LMFDB - Embedded newform 567.2.h.i.352.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(298,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.298"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,4,0,8,-1,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			352.1
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	567.352
Dual form			567.2.h.i.298.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.46050 q^{2} +0.133074 q^{4} +(0.296790 + 0.514055i) q^{5} +(-0.0665372 - 2.64491i) q^{7} +2.72665 q^{8} +(-0.433463 - 0.750780i) q^{10} +(-2.23025 + 3.86291i) q^{11} +(2.25729 - 3.90975i) q^{13} +(0.0971780 + 3.86291i) q^{14} -4.24844 q^{16} +(0.136673 + 0.236725i) q^{17} +(-1.43346 + 2.48283i) q^{19} +(0.0394951 + 0.0684076i) q^{20} +(3.25729 - 5.64180i) q^{22} +(-2.52704 - 4.37697i) q^{23} +(2.32383 - 4.02499i) q^{25} +(-3.29679 + 5.71021i) q^{26} +(-0.00885441 - 0.351971i) q^{28} +(-0.176168 - 0.305132i) q^{29} +2.51459 q^{31} +0.751560 q^{32} +(-0.199612 - 0.345738i) q^{34} +(1.33988 - 0.819187i) q^{35} +(3.32383 - 5.75705i) q^{37} +(2.09358 - 3.62619i) q^{38} +(0.809243 + 1.40165i) q^{40} +(5.44805 - 9.43630i) q^{41} +(-1.69076 - 2.92848i) q^{43} +(-0.296790 + 0.514055i) q^{44} +(3.69076 + 6.39258i) q^{46} +12.4356 q^{47} +(-6.99115 + 0.351971i) q^{49} +(-3.39397 + 5.87852i) q^{50} +(0.300388 - 0.520288i) q^{52} +(-5.66372 - 9.80984i) q^{53} -2.64766 q^{55} +(-0.181424 - 7.21177i) q^{56} +(0.257295 + 0.445647i) q^{58} -8.05408 q^{59} -2.73385 q^{61} -3.67257 q^{62} +7.39922 q^{64} +2.67977 q^{65} +5.86693 q^{67} +(0.0181877 + 0.0315020i) q^{68} +(-1.95691 + 1.19643i) q^{70} +2.60078 q^{71} +(-5.55768 - 9.62619i) q^{73} +(-4.85447 + 8.40819i) q^{74} +(-0.190757 + 0.330401i) q^{76} +(10.3655 + 5.64180i) q^{77} +11.1623 q^{79} +(-1.26089 - 2.18393i) q^{80} +(-7.95691 + 13.7818i) q^{82} +(-8.27188 - 14.3273i) q^{83} +(-0.0811263 + 0.140515i) q^{85} +(2.46936 + 4.27706i) q^{86} +(-6.08113 + 10.5328i) q^{88} +(2.68716 - 4.65430i) q^{89} +(-10.4911 - 5.71021i) q^{91} +(-0.336285 - 0.582462i) q^{92} -18.1623 q^{94} -1.70175 q^{95} +(1.13307 + 1.96254i) q^{97} +(10.2106 - 0.514055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 8 q^{4} - q^{5} - 4 q^{7} + 18 q^{8} + q^{10} - 7 q^{11} - 2 q^{13} - 13 q^{14} + 20 q^{16} - 5 q^{19} + 13 q^{20} + 4 q^{22} - 6 q^{23} + 2 q^{25} - 17 q^{26} - 30 q^{28} - 13 q^{29}+ \cdots + 49 q^{98}+O(q^{100}) $ 6 * q + 4 * q^2 + 8 * q^4 - q^5 - 4 * q^7 + 18 * q^8 + q^10 - 7 * q^11 - 2 * q^13 - 13 * q^14 + 20 * q^16 - 5 * q^19 + 13 * q^20 + 4 * q^22 - 6 * q^23 + 2 * q^25 - 17 * q^26 - 30 * q^28 - 13 * q^29 - 16 * q^31 + 50 * q^32 - 12 * q^34 + 10 * q^35 + 8 * q^37 + 7 * q^38 + 24 * q^40 - 2 * q^41 + 9 * q^43 + q^44 + 3 * q^46 + 18 * q^47 - 12 * q^49 - 4 * q^50 - 9 * q^52 - 24 * q^53 + 8 * q^55 - 51 * q^56 - 14 * q^58 - 30 * q^59 - 2 * q^61 - 42 * q^62 + 66 * q^64 + 20 * q^65 + 28 * q^67 - 39 * q^68 - 7 * q^70 - 6 * q^71 - 7 * q^73 + 18 * q^76 + 10 * q^77 + 12 * q^79 + 16 * q^80 - 43 * q^82 - 3 * q^83 + 27 * q^85 + 32 * q^86 - 9 * q^88 + 5 * q^89 - 33 * q^91 - 12 * q^92 - 54 * q^94 + 32 * q^95 + 14 * q^97 + 49 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.46050			−1.03273			−0.516366	−	0.856368i	$-0.672716\pi$
$2$	−1.46050			−1.03273			−0.516366	+	0.856368i	$0.672716\pi$
$3$		0			0
$3$		0			0
$4$	0.133074			0.0665372
$5$	0.296790	+	0.514055i	0.132728	+	0.229892i	0.924727	−	0.380630i	$-0.124293\pi$
$5$	0.296790	+	0.514055i	0.132728	+	0.229892i	−0.791999	+	0.610522i	$0.790960\pi$
$6$		0			0
$7$	−0.0665372	−	2.64491i	−0.0251487	−	0.999684i
$7$	−0.0665372	−	2.64491i	−0.0251487	−	0.999684i
$8$	2.72665			0.964018
$9$		0			0
$10$	−0.433463	−	0.750780i	−0.137073	−	0.237417i
$11$	−2.23025	+	3.86291i	−0.672446	+	1.16471i	0.304762	+	0.952429i	$0.401423\pi$
$11$	−2.23025	+	3.86291i	−0.672446	+	1.16471i	−0.977208	+	0.212283i	$0.931910\pi$
$12$		0			0
$13$	2.25729	−	3.90975i	0.626061	−	1.08437i	−0.362274	−	0.932072i	$-0.617999\pi$
$13$	2.25729	−	3.90975i	0.626061	−	1.08437i	0.988335	−	0.152298i	$-0.0486672\pi$
$14$	0.0971780	+	3.86291i	0.0259719	+	1.03241i
$15$		0			0
$16$	−4.24844			−1.06211
$17$	0.136673	+	0.236725i	0.0331481	+	0.0574142i	0.882124	−	0.471018i	$-0.156113\pi$
$17$	0.136673	+	0.236725i	0.0331481	+	0.0574142i	−0.848975	+	0.528432i	$0.822780\pi$
$18$		0			0
$19$	−1.43346	+	2.48283i	−0.328859	+	0.569600i	−0.982286	−	0.187389i	$-0.939997\pi$
$19$	−1.43346	+	2.48283i	−0.328859	+	0.569600i	0.653427	+	0.756990i	$0.273331\pi$
$20$	0.0394951	+	0.0684076i	0.00883138	+	0.0152964i
$21$		0			0
$22$	3.25729	−	5.64180i	0.694458	−	1.20284i
$23$	−2.52704	−	4.37697i	−0.526925	−	0.912660i	−0.999508	−	0.0313742i	$-0.990012\pi$
$23$	−2.52704	−	4.37697i	−0.526925	−	0.912660i	0.472583	−	0.881286i	$-0.343322\pi$
$24$		0			0
$25$	2.32383	−	4.02499i	0.464766	−	0.804999i
$26$	−3.29679	+	5.71021i	−0.646554	+	1.11986i
$27$		0			0
$28$	−0.00885441	−	0.351971i	−0.00167333	−	0.0665162i
$29$	−0.176168	−	0.305132i	−0.0327136	−	0.0566616i	0.849205	−	0.528063i	$-0.177082\pi$
$29$	−0.176168	−	0.305132i	−0.0327136	−	0.0566616i	−0.881919	+	0.471402i	$0.843748\pi$
$30$		0			0
$31$	2.51459			0.451634			0.225817	−	0.974170i	$-0.427495\pi$
$31$	2.51459			0.451634			0.225817	+	0.974170i	$0.427495\pi$
$32$	0.751560			0.132858
$33$		0			0
$34$	−0.199612	−	0.345738i	−0.0342331	−	0.0592935i
$35$	1.33988	−	0.819187i	0.226482	−	0.138468i
$36$		0			0
$37$	3.32383	−	5.75705i	0.546435	−	0.946452i	−0.452081	−	0.891977i	$-0.649318\pi$
$37$	3.32383	−	5.75705i	0.546435	−	0.946452i	0.998515	−	0.0544753i	$-0.0173486\pi$
$38$	2.09358	−	3.62619i	0.339623	−	0.588245i
$39$		0			0
$40$	0.809243	+	1.40165i	0.127953	+	0.221620i
$41$	5.44805	−	9.43630i	0.850843	−	1.47370i	−0.0296061	−	0.999562i	$-0.509425\pi$
$41$	5.44805	−	9.43630i	0.850843	−	1.47370i	0.880449	−	0.474141i	$-0.157241\pi$
$42$		0			0
$43$	−1.69076	−	2.92848i	−0.257838	−	0.446589i	0.707824	−	0.706388i	$-0.249677\pi$
$43$	−1.69076	−	2.92848i	−0.257838	−	0.446589i	−0.965663	+	0.259800i	$0.916343\pi$
$44$	−0.296790	+	0.514055i	−0.0447427	+	0.0774967i
$45$		0			0
$46$	3.69076	+	6.39258i	0.544172	+	0.942534i
$47$	12.4356			1.81392			0.906959	−	0.421218i	$-0.138397\pi$
$47$	12.4356			1.81392			0.906959	+	0.421218i	$0.138397\pi$
$48$		0			0
$49$	−6.99115	+	0.351971i	−0.998735	+	0.0502815i
$50$	−3.39397	+	5.87852i	−0.479980	+	0.831349i
$51$		0			0
$52$	0.300388	−	0.520288i	0.0416564	−	0.0721509i
$53$	−5.66372	−	9.80984i	−0.777971	−	1.34749i	−0.933109	−	0.359593i	$-0.882916\pi$
$53$	−5.66372	−	9.80984i	−0.777971	−	1.34749i	0.155138	−	0.987893i	$-0.450418\pi$
$54$		0			0
$55$	−2.64766			−0.357011
$56$	−0.181424	−	7.21177i	−0.0242438	−	0.963713i
$57$		0			0
$58$	0.257295	+	0.445647i	0.0337844	+	0.0585163i
$59$	−8.05408			−1.04855			−0.524276	−	0.851548i	$-0.675664\pi$
$59$	−8.05408			−1.04855			−0.524276	+	0.851548i	$0.675664\pi$
$60$		0			0
$61$	−2.73385			−0.350034			−0.175017	−	0.984565i	$-0.555998\pi$
$61$	−2.73385			−0.350034			−0.175017	+	0.984565i	$0.555998\pi$
$62$	−3.67257			−0.466417
$63$		0			0
$64$	7.39922			0.924903
$65$	2.67977			0.332384
$66$		0			0
$67$	5.86693			0.716759			0.358380	−	0.933576i	$-0.383329\pi$
$67$	5.86693			0.716759			0.358380	+	0.933576i	$0.383329\pi$
$68$	0.0181877	+	0.0315020i	0.00220558	+	0.00382018i
$69$		0			0
$70$	−1.95691	+	1.19643i	−0.233895	+	0.143000i
$71$	2.60078			0.308655			0.154328	−	0.988020i	$-0.450679\pi$
$71$	2.60078			0.308655			0.154328	+	0.988020i	$0.450679\pi$
$72$		0			0
$73$	−5.55768	−	9.62619i	−0.650478	−	1.12666i	−0.983007	−	0.183567i	$-0.941235\pi$
$73$	−5.55768	−	9.62619i	−0.650478	−	1.12666i	0.332530	−	0.943093i	$-0.392098\pi$
$74$	−4.85447	+	8.40819i	−0.564321	+	0.977433i
$75$		0			0
$76$	−0.190757	+	0.330401i	−0.0218814	+	0.0378996i
$77$	10.3655	+	5.64180i	1.18125	+	0.642943i
$78$		0			0
$79$	11.1623			1.25585			0.627926	−	0.778273i	$-0.283904\pi$
$79$	11.1623			1.25585			0.627926	+	0.778273i	$0.283904\pi$
$80$	−1.26089	−	2.18393i	−0.140972	−	0.244171i
$81$		0			0
$82$	−7.95691	+	13.7818i	−0.878693	+	1.52194i
$83$	−8.27188	−	14.3273i	−0.907957	−	1.57263i	−0.816898	−	0.576783i	$-0.804308\pi$
$83$	−8.27188	−	14.3273i	−0.907957	−	1.57263i	−0.0910594	−	0.995845i	$-0.529025\pi$
$84$		0			0
$85$	−0.0811263	+	0.140515i	−0.00879939	+	0.0152410i
$86$	2.46936	+	4.27706i	0.266278	+	0.461207i
$87$		0			0
$88$	−6.08113	+	10.5328i	−0.648250	+	1.12280i
$89$	2.68716	−	4.65430i	0.284838	−	0.493354i	−0.687732	−	0.725965i	$-0.741393\pi$
$89$	2.68716	−	4.65430i	0.284838	−	0.493354i	0.972570	+	0.232611i	$0.0747268\pi$
$90$		0			0
$91$	−10.4911	−	5.71021i	−1.09977	−	0.598592i
$92$	−0.336285	−	0.582462i	−0.0350601	−	0.0607259i
$93$		0			0
$94$	−18.1623			−1.87329
$95$	−1.70175			−0.174596
$96$		0			0
$97$	1.13307	+	1.96254i	0.115046	+	0.199266i	0.917798	−	0.397047i	$-0.129965\pi$
$97$	1.13307	+	1.96254i	0.115046	+	0.199266i	−0.802752	+	0.596313i	$0.796632\pi$
$98$	10.2106	−	0.514055i	1.03143	−	0.0519274i
$99$		0			0
$100$	0.309243	−	0.535624i	0.0309243	−	0.0535624i
$101$	−4.67830	+	8.10306i	−0.465509	+	0.806285i	−0.999224	−	0.0393793i	$-0.987462\pi$
$101$	−4.67830	+	8.10306i	−0.465509	+	0.806285i	0.533716	+	0.845664i	$0.320795\pi$
$102$		0			0
$103$	7.88151	+	13.6512i	0.776589	+	1.34509i	0.933897	+	0.357542i	$0.116385\pi$
$103$	7.88151	+	13.6512i	0.776589	+	1.34509i	−0.157309	+	0.987550i	$0.550282\pi$
$104$	6.15486	−	10.6605i	0.603534	−	1.04535i
$105$		0			0
$106$	8.27188	+	14.3273i	0.803436	+	1.39159i
$107$	−0.512453	+	0.887595i	−0.0495407	+	0.0858070i	−0.889732	−	0.456483i	$-0.849109\pi$
$107$	−0.512453	+	0.887595i	−0.0495407	+	0.0858070i	0.840192	+	0.542290i	$0.182442\pi$
$108$		0			0
$109$	−0.647664	−	1.12179i	−0.0620349	−	0.107448i	0.833340	−	0.552761i	$-0.186426\pi$
$109$	−0.647664	−	1.12179i	−0.0620349	−	0.107448i	−0.895375	+	0.445313i	$0.853092\pi$
$110$	3.86693			0.368697
$111$		0			0
$112$	0.282679	+	11.2368i	0.0267107	+	1.06177i
$113$	−7.14766	+	12.3801i	−0.672396	+	1.16462i	0.304827	+	0.952408i	$0.401401\pi$
$113$	−7.14766	+	12.3801i	−0.672396	+	1.16462i	−0.977223	+	0.212216i	$0.931932\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	−0.0234435	−	0.0406053i	−0.00217667	−	0.00377011i
$117$		0			0
$118$	11.7630			1.08287
$119$	0.617023	−	0.377240i	0.0565624	−	0.0345815i
$120$		0			0
$121$	−4.44805	−	7.70425i	−0.404368	−	0.700387i
$122$	3.99280			0.361491
$123$		0			0
$124$	0.334628			0.0300504
$125$	5.72665			0.512207
$126$		0			0
$127$	12.3346			1.09452			0.547261	−	0.836962i	$-0.315671\pi$
$127$	12.3346			1.09452			0.547261	+	0.836962i	$0.315671\pi$
$128$	−12.3097			−1.08804
$129$		0			0
$130$	−3.91381			−0.343264
$131$	1.59718	+	2.76639i	0.139546	+	0.241701i	0.927325	−	0.374257i	$-0.122102\pi$
$131$	1.59718	+	2.76639i	0.139546	+	0.241701i	−0.787779	+	0.615958i	$0.788769\pi$
$132$		0			0
$133$	6.66225	+	3.62619i	0.577691	+	0.314430i
$134$	−8.56867			−0.740221
$135$		0			0
$136$	0.372660	+	0.645466i	0.0319553	+	0.0553483i
$137$	−5.05408	+	8.75393i	−0.431800	+	0.747899i	−0.997028	−	0.0770354i	$-0.975455\pi$
$137$	−5.05408	+	8.75393i	−0.431800	+	0.747899i	0.565229	+	0.824934i	$0.308788\pi$
$138$		0			0
$139$	−9.03803	+	15.6543i	−0.766596	+	1.32778i	0.172803	+	0.984956i	$0.444718\pi$
$139$	−9.03803	+	15.6543i	−0.766596	+	1.32778i	−0.939399	+	0.342827i	$0.888616\pi$
$140$	0.178304	−	0.109013i	0.0150695	−	0.00921327i
$141$		0			0
$142$	−3.79845			−0.318759
$143$	10.0687	+	17.4395i	0.841985	+	1.45836i
$144$		0			0
$145$	0.104570	−	0.181120i	0.00868405	−	0.0150412i
$146$	8.11702	+	14.0591i	0.671770	+	1.16354i
$147$		0			0
$148$	0.442317	−	0.766116i	0.0363582	−	0.0629743i
$149$	−7.02704	−	12.1712i	−0.575678	−	0.997103i	−0.995968	−	0.0897132i	$-0.971405\pi$
$149$	−7.02704	−	12.1712i	−0.575678	−	0.997103i	0.420290	−	0.907390i	$-0.361928\pi$
$150$		0			0
$151$	−0.190757	+	0.330401i	−0.0155236	+	0.0268877i	−0.873683	−	0.486496i	$-0.838275\pi$
$151$	−0.190757	+	0.330401i	−0.0155236	+	0.0268877i	0.858159	+	0.513384i	$0.171608\pi$
$152$	−3.90856	+	6.76982i	−0.317026	+	0.549105i
$153$		0			0
$154$	−15.1388	−	8.23988i	−1.21992	−	0.663988i
$155$	0.746304	+	1.29264i	0.0599446	+	0.103827i
$156$		0			0
$157$	−7.51459			−0.599729			−0.299865	−	0.953982i	$-0.596942\pi$
$157$	−7.51459			−0.599729			−0.299865	+	0.953982i	$0.596942\pi$
$158$	−16.3025			−1.29696
$159$		0			0
$160$	0.223055	+	0.386343i	0.0176341	+	0.0305431i
$161$	−11.4086	+	6.97504i	−0.899120	+	0.549710i
$162$		0			0
$163$	−7.59572	+	13.1562i	−0.594942	+	1.03047i	0.398613	+	0.917119i	$0.369492\pi$
$163$	−7.59572	+	13.1562i	−0.594942	+	1.03047i	−0.993555	+	0.113351i	$0.963842\pi$
$164$	0.724997	−	1.25573i	0.0566127	−	0.0980561i
$165$		0			0
$166$	12.0811	+	20.9251i	0.937677	+	1.62410i
$167$	−4.47656	+	7.75362i	−0.346406	+	0.599993i	−0.985608	−	0.169046i	$-0.945931\pi$
$167$	−4.47656	+	7.75362i	−0.346406	+	0.599993i	0.639202	+	0.769039i	$0.279265\pi$
$168$		0			0
$169$	−3.69076	−	6.39258i	−0.283904	−	0.491737i
$170$	0.118485	−	0.205223i	0.00908741	−	0.0157399i
$171$		0			0
$172$	−0.224997	−	0.389706i	−0.0171558	−	0.0297148i
$173$	−10.4605			−0.795297			−0.397649	−	0.917538i	$-0.630174\pi$
$173$	−10.4605			−0.795297			−0.397649	+	0.917538i	$0.630174\pi$
$174$		0			0
$175$	−10.8004	−	5.87852i	−0.816433	−	0.444375i
$176$	9.47509	−	16.4113i	0.714212	−	1.23705i
$177$		0			0
$178$	−3.92461	+	6.79762i	−0.294162	+	0.509503i
$179$	4.48395	+	7.76643i	0.335146	+	0.580490i	0.983513	−	0.180838i	$-0.0578810\pi$
$179$	4.48395	+	7.76643i	0.335146	+	0.580490i	−0.648367	+	0.761328i	$0.724548\pi$
$180$		0			0
$181$	5.04689			0.375132			0.187566	−	0.982252i	$-0.439940\pi$
$181$	5.04689			0.375132			0.187566	+	0.982252i	$0.439940\pi$
$182$	15.3224	+	8.33979i	1.13577	+	0.618186i
$183$		0			0
$184$	−6.89037	−	11.9345i	−0.507965	−	0.879821i
$185$	3.94592			0.290109
$186$		0			0
$187$	−1.21926			−0.0891613
$188$	1.65486			0.120693
$189$		0			0
$190$	2.48541			0.180311
$191$	12.1301			0.877707			0.438853	−	0.898559i	$-0.355385\pi$
$191$	12.1301			0.877707			0.438853	+	0.898559i	$0.355385\pi$
$192$		0			0
$193$	17.1623			1.23537			0.617683	−	0.786427i	$-0.288071\pi$
$193$	17.1623			1.23537			0.617683	+	0.786427i	$0.288071\pi$
$194$	−1.65486	−	2.86630i	−0.118812	−	0.205789i
$195$		0			0
$196$	−0.930343	+	0.0468383i	−0.0664531	+	0.00334559i
$197$	0.751560			0.0535464			0.0267732	−	0.999642i	$-0.491477\pi$
$197$	0.751560			0.0535464			0.0267732	+	0.999642i	$0.491477\pi$
$198$		0			0
$199$	−5.14766	−	8.91601i	−0.364908	−	0.632040i	0.623853	−	0.781542i	$-0.285566\pi$
$199$	−5.14766	−	8.91601i	−0.364908	−	0.632040i	−0.988761	+	0.149502i	$0.952233\pi$
$200$	6.33628	−	10.9748i	0.448043	−	0.776033i
$201$		0			0
$202$	6.83269	−	11.8346i	0.480746	−	0.832677i
$203$	−0.795327	+	0.486253i	−0.0558210	+	0.0341282i
$204$		0			0
$205$	6.46770			0.451724
$206$	−11.5110	−	19.9376i	−0.802009	−	1.38912i
$207$		0			0
$208$	−9.58998	+	16.6103i	−0.664946	+	1.15172i
$209$	−6.39397	−	11.0747i	−0.442280	−	0.766051i
$210$		0			0
$211$	8.05768	−	13.9563i	0.554714	−	0.960792i	−0.443212	−	0.896417i	$-0.646161\pi$
$211$	8.05768	−	13.9563i	0.554714	−	0.960792i	0.997926	−	0.0643756i	$-0.0205056\pi$
$212$	−0.753696	−	1.30544i	−0.0517640	−	0.0896580i
$213$		0			0
$214$	0.748440	−	1.29634i	0.0511623	−	0.0886157i
$215$	1.00360	−	1.73828i	0.0684449	−	0.118550i
$216$		0			0
$217$	−0.167314	−	6.65087i	−0.0113580	−	0.451491i
$218$	0.945916	+	1.63837i	0.0640655	+	0.110965i
$219$		0			0
$220$	−0.352336			−0.0237545
$221$	1.23405			0.0830109
$222$		0			0
$223$	3.47656	+	6.02157i	0.232807	+	0.403234i	0.958633	−	0.284644i	$-0.0918755\pi$
$223$	3.47656	+	6.02157i	0.232807	+	0.403234i	−0.725826	+	0.687879i	$0.758542\pi$
$224$	−0.0500067	−	1.98781i	−0.00334121	−	0.132816i
$225$		0			0
$226$	10.4392	−	18.0812i	0.694405	−	1.20274i
$227$	2.64553	−	4.58219i	0.175590	−	0.304131i	−0.764775	−	0.644297i	$-0.777150\pi$
$227$	2.64553	−	4.58219i	0.175590	−	0.304131i	0.940365	+	0.340166i	$0.110483\pi$
$228$		0			0
$229$	−5.86186	−	10.1530i	−0.387363	−	0.670932i	0.604731	−	0.796430i	$-0.293281\pi$
$229$	−5.86186	−	10.1530i	−0.387363	−	0.670932i	−0.992094	+	0.125498i	$0.959947\pi$
$230$	−2.19076	+	3.79450i	−0.144454	+	0.250202i
$231$		0			0
$232$	−0.480350	−	0.831990i	−0.0315365	−	0.0546228i
$233$	1.93560	−	3.35256i	0.126805	−	0.219633i	−0.795632	−	0.605780i	$-0.792861\pi$
$233$	1.93560	−	3.35256i	0.126805	−	0.219633i	0.922437	+	0.386147i	$0.126194\pi$
$234$		0			0
$235$	3.69076	+	6.39258i	0.240758	+	0.417006i
$236$	−1.07179			−0.0697678
$237$		0			0
$238$	−0.901165	+	0.550960i	−0.0584138	+	0.0357135i
$239$	6.19961	−	10.7380i	0.401020	−	0.694586i	−0.592830	−	0.805328i	$-0.701989\pi$
$239$	6.19961	−	10.7380i	0.401020	−	0.694586i	0.993849	+	0.110742i	$0.0353226\pi$
$240$		0			0
$241$	8.28074	−	14.3427i	0.533409	−	0.923892i	−0.465829	−	0.884875i	$-0.654244\pi$
$241$	8.28074	−	14.3427i	0.533409	−	0.923892i	0.999239	−	0.0390173i	$-0.0124227\pi$
$242$	6.49640	+	11.2521i	0.417604	+	0.723312i
$243$		0			0
$244$	−0.363806			−0.0232903
$245$	−2.25583	−	3.48937i	−0.144120	−	0.222928i
$246$		0			0
$247$	6.47150	+	11.2090i	0.411771	+	0.713209i
$248$	6.85641			0.435383
$249$		0			0
$250$	−8.36381			−0.528974
$251$	−1.84922			−0.116722			−0.0583608	−	0.998296i	$-0.518587\pi$
$251$	−1.84922			−0.116722			−0.0583608	+	0.998296i	$0.518587\pi$
$252$		0			0
$253$	22.5438			1.41731
$254$	−18.0148			−1.13035
$255$		0			0
$256$	3.17996			0.198748
$257$	13.4210	+	23.2459i	0.837180	+	1.45004i	0.892243	+	0.451555i	$0.149130\pi$
$257$	13.4210	+	23.2459i	0.837180	+	1.45004i	−0.0550638	+	0.998483i	$0.517536\pi$
$258$		0			0
$259$	−15.4481	−	8.40819i	−0.959895	−	0.522460i
$260$	0.356609			0.0221159
$261$		0			0
$262$	−2.33269	−	4.04033i	−0.144114	−	0.249612i
$263$	10.1424	−	17.5672i	0.625408	−	1.08324i	−0.363054	−	0.931768i	$-0.618266\pi$
$263$	10.1424	−	17.5672i	0.625408	−	1.08324i	0.988462	−	0.151470i	$-0.0484006\pi$
$264$		0			0
$265$	3.36186	−	5.82292i	0.206518	−	0.357699i
$266$	−9.73025	−	5.29606i	−0.596600	−	0.324722i
$267$		0			0
$268$	0.780738			0.0476912
$269$	−4.36333	−	7.55750i	−0.266037	−	0.460789i	0.701798	−	0.712376i	$-0.252381\pi$
$269$	−4.36333	−	7.55750i	−0.266037	−	0.460789i	−0.967835	+	0.251587i	$0.919048\pi$
$270$		0			0
$271$	−12.0957	+	20.9504i	−0.734762	+	1.27265i	0.220065	+	0.975485i	$0.429373\pi$
$271$	−12.0957	+	20.9504i	−0.734762	+	1.27265i	−0.954828	+	0.297161i	$0.903960\pi$
$272$	−0.580647	−	1.00571i	−0.0352069	−	0.0609802i
$273$		0			0
$274$	7.38151	−	12.7852i	0.445934	−	0.772380i
$275$	10.3655	+	17.9535i	0.625061	+	1.08264i
$276$		0			0
$277$	3.55768	−	6.16209i	0.213760	−	0.370244i	−0.739128	−	0.673565i	$-0.764762\pi$
$277$	3.55768	−	6.16209i	0.213760	−	0.370244i	0.952888	+	0.303321i	$0.0980955\pi$
$278$	13.2001	−	22.8632i	0.791689	−	1.37125i
$279$		0			0
$280$	3.65340	−	2.23364i	0.218332	−	0.133485i
$281$	3.94805	+	6.83823i	0.235521	+	0.407934i	0.959424	−	0.281967i	$-0.0909870\pi$
$281$	3.94805	+	6.83823i	0.235521	+	0.407934i	−0.723903	+	0.689902i	$0.757654\pi$
$282$		0			0
$283$	2.20914			0.131320			0.0656599	−	0.997842i	$-0.479085\pi$
$283$	2.20914			0.131320			0.0656599	+	0.997842i	$0.479085\pi$
$284$	0.346097			0.0205371
$285$		0			0
$286$	−14.7053	−	25.4704i	−0.869545	−	1.50610i
$287$	−25.3207	−	13.7818i	−1.49463	−	0.813512i
$288$		0			0
$289$	8.46264	−	14.6577i	0.497802	−	0.862219i
$290$	−0.152725	+	0.264527i	−0.00896830	+	0.0155336i
$291$		0			0
$292$	−0.739586	−	1.28100i	−0.0432810	−	0.0749649i
$293$	−9.59572	+	16.6203i	−0.560588	+	0.970966i	0.436858	+	0.899531i	$0.356091\pi$
$293$	−9.59572	+	16.6203i	−0.560588	+	0.970966i	−0.997445	+	0.0714356i	$0.977242\pi$
$294$		0			0
$295$	−2.39037	−	4.14024i	−0.139173	−	0.241054i
$296$	9.06294	−	15.6975i	0.526773	−	0.912397i
$297$		0			0
$298$	10.2630	+	17.7761i	0.594521	+	1.02974i
$299$	−22.8171			−1.31955
$300$		0			0
$301$	−7.63307	+	4.66676i	−0.439963	+	0.268988i
$302$	0.278602	−	0.482553i	0.0160317	−	0.0277678i
$303$		0			0
$304$	6.08998	−	10.5482i	0.349284	−	0.604978i
$305$	−0.811379	−	1.40535i	−0.0464594	−	0.0804701i
$306$		0			0
$307$	−13.9138			−0.794103			−0.397052	−	0.917796i	$-0.629967\pi$
$307$	−13.9138			−0.794103			−0.397052	+	0.917796i	$0.629967\pi$
$308$	1.37938	+	0.750780i	0.0785974	+	0.0427796i
$309$		0			0
$310$	−1.08998	−	1.88790i	−0.0619067	−	0.107226i
$311$	−10.6549			−0.604182			−0.302091	−	0.953279i	$-0.597685\pi$
$311$	−10.6549			−0.604182			−0.302091	+	0.953279i	$0.597685\pi$
$312$		0			0
$313$	−16.5615			−0.936110			−0.468055	−	0.883699i	$-0.655045\pi$
$313$	−16.5615			−0.936110			−0.468055	+	0.883699i	$0.655045\pi$
$314$	10.9751			0.619360
$315$		0			0
$316$	1.48541			0.0835609
$317$	26.6372			1.49609			0.748046	−	0.663647i	$-0.230992\pi$
$317$	26.6372			1.49609			0.748046	+	0.663647i	$0.230992\pi$
$318$		0			0
$319$	1.57160			0.0879926
$320$	2.19601	+	3.80361i	0.122761	+	0.212628i
$321$		0			0
$322$	16.6623	−	10.1871i	0.928551	−	0.567704i
$323$	−0.783663			−0.0436042
$324$		0			0
$325$	−10.4911	−	18.1712i	−0.581944	−	1.00796i
$326$	11.0936	−	19.2146i	0.614417	−	1.06420i
$327$		0			0
$328$	14.8550	−	25.7295i	0.820227	−	1.42068i
$329$	−0.827430	−	32.8911i	−0.0456177	−	1.81334i
$330$		0			0
$331$	−23.3068			−1.28106			−0.640529	−	0.767934i	$-0.721285\pi$
$331$	−23.3068			−1.28106			−0.640529	+	0.767934i	$0.721285\pi$
$332$	−1.10078	−	1.90660i	−0.0604130	−	0.104638i
$333$		0			0
$334$	6.53803	−	11.3242i	0.357745	−	0.619633i
$335$	1.74124	+	3.01592i	0.0951343	+	0.164777i
$336$		0			0
$337$	11.6192	−	20.1250i	0.632936	−	1.09628i	−0.354013	−	0.935241i	$-0.615183\pi$
$337$	11.6192	−	20.1250i	0.632936	−	1.09628i	0.986948	−	0.161036i	$-0.0514837\pi$
$338$	5.39037	+	9.33639i	0.293197	+	0.507833i
$339$		0			0
$340$	−0.0107958	+	0.0186989i	−0.000585487	+	0.00101409i
$341$	−5.60817	+	9.71363i	−0.303699	+	0.526023i
$342$		0			0
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$	−4.61011	−	7.98494i	−0.248560	−	0.430519i
$345$		0			0
$346$	15.2776			0.821330
$347$	17.1373			0.919981			0.459990	−	0.887924i	$-0.347853\pi$
$347$	17.1373			0.919981			0.459990	+	0.887924i	$0.347853\pi$
$348$		0			0
$349$	9.75729	+	16.9001i	0.522296	+	0.904643i	0.999664	+	0.0259395i	$0.00825772\pi$
$349$	9.75729	+	16.9001i	0.522296	+	0.904643i	−0.477368	+	0.878704i	$0.658409\pi$
$350$	15.7740	+	8.58561i	0.843157	+	0.458920i
$351$		0			0
$352$	−1.67617	+	2.90321i	−0.0893401	+	0.154742i
$353$	−8.03064	+	13.9095i	−0.427428	+	0.740327i	−0.996644	−	0.0818613i	$-0.973914\pi$
$353$	−8.03064	+	13.9095i	−0.427428	+	0.740327i	0.569216	+	0.822188i	$0.307247\pi$
$354$		0			0
$355$	0.771884	+	1.33694i	0.0409673	+	0.0709575i
$356$	0.357592	−	0.619368i	0.0189524	−	0.0328264i
$357$		0			0
$358$	−6.54883	−	11.3429i	−0.346116	−	0.599491i
$359$	−6.93200	+	12.0066i	−0.365857	+	0.633683i	−0.988913	−	0.148494i	$-0.952557\pi$
$359$	−6.93200	+	12.0066i	−0.365857	+	0.633683i	0.623056	+	0.782177i	$0.285891\pi$
$360$		0			0
$361$	5.39037	+	9.33639i	0.283704	+	0.491389i
$362$	−7.37100			−0.387411
$363$		0			0
$364$	−1.39610	−	0.759883i	−0.0731757	−	0.0398287i
$365$	3.29893	−	5.71391i	0.172674	−	0.299080i
$366$		0			0
$367$	−12.6477	+	21.9064i	−0.660203	+	1.14350i	0.320360	+	0.947296i	$0.396196\pi$
$367$	−12.6477	+	21.9064i	−0.660203	+	1.14350i	−0.980562	+	0.196209i	$0.937137\pi$
$368$	10.7360	+	18.5953i	0.559652	+	0.969346i
$369$		0			0
$370$	−5.76303			−0.299606
$371$	−25.5693	+	15.6328i	−1.32749	+	0.811613i
$372$		0			0
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	0.838975	−	0.544170i	$-0.183156\pi$
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	−0.890753	+	0.454488i	$0.849822\pi$
$374$	1.78074			0.0920798
$375$		0			0
$376$	33.9076			1.74865
$377$	−1.59065			−0.0819229
$378$		0			0
$379$	−18.8099			−0.966200			−0.483100	−	0.875565i	$-0.660489\pi$
$379$	−18.8099			−0.966200			−0.483100	+	0.875565i	$0.660489\pi$
$380$	−0.226459			−0.0116171
$381$		0			0
$382$	−17.7161			−0.906437
$383$	−17.5708	−	30.4335i	−0.897826	−	1.55508i	−0.830267	−	0.557366i	$-0.811812\pi$
$383$	−17.5708	−	30.4335i	−0.897826	−	1.55508i	−0.0675593	−	0.997715i	$-0.521521\pi$
$384$		0			0
$385$	0.176168	+	7.00284i	0.00897836	+	0.356898i
$386$	−25.0656			−1.27580
$387$		0			0
$388$	0.150783	+	0.261164i	0.00765486	+	0.0132586i
$389$	4.18929	−	7.25607i	0.212406	−	0.367897i	−0.740061	−	0.672539i	$-0.765204\pi$
$389$	4.18929	−	7.25607i	0.212406	−	0.367897i	0.952467	+	0.304642i	$0.0985368\pi$
$390$		0			0
$391$	0.690757	−	1.19643i	0.0349331	−	0.0605059i
$392$	−19.0624	+	0.959702i	−0.962798	+	0.0484723i
$393$		0			0
$394$	−1.09766			−0.0552992
$395$	3.31284	+	5.73801i	0.166687	+	0.288711i
$396$		0			0
$397$	4.62422	−	8.00938i	0.232083	−	0.401979i	−0.726338	−	0.687338i	$-0.758779\pi$
$397$	4.62422	−	8.00938i	0.232083	−	0.401979i	0.958421	+	0.285358i	$0.0921126\pi$
$398$	7.51819	+	13.0219i	0.376853	+	0.652728i
$399$		0			0
$400$	−9.87266	+	17.0999i	−0.493633	+	0.854997i
$401$	0.0737345	+	0.127712i	0.00368212	+	0.00637763i	0.867861	−	0.496808i	$-0.165495\pi$
$401$	0.0737345	+	0.127712i	0.00368212	+	0.00637763i	−0.864178	+	0.503185i	$0.832161\pi$
$402$		0			0
$403$	5.67617	−	9.83141i	0.282750	−	0.489738i
$404$	−0.622563	+	1.07831i	−0.0309737	+	0.0536480i
$405$		0			0
$406$	1.16158	−	0.710174i	0.0576482	−	0.0352454i
$407$	14.8260	+	25.6793i	0.734896	+	1.27288i
$408$		0			0
$409$	−3.92528			−0.194093			−0.0970463	−	0.995280i	$-0.530940\pi$
$409$	−3.92528			−0.194093			−0.0970463	+	0.995280i	$0.530940\pi$
$410$	−9.44611			−0.466510
$411$		0			0
$412$	1.04883	+	1.81662i	0.0516721	+	0.0894986i
$413$	0.535897	+	21.3024i	0.0263697	+	1.04822i
$414$		0			0
$415$	4.91002	−	8.50440i	0.241023	−	0.417465i
$416$	1.69649	−	2.93841i	0.0831774	−	0.144067i
$417$		0			0
$418$	9.33842	+	16.1746i	0.456757	+	0.791126i
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	0.486928	+	0.873442i	$0.338117\pi$
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	−0.999887	+	0.0150285i	$0.995216\pi$
$420$		0			0
$421$	12.3442	+	21.3807i	0.601617	+	1.04203i	0.992576	+	0.121624i	$0.0388101\pi$
$421$	12.3442	+	21.3807i	0.601617	+	1.04203i	−0.390959	+	0.920408i	$0.627857\pi$
$422$	−11.7683	+	20.3833i	−0.572871	+	0.992242i
$423$		0			0
$424$	−15.4430	−	26.7480i	−0.749978	−	1.29900i
$425$	1.27042			0.0616245
$426$		0			0
$427$	0.181903	+	7.23080i	0.00880290	+	0.349923i
$428$	−0.0681944	+	0.118116i	−0.00329630	+	0.00570936i
$429$		0			0
$430$	−1.46576	+	2.53877i	−0.0706853	+	0.122430i
$431$	2.73745	+	4.74140i	0.131858	+	0.228385i	0.924393	−	0.381442i	$-0.124572\pi$
$431$	2.73745	+	4.74140i	0.131858	+	0.228385i	−0.792535	+	0.609827i	$0.791239\pi$
$432$		0			0
$433$	23.6300			1.13558			0.567792	−	0.823172i	$-0.307798\pi$
$433$	23.6300			1.13558			0.567792	+	0.823172i	$0.307798\pi$
$434$	0.244363	+	9.71363i	0.0117298	+	0.466269i
$435$		0			0
$436$	−0.0861875	−	0.149281i	−0.00412763	−	0.00714927i
$437$	14.4897			0.693136
$438$		0			0
$439$	−5.26615			−0.251340			−0.125670	−	0.992072i	$-0.540108\pi$
$439$	−5.26615			−0.251340			−0.125670	+	0.992072i	$0.540108\pi$
$440$	−7.21926			−0.344165
$441$		0			0
$442$	−1.80233			−0.0857281
$443$	6.03638			0.286797			0.143398	−	0.989665i	$-0.454197\pi$
$443$	6.03638			0.286797			0.143398	+	0.989665i	$0.454197\pi$
$444$		0			0
$445$	3.19008			0.151224
$446$	−5.07753	−	8.79454i	−0.240428	−	0.416433i
$447$		0			0
$448$	−0.492324	−	19.5703i	−0.0232601	−	0.924610i
$449$	22.1445			1.04507			0.522533	−	0.852619i	$-0.324987\pi$
$449$	22.1445			1.04507			0.522533	+	0.852619i	$0.324987\pi$
$450$		0			0
$451$	24.3011	+	42.0907i	1.14429	+	1.98197i
$452$	−0.951172	+	1.64748i	−0.0447393	+	0.0774908i
$453$		0			0
$454$	−3.86381	+	6.69231i	−0.181337	+	0.314086i
$455$	−0.178304	−	7.08775i	−0.00835903	−	0.332279i
$456$		0			0
$457$	−5.33463			−0.249543			−0.124772	−	0.992185i	$-0.539820\pi$
$457$	−5.33463			−0.249543			−0.124772	+	0.992185i	$0.539820\pi$
$458$	8.56128	+	14.8286i	0.400042	+	0.692894i
$459$		0			0
$460$	0.199612	−	0.345738i	0.00930694	−	0.0161201i
$461$	14.8473	+	25.7162i	0.691507	+	1.19772i	0.971344	+	0.237677i	$0.0763860\pi$
$461$	14.8473	+	25.7162i	0.691507	+	1.19772i	−0.279838	+	0.960047i	$0.590281\pi$
$462$		0			0
$463$	−9.29533	+	16.1000i	−0.431990	+	0.748229i	−0.997045	−	0.0768243i	$-0.975522\pi$
$463$	−9.29533	+	16.1000i	−0.431990	+	0.748229i	0.565054	+	0.825054i	$0.308855\pi$
$464$	0.748440	+	1.29634i	0.0347455	+	0.0601809i
$465$		0			0
$466$	−2.82695	+	4.89642i	−0.130956	+	0.226822i
$467$	12.3063	−	21.3152i	0.569468	−	0.986348i	−0.427150	−	0.904181i	$-0.640482\pi$
$467$	12.3063	−	21.3152i	0.569468	−	0.986348i	0.996619	−	0.0821676i	$-0.0261843\pi$
$468$		0			0
$469$	−0.390369	−	15.5175i	−0.0180256	−	0.716532i
$470$	−5.39037	−	9.33639i	−0.248639	−	0.430656i
$471$		0			0
$472$	−21.9607			−1.01082
$473$	15.0833			0.693529
$474$		0			0
$475$	6.66225	+	11.5394i	0.305685	+	0.529462i
$476$	0.0821100	−	0.0502010i	0.00376351	−	0.00230096i
$477$		0			0
$478$	−9.05456	+	15.6830i	−0.414146	+	0.717322i
$479$	−0.178304	+	0.308832i	−0.00814693	+	0.0141109i	−0.870070	−	0.492928i	$-0.835927\pi$
$479$	−0.178304	+	0.308832i	−0.00814693	+	0.0141109i	0.861923	+	0.507039i	$0.169260\pi$
$480$		0			0
$481$	−15.0057	−	25.9907i	−0.684203	−	1.18507i
$482$	−12.0941	+	20.9475i	−0.550869	+	0.954134i
$483$		0			0
$484$	−0.591922	−	1.02524i	−0.0269056	−	0.0466018i
$485$	−0.672570	+	1.16492i	−0.0305398	+	0.0528965i
$486$		0			0
$487$	6.43920	+	11.1530i	0.291788	+	0.505391i	0.974233	−	0.225546i	$-0.0724165\pi$
$487$	6.43920	+	11.1530i	0.291788	+	0.505391i	−0.682445	+	0.730937i	$0.739083\pi$
$488$	−7.45427			−0.337439
$489$		0			0
$490$	3.29465	+	5.09624i	0.148837	+	0.230225i
$491$	2.77694	−	4.80981i	0.125322	−	0.217064i	−0.796537	−	0.604590i	$-0.793337\pi$
$491$	2.77694	−	4.80981i	0.125322	−	0.217064i	0.921859	+	0.387526i	$0.126670\pi$
$492$		0			0
$493$	0.0481549	−	0.0834068i	0.00216879	−	0.00375645i
$494$	−9.45165	−	16.3707i	−0.425250	−	0.736554i
$495$		0			0
$496$	−10.6831			−0.479685
$497$	−0.173048	−	6.87883i	−0.00776229	−	0.308558i
$498$		0			0
$499$	14.0577	+	24.3486i	0.629308	+	1.08999i	0.987691	+	0.156419i	$0.0499951\pi$
$499$	14.0577	+	24.3486i	0.629308	+	1.08999i	−0.358382	+	0.933575i	$0.616672\pi$
$500$	0.762071			0.0340809
$501$		0			0
$502$	2.70079			0.120542
$503$	−16.9430			−0.755451			−0.377725	−	0.925918i	$-0.623294\pi$
$503$	−16.9430			−0.755451			−0.377725	+	0.925918i	$0.623294\pi$
$504$		0			0
$505$	−5.55389			−0.247145
$506$	−32.9253			−1.46371
$507$		0			0
$508$	1.64142			0.0728264
$509$	−11.1513	−	19.3146i	−0.494271	−	0.856102i	0.505707	−	0.862705i	$-0.331232\pi$
$509$	−11.1513	−	19.3146i	−0.494271	−	0.856102i	−0.999978	+	0.00660269i	$0.997898\pi$
$510$		0			0
$511$	−25.0907	+	15.3401i	−1.10995	+	0.678606i
$512$	19.9751			0.882783
$513$		0			0
$514$	−19.6015	−	33.9507i	−0.864583	−	1.49750i
$515$	−4.67830	+	8.10306i	−0.206151	+	0.357064i
$516$		0			0
$517$	−27.7345	+	48.0376i	−1.21976	+	2.11269i
$518$	22.5620	+	12.2802i	0.991315	+	0.539561i
$519$		0			0
$520$	7.30680			0.320424
$521$	6.18044	+	10.7048i	0.270770	+	0.468987i	0.969059	−	0.246828i	$-0.0793884\pi$
$521$	6.18044	+	10.7048i	0.270770	+	0.468987i	−0.698289	+	0.715816i	$0.746055\pi$
$522$		0			0
$523$	−3.09572	+	5.36194i	−0.135366	+	0.234461i	−0.925737	−	0.378167i	$-0.876554\pi$
$523$	−3.09572	+	5.36194i	−0.135366	+	0.234461i	0.790371	+	0.612628i	$0.209888\pi$
$524$	0.212544	+	0.368136i	0.00928501	+	0.0160821i
$525$		0			0
$526$	−14.8130	+	25.6569i	−0.645879	+	1.11870i
$527$	0.343677	+	0.595265i	0.0149708	+	0.0259302i
$528$		0			0
$529$	−1.27188	+	2.20297i	−0.0552993	+	0.0957812i
$530$	−4.91002	+	8.50440i	−0.213278	+	0.369408i
$531$		0			0
$532$	0.886576	+	0.482553i	0.0384379	+	0.0209213i
$533$	−24.5957	−	42.6010i	−1.06536	−	1.84526i
$534$		0			0
$535$	−0.608363			−0.0263018
$536$	15.9971			0.690968
$537$		0			0
$538$	6.37266	+	11.0378i	0.274745	+	0.475872i
$539$	14.2324	−	27.7912i	0.613032	−	1.19705i
$540$		0			0
$541$	−13.4100	+	23.2268i	−0.576542	+	0.998600i	0.419330	+	0.907834i	$0.362265\pi$
$541$	−13.4100	+	23.2268i	−0.576542	+	0.998600i	−0.995872	+	0.0907660i	$0.971068\pi$
$542$	17.6659	−	30.5982i	0.758813	−	1.31430i
$543$		0			0
$544$	0.102718	+	0.177913i	0.00440400	+	0.00762795i
$545$	0.384440	−	0.665869i	0.0164676	−	0.0285227i
$546$		0			0
$547$	7.32957	+	12.6952i	0.313390	+	0.542807i	0.979094	−	0.203409i	$-0.0652021\pi$
$547$	7.32957	+	12.6952i	0.313390	+	0.542807i	−0.665704	+	0.746216i	$0.731869\pi$
$548$	−0.672570	+	1.16492i	−0.0287307	+	0.0497631i
$549$		0			0
$550$	−15.1388	−	26.2212i	−0.645521	−	1.11808i
$551$	1.01012			0.0430327
$552$		0			0
$553$	−0.742705	−	29.5232i	−0.0315830	−	1.25545i
$554$	−5.19601	+	8.99976i	−0.220757	+	0.382363i
$555$		0			0
$556$	−1.20273	+	2.08319i	−0.0510072	+	0.0883470i
$557$	−11.8399	−	20.5073i	−0.501672	−	0.868921i	−0.999998	−	0.00193169i	$-0.999385\pi$
$557$	−11.8399	−	20.5073i	−0.501672	−	0.868921i	0.498326	−	0.866990i	$-0.333948\pi$
$558$		0			0
$559$	−15.2661			−0.645689
$560$	−5.69241	+	3.48027i	−0.240548	+	0.147068i
$561$		0			0
$562$	−5.76615	−	9.98726i	−0.243230	−	0.421287i
$563$	16.3858			0.690579			0.345289	−	0.938496i	$-0.387781\pi$
$563$	16.3858			0.690579			0.345289	+	0.938496i	$0.387781\pi$
$564$		0			0
$565$	−8.48541			−0.356984
$566$	−3.22646			−0.135618
$567$		0			0
$568$	7.09142			0.297549
$569$	15.7879			0.661865			0.330932	−	0.943654i	$-0.392637\pi$
$569$	15.7879			0.661865			0.330932	+	0.943654i	$0.392637\pi$
$570$		0			0
$571$	6.38151			0.267058			0.133529	−	0.991045i	$-0.457369\pi$
$571$	6.38151			0.267058			0.133529	+	0.991045i	$0.457369\pi$
$572$	1.33988	+	2.32075i	0.0560233	+	0.0970353i
$573$		0			0
$574$	36.9810	+	20.1283i	1.54356	+	0.840141i
$575$	−23.4897			−0.979587
$576$		0			0
$577$	18.5203	+	32.0781i	0.771011	+	1.33543i	0.937009	+	0.349304i	$0.113582\pi$
$577$	18.5203	+	32.0781i	0.771011	+	1.33543i	−0.165998	+	0.986126i	$0.553085\pi$
$578$	−12.3597	+	21.4077i	−0.514097	+	0.890442i
$579$		0			0
$580$	0.0139156	−	0.0241025i	0.000577813	−	0.00100080i
$581$	−37.3442	+	22.8317i	−1.54930	+	0.947220i
$582$		0			0
$583$	50.5261			2.09258
$584$	−15.1539	−	26.2473i	−0.627072	−	1.08612i
$585$		0			0
$586$	14.0146	−	24.2740i	0.578937	−	1.00275i
$587$	−6.04689	−	10.4735i	−0.249582	−	0.432288i	0.713828	−	0.700321i	$-0.246960\pi$
$587$	−6.04689	−	10.4735i	−0.249582	−	0.432288i	−0.963410	+	0.268033i	$0.913626\pi$
$588$		0			0
$589$	−3.60457	+	6.24330i	−0.148524	+	0.257251i
$590$	3.49115	+	6.04684i	0.143728	+	0.248945i
$591$		0			0
$592$	−14.1211	+	24.4585i	−0.580374	+	1.00524i
$593$	8.26449	−	14.3145i	0.339382	−	0.587827i	−0.644935	−	0.764238i	$-0.723115\pi$
$593$	8.26449	−	14.3145i	0.339382	−	0.587827i	0.984317	+	0.176411i	$0.0564487\pi$
$594$		0			0
$595$	0.377048	+	0.205223i	0.0154575	+	0.00841331i
$596$	−0.935120	−	1.61968i	−0.0383040	−	0.0663445i
$597$		0			0
$598$	33.3245			1.36274
$599$	8.74825			0.357444			0.178722	−	0.983900i	$-0.442804\pi$
$599$	8.74825			0.357444			0.178722	+	0.983900i	$0.442804\pi$
$600$		0			0
$601$	2.96197	+	5.13028i	0.120821	+	0.209268i	0.920092	−	0.391703i	$-0.128114\pi$
$601$	2.96197	+	5.13028i	0.120821	+	0.209268i	−0.799271	+	0.600971i	$0.794781\pi$
$602$	11.1481	−	6.81583i	0.454364	−	0.277792i
$603$		0			0
$604$	−0.0253849	+	0.0439680i	−0.00103290	+	0.00178903i
$605$	2.64027	−	4.57308i	0.107342	−	0.185922i
$606$		0			0
$607$	0.370719	+	0.642104i	0.0150470	+	0.0260622i	0.873451	−	0.486912i	$-0.161877\pi$
$607$	0.370719	+	0.642104i	0.0150470	+	0.0260622i	−0.858404	+	0.512974i	$0.828544\pi$
$608$	−1.07733	+	1.86600i	−0.0436916	+	0.0756761i
$609$		0			0
$610$	1.18502	+	2.05252i	0.0479802	+	0.0831041i
$611$	28.0708	−	48.6201i	1.13562	−	1.96696i
$612$		0			0
$613$	−2.25350	−	3.90318i	−0.0910181	−	0.157648i	0.816922	−	0.576749i	$-0.195679\pi$
$613$	−2.25350	−	3.90318i	−0.0910181	−	0.157648i	−0.907940	+	0.419101i	$0.862345\pi$
$614$	20.3212			0.820097
$615$		0			0
$616$	28.2630	+	15.3832i	1.13875	+	0.619808i
$617$	−8.60078	+	14.8970i	−0.346254	+	0.599730i	−0.985581	−	0.169205i	$-0.945880\pi$
$617$	−8.60078	+	14.8970i	−0.346254	+	0.599730i	0.639327	+	0.768935i	$0.279213\pi$
$618$		0			0
$619$	−2.24271	+	3.88448i	−0.0901419	+	0.156130i	−0.907571	−	0.419899i	$-0.862065\pi$
$619$	−2.24271	+	3.88448i	−0.0901419	+	0.156130i	0.817429	+	0.576030i	$0.195399\pi$
$620$	0.0993140	+	0.172017i	0.00398855	+	0.00690837i
$621$		0			0
$622$	15.5615			0.623958
$623$	−12.4890	−	6.79762i	−0.500362	−	0.272341i
$624$		0			0
$625$	−9.91955	−	17.1812i	−0.396782	−	0.687246i
$626$	24.1881			0.966752
$627$		0			0
$628$	−1.00000			−0.0399043
$629$	1.81711			0.0724531
$630$		0			0
$631$	−17.3068			−0.688973			−0.344486	−	0.938791i	$-0.611947\pi$
$631$	−17.3068			−0.688973			−0.344486	+	0.938791i	$0.611947\pi$
$632$	30.4356			1.21066
$633$		0			0
$634$	−38.9037			−1.54506
$635$	3.66079	+	6.34067i	0.145274	+	0.251622i
$636$		0			0
$637$	−14.4050	+	28.1281i	−0.570745	+	1.11448i
$638$	−2.29533			−0.0908729
$639$		0			0
$640$	−3.65340	−	6.32787i	−0.144413	−	0.250131i
$641$	21.6608	−	37.5176i	0.855550	−	1.48186i	−0.0205843	−	0.999788i	$-0.506553\pi$
$641$	21.6608	−	37.5176i	0.855550	−	1.48186i	0.876134	−	0.482068i	$-0.160114\pi$
$642$		0			0
$643$	−14.9911	+	25.9654i	−0.591193	+	1.02398i	0.402879	+	0.915253i	$0.368010\pi$
$643$	−14.9911	+	25.9654i	−0.591193	+	1.02398i	−0.994072	+	0.108723i	$0.965324\pi$
$644$	−1.51819	+	0.928200i	−0.0598250	+	0.0365762i
$645$		0			0
$646$	1.14454			0.0450315
$647$	7.08472	+	12.2711i	0.278529	+	0.482427i	0.971019	−	0.239000i	$-0.0768197\pi$
$647$	7.08472	+	12.2711i	0.278529	+	0.482427i	−0.692490	+	0.721427i	$0.743486\pi$
$648$		0			0
$649$	17.9626	−	31.1122i	0.705095	−	1.22126i
$650$	15.3224	+	26.5391i	0.600993	+	1.04095i
$651$		0			0
$652$	−1.01080	+	1.75075i	−0.0395858	+	0.0685647i
$653$	−14.1981	−	24.5919i	−0.555617	−	0.962356i	−0.997855	−	0.0654587i	$-0.979149\pi$
$653$	−14.1981	−	24.5919i	−0.555617	−	0.962356i	0.442239	−	0.896897i	$-0.354184\pi$
$654$		0			0
$655$	−0.948052	+	1.64207i	−0.0370435	+	0.0641611i
$656$	−23.1457	+	40.0896i	−0.903689	+	1.56523i
$657$		0			0
$658$	1.20847	+	48.0376i	0.0471109	+	1.87270i
$659$	4.69961	+	8.13997i	0.183071	+	0.317088i	0.942925	−	0.333006i	$-0.108063\pi$
$659$	4.69961	+	8.13997i	0.183071	+	0.317088i	−0.759854	+	0.650094i	$0.774730\pi$
$660$		0			0
$661$	−12.7161			−0.494601			−0.247300	−	0.968939i	$-0.579543\pi$
$661$	−12.7161			−0.494601			−0.247300	+	0.968939i	$0.579543\pi$
$662$	34.0397			1.32299
$663$		0			0
$664$	−22.5546	−	39.0656i	−0.875287	−	1.51604i
$665$	0.113230	+	4.50098i	0.00439086	+	0.174540i
$666$		0			0
$667$	−0.890369	+	1.54216i	−0.0344752	+	0.0597128i
$668$	−0.595715	+	1.03181i	−0.0230489	+	0.0399219i
$669$		0			0
$670$	−2.54309	−	4.40477i	−0.0982483	−	0.170171i
$671$	6.09718	−	10.5606i	0.235379	−	0.407688i
$672$		0			0
$673$	−17.8961	−	30.9970i	−0.689844	−	1.19485i	−0.971888	−	0.235444i	$-0.924346\pi$
$673$	−17.8961	−	30.9970i	−0.689844	−	1.19485i	0.282044	−	0.959401i	$-0.408988\pi$
$674$	−16.9698	+	29.3926i	−0.653654	+	1.13216i
$675$		0			0
$676$	−0.491146	−	0.850689i	−0.0188902	−	0.0327188i
$677$	10.8918			0.418607			0.209304	−	0.977851i	$-0.432880\pi$
$677$	10.8918			0.418607			0.209304	+	0.977851i	$0.432880\pi$
$678$		0			0
$679$	5.11537	−	3.12747i	0.196310	−	0.120021i
$680$	−0.221203	+	0.383136i	−0.00848276	+	0.0146926i
$681$		0			0
$682$	8.19076	−	14.1868i	0.313640	−	0.543241i
$683$	−17.5079	−	30.3245i	−0.669920	−	1.16034i	−0.977926	−	0.208951i	$-0.932995\pi$
$683$	−17.5079	−	30.3245i	−0.669920	−	1.16034i	0.308006	−	0.951384i	$-0.400338\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	−2.03902	−	26.9720i	−0.0778500	−	1.02979i
$687$		0			0
$688$	7.18308	+	12.4415i	0.273852	+	0.474326i
$689$	−51.1387			−1.94823
$690$		0			0
$691$	8.42082			0.320343			0.160171	−	0.987089i	$-0.448795\pi$
$691$	8.42082			0.320343			0.160171	+	0.987089i	$0.448795\pi$
$692$	−1.39203			−0.0529169
$693$		0			0
$694$	−25.0292			−0.950095
$695$	−10.7296			−0.406996
$696$		0			0
$697$	2.97841			0.112815
$698$	−14.2506	−	24.6827i	−0.539392	−	0.934255i
$699$		0			0
$700$	−1.43726	−	0.782282i	−0.0543232	−	0.0295675i
$701$	42.7453			1.61447			0.807234	−	0.590231i	$-0.200963\pi$
$701$	42.7453			1.61447			0.807234	+	0.590231i	$0.200963\pi$
$702$		0			0
$703$	9.52918	+	16.5050i	0.359400	+	0.622499i
$704$	−16.5021	+	28.5825i	−0.621948	+	1.07724i
$705$		0			0
$706$	11.7288	−	20.3149i	0.441419	−	0.764560i
$707$	21.7432	+	11.8346i	0.817737	+	0.445084i
$708$		0			0
$709$	−24.0862			−0.904576			−0.452288	−	0.891872i	$-0.649392\pi$
$709$	−24.0862			−0.904576			−0.452288	+	0.891872i	$0.649392\pi$
$710$	−1.12734	−	1.95261i	−0.0423083	−	0.0732801i
$711$		0			0
$712$	7.32695	−	12.6907i	0.274589	−	0.475602i
$713$	−6.35447	−	11.0063i	−0.237977	−	0.412188i
$714$		0			0
$715$	−5.97656	+	10.3517i	−0.223511	+	0.387132i
$716$	0.596699	+	1.03351i	0.0222997	+	0.0386242i
$717$		0			0
$718$	10.1242	−	17.5357i	0.377833	−	0.654425i
$719$	−21.0512	+	36.4617i	−0.785076	+	1.35979i	0.143878	+	0.989595i	$0.454043\pi$
$719$	−21.0512	+	36.4617i	−0.785076	+	1.35979i	−0.928954	+	0.370196i	$0.879291\pi$
$720$		0			0
$721$	35.5818	−	21.7542i	1.32514	−	0.810170i
$722$	−7.87266	−	13.6358i	−0.292990	−	0.507474i
$723$		0			0
$724$	0.671612			0.0249603
$725$	−1.63754			−0.0608168
$726$		0			0
$727$	−18.0349	−	31.2374i	−0.668878	−	1.15853i	−0.978218	−	0.207579i	$-0.933442\pi$
$727$	−18.0349	−	31.2374i	−0.668878	−	1.15853i	0.309340	−	0.950951i	$-0.399892\pi$
$728$	−28.6057	−	15.5698i	−1.06020	−	0.577054i
$729$		0			0
$730$	−4.81810	+	8.34519i	−0.178326	+	0.308869i
$731$	0.462162	−	0.800488i	0.0170937	−	0.0296071i
$732$		0			0
$733$	−17.0665	−	29.5601i	−0.630367	−	1.09183i	−0.987477	−	0.157765i	$-0.949571\pi$
$733$	−17.0665	−	29.5601i	−0.630367	−	1.09183i	0.357110	−	0.934062i	$-0.383762\pi$
$734$	18.4720	−	31.9944i	0.681813	−	1.18093i
$735$		0			0
$736$	−1.89922	−	3.28955i	−0.0700063	−	0.121254i
$737$	−13.0847	+	22.6634i	−0.481982	+	0.834817i
$738$		0			0
$739$	−10.9481	−	18.9626i	−0.402731	−	0.697550i	0.591324	−	0.806434i	$-0.298606\pi$
$739$	−10.9481	−	18.9626i	−0.402731	−	0.697550i	−0.994054	+	0.108884i	$0.965272\pi$
$740$	0.525101			0.0193031
$741$		0			0
$742$	37.3442	−	22.8317i	1.37095	−	0.838179i
$743$	14.1426	−	24.4957i	0.518842	−	0.898660i	−0.480919	−	0.876765i	$-0.659697\pi$
$743$	14.1426	−	24.4957i	0.518842	−	0.898660i	0.999760	−	0.0218950i	$-0.00696995\pi$
$744$		0			0
$745$	4.17111	−	7.22457i	0.152818	−	0.264688i
$746$	1.46050	+	2.52967i	0.0534729	+	0.0926177i
$747$		0			0
$748$	−0.162253			−0.00593254
$749$	2.38171	+	1.29634i	0.0870258	+	0.0473671i
$750$		0			0
$751$	7.24844	+	12.5547i	0.264499	+	0.458126i	0.967432	−	0.253130i	$-0.0814600\pi$
$751$	7.24844	+	12.5547i	0.264499	+	0.458126i	−0.702933	+	0.711256i	$0.748127\pi$
$752$	−52.8319			−1.92658
$753$		0			0
$754$	2.32316			0.0846044
$755$	−0.226459			−0.00824169
$756$		0			0
$757$	−38.9646			−1.41619			−0.708096	−	0.706116i	$-0.750446\pi$
$757$	−38.9646			−1.41619			−0.708096	+	0.706116i	$0.750446\pi$
$758$	27.4720			0.997827
$759$		0			0
$760$	−4.64008			−0.168313
$761$	−0.627819	−	1.08741i	−0.0227584	−	0.0394187i	0.854422	−	0.519580i	$-0.173912\pi$
$761$	−0.627819	−	1.08741i	−0.0227584	−	0.0394187i	−0.877180	+	0.480161i	$0.840578\pi$
$762$		0			0
$763$	−2.92393	+	1.78766i	−0.105854	+	0.0647175i
$764$	1.61421			0.0584002
$765$		0			0
$766$	25.6623	+	44.4483i	0.927215	+	1.60598i
$767$	−18.1804	+	31.4894i	−0.656458	+	1.13702i
$768$		0			0
$769$	13.8442	−	23.9788i	0.499233	−	0.864697i	−0.500767	−	0.865582i	$-0.666949\pi$
$769$	13.8442	−	23.9788i	0.499233	−	0.864697i	1.00000		0.000885409i	$0.000281834\pi$
$770$	−0.257295	−	10.2277i	−0.00927225	−	0.368580i
$771$		0			0
$772$	2.28386			0.0821978
$773$	3.95544	+	6.85103i	0.142267	+	0.246414i	0.928350	−	0.371707i	$-0.121227\pi$
$773$	3.95544	+	6.85103i	0.142267	+	0.246414i	−0.786083	+	0.618121i	$0.787894\pi$
$774$		0			0
$775$	5.84348	−	10.1212i	0.209904	−	0.363565i
$776$	3.08950	+	5.35117i	0.110907	+	0.192096i
$777$		0			0
$778$	−6.11849	+	10.5975i	−0.219358	+	0.379940i
$779$	15.6192	+	27.0532i	0.559614	+	0.969281i
$780$		0			0
$781$	−5.80039	+	10.0466i	−0.207554	+	0.359494i
$782$	−1.00885	+	1.74739i	−0.0360766	+	0.0624864i
$783$		0			0
$784$	29.7015	−	1.49533i	1.06077	−	0.0534045i
$785$	−2.23025	−	3.86291i	−0.0796011	−	0.137873i
$786$		0			0
$787$	31.6693			1.12889			0.564444	−	0.825472i	$-0.309091\pi$
$787$	31.6693			1.12889			0.564444	+	0.825472i	$0.309091\pi$
$788$	0.100013			0.00356283
$789$		0			0
$790$	−4.83842	−	8.38039i	−0.172143	−	0.298161i
$791$	33.2199	+	18.0812i	1.18116	+	0.642894i
$792$		0			0
$793$	−6.17111	+	10.6887i	−0.219142	+	0.379566i
$794$	−6.75370	+	11.6977i	−0.239680	+	0.415137i
$795$		0			0
$796$	−0.685023	−	1.18649i	−0.0242800	−	0.0420542i
$797$	16.8961	−	29.2649i	0.598491	−	1.03662i	−0.394553	−	0.918873i	$-0.629101\pi$
$797$	16.8961	−	29.2649i	0.598491	−	1.03662i	0.993044	−	0.117743i	$-0.0375660\pi$
$798$		0			0
$799$	1.69961	+	2.94381i	0.0601279	+	0.104145i
$800$	1.74650	−	3.02502i	0.0617481	−	0.106951i
$801$		0			0
$802$	−0.107690	−	0.186524i	−0.00380265	−	0.00658638i
$803$	49.5801			1.74965
$804$		0			0
$805$	−6.97150	−	3.79450i	−0.245713	−	0.133739i
$806$	−8.29007	+	14.3588i	−0.292005	+	0.505768i
$807$		0			0
$808$	−12.7561	+	22.0942i	−0.448759	+	0.777273i
$809$	18.3801	+	31.8352i	0.646208	+	1.11927i	0.984021	+	0.178052i	$0.0569796\pi$
$809$	18.3801	+	31.8352i	0.646208	+	1.11927i	−0.337813	+	0.941213i	$0.609687\pi$
$810$		0			0
$811$	3.54377			0.124438			0.0622192	−	0.998063i	$-0.480182\pi$
$811$	3.54377			0.124438			0.0622192	+	0.998063i	$0.480182\pi$
$812$	−0.105838	+	0.0647078i	−0.00371418	+	0.00227080i
$813$		0			0
$814$	−21.6534	−	37.5048i	−0.758951	−	1.31454i
$815$	−9.01732			−0.315863
$816$		0			0
$817$	9.69455			0.339169
$818$	5.73289			0.200446
$819$		0			0
$820$	0.860686			0.0300565
$821$	−20.8636			−0.728145			−0.364073	−	0.931371i	$-0.618614\pi$
$821$	−20.8636			−0.728145			−0.364073	+	0.931371i	$0.618614\pi$
$822$		0			0
$823$	45.4006			1.58256			0.791282	−	0.611451i	$-0.209414\pi$
$823$	45.4006			1.58256			0.791282	+	0.611451i	$0.209414\pi$
$824$	21.4902	+	37.2221i	0.748645	+	1.29669i
$825$		0			0
$826$	−0.782679	−	31.1122i	−0.0272329	−	1.08253i
$827$	5.34221			0.185767			0.0928835	−	0.995677i	$-0.470392\pi$
$827$	5.34221			0.185767			0.0928835	+	0.995677i	$0.470392\pi$
$828$		0			0
$829$	−8.45185	−	14.6390i	−0.293545	−	0.508434i	0.681101	−	0.732190i	$-0.261502\pi$
$829$	−8.45185	−	14.6390i	−0.293545	−	0.508434i	−0.974645	+	0.223755i	$0.928168\pi$
$830$	−7.17111	+	12.4207i	−0.248913	+	0.431130i
$831$		0			0
$832$	16.7022	−	28.9291i	0.579046	−	1.00294i
$833$	−1.03882	−	1.60687i	−0.0359930	−	0.0556748i
$834$		0			0
$835$	−5.31438			−0.183912
$836$	−0.850874	−	1.47376i	−0.0294281	−	0.0509709i
$837$		0			0
$838$	15.3353	−	26.5615i	0.529749	−	0.917553i
$839$	−4.91955	−	8.52091i	−0.169842	−	0.294174i	0.768522	−	0.639823i	$-0.220992\pi$
$839$	−4.91955	−	8.52091i	−0.169842	−	0.294174i	−0.938364	+	0.345649i	$0.887659\pi$
$840$		0			0
$841$	14.4379	−	25.0072i	0.497860	−	0.862318i
$842$	−18.0287	−	31.2266i	−0.621310	−	1.07614i
$843$		0			0
$844$	1.07227	−	1.85723i	0.0369091	−	0.0639285i
$845$	2.19076	−	3.79450i	0.0753643	−	0.130535i
$846$		0			0
$847$	−20.0811	+	12.2773i	−0.689996	+	0.421854i
$848$	24.0620	+	41.6765i	0.826291	+	1.43118i
$849$		0			0
$850$	−1.85546			−0.0636416
$851$	−33.5979			−1.15172
$852$		0			0
$853$	27.7434	+	48.0529i	0.949915	+	1.64530i	0.745597	+	0.666397i	$0.232164\pi$
$853$	27.7434	+	48.0529i	0.949915	+	1.64530i	0.204318	+	0.978905i	$0.434502\pi$
$854$	−0.265670	−	10.5606i	−0.00909104	−	0.361377i
$855$		0			0
$856$	−1.39728	+	2.42016i	−0.0477581	+	0.0827195i
$857$	−28.1732	+	48.7975i	−0.962380	+	1.66689i	−0.245884	+	0.969299i	$0.579078\pi$
$857$	−28.1732	+	48.7975i	−0.962380	+	1.66689i	−0.716496	+	0.697591i	$0.754255\pi$
$858$		0			0
$859$	−21.9626	−	38.0404i	−0.749356	−	1.29792i	−0.948132	−	0.317877i	$-0.897030\pi$
$859$	−21.9626	−	38.0404i	−0.749356	−	1.29792i	0.198776	−	0.980045i	$-0.436303\pi$
$860$	0.133553	−	0.231321i	0.00455413	−	0.00788799i
$861$		0			0
$862$	−3.99806	−	6.92484i	−0.136174	−	0.235861i
$863$	5.66372	−	9.80984i	0.192795	−	0.333931i	−0.753380	−	0.657585i	$-0.771578\pi$
$863$	5.66372	−	9.80984i	0.192795	−	0.333931i	0.946175	+	0.323654i	$0.104911\pi$
$864$		0			0
$865$	−3.10457	−	5.37727i	−0.105559	−	0.182833i
$866$	−34.5117			−1.17275
$867$		0			0
$868$	−0.0222652	−	0.885061i	−0.000755730	−	0.0300409i
$869$	−24.8946	+	43.1188i	−0.844493	+	1.46270i
$870$		0			0
$871$	13.2434	−	22.9382i	0.448735	−	0.777231i
$872$	−1.76595	−	3.05872i	−0.0598028	−	0.103581i
$873$		0			0
$874$	−21.1623			−0.715824
$875$	−0.381036	−	15.1465i	−0.0128814	−	0.512045i
$876$		0			0
$877$	23.2307	+	40.2368i	0.784446	+	1.35870i	0.929329	+	0.369252i	$0.120386\pi$
$877$	23.2307	+	40.2368i	0.784446	+	1.35870i	−0.144883	+	0.989449i	$0.546281\pi$
$878$	7.69124			0.259567
$879$		0			0
$880$	11.2484			0.379185
$881$	−21.6578			−0.729669			−0.364835	−	0.931072i	$-0.618874\pi$
$881$	−21.6578			−0.729669			−0.364835	+	0.931072i	$0.618874\pi$
$882$		0			0
$883$	11.4868			0.386560			0.193280	−	0.981144i	$-0.438087\pi$
$883$	11.4868			0.386560			0.193280	+	0.981144i	$0.438087\pi$
$884$	0.164220			0.00552332
$885$		0			0
$886$	−8.81616			−0.296185
$887$	8.92101	+	15.4516i	0.299538	+	0.518815i	0.976030	−	0.217634i	$-0.0698341\pi$
$887$	8.92101	+	15.4516i	0.299538	+	0.518815i	−0.676492	+	0.736450i	$0.736501\pi$
$888$		0			0
$889$	−0.820712	−	32.6240i	−0.0275258	−	1.09418i
$890$	−4.65913			−0.156174
$891$		0			0
$892$	0.462641	+	0.801318i	0.0154904	+	0.0268301i
$893$	−17.8260	+	30.8755i	−0.596523	+	1.03321i
$894$		0			0
$895$	−2.66158	+	4.60999i	−0.0889668	+	0.154095i
$896$	0.819055	+	32.5582i	0.0273627	+	1.08769i
$897$		0			0
$898$	−32.3422			−1.07927
$899$	−0.442991	−	0.767282i	−0.0147746	−	0.0255903i
$900$		0			0
$901$	1.54815	−	2.68148i	0.0515765	−	0.0893331i
$902$	−35.4918	−	61.4736i	−1.18175	−	2.04685i
$903$		0			0
$904$	−19.4892	+	33.7563i	−0.648201	+	1.12272i
$905$	1.49786	+	2.59438i	0.0497907	+	0.0862400i
$906$		0			0
$907$	25.9253	−	44.9039i	0.860835	−	1.49101i	−0.0102894	−	0.999947i	$-0.503275\pi$
$907$	25.9253	−	44.9039i	0.860835	−	1.49101i	0.871124	−	0.491063i	$-0.163391\pi$
$908$	0.352052	−	0.609772i	0.0116833	−	0.0202360i
$909$		0			0
$910$	0.260414	+	10.3517i	0.00863265	+	0.343155i
$911$	−3.24338	−	5.61770i	−0.107458	−	0.186123i	0.807282	−	0.590166i	$-0.200938\pi$
$911$	−3.24338	−	5.61770i	−0.107458	−	0.186123i	−0.914740	+	0.404044i	$0.867604\pi$
$912$		0			0
$913$	73.7936			2.44221
$914$	7.79125			0.257712
$915$		0			0
$916$	−0.780065	−	1.35111i	−0.0257741	−	0.0446420i
$917$	7.21060	−	4.40847i	0.238115	−	0.145580i
$918$		0			0
$919$	5.84221	−	10.1190i	0.192717	−	0.333795i	−0.753433	−	0.657525i	$-0.771603\pi$
$919$	5.84221	−	10.1190i	0.192717	−	0.333795i	0.946150	+	0.323730i	$0.104937\pi$
$920$	4.08998	−	7.08405i	0.134843	−	0.233554i
$921$		0			0
$922$	−21.6845	−	37.5587i	−0.714142	−	1.23693i
$923$	5.87072	−	10.1684i	0.193237	−	0.334696i
$924$		0			0
$925$	−15.4481	−	26.7568i	−0.507929	−	0.879759i
$926$	13.5759	−	23.5141i	0.446131	−	0.772721i
$927$		0			0
$928$	−0.132401	−	0.229325i	−0.00434627	−	0.00752797i
$929$	−1.46050			−0.0479176			−0.0239588	−	0.999713i	$-0.507627\pi$
$929$	−1.46050			−0.0479176			−0.0239588	+	0.999713i	$0.507627\pi$
$930$		0			0
$931$	9.14766	−	17.8624i	0.299803	−	0.585415i
$932$	0.257579	−	0.446140i	0.00843727	−	0.0146138i
$933$		0			0
$934$	−17.9734	+	31.1309i	−0.588109	+	1.01863i
$935$	−0.361864	−	0.626767i	−0.0118342	−	0.0204975i
$936$		0			0
$937$	9.87451			0.322586			0.161293	−	0.986907i	$-0.448434\pi$
$937$	9.87451			0.322586			0.161293	+	0.986907i	$0.448434\pi$
$938$	0.570136	+	22.6634i	0.0186156	+	0.739987i
$939$		0			0
$940$	0.491146	+	0.850689i	0.0160194	+	0.0277464i
$941$	54.1944			1.76669			0.883343	−	0.468728i	$-0.155287\pi$
$941$	54.1944			1.76669			0.883343	+	0.468728i	$0.155287\pi$
$942$		0			0
$943$	−55.0698			−1.79332
$944$	34.2173			1.11368
$945$		0			0
$946$	−22.0292			−0.716230
$947$	−54.8903			−1.78369			−0.891847	−	0.452338i	$-0.850590\pi$
$947$	−54.8903			−1.78369			−0.891847	+	0.452338i	$0.850590\pi$
$948$		0			0
$949$	−50.1813			−1.62895
$950$	−9.73025	−	16.8533i	−0.315691	−	0.546793i
$951$		0			0
$952$	1.68241	−	1.02860i	0.0545271	−	0.0333372i
$953$	−27.0406			−0.875932			−0.437966	−	0.898991i	$-0.644301\pi$
$953$	−27.0406			−0.875932			−0.437966	+	0.898991i	$0.644301\pi$
$954$		0			0
$955$	3.60010	+	6.23556i	0.116497	+	0.201778i
$956$	0.825010	−	1.42896i	0.0266827	−	0.0462158i
$957$		0			0
$958$	0.260414	−	0.451051i	0.00841360	−	0.0145728i
$959$	23.4897	+	12.7852i	0.758521	+	0.412854i
$960$		0			0
$961$	−24.6768			−0.796027
$962$	21.9159	+	37.9595i	0.706599	+	1.22386i
$963$		0			0
$964$	1.10195	−	1.90864i	0.0354916	−	0.0614732i
$965$	5.09358	+	8.82234i	0.163968	+	0.284001i
$966$		0			0
$967$	6.75729	−	11.7040i	0.217300	−	0.376375i	−0.736682	−	0.676240i	$-0.763608\pi$
$967$	6.75729	−	11.7040i	0.217300	−	0.376375i	0.953982	+	0.299865i	$0.0969417\pi$
$968$	−12.1283	−	21.0068i	−0.389818	−	0.675185i
$969$		0			0
$970$	0.982291	−	1.70138i	0.0315395	−	0.0546280i
$971$	−6.46557	+	11.1987i	−0.207490	+	0.359383i	−0.950923	−	0.309427i	$-0.899863\pi$
$971$	−6.46557	+	11.1987i	−0.207490	+	0.359383i	0.743433	+	0.668810i	$0.233196\pi$
$972$		0			0
$973$	42.0057	+	22.8632i	1.34664	+	0.732961i
$974$	−9.40448	−	16.2890i	−0.301339	−	0.521934i
$975$		0			0
$976$	11.6146			0.371774
$977$	−36.5979			−1.17087			−0.585435	−	0.810720i	$-0.699076\pi$
$977$	−36.5979			−1.17087			−0.585435	+	0.810720i	$0.699076\pi$
$978$		0			0
$979$	11.9861	+	20.7605i	0.383077	+	0.663509i
$980$	−0.300194	−	0.464346i	−0.00958933	−	0.0148330i
$981$		0			0
$982$	−4.05574	+	7.02475i	−0.129424	+	0.224169i
$983$	8.61896	−	14.9285i	0.274902	−	0.476145i	−0.695208	−	0.718808i	$-0.744688\pi$
$983$	8.61896	−	14.9285i	0.274902	−	0.476145i	0.970110	+	0.242664i	$0.0780212\pi$
$984$		0			0
$985$	0.223055	+	0.386343i	0.00710713	+	0.0123099i
$986$	−0.0703305	+	0.121816i	−0.00223978	+	0.00387941i
$987$		0			0
$988$	0.861191	+	1.49163i	0.0273981	+	0.0474550i
$989$	−8.54523	+	14.8008i	−0.271722	+	0.470637i
$990$		0			0
$991$	7.67111	+	13.2867i	0.243681	+	0.422067i	0.961760	−	0.273894i	$-0.0883118\pi$
$991$	7.67111	+	13.2867i	0.243681	+	0.422067i	−0.718079	+	0.695961i	$0.754978\pi$
$992$	1.88986			0.0600032
$993$		0			0
$994$	0.252738	+	10.0466i	0.00801637	+	0.318658i
$995$	3.05555	−	5.29236i	0.0968673	−	0.167779i
$996$		0			0
$997$	17.0577	−	29.5448i	0.540222	−	0.935692i	−0.458669	−	0.888607i	$-0.651674\pi$
$997$	17.0577	−	29.5448i	0.540222	−	0.935692i	0.998891	−	0.0470850i	$-0.0149932\pi$
$998$	−20.5313	−	35.5613i	−0.649907	−	1.12567i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.h.i.352.1		6
3.2	odd	2		567.2.h.h.352.3		6
7.4	even	3		567.2.g.h.109.3		6
9.2	odd	6		567.2.g.i.541.1		6
9.4	even	3		189.2.e.e.163.3	yes	6
9.5	odd	6		189.2.e.f.163.1	yes	6
9.7	even	3		567.2.g.h.541.3		6
21.11	odd	6		567.2.g.i.109.1		6
63.4	even	3		189.2.e.e.109.3	✓	6
63.5	even	6		1323.2.a.y.1.3		3
63.11	odd	6		567.2.h.h.298.3		6
63.23	odd	6		1323.2.a.x.1.3		3
63.25	even	3	inner	567.2.h.i.298.1		6
63.32	odd	6		189.2.e.f.109.1	yes	6
63.40	odd	6		1323.2.a.z.1.1		3
63.58	even	3		1323.2.a.ba.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.3	✓	6	63.4	even	3
189.2.e.e.163.3	yes	6	9.4	even	3
189.2.e.f.109.1	yes	6	63.32	odd	6
189.2.e.f.163.1	yes	6	9.5	odd	6
567.2.g.h.109.3		6	7.4	even	3
567.2.g.h.541.3		6	9.7	even	3
567.2.g.i.109.1		6	21.11	odd	6
567.2.g.i.541.1		6	9.2	odd	6
567.2.h.h.298.3		6	63.11	odd	6
567.2.h.h.352.3		6	3.2	odd	2
567.2.h.i.298.1		6	63.25	even	3	inner
567.2.h.i.352.1		6	1.1	even	1	trivial
1323.2.a.x.1.3		3	63.23	odd	6
1323.2.a.y.1.3		3	63.5	even	6
1323.2.a.z.1.1		3	63.40	odd	6
1323.2.a.ba.1.1		3	63.58	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.46050 q^{2} +0.133074 q^{4} +(0.296790 + 0.514055i) q^{5} +(-0.0665372 - 2.64491i) q^{7} +2.72665 q^{8} +(-0.433463 - 0.750780i) q^{10} +(-2.23025 + 3.86291i) q^{11} +(2.25729 - 3.90975i) q^{13} +(0.0971780 + 3.86291i) q^{14} -4.24844 q^{16} +(0.136673 + 0.236725i) q^{17} +(-1.43346 + 2.48283i) q^{19} +(0.0394951 + 0.0684076i) q^{20} +(3.25729 - 5.64180i) q^{22} +(-2.52704 - 4.37697i) q^{23} +(2.32383 - 4.02499i) q^{25} +(-3.29679 + 5.71021i) q^{26} +(-0.00885441 - 0.351971i) q^{28} +(-0.176168 - 0.305132i) q^{29} +2.51459 q^{31} +0.751560 q^{32} +(-0.199612 - 0.345738i) q^{34} +(1.33988 - 0.819187i) q^{35} +(3.32383 - 5.75705i) q^{37} +(2.09358 - 3.62619i) q^{38} +(0.809243 + 1.40165i) q^{40} +(5.44805 - 9.43630i) q^{41} +(-1.69076 - 2.92848i) q^{43} +(-0.296790 + 0.514055i) q^{44} +(3.69076 + 6.39258i) q^{46} +12.4356 q^{47} +(-6.99115 + 0.351971i) q^{49} +(-3.39397 + 5.87852i) q^{50} +(0.300388 - 0.520288i) q^{52} +(-5.66372 - 9.80984i) q^{53} -2.64766 q^{55} +(-0.181424 - 7.21177i) q^{56} +(0.257295 + 0.445647i) q^{58} -8.05408 q^{59} -2.73385 q^{61} -3.67257 q^{62} +7.39922 q^{64} +2.67977 q^{65} +5.86693 q^{67} +(0.0181877 + 0.0315020i) q^{68} +(-1.95691 + 1.19643i) q^{70} +2.60078 q^{71} +(-5.55768 - 9.62619i) q^{73} +(-4.85447 + 8.40819i) q^{74} +(-0.190757 + 0.330401i) q^{76} +(10.3655 + 5.64180i) q^{77} +11.1623 q^{79} +(-1.26089 - 2.18393i) q^{80} +(-7.95691 + 13.7818i) q^{82} +(-8.27188 - 14.3273i) q^{83} +(-0.0811263 + 0.140515i) q^{85} +(2.46936 + 4.27706i) q^{86} +(-6.08113 + 10.5328i) q^{88} +(2.68716 - 4.65430i) q^{89} +(-10.4911 - 5.71021i) q^{91} +(-0.336285 - 0.582462i) q^{92} -18.1623 q^{94} -1.70175 q^{95} +(1.13307 + 1.96254i) q^{97} +(10.2106 - 0.514055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 8 q^{4} - q^{5} - 4 q^{7} + 18 q^{8} + q^{10} - 7 q^{11} - 2 q^{13} - 13 q^{14} + 20 q^{16} - 5 q^{19} + 13 q^{20} + 4 q^{22} - 6 q^{23} + 2 q^{25} - 17 q^{26} - 30 q^{28} - 13 q^{29}+ \cdots + 49 q^{98}+O(q^{100}) \) 6 * q + 4 * q^2 + 8 * q^4 - q^5 - 4 * q^7 + 18 * q^8 + q^10 - 7 * q^11 - 2 * q^13 - 13 * q^14 + 20 * q^16 - 5 * q^19 + 13 * q^20 + 4 * q^22 - 6 * q^23 + 2 * q^25 - 17 * q^26 - 30 * q^28 - 13 * q^29 - 16 * q^31 + 50 * q^32 - 12 * q^34 + 10 * q^35 + 8 * q^37 + 7 * q^38 + 24 * q^40 - 2 * q^41 + 9 * q^43 + q^44 + 3 * q^46 + 18 * q^47 - 12 * q^49 - 4 * q^50 - 9 * q^52 - 24 * q^53 + 8 * q^55 - 51 * q^56 - 14 * q^58 - 30 * q^59 - 2 * q^61 - 42 * q^62 + 66 * q^64 + 20 * q^65 + 28 * q^67 - 39 * q^68 - 7 * q^70 - 6 * q^71 - 7 * q^73 + 18 * q^76 + 10 * q^77 + 12 * q^79 + 16 * q^80 - 43 * q^82 - 3 * q^83 + 27 * q^85 + 32 * q^86 - 9 * q^88 + 5 * q^89 - 33 * q^91 - 12 * q^92 - 54 * q^94 + 32 * q^95 + 14 * q^97 + 49 * q^98

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