LMFDB - Embedded newform 567.2.g.h.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(109,567)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.52751779461$
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			109.3
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.h.541.3

$q$-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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.730252	−	1.26483i	0.516366	−	0.894373i	−0.483453	−	0.875370i	$-0.660618\pi$
$2$	0.730252	−	1.26483i	0.516366	−	0.894373i	0.999819	−	0.0190026i	$-0.00604908\pi$
$3$		0			0
$3$		0			0
$4$	−0.0665372	−	0.115246i	−0.0332686	−	0.0576229i
$5$	−0.593579			−0.265457			−0.132728	−	0.991152i	$-0.542374\pi$
$5$	−0.593579			−0.265457			−0.132728	+	0.991152i	$0.542374\pi$
$6$		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	$-0.265244\pi$
$11$	4.46050			1.34489			0.672446	+	0.740146i	$0.265244\pi$
$12$		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	$-0.0486672\pi$
$14$	−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	$-0.822780\pi$
$17$	0.136673	−	0.236725i	0.0331481	−	0.0574142i	0.882124	+	0.471018i	$0.156113\pi$
$18$		0			0
$19$	−1.43346	−	2.48283i	−0.328859	−	0.569600i	0.653427	−	0.756990i	$-0.273331\pi$
$19$	−1.43346	−	2.48283i	−0.328859	−	0.569600i	−0.982286	+	0.187389i	$0.939997\pi$
$20$	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	$-0.323345\pi$
$23$	5.05408			1.05385			0.526925	+	0.849912i	$0.323345\pi$
$24$		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	$-0.177082\pi$
$29$	−0.176168	−	0.305132i	−0.0327136	−	0.0566616i	−0.881919	+	0.471402i	$0.843748\pi$
$30$		0			0
$31$	−1.25729	−	2.17770i	−0.225817	−	0.391126i	0.730747	−	0.682648i	$-0.239172\pi$
$31$	−1.25729	−	2.17770i	−0.225817	−	0.391126i	−0.956564	+	0.291522i	$0.905838\pi$
$32$	−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	0.998515	+	0.0544753i	$0.0173486\pi$
$37$	3.32383	+	5.75705i	0.546435	+	0.946452i	−0.452081	+	0.891977i	$0.649318\pi$
$38$	−4.18716			−0.679247
$39$		0			0
$40$	−1.61849			−0.255905
$41$	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
$47$	−6.21780	+	10.7695i	−0.906959	+	1.57090i	−0.0886938	+	0.996059i	$0.528269\pi$
$47$	−6.21780	+	10.7695i	−0.906959	+	1.57090i	−0.818265	+	0.574841i	$0.805064\pi$
$48$		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	0.155138	+	0.987893i	$0.450418\pi$
$53$	−5.66372	+	9.80984i	−0.777971	+	1.34749i	−0.933109	+	0.359593i	$0.882916\pi$
$54$		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	0.999601	+	0.0282624i	$0.00899740\pi$
$59$	4.02704	+	6.97504i	0.524276	+	0.908073i	−0.475324	+	0.879811i	$0.657669\pi$
$60$		0			0
$61$	1.36693	−	2.36758i	0.175017	−	0.303138i	−0.765150	−	0.643852i	$-0.777335\pi$
$61$	1.36693	−	2.36758i	0.175017	−	0.303138i	0.940167	+	0.340714i	$0.110669\pi$
$62$	−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	0.629311	−	0.777154i	$-0.283337\pi$
$67$	−2.93346	−	5.08091i	−0.358380	−	0.620732i	−0.987690	+	0.156422i	$0.950004\pi$
$68$	−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	$-0.450679\pi$
$71$	2.60078			0.308655			0.154328	+	0.988020i	$0.450679\pi$
$72$		0			0
$73$	−5.55768	+	9.62619i	−0.650478	+	1.12666i	0.332530	+	0.943093i	$0.392098\pi$
$73$	−5.55768	+	9.62619i	−0.650478	+	1.12666i	−0.983007	+	0.183567i	$0.941235\pi$
$74$	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	0.360042	+	0.932936i	$0.382763\pi$
$79$	−5.58113	+	9.66679i	−0.627926	+	1.08760i	−0.987967	+	0.154663i	$0.950571\pi$
$80$	−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
$86$	−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	$-0.0747268\pi$
$89$	2.68716	+	4.65430i	0.284838	+	0.493354i	−0.687732	+	0.725965i	$0.741393\pi$
$90$		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	0.917798	−	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
$101$	9.35661			0.931017			0.465509	−	0.885043i	$-0.345871\pi$
$101$	9.35661			0.931017			0.465509	+	0.885043i	$0.345871\pi$
$102$		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	$-0.182442\pi$
$107$	−0.512453	−	0.887595i	−0.0495407	−	0.0858070i	−0.889732	+	0.456483i	$0.849109\pi$
$108$		0			0
$109$	−0.647664	+	1.12179i	−0.0620349	+	0.107448i	−0.895375	−	0.445313i	$-0.853092\pi$
$109$	−0.647664	+	1.12179i	−0.0620349	+	0.107448i	0.833340	+	0.552761i	$0.186426\pi$
$110$	−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	0.304827	+	0.952408i	$0.401401\pi$
$113$	−7.14766	+	12.3801i	−0.672396	+	1.16462i	−0.977223	+	0.212216i	$0.931932\pi$
$114$		0			0
$115$	−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	$-0.544564\pi$
$131$	−3.19436			−0.279092			−0.139546	+	0.990216i	$0.544564\pi$
$132$		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	$-0.357879\pi$
$137$	10.1082			0.863599			0.431800	+	0.901970i	$0.357879\pi$
$138$		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	$0.888616\pi$
$140$	0.00525579	−	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	$-0.304738\pi$
$149$	14.0541			1.15136			0.575678	+	0.817677i	$0.304738\pi$
$150$		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	0.976105	−	0.217300i	$-0.0697251\pi$
$157$	3.75729	+	6.50783i	0.299865	+	0.519381i	−0.676240	+	0.736681i	$0.736392\pi$
$158$	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	−0.993555	−	0.113351i	$-0.963842\pi$
$163$	−7.59572	−	13.1562i	−0.594942	−	1.03047i	0.398613	−	0.917119i	$-0.369492\pi$
$164$	−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	$-0.945931\pi$
$167$	−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
$173$	5.23025	−	9.05906i	0.397649	−	0.688748i	−0.595787	−	0.803143i	$-0.703160\pi$
$173$	5.23025	−	9.05906i	0.397649	−	0.688748i	0.993435	+	0.114395i	$0.0364929\pi$
$174$		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	$-0.724548\pi$
$179$	4.48395	−	7.76643i	0.335146	−	0.580490i	0.983513	+	0.180838i	$0.0578810\pi$
$180$		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	$-0.977949\pi$
$191$	−6.06507	+	10.5050i	−0.438853	+	0.760116i	0.558748	+	0.829338i	$0.311282\pi$
$192$		0			0
$193$	−8.58113	−	14.8629i	−0.617683	−	1.06986i	−0.989907	−	0.141716i	$-0.954738\pi$
$193$	−8.58113	−	14.8629i	−0.617683	−	1.06986i	0.372224	−	0.928143i	$-0.378595\pi$
$194$	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	$-0.491477\pi$
$197$	0.751560			0.0535464			0.0267732	+	0.999642i	$0.491477\pi$
$198$		0			0
$199$	−5.14766	+	8.91601i	−0.364908	+	0.632040i	−0.988761	−	0.149502i	$-0.952233\pi$
$199$	−5.14766	+	8.91601i	−0.364908	+	0.632040i	0.623853	+	0.781542i	$0.285566\pi$
$200$	−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	−0.443212	−	0.896417i	$-0.646161\pi$
$211$	8.05768	−	13.9563i	0.554714	−	0.960792i	0.997926	−	0.0643756i	$-0.0205056\pi$
$212$	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	0.958633	−	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
$227$	−5.29105			−0.351180			−0.175590	−	0.984463i	$-0.556183\pi$
$227$	−5.29105			−0.351180			−0.175590	+	0.984463i	$0.556183\pi$
$228$		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	$-0.126194\pi$
$233$	1.93560	+	3.35256i	0.126805	+	0.219633i	−0.795632	+	0.605780i	$0.792861\pi$
$234$		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	$-0.701989\pi$
$239$	6.19961	−	10.7380i	0.401020	−	0.694586i	0.993849	+	0.110742i	$0.0353226\pi$
$240$		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	$-0.518587\pi$
$251$	−1.84922			−0.116722			−0.0583608	+	0.998296i	$0.518587\pi$
$252$		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	$-0.815797\pi$
$257$	−26.8420			−1.67436			−0.837180	+	0.546928i	$0.815797\pi$
$258$		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	$-0.715067\pi$
$263$	−20.2848			−1.25082			−0.625408	+	0.780298i	$0.715067\pi$
$264$		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	$-0.919048\pi$
$269$	−4.36333	+	7.55750i	−0.266037	+	0.460789i	0.701798	+	0.712376i	$0.252381\pi$
$270$		0			0
$271$	−12.0957	−	20.9504i	−0.734762	−	1.27265i	−0.954828	−	0.297161i	$-0.903960\pi$
$271$	−12.0957	−	20.9504i	−0.734762	−	1.27265i	0.220065	−	0.975485i	$-0.429373\pi$
$272$	−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	$-0.0909870\pi$
$281$	3.94805	+	6.83823i	0.235521	+	0.407934i	−0.723903	+	0.689902i	$0.757654\pi$
$282$		0			0
$283$	−1.10457	−	1.91317i	−0.0656599	−	0.113726i	0.831327	−	0.555784i	$-0.187582\pi$
$283$	−1.10457	−	1.91317i	−0.0656599	−	0.113726i	−0.896987	+	0.442058i	$0.854249\pi$
$284$	−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	0.436858	+	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
$299$	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	$-0.0689821\pi$
$311$	5.32743	+	9.22738i	0.302091	+	0.523237i	−0.674519	+	0.738258i	$0.735649\pi$
$312$		0			0
$313$	8.28074	−	14.3427i	0.468055	−	0.810695i	−0.531279	−	0.847197i	$-0.678288\pi$
$313$	8.28074	−	14.3427i	0.468055	−	0.810695i	0.999334	+	0.0365022i	$0.0116216\pi$
$314$	10.9751			0.619360
$315$		0			0
$316$	1.48541			0.0835609
$317$	−13.3186	+	23.0685i	−0.748046	+	1.29565i	0.200712	+	0.979650i	$0.435674\pi$
$317$	−13.3186	+	23.0685i	−0.748046	+	1.29565i	−0.948758	+	0.316003i	$0.897659\pi$
$318$		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	−0.344786	−	0.938681i	$-0.612049\pi$
$331$	11.6534	−	20.1843i	0.640529	−	1.10943i	0.985315	−	0.170747i	$-0.0546181\pi$
$332$	−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	$-0.0514837\pi$
$338$	−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	$-0.318814\pi$
$347$	−8.56867	−	14.8414i	−0.459990	−	0.796727i	−0.998960	+	0.0455985i	$0.985481\pi$
$348$		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
$353$	16.0613			0.854856			0.427428	−	0.904049i	$-0.359420\pi$
$353$	16.0613			0.854856			0.427428	+	0.904049i	$0.359420\pi$
$354$		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	$-0.285891\pi$
$359$	−6.93200	−	12.0066i	−0.365857	−	0.633683i	−0.988913	+	0.148494i	$0.952557\pi$
$360$		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	$-0.145145\pi$
$383$	35.1416			1.79565			0.897826	+	0.440350i	$0.145145\pi$
$384$		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	$-0.568130\pi$
$389$	−8.37859			−0.424811			−0.212406	+	0.977182i	$0.568130\pi$
$390$		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	0.958421	−	0.285358i	$-0.0921126\pi$
$397$	4.62422	+	8.00938i	0.232083	+	0.401979i	−0.726338	+	0.687338i	$0.758779\pi$
$398$	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	$-0.501172\pi$
$401$	−0.147469			−0.00736425			−0.00368212	+	0.999993i	$0.501172\pi$
$402$		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	0.910461	−	0.413595i	$-0.135727\pi$
$409$	1.96264	+	3.39939i	0.0970463	+	0.168089i	−0.813414	+	0.581685i	$0.802394\pi$
$410$	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	0.486928	+	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
$425$	−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	$-0.791239\pi$
$431$	2.73745	−	4.74140i	0.131858	−	0.228385i	0.924393	+	0.381442i	$0.124572\pi$
$432$		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	−0.796325	−	0.604869i	$-0.793225\pi$
$439$	2.63307	−	4.56062i	0.125670	−	0.217666i	0.921995	+	0.387203i	$0.126559\pi$
$440$	−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	$-0.879136\pi$
$443$	−3.01819	+	5.22765i	−0.143398	+	0.248373i	0.785376	+	0.619019i	$0.212470\pi$
$444$		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	$-0.324987\pi$
$449$	22.1445			1.04507			0.522533	+	0.852619i	$0.324987\pi$
$450$		0			0
$451$	24.3011	−	42.0907i	1.14429	−	1.98197i
$452$	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	−0.796872	−	0.604148i	$-0.793513\pi$
$457$	2.66731	−	4.61992i	0.124772	−	0.216111i	0.921644	+	0.388037i	$0.126847\pi$
$458$	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	$0.308855\pi$
$464$	−1.49688			−0.0694909
$465$		0			0
$466$	5.65390			0.261912
$467$	12.3063	+	21.3152i	0.569468	+	0.986348i	0.996619	+	0.0821676i	$0.0261843\pi$
$467$	12.3063	+	21.3152i	0.569468	+	0.986348i	−0.427150	+	0.904181i	$0.640482\pi$
$468$		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	$-0.497407\pi$
$479$	0.356609			0.0162939			0.00814693	+	0.999967i	$0.497407\pi$
$480$		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	−0.682445	−	0.730937i	$-0.739083\pi$
$487$	6.43920	−	11.1530i	0.291788	−	0.505391i	0.974233	+	0.225546i	$0.0724165\pi$
$488$	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	$-0.793337\pi$
$491$	2.77694	−	4.80981i	0.125322	−	0.217064i	0.921859	+	0.387526i	$0.126670\pi$
$492$		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	$-0.623294\pi$
$503$	−16.9430			−0.755451			−0.377725	+	0.925918i	$0.623294\pi$
$504$		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	$-0.335435\pi$
$509$	22.3025			0.988542			0.494271	+	0.869308i	$0.335435\pi$
$510$		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	$-0.746055\pi$
$521$	6.18044	−	10.7048i	0.270770	−	0.468987i	0.969059	+	0.246828i	$0.0793884\pi$
$522$		0			0
$523$	−3.09572	−	5.36194i	−0.135366	−	0.234461i	0.790371	−	0.612628i	$-0.209888\pi$
$523$	−3.09572	−	5.36194i	−0.135366	−	0.234461i	−0.925737	+	0.378167i	$0.876554\pi$
$524$	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	−0.995872	−	0.0907660i	$-0.971068\pi$
$541$	−13.4100	−	23.2268i	−0.576542	−	0.998600i	0.419330	−	0.907834i	$-0.362265\pi$
$542$	−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	0.979094	−	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
$551$	−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	0.498326	+	0.866990i	$0.333948\pi$
$557$	−11.8399	+	20.5073i	−0.501672	+	0.868921i	−0.999998	+	0.00193169i	$0.999385\pi$
$558$		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	$-0.278886\pi$
$563$	−8.19289	−	14.1905i	−0.345289	−	0.598059i	−0.985406	+	0.170219i	$0.945553\pi$
$564$		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	$-0.940697\pi$
$569$	−7.89397	+	13.6728i	−0.330932	+	0.573192i	0.651763	+	0.758423i	$0.274030\pi$
$570$		0			0
$571$	−3.19076	−	5.52655i	−0.133529	−	0.231279i	0.791506	−	0.611162i	$-0.209298\pi$
$571$	−3.19076	−	5.52655i	−0.133529	−	0.231279i	−0.925035	+	0.379883i	$0.875964\pi$
$572$	−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	−0.165998	−	0.986126i	$-0.553085\pi$
$577$	18.5203	−	32.0781i	0.771011	−	1.33543i	0.937009	−	0.349304i	$-0.113582\pi$
$578$	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	$-0.246960\pi$
$587$	−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
$590$	−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	$-0.0564487\pi$
$593$	8.26449	+	14.3145i	0.339382	+	0.587827i	−0.644935	+	0.764238i	$0.723115\pi$
$594$		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	$-0.223863\pi$
$599$	−4.37412	−	7.57620i	−0.178722	−	0.309555i	−0.941443	+	0.337172i	$0.890530\pi$
$600$		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
$605$	−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	−0.907940	−	0.419101i	$-0.862345\pi$
$613$	−2.25350	+	3.90318i	−0.0910181	+	0.157648i	0.816922	+	0.576749i	$0.195679\pi$
$614$	−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	$-0.945880\pi$
$617$	−8.60078	+	14.8970i	−0.346254	+	0.599730i	0.639327	+	0.768935i	$0.279213\pi$
$618$		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	$-0.826781\pi$
$641$	−43.3216			−1.71110			−0.855550	+	0.517721i	$0.826781\pi$
$642$		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	$0.965324\pi$
$644$	−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	$-0.743486\pi$
$647$	7.08472	−	12.2711i	0.278529	−	0.482427i	0.971019	+	0.239000i	$0.0768197\pi$
$648$		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	$-0.312482\pi$
$653$	28.3963			1.11123			0.555617	+	0.831439i	$0.312482\pi$
$654$		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	$-0.108063\pi$
$659$	4.69961	+	8.13997i	0.183071	+	0.317088i	−0.759854	+	0.650094i	$0.774730\pi$
$660$		0			0
$661$	6.35807	+	11.0125i	0.247300	+	0.428337i	0.962776	−	0.270301i	$-0.0871232\pi$
$661$	6.35807	+	11.0125i	0.247300	+	0.428337i	−0.715476	+	0.698638i	$0.753790\pi$
$662$	−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	−0.971888	−	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
$677$	−5.44592	+	9.43260i	−0.209304	+	0.362524i	−0.951495	−	0.307663i	$-0.900453\pi$
$677$	−5.44592	+	9.43260i	−0.209304	+	0.362524i	0.742192	+	0.670188i	$0.233786\pi$
$678$		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	0.308006	+	0.951384i	$0.400338\pi$
$683$	−17.5079	+	30.3245i	−0.669920	+	1.16034i	−0.977926	+	0.208951i	$0.932995\pi$
$684$		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	−0.934930	−	0.354832i	$-0.884538\pi$
$691$	−4.21041	+	7.29264i	−0.160171	+	0.277425i	0.774759	+	0.632257i	$0.217871\pi$
$692$	−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	$-0.200963\pi$
$701$	42.7453			1.61447			0.807234	+	0.590231i	$0.200963\pi$
$702$		0			0
$703$	9.52918	−	16.5050i	0.359400	−	0.622499i
$704$	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	−0.546240	−	0.837629i	$-0.683941\pi$
$709$	12.0431	−	20.8593i	0.452288	−	0.783386i	0.998528	+	0.0542432i	$0.0172746\pi$
$710$	−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	−0.928954	−	0.370196i	$-0.879291\pi$
$719$	−21.0512	−	36.4617i	−0.785076	−	1.35979i	0.143878	−	0.989595i	$-0.454043\pi$
$720$		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	−0.978218	−	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
$731$	−0.924324			−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	−0.994054	−	0.108884i	$-0.965272\pi$
$739$	−10.9481	+	18.9626i	−0.402731	+	0.697550i	0.591324	+	0.806434i	$0.298606\pi$
$740$	−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	−0.480919	−	0.876765i	$-0.659697\pi$
$743$	14.1426	−	24.4957i	0.518842	−	0.898660i	0.999760	−	0.0218950i	$-0.00696995\pi$
$744$		0			0
$745$	−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	$-0.492755\pi$
$761$	1.25564			0.0455168			0.0227584	+	0.999741i	$0.492755\pi$
$762$		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	−0.500767	−	0.865582i	$-0.666949\pi$
$769$	13.8442	−	23.9788i	0.499233	−	0.864697i	1.00000		0.000885409i	$0.000281834\pi$
$770$	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	$-0.787894\pi$
$773$	3.95544	−	6.85103i	0.142267	−	0.246414i	0.928350	+	0.371707i	$0.121227\pi$
$774$		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	−0.997101	−	0.0760866i	$-0.975757\pi$
$787$	−15.8346	−	27.4264i	−0.564444	−	0.977645i	0.432658	−	0.901558i	$-0.357576\pi$
$788$	−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	−0.394553	−	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
$803$	−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	−0.337813	−	0.941213i	$-0.609687\pi$
$809$	18.3801	−	31.8352i	0.646208	−	1.11927i	0.984021	−	0.178052i	$-0.0569796\pi$
$810$		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	$-0.714719\pi$
$821$	10.4318	−	18.0684i	0.364073	−	0.630592i	0.988627	+	0.150389i	$0.0480527\pi$
$822$		0			0
$823$	−22.7003	−	39.3180i	−0.791282	−	1.37054i	−0.925173	−	0.379545i	$-0.876081\pi$
$823$	−22.7003	−	39.3180i	−0.791282	−	1.37054i	0.133891	−	0.990996i	$-0.457253\pi$
$824$	−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	$-0.470392\pi$
$827$	5.34221			0.185767			0.0928835	+	0.995677i	$0.470392\pi$
$828$		0			0
$829$	−8.45185	+	14.6390i	−0.293545	+	0.508434i	−0.974645	−	0.223755i	$-0.928168\pi$
$829$	−8.45185	+	14.6390i	−0.293545	+	0.508434i	0.681101	+	0.732190i	$0.261502\pi$
$830$	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	$-0.220992\pi$
$839$	−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
$842$	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	0.745597	+	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
$857$	56.3465			1.92476			0.962380	−	0.271708i	$-0.0875886\pi$
$857$	56.3465			1.92476			0.962380	+	0.271708i	$0.0875886\pi$
$858$		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	$-0.104911\pi$
$863$	5.66372	+	9.80984i	0.192795	+	0.333931i	−0.753380	+	0.657585i	$0.771578\pi$
$864$		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	$-0.618874\pi$
$881$	−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	$0.438087\pi$
$884$	−0.0821100	+	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	$-0.596833\pi$
$887$	−17.8420			−0.599076			−0.299538	+	0.954084i	$0.596833\pi$
$888$		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	$-0.200938\pi$
$911$	−3.24338	−	5.61770i	−0.107458	−	0.186123i	−0.914740	+	0.404044i	$0.867604\pi$
$912$		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	0.946150	−	0.323730i	$-0.104937\pi$
$919$	5.84221	+	10.1190i	0.192717	+	0.333795i	−0.753433	+	0.657525i	$0.771603\pi$
$920$	−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	$-0.825706\pi$
$929$	0.730252	−	1.26483i	0.0239588	−	0.0414979i	0.877756	+	0.479108i	$0.159040\pi$
$930$		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	−0.847601	−	0.530633i	$-0.821954\pi$
$941$	−27.0972	−	46.9337i	−0.883343	−	1.52999i	−0.0357414	−	0.999361i	$-0.511379\pi$
$942$		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	0.0541875	−	0.998531i	$-0.482743\pi$
$947$	27.4451	−	47.5364i	0.891847	−	1.54472i	0.837659	−	0.546193i	$-0.183924\pi$
$948$		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	$-0.644301\pi$
$953$	−27.0406			−0.875932			−0.437966	+	0.898991i	$0.644301\pi$
$954$		0			0
$955$	3.60010	−	6.23556i	0.116497	−	0.201778i
$956$	−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	−0.736682	−	0.676240i	$-0.763608\pi$
$967$	6.75729	−	11.7040i	0.217300	−	0.376375i	0.953982	+	0.299865i	$0.0969417\pi$
$968$	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	$-0.233196\pi$
$971$	−6.46557	−	11.1987i	−0.207490	−	0.359383i	−0.950923	+	0.309427i	$0.899863\pi$
$972$		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	0.994821	+	0.101641i	$0.0324094\pi$
$977$	18.2989	+	31.6947i	0.585435	+	1.01400i	−0.409387	+	0.912361i	$0.634257\pi$
$978$		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	$-0.588646\pi$
$983$	−17.2379			−0.549805			−0.274902	+	0.961472i	$0.588646\pi$
$984$		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	−0.718079	−	0.695961i	$-0.754978\pi$
$991$	7.67111	−	13.2867i	0.243681	−	0.422067i	0.961760	+	0.273894i	$0.0883118\pi$
$992$	−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.h.109.3		6
3.2	odd	2		567.2.g.i.109.1		6
7.2	even	3		567.2.h.i.352.1		6
9.2	odd	6		567.2.h.h.298.3		6
9.4	even	3		189.2.e.e.109.3	✓	6
9.5	odd	6		189.2.e.f.109.1	yes	6
9.7	even	3		567.2.h.i.298.1		6
21.2	odd	6		567.2.h.h.352.3		6
63.2	odd	6		567.2.g.i.541.1		6
63.4	even	3		1323.2.a.ba.1.1		3
63.16	even	3	inner	567.2.g.h.541.3		6
63.23	odd	6		189.2.e.f.163.1	yes	6
63.31	odd	6		1323.2.a.z.1.1		3
63.32	odd	6		1323.2.a.x.1.3		3
63.58	even	3		189.2.e.e.163.3	yes	6
63.59	even	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	9.4	even	3
189.2.e.e.163.3	yes	6	63.58	even	3
189.2.e.f.109.1	yes	6	9.5	odd	6
189.2.e.f.163.1	yes	6	63.23	odd	6
567.2.g.h.109.3		6	1.1	even	1	trivial
567.2.g.h.541.3		6	63.16	even	3	inner
567.2.g.i.109.1		6	3.2	odd	2
567.2.g.i.541.1		6	63.2	odd	6
567.2.h.h.298.3		6	9.2	odd	6
567.2.h.h.352.3		6	21.2	odd	6
567.2.h.i.298.1		6	9.7	even	3
567.2.h.i.352.1		6	7.2	even	3
1323.2.a.x.1.3		3	63.32	odd	6
1323.2.a.y.1.3		3	63.59	even	6
1323.2.a.z.1.1		3	63.31	odd	6
1323.2.a.ba.1.1		3	63.4	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 $\F_{q}$

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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