LMFDB - Embedded newform 990.2.z.b.701.2

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			701.2
Character	$\chi$	$=$	990.701
Dual form			990.2.z.b.161.2

$q$-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 $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$-1$

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	−0.0126126	−	0.999920i	$-0.504015\pi$
$7$	−1.61538	−	0.524868i	−0.610555	−	0.198381i	−0.597942	+	0.801539i	$0.704015\pi$
$8$	−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	0.918236	+	0.396033i	$0.129613\pi$
$13$	3.64570	+	5.01788i	1.01114	+	1.39171i	0.0928990	+	0.995676i	$0.470387\pi$
$14$	−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	0.999025	+	0.0441490i	$0.0140576\pi$
$17$	5.56507	+	4.04326i	1.34973	+	0.980635i	0.350704	+	0.936486i	$0.385942\pi$
$18$		0			0
$19$	2.46543	−	0.801067i	0.565609	−	0.183777i	−0.0122346	−	0.999925i	$-0.503894\pi$
$19$	2.46543	−	0.801067i	0.565609	−	0.183777i	0.577843	+	0.816148i	$0.303894\pi$
$20$	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	$-0.869257\pi$
$29$	0.320948	−	0.987777i	0.0595986	−	0.183426i	0.976423	+	0.215864i	$0.0692568\pi$
$30$		0			0
$31$	6.40408	−	4.65284i	1.15021	−	0.835675i	0.161699	−	0.986840i	$-0.448303\pi$
$31$	6.40408	−	4.65284i	1.15021	−	0.835675i	0.988508	+	0.151166i	$0.0483026\pi$
$32$	−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	−0.839856	−	0.542810i	$-0.817360\pi$
$37$	0.965076	−	2.97020i	0.158657	−	0.488297i	0.998513	+	0.0545124i	$0.0173604\pi$
$38$	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	0.751618	+	0.659599i	$0.229274\pi$
$41$	3.40165	+	10.4692i	0.531249	+	1.63502i	−0.220369	+	0.975417i	$0.570726\pi$
$42$		0			0
$43$		−	5.33269i		−	0.813228i	−0.913600	−	0.406614i	$-0.866709\pi$
$43$		−	5.33269i		−	0.813228i	0.913600	−	0.406614i	$-0.133291\pi$
$44$	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	$-0.686446\pi$
$47$	−3.49808	+	1.13660i	−0.510248	+	0.165789i	0.0425673	+	0.999094i	$0.486446\pi$
$48$		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	$-0.111698\pi$
$53$	2.34381	+	3.22598i	0.321947	+	0.443122i	−0.617113	+	0.786874i	$0.711698\pi$
$54$		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	$-0.426556\pi$
$59$	−1.21751	−	0.395593i	−0.158506	−	0.0515018i	−0.387195	+	0.921998i	$0.626556\pi$
$60$		0			0
$61$	−5.79653	+	7.97824i	−0.742170	+	1.02151i	0.256321	+	0.966592i	$0.417489\pi$
$61$	−5.79653	+	7.97824i	−0.742170	+	1.02151i	−0.998491	+	0.0549171i	$0.982511\pi$
$62$	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	−0.0632560	+	0.997997i	$0.520148\pi$
$71$	−8.36599	+	11.5148i	−0.992861	+	1.36656i	−0.929605	+	0.368558i	$0.879852\pi$
$72$		0			0
$73$	−4.28390	−	1.39192i	−0.501393	−	0.162912i	0.0473915	−	0.998876i	$-0.484909\pi$
$73$	−4.28390	−	1.39192i	−0.501393	−	0.162912i	−0.548784	+	0.835964i	$0.684909\pi$
$74$	−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	0.988546	−	0.150917i	$-0.0482226\pi$
$79$	4.79552	+	6.60047i	0.539538	+	0.742611i	−0.449008	+	0.893528i	$0.648223\pi$
$80$	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	$-0.362449\pi$
$83$	−2.87351	−	2.08772i	−0.315408	−	0.229158i	−0.734214	+	0.678918i	$0.762449\pi$
$84$		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	0.542896	−	0.839800i	$-0.317328\pi$
$97$	14.8654	−	10.8004i	1.50936	−	1.09661i	0.966461	−	0.256812i	$-0.0826721\pi$
$98$	−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	$-0.820945\pi$
$101$	−6.03094	+	4.38173i	−0.600101	+	0.435999i	0.245814	+	0.969317i	$0.420945\pi$
$102$		0			0
$103$	−3.95198	+	12.1630i	−0.389401	+	1.19845i	0.543837	+	0.839191i	$0.316971\pi$
$103$	−3.95198	+	12.1630i	−0.389401	+	1.19845i	−0.933237	+	0.359261i	$0.883029\pi$
$104$	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	−0.759907	−	0.650032i	$-0.774755\pi$
$107$	−5.45349	−	16.7841i	−0.527209	−	1.62258i	0.232698	−	0.972549i	$-0.425245\pi$
$108$		0			0
$109$		−	14.2681i		−	1.36664i	−0.730119	−	0.683320i	$-0.760535\pi$
$109$		−	14.2681i		−	1.36664i	0.730119	−	0.683320i	$-0.239465\pi$
$110$	−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	$-0.561928\pi$
$113$	2.41268	−	0.783929i	0.226966	−	0.0737458i	0.420292	+	0.907389i	$0.361928\pi$
$114$		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	−0.283441	−	0.958990i	$-0.591476\pi$
$127$	8.07117	−	11.1090i	0.716201	−	0.985766i	0.999641	−	0.0267758i	$-0.00852403\pi$
$128$	−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	$-0.323335\pi$
$131$	12.0625			1.05390			0.526952	+	0.849895i	$0.323335\pi$
$132$		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	$-0.844654\pi$
$137$	−1.92393	+	2.64806i	−0.164373	+	0.226239i	0.718883	+	0.695131i	$0.244654\pi$
$138$		0			0
$139$	14.9675	+	4.86324i	1.26953	+	0.412495i	0.864880	−	0.501978i	$-0.167394\pi$
$139$	14.9675	+	4.86324i	1.26953	+	0.412495i	0.404648	+	0.914473i	$0.367394\pi$
$140$	−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	$-0.512779\pi$
$149$	−12.2411	−	8.89368i	−1.00283	−	0.728598i	−0.962693	+	0.270596i	$0.912779\pi$
$150$		0			0
$151$	−2.96425	+	0.963144i	−0.241227	+	0.0783795i	−0.427136	−	0.904188i	$-0.640477\pi$
$151$	−2.96425	+	0.963144i	−0.241227	+	0.0783795i	0.185908	+	0.982567i	$0.440477\pi$
$152$	−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	0.944086	−	0.329700i	$-0.106948\pi$
$157$	−0.169013	−	0.520169i	−0.0134887	−	0.0415140i	−0.957574	+	0.288186i	$0.906948\pi$
$158$	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	−0.999953	−	0.00966293i	$-0.996924\pi$
$163$	−16.5943	+	12.0565i	−1.29977	+	0.944335i	−0.299813	+	0.953998i	$0.596924\pi$
$164$	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	$-0.459060\pi$
$167$	14.3586	−	10.4321i	1.11110	−	0.807261i	0.982836	+	0.184479i	$0.0590599\pi$
$168$		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	−0.684813	−	0.728719i	$-0.740116\pi$
$173$	−7.35405	−	22.6334i	−0.559118	−	1.72079i	0.125695	−	0.992069i	$-0.459884\pi$
$174$		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	$-0.531697\pi$
$179$	5.41896	−	1.76073i	0.405032	−	0.131603i	0.504446	+	0.863443i	$0.331697\pi$
$180$		0			0
$181$	−5.97112	−	4.33827i	−0.443830	−	0.322461i	0.343325	−	0.939217i	$-0.388447\pi$
$181$	−5.97112	−	4.33827i	−0.443830	−	0.322461i	−0.787155	+	0.616755i	$0.788447\pi$
$182$	−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	$-0.483454\pi$
$191$	−6.81335	−	2.21379i	−0.492997	−	0.160184i	−0.544956	+	0.838465i	$0.683454\pi$
$192$		0			0
$193$	−3.47734	+	4.78614i	−0.250304	+	0.344514i	−0.915618	−	0.402050i	$-0.868298\pi$
$193$	−3.47734	+	4.78614i	−0.250304	+	0.344514i	0.665314	+	0.746564i	$0.268298\pi$
$194$	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	$-0.316044\pi$
$197$	15.3348			1.09256			0.546278	+	0.837604i	$0.316044\pi$
$198$		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	0.627744	−	0.778420i	$-0.283979\pi$
$211$	−4.45306	−	6.12911i	−0.306561	−	0.421945i	−0.934305	+	0.356475i	$0.883979\pi$
$212$	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	−0.924318	−	0.381623i	$-0.875365\pi$
$223$	−5.98584	−	18.4225i	−0.400842	−	1.23366i	0.523476	−	0.852040i	$-0.324635\pi$
$224$	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	−0.533630	−	0.845718i	$-0.679172\pi$
$227$	5.95408	−	18.3248i	0.395186	−	1.21626i	0.928816	−	0.370541i	$-0.120828\pi$
$228$		0			0
$229$	8.65927	−	6.29133i	0.572221	−	0.415743i	−0.263690	−	0.964607i	$-0.584940\pi$
$229$	8.65927	−	6.29133i	0.572221	−	0.415743i	0.835911	+	0.548865i	$0.184940\pi$
$230$	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	$-0.597332\pi$
$233$	7.82880	−	5.68796i	0.512882	−	0.372631i	0.813916	+	0.580983i	$0.197332\pi$
$234$		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	−0.998402	−	0.0565060i	$-0.982004\pi$
$239$	−3.46127	−	10.6527i	−0.223891	−	0.689066i	0.774511	−	0.632560i	$-0.217996\pi$
$240$		0			0
$241$			11.8973i			0.766372i	0.923671	+	0.383186i	$0.125173\pi$
$241$			11.8973i			0.766372i	−0.923671	+	0.383186i	$0.874827\pi$
$242$	−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	−0.999335	−	0.0364742i	$-0.988387\pi$
$251$	−11.4895	−	15.8140i	−0.725212	−	0.998169i	0.274122	−	0.961695i	$-0.411613\pi$
$252$		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	$-0.137202\pi$
$257$	22.4112	+	7.28184i	1.39797	+	0.454229i	0.489438	+	0.872038i	$0.337202\pi$
$258$		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	$-0.481954\pi$
$263$	1.83788			0.113329			0.0566643	+	0.998393i	$0.481954\pi$
$264$		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	$-0.621795\pi$
$269$	10.2392	−	14.0930i	0.624294	−	0.859268i	0.997657	+	0.0684181i	$0.0217952\pi$
$270$		0			0
$271$	−24.4590	−	7.94721i	−1.48578	−	0.482759i	−0.549945	−	0.835201i	$-0.685351\pi$
$271$	−24.4590	−	7.94721i	−1.48578	−	0.482759i	−0.935834	+	0.352442i	$0.885351\pi$
$272$	−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	0.956175	−	0.292797i	$-0.0945859\pi$
$277$	6.36164	+	8.75605i	0.382234	+	0.526100i	−0.573941	+	0.818897i	$0.694586\pi$
$278$	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	$-0.405655\pi$
$281$	−8.83847	−	6.42152i	−0.527259	−	0.383076i	−0.819331	+	0.573320i	$0.805655\pi$
$282$		0			0
$283$	16.3072	−	5.29853i	0.969361	−	0.314965i	0.218803	−	0.975769i	$-0.429785\pi$
$283$	16.3072	−	5.29853i	0.969361	−	0.314965i	0.750558	+	0.660804i	$0.229785\pi$
$284$	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	0.778149	+	0.628080i	$0.216159\pi$
$293$	−3.77542	+	11.6196i	−0.220563	+	0.678822i	−0.998712	+	0.0507424i	$0.983841\pi$
$294$		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	$-0.821751\pi$
$307$		−	18.6138i		−	1.06235i	0.847263	−	0.531173i	$-0.178249\pi$
$308$	−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	$-0.738519\pi$
$311$	−14.1410	+	4.59468i	−0.801862	+	0.260541i	−0.120715	+	0.992687i	$0.538519\pi$
$312$		0			0
$313$	−1.26108	−	0.916230i	−0.0712806	−	0.0517884i	0.551574	−	0.834126i	$-0.314027\pi$
$313$	−1.26108	−	0.916230i	−0.0712806	−	0.0517884i	−0.622855	+	0.782337i	$0.714027\pi$
$314$	−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	−0.999159	−	0.0410064i	$-0.986944\pi$
$317$	−12.9866	−	17.8745i	−0.729401	−	1.00393i	0.269758	−	0.962928i	$-0.413056\pi$
$318$		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	0.358256	−	0.933623i	$-0.383372\pi$
$337$	1.82329	+	0.592422i	0.0993207	+	0.0322713i	−0.258935	+	0.965895i	$0.583372\pi$
$338$	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	$-0.432030\pi$
$347$	−12.1464	−	8.82489i	−0.652054	−	0.473745i	−0.863970	+	0.503543i	$0.832030\pi$
$348$		0			0
$349$	−28.3676	+	9.21718i	−1.51848	+	0.493384i	−0.945344	−	0.326075i	$-0.894274\pi$
$349$	−28.3676	+	9.21718i	−1.51848	+	0.493384i	−0.573137	+	0.819460i	$0.694274\pi$
$350$	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	0.719648	+	0.694339i	$0.244303\pi$
$359$	−5.12869	+	15.7845i	−0.270682	+	0.833073i	−0.990330	+	0.138734i	$0.955697\pi$
$360$		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	−0.535188	−	0.844733i	$-0.679759\pi$
$367$	7.55388	−	23.2485i	0.394310	−	1.21356i	0.929498	−	0.368827i	$-0.120241\pi$
$368$	−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	$-0.963453\pi$
$373$		−	4.42523i		−	0.229130i	0.993416	−	0.114565i	$-0.0365474\pi$
$374$	−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	0.883531	−	0.468373i	$-0.155160\pi$
$379$	13.8438	+	10.0581i	0.711108	+	0.516650i	−0.172423	+	0.985023i	$0.555160\pi$
$380$	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	$-0.313356\pi$
$383$	−8.02094	−	11.0399i	−0.409851	−	0.564111i	−0.963182	+	0.268850i	$0.913356\pi$
$384$		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	$-0.217810\pi$
$389$	20.3193	+	6.60215i	1.03023	+	0.334742i	0.255349	+	0.966849i	$0.417810\pi$
$390$		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	$-0.651477\pi$
$401$	10.5898	−	14.5756i	0.528830	−	0.727872i	0.986952	+	0.161017i	$0.0514775\pi$
$402$		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	0.966750	+	0.255725i	$0.0823140\pi$
$409$	18.4282	+	25.3642i	0.911216	+	1.25418i	−0.0555335	+	0.998457i	$0.517686\pi$
$410$	−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	−0.988367	−	0.152088i	$-0.951400\pi$
$421$	−5.70729	−	17.5652i	−0.278156	−	0.856078i	0.710210	−	0.703989i	$-0.248600\pi$
$422$	−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	0.415485	−	0.909600i	$-0.363612\pi$
$431$	29.2507	−	21.2519i	1.40896	−	1.02367i	0.993473	−	0.114068i	$-0.0363881\pi$
$432$		0			0
$433$	−6.86971	+	21.1428i	−0.330137	+	1.01606i	0.638931	+	0.769264i	$0.279377\pi$
$433$	−6.86971	+	21.1428i	−0.330137	+	1.01606i	−0.969068	+	0.246794i	$0.920623\pi$
$434$	−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	$-0.825139\pi$
$439$		−	21.8795i		−	1.04425i	0.852869	−	0.522125i	$-0.174861\pi$
$440$	−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	$-0.675108\pi$
$443$	−9.35911	+	3.04096i	−0.444665	+	0.144480i	0.0781220	+	0.996944i	$0.475108\pi$
$444$		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	$-0.308914\pi$
$449$	−8.35788	−	11.5036i	−0.394433	−	0.542890i	−0.959336	+	0.282267i	$0.908914\pi$
$450$		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	−0.652314	−	0.757949i	$-0.726202\pi$
$457$	5.77438	−	7.94776i	0.270114	−	0.371780i	0.922428	+	0.386168i	$0.126202\pi$
$458$	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	$-0.623652\pi$
$461$	−16.2650			−0.757535			−0.378768	+	0.925492i	$0.623652\pi$
$462$		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	0.296186	+	0.955130i	$0.404285\pi$
$467$	−15.2076	+	20.9315i	−0.703724	+	0.968592i	−0.999909	+	0.0134620i	$0.995715\pi$
$468$		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	$-0.509102\pi$
$479$	−21.6255	−	15.7119i	−0.988095	−	0.717893i	−0.959503	+	0.281698i	$0.909102\pi$
$480$		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	0.997179	+	0.0750637i	$0.0239160\pi$
$487$	5.17641	+	15.9314i	0.234566	+	0.721918i	−0.762613	+	0.646855i	$0.776084\pi$
$488$	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	0.643197	+	0.765701i	$0.277608\pi$
$491$	−7.25089	+	22.3159i	−0.327228	+	1.00710i	−0.970425	+	0.241404i	$0.922392\pi$
$492$		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	−0.890716	−	0.454559i	$-0.849797\pi$
$499$	2.16842	−	6.67370i	0.0970717	−	0.298756i	0.987788	+	0.155804i	$0.0497967\pi$
$500$	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	$-0.153580\pi$
$503$	−2.32216	−	7.14689i	−0.103540	−	0.318664i	−0.989385	+	0.145318i	$0.953580\pi$
$504$		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	$-0.727500\pi$
$509$	−16.7333	+	5.43697i	−0.741689	+	0.240989i	−0.0862879	+	0.996270i	$0.527500\pi$
$510$		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	$-0.385409\pi$
$521$	1.98950	+	0.646427i	0.0871615	+	0.0283205i	−0.265112	+	0.964218i	$0.585409\pi$
$522$		0			0
$523$	21.8755	−	30.1090i	0.956548	−	1.31657i	0.00799081	−	0.999968i	$-0.497456\pi$
$523$	21.8755	−	30.1090i	0.956548	−	1.31657i	0.948557	−	0.316607i	$-0.102544\pi$
$524$	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	0.915851	−	0.401518i	$-0.131517\pi$
$541$	5.83746	+	8.03457i	0.250972	+	0.345433i	−0.664880	+	0.746951i	$0.731517\pi$
$542$	−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	−0.145056	−	0.989423i	$-0.546336\pi$
$547$	7.46450	−	2.42536i	0.319159	−	0.103701i	0.464215	+	0.885722i	$0.346336\pi$
$548$	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	0.568769	+	0.822497i	$0.307420\pi$
$557$	−8.84622	+	27.2259i	−0.374826	+	1.15360i	−0.943596	+	0.331100i	$0.892580\pi$
$558$		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	$-0.470950\pi$
$563$	25.3031	−	18.3837i	1.06640	−	0.774783i	0.975261	+	0.221056i	$0.0709504\pi$
$564$		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	$-0.187671\pi$
$569$	−4.00931	−	12.3394i	−0.168079	−	0.517295i	−0.999250	+	0.0387226i	$0.987671\pi$
$570$		0			0
$571$			29.2178i			1.22273i	0.791350	+	0.611363i	$0.209379\pi$
$571$			29.2178i			1.22273i	−0.791350	+	0.611363i	$0.790621\pi$
$572$	−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	0.248422	−	0.968652i	$-0.420088\pi$
$577$	−14.3177	−	10.4024i	−0.596054	−	0.433058i	−0.844476	+	0.535593i	$0.820088\pi$
$578$	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	$-0.567199\pi$
$587$	−23.1090	−	7.50856i	−0.953809	−	0.309911i	−0.744262	+	0.667887i	$0.767199\pi$
$588$		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	$-0.271625\pi$
$593$	32.0210			1.31495			0.657473	+	0.753478i	$0.271625\pi$
$594$		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	$-0.962169\pi$
$599$	−14.0322	+	19.3137i	−0.573341	+	0.789136i	0.419605	+	0.907707i	$0.362169\pi$
$600$		0			0
$601$	44.7645	+	14.5449i	1.82598	+	0.593297i	0.999542	+	0.0302696i	$0.00963659\pi$
$601$	44.7645	+	14.5449i	1.82598	+	0.593297i	0.826438	+	0.563027i	$0.190363\pi$
$602$	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	0.326412	−	0.945228i	$-0.394160\pi$
$607$	−16.5913	−	22.8360i	−0.673420	−	0.926883i	−0.999832	+	0.0183447i	$0.994160\pi$
$608$	−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	−0.568609	−	0.822608i	$-0.692518\pi$
$613$	−13.4962	+	4.38519i	−0.545107	+	0.177116i	0.0235020	+	0.999724i	$0.492518\pi$
$614$	−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	0.968439	+	0.249249i	$0.0801837\pi$
$619$	8.24664	+	25.3805i	0.331460	+	1.02013i	−0.636979	+	0.770881i	$0.719816\pi$
$620$	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	0.473339	+	0.880880i	$0.343048\pi$
$631$	−10.7354	+	33.0401i	−0.427369	+	1.31531i	−0.900708	+	0.434425i	$0.856952\pi$
$632$	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	$-0.448259\pi$
$641$	22.0975	−	7.17992i	0.872799	−	0.283590i	0.710964	+	0.703228i	$0.248259\pi$
$642$		0			0
$643$	−7.61817	−	5.53492i	−0.300431	−	0.218276i	0.427349	−	0.904087i	$-0.359448\pi$
$643$	−7.61817	−	5.53492i	−0.300431	−	0.218276i	−0.727780	+	0.685811i	$0.759448\pi$
$644$	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	$-0.210061\pi$
$647$	−0.944989	−	1.30067i	−0.0371513	−	0.0511344i	−0.827189	+	0.561924i	$0.810061\pi$
$648$		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	$-0.387188\pi$
$653$	1.95595	+	0.635525i	0.0765421	+	0.0248700i	−0.270496	+	0.962721i	$0.587188\pi$
$654$		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	$-0.817142\pi$
$659$	−43.1008			−1.67897			−0.839484	+	0.543385i	$0.817142\pi$
$660$		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	0.732128	−	0.681167i	$-0.238527\pi$
$673$	−3.68226	−	5.06820i	−0.141941	−	0.195365i	−0.874069	+	0.485803i	$0.838527\pi$
$674$	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	$-0.505815\pi$
$677$	−25.3638	−	18.4279i	−0.974810	−	0.708241i	−0.956543	+	0.291592i	$0.905815\pi$
$678$		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	−0.905541	−	0.424259i	$-0.860535\pi$
$691$	−20.5530	+	14.9327i	−0.781874	+	0.568065i	0.123667	+	0.992324i	$0.460535\pi$
$692$	−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	0.997241	+	0.0742375i	$0.0236523\pi$
$701$	6.19791	+	19.0752i	0.234092	+	0.720460i	−0.763149	+	0.646223i	$0.776348\pi$
$702$		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	0.188349	−	0.982102i	$-0.439686\pi$
$709$	−18.3056	−	13.2998i	−0.687482	−	0.499485i	−0.875832	+	0.482617i	$0.839686\pi$
$710$	−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	$-0.297310\pi$
$719$	16.1703	+	5.25405i	0.603050	+	0.195943i	0.00844994	+	0.999964i	$0.497310\pi$
$720$		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	0.420386	−	0.907345i	$-0.361895\pi$
$733$	6.15015	+	1.99831i	0.227161	+	0.0738091i	−0.193225	+	0.981155i	$0.561895\pi$
$734$	−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	0.913014	−	0.407929i	$-0.133749\pi$
$739$	6.60348	+	9.08891i	0.242913	+	0.334341i	−0.670101	+	0.742270i	$0.733749\pi$
$740$	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	$-0.0244862\pi$
$743$	33.5835	+	24.3998i	1.23206	+	0.895142i	0.235015	+	0.971992i	$0.424486\pi$
$744$		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	0.942187	−	0.335086i	$-0.108766\pi$
$751$	−0.466342	−	1.43525i	−0.0170171	−	0.0523732i	−0.959204	+	0.282713i	$0.908766\pi$
$752$	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	−0.460998	−	0.887401i	$-0.652509\pi$
$757$	6.61741	−	4.80783i	0.240514	−	0.174744i	0.701512	+	0.712657i	$0.252509\pi$
$758$	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	$-0.628778\pi$
$761$	9.90410	−	7.19575i	0.359023	−	0.260846i	0.752645	+	0.658427i	$0.228778\pi$
$762$		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	$0.309210\pi$
$769$			45.7938i			1.65136i	−0.564135	+	0.825682i	$0.690790\pi$
$770$	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	$-0.526796\pi$
$773$	12.0552	−	3.91696i	0.433594	−	0.140883i	0.517678	+	0.855575i	$0.326796\pi$
$774$		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	−0.559503	−	0.828829i	$-0.689008\pi$
$787$	11.2679	−	15.5089i	0.401656	−	0.552832i	0.961159	+	0.275997i	$0.0890079\pi$
$788$	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	$-0.761546\pi$
$797$	3.99961	−	5.50499i	0.141673	−	0.194997i	0.873957	+	0.486003i	$0.161546\pi$
$798$		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	$-0.214294\pi$
$809$	12.2423	+	8.89457i	0.430417	+	0.312717i	−0.351398	+	0.936226i	$0.614294\pi$
$810$		0			0
$811$	2.61264	−	0.848899i	0.0917423	−	0.0298089i	−0.262786	−	0.964854i	$-0.584641\pi$
$811$	2.61264	−	0.848899i	0.0917423	−	0.0298089i	0.354528	+	0.935045i	$0.384641\pi$
$812$	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	$-0.802885\pi$
$821$	5.31937	−	16.3713i	0.185647	−	0.571364i	0.999959	+	0.00906407i	$0.00288522\pi$
$822$		0			0
$823$	27.4634	−	19.9534i	0.957315	−	0.695530i	0.00478949	−	0.999989i	$-0.498475\pi$
$823$	27.4634	−	19.9534i	0.957315	−	0.695530i	0.952526	+	0.304458i	$0.0984755\pi$
$824$	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	$-0.713283\pi$
$827$	−1.94119	+	1.41036i	−0.0675017	+	0.0490429i	0.553523	+	0.832834i	$0.313283\pi$
$828$		0			0
$829$	−1.84865	+	5.68956i	−0.0642062	+	0.197606i	−0.978013	−	0.208542i	$-0.933128\pi$
$829$	−1.84865	+	5.68956i	−0.0642062	+	0.197606i	0.913807	+	0.406148i	$0.133128\pi$
$830$	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	$-0.725427\pi$
$839$	−21.1525	+	6.87287i	−0.730266	+	0.237278i	−0.0797974	+	0.996811i	$0.525427\pi$
$840$		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	−0.00145281	+	0.999999i	$0.500462\pi$
$853$	−27.8060	+	38.2717i	−0.952059	+	1.31040i	−0.950607	+	0.310398i	$0.899538\pi$
$854$	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	$-0.174165\pi$
$857$	50.0014			1.70802			0.854008	+	0.520260i	$0.174165\pi$
$858$		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	−0.364571	+	0.931176i	$0.618784\pi$
$863$	−33.4166	+	45.9940i	−1.13751	+	1.56565i	−0.772942	+	0.634477i	$0.781216\pi$
$864$		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	−0.305314	−	0.952252i	$-0.598761\pi$
$877$	0.219212	−	0.0712264i	0.00740228	−	0.00240515i	0.312716	+	0.949847i	$0.398761\pi$
$878$	−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	0.993025	+	0.117904i	$0.0376176\pi$
$883$	7.69488	+	23.6824i	0.258953	+	0.796976i	−0.734072	+	0.679072i	$0.762382\pi$
$884$	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	$-0.973619\pi$
$887$	−4.21923	+	12.9855i	−0.141668	+	0.436009i	0.854900	+	0.518794i	$0.173619\pi$
$888$		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	−0.999325	−	0.0367247i	$-0.988308\pi$
$907$	−40.4482	−	29.3874i	−1.34306	−	0.975791i	−0.343736	−	0.939066i	$-0.611692\pi$
$908$	−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	−0.880983	−	0.473148i	$-0.843118\pi$
$911$	−31.9556	−	43.9830i	−1.05873	−	1.45722i	−0.177752	−	0.984075i	$-0.556882\pi$
$912$		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	−0.481414	−	0.876493i	$-0.659877\pi$
$919$	15.1862	−	20.9020i	0.500946	−	0.689492i	0.982360	+	0.187001i	$0.0598767\pi$
$920$	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	$-0.864689\pi$
$929$	−7.23178	+	9.95370i	−0.237267	+	0.326570i	0.673734	+	0.738974i	$0.264689\pi$
$930$		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	−0.977363	−	0.211569i	$-0.932143\pi$
$937$	−26.8318	−	36.9307i	−0.876555	−	1.20647i	0.100808	−	0.994906i	$-0.467857\pi$
$938$	−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	$-0.577768\pi$
$941$	−38.0212	−	27.6240i	−1.23945	−	0.900517i	−0.997562	+	0.0697865i	$0.977768\pi$
$942$		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	−0.756304	−	0.654220i	$-0.772997\pi$
$953$	7.41204	−	22.8119i	0.240100	−	0.738951i	0.996404	−	0.0847307i	$-0.0270030\pi$
$954$		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	$-0.790750\pi$
$967$		−	38.0027i		−	1.22209i	0.791597	−	0.611043i	$-0.209250\pi$
$968$	−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	$-0.529511\pi$
$971$	13.0185	−	4.22996i	0.417783	−	0.135746i	0.510362	+	0.859959i	$0.329511\pi$
$972$		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	$-0.0536145\pi$
$977$	16.3090	+	22.4474i	0.521770	+	0.718155i	−0.464079	+	0.885794i	$0.653614\pi$
$978$		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	$-0.381628\pi$
$983$	3.44009	+	1.11775i	0.109722	+	0.0356507i	−0.253642	+	0.967298i	$0.581628\pi$
$984$		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	0.00406703	−	0.999992i	$-0.498705\pi$
$997$	−18.3270	−	5.95482i	−0.580423	−	0.188591i	−0.584490	+	0.811401i	$0.698705\pi$
$998$	−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.b.701.2	yes	32
3.2	odd	2		990.2.z.a.701.6	yes	32
11.7	odd	10		990.2.z.a.161.6	✓	32
33.29	even	10	inner	990.2.z.b.161.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.z.a.161.6	✓	32	11.7	odd	10
990.2.z.a.701.6	yes	32	3.2	odd	2
990.2.z.b.161.2	yes	32	33.29	even	10	inner
990.2.z.b.701.2	yes	32	1.1	even	1	trivial

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more