LMFDB - Embedded newform 132.2.p.a.101.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [132,2,Mod(17,132)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(132, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("132.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.p (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 12 x^{13} + 23 x^{12} - 72 x^{11} + 146 x^{10} - 176 x^{9} + 223 x^{8} + \cdots + 6561 $ x^16 - 4x^15 + 8x^14 - 12x^13 + 23x^12 - 72x^11 + 146x^10 - 176x^9 + 223x^8 - 528x^7 + 1314x^6 - 1944x^5 + 1863x^4 - 2916x^3 + 5832x^2 - 8748*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.3
Root			$-0.982909 + 1.42615i$ of defining polynomial
Character	$\chi$	$=$	132.101
Dual form			132.2.p.a.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0430774 - 1.73152i) q^{3} +(0.393890 - 0.127982i) q^{5} +(1.02762 - 1.41440i) q^{7} +(-2.99629 - 0.149178i) q^{9} +(2.25433 - 2.43269i) q^{11} +(-2.14565 - 0.697165i) q^{13} +(-0.204636 - 0.687539i) q^{15} +(1.86044 + 5.72585i) q^{17} +(2.08977 + 2.87633i) q^{19} +(-2.40478 - 1.84027i) q^{21} +1.03009i q^{23} +(-3.90632 + 2.83810i) q^{25} +(-0.387377 + 5.18169i) q^{27} +(6.84973 + 4.97662i) q^{29} +(0.334007 - 1.02797i) q^{31} +(-4.11513 - 4.00820i) q^{33} +(0.223751 - 0.688633i) q^{35} +(-6.18282 - 4.49208i) q^{37} +(-1.29958 + 3.68520i) q^{39} +(-2.22248 + 1.61472i) q^{41} +2.87755i q^{43} +(-1.19930 + 0.324713i) q^{45} +(-3.87133 - 5.32843i) q^{47} +(1.21860 + 3.75047i) q^{49} +(9.99453 - 2.97473i) q^{51} +(-6.60630 - 2.14652i) q^{53} +(0.576615 - 1.24673i) q^{55} +(5.07043 - 3.49457i) q^{57} +(6.47553 - 8.91280i) q^{59} +(10.8077 - 3.51165i) q^{61} +(-3.29004 + 4.08464i) q^{63} -0.934375 q^{65} +9.86261 q^{67} +(1.78362 + 0.0443737i) q^{69} +(-15.3680 + 4.99337i) q^{71} +(4.22448 - 5.81450i) q^{73} +(4.74595 + 6.88610i) q^{75} +(-1.12420 - 5.68840i) q^{77} +(-12.1793 - 3.95730i) q^{79} +(8.95549 + 0.893963i) q^{81} +(-3.25369 - 10.0138i) q^{83} +(1.46562 + 2.01725i) q^{85} +(8.91217 - 11.6460i) q^{87} +7.11103i q^{89} +(-3.19098 + 2.31838i) q^{91} +(-1.76555 - 0.622620i) q^{93} +(1.19126 + 0.865501i) q^{95} +(-0.874046 + 2.69004i) q^{97} +(-7.11753 + 6.95275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} + 5 q^{9} + 9 q^{15} - 30 q^{19} - 12 q^{25} + q^{27} - 10 q^{31} - 41 q^{33} - 24 q^{37} - 35 q^{39} + 2 q^{45} + 12 q^{49} - 15 q^{51} + 62 q^{55} + 35 q^{57} + 40 q^{61} + 55 q^{63} + 44 q^{67}+ \cdots - 101 q^{99}+O(q^{100}) $ 16 * q + q^3 + 5 * q^9 + 9 * q^15 - 30 * q^19 - 12 * q^25 + q^27 - 10 * q^31 - 41 * q^33 - 24 * q^37 - 35 * q^39 + 2 * q^45 + 12 * q^49 - 15 * q^51 + 62 * q^55 + 35 * q^57 + 40 * q^61 + 55 * q^63 + 44 * q^67 + 46 * q^69 + 10 * q^73 + 21 * q^75 + 20 * q^79 + 57 * q^81 - 60 * q^85 - 60 * q^91 + 7 * q^93 - 36 * q^97 - 101 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	0.0430774	−	1.73152i	0.0248708	−	0.999691i
$3$	0.0430774	−	1.73152i	0.0248708	−	0.999691i
$4$		0			0
$5$	0.393890	−	0.127982i	0.176153	−	0.0572355i	−0.219613	−	0.975587i	$-0.570479\pi$
$5$	0.393890	−	0.127982i	0.176153	−	0.0572355i	0.395765	+	0.918352i	$0.370479\pi$
$6$		0			0
$7$	1.02762	−	1.41440i	0.388404	−	0.534592i	−0.569383	−	0.822073i	$-0.692818\pi$
$7$	1.02762	−	1.41440i	0.388404	−	0.534592i	0.957786	+	0.287481i	$0.0928178\pi$
$8$		0			0
$9$	−2.99629	−	0.149178i	−0.998763	−	0.0497261i
$10$		0			0
$11$	2.25433	−	2.43269i	0.679706	−	0.733485i
$11$	2.25433	−	2.43269i	0.679706	−	0.733485i
$12$		0			0
$13$	−2.14565	−	0.697165i	−0.595097	−	0.193359i	−0.00404459	−	0.999992i	$-0.501287\pi$
$13$	−2.14565	−	0.697165i	−0.595097	−	0.193359i	−0.591053	+	0.806633i	$0.701287\pi$
$14$		0			0
$15$	−0.204636	−	0.687539i	−0.0528367	−	0.177522i
$16$		0			0
$17$	1.86044	+	5.72585i	0.451223	+	1.38872i	0.875513	+	0.483195i	$0.160524\pi$
$17$	1.86044	+	5.72585i	0.451223	+	1.38872i	−0.424290	+	0.905526i	$0.639476\pi$
$18$		0			0
$19$	2.08977	+	2.87633i	0.479427	+	0.659875i	0.978395	−	0.206746i	$-0.0662873\pi$
$19$	2.08977	+	2.87633i	0.479427	+	0.659875i	−0.498968	+	0.866621i	$0.666287\pi$
$20$		0			0
$21$	−2.40478	−	1.84027i	−0.524766	−	0.401579i
$22$		0			0
$23$			1.03009i			0.214789i	0.994216	+	0.107395i	$0.0342508\pi$
$23$			1.03009i			0.214789i	−0.994216	+	0.107395i	$0.965749\pi$
$24$		0			0
$25$	−3.90632	+	2.83810i	−0.781263	+	0.567621i
$26$		0			0
$27$	−0.387377	+	5.18169i	−0.0745508	+	0.997217i
$28$		0			0
$29$	6.84973	+	4.97662i	1.27196	+	0.924136i	0.999279	−	0.0379677i	$-0.0120884\pi$
$29$	6.84973	+	4.97662i	1.27196	+	0.924136i	0.272685	+	0.962103i	$0.412088\pi$
$30$		0			0
$31$	0.334007	−	1.02797i	0.0599894	−	0.184628i	−0.916571	−	0.399872i	$-0.869055\pi$
$31$	0.334007	−	1.02797i	0.0599894	−	0.184628i	0.976560	+	0.215244i	$0.0690546\pi$
$32$		0			0
$33$	−4.11513	−	4.00820i	−0.716353	−	0.697738i
$34$		0			0
$35$	0.223751	−	0.688633i	0.0378207	−	0.116400i
$36$		0			0
$37$	−6.18282	−	4.49208i	−1.01645	−	0.738493i	−0.0508971	−	0.998704i	$-0.516208\pi$
$37$	−6.18282	−	4.49208i	−1.01645	−	0.738493i	−0.965552	+	0.260210i	$0.916208\pi$
$38$		0			0
$39$	−1.29958	+	3.68520i	−0.208100	+	0.590104i
$40$		0			0
$41$	−2.22248	+	1.61472i	−0.347092	+	0.252177i	−0.747648	−	0.664095i	$-0.768817\pi$
$41$	−2.22248	+	1.61472i	−0.347092	+	0.252177i	0.400556	+	0.916272i	$0.368817\pi$
$42$		0			0
$43$			2.87755i			0.438822i	0.975633	+	0.219411i	$0.0704135\pi$
$43$			2.87755i			0.438822i	−0.975633	+	0.219411i	$0.929587\pi$
$44$		0			0
$45$	−1.19930	+	0.324713i	−0.178781	+	0.0484053i
$46$		0			0
$47$	−3.87133	−	5.32843i	−0.564692	−	0.777232i	0.427222	−	0.904147i	$-0.359492\pi$
$47$	−3.87133	−	5.32843i	−0.564692	−	0.777232i	−0.991914	+	0.126915i	$0.959492\pi$
$48$		0			0
$49$	1.21860	+	3.75047i	0.174086	+	0.535782i
$50$		0			0
$51$	9.99453	−	2.97473i	1.39951	−	0.416545i
$52$		0			0
$53$	−6.60630	−	2.14652i	−0.907445	−	0.294847i	−0.182138	−	0.983273i	$-0.558302\pi$
$53$	−6.60630	−	2.14652i	−0.907445	−	0.294847i	−0.725306	+	0.688426i	$0.758302\pi$
$54$		0			0
$55$	0.576615	−	1.24673i	0.0777507	−	0.168109i
$56$		0			0
$57$	5.07043	−	3.49457i	0.671594	−	0.462867i
$58$		0			0
$59$	6.47553	−	8.91280i	0.843042	−	1.16035i	−0.142311	−	0.989822i	$-0.545453\pi$
$59$	6.47553	−	8.91280i	0.843042	−	1.16035i	0.985353	−	0.170526i	$-0.0545468\pi$
$60$		0			0
$61$	10.8077	−	3.51165i	1.38379	−	0.449620i	0.479876	−	0.877336i	$-0.340682\pi$
$61$	10.8077	−	3.51165i	1.38379	−	0.449620i	0.903913	+	0.427716i	$0.140682\pi$
$62$		0			0
$63$	−3.29004	+	4.08464i	−0.414506	+	0.514617i
$64$		0			0
$65$	−0.934375			−0.115895
$66$		0			0
$67$	9.86261			1.20491			0.602455	−	0.798153i	$-0.294189\pi$
$67$	9.86261			1.20491			0.602455	+	0.798153i	$0.294189\pi$
$68$		0			0
$69$	1.78362	+	0.0443737i	0.214723	+	0.00534197i
$70$		0			0
$71$	−15.3680	+	4.99337i	−1.82385	+	0.592604i	−0.824193	+	0.566309i	$0.808371\pi$
$71$	−15.3680	+	4.99337i	−1.82385	+	0.592604i	−0.999654	+	0.0262952i	$0.991629\pi$
$72$		0			0
$73$	4.22448	−	5.81450i	0.494438	−	0.680536i	−0.486761	−	0.873535i	$-0.661822\pi$
$73$	4.22448	−	5.81450i	0.494438	−	0.680536i	0.981199	+	0.193000i	$0.0618216\pi$
$74$		0			0
$75$	4.74595	+	6.88610i	0.548015	+	0.795139i
$76$		0			0
$77$	−1.12420	−	5.68840i	−0.128115	−	0.648253i
$78$		0			0
$79$	−12.1793	−	3.95730i	−1.37028	−	0.445231i	−0.470817	−	0.882231i	$-0.656041\pi$
$79$	−12.1793	−	3.95730i	−1.37028	−	0.445231i	−0.899461	+	0.437000i	$0.856041\pi$
$80$		0			0
$81$	8.95549	+	0.893963i	0.995055	+	0.0993292i
$82$		0			0
$83$	−3.25369	−	10.0138i	−0.357139	−	1.09916i	−0.954759	−	0.297381i	$-0.903887\pi$
$83$	−3.25369	−	10.0138i	−0.357139	−	1.09916i	0.597620	−	0.801780i	$-0.296113\pi$
$84$		0			0
$85$	1.46562	+	2.01725i	0.158968	+	0.218801i
$86$		0			0
$87$	8.91217	−	11.6460i	0.955485	−	1.24859i
$88$		0			0
$89$			7.11103i			0.753767i	0.926261	+	0.376884i	$0.123004\pi$
$89$			7.11103i			0.753767i	−0.926261	+	0.376884i	$0.876996\pi$
$90$		0			0
$91$	−3.19098	+	2.31838i	−0.334506	+	0.243033i
$92$		0			0
$93$	−1.76555	−	0.622620i	−0.183079	−	0.0645627i
$94$		0			0
$95$	1.19126	+	0.865501i	0.122221	+	0.0887985i
$96$		0			0
$97$	−0.874046	+	2.69004i	−0.0887459	+	0.273132i	−0.985573	−	0.169249i	$-0.945866\pi$
$97$	−0.874046	+	2.69004i	−0.0887459	+	0.273132i	0.896827	+	0.442380i	$0.145866\pi$
$98$		0			0
$99$	−7.11753	+	6.95275i	−0.715338	+	0.698778i
$100$		0			0
$101$	3.25369	−	10.0138i	0.323754	−	0.996414i	−0.648245	−	0.761432i	$-0.724497\pi$
$101$	3.25369	−	10.0138i	0.323754	−	0.996414i	0.972000	−	0.234982i	$-0.0755032\pi$
$102$		0			0
$103$	−8.66248	−	6.29366i	−0.853539	−	0.620133i	0.0725803	−	0.997363i	$-0.476877\pi$
$103$	−8.66248	−	6.29366i	−0.853539	−	0.620133i	−0.926120	+	0.377230i	$0.876877\pi$
$104$		0			0
$105$	−1.18274	−	0.417092i	−0.115424	−	0.0407040i
$106$		0			0
$107$	−13.5394	+	9.83697i	−1.30891	+	0.950976i	−1.00000		0.000117106i	$-0.999963\pi$
$107$	−13.5394	+	9.83697i	−1.30891	+	0.950976i	−0.308906	+	0.951093i	$0.599963\pi$
$108$		0			0
$109$			19.3039i			1.84898i	0.381209	+	0.924489i	$0.375508\pi$
$109$			19.3039i			1.84898i	−0.381209	+	0.924489i	$0.624492\pi$
$110$		0			0
$111$	−8.04444	+	10.5121i	−0.763545	+	0.997768i
$112$		0			0
$113$	0.263124	+	0.362159i	0.0247526	+	0.0340690i	0.821214	−	0.570620i	$-0.193297\pi$
$113$	0.263124	+	0.362159i	0.0247526	+	0.0340690i	−0.796461	+	0.604689i	$0.793297\pi$
$114$		0			0
$115$	0.131834	+	0.405743i	0.0122936	+	0.0378357i
$116$		0			0
$117$	6.32499	+	2.40899i	0.584746	+	0.222711i
$118$		0			0
$119$	10.0104	+	3.25259i	0.917656	+	0.298164i
$120$		0			0
$121$	−0.835996	−	10.9682i	−0.0759996	−	0.997108i
$122$		0			0
$123$	2.70018	+	3.91781i	0.243467	+	0.353257i
$124$		0			0
$125$	−2.39262	+	3.29315i	−0.214002	+	0.294548i
$126$		0			0
$127$	−2.73439	+	0.888458i	−0.242638	+	0.0788379i	−0.427811	−	0.903868i	$-0.640715\pi$
$127$	−2.73439	+	0.888458i	−0.242638	+	0.0788379i	0.185174	+	0.982706i	$0.440715\pi$
$128$		0			0
$129$	4.98251	+	0.123957i	0.438686	+	0.0109138i
$130$		0			0
$131$	8.65271			0.755990			0.377995	−	0.925808i	$-0.376614\pi$
$131$	8.65271			0.755990			0.377995	+	0.925808i	$0.376614\pi$
$132$		0			0
$133$	6.21576			0.538975
$134$		0			0
$135$	0.510582	+	2.09059i	0.0439439	+	0.179930i
$136$		0			0
$137$	2.46591	−	0.801224i	0.210677	−	0.0684532i	−0.201777	−	0.979431i	$-0.564672\pi$
$137$	2.46591	−	0.801224i	0.210677	−	0.0684532i	0.412454	+	0.910978i	$0.364672\pi$
$138$		0			0
$139$	−7.81529	+	10.7568i	−0.662884	+	0.912382i	−0.999573	−	0.0292340i	$-0.990693\pi$
$139$	−7.81529	+	10.7568i	−0.662884	+	0.912382i	0.336688	+	0.941616i	$0.390693\pi$
$140$		0			0
$141$	−9.39303	+	6.47374i	−0.791036	+	0.545187i
$142$		0			0
$143$	−6.53300	+	3.64808i	−0.546317	+	0.305068i
$144$		0			0
$145$	3.33496	+	1.08359i	0.276953	+	0.0899876i
$146$		0			0
$147$	6.54649	−	1.94847i	0.539946	−	0.160707i
$148$		0			0
$149$	2.27994	+	7.01695i	0.186780	+	0.574851i	0.999974	−	0.00714183i	$-0.00227333\pi$
$149$	2.27994	+	7.01695i	0.186780	+	0.574851i	−0.813194	+	0.581992i	$0.802273\pi$
$150$		0			0
$151$	−1.86490	−	2.56681i	−0.151763	−	0.208884i	0.726366	−	0.687309i	$-0.241208\pi$
$151$	−1.86490	−	2.56681i	−0.151763	−	0.208884i	−0.878129	+	0.478425i	$0.841208\pi$
$152$		0			0
$153$	−4.72024	−	17.4338i	−0.381609	−	1.40944i
$154$		0			0
$155$		−	0.447653i		−	0.0359563i
$156$		0			0
$157$	−5.74463	+	4.17372i	−0.458471	+	0.333099i	−0.792931	−	0.609311i	$-0.791446\pi$
$157$	−5.74463	+	4.17372i	−0.458471	+	0.333099i	0.334460	+	0.942410i	$0.391446\pi$
$158$		0			0
$159$	−4.00131	+	11.3464i	−0.317324	+	0.899831i
$160$		0			0
$161$	1.45696	+	1.05854i	0.114824	+	0.0834249i
$162$		0			0
$163$	4.89227	−	15.0569i	0.383192	−	1.17934i	−0.554591	−	0.832123i	$-0.687125\pi$
$163$	4.89227	−	15.0569i	0.383192	−	1.17934i	0.937783	−	0.347221i	$-0.112875\pi$
$164$		0			0
$165$	−2.13389	−	1.05212i	−0.166123	−	0.0819077i
$166$		0			0
$167$	0.207920	−	0.639912i	0.0160893	−	0.0495179i	−0.942690	−	0.333671i	$-0.891712\pi$
$167$	0.207920	−	0.639912i	0.0160893	−	0.0495179i	0.958779	+	0.284153i	$0.0917125\pi$
$168$		0			0
$169$	−6.39943	−	4.64946i	−0.492264	−	0.357651i
$170$		0			0
$171$	−5.83248	−	8.93006i	−0.446021	−	0.682898i
$172$		0			0
$173$	15.0060	−	10.9025i	1.14088	−	0.828900i	0.153641	−	0.988127i	$-0.450900\pi$
$173$	15.0060	−	10.9025i	1.14088	−	0.828900i	0.987242	+	0.159227i	$0.0509000\pi$
$174$		0			0
$175$			8.44157i			0.638123i
$176$		0			0
$177$	−15.1537	−	11.5964i	−1.13902	−	0.871640i
$178$		0			0
$179$	5.03331	+	6.92776i	0.376208	+	0.517805i	0.954575	−	0.297971i	$-0.0963099\pi$
$179$	5.03331	+	6.92776i	0.376208	+	0.517805i	−0.578367	+	0.815777i	$0.696310\pi$
$180$		0			0
$181$	−3.78804	−	11.6584i	−0.281563	−	0.866560i	−0.987408	−	0.158195i	$-0.949433\pi$
$181$	−3.78804	−	11.6584i	−0.281563	−	0.866560i	0.705845	−	0.708366i	$-0.250567\pi$
$182$		0			0
$183$	−5.61490	−	18.8650i	−0.415065	−	1.39454i
$184$		0			0
$185$	−3.01026	−	0.978091i	−0.221318	−	0.0719107i
$186$		0			0
$187$	18.1233	+	8.38206i	1.32530	+	0.612957i
$188$		0			0
$189$	6.93089	+	5.87271i	0.504148	+	0.427177i
$190$		0			0
$191$	0.0771543	−	0.106194i	0.00558269	−	0.00768391i	−0.806217	−	0.591621i	$-0.798488\pi$
$191$	0.0771543	−	0.106194i	0.00558269	−	0.00768391i	0.811799	+	0.583937i	$0.198488\pi$
$192$		0			0
$193$	10.4543	−	3.39680i	0.752515	−	0.244507i	0.0924520	−	0.995717i	$-0.470530\pi$
$193$	10.4543	−	3.39680i	0.752515	−	0.244507i	0.660063	+	0.751210i	$0.270530\pi$
$194$		0			0
$195$	−0.0402505	+	1.61789i	−0.00288240	+	0.115859i
$196$		0			0
$197$	−13.2520			−0.944164			−0.472082	−	0.881555i	$-0.656497\pi$
$197$	−13.2520			−0.944164			−0.472082	+	0.881555i	$0.656497\pi$
$198$		0			0
$199$	9.25589			0.656132			0.328066	−	0.944655i	$-0.393603\pi$
$199$	9.25589			0.656132			0.328066	+	0.944655i	$0.393603\pi$
$200$		0			0
$201$	0.424856	−	17.0773i	0.0299670	−	1.20454i
$202$		0			0
$203$	14.0778	−	4.57417i	0.988071	−	0.321044i
$204$		0			0
$205$	−0.668754	+	0.920461i	−0.0467078	+	0.0642878i
$206$		0			0
$207$	0.153668	−	3.08645i	0.0106806	−	0.214523i
$208$		0			0
$209$	11.7083	+	1.40041i	0.809877	+	0.0968684i
$210$		0			0
$211$	−1.30838	−	0.425117i	−0.0900724	−	0.0292663i	0.263634	−	0.964623i	$-0.415079\pi$
$211$	−1.30838	−	0.425117i	−0.0900724	−	0.0292663i	−0.353707	+	0.935356i	$0.615079\pi$
$212$		0			0
$213$	7.98408	+	26.8250i	0.547060	+	1.83802i
$214$		0			0
$215$	0.368275	+	1.13344i	0.0251162	+	0.0772996i
$216$		0			0
$217$	−1.11072	−	1.52878i	−0.0754007	−	0.103780i
$218$		0			0
$219$	−9.88592	−	7.56523i	−0.668028	−	0.511211i
$220$		0			0
$221$		−	13.5827i		−	0.913672i
$222$		0			0
$223$	12.0113	−	8.72671i	0.804335	−	0.584384i	−0.107847	−	0.994167i	$-0.534396\pi$
$223$	12.0113	−	8.72671i	0.804335	−	0.584384i	0.912183	+	0.409784i	$0.134396\pi$
$224$		0			0
$225$	12.1278	−	7.92104i	0.808522	−	0.528069i
$226$		0			0
$227$	−3.39405	−	2.46592i	−0.225271	−	0.163669i	0.469425	−	0.882972i	$-0.344461\pi$
$227$	−3.39405	−	2.46592i	−0.225271	−	0.163669i	−0.694696	+	0.719303i	$0.744461\pi$
$228$		0			0
$229$	0.966481	−	2.97452i	0.0638669	−	0.196562i	−0.914031	−	0.405644i	$-0.867047\pi$
$229$	0.966481	−	2.97452i	0.0638669	−	0.196562i	0.977898	+	0.209082i	$0.0670474\pi$
$230$		0			0
$231$	−9.89798	+	1.70153i	−0.651239	+	0.111952i
$232$		0			0
$233$	−8.67466	+	26.6978i	−0.568296	+	1.74903i	0.0896546	+	0.995973i	$0.471424\pi$
$233$	−8.67466	+	26.6978i	−0.568296	+	1.74903i	−0.657950	+	0.753061i	$0.728576\pi$
$234$		0			0
$235$	−2.20682	−	1.60335i	−0.143957	−	0.104591i
$236$		0			0
$237$	−7.37677	+	20.9182i	−0.479173	+	1.35878i
$238$		0			0
$239$	13.9530	−	10.1374i	0.902545	−	0.655737i	−0.0365737	−	0.999331i	$-0.511644\pi$
$239$	13.9530	−	10.1374i	0.902545	−	0.655737i	0.939118	+	0.343594i	$0.111644\pi$
$240$		0			0
$241$			14.7794i			0.952024i	0.879439	+	0.476012i	$0.157918\pi$
$241$			14.7794i			0.952024i	−0.879439	+	0.476012i	$0.842082\pi$
$242$		0			0
$243$	1.93369	−	15.4681i	0.124046	−	0.992276i
$244$		0			0
$245$	0.959990	+	1.32131i	0.0613315	+	0.0844155i
$246$		0			0
$247$	−2.47866	−	7.62852i	−0.157713	−	0.485391i
$248$		0			0
$249$	−17.4793	+	5.20245i	−1.10770	+	0.329692i
$250$		0			0
$251$	−1.47665	−	0.479791i	−0.0932051	−	0.0302842i	0.262043	−	0.965056i	$-0.415604\pi$
$251$	−1.47665	−	0.479791i	−0.0932051	−	0.0302842i	−0.355248	+	0.934772i	$0.615604\pi$
$252$		0			0
$253$	2.50590	+	2.32217i	0.157545	+	0.145993i
$254$		0			0
$255$	3.55603	−	2.45084i	0.222687	−	0.153477i
$256$		0			0
$257$	−9.74891	+	13.4182i	−0.608120	+	0.837006i	−0.996421	−	0.0845268i	$-0.973062\pi$
$257$	−9.74891	+	13.4182i	−0.608120	+	0.837006i	0.388301	+	0.921533i	$0.373062\pi$
$258$		0			0
$259$	−12.7072	+	4.12881i	−0.789585	+	0.256552i
$260$		0			0
$261$	−19.7814	−	15.9332i	−1.22444	−	0.986242i
$262$		0			0
$263$	8.42736			0.519654			0.259827	−	0.965655i	$-0.416335\pi$
$263$	8.42736			0.519654			0.259827	+	0.965655i	$0.416335\pi$
$264$		0			0
$265$	−2.87687			−0.176725
$266$		0			0
$267$	12.3129	+	0.306325i	0.753534	+	0.0187468i
$268$		0			0
$269$	23.6131	−	7.67235i	1.43971	−	0.467792i	0.517906	−	0.855438i	$-0.326712\pi$
$269$	23.6131	−	7.67235i	1.43971	−	0.467792i	0.921808	+	0.387646i	$0.126712\pi$
$270$		0			0
$271$	−15.7841	+	21.7250i	−0.958819	+	1.31970i	−0.0113216	+	0.999936i	$0.503604\pi$
$271$	−15.7841	+	21.7250i	−0.958819	+	1.31970i	−0.947497	+	0.319765i	$0.896396\pi$
$272$		0			0
$273$	3.87686	+	5.62511i	0.234638	+	0.340447i
$274$		0			0
$275$	−1.90188	+	15.9009i	−0.114688	+	0.958860i
$276$		0			0
$277$	−22.3433	−	7.25978i	−1.34248	−	0.436198i	−0.452323	−	0.891854i	$-0.649405\pi$
$277$	−22.3433	−	7.25978i	−1.34248	−	0.436198i	−0.890156	+	0.455656i	$0.849405\pi$
$278$		0			0
$279$	−1.15413	+	3.03026i	−0.0690961	+	0.181417i
$280$		0			0
$281$	3.78587	+	11.6517i	0.225846	+	0.695082i	0.998205	+	0.0598957i	$0.0190768\pi$
$281$	3.78587	+	11.6517i	0.225846	+	0.695082i	−0.772359	+	0.635187i	$0.780923\pi$
$282$		0			0
$283$	−0.829965	−	1.14235i	−0.0493363	−	0.0679056i	0.783636	−	0.621220i	$-0.213363\pi$
$283$	−0.829965	−	1.14235i	−0.0493363	−	0.0679056i	−0.832972	+	0.553315i	$0.813363\pi$
$284$		0			0
$285$	1.54994	−	2.02540i	0.0918108	−	0.119974i
$286$		0			0
$287$			4.80278i			0.283499i
$288$		0			0
$289$	−15.5708	+	11.3128i	−0.915928	+	0.665461i
$290$		0			0
$291$	4.62019	+	1.62930i	0.270840	+	0.0955114i
$292$		0			0
$293$	−21.3215	−	15.4909i	−1.24561	−	0.904991i	−0.247654	−	0.968849i	$-0.579660\pi$
$293$	−21.3215	−	15.4909i	−1.24561	−	0.904991i	−0.997959	+	0.0638576i	$0.979660\pi$
$294$		0			0
$295$	1.40996	−	4.33942i	0.0820911	−	0.252651i
$296$		0			0
$297$	11.7322	+	12.6236i	0.680771	+	0.732496i
$298$		0			0
$299$	0.718144	−	2.21022i	0.0415314	−	0.127820i
$300$		0			0
$301$	4.06999	+	2.95702i	0.234590	+	0.170440i
$302$		0			0
$303$	−17.1989	−	6.06519i	−0.988054	−	0.348436i
$304$		0			0
$305$	3.80763	−	2.76640i	0.218024	−	0.158404i
$306$		0			0
$307$		−	6.75671i		−	0.385626i	−0.981236	−	0.192813i	$-0.938239\pi$
$307$		−	6.75671i		−	0.385626i	0.981236	−	0.192813i	$-0.0617611\pi$
$308$		0			0
$309$	−11.2707	+	14.7281i	−0.641169	+	0.837852i
$310$		0			0
$311$	5.64245	+	7.76617i	0.319954	+	0.440379i	0.938453	−	0.345407i	$-0.112259\pi$
$311$	5.64245	+	7.76617i	0.319954	+	0.440379i	−0.618499	+	0.785786i	$0.712259\pi$
$312$		0			0
$313$	−1.98440	−	6.10737i	−0.112165	−	0.345209i	0.879180	−	0.476490i	$-0.158091\pi$
$313$	−1.98440	−	6.10737i	−0.112165	−	0.345209i	−0.991345	+	0.131281i	$0.958091\pi$
$314$		0			0
$315$	−0.773151	+	2.02997i	−0.0435621	+	0.114376i
$316$		0			0
$317$	−12.5082	−	4.06416i	−0.702531	−	0.228266i	−0.0640980	−	0.997944i	$-0.520417\pi$
$317$	−12.5082	−	4.06416i	−0.702531	−	0.228266i	−0.638433	+	0.769677i	$0.720417\pi$
$318$		0			0
$319$	27.5482	−	5.44436i	1.54240	−	0.304825i
$320$		0			0
$321$	16.4496	+	23.8675i	0.918128	+	1.33215i
$322$		0			0
$323$	−12.5815	+	17.3170i	−0.700054	+	0.963541i
$324$		0			0
$325$	10.3602	−	3.36624i	0.574682	−	0.186725i
$326$		0			0
$327$	33.4250	+	0.831562i	1.84841	+	0.0459855i
$328$		0			0
$329$	−11.5148			−0.634830
$330$		0			0
$331$	−4.41807			−0.242839			−0.121420	−	0.992601i	$-0.538745\pi$
$331$	−4.41807			−0.242839			−0.121420	+	0.992601i	$0.538745\pi$
$332$		0			0
$333$	17.8554	+	14.3819i	0.978469	+	0.788124i
$334$		0			0
$335$	3.88478	−	1.26224i	0.212248	−	0.0689636i
$336$		0			0
$337$	−7.57182	+	10.4217i	−0.412463	+	0.567707i	−0.963817	−	0.266565i	$-0.914111\pi$
$337$	−7.57182	+	10.4217i	−0.412463	+	0.567707i	0.551354	+	0.834272i	$0.314111\pi$
$338$		0			0
$339$	0.638418	−	0.440002i	0.0346741	−	0.0238976i
$340$		0			0
$341$	−1.74777	−	3.12991i	−0.0946470	−	0.169494i
$342$		0			0
$343$	18.1960	+	5.91223i	0.982490	+	0.319230i
$344$		0			0
$345$	0.708229	−	0.210794i	0.0381297	−	0.0113488i
$346$		0			0
$347$	−8.44112	−	25.9791i	−0.453143	−	1.39463i	−0.873301	−	0.487181i	$-0.838025\pi$
$347$	−8.44112	−	25.9791i	−0.453143	−	1.39463i	0.420158	−	0.907451i	$-0.361975\pi$
$348$		0			0
$349$	−6.06127	−	8.34262i	−0.324452	−	0.446570i	0.615368	−	0.788240i	$-0.289008\pi$
$349$	−6.06127	−	8.34262i	−0.324452	−	0.446570i	−0.939820	+	0.341670i	$0.889008\pi$
$350$		0			0
$351$	4.44367	−	10.8481i	0.237186	−	0.579026i
$352$		0			0
$353$		−	24.4516i		−	1.30143i	−0.759322	−	0.650715i	$-0.774469\pi$
$353$		−	24.4516i		−	1.30143i	0.759322	−	0.650715i	$-0.225531\pi$
$354$		0			0
$355$	−5.41424	+	3.93367i	−0.287358	+	0.208778i
$356$		0			0
$357$	6.06313	−	17.1931i	0.320895	−	0.909956i
$358$		0			0
$359$	−14.0418	−	10.2020i	−0.741099	−	0.538440i	0.151956	−	0.988387i	$-0.451443\pi$
$359$	−14.0418	−	10.2020i	−0.741099	−	0.538440i	−0.893055	+	0.449947i	$0.851443\pi$
$360$		0			0
$361$	1.96522	−	6.04833i	0.103433	−	0.318333i
$362$		0			0
$363$	−19.0276	+	0.975058i	−0.998690	+	0.0511773i
$364$		0			0
$365$	0.919825	−	2.83093i	0.0481459	−	0.148178i
$366$		0			0
$367$	15.2108	+	11.0513i	0.793999	+	0.576874i	0.909148	−	0.416474i	$-0.136734\pi$
$367$	15.2108	+	11.0513i	0.793999	+	0.576874i	−0.115148	+	0.993348i	$0.536734\pi$
$368$		0			0
$369$	6.90006	−	4.50663i	0.359203	−	0.234606i
$370$		0			0
$371$	−9.82478	+	7.13812i	−0.510077	+	0.370593i
$372$		0			0
$373$		−	4.38788i		−	0.227196i	−0.993527	−	0.113598i	$-0.963762\pi$
$373$		−	4.38788i		−	0.227196i	0.993527	−	0.113598i	$-0.0362376\pi$
$374$		0			0
$375$	5.59907	+	4.28471i	0.289135	+	0.221261i
$376$		0			0
$377$	−11.2276	−	15.4535i	−0.578252	−	0.795896i
$378$		0			0
$379$	−4.75715	−	14.6410i	−0.244358	−	0.752057i	−0.995741	−	0.0921911i	$-0.970613\pi$
$379$	−4.75715	−	14.6410i	−0.244358	−	0.752057i	0.751383	−	0.659866i	$-0.229387\pi$
$380$		0			0
$381$	1.42059	+	4.77291i	0.0727789	+	0.244524i
$382$		0			0
$383$	20.5912	+	6.69047i	1.05216	+	0.341867i	0.783515	−	0.621373i	$-0.213425\pi$
$383$	20.5912	+	6.69047i	1.05216	+	0.341867i	0.268643	+	0.963240i	$0.413425\pi$
$384$		0			0
$385$	−1.17083	−	2.09672i	−0.0596708	−	0.106859i
$386$		0			0
$387$	0.429268	−	8.62196i	0.0218209	−	0.438279i
$388$		0			0
$389$	5.63286	−	7.75297i	0.285597	−	0.393091i	−0.641981	−	0.766721i	$-0.721887\pi$
$389$	5.63286	−	7.75297i	0.285597	−	0.393091i	0.927578	+	0.373630i	$0.121887\pi$
$390$		0			0
$391$	−5.89815	+	1.91643i	−0.298282	+	0.0969178i
$392$		0			0
$393$	0.372736	−	14.9823i	0.0188021	−	0.755757i
$394$		0			0
$395$	−5.30377			−0.266861
$396$		0			0
$397$	4.38148			0.219900			0.109950	−	0.993937i	$-0.464931\pi$
$397$	4.38148			0.219900			0.109950	+	0.993937i	$0.464931\pi$
$398$		0			0
$399$	0.267759	−	10.7627i	0.0134047	−	0.538808i
$400$		0			0
$401$	−13.6643	+	4.43979i	−0.682361	+	0.221712i	−0.629629	−	0.776896i	$-0.716793\pi$
$401$	−13.6643	+	4.43979i	−0.682361	+	0.221712i	−0.0527321	+	0.998609i	$0.516793\pi$
$402$		0			0
$403$	−1.43333	+	1.97280i	−0.0713991	+	0.0982724i
$404$		0			0
$405$	3.64189	−	0.794023i	0.180967	−	0.0394553i
$406$		0			0
$407$	−24.8660	+	4.91427i	−1.23256	+	0.243591i
$408$		0			0
$409$	12.2638	+	3.98476i	0.606408	+	0.197034i	0.596096	−	0.802913i	$-0.296718\pi$
$409$	12.2638	+	3.98476i	0.606408	+	0.197034i	0.0103116	+	0.999947i	$0.496718\pi$
$410$		0			0
$411$	−1.28111	−	4.30428i	−0.0631923	−	0.212314i
$412$		0			0
$413$	−5.95186	−	18.3179i	−0.292872	−	0.901367i
$414$		0			0
$415$	−2.56319	−	3.52793i	−0.125822	−	0.173179i
$416$		0			0
$417$	18.2889	+	13.9957i	0.895614	+	0.685371i
$418$		0			0
$419$			7.17498i			0.350521i	0.984522	+	0.175260i	$0.0560767\pi$
$419$			7.17498i			0.350521i	−0.984522	+	0.175260i	$0.943923\pi$
$420$		0			0
$421$	23.7052	−	17.2229i	1.15532	−	0.839391i	0.166143	−	0.986102i	$-0.446869\pi$
$421$	23.7052	−	17.2229i	1.15532	−	0.839391i	0.989180	+	0.146710i	$0.0468685\pi$
$422$		0			0
$423$	10.8047	+	16.5430i	0.525345	+	0.804350i
$424$		0			0
$425$	−23.5180	−	17.0868i	−1.14079	−	0.828833i
$426$		0			0
$427$	6.13938	−	18.8951i	0.297105	−	0.914396i
$428$		0			0
$429$	6.03528	+	11.4691i	0.291386	+	0.553735i
$430$		0			0
$431$	4.64694	−	14.3018i	0.223835	−	0.688895i	−0.774572	−	0.632485i	$-0.782035\pi$
$431$	4.64694	−	14.3018i	0.223835	−	0.688895i	0.998408	−	0.0564093i	$-0.0179652\pi$
$432$		0			0
$433$	−3.55854	−	2.58543i	−0.171013	−	0.124248i	0.498987	−	0.866610i	$-0.333706\pi$
$433$	−3.55854	−	2.58543i	−0.171013	−	0.124248i	−0.669999	+	0.742362i	$0.733706\pi$
$434$		0			0
$435$	2.01992	−	5.72785i	0.0968478	−	0.274630i
$436$		0			0
$437$	−2.96288	+	2.15266i	−0.141734	+	0.102976i
$438$		0			0
$439$			23.9994i			1.14543i	0.819755	+	0.572715i	$0.194110\pi$
$439$			23.9994i			1.14543i	−0.819755	+	0.572715i	$0.805890\pi$
$440$		0			0
$441$	−3.09180	−	11.4193i	−0.147228	−	0.543776i
$442$		0			0
$443$	16.7454	+	23.0481i	0.795600	+	1.09505i	0.993388	+	0.114804i	$0.0366240\pi$
$443$	16.7454	+	23.0481i	0.795600	+	1.09505i	−0.197789	+	0.980245i	$0.563376\pi$
$444$		0			0
$445$	0.910087	+	2.80096i	0.0431423	+	0.132778i
$446$		0			0
$447$	12.2482	−	3.64549i	0.579318	−	0.172426i
$448$		0			0
$449$	24.0564	+	7.81641i	1.13529	+	0.368879i	0.815585	−	0.578637i	$-0.196415\pi$
$449$	24.0564	+	7.81641i	1.13529	+	0.368879i	0.319708	+	0.947516i	$0.396415\pi$
$450$		0			0
$451$	−1.08207	+	9.04672i	−0.0509525	+	0.425993i
$452$		0			0
$453$	−4.52480	+	3.11852i	−0.212594	+	0.146521i
$454$		0			0
$455$	−0.960182	+	1.32158i	−0.0450140	+	0.0619565i
$456$		0			0
$457$	10.4335	−	3.39004i	0.488057	−	0.158579i	−0.0546427	−	0.998506i	$-0.517402\pi$
$457$	10.4335	−	3.39004i	0.488057	−	0.158579i	0.542700	+	0.839926i	$0.317402\pi$
$458$		0			0
$459$	−30.3903	+	7.42217i	−1.41850	+	0.346437i
$460$		0			0
$461$	12.5522			0.584616			0.292308	−	0.956324i	$-0.405577\pi$
$461$	12.5522			0.584616			0.292308	+	0.956324i	$0.405577\pi$
$462$		0			0
$463$	−25.9141			−1.20433			−0.602165	−	0.798371i	$-0.705695\pi$
$463$	−25.9141			−1.20433			−0.602165	+	0.798371i	$0.705695\pi$
$464$		0			0
$465$	−0.775118	−	0.0192837i	−0.0359452	−	0.000894262i
$466$		0			0
$467$	−18.7784	+	6.10147i	−0.868961	+	0.282342i	−0.709366	−	0.704840i	$-0.751019\pi$
$467$	−18.7784	+	6.10147i	−0.868961	+	0.282342i	−0.159594	+	0.987183i	$0.551019\pi$
$468$		0			0
$469$	10.1350	−	13.9496i	0.467991	−	0.644135i
$470$		0			0
$471$	6.97939	+	10.1267i	0.321593	+	0.466614i
$472$		0			0
$473$	7.00019	+	6.48694i	0.321869	+	0.298270i
$474$		0			0
$475$	−16.3266	−	5.30484i	−0.749117	−	0.243403i
$476$		0			0
$477$	19.4742	+	7.41710i	0.891660	+	0.339606i
$478$		0			0
$479$	−0.740095	−	2.27778i	−0.0338158	−	0.104074i	0.932724	−	0.360591i	$-0.117425\pi$
$479$	−0.740095	−	2.27778i	−0.0338158	−	0.104074i	−0.966540	+	0.256517i	$0.917425\pi$
$480$		0			0
$481$	10.1345	+	13.9489i	0.462092	+	0.636015i
$482$		0			0
$483$	1.89565	−	2.47715i	0.0862548	−	0.112714i
$484$		0			0
$485$			1.17144i			0.0531923i
$486$		0			0
$487$	−4.85737	+	3.52909i	−0.220109	+	0.159918i	−0.692376	−	0.721537i	$-0.743436\pi$
$487$	−4.85737	+	3.52909i	−0.220109	+	0.159918i	0.472267	+	0.881456i	$0.343436\pi$
$488$		0			0
$489$	−25.8604	−	9.11965i	−1.16945	−	0.412405i
$490$		0			0
$491$	23.2904	+	16.9215i	1.05108	+	0.763655i	0.972418	−	0.233246i	$-0.0749347\pi$
$491$	23.2904	+	16.9215i	1.05108	+	0.763655i	0.0786636	+	0.996901i	$0.474935\pi$
$492$		0			0
$493$	−15.7519	+	48.4792i	−0.709428	+	2.18339i
$494$		0			0
$495$	−1.91369	+	3.64954i	−0.0860139	+	0.164034i
$496$		0			0
$497$	−8.72986	+	26.8677i	−0.391588	+	1.20518i
$498$		0			0
$499$	−10.7959	−	7.84368i	−0.483291	−	0.351132i	0.319307	−	0.947651i	$-0.396550\pi$
$499$	−10.7959	−	7.84368i	−0.483291	−	0.351132i	−0.802598	+	0.596520i	$0.796550\pi$
$500$		0			0
$501$	−1.09906	−	0.387583i	−0.0491024	−	0.0173159i
$502$		0			0
$503$	13.4208	−	9.75080i	0.598405	−	0.434767i	−0.246907	−	0.969039i	$-0.579414\pi$
$503$	13.4208	−	9.75080i	0.598405	−	0.434767i	0.845312	+	0.534272i	$0.179414\pi$
$504$		0			0
$505$		−	4.36076i		−	0.194051i
$506$		0			0
$507$	−8.32628	+	10.8804i	−0.369783	+	0.483217i
$508$		0			0
$509$	−4.44881	−	6.12326i	−0.197190	−	0.271409i	0.698959	−	0.715161i	$-0.253647\pi$
$509$	−4.44881	−	6.12326i	−0.197190	−	0.271409i	−0.896149	+	0.443753i	$0.853647\pi$
$510$		0			0
$511$	−3.88285	−	11.9502i	−0.171767	−	0.528645i
$512$		0			0
$513$	−15.7138	+	9.71434i	−0.693780	+	0.428899i
$514$		0			0
$515$	−4.21754	−	1.37036i	−0.185847	−	0.0603853i
$516$		0			0
$517$	−21.6897	−	2.59428i	−0.953912	−	0.114096i
$518$		0			0
$519$	−18.2314	−	26.4527i	−0.800269	−	1.16115i
$520$		0			0
$521$	14.2086	−	19.5565i	0.622490	−	0.856784i	−0.375041	−	0.927008i	$-0.622371\pi$
$521$	14.2086	−	19.5565i	0.622490	−	0.856784i	0.997531	+	0.0702239i	$0.0223714\pi$
$522$		0			0
$523$	−17.0507	+	5.54011i	−0.745576	+	0.242252i	−0.657076	−	0.753824i	$-0.728207\pi$
$523$	−17.0507	+	5.54011i	−0.745576	+	0.242252i	−0.0884994	+	0.996076i	$0.528207\pi$
$524$		0			0
$525$	14.6167	+	0.363641i	0.637925	+	0.0158706i
$526$		0			0
$527$	6.50738			0.283466
$528$		0			0
$529$	21.9389			0.953866
$530$		0			0
$531$	−20.7322	+	25.7393i	−0.899699	+	1.11699i
$532$		0			0
$533$	5.89439	−	1.91520i	0.255314	−	0.0829567i
$534$		0			0
$535$	−4.07408	+	5.60749i	−0.176138	+	0.242433i
$536$		0			0
$537$	12.2123	−	8.41683i	0.527002	−	0.363213i
$538$		0			0
$539$	11.8709	+	5.49032i	0.511315	+	0.236485i
$540$		0			0
$541$	−0.369739	−	0.120136i	−0.0158963	−	0.00516503i	0.301058	−	0.953606i	$-0.402660\pi$
$541$	−0.369739	−	0.120136i	−0.0158963	−	0.00516503i	−0.316954	+	0.948441i	$0.602660\pi$
$542$		0			0
$543$	−20.3498	+	6.05683i	−0.873295	+	0.259923i
$544$		0			0
$545$	2.47056	+	7.60360i	0.105827	+	0.325703i
$546$		0			0
$547$	−14.7588	−	20.3137i	−0.631040	−	0.868551i	0.367059	−	0.930198i	$-0.380365\pi$
$547$	−14.7588	−	20.3137i	−0.631040	−	0.868551i	−0.998098	+	0.0616464i	$0.980365\pi$
$548$		0			0
$549$	−32.9070	+	8.90963i	−1.40443	+	0.380254i
$550$		0			0
$551$			30.1021i			1.28239i
$552$		0			0
$553$	−18.1129	+	13.1598i	−0.770238	+	0.559611i
$554$		0			0
$555$	−1.82325	+	5.17017i	−0.0773928	+	0.219461i
$556$		0			0
$557$	30.2173	+	21.9541i	1.28035	+	0.930227i	0.999563	−	0.0295437i	$-0.00940542\pi$
$557$	30.2173	+	21.9541i	1.28035	+	0.930227i	0.280784	+	0.959771i	$0.409405\pi$
$558$		0			0
$559$	2.00612	−	6.17422i	0.0848500	−	0.261141i
$560$		0			0
$561$	15.2944	−	31.0196i	0.645729	−	1.30965i
$562$		0			0
$563$	−0.597162	+	1.83788i	−0.0251674	+	0.0774573i	−0.962851	−	0.270032i	$-0.912966\pi$
$563$	−0.597162	+	1.83788i	−0.0251674	+	0.0774573i	0.937684	+	0.347489i	$0.112966\pi$
$564$		0			0
$565$	0.149992	+	0.108975i	0.00631020	+	0.00458463i
$566$		0			0
$567$	10.4673	−	11.7480i	0.439583	−	0.493368i
$568$		0			0
$569$	−19.3383	+	14.0501i	−0.810702	+	0.589009i	−0.914034	−	0.405638i	$-0.867050\pi$
$569$	−19.3383	+	14.0501i	−0.810702	+	0.589009i	0.103332	+	0.994647i	$0.467050\pi$
$570$		0			0
$571$		−	24.0487i		−	1.00641i	−0.864167	−	0.503204i	$-0.832154\pi$
$571$		−	24.0487i		−	1.00641i	0.864167	−	0.503204i	$-0.167846\pi$
$572$		0			0
$573$	−0.180553	−	0.138168i	−0.00754269	−	0.00577207i
$574$		0			0
$575$	−2.92351	−	4.02387i	−0.121919	−	0.167807i
$576$		0			0
$577$	9.14804	+	28.1548i	0.380838	+	1.17210i	0.939455	+	0.342673i	$0.111332\pi$
$577$	9.14804	+	28.1548i	0.380838	+	1.17210i	−0.558617	+	0.829426i	$0.688668\pi$
$578$		0			0
$579$	−5.43127	−	18.2481i	−0.225716	−	0.758363i
$580$		0			0
$581$	−17.5071	−	5.68840i	−0.726317	−	0.235995i
$582$		0			0
$583$	−20.1146	+	11.2321i	−0.833061	+	0.465188i
$584$		0			0
$585$	2.79966	+	0.139389i	0.115752	+	0.00576301i
$586$		0			0
$587$	8.50452	−	11.7055i	0.351019	−	0.483136i	−0.596600	−	0.802539i	$-0.703482\pi$
$587$	8.50452	−	11.7055i	0.351019	−	0.483136i	0.947619	+	0.319402i	$0.103482\pi$
$588$		0			0
$589$	3.65477	−	1.18751i	0.150592	−	0.0489304i
$590$		0			0
$591$	−0.570861	+	22.9460i	−0.0234821	+	0.943872i
$592$		0			0
$593$	41.4781			1.70330			0.851650	−	0.524111i	$-0.175602\pi$
$593$	41.4781			1.70330			0.851650	+	0.524111i	$0.175602\pi$
$594$		0			0
$595$	4.35928			0.178713
$596$		0			0
$597$	0.398720	−	16.0267i	0.0163185	−	0.655929i
$598$		0			0
$599$	6.84638	−	2.22452i	0.279736	−	0.0908916i	−0.165789	−	0.986161i	$-0.553017\pi$
$599$	6.84638	−	2.22452i	0.279736	−	0.0908916i	0.445525	+	0.895270i	$0.353017\pi$
$600$		0			0
$601$	18.1873	−	25.0327i	0.741877	−	1.02111i	−0.256631	−	0.966509i	$-0.582613\pi$
$601$	18.1873	−	25.0327i	0.741877	−	1.02111i	0.998508	−	0.0545973i	$-0.0173875\pi$
$602$		0			0
$603$	−29.5512	−	1.47129i	−1.20342	−	0.0599155i
$604$		0			0
$605$	−1.73303	−	4.21326i	−0.0704575	−	0.171293i
$606$		0			0
$607$	42.4533	+	13.7939i	1.72313	+	0.559878i	0.992429	−	0.122824i	$-0.0391949\pi$
$607$	42.4533	+	13.7939i	1.72313	+	0.559878i	0.730698	+	0.682701i	$0.239195\pi$
$608$		0			0
$609$	−7.31380	−	24.5730i	−0.296370	−	0.995750i
$610$		0			0
$611$	4.59174	+	14.1319i	0.185762	+	0.571717i
$612$		0			0
$613$	12.5601	+	17.2874i	0.507296	+	0.698233i	0.983460	−	0.181123i	$-0.0579733\pi$
$613$	12.5601	+	17.2874i	0.507296	+	0.698233i	−0.476164	+	0.879356i	$0.657973\pi$
$614$		0			0
$615$	1.56498	+	1.19761i	0.0631062	+	0.0482922i
$616$		0			0
$617$			12.7339i			0.512647i	0.966591	+	0.256324i	$0.0825113\pi$
$617$			12.7339i			0.512647i	−0.966591	+	0.256324i	$0.917489\pi$
$618$		0			0
$619$	28.3335	−	20.5855i	1.13882	−	0.827402i	0.151867	−	0.988401i	$-0.451471\pi$
$619$	28.3335	−	20.5855i	1.13882	−	0.827402i	0.986955	+	0.160999i	$0.0514715\pi$
$620$		0			0
$621$	−5.33762	−	0.399034i	−0.214191	−	0.0160127i
$622$		0			0
$623$	10.0578	+	7.30743i	0.402958	+	0.292766i
$624$		0			0
$625$	6.93944	−	21.3574i	0.277578	−	0.854296i
$626$		0			0
$627$	2.92919	−	20.2127i	0.116981	−	0.807218i
$628$		0			0
$629$	14.2182	−	43.7591i	0.566917	−	1.74479i
$630$		0			0
$631$	13.8153	+	10.0374i	0.549978	+	0.399582i	0.827777	−	0.561057i	$-0.189605\pi$
$631$	13.8153	+	10.0374i	0.549978	+	0.399582i	−0.277799	+	0.960639i	$0.589605\pi$
$632$		0			0
$633$	−0.792458	+	2.24716i	−0.0314974	+	0.0893166i
$634$		0			0
$635$	−0.963341	+	0.699908i	−0.0382290	+	0.0277750i
$636$		0			0
$637$		−	8.89678i		−	0.352503i
$638$		0			0
$639$	46.7919	−	12.6690i	1.85106	−	0.501178i
$640$		0			0
$641$	−6.73706	−	9.27277i	−0.266098	−	0.366252i	0.654970	−	0.755655i	$-0.272681\pi$
$641$	−6.73706	−	9.27277i	−0.266098	−	0.366252i	−0.921068	+	0.389403i	$0.872681\pi$
$642$		0			0
$643$	11.9065	+	36.6445i	0.469548	+	1.44512i	0.853172	+	0.521630i	$0.174676\pi$
$643$	11.9065	+	36.6445i	0.469548	+	1.44512i	−0.383624	+	0.923489i	$0.625324\pi$
$644$		0			0
$645$	1.97842	−	0.588849i	0.0779004	−	0.0231859i
$646$		0			0
$647$	−19.6211	−	6.37527i	−0.771384	−	0.250638i	−0.103226	−	0.994658i	$-0.532917\pi$
$647$	−19.6211	−	6.37527i	−0.771384	−	0.250638i	−0.668157	+	0.744020i	$0.732917\pi$
$648$		0			0
$649$	−7.08414	−	35.8454i	−0.278077	−	1.40705i
$650$		0			0
$651$	−2.69495	+	1.85738i	−0.105623	+	0.0727963i
$652$		0			0
$653$	−16.3086	+	22.4469i	−0.638206	+	0.878415i	−0.998518	−	0.0544167i	$-0.982670\pi$
$653$	−16.3086	+	22.4469i	−0.638206	+	0.878415i	0.360312	+	0.932832i	$0.382670\pi$
$654$		0			0
$655$	3.40821	−	1.10739i	0.133170	−	0.0432695i
$656$		0			0
$657$	−13.5252	+	16.7917i	−0.527667	+	0.655107i
$658$		0			0
$659$	−31.9195			−1.24341			−0.621703	−	0.783253i	$-0.713559\pi$
$659$	−31.9195			−1.24341			−0.621703	+	0.783253i	$0.713559\pi$
$660$		0			0
$661$	−3.70222			−0.144000			−0.0719998	−	0.997405i	$-0.522938\pi$
$661$	−3.70222			−0.144000			−0.0719998	+	0.997405i	$0.522938\pi$
$662$		0			0
$663$	−23.5187	−	0.585108i	−0.913390	−	0.0227237i
$664$		0			0
$665$	2.44832	−	0.795508i	0.0949419	−	0.0308485i
$666$		0			0
$667$	−5.12638	+	7.05586i	−0.198494	+	0.273204i
$668$		0			0
$669$	−14.5930	−	21.1737i	−0.564199	−	0.818621i
$670$		0			0
$671$	15.8214	−	34.2083i	0.610780	−	1.32060i
$672$		0			0
$673$	−26.8205	−	8.71451i	−1.03385	−	0.335920i	−0.257542	−	0.966267i	$-0.582912\pi$
$673$	−26.8205	−	8.71451i	−1.03385	−	0.335920i	−0.776313	+	0.630347i	$0.782912\pi$
$674$		0			0
$675$	−13.1930	−	21.3407i	−0.507798	−	0.821406i
$676$		0			0
$677$	10.0167	+	30.8282i	0.384972	+	1.18482i	0.936500	+	0.350667i	$0.114045\pi$
$677$	10.0167	+	30.8282i	0.384972	+	1.18482i	−0.551528	+	0.834156i	$0.685955\pi$
$678$		0			0
$679$	2.90659	+	4.00058i	0.111545	+	0.153528i
$680$		0			0
$681$	−4.41599	+	5.77062i	−0.169221	+	0.221131i
$682$		0			0
$683$		−	39.7866i		−	1.52239i	−0.648522	−	0.761196i	$-0.724613\pi$
$683$		−	39.7866i		−	1.52239i	0.648522	−	0.761196i	$-0.275387\pi$
$684$		0			0
$685$	0.868755	−	0.631187i	0.0331934	−	0.0241164i
$686$		0			0
$687$	−5.10880	−	1.80161i	−0.194913	−	0.0687358i
$688$		0			0
$689$	12.6783	+	9.21136i	0.483007	+	0.350925i
$690$		0			0
$691$	−4.17416	+	12.8467i	−0.158792	+	0.488713i	−0.998525	−	0.0542867i	$-0.982712\pi$
$691$	−4.17416	+	12.8467i	−0.158792	+	0.488713i	0.839733	+	0.543000i	$0.182712\pi$
$692$		0			0
$693$	2.51984	+	17.2118i	0.0957210	+	0.653822i
$694$		0			0
$695$	−1.70168	+	5.23722i	−0.0645483	+	0.198659i
$696$		0			0
$697$	−13.3804	−	9.72146i	−0.506820	−	0.368227i
$698$		0			0
$699$	45.8540	+	16.1704i	1.73436	+	0.611620i
$700$		0			0
$701$	9.28637	−	6.74694i	0.350741	−	0.254829i	−0.398439	−	0.917195i	$-0.630448\pi$
$701$	9.28637	−	6.74694i	0.350741	−	0.254829i	0.749180	+	0.662366i	$0.230448\pi$
$702$		0			0
$703$		−	27.1712i		−	1.02478i
$704$		0			0
$705$	−2.87129	+	3.75208i	−0.108139	+	0.141312i
$706$		0			0
$707$	−10.8200	−	14.8924i	−0.406927	−	0.560087i
$708$		0			0
$709$	1.57938	+	4.86082i	0.0593147	+	0.182552i	0.976324	−	0.216315i	$-0.0694037\pi$
$709$	1.57938	+	4.86082i	0.0593147	+	0.182552i	−0.917009	+	0.398866i	$0.869404\pi$
$710$		0			0
$711$	35.9024	+	13.6741i	1.34644	+	0.512818i
$712$		0			0
$713$	1.05890	+	0.344058i	0.0396562	+	0.0128851i
$714$		0			0
$715$	−2.10639	+	2.27305i	−0.0787745	+	0.0850072i
$716$		0			0
$717$	−16.9521	−	24.5965i	−0.633087	−	0.918574i
$718$		0			0
$719$	18.8234	−	25.9082i	0.701994	−	0.966212i	−0.297939	−	0.954585i	$-0.596299\pi$
$719$	18.8234	−	25.9082i	0.701994	−	0.966212i	0.999932	−	0.0116265i	$-0.00370092\pi$
$720$		0			0
$721$	−17.8035	+	5.78470i	−0.663036	+	0.215433i
$722$		0			0
$723$	25.5907	+	0.636658i	0.951729	+	0.0236776i
$724$		0			0
$725$	−40.8814			−1.51830
$726$		0			0
$727$	−4.53747			−0.168285			−0.0841427	−	0.996454i	$-0.526815\pi$
$727$	−4.53747			−0.168285			−0.0841427	+	0.996454i	$0.526815\pi$
$728$		0			0
$729$	−26.6999	−	4.01454i	−0.988884	−	0.148687i
$730$		0			0
$731$	−16.4764	+	5.35350i	−0.609401	+	0.198006i
$732$		0			0
$733$	24.5489	−	33.7887i	0.906736	−	1.24802i	−0.0615329	−	0.998105i	$-0.519599\pi$
$733$	24.5489	−	33.7887i	0.906736	−	1.24802i	0.968269	−	0.249910i	$-0.0804011\pi$
$734$		0			0
$735$	2.32923	−	1.60532i	0.0859148	−	0.0592130i
$736$		0			0
$737$	22.2336	−	23.9927i	0.818984	−	0.883783i
$738$		0			0
$739$	−5.72540	−	1.86030i	−0.210612	−	0.0684321i	0.201811	−	0.979425i	$-0.435317\pi$
$739$	−5.72540	−	1.86030i	−0.210612	−	0.0684321i	−0.412423	+	0.910992i	$0.635317\pi$
$740$		0			0
$741$	−13.3157	+	3.96321i	−0.489163	+	0.145592i
$742$		0			0
$743$	8.03892	+	24.7413i	0.294919	+	0.907669i	0.983248	+	0.182270i	$0.0583445\pi$
$743$	8.03892	+	24.7413i	0.294919	+	0.907669i	−0.688329	+	0.725399i	$0.741655\pi$
$744$		0			0
$745$	1.79609	+	2.47211i	0.0658037	+	0.0905711i
$746$		0			0
$747$	8.25515	+	30.4897i	0.302040	+	1.11556i
$748$		0			0
$749$			29.2588i			1.06909i
$750$		0			0
$751$	−6.08977	+	4.42448i	−0.222219	+	0.161452i	−0.693325	−	0.720625i	$-0.743855\pi$
$751$	−6.08977	+	4.42448i	−0.222219	+	0.161452i	0.471106	+	0.882077i	$0.343855\pi$
$752$		0			0
$753$	−0.894376	+	2.53617i	−0.0325929	+	0.0924231i
$754$		0			0
$755$	−1.06307	−	0.772365i	−0.0386891	−	0.0281093i
$756$		0			0
$757$	−9.14388	+	28.1420i	−0.332340	+	1.02284i	0.635677	+	0.771955i	$0.280721\pi$
$757$	−9.14388	+	28.1420i	−0.332340	+	1.02284i	−0.968017	+	0.250883i	$0.919279\pi$
$758$		0			0
$759$	4.12882	−	4.23897i	0.149867	−	0.153865i
$760$		0			0
$761$	−5.86155	+	18.0400i	−0.212481	+	0.653950i	0.786842	+	0.617155i	$0.211715\pi$
$761$	−5.86155	+	18.0400i	−0.212481	+	0.653950i	−0.999323	+	0.0367949i	$0.988285\pi$
$762$		0			0
$763$	27.3034	+	19.8371i	0.988448	+	0.718150i
$764$		0			0
$765$	−4.09048	−	6.26289i	−0.147892	−	0.226435i
$766$		0			0
$767$	−20.1079	+	14.6093i	−0.726056	+	0.527510i
$768$		0			0
$769$		−	19.9245i		−	0.718496i	−0.933242	−	0.359248i	$-0.883033\pi$
$769$		−	19.9245i		−	0.718496i	0.933242	−	0.359248i	$-0.116967\pi$
$770$		0			0
$771$	22.8139	+	17.4584i	0.821622	+	0.628749i
$772$		0			0
$773$	19.3253	+	26.5990i	0.695083	+	0.956699i	0.999991	+	0.00431740i	$0.00137428\pi$
$773$	19.3253	+	26.5990i	0.695083	+	0.956699i	−0.304908	+	0.952382i	$0.598626\pi$
$774$		0			0
$775$	1.61274	+	4.96351i	0.0579314	+	0.178295i
$776$		0			0
$777$	6.60170	+	22.1805i	0.236835	+	0.795721i
$778$		0			0
$779$	−9.28895	−	3.01816i	−0.332811	−	0.108137i
$780$		0			0
$781$	−22.4972	+	48.6424i	−0.805014	+	1.74056i
$782$		0			0
$783$	−28.4408	+	33.5654i	−1.01639	+	1.19953i
$784$		0			0
$785$	−1.72859	+	2.37920i	−0.0616959	+	0.0849171i
$786$		0			0
$787$	0.983499	−	0.319558i	0.0350580	−	0.0113910i	−0.291436	−	0.956590i	$-0.594133\pi$
$787$	0.983499	−	0.319558i	0.0350580	−	0.0113910i	0.326493	+	0.945199i	$0.394133\pi$
$788$		0			0
$789$	0.363029	−	14.5921i	0.0129242	−	0.519493i
$790$		0			0
$791$	0.782627			0.0278270
$792$		0			0
$793$	−25.6379			−0.910427
$794$		0			0
$795$	−0.123928	+	4.98134i	−0.00439528	+	0.176670i
$796$		0			0
$797$	−28.1611	+	9.15010i	−0.997517	+	0.324113i	−0.761873	−	0.647726i	$-0.775720\pi$
$797$	−28.1611	+	9.15010i	−0.997517	+	0.324113i	−0.235644	+	0.971839i	$0.575720\pi$
$798$		0			0
$799$	23.3074	−	32.0799i	0.824556	−	1.13490i
$800$		0			0
$801$	1.06081	−	21.3067i	0.0374819	−	0.752835i
$802$		0			0
$803$	−4.62152	−	23.3847i	−0.163090	−	0.825227i
$804$		0			0
$805$	0.709356	+	0.230484i	0.0250015	+	0.00812349i
$806$		0			0
$807$	−12.2676	−	41.2169i	−0.431840	−	1.45090i
$808$		0			0
$809$	1.10292	+	3.39445i	0.0387767	+	0.119342i	0.968571	−	0.248737i	$-0.0800155\pi$
$809$	1.10292	+	3.39445i	0.0387767	+	0.119342i	−0.929794	+	0.368079i	$0.880015\pi$
$810$		0			0
$811$	9.86876	+	13.5832i	0.346539	+	0.476970i	0.946337	−	0.323181i	$-0.104752\pi$
$811$	9.86876	+	13.5832i	0.346539	+	0.476970i	−0.599798	+	0.800151i	$0.704752\pi$
$812$		0			0
$813$	36.9372	+	28.2663i	1.29545	+	0.991344i
$814$		0			0
$815$		−	6.55687i		−	0.229677i
$816$		0			0
$817$	−8.27676	+	6.01342i	−0.289567	+	0.210383i
$818$		0			0
$819$	9.90696	−	6.47052i	0.346177	−	0.226098i
$820$		0			0
$821$	37.5702	+	27.2964i	1.31121	+	0.952650i	0.999997	+	0.00230991i	$0.000735269\pi$
$821$	37.5702	+	27.2964i	1.31121	+	0.952650i	0.311213	+	0.950340i	$0.399265\pi$
$822$		0			0
$823$	−7.20739	+	22.1821i	−0.251234	+	0.773218i	0.743314	+	0.668942i	$0.233253\pi$
$823$	−7.20739	+	22.1821i	−0.251234	+	0.773218i	−0.994548	+	0.104276i	$0.966747\pi$
$824$		0			0
$825$	27.4507	+	3.97811i	0.955711	+	0.138500i
$826$		0			0
$827$	4.99681	−	15.3786i	0.173756	−	0.534767i	−0.825818	−	0.563936i	$-0.809286\pi$
$827$	4.99681	−	15.3786i	0.173756	−	0.534767i	0.999574	+	0.0291697i	$0.00928631\pi$
$828$		0			0
$829$	−21.8114	−	15.8469i	−0.757543	−	0.550387i	0.140613	−	0.990065i	$-0.455093\pi$
$829$	−21.8114	−	15.8469i	−0.757543	−	0.550387i	−0.898156	+	0.439678i	$0.855093\pi$
$830$		0			0
$831$	−13.5329	+	38.3750i	−0.469452	+	1.33122i
$832$		0			0
$833$	−19.2075	+	13.9551i	−0.665500	+	0.483514i
$834$		0			0
$835$		−	0.278665i		−	0.00964360i
$836$		0			0
$837$	5.19723	+	2.12893i	0.179642	+	0.0735867i
$838$		0			0
$839$	−33.0491	−	45.4882i	−1.14098	−	1.57043i	−0.765295	−	0.643680i	$-0.777407\pi$
$839$	−33.0491	−	45.4882i	−1.14098	−	1.57043i	−0.375687	−	0.926747i	$-0.622593\pi$
$840$		0			0
$841$	13.1906	+	40.5965i	0.454848	+	1.39988i
$842$		0			0
$843$	20.3382	−	6.05336i	0.700484	−	0.208489i
$844$		0			0
$845$	−3.11572	−	1.01236i	−0.107184	−	0.0348262i
$846$		0			0
$847$	−16.3725	−	10.0887i	−0.562564	−	0.346652i
$848$		0			0
$849$	−2.01375	+	1.38789i	−0.0691116	+	0.0476322i
$850$		0			0
$851$	4.62726	−	6.36887i	0.158620	−	0.218322i
$852$		0			0
$853$	−17.3455	+	5.63590i	−0.593899	+	0.192969i	−0.590518	−	0.807025i	$-0.701076\pi$
$853$	−17.3455	+	5.63590i	−0.593899	+	0.192969i	−0.00338141	+	0.999994i	$0.501076\pi$
$854$		0			0
$855$	−3.44024	−	2.77100i	−0.117654	−	0.0947662i
$856$		0			0
$857$	−8.99814			−0.307370			−0.153685	−	0.988120i	$-0.549114\pi$
$857$	−8.99814			−0.307370			−0.153685	+	0.988120i	$0.549114\pi$
$858$		0			0
$859$	−24.5634			−0.838092			−0.419046	−	0.907965i	$-0.637635\pi$
$859$	−24.5634			−0.838092			−0.419046	+	0.907965i	$0.637635\pi$
$860$		0			0
$861$	8.31609	+	0.206892i	0.283412	+	0.00705085i
$862$		0			0
$863$	7.69272	−	2.49952i	0.261863	−	0.0850845i	−0.175143	−	0.984543i	$-0.556039\pi$
$863$	7.69272	−	2.49952i	0.261863	−	0.0850845i	0.437006	+	0.899459i	$0.356039\pi$
$864$		0			0
$865$	4.51537	−	6.21487i	0.153527	−	0.211312i
$866$		0			0
$867$	18.9176	+	27.4484i	0.642475	+	0.932196i
$868$		0			0
$869$	−37.0831	+	20.7075i	−1.25796	+	0.702453i
$870$		0			0
$871$	−21.1617	−	6.87587i	−0.717038	−	0.232980i
$872$		0			0
$873$	3.02019	−	7.92974i	0.102218	−	0.268381i
$874$		0			0
$875$	2.19913	+	6.76821i	0.0743440	+	0.228807i
$876$		0			0
$877$	1.03938	+	1.43058i	0.0350973	+	0.0483073i	0.826205	−	0.563370i	$-0.190495\pi$
$877$	1.03938	+	1.43058i	0.0350973	+	0.0483073i	−0.791108	+	0.611677i	$0.790495\pi$
$878$		0			0
$879$	−27.7413	+	36.2511i	−0.935690	+	1.22272i
$880$		0			0
$881$		−	5.64608i		−	0.190221i	−0.995467	−	0.0951106i	$-0.969680\pi$
$881$		−	5.64608i		−	0.190221i	0.995467	−	0.0951106i	$-0.0303205\pi$
$882$		0			0
$883$	14.7730	−	10.7332i	0.497150	−	0.361200i	−0.310778	−	0.950483i	$-0.600589\pi$
$883$	14.7730	−	10.7332i	0.497150	−	0.361200i	0.807927	+	0.589282i	$0.200589\pi$
$884$		0			0
$885$	−7.45303	−	2.62830i	−0.250531	−	0.0883493i
$886$		0			0
$887$	−16.0250	−	11.6429i	−0.538068	−	0.390929i	0.285299	−	0.958439i	$-0.407907\pi$
$887$	−16.0250	−	11.6429i	−0.538068	−	0.390929i	−0.823367	+	0.567509i	$0.807907\pi$
$888$		0			0
$889$	−1.55328	+	4.78051i	−0.0520954	+	0.160333i
$890$		0			0
$891$	22.3634	−	19.7707i	0.749201	−	0.662343i
$892$		0			0
$893$	7.23610	−	22.2704i	0.242147	−	0.745252i
$894$		0			0
$895$	2.86920	+	2.08460i	0.0959069	+	0.0696804i
$896$		0			0
$897$	−3.79610	−	1.33869i	−0.126748	−	0.0446975i
$898$		0			0
$899$	7.40367	−	5.37908i	0.246926	−	0.179402i
$900$		0			0
$901$		−	41.8201i		−	1.39323i
$902$		0			0
$903$	5.29545	−	6.91987i	0.176222	−	0.230279i
$904$		0			0
$905$	−2.98414	−	4.10731i	−0.0991961	−	0.136532i
$906$		0			0
$907$	−9.21050	−	28.3470i	−0.305830	−	0.941247i	−0.979366	−	0.202093i	$-0.935226\pi$
$907$	−9.21050	−	28.3470i	−0.305830	−	0.941247i	0.673537	−	0.739154i	$-0.264774\pi$
$908$		0			0
$909$	−11.2428	+	29.5190i	−0.372902	+	0.979082i
$910$		0			0
$911$	−28.2499	−	9.17895i	−0.935962	−	0.304112i	−0.198963	−	0.980007i	$-0.563757\pi$
$911$	−28.2499	−	9.17895i	−0.935962	−	0.304112i	−0.736998	+	0.675895i	$0.763757\pi$
$912$		0			0
$913$	−31.6955	−	14.6592i	−1.04897	−	0.485150i
$914$		0			0
$915$	−4.62604	−	6.71213i	−0.152932	−	0.221896i
$916$		0			0
$917$	8.89169	−	12.2384i	0.293629	−	0.404146i
$918$		0			0
$919$	40.2985	−	13.0938i	1.32932	−	0.431924i	0.443637	−	0.896206i	$-0.353688\pi$
$919$	40.2985	−	13.0938i	1.32932	−	0.431924i	0.885687	+	0.464283i	$0.153688\pi$
$920$		0			0
$921$	−11.6993	−	0.291062i	−0.385507	−	0.00959081i
$922$		0			0
$923$	36.4556			1.19995
$924$		0			0
$925$	36.9010			1.21330
$926$		0			0
$927$	25.0164	+	20.1499i	0.821647	+	0.661809i
$928$		0			0
$929$	−33.1232	+	10.7624i	−1.08674	+	0.353102i	−0.796985	−	0.604000i	$-0.793573\pi$
$929$	−33.1232	+	10.7624i	−1.08674	+	0.353102i	−0.289752	+	0.957102i	$0.593573\pi$
$930$		0			0
$931$	−8.24098	+	11.3427i	−0.270087	+	0.371743i
$932$		0			0
$933$	13.6903	−	9.43544i	0.448200	−	0.308903i
$934$		0			0
$935$	8.21133	+	0.982146i	0.268539	+	0.0321196i
$936$		0			0
$937$	48.0434	+	15.6102i	1.56951	+	0.509964i	0.959327	−	0.282297i	$-0.0910963\pi$
$937$	48.0434	+	15.6102i	1.56951	+	0.509964i	0.610182	+	0.792261i	$0.291096\pi$
$938$		0			0
$939$	−10.6605	+	3.17294i	−0.347892	+	0.103545i
$940$		0			0
$941$	−12.6511	−	38.9362i	−0.412415	−	1.26928i	−0.914542	−	0.404490i	$-0.867449\pi$
$941$	−12.6511	−	38.9362i	−0.412415	−	1.26928i	0.502127	−	0.864794i	$-0.332551\pi$
$942$		0			0
$943$	−1.66331	−	2.28936i	−0.0541650	−	0.0745517i
$944$		0			0
$945$	3.48161	+	1.42617i	0.113257	+	0.0463932i
$946$		0			0
$947$		−	2.82537i		−	0.0918122i	−0.998946	−	0.0459061i	$-0.985382\pi$
$947$		−	2.82537i		−	0.0918122i	0.998946	−	0.0459061i	$-0.0146175\pi$
$948$		0			0
$949$	−13.1179	+	9.53074i	−0.425826	+	0.309381i
$950$		0			0
$951$	−7.57598	+	21.4831i	−0.245668	+	0.696637i
$952$		0			0
$953$	−2.02099	−	1.46833i	−0.0654662	−	0.0475640i	0.554571	−	0.832137i	$-0.312882\pi$
$953$	−2.02099	−	1.46833i	−0.0654662	−	0.0475640i	−0.620037	+	0.784573i	$0.712882\pi$
$954$		0			0
$955$	0.0167993	−	0.0517030i	0.000543614	−	0.00167307i
$956$		0			0
$957$	−8.24028	−	47.9346i	−0.266370	−	1.54950i
$958$		0			0
$959$	1.40077	−	4.31113i	0.0452333	−	0.139214i
$960$		0			0
$961$	24.1344	+	17.5346i	0.778528	+	0.565634i
$962$		0			0
$963$	42.0355	−	27.4546i	1.35457	−	0.884712i
$964$		0			0
$965$	3.68310	−	2.67593i	0.118563	−	0.0861412i
$966$		0			0
$967$		−	16.8424i		−	0.541616i	−0.962633	−	0.270808i	$-0.912709\pi$
$967$		−	16.8424i		−	0.541616i	0.962633	−	0.270808i	$-0.0872909\pi$
$968$		0			0
$969$	29.4426	+	22.5310i	0.945832	+	0.723801i
$970$		0			0
$971$	−18.6779	−	25.7079i	−0.599402	−	0.825006i	0.396251	−	0.918142i	$-0.370311\pi$
$971$	−18.6779	−	25.7079i	−0.599402	−	0.825006i	−0.995653	+	0.0931359i	$0.970311\pi$
$972$		0			0
$973$	7.18328	+	22.1078i	0.230285	+	0.708745i
$974$		0			0
$975$	−5.38241	−	18.0839i	−0.172375	−	0.579148i
$976$		0			0
$977$	5.17367	+	1.68103i	0.165520	+	0.0537808i	0.390605	−	0.920558i	$-0.372266\pi$
$977$	5.17367	+	1.68103i	0.165520	+	0.0537808i	−0.225085	+	0.974339i	$0.572266\pi$
$978$		0			0
$979$	17.2990	+	16.0306i	0.552877	+	0.512340i
$980$		0			0
$981$	2.87972	−	57.8400i	0.0919425	−	1.84669i
$982$		0			0
$983$	−23.4580	+	32.2871i	−0.748193	+	1.02980i	0.249912	+	0.968269i	$0.419598\pi$
$983$	−23.4580	+	32.2871i	−0.748193	+	1.02980i	−0.998105	+	0.0615308i	$0.980402\pi$
$984$		0			0
$985$	−5.21981	+	1.69602i	−0.166317	+	0.0540397i
$986$		0			0
$987$	−0.496027	+	19.9380i	−0.0157887	+	0.634634i
$988$		0			0
$989$	−2.96414			−0.0942541
$990$		0			0
$991$	−44.2995			−1.40722			−0.703610	−	0.710586i	$-0.748430\pi$
$991$	−44.2995			−1.40722			−0.703610	+	0.710586i	$0.748430\pi$
$992$		0			0
$993$	−0.190319	+	7.64996i	−0.00603960	+	0.242764i
$994$		0			0
$995$	3.64580	−	1.18459i	0.115580	−	0.0375541i
$996$		0			0
$997$	25.0872	−	34.5296i	0.794520	−	1.09356i	−0.199011	−	0.979997i	$-0.563773\pi$
$997$	25.0872	−	34.5296i	0.794520	−	1.09356i	0.993531	−	0.113566i	$-0.0362272\pi$
$998$		0			0
$999$	25.6717	−	30.2973i	0.812215	−	0.958565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.p.a.101.3	yes	16
3.2	odd	2	inner	132.2.p.a.101.4	yes	16
4.3	odd	2		528.2.bn.d.497.2		16
11.4	even	5		1452.2.b.e.725.4		16
11.6	odd	10	inner	132.2.p.a.17.4	yes	16
11.7	odd	10		1452.2.b.e.725.3		16
12.11	even	2		528.2.bn.d.497.1		16
33.17	even	10	inner	132.2.p.a.17.3	✓	16
33.26	odd	10		1452.2.b.e.725.2		16
33.29	even	10		1452.2.b.e.725.1		16
44.39	even	10		528.2.bn.d.17.1		16
132.83	odd	10		528.2.bn.d.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.p.a.17.3	✓	16	33.17	even	10	inner
132.2.p.a.17.4	yes	16	11.6	odd	10	inner
132.2.p.a.101.3	yes	16	1.1	even	1	trivial
132.2.p.a.101.4	yes	16	3.2	odd	2	inner
528.2.bn.d.17.1		16	44.39	even	10
528.2.bn.d.17.2		16	132.83	odd	10
528.2.bn.d.497.1		16	12.11	even	2
528.2.bn.d.497.2		16	4.3	odd	2
1452.2.b.e.725.1		16	33.29	even	10
1452.2.b.e.725.2		16	33.26	odd	10
1452.2.b.e.725.3		16	11.7	odd	10
1452.2.b.e.725.4		16	11.4	even	5

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:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0430774 - 1.73152i) q^{3} +(0.393890 - 0.127982i) q^{5} +(1.02762 - 1.41440i) q^{7} +(-2.99629 - 0.149178i) q^{9} +(2.25433 - 2.43269i) q^{11} +(-2.14565 - 0.697165i) q^{13} +(-0.204636 - 0.687539i) q^{15} +(1.86044 + 5.72585i) q^{17} +(2.08977 + 2.87633i) q^{19} +(-2.40478 - 1.84027i) q^{21} +1.03009i q^{23} +(-3.90632 + 2.83810i) q^{25} +(-0.387377 + 5.18169i) q^{27} +(6.84973 + 4.97662i) q^{29} +(0.334007 - 1.02797i) q^{31} +(-4.11513 - 4.00820i) q^{33} +(0.223751 - 0.688633i) q^{35} +(-6.18282 - 4.49208i) q^{37} +(-1.29958 + 3.68520i) q^{39} +(-2.22248 + 1.61472i) q^{41} +2.87755i q^{43} +(-1.19930 + 0.324713i) q^{45} +(-3.87133 - 5.32843i) q^{47} +(1.21860 + 3.75047i) q^{49} +(9.99453 - 2.97473i) q^{51} +(-6.60630 - 2.14652i) q^{53} +(0.576615 - 1.24673i) q^{55} +(5.07043 - 3.49457i) q^{57} +(6.47553 - 8.91280i) q^{59} +(10.8077 - 3.51165i) q^{61} +(-3.29004 + 4.08464i) q^{63} -0.934375 q^{65} +9.86261 q^{67} +(1.78362 + 0.0443737i) q^{69} +(-15.3680 + 4.99337i) q^{71} +(4.22448 - 5.81450i) q^{73} +(4.74595 + 6.88610i) q^{75} +(-1.12420 - 5.68840i) q^{77} +(-12.1793 - 3.95730i) q^{79} +(8.95549 + 0.893963i) q^{81} +(-3.25369 - 10.0138i) q^{83} +(1.46562 + 2.01725i) q^{85} +(8.91217 - 11.6460i) q^{87} +7.11103i q^{89} +(-3.19098 + 2.31838i) q^{91} +(-1.76555 - 0.622620i) q^{93} +(1.19126 + 0.865501i) q^{95} +(-0.874046 + 2.69004i) q^{97} +(-7.11753 + 6.95275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} + 5 q^{9} + 9 q^{15} - 30 q^{19} - 12 q^{25} + q^{27} - 10 q^{31} - 41 q^{33} - 24 q^{37} - 35 q^{39} + 2 q^{45} + 12 q^{49} - 15 q^{51} + 62 q^{55} + 35 q^{57} + 40 q^{61} + 55 q^{63} + 44 q^{67}+ \cdots - 101 q^{99}+O(q^{100}) \) 16 * q + q^3 + 5 * q^9 + 9 * q^15 - 30 * q^19 - 12 * q^25 + q^27 - 10 * q^31 - 41 * q^33 - 24 * q^37 - 35 * q^39 + 2 * q^45 + 12 * q^49 - 15 * q^51 + 62 * q^55 + 35 * q^57 + 40 * q^61 + 55 * q^63 + 44 * q^67 + 46 * q^69 + 10 * q^73 + 21 * q^75 + 20 * q^79 + 57 * q^81 - 60 * q^85 - 60 * q^91 + 7 * q^93 - 36 * q^97 - 101 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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