LMFDB - Embedded newform 990.2.z.a.161.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(161,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.161"); 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.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.6
Character	$\chi$	$=$	990.161
Dual form			990.2.z.a.701.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(-1.61538 + 0.524868i) q^{7} +(0.309017 - 0.951057i) q^{8} -1.00000i q^{10} +(1.21558 + 3.08583i) q^{11} +(3.64570 - 5.01788i) q^{13} +(1.61538 + 0.524868i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-5.56507 + 4.04326i) q^{17} +(2.46543 + 0.801067i) q^{19} +(-0.587785 + 0.809017i) q^{20} +(0.830387 - 3.21099i) q^{22} -0.389823i q^{23} +(-0.309017 + 0.951057i) q^{25} +(-5.89887 + 1.91666i) q^{26} +(-0.998357 - 1.37412i) q^{28} +(-0.320948 - 0.987777i) q^{29} +(6.40408 + 4.65284i) q^{31} +1.00000 q^{32} +6.87881 q^{34} +(-1.37412 - 0.998357i) q^{35} +(0.965076 + 2.97020i) q^{37} +(-1.52372 - 2.09722i) q^{38} +(0.951057 - 0.309017i) q^{40} +(-3.40165 + 10.4692i) q^{41} +5.33269i q^{43} +(-2.55917 + 2.10966i) q^{44} +(-0.229132 + 0.315373i) q^{46} +(3.49808 + 1.13660i) q^{47} +(-3.32916 + 2.41878i) q^{49} +(0.809017 - 0.587785i) q^{50} +(5.89887 + 1.91666i) q^{52} +(-2.34381 + 3.22598i) q^{53} +(-1.78200 + 2.79723i) q^{55} +1.69851i q^{56} +(-0.320948 + 0.987777i) q^{58} +(1.21751 - 0.395593i) q^{59} +(-5.79653 - 7.97824i) q^{61} +(-2.44614 - 7.52845i) q^{62} +(-0.809017 - 0.587785i) q^{64} +6.20244 q^{65} +3.54231 q^{67} +(-5.56507 - 4.04326i) q^{68} +(0.524868 + 1.61538i) q^{70} +(8.36599 + 11.5148i) q^{71} +(-4.28390 + 1.39192i) q^{73} +(0.965076 - 2.97020i) q^{74} +2.59231i q^{76} +(-3.58327 - 4.34677i) q^{77} +(4.79552 - 6.60047i) q^{79} +(-0.951057 - 0.309017i) q^{80} +(8.90564 - 6.47033i) q^{82} +(2.87351 - 2.08772i) q^{83} +(-6.54214 - 2.12567i) q^{85} +(3.13448 - 4.31424i) q^{86} +(3.31044 - 0.202506i) q^{88} +13.5907i q^{89} +(-3.25546 + 10.0193i) q^{91} +(0.370743 - 0.120462i) q^{92} +(-2.16193 - 2.97565i) q^{94} +(0.801067 + 2.46543i) q^{95} +(14.8654 + 10.8004i) q^{97} +4.11507 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) $ 32 * q - 8 * q^2 - 8 * q^4 - 8 * q^8 - 8 * q^16 + 4 * q^17 + 8 * q^25 - 8 * q^29 + 32 * q^31 + 32 * q^32 + 24 * q^34 + 16 * q^37 + 32 * q^41 - 20 * q^46 - 20 * q^47 + 16 * q^49 + 8 * q^50 - 40 * q^53 + 8 * q^55 - 8 * q^58 + 40 * q^59 - 28 * q^62 - 8 * q^64 + 8 * q^65 + 4 * q^68 - 40 * q^71 + 40 * q^73 + 16 * q^74 - 28 * q^77 + 20 * q^79 - 8 * q^82 - 24 * q^83 - 24 * q^91 + 20 * q^94 + 16 * q^95 + 48 * q^97 + 16 * q^98

Character values

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

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.587785	+	0.809017i	0.262866	+	0.361803i
$5$	0.587785	+	0.809017i	0.262866	+	0.361803i
$6$		0			0
$7$	−1.61538	+	0.524868i	−0.610555	+	0.198381i	−0.597942	−	0.801539i	$-0.704015\pi$
$7$	−1.61538	+	0.524868i	−0.610555	+	0.198381i	−0.0126126	+	0.999920i	$0.504015\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	1.21558	+	3.08583i	0.366510	+	0.930414i
$11$	1.21558	+	3.08583i	0.366510	+	0.930414i
$12$		0			0
$13$	3.64570	−	5.01788i	1.01114	−	1.39171i	0.0928990	−	0.995676i	$-0.470387\pi$
$13$	3.64570	−	5.01788i	1.01114	−	1.39171i	0.918236	−	0.396033i	$-0.129613\pi$
$14$	1.61538	+	0.524868i	0.431727	+	0.140277i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−5.56507	+	4.04326i	−1.34973	+	0.980635i	−0.350704	+	0.936486i	$0.614058\pi$
$17$	−5.56507	+	4.04326i	−1.34973	+	0.980635i	−0.999025	+	0.0441490i	$0.985942\pi$
$18$		0			0
$19$	2.46543	+	0.801067i	0.565609	+	0.183777i	0.577843	−	0.816148i	$-0.303894\pi$
$19$	2.46543	+	0.801067i	0.565609	+	0.183777i	−0.0122346	+	0.999925i	$0.503894\pi$
$20$	−0.587785	+	0.809017i	−0.131433	+	0.180902i
$21$		0			0
$22$	0.830387	−	3.21099i	0.177039	−	0.684585i
$23$		−	0.389823i		−	0.0812837i	−0.999174	−	0.0406418i	$-0.987060\pi$
$23$		−	0.389823i		−	0.0812837i	0.999174	−	0.0406418i	$-0.0129403\pi$
$24$		0			0
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	−5.89887	+	1.91666i	−1.15686	+	0.375888i
$27$		0			0
$28$	−0.998357	−	1.37412i	−0.188672	−	0.259684i
$29$	−0.320948	−	0.987777i	−0.0595986	−	0.183426i	0.916825	−	0.399290i	$-0.130743\pi$
$29$	−0.320948	−	0.987777i	−0.0595986	−	0.183426i	−0.976423	+	0.215864i	$0.930743\pi$
$30$		0			0
$31$	6.40408	+	4.65284i	1.15021	+	0.835675i	0.988508	−	0.151166i	$-0.0483026\pi$
$31$	6.40408	+	4.65284i	1.15021	+	0.835675i	0.161699	+	0.986840i	$0.448303\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	6.87881			1.17971
$35$	−1.37412	−	0.998357i	−0.232269	−	0.168753i
$36$		0			0
$37$	0.965076	+	2.97020i	0.158657	+	0.488297i	0.998513	−	0.0545124i	$-0.0173604\pi$
$37$	0.965076	+	2.97020i	0.158657	+	0.488297i	−0.839856	+	0.542810i	$0.817360\pi$
$38$	−1.52372	−	2.09722i	−0.247180	−	0.340214i
$39$		0			0
$40$	0.951057	−	0.309017i	0.150375	−	0.0488599i
$41$	−3.40165	+	10.4692i	−0.531249	+	1.63502i	0.220369	+	0.975417i	$0.429274\pi$
$41$	−3.40165	+	10.4692i	−0.531249	+	1.63502i	−0.751618	+	0.659599i	$0.770726\pi$
$42$		0			0
$43$			5.33269i			0.813228i	0.913600	+	0.406614i	$0.133291\pi$
$43$			5.33269i			0.813228i	−0.913600	+	0.406614i	$0.866709\pi$
$44$	−2.55917	+	2.10966i	−0.385809	+	0.318043i
$45$		0			0
$46$	−0.229132	+	0.315373i	−0.0337837	+	0.0464992i
$47$	3.49808	+	1.13660i	0.510248	+	0.165789i	0.552815	−	0.833304i	$-0.313554\pi$
$47$	3.49808	+	1.13660i	0.510248	+	0.165789i	−0.0425673	+	0.999094i	$0.513554\pi$
$48$		0			0
$49$	−3.32916	+	2.41878i	−0.475595	+	0.345540i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$		0			0
$52$	5.89887	+	1.91666i	0.818026	+	0.265793i
$53$	−2.34381	+	3.22598i	−0.321947	+	0.443122i	−0.939060	−	0.343752i	$-0.888302\pi$
$53$	−2.34381	+	3.22598i	−0.321947	+	0.443122i	0.617113	+	0.786874i	$0.288302\pi$
$54$		0			0
$55$	−1.78200	+	2.79723i	−0.240284	+	0.377178i
$56$			1.69851i			0.226973i
$57$		0			0
$58$	−0.320948	+	0.987777i	−0.0421426	+	0.129701i
$59$	1.21751	−	0.395593i	0.158506	−	0.0515018i	−0.228689	−	0.973500i	$-0.573444\pi$
$59$	1.21751	−	0.395593i	0.158506	−	0.0515018i	0.387195	+	0.921998i	$0.373444\pi$
$60$		0			0
$61$	−5.79653	−	7.97824i	−0.742170	−	1.02151i	−0.998491	−	0.0549171i	$-0.982511\pi$
$61$	−5.79653	−	7.97824i	−0.742170	−	1.02151i	0.256321	−	0.966592i	$-0.417489\pi$
$62$	−2.44614	−	7.52845i	−0.310660	−	0.956114i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	6.20244			0.769317
$66$		0			0
$67$	3.54231			0.432762			0.216381	−	0.976309i	$-0.430575\pi$
$67$	3.54231			0.432762			0.216381	+	0.976309i	$0.430575\pi$
$68$	−5.56507	−	4.04326i	−0.674864	−	0.490318i
$69$		0			0
$70$	0.524868	+	1.61538i	0.0627337	+	0.193074i
$71$	8.36599	+	11.5148i	0.992861	+	1.36656i	0.929605	+	0.368558i	$0.120148\pi$
$71$	8.36599	+	11.5148i	0.992861	+	1.36656i	0.0632560	+	0.997997i	$0.479852\pi$
$72$		0			0
$73$	−4.28390	+	1.39192i	−0.501393	+	0.162912i	−0.548784	−	0.835964i	$-0.684909\pi$
$73$	−4.28390	+	1.39192i	−0.501393	+	0.162912i	0.0473915	+	0.998876i	$0.484909\pi$
$74$	0.965076	−	2.97020i	0.112188	−	0.345278i
$75$		0			0
$76$			2.59231i			0.297358i
$77$	−3.58327	−	4.34677i	−0.408351	−	0.495360i
$78$		0			0
$79$	4.79552	−	6.60047i	0.539538	−	0.742611i	−0.449008	−	0.893528i	$-0.648223\pi$
$79$	4.79552	−	6.60047i	0.539538	−	0.742611i	0.988546	+	0.150917i	$0.0482226\pi$
$80$	−0.951057	−	0.309017i	−0.106331	−	0.0345492i
$81$		0			0
$82$	8.90564	−	6.47033i	0.983464	−	0.714528i
$83$	2.87351	−	2.08772i	0.315408	−	0.229158i	−0.418805	−	0.908076i	$-0.637551\pi$
$83$	2.87351	−	2.08772i	0.315408	−	0.229158i	0.734214	+	0.678918i	$0.237551\pi$
$84$		0			0
$85$	−6.54214	−	2.12567i	−0.709594	−	0.230561i
$86$	3.13448	−	4.31424i	0.338000	−	0.465217i
$87$		0			0
$88$	3.31044	−	0.202506i	0.352894	−	0.0215872i
$89$			13.5907i			1.44061i	0.693658	+	0.720305i	$0.255998\pi$
$89$			13.5907i			1.44061i	−0.693658	+	0.720305i	$0.744002\pi$
$90$		0			0
$91$	−3.25546	+	10.0193i	−0.341265	+	1.05030i
$92$	0.370743	−	0.120462i	0.0386527	−	0.0125590i
$93$		0			0
$94$	−2.16193	−	2.97565i	−0.222986	−	0.306914i
$95$	0.801067	+	2.46543i	0.0821878	+	0.252948i
$96$		0			0
$97$	14.8654	+	10.8004i	1.50936	+	1.09661i	0.966461	+	0.256812i	$0.0826721\pi$
$97$	14.8654	+	10.8004i	1.50936	+	1.09661i	0.542896	+	0.839800i	$0.317328\pi$
$98$	4.11507			0.415685
$99$		0			0
$100$	−1.00000			−0.100000
$101$	6.03094	+	4.38173i	0.600101	+	0.435999i	0.845915	−	0.533318i	$-0.179055\pi$
$101$	6.03094	+	4.38173i	0.600101	+	0.435999i	−0.245814	+	0.969317i	$0.579055\pi$
$102$		0			0
$103$	−3.95198	−	12.1630i	−0.389401	−	1.19845i	−0.933237	−	0.359261i	$-0.883029\pi$
$103$	−3.95198	−	12.1630i	−0.389401	−	1.19845i	0.543837	−	0.839191i	$-0.316971\pi$
$104$	−3.64570	−	5.01788i	−0.357490	−	0.492043i
$105$		0			0
$106$	3.79237	−	1.23221i	0.368347	−	0.119683i
$107$	5.45349	−	16.7841i	0.527209	−	1.62258i	−0.232698	−	0.972549i	$-0.574755\pi$
$107$	5.45349	−	16.7841i	0.527209	−	1.62258i	0.759907	−	0.650032i	$-0.225245\pi$
$108$		0			0
$109$			14.2681i			1.36664i	0.730119	+	0.683320i	$0.239465\pi$
$109$			14.2681i			1.36664i	−0.730119	+	0.683320i	$0.760535\pi$
$110$	3.08583	−	1.21558i	0.294223	−	0.115901i
$111$		0			0
$112$	0.998357	−	1.37412i	0.0943359	−	0.129842i
$113$	−2.41268	−	0.783929i	−0.226966	−	0.0737458i	0.193326	−	0.981135i	$-0.438072\pi$
$113$	−2.41268	−	0.783929i	−0.226966	−	0.0737458i	−0.420292	+	0.907389i	$0.638072\pi$
$114$		0			0
$115$	0.315373	−	0.229132i	0.0294087	−	0.0213667i
$116$	0.840253	−	0.610480i	0.0780155	−	0.0566816i
$117$		0			0
$118$	−1.21751	−	0.395593i	−0.112081	−	0.0364173i
$119$	6.86751	−	9.45232i	0.629544	−	0.866493i
$120$		0			0
$121$	−8.04475	+	7.50213i	−0.731341	+	0.682012i
$122$			9.86165i			0.892831i
$123$		0			0
$124$	−2.44614	+	7.52845i	−0.219670	+	0.676075i
$125$	−0.951057	+	0.309017i	−0.0850651	+	0.0276393i
$126$		0			0
$127$	8.07117	+	11.1090i	0.716201	+	0.985766i	0.999641	+	0.0267758i	$0.00852403\pi$
$127$	8.07117	+	11.1090i	0.716201	+	0.985766i	−0.283441	+	0.958990i	$0.591476\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	−5.01788	−	3.64570i	−0.440097	−	0.319749i
$131$	−12.0625			−1.05390			−0.526952	−	0.849895i	$-0.676665\pi$
$131$	−12.0625			−1.05390			−0.526952	+	0.849895i	$0.676665\pi$
$132$		0			0
$133$	−4.40305			−0.381793
$134$	−2.86579	−	2.08212i	−0.247567	−	0.179868i
$135$		0			0
$136$	2.12567	+	6.54214i	0.182275	+	0.560984i
$137$	1.92393	+	2.64806i	0.164373	+	0.226239i	0.883256	−	0.468891i	$-0.155346\pi$
$137$	1.92393	+	2.64806i	0.164373	+	0.226239i	−0.718883	+	0.695131i	$0.755346\pi$
$138$		0			0
$139$	14.9675	−	4.86324i	1.26953	−	0.412495i	0.404648	−	0.914473i	$-0.367394\pi$
$139$	14.9675	−	4.86324i	1.26953	−	0.412495i	0.864880	+	0.501978i	$0.167394\pi$
$140$	0.524868	−	1.61538i	0.0443594	−	0.136524i
$141$		0			0
$142$		−	14.2331i		−	1.19441i
$143$	19.9160	+	5.15042i	1.66546	+	0.430700i
$144$		0			0
$145$	0.610480	−	0.840253i	0.0506976	−	0.0697792i
$146$	4.28390	+	1.39192i	0.354538	+	0.115196i
$147$		0			0
$148$	−2.52660	+	1.83568i	−0.207685	+	0.150892i
$149$	12.2411	−	8.89368i	1.00283	−	0.728598i	0.0401366	−	0.999194i	$-0.487221\pi$
$149$	12.2411	−	8.89368i	1.00283	−	0.728598i	0.962693	+	0.270596i	$0.0872207\pi$
$150$		0			0
$151$	−2.96425	−	0.963144i	−0.241227	−	0.0783795i	0.185908	−	0.982567i	$-0.440477\pi$
$151$	−2.96425	−	0.963144i	−0.241227	−	0.0783795i	−0.427136	+	0.904188i	$0.640477\pi$
$152$	1.52372	−	2.09722i	0.123590	−	0.170107i
$153$		0			0
$154$	0.343958	+	5.62280i	0.0277169	+	0.453098i
$155$			7.91588i			0.635819i
$156$		0			0
$157$	−0.169013	+	0.520169i	−0.0134887	+	0.0415140i	−0.957574	−	0.288186i	$-0.906948\pi$
$157$	−0.169013	+	0.520169i	−0.0134887	+	0.0415140i	0.944086	+	0.329700i	$0.106948\pi$
$158$	−7.75932	+	2.52115i	−0.617298	+	0.200572i
$159$		0			0
$160$	0.587785	+	0.809017i	0.0464685	+	0.0639584i
$161$	0.204605	+	0.629710i	0.0161252	+	0.0496281i
$162$		0			0
$163$	−16.5943	−	12.0565i	−1.29977	−	0.944335i	−0.299813	−	0.953998i	$-0.596924\pi$
$163$	−16.5943	−	12.0565i	−1.29977	−	0.944335i	−0.999953	+	0.00966293i	$0.996924\pi$
$164$	−11.0080			−0.859579
$165$		0			0
$166$	−3.55185			−0.275677
$167$	−14.3586	−	10.4321i	−1.11110	−	0.807261i	−0.128263	−	0.991740i	$-0.540940\pi$
$167$	−14.3586	−	10.4321i	−1.11110	−	0.807261i	−0.982836	+	0.184479i	$0.940940\pi$
$168$		0			0
$169$	−7.87073	−	24.2236i	−0.605441	−	1.86335i
$170$	4.04326	+	5.56507i	0.310104	+	0.426822i
$171$		0			0
$172$	−5.07169	+	1.64789i	−0.386713	+	0.125651i
$173$	7.35405	−	22.6334i	0.559118	−	1.72079i	−0.125695	−	0.992069i	$-0.540116\pi$
$173$	7.35405	−	22.6334i	0.559118	−	1.72079i	0.684813	−	0.728719i	$-0.259884\pi$
$174$		0			0
$175$		−	1.69851i		−	0.128395i
$176$	−2.79723	−	1.78200i	−0.210849	−	0.134323i
$177$		0			0
$178$	7.98840	−	10.9951i	0.598756	−	0.824117i
$179$	−5.41896	−	1.76073i	−0.405032	−	0.131603i	0.0994139	−	0.995046i	$-0.468303\pi$
$179$	−5.41896	−	1.76073i	−0.405032	−	0.131603i	−0.504446	+	0.863443i	$0.668303\pi$
$180$		0			0
$181$	−5.97112	+	4.33827i	−0.443830	+	0.322461i	−0.787155	−	0.616755i	$-0.788447\pi$
$181$	−5.97112	+	4.33827i	−0.443830	+	0.322461i	0.343325	+	0.939217i	$0.388447\pi$
$182$	8.52290	−	6.19225i	0.631759	−	0.459000i
$183$		0			0
$184$	−0.370743	−	0.120462i	−0.0273316	−	0.00888057i
$185$	−1.83568	+	2.52660i	−0.134962	+	0.185759i
$186$		0			0
$187$	−19.2416	−	12.2580i	−1.40709	−	0.896394i
$188$			3.67810i			0.268253i
$189$		0			0
$190$	0.801067	−	2.46543i	0.0581155	−	0.178861i
$191$	6.81335	−	2.21379i	0.492997	−	0.160184i	−0.0519588	−	0.998649i	$-0.516546\pi$
$191$	6.81335	−	2.21379i	0.492997	−	0.160184i	0.544956	+	0.838465i	$0.316546\pi$
$192$		0			0
$193$	−3.47734	−	4.78614i	−0.250304	−	0.344514i	0.665314	−	0.746564i	$-0.268298\pi$
$193$	−3.47734	−	4.78614i	−0.250304	−	0.344514i	−0.915618	+	0.402050i	$0.868298\pi$
$194$	−5.67809	−	17.4754i	−0.407663	−	1.25466i
$195$		0			0
$196$	−3.32916	−	2.41878i	−0.237797	−	0.172770i
$197$	−15.3348			−1.09256			−0.546278	−	0.837604i	$-0.683956\pi$
$197$	−15.3348			−1.09256			−0.546278	+	0.837604i	$0.683956\pi$
$198$		0			0
$199$	−4.15221			−0.294343			−0.147171	−	0.989111i	$-0.547017\pi$
$199$	−4.15221			−0.294343			−0.147171	+	0.989111i	$0.547017\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$		0			0
$202$	−2.30361	−	7.08979i	−0.162082	−	0.498836i
$203$	1.03690	+	1.42718i	0.0727764	+	0.100168i
$204$		0			0
$205$	−10.4692	+	3.40165i	−0.731201	+	0.237582i
$206$	−3.95198	+	12.1630i	−0.275348	+	0.847433i
$207$		0			0
$208$			6.20244i			0.430062i
$209$	0.524957	+	8.58167i	0.0363121	+	0.593607i
$210$		0			0
$211$	−4.45306	+	6.12911i	−0.306561	+	0.421945i	−0.934305	−	0.356475i	$-0.883979\pi$
$211$	−4.45306	+	6.12911i	−0.306561	+	0.421945i	0.627744	+	0.778420i	$0.283979\pi$
$212$	−3.79237	−	1.23221i	−0.260461	−	0.0846288i
$213$		0			0
$214$	−14.2774	+	10.3732i	−0.975984	+	0.709094i
$215$	−4.31424	+	3.13448i	−0.294229	+	0.213770i
$216$		0			0
$217$	−12.7871	−	4.15479i	−0.868047	−	0.282046i
$218$	8.38660	−	11.5432i	0.568012	−	0.781802i
$219$		0			0
$220$	−3.21099	−	0.830387i	−0.216485	−	0.0559847i
$221$			42.6654i			2.86998i
$222$		0			0
$223$	−5.98584	+	18.4225i	−0.400842	+	1.23366i	0.523476	+	0.852040i	$0.324635\pi$
$223$	−5.98584	+	18.4225i	−0.400842	+	1.23366i	−0.924318	+	0.381623i	$0.875365\pi$
$224$	−1.61538	+	0.524868i	−0.107932	+	0.0350692i
$225$		0			0
$226$	1.49112	+	2.05235i	0.0991879	+	0.136520i
$227$	−5.95408	−	18.3248i	−0.395186	−	1.21626i	−0.928816	−	0.370541i	$-0.879172\pi$
$227$	−5.95408	−	18.3248i	−0.395186	−	1.21626i	0.533630	−	0.845718i	$-0.320828\pi$
$228$		0			0
$229$	8.65927	+	6.29133i	0.572221	+	0.415743i	0.835911	−	0.548865i	$-0.184940\pi$
$229$	8.65927	+	6.29133i	0.572221	+	0.415743i	−0.263690	+	0.964607i	$0.584940\pi$
$230$	−0.389823			−0.0257042
$231$		0			0
$232$	−1.03861			−0.0681881
$233$	−7.82880	−	5.68796i	−0.512882	−	0.372631i	0.301034	−	0.953613i	$-0.402668\pi$
$233$	−7.82880	−	5.68796i	−0.512882	−	0.372631i	−0.813916	+	0.580983i	$0.802668\pi$
$234$		0			0
$235$	1.13660	+	3.49808i	0.0741433	+	0.228190i
$236$	0.752462	+	1.03568i	0.0489811	+	0.0674167i
$237$		0			0
$238$	−11.1119	+	3.61046i	−0.720275	+	0.234032i
$239$	3.46127	−	10.6527i	0.223891	−	0.689066i	−0.774511	−	0.632560i	$-0.782004\pi$
$239$	3.46127	−	10.6527i	0.223891	−	0.689066i	0.998402	−	0.0565060i	$-0.0179960\pi$
$240$		0			0
$241$		−	11.8973i		−	0.766372i	−0.923671	−	0.383186i	$-0.874827\pi$
$241$		−	11.8973i		−	0.766372i	0.923671	−	0.383186i	$-0.125173\pi$
$242$	10.9180	−	1.34077i	0.701835	−	0.0861877i
$243$		0			0
$244$	5.79653	−	7.97824i	0.371085	−	0.510754i
$245$	−3.91367	−	1.27163i	−0.250035	−	0.0812413i
$246$		0			0
$247$	13.0079	−	9.45078i	0.827672	−	0.601339i
$248$	6.40408	−	4.65284i	0.406660	−	0.295456i
$249$		0			0
$250$	0.951057	+	0.309017i	0.0601501	+	0.0195440i
$251$	11.4895	−	15.8140i	0.725212	−	0.998169i	−0.274122	−	0.961695i	$-0.588387\pi$
$251$	11.4895	−	15.8140i	0.725212	−	0.998169i	0.999335	−	0.0364742i	$-0.0116127\pi$
$252$		0			0
$253$	1.20293	−	0.473859i	0.0756275	−	0.0297913i
$254$		−	13.7315i		−	0.861591i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−22.4112	+	7.28184i	−1.39797	+	0.454229i	−0.908535	−	0.417810i	$-0.862798\pi$
$257$	−22.4112	+	7.28184i	−1.39797	+	0.454229i	−0.489438	+	0.872038i	$0.662798\pi$
$258$		0			0
$259$	−3.11792	−	4.29145i	−0.193738	−	0.266658i
$260$	1.91666	+	5.89887i	0.118866	+	0.365832i
$261$		0			0
$262$	9.75875	+	7.09014i	0.602897	+	0.438031i
$263$	−1.83788			−0.113329			−0.0566643	−	0.998393i	$-0.518046\pi$
$263$	−1.83788			−0.113329			−0.0566643	+	0.998393i	$0.518046\pi$
$264$		0			0
$265$	−3.98753			−0.244952
$266$	3.56215	+	2.58805i	0.218409	+	0.158684i
$267$		0			0
$268$	1.09463	+	3.36894i	0.0668654	+	0.205791i
$269$	−10.2392	−	14.0930i	−0.624294	−	0.859268i	0.373362	−	0.927686i	$-0.378205\pi$
$269$	−10.2392	−	14.0930i	−0.624294	−	0.859268i	−0.997657	+	0.0684181i	$0.978205\pi$
$270$		0			0
$271$	−24.4590	+	7.94721i	−1.48578	+	0.482759i	−0.935834	−	0.352442i	$-0.885351\pi$
$271$	−24.4590	+	7.94721i	−1.48578	+	0.482759i	−0.549945	+	0.835201i	$0.685351\pi$
$272$	2.12567	−	6.54214i	0.128888	−	0.396675i
$273$		0			0
$274$		−	3.27319i		−	0.197740i
$275$	−3.31044	+	0.202506i	−0.199627	+	0.0122116i
$276$		0			0
$277$	6.36164	−	8.75605i	0.382234	−	0.526100i	−0.573941	−	0.818897i	$-0.694586\pi$
$277$	6.36164	−	8.75605i	0.382234	−	0.526100i	0.956175	+	0.292797i	$0.0945859\pi$
$278$	−14.9675	−	4.86324i	−0.897692	−	0.291678i
$279$		0			0
$280$	−1.37412	+	0.998357i	−0.0821194	+	0.0596633i
$281$	8.83847	−	6.42152i	0.527259	−	0.383076i	−0.292073	−	0.956396i	$-0.594345\pi$
$281$	8.83847	−	6.42152i	0.527259	−	0.383076i	0.819331	+	0.573320i	$0.194345\pi$
$282$		0			0
$283$	16.3072	+	5.29853i	0.969361	+	0.314965i	0.750558	−	0.660804i	$-0.229785\pi$
$283$	16.3072	+	5.29853i	0.969361	+	0.314965i	0.218803	+	0.975769i	$0.429785\pi$
$284$	−8.36599	+	11.5148i	−0.496430	+	0.683278i
$285$		0			0
$286$	−13.0850	−	15.8731i	−0.773733	−	0.938595i
$287$		−	18.6971i		−	1.10366i
$288$		0			0
$289$	9.36879	−	28.8342i	0.551105	−	1.69613i
$290$	−0.987777	+	0.320948i	−0.0580042	+	0.0188467i
$291$		0			0
$292$	−2.64760	−	3.64410i	−0.154939	−	0.213255i
$293$	3.77542	+	11.6196i	0.220563	+	0.678822i	0.998712	+	0.0507424i	$0.0161588\pi$
$293$	3.77542	+	11.6196i	0.220563	+	0.678822i	−0.778149	+	0.628080i	$0.783841\pi$
$294$		0			0
$295$	1.03568	+	0.752462i	0.0602993	+	0.0438100i
$296$	3.12305			0.181524
$297$		0			0
$298$	−15.1308			−0.876505
$299$	−1.95608	−	1.42118i	−0.113123	−	0.0821888i
$300$		0			0
$301$	−2.79896	−	8.61431i	−0.161329	−	0.496521i
$302$	1.83201	+	2.52154i	0.105420	+	0.145098i
$303$		0			0
$304$	−2.46543	+	0.801067i	−0.141402	+	0.0459444i
$305$	3.04742	−	9.37898i	0.174495	−	0.537039i
$306$		0			0
$307$			18.6138i			1.06235i	0.847263	+	0.531173i	$0.178249\pi$
$307$			18.6138i			1.06235i	−0.847263	+	0.531173i	$0.821751\pi$
$308$	3.02673	−	4.75111i	0.172464	−	0.270720i
$309$		0			0
$310$	4.65284	−	6.40408i	0.264264	−	0.363728i
$311$	14.1410	+	4.59468i	0.801862	+	0.260541i	0.681147	−	0.732147i	$-0.261481\pi$
$311$	14.1410	+	4.59468i	0.801862	+	0.260541i	0.120715	+	0.992687i	$0.461481\pi$
$312$		0			0
$313$	−1.26108	+	0.916230i	−0.0712806	+	0.0517884i	−0.622855	−	0.782337i	$-0.714027\pi$
$313$	−1.26108	+	0.916230i	−0.0712806	+	0.0517884i	0.551574	+	0.834126i	$0.314027\pi$
$314$	0.442482	−	0.321482i	0.0249707	−	0.0181423i
$315$		0			0
$316$	7.75932	+	2.52115i	0.436496	+	0.141826i
$317$	12.9866	−	17.8745i	0.729401	−	1.00393i	−0.269758	−	0.962928i	$-0.586944\pi$
$317$	12.9866	−	17.8745i	0.729401	−	1.00393i	0.999159	−	0.0410064i	$-0.0130564\pi$
$318$		0			0
$319$	2.65798	−	2.19111i	0.148818	−	0.122679i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	0.204605	−	0.629710i	0.0114022	−	0.0350924i
$323$	−16.9592	+	5.51039i	−0.943637	+	0.306606i
$324$		0			0
$325$	3.64570	+	5.01788i	0.202227	+	0.278342i
$326$	6.33846	+	19.5078i	0.351055	+	1.08044i
$327$		0			0
$328$	8.90564	+	6.47033i	0.491732	+	0.357264i
$329$	−6.24728			−0.344424
$330$		0			0
$331$	18.6696			1.02618			0.513088	−	0.858336i	$-0.328501\pi$
$331$	18.6696			1.02618			0.513088	+	0.858336i	$0.328501\pi$
$332$	2.87351	+	2.08772i	0.157704	+	0.114579i
$333$		0			0
$334$	5.48448	+	16.8795i	0.300098	+	0.923606i
$335$	2.08212	+	2.86579i	0.113758	+	0.156575i
$336$		0			0
$337$	1.82329	−	0.592422i	0.0993207	−	0.0322713i	−0.258935	−	0.965895i	$-0.583372\pi$
$337$	1.82329	−	0.592422i	0.0993207	−	0.0322713i	0.358256	+	0.933623i	$0.383372\pi$
$338$	−7.87073	+	24.2236i	−0.428111	+	1.31759i
$339$		0			0
$340$		−	6.87881i		−	0.373056i
$341$	−6.57324	+	25.4178i	−0.355961	+	1.37645i
$342$		0			0
$343$	11.0968	−	15.2735i	0.599172	−	0.824689i
$344$	5.07169	+	1.64789i	0.273447	+	0.0888485i
$345$		0			0
$346$	−19.2531	+	13.9882i	−1.03506	+	0.752012i
$347$	12.1464	−	8.82489i	0.652054	−	0.473745i	−0.211916	−	0.977288i	$-0.567970\pi$
$347$	12.1464	−	8.82489i	0.652054	−	0.473745i	0.863970	+	0.503543i	$0.167970\pi$
$348$		0			0
$349$	−28.3676	−	9.21718i	−1.51848	−	0.493384i	−0.573137	−	0.819460i	$-0.694274\pi$
$349$	−28.3676	−	9.21718i	−1.51848	−	0.493384i	−0.945344	+	0.326075i	$0.894274\pi$
$350$	−0.998357	+	1.37412i	−0.0533645	+	0.0734499i
$351$		0			0
$352$	1.21558	+	3.08583i	0.0647904	+	0.164476i
$353$		−	3.83534i		−	0.204135i	−0.994777	−	0.102067i	$-0.967454\pi$
$353$		−	3.83534i		−	0.204135i	0.994777	−	0.102067i	$-0.0325457\pi$
$354$		0			0
$355$	−4.39826	+	13.5365i	−0.233436	+	0.718441i
$356$	−12.9255	+	4.19975i	−0.685051	+	0.222586i
$357$		0			0
$358$	3.34910	+	4.60964i	0.177006	+	0.243627i
$359$	5.12869	+	15.7845i	0.270682	+	0.833073i	0.990330	+	0.138734i	$0.0443032\pi$
$359$	5.12869	+	15.7845i	0.270682	+	0.833073i	−0.719648	+	0.694339i	$0.755697\pi$
$360$		0			0
$361$	−9.93468	−	7.21797i	−0.522878	−	0.379893i
$362$	7.38071			0.387922
$363$		0			0
$364$	−10.5349			−0.552178
$365$	−3.64410	−	2.64760i	−0.190741	−	0.138582i
$366$		0			0
$367$	7.55388	+	23.2485i	0.394310	+	1.21356i	0.929498	+	0.368827i	$0.120241\pi$
$367$	7.55388	+	23.2485i	0.394310	+	1.21356i	−0.535188	+	0.844733i	$0.679759\pi$
$368$	0.229132	+	0.315373i	0.0119443	+	0.0164400i
$369$		0			0
$370$	2.97020	−	0.965076i	0.154413	−	0.0501719i
$371$	2.09292	−	6.44136i	0.108659	−	0.334419i
$372$		0			0
$373$			4.42523i			0.229130i	0.993416	+	0.114565i	$0.0365474\pi$
$373$			4.42523i			0.229130i	−0.993416	+	0.114565i	$0.963453\pi$
$374$	8.36171	+	21.2269i	0.432374	+	1.09762i
$375$		0			0
$376$	2.16193	−	2.97565i	0.111493	−	0.153457i
$377$	−6.12662	−	1.99066i	−0.315537	−	0.102524i
$378$		0			0
$379$	13.8438	−	10.0581i	0.711108	−	0.516650i	−0.172423	−	0.985023i	$-0.555160\pi$
$379$	13.8438	−	10.0581i	0.711108	−	0.516650i	0.883531	+	0.468373i	$0.155160\pi$
$380$	−2.09722	+	1.52372i	−0.107585	+	0.0781652i
$381$		0			0
$382$	−6.81335	−	2.21379i	−0.348601	−	0.113267i
$383$	8.02094	−	11.0399i	0.409851	−	0.564111i	−0.553331	−	0.832961i	$-0.686644\pi$
$383$	8.02094	−	11.0399i	0.409851	−	0.564111i	0.963182	+	0.268850i	$0.0866437\pi$
$384$		0			0
$385$	1.41042	−	5.45389i	0.0718815	−	0.277956i
$386$			5.91600i			0.301116i
$387$		0			0
$388$	−5.67809	+	17.4754i	−0.288262	+	0.887178i
$389$	−20.3193	+	6.60215i	−1.03023	+	0.334742i	−0.774881	−	0.632107i	$-0.782190\pi$
$389$	−20.3193	+	6.60215i	−1.03023	+	0.334742i	−0.255349	+	0.966849i	$0.582190\pi$
$390$		0			0
$391$	1.57616	+	2.16939i	0.0797096	+	0.109711i
$392$	1.27163	+	3.91367i	0.0642269	+	0.197670i
$393$		0			0
$394$	12.4061	+	9.01354i	0.625009	+	0.454096i
$395$	8.15863			0.410505
$396$		0			0
$397$	−2.86796			−0.143939			−0.0719694	−	0.997407i	$-0.522928\pi$
$397$	−2.86796			−0.143939			−0.0719694	+	0.997407i	$0.522928\pi$
$398$	3.35921	+	2.44061i	0.168382	+	0.122337i
$399$		0			0
$400$	−0.309017	−	0.951057i	−0.0154508	−	0.0475528i
$401$	−10.5898	−	14.5756i	−0.528830	−	0.727872i	0.458121	−	0.888890i	$-0.348523\pi$
$401$	−10.5898	−	14.5756i	−0.528830	−	0.727872i	−0.986952	+	0.161017i	$0.948523\pi$
$402$		0			0
$403$	46.6947	−	15.1720i	2.32603	−	0.755773i
$404$	−2.30361	+	7.08979i	−0.114609	+	0.352730i
$405$		0			0
$406$		−	1.76409i		−	0.0875501i
$407$	−7.99242	+	6.58856i	−0.396169	+	0.326583i
$408$		0			0
$409$	18.4282	−	25.3642i	0.911216	−	1.25418i	−0.0555335	−	0.998457i	$-0.517686\pi$
$409$	18.4282	−	25.3642i	0.911216	−	1.25418i	0.966750	−	0.255725i	$-0.0823140\pi$
$410$	10.4692	+	3.40165i	0.517037	+	0.167996i
$411$		0			0
$412$	10.3464	−	7.51712i	0.509732	−	0.370342i
$413$	−1.75910	+	1.27806i	−0.0865597	+	0.0628893i
$414$		0			0
$415$	3.37801	+	1.09758i	0.165820	+	0.0538782i
$416$	3.64570	−	5.01788i	0.178745	−	0.246022i
$417$		0			0
$418$	4.61948	−	7.25128i	0.225946	−	0.354672i
$419$		−	5.04085i		−	0.246262i	−0.992390	−	0.123131i	$-0.960706\pi$
$419$		−	5.04085i		−	0.246262i	0.992390	−	0.123131i	$-0.0392935\pi$
$420$		0			0
$421$	−5.70729	+	17.5652i	−0.278156	+	0.856078i	0.710210	+	0.703989i	$0.248600\pi$
$421$	−5.70729	+	17.5652i	−0.278156	+	0.856078i	−0.988367	+	0.152088i	$0.951400\pi$
$422$	7.20520	−	2.34111i	0.350743	−	0.113963i
$423$		0			0
$424$	2.34381	+	3.22598i	0.113826	+	0.156667i
$425$	−2.12567	−	6.54214i	−0.103110	−	0.317340i
$426$		0			0
$427$	13.5511	+	9.84545i	0.655783	+	0.476455i
$428$	17.6479			0.853042
$429$		0			0
$430$	5.33269			0.257165
$431$	−29.2507	−	21.2519i	−1.40896	−	1.02367i	−0.993473	−	0.114068i	$-0.963612\pi$
$431$	−29.2507	−	21.2519i	−1.40896	−	1.02367i	−0.415485	−	0.909600i	$-0.636388\pi$
$432$		0			0
$433$	−6.86971	−	21.1428i	−0.330137	−	1.01606i	−0.969068	−	0.246794i	$-0.920623\pi$
$433$	−6.86971	−	21.1428i	−0.330137	−	1.01606i	0.638931	−	0.769264i	$-0.279377\pi$
$434$	7.90288	+	10.8774i	0.379350	+	0.522131i
$435$		0			0
$436$	−13.5698	+	4.40910i	−0.649876	+	0.211157i
$437$	0.312274	−	0.961081i	0.0149381	−	0.0459748i
$438$		0			0
$439$			21.8795i			1.04425i	0.852869	+	0.522125i	$0.174861\pi$
$439$			21.8795i			1.04425i	−0.852869	+	0.522125i	$0.825139\pi$
$440$	2.10966	+	2.55917i	0.100574	+	0.122004i
$441$		0			0
$442$	25.0781	−	34.5170i	1.19284	−	1.64181i
$443$	9.35911	+	3.04096i	0.444665	+	0.144480i	0.522787	−	0.852463i	$-0.324892\pi$
$443$	9.35911	+	3.04096i	0.444665	+	0.144480i	−0.0781220	+	0.996944i	$0.524892\pi$
$444$		0			0
$445$	−10.9951	+	7.98840i	−0.521217	+	0.378687i
$446$	15.6711	−	11.3857i	0.742050	−	0.539131i
$447$		0			0
$448$	1.61538	+	0.524868i	0.0763194	+	0.0247977i
$449$	8.35788	−	11.5036i	0.394433	−	0.542890i	−0.564903	−	0.825157i	$-0.691086\pi$
$449$	8.35788	−	11.5036i	0.394433	−	0.542890i	0.959336	+	0.282267i	$0.0910864\pi$
$450$		0			0
$451$	−36.4412	+	2.22918i	−1.71595	+	0.104968i
$452$		−	2.53685i		−	0.119323i
$453$		0			0
$454$	−5.95408	+	18.3248i	−0.279439	+	0.860025i
$455$	−10.0193	+	3.25546i	−0.469711	+	0.152618i
$456$		0			0
$457$	5.77438	+	7.94776i	0.270114	+	0.371780i	0.922428	−	0.386168i	$-0.126202\pi$
$457$	5.77438	+	7.94776i	0.270114	+	0.371780i	−0.652314	+	0.757949i	$0.726202\pi$
$458$	−3.30755	−	10.1796i	−0.154552	−	0.475661i
$459$		0			0
$460$	0.315373	+	0.229132i	0.0147044	+	0.0106833i
$461$	16.2650			0.757535			0.378768	−	0.925492i	$-0.376348\pi$
$461$	16.2650			0.757535			0.378768	+	0.925492i	$0.376348\pi$
$462$		0			0
$463$	37.4758			1.74165			0.870824	−	0.491594i	$-0.163586\pi$
$463$	37.4758			1.74165			0.870824	+	0.491594i	$0.163586\pi$
$464$	0.840253	+	0.610480i	0.0390078	+	0.0283408i
$465$		0			0
$466$	2.99034	+	9.20331i	0.138525	+	0.426335i
$467$	15.2076	+	20.9315i	0.703724	+	0.968592i	0.999909	+	0.0134620i	$0.00428522\pi$
$467$	15.2076	+	20.9315i	0.703724	+	0.968592i	−0.296186	+	0.955130i	$0.595715\pi$
$468$		0			0
$469$	−5.72217	+	1.85924i	−0.264225	+	0.0858519i
$470$	1.13660	−	3.49808i	0.0524272	−	0.161354i
$471$		0			0
$472$		−	1.28017i		−	0.0589244i
$473$	−16.4558	+	6.48229i	−0.756639	+	0.298056i
$474$		0			0
$475$	−1.52372	+	2.09722i	−0.0699131	+	0.0962271i
$476$	11.1119	+	3.61046i	0.509312	+	0.165485i
$477$		0			0
$478$	−9.06173	+	6.58374i	−0.414474	+	0.301133i
$479$	21.6255	−	15.7119i	0.988095	−	0.717893i	0.0285918	−	0.999591i	$-0.490898\pi$
$479$	21.6255	−	15.7119i	0.988095	−	0.717893i	0.959503	+	0.281698i	$0.0908977\pi$
$480$		0			0
$481$	18.4225	+	5.98582i	0.839992	+	0.272930i
$482$	−6.99305	+	9.62511i	−0.318525	+	0.438412i
$483$		0			0
$484$	−9.62092	−	5.33273i	−0.437314	−	0.242397i
$485$			18.3747i			0.834352i
$486$		0			0
$487$	5.17641	−	15.9314i	0.234566	−	0.721918i	−0.762613	−	0.646855i	$-0.776084\pi$
$487$	5.17641	−	15.9314i	0.234566	−	0.721918i	0.997179	−	0.0750637i	$-0.0239160\pi$
$488$	−9.37898	+	3.04742i	−0.424567	+	0.137950i
$489$		0			0
$490$	2.41878	+	3.32916i	0.109269	+	0.150396i
$491$	7.25089	+	22.3159i	0.327228	+	1.00710i	0.970425	+	0.241404i	$0.0776077\pi$
$491$	7.25089	+	22.3159i	0.327228	+	1.00710i	−0.643197	+	0.765701i	$0.722392\pi$
$492$		0			0
$493$	5.77994	+	4.19937i	0.260315	+	0.189130i
$494$	−16.0786			−0.723411
$495$		0			0
$496$	−7.91588			−0.355434
$497$	−19.5580	−	14.2097i	−0.877295	−	0.637392i
$498$		0			0
$499$	2.16842	+	6.67370i	0.0970717	+	0.298756i	0.987788	−	0.155804i	$-0.0497967\pi$
$499$	2.16842	+	6.67370i	0.0970717	+	0.298756i	−0.890716	+	0.454559i	$0.849797\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$		0			0
$502$	−18.5904	+	6.04040i	−0.829732	+	0.269596i
$503$	2.32216	−	7.14689i	0.103540	−	0.318664i	−0.885845	−	0.463982i	$-0.846420\pi$
$503$	2.32216	−	7.14689i	0.103540	−	0.318664i	0.989385	+	0.145318i	$0.0464204\pi$
$504$		0			0
$505$			7.45465i			0.331727i
$506$	−1.25172	−	0.323704i	−0.0556456	−	0.0143904i
$507$		0			0
$508$	−8.07117	+	11.1090i	−0.358100	+	0.492883i
$509$	16.7333	+	5.43697i	0.741689	+	0.240989i	0.655401	−	0.755281i	$-0.272500\pi$
$509$	16.7333	+	5.43697i	0.741689	+	0.240989i	0.0862879	+	0.996270i	$0.472500\pi$
$510$		0			0
$511$	6.18954	−	4.49696i	0.273809	−	0.198934i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	22.4112	+	7.28184i	0.988516	+	0.321188i
$515$	7.51712	−	10.3464i	0.331244	−	0.455918i
$516$		0			0
$517$	0.744837	+	12.1761i	0.0327579	+	0.535505i
$518$			5.30452i			0.233067i
$519$		0			0
$520$	1.91666	−	5.89887i	0.0840510	−	0.258682i
$521$	−1.98950	+	0.646427i	−0.0871615	+	0.0283205i	−0.352273	−	0.935897i	$-0.614591\pi$
$521$	−1.98950	+	0.646427i	−0.0871615	+	0.0283205i	0.265112	+	0.964218i	$0.414591\pi$
$522$		0			0
$523$	21.8755	+	30.1090i	0.956548	+	1.31657i	0.948557	+	0.316607i	$0.102544\pi$
$523$	21.8755	+	30.1090i	0.956548	+	1.31657i	0.00799081	+	0.999968i	$0.497456\pi$
$524$	−3.72751	−	11.4721i	−0.162837	−	0.501161i
$525$		0			0
$526$	1.48688	+	1.08028i	0.0648310	+	0.0471025i
$527$	−54.4519			−2.37196
$528$		0			0
$529$	22.8480			0.993393
$530$	3.22598	+	2.34381i	0.140128	+	0.101809i
$531$		0			0
$532$	−1.36062	−	4.18755i	−0.0589903	−	0.181553i
$533$	40.1318	+	55.2367i	1.73830	+	2.39257i
$534$		0			0
$535$	16.7841	−	5.45349i	0.725640	−	0.235775i
$536$	1.09463	−	3.36894i	0.0472810	−	0.145516i
$537$		0			0
$538$			17.4199i			0.751027i
$539$	−11.5108	−	7.33304i	−0.495805	−	0.315856i
$540$		0			0
$541$	5.83746	−	8.03457i	0.250972	−	0.345433i	−0.664880	−	0.746951i	$-0.731517\pi$
$541$	5.83746	−	8.03457i	0.250972	−	0.345433i	0.915851	+	0.401518i	$0.131517\pi$
$542$	24.4590	+	7.94721i	1.05060	+	0.341362i
$543$		0			0
$544$	−5.56507	+	4.04326i	−0.238601	+	0.173353i
$545$	−11.5432	+	8.38660i	−0.494455	+	0.359243i
$546$		0			0
$547$	7.46450	+	2.42536i	0.319159	+	0.103701i	0.464215	−	0.885722i	$-0.346336\pi$
$547$	7.46450	+	2.42536i	0.319159	+	0.103701i	−0.145056	+	0.989423i	$0.546336\pi$
$548$	−1.92393	+	2.64806i	−0.0821863	+	0.113120i
$549$		0			0
$550$	2.79723	+	1.78200i	0.119274	+	0.0759845i
$551$		−	2.69240i		−	0.114700i
$552$		0			0
$553$	−4.28220	+	13.1793i	−0.182098	+	0.560439i
$554$	−10.2934	+	3.34451i	−0.437323	+	0.142095i
$555$		0			0
$556$	9.25043	+	12.7321i	0.392306	+	0.539963i
$557$	8.84622	+	27.2259i	0.374826	+	1.15360i	0.943596	+	0.331100i	$0.107420\pi$
$557$	8.84622	+	27.2259i	0.374826	+	1.15360i	−0.568769	+	0.822497i	$0.692580\pi$
$558$		0			0
$559$	26.7588	+	19.4414i	1.13178	+	0.822284i
$560$	1.69851			0.0717750
$561$		0			0
$562$	−10.9249			−0.460841
$563$	−25.3031	−	18.3837i	−1.06640	−	0.774783i	−0.0911355	−	0.995838i	$-0.529050\pi$
$563$	−25.3031	−	18.3837i	−1.06640	−	0.774783i	−0.975261	+	0.221056i	$0.929050\pi$
$564$		0			0
$565$	−0.783929	−	2.41268i	−0.0329801	−	0.101502i
$566$	−10.0784	−	13.8717i	−0.423626	−	0.583072i
$567$		0			0
$568$	13.5365	−	4.39826i	0.567977	−	0.184547i
$569$	4.00931	−	12.3394i	0.168079	−	0.517295i	−0.831171	−	0.556017i	$-0.812329\pi$
$569$	4.00931	−	12.3394i	0.168079	−	0.517295i	0.999250	+	0.0387226i	$0.0123289\pi$
$570$		0			0
$571$		−	29.2178i		−	1.22273i	−0.791350	−	0.611363i	$-0.790621\pi$
$571$		−	29.2178i		−	1.22273i	0.791350	−	0.611363i	$-0.209379\pi$
$572$	1.25603	+	20.5328i	0.0525172	+	0.858518i
$573$		0			0
$574$	−10.9899	+	15.1263i	−0.458709	+	0.631359i
$575$	0.370743	+	0.120462i	0.0154611	+	0.00502361i
$576$		0			0
$577$	−14.3177	+	10.4024i	−0.596054	+	0.433058i	−0.844476	−	0.535593i	$-0.820088\pi$
$577$	−14.3177	+	10.4024i	−0.596054	+	0.433058i	0.248422	+	0.968652i	$0.420088\pi$
$578$	−24.5278	+	17.8205i	−1.02022	+	0.741235i
$579$		0			0
$580$	0.987777	+	0.320948i	0.0410152	+	0.0133266i
$581$	−3.54602	+	4.88067i	−0.147114	+	0.202484i
$582$		0			0
$583$	−12.8039	−	3.31119i	−0.530284	−	0.137136i
$584$			4.50436i			0.186392i
$585$		0			0
$586$	3.77542	−	11.6196i	0.155961	−	0.480000i
$587$	23.1090	−	7.50856i	0.953809	−	0.309911i	0.209547	−	0.977799i	$-0.432801\pi$
$587$	23.1090	−	7.50856i	0.953809	−	0.309911i	0.744262	+	0.667887i	$0.232801\pi$
$588$		0			0
$589$	12.0616	+	16.6014i	0.496989	+	0.684047i
$590$	−0.395593	−	1.21751i	−0.0162863	−	0.0501241i
$591$		0			0
$592$	−2.52660	−	1.83568i	−0.103843	−	0.0754461i
$593$	−32.0210			−1.31495			−0.657473	−	0.753478i	$-0.728375\pi$
$593$	−32.0210			−1.31495			−0.657473	+	0.753478i	$0.728375\pi$
$594$		0			0
$595$	11.6837			0.478985
$596$	12.2411	+	8.89368i	0.501415	+	0.364299i
$597$		0			0
$598$	0.747157	+	2.29951i	0.0305535	+	0.0940341i
$599$	14.0322	+	19.3137i	0.573341	+	0.789136i	0.992946	−	0.118571i	$-0.0378314\pi$
$599$	14.0322	+	19.3137i	0.573341	+	0.789136i	−0.419605	+	0.907707i	$0.637831\pi$
$600$		0			0
$601$	44.7645	−	14.5449i	1.82598	−	0.593297i	0.826438	−	0.563027i	$-0.190363\pi$
$601$	44.7645	−	14.5449i	1.82598	−	0.593297i	0.999542	−	0.0302696i	$-0.00963659\pi$
$602$	−2.79896	+	8.61431i	−0.114077	+	0.351093i
$603$		0			0
$604$		−	3.11680i		−	0.126821i
$605$	−10.7979	−	2.09870i	−0.438999	−	0.0853242i
$606$		0			0
$607$	−16.5913	+	22.8360i	−0.673420	+	0.926883i	−0.999832	−	0.0183447i	$-0.994160\pi$
$607$	−16.5913	+	22.8360i	−0.673420	+	0.926883i	0.326412	+	0.945228i	$0.394160\pi$
$608$	2.46543	+	0.801067i	0.0999864	+	0.0324876i
$609$		0			0
$610$	−7.97824	+	5.79653i	−0.323029	+	0.234695i
$611$	18.4563	−	13.4093i	0.746660	−	0.542480i
$612$		0			0
$613$	−13.4962	−	4.38519i	−0.545107	−	0.177116i	0.0235020	−	0.999724i	$-0.492518\pi$
$613$	−13.4962	−	4.38519i	−0.545107	−	0.177116i	−0.568609	+	0.822608i	$0.692518\pi$
$614$	10.9409	−	15.0589i	0.441540	−	0.607727i
$615$		0			0
$616$	−5.24131	+	2.06466i	−0.211178	+	0.0831877i
$617$			11.3503i			0.456947i	0.973550	+	0.228473i	$0.0733733\pi$
$617$			11.3503i			0.456947i	−0.973550	+	0.228473i	$0.926627\pi$
$618$		0			0
$619$	8.24664	−	25.3805i	0.331460	−	1.02013i	−0.636979	−	0.770881i	$-0.719816\pi$
$619$	8.24664	−	25.3805i	0.331460	−	1.02013i	0.968439	−	0.249249i	$-0.0801837\pi$
$620$	−7.52845	+	2.44614i	−0.302350	+	0.0982394i
$621$		0			0
$622$	−8.73961	−	12.0290i	−0.350426	−	0.482320i
$623$	−7.13331	−	21.9541i	−0.285790	−	0.879571i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	1.55878			0.0623015
$627$		0			0
$628$	−0.546938			−0.0218252
$629$	−17.3800	−	12.6273i	−0.692986	−	0.503484i
$630$		0			0
$631$	−10.7354	−	33.0401i	−0.427369	−	1.31531i	−0.900708	−	0.434425i	$-0.856952\pi$
$631$	−10.7354	−	33.0401i	−0.427369	−	1.31531i	0.473339	−	0.880880i	$-0.343048\pi$
$632$	−4.79552	−	6.60047i	−0.190756	−	0.262553i
$633$		0			0
$634$	−21.0128	+	6.82747i	−0.834525	+	0.271153i
$635$	−4.24327	+	13.0594i	−0.168389	+	0.518248i
$636$		0			0
$637$			25.5235i			1.01128i
$638$	−3.43825	+	0.210325i	−0.136122	+	0.00832683i
$639$		0			0
$640$	−0.587785	+	0.809017i	−0.0232343	+	0.0319792i
$641$	−22.0975	−	7.17992i	−0.872799	−	0.283590i	−0.161835	−	0.986818i	$-0.551741\pi$
$641$	−22.0975	−	7.17992i	−0.872799	−	0.283590i	−0.710964	+	0.703228i	$0.751741\pi$
$642$		0			0
$643$	−7.61817	+	5.53492i	−0.300431	+	0.218276i	−0.727780	−	0.685811i	$-0.759448\pi$
$643$	−7.61817	+	5.53492i	−0.300431	+	0.218276i	0.427349	+	0.904087i	$0.359448\pi$
$644$	−0.535664	+	0.389182i	−0.0211081	+	0.0153359i
$645$		0			0
$646$	16.9592	+	5.51039i	0.667252	+	0.216803i
$647$	0.944989	−	1.30067i	0.0371513	−	0.0511344i	−0.790037	−	0.613059i	$-0.789939\pi$
$647$	0.944989	−	1.30067i	0.0371513	−	0.0511344i	0.827189	+	0.561924i	$0.189939\pi$
$648$		0			0
$649$	2.70071	+	3.27616i	0.106012	+	0.128601i
$650$		−	6.20244i		−	0.243280i
$651$		0			0
$652$	6.33846	−	19.5078i	0.248233	−	0.763983i
$653$	−1.95595	+	0.635525i	−0.0765421	+	0.0248700i	−0.347038	−	0.937851i	$-0.612812\pi$
$653$	−1.95595	+	0.635525i	−0.0765421	+	0.0248700i	0.270496	+	0.962721i	$0.412812\pi$
$654$		0			0
$655$	−7.09014	−	9.75875i	−0.277035	−	0.381306i
$656$	−3.40165	−	10.4692i	−0.132812	−	0.408754i
$657$		0			0
$658$	5.05416	+	3.67206i	0.197031	+	0.143152i
$659$	43.1008			1.67897			0.839484	−	0.543385i	$-0.182858\pi$
$659$	43.1008			1.67897			0.839484	+	0.543385i	$0.182858\pi$
$660$		0			0
$661$	27.8596			1.08361			0.541807	−	0.840503i	$-0.317740\pi$
$661$	27.8596			1.08361			0.541807	+	0.840503i	$0.317740\pi$
$662$	−15.1041	−	10.9737i	−0.587036	−	0.426507i
$663$		0			0
$664$	−1.09758	−	3.37801i	−0.0425944	−	0.131092i
$665$	−2.58805	−	3.56215i	−0.100360	−	0.138134i
$666$		0			0
$667$	−0.385058	+	0.125113i	−0.0149095	+	0.00484439i
$668$	5.48448	−	16.8795i	0.212201	−	0.653088i
$669$		0			0
$670$		−	3.54231i		−	0.136851i
$671$	17.5734	−	27.5853i	0.678414	−	1.06492i
$672$		0			0
$673$	−3.68226	+	5.06820i	−0.141941	+	0.195365i	−0.874069	−	0.485803i	$-0.838527\pi$
$673$	−3.68226	+	5.06820i	−0.141941	+	0.195365i	0.732128	+	0.681167i	$0.238527\pi$
$674$	−1.82329	−	0.592422i	−0.0702304	−	0.0228192i
$675$		0			0
$676$	20.6058	−	14.9710i	0.792532	−	0.575808i
$677$	25.3638	−	18.4279i	0.974810	−	0.708241i	0.0182674	−	0.999833i	$-0.494185\pi$
$677$	25.3638	−	18.4279i	0.974810	−	0.708241i	0.956543	+	0.291592i	$0.0941850\pi$
$678$		0			0
$679$	−29.6821	−	9.64428i	−1.13909	−	0.370114i
$680$	−4.04326	+	5.56507i	−0.155052	+	0.213411i
$681$		0			0
$682$	20.2581	−	16.6998i	0.775722	−	0.639468i
$683$			29.4142i			1.12550i	0.826627	+	0.562751i	$0.190257\pi$
$683$			29.4142i			1.12550i	−0.826627	+	0.562751i	$0.809743\pi$
$684$		0			0
$685$	−1.01147	+	3.11299i	−0.0386463	+	0.118941i
$686$	−17.9550	+	5.83394i	−0.685526	+	0.222741i
$687$		0			0
$688$	−3.13448	−	4.31424i	−0.119501	−	0.164479i
$689$	7.64273	+	23.5219i	0.291165	+	0.896113i
$690$		0			0
$691$	−20.5530	−	14.9327i	−0.781874	−	0.568065i	0.123667	−	0.992324i	$-0.460535\pi$
$691$	−20.5530	−	14.9327i	−0.781874	−	0.568065i	−0.905541	+	0.424259i	$0.860535\pi$
$692$	23.7982			0.904672
$693$		0			0
$694$	−15.0138			−0.569916
$695$	12.7321	+	9.25043i	0.482957	+	0.350889i
$696$		0			0
$697$	−23.3993	−	72.0157i	−0.886313	−	2.72779i
$698$	17.5321	+	24.1309i	0.663601	+	0.913368i
$699$		0			0
$700$	1.61538	−	0.524868i	0.0610555	−	0.0198381i
$701$	−6.19791	+	19.0752i	−0.234092	+	0.720460i	0.763149	+	0.646223i	$0.223652\pi$
$701$	−6.19791	+	19.0752i	−0.234092	+	0.720460i	−0.997241	+	0.0742375i	$0.976348\pi$
$702$		0			0
$703$			8.09591i			0.305343i
$704$	0.830387	−	3.21099i	0.0312964	−	0.121019i
$705$		0			0
$706$	−2.25436	+	3.10286i	−0.0848439	+	0.116778i
$707$	−12.0421	−	3.91270i	−0.452888	−	0.147152i
$708$		0			0
$709$	−18.3056	+	13.2998i	−0.687482	+	0.499485i	−0.875832	−	0.482617i	$-0.839686\pi$
$709$	−18.3056	+	13.2998i	−0.687482	+	0.499485i	0.188349	+	0.982102i	$0.439686\pi$
$710$	11.5148	−	8.36599i	0.432143	−	0.313970i
$711$		0			0
$712$	12.9255	+	4.19975i	0.484404	+	0.157392i
$713$	1.81378	−	2.49646i	0.0679267	−	0.0934931i
$714$		0			0
$715$	7.53953	+	19.1397i	0.281962	+	0.715784i
$716$		−	5.69783i		−	0.212938i
$717$		0			0
$718$	5.12869	−	15.7845i	0.191401	−	0.589072i
$719$	−16.1703	+	5.25405i	−0.603050	+	0.195943i	−0.594600	−	0.804021i	$-0.702690\pi$
$719$	−16.1703	+	5.25405i	−0.603050	+	0.195943i	−0.00844994	+	0.999964i	$0.502690\pi$
$720$		0			0
$721$	12.7679	+	17.5735i	0.475501	+	0.654471i
$722$	3.79471	+	11.6789i	0.141224	+	0.434644i
$723$		0			0
$724$	−5.97112	−	4.33827i	−0.221915	−	0.161231i
$725$	1.03861			0.0385730
$726$		0			0
$727$	−49.7264			−1.84425			−0.922124	−	0.386893i	$-0.873548\pi$
$727$	−49.7264			−1.84425			−0.922124	+	0.386893i	$0.873548\pi$
$728$	8.52290	+	6.19225i	0.315880	+	0.229500i
$729$		0			0
$730$	1.39192	+	4.28390i	0.0515174	+	0.158554i
$731$	−21.5615	−	29.6768i	−0.797481	−	1.09764i
$732$		0			0
$733$	6.15015	−	1.99831i	0.227161	−	0.0738091i	−0.193225	−	0.981155i	$-0.561895\pi$
$733$	6.15015	−	1.99831i	0.227161	−	0.0738091i	0.420386	+	0.907345i	$0.361895\pi$
$734$	7.55388	−	23.2485i	0.278819	−	0.858116i
$735$		0			0
$736$		−	0.389823i		−	0.0143691i
$737$	4.30595	+	10.9310i	0.158612	+	0.402648i
$738$		0			0
$739$	6.60348	−	9.08891i	0.242913	−	0.334341i	−0.670101	−	0.742270i	$-0.733749\pi$
$739$	6.60348	−	9.08891i	0.242913	−	0.334341i	0.913014	+	0.407929i	$0.133749\pi$
$740$	−2.97020	−	0.965076i	−0.109187	−	0.0354769i
$741$		0			0
$742$	−5.47935	+	3.98098i	−0.201153	+	0.146146i
$743$	−33.5835	+	24.3998i	−1.23206	+	0.895142i	−0.997043	−	0.0768497i	$-0.975514\pi$
$743$	−33.5835	+	24.3998i	−1.23206	+	0.895142i	−0.235015	+	0.971992i	$0.575514\pi$
$744$		0			0
$745$	14.3903	+	4.67568i	0.527219	+	0.171304i
$746$	2.60109	−	3.58009i	0.0952326	−	0.131076i
$747$		0			0
$748$	5.71207	−	22.0878i	0.208854	−	0.807610i
$749$			29.9750i			1.09526i
$750$		0			0
$751$	−0.466342	+	1.43525i	−0.0170171	+	0.0523732i	−0.959204	−	0.282713i	$-0.908766\pi$
$751$	−0.466342	+	1.43525i	−0.0170171	+	0.0523732i	0.942187	+	0.335086i	$0.108766\pi$
$752$	−3.49808	+	1.13660i	−0.127562	+	0.0414474i
$753$		0			0
$754$	3.78646	+	5.21162i	0.137895	+	0.189796i
$755$	−0.963144	−	2.96425i	−0.0350524	−	0.107880i
$756$		0			0
$757$	6.61741	+	4.80783i	0.240514	+	0.174744i	0.701512	−	0.712657i	$-0.252509\pi$
$757$	6.61741	+	4.80783i	0.240514	+	0.174744i	−0.460998	+	0.887401i	$0.652509\pi$
$758$	−17.1119			−0.621531
$759$		0			0
$760$	2.59231			0.0940329
$761$	−9.90410	−	7.19575i	−0.359023	−	0.260846i	0.393621	−	0.919273i	$-0.371222\pi$
$761$	−9.90410	−	7.19575i	−0.359023	−	0.260846i	−0.752645	+	0.658427i	$0.771222\pi$
$762$		0			0
$763$	−7.48888	−	23.0484i	−0.271116	−	0.834409i
$764$	4.21088	+	5.79578i	0.152344	+	0.209684i
$765$		0			0
$766$	−12.9781	+	4.21686i	−0.468920	+	0.152361i
$767$	2.45364	−	7.55152i	0.0885958	−	0.272670i
$768$		0			0
$769$		−	45.7938i		−	1.65136i	−0.564135	−	0.825682i	$-0.690790\pi$
$769$		−	45.7938i		−	1.65136i	0.564135	−	0.825682i	$-0.309210\pi$
$770$	−4.34677	+	3.58327i	−0.156647	+	0.129132i
$771$		0			0
$772$	3.47734	−	4.78614i	0.125152	−	0.172257i
$773$	−12.0552	−	3.91696i	−0.433594	−	0.140883i	0.0840840	−	0.996459i	$-0.473204\pi$
$773$	−12.0552	−	3.91696i	−0.433594	−	0.140883i	−0.517678	+	0.855575i	$0.673204\pi$
$774$		0			0
$775$	−6.40408	+	4.65284i	−0.230041	+	0.167135i
$776$	14.8654	−	10.8004i	0.533638	−	0.387711i
$777$		0			0
$778$	20.3193	+	6.60215i	0.728483	+	0.236698i
$779$	−16.7731	+	23.0862i	−0.600958	+	0.827148i
$780$		0			0
$781$	−25.3633	+	39.8132i	−0.907569	+	1.42463i
$782$		−	2.68152i		−	0.0958909i
$783$		0			0
$784$	1.27163	−	3.91367i	0.0454153	−	0.139774i
$785$	−0.520169	+	0.169013i	−0.0185656	+	0.00603233i
$786$		0			0
$787$	11.2679	+	15.5089i	0.401656	+	0.552832i	0.961159	−	0.275997i	$-0.0890079\pi$
$787$	11.2679	+	15.5089i	0.401656	+	0.552832i	−0.559503	+	0.828829i	$0.689008\pi$
$788$	−4.73870	−	14.5842i	−0.168809	−	0.519541i
$789$		0			0
$790$	−6.60047	−	4.79552i	−0.234834	−	0.170617i
$791$	4.30885			0.153205
$792$		0			0
$793$	−61.1662			−2.17208
$794$	2.32023	+	1.68575i	0.0823419	+	0.0598249i
$795$		0			0
$796$	−1.28310	−	3.94899i	−0.0454784	−	0.139968i
$797$	−3.99961	−	5.50499i	−0.141673	−	0.194997i	0.732284	−	0.681000i	$-0.238454\pi$
$797$	−3.99961	−	5.50499i	−0.141673	−	0.194997i	−0.873957	+	0.486003i	$0.838454\pi$
$798$		0			0
$799$	−24.0626	+	7.81842i	−0.851275	+	0.276596i
$800$	−0.309017	+	0.951057i	−0.0109254	+	0.0336249i
$801$		0			0
$802$			18.0165i			0.636184i
$803$	−9.50266	−	11.5274i	−0.335341	−	0.406794i
$804$		0			0
$805$	−0.389182	+	0.535664i	−0.0137169	+	0.0188797i
$806$	−46.6947	−	15.1720i	−1.64475	−	0.534412i
$807$		0			0
$808$	6.03094	−	4.38173i	0.212168	−	0.154149i
$809$	−12.2423	+	8.89457i	−0.430417	+	0.312717i	−0.781816	−	0.623509i	$-0.785706\pi$
$809$	−12.2423	+	8.89457i	−0.430417	+	0.312717i	0.351398	+	0.936226i	$0.385706\pi$
$810$		0			0
$811$	2.61264	+	0.848899i	0.0917423	+	0.0298089i	0.354528	−	0.935045i	$-0.384641\pi$
$811$	2.61264	+	0.848899i	0.0917423	+	0.0298089i	−0.262786	+	0.964854i	$0.584641\pi$
$812$	−1.03690	+	1.42718i	−0.0363882	+	0.0500841i
$813$		0			0
$814$	10.3387	−	0.632436i	0.362370	−	0.0221669i
$815$		−	20.5117i		−	0.718493i
$816$		0			0
$817$	−4.27185	+	13.1474i	−0.149453	+	0.459969i
$818$	−29.8175	+	9.68828i	−1.04254	+	0.338743i
$819$		0			0
$820$	−6.47033	−	8.90564i	−0.225954	−	0.310998i
$821$	−5.31937	−	16.3713i	−0.185647	−	0.571364i	0.814311	−	0.580428i	$-0.197115\pi$
$821$	−5.31937	−	16.3713i	−0.185647	−	0.571364i	−0.999959	+	0.00906407i	$0.997115\pi$
$822$		0			0
$823$	27.4634	+	19.9534i	0.957315	+	0.695530i	0.952526	−	0.304458i	$-0.0984755\pi$
$823$	27.4634	+	19.9534i	0.957315	+	0.695530i	0.00478949	+	0.999989i	$0.498475\pi$
$824$	−12.7889			−0.445522
$825$		0			0
$826$	2.17437			0.0756560
$827$	1.94119	+	1.41036i	0.0675017	+	0.0490429i	0.621024	−	0.783791i	$-0.286717\pi$
$827$	1.94119	+	1.41036i	0.0675017	+	0.0490429i	−0.553523	+	0.832834i	$0.686717\pi$
$828$		0			0
$829$	−1.84865	−	5.68956i	−0.0642062	−	0.197606i	0.913807	−	0.406148i	$-0.133128\pi$
$829$	−1.84865	−	5.68956i	−0.0642062	−	0.197606i	−0.978013	+	0.208542i	$0.933128\pi$
$830$	−2.08772	−	2.87351i	−0.0724660	−	0.0997409i
$831$		0			0
$832$	−5.89887	+	1.91666i	−0.204506	+	0.0664482i
$833$	8.74729	−	26.9214i	0.303075	−	0.932770i
$834$		0			0
$835$		−	17.7482i		−	0.614201i
$836$	−7.99943	+	3.15115i	−0.276666	+	0.108985i
$837$		0			0
$838$	−2.96294	+	4.07814i	−0.102353	+	0.140877i
$839$	21.1525	+	6.87287i	0.730266	+	0.237278i	0.650468	−	0.759533i	$-0.274573\pi$
$839$	21.1525	+	6.87287i	0.730266	+	0.237278i	0.0797974	+	0.996811i	$0.474573\pi$
$840$		0			0
$841$	22.5888	−	16.4117i	0.778924	−	0.565921i
$842$	14.9419	−	10.8559i	0.514932	−	0.374120i
$843$		0			0
$844$	−7.20520	−	2.34111i	−0.248013	−	0.0805843i
$845$	14.9710	−	20.6058i	0.515019	−	0.708862i
$846$		0			0
$847$	9.05768	−	16.3412i	0.311225	−	0.561490i
$848$		−	3.98753i		−	0.136932i
$849$		0			0
$850$	−2.12567	+	6.54214i	−0.0729099	+	0.224393i
$851$	1.15785	−	0.376208i	0.0396906	−	0.0128963i
$852$		0			0
$853$	−27.8060	−	38.2717i	−0.952059	−	1.31040i	−0.950607	−	0.310398i	$-0.899538\pi$
$853$	−27.8060	−	38.2717i	−0.952059	−	1.31040i	−0.00145281	−	0.999999i	$-0.500462\pi$
$854$	−5.17606	−	15.9303i	−0.177121	−	0.545123i
$855$		0			0
$856$	−14.2774	−	10.3732i	−0.487992	−	0.354547i
$857$	−50.0014			−1.70802			−0.854008	−	0.520260i	$-0.825835\pi$
$857$	−50.0014			−1.70802			−0.854008	+	0.520260i	$0.825835\pi$
$858$		0			0
$859$	−43.1879			−1.47355			−0.736776	−	0.676137i	$-0.763653\pi$
$859$	−43.1879			−1.47355			−0.736776	+	0.676137i	$0.763653\pi$
$860$	−4.31424	−	3.13448i	−0.147114	−	0.106885i
$861$		0			0
$862$	11.1728	+	34.3863i	0.380546	+	1.17120i
$863$	33.4166	+	45.9940i	1.13751	+	1.56565i	0.772942	+	0.634477i	$0.218784\pi$
$863$	33.4166	+	45.9940i	1.13751	+	1.56565i	0.364571	+	0.931176i	$0.381216\pi$
$864$		0			0
$865$	22.6334	−	7.35405i	0.769560	−	0.250045i
$866$	−6.86971	+	21.1428i	−0.233442	+	0.718462i
$867$		0			0
$868$		−	13.4452i		−	0.456359i
$869$	26.1973	+	6.77482i	0.888682	+	0.229820i
$870$		0			0
$871$	12.9142	−	17.7749i	0.437581	−	0.602279i
$872$	13.5698	+	4.40910i	0.459532	+	0.149311i
$873$		0			0
$874$	−0.817545	+	0.593981i	−0.0276539	+	0.0200917i
$875$	1.37412	−	0.998357i	0.0464538	−	0.0337506i
$876$		0			0
$877$	0.219212	+	0.0712264i	0.00740228	+	0.00240515i	0.312716	−	0.949847i	$-0.398761\pi$
$877$	0.219212	+	0.0712264i	0.00740228	+	0.00240515i	−0.305314	+	0.952252i	$0.598761\pi$
$878$	12.8604	−	17.7009i	0.434019	−	0.597376i
$879$		0			0
$880$	−0.202506	−	3.31044i	−0.00682647	−	0.111595i
$881$		−	0.767691i		−	0.0258642i	−0.999916	−	0.0129321i	$-0.995883\pi$
$881$		−	0.767691i		−	0.0258642i	0.999916	−	0.0129321i	$-0.00411652\pi$
$882$		0			0
$883$	7.69488	−	23.6824i	0.258953	−	0.796976i	−0.734072	−	0.679072i	$-0.762382\pi$
$883$	7.69488	−	23.6824i	0.258953	−	0.796976i	0.993025	−	0.117904i	$-0.0376176\pi$
$884$	−40.5772	+	13.1843i	−1.36476	+	0.443437i
$885$		0			0
$886$	−5.78425	−	7.96134i	−0.194326	−	0.267466i
$887$	4.21923	+	12.9855i	0.141668	+	0.436009i	0.996567	−	0.0827845i	$-0.0263813\pi$
$887$	4.21923	+	12.9855i	0.141668	+	0.436009i	−0.854900	+	0.518794i	$0.826381\pi$
$888$		0			0
$889$	−18.8687	−	13.7089i	−0.632837	−	0.459783i
$890$	13.5907			0.455561
$891$		0			0
$892$	−19.3706			−0.648575
$893$	7.71379	+	5.60440i	0.258132	+	0.187544i
$894$		0			0
$895$	−1.76073	−	5.41896i	−0.0588546	−	0.181136i
$896$	−0.998357	−	1.37412i	−0.0333528	−	0.0459062i
$897$		0			0
$898$	−13.5233	+	4.39400i	−0.451280	+	0.146630i
$899$	2.54059	−	7.81912i	0.0847333	−	0.260782i
$900$		0			0
$901$		−	27.4295i		−	0.913808i
$902$	30.7918	+	19.6162i	1.02526	+	0.653147i
$903$		0			0
$904$	−1.49112	+	2.05235i	−0.0495940	+	0.0682602i
$905$	−7.01948	−	2.28077i	−0.233335	−	0.0758152i
$906$		0			0
$907$	−40.4482	+	29.3874i	−1.34306	+	0.975791i	−0.343736	+	0.939066i	$0.611692\pi$
$907$	−40.4482	+	29.3874i	−1.34306	+	0.975791i	−0.999325	+	0.0367247i	$0.988308\pi$
$908$	15.5880	−	11.3253i	0.517306	−	0.375845i
$909$		0			0
$910$	10.0193	+	3.25546i	0.332135	+	0.107917i
$911$	31.9556	−	43.9830i	1.05873	−	1.45722i	0.177752	−	0.984075i	$-0.443118\pi$
$911$	31.9556	−	43.9830i	1.05873	−	1.45722i	0.880983	−	0.473148i	$-0.156882\pi$
$912$		0			0
$913$	9.93534	+	6.32938i	0.328812	+	0.209472i
$914$		−	9.82397i		−	0.324948i
$915$		0			0
$916$	−3.30755	+	10.1796i	−0.109284	+	0.336343i
$917$	19.4854	−	6.33120i	0.643466	−	0.209075i
$918$		0			0
$919$	15.1862	+	20.9020i	0.500946	+	0.689492i	0.982360	−	0.187001i	$-0.0598767\pi$
$919$	15.1862	+	20.9020i	0.500946	+	0.689492i	−0.481414	+	0.876493i	$0.659877\pi$
$920$	−0.120462	−	0.370743i	−0.00397151	−	0.0122231i
$921$		0			0
$922$	−13.1586	−	9.56031i	−0.433357	−	0.314852i
$923$	88.2797			2.90576
$924$		0			0
$925$	−3.12305			−0.102685
$926$	−30.3186	−	22.0277i	−0.996330	−	0.723876i
$927$		0			0
$928$	−0.320948	−	0.987777i	−0.0105356	−	0.0324254i
$929$	7.23178	+	9.95370i	0.237267	+	0.326570i	0.911001	−	0.412404i	$-0.135311\pi$
$929$	7.23178	+	9.95370i	0.237267	+	0.326570i	−0.673734	+	0.738974i	$0.735311\pi$
$930$		0			0
$931$	−10.1454	+	3.29645i	−0.332503	+	0.108037i
$932$	2.99034	−	9.20331i	0.0979518	−	0.301464i
$933$		0			0
$934$		−	25.8727i		−	0.846581i
$935$	−1.39300	−	22.7719i	−0.0455559	−	0.744720i
$936$		0			0
$937$	−26.8318	+	36.9307i	−0.876555	+	1.20647i	0.100808	+	0.994906i	$0.467857\pi$
$937$	−26.8318	+	36.9307i	−0.876555	+	1.20647i	−0.977363	+	0.211569i	$0.932143\pi$
$938$	5.72217	+	1.85924i	0.186835	+	0.0607065i
$939$		0			0
$940$	−2.97565	+	2.16193i	−0.0970549	+	0.0705145i
$941$	38.0212	−	27.6240i	1.23945	−	0.900517i	0.241893	−	0.970303i	$-0.422232\pi$
$941$	38.0212	−	27.6240i	1.23945	−	0.900517i	0.997562	+	0.0697865i	$0.0222318\pi$
$942$		0			0
$943$	4.08114	+	1.32604i	0.132900	+	0.0431819i
$944$	−0.752462	+	1.03568i	−0.0244906	+	0.0337084i
$945$		0			0
$946$	17.1232	+	4.42820i	0.556724	+	0.143973i
$947$			21.0266i			0.683274i	0.939832	+	0.341637i	$0.110981\pi$
$947$			21.0266i			0.683274i	−0.939832	+	0.341637i	$0.889019\pi$
$948$		0			0
$949$	−8.63332	+	26.5706i	−0.280249	+	0.862519i
$950$	2.46543	−	0.801067i	0.0799892	−	0.0259901i
$951$		0			0
$952$	−6.86751	−	9.45232i	−0.222577	−	0.306351i
$953$	−7.41204	−	22.8119i	−0.240100	−	0.738951i	−0.996404	−	0.0847307i	$-0.972997\pi$
$953$	−7.41204	−	22.8119i	−0.240100	−	0.738951i	0.756304	−	0.654220i	$-0.227003\pi$
$954$		0			0
$955$	5.79578	+	4.21088i	0.187547	+	0.136261i
$956$	11.2009			0.362264
$957$		0			0
$958$	−26.7306			−0.863627
$959$	−4.49776	−	3.26781i	−0.145240	−	0.105523i
$960$		0			0
$961$	9.78385	+	30.1116i	0.315608	+	0.971342i
$962$	−11.3857	−	15.6711i	−0.367090	−	0.505256i
$963$		0			0
$964$	11.3150	−	3.67647i	0.364432	−	0.118411i
$965$	1.82814	−	5.62645i	0.0588500	−	0.181122i
$966$		0			0
$967$			38.0027i			1.22209i	0.791597	+	0.611043i	$0.209250\pi$
$967$			38.0027i			1.22209i	−0.791597	+	0.611043i	$0.790750\pi$
$968$	4.64899	+	9.96930i	0.149424	+	0.320425i
$969$		0			0
$970$	10.8004	−	14.8654i	0.346779	−	0.477301i
$971$	−13.0185	−	4.22996i	−0.417783	−	0.135746i	0.0925797	−	0.995705i	$-0.470489\pi$
$971$	−13.0185	−	4.22996i	−0.417783	−	0.135746i	−0.510362	+	0.859959i	$0.670489\pi$
$972$		0			0
$973$	−21.6256	+	15.7119i	−0.693285	+	0.503701i
$974$	−13.5520	+	9.84612i	−0.434235	+	0.315490i
$975$		0			0
$976$	9.37898	+	3.04742i	0.300214	+	0.0975454i
$977$	−16.3090	+	22.4474i	−0.521770	+	0.718155i	−0.985848	−	0.167640i	$-0.946386\pi$
$977$	−16.3090	+	22.4474i	−0.521770	+	0.718155i	0.464079	+	0.885794i	$0.346386\pi$
$978$		0			0
$979$	−41.9386	+	16.5205i	−1.34036	+	0.527998i
$980$		−	4.11507i		−	0.131451i
$981$		0			0
$982$	7.25089	−	22.3159i	0.231385	−	0.712130i
$983$	−3.44009	+	1.11775i	−0.109722	+	0.0356507i	−0.363363	−	0.931648i	$-0.618372\pi$
$983$	−3.44009	+	1.11775i	−0.109722	+	0.0356507i	0.253642	+	0.967298i	$0.418372\pi$
$984$		0			0
$985$	−9.01354	−	12.4061i	−0.287195	−	0.395290i
$986$	−2.20774	−	6.79473i	−0.0703088	−	0.216388i
$987$		0			0
$988$	13.0079	+	9.45078i	0.413836	+	0.300669i
$989$	2.07881			0.0661022
$990$		0			0
$991$	−24.7402			−0.785899			−0.392950	−	0.919560i	$-0.628545\pi$
$991$	−24.7402			−0.785899			−0.392950	+	0.919560i	$0.628545\pi$
$992$	6.40408	+	4.65284i	0.203330	+	0.147728i
$993$		0			0
$994$	7.47048	+	22.9918i	0.236949	+	0.729255i
$995$	−2.44061	−	3.35921i	−0.0773726	−	0.106494i
$996$		0			0
$997$	−18.3270	+	5.95482i	−0.580423	+	0.188591i	−0.584490	−	0.811401i	$-0.698705\pi$
$997$	−18.3270	+	5.95482i	−0.580423	+	0.188591i	0.00406703	+	0.999992i	$0.498705\pi$
$998$	2.16842	−	6.67370i	0.0686400	−	0.211252i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.z.a.161.6	✓	32
3.2	odd	2		990.2.z.b.161.2	yes	32
11.8	odd	10		990.2.z.b.701.2	yes	32
33.8	even	10	inner	990.2.z.a.701.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.z.a.161.6	✓	32	1.1	even	1	trivial
990.2.z.a.701.6	yes	32	33.8	even	10	inner
990.2.z.b.161.2	yes	32	3.2	odd	2
990.2.z.b.701.2	yes	32	11.8	odd	10

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.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(-1.61538 + 0.524868i) q^{7} +(0.309017 - 0.951057i) q^{8} -1.00000i q^{10} +(1.21558 + 3.08583i) q^{11} +(3.64570 - 5.01788i) q^{13} +(1.61538 + 0.524868i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-5.56507 + 4.04326i) q^{17} +(2.46543 + 0.801067i) q^{19} +(-0.587785 + 0.809017i) q^{20} +(0.830387 - 3.21099i) q^{22} -0.389823i q^{23} +(-0.309017 + 0.951057i) q^{25} +(-5.89887 + 1.91666i) q^{26} +(-0.998357 - 1.37412i) q^{28} +(-0.320948 - 0.987777i) q^{29} +(6.40408 + 4.65284i) q^{31} +1.00000 q^{32} +6.87881 q^{34} +(-1.37412 - 0.998357i) q^{35} +(0.965076 + 2.97020i) q^{37} +(-1.52372 - 2.09722i) q^{38} +(0.951057 - 0.309017i) q^{40} +(-3.40165 + 10.4692i) q^{41} +5.33269i q^{43} +(-2.55917 + 2.10966i) q^{44} +(-0.229132 + 0.315373i) q^{46} +(3.49808 + 1.13660i) q^{47} +(-3.32916 + 2.41878i) q^{49} +(0.809017 - 0.587785i) q^{50} +(5.89887 + 1.91666i) q^{52} +(-2.34381 + 3.22598i) q^{53} +(-1.78200 + 2.79723i) q^{55} +1.69851i q^{56} +(-0.320948 + 0.987777i) q^{58} +(1.21751 - 0.395593i) q^{59} +(-5.79653 - 7.97824i) q^{61} +(-2.44614 - 7.52845i) q^{62} +(-0.809017 - 0.587785i) q^{64} +6.20244 q^{65} +3.54231 q^{67} +(-5.56507 - 4.04326i) q^{68} +(0.524868 + 1.61538i) q^{70} +(8.36599 + 11.5148i) q^{71} +(-4.28390 + 1.39192i) q^{73} +(0.965076 - 2.97020i) q^{74} +2.59231i q^{76} +(-3.58327 - 4.34677i) q^{77} +(4.79552 - 6.60047i) q^{79} +(-0.951057 - 0.309017i) q^{80} +(8.90564 - 6.47033i) q^{82} +(2.87351 - 2.08772i) q^{83} +(-6.54214 - 2.12567i) q^{85} +(3.13448 - 4.31424i) q^{86} +(3.31044 - 0.202506i) q^{88} +13.5907i q^{89} +(-3.25546 + 10.0193i) q^{91} +(0.370743 - 0.120462i) q^{92} +(-2.16193 - 2.97565i) q^{94} +(0.801067 + 2.46543i) q^{95} +(14.8654 + 10.8004i) q^{97} +4.11507 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) \) 32 * q - 8 * q^2 - 8 * q^4 - 8 * q^8 - 8 * q^16 + 4 * q^17 + 8 * q^25 - 8 * q^29 + 32 * q^31 + 32 * q^32 + 24 * q^34 + 16 * q^37 + 32 * q^41 - 20 * q^46 - 20 * q^47 + 16 * q^49 + 8 * q^50 - 40 * q^53 + 8 * q^55 - 8 * q^58 + 40 * q^59 - 28 * q^62 - 8 * q^64 + 8 * q^65 + 4 * q^68 - 40 * q^71 + 40 * q^73 + 16 * q^74 - 28 * q^77 + 20 * q^79 - 8 * q^82 - 24 * q^83 - 24 * q^91 + 20 * q^94 + 16 * q^95 + 48 * q^97 + 16 * q^98

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