LMFDB - Embedded newform 585.2.bs.b.334.7

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			334.7
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.b.289.7

$q$-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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.521384	+	0.301021i	0.368674	+	0.212854i	0.672879	−	0.739752i	$-0.265057\pi$
$2$	0.521384	+	0.301021i	0.368674	+	0.212854i	−0.304205	+	0.952607i	$0.598391\pi$
$3$		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	−0.952462	−	0.304657i	$-0.901458\pi$
$7$	−3.08191	+	1.77934i	−1.16485	+	0.672528i	−0.212390	+	0.977185i	$0.568125\pi$
$8$		−	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	−0.598726	−	0.800954i	$-0.704326\pi$
$11$	1.30769	−	2.26499i	0.394284	−	0.682920i	0.993010	+	0.118034i	$0.0376593\pi$
$12$		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	−0.717032	−	0.697041i	$-0.754500\pi$
$17$	−1.94566	+	1.12333i	−0.471893	+	0.272447i	0.245139	+	0.969488i	$0.421166\pi$
$18$		0			0
$19$	−4.00873	−	6.94332i	−0.919666	−	1.59291i	−0.799923	−	0.600103i	$-0.795126\pi$
$19$	−4.00873	−	6.94332i	−0.919666	−	1.59291i	−0.119743	−	0.992805i	$-0.538207\pi$
$20$	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	0.343338	−	0.939212i	$-0.388442\pi$
$23$	−1.43095	−	0.826160i	−0.298374	−	0.172266i	−0.641712	+	0.766946i	$0.721776\pi$
$24$		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	−0.995928	−	0.0901479i	$-0.971266\pi$
$29$	−2.26120	+	3.91651i	−0.419894	+	0.727277i	0.576035	+	0.817425i	$0.304599\pi$
$30$		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	0.768885	−	0.639387i	$-0.220812\pi$
$37$	3.64724	+	2.10574i	0.599603	+	0.346181i	−0.169283	+	0.985568i	$0.554145\pi$
$38$		−	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	−0.894774	−	0.446518i	$-0.852664\pi$
$41$	−0.388612	+	0.673096i	−0.0606910	+	0.105120i	0.834083	+	0.551638i	$0.185997\pi$
$42$		0			0
$43$	0.197117	−	0.113806i	0.0300601	−	0.0173552i	−0.484895	−	0.874573i	$-0.661142\pi$
$43$	0.197117	−	0.113806i	0.0300601	−	0.0173552i	0.514955	+	0.857217i	$0.327809\pi$
$44$	−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	$0.0737243\pi$
$47$			3.14738i			0.459093i	−0.973298	+	0.229547i	$0.926276\pi$
$48$		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	$0.145454\pi$
$53$			6.42424i			0.882437i	−0.897400	+	0.441218i	$0.854546\pi$
$54$		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	0.908640	+	0.417580i	$0.137122\pi$
$59$	6.26747	+	10.8556i	0.815955	+	1.41328i	−0.0926855	+	0.995695i	$0.529545\pi$
$60$		0			0
$61$	−1.46568	−	2.53863i	−0.187661	−	0.325038i	0.756809	−	0.653636i	$-0.226757\pi$
$61$	−1.46568	−	2.53863i	−0.187661	−	0.325038i	−0.944470	+	0.328598i	$0.893424\pi$
$62$	−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	0.439597	−	0.898195i	$-0.355121\pi$
$67$	−0.969664	−	0.559836i	−0.118463	−	0.0683948i	−0.558061	+	0.829800i	$0.688454\pi$
$68$	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	−0.977154	−	0.212531i	$-0.931829\pi$
$71$	−5.66772	−	9.81678i	−0.672635	−	1.16504i	0.304520	−	0.952506i	$-0.401504\pi$
$72$		0			0
$73$		−	12.4350i		−	1.45541i	−0.685890	−	0.727705i	$-0.740587\pi$
$73$		−	12.4350i		−	1.45541i	0.685890	−	0.727705i	$-0.259413\pi$
$74$	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	$-0.777286\pi$
$83$		−	11.7337i		−	1.28794i	0.765050	−	0.643971i	$-0.222714\pi$
$84$		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	0.100919	−	0.994895i	$-0.467822\pi$
$89$	8.60439	−	14.9032i	0.912064	−	1.57974i	0.811144	−	0.584846i	$-0.198845\pi$
$90$		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	−0.930129	−	0.367233i	$-0.880305\pi$
$97$	−10.6088	+	6.12499i	−1.07716	+	0.621899i	−0.147032	+	0.989132i	$0.546972\pi$
$98$	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	0.0165815	+	0.999863i	$0.494722\pi$
$101$	−8.61893	+	14.9284i	−0.857616	+	1.48543i	−0.874197	+	0.485571i	$0.838612\pi$
$102$		0			0
$103$		−	2.80894i		−	0.276773i	−0.990378	−	0.138387i	$-0.955808\pi$
$103$		−	2.80894i		−	0.276773i	0.990378	−	0.138387i	$-0.0441917\pi$
$104$	−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	0.853852	−	0.520516i	$-0.174261\pi$
$107$	8.58556	+	4.95687i	0.829997	+	0.479199i	−0.0238546	+	0.999715i	$0.507594\pi$
$108$		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	−0.189462	−	0.981888i	$-0.560674\pi$
$113$	6.01823	−	3.47463i	0.566148	−	0.326866i	0.755609	+	0.655023i	$0.227341\pi$
$114$		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	0.257533	−	0.966270i	$-0.417091\pi$
$127$	−5.07705	−	2.93124i	−0.450515	−	0.260105i	−0.708048	+	0.706165i	$0.750424\pi$
$128$	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	−0.989635	−	0.143603i	$-0.954131\pi$
$137$	−15.9194	+	9.19109i	−1.36009	+	0.785248i	−0.370454	+	0.928851i	$0.620798\pi$
$138$		0			0
$139$	2.15531	+	3.73311i	0.182811	+	0.316638i	0.942837	−	0.333255i	$-0.108147\pi$
$139$	2.15531	+	3.73311i	0.182811	+	0.316638i	−0.760026	+	0.649893i	$0.774814\pi$
$140$	−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	0.908620	−	0.417623i	$-0.137137\pi$
$149$	1.13079	+	1.95858i	0.0926377	+	0.160453i	−0.815983	+	0.578077i	$0.803804\pi$
$150$		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	$0.0840137\pi$
$157$			6.53771i			0.521766i	−0.965370	+	0.260883i	$0.915986\pi$
$158$	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	−0.994331	−	0.106331i	$-0.966090\pi$
$163$	−17.8665	+	10.3152i	−1.39941	+	0.807950i	−0.405080	+	0.914281i	$0.632756\pi$
$164$	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	−0.307988	−	0.951390i	$-0.599656\pi$
$167$	−16.6176	−	9.59418i	−1.28591	−	0.742420i	−0.977922	+	0.208970i	$0.932989\pi$
$168$		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	−0.974936	−	0.222485i	$-0.928583\pi$
$173$	−16.7006	+	9.64212i	−1.26973	+	0.733077i	−0.294791	+	0.955562i	$0.595250\pi$
$174$		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	−0.739164	−	0.673525i	$-0.764779\pi$
$179$	2.85922	−	4.95232i	0.213708	−	0.370153i	0.952872	+	0.303372i	$0.0981125\pi$
$180$		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	0.985710	+	0.168449i	$0.0538758\pi$
$191$	8.82751	+	15.2897i	0.638736	+	1.10632i	−0.346974	+	0.937875i	$0.612791\pi$
$192$		0			0
$193$	−3.17329	−	1.83210i	−0.228418	−	0.131877i	0.381424	−	0.924400i	$-0.375434\pi$
$193$	−3.17329	−	1.83210i	−0.228418	−	0.131877i	−0.609842	+	0.792523i	$0.708767\pi$
$194$	−7.37502			−0.529495
$195$		0			0
$196$	−9.27542			−0.662530
$197$	−6.03467	−	3.48412i	−0.429952	−	0.248233i	0.269374	−	0.963036i	$-0.413183\pi$
$197$	−6.03467	−	3.48412i	−0.429952	−	0.248233i	−0.699326	+	0.714803i	$0.746517\pi$
$198$		0			0
$199$	−3.68996	−	6.39119i	−0.261574	−	0.453060i	0.705086	−	0.709122i	$-0.250908\pi$
$199$	−3.68996	−	6.39119i	−0.261574	−	0.453060i	−0.966660	+	0.256062i	$0.917575\pi$
$200$	−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	−0.0370857	−	0.999312i	$-0.511807\pi$
$211$	12.3017	−	21.3072i	0.846887	−	1.46685i	0.883973	−	0.467539i	$-0.154859\pi$
$212$	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	0.483824	−	0.875166i	$-0.339248\pi$
$223$	−0.480551	−	0.277446i	−0.0321801	−	0.0185792i	−0.516004	+	0.856586i	$0.672581\pi$
$224$	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	−0.542822	−	0.839848i	$-0.682644\pi$
$227$	−1.30934	+	0.755945i	−0.0869037	+	0.0501739i	0.455918	+	0.890022i	$0.349311\pi$
$228$		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	$-0.879836\pi$
$233$		−	11.2530i		−	0.737206i	0.929587	−	0.368603i	$-0.120164\pi$
$234$		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	−0.981907	−	0.189366i	$-0.939357\pi$
$241$	−10.1675	−	17.6107i	−0.654949	−	1.13440i	0.326958	−	0.945039i	$-0.393977\pi$
$242$			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	−0.993560	−	0.113304i	$-0.963857\pi$
$251$	−9.42506	−	16.3247i	−0.594904	−	1.03040i	0.398656	−	0.917101i	$-0.369477\pi$
$252$		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	0.999203	+	0.0399265i	$0.0127124\pi$
$257$	24.5820	+	14.1924i	1.53338	+	0.885298i	0.534179	+	0.845372i	$0.320621\pi$
$258$		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	0.829978	−	0.557796i	$-0.188353\pi$
$263$	12.3560	+	7.13372i	0.761901	+	0.439884i	−0.0680767	+	0.997680i	$0.521686\pi$
$264$		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	−0.933055	−	0.359735i	$-0.882867\pi$
$269$	−12.7612	−	22.1031i	−0.778067	−	1.34765i	0.154988	−	0.987916i	$-0.450466\pi$
$270$		0			0
$271$	3.91226	−	6.77623i	0.237653	−	0.411627i	−0.722387	−	0.691488i	$-0.756955\pi$
$271$	3.91226	−	6.77623i	0.237653	−	0.411627i	0.960040	+	0.279862i	$0.0902886\pi$
$272$		−	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	0.100578	−	0.994929i	$-0.467931\pi$
$277$	16.8514	−	9.72915i	1.01250	−	0.584568i	0.911923	+	0.410361i	$0.134597\pi$
$278$			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	−0.346899	−	0.937903i	$-0.612765\pi$
$283$	−22.4177	−	12.9429i	−1.33260	−	0.769374i	−0.985697	+	0.168528i	$0.946099\pi$
$284$	−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	−0.597997	−	0.801499i	$-0.704036\pi$
$293$	−3.47269	+	2.00496i	−0.202877	+	0.117131i	0.395120	+	0.918630i	$0.370703\pi$
$294$		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	$-0.751096\pi$
$307$		−	24.6936i		−	1.40934i	0.709537	−	0.704668i	$-0.248904\pi$
$308$	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	$-0.944271\pi$
$313$		−	6.16331i		−	0.348371i	0.984713	−	0.174185i	$-0.0557292\pi$
$314$	−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	$-0.881347\pi$
$317$		−	12.9683i		−	0.728371i	0.931326	−	0.364186i	$-0.118653\pi$
$318$		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	0.678277	−	0.734806i	$-0.262727\pi$
$331$	−5.40749	−	9.36605i	−0.297223	−	0.514805i	−0.975499	+	0.220002i	$0.929394\pi$
$332$	−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	$-0.966629\pi$
$337$		−	3.84210i		−	0.209292i	0.994510	−	0.104646i	$-0.0333710\pi$
$338$	−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	−0.746400	−	0.665497i	$-0.768219\pi$
$347$	−10.1199	+	5.84271i	−0.543263	+	0.313653i	0.203137	+	0.979150i	$0.434886\pi$
$348$		0			0
$349$	0.812876	−	1.40794i	0.0435122	−	0.0753654i	−0.843449	−	0.537209i	$-0.819479\pi$
$349$	0.812876	−	1.40794i	0.0435122	−	0.0753654i	0.886961	+	0.461844i	$0.152812\pi$
$350$	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	0.274671	−	0.961538i	$-0.411431\pi$
$353$	−7.90443	−	4.56363i	−0.420710	−	0.242897i	−0.695381	+	0.718641i	$0.744764\pi$
$354$		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	0.0646267	−	0.997910i	$-0.479414\pi$
$367$	−14.6989	−	8.48640i	−0.767275	−	0.442986i	−0.831902	+	0.554923i	$0.812748\pi$
$368$	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	−0.812291	−	0.583252i	$-0.801780\pi$
$373$	−13.7766	+	7.95393i	−0.713326	+	0.411839i	0.0989655	+	0.995091i	$0.468447\pi$
$374$	−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	−0.464543	−	0.885551i	$-0.653781\pi$
$379$	10.4083	−	18.0277i	0.534638	−	0.926020i	0.999181	−	0.0404693i	$-0.0128853\pi$
$380$	−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	−0.927266	−	0.374403i	$-0.877848\pi$
$383$	−20.8749	+	12.0521i	−1.06666	+	0.615834i	−0.139391	+	0.990237i	$0.544514\pi$
$384$		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	−0.193079	−	0.981183i	$-0.561847\pi$
$397$	11.1601	−	6.44331i	0.560111	−	0.323380i	0.753190	+	0.657803i	$0.228514\pi$
$398$		−	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	−0.993427	−	0.114464i	$-0.963485\pi$
$401$	−7.96163	+	13.7899i	−0.397585	+	0.688637i	0.595843	+	0.803101i	$0.296818\pi$
$402$		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	0.914994	−	0.403468i	$-0.132195\pi$
$409$	2.18586	+	3.78602i	0.108084	+	0.187206i	−0.806910	+	0.590674i	$0.798862\pi$
$410$	−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	−0.954983	−	0.296659i	$-0.904127\pi$
$419$	−4.51510	+	7.82039i	−0.220577	+	0.382051i	0.734406	+	0.678710i	$0.237461\pi$
$420$		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	−0.801532	−	0.597952i	$-0.795981\pi$
$431$	2.43056	−	4.20985i	0.117076	−	0.202782i	0.918608	+	0.395171i	$0.129315\pi$
$432$		0			0
$433$	2.66886	−	1.54087i	0.128257	−	0.0740494i	−0.434499	−	0.900673i	$-0.643074\pi$
$433$	2.66886	−	1.54087i	0.128257	−	0.0740494i	0.562756	+	0.826623i	$0.309741\pi$
$434$	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	−0.816531	−	0.577301i	$-0.804106\pi$
$439$	1.92116	−	3.32754i	0.0916918	−	0.158815i	0.908223	+	0.418486i	$0.137439\pi$
$440$	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	$-0.943718\pi$
$443$		−	7.40427i		−	0.351788i	0.984409	−	0.175894i	$-0.0562815\pi$
$444$		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	0.995273	+	0.0971206i	$0.0309632\pi$
$449$	12.3270	+	21.3509i	0.581745	+	1.00761i	−0.413527	+	0.910492i	$0.635703\pi$
$450$		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	−0.212079	−	0.977252i	$-0.568023\pi$
$457$	−24.8930	−	14.3720i	−1.16444	−	0.672292i	−0.952365	+	0.304960i	$0.901357\pi$
$458$	−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	0.908641	−	0.417578i	$-0.137121\pi$
$461$	1.99008	+	3.44692i	0.0926874	+	0.160539i	−0.815954	+	0.578117i	$0.803788\pi$
$462$		0			0
$463$		−	13.1195i		−	0.609717i	−0.952398	−	0.304859i	$-0.901391\pi$
$463$		−	13.1195i		−	0.609717i	0.952398	−	0.304859i	$-0.0986092\pi$
$464$	−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	$-0.911102\pi$
$467$		−	11.9144i		−	0.551332i	0.961253	−	0.275666i	$-0.0888984\pi$
$468$		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	−0.180934	+	0.983495i	$0.557912\pi$
$479$	−20.6210	+	35.7167i	−0.942199	+	1.63194i	−0.761265	+	0.648441i	$0.775421\pi$
$480$		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	−0.188097	−	0.982151i	$-0.560232\pi$
$487$	12.5440	−	7.24227i	0.568422	−	0.328179i	0.756519	+	0.653972i	$0.226898\pi$
$488$	−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	−0.594573	−	0.804042i	$-0.702679\pi$
$491$	8.84200	−	15.3148i	0.399034	−	0.691147i	0.993607	+	0.112894i	$0.0360122\pi$
$492$		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	−0.688717	−	0.725031i	$-0.741826\pi$
$503$	−9.08724	+	5.24652i	−0.405180	+	0.233931i	0.283537	+	0.958961i	$0.408492\pi$
$504$		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	−0.999991	−	0.00426454i	$-0.998643\pi$
$509$	−11.1971	+	19.3939i	−0.496302	+	0.859621i	0.503689	+	0.863885i	$0.331976\pi$
$510$		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	0.856150	−	0.516728i	$-0.172850\pi$
$523$	19.1352	+	11.0477i	0.836725	+	0.483083i	−0.0194246	+	0.999811i	$0.506183\pi$
$524$	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	$-0.955548\pi$
$547$		−	6.51100i		−	0.278390i	0.990265	−	0.139195i	$-0.0444515\pi$
$548$	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	0.433092	−	0.901350i	$-0.357423\pi$
$557$	−3.09063	−	1.78437i	−0.130954	−	0.0756064i	−0.564046	+	0.825743i	$0.690756\pi$
$558$		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	−0.186829	−	0.982392i	$-0.559821\pi$
$563$	13.5374	−	7.81582i	0.570533	−	0.329397i	0.757362	+	0.652995i	$0.226488\pi$
$564$		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	−0.779381	−	0.626551i	$-0.784466\pi$
$569$	3.64767	−	6.31796i	0.152918	−	0.264863i	0.932299	+	0.361688i	$0.117799\pi$
$570$		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	$0.301661\pi$
$577$			39.0134i			1.62415i	−0.583555	+	0.812074i	$0.698339\pi$
$578$	−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	0.710588	−	0.703609i	$-0.248429\pi$
$587$	11.0611	+	6.38611i	0.456539	+	0.263583i	−0.254049	+	0.967191i	$0.581762\pi$
$588$		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	$-0.983546\pi$
$593$		−	2.51648i		−	0.103339i	0.998664	−	0.0516697i	$-0.0164543\pi$
$594$		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	−0.0900081	+	0.995941i	$0.528689\pi$
$601$	−22.2480	+	38.5346i	−0.907514	+	1.57186i	−0.817506	+	0.575920i	$0.804644\pi$
$602$	−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	0.402534	−	0.915405i	$-0.368129\pi$
$607$	34.4077	−	19.8653i	1.39657	−	0.806307i	0.994031	+	0.109097i	$0.0347961\pi$
$608$	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	0.316458	−	0.948606i	$-0.397506\pi$
$613$	−8.58710	−	4.95776i	−0.346830	−	0.200242i	−0.663288	+	0.748364i	$0.730840\pi$
$614$	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	0.282344	−	0.959313i	$-0.408888\pi$
$617$	31.1563	−	17.9881i	1.25431	−	0.724174i	0.971962	+	0.235140i	$0.0755548\pi$
$618$		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	0.998135	+	0.0610440i	$0.0194430\pi$
$631$	13.8644	+	24.0138i	0.551933	+	0.955976i	−0.446202	+	0.894932i	$0.647224\pi$
$632$		−	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	0.896108	−	0.443836i	$-0.146383\pi$
$641$	1.61226	+	2.79251i	0.0636803	+	0.110297i	−0.832428	+	0.554134i	$0.813050\pi$
$642$		0			0
$643$	5.46209	−	3.15354i	0.215404	−	0.124363i	−0.388417	−	0.921484i	$-0.626978\pi$
$643$	5.46209	−	3.15354i	0.215404	−	0.124363i	0.603820	+	0.797121i	$0.293644\pi$
$644$	−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	0.275664	−	0.961254i	$-0.411102\pi$
$647$	−10.6571	−	6.15288i	−0.418974	−	0.241895i	−0.694638	+	0.719359i	$0.744436\pi$
$648$		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	0.228076	−	0.973643i	$-0.426757\pi$
$653$	−12.8047	−	7.39280i	−0.501087	−	0.289302i	−0.729162	+	0.684341i	$0.760090\pi$
$654$		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	0.949473	−	0.313848i	$-0.101618\pi$
$659$	5.20958	+	9.02326i	0.202937	+	0.351496i	−0.746537	+	0.665344i	$0.768285\pi$
$660$		0			0
$661$	−1.78786	+	3.09666i	−0.0695396	+	0.120446i	−0.898699	−	0.438567i	$-0.855486\pi$
$661$	−1.78786	+	3.09666i	−0.0695396	+	0.120446i	0.829159	+	0.559013i	$0.188820\pi$
$662$		−	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	0.586560	−	0.809906i	$-0.300482\pi$
$673$	4.62917	+	2.67265i	0.178441	+	0.103023i	−0.408119	+	0.912929i	$0.633815\pi$
$674$	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	$-0.802934\pi$
$677$		−	30.1981i		−	1.16061i	0.814400	−	0.580304i	$-0.197066\pi$
$678$		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	−0.562848	−	0.826561i	$-0.690294\pi$
$683$	−3.35693	+	1.93812i	−0.128449	+	0.0741602i	0.434399	+	0.900721i	$0.356961\pi$
$684$		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	−0.213545	−	0.976933i	$-0.568501\pi$
$691$	19.4333	−	33.6594i	0.739277	−	1.28046i	0.952821	−	0.303532i	$-0.0981658\pi$
$692$	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	0.919726	−	0.392562i	$-0.128411\pi$
$709$	3.19243	+	5.52946i	0.119894	+	0.207663i	−0.799831	+	0.600225i	$0.795078\pi$
$710$	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	0.968300	−	0.249790i	$-0.0803617\pi$
$719$	7.18151	+	12.4387i	0.267825	+	0.463887i	−0.700475	+	0.713677i	$0.747028\pi$
$720$		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	$0.0765528\pi$
$727$			12.8444i			0.476372i	−0.971220	+	0.238186i	$0.923447\pi$
$728$	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	$0.0194584\pi$
$733$			3.30801i			0.122184i	−0.998132	+	0.0610922i	$0.980542\pi$
$734$	−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	−0.899740	−	0.436425i	$-0.856244\pi$
$739$	−1.95497	+	3.38611i	−0.0719147	+	0.124560i	0.827826	+	0.560985i	$0.189578\pi$
$740$	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	−0.180515	−	0.983572i	$-0.557776\pi$
$743$	−30.5991	−	17.6664i	−1.12257	−	0.648116i	−0.942056	+	0.335456i	$0.891110\pi$
$744$		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	−0.835905	−	0.548874i	$-0.815057\pi$
$751$	1.57264	−	2.72389i	0.0573864	−	0.0993962i	0.893291	+	0.449478i	$0.148390\pi$
$752$	−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	0.790843	−	0.612019i	$-0.209643\pi$
$757$	18.0555	+	10.4244i	0.656240	+	0.378880i	−0.134603	+	0.990900i	$0.542976\pi$
$758$	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	−0.916002	−	0.401173i	$-0.868603\pi$
$761$	−22.2187	−	38.4839i	−0.805427	−	1.39504i	0.110576	−	0.993868i	$-0.464731\pi$
$762$		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	−0.996579	−	0.0826421i	$-0.973664\pi$
$769$	−11.8333	+	20.4959i	−0.426719	+	0.739100i	0.569860	+	0.821742i	$0.306997\pi$
$770$	−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	−0.765812	−	0.643064i	$-0.777663\pi$
$773$	−16.4540	+	9.49970i	−0.591808	+	0.341680i	0.174004	+	0.984745i	$0.444329\pi$
$774$		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	0.366574	−	0.930389i	$-0.380531\pi$
$787$	38.0294	−	21.9563i	1.35560	−	0.782657i	0.989027	+	0.147732i	$0.0471972\pi$
$788$			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	−0.758495	−	0.651678i	$-0.774065\pi$
$797$	−16.1870	+	9.34557i	−0.573373	+	0.331037i	0.185122	+	0.982715i	$0.440732\pi$
$798$		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	−0.971843	−	0.235631i	$-0.924284\pi$
$809$	−8.01688	+	13.8856i	−0.281859	+	0.488193i	0.689984	+	0.723825i	$0.257618\pi$
$810$		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	−0.479803	−	0.877376i	$-0.659292\pi$
$821$	14.8976	−	25.8033i	0.519929	−	0.900543i	0.999732	−	0.0231666i	$-0.00737483\pi$
$822$		0			0
$823$	−45.0733	+	26.0231i	−1.57116	+	0.907108i	−0.575130	+	0.818062i	$0.695048\pi$
$823$	−45.0733	+	26.0231i	−1.57116	+	0.907108i	−0.996028	+	0.0890459i	$0.971618\pi$
$824$	−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	$0.0677071\pi$
$827$			12.1419i			0.422215i	−0.977463	+	0.211108i	$0.932293\pi$
$828$		0			0
$829$	−10.2500	+	17.7535i	−0.355997	+	0.616604i	−0.987288	−	0.158941i	$-0.949192\pi$
$829$	−10.2500	+	17.7535i	−0.355997	+	0.616604i	0.631291	+	0.775546i	$0.282525\pi$
$830$	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	0.981519	−	0.191366i	$-0.0612916\pi$
$839$	9.41471	+	16.3068i	0.325032	+	0.562972i	−0.656487	+	0.754337i	$0.727958\pi$
$840$		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	$0.156964\pi$
$853$			27.6509i			0.946748i	−0.880861	+	0.473374i	$0.843036\pi$
$854$	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	$0.207601\pi$
$857$			35.5356i			1.21387i	−0.794751	+	0.606936i	$0.792399\pi$
$858$		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	$0.221159\pi$
$863$			37.6157i			1.28045i	−0.768187	+	0.640226i	$0.778841\pi$
$864$		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	−0.519803	−	0.854286i	$-0.673995\pi$
$877$	−1.18072	+	0.681691i	−0.0398702	+	0.0230191i	0.479932	+	0.877305i	$0.340661\pi$
$878$	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	0.104580	+	0.994517i	$0.466650\pi$
$881$	−24.0121	+	41.5901i	−0.808987	+	1.40121i	−0.913566	+	0.406690i	$0.866683\pi$
$882$		0			0
$883$			26.6427i			0.896597i	0.893884	+	0.448299i	$0.147970\pi$
$883$			26.6427i			0.896597i	−0.893884	+	0.448299i	$0.852030\pi$
$884$	−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	0.211880	−	0.977296i	$-0.432042\pi$
$887$	−15.7414	−	9.08828i	−0.528543	−	0.305155i	−0.740423	+	0.672141i	$0.765375\pi$
$888$		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	0.0503208	−	0.998733i	$-0.483976\pi$
$907$	−23.7753	−	13.7267i	−0.789447	−	0.455787i	−0.839768	+	0.542946i	$0.817309\pi$
$908$	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	0.996841	−	0.0794191i	$-0.0253065\pi$
$919$	13.0246	+	22.5593i	0.429642	+	0.744161i	−0.567200	+	0.823580i	$0.691973\pi$
$920$	−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	0.720374	−	0.693585i	$-0.243970\pi$
$929$	−7.32957	−	12.6952i	−0.240475	−	0.416516i	−0.960850	+	0.277070i	$0.910637\pi$
$930$		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	$0.407179\pi$
$937$			58.6364i			1.91557i	−0.287489	+	0.957784i	$0.592821\pi$
$938$	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	0.492588	−	0.870262i	$-0.336051\pi$
$947$	−0.455045	−	0.262720i	−0.0147870	−	0.00853726i	−0.507375	+	0.861725i	$0.669384\pi$
$948$		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	−0.0776460	−	0.996981i	$-0.524740\pi$
$953$	23.0586	−	13.3129i	0.746942	−	0.431247i	0.824588	+	0.565734i	$0.191407\pi$
$954$		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	$-0.886017\pi$
$967$		−	21.7977i		−	0.700967i	0.936569	−	0.350484i	$-0.113983\pi$
$968$	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	0.996961	+	0.0779030i	$0.0248224\pi$
$971$	17.6354	+	30.5454i	0.565946	+	0.980248i	−0.431015	+	0.902345i	$0.641844\pi$
$972$		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	0.800287	−	0.599617i	$-0.204680\pi$
$977$	21.2906	+	12.2921i	0.681147	+	0.393261i	−0.119140	+	0.992877i	$0.538014\pi$
$978$		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	$-0.807996\pi$
$983$		−	35.5716i		−	1.13456i	0.823526	−	0.567279i	$-0.192004\pi$
$984$		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	−0.341865	−	0.939749i	$-0.611058\pi$
$991$	20.2390	−	35.0550i	0.642914	−	1.11356i	0.984779	−	0.173811i	$-0.0556082\pi$
$992$	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	−0.0825297	−	0.996589i	$-0.526300\pi$
$997$	23.3429	−	13.4770i	0.739277	−	0.426822i	0.821806	+	0.569767i	$0.192967\pi$
$998$	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.334.7		24
3.2	odd	2		195.2.ba.a.139.6	yes	24
5.4	even	2	inner	585.2.bs.b.334.6		24
13.3	even	3	inner	585.2.bs.b.289.6		24
15.2	even	4		975.2.i.o.451.4		12
15.8	even	4		975.2.i.q.451.3		12
15.14	odd	2		195.2.ba.a.139.7	yes	24
39.29	odd	6		195.2.ba.a.94.7	yes	24
65.29	even	6	inner	585.2.bs.b.289.7		24
195.29	odd	6		195.2.ba.a.94.6	✓	24
195.68	even	12		975.2.i.q.601.3		12
195.107	even	12		975.2.i.o.601.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.6	✓	24	195.29	odd	6
195.2.ba.a.94.7	yes	24	39.29	odd	6
195.2.ba.a.139.6	yes	24	3.2	odd	2
195.2.ba.a.139.7	yes	24	15.14	odd	2
585.2.bs.b.289.6		24	13.3	even	3	inner
585.2.bs.b.289.7		24	65.29	even	6	inner
585.2.bs.b.334.6		24	5.4	even	2	inner
585.2.bs.b.334.7		24	1.1	even	1	trivial
975.2.i.o.451.4		12	15.2	even	4
975.2.i.o.601.4		12	195.107	even	12
975.2.i.q.451.3		12	15.8	even	4
975.2.i.q.601.3		12	195.68	even	12

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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