LMFDB - Embedded newform 729.2.e.t.325.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			325.2
Root			$1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.t.406.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.595778 - 0.499917i) q^{2} +(-0.242262 + 1.37394i) q^{4} +(-2.23304 + 0.812759i) q^{5} +(-0.434359 - 2.46337i) q^{7} +(1.32025 + 2.28674i) q^{8} +O(q^{10})$	\(q+(0.595778 - 0.499917i) q^{2} +(-0.242262 + 1.37394i) q^{4} +(-2.23304 + 0.812759i) q^{5} +(-0.434359 - 2.46337i) q^{7} +(1.32025 + 2.28674i) q^{8} +(-0.924081 + 1.60056i) q^{10} +(-2.95192 - 1.07441i) q^{11} +(1.02392 + 0.859169i) q^{13} +(-1.49026 - 1.25048i) q^{14} +(-0.692233 - 0.251952i) q^{16} +(-3.13726 + 5.43389i) q^{17} +(-4.03234 - 6.98422i) q^{19} +(-0.575699 - 3.26495i) q^{20} +(-2.29581 + 0.835605i) q^{22} +(0.704074 - 3.99300i) q^{23} +(0.495652 - 0.415902i) q^{25} +1.03954 q^{26} +3.48975 q^{28} +(-7.11443 + 5.96971i) q^{29} +(0.491741 - 2.78880i) q^{31} +(-5.50090 + 2.00216i) q^{32} +(0.847385 + 4.80576i) q^{34} +(2.97207 + 5.14778i) q^{35} +(-2.76596 + 4.79078i) q^{37} +(-5.89391 - 2.14521i) q^{38} +(-4.80674 - 4.03334i) q^{40} +(-5.44333 - 4.56750i) q^{41} +(-2.19597 - 0.799267i) q^{43} +(2.19131 - 3.79547i) q^{44} +(-1.57670 - 2.73092i) q^{46} +(-0.801248 - 4.54411i) q^{47} +(0.698301 - 0.254161i) q^{49} +(0.0873823 - 0.495570i) q^{50} +(-1.42850 + 1.19865i) q^{52} +0.135496 q^{53} +7.46499 q^{55} +(5.05964 - 4.24554i) q^{56} +(-1.25426 + 7.11324i) q^{58} +(3.75759 - 1.36765i) q^{59} +(0.0593526 + 0.336605i) q^{61} +(-1.10120 - 1.90733i) q^{62} +(-1.53974 + 2.66690i) q^{64} +(-2.98474 - 1.08636i) q^{65} +(7.75461 + 6.50689i) q^{67} +(-6.70579 - 5.62682i) q^{68} +(4.34415 + 1.58114i) q^{70} +(-4.09540 + 7.09344i) q^{71} +(6.15722 + 10.6646i) q^{73} +(0.747095 + 4.23698i) q^{74} +(10.5728 - 3.84817i) q^{76} +(-1.36448 + 7.73837i) q^{77} +(3.12600 - 2.62302i) q^{79} +1.75056 q^{80} -5.52638 q^{82} +(0.699573 - 0.587012i) q^{83} +(2.58917 - 14.6839i) q^{85} +(-1.70788 + 0.621616i) q^{86} +(-1.44038 - 8.16879i) q^{88} +(1.86437 + 3.22919i) q^{89} +(1.67171 - 2.89548i) q^{91} +(5.31556 + 1.93471i) q^{92} +(-2.74904 - 2.30672i) q^{94} +(14.6809 + 12.3187i) q^{95} +(5.63467 + 2.05085i) q^{97} +(0.288973 - 0.500515i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.595778	−	0.499917i	0.421278	−	0.353495i	−0.407371	−	0.913263i	$-0.633554\pi$
$2$	0.595778	−	0.499917i	0.421278	−	0.353495i	0.828649	+	0.559768i	$0.189110\pi$
$3$		0			0
$3$		0			0
$4$	−0.242262	+	1.37394i	−0.121131	+	0.686969i
$5$	−2.23304	+	0.812759i	−0.998644	+	0.363477i	−0.789062	−	0.614314i	$-0.789433\pi$
$5$	−2.23304	+	0.812759i	−0.998644	+	0.363477i	−0.209583	+	0.977791i	$0.567211\pi$
$6$		0			0
$7$	−0.434359	−	2.46337i	−0.164172	−	0.931068i	−0.949914	−	0.312513i	$-0.898829\pi$
$7$	−0.434359	−	2.46337i	−0.164172	−	0.931068i	0.785741	−	0.618555i	$-0.212282\pi$
$8$	1.32025	+	2.28674i	0.466780	+	0.808486i
$9$		0			0
$10$	−0.924081	+	1.60056i	−0.292220	+	0.506140i
$11$	−2.95192	−	1.07441i	−0.890038	−	0.323947i	−0.143784	−	0.989609i	$-0.545927\pi$
$11$	−2.95192	−	1.07441i	−0.890038	−	0.323947i	−0.746254	+	0.665662i	$0.768149\pi$
$12$		0			0
$13$	1.02392	+	0.859169i	0.283984	+	0.238291i	0.773641	−	0.633624i	$-0.218434\pi$
$13$	1.02392	+	0.859169i	0.283984	+	0.238291i	−0.489657	+	0.871915i	$0.662878\pi$
$14$	−1.49026	−	1.25048i	−0.398290	−	0.334205i
$15$		0			0
$16$	−0.692233	−	0.251952i	−0.173058	−	0.0629881i
$17$	−3.13726	+	5.43389i	−0.760897	+	1.31791i	0.181492	+	0.983392i	$0.441907\pi$
$17$	−3.13726	+	5.43389i	−0.760897	+	1.31791i	−0.942389	+	0.334520i	$0.891426\pi$
$18$		0			0
$19$	−4.03234	−	6.98422i	−0.925083	−	1.60229i	−0.791427	−	0.611263i	$-0.790662\pi$
$19$	−4.03234	−	6.98422i	−0.925083	−	1.60229i	−0.133656	−	0.991028i	$-0.542672\pi$
$20$	−0.575699	−	3.26495i	−0.128730	−	0.730066i
$21$		0			0
$22$	−2.29581	+	0.835605i	−0.489467	+	0.178152i
$23$	0.704074	−	3.99300i	0.146810	−	0.832598i	−0.819087	−	0.573669i	$-0.805519\pi$
$23$	0.704074	−	3.99300i	0.146810	−	0.832598i	0.965896	−	0.258929i	$-0.0833695\pi$
$24$		0			0
$25$	0.495652	−	0.415902i	0.0991305	−	0.0831803i
$26$	1.03954			0.203871
$27$		0			0
$28$	3.48975			0.659501
$29$	−7.11443	+	5.96971i	−1.32112	+	1.10855i	−0.335049	+	0.942201i	$0.608753\pi$
$29$	−7.11443	+	5.96971i	−1.32112	+	1.10855i	−0.986067	+	0.166347i	$0.946803\pi$
$30$		0			0
$31$	0.491741	−	2.78880i	0.0883192	−	0.500883i	−0.908272	−	0.418381i	$-0.862598\pi$
$31$	0.491741	−	2.78880i	0.0883192	−	0.500883i	0.996591	−	0.0825022i	$-0.0262912\pi$
$32$	−5.50090	+	2.00216i	−0.972430	+	0.353936i
$33$		0			0
$34$	0.847385	+	4.80576i	0.145325	+	0.824181i
$35$	2.97207	+	5.14778i	0.502372	+	0.870133i
$36$		0			0
$37$	−2.76596	+	4.79078i	−0.454720	+	0.787599i	−0.998672	−	0.0515178i	$-0.983594\pi$
$37$	−2.76596	+	4.79078i	−0.454720	+	0.787599i	0.543952	+	0.839117i	$0.316927\pi$
$38$	−5.89391	−	2.14521i	−0.956119	−	0.347999i
$39$		0			0
$40$	−4.80674	−	4.03334i	−0.760013	−	0.637726i
$41$	−5.44333	−	4.56750i	−0.850105	−	0.713323i	0.109708	−	0.993964i	$-0.465009\pi$
$41$	−5.44333	−	4.56750i	−0.850105	−	0.713323i	−0.959813	+	0.280641i	$0.909453\pi$
$42$		0			0
$43$	−2.19597	−	0.799267i	−0.334882	−	0.121887i	0.169106	−	0.985598i	$-0.445912\pi$
$43$	−2.19597	−	0.799267i	−0.334882	−	0.121887i	−0.503988	+	0.863711i	$0.668134\pi$
$44$	2.19131	−	3.79547i	0.330353	−	0.572188i
$45$		0			0
$46$	−1.57670	−	2.73092i	−0.232471	−	0.402652i
$47$	−0.801248	−	4.54411i	−0.116874	−	0.662826i	−0.985805	−	0.167893i	$-0.946304\pi$
$47$	−0.801248	−	4.54411i	−0.116874	−	0.662826i	0.868931	−	0.494933i	$-0.164807\pi$
$48$		0			0
$49$	0.698301	−	0.254161i	0.0997573	−	0.0363087i
$50$	0.0873823	−	0.495570i	0.0123577	−	0.0700842i
$51$		0			0
$52$	−1.42850	+	1.19865i	−0.198097	+	0.166224i
$53$	0.135496			0.0186118			0.00930588	−	0.999957i	$-0.497038\pi$
$53$	0.135496			0.0186118			0.00930588	+	0.999957i	$0.497038\pi$
$54$		0			0
$55$	7.46499			1.00658
$56$	5.05964	−	4.24554i	0.676123	−	0.567335i
$57$		0			0
$58$	−1.25426	+	7.11324i	−0.164692	+	0.934015i
$59$	3.75759	−	1.36765i	0.489196	−	0.178053i	−0.0856324	−	0.996327i	$-0.527291\pi$
$59$	3.75759	−	1.36765i	0.489196	−	0.178053i	0.574828	+	0.818274i	$0.305069\pi$
$60$		0			0
$61$	0.0593526	+	0.336605i	0.00759932	+	0.0430979i	0.988372	−	0.152058i	$-0.0485899\pi$
$61$	0.0593526	+	0.336605i	0.00759932	+	0.0430979i	−0.980772	+	0.195156i	$0.937479\pi$
$62$	−1.10120	−	1.90733i	−0.139852	−	0.242232i
$63$		0			0
$64$	−1.53974	+	2.66690i	−0.192467	+	0.333363i
$65$	−2.98474	−	1.08636i	−0.370212	−	0.134746i
$66$		0			0
$67$	7.75461	+	6.50689i	0.947376	+	0.794943i	0.978854	−	0.204562i	$-0.0655769\pi$
$67$	7.75461	+	6.50689i	0.947376	+	0.794943i	−0.0314778	+	0.999504i	$0.510021\pi$
$68$	−6.70579	−	5.62682i	−0.813196	−	0.682353i
$69$		0			0
$70$	4.34415	+	1.58114i	0.519225	+	0.188983i
$71$	−4.09540	+	7.09344i	−0.486035	+	0.841837i	−0.999871	−	0.0160515i	$-0.994890\pi$
$71$	−4.09540	+	7.09344i	−0.486035	+	0.841837i	0.513837	+	0.857888i	$0.328224\pi$
$72$		0			0
$73$	6.15722	+	10.6646i	0.720648	+	1.24820i	0.960740	+	0.277449i	$0.0894890\pi$
$73$	6.15722	+	10.6646i	0.720648	+	1.24820i	−0.240092	+	0.970750i	$0.577178\pi$
$74$	0.747095	+	4.23698i	0.0868480	+	0.492539i
$75$		0			0
$76$	10.5728	−	3.84817i	1.21278	−	0.441416i
$77$	−1.36448	+	7.73837i	−0.155497	+	0.881869i
$78$		0			0
$79$	3.12600	−	2.62302i	0.351702	−	0.295113i	−0.449771	−	0.893144i	$-0.648494\pi$
$79$	3.12600	−	2.62302i	0.351702	−	0.295113i	0.801473	+	0.598031i	$0.204050\pi$
$80$	1.75056			0.195718
$81$		0			0
$82$	−5.52638			−0.610287
$83$	0.699573	−	0.587012i	0.0767881	−	0.0644329i	−0.603586	−	0.797298i	$-0.706262\pi$
$83$	0.699573	−	0.587012i	0.0767881	−	0.0644329i	0.680374	+	0.732865i	$0.261817\pi$
$84$		0			0
$85$	2.58917	−	14.6839i	0.280835	−	1.59269i
$86$	−1.70788	+	0.621616i	−0.184165	+	0.0670306i
$87$		0			0
$88$	−1.44038	−	8.16879i	−0.153545	−	0.870795i
$89$	1.86437	+	3.22919i	0.197623	+	0.342293i	0.947757	−	0.318992i	$-0.103344\pi$
$89$	1.86437	+	3.22919i	0.197623	+	0.342293i	−0.750134	+	0.661286i	$0.770011\pi$
$90$		0			0
$91$	1.67171	−	2.89548i	0.175243	−	0.303529i
$92$	5.31556	+	1.93471i	0.554186	+	0.201707i
$93$		0			0
$94$	−2.74904	−	2.30672i	−0.283542	−	0.237920i
$95$	14.6809	+	12.3187i	1.50622	+	1.26387i
$96$		0			0
$97$	5.63467	+	2.05085i	0.572115	+	0.208233i	0.611845	−	0.790978i	$-0.290428\pi$
$97$	5.63467	+	2.05085i	0.572115	+	0.208233i	−0.0397303	+	0.999210i	$0.512650\pi$
$98$	0.288973	−	0.500515i	0.0291907	−	0.0505597i
$99$		0			0
$100$	0.451345	+	0.781752i	0.0451345	+	0.0781752i
$101$	1.77498	+	10.0664i	0.176617	+	1.00165i	0.936261	+	0.351306i	$0.114262\pi$
$101$	1.77498	+	10.0664i	0.176617	+	1.00165i	−0.759643	+	0.650340i	$0.774626\pi$
$102$		0			0
$103$	−8.01939	+	2.91882i	−0.790174	+	0.287600i	−0.705409	−	0.708801i	$-0.749236\pi$
$103$	−8.01939	+	2.91882i	−0.790174	+	0.287600i	−0.0847658	+	0.996401i	$0.527014\pi$
$104$	−0.612870	+	3.47576i	−0.0600968	+	0.340826i
$105$		0			0
$106$	0.0807253	−	0.0677366i	0.00784073	−	0.00657916i
$107$	−7.74500			−0.748738			−0.374369	−	0.927280i	$-0.622141\pi$
$107$	−7.74500			−0.748738			−0.374369	+	0.927280i	$0.622141\pi$
$108$		0			0
$109$	1.25438			0.120148			0.0600738	−	0.998194i	$-0.480866\pi$
$109$	1.25438			0.120148			0.0600738	+	0.998194i	$0.480866\pi$
$110$	4.44747	−	3.73187i	0.424050	−	0.355820i
$111$		0			0
$112$	−0.319975	+	1.81467i	−0.0302348	+	0.171470i
$113$	16.6897	−	6.07454i	1.57003	−	0.571445i	0.597025	−	0.802223i	$-0.296349\pi$
$113$	16.6897	−	6.07454i	1.57003	−	0.571445i	0.973006	+	0.230778i	$0.0741271\pi$
$114$		0			0
$115$	1.67312	+	9.48876i	0.156020	+	0.884831i
$116$	−6.47846	−	11.2210i	−0.601509	−	1.04185i
$117$		0			0
$118$	1.55497	−	2.69329i	0.143147	−	0.247938i
$119$	14.7484	+	5.36798i	1.35198	+	0.492082i
$120$		0			0
$121$	−0.867002	−	0.727501i	−0.0788184	−	0.0661365i
$122$	0.203636	+	0.170871i	0.0184363	+	0.0154699i
$123$		0			0
$124$	3.71250	+	1.35124i	0.333393	+	0.121345i
$125$	5.17209	−	8.95832i	0.462606	−	0.801256i
$126$		0			0
$127$	1.98279	+	3.43429i	0.175944	+	0.304744i	0.940488	−	0.339828i	$-0.110369\pi$
$127$	1.98279	+	3.43429i	0.175944	+	0.304744i	−0.764543	+	0.644572i	$0.777036\pi$
$128$	−1.61716	−	9.17137i	−0.142938	−	0.810643i
$129$		0			0
$130$	−2.32133	+	0.844896i	−0.203594	+	0.0741022i
$131$	−0.0177987	+	0.100941i	−0.00155508	+	0.00881927i	−0.985575	−	0.169237i	$-0.945870\pi$
$131$	−0.0177987	+	0.100941i	−0.00155508	+	0.00881927i	0.984020	+	0.178056i	$0.0569808\pi$
$132$		0			0
$133$	−15.4533	+	12.9668i	−1.33997	+	1.12437i
$134$	7.87292			0.680117
$135$		0			0
$136$	−16.5679			−1.42068
$137$	−5.83691	+	4.89775i	−0.498681	+	0.418443i	−0.857125	−	0.515108i	$-0.827752\pi$
$137$	−5.83691	+	4.89775i	−0.498681	+	0.418443i	0.358444	+	0.933551i	$0.383307\pi$
$138$		0			0
$139$	−1.81301	+	10.2821i	−0.153778	+	0.872117i	0.806117	+	0.591756i	$0.201565\pi$
$139$	−1.81301	+	10.2821i	−0.153778	+	0.872117i	−0.959895	+	0.280361i	$0.909546\pi$
$140$	−7.79274	+	2.83633i	−0.658607	+	0.239713i
$141$		0			0
$142$	1.10618	+	6.27347i	0.0928288	+	0.526458i
$143$	−2.09943	−	3.63631i	−0.175563	−	0.304084i
$144$		0			0
$145$	11.0348	−	19.1129i	0.916394	−	1.58724i
$146$	8.99975	+	3.27564i	0.744825	+	0.271094i
$147$		0			0
$148$	−5.91214	−	4.96087i	−0.485975	−	0.407781i
$149$	6.91936	+	5.80603i	0.566856	+	0.475648i	0.880601	−	0.473859i	$-0.157139\pi$
$149$	6.91936	+	5.80603i	0.566856	+	0.475648i	−0.313745	+	0.949507i	$0.601584\pi$
$150$		0			0
$151$	−22.4496	−	8.17099i	−1.82692	−	0.664946i	−0.993708	−	0.111998i	$-0.964275\pi$
$151$	−22.4496	−	8.17099i	−1.82692	−	0.664946i	−0.833216	−	0.552948i	$-0.813503\pi$
$152$	10.6474	−	18.4419i	0.863620	−	1.49583i
$153$		0			0
$154$	3.05561	+	5.29248i	0.246228	+	0.426480i
$155$	1.16855	+	6.62716i	0.0938599	+	0.532306i
$156$		0			0
$157$	−2.54843	+	0.927554i	−0.203387	+	0.0740269i	−0.441705	−	0.897160i	$-0.645626\pi$
$157$	−2.54843	+	0.927554i	−0.203387	+	0.0740269i	0.238318	+	0.971187i	$0.423404\pi$
$158$	0.551105	−	3.12547i	0.0438436	−	0.248649i
$159$		0			0
$160$	10.6564	−	8.94180i	0.842465	−	0.706912i
$161$	−10.1421			−0.799308
$162$		0			0
$163$	−22.0489			−1.72701			−0.863504	−	0.504343i	$-0.831735\pi$
$163$	−22.0489			−1.72701			−0.863504	+	0.504343i	$0.831735\pi$
$164$	7.59416	−	6.37226i	0.593005	−	0.497590i
$165$		0			0
$166$	0.123333	−	0.699457i	0.00957251	−	0.0542884i
$167$	8.41101	−	3.06136i	0.650863	−	0.236895i	0.00457649	−	0.999990i	$-0.498543\pi$
$167$	8.41101	−	3.06136i	0.650863	−	0.236895i	0.646287	+	0.763095i	$0.276321\pi$
$168$		0			0
$169$	−1.94719	−	11.0431i	−0.149784	−	0.849466i
$170$	−5.79816	−	10.0427i	−0.444699	−	0.770241i
$171$		0			0
$172$	1.63014	−	2.82349i	0.124297	−	0.215289i
$173$	2.47538	+	0.900966i	0.188200	+	0.0684992i	0.434401	−	0.900720i	$-0.356960\pi$
$173$	2.47538	+	0.900966i	0.188200	+	0.0684992i	−0.246201	+	0.969219i	$0.579182\pi$
$174$		0			0
$175$	−1.23981	−	1.04033i	−0.0937211	−	0.0786413i
$176$	1.77272	+	1.48749i	0.133624	+	0.112124i
$177$		0			0
$178$	2.72508	+	0.991847i	0.204253	+	0.0743421i
$179$	1.84227	−	3.19090i	0.137697	−	0.238499i	−0.788927	−	0.614487i	$-0.789363\pi$
$179$	1.84227	−	3.19090i	0.137697	−	0.238499i	0.926625	+	0.375988i	$0.122697\pi$
$180$		0			0
$181$	0.134255	+	0.232536i	0.00997906	+	0.0172842i	0.870972	−	0.491333i	$-0.163490\pi$
$181$	0.134255	+	0.232536i	0.00997906	+	0.0172842i	−0.860993	+	0.508617i	$0.830157\pi$
$182$	−0.451534	−	2.56078i	−0.0334699	−	0.189817i
$183$		0			0
$184$	10.0605	−	3.66173i	0.741672	−	0.269946i
$185$	2.28273	−	12.9460i	0.167830	−	0.951811i
$186$		0			0
$187$	15.0992	−	12.6697i	1.10416	−	0.926502i
$188$	6.43743			0.469498
$189$		0			0
$190$	14.9049			1.08131
$191$	1.83696	−	1.54140i	0.132918	−	0.111531i	−0.573905	−	0.818922i	$-0.694572\pi$
$191$	1.83696	−	1.54140i	0.132918	−	0.111531i	0.706823	+	0.707390i	$0.250128\pi$
$192$		0			0
$193$	0.0861647	−	0.488664i	0.00620227	−	0.0351748i	−0.981550	−	0.191208i	$-0.938760\pi$
$193$	0.0861647	−	0.488664i	0.00620227	−	0.0351748i	0.987752	+	0.156033i	$0.0498706\pi$
$194$	4.38227	−	1.59502i	0.314629	−	0.114515i
$195$		0			0
$196$	0.180029	+	1.02099i	0.0128592	+	0.0729282i
$197$	−11.0734	−	19.1797i	−0.788946	−	1.36649i	−0.926613	−	0.376016i	$-0.877294\pi$
$197$	−11.0734	−	19.1797i	−0.788946	−	1.36649i	0.137667	−	0.990479i	$-0.456040\pi$
$198$		0			0
$199$	−1.06624	+	1.84677i	−0.0755834	+	0.130914i	−0.901340	−	0.433113i	$-0.857415\pi$
$199$	−1.06624	+	1.84677i	−0.0755834	+	0.130914i	0.825756	+	0.564027i	$0.190749\pi$
$200$	1.60545	+	0.584335i	0.113522	+	0.0413187i
$201$		0			0
$202$	6.08987	+	5.11001i	0.428482	+	0.359539i
$203$	17.7959	+	14.9325i	1.24902	+	1.04806i
$204$		0			0
$205$	15.8674	+	5.77527i	1.10823	+	0.403362i
$206$	−3.31861	+	5.74800i	−0.231218	+	0.400482i
$207$		0			0
$208$	−0.492320	−	0.852724i	−0.0341363	−	0.0591257i
$209$	4.39923	+	24.9493i	0.304301	+	1.72578i
$210$		0			0
$211$	−18.8019	+	6.84334i	−1.29438	+	0.471115i	−0.895162	−	0.445742i	$-0.852940\pi$
$211$	−18.8019	+	6.84334i	−1.29438	+	0.471115i	−0.399216	+	0.916857i	$0.630718\pi$
$212$	−0.0328255	+	0.186163i	−0.00225446	+	0.0127857i
$213$		0			0
$214$	−4.61430	+	3.87186i	−0.315427	+	0.264675i
$215$	5.55329			0.378731
$216$		0			0
$217$	−7.08345			−0.480856
$218$	0.747330	−	0.627084i	0.0506156	−	0.0424715i
$219$		0			0
$220$	−1.80848	+	10.2564i	−0.121928	+	0.691488i
$221$	−7.88093	+	2.86842i	−0.530129	+	0.192951i
$222$		0			0
$223$	−2.30578	−	13.0767i	−0.154407	−	0.875683i	−0.959326	−	0.282299i	$-0.908903\pi$
$223$	−2.30578	−	13.0767i	−0.154407	−	0.875683i	0.804920	−	0.593384i	$-0.202208\pi$
$224$	7.32144	+	12.6811i	0.489185	+	0.847292i
$225$		0			0
$226$	6.90656	−	11.9625i	0.459418	−	0.795735i
$227$	−11.7188	−	4.26531i	−0.777807	−	0.283099i	−0.0775490	−	0.996989i	$-0.524709\pi$
$227$	−11.7188	−	4.26531i	−0.777807	−	0.283099i	−0.700258	+	0.713890i	$0.746932\pi$
$228$		0			0
$229$	19.6579	+	16.4949i	1.29903	+	1.09002i	0.990312	+	0.138862i	$0.0443445\pi$
$229$	19.6579	+	16.4949i	1.29903	+	1.09002i	0.308719	+	0.951153i	$0.400100\pi$
$230$	5.74040	+	4.81677i	0.378511	+	0.317608i
$231$		0			0
$232$	−23.0440	−	8.38735i	−1.51292	−	0.550656i
$233$	−2.69821	+	4.67344i	−0.176766	+	0.306167i	−0.940771	−	0.339043i	$-0.889897\pi$
$233$	−2.69821	+	4.67344i	−0.176766	+	0.306167i	0.764005	+	0.645210i	$0.223230\pi$
$234$		0			0
$235$	5.48248	+	9.49593i	0.357637	+	0.619446i
$236$	0.968743	+	5.49402i	0.0630598	+	0.357630i
$237$		0			0
$238$	11.4703	−	4.17485i	0.743510	−	0.270616i
$239$	−1.45362	+	8.24387i	−0.0940266	+	0.533252i	0.901015	+	0.433789i	$0.142824\pi$
$239$	−1.45362	+	8.24387i	−0.0940266	+	0.533252i	−0.995041	+	0.0994629i	$0.968288\pi$
$240$		0			0
$241$	−0.338737	+	0.284234i	−0.0218200	+	0.0183091i	−0.653632	−	0.756812i	$-0.726756\pi$
$241$	−0.338737	+	0.284234i	−0.0218200	+	0.0183091i	0.631812	+	0.775121i	$0.282311\pi$
$242$	−0.880231			−0.0565834
$243$		0			0
$244$	−0.476854			−0.0305274
$245$	−1.35276	+	1.13510i	−0.0864246	+	0.0725189i
$246$		0			0
$247$	1.87184	−	10.6157i	0.119102	−	0.675463i
$248$	7.02649	−	2.55743i	0.446183	−	0.162397i
$249$		0			0
$250$	−1.39700	−	7.92278i	−0.0883540	−	0.501080i
$251$	8.51427	+	14.7471i	0.537416	+	0.930832i	0.999042	+	0.0437571i	$0.0139328\pi$
$251$	8.51427	+	14.7471i	0.537416	+	0.930832i	−0.461626	+	0.887074i	$0.652734\pi$
$252$		0			0
$253$	−6.36850	+	11.0306i	−0.400384	+	0.693486i
$254$	2.89816	+	1.05484i	0.181847	+	0.0661869i
$255$		0			0
$256$	−10.2664	−	8.61455i	−0.641651	−	0.538409i
$257$	−15.9925	−	13.4193i	−0.997584	−	0.837073i	−0.0109365	−	0.999940i	$-0.503481\pi$
$257$	−15.9925	−	13.4193i	−0.997584	−	0.837073i	−0.986648	+	0.162867i	$0.947926\pi$
$258$		0			0
$259$	13.0029	+	4.73267i	0.807961	+	0.294074i
$260$	2.21568	−	3.83767i	0.137411	−	0.238002i
$261$		0			0
$262$	0.0398582	+	0.0690364i	0.00246245	+	0.00426508i
$263$	−3.36731	−	19.0970i	−0.207637	−	1.17757i	−0.893236	−	0.449589i	$-0.851571\pi$
$263$	−3.36731	−	19.0970i	−0.207637	−	1.17757i	0.685599	−	0.727980i	$-0.259541\pi$
$264$		0			0
$265$	−0.302567	+	0.110125i	−0.0185865	+	0.00676495i
$266$	−2.72438	+	15.4507i	−0.167042	+	0.947343i
$267$		0			0
$268$	−10.8187	+	9.07797i	−0.660857	+	0.554525i
$269$	−18.6791			−1.13889			−0.569443	−	0.822031i	$-0.692841\pi$
$269$	−18.6791			−1.13889			−0.569443	+	0.822031i	$0.692841\pi$
$270$		0			0
$271$	12.9378			0.785917			0.392958	−	0.919556i	$-0.371452\pi$
$271$	12.9378			0.785917			0.392958	+	0.919556i	$0.371452\pi$
$272$	3.54080	−	2.97108i	0.214692	−	0.180148i
$273$		0			0
$274$	−1.02903	+	5.83594i	−0.0621662	+	0.352562i
$275$	−1.90998	+	0.695175i	−0.115176	+	0.0419206i
$276$		0			0
$277$	1.81312	+	10.2827i	0.108940	+	0.617828i	0.989573	+	0.144030i	$0.0460061\pi$
$277$	1.81312	+	10.2827i	0.108940	+	0.617828i	−0.880634	+	0.473798i	$0.842883\pi$
$278$	4.06005	+	7.03221i	0.243505	+	0.421764i
$279$		0			0
$280$	−7.84776	+	13.5927i	−0.468994	+	0.812321i
$281$	13.4806	+	4.90655i	0.804187	+	0.292700i	0.711221	−	0.702969i	$-0.248143\pi$
$281$	13.4806	+	4.90655i	0.804187	+	0.292700i	0.0929668	+	0.995669i	$0.470365\pi$
$282$		0			0
$283$	−14.3194	−	12.0154i	−0.851198	−	0.714240i	0.108855	−	0.994058i	$-0.465282\pi$
$283$	−14.3194	−	12.0154i	−0.851198	−	0.714240i	−0.960053	+	0.279818i	$0.909726\pi$
$284$	−8.75378	−	7.34530i	−0.519441	−	0.435863i
$285$		0			0
$286$	−3.06864	−	1.11689i	−0.181453	−	0.0660434i
$287$	−8.88709	+	15.3929i	−0.524588	+	0.908614i
$288$		0			0
$289$	−11.1848	−	19.3726i	−0.657929	−	1.13957i
$290$	−2.98055	−	16.9035i	−0.175024	−	0.992610i
$291$		0			0
$292$	−16.1442	+	5.87600i	−0.944766	+	0.343867i
$293$	1.87335	−	10.6243i	0.109442	−	0.620677i	−0.879911	−	0.475139i	$-0.842398\pi$
$293$	1.87335	−	10.6243i	0.109442	−	0.620677i	0.989353	−	0.145538i	$-0.0464913\pi$
$294$		0			0
$295$	−7.27926	+	6.10802i	−0.423815	+	0.355623i
$296$	−14.6070			−0.849017
$297$		0			0
$298$	7.02493			0.406943
$299$	4.15158	−	3.48359i	0.240092	−	0.201461i
$300$		0			0
$301$	−1.01506	+	5.75666i	−0.0585068	+	0.331809i
$302$	−17.4598	+	6.35485i	−1.00470	+	0.365680i
$303$		0			0
$304$	1.03163	+	5.85067i	0.0591681	+	0.335559i
$305$	−0.406116	−	0.703413i	−0.0232541	−	0.0402773i
$306$		0			0
$307$	−0.0248747	+	0.0430843i	−0.00141967	+	0.00245895i	−0.866734	−	0.498770i	$-0.833785\pi$
$307$	−0.0248747	+	0.0430843i	−0.00141967	+	0.00245895i	0.865315	+	0.501229i	$0.167119\pi$
$308$	−10.3015	−	3.74943i	−0.586981	−	0.213644i
$309$		0			0
$310$	4.00922	+	3.36413i	0.227708	+	0.191070i
$311$	−10.1389	−	8.50759i	−0.574927	−	0.482421i	0.308350	−	0.951273i	$-0.400223\pi$
$311$	−10.1389	−	8.50759i	−0.574927	−	0.482421i	−0.883277	+	0.468852i	$0.844668\pi$
$312$		0			0
$313$	14.1733	+	5.15866i	0.801123	+	0.291585i	0.709952	−	0.704250i	$-0.248717\pi$
$313$	14.1733	+	5.15866i	0.801123	+	0.291585i	0.0911710	+	0.995835i	$0.470939\pi$
$314$	−1.05460	+	1.82662i	−0.0595145	+	0.103082i
$315$		0			0
$316$	2.84656	+	4.93038i	0.160131	+	0.277356i
$317$	−1.49873	−	8.49970i	−0.0841769	−	0.477391i	−0.997531	−	0.0702251i	$-0.977628\pi$
$317$	−1.49873	−	8.49970i	−0.0841769	−	0.477391i	0.913354	−	0.407166i	$-0.133483\pi$
$318$		0			0
$319$	27.4152	−	9.97831i	1.53496	−	0.558678i
$320$	1.27074	−	7.20673i	0.0710365	−	0.402868i
$321$		0			0
$322$	−6.04242	+	5.07019i	−0.336731	+	0.282551i
$323$	50.6020			2.81557
$324$		0			0
$325$	0.864837			0.0479725
$326$	−13.1363	+	11.0226i	−0.727551	+	0.610488i
$327$		0			0
$328$	3.25812	−	18.4777i	0.179900	−	1.02026i
$329$	−10.8458	+	3.94755i	−0.597949	+	0.217636i
$330$		0			0
$331$	5.38752	+	30.5541i	0.296125	+	1.67941i	0.662596	+	0.748977i	$0.269455\pi$
$331$	5.38752	+	30.5541i	0.296125	+	1.67941i	−0.366471	+	0.930430i	$0.619434\pi$
$332$	0.637037	+	1.10338i	0.0349619	+	0.0605559i
$333$		0			0
$334$	3.48067	−	6.02869i	0.190454	−	0.329875i
$335$	−22.6048	−	8.22749i	−1.23503	−	0.449516i
$336$		0			0
$337$	−18.2834	−	15.3416i	−0.995962	−	0.835711i	−0.00954207	−	0.999954i	$-0.503037\pi$
$337$	−18.2834	−	15.3416i	−0.995962	−	0.835711i	−0.986420	+	0.164243i	$0.947482\pi$
$338$	−6.68070	−	5.60578i	−0.363382	−	0.304914i
$339$		0			0
$340$	19.5475	+	7.11471i	1.06011	+	0.385850i
$341$	−4.44790	+	7.70399i	−0.240867	+	0.417194i
$342$		0			0
$343$	−9.68422	−	16.7736i	−0.522899	−	0.905688i
$344$	−1.07151	−	6.07685i	−0.0577721	−	0.327642i
$345$		0			0
$346$	1.92519	−	0.700711i	0.103499	−	0.0376704i
$347$	−3.80485	+	21.5784i	−0.204255	+	1.15839i	0.694353	+	0.719634i	$0.255691\pi$
$347$	−3.80485	+	21.5784i	−0.204255	+	1.15839i	−0.898608	+	0.438752i	$0.855420\pi$
$348$		0			0
$349$	12.1394	−	10.1862i	0.649807	−	0.545253i	−0.257205	−	0.966357i	$-0.582802\pi$
$349$	12.1394	−	10.1862i	0.649807	−	0.545253i	0.907012	+	0.421104i	$0.138357\pi$
$350$	−1.25873			−0.0672819
$351$		0			0
$352$	18.3894			0.980157
$353$	−9.88725	+	8.29639i	−0.526245	+	0.441572i	−0.866802	−	0.498652i	$-0.833829\pi$
$353$	−9.88725	+	8.29639i	−0.526245	+	0.441572i	0.340557	+	0.940224i	$0.389384\pi$
$354$		0			0
$355$	3.37992	−	19.1685i	0.179388	−	1.01736i
$356$	−4.88837	+	1.77922i	−0.259083	+	0.0942985i
$357$		0			0
$358$	−0.497603	−	2.82204i	−0.0262991	−	0.149150i
$359$	12.9142	+	22.3681i	0.681588	+	1.18054i	0.974496	+	0.224404i	$0.0720435\pi$
$359$	12.9142	+	22.3681i	0.681588	+	1.18054i	−0.292909	+	0.956140i	$0.594623\pi$
$360$		0			0
$361$	−23.0196	+	39.8711i	−1.21156	+	2.09848i
$362$	0.196234	+	0.0714235i	0.0103138	+	0.00375393i
$363$		0			0
$364$	3.57322	+	2.99829i	0.187288	+	0.157153i
$365$	−22.4171	−	18.8101i	−1.17336	−	0.984568i
$366$		0			0
$367$	−15.0112	−	5.46363i	−0.783578	−	0.285199i	−0.0809141	−	0.996721i	$-0.525784\pi$
$367$	−15.0112	−	5.46363i	−0.783578	−	0.285199i	−0.702664	+	0.711522i	$0.748006\pi$
$368$	−1.49343	+	2.58669i	−0.0778503	+	0.134841i
$369$		0			0
$370$	−5.11194	−	8.85413i	−0.265757	−	0.460304i
$371$	−0.0588538	−	0.333777i	−0.00305554	−	0.0173288i
$372$		0			0
$373$	−1.71641	+	0.624722i	−0.0888724	+	0.0323469i	−0.386074	−	0.922468i	$-0.626169\pi$
$373$	−1.71641	+	0.624722i	−0.0888724	+	0.0323469i	0.297201	+	0.954815i	$0.403947\pi$
$374$	2.66195	−	15.0967i	0.137646	−	0.780630i
$375$		0			0
$376$	9.33336	−	7.83162i	0.481331	−	0.403885i
$377$	−12.4136			−0.639332
$378$		0			0
$379$	1.14694			0.0589141			0.0294571	−	0.999566i	$-0.490622\pi$
$379$	1.14694			0.0589141			0.0294571	+	0.999566i	$0.490622\pi$
$380$	−20.4817	+	17.1862i	−1.05069	+	0.881635i
$381$		0			0
$382$	0.323852	−	1.83666i	0.0165697	−	0.0939716i
$383$	20.5112	−	7.46546i	1.04807	−	0.381467i	0.240138	−	0.970739i	$-0.422807\pi$
$383$	20.5112	−	7.46546i	1.04807	−	0.381467i	0.807935	+	0.589272i	$0.200585\pi$
$384$		0			0
$385$	−3.24249	−	18.3891i	−0.165253	−	0.937194i
$386$	−0.192957	−	0.334210i	−0.00982123	−	0.0170109i
$387$		0			0
$388$	−4.18281	+	7.24484i	−0.212350	+	0.367801i
$389$	−24.6164	−	8.95962i	−1.24810	−	0.454271i	−0.368340	−	0.929691i	$-0.620074\pi$
$389$	−24.6164	−	8.95962i	−1.24810	−	0.454271i	−0.879759	+	0.475420i	$0.842296\pi$
$390$		0			0
$391$	19.4887	+	16.3529i	0.985584	+	0.827003i
$392$	1.50313	+	1.26128i	0.0759197	+	0.0637042i
$393$		0			0
$394$	−16.1855	−	5.89104i	−0.815414	−	0.296787i
$395$	−4.84858	+	8.39798i	−0.243958	+	0.422548i
$396$		0			0
$397$	−2.09915	−	3.63584i	−0.105353	−	0.182478i	0.808529	−	0.588456i	$-0.200264\pi$
$397$	−2.09915	−	3.63584i	−0.105353	−	0.182478i	−0.913883	+	0.405979i	$0.866931\pi$
$398$	0.287994	+	1.63330i	0.0144358	+	0.0818697i
$399$		0			0
$400$	−0.447894	+	0.163020i	−0.0223947	+	0.00815101i
$401$	1.35963	−	7.71086i	0.0678968	−	0.385062i	−0.931856	−	0.362828i	$-0.881811\pi$
$401$	1.35963	−	7.71086i	0.0678968	−	0.385062i	0.999753	−	0.0222335i	$-0.00707774\pi$
$402$		0			0
$403$	2.89955	−	2.43301i	0.144437	−	0.121197i
$404$	−14.2606			−0.709493
$405$		0			0
$406$	18.0674			0.896669
$407$	13.3122	−	11.1702i	0.659859	−	0.553687i
$408$		0			0
$409$	−3.02651	+	17.1642i	−0.149651	+	0.848716i	0.813863	+	0.581057i	$0.197361\pi$
$409$	−3.02651	+	17.1642i	−0.149651	+	0.848716i	−0.963514	+	0.267658i	$0.913750\pi$
$410$	12.3406	−	4.49161i	0.609459	−	0.221825i
$411$		0			0
$412$	−2.06748	−	11.7253i	−0.101857	−	0.577662i
$413$	−5.00118	−	8.66229i	−0.246092	−	0.426243i
$414$		0			0
$415$	−1.08507	+	1.87940i	−0.0532642	+	0.0922563i
$416$	−7.35266	−	2.67615i	−0.360494	−	0.131209i
$417$		0			0
$418$	15.0935	+	12.6650i	0.738249	+	0.619464i
$419$	−8.79662	−	7.38124i	−0.429743	−	0.360597i	0.402112	−	0.915591i	$-0.368276\pi$
$419$	−8.79662	−	7.38124i	−0.429743	−	0.360597i	−0.831855	+	0.554993i	$0.812721\pi$
$420$		0			0
$421$	−6.85151	−	2.49375i	−0.333922	−	0.121538i	0.169617	−	0.985510i	$-0.445747\pi$
$421$	−6.85151	−	2.49375i	−0.333922	−	0.121538i	−0.503539	+	0.863972i	$0.667969\pi$
$422$	−7.78066	+	13.4765i	−0.378757	+	0.656026i
$423$		0			0
$424$	0.178889	+	0.309844i	0.00868759	+	0.0150474i
$425$	0.704975	+	3.99811i	0.0341963	+	0.193937i
$426$		0			0
$427$	0.803405	−	0.292416i	0.0388795	−	0.0141510i
$428$	1.87632	−	10.6411i	0.0906954	−	0.514359i
$429$		0			0
$430$	3.30853	−	2.77618i	0.159551	−	0.133879i
$431$	−0.389084			−0.0187415			−0.00937075	−	0.999956i	$-0.502983\pi$
$431$	−0.389084			−0.0187415			−0.00937075	+	0.999956i	$0.502983\pi$
$432$		0			0
$433$	24.1011			1.15822			0.579112	−	0.815248i	$-0.303400\pi$
$433$	24.1011			1.15822			0.579112	+	0.815248i	$0.303400\pi$
$434$	−4.22016	+	3.54113i	−0.202574	+	0.169980i
$435$		0			0
$436$	−0.303888	+	1.72344i	−0.0145536	+	0.0825376i
$437$	−30.7271	+	11.1837i	−1.46988	+	0.534991i
$438$		0			0
$439$	6.36691	+	36.1086i	0.303876	+	1.72337i	0.628748	+	0.777609i	$0.283568\pi$
$439$	6.36691	+	36.1086i	0.303876	+	1.72337i	−0.324871	+	0.945758i	$0.605321\pi$
$440$	9.85567	+	17.0705i	0.469851	+	0.813805i
$441$		0			0
$442$	−3.26131	+	5.64875i	−0.155125	+	0.268684i
$443$	−35.5078	−	12.9238i	−1.68703	−	0.614028i	−0.692782	−	0.721147i	$-0.743615\pi$
$443$	−35.5078	−	12.9238i	−1.68703	−	0.614028i	−0.994246	+	0.107118i	$0.965838\pi$
$444$		0			0
$445$	−6.78776	−	5.69561i	−0.321771	−	0.269998i
$446$	−7.91101	−	6.63813i	−0.374597	−	0.314324i
$447$		0			0
$448$	7.23838	+	2.63456i	0.341981	+	0.124471i
$449$	5.89289	−	10.2068i	0.278103	−	0.481688i	−0.692811	−	0.721120i	$-0.743628\pi$
$449$	5.89289	−	10.2068i	0.278103	−	0.481688i	0.970913	+	0.239432i	$0.0769611\pi$
$450$		0			0
$451$	11.1609	+	19.3313i	0.525547	+	0.910274i
$452$	4.30276	+	24.4022i	0.202385	+	1.14778i
$453$		0			0
$454$	−9.11412	+	3.31727i	−0.427747	+	0.155687i
$455$	−1.37965	+	7.82441i	−0.0646792	+	0.366814i
$456$		0			0
$457$	−15.2105	+	12.7631i	−0.711517	+	0.597034i	−0.925024	−	0.379908i	$-0.875956\pi$
$457$	−15.2105	+	12.7631i	−0.711517	+	0.597034i	0.213507	+	0.976942i	$0.431511\pi$
$458$	19.9578			0.932568
$459$		0			0
$460$	−13.4423			−0.626750
$461$	5.85398	−	4.91207i	0.272647	−	0.228778i	−0.496204	−	0.868206i	$-0.665273\pi$
$461$	5.85398	−	4.91207i	0.272647	−	0.228778i	0.768851	+	0.639428i	$0.220829\pi$
$462$		0			0
$463$	−2.77046	+	15.7120i	−0.128754	+	0.730200i	0.850253	+	0.526374i	$0.176449\pi$
$463$	−2.77046	+	15.7120i	−0.128754	+	0.730200i	−0.979007	+	0.203826i	$0.934662\pi$
$464$	6.42893	−	2.33994i	0.298455	−	0.108629i
$465$		0			0
$466$	0.728797	+	4.13321i	0.0337609	+	0.191467i
$467$	13.0703	+	22.6385i	0.604822	+	1.04758i	0.992080	+	0.125611i	$0.0400892\pi$
$467$	13.0703	+	22.6385i	0.604822	+	1.04758i	−0.387257	+	0.921972i	$0.626577\pi$
$468$		0			0
$469$	12.6606	−	21.9288i	0.584613	−	1.01258i
$470$	8.01351	+	2.91668i	0.369636	+	0.134536i
$471$		0			0
$472$	8.08842	+	6.78699i	0.372300	+	0.312397i
$473$	5.62359	+	4.71875i	0.258573	+	0.216968i
$474$		0			0
$475$	−4.90339	−	1.78469i	−0.224983	−	0.0818871i
$476$	−10.9483	+	18.9629i	−0.501812	+	0.869164i
$477$		0			0
$478$	3.25522	+	5.63820i	0.148890	+	0.257885i
$479$	−6.83310	−	38.7525i	−0.312213	−	1.77065i	−0.587442	−	0.809267i	$-0.699865\pi$
$479$	−6.83310	−	38.7525i	−0.312213	−	1.77065i	0.275229	−	0.961379i	$-0.411246\pi$
$480$		0			0
$481$	−6.94820	+	2.52894i	−0.316811	+	0.115310i
$482$	−0.0597185	+	0.338680i	−0.00272010	+	0.0154265i
$483$		0			0
$484$	1.20958	−	1.01496i	0.0549811	−	0.0461346i
$485$	−14.2493			−0.647027
$486$		0			0
$487$	11.7133			0.530779			0.265389	−	0.964141i	$-0.414500\pi$
$487$	11.7133			0.530779			0.265389	+	0.964141i	$0.414500\pi$
$488$	−0.691370	+	0.580128i	−0.0312968	+	0.0262612i
$489$		0			0
$490$	−0.238488	+	1.35253i	−0.0107738	+	0.0611013i
$491$	−36.2250	+	13.1848i	−1.63481	+	0.595023i	−0.986121	−	0.166030i	$-0.946905\pi$
$491$	−36.2250	+	13.1848i	−1.63481	+	0.595023i	−0.648691	+	0.761052i	$0.724683\pi$
$492$		0			0
$493$	−10.1190	−	57.3876i	−0.455736	−	2.58461i
$494$	−4.19178	−	7.26038i	−0.188597	−	0.326660i
$495$		0			0
$496$	−1.04304	+	1.80660i	−0.0468340	+	0.0811189i
$497$	19.2527	+	7.00740i	0.863601	+	0.314325i
$498$		0			0
$499$	−22.6455	−	19.0018i	−1.01375	−	0.850638i	−0.0249220	−	0.999689i	$-0.507934\pi$
$499$	−22.6455	−	19.0018i	−1.01375	−	0.850638i	−0.988830	+	0.149051i	$0.952378\pi$
$500$	11.0552	+	9.27638i	0.494402	+	0.414853i
$501$		0			0
$502$	12.4450	+	4.52959i	0.555445	+	0.202166i
$503$	17.7888	−	30.8110i	0.793161	−	1.37380i	−0.130839	−	0.991404i	$-0.541767\pi$
$503$	17.7888	−	30.8110i	0.793161	−	1.37380i	0.924000	−	0.382392i	$-0.124900\pi$
$504$		0			0
$505$	−12.1452	−	21.0361i	−0.540453	−	0.936092i
$506$	1.72015	+	9.75548i	0.0764702	+	0.433684i
$507$		0			0
$508$	−5.19886	+	1.89223i	−0.230662	+	0.0839541i
$509$	4.92854	−	27.9512i	0.218454	−	1.23891i	−0.656358	−	0.754450i	$-0.727904\pi$
$509$	4.92854	−	27.9512i	0.218454	−	1.23891i	0.874812	−	0.484463i	$-0.160985\pi$
$510$		0			0
$511$	23.5965	−	19.7998i	1.04385	−	0.875892i
$512$	8.20265			0.362510
$513$		0			0
$514$	−16.2365			−0.716161
$515$	15.5353	−	13.0357i	0.684567	−	0.574420i
$516$		0			0
$517$	−2.51702	+	14.2747i	−0.110698	+	0.627801i
$518$	10.1128	−	3.68075i	0.444330	−	0.161723i
$519$		0			0
$520$	−1.45639	−	8.25961i	−0.0638670	−	0.362208i
$521$	−12.7176	−	22.0275i	−0.557167	−	0.965041i	−0.997731	−	0.0673204i	$-0.978555\pi$
$521$	−12.7176	−	22.0275i	−0.557167	−	0.965041i	0.440565	−	0.897721i	$-0.354778\pi$
$522$		0			0
$523$	−4.20395	+	7.28145i	−0.183826	+	0.318396i	−0.943180	−	0.332282i	$-0.892182\pi$
$523$	−4.20395	+	7.28145i	−0.183826	+	0.318396i	0.759354	+	0.650677i	$0.225515\pi$
$524$	−0.134375	−	0.0489085i	−0.00587020	−	0.00213658i
$525$		0			0
$526$	−11.5531	−	9.69416i	−0.503737	−	0.422686i
$527$	13.6113	+	11.4212i	0.592918	+	0.497517i
$528$		0			0
$529$	6.16460	+	2.24373i	0.268026	+	0.0975535i
$530$	−0.125209	+	0.216868i	−0.00543873	+	0.00942016i
$531$		0			0
$532$	−14.0719	−	24.3732i	−0.610093	−	1.05671i
$533$	−1.64927	−	9.35348i	−0.0714379	−	0.405144i
$534$		0			0
$535$	17.2949	−	6.29482i	0.747723	−	0.272149i
$536$	−4.64155	+	26.3235i	−0.200484	+	1.13700i
$537$		0			0
$538$	−11.1286	+	9.33801i	−0.479788	+	0.402590i
$539$	−2.33440			−0.100550
$540$		0			0
$541$	−12.8635			−0.553043			−0.276522	−	0.961008i	$-0.589182\pi$
$541$	−12.8635			−0.553043			−0.276522	+	0.961008i	$0.589182\pi$
$542$	7.70806	−	6.46783i	0.331090	−	0.277817i
$543$		0			0
$544$	6.37820	−	36.1726i	0.273463	−	1.55089i
$545$	−2.80107	+	1.01951i	−0.119985	+	0.0436708i
$546$		0			0
$547$	2.27340	+	12.8931i	0.0972034	+	0.551268i	0.994050	+	0.108926i	$0.0347411\pi$
$547$	2.27340	+	12.8931i	0.0972034	+	0.551268i	−0.896847	+	0.442342i	$0.854148\pi$
$548$	−5.31514	−	9.20609i	−0.227051	−	0.393265i
$549$		0			0
$550$	−0.790392	+	1.36900i	−0.0337024	+	0.0583743i
$551$	70.3817	+	25.6168i	2.99836	+	1.09131i
$552$		0			0
$553$	−7.81929	−	6.56116i	−0.332510	−	0.279009i
$554$	6.22071	+	5.21980i	0.264293	+	0.221768i
$555$		0			0
$556$	−13.6878	−	4.98193i	−0.580490	−	0.211281i
$557$	2.29110	−	3.96830i	0.0970769	−	0.168142i	−0.813397	−	0.581710i	$-0.802384\pi$
$557$	2.29110	−	3.96830i	0.0970769	−	0.168142i	0.910474	+	0.413567i	$0.135717\pi$
$558$		0			0
$559$	−1.56179	−	2.70509i	−0.0660565	−	0.114413i
$560$	−0.760371	−	4.31228i	−0.0321316	−	0.182227i
$561$		0			0
$562$	10.4843	−	3.81598i	0.442255	−	0.160968i
$563$	−2.13308	+	12.0973i	−0.0898986	+	0.509840i	0.906293	+	0.422650i	$0.138900\pi$
$563$	−2.13308	+	12.0973i	−0.0898986	+	0.509840i	−0.996192	+	0.0871905i	$0.972211\pi$
$564$		0			0
$565$	−32.3315	+	27.1293i	−1.36020	+	1.14134i
$566$	−14.5378			−0.611071
$567$		0			0
$568$	−21.6278			−0.907484
$569$	−11.1028	+	9.31634i	−0.465453	+	0.390561i	−0.845133	−	0.534557i	$-0.820479\pi$
$569$	−11.1028	+	9.31634i	−0.465453	+	0.390561i	0.379680	+	0.925118i	$0.376034\pi$
$570$		0			0
$571$	−3.82814	+	21.7104i	−0.160203	+	0.908554i	0.793672	+	0.608346i	$0.208167\pi$
$571$	−3.82814	+	21.7104i	−0.160203	+	0.908554i	−0.953874	+	0.300207i	$0.902944\pi$
$572$	5.50467	−	2.00354i	0.230162	−	0.0837721i
$573$		0			0
$574$	2.40044	+	13.6135i	0.100192	+	0.568218i
$575$	−1.31172	−	2.27197i	−0.0547025	−	0.0947475i
$576$		0			0
$577$	15.7418	−	27.2655i	0.655338	−	1.13508i	−0.326471	−	0.945207i	$-0.605859\pi$
$577$	15.7418	−	27.2655i	0.655338	−	1.13508i	0.981809	−	0.189872i	$-0.0608072\pi$
$578$	−16.3483	−	5.95031i	−0.680001	−	0.247500i
$579$		0			0
$580$	23.5866	+	19.7915i	0.979380	+	0.821798i
$581$	−1.74990	−	1.46834i	−0.0725979	−	0.0609169i
$582$		0			0
$583$	−0.399973	−	0.145578i	−0.0165652	−	0.00602923i
$584$	−16.2582	+	28.1600i	−0.672768	+	1.16527i
$585$		0			0
$586$	−4.19516	−	7.26623i	−0.173300	−	0.300165i
$587$	2.49523	+	14.1511i	0.102989	+	0.584080i	0.992004	+	0.126203i	$0.0402790\pi$
$587$	2.49523	+	14.1511i	0.102989	+	0.584080i	−0.889015	+	0.457877i	$0.848610\pi$
$588$		0			0
$589$	−21.4605	+	7.81097i	−0.884263	+	0.321845i
$590$	−1.28332	+	7.27804i	−0.0528333	+	0.299632i
$591$		0			0
$592$	3.12173	−	2.61944i	0.128302	−	0.107659i
$593$	41.0988			1.68772			0.843862	−	0.536560i	$-0.180276\pi$
$593$	41.0988			1.68772			0.843862	+	0.536560i	$0.180276\pi$
$594$		0			0
$595$	−37.2966			−1.52901
$596$	−9.65342	+	8.10018i	−0.395419	+	0.331796i
$597$		0			0
$598$	0.731913	−	4.15089i	0.0299301	−	0.169742i
$599$	8.04580	−	2.92843i	0.328742	−	0.119652i	−0.172376	−	0.985031i	$-0.555144\pi$
$599$	8.04580	−	2.92843i	0.328742	−	0.119652i	0.501118	+	0.865379i	$0.332922\pi$
$600$		0			0
$601$	−0.283951	−	1.61037i	−0.0115826	−	0.0656883i	0.978469	−	0.206396i	$-0.0661734\pi$
$601$	−0.283951	−	1.61037i	−0.0115826	−	0.0656883i	−0.990051	+	0.140707i	$0.955062\pi$
$602$	2.27311	+	3.93713i	0.0926449	+	0.160466i
$603$		0			0
$604$	16.6651	−	28.8648i	0.678094	−	1.17449i
$605$	2.52733	+	0.919873i	0.102751	+	0.0373982i
$606$		0			0
$607$	5.03248	+	4.22275i	0.204262	+	0.171396i	0.739180	−	0.673508i	$-0.235213\pi$
$607$	5.03248	+	4.22275i	0.204262	+	0.171396i	−0.534918	+	0.844904i	$0.679658\pi$
$608$	36.1651	+	30.3461i	1.46669	+	1.23070i
$609$		0			0
$610$	−0.593602	−	0.216054i	−0.0240343	−	0.00874775i
$611$	3.08374	−	5.34120i	0.124755	−	0.216082i
$612$		0			0
$613$	13.1363	+	22.7527i	0.530569	+	0.918973i	0.999364	+	0.0356656i	$0.0113551\pi$
$613$	13.1363	+	22.7527i	0.530569	+	0.918973i	−0.468795	+	0.883307i	$0.655312\pi$
$614$	0.00671875	+	0.0381039i	0.000271147	+	0.00153775i
$615$		0			0
$616$	−19.4971	+	7.09638i	−0.785562	+	0.285921i
$617$	1.08930	−	6.17772i	0.0438535	−	0.248706i	−0.954998	−	0.296611i	$-0.904143\pi$
$617$	1.08930	−	6.17772i	0.0438535	−	0.248706i	0.998852	+	0.0479054i	$0.0152546\pi$
$618$		0			0
$619$	3.78493	−	3.17593i	0.152129	−	0.127651i	−0.563546	−	0.826084i	$-0.690563\pi$
$619$	3.78493	−	3.17593i	0.152129	−	0.127651i	0.715676	+	0.698433i	$0.246119\pi$
$620$	−9.38839			−0.377047
$621$		0			0
$622$	−10.2936			−0.412738
$623$	7.14489	−	5.99528i	0.286254	−	0.240196i
$624$		0			0
$625$	−4.83028	+	27.3939i	−0.193211	+	1.09576i
$626$	11.0230	−	4.01206i	0.440569	−	0.160354i
$627$		0			0
$628$	−0.657012	−	3.72610i	−0.0262176	−	0.148688i
$629$	−17.3550	−	30.0598i	−0.691991	−	1.19856i
$630$		0			0
$631$	3.46210	−	5.99653i	0.137824	−	0.238718i	−0.788849	−	0.614587i	$-0.789322\pi$
$631$	3.46210	−	5.99653i	0.137824	−	0.238718i	0.926673	+	0.375869i	$0.122656\pi$
$632$	10.1253	+	3.68530i	0.402762	+	0.146593i
$633$		0			0
$634$	−5.14205	−	4.31469i	−0.204217	−	0.171358i
$635$	−7.21889	−	6.05737i	−0.286473	−	0.240379i
$636$		0			0
$637$	0.933370	+	0.339719i	0.0369815	+	0.0134601i
$638$	11.3450	−	19.6502i	0.449154	−	0.777957i
$639$		0			0
$640$	11.0653	+	19.1657i	0.437394	+	0.757589i
$641$	5.88995	+	33.4036i	0.232639	+	1.31936i	0.847529	+	0.530749i	$0.178089\pi$
$641$	5.88995	+	33.4036i	0.232639	+	1.31936i	−0.614890	+	0.788613i	$0.710800\pi$
$642$		0			0
$643$	−7.25745	+	2.64150i	−0.286206	+	0.104170i	−0.481134	−	0.876647i	$-0.659775\pi$
$643$	−7.25745	+	2.64150i	−0.286206	+	0.104170i	0.194928	+	0.980818i	$0.437553\pi$
$644$	2.45704	−	13.9346i	0.0968210	−	0.549099i
$645$		0			0
$646$	30.1476	−	25.2968i	1.18614	−	0.995289i
$647$	−35.1862			−1.38331			−0.691655	−	0.722228i	$-0.743118\pi$
$647$	−35.1862			−1.38331			−0.691655	+	0.722228i	$0.743118\pi$
$648$		0			0
$649$	−12.5615			−0.493083
$650$	0.515251	−	0.432347i	0.0202098	−	0.0169580i
$651$		0			0
$652$	5.34163	−	30.2939i	0.209194	−	1.18640i
$653$	18.3353	−	6.67349i	0.717514	−	0.261154i	0.0426440	−	0.999090i	$-0.486422\pi$
$653$	18.3353	−	6.67349i	0.717514	−	0.261154i	0.674870	+	0.737937i	$0.264200\pi$
$654$		0			0
$655$	−0.0422958	−	0.239871i	−0.00165263	−	0.00937255i
$656$	2.61726	+	4.53323i	0.102187	+	0.176993i
$657$		0			0
$658$	−4.48824	+	7.77386i	−0.174970	+	0.303057i
$659$	21.6942	+	7.89603i	0.845085	+	0.307586i	0.728035	−	0.685540i	$-0.240434\pi$
$659$	21.6942	+	7.89603i	0.845085	+	0.307586i	0.117050	+	0.993126i	$0.462656\pi$
$660$		0			0
$661$	−5.26760	−	4.42004i	−0.204886	−	0.171920i	0.534571	−	0.845123i	$-0.320473\pi$
$661$	−5.26760	−	4.42004i	−0.204886	−	0.171920i	−0.739457	+	0.673204i	$0.764918\pi$
$662$	18.4843	+	15.5102i	0.718412	+	0.602819i
$663$		0			0
$664$	2.26596	+	0.824741i	0.0879362	+	0.0320062i
$665$	23.9688	−	41.5152i	0.929471	−	1.60989i
$666$		0			0
$667$	18.8280	+	32.6110i	0.729023	+	1.26270i
$668$	2.16844	+	12.2978i	0.0838995	+	0.475818i
$669$		0			0
$670$	−17.5805	+	6.39879i	−0.679195	+	0.247207i
$671$	0.186449	−	1.05740i	0.00719777	−	0.0408206i
$672$		0			0
$673$	−23.4964	+	19.7158i	−0.905718	+	0.759988i	−0.971300	−	0.237859i	$-0.923554\pi$
$673$	−23.4964	+	19.7158i	−0.905718	+	0.759988i	0.0655815	+	0.997847i	$0.479110\pi$
$674$	−18.5624			−0.714997
$675$		0			0
$676$	15.6442			0.601700
$677$	10.4059	−	8.73161i	0.399932	−	0.335583i	−0.420535	−	0.907276i	$-0.638158\pi$
$677$	10.4059	−	8.73161i	0.399932	−	0.335583i	0.820467	+	0.571693i	$0.193713\pi$
$678$		0			0
$679$	2.60455	−	14.7711i	0.0999534	−	0.566864i
$680$	36.9967	−	13.4657i	1.41876	−	0.516386i
$681$		0			0
$682$	1.20139	+	6.81344i	0.0460037	+	0.260900i
$683$	−3.03350	−	5.25418i	−0.116074	−	0.201045i	0.802135	−	0.597143i	$-0.203698\pi$
$683$	−3.03350	−	5.25418i	−0.116074	−	0.201045i	−0.918208	+	0.396098i	$0.870364\pi$
$684$		0			0
$685$	9.05335	−	15.6809i	0.345911	−	0.599135i
$686$	−14.1550	−	5.15201i	−0.540442	−	0.196705i
$687$		0			0
$688$	1.31875	+	1.10656i	0.0502767	+	0.0421871i
$689$	0.138736	+	0.116414i	0.00528544	+	0.00443501i
$690$		0			0
$691$	−19.4188	−	7.06787i	−0.738727	−	0.268875i	−0.0548728	−	0.998493i	$-0.517475\pi$
$691$	−19.4188	−	7.06787i	−0.738727	−	0.268875i	−0.683854	+	0.729619i	$0.739698\pi$
$692$	−1.83756	+	3.18275i	−0.0698537	+	0.120990i
$693$		0			0
$694$	8.52054	+	14.7580i	0.323435	+	0.560206i
$695$	−4.30835	−	24.4339i	−0.163425	−	0.926830i
$696$		0			0
$697$	41.8964	−	15.2490i	1.58694	−	0.577599i
$698$	2.14015	−	12.1374i	0.0810058	−	0.459407i
$699$		0			0
$700$	1.72970	−	1.45139i	0.0653766	−	0.0548575i
$701$	−11.0222			−0.416303			−0.208151	−	0.978097i	$-0.566745\pi$
$701$	−11.0222			−0.416303			−0.208151	+	0.978097i	$0.566745\pi$
$702$		0			0
$703$	44.6131			1.68262
$704$	7.41054	−	6.21818i	0.279295	−	0.234356i
$705$		0			0
$706$	−1.74310	+	9.88560i	−0.0656024	+	0.372050i
$707$	24.0264	−	8.74489i	0.903605	−	0.328885i
$708$		0			0
$709$	−1.90795	−	10.8205i	−0.0716546	−	0.406373i	−0.999446	−	0.0332746i	$-0.989406\pi$
$709$	−1.90795	−	10.8205i	−0.0716546	−	0.406373i	0.927792	−	0.373099i	$-0.121705\pi$
$710$	−7.56897	−	13.1098i	−0.284058	−	0.492003i
$711$		0			0
$712$	−4.92288	+	8.52669i	−0.184493	+	0.319551i
$713$	−10.7895	−	3.92704i	−0.404068	−	0.147069i
$714$		0			0
$715$	7.64354	+	6.41369i	0.285852	+	0.239858i
$716$	3.93778	+	3.30419i	0.147162	+	0.123483i
$717$		0			0
$718$	18.8762	+	6.87038i	0.704454	+	0.256400i
$719$	16.3529	−	28.3240i	0.609859	−	1.05631i	−0.381404	−	0.924408i	$-0.624559\pi$
$719$	16.3529	−	28.3240i	0.609859	−	1.05631i	0.991263	−	0.131898i	$-0.0421072\pi$
$720$		0			0
$721$	10.6734	+	18.4870i	0.397500	+	0.688490i
$722$	6.21768	+	35.2622i	0.231398	+	1.31232i
$723$		0			0
$724$	−0.352014	+	0.128123i	−0.0130825	+	0.00476164i
$725$	−1.04347	+	5.91781i	−0.0387535	+	0.219782i
$726$		0			0
$727$	29.4625	−	24.7220i	1.09271	−	0.916888i	0.0957920	−	0.995401i	$-0.469462\pi$
$727$	29.4625	−	24.7220i	1.09271	−	0.916888i	0.996913	+	0.0785129i	$0.0250172\pi$
$728$	8.82830			0.327199
$729$		0			0
$730$	−22.7591			−0.842352
$731$	11.2325	−	9.42515i	0.415447	−	0.348602i
$732$		0			0
$733$	2.44978	−	13.8934i	0.0904849	−	0.513165i	−0.905553	−	0.424233i	$-0.860544\pi$
$733$	2.44978	−	13.8934i	0.0904849	−	0.513165i	0.996038	−	0.0889317i	$-0.0283453\pi$
$734$	−11.6747	+	4.24924i	−0.430921	+	0.156842i
$735$		0			0
$736$	4.12160	+	23.3748i	0.151924	+	0.861605i
$737$	−15.8999	−	27.5395i	−0.585681	−	1.01443i
$738$		0			0
$739$	5.92286	−	10.2587i	0.217876	−	0.377372i	−0.736283	−	0.676674i	$-0.763421\pi$
$739$	5.92286	−	10.2587i	0.217876	−	0.377372i	0.954158	+	0.299302i	$0.0967539\pi$
$740$	17.2340	+	6.27267i	0.633535	+	0.230588i
$741$		0			0
$742$	−0.201924	−	0.169435i	−0.00741288	−	0.00622014i
$743$	16.6749	+	13.9919i	0.611743	+	0.513314i	0.895196	−	0.445673i	$-0.147035\pi$
$743$	16.6749	+	13.9919i	0.611743	+	0.513314i	−0.283453	+	0.958986i	$0.591480\pi$
$744$		0			0
$745$	−20.1701	−	7.34131i	−0.738974	−	0.268965i
$746$	−0.710290	+	1.23026i	−0.0260056	+	0.0450429i
$747$		0			0
$748$	13.7494	+	23.8147i	0.502729	+	0.870753i
$749$	3.36412	+	19.0788i	0.122922	+	0.697126i
$750$		0			0
$751$	39.9830	−	14.5526i	1.45900	−	0.531033i	0.513911	−	0.857844i	$-0.328196\pi$
$751$	39.9830	−	14.5526i	1.45900	−	0.531033i	0.945090	+	0.326811i	$0.105974\pi$
$752$	−0.590247	+	3.34746i	−0.0215241	+	0.122069i
$753$		0			0
$754$	−7.39574	+	6.20576i	−0.269337	+	0.226000i
$755$	56.7719			2.06614
$756$		0			0
$757$	−20.6382			−0.750110			−0.375055	−	0.927003i	$-0.622376\pi$
$757$	−20.6382			−0.750110			−0.375055	+	0.927003i	$0.622376\pi$
$758$	0.683318	−	0.573372i	0.0248192	−	0.0208258i
$759$		0			0
$760$	−8.78728	+	49.8352i	−0.318748	+	1.80771i
$761$	−46.4631	+	16.9112i	−1.68429	+	0.613030i	−0.993887	−	0.110398i	$-0.964787\pi$
$761$	−46.4631	+	16.9112i	−1.68429	+	0.613030i	−0.690400	+	0.723428i	$0.742565\pi$
$762$		0			0
$763$	−0.544851	−	3.09000i	−0.0197249	−	0.111866i
$764$	1.67275	+	2.89729i	0.0605181	+	0.104820i
$765$		0			0
$766$	8.48799	−	14.7016i	0.306684	−	0.531192i
$767$	5.02250	+	1.82804i	0.181352	+	0.0660067i
$768$		0			0
$769$	16.9553	+	14.2272i	0.611424	+	0.513046i	0.895095	−	0.445876i	$-0.147108\pi$
$769$	16.9553	+	14.2272i	0.611424	+	0.513046i	−0.283670	+	0.958922i	$0.591552\pi$
$770$	−11.1248	−	9.33482i	−0.400910	−	0.336403i
$771$		0			0
$772$	0.650520	+	0.236770i	0.0234127	+	0.00852153i
$773$	10.9836	−	19.0241i	0.395051	−	0.684248i	−0.598057	−	0.801454i	$-0.704060\pi$
$773$	10.9836	−	19.0241i	0.395051	−	0.684248i	0.993108	+	0.117206i	$0.0373936\pi$
$774$		0			0
$775$	−0.916134	−	1.58679i	−0.0329085	−	0.0569992i
$776$	2.74941	+	15.5927i	0.0986982	+	0.559745i
$777$		0			0
$778$	−19.1449	+	6.96819i	−0.686379	+	0.249822i
$779$	−9.95104	+	56.4351i	−0.356533	+	2.02200i
$780$		0			0
$781$	19.7106	−	16.5391i	0.705300	−	0.591817i
$782$	19.7860			0.707547
$783$		0			0
$784$	−0.547423			−0.0195508
$785$	4.93687	−	4.14253i	0.176204	−	0.147853i
$786$		0			0
$787$	0.0929939	−	0.527395i	0.00331488	−	0.0187996i	−0.983105	−	0.183040i	$-0.941406\pi$
$787$	0.0929939	−	0.527395i	0.00331488	−	0.0187996i	0.986420	+	0.164240i	$0.0525173\pi$
$788$	29.0343	−	10.5676i	1.03430	−	0.376456i
$789$		0			0
$790$	1.30962	+	7.42721i	0.0465941	+	0.264248i
$791$	−22.2132	−	38.4744i	−0.789810	−	1.36799i
$792$		0			0
$793$	−0.228429	+	0.395650i	−0.00811174	+	0.0140500i
$794$	−3.06825	−	1.11675i	−0.108888	−	0.0396320i
$795$		0			0
$796$	−2.27904	−	1.91234i	−0.0807785	−	0.0677812i
$797$	−30.7176	−	25.7751i	−1.08807	−	0.913001i	−0.0915068	−	0.995804i	$-0.529168\pi$
$797$	−30.7176	−	25.7751i	−1.08807	−	0.913001i	−0.996566	+	0.0828030i	$0.973613\pi$
$798$		0			0
$799$	27.2059	+	9.90214i	0.962476	+	0.350312i
$800$	−1.89383	+	3.28021i	−0.0669570	+	0.115973i
$801$		0			0
$802$	−3.04475	−	5.27366i	−0.107514	−	0.186219i
$803$	−6.71744	−	38.0965i	−0.237053	−	1.34440i
$804$		0			0
$805$	22.6476	−	8.24306i	0.798224	−	0.290530i
$806$	0.511184	−	2.89907i	0.0180057	−	0.102115i
$807$		0			0
$808$	−20.6759	+	17.3491i	−0.727376	+	0.610341i
$809$	−17.1826			−0.604110			−0.302055	−	0.953291i	$-0.597673\pi$
$809$	−17.1826			−0.604110			−0.302055	+	0.953291i	$0.597673\pi$
$810$		0			0
$811$	−19.6169			−0.688842			−0.344421	−	0.938815i	$-0.611925\pi$
$811$	−19.6169			−0.688842			−0.344421	+	0.938815i	$0.611925\pi$
$812$	−24.8276	+	20.8328i	−0.871277	+	0.731089i
$813$		0			0
$814$	2.34690	−	13.3099i	0.0822588	−	0.466513i
$815$	49.2361	−	17.9205i	1.72467	−	0.627727i
$816$		0			0
$817$	3.27264	+	18.5601i	0.114495	+	0.649334i
$818$	6.77755	+	11.7391i	0.236971	+	0.410446i
$819$		0			0
$820$	−11.7789	+	20.4017i	−0.411338	+	0.712459i
$821$	33.7405	+	12.2806i	1.17755	+	0.428594i	0.855337	−	0.518072i	$-0.173350\pi$
$821$	33.7405	+	12.2806i	1.17755	+	0.428594i	0.322216	+	0.946666i	$0.395572\pi$
$822$		0			0
$823$	−19.7778	−	16.5955i	−0.689410	−	0.578484i	0.229329	−	0.973349i	$-0.426347\pi$
$823$	−19.7778	−	16.5955i	−0.689410	−	0.578484i	−0.918739	+	0.394865i	$0.870791\pi$
$824$	−17.2622	−	14.4847i	−0.601358	−	0.504599i
$825$		0			0
$826$	−7.31001	−	2.66063i	−0.254348	−	0.0925750i
$827$	−12.4793	+	21.6148i	−0.433948	+	0.751619i	−0.997209	−	0.0746593i	$-0.976213\pi$
$827$	−12.4793	+	21.6148i	−0.433948	+	0.751619i	0.563261	+	0.826279i	$0.309546\pi$
$828$		0			0
$829$	−1.39964	−	2.42424i	−0.0486114	−	0.0841974i	0.840696	−	0.541508i	$-0.182146\pi$
$829$	−1.39964	−	2.42424i	−0.0486114	−	0.0841974i	−0.889307	+	0.457310i	$0.848813\pi$
$830$	0.293082	+	1.66215i	0.0101730	+	0.0576942i
$831$		0			0
$832$	−3.86789	+	1.40780i	−0.134095	+	0.0488065i
$833$	−0.809669	+	4.59186i	−0.0280534	+	0.159098i
$834$		0			0
$835$	−16.2939	+	13.6722i	−0.563875	+	0.473147i
$836$	−35.3445			−1.22242
$837$		0			0
$838$	−8.93083			−0.308511
$839$	34.2482	−	28.7377i	1.18238	−	0.992134i	0.182419	−	0.983221i	$-0.441607\pi$
$839$	34.2482	−	28.7377i	1.18238	−	0.992134i	0.999960	−	0.00891362i	$-0.00283733\pi$
$840$		0			0
$841$	9.94181	−	56.3828i	0.342821	−	1.94423i
$842$	−5.32864	+	1.93947i	−0.183637	+	0.0668385i
$843$		0			0
$844$	−4.84732	−	27.4905i	−0.166852	−	0.946263i
$845$	13.3235	+	23.0770i	0.458342	+	0.793872i
$846$		0			0
$847$	−1.41552	+	2.45175i	−0.0486378	+	0.0842431i
$848$	−0.0937946	−	0.0341384i	−0.00322092	−	0.00117232i
$849$		0			0
$850$	2.41873	+	2.02956i	0.0829618	+	0.0696132i
$851$	17.1821	+	14.4175i	0.588996	+	0.494226i
$852$		0			0
$853$	40.8907	+	14.8830i	1.40007	+	0.509584i	0.928199	−	0.372084i	$-0.121357\pi$
$853$	40.8907	+	14.8830i	1.40007	+	0.509584i	0.471871	+	0.881668i	$0.343579\pi$
$854$	0.332467	−	0.575850i	0.0113768	−	0.0197052i
$855$		0			0
$856$	−10.2254	−	17.7108i	−0.349496	−	0.605344i
$857$	−1.26945	−	7.19944i	−0.0433638	−	0.245928i	0.955419	−	0.295253i	$-0.0954040\pi$
$857$	−1.26945	−	7.19944i	−0.0433638	−	0.245928i	−0.998783	+	0.0493252i	$0.984293\pi$
$858$		0			0
$859$	9.08034	−	3.30497i	0.309817	−	0.112764i	−0.182432	−	0.983218i	$-0.558397\pi$
$859$	9.08034	−	3.30497i	0.309817	−	0.112764i	0.492249	+	0.870454i	$0.336175\pi$
$860$	−1.34535	+	7.62987i	−0.0458761	+	0.260176i
$861$		0			0
$862$	−0.231807	+	0.194510i	−0.00789539	+	0.00662502i
$863$	−3.15525			−0.107406			−0.0537030	−	0.998557i	$-0.517102\pi$
$863$	−3.15525			−0.107406			−0.0537030	+	0.998557i	$0.517102\pi$
$864$		0			0
$865$	−6.25989			−0.212843
$866$	14.3589	−	12.0485i	0.487934	−	0.409426i
$867$		0			0
$868$	1.71605	−	9.73221i	0.0582466	−	0.330333i
$869$	−12.0459	+	4.38435i	−0.408629	+	0.148729i
$870$		0			0
$871$	2.34956	+	13.3250i	0.0796119	+	0.451502i
$872$	1.65609	+	2.86844i	0.0560824	+	0.0971376i
$873$		0			0
$874$	−12.7156	+	22.0240i	−0.430110	+	0.744973i
$875$	−24.3142	−	8.84966i	−0.821971	−	0.299173i
$876$		0			0
$877$	−40.5413	−	34.0182i	−1.36898	−	1.14871i	−0.973093	−	0.230413i	$-0.925992\pi$
$877$	−40.5413	−	34.0182i	−1.36898	−	1.14871i	−0.395888	−	0.918299i	$-0.629563\pi$
$878$	21.8445	+	18.3297i	0.737218	+	0.618599i
$879$		0			0
$880$	−5.16751	−	1.88082i	−0.174197	−	0.0634024i
$881$	−18.3507	+	31.7843i	−0.618250	+	1.07084i	0.371555	+	0.928411i	$0.378825\pi$
$881$	−18.3507	+	31.7843i	−0.618250	+	1.07084i	−0.989805	+	0.142430i	$0.954508\pi$
$882$		0			0
$883$	−14.9551	−	25.9031i	−0.503280	−	0.871707i	−0.999993	−	0.00379204i	$-0.998793\pi$
$883$	−14.9551	−	25.9031i	−0.503280	−	0.871707i	0.496712	−	0.867915i	$-0.334540\pi$
$884$	−2.03178	−	11.5228i	−0.0683362	−	0.387554i
$885$		0			0
$886$	−27.6156	+	10.0513i	−0.927764	+	0.337679i
$887$	9.68114	−	54.9045i	0.325061	−	1.84351i	−0.184185	−	0.982892i	$-0.558965\pi$
$887$	9.68114	−	54.9045i	0.325061	−	1.84351i	0.509246	−	0.860621i	$-0.329924\pi$
$888$		0			0
$889$	7.59871	−	6.37607i	0.254852	−	0.213847i
$890$	−6.89133			−0.230998
$891$		0			0
$892$	18.5252			0.620270
$893$	−28.5061	+	23.9195i	−0.953922	+	0.800435i
$894$		0			0
$895$	−1.52042	+	8.62271i	−0.0508219	+	0.288225i
$896$	−21.8901	+	7.96735i	−0.731297	+	0.266170i
$897$		0			0
$898$	−1.59169	−	9.02693i	−0.0531154	−	0.301233i
$899$	13.1499	+	22.7763i	0.438573	+	0.759631i
$900$		0			0
$901$	−0.425085	+	0.736269i	−0.0141616	+	0.0245287i
$902$	16.3134	+	5.93761i	0.543178	+	0.197701i
$903$		0			0
$904$	35.9255	+	30.1451i	1.19486	+	1.00261i
$905$	−0.488791	−	0.410144i	−0.0162480	−	0.0136337i
$906$		0			0
$907$	−33.8305	−	12.3133i	−1.12332	−	0.408856i	−0.287459	−	0.957793i	$-0.592811\pi$
$907$	−33.8305	−	12.3133i	−1.12332	−	0.408856i	−0.835864	+	0.548937i	$0.815033\pi$
$908$	8.69930	−	15.0676i	0.288696	−	0.500037i
$909$		0			0
$910$	3.08959	+	5.35132i	0.102419	+	0.177395i
$911$	−2.84381	−	16.1280i	−0.0942195	−	0.534345i	−0.994984	−	0.100037i	$-0.968104\pi$
$911$	−2.84381	−	16.1280i	−0.0942195	−	0.534345i	0.900764	−	0.434308i	$-0.143007\pi$
$912$		0			0
$913$	−2.69578	+	0.981183i	−0.0892173	+	0.0324724i
$914$	−2.68158	+	15.2080i	−0.0886986	+	0.503035i
$915$		0			0
$916$	−27.4254	+	23.0126i	−0.906160	+	0.760358i
$917$	0.256387			0.00846665
$918$		0			0
$919$	19.5368			0.644461			0.322231	−	0.946661i	$-0.395567\pi$
$919$	19.5368			0.644461			0.322231	+	0.946661i	$0.395567\pi$
$920$	−19.4894	+	16.3536i	−0.642547	+	0.539161i
$921$		0			0
$922$	1.03204	−	5.85301i	0.0339885	−	0.192758i
$923$	−10.2878	+	3.74446i	−0.338628	+	0.123250i
$924$		0			0
$925$	0.621539	+	3.52493i	0.0204361	+	0.115899i
$926$	6.20413	+	10.7459i	0.203880	+	0.353131i
$927$		0			0
$928$	27.1834	−	47.0830i	0.892339	−	1.54558i
$929$	10.1028	+	3.67710i	0.331461	+	0.120642i	0.502389	−	0.864642i	$-0.332454\pi$
$929$	10.1028	+	3.67710i	0.331461	+	0.120642i	−0.170929	+	0.985283i	$0.554677\pi$
$930$		0			0
$931$	−4.59090	−	3.85223i	−0.150461	−	0.126252i
$932$	−5.76734	−	4.83937i	−0.188915	−	0.158519i
$933$		0			0
$934$	19.1043	+	6.95341i	0.625113	+	0.227523i
$935$	−23.4196	+	40.5639i	−0.765903	+	1.32658i
$936$		0			0
$937$	14.2219	+	24.6330i	0.464609	+	0.804727i	0.999184	−	0.0403947i	$-0.0128615\pi$
$937$	14.2219	+	24.6330i	0.464609	+	0.804727i	−0.534575	+	0.845121i	$0.679528\pi$
$938$	−3.41968	−	19.3940i	−0.111656	−	0.633235i
$939$		0			0
$940$	−14.3750	+	5.23208i	−0.468861	+	0.170651i
$941$	−4.82057	+	27.3388i	−0.157146	+	0.891219i	0.799652	+	0.600464i	$0.205018\pi$
$941$	−4.82057	+	27.3388i	−0.157146	+	0.891219i	−0.956798	+	0.290755i	$0.906094\pi$
$942$		0			0
$943$	−22.0705	+	18.5194i	−0.718715	+	0.603073i
$944$	−2.94571			−0.0958746
$945$		0			0
$946$	5.70939			0.185628
$947$	−32.5381	+	27.3027i	−1.05735	+	0.887220i	−0.993847	−	0.110762i	$-0.964671\pi$
$947$	−32.5381	+	27.3027i	−1.05735	+	0.887220i	−0.0635006	+	0.997982i	$0.520226\pi$
$948$		0			0
$949$	−2.85822	+	16.2098i	−0.0927818	+	0.526192i
$950$	−3.81353	+	1.38801i	−0.123727	+	0.0450330i
$951$		0			0
$952$	7.19642	+	40.8129i	0.233237	+	1.32275i
$953$	24.5758	+	42.5665i	0.796088	+	1.37886i	0.922146	+	0.386842i	$0.126434\pi$
$953$	24.5758	+	42.5665i	0.796088	+	1.37886i	−0.126058	+	0.992023i	$0.540233\pi$
$954$		0			0
$955$	−2.84922	+	4.93500i	−0.0921987	+	0.159693i
$956$	−10.9744	−	3.99436i	−0.354937	−	0.129187i
$957$		0			0
$958$	−23.4440	−	19.6719i	−0.757442	−	0.635569i
$959$	14.6003	+	12.2511i	0.471469	+	0.395609i
$960$		0			0
$961$	21.5949	+	7.85989i	0.696609	+	0.253545i
$962$	−2.87532	+	4.98021i	−0.0927041	+	0.160568i
$963$		0			0
$964$	−0.308456	−	0.534262i	−0.00993471	−	0.0172074i
$965$	0.204757	+	1.16124i	0.00659137	+	0.0373815i
$966$		0			0
$967$	−45.0930	+	16.4125i	−1.45009	+	0.527791i	−0.942617	−	0.333875i	$-0.891644\pi$
$967$	−45.0930	+	16.4125i	−1.45009	+	0.527791i	−0.507476	+	0.861666i	$0.669422\pi$
$968$	0.518948	−	2.94310i	0.0166796	−	0.0945947i
$969$		0			0
$970$	−8.48940	+	7.12346i	−0.272578	+	0.228720i
$971$	28.9682			0.929633			0.464817	−	0.885407i	$-0.346120\pi$
$971$	28.9682			0.929633			0.464817	+	0.885407i	$0.346120\pi$
$972$		0			0
$973$	26.1162			0.837247
$974$	6.97850	−	5.85566i	0.223606	−	0.187627i
$975$		0			0
$976$	0.0437226	−	0.247963i	0.00139953	−	0.00793712i
$977$	−14.2807	+	5.19774i	−0.456879	+	0.166290i	−0.560199	−	0.828358i	$-0.689276\pi$
$977$	−14.2807	+	5.19774i	−0.456879	+	0.166290i	0.103320	+	0.994648i	$0.467053\pi$
$978$		0			0
$979$	−2.03401	−	11.5354i	−0.0650071	−	0.368674i
$980$	−1.23183	−	2.13360i	−0.0393495	−	0.0681553i
$981$		0			0
$982$	−14.9907	+	25.9647i	−0.478373	+	0.828567i
$983$	−36.2460	−	13.1925i	−1.15607	−	0.420774i	−0.308377	−	0.951264i	$-0.599786\pi$
$983$	−36.2460	−	13.1925i	−1.15607	−	0.420774i	−0.847691	+	0.530490i	$0.822008\pi$
$984$		0			0
$985$	40.3157	+	33.8289i	1.28457	+	1.07788i
$986$	−34.7177	−	29.1316i	−1.10564	−	0.927739i
$987$		0			0
$988$	14.1319	+	5.14358i	0.449595	+	0.163639i
$989$	−4.73760	+	8.20576i	−0.150647	+	0.260928i
$990$		0			0
$991$	−25.5171	−	44.1968i	−0.810576	−	1.40396i	−0.912461	−	0.409163i	$-0.865821\pi$
$991$	−25.5171	−	44.1968i	−0.810576	−	1.40396i	0.101885	−	0.994796i	$-0.467512\pi$
$992$	2.87862	+	16.3254i	0.0913961	+	0.518333i
$993$		0			0
$994$	14.9734	−	5.44988i	0.474928	−	0.172860i
$995$	0.879961	−	4.99050i	0.0278966	−	0.158210i
$996$		0			0
$997$	24.3581	−	20.4389i	0.771429	−	0.647306i	−0.169645	−	0.985505i	$-0.554262\pi$
$997$	24.3581	−	20.4389i	0.771429	−	0.647306i	0.941075	+	0.338199i	$0.109818\pi$
$998$	−22.9910			−0.727768
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.t.325.2		12
3.2	odd	2		729.2.e.k.325.1		12
9.2	odd	6		729.2.e.l.568.2		12
9.4	even	3		729.2.e.j.82.2		12
9.5	odd	6		729.2.e.u.82.1		12
9.7	even	3		729.2.e.s.568.1		12
27.2	odd	18		729.2.e.l.163.2		12
27.4	even	9		729.2.a.b.1.5	✓	6
27.5	odd	18		729.2.c.a.244.5		12
27.7	even	9		729.2.e.j.649.2		12
27.11	odd	18		729.2.e.k.406.1		12
27.13	even	9		729.2.c.d.487.2		12
27.14	odd	18		729.2.c.a.487.5		12
27.16	even	9	inner	729.2.e.t.406.2		12
27.20	odd	18		729.2.e.u.649.1		12
27.22	even	9		729.2.c.d.244.2		12
27.23	odd	18		729.2.a.e.1.2	yes	6
27.25	even	9		729.2.e.s.163.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.5	✓	6	27.4	even	9
729.2.a.e.1.2	yes	6	27.23	odd	18
729.2.c.a.244.5		12	27.5	odd	18
729.2.c.a.487.5		12	27.14	odd	18
729.2.c.d.244.2		12	27.22	even	9
729.2.c.d.487.2		12	27.13	even	9
729.2.e.j.82.2		12	9.4	even	3
729.2.e.j.649.2		12	27.7	even	9
729.2.e.k.325.1		12	3.2	odd	2
729.2.e.k.406.1		12	27.11	odd	18
729.2.e.l.163.2		12	27.2	odd	18
729.2.e.l.568.2		12	9.2	odd	6
729.2.e.s.163.1		12	27.25	even	9
729.2.e.s.568.1		12	9.7	even	3
729.2.e.t.325.2		12	1.1	even	1	trivial
729.2.e.t.406.2		12	27.16	even	9	inner
729.2.e.u.82.1		12	9.5	odd	6
729.2.e.u.649.1		12	27.20	odd	18

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.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.595778 - 0.499917i) q^{2} +(-0.242262 + 1.37394i) q^{4} +(-2.23304 + 0.812759i) q^{5} +(-0.434359 - 2.46337i) q^{7} +(1.32025 + 2.28674i) q^{8} +O(q^{10})\)	\(q+(0.595778 - 0.499917i) q^{2} +(-0.242262 + 1.37394i) q^{4} +(-2.23304 + 0.812759i) q^{5} +(-0.434359 - 2.46337i) q^{7} +(1.32025 + 2.28674i) q^{8} +(-0.924081 + 1.60056i) q^{10} +(-2.95192 - 1.07441i) q^{11} +(1.02392 + 0.859169i) q^{13} +(-1.49026 - 1.25048i) q^{14} +(-0.692233 - 0.251952i) q^{16} +(-3.13726 + 5.43389i) q^{17} +(-4.03234 - 6.98422i) q^{19} +(-0.575699 - 3.26495i) q^{20} +(-2.29581 + 0.835605i) q^{22} +(0.704074 - 3.99300i) q^{23} +(0.495652 - 0.415902i) q^{25} +1.03954 q^{26} +3.48975 q^{28} +(-7.11443 + 5.96971i) q^{29} +(0.491741 - 2.78880i) q^{31} +(-5.50090 + 2.00216i) q^{32} +(0.847385 + 4.80576i) q^{34} +(2.97207 + 5.14778i) q^{35} +(-2.76596 + 4.79078i) q^{37} +(-5.89391 - 2.14521i) q^{38} +(-4.80674 - 4.03334i) q^{40} +(-5.44333 - 4.56750i) q^{41} +(-2.19597 - 0.799267i) q^{43} +(2.19131 - 3.79547i) q^{44} +(-1.57670 - 2.73092i) q^{46} +(-0.801248 - 4.54411i) q^{47} +(0.698301 - 0.254161i) q^{49} +(0.0873823 - 0.495570i) q^{50} +(-1.42850 + 1.19865i) q^{52} +0.135496 q^{53} +7.46499 q^{55} +(5.05964 - 4.24554i) q^{56} +(-1.25426 + 7.11324i) q^{58} +(3.75759 - 1.36765i) q^{59} +(0.0593526 + 0.336605i) q^{61} +(-1.10120 - 1.90733i) q^{62} +(-1.53974 + 2.66690i) q^{64} +(-2.98474 - 1.08636i) q^{65} +(7.75461 + 6.50689i) q^{67} +(-6.70579 - 5.62682i) q^{68} +(4.34415 + 1.58114i) q^{70} +(-4.09540 + 7.09344i) q^{71} +(6.15722 + 10.6646i) q^{73} +(0.747095 + 4.23698i) q^{74} +(10.5728 - 3.84817i) q^{76} +(-1.36448 + 7.73837i) q^{77} +(3.12600 - 2.62302i) q^{79} +1.75056 q^{80} -5.52638 q^{82} +(0.699573 - 0.587012i) q^{83} +(2.58917 - 14.6839i) q^{85} +(-1.70788 + 0.621616i) q^{86} +(-1.44038 - 8.16879i) q^{88} +(1.86437 + 3.22919i) q^{89} +(1.67171 - 2.89548i) q^{91} +(5.31556 + 1.93471i) q^{92} +(-2.74904 - 2.30672i) q^{94} +(14.6809 + 12.3187i) q^{95} +(5.63467 + 2.05085i) q^{97} +(0.288973 - 0.500515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} + 6 q^{7} + 6 q^{8} - 6 q^{10} - 15 q^{11} - 3 q^{13} - 21 q^{14} + 9 q^{16} - 9 q^{17} - 12 q^{19} - 3 q^{20} + 33 q^{22} + 15 q^{23} - 12 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} - 12 q^{31} - 27 q^{32} + 27 q^{34} + 30 q^{35} - 3 q^{37} - 39 q^{38} + 24 q^{40} - 39 q^{41} + 24 q^{43} - 33 q^{44} + 3 q^{46} - 42 q^{47} - 30 q^{49} - 15 q^{50} - 45 q^{52} + 18 q^{53} + 30 q^{55} + 12 q^{56} - 30 q^{58} + 15 q^{59} - 3 q^{61} - 30 q^{62} - 6 q^{64} - 6 q^{65} - 3 q^{67} + 36 q^{68} - 75 q^{70} - 12 q^{73} + 60 q^{74} + 30 q^{76} + 33 q^{77} + 33 q^{79} + 42 q^{80} - 42 q^{82} - 33 q^{83} - 18 q^{85} - 30 q^{86} - 42 q^{88} - 9 q^{89} - 18 q^{91} + 33 q^{92} - 66 q^{94} + 12 q^{95} + 15 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 + 6 * q^5 + 6 * q^7 + 6 * q^8 - 6 * q^10 - 15 * q^11 - 3 * q^13 - 21 * q^14 + 9 * q^16 - 9 * q^17 - 12 * q^19 - 3 * q^20 + 33 * q^22 + 15 * q^23 - 12 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 - 12 * q^31 - 27 * q^32 + 27 * q^34 + 30 * q^35 - 3 * q^37 - 39 * q^38 + 24 * q^40 - 39 * q^41 + 24 * q^43 - 33 * q^44 + 3 * q^46 - 42 * q^47 - 30 * q^49 - 15 * q^50 - 45 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 - 30 * q^58 + 15 * q^59 - 3 * q^61 - 30 * q^62 - 6 * q^64 - 6 * q^65 - 3 * q^67 + 36 * q^68 - 75 * q^70 - 12 * q^73 + 60 * q^74 + 30 * q^76 + 33 * q^77 + 33 * q^79 + 42 * q^80 - 42 * q^82 - 33 * q^83 - 18 * q^85 - 30 * q^86 - 42 * q^88 - 9 * q^89 - 18 * q^91 + 33 * q^92 - 66 * q^94 + 12 * q^95 + 15 * q^97 + 18 * q^98

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