LMFDB - Embedded newform 864.2.bk.a.37.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(37,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("864.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bk (of order $24$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			37.13
Character	$\chi$	$=$	864.37
Dual form			864.2.bk.a.397.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.917969 + 1.07579i) q^{2} +(-0.314664 - 1.97509i) q^{4} +(2.56852 - 1.97090i) q^{5} +(-0.846806 + 3.16032i) q^{7} +(2.41364 + 1.47456i) q^{8} +O(q^{10})$	\(q+(-0.917969 + 1.07579i) q^{2} +(-0.314664 - 1.97509i) q^{4} +(2.56852 - 1.97090i) q^{5} +(-0.846806 + 3.16032i) q^{7} +(2.41364 + 1.47456i) q^{8} +(-0.237547 + 4.57243i) q^{10} +(-3.18352 + 0.419118i) q^{11} +(-0.765734 + 5.81632i) q^{13} +(-2.62251 - 3.81207i) q^{14} +(-3.80197 + 1.24298i) q^{16} -3.19756i q^{17} +(-0.917962 + 0.380232i) q^{19} +(-4.70093 - 4.45290i) q^{20} +(2.47149 - 3.80954i) q^{22} +(1.96087 + 7.31806i) q^{23} +(1.41878 - 5.29496i) q^{25} +(-5.55425 - 6.16298i) q^{26} +(6.50839 + 0.678079i) q^{28} +(-0.633433 + 0.825505i) q^{29} +(-1.14946 + 1.99093i) q^{31} +(2.15290 - 5.23116i) q^{32} +(3.43992 + 2.93526i) q^{34} +(4.05363 + 9.78633i) q^{35} +(10.0952 + 4.18156i) q^{37} +(0.433609 - 1.33658i) q^{38} +(9.10571 - 0.969602i) q^{40} +(1.82855 + 6.82422i) q^{41} +(1.04212 - 0.137198i) q^{43} +(1.82953 + 6.15585i) q^{44} +(-9.67274 - 4.60827i) q^{46} +(-5.34450 + 3.08565i) q^{47} +(-3.20839 - 1.85236i) q^{49} +(4.39389 + 6.38693i) q^{50} +(11.7287 - 0.317796i) q^{52} +(5.16512 - 12.4697i) q^{53} +(-7.35090 + 7.35090i) q^{55} +(-6.70397 + 6.37923i) q^{56} +(-0.306602 - 1.43923i) q^{58} +(-0.679702 + 0.521554i) q^{59} +(-3.51653 + 4.58283i) q^{61} +(-1.08666 - 3.06419i) q^{62} +(3.65135 + 7.11812i) q^{64} +(9.49657 + 16.4485i) q^{65} +(6.81006 + 0.896561i) q^{67} +(-6.31548 + 1.00616i) q^{68} +(-14.2492 - 4.62268i) q^{70} +(-2.92094 - 2.92094i) q^{71} +(-4.48292 + 4.48292i) q^{73} +(-13.7656 + 7.02178i) q^{74} +(1.03984 + 1.69341i) q^{76} +(1.37127 - 10.4159i) q^{77} +(7.00349 - 4.04346i) q^{79} +(-7.31567 + 10.6859i) q^{80} +(-9.02000 - 4.29729i) q^{82} +(1.27984 + 0.982054i) q^{83} +(-6.30207 - 8.21301i) q^{85} +(-0.809039 + 1.24705i) q^{86} +(-8.30188 - 3.68268i) q^{88} +(-1.97258 - 1.97258i) q^{89} +(-17.7330 - 7.34527i) q^{91} +(13.8368 - 6.17563i) q^{92} +(1.58657 - 8.58212i) q^{94} +(-1.60841 + 2.78584i) q^{95} +(-0.192235 - 0.332960i) q^{97} +(4.93796 - 1.75115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	$ 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) $ 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.917969	+	1.07579i	−0.649102	+	0.760701i
$2$	−0.917969	+	1.07579i	−0.649102	+	0.760701i
$3$		0			0
$3$		0			0
$4$	−0.314664	−	1.97509i	−0.157332	−	0.987546i
$5$	2.56852	−	1.97090i	1.14868	−	0.881412i	0.154377	−	0.988012i	$-0.450663\pi$
$5$	2.56852	−	1.97090i	1.14868	−	0.881412i	0.994302	+	0.106600i	$0.0339964\pi$
$6$		0			0
$7$	−0.846806	+	3.16032i	−0.320063	+	1.19449i	0.599120	+	0.800659i	$0.295517\pi$
$7$	−0.846806	+	3.16032i	−0.320063	+	1.19449i	−0.919183	+	0.393831i	$0.871150\pi$
$8$	2.41364	+	1.47456i	0.853352	+	0.521336i
$9$		0			0
$10$	−0.237547	+	4.57243i	−0.0751189	+	1.44593i
$11$	−3.18352	+	0.419118i	−0.959866	+	0.126369i	−0.594147	−	0.804357i	$-0.702510\pi$
$11$	−3.18352	+	0.419118i	−0.959866	+	0.126369i	−0.365719	+	0.930725i	$0.619177\pi$
$12$		0			0
$13$	−0.765734	+	5.81632i	−0.212376	+	1.61316i	0.470347	+	0.882481i	$0.344129\pi$
$13$	−0.765734	+	5.81632i	−0.212376	+	1.61316i	−0.682724	+	0.730677i	$0.739205\pi$
$14$	−2.62251	−	3.81207i	−0.700896	−	1.01882i
$15$		0			0
$16$	−3.80197	+	1.24298i	−0.950493	+	0.310745i
$17$		−	3.19756i		−	0.775523i	−0.921760	−	0.387761i	$-0.873248\pi$
$17$		−	3.19756i		−	0.775523i	0.921760	−	0.387761i	$-0.126752\pi$
$18$		0			0
$19$	−0.917962	+	0.380232i	−0.210595	+	0.0872312i	−0.485487	−	0.874244i	$-0.661358\pi$
$19$	−0.917962	+	0.380232i	−0.210595	+	0.0872312i	0.274892	+	0.961475i	$0.411358\pi$
$20$	−4.70093	−	4.45290i	−1.05116	−	0.995698i
$21$		0			0
$22$	2.47149	−	3.80954i	0.526922	−	0.812197i
$23$	1.96087	+	7.31806i	0.408869	+	1.52592i	0.796806	+	0.604235i	$0.206521\pi$
$23$	1.96087	+	7.31806i	0.408869	+	1.52592i	−0.387937	+	0.921686i	$0.626812\pi$
$24$		0			0
$25$	1.41878	−	5.29496i	0.283756	−	1.05899i
$26$	−5.55425	−	6.16298i	−1.08928	−	1.20866i
$27$		0			0
$28$	6.50839	+	0.678079i	1.22997	+	0.128145i
$29$	−0.633433	+	0.825505i	−0.117625	+	0.153293i	−0.848455	−	0.529268i	$-0.822467\pi$
$29$	−0.633433	+	0.825505i	−0.117625	+	0.153293i	0.730830	+	0.682560i	$0.239133\pi$
$30$		0			0
$31$	−1.14946	+	1.99093i	−0.206450	+	0.357581i	−0.950594	−	0.310438i	$-0.899524\pi$
$31$	−1.14946	+	1.99093i	−0.206450	+	0.357581i	0.744144	+	0.668019i	$0.232858\pi$
$32$	2.15290	−	5.23116i	0.380583	−	0.924747i
$33$		0			0
$34$	3.43992	+	2.93526i	0.589941	+	0.503394i
$35$	4.05363	+	9.78633i	0.685189	+	1.65419i
$36$		0			0
$37$	10.0952	+	4.18156i	1.65964	+	0.687444i	0.998050	−	0.0624246i	$-0.0198833\pi$
$37$	10.0952	+	4.18156i	1.65964	+	0.687444i	0.661587	+	0.749869i	$0.269883\pi$
$38$	0.433609	−	1.33658i	0.0703407	−	0.216822i
$39$		0			0
$40$	9.10571	−	0.969602i	1.43974	−	0.153308i
$41$	1.82855	+	6.82422i	0.285571	+	1.06576i	0.948421	+	0.317013i	$0.102680\pi$
$41$	1.82855	+	6.82422i	0.285571	+	1.06576i	−0.662851	+	0.748752i	$0.730654\pi$
$42$		0			0
$43$	1.04212	−	0.137198i	0.158922	−	0.0209225i	−0.0506453	−	0.998717i	$-0.516128\pi$
$43$	1.04212	−	0.137198i	0.158922	−	0.0209225i	0.209567	+	0.977794i	$0.432794\pi$
$44$	1.82953	+	6.15585i	0.275813	+	0.928030i
$45$		0			0
$46$	−9.67274	−	4.60827i	−1.42617	−	0.679452i
$47$	−5.34450	+	3.08565i	−0.779576	+	0.450088i	−0.836280	−	0.548303i	$-0.815274\pi$
$47$	−5.34450	+	3.08565i	−0.779576	+	0.450088i	0.0567040	+	0.998391i	$0.481941\pi$
$48$		0			0
$49$	−3.20839	−	1.85236i	−0.458341	−	0.264623i
$50$	4.39389	+	6.38693i	0.621390	+	0.903248i
$51$		0			0
$52$	11.7287	−	0.317796i	1.62648	−	0.0440703i
$53$	5.16512	−	12.4697i	0.709484	−	1.71285i	0.00819895	−	0.999966i	$-0.497390\pi$
$53$	5.16512	−	12.4697i	0.709484	−	1.71285i	0.701285	−	0.712881i	$-0.252610\pi$
$54$		0			0
$55$	−7.35090	+	7.35090i	−0.991195	+	0.991195i
$56$	−6.70397	+	6.37923i	−0.895856	+	0.852460i
$57$		0			0
$58$	−0.306602	−	1.43923i	−0.0402588	−	0.188980i
$59$	−0.679702	+	0.521554i	−0.0884896	+	0.0679005i	−0.652059	−	0.758168i	$-0.726094\pi$
$59$	−0.679702	+	0.521554i	−0.0884896	+	0.0679005i	0.563569	+	0.826069i	$0.309428\pi$
$60$		0			0
$61$	−3.51653	+	4.58283i	−0.450245	+	0.586771i	−0.962235	−	0.272220i	$-0.912242\pi$
$61$	−3.51653	+	4.58283i	−0.450245	+	0.586771i	0.511989	+	0.858992i	$0.328909\pi$
$62$	−1.08666	−	3.06419i	−0.138005	−	0.389153i
$63$		0			0
$64$	3.65135	+	7.11812i	0.456418	+	0.889765i
$65$	9.49657	+	16.4485i	1.17791	+	2.04019i
$66$		0			0
$67$	6.81006	+	0.896561i	0.831981	+	0.109532i	0.534471	−	0.845187i	$-0.320511\pi$
$67$	6.81006	+	0.896561i	0.831981	+	0.109532i	0.297509	+	0.954719i	$0.403844\pi$
$68$	−6.31548	+	1.00616i	−0.765864	+	0.122015i
$69$		0			0
$70$	−14.2492	−	4.62268i	−1.70310	−	0.552516i
$71$	−2.92094	−	2.92094i	−0.346652	−	0.346652i	0.512209	−	0.858861i	$-0.328827\pi$
$71$	−2.92094	−	2.92094i	−0.346652	−	0.346652i	−0.858861	+	0.512209i	$0.828827\pi$
$72$		0			0
$73$	−4.48292	+	4.48292i	−0.524687	+	0.524687i	−0.918983	−	0.394297i	$-0.870988\pi$
$73$	−4.48292	+	4.48292i	−0.524687	+	0.524687i	0.394297	+	0.918983i	$0.370988\pi$
$74$	−13.7656	+	7.02178i	−1.60021	+	0.816266i
$75$		0			0
$76$	1.03984	+	1.69341i	0.119278	+	0.194248i
$77$	1.37127	−	10.4159i	0.156271	−	1.18700i
$78$		0			0
$79$	7.00349	−	4.04346i	0.787954	−	0.454925i	−0.0512879	−	0.998684i	$-0.516333\pi$
$79$	7.00349	−	4.04346i	0.787954	−	0.454925i	0.839242	+	0.543759i	$0.182999\pi$
$80$	−7.31567	+	10.6859i	−0.817916	+	1.19472i
$81$		0			0
$82$	−9.02000	−	4.29729i	−0.996093	−	0.474556i
$83$	1.27984	+	0.982054i	0.140480	+	0.107794i	0.676611	−	0.736341i	$-0.263448\pi$
$83$	1.27984	+	0.982054i	0.140480	+	0.107794i	−0.536131	+	0.844135i	$0.680115\pi$
$84$		0			0
$85$	−6.30207	−	8.21301i	−0.683555	−	0.890826i
$86$	−0.809039	+	1.24705i	−0.0872409	+	0.134473i
$87$		0			0
$88$	−8.30188	−	3.68268i	−0.884984	−	0.392575i
$89$	−1.97258	−	1.97258i	−0.209093	−	0.209093i	0.594789	−	0.803882i	$-0.297236\pi$
$89$	−1.97258	−	1.97258i	−0.209093	−	0.209093i	−0.803882	+	0.594789i	$0.797236\pi$
$90$		0			0
$91$	−17.7330	−	7.34527i	−1.85893	−	0.769993i
$92$	13.8368	−	6.17563i	1.44259	−	0.643854i
$93$		0			0
$94$	1.58657	−	8.58212i	0.163642	−	0.885178i
$95$	−1.60841	+	2.78584i	−0.165019	+	0.285822i
$96$		0			0
$97$	−0.192235	−	0.332960i	−0.0195185	−	0.0338070i	0.856101	−	0.516808i	$-0.172880\pi$
$97$	−0.192235	−	0.332960i	−0.0195185	−	0.0338070i	−0.875620	+	0.483001i	$0.839547\pi$
$98$	4.93796	−	1.75115i	0.498810	−	0.176893i
$99$		0			0
$100$	−10.9045	−	1.13609i	−1.09045	−	0.113609i
$101$	−0.0939354	−	0.713510i	−0.00934692	−	0.0709969i	0.986136	−	0.165941i	$-0.0530661\pi$
$101$	−0.0939354	−	0.713510i	−0.00934692	−	0.0709969i	−0.995483	+	0.0949440i	$0.969733\pi$
$102$		0			0
$103$	−8.79709	+	2.35717i	−0.866803	+	0.232259i	−0.664705	−	0.747106i	$-0.731443\pi$
$103$	−8.79709	+	2.35717i	−0.866803	+	0.232259i	−0.202098	+	0.979365i	$0.564776\pi$
$104$	−10.4247	+	12.9094i	−1.02223	+	1.26587i
$105$		0			0
$106$	8.67341	+	17.0034i	0.842436	+	1.65152i
$107$	0.118579	−	0.286276i	0.0114635	−	0.0276753i	−0.918044	−	0.396478i	$-0.870232\pi$
$107$	0.118579	−	0.286276i	0.0114635	−	0.0276753i	0.929508	+	0.368803i	$0.120232\pi$
$108$		0			0
$109$	−6.88950	+	2.85373i	−0.659895	+	0.273337i	−0.687394	−	0.726284i	$-0.741246\pi$
$109$	−6.88950	+	2.85373i	−0.659895	+	0.273337i	0.0274995	+	0.999622i	$0.491246\pi$
$110$	−1.16015	−	14.6559i	−0.110616	−	1.39739i
$111$		0			0
$112$	−0.708690	−	13.0680i	−0.0669649	−	1.23481i
$113$	−13.3738	−	7.72138i	−1.25810	−	0.726367i	−0.285398	−	0.958409i	$-0.592126\pi$
$113$	−13.3738	−	7.72138i	−1.25810	−	0.726367i	−0.972706	+	0.232043i	$0.925459\pi$
$114$		0			0
$115$	19.4597	+	14.9319i	1.81462	+	1.39241i
$116$	1.82977	+	0.991330i	0.169890	+	0.0920427i
$117$		0			0
$118$	0.0628614	−	1.20999i	0.00578686	−	0.111389i
$119$	10.1053	+	2.70771i	0.926354	+	0.248216i
$120$		0			0
$121$	−0.666075	+	0.178474i	−0.0605523	+	0.0162249i
$122$	−1.70211	−	7.98996i	−0.154102	−	0.723377i
$123$		0			0
$124$	4.29396	+	1.64382i	0.385609	+	0.147619i
$125$	−0.596868	−	1.44097i	−0.0533855	−	0.128884i
$126$		0			0
$127$	5.50843			0.488794			0.244397	−	0.969675i	$-0.421410\pi$
$127$	5.50843			0.488794			0.244397	+	0.969675i	$0.421410\pi$
$128$	−11.0095	−	2.60612i	−0.973108	−	0.230351i
$129$		0			0
$130$	−26.4128	−	4.88291i	−2.31656	−	0.428260i
$131$	11.3324	+	1.49194i	0.990116	+	0.130351i	0.608147	−	0.793824i	$-0.291913\pi$
$131$	11.3324	+	1.49194i	0.990116	+	0.130351i	0.381968	+	0.924175i	$0.375246\pi$
$132$		0			0
$133$	−0.424321	−	3.22304i	−0.0367933	−	0.279473i
$134$	−7.21594	+	6.50320i	−0.623362	+	0.561791i
$135$		0			0
$136$	4.71500	−	7.71777i	0.404308	−	0.661794i
$137$	−0.490612	−	0.131459i	−0.0419158	−	0.0112313i	0.237800	−	0.971314i	$-0.423574\pi$
$137$	−0.490612	−	0.131459i	−0.0419158	−	0.0112313i	−0.279716	+	0.960083i	$0.590240\pi$
$138$		0			0
$139$	7.45182	+	9.71140i	0.632055	+	0.823710i	0.994102	−	0.108450i	$-0.0345886\pi$
$139$	7.45182	+	9.71140i	0.632055	+	0.823710i	−0.362047	+	0.932160i	$0.617922\pi$
$140$	18.0534	−	11.0857i	1.52579	−	0.936913i
$141$		0			0
$142$	5.82367	−	0.460996i	0.488712	−	0.0386859i
$143$		−	18.8373i		−	1.57525i
$144$		0			0
$145$			3.36876i			0.279760i
$146$	−0.707514	−	8.93789i	−0.0585543	−	0.739705i
$147$		0			0
$148$	5.08237	−	21.2547i	0.417768	−	1.74712i
$149$	−2.31891	−	3.02206i	−0.189972	−	0.247577i	0.688650	−	0.725094i	$-0.258204\pi$
$149$	−2.31891	−	3.02206i	−0.189972	−	0.247577i	−0.878622	+	0.477517i	$0.841537\pi$
$150$		0			0
$151$	15.5031	+	4.15404i	1.26162	+	0.338051i	0.826816	−	0.562472i	$-0.190150\pi$
$151$	15.5031	+	4.15404i	1.26162	+	0.338051i	0.434808	+	0.900523i	$0.356816\pi$
$152$	−2.77631	−	0.435844i	−0.225188	−	0.0353516i
$153$		0			0
$154$	9.94652	+	11.0366i	0.801513	+	0.889358i
$155$	0.971492	+	7.37922i	0.0780321	+	0.592713i
$156$		0			0
$157$	7.56916	+	0.996498i	0.604084	+	0.0795292i	0.426364	−	0.904552i	$-0.359794\pi$
$157$	7.56916	+	0.996498i	0.604084	+	0.0795292i	0.177721	+	0.984081i	$0.443128\pi$
$158$	−2.07905	+	11.2461i	−0.165401	+	0.894690i
$159$		0			0
$160$	−4.78029	−	17.6795i	−0.377915	−	1.39769i
$161$	−24.7879			−1.95356
$162$		0			0
$163$	1.18238	+	2.85452i	0.0926111	+	0.223583i	0.963397	−	0.268080i	$-0.0863892\pi$
$163$	1.18238	+	2.85452i	0.0926111	+	0.223583i	−0.870786	+	0.491663i	$0.836389\pi$
$164$	12.9031	−	5.75888i	1.00756	−	0.449693i
$165$		0			0
$166$	−2.23134	+	0.475346i	−0.173185	+	0.0368940i
$167$	−1.66677	+	0.446610i	−0.128979	+	0.0345597i	−0.322731	−	0.946491i	$-0.604601\pi$
$167$	−1.66677	+	0.446610i	−0.128979	+	0.0345597i	0.193752	+	0.981050i	$0.437934\pi$
$168$		0			0
$169$	−20.6862	−	5.54286i	−1.59125	−	0.426374i
$170$	14.6206	+	0.759571i	1.12135	+	0.0582564i
$171$		0			0
$172$	−0.598897	−	2.01511i	−0.0456655	−	0.153651i
$173$	11.1819	+	8.58019i	0.850146	+	0.652340i	0.939080	−	0.343697i	$-0.111679\pi$
$173$	11.1819	+	8.58019i	0.850146	+	0.652340i	−0.0889343	+	0.996037i	$0.528346\pi$
$174$		0			0
$175$	15.5324	+	8.96762i	1.17414	+	0.677888i
$176$	11.5827	−	5.55053i	0.873078	−	0.418387i
$177$		0			0
$178$	3.93285	−	0.311320i	0.294779	−	0.0233345i
$179$	−20.8995	+	8.65686i	−1.56210	+	0.647044i	−0.985453	−	0.169947i	$-0.945640\pi$
$179$	−20.8995	+	8.65686i	−1.56210	+	0.647044i	−0.576650	+	0.816991i	$0.695640\pi$
$180$		0			0
$181$	6.90156	−	16.6618i	0.512989	−	1.23846i	−0.429147	−	0.903234i	$-0.641186\pi$
$181$	6.90156	−	16.6618i	0.512989	−	1.23846i	0.942136	−	0.335230i	$-0.108814\pi$
$182$	24.1804	−	12.3344i	1.79237	−	0.914284i
$183$		0			0
$184$	−6.05808	+	20.5546i	−0.446608	+	1.51531i
$185$	34.1711	−	9.15612i	2.51231	−	0.673172i
$186$		0			0
$187$	1.34015	+	10.1795i	0.0980018	+	0.744398i
$188$	7.77617	+	9.58494i	0.567135	+	0.699054i
$189$		0			0
$190$	−1.52052	−	4.28763i	−0.110310	−	0.311058i
$191$	−5.92947	−	10.2701i	−0.429041	−	0.743121i	0.567747	−	0.823203i	$-0.307815\pi$
$191$	−5.92947	−	10.2701i	−0.429041	−	0.743121i	−0.996788	+	0.0800819i	$0.974482\pi$
$192$		0			0
$193$	6.24993	−	10.8252i	0.449880	−	0.779215i	−0.548498	−	0.836152i	$-0.684800\pi$
$193$	6.24993	−	10.8252i	0.449880	−	0.779215i	0.998378	+	0.0569372i	$0.0181335\pi$
$194$	0.534662	+	0.0988424i	0.0383865	+	0.00709647i
$195$		0			0
$196$	−2.64902	+	6.91973i	−0.189216	+	0.494267i
$197$	14.0411	+	5.81603i	1.00039	+	0.414375i	0.821940	−	0.569574i	$-0.192892\pi$
$197$	14.0411	+	5.81603i	1.00039	+	0.414375i	0.178450	+	0.983949i	$0.442892\pi$
$198$		0			0
$199$	−1.49055	−	1.49055i	−0.105662	−	0.105662i	0.652299	−	0.757961i	$-0.273805\pi$
$199$	−1.49055	−	1.49055i	−0.105662	−	0.105662i	−0.757961	+	0.652299i	$0.773805\pi$
$200$	11.2322	−	10.6881i	0.794235	−	0.755761i
$201$		0			0
$202$	0.853820	+	0.553925i	0.0600745	+	0.0389741i
$203$	−2.07247	−	2.70090i	−0.145459	−	0.189566i
$204$		0			0
$205$	18.1465	+	13.9243i	1.26741	+	0.972515i
$206$	5.53963	−	11.6277i	0.385964	−	0.810138i
$207$		0			0
$208$	−4.31829	−	23.0653i	−0.299419	−	1.59929i
$209$	2.76298	−	1.59521i	0.191120	−	0.110343i
$210$		0			0
$211$	2.36500	−	17.9639i	0.162813	−	1.23669i	−0.693586	−	0.720374i	$-0.743970\pi$
$211$	2.36500	−	17.9639i	0.162813	−	1.23669i	0.856399	−	0.516315i	$-0.172697\pi$
$212$	−26.2541	−	6.27782i	−1.80314	−	0.431162i
$213$		0			0
$214$	0.199122	+	0.390360i	0.0136117	+	0.0266844i
$215$	2.40631	−	2.40631i	0.164109	−	0.164109i
$216$		0			0
$217$	−5.31860	−	5.31860i	−0.361050	−	0.361050i
$218$	3.25433	−	10.0313i	0.220411	−	0.679407i
$219$		0			0
$220$	16.8318	+	12.2056i	1.13480	+	0.822903i
$221$	18.5981	+	2.44848i	1.25104	+	0.164703i
$222$		0			0
$223$	−11.6777	−	20.2264i	−0.781997	−	1.35446i	−0.930776	−	0.365589i	$-0.880868\pi$
$223$	−11.6777	−	20.2264i	−0.781997	−	1.35446i	0.148779	−	0.988870i	$-0.452466\pi$
$224$	14.7091	+	11.2336i	0.982790	+	0.750580i
$225$		0			0
$226$	20.5834	−	7.29949i	1.36919	−	0.485555i
$227$	−1.05713	+	1.37767i	−0.0701639	+	0.0914393i	−0.827117	−	0.562030i	$-0.810021\pi$
$227$	−1.05713	+	1.37767i	−0.0701639	+	0.0914393i	0.756953	+	0.653469i	$0.226687\pi$
$228$		0			0
$229$	−14.8485	+	11.3937i	−0.981217	+	0.752915i	−0.969013	−	0.247011i	$-0.920552\pi$
$229$	−14.8485	+	11.3937i	−0.981217	+	0.752915i	−0.0122047	+	0.999926i	$0.503885\pi$
$230$	−33.9271	+	7.22754i	−2.23709	+	0.476570i
$231$		0			0
$232$	−2.74614	+	1.05844i	−0.180293	+	0.0694901i
$233$	2.43002	−	2.43002i	0.159196	−	0.159196i	−0.623014	−	0.782210i	$-0.714092\pi$
$233$	2.43002	−	2.43002i	0.159196	−	0.159196i	0.782210	+	0.623014i	$0.214092\pi$
$234$		0			0
$235$	−7.64598	+	18.4590i	−0.498769	+	1.20413i
$236$	1.24399	+	1.17836i	0.0809771	+	0.0767046i
$237$		0			0
$238$	−12.1893	+	8.38565i	−0.790117	+	0.543561i
$239$	6.39630	+	3.69291i	0.413742	+	0.238874i	0.692396	−	0.721517i	$-0.256555\pi$
$239$	6.39630	+	3.69291i	0.413742	+	0.238874i	−0.278654	+	0.960392i	$0.589888\pi$
$240$		0			0
$241$	11.9933	−	6.92431i	0.772554	−	0.446034i	−0.0612310	−	0.998124i	$-0.519503\pi$
$241$	11.9933	−	6.92431i	0.772554	−	0.446034i	0.833785	+	0.552089i	$0.186169\pi$
$242$	0.419435	−	0.880393i	0.0269623	−	0.0565938i
$243$		0			0
$244$	10.1580	+	5.50341i	0.650302	+	0.352320i
$245$	−11.8916	+	1.56556i	−0.759729	+	0.100020i
$246$		0			0
$247$	−1.50864	−	5.63032i	−0.0959924	−	0.358249i
$248$	−5.71013	+	3.11044i	−0.362594	+	0.197513i
$249$		0			0
$250$	2.09809	+	0.680657i	0.132695	+	0.0430485i
$251$	−1.73159	−	0.717250i	−0.109297	−	0.0452724i	0.327365	−	0.944898i	$-0.393839\pi$
$251$	−1.73159	−	0.717250i	−0.109297	−	0.0452724i	−0.436662	+	0.899626i	$0.643839\pi$
$252$		0			0
$253$	−9.30958	−	22.4753i	−0.585288	−	1.41301i
$254$	−5.05657	+	5.92594i	−0.317278	+	0.371826i
$255$		0			0
$256$	12.9100	−	9.45156i	0.806875	−	0.590723i
$257$	−2.38358	+	4.12849i	−0.148684	+	0.257528i	−0.930741	−	0.365678i	$-0.880837\pi$
$257$	−2.38358	+	4.12849i	−0.148684	+	0.257528i	0.782057	+	0.623206i	$0.214170\pi$
$258$		0			0
$259$	−21.7637	+	28.3631i	−1.35233	+	1.76239i
$260$	29.4992	−	23.9324i	1.82946	−	1.48422i
$261$		0			0
$262$	−12.0078	+	10.8218i	−0.741845	+	0.668571i
$263$	3.27806	−	12.2339i	0.202134	−	0.754373i	−0.788171	−	0.615457i	$-0.788972\pi$
$263$	3.27806	−	12.2339i	0.202134	−	0.754373i	0.990304	−	0.138916i	$-0.0443618\pi$
$264$		0			0
$265$	−11.3098	−	42.2087i	−0.694754	−	2.59286i
$266$	3.85684	+	2.50217i	0.236478	+	0.153418i
$267$		0			0
$268$	−0.372092	−	13.7326i	−0.0227291	−	0.838852i
$269$	21.8241	−	9.03984i	1.33064	−	0.551169i	0.399801	−	0.916602i	$-0.369079\pi$
$269$	21.8241	−	9.03984i	1.33064	−	0.551169i	0.930838	+	0.365433i	$0.119079\pi$
$270$		0			0
$271$		−	29.6716i		−	1.80242i	−0.433383	−	0.901210i	$-0.642680\pi$
$271$		−	29.6716i		−	1.80242i	0.433383	−	0.901210i	$-0.357320\pi$
$272$	3.97451	+	12.1570i	0.240990	+	0.737129i
$273$		0			0
$274$	0.591790	−	0.407122i	0.0357513	−	0.0245951i
$275$	−2.29750	+	17.4512i	−0.138544	+	1.05235i
$276$		0			0
$277$	−14.5874	+	1.92047i	−0.876474	+	0.115390i	−0.555320	−	0.831637i	$-0.687404\pi$
$277$	−14.5874	+	1.92047i	−0.876474	+	0.115390i	−0.321154	+	0.947027i	$0.604071\pi$
$278$	−17.2880	−	0.898148i	−1.03687	−	0.0538673i
$279$		0			0
$280$	−4.64651	+	29.5980i	−0.277682	+	1.76882i
$281$	−0.366424	+	1.36751i	−0.0218591	+	0.0815791i	−0.975994	−	0.217799i	$-0.930112\pi$
$281$	−0.366424	+	1.36751i	−0.0218591	+	0.0815791i	0.954135	+	0.299378i	$0.0967791\pi$
$282$		0			0
$283$	2.88747	−	2.21563i	0.171642	−	0.131706i	−0.519368	−	0.854551i	$-0.673833\pi$
$283$	2.88747	−	2.21563i	0.171642	−	0.131706i	0.691010	+	0.722845i	$0.257166\pi$
$284$	−4.85002	+	6.68825i	−0.287795	+	0.396875i
$285$		0			0
$286$	20.2650	+	17.2921i	1.19830	+	1.02250i
$287$	−23.1152			−1.36445
$288$		0			0
$289$	6.77560			0.398565
$290$	−3.62409	−	3.09242i	−0.212814	−	0.181593i
$291$		0			0
$292$	10.2648	+	7.44357i	0.600702	+	0.435602i
$293$	−17.5365	+	13.4562i	−1.02449	+	0.786120i	−0.977105	−	0.212757i	$-0.931756\pi$
$293$	−17.5365	+	13.4562i	−1.02449	+	0.786120i	−0.0473862	+	0.998877i	$0.515089\pi$
$294$		0			0
$295$	−0.717902	+	2.67925i	−0.0417979	+	0.155992i
$296$	18.2002	+	24.9787i	1.05786	+	1.45186i
$297$		0			0
$298$	5.37980	+	0.279491i	0.311643	+	0.0161905i
$299$	−44.0657	+	5.80136i	−2.54839	+	0.335501i
$300$		0			0
$301$	−0.448885	+	3.40962i	−0.0258733	+	0.196527i
$302$	−18.7003	+	12.8649i	−1.07608	+	0.740289i
$303$		0			0
$304$	3.01744	−	2.58664i	0.173062	−	0.148354i
$305$			18.7018i			1.07086i
$306$		0			0
$307$	−3.09982	+	1.28399i	−0.176916	+	0.0732812i	−0.469383	−	0.882994i	$-0.655524\pi$
$307$	−3.09982	+	1.28399i	−0.176916	+	0.0732812i	0.292467	+	0.956276i	$0.405524\pi$
$308$	−21.0037	+	0.569107i	−1.19680	+	0.0324279i
$309$		0			0
$310$	−8.83031	−	5.72877i	−0.501528	−	0.325372i
$311$	−5.76600	−	21.5190i	−0.326960	−	1.22023i	−0.912327	−	0.409463i	$-0.865716\pi$
$311$	−5.76600	−	21.5190i	−0.326960	−	1.22023i	0.585367	−	0.810769i	$-0.300951\pi$
$312$		0			0
$313$	2.92455	−	10.9146i	0.165305	−	0.616928i	−0.832696	−	0.553731i	$-0.813204\pi$
$313$	2.92455	−	10.9146i	0.165305	−	0.616928i	0.998001	−	0.0631970i	$-0.0201296\pi$
$314$	−8.02028	+	7.22810i	−0.452611	+	0.407905i
$315$		0			0
$316$	−10.1900	−	12.5602i	−0.573230	−	0.706566i
$317$	1.63700	−	2.13338i	0.0919432	−	0.119823i	−0.745116	−	0.666935i	$-0.767606\pi$
$317$	1.63700	−	2.13338i	0.0919432	−	0.119823i	0.837060	+	0.547112i	$0.184273\pi$
$318$		0			0
$319$	1.67056	−	2.89349i	0.0935333	−	0.162004i
$320$	23.4077	+	11.0866i	1.30853	+	0.619762i
$321$		0			0
$322$	22.7545	−	26.6667i	1.26806	−	1.48608i
$323$	1.21582	+	2.93524i	0.0676498	+	0.163321i
$324$		0			0
$325$	29.7108	+	12.3066i	1.64806	+	0.682649i
$326$	−4.15626	−	1.34836i	−0.230194	−	0.0746789i
$327$		0			0
$328$	−5.64927	+	19.1675i	−0.311929	+	1.05835i
$329$	−5.22590	−	19.5033i	−0.288113	−	1.07525i
$330$		0			0
$331$	−33.1359	+	4.36242i	−1.82131	+	0.239780i	−0.962264	−	0.272116i	$-0.912277\pi$
$331$	−33.1359	+	4.36242i	−1.82131	+	0.239780i	−0.859047	+	0.511896i	$0.828943\pi$
$332$	1.53693	−	2.83681i	0.0843498	−	0.155690i
$333$		0			0
$334$	1.04958	−	2.20308i	0.0574307	−	0.120547i
$335$	19.2588	−	11.1191i	1.05222	−	0.607501i
$336$		0			0
$337$	−6.19798	−	3.57841i	−0.337626	−	0.194928i	0.321596	−	0.946877i	$-0.395781\pi$
$337$	−6.19798	−	3.57841i	−0.337626	−	0.194928i	−0.659222	+	0.751949i	$0.729114\pi$
$338$	24.9523	−	17.1660i	1.35723	−	0.933705i
$339$		0			0
$340$	−14.2384	+	15.0315i	−0.772186	+	0.815197i
$341$	2.82490	−	6.81991i	0.152977	−	0.369319i
$342$		0			0
$343$	−7.62367	+	7.62367i	−0.411640	+	0.411640i
$344$	2.71762	+	1.20552i	0.146524	+	0.0649975i
$345$		0			0
$346$	−19.4952	+	4.15309i	−1.04807	+	0.223272i
$347$	23.2842	−	17.8666i	1.24996	−	0.959129i	0.250003	−	0.968245i	$-0.419568\pi$
$347$	23.2842	−	17.8666i	1.24996	−	0.959129i	0.999958	+	0.00911603i	$0.00290176\pi$
$348$		0			0
$349$	18.1221	−	23.6172i	0.970054	−	1.26420i	0.00559057	−	0.999984i	$-0.498220\pi$
$349$	18.1221	−	23.6172i	0.970054	−	1.26420i	0.964464	−	0.264215i	$-0.0851129\pi$
$350$	−23.9055	+	8.47763i	−1.27781	+	0.453148i
$351$		0			0
$352$	−4.66133	+	17.5558i	−0.248450	+	0.935727i
$353$	−7.49907	−	12.9888i	−0.399135	−	0.691322i	0.594484	−	0.804107i	$-0.297356\pi$
$353$	−7.49907	−	12.9888i	−0.399135	−	0.691322i	−0.993619	+	0.112785i	$0.964023\pi$
$354$		0			0
$355$	−13.2594	−	1.74563i	−0.703736	−	0.0926486i
$356$	−3.27532	+	4.51672i	−0.173592	+	0.239386i
$357$		0			0
$358$	9.87212	−	30.4303i	0.521758	−	1.60829i
$359$	6.56704	+	6.56704i	0.346595	+	0.346595i	0.858840	−	0.512245i	$-0.171186\pi$
$359$	6.56704	+	6.56704i	0.346595	+	0.346595i	−0.512245	+	0.858840i	$0.671186\pi$
$360$		0			0
$361$	−12.7370	+	12.7370i	−0.670366	+	0.670366i
$362$	11.5893	+	22.7197i	0.609119	+	1.19412i
$363$		0			0
$364$	−8.92762	+	37.3357i	−0.467934	+	1.95692i
$365$	−2.67911	+	20.3499i	−0.140231	+	1.06516i
$366$		0			0
$367$	11.4275	−	6.59770i	0.596513	−	0.344397i	−0.171156	−	0.985244i	$-0.554750\pi$
$367$	11.4275	−	6.59770i	0.596513	−	0.344397i	0.767669	+	0.640847i	$0.221417\pi$
$368$	−16.5514	−	25.3857i	−0.862800	−	1.32332i
$369$		0			0
$370$	−21.5179	+	45.1661i	−1.11866	+	2.34807i
$371$	35.0345	+	26.8829i	1.81890	+	1.39569i
$372$		0			0
$373$	9.34594	+	12.1799i	0.483914	+	0.630649i	0.969954	−	0.243287i	$-0.0782257\pi$
$373$	9.34594	+	12.1799i	0.483914	+	0.630649i	−0.486040	+	0.873937i	$0.661559\pi$
$374$	−12.1812	−	7.90273i	−0.629877	−	0.408640i
$375$		0			0
$376$	−17.4497	−	0.433130i	−0.899900	−	0.0223370i
$377$	−4.31637	−	4.31637i	−0.222304	−	0.222304i
$378$		0			0
$379$	27.7834	+	11.5083i	1.42714	+	0.591140i	0.956643	−	0.291263i	$-0.0940754\pi$
$379$	27.7834	+	11.5083i	1.42714	+	0.591140i	0.470495	+	0.882403i	$0.344075\pi$
$380$	6.00840	+	2.30015i	0.308225	+	0.117995i
$381$		0			0
$382$	16.4916	+	3.04879i	0.843785	+	0.155990i
$383$	4.98005	−	8.62570i	0.254469	−	0.440752i	−0.710282	−	0.703917i	$-0.751433\pi$
$383$	4.98005	−	8.62570i	0.254469	−	0.440752i	0.964751	+	0.263164i	$0.0847661\pi$
$384$		0			0
$385$	−17.0064	−	29.4560i	−0.866728	−	1.50122i
$386$	5.90843	+	16.6608i	0.300731	+	0.848014i
$387$		0			0
$388$	−0.597138	+	0.484452i	−0.0303151	+	0.0245943i
$389$	−1.06373	−	8.07985i	−0.0539334	−	0.409665i	−0.997022	−	0.0771221i	$-0.975427\pi$
$389$	−1.06373	−	8.07985i	−0.0539334	−	0.409665i	0.943088	−	0.332542i	$-0.107906\pi$
$390$		0			0
$391$	23.3999	−	6.27000i	1.18339	−	0.317087i
$392$	−5.01248	−	9.20190i	−0.253169	−	0.464766i
$393$		0			0
$394$	−19.1462	+	9.76643i	−0.964571	+	0.492026i
$395$	10.0194	−	24.1889i	0.504129	−	1.21707i
$396$		0			0
$397$	31.6589	−	13.1136i	1.58892	−	0.658150i	0.599122	−	0.800658i	$-0.295516\pi$
$397$	31.6589	−	13.1136i	1.58892	−	0.658150i	0.989794	+	0.142507i	$0.0455164\pi$
$398$	2.97180	−	0.235245i	0.148963	−	0.0117917i
$399$		0			0
$400$	1.18738	+	21.8948i	0.0593688	+	1.09474i
$401$	−30.2179	−	17.4463i	−1.50901	−	0.871227i	−0.999945	−	0.0104983i	$-0.996658\pi$
$401$	−30.2179	−	17.4463i	−1.50901	−	0.871227i	−0.509064	−	0.860729i	$-0.670008\pi$
$402$		0			0
$403$	−10.6997	−	8.21017i	−0.532990	−	0.408978i
$404$	−1.37969	+	0.410047i	−0.0686421	+	0.0204006i
$405$		0			0
$406$	4.80807	+	0.249789i	0.238621	+	0.0123968i
$407$	−33.8907	−	9.08099i	−1.67990	−	0.450128i
$408$		0			0
$409$	−5.70295	+	1.52810i	−0.281993	+	0.0755597i	−0.397043	−	0.917800i	$-0.629964\pi$
$409$	−5.70295	+	1.52810i	−0.281993	+	0.0755597i	0.115051	+	0.993360i	$0.463297\pi$
$410$	−31.6376	+	6.73981i	−1.56247	+	0.332856i
$411$		0			0
$412$	7.42376	+	16.6333i	0.365743	+	0.819466i
$413$	−1.07270	−	2.58973i	−0.0527842	−	0.127432i
$414$		0			0
$415$	5.22282			0.256378
$416$	28.7776	+	16.5277i	1.41094	+	0.810335i
$417$		0			0
$418$	−0.820218	+	4.43675i	−0.0401182	+	0.217009i
$419$	26.8756	+	3.53824i	1.31296	+	0.172854i	0.754292	−	0.656539i	$-0.227980\pi$
$419$	26.8756	+	3.53824i	1.31296	+	0.172854i	0.558666	+	0.829393i	$0.311313\pi$
$420$		0			0
$421$	0.0992683	+	0.754018i	0.00483804	+	0.0367486i	0.993694	−	0.112129i	$-0.0357671\pi$
$421$	0.0992683	+	0.754018i	0.00483804	+	0.0367486i	−0.988856	+	0.148878i	$0.952434\pi$
$422$	17.1545	+	19.0346i	0.835068	+	0.926590i
$423$		0			0
$424$	30.8541	−	22.4812i	1.49841	−	1.09178i
$425$	−16.9310	−	4.53664i	−0.821273	−	0.220059i
$426$		0			0
$427$	−11.5054	−	14.9941i	−0.556786	−	0.725617i
$428$	−0.602734	−	0.144124i	−0.0291342	−	0.00696651i
$429$		0			0
$430$	0.379774	+	4.79761i	0.0183143	+	0.231361i
$431$			28.0930i			1.35319i	0.736355	+	0.676596i	$0.236546\pi$
$431$			28.0930i			1.35319i	−0.736355	+	0.676596i	$0.763454\pi$
$432$		0			0
$433$			28.2028i			1.35534i	0.735367	+	0.677669i	$0.237010\pi$
$433$			28.2028i			1.35534i	−0.735367	+	0.677669i	$0.762990\pi$
$434$	10.6040	−	0.839405i	0.509010	−	0.0402927i
$435$		0			0
$436$	7.80425	+	12.7094i	0.373756	+	0.608672i
$437$	−4.58256	−	5.97211i	−0.219214	−	0.285685i
$438$		0			0
$439$	10.4276	+	2.79407i	0.497682	+	0.133354i	0.498924	−	0.866646i	$-0.333729\pi$
$439$	10.4276	+	2.79407i	0.497682	+	0.133354i	−0.00124189	+	0.999999i	$0.500395\pi$
$440$	−28.5818	+	6.90311i	−1.36258	+	0.329093i
$441$		0			0
$442$	−19.7065	+	17.7600i	−0.937343	+	0.844759i
$443$	−0.941018	−	7.14774i	−0.0447091	−	0.339599i	−0.999151	−	0.0412020i	$-0.986881\pi$
$443$	−0.941018	−	7.14774i	−0.0447091	−	0.339599i	0.954442	−	0.298397i	$-0.0964521\pi$
$444$		0			0
$445$	−8.95435	−	1.17886i	−0.424477	−	0.0558835i
$446$	32.4792	+	6.00440i	1.53794	+	0.284317i
$447$		0			0
$448$	−25.5876	+	5.51177i	−1.20890	+	0.260407i
$449$	−12.9753			−0.612344			−0.306172	−	0.951976i	$-0.599048\pi$
$449$	−12.9753			−0.612344			−0.306172	+	0.951976i	$0.599048\pi$
$450$		0			0
$451$	−8.68135	−	20.9586i	−0.408789	−	0.986904i
$452$	−11.0422	+	28.8442i	−0.519380	+	1.35672i
$453$		0			0
$454$	−0.511683	−	2.40191i	−0.0240145	−	0.112727i
$455$	−60.0245	+	16.0835i	−2.81399	+	0.754007i
$456$		0			0
$457$	17.3412	+	4.64656i	0.811187	+	0.217357i	0.640490	−	0.767967i	$-0.278731\pi$
$457$	17.3412	+	4.64656i	0.811187	+	0.217357i	0.170697	+	0.985324i	$0.445398\pi$
$458$	1.37325	−	26.4330i	0.0641676	−	1.23513i
$459$		0			0
$460$	23.3687	−	43.1332i	1.08957	−	2.01110i
$461$	−8.73140	−	6.69984i	−0.406662	−	0.312043i	0.385097	−	0.922876i	$-0.374168\pi$
$461$	−8.73140	−	6.69984i	−0.406662	−	0.312043i	−0.791759	+	0.610833i	$0.790835\pi$
$462$		0			0
$463$	16.6538	+	9.61509i	0.773969	+	0.446851i	0.834288	−	0.551328i	$-0.185879\pi$
$463$	16.6538	+	9.61509i	0.773969	+	0.446851i	−0.0603199	+	0.998179i	$0.519212\pi$
$464$	1.38221	−	3.92589i	0.0641673	−	0.182255i
$465$		0			0
$466$	0.383517	+	4.84489i	0.0177661	+	0.224435i
$467$	−36.6428	+	15.1780i	−1.69563	+	0.702352i	−0.999873	−	0.0159280i	$-0.994930\pi$
$467$	−36.6428	+	15.1780i	−1.69563	+	0.702352i	−0.695754	+	0.718280i	$0.744930\pi$
$468$		0			0
$469$	−8.60022	+	20.7628i	−0.397121	+	0.958736i
$470$	−12.8393	−	25.1703i	−0.592234	−	1.16102i
$471$		0			0
$472$	−2.40962	+	0.256583i	−0.110912	+	0.0118102i
$473$	−3.26011	+	0.873543i	−0.149900	+	0.0401656i
$474$		0			0
$475$	0.710929	+	5.40004i	0.0326196	+	0.247771i
$476$	2.16820	−	20.8110i	0.0993792	−	0.953869i
$477$		0			0
$478$	−9.84442	+	3.49113i	−0.450273	+	0.159680i
$479$	10.4848	+	18.1603i	0.479065	+	0.829764i	0.999712	−	0.0240077i	$-0.00764263\pi$
$479$	10.4848	+	18.1603i	0.479065	+	0.829764i	−0.520647	+	0.853772i	$0.674309\pi$
$480$		0			0
$481$	−32.0515	+	55.5149i	−1.46142	+	2.53126i
$482$	−3.56031	+	19.2586i	−0.162168	+	0.877204i
$483$		0			0
$484$	0.562093	+	1.25940i	0.0255497	+	0.0572454i
$485$	−1.14999	−	0.476341i	−0.0522183	−	0.0216295i
$486$		0			0
$487$	−21.4292	−	21.4292i	−0.971049	−	0.971049i	0.0285433	−	0.999593i	$-0.490913\pi$
$487$	−21.4292	−	21.4292i	−0.971049	−	0.971049i	−0.999593	+	0.0285433i	$0.990913\pi$
$488$	−15.2453	+	5.87599i	−0.690123	+	0.265993i
$489$		0			0
$490$	9.23194	−	14.2301i	0.417056	−	0.642850i
$491$	8.09015	+	10.5433i	0.365103	+	0.475812i	0.939394	−	0.342839i	$-0.111389\pi$
$491$	8.09015	+	10.5433i	0.365103	+	0.475812i	−0.574291	+	0.818652i	$0.694722\pi$
$492$		0			0
$493$	2.63960	+	2.02544i	0.118882	+	0.0912212i
$494$	7.44195	+	3.54548i	0.334829	+	0.159519i
$495$		0			0
$496$	1.89554	−	8.99821i	0.0851122	−	0.404032i
$497$	11.7046	−	6.75766i	0.525023	−	0.303122i
$498$		0			0
$499$	−3.11079	+	23.6288i	−0.139258	+	1.05777i	0.768967	+	0.639288i	$0.220771\pi$
$499$	−3.11079	+	23.6288i	−0.139258	+	1.05777i	−0.908225	+	0.418482i	$0.862562\pi$
$500$	−2.65823	+	1.63229i	−0.118880	+	0.0729982i
$501$		0			0
$502$	2.36116	−	1.20443i	0.105384	−	0.0537561i
$503$	−13.9955	+	13.9955i	−0.624028	+	0.624028i	−0.946559	−	0.322531i	$-0.895466\pi$
$503$	−13.9955	+	13.9955i	−0.624028	+	0.624028i	0.322531	+	0.946559i	$0.395466\pi$
$504$		0			0
$505$	−1.64753	−	1.64753i	−0.0733142	−	0.0733142i
$506$	32.7247	+	10.6165i	1.45479	+	0.471959i
$507$		0			0
$508$	−1.73331	−	10.8797i	−0.0769031	−	0.482707i
$509$	29.1868	+	3.84251i	1.29368	+	0.170316i	0.745760	−	0.666214i	$-0.232086\pi$
$509$	29.1868	+	3.84251i	1.29368	+	0.170316i	0.547920	+	0.836531i	$0.315420\pi$
$510$		0			0
$511$	−10.3713	−	17.9637i	−0.458800	−	0.794665i
$512$	−1.68304	+	22.5647i	−0.0743808	+	0.997230i
$513$		0			0
$514$	−2.25334	−	6.35407i	−0.0993908	−	0.280266i
$515$	−17.9498	+	23.3926i	−0.790962	+	1.03080i
$516$		0			0
$517$	15.7211	−	12.0632i	0.691411	−	0.530539i
$518$	−10.5344	−	49.4497i	−0.462853	−	2.17270i
$519$		0			0
$520$	−1.33302	+	53.7042i	−0.0584570	+	2.35508i
$521$	−24.3784	+	24.3784i	−1.06804	+	1.06804i	−0.0705269	+	0.997510i	$0.522468\pi$
$521$	−24.3784	+	24.3784i	−1.06804	+	1.06804i	−0.997510	+	0.0705269i	$0.977532\pi$
$522$		0			0
$523$	−3.69577	+	8.92238i	−0.161605	+	0.390148i	−0.983852	−	0.178981i	$-0.942720\pi$
$523$	−3.69577	+	8.92238i	−0.161605	+	0.390148i	0.822248	+	0.569130i	$0.192720\pi$
$524$	−0.619186	−	22.8520i	−0.0270493	−	0.998293i
$525$		0			0
$526$	10.1520	+	14.7568i	0.442647	+	0.643429i
$527$	6.36611	+	3.67548i	0.277312	+	0.160106i
$528$		0			0
$529$	−29.7904	+	17.1995i	−1.29524	+	0.747804i
$530$	55.7899	+	26.5793i	2.42336	+	1.15453i
$531$		0			0
$532$	−6.23228	+	1.85225i	−0.270204	+	0.0803051i
$533$	−41.0921	+	5.40987i	−1.77990	+	0.234328i
$534$		0			0
$535$	−0.259647	−	0.969014i	−0.0112255	−	0.0418941i
$536$	15.1150	+	12.2058i	0.652869	+	0.527211i
$537$		0			0
$538$	−10.3089	+	31.7765i	−0.444446	+	1.36998i
$539$	10.9903	+	4.55234i	0.473386	+	0.196083i
$540$		0			0
$541$	14.1287	+	34.1097i	0.607440	+	1.46649i	0.865774	+	0.500434i	$0.166826\pi$
$541$	14.1287	+	34.1097i	0.607440	+	1.46649i	−0.258334	+	0.966056i	$0.583174\pi$
$542$	31.9205	+	27.2376i	1.37110	+	1.16995i
$543$		0			0
$544$	−16.7269	−	6.88404i	−0.717162	−	0.295151i
$545$	−12.0715	+	20.9084i	−0.517084	+	0.895616i
$546$		0			0
$547$	17.9360	−	23.3746i	0.766887	−	0.999426i	−0.232752	−	0.972536i	$-0.574773\pi$
$547$	17.9360	−	23.3746i	0.766887	−	0.999426i	0.999638	−	0.0268901i	$-0.00856042\pi$
$548$	−0.105266	+	1.01037i	−0.00449673	+	0.0431608i
$549$		0			0
$550$	−16.6649	−	18.4913i	−0.710594	−	0.788473i
$551$	0.267583	−	0.998634i	0.0113994	−	0.0425432i
$552$		0			0
$553$	6.84806	+	25.5573i	0.291209	+	1.08681i
$554$	11.3248	−	17.4560i	0.481144	−	0.741634i
$555$		0			0
$556$	16.8361	−	17.7739i	0.714009	−	0.753779i
$557$	5.54466	−	2.29667i	0.234935	−	0.0973132i	−0.262110	−	0.965038i	$-0.584418\pi$
$557$	5.54466	−	2.29667i	0.234935	−	0.0973132i	0.497045	+	0.867725i	$0.334418\pi$
$558$		0			0
$559$			6.16637i			0.260810i
$560$	−27.5760	−	32.1688i	−1.16530	−	1.35938i
$561$		0			0
$562$	−1.13480	−	1.64953i	−0.0478685	−	0.0695814i
$563$	5.27480	−	40.0661i	0.222306	−	1.68859i	−0.408590	−	0.912718i	$-0.633979\pi$
$563$	5.27480	−	40.0661i	0.222306	−	1.68859i	0.630896	−	0.775867i	$-0.282687\pi$
$564$		0			0
$565$	−49.5690	+	6.52589i	−2.08539	+	0.274546i
$566$	−0.267044	+	5.14021i	−0.0112247	+	0.216059i
$567$		0			0
$568$	−2.74301	−	11.3572i	−0.115094	−	0.476539i
$569$	0.244879	−	0.913900i	0.0102659	−	0.0383127i	−0.960603	−	0.277924i	$-0.910353\pi$
$569$	0.244879	−	0.913900i	0.0102659	−	0.0383127i	0.970869	+	0.239612i	$0.0770202\pi$
$570$		0			0
$571$	11.2883	−	8.66182i	0.472401	−	0.362486i	−0.344955	−	0.938619i	$-0.612106\pi$
$571$	11.2883	−	8.66182i	0.472401	−	0.362486i	0.817356	+	0.576133i	$0.195439\pi$
$572$	−37.2054	+	5.92742i	−1.55563	+	0.247838i
$573$		0			0
$574$	21.2190	−	24.8672i	0.885665	−	1.03794i
$575$	41.5309			1.73196
$576$		0			0
$577$	42.7863			1.78122			0.890608	−	0.454771i	$-0.150279\pi$
$577$	42.7863			1.78122			0.890608	+	0.454771i	$0.150279\pi$
$578$	−6.21979	+	7.28915i	−0.258709	+	0.303189i
$579$		0			0
$580$	6.65361	−	1.06003i	0.276276	−	0.0440153i
$581$	−4.18738	+	3.21309i	−0.173722	+	0.133301i
$582$		0			0
$583$	−11.2170	+	41.8623i	−0.464560	+	1.73376i
$584$	−17.4305	+	4.20984i	−0.721280	+	0.174204i
$585$		0			0
$586$	1.62184	−	31.2180i	0.0669976	−	1.28960i
$587$	5.17681	−	0.681539i	0.213670	−	0.0281301i	−0.0229314	−	0.999737i	$-0.507300\pi$
$587$	5.17681	−	0.681539i	0.213670	−	0.0281301i	0.236601	+	0.971607i	$0.423967\pi$
$588$		0			0
$589$	0.298148	−	2.26466i	0.0122850	−	0.0933136i
$590$	−2.22330	−	3.23178i	−0.0915320	−	0.133050i
$591$		0			0
$592$	−43.5792	−	3.35005i	−1.79109	−	0.137686i
$593$			3.77979i			0.155217i	0.996984	+	0.0776086i	$0.0247285\pi$
$593$			3.77979i			0.155217i	−0.996984	+	0.0776086i	$0.975272\pi$
$594$		0			0
$595$	31.2924	−	12.9617i	1.28286	−	0.531379i
$596$	−5.23916	+	5.53099i	−0.214604	+	0.226558i
$597$		0			0
$598$	34.2099	−	52.7311i	1.39895	−	2.15633i
$599$	−8.51319	−	31.7717i	−0.347839	−	1.29815i	−0.889260	−	0.457402i	$-0.848780\pi$
$599$	−8.51319	−	31.7717i	−0.347839	−	1.29815i	0.541420	−	0.840752i	$-0.317887\pi$
$600$		0			0
$601$	6.62862	−	24.7383i	0.270387	−	1.00910i	−0.688483	−	0.725252i	$-0.741723\pi$
$601$	6.62862	−	24.7383i	0.270387	−	1.00910i	0.958870	−	0.283846i	$-0.0916103\pi$
$602$	−3.25599	−	3.61284i	−0.132704	−	0.147248i
$603$		0			0
$604$	3.32634	−	31.9272i	0.135347	−	1.29910i
$605$	−1.35907	+	1.77118i	−0.0552543	+	0.0720087i
$606$		0			0
$607$	12.5507	−	21.7385i	0.509419	−	0.882339i	−0.490522	−	0.871429i	$-0.663194\pi$
$607$	12.5507	−	21.7385i	0.509419	−	0.882339i	0.999940	−	0.0109103i	$-0.00347291\pi$
$608$	0.0127722	+	5.62060i	0.000517980	+	0.227946i
$609$		0			0
$610$	−20.1193	−	17.1677i	−0.814607	−	0.695100i
$611$	−13.8547	−	33.4482i	−0.560500	−	1.35317i
$612$		0			0
$613$	−15.0232	−	6.22283i	−0.606783	−	0.251338i	0.0580695	−	0.998313i	$-0.481505\pi$
$613$	−15.0232	−	6.22283i	−0.606783	−	0.251338i	−0.664852	+	0.746975i	$0.731505\pi$
$614$	1.46424	−	4.51344i	0.0590918	−	0.182147i
$615$		0			0
$616$	18.6686	−	23.1181i	0.752178	−	0.931456i
$617$	4.14237	+	15.4595i	0.166765	+	0.622377i	0.997808	+	0.0661689i	$0.0210776\pi$
$617$	4.14237	+	15.4595i	0.166765	+	0.622377i	−0.831043	+	0.556208i	$0.812256\pi$
$618$		0			0
$619$	−21.4206	+	2.82008i	−0.860967	+	0.113349i	−0.548064	−	0.836436i	$-0.684635\pi$
$619$	−21.4206	+	2.82008i	−0.860967	+	0.113349i	−0.312903	+	0.949785i	$0.601302\pi$
$620$	14.2689	−	4.24076i	0.573054	−	0.170313i
$621$		0			0
$622$	28.4430	+	13.5508i	1.14046	+	0.543336i
$623$	7.90437	−	4.56359i	0.316682	−	0.182836i
$624$		0			0
$625$	19.3636	+	11.1796i	0.774544	+	0.447183i
$626$	9.05717	+	13.1654i	0.361998	+	0.526197i
$627$		0			0
$628$	−0.413568	−	15.2633i	−0.0165032	−	0.609073i
$629$	13.3708	−	32.2799i	0.533128	−	1.28709i
$630$		0			0
$631$	8.06758	−	8.06758i	0.321165	−	0.321165i	−0.528049	−	0.849214i	$-0.677076\pi$
$631$	8.06758	−	8.06758i	0.321165	−	0.321165i	0.849214	+	0.528049i	$0.177076\pi$
$632$	22.8662	+	0.567577i	0.909570	+	0.0225770i
$633$		0			0
$634$	0.792362	+	3.71946i	0.0314687	+	0.147719i
$635$	14.1485	−	10.8566i	0.561468	−	0.430829i
$636$		0			0
$637$	13.2307	−	17.2426i	0.524220	−	0.683177i
$638$	1.57928	+	4.45331i	0.0625243	+	0.176308i
$639$		0			0
$640$	−33.4144	+	15.0046i	−1.32082	+	0.593110i
$641$	2.19241	+	3.79736i	0.0865949	+	0.149987i	0.906070	−	0.423128i	$-0.139068\pi$
$641$	2.19241	+	3.79736i	0.0865949	+	0.149987i	−0.819475	+	0.573115i	$0.805735\pi$
$642$		0			0
$643$	16.6052	+	2.18611i	0.654843	+	0.0862118i	0.450625	−	0.892714i	$-0.351201\pi$
$643$	16.6052	+	2.18611i	0.654843	+	0.0862118i	0.204219	+	0.978925i	$0.434535\pi$
$644$	7.79987	+	48.9584i	0.307358	+	1.92923i
$645$		0			0
$646$	−4.27379	−	1.38649i	−0.168150	−	0.0545508i
$647$	−9.86054	−	9.86054i	−0.387658	−	0.387658i	0.486193	−	0.873851i	$-0.338385\pi$
$647$	−9.86054	−	9.86054i	−0.387658	−	0.387658i	−0.873851	+	0.486193i	$0.838385\pi$
$648$		0			0
$649$	1.94525	−	1.94525i	0.0763577	−	0.0763577i
$650$	−40.5130	+	20.6656i	−1.58905	+	0.810572i
$651$		0			0
$652$	5.26588	−	3.23352i	0.206228	−	0.126634i
$653$	2.61721	−	19.8797i	0.102419	−	0.777951i	−0.860745	−	0.509037i	$-0.830002\pi$
$653$	2.61721	−	19.8797i	0.102419	−	0.777951i	0.963164	−	0.268915i	$-0.0866650\pi$
$654$		0			0
$655$	32.0480	−	18.5029i	1.25222	−	0.722968i
$656$	−15.4345	−	23.6727i	−0.602615	−	0.924262i
$657$		0			0
$658$	25.7788	+	12.2815i	1.00496	+	0.478781i
$659$	6.83899	+	5.24774i	0.266409	+	0.204423i	0.733324	−	0.679879i	$-0.237968\pi$
$659$	6.83899	+	5.24774i	0.266409	+	0.204423i	−0.466915	+	0.884302i	$0.654634\pi$
$660$		0			0
$661$	20.6243	+	26.8781i	0.802191	+	1.04544i	0.997900	+	0.0647741i	$0.0206327\pi$
$661$	20.6243	+	26.8781i	0.802191	+	1.04544i	−0.195708	+	0.980662i	$0.562701\pi$
$662$	25.7246	−	39.6519i	0.999817	−	1.54112i
$663$		0			0
$664$	1.64097	+	4.25752i	0.0636821	+	0.165224i
$665$	−7.44216	−	7.44216i	−0.288594	−	0.288594i
$666$		0			0
$667$	−7.28318	−	3.01679i	−0.282006	−	0.116811i
$668$	1.40657	+	3.15149i	0.0544218	+	0.121935i
$669$		0			0
$670$	−5.71717	+	30.9255i	−0.220873	+	1.19476i
$671$	9.27418	−	16.0634i	0.358026	−	0.620119i
$672$		0			0
$673$	18.8856	+	32.7108i	0.727987	+	1.26091i	0.957733	+	0.287660i	$0.0928772\pi$
$673$	18.8856	+	32.7108i	0.727987	+	1.26091i	−0.229746	+	0.973251i	$0.573790\pi$
$674$	9.53919	−	3.38288i	0.367436	−	0.130304i
$675$		0			0
$676$	−4.43844	+	42.6014i	−0.170709	+	1.63851i
$677$	3.93829	+	29.9143i	0.151361	+	1.14970i	0.883462	+	0.468503i	$0.155206\pi$
$677$	3.93829	+	29.9143i	0.151361	+	1.14970i	−0.732101	+	0.681196i	$0.761460\pi$
$678$		0			0
$679$	1.21505	−	0.325571i	0.0466292	−	0.0124943i
$680$	−3.10036	−	29.1161i	−0.118893	−	1.11655i
$681$		0			0
$682$	4.74364	+	9.29947i	0.181643	+	0.356095i
$683$	7.16855	−	17.3064i	0.274297	−	0.662211i	−0.725361	−	0.688369i	$-0.758327\pi$
$683$	7.16855	−	17.3064i	0.274297	−	0.662211i	0.999658	+	0.0261574i	$0.00832712\pi$
$684$		0			0
$685$	−1.51924	+	0.629290i	−0.0580472	+	0.0240439i
$686$	−1.20320	−	15.1998i	−0.0459384	−	0.580331i
$687$		0			0
$688$	−3.79158	+	1.81696i	−0.144553	+	0.0692710i
$689$	68.5728	+	39.5905i	2.61242	+	1.50828i
$690$		0			0
$691$	10.0619	+	7.72073i	0.382771	+	0.293711i	0.782168	−	0.623068i	$-0.214114\pi$
$691$	10.0619	+	7.72073i	0.382771	+	0.293711i	−0.399397	+	0.916778i	$0.630780\pi$
$692$	13.4281	−	24.7852i	0.510460	−	0.942192i
$693$		0			0
$694$	−2.15341	+	41.4500i	−0.0817424	+	1.57342i
$695$	38.2803	+	10.2572i	1.45206	+	0.389077i
$696$		0			0
$697$	21.8209	−	5.84689i	0.826524	−	0.221467i
$698$	8.77169	+	41.1755i	0.332013	+	1.55852i
$699$		0			0
$700$	12.8244	−	33.4996i	0.484716	−	1.26617i
$701$	0.135361	+	0.326791i	0.00511253	+	0.0123427i	0.926415	−	0.376504i	$-0.122874\pi$
$701$	0.135361	+	0.326791i	0.00511253	+	0.0123427i	−0.921303	+	0.388846i	$0.872874\pi$
$702$		0			0
$703$	−10.8569			−0.409477
$704$	−14.6075	−	21.1303i	−0.550539	−	0.796378i
$705$		0			0
$706$	20.8571	+	3.85584i	0.784969	+	0.145116i
$707$	2.33447	+	0.307339i	0.0877967	+	0.0115587i
$708$		0			0
$709$	−3.45282	−	26.2267i	−0.129673	−	0.984966i	−0.925315	−	0.379199i	$-0.876200\pi$
$709$	−3.45282	−	26.2267i	−0.129673	−	0.984966i	0.795642	−	0.605767i	$-0.207134\pi$
$710$	14.0497	−	12.6619i	0.527274	−	0.475194i
$711$		0			0
$712$	−1.85241	−	7.66977i	−0.0694221	−	0.287437i
$713$	−16.8237	−	4.50789i	−0.630051	−	0.168822i
$714$		0			0
$715$	−37.1264	−	48.3840i	−1.38845	−	1.80946i
$716$	23.6744	+	38.5544i	0.884755	+	1.44085i
$717$		0			0
$718$	−13.0931	+	1.03644i	−0.488631	+	0.0386795i
$719$		−	18.7851i		−	0.700565i	−0.936644	−	0.350282i	$-0.886086\pi$
$719$		−	18.7851i		−	0.700565i	0.936644	−	0.350282i	$-0.113914\pi$
$720$		0			0
$721$		−	29.7977i		−	1.10973i
$722$	−2.01020	−	25.3945i	−0.0748119	−	0.945084i
$723$		0			0
$724$	−35.0803	−	8.38832i	−1.30375	−	0.311750i
$725$	3.47232	+	4.52521i	0.128959	+	0.168062i
$726$		0			0
$727$	−6.30762	−	1.69012i	−0.233937	−	0.0626831i	0.139946	−	0.990159i	$-0.455307\pi$
$727$	−6.30762	−	1.69012i	−0.233937	−	0.0626831i	−0.373883	+	0.927476i	$0.621974\pi$
$728$	−31.9702	−	43.8773i	−1.18489	−	1.62620i
$729$		0			0
$730$	−19.4329	−	21.5627i	−0.719245	−	0.798073i
$731$	−0.438699	−	3.33225i	−0.0162259	−	0.123248i
$732$		0			0
$733$	−25.6331	−	3.37467i	−0.946781	−	0.124646i	−0.358704	−	0.933451i	$-0.616781\pi$
$733$	−25.6331	−	3.37467i	−0.946781	−	0.124646i	−0.588077	+	0.808805i	$0.700115\pi$
$734$	−3.39238	+	18.3502i	−0.125215	+	0.677317i
$735$		0			0
$736$	42.5035	+	5.49746i	1.56670	+	0.202639i
$737$	−22.0557			−0.812432
$738$		0			0
$739$	−12.9826	−	31.3427i	−0.477572	−	1.15296i	−0.960744	−	0.277436i	$-0.910515\pi$
$739$	−12.9826	−	31.3427i	−0.477572	−	1.15296i	0.483172	−	0.875525i	$-0.339485\pi$
$740$	−28.8366	−	64.6100i	−1.06005	−	2.37511i
$741$		0			0
$742$	−61.0810	+	13.0122i	−2.24236	+	0.477693i
$743$	−28.4651	+	7.62720i	−1.04428	+	0.279815i	−0.739887	−	0.672731i	$-0.765121\pi$
$743$	−28.4651	+	7.62720i	−1.04428	+	0.279815i	−0.304395	+	0.952546i	$0.598454\pi$
$744$		0			0
$745$	−11.9123	−	3.19190i	−0.436434	−	0.116942i
$746$	−21.6823	−	1.12644i	−0.793846	−	0.0412419i
$747$		0			0
$748$	19.6837	−	5.85005i	0.719708	−	0.213899i
$749$	0.804311	+	0.617170i	0.0293889	+	0.0225509i
$750$		0			0
$751$	−21.6131	−	12.4783i	−0.788672	−	0.455340i	0.0508231	−	0.998708i	$-0.483816\pi$
$751$	−21.6131	−	12.4783i	−0.788672	−	0.455340i	−0.839495	+	0.543368i	$0.817149\pi$
$752$	16.4843	−	18.3747i	0.601119	−	0.670056i
$753$		0			0
$754$	8.60581	−	0.681228i	0.313405	−	0.0248088i
$755$	48.0073	−	19.8853i	1.74716	−	0.723699i
$756$		0			0
$757$	−3.98806	+	9.62802i	−0.144948	+	0.349936i	−0.979634	−	0.200790i	$-0.935649\pi$
$757$	−3.98806	+	9.62802i	−0.144948	+	0.349936i	0.834686	+	0.550726i	$0.185649\pi$
$758$	−37.8848	+	19.3250i	−1.37604	+	0.701915i
$759$		0			0
$760$	−7.99001	+	4.35234i	−0.289828	+	0.157876i
$761$	−32.2417	+	8.63913i	−1.16876	+	0.313168i	−0.790459	−	0.612514i	$-0.790158\pi$
$761$	−32.2417	+	8.63913i	−1.16876	+	0.313168i	−0.378301	+	0.925683i	$0.623492\pi$
$762$		0			0
$763$	−3.18462	−	24.1896i	−0.115291	−	0.875723i
$764$	−18.4187	+	14.9429i	−0.666364	+	0.540615i
$765$		0			0
$766$	4.70794	+	13.2756i	0.170105	+	0.479668i
$767$	−2.51305	−	4.35274i	−0.0907411	−	0.157168i
$768$		0			0
$769$	−8.08638	+	14.0060i	−0.291602	+	0.505070i	−0.974189	−	0.225735i	$-0.927522\pi$
$769$	−8.08638	+	14.0060i	−0.291602	+	0.505070i	0.682587	+	0.730805i	$0.260855\pi$
$770$	47.3000	+	8.74429i	1.70457	+	0.315123i
$771$		0			0
$772$	−23.3474	−	8.93788i	−0.840291	−	0.321681i
$773$	25.4216	+	10.5300i	0.914351	+	0.378737i	0.789721	−	0.613467i	$-0.210226\pi$
$773$	25.4216	+	10.5300i	0.914351	+	0.378737i	0.124630	+	0.992203i	$0.460226\pi$
$774$		0			0
$775$	8.91105	+	8.91105i	0.320094	+	0.320094i
$776$	0.0269838	−	1.08711i	0.000968661	−	0.0390249i
$777$		0			0
$778$	9.66872	+	6.27270i	0.346641	+	0.224887i
$779$	−4.27332	−	5.56910i	−0.153108	−	0.199534i
$780$		0			0
$781$	10.5231	+	8.07465i	0.376546	+	0.288934i
$782$	−14.7352	+	30.9292i	−0.526930	+	1.10603i
$783$		0			0
$784$	14.5007	+	3.05467i	0.517881	+	0.109095i
$785$	21.4056	−	12.3585i	0.763997	−	0.441094i
$786$		0			0
$787$	−4.08448	+	31.0247i	−0.145596	+	1.10591i	0.750125	+	0.661296i	$0.229993\pi$
$787$	−4.08448	+	31.0247i	−0.145596	+	1.10591i	−0.895721	+	0.444616i	$0.853340\pi$
$788$	7.06895	−	29.5626i	0.251821	−	1.05313i
$789$		0			0
$790$	16.8248	+	32.9834i	0.598599	+	1.17350i
$791$	35.7271	−	35.7271i	1.27031	−	1.27031i
$792$		0			0
$793$	−23.9625	−	23.9625i	−0.850934	−	0.850934i
$794$	−14.9544	+	46.0963i	−0.530713	+	1.63590i
$795$		0			0
$796$	−2.47494	+	3.41299i	−0.0877221	+	0.120970i
$797$	12.7183	+	1.67440i	0.450507	+	0.0593103i	0.352366	−	0.935862i	$-0.385377\pi$
$797$	12.7183	+	1.67440i	0.450507	+	0.0593103i	0.0981406	+	0.995173i	$0.468711\pi$
$798$		0			0
$799$	9.86656	+	17.0894i	0.349054	+	0.604579i
$800$	−24.6443	−	18.8214i	−0.871307	−	0.665437i
$801$		0			0
$802$	46.5077	−	16.4930i	1.64224	−	0.582389i
$803$	12.3926	−	16.1503i	0.437325	−	0.569933i
$804$		0			0
$805$	−63.6683	+	48.8544i	−2.24401	+	1.72189i
$806$	18.6544	−	3.97399i	0.657075	−	0.139978i
$807$		0			0
$808$	0.825387	−	1.86067i	0.0290370	−	0.0654582i
$809$	16.2429	−	16.2429i	0.571069	−	0.571069i	−0.361358	−	0.932427i	$-0.617687\pi$
$809$	16.2429	−	16.2429i	0.571069	−	0.571069i	0.932427	+	0.361358i	$0.117687\pi$
$810$		0			0
$811$	−1.39355	+	3.36433i	−0.0489342	+	0.118138i	−0.946456	−	0.322832i	$-0.895365\pi$
$811$	−1.39355	+	3.36433i	−0.0489342	+	0.118138i	0.897522	+	0.440969i	$0.145365\pi$
$812$	−4.68238	+	4.94319i	−0.164319	+	0.173472i
$813$		0			0
$814$	40.8799	−	28.1233i	1.43284	−	0.985723i
$815$	8.66293	+	5.00154i	0.303449	+	0.175196i
$816$		0			0
$817$	−0.904460	+	0.522190i	−0.0316431	+	0.0182691i
$818$	3.59121	−	7.53794i	0.125564	−	0.263558i
$819$		0			0
$820$	21.7917	−	40.2225i	0.761000	−	1.40463i
$821$	43.6603	−	5.74799i	1.52375	−	0.200606i	0.678353	−	0.734736i	$-0.262694\pi$
$821$	43.6603	−	5.74799i	1.52375	−	0.200606i	0.845402	+	0.534130i	$0.179361\pi$
$822$		0			0
$823$	−14.0980	−	52.6145i	−0.491426	−	1.83403i	−0.549190	−	0.835697i	$-0.685064\pi$
$823$	−14.0980	−	52.6145i	−0.491426	−	1.83403i	0.0577638	−	0.998330i	$-0.481603\pi$
$824$	−24.7088	−	7.28246i	−0.860773	−	0.253696i
$825$		0			0
$826$	3.77073	+	1.22329i	0.131200	+	0.0425637i
$827$	33.5301	+	13.8886i	1.16596	+	0.482955i	0.879854	−	0.475244i	$-0.157640\pi$
$827$	33.5301	+	13.8886i	1.16596	+	0.482955i	0.286102	+	0.958199i	$0.407640\pi$
$828$		0			0
$829$	2.85146	+	6.88403i	0.0990352	+	0.239092i	0.965630	−	0.259920i	$-0.0836962\pi$
$829$	2.85146	+	6.88403i	0.0990352	+	0.239092i	−0.866595	+	0.499012i	$0.833696\pi$
$830$	−4.79439	+	5.61868i	−0.166416	+	0.195027i
$831$		0			0
$832$	−44.1973	+	15.7868i	−1.53226	+	0.547310i
$833$	−5.92305	+	10.2590i	−0.205221	+	0.355454i
$834$		0			0
$835$	−3.40092	+	4.43216i	−0.117694	+	0.153381i
$836$	−4.02010	−	4.95519i	−0.139038	−	0.171379i
$837$		0			0
$838$	−28.4774	+	25.6646i	−0.983735	+	0.886568i
$839$	−0.546077	+	2.03799i	−0.0188527	+	0.0703591i	−0.974711	−	0.223468i	$-0.928262\pi$
$839$	−0.546077	+	2.03799i	−0.0188527	+	0.0703591i	0.955859	+	0.293827i	$0.0949289\pi$
$840$		0			0
$841$	7.22553	+	26.9660i	0.249156	+	0.929864i
$842$	−0.902293	−	0.585373i	−0.0310951	−	0.0201733i
$843$		0			0
$844$	−36.2246	+	0.981525i	−1.24690	+	0.0337855i
$845$	−64.0575	+	26.5335i	−2.20365	+	0.912780i
$846$		0			0
$847$		−	2.25615i		−	0.0775221i
$848$	−4.13804	+	53.8297i	−0.142101	+	1.84852i
$849$		0			0
$850$	20.4226	−	14.0497i	0.700490	−	0.481902i
$851$	−10.8056	+	82.0766i	−0.370411	+	2.81355i
$852$		0			0
$853$	20.8983	−	2.75131i	0.715544	−	0.0942032i	0.236041	−	0.971743i	$-0.424150\pi$
$853$	20.8983	−	2.75131i	0.715544	−	0.0942032i	0.479503	+	0.877540i	$0.340817\pi$
$854$	26.6922	+	1.38672i	0.913389	+	0.0474524i
$855$		0			0
$856$	0.708339	−	0.516116i	0.0242105	−	0.0176405i
$857$	10.7958	−	40.2904i	0.368777	−	1.37630i	−0.493450	−	0.869774i	$-0.664264\pi$
$857$	10.7958	−	40.2904i	0.368777	−	1.37630i	0.862227	−	0.506521i	$-0.169069\pi$
$858$		0			0
$859$	13.1864	−	10.1183i	0.449914	−	0.345231i	−0.358819	−	0.933407i	$-0.616820\pi$
$859$	13.1864	−	10.1183i	0.449914	−	0.345231i	0.808733	+	0.588176i	$0.200154\pi$
$860$	−5.50986	−	3.99550i	−0.187885	−	0.136246i
$861$		0			0
$862$	−30.2223	−	25.7885i	−1.02937	−	0.878360i
$863$	−0.332738			−0.0113265			−0.00566326	−	0.999984i	$-0.501803\pi$
$863$	−0.332738			−0.0113265			−0.00566326	+	0.999984i	$0.501803\pi$
$864$		0			0
$865$	45.6317			1.55153
$866$	−30.3403	−	25.8893i	−1.03101	−	0.879753i
$867$		0			0
$868$	−8.83115	+	12.1783i	−0.299749	+	0.413358i
$869$	−20.6010	+	15.8077i	−0.698842	+	0.536240i
$870$		0			0
$871$	−10.4294	+	38.9230i	−0.353386	+	1.31885i
$872$	−20.8368	−	3.27111i	−0.705623	−	0.110774i
$873$		0			0
$874$	10.6314	+	0.552324i	0.359613	+	0.0186826i
$875$	5.05935	−	0.666077i	0.171037	−	0.0225175i
$876$		0			0
$877$	0.723680	−	5.49690i	0.0244369	−	0.185617i	−0.974873	−	0.222762i	$-0.928493\pi$
$877$	0.723680	−	5.49690i	0.0244369	−	0.185617i	0.999310	+	0.0371446i	$0.0118262\pi$
$878$	−12.5781	+	8.65308i	−0.424489	+	0.292027i
$879$		0			0
$880$	18.8109	−	37.0849i	0.634115	−	1.25013i
$881$			40.7751i			1.37375i	0.726777	+	0.686874i	$0.241017\pi$
$881$			40.7751i			1.37375i	−0.726777	+	0.686874i	$0.758983\pi$
$882$		0			0
$883$	−8.08271	+	3.34797i	−0.272005	+	0.112668i	−0.514517	−	0.857480i	$-0.672029\pi$
$883$	−8.08271	+	3.34797i	−0.272005	+	0.112668i	0.242512	+	0.970148i	$0.422029\pi$
$884$	−1.01617	−	37.5033i	−0.0341776	−	1.26137i
$885$		0			0
$886$	8.55332	+	5.54907i	0.287354	+	0.186424i
$887$	7.86310	+	29.3455i	0.264017	+	0.985325i	0.962849	+	0.270039i	$0.0870366\pi$
$887$	7.86310	+	29.3455i	0.264017	+	0.985325i	−0.698832	+	0.715285i	$0.746297\pi$
$888$		0			0
$889$	−4.66458	+	17.4084i	−0.156445	+	0.583860i
$890$	9.48803	−	8.55088i	0.318040	−	0.286626i
$891$		0			0
$892$	−36.2744	+	29.4291i	−1.21456	+	0.985358i
$893$	3.73279	−	4.86466i	0.124913	−	0.162790i
$894$		0			0
$895$	−36.6191	+	63.4262i	−1.22404	+	2.12010i
$896$	17.5591	−	32.5866i	0.586607	−	1.08864i
$897$		0			0
$898$	11.9110	−	13.9588i	0.397474	−	0.465811i
$899$	−0.915414	−	2.21001i	−0.0305308	−	0.0737078i
$900$		0			0
$901$	−39.8727	−	16.5158i	−1.32835	−	0.550221i
$902$	30.5164	+	9.90005i	1.01608	+	0.329635i
$903$		0			0
$904$	−20.8940	−	38.3572i	−0.694924	−	1.27574i
$905$	−15.1120	−	56.3986i	−0.502338	−	1.87475i
$906$		0			0
$907$	40.0585	−	5.27381i	1.33012	−	0.175114i	0.568258	−	0.822851i	$-0.307618\pi$
$907$	40.0585	−	5.27381i	1.33012	−	0.175114i	0.761864	+	0.647737i	$0.224284\pi$
$908$	3.05367	+	1.65441i	0.101340	+	0.0549037i
$909$		0			0
$910$	37.7981	−	79.3382i	1.25300	−	2.63003i
$911$	7.74287	−	4.47035i	0.256533	−	0.148109i	−0.366219	−	0.930529i	$-0.619348\pi$
$911$	7.74287	−	4.47035i	0.256533	−	0.148109i	0.622752	+	0.782419i	$0.286015\pi$
$912$		0			0
$913$	−4.48598	−	2.58998i	−0.148464	−	0.0857159i
$914$	−20.9174	+	14.3901i	−0.691887	+	0.475984i
$915$		0			0
$916$	27.1758	+	25.7420i	0.897915	+	0.850539i
$917$	−14.3113	+	34.5506i	−0.472602	+	1.14096i
$918$		0			0
$919$	14.7125	−	14.7125i	0.485319	−	0.485319i	−0.421506	−	0.906825i	$-0.638498\pi$
$919$	14.7125	−	14.7125i	0.485319	−	0.485319i	0.906825	+	0.421506i	$0.138498\pi$
$920$	24.9507	+	64.7348i	0.822600	+	2.13424i
$921$		0			0
$922$	15.2228	−	3.24294i	0.501336	−	0.106800i
$923$	19.2258	−	14.7525i	0.632826	−	0.485584i
$924$		0			0
$925$	36.4640	−	47.5209i	1.19893	−	1.56248i
$926$	−25.6315	+	9.08972i	−0.842305	+	0.298707i
$927$		0			0
$928$	2.95463	+	5.09082i	0.0969905	+	0.167114i
$929$	13.7882	+	23.8819i	0.452376	+	0.783539i	0.998533	−	0.0541440i	$-0.0172430\pi$
$929$	13.7882	+	23.8819i	0.452376	+	0.783539i	−0.546157	+	0.837683i	$0.683910\pi$
$930$		0			0
$931$	3.64950	+	0.480466i	0.119608	+	0.0157467i
$932$	−5.56416	−	4.03488i	−0.182260	−	0.132167i
$933$		0			0
$934$	17.3086	−	53.3530i	0.566356	−	1.74576i
$935$	23.5049	+	23.5049i	0.768694	+	0.768694i
$936$		0			0
$937$	13.3238	−	13.3238i	0.435269	−	0.435269i	−0.455147	−	0.890416i	$-0.650413\pi$
$937$	13.3238	−	13.3238i	0.435269	−	0.435269i	0.890416	+	0.455147i	$0.150413\pi$
$938$	−14.4417	−	28.3117i	−0.471539	−	0.924408i
$939$		0			0
$940$	38.8642	+	9.29312i	1.26761	+	0.303108i
$941$	−5.87578	+	44.6310i	−0.191545	+	1.45493i	0.577844	+	0.816148i	$0.303894\pi$
$941$	−5.87578	+	44.6310i	−0.191545	+	1.45493i	−0.769389	+	0.638781i	$0.779439\pi$
$942$		0			0
$943$	−46.3545	+	26.7628i	−1.50951	+	0.871517i
$944$	1.93593	−	2.82779i	0.0630090	−	0.0920367i
$945$		0			0
$946$	2.05293	−	4.30909i	0.0667464	−	0.140101i
$947$	−18.2380	−	13.9945i	−0.592656	−	0.454761i	0.268374	−	0.963315i	$-0.413514\pi$
$947$	−18.2380	−	13.9945i	−0.592656	−	0.454761i	−0.861030	+	0.508554i	$0.830180\pi$
$948$		0			0
$949$	−22.6414	−	29.5069i	−0.734971	−	0.957833i
$950$	−6.46194	−	4.19226i	−0.209653	−	0.136015i
$951$		0			0
$952$	20.3980	+	21.4364i	0.661102	+	0.694757i
$953$	24.0511	+	24.0511i	0.779093	+	0.779093i	0.979677	−	0.200584i	$-0.0642839\pi$
$953$	24.0511	+	24.0511i	0.779093	+	0.779093i	−0.200584	+	0.979677i	$0.564284\pi$
$954$		0			0
$955$	−35.4714	−	14.6927i	−1.14783	−	0.475445i
$956$	5.28114	−	13.7953i	0.170804	−	0.446172i
$957$		0			0
$958$	−29.1615	−	5.39105i	−0.942164	−	0.174177i
$959$	0.830907	−	1.43917i	0.0268314	−	0.0464733i
$960$		0			0
$961$	12.8575	+	22.2698i	0.414757	+	0.718381i
$962$	−30.3002	−	85.4418i	−0.976918	−	2.75475i
$963$		0			0
$964$	−17.4500	−	21.5090i	−0.562027	−	0.692757i
$965$	−5.28226	−	40.1227i	−0.170042	−	1.29160i
$966$		0			0
$967$	24.5959	−	6.59045i	0.790950	−	0.211934i	0.159343	−	0.987223i	$-0.449062\pi$
$967$	24.5959	−	6.59045i	0.790950	−	0.211934i	0.631607	+	0.775289i	$0.282396\pi$
$968$	−1.87084	−	0.551394i	−0.0601310	−	0.0177225i
$969$		0			0
$970$	1.56810	−	0.799885i	0.0503487	−	0.0256828i
$971$	−13.5920	+	32.8139i	−0.436187	+	1.05305i	0.541067	+	0.840979i	$0.318020\pi$
$971$	−13.5920	+	32.8139i	−0.436187	+	1.05305i	−0.977255	+	0.212070i	$0.931980\pi$
$972$		0			0
$973$	−37.0014	+	15.3265i	−1.18621	+	0.491345i
$974$	42.7247	−	3.38205i	1.36899	−	0.108368i
$975$		0			0
$976$	7.67338	−	21.7948i	0.245619	−	0.697634i
$977$	−14.9389	−	8.62499i	−0.477938	−	0.275938i	0.241619	−	0.970371i	$-0.422322\pi$
$977$	−14.9389	−	8.62499i	−0.477938	−	0.275938i	−0.719557	+	0.694433i	$0.755655\pi$
$978$		0			0
$979$	7.10647	+	5.45298i	0.227124	+	0.174278i
$980$	6.83401	+	22.9944i	0.218304	+	0.734531i
$981$		0			0
$982$	−18.7689	−	0.975084i	−0.598940	−	0.0311162i
$983$	8.27282	+	2.21670i	0.263862	+	0.0707016i	0.388324	−	0.921523i	$-0.373054\pi$
$983$	8.27282	+	2.21670i	0.263862	+	0.0707016i	−0.124462	+	0.992224i	$0.539721\pi$
$984$		0			0
$985$	47.5278	−	12.7350i	1.51436	−	0.405772i
$986$	−4.60203	+	0.980378i	−0.146559	+	0.0312216i
$987$		0			0
$988$	−10.6457	+	4.75136i	−0.338684	+	0.151161i
$989$	3.04748	+	7.35728i	0.0969044	+	0.233948i
$990$		0			0
$991$	−61.2959			−1.94713			−0.973564	−	0.228414i	$-0.926646\pi$
$991$	−61.2959			−1.94713			−0.973564	+	0.228414i	$0.926646\pi$
$992$	7.94017	+	10.2993i	0.252101	+	0.327003i
$993$		0			0
$994$	−3.47462	+	18.7951i	−0.110208	+	0.596143i
$995$	−6.76622	−	0.890790i	−0.214504	−	0.0282399i
$996$		0			0
$997$	6.83025	+	51.8809i	0.216316	+	1.64308i	0.663164	+	0.748474i	$0.269213\pi$
$997$	6.83025	+	51.8809i	0.216316	+	1.64308i	−0.446848	+	0.894610i	$0.647454\pi$
$998$	−22.5641	−	25.0371i	−0.714254	−	0.792535i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bk.a.37.13		368
3.2	odd	2		288.2.bc.a.229.34	yes	368
9.2	odd	6		288.2.bc.a.133.3	yes	368
9.7	even	3	inner	864.2.bk.a.613.44		368
32.13	even	8	inner	864.2.bk.a.685.44		368
96.77	odd	8		288.2.bc.a.13.3	✓	368
288.173	odd	24		288.2.bc.a.205.34	yes	368
288.205	even	24	inner	864.2.bk.a.397.13		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.3	✓	368	96.77	odd	8
288.2.bc.a.133.3	yes	368	9.2	odd	6
288.2.bc.a.205.34	yes	368	288.173	odd	24
288.2.bc.a.229.34	yes	368	3.2	odd	2
864.2.bk.a.37.13		368	1.1	even	1	trivial
864.2.bk.a.397.13		368	288.205	even	24	inner
864.2.bk.a.613.44		368	9.7	even	3	inner
864.2.bk.a.685.44		368	32.13	even	8	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.bk (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.917969 + 1.07579i) q^{2} +(-0.314664 - 1.97509i) q^{4} +(2.56852 - 1.97090i) q^{5} +(-0.846806 + 3.16032i) q^{7} +(2.41364 + 1.47456i) q^{8} +O(q^{10})\)	\(q+(-0.917969 + 1.07579i) q^{2} +(-0.314664 - 1.97509i) q^{4} +(2.56852 - 1.97090i) q^{5} +(-0.846806 + 3.16032i) q^{7} +(2.41364 + 1.47456i) q^{8} +(-0.237547 + 4.57243i) q^{10} +(-3.18352 + 0.419118i) q^{11} +(-0.765734 + 5.81632i) q^{13} +(-2.62251 - 3.81207i) q^{14} +(-3.80197 + 1.24298i) q^{16} -3.19756i q^{17} +(-0.917962 + 0.380232i) q^{19} +(-4.70093 - 4.45290i) q^{20} +(2.47149 - 3.80954i) q^{22} +(1.96087 + 7.31806i) q^{23} +(1.41878 - 5.29496i) q^{25} +(-5.55425 - 6.16298i) q^{26} +(6.50839 + 0.678079i) q^{28} +(-0.633433 + 0.825505i) q^{29} +(-1.14946 + 1.99093i) q^{31} +(2.15290 - 5.23116i) q^{32} +(3.43992 + 2.93526i) q^{34} +(4.05363 + 9.78633i) q^{35} +(10.0952 + 4.18156i) q^{37} +(0.433609 - 1.33658i) q^{38} +(9.10571 - 0.969602i) q^{40} +(1.82855 + 6.82422i) q^{41} +(1.04212 - 0.137198i) q^{43} +(1.82953 + 6.15585i) q^{44} +(-9.67274 - 4.60827i) q^{46} +(-5.34450 + 3.08565i) q^{47} +(-3.20839 - 1.85236i) q^{49} +(4.39389 + 6.38693i) q^{50} +(11.7287 - 0.317796i) q^{52} +(5.16512 - 12.4697i) q^{53} +(-7.35090 + 7.35090i) q^{55} +(-6.70397 + 6.37923i) q^{56} +(-0.306602 - 1.43923i) q^{58} +(-0.679702 + 0.521554i) q^{59} +(-3.51653 + 4.58283i) q^{61} +(-1.08666 - 3.06419i) q^{62} +(3.65135 + 7.11812i) q^{64} +(9.49657 + 16.4485i) q^{65} +(6.81006 + 0.896561i) q^{67} +(-6.31548 + 1.00616i) q^{68} +(-14.2492 - 4.62268i) q^{70} +(-2.92094 - 2.92094i) q^{71} +(-4.48292 + 4.48292i) q^{73} +(-13.7656 + 7.02178i) q^{74} +(1.03984 + 1.69341i) q^{76} +(1.37127 - 10.4159i) q^{77} +(7.00349 - 4.04346i) q^{79} +(-7.31567 + 10.6859i) q^{80} +(-9.02000 - 4.29729i) q^{82} +(1.27984 + 0.982054i) q^{83} +(-6.30207 - 8.21301i) q^{85} +(-0.809039 + 1.24705i) q^{86} +(-8.30188 - 3.68268i) q^{88} +(-1.97258 - 1.97258i) q^{89} +(-17.7330 - 7.34527i) q^{91} +(13.8368 - 6.17563i) q^{92} +(1.58657 - 8.58212i) q^{94} +(-1.60841 + 2.78584i) q^{95} +(-0.192235 - 0.332960i) q^{97} +(4.93796 - 1.75115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8}+O(q^{10}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8	\( 368 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 16 q^{8} - 16 q^{10} + 4 q^{11} - 4 q^{13} + 4 q^{14} - 4 q^{16} - 16 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{25} + 16 q^{26} - 16 q^{28} + 4 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{34} + 16 q^{35} - 16 q^{37} + 60 q^{38} - 4 q^{40} + 4 q^{41} - 4 q^{43} + 104 q^{44} - 16 q^{46} - 48 q^{50} - 4 q^{52} + 16 q^{53} - 16 q^{55} + 84 q^{56} - 40 q^{58} + 4 q^{59} - 4 q^{61} + 24 q^{62} - 16 q^{64} + 8 q^{65} - 4 q^{67} - 12 q^{68} - 4 q^{70} + 16 q^{71} - 16 q^{73} + 4 q^{74} + 20 q^{76} + 4 q^{77} - 48 q^{80} - 16 q^{82} - 36 q^{83} + 16 q^{85} - 100 q^{86} - 4 q^{88} + 16 q^{89} - 16 q^{91} + 80 q^{92} - 20 q^{94} + 136 q^{95} - 8 q^{97} - 104 q^{98}+O(q^{100}) \) 368 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 - 4 * q^7 + 16 * q^8 - 16 * q^10 + 4 * q^11 - 4 * q^13 + 4 * q^14 - 4 * q^16 - 16 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^25 + 16 * q^26 - 16 * q^28 + 4 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^34 + 16 * q^35 - 16 * q^37 + 60 * q^38 - 4 * q^40 + 4 * q^41 - 4 * q^43 + 104 * q^44 - 16 * q^46 - 48 * q^50 - 4 * q^52 + 16 * q^53 - 16 * q^55 + 84 * q^56 - 40 * q^58 + 4 * q^59 - 4 * q^61 + 24 * q^62 - 16 * q^64 + 8 * q^65 - 4 * q^67 - 12 * q^68 - 4 * q^70 + 16 * q^71 - 16 * q^73 + 4 * q^74 + 20 * q^76 + 4 * q^77 - 48 * q^80 - 16 * q^82 - 36 * q^83 + 16 * q^85 - 100 * q^86 - 4 * q^88 + 16 * q^89 - 16 * q^91 + 80 * q^92 - 20 * q^94 + 136 * q^95 - 8 * q^97 - 104 * q^98

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