LMFDB - Embedded newform 729.2.c.d.487.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(244,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.244"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,3,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.1
Root			$1.22778i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.d.244.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22889 + 2.12851i) q^{2} +(-2.02036 - 3.49937i) q^{4} +(-1.54013 - 2.66759i) q^{5} +(1.32933 - 2.30247i) q^{7} +5.01568 q^{8} +7.57064 q^{10} +(-1.71717 + 2.97423i) q^{11} +(1.67198 + 2.89595i) q^{13} +(3.26722 + 5.65899i) q^{14} +(-2.12302 + 3.67717i) q^{16} -2.57282 q^{17} -2.09676 q^{19} +(-6.22325 + 10.7790i) q^{20} +(-4.22044 - 7.31002i) q^{22} +(0.267222 + 0.462842i) q^{23} +(-2.24401 + 3.88674i) q^{25} -8.21874 q^{26} -10.7430 q^{28} +(1.26545 - 2.19182i) q^{29} +(-3.85735 - 6.68113i) q^{31} +(-0.202245 - 0.350299i) q^{32} +(3.16172 - 5.47626i) q^{34} -8.18939 q^{35} -10.2957 q^{37} +(2.57670 - 4.46298i) q^{38} +(-7.72481 - 13.3798i) q^{40} +(-2.44250 - 4.23054i) q^{41} +(-1.37075 + 2.37420i) q^{43} +13.8772 q^{44} -1.31355 q^{46} +(-2.82900 + 4.89997i) q^{47} +(-0.0342555 - 0.0593322i) q^{49} +(-5.51530 - 9.55279i) q^{50} +(6.75601 - 11.7018i) q^{52} -6.42657 q^{53} +10.5787 q^{55} +(6.66751 - 11.5485i) q^{56} +(3.11020 + 5.38703i) q^{58} +(0.827475 + 1.43323i) q^{59} +(-7.18610 + 12.4467i) q^{61} +18.9611 q^{62} -7.49791 q^{64} +(5.15013 - 8.92029i) q^{65} +(2.93949 + 5.09135i) q^{67} +(5.19803 + 9.00325i) q^{68} +(10.0639 - 17.4312i) q^{70} -14.8163 q^{71} +1.88140 q^{73} +(12.6523 - 21.9144i) q^{74} +(4.23623 + 7.33736i) q^{76} +(4.56538 + 7.90748i) q^{77} +(-8.59674 + 14.8900i) q^{79} +13.0789 q^{80} +12.0063 q^{82} +(1.98439 - 3.43707i) q^{83} +(3.96248 + 6.86321i) q^{85} +(-3.36900 - 5.83528i) q^{86} +(-8.61278 + 14.9178i) q^{88} -5.09880 q^{89} +8.89047 q^{91} +(1.07977 - 1.87022i) q^{92} +(-6.95308 - 12.0431i) q^{94} +(3.22929 + 5.59330i) q^{95} +(5.31594 - 9.20748i) q^{97} +0.168385 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots - 36 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.22889	+	2.12851i	−0.868960	+	1.50508i	−0.00589892	+	0.999983i	$0.501878\pi$
$2$	−1.22889	+	2.12851i	−0.868960	+	1.50508i	−0.863061	+	0.505100i	$0.831456\pi$
$3$		0			0
$3$		0			0
$4$	−2.02036	−	3.49937i	−1.01018	−	1.74969i
$5$	−1.54013	−	2.66759i	−0.688768	−	1.19298i	−0.972237	−	0.233999i	$-0.924819\pi$
$5$	−1.54013	−	2.66759i	−0.688768	−	1.19298i	0.283469	−	0.958981i	$-0.408515\pi$
$6$		0			0
$7$	1.32933	−	2.30247i	0.502441	−	0.870253i	−0.497555	−	0.867432i	$-0.665769\pi$
$7$	1.32933	−	2.30247i	0.502441	−	0.870253i	0.999996	−	0.00282076i	$-0.000897877\pi$
$8$	5.01568			1.77331
$9$		0			0
$10$	7.57064			2.39405
$11$	−1.71717	+	2.97423i	−0.517746	+	0.896763i	0.482041	+	0.876149i	$0.339896\pi$
$11$	−1.71717	+	2.97423i	−0.517746	+	0.896763i	−0.999788	+	0.0206144i	$0.993438\pi$
$12$		0			0
$13$	1.67198	+	2.89595i	0.463723	+	0.803192i	0.999143	−	0.0413939i	$-0.0131799\pi$
$13$	1.67198	+	2.89595i	0.463723	+	0.803192i	−0.535420	+	0.844586i	$0.679847\pi$
$14$	3.26722	+	5.65899i	0.873202	+	1.51243i
$15$		0			0
$16$	−2.12302	+	3.67717i	−0.530754	+	0.919293i
$17$	−2.57282			−0.624000			−0.312000	−	0.950082i	$-0.600999\pi$
$17$	−2.57282			−0.624000			−0.312000	+	0.950082i	$0.600999\pi$
$18$		0			0
$19$	−2.09676			−0.481030			−0.240515	−	0.970645i	$-0.577316\pi$
$19$	−2.09676			−0.481030			−0.240515	+	0.970645i	$0.577316\pi$
$20$	−6.22325	+	10.7790i	−1.39156	+	2.41026i
$21$		0			0
$22$	−4.22044	−	7.31002i	−0.899802	−	1.55850i
$23$	0.267222	+	0.462842i	0.0557196	+	0.0965093i	0.892540	−	0.450969i	$-0.148921\pi$
$23$	0.267222	+	0.462842i	0.0557196	+	0.0965093i	−0.836820	+	0.547478i	$0.815588\pi$
$24$		0			0
$25$	−2.24401	+	3.88674i	−0.448802	+	0.777348i
$26$	−8.21874			−1.61183
$27$		0			0
$28$	−10.7430			−2.03023
$29$	1.26545	−	2.19182i	0.234988	−	0.407010i	−0.724281	−	0.689504i	$-0.757828\pi$
$29$	1.26545	−	2.19182i	0.234988	−	0.407010i	0.959269	+	0.282494i	$0.0911617\pi$
$30$		0			0
$31$	−3.85735	−	6.68113i	−0.692801	−	1.19997i	−0.970917	−	0.239418i	$-0.923043\pi$
$31$	−3.85735	−	6.68113i	−0.692801	−	1.19997i	0.278116	−	0.960548i	$-0.410290\pi$
$32$	−0.202245	−	0.350299i	−0.0357522	−	0.0619247i
$33$		0			0
$34$	3.16172	−	5.47626i	0.542231	−	0.939171i
$35$	−8.18939			−1.38426
$36$		0			0
$37$	−10.2957			−1.69260			−0.846298	−	0.532709i	$-0.821174\pi$
$37$	−10.2957			−1.69260			−0.846298	+	0.532709i	$0.821174\pi$
$38$	2.57670	−	4.46298i	0.417996	−	0.723991i
$39$		0			0
$40$	−7.72481	−	13.3798i	−1.22140	−	2.11553i
$41$	−2.44250	−	4.23054i	−0.381455	−	0.660699i	0.609816	−	0.792543i	$-0.291244\pi$
$41$	−2.44250	−	4.23054i	−0.381455	−	0.660699i	−0.991270	+	0.131844i	$0.957910\pi$
$42$		0			0
$43$	−1.37075	+	2.37420i	−0.209037	+	0.362062i	−0.951411	−	0.307923i	$-0.900366\pi$
$43$	−1.37075	+	2.37420i	−0.209037	+	0.362062i	0.742375	+	0.669985i	$0.233699\pi$
$44$	13.8772			2.09207
$45$		0			0
$46$	−1.31355			−0.193673
$47$	−2.82900	+	4.89997i	−0.412652	+	0.714734i	−0.995179	−	0.0980775i	$-0.968731\pi$
$47$	−2.82900	+	4.89997i	−0.412652	+	0.714734i	0.582527	+	0.812811i	$0.302064\pi$
$48$		0			0
$49$	−0.0342555	−	0.0593322i	−0.00489364	−	0.00847603i
$50$	−5.51530	−	9.55279i	−0.779982	−	1.35097i
$51$		0			0
$52$	6.75601	−	11.7018i	0.936890	−	1.62274i
$53$	−6.42657			−0.882758			−0.441379	−	0.897321i	$-0.645511\pi$
$53$	−6.42657			−0.882758			−0.441379	+	0.897321i	$0.645511\pi$
$54$		0			0
$55$	10.5787			1.42643
$56$	6.66751	−	11.5485i	0.890984	−	1.54323i
$57$		0			0
$58$	3.11020	+	5.38703i	0.408390	+	0.707351i
$59$	0.827475	+	1.43323i	0.107728	+	0.186590i	0.914850	−	0.403795i	$-0.132309\pi$
$59$	0.827475	+	1.43323i	0.107728	+	0.186590i	−0.807121	+	0.590385i	$0.798976\pi$
$60$		0			0
$61$	−7.18610	+	12.4467i	−0.920086	+	1.59364i	−0.120808	+	0.992676i	$0.538548\pi$
$61$	−7.18610	+	12.4467i	−0.920086	+	1.59364i	−0.799279	+	0.600960i	$0.794785\pi$
$62$	18.9611			2.40806
$63$		0			0
$64$	−7.49791			−0.937239
$65$	5.15013	−	8.92029i	0.638795	−	1.10643i
$66$		0			0
$67$	2.93949	+	5.09135i	0.359116	+	0.622007i	0.987813	−	0.155643i	$-0.0497449\pi$
$67$	2.93949	+	5.09135i	0.359116	+	0.622007i	−0.628697	+	0.777650i	$0.716412\pi$
$68$	5.19803	+	9.00325i	0.630354	+	1.09180i
$69$		0			0
$70$	10.0639	−	17.4312i	1.20287	−	2.08343i
$71$	−14.8163			−1.75837			−0.879184	−	0.476483i	$-0.841911\pi$
$71$	−14.8163			−1.75837			−0.879184	+	0.476483i	$0.841911\pi$
$72$		0			0
$73$	1.88140			0.220201			0.110101	−	0.993920i	$-0.464883\pi$
$73$	1.88140			0.220201			0.110101	+	0.993920i	$0.464883\pi$
$74$	12.6523	−	21.9144i	1.47080	−	2.54750i
$75$		0			0
$76$	4.23623	+	7.33736i	0.485928	+	0.841653i
$77$	4.56538	+	7.90748i	0.520274	+	0.901141i
$78$		0			0
$79$	−8.59674	+	14.8900i	−0.967209	+	1.67526i	−0.263651	+	0.964618i	$0.584927\pi$
$79$	−8.59674	+	14.8900i	−0.967209	+	1.67526i	−0.703558	+	0.710637i	$0.748407\pi$
$80$	13.0789			1.46227
$81$		0			0
$82$	12.0063			1.32588
$83$	1.98439	−	3.43707i	0.217815	−	0.377267i	−0.736324	−	0.676629i	$-0.763440\pi$
$83$	1.98439	−	3.43707i	0.217815	−	0.377267i	0.954140	+	0.299361i	$0.0967736\pi$
$84$		0			0
$85$	3.96248	+	6.86321i	0.429791	+	0.744420i
$86$	−3.36900	−	5.83528i	−0.363289	−	0.629235i
$87$		0			0
$88$	−8.61278	+	14.9178i	−0.918126	+	1.59024i
$89$	−5.09880			−0.540471			−0.270236	−	0.962794i	$-0.587102\pi$
$89$	−5.09880			−0.540471			−0.270236	+	0.962794i	$0.587102\pi$
$90$		0			0
$91$	8.89047			0.931974
$92$	1.07977	−	1.87022i	0.112574	−	0.194984i
$93$		0			0
$94$	−6.95308	−	12.0431i	−0.717156	−	1.24215i
$95$	3.22929	+	5.59330i	0.331318	+	0.573860i
$96$		0			0
$97$	5.31594	−	9.20748i	0.539752	−	0.934878i	−0.459165	−	0.888351i	$-0.651851\pi$
$97$	5.31594	−	9.20748i	0.539752	−	0.934878i	0.998917	−	0.0465267i	$-0.0148153\pi$
$98$	0.168385			0.0170095
$99$		0			0
$100$	18.1349			1.81349
$101$	2.82904	−	4.90005i	0.281500	−	0.487573i	−0.690254	−	0.723567i	$-0.742501\pi$
$101$	2.82904	−	4.90005i	0.281500	−	0.487573i	0.971755	+	0.235994i	$0.0758346\pi$
$102$		0			0
$103$	−5.18527	−	8.98115i	−0.510920	−	0.884939i	−0.999920	−	0.0126554i	$-0.995972\pi$
$103$	−5.18527	−	8.98115i	−0.510920	−	0.884939i	0.489000	−	0.872284i	$-0.337362\pi$
$104$	8.38611	+	14.5252i	0.822326	+	1.42431i
$105$		0			0
$106$	7.89758	−	13.6790i	0.767081	−	1.32862i
$107$	14.2457			1.37719			0.688594	−	0.725147i	$-0.258228\pi$
$107$	14.2457			1.37719			0.688594	+	0.725147i	$0.258228\pi$
$108$		0			0
$109$	5.76064			0.551769			0.275884	−	0.961191i	$-0.411029\pi$
$109$	5.76064			0.551769			0.275884	+	0.961191i	$0.411029\pi$
$110$	−13.0001	+	22.5168i	−1.23951	+	2.14689i
$111$		0			0
$112$	5.64439	+	9.77638i	0.533345	+	0.923781i
$113$	−5.70835	−	9.88715i	−0.536996	−	0.930104i	−0.999064	−	0.0432598i	$-0.986226\pi$
$113$	−5.70835	−	9.88715i	−0.536996	−	0.930104i	0.462068	−	0.886845i	$-0.347108\pi$
$114$		0			0
$115$	0.823114	−	1.42568i	0.0767558	−	0.132945i
$116$	−10.2267			−0.949521
$117$		0			0
$118$	−4.06752			−0.374445
$119$	−3.42013	+	5.92384i	−0.313523	+	0.543038i
$120$		0			0
$121$	−0.397348	−	0.688227i	−0.0361225	−	0.0625661i
$122$	−17.6619	−	30.5914i	−1.59904	−	2.76961i
$123$		0			0
$124$	−15.5865	+	26.9966i	−1.39971	+	2.42437i
$125$	−1.57703			−0.141054
$126$		0			0
$127$	2.59019			0.229843			0.114921	−	0.993375i	$-0.463338\pi$
$127$	2.59019			0.229843			0.114921	+	0.993375i	$0.463338\pi$
$128$	9.61864	−	16.6600i	0.850175	−	1.47255i
$129$		0			0
$130$	12.6579	+	21.9242i	1.11017	+	1.92288i
$131$	−2.20549	−	3.82003i	−0.192695	−	0.333757i	0.753448	−	0.657508i	$-0.228389\pi$
$131$	−2.20549	−	3.82003i	−0.192695	−	0.333757i	−0.946142	+	0.323751i	$0.895056\pi$
$132$		0			0
$133$	−2.78730	+	4.82774i	−0.241689	+	0.418618i
$134$	−14.4493			−1.24823
$135$		0			0
$136$	−12.9044			−1.10655
$137$	9.08384	−	15.7337i	0.776085	−	1.34422i	−0.158098	−	0.987423i	$-0.550536\pi$
$137$	9.08384	−	15.7337i	0.776085	−	1.34422i	0.934183	−	0.356795i	$-0.116131\pi$
$138$		0			0
$139$	−0.978972	−	1.69563i	−0.0830353	−	0.143821i	0.821517	−	0.570184i	$-0.193128\pi$
$139$	−0.978972	−	1.69563i	−0.0830353	−	0.143821i	−0.904552	+	0.426363i	$0.859795\pi$
$140$	16.5456	+	28.6578i	1.39836	+	2.42202i
$141$		0			0
$142$	18.2076	−	31.5365i	1.52795	−	2.64649i
$143$	−11.4843			−0.960364
$144$		0			0
$145$	−7.79582			−0.647407
$146$	−2.31204	+	4.00457i	−0.191346	+	0.331421i
$147$		0			0
$148$	20.8010	+	36.0284i	1.70983	+	2.96151i
$149$	3.65759	+	6.33514i	0.299642	+	0.518995i	0.976054	−	0.217528i	$-0.0697995\pi$
$149$	3.65759	+	6.33514i	0.299642	+	0.518995i	−0.676412	+	0.736523i	$0.736466\pi$
$150$		0			0
$151$	−2.42549	+	4.20108i	−0.197384	+	0.341879i	−0.947679	−	0.319224i	$-0.896578\pi$
$151$	−2.42549	+	4.20108i	−0.197384	+	0.341879i	0.750296	+	0.661103i	$0.229911\pi$
$152$	−10.5167			−0.853017
$153$		0			0
$154$	−22.4415			−1.80839
$155$	−11.8817	+	20.5796i	−0.954357	+	1.65300i
$156$		0			0
$157$	−0.738351	−	1.27886i	−0.0589269	−	0.102064i	0.835057	−	0.550163i	$-0.185435\pi$
$157$	−0.738351	−	1.27886i	−0.0589269	−	0.102064i	−0.893984	+	0.448099i	$0.852101\pi$
$158$	−21.1290	−	36.5965i	−1.68093	−	2.91146i
$159$		0			0
$160$	−0.622969	+	1.07901i	−0.0492500	+	0.0853035i
$161$	1.42091			0.111983
$162$		0			0
$163$	−17.2536			−1.35141			−0.675703	−	0.737174i	$-0.736160\pi$
$163$	−17.2536			−1.35141			−0.675703	+	0.737174i	$0.736160\pi$
$164$	−9.86949	+	17.0945i	−0.770678	+	1.33485i
$165$		0			0
$166$	4.87722	+	8.44759i	0.378546	+	0.655660i
$167$	3.42018	+	5.92393i	0.264662	+	0.458407i	0.967475	−	0.252967i	$-0.0814064\pi$
$167$	3.42018	+	5.92393i	0.264662	+	0.458407i	−0.702813	+	0.711374i	$0.748073\pi$
$168$		0			0
$169$	0.908979	−	1.57440i	0.0699214	−	0.121107i
$170$	−19.4779			−1.49388
$171$		0			0
$172$	11.0776			0.844661
$173$	−11.9837	+	20.7564i	−0.911103	+	1.57808i	−0.0985945	+	0.995128i	$0.531435\pi$
$173$	−11.9837	+	20.7564i	−0.911103	+	1.57808i	−0.812509	+	0.582949i	$0.801899\pi$
$174$		0			0
$175$	5.96608	+	10.3335i	0.450993	+	0.781143i
$176$	−7.29116	−	12.6287i	−0.549592	−	0.951921i
$177$		0			0
$178$	6.26588	−	10.8528i	0.469648	−	0.813454i
$179$	20.5722			1.53764			0.768820	−	0.639466i	$-0.220844\pi$
$179$	20.5722			1.53764			0.768820	+	0.639466i	$0.220844\pi$
$180$		0			0
$181$	−15.4701			−1.14989			−0.574943	−	0.818194i	$-0.694976\pi$
$181$	−15.4701			−1.14989			−0.574943	+	0.818194i	$0.694976\pi$
$182$	−10.9254	+	18.9234i	−0.809848	+	1.40270i
$183$		0			0
$184$	1.34030	+	2.32147i	0.0988083	+	0.171141i
$185$	15.8567	+	27.4646i	1.16581	+	2.01924i
$186$		0			0
$187$	4.41797	−	7.65214i	0.323074	−	0.559580i
$188$	22.8624			1.66741
$189$		0			0
$190$	−15.8738			−1.15161
$191$	−5.47542	+	9.48371i	−0.396188	+	0.686217i	−0.993252	−	0.115976i	$-0.963000\pi$
$191$	−5.47542	+	9.48371i	−0.396188	+	0.686217i	0.597064	+	0.802193i	$0.296334\pi$
$192$		0			0
$193$	−0.572426	−	0.991470i	−0.0412041	−	0.0713676i	0.844688	−	0.535259i	$-0.179786\pi$
$193$	−0.572426	−	0.991470i	−0.0412041	−	0.0713676i	−0.885892	+	0.463892i	$0.846453\pi$
$194$	13.0655	+	22.6300i	0.938045	+	1.62474i
$195$		0			0
$196$	−0.138417	+	0.239745i	−0.00988693	+	0.0171247i
$197$	5.04195			0.359224			0.179612	−	0.983738i	$-0.442516\pi$
$197$	5.04195			0.359224			0.179612	+	0.983738i	$0.442516\pi$
$198$		0			0
$199$	13.7258			0.972997			0.486499	−	0.873681i	$-0.338274\pi$
$199$	13.7258			0.972997			0.486499	+	0.873681i	$0.338274\pi$
$200$	−11.2552	+	19.4946i	−0.795866	+	1.37848i
$201$		0			0
$202$	6.95320	+	12.0433i	0.489225	+	0.847363i
$203$	−3.36440	−	5.82732i	−0.236135	−	0.408997i
$204$		0			0
$205$	−7.52355	+	13.0312i	−0.525468	+	0.910137i
$206$	25.4886			1.77588
$207$		0			0
$208$	−14.1985			−0.984492
$209$	3.60050	−	6.23625i	0.249052	−	0.431370i
$210$		0			0
$211$	2.91757	+	5.05337i	0.200854	+	0.347888i	0.948804	−	0.315866i	$-0.102295\pi$
$211$	2.91757	+	5.05337i	0.200854	+	0.347888i	−0.747950	+	0.663755i	$0.768962\pi$
$212$	12.9840	+	22.4890i	0.891746	+	1.54455i
$213$		0			0
$214$	−17.5065	+	30.3222i	−1.19672	+	2.07278i
$215$	8.44451			0.575911
$216$		0			0
$217$	−20.5108			−1.39237
$218$	−7.07922	+	12.2616i	−0.479465	+	0.830458i
$219$		0			0
$220$	−21.3728	−	37.0187i	−1.44095	−	2.49580i
$221$	−4.30170	−	7.45075i	−0.289363	−	0.501192i
$222$		0			0
$223$	−4.36434	+	7.55926i	−0.292258	+	0.506205i	−0.974343	−	0.225067i	$-0.927740\pi$
$223$	−4.36434	+	7.55926i	−0.292258	+	0.506205i	0.682085	+	0.731272i	$0.261073\pi$
$224$	−1.07541			−0.0718536
$225$		0			0
$226$	28.0598			1.86651
$227$	12.1413	−	21.0293i	0.805844	−	1.39576i	−0.109876	−	0.993945i	$-0.535045\pi$
$227$	12.1413	−	21.0293i	0.805844	−	1.39576i	0.915720	−	0.401817i	$-0.131621\pi$
$228$		0			0
$229$	−9.07571	−	15.7196i	−0.599740	−	1.03878i	−0.992859	−	0.119293i	$-0.961937\pi$
$229$	−9.07571	−	15.7196i	−0.599740	−	1.03878i	0.393119	−	0.919488i	$-0.371396\pi$
$230$	2.02304	+	3.50401i	0.133395	+	0.231048i
$231$		0			0
$232$	6.34708	−	10.9935i	0.416706	−	0.721756i
$233$	−10.5380			−0.690367			−0.345183	−	0.938535i	$-0.612183\pi$
$233$	−10.5380			−0.690367			−0.345183	+	0.938535i	$0.612183\pi$
$234$		0			0
$235$	17.4281			1.13688
$236$	3.34360	−	5.79129i	0.217650	−	0.376981i
$237$		0			0
$238$	−8.40597	−	14.5596i	−0.544878	−	0.943756i
$239$	−4.76830	−	8.25894i	−0.308436	−	0.534226i	0.669585	−	0.742736i	$-0.266472\pi$
$239$	−4.76830	−	8.25894i	−0.308436	−	0.534226i	−0.978020	+	0.208509i	$0.933139\pi$
$240$		0			0
$241$	3.51864	−	6.09446i	0.226656	−	0.392579i	−0.730159	−	0.683277i	$-0.760554\pi$
$241$	3.51864	−	6.09446i	0.226656	−	0.392579i	0.956815	+	0.290698i	$0.0938875\pi$
$242$	1.95320			0.125556
$243$		0			0
$244$	58.0742			3.71782
$245$	−0.105516	+	0.182759i	−0.00674116	+	0.0116760i
$246$		0			0
$247$	−3.50574	−	6.07212i	−0.223065	−	0.386360i
$248$	−19.3472	−	33.5104i	−1.22855	−	2.12791i
$249$		0			0
$250$	1.93801	−	3.35673i	0.122570	−	0.212298i
$251$	15.5870			0.983843			0.491921	−	0.870640i	$-0.336295\pi$
$251$	15.5870			0.983843			0.491921	+	0.870640i	$0.336295\pi$
$252$		0			0
$253$	−1.83546			−0.115395
$254$	−3.18308	+	5.51325i	−0.199724	+	0.345932i
$255$		0			0
$256$	16.1427	+	27.9599i	1.00892	+	1.74750i
$257$	−6.09489	−	10.5567i	−0.380189	−	0.658506i	0.610900	−	0.791708i	$-0.290808\pi$
$257$	−6.09489	−	10.5567i	−0.380189	−	0.658506i	−0.991089	+	0.133201i	$0.957474\pi$
$258$		0			0
$259$	−13.6864	+	23.7055i	−0.850430	+	1.47299i
$260$	−41.6206			−2.58120
$261$		0			0
$262$	10.8413			0.669776
$263$	3.44482	−	5.96660i	0.212417	−	0.367916i	−0.740054	−	0.672548i	$-0.765200\pi$
$263$	3.44482	−	5.96660i	0.212417	−	0.367916i	0.952470	+	0.304632i	$0.0985333\pi$
$264$		0			0
$265$	9.89777	+	17.1434i	0.608015	+	1.05311i
$266$	−6.85059	−	11.8656i	−0.420037	−	0.727525i
$267$		0			0
$268$	11.8777	−	20.5728i	0.725545	−	1.25668i
$269$	7.05875			0.430380			0.215190	−	0.976572i	$-0.430963\pi$
$269$	7.05875			0.430380			0.215190	+	0.976572i	$0.430963\pi$
$270$		0			0
$271$	23.7575			1.44316			0.721581	−	0.692330i	$-0.243416\pi$
$271$	23.7575			1.44316			0.721581	+	0.692330i	$0.243416\pi$
$272$	5.46213	−	9.46070i	0.331191	−	0.573639i
$273$		0			0
$274$	22.3262	+	38.6701i	1.34877	+	2.33614i
$275$	−7.70669	−	13.3484i	−0.464731	−	0.804938i
$276$		0			0
$277$	0.0522319	−	0.0904682i	0.00313831	−	0.00543571i	−0.864452	−	0.502715i	$-0.832334\pi$
$277$	0.0522319	−	0.0904682i	0.00313831	−	0.00543571i	0.867590	+	0.497280i	$0.165668\pi$
$278$	4.81221			0.288617
$279$		0			0
$280$	−41.0754			−2.45472
$281$	−4.07610	+	7.06001i	−0.243160	+	0.421165i	−0.961613	−	0.274411i	$-0.911517\pi$
$281$	−4.07610	+	7.06001i	−0.243160	+	0.421165i	0.718453	+	0.695576i	$0.244851\pi$
$282$		0			0
$283$	−11.8080	−	20.4520i	−0.701912	−	1.21575i	−0.967794	−	0.251742i	$-0.918996\pi$
$283$	−11.8080	−	20.4520i	−0.701912	−	1.21575i	0.265882	−	0.964006i	$-0.414337\pi$
$284$	29.9343	+	51.8477i	1.77627	+	3.07659i
$285$		0			0
$286$	14.1130	−	24.4444i	0.834518	−	1.44543i
$287$	−12.9876			−0.766634
$288$		0			0
$289$	−10.3806			−0.610624
$290$	9.58024	−	16.5935i	0.562571	−	0.974402i
$291$		0			0
$292$	−3.80111	−	6.58372i	−0.222443	−	0.385283i
$293$	−10.8129	−	18.7285i	−0.631695	−	1.09413i	−0.987205	−	0.159455i	$-0.949026\pi$
$293$	−10.8129	−	18.7285i	−0.631695	−	1.09413i	0.355510	−	0.934672i	$-0.384307\pi$
$294$		0			0
$295$	2.54884	−	4.41472i	0.148399	−	0.257035i
$296$	−51.6398			−3.00150
$297$		0			0
$298$	−17.9792			−1.04151
$299$	−0.893579	+	1.54772i	−0.0516770	+	0.0895072i
$300$		0			0
$301$	3.64435	+	6.31221i	0.210057	+	0.363830i
$302$	−5.96135	−	10.3254i	−0.343037	−	0.594158i
$303$		0			0
$304$	4.45146	−	7.71016i	0.255309	−	0.442208i
$305$	44.2702			2.53490
$306$		0			0
$307$	16.3599			0.933711			0.466855	−	0.884334i	$-0.345387\pi$
$307$	16.3599			0.933711			0.466855	+	0.884334i	$0.345387\pi$
$308$	18.4475	−	31.9520i	1.05114	−	1.82063i
$309$		0			0
$310$	−29.2026	−	50.5804i	−1.65860	−	2.87277i
$311$	−3.87743	−	6.71591i	−0.219869	−	0.380824i	0.734899	−	0.678177i	$-0.237230\pi$
$311$	−3.87743	−	6.71591i	−0.219869	−	0.380824i	−0.954768	+	0.297353i	$0.903896\pi$
$312$		0			0
$313$	−7.70903	+	13.3524i	−0.435740	+	0.754724i	−0.997356	−	0.0726744i	$-0.976847\pi$
$313$	−7.70903	+	13.3524i	−0.435740	+	0.754724i	0.561616	+	0.827398i	$0.310180\pi$
$314$	3.62942			0.204820
$315$		0			0
$316$	69.4742			3.90823
$317$	4.31810	−	7.47917i	0.242529	−	0.420072i	−0.718905	−	0.695108i	$-0.755356\pi$
$317$	4.31810	−	7.47917i	0.242529	−	0.420072i	0.961434	+	0.275036i	$0.0886898\pi$
$318$		0			0
$319$	4.34598	+	7.52745i	0.243328	+	0.421456i
$320$	11.5478	+	20.0013i	0.645540	+	1.11811i
$321$		0			0
$322$	−1.74615	+	3.02442i	−0.0973090	+	0.168544i
$323$	5.39459			0.300163
$324$		0			0
$325$	−15.0077			−0.832480
$326$	21.2029	−	36.7244i	1.17432	−	2.03398i
$327$		0			0
$328$	−12.2508	−	21.2190i	−0.676438	−	1.17163i
$329$	7.52136	+	13.0274i	0.414666	+	0.718223i
$330$		0			0
$331$	−10.2723	+	17.7921i	−0.564614	+	0.977941i	0.432471	+	0.901648i	$0.357642\pi$
$331$	−10.2723	+	17.7921i	−0.564614	+	0.977941i	−0.997085	+	0.0762930i	$0.975692\pi$
$332$	−16.0368			−0.880133
$333$		0			0
$334$	−16.8122			−0.919921
$335$	9.05441	−	15.6827i	0.494695	−	0.856837i
$336$		0			0
$337$	−7.98910	−	13.8375i	−0.435194	−	0.753778i	0.562117	−	0.827057i	$-0.309987\pi$
$337$	−7.98910	−	13.8375i	−0.435194	−	0.753778i	−0.997311	+	0.0732792i	$0.976654\pi$
$338$	2.23408	+	3.86954i	0.121518	+	0.210475i
$339$		0			0
$340$	16.0113	−	27.7324i	0.868335	−	1.50400i
$341$	26.4949			1.43478
$342$		0			0
$343$	18.4285			0.995047
$344$	−6.87522	+	11.9082i	−0.370687	+	0.642049i
$345$		0			0
$346$	−29.4534	−	51.0148i	−1.58342	−	2.74257i
$347$	−4.90214	−	8.49075i	−0.263161	−	0.455807i	0.703920	−	0.710280i	$-0.251432\pi$
$347$	−4.90214	−	8.49075i	−0.263161	−	0.455807i	−0.967080	+	0.254472i	$0.918098\pi$
$348$		0			0
$349$	4.71749	−	8.17093i	0.252521	−	0.437380i	−0.711698	−	0.702486i	$-0.752074\pi$
$349$	4.71749	−	8.17093i	0.252521	−	0.437380i	0.964219	+	0.265106i	$0.0854069\pi$
$350$	−29.3267			−1.56758
$351$		0			0
$352$	1.38916			0.0740424
$353$	−1.69258	+	2.93164i	−0.0900870	+	0.156035i	−0.907548	−	0.419949i	$-0.862048\pi$
$353$	−1.69258	+	2.93164i	−0.0900870	+	0.156035i	0.817461	+	0.575985i	$0.195381\pi$
$354$		0			0
$355$	22.8190	+	39.5237i	1.21111	+	2.09770i
$356$	10.3014	+	17.8426i	0.545975	+	0.945656i
$357$		0			0
$358$	−25.2811	+	43.7881i	−1.33615	+	2.31427i
$359$	−35.2273			−1.85923			−0.929614	−	0.368535i	$-0.879859\pi$
$359$	−35.2273			−1.85923			−0.929614	+	0.368535i	$0.879859\pi$
$360$		0			0
$361$	−14.6036			−0.768610
$362$	19.0112	−	32.9283i	0.999205	−	1.73067i
$363$		0			0
$364$	−17.9620	−	31.1111i	−0.941464	−	1.63066i
$365$	−2.89760	−	5.01879i	−0.151667	−	0.262696i
$366$		0			0
$367$	15.7727	−	27.3191i	0.823329	−	1.42605i	−0.0798606	−	0.996806i	$-0.525448\pi$
$367$	15.7727	−	27.3191i	0.823329	−	1.42605i	0.903190	−	0.429242i	$-0.141219\pi$
$368$	−2.26927			−0.118294
$369$		0			0
$370$	−77.9447			−4.05215
$371$	−8.54306	+	14.7970i	−0.443534	+	0.768223i
$372$		0			0
$373$	−7.22116	−	12.5074i	−0.373897	−	0.647609i	0.616264	−	0.787540i	$-0.288645\pi$
$373$	−7.22116	−	12.5074i	−0.373897	−	0.647609i	−0.990161	+	0.139931i	$0.955312\pi$
$374$	10.8584	+	18.8074i	0.561476	+	0.972505i
$375$		0			0
$376$	−14.1894	+	24.5767i	−0.731760	+	1.26745i
$377$	8.46320			0.435877
$378$		0			0
$379$	1.00099			0.0514176			0.0257088	−	0.999669i	$-0.491816\pi$
$379$	1.00099			0.0514176			0.0257088	+	0.999669i	$0.491816\pi$
$380$	13.0487	−	22.6010i	0.669384	−	1.15941i
$381$		0			0
$382$	−13.4574	−	23.3090i	−0.688543	−	1.19259i
$383$	2.05867	+	3.56572i	0.105193	+	0.182200i	0.913817	−	0.406126i	$-0.133121\pi$
$383$	2.05867	+	3.56572i	0.105193	+	0.182200i	−0.808624	+	0.588326i	$0.799787\pi$
$384$		0			0
$385$	14.0626	−	24.3571i	0.716696	−	1.24135i
$386$	2.81380			0.143219
$387$		0			0
$388$	−42.9605			−2.18099
$389$	−7.75996	+	13.4406i	−0.393445	+	0.681468i	−0.992901	−	0.118940i	$-0.962050\pi$
$389$	−7.75996	+	13.4406i	−0.393445	+	0.681468i	0.599456	+	0.800408i	$0.295384\pi$
$390$		0			0
$391$	−0.687514	−	1.19081i	−0.0347691	−	0.0602218i
$392$	−0.171815	−	0.297591i	−0.00867794	−	0.0150306i
$393$		0			0
$394$	−6.19602	+	10.7318i	−0.312151	+	0.540662i
$395$	52.9605			2.66473
$396$		0			0
$397$	−1.54893			−0.0777384			−0.0388692	−	0.999244i	$-0.512376\pi$
$397$	−1.54893			−0.0777384			−0.0388692	+	0.999244i	$0.512376\pi$
$398$	−16.8676	+	29.2155i	−0.845495	+	1.46444i
$399$		0			0
$400$	−9.52814	−	16.5032i	−0.476407	−	0.825161i
$401$	3.97369	+	6.88263i	0.198437	+	0.343702i	0.948022	−	0.318206i	$-0.103080\pi$
$401$	3.97369	+	6.88263i	0.198437	+	0.343702i	−0.749585	+	0.661908i	$0.769747\pi$
$402$		0			0
$403$	12.8988	−	22.3414i	0.642536	−	1.11290i
$404$	−22.8628			−1.13747
$405$		0			0
$406$	16.5380			0.820766
$407$	17.6794	−	30.6216i	0.876336	−	1.51786i
$408$		0			0
$409$	−13.2277	−	22.9110i	−0.654068	−	1.13288i	−0.982127	−	0.188221i	$-0.939728\pi$
$409$	−13.2277	−	22.9110i	−0.654068	−	1.13288i	0.328059	−	0.944657i	$-0.393606\pi$
$410$	−18.4913	−	32.0279i	−0.913221	−	1.58174i
$411$		0			0
$412$	−20.9523	+	36.2904i	−1.03224	+	1.78790i
$413$	4.39996			0.216508
$414$		0			0
$415$	−12.2249			−0.600097
$416$	0.676299	−	1.17138i	0.0331583	−	0.0574319i
$417$		0			0
$418$	8.84927	+	15.3274i	0.432832	+	0.749687i
$419$	19.1700	+	33.2034i	0.936516	+	1.62209i	0.771909	+	0.635733i	$0.219302\pi$
$419$	19.1700	+	33.2034i	0.936516	+	1.62209i	0.164607	+	0.986359i	$0.447364\pi$
$420$		0			0
$421$	−3.67225	+	6.36052i	−0.178974	+	0.309993i	−0.941530	−	0.336930i	$-0.890611\pi$
$421$	−3.67225	+	6.36052i	−0.178974	+	0.309993i	0.762555	+	0.646923i	$0.223945\pi$
$422$	−14.3415			−0.698134
$423$		0			0
$424$	−32.2337			−1.56540
$425$	5.77343	−	9.99987i	0.280052	−	0.485065i
$426$		0			0
$427$	19.1055	+	33.0916i	0.924578	+	1.60142i
$428$	−28.7816	−	49.8512i	−1.39121	−	2.40965i
$429$		0			0
$430$	−10.3774	+	17.9742i	−0.500443	+	0.866793i
$431$	15.8463			0.763289			0.381644	−	0.924309i	$-0.375358\pi$
$431$	15.8463			0.763289			0.381644	+	0.924309i	$0.375358\pi$
$432$		0			0
$433$	−23.8507			−1.14619			−0.573097	−	0.819488i	$-0.694258\pi$
$433$	−23.8507			−1.14619			−0.573097	+	0.819488i	$0.694258\pi$
$434$	25.2056	−	43.6575i	1.20991	−	2.09562i
$435$		0			0
$436$	−11.6386	−	20.1586i	−0.557387	−	0.965423i
$437$	−0.560301	−	0.970470i	−0.0268028	−	0.0464239i
$438$		0			0
$439$	10.7350	−	18.5935i	0.512352	−	0.887420i	−0.487545	−	0.873098i	$-0.662108\pi$
$439$	10.7350	−	18.5935i	0.512352	−	0.887420i	0.999897	−	0.0143222i	$-0.00455904\pi$
$440$	53.0593			2.52950
$441$		0			0
$442$	21.1453			1.00578
$443$	15.7740	−	27.3213i	0.749443	−	1.29807i	−0.198646	−	0.980071i	$-0.563655\pi$
$443$	15.7740	−	27.3213i	0.749443	−	1.29807i	0.948090	−	0.318003i	$-0.103012\pi$
$444$		0			0
$445$	7.85282	+	13.6015i	0.372259	+	0.644772i
$446$	−10.7266	−	18.5791i	−0.507921	−	0.879744i
$447$		0			0
$448$	−9.96723	+	17.2637i	−0.470907	+	0.815635i
$449$	−20.7898			−0.981130			−0.490565	−	0.871405i	$-0.663210\pi$
$449$	−20.7898			−0.981130			−0.490565	+	0.871405i	$0.663210\pi$
$450$		0			0
$451$	16.7768			0.789988
$452$	−23.0659	+	39.9513i	−1.08493	+	1.87915i
$453$		0			0
$454$	29.8407	+	51.6855i	1.40049	+	2.42572i
$455$	−13.6925	−	23.7161i	−0.641914	−	1.11183i
$456$		0			0
$457$	8.71387	−	15.0929i	0.407618	−	0.706014i	−0.587005	−	0.809584i	$-0.699693\pi$
$457$	8.71387	−	15.0929i	0.407618	−	0.706014i	0.994622	+	0.103569i	$0.0330263\pi$
$458$	44.6124			2.08460
$459$		0			0
$460$	−6.65196			−0.310149
$461$	−15.5022	+	26.8507i	−0.722011	+	1.25056i	0.238181	+	0.971221i	$0.423449\pi$
$461$	−15.5022	+	26.8507i	−0.722011	+	1.25056i	−0.960193	+	0.279339i	$0.909885\pi$
$462$		0			0
$463$	−3.24398	−	5.61873i	−0.150760	−	0.261125i	0.780747	−	0.624847i	$-0.214839\pi$
$463$	−3.24398	−	5.61873i	−0.150760	−	0.261125i	−0.931507	+	0.363723i	$0.881506\pi$
$464$	5.37313	+	9.30653i	0.249441	+	0.432045i
$465$		0			0
$466$	12.9501	−	22.4302i	0.599901	−	1.03906i
$467$	−1.94390			−0.0899530			−0.0449765	−	0.998988i	$-0.514321\pi$
$467$	−1.94390			−0.0899530			−0.0449765	+	0.998988i	$0.514321\pi$
$468$		0			0
$469$	15.6303			0.721738
$470$	−21.4173	+	37.0959i	−0.987907	+	1.71111i
$471$		0			0
$472$	4.15035	+	7.18862i	0.191035	+	0.330883i
$473$	−4.70761	−	8.15381i	−0.216456	−	0.374913i
$474$		0			0
$475$	4.70516	−	8.14957i	0.215887	−	0.373928i
$476$	27.6397			1.26686
$477$		0			0
$478$	23.4390			1.07207
$479$	0.664695	−	1.15129i	0.0303707	−	0.0526036i	−0.850441	−	0.526071i	$-0.823665\pi$
$479$	0.664695	−	1.15129i	0.0303707	−	0.0526036i	0.880811	+	0.473468i	$0.156998\pi$
$480$		0			0
$481$	−17.2141	−	29.8157i	−0.784896	−	1.35948i
$482$	8.64808	+	14.9789i	0.393909	+	0.682271i
$483$		0			0
$484$	−1.60558	+	2.78094i	−0.0729807	+	0.126406i
$485$	−32.7490			−1.48705
$486$		0			0
$487$	21.2040			0.960844			0.480422	−	0.877037i	$-0.340484\pi$
$487$	21.2040			0.960844			0.480422	+	0.877037i	$0.340484\pi$
$488$	−36.0432	+	62.4287i	−1.63160	+	2.82601i
$489$		0			0
$490$	−0.259336	−	0.449183i	−0.0117156	−	0.0202920i
$491$	13.5051	+	23.3915i	0.609475	+	1.05564i	0.991327	+	0.131419i	$0.0419532\pi$
$491$	13.5051	+	23.3915i	0.609475	+	1.05564i	−0.381852	+	0.924224i	$0.624713\pi$
$492$		0			0
$493$	−3.25576	+	5.63915i	−0.146632	+	0.253975i
$494$	17.2328			0.775338
$495$		0			0
$496$	32.7569			1.47083
$497$	−19.6958	+	34.1141i	−0.883476	+	1.53022i
$498$		0			0
$499$	−7.51946	−	13.0241i	−0.336617	−	0.583038i	0.647177	−	0.762340i	$-0.275949\pi$
$499$	−7.51946	−	13.0241i	−0.336617	−	0.583038i	−0.983794	+	0.179302i	$0.942616\pi$
$500$	3.18618	+	5.51863i	0.142490	+	0.246801i
$501$		0			0
$502$	−19.1548	+	33.1771i	−0.854920	+	1.48076i
$503$	−4.60650			−0.205394			−0.102697	−	0.994713i	$-0.532747\pi$
$503$	−4.60650			−0.205394			−0.102697	+	0.994713i	$0.532747\pi$
$504$		0			0
$505$	−17.4284			−0.775554
$506$	2.25559	−	3.90680i	0.100273	−	0.173678i
$507$		0			0
$508$	−5.23314	−	9.06406i	−0.232183	−	0.402153i
$509$	14.8983	+	25.8047i	0.660357	+	1.14377i	0.980522	+	0.196410i	$0.0629283\pi$
$509$	14.8983	+	25.8047i	0.660357	+	1.14377i	−0.320165	+	0.947362i	$0.603738\pi$
$510$		0			0
$511$	2.50101	−	4.33187i	0.110638	−	0.191631i
$512$	−40.8760			−1.80648
$513$		0			0
$514$	29.9599			1.32147
$515$	−15.9720	+	27.6643i	−0.703810	+	1.21904i
$516$		0			0
$517$	−9.71574	−	16.8282i	−0.427298	−	0.740102i
$518$	−33.6382	−	58.2631i	−1.47798	−	2.55993i
$519$		0			0
$520$	25.8314	−	44.7413i	1.13278	−	1.96204i
$521$	11.7621			0.515306			0.257653	−	0.966237i	$-0.417051\pi$
$521$	11.7621			0.515306			0.257653	+	0.966237i	$0.417051\pi$
$522$		0			0
$523$	29.3853			1.28493			0.642464	−	0.766316i	$-0.277912\pi$
$523$	29.3853			1.28493			0.642464	+	0.766316i	$0.277912\pi$
$524$	−8.91180	+	15.4357i	−0.389314	+	0.674311i
$525$		0			0
$526$	8.46663	+	14.6646i	0.369163	+	0.639409i
$527$	9.92426	+	17.1893i	0.432308	+	0.748779i
$528$		0			0
$529$	11.3572	−	19.6712i	0.493791	−	0.855270i
$530$	−48.6533			−2.11336
$531$		0			0
$532$	22.5254			0.976601
$533$	8.16762	−	14.1467i	0.353779	−	0.612763i
$534$		0			0
$535$	−21.9403	−	38.0017i	−0.948562	−	1.64296i
$536$	14.7436	+	25.5366i	0.636825	+	1.10301i
$537$		0			0
$538$	−8.67446	+	15.0246i	−0.373983	+	0.647757i
$539$	0.235290			0.0101347
$540$		0			0
$541$	−22.9116			−0.985046			−0.492523	−	0.870300i	$-0.663925\pi$
$541$	−22.9116			−0.985046			−0.492523	+	0.870300i	$0.663925\pi$
$542$	−29.1954	+	50.5679i	−1.25405	+	2.17208i
$543$		0			0
$544$	0.520340	+	0.901256i	0.0223094	+	0.0386410i
$545$	−8.87214	−	15.3670i	−0.380041	−	0.658250i
$546$		0			0
$547$	6.87885	−	11.9145i	0.294118	−	0.509428i	−0.680661	−	0.732598i	$-0.738307\pi$
$547$	6.87885	−	11.9145i	0.294118	−	0.509428i	0.974779	+	0.223171i	$0.0716407\pi$
$548$	−73.4107			−3.13595
$549$		0			0
$550$	37.8829			1.61533
$551$	−2.65334	+	4.59572i	−0.113036	+	0.195784i
$552$		0			0
$553$	22.8559	+	39.5875i	0.971931	+	1.68343i
$554$	0.128375	+	0.222352i	0.00545413	+	0.00944682i
$555$		0			0
$556$	−3.95576	+	6.85158i	−0.167762	+	0.290572i
$557$	−21.9041			−0.928105			−0.464053	−	0.885808i	$-0.653605\pi$
$557$	−21.9041			−0.928105			−0.464053	+	0.885808i	$0.653605\pi$
$558$		0			0
$559$	−9.16742			−0.387741
$560$	17.3862	−	30.1138i	0.734702	−	1.27254i
$561$		0			0
$562$	−10.0182	−	17.3520i	−0.422592	−	0.731951i
$563$	7.28421	+	12.6166i	0.306993	+	0.531727i	0.977703	−	0.209992i	$-0.0673438\pi$
$563$	7.28421	+	12.6166i	0.306993	+	0.531727i	−0.670710	+	0.741720i	$0.734011\pi$
$564$		0			0
$565$	−17.5832	+	30.4550i	−0.739731	+	1.28125i
$566$	58.0431			2.43973
$567$		0			0
$568$	−74.3137			−3.11813
$569$	−11.1785	+	19.3618i	−0.468628	+	0.811687i	−0.999357	−	0.0358544i	$-0.988585\pi$
$569$	−11.1785	+	19.3618i	−0.468628	+	0.811687i	0.530729	+	0.847541i	$0.321918\pi$
$570$		0			0
$571$	7.71307	+	13.3594i	0.322782	+	0.559075i	0.981061	−	0.193699i	$-0.0620486\pi$
$571$	7.71307	+	13.3594i	0.322782	+	0.559075i	−0.658279	+	0.752774i	$0.728715\pi$
$572$	23.2024	+	40.1878i	0.970143	+	1.68034i
$573$		0			0
$574$	15.9604	−	27.6442i	0.666174	−	1.15385i
$575$	−2.39860			−0.100028
$576$		0			0
$577$	32.8081			1.36582			0.682909	−	0.730503i	$-0.260714\pi$
$577$	32.8081			1.36582			0.682909	+	0.730503i	$0.260714\pi$
$578$	12.7567	−	22.0952i	0.530608	−	0.919040i
$579$		0			0
$580$	15.7504	+	27.2805i	0.654000	+	1.13276i
$581$	−5.27584	−	9.13802i	−0.218879	−	0.379109i
$582$		0			0
$583$	11.0355	−	19.1141i	0.457045	−	0.791625i
$584$	9.43650			0.390485
$585$		0			0
$586$	53.1515			2.19567
$587$	15.1171	−	26.1836i	0.623951	−	1.08071i	−0.364792	−	0.931089i	$-0.618860\pi$
$587$	15.1171	−	26.1836i	0.623951	−	1.08071i	0.988743	−	0.149625i	$-0.0478068\pi$
$588$		0			0
$589$	8.08795	+	14.0087i	0.333258	+	0.577220i
$590$	6.26451	+	10.8505i	0.257906	+	0.446706i
$591$		0			0
$592$	21.8579	−	37.8589i	0.898353	−	1.55599i
$593$	−41.1023			−1.68787			−0.843935	−	0.536446i	$-0.819766\pi$
$593$	−41.1023			−1.68787			−0.843935	+	0.536446i	$0.819766\pi$
$594$		0			0
$595$	21.0698			0.863778
$596$	14.7793	−	25.5986i	0.605386	−	1.04856i
$597$		0			0
$598$	−2.19623	−	3.80398i	−0.0898105	−	0.155556i
$599$	18.2753	+	31.6537i	0.746707	+	1.29333i	0.949393	+	0.314091i	$0.101700\pi$
$599$	18.2753	+	31.6537i	0.746707	+	1.29333i	−0.202686	+	0.979244i	$0.564967\pi$
$600$		0			0
$601$	−1.97290	+	3.41717i	−0.0804764	+	0.139389i	−0.903455	−	0.428684i	$-0.858977\pi$
$601$	−1.97290	+	3.41717i	−0.0804764	+	0.139389i	0.822978	+	0.568073i	$0.192311\pi$
$602$	−17.9141			−0.730125
$603$		0			0
$604$	19.6015			0.797575
$605$	−1.22394	+	2.11992i	−0.0497601	+	0.0861870i
$606$		0			0
$607$	−5.00576	−	8.67023i	−0.203178	−	0.351914i	0.746373	−	0.665528i	$-0.231794\pi$
$607$	−5.00576	−	8.67023i	−0.203178	−	0.351914i	−0.949551	+	0.313614i	$0.898460\pi$
$608$	0.424060	+	0.734494i	0.0171979	+	0.0297877i
$609$		0			0
$610$	−54.4034	+	94.2294i	−2.20273	+	3.81524i
$611$	−18.9201			−0.765425
$612$		0			0
$613$	−18.7568			−0.757578			−0.378789	−	0.925483i	$-0.623659\pi$
$613$	−18.7568			−0.757578			−0.378789	+	0.925483i	$0.623659\pi$
$614$	−20.1046	+	34.8223i	−0.811357	+	1.40531i
$615$		0			0
$616$	22.8985	+	39.6614i	0.922608	+	1.59800i
$617$	−11.5050	−	19.9273i	−0.463175	−	0.802243i	0.535942	−	0.844255i	$-0.319957\pi$
$617$	−11.5050	−	19.9273i	−0.463175	−	0.802243i	−0.999117	+	0.0420119i	$0.986623\pi$
$618$		0			0
$619$	−3.70701	+	6.42073i	−0.148997	+	0.258071i	−0.930857	−	0.365383i	$-0.880938\pi$
$619$	−3.70701	+	6.42073i	−0.148997	+	0.258071i	0.781860	+	0.623454i	$0.214271\pi$
$620$	96.0211			3.85630
$621$		0			0
$622$	19.0598			0.764229
$623$	−6.77800	+	11.7398i	−0.271555	+	0.470347i
$624$		0			0
$625$	13.6489	+	23.6406i	0.545956	+	0.945623i
$626$	−18.9472	−	32.8175i	−0.757281	−	1.31165i
$627$		0			0
$628$	−2.98348	+	5.16754i	−0.119054	+	0.206207i
$629$	26.4889			1.05618
$630$		0			0
$631$	−30.9924			−1.23379			−0.616894	−	0.787046i	$-0.711609\pi$
$631$	−30.9924			−1.23379			−0.616894	+	0.787046i	$0.711609\pi$
$632$	−43.1185	+	74.6835i	−1.71516	+	2.97075i
$633$		0			0
$634$	10.6130	+	18.3822i	0.421496	+	0.730052i
$635$	−3.98924	−	6.90957i	−0.158308	−	0.274198i
$636$		0			0
$637$	0.114549	−	0.198404i	0.00453859	−	0.00786106i
$638$	−21.3630			−0.845769
$639$		0			0
$640$	−59.2559			−2.34229
$641$	−17.6731	+	30.6106i	−0.698044	+	1.20905i	0.271100	+	0.962551i	$0.412613\pi$
$641$	−17.6731	+	30.6106i	−0.698044	+	1.20905i	−0.969144	+	0.246496i	$0.920721\pi$
$642$		0			0
$643$	9.85047	+	17.0615i	0.388465	+	0.672840i	0.992243	−	0.124312i	$-0.0396723\pi$
$643$	9.85047	+	17.0615i	0.388465	+	0.672840i	−0.603779	+	0.797152i	$0.706339\pi$
$644$	−2.87075	−	4.97229i	−0.113124	−	0.195936i
$645$		0			0
$646$	−6.62938	+	11.4824i	−0.260830	+	0.451770i
$647$	−46.8317			−1.84114			−0.920572	−	0.390572i	$-0.872277\pi$
$647$	−46.8317			−1.84114			−0.920572	+	0.390572i	$0.872277\pi$
$648$		0			0
$649$	−5.68366			−0.223103
$650$	18.4429	−	31.9441i	0.723391	−	1.25295i
$651$		0			0
$652$	34.8586	+	60.3768i	1.36517	+	2.36454i
$653$	8.66336	+	15.0054i	0.339023	+	0.587206i	0.984249	−	0.176786i	$-0.0565701\pi$
$653$	8.66336	+	15.0054i	0.339023	+	0.587206i	−0.645226	+	0.763992i	$0.723237\pi$
$654$		0			0
$655$	−6.79350	+	11.7667i	−0.265444	+	0.459762i
$656$	20.7419			0.809835
$657$		0			0
$658$	−36.9719			−1.44131
$659$	21.8671	−	37.8749i	0.851821	−	1.47540i	−0.0277419	−	0.999615i	$-0.508832\pi$
$659$	21.8671	−	37.8749i	0.851821	−	1.47540i	0.879563	−	0.475782i	$-0.157835\pi$
$660$		0			0
$661$	4.54343	+	7.86945i	0.176719	+	0.306086i	0.940755	−	0.339088i	$-0.110118\pi$
$661$	4.54343	+	7.86945i	0.176719	+	0.306086i	−0.764036	+	0.645174i	$0.776785\pi$
$662$	−25.2470	−	43.7292i	−0.981254	−	1.69958i
$663$		0			0
$664$	9.95308	−	17.2392i	0.386254	−	0.669012i
$665$	17.1712			0.665871
$666$		0			0
$667$	1.35262			0.0523737
$668$	13.8200	−	23.9370i	0.534713	−	0.926150i
$669$		0			0
$670$	22.2538	+	38.5448i	0.859740	+	1.48911i
$671$	−24.6795	−	42.7462i	−0.952743	−	1.65020i
$672$		0			0
$673$	−3.74834	+	6.49232i	−0.144488	+	0.250261i	−0.929182	−	0.369623i	$-0.879487\pi$
$673$	−3.74834	+	6.49232i	−0.144488	+	0.250261i	0.784694	+	0.619884i	$0.212820\pi$
$674$	39.2711			1.51266
$675$		0			0
$676$	−7.34587			−0.282534
$677$	7.68128	−	13.3044i	0.295215	−	0.511328i	−0.679820	−	0.733379i	$-0.737942\pi$
$677$	7.68128	−	13.3044i	0.295215	−	0.511328i	0.975035	+	0.222051i	$0.0712753\pi$
$678$		0			0
$679$	−14.1333	−	24.4796i	−0.542387	−	0.939441i
$680$	19.8745	+	34.4237i	0.762153	+	1.32009i
$681$		0			0
$682$	−32.5595	+	56.3946i	−1.24677	+	2.15946i
$683$	−6.62157			−0.253367			−0.126684	−	0.991943i	$-0.540433\pi$
$683$	−6.62157			−0.253367			−0.126684	+	0.991943i	$0.540433\pi$
$684$		0			0
$685$	−55.9612			−2.13817
$686$	−22.6467	+	39.2253i	−0.864656	+	1.49763i
$687$		0			0
$688$	−5.82023	−	10.0809i	−0.221894	−	0.384332i
$689$	−10.7451	−	18.6110i	−0.409355	−	0.709024i
$690$		0			0
$691$	9.32843	−	16.1573i	0.354870	−	0.614653i	−0.632226	−	0.774784i	$-0.717858\pi$
$691$	9.32843	−	16.1573i	0.354870	−	0.614653i	0.987096	+	0.160131i	$0.0511918\pi$
$692$	96.8457			3.68152
$693$		0			0
$694$	24.0968			0.914704
$695$	−3.01549	+	5.22298i	−0.114384	+	0.198119i
$696$		0			0
$697$	6.28412	+	10.8844i	0.238028	+	0.412276i
$698$	11.5946	+	20.0824i	0.438862	+	0.760131i
$699$		0			0
$700$	24.1073	−	41.7551i	0.911170	−	1.57819i
$701$	−24.8903			−0.940092			−0.470046	−	0.882642i	$-0.655763\pi$
$701$	−24.8903			−0.940092			−0.470046	+	0.882642i	$0.655763\pi$
$702$		0			0
$703$	21.5876			0.814190
$704$	12.8752	−	22.3005i	0.485252	−	0.840481i
$705$		0			0
$706$	−4.16001	−	7.20535i	−0.156564	−	0.271177i
$707$	−7.52149	−	13.0276i	−0.282875	−	0.489953i
$708$		0			0
$709$	13.0894	−	22.6715i	0.491582	−	0.851445i	−0.508371	−	0.861138i	$-0.669752\pi$
$709$	13.0894	−	22.6715i	0.491582	−	0.851445i	0.999953	+	0.00969346i	$0.00308557\pi$
$710$	−112.169			−4.20961
$711$		0			0
$712$	−25.5739			−0.958424
$713$	2.06154	−	3.57069i	0.0772052	−	0.133723i
$714$		0			0
$715$	17.6873	+	30.6353i	0.661468	+	1.14570i
$716$	−41.5634	−	71.9899i	−1.55330	−	2.69039i
$717$		0			0
$718$	43.2907	−	74.9817i	1.61559	−	2.79829i
$719$	−21.0290			−0.784251			−0.392125	−	0.919912i	$-0.628260\pi$
$719$	−21.0290			−0.784251			−0.392125	+	0.919912i	$0.628260\pi$
$720$		0			0
$721$	−27.5718			−1.02683
$722$	17.9463	−	31.0838i	0.667891	−	1.15682i
$723$		0			0
$724$	31.2553	+	54.1358i	1.16159	+	2.01194i
$725$	5.67935	+	9.83692i	0.210926	+	0.365334i
$726$		0			0
$727$	−20.6978	+	35.8497i	−0.767640	+	1.32959i	0.171199	+	0.985236i	$0.445236\pi$
$727$	−20.6978	+	35.8497i	−0.767640	+	1.32959i	−0.938839	+	0.344356i	$0.888097\pi$
$728$	44.5918			1.65268
$729$		0			0
$730$	14.2434			0.527171
$731$	3.52668	−	6.10838i	0.130439	−	0.225927i
$732$		0			0
$733$	−16.8134	−	29.1216i	−0.621016	−	1.07563i	−0.989297	−	0.145916i	$-0.953387\pi$
$733$	−16.8134	−	29.1216i	−0.621016	−	1.07563i	0.368281	−	0.929714i	$-0.379946\pi$
$734$	38.7660	+	67.1447i	1.43088	+	2.47836i
$735$		0			0
$736$	0.108089	−	0.187215i	0.00398421	−	0.00690085i
$737$	−20.1904			−0.743724
$738$		0			0
$739$	−12.9454			−0.476202			−0.238101	−	0.971240i	$-0.576525\pi$
$739$	−12.9454			−0.476202			−0.238101	+	0.971240i	$0.576525\pi$
$740$	64.0725	−	110.977i	2.35535	−	4.07959i
$741$		0			0
$742$	−20.9970	−	36.3679i	−0.770826	−	1.33511i
$743$	−0.0439646	−	0.0761489i	−0.00161290	−	0.00279363i	0.865218	−	0.501396i	$-0.167180\pi$
$743$	−0.0439646	−	0.0761489i	−0.00161290	−	0.00279363i	−0.866831	+	0.498603i	$0.833847\pi$
$744$		0			0
$745$	11.2664	−	19.5139i	0.412767	−	0.714934i
$746$	35.4962			1.29961
$747$		0			0
$748$	−35.7036			−1.30545
$749$	18.9373	−	32.8004i	0.691955	−	1.19850i
$750$		0			0
$751$	−24.9480	−	43.2112i	−0.910366	−	1.57680i	−0.813548	−	0.581498i	$-0.802467\pi$
$751$	−24.9480	−	43.2112i	−0.910366	−	1.57680i	−0.0968179	−	0.995302i	$-0.530866\pi$
$752$	−12.0120	−	20.8054i	−0.438033	−	0.758696i
$753$		0			0
$754$	−10.4004	+	18.0140i	−0.378759	+	0.656031i
$755$	14.9423			0.543806
$756$		0			0
$757$	−11.8679			−0.431348			−0.215674	−	0.976465i	$-0.569195\pi$
$757$	−11.8679			−0.431348			−0.215674	+	0.976465i	$0.569195\pi$
$758$	−1.23011	+	2.13062i	−0.0446798	+	0.0773877i
$759$		0			0
$760$	16.1971	+	28.0542i	0.587530	+	1.01763i
$761$	1.89515	+	3.28250i	0.0686992	+	0.118990i	0.898329	−	0.439323i	$-0.144782\pi$
$761$	1.89515	+	3.28250i	0.0686992	+	0.118990i	−0.829630	+	0.558314i	$0.811448\pi$
$762$		0			0
$763$	7.65781	−	13.2637i	0.277231	−	0.480179i
$764$	44.2494			1.60089
$765$		0			0
$766$	−10.1196			−0.365634
$767$	−2.76704	+	4.79265i	−0.0999120	+	0.173053i
$768$		0			0
$769$	−3.13475	−	5.42955i	−0.113042	−	0.195795i	0.803953	−	0.594692i	$-0.202726\pi$
$769$	−3.13475	−	5.42955i	−0.113042	−	0.195795i	−0.916995	+	0.398898i	$0.869393\pi$
$770$	34.5629	+	59.8646i	1.24556	+	2.15737i
$771$		0			0
$772$	−2.31302	+	4.00626i	−0.0832473	+	0.144189i
$773$	1.29536			0.0465907			0.0232954	−	0.999729i	$-0.492584\pi$
$773$	1.29536			0.0465907			0.0232954	+	0.999729i	$0.492584\pi$
$774$		0			0
$775$	34.6237			1.24372
$776$	26.6631	−	46.1818i	0.957148	−	1.65783i
$777$		0			0
$778$	−19.0723	−	33.0343i	−0.683777	−	1.18434i
$779$	5.12135	+	8.87044i	0.183491	+	0.317816i
$780$		0			0
$781$	25.4421	−	44.0669i	0.910388	−	1.57684i
$782$	3.37953			0.120852
$783$		0			0
$784$	0.290900			0.0103893
$785$	−2.27432	+	3.93923i	−0.0811738	+	0.140597i
$786$		0			0
$787$	6.19611	+	10.7320i	0.220867	+	0.382554i	0.955072	−	0.296375i	$-0.0957778\pi$
$787$	6.19611	+	10.7320i	0.220867	+	0.382554i	−0.734204	+	0.678929i	$0.762445\pi$
$788$	−10.1866	−	17.6437i	−0.362882	−	0.628529i
$789$		0			0
$790$	−65.0828	+	112.727i	−2.31554	+	4.01064i
$791$	−30.3532			−1.07924
$792$		0			0
$793$	−48.0600			−1.70666
$794$	1.90347	−	3.29690i	0.0675515	−	0.117003i
$795$		0			0
$796$	−27.7311	−	48.0318i	−0.982904	−	1.70244i
$797$	12.1914	+	21.1160i	0.431840	+	0.747968i	0.997032	−	0.0769910i	$-0.0245313\pi$
$797$	12.1914	+	21.1160i	0.431840	+	0.747968i	−0.565192	+	0.824959i	$0.691198\pi$
$798$		0			0
$799$	7.27850	−	12.6067i	0.257495	−	0.445994i
$800$	1.81536			0.0641827
$801$		0			0
$802$	−19.5330			−0.689734
$803$	−3.23068	+	5.59570i	−0.114008	+	0.197468i
$804$		0			0
$805$	−2.18839	−	3.79040i	−0.0771305	−	0.133594i
$806$	31.7026	+	54.9104i	1.11668	+	1.93414i
$807$		0			0
$808$	14.1896	−	24.5771i	0.499188	−	0.864619i
$809$	−24.1156			−0.847861			−0.423930	−	0.905695i	$-0.639350\pi$
$809$	−24.1156			−0.847861			−0.423930	+	0.905695i	$0.639350\pi$
$810$		0			0
$811$	48.1121			1.68944			0.844721	−	0.535206i	$-0.179766\pi$
$811$	48.1121			1.68944			0.844721	+	0.535206i	$0.179766\pi$
$812$	−13.5946	+	23.5466i	−0.477078	+	0.826324i
$813$		0			0
$814$	43.4523	+	75.2615i	1.52300	+	2.63791i
$815$	26.5728	+	46.0255i	0.930805	+	1.61220i
$816$		0			0
$817$	2.87413	−	4.97814i	0.100553	−	0.174163i
$818$	65.0218			2.27343
$819$		0			0
$820$	60.8013			2.12327
$821$	−8.46941	+	14.6695i	−0.295585	+	0.511968i	−0.975121	−	0.221675i	$-0.928848\pi$
$821$	−8.46941	+	14.6695i	−0.295585	+	0.511968i	0.679536	+	0.733642i	$0.262181\pi$
$822$		0			0
$823$	−5.77797	−	10.0077i	−0.201407	−	0.348848i	0.747575	−	0.664178i	$-0.231218\pi$
$823$	−5.77797	−	10.0077i	−0.201407	−	0.348848i	−0.948982	+	0.315330i	$0.897885\pi$
$824$	−26.0077	−	45.0466i	−0.906020	−	1.56927i
$825$		0			0
$826$	−5.40709	+	9.36535i	−0.188137	+	0.325862i
$827$	10.2374			0.355988			0.177994	−	0.984032i	$-0.443039\pi$
$827$	10.2374			0.355988			0.177994	+	0.984032i	$0.443039\pi$
$828$		0			0
$829$	9.35244			0.324824			0.162412	−	0.986723i	$-0.448073\pi$
$829$	9.35244			0.324824			0.162412	+	0.986723i	$0.448073\pi$
$830$	15.0231	−	26.0208i	0.521460	−	0.903195i
$831$		0			0
$832$	−12.5363	−	21.7136i	−0.434620	−	0.752783i
$833$	0.0881331	+	0.152651i	0.00305363	+	0.00528904i
$834$		0			0
$835$	10.5351	−	18.2473i	0.364581	−	0.631472i
$836$	−29.0973			−1.00635
$837$		0			0
$838$	−94.2316			−3.25518
$839$	5.92256	−	10.2582i	0.204469	−	0.354151i	−0.745494	−	0.666512i	$-0.767786\pi$
$839$	5.92256	−	10.2582i	0.204469	−	0.354151i	0.949964	+	0.312361i	$0.101120\pi$
$840$		0			0
$841$	11.2973	+	19.5675i	0.389562	+	0.674741i
$842$	−9.02561	−	15.6328i	−0.311043	−	0.538742i
$843$		0			0
$844$	11.7891	−	20.4193i	0.405797	−	0.702862i
$845$	−5.59979			−0.192639
$846$		0			0
$847$	−2.11283			−0.0725978
$848$	13.6437	−	23.6316i	0.468527	−	0.811513i
$849$		0			0
$850$	14.1899	+	24.5776i	0.486709	+	0.843004i
$851$	−2.75123	−	4.76527i	−0.0943109	−	0.163351i
$852$		0			0
$853$	18.6356	−	32.2779i	0.638072	−	1.10517i	−0.347783	−	0.937575i	$-0.613065\pi$
$853$	18.6356	−	32.2779i	0.638072	−	1.10517i	0.985855	−	0.167599i	$-0.0536012\pi$
$854$	−93.9144			−3.21368
$855$		0			0
$856$	71.4521			2.44218
$857$	20.7159	−	35.8810i	0.707642	−	1.22567i	−0.258087	−	0.966122i	$-0.583092\pi$
$857$	20.7159	−	35.8810i	0.707642	−	1.22567i	0.965729	−	0.259551i	$-0.0835746\pi$
$858$		0			0
$859$	4.62925	+	8.01810i	0.157948	+	0.273574i	0.934129	−	0.356937i	$-0.116179\pi$
$859$	4.62925	+	8.01810i	0.157948	+	0.273574i	−0.776180	+	0.630511i	$0.782845\pi$
$860$	−17.0610	−	29.5505i	−0.581775	−	1.00766i
$861$		0			0
$862$	−19.4734	+	33.7290i	−0.663267	+	1.14881i
$863$	51.4748			1.75222			0.876110	−	0.482110i	$-0.160130\pi$
$863$	51.4748			1.75222			0.876110	+	0.482110i	$0.160130\pi$
$864$		0			0
$865$	73.8258			2.51015
$866$	29.3100	−	50.7665i	0.995996	−	1.72512i
$867$		0			0
$868$	41.4393	+	71.7750i	1.40654	+	2.43620i
$869$	−29.5241	−	51.1373i	−1.00154	−	1.73471i
$870$		0			0
$871$	−9.82953	+	17.0252i	−0.333061	+	0.576878i
$872$	28.8935			0.978458
$873$		0			0
$874$	2.75421			0.0931624
$875$	−2.09640	+	3.63108i	−0.0708714	+	0.122753i
$876$		0			0
$877$	12.4495	+	21.5632i	0.420390	+	0.728137i	0.995978	−	0.0896030i	$-0.0285598\pi$
$877$	12.4495	+	21.5632i	0.420390	+	0.728137i	−0.575587	+	0.817740i	$0.695226\pi$
$878$	26.3843	+	45.6989i	0.890427	+	1.54226i
$879$		0			0
$880$	−22.4587	+	38.8996i	−0.757082	+	1.31131i
$881$	−1.43361			−0.0482997			−0.0241498	−	0.999708i	$-0.507688\pi$
$881$	−1.43361			−0.0482997			−0.0241498	+	0.999708i	$0.507688\pi$
$882$		0			0
$883$	26.2046			0.881855			0.440928	−	0.897543i	$-0.354650\pi$
$883$	26.2046			0.881855			0.440928	+	0.897543i	$0.354650\pi$
$884$	−17.3820	+	30.1065i	−0.584619	+	1.01259i
$885$		0			0
$886$	38.7691	+	67.1500i	1.30247	+	2.25595i
$887$	−21.6863	−	37.5617i	−0.728154	−	1.26120i	−0.957663	−	0.287893i	$-0.907045\pi$
$887$	−21.6863	−	37.5617i	−0.728154	−	1.26120i	0.229509	−	0.973307i	$-0.426288\pi$
$888$		0			0
$889$	3.44323	−	5.96385i	0.115482	−	0.200021i
$890$	−38.6011			−1.29391
$891$		0			0
$892$	35.2702			1.18093
$893$	5.93174	−	10.2741i	0.198498	−	0.343809i
$894$		0			0
$895$	−31.6839	−	54.8781i	−1.05908	−	1.83437i
$896$	−25.5728	−	44.2933i	−0.854326	−	1.47974i
$897$		0			0
$898$	25.5484	−	44.2512i	0.852563	−	1.47668i
$899$	−19.5251			−0.651198
$900$		0			0
$901$	16.5344			0.550841
$902$	−20.6169	+	35.7095i	−0.686467	+	1.18900i
$903$		0			0
$904$	−28.6313	−	49.5908i	−0.952261	−	1.64936i
$905$	23.8260	+	41.2679i	0.792004	+	1.37179i
$906$		0			0
$907$	−11.9359	+	20.6736i	−0.396325	+	0.686454i	−0.993269	−	0.115828i	$-0.963048\pi$
$907$	−11.9359	+	20.6736i	−0.396325	+	0.686454i	0.596945	+	0.802282i	$0.296381\pi$
$908$	−98.1191			−3.25620
$909$		0			0
$910$	67.3065			2.23119
$911$	−2.16026	+	3.74168i	−0.0715726	+	0.123967i	−0.899591	−	0.436734i	$-0.856135\pi$
$911$	−2.16026	+	3.74168i	−0.0715726	+	0.123967i	0.828018	+	0.560701i	$0.189468\pi$
$912$		0			0
$913$	6.81508	+	11.8041i	0.225546	+	0.390657i
$914$	21.4169	+	37.0951i	0.708406	+	1.22700i
$915$		0			0
$916$	−36.6725	+	63.5186i	−1.21169	+	2.09871i
$917$	−11.7273			−0.387271
$918$		0			0
$919$	3.56151			0.117483			0.0587417	−	0.998273i	$-0.481291\pi$
$919$	3.56151			0.117483			0.0587417	+	0.998273i	$0.481291\pi$
$920$	4.12848	−	7.15074i	0.136112	−	0.235753i
$921$		0			0
$922$	−38.1012	−	65.9933i	−1.25480	−	2.17337i
$923$	−24.7725	−	42.9072i	−0.815396	−	1.41231i
$924$		0			0
$925$	23.1036	−	40.0166i	0.759641	−	1.31574i
$926$	15.9460			0.524019
$927$		0			0
$928$	−1.02372			−0.0336053
$929$	16.6629	−	28.8610i	0.546692	−	0.946898i	−0.451807	−	0.892116i	$-0.649220\pi$
$929$	16.6629	−	28.8610i	0.546692	−	0.946898i	0.998498	−	0.0547818i	$-0.0174463\pi$
$930$		0			0
$931$	0.0718256	+	0.124406i	0.00235399	+	0.00407723i
$932$	21.2906	+	36.8764i	0.697396	+	1.20793i
$933$		0			0
$934$	2.38885	−	4.13761i	0.0781655	−	0.135387i
$935$	−27.2170			−0.890091
$936$		0			0
$937$	26.0594			0.851322			0.425661	−	0.904883i	$-0.360042\pi$
$937$	26.0594			0.851322			0.425661	+	0.904883i	$0.360042\pi$
$938$	−19.2079	+	33.2691i	−0.627161	+	1.08628i
$939$		0			0
$940$	−35.2111	−	60.9875i	−1.14846	−	1.98919i
$941$	11.9968	+	20.7790i	0.391084	+	0.677377i	0.992593	−	0.121489i	$-0.0387669\pi$
$941$	11.9968	+	20.7790i	0.391084	+	0.677377i	−0.601509	+	0.798866i	$0.705434\pi$
$942$		0			0
$943$	1.30538	−	2.26099i	0.0425091	−	0.0736279i
$944$	−7.02697			−0.228708
$945$		0			0
$946$	23.1406			0.752366
$947$	−14.9423	+	25.8809i	−0.485561	+	0.841016i	−0.999862	−	0.0165935i	$-0.994718\pi$
$947$	−14.9423	+	25.8809i	−0.485561	+	0.841016i	0.514302	+	0.857609i	$0.328051\pi$
$948$		0			0
$949$	3.14566	+	5.44844i	0.102112	+	0.176864i
$950$	11.5643	+	20.0299i	0.375195	+	0.649857i
$951$		0			0
$952$	−17.1543	+	29.7121i	−0.555974	+	0.962975i
$953$	−10.1934			−0.330196			−0.165098	−	0.986277i	$-0.552794\pi$
$953$	−10.1934			−0.330196			−0.165098	+	0.986277i	$0.552794\pi$
$954$		0			0
$955$	33.7315			1.09153
$956$	−19.2674	+	33.3721i	−0.623153	+	1.07933i
$957$		0			0
$958$	1.63368	+	2.82962i	0.0527819	+	0.0914209i
$959$	−24.1509	−	41.8306i	−0.779874	−	1.35078i
$960$		0			0
$961$	−14.2583	+	24.6961i	−0.459945	+	0.796649i
$962$	84.6174			2.72817
$963$		0			0
$964$	−28.4357			−0.915854
$965$	−1.76322	+	3.05399i	−0.0567601	+	0.0983114i
$966$		0			0
$967$	9.38330	+	16.2524i	0.301747	+	0.522641i	0.976532	−	0.215374i	$-0.0690970\pi$
$967$	9.38330	+	16.2524i	0.301747	+	0.522641i	−0.674785	+	0.738014i	$0.735764\pi$
$968$	−1.99297	−	3.45193i	−0.0640565	−	0.110949i
$969$		0			0
$970$	40.2450	−	69.7065i	1.29219	−	2.23814i
$971$	−51.9535			−1.66727			−0.833633	−	0.552319i	$-0.813743\pi$
$971$	−51.9535			−1.66727			−0.833633	+	0.552319i	$0.813743\pi$
$972$		0			0
$973$	−5.20552			−0.166881
$974$	−26.0575	+	45.1328i	−0.834935	+	1.44615i
$975$		0			0
$976$	−30.5124	−	52.8491i	−0.976679	−	1.69166i
$977$	−16.2920	−	28.2186i	−0.521229	−	0.902794i	−0.999695	−	0.0246887i	$-0.992141\pi$
$977$	−16.2920	−	28.2186i	−0.521229	−	0.902794i	0.478467	−	0.878106i	$-0.341193\pi$
$978$		0			0
$979$	8.75550	−	15.1650i	0.279827	−	0.484675i
$980$	0.852722			0.0272392
$981$		0			0
$982$	−66.3852			−2.11844
$983$	−17.5397	+	30.3797i	−0.559431	+	0.968962i	0.438114	+	0.898920i	$0.355647\pi$
$983$	−17.5397	+	30.3797i	−0.559431	+	0.968962i	−0.997544	+	0.0700424i	$0.977687\pi$
$984$		0			0
$985$	−7.76526	−	13.4498i	−0.247422	−	0.428547i
$986$	−8.00198	−	13.8598i	−0.254835	−	0.441387i
$987$		0			0
$988$	−14.1658	+	24.5358i	−0.450673	+	0.780588i
$989$	−1.46517			−0.0465898
$990$		0			0
$991$	−54.7635			−1.73962			−0.869810	−	0.493386i	$-0.835759\pi$
$991$	−54.7635			−1.73962			−0.869810	+	0.493386i	$0.835759\pi$
$992$	−1.56026	+	2.70245i	−0.0495384	+	0.0858030i
$993$		0			0
$994$	−48.4080	−	83.8452i	−1.53541	−	2.65941i
$995$	−21.1396	−	36.6148i	−0.670169	−	1.16077i
$996$		0			0
$997$	−25.1650	+	43.5871i	−0.796984	+	1.38042i	0.124587	+	0.992209i	$0.460239\pi$
$997$	−25.1650	+	43.5871i	−0.796984	+	1.38042i	−0.921571	+	0.388209i	$0.873094\pi$
$998$	36.9625			1.17003
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.d.487.1		12
3.2	odd	2		729.2.c.a.487.6		12
9.2	odd	6		729.2.a.e.1.1	yes	6
9.4	even	3	inner	729.2.c.d.244.1		12
9.5	odd	6		729.2.c.a.244.6		12
9.7	even	3		729.2.a.b.1.6	✓	6
27.2	odd	18		729.2.e.l.325.1		12
27.4	even	9		729.2.e.j.163.1		12
27.5	odd	18		729.2.e.l.406.1		12
27.7	even	9		729.2.e.t.82.2		12
27.11	odd	18		729.2.e.u.568.2		12
27.13	even	9		729.2.e.t.649.2		12
27.14	odd	18		729.2.e.k.649.1		12
27.16	even	9		729.2.e.j.568.1		12
27.20	odd	18		729.2.e.k.82.1		12
27.22	even	9		729.2.e.s.406.2		12
27.23	odd	18		729.2.e.u.163.2		12
27.25	even	9		729.2.e.s.325.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.6	✓	6	9.7	even	3
729.2.a.e.1.1	yes	6	9.2	odd	6
729.2.c.a.244.6		12	9.5	odd	6
729.2.c.a.487.6		12	3.2	odd	2
729.2.c.d.244.1		12	9.4	even	3	inner
729.2.c.d.487.1		12	1.1	even	1	trivial
729.2.e.j.163.1		12	27.4	even	9
729.2.e.j.568.1		12	27.16	even	9
729.2.e.k.82.1		12	27.20	odd	18
729.2.e.k.649.1		12	27.14	odd	18
729.2.e.l.325.1		12	27.2	odd	18
729.2.e.l.406.1		12	27.5	odd	18
729.2.e.s.325.2		12	27.25	even	9
729.2.e.s.406.2		12	27.22	even	9
729.2.e.t.82.2		12	27.7	even	9
729.2.e.t.649.2		12	27.13	even	9
729.2.e.u.163.2		12	27.23	odd	18
729.2.e.u.568.2		12	27.11	odd	18

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22889 + 2.12851i) q^{2} +(-2.02036 - 3.49937i) q^{4} +(-1.54013 - 2.66759i) q^{5} +(1.32933 - 2.30247i) q^{7} +5.01568 q^{8} +7.57064 q^{10} +(-1.71717 + 2.97423i) q^{11} +(1.67198 + 2.89595i) q^{13} +(3.26722 + 5.65899i) q^{14} +(-2.12302 + 3.67717i) q^{16} -2.57282 q^{17} -2.09676 q^{19} +(-6.22325 + 10.7790i) q^{20} +(-4.22044 - 7.31002i) q^{22} +(0.267222 + 0.462842i) q^{23} +(-2.24401 + 3.88674i) q^{25} -8.21874 q^{26} -10.7430 q^{28} +(1.26545 - 2.19182i) q^{29} +(-3.85735 - 6.68113i) q^{31} +(-0.202245 - 0.350299i) q^{32} +(3.16172 - 5.47626i) q^{34} -8.18939 q^{35} -10.2957 q^{37} +(2.57670 - 4.46298i) q^{38} +(-7.72481 - 13.3798i) q^{40} +(-2.44250 - 4.23054i) q^{41} +(-1.37075 + 2.37420i) q^{43} +13.8772 q^{44} -1.31355 q^{46} +(-2.82900 + 4.89997i) q^{47} +(-0.0342555 - 0.0593322i) q^{49} +(-5.51530 - 9.55279i) q^{50} +(6.75601 - 11.7018i) q^{52} -6.42657 q^{53} +10.5787 q^{55} +(6.66751 - 11.5485i) q^{56} +(3.11020 + 5.38703i) q^{58} +(0.827475 + 1.43323i) q^{59} +(-7.18610 + 12.4467i) q^{61} +18.9611 q^{62} -7.49791 q^{64} +(5.15013 - 8.92029i) q^{65} +(2.93949 + 5.09135i) q^{67} +(5.19803 + 9.00325i) q^{68} +(10.0639 - 17.4312i) q^{70} -14.8163 q^{71} +1.88140 q^{73} +(12.6523 - 21.9144i) q^{74} +(4.23623 + 7.33736i) q^{76} +(4.56538 + 7.90748i) q^{77} +(-8.59674 + 14.8900i) q^{79} +13.0789 q^{80} +12.0063 q^{82} +(1.98439 - 3.43707i) q^{83} +(3.96248 + 6.86321i) q^{85} +(-3.36900 - 5.83528i) q^{86} +(-8.61278 + 14.9178i) q^{88} -5.09880 q^{89} +8.89047 q^{91} +(1.07977 - 1.87022i) q^{92} +(-6.95308 - 12.0431i) q^{94} +(3.22929 + 5.59330i) q^{95} +(5.31594 - 9.20748i) q^{97} +0.168385 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots - 36 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Introduction

L-functions

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