LMFDB - Embedded newform 729.2.e.s.163.1

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			163.1
Root			$1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.s.568.1

$q$-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	−0.587223	−	0.809425i	$-0.699779\pi$
$2$	−0.730829	+	0.266000i	−0.516774	+	0.188091i	0.0704490	+	0.997515i	$0.477557\pi$
$3$		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	$0.122766\pi$
$5$	0.412648	+	2.34025i	0.184542	+	1.04659i	−0.742000	+	0.670399i	$0.766123\pi$
$6$		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	$-0.787406\pi$
$11$	0.545493	−	3.09365i	0.164472	−	0.932769i	0.949607	−	0.313444i	$-0.101483\pi$
$12$		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	$-0.891426\pi$
$17$	−3.13726	−	5.43389i	−0.760897	−	1.31791i	0.181492	−	0.983392i	$-0.441907\pi$
$18$		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	−0.258709	−	0.965955i	$-0.583297\pi$
$23$	3.10600	−	2.60625i	0.647646	−	0.543440i	0.906356	+	0.422515i	$0.138853\pi$
$24$		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	0.637095	−	0.770786i	$-0.280136\pi$
$29$	8.72714	−	3.17642i	1.62059	−	0.589846i	0.983494	+	0.180939i	$0.0579138\pi$
$30$		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	0.805944	−	0.591992i	$-0.201658\pi$
$41$	6.67723	+	2.43031i	1.04281	+	0.379551i	0.236864	+	0.971543i	$0.423880\pi$
$42$		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	0.347503	−	0.937679i	$-0.387030\pi$
$47$	−3.53469	−	2.96595i	−0.515587	−	0.432629i	−0.863090	+	0.505050i	$0.831474\pi$
$48$		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	$-0.497038\pi$
$53$	0.135496			0.0186118			0.00930588	+	0.999957i	$0.497038\pi$
$54$		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	$-0.971736\pi$
$59$	−0.694374	−	3.93799i	−0.0903998	−	0.512682i	0.905661	−	0.424004i	$-0.139376\pi$
$60$		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	0.513837	−	0.857888i	$-0.328224\pi$
$71$	−4.09540	−	7.09344i	−0.486035	−	0.841837i	−0.999871	+	0.0160515i	$0.994890\pi$
$72$		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	−0.388688	−	0.921370i	$-0.627071\pi$
$83$	−0.858154	+	0.312342i	−0.0941946	+	0.0342840i	0.294493	+	0.955654i	$0.404849\pi$
$84$		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	−0.750134	−	0.661286i	$-0.770011\pi$
$89$	1.86437	−	3.22919i	0.197623	−	0.342293i	0.947757	+	0.318992i	$0.103344\pi$
$90$		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	0.943033	−	0.332700i	$-0.107960\pi$
$101$	7.83029	+	6.57039i	0.779143	+	0.653778i	−0.163890	+	0.986479i	$0.552404\pi$
$102$		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	$-0.622141\pi$
$107$	−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	$0.480866\pi$
$110$	−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	$-0.740794\pi$
$113$	−3.08413	−	17.4909i	−0.290130	−	1.64541i	0.396233	−	0.918150i	$-0.370317\pi$
$114$		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	−0.646211	−	0.763159i	$-0.723648\pi$
$131$	−0.0785183	+	0.0658847i	−0.00686018	+	0.00575637i	0.639351	+	0.768915i	$0.279203\pi$
$132$		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	−0.0175340	−	0.999846i	$-0.505582\pi$
$137$	7.16003	−	2.60604i	0.611723	−	0.222649i	0.629257	+	0.777197i	$0.283359\pi$
$138$		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	−0.0299267	−	0.999552i	$-0.509527\pi$
$149$	−8.48785	−	3.08932i	−0.695352	−	0.253087i	−0.665425	+	0.746465i	$0.731750\pi$
$150$		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	$-0.942988\pi$
$167$	−1.55429	−	8.81482i	−0.120275	−	0.682111i	0.863728	−	0.503958i	$-0.168123\pi$
$168$		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	−0.997247	−	0.0741575i	$-0.976373\pi$
$173$	−0.457433	+	2.59423i	−0.0347780	+	0.197236i	0.962469	+	0.271393i	$0.0874843\pi$
$174$		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	0.926625	−	0.375988i	$-0.122697\pi$
$179$	1.84227	+	3.19090i	0.137697	+	0.238499i	−0.788927	+	0.614487i	$0.789363\pi$
$180$		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	−0.422255	−	0.906477i	$-0.638761\pi$
$191$	−2.25337	+	0.820159i	−0.163048	+	0.0593447i	0.259207	+	0.965822i	$0.416539\pi$
$192$		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	$0.456040\pi$
$197$	−11.0734	+	19.1797i	−0.788946	+	1.36649i	−0.926613	+	0.376016i	$0.877294\pi$
$198$		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	$-0.808624\pi$
$227$	2.16555	−	12.2815i	0.143733	−	0.815150i	0.968376	−	0.249496i	$-0.0802650\pi$
$228$		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	0.764005	−	0.645210i	$-0.223230\pi$
$233$	−2.69821	−	4.67344i	−0.176766	−	0.306167i	−0.940771	+	0.339043i	$0.889897\pi$
$234$		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	−0.826179	−	0.563407i	$-0.809490\pi$
$239$	−6.41259	+	5.38080i	−0.414796	+	0.348055i	0.411383	+	0.911462i	$0.365046\pi$
$240$		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	$-0.652734\pi$
$251$	8.51427	−	14.7471i	0.537416	−	0.930832i	0.999042	−	0.0437571i	$-0.0139328\pi$
$252$		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	0.871442	−	0.490499i	$-0.163185\pi$
$257$	19.6177	+	7.14026i	1.22372	+	0.445397i	0.352277	+	0.935896i	$0.385408\pi$
$258$		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	0.0572625	−	0.998359i	$-0.481763\pi$
$263$	−14.8548	−	12.4647i	−0.915986	−	0.768603i	−0.973248	+	0.229756i	$0.926207\pi$
$264$		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	$-0.692841\pi$
$269$	−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	$0.371452\pi$
$272$	−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	$0.196302\pi$
$281$	−2.49112	+	14.1278i	−0.148608	+	0.842797i	−0.964399	+	0.264451i	$0.914809\pi$
$282$		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	−0.368637	−	0.929574i	$-0.620175\pi$
$293$	8.26423	−	6.93451i	0.482801	−	0.405118i	0.851438	+	0.524455i	$0.175731\pi$
$294$		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	0.669652	−	0.742675i	$-0.266443\pi$
$311$	12.4373	+	4.52679i	0.705252	+	0.256691i	0.0356007	+	0.999366i	$0.488666\pi$
$312$		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	0.437949	−	0.899000i	$-0.355705\pi$
$317$	−6.61159	−	5.54779i	−0.371344	−	0.311595i	−0.809293	+	0.587405i	$0.800150\pi$
$318$		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	−0.970398	−	0.241510i	$-0.922357\pi$
$347$	−16.7850	+	14.0843i	−0.901065	+	0.756083i	0.0693332	+	0.997594i	$0.477913\pi$
$348$		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	0.00155627	−	0.999999i	$-0.499505\pi$
$353$	12.1285	−	4.41442i	0.645535	−	0.234956i	0.643979	+	0.765043i	$0.277282\pi$
$354$		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	$-0.594623\pi$
$359$	12.9142	−	22.3681i	0.681588	−	1.18054i	0.974496	−	0.224404i	$-0.0720435\pi$
$360$		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	$-0.867252\pi$
$383$	−3.79031	−	21.4959i	−0.193676	−	1.09839i	0.720616	−	0.693335i	$-0.243859\pi$
$384$		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	$-0.713260\pi$
$389$	4.54892	−	25.7982i	0.230639	−	1.30802i	0.851605	−	0.524183i	$-0.175629\pi$
$390$		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	−0.480622	−	0.876928i	$-0.659589\pi$
$401$	5.99798	−	5.03290i	0.299525	−	0.251331i	0.780147	+	0.625597i	$0.215144\pi$
$402$		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	0.591869	−	0.806034i	$-0.298390\pi$
$419$	10.7907	+	3.92748i	0.527158	+	0.191870i	−0.0647110	+	0.997904i	$0.520613\pi$
$420$		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	$-0.502983\pi$
$431$	−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	$0.303400\pi$
$434$	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	$-0.589718\pi$
$443$	6.56158	−	37.2126i	0.311750	−	1.76802i	0.589890	−	0.807483i	$-0.299171\pi$
$444$		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	0.970913	−	0.239432i	$-0.0769611\pi$
$449$	5.89289	+	10.2068i	0.278103	+	0.481688i	−0.692811	+	0.721120i	$0.743628\pi$
$450$		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	−0.503786	−	0.863828i	$-0.668060\pi$
$461$	−7.18097	+	2.61366i	−0.334451	+	0.121730i	0.169335	+	0.985558i	$0.445838\pi$
$462$		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	$-0.626577\pi$
$467$	13.0703	−	22.6385i	0.604822	−	1.04758i	0.992080	−	0.125611i	$-0.0400892\pi$
$468$		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	$-0.922087\pi$
$479$	−30.1441	−	25.2939i	−1.37732	−	1.15571i	−0.407125	−	0.913373i	$-0.633469\pi$
$480$		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	$0.280239\pi$
$491$	6.69411	+	37.9642i	0.302101	+	1.71330i	−0.334745	+	0.942309i	$0.608650\pi$
$492$		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	$0.124900\pi$
$503$	17.7888	+	30.8110i	0.793161	+	1.37380i	−0.130839	+	0.991404i	$0.541767\pi$
$504$		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	−0.0178483	−	0.999841i	$-0.505682\pi$
$509$	21.7421	−	18.2438i	0.963703	−	0.808643i	0.981552	+	0.191198i	$0.0612372\pi$
$510$		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	$0.354778\pi$
$521$	−12.7176	+	22.0275i	−0.557167	+	0.965041i	−0.997731	+	0.0673204i	$0.978555\pi$
$522$		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	0.910474	−	0.413567i	$-0.135717\pi$
$557$	2.29110	+	3.96830i	0.0970769	+	0.168142i	−0.813397	+	0.581710i	$0.802384\pi$
$558$		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	−0.819172	−	0.573548i	$-0.805567\pi$
$563$	−9.41003	+	7.89595i	−0.396585	+	0.332775i	0.422587	+	0.906323i	$0.361122\pi$
$564$		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	−0.0403732	−	0.999185i	$-0.512855\pi$
$569$	13.6196	−	4.95712i	0.570963	−	0.207813i	0.611336	+	0.791371i	$0.290632\pi$
$570$		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	0.841041	−	0.540971i	$-0.181943\pi$
$587$	11.0076	+	9.23650i	0.454334	+	0.381231i	−0.386707	+	0.922202i	$0.626388\pi$
$588$		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	$-0.180276\pi$
$593$	41.0988			1.68772			0.843862	+	0.536560i	$0.180276\pi$
$594$		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	$-0.999589\pi$
$599$	−1.48680	−	8.43208i	−0.0607491	−	0.344525i	0.939250	−	0.343234i	$-0.111522\pi$
$600$		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	−0.540913	−	0.841078i	$-0.681921\pi$
$617$	4.80542	−	4.03222i	0.193459	−	0.162331i	0.734372	+	0.678747i	$0.237477\pi$
$618$		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	0.990404	−	0.138204i	$-0.0441329\pi$
$641$	25.9834	+	21.8026i	1.02628	+	0.861152i	0.0358777	+	0.999356i	$0.488577\pi$
$642$		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	$-0.743118\pi$
$647$	−35.1862			−1.38331			−0.691655	+	0.722228i	$0.743118\pi$
$648$		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	$-0.930866\pi$
$653$	−3.38822	−	19.2155i	−0.132591	−	0.751962i	0.843916	−	0.536476i	$-0.180245\pi$
$654$		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	$0.204010\pi$
$659$	−4.00892	+	22.7357i	−0.156165	+	0.885658i	−0.957713	+	0.287726i	$0.907101\pi$
$660$		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	−0.575457	−	0.817832i	$-0.695176\pi$
$677$	−12.7648	+	4.64599i	−0.490589	+	0.178560i	0.0848672	+	0.996392i	$0.472953\pi$
$678$		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	−0.918208	−	0.396098i	$-0.870364\pi$
$683$	−3.03350	+	5.25418i	−0.116074	+	0.201045i	0.802135	+	0.597143i	$0.203698\pi$
$684$		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	$-0.566745\pi$
$701$	−11.0222			−0.416303			−0.208151	+	0.978097i	$0.566745\pi$
$702$		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	$0.0421072\pi$
$719$	16.3529	+	28.3240i	0.609859	+	1.05631i	−0.381404	+	0.924408i	$0.624559\pi$
$720$		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	−0.0616343	−	0.998099i	$-0.519631\pi$
$743$	−20.4548	−	7.44494i	−0.750414	−	0.273129i	−0.688780	+	0.724970i	$0.741853\pi$
$744$		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	$0.298121\pi$
$761$	8.58604	+	48.6938i	0.311244	+	1.76515i	−0.281307	+	0.959618i	$0.590768\pi$
$762$		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	0.993108	−	0.117206i	$-0.0373936\pi$
$773$	10.9836	+	19.0241i	0.395051	+	0.684248i	−0.598057	+	0.801454i	$0.704060\pi$
$774$		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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more