LMFDB - Embedded newform 920.2.bv.a.617.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			617.18
Character	$\chi$	$=$	920.617
Dual form			920.2.bv.a.753.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0224040 + 0.0410298i) q^{3} +(2.13690 - 0.658540i) q^{5} +(2.31180 + 1.73059i) q^{7} +(1.62074 + 2.52192i) q^{9} +(0.565611 + 0.258306i) q^{11} +(0.666316 + 0.890094i) q^{13} +(-0.0208552 + 0.102430i) q^{15} +(-2.08532 - 0.149145i) q^{17} +(-1.43969 + 1.66149i) q^{19} +(-0.122799 + 0.0560805i) q^{21} +(-2.25231 + 4.23404i) q^{23} +(4.13265 - 2.81446i) q^{25} +(-0.279672 + 0.0200025i) q^{27} +(1.86944 - 1.61988i) q^{29} +(-8.11526 - 2.38286i) q^{31} +(-0.0232702 + 0.0174198i) q^{33} +(6.07973 + 2.17568i) q^{35} +(0.190749 - 0.876858i) q^{37} +(-0.0514485 + 0.00739718i) q^{39} +(6.19326 + 3.98017i) q^{41} +(-5.01600 - 2.73894i) q^{43} +(5.12414 + 4.32176i) q^{45} +(1.83333 + 1.83333i) q^{47} +(0.377336 + 1.28509i) q^{49} +(0.0528390 - 0.0822190i) q^{51} +(1.91884 - 2.56327i) q^{53} +(1.37876 + 0.179495i) q^{55} +(-0.0359158 - 0.0962940i) q^{57} +(6.13247 + 0.881716i) q^{59} +(3.88373 - 13.2268i) q^{61} +(-0.617588 + 8.63501i) q^{63} +(2.01001 + 1.46324i) q^{65} +(12.7829 + 4.76778i) q^{67} +(-0.123261 - 0.187271i) q^{69} +(-0.404054 - 0.884756i) q^{71} +(-0.272310 - 3.80740i) q^{73} +(0.0228892 + 0.232617i) q^{75} +(0.860556 + 1.57599i) q^{77} +(-0.310067 + 2.15657i) q^{79} +(-3.73057 + 8.16880i) q^{81} +(-10.2708 - 2.23428i) q^{83} +(-4.55434 + 1.05456i) q^{85} +(0.0245804 + 0.112994i) q^{87} +(9.66802 - 2.83879i) q^{89} +3.21083i q^{91} +(0.279582 - 0.279582i) q^{93} +(-1.98230 + 4.49852i) q^{95} +(-10.7495 + 2.33842i) q^{97} +(0.265282 + 1.84507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.0224040	+	0.0410298i	−0.0129349	+	0.0236886i	−0.884067	−	0.467361i	$-0.845205\pi$
$3$	−0.0224040	+	0.0410298i	−0.0129349	+	0.0236886i	0.871132	+	0.491050i	$0.163387\pi$
$4$		0			0
$5$	2.13690	−	0.658540i	0.955649	−	0.294508i
$5$	2.13690	−	0.658540i	0.955649	−	0.294508i
$6$		0			0
$7$	2.31180	+	1.73059i	0.873777	+	0.654101i	0.939055	−	0.343766i	$-0.111703\pi$
$7$	2.31180	+	1.73059i	0.873777	+	0.654101i	−0.0652785	+	0.997867i	$0.520794\pi$
$8$		0			0
$9$	1.62074	+	2.52192i	0.540247	+	0.840641i
$10$		0			0
$11$	0.565611	+	0.258306i	0.170538	+	0.0778822i	0.498855	−	0.866686i	$-0.333754\pi$
$11$	0.565611	+	0.258306i	0.170538	+	0.0778822i	−0.328317	+	0.944568i	$0.606481\pi$
$12$		0			0
$13$	0.666316	+	0.890094i	0.184803	+	0.246868i	0.883369	−	0.468677i	$-0.155269\pi$
$13$	0.666316	+	0.890094i	0.184803	+	0.246868i	−0.698567	+	0.715545i	$0.746178\pi$
$14$		0			0
$15$	−0.0208552	+	0.102430i	−0.00538479	+	0.0264474i
$16$		0			0
$17$	−2.08532	−	0.149145i	−0.505765	−	0.0361730i	−0.183874	−	0.982950i	$-0.558864\pi$
$17$	−2.08532	−	0.149145i	−0.505765	−	0.0361730i	−0.321891	+	0.946777i	$0.604318\pi$
$18$		0			0
$19$	−1.43969	+	1.66149i	−0.330287	+	0.381171i	−0.896467	−	0.443110i	$-0.853875\pi$
$19$	−1.43969	+	1.66149i	−0.330287	+	0.381171i	0.566180	+	0.824281i	$0.308421\pi$
$20$		0			0
$21$	−0.122799	+	0.0560805i	−0.0267970	+	0.0122378i
$22$		0			0
$23$	−2.25231	+	4.23404i	−0.469639	+	0.882859i
$23$	−2.25231	+	4.23404i	−0.469639	+	0.882859i
$24$		0			0
$25$	4.13265	−	2.81446i	0.826530	−	0.562893i
$26$		0			0
$27$	−0.279672	+	0.0200025i	−0.0538229	+	0.00384949i
$28$		0			0
$29$	1.86944	−	1.61988i	0.347145	−	0.300803i	−0.463783	−	0.885949i	$-0.653508\pi$
$29$	1.86944	−	1.61988i	0.347145	−	0.300803i	0.810928	+	0.585146i	$0.198963\pi$
$30$		0			0
$31$	−8.11526	−	2.38286i	−1.45754	−	0.427974i	−0.545516	−	0.838101i	$-0.683666\pi$
$31$	−8.11526	−	2.38286i	−1.45754	−	0.427974i	−0.912028	+	0.410127i	$0.865484\pi$
$32$		0			0
$33$	−0.0232702	+	0.0174198i	−0.00405082	+	0.00303241i
$34$		0			0
$35$	6.07973	+	2.17568i	1.02766	+	0.367757i
$36$		0			0
$37$	0.190749	−	0.876858i	0.0313589	−	0.144155i	−0.958805	−	0.284064i	$-0.908317\pi$
$37$	0.190749	−	0.876858i	0.0313589	−	0.144155i	0.990164	+	0.139909i	$0.0446810\pi$
$38$		0			0
$39$	−0.0514485	+	0.00739718i	−0.00823836	+	0.00118450i
$40$		0			0
$41$	6.19326	+	3.98017i	0.967225	+	0.621597i	0.925988	−	0.377552i	$-0.123234\pi$
$41$	6.19326	+	3.98017i	0.967225	+	0.621597i	0.0412362	+	0.999149i	$0.486870\pi$
$42$		0			0
$43$	−5.01600	−	2.73894i	−0.764933	−	0.417685i	0.0488854	−	0.998804i	$-0.484433\pi$
$43$	−5.01600	−	2.73894i	−0.764933	−	0.417685i	−0.813818	+	0.581119i	$0.802615\pi$
$44$		0			0
$45$	5.12414	+	4.32176i	0.763862	+	0.644250i
$46$		0			0
$47$	1.83333	+	1.83333i	0.267418	+	0.267418i	0.828059	−	0.560641i	$-0.189445\pi$
$47$	1.83333	+	1.83333i	0.267418	+	0.267418i	−0.560641	+	0.828059i	$0.689445\pi$
$48$		0			0
$49$	0.377336	+	1.28509i	0.0539051	+	0.183584i
$50$		0			0
$51$	0.0528390	−	0.0822190i	0.00739893	−	0.0115130i
$52$		0			0
$53$	1.91884	−	2.56327i	0.263573	−	0.352092i	−0.649158	−	0.760654i	$-0.724879\pi$
$53$	1.91884	−	2.56327i	0.263573	−	0.352092i	0.912731	+	0.408561i	$0.133969\pi$
$54$		0			0
$55$	1.37876	+	0.179495i	0.185912	+	0.0242031i
$56$		0			0
$57$	−0.0359158	−	0.0962940i	−0.00475717	−	0.0127545i
$58$		0			0
$59$	6.13247	+	0.881716i	0.798379	+	0.114790i	0.529418	−	0.848361i	$-0.322410\pi$
$59$	6.13247	+	0.881716i	0.798379	+	0.114790i	0.268962	+	0.963151i	$0.413320\pi$
$60$		0			0
$61$	3.88373	−	13.2268i	0.497260	−	1.69351i	−0.202624	−	0.979257i	$-0.564947\pi$
$61$	3.88373	−	13.2268i	0.497260	−	1.69351i	0.699884	−	0.714256i	$-0.253235\pi$
$62$		0			0
$63$	−0.617588	+	8.63501i	−0.0778088	+	1.08791i
$64$		0			0
$65$	2.01001	+	1.46324i	0.249311	+	0.181493i
$66$		0			0
$67$	12.7829	+	4.76778i	1.56168	+	0.582477i	0.973987	−	0.226605i	$-0.0727627\pi$
$67$	12.7829	+	4.76778i	1.56168	+	0.582477i	0.587695	+	0.809082i	$0.300035\pi$
$68$		0			0
$69$	−0.123261	−	0.187271i	−0.0148389	−	0.0225448i
$70$		0			0
$71$	−0.404054	−	0.884756i	−0.0479524	−	0.105001i	0.884139	−	0.467223i	$-0.154746\pi$
$71$	−0.404054	−	0.884756i	−0.0479524	−	0.105001i	−0.932092	+	0.362222i	$0.882018\pi$
$72$		0			0
$73$	−0.272310	−	3.80740i	−0.0318715	−	0.445622i	−0.988184	−	0.153275i	$-0.951018\pi$
$73$	−0.272310	−	3.80740i	−0.0318715	−	0.445622i	0.956312	−	0.292348i	$-0.0944364\pi$
$74$		0			0
$75$	0.0228892	+	0.232617i	0.00264301	+	0.0268603i
$76$		0			0
$77$	0.860556	+	1.57599i	0.0980695	+	0.179601i
$78$		0			0
$79$	−0.310067	+	2.15657i	−0.0348853	+	0.242633i	−0.999801	−	0.0199256i	$-0.993657\pi$
$79$	−0.310067	+	2.15657i	−0.0348853	+	0.242633i	0.964916	+	0.262558i	$0.0845662\pi$
$80$		0			0
$81$	−3.73057	+	8.16880i	−0.414507	+	0.907645i
$82$		0			0
$83$	−10.2708	−	2.23428i	−1.12737	−	0.245244i	−0.390053	−	0.920792i	$-0.627543\pi$
$83$	−10.2708	−	2.23428i	−1.12737	−	0.245244i	−0.737316	+	0.675548i	$0.763907\pi$
$84$		0			0
$85$	−4.55434	+	1.05456i	−0.493987	+	0.114383i
$86$		0			0
$87$	0.0245804	+	0.112994i	0.00263530	+	0.0121143i
$88$		0			0
$89$	9.66802	−	2.83879i	1.02481	−	0.300911i	0.274210	−	0.961670i	$-0.411584\pi$
$89$	9.66802	−	2.83879i	1.02481	−	0.300911i	0.750598	+	0.660759i	$0.229765\pi$
$90$		0			0
$91$			3.21083i			0.336587i
$92$		0			0
$93$	0.279582	−	0.279582i	0.0289913	−	0.0289913i
$94$		0			0
$95$	−1.98230	+	4.49852i	−0.203380	+	0.461538i
$96$		0			0
$97$	−10.7495	+	2.33842i	−1.09145	+	0.237430i	−0.722050	−	0.691841i	$-0.756800\pi$
$97$	−10.7495	+	2.33842i	−1.09145	+	0.237430i	−0.369399	+	0.929271i	$0.620436\pi$
$98$		0			0
$99$	0.265282	+	1.84507i	0.0266618	+	0.185437i
$100$		0			0
$101$	3.59659	−	2.31139i	0.357874	−	0.229991i	−0.349332	−	0.936999i	$-0.613592\pi$
$101$	3.59659	−	2.31139i	0.357874	−	0.229991i	0.707206	+	0.707007i	$0.249955\pi$
$102$		0			0
$103$	3.53500	−	1.31849i	0.348314	−	0.129915i	−0.169217	−	0.985579i	$-0.554124\pi$
$103$	3.53500	−	1.31849i	0.348314	−	0.129915i	0.517531	+	0.855664i	$0.326851\pi$
$104$		0			0
$105$	−0.225478	+	0.200706i	−0.0220044	+	0.0195869i
$106$		0			0
$107$	−7.23107	+	3.94846i	−0.699054	+	0.381712i	−0.789133	−	0.614222i	$-0.789470\pi$
$107$	−7.23107	+	3.94846i	−0.699054	+	0.381712i	0.0900793	+	0.995935i	$0.471288\pi$
$108$		0			0
$109$	9.46629	+	10.9247i	0.906706	+	1.04639i	0.998717	+	0.0506366i	$0.0161250\pi$
$109$	9.46629	+	10.9247i	0.906706	+	1.04639i	−0.0920111	+	0.995758i	$0.529330\pi$
$110$		0			0
$111$	0.0317038	+	0.0274715i	0.00300919	+	0.00260748i
$112$		0			0
$113$	4.63290	−	12.4213i	0.435826	−	1.16850i	−0.514569	−	0.857449i	$-0.672048\pi$
$113$	4.63290	−	12.4213i	0.435826	−	1.16850i	0.950395	−	0.311046i	$-0.100679\pi$
$114$		0			0
$115$	−2.02466	+	10.5309i	−0.188801	+	0.982015i
$116$		0			0
$117$	−1.16482	+	3.12301i	−0.107688	+	0.288722i
$118$		0			0
$119$	−4.56273	−	3.95363i	−0.418265	−	0.362429i
$120$		0			0
$121$	−6.95027	−	8.02104i	−0.631843	−	0.729186i
$122$		0			0
$123$	−0.302059	+	0.164937i	−0.0272358	+	0.0148719i
$124$		0			0
$125$	6.97760	−	8.73573i	0.624096	−	0.781348i
$126$		0			0
$127$	−6.24728	+	2.33011i	−0.554356	+	0.206764i	−0.611000	−	0.791630i	$-0.709233\pi$
$127$	−6.24728	+	2.33011i	−0.554356	+	0.206764i	0.0566443	+	0.998394i	$0.481960\pi$
$128$		0			0
$129$	0.224757	−	0.144442i	0.0197887	−	0.0127174i
$130$		0			0
$131$	−1.65287	−	11.4959i	−0.144412	−	1.00440i	−0.925165	−	0.379565i	$-0.876074\pi$
$131$	−1.65287	−	11.4959i	−0.144412	−	1.00440i	0.780753	−	0.624839i	$-0.214836\pi$
$132$		0			0
$133$	−6.20361	+	1.34951i	−0.537921	+	0.117018i
$134$		0			0
$135$	−0.584458	+	0.226919i	−0.0503021	+	0.0195301i
$136$		0			0
$137$	−13.8908	+	13.8908i	−1.18677	+	1.18677i	−0.208819	+	0.977954i	$0.566962\pi$
$137$	−13.8908	+	13.8908i	−1.18677	+	1.18677i	−0.977954	+	0.208819i	$0.933038\pi$
$138$		0			0
$139$		−	12.3148i		−	1.04453i	−0.852784	−	0.522264i	$-0.825088\pi$
$139$		−	12.3148i		−	1.04453i	0.852784	−	0.522264i	$-0.174912\pi$
$140$		0			0
$141$	−0.116295	+	0.0341473i	−0.00979380	+	0.00287572i
$142$		0			0
$143$	0.146959	+	0.675560i	0.0122893	+	0.0564932i
$144$		0			0
$145$	2.92804	−	4.69260i	0.243160	−	0.389699i
$146$		0			0
$147$	−0.0611807	−	0.0133091i	−0.00504610	−	0.00109771i
$148$		0			0
$149$	3.32109	−	7.27217i	0.272074	−	0.595759i	−0.723439	−	0.690389i	$-0.757439\pi$
$149$	3.32109	−	7.27217i	0.272074	−	0.595759i	0.995513	+	0.0946298i	$0.0301667\pi$
$150$		0			0
$151$	3.34577	−	23.2704i	0.272275	−	1.89372i	−0.152318	−	0.988332i	$-0.548674\pi$
$151$	3.34577	−	23.2704i	0.272275	−	1.89372i	0.424593	−	0.905384i	$-0.360417\pi$
$152$		0			0
$153$	−3.00364	−	5.50075i	−0.242830	−	0.444709i
$154$		0			0
$155$	−18.9107	+	0.252311i	−1.51894	+	0.0202661i
$156$		0			0
$157$	0.434190	+	6.07076i	0.0346521	+	0.484500i	0.984914	+	0.173047i	$0.0553611\pi$
$157$	0.434190	+	6.07076i	0.0346521	+	0.484500i	−0.950262	+	0.311453i	$0.899184\pi$
$158$		0			0
$159$	0.0621809	+	0.136157i	0.00493127	+	0.0107980i
$160$		0			0
$161$	−12.5343	+	5.89042i	−0.987838	+	0.464230i
$162$		0			0
$163$	−7.57095	−	2.82382i	−0.593003	−	0.221179i	0.0350031	−	0.999387i	$-0.488856\pi$
$163$	−7.57095	−	2.82382i	−0.593003	−	0.221179i	−0.628006	+	0.778209i	$0.716129\pi$
$164$		0			0
$165$	−0.0382543	+	0.0525488i	−0.00297809	+	0.00409092i
$166$		0			0
$167$	−0.592237	+	8.28055i	−0.0458287	+	0.640768i	0.921683	+	0.387943i	$0.126814\pi$
$167$	−0.592237	+	8.28055i	−0.0458287	+	0.640768i	−0.967512	+	0.252825i	$0.918640\pi$
$168$		0			0
$169$	3.31423	−	11.2872i	0.254941	−	0.868249i
$170$		0			0
$171$	−6.52350	−	0.937938i	−0.498864	−	0.0717259i
$172$		0			0
$173$	0.906895	+	2.43148i	0.0689499	+	0.184862i	0.966854	−	0.255329i	$-0.0821836\pi$
$173$	0.906895	+	2.43148i	0.0689499	+	0.184862i	−0.897904	+	0.440190i	$0.854911\pi$
$174$		0			0
$175$	14.4245	+	0.645451i	1.09039	+	0.0487915i
$176$		0			0
$177$	−0.173568	+	0.231860i	−0.0130462	+	0.0174277i
$178$		0			0
$179$	0.0260598	−	0.0405498i	0.00194780	−	0.00303084i	−0.840278	−	0.542155i	$-0.817608\pi$
$179$	0.0260598	−	0.0405498i	0.00194780	−	0.00303084i	0.842226	+	0.539125i	$0.181245\pi$
$180$		0			0
$181$	−1.62901	−	5.54788i	−0.121083	−	0.412371i	0.876536	−	0.481336i	$-0.159848\pi$
$181$	−1.62901	−	5.54788i	−0.121083	−	0.412371i	−0.997619	+	0.0689653i	$0.978030\pi$
$182$		0			0
$183$	0.455681	+	0.455681i	0.0336849	+	0.0336849i
$184$		0			0
$185$	−0.169836	−	1.99937i	−0.0124866	−	0.146997i
$186$		0			0
$187$	−1.14096	−	0.623010i	−0.0834350	−	0.0455590i
$188$		0			0
$189$	−0.681161	−	0.437756i	−0.0495472	−	0.0318420i
$190$		0			0
$191$	8.15000	−	1.17179i	0.589713	−	0.0847880i	0.159003	−	0.987278i	$-0.449172\pi$
$191$	8.15000	−	1.17179i	0.589713	−	0.0847880i	0.430710	+	0.902490i	$0.358263\pi$
$192$		0			0
$193$	3.29926	−	15.1665i	0.237486	−	1.09171i	−0.691726	−	0.722160i	$-0.743149\pi$
$193$	3.29926	−	15.1665i	0.237486	−	1.09171i	0.929212	−	0.369546i	$-0.120487\pi$
$194$		0			0
$195$	−0.105069	+	0.0496879i	−0.00752414	+	0.00355823i
$196$		0			0
$197$	−2.21376	+	1.65720i	−0.157724	+	0.118070i	−0.675225	−	0.737612i	$-0.735953\pi$
$197$	−2.21376	+	1.65720i	−0.157724	+	0.118070i	0.517501	+	0.855683i	$0.326862\pi$
$198$		0			0
$199$	−18.4366	−	5.41346i	−1.30693	−	0.383750i	−0.447173	−	0.894448i	$-0.647569\pi$
$199$	−18.4366	−	5.41346i	−1.30693	−	0.383750i	−0.859760	+	0.510698i	$0.829387\pi$
$200$		0			0
$201$	−0.482010	+	0.417664i	−0.0339983	+	0.0294597i
$202$		0			0
$203$	7.12509	−	0.509597i	0.500083	−	0.0357667i
$204$		0			0
$205$	15.8555	+	4.42669i	1.10739	+	0.309173i
$206$		0			0
$207$	−14.3283	+	1.18214i	−0.995888	+	0.0821641i
$208$		0			0
$209$	−1.24347	+	0.567876i	−0.0860129	+	0.0392808i
$210$		0			0
$211$	1.83738	−	2.12045i	0.126490	−	0.145978i	−0.688972	−	0.724788i	$-0.741938\pi$
$211$	1.83738	−	2.12045i	0.126490	−	0.145978i	0.815462	+	0.578811i	$0.196483\pi$
$212$		0			0
$213$	0.0453538	+	0.00324377i	0.00310759	+	0.000222259i
$214$		0			0
$215$	−12.5224	−	2.54960i	−0.854019	−	0.173881i
$216$		0			0
$217$	−14.6371	−	19.5529i	−0.993630	−	1.32733i
$218$		0			0
$219$	0.162318	+	0.0741280i	0.0109684	+	0.00500911i
$220$		0			0
$221$	−1.25673	−	1.95551i	−0.0845369	−	0.131542i
$222$		0			0
$223$	−12.6841	−	9.49522i	−0.849392	−	0.635847i	0.0832984	−	0.996525i	$-0.473455\pi$
$223$	−12.6841	−	9.49522i	−0.849392	−	0.635847i	−0.932691	+	0.360678i	$0.882545\pi$
$224$		0			0
$225$	13.7958	+	5.86070i	0.919721	+	0.390714i
$226$		0			0
$227$	−6.23822	+	11.4244i	−0.414045	+	0.758267i	−0.998589	−	0.0530949i	$-0.983091\pi$
$227$	−6.23822	+	11.4244i	−0.414045	+	0.758267i	0.584544	+	0.811362i	$0.301273\pi$
$228$		0			0
$229$	−1.27982			−0.0845730			−0.0422865	−	0.999106i	$-0.513464\pi$
$229$	−1.27982			−0.0845730			−0.0422865	+	0.999106i	$0.513464\pi$
$230$		0			0
$231$	−0.0839425			−0.00552301
$232$		0			0
$233$	−7.58228	+	13.8859i	−0.496731	+	0.909696i	0.502257	+	0.864719i	$0.332503\pi$
$233$	−7.58228	+	13.8859i	−0.496731	+	0.909696i	−0.998988	+	0.0449770i	$0.985679\pi$
$234$		0			0
$235$	5.12495	+	2.71031i	0.334315	+	0.176801i
$236$		0			0
$237$	−0.0815368	−	0.0610377i	−0.00529638	−	0.00396482i
$238$		0			0
$239$	4.50993	+	7.01758i	0.291723	+	0.453930i	0.955920	−	0.293628i	$-0.0948627\pi$
$239$	4.50993	+	7.01758i	0.291723	+	0.453930i	−0.664197	+	0.747558i	$0.731226\pi$
$240$		0			0
$241$	−13.2858	−	6.06744i	−0.855816	−	0.390838i	−0.0613278	−	0.998118i	$-0.519534\pi$
$241$	−13.2858	−	6.06744i	−0.855816	−	0.390838i	−0.794488	+	0.607280i	$0.792261\pi$
$242$		0			0
$243$	−0.755673	−	1.00946i	−0.0484765	−	0.0647570i
$244$		0			0
$245$	1.65261	+	2.49761i	0.105581	+	0.159566i
$246$		0			0
$247$	−2.43817	−	0.174381i	−0.155137	−	0.0110956i
$248$		0			0
$249$	0.321779	−	0.371353i	0.0203919	−	0.0235335i
$250$		0			0
$251$	7.92879	−	3.62096i	0.500461	−	0.228553i	−0.149157	−	0.988813i	$-0.547656\pi$
$251$	7.92879	−	3.62096i	0.500461	−	0.228553i	0.649618	+	0.760261i	$0.274929\pi$
$252$		0			0
$253$	−2.36761	+	1.81304i	−0.148850	+	0.113985i
$254$		0			0
$255$	0.0587668	−	0.210490i	0.00368012	−	0.0131814i
$256$		0			0
$257$	−20.5547	+	1.47010i	−1.28217	+	0.0917025i	−0.695737	−	0.718297i	$-0.744922\pi$
$257$	−20.5547	+	1.47010i	−1.28217	+	0.0917025i	−0.586431	+	0.809999i	$0.699467\pi$
$258$		0			0
$259$	1.95845	−	1.69701i	0.121692	−	0.105447i
$260$		0			0
$261$	7.11507	+	2.08917i	0.440412	+	0.129317i
$262$		0			0
$263$	4.58938	−	3.43557i	0.282993	−	0.211846i	−0.448346	−	0.893860i	$-0.647987\pi$
$263$	4.58938	−	3.43557i	0.282993	−	0.211846i	0.731339	+	0.682014i	$0.238896\pi$
$264$		0			0
$265$	2.41235	−	6.74108i	0.148189	−	0.414101i
$266$		0			0
$267$	−0.100127	+	0.460277i	−0.00612769	+	0.0281685i
$268$		0			0
$269$	−5.04128	+	0.724827i	−0.307373	+	0.0441935i	−0.294275	−	0.955721i	$-0.595078\pi$
$269$	−5.04128	+	0.724827i	−0.307373	+	0.0441935i	−0.0130973	+	0.999914i	$0.504169\pi$
$270$		0			0
$271$	17.3028	+	11.1198i	1.05107	+	0.675481i	0.947700	−	0.319162i	$-0.103401\pi$
$271$	17.3028	+	11.1198i	1.05107	+	0.675481i	0.103369	+	0.994643i	$0.467038\pi$
$272$		0			0
$273$	−0.131740	−	0.0719355i	−0.00797327	−	0.00435373i
$274$		0			0
$275$	3.06447	−	0.524404i	0.184794	−	0.0316228i
$276$		0			0
$277$	19.5001	+	19.5001i	1.17165	+	1.17165i	0.981817	+	0.189831i	$0.0607940\pi$
$277$	19.5001	+	19.5001i	1.17165	+	1.17165i	0.189831	+	0.981817i	$0.439206\pi$
$278$		0			0
$279$	−7.14336	−	24.3280i	−0.427662	−	1.45648i
$280$		0			0
$281$	−15.2584	+	23.7425i	−0.910239	+	1.41636i	−0.00103862	+	0.999999i	$0.500331\pi$
$281$	−15.2584	+	23.7425i	−0.910239	+	1.41636i	−0.909200	+	0.416360i	$0.863306\pi$
$282$		0			0
$283$	−7.93155	+	10.5953i	−0.471482	+	0.629826i	−0.971741	−	0.236050i	$-0.924147\pi$
$283$	−7.93155	+	10.5953i	−0.471482	+	0.629826i	0.500259	+	0.865876i	$0.333238\pi$
$284$		0			0
$285$	−0.140162	−	0.182118i	−0.00830247	−	0.0107878i
$286$		0			0
$287$	7.42952	+	19.9193i	0.438551	+	1.17580i
$288$		0			0
$289$	−12.5006	−	1.79732i	−0.735331	−	0.105725i
$290$		0			0
$291$	0.144887	−	0.493441i	0.00849345	−	0.0289260i
$292$		0			0
$293$	1.13358	−	15.8495i	0.0662245	−	0.925940i	−0.850386	−	0.526159i	$-0.823632\pi$
$293$	1.13358	−	15.8495i	0.0662245	−	0.925940i	0.916611	−	0.399781i	$-0.130914\pi$
$294$		0			0
$295$	13.6851	−	2.15434i	0.796777	−	0.125431i
$296$		0			0
$297$	−0.163352	−	0.0609273i	−0.00947867	−	0.00353536i
$298$		0			0
$299$	−5.26944	+	0.816442i	−0.304740	+	0.0472161i
$300$		0			0
$301$	−6.85599	−	15.0125i	−0.395172	−	0.865307i
$302$		0			0
$303$	0.0142579	+	0.199352i	0.000819095	+	0.0114524i
$304$		0			0
$305$	−0.411232	−	30.8218i	−0.0235471	−	1.76485i
$306$		0			0
$307$	−5.46708	−	10.0122i	−0.312023	−	0.571427i	0.673861	−	0.738858i	$-0.264635\pi$
$307$	−5.46708	−	10.0122i	−0.312023	−	0.571427i	−0.985884	+	0.167431i	$0.946453\pi$
$308$		0			0
$309$	−0.0251008	+	0.174580i	−0.00142794	+	0.00993151i
$310$		0			0
$311$	4.59387	−	10.0592i	0.260494	−	0.570403i	−0.733518	−	0.679670i	$-0.762123\pi$
$311$	4.59387	−	10.0592i	0.260494	−	0.570403i	0.994012	+	0.109267i	$0.0348503\pi$
$312$		0			0
$313$	−15.0197	−	3.26733i	−0.848963	−	0.184681i	−0.233021	−	0.972472i	$-0.574861\pi$
$313$	−15.0197	−	3.26733i	−0.848963	−	0.184681i	−0.615942	+	0.787791i	$0.711225\pi$
$314$		0			0
$315$	4.36678	+	18.8588i	0.246040	+	1.06257i
$316$		0			0
$317$	5.03014	+	23.1232i	0.282521	+	1.29873i	0.871426	+	0.490526i	$0.163195\pi$
$317$	5.03014	+	23.1232i	0.282521	+	1.29873i	−0.588905	+	0.808202i	$0.700441\pi$
$318$		0			0
$319$	1.47580	−	0.433333i	0.0826288	−	0.0242620i
$320$		0			0
$321$		−	0.385151i		−	0.0214970i
$322$		0			0
$323$	3.25002	−	3.25002i	0.180836	−	0.180836i
$324$		0			0
$325$	5.25879	+	1.80312i	0.291705	+	0.100019i
$326$		0			0
$327$	−0.660320	+	0.143644i	−0.0365158	+	0.00794353i
$328$		0			0
$329$	1.06554	+	7.41101i	0.0587453	+	0.408582i
$330$		0			0
$331$	0.748852	−	0.481258i	0.0411606	−	0.0264523i	−0.519899	−	0.854228i	$-0.674030\pi$
$331$	0.748852	−	0.481258i	0.0411606	−	0.0264523i	0.561059	+	0.827776i	$0.310394\pi$
$332$		0			0
$333$	2.52052	−	0.940106i	0.138124	−	0.0515175i
$334$		0			0
$335$	30.4555	+	1.77019i	1.66396	+	0.0967158i
$336$		0			0
$337$	−9.68813	+	5.29012i	−0.527746	+	0.288171i	−0.720950	−	0.692987i	$-0.756294\pi$
$337$	−9.68813	+	5.29012i	−0.527746	+	0.288171i	0.193203	+	0.981159i	$0.438112\pi$
$338$		0			0
$339$	0.405847	+	0.468373i	0.0220426	+	0.0254385i
$340$		0			0
$341$	−3.97458	−	3.44399i	−0.215235	−	0.186503i
$342$		0			0
$343$	5.71262	−	15.3161i	0.308453	−	0.826994i
$344$		0			0
$345$	−0.386722	−	0.319007i	−0.0208204	−	0.0171747i
$346$		0			0
$347$	−2.81036	+	7.53487i	−0.150868	+	0.404493i	−0.990295	−	0.138979i	$-0.955618\pi$
$347$	−2.81036	+	7.53487i	−0.150868	+	0.404493i	0.839427	+	0.543472i	$0.182891\pi$
$348$		0			0
$349$	19.0865	+	16.5386i	1.02168	+	0.885289i	0.993445	−	0.114313i	$-0.0364666\pi$
$349$	19.0865	+	16.5386i	1.02168	+	0.885289i	0.0282326	+	0.999601i	$0.491012\pi$
$350$		0			0
$351$	−0.204154	−	0.235606i	−0.0108969	−	0.0125757i
$352$		0			0
$353$	−24.4128	+	13.3304i	−1.29936	+	0.709507i	−0.971908	−	0.235360i	$-0.924373\pi$
$353$	−24.4128	+	13.3304i	−1.29936	+	0.709507i	−0.327456	+	0.944866i	$0.606191\pi$
$354$		0			0
$355$	−1.44607	−	1.62454i	−0.0767494	−	0.0862219i
$356$		0			0
$357$	0.264440	−	0.0986311i	0.0139957	−	0.00522011i
$358$		0			0
$359$	15.5908	−	10.0196i	0.822853	−	0.528816i	−0.0601462	−	0.998190i	$-0.519157\pi$
$359$	15.5908	−	10.0196i	0.822853	−	0.528816i	0.883000	+	0.469374i	$0.155520\pi$
$360$		0			0
$361$	2.01614	+	14.0226i	0.106113	+	0.738030i
$362$		0			0
$363$	0.484816	−	0.105465i	0.0254462	−	0.00553549i
$364$		0			0
$365$	−3.08922	−	7.95669i	−0.161697	−	0.416472i
$366$		0			0
$367$	14.6761	−	14.6761i	0.766085	−	0.766085i	−0.211330	−	0.977415i	$-0.567779\pi$
$367$	14.6761	−	14.6761i	0.766085	−	0.766085i	0.977415	+	0.211330i	$0.0677793\pi$
$368$		0			0
$369$			22.0697i			1.14890i
$370$		0			0
$371$	8.87194	−	2.60504i	0.460608	−	0.135247i
$372$		0			0
$373$	−2.13339	−	9.80702i	−0.110463	−	0.507788i	−0.998817	−	0.0486298i	$-0.984515\pi$
$373$	−2.13339	−	9.80702i	−0.110463	−	0.507788i	0.888354	−	0.459159i	$-0.151849\pi$
$374$		0			0
$375$	0.202100	+	0.482005i	0.0104364	+	0.0248906i
$376$		0			0
$377$	2.68748	+	0.584625i	0.138412	+	0.0301097i
$378$		0			0
$379$	9.57218	−	20.9601i	0.491690	−	1.07665i	−0.487392	−	0.873183i	$-0.662052\pi$
$379$	9.57218	−	20.9601i	0.491690	−	1.07665i	0.979082	−	0.203467i	$-0.0652210\pi$
$380$		0			0
$381$	0.0443597	−	0.308529i	0.00227262	−	0.0158064i
$382$		0			0
$383$	11.7921	+	21.5957i	0.602549	+	1.10349i	0.983843	+	0.179032i	$0.0572967\pi$
$383$	11.7921	+	21.5957i	0.602549	+	1.10349i	−0.381294	+	0.924454i	$0.624521\pi$
$384$		0			0
$385$	2.87677	+	2.80102i	0.146614	+	0.142753i
$386$		0			0
$387$	−1.22224	−	17.0891i	−0.0621297	−	0.868687i
$388$		0			0
$389$	5.42505	+	11.8792i	0.275061	+	0.602300i	0.995866	−	0.0908387i	$-0.0289548\pi$
$389$	5.42505	+	11.8792i	0.275061	+	0.602300i	−0.720805	+	0.693138i	$0.756227\pi$
$390$		0			0
$391$	5.32828	−	8.49342i	0.269463	−	0.429531i
$392$		0			0
$393$	0.508707	+	0.189738i	0.0256609	+	0.00957101i
$394$		0			0
$395$	0.757604	+	4.81255i	0.0381192	+	0.242146i
$396$		0			0
$397$	0.516506	−	7.22169i	0.0259227	−	0.362446i	−0.967890	−	0.251375i	$-0.919117\pi$
$397$	0.516506	−	7.22169i	0.0259227	−	0.362446i	0.993812	−	0.111071i	$-0.0354282\pi$
$398$		0			0
$399$	0.0836153	−	0.284768i	0.00418600	−	0.0142562i
$400$		0			0
$401$	−37.5899	−	5.40462i	−1.87715	−	0.269894i	−0.893377	−	0.449307i	$-0.851671\pi$
$401$	−37.5899	−	5.40462i	−1.87715	−	0.269894i	−0.983774	+	0.179413i	$0.942580\pi$
$402$		0			0
$403$	−3.28636	−	8.81108i	−0.163705	−	0.438911i
$404$		0			0
$405$	−2.59235	+	19.9126i	−0.128815	+	0.989465i
$406$		0			0
$407$	0.334387	−	0.446689i	0.0165750	−	0.0221416i
$408$		0			0
$409$	−8.61194	+	13.4004i	−0.425833	+	0.662609i	−0.986185	−	0.165645i	$-0.947029\pi$
$409$	−8.61194	+	13.4004i	−0.425833	+	0.662609i	0.560352	+	0.828254i	$0.310666\pi$
$410$		0			0
$411$	−0.258728	−	0.881148i	−0.0127621	−	0.0434638i
$412$		0			0
$413$	12.6511	+	12.6511i	0.622521	+	0.622521i
$414$		0			0
$415$	−23.4190	+	1.98932i	−1.14959	+	0.0976520i
$416$		0			0
$417$	0.505274	+	0.275901i	0.0247434	+	0.0135109i
$418$		0			0
$419$	−10.2159	−	6.56534i	−0.499078	−	0.320738i	0.266770	−	0.963760i	$-0.414044\pi$
$419$	−10.2159	−	6.56534i	−0.499078	−	0.320738i	−0.765847	+	0.643023i	$0.777680\pi$
$420$		0			0
$421$	24.3000	−	3.49382i	1.18431	−	0.170278i	0.478117	−	0.878296i	$-0.341320\pi$
$421$	24.3000	−	3.49382i	1.18431	−	0.170278i	0.706194	+	0.708018i	$0.250410\pi$
$422$		0			0
$423$	−1.65216	+	7.59485i	−0.0803307	+	0.369274i
$424$		0			0
$425$	−9.03767	+	5.25270i	−0.438392	+	0.254793i
$426$		0			0
$427$	31.8685	−	23.8564i	1.54222	−	1.15449i
$428$		0			0
$429$	−0.0310106	−	0.00910553i	−0.00149721	−	0.000439619i
$430$		0			0
$431$	−4.43914	+	3.84653i	−0.213826	+	0.185281i	−0.755188	−	0.655509i	$-0.772454\pi$
$431$	−4.43914	+	3.84653i	−0.213826	+	0.185281i	0.541362	+	0.840790i	$0.317909\pi$
$432$		0			0
$433$	−16.3463	+	1.16911i	−0.785555	+	0.0561840i	−0.458353	−	0.888770i	$-0.651560\pi$
$433$	−16.3463	+	1.16911i	−0.785555	+	0.0561840i	−0.327202	+	0.944954i	$0.606106\pi$
$434$		0			0
$435$	0.126937	+	0.225270i	0.00608617	+	0.0108009i
$436$		0			0
$437$	−3.79218	−	9.83787i	−0.181405	−	0.470609i
$438$		0			0
$439$	−8.36448	+	3.81993i	−0.399215	+	0.182315i	−0.604897	−	0.796303i	$-0.706786\pi$
$439$	−8.36448	+	3.81993i	−0.399215	+	0.182315i	0.205682	+	0.978619i	$0.434059\pi$
$440$		0			0
$441$	−2.62933	+	3.03440i	−0.125206	+	0.144495i
$442$		0			0
$443$	27.1784	+	1.94384i	1.29129	+	0.0923546i	0.700021	−	0.714122i	$-0.253174\pi$
$443$	27.1784	+	1.94384i	1.29129	+	0.0923546i	0.591265	+	0.806477i	$0.298629\pi$
$444$		0			0
$445$	18.7901	−	12.4330i	0.890736	−	0.589380i
$446$		0			0
$447$	0.223970	+	0.299189i	0.0105934	+	0.0141512i
$448$		0			0
$449$	9.78375	+	4.46809i	0.461724	+	0.210862i	0.632675	−	0.774417i	$-0.281957\pi$
$449$	9.78375	+	4.46809i	0.461724	+	0.210862i	−0.170951	+	0.985279i	$0.554684\pi$
$450$		0			0
$451$	2.47488	+	3.85098i	0.116537	+	0.181336i
$452$		0			0
$453$	0.879821	+	0.658626i	0.0413376	+	0.0309449i
$454$		0			0
$455$	2.11446	+	6.86122i	0.0991276	+	0.321659i
$456$		0			0
$457$	10.5034	−	19.2356i	0.491330	−	0.899804i	−0.507932	−	0.861397i	$-0.669590\pi$
$457$	10.5034	−	19.2356i	0.491330	−	0.899804i	0.999262	−	0.0384067i	$-0.0122282\pi$
$458$		0			0
$459$	0.586190			0.0273610
$460$		0			0
$461$	5.44735			0.253709			0.126854	−	0.991921i	$-0.459512\pi$
$461$	5.44735			0.253709			0.126854	+	0.991921i	$0.459512\pi$
$462$		0			0
$463$	−7.65647	+	14.0218i	−0.355826	+	0.651647i	−0.992873	−	0.119178i	$-0.961974\pi$
$463$	−7.65647	+	14.0218i	−0.355826	+	0.651647i	0.637046	+	0.770825i	$0.280156\pi$
$464$		0			0
$465$	0.413322	−	0.781555i	0.0191674	−	0.0362437i
$466$		0			0
$467$	27.3138	+	20.4468i	1.26393	+	0.946166i	0.999832	−	0.0183300i	$-0.00583496\pi$
$467$	27.3138	+	20.4468i	1.26393	+	0.946166i	0.264098	+	0.964496i	$0.414926\pi$
$468$		0			0
$469$	21.3004	+	33.1441i	0.983562	+	1.53045i
$470$		0			0
$471$	−0.258810	−	0.118195i	−0.0119253	−	0.00544612i
$472$		0			0
$473$	−2.12962	−	2.84484i	−0.0979200	−	0.130806i
$474$		0			0
$475$	−1.27353	+	10.9183i	−0.0584333	+	0.500965i
$476$		0			0
$477$	9.57431	+	0.684768i	0.438378	+	0.0313534i
$478$		0			0
$479$	7.08995	−	8.18224i	0.323948	−	0.373856i	−0.570293	−	0.821441i	$-0.693170\pi$
$479$	7.08995	−	8.18224i	0.323948	−	0.373856i	0.894241	+	0.447585i	$0.147716\pi$
$480$		0			0
$481$	0.907585	−	0.414480i	0.0413823	−	0.0188987i
$482$		0			0
$483$	0.0391346	−	0.646248i	0.00178068	−	0.0294053i
$484$		0			0
$485$	−21.4307	+	12.0759i	−0.973117	+	0.548341i
$486$		0			0
$487$	−17.3804	+	1.24307i	−0.787581	+	0.0563289i	−0.459335	−	0.888263i	$-0.651912\pi$
$487$	−17.3804	+	1.24307i	−0.787581	+	0.0563289i	−0.328246	+	0.944592i	$0.606458\pi$
$488$		0			0
$489$	0.285480	−	0.247370i	0.0129099	−	0.0111865i
$490$		0			0
$491$	8.92733	+	2.62130i	0.402885	+	0.118298i	0.476896	−	0.878960i	$-0.341762\pi$
$491$	8.92733	+	2.62130i	0.402885	+	0.118298i	−0.0740112	+	0.997257i	$0.523580\pi$
$492$		0			0
$493$	−4.13997	+	3.09915i	−0.186455	+	0.139579i
$494$		0			0
$495$	1.78193	+	3.76803i	0.0800920	+	0.169360i
$496$		0			0
$497$	0.597057	−	2.74463i	0.0267817	−	0.123113i
$498$		0			0
$499$	8.96005	−	1.28826i	0.401107	−	0.0576705i	0.0611905	−	0.998126i	$-0.480510\pi$
$499$	8.96005	−	1.28826i	0.401107	−	0.0576705i	0.339916	+	0.940456i	$0.389601\pi$
$500$		0			0
$501$	−0.326481	−	0.209817i	−0.0145861	−	0.00937392i
$502$		0			0
$503$	−4.76877	−	2.60394i	−0.212629	−	0.116104i	0.369406	−	0.929268i	$-0.379561\pi$
$503$	−4.76877	−	2.60394i	−0.212629	−	0.116104i	−0.582034	+	0.813164i	$0.697743\pi$
$504$		0			0
$505$	6.16339	−	7.30769i	0.274267	−	0.325188i
$506$		0			0
$507$	0.388862	+	0.388862i	0.0172699	+	0.0172699i
$508$		0			0
$509$	7.09233	+	24.1543i	0.314362	+	1.07062i	0.953466	+	0.301499i	$0.0974870\pi$
$509$	7.09233	+	24.1543i	0.314362	+	1.07062i	−0.639104	+	0.769120i	$0.720695\pi$
$510$		0			0
$511$	5.95951	−	9.27318i	0.263633	−	0.410222i
$512$		0			0
$513$	0.369406	−	0.493469i	0.0163097	−	0.0217872i
$514$		0			0
$515$	6.68566	−	5.14541i	0.294605	−	0.226734i
$516$		0			0
$517$	0.563391	+	1.51051i	0.0247779	+	0.0664321i
$518$		0			0
$519$	−0.120081	−	0.0172651i	−0.00527098	−	0.000757853i
$520$		0			0
$521$	−10.1091	+	34.4283i	−0.442886	+	1.50833i	0.371735	+	0.928339i	$0.378763\pi$
$521$	−10.1091	+	34.4283i	−0.442886	+	1.50833i	−0.814621	+	0.579994i	$0.803055\pi$
$522$		0			0
$523$	2.87793	−	40.2388i	0.125843	−	1.75952i	−0.407115	−	0.913377i	$-0.633465\pi$
$523$	2.87793	−	40.2388i	0.125843	−	1.75952i	0.532958	−	0.846142i	$-0.321080\pi$
$524$		0			0
$525$	−0.349650	+	0.577375i	−0.0152600	+	0.0251987i
$526$		0			0
$527$	16.5676	+	6.17938i	0.721694	+	0.269178i
$528$		0			0
$529$	−12.8542	−	19.0727i	−0.558879	−	0.829250i
$530$		0			0
$531$	7.71552	+	16.8946i	0.334825	+	0.733165i
$532$		0			0
$533$	0.583946	+	8.16463i	0.0252935	+	0.353649i
$534$		0			0
$535$	−12.8518	+	13.1994i	−0.555633	+	0.570660i
$536$		0			0
$537$	0.00107991	+	0.00197771i	4.66015e−5	+	8.53444e-5i
$538$		0			0
$539$	−0.118520	+	0.824327i	−0.00510503	+	0.0355063i
$540$		0			0
$541$	9.00737	−	19.7234i	0.387257	−	0.847975i	−0.611148	−	0.791516i	$-0.709292\pi$
$541$	9.00737	−	19.7234i	0.387257	−	0.847975i	0.998405	−	0.0564583i	$-0.0179808\pi$
$542$		0			0
$543$	0.264125	+	0.0574569i	0.0113347	+	0.00246571i
$544$		0			0
$545$	27.4228	+	17.1110i	1.17466	+	0.732954i
$546$		0			0
$547$	2.31948	+	10.6625i	0.0991738	+	0.455895i	0.999774	+	0.0212467i	$0.00676354\pi$
$547$	2.31948	+	10.6625i	0.0991738	+	0.455895i	−0.900600	+	0.434648i	$0.856873\pi$
$548$		0			0
$549$	39.6514	−	11.6427i	1.69228	−	0.496898i
$550$		0			0
$551$			5.43816i			0.231673i
$552$		0			0
$553$	−4.44894	+	4.44894i	−0.189188	+	0.189188i
$554$		0			0
$555$	0.0858388	+	0.0378255i	0.00364366	+	0.00160560i
$556$		0			0
$557$	−10.1142	+	2.20022i	−0.428554	+	0.0932263i	−0.421669	−	0.906750i	$-0.638555\pi$
$557$	−10.1142	+	2.20022i	−0.428554	+	0.0932263i	−0.00688568	+	0.999976i	$0.502192\pi$
$558$		0			0
$559$	−0.904324	−	6.28971i	−0.0382488	−	0.266027i
$560$		0			0
$561$	0.0511240	−	0.0328554i	0.00215846	−	0.00138716i
$562$		0			0
$563$	−15.4906	+	5.77770i	−0.652851	+	0.243501i	−0.653996	−	0.756498i	$-0.726908\pi$
$563$	−15.4906	+	5.77770i	−0.652851	+	0.243501i	0.00114429	+	0.999999i	$0.499636\pi$
$564$		0			0
$565$	1.72011	−	29.5939i	0.0723655	−	1.24503i
$566$		0			0
$567$	−22.7611	+	12.4285i	−0.955878	+	0.521949i
$568$		0			0
$569$	3.37859	+	3.89910i	0.141638	+	0.163459i	0.822136	−	0.569291i	$-0.192782\pi$
$569$	3.37859	+	3.89910i	0.141638	+	0.163459i	−0.680498	+	0.732750i	$0.738237\pi$
$570$		0			0
$571$	−13.9138	−	12.0564i	−0.582275	−	0.504544i	0.313182	−	0.949693i	$-0.398605\pi$
$571$	−13.9138	−	12.0564i	−0.582275	−	0.504544i	−0.895456	+	0.445149i	$0.853151\pi$
$572$		0			0
$573$	−0.134514	+	0.360646i	−0.00561940	+	0.0150662i
$574$		0			0
$575$	2.60855	+	23.8369i	0.108784	+	0.994065i
$576$		0			0
$577$	−11.0657	+	29.6682i	−0.460670	+	1.23510i	0.474296	+	0.880365i	$0.342703\pi$
$577$	−11.0657	+	29.6682i	−0.460670	+	1.23510i	−0.934966	+	0.354738i	$0.884570\pi$
$578$		0			0
$579$	0.548361	+	0.475158i	0.0227891	+	0.0197469i
$580$		0			0
$581$	−19.8774	−	22.9398i	−0.824654	−	0.951702i
$582$		0			0
$583$	1.74743	−	0.954166i	0.0723710	−	0.0395175i
$584$		0			0
$585$	−0.432477	+	7.44063i	−0.0178807	+	0.307632i
$586$		0			0
$587$	16.4230	−	6.12545i	0.677848	−	0.252824i	0.0131249	−	0.999914i	$-0.495822\pi$
$587$	16.4230	−	6.12545i	0.677848	−	0.252824i	0.664723	+	0.747089i	$0.268549\pi$
$588$		0			0
$589$	15.6425	−	10.0528i	0.644539	−	0.414220i
$590$		0			0
$591$	−0.0183976	−	0.127958i	−0.000756775	−	0.00526349i
$592$		0			0
$593$	−0.0623474	+	0.0135628i	−0.00256030	+	0.000556959i	−0.213845	−	0.976868i	$-0.568599\pi$
$593$	−0.0623474	+	0.0135628i	−0.00256030	+	0.000556959i	0.211285	+	0.977425i	$0.432235\pi$
$594$		0			0
$595$	−12.3537	−	5.44376i	−0.506453	−	0.223172i
$596$		0			0
$597$	0.635166	−	0.635166i	0.0259956	−	0.0259956i
$598$		0			0
$599$			22.7964i			0.931437i	0.884933	+	0.465719i	$0.154204\pi$
$599$			22.7964i			0.931437i	−0.884933	+	0.465719i	$0.845796\pi$
$600$		0			0
$601$	35.2693	−	10.3560i	1.43867	−	0.422430i	0.532888	−	0.846186i	$-0.321107\pi$
$601$	35.2693	−	10.3560i	1.43867	−	0.422430i	0.905777	+	0.423755i	$0.139288\pi$
$602$		0			0
$603$	8.69382	+	39.9649i	0.354040	+	1.62749i
$604$		0			0
$605$	−20.1342	−	12.5631i	−0.818571	−	0.510763i
$606$		0			0
$607$	28.8501	+	6.27596i	1.17099	+	0.254733i	0.755676	−	0.654945i	$-0.227308\pi$
$607$	28.8501	+	6.27596i	1.17099	+	0.254733i	0.415313	+	0.909678i	$0.363672\pi$
$608$		0			0
$609$	−0.138722	+	0.303758i	−0.00562129	+	0.0123089i
$610$		0			0
$611$	−0.410258	+	2.85341i	−0.0165973	+	0.115437i
$612$		0			0
$613$	12.2521	+	22.4381i	0.494859	+	0.906267i	0.999088	+	0.0426970i	$0.0135950\pi$
$613$	12.2521	+	22.4381i	0.494859	+	0.906267i	−0.504229	+	0.863570i	$0.668223\pi$
$614$		0			0
$615$	−0.536852	+	0.551371i	−0.0216479	+	0.0222334i
$616$		0			0
$617$	−2.14810	−	30.0344i	−0.0864793	−	1.20914i	−0.836591	−	0.547828i	$-0.815455\pi$
$617$	−2.14810	−	30.0344i	−0.0864793	−	1.20914i	0.750112	−	0.661311i	$-0.230000\pi$
$618$		0			0
$619$	14.7832	+	32.3707i	0.594188	+	1.30109i	0.932878	+	0.360192i	$0.117289\pi$
$619$	14.7832	+	32.3707i	0.594188	+	1.30109i	−0.338691	+	0.940898i	$0.609984\pi$
$620$		0			0
$621$	0.545216	−	1.22920i	0.0218788	−	0.0493259i
$622$		0			0
$623$	27.2633	+	10.1687i	1.09228	+	0.407399i
$624$		0			0
$625$	9.15759	−	23.2624i	0.366303	−	0.930495i
$626$		0			0
$627$	0.00455893	−	0.0637422i	0.000182066	−	0.00254562i
$628$		0			0
$629$	−0.528552	+	1.80008i	−0.0210748	+	0.0717740i
$630$		0			0
$631$	−44.0286	−	6.33036i	−1.75275	−	0.252008i	−0.810220	−	0.586125i	$-0.800653\pi$
$631$	−44.0286	−	6.33036i	−1.75275	−	0.252008i	−0.942531	+	0.334118i	$0.891562\pi$
$632$		0			0
$633$	0.0458371	+	0.122894i	0.00182186	+	0.00488459i
$634$		0			0
$635$	−11.8153	+	9.09329i	−0.468876	+	0.360856i
$636$		0			0
$637$	−0.892423	+	1.19214i	−0.0353591	+	0.0472342i
$638$		0			0
$639$	1.57642	−	2.45295i	0.0623621	−	0.0970373i
$640$		0			0
$641$	3.57248	+	12.1667i	0.141104	+	0.480557i	0.999472	−	0.0324770i	$-0.0103396\pi$
$641$	3.57248	+	12.1667i	0.141104	+	0.480557i	−0.858368	+	0.513034i	$0.828521\pi$
$642$		0			0
$643$	−25.5764	−	25.5764i	−1.00863	−	1.00863i	−0.999962	−	0.00867061i	$-0.997240\pi$
$643$	−25.5764	−	25.5764i	−1.00863	−	1.00863i	−0.00867061	−	0.999962i	$-0.502760\pi$
$644$		0			0
$645$	0.385161	−	0.456670i	0.0151657	−	0.0179814i
$646$		0			0
$647$	7.68042	+	4.19382i	0.301948	+	0.164876i	0.623080	−	0.782158i	$-0.285881\pi$
$647$	7.68042	+	4.19382i	0.301948	+	0.164876i	−0.321131	+	0.947035i	$0.604063\pi$
$648$		0			0
$649$	3.24084	+	2.08276i	0.127214	+	0.0817555i
$650$		0			0
$651$	1.13018	−	0.162495i	0.0442952	−	0.00636869i
$652$		0			0
$653$	3.73723	−	17.1798i	0.146249	−	0.672296i	−0.844383	−	0.535740i	$-0.820033\pi$
$653$	3.73723	−	17.1798i	0.146249	−	0.672296i	0.990632	−	0.136556i	$-0.0436035\pi$
$654$		0			0
$655$	−11.1025	−	23.4771i	−0.433812	−	0.917328i
$656$		0			0
$657$	9.16062	−	6.85755i	0.357390	−	0.267539i
$658$		0			0
$659$	−45.1308	−	13.2516i	−1.75805	−	0.516210i	−0.766085	−	0.642739i	$-0.777798\pi$
$659$	−45.1308	−	13.2516i	−1.75805	−	0.516210i	−0.991963	+	0.126529i	$0.959616\pi$
$660$		0			0
$661$	−5.93565	+	5.14327i	−0.230870	+	0.200050i	−0.762612	−	0.646857i	$-0.776083\pi$
$661$	−5.93565	+	5.14327i	−0.230870	+	0.200050i	0.531742	+	0.846907i	$0.321538\pi$
$662$		0			0
$663$	0.108390	−	0.00775221i	0.00420952	−	0.000301071i
$664$		0			0
$665$	−12.3678	+	6.96910i	−0.479601	+	0.270250i
$666$		0			0
$667$	2.64807	+	11.5637i	0.102534	+	0.447749i
$668$		0			0
$669$	0.673762	−	0.307697i	0.0260492	−	0.0118963i
$670$		0			0
$671$	5.61323	−	6.47801i	0.216696	−	0.250081i
$672$		0			0
$673$	26.0220	+	1.86113i	1.00307	+	0.0717412i	0.563202	−	0.826319i	$-0.309569\pi$
$673$	26.0220	+	1.86113i	1.00307	+	0.0717412i	0.439872	+	0.898061i	$0.355024\pi$
$674$		0			0
$675$	−1.09949	+	0.869791i	−0.0423194	+	0.0334783i
$676$		0			0
$677$	−29.1494	−	38.9391i	−1.12030	−	1.49655i	−0.844669	−	0.535289i	$-0.820203\pi$
$677$	−29.1494	−	38.9391i	−1.12030	−	1.49655i	−0.275635	−	0.961262i	$-0.588888\pi$
$678$		0			0
$679$	−28.8976	−	13.1971i	−1.10899	−	0.506457i
$680$		0			0
$681$	−0.328982	−	0.511906i	−0.0126066	−	0.0196163i
$682$		0			0
$683$	33.9979	+	25.4505i	1.30089	+	0.973837i	0.999795	+	0.0202434i	$0.00644413\pi$
$683$	33.9979	+	25.4505i	1.30089	+	0.973837i	0.301098	+	0.953593i	$0.402647\pi$
$684$		0			0
$685$	−20.5356	+	38.8309i	−0.784625	+	1.48365i
$686$		0			0
$687$	0.0286731	−	0.0525109i	0.00109395	−	0.00200341i
$688$		0			0
$689$	3.56011			0.135629
$690$		0			0
$691$	18.2417			0.693947			0.346974	−	0.937875i	$-0.387209\pi$
$691$	18.2417			0.693947			0.346974	+	0.937875i	$0.387209\pi$
$692$		0			0
$693$	−2.57979	+	4.72453i	−0.0979980	+	0.179470i
$694$		0			0
$695$	−8.10979	−	26.3154i	−0.307622	−	0.998202i
$696$		0			0
$697$	−12.3213	−	9.22363i	−0.466703	−	0.349370i
$698$		0			0
$699$	−0.399863	−	0.622199i	−0.0151242	−	0.0235337i
$700$		0			0
$701$	−5.66689	−	2.58798i	−0.214036	−	0.0977468i	0.305512	−	0.952188i	$-0.401172\pi$
$701$	−5.66689	−	2.58798i	−0.214036	−	0.0977468i	−0.519548	+	0.854441i	$0.673900\pi$
$702$		0			0
$703$	1.18227	+	1.57933i	0.0445902	+	0.0595655i
$704$		0			0
$705$	−0.226023	+	0.149554i	−0.00851251	+	0.00563253i
$706$		0			0
$707$	12.3146	+	0.880760i	0.463139	+	0.0331244i
$708$		0			0
$709$	−21.3230	+	24.6080i	−0.800801	+	0.924174i	−0.998425	−	0.0561043i	$-0.982132\pi$
$709$	−21.3230	+	24.6080i	−0.800801	+	0.924174i	0.197624	+	0.980278i	$0.436678\pi$
$710$		0			0
$711$	−5.94123	+	2.71327i	−0.222814	+	0.101756i
$712$		0			0
$713$	28.3672	−	28.9934i	1.06236	−	1.08581i
$714$		0			0
$715$	0.758920	+	1.34682i	0.0283820	+	0.0503684i
$716$		0			0
$717$	−0.388971	+	0.0278197i	−0.0145264	+	0.00103895i
$718$		0			0
$719$	30.4326	−	26.3700i	1.13494	−	0.983435i	0.134972	−	0.990849i	$-0.456906\pi$
$719$	30.4326	−	26.3700i	1.13494	−	0.983435i	0.999973	+	0.00741457i	$0.00236015\pi$
$720$		0			0
$721$	10.4540	+	3.06956i	0.389326	+	0.114316i
$722$		0			0
$723$	0.546602	−	0.409181i	0.0203283	−	0.0152176i
$724$		0			0
$725$	3.16664	−	11.9558i	0.117606	−	0.444029i
$726$		0			0
$727$	10.3007	−	47.3516i	0.382032	−	1.75617i	−0.237679	−	0.971344i	$-0.576387\pi$
$727$	10.3007	−	47.3516i	0.382032	−	1.75617i	0.619711	−	0.784830i	$-0.287250\pi$
$728$		0			0
$729$	−26.6084	+	3.82572i	−0.985498	+	0.141693i
$730$		0			0
$731$	10.0515	+	6.45970i	0.371768	+	0.238920i
$732$		0			0
$733$	−20.1241	−	10.9886i	−0.743301	−	0.405873i	0.0625110	−	0.998044i	$-0.480089\pi$
$733$	−20.1241	−	10.9886i	−0.743301	−	0.405873i	−0.805812	+	0.592171i	$0.798271\pi$
$734$		0			0
$735$	−0.139501	+	0.0118499i	−0.00514559	+	0.000437090i
$736$		0			0
$737$	5.99861	+	5.99861i	0.220962	+	0.220962i
$738$		0			0
$739$	−12.6529	−	43.0918i	−0.465444	−	1.58516i	−0.773504	−	0.633791i	$-0.781498\pi$
$739$	−12.6529	−	43.0918i	−0.465444	−	1.58516i	0.308060	−	0.951367i	$-0.400320\pi$
$740$		0			0
$741$	0.0617794	−	0.0961307i	0.00226952	−	0.00353145i
$742$		0			0
$743$	−6.70612	+	8.95832i	−0.246024	+	0.328649i	−0.906506	−	0.422192i	$-0.861261\pi$
$743$	−6.70612	+	8.95832i	−0.246024	+	0.328649i	0.660483	+	0.750841i	$0.270352\pi$
$744$		0			0
$745$	2.30780	−	17.7269i	0.0845514	−	0.649464i
$746$		0			0
$747$	−11.0117	−	29.5234i	−0.402895	−	1.08020i
$748$		0			0
$749$	−23.5499	−	3.38597i	−0.860495	−	0.123721i
$750$		0			0
$751$	−11.4649	+	39.0458i	−0.418359	+	1.42480i	0.433559	+	0.901125i	$0.357258\pi$
$751$	−11.4649	+	39.0458i	−0.418359	+	1.42480i	−0.851918	+	0.523675i	$0.824561\pi$
$752$		0			0
$753$	−0.0290692	+	0.406441i	−0.00105934	+	0.0148115i
$754$		0			0
$755$	−8.17490	−	51.9297i	−0.297515	−	1.88991i
$756$		0			0
$757$	−5.75625	−	2.14697i	−0.209215	−	0.0780330i	0.242672	−	0.970108i	$-0.421976\pi$
$757$	−5.75625	−	2.14697i	−0.209215	−	0.0780330i	−0.451887	+	0.892075i	$0.649249\pi$
$758$		0			0
$759$	−0.0213447	−	0.137762i	−0.000774763	−	0.00500044i
$760$		0			0
$761$	4.22538	+	9.25230i	0.153170	+	0.335396i	0.970625	−	0.240597i	$-0.0773431\pi$
$761$	4.22538	+	9.25230i	0.153170	+	0.335396i	−0.817455	+	0.575992i	$0.804616\pi$
$762$		0			0
$763$	2.97800	+	41.6379i	0.107811	+	1.50739i
$764$		0			0
$765$	−10.0409	−	9.77651i	−0.363030	−	0.353471i
$766$		0			0
$767$	3.30135	+	6.04597i	0.119205	+	0.218307i
$768$		0			0
$769$	2.92270	−	20.3278i	0.105395	−	0.733039i	−0.866764	−	0.498718i	$-0.833804\pi$
$769$	2.92270	−	20.3278i	0.105395	−	0.733039i	0.972159	−	0.234321i	$-0.0752866\pi$
$770$		0			0
$771$	0.400189	−	0.876293i	0.0144125	−	0.0315589i
$772$		0			0
$773$	19.6869	+	4.28263i	0.708090	+	0.154036i	0.552167	−	0.833734i	$-0.313801\pi$
$773$	19.6869	+	4.28263i	0.708090	+	0.154036i	0.155923	+	0.987769i	$0.450165\pi$
$774$		0			0
$775$	−40.2440	+	12.9926i	−1.44561	+	0.466708i
$776$		0			0
$777$	0.0257509	+	0.118375i	0.000923807	+	0.00424667i
$778$		0			0
$779$	−15.5293	+	4.55983i	−0.556397	+	0.163373i
$780$		0			0
$781$		−	0.604797i		−	0.0216413i
$782$		0			0
$783$	−0.490427	+	0.490427i	−0.0175264	+	0.0175264i
$784$		0			0
$785$	4.92566	+	12.6867i	0.175804	+	0.452806i
$786$		0			0
$787$	−42.0079	+	9.13827i	−1.49742	+	0.325744i	−0.885300	−	0.465020i	$-0.846047\pi$
$787$	−42.0079	+	9.13827i	−1.49742	+	0.325744i	−0.612121	+	0.790764i	$0.709683\pi$
$788$		0			0
$789$	0.0381403	+	0.265272i	0.00135783	+	0.00944393i
$790$		0			0
$791$	32.2064	−	20.6978i	1.14513	−	0.735930i
$792$		0			0
$793$	14.3608	−	5.35632i	0.509969	−	0.190208i
$794$		0			0
$795$	0.222539	+	0.250005i	0.00789265	+	0.00886677i
$796$		0			0
$797$	−44.1371	+	24.1007i	−1.56342	+	0.853690i	−0.563802	+	0.825910i	$0.690662\pi$
$797$	−44.1371	+	24.1007i	−1.56342	+	0.853690i	−0.999614	+	0.0277795i	$0.991156\pi$
$798$		0			0
$799$	−3.54965	−	4.09651i	−0.125577	−	0.144924i
$800$		0			0
$801$	22.8286	+	19.7811i	0.806607	+	0.698929i
$802$		0			0
$803$	0.829452	−	2.22385i	0.0292707	−	0.0784778i
$804$		0			0
$805$	−22.9053	+	20.8415i	−0.807307	+	0.734567i
$806$		0			0
$807$	0.0832053	−	0.223082i	0.00292897	−	0.00785286i
$808$		0			0
$809$	−34.4294	−	29.8333i	−1.21047	−	1.04888i	−0.997416	−	0.0718416i	$-0.977112\pi$
$809$	−34.4294	−	29.8333i	−1.21047	−	1.04888i	−0.213057	−	0.977040i	$-0.568342\pi$
$810$		0			0
$811$	−34.8890	−	40.2641i	−1.22512	−	1.41386i	−0.879776	−	0.475388i	$-0.842308\pi$
$811$	−34.8890	−	40.2641i	−1.22512	−	1.41386i	−0.345344	−	0.938476i	$-0.612238\pi$
$812$		0			0
$813$	−0.843896	+	0.460802i	−0.0295967	+	0.0161610i
$814$		0			0
$815$	−18.0379	−	1.04843i	−0.631841	−	0.0367250i
$816$		0			0
$817$	11.7722	−	4.39080i	0.411857	−	0.153615i
$818$		0			0
$819$	−8.09747	+	5.20393i	−0.282949	+	0.181840i
$820$		0			0
$821$	0.848233	+	5.89959i	0.0296035	+	0.205897i	0.999255	−	0.0385944i	$-0.0122880\pi$
$821$	0.848233	+	5.89959i	0.0296035	+	0.205897i	−0.969651	+	0.244492i	$0.921379\pi$
$822$		0			0
$823$	−1.10009	+	0.239309i	−0.0383466	+	0.00834179i	−0.231698	−	0.972788i	$-0.574428\pi$
$823$	−1.10009	+	0.239309i	−0.0383466	+	0.00834179i	0.193351	+	0.981130i	$0.438064\pi$
$824$		0			0
$825$	−0.0471400	+	0.137483i	−0.00164120	+	0.00478655i
$826$		0			0
$827$	−2.56413	+	2.56413i	−0.0891635	+	0.0891635i	−0.750282	−	0.661118i	$-0.770082\pi$
$827$	−2.56413	+	2.56413i	−0.0891635	+	0.0891635i	0.661118	+	0.750282i	$0.270082\pi$
$828$		0			0
$829$		−	6.22752i		−	0.216291i	−0.994135	−	0.108145i	$-0.965509\pi$
$829$		−	6.22752i		−	0.216291i	0.994135	−	0.108145i	$-0.0344912\pi$
$830$		0			0
$831$	−1.23697	+	0.363206i	−0.0429099	+	0.0125995i
$832$		0			0
$833$	−0.595202	−	2.73610i	−0.0206225	−	0.0948002i
$834$		0			0
$835$	4.18753	+	18.0847i	0.144915	+	0.625846i
$836$		0			0
$837$	2.31728	+	0.504092i	0.0800968	+	0.0174240i
$838$		0			0
$839$	−15.7581	+	34.5054i	−0.544030	+	1.19126i	0.415484	+	0.909600i	$0.363612\pi$
$839$	−15.7581	+	34.5054i	−0.544030	+	1.19126i	−0.959514	+	0.281659i	$0.909115\pi$
$840$		0			0
$841$	−3.25634	+	22.6483i	−0.112287	+	0.780976i
$842$		0			0
$843$	−0.632302	−	1.15798i	−0.0217777	−	0.0398828i
$844$		0			0
$845$	−0.350931	−	26.3022i	−0.0120724	−	0.904824i
$846$		0			0
$847$	−2.18649	−	30.5711i	−0.0751286	−	1.05043i
$848$		0			0
$849$	−0.257026	−	0.562808i	−0.00882110	−	0.0193155i
$850$		0			0
$851$	3.28303	+	2.78259i	0.112541	+	0.0953861i
$852$		0			0
$853$	25.7340	+	9.59827i	0.881114	+	0.328638i	0.748979	−	0.662593i	$-0.230544\pi$
$853$	25.7340	+	9.59827i	0.881114	+	0.328638i	0.132134	+	0.991232i	$0.457817\pi$
$854$		0			0
$855$	−14.5577	+	2.29171i	−0.497863	+	0.0783749i
$856$		0			0
$857$	−0.875592	+	12.2424i	−0.0299097	+	0.418192i	0.960335	+	0.278850i	$0.0899532\pi$
$857$	−0.875592	+	12.2424i	−0.0299097	+	0.418192i	−0.990244	+	0.139342i	$0.955501\pi$
$858$		0			0
$859$	5.72595	−	19.5008i	0.195367	−	0.665359i	−0.802289	−	0.596935i	$-0.796385\pi$
$859$	5.72595	−	19.5008i	0.195367	−	0.665359i	0.997656	−	0.0684234i	$-0.0217969\pi$
$860$		0			0
$861$	−0.983737	−	0.141440i	−0.0335257	−	0.00482026i
$862$		0			0
$863$	−6.74716	−	18.0898i	−0.229676	−	0.615785i	0.770078	−	0.637949i	$-0.220217\pi$
$863$	−6.74716	−	18.0898i	−0.229676	−	0.615785i	−0.999754	+	0.0221643i	$0.992944\pi$
$864$		0			0
$865$	3.53917	+	4.59859i	0.120335	+	0.156357i
$866$		0			0
$867$	0.353808	−	0.472632i	0.0120159	−	0.0160514i
$868$		0			0
$869$	−0.732431	+	1.13969i	−0.0248460	+	0.0386612i
$870$		0			0
$871$	4.27369	+	14.5548i	0.144808	+	0.493172i
$872$		0			0
$873$	−23.3195	−	23.3195i	−0.789246	−	0.789246i
$874$		0			0
$875$	31.2488	−	8.11987i	1.05640	−	0.274502i
$876$		0			0
$877$	9.46774	+	5.16978i	0.319703	+	0.174571i	0.631085	−	0.775714i	$-0.282610\pi$
$877$	9.46774	+	5.16978i	0.319703	+	0.174571i	−0.311382	+	0.950285i	$0.600792\pi$
$878$		0			0
$879$	0.624907	+	0.401604i	0.0210776	+	0.0135458i
$880$		0			0
$881$	−0.0444367	+	0.00638903i	−0.00149711	+	0.000215252i	−0.143063	−	0.989714i	$-0.545695\pi$
$881$	−0.0444367	+	0.00638903i	−0.00149711	+	0.000215252i	0.141566	+	0.989929i	$0.454786\pi$
$882$		0			0
$883$	−5.72351	+	26.3106i	−0.192612	+	0.885421i	0.774799	+	0.632208i	$0.217851\pi$
$883$	−5.72351	+	26.3106i	−0.192612	+	0.885421i	−0.967411	+	0.253213i	$0.918513\pi$
$884$		0			0
$885$	−0.218208	+	0.609763i	−0.00733499	+	0.0204970i
$886$		0			0
$887$	33.9162	−	25.3893i	1.13879	−	0.852490i	0.148150	−	0.988965i	$-0.452668\pi$
$887$	33.9162	−	25.3893i	1.13879	−	0.852490i	0.990644	+	0.136475i	$0.0435772\pi$
$888$		0			0
$889$	−18.4749	−	5.42472i	−0.619628	−	0.181939i
$890$		0			0
$891$	−4.22010	+	3.65674i	−0.141379	+	0.122505i
$892$		0			0
$893$	−5.68546	+	0.406632i	−0.190257	+	0.0136074i
$894$		0			0
$895$	0.0289834	−	0.103812i	0.000968808	−	0.00347006i
$896$		0			0
$897$	0.0845580	−	0.234496i	0.00282331	−	0.00782959i
$898$		0			0
$899$	−19.0309	+	8.69111i	−0.634716	+	0.289865i
$900$		0			0
$901$	−4.38370	+	5.05906i	−0.146042	+	0.168542i
$902$		0			0
$903$	0.769562	+	0.0550402i	0.0256094	+	0.00183162i
$904$		0			0
$905$	−7.13452	−	10.7825i	−0.237160	−	0.358422i
$906$		0			0
$907$	6.66578	+	8.90444i	0.221334	+	0.295667i	0.897440	−	0.441137i	$-0.145425\pi$
$907$	6.66578	+	8.90444i	0.221334	+	0.295667i	−0.676106	+	0.736804i	$0.736334\pi$
$908$		0			0
$909$	11.6583	+	5.32415i	0.386680	+	0.176591i
$910$		0			0
$911$	12.2990	+	19.1376i	0.407485	+	0.634059i	0.982973	−	0.183752i	$-0.0588242\pi$
$911$	12.2990	+	19.1376i	0.407485	+	0.634059i	−0.575488	+	0.817810i	$0.695188\pi$
$912$		0			0
$913$	−5.23216	−	3.91675i	−0.173159	−	0.129625i
$914$		0			0
$915$	1.27383	+	0.673658i	0.0421114	+	0.0222705i
$916$		0			0
$917$	16.0736	−	29.4367i	0.530799	−	0.972085i
$918$		0			0
$919$	−17.6471			−0.582125			−0.291063	−	0.956704i	$-0.594009\pi$
$919$	−17.6471			−0.582125			−0.291063	+	0.956704i	$0.594009\pi$
$920$		0			0
$921$	0.533283			0.0175723
$922$		0			0
$923$	0.518288	−	0.949173i	0.0170596	−	0.0312424i
$924$		0			0
$925$	−1.67959	−	4.16060i	−0.0552245	−	0.136800i
$926$		0			0
$927$	9.05445	+	6.77808i	0.297387	+	0.222621i
$928$		0			0
$929$	−4.94656	−	7.69700i	−0.162292	−	0.252531i	0.750578	−	0.660782i	$-0.229775\pi$
$929$	−4.94656	−	7.69700i	−0.162292	−	0.252531i	−0.912870	+	0.408251i	$0.866139\pi$
$930$		0			0
$931$	−2.67840	−	1.22318i	−0.0877810	−	0.0400882i
$932$		0			0
$933$	0.309805	+	0.413851i	0.0101426	+	0.0135489i
$934$		0			0
$935$	−2.84838	−	0.579941i	−0.0931521	−	0.0189661i
$936$		0			0
$937$	8.21678	+	0.587675i	0.268430	+	0.0191985i	0.204906	−	0.978782i	$-0.434311\pi$
$937$	8.21678	+	0.587675i	0.268430	+	0.0191985i	0.0635248	+	0.997980i	$0.479766\pi$
$938$		0			0
$939$	0.470559	−	0.543054i	0.0153561	−	0.0177219i
$940$		0			0
$941$	−28.3568	+	12.9501i	−0.924405	+	0.422162i	−0.819994	−	0.572373i	$-0.806023\pi$
$941$	−28.3568	+	12.9501i	−0.924405	+	0.422162i	−0.104411	+	0.994534i	$0.533296\pi$
$942$		0			0
$943$	−30.8013	+	17.2579i	−1.00303	+	0.561996i
$944$		0			0
$945$	−1.74385	−	0.486866i	−0.0567274	−	0.0158378i
$946$		0			0
$947$	−32.2017	+	2.30311i	−1.04641	+	0.0748411i	−0.583944	−	0.811794i	$-0.698491\pi$
$947$	−32.2017	+	2.30311i	−1.04641	+	0.0748411i	−0.462470	+	0.886635i	$0.653037\pi$
$948$		0			0
$949$	3.20750	−	2.77931i	0.104120	−	0.0902203i
$950$		0			0
$951$	−1.06144	−	0.311666i	−0.0344194	−	0.0101065i
$952$		0			0
$953$	31.0797	−	23.2659i	1.00677	−	0.753658i	0.0374085	−	0.999300i	$-0.488090\pi$
$953$	31.0797	−	23.2659i	1.00677	−	0.753658i	0.969361	+	0.245642i	$0.0789988\pi$
$954$		0			0
$955$	16.6440	−	7.87110i	0.538588	−	0.254703i
$956$		0			0
$957$	−0.0152841	+	0.0702601i	−0.000494066	+	0.00227119i
$958$		0			0
$959$	−56.1521	+	8.07345i	−1.81325	+	0.260705i
$960$		0			0
$961$	34.1006	+	21.9151i	1.10002	+	0.706940i
$962$		0			0
$963$	−21.6774	−	11.8368i	−0.698544	−	0.381434i
$964$		0			0
$965$	−2.93755	−	34.5819i	−0.0945630	−	1.11323i
$966$		0			0
$967$	10.2193	+	10.2193i	0.328630	+	0.328630i	0.852065	−	0.523435i	$-0.175350\pi$
$967$	10.2193	+	10.2193i	0.328630	+	0.328630i	−0.523435	+	0.852065i	$0.675350\pi$
$968$		0			0
$969$	0.0605343	+	0.206161i	0.00194464	+	0.00662284i
$970$		0			0
$971$	−4.46633	+	6.94974i	−0.143331	+	0.223028i	−0.905495	−	0.424356i	$-0.860501\pi$
$971$	−4.46633	+	6.94974i	−0.143331	+	0.223028i	0.762164	+	0.647384i	$0.224137\pi$
$972$		0			0
$973$	21.3119	−	28.4693i	0.683227	−	0.912684i
$974$		0			0
$975$	−0.191800	+	0.175370i	−0.00614251	+	0.00561634i
$976$		0			0
$977$	−5.49131	−	14.7228i	−0.175683	−	0.471024i	0.819026	−	0.573756i	$-0.194514\pi$
$977$	−5.49131	−	14.7228i	−0.175683	−	0.471024i	−0.994709	+	0.102732i	$0.967241\pi$
$978$		0			0
$979$	6.20162	+	0.891658i	0.198205	+	0.0284975i
$980$		0			0
$981$	−12.2088	+	41.5793i	−0.389797	+	1.32753i
$982$		0			0
$983$	0.0879238	−	1.22934i	0.00280433	−	0.0392097i	−0.995857	−	0.0909303i	$-0.971016\pi$
$983$	0.0879238	−	1.22934i	0.00280433	−	0.0392097i	0.998662	+	0.0517205i	$0.0164705\pi$
$984$		0			0
$985$	−3.63924	+	4.99911i	−0.115956	+	0.159285i
$986$		0			0
$987$	−0.327945	−	0.122317i	−0.0104386	−	0.00389340i
$988$		0			0
$989$	22.8944	−	15.0690i	0.727999	−	0.479166i
$990$		0			0
$991$	23.7777	+	52.0659i	0.755323	+	1.65393i	0.756557	+	0.653927i	$0.226880\pi$
$991$	23.7777	+	52.0659i	0.755323	+	1.65393i	−0.00123431	+	0.999999i	$0.500393\pi$
$992$		0			0
$993$	0.00296867	+	0.0415074i	9.42078e−5	+	0.00131720i
$994$		0			0
$995$	−42.9620	+	0.573209i	−1.36199	+	0.0181720i
$996$		0			0
$997$	−26.6669	−	48.8369i	−0.844551	−	1.54668i	−0.837325	−	0.546705i	$-0.815882\pi$
$997$	−26.6669	−	48.8369i	−0.844551	−	1.54668i	−0.00722554	−	0.999974i	$-0.502300\pi$
$998$		0			0
$999$	−0.0358077	+	0.249048i	−0.00113291	+	0.00787954i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.617.18	yes	720
5.3	odd	4	inner	920.2.bv.a.433.18	yes	720
23.17	odd	22	inner	920.2.bv.a.17.18	✓	720
115.63	even	44	inner	920.2.bv.a.753.18	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.18	✓	720	23.17	odd	22	inner
920.2.bv.a.433.18	yes	720	5.3	odd	4	inner
920.2.bv.a.617.18	yes	720	1.1	even	1	trivial
920.2.bv.a.753.18	yes	720	115.63	even	44	inner

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0224040 + 0.0410298i) q^{3} +(2.13690 - 0.658540i) q^{5} +(2.31180 + 1.73059i) q^{7} +(1.62074 + 2.52192i) q^{9} +(0.565611 + 0.258306i) q^{11} +(0.666316 + 0.890094i) q^{13} +(-0.0208552 + 0.102430i) q^{15} +(-2.08532 - 0.149145i) q^{17} +(-1.43969 + 1.66149i) q^{19} +(-0.122799 + 0.0560805i) q^{21} +(-2.25231 + 4.23404i) q^{23} +(4.13265 - 2.81446i) q^{25} +(-0.279672 + 0.0200025i) q^{27} +(1.86944 - 1.61988i) q^{29} +(-8.11526 - 2.38286i) q^{31} +(-0.0232702 + 0.0174198i) q^{33} +(6.07973 + 2.17568i) q^{35} +(0.190749 - 0.876858i) q^{37} +(-0.0514485 + 0.00739718i) q^{39} +(6.19326 + 3.98017i) q^{41} +(-5.01600 - 2.73894i) q^{43} +(5.12414 + 4.32176i) q^{45} +(1.83333 + 1.83333i) q^{47} +(0.377336 + 1.28509i) q^{49} +(0.0528390 - 0.0822190i) q^{51} +(1.91884 - 2.56327i) q^{53} +(1.37876 + 0.179495i) q^{55} +(-0.0359158 - 0.0962940i) q^{57} +(6.13247 + 0.881716i) q^{59} +(3.88373 - 13.2268i) q^{61} +(-0.617588 + 8.63501i) q^{63} +(2.01001 + 1.46324i) q^{65} +(12.7829 + 4.76778i) q^{67} +(-0.123261 - 0.187271i) q^{69} +(-0.404054 - 0.884756i) q^{71} +(-0.272310 - 3.80740i) q^{73} +(0.0228892 + 0.232617i) q^{75} +(0.860556 + 1.57599i) q^{77} +(-0.310067 + 2.15657i) q^{79} +(-3.73057 + 8.16880i) q^{81} +(-10.2708 - 2.23428i) q^{83} +(-4.55434 + 1.05456i) q^{85} +(0.0245804 + 0.112994i) q^{87} +(9.66802 - 2.83879i) q^{89} +3.21083i q^{91} +(0.279582 - 0.279582i) q^{93} +(-1.98230 + 4.49852i) q^{95} +(-10.7495 + 2.33842i) q^{97} +(0.265282 + 1.84507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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