LMFDB - Embedded newform 864.2.bi.a.95.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.13
Character	$\chi$	$=$	864.95
Dual form			864.2.bi.a.191.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.639313 + 1.60974i) q^{3} +(1.25880 - 1.50018i) q^{5} +(-0.917368 + 2.52045i) q^{7} +(-2.18256 - 2.05826i) q^{9} +O(q^{10})$	\(q+(-0.639313 + 1.60974i) q^{3} +(1.25880 - 1.50018i) q^{5} +(-0.917368 + 2.52045i) q^{7} +(-2.18256 - 2.05826i) q^{9} +(-1.09748 + 0.920894i) q^{11} +(-0.343327 + 1.94711i) q^{13} +(1.61014 + 2.98543i) q^{15} +(-0.116347 - 0.0671731i) q^{17} +(-2.14430 + 1.23801i) q^{19} +(-3.47079 - 3.08808i) q^{21} +(-3.02806 + 1.10212i) q^{23} +(0.202279 + 1.14718i) q^{25} +(4.70861 - 2.19749i) q^{27} +(-6.97586 + 1.23003i) q^{29} +(2.22686 + 6.11824i) q^{31} +(-0.780772 - 2.35540i) q^{33} +(2.62634 + 4.54896i) q^{35} +(-3.97244 + 6.88048i) q^{37} +(-2.91485 - 1.79748i) q^{39} +(6.86694 + 1.21083i) q^{41} +(-7.29062 - 8.68863i) q^{43} +(-5.83517 + 0.683287i) q^{45} +(3.00673 + 1.09436i) q^{47} +(-0.148783 - 0.124844i) q^{49} +(0.182514 - 0.144345i) q^{51} -7.88980i q^{53} +2.80564i q^{55} +(-0.622004 - 4.24325i) q^{57} +(0.194256 + 0.163001i) q^{59} +(-11.8108 - 4.29879i) q^{61} +(7.18995 - 3.61284i) q^{63} +(2.48883 + 2.96607i) q^{65} +(-4.87904 - 0.860306i) q^{67} +(0.161740 - 5.57900i) q^{69} +(-4.05398 + 7.02170i) q^{71} +(2.90548 + 5.03244i) q^{73} +(-1.97599 - 0.407791i) q^{75} +(-1.31427 - 3.61094i) q^{77} +(-11.3726 + 2.00530i) q^{79} +(0.527112 + 8.98455i) q^{81} +(2.29255 + 13.0017i) q^{83} +(-0.247230 + 0.0899843i) q^{85} +(2.47972 - 12.0157i) q^{87} +(-3.88936 + 2.24553i) q^{89} +(-4.59262 - 2.65155i) q^{91} +(-11.2725 - 0.326799i) q^{93} +(-0.842004 + 4.77524i) q^{95} +(2.93284 - 2.46095i) q^{97} +(4.29075 + 0.248995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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			0
$2$		0			0
$3$	−0.639313	+	1.60974i	−0.369108	+	0.929387i
$3$	−0.639313	+	1.60974i	−0.369108	+	0.929387i
$4$		0			0
$5$	1.25880	−	1.50018i	0.562953	−	0.670901i	−0.407216	−	0.913332i	$-0.633500\pi$
$5$	1.25880	−	1.50018i	0.562953	−	0.670901i	0.970169	+	0.242431i	$0.0779448\pi$
$6$		0			0
$7$	−0.917368	+	2.52045i	−0.346733	+	0.952640i	0.636659	+	0.771145i	$0.280316\pi$
$7$	−0.917368	+	2.52045i	−0.346733	+	0.952640i	−0.983392	+	0.181495i	$0.941906\pi$
$8$		0			0
$9$	−2.18256	−	2.05826i	−0.727519	−	0.686087i
$10$		0			0
$11$	−1.09748	+	0.920894i	−0.330902	+	0.277660i	−0.793067	−	0.609134i	$-0.791517\pi$
$11$	−1.09748	+	0.920894i	−0.330902	+	0.277660i	0.462165	+	0.886794i	$0.347073\pi$
$12$		0			0
$13$	−0.343327	+	1.94711i	−0.0952219	+	0.540030i	0.899457	+	0.437009i	$0.143962\pi$
$13$	−0.343327	+	1.94711i	−0.0952219	+	0.540030i	−0.994679	+	0.103021i	$0.967149\pi$
$14$		0			0
$15$	1.61014	+	2.98543i	0.415736	+	0.770836i
$16$		0			0
$17$	−0.116347	−	0.0671731i	−0.0282183	−	0.0162919i	0.485824	−	0.874056i	$-0.338519\pi$
$17$	−0.116347	−	0.0671731i	−0.0282183	−	0.0162919i	−0.514043	+	0.857765i	$0.671853\pi$
$18$		0			0
$19$	−2.14430	+	1.23801i	−0.491935	+	0.284019i	−0.725377	−	0.688352i	$-0.758335\pi$
$19$	−2.14430	+	1.23801i	−0.491935	+	0.284019i	0.233442	+	0.972371i	$0.425001\pi$
$20$		0			0
$21$	−3.47079	−	3.08808i	−0.757389	−	0.673875i
$22$		0			0
$23$	−3.02806	+	1.10212i	−0.631393	+	0.229808i	−0.637838	−	0.770171i	$-0.720171\pi$
$23$	−3.02806	+	1.10212i	−0.631393	+	0.229808i	0.00644430	+	0.999979i	$0.497949\pi$
$24$		0			0
$25$	0.202279	+	1.14718i	0.0404558	+	0.229436i
$26$		0			0
$27$	4.70861	−	2.19749i	0.906173	−	0.422906i
$28$		0			0
$29$	−6.97586	+	1.23003i	−1.29539	+	0.228411i	−0.778501	−	0.627644i	$-0.784019\pi$
$29$	−6.97586	+	1.23003i	−1.29539	+	0.228411i	−0.516884	+	0.856055i	$0.672908\pi$
$30$		0			0
$31$	2.22686	+	6.11824i	0.399955	+	1.09887i	0.962306	+	0.271969i	$0.0876749\pi$
$31$	2.22686	+	6.11824i	0.399955	+	1.09887i	−0.562351	+	0.826899i	$0.690103\pi$
$32$		0			0
$33$	−0.780772	−	2.35540i	−0.135915	−	0.410023i
$34$		0			0
$35$	2.62634	+	4.54896i	0.443933	+	0.768915i
$36$		0			0
$37$	−3.97244	+	6.88048i	−0.653066	+	1.13114i	0.329309	+	0.944222i	$0.393184\pi$
$37$	−3.97244	+	6.88048i	−0.653066	+	1.13114i	−0.982375	+	0.186921i	$0.940149\pi$
$38$		0			0
$39$	−2.91485	−	1.79748i	−0.466750	−	0.287827i
$40$		0			0
$41$	6.86694	+	1.21083i	1.07244	+	0.189099i	0.681868	−	0.731475i	$-0.261168\pi$
$41$	6.86694	+	1.21083i	1.07244	+	0.189099i	0.390568	+	0.920574i	$0.372279\pi$
$42$		0			0
$43$	−7.29062	−	8.68863i	−1.11181	−	1.32500i	−0.940503	−	0.339785i	$-0.889646\pi$
$43$	−7.29062	−	8.68863i	−1.11181	−	1.32500i	−0.171307	−	0.985218i	$-0.554799\pi$
$44$		0			0
$45$	−5.83517	+	0.683287i	−0.869856	+	0.101858i
$46$		0			0
$47$	3.00673	+	1.09436i	0.438576	+	0.159629i	0.551865	−	0.833933i	$-0.313916\pi$
$47$	3.00673	+	1.09436i	0.438576	+	0.159629i	−0.113289	+	0.993562i	$0.536139\pi$
$48$		0			0
$49$	−0.148783	−	0.124844i	−0.0212548	−	0.0178349i
$50$		0			0
$51$	0.182514	−	0.144345i	0.0255571	−	0.0202123i
$52$		0			0
$53$		−	7.88980i		−	1.08375i	−0.840460	−	0.541874i	$-0.817715\pi$
$53$		−	7.88980i		−	1.08375i	0.840460	−	0.541874i	$-0.182285\pi$
$54$		0			0
$55$			2.80564i			0.378312i
$56$		0			0
$57$	−0.622004	−	4.24325i	−0.0823864	−	0.562032i
$58$		0			0
$59$	0.194256	+	0.163001i	0.0252900	+	0.0212209i	0.655345	−	0.755330i	$-0.272523\pi$
$59$	0.194256	+	0.163001i	0.0252900	+	0.0212209i	−0.630055	+	0.776551i	$0.716968\pi$
$60$		0			0
$61$	−11.8108	−	4.29879i	−1.51222	−	0.550404i	−0.553030	−	0.833161i	$-0.686529\pi$
$61$	−11.8108	−	4.29879i	−1.51222	−	0.550404i	−0.959191	+	0.282757i	$0.908751\pi$
$62$		0			0
$63$	7.18995	−	3.61284i	0.905849	−	0.455175i
$64$		0			0
$65$	2.48883	+	2.96607i	0.308701	+	0.367896i
$66$		0			0
$67$	−4.87904	−	0.860306i	−0.596070	−	0.105103i	−0.132529	−	0.991179i	$-0.542310\pi$
$67$	−4.87904	−	0.860306i	−0.596070	−	0.105103i	−0.463540	+	0.886076i	$0.653421\pi$
$68$		0			0
$69$	0.161740	−	5.57900i	0.0194713	−	0.671633i
$70$		0			0
$71$	−4.05398	+	7.02170i	−0.481119	+	0.833323i	−0.999765	−	0.0216663i	$-0.993103\pi$
$71$	−4.05398	+	7.02170i	−0.481119	+	0.833323i	0.518646	+	0.854989i	$0.326436\pi$
$72$		0			0
$73$	2.90548	+	5.03244i	0.340061	+	0.589003i	0.984444	−	0.175700i	$-0.0562189\pi$
$73$	2.90548	+	5.03244i	0.340061	+	0.589003i	−0.644383	+	0.764703i	$0.722886\pi$
$74$		0			0
$75$	−1.97599	−	0.407791i	−0.228168	−	0.0470876i
$76$		0			0
$77$	−1.31427	−	3.61094i	−0.149775	−	0.411505i
$78$		0			0
$79$	−11.3726	+	2.00530i	−1.27952	+	0.225614i	−0.771777	−	0.635893i	$-0.780632\pi$
$79$	−11.3726	+	2.00530i	−1.27952	+	0.225614i	−0.507745	+	0.861507i	$0.669521\pi$
$80$		0			0
$81$	0.527112	+	8.98455i	0.0585681	+	0.998283i
$82$		0			0
$83$	2.29255	+	13.0017i	0.251640	+	1.42712i	0.804553	+	0.593880i	$0.202405\pi$
$83$	2.29255	+	13.0017i	0.251640	+	1.42712i	−0.552914	+	0.833238i	$0.686484\pi$
$84$		0			0
$85$	−0.247230	+	0.0899843i	−0.0268158	+	0.00976017i
$86$		0			0
$87$	2.47972	−	12.0157i	0.265854	−	1.28822i
$88$		0			0
$89$	−3.88936	+	2.24553i	−0.412272	+	0.238025i	−0.691765	−	0.722122i	$-0.743167\pi$
$89$	−3.88936	+	2.24553i	−0.412272	+	0.238025i	0.279494	+	0.960148i	$0.409833\pi$
$90$		0			0
$91$	−4.59262	−	2.65155i	−0.481438	−	0.277958i
$92$		0			0
$93$	−11.2725	−	0.326799i	−1.16890	−	0.0338875i
$94$		0			0
$95$	−0.842004	+	4.77524i	−0.0863878	+	0.489929i
$96$		0			0
$97$	2.93284	−	2.46095i	0.297785	−	0.249871i	−0.481637	−	0.876371i	$-0.659958\pi$
$97$	2.93284	−	2.46095i	0.297785	−	0.249871i	0.779422	+	0.626500i	$0.215513\pi$
$98$		0			0
$99$	4.29075	+	0.248995i	0.431237	+	0.0250250i
$100$		0			0
$101$	−1.33897	+	3.67879i	−0.133233	+	0.366054i	−0.988312	−	0.152443i	$-0.951286\pi$
$101$	−1.33897	+	3.67879i	−0.133233	+	0.366054i	0.855080	+	0.518497i	$0.173508\pi$
$102$		0			0
$103$	4.65908	−	5.55248i	0.459073	−	0.547102i	−0.486001	−	0.873958i	$-0.661545\pi$
$103$	4.65908	−	5.55248i	0.459073	−	0.547102i	0.945074	+	0.326856i	$0.105989\pi$
$104$		0			0
$105$	−9.00172	+	1.31953i	−0.878478	+	0.128773i
$106$		0			0
$107$	15.7876			1.52624			0.763122	−	0.646254i	$-0.223665\pi$
$107$	15.7876			1.52624			0.763122	+	0.646254i	$0.223665\pi$
$108$		0			0
$109$	−2.10310			−0.201441			−0.100720	−	0.994915i	$-0.532115\pi$
$109$	−2.10310			−0.201441			−0.100720	+	0.994915i	$0.532115\pi$
$110$		0			0
$111$	−8.53617	−	10.7934i	−0.810218	−	1.02446i
$112$		0			0
$113$	12.5413	−	14.9461i	1.17978	−	1.40601i	0.285578	−	0.958355i	$-0.407814\pi$
$113$	12.5413	−	14.9461i	1.17978	−	1.40601i	0.894206	−	0.447656i	$-0.147741\pi$
$114$		0			0
$115$	−2.15834	+	5.92998i	−0.201266	+	0.552974i
$116$		0			0
$117$	4.75699	−	3.54301i	0.439784	−	0.327552i
$118$		0			0
$119$	0.276040	−	0.231625i	0.0253045	−	0.0212330i
$120$		0			0
$121$	−1.55372	+	8.81156i	−0.141247	+	0.801051i
$122$		0			0
$123$	−6.33925	+	10.2799i	−0.571591	+	0.926910i
$124$		0			0
$125$	10.4555	+	6.03648i	0.935168	+	0.539920i
$126$		0			0
$127$	4.52975	−	2.61525i	0.401950	−	0.232066i	−0.285375	−	0.958416i	$-0.592118\pi$
$127$	4.52975	−	2.61525i	0.401950	−	0.232066i	0.687325	+	0.726350i	$0.258785\pi$
$128$		0			0
$129$	18.6475	−	6.18129i	1.64182	−	0.544232i
$130$		0			0
$131$	5.33274	−	1.94096i	0.465924	−	0.169582i	−0.0983810	−	0.995149i	$-0.531366\pi$
$131$	5.33274	−	1.94096i	0.465924	−	0.169582i	0.564305	+	0.825566i	$0.309144\pi$
$132$		0			0
$133$	−1.15323	−	6.54030i	−0.0999978	−	0.567116i
$134$		0			0
$135$	2.63058	−	9.82997i	0.226405	−	0.846029i
$136$		0			0
$137$	15.7082	−	2.76978i	1.34204	−	0.236638i	0.543920	−	0.839137i	$-0.316939\pi$
$137$	15.7082	−	2.76978i	1.34204	−	0.236638i	0.798120	+	0.602499i	$0.205828\pi$
$138$		0			0
$139$	−5.94211	−	16.3258i	−0.504003	−	1.38474i	−0.887334	−	0.461127i	$-0.847445\pi$
$139$	−5.94211	−	16.3258i	−0.504003	−	1.38474i	0.383331	−	0.923611i	$-0.374777\pi$
$140$		0			0
$141$	−3.68388	+	4.14043i	−0.310239	+	0.348687i
$142$		0			0
$143$	−1.41628	−	2.45308i	−0.118436	−	0.205137i
$144$		0			0
$145$	−6.93595	+	12.0134i	−0.575999	+	0.997660i
$146$		0			0
$147$	0.296086	−	0.159689i	0.0244208	−	0.0131709i
$148$		0			0
$149$	16.5852	+	2.92443i	1.35872	+	0.239578i	0.805073	−	0.593176i	$-0.202126\pi$
$149$	16.5852	+	2.92443i	1.35872	+	0.239578i	0.553643	+	0.832754i	$0.313237\pi$
$150$		0			0
$151$	−3.36603	−	4.01148i	−0.273924	−	0.326449i	0.611491	−	0.791251i	$-0.290570\pi$
$151$	−3.36603	−	4.01148i	−0.273924	−	0.326449i	−0.885415	+	0.464802i	$0.846126\pi$
$152$		0			0
$153$	0.115675	+	0.386082i	0.00935174	+	0.0312129i
$154$		0			0
$155$	11.9816	+	4.36096i	0.962388	+	0.350281i
$156$		0			0
$157$	13.3353	+	11.1896i	1.06427	+	0.893031i	0.994521	−	0.104534i	$-0.0333350\pi$
$157$	13.3353	+	11.1896i	1.06427	+	0.893031i	0.0697511	+	0.997564i	$0.477779\pi$
$158$		0			0
$159$	12.7006	+	5.04405i	1.00722	+	0.400020i
$160$		0			0
$161$		−	8.64311i		−	0.681173i
$162$		0			0
$163$			4.36267i			0.341711i	0.985296	+	0.170855i	$0.0546531\pi$
$163$			4.36267i			0.341711i	−0.985296	+	0.170855i	$0.945347\pi$
$164$		0			0
$165$	−4.51636	−	1.79368i	−0.351598	−	0.139638i
$166$		0			0
$167$	−9.11224	−	7.64608i	−0.705126	−	0.591671i	0.218101	−	0.975926i	$-0.430014\pi$
$167$	−9.11224	−	7.64608i	−0.705126	−	0.591671i	−0.923227	+	0.384255i	$0.874458\pi$
$168$		0			0
$169$	8.54265	+	3.10927i	0.657127	+	0.239175i
$170$		0			0
$171$	7.22820	+	1.71150i	0.552754	+	0.130881i
$172$		0			0
$173$	3.10857	+	3.70465i	0.236340	+	0.281659i	0.871158	−	0.491002i	$-0.163369\pi$
$173$	3.10857	+	3.70465i	0.236340	+	0.281659i	−0.634818	+	0.772662i	$0.718925\pi$
$174$		0			0
$175$	−3.07698	−	0.542554i	−0.232598	−	0.0410132i
$176$		0			0
$177$	−0.386580	+	0.208495i	−0.0290571	+	0.0156714i
$178$		0			0
$179$	−10.1656	+	17.6073i	−0.759812	+	1.31603i	0.183135	+	0.983088i	$0.441376\pi$
$179$	−10.1656	+	17.6073i	−0.759812	+	1.31603i	−0.942946	+	0.332944i	$0.891958\pi$
$180$		0			0
$181$	5.61981	+	9.73380i	0.417717	+	0.723508i	0.995709	−	0.0925348i	$-0.0294969\pi$
$181$	5.61981	+	9.73380i	0.417717	+	0.723508i	−0.577992	+	0.816042i	$0.696164\pi$
$182$		0			0
$183$	14.4708	−	16.2641i	1.06971	−	1.20228i
$184$		0			0
$185$	5.32144	+	14.6205i	0.391240	+	1.07492i
$186$		0			0
$187$	0.189548	−	0.0334224i	0.0138611	−	0.00244409i
$188$		0			0
$189$	1.21912	+	13.8837i	0.0886777	+	1.00989i
$190$		0			0
$191$	1.24356	+	7.05261i	0.0899812	+	0.510309i	0.996170	+	0.0874357i	$0.0278672\pi$
$191$	1.24356	+	7.05261i	0.0899812	+	0.510309i	−0.906189	+	0.422873i	$0.861022\pi$
$192$		0			0
$193$	14.1335	−	5.14418i	1.01735	−	0.370287i	0.221101	−	0.975251i	$-0.429035\pi$
$193$	14.1335	−	5.14418i	1.01735	−	0.370287i	0.796253	+	0.604964i	$0.206813\pi$
$194$		0			0
$195$	−6.36576	+	2.11013i	−0.455862	+	0.151110i
$196$		0			0
$197$	5.09671	−	2.94259i	0.363126	−	0.209651i	−0.307325	−	0.951605i	$-0.599434\pi$
$197$	5.09671	−	2.94259i	0.363126	−	0.209651i	0.670451	+	0.741954i	$0.266101\pi$
$198$		0			0
$199$	10.5139	+	6.07023i	0.745314	+	0.430307i	0.823998	−	0.566592i	$-0.191739\pi$
$199$	10.5139	+	6.07023i	0.745314	+	0.430307i	−0.0786843	+	0.996900i	$0.525072\pi$
$200$		0			0
$201$	4.50411	−	7.30400i	0.317695	−	0.515185i
$202$		0			0
$203$	3.29920	−	18.7107i	0.231558	−	1.31323i
$204$		0			0
$205$	10.4606	−	8.77746i	0.730598	−	0.613045i
$206$		0			0
$207$	8.87736	+	3.82709i	0.617019	+	0.266001i
$208$		0			0
$209$	1.21324	−	3.33336i	0.0839219	−	0.230573i
$210$		0			0
$211$	13.6424	−	16.2584i	0.939181	−	1.11927i	−0.0535077	−	0.998567i	$-0.517040\pi$
$211$	13.6424	−	16.2584i	0.939181	−	1.11927i	0.992688	−	0.120705i	$-0.0385154\pi$
$212$		0			0
$213$	−8.71139	−	11.0149i	−0.596894	−	0.754731i
$214$		0			0
$215$	−22.2120			−1.51484
$216$		0			0
$217$	−17.4636			−1.18550
$218$		0			0
$219$	−9.95847	+	1.45978i	−0.672931	+	0.0986427i
$220$		0			0
$221$	0.170738	−	0.203478i	0.0114851	−	0.0136874i
$222$		0			0
$223$	−4.98071	+	13.6844i	−0.333533	+	0.916374i	0.653652	+	0.756795i	$0.273236\pi$
$223$	−4.98071	+	13.6844i	−0.333533	+	0.916374i	−0.987185	+	0.159579i	$0.948986\pi$
$224$		0			0
$225$	1.91971	−	2.92013i	0.127981	−	0.194676i
$226$		0			0
$227$	22.8728	−	19.1925i	1.51812	−	1.27385i	0.672457	−	0.740136i	$-0.265239\pi$
$227$	22.8728	−	19.1925i	1.51812	−	1.27385i	0.845663	−	0.533718i	$-0.179205\pi$
$228$		0			0
$229$	−4.86473	+	27.5893i	−0.321471	+	1.82315i	0.211927	+	0.977286i	$0.432026\pi$
$229$	−4.86473	+	27.5893i	−0.321471	+	1.82315i	−0.533397	+	0.845865i	$0.679085\pi$
$230$		0			0
$231$	6.65292	+	0.192875i	0.437730	+	0.0126902i
$232$		0			0
$233$	−13.7921	−	7.96289i	−0.903553	−	0.521667i	−0.0252017	−	0.999682i	$-0.508023\pi$
$233$	−13.7921	−	7.96289i	−0.903553	−	0.521667i	−0.878351	+	0.478016i	$0.841356\pi$
$234$		0			0
$235$	5.42661	−	3.13305i	0.353993	−	0.204378i
$236$		0			0
$237$	4.04265	−	19.5891i	0.262599	−	1.27245i
$238$		0			0
$239$	−2.74901	+	1.00056i	−0.177819	+	0.0647208i	−0.429395	−	0.903117i	$-0.641273\pi$
$239$	−2.74901	+	1.00056i	−0.177819	+	0.0647208i	0.251576	+	0.967837i	$0.419051\pi$
$240$		0			0
$241$	3.48514	+	19.7652i	0.224498	+	1.27319i	0.863643	+	0.504103i	$0.168177\pi$
$241$	3.48514	+	19.7652i	0.224498	+	1.27319i	−0.639146	+	0.769086i	$0.720712\pi$
$242$		0			0
$243$	−14.7998	−	4.89543i	−0.949409	−	0.314042i
$244$		0			0
$245$	−0.374577	+	0.0660480i	−0.0239309	+	0.00421965i
$246$		0			0
$247$	−1.67434	−	4.60022i	−0.106536	−	0.292705i
$248$		0			0
$249$	−22.3950	−	4.62173i	−1.41923	−	0.292890i
$250$		0			0
$251$	−8.25781	−	14.3029i	−0.521228	−	0.902794i	−0.999695	−	0.0246881i	$-0.992141\pi$
$251$	−8.25781	−	14.3029i	−0.521228	−	0.902794i	0.478467	−	0.878105i	$-0.341193\pi$
$252$		0			0
$253$	2.30829	−	3.99808i	0.145121	−	0.251357i
$254$		0			0
$255$	0.0132055	−	0.455505i	0.000826962	−	0.0285248i
$256$		0			0
$257$	−10.9724	−	1.93474i	−0.684442	−	0.120686i	−0.179394	−	0.983777i	$-0.557414\pi$
$257$	−10.9724	−	1.93474i	−0.684442	−	0.120686i	−0.505047	+	0.863092i	$0.668525\pi$
$258$		0			0
$259$	−13.6977	−	16.3243i	−0.851133	−	1.01434i
$260$		0			0
$261$	17.7569	+	11.6735i	1.09913	+	0.722574i
$262$		0			0
$263$	5.59912	+	2.03791i	0.345256	+	0.125663i	0.508828	−	0.860868i	$-0.330079\pi$
$263$	5.59912	+	2.03791i	0.345256	+	0.125663i	−0.163571	+	0.986532i	$0.552301\pi$
$264$		0			0
$265$	−11.8361	−	9.93169i	−0.727087	−	0.610099i
$266$		0			0
$267$	−1.12820	−	7.69648i	−0.0690448	−	0.471017i
$268$		0			0
$269$		−	7.75790i		−	0.473008i	−0.971631	−	0.236504i	$-0.923998\pi$
$269$		−	7.75790i		−	0.473008i	0.971631	−	0.236504i	$-0.0760016\pi$
$270$		0			0
$271$			13.1956i			0.801578i	0.916170	+	0.400789i	$0.131264\pi$
$271$			13.1956i			0.801578i	−0.916170	+	0.400789i	$0.868736\pi$
$272$		0			0
$273$	7.20445	−	5.69778i	0.436033	−	0.344845i
$274$		0			0
$275$	−1.27843	−	1.07273i	−0.0770922	−	0.0646881i
$276$		0			0
$277$	−13.3320	−	4.85246i	−0.801043	−	0.291556i	−0.0911244	−	0.995840i	$-0.529046\pi$
$277$	−13.3320	−	4.85246i	−0.801043	−	0.291556i	−0.709919	+	0.704284i	$0.751268\pi$
$278$		0			0
$279$	7.73270	−	17.9369i	0.462945	−	1.07385i
$280$		0			0
$281$	11.2066	+	13.3555i	0.668531	+	0.796724i	0.988583	−	0.150675i	$-0.0481449\pi$
$281$	11.2066	+	13.3555i	0.668531	+	0.796724i	−0.320052	+	0.947400i	$0.603700\pi$
$282$		0			0
$283$	−26.0366	−	4.59096i	−1.54772	−	0.272904i	−0.666459	−	0.745541i	$-0.732191\pi$
$283$	−26.0366	−	4.59096i	−1.54772	−	0.272904i	−0.881257	+	0.472637i	$0.843302\pi$
$284$		0			0
$285$	−7.14861	−	4.40829i	−0.423447	−	0.261124i
$286$		0			0
$287$	−9.35134	+	16.1970i	−0.551992	+	0.956078i
$288$		0			0
$289$	−8.49098	−	14.7068i	−0.499469	−	0.865106i
$290$		0			0
$291$	2.08649	+	6.29444i	0.122312	+	0.368987i
$292$		0			0
$293$	−7.78643	−	21.3931i	−0.454888	−	1.24980i	−0.929245	−	0.369463i	$-0.879542\pi$
$293$	−7.78643	−	21.3931i	−0.454888	−	1.24980i	0.474357	−	0.880333i	$-0.342681\pi$
$294$		0			0
$295$	0.489060	−	0.0862346i	0.0284742	−	0.00502077i
$296$		0			0
$297$	−3.14395	+	6.74783i	−0.182431	+	0.391549i
$298$		0			0
$299$	−1.10634	−	6.27434i	−0.0639810	−	0.362854i
$300$		0			0
$301$	28.5874	−	10.4050i	1.64775	−	0.599732i
$302$		0			0
$303$	−5.06590	−	4.50730i	−0.291028	−	0.258938i
$304$		0			0
$305$	−21.3164	+	12.3071i	−1.22058	+	0.704700i
$306$		0			0
$307$	11.9395	+	6.89327i	0.681423	+	0.393420i	0.800391	−	0.599478i	$-0.204625\pi$
$307$	11.9395	+	6.89327i	0.681423	+	0.393420i	−0.118968	+	0.992898i	$0.537959\pi$
$308$		0			0
$309$	5.95946	+	11.0497i	0.339022	+	0.628596i
$310$		0			0
$311$	4.12670	−	23.4037i	0.234004	−	1.32710i	−0.610698	−	0.791864i	$-0.709111\pi$
$311$	4.12670	−	23.4037i	0.234004	−	1.32710i	0.844702	−	0.535237i	$-0.179778\pi$
$312$		0			0
$313$	13.5559	−	11.3747i	0.766225	−	0.642939i	−0.173514	−	0.984831i	$-0.555512\pi$
$313$	13.5559	−	11.3747i	0.766225	−	0.642939i	0.939739	+	0.341893i	$0.111068\pi$
$314$		0			0
$315$	3.63081	−	15.3341i	0.204573	−	0.863977i
$316$		0			0
$317$	−11.4288	+	31.4003i	−0.641904	+	1.76362i	0.00375854	+	0.999993i	$0.498804\pi$
$317$	−11.4288	+	31.4003i	−0.641904	+	1.76362i	−0.645662	+	0.763623i	$0.723419\pi$
$318$		0			0
$319$	6.52313	−	7.77397i	0.365225	−	0.435259i
$320$		0			0
$321$	−10.0932	+	25.4140i	−0.563348	+	1.41847i
$322$		0			0
$323$	0.332644			0.0185088
$324$		0			0
$325$	−2.30313			−0.127755
$326$		0			0
$327$	1.34454	−	3.38546i	0.0743533	−	0.187216i
$328$		0			0
$329$	−5.51655	+	6.57437i	−0.304137	+	0.362457i
$330$		0			0
$331$	−4.89541	+	13.4500i	−0.269076	+	0.739281i	0.729399	+	0.684088i	$0.239800\pi$
$331$	−4.89541	+	13.4500i	−0.269076	+	0.739281i	−0.998476	+	0.0551929i	$0.982423\pi$
$332$		0			0
$333$	22.8319	−	6.84070i	1.25118	−	0.374868i
$334$		0			0
$335$	−7.43235	+	6.23649i	−0.406073	+	0.340736i
$336$		0			0
$337$	0.470811	−	2.67010i	0.0256467	−	0.145450i	−0.969295	−	0.245899i	$-0.920917\pi$
$337$	0.470811	−	2.67010i	0.0256467	−	0.145450i	0.994942	+	0.100449i	$0.0320280\pi$
$338$		0			0
$339$	16.0416	+	29.7435i	0.871261	+	1.61545i
$340$		0			0
$341$	−8.07818	−	4.66394i	−0.437458	−	0.252567i
$342$		0			0
$343$	−15.8089	+	9.12724i	−0.853598	+	0.492825i
$344$		0			0
$345$	−8.16591	−	7.26549i	−0.439638	−	0.391161i
$346$		0			0
$347$	14.0854	−	5.12665i	0.756142	−	0.275213i	0.0649538	−	0.997888i	$-0.479310\pi$
$347$	14.0854	−	5.12665i	0.756142	−	0.275213i	0.691188	+	0.722675i	$0.257088\pi$
$348$		0			0
$349$	−2.93512	−	16.6459i	−0.157113	−	0.891033i	−0.956828	−	0.290653i	$-0.906127\pi$
$349$	−2.93512	−	16.6459i	−0.157113	−	0.891033i	0.799715	−	0.600379i	$-0.204984\pi$
$350$		0			0
$351$	2.66214	+	9.92263i	0.142095	+	0.529631i
$352$		0			0
$353$	−14.5351	+	2.56293i	−0.773625	+	0.136411i	−0.546505	−	0.837456i	$-0.684042\pi$
$353$	−14.5351	+	2.56293i	−0.773625	+	0.136411i	−0.227120	+	0.973867i	$0.572931\pi$
$354$		0			0
$355$	5.43066	+	14.9206i	0.288230	+	0.791905i
$356$		0			0
$357$	0.196381	+	0.592434i	0.0103936	+	0.0313549i
$358$		0			0
$359$	7.79307	+	13.4980i	0.411303	+	0.712397i	0.995032	−	0.0995508i	$-0.0317406\pi$
$359$	7.79307	+	13.4980i	0.411303	+	0.712397i	−0.583730	+	0.811948i	$0.698407\pi$
$360$		0			0
$361$	−6.43466	+	11.1452i	−0.338666	+	0.586587i
$362$		0			0
$363$	−13.1911	−	8.13443i	−0.692351	−	0.426947i
$364$		0			0
$365$	11.2070	+	1.97610i	0.586601	+	0.103434i
$366$		0			0
$367$	18.7485	+	22.3436i	0.978663	+	1.16632i	0.986066	+	0.166352i	$0.0531989\pi$
$367$	18.7485	+	22.3436i	0.978663	+	1.16632i	−0.00740359	+	0.999973i	$0.502357\pi$
$368$		0			0
$369$	−12.4953	−	16.7767i	−0.650479	−	0.873358i
$370$		0			0
$371$	19.8858	+	7.23785i	1.03242	+	0.375771i
$372$		0			0
$373$	1.87518	+	1.57347i	0.0970933	+	0.0814710i	0.690042	−	0.723769i	$-0.257592\pi$
$373$	1.87518	+	1.57347i	0.0970933	+	0.0814710i	−0.592949	+	0.805240i	$0.702036\pi$
$374$		0			0
$375$	−16.4015	+	12.9715i	−0.846972	+	0.669844i
$376$		0			0
$377$		−	14.0051i		−	0.721297i
$378$		0			0
$379$		−	6.41012i		−	0.329266i	−0.986355	−	0.164633i	$-0.947356\pi$
$379$		−	6.41012i		−	0.329266i	0.986355	−	0.164633i	$-0.0526439\pi$
$380$		0			0
$381$	1.31396	+	8.96370i	0.0673162	+	0.459224i
$382$		0			0
$383$	−1.56795	−	1.31566i	−0.0801182	−	0.0672272i	0.601849	−	0.798610i	$-0.294431\pi$
$383$	−1.56795	−	1.31566i	−0.0801182	−	0.0672272i	−0.681967	+	0.731383i	$0.738875\pi$
$384$		0			0
$385$	−7.07147	−	2.57380i	−0.360395	−	0.131173i
$386$		0			0
$387$	−1.97127	+	33.9694i	−0.100205	+	1.72676i
$388$		0			0
$389$	3.33911	+	3.97940i	0.169300	+	0.201763i	0.844023	−	0.536308i	$-0.180181\pi$
$389$	3.33911	+	3.97940i	0.169300	+	0.201763i	−0.674723	+	0.738071i	$0.735737\pi$
$390$		0			0
$391$	0.426339	+	0.0751751i	0.0215609	+	0.00380177i
$392$		0			0
$393$	−0.284843	+	9.82524i	−0.0143684	+	0.495618i
$394$		0			0
$395$	−11.3076	+	19.5853i	−0.568946	+	0.985443i
$396$		0			0
$397$	−8.92858	−	15.4648i	−0.448113	−	0.776154i	0.550150	−	0.835066i	$-0.314570\pi$
$397$	−8.92858	−	15.4648i	−0.448113	−	0.776154i	−0.998263	+	0.0589115i	$0.981237\pi$
$398$		0			0
$399$	11.2655	+	2.32489i	0.563980	+	0.116390i
$400$		0			0
$401$	5.45735	+	14.9939i	0.272527	+	0.748762i	0.998157	+	0.0606770i	$0.0193260\pi$
$401$	5.45735	+	14.9939i	0.272527	+	0.748762i	−0.725631	+	0.688085i	$0.758452\pi$
$402$		0			0
$403$	−12.6774	+	2.23537i	−0.631507	+	0.111352i
$404$		0			0
$405$	14.1420	+	10.5190i	0.702721	+	0.522693i
$406$		0			0
$407$	−1.97652	−	11.2094i	−0.0979723	−	0.555628i
$408$		0			0
$409$	34.0448	−	12.3913i	1.68341	−	0.612710i	0.689635	−	0.724157i	$-0.257771\pi$
$409$	34.0448	−	12.3913i	1.68341	−	0.612710i	0.993770	+	0.111447i	$0.0355486\pi$
$410$		0			0
$411$	−5.58381	+	27.0569i	−0.275429	+	1.33462i
$412$		0			0
$413$	−0.589039	+	0.340082i	−0.0289847	+	0.0167343i
$414$		0			0
$415$	22.3907	+	12.9273i	1.09912	+	0.634575i
$416$		0			0
$417$	30.0793	+	0.872027i	1.47299	+	0.0427033i
$418$		0			0
$419$	−2.68431	+	15.2235i	−0.131137	+	0.743717i	0.846335	+	0.532652i	$0.178804\pi$
$419$	−2.68431	+	15.2235i	−0.131137	+	0.743717i	−0.977472	+	0.211065i	$0.932307\pi$
$420$		0			0
$421$	−14.8837	+	12.4889i	−0.725386	+	0.608671i	−0.928870	−	0.370407i	$-0.879218\pi$
$421$	−14.8837	+	12.4889i	−0.725386	+	0.608671i	0.203483	+	0.979078i	$0.434774\pi$
$422$		0			0
$423$	−4.30988	−	8.57714i	−0.209553	−	0.417035i
$424$		0			0
$425$	0.0535251	−	0.147059i	0.00259635	−	0.00713341i
$426$		0			0
$427$	21.6698	−	25.8250i	1.04867	−	1.24976i
$428$		0			0
$429$	4.85428	−	0.711573i	0.234367	−	0.0343551i
$430$		0			0
$431$	−23.6619			−1.13975			−0.569877	−	0.821730i	$-0.693009\pi$
$431$	−23.6619			−1.13975			−0.569877	+	0.821730i	$0.693009\pi$
$432$		0			0
$433$	−37.7192			−1.81267			−0.906335	−	0.422559i	$-0.861132\pi$
$433$	−37.7192			−1.81267			−0.906335	+	0.422559i	$0.861132\pi$
$434$		0			0
$435$	−14.9043	−	18.8454i	−0.714606	−	0.903570i
$436$		0			0
$437$	5.12861	−	6.11204i	0.245335	−	0.292379i
$438$		0			0
$439$	10.0968	−	27.7407i	0.481893	−	1.32399i	−0.425975	−	0.904735i	$-0.640069\pi$
$439$	10.0968	−	27.7407i	0.481893	−	1.32399i	0.907868	−	0.419256i	$-0.137709\pi$
$440$		0			0
$441$	0.0677663	+	0.578714i	0.00322697	+	0.0275578i
$442$		0			0
$443$	−11.3998	+	9.56559i	−0.541622	+	0.454475i	−0.872092	−	0.489341i	$-0.837237\pi$
$443$	−11.3998	+	9.56559i	−0.541622	+	0.454475i	0.330470	+	0.943817i	$0.392793\pi$
$444$		0			0
$445$	−1.52724	+	8.66142i	−0.0723982	+	0.410591i
$446$		0			0
$447$	−15.3107	+	24.8284i	−0.724174	+	1.17434i
$448$		0			0
$449$	−30.0475	−	17.3479i	−1.41803	−	0.818700i	−0.421904	−	0.906641i	$-0.638638\pi$
$449$	−30.0475	−	17.3479i	−1.41803	−	0.818700i	−0.996126	+	0.0879412i	$0.971971\pi$
$450$		0			0
$451$	−8.65137	+	4.99487i	−0.407377	+	0.235199i
$452$		0			0
$453$	8.60940	−	2.85386i	0.404505	−	0.134086i
$454$		0			0
$455$	−9.75901	+	3.55199i	−0.457509	+	0.166520i
$456$		0			0
$457$	−7.08043	−	40.1551i	−0.331209	−	1.87838i	−0.461866	−	0.886950i	$-0.652820\pi$
$457$	−7.08043	−	40.1551i	−0.331209	−	1.87838i	0.130658	−	0.991428i	$-0.458291\pi$
$458$		0			0
$459$	−0.695446	−	0.0606209i	−0.0324607	−	0.00282954i
$460$		0			0
$461$	−12.2778	+	2.16490i	−0.571832	+	0.100829i	−0.452085	−	0.891975i	$-0.649320\pi$
$461$	−12.2778	+	2.16490i	−0.571832	+	0.100829i	−0.119747	+	0.992804i	$0.538208\pi$
$462$		0			0
$463$	4.39841	+	12.0845i	0.204412	+	0.561616i	0.998961	−	0.0455839i	$-0.0145148\pi$
$463$	4.39841	+	12.0845i	0.204412	+	0.561616i	−0.794549	+	0.607200i	$0.792293\pi$
$464$		0			0
$465$	−14.6800	+	16.4994i	−0.680771	+	0.765139i
$466$		0			0
$467$	−2.00758	−	3.47722i	−0.0928995	−	0.160907i	0.815830	−	0.578291i	$-0.196280\pi$
$467$	−2.00758	−	3.47722i	−0.0928995	−	0.160907i	−0.908730	+	0.417384i	$0.862947\pi$
$468$		0			0
$469$	6.64423	−	11.5081i	0.306802	−	0.531397i
$470$		0			0
$471$	−26.5379	+	14.3127i	−1.22280	+	0.659496i
$472$		0			0
$473$	16.0026	+	2.82169i	0.735801	+	0.129742i
$474$		0			0
$475$	−1.85397	−	2.20947i	−0.0850659	−	0.101378i
$476$		0			0
$477$	−16.2393	+	17.2199i	−0.743546	+	0.788447i
$478$		0			0
$479$	4.21883	+	1.53553i	0.192763	+	0.0701601i	0.436598	−	0.899657i	$-0.356183\pi$
$479$	4.21883	+	1.53553i	0.192763	+	0.0701601i	−0.243835	+	0.969817i	$0.578405\pi$
$480$		0			0
$481$	−12.0332	−	10.0970i	−0.548665	−	0.460385i
$482$		0			0
$483$	13.9132	+	5.52565i	0.633073	+	0.251426i
$484$		0			0
$485$		−	7.49763i		−	0.340450i
$486$		0			0
$487$			31.5551i			1.42990i	0.699176	+	0.714950i	$0.253550\pi$
$487$			31.5551i			1.42990i	−0.699176	+	0.714950i	$0.746450\pi$
$488$		0			0
$489$	−7.02279	−	2.78911i	−0.317581	−	0.126128i
$490$		0			0
$491$	−4.84498	−	4.06542i	−0.218651	−	0.183470i	0.526882	−	0.849938i	$-0.323361\pi$
$491$	−4.84498	−	4.06542i	−0.218651	−	0.183470i	−0.745534	+	0.666468i	$0.767805\pi$
$492$		0			0
$493$	0.894247	+	0.325479i	0.0402749	+	0.0146589i
$494$		0			0
$495$	5.77474	−	6.12347i	0.259555	−	0.275229i
$496$		0			0
$497$	−13.9788	−	16.6593i	−0.627037	−	0.747273i
$498$		0			0
$499$	17.5088	+	3.08728i	0.783802	+	0.138205i	0.551207	−	0.834368i	$-0.314167\pi$
$499$	17.5088	+	3.08728i	0.783802	+	0.138205i	0.232595	+	0.972574i	$0.425278\pi$
$500$		0			0
$501$	18.1338	−	9.78014i	0.810159	−	0.436945i
$502$		0			0
$503$	11.6709	−	20.2147i	0.520382	−	0.901328i	−0.479337	−	0.877631i	$-0.659123\pi$
$503$	11.6709	−	20.2147i	0.520382	−	0.901328i	0.999719	−	0.0236969i	$-0.00754367\pi$
$504$		0			0
$505$	3.83336	+	6.63957i	0.170582	+	0.295457i
$506$		0			0
$507$	−10.4666	+	11.7637i	−0.464836	+	0.522444i
$508$		0			0
$509$	−6.13820	−	16.8646i	−0.272071	−	0.747509i	−0.998201	−	0.0599518i	$-0.980905\pi$
$509$	−6.13820	−	16.8646i	−0.272071	−	0.747509i	0.726130	−	0.687557i	$-0.241317\pi$
$510$		0			0
$511$	−15.3494	+	2.70652i	−0.679018	+	0.119729i
$512$		0			0
$513$	−7.37616	+	10.5414i	−0.325665	+	0.465413i
$514$		0			0
$515$	−2.46486	−	13.9789i	−0.108615	−	0.615985i
$516$		0			0
$517$	−4.30761	+	1.56784i	−0.189448	+	0.0689536i
$518$		0			0
$519$	−7.95089	+	2.63557i	−0.349005	+	0.115689i
$520$		0			0
$521$	−19.1823	+	11.0749i	−0.840392	+	0.485201i	−0.857397	−	0.514655i	$-0.827920\pi$
$521$	−19.1823	+	11.0749i	−0.840392	+	0.485201i	0.0170055	+	0.999855i	$0.494587\pi$
$522$		0			0
$523$	14.9975	+	8.65882i	0.655796	+	0.378624i	0.790673	−	0.612238i	$-0.209731\pi$
$523$	14.9975	+	8.65882i	0.655796	+	0.378624i	−0.134877	+	0.990862i	$0.543064\pi$
$524$		0			0
$525$	2.84052	−	4.60628i	0.123971	−	0.201035i
$526$		0			0
$527$	0.151892	−	0.861425i	0.00661654	−	0.0375243i
$528$		0			0
$529$	−9.66457	+	8.10954i	−0.420199	+	0.352589i
$530$		0			0
$531$	−0.0884780	−	0.755589i	−0.00383962	−	0.0327898i
$532$		0			0
$533$	−4.71522	+	12.9550i	−0.204239	+	0.561142i
$534$		0			0
$535$	19.8734	−	23.6842i	0.859204	−	1.02396i
$536$		0			0
$537$	−21.8443	−	27.6206i	−0.942651	−	1.19192i
$538$		0			0
$539$	0.278255			0.0119853
$540$		0			0
$541$	23.1186			0.993946			0.496973	−	0.867766i	$-0.334445\pi$
$541$	23.1186			0.993946			0.496973	+	0.867766i	$0.334445\pi$
$542$		0			0
$543$	−19.2618	+	2.82352i	−0.826601	+	0.121169i
$544$		0			0
$545$	−2.64739	+	3.15504i	−0.113402	+	0.135147i
$546$		0			0
$547$	−1.67406	+	4.59944i	−0.0715776	+	0.196658i	−0.970323	−	0.241814i	$-0.922258\pi$
$547$	−1.67406	+	4.59944i	−0.0715776	+	0.196658i	0.898745	+	0.438471i	$0.144480\pi$
$548$		0			0
$549$	16.9298	+	33.6921i	0.722545	+	1.43795i
$550$		0			0
$551$	13.4355	−	11.2737i	0.572373	−	0.480278i
$552$		0			0
$553$	5.37864	−	30.5038i	0.228723	−	1.29715i
$554$		0			0
$555$	−26.9374	−	0.780941i	−1.14343	−	0.0331491i
$556$		0			0
$557$	15.8463	+	9.14884i	0.671427	+	0.387649i	0.796617	−	0.604484i	$-0.206621\pi$
$557$	15.8463	+	9.14884i	0.671427	+	0.387649i	−0.125190	+	0.992133i	$0.539954\pi$
$558$		0			0
$559$	19.4208	−	11.2126i	0.821410	−	0.474242i
$560$		0			0
$561$	−0.0673789	+	0.326491i	−0.00284474	+	0.0137845i
$562$		0			0
$563$	−18.2238	+	6.63293i	−0.768043	+	0.279545i	−0.696178	−	0.717870i	$-0.745117\pi$
$563$	−18.2238	+	6.63293i	−0.768043	+	0.279545i	−0.0718654	+	0.997414i	$0.522895\pi$
$564$		0			0
$565$	−6.63489	−	37.6284i	−0.279132	−	1.58304i
$566$		0			0
$567$	−23.1287	−	6.91358i	−0.971312	−	0.290343i
$568$		0			0
$569$	−4.56223	+	0.804445i	−0.191259	+	0.0337241i	−0.268457	−	0.963292i	$-0.586514\pi$
$569$	−4.56223	+	0.804445i	−0.191259	+	0.0337241i	0.0771982	+	0.997016i	$0.475403\pi$
$570$		0			0
$571$	5.08817	+	13.9796i	0.212933	+	0.585029i	0.999471	−	0.0325126i	$-0.0103509\pi$
$571$	5.08817	+	13.9796i	0.212933	+	0.585029i	−0.786538	+	0.617542i	$0.788129\pi$
$572$		0			0
$573$	−12.1479	−	2.50700i	−0.507487	−	0.104732i
$574$		0			0
$575$	−1.87685	−	3.25079i	−0.0782699	−	0.135567i
$576$		0			0
$577$	−18.5993	+	32.2150i	−0.774300	+	1.34113i	0.160888	+	0.986973i	$0.448564\pi$
$577$	−18.5993	+	32.2150i	−0.774300	+	1.34113i	−0.935187	+	0.354153i	$0.884769\pi$
$578$		0			0
$579$	−0.754928	+	26.0401i	−0.0313737	+	1.08219i
$580$		0			0
$581$	−34.8731	−	6.14908i	−1.44678	−	0.255107i
$582$		0			0
$583$	7.26567	+	8.65889i	0.300913	+	0.358615i
$584$		0			0
$585$	0.672941	−	11.5963i	0.0278227	−	0.479448i
$586$		0			0
$587$	−4.34575	−	1.58172i	−0.179368	−	0.0652847i	0.250775	−	0.968045i	$-0.419315\pi$
$587$	−4.34575	−	1.58172i	−0.179368	−	0.0652847i	−0.430143	+	0.902761i	$0.641537\pi$
$588$		0			0
$589$	−12.3495	−	10.3624i	−0.508852	−	0.426977i
$590$		0			0
$591$	1.47842	+	10.0856i	0.0608141	+	0.414868i
$592$		0			0
$593$		−	32.7828i		−	1.34623i	−0.739539	−	0.673114i	$-0.764956\pi$
$593$		−	32.7828i		−	1.34623i	0.739539	−	0.673114i	$-0.235044\pi$
$594$		0			0
$595$		−	0.705679i		−	0.0289300i
$596$		0			0
$597$	−16.4932	+	13.0440i	−0.675023	+	0.533855i
$598$		0			0
$599$	−26.9780	−	22.6372i	−1.10229	−	0.924930i	−0.104712	−	0.994503i	$-0.533392\pi$
$599$	−26.9780	−	22.6372i	−1.10229	−	0.924930i	−0.997577	+	0.0695721i	$0.977837\pi$
$600$		0			0
$601$	8.77293	+	3.19308i	0.357855	+	0.130249i	0.514690	−	0.857376i	$-0.327907\pi$
$601$	8.77293	+	3.19308i	0.357855	+	0.130249i	−0.156835	+	0.987625i	$0.550129\pi$
$602$		0			0
$603$	8.87805	+	11.9200i	0.361542	+	0.485420i
$604$		0			0
$605$	11.2631	+	13.4229i	0.457911	+	0.545717i
$606$		0			0
$607$	−9.50803	−	1.67652i	−0.385919	−	0.0680479i	−0.0226772	−	0.999743i	$-0.507219\pi$
$607$	−9.50803	−	1.67652i	−0.385919	−	0.0680479i	−0.363242	+	0.931695i	$0.618330\pi$
$608$		0			0
$609$	28.0102	+	17.2729i	1.13503	+	0.699932i
$610$		0			0
$611$	−3.16313	+	5.47870i	−0.127966	+	0.221644i
$612$		0			0
$613$	9.54994	+	16.5410i	0.385719	+	0.668084i	0.991869	−	0.127266i	$-0.0406202\pi$
$613$	9.54994	+	16.5410i	0.385719	+	0.668084i	−0.606150	+	0.795350i	$0.707287\pi$
$614$		0			0
$615$	7.44189	+	22.4504i	0.300086	+	0.905287i
$616$		0			0
$617$	12.3995	+	34.0673i	0.499184	+	1.37150i	0.892065	+	0.451907i	$0.149256\pi$
$617$	12.3995	+	34.0673i	0.499184	+	1.37150i	−0.392881	+	0.919589i	$0.628522\pi$
$618$		0			0
$619$	17.9772	−	3.16986i	0.722564	−	0.127407i	0.199741	−	0.979849i	$-0.435990\pi$
$619$	17.9772	−	3.16986i	0.722564	−	0.127407i	0.522823	+	0.852441i	$0.324879\pi$
$620$		0			0
$621$	−11.8361	+	11.8436i	−0.474964	+	0.475267i
$622$		0			0
$623$	−2.09175	−	11.8629i	−0.0838043	−	0.475278i
$624$		0			0
$625$	16.7441	−	6.09434i	0.669763	−	0.243774i
$626$		0			0
$627$	4.59022	+	4.08408i	0.183316	+	0.163102i
$628$		0			0
$629$	0.924366	−	0.533683i	0.0368569	−	0.0212793i
$630$		0			0
$631$	3.70385	+	2.13842i	0.147448	+	0.0851291i	0.571909	−	0.820317i	$-0.306203\pi$
$631$	3.70385	+	2.13842i	0.147448	+	0.0851291i	−0.424461	+	0.905446i	$0.639536\pi$
$632$		0			0
$633$	17.4501	+	32.3550i	0.693578	+	1.28599i
$634$		0			0
$635$	1.77870	−	10.0875i	0.0705856	−	0.400311i
$636$		0			0
$637$	0.294166	−	0.246835i	0.0116553	−	0.00977994i
$638$		0			0
$639$	23.3006	−	6.98111i	0.921756	−	0.276168i
$640$		0			0
$641$	−1.89651	+	5.21062i	−0.0749077	+	0.205807i	−0.971495	−	0.237060i	$-0.923816\pi$
$641$	−1.89651	+	5.21062i	−0.0749077	+	0.205807i	0.896587	+	0.442867i	$0.146039\pi$
$642$		0			0
$643$	4.61815	−	5.50370i	0.182122	−	0.217045i	−0.667258	−	0.744827i	$-0.732532\pi$
$643$	4.61815	−	5.50370i	0.182122	−	0.217045i	0.849380	+	0.527782i	$0.176976\pi$
$644$		0			0
$645$	14.2004	−	35.7556i	0.559140	−	1.40787i
$646$		0			0
$647$	23.4676			0.922606			0.461303	−	0.887243i	$-0.347382\pi$
$647$	23.4676			0.922606			0.461303	+	0.887243i	$0.347382\pi$
$648$		0			0
$649$	−0.363299			−0.0142607
$650$		0			0
$651$	11.1647	−	28.1119i	0.437578	−	1.10179i
$652$		0			0
$653$	14.6044	−	17.4049i	0.571515	−	0.681104i	−0.400427	−	0.916329i	$-0.631138\pi$
$653$	14.6044	−	17.4049i	0.571515	−	0.681104i	0.971941	+	0.235224i	$0.0755825\pi$
$654$		0			0
$655$	3.80107	−	10.4434i	0.148520	−	0.408056i
$656$		0			0
$657$	4.01671	−	16.9638i	0.156707	−	0.661823i
$658$		0			0
$659$	15.7748	−	13.2366i	0.614499	−	0.515626i	−0.281570	−	0.959541i	$-0.590855\pi$
$659$	15.7748	−	13.2366i	0.614499	−	0.515626i	0.896069	+	0.443915i	$0.146411\pi$
$660$		0			0
$661$	−4.10846	+	23.3002i	−0.159801	+	0.906275i	0.794464	+	0.607311i	$0.207752\pi$
$661$	−4.10846	+	23.3002i	−0.159801	+	0.906275i	−0.954265	+	0.298963i	$0.903359\pi$
$662$		0			0
$663$	0.218393	+	0.404932i	0.00848166	+	0.0157262i
$664$		0			0
$665$	−11.2633	−	6.50288i	−0.436773	−	0.252171i
$666$		0			0
$667$	19.7677	−	11.4129i	0.765407	−	0.441908i
$668$		0			0
$669$	−18.8441	−	16.7663i	−0.728556	−	0.648221i
$670$		0			0
$671$	16.9209	−	6.15869i	0.653223	−	0.237754i
$672$		0			0
$673$	−0.175818	−	0.997115i	−0.00677730	−	0.0384360i	0.981232	−	0.192833i	$-0.0617676\pi$
$673$	−0.175818	−	0.997115i	−0.00677730	−	0.0384360i	−0.988009	+	0.154397i	$0.950656\pi$
$674$		0			0
$675$	3.47337	+	4.95713i	0.133690	+	0.190800i
$676$		0			0
$677$	−34.3106	+	6.04989i	−1.31867	+	0.232516i	−0.788320	−	0.615266i	$-0.789049\pi$
$677$	−34.3106	+	6.04989i	−1.31867	+	0.232516i	−0.530345	+	0.847782i	$0.677938\pi$
$678$		0			0
$679$	3.51219	+	9.64966i	0.134786	+	0.370320i
$680$		0			0
$681$	16.2722	+	49.0894i	0.623553	+	1.88111i
$682$		0			0
$683$	−7.09514	−	12.2891i	−0.271488	−	0.470231i	0.697755	−	0.716336i	$-0.254182\pi$
$683$	−7.09514	−	12.2891i	−0.271488	−	0.470231i	−0.969243	+	0.246106i	$0.920849\pi$
$684$		0			0
$685$	15.6183	−	27.0517i	0.596745	−	1.03359i
$686$		0			0
$687$	−41.3016	−	25.4692i	−1.57575	−	0.971709i
$688$		0			0
$689$	15.3623	+	2.70879i	0.585257	+	0.103197i
$690$		0			0
$691$	−3.40417	−	4.05693i	−0.129501	−	0.154333i	0.697397	−	0.716685i	$-0.254341\pi$
$691$	−3.40417	−	4.05693i	−0.129501	−	0.154333i	−0.826898	+	0.562351i	$0.809897\pi$
$692$		0			0
$693$	−4.56378	+	10.5862i	−0.173364	+	0.402136i
$694$		0			0
$695$	−31.9716	−	11.6367i	−1.21275	−	0.441406i
$696$		0			0
$697$	−0.717615	−	0.602150i	−0.0271816	−	0.0228081i
$698$		0			0
$699$	21.6357	−	17.1110i	0.818338	−	0.647199i
$700$		0			0
$701$			40.3475i			1.52391i	0.647633	+	0.761953i	$0.275759\pi$
$701$			40.3475i			1.52391i	−0.647633	+	0.761953i	$0.724241\pi$
$702$		0			0
$703$		−	19.6717i		−	0.741932i
$704$		0			0
$705$	1.57412	+	10.7385i	0.0592846	+	0.404434i
$706$		0			0
$707$	−8.04388	−	6.74962i	−0.302521	−	0.253845i
$708$		0			0
$709$	−12.7194	−	4.62947i	−0.477686	−	0.173863i	0.0919451	−	0.995764i	$-0.470692\pi$
$709$	−12.7194	−	4.62947i	−0.477686	−	0.173863i	−0.569631	+	0.821901i	$0.692914\pi$
$710$		0			0
$711$	28.9489	+	19.0312i	1.08567	+	0.713726i
$712$		0			0
$713$	−13.4861	−	16.0721i	−0.505058	−	0.601905i
$714$		0			0
$715$	−5.46288	−	0.963253i	−0.204300	−	0.0360236i
$716$		0			0
$717$	0.146836	−	5.06488i	0.00548368	−	0.189151i
$718$		0			0
$719$	21.8364	−	37.8218i	0.814361	−	1.41051i	−0.0954248	−	0.995437i	$-0.530421\pi$
$719$	21.8364	−	37.8218i	0.814361	−	1.41051i	0.909786	−	0.415078i	$-0.136246\pi$
$720$		0			0
$721$	9.72064	+	16.8366i	0.362016	+	0.627029i
$722$		0			0
$723$	−34.0450	−	7.02597i	−1.26615	−	0.261299i
$724$		0			0
$725$	−2.82214	−	7.75377i	−0.104812	−	0.287968i
$726$		0			0
$727$	−16.0849	+	2.83621i	−0.596557	+	0.105189i	−0.463770	−	0.885956i	$-0.653504\pi$
$727$	−16.0849	+	2.83621i	−0.596557	+	0.105189i	−0.132787	+	0.991145i	$0.542393\pi$
$728$		0			0
$729$	17.3421	−	20.6942i	0.642300	−	0.766453i
$730$		0			0
$731$	0.264602	+	1.50063i	0.00978665	+	0.0555029i
$732$		0			0
$733$	22.5128	−	8.19400i	0.831531	−	0.302652i	0.109044	−	0.994037i	$-0.465221\pi$
$733$	22.5128	−	8.19400i	0.831531	−	0.302652i	0.722487	+	0.691385i	$0.242999\pi$
$734$		0			0
$735$	0.133152	−	0.645199i	0.00491137	−	0.0237985i
$736$		0			0
$737$	6.14690	−	3.54891i	0.226424	−	0.130726i
$738$		0			0
$739$	−18.3316	−	10.5838i	−0.674339	−	0.389330i	0.123380	−	0.992360i	$-0.460627\pi$
$739$	−18.3316	−	10.5838i	−0.674339	−	0.389330i	−0.797719	+	0.603030i	$0.793960\pi$
$740$		0			0
$741$	8.47561	+	0.245716i	0.311359	+	0.00902660i
$742$		0			0
$743$	5.11590	−	29.0137i	0.187684	−	1.06441i	−0.734774	−	0.678312i	$-0.762712\pi$
$743$	5.11590	−	29.0137i	0.187684	−	1.06441i	0.922458	−	0.386097i	$-0.126177\pi$
$744$		0			0
$745$	25.2647	−	21.1996i	0.925627	−	0.776693i
$746$		0			0
$747$	21.7572	−	33.0955i	0.796056	−	1.21090i
$748$		0			0
$749$	−14.4830	+	39.7918i	−0.529199	+	1.45396i
$750$		0			0
$751$	20.6116	−	24.5639i	0.752127	−	0.896350i	−0.245196	−	0.969474i	$-0.578852\pi$
$751$	20.6116	−	24.5639i	0.752127	−	0.896350i	0.997323	+	0.0731237i	$0.0232968\pi$
$752$		0			0
$753$	28.3034	−	4.14890i	1.03143	−	0.151194i
$754$		0			0
$755$	−10.2551			−0.373221
$756$		0			0
$757$	10.5411			0.383123			0.191561	−	0.981481i	$-0.438645\pi$
$757$	10.5411			0.383123			0.191561	+	0.981481i	$0.438645\pi$
$758$		0			0
$759$	4.96016	+	6.27178i	0.180042	+	0.227651i
$760$		0			0
$761$	−16.0147	+	19.0855i	−0.580531	+	0.691850i	−0.973757	−	0.227592i	$-0.926915\pi$
$761$	−16.0147	+	19.0855i	−0.580531	+	0.691850i	0.393225	+	0.919442i	$0.371359\pi$
$762$		0			0
$763$	1.92932	−	5.30076i	0.0698461	−	0.191901i
$764$		0			0
$765$	0.724804	+	0.312468i	0.0262054	+	0.0112973i
$766$		0			0
$767$	−0.384073	+	0.322276i	−0.0138681	+	0.0116367i
$768$		0			0
$769$	−4.79307	+	27.1829i	−0.172843	+	0.980239i	0.767762	+	0.640735i	$0.221370\pi$
$769$	−4.79307	+	27.1829i	−0.172843	+	0.980239i	−0.940605	+	0.339504i	$0.889741\pi$
$770$		0			0
$771$	10.1293	−	16.4259i	0.364796	−	0.591565i
$772$		0			0
$773$	−30.1712	−	17.4193i	−1.08518	−	0.626530i	−0.152892	−	0.988243i	$-0.548859\pi$
$773$	−30.1712	−	17.4193i	−1.08518	−	0.626530i	−0.932290	+	0.361713i	$0.882192\pi$
$774$		0			0
$775$	−6.56829	+	3.79220i	−0.235940	+	0.136220i
$776$		0			0
$777$	35.0350	−	11.6135i	1.25687	−	0.416631i
$778$		0			0
$779$	−16.2238	+	5.90497i	−0.581277	+	0.211568i
$780$		0			0
$781$	−2.01709	−	11.4395i	−0.0721770	−	0.409336i
$782$		0			0
$783$	−30.1437	+	21.1211i	−1.07725	+	0.754807i
$784$		0			0
$785$	33.5730	−	5.91982i	1.19827	−	0.211287i
$786$		0			0
$787$	13.8245	+	37.9826i	0.492791	+	1.35393i	0.898116	+	0.439760i	$0.144936\pi$
$787$	13.8245	+	37.9826i	0.492791	+	1.35393i	−0.405324	+	0.914173i	$0.632841\pi$
$788$		0			0
$789$	−6.86011	+	7.71029i	−0.244226	+	0.274494i
$790$		0			0
$791$	26.1659	+	45.3207i	0.930353	+	1.61142i
$792$		0			0
$793$	12.4252	−	21.5211i	0.441231	−	0.764235i
$794$		0			0
$795$	23.5545	−	12.7037i	0.835391	−	0.450553i
$796$		0			0
$797$	15.6485	+	2.75925i	0.554297	+	0.0977376i	0.443779	−	0.896136i	$-0.353638\pi$
$797$	15.6485	+	2.75925i	0.554297	+	0.0977376i	0.110519	+	0.993874i	$0.464749\pi$
$798$		0			0
$799$	−0.276313	−	0.329297i	−0.00977525	−	0.0116497i
$800$		0			0
$801$	13.1106	+	3.10434i	0.463242	+	0.109687i
$802$		0			0
$803$	−7.82306	−	2.84736i	−0.276070	−	0.100481i
$804$		0			0
$805$	−12.9662	−	10.8800i	−0.456999	−	0.383468i
$806$		0			0
$807$	12.4882	+	4.95973i	0.439607	+	0.174591i
$808$		0			0
$809$			53.0647i			1.86565i	0.360323	+	0.932827i	$0.382666\pi$
$809$			53.0647i			1.86565i	−0.360323	+	0.932827i	$0.617334\pi$
$810$		0			0
$811$			35.6438i			1.25162i	0.779975	+	0.625811i	$0.215232\pi$
$811$			35.6438i			1.25162i	−0.779975	+	0.625811i	$0.784768\pi$
$812$		0			0
$813$	−21.2416	−	8.43614i	−0.744976	−	0.295868i
$814$		0			0
$815$	6.54479	+	5.49173i	0.229254	+	0.192367i
$816$		0			0
$817$	26.3899	+	9.60513i	0.923265	+	0.336041i
$818$		0			0
$819$	4.56607	+	15.2400i	0.159552	+	0.532528i
$820$		0			0
$821$	−0.0410674	−	0.0489422i	−0.00143326	−	0.00170809i	0.765327	−	0.643641i	$-0.222577\pi$
$821$	−0.0410674	−	0.0489422i	−0.00143326	−	0.00170809i	−0.766761	+	0.641933i	$0.778133\pi$
$822$		0			0
$823$	−39.3284	−	6.93466i	−1.37090	−	0.241727i	−0.560768	−	0.827973i	$-0.689494\pi$
$823$	−39.3284	−	6.93466i	−1.37090	−	0.241727i	−0.810133	+	0.586246i	$0.800605\pi$
$824$		0			0
$825$	2.54414	−	1.37214i	0.0885756	−	0.0477716i
$826$		0			0
$827$	15.0175	−	26.0111i	0.522210	−	0.904494i	−0.477456	−	0.878656i	$-0.658441\pi$
$827$	15.0175	−	26.0111i	0.522210	−	0.904494i	0.999666	−	0.0258385i	$-0.00822557\pi$
$828$		0			0
$829$	−13.4305	−	23.2622i	−0.466459	−	0.807930i	0.532807	−	0.846237i	$-0.321137\pi$
$829$	−13.4305	−	23.2622i	−0.466459	−	0.807930i	−0.999266	+	0.0383063i	$0.987804\pi$
$830$		0			0
$831$	16.3345	−	18.3589i	0.566639	−	0.636863i
$832$		0			0
$833$	0.00892436	+	0.0245195i	0.000309211	+	0.000849550i
$834$		0			0
$835$	−22.9410	+	4.04512i	−0.793906	+	0.139987i
$836$		0			0
$837$	23.9302	+	23.9149i	0.827147	+	0.826621i
$838$		0			0
$839$	9.78067	+	55.4690i	0.337666	+	1.91500i	0.399136	+	0.916892i	$0.369310\pi$
$839$	9.78067	+	55.4690i	0.337666	+	1.91500i	−0.0614693	+	0.998109i	$0.519579\pi$
$840$		0			0
$841$	19.8986	−	7.24249i	0.686158	−	0.249741i
$842$		0			0
$843$	−28.6635	+	9.50144i	−0.987225	+	0.327247i
$844$		0			0
$845$	15.4180	−	8.90157i	0.530394	−	0.306223i
$846$		0			0
$847$	−20.7838	−	11.9995i	−0.714138	−	0.412308i
$848$		0			0
$849$	24.0358	−	38.9773i	0.824907	−	1.33770i
$850$		0			0
$851$	4.44566	−	25.2126i	0.152395	−	0.864276i
$852$		0			0
$853$	6.59941	−	5.53757i	0.225960	−	0.189603i	−0.522778	−	0.852469i	$-0.675105\pi$
$853$	6.59941	−	5.53757i	0.225960	−	0.189603i	0.748738	+	0.662866i	$0.230660\pi$
$854$		0			0
$855$	11.6664	−	8.68917i	0.398983	−	0.297163i
$856$		0			0
$857$	4.48740	−	12.3290i	0.153287	−	0.421152i	−0.839151	−	0.543898i	$-0.816948\pi$
$857$	4.48740	−	12.3290i	0.153287	−	0.421152i	0.992438	+	0.122746i	$0.0391701\pi$
$858$		0			0
$859$	−1.27842	+	1.52357i	−0.0436193	+	0.0519834i	−0.787413	−	0.616426i	$-0.788580\pi$
$859$	−1.27842	+	1.52357i	−0.0436193	+	0.0519834i	0.743794	+	0.668409i	$0.233024\pi$
$860$		0			0
$861$	−20.0946	−	25.4082i	−0.684822	−	0.865910i
$862$		0			0
$863$	−34.7384			−1.18251			−0.591255	−	0.806485i	$-0.701367\pi$
$863$	−34.7384			−1.18251			−0.591255	+	0.806485i	$0.701367\pi$
$864$		0			0
$865$	9.47071			0.322014
$866$		0			0
$867$	29.1026	−	4.26605i	0.988376	−	0.144883i
$868$		0			0
$869$	10.6346	−	12.6738i	0.360753	−	0.429929i
$870$		0			0
$871$	3.35022	−	9.20464i	0.113518	−	0.311887i
$872$		0			0
$873$	−11.4664	−	0.665401i	−0.388078	−	0.0225204i
$874$		0			0
$875$	−24.8062	+	20.8149i	−0.838602	+	0.703671i
$876$		0			0
$877$	−8.29844	+	47.0628i	−0.280218	+	1.58920i	0.441663	+	0.897181i	$0.354389\pi$
$877$	−8.29844	+	47.0628i	−0.280218	+	1.58920i	−0.721881	+	0.692017i	$0.756722\pi$
$878$		0			0
$879$	39.4153	+	1.14269i	1.32945	+	0.0385419i
$880$		0			0
$881$	10.5236	+	6.07578i	0.354548	+	0.204698i	0.666687	−	0.745338i	$-0.267712\pi$
$881$	10.5236	+	6.07578i	0.354548	+	0.204698i	−0.312139	+	0.950037i	$0.601045\pi$
$882$		0			0
$883$	16.1433	−	9.32035i	0.543266	−	0.313655i	−0.203136	−	0.979151i	$-0.565113\pi$
$883$	16.1433	−	9.32035i	0.543266	−	0.313655i	0.746401	+	0.665496i	$0.231780\pi$
$884$		0			0
$885$	−0.173847	+	0.842393i	−0.00584381	+	0.0283167i
$886$		0			0
$887$	10.2255	−	3.72179i	0.343340	−	0.124966i	−0.164594	−	0.986361i	$-0.552632\pi$
$887$	10.2255	−	3.72179i	0.343340	−	0.124966i	0.507934	+	0.861396i	$0.330409\pi$
$888$		0			0
$889$	2.43616	+	13.8161i	0.0817061	+	0.463379i
$890$		0			0
$891$	−8.85232	−	9.37494i	−0.296564	−	0.314072i
$892$		0			0
$893$	−7.80214	+	1.37573i	−0.261089	+	0.0460370i
$894$		0			0
$895$	13.6177	+	37.4143i	0.455189	+	1.25062i
$896$		0			0
$897$	10.8074	+	2.23035i	0.360848	+	0.0744692i
$898$		0			0
$899$	−23.0599	−	39.9409i	−0.769090	−	1.33210i
$900$		0			0
$901$	−0.529982	+	0.917957i	−0.0176563	+	0.0305816i
$902$		0			0
$903$	−1.52697	+	52.6705i	−0.0508143	+	1.75276i
$904$		0			0
$905$	21.6767	+	3.82218i	0.720557	+	0.127054i
$906$		0			0
$907$	20.7508	+	24.7298i	0.689018	+	0.821139i	0.991237	−	0.132099i	$-0.0421717\pi$
$907$	20.7508	+	24.7298i	0.689018	+	0.821139i	−0.302219	+	0.953239i	$0.597727\pi$
$908$		0			0
$909$	10.4943	−	5.27322i	0.348074	−	0.174902i
$910$		0			0
$911$	46.9210	+	17.0778i	1.55456	+	0.565814i	0.969482	−	0.245163i	$-0.0788414\pi$
$911$	46.9210	+	17.0778i	1.55456	+	0.565814i	0.585079	+	0.810976i	$0.301064\pi$
$912$		0			0
$913$	−14.4892	−	12.1579i	−0.479522	−	0.402367i
$914$		0			0
$915$	−6.18333	−	42.1821i	−0.204415	−	1.39450i
$916$		0			0
$917$			15.2215i			0.502658i
$918$		0			0
$919$		−	29.9954i		−	0.989457i	−0.869048	−	0.494728i	$-0.835268\pi$
$919$		−	29.9954i		−	0.989457i	0.869048	−	0.494728i	$-0.164732\pi$
$920$		0			0
$921$	−18.7295	+	14.8126i	−0.617158	+	0.488091i
$922$		0			0
$923$	−12.2802	−	10.3043i	−0.404206	−	0.339169i
$924$		0			0
$925$	−8.69670	−	3.16534i	−0.285946	−	0.104076i
$926$		0			0
$927$	−21.5972	+	2.52899i	−0.709344	+	0.0830629i
$928$		0			0
$929$	−4.56040	−	5.43487i	−0.149622	−	0.178312i	0.686028	−	0.727576i	$-0.259353\pi$
$929$	−4.56040	−	5.43487i	−0.149622	−	0.178312i	−0.835649	+	0.549263i	$0.814908\pi$
$930$		0			0
$931$	0.473594	+	0.0835073i	0.0155214	+	0.00273684i
$932$		0			0
$933$	35.0357	+	21.6052i	1.14702	+	0.707323i
$934$		0			0
$935$	0.188463	−	0.326428i	0.00616342	−	0.0106753i
$936$		0			0
$937$	6.25375	+	10.8318i	0.204301	+	0.353860i	0.949910	−	0.312524i	$-0.101175\pi$
$937$	6.25375	+	10.8318i	0.204301	+	0.353860i	−0.745609	+	0.666384i	$0.767841\pi$
$938$		0			0
$939$	9.64398	+	29.0936i	0.314719	+	0.949433i
$940$		0			0
$941$	−11.7008	−	32.1476i	−0.381435	−	1.04798i	−0.970753	−	0.240082i	$-0.922826\pi$
$941$	−11.7008	−	32.1476i	−0.381435	−	1.04798i	0.589318	−	0.807901i	$-0.299397\pi$
$942$		0			0
$943$	−22.1280	+	3.90176i	−0.720586	+	0.127059i
$944$		0			0
$945$	22.3627	+	15.6479i	0.727459	+	0.509028i
$946$		0			0
$947$	0.312265	+	1.77094i	0.0101473	+	0.0575480i	0.989461	−	0.144800i	$-0.0462539\pi$
$947$	0.312265	+	1.77094i	0.0101473	+	0.0575480i	−0.979314	+	0.202348i	$0.935143\pi$
$948$		0			0
$949$	−10.7962	+	3.92951i	−0.350461	+	0.127557i
$950$		0			0
$951$	−43.2399	−	38.4720i	−1.40215	−	1.24754i
$952$		0			0
$953$	20.4099	−	11.7837i	0.661142	−	0.381711i	−0.131570	−	0.991307i	$-0.542002\pi$
$953$	20.4099	−	11.7837i	0.661142	−	0.381711i	0.792712	+	0.609596i	$0.208668\pi$
$954$		0			0
$955$	12.1456	+	7.01225i	0.393022	+	0.226911i
$956$		0			0
$957$	8.34378	+	15.4706i	0.269716	+	0.500093i
$958$		0			0
$959$	−7.42911	+	42.1325i	−0.239898	+	1.36053i
$960$		0			0
$961$	−8.72658	+	7.32247i	−0.281503	+	0.236209i
$962$		0			0
$963$	−34.4573	−	32.4950i	−1.11037	−	1.04714i
$964$		0			0
$965$	10.0741	−	27.6784i	0.324297	−	0.890998i
$966$		0			0
$967$	8.29004	−	9.87968i	0.266590	−	0.317709i	−0.616098	−	0.787670i	$-0.711287\pi$
$967$	8.29004	−	9.87968i	0.266590	−	0.317709i	0.882687	+	0.469961i	$0.155732\pi$
$968$		0			0
$969$	−0.212664	+	0.535472i	−0.00683174	+	0.0172018i
$970$		0			0
$971$	22.9545			0.736646			0.368323	−	0.929698i	$-0.379932\pi$
$971$	22.9545			0.736646			0.368323	+	0.929698i	$0.379932\pi$
$972$		0			0
$973$	46.5995			1.49391
$974$		0			0
$975$	1.47242	−	3.70746i	0.0471553	−	0.118734i
$976$		0			0
$977$	10.4177	−	12.4154i	0.333292	−	0.397202i	−0.573206	−	0.819411i	$-0.694301\pi$
$977$	10.4177	−	12.4154i	0.333292	−	0.397202i	0.906499	+	0.422209i	$0.138745\pi$
$978$		0			0
$979$	2.20060	−	6.04611i	0.0703316	−	0.193235i
$980$		0			0
$981$	4.59014	+	4.32874i	0.146552	+	0.138206i
$982$		0			0
$983$	25.0921	−	21.0548i	0.800314	−	0.671543i	−0.147961	−	0.988993i	$-0.547271\pi$
$983$	25.0921	−	21.0548i	0.800314	−	0.671543i	0.948275	+	0.317450i	$0.102827\pi$
$984$		0			0
$985$	2.00133	−	11.3501i	0.0637678	−	0.361645i
$986$		0			0
$987$	−7.05626	−	13.0833i	−0.224603	−	0.416447i
$988$		0			0
$989$	31.6523	+	18.2745i	1.00649	+	0.581095i
$990$		0			0
$991$	23.1547	−	13.3684i	0.735534	−	0.424661i	−0.0849094	−	0.996389i	$-0.527060\pi$
$991$	23.1547	−	13.3684i	0.735534	−	0.424661i	0.820443	+	0.571728i	$0.193727\pi$
$992$		0			0
$993$	−18.5214	−	16.4792i	−0.587760	−	0.522950i
$994$		0			0
$995$	22.3414	−	8.13161i	0.708270	−	0.257789i
$996$		0			0
$997$	5.58314	+	31.6636i	0.176820	+	1.00280i	0.936022	+	0.351941i	$0.114478\pi$
$997$	5.58314	+	31.6636i	0.176820	+	1.00280i	−0.759202	+	0.650855i	$0.774411\pi$
$998$		0			0
$999$	−3.58496	+	41.1269i	−0.113423	+	1.30120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.95.13	✓	216
4.3	odd	2	inner	864.2.bi.a.95.24	yes	216
27.2	odd	18	inner	864.2.bi.a.191.24	yes	216
108.83	even	18	inner	864.2.bi.a.191.13	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.95.13	✓	216	1.1	even	1	trivial
864.2.bi.a.95.24	yes	216	4.3	odd	2	inner
864.2.bi.a.191.13	yes	216	108.83	even	18	inner
864.2.bi.a.191.24	yes	216	27.2	odd	18	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.639313 + 1.60974i) q^{3} +(1.25880 - 1.50018i) q^{5} +(-0.917368 + 2.52045i) q^{7} +(-2.18256 - 2.05826i) q^{9} +O(q^{10})\)	\(q+(-0.639313 + 1.60974i) q^{3} +(1.25880 - 1.50018i) q^{5} +(-0.917368 + 2.52045i) q^{7} +(-2.18256 - 2.05826i) q^{9} +(-1.09748 + 0.920894i) q^{11} +(-0.343327 + 1.94711i) q^{13} +(1.61014 + 2.98543i) q^{15} +(-0.116347 - 0.0671731i) q^{17} +(-2.14430 + 1.23801i) q^{19} +(-3.47079 - 3.08808i) q^{21} +(-3.02806 + 1.10212i) q^{23} +(0.202279 + 1.14718i) q^{25} +(4.70861 - 2.19749i) q^{27} +(-6.97586 + 1.23003i) q^{29} +(2.22686 + 6.11824i) q^{31} +(-0.780772 - 2.35540i) q^{33} +(2.62634 + 4.54896i) q^{35} +(-3.97244 + 6.88048i) q^{37} +(-2.91485 - 1.79748i) q^{39} +(6.86694 + 1.21083i) q^{41} +(-7.29062 - 8.68863i) q^{43} +(-5.83517 + 0.683287i) q^{45} +(3.00673 + 1.09436i) q^{47} +(-0.148783 - 0.124844i) q^{49} +(0.182514 - 0.144345i) q^{51} -7.88980i q^{53} +2.80564i q^{55} +(-0.622004 - 4.24325i) q^{57} +(0.194256 + 0.163001i) q^{59} +(-11.8108 - 4.29879i) q^{61} +(7.18995 - 3.61284i) q^{63} +(2.48883 + 2.96607i) q^{65} +(-4.87904 - 0.860306i) q^{67} +(0.161740 - 5.57900i) q^{69} +(-4.05398 + 7.02170i) q^{71} +(2.90548 + 5.03244i) q^{73} +(-1.97599 - 0.407791i) q^{75} +(-1.31427 - 3.61094i) q^{77} +(-11.3726 + 2.00530i) q^{79} +(0.527112 + 8.98455i) q^{81} +(2.29255 + 13.0017i) q^{83} +(-0.247230 + 0.0899843i) q^{85} +(2.47972 - 12.0157i) q^{87} +(-3.88936 + 2.24553i) q^{89} +(-4.59262 - 2.65155i) q^{91} +(-11.2725 - 0.326799i) q^{93} +(-0.842004 + 4.77524i) q^{95} +(2.93284 - 2.46095i) q^{97} +(4.29075 + 0.248995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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