LMFDB - Embedded newform 891.2.u.e.512.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, degree $8$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			512.4
Character	$\chi$	$=$	891.512
Dual form			891.2.u.e.134.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.607139 - 0.129051i) q^{2} +(-1.47513 - 0.656769i) q^{4} +(-0.776244 - 3.65194i) q^{5} +(2.20625 - 0.231886i) q^{7} +(1.81517 + 1.31880i) q^{8} +O(q^{10})$	\(q+(-0.607139 - 0.129051i) q^{2} +(-1.47513 - 0.656769i) q^{4} +(-0.776244 - 3.65194i) q^{5} +(2.20625 - 0.231886i) q^{7} +(1.81517 + 1.31880i) q^{8} +2.31741i q^{10} +(3.15510 + 1.02242i) q^{11} +(4.58440 + 4.12782i) q^{13} +(-1.36942 - 0.143932i) q^{14} +(1.22906 + 1.36501i) q^{16} +(-0.0962825 + 0.296327i) q^{17} +(1.44540 - 1.98943i) q^{19} +(-1.25342 + 5.89689i) q^{20} +(-1.78364 - 1.02792i) q^{22} +(7.72848 - 4.46204i) q^{23} +(-8.16640 + 3.63592i) q^{25} +(-2.25067 - 3.09778i) q^{26} +(-3.40679 - 1.10693i) q^{28} +(-0.690036 - 6.56526i) q^{29} +(-0.721480 + 0.801285i) q^{31} +(-2.81373 - 4.87352i) q^{32} +(0.0966983 - 0.167486i) q^{34} +(-2.55942 - 7.87708i) q^{35} +(-3.01593 + 2.19120i) q^{37} +(-1.13430 + 1.02133i) q^{38} +(3.40716 - 7.65260i) q^{40} +(0.436738 - 4.15528i) q^{41} +(4.12066 + 2.37906i) q^{43} +(-3.98268 - 3.58037i) q^{44} +(-5.26809 + 1.71171i) q^{46} +(-0.585996 - 1.31617i) q^{47} +(-2.03329 + 0.432188i) q^{49} +(5.42736 - 1.15362i) q^{50} +(-4.05156 - 9.09995i) q^{52} +(-5.61052 + 1.82297i) q^{53} +(1.28469 - 12.3159i) q^{55} +(4.31052 + 2.48868i) q^{56} +(-0.428307 + 4.07507i) q^{58} +(-2.27545 + 5.11074i) q^{59} +(1.11847 - 1.00708i) q^{61} +(0.541446 - 0.393383i) q^{62} +(-0.0558176 - 0.171789i) q^{64} +(11.5159 - 19.9462i) q^{65} +(-1.39875 - 2.42271i) q^{67} +(0.336647 - 0.373885i) q^{68} +(0.537375 + 5.11278i) q^{70} +(-6.47873 - 2.10507i) q^{71} +(5.66251 + 7.79378i) q^{73} +(2.11386 - 0.941153i) q^{74} +(-3.43875 + 1.98536i) q^{76} +(7.19801 + 1.52409i) q^{77} +(1.03441 - 4.86651i) q^{79} +(4.03089 - 5.54804i) q^{80} +(-0.801405 + 2.46647i) q^{82} +(8.96283 + 9.95424i) q^{83} +(1.15691 + 0.121596i) q^{85} +(-2.19479 - 1.97620i) q^{86} +(4.37867 + 6.01680i) q^{88} +3.05090i q^{89} +(11.0715 + 8.04392i) q^{91} +(-14.3310 + 1.50625i) q^{92} +(0.185928 + 0.874721i) q^{94} +(-8.38726 - 3.73425i) q^{95} +(14.3958 + 3.05992i) q^{97} +1.29026 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{4}+O(q^{10}) $ 64 * q + 8 * q^4	$ 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70} + 160 q^{73} + 60 q^{79} + 144 q^{82} + 20 q^{85} + 24 q^{88} + 48 q^{91} - 20 q^{94} + 24 q^{97}+O(q^{100}) $ 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.607139	−	0.129051i	−0.429312	−	0.0912531i	−0.0118125	−	0.999930i	$-0.503760\pi$
$2$	−0.607139	−	0.129051i	−0.429312	−	0.0912531i	−0.417500	+	0.908677i	$0.637093\pi$
$3$		0			0
$3$		0			0
$4$	−1.47513	−	0.656769i	−0.737564	−	0.328385i
$5$	−0.776244	−	3.65194i	−0.347147	−	1.63320i	−0.712033	−	0.702146i	$-0.752225\pi$
$5$	−0.776244	−	3.65194i	−0.347147	−	1.63320i	0.364886	−	0.931052i	$-0.381108\pi$
$6$		0			0
$7$	2.20625	−	0.231886i	0.833882	−	0.0876446i	0.322042	−	0.946725i	$-0.395631\pi$
$7$	2.20625	−	0.231886i	0.833882	−	0.0876446i	0.511840	+	0.859081i	$0.328964\pi$
$8$	1.81517	+	1.31880i	0.641759	+	0.466265i
$9$		0			0
$10$			2.31741i			0.732830i
$11$	3.15510	+	1.02242i	0.951298	+	0.308271i
$11$	3.15510	+	1.02242i	0.951298	+	0.308271i
$12$		0			0
$13$	4.58440	+	4.12782i	1.27148	+	1.14485i	0.982247	+	0.187593i	$0.0600685\pi$
$13$	4.58440	+	4.12782i	1.27148	+	1.14485i	0.289238	+	0.957257i	$0.406598\pi$
$14$	−1.36942	−	0.143932i	−0.365994	−	0.0384675i
$15$		0			0
$16$	1.22906	+	1.36501i	0.307265	+	0.341253i
$17$	−0.0962825	+	0.296327i	−0.0233519	+	0.0718699i	−0.962053	−	0.272861i	$-0.912030\pi$
$17$	−0.0962825	+	0.296327i	−0.0233519	+	0.0718699i	0.938701	+	0.344731i	$0.112030\pi$
$18$		0			0
$19$	1.44540	−	1.98943i	0.331598	−	0.456406i	−0.610366	−	0.792120i	$-0.708977\pi$
$19$	1.44540	−	1.98943i	0.331598	−	0.456406i	0.941964	+	0.335714i	$0.108977\pi$
$20$	−1.25342	+	5.89689i	−0.280274	+	1.31859i
$21$		0			0
$22$	−1.78364	−	1.02792i	−0.380273	−	0.219154i
$23$	7.72848	−	4.46204i	1.61150	−	0.930399i	0.622475	−	0.782639i	$-0.286127\pi$
$23$	7.72848	−	4.46204i	1.61150	−	0.930399i	0.989023	−	0.147760i	$-0.0472063\pi$
$24$		0			0
$25$	−8.16640	+	3.63592i	−1.63328	+	0.727183i
$26$	−2.25067	−	3.09778i	−0.441393	−	0.607525i
$27$		0			0
$28$	−3.40679	−	1.10693i	−0.643822	−	0.209191i
$29$	−0.690036	−	6.56526i	−0.128136	−	1.21914i	−0.849880	−	0.526977i	$-0.823326\pi$
$29$	−0.690036	−	6.56526i	−0.128136	−	1.21914i	0.721743	−	0.692161i	$-0.243341\pi$
$30$		0			0
$31$	−0.721480	+	0.801285i	−0.129582	+	0.143915i	−0.804444	−	0.594029i	$-0.797536\pi$
$31$	−0.721480	+	0.801285i	−0.129582	+	0.143915i	0.674862	+	0.737944i	$0.264203\pi$
$32$	−2.81373	−	4.87352i	−0.497401	−	0.861524i
$33$		0			0
$34$	0.0966983	−	0.167486i	0.0165836	−	0.0287237i
$35$	−2.55942	−	7.87708i	−0.432621	−	1.33147i
$36$		0			0
$37$	−3.01593	+	2.19120i	−0.495815	+	0.360231i	−0.807416	−	0.589982i	$-0.799135\pi$
$37$	−3.01593	+	2.19120i	−0.495815	+	0.360231i	0.311601	+	0.950213i	$0.399135\pi$
$38$	−1.13430	+	1.02133i	−0.184008	+	0.165681i
$39$		0			0
$40$	3.40716	−	7.65260i	0.538719	−	1.20998i
$41$	0.436738	−	4.15528i	0.0682070	−	0.648946i	−0.905998	−	0.423282i	$-0.860878\pi$
$41$	0.436738	−	4.15528i	0.0682070	−	0.648946i	0.974205	−	0.225664i	$-0.0724552\pi$
$42$		0			0
$43$	4.12066	+	2.37906i	0.628394	+	0.362803i	0.780130	−	0.625618i	$-0.215153\pi$
$43$	4.12066	+	2.37906i	0.628394	+	0.362803i	−0.151736	+	0.988421i	$0.548486\pi$
$44$	−3.98268	−	3.58037i	−0.600412	−	0.539762i
$45$		0			0
$46$	−5.26809	+	1.71171i	−0.776738	+	0.252377i
$47$	−0.585996	−	1.31617i	−0.0854763	−	0.191983i	0.865750	−	0.500477i	$-0.166842\pi$
$47$	−0.585996	−	1.31617i	−0.0854763	−	0.191983i	−0.951226	+	0.308494i	$0.900175\pi$
$48$		0			0
$49$	−2.03329	+	0.432188i	−0.290469	+	0.0617412i
$50$	5.42736	−	1.15362i	0.767545	−	0.163147i
$51$		0			0
$52$	−4.05156	−	9.09995i	−0.561850	−	1.26194i
$53$	−5.61052	+	1.82297i	−0.770664	+	0.250404i	−0.667849	−	0.744297i	$-0.732785\pi$
$53$	−5.61052	+	1.82297i	−0.770664	+	0.250404i	−0.102815	+	0.994701i	$0.532785\pi$
$54$		0			0
$55$	1.28469	−	12.3159i	0.173228	−	1.66067i
$56$	4.31052	+	2.48868i	0.576017	+	0.332564i
$57$		0			0
$58$	−0.428307	+	4.07507i	−0.0562395	+	0.535083i
$59$	−2.27545	+	5.11074i	−0.296238	+	0.665361i	−0.998936	−	0.0461273i	$-0.985312\pi$
$59$	−2.27545	+	5.11074i	−0.296238	+	0.665361i	0.702698	+	0.711489i	$0.251979\pi$
$60$		0			0
$61$	1.11847	−	1.00708i	0.143206	−	0.128943i	−0.594414	−	0.804159i	$-0.702616\pi$
$61$	1.11847	−	1.00708i	0.143206	−	0.128943i	0.737620	+	0.675216i	$0.235949\pi$
$62$	0.541446	−	0.393383i	0.0687637	−	0.0499597i
$63$		0			0
$64$	−0.0558176	−	0.171789i	−0.00697720	−	0.0214736i
$65$	11.5159	−	19.9462i	1.42838	−	2.47402i
$66$		0			0
$67$	−1.39875	−	2.42271i	−0.170885	−	0.295981i	0.767845	−	0.640636i	$-0.221329\pi$
$67$	−1.39875	−	2.42271i	−0.170885	−	0.295981i	−0.938729	+	0.344655i	$0.887996\pi$
$68$	0.336647	−	0.373885i	0.0408245	−	0.0453402i
$69$		0			0
$70$	0.537375	+	5.11278i	0.0642286	+	0.611094i
$71$	−6.47873	−	2.10507i	−0.768884	−	0.249826i	−0.101797	−	0.994805i	$-0.532459\pi$
$71$	−6.47873	−	2.10507i	−0.768884	−	0.249826i	−0.667087	+	0.744980i	$0.732459\pi$
$72$		0			0
$73$	5.66251	+	7.79378i	0.662747	+	0.912193i	0.999568	−	0.0293753i	$-0.00935180\pi$
$73$	5.66251	+	7.79378i	0.662747	+	0.912193i	−0.336821	+	0.941569i	$0.609352\pi$
$74$	2.11386	−	0.941153i	0.245732	−	0.109407i
$75$		0			0
$76$	−3.43875	+	1.98536i	−0.394452	+	0.227737i
$77$	7.19801	+	1.52409i	0.820289	+	0.173686i
$78$		0			0
$79$	1.03441	−	4.86651i	0.116380	−	0.547525i	−0.880866	−	0.473365i	$-0.843039\pi$
$79$	1.03441	−	4.86651i	0.116380	−	0.547525i	0.997246	−	0.0741597i	$-0.0236275\pi$
$80$	4.03089	−	5.54804i	0.450667	−	0.620290i
$81$		0			0
$82$	−0.801405	+	2.46647i	−0.0885004	+	0.272376i
$83$	8.96283	+	9.95424i	0.983799	+	1.09262i	0.995695	+	0.0926900i	$0.0295466\pi$
$83$	8.96283	+	9.95424i	0.983799	+	1.09262i	−0.0118962	+	0.999929i	$0.503787\pi$
$84$		0			0
$85$	1.15691	+	0.121596i	0.125484	+	0.0131889i
$86$	−2.19479	−	1.97620i	−0.236670	−	0.213099i
$87$		0			0
$88$	4.37867	+	6.01680i	0.466768	+	0.641393i
$89$			3.05090i			0.323394i	0.986840	+	0.161697i	$0.0516968\pi$
$89$			3.05090i			0.323394i	−0.986840	+	0.161697i	$0.948303\pi$
$90$		0			0
$91$	11.0715	+	8.04392i	1.16061	+	0.843231i
$92$	−14.3310	+	1.50625i	−1.49411	+	0.157037i
$93$		0			0
$94$	0.185928	+	0.874721i	0.0191770	+	0.0902206i
$95$	−8.38726	−	3.73425i	−0.860515	−	0.383126i
$96$		0			0
$97$	14.3958	+	3.05992i	1.46167	+	0.310688i	0.869022	−	0.494774i	$-0.164749\pi$
$97$	14.3958	+	3.05992i	1.46167	+	0.310688i	0.592648	+	0.805461i	$0.298082\pi$
$98$	1.29026			0.130336
$99$		0			0
$100$	14.4344			1.44344
$101$	−6.41057	−	1.36261i	−0.637876	−	0.135585i	−0.122389	−	0.992482i	$-0.539056\pi$
$101$	−6.41057	−	1.36261i	−0.637876	−	0.135585i	−0.515487	+	0.856898i	$0.672389\pi$
$102$		0			0
$103$	−8.00445	−	3.56381i	−0.788702	−	0.351153i	−0.0274620	−	0.999623i	$-0.508743\pi$
$103$	−8.00445	−	3.56381i	−0.788702	−	0.351153i	−0.761240	+	0.648470i	$0.775409\pi$
$104$	2.87771	+	13.5386i	0.282183	+	1.32757i
$105$		0			0
$106$	3.64162	−	0.382750i	0.353705	−	0.0371759i
$107$	0.618545	+	0.449399i	0.0597970	+	0.0434451i	0.617282	−	0.786742i	$-0.288234\pi$
$107$	0.618545	+	0.449399i	0.0597970	+	0.0434451i	−0.557485	+	0.830187i	$0.688234\pi$
$108$		0			0
$109$		−	4.39272i		−	0.420746i	−0.977621	−	0.210373i	$-0.932532\pi$
$109$		−	4.39272i		−	0.420746i	0.977621	−	0.210373i	$-0.0674678\pi$
$110$	−2.36937	+	7.31167i	−0.225911	+	0.697140i
$111$		0			0
$112$	3.02814	+	2.72655i	0.286132	+	0.257634i
$113$	5.98198	+	0.628732i	0.562738	+	0.0591461i	0.381627	−	0.924317i	$-0.375364\pi$
$113$	5.98198	+	0.628732i	0.562738	+	0.0591461i	0.181111	+	0.983463i	$0.442031\pi$
$114$		0			0
$115$	−22.2943	−	24.7603i	−2.07895	−	2.30891i
$116$	−3.29397	+	10.1378i	−0.305837	+	0.941269i
$117$		0			0
$118$	2.04106	−	2.80928i	0.187895	−	0.258615i
$119$	−0.143709	+	0.676097i	−0.0131738	+	0.0619777i
$120$		0			0
$121$	8.90931	+	6.45168i	0.809937	+	0.586516i
$122$	−0.809034	+	0.467096i	−0.0732465	+	0.0422889i
$123$		0			0
$124$	1.59053	−	0.708152i	0.142834	−	0.0635939i
$125$	8.64472	+	11.8984i	0.773207	+	1.06423i
$126$		0			0
$127$	−10.7264	−	3.48521i	−0.951811	−	0.309262i	−0.208360	−	0.978052i	$-0.566813\pi$
$127$	−10.7264	−	3.48521i	−0.951811	−	0.309262i	−0.743451	+	0.668790i	$0.766813\pi$
$128$	1.18818	+	11.3048i	0.105021	+	0.999208i
$129$		0			0
$130$	−9.56585	+	10.6240i	−0.838981	+	0.931782i
$131$	−8.59104	−	14.8801i	−0.750603	−	1.30008i	−0.947531	−	0.319664i	$-0.896430\pi$
$131$	−8.59104	−	14.8801i	−0.750603	−	1.30008i	0.196928	−	0.980418i	$-0.436903\pi$
$132$		0			0
$133$	2.72760	−	4.72433i	0.236513	−	0.409652i
$134$	0.536583	+	1.65143i	0.0463537	+	0.142662i
$135$		0			0
$136$	−0.565564	+	0.410906i	−0.0484967	+	0.0352349i
$137$	−1.01033	+	0.909706i	−0.0863184	+	0.0777214i	−0.711160	−	0.703030i	$-0.751830\pi$
$137$	−1.01033	+	0.909706i	−0.0863184	+	0.0777214i	0.624842	+	0.780751i	$0.285163\pi$
$138$		0			0
$139$	4.90673	−	11.0207i	0.416183	−	0.934763i	−0.576841	−	0.816856i	$-0.695715\pi$
$139$	4.90673	−	11.0207i	0.416183	−	0.934763i	0.993025	−	0.117907i	$-0.0376185\pi$
$140$	−1.39795	+	13.3006i	−0.118149	+	1.12411i
$141$		0			0
$142$	3.66183	+	2.11416i	0.307294	+	0.177416i
$143$	10.2439	+	17.7109i	0.856637	+	1.48106i
$144$		0			0
$145$	−23.4403	+	7.61622i	−1.94661	+	0.632492i
$146$	−2.43213	−	5.46266i	−0.201285	−	0.452093i
$147$		0			0
$148$	5.88799	−	1.25153i	0.483990	−	0.102875i
$149$	−14.3002	+	3.03960i	−1.17152	+	0.249013i	−0.752267	−	0.658858i	$-0.771040\pi$
$149$	−14.3002	+	3.03960i	−1.17152	+	0.249013i	−0.419249	+	0.907872i	$0.637706\pi$
$150$		0			0
$151$	−1.13147	−	2.54132i	−0.0920775	−	0.206809i	0.861636	−	0.507527i	$-0.169440\pi$
$151$	−1.13147	−	2.54132i	−0.0920775	−	0.206809i	−0.953713	+	0.300718i	$0.902774\pi$
$152$	5.24730	−	1.70495i	0.425613	−	0.138290i
$153$		0			0
$154$	−4.17351	−	1.85425i	−0.336311	−	0.149419i
$155$	3.48629	+	2.01281i	0.280026	+	0.161673i
$156$		0			0
$157$	1.85052	−	17.6065i	0.147688	−	1.40516i	−0.630044	−	0.776559i	$-0.716963\pi$
$157$	1.85052	−	17.6065i	0.147688	−	1.40516i	0.777732	−	0.628596i	$-0.216370\pi$
$158$	−1.25606	+	2.82115i	−0.0999266	+	0.224439i
$159$		0			0
$160$	−15.6137	+	14.0586i	−1.23437	+	1.11143i
$161$	16.0162	−	11.6365i	1.26226	−	0.917083i
$162$		0			0
$163$	0.454189	+	1.39785i	0.0355748	+	0.109488i	0.967267	−	0.253761i	$-0.0816675\pi$
$163$	0.454189	+	1.39785i	0.0355748	+	0.109488i	−0.931692	+	0.363249i	$0.881668\pi$
$164$	−3.37330	+	5.84273i	−0.263411	+	0.456241i
$165$		0			0
$166$	−4.15708	−	7.20027i	−0.322652	−	0.558849i
$167$	−6.01213	+	6.67715i	−0.465233	+	0.516693i	−0.929410	−	0.369049i	$-0.879683\pi$
$167$	−6.01213	+	6.67715i	−0.465233	+	0.516693i	0.464177	+	0.885742i	$0.346350\pi$
$168$		0			0
$169$	2.61903	+	24.9184i	0.201463	+	1.91680i
$170$	−0.686712	−	0.223126i	−0.0526684	−	0.0171130i
$171$		0			0
$172$	−4.51600	−	6.21574i	−0.344342	−	0.473946i
$173$	−6.02423	+	2.68216i	−0.458014	+	0.203921i	−0.622757	−	0.782416i	$-0.713987\pi$
$173$	−6.02423	+	2.68216i	−0.458014	+	0.203921i	0.164743	+	0.986337i	$0.447321\pi$
$174$		0			0
$175$	−17.1740	+	9.91540i	−1.29823	+	0.749534i
$176$	2.48219	+	5.56336i	0.187102	+	0.419354i
$177$		0			0
$178$	0.393722	−	1.85232i	0.0295107	−	0.138837i
$179$	−0.750385	+	1.03282i	−0.0560864	+	0.0771963i	−0.836139	−	0.548518i	$-0.815192\pi$
$179$	−0.750385	+	1.03282i	−0.0560864	+	0.0771963i	0.780053	+	0.625714i	$0.215192\pi$
$180$		0			0
$181$	6.39068	−	19.6685i	0.475016	−	1.46195i	−0.370921	−	0.928664i	$-0.620958\pi$
$181$	6.39068	−	19.6685i	0.475016	−	1.46195i	0.845937	−	0.533283i	$-0.179042\pi$
$182$	−5.68386	−	6.31257i	−0.421316	−	0.467919i
$183$		0			0
$184$	19.9130	+	2.09294i	1.46801	+	0.154294i
$185$	10.3432	+	9.31309i	0.760450	+	0.684712i
$186$		0			0
$187$	−0.606752	+	0.836500i	−0.0443701	+	0.0611709i
$188$			2.32638i			0.169669i
$189$		0			0
$190$	4.61032	+	3.34960i	0.334468	+	0.243005i
$191$	−6.69305	+	0.703468i	−0.484292	+	0.0509012i	−0.343529	−	0.939142i	$-0.611622\pi$
$191$	−6.69305	+	0.703468i	−0.484292	+	0.0509012i	−0.140763	+	0.990043i	$0.544956\pi$
$192$		0			0
$193$	−3.28299	−	15.4453i	−0.236315	−	1.11177i	−0.922994	−	0.384814i	$-0.874266\pi$
$193$	−3.28299	−	15.4453i	−0.236315	−	1.11177i	0.686679	−	0.726961i	$-0.259068\pi$
$194$	−8.34535	−	3.71559i	−0.599161	−	0.266764i
$195$		0			0
$196$	3.28320	+	0.697867i	0.234515	+	0.0498476i
$197$	2.09103			0.148980			0.0744900	−	0.997222i	$-0.476267\pi$
$197$	2.09103			0.148980			0.0744900	+	0.997222i	$0.476267\pi$
$198$		0			0
$199$	−3.76773			−0.267087			−0.133544	−	0.991043i	$-0.542636\pi$
$199$	−3.76773			−0.267087			−0.133544	+	0.991043i	$0.542636\pi$
$200$	−19.6184	−	4.17003i	−1.38723	−	0.294865i
$201$		0			0
$202$	3.71626	+	1.65459i	0.261475	+	0.116416i
$203$	−3.04478	−	14.3246i	−0.213702	−	1.00539i
$204$		0			0
$205$	−15.5139	+	1.63057i	−1.08354	+	0.113884i
$206$	4.39990	+	3.19671i	0.306556	+	0.222726i
$207$		0			0
$208$			11.3311i			0.785670i
$209$	6.59443	−	4.79903i	0.456146	−	0.331956i
$210$		0			0
$211$	8.09236	+	7.28640i	0.557101	+	0.501616i	0.898898	−	0.438158i	$-0.144369\pi$
$211$	8.09236	+	7.28640i	0.557101	+	0.501616i	−0.341797	+	0.939774i	$0.611035\pi$
$212$	9.47350	+	0.995705i	0.650642	+	0.0683853i
$213$		0			0
$214$	−0.317547	−	0.352672i	−0.0217071	−	0.0241082i
$215$	5.48956	−	16.8951i	0.374385	−	1.15224i
$216$		0			0
$217$	−1.40596	+	1.93513i	−0.0954425	+	0.131365i
$218$	−0.566886	+	2.66699i	−0.0383944	+	0.180631i
$219$		0			0
$220$	−9.98378	+	17.3238i	−0.673107	+	1.16797i
$221$	−1.66458	+	0.961046i	−0.111972	+	0.0646470i
$222$		0			0
$223$	10.3750	−	4.61926i	0.694764	−	0.309329i	−0.0288010	−	0.999585i	$-0.509169\pi$
$223$	10.3750	−	4.61926i	0.694764	−	0.309329i	0.723565	+	0.690256i	$0.242502\pi$
$224$	−7.33787	−	10.0997i	−0.490282	−	0.674815i
$225$		0			0
$226$	−3.55076	−	1.15371i	−0.236193	−	0.0767437i
$227$	−1.11988	−	10.6550i	−0.0743292	−	0.707195i	−0.966704	−	0.255899i	$-0.917629\pi$
$227$	−1.11988	−	10.6550i	−0.0743292	−	0.707195i	0.892374	−	0.451296i	$-0.149038\pi$
$228$		0			0
$229$	−13.1650	+	14.6213i	−0.869971	+	0.966200i	−0.999679	−	0.0253520i	$-0.991929\pi$
$229$	−13.1650	+	14.6213i	−0.869971	+	0.966200i	0.129708	+	0.991552i	$0.458596\pi$
$230$	10.3404	+	17.9101i	0.681825	+	1.18095i
$231$		0			0
$232$	7.40571	−	12.8271i	0.486209	−	0.842138i
$233$	6.22888	+	19.1705i	0.408068	+	1.25590i	0.918306	+	0.395871i	$0.129557\pi$
$233$	6.22888	+	19.1705i	0.408068	+	1.25590i	−0.510238	+	0.860033i	$0.670443\pi$
$234$		0			0
$235$	−4.35170	+	3.16169i	−0.283874	+	0.206246i
$236$	6.71315	−	6.04454i	0.436989	−	0.393466i
$237$		0			0
$238$	0.174502	−	0.391939i	0.0113113	−	0.0254056i
$239$	−1.79773	+	17.1043i	−0.116286	+	1.10638i	0.768327	+	0.640058i	$0.221090\pi$
$239$	−1.79773	+	17.1043i	−0.116286	+	1.10638i	−0.884612	+	0.466327i	$0.845577\pi$
$240$		0			0
$241$	17.7792	+	10.2648i	1.14526	+	0.661215i	0.947727	−	0.319081i	$-0.103374\pi$
$241$	17.7792	+	10.2648i	1.14526	+	0.661215i	0.197531	+	0.980297i	$0.436708\pi$
$242$	−4.57659	−	5.06683i	−0.294194	−	0.325708i
$243$		0			0
$244$	−2.31131	+	0.750990i	−0.147966	+	0.0480772i
$245$	3.15665	+	7.08996i	0.201671	+	0.452961i
$246$		0			0
$247$	14.8383	−	3.15398i	0.944139	−	0.200683i
$248$	−2.36634	+	0.502981i	−0.150263	+	0.0319394i
$249$		0			0
$250$	−3.71304	−	8.33962i	−0.234833	−	0.527444i
$251$	6.04667	−	1.96468i	0.381662	−	0.124010i	−0.111901	−	0.993719i	$-0.535694\pi$
$251$	6.04667	−	1.96468i	0.381662	−	0.124010i	0.493563	+	0.869710i	$0.335694\pi$
$252$		0			0
$253$	28.9462	−	6.17642i	1.81983	−	0.388308i
$254$	6.06263	+	3.50026i	0.380403	+	0.219626i
$255$		0			0
$256$	0.699743	−	6.65761i	0.0437339	−	0.416101i
$257$	−5.63007	+	12.6453i	−0.351194	+	0.788794i	0.648427	+	0.761276i	$0.275427\pi$
$257$	−5.63007	+	12.6453i	−0.351194	+	0.788794i	−0.999621	+	0.0275179i	$0.991240\pi$
$258$		0			0
$259$	−6.14577	+	5.53367i	−0.381879	+	0.343846i
$260$	−30.0875	+	21.8598i	−1.86595	+	1.35569i
$261$		0			0
$262$	3.29566	+	10.1430i	0.203606	+	0.626636i
$263$	−7.71773	+	13.3675i	−0.475896	+	0.824275i	−0.999619	−	0.0276132i	$-0.991209\pi$
$263$	−7.71773	+	13.3675i	−0.475896	+	0.824275i	0.523723	+	0.851889i	$0.324543\pi$
$264$		0			0
$265$	11.0125	+	19.0742i	0.676493	+	1.17172i
$266$	−2.26571	+	2.51633i	−0.138920	+	0.154286i
$267$		0			0
$268$	0.472177	+	4.49247i	0.0288428	+	0.274421i
$269$	5.84229	+	1.89827i	0.356211	+	0.115740i	0.481655	−	0.876361i	$-0.340036\pi$
$269$	5.84229	+	1.89827i	0.356211	+	0.115740i	−0.125445	+	0.992101i	$0.540036\pi$
$270$		0			0
$271$	11.0715	+	15.2386i	0.672546	+	0.925680i	0.999815	−	0.0192514i	$-0.00612829\pi$
$271$	11.0715	+	15.2386i	0.672546	+	0.925680i	−0.327269	+	0.944931i	$0.606128\pi$
$272$	−0.522826	+	0.232777i	−0.0317010	+	0.0141142i
$273$		0			0
$274$	0.730810	−	0.421933i	0.0441498	−	0.0254899i
$275$	−29.4833	+	3.12218i	−1.77791	+	0.188275i
$276$		0			0
$277$	−1.14030	+	5.36469i	−0.0685140	+	0.322333i	−0.999036	−	0.0439036i	$-0.986021\pi$
$277$	−1.14030	+	5.36469i	−0.0685140	+	0.322333i	0.930522	+	0.366236i	$0.119354\pi$
$278$	−4.40130	+	6.05787i	−0.263973	+	0.363327i
$279$		0			0
$280$	5.74250	−	17.6736i	0.343180	−	1.05620i
$281$	−17.4638	−	19.3955i	−1.04180	−	1.15704i	−0.987356	−	0.158521i	$-0.949327\pi$
$281$	−17.4638	−	19.3955i	−1.04180	−	1.15704i	−0.0544463	−	0.998517i	$-0.517339\pi$
$282$		0			0
$283$	−17.1513	−	1.80267i	−1.01954	−	0.107158i	−0.420017	−	0.907516i	$-0.637976\pi$
$283$	−17.1513	−	1.80267i	−1.01954	−	0.107158i	−0.599522	+	0.800359i	$0.704642\pi$
$284$	8.17442	+	7.36028i	0.485062	+	0.436752i
$285$		0			0
$286$	−3.93385	−	12.0749i	−0.232614	−	0.714006i
$287$		−	9.26884i		−	0.547122i
$288$		0			0
$289$	13.6747	+	9.93529i	0.804397	+	0.584429i
$290$	15.2144	−	1.59910i	0.893420	−	0.0939023i
$291$		0			0
$292$	−3.23422	−	15.2158i	−0.189268	−	0.890437i
$293$	24.8046	+	11.0437i	1.44910	+	0.645182i	0.972280	−	0.233818i	$-0.0751219\pi$
$293$	24.8046	+	11.0437i	1.44910	+	0.645182i	0.476822	+	0.879000i	$0.341789\pi$
$294$		0			0
$295$	20.4304	+	4.34262i	1.18951	+	0.252837i
$296$	−8.36416			−0.486157
$297$		0			0
$298$	9.07446			0.525669
$299$	53.8489	+	11.4459i	3.11416	+	0.661936i
$300$		0			0
$301$	9.64285	+	4.29327i	0.555804	+	0.247460i
$302$	0.358997	+	1.68895i	0.0206580	+	0.0971882i
$303$		0			0
$304$	4.49208	−	0.472136i	0.257638	−	0.0270789i
$305$	−4.54600	−	3.30286i	−0.260303	−	0.189121i
$306$		0			0
$307$			14.5585i			0.830895i	0.909617	+	0.415448i	$0.136375\pi$
$307$			14.5585i			0.830895i	−0.909617	+	0.415448i	$0.863625\pi$
$308$	−9.61701	−	6.97565i	−0.547980	−	0.397475i
$309$		0			0
$310$	−1.85691	−	1.67197i	−0.105465	−	0.0949614i
$311$	−4.35726	−	0.457966i	−0.247078	−	0.0259689i	−0.0198199	−	0.999804i	$-0.506309\pi$
$311$	−4.35726	−	0.457966i	−0.247078	−	0.0259689i	−0.227258	+	0.973835i	$0.572976\pi$
$312$		0			0
$313$	−3.77269	−	4.18999i	−0.213245	−	0.236832i	0.627027	−	0.778997i	$-0.284271\pi$
$313$	−3.77269	−	4.18999i	−0.213245	−	0.236832i	−0.840272	+	0.542165i	$0.817605\pi$
$314$	−3.39567	+	10.4508i	−0.191629	+	0.589773i
$315$		0			0
$316$	−4.72205	+	6.49935i	−0.265636	+	0.365617i
$317$	3.30773	−	15.5617i	0.185781	−	0.874030i	−0.782204	−	0.623022i	$-0.785905\pi$
$317$	3.30773	−	15.5617i	0.185781	−	0.874030i	0.967985	−	0.251008i	$-0.0807620\pi$
$318$		0			0
$319$	4.53532	−	21.4195i	0.253929	−	1.19926i
$320$	−0.584035	+	0.337193i	−0.0326486	+	0.0188497i
$321$		0			0
$322$	−11.2258	+	4.99804i	−0.625588	+	0.278530i
$323$	0.450354	+	0.619859i	0.0250584	+	0.0344899i
$324$		0			0
$325$	−52.4465	−	17.0409i	−2.90921	−	0.945259i
$326$	−0.0953614	−	0.907303i	−0.00528158	−	0.0502509i
$327$		0			0
$328$	6.27273	−	6.96657i	0.346353	−	0.384664i
$329$	−1.59805	−	2.76791i	−0.0881035	−	0.152600i
$330$		0			0
$331$	−9.89275	+	17.1347i	−0.543755	+	0.941811i	0.454930	+	0.890527i	$0.349664\pi$
$331$	−9.89275	+	17.1347i	−0.543755	+	0.941811i	−0.998684	+	0.0512832i	$0.983669\pi$
$332$	−6.68369	−	20.5703i	−0.366815	−	1.12894i
$333$		0			0
$334$	4.51189	−	3.27808i	0.246880	−	0.179369i
$335$	−7.76183	+	6.98878i	−0.424074	+	0.381838i
$336$		0			0
$337$	−9.70893	+	21.8066i	−0.528879	+	1.18788i	0.429678	+	0.902982i	$0.358627\pi$
$337$	−9.70893	+	21.8066i	−0.528879	+	1.18788i	−0.958557	+	0.284900i	$0.908040\pi$
$338$	1.62564	−	15.4669i	0.0884230	−	0.841288i
$339$		0			0
$340$	−1.62673	−	0.939191i	−0.0882216	−	0.0509348i
$341$	−3.09559	+	1.79048i	−0.167636	+	0.0969598i
$342$		0			0
$343$	−19.1545	+	6.22366i	−1.03424	+	0.336046i
$344$	4.34218	+	9.75271i	0.234115	+	0.525831i
$345$		0			0
$346$	4.00368	−	0.851009i	0.215239	−	0.0457505i
$347$	16.9727	−	3.60765i	0.911141	−	0.193669i	0.271586	−	0.962414i	$-0.412452\pi$
$347$	16.9727	−	3.60765i	0.911141	−	0.193669i	0.639555	+	0.768745i	$0.279119\pi$
$348$		0			0
$349$	−4.53784	−	10.1921i	−0.242905	−	0.545573i	0.750415	−	0.660967i	$-0.229854\pi$
$349$	−4.53784	−	10.1921i	−0.242905	−	0.545573i	−0.993320	+	0.115394i	$0.963187\pi$
$350$	11.7066	−	3.80370i	0.625743	−	0.203316i
$351$		0			0
$352$	−3.89480	−	18.2532i	−0.207594	−	0.972901i
$353$	−20.3046	−	11.7228i	−1.08070	−	0.623944i	−0.149617	−	0.988744i	$-0.547804\pi$
$353$	−20.3046	−	11.7228i	−1.08070	−	0.623944i	−0.931086	+	0.364800i	$0.881137\pi$
$354$		0			0
$355$	−2.65851	+	25.2940i	−0.141099	+	1.34247i
$356$	2.00373	−	4.50046i	0.106198	−	0.238524i
$357$		0			0
$358$	0.588874	−	0.530225i	0.0311230	−	0.0280232i
$359$	−14.8582	+	10.7951i	−0.784184	+	0.569743i	−0.906232	−	0.422781i	$-0.861054\pi$
$359$	−14.8582	+	10.7951i	−0.784184	+	0.569743i	0.122048	+	0.992524i	$0.461054\pi$
$360$		0			0
$361$	4.00269	+	12.3190i	0.210668	+	0.648370i
$362$	−6.41828	+	11.1168i	−0.337337	+	0.584285i
$363$		0			0
$364$	−11.0489	−	19.1372i	−0.579119	−	1.00306i
$365$	24.0670	−	26.7291i	1.25972	−	1.39906i
$366$		0			0
$367$	−1.41118	−	13.4265i	−0.0736632	−	0.700859i	−0.967570	−	0.252605i	$-0.918713\pi$
$367$	−1.41118	−	13.4265i	−0.0736632	−	0.700859i	0.893906	−	0.448254i	$-0.147954\pi$
$368$	15.5895	+	5.06533i	0.812659	+	0.264049i
$369$		0			0
$370$	−5.07791	−	6.98915i	−0.263988	−	0.363348i
$371$	−11.9555	+	5.32291i	−0.620696	+	0.276352i
$372$		0			0
$373$	24.4937	−	14.1414i	1.26823	−	0.732215i	0.293581	−	0.955934i	$-0.405153\pi$
$373$	24.4937	−	14.1414i	1.26823	−	0.732215i	0.974654	+	0.223719i	$0.0718197\pi$
$374$	0.476334	−	0.429570i	0.0246307	−	0.0222125i
$375$		0			0
$376$	0.672078	−	3.16188i	0.0346598	−	0.163061i
$377$	23.9368	−	32.9461i	1.23281	−	1.69681i
$378$		0			0
$379$	−0.0682032	+	0.209908i	−0.00350336	+	0.0107822i	−0.952793	−	0.303621i	$-0.901804\pi$
$379$	−0.0682032	+	0.209908i	−0.00350336	+	0.0107822i	0.949290	+	0.314403i	$0.101804\pi$
$380$	9.91974	+	11.0170i	0.508872	+	0.565160i
$381$		0			0
$382$	4.15440	+	0.436645i	0.212557	+	0.0223407i
$383$	−28.6768	−	25.8207i	−1.46532	−	1.31938i	−0.844672	−	0.535284i	$-0.820205\pi$
$383$	−28.6768	−	25.8207i	−1.46532	−	1.31938i	−0.620644	−	0.784093i	$-0.713129\pi$
$384$		0			0
$385$	−0.0215298	−	27.4698i	−0.00109726	−	1.39999i
$386$			9.80110i			0.498863i
$387$		0			0
$388$	−19.2260	−	13.9685i	−0.976050	−	0.709142i
$389$	36.1590	−	3.80046i	1.83333	−	0.192691i	0.876124	−	0.482086i	$-0.160121\pi$
$389$	36.1590	−	3.80046i	1.83333	−	0.192691i	0.957210	+	0.289395i	$0.0934541\pi$
$390$		0			0
$391$	0.578105	+	2.71977i	0.0292360	+	0.137545i
$392$	−4.26073	−	1.89700i	−0.215199	−	0.0958128i
$393$		0			0
$394$	−1.26955	−	0.269851i	−0.0639589	−	0.0135949i
$395$	−18.5752			−0.934617
$396$		0			0
$397$	22.4527			1.12687			0.563434	−	0.826161i	$-0.309480\pi$
$397$	22.4527			1.12687			0.563434	+	0.826161i	$0.309480\pi$
$398$	2.28753	+	0.486230i	0.114664	+	0.0243725i
$399$		0			0
$400$	−15.0001	−	6.67846i	−0.750004	−	0.333923i
$401$	−5.72301	−	26.9246i	−0.285793	−	1.34455i	−0.853402	−	0.521253i	$-0.825465\pi$
$401$	−5.72301	−	26.9246i	−0.285793	−	1.34455i	0.567609	−	0.823298i	$-0.307869\pi$
$402$		0			0
$403$	−6.61511	+	0.695277i	−0.329522	+	0.0346342i
$404$	8.56149	+	6.22029i	0.425950	+	0.309471i
$405$		0			0
$406$			9.08993i			0.451126i
$407$	−11.7559	+	3.82991i	−0.582717	+	0.189841i
$408$		0			0
$409$	−29.6933	−	26.7360i	−1.46824	−	1.32201i	−0.838082	−	0.545544i	$-0.816323\pi$
$409$	−29.6933	−	26.7360i	−1.46824	−	1.32201i	−0.630158	−	0.776467i	$-0.717010\pi$
$410$	9.62950	+	1.01210i	0.475567	+	0.0499841i
$411$		0			0
$412$	9.46699	+	10.5142i	0.466405	+	0.517995i
$413$	−3.83509	+	11.8032i	−0.188712	+	0.580797i
$414$		0			0
$415$	29.3949	−	40.4587i	1.44294	−	1.98604i
$416$	7.21772	−	33.9567i	0.353878	−	1.66486i
$417$		0			0
$418$	−4.62305	+	2.06266i	−0.226121	+	0.100888i
$419$	−21.9499	+	12.6728i	−1.07232	+	0.619105i	−0.928815	−	0.370544i	$-0.879171\pi$
$419$	−21.9499	+	12.6728i	−1.07232	+	0.619105i	−0.143507	+	0.989649i	$0.545838\pi$
$420$		0			0
$421$	−13.6093	+	6.05927i	−0.663278	+	0.295311i	−0.710628	−	0.703568i	$-0.751589\pi$
$421$	−13.6093	+	6.05927i	−0.663278	+	0.295311i	0.0473497	+	0.998878i	$0.484922\pi$
$422$	−3.97287	−	5.46819i	−0.193396	−	0.266187i
$423$		0			0
$424$	−12.5882	−	4.09014i	−0.611335	−	0.198635i
$425$	−0.291139	−	2.77000i	−0.0141223	−	0.134365i
$426$		0			0
$427$	2.23410	−	2.48122i	0.108116	−	0.120075i
$428$	−0.617281	−	1.06916i	−0.0298374	−	0.0516799i
$429$		0			0
$430$	−5.51327	+	9.54926i	−0.265873	+	0.460506i
$431$	4.81473	+	14.8182i	0.231917	+	0.713768i	0.997515	+	0.0704489i	$0.0224432\pi$
$431$	4.81473	+	14.8182i	0.231917	+	0.713768i	−0.765598	+	0.643319i	$0.777557\pi$
$432$		0			0
$433$	−8.59479	+	6.24448i	−0.413039	+	0.300091i	−0.774831	−	0.632168i	$-0.782165\pi$
$433$	−8.59479	+	6.24448i	−0.413039	+	0.300091i	0.361792	+	0.932259i	$0.382165\pi$
$434$	1.10334	−	0.993454i	0.0529621	−	0.0476873i
$435$		0			0
$436$	−2.88500	+	6.47982i	−0.138166	+	0.310327i
$437$	2.29387	−	21.8247i	0.109731	−	1.04402i
$438$		0			0
$439$	15.4266	+	8.90653i	0.736270	+	0.425085i	0.820711	−	0.571343i	$-0.193577\pi$
$439$	15.4266	+	8.90653i	0.736270	+	0.425085i	−0.0844418	+	0.996428i	$0.526911\pi$
$440$	18.5741	−	20.6612i	0.885486	−	0.984983i
$441$		0			0
$442$	1.13466	−	0.368672i	0.0539701	−	0.0175359i
$443$	7.45041	+	16.7339i	0.353980	+	0.795051i	0.999510	+	0.0313162i	$0.00996988\pi$
$443$	7.45041	+	16.7339i	0.353980	+	0.795051i	−0.645530	+	0.763735i	$0.723363\pi$
$444$		0			0
$445$	11.1417	−	2.36824i	0.528167	−	0.112265i
$446$	−6.89521	+	1.46562i	−0.326498	+	0.0693992i
$447$		0			0
$448$	−0.162983	−	0.366065i	−0.00770021	−	0.0172950i
$449$	−13.4434	+	4.36802i	−0.634433	+	0.206140i	−0.608538	−	0.793525i	$-0.708244\pi$
$449$	−13.4434	+	4.36802i	−0.634433	+	0.206140i	−0.0258953	+	0.999665i	$0.508244\pi$
$450$		0			0
$451$	5.62640	−	12.6638i	0.264937	−	0.596315i
$452$	−8.41126	−	4.85624i	−0.395632	−	0.228418i
$453$		0			0
$454$	−0.695114	+	6.61357i	−0.0326233	+	0.310390i
$455$	20.7817	−	46.6765i	0.974263	−	2.18823i
$456$		0			0
$457$	−6.43116	+	5.79065i	−0.300837	+	0.270875i	−0.805699	−	0.592325i	$-0.798210\pi$
$457$	−6.43116	+	5.79065i	−0.300837	+	0.270875i	0.504862	+	0.863200i	$0.331543\pi$
$458$	9.87990	−	7.17817i	0.461658	−	0.335414i
$459$		0			0
$460$	16.6251	+	51.1668i	0.775150	+	2.38567i
$461$	−18.1341	+	31.4092i	−0.844590	+	1.46287i	0.0413877	+	0.999143i	$0.486822\pi$
$461$	−18.1341	+	31.4092i	−0.844590	+	1.46287i	−0.885977	+	0.463729i	$0.846511\pi$
$462$		0			0
$463$	14.1514	+	24.5109i	0.657669	+	1.13912i	0.981217	+	0.192905i	$0.0617908\pi$
$463$	14.1514	+	24.5109i	0.657669	+	1.13912i	−0.323548	+	0.946212i	$0.604876\pi$
$464$	8.11354	−	9.01100i	0.376662	−	0.418325i
$465$		0			0
$466$	−1.30781	−	12.4430i	−0.0605833	−	0.576412i
$467$	−26.4483	−	8.59356i	−1.22388	−	0.397662i	−0.375386	−	0.926869i	$-0.622490\pi$
$467$	−26.4483	−	8.59356i	−1.22388	−	0.397662i	−0.848493	+	0.529206i	$0.822490\pi$
$468$		0			0
$469$	−3.64778	−	5.02074i	−0.168439	−	0.231836i
$470$	3.05011	−	1.35800i	0.140691	−	0.0626396i
$471$		0			0
$472$	−10.8703	+	6.27600i	−0.500348	+	0.288876i
$473$	10.5687	+	11.7192i	0.485948	+	0.538850i
$474$		0			0
$475$	−4.57036	+	21.5018i	−0.209702	+	0.986572i
$476$	0.656028	−	0.902945i	0.0300690	−	0.0413864i
$477$		0			0
$478$	3.29881	−	10.1527i	0.150884	−	0.464373i
$479$	−4.96151	−	5.51031i	−0.226697	−	0.251773i	0.619056	−	0.785347i	$-0.287515\pi$
$479$	−4.96151	−	5.51031i	−0.226697	−	0.251773i	−0.845753	+	0.533574i	$0.820849\pi$
$480$		0			0
$481$	−22.8711	−	2.40385i	−1.04283	−	0.109606i
$482$	−9.46975	−	8.52660i	−0.431335	−	0.388376i
$483$		0			0
$484$	−8.90511	−	15.3684i	−0.404778	−	0.698564i
$485$		−	54.9478i		−	2.49505i
$486$		0			0
$487$	15.0683	+	10.9477i	0.682808	+	0.496089i	0.874288	−	0.485408i	$-0.161329\pi$
$487$	15.0683	+	10.9477i	0.682808	+	0.496089i	−0.191480	+	0.981496i	$0.561329\pi$
$488$	3.35835	−	0.352977i	0.152025	−	0.0159785i
$489$		0			0
$490$	−1.00156	−	4.71196i	−0.0452458	−	0.212865i
$491$	19.5154	+	8.68880i	0.880716	+	0.392120i	0.796722	−	0.604346i	$-0.206566\pi$
$491$	19.5154	+	8.68880i	0.880716	+	0.392120i	0.0839943	+	0.996466i	$0.473232\pi$
$492$		0			0
$493$	2.01190	+	0.427643i	0.0906115	+	0.0192601i
$494$	−9.41594			−0.423643
$495$		0			0
$496$	−1.98051			−0.0889273
$497$	−14.7818	−	3.14197i	−0.663055	−	0.140937i
$498$		0			0
$499$	10.9153	+	4.85982i	0.488637	+	0.217555i	0.636240	−	0.771491i	$-0.280489\pi$
$499$	10.9153	+	4.85982i	0.488637	+	0.217555i	−0.147602	+	0.989047i	$0.547156\pi$
$500$	−4.93754	−	23.2293i	−0.220813	−	1.03885i
$501$		0			0
$502$	−3.92471	+	0.412504i	−0.175168	+	0.0184109i
$503$	−21.5801	−	15.6789i	−0.962210	−	0.699087i	−0.00854739	−	0.999963i	$-0.502721\pi$
$503$	−21.5801	−	15.6789i	−0.962210	−	0.699087i	−0.953663	+	0.300877i	$0.902721\pi$
$504$		0			0
$505$			24.4688i			1.08885i
$506$	−18.3714	+	0.0143988i	−0.816710	+	0.000640106i
$507$		0			0
$508$	13.5338	+	12.1859i	0.600465	+	0.540661i
$509$	25.7218	+	2.70347i	1.14010	+	0.119829i	0.655702	−	0.755020i	$-0.272373\pi$
$509$	25.7218	+	2.70347i	1.14010	+	0.119829i	0.484395	+	0.874849i	$0.339040\pi$
$510$		0			0
$511$	14.3002	+	15.8819i	0.632602	+	0.702576i
$512$	5.74119	−	17.6696i	0.253727	−	0.780892i
$513$		0			0
$514$	5.05013	−	6.95091i	0.222752	−	0.306591i
$515$	−6.80143	+	31.9982i	−0.299707	+	1.41001i
$516$		0			0
$517$	−0.503198	−	4.75178i	−0.0221306	−	0.208983i
$518$	4.44546	−	2.56659i	0.195322	−	0.112769i
$519$		0			0
$520$	47.2083	−	21.0185i	2.07022	−	0.921722i
$521$	13.0853	+	18.0103i	0.573276	+	0.789047i	0.992938	−	0.118634i	$-0.0378514\pi$
$521$	13.0853	+	18.0103i	0.573276	+	0.789047i	−0.419662	+	0.907680i	$0.637851\pi$
$522$		0			0
$523$	−27.2570	−	8.85633i	−1.19186	−	0.387260i	−0.355103	−	0.934827i	$-0.615554\pi$
$523$	−27.2570	−	8.85633i	−1.19186	−	0.387260i	−0.836762	+	0.547567i	$0.815554\pi$
$524$	2.90008	+	27.5924i	0.126691	+	1.20538i
$525$		0			0
$526$	6.41083	−	7.11995i	0.279525	−	0.310444i
$527$	−0.167977	−	0.290944i	−0.00731717	−	0.0126737i
$528$		0			0
$529$	28.3196	−	49.0509i	1.23129	−	2.13265i
$530$	−4.22457	−	13.0019i	−0.183503	−	0.564766i
$531$		0			0
$532$	−7.12635	+	5.17759i	−0.308966	+	0.224477i
$533$	19.1544	−	17.2467i	0.829670	−	0.747038i
$534$		0			0
$535$	1.16104	−	2.60774i	0.0501961	−	0.112742i
$536$	0.656092	−	6.24230i	0.0283389	−	0.269626i
$537$		0			0
$538$	−3.30211	−	1.90647i	−0.142364	−	0.0821938i
$539$	−6.85710	−	0.715277i	−0.295356	−	0.0308092i
$540$		0			0
$541$	27.0426	−	8.78666i	1.16265	−	0.377768i	0.336755	−	0.941592i	$-0.390670\pi$
$541$	27.0426	−	8.78666i	1.16265	−	0.377768i	0.825895	+	0.563824i	$0.190670\pi$
$542$	−4.75538	−	10.6807i	−0.204261	−	0.458777i
$543$		0			0
$544$	1.71507	−	0.364549i	0.0735329	−	0.0156299i
$545$	−16.0419	+	3.40982i	−0.687161	+	0.146061i
$546$		0			0
$547$	7.26651	+	16.3209i	0.310694	+	0.697830i	0.999636	−	0.0269869i	$-0.00859123\pi$
$547$	7.26651	+	16.3209i	0.310694	+	0.697830i	−0.688942	+	0.724816i	$0.741925\pi$
$548$	2.08783	−	0.678378i	0.0891878	−	0.0289789i
$549$		0			0
$550$	18.3034	+	1.90926i	0.780458	+	0.0814110i
$551$	−14.0585	−	8.11667i	−0.598911	−	0.345782i
$552$		0			0
$553$	1.15368	−	10.9766i	0.0490596	−	0.466771i
$554$	1.38464	−	3.10995i	0.0588277	−	0.132129i
$555$		0			0
$556$	−14.4761	+	13.0343i	−0.613924	+	0.552779i
$557$	27.7784	−	20.1822i	1.17701	−	0.855148i	0.185179	−	0.982705i	$-0.440713\pi$
$557$	27.7784	−	20.1822i	1.17701	−	0.855148i	0.991831	+	0.127556i	$0.0407134\pi$
$558$		0			0
$559$	9.07042	+	27.9159i	0.383638	+	1.18072i
$560$	7.60662	−	13.1750i	0.321438	−	0.556747i
$561$		0			0
$562$	8.09993	+	14.0295i	0.341675	+	0.591798i
$563$	−0.0657990	+	0.0730772i	−0.00277310	+	0.00307984i	−0.744530	−	0.667589i	$-0.767326\pi$
$563$	−0.0657990	+	0.0730772i	−0.00277310	+	0.00307984i	0.741757	+	0.670669i	$0.233993\pi$
$564$		0			0
$565$	−2.34739	−	22.3339i	−0.0987554	−	0.939595i
$566$	10.1806	+	3.30787i	0.427922	+	0.139040i
$567$		0			0
$568$	−8.98384	−	12.3652i	−0.376953	−	0.518832i
$569$	31.9277	−	14.2151i	1.33848	−	0.595930i	0.392380	−	0.919803i	$-0.371652\pi$
$569$	31.9277	−	14.2151i	1.33848	−	0.595930i	0.946100	+	0.323873i	$0.104985\pi$
$570$		0			0
$571$	−7.73170	+	4.46390i	−0.323562	+	0.186808i	−0.652979	−	0.757376i	$-0.726481\pi$
$571$	−7.73170	+	4.46390i	−0.323562	+	0.186808i	0.329417	+	0.944184i	$0.393148\pi$
$572$	−3.47909	−	32.8536i	−0.145468	−	1.37368i
$573$		0			0
$574$	−1.19616	+	5.62748i	−0.0499266	+	0.234886i
$575$	−46.8903	+	64.5389i	−1.95546	+	2.69146i
$576$		0			0
$577$	−1.57214	+	4.83854i	−0.0654489	+	0.201431i	−0.978433	−	0.206564i	$-0.933772\pi$
$577$	−1.57214	+	4.83854i	−0.0654489	+	0.201431i	0.912984	+	0.407995i	$0.133772\pi$
$578$	−7.02031	−	7.79685i	−0.292006	−	0.324306i
$579$		0			0
$580$	39.5795	+	4.15998i	1.64345	+	0.172734i
$581$	22.0825	+	19.8831i	0.916135	+	0.824891i
$582$		0			0
$583$	−19.5656	+	0.0153347i	−0.810324	+	0.000635100i
$584$			21.6147i			0.894424i
$585$		0			0
$586$	−13.6347	−	9.90616i	−0.563242	−	0.409220i
$587$	−3.40633	+	0.358020i	−0.140594	+	0.0147771i	−0.174564	−	0.984646i	$-0.555852\pi$
$587$	−3.40633	+	0.358020i	−0.140594	+	0.0147771i	0.0339698	+	0.999423i	$0.489185\pi$
$588$		0			0
$589$	0.551268	+	2.59351i	0.0227146	+	0.106864i
$590$	−11.8437	−	5.27315i	−0.487597	−	0.217092i
$591$		0			0
$592$	−6.69777	−	1.42365i	−0.275277	−	0.0585118i
$593$	16.6897			0.685365			0.342683	−	0.939451i	$-0.388664\pi$
$593$	16.6897			0.685365			0.342683	+	0.939451i	$0.388664\pi$
$594$		0			0
$595$	2.58062			0.105795
$596$	23.0909	+	4.90812i	0.945840	+	0.201044i
$597$		0			0
$598$	−31.2167	−	13.8986i	−1.27654	−	0.568354i
$599$	10.0293	+	47.1839i	0.409784	+	1.92788i	0.370992	+	0.928636i	$0.379018\pi$
$599$	10.0293	+	47.1839i	0.409784	+	1.92788i	0.0387921	+	0.999247i	$0.487649\pi$
$600$		0			0
$601$	−18.8072	+	1.97671i	−0.767161	+	0.0806318i	−0.480021	−	0.877257i	$-0.659371\pi$
$601$	−18.8072	+	1.97671i	−0.767161	+	0.0806318i	−0.287139	+	0.957889i	$0.592704\pi$
$602$	−5.30050	−	3.85104i	−0.216032	−	0.156956i
$603$		0			0
$604$			4.49188i			0.182772i
$605$	16.6454	−	37.5444i	0.676730	−	1.52640i
$606$		0			0
$607$	−26.6309	−	23.9786i	−1.08092	−	0.973261i	−0.0811909	−	0.996699i	$-0.525872\pi$
$607$	−26.6309	−	23.9786i	−1.08092	−	0.973261i	−0.999725	+	0.0234373i	$0.992539\pi$
$608$	−13.7625	−	1.44649i	−0.558142	−	0.0586631i
$609$		0			0
$610$	2.33382	+	2.59196i	0.0944934	+	0.104946i
$611$	2.74646	−	8.45274i	0.111110	−	0.341961i
$612$		0			0
$613$	−0.393669	+	0.541839i	−0.0159002	+	0.0218847i	−0.816893	−	0.576789i	$-0.804305\pi$
$613$	−0.393669	+	0.541839i	−0.0159002	+	0.0218847i	0.800993	+	0.598674i	$0.204305\pi$
$614$	1.87879	−	8.83901i	0.0758218	−	0.356713i
$615$		0			0
$616$	11.0556	+	12.2592i	0.445444	+	0.493937i
$617$	9.40017	−	5.42719i	0.378436	−	0.218490i	−0.298701	−	0.954347i	$-0.596553\pi$
$617$	9.40017	−	5.42719i	0.378436	−	0.218490i	0.677138	+	0.735856i	$0.263220\pi$
$618$		0			0
$619$	25.3410	−	11.2825i	1.01854	−	0.453483i	0.171597	−	0.985167i	$-0.445107\pi$
$619$	25.3410	−	11.2825i	1.01854	−	0.453483i	0.846943	+	0.531684i	$0.178441\pi$
$620$	−3.82077	−	5.25884i	−0.153446	−	0.211200i
$621$		0			0
$622$	2.58636	+	0.840360i	0.103704	+	0.0336953i
$623$	0.707459	+	6.73102i	0.0283438	+	0.269673i
$624$		0			0
$625$	6.83439	−	7.59036i	0.273376	−	0.303614i
$626$	1.74982	+	3.03078i	0.0699369	+	0.121134i
$627$		0			0
$628$	−14.2932	+	24.7565i	−0.570360	+	0.987893i
$629$	−0.358931	−	1.10467i	−0.0143115	−	0.0440463i
$630$		0			0
$631$	−35.5496	+	25.8283i	−1.41521	+	1.02821i	−0.422667	+	0.906285i	$0.638906\pi$
$631$	−35.5496	+	25.8283i	−1.41521	+	1.02821i	−0.992540	+	0.121923i	$0.961094\pi$
$632$	8.29556	−	7.46935i	0.329980	−	0.297115i
$633$		0			0
$634$	−4.01651	+	9.02122i	−0.159516	+	0.358279i
$635$	−4.40150	+	41.8775i	−0.174668	+	1.66186i
$636$		0			0
$637$	−11.1054	−	6.41170i	−0.440012	−	0.254041i
$638$	−5.51779	+	12.4193i	−0.218451	+	0.491687i
$639$		0			0
$640$	40.3620	−	13.1144i	1.59545	−	0.518392i
$641$	5.73076	+	12.8715i	0.226351	+	0.508393i	0.990643	−	0.136477i	$-0.0435780\pi$
$641$	5.73076	+	12.8715i	0.226351	+	0.508393i	−0.764292	+	0.644870i	$0.776911\pi$
$642$		0			0
$643$	−28.6159	+	6.08250i	−1.12850	+	0.239871i	−0.734083	−	0.679060i	$-0.762388\pi$
$643$	−28.6159	+	6.08250i	−1.12850	+	0.239871i	−0.394419	+	0.918931i	$0.629054\pi$
$644$	−31.2685	+	6.64632i	−1.23215	+	0.261902i
$645$		0			0
$646$	−0.193434	−	0.434459i	−0.00761055	−	0.0170936i
$647$	−39.3432	+	12.7834i	−1.54674	+	0.502566i	−0.953226	−	0.302258i	$-0.902260\pi$
$647$	−39.3432	+	12.7834i	−1.54674	+	0.502566i	−0.593513	+	0.804824i	$0.702260\pi$
$648$		0			0
$649$	−12.4046	+	13.7984i	−0.486923	+	0.541635i
$650$	29.6432	+	17.1145i	1.16270	+	0.671285i
$651$		0			0
$652$	0.248078	−	2.36030i	0.00971548	−	0.0924367i
$653$	−11.1095	+	24.9524i	−0.434749	+	0.976463i	0.554762	+	0.832009i	$0.312809\pi$
$653$	−11.1095	+	24.9524i	−0.434749	+	0.976463i	−0.989512	+	0.144454i	$0.953857\pi$
$654$		0			0
$655$	−47.6726	+	42.9246i	−1.86272	+	1.67720i
$656$	6.20878	−	4.51094i	0.242412	−	0.176123i
$657$		0			0
$658$	0.613038	+	1.88674i	0.0238987	+	0.0735526i
$659$	−0.320896	+	0.555808i	−0.0125003	+	0.0216512i	−0.872208	−	0.489135i	$-0.837312\pi$
$659$	−0.320896	+	0.555808i	−0.0125003	+	0.0216512i	0.859708	+	0.510787i	$0.170646\pi$
$660$		0			0
$661$	4.12078	+	7.13740i	0.160280	+	0.277613i	0.934969	−	0.354729i	$-0.115427\pi$
$661$	4.12078	+	7.13740i	0.160280	+	0.277613i	−0.774689	+	0.632342i	$0.782094\pi$
$662$	8.21753	−	9.12650i	0.319384	−	0.354711i
$663$		0			0
$664$	3.14144	+	29.8888i	0.121911	+	1.15991i
$665$	−19.3703	−	6.29378i	−0.751147	−	0.244063i
$666$		0			0
$667$	−34.6273	−	47.6604i	−1.34078	−	1.84542i
$668$	13.2540	−	5.90106i	0.512813	−	0.228319i
$669$		0			0
$670$	5.61442	−	3.24149i	0.216904	−	0.125230i
$671$	4.55855	−	2.03388i	0.175981	−	0.0785171i
$672$		0			0
$673$	−3.08146	+	14.4971i	−0.118782	+	0.558824i	0.878000	+	0.478660i	$0.158878\pi$
$673$	−3.08146	+	14.4971i	−0.118782	+	0.558824i	−0.996782	+	0.0801633i	$0.974456\pi$
$674$	8.70884	−	11.9867i	0.335452	−	0.461710i
$675$		0			0
$676$	12.5022	−	38.4778i	0.480854	−	1.47992i
$677$	−4.21333	−	4.67938i	−0.161931	−	0.179843i	0.656719	−	0.754136i	$-0.271944\pi$
$677$	−4.21333	−	4.67938i	−0.161931	−	0.179843i	−0.818650	+	0.574292i	$0.805277\pi$
$678$		0			0
$679$	32.4702	+	3.41275i	1.24609	+	0.130969i
$680$	1.93962	+	1.74644i	0.0743811	+	0.0669731i
$681$		0			0
$682$	2.11052	−	0.687579i	0.0808160	−	0.0263287i
$683$			14.1497i			0.541422i	0.962661	+	0.270711i	$0.0872588\pi$
$683$			14.1497i			0.541422i	−0.962661	+	0.270711i	$0.912741\pi$
$684$		0			0
$685$	4.10646	+	2.98352i	0.156900	+	0.113994i
$686$	12.4326	−	1.30672i	0.474679	−	0.0498907i
$687$		0			0
$688$	1.81709	+	8.54875i	0.0692760	+	0.325918i
$689$	−33.2457	−	14.8020i	−1.26656	−	0.563910i
$690$		0			0
$691$	25.1921	+	5.35475i	0.958354	+	0.203704i	0.660432	−	0.750886i	$-0.270373\pi$
$691$	25.1921	+	5.35475i	0.958354	+	0.203704i	0.297922	+	0.954590i	$0.403707\pi$
$692$	10.6481			0.404779
$693$		0			0
$694$	−10.7703			−0.408837
$695$	−44.0558	−	9.36434i	−1.67113	−	0.355210i
$696$		0			0
$697$	1.18927	+	0.529498i	0.0450469	+	0.0200562i
$698$	1.43979	+	6.77366i	0.0544967	+	0.256387i
$699$		0			0
$700$	31.8459	−	3.34714i	1.20366	−	0.126510i
$701$	8.55571	+	6.21609i	0.323145	+	0.234778i	0.737516	−	0.675329i	$-0.235999\pi$
$701$	8.55571	+	6.21609i	0.323145	+	0.234778i	−0.414371	+	0.910108i	$0.635999\pi$
$702$		0			0
$703$			9.16714i			0.345745i
$704$	−0.000469536	−	0.599081i	−1.76963e−5	−	0.0225787i
$705$		0			0
$706$	10.8148	+	9.73773i	0.407022	+	0.366484i
$707$	−14.4593	−	1.51973i	−0.543796	−	0.0571553i
$708$		0			0
$709$	−17.4499	−	19.3800i	−0.655344	−	0.727833i	0.320270	−	0.947326i	$-0.396226\pi$
$709$	−17.4499	−	19.3800i	−0.655344	−	0.727833i	−0.975614	+	0.219493i	$0.929560\pi$
$710$	4.87831	−	15.0139i	0.183080	−	0.563462i
$711$		0			0
$712$	−4.02351	+	5.53789i	−0.150788	+	0.207541i
$713$	−2.00058	+	9.41199i	−0.0749223	+	0.352482i
$714$		0			0
$715$	56.7273	−	51.1580i	2.12148	−	1.91320i
$716$	1.78523	−	1.03071i	0.0667173	−	0.0385193i
$717$		0			0
$718$	10.4141	−	4.63666i	0.388651	−	0.173038i
$719$	8.91625	+	12.2722i	0.332520	+	0.457675i	0.942238	−	0.334944i	$-0.108717\pi$
$719$	8.91625	+	12.2722i	0.332520	+	0.457675i	−0.609718	+	0.792618i	$0.708717\pi$
$720$		0			0
$721$	−18.4862	−	6.00653i	−0.688461	−	0.223695i
$722$	−0.840404	−	7.99591i	−0.0312766	−	0.297577i
$723$		0			0
$724$	−22.3447	+	24.8163i	−0.830435	+	0.922292i
$725$	29.5058	+	51.1056i	1.09582	+	1.89801i
$726$		0			0
$727$	8.28230	−	14.3454i	0.307174	−	0.532040i	−0.670569	−	0.741847i	$-0.733950\pi$
$727$	8.28230	−	14.3454i	0.307174	−	0.532040i	0.977743	+	0.209807i	$0.0672834\pi$
$728$	9.48835	+	29.2021i	0.351662	+	1.08230i
$729$		0			0
$730$	−18.0614	+	13.1224i	−0.668483	+	0.485681i
$731$	−1.10173	+	0.991999i	−0.0407488	+	0.0366904i
$732$		0			0
$733$	−9.20266	+	20.6695i	−0.339908	+	0.763446i	0.660018	+	0.751250i	$0.270549\pi$
$733$	−9.20266	+	20.6695i	−0.339908	+	0.763446i	−0.999926	+	0.0121956i	$0.996118\pi$
$734$	−0.875926	+	8.33388i	−0.0323310	+	0.307609i
$735$		0			0
$736$	−43.4916	−	25.1099i	−1.60312	−	0.925563i
$737$	−1.93618	−	9.07401i	−0.0713199	−	0.334245i
$738$		0			0
$739$	−29.5613	+	9.60506i	−1.08743	+	0.353328i	−0.797253	−	0.603645i	$-0.793714\pi$
$739$	−29.5613	+	9.60506i	−1.08743	+	0.353328i	−0.290178	+	0.956973i	$0.593714\pi$
$740$	−9.14104	−	20.5311i	−0.336031	−	0.754738i
$741$		0			0
$742$	7.94555	−	1.68888i	0.291690	−	0.0620007i
$743$	46.0242	−	9.78274i	1.68846	−	0.358894i	0.739227	−	0.673456i	$-0.235191\pi$
$743$	46.0242	−	9.78274i	1.68846	−	0.358894i	0.949237	+	0.314562i	$0.101858\pi$
$744$		0			0
$745$	22.2009	+	49.8639i	0.813376	+	1.82687i
$746$	−16.6960	+	5.42487i	−0.611285	+	0.198619i
$747$		0			0
$748$	1.44442	−	0.835448i	0.0528134	−	0.0305470i
$749$	1.46887	+	0.848053i	0.0536714	+	0.0309872i
$750$		0			0
$751$	−3.81772	+	36.3232i	−0.139311	+	1.32545i	0.671875	+	0.740664i	$0.265489\pi$
$751$	−3.81772	+	36.3232i	−0.139311	+	1.32545i	−0.811186	+	0.584788i	$0.801178\pi$
$752$	1.07636	−	2.41754i	0.0392508	−	0.0881587i
$753$		0			0
$754$	−18.7847	+	16.9138i	−0.684098	+	0.615964i
$755$	−8.40245	+	6.10474i	−0.305796	+	0.222174i
$756$		0			0
$757$	−8.52322	−	26.2318i	−0.309782	−	0.953409i	−0.977849	−	0.209309i	$-0.932878\pi$
$757$	−8.52322	−	26.2318i	−0.309782	−	0.953409i	0.668068	−	0.744100i	$-0.267122\pi$
$758$	0.0684977	−	0.118642i	0.00248795	−	0.00430925i
$759$		0			0
$760$	−10.2996	−	17.8394i	−0.373605	−	0.647103i
$761$	−35.2659	+	39.1668i	−1.27839	+	1.41979i	−0.419399	+	0.907802i	$0.637759\pi$
$761$	−35.2659	+	39.1668i	−1.27839	+	1.41979i	−0.858990	+	0.511993i	$0.828908\pi$
$762$		0			0
$763$	−1.01861	−	9.69141i	−0.0368761	−	0.350853i
$764$	10.3351	+	3.35808i	0.373912	+	0.121491i
$765$		0			0
$766$	14.0786	+	19.3775i	0.508681	+	0.700139i
$767$	−31.5277	+	14.0371i	−1.13840	+	0.506849i
$768$		0			0
$769$	−15.7023	+	9.06575i	−0.566241	+	0.326919i	−0.755647	−	0.654980i	$-0.772677\pi$
$769$	−15.7023	+	9.06575i	−0.566241	+	0.326919i	0.189406	+	0.981899i	$0.439344\pi$
$770$	−3.53194	+	16.6808i	−0.127282	+	0.601133i
$771$		0			0
$772$	−5.30114	+	24.9399i	−0.190792	+	0.897607i
$773$	8.15106	−	11.2190i	0.293173	−	0.403518i	−0.636868	−	0.770973i	$-0.719771\pi$
$773$	8.15106	−	11.2190i	0.293173	−	0.403518i	0.930042	+	0.367454i	$0.119771\pi$
$774$		0			0
$775$	2.97849	−	9.16686i	0.106991	−	0.329283i
$776$	22.0954	+	24.5394i	0.793177	+	0.880913i
$777$		0			0
$778$	−22.4440	−	2.35896i	−0.804656	−	0.0845727i
$779$	−7.63537	−	6.87492i	−0.273565	−	0.246319i
$780$		0			0
$781$	−18.2888	−	13.2657i	−0.654424	−	0.474684i
$782$		−	1.72589i		−	0.0617175i
$783$		0			0
$784$	−3.08897	−	2.24427i	−0.110320	−	0.0801525i
$785$	−65.7346	+	6.90898i	−2.34617	+	0.246592i
$786$		0			0
$787$	0.139682	+	0.657150i	0.00497911	+	0.0234249i	0.980567	−	0.196184i	$-0.0628551\pi$
$787$	0.139682	+	0.657150i	0.00497911	+	0.0234249i	−0.975588	+	0.219609i	$0.929522\pi$
$788$	−3.08454	−	1.37333i	−0.109882	−	0.0489227i
$789$		0			0
$790$	11.2777	+	2.39715i	0.401243	+	0.0852867i
$791$	13.3435			0.474441
$792$		0			0
$793$	9.28457			0.329705
$794$	−13.6319	−	2.89755i	−0.483778	−	0.102830i
$795$		0			0
$796$	5.55788	+	2.47453i	0.196994	+	0.0877073i
$797$	1.09274	+	5.14095i	0.0387069	+	0.182102i	0.993254	−	0.115958i	$-0.0369938\pi$
$797$	1.09274	+	5.14095i	0.0387069	+	0.182102i	−0.954547	+	0.298060i	$0.903660\pi$
$798$		0			0
$799$	0.446438	−	0.0469225i	0.0157938	−	0.00166000i
$800$	40.6977	+	29.5686i	1.43888	+	1.04541i
$801$		0			0
$802$			17.0856i			0.603312i
$803$	9.89727	+	30.3796i	0.349267	+	1.07207i
$804$		0			0
$805$	−54.9282	−	49.4576i	−1.93597	−	1.74315i
$806$	4.10602	+	0.431560i	0.144628	+	0.0152011i
$807$		0			0
$808$	−9.83926	−	10.9276i	−0.346144	−	0.384432i
$809$	−8.82483	+	27.1600i	−0.310265	+	0.954896i	0.667395	+	0.744704i	$0.267409\pi$
$809$	−8.82483	+	27.1600i	−0.310265	+	0.954896i	−0.977660	+	0.210193i	$0.932591\pi$
$810$		0			0
$811$	13.6775	−	18.8255i	0.480283	−	0.661053i	−0.498276	−	0.867018i	$-0.666033\pi$
$811$	13.6775	−	18.8255i	0.480283	−	0.661053i	0.978559	+	0.205965i	$0.0660335\pi$
$812$	−4.91649	+	23.1303i	−0.172535	+	0.811713i
$813$		0			0
$814$	7.63171	−	0.808173i	0.267491	−	0.0283264i
$815$	4.75231	−	2.74375i	0.166466	−	0.0961092i
$816$		0			0
$817$	10.6890	−	4.75904i	0.373960	−	0.166498i
$818$	14.5777	+	20.0644i	0.509696	+	0.701536i
$819$		0			0
$820$	23.9558	+	7.78372i	0.836574	+	0.271819i
$821$	2.24547	+	21.3642i	0.0783675	+	0.745617i	0.961186	+	0.275902i	$0.0889765\pi$
$821$	2.24547	+	21.3642i	0.0783675	+	0.745617i	−0.882818	+	0.469715i	$0.844357\pi$
$822$		0			0
$823$	32.4175	−	36.0033i	1.13000	−	1.25500i	0.166867	−	0.985979i	$-0.446635\pi$
$823$	32.4175	−	36.0033i	1.13000	−	1.25500i	0.963136	−	0.269016i	$-0.0866984\pi$
$824$	−9.82949	−	17.0252i	−0.342426	−	0.593100i
$825$		0			0
$826$	3.85165	−	6.67125i	0.134016	−	0.232122i
$827$	−12.2819	−	37.7998i	−0.427084	−	1.31443i	−0.900985	−	0.433851i	$-0.857155\pi$
$827$	−12.2819	−	37.7998i	−0.427084	−	1.31443i	0.473901	−	0.880578i	$-0.342845\pi$
$828$		0			0
$829$	27.8772	−	20.2540i	0.968215	−	0.703450i	0.0131712	−	0.999913i	$-0.495807\pi$
$829$	27.8772	−	20.2540i	0.968215	−	0.703450i	0.955044	+	0.296464i	$0.0958074\pi$
$830$	−23.0681	+	20.7706i	−0.800704	+	0.720957i
$831$		0			0
$832$	0.453223	−	1.01795i	0.0157127	−	0.0352912i
$833$	0.0677008	−	0.644130i	0.00234569	−	0.0223178i
$834$		0			0
$835$	29.0514	+	16.7729i	1.00537	+	0.580449i
$836$	−12.8795	+	2.74817i	−0.445446	+	0.0950474i
$837$		0			0
$838$	14.9621	−	4.86147i	0.516856	−	0.167937i
$839$	−10.6838	−	23.9961i	−0.368844	−	0.828438i	−0.998663	−	0.0516955i	$-0.983537\pi$
$839$	−10.6838	−	23.9961i	−0.368844	−	0.828438i	0.629819	−	0.776742i	$-0.283129\pi$
$840$		0			0
$841$	−14.2601	+	3.03109i	−0.491729	+	0.104520i
$842$	9.04471	−	1.92251i	0.311701	−	0.0662542i
$843$		0			0
$844$	−7.15179	−	16.0632i	−0.246175	−	0.552917i
$845$	88.9674	−	28.9073i	3.06057	−	0.994440i
$846$		0			0
$847$	21.1522	+	12.1680i	0.726797	+	0.418099i
$848$	−9.38404	−	5.41788i	−0.322249	−	0.186051i
$849$		0			0
$850$	−0.180711	+	1.71935i	−0.00619833	+	0.0589731i
$851$	−13.5313	+	30.3918i	−0.463847	+	1.04182i
$852$		0			0
$853$	30.3073	−	27.2888i	1.03770	−	0.934350i	0.0398060	−	0.999207i	$-0.487326\pi$
$853$	30.3073	−	27.2888i	1.03770	−	0.934350i	0.997895	+	0.0648576i	$0.0206593\pi$
$854$	−1.67661	+	1.21813i	−0.0573726	+	0.0416836i
$855$		0			0
$856$	0.530097	+	1.63147i	0.0181183	+	0.0557625i
$857$	22.9703	−	39.7858i	0.784651	−	1.35906i	−0.144556	−	0.989497i	$-0.546175\pi$
$857$	22.9703	−	39.7858i	0.784651	−	1.35906i	0.929207	−	0.369559i	$-0.120491\pi$
$858$		0			0
$859$	9.12751	+	15.8093i	0.311427	+	0.539407i	0.978671	−	0.205432i	$-0.0658598\pi$
$859$	9.12751	+	15.8093i	0.311427	+	0.539407i	−0.667245	+	0.744838i	$0.732527\pi$
$860$	−19.1940	+	21.3171i	−0.654510	+	0.726907i
$861$		0			0
$862$	−1.01090	−	9.61806i	−0.0344314	−	0.327592i
$863$	18.5553	+	6.02899i	0.631631	+	0.205229i	0.607297	−	0.794475i	$-0.292254\pi$
$863$	18.5553	+	6.02899i	0.631631	+	0.205229i	0.0243334	+	0.999704i	$0.492254\pi$
$864$		0			0
$865$	14.4714	+	19.9181i	0.492042	+	0.677237i
$866$	6.02409	−	2.68210i	0.204707	−	0.0911414i
$867$		0			0
$868$	3.34490	−	1.93118i	0.113533	−	0.0655485i
$869$	8.23928	−	14.2967i	0.279498	−	0.484983i
$870$		0			0
$871$	3.58806	−	16.8805i	0.121577	−	0.571973i
$872$	5.79310	−	7.97352i	0.196179	−	0.270017i
$873$		0			0
$874$	−4.20920	+	12.9546i	−0.142378	+	0.438196i
$875$	21.8314	+	24.2463i	0.738038	+	0.819674i
$876$		0			0
$877$	−20.3710	−	2.14108i	−0.687880	−	0.0722991i	−0.245861	−	0.969305i	$-0.579071\pi$
$877$	−20.3710	−	2.14108i	−0.687880	−	0.0722991i	−0.442018	+	0.897006i	$0.645737\pi$
$878$	−8.21667	−	7.39832i	−0.277299	−	0.249681i
$879$		0			0
$880$	18.3903	−	13.3834i	0.619936	−	0.451153i
$881$			38.0577i			1.28220i	0.767459	+	0.641099i	$0.221521\pi$
$881$			38.0577i			1.28220i	−0.767459	+	0.641099i	$0.778479\pi$
$882$		0			0
$883$	17.6981	+	12.8584i	0.595590	+	0.432721i	0.844311	−	0.535854i	$-0.180010\pi$
$883$	17.6981	+	12.8584i	0.595590	+	0.432721i	−0.248721	+	0.968575i	$0.580010\pi$
$884$	3.08665	−	0.324420i	0.103815	−	0.0109114i
$885$		0			0
$886$	−2.36390	−	11.1213i	−0.0794168	−	0.373627i
$887$	30.9486	+	13.7792i	1.03915	+	0.462660i	0.854122	−	0.520073i	$-0.174095\pi$
$887$	30.9486	+	13.7792i	1.03915	+	0.462660i	0.185030	+	0.982733i	$0.440762\pi$
$888$		0			0
$889$	−24.4732	−	5.20193i	−0.820804	−	0.174467i
$890$	−7.07018			−0.236993
$891$		0			0
$892$	−18.3383			−0.614011
$893$	−3.46542	−	0.736599i	−0.115966	−	0.0246493i
$894$		0			0
$895$	4.35427	+	1.93864i	0.145547	+	0.0648017i
$896$	5.24282	+	24.6655i	0.175150	+	0.824018i
$897$		0			0
$898$	8.72571	−	0.917109i	0.291181	−	0.0306043i
$899$	5.75849	+	4.18379i	0.192056	+	0.139537i
$900$		0			0
$901$		−	1.83807i		−	0.0612349i
$902$	−5.05029	+	6.96259i	−0.168156	+	0.231829i
$903$		0			0
$904$	10.0291	+	9.03028i	0.333564	+	0.300343i
$905$	−76.7889	−	8.07084i	−2.55255	−	0.268284i
$906$		0			0
$907$	−10.8902	−	12.0948i	−0.361602	−	0.401600i	0.534701	−	0.845041i	$-0.320424\pi$
$907$	−10.8902	−	12.0948i	−0.361602	−	0.401600i	−0.896303	+	0.443441i	$0.853757\pi$
$908$	−5.34588	+	16.4529i	−0.177409	+	0.546010i
$909$		0			0
$910$	−18.6411	+	25.6572i	−0.617945	+	0.850529i
$911$	−3.44054	+	16.1865i	−0.113990	+	0.536282i	0.883682	+	0.468088i	$0.155057\pi$
$911$	−3.44054	+	16.1865i	−0.113990	+	0.536282i	−0.997672	+	0.0681939i	$0.978276\pi$
$912$		0			0
$913$	18.1012	+	40.5704i	0.599063	+	1.34268i
$914$	4.65190	−	2.68578i	0.153871	−	0.0888376i
$915$		0			0
$916$	29.0229	−	12.9218i	0.958944	−	0.426949i
$917$	−22.4044	−	30.8371i	−0.739860	−	1.01833i
$918$		0			0
$919$	30.9592	+	10.0592i	1.02125	+	0.331824i	0.771325	−	0.636441i	$-0.219594\pi$
$919$	30.9592	+	10.0592i	1.02125	+	0.331824i	0.249924	+	0.968265i	$0.419594\pi$
$920$	−7.81406	−	74.3458i	−0.257622	−	2.45111i
$921$		0			0
$922$	15.0633	−	16.7295i	0.496084	−	0.550957i
$923$	−21.0118	−	36.3935i	−0.691612	−	1.19791i
$924$		0			0
$925$	16.6623	−	28.8599i	0.547852	−	0.948907i
$926$	−5.42868	−	16.7078i	−0.178397	−	0.549051i
$927$		0			0
$928$	−30.0543	+	21.8357i	−0.986581	+	0.716793i
$929$	−38.5410	+	34.7024i	−1.26449	+	1.13855i	−0.280589	+	0.959828i	$0.590530\pi$
$929$	−38.5410	+	34.7024i	−1.26449	+	1.13855i	−0.983900	+	0.178722i	$0.942804\pi$
$930$		0			0
$931$	−2.07911	+	4.66976i	−0.0681401	+	0.153045i
$932$	3.40222	−	32.3699i	0.111443	−	1.06031i
$933$		0			0
$934$	14.9488	+	8.63067i	0.489138	+	0.282404i
$935$	3.52584	+	1.56649i	0.115307	+	0.0512298i
$936$		0			0
$937$	4.46609	−	1.45112i	0.145901	−	0.0474061i	−0.235156	−	0.971958i	$-0.575560\pi$
$937$	4.46609	−	1.45112i	0.145901	−	0.0474061i	0.381057	+	0.924552i	$0.375560\pi$
$938$	1.56678	+	3.51904i	0.0511571	+	0.114901i
$939$		0			0
$940$	8.49581	−	1.80584i	0.277103	−	0.0589000i
$941$	−8.81457	+	1.87360i	−0.287347	+	0.0610775i	−0.349330	−	0.937000i	$-0.613591\pi$
$941$	−8.81457	+	1.87360i	−0.287347	+	0.0610775i	0.0619832	+	0.998077i	$0.480257\pi$
$942$		0			0
$943$	−15.1657	−	34.0627i	−0.493863	−	1.10924i
$944$	−9.77287	+	3.17540i	−0.318080	+	0.103350i
$945$		0			0
$946$	−4.90427	−	8.47910i	−0.159452	−	0.275679i
$947$	−28.1466	−	16.2504i	−0.914641	−	0.528068i	−0.0327198	−	0.999465i	$-0.510417\pi$
$947$	−28.1466	−	16.2504i	−0.914641	−	0.528068i	−0.881922	+	0.471396i	$0.843750\pi$
$948$		0			0
$949$	−6.21205	+	59.1037i	−0.201652	+	1.91859i
$950$	5.54968	−	12.4648i	0.180056	−	0.404411i
$951$		0			0
$952$	−1.15249	+	1.03771i	−0.0373524	+	0.0336323i
$953$	−9.17192	+	6.66379i	−0.297108	+	0.215861i	−0.726345	−	0.687331i	$-0.758782\pi$
$953$	−9.17192	+	6.66379i	−0.297108	+	0.215861i	0.429237	+	0.903192i	$0.358782\pi$
$954$		0			0
$955$	7.76447	+	23.8966i	0.251252	+	0.773275i
$956$	13.8855	−	24.0503i	0.449088	−	0.777843i
$957$		0			0
$958$	2.30121	+	3.98581i	0.0743488	+	0.128776i
$959$	−2.01809	+	2.24132i	−0.0651675	+	0.0723758i
$960$		0			0
$961$	3.11886	+	29.6740i	0.100608	+	0.957224i
$962$	13.5757	+	4.41102i	0.437699	+	0.142217i
$963$		0			0
$964$	−19.4850	−	26.8187i	−0.627568	−	0.863774i
$965$	−53.8568	+	23.9786i	−1.73371	+	0.771899i
$966$		0			0
$967$	−4.25298	+	2.45546i	−0.136767	+	0.0789623i	−0.566822	−	0.823840i	$-0.691827\pi$
$967$	−4.25298	+	2.45546i	−0.136767	+	0.0789623i	0.430055	+	0.902802i	$0.358494\pi$
$968$	7.66344	+	23.4605i	0.246312	+	0.754048i
$969$		0			0
$970$	−7.09109	+	33.3610i	−0.227681	+	1.07116i
$971$	6.66140	−	9.16863i	0.213774	−	0.294235i	−0.688641	−	0.725103i	$-0.741792\pi$
$971$	6.66140	−	9.16863i	0.213774	−	0.294235i	0.902415	+	0.430867i	$0.141792\pi$
$972$		0			0
$973$	8.26991	−	25.4522i	0.265121	−	0.815959i
$974$	−7.73570	−	8.59137i	−0.247868	−	0.275285i
$975$		0			0
$976$	2.74934	+	0.288968i	0.0880044	+	0.00924963i
$977$	22.1946	+	19.9841i	0.710067	+	0.639347i	0.942864	−	0.333178i	$-0.108121\pi$
$977$	22.1946	+	19.9841i	0.710067	+	0.639347i	−0.232797	+	0.972525i	$0.574788\pi$
$978$		0			0
$979$	−3.11930	+	9.62588i	−0.0996932	+	0.307644i
$980$		−	12.5318i		−	0.400313i
$981$		0			0
$982$	−10.7272	−	7.79379i	−0.342320	−	0.248710i
$983$	6.68789	−	0.702926i	0.213311	−	0.0224199i	0.00272968	−	0.999996i	$-0.499131\pi$
$983$	6.68789	−	0.702926i	0.213311	−	0.0224199i	0.210581	+	0.977576i	$0.432464\pi$
$984$		0			0
$985$	−1.62315	−	7.63633i	−0.0517179	−	0.243314i
$986$	−1.16632	−	0.519277i	−0.0371431	−	0.0165372i
$987$		0			0
$988$	−23.9598	−	5.09282i	−0.762264	−	0.162024i
$989$	42.4618			1.35021
$990$		0			0
$991$	−6.33993			−0.201395			−0.100697	−	0.994917i	$-0.532107\pi$
$991$	−6.33993			−0.201395			−0.100697	+	0.994917i	$0.532107\pi$
$992$	5.93513	+	1.26155i	0.188440	+	0.0400542i
$993$		0			0
$994$	8.56914	+	3.81523i	0.271797	+	0.121012i
$995$	2.92468	+	13.7595i	0.0927185	+	0.436206i
$996$		0			0
$997$	−6.71660	+	0.705943i	−0.212717	+	0.0223575i	−0.210287	−	0.977640i	$-0.567440\pi$
$997$	−6.71660	+	0.705943i	−0.212717	+	0.0223575i	−0.00242948	+	0.999997i	$0.500773\pi$
$998$	−5.99996	−	4.35922i	−0.189925	−	0.137989i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.e.512.4		64
3.2	odd	2	inner	891.2.u.e.512.5		64
9.2	odd	6		297.2.k.a.215.4	yes	32
9.4	even	3	inner	891.2.u.e.215.5		64
9.5	odd	6	inner	891.2.u.e.215.4		64
9.7	even	3		297.2.k.a.215.5	yes	32
11.2	odd	10	inner	891.2.u.e.431.4		64
33.2	even	10	inner	891.2.u.e.431.5		64
99.2	even	30		297.2.k.a.134.5	yes	32
99.13	odd	30	inner	891.2.u.e.134.5		64
99.68	even	30	inner	891.2.u.e.134.4		64
99.79	odd	30		297.2.k.a.134.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.a.134.4	✓	32	99.79	odd	30
297.2.k.a.134.5	yes	32	99.2	even	30
297.2.k.a.215.4	yes	32	9.2	odd	6
297.2.k.a.215.5	yes	32	9.7	even	3
891.2.u.e.134.4		64	99.68	even	30	inner
891.2.u.e.134.5		64	99.13	odd	30	inner
891.2.u.e.215.4		64	9.5	odd	6	inner
891.2.u.e.215.5		64	9.4	even	3	inner
891.2.u.e.431.4		64	11.2	odd	10	inner
891.2.u.e.431.5		64	33.2	even	10	inner
891.2.u.e.512.4		64	1.1	even	1	trivial
891.2.u.e.512.5		64	3.2	odd	2	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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.607139 - 0.129051i) q^{2} +(-1.47513 - 0.656769i) q^{4} +(-0.776244 - 3.65194i) q^{5} +(2.20625 - 0.231886i) q^{7} +(1.81517 + 1.31880i) q^{8} +O(q^{10})\)	\(q+(-0.607139 - 0.129051i) q^{2} +(-1.47513 - 0.656769i) q^{4} +(-0.776244 - 3.65194i) q^{5} +(2.20625 - 0.231886i) q^{7} +(1.81517 + 1.31880i) q^{8} +2.31741i q^{10} +(3.15510 + 1.02242i) q^{11} +(4.58440 + 4.12782i) q^{13} +(-1.36942 - 0.143932i) q^{14} +(1.22906 + 1.36501i) q^{16} +(-0.0962825 + 0.296327i) q^{17} +(1.44540 - 1.98943i) q^{19} +(-1.25342 + 5.89689i) q^{20} +(-1.78364 - 1.02792i) q^{22} +(7.72848 - 4.46204i) q^{23} +(-8.16640 + 3.63592i) q^{25} +(-2.25067 - 3.09778i) q^{26} +(-3.40679 - 1.10693i) q^{28} +(-0.690036 - 6.56526i) q^{29} +(-0.721480 + 0.801285i) q^{31} +(-2.81373 - 4.87352i) q^{32} +(0.0966983 - 0.167486i) q^{34} +(-2.55942 - 7.87708i) q^{35} +(-3.01593 + 2.19120i) q^{37} +(-1.13430 + 1.02133i) q^{38} +(3.40716 - 7.65260i) q^{40} +(0.436738 - 4.15528i) q^{41} +(4.12066 + 2.37906i) q^{43} +(-3.98268 - 3.58037i) q^{44} +(-5.26809 + 1.71171i) q^{46} +(-0.585996 - 1.31617i) q^{47} +(-2.03329 + 0.432188i) q^{49} +(5.42736 - 1.15362i) q^{50} +(-4.05156 - 9.09995i) q^{52} +(-5.61052 + 1.82297i) q^{53} +(1.28469 - 12.3159i) q^{55} +(4.31052 + 2.48868i) q^{56} +(-0.428307 + 4.07507i) q^{58} +(-2.27545 + 5.11074i) q^{59} +(1.11847 - 1.00708i) q^{61} +(0.541446 - 0.393383i) q^{62} +(-0.0558176 - 0.171789i) q^{64} +(11.5159 - 19.9462i) q^{65} +(-1.39875 - 2.42271i) q^{67} +(0.336647 - 0.373885i) q^{68} +(0.537375 + 5.11278i) q^{70} +(-6.47873 - 2.10507i) q^{71} +(5.66251 + 7.79378i) q^{73} +(2.11386 - 0.941153i) q^{74} +(-3.43875 + 1.98536i) q^{76} +(7.19801 + 1.52409i) q^{77} +(1.03441 - 4.86651i) q^{79} +(4.03089 - 5.54804i) q^{80} +(-0.801405 + 2.46647i) q^{82} +(8.96283 + 9.95424i) q^{83} +(1.15691 + 0.121596i) q^{85} +(-2.19479 - 1.97620i) q^{86} +(4.37867 + 6.01680i) q^{88} +3.05090i q^{89} +(11.0715 + 8.04392i) q^{91} +(-14.3310 + 1.50625i) q^{92} +(0.185928 + 0.874721i) q^{94} +(-8.38726 - 3.73425i) q^{95} +(14.3958 + 3.05992i) q^{97} +1.29026 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{4}+O(q^{10}) \) 64 * q + 8 * q^4	\( 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70} + 160 q^{73} + 60 q^{79} + 144 q^{82} + 20 q^{85} + 24 q^{88} + 48 q^{91} - 20 q^{94} + 24 q^{97}+O(q^{100}) \) 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Introduction

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