LMFDB - Embedded newform 192.2.r.a.133.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			133.14
Character	$\chi$	$=$	192.133
Dual form			192.2.r.a.13.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11696 - 0.867416i) q^{2} +(0.831470 + 0.555570i) q^{3} +(0.495179 - 1.93773i) q^{4} +(-0.668642 - 0.133001i) q^{5} +(1.41063 - 0.100683i) q^{6} +(0.440731 - 1.06402i) q^{7} +(-1.12772 - 2.59388i) q^{8} +(0.382683 + 0.923880i) q^{9} +O(q^{10})$	\(q+(1.11696 - 0.867416i) q^{2} +(0.831470 + 0.555570i) q^{3} +(0.495179 - 1.93773i) q^{4} +(-0.668642 - 0.133001i) q^{5} +(1.41063 - 0.100683i) q^{6} +(0.440731 - 1.06402i) q^{7} +(-1.12772 - 2.59388i) q^{8} +(0.382683 + 0.923880i) q^{9} +(-0.862210 + 0.431434i) q^{10} +(1.16209 + 1.73918i) q^{11} +(1.48827 - 1.33606i) q^{12} +(1.13856 - 0.226473i) q^{13} +(-0.430670 - 1.57076i) q^{14} +(-0.482064 - 0.482064i) q^{15} +(-3.50959 - 1.91905i) q^{16} +(-4.47057 + 4.47057i) q^{17} +(1.22883 + 0.699987i) q^{18} +(0.731601 + 3.67801i) q^{19} +(-0.588818 + 1.22979i) q^{20} +(0.957593 - 0.639843i) q^{21} +(2.80659 + 0.934580i) q^{22} +(1.46515 - 0.606887i) q^{23} +(0.503417 - 2.78327i) q^{24} +(-4.19001 - 1.73556i) q^{25} +(1.07527 - 1.24056i) q^{26} +(-0.195090 + 0.980785i) q^{27} +(-1.84354 - 1.38090i) q^{28} +(-3.43347 + 5.13856i) q^{29} +(-0.956594 - 0.120294i) q^{30} -6.02971i q^{31} +(-5.58467 + 0.900787i) q^{32} +2.09170i q^{33} +(-1.11559 + 8.87128i) q^{34} +(-0.436207 + 0.652830i) q^{35} +(1.97973 - 0.284051i) q^{36} +(0.203687 - 1.02400i) q^{37} +(4.00753 + 3.47357i) q^{38} +(1.07250 + 0.444243i) q^{39} +(0.409054 + 1.88437i) q^{40} +(-6.26769 + 2.59616i) q^{41} +(0.514578 - 1.54531i) q^{42} +(7.89573 - 5.27576i) q^{43} +(3.94551 - 1.39060i) q^{44} +(-0.133001 - 0.668642i) q^{45} +(1.11009 - 1.94876i) q^{46} +(0.154883 - 0.154883i) q^{47} +(-1.85196 - 3.54546i) q^{48} +(4.01185 + 4.01185i) q^{49} +(-6.18550 + 1.69594i) q^{50} +(-6.20086 + 1.23343i) q^{51} +(0.124946 - 2.31836i) q^{52} +(-4.50589 - 6.74354i) q^{53} +(0.632842 + 1.26472i) q^{54} +(-0.545706 - 1.31745i) q^{55} +(-3.25697 + 0.0567146i) q^{56} +(-1.43509 + 3.46461i) q^{57} +(0.622228 + 8.71779i) q^{58} +(5.69944 + 1.13369i) q^{59} +(-1.17282 + 0.695401i) q^{60} +(9.02079 + 6.02750i) q^{61} +(-5.23027 - 6.73492i) q^{62} +1.15169 q^{63} +(-5.45648 + 5.85037i) q^{64} -0.791408 q^{65} +(1.81437 + 2.33634i) q^{66} +(1.77800 + 1.18802i) q^{67} +(6.44903 + 10.8765i) q^{68} +(1.55540 + 0.309388i) q^{69} +(0.0790513 + 1.10756i) q^{70} +(3.89298 - 9.39848i) q^{71} +(1.96488 - 2.03452i) q^{72} +(-1.36156 - 3.28710i) q^{73} +(-0.660728 - 1.32045i) q^{74} +(-2.51964 - 3.77090i) q^{75} +(7.48926 + 0.403628i) q^{76} +(2.36269 - 0.469969i) q^{77} +(1.58328 - 0.434102i) q^{78} +(-6.41645 - 6.41645i) q^{79} +(2.09143 + 1.74994i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(-4.74878 + 8.33649i) q^{82} +(1.53602 + 7.72209i) q^{83} +(-0.765663 - 2.17239i) q^{84} +(3.58380 - 2.39462i) q^{85} +(4.24290 - 12.7417i) q^{86} +(-5.70966 + 2.36502i) q^{87} +(3.20073 - 4.97564i) q^{88} +(-10.4082 - 4.31121i) q^{89} +(-0.728547 - 0.631476i) q^{90} +(0.260826 - 1.31126i) q^{91} +(-0.450468 - 3.13959i) q^{92} +(3.34993 - 5.01352i) q^{93} +(0.0386495 - 0.307346i) q^{94} -2.55657i q^{95} +(-5.14394 - 2.35370i) q^{96} -12.9952i q^{97} +(7.96101 + 1.00112i) q^{98} +(-1.16209 + 1.73918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{16}\right)$

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 $

$2$	1.11696	−	0.867416i	0.789807	−	0.613356i
$2$	1.11696	−	0.867416i	0.789807	−	0.613356i
$3$	0.831470	+	0.555570i	0.480049	+	0.320759i
$3$	0.831470	+	0.555570i	0.480049	+	0.320759i
$4$	0.495179	−	1.93773i	0.247590	−	0.968865i
$5$	−0.668642	−	0.133001i	−0.299026	−	0.0594799i	0.0432973	−	0.999062i	$-0.486214\pi$
$5$	−0.668642	−	0.133001i	−0.299026	−	0.0594799i	−0.342323	+	0.939582i	$0.611214\pi$
$6$	1.41063	−	0.100683i	0.575885	−	0.0411035i
$7$	0.440731	−	1.06402i	0.166581	−	0.402162i	−0.818441	−	0.574590i	$-0.805161\pi$
$7$	0.440731	−	1.06402i	0.166581	−	0.402162i	0.985022	+	0.172429i	$0.0551614\pi$
$8$	−1.12772	−	2.59388i	−0.398711	−	0.917077i
$9$	0.382683	+	0.923880i	0.127561	+	0.307960i
$10$	−0.862210	+	0.431434i	−0.272655	+	0.136431i
$11$	1.16209	+	1.73918i	0.350382	+	0.524384i	0.964239	−	0.265033i	$-0.0853829\pi$
$11$	1.16209	+	1.73918i	0.350382	+	0.524384i	−0.613857	+	0.789417i	$0.710383\pi$
$12$	1.48827	−	1.33606i	0.429627	−	0.385686i
$13$	1.13856	−	0.226473i	0.315779	−	0.0628123i	−0.0346564	−	0.999399i	$-0.511034\pi$
$13$	1.13856	−	0.226473i	0.315779	−	0.0628123i	0.350435	+	0.936587i	$0.386034\pi$
$14$	−0.430670	−	1.57076i	−0.115101	−	0.419803i
$15$	−0.482064	−	0.482064i	−0.124468	−	0.124468i
$16$	−3.50959	−	1.91905i	−0.877399	−	0.479762i
$17$	−4.47057	+	4.47057i	−1.08427	+	1.08427i	−0.0881675	+	0.996106i	$0.528101\pi$
$17$	−4.47057	+	4.47057i	−1.08427	+	1.08427i	−0.996106	+	0.0881675i	$0.971899\pi$
$18$	1.22883	+	0.699987i	0.289638	+	0.164988i
$19$	0.731601	+	3.67801i	0.167841	+	0.843793i	0.969326	+	0.245778i	$0.0790435\pi$
$19$	0.731601	+	3.67801i	0.167841	+	0.843793i	−0.801485	+	0.598014i	$0.795957\pi$
$20$	−0.588818	+	1.22979i	−0.131664	+	0.274989i
$21$	0.957593	−	0.639843i	0.208964	−	0.139625i
$22$	2.80659	+	0.934580i	0.598368	+	0.199253i
$23$	1.46515	−	0.606887i	0.305506	−	0.126545i	−0.224664	−	0.974436i	$-0.572128\pi$
$23$	1.46515	−	0.606887i	0.305506	−	0.126545i	0.530169	+	0.847892i	$0.322128\pi$
$24$	0.503417	−	2.78327i	0.102759	−	0.568132i
$25$	−4.19001	−	1.73556i	−0.838001	−	0.347111i
$26$	1.07527	−	1.24056i	0.210878	−	0.243294i
$27$	−0.195090	+	0.980785i	−0.0375451	+	0.188752i
$28$	−1.84354	−	1.38090i	−0.348397	−	0.260965i
$29$	−3.43347	+	5.13856i	−0.637580	+	0.954206i	0.362176	+	0.932110i	$0.382034\pi$
$29$	−3.43347	+	5.13856i	−0.637580	+	0.954206i	−0.999756	+	0.0220962i	$0.992966\pi$
$30$	−0.956594	−	0.120294i	−0.174649	−	0.0219626i
$31$		−	6.02971i		−	1.08297i	−0.840711	−	0.541484i	$-0.817863\pi$
$31$		−	6.02971i		−	1.08297i	0.840711	−	0.541484i	$-0.182137\pi$
$32$	−5.58467	+	0.900787i	−0.987240	+	0.159238i
$33$			2.09170i			0.364118i
$34$	−1.11559	+	8.87128i	−0.191321	+	1.52141i
$35$	−0.436207	+	0.652830i	−0.0737325	+	0.110348i
$36$	1.97973	−	0.284051i	0.329954	−	0.0473418i
$37$	0.203687	−	1.02400i	0.0334859	−	0.168345i	−0.960424	−	0.278543i	$-0.910148\pi$
$37$	0.203687	−	1.02400i	0.0334859	−	0.168345i	0.993910	+	0.110198i	$0.0351485\pi$
$38$	4.00753	+	3.47357i	0.650107	+	0.563487i
$39$	1.07250	+	0.444243i	0.171737	+	0.0711358i
$40$	0.409054	+	1.88437i	0.0646771	+	0.297945i
$41$	−6.26769	+	2.59616i	−0.978848	+	0.405452i	−0.813999	−	0.580866i	$-0.802714\pi$
$41$	−6.26769	+	2.59616i	−0.978848	+	0.405452i	−0.164849	+	0.986319i	$0.552714\pi$
$42$	0.514578	−	1.54531i	0.0794012	−	0.238446i
$43$	7.89573	−	5.27576i	1.20409	−	0.804546i	0.218854	−	0.975758i	$-0.429768\pi$
$43$	7.89573	−	5.27576i	1.20409	−	0.804546i	0.985234	+	0.171212i	$0.0547682\pi$
$44$	3.94551	−	1.39060i	0.594808	−	0.209641i
$45$	−0.133001	−	0.668642i	−0.0198266	−	0.0996752i
$46$	1.11009	−	1.94876i	0.163674	−	0.287330i
$47$	0.154883	−	0.154883i	0.0225920	−	0.0225920i	−0.695721	−	0.718313i	$-0.744915\pi$
$47$	0.154883	−	0.154883i	0.0225920	−	0.0225920i	0.718313	+	0.695721i	$0.244915\pi$
$48$	−1.85196	−	3.54546i	−0.267307	−	0.511743i
$49$	4.01185	+	4.01185i	0.573122	+	0.573122i
$50$	−6.18550	+	1.69594i	−0.874762	+	0.239842i
$51$	−6.20086	+	1.23343i	−0.868294	+	0.172715i
$52$	0.124946	−	2.31836i	0.0173269	−	0.321499i
$53$	−4.50589	−	6.74354i	−0.618932	−	0.926297i	−0.999998	−	0.00174951i	$-0.999443\pi$
$53$	−4.50589	−	6.74354i	−0.618932	−	0.926297i	0.381067	−	0.924548i	$-0.375557\pi$
$54$	0.632842	+	1.26472i	0.0861188	+	0.172106i
$55$	−0.545706	−	1.31745i	−0.0735829	−	0.177645i
$56$	−3.25697	+	0.0567146i	−0.435231	+	0.00757880i
$57$	−1.43509	+	3.46461i	−0.190082	+	0.458898i
$58$	0.622228	+	8.71779i	0.0817026	+	1.14470i
$59$	5.69944	+	1.13369i	0.742004	+	0.147594i	0.551596	−	0.834111i	$-0.314019\pi$
$59$	5.69944	+	1.13369i	0.742004	+	0.147594i	0.190408	+	0.981705i	$0.439019\pi$
$60$	−1.17282	+	0.695401i	−0.151410	+	0.0897759i
$61$	9.02079	+	6.02750i	1.15499	+	0.771742i	0.977199	−	0.212325i	$-0.0681037\pi$
$61$	9.02079	+	6.02750i	1.15499	+	0.771742i	0.177795	+	0.984068i	$0.443104\pi$
$62$	−5.23027	−	6.73492i	−0.664245	−	0.855336i
$63$	1.15169			0.145099
$64$	−5.45648	+	5.85037i	−0.682059	+	0.731297i
$65$	−0.791408			−0.0981621
$66$	1.81437	+	2.33634i	0.223334	+	0.287583i
$67$	1.77800	+	1.18802i	0.217217	+	0.145140i	0.659419	−	0.751776i	$-0.270802\pi$
$67$	1.77800	+	1.18802i	0.217217	+	0.145140i	−0.442202	+	0.896916i	$0.645802\pi$
$68$	6.44903	+	10.8765i	0.782059	+	1.31897i
$69$	1.55540	+	0.309388i	0.187248	+	0.0372460i
$70$	0.0790513	+	1.10756i	0.00944843	+	0.132378i
$71$	3.89298	−	9.39848i	0.462011	−	1.11539i	−0.505559	−	0.862792i	$-0.668714\pi$
$71$	3.89298	−	9.39848i	0.462011	−	1.11539i	0.967570	−	0.252602i	$-0.0812863\pi$
$72$	1.96488	−	2.03452i	0.231563	−	0.239770i
$73$	−1.36156	−	3.28710i	−0.159359	−	0.384726i	0.823952	−	0.566660i	$-0.191765\pi$
$73$	−1.36156	−	3.28710i	−0.159359	−	0.384726i	−0.983311	+	0.181933i	$0.941765\pi$
$74$	−0.660728	−	1.32045i	−0.0768080	−	0.153499i
$75$	−2.51964	−	3.77090i	−0.290943	−	0.435427i
$76$	7.48926	+	0.403628i	0.859077	+	0.0462993i
$77$	2.36269	−	0.469969i	0.269254	−	0.0535580i
$78$	1.58328	−	0.434102i	0.179271	−	0.0491523i
$79$	−6.41645	−	6.41645i	−0.721907	−	0.721907i	0.247086	−	0.968994i	$-0.420527\pi$
$79$	−6.41645	−	6.41645i	−0.721907	−	0.721907i	−0.968994	+	0.247086i	$0.920527\pi$
$80$	2.09143	+	1.74994i	0.233829	+	0.195649i
$81$	−0.707107	+	0.707107i	−0.0785674	+	0.0785674i
$82$	−4.74878	+	8.33649i	−0.524415	+	0.920611i
$83$	1.53602	+	7.72209i	0.168600	+	0.847609i	0.968794	+	0.247868i	$0.0797299\pi$
$83$	1.53602	+	7.72209i	0.168600	+	0.847609i	−0.800194	+	0.599741i	$0.795270\pi$
$84$	−0.765663	−	2.17239i	−0.0835406	−	0.237027i
$85$	3.58380	−	2.39462i	0.388718	−	0.259733i
$86$	4.24290	−	12.7417i	0.457524	−	1.37397i
$87$	−5.70966	+	2.36502i	−0.612140	+	0.253557i
$88$	3.20073	−	4.97564i	0.341199	−	0.530405i
$89$	−10.4082	−	4.31121i	−1.10326	−	0.456987i	−0.244651	−	0.969611i	$-0.578674\pi$
$89$	−10.4082	−	4.31121i	−1.10326	−	0.456987i	−0.858613	+	0.512624i	$0.828674\pi$
$90$	−0.728547	−	0.631476i	−0.0767956	−	0.0665634i
$91$	0.260826	−	1.31126i	0.0273420	−	0.137457i
$92$	−0.450468	−	3.13959i	−0.0469646	−	0.327325i
$93$	3.34993	−	5.01352i	0.347372	−	0.519878i
$94$	0.0386495	−	0.307346i	0.00398639	−	0.0317003i
$95$		−	2.55657i		−	0.262299i
$96$	−5.14394	−	2.35370i	−0.525001	−	0.240224i
$97$		−	12.9952i		−	1.31946i	−0.751501	−	0.659731i	$-0.770670\pi$
$97$		−	12.9952i		−	1.31946i	0.751501	−	0.659731i	$-0.229330\pi$
$98$	7.96101	+	1.00112i	0.804183	+	0.101128i
$99$	−1.16209	+	1.73918i	−0.116794	+	0.174795i
$100$	−5.43784	+	7.25969i	−0.543784	+	0.725969i
$101$	1.73740	−	8.73448i	0.172877	−	0.869113i	−0.792823	−	0.609453i	$-0.791389\pi$
$101$	1.73740	−	8.73448i	0.172877	−	0.869113i	0.965700	−	0.259661i	$-0.0836107\pi$
$102$	−5.85619	+	6.75641i	−0.579849	+	0.668984i
$103$	1.79136	+	0.742006i	0.176508	+	0.0731120i	0.469187	−	0.883099i	$-0.344547\pi$
$103$	1.79136	+	0.742006i	0.176508	+	0.0731120i	−0.292679	+	0.956211i	$0.594547\pi$
$104$	−1.87142	−	2.69789i	−0.183508	−	0.264550i
$105$	−0.725386	+	0.300465i	−0.0707904	+	0.0293224i
$106$	−10.8823	−	3.62376i	−1.05699	−	0.351970i
$107$	10.7964	−	7.21394i	1.04373	−	0.697398i	0.0893526	−	0.996000i	$-0.471520\pi$
$107$	10.7964	−	7.21394i	1.04373	−	0.697398i	0.954378	+	0.298602i	$0.0965202\pi$
$108$	1.80389	+	0.863697i	0.173580	+	0.0831093i
$109$	−1.32459	−	6.65919i	−0.126873	−	0.637835i	−0.990923	−	0.134429i	$-0.957080\pi$
$109$	−1.32459	−	6.65919i	−0.126873	−	0.637835i	0.864050	−	0.503406i	$-0.167920\pi$
$110$	−1.75231	−	0.998179i	−0.167076	−	0.0951727i
$111$	0.738266	−	0.738266i	0.0700731	−	0.0700731i
$112$	−3.58869	+	2.88849i	−0.339100	+	0.272937i
$113$	0.344056	+	0.344056i	0.0323661	+	0.0323661i	0.723105	−	0.690739i	$-0.242714\pi$
$113$	0.344056	+	0.344056i	0.0323661	+	0.0323661i	−0.690739	+	0.723105i	$0.742714\pi$
$114$	1.40233	+	5.11463i	0.131340	+	0.479029i
$115$	−1.06038	+	0.210923i	−0.0988809	+	0.0196686i
$116$	8.25695	+	9.19765i	0.766639	+	0.853981i
$117$	0.644941	+	0.965222i	0.0596248	+	0.0892348i
$118$	7.34941	−	3.67751i	0.676568	−	0.338542i
$119$	2.78646	+	6.72710i	0.255434	+	0.616672i
$120$	−0.706783	+	1.79405i	−0.0645202	+	0.163774i
$121$	2.53520	−	6.12051i	0.230473	−	0.556410i
$122$	15.3042	−	1.09233i	1.38557	−	0.0988947i
$123$	−6.65374	−	1.32351i	−0.599948	−	0.119337i
$124$	−11.6840	−	2.98579i	−1.04925	−	0.268132i
$125$	5.40502	+	3.61152i	0.483439	+	0.323024i
$126$	1.28638	−	0.998991i	0.114600	−	0.0889972i
$127$	−18.6929			−1.65873			−0.829364	−	0.558709i	$-0.811297\pi$
$127$	−18.6929			−1.65873			−0.829364	+	0.558709i	$0.811297\pi$
$128$	−1.01993	+	11.2676i	−0.0901502	+	0.995928i
$129$	9.49612			0.836086
$130$	−0.883967	+	0.686480i	−0.0775291	+	0.0602083i
$131$	−5.80567	−	3.87922i	−0.507244	−	0.338929i	0.275472	−	0.961309i	$-0.411166\pi$
$131$	−5.80567	−	3.87922i	−0.507244	−	0.338929i	−0.782715	+	0.622380i	$0.786166\pi$
$132$	4.05315	+	1.03577i	0.352781	+	0.0901519i
$133$	4.23591	+	0.842575i	0.367300	+	0.0730605i
$134$	3.01645	−	0.215298i	0.260582	−	0.0185989i
$135$	0.260891	−	0.629847i	0.0224539	−	0.0542086i
$136$	16.6377	+	6.55458i	1.42667	+	0.562050i
$137$	4.83221	+	11.6660i	0.412843	+	0.996692i	0.984371	+	0.176109i	$0.0563511\pi$
$137$	4.83221	+	11.6660i	0.412843	+	0.996692i	−0.571527	+	0.820583i	$0.693649\pi$
$138$	2.00568	−	1.00361i	0.170735	−	0.0854326i
$139$	8.23383	+	12.3228i	0.698384	+	1.04521i	0.995898	+	0.0904879i	$0.0288426\pi$
$139$	8.23383	+	12.3228i	0.698384	+	1.04521i	−0.297514	+	0.954718i	$0.596157\pi$
$140$	1.04901	+	1.16852i	0.0886574	+	0.0987580i
$141$	0.214829	−	0.0427321i	0.0180919	−	0.00359870i
$142$	−3.80411	−	13.8745i	−0.319234	−	1.16432i
$143$	1.71698	+	1.71698i	0.143581	+	0.143581i
$144$	0.429905	−	3.97683i	0.0358254	−	0.331403i
$145$	2.97920	−	2.97920i	0.247409	−	0.247409i
$146$	−4.37209	−	2.49051i	−0.361837	−	0.206116i
$147$	1.10687	+	5.56460i	0.0912929	+	0.458961i
$148$	−1.88338	−	0.901756i	−0.154813	−	0.0741239i
$149$	18.8895	−	12.6215i	1.54748	−	1.03400i	0.570343	−	0.821406i	$-0.306810\pi$
$149$	18.8895	−	12.6215i	1.54748	−	1.03400i	0.977142	−	0.212590i	$-0.0681898\pi$
$150$	−6.08527	−	2.02636i	−0.496860	−	0.165452i
$151$	−17.0280	+	7.05323i	−1.38572	+	0.573984i	−0.946004	−	0.324154i	$-0.894921\pi$
$151$	−17.0280	+	7.05323i	−1.38572	+	0.573984i	−0.439715	+	0.898137i	$0.644921\pi$
$152$	8.71528	−	6.04547i	0.706903	−	0.490352i
$153$	−5.84108	−	2.41946i	−0.472224	−	0.195601i
$154$	2.23137	−	2.57437i	0.179809	−	0.207449i
$155$	−0.801959	+	4.03172i	−0.0644149	+	0.323835i
$156$	1.39190	−	1.85823i	0.111441	−	0.148777i
$157$	−11.9907	+	17.9454i	−0.956964	+	1.43220i	−0.0559374	+	0.998434i	$0.517815\pi$
$157$	−11.9907	+	17.9454i	−0.956964	+	1.43220i	−0.901027	+	0.433764i	$0.857185\pi$
$158$	−12.7326	−	1.60116i	−1.01295	−	0.127381i
$159$		−	8.11039i		−	0.643196i
$160$	3.85395	+	0.140464i	0.304682	+	0.0111047i
$161$		−	1.82643i		−	0.143943i
$162$	−0.176451	+	1.40316i	−0.0138633	+	0.110243i
$163$	1.37702	−	2.06085i	0.107856	−	0.161418i	−0.773615	−	0.633656i	$-0.781554\pi$
$163$	1.37702	−	2.06085i	0.107856	−	0.161418i	0.881471	+	0.472238i	$0.156554\pi$
$164$	1.92703	+	13.4307i	0.150476	+	1.04876i
$165$	0.278198	−	1.39860i	0.0216577	−	0.108881i
$166$	8.41393	+	7.29286i	0.653047	+	0.566036i
$167$	23.4325	+	9.70606i	1.81326	+	0.751078i	0.980233	+	0.197849i	$0.0633956\pi$
$167$	23.4325	+	9.70606i	1.81326	+	0.751078i	0.833029	+	0.553229i	$0.186604\pi$
$168$	−2.73958	−	1.76232i	−0.211363	−	0.135966i
$169$	−10.7654	+	4.45918i	−0.828109	+	0.343014i
$170$	1.92582	−	5.78333i	0.147703	−	0.443561i
$171$	−3.11806	+	2.08342i	−0.238444	+	0.159323i
$172$	−6.31319	−	17.9122i	−0.481377	−	1.36580i
$173$	1.07935	+	5.42627i	0.0820616	+	0.412552i	0.999879	+	0.0155491i	$0.00494963\pi$
$173$	1.07935	+	5.42627i	0.0820616	+	0.412552i	−0.917817	+	0.397003i	$0.870050\pi$
$174$	−4.32598	+	7.59427i	−0.327952	+	0.575720i
$175$	−3.69333	+	3.69333i	−0.279190	+	0.279190i
$176$	−0.740872	−	8.33393i	−0.0558454	−	0.628194i
$177$	4.10907	+	4.10907i	0.308857	+	0.308857i
$178$	−15.3651	+	4.21279i	−1.15166	+	0.315762i
$179$	−23.0535	+	4.58562i	−1.72310	+	0.342746i	−0.954778	−	0.297320i	$-0.903907\pi$
$179$	−23.0535	+	4.58562i	−1.72310	+	0.342746i	−0.768320	+	0.640066i	$0.778907\pi$
$180$	−1.36151	−	0.0733774i	−0.101481	−	0.00546923i
$181$	3.93657	+	5.89150i	0.292603	+	0.437912i	0.948424	−	0.317005i	$-0.102677\pi$
$181$	3.93657	+	5.89150i	0.292603	+	0.437912i	−0.655821	+	0.754917i	$0.727677\pi$
$182$	−0.846077	−	1.69086i	−0.0627154	−	0.125335i
$183$	4.15181	+	10.0234i	0.306911	+	0.740948i
$184$	−3.22648	−	3.11604i	−0.237860	−	0.229718i
$185$	−0.272387	+	0.657601i	−0.0200263	+	0.0483478i
$186$	−0.607088	−	8.50567i	−0.0445138	−	0.623666i
$187$	−12.9703	−	2.57996i	−0.948485	−	0.188665i
$188$	−0.223427	−	0.376816i	−0.0162951	−	0.0274822i
$189$	0.957593	+	0.639843i	0.0696546	+	0.0465417i
$190$	−2.21761	−	2.85558i	−0.160882	−	0.207165i
$191$	−5.06823			−0.366724			−0.183362	−	0.983045i	$-0.558698\pi$
$191$	−5.06823			−0.366724			−0.183362	+	0.983045i	$0.558698\pi$
$192$	−7.78719	+	1.83295i	−0.561992	+	0.132282i
$193$	12.4982			0.899642			0.449821	−	0.893119i	$-0.351488\pi$
$193$	12.4982			0.899642			0.449821	+	0.893119i	$0.351488\pi$
$194$	−11.2722	−	14.5151i	−0.809300	−	1.04212i
$195$	−0.658032	−	0.439683i	−0.0471226	−	0.0314863i
$196$	9.76048	−	5.78730i	0.697177	−	0.413379i
$197$	−23.9310	−	4.76017i	−1.70501	−	0.339148i	−0.756044	−	0.654520i	$-0.772871\pi$
$197$	−23.9310	−	4.76017i	−1.70501	−	0.339148i	−0.948968	+	0.315372i	$0.897871\pi$
$198$	0.210598	+	2.95060i	0.0149665	+	0.209690i
$199$	−7.19400	+	17.3679i	−0.509969	+	1.23117i	0.433932	+	0.900946i	$0.357126\pi$
$199$	−7.19400	+	17.3679i	−0.509969	+	1.23117i	−0.943901	+	0.330229i	$0.892874\pi$
$200$	0.223336	+	12.8256i	0.0157923	+	0.906908i
$201$	0.818323	+	1.97561i	0.0577200	+	0.139348i
$202$	−5.63583	−	11.2631i	−0.396536	−	0.792467i
$203$	3.95429	+	5.91801i	0.277537	+	0.415363i
$204$	−0.680488	+	12.6264i	−0.0476437	+	0.884022i
$205$	4.53613	−	0.902292i	0.316817	−	0.0630188i
$206$	2.64450	−	0.725067i	0.184251	−	0.0505178i
$207$	1.12138	+	1.12138i	0.0779413	+	0.0779413i
$208$	−4.43049	−	1.39012i	−0.307199	−	0.0963872i
$209$	−5.54655	+	5.54655i	−0.383663	+	0.383663i
$210$	−0.549596	+	0.964817i	−0.0379257	+	0.0665787i
$211$	3.77623	+	18.9844i	0.259966	+	1.30694i	0.861363	+	0.507989i	$0.169611\pi$
$211$	3.77623	+	18.9844i	0.259966	+	1.30694i	−0.601397	+	0.798950i	$0.705389\pi$
$212$	−15.2984	+	5.39194i	−1.05070	+	0.370320i
$213$	8.45841	−	5.65173i	0.579560	−	0.387250i
$214$	5.80164	−	17.4227i	0.396592	−	1.19099i
$215$	−5.98110	+	2.47745i	−0.407908	+	0.168961i
$216$	2.76405	−	0.600014i	0.188070	−	0.0408258i
$217$	−6.41574	−	2.65748i	−0.435529	−	0.180402i
$218$	−7.25580	−	6.28904i	−0.491425	−	0.425948i
$219$	0.694118	−	3.48957i	0.0469042	−	0.235803i
$220$	−2.82308	+	0.405056i	−0.190332	+	0.0273089i
$221$	−4.07754	+	6.10247i	−0.274285	+	0.410496i
$222$	0.184227	−	1.46499i	0.0123645	−	0.0983239i
$223$		−	17.2703i		−	1.15651i	−0.815857	−	0.578254i	$-0.803734\pi$
$223$		−	17.2703i		−	1.15651i	0.815857	−	0.578254i	$-0.196266\pi$
$224$	−1.50289	+	6.33921i	−0.100416	+	0.423556i
$225$		−	4.53523i		−	0.302349i
$226$	0.682735	+	0.0858556i	0.0454148	+	0.00571103i
$227$	5.86944	−	8.78423i	0.389568	−	0.583030i	−0.583908	−	0.811820i	$-0.698477\pi$
$227$	5.86944	−	8.78423i	0.389568	−	0.583030i	0.973476	+	0.228790i	$0.0734770\pi$
$228$	6.00285	+	4.49641i	0.397548	+	0.297782i
$229$	−2.52966	+	12.7175i	−0.167165	+	0.840393i	0.802631	+	0.596475i	$0.203433\pi$
$229$	−2.52966	+	12.7175i	−0.167165	+	0.840393i	−0.969796	+	0.243918i	$0.921567\pi$
$230$	−1.00144	+	1.15538i	−0.0660330	+	0.0761836i
$231$	2.22561	+	0.921878i	0.146434	+	0.0606551i
$232$	17.2008	+	3.11116i	1.12929	+	0.204258i
$233$	25.2224	−	10.4475i	1.65237	−	0.684436i	0.654917	−	0.755701i	$-0.272704\pi$
$233$	25.2224	−	10.4475i	1.65237	−	0.684436i	0.997457	+	0.0712652i	$0.0227037\pi$
$234$	1.55762	+	0.518678i	0.101825	+	0.0339071i
$235$	−0.124161	+	0.0829617i	−0.00809936	+	0.00541182i
$236$	5.01903	−	10.4826i	0.326711	−	0.682359i
$237$	−1.77030	−	8.89988i	−0.114993	−	0.578109i
$238$	8.94754	+	5.09686i	0.579983	+	0.330380i
$239$	−4.88796	+	4.88796i	−0.316176	+	0.316176i	−0.847296	−	0.531121i	$-0.821771\pi$
$239$	−4.88796	+	4.88796i	−0.316176	+	0.316176i	0.531121	+	0.847296i	$0.321771\pi$
$240$	0.766745	+	2.61695i	0.0494932	+	0.168924i
$241$	13.5225	+	13.5225i	0.871063	+	0.871063i	0.992588	−	0.121525i	$-0.0387785\pi$
$241$	13.5225	+	13.5225i	0.871063	+	0.871063i	−0.121525	+	0.992588i	$0.538778\pi$
$242$	−2.47732	−	9.03541i	−0.159248	−	0.580818i
$243$	−0.980785	+	0.195090i	−0.0629174	+	0.0125150i
$244$	16.1466	−	14.4952i	1.03368	−	0.927958i
$245$	−2.14891	−	3.21607i	−0.137289	−	0.205467i
$246$	−8.57997	+	4.29326i	−0.547039	+	0.273728i
$247$	1.66594	+	4.02193i	0.106001	+	0.255909i
$248$	−15.6404	+	6.79986i	−0.993165	+	0.431791i
$249$	−3.01301	+	7.27405i	−0.190942	+	0.460974i
$250$	9.16985	−	0.654494i	0.579952	−	0.0413938i
$251$	−7.53300	−	1.49841i	−0.475479	−	0.0945786i	−0.0484672	−	0.998825i	$-0.515434\pi$
$251$	−7.53300	−	1.49841i	−0.475479	−	0.0945786i	−0.427012	+	0.904246i	$0.640434\pi$
$252$	0.570292	−	2.23166i	0.0359250	−	0.140581i
$253$	2.75812	+	1.84292i	0.173402	+	0.115863i
$254$	−20.8792	+	16.2145i	−1.31007	+	1.01739i
$255$	4.31020			0.269915
$256$	8.63451	+	13.4702i	0.539657	+	0.841885i
$257$	3.71961			0.232023			0.116011	−	0.993248i	$-0.462989\pi$
$257$	3.71961			0.232023			0.116011	+	0.993248i	$0.462989\pi$
$258$	10.6067	−	8.23708i	0.660347	−	0.512818i
$259$	−0.999789	−	0.668038i	−0.0621239	−	0.0415098i
$260$	−0.391889	+	1.53353i	−0.0243039	+	0.0951058i
$261$	−6.06134	−	1.20568i	−0.375188	−	0.0746295i
$262$	−9.84958	+	0.703009i	−0.608509	+	0.0434320i
$263$	11.3655	−	27.4387i	0.700826	−	1.69194i	−0.0209159	−	0.999781i	$-0.506658\pi$
$263$	11.3655	−	27.4387i	0.700826	−	1.69194i	0.721742	−	0.692162i	$-0.243342\pi$
$264$	5.42563	−	2.35886i	0.333924	−	0.145178i
$265$	2.11593	+	5.10830i	0.129980	+	0.313801i
$266$	5.46219	−	2.73318i	0.334908	−	0.167582i
$267$	−6.25890	−	9.36711i	−0.383039	−	0.573258i
$268$	3.18249	−	2.85700i	0.194402	−	0.174519i
$269$	−17.8570	+	3.55197i	−1.08876	+	0.216568i	−0.706659	−	0.707554i	$-0.749799\pi$
$269$	−17.8570	+	3.55197i	−1.08876	+	0.216568i	−0.382099	+	0.924121i	$0.624799\pi$
$270$	−0.254935	−	0.929812i	−0.0155149	−	0.0565866i
$271$	18.6968	+	18.6968i	1.13575	+	1.13575i	0.989204	+	0.146544i	$0.0468151\pi$
$271$	18.6968	+	18.6968i	1.13575	+	1.13575i	0.146544	+	0.989204i	$0.453185\pi$
$272$	24.2691	−	7.11066i	1.47153	−	0.431147i
$273$	0.945366	−	0.945366i	0.0572162	−	0.0572162i
$274$	15.5166	+	8.83885i	0.937393	+	0.533974i
$275$	−1.85069	−	9.30406i	−0.111601	−	0.561056i
$276$	1.36971	−	2.86074i	0.0824470	−	0.172196i
$277$	−15.6474	+	10.4552i	−0.940158	+	0.628194i	−0.928338	−	0.371736i	$-0.878763\pi$
$277$	−15.6474	+	10.4552i	−0.940158	+	0.628194i	−0.0118201	+	0.999930i	$0.503763\pi$
$278$	19.8858	+	6.62186i	1.19267	+	0.397153i
$279$	5.57073	−	2.30747i	0.333511	−	0.138145i
$280$	2.18529	+	0.395259i	0.130596	+	0.0236212i
$281$	2.97902	+	1.23395i	0.177714	+	0.0736114i	0.469766	−	0.882791i	$-0.344338\pi$
$281$	2.97902	+	1.23395i	0.177714	+	0.0736114i	−0.292053	+	0.956402i	$0.594338\pi$
$282$	0.202888	−	0.234076i	0.0120818	−	0.0139390i
$283$	3.89011	−	19.5569i	0.231243	−	1.16254i	−0.674357	−	0.738405i	$-0.735579\pi$
$283$	3.89011	−	19.5569i	0.231243	−	1.16254i	0.905600	−	0.424132i	$-0.139421\pi$
$284$	−16.2840	−	12.1975i	−0.966277	−	0.723787i
$285$	1.42036	−	2.12571i	0.0841346	−	0.125916i
$286$	3.40712	+	0.428454i	0.201468	+	0.0253350i
$287$			7.81315i			0.461196i
$288$	−2.96938	−	4.81485i	−0.174972	−	0.283718i
$289$		−	22.9720i		−	1.35130i
$290$	0.743428	−	5.91184i	0.0436556	−	0.347155i
$291$	7.21975	−	10.8051i	0.423229	−	0.633407i
$292$	−7.04373	+	1.01063i	−0.412203	+	0.0591429i
$293$	0.866994	−	4.35867i	0.0506503	−	0.254636i	−0.947161	−	0.320758i	$-0.896062\pi$
$293$	0.866994	−	4.35867i	0.0506503	−	0.254636i	0.997812	+	0.0661214i	$0.0210625\pi$
$294$	6.06315	+	5.25530i	0.353610	+	0.306495i
$295$	−3.66010	−	1.51607i	−0.213100	−	0.0882687i
$296$	−2.88585	+	0.626453i	−0.167737	+	0.0364119i
$297$	−1.93248	+	0.800459i	−0.112134	+	0.0464473i
$298$	10.1506	−	30.4827i	0.588007	−	1.76582i
$299$	1.53072	−	1.02279i	0.0885237	−	0.0591497i
$300$	−8.55467	+	3.01510i	−0.493904	+	0.174077i
$301$	−2.13362	−	10.7264i	−0.122980	−	0.618260i
$302$	−12.9014	+	22.6485i	−0.742394	+	1.30328i
$303$	6.29721	−	6.29721i	0.361765	−	0.361765i
$304$	4.49065	−	14.3123i	0.257556	−	0.820866i
$305$	−5.23001	−	5.23001i	−0.299470	−	0.299470i
$306$	−8.62291	+	2.36422i	−0.492939	+	0.135154i
$307$	23.6281	−	4.69992i	1.34853	−	0.268238i	0.532586	−	0.846376i	$-0.321220\pi$
$307$	23.6281	−	4.69992i	1.34853	−	0.268238i	0.815939	+	0.578137i	$0.196220\pi$
$308$	0.259284	−	4.81098i	0.0147741	−	0.274131i
$309$	1.07723	+	1.61218i	0.0612812	+	0.0917138i
$310$	2.60142	+	5.19888i	0.147751	+	0.295277i
$311$	5.97793	+	14.4320i	0.338977	+	0.818364i	0.997814	+	0.0660782i	$0.0210487\pi$
$311$	5.97793	+	14.4320i	0.338977	+	0.818364i	−0.658837	+	0.752286i	$0.728951\pi$
$312$	−0.0571664	−	3.28292i	−0.00323641	−	0.185859i
$313$	6.58613	−	15.9003i	0.372270	−	0.898740i	−0.621095	−	0.783736i	$-0.713312\pi$
$313$	6.58613	−	15.9003i	0.372270	−	0.898740i	0.993365	−	0.115004i	$-0.0366882\pi$
$314$	2.17301	+	30.4451i	0.122630	+	1.71812i
$315$	−0.770066	−	0.153176i	−0.0433883	−	0.00863047i
$316$	−15.6107	+	9.25606i	−0.878168	+	0.520694i
$317$	2.25812	+	1.50882i	0.126828	+	0.0847441i	0.617366	−	0.786676i	$-0.288200\pi$
$317$	2.25812	+	1.50882i	0.126828	+	0.0847441i	−0.490538	+	0.871420i	$0.663200\pi$
$318$	−7.03508	−	9.05895i	−0.394508	−	0.508001i
$319$	−12.9269			−0.723767
$320$	4.42653	−	3.18609i	0.247451	−	0.178108i
$321$	12.9848			0.724738
$322$	−1.58427	−	2.04004i	−0.0882880	−	0.113687i
$323$	−19.7135	−	13.1721i	−1.09689	−	0.732916i
$324$	1.02004	+	1.72033i	0.0566687	+	0.0955737i
$325$	−5.16362	−	1.02711i	−0.286426	−	0.0569737i
$326$	−0.249548	−	3.49632i	−0.0138212	−	0.193643i
$327$	2.59829	−	6.27282i	0.143686	−	0.346888i
$328$	13.8024	+	13.3299i	0.762108	+	0.736021i
$329$	−0.0965368	−	0.233060i	−0.00532225	−	0.0128490i
$330$	−0.902430	−	1.80348i	−0.0496772	−	0.0992786i
$331$	−2.90458	−	4.34702i	−0.159650	−	0.238934i	0.743017	−	0.669272i	$-0.233394\pi$
$331$	−2.90458	−	4.34702i	−0.159650	−	0.238934i	−0.902667	+	0.430339i	$0.858394\pi$
$332$	15.7239	+	0.847429i	0.862962	+	0.0465087i
$333$	1.02400	−	0.203687i	0.0561151	−	0.0111620i
$334$	34.5923	−	9.48449i	1.89280	−	0.518968i
$335$	−1.03084	−	1.03084i	−0.0563206	−	0.0563206i
$336$	−4.58865	+	0.407923i	−0.250331	+	0.0222540i
$337$	3.47075	−	3.47075i	0.189064	−	0.189064i	−0.606228	−	0.795291i	$-0.707318\pi$
$337$	3.47075	−	3.47075i	0.189064	−	0.189064i	0.795291	+	0.606228i	$0.207318\pi$
$338$	−8.15652	+	14.3188i	−0.443656	+	0.778840i
$339$	0.0949248	+	0.477219i	0.00515561	+	0.0259190i
$340$	−2.86550	−	8.13021i	−0.155404	−	0.440922i
$341$	10.4868	−	7.00705i	0.567891	−	0.379453i
$342$	−1.67554	+	5.03175i	−0.0906030	+	0.272086i
$343$	13.4850	−	5.58566i	0.728120	−	0.301597i
$344$	−22.5889	−	14.5310i	−1.21791	−	0.783460i
$345$	−0.998856	−	0.413740i	−0.0537766	−	0.0222750i
$346$	5.91242	+	5.12466i	0.317854	+	0.275503i
$347$	0.825800	−	4.15158i	0.0443313	−	0.222868i	−0.952269	−	0.305261i	$-0.901256\pi$
$347$	0.825800	−	4.15158i	0.0443313	−	0.222868i	0.996600	+	0.0823928i	$0.0262562\pi$
$348$	1.75546	+	12.2349i	0.0941026	+	0.655859i
$349$	−15.6757	+	23.4603i	−0.839100	+	1.25580i	0.125502	+	0.992093i	$0.459946\pi$
$349$	−15.6757	+	23.4603i	−0.839100	+	1.25580i	−0.964602	+	0.263709i	$0.915054\pi$
$350$	−0.921633	+	7.32895i	−0.0492634	+	0.391749i
$351$			1.16086i			0.0619623i
$352$	−8.05651	−	8.66599i	−0.429413	−	0.461899i
$353$			3.15845i			0.168107i	0.996461	+	0.0840536i	$0.0267867\pi$
$353$			3.15845i			0.168107i	−0.996461	+	0.0840536i	$0.973213\pi$
$354$	8.15392	+	1.02538i	0.433376	+	0.0544981i
$355$	−3.85302	+	5.76644i	−0.204497	+	0.306051i
$356$	−13.5079	+	18.0334i	−0.715916	+	0.955769i
$357$	−1.42052	+	7.14145i	−0.0751820	+	0.377966i
$358$	−21.7721	+	25.1189i	−1.15069	+	1.32757i
$359$	1.03697	+	0.429528i	0.0547293	+	0.0226696i	0.409880	−	0.912139i	$-0.365571\pi$
$359$	1.03697	+	0.429528i	0.0547293	+	0.0226696i	−0.355151	+	0.934809i	$0.615571\pi$
$360$	−1.58439	+	1.09903i	−0.0835047	+	0.0579241i
$361$	4.56122	−	1.88932i	0.240064	−	0.0994378i
$362$	9.50736	+	3.16590i	0.499695	+	0.166396i
$363$	5.50832	−	3.68054i	0.289112	−	0.193178i
$364$	−2.41171	−	1.15472i	−0.126408	−	0.0605238i
$365$	0.473209	+	2.37898i	0.0247689	+	0.124522i
$366$	13.3318	+	7.59430i	0.696865	+	0.396961i
$367$	12.6171	−	12.6171i	0.658609	−	0.658609i	−0.296442	−	0.955051i	$-0.595800\pi$
$367$	12.6171	−	12.6171i	0.658609	−	0.658609i	0.955051	+	0.296442i	$0.0958000\pi$
$368$	−6.30674	−	0.681775i	−0.328762	−	0.0355400i
$369$	−4.79708	−	4.79708i	−0.249726	−	0.249726i
$370$	0.266169	+	0.970784i	0.0138375	+	0.0504687i
$371$	−9.16115	+	1.82227i	−0.475623	+	0.0946074i
$372$	−8.05604	−	8.97385i	−0.417686	−	0.465273i
$373$	2.62282	+	3.92533i	0.135804	+	0.203246i	0.893138	−	0.449782i	$-0.148498\pi$
$373$	2.62282	+	3.92533i	0.135804	+	0.203246i	−0.757334	+	0.653028i	$0.773498\pi$
$374$	−16.7252	+	8.36898i	−0.864839	+	0.432749i
$375$	2.48766	+	6.00573i	0.128462	+	0.310135i
$376$	−0.576414	−	0.227083i	−0.0297263	−	0.0117109i
$377$	−2.74546	+	6.62813i	−0.141398	+	0.341366i
$378$	1.62460	−	0.115955i	0.0835603	−	0.00596408i
$379$	−5.45195	−	1.08446i	−0.280048	−	0.0557049i	0.0530681	−	0.998591i	$-0.483100\pi$
$379$	−5.45195	−	1.08446i	−0.280048	−	0.0557049i	−0.333116	+	0.942886i	$0.608100\pi$
$380$	−4.95395	−	1.26596i	−0.254132	−	0.0649425i
$381$	−15.5426	−	10.3852i	−0.796271	−	0.532051i
$382$	−5.66098	+	4.39626i	−0.289641	+	0.224932i
$383$	−1.01686			−0.0519591			−0.0259796	−	0.999662i	$-0.508270\pi$
$383$	−1.01686			−0.0519591			−0.0259796	+	0.999662i	$0.508270\pi$
$384$	−7.10801	+	8.80206i	−0.362729	+	0.449178i
$385$	−1.64230			−0.0836995
$386$	13.9600	−	10.8412i	0.710544	−	0.551801i
$387$	7.89573	+	5.27576i	0.401363	+	0.268182i
$388$	−25.1812	−	6.43496i	−1.27838	−	0.326685i
$389$	−13.7375	−	2.73255i	−0.696516	−	0.138546i	−0.165881	−	0.986146i	$-0.553047\pi$
$389$	−13.7375	−	2.73255i	−0.696516	−	0.138546i	−0.530636	+	0.847600i	$0.678047\pi$
$390$	−1.11638	+	0.0796811i	−0.0565301	+	0.00403481i
$391$	−3.83695	+	9.26321i	−0.194043	+	0.468461i
$392$	5.88202	−	14.9306i	0.297087	−	0.754107i
$393$	−2.67206	−	6.45091i	−0.134787	−	0.325406i
$394$	−30.8589	+	15.4412i	−1.55465	+	0.777918i
$395$	3.43691	+	5.14370i	0.172930	+	0.258808i
$396$	2.79463	+	3.11302i	0.140435	+	0.156435i
$397$	−27.7166	+	5.51318i	−1.39106	+	0.276698i	−0.833077	−	0.553157i	$-0.813423\pi$
$397$	−27.7166	+	5.51318i	−1.39106	+	0.276698i	−0.557979	+	0.829855i	$0.688423\pi$
$398$	7.02977	+	25.6393i	0.352371	+	1.28518i
$399$	3.05392	+	3.05392i	0.152887	+	0.152887i
$400$	11.3746	+	14.1319i	0.568730	+	0.706596i
$401$	−10.1050	+	10.1050i	−0.504619	+	0.504619i	−0.912870	−	0.408251i	$-0.866139\pi$
$401$	−10.1050	+	10.1050i	−0.504619	+	0.504619i	0.408251	+	0.912870i	$0.366139\pi$
$402$	2.62770	+	1.49684i	0.131058	+	0.0746555i
$403$	−1.36557	−	6.86517i	−0.0680238	−	0.341979i
$404$	−16.0647	−	7.69174i	−0.799251	−	0.382678i
$405$	0.566847	−	0.378755i	0.0281669	−	0.0188205i
$406$	9.55014	+	3.18014i	0.473965	+	0.157828i
$407$	2.01763	−	0.835731i	0.100010	−	0.0414256i
$408$	10.1922	+	14.6934i	0.504591	+	0.727429i
$409$	−26.1539	−	10.8333i	−1.29323	−	0.535673i	−0.373282	−	0.927718i	$-0.621768\pi$
$409$	−26.1539	−	10.8333i	−1.29323	−	0.535673i	−0.919946	+	0.392045i	$0.871768\pi$
$410$	4.28399	−	4.94253i	0.211571	−	0.244094i
$411$	−2.46344	+	12.3845i	−0.121512	+	0.610884i
$412$	2.32485	−	3.10375i	0.114537	−	0.152911i
$413$	3.71819	−	5.56467i	0.182960	−	0.273819i
$414$	2.22524	+	0.279829i	0.109364	+	0.0137528i
$415$		−	5.36760i		−	0.263485i
$416$	−6.15447	+	2.29038i	−0.301747	+	0.112295i
$417$			14.8205i			0.725763i
$418$	−1.38408	+	11.0064i	−0.0676978	+	0.538341i
$419$	10.2513	−	15.3421i	0.500807	−	0.749511i	−0.491823	−	0.870695i	$-0.663669\pi$
$419$	10.2513	−	15.3421i	0.500807	−	0.749511i	0.992630	+	0.121185i	$0.0386693\pi$
$420$	0.223023	+	1.55439i	0.0108824	+	0.0758463i
$421$	−3.15120	+	15.8421i	−0.153580	+	0.772098i	0.824823	+	0.565391i	$0.191275\pi$
$421$	−3.15120	+	15.8421i	−0.153580	+	0.772098i	−0.978403	+	0.206707i	$0.933725\pi$
$422$	20.6852	+	17.9292i	1.00694	+	0.872778i
$423$	0.202364	+	0.0838221i	0.00983930	+	0.00407557i
$424$	−12.4106	+	19.2926i	−0.602711	+	0.936933i
$425$	26.4907	−	10.9728i	1.28499	−	0.532258i
$426$	4.54527	−	13.6497i	0.220219	−	0.661329i
$427$	10.3891	−	6.94179i	0.502765	−	0.335937i
$428$	−8.63251	−	24.4928i	−0.417268	−	1.18390i
$429$	0.473714	+	2.38152i	0.0228711	+	0.114981i
$430$	−4.53164	+	7.95530i	−0.218535	+	0.383639i
$431$	−22.1443	+	22.1443i	−1.06665	+	1.06665i	−0.0690385	+	0.997614i	$0.521993\pi$
$431$	−22.1443	+	22.1443i	−1.06665	+	1.06665i	−0.997614	+	0.0690385i	$0.978007\pi$
$432$	2.56686	−	3.06777i	0.123498	−	0.147598i
$433$	−10.4560	−	10.4560i	−0.502484	−	0.502484i	0.409725	−	0.912209i	$-0.365625\pi$
$433$	−10.4560	−	10.4560i	−0.502484	−	0.502484i	−0.912209	+	0.409725i	$0.865625\pi$
$434$	−9.47124	+	2.59682i	−0.454634	+	0.124651i
$435$	4.13227	−	0.821959i	0.198127	−	0.0394099i
$436$	−13.5596	−	0.730785i	−0.649388	−	0.0349983i
$437$	3.30404	+	4.94485i	0.158054	+	0.236544i
$438$	−2.25161	−	4.49978i	−0.107586	−	0.215008i
$439$	−7.07243	−	17.0744i	−0.337549	−	0.814915i	−0.997950	−	0.0640017i	$-0.979614\pi$
$439$	−7.07243	−	17.0744i	−0.337549	−	0.814915i	0.660401	−	0.750913i	$-0.270386\pi$
$440$	−2.80191	+	2.90122i	−0.133576	+	0.138310i
$441$	−2.17120	+	5.24174i	−0.103390	+	0.249607i
$442$	0.738948	+	10.3531i	0.0351482	+	0.492447i
$443$	−3.44920	−	0.686089i	−0.163877	−	0.0325971i	0.112470	−	0.993655i	$-0.464124\pi$
$443$	−3.44920	−	0.686089i	−0.163877	−	0.0325971i	−0.276347	+	0.961058i	$0.589124\pi$
$444$	−1.06499	−	1.79613i	−0.0505420	−	0.0852407i
$445$	6.38595	+	4.26695i	0.302723	+	0.202273i
$446$	−14.9806	−	19.2902i	−0.709351	−	0.913418i
$447$	22.7182			1.07453
$448$	3.82007	+	8.38424i	0.180482	+	0.396118i
$449$	−5.30318			−0.250273			−0.125136	−	0.992140i	$-0.539937\pi$
$449$	−5.30318			−0.250273			−0.125136	+	0.992140i	$0.539937\pi$
$450$	−3.93393	−	5.06565i	−0.185447	−	0.238797i
$451$	−11.7988	−	7.88370i	−0.555583	−	0.371229i
$452$	0.837057	−	0.496318i	0.0393718	−	0.0233448i
$453$	−18.0768	−	3.59571i	−0.849324	−	0.168941i
$454$	−1.06368	−	14.9028i	−0.0499211	−	0.699425i
$455$	−0.348798	+	0.842074i	−0.0163519	+	0.0394770i
$456$	10.6052	−	0.184671i	0.496633	−	0.00864801i
$457$	7.47433	+	18.0446i	0.349635	+	0.844092i	0.996663	+	0.0816266i	$0.0260115\pi$
$457$	7.47433	+	18.0446i	0.349635	+	0.844092i	−0.647028	+	0.762466i	$0.723989\pi$
$458$	8.20580	+	16.3991i	0.383432	+	0.766279i
$459$	−3.51251	−	5.25684i	−0.163950	−	0.245368i
$460$	−0.116367	+	2.15917i	−0.00542564	+	0.100672i
$461$	20.1285	−	4.00381i	0.937478	−	0.186476i	0.297371	−	0.954762i	$-0.403890\pi$
$461$	20.1285	−	4.00381i	0.937478	−	0.186476i	0.640107	+	0.768286i	$0.278890\pi$
$462$	3.28556	−	0.900833i	0.152858	−	0.0419105i
$463$	28.0958	+	28.0958i	1.30572	+	1.30572i	0.924472	+	0.381250i	$0.124506\pi$
$463$	28.0958	+	28.0958i	1.30572	+	1.30572i	0.381250	+	0.924472i	$0.375494\pi$
$464$	21.9112	−	11.4453i	1.01720	−	0.531332i
$465$	−2.90671	+	2.90671i	−0.134795	+	0.134795i
$466$	19.1100	−	33.5477i	0.885254	−	1.55407i
$467$	−1.15407	−	5.80190i	−0.0534040	−	0.268480i	0.944853	−	0.327494i	$-0.106204\pi$
$467$	−1.15407	−	5.80190i	−0.0534040	−	0.268480i	−0.998257	+	0.0590143i	$0.981204\pi$
$468$	2.18970	−	0.771763i	0.101219	−	0.0356748i
$469$	2.04770	−	1.36823i	0.0945538	−	0.0631789i
$470$	−0.0667200	+	0.200364i	−0.00307756	+	0.00924209i
$471$	−19.9398	+	8.25936i	−0.918780	+	0.380571i
$472$	−3.48674	−	16.0622i	−0.160490	−	0.739322i
$473$	18.3510	+	7.60125i	0.843782	+	0.349506i
$474$	−9.69724	−	8.40518i	−0.445409	−	0.386063i
$475$	3.31798	−	16.6806i	0.152239	−	0.765359i
$476$	14.4151	−	2.06828i	0.660715	−	0.0947994i
$477$	4.50589	−	6.74354i	0.206311	−	0.308766i
$478$	−1.21974	+	9.69952i	−0.0557896	+	0.443646i
$479$		−	3.77171i		−	0.172334i	−0.996281	−	0.0861670i	$-0.972538\pi$
$479$		−	3.77171i		−	0.172334i	0.996281	−	0.0861670i	$-0.0274619\pi$
$480$	3.12641	+	2.25793i	0.142700	+	0.103060i
$481$		−	1.21202i		−	0.0552632i
$482$	26.8337	+	3.37441i	1.22224	+	0.153700i
$483$	1.01471	−	1.51862i	0.0461708	−	0.0690995i
$484$	−10.6045	−	7.94328i	−0.482024	−	0.361058i
$485$	−1.72838	+	8.68914i	−0.0784815	+	0.394553i
$486$	−0.926269	+	1.06866i	−0.0420164	+	0.0484752i
$487$	6.52856	+	2.70422i	0.295837	+	0.122540i	0.525665	−	0.850691i	$-0.323816\pi$
$487$	6.52856	+	2.70422i	0.295837	+	0.122540i	−0.229828	+	0.973231i	$0.573816\pi$
$488$	5.46167	−	30.1962i	0.247238	−	1.36692i
$489$	2.28989	−	0.948505i	0.103553	−	0.0428929i
$490$	−5.18991	−	1.72821i	−0.234456	−	0.0780726i
$491$	3.44645	−	2.30285i	0.155536	−	0.103926i	−0.475367	−	0.879788i	$-0.657685\pi$
$491$	3.44645	−	2.30285i	0.155536	−	0.103926i	0.630903	+	0.775862i	$0.282685\pi$
$492$	−5.85940	+	12.2378i	−0.264162	+	0.551722i
$493$	−7.62270	−	38.3219i	−0.343309	−	1.72593i
$494$	5.34947	+	3.04726i	0.240684	+	0.137103i
$495$	1.00833	−	1.00833i	0.0453212	−	0.0453212i
$496$	−11.5713	+	21.1619i	−0.519567	+	0.950195i
$497$	−8.28441	−	8.28441i	−0.371607	−	0.371607i
$498$	2.94423	+	10.7383i	0.131934	+	0.481196i
$499$	23.8975	−	4.75351i	1.06980	−	0.212796i	0.371377	−	0.928482i	$-0.378886\pi$
$499$	23.8975	−	4.75351i	1.06980	−	0.212796i	0.698422	+	0.715686i	$0.253886\pi$
$500$	9.67460	−	8.68511i	0.432661	−	0.388410i
$501$	14.0910	+	21.0887i	0.629540	+	0.942174i
$502$	−9.71377	+	4.86059i	−0.433547	+	0.216939i
$503$	−14.9766	−	36.1567i	−0.667773	−	1.61215i	−0.785328	−	0.619080i	$-0.787506\pi$
$503$	−14.9766	−	36.1567i	−0.667773	−	1.61215i	0.117555	−	0.993066i	$-0.462494\pi$
$504$	−1.29879	−	2.98734i	−0.0578525	−	0.133067i
$505$	−2.32339	+	5.60916i	−0.103390	+	0.249604i
$506$	4.67928	−	0.333981i	0.208019	−	0.0148473i
$507$	−11.4285	−	2.27327i	−0.507558	−	0.100959i
$508$	−9.25635	+	36.2218i	−0.410684	+	1.60708i
$509$	22.0659	+	14.7440i	0.978053	+	0.653514i	0.938346	−	0.345697i	$-0.112357\pi$
$509$	22.0659	+	14.7440i	0.978053	+	0.653514i	0.0397072	+	0.999211i	$0.487357\pi$
$510$	4.81431	−	3.73874i	0.213181	−	0.165554i
$511$	−4.09763			−0.181268
$512$	21.3286	+	7.55586i	0.942600	+	0.333925i
$513$	−3.75006			−0.165569
$514$	4.15464	−	3.22645i	0.183253	−	0.142312i
$515$	−1.09909	−	0.734389i	−0.0484317	−	0.0323611i
$516$	4.70228	−	18.4009i	0.207006	−	0.810055i
$517$	0.449358	+	0.0893828i	0.0197627	+	0.00393105i
$518$	−1.69619	+	0.121065i	−0.0745262	+	0.00531927i
$519$	−2.11723	+	5.11144i	−0.0929359	+	0.224367i
$520$	0.892490	+	2.05282i	0.0391383	+	0.0900221i
$521$	2.48332	+	5.99527i	0.108796	+	0.262658i	0.968896	−	0.247469i	$-0.0795987\pi$
$521$	2.48332	+	5.99527i	0.108796	+	0.262658i	−0.860100	+	0.510126i	$0.829599\pi$
$522$	−7.81607	+	3.91102i	−0.342100	+	0.171181i
$523$	21.0387	+	31.4867i	0.919960	+	1.37682i	0.926279	+	0.376837i	$0.122988\pi$
$523$	21.0387	+	31.4867i	0.919960	+	1.37682i	−0.00631956	+	0.999980i	$0.502012\pi$
$524$	−10.3917	+	9.32891i	−0.453965	+	0.407535i
$525$	−5.12280	+	1.01899i	−0.223577	+	0.0444723i
$526$	−11.1060	−	40.5064i	−0.484246	−	1.76616i
$527$	26.9563	+	26.9563i	1.17423	+	1.17423i
$528$	4.01407	−	7.34102i	0.174690	−	0.319477i
$529$	−14.4851	+	14.4851i	−0.629787	+	0.629787i
$530$	6.79442	+	3.87036i	0.295131	+	0.168118i
$531$	1.13369	+	5.69944i	0.0491980	+	0.247335i
$532$	3.73022	−	7.79083i	0.161726	−	0.337775i
$533$	−6.54816	+	4.37534i	−0.283632	+	0.189517i
$534$	−15.1161	−	5.03357i	−0.654138	−	0.217824i
$535$	−8.17841	+	3.38761i	−0.353583	+	0.146459i
$536$	1.07650	−	5.95168i	0.0464975	−	0.257073i
$537$	−21.7159	−	8.99502i	−0.937111	−	0.388164i
$538$	−16.8644	+	19.4568i	−0.727076	+	0.838843i
$539$	−2.31523	+	11.6395i	−0.0997242	+	0.501347i
$540$	−1.09129	−	0.817424i	−0.0469614	−	0.0351763i
$541$	14.8610	−	22.2411i	0.638925	−	0.956219i	−0.360797	−	0.932644i	$-0.617495\pi$
$541$	14.8610	−	22.2411i	0.638925	−	0.956219i	0.999722	−	0.0235744i	$-0.00750466\pi$
$542$	37.1014	+	4.66559i	1.59364	+	0.200404i
$543$			7.08564i			0.304074i
$544$	20.9397	−	28.9937i	0.897780	−	1.24310i
$545$			4.62878i			0.198275i
$546$	0.235906	−	1.87596i	0.0100959	−	0.0802836i
$547$	6.16715	−	9.22980i	0.263688	−	0.394638i	−0.675873	−	0.737018i	$-0.736233\pi$
$547$	6.16715	−	9.22980i	0.263688	−	0.394638i	0.939561	+	0.342381i	$0.111233\pi$
$548$	24.9983	−	3.58676i	1.06788	−	0.153219i
$549$	−2.11658	+	10.6407i	−0.0903333	+	0.454136i
$550$	−10.1376	−	8.78690i	−0.432270	−	0.374675i
$551$	−21.4116	−	8.86897i	−0.912164	−	0.377831i
$552$	−0.951545	−	4.38343i	−0.0405004	−	0.186571i
$553$	−9.65517	+	3.99930i	−0.410579	+	0.170068i
$554$	−8.40837	+	25.2508i	−0.357237	+	1.07280i
$555$	−0.591825	+	0.395445i	−0.0251216	+	0.0167857i
$556$	27.9555	−	9.85294i	1.18558	−	0.417858i
$557$	4.91160	+	24.6923i	0.208111	+	1.04625i	0.933683	+	0.358099i	$0.116575\pi$
$557$	4.91160	+	24.6923i	0.208111	+	1.04625i	−0.725572	+	0.688146i	$0.758425\pi$
$558$	4.22072	−	7.40948i	0.178677	−	0.313668i
$559$	7.79492	−	7.79492i	0.329690	−	0.329690i
$560$	2.78372	−	1.45407i	0.117634	−	0.0614456i
$561$	−9.35109	−	9.35109i	−0.394803	−	0.394803i
$562$	4.39779	−	1.20578i	0.185509	−	0.0508629i
$563$	−12.3496	+	2.45650i	−0.520475	+	0.103529i	−0.448335	−	0.893866i	$-0.647983\pi$
$563$	−12.3496	+	2.45650i	−0.520475	+	0.103529i	−0.0721401	+	0.997395i	$0.522983\pi$
$564$	0.0235755	−	0.437441i	0.000992709	−	0.0184196i
$565$	−0.184290	−	0.275810i	−0.00775315	−	0.0116034i
$566$	−12.6189	−	25.2185i	−0.530412	−	1.06001i
$567$	0.440731	+	1.06402i	0.0185090	+	0.0446846i
$568$	−28.7688	+	0.500959i	−1.20711	+	0.0210198i
$569$	9.08881	−	21.9423i	0.381023	−	0.919870i	−0.610746	−	0.791827i	$-0.709130\pi$
$569$	9.08881	−	21.9423i	0.381023	−	0.919870i	0.991769	−	0.128044i	$-0.0408697\pi$
$570$	−0.257403	−	3.60637i	−0.0107814	−	0.151054i
$571$	−30.7371	−	6.11399i	−1.28631	−	0.255863i	−0.495866	−	0.868399i	$-0.665149\pi$
$571$	−30.7371	−	6.11399i	−1.28631	−	0.255863i	−0.790442	+	0.612536i	$0.790149\pi$
$572$	4.17725	−	2.47683i	0.174660	−	0.103561i
$573$	−4.21408	−	2.81576i	−0.176046	−	0.117630i
$574$	6.77725	+	8.72695i	0.282877	+	0.364256i
$575$	−7.19229			−0.299939
$576$	−7.49314	−	2.80228i	−0.312214	−	0.116762i
$577$	−17.6921			−0.736533			−0.368267	−	0.929720i	$-0.620049\pi$
$577$	−17.6921			−0.736533			−0.368267	+	0.929720i	$0.620049\pi$
$578$	−19.9263	−	25.6588i	−0.828825	−	1.06726i
$579$	10.3919	+	6.94364i	0.431873	+	0.288568i
$580$	−4.29764	−	7.24812i	−0.178450	−	0.300962i
$581$	8.89343	+	1.76901i	0.368961	+	0.0733910i
$582$	−1.30839	−	18.3314i	−0.0542346	−	0.759859i
$583$	6.49203	−	15.6732i	0.268873	−	0.649116i
$584$	−6.99090	+	7.23868i	−0.289285	+	0.299539i
$585$	−0.302859	−	0.731166i	−0.0125217	−	0.0302300i
$586$	−2.81239	−	5.62049i	−0.116179	−	0.232180i
$587$	8.06620	+	12.0719i	0.332928	+	0.498262i	0.959733	−	0.280915i	$-0.0906378\pi$
$587$	8.06620	+	12.0719i	0.332928	+	0.498262i	−0.626805	+	0.779176i	$0.715638\pi$
$588$	11.3308	+	0.610664i	0.467274	+	0.0251834i
$589$	22.1773	−	4.41135i	0.913801	−	0.181766i
$590$	−5.40323	+	1.48146i	−0.222448	+	0.0609906i
$591$	−17.2533	−	17.2533i	−0.709705	−	0.709705i
$592$	−2.67997	+	3.20295i	−0.110146	+	0.131641i
$593$	−12.6582	+	12.6582i	−0.519810	+	0.519810i	−0.917514	−	0.397704i	$-0.869807\pi$
$593$	−12.6582	+	12.6582i	−0.519810	+	0.519810i	0.397704	+	0.917514i	$0.369807\pi$
$594$	−1.46416	+	2.57034i	−0.0600753	+	0.105462i
$595$	−0.968429	−	4.86862i	−0.0397017	−	0.199594i
$596$	−15.1035	−	42.8526i	−0.618661	−	1.75531i
$597$	−15.6307	+	10.4441i	−0.639720	+	0.427447i
$598$	0.822557	−	2.47018i	0.0336369	−	0.101013i
$599$	−1.63778	+	0.678392i	−0.0669180	+	0.0277183i	−0.415891	−	0.909414i	$-0.636530\pi$
$599$	−1.63778	+	0.678392i	−0.0669180	+	0.0277183i	0.348973	+	0.937133i	$0.386530\pi$
$600$	−6.93984	+	10.7882i	−0.283318	+	0.440426i
$601$	32.5188	+	13.4697i	1.32647	+	0.549441i	0.929646	−	0.368454i	$-0.120113\pi$
$601$	32.5188	+	13.4697i	1.32647	+	0.549441i	0.396822	+	0.917895i	$0.370113\pi$
$602$	−11.6874	−	10.1302i	−0.476343	−	0.412876i
$603$	−0.417177	+	2.09729i	−0.0169888	+	0.0854083i
$604$	5.23534	+	36.4883i	0.213023	+	1.48469i
$605$	−2.50917	+	3.75525i	−0.102012	+	0.152672i
$606$	1.57140	−	12.4960i	0.0638339	−	0.507615i
$607$		−	4.72069i		−	0.191607i	−0.995400	−	0.0958035i	$-0.969458\pi$
$607$		−	4.72069i		−	0.191607i	0.995400	−	0.0958035i	$-0.0305420\pi$
$608$	−7.39885	−	19.8815i	−0.300063	−	0.806299i
$609$			7.11753i			0.288417i
$610$	−10.3783	−	1.30510i	−0.420205	−	0.0528418i
$611$	0.141266	−	0.211420i	0.00571502	−	0.00855314i
$612$	−7.58064	+	10.1204i	−0.306429	+	0.409092i
$613$	3.01668	−	15.1659i	0.121842	−	0.612543i	−0.870818	−	0.491606i	$-0.836410\pi$
$613$	3.01668	−	15.1659i	0.121842	−	0.612543i	0.992660	−	0.120937i	$-0.0385900\pi$
$614$	22.3147	−	25.7450i	0.900549	−	1.03898i
$615$	4.27294	+	1.76991i	0.172302	+	0.0713697i
$616$	−3.88351	−	5.59856i	−0.156471	−	0.225572i
$617$	28.8876	−	11.9656i	1.16297	−	0.481718i	0.284107	−	0.958793i	$-0.408303\pi$
$617$	28.8876	−	11.9656i	1.16297	−	0.481718i	0.878862	+	0.477075i	$0.158303\pi$
$618$	2.60165	+	0.866333i	0.104654	+	0.0348490i
$619$	−10.6078	+	7.08793i	−0.426365	+	0.284888i	−0.750182	−	0.661232i	$-0.770034\pi$
$619$	−10.6078	+	7.08793i	−0.426365	+	0.284888i	0.323816	+	0.946120i	$0.395034\pi$
$620$	7.41527	+	3.55040i	0.297804	+	0.142588i
$621$	0.309388	+	1.55540i	0.0124153	+	0.0624160i
$622$	19.1956	+	10.9346i	0.769675	+	0.438436i
$623$	−9.17442	+	9.17442i	−0.367565	+	0.367565i
$624$	−2.91151	−	3.61729i	−0.116554	−	0.144807i
$625$	12.9008	+	12.9008i	0.516031	+	0.516031i
$626$	−6.43578	−	23.4729i	−0.257226	−	0.938165i
$627$	−7.69328	+	1.53029i	−0.307240	+	0.0611139i
$628$	28.8358	+	32.1210i	1.15067	+	1.28177i
$629$	3.66729	+	5.48848i	0.146224	+	0.218840i
$630$	−0.992996	+	0.496877i	−0.0395619	+	0.0197961i
$631$	2.52703	+	6.10078i	0.100599	+	0.242868i	0.966164	−	0.257929i	$-0.0830401\pi$
$631$	2.52703	+	6.10078i	0.100599	+	0.242868i	−0.865564	+	0.500798i	$0.833040\pi$
$632$	−9.40755	+	23.8795i	−0.374212	+	0.949877i
$633$	−7.40734	+	17.8829i	−0.294415	+	0.710782i
$634$	3.83099	−	0.273435i	0.152148	−	0.0108595i
$635$	12.4989	+	2.48618i	0.496002	+	0.0986610i
$636$	−15.7158	−	4.01610i	−0.623170	−	0.159249i
$637$	5.47630	+	3.65915i	0.216979	+	0.144981i
$638$	−14.4388	+	11.2130i	−0.571636	+	0.443926i
$639$	10.1728			0.402431
$640$	2.18058	−	7.39836i	0.0861949	−	0.292446i
$641$	5.36117			0.211753			0.105877	−	0.994379i	$-0.466235\pi$
$641$	5.36117			0.211753			0.105877	+	0.994379i	$0.466235\pi$
$642$	14.5034	−	11.2632i	0.572403	−	0.444522i
$643$	14.9450	+	9.98590i	0.589371	+	0.393805i	0.814193	−	0.580595i	$-0.197180\pi$
$643$	14.9450	+	9.98590i	0.589371	+	0.393805i	−0.224821	+	0.974400i	$0.572180\pi$
$644$	−3.53912	−	0.904409i	−0.139461	−	0.0356387i
$645$	−6.34950	−	1.26299i	−0.250011	−	0.0497303i
$646$	−33.4448	+	2.38711i	−1.31587	+	0.0939194i
$647$	−0.650809	+	1.57119i	−0.0255859	+	0.0617699i	−0.936156	−	0.351585i	$-0.885643\pi$
$647$	−0.650809	+	1.57119i	−0.0255859	+	0.0617699i	0.910570	+	0.413354i	$0.135643\pi$
$648$	2.63158	+	1.03673i	0.103378	+	0.0407267i
$649$	4.65155	+	11.2298i	0.182589	+	0.440809i
$650$	−6.65846	+	3.33177i	−0.261166	+	0.130683i
$651$	−3.85807	−	5.77401i	−0.151210	−	0.226301i
$652$	−3.31150	−	3.68878i	−0.129688	−	0.144464i
$653$	8.55252	−	1.70120i	0.334686	−	0.0665732i	−0.0248867	−	0.999690i	$-0.507922\pi$
$653$	8.55252	−	1.70120i	0.334686	−	0.0665732i	0.359573	+	0.933117i	$0.382922\pi$
$654$	−2.53897	−	9.26025i	−0.0992816	−	0.362105i
$655$	3.36597	+	3.36597i	0.131519	+	0.131519i
$656$	26.9792	+	2.91652i	1.05336	+	0.113871i
$657$	2.51584	−	2.51584i	0.0981522	−	0.0981522i
$658$	−0.309988	−	0.176581i	−0.0120846	−	0.00688383i
$659$	2.29945	+	11.5601i	0.0895740	+	0.450319i	0.999377	+	0.0352795i	$0.0112322\pi$
$659$	2.29945	+	11.5601i	0.0895740	+	0.450319i	−0.909804	+	0.415039i	$0.863768\pi$
$660$	−2.57235	−	1.23163i	−0.100128	−	0.0479411i
$661$	−15.6360	+	10.4476i	−0.608170	+	0.406366i	−0.821168	−	0.570686i	$-0.806677\pi$
$661$	−15.6360	+	10.4476i	−0.608170	+	0.406366i	0.212998	+	0.977053i	$0.431677\pi$
$662$	−7.01496	−	2.33594i	−0.272644	−	0.0907890i
$663$	−6.78070	+	2.80866i	−0.263340	+	0.109079i
$664$	18.2980	−	12.6926i	0.710100	−	0.492570i
$665$	−2.72024	−	1.12676i	−0.105487	−	0.0436940i
$666$	0.967085	−	1.11575i	0.0374738	−	0.0432343i
$667$	−1.91205	+	9.61251i	−0.0740348	+	0.372198i
$668$	30.4110	−	40.5996i	1.17664	−	1.57085i
$669$	9.59489	−	14.3598i	0.370960	−	0.555181i
$670$	−2.04556	−	0.257234i	−0.0790269	−	0.00993783i
$671$			22.6933i			0.876065i
$672$	−4.77148	+	4.43590i	−0.184064	+	0.171119i
$673$		−	3.77219i		−	0.145407i	−0.997354	−	0.0727036i	$-0.976837\pi$
$673$		−	3.77219i		−	0.145407i	0.997354	−	0.0727036i	$-0.0231627\pi$
$674$	0.866089	−	6.88725i	0.0333605	−	0.265287i
$675$	2.51964	−	3.77090i	0.0969809	−	0.145142i
$676$	3.30988	+	23.0686i	0.127303	+	0.887252i
$677$	0.0293360	−	0.147482i	0.00112747	−	0.00566819i	−0.980217	−	0.197924i	$-0.936580\pi$
$677$	0.0293360	−	0.147482i	0.00112747	−	0.00566819i	0.981345	+	0.192255i	$0.0615802\pi$
$678$	0.519974	+	0.450693i	0.0199695	+	0.0173088i
$679$	−13.8272	−	5.72739i	−0.530637	−	0.219797i
$680$	−10.2529	−	6.59550i	−0.393181	−	0.252926i
$681$	9.76051	−	4.04294i	0.374024	−	0.154926i
$682$	5.63525	−	16.9230i	0.215785	−	0.648014i
$683$	−24.9296	+	16.6574i	−0.953904	+	0.637378i	−0.932030	−	0.362382i	$-0.881963\pi$
$683$	−24.9296	+	16.6574i	−0.953904	+	0.637378i	−0.0218747	+	0.999761i	$0.506963\pi$
$684$	2.49311	+	7.07363i	0.0953265	+	0.270467i
$685$	−1.67943	−	8.44305i	−0.0641676	−	0.322592i
$686$	10.2170	−	17.9360i	0.390088	−	0.684800i
$687$	−9.16877	+	9.16877i	−0.349810	+	0.349810i
$688$	−37.8353	+	3.36349i	−1.44246	+	0.128232i
$689$	−6.65745	−	6.65745i	−0.253629	−	0.253629i
$690$	−1.47456	+	0.404295i	−0.0561356	+	0.0153912i
$691$	3.35115	−	0.666585i	0.127484	−	0.0253581i	−0.130936	−	0.991391i	$-0.541798\pi$
$691$	3.35115	−	0.666585i	0.127484	−	0.0253581i	0.258420	+	0.966033i	$0.416798\pi$
$692$	11.0491	+	0.595484i	0.420025	+	0.0226369i
$693$	1.33836	+	2.00300i	0.0508400	+	0.0760875i
$694$	−2.67876	−	5.35344i	−0.101684	−	0.203214i
$695$	−3.86653	−	9.33464i	−0.146666	−	0.354083i
$696$	12.5735	+	12.1431i	0.476597	+	0.460283i
$697$	16.4138	−	39.6265i	0.621718	−	1.50096i
$698$	2.84081	+	39.8015i	0.107526	+	1.50651i
$699$	26.7760	+	5.32607i	1.01276	+	0.201450i
$700$	5.32782	+	8.98555i	0.201373	+	0.339622i
$701$	−25.2307	−	16.8586i	−0.952949	−	0.636740i	−0.0211737	−	0.999776i	$-0.506740\pi$
$701$	−25.2307	−	16.8586i	−0.952949	−	0.636740i	−0.931775	+	0.363036i	$0.881740\pi$
$702$	1.00695	+	1.29663i	0.0380049	+	0.0489382i
$703$	3.91531			0.147669
$704$	−16.5158	−	2.69118i	−0.622462	−	0.101428i
$705$	−0.149327			−0.00562398
$706$	2.73969	+	3.52785i	0.103110	+	0.132772i
$707$	−8.52793	−	5.69818i	−0.320726	−	0.214302i
$708$	9.99700	−	5.92754i	0.375710	−	0.222771i
$709$	39.8461	+	7.92589i	1.49645	+	0.297663i	0.874359	−	0.485280i	$-0.161282\pi$
$709$	39.8461	+	7.92589i	1.49645	+	0.297663i	0.622094	+	0.782943i	$0.286282\pi$
$710$	0.698259	+	9.78303i	0.0262052	+	0.367151i
$711$	3.47256	−	8.38350i	0.130231	−	0.314406i
$712$	0.554778	+	31.8595i	0.0207912	+	1.19398i
$713$	−3.65935	−	8.83446i	−0.137044	−	0.330853i
$714$	4.60795	+	9.20887i	0.172448	+	0.344633i
$715$	−0.919684	−	1.37640i	−0.0343942	−	0.0514746i
$716$	−2.52991	+	46.9421i	−0.0945472	+	1.75431i
$717$	−6.77979	+	1.34858i	−0.253196	+	0.0503638i
$718$	1.53083	−	0.419723i	0.0571302	−	0.0156639i
$719$	−22.4551	−	22.4551i	−0.837433	−	0.837433i	0.151087	−	0.988520i	$-0.451723\pi$
$719$	−22.4551	−	22.4551i	−0.837433	−	0.837433i	−0.988520	+	0.151087i	$0.951723\pi$
$720$	−0.816376	+	2.60190i	−0.0304245	+	0.0969670i
$721$	1.57902	−	1.57902i	0.0588057	−	0.0588057i
$722$	3.45585	−	6.06676i	0.128614	−	0.225781i
$723$	3.73086	+	18.7563i	0.138752	+	0.697554i
$724$	13.3654	−	4.71067i	0.496723	−	0.175071i
$725$	23.3045	−	15.5716i	0.865509	−	0.578314i
$726$	2.95999	−	8.88900i	0.109855	−	0.329902i
$727$	3.26753	−	1.35346i	0.121186	−	0.0501969i	−0.321266	−	0.946989i	$-0.604109\pi$
$727$	3.26753	−	1.35346i	0.121186	−	0.0501969i	0.442453	+	0.896792i	$0.354109\pi$
$728$	−3.69540	+	0.802188i	−0.136961	+	0.0297311i
$729$	−0.923880	−	0.382683i	−0.0342178	−	0.0141735i
$730$	2.59212	+	2.24675i	0.0959387	+	0.0831559i
$731$	−11.7128	+	58.8841i	−0.433213	+	2.17791i
$732$	21.4785	−	3.08173i	0.793867	−	0.113904i
$733$	22.0856	−	33.0535i	0.815752	−	1.22086i	−0.156675	−	0.987650i	$-0.550078\pi$
$733$	22.0856	−	33.0535i	0.815752	−	1.22086i	0.972427	−	0.233208i	$-0.0749224\pi$
$734$	3.14848	−	25.0371i	0.116212	−	0.924136i
$735$		−	3.86794i		−	0.142671i
$736$	−7.63573	+	4.70906i	−0.281457	+	0.173578i
$737$			4.47285i			0.164759i
$738$	−9.51919	−	1.19706i	−0.350406	−	0.0440645i
$739$	−19.2682	+	28.8369i	−0.708792	+	1.06078i	0.285937	+	0.958248i	$0.407695\pi$
$739$	−19.2682	+	28.8369i	−0.708792	+	1.06078i	−0.994730	+	0.102534i	$0.967305\pi$
$740$	1.13937	+	0.853444i	0.0418842	+	0.0313732i
$741$	−0.849288	+	4.26966i	−0.0311994	+	0.156850i
$742$	−8.65194	+	9.98192i	−0.317623	+	0.366448i
$743$	−32.8287	−	13.5981i	−1.20437	−	0.498865i	−0.311959	−	0.950095i	$-0.600985\pi$
$743$	−32.8287	−	13.5981i	−1.20437	−	0.498865i	−0.892408	+	0.451230i	$0.850985\pi$
$744$	−16.7823	−	3.03546i	−0.615269	−	0.111285i
$745$	−14.3090	+	5.92696i	−0.524240	+	0.217147i
$746$	6.33446	+	2.10934i	0.231921	+	0.0772284i
$747$	−6.54647	+	4.37421i	−0.239523	+	0.160044i
$748$	−11.4219	+	23.8555i	−0.417626	+	0.872242i
$749$	−2.91745	−	14.6670i	−0.106601	−	0.535922i
$750$	7.98807	+	4.55030i	0.291683	+	0.166154i
$751$	18.7680	−	18.7680i	0.684856	−	0.684856i	−0.276235	−	0.961090i	$-0.589087\pi$
$751$	18.7680	−	18.7680i	0.684856	−	0.684856i	0.961090	+	0.276235i	$0.0890867\pi$
$752$	−0.840805	+	0.246349i	−0.0306610	+	0.00898342i
$753$	−5.43099	−	5.43099i	−0.197916	−	0.197916i
$754$	2.68279	+	9.78478i	0.0977013	+	0.356341i
$755$	12.3237	−	2.45134i	0.448506	−	0.0892134i
$756$	1.71402	−	1.53872i	0.0623384	−	0.0559627i
$757$	−15.4468	−	23.1177i	−0.561422	−	0.840228i	0.436817	−	0.899551i	$-0.356106\pi$
$757$	−15.4468	−	23.1177i	−0.561422	−	0.840228i	−0.998239	+	0.0593228i	$0.981106\pi$
$758$	−7.03026	+	3.51781i	−0.255350	+	0.127773i
$759$	1.26942	+	3.06466i	0.0460772	+	0.111240i
$760$	−6.63145	+	2.88311i	−0.240548	+	0.104581i
$761$	−9.50616	+	22.9499i	−0.344598	+	0.831933i	0.652640	+	0.757668i	$0.273661\pi$
$761$	−9.50616	+	22.9499i	−0.344598	+	0.831933i	−0.997239	+	0.0742655i	$0.976339\pi$
$762$	−26.3687	+	1.88205i	−0.955237	+	0.0681796i
$763$	−7.66930	−	1.52552i	−0.277647	−	0.0552275i
$764$	−2.50968	+	9.82085i	−0.0907971	+	0.355306i
$765$	3.58380	+	2.39462i	0.129573	+	0.0865777i
$766$	−1.13579	+	0.882040i	−0.0410377	+	0.0318694i
$767$	6.74589			0.243580
$768$	−0.304287	+	15.9971i	−0.0109800	+	0.577246i
$769$	−31.3503			−1.13052			−0.565260	−	0.824913i	$-0.691224\pi$
$769$	−31.3503			−1.13052			−0.565260	+	0.824913i	$0.691224\pi$
$770$	−1.83438	+	1.42456i	−0.0661064	+	0.0513376i
$771$	3.09274	+	2.06650i	0.111382	+	0.0744233i
$772$	6.18887	−	24.2182i	0.222742	−	0.871632i
$773$	5.74188	+	1.14213i	0.206521	+	0.0410796i	0.297267	−	0.954795i	$-0.403925\pi$
$773$	5.74188	+	1.14213i	0.206521	+	0.0410796i	−0.0907456	+	0.995874i	$0.528925\pi$
$774$	13.3955	−	0.956095i	0.481490	−	0.0343661i
$775$	−10.4649	+	25.2645i	−0.375911	+	0.907529i
$776$	−33.7081	+	14.6550i	−1.21005	+	0.526084i
$777$	−0.460152	−	1.11091i	−0.0165079	−	0.0398535i
$778$	−17.7144	+	8.86395i	−0.635091	+	0.317788i
$779$	−14.1341	−	21.1532i	−0.506408	−	0.757894i
$780$	−1.17783	+	1.05737i	−0.0421731	+	0.0378598i
$781$	20.8697	−	4.15123i	0.746775	−	0.148543i
$782$	3.74936	+	13.6748i	0.134077	+	0.489011i
$783$	−4.36998	−	4.36998i	−0.156170	−	0.156170i
$784$	−6.38104	−	21.7789i	−0.227894	−	0.777819i
$785$	10.4043	−	10.4043i	0.371344	−	0.371344i
$786$	−8.58019	−	4.88760i	−0.306045	−	0.174335i
$787$	−1.14177	−	5.74008i	−0.0406998	−	0.204612i	0.955085	−	0.296332i	$-0.0957635\pi$
$787$	−1.14177	−	5.74008i	−0.0406998	−	0.204612i	−0.995785	+	0.0917202i	$0.970763\pi$
$788$	−21.0741	+	44.0147i	−0.750732	+	1.56796i
$789$	24.6942	−	16.5001i	0.879136	−	0.587420i
$790$	8.30061	+	2.76406i	0.295322	+	0.0983407i
$791$	0.517719	−	0.214446i	0.0184080	−	0.00762482i
$792$	5.82176	+	1.05300i	0.206867	+	0.0374166i
$793$	11.6357	+	4.81969i	0.413198	+	0.171152i
$794$	−26.1760	+	30.1998i	−0.928951	+	1.07175i
$795$	−1.07869	+	5.42295i	−0.0382572	+	0.192332i
$796$	30.0919	+	22.5402i	1.06658	+	0.798917i
$797$	12.0226	−	17.9930i	0.425861	−	0.637346i	−0.555047	−	0.831819i	$-0.687300\pi$
$797$	12.0226	−	17.9930i	0.425861	−	0.637346i	0.980908	+	0.194473i	$0.0622998\pi$
$798$	6.06012	+	0.762075i	0.214526	+	0.0269772i
$799$			1.38483i			0.0489918i
$800$	24.9632	+	5.91822i	0.882582	+	0.209241i
$801$		−	11.2657i		−	0.398055i
$802$	−2.52160	+	20.0521i	−0.0890406	+	0.708063i
$803$	4.13462	−	6.18790i	0.145908	−	0.218366i
$804$	4.23341	−	0.607409i	0.149301	−	0.0214217i
$805$	−0.242917	+	1.22123i	−0.00856169	+	0.0430425i
$806$	−7.48024	−	6.48358i	−0.263480	−	0.228374i
$807$	−16.8209	−	6.96744i	−0.592124	−	0.245266i
$808$	−24.6155	+	5.34348i	−0.865972	+	0.187983i
$809$	−23.6079	+	9.77871i	−0.830010	+	0.343801i	−0.756907	−	0.653523i	$-0.773290\pi$
$809$	−23.6079	+	9.77871i	−0.830010	+	0.343801i	−0.0731031	+	0.997324i	$0.523290\pi$
$810$	0.304605	−	0.914745i	0.0107027	−	0.0321409i
$811$	−38.9715	+	26.0399i	−1.36847	+	0.914384i	−0.999884	−	0.0152083i	$-0.995159\pi$
$811$	−38.9715	+	26.0399i	−1.36847	+	0.914384i	−0.368588	+	0.929593i	$0.620159\pi$
$812$	13.4256	−	4.73186i	0.471146	−	0.166056i
$813$	5.15843	+	25.9332i	0.180914	+	0.909516i
$814$	1.52868	−	2.68360i	0.0535802	−	0.0940602i
$815$	−1.19483	+	1.19483i	−0.0418529	+	0.0418529i
$816$	24.1295	+	7.57092i	0.844702	+	0.265035i
$817$	25.1808	+	25.1808i	0.880965	+	0.880965i
$818$	−38.6098	+	10.5860i	−1.34996	+	0.370131i
$819$	1.31126	−	0.260826i	0.0458192	−	0.00911400i
$820$	0.497799	−	9.23659i	0.0173839	−	0.322556i
$821$	0.606218	+	0.907270i	0.0211572	+	0.0316639i	0.841897	−	0.539638i	$-0.181439\pi$
$821$	0.606218	+	0.907270i	0.0211572	+	0.0316639i	−0.820740	+	0.571301i	$0.806439\pi$
$822$	7.99100	+	15.9698i	0.278718	+	0.557011i
$823$	−20.6385	−	49.8257i	−0.719412	−	1.73681i	−0.675020	−	0.737799i	$-0.735865\pi$
$823$	−20.6385	−	49.8257i	−0.719412	−	1.73681i	−0.0443915	−	0.999014i	$-0.514135\pi$
$824$	−0.0954834	−	5.48336i	−0.00332632	−	0.191022i
$825$	3.63026	−	8.76423i	0.126390	−	0.305131i
$826$	−0.673826	−	9.44071i	−0.0234454	−	0.328484i
$827$	3.92291	+	0.780314i	0.136413	+	0.0271342i	0.262824	−	0.964844i	$-0.415346\pi$
$827$	3.92291	+	0.780314i	0.136413	+	0.0271342i	−0.126412	+	0.991978i	$0.540346\pi$
$828$	2.72822	−	1.61765i	0.0948121	−	0.0562172i
$829$	−21.3565	−	14.2699i	−0.741741	−	0.495615i	0.126372	−	0.991983i	$-0.459667\pi$
$829$	−21.3565	−	14.2699i	−0.741741	−	0.495615i	−0.868112	+	0.496368i	$0.834667\pi$
$830$	−4.65594	−	5.99537i	−0.161610	−	0.208102i
$831$	−18.8189			−0.652821
$832$	−4.88756	+	7.89673i	−0.169446	+	0.273770i
$833$	−35.8706			−1.24284
$834$	12.8555	+	16.5538i	0.445151	+	0.573212i
$835$	−14.3770	−	9.60643i	−0.497538	−	0.332444i
$836$	8.00118	+	13.4942i	0.276726	+	0.466708i
$837$	5.91386	+	1.17634i	0.204413	+	0.0406602i
$838$	−1.85778	−	26.0286i	−0.0641758	−	0.899142i
$839$	9.38471	−	22.6567i	0.323996	−	0.782196i	−0.675018	−	0.737801i	$-0.735864\pi$
$839$	9.38471	−	22.6567i	0.323996	−	0.782196i	0.999014	−	0.0443946i	$-0.0141359\pi$
$840$	1.59741	+	1.54273i	0.0551158	+	0.0532291i
$841$	−3.51820	−	8.49370i	−0.121317	−	0.292886i
$842$	10.2220	+	20.4284i	0.352272	+	0.704008i
$843$	1.79142	+	2.68105i	0.0616998	+	0.0923403i
$844$	38.6565	+	2.08337i	1.33061	+	0.0717124i
$845$	7.79128	−	1.54978i	0.268028	−	0.0533141i
$846$	0.298741	−	0.0819086i	0.0102709	−	0.00281608i
$847$	−5.39500	−	5.39500i	−0.185375	−	0.185375i
$848$	2.87267	+	32.3141i	0.0986480	+	1.10967i
$849$	14.0997	−	14.0997i	0.483902	−	0.483902i
$850$	20.0709	−	35.2345i	0.688427	−	1.20853i
$851$	−0.323021	−	1.62394i	−0.0110730	−	0.0556679i
$852$	−6.76309	−	19.1887i	−0.231700	−	0.657395i
$853$	−15.9216	+	10.6385i	−0.545147	+	0.364255i	−0.797443	−	0.603395i	$-0.793814\pi$
$853$	−15.9216	+	10.6385i	−0.545147	+	0.364255i	0.252296	+	0.967650i	$0.418814\pi$
$854$	5.58277	−	16.7654i	0.191038	−	0.573699i
$855$	2.36197	−	0.978358i	0.0807775	−	0.0334591i
$856$	−30.8875	−	19.8694i	−1.05571	−	0.679121i
$857$	35.0567	+	14.5209i	1.19751	+	0.496026i	0.890195	−	0.455581i	$-0.150568\pi$
$857$	35.0567	+	14.5209i	1.19751	+	0.496026i	0.307318	+	0.951607i	$0.400568\pi$
$858$	2.59488	+	2.24914i	0.0885879	+	0.0767845i
$859$	1.81035	−	9.10123i	0.0617683	−	0.310530i	−0.937533	−	0.347895i	$-0.886896\pi$
$859$	1.81035	−	9.10123i	0.0617683	−	0.310530i	0.999302	+	0.0373652i	$0.0118965\pi$
$860$	1.83892	+	12.8165i	0.0627065	+	0.437040i
$861$	−4.34076	+	6.49640i	−0.147933	+	0.221397i
$862$	−5.52588	+	43.9425i	−0.188212	+	1.49669i
$863$			17.9537i			0.611152i	0.952168	+	0.305576i	$0.0988490\pi$
$863$			17.9537i			0.611152i	−0.952168	+	0.305576i	$0.901151\pi$
$864$	0.206037	−	5.65310i	0.00700952	−	0.192322i
$865$		−	3.77179i		−	0.128245i
$866$	−20.7486	−	2.60919i	−0.705067	−	0.0886640i
$867$	12.7626	−	19.1006i	0.433440	−	0.648689i
$868$	−8.32643	+	11.1160i	−0.282617	+	0.377303i
$869$	3.70293	−	18.6159i	0.125613	−	0.631500i
$870$	3.90258	−	4.50248i	0.132310	−	0.152649i
$871$	2.29341	+	0.949960i	0.0777091	+	0.0321882i
$872$	−15.7794	+	10.9456i	−0.534358	+	0.370664i
$873$	12.0060	−	4.97305i	0.406342	−	0.168312i
$874$	7.97971	+	2.65720i	0.269918	+	0.0898810i
$875$	6.22489	−	4.15934i	0.210440	−	0.140611i
$876$	−6.41813	−	3.07298i	−0.216849	−	0.103826i
$877$	−11.0863	−	55.7344i	−0.374357	−	1.88202i	−0.463660	−	0.886013i	$-0.653464\pi$
$877$	−11.0863	−	55.7344i	−0.374357	−	1.88202i	0.0893033	−	0.996004i	$-0.471536\pi$
$878$	−22.7102	−	12.9366i	−0.766431	−	0.436588i
$879$	3.14243	−	3.14243i	0.105991	−	0.105991i
$880$	−0.613044	+	5.67095i	−0.0206657	+	0.191168i
$881$	−34.4525	−	34.4525i	−1.16073	−	1.16073i	−0.984315	−	0.176418i	$-0.943549\pi$
$881$	−34.4525	−	34.4525i	−1.16073	−	1.16073i	−0.176418	−	0.984315i	$-0.556451\pi$
$882$	2.12163	+	7.73812i	0.0714392	+	0.260556i
$883$	41.2464	−	8.20441i	1.38805	−	0.276101i	0.556177	−	0.831064i	$-0.312268\pi$
$883$	41.2464	−	8.20441i	1.38805	−	0.276101i	0.831875	+	0.554964i	$0.187268\pi$
$884$	9.80582	+	10.9230i	0.329805	+	0.367380i
$885$	−2.20099	−	3.29401i	−0.0739853	−	0.110727i
$886$	−4.44773	+	2.22556i	−0.149425	+	0.0747693i
$887$	5.01242	+	12.1011i	0.168301	+	0.406314i	0.985416	−	0.170160i	$-0.0544284\pi$
$887$	5.01242	+	12.1011i	0.168301	+	0.406314i	−0.817116	+	0.576474i	$0.804428\pi$
$888$	−2.74754	−	1.08242i	−0.0922013	−	0.0363235i
$889$	−8.23856	+	19.8896i	−0.276312	+	0.667077i
$890$	10.8340	−	0.773275i	0.363158	−	0.0259202i
$891$	−2.05151	−	0.408070i	−0.0687281	−	0.0136709i
$892$	−33.4653	−	8.55192i	−1.12050	−	0.286339i
$893$	0.682974	+	0.456348i	0.0228548	+	0.0152711i
$894$	25.3752	−	19.7061i	0.848673	−	0.659070i
$895$	16.0244			0.535637
$896$	11.5395	+	6.05123i	0.385507	+	0.202158i
$897$	1.84098			0.0614685
$898$	−5.92342	+	4.60006i	−0.197667	+	0.153506i
$899$	30.9840	+	20.7029i	1.03338	+	0.690479i
$900$	−8.78805	−	2.24575i	−0.292935	−	0.0748584i
$901$	50.2914	+	10.0036i	1.67545	+	0.333268i
$902$	−20.0172	+	1.42872i	−0.666499	+	0.0475711i
$903$	4.18524	−	10.1041i	0.139276	−	0.336242i
$904$	0.504441	−	1.28044i	0.0167775	−	0.0425869i
$905$	−1.84858	−	4.46287i	−0.0614489	−	0.148351i
$906$	−23.3100	+	11.6639i	−0.774423	+	0.387507i
$907$	−2.99394	−	4.48075i	−0.0994122	−	0.148781i	0.778429	−	0.627733i	$-0.216017\pi$
$907$	−2.99394	−	4.48075i	−0.0994122	−	0.148781i	−0.877841	+	0.478952i	$0.841017\pi$
$908$	−14.1150	−	15.7231i	−0.468424	−	0.521791i
$909$	8.73448	−	1.73740i	0.289704	−	0.0576258i
$910$	0.340836	+	1.24311i	0.0112986	+	0.0412088i
$911$	−30.2796	−	30.2796i	−1.00321	−	1.00321i	−0.999995	−	0.00321177i	$-0.998978\pi$
$911$	−30.2796	−	30.2796i	−1.00321	−	1.00321i	−0.00321177	−	0.999995i	$-0.501022\pi$
$912$	11.6853	−	9.40536i	0.386940	−	0.311443i
$913$	−11.6451	+	11.6451i	−0.385398	+	0.385398i
$914$	24.0007	+	13.6717i	0.793873	+	0.452220i
$915$	−1.44296	−	7.25424i	−0.0477027	−	0.239818i
$916$	23.3904	+	11.1992i	0.772839	+	0.370032i
$917$	−6.68631	+	4.46765i	−0.220801	+	0.147535i
$918$	−8.48318	−	2.82485i	−0.279987	−	0.0932339i
$919$	42.9377	−	17.7854i	1.41638	−	0.586685i	0.462434	−	0.886654i	$-0.346976\pi$
$919$	42.9377	−	17.7854i	1.41638	−	0.586685i	0.953949	+	0.299968i	$0.0969761\pi$
$920$	1.74293	+	2.51264i	0.0574626	+	0.0828393i
$921$	22.2572	+	9.21922i	0.733398	+	0.303784i
$922$	19.0097	−	21.9319i	0.626050	−	0.722287i
$923$	2.30387	−	11.5824i	0.0758329	−	0.381238i
$924$	2.88843	−	3.85614i	0.0950222	−	0.126858i
$925$	−2.63067	+	3.93707i	−0.0864958	+	0.129450i
$926$	55.7525	+	7.01101i	1.83214	+	0.230396i
$927$			1.93896i			0.0636836i
$928$	14.5461	−	31.7900i	0.477499	−	1.04356i
$929$			2.55172i			0.0837194i	0.999123	+	0.0418597i	$0.0133282\pi$
$929$			2.55172i			0.0837194i	−0.999123	+	0.0418597i	$0.986672\pi$
$930$	−0.725339	+	5.76799i	−0.0237848	+	0.189140i
$931$	−11.8205	+	17.6907i	−0.387403	+	0.579789i
$932$	−7.75474	−	54.0476i	−0.254015	−	1.77039i
$933$	−3.04752	+	15.3209i	−0.0997714	+	0.501585i
$934$	−6.32171	−	5.47941i	−0.206853	−	0.179292i
$935$	8.32937	+	3.45014i	0.272400	+	0.112832i
$936$	1.77636	−	2.76141i	0.0580621	−	0.0902594i
$937$	−47.0690	+	19.4966i	−1.53768	+	0.636927i	−0.981036	−	0.193825i	$-0.937911\pi$
$937$	−47.0690	+	19.4966i	−1.53768	+	0.636927i	−0.556642	+	0.830752i	$0.687911\pi$
$938$	1.10036	−	3.30445i	0.0359282	−	0.107894i
$939$	14.3099	−	9.56158i	0.466987	−	0.312031i
$940$	0.0992754	+	0.281671i	0.00323801	+	0.00918710i
$941$	4.67122	+	23.4838i	0.152277	+	0.765550i	0.979146	+	0.203156i	$0.0651197\pi$
$941$	4.67122	+	23.4838i	0.152277	+	0.765550i	−0.826869	+	0.562394i	$0.809880\pi$
$942$	−15.1076	+	26.5215i	−0.492233	+	0.864116i
$943$	−7.60755	+	7.60755i	−0.247736	+	0.247736i
$944$	−17.8271	−	14.9163i	−0.580224	−	0.485484i
$945$	−0.555187	−	0.555187i	−0.0180602	−	0.0180602i
$946$	27.0907	−	7.42772i	0.880796	−	0.241496i
$947$	10.1946	−	2.02783i	0.331279	−	0.0658955i	−0.0266486	−	0.999645i	$-0.508484\pi$
$947$	10.1946	−	2.02783i	0.331279	−	0.0658955i	0.357927	+	0.933749i	$0.383484\pi$
$948$	−18.1222	−	0.976681i	−0.588581	−	0.0317211i
$949$	−2.29466	−	3.43420i	−0.0744877	−	0.111479i
$950$	−10.7630	−	21.5096i	−0.349197	−	0.697862i
$951$	1.03930	+	2.50908i	0.0337015	+	0.0813626i
$952$	14.3070	−	14.8141i	0.463691	−	0.480126i
$953$	−4.80748	+	11.6063i	−0.155730	+	0.375965i	−0.982418	−	0.186696i	$-0.940222\pi$
$953$	−4.80748	+	11.6063i	−0.155730	+	0.375965i	0.826688	+	0.562660i	$0.190222\pi$
$954$	−0.816576	−	11.4407i	−0.0264376	−	0.370407i
$955$	3.38883	+	0.674080i	0.109660	+	0.0218127i
$956$	7.05113	+	11.8920i	0.228050	+	0.384613i
$957$	−10.7483	−	7.18179i	−0.347444	−	0.232154i
$958$	−3.27164	−	4.21284i	−0.105702	−	0.136111i
$959$	14.5425			0.469603
$960$	5.45062	−	0.189884i	0.175918	−	0.00612849i
$961$	−5.35746			−0.172821
$962$	−1.05132	−	1.35377i	−0.0338960	−	0.0436472i
$963$	10.7964	+	7.21394i	0.347910	+	0.232466i
$964$	32.8991	−	19.5069i	1.05961	−	0.628276i
$965$	−8.35684	−	1.66228i	−0.269016	−	0.0535106i
$966$	−0.183890	−	2.57640i	−0.00591655	−	0.0828944i
$967$	−8.68667	+	20.9715i	−0.279344	+	0.674397i	−0.999818	−	0.0190855i	$-0.993925\pi$
$967$	−8.68667	+	20.9715i	−0.279344	+	0.674397i	0.720473	+	0.693482i	$0.243925\pi$
$968$	−18.7349	+	0.326237i	−0.602163	+	0.0104856i
$969$	−9.07312	−	21.9044i	−0.291470	−	0.703672i
$970$	5.60657	+	11.2046i	0.180016	+	0.359758i
$971$	0.317227	+	0.474764i	0.0101803	+	0.0152359i	0.836525	−	0.547929i	$-0.184584\pi$
$971$	0.317227	+	0.474764i	0.0101803	+	0.0152359i	−0.826345	+	0.563165i	$0.809584\pi$
$972$	−0.107632	+	1.99710i	−0.00345231	+	0.0640571i
$973$	16.7406	−	3.32991i	0.536679	−	0.106752i
$974$	9.63779	−	2.64248i	0.308815	−	0.0846707i
$975$	−3.72276	−	3.72276i	−0.119224	−	0.119224i
$976$	−20.0923	−	38.4654i	−0.643138	−	1.23125i
$977$	−10.1697	+	10.1697i	−0.325356	+	0.325356i	−0.850818	−	0.525461i	$-0.823893\pi$
$977$	−10.1697	+	10.1697i	−0.325356	+	0.325356i	0.525461	+	0.850818i	$0.323893\pi$
$978$	1.73496	−	3.04573i	0.0554780	−	0.0973917i
$979$	−4.59721	−	23.1117i	−0.146927	−	0.738654i
$980$	−7.29598	+	2.57148i	−0.233062	+	0.0821428i
$981$	5.64539	−	3.77213i	0.180243	−	0.120435i
$982$	1.85201	−	5.56169i	0.0591000	−	0.177481i
$983$	−9.71143	+	4.02261i	−0.309746	+	0.128301i	−0.532141	−	0.846655i	$-0.678613\pi$
$983$	−9.71143	+	4.02261i	−0.309746	+	0.128301i	0.222395	+	0.974957i	$0.428613\pi$
$984$	4.07055	+	18.7516i	0.129764	+	0.597779i
$985$	15.3682	+	6.36570i	0.489670	+	0.202828i
$986$	−41.7552	−	36.1918i	−1.32976	−	1.15258i
$987$	0.0492140	−	0.247416i	0.00156650	−	0.00787533i
$988$	8.61836	−	1.23656i	0.274186	−	0.0393403i
$989$	8.36668	−	12.5216i	0.266045	−	0.398164i
$990$	0.251619	−	2.00091i	0.00799698	−	0.0635930i
$991$			5.97690i			0.189862i	0.995484	+	0.0949312i	$0.0302631\pi$
$991$			5.97690i			0.189862i	−0.995484	+	0.0949312i	$0.969737\pi$
$992$	5.43149	+	33.6740i	0.172450	+	1.06915i
$993$		−	5.22811i		−	0.165909i
$994$	−16.4393	−	2.06729i	−0.521424	−	0.0655704i
$995$	7.12015	−	10.6561i	0.225724	−	0.337820i
$996$	12.6032	+	9.44036i	0.399346	+	0.299129i
$997$	0.256966	−	1.29186i	0.00813820	−	0.0409135i	−0.976503	−	0.215505i	$-0.930860\pi$
$997$	0.256966	−	1.29186i	0.00813820	−	0.0409135i	0.984641	+	0.174591i	$0.0558604\pi$
$998$	22.5692	−	26.0385i	0.714415	−	0.824235i
$999$	0.964591	+	0.399546i	0.0305183	+	0.0126411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.133.14	yes	128
3.2	odd	2		576.2.bd.b.325.3		128
4.3	odd	2		768.2.r.a.625.4		128
64.13	even	16	inner	192.2.r.a.13.14	✓	128
64.51	odd	16		768.2.r.a.145.4		128
192.77	odd	16		576.2.bd.b.397.3		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.13.14	✓	128	64.13	even	16	inner
192.2.r.a.133.14	yes	128	1.1	even	1	trivial
576.2.bd.b.325.3		128	3.2	odd	2
576.2.bd.b.397.3		128	192.77	odd	16
768.2.r.a.145.4		128	64.51	odd	16
768.2.r.a.625.4		128	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11696 - 0.867416i) q^{2} +(0.831470 + 0.555570i) q^{3} +(0.495179 - 1.93773i) q^{4} +(-0.668642 - 0.133001i) q^{5} +(1.41063 - 0.100683i) q^{6} +(0.440731 - 1.06402i) q^{7} +(-1.12772 - 2.59388i) q^{8} +(0.382683 + 0.923880i) q^{9} +O(q^{10})\)	\(q+(1.11696 - 0.867416i) q^{2} +(0.831470 + 0.555570i) q^{3} +(0.495179 - 1.93773i) q^{4} +(-0.668642 - 0.133001i) q^{5} +(1.41063 - 0.100683i) q^{6} +(0.440731 - 1.06402i) q^{7} +(-1.12772 - 2.59388i) q^{8} +(0.382683 + 0.923880i) q^{9} +(-0.862210 + 0.431434i) q^{10} +(1.16209 + 1.73918i) q^{11} +(1.48827 - 1.33606i) q^{12} +(1.13856 - 0.226473i) q^{13} +(-0.430670 - 1.57076i) q^{14} +(-0.482064 - 0.482064i) q^{15} +(-3.50959 - 1.91905i) q^{16} +(-4.47057 + 4.47057i) q^{17} +(1.22883 + 0.699987i) q^{18} +(0.731601 + 3.67801i) q^{19} +(-0.588818 + 1.22979i) q^{20} +(0.957593 - 0.639843i) q^{21} +(2.80659 + 0.934580i) q^{22} +(1.46515 - 0.606887i) q^{23} +(0.503417 - 2.78327i) q^{24} +(-4.19001 - 1.73556i) q^{25} +(1.07527 - 1.24056i) q^{26} +(-0.195090 + 0.980785i) q^{27} +(-1.84354 - 1.38090i) q^{28} +(-3.43347 + 5.13856i) q^{29} +(-0.956594 - 0.120294i) q^{30} -6.02971i q^{31} +(-5.58467 + 0.900787i) q^{32} +2.09170i q^{33} +(-1.11559 + 8.87128i) q^{34} +(-0.436207 + 0.652830i) q^{35} +(1.97973 - 0.284051i) q^{36} +(0.203687 - 1.02400i) q^{37} +(4.00753 + 3.47357i) q^{38} +(1.07250 + 0.444243i) q^{39} +(0.409054 + 1.88437i) q^{40} +(-6.26769 + 2.59616i) q^{41} +(0.514578 - 1.54531i) q^{42} +(7.89573 - 5.27576i) q^{43} +(3.94551 - 1.39060i) q^{44} +(-0.133001 - 0.668642i) q^{45} +(1.11009 - 1.94876i) q^{46} +(0.154883 - 0.154883i) q^{47} +(-1.85196 - 3.54546i) q^{48} +(4.01185 + 4.01185i) q^{49} +(-6.18550 + 1.69594i) q^{50} +(-6.20086 + 1.23343i) q^{51} +(0.124946 - 2.31836i) q^{52} +(-4.50589 - 6.74354i) q^{53} +(0.632842 + 1.26472i) q^{54} +(-0.545706 - 1.31745i) q^{55} +(-3.25697 + 0.0567146i) q^{56} +(-1.43509 + 3.46461i) q^{57} +(0.622228 + 8.71779i) q^{58} +(5.69944 + 1.13369i) q^{59} +(-1.17282 + 0.695401i) q^{60} +(9.02079 + 6.02750i) q^{61} +(-5.23027 - 6.73492i) q^{62} +1.15169 q^{63} +(-5.45648 + 5.85037i) q^{64} -0.791408 q^{65} +(1.81437 + 2.33634i) q^{66} +(1.77800 + 1.18802i) q^{67} +(6.44903 + 10.8765i) q^{68} +(1.55540 + 0.309388i) q^{69} +(0.0790513 + 1.10756i) q^{70} +(3.89298 - 9.39848i) q^{71} +(1.96488 - 2.03452i) q^{72} +(-1.36156 - 3.28710i) q^{73} +(-0.660728 - 1.32045i) q^{74} +(-2.51964 - 3.77090i) q^{75} +(7.48926 + 0.403628i) q^{76} +(2.36269 - 0.469969i) q^{77} +(1.58328 - 0.434102i) q^{78} +(-6.41645 - 6.41645i) q^{79} +(2.09143 + 1.74994i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(-4.74878 + 8.33649i) q^{82} +(1.53602 + 7.72209i) q^{83} +(-0.765663 - 2.17239i) q^{84} +(3.58380 - 2.39462i) q^{85} +(4.24290 - 12.7417i) q^{86} +(-5.70966 + 2.36502i) q^{87} +(3.20073 - 4.97564i) q^{88} +(-10.4082 - 4.31121i) q^{89} +(-0.728547 - 0.631476i) q^{90} +(0.260826 - 1.31126i) q^{91} +(-0.450468 - 3.13959i) q^{92} +(3.34993 - 5.01352i) q^{93} +(0.0386495 - 0.307346i) q^{94} -2.55657i q^{95} +(-5.14394 - 2.35370i) q^{96} -12.9952i q^{97} +(7.96101 + 1.00112i) q^{98} +(-1.16209 + 1.73918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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