LMFDB - Embedded newform 585.2.bs.b.289.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.7
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.b.334.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.521384 - 0.301021i) q^{2} +(-0.818772 + 1.41816i) q^{4} +(-0.446511 - 2.19103i) q^{5} +(-3.08191 - 1.77934i) q^{7} +2.18996i q^{8} +O(q^{10})$	\(q+(0.521384 - 0.301021i) q^{2} +(-0.818772 + 1.41816i) q^{4} +(-0.446511 - 2.19103i) q^{5} +(-3.08191 - 1.77934i) q^{7} +2.18996i q^{8} +(-0.892352 - 1.00796i) q^{10} +(1.30769 + 2.26499i) q^{11} +(-2.88598 + 2.16128i) q^{13} -2.14248 q^{14} +(-0.978320 - 1.69450i) q^{16} +(-1.94566 - 1.12333i) q^{17} +(-4.00873 + 6.94332i) q^{19} +(3.47282 + 1.16074i) q^{20} +(1.36362 + 0.787287i) q^{22} +(-1.43095 + 0.826160i) q^{23} +(-4.60126 + 1.95664i) q^{25} +(-0.854110 + 1.99560i) q^{26} +(5.04676 - 2.91375i) q^{28} +(-2.26120 - 3.91651i) q^{29} -4.05655 q^{31} +(-4.81328 - 2.77895i) q^{32} -1.35258 q^{34} +(-2.52249 + 7.54706i) q^{35} +(3.64724 - 2.10574i) q^{37} +4.82685i q^{38} +(4.79827 - 0.977840i) q^{40} +(-0.388612 - 0.673096i) q^{41} +(0.197117 + 0.113806i) q^{43} -4.28281 q^{44} +(-0.497384 + 0.861494i) q^{46} -3.14738i q^{47} +(2.83211 + 4.90536i) q^{49} +(-1.81003 + 2.40524i) q^{50} +(-0.702078 - 5.86236i) q^{52} -6.42424i q^{53} +(4.37877 - 3.87654i) q^{55} +(3.89668 - 6.74925i) q^{56} +(-2.35791 - 1.36134i) q^{58} +(6.26747 - 10.8556i) q^{59} +(-1.46568 + 2.53863i) q^{61} +(-2.11502 + 1.22111i) q^{62} +0.567189 q^{64} +(6.02406 + 5.35823i) q^{65} +(-0.969664 + 0.559836i) q^{67} +(3.18611 - 1.83950i) q^{68} +(0.956640 + 4.69425i) q^{70} +(-5.66772 + 9.81678i) q^{71} +12.4350i q^{73} +(1.26774 - 2.19579i) q^{74} +(-6.56447 - 11.3700i) q^{76} -9.30732i q^{77} +14.8640 q^{79} +(-3.27588 + 2.90015i) q^{80} +(-0.405233 - 0.233961i) q^{82} +11.7337i q^{83} +(-1.59249 + 4.76459i) q^{85} +0.137032 q^{86} +(-4.96023 + 2.86379i) q^{88} +(8.60439 + 14.9032i) q^{89} +(12.7400 - 1.52574i) q^{91} -2.70575i q^{92} +(-0.947430 - 1.64100i) q^{94} +(17.0030 + 5.68299i) q^{95} +(-10.6088 - 6.12499i) q^{97} +(2.95324 + 1.70505i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) $ 24 * q + 8 * q^4 - 4 * q^5	$ 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) $ 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.521384	−	0.301021i	0.368674	−	0.212854i	−0.304205	−	0.952607i	$-0.598391\pi$
$2$	0.521384	−	0.301021i	0.368674	−	0.212854i	0.672879	+	0.739752i	$0.265057\pi$
$3$		0			0
$3$		0			0
$4$	−0.818772	+	1.41816i	−0.409386	+	0.709078i
$5$	−0.446511	−	2.19103i	−0.199686	−	0.979860i
$5$	−0.446511	−	2.19103i	−0.199686	−	0.979860i
$6$		0			0
$7$	−3.08191	−	1.77934i	−1.16485	−	0.672528i	−0.212390	−	0.977185i	$-0.568125\pi$
$7$	−3.08191	−	1.77934i	−1.16485	−	0.672528i	−0.952462	+	0.304657i	$0.901458\pi$
$8$			2.18996i			0.774267i
$9$		0			0
$10$	−0.892352	−	1.00796i	−0.282186	−	0.318745i
$11$	1.30769	+	2.26499i	0.394284	+	0.682920i	0.993010	−	0.118034i	$-0.0376593\pi$
$11$	1.30769	+	2.26499i	0.394284	+	0.682920i	−0.598726	+	0.800954i	$0.704326\pi$
$12$		0			0
$13$	−2.88598	+	2.16128i	−0.800426	+	0.599432i
$13$	−2.88598	+	2.16128i	−0.800426	+	0.599432i
$14$	−2.14248			−0.572602
$15$		0			0
$16$	−0.978320	−	1.69450i	−0.244580	−	0.423625i
$17$	−1.94566	−	1.12333i	−0.471893	−	0.272447i	0.245139	−	0.969488i	$-0.421166\pi$
$17$	−1.94566	−	1.12333i	−0.471893	−	0.272447i	−0.717032	+	0.697041i	$0.754500\pi$
$18$		0			0
$19$	−4.00873	+	6.94332i	−0.919666	+	1.59291i	−0.119743	+	0.992805i	$0.538207\pi$
$19$	−4.00873	+	6.94332i	−0.919666	+	1.59291i	−0.799923	+	0.600103i	$0.795126\pi$
$20$	3.47282	+	1.16074i	0.776545	+	0.259548i
$21$		0			0
$22$	1.36362	+	0.787287i	0.290725	+	0.167850i
$23$	−1.43095	+	0.826160i	−0.298374	+	0.172266i	−0.641712	−	0.766946i	$-0.721776\pi$
$23$	−1.43095	+	0.826160i	−0.298374	+	0.172266i	0.343338	+	0.939212i	$0.388442\pi$
$24$		0			0
$25$	−4.60126	+	1.95664i	−0.920251	+	0.391328i
$26$	−0.854110	+	1.99560i	−0.167505	+	0.391369i
$27$		0			0
$28$	5.04676	−	2.91375i	0.953749	−	0.550647i
$29$	−2.26120	−	3.91651i	−0.419894	−	0.727277i	0.576035	−	0.817425i	$-0.304599\pi$
$29$	−2.26120	−	3.91651i	−0.419894	−	0.727277i	−0.995928	+	0.0901479i	$0.971266\pi$
$30$		0			0
$31$	−4.05655			−0.728577			−0.364289	−	0.931286i	$-0.618688\pi$
$31$	−4.05655			−0.728577			−0.364289	+	0.931286i	$0.618688\pi$
$32$	−4.81328	−	2.77895i	−0.850876	−	0.491253i
$33$		0			0
$34$	−1.35258			−0.231966
$35$	−2.52249	+	7.54706i	−0.426379	+	1.27569i
$36$		0			0
$37$	3.64724	−	2.10574i	0.599603	−	0.346181i	−0.169283	−	0.985568i	$-0.554145\pi$
$37$	3.64724	−	2.10574i	0.599603	−	0.346181i	0.768885	+	0.639387i	$0.220812\pi$
$38$			4.82685i			0.783019i
$39$		0			0
$40$	4.79827	−	0.977840i	0.758673	−	0.154610i
$41$	−0.388612	−	0.673096i	−0.0606910	−	0.105120i	0.834083	−	0.551638i	$-0.185997\pi$
$41$	−0.388612	−	0.673096i	−0.0606910	−	0.105120i	−0.894774	+	0.446518i	$0.852664\pi$
$42$		0			0
$43$	0.197117	+	0.113806i	0.0300601	+	0.0173552i	0.514955	−	0.857217i	$-0.327809\pi$
$43$	0.197117	+	0.113806i	0.0300601	+	0.0173552i	−0.484895	+	0.874573i	$0.661142\pi$
$44$	−4.28281			−0.645658
$45$		0			0
$46$	−0.497384	+	0.861494i	−0.0733352	+	0.127020i
$47$		−	3.14738i		−	0.459093i	−0.973298	−	0.229547i	$-0.926276\pi$
$47$		−	3.14738i		−	0.459093i	0.973298	−	0.229547i	$-0.0737243\pi$
$48$		0			0
$49$	2.83211	+	4.90536i	0.404588	+	0.700766i
$50$	−1.81003	+	2.40524i	−0.255977	+	0.340152i
$51$		0			0
$52$	−0.702078	−	5.86236i	−0.0973607	−	0.812963i
$53$		−	6.42424i		−	0.882437i	−0.897400	−	0.441218i	$-0.854546\pi$
$53$		−	6.42424i		−	0.882437i	0.897400	−	0.441218i	$-0.145454\pi$
$54$		0			0
$55$	4.37877	−	3.87654i	0.590433	−	0.522712i
$56$	3.89668	−	6.74925i	0.520716	−	0.901907i
$57$		0			0
$58$	−2.35791	−	1.36134i	−0.309608	−	0.178752i
$59$	6.26747	−	10.8556i	0.815955	−	1.41328i	−0.0926855	−	0.995695i	$-0.529545\pi$
$59$	6.26747	−	10.8556i	0.815955	−	1.41328i	0.908640	−	0.417580i	$-0.137122\pi$
$60$		0			0
$61$	−1.46568	+	2.53863i	−0.187661	+	0.325038i	−0.944470	−	0.328598i	$-0.893424\pi$
$61$	−1.46568	+	2.53863i	−0.187661	+	0.325038i	0.756809	+	0.653636i	$0.226757\pi$
$62$	−2.11502	+	1.22111i	−0.268608	+	0.155081i
$63$		0			0
$64$	0.567189			0.0708986
$65$	6.02406	+	5.35823i	0.747193	+	0.664607i
$66$		0			0
$67$	−0.969664	+	0.559836i	−0.118463	+	0.0683948i	−0.558061	−	0.829800i	$-0.688454\pi$
$67$	−0.969664	+	0.559836i	−0.118463	+	0.0683948i	0.439597	+	0.898195i	$0.355121\pi$
$68$	3.18611	−	1.83950i	0.386373	−	0.223072i
$69$		0			0
$70$	0.956640	+	4.69425i	0.114340	+	0.561070i
$71$	−5.66772	+	9.81678i	−0.672635	+	1.16504i	0.304520	+	0.952506i	$0.401504\pi$
$71$	−5.66772	+	9.81678i	−0.672635	+	1.16504i	−0.977154	+	0.212531i	$0.931829\pi$
$72$		0			0
$73$			12.4350i			1.45541i	0.685890	+	0.727705i	$0.259413\pi$
$73$			12.4350i			1.45541i	−0.685890	+	0.727705i	$0.740587\pi$
$74$	1.26774	−	2.19579i	0.147372	−	0.255256i
$75$		0			0
$76$	−6.56447	−	11.3700i	−0.752997	−	1.30423i
$77$		−	9.30732i		−	1.06067i
$78$		0			0
$79$	14.8640			1.67234			0.836168	−	0.548474i	$-0.184791\pi$
$79$	14.8640			1.67234			0.836168	+	0.548474i	$0.184791\pi$
$80$	−3.27588	+	2.90015i	−0.366254	+	0.324246i
$81$		0			0
$82$	−0.405233	−	0.233961i	−0.0447505	−	0.0258367i
$83$			11.7337i			1.28794i	0.765050	+	0.643971i	$0.222714\pi$
$83$			11.7337i			1.28794i	−0.765050	+	0.643971i	$0.777286\pi$
$84$		0			0
$85$	−1.59249	+	4.76459i	−0.172730	+	0.516793i
$86$	0.137032			0.0147765
$87$		0			0
$88$	−4.96023	+	2.86379i	−0.528762	+	0.305281i
$89$	8.60439	+	14.9032i	0.912064	+	1.57974i	0.811144	+	0.584846i	$0.198845\pi$
$89$	8.60439	+	14.9032i	0.912064	+	1.57974i	0.100919	+	0.994895i	$0.467822\pi$
$90$		0			0
$91$	12.7400	−	1.52574i	1.33551	−	0.159941i
$92$		−	2.70575i		−	0.282094i
$93$		0			0
$94$	−0.947430	−	1.64100i	−0.0977200	−	0.169256i
$95$	17.0030	+	5.68299i	1.74447	+	0.583063i
$96$		0			0
$97$	−10.6088	−	6.12499i	−1.07716	−	0.621899i	−0.147032	−	0.989132i	$-0.546972\pi$
$97$	−10.6088	−	6.12499i	−1.07716	−	0.621899i	−0.930129	+	0.367233i	$0.880305\pi$
$98$	2.95324	+	1.70505i	0.298322	+	0.172236i
$99$		0			0
$100$	0.992561	−	8.12734i	0.0992561	−	0.812734i
$101$	−8.61893	−	14.9284i	−0.857616	−	1.48543i	−0.874197	−	0.485571i	$-0.838612\pi$
$101$	−8.61893	−	14.9284i	−0.857616	−	1.48543i	0.0165815	−	0.999863i	$-0.494722\pi$
$102$		0			0
$103$			2.80894i			0.276773i	0.990378	+	0.138387i	$0.0441917\pi$
$103$			2.80894i			0.276773i	−0.990378	+	0.138387i	$0.955808\pi$
$104$	−4.73312	−	6.32016i	−0.464120	−	0.619743i
$105$		0			0
$106$	−1.93383	−	3.34950i	−0.187830	−	0.325332i
$107$	8.58556	−	4.95687i	0.829997	−	0.479199i	−0.0238546	−	0.999715i	$-0.507594\pi$
$107$	8.58556	−	4.95687i	0.829997	−	0.479199i	0.853852	+	0.520516i	$0.174261\pi$
$108$		0			0
$109$	−7.17060			−0.686819			−0.343409	−	0.939186i	$-0.611582\pi$
$109$	−7.17060			−0.686819			−0.343409	+	0.939186i	$0.611582\pi$
$110$	1.11610	−	3.33927i	0.106416	−	0.318387i
$111$		0			0
$112$			6.96306i			0.657948i
$113$	6.01823	+	3.47463i	0.566148	+	0.326866i	0.755609	−	0.655023i	$-0.227341\pi$
$113$	6.01823	+	3.47463i	0.566148	+	0.326866i	−0.189462	+	0.981888i	$0.560674\pi$
$114$		0			0
$115$	2.44908	+	2.76637i	0.228378	+	0.257966i
$116$	7.40562			0.687595
$117$		0			0
$118$		−	7.54657i		−	0.694718i
$119$	3.99757	+	6.92400i	0.366457	+	0.634722i
$120$		0			0
$121$	2.07988	−	3.60246i	0.189080	−	0.327497i
$122$			1.76480i			0.159778i
$123$		0			0
$124$	3.32139	−	5.75281i	0.298269	−	0.516618i
$125$	6.34158	+	9.20785i	0.567208	+	0.823575i
$126$		0			0
$127$	−5.07705	+	2.93124i	−0.450515	+	0.260105i	−0.708048	−	0.706165i	$-0.750424\pi$
$127$	−5.07705	+	2.93124i	−0.450515	+	0.260105i	0.257533	+	0.966270i	$0.417091\pi$
$128$	9.92228	−	5.72863i	0.877014	−	0.506344i
$129$		0			0
$130$	4.75380	+	0.980327i	0.416935	+	0.0859803i
$131$	−10.0136			−0.874892			−0.437446	−	0.899245i	$-0.644117\pi$
$131$	−10.0136			−0.874892			−0.437446	+	0.899245i	$0.644117\pi$
$132$		0			0
$133$	24.7091	−	14.2658i	2.14255	−	1.23700i
$134$	−0.337045	+	0.583779i	−0.0291163	+	0.0504309i
$135$		0			0
$136$	2.46004	−	4.26092i	0.210947	−	0.365371i
$137$	−15.9194	−	9.19109i	−1.36009	−	0.785248i	−0.370454	−	0.928851i	$-0.620798\pi$
$137$	−15.9194	−	9.19109i	−1.36009	−	0.785248i	−0.989635	+	0.143603i	$0.954131\pi$
$138$		0			0
$139$	2.15531	−	3.73311i	0.182811	−	0.316638i	−0.760026	−	0.649893i	$-0.774814\pi$
$139$	2.15531	−	3.73311i	0.182811	−	0.316638i	0.942837	+	0.333255i	$0.108147\pi$
$140$	−8.63756	−	9.75661i	−0.730007	−	0.824584i
$141$		0			0
$142$			6.82442i			0.572693i
$143$	−8.66925	−	3.71041i	−0.724959	−	0.310280i
$144$		0			0
$145$	−7.57155	+	6.70312i	−0.628783	+	0.556664i
$146$	3.74321	+	6.48343i	0.309790	+	0.536572i
$147$		0			0
$148$			6.89647i			0.566886i
$149$	1.13079	−	1.95858i	0.0926377	−	0.160453i	−0.815983	−	0.578077i	$-0.803804\pi$
$149$	1.13079	−	1.95858i	0.0926377	−	0.160453i	0.908620	+	0.417623i	$0.137137\pi$
$150$		0			0
$151$	8.52523			0.693773			0.346886	−	0.937907i	$-0.387239\pi$
$151$	8.52523			0.693773			0.346886	+	0.937907i	$0.387239\pi$
$152$	−15.2056	−	8.77895i	−1.23334	−	0.712067i
$153$		0			0
$154$	−2.80170	−	4.85269i	−0.225768	−	0.391041i
$155$	1.81129	+	8.88803i	0.145487	+	0.713904i
$156$		0			0
$157$		−	6.53771i		−	0.521766i	−0.965370	−	0.260883i	$-0.915986\pi$
$157$		−	6.53771i		−	0.521766i	0.965370	−	0.260883i	$-0.0840137\pi$
$158$	7.74988	−	4.47439i	0.616547	−	0.355964i
$159$		0			0
$160$	−3.93959	+	11.7869i	−0.311452	+	0.931835i
$161$	5.88008			0.463416
$162$		0			0
$163$	−17.8665	−	10.3152i	−1.39941	−	0.807950i	−0.405080	−	0.914281i	$-0.632756\pi$
$163$	−17.8665	−	10.3152i	−1.39941	−	0.807950i	−0.994331	+	0.106331i	$0.966090\pi$
$164$	1.27274			0.0993843
$165$		0			0
$166$	3.53210	+	6.11777i	0.274144	+	0.474831i
$167$	−16.6176	+	9.59418i	−1.28591	+	0.742420i	−0.977922	−	0.208970i	$-0.932989\pi$
$167$	−16.6176	+	9.59418i	−1.28591	+	0.742420i	−0.307988	+	0.951390i	$0.599656\pi$
$168$		0			0
$169$	3.65771	−	12.4748i	0.281362	−	0.959602i
$170$	0.603944	+	2.96356i	0.0463204	+	0.227295i
$171$		0			0
$172$	−0.322788	+	0.186362i	−0.0246123	+	0.0142099i
$173$	−16.7006	−	9.64212i	−1.26973	−	0.733077i	−0.294791	−	0.955562i	$-0.595250\pi$
$173$	−16.7006	−	9.64212i	−1.26973	−	0.733077i	−0.974936	+	0.222485i	$0.928583\pi$
$174$		0			0
$175$	17.6622	+	2.15702i	1.33514	+	0.163055i
$176$	2.55868	−	4.43177i	0.192868	−	0.334057i
$177$		0			0
$178$	8.97239	+	5.18021i	0.672509	+	0.388273i
$179$	2.85922	+	4.95232i	0.213708	+	0.370153i	0.952872	−	0.303372i	$-0.0981125\pi$
$179$	2.85922	+	4.95232i	0.213708	+	0.370153i	−0.739164	+	0.673525i	$0.764779\pi$
$180$		0			0
$181$	−5.05252			−0.375551			−0.187775	−	0.982212i	$-0.560128\pi$
$181$	−5.05252			−0.375551			−0.187775	+	0.982212i	$0.560128\pi$
$182$	6.18314	−	4.63051i	0.458325	−	0.343236i
$183$		0			0
$184$	−1.80926	−	3.13372i	−0.133380	−	0.231021i
$185$	−6.24227	−	7.05099i	−0.458941	−	0.518399i
$186$		0			0
$187$		−	5.87588i		−	0.429687i
$188$	4.46348	+	2.57699i	0.325533	+	0.187946i
$189$		0			0
$190$	10.5758	−	2.15524i	0.767249	−	0.156358i
$191$	8.82751	−	15.2897i	0.638736	−	1.10632i	−0.346974	−	0.937875i	$-0.612791\pi$
$191$	8.82751	−	15.2897i	0.638736	−	1.10632i	0.985710	−	0.168449i	$-0.0538758\pi$
$192$		0			0
$193$	−3.17329	+	1.83210i	−0.228418	+	0.131877i	−0.609842	−	0.792523i	$-0.708767\pi$
$193$	−3.17329	+	1.83210i	−0.228418	+	0.131877i	0.381424	+	0.924400i	$0.375434\pi$
$194$	−7.37502			−0.529495
$195$		0			0
$196$	−9.27542			−0.662530
$197$	−6.03467	+	3.48412i	−0.429952	+	0.248233i	−0.699326	−	0.714803i	$-0.746517\pi$
$197$	−6.03467	+	3.48412i	−0.429952	+	0.248233i	0.269374	+	0.963036i	$0.413183\pi$
$198$		0			0
$199$	−3.68996	+	6.39119i	−0.261574	+	0.453060i	−0.966660	−	0.256062i	$-0.917575\pi$
$199$	−3.68996	+	6.39119i	−0.261574	+	0.453060i	0.705086	+	0.709122i	$0.250908\pi$
$200$	−4.28496	−	10.0766i	−0.302992	−	0.712520i
$201$		0			0
$202$	−8.98755	−	5.18897i	−0.632362	−	0.365094i
$203$			16.0938i			1.12956i
$204$		0			0
$205$	−1.30126	+	1.15201i	−0.0908837	+	0.0804597i
$206$	0.845552	+	1.46454i	0.0589124	+	0.102039i
$207$		0			0
$208$	6.48570	+	2.77586i	0.449703	+	0.192471i
$209$	−20.9687			−1.45044
$210$		0			0
$211$	12.3017	+	21.3072i	0.846887	+	1.46685i	0.883973	+	0.467539i	$0.154859\pi$
$211$	12.3017	+	21.3072i	0.846887	+	1.46685i	−0.0370857	+	0.999312i	$0.511807\pi$
$212$	9.11056	+	5.25999i	0.625716	+	0.361257i
$213$		0			0
$214$	2.98425	−	5.16887i	0.203999	−	0.353337i
$215$	0.161337	−	0.482705i	0.0110031	−	0.0329202i
$216$		0			0
$217$	12.5019	+	7.21798i	0.848685	+	0.489989i
$218$	−3.73864	+	2.15850i	−0.253212	+	0.146192i
$219$		0			0
$220$	1.91232	+	9.38378i	0.128929	+	0.632654i
$221$	8.04297	−	0.963229i	0.541029	−	0.0647938i
$222$		0			0
$223$	−0.480551	+	0.277446i	−0.0321801	+	0.0185792i	−0.516004	−	0.856586i	$-0.672581\pi$
$223$	−0.480551	+	0.277446i	−0.0321801	+	0.0185792i	0.483824	+	0.875166i	$0.339248\pi$
$224$	9.88940	+	17.1289i	0.660763	+	1.14448i
$225$		0			0
$226$	4.18375			0.278299
$227$	−1.30934	−	0.755945i	−0.0869037	−	0.0501739i	0.455918	−	0.890022i	$-0.349311\pi$
$227$	−1.30934	−	0.755945i	−0.0869037	−	0.0501739i	−0.542822	+	0.839848i	$0.682644\pi$
$228$		0			0
$229$	−5.42263			−0.358337			−0.179169	−	0.983818i	$-0.557341\pi$
$229$	−5.42263			−0.358337			−0.179169	+	0.983818i	$0.557341\pi$
$230$	2.10965	+	0.705118i	0.139106	+	0.0464941i
$231$		0			0
$232$	8.57699	−	4.95193i	0.563107	−	0.325110i
$233$			11.2530i			0.737206i	0.929587	+	0.368603i	$0.120164\pi$
$233$			11.2530i			0.737206i	−0.929587	+	0.368603i	$0.879836\pi$
$234$		0			0
$235$	−6.89603	+	1.40534i	−0.449847	+	0.0916744i
$236$	10.2633	+	17.7765i	0.668081	+	1.15715i
$237$		0			0
$238$	4.16854	+	2.40671i	0.270207	+	0.156004i
$239$	17.9281			1.15967			0.579837	−	0.814733i	$-0.303116\pi$
$239$	17.9281			1.15967			0.579837	+	0.814733i	$0.303116\pi$
$240$		0			0
$241$	−10.1675	+	17.6107i	−0.654949	+	1.13440i	0.326958	+	0.945039i	$0.393977\pi$
$241$	−10.1675	+	17.6107i	−0.654949	+	1.13440i	−0.981907	+	0.189366i	$0.939357\pi$
$242$		−	2.50436i		−	0.160986i
$243$		0			0
$244$	−2.40011	−	4.15711i	−0.153651	−	0.266132i
$245$	9.48325	−	8.39555i	0.605863	−	0.536372i
$246$		0			0
$247$	−3.43739	−	28.7023i	−0.218716	−	1.82628i
$248$		−	8.88367i		−	0.564113i
$249$		0			0
$250$	6.07816	+	2.89188i	0.384416	+	0.182898i
$251$	−9.42506	+	16.3247i	−0.594904	+	1.03040i	0.398656	+	0.917101i	$0.369477\pi$
$251$	−9.42506	+	16.3247i	−0.594904	+	1.03040i	−0.993560	+	0.113304i	$0.963857\pi$
$252$		0			0
$253$	−3.74249	−	2.16073i	−0.235288	−	0.135844i
$254$	−1.76473	+	3.05660i	−0.110729	+	0.191788i
$255$		0			0
$256$	2.88169	−	4.99124i	0.180106	−	0.311952i
$257$	24.5820	−	14.1924i	1.53338	−	0.885298i	0.534179	−	0.845372i	$-0.320621\pi$
$257$	24.5820	−	14.1924i	1.53338	−	0.885298i	0.999203	−	0.0399265i	$-0.0127124\pi$
$258$		0			0
$259$	−14.9873			−0.931265
$260$	−12.5311	+	4.15588i	−0.777148	+	0.257737i
$261$		0			0
$262$	−5.22093	+	3.01431i	−0.322550	+	0.186224i
$263$	12.3560	−	7.13372i	0.761901	−	0.439884i	−0.0680767	−	0.997680i	$-0.521686\pi$
$263$	12.3560	−	7.13372i	0.761901	−	0.439884i	0.829978	+	0.557796i	$0.188353\pi$
$264$		0			0
$265$	−14.0757	+	2.86849i	−0.864664	+	0.176210i
$266$	8.58862	−	14.8759i	0.526602	−	0.912102i
$267$		0			0
$268$		−	1.83351i		−	0.112000i
$269$	−12.7612	+	22.1031i	−0.778067	+	1.34765i	0.154988	+	0.987916i	$0.450466\pi$
$269$	−12.7612	+	22.1031i	−0.778067	+	1.34765i	−0.933055	+	0.359735i	$0.882867\pi$
$270$		0			0
$271$	3.91226	+	6.77623i	0.237653	+	0.411627i	0.960040	−	0.279862i	$-0.0902886\pi$
$271$	3.91226	+	6.77623i	0.237653	+	0.411627i	−0.722387	+	0.691488i	$0.756955\pi$
$272$			4.39590i			0.266541i
$273$		0			0
$274$	−11.0669			−0.668573
$275$	−10.4488	−	7.86311i	−0.630086	−	0.474163i
$276$		0			0
$277$	16.8514	+	9.72915i	1.01250	+	0.584568i	0.911923	−	0.410361i	$-0.134597\pi$
$277$	16.8514	+	9.72915i	1.01250	+	0.584568i	0.100578	+	0.994929i	$0.467931\pi$
$278$		−	2.59518i		−	0.155648i
$279$		0			0
$280$	−16.5278	−	5.52415i	−0.987722	−	0.330131i
$281$	−23.1248			−1.37951			−0.689754	−	0.724043i	$-0.742282\pi$
$281$	−23.1248			−1.37951			−0.689754	+	0.724043i	$0.742282\pi$
$282$		0			0
$283$	−22.4177	+	12.9429i	−1.33260	+	0.769374i	−0.985697	−	0.168528i	$-0.946099\pi$
$283$	−22.4177	+	12.9429i	−1.33260	+	0.769374i	−0.346899	+	0.937903i	$0.612765\pi$
$284$	−9.28114	−	16.0754i	−0.550735	−	0.953900i
$285$		0			0
$286$	−5.63693	+	0.675080i	−0.333318	+	0.0399183i
$287$			2.76590i			0.163266i
$288$		0			0
$289$	−5.97626	−	10.3512i	−0.351545	−	0.608894i
$290$	−1.92991	+	5.77410i	−0.113328	+	0.339067i
$291$		0			0
$292$	−17.6348	−	10.1815i	−1.03200	−	0.595825i
$293$	−3.47269	−	2.00496i	−0.202877	−	0.117131i	0.395120	−	0.918630i	$-0.370703\pi$
$293$	−3.47269	−	2.00496i	−0.202877	−	0.117131i	−0.597997	+	0.801499i	$0.704036\pi$
$294$		0			0
$295$	−26.5834	−	8.88510i	−1.54775	−	0.517311i
$296$	4.61147	+	7.98730i	0.268036	+	0.464252i
$297$		0			0
$298$		−	1.36156i		−	0.0788733i
$299$	2.34412	−	5.47697i	0.135564	−	0.316741i
$300$		0			0
$301$	−0.404998	−	0.701477i	−0.0233437	−	0.0404325i
$302$	4.44492	−	2.56628i	0.255776	−	0.147673i
$303$		0			0
$304$	15.6873			0.899728
$305$	6.21666	+	2.07782i	0.355965	+	0.118976i
$306$		0			0
$307$			24.6936i			1.40934i	0.709537	+	0.704668i	$0.248904\pi$
$307$			24.6936i			1.40934i	−0.709537	+	0.704668i	$0.751096\pi$
$308$	13.1992	+	7.62058i	0.752096	+	0.434223i
$309$		0			0
$310$	3.61987	+	4.08884i	0.205595	+	0.232231i
$311$	11.7458			0.666041			0.333021	−	0.942920i	$-0.391932\pi$
$311$	11.7458			0.666041			0.333021	+	0.942920i	$0.391932\pi$
$312$		0			0
$313$			6.16331i			0.348371i	0.984713	+	0.174185i	$0.0557292\pi$
$313$			6.16331i			0.348371i	−0.984713	+	0.174185i	$0.944271\pi$
$314$	−1.96799	−	3.40866i	−0.111060	−	0.192362i
$315$		0			0
$316$	−12.1703	+	21.0795i	−0.684631	+	1.18582i
$317$			12.9683i			0.728371i	0.931326	+	0.364186i	$0.118653\pi$
$317$			12.9683i			0.728371i	−0.931326	+	0.364186i	$0.881347\pi$
$318$		0			0
$319$	5.91390	−	10.2432i	0.331115	−	0.573508i
$320$	−0.253256	−	1.24273i	−0.0141574	−	0.0694707i
$321$		0			0
$322$	3.06578	−	1.77003i	0.170849	−	0.0986400i
$323$	15.5993	−	9.00625i	0.867967	−	0.501121i
$324$		0			0
$325$	9.05026	−	15.5914i	0.502018	−	0.864857i
$326$	−12.4204			−0.687903
$327$		0			0
$328$	1.47405	−	0.851044i	0.0813909	−	0.0469911i
$329$	−5.60027	+	9.69996i	−0.308753	+	0.534776i
$330$		0			0
$331$	−5.40749	+	9.36605i	−0.297223	+	0.514805i	−0.975499	−	0.220002i	$-0.929394\pi$
$331$	−5.40749	+	9.36605i	−0.297223	+	0.514805i	0.678277	+	0.734806i	$0.262727\pi$
$332$	−16.6402	−	9.60724i	−0.913251	−	0.527266i
$333$		0			0
$334$	−5.77611	+	10.0045i	−0.316055	+	0.547423i
$335$	1.65959	+	1.87459i	0.0906728	+	0.102420i
$336$		0			0
$337$			3.84210i			0.209292i	0.994510	+	0.104646i	$0.0333710\pi$
$337$			3.84210i			0.209292i	−0.994510	+	0.104646i	$0.966629\pi$
$338$	−1.84812	−	7.60523i	−0.100524	−	0.413670i
$339$		0			0
$340$	−5.45304	−	6.15952i	−0.295733	−	0.334047i
$341$	−5.30472	−	9.18804i	−0.287266	−	0.497560i
$342$		0			0
$343$			4.75359i			0.256670i
$344$	−0.249229	+	0.431678i	−0.0134375	+	0.0232745i
$345$		0			0
$346$	−11.6099			−0.624154
$347$	−10.1199	−	5.84271i	−0.543263	−	0.313653i	0.203137	−	0.979150i	$-0.434886\pi$
$347$	−10.1199	−	5.84271i	−0.543263	−	0.313653i	−0.746400	+	0.665497i	$0.768219\pi$
$348$		0			0
$349$	0.812876	+	1.40794i	0.0435122	+	0.0753654i	0.886961	−	0.461844i	$-0.152812\pi$
$349$	0.812876	+	1.40794i	0.0435122	+	0.0753654i	−0.843449	+	0.537209i	$0.819479\pi$
$350$	9.85810	−	4.19206i	0.526938	−	0.224075i
$351$		0			0
$352$		−	14.5360i		−	0.774773i
$353$	−7.90443	+	4.56363i	−0.420710	+	0.242897i	−0.695381	−	0.718641i	$-0.744764\pi$
$353$	−7.90443	+	4.56363i	−0.420710	+	0.242897i	0.274671	+	0.961538i	$0.411431\pi$
$354$		0			0
$355$	24.0396	+	8.03487i	1.27589	+	0.426446i
$356$	−28.1801			−1.49354
$357$		0			0
$358$	2.98151	+	1.72137i	0.157577	+	0.0909774i
$359$	23.8361			1.25802			0.629011	−	0.777396i	$-0.283460\pi$
$359$	23.8361			1.25802			0.629011	+	0.777396i	$0.283460\pi$
$360$		0			0
$361$	−22.6398	−	39.2133i	−1.19157	−	2.06386i
$362$	−2.63431	+	1.52092i	−0.138456	+	0.0799376i
$363$		0			0
$364$	−8.26740	+	19.3165i	−0.433329	+	1.01246i
$365$	27.2456	−	5.55237i	1.42610	−	0.290625i
$366$		0			0
$367$	−14.6989	+	8.48640i	−0.767275	+	0.442986i	−0.831902	−	0.554923i	$-0.812748\pi$
$367$	−14.6989	+	8.48640i	−0.767275	+	0.442986i	0.0646267	+	0.997910i	$0.479414\pi$
$368$	2.79986	+	1.61650i	0.145953	+	0.0842658i
$369$		0			0
$370$	−5.37712	−	1.79722i	−0.279543	−	0.0934331i
$371$	−11.4309	+	19.7989i	−0.593463	+	1.02791i
$372$		0			0
$373$	−13.7766	−	7.95393i	−0.713326	−	0.411839i	0.0989655	−	0.995091i	$-0.468447\pi$
$373$	−13.7766	−	7.95393i	−0.713326	−	0.411839i	−0.812291	+	0.583252i	$0.801780\pi$
$374$	−1.76876	−	3.06359i	−0.0914606	−	0.158414i
$375$		0			0
$376$	6.89264			0.355461
$377$	14.9904	+	6.41586i	0.772047	+	0.330434i
$378$		0			0
$379$	10.4083	+	18.0277i	0.534638	+	0.926020i	0.999181	+	0.0404693i	$0.0128853\pi$
$379$	10.4083	+	18.0277i	0.534638	+	0.926020i	−0.464543	+	0.885551i	$0.653781\pi$
$380$	−21.9809	+	19.4598i	−1.12760	+	0.998267i
$381$		0			0
$382$		−	10.6291i		−	0.543831i
$383$	−20.8749	−	12.0521i	−1.06666	−	0.615834i	−0.139391	−	0.990237i	$-0.544514\pi$
$383$	−20.8749	−	12.0521i	−1.06666	−	0.615834i	−0.927266	+	0.374403i	$0.877848\pi$
$384$		0			0
$385$	−20.3927	+	4.15582i	−1.03931	+	0.211800i
$386$	−1.10300	+	1.91046i	−0.0561413	+	0.0972396i
$387$		0			0
$388$	17.3724	−	10.0300i	0.881949	−	0.509194i
$389$	−17.6045			−0.892583			−0.446292	−	0.894888i	$-0.647256\pi$
$389$	−17.6045			−0.892583			−0.446292	+	0.894888i	$0.647256\pi$
$390$		0			0
$391$	3.71220			0.187734
$392$	−10.7425	+	6.20221i	−0.542580	+	0.313259i
$393$		0			0
$394$	−2.09759	+	3.63313i	−0.105675	+	0.183034i
$395$	−6.63696	−	32.5676i	−0.333941	−	1.63865i
$396$		0			0
$397$	11.1601	+	6.44331i	0.560111	+	0.323380i	0.753190	−	0.657803i	$-0.228514\pi$
$397$	11.1601	+	6.44331i	0.560111	+	0.323380i	−0.193079	+	0.981183i	$0.561847\pi$
$398$			4.44303i			0.222709i
$399$		0			0
$400$	7.81703	+	5.88261i	0.390852	+	0.294130i
$401$	−7.96163	−	13.7899i	−0.397585	−	0.688637i	0.595843	−	0.803101i	$-0.296818\pi$
$401$	−7.96163	−	13.7899i	−0.397585	−	0.688637i	−0.993427	+	0.114464i	$0.963485\pi$
$402$		0			0
$403$	11.7071	−	8.76735i	0.583172	−	0.436733i
$404$	28.2278			1.40438
$405$		0			0
$406$	4.84457	+	8.39104i	0.240432	+	0.416440i
$407$	9.53893	+	5.50731i	0.472827	+	0.272987i
$408$		0			0
$409$	2.18586	−	3.78602i	0.108084	−	0.187206i	−0.806910	−	0.590674i	$-0.798862\pi$
$409$	2.18586	−	3.78602i	0.108084	−	0.187206i	0.914994	+	0.403468i	$0.132195\pi$
$410$	−0.331676	+	0.992345i	−0.0163803	+	0.0490084i
$411$		0			0
$412$	−3.98352	−	2.29988i	−0.196254	−	0.113307i
$413$	−38.6315	+	22.3039i	−1.90093	+	1.09750i
$414$		0			0
$415$	25.7090	−	5.23923i	1.26200	−	0.257184i
$416$	19.8971	−	2.38288i	0.975536	−	0.116831i
$417$		0			0
$418$	−10.9328	+	6.31204i	−0.534739	+	0.308732i
$419$	−4.51510	−	7.82039i	−0.220577	−	0.382051i	0.734406	−	0.678710i	$-0.237461\pi$
$419$	−4.51510	−	7.82039i	−0.220577	−	0.382051i	−0.954983	+	0.296659i	$0.904127\pi$
$420$		0			0
$421$	15.7927			0.769689			0.384845	−	0.922981i	$-0.374255\pi$
$421$	15.7927			0.769689			0.384845	+	0.922981i	$0.374255\pi$
$422$	12.8279	+	7.40618i	0.624451	+	0.360527i
$423$		0			0
$424$	14.0688			0.683241
$425$	11.1504	+	1.36176i	0.540876	+	0.0660552i
$426$		0			0
$427$	9.03417	−	5.21588i	0.437194	−	0.252414i
$428$			16.2342i			0.784710i
$429$		0			0
$430$	−0.0611861	−	0.300241i	−0.00295066	−	0.0144789i
$431$	2.43056	+	4.20985i	0.117076	+	0.202782i	0.918608	−	0.395171i	$-0.129315\pi$
$431$	2.43056	+	4.20985i	0.117076	+	0.202782i	−0.801532	+	0.597952i	$0.795981\pi$
$432$		0			0
$433$	2.66886	+	1.54087i	0.128257	+	0.0740494i	0.562756	−	0.826623i	$-0.309741\pi$
$433$	2.66886	+	1.54087i	0.128257	+	0.0740494i	−0.434499	+	0.900673i	$0.643074\pi$
$434$	8.69107			0.417185
$435$		0			0
$436$	5.87109	−	10.1690i	0.281174	−	0.487008i
$437$		−	13.2474i		−	0.633710i
$438$		0			0
$439$	1.92116	+	3.32754i	0.0916918	+	0.158815i	0.908223	−	0.418486i	$-0.137439\pi$
$439$	1.92116	+	3.32754i	0.0916918	+	0.158815i	−0.816531	+	0.577301i	$0.804106\pi$
$440$	8.48946	+	9.58932i	0.404719	+	0.457153i
$441$		0			0
$442$	3.90353	−	2.92332i	0.185672	−	0.139048i
$443$			7.40427i			0.351788i	0.984409	+	0.175894i	$0.0562815\pi$
$443$			7.40427i			0.351788i	−0.984409	+	0.175894i	$0.943718\pi$
$444$		0			0
$445$	28.8116	−	25.5070i	1.36580	−	1.20915i
$446$	−0.167035	+	0.289312i	−0.00790931	+	0.0136993i
$447$		0			0
$448$	−1.74803	−	1.00922i	−0.0825865	−	0.0476813i
$449$	12.3270	−	21.3509i	0.581745	−	1.00761i	−0.413527	−	0.910492i	$-0.635703\pi$
$449$	12.3270	−	21.3509i	0.581745	−	1.00761i	0.995273	−	0.0971206i	$-0.0309632\pi$
$450$		0			0
$451$	1.01637	−	1.76041i	0.0478590	−	0.0828942i
$452$	−9.85512	+	5.68986i	−0.463546	+	0.267628i
$453$		0			0
$454$	−0.910223			−0.0427189
$455$	−9.03150	−	27.2325i	−0.423403	−	1.27668i
$456$		0			0
$457$	−24.8930	+	14.3720i	−1.16444	+	0.672292i	−0.952365	−	0.304960i	$-0.901357\pi$
$457$	−24.8930	+	14.3720i	−1.16444	+	0.672292i	−0.212079	+	0.977252i	$0.568023\pi$
$458$	−2.82727	+	1.63233i	−0.132110	+	0.0762736i
$459$		0			0
$460$	−5.92838	+	1.20815i	−0.276412	+	0.0563301i
$461$	1.99008	−	3.44692i	0.0926874	−	0.160539i	−0.815954	−	0.578117i	$-0.803788\pi$
$461$	1.99008	−	3.44692i	0.0926874	−	0.160539i	0.908641	+	0.417578i	$0.137121\pi$
$462$		0			0
$463$			13.1195i			0.609717i	0.952398	+	0.304859i	$0.0986092\pi$
$463$			13.1195i			0.609717i	−0.952398	+	0.304859i	$0.901391\pi$
$464$	−4.42435	+	7.66320i	−0.205395	+	0.355755i
$465$		0			0
$466$	3.38738	+	5.86712i	0.156917	+	0.271789i
$467$			11.9144i			0.551332i	0.961253	+	0.275666i	$0.0888984\pi$
$467$			11.9144i			0.551332i	−0.961253	+	0.275666i	$0.911102\pi$
$468$		0			0
$469$	3.98456			0.183990
$470$	−3.17244	+	2.80857i	−0.146334	+	0.129550i
$471$		0			0
$472$	23.7732	+	13.7255i	1.09425	+	0.631767i
$473$			0.595290i			0.0273715i
$474$		0			0
$475$	4.85960	−	39.7917i	0.222974	−	1.82577i
$476$	−13.0924			−0.600089
$477$		0			0
$478$	9.34744	−	5.39675i	0.427542	−	0.246842i
$479$	−20.6210	−	35.7167i	−0.942199	−	1.63194i	−0.761265	−	0.648441i	$-0.775421\pi$
$479$	−20.6210	−	35.7167i	−0.942199	−	1.63194i	−0.180934	−	0.983495i	$-0.557912\pi$
$480$		0			0
$481$	−5.97476	+	13.9598i	−0.272425	+	0.636513i
$482$			12.2426i			0.557635i
$483$		0			0
$484$	3.40590	+	5.89919i	0.154814	+	0.268145i
$485$	−8.68312	+	25.9791i	−0.394280	+	1.17965i
$486$		0			0
$487$	12.5440	+	7.24227i	0.568422	+	0.328179i	0.756519	−	0.653972i	$-0.226898\pi$
$487$	12.5440	+	7.24227i	0.568422	+	0.328179i	−0.188097	+	0.982151i	$0.560232\pi$
$488$	−5.55948	−	3.20977i	−0.251666	−	0.145299i
$489$		0			0
$490$	2.41718	−	7.23197i	0.109197	−	0.326707i
$491$	8.84200	+	15.3148i	0.399034	+	0.691147i	0.993607	−	0.112894i	$-0.0360122\pi$
$491$	8.84200	+	15.3148i	0.399034	+	0.691147i	−0.594573	+	0.804042i	$0.702679\pi$
$492$		0			0
$493$			10.1603i			0.457596i
$494$	−10.4322	−	13.9302i	−0.469367	−	0.626749i
$495$		0			0
$496$	3.96860	+	6.87382i	0.178196	+	0.308644i
$497$	34.9348	−	20.1696i	1.56704	−	0.904731i
$498$		0			0
$499$	0.690775			0.0309233			0.0154617	−	0.999880i	$-0.495078\pi$
$499$	0.690775			0.0309233			0.0154617	+	0.999880i	$0.495078\pi$
$500$	−18.2505	+	1.45421i	−0.816185	+	0.0650342i
$501$		0			0
$502$			11.3486i			0.506512i
$503$	−9.08724	−	5.24652i	−0.405180	−	0.233931i	0.283537	−	0.958961i	$-0.408492\pi$
$503$	−9.08724	−	5.24652i	−0.405180	−	0.233931i	−0.688717	+	0.725031i	$0.741826\pi$
$504$		0			0
$505$	−28.8602	+	25.5501i	−1.28426	+	1.13696i
$506$	−2.60170			−0.115660
$507$		0			0
$508$		−	9.60006i		−	0.425934i
$509$	−11.1971	−	19.3939i	−0.496302	−	0.859621i	0.503689	−	0.863885i	$-0.331976\pi$
$509$	−11.1971	−	19.3939i	−0.496302	−	0.859621i	−0.999991	+	0.00426454i	$0.998643\pi$
$510$		0			0
$511$	22.1262	−	38.3236i	0.978804	−	1.69534i
$512$			19.4447i			0.859344i
$513$		0			0
$514$	8.54444	−	14.7994i	0.376879	−	0.652774i
$515$	6.15449	−	1.25422i	0.271199	−	0.0552677i
$516$		0			0
$517$	7.12879	−	4.11581i	0.313524	−	0.181013i
$518$	−7.81414	+	4.51149i	−0.343334	+	0.198224i
$519$		0			0
$520$	−11.7343	+	13.1924i	−0.514583	+	0.578527i
$521$	24.8874			1.09034			0.545168	−	0.838327i	$-0.316466\pi$
$521$	24.8874			1.09034			0.545168	+	0.838327i	$0.316466\pi$
$522$		0			0
$523$	19.1352	−	11.0477i	0.836725	−	0.483083i	−0.0194246	−	0.999811i	$-0.506183\pi$
$523$	19.1352	−	11.0477i	0.836725	−	0.483083i	0.856150	+	0.516728i	$0.172850\pi$
$524$	8.19885	−	14.2008i	0.358168	−	0.620366i
$525$		0			0
$526$	4.29480	−	7.43882i	0.187262	−	0.324348i
$527$	7.89268	+	4.55684i	0.343810	+	0.198499i
$528$		0			0
$529$	−10.1349	+	17.5542i	−0.440649	+	0.763226i
$530$	−6.47538	+	5.73268i	−0.281273	+	0.249012i
$531$		0			0
$532$			46.7218i			2.02565i
$533$	2.57628	+	1.10264i	0.111591	+	0.0477606i
$534$		0			0
$535$	−14.6942	−	16.5979i	−0.635287	−	0.717592i
$536$	−1.22602	−	2.12352i	−0.0529559	−	0.0917223i
$537$		0			0
$538$			15.3656i			0.662459i
$539$	−7.40707	+	12.8294i	−0.319045	+	0.552602i
$540$		0			0
$541$	−11.0259			−0.474039			−0.237020	−	0.971505i	$-0.576171\pi$
$541$	−11.0259			−0.474039			−0.237020	+	0.971505i	$0.576171\pi$
$542$	4.07958	+	2.35535i	0.175233	+	0.101171i
$543$		0			0
$544$	6.24335	+	10.8138i	0.267681	+	0.463638i
$545$	3.20175	+	15.7110i	0.137148	+	0.672986i
$546$		0			0
$547$			6.51100i			0.278390i	0.990265	+	0.139195i	$0.0444515\pi$
$547$			6.51100i			0.278390i	−0.990265	+	0.139195i	$0.955548\pi$
$548$	26.0688	−	15.0508i	1.11360	−	0.642939i
$549$		0			0
$550$	−7.81480	−	0.954393i	−0.333224	−	0.0406954i
$551$	36.2581			1.54465
$552$		0			0
$553$	−45.8096	−	26.4482i	−1.94802	−	1.12469i
$554$	11.7147			0.497711
$555$		0			0
$556$	3.52942	+	6.11313i	0.149681	+	0.259254i
$557$	−3.09063	+	1.78437i	−0.130954	+	0.0756064i	−0.564046	−	0.825743i	$-0.690756\pi$
$557$	−3.09063	+	1.78437i	−0.130954	+	0.0756064i	0.433092	+	0.901350i	$0.357423\pi$
$558$		0			0
$559$	−0.814841	+	0.0975856i	−0.0344641	+	0.00412743i
$560$	15.2563	−	3.10908i	0.644697	−	0.131383i
$561$		0			0
$562$	−12.0569	+	6.96105i	−0.508590	+	0.293634i
$563$	13.5374	+	7.81582i	0.570533	+	0.329397i	0.757362	−	0.652995i	$-0.226488\pi$
$563$	13.5374	+	7.81582i	0.570533	+	0.329397i	−0.186829	+	0.982392i	$0.559821\pi$
$564$		0			0
$565$	4.92582	−	14.7376i	0.207231	−	0.620016i
$566$	−7.79217	+	13.4964i	−0.327529	+	0.567297i
$567$		0			0
$568$	−21.4983	−	12.4121i	−0.902050	−	0.520799i
$569$	3.64767	+	6.31796i	0.152918	+	0.264863i	0.932299	−	0.361688i	$-0.117799\pi$
$569$	3.64767	+	6.31796i	0.152918	+	0.264863i	−0.779381	+	0.626551i	$0.784466\pi$
$570$		0			0
$571$	−4.57292			−0.191371			−0.0956853	−	0.995412i	$-0.530504\pi$
$571$	−4.57292			−0.191371			−0.0956853	+	0.995412i	$0.530504\pi$
$572$	12.3601	−	9.25636i	0.516801	−	0.387028i
$573$		0			0
$574$	0.832594	+	1.44210i	0.0347518	+	0.0601919i
$575$	4.96768	−	6.60123i	0.207166	−	0.275290i
$576$		0			0
$577$		−	39.0134i		−	1.62415i	−0.583555	−	0.812074i	$-0.698339\pi$
$577$		−	39.0134i		−	1.62415i	0.583555	−	0.812074i	$-0.301661\pi$
$578$	−6.23186	−	3.59797i	−0.259211	−	0.149656i
$579$		0			0
$580$	−3.30669	−	16.2260i	−0.137303	−	0.673747i
$581$	20.8783	−	36.1622i	0.866177	−	1.50026i
$582$		0			0
$583$	14.5508	−	8.40092i	0.602634	−	0.347931i
$584$	−27.2322			−1.12688
$585$		0			0
$586$	−2.41414			−0.0997274
$587$	11.0611	−	6.38611i	0.456539	−	0.263583i	−0.254049	−	0.967191i	$-0.581762\pi$
$587$	11.0611	−	6.38611i	0.456539	−	0.263583i	0.710588	+	0.703609i	$0.248429\pi$
$588$		0			0
$589$	16.2616	−	28.1659i	0.670048	−	1.16056i
$590$	−16.5348	+	3.36962i	−0.680726	+	0.138725i
$591$		0			0
$592$	−7.13634	−	4.12017i	−0.293302	−	0.169338i
$593$			2.51648i			0.103339i	0.998664	+	0.0516697i	$0.0164543\pi$
$593$			2.51648i			0.103339i	−0.998664	+	0.0516697i	$0.983546\pi$
$594$		0			0
$595$	13.3858	−	11.8505i	0.548762	−	0.485821i
$596$	1.85171	+	3.20726i	0.0758491	+	0.131375i
$597$		0			0
$598$	−0.426495	−	3.56124i	−0.0174407	−	0.145630i
$599$	20.2305			0.826594			0.413297	−	0.910596i	$-0.364377\pi$
$599$	20.2305			0.826594			0.413297	+	0.910596i	$0.364377\pi$
$600$		0			0
$601$	−22.2480	−	38.5346i	−0.907514	−	1.57186i	−0.817506	−	0.575920i	$-0.804644\pi$
$601$	−22.2480	−	38.5346i	−0.907514	−	1.57186i	−0.0900081	−	0.995941i	$-0.528689\pi$
$602$	−0.422319	−	0.243826i	−0.0172124	−	0.00993761i
$603$		0			0
$604$	−6.98022	+	12.0901i	−0.284021	+	0.491939i
$605$	−8.82181	−	2.94855i	−0.358657	−	0.119876i
$606$		0			0
$607$	34.4077	+	19.8653i	1.39657	+	0.806307i	0.994031	−	0.109097i	$-0.0347961\pi$
$607$	34.4077	+	19.8653i	1.39657	+	0.806307i	0.402534	+	0.915405i	$0.368129\pi$
$608$	38.5903	−	22.2801i	1.56504	−	0.903578i
$609$		0			0
$610$	3.86674	−	0.788002i	0.156560	−	0.0319053i
$611$	6.80239	+	9.08328i	0.275195	+	0.367470i
$612$		0			0
$613$	−8.58710	+	4.95776i	−0.346830	+	0.200242i	−0.663288	−	0.748364i	$-0.730840\pi$
$613$	−8.58710	+	4.95776i	−0.346830	+	0.200242i	0.316458	+	0.948606i	$0.397506\pi$
$614$	7.43329	+	12.8748i	0.299983	+	0.519586i
$615$		0			0
$616$	20.3826			0.821240
$617$	31.1563	+	17.9881i	1.25431	+	0.724174i	0.971962	−	0.235140i	$-0.0755548\pi$
$617$	31.1563	+	17.9881i	1.25431	+	0.724174i	0.282344	+	0.959313i	$0.408888\pi$
$618$		0			0
$619$	−30.5783			−1.22905			−0.614523	−	0.788899i	$-0.710651\pi$
$619$	−30.5783			−1.22905			−0.614523	+	0.788899i	$0.710651\pi$
$620$	−14.0876	−	4.70858i	−0.565773	−	0.189101i
$621$		0			0
$622$	6.12406	−	3.53573i	0.245552	−	0.141770i
$623$		−	61.2406i		−	2.45355i
$624$		0			0
$625$	17.3431	−	18.0060i	0.693725	−	0.720240i
$626$	1.85529	+	3.21345i	0.0741522	+	0.128435i
$627$		0			0
$628$	9.27149	+	5.35290i	0.369973	+	0.213604i
$629$	−9.46173			−0.377264
$630$		0			0
$631$	13.8644	−	24.0138i	0.551933	−	0.955976i	−0.446202	−	0.894932i	$-0.647224\pi$
$631$	13.8644	−	24.0138i	0.551933	−	0.955976i	0.998135	−	0.0610440i	$-0.0194430\pi$
$632$			32.5516i			1.29483i
$633$		0			0
$634$	3.90373	+	6.76146i	0.155037	+	0.268532i
$635$	8.68939	+	9.81516i	0.344828	+	0.389503i
$636$		0			0
$637$	−18.7753	−	8.03576i	−0.743904	−	0.318388i
$638$		−	7.12084i		−	0.281917i
$639$		0			0
$640$	−16.9820	−	19.1822i	−0.671274	−	0.758241i
$641$	1.61226	−	2.79251i	0.0636803	−	0.110297i	−0.832428	−	0.554134i	$-0.813050\pi$
$641$	1.61226	−	2.79251i	0.0636803	−	0.110297i	0.896108	+	0.443836i	$0.146383\pi$
$642$		0			0
$643$	5.46209	+	3.15354i	0.215404	+	0.124363i	0.603820	−	0.797121i	$-0.293644\pi$
$643$	5.46209	+	3.15354i	0.215404	+	0.124363i	−0.388417	+	0.921484i	$0.626978\pi$
$644$	−4.81445	+	8.33887i	−0.189716	+	0.328598i
$645$		0			0
$646$	5.42215	−	9.39143i	0.213332	−	0.369501i
$647$	−10.6571	+	6.15288i	−0.418974	+	0.241895i	−0.694638	−	0.719359i	$-0.744436\pi$
$647$	−10.6571	+	6.15288i	−0.418974	+	0.241895i	0.275664	+	0.961254i	$0.411102\pi$
$648$		0			0
$649$	32.7837			1.28687
$650$	0.0253076	−	10.8535i	0.000992645	−	0.425707i
$651$		0			0
$652$	29.2572	−	16.8916i	1.14580	−	0.661527i
$653$	−12.8047	+	7.39280i	−0.501087	+	0.289302i	−0.729162	−	0.684341i	$-0.760090\pi$
$653$	−12.8047	+	7.39280i	−0.501087	+	0.289302i	0.228076	+	0.973643i	$0.426757\pi$
$654$		0			0
$655$	4.47118	+	21.9401i	0.174703	+	0.857271i
$656$	−0.760375	+	1.31701i	−0.0296876	+	0.0514205i
$657$		0			0
$658$			6.74321i			0.262878i
$659$	5.20958	−	9.02326i	0.202937	−	0.351496i	−0.746537	−	0.665344i	$-0.768285\pi$
$659$	5.20958	−	9.02326i	0.202937	−	0.351496i	0.949473	+	0.313848i	$0.101618\pi$
$660$		0			0
$661$	−1.78786	−	3.09666i	−0.0695396	−	0.120446i	0.829159	−	0.559013i	$-0.188820\pi$
$661$	−1.78786	−	3.09666i	−0.0695396	−	0.120446i	−0.898699	+	0.438567i	$0.855486\pi$
$662$			6.51108i			0.253060i
$663$		0			0
$664$	−25.6963			−0.997211
$665$	−42.2897	−	47.7686i	−1.63993	−	1.85239i
$666$		0			0
$667$	6.47133	+	3.73622i	0.250571	+	0.144667i
$668$		−	31.4218i		−	1.21575i
$669$		0			0
$670$	1.42957	+	0.477814i	0.0552293	+	0.0184595i
$671$	−7.66661			−0.295966
$672$		0			0
$673$	4.62917	−	2.67265i	0.178441	−	0.103023i	−0.408119	−	0.912929i	$-0.633815\pi$
$673$	4.62917	−	2.67265i	0.178441	−	0.103023i	0.586560	+	0.809906i	$0.300482\pi$
$674$	1.15655	+	2.00321i	0.0445488	+	0.0771607i
$675$		0			0
$676$	14.6964	+	15.4012i	0.565246	+	0.592355i
$677$			30.1981i			1.16061i	0.814400	+	0.580304i	$0.197066\pi$
$677$			30.1981i			1.16061i	−0.814400	+	0.580304i	$0.802934\pi$
$678$		0			0
$679$	21.7969	+	37.7534i	0.836489	+	1.44884i
$680$	−10.4343	−	3.48749i	−0.400135	−	0.133739i
$681$		0			0
$682$	−5.53159	−	3.19367i	−0.211816	−	0.122292i
$683$	−3.35693	−	1.93812i	−0.128449	−	0.0741602i	0.434399	−	0.900721i	$-0.356961\pi$
$683$	−3.35693	−	1.93812i	−0.128449	−	0.0741602i	−0.562848	+	0.826561i	$0.690294\pi$
$684$		0			0
$685$	−13.0298	+	38.9839i	−0.497843	+	1.48950i
$686$	1.43093	+	2.47845i	0.0546333	+	0.0946276i
$687$		0			0
$688$		−	0.445353i		−	0.0169789i
$689$	13.8846	+	18.5402i	0.528961	+	0.706325i
$690$		0			0
$691$	19.4333	+	33.6594i	0.739277	+	1.28046i	0.952821	+	0.303532i	$0.0981658\pi$
$691$	19.4333	+	33.6594i	0.739277	+	1.28046i	−0.213545	+	0.976933i	$0.568501\pi$
$692$	27.3481	−	15.7894i	1.03962	−	0.600223i
$693$		0			0
$694$	−7.03512			−0.267049
$695$	−9.14173	−	3.05548i	−0.346766	−	0.115901i
$696$		0			0
$697$			1.74616i			0.0661405i
$698$	0.847642	+	0.489386i	0.0320837	+	0.0185235i
$699$		0			0
$700$	−17.5203	+	23.2816i	−0.662205	+	0.879962i
$701$	−18.2792			−0.690396			−0.345198	−	0.938530i	$-0.612188\pi$
$701$	−18.2792			−0.690396			−0.345198	+	0.938530i	$0.612188\pi$
$702$		0			0
$703$			33.7653i			1.27348i
$704$	0.741709	+	1.28468i	0.0279542	+	0.0484181i
$705$		0			0
$706$	−2.74750	+	4.75881i	−0.103403	+	0.179100i
$707$			61.3441i			2.30708i
$708$		0			0
$709$	3.19243	−	5.52946i	0.119894	−	0.207663i	−0.799831	−	0.600225i	$-0.795078\pi$
$709$	3.19243	−	5.52946i	0.119894	−	0.207663i	0.919726	+	0.392562i	$0.128411\pi$
$710$	14.9525	−	3.04718i	0.561159	−	0.114359i
$711$		0			0
$712$	−32.6375	+	18.8433i	−1.22314	+	0.706181i
$713$	5.80472	−	3.35136i	0.217389	−	0.125509i
$714$		0			0
$715$	−4.25872	+	20.6514i	−0.159267	+	0.772317i
$716$	−9.36420			−0.349957
$717$		0			0
$718$	12.4278	−	7.17519i	0.463801	−	0.267776i
$719$	7.18151	−	12.4387i	0.267825	−	0.463887i	−0.700475	−	0.713677i	$-0.747028\pi$
$719$	7.18151	−	12.4387i	0.267825	−	0.463887i	0.968300	+	0.249790i	$0.0803617\pi$
$720$		0			0
$721$	4.99807	−	8.65691i	0.186138	−	0.322400i
$722$	−23.6081	−	13.6301i	−0.878603	−	0.507262i
$723$		0			0
$724$	4.13686	−	7.16526i	0.153745	−	0.266295i
$725$	18.0675	+	13.5965i	0.671012	+	0.504962i
$726$		0			0
$727$		−	12.8444i		−	0.476372i	−0.971220	−	0.238186i	$-0.923447\pi$
$727$		−	12.8444i		−	0.476372i	0.971220	−	0.238186i	$-0.0765528\pi$
$728$	3.34132	+	27.9000i	0.123837	+	1.03404i
$729$		0			0
$730$	12.5340	−	11.0964i	0.463905	−	0.410697i
$731$	−0.255682	−	0.442855i	−0.00945675	−	0.0163796i
$732$		0			0
$733$		−	3.30801i		−	0.122184i	−0.998132	−	0.0610922i	$-0.980542\pi$
$733$		−	3.30801i		−	0.122184i	0.998132	−	0.0610922i	$-0.0194584\pi$
$734$	−5.10918	+	8.84935i	−0.188583	+	0.326636i
$735$		0			0
$736$	9.18343			0.338506
$737$	−2.53604	−	1.46419i	−0.0934164	−	0.0539340i
$738$		0			0
$739$	−1.95497	−	3.38611i	−0.0719147	−	0.124560i	0.827826	−	0.560985i	$-0.189578\pi$
$739$	−1.95497	−	3.38611i	−0.0719147	−	0.124560i	−0.899740	+	0.436425i	$0.856244\pi$
$740$	15.1104	−	3.07935i	0.555469	−	0.113199i
$741$		0			0
$742$			13.7638i			0.505285i
$743$	−30.5991	+	17.6664i	−1.12257	+	0.648116i	−0.942056	−	0.335456i	$-0.891110\pi$
$743$	−30.5991	+	17.6664i	−1.12257	+	0.648116i	−0.180515	+	0.983572i	$0.557776\pi$
$744$		0			0
$745$	−4.79622	−	1.60306i	−0.175720	−	0.0587317i
$746$	−9.57721			−0.350647
$747$		0			0
$748$	8.33290	+	4.81100i	0.304681	+	0.175908i
$749$	−35.2799			−1.28910
$750$		0			0
$751$	1.57264	+	2.72389i	0.0573864	+	0.0993962i	0.893291	−	0.449478i	$-0.148390\pi$
$751$	1.57264	+	2.72389i	0.0573864	+	0.0993962i	−0.835905	+	0.548874i	$0.815057\pi$
$752$	−5.33324	+	3.07915i	−0.194483	+	0.112285i
$753$		0			0
$754$	9.74710	−	1.16732i	0.354968	−	0.0425111i
$755$	−3.80661	−	18.6791i	−0.138537	−	0.679800i
$756$		0			0
$757$	18.0555	−	10.4244i	0.656240	−	0.378880i	−0.134603	−	0.990900i	$-0.542976\pi$
$757$	18.0555	−	10.4244i	0.656240	−	0.378880i	0.790843	+	0.612019i	$0.209643\pi$
$758$	10.8534	+	6.26623i	0.394215	+	0.227600i
$759$		0			0
$760$	−12.4455	+	37.2358i	−0.451446	+	1.35069i
$761$	−22.2187	+	38.4839i	−0.805427	+	1.39504i	0.110576	+	0.993868i	$0.464731\pi$
$761$	−22.2187	+	38.4839i	−0.805427	+	1.39504i	−0.916002	+	0.401173i	$0.868603\pi$
$762$		0			0
$763$	22.0991	+	12.7589i	0.800042	+	0.461905i
$764$	14.4554	+	25.0376i	0.522979	+	0.905827i
$765$		0			0
$766$	−14.5118			−0.524332
$767$	5.37421	+	44.8747i	0.194051	+	1.62033i
$768$		0			0
$769$	−11.8333	−	20.4959i	−0.426719	−	0.739100i	0.569860	−	0.821742i	$-0.306997\pi$
$769$	−11.8333	−	20.4959i	−0.426719	−	0.739100i	−0.996579	+	0.0826421i	$0.973664\pi$
$770$	−9.38142	+	8.30541i	−0.338083	+	0.299306i
$771$		0			0
$772$		−	6.00029i		−	0.215955i
$773$	−16.4540	−	9.49970i	−0.591808	−	0.341680i	0.174004	−	0.984745i	$-0.444329\pi$
$773$	−16.4540	−	9.49970i	−0.591808	−	0.341680i	−0.765812	+	0.643064i	$0.777663\pi$
$774$		0			0
$775$	18.6652	−	7.93721i	0.670474	−	0.285113i
$776$	13.4135	−	23.2328i	0.481516	−	0.834010i
$777$		0			0
$778$	−9.17871	+	5.29933i	−0.329073	+	0.189990i
$779$	6.23137			0.223262
$780$		0			0
$781$	−29.6465			−1.06084
$782$	1.93548	−	1.11745i	0.0692127	−	0.0399600i
$783$		0			0
$784$	5.54143	−	9.59804i	0.197908	−	0.342787i
$785$	−14.3244	+	2.91916i	−0.511258	+	0.104189i
$786$		0			0
$787$	38.0294	+	21.9563i	1.35560	+	0.782657i	0.989027	−	0.147732i	$-0.0471972\pi$
$787$	38.0294	+	21.9563i	1.35560	+	0.782657i	0.366574	+	0.930389i	$0.380531\pi$
$788$		−	11.4108i		−	0.406493i
$789$		0			0
$790$	−13.2640	−	14.9824i	−0.471910	−	0.533049i
$791$	−12.3651	−	21.4170i	−0.439652	−	0.761500i
$792$		0			0
$793$	−1.25678	−	10.4942i	−0.0446297	−	0.372658i
$794$	7.75829			0.275332
$795$		0			0
$796$	−6.04247	−	10.4659i	−0.214170	−	0.370953i
$797$	−16.1870	−	9.34557i	−0.573373	−	0.331037i	0.185122	−	0.982715i	$-0.440732\pi$
$797$	−16.1870	−	9.34557i	−0.573373	−	0.331037i	−0.758495	+	0.651678i	$0.774065\pi$
$798$		0			0
$799$	−3.53555	+	6.12375i	−0.125079	+	0.216643i
$800$	27.5845	+	3.36880i	0.975261	+	0.119105i
$801$		0			0
$802$	−8.30214	−	4.79324i	−0.293159	−	0.169255i
$803$	−28.1652	+	16.2612i	−0.993928	+	0.573845i
$804$		0			0
$805$	−2.62552	−	12.8835i	−0.0925375	−	0.454082i
$806$	3.46474	−	8.09525i	0.122040	−	0.285143i
$807$		0			0
$808$	32.6926	−	18.8751i	1.15012	−	0.664023i
$809$	−8.01688	−	13.8856i	−0.281859	−	0.488193i	0.689984	−	0.723825i	$-0.257618\pi$
$809$	−8.01688	−	13.8856i	−0.281859	−	0.488193i	−0.971843	+	0.235631i	$0.924284\pi$
$810$		0			0
$811$	−46.1871			−1.62185			−0.810923	−	0.585152i	$-0.801035\pi$
$811$	−46.1871			−1.62185			−0.810923	+	0.585152i	$0.801035\pi$
$812$	−22.8235	−	13.1771i	−0.800947	−	0.462427i
$813$		0			0
$814$	6.63127			0.232426
$815$	−14.6234	+	43.7519i	−0.512236	+	1.53256i
$816$		0			0
$817$	−1.58038	+	0.912431i	−0.0552904	+	0.0319219i
$818$		−	2.63196i		−	0.0920243i
$819$		0			0
$820$	−0.568292	−	2.78862i	−0.0198456	−	0.0973827i
$821$	14.8976	+	25.8033i	0.519929	+	0.900543i	0.999732	+	0.0231666i	$0.00737483\pi$
$821$	14.8976	+	25.8033i	0.519929	+	0.900543i	−0.479803	+	0.877376i	$0.659292\pi$
$822$		0			0
$823$	−45.0733	−	26.0231i	−1.57116	−	0.907108i	−0.996028	−	0.0890459i	$-0.971618\pi$
$823$	−45.0733	−	26.0231i	−1.57116	−	0.907108i	−0.575130	−	0.818062i	$-0.695048\pi$
$824$	−6.15147			−0.214296
$825$		0			0
$826$	−13.4279	+	23.2578i	−0.467217	+	0.809244i
$827$		−	12.1419i		−	0.422215i	−0.977463	−	0.211108i	$-0.932293\pi$
$827$		−	12.1419i		−	0.422215i	0.977463	−	0.211108i	$-0.0677071\pi$
$828$		0			0
$829$	−10.2500	−	17.7535i	−0.355997	−	0.616604i	0.631291	−	0.775546i	$-0.282525\pi$
$829$	−10.2500	−	17.7535i	−0.355997	−	0.616604i	−0.987288	+	0.158941i	$0.949192\pi$
$830$	11.8271	−	10.4706i	0.410526	−	0.363440i
$831$		0			0
$832$	−1.63689	+	1.22586i	−0.0567491	+	0.0424989i
$833$		−	12.7256i		−	0.440915i
$834$		0			0
$835$	28.4411	+	32.1258i	0.984246	+	1.11176i
$836$	17.1686	−	29.7369i	0.593789	−	1.02847i
$837$		0			0
$838$	−4.70821	−	2.71829i	−0.162642	−	0.0939016i
$839$	9.41471	−	16.3068i	0.325032	−	0.562972i	−0.656487	−	0.754337i	$-0.727958\pi$
$839$	9.41471	−	16.3068i	0.325032	−	0.562972i	0.981519	+	0.191366i	$0.0612916\pi$
$840$		0			0
$841$	4.27397	−	7.40274i	0.147378	−	0.255267i
$842$	8.23407	−	4.75394i	0.283765	−	0.163832i
$843$		0			0
$844$	−40.2893			−1.38681
$845$	−28.9660	−	2.44402i	−0.996459	−	0.0840769i
$846$		0			0
$847$	−12.8200	+	7.40164i	−0.440501	+	0.254323i
$848$	−10.8859	+	6.28496i	−0.373822	+	0.215826i
$849$		0			0
$850$	6.22359	−	2.64652i	0.213467	−	0.0907750i
$851$	−3.47935	+	6.02641i	−0.119271	+	0.206583i
$852$		0			0
$853$		−	27.6509i		−	0.946748i	−0.880861	−	0.473374i	$-0.843036\pi$
$853$		−	27.6509i		−	0.946748i	0.880861	−	0.473374i	$-0.156964\pi$
$854$	3.14018	−	5.43896i	0.107455	−	0.186117i
$855$		0			0
$856$	10.8553	+	18.8020i	0.371028	+	0.642639i
$857$		−	35.5356i		−	1.21387i	−0.794751	−	0.606936i	$-0.792399\pi$
$857$		−	35.5356i		−	1.21387i	0.794751	−	0.606936i	$-0.207601\pi$
$858$		0			0
$859$	−14.8039			−0.505101			−0.252550	−	0.967584i	$-0.581269\pi$
$859$	−14.8039			−0.505101			−0.252550	+	0.967584i	$0.581269\pi$
$860$	0.552453	+	0.624026i	0.0188385	+	0.0212791i
$861$		0			0
$862$	2.53451	+	1.46330i	0.0863258	+	0.0498402i
$863$		−	37.6157i		−	1.28045i	−0.768187	−	0.640226i	$-0.778841\pi$
$863$		−	37.6157i		−	1.28045i	0.768187	−	0.640226i	$-0.221159\pi$
$864$		0			0
$865$	−13.6692	+	40.8970i	−0.464767	+	1.39054i
$866$	1.85534			0.0630469
$867$		0			0
$868$	−20.4724	+	11.8198i	−0.694880	+	0.401189i
$869$	19.4376	+	33.6669i	0.659375	+	1.14207i
$870$		0			0
$871$	1.58846	−	3.71139i	0.0538230	−	0.125756i
$872$		−	15.7033i		−	0.531781i
$873$		0			0
$874$	−3.98775	−	6.90699i	−0.134888	−	0.233633i
$875$	−3.16026	−	39.6616i	−0.106836	−	1.34081i
$876$		0			0
$877$	−1.18072	−	0.681691i	−0.0398702	−	0.0230191i	0.479932	−	0.877305i	$-0.340661\pi$
$877$	−1.18072	−	0.681691i	−0.0398702	−	0.0230191i	−0.519803	+	0.854286i	$0.673995\pi$
$878$	2.00332	+	1.15662i	0.0676088	+	0.0390340i
$879$		0			0
$880$	−10.8526	−	3.62733i	−0.365842	−	0.122277i
$881$	−24.0121	−	41.5901i	−0.808987	−	1.40121i	−0.913566	−	0.406690i	$-0.866683\pi$
$881$	−24.0121	−	41.5901i	−0.808987	−	1.40121i	0.104580	−	0.994517i	$-0.466650\pi$
$882$		0			0
$883$		−	26.6427i		−	0.896597i	−0.893884	−	0.448299i	$-0.852030\pi$
$883$		−	26.6427i		−	0.896597i	0.893884	−	0.448299i	$-0.147970\pi$
$884$	−5.21935	+	12.1948i	−0.175546	+	0.410157i
$885$		0			0
$886$	2.22884	+	3.86047i	0.0748795	+	0.129695i
$887$	−15.7414	+	9.08828i	−0.528543	+	0.305155i	−0.740423	−	0.672141i	$-0.765375\pi$
$887$	−15.7414	+	9.08828i	−0.528543	+	0.305155i	0.211880	+	0.977296i	$0.432042\pi$
$888$		0			0
$889$	20.8627			0.699712
$890$	7.34375	−	21.9718i	0.246163	−	0.736497i
$891$		0			0
$892$		−	0.908661i		−	0.0304242i
$893$	21.8533	+	12.6170i	0.731293	+	0.422212i
$894$		0			0
$895$	9.57402	−	8.47591i	0.320024	−	0.283318i
$896$	−40.7728			−1.36212
$897$		0			0
$898$		−	14.8427i		−	0.495308i
$899$	9.17266	+	15.8875i	0.305925	+	0.529878i
$900$		0			0
$901$	−7.21653	+	12.4994i	−0.240418	+	0.416415i
$902$		−	1.22380i		−	0.0407480i
$903$		0			0
$904$	−7.60929	+	13.1797i	−0.253081	+	0.438349i
$905$	2.25601	+	11.0702i	0.0749922	+	0.367987i
$906$		0			0
$907$	−23.7753	+	13.7267i	−0.789447	+	0.455787i	−0.839768	−	0.542946i	$-0.817309\pi$
$907$	−23.7753	+	13.7267i	−0.789447	+	0.455787i	0.0503208	+	0.998733i	$0.483976\pi$
$908$	2.14410	−	1.23789i	0.0711543	−	0.0410810i
$909$		0			0
$910$	−12.9064	−	11.4799i	−0.427844	−	0.380555i
$911$	−52.6351			−1.74388			−0.871939	−	0.489615i	$-0.837137\pi$
$911$	−52.6351			−1.74388			−0.871939	+	0.489615i	$0.837137\pi$
$912$		0			0
$913$	−26.5767	+	15.3441i	−0.879561	+	0.507815i
$914$	−8.65254	+	14.9866i	−0.286201	+	0.495714i
$915$		0			0
$916$	4.43990	−	7.69013i	0.146698	−	0.254089i
$917$	30.8610	+	17.8176i	1.01912	+	0.588389i
$918$		0			0
$919$	13.0246	−	22.5593i	0.429642	−	0.744161i	−0.567200	−	0.823580i	$-0.691973\pi$
$919$	13.0246	−	22.5593i	0.429642	−	0.744161i	0.996841	+	0.0794191i	$0.0253065\pi$
$920$	−6.05824	+	5.36338i	−0.199734	+	0.176825i
$921$		0			0
$922$		−	2.39623i		−	0.0789156i
$923$	−4.85994	−	40.5805i	−0.159967	−	1.33572i
$924$		0			0
$925$	−12.6617	+	16.8254i	−0.416315	+	0.553215i
$926$	3.94926	+	6.84033i	0.129781	+	0.224787i
$927$		0			0
$928$			25.1350i			0.825097i
$929$	−7.32957	+	12.6952i	−0.240475	+	0.416516i	−0.960850	−	0.277070i	$-0.910637\pi$
$929$	−7.32957	+	12.6952i	−0.240475	+	0.416516i	0.720374	+	0.693585i	$0.243970\pi$
$930$		0			0
$931$	−45.4127			−1.48834
$932$	−15.9584	−	9.21361i	−0.522736	−	0.301802i
$933$		0			0
$934$	3.58649	+	6.21198i	0.117353	+	0.203262i
$935$	−12.8742	+	2.62364i	−0.421033	+	0.0858023i
$936$		0			0
$937$		−	58.6364i		−	1.91557i	−0.287489	−	0.957784i	$-0.592821\pi$
$937$		−	58.6364i		−	1.91557i	0.287489	−	0.957784i	$-0.407179\pi$
$938$	2.07749	−	1.19944i	0.0678323	−	0.0391630i
$939$		0			0
$940$	3.65328	−	10.9303i	0.119157	−	0.356507i
$941$	23.6082			0.769604			0.384802	−	0.922999i	$-0.374270\pi$
$941$	23.6082			0.769604			0.384802	+	0.922999i	$0.374270\pi$
$942$		0			0
$943$	1.11217	+	0.642112i	0.0362173	+	0.0209100i
$944$	−24.5264			−0.798265
$945$		0			0
$946$	0.179195	+	0.310375i	0.00582614	+	0.0100912i
$947$	−0.455045	+	0.262720i	−0.0147870	+	0.00853726i	−0.507375	−	0.861725i	$-0.669384\pi$
$947$	−0.455045	+	0.262720i	−0.0147870	+	0.00853726i	0.492588	+	0.870262i	$0.336051\pi$
$948$		0			0
$949$	−26.8756	−	35.8872i	−0.872419	−	1.16495i
$950$	−9.44442	−	22.2096i	−0.306417	−	0.720574i
$951$		0			0
$952$	−15.1633	+	8.75452i	−0.491444	+	0.283735i
$953$	23.0586	+	13.3129i	0.746942	+	0.431247i	0.824588	−	0.565734i	$-0.191407\pi$
$953$	23.0586	+	13.3129i	0.746942	+	0.431247i	−0.0776460	+	0.996981i	$0.524740\pi$
$954$		0			0
$955$	−37.4418	−	12.5144i	−1.21159	−	0.404955i
$956$	−14.6790	+	25.4249i	−0.474754	+	0.822299i
$957$		0			0
$958$	−21.5030	−	12.4147i	−0.694729	−	0.401102i
$959$	32.7082	+	56.6522i	1.05620	+	1.82940i
$960$		0			0
$961$	−14.5444			−0.469175
$962$	1.08706	+	9.07696i	0.0350482	+	0.292653i
$963$		0			0
$964$	−16.6498	−	28.8383i	−0.536254	−	0.928819i
$965$	5.43110	+	6.13473i	0.174833	+	0.197484i
$966$		0			0
$967$			21.7977i			0.700967i	0.936569	+	0.350484i	$0.113983\pi$
$967$			21.7977i			0.700967i	−0.936569	+	0.350484i	$0.886017\pi$
$968$	7.88924	+	4.55485i	0.253570	+	0.146399i
$969$		0			0
$970$	3.29303	+	16.1589i	0.105733	+	0.518831i
$971$	17.6354	−	30.5454i	0.565946	−	0.980248i	−0.431015	−	0.902345i	$-0.641844\pi$
$971$	17.6354	−	30.5454i	0.565946	−	0.980248i	0.996961	−	0.0779030i	$-0.0248224\pi$
$972$		0			0
$973$	−13.2849	+	7.67007i	−0.425896	+	0.245891i
$974$	8.72032			0.279417
$975$		0			0
$976$	5.73560			0.183592
$977$	21.2906	−	12.2921i	0.681147	−	0.393261i	−0.119140	−	0.992877i	$-0.538014\pi$
$977$	21.2906	−	12.2921i	0.681147	−	0.393261i	0.800287	+	0.599617i	$0.204680\pi$
$978$		0			0
$979$	−22.5038	+	38.9777i	−0.719224	+	1.24573i
$980$	4.14158	+	20.3228i	0.132298	+	0.649187i
$981$		0			0
$982$	9.22016	+	5.32326i	0.294227	+	0.169872i
$983$			35.5716i			1.13456i	0.823526	+	0.567279i	$0.192004\pi$
$983$			35.5716i			1.13456i	−0.823526	+	0.567279i	$0.807996\pi$
$984$		0			0
$985$	10.3284	+	11.6665i	0.329089	+	0.371724i
$986$	3.05846	+	5.29741i	0.0974012	+	0.168704i
$987$		0			0
$988$	43.5187	+	18.6259i	1.38451	+	0.592567i
$989$	−0.376086			−0.0119589
$990$		0			0
$991$	20.2390	+	35.0550i	0.642914	+	1.11356i	0.984779	+	0.173811i	$0.0556082\pi$
$991$	20.2390	+	35.0550i	0.642914	+	1.11356i	−0.341865	+	0.939749i	$0.611058\pi$
$992$	19.5253	+	11.2729i	0.619929	+	0.357916i
$993$		0			0
$994$	12.1430	−	21.0323i	0.385152	−	0.667103i
$995$	15.6509	+	5.23108i	0.496168	+	0.165836i
$996$		0			0
$997$	23.3429	+	13.4770i	0.739277	+	0.426822i	0.821806	−	0.569767i	$-0.192967\pi$
$997$	23.3429	+	13.4770i	0.739277	+	0.426822i	−0.0825297	+	0.996589i	$0.526300\pi$
$998$	0.360159	−	0.207938i	0.0114006	−	0.00658216i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.b.289.7		24
3.2	odd	2		195.2.ba.a.94.6	✓	24
5.4	even	2	inner	585.2.bs.b.289.6		24
13.9	even	3	inner	585.2.bs.b.334.6		24
15.2	even	4		975.2.i.q.601.3		12
15.8	even	4		975.2.i.o.601.4		12
15.14	odd	2		195.2.ba.a.94.7	yes	24
39.35	odd	6		195.2.ba.a.139.7	yes	24
65.9	even	6	inner	585.2.bs.b.334.7		24
195.74	odd	6		195.2.ba.a.139.6	yes	24
195.113	even	12		975.2.i.o.451.4		12
195.152	even	12		975.2.i.q.451.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.6	✓	24	3.2	odd	2
195.2.ba.a.94.7	yes	24	15.14	odd	2
195.2.ba.a.139.6	yes	24	195.74	odd	6
195.2.ba.a.139.7	yes	24	39.35	odd	6
585.2.bs.b.289.6		24	5.4	even	2	inner
585.2.bs.b.289.7		24	1.1	even	1	trivial
585.2.bs.b.334.6		24	13.9	even	3	inner
585.2.bs.b.334.7		24	65.9	even	6	inner
975.2.i.o.451.4		12	195.113	even	12
975.2.i.o.601.4		12	15.8	even	4
975.2.i.q.451.3		12	195.152	even	12
975.2.i.q.601.3		12	15.2	even	4

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.521384 - 0.301021i) q^{2} +(-0.818772 + 1.41816i) q^{4} +(-0.446511 - 2.19103i) q^{5} +(-3.08191 - 1.77934i) q^{7} +2.18996i q^{8} +O(q^{10})\)	\(q+(0.521384 - 0.301021i) q^{2} +(-0.818772 + 1.41816i) q^{4} +(-0.446511 - 2.19103i) q^{5} +(-3.08191 - 1.77934i) q^{7} +2.18996i q^{8} +(-0.892352 - 1.00796i) q^{10} +(1.30769 + 2.26499i) q^{11} +(-2.88598 + 2.16128i) q^{13} -2.14248 q^{14} +(-0.978320 - 1.69450i) q^{16} +(-1.94566 - 1.12333i) q^{17} +(-4.00873 + 6.94332i) q^{19} +(3.47282 + 1.16074i) q^{20} +(1.36362 + 0.787287i) q^{22} +(-1.43095 + 0.826160i) q^{23} +(-4.60126 + 1.95664i) q^{25} +(-0.854110 + 1.99560i) q^{26} +(5.04676 - 2.91375i) q^{28} +(-2.26120 - 3.91651i) q^{29} -4.05655 q^{31} +(-4.81328 - 2.77895i) q^{32} -1.35258 q^{34} +(-2.52249 + 7.54706i) q^{35} +(3.64724 - 2.10574i) q^{37} +4.82685i q^{38} +(4.79827 - 0.977840i) q^{40} +(-0.388612 - 0.673096i) q^{41} +(0.197117 + 0.113806i) q^{43} -4.28281 q^{44} +(-0.497384 + 0.861494i) q^{46} -3.14738i q^{47} +(2.83211 + 4.90536i) q^{49} +(-1.81003 + 2.40524i) q^{50} +(-0.702078 - 5.86236i) q^{52} -6.42424i q^{53} +(4.37877 - 3.87654i) q^{55} +(3.89668 - 6.74925i) q^{56} +(-2.35791 - 1.36134i) q^{58} +(6.26747 - 10.8556i) q^{59} +(-1.46568 + 2.53863i) q^{61} +(-2.11502 + 1.22111i) q^{62} +0.567189 q^{64} +(6.02406 + 5.35823i) q^{65} +(-0.969664 + 0.559836i) q^{67} +(3.18611 - 1.83950i) q^{68} +(0.956640 + 4.69425i) q^{70} +(-5.66772 + 9.81678i) q^{71} +12.4350i q^{73} +(1.26774 - 2.19579i) q^{74} +(-6.56447 - 11.3700i) q^{76} -9.30732i q^{77} +14.8640 q^{79} +(-3.27588 + 2.90015i) q^{80} +(-0.405233 - 0.233961i) q^{82} +11.7337i q^{83} +(-1.59249 + 4.76459i) q^{85} +0.137032 q^{86} +(-4.96023 + 2.86379i) q^{88} +(8.60439 + 14.9032i) q^{89} +(12.7400 - 1.52574i) q^{91} -2.70575i q^{92} +(-0.947430 - 1.64100i) q^{94} +(17.0030 + 5.68299i) q^{95} +(-10.6088 - 6.12499i) q^{97} +(2.95324 + 1.70505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} - 4 q^{5}+O(q^{10}) \) 24 * q + 8 * q^4 - 4 * q^5	\( 24 q + 8 q^{4} - 4 q^{5} - 4 q^{10} - 4 q^{11} - 24 q^{14} + 16 q^{16} - 16 q^{19} + 16 q^{20} - 16 q^{25} + 48 q^{26} + 12 q^{29} + 8 q^{31} - 32 q^{34} - 10 q^{35} - 48 q^{40} + 40 q^{41} - 40 q^{44} - 24 q^{46} - 16 q^{49} - 20 q^{50} + 20 q^{55} + 24 q^{56} - 12 q^{59} + 20 q^{61} + 48 q^{64} - 14 q^{65} - 56 q^{70} - 4 q^{71} + 12 q^{74} + 8 q^{76} + 136 q^{79} + 4 q^{80} - 4 q^{85} - 48 q^{86} + 64 q^{89} + 60 q^{91} - 48 q^{94} + 28 q^{95}+O(q^{100}) \) 24 * q + 8 * q^4 - 4 * q^5 - 4 * q^10 - 4 * q^11 - 24 * q^14 + 16 * q^16 - 16 * q^19 + 16 * q^20 - 16 * q^25 + 48 * q^26 + 12 * q^29 + 8 * q^31 - 32 * q^34 - 10 * q^35 - 48 * q^40 + 40 * q^41 - 40 * q^44 - 24 * q^46 - 16 * q^49 - 20 * q^50 + 20 * q^55 + 24 * q^56 - 12 * q^59 + 20 * q^61 + 48 * q^64 - 14 * q^65 - 56 * q^70 - 4 * q^71 + 12 * q^74 + 8 * q^76 + 136 * q^79 + 4 * q^80 - 4 * q^85 - 48 * q^86 + 64 * q^89 + 60 * q^91 - 48 * q^94 + 28 * q^95

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