0.138144	+	0.110841i
$981$	−23.1519	+	40.3306i	−0.739185	+	1.28766i
$982$			36.6867i			1.17072i
$983$	14.0687	+	24.3676i	0.448721	+	0.777207i	0.998303	−	0.0582323i	$-0.0185464\pi$
$983$	14.0687	+	24.3676i	0.448721	+	0.777207i	−0.549582	+	0.835440i	$0.685213\pi$
$984$	−11.2835	−	11.2556i	−0.359706	−	0.358817i
$985$	−20.0804	−	51.6156i	−0.639816	−	1.64461i
$986$	−3.84173	+	6.65407i	−0.122346	+	0.211909i
$987$	1.25040	−	1.25350i	0.0398008	−	0.0398994i
$988$	−11.9945	+	6.92502i	−0.381595	+	0.220314i
$989$	−19.9201			−0.633422
$990$	−12.2419	+	18.5778i	−0.389074	+	0.590442i
$991$	57.5103			1.82687			0.913437	−	0.406980i	$-0.133418\pi$
$991$	57.5103			1.82687			0.913437	+	0.406980i	$0.133418\pi$
$992$	6.09138	−	3.51686i	0.193401	−	0.111660i
$993$	−2.89862	−	10.7645i	−0.0919848	−	0.341600i
$994$	13.3043	−	23.0437i	0.421987	−	0.730903i
$995$	4.97501	−	1.93547i	0.157718	−	0.0613585i
$996$	−3.98299	+	14.9386i	−0.126206	+	0.473349i
$997$	8.64274	+	14.9697i	0.273718	+	0.474094i	0.969811	−	0.243858i	$-0.0784131\pi$
$997$	8.64274	+	14.9697i	0.273718	+	0.474094i	−0.696093	+	0.717952i	$0.745080\pi$
$998$			10.5111i			0.332723i
$999$	−17.4661	+	17.5963i	−0.552605	+	0.556723i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.329.70	yes	144
5.4	even	2	inner	990.2.o.a.329.3	✓	144
9.2	odd	6	inner	990.2.o.a.659.39	yes	144
11.10	odd	2	inner	990.2.o.a.329.34	yes	144
45.29	odd	6	inner	990.2.o.a.659.34	yes	144
55.54	odd	2	inner	990.2.o.a.329.39	yes	144
99.65	even	6	inner	990.2.o.a.659.3	yes	144
495.164	even	6	inner	990.2.o.a.659.70	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.3	✓	144	5.4	even	2	inner
990.2.o.a.329.34	yes	144	11.10	odd	2	inner
990.2.o.a.329.39	yes	144	55.54	odd	2	inner
990.2.o.a.329.70	yes	144	1.1	even	1	trivial
990.2.o.a.659.3	yes	144	99.65	even	6	inner
990.2.o.a.659.34	yes	144	45.29	odd	6	inner
990.2.o.a.659.39	yes	144	9.2	odd	6	inner
990.2.o.a.659.70	yes	144	495.164	even	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(1.67359 + 0.446217i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.08392 + 0.810725i) q^{5} +(1.67248 - 0.450358i) q^{6} +(-1.06306 - 1.84128i) q^{7} -1.00000i q^{8} +(2.60178 + 1.49356i) q^{9} +(-1.39937 + 1.74407i) q^{10} +(2.70959 - 1.91262i) q^{11} +(1.22323 - 1.22626i) q^{12} +(2.63748 - 4.56825i) q^{13} +(-1.84128 - 1.06306i) q^{14} +(-3.84938 + 0.426938i) q^{15} +(-0.500000 - 0.866025i) q^{16} +0.850639i q^{17} +(2.99999 - 0.00742535i) q^{18} -2.62562i q^{19} +(-0.339852 + 2.21009i) q^{20} +(-0.957517 - 3.55589i) q^{21} +(1.39026 - 3.01117i) q^{22} +(1.13469 - 1.96534i) q^{23} +(0.446217 - 1.67359i) q^{24} +(3.68545 - 3.37897i) q^{25} -5.27496i q^{26} +(3.68785 + 3.66057i) q^{27} -2.12612 q^{28} +(4.51629 + 7.82244i) q^{29} +(-3.12019 + 2.29443i) q^{30} +(-3.51686 + 6.09138i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.38818 - 1.99188i) q^{33} +(0.425319 + 0.736675i) q^{34} +(3.70811 + 2.97523i) q^{35} +(2.59436 - 1.50643i) q^{36} +4.77143i q^{37} +(-1.31281 - 2.27385i) q^{38} +(6.45248 - 6.46847i) q^{39} +(0.810725 + 2.08392i) q^{40} +(4.60079 - 7.96881i) q^{41} +(-2.60718 - 2.60074i) q^{42} +(-4.38888 - 7.60176i) q^{43} +(-0.301586 - 3.30288i) q^{44} +(-6.63278 - 1.00314i) q^{45} -2.26938i q^{46} +(0.240394 + 0.416375i) q^{47} +(-0.450358 - 1.67248i) q^{48} +(1.23980 - 2.14739i) q^{49} +(1.50221 - 4.76900i) q^{50} +(-0.379569 + 1.42362i) q^{51} +(-2.63748 - 4.56825i) q^{52} -9.77771 q^{53} +(5.02406 + 1.32622i) q^{54} +(-4.09596 + 6.18249i) q^{55} +(-1.84128 + 1.06306i) q^{56} +(1.17160 - 4.39420i) q^{57} +(7.82244 + 4.51629i) q^{58} +(8.28833 + 4.78527i) q^{59} +(-1.55495 + 3.54713i) q^{60} +(5.31642 - 3.06944i) q^{61} +7.03372i q^{62} +(-0.0157872 - 6.37835i) q^{63} -1.00000 q^{64} +(-1.79270 + 11.6581i) q^{65} +(3.67036 - 4.41910i) q^{66} +(-2.27943 - 1.31603i) q^{67} +(0.736675 + 0.425319i) q^{68} +(2.77597 - 2.78285i) q^{69} +(4.69893 + 0.722567i) q^{70} +12.5151i q^{71} +(1.49356 - 2.60178i) q^{72} -6.05548 q^{73} +(2.38572 + 4.13218i) q^{74} +(7.67567 - 4.01049i) q^{75} +(-2.27385 - 1.31281i) q^{76} +(-6.40213 - 2.95587i) q^{77} +(2.35378 - 8.82810i) q^{78} +(-11.3092 + 6.52938i) q^{79} +(1.74407 + 1.39937i) q^{80} +(4.53853 + 7.77186i) q^{81} -9.20159i q^{82} +(-7.73026 + 4.46307i) q^{83} +(-3.55825 - 0.948713i) q^{84} +(-0.689634 - 1.77266i) q^{85} +(-7.60176 - 4.38888i) q^{86} +(4.06789 + 15.1068i) q^{87} +(-1.91262 - 2.70959i) q^{88} -8.26439i q^{89} +(-6.24572 + 2.44764i) q^{90} -11.2152 q^{91} +(-1.13469 - 1.96534i) q^{92} +(-8.60384 + 8.62516i) q^{93} +(0.416375 + 0.240394i) q^{94} +(2.12866 + 5.47158i) q^{95} +(-1.22626 - 1.22323i) q^{96} +(-10.8929 + 6.28902i) q^{97} -2.47959i q^{98} +(9.90638 - 0.929280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

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