LMFDB - Embedded newform 729.2.g.d.703.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			703.6
Character	$\chi$	$=$	729.703
Dual form			729.2.g.d.28.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.890910 + 0.585961i) q^{2} +(-0.341789 - 0.792356i) q^{4} +(0.585850 + 0.620965i) q^{5} +(0.284505 - 0.0332539i) q^{7} +(0.530120 - 3.00646i) q^{8} +(0.158079 + 0.896509i) q^{10} +(-0.519011 - 1.73362i) q^{11} +(-0.325075 - 5.58132i) q^{13} +(0.272954 + 0.137083i) q^{14} +(1.04960 - 1.11251i) q^{16} +(4.42908 + 1.61205i) q^{17} +(-1.75427 + 0.638503i) q^{19} +(0.291788 - 0.676441i) q^{20} +(0.553440 - 1.84862i) q^{22} +(1.34612 + 0.157339i) q^{23} +(0.248347 - 4.26396i) q^{25} +(2.98082 - 5.16294i) q^{26} +(-0.123590 - 0.214064i) q^{28} +(5.35083 - 2.68729i) q^{29} +(-2.54206 + 3.41458i) q^{31} +(-4.35412 + 1.03194i) q^{32} +(3.00131 + 4.03146i) q^{34} +(0.187327 + 0.157186i) q^{35} +(-5.46107 + 4.58238i) q^{37} +(-1.93704 - 0.459086i) q^{38} +(2.17748 - 1.43215i) q^{40} +(9.58849 - 6.30645i) q^{41} +(12.3767 + 2.93332i) q^{43} +(-1.19625 + 1.00377i) q^{44} +(1.10708 + 0.928949i) q^{46} +(-1.22397 - 1.64408i) q^{47} +(-6.73148 + 1.59539i) q^{49} +(2.71977 - 3.65328i) q^{50} +(-4.31129 + 2.16521i) q^{52} +(-1.54131 - 2.66962i) q^{53} +(0.772454 - 1.33793i) q^{55} +(0.0508455 - 0.872983i) q^{56} +(6.34175 + 0.741244i) q^{58} +(0.361763 - 1.20837i) q^{59} +(1.09744 - 2.54416i) q^{61} +(-4.26556 + 1.55254i) q^{62} +(-7.35831 - 2.67821i) q^{64} +(3.27536 - 3.47168i) q^{65} +(-5.61273 - 2.81882i) q^{67} +(-0.236491 - 4.06039i) q^{68} +(0.0747867 + 0.249805i) q^{70} +(2.24048 + 12.7064i) q^{71} +(-1.11508 + 6.32396i) q^{73} +(-7.55042 + 0.882517i) q^{74} +(1.10551 + 1.17178i) q^{76} +(-0.205311 - 0.475965i) q^{77} +(-5.95312 - 3.91543i) q^{79} +1.30574 q^{80} +12.2378 q^{82} +(11.3260 + 7.44925i) q^{83} +(1.59375 + 3.69472i) q^{85} +(9.30768 + 9.86557i) q^{86} +(-5.48720 + 0.641362i) q^{88} +(-0.0750415 + 0.425581i) q^{89} +(-0.278086 - 1.57711i) q^{91} +(-0.335421 - 1.12038i) q^{92} +(-0.127083 - 2.18193i) q^{94} +(-1.42423 - 0.715275i) q^{95} +(-6.92494 + 7.34001i) q^{97} +(-6.93197 - 2.52303i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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 $

$2$	0.890910	+	0.585961i	0.629968	+	0.414337i	0.823945	−	0.566669i	$-0.191768\pi$
$2$	0.890910	+	0.585961i	0.629968	+	0.414337i	−0.193977	+	0.981006i	$0.562139\pi$
$3$		0			0
$3$		0			0
$4$	−0.341789	−	0.792356i	−0.170894	−	0.396178i
$5$	0.585850	+	0.620965i	0.262000	+	0.277704i	0.844998	−	0.534770i	$-0.179602\pi$
$5$	0.585850	+	0.620965i	0.262000	+	0.277704i	−0.582998	+	0.812474i	$0.698120\pi$
$6$		0			0
$7$	0.284505	−	0.0332539i	0.107533	−	0.0125688i	−0.0621562	−	0.998066i	$-0.519798\pi$
$7$	0.284505	−	0.0332539i	0.107533	−	0.0125688i	0.169689	+	0.985498i	$0.445724\pi$
$8$	0.530120	−	3.00646i	0.187426	−	1.06295i
$9$		0			0
$10$	0.158079	+	0.896509i	0.0499889	+	0.283501i
$11$	−0.519011	−	1.73362i	−0.156488	−	0.522706i	0.843406	−	0.537277i	$-0.180547\pi$
$11$	−0.519011	−	1.73362i	−0.156488	−	0.522706i	−0.999894	+	0.0145710i	$0.995362\pi$
$12$		0			0
$13$	−0.325075	−	5.58132i	−0.0901596	−	1.54798i	−0.675602	−	0.737266i	$-0.736116\pi$
$13$	−0.325075	−	5.58132i	−0.0901596	−	1.54798i	0.585443	−	0.810714i	$-0.300921\pi$
$14$	0.272954	+	0.137083i	0.0729501	+	0.0366369i
$15$		0			0
$16$	1.04960	−	1.11251i	0.262400	−	0.278128i
$17$	4.42908	+	1.61205i	1.07421	+	0.390980i	0.817749	−	0.575574i	$-0.195222\pi$
$17$	4.42908	+	1.61205i	1.07421	+	0.390980i	0.256460	+	0.966555i	$0.417444\pi$
$18$		0			0
$19$	−1.75427	+	0.638503i	−0.402458	+	0.146483i	−0.535315	−	0.844652i	$-0.679807\pi$
$19$	−1.75427	+	0.638503i	−0.402458	+	0.146483i	0.132857	+	0.991135i	$0.457585\pi$
$20$	0.291788	−	0.676441i	0.0652458	−	0.151257i
$21$		0			0
$22$	0.553440	−	1.84862i	0.117994	−	0.394127i
$23$	1.34612	+	0.157339i	0.280686	+	0.0328074i	0.255271	−	0.966870i	$-0.417835\pi$
$23$	1.34612	+	0.157339i	0.280686	+	0.0328074i	0.0254146	+	0.999677i	$0.491909\pi$
$24$		0			0
$25$	0.248347	−	4.26396i	0.0496694	−	0.852791i
$26$	2.98082	−	5.16294i	0.584587	−	1.01254i
$27$		0			0
$28$	−0.123590	−	0.214064i	−0.0233563	−	0.0404542i
$29$	5.35083	−	2.68729i	0.993624	−	0.499017i	0.123762	−	0.992312i	$-0.460504\pi$
$29$	5.35083	−	2.68729i	0.993624	−	0.499017i	0.869862	+	0.493295i	$0.164208\pi$
$30$		0			0
$31$	−2.54206	+	3.41458i	−0.456568	+	0.613277i	−0.969482	−	0.245163i	$-0.921159\pi$
$31$	−2.54206	+	3.41458i	−0.456568	+	0.613277i	0.512914	+	0.858440i	$0.328566\pi$
$32$	−4.35412	+	1.03194i	−0.769706	+	0.182424i
$33$		0			0
$34$	3.00131	+	4.03146i	0.514721	+	0.691390i
$35$	0.187327	+	0.157186i	0.0316641	+	0.0265693i
$36$		0			0
$37$	−5.46107	+	4.58238i	−0.897794	+	0.753339i	−0.969758	−	0.244068i	$-0.921518\pi$
$37$	−5.46107	+	4.58238i	−0.897794	+	0.753339i	0.0719637	+	0.997407i	$0.477073\pi$
$38$	−1.93704	−	0.459086i	−0.314229	−	0.0744736i
$39$		0			0
$40$	2.17748	−	1.43215i	0.344290	−	0.226443i
$41$	9.58849	−	6.30645i	1.49747	−	0.984902i	0.504907	−	0.863174i	$-0.331527\pi$
$41$	9.58849	−	6.30645i	1.49747	−	0.984902i	0.992563	−	0.121728i	$-0.0388437\pi$
$42$		0			0
$43$	12.3767	+	2.93332i	1.88742	+	0.447328i	0.999910	−	0.0134525i	$-0.00428219\pi$
$43$	12.3767	+	2.93332i	1.88742	+	0.447328i	0.887514	+	0.460780i	$0.152430\pi$
$44$	−1.19625	+	1.00377i	−0.180342	+	0.151325i
$45$		0			0
$46$	1.10708	+	0.928949i	0.163230	+	0.136966i
$47$	−1.22397	−	1.64408i	−0.178535	−	0.239814i	0.703843	−	0.710356i	$-0.251466\pi$
$47$	−1.22397	−	1.64408i	−0.178535	−	0.239814i	−0.882378	+	0.470542i	$0.844059\pi$
$48$		0			0
$49$	−6.73148	+	1.59539i	−0.961640	+	0.227913i
$50$	2.71977	−	3.65328i	0.384633	−	0.516652i
$51$		0			0
$52$	−4.31129	+	2.16521i	−0.597868	+	0.300261i
$53$	−1.54131	−	2.66962i	−0.211715	−	0.366701i	0.740537	−	0.672016i	$-0.234571\pi$
$53$	−1.54131	−	2.66962i	−0.211715	−	0.366701i	−0.952251	+	0.305315i	$0.901238\pi$
$54$		0			0
$55$	0.772454	−	1.33793i	0.104158	−	0.180406i
$56$	0.0508455	−	0.872983i	0.00679452	−	0.116657i
$57$		0			0
$58$	6.34175	+	0.741244i	0.832713	+	0.0973301i
$59$	0.361763	−	1.20837i	0.0470975	−	0.157317i	−0.931206	−	0.364493i	$-0.881242\pi$
$59$	0.361763	−	1.20837i	0.0470975	−	0.157317i	0.978304	+	0.207177i	$0.0664275\pi$
$60$		0			0
$61$	1.09744	−	2.54416i	0.140513	−	0.325747i	−0.833399	−	0.552672i	$-0.813608\pi$
$61$	1.09744	−	2.54416i	0.140513	−	0.325747i	0.973912	+	0.226926i	$0.0728674\pi$
$62$	−4.26556	+	1.55254i	−0.541726	+	0.197172i
$63$		0			0
$64$	−7.35831	−	2.67821i	−0.919789	−	0.334776i
$65$	3.27536	−	3.47168i	0.406258	−	0.430609i
$66$		0			0
$67$	−5.61273	−	2.81882i	−0.685705	−	0.344374i	0.0716021	−	0.997433i	$-0.477189\pi$
$67$	−5.61273	−	2.81882i	−0.685705	−	0.344374i	−0.757307	+	0.653060i	$0.773485\pi$
$68$	−0.236491	−	4.06039i	−0.0286787	−	0.492395i
$69$		0			0
$70$	0.0747867	+	0.249805i	0.00893872	+	0.0298574i
$71$	2.24048	+	12.7064i	0.265896	+	1.50797i	0.766472	+	0.642278i	$0.222011\pi$
$71$	2.24048	+	12.7064i	0.265896	+	1.50797i	−0.500576	+	0.865693i	$0.666878\pi$
$72$		0			0
$73$	−1.11508	+	6.32396i	−0.130511	+	0.740164i	0.847370	+	0.531002i	$0.178184\pi$
$73$	−1.11508	+	6.32396i	−0.130511	+	0.740164i	−0.977881	+	0.209161i	$0.932927\pi$
$74$	−7.55042	+	0.882517i	−0.877718	+	0.102591i
$75$		0			0
$76$	1.10551	+	1.17178i	0.126811	+	0.134412i
$77$	−0.205311	−	0.475965i	−0.0233974	−	0.0542412i
$78$		0			0
$79$	−5.95312	−	3.91543i	−0.669778	−	0.440520i	0.168545	−	0.985694i	$-0.446093\pi$
$79$	−5.95312	−	3.91543i	−0.669778	−	0.440520i	−0.838323	+	0.545174i	$0.816464\pi$
$80$	1.30574			0.145986
$81$		0			0
$82$	12.2378			1.35144
$83$	11.3260	+	7.44925i	1.24319	+	0.817661i	0.988772	−	0.149433i	$-0.0477447\pi$
$83$	11.3260	+	7.44925i	1.24319	+	0.817661i	0.254421	+	0.967094i	$0.418115\pi$
$84$		0			0
$85$	1.59375	+	3.69472i	0.172866	+	0.400749i
$86$	9.30768	+	9.86557i	1.00367	+	1.06383i
$87$		0			0
$88$	−5.48720	+	0.641362i	−0.584937	+	0.0683694i
$89$	−0.0750415	+	0.425581i	−0.00795438	+	0.0451115i	−0.988527	−	0.151047i	$-0.951736\pi$
$89$	−0.0750415	+	0.425581i	−0.00795438	+	0.0451115i	0.980572	+	0.196158i	$0.0628467\pi$
$90$		0			0
$91$	−0.278086	−	1.57711i	−0.0291514	−	0.165326i
$92$	−0.335421	−	1.12038i	−0.0349700	−	0.116808i
$93$		0			0
$94$	−0.127083	−	2.18193i	−0.0131076	−	0.225049i
$95$	−1.42423	−	0.715275i	−0.146123	−	0.0733857i
$96$		0			0
$97$	−6.92494	+	7.34001i	−0.703121	+	0.745265i	−0.976234	−	0.216717i	$-0.930465\pi$
$97$	−6.92494	+	7.34001i	−0.703121	+	0.745265i	0.273114	+	0.961982i	$0.411947\pi$
$98$	−6.93197	−	2.52303i	−0.700235	−	0.254865i
$99$		0			0
$100$	−3.46345	+	1.26059i	−0.346345	+	0.126059i
$101$	−3.67502	+	8.51965i	−0.365678	+	0.847737i	0.631689	+	0.775222i	$0.282362\pi$
$101$	−3.67502	+	8.51965i	−0.365678	+	0.847737i	−0.997367	+	0.0725151i	$0.976897\pi$
$102$		0			0
$103$	−4.20365	+	14.0412i	−0.414198	+	1.38352i	0.455634	+	0.890167i	$0.349413\pi$
$103$	−4.20365	+	14.0412i	−0.414198	+	1.38352i	−0.869831	+	0.493349i	$0.835772\pi$
$104$	−16.9524	−	1.98145i	−1.66232	−	0.194297i
$105$		0			0
$106$	0.191128	−	3.28154i	0.0185640	−	0.318731i
$107$	0.0376376	−	0.0651902i	0.00363856	−	0.00630218i	−0.864200	−	0.503148i	$-0.832175\pi$
$107$	0.0376376	−	0.0651902i	0.00363856	−	0.00630218i	0.867839	+	0.496846i	$0.165508\pi$
$108$		0			0
$109$	−2.64599	−	4.58298i	−0.253440	−	0.438970i	0.711031	−	0.703161i	$-0.248229\pi$
$109$	−2.64599	−	4.58298i	−0.253440	−	0.438970i	−0.964470	+	0.264191i	$0.914895\pi$
$110$	1.47216	−	0.739347i	0.140365	−	0.0704939i
$111$		0			0
$112$	0.261622	−	0.351419i	0.0247210	−	0.0332060i
$113$	−18.0181	+	4.27037i	−1.69500	+	0.401722i	−0.960807	−	0.277219i	$-0.910587\pi$
$113$	−18.0181	+	4.27037i	−1.69500	+	0.401722i	−0.734193	+	0.678941i	$0.762439\pi$
$114$		0			0
$115$	0.690923	+	0.928071i	0.0644289	+	0.0865430i
$116$	−3.95814	−	3.32128i	−0.367504	−	0.308373i
$117$		0			0
$118$	1.03036	−	0.864571i	0.0948520	−	0.0795903i
$119$	1.31370	+	0.311354i	0.120427	+	0.0285417i
$120$		0			0
$121$	6.45430	−	4.24506i	0.586755	−	0.385915i
$122$	2.46850	−	1.62356i	0.223488	−	0.146990i
$123$		0			0
$124$	3.57441	+	0.847151i	0.320992	+	0.0760764i
$125$	6.06315	−	5.08759i	0.542305	−	0.455048i
$126$		0			0
$127$	8.52895	+	7.15664i	0.756822	+	0.635049i	0.937297	−	0.348531i	$-0.113319\pi$
$127$	8.52895	+	7.15664i	0.756822	+	0.635049i	−0.180476	+	0.983579i	$0.557764\pi$
$128$	0.357982	+	0.480853i	0.0316414	+	0.0425018i
$129$		0			0
$130$	4.95232	−	1.17372i	0.434347	−	0.102942i
$131$	0.164790	−	0.221351i	0.0143977	−	0.0193395i	−0.794866	−	0.606785i	$-0.792459\pi$
$131$	0.164790	−	0.221351i	0.0143977	−	0.0193395i	0.809264	+	0.587445i	$0.199866\pi$
$132$		0			0
$133$	−0.477868	+	0.239994i	−0.0414364	+	0.0208101i
$134$	−3.34872	−	5.80016i	−0.289285	−	0.501057i
$135$		0			0
$136$	7.19452	−	12.4613i	0.616925	−	1.06855i
$137$	−0.612702	+	10.5197i	−0.0523466	+	0.898757i	0.865274	+	0.501299i	$0.167144\pi$
$137$	−0.612702	+	10.5197i	−0.0523466	+	0.898757i	−0.917621	+	0.397458i	$0.869893\pi$
$138$		0			0
$139$	−0.538250	−	0.0629124i	−0.0456537	−	0.00533616i	0.0932354	−	0.995644i	$-0.470279\pi$
$139$	−0.538250	−	0.0629124i	−0.0456537	−	0.00533616i	−0.138889	+	0.990308i	$0.544353\pi$
$140$	0.0605210	−	0.202154i	0.00511496	−	0.0170851i
$141$		0			0
$142$	−5.44938	+	12.6331i	−0.457302	+	1.06014i
$143$	−9.50717	+	3.46033i	−0.795029	+	0.289367i
$144$		0			0
$145$	4.80349	+	1.74833i	0.398908	+	0.145191i
$146$	−4.69903	+	4.98068i	−0.388895	+	0.412204i
$147$		0			0
$148$	5.49741	+	2.76090i	0.451884	+	0.226945i
$149$	1.14216	+	19.6101i	0.0935693	+	1.60652i	0.639566	+	0.768736i	$0.279114\pi$
$149$	1.14216	+	19.6101i	0.0935693	+	1.60652i	−0.545997	+	0.837787i	$0.683849\pi$
$150$		0			0
$151$	−4.25389	−	14.2090i	−0.346177	−	1.15631i	−0.936947	−	0.349471i	$-0.886361\pi$
$151$	−4.25389	−	14.2090i	−0.346177	−	1.15631i	0.590770	−	0.806840i	$-0.298824\pi$
$152$	0.989660	+	5.61264i	0.0802720	+	0.455245i
$153$		0			0
$154$	0.0959829	−	0.544346i	0.00773452	−	0.0438647i
$155$	−3.60960	+	0.421902i	−0.289930	+	0.0338880i
$156$		0			0
$157$	−4.00801	−	4.24824i	−0.319874	−	0.339047i	0.547406	−	0.836867i	$-0.315615\pi$
$157$	−4.00801	−	4.24824i	−0.319874	−	0.339047i	−0.867280	+	0.497820i	$0.834134\pi$
$158$	−3.00941	−	6.97659i	−0.239415	−	0.555027i
$159$		0			0
$160$	−3.19166	−	2.09919i	−0.252323	−	0.165955i
$161$	0.388211			0.0305953
$162$		0			0
$163$	−6.88988			−0.539657			−0.269828	−	0.962908i	$-0.586967\pi$
$163$	−6.88988			−0.539657			−0.269828	+	0.962908i	$0.586967\pi$
$164$	−8.27419	−	5.44202i	−0.646106	−	0.424951i
$165$		0			0
$166$	5.72551	+	13.2732i	0.444385	+	1.03020i
$167$	12.1766	+	12.9064i	0.942252	+	0.998728i	1.00000		0.000397221i	$0.000126439\pi$
$167$	12.1766	+	12.9064i	0.942252	+	0.998728i	−0.0577483	+	0.998331i	$0.518392\pi$
$168$		0			0
$169$	−18.1334	+	2.11949i	−1.39488	+	0.163038i
$170$	−0.745077	+	4.22554i	−0.0571448	+	0.324084i
$171$		0			0
$172$	−1.90597	−	10.8093i	−0.145329	−	0.824202i
$173$	−4.01157	−	13.3996i	−0.304994	−	1.01875i	−0.963842	−	0.266474i	$-0.914141\pi$
$173$	−4.01157	−	13.3996i	−0.304994	−	1.01875i	0.658848	−	0.752276i	$-0.271044\pi$
$174$		0			0
$175$	−0.0711371	−	1.22138i	−0.00537746	−	0.0923274i
$176$	−2.47343	−	1.24220i	−0.186442	−	0.0936345i
$177$		0			0
$178$	−0.316229	+	0.335183i	−0.0237024	+	0.0251230i
$179$	9.85261	+	3.58606i	0.736418	+	0.268034i	0.682879	−	0.730531i	$-0.260728\pi$
$179$	9.85261	+	3.58606i	0.736418	+	0.268034i	0.0535392	+	0.998566i	$0.482950\pi$
$180$		0			0
$181$	11.6610	−	4.24426i	0.866755	−	0.315473i	0.129903	−	0.991527i	$-0.458533\pi$
$181$	11.6610	−	4.24426i	0.866755	−	0.315473i	0.736852	+	0.676054i	$0.236311\pi$
$182$	0.676372	−	1.56801i	0.0501361	−	0.116228i
$183$		0			0
$184$	1.18664	−	3.96365i	0.0874803	−	0.292204i
$185$	−6.04487	−	0.706543i	−0.444427	−	0.0519461i
$186$		0			0
$187$	0.495943	−	8.51501i	0.0362669	−	0.622679i
$188$	−0.884358	+	1.53175i	−0.0644984	+	0.111715i
$189$		0			0
$190$	−0.849737	−	1.47179i	−0.0616464	−	0.106775i
$191$	−12.6284	+	6.34222i	−0.913759	+	0.458907i	−0.842589	−	0.538557i	$-0.818970\pi$
$191$	−12.6284	+	6.34222i	−0.913759	+	0.458907i	−0.0711702	+	0.997464i	$0.522673\pi$
$192$		0			0
$193$	13.1675	−	17.6871i	0.947820	−	1.27314i	−0.0141245	−	0.999900i	$-0.504496\pi$
$193$	13.1675	−	17.6871i	0.947820	−	1.27314i	0.961945	−	0.273243i	$-0.0880965\pi$
$194$	−10.4705	+	2.48154i	−0.751735	+	0.178164i
$195$		0			0
$196$	3.56486	+	4.78844i	0.254633	+	0.342031i
$197$	−1.28639	−	1.07941i	−0.0916516	−	0.0769049i	0.595811	−	0.803125i	$-0.296831\pi$
$197$	−1.28639	−	1.07941i	−0.0916516	−	0.0769049i	−0.687462	+	0.726220i	$0.741275\pi$
$198$		0			0
$199$	8.18059	−	6.86433i	0.579906	−	0.486599i	−0.305010	−	0.952349i	$-0.598660\pi$
$199$	8.18059	−	6.86433i	0.579906	−	0.486599i	0.884916	+	0.465750i	$0.154215\pi$
$200$	−12.6878	−	3.00706i	−0.897161	−	0.212631i
$201$		0			0
$202$	−8.26629	+	5.43682i	−0.581614	+	0.382534i
$203$	1.43298	−	0.942484i	0.100575	−	0.0661494i
$204$		0			0
$205$	9.53350	+	2.25948i	0.665849	+	0.157809i
$206$	−11.9726	+	10.0462i	−0.834173	+	0.699954i
$207$		0			0
$208$	−6.55049	−	5.49652i	−0.454195	−	0.381115i
$209$	2.01741	+	2.70985i	0.139547	+	0.187444i
$210$		0			0
$211$	−10.1652	+	2.40919i	−0.699798	+	0.165855i	−0.565089	−	0.825030i	$-0.691158\pi$
$211$	−10.1652	+	2.40919i	−0.699798	+	0.165855i	−0.134709	+	0.990885i	$0.543010\pi$
$212$	−1.58849	+	2.13371i	−0.109098	+	0.146544i
$213$		0			0
$214$	0.0717306	−	0.0360245i	0.00490341	−	0.00246258i
$215$	5.42938	+	9.40396i	0.370281	+	0.641345i
$216$		0			0
$217$	−0.609682	+	1.05600i	−0.0413879	+	0.0716860i
$218$	0.328112	−	5.63347i	0.0222226	−	0.381547i
$219$		0			0
$220$	−1.32413	−	0.154769i	−0.0892730	−	0.0104345i
$221$	7.55761	−	25.2442i	0.508380	−	1.69811i
$222$		0			0
$223$	5.39966	−	12.5178i	0.361588	−	0.838256i	−0.636184	−	0.771538i	$-0.719488\pi$
$223$	5.39966	−	12.5178i	0.361588	−	0.838256i	0.997772	−	0.0667182i	$-0.0212528\pi$
$224$	−1.20445	+	0.438385i	−0.0804759	+	0.0292908i
$225$		0			0
$226$	−18.5548	−	6.75338i	−1.23424	−	0.449228i
$227$	8.98971	−	9.52854i	0.596668	−	0.632431i	−0.356708	−	0.934216i	$-0.616101\pi$
$227$	8.98971	−	9.52854i	0.596668	−	0.632431i	0.953376	+	0.301785i	$0.0975824\pi$
$228$		0			0
$229$	1.54142	+	0.774128i	0.101860	+	0.0511559i	0.499000	−	0.866602i	$-0.333701\pi$
$229$	1.54142	+	0.774128i	0.101860	+	0.0511559i	−0.397140	+	0.917758i	$0.629997\pi$
$230$	0.0717373	+	1.23168i	0.00473021	+	0.0812146i
$231$		0			0
$232$	−5.24264	−	17.5116i	−0.344196	−	1.14970i
$233$	−4.21198	−	23.8873i	−0.275936	−	1.56491i	−0.735972	−	0.677011i	$-0.763275\pi$
$233$	−4.21198	−	23.8873i	−0.275936	−	1.56491i	0.460036	−	0.887900i	$-0.347836\pi$
$234$		0			0
$235$	0.303852	−	1.72323i	0.0198211	−	0.112411i
$236$	−1.08111	+	0.126363i	−0.0703741	+	0.00822555i
$237$		0			0
$238$	0.987951	+	1.04717i	0.0640394	+	0.0678778i
$239$	8.77100	+	20.3335i	0.567349	+	1.31526i	0.924488	+	0.381211i	$0.124493\pi$
$239$	8.77100	+	20.3335i	0.567349	+	1.31526i	−0.357139	+	0.934051i	$0.616248\pi$
$240$		0			0
$241$	15.1000	+	9.93144i	0.972677	+	0.639740i	0.933153	−	0.359479i	$-0.117045\pi$
$241$	15.1000	+	9.93144i	0.972677	+	0.639740i	0.0395241	+	0.999219i	$0.487416\pi$
$242$	8.23764			0.529536
$243$		0			0
$244$	−2.39098			−0.153067
$245$	−4.93432	−	3.24535i	−0.315242	−	0.207338i
$246$		0			0
$247$	4.13396	+	9.58361i	0.263038	+	0.609790i
$248$	8.91821	+	9.45275i	0.566307	+	0.600250i
$249$		0			0
$250$	8.38285	−	0.979815i	0.530178	−	0.0619689i
$251$	−1.74420	+	9.89185i	−0.110093	+	0.624368i	0.878970	+	0.476876i	$0.158231\pi$
$251$	−1.74420	+	9.89185i	−0.110093	+	0.624368i	−0.989063	+	0.147492i	$0.952880\pi$
$252$		0			0
$253$	−0.425886	−	2.41532i	−0.0267752	−	0.151850i
$254$	3.40502	+	11.3735i	0.213650	+	0.713640i
$255$		0			0
$256$	0.947781	+	16.2728i	0.0592363	+	1.01705i
$257$	−8.19846	−	4.11742i	−0.511406	−	0.256838i	0.174331	−	0.984687i	$-0.444224\pi$
$257$	−8.19846	−	4.11742i	−0.511406	−	0.256838i	−0.685737	+	0.727849i	$0.740520\pi$
$258$		0			0
$259$	−1.40132	+	1.48531i	−0.0870739	+	0.0922929i
$260$	−3.87029	−	1.40867i	−0.240025	−	0.0873620i
$261$		0			0
$262$	0.276516	−	0.100643i	0.0170832	−	0.00621777i
$263$	−9.41306	+	21.8219i	−0.580434	+	1.34560i	0.334653	+	0.942342i	$0.391381\pi$
$263$	−9.41306	+	21.8219i	−0.580434	+	1.34560i	−0.915087	+	0.403257i	$0.867878\pi$
$264$		0			0
$265$	0.754766	−	2.52109i	0.0463649	−	0.154870i
$266$	−0.566364	−	0.0661985i	−0.0347260	−	0.00405889i
$267$		0			0
$268$	−0.315139	+	5.41072i	−0.0192502	+	0.330513i
$269$	3.35091	−	5.80395i	0.204309	−	0.353873i	−0.745604	−	0.666390i	$-0.767839\pi$
$269$	3.35091	−	5.80395i	0.204309	−	0.353873i	0.949912	+	0.312517i	$0.101172\pi$
$270$		0			0
$271$	4.74494	+	8.21848i	0.288235	+	0.499237i	0.973388	−	0.229161i	$-0.0735984\pi$
$271$	4.74494	+	8.21848i	0.288235	+	0.499237i	−0.685154	+	0.728398i	$0.740265\pi$
$272$	6.44220	−	3.23539i	0.390616	−	0.196175i
$273$		0			0
$274$	−6.70998	+	9.01307i	−0.405365	+	0.544499i
$275$	−7.52097	+	1.78250i	−0.453532	+	0.107489i
$276$		0			0
$277$	−0.827868	−	1.11202i	−0.0497418	−	0.0668148i	0.776556	−	0.630048i	$-0.216965\pi$
$277$	−0.827868	−	1.11202i	−0.0497418	−	0.0668148i	−0.826298	+	0.563233i	$0.809557\pi$
$278$	−0.442668	−	0.371442i	−0.0265494	−	0.0222776i
$279$		0			0
$280$	0.571880	−	0.479864i	0.0341764	−	0.0286774i
$281$	15.5815	+	3.69287i	0.929512	+	0.220298i	0.667366	−	0.744730i	$-0.267422\pi$
$281$	15.5815	+	3.69287i	0.929512	+	0.220298i	0.262146	+	0.965028i	$0.415570\pi$
$282$		0			0
$283$	0.262449	−	0.172616i	0.0156010	−	0.0102609i	−0.541685	−	0.840582i	$-0.682213\pi$
$283$	0.262449	−	0.172616i	0.0156010	−	0.0102609i	0.557286	+	0.830321i	$0.311843\pi$
$284$	9.30221	−	6.11816i	0.551985	−	0.363046i
$285$		0			0
$286$	−10.4976	−	2.48799i	−0.620739	−	0.147118i
$287$	2.51826	−	2.11307i	0.148648	−	0.124731i
$288$		0			0
$289$	3.99528	+	3.35244i	0.235016	+	0.197202i
$290$	3.25503	+	4.37226i	0.191142	+	0.256748i
$291$		0			0
$292$	5.39195	−	1.27792i	0.315540	−	0.0747844i
$293$	11.1446	−	14.9698i	0.651076	−	0.874547i	−0.346915	−	0.937897i	$-0.612771\pi$
$293$	11.1446	−	14.9698i	0.651076	−	0.874547i	0.997991	+	0.0633491i	$0.0201782\pi$
$294$		0			0
$295$	0.962295	−	0.483283i	0.0560270	−	0.0281378i
$296$	10.8817	+	18.8477i	0.632488	+	1.09550i
$297$		0			0
$298$	−10.4732	+	18.1401i	−0.606696	+	1.05083i
$299$	0.440569	−	7.56428i	0.0254788	−	0.437454i
$300$		0			0
$301$	3.61877	+	0.422974i	0.208583	+	0.0243798i
$302$	4.53607	−	15.1515i	0.261022	−	0.871873i
$303$		0			0
$304$	−1.13095	+	2.62183i	−0.0648642	+	0.150372i
$305$	2.22277	−	0.809023i	0.127276	−	0.0463245i
$306$		0			0
$307$	25.4414	+	9.25992i	1.45202	+	0.528491i	0.943154	−	0.332356i	$-0.107843\pi$
$307$	25.4414	+	9.25992i	1.45202	+	0.528491i	0.508864	+	0.860847i	$0.330066\pi$
$308$	−0.306960	+	0.325359i	−0.0174907	+	0.0185391i
$309$		0			0
$310$	−3.46305	−	1.73921i	−0.196688	−	0.0987804i
$311$	0.719941	+	12.3609i	0.0408241	+	0.700923i	0.955183	+	0.296017i	$0.0956586\pi$
$311$	0.719941	+	12.3609i	0.0408241	+	0.700923i	−0.914359	+	0.404906i	$0.867304\pi$
$312$		0			0
$313$	6.15560	+	20.5611i	0.347935	+	1.16218i	0.935595	+	0.353076i	$0.114864\pi$
$313$	6.15560	+	20.5611i	0.347935	+	1.16218i	−0.587660	+	0.809108i	$0.699951\pi$
$314$	−1.08147	−	6.13334i	−0.0610311	−	0.346124i
$315$		0			0
$316$	−1.06770	+	6.05524i	−0.0600629	+	0.340634i
$317$	23.4460	−	2.74044i	1.31686	−	0.153919i	0.571511	−	0.820595i	$-0.306358\pi$
$317$	23.4460	−	2.74044i	1.31686	−	0.153919i	0.745348	+	0.666676i	$0.232283\pi$
$318$		0			0
$319$	−7.43587	−	7.88156i	−0.416329	−	0.441283i
$320$	−2.64780	−	6.13828i	−0.148016	−	0.343140i
$321$		0			0
$322$	0.345861	+	0.227476i	0.0192741	+	0.0126768i
$323$	−8.79912			−0.489596
$324$		0			0
$325$	−23.8792			−1.32458
$326$	−6.13826	−	4.03720i	−0.339967	−	0.223600i
$327$		0			0
$328$	−13.8770	−	32.1706i	−0.766232	−	1.77633i
$329$	−0.402900	−	0.427049i	−0.0222126	−	0.0235439i
$330$		0			0
$331$	0.842076	−	0.0984246i	0.0462847	−	0.00540990i	−0.0929190	−	0.995674i	$-0.529620\pi$
$331$	0.842076	−	0.0984246i	0.0462847	−	0.00540990i	0.139204	+	0.990264i	$0.455546\pi$
$332$	2.03134	−	11.5203i	0.111484	−	0.632259i
$333$		0			0
$334$	3.28558	+	18.6334i	0.179779	+	1.01958i
$335$	−1.53783	−	5.13672i	−0.0840207	−	0.280649i
$336$		0			0
$337$	−0.118835	−	2.04032i	−0.00647336	−	0.111143i	0.993524	−	0.113626i	$-0.0362467\pi$
$337$	−0.118835	−	2.04032i	−0.00647336	−	0.111143i	−0.999997	+	0.00248306i	$0.999210\pi$
$338$	−17.3971	−	8.73718i	−0.946280	−	0.475240i
$339$		0			0
$340$	2.38281	−	2.52563i	0.129226	−	0.136972i
$341$	7.23894	+	2.63476i	0.392011	+	0.142680i
$342$		0			0
$343$	−3.74626	+	1.36353i	−0.202279	+	0.0736236i
$344$	15.3801	−	35.6550i	0.829237	−	1.92239i
$345$		0			0
$346$	4.27767	−	14.2884i	0.229969	−	0.768151i
$347$	6.45936	+	0.754991i	0.346757	+	0.0405300i	0.287689	−	0.957724i	$-0.407113\pi$
$347$	6.45936	+	0.754991i	0.346757	+	0.0405300i	0.0590678	+	0.998254i	$0.481187\pi$
$348$		0			0
$349$	−0.384965	+	6.60959i	−0.0206067	+	0.353803i	0.972206	+	0.234126i	$0.0752229\pi$
$349$	−0.384965	+	6.60959i	−0.0206067	+	0.353803i	−0.992813	+	0.119677i	$0.961814\pi$
$350$	0.652302	−	1.12982i	0.0348670	−	0.0603914i
$351$		0			0
$352$	4.04883	+	7.01279i	0.215804	+	0.373783i
$353$	−0.270111	+	0.135655i	−0.0143765	+	0.00722017i	−0.455973	−	0.889994i	$-0.650709\pi$
$353$	−0.270111	+	0.135655i	−0.0143765	+	0.00722017i	0.441596	+	0.897214i	$0.354412\pi$
$354$		0			0
$355$	−6.57763	+	8.83530i	−0.349105	+	0.468929i
$356$	0.362860	−	0.0859995i	0.0192316	−	0.00455796i
$357$		0			0
$358$	6.67650	+	8.96809i	0.352864	+	0.473978i
$359$	3.14494	+	2.63892i	0.165984	+	0.139277i	0.721996	−	0.691897i	$-0.243225\pi$
$359$	3.14494	+	2.63892i	0.165984	+	0.139277i	−0.556012	+	0.831174i	$0.687669\pi$
$360$		0			0
$361$	−11.8851	+	9.97274i	−0.625529	+	0.524881i
$362$	12.8759	+	3.05164i	0.676740	+	0.160390i
$363$		0			0
$364$	−1.15458	+	0.759381i	−0.0605166	+	0.0398024i
$365$	−4.58023	+	3.01246i	−0.239740	+	0.157680i
$366$		0			0
$367$	−8.75239	−	2.07435i	−0.456871	−	0.108280i	−0.00426466	−	0.999991i	$-0.501357\pi$
$367$	−8.75239	−	2.07435i	−0.456871	−	0.108280i	−0.452606	+	0.891711i	$0.649506\pi$
$368$	1.58793	−	1.33243i	0.0827767	−	0.0694579i
$369$		0			0
$370$	−4.97142	−	4.17152i	−0.258452	−	0.216867i
$371$	−0.527285	−	0.708267i	−0.0273753	−	0.0367714i
$372$		0			0
$373$	5.11858	−	1.21313i	0.265030	−	0.0628133i	−0.0959522	−	0.995386i	$-0.530590\pi$
$373$	5.11858	−	1.21313i	0.265030	−	0.0628133i	0.360982	+	0.932573i	$0.382441\pi$
$374$	5.43130	−	7.29550i	0.280846	−	0.377242i
$375$		0			0
$376$	−5.59173	+	2.80827i	−0.288371	+	0.144826i
$377$	−16.7380	−	28.9911i	−0.862053	−	1.49312i
$378$		0			0
$379$	−3.76722	+	6.52502i	−0.193509	+	0.335168i	−0.946411	−	0.322965i	$-0.895320\pi$
$379$	−3.76722	+	6.52502i	−0.193509	+	0.335168i	0.752902	+	0.658133i	$0.228654\pi$
$380$	−0.0799664	+	1.37297i	−0.00410219	+	0.0704319i
$381$		0			0
$382$	−14.9671	−	1.74940i	−0.765782	−	0.0895070i
$383$	10.2165	−	34.1256i	0.522040	−	1.74374i	−0.135955	−	0.990715i	$-0.543410\pi$
$383$	10.2165	−	34.1256i	0.522040	−	1.74374i	0.657996	−	0.753022i	$-0.271404\pi$
$384$		0			0
$385$	0.175276	−	0.406335i	0.00893288	−	0.0207088i
$386$	22.0950	−	8.04193i	1.12461	−	0.409324i
$387$		0			0
$388$	8.18276	+	2.97828i	0.415417	+	0.151199i
$389$	−8.68991	+	9.21077i	−0.440596	+	0.467005i	−0.909173	−	0.416418i	$-0.863285\pi$
$389$	−8.68991	+	9.21077i	−0.440596	+	0.467005i	0.468577	+	0.883423i	$0.344767\pi$
$390$		0			0
$391$	5.70844	+	2.86689i	0.288688	+	0.144985i
$392$	1.22798	+	21.0837i	0.0620226	+	1.06489i
$393$		0			0
$394$	−0.513567	−	1.71543i	−0.0258731	−	0.0864223i
$395$	−1.05629	−	5.99053i	−0.0531478	−	0.301416i
$396$		0			0
$397$	1.88601	−	10.6961i	0.0946564	−	0.536823i	−0.900196	−	0.435486i	$-0.856577\pi$
$397$	1.88601	−	10.6961i	0.0946564	−	0.536823i	0.994852	−	0.101337i	$-0.0323122\pi$
$398$	11.3104	−	1.32200i	0.566939	−	0.0662656i
$399$		0			0
$400$	−4.48304	−	4.75175i	−0.224152	−	0.237587i
$401$	2.27311	+	5.26965i	0.113514	+	0.263154i	0.965497	−	0.260415i	$-0.0838594\pi$
$401$	2.27311	+	5.26965i	0.113514	+	0.263154i	−0.851983	+	0.523569i	$0.824600\pi$
$402$		0			0
$403$	19.8842	+	13.0781i	0.990505	+	0.651465i
$404$	8.00667			0.398347
$405$		0			0
$406$	1.82891			0.0907674
$407$	10.7785	+	7.08910i	0.534268	+	0.351394i
$408$		0			0
$409$	−11.7085	−	27.1434i	−0.578948	−	1.34215i	−0.916193	−	0.400737i	$-0.868754\pi$
$409$	−11.7085	−	27.1434i	−0.578948	−	1.34215i	0.337245	−	0.941417i	$-0.390505\pi$
$410$	7.16952	+	7.59925i	0.354078	+	0.375300i
$411$		0			0
$412$	12.5624	−	1.46833i	0.618903	−	0.0723394i
$413$	0.0627404	−	0.355818i	0.00308725	−	0.0175087i
$414$		0			0
$415$	2.00964	+	11.3972i	0.0986491	+	0.559467i
$416$	7.17503	+	23.9663i	0.351785	+	1.17504i
$417$		0			0
$418$	0.209464	+	3.59636i	0.0102452	+	0.175904i
$419$	−7.98438	−	4.00990i	−0.390062	−	0.195897i	0.242949	−	0.970039i	$-0.421885\pi$
$419$	−7.98438	−	4.00990i	−0.390062	−	0.195897i	−0.633012	+	0.774142i	$0.718181\pi$
$420$		0			0
$421$	−1.73759	+	1.84173i	−0.0846848	+	0.0897606i	−0.768330	−	0.640054i	$-0.778912\pi$
$421$	−1.73759	+	1.84173i	−0.0846848	+	0.0897606i	0.683645	+	0.729814i	$0.260394\pi$
$422$	−10.4679	−	3.81001i	−0.509570	−	0.185468i
$423$		0			0
$424$	−8.84319	+	3.21866i	−0.429463	+	0.156312i
$425$	7.97367	−	18.4851i	0.386780	−	0.896657i
$426$		0			0
$427$	0.227626	−	0.760322i	0.0110156	−	0.0367946i
$428$	−0.0645180	−	0.00754107i	−0.00311860	−	0.000364511i
$429$		0			0
$430$	−0.673263	+	11.5595i	−0.0324676	+	0.557448i
$431$	−14.8594	+	25.7372i	−0.715750	+	1.23972i	0.246919	+	0.969036i	$0.420582\pi$
$431$	−14.8594	+	25.7372i	−0.715750	+	1.23972i	−0.962669	+	0.270680i	$0.912751\pi$
$432$		0			0
$433$	0.612994	+	1.06174i	0.0294586	+	0.0510238i	0.880379	−	0.474271i	$-0.157288\pi$
$433$	0.612994	+	1.06174i	0.0294586	+	0.0510238i	−0.850920	+	0.525295i	$0.823955\pi$
$434$	−1.16195	+	0.583551i	−0.0557752	+	0.0280114i
$435$		0			0
$436$	−2.72698	+	3.66298i	−0.130599	+	0.175425i
$437$	−2.46193	+	0.583487i	−0.117770	+	0.0279120i
$438$		0			0
$439$	−10.3661	−	13.9241i	−0.494748	−	0.664562i	0.482689	−	0.875792i	$-0.339660\pi$
$439$	−10.3661	−	13.9241i	−0.494748	−	0.664562i	−0.977436	+	0.211231i	$0.932253\pi$
$440$	−3.61294	−	3.03162i	−0.172240	−	0.144527i
$441$		0			0
$442$	21.5252	−	18.0618i	1.02385	−	0.859113i
$443$	−11.6619	−	2.76392i	−0.554073	−	0.131318i	−0.0559651	−	0.998433i	$-0.517824\pi$
$443$	−11.6619	−	2.76392i	−0.554073	−	0.131318i	−0.498108	+	0.867115i	$0.665972\pi$
$444$		0			0
$445$	−0.308234	+	0.202729i	−0.0146117	+	0.00961027i
$446$	12.1456	−	7.98827i	0.575109	−	0.378255i
$447$		0			0
$448$	−2.18254	−	0.517271i	−0.103115	−	0.0244388i
$449$	15.0015	−	12.5878i	0.707965	−	0.594053i	−0.216063	−	0.976380i	$-0.569322\pi$
$449$	15.0015	−	12.5878i	0.707965	−	0.594053i	0.924027	+	0.382327i	$0.124877\pi$
$450$		0			0
$451$	−15.9095	−	13.3497i	−0.749150	−	0.628611i
$452$	9.54203	+	12.8172i	0.448820	+	0.602869i
$453$		0			0
$454$	13.5924	−	3.22145i	0.637921	−	0.151190i
$455$	0.816411	−	1.09663i	0.0382739	−	0.0514108i
$456$		0			0
$457$	21.4625	−	10.7789i	1.00397	−	0.504215i	0.130689	−	0.991423i	$-0.458281\pi$
$457$	21.4625	−	10.7789i	1.00397	−	0.504215i	0.873286	+	0.487208i	$0.161985\pi$
$458$	0.919654	+	1.59289i	0.0429726	+	0.0744308i
$459$		0			0
$460$	0.499212	−	0.864661i	0.0232759	−	0.0403150i
$461$	0.823736	−	14.1430i	0.0383652	−	0.658705i	−0.923232	−	0.384242i	$-0.874463\pi$
$461$	0.823736	−	14.1430i	0.0383652	−	0.658705i	0.961598	−	0.274463i	$-0.0885001\pi$
$462$		0			0
$463$	10.9340	+	1.27800i	0.508147	+	0.0593938i	0.366304	−	0.930495i	$-0.380623\pi$
$463$	10.9340	+	1.27800i	0.508147	+	0.0593938i	0.141843	+	0.989889i	$0.454697\pi$
$464$	2.62660	−	8.77345i	0.121937	−	0.407297i
$465$		0			0
$466$	10.2445	−	23.7495i	0.474569	−	1.10018i
$467$	36.6170	−	13.3275i	1.69443	−	0.616723i	0.699261	−	0.714867i	$-0.253513\pi$
$467$	36.6170	−	13.3275i	1.69443	−	0.616723i	0.995172	+	0.0981436i	$0.0312904\pi$
$468$		0			0
$469$	−1.69059	−	0.615324i	−0.0780642	−	0.0284130i
$470$	1.28045	−	1.35720i	0.0590628	−	0.0626029i
$471$		0			0
$472$	−3.44115	−	1.72821i	−0.158392	−	0.0795472i
$473$	−1.33837	−	22.9789i	−0.0615381	−	1.05657i
$474$		0			0
$475$	2.28688	+	7.63872i	0.104929	+	0.350488i
$476$	−0.202307	−	1.14734i	−0.00927272	−	0.0525882i
$477$		0			0
$478$	−4.10044	+	23.2547i	−0.187550	+	1.06365i
$479$	−14.0251	+	1.63930i	−0.640825	+	0.0749017i	−0.430299	−	0.902686i	$-0.641592\pi$
$479$	−14.0251	+	1.63930i	−0.640825	+	0.0749017i	−0.210526	+	0.977588i	$0.567518\pi$
$480$		0			0
$481$	27.3510	+	28.9904i	1.24710	+	1.32185i
$482$	7.63332	+	17.6960i	0.347688	+	0.806032i
$483$		0			0
$484$	−5.56961	−	3.66319i	−0.253164	−	0.166509i
$485$	−8.61486			−0.391181
$486$		0			0
$487$	−11.6224			−0.526663			−0.263332	−	0.964705i	$-0.584821\pi$
$487$	−11.6224			−0.526663			−0.263332	+	0.964705i	$0.584821\pi$
$488$	−7.06715	−	4.64814i	−0.319915	−	0.210411i
$489$		0			0
$490$	−2.49438	−	5.78263i	−0.112685	−	0.261233i
$491$	3.60508	+	3.82116i	0.162695	+	0.172447i	0.803593	−	0.595180i	$-0.202919\pi$
$491$	3.60508	+	3.82116i	0.162695	+	0.172447i	−0.640898	+	0.767626i	$0.721438\pi$
$492$		0			0
$493$	28.0313	−	3.27639i	1.26247	−	0.147561i
$494$	−1.93263	+	10.9605i	−0.0869530	+	0.493135i
$495$		0			0
$496$	1.13061	+	6.41203i	0.0507660	+	0.287909i
$497$	1.05997	+	3.54053i	0.0475460	+	0.158815i
$498$		0			0
$499$	−0.320759	−	5.50722i	−0.0143592	−	0.246537i	−0.997848	−	0.0655687i	$-0.979114\pi$
$499$	−0.320759	−	5.50722i	−0.0143592	−	0.246537i	0.983489	−	0.180968i	$-0.0579232\pi$
$500$	−6.10350	−	3.06529i	−0.272957	−	0.137084i
$501$		0			0
$502$	−7.35016	+	7.79071i	−0.328054	+	0.347717i
$503$	−31.2754	−	11.3833i	−1.39450	−	0.507557i	−0.467959	−	0.883750i	$-0.655011\pi$
$503$	−31.2754	−	11.3833i	−1.39450	−	0.507557i	−0.926541	+	0.376193i	$0.877233\pi$
$504$		0			0
$505$	−7.44341	+	2.70918i	−0.331227	+	0.120557i
$506$	1.03586	−	2.40139i	0.0460495	−	0.106755i
$507$		0			0
$508$	2.75550	−	9.20402i	0.122256	−	0.408362i
$509$	21.9142	+	2.56140i	0.971328	+	0.113532i	0.586932	−	0.809636i	$-0.300336\pi$
$509$	21.9142	+	2.56140i	0.971328	+	0.113532i	0.384396	+	0.923168i	$0.374410\pi$
$510$		0			0
$511$	−0.106951	+	1.83628i	−0.00473124	+	0.0812323i
$512$	−8.09134	+	14.0146i	−0.357590	+	0.619364i
$513$		0			0
$514$	−4.89144	−	8.47222i	−0.215752	−	0.373694i
$515$	−11.1818	+	5.61570i	−0.492728	+	0.247457i
$516$		0			0
$517$	−2.21496	+	2.97520i	−0.0974137	+	0.130849i
$518$	−2.11879	+	0.502162i	−0.0930942	+	0.0220637i
$519$		0			0
$520$	−8.70114	−	11.6877i	−0.381570	−	0.512538i
$521$	21.4866	+	18.0294i	0.941345	+	0.789882i	0.977819	−	0.209453i	$-0.0671682\pi$
$521$	21.4866	+	18.0294i	0.941345	+	0.789882i	−0.0364742	+	0.999335i	$0.511613\pi$
$522$		0			0
$523$	−6.29841	+	5.28500i	−0.275410	+	0.231097i	−0.770022	−	0.638017i	$-0.779755\pi$
$523$	−6.29841	+	5.28500i	−0.275410	+	0.231097i	0.494612	+	0.869114i	$0.335310\pi$
$524$	−0.231712	−	0.0549167i	−0.0101224	−	0.00239905i
$525$		0			0
$526$	−21.1730	+	13.9257i	−0.923186	+	0.607189i
$527$	−16.7635	+	11.0255i	−0.730229	+	0.480279i
$528$		0			0
$529$	−20.5927	−	4.88057i	−0.895337	−	0.212199i
$530$	2.14969	−	1.80381i	0.0933766	−	0.0783523i
$531$		0			0
$532$	0.353491	+	0.296614i	0.0153258	+	0.0128598i
$533$	−38.3153	−	51.4664i	−1.65962	−	2.22926i
$534$		0			0
$535$	0.0625308	−	0.0148201i	0.00270344	−	0.000640728i
$536$	−11.4501	+	15.3802i	−0.494569	+	0.664322i
$537$		0			0
$538$	6.38625	−	3.20729i	0.275331	−	0.138276i
$539$	6.25951	+	10.8418i	0.269616	+	0.466989i
$540$		0			0
$541$	0.833782	−	1.44415i	0.0358471	−	0.0620889i	−0.847545	−	0.530723i	$-0.821920\pi$
$541$	0.833782	−	1.44415i	0.0358471	−	0.0620889i	0.883392	+	0.468634i	$0.155254\pi$
$542$	−0.588390	+	10.1023i	−0.0252735	+	0.433930i
$543$		0			0
$544$	−20.9483	−	2.44850i	−0.898150	−	0.104979i
$545$	1.29572	−	4.32801i	0.0555025	−	0.185391i
$546$		0			0
$547$	7.06785	−	16.3851i	0.302199	−	0.700577i	−0.697675	−	0.716414i	$-0.745782\pi$
$547$	7.06785	−	16.3851i	0.302199	−	0.700577i	0.999875	+	0.0158373i	$0.00504139\pi$
$548$	8.54475	−	3.11003i	0.365013	−	0.132854i
$549$		0			0
$550$	−7.74498	−	2.81894i	−0.330247	−	0.120200i
$551$	−7.67098	+	8.13076i	−0.326795	+	0.346382i
$552$		0			0
$553$	−1.82390	−	0.915996i	−0.0775600	−	0.0389521i
$554$	−0.0859560	−	1.47581i	−0.00365192	−	0.0627010i
$555$		0			0
$556$	0.134119	+	0.447988i	0.00568790	+	0.0189989i
$557$	3.03540	+	17.2146i	0.128614	+	0.729407i	0.979095	+	0.203402i	$0.0651997\pi$
$557$	3.03540	+	17.2146i	0.128614	+	0.729407i	−0.850481	+	0.526005i	$0.823689\pi$
$558$		0			0
$559$	12.3485	−	70.0317i	0.522285	−	2.96203i
$560$	0.371490	−	0.0434210i	0.0156983	−	0.00183487i
$561$		0			0
$562$	11.7178	+	12.4201i	0.494285	+	0.523912i
$563$	13.6909	+	31.7390i	0.577002	+	1.33764i	0.917628	+	0.397441i	$0.130102\pi$
$563$	13.6909	+	31.7390i	0.577002	+	1.33764i	−0.340626	+	0.940199i	$0.610639\pi$
$564$		0			0
$565$	−13.2076	−	8.68681i	−0.555650	−	0.365457i
$566$	0.334965			0.0140796
$567$		0			0
$568$	39.3890			1.65273
$569$	−21.3130	−	14.0178i	−0.893489	−	0.587657i	0.0176099	−	0.999845i	$-0.494394\pi$
$569$	−21.3130	−	14.0178i	−0.893489	−	0.587657i	−0.911099	+	0.412188i	$0.864765\pi$
$570$		0			0
$571$	8.79169	+	20.3814i	0.367921	+	0.852936i	0.997131	+	0.0757007i	$0.0241194\pi$
$571$	8.79169	+	20.3814i	0.367921	+	0.852936i	−0.629210	+	0.777235i	$0.716621\pi$
$572$	5.99126	+	6.35036i	0.250507	+	0.265522i
$573$		0			0
$574$	3.48172	−	0.406955i	0.145324	−	0.0169860i
$575$	1.00519	−	5.70073i	0.0419194	−	0.237737i
$576$		0			0
$577$	−3.76924	−	21.3764i	−0.156915	−	0.889911i	−0.957014	−	0.290042i	$-0.906331\pi$
$577$	−3.76924	−	21.3764i	−0.156915	−	0.889911i	0.800098	−	0.599869i	$-0.204781\pi$
$578$	1.59504	+	5.32779i	0.0663448	+	0.221607i
$579$		0			0
$580$	−0.256483	−	4.40364i	−0.0106499	−	0.182851i
$581$	3.47003	+	1.74272i	0.143961	+	0.0723000i
$582$		0			0
$583$	−3.82815	+	4.05760i	−0.158546	+	0.168049i
$584$	18.4216	+	6.70492i	0.762292	+	0.277452i
$585$		0			0
$586$	18.7006	−	6.80646i	0.772515	−	0.281172i
$587$	−8.05782	+	18.6801i	−0.332582	+	0.771012i	0.667079	+	0.744987i	$0.267544\pi$
$587$	−8.05782	+	18.6801i	−0.332582	+	0.771012i	−0.999661	+	0.0260249i	$0.991715\pi$
$588$		0			0
$589$	2.27925	−	7.61323i	0.0939149	−	0.313698i
$590$	1.14050	+	0.133306i	0.0469538	+	0.00548811i
$591$		0			0
$592$	−0.633990	+	10.8852i	−0.0260568	+	0.447378i
$593$	0.579087	−	1.00301i	0.0237803	−	0.0411886i	−0.853890	−	0.520453i	$-0.825763\pi$
$593$	0.579087	−	1.00301i	0.0237803	−	0.0411886i	0.877671	+	0.479264i	$0.159096\pi$
$594$		0			0
$595$	0.576294	+	0.998171i	0.0236258	+	0.0409210i
$596$	15.1478	−	7.60752i	0.620479	−	0.311616i
$597$		0			0
$598$	4.82488	−	6.48094i	0.197304	−	0.265025i
$599$	−44.1467	+	10.4629i	−1.80378	+	0.427505i	−0.988458	−	0.151498i	$-0.951590\pi$
$599$	−44.1467	+	10.4629i	−1.80378	+	0.427505i	−0.815326	+	0.579002i	$0.803442\pi$
$600$		0			0
$601$	−19.5190	−	26.2185i	−0.796195	−	1.06948i	−0.995975	−	0.0896345i	$-0.971430\pi$
$601$	−19.5190	−	26.2185i	−0.796195	−	1.06948i	0.199780	−	0.979841i	$-0.435977\pi$
$602$	2.97615	+	2.49729i	0.121299	+	0.101782i
$603$		0			0
$604$	−9.80464	+	8.22707i	−0.398945	+	0.334755i
$605$	6.41729	+	1.52093i	0.260900	+	0.0618344i
$606$		0			0
$607$	−0.512985	+	0.337395i	−0.0208214	+	0.0136945i	−0.559877	−	0.828576i	$-0.689152\pi$
$607$	−0.512985	+	0.337395i	−0.0208214	+	0.0136945i	0.539056	+	0.842270i	$0.318781\pi$
$608$	6.97941	−	4.59043i	0.283052	−	0.186167i
$609$		0			0
$610$	2.45435	+	0.581691i	0.0993736	+	0.0235520i
$611$	−8.77827	+	7.36585i	−0.355131	+	0.297990i
$612$		0			0
$613$	−15.6352	−	13.1195i	−0.631499	−	0.529891i	0.269895	−	0.962890i	$-0.413011\pi$
$613$	−15.6352	−	13.1195i	−0.631499	−	0.529891i	−0.901394	+	0.432999i	$0.857455\pi$
$614$	17.2401	+	23.1574i	0.695752	+	0.934557i
$615$		0			0
$616$	−1.53981	+	0.364942i	−0.0620407	+	0.0147039i
$617$	5.77352	−	7.75518i	0.232433	−	0.312212i	−0.670570	−	0.741847i	$-0.733950\pi$
$617$	5.77352	−	7.75518i	0.232433	−	0.312212i	0.903003	+	0.429635i	$0.141358\pi$
$618$		0			0
$619$	−24.0046	+	12.0556i	−0.964828	+	0.484555i	−0.860200	−	0.509957i	$-0.829661\pi$
$619$	−24.0046	+	12.0556i	−0.964828	+	0.484555i	−0.104628	+	0.994511i	$0.533365\pi$
$620$	1.56802	+	2.71589i	0.0629732	+	0.109073i
$621$		0			0
$622$	−6.60160	+	11.4343i	−0.264700	+	0.458474i
$623$	−0.00719746	+	0.123576i	−0.000288360	+	0.00495095i
$624$		0			0
$625$	−14.5002	−	1.69483i	−0.580008	−	0.0677932i
$626$	−6.56393	+	21.9251i	−0.262347	+	0.876302i
$627$		0			0
$628$	−1.99623	+	4.62778i	−0.0796581	+	0.184668i
$629$	−31.5746	+	11.4922i	−1.25896	+	0.458224i
$630$		0			0
$631$	29.6208	+	10.7811i	1.17918	+	0.429188i	0.855914	−	0.517119i	$-0.172996\pi$
$631$	29.6208	+	10.7811i	1.17918	+	0.429188i	0.323270	+	0.946307i	$0.395218\pi$
$632$	−14.9275	+	15.8222i	−0.593782	+	0.629372i
$633$		0			0
$634$	22.4941	+	11.2969i	0.893354	+	0.448659i
$635$	0.552665	+	9.48889i	0.0219318	+	0.376555i
$636$		0			0
$637$	11.0926	+	37.0519i	0.439505	+	1.46805i
$638$	−2.00641	−	11.3789i	−0.0794344	−	0.450495i
$639$		0			0
$640$	−0.0888692	+	0.504002i	−0.00351286	+	0.0199224i
$641$	11.2656	−	1.31676i	0.444965	−	0.0520089i	0.109339	−	0.994004i	$-0.465126\pi$
$641$	11.2656	−	1.31676i	0.444965	−	0.0520089i	0.335625	+	0.941996i	$0.391052\pi$
$642$		0			0
$643$	−9.07210	−	9.61586i	−0.357769	−	0.379213i	0.523342	−	0.852123i	$-0.324685\pi$
$643$	−9.07210	−	9.61586i	−0.357769	−	0.379213i	−0.881111	+	0.472910i	$0.843204\pi$
$644$	−0.132686	−	0.307601i	−0.00522857	−	0.0121212i
$645$		0			0
$646$	−7.83922	−	5.15594i	−0.308430	−	0.202858i
$647$	−36.5943			−1.43867			−0.719336	−	0.694663i	$-0.755554\pi$
$647$	−36.5943			−1.43867			−0.719336	+	0.694663i	$0.755554\pi$
$648$		0			0
$649$	−2.28261			−0.0896005
$650$	−21.2743	−	13.9923i	−0.834445	−	0.548823i
$651$		0			0
$652$	2.35488	+	5.45923i	0.0922244	+	0.213800i
$653$	−18.7327	−	19.8555i	−0.733069	−	0.777008i	0.248394	−	0.968659i	$-0.420097\pi$
$653$	−18.7327	−	19.8555i	−0.733069	−	0.777008i	−0.981463	+	0.191651i	$0.938616\pi$
$654$		0			0
$655$	0.233993	−	0.0273499i	0.00914287	−	0.00106865i
$656$	3.04809	−	17.2866i	0.119008	−	0.674928i
$657$		0			0
$658$	−0.108714	−	0.616545i	−0.00423809	−	0.0240354i
$659$	4.23303	+	14.1393i	0.164895	+	0.550789i	1.00000		0.000697383i	$0.000221984\pi$
$659$	4.23303	+	14.1393i	0.164895	+	0.550789i	−0.835104	+	0.550091i	$0.814593\pi$
$660$		0			0
$661$	1.61762	+	27.7734i	0.0629181	+	1.08026i	0.871029	+	0.491232i	$0.163453\pi$
$661$	1.61762	+	27.7734i	0.0629181	+	1.08026i	−0.808111	+	0.589030i	$0.799510\pi$
$662$	0.807887	+	0.405736i	0.0313994	+	0.0157694i
$663$		0			0
$664$	28.4000	−	30.1023i	1.10214	−	1.16820i
$665$	−0.428987	−	0.156138i	−0.0166354	−	0.00605479i
$666$		0			0
$667$	7.62568	−	2.77552i	0.295267	−	0.107469i
$668$	6.06466	−	14.0595i	0.234649	−	0.543977i
$669$		0			0
$670$	1.63984	−	5.47746i	0.0633527	−	0.211613i
$671$	−4.98019	−	0.582101i	−0.192258	−	0.0224718i
$672$		0			0
$673$	−1.91225	+	32.8321i	−0.0737118	+	1.26558i	0.735280	+	0.677763i	$0.237051\pi$
$673$	−1.91225	+	32.8321i	−0.0737118	+	1.26558i	−0.808992	+	0.587820i	$0.799986\pi$
$674$	1.08967	−	1.88737i	0.0419727	−	0.0726989i
$675$		0			0
$676$	7.87718	+	13.6437i	0.302968	+	0.524757i
$677$	−21.5460	+	10.8208i	−0.828081	+	0.415878i	−0.811762	−	0.583989i	$-0.801491\pi$
$677$	−21.5460	+	10.8208i	−0.828081	+	0.415878i	−0.0163192	+	0.999867i	$0.505195\pi$
$678$		0			0
$679$	−1.72610	+	2.31855i	−0.0662416	+	0.0889779i
$680$	11.9529	−	2.83290i	0.458374	−	0.108637i
$681$		0			0
$682$	4.90538	+	6.58907i	0.187837	+	0.252308i
$683$	−10.1873	−	8.54816i	−0.389806	−	0.327086i	0.426731	−	0.904378i	$-0.359665\pi$
$683$	−10.1873	−	8.54816i	−0.389806	−	0.327086i	−0.816538	+	0.577292i	$0.804109\pi$
$684$		0			0
$685$	−6.89130	+	5.78249i	−0.263303	+	0.220938i
$686$	−4.13656	−	0.980382i	−0.157934	−	0.0374311i
$687$		0			0
$688$	16.2539	−	10.6904i	0.619675	−	0.407567i
$689$	−14.3990	+	9.47035i	−0.548557	+	0.360792i
$690$		0			0
$691$	−42.6555	−	10.1095i	−1.62269	−	0.384585i	−0.684038	−	0.729447i	$-0.739778\pi$
$691$	−42.6555	−	10.1095i	−1.62269	−	0.384585i	−0.938654	+	0.344862i	$0.887926\pi$
$692$	−9.24612	+	7.75841i	−0.351485	+	0.294931i
$693$		0			0
$694$	5.31231	+	4.45756i	0.201653	+	0.169207i
$695$	−0.276267	−	0.371091i	−0.0104794	−	0.0140763i
$696$		0			0
$697$	52.6345	−	12.4746i	1.99367	−	0.472510i
$698$	−4.21593	+	5.66297i	−0.159575	+	0.214347i
$699$		0			0
$700$	−0.943452	+	0.473819i	−0.0356591	+	0.0179087i
$701$	−3.65194	−	6.32534i	−0.137932	−	0.238905i	0.788782	−	0.614673i	$-0.210712\pi$
$701$	−3.65194	−	6.32534i	−0.137932	−	0.238905i	−0.926714	+	0.375768i	$0.877379\pi$
$702$		0			0
$703$	6.65434	−	11.5257i	0.250973	−	0.434699i
$704$	−0.823941	+	14.1465i	−0.0310535	+	0.533167i
$705$		0			0
$706$	−0.320133	−	0.0374181i	−0.0120484	−	0.00140825i
$707$	−0.762251	+	2.54609i	−0.0286674	+	0.0957558i
$708$		0			0
$709$	−17.3188	+	40.1494i	−0.650420	+	1.50784i	0.198931	+	0.980014i	$0.436253\pi$
$709$	−17.3188	+	40.1494i	−0.650420	+	1.50784i	−0.849350	+	0.527829i	$0.823006\pi$
$710$	−11.0372	+	4.01722i	−0.414219	+	0.150764i
$711$		0			0
$712$	1.23971	+	0.451219i	0.0464602	+	0.0169101i
$713$	−3.95917	+	4.19647i	−0.148272	+	0.157159i
$714$		0			0
$715$	−7.71852	−	3.87638i	−0.288656	−	0.144969i
$716$	−0.526080	−	9.03245i	−0.0196605	−	0.337558i
$717$		0			0
$718$	1.25556	+	4.19385i	0.0468569	+	0.156513i
$719$	−1.93615	−	10.9804i	−0.0722061	−	0.409501i	−0.999391	−	0.0348968i	$-0.988890\pi$
$719$	−1.93615	−	10.9804i	−0.0722061	−	0.409501i	0.927185	−	0.374604i	$-0.122221\pi$
$720$		0			0
$721$	−0.729037	+	4.13457i	−0.0271508	+	0.153980i
$722$	−16.4321	+	1.92064i	−0.611541	+	0.0714789i
$723$		0			0
$724$	−7.34856	−	7.78902i	−0.273107	−	0.289477i
$725$	−10.1296	−	23.4831i	−0.376204	−	0.872140i
$726$		0			0
$727$	−24.3067	−	15.9867i	−0.901484	−	0.592916i	0.0119379	−	0.999929i	$-0.496200\pi$
$727$	−24.3067	−	15.9867i	−0.901484	−	0.592916i	−0.913422	+	0.407013i	$0.866570\pi$
$728$	−4.88893			−0.181196
$729$		0			0
$730$	−5.84576			−0.216361
$731$	50.0886	+	32.9438i	1.85259	+	1.21847i
$732$		0			0
$733$	6.87604	+	15.9405i	0.253972	+	0.588774i	0.996732	−	0.0807844i	$-0.0257425\pi$
$733$	6.87604	+	15.9405i	0.253972	+	0.588774i	−0.742759	+	0.669559i	$0.766483\pi$
$734$	−6.58210	−	6.97662i	−0.242950	−	0.257512i
$735$		0			0
$736$	−6.02353	+	0.704050i	−0.222030	+	0.0259516i
$737$	−1.97369	+	11.1933i	−0.0727017	+	0.412312i
$738$		0			0
$739$	3.59215	+	20.3721i	0.132139	+	0.749400i	0.976809	+	0.214112i	$0.0686857\pi$
$739$	3.59215	+	20.3721i	0.132139	+	0.749400i	−0.844670	+	0.535288i	$0.820203\pi$
$740$	1.50623	+	5.03117i	0.0553703	+	0.184950i
$741$		0			0
$742$	−0.0547471	−	0.939971i	−0.00200983	−	0.0345074i
$743$	−34.0508	−	17.1009i	−1.24920	−	0.627373i	−0.303632	−	0.952790i	$-0.598199\pi$
$743$	−34.0508	−	17.1009i	−1.24920	−	0.627373i	−0.945571	+	0.325417i	$0.894495\pi$
$744$		0			0
$745$	−11.5081	+	12.1978i	−0.421623	+	0.446894i
$746$	5.27104	+	1.91850i	0.192986	+	0.0702413i
$747$		0			0
$748$	−6.91643	+	2.51737i	−0.252890	+	0.0920443i
$749$	0.00854027	−	0.0197986i	0.000312055	−	0.000723424i
$750$		0			0
$751$	−9.82318	+	32.8117i	−0.358453	+	1.19732i	0.568672	+	0.822564i	$0.307457\pi$
$751$	−9.82318	+	32.8117i	−0.358453	+	1.19732i	−0.927125	+	0.374752i	$0.877728\pi$
$752$	−3.11375	−	0.363945i	−0.113547	−	0.0132717i
$753$		0			0
$754$	2.07558	−	35.6363i	0.0755881	−	1.29780i
$755$	6.33114	−	10.9659i	0.230414	−	0.399088i
$756$		0			0
$757$	−14.5877	−	25.2666i	−0.530198	−	0.918330i	−0.999379	−	0.0352284i	$-0.988784\pi$
$757$	−14.5877	−	25.2666i	−0.530198	−	0.918330i	0.469181	−	0.883102i	$-0.344549\pi$
$758$	−7.17966	+	3.60576i	−0.260777	+	0.130967i
$759$		0			0
$760$	−2.90546	+	3.90271i	−0.105392	+	0.141566i
$761$	12.0070	−	2.84572i	0.435255	−	0.103157i	−0.00714662	−	0.999974i	$-0.502275\pi$
$761$	12.0070	−	2.84572i	0.435255	−	0.103157i	0.442401	+	0.896817i	$0.354127\pi$
$762$		0			0
$763$	−0.905200	−	1.21589i	−0.0327704	−	0.0440183i
$764$	9.34155	+	7.83849i	0.337965	+	0.283587i
$765$		0			0
$766$	29.0983	−	24.4163i	1.05136	−	0.882198i
$767$	−6.86191	−	1.62630i	−0.247769	−	0.0587224i
$768$		0			0
$769$	−2.31777	+	1.52442i	−0.0835810	+	0.0549721i	−0.590612	−	0.806956i	$-0.701113\pi$
$769$	−2.31777	+	1.52442i	−0.0835810	+	0.0549721i	0.507031	+	0.861928i	$0.330743\pi$
$770$	0.394251	−	0.259303i	0.0142078	−	0.00934464i
$771$		0			0
$772$	−18.5150	−	4.38813i	−0.666369	−	0.157932i
$773$	−21.3606	+	17.9237i	−0.768287	+	0.644669i	−0.940270	−	0.340431i	$-0.889427\pi$
$773$	−21.3606	+	17.9237i	−0.768287	+	0.644669i	0.171983	+	0.985100i	$0.444983\pi$
$774$		0			0
$775$	13.9283	+	11.6872i	0.500320	+	0.419818i
$776$	18.3964	+	24.7107i	0.660392	+	0.887061i
$777$		0			0
$778$	−13.1391	+	3.11402i	−0.471059	+	0.111643i
$779$	−12.7941	+	17.1855i	−0.458398	+	0.615735i
$780$		0			0
$781$	20.8652	−	10.4789i	0.746616	−	0.374964i
$782$	3.40582	+	5.89906i	0.121792	+	0.210950i
$783$		0			0
$784$	−5.29048	+	9.16338i	−0.188946	+	0.327263i
$785$	0.289916	−	4.97767i	0.0103476	−	0.177661i
$786$		0			0
$787$	1.39131	+	0.162621i	0.0495950	+	0.00579682i	0.140854	−	0.990030i	$-0.455015\pi$
$787$	1.39131	+	0.162621i	0.0495950	+	0.00579682i	−0.0912592	+	0.995827i	$0.529089\pi$
$788$	−0.415603	+	1.38821i	−0.0148052	+	0.0494530i
$789$		0			0
$790$	2.56915	−	5.95597i	0.0914064	−	0.211904i
$791$	−4.98424	+	1.81411i	−0.177219	+	0.0645025i
$792$		0			0
$793$	−14.5565	−	5.29815i	−0.516918	−	0.188143i
$794$	7.94778	−	8.42415i	0.282056	−	0.298962i
$795$		0			0
$796$	−8.23503	−	4.13579i	−0.291883	−	0.146589i
$797$	0.651880	+	11.1924i	0.0230908	+	0.396453i	0.989975	+	0.141240i	$0.0451088\pi$
$797$	0.651880	+	11.1924i	0.0230908	+	0.396453i	−0.966885	+	0.255214i	$0.917854\pi$
$798$		0			0
$799$	−2.77073	−	9.25489i	−0.0980214	−	0.327414i
$800$	3.31883	+	18.8220i	0.117338	+	0.665460i
$801$		0			0
$802$	−1.06268	+	6.02674i	−0.0375244	+	0.212812i
$803$	11.5421	−	1.34908i	0.407311	−	0.0476078i
$804$		0			0
$805$	0.227433	+	0.241065i	0.00801597	+	0.00849643i
$806$	10.0518	+	23.3028i	0.354061	+	0.820805i
$807$		0			0
$808$	23.6658	+	15.5652i	0.832560	+	0.547583i
$809$	2.44943			0.0861173			0.0430587	−	0.999073i	$-0.486290\pi$
$809$	2.44943			0.0861173			0.0430587	+	0.999073i	$0.486290\pi$
$810$		0			0
$811$	11.9053			0.418050			0.209025	−	0.977910i	$-0.432971\pi$
$811$	11.9053			0.418050			0.209025	+	0.977910i	$0.432971\pi$
$812$	−1.23656	−	0.813297i	−0.0433947	−	0.0285411i
$813$		0			0
$814$	5.44870	+	12.6315i	0.190977	+	0.442734i
$815$	−4.03644	−	4.27837i	−0.141390	−	0.149865i
$816$		0			0
$817$	−23.5850	+	2.75669i	−0.825135	+	0.0964444i
$818$	5.47372	−	31.0430i	0.191384	−	1.08539i
$819$		0			0
$820$	−1.46813	−	8.32619i	−0.0512694	−	0.290763i
$821$	−6.96784	−	23.2742i	−0.243179	−	0.812275i	−0.989228	−	0.146384i	$-0.953237\pi$
$821$	−6.96784	−	23.2742i	−0.243179	−	0.812275i	0.746049	−	0.665891i	$-0.231949\pi$
$822$		0			0
$823$	−1.80431	−	30.9788i	−0.0628944	−	1.07985i	−0.871148	−	0.491020i	$-0.836624\pi$
$823$	−1.80431	−	30.9788i	−0.0628944	−	1.07985i	0.808254	−	0.588834i	$-0.200413\pi$
$824$	39.9858	+	20.0816i	1.39297	+	0.699576i
$825$		0			0
$826$	0.264392	−	0.280239i	0.00919936	−	0.00975075i
$827$	9.52144	+	3.46552i	0.331093	+	0.120508i	0.502217	−	0.864741i	$-0.332518\pi$
$827$	9.52144	+	3.46552i	0.331093	+	0.120508i	−0.171124	+	0.985249i	$0.554740\pi$
$828$		0			0
$829$	−16.7991	+	6.11438i	−0.583458	+	0.212361i	−0.616850	−	0.787081i	$-0.711591\pi$
$829$	−16.7991	+	6.11438i	−0.583458	+	0.212361i	0.0333918	+	0.999442i	$0.489369\pi$
$830$	−4.88791	+	11.3315i	−0.169662	+	0.393320i
$831$		0			0
$832$	−12.5559	+	41.9397i	−0.435298	+	1.45400i
$833$	−32.3861	−	3.78539i	−1.12211	−	0.131156i
$834$		0			0
$835$	−0.880782	+	15.1224i	−0.0304807	+	0.523334i
$836$	1.45764	−	2.52470i	0.0504135	−	0.0873187i
$837$		0			0
$838$	−4.76371	−	8.25099i	−0.164560	−	0.285026i
$839$	22.0336	−	11.0657i	0.760685	−	0.382030i	−0.0257780	−	0.999668i	$-0.508206\pi$
$839$	22.0336	−	11.0657i	0.760685	−	0.382030i	0.786463	+	0.617637i	$0.211910\pi$
$840$		0			0
$841$	4.09225	−	5.49684i	0.141112	−	0.189546i
$842$	−2.62722	+	0.622662i	−0.0905399	+	0.0214583i
$843$		0			0
$844$	5.38327	+	7.23098i	0.185300	+	0.248901i
$845$	−11.9396	−	10.0185i	−0.410734	−	0.344647i
$846$		0			0
$847$	1.69512	−	1.42237i	0.0582450	−	0.0488734i
$848$	−4.58775	−	1.08732i	−0.157544	−	0.0373386i
$849$		0			0
$850$	17.9353	−	11.7963i	0.615177	−	0.404608i
$851$	−8.07225	+	5.30920i	−0.276713	+	0.181997i
$852$		0			0
$853$	2.02471	+	0.479866i	0.0693249	+	0.0164303i	0.265132	−	0.964212i	$-0.414584\pi$
$853$	2.02471	+	0.479866i	0.0693249	+	0.0164303i	−0.195807	+	0.980642i	$0.562733\pi$
$854$	0.648313	−	0.543999i	0.0221848	−	0.0186153i
$855$		0			0
$856$	−0.176040	−	0.147715i	−0.00601691	−	0.00504879i
$857$	−7.38060	−	9.91387i	−0.252117	−	0.338651i	0.657989	−	0.753027i	$-0.271407\pi$
$857$	−7.38060	−	9.91387i	−0.252117	−	0.338651i	−0.910106	+	0.414376i	$0.864000\pi$
$858$		0			0
$859$	−38.1158	+	9.03362i	−1.30050	+	0.308223i	−0.821809	−	0.569763i	$-0.807035\pi$
$859$	−38.1158	+	9.03362i	−1.30050	+	0.308223i	−0.478686	+	0.877986i	$0.658887\pi$
$860$	5.59558	−	7.51617i	0.190808	−	0.256299i
$861$		0			0
$862$	−28.3193	+	14.2225i	−0.964560	+	0.484420i
$863$	12.2220	+	21.1691i	0.416040	+	0.720603i	0.995537	−	0.0943715i	$-0.0300842\pi$
$863$	12.2220	+	21.1691i	0.416040	+	0.720603i	−0.579497	+	0.814975i	$0.696751\pi$
$864$		0			0
$865$	5.97048	−	10.3412i	0.203003	−	0.351611i
$866$	−0.0760135	+	1.30510i	−0.00258304	+	0.0443491i
$867$		0			0
$868$	1.04511	+	0.122156i	0.0354734	+	0.00414624i
$869$	−3.69812	+	12.3526i	−0.125450	+	0.419033i
$870$		0			0
$871$	−13.9082	+	32.2428i	−0.471261	+	1.09251i
$872$	−15.1813	+	5.52553i	−0.514102	+	0.187118i
$873$		0			0
$874$	−2.53525	−	0.922757i	−0.0857563	−	0.0312127i
$875$	1.55582	−	1.64907i	0.0525962	−	0.0557488i
$876$		0			0
$877$	−12.1192	−	6.08649i	−0.409236	−	0.205526i	0.232258	−	0.972654i	$-0.425389\pi$
$877$	−12.1192	−	6.08649i	−0.409236	−	0.205526i	−0.641494	+	0.767128i	$0.721685\pi$
$878$	−1.07629	−	18.4793i	−0.0363232	−	0.623645i
$879$		0			0
$880$	−0.677694	−	2.26366i	−0.0228451	−	0.0763079i
$881$	−2.84380	−	16.1280i	−0.0958101	−	0.543366i	−0.994496	−	0.104774i	$-0.966588\pi$
$881$	−2.84380	−	16.1280i	−0.0958101	−	0.543366i	0.898686	−	0.438593i	$-0.144523\pi$
$882$		0			0
$883$	−7.98860	+	45.3056i	−0.268838	+	1.52465i	0.489042	+	0.872260i	$0.337347\pi$
$883$	−7.98860	+	45.3056i	−0.268838	+	1.52465i	−0.757880	+	0.652394i	$0.773765\pi$
$884$	−22.5855	+	2.63986i	−0.759631	+	0.0887882i
$885$		0			0
$886$	−8.77015	−	9.29581i	−0.294639	−	0.312299i
$887$	−19.5768	−	45.3842i	−0.657325	−	1.52385i	−0.841098	−	0.540882i	$-0.818090\pi$
$887$	−19.5768	−	45.3842i	−0.657325	−	1.52385i	0.183773	−	0.982969i	$-0.441169\pi$
$888$		0			0
$889$	2.66452	+	1.75248i	0.0893651	+	0.0587763i
$890$	−0.393400			−0.0131868
$891$		0			0
$892$	−11.7641			−0.393892
$893$	3.19694	+	2.10266i	0.106981	+	0.0703628i
$894$		0			0
$895$	3.54534	+	8.21901i	0.118508	+	0.274731i
$896$	0.117838	+	0.124901i	0.00393669	+	0.00417265i
$897$		0			0
$898$	20.7409	−	2.42427i	0.692133	−	0.0808988i
$899$	−4.42618	+	25.1021i	−0.147621	+	0.837201i
$900$		0			0
$901$	−2.52300	−	14.3086i	−0.0840532	−	0.476690i
$902$	−6.35156	−	21.2157i	−0.211484	−	0.706406i
$903$		0			0
$904$	3.28694	+	56.4345i	0.109322	+	1.87698i
$905$	9.46713	+	4.75457i	0.314698	+	0.158047i
$906$		0			0
$907$	32.8053	−	34.7716i	1.08928	−	1.15457i	0.102134	−	0.994771i	$-0.467433\pi$
$907$	32.8053	−	34.7716i	1.08928	−	1.15457i	0.987149	−	0.159802i	$-0.0510856\pi$
$908$	−10.6226	−	3.86630i	−0.352523	−	0.128308i
$909$		0			0
$910$	1.36993	−	0.498614i	0.0454127	−	0.0165289i
$911$	−13.1560	+	30.4989i	−0.435876	+	1.01047i	0.548780	+	0.835967i	$0.315093\pi$
$911$	−13.1560	+	30.4989i	−0.435876	+	1.01047i	−0.984656	+	0.174508i	$0.944167\pi$
$912$		0			0
$913$	7.03582	−	23.5013i	0.232852	−	0.777778i
$914$	25.4372	+	2.97318i	0.841387	+	0.0983441i
$915$		0			0
$916$	0.0865461	−	1.48594i	0.00285956	−	0.0490968i
$917$	0.0395228	−	0.0684554i	0.00130516	−	0.00226060i
$918$		0			0
$919$	13.4983	+	23.3798i	0.445268	+	0.771228i	0.998071	−	0.0620848i	$-0.0197749\pi$
$919$	13.4983	+	23.3798i	0.445268	+	0.771228i	−0.552802	+	0.833312i	$0.686442\pi$
$920$	3.15648	−	1.58525i	0.104066	−	0.0522640i
$921$		0			0
$922$	9.02111	−	12.1175i	0.297094	−	0.399067i
$923$	70.1901	−	16.6354i	2.31034	−	0.547560i
$924$		0			0
$925$	18.1828	+	24.4238i	0.597848	+	0.803049i
$926$	8.99236	+	7.54549i	0.295507	+	0.247960i
$927$		0			0
$928$	−20.5250	+	17.2225i	−0.673766	+	0.565357i
$929$	0.850096	+	0.201476i	0.0278907	+	0.00661023i	0.244538	−	0.969640i	$-0.421364\pi$
$929$	0.850096	+	0.201476i	0.0278907	+	0.00661023i	−0.216647	+	0.976250i	$0.569512\pi$
$930$		0			0
$931$	10.7902	−	7.09682i	0.353634	−	0.232589i
$932$	−17.4877	+	11.5018i	−0.572828	+	0.376755i
$933$		0			0
$934$	40.4318	+	9.58252i	1.32297	+	0.313550i
$935$	5.57807	−	4.68056i	0.182422	−	0.153071i
$936$		0			0
$937$	12.6271	+	10.5954i	0.412511	+	0.346138i	0.825306	−	0.564686i	$-0.191003\pi$
$937$	12.6271	+	10.5954i	0.412511	+	0.346138i	−0.412795	+	0.910824i	$0.635447\pi$
$938$	−1.14561	−	1.53882i	−0.0374054	−	0.0502442i
$939$		0			0
$940$	−1.46927	+	0.348222i	−0.0479222	+	0.0113578i
$941$	18.1527	−	24.3833i	0.591760	−	0.794872i	−0.400860	−	0.916140i	$-0.631288\pi$
$941$	18.1527	−	24.3833i	0.591760	−	0.794872i	0.992620	+	0.121267i	$0.0386959\pi$
$942$		0			0
$943$	13.8995	−	6.98060i	0.452631	−	0.227320i
$944$	−0.964622	−	1.67077i	−0.0313958	−	0.0543791i
$945$		0			0
$946$	12.2723	−	21.2563i	0.399008	−	0.691102i
$947$	0.743799	−	12.7705i	0.0241702	−	0.414987i	−0.964422	−	0.264368i	$-0.914837\pi$
$947$	0.743799	−	12.7705i	0.0241702	−	0.414987i	0.988592	−	0.150618i	$-0.0481265\pi$
$948$		0			0
$949$	35.6585	+	4.16789i	1.15753	+	0.135295i
$950$	−2.43858	+	8.14543i	−0.0791181	+	0.264273i
$951$		0			0
$952$	1.63249	−	3.78455i	0.0529095	−	0.122658i
$953$	−28.8328	+	10.4943i	−0.933986	+	0.339943i	−0.763788	−	0.645467i	$-0.776663\pi$
$953$	−28.8328	+	10.4943i	−0.933986	+	0.339943i	−0.170198	+	0.985410i	$0.554441\pi$
$954$		0			0
$955$	−11.3367	−	4.12620i	−0.366845	−	0.133521i
$956$	13.1135	−	13.8995i	0.424121	−	0.449542i
$957$		0			0
$958$	−13.4557	−	6.75771i	−0.434734	−	0.218332i
$959$	0.175504	+	3.01328i	0.00566731	+	0.0973039i
$960$		0			0
$961$	3.69361	+	12.3375i	0.119149	+	0.397985i
$962$	7.38006	+	41.8544i	0.237943	+	1.34944i
$963$		0			0
$964$	2.70821	−	15.3590i	0.0872257	−	0.494681i
$965$	18.6973	−	2.18540i	0.601886	−	0.0703504i
$966$		0			0
$967$	−11.6005	−	12.2958i	−0.373047	−	0.395407i	0.513466	−	0.858110i	$-0.328361\pi$
$967$	−11.6005	−	12.2958i	−0.373047	−	0.395407i	−0.886513	+	0.462703i	$0.846880\pi$
$968$	−9.34106	−	21.6550i	−0.300233	−	0.696019i
$969$		0			0
$970$	−7.67506	−	5.04797i	−0.246431	−	0.162081i
$971$	53.7751			1.72572			0.862862	−	0.505439i	$-0.168670\pi$
$971$	53.7751			1.72572			0.862862	+	0.505439i	$0.168670\pi$
$972$		0			0
$973$	−0.155227			−0.00497635
$974$	−10.3545	−	6.81029i	−0.331781	−	0.218216i
$975$		0			0
$976$	−1.67853	−	3.89128i	−0.0537286	−	0.124557i
$977$	10.1987	+	10.8100i	0.326285	+	0.345841i	0.869663	−	0.493647i	$-0.164336\pi$
$977$	10.1987	+	10.8100i	0.326285	+	0.345841i	−0.543378	+	0.839488i	$0.682855\pi$
$978$		0			0
$979$	0.776743	−	0.0907883i	0.0248248	−	0.00290161i
$980$	−0.884978	+	5.01896i	−0.0282696	+	0.160325i
$981$		0			0
$982$	0.972752	+	5.51675i	0.0310418	+	0.176047i
$983$	−5.10312	−	17.0456i	−0.162764	−	0.543671i	0.837231	−	0.546850i	$-0.184173\pi$
$983$	−5.10312	−	17.0456i	−0.162764	−	0.543671i	−0.999995	+	0.00317929i	$0.998988\pi$
$984$		0			0
$985$	−0.0833566	−	1.43118i	−0.00265596	−	0.0456011i
$986$	26.8932	+	13.5063i	0.856454	+	0.430127i
$987$		0			0
$988$	6.18068	−	6.55114i	0.196634	−	0.208420i
$989$	16.1990	+	5.89594i	0.515097	+	0.187480i
$990$		0			0
$991$	12.0174	−	4.37398i	0.381746	−	0.138944i	−0.144017	−	0.989575i	$-0.546002\pi$
$991$	12.0174	−	4.37398i	0.381746	−	0.138944i	0.525763	+	0.850631i	$0.323780\pi$
$992$	7.54477	−	17.4907i	0.239547	−	0.555332i
$993$		0			0
$994$	−1.13028	+	3.77539i	−0.0358503	+	0.119748i
$995$	9.05510	+	1.05839i	0.287066	+	0.0335532i
$996$		0			0
$997$	3.57455	−	61.3726i	0.113207	−	1.94369i	−0.171733	−	0.985144i	$-0.554937\pi$
$997$	3.57455	−	61.3726i	0.113207	−	1.94369i	0.284940	−	0.958545i	$-0.408026\pi$
$998$	2.94125	−	5.09439i	0.0931036	−	0.161260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.703.6		144
3.2	odd	2		729.2.g.a.703.3		144
9.2	odd	6		243.2.g.a.235.3		144
9.4	even	3		729.2.g.c.460.3		144
9.5	odd	6		729.2.g.b.460.6		144
9.7	even	3		81.2.g.a.79.6	yes	144
81.13	even	27		81.2.g.a.40.6	✓	144
81.14	odd	54		729.2.g.a.28.3		144
81.38	odd	54		6561.2.a.d.1.46		72
81.40	even	27		729.2.g.c.271.3		144
81.41	odd	54		729.2.g.b.271.6		144
81.43	even	27		6561.2.a.c.1.27		72
81.67	even	27	inner	729.2.g.d.28.6		144
81.68	odd	54		243.2.g.a.91.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.6	✓	144	81.13	even	27
81.2.g.a.79.6	yes	144	9.7	even	3
243.2.g.a.91.3		144	81.68	odd	54
243.2.g.a.235.3		144	9.2	odd	6
729.2.g.a.28.3		144	81.14	odd	54
729.2.g.a.703.3		144	3.2	odd	2
729.2.g.b.271.6		144	81.41	odd	54
729.2.g.b.460.6		144	9.5	odd	6
729.2.g.c.271.3		144	81.40	even	27
729.2.g.c.460.3		144	9.4	even	3
729.2.g.d.28.6		144	81.67	even	27	inner
729.2.g.d.703.6		144	1.1	even	1	trivial
6561.2.a.c.1.27		72	81.43	even	27
6561.2.a.d.1.46		72	81.38	odd	54

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.890910 + 0.585961i) q^{2} +(-0.341789 - 0.792356i) q^{4} +(0.585850 + 0.620965i) q^{5} +(0.284505 - 0.0332539i) q^{7} +(0.530120 - 3.00646i) q^{8} +(0.158079 + 0.896509i) q^{10} +(-0.519011 - 1.73362i) q^{11} +(-0.325075 - 5.58132i) q^{13} +(0.272954 + 0.137083i) q^{14} +(1.04960 - 1.11251i) q^{16} +(4.42908 + 1.61205i) q^{17} +(-1.75427 + 0.638503i) q^{19} +(0.291788 - 0.676441i) q^{20} +(0.553440 - 1.84862i) q^{22} +(1.34612 + 0.157339i) q^{23} +(0.248347 - 4.26396i) q^{25} +(2.98082 - 5.16294i) q^{26} +(-0.123590 - 0.214064i) q^{28} +(5.35083 - 2.68729i) q^{29} +(-2.54206 + 3.41458i) q^{31} +(-4.35412 + 1.03194i) q^{32} +(3.00131 + 4.03146i) q^{34} +(0.187327 + 0.157186i) q^{35} +(-5.46107 + 4.58238i) q^{37} +(-1.93704 - 0.459086i) q^{38} +(2.17748 - 1.43215i) q^{40} +(9.58849 - 6.30645i) q^{41} +(12.3767 + 2.93332i) q^{43} +(-1.19625 + 1.00377i) q^{44} +(1.10708 + 0.928949i) q^{46} +(-1.22397 - 1.64408i) q^{47} +(-6.73148 + 1.59539i) q^{49} +(2.71977 - 3.65328i) q^{50} +(-4.31129 + 2.16521i) q^{52} +(-1.54131 - 2.66962i) q^{53} +(0.772454 - 1.33793i) q^{55} +(0.0508455 - 0.872983i) q^{56} +(6.34175 + 0.741244i) q^{58} +(0.361763 - 1.20837i) q^{59} +(1.09744 - 2.54416i) q^{61} +(-4.26556 + 1.55254i) q^{62} +(-7.35831 - 2.67821i) q^{64} +(3.27536 - 3.47168i) q^{65} +(-5.61273 - 2.81882i) q^{67} +(-0.236491 - 4.06039i) q^{68} +(0.0747867 + 0.249805i) q^{70} +(2.24048 + 12.7064i) q^{71} +(-1.11508 + 6.32396i) q^{73} +(-7.55042 + 0.882517i) q^{74} +(1.10551 + 1.17178i) q^{76} +(-0.205311 - 0.475965i) q^{77} +(-5.95312 - 3.91543i) q^{79} +1.30574 q^{80} +12.2378 q^{82} +(11.3260 + 7.44925i) q^{83} +(1.59375 + 3.69472i) q^{85} +(9.30768 + 9.86557i) q^{86} +(-5.48720 + 0.641362i) q^{88} +(-0.0750415 + 0.425581i) q^{89} +(-0.278086 - 1.57711i) q^{91} +(-0.335421 - 1.12038i) q^{92} +(-0.127083 - 2.18193i) q^{94} +(-1.42423 - 0.715275i) q^{95} +(-6.92494 + 7.34001i) q^{97} +(-6.93197 - 2.52303i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

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