LMFDB - Embedded newform 1323.2.h.c.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	1323.226
Dual form			1323.2.h.c.802.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.34730 q^{2} -0.184793 q^{4} +(1.26604 + 2.19285i) q^{5} +2.94356 q^{8} +O(q^{10})$	\(q-1.34730 q^{2} -0.184793 q^{4} +(1.26604 + 2.19285i) q^{5} +2.94356 q^{8} +(-1.70574 - 2.95442i) q^{10} +(0.233956 - 0.405223i) q^{11} +(-2.91147 + 5.04282i) q^{13} -3.59627 q^{16} +(1.93969 + 3.35965i) q^{17} +(1.09240 - 1.89209i) q^{19} +(-0.233956 - 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(-0.0530334 - 0.0918566i) q^{23} +(-0.705737 + 1.22237i) q^{25} +(3.92262 - 6.79417i) q^{26} +(4.39053 + 7.60462i) q^{29} -7.68004 q^{31} -1.04189 q^{32} +(-2.61334 - 4.52644i) q^{34} +(3.84002 - 6.65111i) q^{37} +(-1.47178 + 2.54920i) q^{38} +(3.72668 + 6.45480i) q^{40} +(-1.11334 + 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +(-0.0432332 + 0.0748822i) q^{44} +(0.0714517 + 0.123758i) q^{46} +5.33275 q^{47} +(0.950837 - 1.64690i) q^{50} +(0.538019 - 0.931876i) q^{52} +(-0.358441 - 0.620838i) q^{53} +1.18479 q^{55} +(-5.91534 - 10.2457i) q^{58} -0.736482 q^{59} +0.958111 q^{61} +10.3473 q^{62} +8.59627 q^{64} -14.7442 q^{65} -9.63816 q^{67} +(-0.358441 - 0.620838i) q^{68} -13.2344 q^{71} +(5.13429 + 8.89284i) q^{73} +(-5.17365 + 8.96102i) q^{74} +(-0.201867 + 0.349643i) q^{76} -12.6382 q^{79} +(-4.55303 - 7.88609i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(0.826352 + 1.43128i) q^{86} +(0.688663 - 1.19280i) q^{88} +(-4.05690 + 7.02676i) q^{89} +(0.00980018 + 0.0169744i) q^{92} -7.18479 q^{94} +5.53209 q^{95} +(6.80200 + 11.7814i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 + 3 * q^5 - 12 * q^8	$ 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38} + 9 q^{40} + 3 q^{43} + 15 q^{44} - 6 q^{47} - 6 q^{50} + 21 q^{52} + 6 q^{53} + 9 q^{58} + 6 q^{59} + 12 q^{61} + 60 q^{62} + 24 q^{64} - 30 q^{65} - 24 q^{67} + 6 q^{68} - 18 q^{71} + 21 q^{73} - 30 q^{74} - 15 q^{76} - 42 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 12 q^{89} + 3 q^{92} - 36 q^{94} + 24 q^{95} + 3 q^{97}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 + 3 * q^5 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 6 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 3 * q^26 + 9 * q^29 - 6 * q^31 - 9 * q^34 + 3 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 + 15 * q^44 - 6 * q^47 - 6 * q^50 + 21 * q^52 + 6 * q^53 + 9 * q^58 + 6 * q^59 + 12 * q^61 + 60 * q^62 + 24 * q^64 - 30 * q^65 - 24 * q^67 + 6 * q^68 - 18 * q^71 + 21 * q^73 - 30 * q^74 - 15 * q^76 - 42 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 12 * q^89 + 3 * q^92 - 36 * q^94 + 24 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.34730			−0.952682			−0.476341	−	0.879261i	$-0.658037\pi$
$2$	−1.34730			−0.952682			−0.476341	+	0.879261i	$0.658037\pi$
$3$		0			0
$3$		0			0
$4$	−0.184793			−0.0923963
$5$	1.26604	+	2.19285i	0.566192	+	0.980674i	0.996938	+	0.0782003i	$0.0249174\pi$
$5$	1.26604	+	2.19285i	0.566192	+	0.980674i	−0.430745	+	0.902473i	$0.641749\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.94356			1.04071
$9$		0			0
$10$	−1.70574	−	2.95442i	−0.539401	−	0.934271i
$11$	0.233956	−	0.405223i	0.0705403	−	0.122179i	−0.828598	−	0.559844i	$-0.810861\pi$
$11$	0.233956	−	0.405223i	0.0705403	−	0.122179i	0.899138	+	0.437665i	$0.144194\pi$
$12$		0			0
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	0.107094	+	0.994249i	$0.465845\pi$
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	−0.914592	+	0.404378i	$0.867488\pi$
$14$		0			0
$15$		0			0
$16$	−3.59627			−0.899067
$17$	1.93969	+	3.35965i	0.470445	+	0.814834i	0.999429	−	0.0337978i	$-0.0107602\pi$
$17$	1.93969	+	3.35965i	0.470445	+	0.814834i	−0.528984	+	0.848632i	$0.677427\pi$
$18$		0			0
$19$	1.09240	−	1.89209i	0.250613	−	0.434074i	−0.713082	−	0.701081i	$-0.752701\pi$
$19$	1.09240	−	1.89209i	0.250613	−	0.434074i	0.963695	+	0.267007i	$0.0860345\pi$
$20$	−0.233956	−	0.405223i	−0.0523141	−	0.0906106i
$21$		0			0
$22$	−0.315207	+	0.545955i	−0.0672025	+	0.116398i
$23$	−0.0530334	−	0.0918566i	−0.0110582	−	0.0191534i	0.860443	−	0.509546i	$-0.170187\pi$
$23$	−0.0530334	−	0.0918566i	−0.0110582	−	0.0191534i	−0.871502	+	0.490393i	$0.836853\pi$
$24$		0			0
$25$	−0.705737	+	1.22237i	−0.141147	+	0.244474i
$26$	3.92262	−	6.79417i	0.769289	−	1.33245i
$27$		0			0
$28$		0			0
$29$	4.39053	+	7.60462i	0.815301	+	1.41214i	0.909112	+	0.416552i	$0.136762\pi$
$29$	4.39053	+	7.60462i	0.815301	+	1.41214i	−0.0938108	+	0.995590i	$0.529905\pi$
$30$		0			0
$31$	−7.68004			−1.37938			−0.689688	−	0.724106i	$-0.742252\pi$
$31$	−7.68004			−1.37938			−0.689688	+	0.724106i	$0.742252\pi$
$32$	−1.04189			−0.184182
$33$		0			0
$34$	−2.61334	−	4.52644i	−0.448184	−	0.776278i
$35$		0			0
$36$		0			0
$37$	3.84002	−	6.65111i	0.631296	−	1.09344i	−0.355991	−	0.934489i	$-0.615857\pi$
$37$	3.84002	−	6.65111i	0.631296	−	1.09344i	0.987287	−	0.158947i	$-0.0508099\pi$
$38$	−1.47178	+	2.54920i	−0.238754	+	0.413535i
$39$		0			0
$40$	3.72668	+	6.45480i	0.589240	+	1.02059i
$41$	−1.11334	+	1.92836i	−0.173875	+	0.301160i	−0.939771	−	0.341804i	$-0.888962\pi$
$41$	−1.11334	+	1.92836i	−0.173875	+	0.301160i	0.765897	+	0.642964i	$0.222295\pi$
$42$		0			0
$43$	−0.613341	−	1.06234i	−0.0935336	−	0.162005i	0.815462	−	0.578811i	$-0.196483\pi$
$43$	−0.613341	−	1.06234i	−0.0935336	−	0.162005i	−0.908996	+	0.416806i	$0.863150\pi$
$44$	−0.0432332	+	0.0748822i	−0.00651766	+	0.0112889i
$45$		0			0
$46$	0.0714517	+	0.123758i	0.0105350	+	0.0182471i
$47$	5.33275			0.777861			0.388931	−	0.921267i	$-0.372845\pi$
$47$	5.33275			0.777861			0.388931	+	0.921267i	$0.372845\pi$
$48$		0			0
$49$		0			0
$50$	0.950837	−	1.64690i	0.134469	−	0.232907i
$51$		0			0
$52$	0.538019	−	0.931876i	0.0746098	−	0.129228i
$53$	−0.358441	−	0.620838i	−0.0492356	−	0.0852786i	0.840357	−	0.542033i	$-0.182345\pi$
$53$	−0.358441	−	0.620838i	−0.0492356	−	0.0852786i	−0.889593	+	0.456754i	$0.849012\pi$
$54$		0			0
$55$	1.18479			0.159757
$56$		0			0
$57$		0			0
$58$	−5.91534	−	10.2457i	−0.776723	−	1.34532i
$59$	−0.736482			−0.0958818			−0.0479409	−	0.998850i	$-0.515266\pi$
$59$	−0.736482			−0.0958818			−0.0479409	+	0.998850i	$0.515266\pi$
$60$		0			0
$61$	0.958111			0.122674			0.0613368	−	0.998117i	$-0.480464\pi$
$61$	0.958111			0.122674			0.0613368	+	0.998117i	$0.480464\pi$
$62$	10.3473			1.31411
$63$		0			0
$64$	8.59627			1.07453
$65$	−14.7442			−1.82880
$66$		0			0
$67$	−9.63816			−1.17749			−0.588744	−	0.808320i	$-0.700377\pi$
$67$	−9.63816			−1.17749			−0.588744	+	0.808320i	$0.700377\pi$
$68$	−0.358441	−	0.620838i	−0.0434673	−	0.0752876i
$69$		0			0
$70$		0			0
$71$	−13.2344			−1.57064			−0.785318	−	0.619092i	$-0.787501\pi$
$71$	−13.2344			−1.57064			−0.785318	+	0.619092i	$0.787501\pi$
$72$		0			0
$73$	5.13429	+	8.89284i	0.600923	+	1.04083i	0.992682	+	0.120761i	$0.0385334\pi$
$73$	5.13429	+	8.89284i	0.600923	+	1.04083i	−0.391759	+	0.920068i	$0.628133\pi$
$74$	−5.17365	+	8.96102i	−0.601424	+	1.04170i
$75$		0			0
$76$	−0.201867	+	0.349643i	−0.0231557	+	0.0401068i
$77$		0			0
$78$		0			0
$79$	−12.6382			−1.42190			−0.710952	−	0.703241i	$-0.751736\pi$
$79$	−12.6382			−1.42190			−0.710952	+	0.703241i	$0.751736\pi$
$80$	−4.55303	−	7.88609i	−0.509045	−	0.881691i
$81$		0			0
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	−1.36571	−	2.36549i	−0.149907	−	0.259646i	0.781286	−	0.624173i	$-0.214564\pi$
$83$	−1.36571	−	2.36549i	−0.149907	−	0.259646i	−0.931193	+	0.364527i	$0.881231\pi$
$84$		0			0
$85$	−4.91147	+	8.50692i	−0.532724	+	0.922705i
$86$	0.826352	+	1.43128i	0.0891078	+	0.154339i
$87$		0			0
$88$	0.688663	−	1.19280i	0.0734117	−	0.127153i
$89$	−4.05690	+	7.02676i	−0.430031	+	0.744835i	−0.996875	−	0.0789894i	$-0.974831\pi$
$89$	−4.05690	+	7.02676i	−0.430031	+	0.744835i	0.566845	+	0.823825i	$0.308164\pi$
$90$		0			0
$91$		0			0
$92$	0.00980018	+	0.0169744i	0.00102174	+	0.00176970i
$93$		0			0
$94$	−7.18479			−0.741055
$95$	5.53209			0.567580
$96$		0			0
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	0.971629	+	0.236511i	$0.0760039\pi$
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	−0.280990	+	0.959711i	$0.590663\pi$
$98$		0			0
$99$		0			0
$100$	0.130415	−	0.225885i	0.0130415	−	0.0225885i
$101$	−4.78699	+	8.29131i	−0.476323	+	0.825016i	−0.999632	−	0.0271271i	$-0.991364\pi$
$101$	−4.78699	+	8.29131i	−0.476323	+	0.825016i	0.523309	+	0.852143i	$0.324697\pi$
$102$		0			0
$103$	−1.52094	−	2.63435i	−0.149863	−	0.259571i	0.781314	−	0.624139i	$-0.214550\pi$
$103$	−1.52094	−	2.63435i	−0.149863	−	0.259571i	−0.931177	+	0.364568i	$0.881217\pi$
$104$	−8.57011	+	14.8439i	−0.840368	+	1.45556i
$105$		0			0
$106$	0.482926	+	0.836452i	0.0469059	+	0.0812434i
$107$	−3.25877	+	5.64436i	−0.315037	+	0.545660i	−0.979445	−	0.201709i	$-0.935350\pi$
$107$	−3.25877	+	5.64436i	−0.315037	+	0.545660i	0.664408	+	0.747370i	$0.268684\pi$
$108$		0			0
$109$	−5.31908	−	9.21291i	−0.509475	−	0.882437i	−0.999940	−	0.0109759i	$-0.996506\pi$
$109$	−5.31908	−	9.21291i	−0.509475	−	0.882437i	0.490465	−	0.871461i	$-0.336827\pi$
$110$	−1.59627			−0.152198
$111$		0			0
$112$		0			0
$113$	2.58853	−	4.48346i	0.243508	−	0.421768i	−0.718203	−	0.695834i	$-0.755035\pi$
$113$	2.58853	−	4.48346i	0.243508	−	0.421768i	0.961711	+	0.274065i	$0.0883684\pi$
$114$		0			0
$115$	0.134285	−	0.232589i	0.0125222	−	0.0216890i
$116$	−0.811337	−	1.40528i	−0.0753308	−	0.130477i
$117$		0			0
$118$	0.992259			0.0913449
$119$		0			0
$120$		0			0
$121$	5.39053	+	9.33667i	0.490048	+	0.848788i
$122$	−1.29086			−0.116869
$123$		0			0
$124$	1.41921			0.127449
$125$	9.08647			0.812718
$126$		0			0
$127$	−8.88207			−0.788157			−0.394078	−	0.919077i	$-0.628936\pi$
$127$	−8.88207			−0.788157			−0.394078	+	0.919077i	$0.628936\pi$
$128$	−9.49794			−0.839507
$129$		0			0
$130$	19.8648			1.74226
$131$	5.68139	+	9.84045i	0.496385	+	0.859764i	0.999991	−	0.00416893i	$-0.00132701\pi$
$131$	5.68139	+	9.84045i	0.496385	+	0.859764i	−0.503606	+	0.863933i	$0.667994\pi$
$132$		0			0
$133$		0			0
$134$	12.9855			1.12177
$135$		0			0
$136$	5.70961	+	9.88933i	0.489595	+	0.848003i
$137$	−2.86231	+	4.95767i	−0.244544	+	0.423562i	−0.962003	−	0.273038i	$-0.911972\pi$
$137$	−2.86231	+	4.95767i	−0.244544	+	0.423562i	0.717459	+	0.696600i	$0.245305\pi$
$138$		0			0
$139$	0.461981	−	0.800175i	0.0391847	−	0.0678700i	−0.845768	−	0.533551i	$-0.820857\pi$
$139$	0.461981	−	0.800175i	0.0391847	−	0.0678700i	0.884953	+	0.465681i	$0.154191\pi$
$140$		0			0
$141$		0			0
$142$	17.8307			1.49632
$143$	1.36231	+	2.35959i	0.113922	+	0.197319i
$144$		0			0
$145$	−11.1172	+	19.2556i	−0.923234	+	1.59909i
$146$	−6.91740	−	11.9813i	−0.572488	−	0.991579i
$147$		0			0
$148$	−0.709607	+	1.22908i	−0.0583294	+	0.101029i
$149$	4.36231	+	7.55574i	0.357374	+	0.618991i	0.987521	−	0.157485i	$-0.0503387\pi$
$149$	4.36231	+	7.55574i	0.357374	+	0.618991i	−0.630147	+	0.776476i	$0.717005\pi$
$150$		0			0
$151$	−9.21348	+	15.9582i	−0.749782	+	1.29866i	0.198145	+	0.980173i	$0.436508\pi$
$151$	−9.21348	+	15.9582i	−0.749782	+	1.29866i	−0.947927	+	0.318488i	$0.896825\pi$
$152$	3.21554	−	5.56947i	0.260815	−	0.451744i
$153$		0			0
$154$		0			0
$155$	−9.72328	−	16.8412i	−0.780992	−	1.35272i
$156$		0			0
$157$	4.92396			0.392975			0.196488	−	0.980506i	$-0.437046\pi$
$157$	4.92396			0.392975			0.196488	+	0.980506i	$0.437046\pi$
$158$	17.0273			1.35462
$159$		0			0
$160$	−1.31908	−	2.28471i	−0.104282	−	0.180622i
$161$		0			0
$162$		0			0
$163$	−3.81908	+	6.61484i	−0.299133	+	0.518114i	−0.975938	−	0.218049i	$-0.930031\pi$
$163$	−3.81908	+	6.61484i	−0.299133	+	0.518114i	0.676805	+	0.736163i	$0.263364\pi$
$164$	0.205737	−	0.356347i	0.0160654	−	0.0278260i
$165$		0			0
$166$	1.84002	+	3.18701i	0.142813	+	0.247360i
$167$	−2.82770	+	4.89771i	−0.218814	+	0.378996i	−0.954446	−	0.298385i	$-0.903552\pi$
$167$	−2.82770	+	4.89771i	−0.218814	+	0.378996i	0.735632	+	0.677382i	$0.236885\pi$
$168$		0			0
$169$	−10.4534	−	18.1058i	−0.804105	−	1.39275i
$170$	6.61721	−	11.4613i	0.507517	−	0.879045i
$171$		0			0
$172$	0.113341	+	0.196312i	0.00864215	+	0.0149687i
$173$	−21.0692			−1.60186			−0.800932	−	0.598755i	$-0.795662\pi$
$173$	−21.0692			−1.60186			−0.800932	+	0.598755i	$0.795662\pi$
$174$		0			0
$175$		0			0
$176$	−0.841367	+	1.45729i	−0.0634204	+	0.109847i
$177$		0			0
$178$	5.46585	−	9.46713i	0.409683	−	0.709592i
$179$	−2.56031	−	4.43458i	−0.191366	−	0.331456i	0.754337	−	0.656487i	$-0.227959\pi$
$179$	−2.56031	−	4.43458i	−0.191366	−	0.331456i	−0.945703	+	0.325031i	$0.894625\pi$
$180$		0			0
$181$	−0.319955			−0.0237821			−0.0118910	−	0.999929i	$-0.503785\pi$
$181$	−0.319955			−0.0237821			−0.0118910	+	0.999929i	$0.503785\pi$
$182$		0			0
$183$		0			0
$184$	−0.156107	−	0.270386i	−0.0115084	−	0.0199331i
$185$	19.4466			1.42974
$186$		0			0
$187$	1.81521			0.132741
$188$	−0.985452			−0.0718715
$189$		0			0
$190$	−7.45336			−0.540724
$191$	15.5672			1.12640			0.563200	−	0.826320i	$-0.309570\pi$
$191$	15.5672			1.12640			0.563200	+	0.826320i	$0.309570\pi$
$192$		0			0
$193$	6.04189			0.434905			0.217452	−	0.976071i	$-0.430225\pi$
$193$	6.04189			0.434905			0.217452	+	0.976071i	$0.430225\pi$
$194$	−9.16431	−	15.8731i	−0.657959	−	1.13962i
$195$		0			0
$196$		0			0
$197$	−25.2344			−1.79788			−0.898939	−	0.438074i	$-0.855661\pi$
$197$	−25.2344			−1.79788			−0.898939	+	0.438074i	$0.855661\pi$
$198$		0			0
$199$	−1.52094	−	2.63435i	−0.107817	−	0.186744i	0.807069	−	0.590458i	$-0.201053\pi$
$199$	−1.52094	−	2.63435i	−0.107817	−	0.186744i	−0.914886	+	0.403713i	$0.867719\pi$
$200$	−2.07738	+	3.59813i	−0.146893	+	0.254426i
$201$		0			0
$202$	6.44949	−	11.1708i	0.453785	−	0.785978i
$203$		0			0
$204$		0			0
$205$	−5.63816			−0.393786
$206$	2.04916	+	3.54925i	0.142772	+	0.247288i
$207$		0			0
$208$	10.4704	−	18.1353i	0.725994	−	1.25746i
$209$	−0.511144	−	0.885328i	−0.0353566	−	0.0612394i
$210$		0			0
$211$	2.72668	−	4.72275i	0.187713	−	0.325128i	−0.756775	−	0.653676i	$-0.773226\pi$
$211$	2.72668	−	4.72275i	0.187713	−	0.325128i	0.944487	+	0.328548i	$0.106559\pi$
$212$	0.0662372	+	0.114726i	0.00454919	+	0.00787942i
$213$		0			0
$214$	4.39053	−	7.60462i	0.300130	−	0.519841i
$215$	1.55303	−	2.68993i	0.105916	−	0.183452i
$216$		0			0
$217$		0			0
$218$	7.16637	+	12.4125i	0.485368	+	0.840682i
$219$		0			0
$220$	−0.218941			−0.0147610
$221$	−22.5895			−1.51953
$222$		0			0
$223$	−7.09627	−	12.2911i	−0.475201	−	0.823073i	0.524395	−	0.851475i	$-0.324291\pi$
$223$	−7.09627	−	12.2911i	−0.475201	−	0.823073i	−0.999597	+	0.0284023i	$0.990958\pi$
$224$		0			0
$225$		0			0
$226$	−3.48751	+	6.04055i	−0.231986	+	0.401811i
$227$	−1.44697	+	2.50622i	−0.0960385	+	0.166344i	−0.910042	−	0.414517i	$-0.863951\pi$
$227$	−1.44697	+	2.50622i	−0.0960385	+	0.166344i	0.814003	+	0.580861i	$0.197284\pi$
$228$		0			0
$229$	−4.58378	−	7.93934i	−0.302905	−	0.524646i	0.673888	−	0.738834i	$-0.264623\pi$
$229$	−4.58378	−	7.93934i	−0.302905	−	0.524646i	−0.976793	+	0.214187i	$0.931290\pi$
$230$	−0.180922	+	0.313366i	−0.0119297	+	0.0206628i
$231$		0			0
$232$	12.9238	+	22.3847i	0.848489	+	1.46963i
$233$	6.63563	−	11.4932i	0.434715	−	0.752948i	−0.562558	−	0.826758i	$-0.690183\pi$
$233$	6.63563	−	11.4932i	0.434715	−	0.752948i	0.997272	+	0.0738103i	$0.0235159\pi$
$234$		0			0
$235$	6.75150	+	11.6939i	0.440419	+	0.762828i
$236$	0.136096			0.00885912
$237$		0			0
$238$		0			0
$239$	4.76857	−	8.25941i	0.308453	−	0.534257i	−0.669571	−	0.742748i	$-0.733522\pi$
$239$	4.76857	−	8.25941i	0.308453	−	0.534257i	0.978024	+	0.208491i	$0.0668553\pi$
$240$		0			0
$241$	4.47906	−	7.75795i	0.288521	−	0.499734i	−0.684936	−	0.728604i	$-0.740170\pi$
$241$	4.47906	−	7.75795i	0.288521	−	0.499734i	0.973457	+	0.228870i	$0.0735031\pi$
$242$	−7.26264	−	12.5793i	−0.466860	−	0.808626i
$243$		0			0
$244$	−0.177052			−0.0113346
$245$		0			0
$246$		0			0
$247$	6.36097	+	11.0175i	0.404739	+	0.701028i
$248$	−22.6067			−1.43553
$249$		0			0
$250$	−12.2422			−0.774262
$251$	24.9982			1.57788			0.788938	−	0.614473i	$-0.210631\pi$
$251$	24.9982			1.57788			0.788938	+	0.614473i	$0.210631\pi$
$252$		0			0
$253$	−0.0496299			−0.00312020
$254$	11.9668			0.750863
$255$		0			0
$256$	−4.39599			−0.274750
$257$	5.42602	+	9.39815i	0.338466	+	0.586240i	0.984144	−	0.177369i	$-0.0567587\pi$
$257$	5.42602	+	9.39815i	0.338466	+	0.586240i	−0.645678	+	0.763609i	$0.723425\pi$
$258$		0			0
$259$		0			0
$260$	2.72462			0.168974
$261$		0			0
$262$	−7.65451	−	13.2580i	−0.472897	−	0.819082i
$263$	13.0437	−	22.5924i	0.804309	−	1.39310i	−0.112448	−	0.993658i	$-0.535869\pi$
$263$	13.0437	−	22.5924i	0.804309	−	1.39310i	0.916757	−	0.399446i	$-0.130798\pi$
$264$		0			0
$265$	0.907604	−	1.57202i	0.0557537	−	0.0965682i
$266$		0			0
$267$		0			0
$268$	1.78106			0.108796
$269$	−3.81655	−	6.61046i	−0.232699	−	0.403047i	0.725902	−	0.687798i	$-0.241422\pi$
$269$	−3.81655	−	6.61046i	−0.232699	−	0.403047i	−0.958602	+	0.284751i	$0.908089\pi$
$270$		0			0
$271$	−1.70187	+	2.94772i	−0.103381	+	0.179061i	−0.913076	−	0.407790i	$-0.866299\pi$
$271$	−1.70187	+	2.94772i	−0.103381	+	0.179061i	0.809695	+	0.586852i	$0.199633\pi$
$272$	−6.97565	−	12.0822i	−0.422961	−	0.732590i
$273$		0			0
$274$	3.85638	−	6.67945i	0.232973	−	0.403520i
$275$	0.330222	+	0.571962i	0.0199131	+	0.0344906i
$276$		0			0
$277$	2.86097	−	4.95534i	0.171899	−	0.297738i	−0.767185	−	0.641426i	$-0.778343\pi$
$277$	2.86097	−	4.95534i	0.171899	−	0.297738i	0.939084	+	0.343689i	$0.111676\pi$
$278$	−0.622426	+	1.07807i	−0.0373306	+	0.0646585i
$279$		0			0
$280$		0			0
$281$	14.1887	+	24.5755i	0.846425	+	1.46605i	0.884378	+	0.466771i	$0.154583\pi$
$281$	14.1887	+	24.5755i	0.846425	+	1.46605i	−0.0379535	+	0.999280i	$0.512084\pi$
$282$		0			0
$283$	4.57129			0.271735			0.135867	−	0.990727i	$-0.456618\pi$
$283$	4.57129			0.271735			0.135867	+	0.990727i	$0.456618\pi$
$284$	2.44562			0.145121
$285$		0			0
$286$	−1.83544	−	3.17907i	−0.108532	−	0.187982i
$287$		0			0
$288$		0			0
$289$	0.975185	−	1.68907i	0.0573638	−	0.0993571i
$290$	14.9782	−	25.9430i	0.879549	−	1.52342i
$291$		0			0
$292$	−0.948778	−	1.64333i	−0.0555230	−	0.0961687i
$293$	2.16385	−	3.74789i	0.126413	−	0.218954i	−0.795871	−	0.605466i	$-0.792987\pi$
$293$	2.16385	−	3.74789i	0.126413	−	0.218954i	0.922285	+	0.386512i	$0.126320\pi$
$294$		0			0
$295$	−0.932419	−	1.61500i	−0.0542875	−	0.0940287i
$296$	11.3033	−	19.5780i	0.656994	−	1.13795i
$297$		0			0
$298$	−5.87733	−	10.1798i	−0.340464	−	0.589702i
$299$	0.617622			0.0357180
$300$		0			0
$301$		0			0
$302$	12.4133	−	21.5004i	0.714304	−	1.23721i
$303$		0			0
$304$	−3.92855	+	6.80445i	−0.225318	+	0.390262i
$305$	1.21301	+	2.10100i	0.0694568	+	0.120303i
$306$		0			0
$307$	12.3773			0.706411			0.353206	−	0.935546i	$-0.385092\pi$
$307$	12.3773			0.706411			0.353206	+	0.935546i	$0.385092\pi$
$308$		0			0
$309$		0			0
$310$	13.1001	+	22.6901i	0.744038	+	1.28871i
$311$	21.9855			1.24668			0.623340	−	0.781951i	$-0.285775\pi$
$311$	21.9855			1.24668			0.623340	+	0.781951i	$0.285775\pi$
$312$		0			0
$313$	−13.8898			−0.785099			−0.392549	−	0.919731i	$-0.628407\pi$
$313$	−13.8898			−0.785099			−0.392549	+	0.919731i	$0.628407\pi$
$314$	−6.63404			−0.374380
$315$		0			0
$316$	2.33544			0.131379
$317$	6.18210			0.347222			0.173611	−	0.984814i	$-0.444457\pi$
$317$	6.18210			0.347222			0.173611	+	0.984814i	$0.444457\pi$
$318$		0			0
$319$	4.10876			0.230046
$320$	10.8833	+	18.8504i	0.608392	+	1.05377i
$321$		0			0
$322$		0			0
$323$	8.47565			0.471598
$324$		0			0
$325$	−4.10947	−	7.11781i	−0.227952	−	0.394825i
$326$	5.14543	−	8.91215i	0.284979	−	0.493598i
$327$		0			0
$328$	−3.27719	+	5.67626i	−0.180952	+	0.313419i
$329$		0			0
$330$		0			0
$331$	10.7314			0.589853			0.294926	−	0.955520i	$-0.404705\pi$
$331$	10.7314			0.589853			0.294926	+	0.955520i	$0.404705\pi$
$332$	0.252374	+	0.437124i	0.0138508	+	0.0239903i
$333$		0			0
$334$	3.80974	−	6.59867i	0.208460	−	0.361063i
$335$	−12.2023	−	21.1351i	−0.666685	−	1.15473i
$336$		0			0
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	−0.493518	−	0.869735i	$-0.664289\pi$
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	0.999972	−	0.00746831i	$-0.00237726\pi$
$338$	14.0838	+	24.3938i	0.766057	+	1.32685i
$339$		0			0
$340$	0.907604	−	1.57202i	0.0492217	−	0.0852545i
$341$	−1.79679	+	3.11213i	−0.0973016	+	0.168531i
$342$		0			0
$343$		0			0
$344$	−1.80541	−	3.12706i	−0.0973410	−	0.168600i
$345$		0			0
$346$	28.3865			1.52607
$347$	20.4124			1.09580			0.547898	−	0.836545i	$-0.315428\pi$
$347$	20.4124			1.09580			0.547898	+	0.836545i	$0.315428\pi$
$348$		0			0
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	0.909750	−	0.415157i	$-0.136274\pi$
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	−0.814412	+	0.580288i	$0.802940\pi$
$350$		0			0
$351$		0			0
$352$	−0.243756	+	0.422197i	−0.0129922	+	0.0225032i
$353$	5.01114	−	8.67956i	0.266716	−	0.461966i	−0.701296	−	0.712871i	$-0.747395\pi$
$353$	5.01114	−	8.67956i	0.266716	−	0.461966i	0.968012	+	0.250904i	$0.0807280\pi$
$354$		0			0
$355$	−16.7554	−	29.0211i	−0.889283	−	1.54028i
$356$	0.749686	−	1.29849i	0.0397333	−	0.0688200i
$357$		0			0
$358$	3.44949	+	5.97470i	0.182311	+	0.315773i
$359$	4.74035	−	8.21053i	0.250186	−	0.433335i	−0.713391	−	0.700766i	$-0.752841\pi$
$359$	4.74035	−	8.21053i	0.250186	−	0.433335i	0.963577	+	0.267431i	$0.0861748\pi$
$360$		0			0
$361$	7.11334	+	12.3207i	0.374386	+	0.648456i
$362$	0.431074			0.0226568
$363$		0			0
$364$		0			0
$365$	−13.0005	+	22.5175i	−0.680476	+	1.17862i
$366$		0			0
$367$	−8.06670	+	13.9719i	−0.421079	+	0.729329i	−0.996045	−	0.0888474i	$-0.971682\pi$
$367$	−8.06670	+	13.9719i	−0.421079	+	0.729329i	0.574967	+	0.818177i	$0.305015\pi$
$368$	0.190722	+	0.330341i	0.00994209	+	0.0172202i
$369$		0			0
$370$	−26.2003			−1.36209
$371$		0			0
$372$		0			0
$373$	−7.02481	−	12.1673i	−0.363731	−	0.630001i	0.624841	−	0.780752i	$-0.285164\pi$
$373$	−7.02481	−	12.1673i	−0.363731	−	0.630001i	−0.988572	+	0.150752i	$0.951831\pi$
$374$	−2.44562			−0.126460
$375$		0			0
$376$	15.6973			0.809525
$377$	−51.1317			−2.63341
$378$		0			0
$379$	16.0574			0.824812			0.412406	−	0.911000i	$-0.364689\pi$
$379$	16.0574			0.824812			0.412406	+	0.911000i	$0.364689\pi$
$380$	−1.02229			−0.0524423
$381$		0			0
$382$	−20.9736			−1.07310
$383$	−16.0103	−	27.7306i	−0.818086	−	1.41697i	−0.907090	−	0.420936i	$-0.861702\pi$
$383$	−16.0103	−	27.7306i	−0.818086	−	1.41697i	0.0890039	−	0.996031i	$-0.471632\pi$
$384$		0			0
$385$		0			0
$386$	−8.14022			−0.414326
$387$		0			0
$388$	−1.25696	−	2.17712i	−0.0638124	−	0.110526i
$389$	−15.0214	+	26.0178i	−0.761616	+	1.31916i	0.180402	+	0.983593i	$0.442260\pi$
$389$	−15.0214	+	26.0178i	−0.761616	+	1.31916i	−0.942017	+	0.335564i	$0.891073\pi$
$390$		0			0
$391$	0.205737	−	0.356347i	0.0104046	−	0.0180212i
$392$		0			0
$393$		0			0
$394$	33.9982			1.71281
$395$	−16.0005	−	27.7136i	−0.805071	−	1.39442i
$396$		0			0
$397$	6.15998	−	10.6694i	0.309160	−	0.535482i	−0.669019	−	0.743246i	$-0.733285\pi$
$397$	6.15998	−	10.6694i	0.309160	−	0.535482i	0.978179	+	0.207764i	$0.0666187\pi$
$398$	2.04916	+	3.54925i	0.102715	+	0.177908i
$399$		0			0
$400$	2.53802	−	4.39598i	0.126901	−	0.219799i
$401$	10.4880	+	18.1657i	0.523745	+	0.907152i	0.999618	+	0.0276385i	$0.00879873\pi$
$401$	10.4880	+	18.1657i	0.523745	+	0.907152i	−0.475873	+	0.879514i	$0.657868\pi$
$402$		0			0
$403$	22.3603	−	38.7291i	1.11384	−	1.92923i
$404$	0.884600	−	1.53217i	0.0440105	−	0.0762284i
$405$		0			0
$406$		0			0
$407$	−1.79679	−	3.11213i	−0.0890635	−	0.154263i
$408$		0			0
$409$	25.6614			1.26887			0.634437	−	0.772975i	$-0.281232\pi$
$409$	25.6614			1.26887			0.634437	+	0.772975i	$0.281232\pi$
$410$	7.59627			0.375153
$411$		0			0
$412$	0.281059	+	0.486809i	0.0138468	+	0.0239833i
$413$		0			0
$414$		0			0
$415$	3.45811	−	5.98962i	0.169752	−	0.294019i
$416$	3.03343	−	5.25406i	0.148726	−	0.257601i
$417$		0			0
$418$	0.688663	+	1.19280i	0.0336836	+	0.0583417i
$419$	−0.739885	+	1.28152i	−0.0361458	+	0.0626063i	−0.883532	−	0.468370i	$-0.844841\pi$
$419$	−0.739885	+	1.28152i	−0.0361458	+	0.0626063i	0.847387	+	0.530976i	$0.178175\pi$
$420$		0			0
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	0.660965	−	0.750417i	$-0.270147\pi$
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	−0.980363	+	0.197203i	$0.936814\pi$
$422$	−3.67365	+	6.36295i	−0.178830	+	0.309743i
$423$		0			0
$424$	−1.05509	−	1.82747i	−0.0512398	−	0.0887500i
$425$	−5.47565			−0.265608
$426$		0			0
$427$		0			0
$428$	0.602196	−	1.04303i	0.0291083	−	0.0504170i
$429$		0			0
$430$	−2.09240	+	3.62414i	−0.100904	+	0.174771i
$431$	8.86349	+	15.3520i	0.426939	+	0.739481i	0.996599	−	0.0823997i	$-0.0262584\pi$
$431$	8.86349	+	15.3520i	0.426939	+	0.739481i	−0.569660	+	0.821881i	$0.692925\pi$
$432$		0			0
$433$	−5.83843			−0.280577			−0.140289	−	0.990111i	$-0.544803\pi$
$433$	−5.83843			−0.280577			−0.140289	+	0.990111i	$0.544803\pi$
$434$		0			0
$435$		0			0
$436$	0.982926	+	1.70248i	0.0470736	+	0.0815339i
$437$	−0.231734			−0.0110853
$438$		0			0
$439$	29.8553			1.42492			0.712459	−	0.701714i	$-0.247582\pi$
$439$	29.8553			1.42492			0.712459	+	0.701714i	$0.247582\pi$
$440$	3.48751			0.166261
$441$		0			0
$442$	30.4347			1.44763
$443$	−10.6655			−0.506733			−0.253367	−	0.967370i	$-0.581538\pi$
$443$	−10.6655			−0.506733			−0.253367	+	0.967370i	$0.581538\pi$
$444$		0			0
$445$	−20.5449			−0.973921
$446$	9.56077	+	16.5597i	0.452716	+	0.784127i
$447$		0			0
$448$		0			0
$449$	−3.55438			−0.167741			−0.0838707	−	0.996477i	$-0.526728\pi$
$449$	−3.55438			−0.167741			−0.0838707	+	0.996477i	$0.526728\pi$
$450$		0			0
$451$	0.520945	+	0.902302i	0.0245303	+	0.0424878i
$452$	−0.478340	+	0.828510i	−0.0224992	+	0.0389698i
$453$		0			0
$454$	1.94949	−	3.37662i	0.0914942	−	0.158473i
$455$		0			0
$456$		0			0
$457$	5.02322			0.234976			0.117488	−	0.993074i	$-0.462516\pi$
$457$	5.02322			0.234976			0.117488	+	0.993074i	$0.462516\pi$
$458$	6.17571	+	10.6966i	0.288572	+	0.499821i
$459$		0			0
$460$	−0.0248149	+	0.0429807i	−0.00115700	+	0.00200399i
$461$	9.23055	+	15.9878i	0.429910	+	0.744625i	0.996865	−	0.0791233i	$-0.0252121\pi$
$461$	9.23055	+	15.9878i	0.429910	+	0.744625i	−0.566955	+	0.823749i	$0.691879\pi$
$462$		0			0
$463$	7.11721	−	12.3274i	0.330765	−	0.572902i	−0.651897	−	0.758307i	$-0.726027\pi$
$463$	7.11721	−	12.3274i	0.330765	−	0.572902i	0.982662	+	0.185406i	$0.0593600\pi$
$464$	−15.7895	−	27.3482i	−0.733010	−	1.26961i
$465$		0			0
$466$	−8.94016	+	15.4848i	−0.414145	+	0.717320i
$467$	−1.68433	+	2.91734i	−0.0779413	+	0.134998i	−0.902362	−	0.430980i	$-0.858168\pi$
$467$	−1.68433	+	2.91734i	−0.0779413	+	0.134998i	0.824420	+	0.565978i	$0.191501\pi$
$468$		0			0
$469$		0			0
$470$	−9.09627	−	15.7552i	−0.419579	−	0.726733i
$471$		0			0
$472$	−2.16788			−0.0997848
$473$	−0.573978			−0.0263915
$474$		0			0
$475$	1.54189	+	2.67063i	0.0707467	+	0.122537i
$476$		0			0
$477$		0			0
$478$	−6.42468	+	11.1279i	−0.293858	+	0.508977i
$479$	−18.3833	+	31.8407i	−0.839952	+	1.45484i	0.0499812	+	0.998750i	$0.484084\pi$
$479$	−18.3833	+	31.8407i	−0.839952	+	1.45484i	−0.889934	+	0.456090i	$0.849249\pi$
$480$		0			0
$481$	22.3603	+	38.7291i	1.01954	+	1.76589i
$482$	−6.03462	+	10.4523i	−0.274869	+	0.476087i
$483$		0			0
$484$	−0.996130	−	1.72535i	−0.0452786	−	0.0784249i
$485$	−17.2233	+	29.8316i	−0.782069	+	1.35458i
$486$		0			0
$487$	18.7087	+	32.4045i	0.847773	+	1.46839i	0.883191	+	0.469014i	$0.155391\pi$
$487$	18.7087	+	32.4045i	0.847773	+	1.46839i	−0.0354172	+	0.999373i	$0.511276\pi$
$488$	2.82026			0.127667
$489$		0			0
$490$		0			0
$491$	−13.3353	+	23.0974i	−0.601813	+	1.04237i	0.390734	+	0.920504i	$0.372221\pi$
$491$	−13.3353	+	23.0974i	−0.601813	+	1.04237i	−0.992547	+	0.121866i	$0.961112\pi$
$492$		0			0
$493$	−17.0326	+	29.5013i	−0.767108	+	1.32867i
$494$	−8.57011	−	14.8439i	−0.385587	−	0.667857i
$495$		0			0
$496$	27.6195			1.24015
$497$		0			0
$498$		0			0
$499$	−16.8726	−	29.2242i	−0.755320	−	1.30825i	−0.945215	−	0.326449i	$-0.894148\pi$
$499$	−16.8726	−	29.2242i	−0.755320	−	1.30825i	0.189895	−	0.981804i	$-0.439185\pi$
$500$	−1.67911			−0.0750921
$501$		0			0
$502$	−33.6800			−1.50321
$503$	32.0401			1.42860			0.714299	−	0.699840i	$-0.246745\pi$
$503$	32.0401			1.42860			0.714299	+	0.699840i	$0.246745\pi$
$504$		0			0
$505$	−24.2422			−1.07876
$506$	0.0668661			0.00297256
$507$		0			0
$508$	1.64134			0.0728227
$509$	−3.96926	−	6.87495i	−0.175934	−	0.304727i	0.764550	−	0.644564i	$-0.222961\pi$
$509$	−3.96926	−	6.87495i	−0.175934	−	0.304727i	−0.940484	+	0.339838i	$0.889628\pi$
$510$		0			0
$511$		0			0
$512$	24.9186			1.10126
$513$		0			0
$514$	−7.31046	−	12.6621i	−0.322451	−	0.558501i
$515$	3.85117	−	6.67042i	0.169703	−	0.293934i
$516$		0			0
$517$	1.24763	−	2.16095i	0.0548705	−	0.0950386i
$518$		0			0
$519$		0			0
$520$	−43.4005			−1.90324
$521$	−7.33750	−	12.7089i	−0.321462	−	0.556788i	0.659328	−	0.751855i	$-0.270841\pi$
$521$	−7.33750	−	12.7089i	−0.321462	−	0.556788i	−0.980790	+	0.195067i	$0.937507\pi$
$522$		0			0
$523$	−14.1716	+	24.5459i	−0.619680	+	1.07332i	0.369864	+	0.929086i	$0.379404\pi$
$523$	−14.1716	+	24.5459i	−0.619680	+	1.07332i	−0.989544	+	0.144232i	$0.953929\pi$
$524$	−1.04988	−	1.81844i	−0.0458641	−	0.0794390i
$525$		0			0
$526$	−17.5737	+	30.4386i	−0.766251	+	1.32719i
$527$	−14.8969	−	25.8022i	−0.648920	−	1.12396i
$528$		0			0
$529$	11.4944	−	19.9088i	0.499755	−	0.865602i
$530$	−1.22281	+	2.11797i	−0.0531155	+	0.0919988i
$531$		0			0
$532$		0			0
$533$	−6.48293	−	11.2288i	−0.280807	−	0.486371i
$534$		0			0
$535$	−16.5030			−0.713487
$536$	−28.3705			−1.22542
$537$		0			0
$538$	5.14203	+	8.90625i	0.221688	+	0.383976i
$539$		0			0
$540$		0			0
$541$	−5.64290	+	9.77380i	−0.242607	+	0.420208i	−0.961456	−	0.274958i	$-0.911336\pi$
$541$	−5.64290	+	9.77380i	−0.242607	+	0.420208i	0.718849	+	0.695166i	$0.244669\pi$
$542$	2.29292	−	3.97145i	0.0984893	−	0.170588i
$543$		0			0
$544$	−2.02094	−	3.50038i	−0.0866473	−	0.150077i
$545$	13.4684	−	23.3279i	0.576922	−	0.999258i
$546$		0			0
$547$	14.6202	+	25.3229i	0.625115	+	1.08273i	0.988519	+	0.151099i	$0.0482812\pi$
$547$	14.6202	+	25.3229i	0.625115	+	1.08273i	−0.363404	+	0.931632i	$0.618385\pi$
$548$	0.528934	−	0.916140i	0.0225949	−	0.0391356i
$549$		0			0
$550$	−0.444907	−	0.770602i	−0.0189709	−	0.0328586i
$551$	19.1848			0.817300
$552$		0			0
$553$		0			0
$554$	−3.85457	+	6.67631i	−0.163765	+	0.283649i
$555$		0			0
$556$	−0.0853707	+	0.147866i	−0.00362052	+	0.00627093i
$557$	−0.387841	−	0.671761i	−0.0164334	−	0.0284634i	0.857692	−	0.514164i	$-0.171898\pi$
$557$	−0.387841	−	0.671761i	−0.0164334	−	0.0284634i	−0.874125	+	0.485701i	$0.838564\pi$
$558$		0			0
$559$	7.14290			0.302113
$560$		0			0
$561$		0			0
$562$	−19.1163	−	33.1105i	−0.806374	−	1.39668i
$563$	−24.9522			−1.05161			−0.525806	−	0.850605i	$-0.676236\pi$
$563$	−24.9522			−1.05161			−0.525806	+	0.850605i	$0.676236\pi$
$564$		0			0
$565$	13.1088			0.551489
$566$	−6.15888			−0.258877
$567$		0			0
$568$	−38.9564			−1.63457
$569$	24.8033			1.03981			0.519905	−	0.854224i	$-0.325967\pi$
$569$	24.8033			1.03981			0.519905	+	0.854224i	$0.325967\pi$
$570$		0			0
$571$	8.79654			0.368124			0.184062	−	0.982915i	$-0.441075\pi$
$571$	8.79654			0.368124			0.184062	+	0.982915i	$0.441075\pi$
$572$	−0.251745	−	0.436035i	−0.0105260	−	0.0182315i
$573$		0			0
$574$		0			0
$575$	0.149711			0.00624336
$576$		0			0
$577$	6.43717	+	11.1495i	0.267983	+	0.464160i	0.968341	−	0.249632i	$-0.0803096\pi$
$577$	6.43717	+	11.1495i	0.267983	+	0.464160i	−0.700358	+	0.713792i	$0.746976\pi$
$578$	−1.31386	+	2.27568i	−0.0546495	+	0.0946557i
$579$		0			0
$580$	2.05438	−	3.55829i	0.0853034	−	0.147750i
$581$		0			0
$582$		0			0
$583$	−0.335437			−0.0138924
$584$	15.1131	+	26.1766i	0.625384	+	1.08320i
$585$		0			0
$586$	−2.91534	+	5.04952i	−0.120432	+	0.208594i
$587$	22.4315	+	38.8526i	0.925849	+	1.60362i	0.790190	+	0.612861i	$0.209982\pi$
$587$	22.4315	+	38.8526i	0.925849	+	1.60362i	0.135658	+	0.990756i	$0.456685\pi$
$588$		0			0
$589$	−8.38965	+	14.5313i	−0.345690	+	0.598752i
$590$	1.25624	+	2.17588i	0.0517188	+	0.0895795i
$591$		0			0
$592$	−13.8097	+	23.9192i	−0.567577	+	0.983072i
$593$	1.88026	−	3.25671i	0.0772131	−	0.133737i	−0.824833	−	0.565376i	$-0.808731\pi$
$593$	1.88026	−	3.25671i	0.0772131	−	0.133737i	0.902047	+	0.431639i	$0.142064\pi$
$594$		0			0
$595$		0			0
$596$	−0.806123	−	1.39625i	−0.0330201	−	0.0571924i
$597$		0			0
$598$	−0.832119			−0.0340279
$599$	3.69047			0.150789			0.0753943	−	0.997154i	$-0.475978\pi$
$599$	3.69047			0.150789			0.0753943	+	0.997154i	$0.475978\pi$
$600$		0			0
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	0.998107	−	0.0615091i	$-0.0195913\pi$
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	−0.552322	+	0.833631i	$0.686258\pi$
$602$		0			0
$603$		0			0
$604$	1.70258	−	2.94896i	0.0692771	−	0.119991i
$605$	−13.6493	+	23.6413i	−0.554923	+	0.961155i
$606$		0			0
$607$	−12.1973	−	21.1263i	−0.495072	−	0.857490i	0.504911	−	0.863171i	$-0.331525\pi$
$607$	−12.1973	−	21.1263i	−0.495072	−	0.857490i	−0.999984	+	0.00568063i	$0.998192\pi$
$608$	−1.13816	+	1.97134i	−0.0461583	+	0.0799485i
$609$		0			0
$610$	−1.63429	−	2.83067i	−0.0661703	−	0.114610i
$611$	−15.5262	+	26.8921i	−0.628121	+	1.08794i
$612$		0			0
$613$	−21.0107	−	36.3917i	−0.848616	−	1.46985i	−0.882444	−	0.470418i	$-0.844103\pi$
$613$	−21.0107	−	36.3917i	−0.848616	−	1.46985i	0.0338284	−	0.999428i	$-0.489230\pi$
$614$	−16.6759			−0.672986
$615$		0			0
$616$		0			0
$617$	23.2049	−	40.1920i	0.934192	−	1.61807i	0.158125	−	0.987419i	$-0.449455\pi$
$617$	23.2049	−	40.1920i	0.934192	−	1.61807i	0.776068	−	0.630650i	$-0.217212\pi$
$618$		0			0
$619$	13.6047	−	23.5641i	0.546820	−	0.947120i	−0.451670	−	0.892185i	$-0.649172\pi$
$619$	13.6047	−	23.5641i	0.546820	−	0.947120i	0.998490	−	0.0549349i	$-0.0174951\pi$
$620$	1.79679	+	3.11213i	0.0721608	+	0.124986i
$621$		0			0
$622$	−29.6209			−1.18769
$623$		0			0
$624$		0			0
$625$	15.0326	+	26.0372i	0.601302	+	1.04149i
$626$	18.7137			0.747950
$627$		0			0
$628$	−0.909912			−0.0363094
$629$	29.7939			1.18796
$630$		0			0
$631$	−29.6023			−1.17845			−0.589224	−	0.807970i	$-0.700566\pi$
$631$	−29.6023			−1.17845			−0.589224	+	0.807970i	$0.700566\pi$
$632$	−37.2012			−1.47978
$633$		0			0
$634$	−8.32913			−0.330792
$635$	−11.2451	−	19.4771i	−0.446248	−	0.772925i
$636$		0			0
$637$		0			0
$638$	−5.53571			−0.219161
$639$		0			0
$640$	−12.0248	−	20.8276i	−0.475323	−	0.823283i
$641$	−0.139500	+	0.241621i	−0.00550991	+	0.00954345i	−0.868767	−	0.495221i	$-0.835087\pi$
$641$	−0.139500	+	0.241621i	−0.00550991	+	0.00954345i	0.863257	+	0.504764i	$0.168421\pi$
$642$		0			0
$643$	9.12196	−	15.7997i	0.359735	−	0.623079i	−0.628181	−	0.778067i	$-0.716200\pi$
$643$	9.12196	−	15.7997i	0.359735	−	0.623079i	0.987916	+	0.154988i	$0.0495338\pi$
$644$		0			0
$645$		0			0
$646$	−11.4192			−0.449283
$647$	11.2285	+	19.4483i	0.441438	+	0.764592i	0.997796	−	0.0663498i	$-0.0211353\pi$
$647$	11.2285	+	19.4483i	0.441438	+	0.764592i	−0.556359	+	0.830942i	$0.687802\pi$
$648$		0			0
$649$	−0.172304	+	0.298439i	−0.00676352	+	0.0117148i
$650$	5.53667	+	9.58980i	0.217166	+	0.376143i
$651$		0			0
$652$	0.705737	−	1.22237i	0.0276388	−	0.0478718i
$653$	−25.2656	−	43.7614i	−0.988721	−	1.71251i	−0.624066	−	0.781372i	$-0.714520\pi$
$653$	−25.2656	−	43.7614i	−0.988721	−	1.71251i	−0.364655	−	0.931143i	$-0.618813\pi$
$654$		0			0
$655$	−14.3858	+	24.9169i	−0.562099	+	0.973584i
$656$	4.00387	−	6.93491i	0.156325	−	0.270763i
$657$		0			0
$658$		0			0
$659$	−1.33631	−	2.31456i	−0.0520554	−	0.0901626i	0.838824	−	0.544403i	$-0.183244\pi$
$659$	−1.33631	−	2.31456i	−0.0520554	−	0.0901626i	−0.890879	+	0.454241i	$0.849911\pi$
$660$		0			0
$661$	−34.6100			−1.34617			−0.673086	−	0.739564i	$-0.735032\pi$
$661$	−34.6100			−1.34617			−0.673086	+	0.739564i	$0.735032\pi$
$662$	−14.4584			−0.561942
$663$		0			0
$664$	−4.02007	−	6.96296i	−0.156009	−	0.270215i
$665$		0			0
$666$		0			0
$667$	0.465690	−	0.806598i	0.0180316	−	0.0312316i
$668$	0.522537	−	0.905061i	0.0202176	−	0.0350179i
$669$		0			0
$670$	16.4402	+	28.4752i	0.635139	+	1.10009i
$671$	0.224155	−	0.388249i	0.00865342	−	0.0149882i
$672$		0			0
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	0.661869	−	0.749619i	$-0.269763\pi$
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	−0.980124	+	0.198386i	$0.936430\pi$
$674$	−12.5262	+	21.6959i	−0.482490	+	0.835697i
$675$		0			0
$676$	1.93170	+	3.34581i	0.0742963	+	0.128685i
$677$	43.7579			1.68175			0.840877	−	0.541226i	$-0.182040\pi$
$677$	43.7579			1.68175			0.840877	+	0.541226i	$0.182040\pi$
$678$		0			0
$679$		0			0
$680$	−14.4572	+	25.0407i	−0.554410	+	0.960266i
$681$		0			0
$682$	2.42081	−	4.19296i	0.0926975	−	0.160557i
$683$	14.1206	+	24.4576i	0.540310	+	0.935845i	0.998886	+	0.0471895i	$0.0150265\pi$
$683$	14.1206	+	24.4576i	0.540310	+	0.935845i	−0.458576	+	0.888655i	$0.651640\pi$
$684$		0			0
$685$	−14.4953			−0.553835
$686$		0			0
$687$		0			0
$688$	2.20574	+	3.82045i	0.0840929	+	0.145653i
$689$	4.17436			0.159031
$690$		0			0
$691$	−29.0651			−1.10569			−0.552844	−	0.833284i	$-0.686458\pi$
$691$	−29.0651			−1.10569			−0.552844	+	0.833284i	$0.686458\pi$
$692$	3.89344			0.148006
$693$		0			0
$694$	−27.5016			−1.04395
$695$	2.33956			0.0887444
$696$		0			0
$697$	−8.63816			−0.327193
$698$	−2.39961	−	4.15625i	−0.0908268	−	0.157317i
$699$		0			0
$700$		0			0
$701$	1.10876			0.0418771			0.0209386	−	0.999781i	$-0.493335\pi$
$701$	1.10876			0.0418771			0.0209386	+	0.999781i	$0.493335\pi$
$702$		0			0
$703$	−8.38965	−	14.5313i	−0.316422	−	0.548059i
$704$	2.01114	−	3.48340i	0.0757979	−	0.131286i
$705$		0			0
$706$	−6.75150	+	11.6939i	−0.254096	+	0.440107i
$707$		0			0
$708$		0			0
$709$	−18.4688			−0.693612			−0.346806	−	0.937937i	$-0.612734\pi$
$709$	−18.4688			−0.693612			−0.346806	+	0.937937i	$0.612734\pi$
$710$	22.5744	+	39.1001i	0.847204	+	1.46740i
$711$		0			0
$712$	−11.9418	+	20.6837i	−0.447536	+	0.775155i
$713$	0.407299	+	0.705463i	0.0152535	+	0.0264198i
$714$		0			0
$715$	−3.44949	+	5.97470i	−0.129004	+	0.223441i
$716$	0.473126	+	0.819478i	0.0176815	+	0.0306253i
$717$		0			0
$718$	−6.38666	+	11.0620i	−0.238348	+	0.412831i
$719$	−16.8885	+	29.2517i	−0.629834	+	1.09090i	0.357751	+	0.933817i	$0.383544\pi$
$719$	−16.8885	+	29.2517i	−0.629834	+	1.09090i	−0.987585	+	0.157087i	$0.949790\pi$
$720$		0			0
$721$		0			0
$722$	−9.58378	−	16.5996i	−0.356671	−	0.617773i
$723$		0			0
$724$	0.0591253			0.00219738
$725$	−12.3942			−0.460310
$726$		0			0
$727$	−8.40214	−	14.5529i	−0.311618	−	0.539738i	0.667095	−	0.744973i	$-0.267538\pi$
$727$	−8.40214	−	14.5529i	−0.311618	−	0.539738i	−0.978713	+	0.205234i	$0.934204\pi$
$728$		0			0
$729$		0			0
$730$	17.5155	−	30.3377i	0.648277	−	1.12285i
$731$	2.37939	−	4.12122i	0.0880047	−	0.152429i
$732$		0			0
$733$	6.81820	+	11.8095i	0.251836	+	0.436193i	0.964031	−	0.265789i	$-0.0856323\pi$
$733$	6.81820	+	11.8095i	0.251836	+	0.436193i	−0.712195	+	0.701981i	$0.752299\pi$
$734$	10.8682	−	18.8243i	0.401154	−	0.694819i
$735$		0			0
$736$	0.0552549	+	0.0957044i	0.00203672	+	0.00352771i
$737$	−2.25490	+	3.90560i	−0.0830603	+	0.143865i
$738$		0			0
$739$	16.0209	+	27.7491i	0.589340	+	1.02077i	0.994319	+	0.106441i	$0.0339455\pi$
$739$	16.0209	+	27.7491i	0.589340	+	1.02077i	−0.404979	+	0.914326i	$0.632721\pi$
$740$	−3.59358			−0.132103
$741$		0			0
$742$		0			0
$743$	16.8764	−	29.2309i	0.619137	−	1.07238i	−0.370507	−	0.928830i	$-0.620816\pi$
$743$	16.8764	−	29.2309i	0.619137	−	1.07238i	0.989644	−	0.143547i	$-0.0458507\pi$
$744$		0			0
$745$	−11.0458	+	19.1318i	−0.404685	+	0.700936i
$746$	9.46451	+	16.3930i	0.346520	+	0.600191i
$747$		0			0
$748$	−0.335437			−0.0122648
$749$		0			0
$750$		0			0
$751$	−13.0582	−	22.6175i	−0.476502	−	0.825326i	0.523135	−	0.852250i	$-0.324762\pi$
$751$	−13.0582	−	22.6175i	−0.476502	−	0.825326i	−0.999637	+	0.0269236i	$0.991429\pi$
$752$	−19.1780			−0.699349
$753$		0			0
$754$	68.8895			2.50881
$755$	−46.6587			−1.69808
$756$		0			0
$757$	35.6536			1.29585			0.647927	−	0.761703i	$-0.275636\pi$
$757$	35.6536			1.29585			0.647927	+	0.761703i	$0.275636\pi$
$758$	−21.6340			−0.785784
$759$		0			0
$760$	16.2841			0.590685
$761$	20.3824	+	35.3033i	0.738861	+	1.27974i	0.953009	+	0.302943i	$0.0979692\pi$
$761$	20.3824	+	35.3033i	0.738861	+	1.27974i	−0.214148	+	0.976801i	$0.568698\pi$
$762$		0			0
$763$		0			0
$764$	−2.87670			−0.104075
$765$		0			0
$766$	21.5706	+	37.3613i	0.779377	+	1.34992i
$767$	2.14425	−	3.71395i	0.0774243	−	0.134103i
$768$		0			0
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	0.253639	+	0.967299i	$0.418373\pi$
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	−0.964525	+	0.263992i	$0.914961\pi$
$770$		0			0
$771$		0			0
$772$	−1.11650			−0.0401836
$773$	12.4513	+	21.5663i	0.447842	+	0.775686i	0.998245	−	0.0592135i	$-0.0188593\pi$
$773$	12.4513	+	21.5663i	0.447842	+	0.775686i	−0.550403	+	0.834899i	$0.685526\pi$
$774$		0			0
$775$	5.42009	−	9.38788i	0.194695	−	0.337222i
$776$	20.0221	+	34.6793i	0.718752	+	1.24492i
$777$		0			0
$778$	20.2383	−	35.0538i	0.725578	−	1.25674i
$779$	2.43242	+	4.21307i	0.0871504	+	0.150949i
$780$		0			0
$781$	−3.09627	+	5.36289i	−0.110793	+	0.191899i
$782$	−0.277189	+	0.480105i	−0.00991225	+	0.0171685i
$783$		0			0
$784$		0			0
$785$	6.23396	+	10.7975i	0.222499	+	0.385380i
$786$		0			0
$787$	−30.7050			−1.09452			−0.547258	−	0.836964i	$-0.684328\pi$
$787$	−30.7050			−1.09452			−0.547258	+	0.836964i	$0.684328\pi$
$788$	4.66313			0.166117
$789$		0			0
$790$	21.5574	+	37.3385i	0.766977	+	1.32844i
$791$		0			0
$792$		0			0
$793$	−2.78952	+	4.83158i	−0.0990586	+	0.171575i
$794$	−8.29932	+	14.3748i	−0.294532	+	0.510144i
$795$		0			0
$796$	0.281059	+	0.486809i	0.00996188	+	0.0172545i
$797$	−5.50686	+	9.53817i	−0.195063	+	0.337859i	−0.946921	−	0.321466i	$-0.895825\pi$
$797$	−5.50686	+	9.53817i	−0.195063	+	0.337859i	0.751858	+	0.659325i	$0.229158\pi$
$798$		0			0
$799$	10.3439	+	17.9161i	0.365941	+	0.633828i
$800$	0.735300	−	1.27358i	0.0259968	−	0.0450277i
$801$		0			0
$802$	−14.1304	−	24.4746i	−0.498962	−	0.864228i
$803$	4.80478			0.169557
$804$		0			0
$805$		0			0
$806$	−30.1259	+	52.1796i	−1.06114	+	1.83795i
$807$		0			0
$808$	−14.0908	+	24.4060i	−0.495713	+	0.858600i
$809$	8.49407	+	14.7122i	0.298636	+	0.517252i	0.975824	−	0.218558i	$-0.0701352\pi$
$809$	8.49407	+	14.7122i	0.298636	+	0.517252i	−0.677188	+	0.735810i	$0.736802\pi$
$810$		0			0
$811$	37.9796			1.33364			0.666822	−	0.745217i	$-0.267654\pi$
$811$	37.9796			1.33364			0.666822	+	0.745217i	$0.267654\pi$
$812$		0			0
$813$		0			0
$814$	2.42081	+	4.19296i	0.0848493	+	0.146963i
$815$	−19.3405			−0.677468
$816$		0			0
$817$	−2.68004			−0.0937629
$818$	−34.5735			−1.20883
$819$		0			0
$820$	1.04189			0.0363843
$821$	−8.27868			−0.288928			−0.144464	−	0.989510i	$-0.546146\pi$
$821$	−8.27868			−0.288928			−0.144464	+	0.989510i	$0.546146\pi$
$822$		0			0
$823$	54.5526			1.90158			0.950792	−	0.309829i	$-0.100272\pi$
$823$	54.5526			1.90158			0.950792	+	0.309829i	$0.100272\pi$
$824$	−4.47700	−	7.75438i	−0.155964	−	0.270137i
$825$		0			0
$826$		0			0
$827$	31.8708			1.10826			0.554129	−	0.832431i	$-0.313052\pi$
$827$	31.8708			1.10826			0.554129	+	0.832431i	$0.313052\pi$
$828$		0			0
$829$	0.176174	+	0.305143i	0.00611879	+	0.0105981i	0.869069	−	0.494692i	$-0.164719\pi$
$829$	0.176174	+	0.305143i	0.00611879	+	0.0105981i	−0.862950	+	0.505290i	$0.831386\pi$
$830$	−4.65910	+	8.06980i	−0.161720	+	0.280107i
$831$		0			0
$832$	−25.0278	+	43.3494i	−0.867683	+	1.50287i
$833$		0			0
$834$		0			0
$835$	−14.3200			−0.495562
$836$	0.0944557	+	0.163602i	0.00326682	+	0.00565829i
$837$		0			0
$838$	0.996845	−	1.72659i	0.0344354	−	0.0596439i
$839$	12.5077	+	21.6640i	0.431815	+	0.747926i	0.997030	−	0.0770182i	$-0.0245399\pi$
$839$	12.5077	+	21.6640i	0.431815	+	0.747926i	−0.565215	+	0.824944i	$0.691207\pi$
$840$		0			0
$841$	−24.0535	+	41.6619i	−0.829431	+	1.43662i
$842$	8.82951	+	15.2932i	0.304285	+	0.527037i
$843$		0			0
$844$	−0.503870	+	0.872729i	−0.0173439	+	0.0300406i
$845$	26.4688	−	45.8454i	0.910556	−	1.57713i
$846$		0			0
$847$		0			0
$848$	1.28905	+	2.23270i	0.0442661	+	0.0766711i
$849$		0			0
$850$	7.37733			0.253040
$851$	−0.814598			−0.0279241
$852$		0			0
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	−0.977640	−	0.210286i	$-0.932560\pi$
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	0.306706	−	0.951804i	$-0.400773\pi$
$854$		0			0
$855$		0			0
$856$	−9.59240	+	16.6145i	−0.327861	+	0.567873i
$857$	8.20368	−	14.2092i	0.280232	−	0.485377i	−0.691210	−	0.722654i	$-0.742922\pi$
$857$	8.20368	−	14.2092i	0.280232	−	0.485377i	0.971442	+	0.237278i	$0.0762552\pi$
$858$		0			0
$859$	13.4162	+	23.2376i	0.457756	+	0.792856i	0.998842	−	0.0481111i	$-0.0153201\pi$
$859$	13.4162	+	23.2376i	0.457756	+	0.792856i	−0.541086	+	0.840967i	$0.681987\pi$
$860$	−0.286989	+	0.497079i	−0.00978624	+	0.0169503i
$861$		0			0
$862$	−11.9418	−	20.6837i	−0.406738	−	0.704490i
$863$	7.25284	−	12.5623i	0.246890	−	0.427625i	−0.715772	−	0.698334i	$-0.753925\pi$
$863$	7.25284	−	12.5623i	0.246890	−	0.427625i	0.962661	+	0.270709i	$0.0872582\pi$
$864$		0			0
$865$	−26.6746	−	46.2017i	−0.906963	−	1.57091i
$866$	7.86610			0.267301
$867$		0			0
$868$		0			0
$869$	−2.95677	+	5.12127i	−0.100301	+	0.173727i
$870$		0			0
$871$	28.0612	−	48.6035i	0.950819	−	1.64687i
$872$	−15.6570	−	27.1188i	−0.530214	−	0.918358i
$873$		0			0
$874$	0.312214			0.0105608
$875$		0			0
$876$		0			0
$877$	−9.45723	−	16.3804i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270131\pi$
$877$	−9.45723	−	16.3804i	−0.319348	−	0.553127i	−0.980352	+	0.197255i	$0.936797\pi$
$878$	−40.2240			−1.35749
$879$		0			0
$880$	−4.26083			−0.143633
$881$	−53.8976			−1.81585			−0.907927	−	0.419128i	$-0.862336\pi$
$881$	−53.8976			−1.81585			−0.907927	+	0.419128i	$0.862336\pi$
$882$		0			0
$883$	43.4252			1.46137			0.730687	−	0.682712i	$-0.239200\pi$
$883$	43.4252			1.46137			0.730687	+	0.682712i	$0.239200\pi$
$884$	4.17436			0.140399
$885$		0			0
$886$	14.3696			0.482756
$887$	−19.4800	−	33.7403i	−0.654074	−	1.13289i	−0.982125	−	0.188229i	$-0.939725\pi$
$887$	−19.4800	−	33.7403i	−0.654074	−	1.13289i	0.328051	−	0.944660i	$-0.393608\pi$
$888$		0			0
$889$		0			0
$890$	27.6800			0.927837
$891$		0			0
$892$	1.31134	+	2.27130i	0.0439068	+	0.0760488i
$893$	5.82547	−	10.0900i	0.194942	−	0.337650i
$894$		0			0
$895$	6.48293	−	11.2288i	0.216700	−	0.375336i
$896$		0			0
$897$		0			0
$898$	4.78880			0.159804
$899$	−33.7195	−	58.4038i	−1.12461	−	1.94788i
$900$		0			0
$901$	1.39053	−	2.40847i	0.0463253	−	0.0802377i
$902$	−0.701867	−	1.21567i	−0.0233696	−	0.0404773i
$903$		0			0
$904$	7.61949	−	13.1973i	0.253420	−	0.438937i
$905$	−0.405078	−	0.701615i	−0.0134652	−	0.0233225i
$906$		0			0
$907$	−17.2638	+	29.9018i	−0.573236	+	0.992874i	0.422995	+	0.906132i	$0.360979\pi$
$907$	−17.2638	+	29.9018i	−0.573236	+	0.992874i	−0.996231	+	0.0867416i	$0.972355\pi$
$908$	0.267389	−	0.463131i	0.00887360	−	0.0153695i
$909$		0			0
$910$		0			0
$911$	23.2631	+	40.2929i	0.770741	+	1.33496i	0.937157	+	0.348907i	$0.113447\pi$
$911$	23.2631	+	40.2929i	0.770741	+	1.33496i	−0.166416	+	0.986056i	$0.553220\pi$
$912$		0			0
$913$	−1.27807			−0.0422978
$914$	−6.76777			−0.223858
$915$		0			0
$916$	0.847048	+	1.46713i	0.0279873	+	0.0484753i
$917$		0			0
$918$		0			0
$919$	4.97818	−	8.62246i	0.164215	−	0.284429i	−0.772161	−	0.635427i	$-0.780824\pi$
$919$	4.97818	−	8.62246i	0.164215	−	0.284429i	0.936376	+	0.350998i	$0.114158\pi$
$920$	0.395277	−	0.684640i	0.0130319	−	0.0225719i
$921$		0			0
$922$	−12.4363	−	21.5403i	−0.409567	−	0.709391i
$923$	38.5317	−	66.7388i	1.26829	−	2.19674i
$924$		0			0
$925$	5.42009	+	9.38788i	0.178212	+	0.308671i
$926$	−9.58899	+	16.6086i	−0.315114	+	0.545793i
$927$		0			0
$928$	−4.57444	−	7.92317i	−0.150164	−	0.260091i
$929$	−9.04601			−0.296790			−0.148395	−	0.988928i	$-0.547411\pi$
$929$	−9.04601			−0.296790			−0.148395	+	0.988928i	$0.547411\pi$
$930$		0			0
$931$		0			0
$932$	−1.22621	+	2.12387i	−0.0401660	+	0.0695696i
$933$		0			0
$934$	2.26929	−	3.93052i	0.0742533	−	0.128610i
$935$	2.29813	+	3.98048i	0.0751570	+	0.130176i
$936$		0			0
$937$	−24.3928			−0.796878			−0.398439	−	0.917195i	$-0.630448\pi$
$937$	−24.3928			−0.796878			−0.398439	+	0.917195i	$0.630448\pi$
$938$		0			0
$939$		0			0
$940$	−1.24763	−	2.16095i	−0.0406931	−	0.0704825i
$941$	59.5381			1.94089			0.970443	−	0.241331i	$-0.0775839\pi$
$941$	59.5381			1.94089			0.970443	+	0.241331i	$0.0775839\pi$
$942$		0			0
$943$	0.236177			0.00769098
$944$	2.64858			0.0862041
$945$		0			0
$946$	0.773318			0.0251428
$947$	−8.64858			−0.281041			−0.140521	−	0.990078i	$-0.544878\pi$
$947$	−8.64858			−0.281041			−0.140521	+	0.990078i	$0.544878\pi$
$948$		0			0
$949$	−59.7934			−1.94097
$950$	−2.07738	−	3.59813i	−0.0673992	−	0.116739i
$951$		0			0
$952$		0			0
$953$	−3.78249			−0.122527			−0.0612634	−	0.998122i	$-0.519513\pi$
$953$	−3.78249			−0.122527			−0.0612634	+	0.998122i	$0.519513\pi$
$954$		0			0
$955$	19.7087	+	34.1365i	0.637760	+	1.10463i
$956$	−0.881196	+	1.52628i	−0.0284999	+	0.0493633i
$957$		0			0
$958$	24.7677	−	42.8989i	0.800208	−	1.38600i
$959$		0			0
$960$		0			0
$961$	27.9831			0.902680
$962$	−30.1259	−	52.1796i	−0.971298	−	1.68234i
$963$		0			0
$964$	−0.827696	+	1.43361i	−0.0266583	+	0.0461735i
$965$	7.64930	+	13.2490i	0.246240	+	0.426500i
$966$		0			0
$967$	16.4745	−	28.5346i	0.529783	−	0.917611i	−0.469613	−	0.882872i	$-0.655607\pi$
$967$	16.4745	−	28.5346i	0.529783	−	0.917611i	0.999396	−	0.0347392i	$-0.0110601\pi$
$968$	15.8674	+	27.4831i	0.509996	+	0.883340i
$969$		0			0
$970$	23.2049	−	40.1920i	0.745063	−	1.29049i
$971$	−27.7285	+	48.0272i	−0.889850	+	1.54126i	−0.0497974	+	0.998759i	$0.515858\pi$
$971$	−27.7285	+	48.0272i	−0.889850	+	1.54126i	−0.840052	+	0.542506i	$0.817476\pi$
$972$		0			0
$973$		0			0
$974$	−25.2062	−	43.6584i	−0.807659	−	1.39891i
$975$		0			0
$976$	−3.44562			−0.110292
$977$	−56.5485			−1.80915			−0.904573	−	0.426318i	$-0.859811\pi$
$977$	−56.5485			−1.80915			−0.904573	+	0.426318i	$0.859811\pi$
$978$		0			0
$979$	1.89827	+	3.28790i	0.0606690	+	0.105082i
$980$		0			0
$981$		0			0
$982$	17.9666	−	31.1190i	0.573336	−	0.993047i
$983$	14.4987	−	25.1124i	0.462435	−	0.800961i	−0.536646	−	0.843807i	$-0.680309\pi$
$983$	14.4987	−	25.1124i	0.462435	−	0.800961i	0.999082	+	0.0428458i	$0.0136424\pi$
$984$		0			0
$985$	−31.9479	−	55.3354i	−1.01794	−	1.76313i
$986$	22.9479	−	39.7469i	0.730810	−	1.26580i
$987$		0			0
$988$	−1.17546	−	2.03596i	−0.0373963	−	0.0647724i
$989$	−0.0650551	+	0.112679i	−0.00206863	+	0.00358298i
$990$		0			0
$991$	−3.40461	−	5.89696i	−0.108151	−	0.187323i	0.806870	−	0.590729i	$-0.201160\pi$
$991$	−3.40461	−	5.89696i	−0.108151	−	0.187323i	−0.915021	+	0.403406i	$0.867826\pi$
$992$	8.00175			0.254056
$993$		0			0
$994$		0			0
$995$	3.85117	−	6.67042i	0.122090	−	0.211466i
$996$		0			0
$997$	19.4688	−	33.7210i	0.616585	−	1.06796i	−0.373520	−	0.927622i	$-0.621849\pi$
$997$	19.4688	−	33.7210i	0.616585	−	1.06796i	0.990104	−	0.140333i	$-0.0448175\pi$
$998$	22.7324	+	39.3736i	0.719580	+	1.24635i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.c.226.2		6
3.2	odd	2		441.2.h.d.373.2		6
7.2	even	3		189.2.f.b.64.2		6
7.3	odd	6		1323.2.g.e.361.2		6
7.4	even	3		1323.2.g.d.361.2		6
7.5	odd	6		1323.2.f.d.442.2		6
7.6	odd	2		1323.2.h.b.226.2		6
9.2	odd	6		441.2.g.c.79.2		6
9.7	even	3		1323.2.g.d.667.2		6
21.2	odd	6		63.2.f.a.22.2	✓	6
21.5	even	6		441.2.f.c.148.2		6
21.11	odd	6		441.2.g.c.67.2		6
21.17	even	6		441.2.g.b.67.2		6
21.20	even	2		441.2.h.e.373.2		6
28.23	odd	6		3024.2.r.k.1009.3		6
63.2	odd	6		63.2.f.a.43.2	yes	6
63.5	even	6		3969.2.a.q.1.2		3
63.11	odd	6		441.2.h.d.214.2		6
63.16	even	3		189.2.f.b.127.2		6
63.20	even	6		441.2.g.b.79.2		6
63.23	odd	6		567.2.a.h.1.2		3
63.25	even	3	inner	1323.2.h.c.802.2		6
63.34	odd	6		1323.2.g.e.667.2		6
63.38	even	6		441.2.h.e.214.2		6
63.40	odd	6		3969.2.a.l.1.2		3
63.47	even	6		441.2.f.c.295.2		6
63.52	odd	6		1323.2.h.b.802.2		6
63.58	even	3		567.2.a.c.1.2		3
63.61	odd	6		1323.2.f.d.883.2		6
84.23	even	6		1008.2.r.h.337.1		6
252.23	even	6		9072.2.a.ca.1.3		3
252.79	odd	6		3024.2.r.k.2017.3		6
252.191	even	6		1008.2.r.h.673.1		6
252.247	odd	6		9072.2.a.bs.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.2	✓	6	21.2	odd	6
63.2.f.a.43.2	yes	6	63.2	odd	6
189.2.f.b.64.2		6	7.2	even	3
189.2.f.b.127.2		6	63.16	even	3
441.2.f.c.148.2		6	21.5	even	6
441.2.f.c.295.2		6	63.47	even	6
441.2.g.b.67.2		6	21.17	even	6
441.2.g.b.79.2		6	63.20	even	6
441.2.g.c.67.2		6	21.11	odd	6
441.2.g.c.79.2		6	9.2	odd	6
441.2.h.d.214.2		6	63.11	odd	6
441.2.h.d.373.2		6	3.2	odd	2
441.2.h.e.214.2		6	63.38	even	6
441.2.h.e.373.2		6	21.20	even	2
567.2.a.c.1.2		3	63.58	even	3
567.2.a.h.1.2		3	63.23	odd	6
1008.2.r.h.337.1		6	84.23	even	6
1008.2.r.h.673.1		6	252.191	even	6
1323.2.f.d.442.2		6	7.5	odd	6
1323.2.f.d.883.2		6	63.61	odd	6
1323.2.g.d.361.2		6	7.4	even	3
1323.2.g.d.667.2		6	9.7	even	3
1323.2.g.e.361.2		6	7.3	odd	6
1323.2.g.e.667.2		6	63.34	odd	6
1323.2.h.b.226.2		6	7.6	odd	2
1323.2.h.b.802.2		6	63.52	odd	6
1323.2.h.c.226.2		6	1.1	even	1	trivial
1323.2.h.c.802.2		6	63.25	even	3	inner
3024.2.r.k.1009.3		6	28.23	odd	6
3024.2.r.k.2017.3		6	252.79	odd	6
3969.2.a.l.1.2		3	63.40	odd	6
3969.2.a.q.1.2		3	63.5	even	6
9072.2.a.bs.1.1		3	252.247	odd	6
9072.2.a.ca.1.3		3	252.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.34730 q^{2} -0.184793 q^{4} +(1.26604 + 2.19285i) q^{5} +2.94356 q^{8} +O(q^{10})\)	\(q-1.34730 q^{2} -0.184793 q^{4} +(1.26604 + 2.19285i) q^{5} +2.94356 q^{8} +(-1.70574 - 2.95442i) q^{10} +(0.233956 - 0.405223i) q^{11} +(-2.91147 + 5.04282i) q^{13} -3.59627 q^{16} +(1.93969 + 3.35965i) q^{17} +(1.09240 - 1.89209i) q^{19} +(-0.233956 - 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(-0.0530334 - 0.0918566i) q^{23} +(-0.705737 + 1.22237i) q^{25} +(3.92262 - 6.79417i) q^{26} +(4.39053 + 7.60462i) q^{29} -7.68004 q^{31} -1.04189 q^{32} +(-2.61334 - 4.52644i) q^{34} +(3.84002 - 6.65111i) q^{37} +(-1.47178 + 2.54920i) q^{38} +(3.72668 + 6.45480i) q^{40} +(-1.11334 + 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +(-0.0432332 + 0.0748822i) q^{44} +(0.0714517 + 0.123758i) q^{46} +5.33275 q^{47} +(0.950837 - 1.64690i) q^{50} +(0.538019 - 0.931876i) q^{52} +(-0.358441 - 0.620838i) q^{53} +1.18479 q^{55} +(-5.91534 - 10.2457i) q^{58} -0.736482 q^{59} +0.958111 q^{61} +10.3473 q^{62} +8.59627 q^{64} -14.7442 q^{65} -9.63816 q^{67} +(-0.358441 - 0.620838i) q^{68} -13.2344 q^{71} +(5.13429 + 8.89284i) q^{73} +(-5.17365 + 8.96102i) q^{74} +(-0.201867 + 0.349643i) q^{76} -12.6382 q^{79} +(-4.55303 - 7.88609i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(0.826352 + 1.43128i) q^{86} +(0.688663 - 1.19280i) q^{88} +(-4.05690 + 7.02676i) q^{89} +(0.00980018 + 0.0169744i) q^{92} -7.18479 q^{94} +5.53209 q^{95} +(6.80200 + 11.7814i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 + 3 * q^5 - 12 * q^8	\( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38} + 9 q^{40} + 3 q^{43} + 15 q^{44} - 6 q^{47} - 6 q^{50} + 21 q^{52} + 6 q^{53} + 9 q^{58} + 6 q^{59} + 12 q^{61} + 60 q^{62} + 24 q^{64} - 30 q^{65} - 24 q^{67} + 6 q^{68} - 18 q^{71} + 21 q^{73} - 30 q^{74} - 15 q^{76} - 42 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 12 q^{89} + 3 q^{92} - 36 q^{94} + 24 q^{95} + 3 q^{97}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 + 3 * q^5 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 6 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 3 * q^26 + 9 * q^29 - 6 * q^31 - 9 * q^34 + 3 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 + 15 * q^44 - 6 * q^47 - 6 * q^50 + 21 * q^52 + 6 * q^53 + 9 * q^58 + 6 * q^59 + 12 * q^61 + 60 * q^62 + 24 * q^64 - 30 * q^65 - 24 * q^67 + 6 * q^68 - 18 * q^71 + 21 * q^73 - 30 * q^74 - 15 * q^76 - 42 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 12 * q^89 + 3 * q^92 - 36 * q^94 + 24 * q^95 + 3 * q^97

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