LMFDB - Embedded newform 567.2.g.i.541.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(109,567)] 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("567.109"); 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([2, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [6,2,0,-4,-2,0,2] 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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	567.541
Dual form			567.2.g.i.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.730252 - 1.26483i) q^{2} +(-0.0665372 + 0.115246i) q^{4} +0.593579 q^{5} +(-2.25729 + 1.38008i) q^{7} -2.72665 q^{8} +(-0.433463 - 0.750780i) q^{10} -4.46050 q^{11} +(2.25729 + 3.90975i) q^{13} +(3.39397 + 1.84730i) q^{14} +(2.12422 + 3.67926i) q^{16} +(-0.136673 - 0.236725i) q^{17} +(-1.43346 + 2.48283i) q^{19} +(-0.0394951 + 0.0684076i) q^{20} +(3.25729 + 5.64180i) q^{22} -5.05408 q^{23} -4.64766 q^{25} +(3.29679 - 5.71021i) q^{26} +(-0.00885441 - 0.351971i) q^{28} +(0.176168 - 0.305132i) q^{29} +(-1.25729 + 2.17770i) q^{31} +(0.375780 - 0.650870i) q^{32} +(-0.199612 + 0.345738i) q^{34} +(-1.33988 + 0.819187i) q^{35} +(3.32383 - 5.75705i) q^{37} +4.18716 q^{38} -1.61849 q^{40} +(-5.44805 - 9.43630i) q^{41} +(-1.69076 + 2.92848i) q^{43} +(0.296790 - 0.514055i) q^{44} +(3.69076 + 6.39258i) q^{46} +(6.21780 + 10.7695i) q^{47} +(3.19076 - 6.23049i) q^{49} +(3.39397 + 5.87852i) q^{50} -0.600777 q^{52} +(5.66372 + 9.80984i) q^{53} -2.64766 q^{55} +(6.15486 - 3.76300i) q^{56} -0.514589 q^{58} +(-4.02704 + 6.97504i) q^{59} +(1.36693 + 2.36758i) q^{61} +3.67257 q^{62} +7.39922 q^{64} +(1.33988 + 2.32075i) q^{65} +(-2.93346 + 5.08091i) q^{67} +0.0363754 q^{68} +(2.01459 + 1.09652i) q^{70} -2.60078 q^{71} +(-5.55768 - 9.62619i) q^{73} -9.70895 q^{74} +(-0.190757 - 0.330401i) q^{76} +(10.0687 - 6.15585i) q^{77} +(-5.58113 - 9.66679i) q^{79} +(1.26089 + 2.18393i) q^{80} +(-7.95691 + 13.7818i) q^{82} +(8.27188 - 14.3273i) q^{83} +(-0.0811263 - 0.140515i) q^{85} +4.93872 q^{86} +12.1623 q^{88} +(-2.68716 + 4.65430i) q^{89} +(-10.4911 - 5.71021i) q^{91} +(0.336285 - 0.582462i) q^{92} +(9.08113 - 15.7290i) q^{94} +(-0.850874 + 1.47376i) q^{95} +(1.13307 - 1.96254i) q^{97} +(-10.2106 + 0.514055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 4 q^{4} - 2 q^{5} + 2 q^{7} - 18 q^{8} + q^{10} - 14 q^{11} - 2 q^{13} + 4 q^{14} - 10 q^{16} - 5 q^{19} - 13 q^{20} + 4 q^{22} - 12 q^{23} - 4 q^{25} + 17 q^{26} - 30 q^{28} + 13 q^{29}+ \cdots - 49 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 4 * q^4 - 2 * q^5 + 2 * q^7 - 18 * q^8 + q^10 - 14 * q^11 - 2 * q^13 + 4 * q^14 - 10 * q^16 - 5 * q^19 - 13 * q^20 + 4 * q^22 - 12 * q^23 - 4 * q^25 + 17 * q^26 - 30 * q^28 + 13 * q^29 + 8 * q^31 + 25 * q^32 - 12 * q^34 - 10 * q^35 + 8 * q^37 + 14 * q^38 - 48 * q^40 + 2 * q^41 + 9 * q^43 - q^44 + 3 * q^46 + 9 * q^47 + 4 * q^50 + 18 * q^52 + 24 * q^53 + 8 * q^55 - 3 * q^56 + 28 * q^58 - 15 * q^59 + q^61 + 42 * q^62 + 66 * q^64 + 10 * q^65 - 14 * q^67 - 78 * q^68 - 19 * q^70 + 6 * q^71 - 7 * q^73 + 18 * q^76 + 11 * q^77 - 6 * q^79 - 16 * q^80 - 43 * q^82 + 3 * q^83 + 27 * q^85 + 64 * q^86 + 18 * q^88 - 5 * q^89 - 33 * q^91 + 12 * q^92 + 27 * q^94 + 16 * q^95 + 14 * q^97 - 49 * q^98

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.730252	−	1.26483i	−0.516366	−	0.894373i	−0.999819	−	0.0190026i	$-0.993951\pi$
$2$	−0.730252	−	1.26483i	−0.516366	−	0.894373i	0.483453	−	0.875370i	$-0.339382\pi$
$3$		0			0
$3$		0			0
$4$	−0.0665372	+	0.115246i	−0.0332686	+	0.0576229i
$5$	0.593579			0.265457			0.132728	−	0.991152i	$-0.457626\pi$
$5$	0.593579			0.265457			0.132728	+	0.991152i	$0.457626\pi$
$6$		0			0
$7$	−2.25729	+	1.38008i	−0.853177	+	0.521621i
$7$	−2.25729	+	1.38008i	−0.853177	+	0.521621i
$8$	−2.72665			−0.964018
$9$		0			0
$10$	−0.433463	−	0.750780i	−0.137073	−	0.237417i
$11$	−4.46050			−1.34489			−0.672446	−	0.740146i	$-0.734756\pi$
$11$	−4.46050			−1.34489			−0.672446	+	0.740146i	$0.734756\pi$
$12$		0			0
$13$	2.25729	+	3.90975i	0.626061	+	1.08437i	0.988335	+	0.152298i	$0.0486672\pi$
$13$	2.25729	+	3.90975i	0.626061	+	1.08437i	−0.362274	+	0.932072i	$0.617999\pi$
$14$	3.39397	+	1.84730i	0.907076	+	0.493711i
$15$		0			0
$16$	2.12422	+	3.67926i	0.531055	+	0.919814i
$17$	−0.136673	−	0.236725i	−0.0331481	−	0.0574142i	0.848975	−	0.528432i	$-0.177220\pi$
$17$	−0.136673	−	0.236725i	−0.0331481	−	0.0574142i	−0.882124	+	0.471018i	$0.843887\pi$
$18$		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
$23$	−5.05408			−1.05385			−0.526925	−	0.849912i	$-0.676655\pi$
$23$	−5.05408			−1.05385			−0.526925	+	0.849912i	$0.676655\pi$
$24$		0			0
$25$	−4.64766			−0.929533
$26$	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	$-0.822918\pi$
$29$	0.176168	−	0.305132i	0.0327136	−	0.0566616i	0.881919	+	0.471402i	$0.156252\pi$
$30$		0			0
$31$	−1.25729	+	2.17770i	−0.225817	+	0.391126i	−0.956564	−	0.291522i	$-0.905838\pi$
$31$	−1.25729	+	2.17770i	−0.225817	+	0.391126i	0.730747	+	0.682648i	$0.239172\pi$
$32$	0.375780	−	0.650870i	0.0664291	−	0.115059i
$33$		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	$-0.0173486\pi$
$38$	4.18716			0.679247
$39$		0			0
$40$	−1.61849			−0.255905
$41$	−5.44805	−	9.43630i	−0.850843	−	1.47370i	−0.880449	−	0.474141i	$-0.842759\pi$
$41$	−5.44805	−	9.43630i	−0.850843	−	1.47370i	0.0296061	−	0.999562i	$-0.490575\pi$
$42$		0			0
$43$	−1.69076	+	2.92848i	−0.257838	+	0.446589i	−0.965663	−	0.259800i	$-0.916343\pi$
$43$	−1.69076	+	2.92848i	−0.257838	+	0.446589i	0.707824	+	0.706388i	$0.249677\pi$
$44$	0.296790	−	0.514055i	0.0447427	−	0.0774967i
$45$		0			0
$46$	3.69076	+	6.39258i	0.544172	+	0.942534i
$47$	6.21780	+	10.7695i	0.906959	+	1.57090i	0.818265	+	0.574841i	$0.194936\pi$
$47$	6.21780	+	10.7695i	0.906959	+	1.57090i	0.0886938	+	0.996059i	$0.471731\pi$
$48$		0			0
$49$	3.19076	−	6.23049i	0.455822	−	0.890071i
$50$	3.39397	+	5.87852i	0.479980	+	0.831349i
$51$		0			0
$52$	−0.600777			−0.0833127
$53$	5.66372	+	9.80984i	0.777971	+	1.34749i	0.933109	+	0.359593i	$0.117084\pi$
$53$	5.66372	+	9.80984i	0.777971	+	1.34749i	−0.155138	+	0.987893i	$0.549582\pi$
$54$		0			0
$55$	−2.64766			−0.357011
$56$	6.15486	−	3.76300i	0.822478	−	0.502852i
$57$		0			0
$58$	−0.514589			−0.0675689
$59$	−4.02704	+	6.97504i	−0.524276	+	0.908073i	0.475324	+	0.879811i	$0.342331\pi$
$59$	−4.02704	+	6.97504i	−0.524276	+	0.908073i	−0.999601	+	0.0282624i	$0.991003\pi$
$60$		0			0
$61$	1.36693	+	2.36758i	0.175017	+	0.303138i	0.940167	−	0.340714i	$-0.110669\pi$
$61$	1.36693	+	2.36758i	0.175017	+	0.303138i	−0.765150	+	0.643852i	$0.777335\pi$
$62$	3.67257			0.466417
$63$		0			0
$64$	7.39922			0.924903
$65$	1.33988	+	2.32075i	0.166192	+	0.287853i
$66$		0			0
$67$	−2.93346	+	5.08091i	−0.358380	+	0.620732i	−0.987690	−	0.156422i	$-0.950004\pi$
$67$	−2.93346	+	5.08091i	−0.358380	+	0.620732i	0.629311	+	0.777154i	$0.283337\pi$
$68$	0.0363754			0.00441117
$69$		0			0
$70$	2.01459	+	1.09652i	0.240789	+	0.131059i
$71$	−2.60078			−0.308655			−0.154328	−	0.988020i	$-0.549321\pi$
$71$	−2.60078			−0.308655			−0.154328	+	0.988020i	$0.549321\pi$
$72$		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	$-0.392098\pi$
$74$	−9.70895			−1.12864
$75$		0			0
$76$	−0.190757	−	0.330401i	−0.0218814	−	0.0378996i
$77$	10.0687	−	6.15585i	1.14743	−	0.701525i
$78$		0			0
$79$	−5.58113	−	9.66679i	−0.627926	−	1.08760i	−0.987967	−	0.154663i	$-0.950571\pi$
$79$	−5.58113	−	9.66679i	−0.627926	−	1.08760i	0.360042	−	0.932936i	$-0.382763\pi$
$80$	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	0.0910594	−	0.995845i	$-0.470975\pi$
$83$	8.27188	−	14.3273i	0.907957	−	1.57263i	0.816898	−	0.576783i	$-0.195692\pi$
$84$		0			0
$85$	−0.0811263	−	0.140515i	−0.00879939	−	0.0152410i
$86$	4.93872			0.532556
$87$		0			0
$88$	12.1623			1.29650
$89$	−2.68716	+	4.65430i	−0.284838	+	0.493354i	−0.972570	−	0.232611i	$-0.925273\pi$
$89$	−2.68716	+	4.65430i	−0.284838	+	0.493354i	0.687732	+	0.725965i	$0.258607\pi$
$90$		0			0
$91$	−10.4911	−	5.71021i	−1.09977	−	0.598592i
$92$	0.336285	−	0.582462i	0.0350601	−	0.0607259i
$93$		0			0
$94$	9.08113	−	15.7290i	0.936647	−	1.62232i
$95$	−0.850874	+	1.47376i	−0.0872978	+	0.151204i
$96$		0			0
$97$	1.13307	−	1.96254i	0.115046	−	0.199266i	−0.802752	−	0.596313i	$-0.796632\pi$
$97$	1.13307	−	1.96254i	0.115046	−	0.199266i	0.917798	+	0.397047i	$0.129965\pi$
$98$	−10.2106	+	0.514055i	−1.03143	+	0.0519274i
$99$		0			0
$100$	0.309243	−	0.535624i	0.0309243	−	0.0535624i
$101$	−9.35661			−0.931017			−0.465509	−	0.885043i	$-0.654129\pi$
$101$	−9.35661			−0.931017			−0.465509	+	0.885043i	$0.654129\pi$
$102$		0			0
$103$	−15.7630			−1.55318			−0.776589	−	0.630008i	$-0.783052\pi$
$103$	−15.7630			−1.55318			−0.776589	+	0.630008i	$0.783052\pi$
$104$	−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	−0.840192	−	0.542290i	$-0.817558\pi$
$107$	0.512453	−	0.887595i	0.0495407	−	0.0858070i	0.889732	+	0.456483i	$0.150891\pi$
$108$		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	$0.853092\pi$
$110$	1.93346	+	3.34886i	0.184348	+	0.319301i
$111$		0			0
$112$	−9.87266	−	5.37357i	−0.932879	−	0.507755i
$113$	7.14766	+	12.3801i	0.672396	+	1.16462i	0.977223	+	0.212216i	$0.0680679\pi$
$113$	7.14766	+	12.3801i	0.672396	+	1.16462i	−0.304827	+	0.952408i	$0.598599\pi$
$114$		0			0
$115$	−3.00000			−0.279751
$116$	0.0234435	+	0.0406053i	0.00217667	+	0.00377011i
$117$		0			0
$118$	11.7630			1.08287
$119$	0.635211	+	0.345738i	0.0582297	+	0.0316937i
$120$		0			0
$121$	8.89610			0.808737
$122$	1.99640	−	3.45787i	0.180746	−	0.313061i
$123$		0			0
$124$	−0.167314	−	0.289796i	−0.0150252	−	0.0260245i
$125$	−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	$0.315671\pi$
$128$	−6.15486	−	10.6605i	−0.544018	−	0.942267i
$129$		0			0
$130$	1.95691	−	3.38946i	0.171632	−	0.297275i
$131$	3.19436			0.279092			0.139546	−	0.990216i	$-0.455436\pi$
$131$	3.19436			0.279092			0.139546	+	0.990216i	$0.455436\pi$
$132$		0			0
$133$	−0.190757	−	7.58277i	−0.0165408	−	0.657510i
$134$	8.56867			0.740221
$135$		0			0
$136$	0.372660	+	0.645466i	0.0319553	+	0.0553483i
$137$	−10.1082			−0.863599			−0.431800	−	0.901970i	$-0.642121\pi$
$137$	−10.1082			−0.863599			−0.431800	+	0.901970i	$0.642121\pi$
$138$		0			0
$139$	−9.03803	−	15.6543i	−0.766596	−	1.32778i	−0.939399	−	0.342827i	$-0.888616\pi$
$139$	−9.03803	−	15.6543i	−0.766596	−	1.32778i	0.172803	−	0.984956i	$-0.444718\pi$
$140$	−0.00525579	−	0.208922i	−0.000444196	−	0.0176572i
$141$		0			0
$142$	1.89922	+	3.28955i	0.159379	+	0.276053i
$143$	−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
$149$	−14.0541			−1.15136			−0.575678	−	0.817677i	$-0.695262\pi$
$149$	−14.0541			−1.15136			−0.575678	+	0.817677i	$0.695262\pi$
$150$		0			0
$151$	0.381515			0.0310472			0.0155236	−	0.999880i	$-0.495058\pi$
$151$	0.381515			0.0310472			0.0155236	+	0.999880i	$0.495058\pi$
$152$	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
$157$	3.75729	−	6.50783i	0.299865	−	0.519381i	−0.676240	−	0.736681i	$-0.736392\pi$
$157$	3.75729	−	6.50783i	0.299865	−	0.519381i	0.976105	+	0.217300i	$0.0697251\pi$
$158$	−8.15126	+	14.1184i	−0.648480	+	1.12320i
$159$		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	$0.963842\pi$
$164$	1.44999			0.113225
$165$		0			0
$166$	−24.1623			−1.87535
$167$	4.47656	+	7.75362i	0.346406	+	0.599993i	0.985608	−	0.169046i	$-0.0540685\pi$
$167$	4.47656	+	7.75362i	0.346406	+	0.599993i	−0.639202	+	0.769039i	$0.720735\pi$
$168$		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
$173$	−5.23025	−	9.05906i	−0.397649	−	0.688748i	0.595787	−	0.803143i	$-0.296840\pi$
$173$	−5.23025	−	9.05906i	−0.397649	−	0.688748i	−0.993435	+	0.114395i	$0.963507\pi$
$174$		0			0
$175$	10.4911	−	6.41415i	0.793056	−	0.484864i
$176$	−9.47509	−	16.4113i	−0.714212	−	1.23705i
$177$		0			0
$178$	7.84922			0.588324
$179$	−4.48395	−	7.76643i	−0.335146	−	0.580490i	0.648367	−	0.761328i	$-0.275452\pi$
$179$	−4.48395	−	7.76643i	−0.335146	−	0.580490i	−0.983513	+	0.180838i	$0.942119\pi$
$180$		0			0
$181$	5.04689			0.375132			0.187566	−	0.982252i	$-0.439940\pi$
$181$	5.04689			0.375132			0.187566	+	0.982252i	$0.439940\pi$
$182$	0.438719	+	17.4395i	0.0325200	+	1.29270i
$183$		0			0
$184$	13.7807			1.01593
$185$	1.97296	−	3.41726i	0.145055	−	0.251242i
$186$		0			0
$187$	0.609631	+	1.05591i	0.0445806	+	0.0772159i
$188$	−1.65486			−0.120693
$189$		0			0
$190$	2.48541			0.180311
$191$	6.06507	+	10.5050i	0.438853	+	0.760116i	0.997601	−	0.0692211i	$-0.0220514\pi$
$191$	6.06507	+	10.5050i	0.438853	+	0.760116i	−0.558748	+	0.829338i	$0.688718\pi$
$192$		0			0
$193$	−8.58113	+	14.8629i	−0.617683	+	1.06986i	0.372224	+	0.928143i	$0.378595\pi$
$193$	−8.58113	+	14.8629i	−0.617683	+	1.06986i	−0.989907	+	0.141716i	$0.954738\pi$
$194$	−3.30972			−0.237624
$195$		0			0
$196$	0.505735	+	0.782282i	0.0361239	+	0.0558773i
$197$	−0.751560			−0.0535464			−0.0267732	−	0.999642i	$-0.508523\pi$
$197$	−0.751560			−0.0535464			−0.0267732	+	0.999642i	$0.508523\pi$
$198$		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	$0.952233\pi$
$200$	12.6726			0.896086
$201$		0			0
$202$	6.83269	+	11.8346i	0.480746	+	0.832677i
$203$	0.0234435	+	0.931900i	0.00164541	+	0.0654065i
$204$		0			0
$205$	−3.23385	−	5.60119i	−0.225862	−	0.391204i
$206$	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	0.997926	+	0.0643756i	$0.0205056\pi$
$211$	8.05768	+	13.9563i	0.554714	+	0.960792i	−0.443212	+	0.896417i	$0.646161\pi$
$212$	−1.50739			−0.103528
$213$		0			0
$214$	−1.49688			−0.102325
$215$	−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
$220$	0.176168	−	0.305132i	0.0118773	−	0.0205720i
$221$	0.617023	−	1.06871i	0.0415054	−	0.0718895i
$222$		0			0
$223$	3.47656	−	6.02157i	0.232807	−	0.403234i	−0.725826	−	0.687879i	$-0.758542\pi$
$223$	3.47656	−	6.02157i	0.232807	−	0.403234i	0.958633	+	0.284644i	$0.0918755\pi$
$224$	0.0500067	+	1.98781i	0.00334121	+	0.132816i
$225$		0			0
$226$	10.4392	−	18.0812i	0.694405	−	1.20274i
$227$	5.29105			0.351180			0.175590	−	0.984463i	$-0.443817\pi$
$227$	5.29105			0.351180			0.175590	+	0.984463i	$0.443817\pi$
$228$		0			0
$229$	11.7237			0.774726			0.387363	−	0.921927i	$-0.373386\pi$
$229$	11.7237			0.774726			0.387363	+	0.921927i	$0.373386\pi$
$230$	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	−0.922437	−	0.386147i	$-0.873806\pi$
$233$	−1.93560	+	3.35256i	−0.126805	+	0.219633i	0.795632	+	0.605780i	$0.207139\pi$
$234$		0			0
$235$	3.69076	+	6.39258i	0.240758	+	0.417006i
$236$	−0.535897	−	0.928200i	−0.0348839	−	0.0604207i
$237$		0			0
$238$	−0.0265632	−	1.05591i	−0.00172184	−	0.0684446i
$239$	−6.19961	−	10.7380i	−0.401020	−	0.694586i	0.592830	−	0.805328i	$-0.298011\pi$
$239$	−6.19961	−	10.7380i	−0.401020	−	0.694586i	−0.993849	+	0.110742i	$0.964677\pi$
$240$		0			0
$241$	−16.5615			−1.06682			−0.533409	−	0.845857i	$-0.679089\pi$
$241$	−16.5615			−1.06682			−0.533409	+	0.845857i	$0.679089\pi$
$242$	−6.49640	−	11.2521i	−0.417604	−	0.723312i
$243$		0			0
$244$	−0.363806			−0.0232903
$245$	1.89397	−	3.69829i	0.121001	−	0.236275i
$246$		0			0
$247$	−12.9430			−0.823543
$248$	3.42821	−	5.93783i	0.217691	−	0.377052i
$249$		0			0
$250$	4.18190	+	7.24327i	0.264487	+	0.458105i
$251$	1.84922			0.116722			0.0583608	−	0.998296i	$-0.481413\pi$
$251$	1.84922			0.116722			0.0583608	+	0.998296i	$0.481413\pi$
$252$		0			0
$253$	22.5438			1.41731
$254$	−9.00739	−	15.6013i	−0.565174	−	0.978910i
$255$		0			0
$256$	−1.58998	+	2.75393i	−0.0993738	+	0.172120i
$257$	26.8420			1.67436			0.837180	−	0.546928i	$-0.184203\pi$
$257$	26.8420			1.67436			0.837180	+	0.546928i	$0.184203\pi$
$258$		0			0
$259$	0.442317	+	17.5825i	0.0274843	+	1.09252i
$260$	−0.356609			−0.0221159
$261$		0			0
$262$	−2.33269	−	4.04033i	−0.144114	−	0.249612i
$263$	20.2848			1.25082			0.625408	−	0.780298i	$-0.284933\pi$
$263$	20.2848			1.25082			0.625408	+	0.780298i	$0.284933\pi$
$264$		0			0
$265$	3.36186	+	5.82292i	0.206518	+	0.357699i
$266$	−9.45165	+	5.77861i	−0.579518	+	0.354310i
$267$		0			0
$268$	−0.390369	−	0.676139i	−0.0238456	−	0.0413018i
$269$	4.36333	+	7.55750i	0.266037	+	0.460789i	0.967835	−	0.251587i	$-0.0809524\pi$
$269$	4.36333	+	7.55750i	0.266037	+	0.460789i	−0.701798	+	0.712376i	$0.747619\pi$
$270$		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
$275$	20.7309			1.25012
$276$		0			0
$277$	−7.11537			−0.427521			−0.213760	−	0.976886i	$-0.568571\pi$
$277$	−7.11537			−0.427521			−0.213760	+	0.976886i	$0.568571\pi$
$278$	−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	$-0.909013\pi$
$281$	−3.94805	+	6.83823i	−0.235521	+	0.407934i	0.723903	+	0.689902i	$0.242346\pi$
$282$		0			0
$283$	−1.10457	+	1.91317i	−0.0656599	+	0.113726i	−0.896987	−	0.442058i	$-0.854249\pi$
$283$	−1.10457	+	1.91317i	−0.0656599	+	0.113726i	0.831327	+	0.555784i	$0.187582\pi$
$284$	0.173048	−	0.299729i	0.0102685	−	0.0177856i
$285$		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
$290$	−0.305449			−0.0179366
$291$		0			0
$292$	1.47917			0.0865620
$293$	9.59572	+	16.6203i	0.560588	+	0.970966i	0.997445	+	0.0714356i	$0.0227581\pi$
$293$	9.59572	+	16.6203i	0.560588	+	0.970966i	−0.436858	+	0.899531i	$0.643909\pi$
$294$		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
$299$	−11.4086	−	19.7602i	−0.659774	−	1.14276i
$300$		0			0
$301$	−0.224997	−	8.94382i	−0.0129686	−	0.515513i
$302$	−0.278602	−	0.482553i	−0.0160317	−	0.0277678i
$303$		0			0
$304$	−12.1800			−0.698569
$305$	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	$0.629967\pi$
$308$	0.0394951	+	1.56997i	0.00225044	+	0.0894572i
$309$		0			0
$310$	2.17996			0.123813
$311$	−5.32743	+	9.22738i	−0.302091	+	0.523237i	−0.976609	−	0.215021i	$-0.931018\pi$
$311$	−5.32743	+	9.22738i	−0.302091	+	0.523237i	0.674519	+	0.738258i	$0.264351\pi$
$312$		0			0
$313$	8.28074	+	14.3427i	0.468055	+	0.810695i	0.999334	−	0.0365022i	$-0.0116216\pi$
$313$	8.28074	+	14.3427i	0.468055	+	0.810695i	−0.531279	+	0.847197i	$0.678288\pi$
$314$	−10.9751			−0.619360
$315$		0			0
$316$	1.48541			0.0835609
$317$	13.3186	+	23.0685i	0.748046	+	1.29565i	0.948758	+	0.316003i	$0.102341\pi$
$317$	13.3186	+	23.0685i	0.748046	+	1.29565i	−0.200712	+	0.979650i	$0.564326\pi$
$318$		0			0
$319$	−0.785799	+	1.36104i	−0.0439963	+	0.0762038i
$320$	4.39203			0.245522
$321$		0			0
$322$	−17.1534	−	9.33639i	−0.955922	−	0.520297i
$323$	0.783663			0.0436042
$324$		0			0
$325$	−10.4911	−	18.1712i	−0.581944	−	1.00796i
$326$	22.1872			1.22883
$327$		0			0
$328$	14.8550	+	25.7295i	0.820227	+	1.42068i
$329$	−28.8982	−	15.7290i	−1.59321	−	0.867166i
$330$		0			0
$331$	11.6534	+	20.1843i	0.640529	+	1.10943i	0.985315	+	0.170747i	$0.0546181\pi$
$331$	11.6534	+	20.1843i	0.640529	+	1.10943i	−0.344786	+	0.938681i	$0.612049\pi$
$332$	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	0.986948	+	0.161036i	$0.0514837\pi$
$337$	11.6192	+	20.1250i	0.632936	+	1.09628i	−0.354013	+	0.935241i	$0.615183\pi$
$338$	10.7807			0.586395
$339$		0			0
$340$	0.0215917			0.00117097
$341$	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
$346$	−7.63881	+	13.2308i	−0.410665	+	0.711293i
$347$	8.56867	−	14.8414i	0.459990	−	0.796727i	−0.538969	−	0.842325i	$-0.681186\pi$
$347$	8.56867	−	14.8414i	0.459990	−	0.796727i	0.998960	+	0.0455985i	$0.0145195\pi$
$348$		0			0
$349$	9.75729	−	16.9001i	0.522296	−	0.904643i	−0.477368	−	0.878704i	$-0.658409\pi$
$349$	9.75729	−	16.9001i	0.522296	−	0.904643i	0.999664	−	0.0259395i	$-0.00825772\pi$
$350$	−15.7740	−	8.58561i	−0.843157	−	0.458920i
$351$		0			0
$352$	−1.67617	+	2.90321i	−0.0893401	+	0.154742i
$353$	−16.0613			−0.854856			−0.427428	−	0.904049i	$-0.640580\pi$
$353$	−16.0613			−0.854856			−0.427428	+	0.904049i	$0.640580\pi$
$354$		0			0
$355$	−1.54377			−0.0819347
$356$	−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	−0.623056	−	0.782177i	$-0.714109\pi$
$359$	6.93200	−	12.0066i	0.365857	−	0.633683i	0.988913	+	0.148494i	$0.0474426\pi$
$360$		0			0
$361$	5.39037	+	9.33639i	0.283704	+	0.491389i
$362$	−3.68550	−	6.38348i	−0.193706	−	0.335508i
$363$		0			0
$364$	1.35613	−	0.829120i	0.0710805	−	0.0434577i
$365$	−3.29893	−	5.71391i	−0.172674	−	0.299080i
$366$		0			0
$367$	25.2953			1.32041			0.660203	−	0.751088i	$-0.270470\pi$
$367$	25.2953			1.32041			0.660203	+	0.751088i	$0.270470\pi$
$368$	−10.7360	−	18.5953i	−0.559652	−	0.969346i
$369$		0			0
$370$	−5.76303			−0.299606
$371$	−26.3230	−	14.3273i	−1.36662	−	0.743838i
$372$		0			0
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$	0.890369	−	1.54216i	0.0460399	−	0.0797434i
$375$		0			0
$376$	−16.9538	−	29.3648i	−0.874325	−	1.51437i
$377$	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	$0.660489\pi$
$380$	−0.113230	−	0.196119i	−0.00580856	−	0.0100607i
$381$		0			0
$382$	8.85807	−	15.3426i	0.453218	−	0.784997i
$383$	−35.1416			−1.79565			−0.897826	−	0.440350i	$-0.854855\pi$
$383$	−35.1416			−1.79565			−0.897826	+	0.440350i	$0.854855\pi$
$384$		0			0
$385$	5.97656	−	3.65399i	0.304594	−	0.186224i
$386$	25.0656			1.27580
$387$		0			0
$388$	0.150783	+	0.261164i	0.00765486	+	0.0132586i
$389$	8.37859			0.424811			0.212406	−	0.977182i	$-0.431870\pi$
$389$	8.37859			0.424811			0.212406	+	0.977182i	$0.431870\pi$
$390$		0			0
$391$	0.690757	+	1.19643i	0.0349331	+	0.0605059i
$392$	−8.70009	+	16.9884i	−0.439421	+	0.858044i
$393$		0			0
$394$	0.548828	+	0.950599i	0.0276496	+	0.0478905i
$395$	−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
$401$	0.147469			0.00736425			0.00368212	−	0.999993i	$-0.498828\pi$
$401$	0.147469			0.00736425			0.00368212	+	0.999993i	$0.498828\pi$
$402$		0			0
$403$	−11.3523			−0.565500
$404$	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
$409$	1.96264	−	3.39939i	0.0970463	−	0.168089i	−0.813414	−	0.581685i	$-0.802394\pi$
$409$	1.96264	−	3.39939i	0.0970463	−	0.168089i	0.910461	+	0.413595i	$0.135727\pi$
$410$	−4.72306	+	8.18057i	−0.233255	+	0.404010i
$411$		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
$416$	3.39298			0.166355
$417$		0			0
$418$	−18.6768			−0.913514
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	0.999887	+	0.0150285i	$0.00478389\pi$
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	−0.486928	+	0.873442i	$0.661883\pi$
$420$		0			0
$421$	12.3442	−	21.3807i	0.601617	−	1.04203i	−0.390959	−	0.920408i	$-0.627857\pi$
$421$	12.3442	−	21.3807i	0.601617	−	1.04203i	0.992576	−	0.121624i	$-0.0388101\pi$
$422$	11.7683	−	20.3833i	0.572871	−	0.992242i
$423$		0			0
$424$	−15.4430	−	26.7480i	−0.749978	−	1.29900i
$425$	0.635211	+	1.10022i	0.0308122	+	0.0533684i
$426$		0			0
$427$	−6.35301	−	3.45787i	−0.307444	−	0.167338i
$428$	0.0681944	+	0.118116i	0.00329630	+	0.00570936i
$429$		0			0
$430$	2.93152			0.141371
$431$	−2.73745	−	4.74140i	−0.131858	−	0.228385i	0.792535	−	0.609827i	$-0.208761\pi$
$431$	−2.73745	−	4.74140i	−0.131858	−	0.228385i	−0.924393	+	0.381442i	$0.875428\pi$
$432$		0			0
$433$	23.6300			1.13558			0.567792	−	0.823172i	$-0.307798\pi$
$433$	23.6300			1.13558			0.567792	+	0.823172i	$0.307798\pi$
$434$	−8.29007	+	5.06844i	−0.397936	+	0.243293i
$435$		0			0
$436$	0.172375			0.00825526
$437$	7.24484	−	12.5484i	0.346568	−	0.600273i
$438$		0			0
$439$	2.63307	+	4.56062i	0.125670	+	0.217666i	0.921995	−	0.387203i	$-0.126559\pi$
$439$	2.63307	+	4.56062i	0.125670	+	0.217666i	−0.796325	+	0.604869i	$0.793225\pi$
$440$	7.21926			0.344165
$441$		0			0
$442$	−1.80233			−0.0857281
$443$	3.01819	+	5.22765i	0.143398	+	0.248373i	0.928774	−	0.370646i	$-0.120864\pi$
$443$	3.01819	+	5.22765i	0.143398	+	0.248373i	−0.785376	+	0.619019i	$0.787530\pi$
$444$		0			0
$445$	−1.59504	+	2.76269i	−0.0756122	+	0.130964i
$446$	−10.1551			−0.480856
$447$		0			0
$448$	−16.7022	+	10.2115i	−0.789106	+	0.482449i
$449$	−22.1445			−1.04507			−0.522533	−	0.852619i	$-0.675013\pi$
$449$	−22.1445			−1.04507			−0.522533	+	0.852619i	$0.675013\pi$
$450$		0			0
$451$	24.3011	+	42.0907i	1.14429	+	1.98197i
$452$	−1.90234			−0.0894787
$453$		0			0
$454$	−3.86381	−	6.69231i	−0.181337	−	0.314086i
$455$	−6.22733	−	3.38946i	−0.291942	−	0.158900i
$456$		0			0
$457$	2.66731	+	4.61992i	0.124772	+	0.216111i	0.921644	−	0.388037i	$-0.126847\pi$
$457$	2.66731	+	4.61992i	0.124772	+	0.216111i	−0.796872	+	0.604148i	$0.793513\pi$
$458$	−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	0.279838	+	0.960047i	$0.409719\pi$
$461$	−14.8473	+	25.7162i	−0.691507	+	1.19772i	−0.971344	+	0.237677i	$0.923614\pi$
$462$		0			0
$463$	−9.29533	−	16.1000i	−0.431990	−	0.748229i	0.565054	−	0.825054i	$-0.308855\pi$
$463$	−9.29533	−	16.1000i	−0.431990	−	0.748229i	−0.997045	+	0.0768243i	$0.975522\pi$
$464$	1.49688			0.0694909
$465$		0			0
$466$	5.65390			0.261912
$467$	−12.3063	+	21.3152i	−0.569468	+	0.986348i	0.427150	+	0.904181i	$0.359518\pi$
$467$	−12.3063	+	21.3152i	−0.569468	+	0.986348i	−0.996619	+	0.0821676i	$0.973816\pi$
$468$		0			0
$469$	−0.390369	−	15.5175i	−0.0180256	−	0.716532i
$470$	5.39037	−	9.33639i	0.248639	−	0.430656i
$471$		0			0
$472$	10.9803	−	19.0185i	0.505412	−	0.875399i
$473$	7.54163	−	13.0625i	0.346765	−	0.600614i
$474$		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
$479$	−0.356609			−0.0162939			−0.00814693	−	0.999967i	$-0.502593\pi$
$479$	−0.356609			−0.0162939			−0.00814693	+	0.999967i	$0.502593\pi$
$480$		0			0
$481$	30.0115			1.36841
$482$	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	$0.739083\pi$
$488$	−3.72713	−	6.45558i	−0.168719	−	0.292231i
$489$		0			0
$490$	−6.06080	+	0.305132i	−0.273799	+	0.0137845i
$491$	−2.77694	−	4.80981i	−0.125322	−	0.217064i	0.796537	−	0.604590i	$-0.206663\pi$
$491$	−2.77694	−	4.80981i	−0.125322	−	0.217064i	−0.921859	+	0.387526i	$0.873330\pi$
$492$		0			0
$493$	−0.0963098			−0.00433758
$494$	9.45165	+	16.3707i	0.425250	+	0.736554i
$495$		0			0
$496$	−10.6831			−0.479685
$497$	5.87072	−	3.58928i	0.263338	−	0.161001i
$498$		0			0
$499$	−28.1154			−1.25862			−0.629308	−	0.777156i	$-0.716662\pi$
$499$	−28.1154			−1.25862			−0.629308	+	0.777156i	$0.716662\pi$
$500$	0.381036	−	0.659973i	0.0170404	−	0.0295149i
$501$		0			0
$502$	−1.35040	−	2.33895i	−0.0602711	−	0.104393i
$503$	16.9430			0.755451			0.377725	−	0.925918i	$-0.376706\pi$
$503$	16.9430			0.755451			0.377725	+	0.925918i	$0.376706\pi$
$504$		0			0
$505$	−5.55389			−0.247145
$506$	−16.4626	−	28.5141i	−0.731854	−	1.26761i
$507$		0			0
$508$	−0.820712	+	1.42151i	−0.0364132	+	0.0630695i
$509$	−22.3025			−0.988542			−0.494271	−	0.869308i	$-0.664565\pi$
$509$	−22.3025			−0.988542			−0.494271	+	0.869308i	$0.664565\pi$
$510$		0			0
$511$	25.8302	+	14.0591i	1.14266	+	0.621938i
$512$	−19.9751			−0.882783
$513$		0			0
$514$	−19.6015	−	33.9507i	−0.864583	−	1.49750i
$515$	−9.35661			−0.412301
$516$		0			0
$517$	−27.7345	−	48.0376i	−1.21976	−	2.11269i
$518$	21.9159	−	13.3991i	0.962931	−	0.588724i
$519$		0			0
$520$	−3.65340	−	6.32787i	−0.160212	−	0.277496i
$521$	−6.18044	−	10.7048i	−0.270770	−	0.468987i	0.698289	−	0.715816i	$-0.253945\pi$
$521$	−6.18044	−	10.7048i	−0.270770	−	0.468987i	−0.969059	+	0.246828i	$0.920612\pi$
$522$		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
$527$	0.687353			0.0299416
$528$		0			0
$529$	2.54377			0.110599
$530$	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
$535$	0.304182	−	0.526858i	0.0131509	−	0.0227781i
$536$	7.99854	−	13.8539i	0.345484	−	0.598396i
$537$		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	$0.971068\pi$
$542$	35.3317			1.51763
$543$		0			0
$544$	−0.205436			−0.00880800
$545$	−0.384440	−	0.665869i	−0.0164676	−	0.0285227i
$546$		0			0
$547$	7.32957	−	12.6952i	0.313390	−	0.542807i	−0.665704	−	0.746216i	$-0.731869\pi$
$547$	7.32957	−	12.6952i	0.313390	−	0.542807i	0.979094	+	0.203409i	$0.0652021\pi$
$548$	0.672570	−	1.16492i	0.0287307	−	0.0497631i
$549$		0			0
$550$	−15.1388	−	26.2212i	−0.645521	−	1.11808i
$551$	0.505061	+	0.874792i	0.0215163	+	0.0372674i
$552$		0			0
$553$	25.9392	+	14.1184i	1.10305	+	0.600375i
$554$	5.19601	+	8.99976i	0.220757	+	0.382363i
$555$		0			0
$556$	2.40546			0.102014
$557$	11.8399	+	20.5073i	0.501672	+	0.868921i	0.999998	+	0.00193169i	$0.000614877\pi$
$557$	11.8399	+	20.5073i	0.501672	+	0.868921i	−0.498326	+	0.866990i	$0.666052\pi$
$558$		0			0
$559$	−15.2661			−0.645689
$560$	−5.86021	−	3.18964i	−0.247639	−	0.134787i
$561$		0			0
$562$	11.5323			0.486461
$563$	8.19289	−	14.1905i	0.345289	−	0.598059i	−0.640117	−	0.768277i	$-0.721114\pi$
$563$	8.19289	−	14.1905i	0.345289	−	0.598059i	0.985406	+	0.170219i	$0.0544475\pi$
$564$		0			0
$565$	4.24271	+	7.34858i	0.178492	+	0.309157i
$566$	3.22646			0.135618
$567$		0			0
$568$	7.09142			0.297549
$569$	7.89397	+	13.6728i	0.330932	+	0.573192i	0.982695	−	0.185231i	$-0.0593035\pi$
$569$	7.89397	+	13.6728i	0.330932	+	0.573192i	−0.651763	+	0.758423i	$0.725970\pi$
$570$		0			0
$571$	−3.19076	+	5.52655i	−0.133529	+	0.231279i	−0.925035	−	0.379883i	$-0.875964\pi$
$571$	−3.19076	+	5.52655i	−0.133529	+	0.231279i	0.791506	+	0.611162i	$0.209298\pi$
$572$	2.67977			0.112047
$573$		0			0
$574$	−1.05886	−	42.0907i	−0.0441960	−	1.75683i
$575$	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	$0.553085\pi$
$578$	−24.7195			−1.02819
$579$		0			0
$580$	0.0139156	+	0.0241025i	0.000577813	+	0.00100080i
$581$	1.10078	+	43.7569i	0.0456679	+	1.81534i
$582$		0			0
$583$	−25.2630	−	43.7569i	−1.04629	−	1.81222i
$584$	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	$-0.753040\pi$
$587$	6.04689	−	10.4735i	0.249582	−	0.432288i	0.963410	+	0.268033i	$0.0863735\pi$
$588$		0			0
$589$	−3.60457	−	6.24330i	−0.148524	−	0.257251i
$590$	6.98229			0.287456
$591$		0			0
$592$	28.2422			1.16075
$593$	−8.26449	+	14.3145i	−0.339382	+	0.587827i	−0.984317	−	0.176411i	$-0.943551\pi$
$593$	−8.26449	+	14.3145i	−0.339382	+	0.587827i	0.644935	+	0.764238i	$0.276885\pi$
$594$		0			0
$595$	0.377048	+	0.205223i	0.0154575	+	0.00841331i
$596$	0.935120	−	1.61968i	0.0383040	−	0.0663445i
$597$		0			0
$598$	−16.6623	+	28.8599i	−0.681370	+	1.18017i
$599$	4.37412	−	7.57620i	0.178722	−	0.309555i	−0.762721	−	0.646727i	$-0.776137\pi$
$599$	4.37412	−	7.57620i	0.178722	−	0.309555i	0.941443	+	0.337172i	$0.109470\pi$
$600$		0			0
$601$	2.96197	−	5.13028i	0.120821	−	0.209268i	−0.799271	−	0.600971i	$-0.794781\pi$
$601$	2.96197	−	5.13028i	0.120821	−	0.209268i	0.920092	+	0.391703i	$0.128114\pi$
$602$	−11.1481	+	6.81583i	−0.454364	+	0.277792i
$603$		0			0
$604$	−0.0253849	+	0.0439680i	−0.00103290	+	0.00178903i
$605$	5.28054			0.214685
$606$		0			0
$607$	−0.741438			−0.0300940			−0.0150470	−	0.999887i	$-0.504790\pi$
$607$	−0.741438			−0.0300940			−0.0150470	+	0.999887i	$0.504790\pi$
$608$	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	$0.862345\pi$
$614$	10.1606	+	17.5987i	0.410048	+	0.710224i
$615$		0			0
$616$	−27.4538	+	16.7849i	−1.10614	+	0.676282i
$617$	8.60078	+	14.8970i	0.346254	+	0.599730i	0.985581	−	0.169205i	$-0.0541201\pi$
$617$	8.60078	+	14.8970i	0.346254	+	0.599730i	−0.639327	+	0.768935i	$0.720787\pi$
$618$		0			0
$619$	4.48541			0.180284			0.0901419	−	0.995929i	$-0.471268\pi$
$619$	4.48541			0.180284			0.0901419	+	0.995929i	$0.471268\pi$
$620$	−0.0993140	−	0.172017i	−0.00398855	−	0.00690837i
$621$		0			0
$622$	15.5615			0.623958
$623$	−0.357592	−	14.2146i	−0.0143266	−	0.569496i
$624$		0			0
$625$	19.8391			0.793564
$626$	12.0941	−	20.9475i	0.483376	−	0.837231i
$627$		0			0
$628$	0.500000	+	0.866025i	0.0199522	+	0.0345582i
$629$	−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	$0.611947\pi$
$632$	15.2178	+	26.3580i	0.605332	+	1.04847i
$633$		0			0
$634$	19.4518	−	33.6916i	0.772531	−	1.33806i
$635$	7.32158			0.290548
$636$		0			0
$637$	31.5621	−	1.58900i	1.25054	−	0.0629586i
$638$	2.29533			0.0908729
$639$		0			0
$640$	−3.65340	−	6.32787i	−0.144413	−	0.250131i
$641$	43.3216			1.71110			0.855550	−	0.517721i	$-0.173219\pi$
$641$	43.3216			1.71110			0.855550	+	0.517721i	$0.173219\pi$
$642$		0			0
$643$	−14.9911	−	25.9654i	−0.591193	−	1.02398i	−0.994072	−	0.108723i	$-0.965324\pi$
$643$	−14.9911	−	25.9654i	−0.591193	−	1.02398i	0.402879	−	0.915253i	$-0.368010\pi$
$644$	0.0447509	+	1.77889i	0.00176343	+	0.0700981i
$645$		0			0
$646$	−0.572272	−	0.991204i	−0.0225157	−	0.0389984i
$647$	−7.08472	−	12.2711i	−0.278529	−	0.482427i	0.692490	−	0.721427i	$-0.256514\pi$
$647$	−7.08472	−	12.2711i	−0.278529	−	0.482427i	−0.971019	+	0.239000i	$0.923180\pi$
$648$		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
$653$	−28.3963			−1.11123			−0.555617	−	0.831439i	$-0.687518\pi$
$653$	−28.3963			−1.11123			−0.555617	+	0.831439i	$0.687518\pi$
$654$		0			0
$655$	1.89610			0.0740869
$656$	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	$-0.891937\pi$
$659$	−4.69961	+	8.13997i	−0.183071	+	0.317088i	0.759854	+	0.650094i	$0.225270\pi$
$660$		0			0
$661$	6.35807	−	11.0125i	0.247300	−	0.428337i	−0.715476	−	0.698638i	$-0.753790\pi$
$661$	6.35807	−	11.0125i	0.247300	−	0.428337i	0.962776	+	0.270301i	$0.0871232\pi$
$662$	17.0198	−	29.4792i	0.661495	−	1.14574i
$663$		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
$668$	−1.19143			−0.0460978
$669$		0			0
$670$	5.08619			0.196497
$671$	−6.09718	−	10.5606i	−0.235379	−	0.407688i
$672$		0			0
$673$	−17.8961	+	30.9970i	−0.689844	+	1.19485i	0.282044	+	0.959401i	$0.408988\pi$
$673$	−17.8961	+	30.9970i	−0.689844	+	1.19485i	−0.971888	+	0.235444i	$0.924346\pi$
$674$	16.9698	−	29.3926i	0.653654	−	1.13216i
$675$		0			0
$676$	−0.491146	−	0.850689i	−0.0188902	−	0.0327188i
$677$	5.44592	+	9.43260i	0.209304	+	0.362524i	0.951495	−	0.307663i	$-0.0995470\pi$
$677$	5.44592	+	9.43260i	0.209304	+	0.362524i	−0.742192	+	0.670188i	$0.766214\pi$
$678$		0			0
$679$	0.150783	+	5.99377i	0.00578653	+	0.230020i
$680$	0.221203	+	0.383136i	0.00848276	+	0.0146926i
$681$		0			0
$682$	−16.3815			−0.627281
$683$	17.5079	+	30.3245i	0.669920	+	1.16034i	0.977926	+	0.208951i	$0.0670050\pi$
$683$	17.5079	+	30.3245i	0.669920	+	1.16034i	−0.308006	+	0.951384i	$0.599662\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	22.3389	−	15.2518i	0.852903	−	0.582317i
$687$		0			0
$688$	−14.3662			−0.547705
$689$	−25.5693	+	44.2874i	−0.974115	+	1.68722i
$690$		0			0
$691$	−4.21041	−	7.29264i	−0.160171	−	0.277425i	0.774759	−	0.632257i	$-0.217871\pi$
$691$	−4.21041	−	7.29264i	−0.160171	−	0.277425i	−0.934930	+	0.354832i	$0.884538\pi$
$692$	1.39203			0.0529169
$693$		0			0
$694$	−25.0292			−0.950095
$695$	−5.36479	−	9.29209i	−0.203498	−	0.352469i
$696$		0			0
$697$	−1.48920	+	2.57938i	−0.0564076	+	0.0977009i
$698$	−28.5012			−1.07878
$699$		0			0
$700$	0.0411523	+	1.63584i	0.00155541	+	0.0618290i
$701$	−42.7453			−1.61447			−0.807234	−	0.590231i	$-0.799037\pi$
$701$	−42.7453			−1.61447			−0.807234	+	0.590231i	$0.799037\pi$
$702$		0			0
$703$	9.52918	+	16.5050i	0.359400	+	0.622499i
$704$	−33.0043			−1.24390
$705$		0			0
$706$	11.7288	+	20.3149i	0.441419	+	0.764560i
$707$	21.1206	−	12.9129i	0.794323	−	0.485638i
$708$		0			0
$709$	12.0431	+	20.8593i	0.452288	+	0.783386i	0.998528	−	0.0542432i	$-0.0172746\pi$
$709$	12.0431	+	20.8593i	0.452288	+	0.783386i	−0.546240	+	0.837629i	$0.683941\pi$
$710$	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
$716$	1.19340			0.0445994
$717$		0			0
$718$	−20.2484			−0.755665
$719$	21.0512	−	36.4617i	0.785076	−	1.35979i	−0.143878	−	0.989595i	$-0.545957\pi$
$719$	21.0512	−	36.4617i	0.785076	−	1.35979i	0.928954	−	0.370196i	$-0.120709\pi$
$720$		0			0
$721$	35.5818	−	21.7542i	1.32514	−	0.810170i
$722$	7.87266	−	13.6358i	0.292990	−	0.507474i
$723$		0			0
$724$	−0.335806	+	0.581633i	−0.0124801	+	0.0216162i
$725$	−0.818771	+	1.41815i	−0.0304084	+	0.0526689i
$726$		0			0
$727$	−18.0349	+	31.2374i	−0.668878	+	1.15853i	0.309340	+	0.950951i	$0.399892\pi$
$727$	−18.0349	+	31.2374i	−0.668878	+	1.15853i	−0.978218	+	0.207579i	$0.933442\pi$
$728$	28.6057	+	15.5698i	1.06020	+	0.577054i
$729$		0			0
$730$	−4.81810	+	8.34519i	−0.178326	+	0.308869i
$731$	0.924324			0.0341874
$732$		0			0
$733$	34.1331			1.26073			0.630367	−	0.776297i	$-0.282904\pi$
$733$	34.1331			1.26073			0.630367	+	0.776297i	$0.282904\pi$
$734$	−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	$0.965272\pi$
$740$	0.262550	+	0.454751i	0.00965154	+	0.0167170i
$741$		0			0
$742$	1.10078	+	43.7569i	0.0404108	+	1.60636i
$743$	−14.1426	−	24.4957i	−0.518842	−	0.898660i	−0.999760	−	0.0218950i	$-0.993030\pi$
$743$	−14.1426	−	24.4957i	−0.518842	−	0.898660i	0.480919	−	0.876765i	$-0.340303\pi$
$744$		0			0
$745$	−8.34221			−0.305635
$746$	−1.46050	−	2.52967i	−0.0534729	−	0.0926177i
$747$		0			0
$748$	−0.162253			−0.00593254
$749$	0.0681944	+	2.71079i	0.00249177	+	0.0990501i
$750$		0			0
$751$	−14.4969			−0.528999			−0.264499	−	0.964386i	$-0.585207\pi$
$751$	−14.4969			−0.528999			−0.264499	+	0.964386i	$0.585207\pi$
$752$	−26.4159	+	45.7538i	−0.963291	+	1.66847i
$753$		0			0
$754$	−1.16158	−	2.01191i	−0.0423022	−	0.0732696i
$755$	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	$0.750446\pi$
$758$	13.7360	+	23.7914i	0.498914	+	0.864144i
$759$		0			0
$760$	2.32004	−	4.01842i	0.0841566	−	0.145764i
$761$	−1.25564			−0.0455168			−0.0227584	−	0.999741i	$-0.507245\pi$
$761$	−1.25564			−0.0455168			−0.0227584	+	0.999741i	$0.507245\pi$
$762$		0			0
$763$	3.01012	+	1.63837i	0.108974	+	0.0593131i
$764$	−1.61421			−0.0584002
$765$		0			0
$766$	25.6623	+	44.4483i	0.927215	+	1.60598i
$767$	−36.3609			−1.31292
$768$		0			0
$769$	13.8442	+	23.9788i	0.499233	+	0.864697i	1.00000		0.000885409i	$-0.000281834\pi$
$769$	13.8442	+	23.9788i	0.499233	+	0.864697i	−0.500767	+	0.865582i	$0.666949\pi$
$770$	−8.98608	−	4.89102i	−0.323836	−	0.176260i
$771$		0			0
$772$	−1.14193	−	1.97788i	−0.0410989	−	0.0711854i
$773$	−3.95544	−	6.85103i	−0.142267	−	0.246414i	0.786083	−	0.618121i	$-0.212106\pi$
$773$	−3.95544	−	6.85103i	−0.142267	−	0.246414i	−0.928350	+	0.371707i	$0.878773\pi$
$774$		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
$779$	31.2383			1.11923
$780$		0			0
$781$	11.6008			0.415108
$782$	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
$787$	−15.8346	+	27.4264i	−0.564444	+	0.977645i	0.432658	+	0.901558i	$0.357576\pi$
$787$	−15.8346	+	27.4264i	−0.564444	+	0.977645i	−0.997101	+	0.0760866i	$0.975757\pi$
$788$	0.0500067	−	0.0866142i	0.00178142	−	0.00308550i
$789$		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
$794$	−13.5074			−0.479359
$795$		0			0
$796$	1.37005			0.0485600
$797$	−16.8961	−	29.2649i	−0.598491	−	1.03662i	−0.993044	−	0.117743i	$-0.962434\pi$
$797$	−16.8961	−	29.2649i	−0.598491	−	1.03662i	0.394553	−	0.918873i	$-0.370899\pi$
$798$		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
$803$	24.7901	+	42.9377i	0.874823	+	1.51524i
$804$		0			0
$805$	6.77188	−	4.14024i	0.238678	−	0.145924i
$806$	8.29007	+	14.3588i	0.292005	+	0.505768i
$807$		0			0
$808$	25.5122			0.897517
$809$	−18.3801	−	31.8352i	−0.646208	−	1.11927i	−0.984021	−	0.178052i	$-0.943020\pi$
$809$	−18.3801	−	31.8352i	−0.646208	−	1.11927i	0.337813	−	0.941213i	$-0.390313\pi$
$810$		0			0
$811$	3.54377			0.124438			0.0622192	−	0.998063i	$-0.480182\pi$
$811$	3.54377			0.124438			0.0622192	+	0.998063i	$0.480182\pi$
$812$	−0.108957	−	0.0593043i	−0.00382366	−	0.00208117i
$813$		0			0
$814$	43.3068			1.51790
$815$	−4.50866	+	7.80923i	−0.157931	+	0.273545i
$816$		0			0
$817$	−4.84728	−	8.39573i	−0.169585	−	0.293729i
$818$	−5.73289			−0.200446
$819$		0			0
$820$	0.860686			0.0300565
$821$	−10.4318	−	18.0684i	−0.364073	−	0.630592i	0.624554	−	0.780981i	$-0.285281\pi$
$821$	−10.4318	−	18.0684i	−0.364073	−	0.630592i	−0.988627	+	0.150389i	$0.951947\pi$
$822$		0			0
$823$	−22.7003	+	39.3180i	−0.791282	+	1.37054i	0.133891	+	0.990996i	$0.457253\pi$
$823$	−22.7003	+	39.3180i	−0.791282	+	1.37054i	−0.925173	+	0.379545i	$0.876081\pi$
$824$	42.9803			1.49729
$825$		0			0
$826$	−26.5526	+	16.2339i	−0.923884	+	0.564850i
$827$	−5.34221			−0.185767			−0.0928835	−	0.995677i	$-0.529608\pi$
$827$	−5.34221			−0.185767			−0.0928835	+	0.995677i	$0.529608\pi$
$828$		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	$0.928168\pi$
$830$	−14.3422			−0.497826
$831$		0			0
$832$	16.7022	+	28.9291i	0.579046	+	1.00294i
$833$	−1.91100	+	0.0962098i	−0.0662123	+	0.00333347i
$834$		0			0
$835$	2.65719	+	4.60239i	0.0919559	+	0.159272i
$836$	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	$-0.779008\pi$
$839$	4.91955	−	8.52091i	0.169842	−	0.294174i	0.938364	+	0.345649i	$0.112341\pi$
$840$		0			0
$841$	14.4379	+	25.0072i	0.497860	+	0.862318i
$842$	−36.0574			−1.24262
$843$		0			0
$844$	−2.14454			−0.0738182
$845$	−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
$850$	0.927728	−	1.60687i	0.0318208	−	0.0551153i
$851$	−16.7989	+	29.0966i	−0.575860	+	0.997418i
$852$		0			0
$853$	27.7434	−	48.0529i	0.949915	−	1.64530i	0.204318	−	0.978905i	$-0.434502\pi$
$853$	27.7434	−	48.0529i	0.949915	−	1.64530i	0.745597	−	0.666397i	$-0.232164\pi$
$854$	0.265670	+	10.5606i	0.00909104	+	0.361377i
$855$		0			0
$856$	−1.39728	+	2.42016i	−0.0477581	+	0.0827195i
$857$	−56.3465			−1.92476			−0.962380	−	0.271708i	$-0.912411\pi$
$857$	−56.3465			−1.92476			−0.962380	+	0.271708i	$0.912411\pi$
$858$		0			0
$859$	43.9253			1.49871			0.749356	−	0.662168i	$-0.230363\pi$
$859$	43.9253			1.49871			0.749356	+	0.662168i	$0.230363\pi$
$860$	−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	−0.946175	−	0.323654i	$-0.895089\pi$
$863$	−5.66372	+	9.80984i	−0.192795	+	0.333931i	0.753380	+	0.657585i	$0.228422\pi$
$864$		0			0
$865$	−3.10457	−	5.37727i	−0.105559	−	0.182833i
$866$	−17.2558	−	29.8880i	−0.586377	−	1.01563i
$867$		0			0
$868$	0.777618	+	0.423249i	0.0263941	+	0.0143660i
$869$	24.8946	+	43.1188i	0.844493	+	1.46270i
$870$		0			0
$871$	−26.4868			−0.897470
$872$	1.76595	+	3.05872i	0.0598028	+	0.103581i
$873$		0			0
$874$	−21.1623			−0.715824
$875$	12.9267	−	7.90324i	0.437004	−	0.267178i
$876$		0			0
$877$	−46.4615			−1.56889			−0.784446	−	0.620197i	$-0.787053\pi$
$877$	−46.4615			−1.56889			−0.784446	+	0.620197i	$0.787053\pi$
$878$	3.84562	−	6.66081i	0.129783	−	0.224791i
$879$		0			0
$880$	−5.62422	−	9.74143i	−0.189592	−	0.328384i
$881$	21.6578			0.729669			0.364835	−	0.931072i	$-0.381126\pi$
$881$	21.6578			0.729669			0.364835	+	0.931072i	$0.381126\pi$
$882$		0			0
$883$	11.4868			0.386560			0.193280	−	0.981144i	$-0.438087\pi$
$883$	11.4868			0.386560			0.193280	+	0.981144i	$0.438087\pi$
$884$	0.0821100	+	0.142219i	0.00276166	+	0.00478333i
$885$		0			0
$886$	4.40808	−	7.63501i	0.148092	−	0.256503i
$887$	17.8420			0.599076			0.299538	−	0.954084i	$-0.403167\pi$
$887$	17.8420			0.599076			0.299538	+	0.954084i	$0.403167\pi$
$888$		0			0
$889$	−27.8429	+	17.0228i	−0.933820	+	0.570926i
$890$	4.65913			0.156174
$891$		0			0
$892$	0.462641	+	0.801318i	0.0154904	+	0.0268301i
$893$	−35.6519			−1.19305
$894$		0			0
$895$	−2.66158	−	4.60999i	−0.0889668	−	0.154095i
$896$	28.6057	+	15.5698i	0.955650	+	0.520149i
$897$		0			0
$898$	16.1711	+	28.0092i	0.539637	+	0.934678i
$899$	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
$905$	2.99573			0.0995814
$906$		0			0
$907$	−51.8506			−1.72167			−0.860835	−	0.508884i	$-0.830058\pi$
$907$	−51.8506			−1.72167			−0.860835	+	0.508884i	$0.830058\pi$
$908$	−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	$-0.799062\pi$
$911$	3.24338	−	5.61770i	0.107458	−	0.186123i	0.914740	+	0.404044i	$0.132396\pi$
$912$		0			0
$913$	−36.8968	+	63.9071i	−1.22111	+	2.11502i
$914$	3.89562	−	6.74742i	0.128856	−	0.223185i
$915$		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	$0.104937\pi$
$920$	8.17996			0.269685
$921$		0			0
$922$	43.3690			1.42828
$923$	−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
$929$	−0.730252	−	1.26483i	−0.0239588	−	0.0414979i	0.853797	−	0.520605i	$-0.174294\pi$
$929$	−0.730252	−	1.26483i	−0.0239588	−	0.0414979i	−0.877756	+	0.479108i	$0.840960\pi$
$930$		0			0
$931$	10.8954	+	16.8533i	0.357083	+	0.552344i
$932$	−0.257579	−	0.446140i	−0.00843727	−	0.0146138i
$933$		0			0
$934$	35.9469			1.17622
$935$	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	$0.448434\pi$
$938$	−19.3420	+	11.8255i	−0.631539	+	0.386115i
$939$		0			0
$940$	−0.982291			−0.0320388
$941$	27.0972	−	46.9337i	0.883343	−	1.52999i	0.0357414	−	0.999361i	$-0.488621\pi$
$941$	27.0972	−	46.9337i	0.883343	−	1.52999i	0.847601	−	0.530633i	$-0.178046\pi$
$942$		0			0
$943$	27.5349	+	47.6919i	0.896660	+	1.55306i
$944$	−34.2173			−1.11368
$945$		0			0
$946$	−22.0292			−0.716230
$947$	−27.4451	−	47.5364i	−0.891847	−	1.54472i	−0.837659	−	0.546193i	$-0.816076\pi$
$947$	−27.4451	−	47.5364i	−0.891847	−	1.54472i	−0.0541875	−	0.998531i	$-0.517257\pi$
$948$		0			0
$949$	25.0907	−	43.4583i	0.814477	−	1.41072i
$950$	−19.4605			−0.631382
$951$		0			0
$952$	−1.73200	−	0.942707i	−0.0561344	−	0.0305533i
$953$	27.0406			0.875932			0.437966	−	0.898991i	$-0.355699\pi$
$953$	27.0406			0.875932			0.437966	+	0.898991i	$0.355699\pi$
$954$		0			0
$955$	3.60010	+	6.23556i	0.116497	+	0.201778i
$956$	1.65002			0.0533655
$957$		0			0
$958$	0.260414	+	0.451051i	0.00841360	+	0.0145728i
$959$	22.8171	−	13.9501i	0.736803	−	0.450472i
$960$		0			0
$961$	12.3384	+	21.3708i	0.398014	+	0.689380i
$962$	−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	0.953982	−	0.299865i	$-0.0969417\pi$
$967$	6.75729	+	11.7040i	0.217300	+	0.376375i	−0.736682	+	0.676240i	$0.763608\pi$
$968$	−24.2566			−0.779636
$969$		0			0
$970$	−1.96458			−0.0630789
$971$	6.46557	−	11.1987i	0.207490	−	0.359383i	−0.743433	−	0.668810i	$-0.766804\pi$
$971$	6.46557	−	11.1987i	0.207490	−	0.359383i	0.950923	+	0.309427i	$0.100137\pi$
$972$		0			0
$973$	42.0057	+	22.8632i	1.34664	+	0.732961i
$974$	9.40448	−	16.2890i	0.301339	−	0.521934i
$975$		0			0
$976$	−5.80730	+	10.0585i	−0.185887	+	0.321966i
$977$	−18.2989	+	31.6947i	−0.585435	+	1.01400i	0.409387	+	0.912361i	$0.365743\pi$
$977$	−18.2989	+	31.6947i	−0.585435	+	1.01400i	−0.994821	+	0.101641i	$0.967591\pi$
$978$		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
$983$	17.2379			0.549805			0.274902	−	0.961472i	$-0.411354\pi$
$983$	17.2379			0.549805			0.274902	+	0.961472i	$0.411354\pi$
$984$		0			0
$985$	−0.446110			−0.0142143
$986$	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	$0.754978\pi$
$992$	0.944932	+	1.63667i	0.0300016	+	0.0519643i
$993$		0			0
$994$	−8.82695	−	4.80441i	−0.279974	−	0.152387i
$995$	−3.05555	−	5.29236i	−0.0968673	−	0.167779i
$996$		0			0
$997$	−34.1154			−1.08044			−0.540222	−	0.841522i	$-0.681660\pi$
$997$	−34.1154			−1.08044			−0.540222	+	0.841522i	$0.681660\pi$
$998$	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.g.i.541.1		6
3.2	odd	2		567.2.g.h.541.3		6
7.4	even	3		567.2.h.h.298.3		6
9.2	odd	6		189.2.e.e.163.3	yes	6
9.4	even	3		567.2.h.h.352.3		6
9.5	odd	6		567.2.h.i.352.1		6
9.7	even	3		189.2.e.f.163.1	yes	6
21.11	odd	6		567.2.h.i.298.1		6
63.2	odd	6		1323.2.a.ba.1.1		3
63.4	even	3	inner	567.2.g.i.109.1		6
63.11	odd	6		189.2.e.e.109.3	✓	6
63.16	even	3		1323.2.a.x.1.3		3
63.25	even	3		189.2.e.f.109.1	yes	6
63.32	odd	6		567.2.g.h.109.3		6
63.47	even	6		1323.2.a.z.1.1		3
63.61	odd	6		1323.2.a.y.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.3	✓	6	63.11	odd	6
189.2.e.e.163.3	yes	6	9.2	odd	6
189.2.e.f.109.1	yes	6	63.25	even	3
189.2.e.f.163.1	yes	6	9.7	even	3
567.2.g.h.109.3		6	63.32	odd	6
567.2.g.h.541.3		6	3.2	odd	2
567.2.g.i.109.1		6	63.4	even	3	inner
567.2.g.i.541.1		6	1.1	even	1	trivial
567.2.h.h.298.3		6	7.4	even	3
567.2.h.h.352.3		6	9.4	even	3
567.2.h.i.298.1		6	21.11	odd	6
567.2.h.i.352.1		6	9.5	odd	6
1323.2.a.x.1.3		3	63.16	even	3
1323.2.a.y.1.3		3	63.61	odd	6
1323.2.a.z.1.1		3	63.47	even	6
1323.2.a.ba.1.1		3	63.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.730252 - 1.26483i) q^{2} +(-0.0665372 + 0.115246i) q^{4} +0.593579 q^{5} +(-2.25729 + 1.38008i) q^{7} -2.72665 q^{8} +(-0.433463 - 0.750780i) q^{10} -4.46050 q^{11} +(2.25729 + 3.90975i) q^{13} +(3.39397 + 1.84730i) q^{14} +(2.12422 + 3.67926i) q^{16} +(-0.136673 - 0.236725i) q^{17} +(-1.43346 + 2.48283i) q^{19} +(-0.0394951 + 0.0684076i) q^{20} +(3.25729 + 5.64180i) q^{22} -5.05408 q^{23} -4.64766 q^{25} +(3.29679 - 5.71021i) q^{26} +(-0.00885441 - 0.351971i) q^{28} +(0.176168 - 0.305132i) q^{29} +(-1.25729 + 2.17770i) q^{31} +(0.375780 - 0.650870i) q^{32} +(-0.199612 + 0.345738i) q^{34} +(-1.33988 + 0.819187i) q^{35} +(3.32383 - 5.75705i) q^{37} +4.18716 q^{38} -1.61849 q^{40} +(-5.44805 - 9.43630i) q^{41} +(-1.69076 + 2.92848i) q^{43} +(0.296790 - 0.514055i) q^{44} +(3.69076 + 6.39258i) q^{46} +(6.21780 + 10.7695i) q^{47} +(3.19076 - 6.23049i) q^{49} +(3.39397 + 5.87852i) q^{50} -0.600777 q^{52} +(5.66372 + 9.80984i) q^{53} -2.64766 q^{55} +(6.15486 - 3.76300i) q^{56} -0.514589 q^{58} +(-4.02704 + 6.97504i) q^{59} +(1.36693 + 2.36758i) q^{61} +3.67257 q^{62} +7.39922 q^{64} +(1.33988 + 2.32075i) q^{65} +(-2.93346 + 5.08091i) q^{67} +0.0363754 q^{68} +(2.01459 + 1.09652i) q^{70} -2.60078 q^{71} +(-5.55768 - 9.62619i) q^{73} -9.70895 q^{74} +(-0.190757 - 0.330401i) q^{76} +(10.0687 - 6.15585i) q^{77} +(-5.58113 - 9.66679i) q^{79} +(1.26089 + 2.18393i) q^{80} +(-7.95691 + 13.7818i) q^{82} +(8.27188 - 14.3273i) q^{83} +(-0.0811263 - 0.140515i) q^{85} +4.93872 q^{86} +12.1623 q^{88} +(-2.68716 + 4.65430i) q^{89} +(-10.4911 - 5.71021i) q^{91} +(0.336285 - 0.582462i) q^{92} +(9.08113 - 15.7290i) q^{94} +(-0.850874 + 1.47376i) q^{95} +(1.13307 - 1.96254i) q^{97} +(-10.2106 + 0.514055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 4 q^{4} - 2 q^{5} + 2 q^{7} - 18 q^{8} + q^{10} - 14 q^{11} - 2 q^{13} + 4 q^{14} - 10 q^{16} - 5 q^{19} - 13 q^{20} + 4 q^{22} - 12 q^{23} - 4 q^{25} + 17 q^{26} - 30 q^{28} + 13 q^{29}+ \cdots - 49 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 4 * q^4 - 2 * q^5 + 2 * q^7 - 18 * q^8 + q^10 - 14 * q^11 - 2 * q^13 + 4 * q^14 - 10 * q^16 - 5 * q^19 - 13 * q^20 + 4 * q^22 - 12 * q^23 - 4 * q^25 + 17 * q^26 - 30 * q^28 + 13 * q^29 + 8 * q^31 + 25 * q^32 - 12 * q^34 - 10 * q^35 + 8 * q^37 + 14 * q^38 - 48 * q^40 + 2 * q^41 + 9 * q^43 - q^44 + 3 * q^46 + 9 * q^47 + 4 * q^50 + 18 * q^52 + 24 * q^53 + 8 * q^55 - 3 * q^56 + 28 * q^58 - 15 * q^59 + q^61 + 42 * q^62 + 66 * q^64 + 10 * q^65 - 14 * q^67 - 78 * q^68 - 19 * q^70 + 6 * q^71 - 7 * q^73 + 18 * q^76 + 11 * q^77 - 6 * q^79 - 16 * q^80 - 43 * q^82 + 3 * q^83 + 27 * q^85 + 64 * q^86 + 18 * q^88 - 5 * q^89 - 33 * q^91 + 12 * q^92 + 27 * q^94 + 16 * q^95 + 14 * q^97 - 49 * q^98

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