LMFDB - Embedded newform 729.2.e.l.163.2

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			163.2
Root			$-1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.l.568.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.730829 - 0.266000i) q^{2} +(-1.06873 + 0.896774i) q^{4} +(-0.412648 - 2.34025i) q^{5} +(-1.91617 - 1.60785i) q^{7} +(-1.32025 + 2.28674i) q^{8} +O(q^{10})$	\(q+(0.730829 - 0.266000i) q^{2} +(-1.06873 + 0.896774i) q^{4} +(-0.412648 - 2.34025i) q^{5} +(-1.91617 - 1.60785i) q^{7} +(-1.32025 + 2.28674i) q^{8} +(-0.924081 - 1.60056i) q^{10} +(-0.545493 + 3.09365i) q^{11} +(-1.25602 - 0.457154i) q^{13} +(-1.82808 - 0.665366i) q^{14} +(0.127919 - 0.725467i) q^{16} +(3.13726 + 5.43389i) q^{17} +(-4.03234 + 6.98422i) q^{19} +(2.53968 + 2.13105i) q^{20} +(0.424248 + 2.40603i) q^{22} +(-3.10600 + 2.60625i) q^{23} +(-0.608008 + 0.221297i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(-8.72714 + 3.17642i) q^{29} +(2.16930 - 1.82026i) q^{31} +(-1.01652 - 5.76500i) q^{32} +(3.73822 + 3.13674i) q^{34} +(-2.97207 + 5.14778i) q^{35} +(-2.76596 - 4.79078i) q^{37} +(-1.08915 + 6.17688i) q^{38} +(5.89634 + 2.14609i) q^{40} +(-6.67723 - 2.43031i) q^{41} +(0.405799 - 2.30140i) q^{43} +(-2.19131 - 3.79547i) q^{44} +(-1.57670 + 2.73092i) q^{46} +(3.53469 + 2.96595i) q^{47} +(-0.129041 - 0.731827i) q^{49} +(-0.385485 + 0.323460i) q^{50} +(1.75232 - 0.637791i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(6.20657 - 2.25901i) q^{56} +(-5.53312 + 4.64284i) q^{58} +(0.694374 + 3.93799i) q^{59} +(0.261833 + 0.219704i) q^{61} +(1.10120 - 1.90733i) q^{62} +(-1.53974 - 2.66690i) q^{64} +(-0.551558 + 3.12804i) q^{65} +(-9.51243 - 3.46224i) q^{67} +(-8.22586 - 2.99397i) q^{68} +(-0.802767 + 4.55272i) q^{70} +(4.09540 + 7.09344i) q^{71} +(6.15722 - 10.6646i) q^{73} +(-3.29579 - 2.76550i) q^{74} +(-1.95377 - 11.0804i) q^{76} +(6.01939 - 5.05086i) q^{77} +(-3.83460 + 1.39568i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(0.858154 - 0.312342i) q^{83} +(11.4221 - 9.58424i) q^{85} +(-0.315603 - 1.78987i) q^{86} +(-6.35419 - 5.33180i) q^{88} +(-1.86437 + 3.22919i) q^{89} +(1.67171 + 2.89548i) q^{91} +(0.982276 - 5.57076i) q^{92} +(3.37220 + 1.22738i) q^{94} +(18.0087 + 6.55465i) q^{95} +(-1.04125 + 5.90520i) q^{97} +(-0.288973 - 0.500515i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 12 * q^5 - 3 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} + 27 q^{16} + 9 q^{17} - 12 q^{19} + 39 q^{20} - 39 q^{22} + 21 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} + 6 q^{31} + 27 q^{32} - 18 q^{34} - 30 q^{35} - 3 q^{37} + 3 q^{38} + 33 q^{40} - 15 q^{41} - 30 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} - 3 q^{49} + 6 q^{50} - 18 q^{53} + 30 q^{55} + 15 q^{56} - 3 q^{58} + 30 q^{59} - 30 q^{61} + 30 q^{62} - 6 q^{64} - 12 q^{65} - 39 q^{67} + 18 q^{68} + 51 q^{70} - 12 q^{73} + 57 q^{74} + 57 q^{76} - 24 q^{77} + 15 q^{79} - 42 q^{80} - 42 q^{82} - 21 q^{83} + 54 q^{85} - 60 q^{86} + 12 q^{88} + 9 q^{89} - 18 q^{91} - 15 q^{92} + 33 q^{94} + 42 q^{95} - 12 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 + 12 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 3 * q^11 + 6 * q^13 - 6 * q^14 + 27 * q^16 + 9 * q^17 - 12 * q^19 + 39 * q^20 - 39 * q^22 + 21 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 + 6 * q^31 + 27 * q^32 - 18 * q^34 - 30 * q^35 - 3 * q^37 + 3 * q^38 + 33 * q^40 - 15 * q^41 - 30 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 - 3 * q^49 + 6 * q^50 - 18 * q^53 + 30 * q^55 + 15 * q^56 - 3 * q^58 + 30 * q^59 - 30 * q^61 + 30 * q^62 - 6 * q^64 - 12 * q^65 - 39 * q^67 + 18 * q^68 + 51 * q^70 - 12 * q^73 + 57 * q^74 + 57 * q^76 - 24 * q^77 + 15 * q^79 - 42 * q^80 - 42 * q^82 - 21 * q^83 + 54 * q^85 - 60 * q^86 + 12 * q^88 + 9 * q^89 - 18 * q^91 - 15 * q^92 + 33 * q^94 + 42 * q^95 - 12 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.730829	−	0.266000i	0.516774	−	0.188091i	−0.0704490	−	0.997515i	$-0.522443\pi$
$2$	0.730829	−	0.266000i	0.516774	−	0.188091i	0.587223	+	0.809425i	$0.300221\pi$
$3$		0			0
$3$		0			0
$4$	−1.06873	+	0.896774i	−0.534367	+	0.448387i
$5$	−0.412648	−	2.34025i	−0.184542	−	1.04659i	−0.926542	−	0.376190i	$-0.877234\pi$
$5$	−0.412648	−	2.34025i	−0.184542	−	1.04659i	0.742000	−	0.670399i	$-0.233877\pi$
$6$		0			0
$7$	−1.91617	−	1.60785i	−0.724242	−	0.607712i	0.204313	−	0.978906i	$-0.434504\pi$
$7$	−1.91617	−	1.60785i	−0.724242	−	0.607712i	−0.928555	+	0.371194i	$0.878948\pi$
$8$	−1.32025	+	2.28674i	−0.466780	+	0.808486i
$9$		0			0
$10$	−0.924081	−	1.60056i	−0.292220	−	0.506140i
$11$	−0.545493	+	3.09365i	−0.164472	+	0.932769i	0.785134	+	0.619326i	$0.212594\pi$
$11$	−0.545493	+	3.09365i	−0.164472	+	0.932769i	−0.949607	+	0.313444i	$0.898517\pi$
$12$		0			0
$13$	−1.25602	−	0.457154i	−0.348358	−	0.126792i	0.161915	−	0.986805i	$-0.448233\pi$
$13$	−1.25602	−	0.457154i	−0.348358	−	0.126792i	−0.510272	+	0.860013i	$0.670455\pi$
$14$	−1.82808	−	0.665366i	−0.488575	−	0.177827i
$15$		0			0
$16$	0.127919	−	0.725467i	0.0319799	−	0.181367i
$17$	3.13726	+	5.43389i	0.760897	+	1.31791i	0.942389	+	0.334520i	$0.108574\pi$
$17$	3.13726	+	5.43389i	0.760897	+	1.31791i	−0.181492	+	0.983392i	$0.558093\pi$
$18$		0			0
$19$	−4.03234	+	6.98422i	−0.925083	+	1.60229i	−0.133656	+	0.991028i	$0.542672\pi$
$19$	−4.03234	+	6.98422i	−0.925083	+	1.60229i	−0.791427	+	0.611263i	$0.790662\pi$
$20$	2.53968	+	2.13105i	0.567890	+	0.476516i
$21$		0			0
$22$	0.424248	+	2.40603i	0.0904499	+	0.512967i
$23$	−3.10600	+	2.60625i	−0.647646	+	0.543440i	−0.906356	−	0.422515i	$-0.861147\pi$
$23$	−3.10600	+	2.60625i	−0.647646	+	0.543440i	0.258709	+	0.965955i	$0.416703\pi$
$24$		0			0
$25$	−0.608008	+	0.221297i	−0.121602	+	0.0442593i
$26$	−1.03954			−0.203871
$27$		0			0
$28$	3.48975			0.659501
$29$	−8.72714	+	3.17642i	−1.62059	+	0.589846i	−0.983494	−	0.180939i	$-0.942086\pi$
$29$	−8.72714	+	3.17642i	−1.62059	+	0.589846i	−0.637095	+	0.770786i	$0.719864\pi$
$30$		0			0
$31$	2.16930	−	1.82026i	0.389618	−	0.326928i	−0.426846	−	0.904324i	$-0.640376\pi$
$31$	2.16930	−	1.82026i	0.389618	−	0.326928i	0.816464	+	0.577396i	$0.195931\pi$
$32$	−1.01652	−	5.76500i	−0.179698	−	1.01912i
$33$		0			0
$34$	3.73822	+	3.13674i	0.641099	+	0.537946i
$35$	−2.97207	+	5.14778i	−0.502372	+	0.870133i
$36$		0			0
$37$	−2.76596	−	4.79078i	−0.454720	−	0.787599i	0.543952	−	0.839117i	$-0.316927\pi$
$37$	−2.76596	−	4.79078i	−0.454720	−	0.787599i	−0.998672	+	0.0515178i	$0.983594\pi$
$38$	−1.08915	+	6.17688i	−0.176684	+	1.00202i
$39$		0			0
$40$	5.89634	+	2.14609i	0.932294	+	0.339327i
$41$	−6.67723	−	2.43031i	−1.04281	−	0.379551i	−0.236864	−	0.971543i	$-0.576120\pi$
$41$	−6.67723	−	2.43031i	−1.04281	−	0.379551i	−0.805944	+	0.591992i	$0.798342\pi$
$42$		0			0
$43$	0.405799	−	2.30140i	0.0618837	−	0.350960i	−0.938106	−	0.346349i	$-0.887421\pi$
$43$	0.405799	−	2.30140i	0.0618837	−	0.350960i	0.999989	−	0.00461079i	$-0.00146766\pi$
$44$	−2.19131	−	3.79547i	−0.330353	−	0.572188i
$45$		0			0
$46$	−1.57670	+	2.73092i	−0.232471	+	0.402652i
$47$	3.53469	+	2.96595i	0.515587	+	0.432629i	0.863090	−	0.505050i	$-0.168526\pi$
$47$	3.53469	+	2.96595i	0.515587	+	0.432629i	−0.347503	+	0.937679i	$0.612970\pi$
$48$		0			0
$49$	−0.129041	−	0.731827i	−0.0184344	−	0.104547i
$50$	−0.385485	+	0.323460i	−0.0545158	+	0.0457442i
$51$		0			0
$52$	1.75232	−	0.637791i	0.243003	−	0.0884457i
$53$	−0.135496			−0.0186118			−0.00930588	−	0.999957i	$-0.502962\pi$
$53$	−0.135496			−0.0186118			−0.00930588	+	0.999957i	$0.502962\pi$
$54$		0			0
$55$	7.46499			1.00658
$56$	6.20657	−	2.25901i	0.829388	−	0.301873i
$57$		0			0
$58$	−5.53312	+	4.64284i	−0.726534	+	0.609635i
$59$	0.694374	+	3.93799i	0.0903998	+	0.512682i	0.996060	+	0.0886789i	$0.0282645\pi$
$59$	0.694374	+	3.93799i	0.0903998	+	0.512682i	−0.905661	+	0.424004i	$0.860624\pi$
$60$		0			0
$61$	0.261833	+	0.219704i	0.0335242	+	0.0281302i	0.659396	−	0.751796i	$-0.270812\pi$
$61$	0.261833	+	0.219704i	0.0335242	+	0.0281302i	−0.625872	+	0.779926i	$0.715257\pi$
$62$	1.10120	−	1.90733i	0.139852	−	0.242232i
$63$		0			0
$64$	−1.53974	−	2.66690i	−0.192467	−	0.333363i
$65$	−0.551558	+	3.12804i	−0.0684124	+	0.387986i
$66$		0			0
$67$	−9.51243	−	3.46224i	−1.16213	−	0.422980i	−0.312271	−	0.949993i	$-0.601090\pi$
$67$	−9.51243	−	3.46224i	−1.16213	−	0.422980i	−0.849857	+	0.527013i	$0.823312\pi$
$68$	−8.22586	−	2.99397i	−0.997533	−	0.363072i
$69$		0			0
$70$	−0.802767	+	4.55272i	−0.0959490	+	0.544154i
$71$	4.09540	+	7.09344i	0.486035	+	0.841837i	0.999871	−	0.0160515i	$-0.00510955\pi$
$71$	4.09540	+	7.09344i	0.486035	+	0.841837i	−0.513837	+	0.857888i	$0.671776\pi$
$72$		0			0
$73$	6.15722	−	10.6646i	0.720648	−	1.24820i	−0.240092	−	0.970750i	$-0.577178\pi$
$73$	6.15722	−	10.6646i	0.720648	−	1.24820i	0.960740	−	0.277449i	$-0.0894890\pi$
$74$	−3.29579	−	2.76550i	−0.383128	−	0.321482i
$75$		0			0
$76$	−1.95377	−	11.0804i	−0.224113	−	1.27101i
$77$	6.01939	−	5.05086i	0.685973	−	0.575599i
$78$		0			0
$79$	−3.83460	+	1.39568i	−0.431426	+	0.157026i	−0.548600	−	0.836085i	$-0.684839\pi$
$79$	−3.83460	+	1.39568i	−0.431426	+	0.157026i	0.117173	+	0.993111i	$0.462617\pi$
$80$	−1.75056			−0.195718
$81$		0			0
$82$	−5.52638			−0.610287
$83$	0.858154	−	0.312342i	0.0941946	−	0.0342840i	−0.294493	−	0.955654i	$-0.595151\pi$
$83$	0.858154	−	0.312342i	0.0941946	−	0.0342840i	0.388688	+	0.921370i	$0.372929\pi$
$84$		0			0
$85$	11.4221	−	9.58424i	1.23890	−	1.03956i
$86$	−0.315603	−	1.78987i	−0.0340323	−	0.193007i
$87$		0			0
$88$	−6.35419	−	5.33180i	−0.677359	−	0.568371i
$89$	−1.86437	+	3.22919i	−0.197623	+	0.342293i	−0.947757	−	0.318992i	$-0.896656\pi$
$89$	−1.86437	+	3.22919i	−0.197623	+	0.342293i	0.750134	+	0.661286i	$0.229989\pi$
$90$		0			0
$91$	1.67171	+	2.89548i	0.175243	+	0.303529i
$92$	0.982276	−	5.57076i	0.102409	−	0.580792i
$93$		0			0
$94$	3.37220	+	1.22738i	0.347816	+	0.126595i
$95$	18.0087	+	6.55465i	1.84766	+	0.672492i
$96$		0			0
$97$	−1.04125	+	5.90520i	−0.105722	+	0.599582i	0.885207	+	0.465198i	$0.154017\pi$
$97$	−1.04125	+	5.90520i	−0.105722	+	0.599582i	−0.990929	+	0.134384i	$0.957094\pi$
$98$	−0.288973	−	0.500515i	−0.0291907	−	0.0505597i
$99$		0			0
$100$	0.451345	−	0.781752i	0.0451345	−	0.0781752i
$101$	−7.83029	−	6.57039i	−0.779143	−	0.653778i	0.163890	−	0.986479i	$-0.447596\pi$
$101$	−7.83029	−	6.57039i	−0.779143	−	0.653778i	−0.943033	+	0.332700i	$0.892040\pi$
$102$		0			0
$103$	1.48192	+	8.40441i	0.146018	+	0.828111i	0.966544	+	0.256501i	$0.0825698\pi$
$103$	1.48192	+	8.40441i	0.146018	+	0.828111i	−0.820526	+	0.571610i	$0.806319\pi$
$104$	2.70366	−	2.26864i	0.265116	−	0.222458i
$105$		0			0
$106$	−0.0990242	+	0.0360419i	−0.00961808	+	0.00350070i
$107$	7.74500			0.748738			0.374369	−	0.927280i	$-0.377859\pi$
$107$	7.74500			0.748738			0.374369	+	0.927280i	$0.377859\pi$
$108$		0			0
$109$	1.25438			0.120148			0.0600738	−	0.998194i	$-0.480866\pi$
$109$	1.25438			0.120148			0.0600738	+	0.998194i	$0.480866\pi$
$110$	5.45563	−	1.98569i	0.520174	−	0.189328i
$111$		0			0
$112$	−1.41156	+	1.18444i	−0.133380	+	0.111919i
$113$	3.08413	+	17.4909i	0.290130	+	1.64541i	0.686363	+	0.727259i	$0.259206\pi$
$113$	3.08413	+	17.4909i	0.290130	+	1.64541i	−0.396233	+	0.918150i	$0.629683\pi$
$114$		0			0
$115$	7.38094	+	6.19335i	0.688276	+	0.577532i
$116$	6.47846	−	11.2210i	0.601509	−	1.04185i
$117$		0			0
$118$	1.55497	+	2.69329i	0.143147	+	0.247938i
$119$	2.72540	−	15.4565i	0.249837	−	1.41689i
$120$		0			0
$121$	1.06354	+	0.387095i	0.0966851	+	0.0351905i
$122$	0.249796	+	0.0909183i	0.0226155	+	0.00823136i
$123$		0			0
$124$	−0.686043	+	3.89074i	−0.0616085	+	0.349399i
$125$	−5.17209	−	8.95832i	−0.462606	−	0.801256i
$126$		0			0
$127$	1.98279	−	3.43429i	0.175944	−	0.304744i	−0.764543	−	0.644572i	$-0.777036\pi$
$127$	1.98279	−	3.43429i	0.175944	−	0.304744i	0.940488	+	0.339828i	$0.110369\pi$
$128$	7.13406	+	5.98619i	0.630568	+	0.529109i
$129$		0			0
$130$	0.428965	+	2.43278i	0.0376227	+	0.213369i
$131$	0.0785183	−	0.0658847i	0.00686018	−	0.00575637i	−0.639351	−	0.768915i	$-0.720797\pi$
$131$	0.0785183	−	0.0658847i	0.00686018	−	0.00575637i	0.646211	+	0.763159i	$0.276352\pi$
$132$		0			0
$133$	18.9563	−	6.89951i	1.64372	−	0.598263i
$134$	−7.87292			−0.680117
$135$		0			0
$136$	−16.5679			−1.42068
$137$	−7.16003	+	2.60604i	−0.611723	+	0.222649i	−0.629257	−	0.777197i	$-0.716641\pi$
$137$	−7.16003	+	2.60604i	−0.611723	+	0.222649i	0.0175340	+	0.999846i	$0.494418\pi$
$138$		0			0
$139$	−7.99806	+	6.71117i	−0.678387	+	0.569234i	−0.915535	−	0.402239i	$-0.868232\pi$
$139$	−7.99806	+	6.71117i	−0.678387	+	0.569234i	0.237148	+	0.971474i	$0.423787\pi$
$140$	−1.44004	−	8.16687i	−0.121706	−	0.690227i
$141$		0			0
$142$	4.87990	+	4.09472i	0.409512	+	0.343621i
$143$	2.09943	−	3.63631i	0.175563	−	0.304084i
$144$		0			0
$145$	11.0348	+	19.1129i	0.916394	+	1.58724i
$146$	1.66309	−	9.43184i	0.137638	−	0.780584i
$147$		0			0
$148$	7.25231	+	2.63963i	0.596136	+	0.216976i
$149$	8.48785	+	3.08932i	0.695352	+	0.253087i	0.665425	−	0.746465i	$-0.268250\pi$
$149$	8.48785	+	3.08932i	0.695352	+	0.253087i	0.0299267	+	0.999552i	$0.490473\pi$
$150$		0			0
$151$	4.14852	−	23.5274i	0.337602	−	1.91464i	−0.0622588	−	0.998060i	$-0.519830\pi$
$151$	4.14852	−	23.5274i	0.337602	−	1.91464i	0.399861	−	0.916576i	$-0.369058\pi$
$152$	−10.6474	−	18.4419i	−0.863620	−	1.49583i
$153$		0			0
$154$	3.05561	−	5.29248i	0.246228	−	0.426480i
$155$	−5.15501	−	4.32557i	−0.414061	−	0.347438i
$156$		0			0
$157$	0.470932	+	2.67079i	0.0375844	+	0.213152i	0.997816	−	0.0660524i	$-0.0210404\pi$
$157$	0.470932	+	2.67079i	0.0375844	+	0.213152i	−0.960232	+	0.279204i	$0.909929\pi$
$158$	−2.43119	+	2.04001i	−0.193415	+	0.162294i
$159$		0			0
$160$	−13.0720	+	4.75783i	−1.03344	+	0.376140i
$161$	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	$0.831735\pi$
$164$	9.31562	−	3.39061i	0.727428	−	0.264762i
$165$		0			0
$166$	0.544081	−	0.456538i	0.0422289	−	0.0354342i
$167$	1.55429	+	8.81482i	0.120275	+	0.682111i	0.984003	+	0.178153i	$0.0570123\pi$
$167$	1.55429	+	8.81482i	0.120275	+	0.682111i	−0.863728	+	0.503958i	$0.831877\pi$
$168$		0			0
$169$	−8.58998	−	7.20785i	−0.660768	−	0.554450i
$170$	5.79816	−	10.0427i	0.444699	−	0.770241i
$171$		0			0
$172$	1.63014	+	2.82349i	0.124297	+	0.215289i
$173$	0.457433	−	2.59423i	0.0347780	−	0.197236i	−0.962469	−	0.271393i	$-0.912516\pi$
$173$	0.457433	−	2.59423i	0.0347780	−	0.197236i	0.997247	+	0.0741575i	$0.0236268\pi$
$174$		0			0
$175$	1.52086	+	0.553546i	0.114966	+	0.0418442i
$176$	2.17456	+	0.791475i	0.163914	+	0.0596597i
$177$		0			0
$178$	−0.503574	+	2.85591i	−0.0377445	+	0.214059i
$179$	−1.84227	−	3.19090i	−0.137697	−	0.238499i	0.788927	−	0.614487i	$-0.210637\pi$
$179$	−1.84227	−	3.19090i	−0.137697	−	0.238499i	−0.926625	+	0.375988i	$0.877303\pi$
$180$		0			0
$181$	0.134255	−	0.232536i	0.00997906	−	0.0172842i	−0.860993	−	0.508617i	$-0.830157\pi$
$181$	0.134255	−	0.232536i	0.00997906	−	0.0172842i	0.870972	+	0.491333i	$0.163490\pi$
$182$	1.99193	+	1.67143i	0.147652	+	0.123895i
$183$		0			0
$184$	−1.85911	−	10.5435i	−0.137055	−	0.777280i
$185$	−10.0702	+	8.44992i	−0.740378	+	0.621251i
$186$		0			0
$187$	−18.5219	+	6.74142i	−1.35445	+	0.492981i
$188$	−6.43743			−0.469498
$189$		0			0
$190$	14.9049			1.08131
$191$	2.25337	−	0.820159i	0.163048	−	0.0593447i	−0.259207	−	0.965822i	$-0.583461\pi$
$191$	2.25337	−	0.820159i	0.163048	−	0.0593447i	0.422255	+	0.906477i	$0.361239\pi$
$192$		0			0
$193$	0.380113	−	0.318953i	0.0273612	−	0.0229587i	−0.629005	−	0.777402i	$-0.716537\pi$
$193$	0.380113	−	0.318953i	0.0273612	−	0.0229587i	0.656366	+	0.754443i	$0.272093\pi$
$194$	0.809811	+	4.59266i	0.0581410	+	0.329734i
$195$		0			0
$196$	0.794193	+	0.666407i	0.0567281	+	0.0476005i
$197$	11.0734	−	19.1797i	0.788946	−	1.36649i	−0.137667	−	0.990479i	$-0.543960\pi$
$197$	11.0734	−	19.1797i	0.788946	−	1.36649i	0.926613	−	0.376016i	$-0.122706\pi$
$198$		0			0
$199$	−1.06624	−	1.84677i	−0.0755834	−	0.130914i	0.825756	−	0.564027i	$-0.190749\pi$
$199$	−1.06624	−	1.84677i	−0.0755834	−	0.130914i	−0.901340	+	0.433113i	$0.857415\pi$
$200$	0.296675	−	1.68253i	0.0209781	−	0.118972i
$201$		0			0
$202$	−7.47033	−	2.71898i	−0.525610	−	0.191307i
$203$	21.8299	+	7.94542i	1.53216	+	0.557659i
$204$		0			0
$205$	−2.93218	+	16.6292i	−0.204792	+	1.16144i
$206$	3.31861	+	5.74800i	0.231218	+	0.400482i
$207$		0			0
$208$	−0.492320	+	0.852724i	−0.0341363	+	0.0591257i
$209$	−19.4071	−	16.2845i	−1.34242	−	1.12642i
$210$		0			0
$211$	3.47445	+	19.7046i	0.239191	+	1.35652i	0.833605	+	0.552362i	$0.186273\pi$
$211$	3.47445	+	19.7046i	0.239191	+	1.35652i	−0.594413	+	0.804160i	$0.702616\pi$
$212$	0.144809	−	0.121509i	0.00994551	−	0.00834527i
$213$		0			0
$214$	5.66028	−	2.06017i	0.386929	−	0.140830i
$215$	−5.55329			−0.378731
$216$		0			0
$217$	−7.08345			−0.480856
$218$	0.916736	−	0.333664i	0.0620892	−	0.0225986i
$219$		0			0
$220$	−7.97808	+	6.69441i	−0.537882	+	0.451337i
$221$	−1.45634	−	8.25930i	−0.0979638	−	0.555580i
$222$		0			0
$223$	−10.1719	−	8.53523i	−0.681160	−	0.571561i	0.235185	−	0.971951i	$-0.424430\pi$
$223$	−10.1719	−	8.53523i	−0.681160	−	0.571561i	−0.916345	+	0.400389i	$0.868875\pi$
$224$	−7.32144	+	12.6811i	−0.489185	+	0.847292i
$225$		0			0
$226$	6.90656	+	11.9625i	0.459418	+	0.795735i
$227$	−2.16555	+	12.2815i	−0.143733	+	0.815150i	0.824643	+	0.565654i	$0.191376\pi$
$227$	−2.16555	+	12.2815i	−0.143733	+	0.815150i	−0.968376	+	0.249496i	$0.919735\pi$
$228$		0			0
$229$	−24.1140	−	8.77677i	−1.59350	−	0.579985i	−0.615414	−	0.788204i	$-0.711011\pi$
$229$	−24.1140	−	8.77677i	−1.59350	−	0.579985i	−0.978082	+	0.208219i	$0.933233\pi$
$230$	7.04164	+	2.56295i	0.464312	+	0.168996i
$231$		0			0
$232$	4.25837	−	24.1504i	0.279576	−	1.58555i
$233$	2.69821	+	4.67344i	0.176766	+	0.306167i	0.940771	−	0.339043i	$-0.110103\pi$
$233$	2.69821	+	4.67344i	0.176766	+	0.306167i	−0.764005	+	0.645210i	$0.776770\pi$
$234$		0			0
$235$	5.48248	−	9.49593i	0.357637	−	0.619446i
$236$	−4.27359	−	3.58596i	−0.278187	−	0.233426i
$237$		0			0
$238$	−2.11963	−	12.0210i	−0.137395	−	0.779206i
$239$	6.41259	−	5.38080i	0.414796	−	0.348055i	−0.411383	−	0.911462i	$-0.634954\pi$
$239$	6.41259	−	5.38080i	0.414796	−	0.348055i	0.826179	+	0.563407i	$0.190510\pi$
$240$		0			0
$241$	0.415522	−	0.151238i	0.0267661	−	0.00974208i	−0.328602	−	0.944468i	$-0.606578\pi$
$241$	0.415522	−	0.151238i	0.0267661	−	0.00974208i	0.355369	+	0.934726i	$0.384355\pi$
$242$	0.880231			0.0565834
$243$		0			0
$244$	−0.476854			−0.0305274
$245$	−1.65941	+	0.603974i	−0.106016	+	0.0385865i
$246$		0			0
$247$	8.25758	−	6.92893i	0.525417	−	0.440877i
$248$	1.29844	+	7.36384i	0.0824512	+	0.467604i
$249$		0			0
$250$	−6.16283	−	5.17123i	−0.389771	−	0.327057i
$251$	−8.51427	+	14.7471i	−0.537416	+	0.930832i	0.461626	+	0.887074i	$0.347266\pi$
$251$	−8.51427	+	14.7471i	−0.537416	+	0.930832i	−0.999042	+	0.0437571i	$0.986067\pi$
$252$		0			0
$253$	−6.36850	−	11.0306i	−0.400384	−	0.693486i
$254$	0.535559	−	3.03730i	0.0336039	−	0.190577i
$255$		0			0
$256$	12.5936	+	4.58371i	0.787102	+	0.286482i
$257$	−19.6177	−	7.14026i	−1.22372	−	0.445397i	−0.352277	−	0.935896i	$-0.614592\pi$
$257$	−19.6177	−	7.14026i	−1.22372	−	0.445397i	−0.871442	+	0.490499i	$0.836815\pi$
$258$		0			0
$259$	−2.40284	+	13.6272i	−0.149305	+	0.846751i
$260$	−2.21568	−	3.83767i	−0.137411	−	0.238002i
$261$		0			0
$262$	0.0398582	−	0.0690364i	0.00246245	−	0.00426508i
$263$	14.8548	+	12.4647i	0.915986	+	0.768603i	0.973248	−	0.229756i	$-0.0737927\pi$
$263$	14.8548	+	12.4647i	0.915986	+	0.768603i	−0.0572625	+	0.998359i	$0.518237\pi$
$264$		0			0
$265$	0.0559121	+	0.317093i	0.00343465	+	0.0194789i
$266$	12.0185	−	10.0847i	0.736902	−	0.618334i
$267$		0			0
$268$	13.2711	−	4.83029i	0.810662	−	0.295057i
$269$	18.6791			1.13889			0.569443	−	0.822031i	$-0.307159\pi$
$269$	18.6791			1.13889			0.569443	+	0.822031i	$0.307159\pi$
$270$		0			0
$271$	12.9378			0.785917			0.392958	−	0.919556i	$-0.371452\pi$
$271$	12.9378			0.785917			0.392958	+	0.919556i	$0.371452\pi$
$272$	4.34343	−	1.58088i	0.263359	−	0.0958548i
$273$		0			0
$274$	−4.53956	+	3.80914i	−0.274245	+	0.230119i
$275$	−0.352950	−	2.00168i	−0.0212837	−	0.120706i
$276$		0			0
$277$	7.99852	+	6.71156i	0.480585	+	0.403258i	0.850638	−	0.525752i	$-0.176216\pi$
$277$	7.99852	+	6.71156i	0.480585	+	0.403258i	−0.370053	+	0.929011i	$0.620661\pi$
$278$	−4.06005	+	7.03221i	−0.243505	+	0.421764i
$279$		0			0
$280$	−7.84776	−	13.5927i	−0.468994	−	0.812321i
$281$	2.49112	−	14.1278i	0.148608	−	0.842797i	−0.815791	−	0.578346i	$-0.803698\pi$
$281$	2.49112	−	14.1278i	0.148608	−	0.842797i	0.964399	−	0.264451i	$-0.0851906\pi$
$282$		0			0
$283$	17.5653	+	6.39325i	1.04415	+	0.380039i	0.806452	−	0.591300i	$-0.201385\pi$
$283$	17.5653	+	6.39325i	1.04415	+	0.380039i	0.237697	+	0.971339i	$0.423607\pi$
$284$	−10.7381	−	3.90835i	−0.637189	−	0.231918i
$285$		0			0
$286$	0.567062	−	3.21597i	0.0335311	−	0.190164i
$287$	8.88709	+	15.3929i	0.524588	+	0.908614i
$288$		0			0
$289$	−11.1848	+	19.3726i	−0.657929	+	1.13957i
$290$	13.1486	+	11.0330i	0.772114	+	0.647880i
$291$		0			0
$292$	2.98332	+	16.9193i	0.174586	+	0.990125i
$293$	−8.26423	+	6.93451i	−0.482801	+	0.405118i	−0.851438	−	0.524455i	$-0.824269\pi$
$293$	−8.26423	+	6.93451i	−0.482801	+	0.405118i	0.368637	+	0.929574i	$0.379825\pi$
$294$		0			0
$295$	8.92933	−	3.25001i	0.519886	−	0.189223i
$296$	14.6070			0.849017
$297$		0			0
$298$	7.02493			0.406943
$299$	5.09266	−	1.85358i	0.294516	−	0.107195i
$300$		0			0
$301$	−4.47789	+	3.75740i	−0.258101	+	0.216573i
$302$	−3.22644	−	18.2981i	−0.185661	−	1.05293i
$303$		0			0
$304$	4.55101	+	3.81875i	0.261018	+	0.219020i
$305$	0.406116	−	0.703413i	0.0232541	−	0.0402773i
$306$		0			0
$307$	−0.0248747	−	0.0430843i	−0.00141967	−	0.00245895i	0.865315	−	0.501229i	$-0.167119\pi$
$307$	−0.0248747	−	0.0430843i	−0.00141967	−	0.00245895i	−0.866734	+	0.498770i	$0.833785\pi$
$308$	−1.90364	+	10.7961i	−0.108470	+	0.615162i
$309$		0			0
$310$	−4.91804	−	1.79002i	−0.279326	−	0.101666i
$311$	−12.4373	−	4.52679i	−0.705252	−	0.256691i	−0.0356007	−	0.999366i	$-0.511334\pi$
$311$	−12.4373	−	4.52679i	−0.705252	−	0.256691i	−0.669652	+	0.742675i	$0.733557\pi$
$312$		0			0
$313$	−2.61912	+	14.8538i	−0.148041	+	0.839585i	0.816833	+	0.576874i	$0.195728\pi$
$313$	−2.61912	+	14.8538i	−0.148041	+	0.839585i	−0.964875	+	0.262711i	$0.915383\pi$
$314$	1.05460	+	1.82662i	0.0595145	+	0.103082i
$315$		0			0
$316$	2.84656	−	4.93038i	0.160131	−	0.277356i
$317$	6.61159	+	5.54779i	0.371344	+	0.311595i	0.809293	−	0.587405i	$-0.199850\pi$
$317$	6.61159	+	5.54779i	0.371344	+	0.311595i	−0.437949	+	0.899000i	$0.644295\pi$
$318$		0			0
$319$	−5.06612	−	28.7314i	−0.283648	−	1.60865i
$320$	−5.60584	+	4.70386i	−0.313376	+	0.262954i
$321$		0			0
$322$	7.41213	−	2.69779i	0.413062	−	0.150342i
$323$	−50.6020			−2.81557
$324$		0			0
$325$	0.864837			0.0479725
$326$	−16.1140	+	5.86502i	−0.892473	+	0.324834i
$327$		0			0
$328$	14.3731	−	12.0605i	0.793624	−	0.665929i
$329$	−2.00422	−	11.3665i	−0.110496	−	0.626656i
$330$		0			0
$331$	23.7669	+	19.9428i	1.30635	+	1.09615i	0.989011	+	0.147842i	$0.0472326\pi$
$331$	23.7669	+	19.9428i	1.30635	+	1.09615i	0.317336	+	0.948313i	$0.397212\pi$
$332$	−0.637037	+	1.10338i	−0.0349619	+	0.0605559i
$333$		0			0
$334$	3.48067	+	6.02869i	0.190454	+	0.329875i
$335$	−4.17721	+	23.6901i	−0.228225	+	1.29433i
$336$		0			0
$337$	22.4279	+	8.16311i	1.22173	+	0.444673i	0.870757	−	0.491714i	$-0.163629\pi$
$337$	22.4279	+	8.16311i	1.22173	+	0.444673i	0.350971	+	0.936386i	$0.385852\pi$
$338$	−8.19510	−	2.98277i	−0.445755	−	0.162241i
$339$		0			0
$340$	−3.61223	+	20.4860i	−0.195901	+	1.11101i
$341$	4.44790	+	7.70399i	0.240867	+	0.417194i
$342$		0			0
$343$	−9.68422	+	16.7736i	−0.522899	+	0.905688i
$344$	4.72695	+	3.96638i	0.254860	+	0.213853i
$345$		0			0
$346$	−0.355760	−	2.01762i	−0.0191258	−	0.108468i
$347$	16.7850	−	14.0843i	0.901065	−	0.756083i	−0.0693332	−	0.997594i	$-0.522087\pi$
$347$	16.7850	−	14.0843i	0.901065	−	0.756083i	0.970398	+	0.241510i	$0.0776427\pi$
$348$		0			0
$349$	−14.8912	+	5.41995i	−0.797107	+	0.290123i	−0.708287	−	0.705925i	$-0.750532\pi$
$349$	−14.8912	+	5.41995i	−0.797107	+	0.290123i	−0.0888197	+	0.996048i	$0.528309\pi$
$350$	1.25873			0.0672819
$351$		0			0
$352$	18.3894			0.980157
$353$	−12.1285	+	4.41442i	−0.645535	+	0.234956i	−0.643979	−	0.765043i	$-0.722718\pi$
$353$	−12.1285	+	4.41442i	−0.645535	+	0.234956i	−0.00155627	+	0.999999i	$0.500495\pi$
$354$		0			0
$355$	14.9104	−	12.5113i	0.791364	−	0.664033i
$356$	−0.903334	−	5.12306i	−0.0478766	−	0.271522i
$357$		0			0
$358$	−2.19516	−	1.84196i	−0.116018	−	0.0973505i
$359$	−12.9142	+	22.3681i	−0.681588	+	1.18054i	0.292909	+	0.956140i	$0.405377\pi$
$359$	−12.9142	+	22.3681i	−0.681588	+	1.18054i	−0.974496	+	0.224404i	$0.927956\pi$
$360$		0			0
$361$	−23.0196	−	39.8711i	−1.21156	−	2.09848i
$362$	0.0362626	−	0.205656i	0.00190592	−	0.0108090i
$363$		0			0
$364$	−4.38320	−	1.59536i	−0.229742	−	0.0836193i
$365$	−27.4986	−	10.0087i	−1.43934	−	0.523878i
$366$		0			0
$367$	2.77396	−	15.7319i	0.144799	−	0.821198i	−0.822729	−	0.568434i	$-0.807549\pi$
$367$	2.77396	−	15.7319i	0.144799	−	0.821198i	0.967528	−	0.252764i	$-0.0813395\pi$
$368$	1.49343	+	2.58669i	0.0778503	+	0.134841i
$369$		0			0
$370$	−5.11194	+	8.85413i	−0.265757	+	0.460304i
$371$	0.259632	+	0.217857i	0.0134794	+	0.0113106i
$372$		0			0
$373$	0.317180	+	1.79882i	0.0164229	+	0.0931392i	0.991918	−	0.126884i	$-0.0404977\pi$
$373$	0.317180	+	1.79882i	0.0164229	+	0.0931392i	−0.975495	+	0.220023i	$0.929387\pi$
$374$	−11.7431	+	9.85365i	−0.607222	+	0.509520i
$375$		0			0
$376$	−11.4491	+	4.16712i	−0.590440	+	0.214903i
$377$	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	$0.490622\pi$
$380$	−25.1246	+	9.14460i	−1.28886	+	0.469108i
$381$		0			0
$382$	1.42867	−	1.19879i	0.0730969	−	0.0613356i
$383$	3.79031	+	21.4959i	0.193676	+	1.09839i	0.914292	+	0.405056i	$0.132748\pi$
$383$	3.79031	+	21.4959i	0.193676	+	1.09839i	−0.720616	+	0.693335i	$0.756141\pi$
$384$		0			0
$385$	−14.3042	−	12.0026i	−0.729007	−	0.611710i
$386$	0.192957	−	0.334210i	0.00982123	−	0.0170109i
$387$		0			0
$388$	−4.18281	−	7.24484i	−0.212350	−	0.367801i
$389$	−4.54892	+	25.7982i	−0.230639	+	1.30802i	0.620966	+	0.783837i	$0.286740\pi$
$389$	−4.54892	+	25.7982i	−0.230639	+	1.30802i	−0.851605	+	0.524183i	$0.824371\pi$
$390$		0			0
$391$	−23.9064	−	8.70121i	−1.20900	−	0.440039i
$392$	1.84387	+	0.671112i	0.0931293	+	0.0338963i
$393$		0			0
$394$	2.99096	−	16.9626i	0.150682	−	0.854563i
$395$	4.84858	+	8.39798i	0.243958	+	0.422548i
$396$		0			0
$397$	−2.09915	+	3.63584i	−0.105353	+	0.182478i	−0.913883	−	0.405979i	$-0.866931\pi$
$397$	−2.09915	+	3.63584i	−0.105353	+	0.182478i	0.808529	+	0.588456i	$0.200264\pi$
$398$	−1.27048	−	1.06606i	−0.0636833	−	0.0534366i
$399$		0			0
$400$	0.0827675	+	0.469398i	0.00413838	+	0.0234699i
$401$	−5.99798	+	5.03290i	−0.299525	+	0.251331i	−0.780147	−	0.625597i	$-0.784856\pi$
$401$	−5.99798	+	5.03290i	−0.299525	+	0.251331i	0.480622	+	0.876928i	$0.340411\pi$
$402$		0			0
$403$	−3.55683	+	1.29458i	−0.177178	+	0.0644876i
$404$	14.2606			0.709493
$405$		0			0
$406$	18.0674			0.896669
$407$	16.3298	−	5.94355i	0.809437	−	0.294611i
$408$		0			0
$409$	−13.3514	+	11.2031i	−0.660183	+	0.553960i	−0.910142	−	0.414297i	$-0.864028\pi$
$409$	−13.3514	+	11.2031i	−0.660183	+	0.553960i	0.249958	+	0.968257i	$0.419583\pi$
$410$	2.28045	+	12.9331i	0.112624	+	0.638720i
$411$		0			0
$412$	−9.12063	−	7.65312i	−0.449341	−	0.377042i
$413$	5.00118	−	8.66229i	0.246092	−	0.426243i
$414$		0			0
$415$	−1.08507	−	1.87940i	−0.0532642	−	0.0922563i
$416$	−1.35872	+	7.70567i	−0.0666166	+	0.377802i
$417$		0			0
$418$	−18.5150	−	6.73889i	−0.905596	−	0.329610i
$419$	−10.7907	−	3.92748i	−0.527158	−	0.191870i	0.0647110	−	0.997904i	$-0.479387\pi$
$419$	−10.7907	−	3.92748i	−0.527158	−	0.191870i	−0.591869	+	0.806034i	$0.701610\pi$
$420$		0			0
$421$	1.26611	−	7.18046i	0.0617064	−	0.349954i	−0.938285	−	0.345862i	$-0.887586\pi$
$421$	1.26611	−	7.18046i	0.0617064	−	0.349954i	0.999992	−	0.00409180i	$-0.00130246\pi$
$422$	7.78066	+	13.4765i	0.378757	+	0.656026i
$423$		0			0
$424$	0.178889	−	0.309844i	0.00868759	−	0.0150474i
$425$	−3.10998	−	2.60958i	−0.150856	−	0.126583i
$426$		0			0
$427$	−0.148463	−	0.841977i	−0.00718464	−	0.0407461i
$428$	−8.27734	+	6.94552i	−0.400101	+	0.335724i
$429$		0			0
$430$	−4.05851	+	1.47718i	−0.195719	+	0.0712358i
$431$	0.389084			0.0187415			0.00937075	−	0.999956i	$-0.497017\pi$
$431$	0.389084			0.0187415			0.00937075	+	0.999956i	$0.497017\pi$
$432$		0			0
$433$	24.1011			1.15822			0.579112	−	0.815248i	$-0.303400\pi$
$433$	24.1011			1.15822			0.579112	+	0.815248i	$0.303400\pi$
$434$	−5.17679	+	1.88420i	−0.248494	+	0.0904444i
$435$		0			0
$436$	−1.34059	+	1.12489i	−0.0642028	+	0.0538726i
$437$	−5.67813	−	32.2023i	−0.271622	−	1.54044i
$438$		0			0
$439$	28.0875	+	23.5682i	1.34054	+	1.12485i	0.981486	+	0.191532i	$0.0613457\pi$
$439$	28.0875	+	23.5682i	1.34054	+	1.12485i	0.359056	+	0.933316i	$0.383099\pi$
$440$	−9.85567	+	17.0705i	−0.469851	+	0.813805i
$441$		0			0
$442$	−3.26131	−	5.64875i	−0.155125	−	0.268684i
$443$	−6.56158	+	37.2126i	−0.311750	+	1.76802i	0.278140	+	0.960540i	$0.410282\pi$
$443$	−6.56158	+	37.2126i	−0.311750	+	1.76802i	−0.589890	+	0.807483i	$0.700829\pi$
$444$		0			0
$445$	8.32642	+	3.03057i	0.394710	+	0.143663i
$446$	−9.70429	−	3.53207i	−0.459512	−	0.167249i
$447$		0			0
$448$	−1.33760	+	7.58590i	−0.0631956	+	0.358400i
$449$	−5.89289	−	10.2068i	−0.278103	−	0.481688i	0.692811	−	0.721120i	$-0.256372\pi$
$449$	−5.89289	−	10.2068i	−0.278103	−	0.481688i	−0.970913	+	0.239432i	$0.923039\pi$
$450$		0			0
$451$	11.1609	−	19.3313i	0.525547	−	0.910274i
$452$	−18.9815	−	15.9274i	−0.892816	−	0.749162i
$453$		0			0
$454$	1.68422	+	9.55170i	0.0790444	+	0.448283i
$455$	6.08631	−	5.10702i	0.285331	−	0.239421i
$456$		0			0
$457$	18.6584	−	6.79112i	0.872805	−	0.317675i	0.133503	−	0.991048i	$-0.457378\pi$
$457$	18.6584	−	6.79112i	0.872805	−	0.317675i	0.739303	+	0.673373i	$0.235155\pi$
$458$	−19.9578			−0.932568
$459$		0			0
$460$	−13.4423			−0.626750
$461$	7.18097	−	2.61366i	0.334451	−	0.121730i	−0.169335	−	0.985558i	$-0.554162\pi$
$461$	7.18097	−	2.61366i	0.334451	−	0.121730i	0.503786	+	0.863828i	$0.331940\pi$
$462$		0			0
$463$	−12.2218	+	10.2553i	−0.567995	+	0.476604i	−0.880980	−	0.473154i	$-0.843115\pi$
$463$	−12.2218	+	10.2553i	−0.567995	+	0.476604i	0.312985	+	0.949758i	$0.398671\pi$
$464$	1.18802	+	6.73758i	0.0551523	+	0.312784i
$465$		0			0
$466$	3.21507	+	2.69776i	0.148935	+	0.124971i
$467$	−13.0703	+	22.6385i	−0.604822	+	1.04758i	0.387257	+	0.921972i	$0.373423\pi$
$467$	−13.0703	+	22.6385i	−0.604822	+	1.04758i	−0.992080	+	0.125611i	$0.959911\pi$
$468$		0			0
$469$	12.6606	+	21.9288i	0.584613	+	1.01258i
$470$	1.48084	−	8.39825i	0.0683059	−	0.387382i
$471$		0			0
$472$	−9.92192	−	3.61128i	−0.456693	−	0.166223i
$473$	6.89835	+	2.51080i	0.317187	+	0.115446i
$474$		0			0
$475$	0.906110	−	5.13881i	0.0415752	−	0.235785i
$476$	10.9483	+	18.9629i	0.501812	+	0.869164i
$477$		0			0
$478$	3.25522	−	5.63820i	0.148890	−	0.257885i
$479$	30.1441	+	25.2939i	1.37732	+	1.15571i	0.970193	+	0.242334i	$0.0779130\pi$
$479$	30.1441	+	25.2939i	1.37732	+	1.15571i	0.407125	+	0.913373i	$0.366531\pi$
$480$		0			0
$481$	1.28398	+	7.28179i	0.0585442	+	0.332021i
$482$	0.263447	−	0.221058i	0.0119997	−	0.0100689i
$483$		0			0
$484$	−1.48377	+	0.540049i	−0.0674442	+	0.0245477i
$485$	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	$0.414500\pi$
$488$	−0.848091	+	0.308680i	−0.0383913	+	0.0139733i
$489$		0			0
$490$	−1.05208	+	0.882804i	−0.0475284	+	0.0398810i
$491$	−6.69411	−	37.9642i	−0.302101	−	1.71330i	−0.636846	−	0.770991i	$-0.719761\pi$
$491$	−6.69411	−	37.9642i	−0.302101	−	1.71330i	0.334745	−	0.942309i	$-0.391350\pi$
$492$		0			0
$493$	−44.6396	−	37.4571i	−2.01047	−	1.68698i
$494$	4.19178	−	7.26038i	0.188597	−	0.326660i
$495$		0			0
$496$	−1.04304	−	1.80660i	−0.0468340	−	0.0811189i
$497$	3.55775	−	20.1770i	0.159587	−	0.905063i
$498$		0			0
$499$	27.7788	+	10.1107i	1.24355	+	0.452615i	0.878217	−	0.478262i	$-0.158733\pi$
$499$	27.7788	+	10.1107i	1.24355	+	0.452615i	0.365333	+	0.930877i	$0.380955\pi$
$500$	13.5612	+	4.93586i	0.606474	+	0.220738i
$501$		0			0
$502$	−2.29973	+	13.0424i	−0.102642	+	0.582113i
$503$	−17.7888	−	30.8110i	−0.793161	−	1.37380i	−0.924000	−	0.382392i	$-0.875100\pi$
$503$	−17.7888	−	30.8110i	−0.793161	−	1.37380i	0.130839	−	0.991404i	$-0.458233\pi$
$504$		0			0
$505$	−12.1452	+	21.0361i	−0.540453	+	0.936092i
$506$	−7.58842	−	6.36744i	−0.337346	−	0.283067i
$507$		0			0
$508$	0.960710	+	5.44846i	0.0426246	+	0.241736i
$509$	−21.7421	+	18.2438i	−0.963703	+	0.808643i	−0.981552	−	0.191198i	$-0.938763\pi$
$509$	−21.7421	+	18.2438i	−0.963703	+	0.808643i	0.0178483	+	0.999841i	$0.494318\pi$
$510$		0			0
$511$	−28.9454	+	10.5353i	−1.28047	+	0.466053i
$512$	−8.20265			−0.362510
$513$		0			0
$514$	−16.2365			−0.716161
$515$	19.0569	−	6.93613i	0.839746	−	0.305642i
$516$		0			0
$517$	−11.1038	+	9.31716i	−0.488343	+	0.409768i
$518$	1.86877	+	10.5983i	0.0821088	+	0.465662i
$519$		0			0
$520$	−6.42484	−	5.39108i	−0.281748	−	0.236414i
$521$	12.7176	−	22.0275i	0.557167	−	0.965041i	−0.440565	−	0.897721i	$-0.645222\pi$
$521$	12.7176	−	22.0275i	0.557167	−	0.965041i	0.997731	−	0.0673204i	$-0.0214450\pi$
$522$		0			0
$523$	−4.20395	−	7.28145i	−0.183826	−	0.318396i	0.759354	−	0.650677i	$-0.225515\pi$
$523$	−4.20395	−	7.28145i	−0.183826	−	0.318396i	−0.943180	+	0.332282i	$0.892182\pi$
$524$	−0.0248315	+	0.140826i	−0.00108477	+	0.00615203i
$525$		0			0
$526$	14.1719	+	5.15816i	0.617925	+	0.224906i
$527$	16.6967	+	6.07712i	0.727322	+	0.264723i
$528$		0			0
$529$	−1.13917	+	6.46057i	−0.0495292	+	0.280894i
$530$	0.125209	+	0.216868i	0.00543873	+	0.00942016i
$531$		0			0
$532$	−14.0719	+	24.3732i	−0.610093	+	1.05671i
$533$	7.27572	+	6.10505i	0.315146	+	0.264439i
$534$		0			0
$535$	−3.19596	−	18.1252i	−0.138174	−	0.783621i
$536$	20.4761	−	17.1815i	0.884432	−	0.742126i
$537$		0			0
$538$	13.6513	−	4.96865i	0.588547	−	0.214214i
$539$	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	$0.589182\pi$
$542$	9.45534	−	3.44146i	0.406142	−	0.147823i
$543$		0			0
$544$	28.1373	−	23.6100i	1.20638	−	1.01227i
$545$	−0.517617	−	2.93555i	−0.0221723	−	0.125745i
$546$		0			0
$547$	10.0290	+	8.41535i	0.428810	+	0.359814i	0.831503	−	0.555521i	$-0.187481\pi$
$547$	10.0290	+	8.41535i	0.428810	+	0.359814i	−0.402692	+	0.915335i	$0.631926\pi$
$548$	5.31514	−	9.20609i	0.227051	−	0.393265i
$549$		0			0
$550$	−0.790392	−	1.36900i	−0.0337024	−	0.0583743i
$551$	13.0060	−	73.7607i	0.554074	−	3.14231i
$552$		0			0
$553$	9.59178	+	3.49112i	0.407884	+	0.148458i
$554$	7.63083	+	2.77740i	0.324203	+	0.118000i
$555$		0			0
$556$	2.52939	−	14.3449i	0.107270	−	0.608360i
$557$	−2.29110	−	3.96830i	−0.0970769	−	0.168142i	0.813397	−	0.581710i	$-0.197616\pi$
$557$	−2.29110	−	3.96830i	−0.0970769	−	0.168142i	−0.910474	+	0.413567i	$0.864283\pi$
$558$		0			0
$559$	−1.56179	+	2.70509i	−0.0660565	+	0.114413i
$560$	3.35436	+	2.81464i	0.141748	+	0.118940i
$561$		0			0
$562$	−1.93743	−	10.9877i	−0.0817254	−	0.463488i
$563$	9.41003	−	7.89595i	0.396585	−	0.332775i	−0.422587	−	0.906323i	$-0.638878\pi$
$563$	9.41003	−	7.89595i	0.396585	−	0.332775i	0.819172	+	0.573548i	$0.194433\pi$
$564$		0			0
$565$	39.6604	−	14.4352i	1.66853	−	0.607294i
$566$	14.5378			0.611071
$567$		0			0
$568$	−21.6278			−0.907484
$569$	−13.6196	+	4.95712i	−0.570963	+	0.207813i	−0.611336	−	0.791371i	$-0.709368\pi$
$569$	−13.6196	+	4.95712i	−0.570963	+	0.207813i	0.0403732	+	0.999185i	$0.487145\pi$
$570$		0			0
$571$	−16.8877	+	14.1705i	−0.706729	+	0.593016i	−0.923679	−	0.383166i	$-0.874834\pi$
$571$	−16.8877	+	14.1705i	−0.706729	+	0.593016i	0.216950	+	0.976183i	$0.430389\pi$
$572$	1.01722	+	5.76896i	0.0425322	+	0.241212i
$573$		0			0
$574$	10.5895	+	8.88561i	0.441996	+	0.370878i
$575$	1.31172	−	2.27197i	0.0547025	−	0.0947475i
$576$		0			0
$577$	15.7418	+	27.2655i	0.655338	+	1.13508i	0.981809	+	0.189872i	$0.0608072\pi$
$577$	15.7418	+	27.2655i	0.655338	+	1.13508i	−0.326471	+	0.945207i	$0.605859\pi$
$578$	−3.02105	+	17.1332i	−0.125659	+	0.712648i
$579$		0			0
$580$	−28.9333	−	10.5308i	−1.20139	−	0.437269i
$581$	−2.14657	−	0.781286i	−0.0890545	−	0.0324132i
$582$		0			0
$583$	0.0739120	−	0.419176i	0.00306112	−	0.0173605i
$584$	16.2582	+	28.1600i	0.672768	+	1.16527i
$585$		0			0
$586$	−4.19516	+	7.26623i	−0.173300	+	0.300165i
$587$	−11.0076	−	9.23650i	−0.454334	−	0.381231i	0.386707	−	0.922202i	$-0.373612\pi$
$587$	−11.0076	−	9.23650i	−0.454334	−	0.381231i	−0.841041	+	0.540971i	$0.818057\pi$
$588$		0			0
$589$	3.96573	+	22.4908i	0.163405	+	0.926717i
$590$	5.66131	−	4.75041i	0.233073	−	0.195571i
$591$		0			0
$592$	−3.82937	+	1.39378i	−0.157386	+	0.0572839i
$593$	−41.0988			−1.68772			−0.843862	−	0.536560i	$-0.819724\pi$
$593$	−41.0988			−1.68772			−0.843862	+	0.536560i	$0.819724\pi$
$594$		0			0
$595$	−37.2966			−1.52901
$596$	−11.8417	+	4.31002i	−0.485054	+	0.176545i
$597$		0			0
$598$	3.22882	−	2.70930i	0.132036	−	0.110791i
$599$	1.48680	+	8.43208i	0.0607491	+	0.344525i	0.999999	+	0.00129176i	$0.000411180\pi$
$599$	1.48680	+	8.43208i	0.0607491	+	0.344525i	−0.939250	+	0.343234i	$0.888478\pi$
$600$		0			0
$601$	−1.25264	−	1.05109i	−0.0510964	−	0.0428750i	0.616882	−	0.787056i	$-0.288396\pi$
$601$	−1.25264	−	1.05109i	−0.0510964	−	0.0428750i	−0.667978	+	0.744181i	$0.732840\pi$
$602$	−2.27311	+	3.93713i	−0.0926449	+	0.160466i
$603$		0			0
$604$	16.6651	+	28.8648i	0.678094	+	1.17449i
$605$	0.467032	−	2.64867i	0.0189875	−	0.107684i
$606$		0			0
$607$	−6.17325	−	2.24688i	−0.250564	−	0.0911980i	0.213685	−	0.976903i	$-0.431453\pi$
$607$	−6.17325	−	2.24688i	−0.250564	−	0.0911980i	−0.464249	+	0.885705i	$0.653676\pi$
$608$	44.3630	+	16.1468i	1.79916	+	0.654840i
$609$		0			0
$610$	0.109693	−	0.622102i	0.00444135	−	0.0251882i
$611$	−3.08374	−	5.34120i	−0.124755	−	0.216082i
$612$		0			0
$613$	13.1363	−	22.7527i	0.530569	−	0.918973i	−0.468795	−	0.883307i	$-0.655312\pi$
$613$	13.1363	−	22.7527i	0.530569	−	0.918973i	0.999364	−	0.0356656i	$-0.0113551\pi$
$614$	−0.0296396	−	0.0248706i	−0.00119616	−	0.00100369i
$615$		0			0
$616$	3.60293	+	20.4332i	0.145166	+	0.823277i
$617$	−4.80542	+	4.03222i	−0.193459	+	0.162331i	−0.734372	−	0.678747i	$-0.762523\pi$
$617$	−4.80542	+	4.03222i	−0.193459	+	0.162331i	0.540913	+	0.841078i	$0.318079\pi$
$618$		0			0
$619$	−4.64290	+	1.68988i	−0.186614	+	0.0679219i	−0.433637	−	0.901088i	$-0.642770\pi$
$619$	−4.64290	+	1.68988i	−0.186614	+	0.0679219i	0.247023	+	0.969010i	$0.420548\pi$
$620$	9.38839			0.377047
$621$		0			0
$622$	−10.2936			−0.412738
$623$	8.76451	−	3.19002i	0.351143	−	0.127805i
$624$		0			0
$625$	−21.3087	+	17.8801i	−0.852347	+	0.715204i
$626$	2.03698	+	11.5523i	0.0814139	+	0.461721i
$627$		0			0
$628$	−2.89839	−	2.43204i	−0.115658	−	0.0970489i
$629$	17.3550	−	30.0598i	0.691991	−	1.19856i
$630$		0			0
$631$	3.46210	+	5.99653i	0.137824	+	0.238718i	0.926673	−	0.375869i	$-0.122656\pi$
$631$	3.46210	+	5.99653i	0.137824	+	0.238718i	−0.788849	+	0.614587i	$0.789322\pi$
$632$	1.87108	−	10.6114i	0.0744274	−	0.422099i
$633$		0			0
$634$	6.30766	+	2.29580i	0.250509	+	0.0911779i
$635$	−8.85528	−	3.22306i	−0.351411	−	0.127903i
$636$		0			0
$637$	−0.172480	+	0.978181i	−0.00683390	+	0.0387570i
$638$	−11.3450	−	19.6502i	−0.449154	−	0.777957i
$639$		0			0
$640$	11.0653	−	19.1657i	0.437394	−	0.757589i
$641$	−25.9834	−	21.8026i	−1.02628	−	0.861152i	−0.0358777	−	0.999356i	$-0.511423\pi$
$641$	−25.9834	−	21.8026i	−1.02628	−	0.861152i	−0.990404	+	0.138204i	$0.955867\pi$
$642$		0			0
$643$	1.34112	+	7.60588i	0.0528887	+	0.299947i	0.999766	−	0.0216494i	$-0.00689176\pi$
$643$	1.34112	+	7.60588i	0.0528887	+	0.299947i	−0.946877	+	0.321596i	$0.895781\pi$
$644$	−10.8392	+	9.09515i	−0.427123	+	0.358399i
$645$		0			0
$646$	−36.9814	+	13.4601i	−1.45502	+	0.529582i
$647$	35.1862			1.38331			0.691655	−	0.722228i	$-0.256882\pi$
$647$	35.1862			1.38331			0.691655	+	0.722228i	$0.256882\pi$
$648$		0			0
$649$	−12.5615			−0.493083
$650$	0.632049	−	0.230047i	0.0247910	−	0.00902318i
$651$		0			0
$652$	23.5644	−	19.7729i	0.922855	−	0.774367i
$653$	3.38822	+	19.2155i	0.132591	+	0.751962i	0.976507	+	0.215486i	$0.0691337\pi$
$653$	3.38822	+	19.2155i	0.132591	+	0.751962i	−0.843916	+	0.536476i	$0.819755\pi$
$654$		0			0
$655$	−0.186587	−	0.156565i	−0.00729055	−	0.00611750i
$656$	−2.61726	+	4.53323i	−0.102187	+	0.176993i
$657$		0			0
$658$	−4.48824	−	7.77386i	−0.174970	−	0.303057i
$659$	4.00892	−	22.7357i	0.156165	−	0.885658i	−0.801547	−	0.597931i	$-0.795990\pi$
$659$	4.00892	−	22.7357i	0.156165	−	0.885658i	0.957713	−	0.287726i	$-0.0928993\pi$
$660$		0			0
$661$	6.46166	+	2.35185i	0.251330	+	0.0914765i	0.464613	−	0.885514i	$-0.346194\pi$
$661$	6.46166	+	2.35185i	0.251330	+	0.0914765i	−0.213283	+	0.976990i	$0.568416\pi$
$662$	22.6743	+	8.25278i	0.881263	+	0.320753i
$663$		0			0
$664$	−0.418732	+	2.37475i	−0.0162500	+	0.0921581i
$665$	−23.9688	−	41.5152i	−0.929471	−	1.60989i
$666$		0			0
$667$	18.8280	−	32.6110i	0.729023	−	1.26270i
$668$	−9.56602	−	8.02685i	−0.370121	−	0.310568i
$669$		0			0
$670$	3.24875	+	18.4246i	0.125510	+	0.711803i
$671$	−0.822513	+	0.690170i	−0.0317528	+	0.0266437i
$672$		0			0
$673$	28.8226	−	10.4906i	1.11103	−	0.404381i	0.279657	−	0.960100i	$-0.409779\pi$
$673$	28.8226	−	10.4906i	1.11103	−	0.404381i	0.831370	+	0.555719i	$0.187557\pi$
$674$	18.5624			0.714997
$675$		0			0
$676$	15.6442			0.601700
$677$	12.7648	−	4.64599i	0.490589	−	0.178560i	−0.0848672	−	0.996392i	$-0.527047\pi$
$677$	12.7648	−	4.64599i	0.490589	−	0.178560i	0.575457	+	0.817832i	$0.304824\pi$
$678$		0			0
$679$	11.4899	−	9.64117i	0.440942	−	0.369994i
$680$	6.83671	+	38.7729i	0.262176	+	1.48687i
$681$		0			0
$682$	5.29992	+	4.44716i	0.202944	+	0.170290i
$683$	3.03350	−	5.25418i	0.116074	−	0.201045i	−0.802135	−	0.597143i	$-0.796302\pi$
$683$	3.03350	−	5.25418i	0.116074	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$684$		0			0
$685$	9.05335	+	15.6809i	0.345911	+	0.599135i
$686$	−2.61574	+	14.8346i	−0.0998696	+	0.566388i
$687$		0			0
$688$	−1.61768	−	0.588787i	−0.0616735	−	0.0224473i
$689$	0.170186	+	0.0619425i	0.00648355	+	0.00235982i
$690$		0			0
$691$	3.58845	−	20.3511i	0.136511	−	0.774194i	−0.837284	−	0.546768i	$-0.815858\pi$
$691$	3.58845	−	20.3511i	0.136511	−	0.774194i	0.973795	−	0.227426i	$-0.0730309\pi$
$692$	1.83756	+	3.18275i	0.0698537	+	0.120990i
$693$		0			0
$694$	8.52054	−	14.7580i	0.323435	−	0.560206i
$695$	19.0062	+	15.9481i	0.720945	+	0.604945i
$696$		0			0
$697$	−7.74214	−	43.9079i	−0.293255	−	1.66313i
$698$	−9.44121	+	7.92211i	−0.357355	+	0.299856i
$699$		0			0
$700$	−2.12180	+	0.772270i	−0.0801963	+	0.0291891i
$701$	11.0222			0.416303			0.208151	−	0.978097i	$-0.433255\pi$
$701$	11.0222			0.416303			0.208151	+	0.978097i	$0.433255\pi$
$702$		0			0
$703$	44.6131			1.68262
$704$	9.09037	−	3.30862i	0.342606	−	0.124698i
$705$		0			0
$706$	−7.68963	+	6.45237i	−0.289403	+	0.242838i
$707$	4.43990	+	25.1799i	0.166980	+	0.946988i
$708$		0			0
$709$	−8.41687	−	7.06260i	−0.316102	−	0.265241i	0.470906	−	0.882183i	$-0.343927\pi$
$709$	−8.41687	−	7.06260i	−0.316102	−	0.265241i	−0.787009	+	0.616942i	$0.788371\pi$
$710$	7.56897	−	13.1098i	0.284058	−	0.492003i
$711$		0			0
$712$	−4.92288	−	8.52669i	−0.184493	−	0.319551i
$713$	−1.99381	+	11.3075i	−0.0746688	+	0.423468i
$714$		0			0
$715$	−9.37618	−	3.41265i	−0.350649	−	0.127626i
$716$	4.83040	+	1.75812i	0.180521	+	0.0657041i
$717$		0			0
$718$	−3.48818	+	19.7825i	−0.130178	+	0.738275i
$719$	−16.3529	−	28.3240i	−0.609859	−	1.05631i	−0.991263	−	0.131898i	$-0.957893\pi$
$719$	−16.3529	−	28.3240i	−0.609859	−	1.05631i	0.381404	−	0.924408i	$-0.375441\pi$
$720$		0			0
$721$	10.6734	−	18.4870i	0.397500	−	0.688490i
$722$	−27.4291	−	23.0158i	−1.02081	−	0.856558i
$723$		0			0
$724$	0.0650496	+	0.368915i	0.00241755	+	0.0137106i
$725$	4.60324	−	3.86257i	0.170960	−	0.143452i
$726$		0			0
$727$	−36.1412	+	13.1543i	−1.34040	+	0.487866i	−0.909939	−	0.414742i	$-0.863872\pi$
$727$	−36.1412	+	13.1543i	−1.34040	+	0.487866i	−0.430462	+	0.902609i	$0.641649\pi$
$728$	−8.82830			−0.327199
$729$		0			0
$730$	−22.7591			−0.842352
$731$	13.7786	−	5.01502i	0.509622	−	0.185487i
$732$		0			0
$733$	10.8072	−	9.06829i	0.399172	−	0.334945i	−0.421002	−	0.907060i	$-0.638321\pi$
$733$	10.8072	−	9.06829i	0.399172	−	0.334945i	0.820173	+	0.572115i	$0.193877\pi$
$734$	−2.15740	−	12.2352i	−0.0796309	−	0.451609i
$735$		0			0
$736$	18.1823	+	15.2568i	0.670210	+	0.562373i
$737$	15.8999	−	27.5395i	0.585681	−	1.01443i
$738$		0			0
$739$	5.92286	+	10.2587i	0.217876	+	0.377372i	0.954158	−	0.299302i	$-0.0967539\pi$
$739$	5.92286	+	10.2587i	0.217876	+	0.377372i	−0.736283	+	0.676674i	$0.763421\pi$
$740$	3.18472	−	18.0614i	0.117073	−	0.663951i
$741$		0			0
$742$	0.247697	+	0.0901543i	0.00909324	+	0.00330967i
$743$	20.4548	+	7.44494i	0.750414	+	0.273129i	0.688780	−	0.724970i	$-0.258147\pi$
$743$	20.4548	+	7.44494i	0.750414	+	0.273129i	0.0616343	+	0.998099i	$0.480369\pi$
$744$		0			0
$745$	3.72728	−	21.1385i	0.136557	−	0.774453i
$746$	0.710290	+	1.23026i	0.0260056	+	0.0450429i
$747$		0			0
$748$	13.7494	−	23.8147i	0.502729	−	0.870753i
$749$	−14.8407	−	12.4528i	−0.542268	−	0.455017i
$750$		0			0
$751$	−7.38856	−	41.9026i	−0.269612	−	1.52905i	−0.755571	−	0.655066i	$-0.772641\pi$
$751$	−7.38856	−	41.9026i	−0.269612	−	1.52905i	0.485959	−	0.873982i	$-0.338470\pi$
$752$	2.60386	−	2.18490i	0.0949530	−	0.0796750i
$753$		0			0
$754$	9.07221	−	3.30202i	0.330391	−	0.120252i
$755$	−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	$0.622376\pi$
$758$	0.838214	−	0.305085i	0.0304453	−	0.0110812i
$759$		0			0
$760$	−38.7649	+	32.5276i	−1.40615	+	1.17990i
$761$	−8.58604	−	48.6938i	−0.311244	−	1.76515i	−0.592551	−	0.805533i	$-0.701879\pi$
$761$	−8.58604	−	48.6938i	−0.311244	−	1.76515i	0.281307	−	0.959618i	$-0.409232\pi$
$762$		0			0
$763$	−2.40359	−	2.01686i	−0.0870160	−	0.0730151i
$764$	−1.67275	+	2.89729i	−0.0605181	+	0.104820i
$765$		0			0
$766$	8.48799	+	14.7016i	0.306684	+	0.531192i
$767$	0.928121	−	5.26363i	0.0335125	−	0.190059i
$768$		0			0
$769$	−20.7988	−	7.57014i	−0.750023	−	0.272986i	−0.0614076	−	0.998113i	$-0.519559\pi$
$769$	−20.7988	−	7.57014i	−0.750023	−	0.272986i	−0.688616	+	0.725127i	$0.741781\pi$
$770$	−13.6466	−	4.96695i	−0.491789	−	0.178997i
$771$		0			0
$772$	−0.120211	+	0.681752i	−0.00432650	+	0.0245368i
$773$	−10.9836	−	19.0241i	−0.395051	−	0.684248i	0.598057	−	0.801454i	$-0.295940\pi$
$773$	−10.9836	−	19.0241i	−0.395051	−	0.684248i	−0.993108	+	0.117206i	$0.962606\pi$
$774$		0			0
$775$	−0.916134	+	1.58679i	−0.0329085	+	0.0569992i
$776$	−12.1290	−	10.1774i	−0.435405	−	0.365348i
$777$		0			0
$778$	3.53784	+	20.0641i	0.126838	+	0.719333i
$779$	43.8988	−	36.8354i	1.57284	−	1.31977i
$780$		0			0
$781$	−24.1786	+	8.80029i	−0.865179	+	0.314899i
$782$	−19.7860			−0.707547
$783$		0			0
$784$	−0.547423			−0.0195508
$785$	6.05597	−	2.20419i	0.216147	−	0.0786710i
$786$		0			0
$787$	0.410240	−	0.344232i	0.0146235	−	0.0122706i	−0.635447	−	0.772145i	$-0.719184\pi$
$787$	0.410240	−	0.344232i	0.0146235	−	0.0122706i	0.650070	+	0.759874i	$0.274740\pi$
$788$	5.36533	+	30.4283i	0.191132	+	1.08396i
$789$		0			0
$790$	5.77735	+	4.84777i	0.205549	+	0.172476i
$791$	22.2132	−	38.4744i	0.789810	−	1.36799i
$792$		0			0
$793$	−0.228429	−	0.395650i	−0.00811174	−	0.0140500i
$794$	−0.566989	+	3.21555i	−0.0201217	+	0.114116i
$795$		0			0
$796$	2.79566	+	1.01754i	0.0990895	+	0.0360656i
$797$	−37.6807	−	13.7147i	−1.33472	−	0.485798i	−0.426573	−	0.904453i	$-0.640279\pi$
$797$	−37.6807	−	13.7147i	−1.33472	−	0.485798i	−0.908145	+	0.418655i	$0.862502\pi$
$798$		0			0
$799$	−5.02745	+	28.5121i	−0.177858	+	1.00868i
$800$	1.89383	+	3.28021i	0.0669570	+	0.115973i
$801$		0			0
$802$	−3.04475	+	5.27366i	−0.107514	+	0.186219i
$803$	29.6338	+	24.8657i	1.04576	+	0.877493i
$804$		0			0
$805$	−4.18511	−	23.7350i	−0.147506	−	0.836547i
$806$	−2.25508	+	1.89223i	−0.0794317	+	0.0666511i
$807$		0			0
$808$	25.3628	−	9.23129i	0.892259	−	0.324756i
$809$	17.1826			0.604110			0.302055	−	0.953291i	$-0.402327\pi$
$809$	17.1826			0.604110			0.302055	+	0.953291i	$0.402327\pi$
$810$		0			0
$811$	−19.6169			−0.688842			−0.344421	−	0.938815i	$-0.611925\pi$
$811$	−19.6169			−0.688842			−0.344421	+	0.938815i	$0.611925\pi$
$812$	−30.4555	+	11.0849i	−1.06878	+	0.389004i
$813$		0			0
$814$	10.3533	−	8.68745i	0.362883	−	0.304495i
$815$	9.09846	+	51.6000i	0.318705	+	1.80747i
$816$		0			0
$817$	14.4372	+	12.1142i	0.505092	+	0.423823i
$818$	−6.77755	+	11.7391i	−0.236971	+	0.410446i
$819$		0			0
$820$	−11.7789	−	20.4017i	−0.411338	−	0.712459i
$821$	6.23500	−	35.3604i	0.217603	−	1.23409i	−0.658729	−	0.752380i	$-0.728906\pi$
$821$	6.23500	−	35.3604i	0.217603	−	1.23409i	0.876332	−	0.481708i	$-0.159983\pi$
$822$		0			0
$823$	24.2610	+	8.83030i	0.845687	+	0.307805i	0.728280	−	0.685279i	$-0.240320\pi$
$823$	24.2610	+	8.83030i	0.845687	+	0.307805i	0.117406	+	0.993084i	$0.462542\pi$
$824$	−21.1752	−	7.70716i	−0.737675	−	0.268492i
$825$		0			0
$826$	1.35084	−	7.66097i	0.0470016	−	0.266559i
$827$	12.4793	+	21.6148i	0.433948	+	0.751619i	0.997209	−	0.0746593i	$-0.0237869\pi$
$827$	12.4793	+	21.6148i	0.433948	+	0.751619i	−0.563261	+	0.826279i	$0.690454\pi$
$828$		0			0
$829$	−1.39964	+	2.42424i	−0.0486114	+	0.0841974i	−0.889307	−	0.457310i	$-0.848813\pi$
$829$	−1.39964	+	2.42424i	−0.0486114	+	0.0841974i	0.840696	+	0.541508i	$0.182146\pi$
$830$	−1.29293	−	1.08489i	−0.0448781	−	0.0376572i
$831$		0			0
$832$	0.714756	+	4.05359i	0.0247797	+	0.140533i
$833$	3.57183	−	2.99712i	0.123757	−	0.103844i
$834$		0			0
$835$	19.9875	−	7.27485i	0.691695	−	0.251756i
$836$	35.3445			1.22242
$837$		0			0
$838$	−8.93083			−0.308511
$839$	42.0117	−	15.2910i	1.45040	−	0.527904i	0.507700	−	0.861534i	$-0.330496\pi$
$839$	42.0117	−	15.2910i	1.45040	−	0.527904i	0.942704	+	0.333630i	$0.108274\pi$
$840$		0			0
$841$	43.8580	−	36.8013i	1.51235	−	1.26901i
$842$	−0.984694	−	5.58447i	−0.0339348	−	0.192454i
$843$		0			0
$844$	−21.3838	−	17.9432i	−0.736062	−	0.617630i
$845$	−13.3235	+	23.0770i	−0.458342	+	0.793872i
$846$		0			0
$847$	−1.41552	−	2.45175i	−0.0486378	−	0.0842431i
$848$	−0.0173325	+	0.0982977i	−0.000595202	+	0.00337556i
$849$		0			0
$850$	−2.96701	−	1.07990i	−0.101768	−	0.0370404i
$851$	21.0770	+	7.67140i	0.722510	+	0.262972i
$852$		0			0
$853$	−7.55629	+	42.8539i	−0.258723	+	1.46729i	0.527611	+	0.849486i	$0.323088\pi$
$853$	−7.55629	+	42.8539i	−0.258723	+	1.46729i	−0.786333	+	0.617802i	$0.788023\pi$
$854$	−0.332467	−	0.575850i	−0.0113768	−	0.0197052i
$855$		0			0
$856$	−10.2254	+	17.7108i	−0.349496	+	0.605344i
$857$	5.60017	+	4.69910i	0.191298	+	0.160518i	0.733406	−	0.679791i	$-0.237929\pi$
$857$	5.60017	+	4.69910i	0.191298	+	0.160518i	−0.542108	+	0.840309i	$0.682374\pi$
$858$		0			0
$859$	−1.67798	−	9.51629i	−0.0572519	−	0.324692i	0.942708	−	0.333618i	$-0.108270\pi$
$859$	−1.67798	−	9.51629i	−0.0572519	−	0.324692i	−0.999960	+	0.00892654i	$0.997159\pi$
$860$	5.93499	−	4.98005i	0.202381	−	0.169818i
$861$		0			0
$862$	0.284354	−	0.103496i	0.00968513	−	0.00352510i
$863$	3.15525			0.107406			0.0537030	−	0.998557i	$-0.482898\pi$
$863$	3.15525			0.107406			0.0537030	+	0.998557i	$0.482898\pi$
$864$		0			0
$865$	−6.25989			−0.212843
$866$	17.6138	−	6.41089i	0.598540	−	0.217851i
$867$		0			0
$868$	7.57032	−	6.35225i	0.256953	−	0.215609i
$869$	−2.22599	−	12.6242i	−0.0755116	−	0.428248i
$870$		0			0
$871$	10.3650	+	8.69730i	0.351206	+	0.294697i
$872$	−1.65609	+	2.86844i	−0.0560824	+	0.0971376i
$873$		0			0
$874$	−12.7156	−	22.0240i	−0.430110	−	0.744973i
$875$	−4.49309	+	25.4816i	−0.151894	+	0.861435i
$876$		0			0
$877$	49.7312	+	18.1007i	1.67930	+	0.611217i	0.993214	−	0.116300i	$-0.0371034\pi$
$877$	49.7312	+	18.1007i	1.67930	+	0.611217i	0.686090	+	0.727517i	$0.259326\pi$
$878$	26.7963	+	9.75305i	0.904331	+	0.329150i
$879$		0			0
$880$	0.954918	−	5.41561i	0.0321903	−	0.182560i
$881$	18.3507	+	31.7843i	0.618250	+	1.07084i	0.989805	+	0.142430i	$0.0454915\pi$
$881$	18.3507	+	31.7843i	0.618250	+	1.07084i	−0.371555	+	0.928411i	$0.621175\pi$
$882$		0			0
$883$	−14.9551	+	25.9031i	−0.503280	+	0.871707i	0.496712	+	0.867915i	$0.334540\pi$
$883$	−14.9551	+	25.9031i	−0.503280	+	0.871707i	−0.999993	+	0.00379204i	$0.998793\pi$
$884$	8.96316	+	7.52098i	0.301464	+	0.252958i
$885$		0			0
$886$	5.10316	+	28.9414i	0.171444	+	0.972307i
$887$	−42.7081	+	35.8364i	−1.43400	+	1.20327i	−0.490696	+	0.871331i	$0.663258\pi$
$887$	−42.7081	+	35.8364i	−1.43400	+	1.20327i	−0.943302	+	0.331937i	$0.892298\pi$
$888$		0			0
$889$	−9.32120	+	3.39264i	−0.312623	+	0.113785i
$890$	6.89133			0.230998
$891$		0			0
$892$	18.5252			0.620270
$893$	−34.9680	+	12.7273i	−1.17016	+	0.425903i
$894$		0			0
$895$	−6.70728	+	5.62807i	−0.224199	+	0.188126i
$896$	−4.04513	−	22.9411i	−0.135138	−	0.766407i
$897$		0			0
$898$	−7.02170	−	5.89191i	−0.234317	−	0.196616i
$899$	−13.1499	+	22.7763i	−0.438573	+	0.759631i
$900$		0			0
$901$	−0.425085	−	0.736269i	−0.0141616	−	0.0245287i
$902$	3.01460	−	17.0967i	0.100375	−	0.569257i
$903$		0			0
$904$	−44.0691	−	16.0399i	−1.46572	−	0.533478i
$905$	−0.599591	−	0.218233i	−0.0199311	−	0.00725432i
$906$		0			0
$907$	6.25162	−	35.4547i	0.207582	−	1.17725i	−0.685743	−	0.727843i	$-0.740523\pi$
$907$	6.25162	−	35.4547i	0.207582	−	1.17725i	0.893325	−	0.449411i	$-0.148366\pi$
$908$	−8.69930	−	15.0676i	−0.288696	−	0.500037i
$909$		0			0
$910$	3.08959	−	5.35132i	0.102419	−	0.177395i
$911$	12.5454	+	10.5268i	0.415647	+	0.348769i	0.826504	−	0.562930i	$-0.190326\pi$
$911$	12.5454	+	10.5268i	0.415647	+	0.348769i	−0.410857	+	0.911700i	$0.634771\pi$
$912$		0			0
$913$	0.498160	+	2.82520i	0.0164867	+	0.0935006i
$914$	11.8297	−	9.92630i	0.391292	−	0.328333i
$915$		0			0
$916$	33.6422	−	12.2448i	1.11157	−	0.404578i
$917$	−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	$0.395567\pi$
$920$	−23.9073	+	8.70155i	−0.788200	+	0.286881i
$921$		0			0
$922$	4.55283	−	3.82028i	0.149939	−	0.125814i
$923$	−1.90111	−	10.7817i	−0.0625759	−	0.354885i
$924$		0			0
$925$	2.74191	+	2.30073i	0.0901533	+	0.0756476i
$926$	−6.20413	+	10.7459i	−0.203880	+	0.353131i
$927$		0			0
$928$	27.1834	+	47.0830i	0.892339	+	1.54558i
$929$	1.86691	−	10.5878i	0.0612514	−	0.347374i	−0.938745	−	0.344613i	$-0.888010\pi$
$929$	1.86691	−	10.5878i	0.0612514	−	0.347374i	0.999996	−	0.00276093i	$-0.000878834\pi$
$930$		0			0
$931$	5.63158	+	2.04973i	0.184568	+	0.0671771i
$932$	−7.07469	−	2.57498i	−0.231739	−	0.0843461i
$933$		0			0
$934$	−3.53034	+	20.0216i	−0.115516	+	0.655125i
$935$	23.4196	+	40.5639i	0.765903	+	1.32658i
$936$		0			0
$937$	14.2219	−	24.6330i	0.464609	−	0.804727i	−0.534575	−	0.845121i	$-0.679528\pi$
$937$	14.2219	−	24.6330i	0.464609	−	0.804727i	0.999184	+	0.0403947i	$0.0128615\pi$
$938$	15.0858	+	12.6585i	0.492570	+	0.413315i
$939$		0			0
$940$	2.65639	+	15.0652i	0.0866420	+	0.491371i
$941$	21.2658	−	17.8441i	0.693245	−	0.581702i	−0.226598	−	0.973988i	$-0.572760\pi$
$941$	21.2658	−	17.8441i	0.693245	−	0.581702i	0.919843	+	0.392287i	$0.128316\pi$
$942$		0			0
$943$	27.0735	−	9.85395i	0.881634	−	0.320889i
$944$	2.94571			0.0958746
$945$		0			0
$946$	5.70939			0.185628
$947$	−39.9139	+	14.5275i	−1.29703	+	0.472080i	−0.896028	−	0.443998i	$-0.853560\pi$
$947$	−39.9139	+	14.5275i	−1.29703	+	0.472080i	−0.401001	+	0.916078i	$0.631338\pi$
$948$		0			0
$949$	−12.6090	+	10.5802i	−0.409305	+	0.343447i
$950$	−0.704711	−	3.99662i	−0.0228639	−	0.129667i
$951$		0			0
$952$	31.7468	+	26.6387i	1.02892	+	0.863367i
$953$	−24.5758	+	42.5665i	−0.796088	+	1.37886i	0.126058	+	0.992023i	$0.459767\pi$
$953$	−24.5758	+	42.5665i	−0.796088	+	1.37886i	−0.922146	+	0.386842i	$0.873566\pi$
$954$		0			0
$955$	−2.84922	−	4.93500i	−0.0921987	−	0.159693i
$956$	−2.02799	+	11.5013i	−0.0655898	+	0.371978i
$957$		0			0
$958$	28.7583	+	10.4672i	0.929140	+	0.338179i
$959$	17.9099	+	6.51868i	0.578342	+	0.210499i
$960$		0			0
$961$	−3.99057	+	22.6317i	−0.128728	+	0.730054i
$962$	2.87532	+	4.98021i	0.0927041	+	0.160568i
$963$		0			0
$964$	−0.308456	+	0.534262i	−0.00993471	+	0.0172074i
$965$	−0.903282	−	0.757943i	−0.0290777	−	0.0243991i
$966$		0			0
$967$	8.33285	+	47.2580i	0.267967	+	1.51971i	0.760453	+	0.649393i	$0.224977\pi$
$967$	8.33285	+	47.2580i	0.267967	+	1.51971i	−0.492486	+	0.870320i	$0.663912\pi$
$968$	−2.28932	+	1.92097i	−0.0735817	+	0.0617423i
$969$		0			0
$970$	10.4138	−	3.79031i	0.334367	−	0.121700i
$971$	−28.9682			−0.929633			−0.464817	−	0.885407i	$-0.653880\pi$
$971$	−28.9682			−0.929633			−0.464817	+	0.885407i	$0.653880\pi$
$972$		0			0
$973$	26.1162			0.837247
$974$	8.56040	−	3.11573i	0.274293	−	0.0998344i
$975$		0			0
$976$	0.192881	−	0.161847i	0.00617398	−	0.00518058i
$977$	−2.63896	−	14.9663i	−0.0844278	−	0.478814i	−0.997479	−	0.0709681i	$-0.977391\pi$
$977$	−2.63896	−	14.9663i	−0.0844278	−	0.478814i	0.913051	−	0.407846i	$-0.133720\pi$
$978$		0			0
$979$	−8.97296	−	7.52921i	−0.286777	−	0.240635i
$980$	1.23183	−	2.13360i	0.0393495	−	0.0681553i
$981$		0			0
$982$	−14.9907	−	25.9647i	−0.478373	−	0.828567i
$983$	−6.69799	+	37.9862i	−0.213633	+	1.21157i	0.669631	+	0.742694i	$0.266452\pi$
$983$	−6.69799	+	37.9862i	−0.213633	+	1.21157i	−0.883263	+	0.468877i	$0.844659\pi$
$984$		0			0
$985$	−49.4545	−	18.0000i	−1.57575	−	0.573527i
$986$	−42.5875	−	15.5006i	−1.35626	−	0.493639i
$987$		0			0
$988$	−2.61147	+	14.8104i	−0.0830818	+	0.471180i
$989$	4.73760	+	8.20576i	0.150647	+	0.260928i
$990$		0			0
$991$	−25.5171	+	44.1968i	−0.810576	+	1.40396i	0.101885	+	0.994796i	$0.467512\pi$
$991$	−25.5171	+	44.1968i	−0.810576	+	1.40396i	−0.912461	+	0.409163i	$0.865821\pi$
$992$	−12.6989	−	10.6557i	−0.403192	−	0.338318i
$993$		0			0
$994$	−2.76698	−	15.6923i	−0.0877632	−	0.497730i
$995$	−3.88192	+	3.25732i	−0.123065	+	0.103264i
$996$		0			0
$997$	−29.8797	+	10.8753i	−0.946298	+	0.344424i	−0.768650	−	0.639670i	$-0.779071\pi$
$997$	−29.8797	+	10.8753i	−0.946298	+	0.344424i	−0.177648	+	0.984094i	$0.556849\pi$
$998$	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.l.163.2		12
3.2	odd	2		729.2.e.s.163.1		12
9.2	odd	6		729.2.e.t.406.2		12
9.4	even	3		729.2.e.u.649.1		12
9.5	odd	6		729.2.e.j.649.2		12
9.7	even	3		729.2.e.k.406.1		12
27.2	odd	18		729.2.a.b.1.5	✓	6
27.4	even	9	inner	729.2.e.l.568.2		12
27.5	odd	18		729.2.e.j.82.2		12
27.7	even	9		729.2.c.a.487.5		12
27.11	odd	18		729.2.c.d.244.2		12
27.13	even	9		729.2.e.k.325.1		12
27.14	odd	18		729.2.e.t.325.2		12
27.16	even	9		729.2.c.a.244.5		12
27.20	odd	18		729.2.c.d.487.2		12
27.22	even	9		729.2.e.u.82.1		12
27.23	odd	18		729.2.e.s.568.1		12
27.25	even	9		729.2.a.e.1.2	yes	6

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

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)

\(f(q)\)	\(=\)	\(q+(0.730829 - 0.266000i) q^{2} +(-1.06873 + 0.896774i) q^{4} +(-0.412648 - 2.34025i) q^{5} +(-1.91617 - 1.60785i) q^{7} +(-1.32025 + 2.28674i) q^{8} +O(q^{10})\)	\(q+(0.730829 - 0.266000i) q^{2} +(-1.06873 + 0.896774i) q^{4} +(-0.412648 - 2.34025i) q^{5} +(-1.91617 - 1.60785i) q^{7} +(-1.32025 + 2.28674i) q^{8} +(-0.924081 - 1.60056i) q^{10} +(-0.545493 + 3.09365i) q^{11} +(-1.25602 - 0.457154i) q^{13} +(-1.82808 - 0.665366i) q^{14} +(0.127919 - 0.725467i) q^{16} +(3.13726 + 5.43389i) q^{17} +(-4.03234 + 6.98422i) q^{19} +(2.53968 + 2.13105i) q^{20} +(0.424248 + 2.40603i) q^{22} +(-3.10600 + 2.60625i) q^{23} +(-0.608008 + 0.221297i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(-8.72714 + 3.17642i) q^{29} +(2.16930 - 1.82026i) q^{31} +(-1.01652 - 5.76500i) q^{32} +(3.73822 + 3.13674i) q^{34} +(-2.97207 + 5.14778i) q^{35} +(-2.76596 - 4.79078i) q^{37} +(-1.08915 + 6.17688i) q^{38} +(5.89634 + 2.14609i) q^{40} +(-6.67723 - 2.43031i) q^{41} +(0.405799 - 2.30140i) q^{43} +(-2.19131 - 3.79547i) q^{44} +(-1.57670 + 2.73092i) q^{46} +(3.53469 + 2.96595i) q^{47} +(-0.129041 - 0.731827i) q^{49} +(-0.385485 + 0.323460i) q^{50} +(1.75232 - 0.637791i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(6.20657 - 2.25901i) q^{56} +(-5.53312 + 4.64284i) q^{58} +(0.694374 + 3.93799i) q^{59} +(0.261833 + 0.219704i) q^{61} +(1.10120 - 1.90733i) q^{62} +(-1.53974 - 2.66690i) q^{64} +(-0.551558 + 3.12804i) q^{65} +(-9.51243 - 3.46224i) q^{67} +(-8.22586 - 2.99397i) q^{68} +(-0.802767 + 4.55272i) q^{70} +(4.09540 + 7.09344i) q^{71} +(6.15722 - 10.6646i) q^{73} +(-3.29579 - 2.76550i) q^{74} +(-1.95377 - 11.0804i) q^{76} +(6.01939 - 5.05086i) q^{77} +(-3.83460 + 1.39568i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(0.858154 - 0.312342i) q^{83} +(11.4221 - 9.58424i) q^{85} +(-0.315603 - 1.78987i) q^{86} +(-6.35419 - 5.33180i) q^{88} +(-1.86437 + 3.22919i) q^{89} +(1.67171 + 2.89548i) q^{91} +(0.982276 - 5.57076i) q^{92} +(3.37220 + 1.22738i) q^{94} +(18.0087 + 6.55465i) q^{95} +(-1.04125 + 5.90520i) q^{97} +(-0.288973 - 0.500515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 12 * q^5 - 3 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} + 27 q^{16} + 9 q^{17} - 12 q^{19} + 39 q^{20} - 39 q^{22} + 21 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} + 6 q^{31} + 27 q^{32} - 18 q^{34} - 30 q^{35} - 3 q^{37} + 3 q^{38} + 33 q^{40} - 15 q^{41} - 30 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} - 3 q^{49} + 6 q^{50} - 18 q^{53} + 30 q^{55} + 15 q^{56} - 3 q^{58} + 30 q^{59} - 30 q^{61} + 30 q^{62} - 6 q^{64} - 12 q^{65} - 39 q^{67} + 18 q^{68} + 51 q^{70} - 12 q^{73} + 57 q^{74} + 57 q^{76} - 24 q^{77} + 15 q^{79} - 42 q^{80} - 42 q^{82} - 21 q^{83} + 54 q^{85} - 60 q^{86} + 12 q^{88} + 9 q^{89} - 18 q^{91} - 15 q^{92} + 33 q^{94} + 42 q^{95} - 12 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 12 * q^5 - 3 * q^7 - 6 * q^8 - 6 * q^10 - 3 * q^11 + 6 * q^13 - 6 * q^14 + 27 * q^16 + 9 * q^17 - 12 * q^19 + 39 * q^20 - 39 * q^22 + 21 * q^23 + 6 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 + 6 * q^31 + 27 * q^32 - 18 * q^34 - 30 * q^35 - 3 * q^37 + 3 * q^38 + 33 * q^40 - 15 * q^41 - 30 * q^43 + 33 * q^44 + 3 * q^46 - 21 * q^47 - 3 * q^49 + 6 * q^50 - 18 * q^53 + 30 * q^55 + 15 * q^56 - 3 * q^58 + 30 * q^59 - 30 * q^61 + 30 * q^62 - 6 * q^64 - 12 * q^65 - 39 * q^67 + 18 * q^68 + 51 * q^70 - 12 * q^73 + 57 * q^74 + 57 * q^76 - 24 * q^77 + 15 * q^79 - 42 * q^80 - 42 * q^82 - 21 * q^83 + 54 * q^85 - 60 * q^86 + 12 * q^88 + 9 * q^89 - 18 * q^91 - 15 * q^92 + 33 * q^94 + 42 * q^95 - 12 * q^97 - 18 * q^98

Introduction

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