LMFDB - Embedded newform 414.2.i.e.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			307.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	414.307
Dual form			414.2.i.e.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(-0.698939 - 0.806618i) q^{5} +(3.72270 + 2.39243i) q^{7} +(-0.415415 + 0.909632i) q^{8} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(-0.698939 - 0.806618i) q^{5} +(3.72270 + 2.39243i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.897877 + 0.577031i) q^{10} +(-0.234769 - 1.63285i) q^{11} +(4.60260 - 2.95791i) q^{13} +(2.89788 - 3.34433i) q^{14} +(0.841254 + 0.540641i) q^{16} +(3.76709 - 1.10612i) q^{17} +(-6.33409 - 1.85986i) q^{19} +(0.443376 + 0.970858i) q^{20} -1.64964 q^{22} +(4.78492 + 0.323343i) q^{23} +(0.549456 - 3.82155i) q^{25} +(-2.27279 - 4.97671i) q^{26} +(-2.89788 - 3.34433i) q^{28} +(-6.14024 + 1.80294i) q^{29} +(-1.25244 + 2.74246i) q^{31} +(0.654861 - 0.755750i) q^{32} +(-0.558746 - 3.88617i) q^{34} +(-0.672158 - 4.67496i) q^{35} +(1.44774 - 1.67078i) q^{37} +(-2.74236 + 6.00493i) q^{38} +(1.02408 - 0.300696i) q^{40} +(2.67954 + 3.09235i) q^{41} +(-1.21021 - 2.64998i) q^{43} +(-0.234769 + 1.63285i) q^{44} +(1.00102 - 4.69020i) q^{46} +9.62306 q^{47} +(5.22685 + 11.4452i) q^{49} +(-3.70446 - 1.08773i) q^{50} +(-5.24950 + 1.54139i) q^{52} +(1.87633 + 1.20584i) q^{53} +(-1.15300 + 1.33063i) q^{55} +(-3.72270 + 2.39243i) q^{56} +(0.910738 + 6.33432i) q^{58} +(-8.20397 + 5.27237i) q^{59} +(-0.647821 + 1.41853i) q^{61} +(2.53631 + 1.62999i) q^{62} +(-0.654861 - 0.755750i) q^{64} +(-5.60284 - 1.64514i) q^{65} +(-1.71423 + 11.9227i) q^{67} -3.92613 q^{68} -4.72304 q^{70} +(-0.749168 + 5.21058i) q^{71} +(-6.89449 - 2.02441i) q^{73} +(-1.44774 - 1.67078i) q^{74} +(5.55353 + 3.56904i) q^{76} +(3.03252 - 6.64029i) q^{77} +(2.26617 - 1.45638i) q^{79} +(-0.151894 - 1.05645i) q^{80} +(3.44222 - 2.21218i) q^{82} +(3.62690 - 4.18567i) q^{83} +(-3.52518 - 2.26550i) q^{85} +(-2.79524 + 0.820757i) q^{86} +(1.58282 + 0.464758i) q^{88} +(-4.70504 - 10.3026i) q^{89} +24.2107 q^{91} +(-4.50000 - 1.65831i) q^{92} +(1.36950 - 9.52511i) q^{94} +(2.92694 + 6.40911i) q^{95} +(-7.84485 - 9.05344i) q^{97} +(12.0726 - 3.54482i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{4} + 2 q^{5} + q^{8}+O(q^{10}) $ 10 * q + q^2 - q^4 + 2 * q^5 + q^8	$ 10 q + q^{2} - q^{4} + 2 q^{5} + q^{8} + 9 q^{10} - 11 q^{11} + 13 q^{13} + 11 q^{14} - q^{16} + 24 q^{17} - 14 q^{19} + 13 q^{20} + 22 q^{22} + 10 q^{23} - 43 q^{25} + 9 q^{26} - 11 q^{28} - 13 q^{29} + 8 q^{31} + q^{32} + 9 q^{34} - 13 q^{37} + 3 q^{38} + 9 q^{40} + 10 q^{41} - 8 q^{43} - 11 q^{44} + q^{46} + 8 q^{47} + 29 q^{49} - 23 q^{50} + 2 q^{52} + 35 q^{53} - 11 q^{55} + 13 q^{58} - 37 q^{59} - 2 q^{61} - 8 q^{62} - q^{64} - 37 q^{65} + 14 q^{67} + 2 q^{68} - 22 q^{70} - 44 q^{71} - 49 q^{73} + 13 q^{74} + 8 q^{76} - 44 q^{77} - 8 q^{79} + 2 q^{80} + 12 q^{82} + 17 q^{83} - 37 q^{85} - 14 q^{86} - 59 q^{89} + 66 q^{91} - 45 q^{92} - 19 q^{94} + 28 q^{95} - 21 q^{97} + 26 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^4 + 2 * q^5 + q^8 + 9 * q^10 - 11 * q^11 + 13 * q^13 + 11 * q^14 - q^16 + 24 * q^17 - 14 * q^19 + 13 * q^20 + 22 * q^22 + 10 * q^23 - 43 * q^25 + 9 * q^26 - 11 * q^28 - 13 * q^29 + 8 * q^31 + q^32 + 9 * q^34 - 13 * q^37 + 3 * q^38 + 9 * q^40 + 10 * q^41 - 8 * q^43 - 11 * q^44 + q^46 + 8 * q^47 + 29 * q^49 - 23 * q^50 + 2 * q^52 + 35 * q^53 - 11 * q^55 + 13 * q^58 - 37 * q^59 - 2 * q^61 - 8 * q^62 - q^64 - 37 * q^65 + 14 * q^67 + 2 * q^68 - 22 * q^70 - 44 * q^71 - 49 * q^73 + 13 * q^74 + 8 * q^76 - 44 * q^77 - 8 * q^79 + 2 * q^80 + 12 * q^82 + 17 * q^83 - 37 * q^85 - 14 * q^86 - 59 * q^89 + 66 * q^91 - 45 * q^92 - 19 * q^94 + 28 * q^95 - 21 * q^97 + 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$		0			0
$3$		0			0
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−0.698939	−	0.806618i	−0.312575	−	0.360731i	0.577624	−	0.816303i	$-0.303980\pi$
$5$	−0.698939	−	0.806618i	−0.312575	−	0.360731i	−0.890199	+	0.455572i	$0.849435\pi$
$6$		0			0
$7$	3.72270	+	2.39243i	1.40705	+	0.904255i	0.999958	−	0.00913325i	$-0.00290725\pi$
$7$	3.72270	+	2.39243i	1.40705	+	0.904255i	0.407090	+	0.913388i	$0.366544\pi$
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$		0			0
$10$	−0.897877	+	0.577031i	−0.283934	+	0.182473i
$11$	−0.234769	−	1.63285i	−0.0707855	−	0.492324i	−0.994116	−	0.108318i	$-0.965453\pi$
$11$	−0.234769	−	1.63285i	−0.0707855	−	0.492324i	0.923331	−	0.384005i	$-0.125456\pi$
$12$		0			0
$13$	4.60260	−	2.95791i	1.27653	−	0.820377i	0.286075	−	0.958207i	$-0.407649\pi$
$13$	4.60260	−	2.95791i	1.27653	−	0.820377i	0.990456	+	0.137830i	$0.0440128\pi$
$14$	2.89788	−	3.34433i	0.774490	−	0.893809i
$15$		0			0
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	3.76709	−	1.10612i	0.913654	−	0.268273i	0.209076	−	0.977899i	$-0.432954\pi$
$17$	3.76709	−	1.10612i	0.913654	−	0.268273i	0.704578	+	0.709626i	$0.251136\pi$
$18$		0			0
$19$	−6.33409	−	1.85986i	−1.45314	−	0.426680i	−0.542561	−	0.840017i	$-0.682545\pi$
$19$	−6.33409	−	1.85986i	−1.45314	−	0.426680i	−0.910578	+	0.413337i	$0.864363\pi$
$20$	0.443376	+	0.970858i	0.0991419	+	0.217091i
$21$		0			0
$22$	−1.64964			−0.351705
$23$	4.78492	+	0.323343i	0.997725	+	0.0674216i
$23$	4.78492	+	0.323343i	0.997725	+	0.0674216i
$24$		0			0
$25$	0.549456	−	3.82155i	0.109891	−	0.764311i
$26$	−2.27279	−	4.97671i	−0.445730	−	0.976012i
$27$		0			0
$28$	−2.89788	−	3.34433i	−0.547647	−	0.632019i
$29$	−6.14024	+	1.80294i	−1.14021	+	0.334797i	−0.796714	−	0.604356i	$-0.793430\pi$
$29$	−6.14024	+	1.80294i	−1.14021	+	0.334797i	−0.343499	+	0.939153i	$0.611612\pi$
$30$		0			0
$31$	−1.25244	+	2.74246i	−0.224945	+	0.492561i	−0.988130	−	0.153619i	$-0.950907\pi$
$31$	−1.25244	+	2.74246i	−0.224945	+	0.492561i	0.763185	+	0.646180i	$0.223634\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$		0			0
$34$	−0.558746	−	3.88617i	−0.0958242	−	0.666472i
$35$	−0.672158	−	4.67496i	−0.113615	−	0.790213i
$36$		0			0
$37$	1.44774	−	1.67078i	0.238007	−	0.274674i	−0.624163	−	0.781294i	$-0.714560\pi$
$37$	1.44774	−	1.67078i	0.238007	−	0.274674i	0.862169	+	0.506620i	$0.169105\pi$
$38$	−2.74236	+	6.00493i	−0.444869	+	0.974128i
$39$		0			0
$40$	1.02408	−	0.300696i	0.161921	−	0.0475442i
$41$	2.67954	+	3.09235i	0.418474	+	0.482945i	0.925371	−	0.379062i	$-0.123753\pi$
$41$	2.67954	+	3.09235i	0.418474	+	0.482945i	−0.506898	+	0.862006i	$0.669208\pi$
$42$		0			0
$43$	−1.21021	−	2.64998i	−0.184555	−	0.404119i	0.794629	−	0.607096i	$-0.207666\pi$
$43$	−1.21021	−	2.64998i	−0.184555	−	0.404119i	−0.979183	+	0.202977i	$0.934938\pi$
$44$	−0.234769	+	1.63285i	−0.0353927	+	0.246162i
$45$		0			0
$46$	1.00102	−	4.69020i	0.147592	−	0.691532i
$47$	9.62306			1.40367			0.701834	−	0.712341i	$-0.252365\pi$
$47$	9.62306			1.40367			0.701834	+	0.712341i	$0.252365\pi$
$48$		0			0
$49$	5.22685	+	11.4452i	0.746692	+	1.63503i
$50$	−3.70446	−	1.08773i	−0.523890	−	0.153828i
$51$		0			0
$52$	−5.24950	+	1.54139i	−0.727975	+	0.213753i
$53$	1.87633	+	1.20584i	0.257734	+	0.165635i	0.663127	−	0.748507i	$-0.269229\pi$
$53$	1.87633	+	1.20584i	0.257734	+	0.165635i	−0.405393	+	0.914142i	$0.632865\pi$
$54$		0			0
$55$	−1.15300	+	1.33063i	−0.155470	+	0.179422i
$56$	−3.72270	+	2.39243i	−0.497467	+	0.319702i
$57$		0			0
$58$	0.910738	+	6.33432i	0.119586	+	0.831737i
$59$	−8.20397	+	5.27237i	−1.06807	+	0.686405i	−0.951771	−	0.306810i	$-0.900738\pi$
$59$	−8.20397	+	5.27237i	−1.06807	+	0.686405i	−0.116296	+	0.993215i	$0.537102\pi$
$60$		0			0
$61$	−0.647821	+	1.41853i	−0.0829450	+	0.181624i	−0.946560	−	0.322528i	$-0.895468\pi$
$61$	−0.647821	+	1.41853i	−0.0829450	+	0.181624i	0.863615	+	0.504152i	$0.168195\pi$
$62$	2.53631	+	1.62999i	0.322111	+	0.207008i
$63$		0			0
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−5.60284	−	1.64514i	−0.694947	−	0.204055i
$66$		0			0
$67$	−1.71423	+	11.9227i	−0.209426	+	1.45659i	0.565610	+	0.824673i	$0.308641\pi$
$67$	−1.71423	+	11.9227i	−0.209426	+	1.45659i	−0.775036	+	0.631917i	$0.782268\pi$
$68$	−3.92613			−0.476113
$69$		0			0
$70$	−4.72304			−0.564511
$71$	−0.749168	+	5.21058i	−0.0889098	+	0.618382i	0.895836	+	0.444384i	$0.146577\pi$
$71$	−0.749168	+	5.21058i	−0.0889098	+	0.618382i	−0.984746	+	0.173997i	$0.944332\pi$
$72$		0			0
$73$	−6.89449	−	2.02441i	−0.806939	−	0.236939i	−0.147856	−	0.989009i	$-0.547237\pi$
$73$	−6.89449	−	2.02441i	−0.806939	−	0.236939i	−0.659083	+	0.752070i	$0.729055\pi$
$74$	−1.44774	−	1.67078i	−0.168296	−	0.194224i
$75$		0			0
$76$	5.55353	+	3.56904i	0.637034	+	0.409397i
$77$	3.03252	−	6.64029i	0.345588	−	0.756731i
$78$		0			0
$79$	2.26617	−	1.45638i	0.254964	−	0.163856i	−0.406915	−	0.913466i	$-0.633395\pi$
$79$	2.26617	−	1.45638i	0.254964	−	0.163856i	0.661879	+	0.749610i	$0.269759\pi$
$80$	−0.151894	−	1.05645i	−0.0169823	−	0.118114i
$81$		0			0
$82$	3.44222	−	2.21218i	0.380129	−	0.244294i
$83$	3.62690	−	4.18567i	0.398104	−	0.459436i	−0.520939	−	0.853594i	$-0.674418\pi$
$83$	3.62690	−	4.18567i	0.398104	−	0.459436i	0.919043	+	0.394157i	$0.128964\pi$
$84$		0			0
$85$	−3.52518	−	2.26550i	−0.382360	−	0.245728i
$86$	−2.79524	+	0.820757i	−0.301419	+	0.0885045i
$87$		0			0
$88$	1.58282	+	0.464758i	0.168729	+	0.0495434i
$89$	−4.70504	−	10.3026i	−0.498733	−	1.09207i	−0.976879	−	0.213792i	$-0.931418\pi$
$89$	−4.70504	−	10.3026i	−0.498733	−	1.09207i	0.478146	−	0.878280i	$-0.341309\pi$
$90$		0			0
$91$	24.2107			2.53797
$92$	−4.50000	−	1.65831i	−0.469157	−	0.172891i
$93$		0			0
$94$	1.36950	−	9.52511i	0.141254	−	0.982440i
$95$	2.92694	+	6.40911i	0.300298	+	0.657561i
$96$		0			0
$97$	−7.84485	−	9.05344i	−0.796524	−	0.919238i	0.201661	−	0.979455i	$-0.435366\pi$
$97$	−7.84485	−	9.05344i	−0.796524	−	0.919238i	−0.998185	+	0.0602176i	$0.980821\pi$
$98$	12.0726	−	3.54482i	1.21951	−	0.358081i
$99$		0			0
$100$	−1.60386	+	3.51195i	−0.160386	+	0.351195i
$101$	−12.0894	+	13.9519i	−1.20294	+	1.38826i	−0.302570	+	0.953127i	$0.597845\pi$
$101$	−12.0894	+	13.9519i	−1.20294	+	1.38826i	−0.900365	+	0.435135i	$0.856701\pi$
$102$		0			0
$103$	1.62633	+	11.3114i	0.160247	+	1.11455i	0.898166	+	0.439656i	$0.144900\pi$
$103$	1.62633	+	11.3114i	0.160247	+	1.11455i	−0.737919	+	0.674889i	$0.764191\pi$
$104$	0.778622	+	5.41543i	0.0763501	+	0.531027i
$105$		0			0
$106$	1.46060	−	1.68562i	0.141866	−	0.163722i
$107$	−6.17478	+	13.5209i	−0.596938	+	1.30711i	0.334219	+	0.942495i	$0.391528\pi$
$107$	−6.17478	+	13.5209i	−0.596938	+	1.30711i	−0.931157	+	0.364618i	$0.881200\pi$
$108$		0			0
$109$	−11.7854	+	3.46052i	−1.12884	+	0.331458i	−0.792252	−	0.610194i	$-0.791092\pi$
$109$	−11.7854	+	3.46052i	−1.12884	+	0.331458i	−0.336589	+	0.941652i	$0.609273\pi$
$110$	1.15300	+	1.33063i	0.109934	+	0.126871i
$111$		0			0
$112$	1.83829	+	4.02529i	0.173702	+	0.380354i
$113$	−0.429025	+	2.98393i	−0.0403593	+	0.280705i	−1.00000		0.000524443i	$-0.999833\pi$
$113$	−0.429025	+	2.98393i	−0.0403593	+	0.280705i	0.959641	+	0.281229i	$0.0907422\pi$
$114$		0			0
$115$	−3.08355	−	4.08560i	−0.287543	−	0.380984i
$116$	6.39946			0.594175
$117$		0			0
$118$	4.05116	+	8.87081i	0.372940	+	0.816624i
$119$	16.6701	+	4.89477i	1.52814	+	0.448703i
$120$		0			0
$121$	7.94333	−	2.33237i	0.722121	−	0.212034i
$122$	1.31190	+	0.843105i	0.118774	+	0.0763311i
$123$		0			0
$124$	1.97435	−	2.27852i	0.177302	−	0.204617i
$125$	−7.95596	+	5.11298i	−0.711603	+	0.457319i
$126$		0			0
$127$	0.775959	+	5.39691i	0.0688552	+	0.478899i	0.994850	+	0.101362i	$0.0323199\pi$
$127$	0.775959	+	5.39691i	0.0688552	+	0.478899i	−0.925994	+	0.377537i	$0.876771\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$		0			0
$130$	−2.42576	+	5.31168i	−0.212754	+	0.465865i
$131$	7.29997	+	4.69140i	0.637801	+	0.409890i	0.819190	−	0.573522i	$-0.194423\pi$
$131$	7.29997	+	4.69140i	0.637801	+	0.409890i	−0.181389	+	0.983411i	$0.558059\pi$
$132$		0			0
$133$	−19.1303	−	22.0776i	−1.65881	−	1.91437i
$134$	11.5574	+	3.39356i	0.998406	+	0.293159i
$135$		0			0
$136$	−0.558746	+	3.88617i	−0.0479121	+	0.333236i
$137$	−8.98175			−0.767363			−0.383682	−	0.923465i	$-0.625344\pi$
$137$	−8.98175			−0.767363			−0.383682	+	0.923465i	$0.625344\pi$
$138$		0			0
$139$	3.06287			0.259789			0.129895	−	0.991528i	$-0.458536\pi$
$139$	3.06287			0.259789			0.129895	+	0.991528i	$0.458536\pi$
$140$	−0.672158	+	4.67496i	−0.0568077	+	0.395106i
$141$		0			0
$142$	5.05092	+	1.48308i	0.423864	+	0.124458i
$143$	−5.91038	−	6.82094i	−0.494251	−	0.570396i
$144$		0			0
$145$	5.74593	+	3.69269i	0.477174	+	0.306661i
$146$	−2.98499	+	6.53621i	−0.247039	+	0.540941i
$147$		0			0
$148$	−1.85981	+	1.19523i	−0.152875	+	0.0982470i
$149$	−2.90507	−	20.2052i	−0.237993	−	1.65528i	−0.661915	−	0.749579i	$-0.730256\pi$
$149$	−2.90507	−	20.2052i	−0.237993	−	1.65528i	0.423922	−	0.905699i	$-0.360653\pi$
$150$		0			0
$151$	−10.6960	+	6.87389i	−0.870427	+	0.559390i	−0.897883	−	0.440233i	$-0.854896\pi$
$151$	−10.6960	+	6.87389i	−0.870427	+	0.559390i	0.0274562	+	0.999623i	$0.491259\pi$
$152$	4.32306	−	4.98908i	0.350646	−	0.404667i
$153$		0			0
$154$	−6.14113	−	3.94666i	−0.494866	−	0.318031i
$155$	3.08750	−	0.906571i	0.247994	−	0.0728176i
$156$		0			0
$157$	1.09842	+	0.322526i	0.0876638	+	0.0257404i	0.325270	−	0.945621i	$-0.394545\pi$
$157$	1.09842	+	0.322526i	0.0876638	+	0.0257404i	−0.237607	+	0.971361i	$0.576363\pi$
$158$	−1.11905	−	2.45037i	−0.0890266	−	0.194941i
$159$		0			0
$160$	−1.06731			−0.0843782
$161$	17.0392	+	12.6513i	1.34288	+	0.997063i
$162$		0			0
$163$	−0.683592	+	4.75449i	−0.0535431	+	0.372400i	0.945379	+	0.325974i	$0.105692\pi$
$163$	−0.683592	+	4.75449i	−0.0535431	+	0.372400i	−0.998922	+	0.0464260i	$0.985217\pi$
$164$	−1.69978	−	3.72201i	−0.132731	−	0.290640i
$165$		0			0
$166$	−3.62690	−	4.18567i	−0.281502	−	0.324871i
$167$	11.2720	−	3.30976i	0.872254	−	0.256117i	0.185180	−	0.982705i	$-0.440713\pi$
$167$	11.2720	−	3.30976i	0.872254	−	0.256117i	0.687074	+	0.726588i	$0.258895\pi$
$168$		0			0
$169$	7.03429	−	15.4029i	0.541099	−	1.18484i
$170$	−2.74412	+	3.16689i	−0.210465	+	0.242889i
$171$		0			0
$172$	0.414598	+	2.88359i	0.0316128	+	0.219872i
$173$	−0.728537	−	5.06708i	−0.0553896	−	0.385243i	−0.998593	−	0.0530276i	$-0.983113\pi$
$173$	−0.728537	−	5.06708i	−0.0553896	−	0.385243i	0.943203	−	0.332216i	$-0.107796\pi$
$174$		0			0
$175$	11.1883	−	12.9120i	0.845754	−	0.976052i
$176$	0.685287	−	1.50057i	0.0516554	−	0.113110i
$177$		0			0
$178$	−10.8673	+	3.19093i	−0.814540	+	0.239171i
$179$	−12.2769	−	14.1683i	−0.917619	−	1.05899i	−0.998062	−	0.0622298i	$-0.980179\pi$
$179$	−12.2769	−	14.1683i	−0.917619	−	1.05899i	0.0804426	−	0.996759i	$-0.474367\pi$
$180$		0			0
$181$	−3.01827	−	6.60909i	−0.224346	−	0.491250i	0.763669	−	0.645608i	$-0.223396\pi$
$181$	−3.01827	−	6.60909i	−0.224346	−	0.491250i	−0.988015	+	0.154359i	$0.950669\pi$
$182$	3.44554	−	23.9643i	0.255401	−	1.77635i
$183$		0			0
$184$	−2.28185	+	4.21819i	−0.168220	+	0.310969i
$185$	−2.35956			−0.173478
$186$		0			0
$187$	−2.69052	−	5.89142i	−0.196751	−	0.430824i
$188$	−9.23326	−	2.71113i	−0.673404	−	0.197729i
$189$		0			0
$190$	6.76043	−	1.98504i	0.490453	−	0.144010i
$191$	−21.1841	−	13.6142i	−1.53283	−	0.985090i	−0.989332	−	0.145681i	$-0.953463\pi$
$191$	−21.1841	−	13.6142i	−1.53283	−	0.985090i	−0.543499	−	0.839410i	$-0.682901\pi$
$192$		0			0
$193$	−11.0715	+	12.7772i	−0.796948	+	0.919727i	−0.998210	−	0.0598109i	$-0.980950\pi$
$193$	−11.0715	+	12.7772i	−0.796948	+	0.919727i	0.201262	+	0.979537i	$0.435496\pi$
$194$	−10.0777	+	6.47656i	−0.723539	+	0.464990i
$195$		0			0
$196$	−1.79064	−	12.4542i	−0.127903	−	0.889583i
$197$	10.8033	−	6.94289i	0.769706	−	0.494660i	−0.0958965	−	0.995391i	$-0.530572\pi$
$197$	10.8033	−	6.94289i	0.769706	−	0.494660i	0.865603	+	0.500731i	$0.166935\pi$
$198$		0			0
$199$	5.65154	−	12.3751i	0.400627	−	0.877251i	−0.596579	−	0.802554i	$-0.703474\pi$
$199$	5.65154	−	12.3751i	0.400627	−	0.877251i	0.997206	−	0.0746967i	$-0.0237989\pi$
$200$	3.24796	+	2.08733i	0.229665	+	0.147597i
$201$		0			0
$202$	12.0894	+	13.9519i	0.850604	+	0.981649i
$203$	−27.1717	−	7.97832i	−1.90708	−	0.559968i
$204$		0			0
$205$	0.621515	−	4.32273i	0.0434085	−	0.301913i
$206$	11.4277			0.796207
$207$		0			0
$208$	5.47112			0.379354
$209$	−1.54982	+	10.7793i	−0.107204	+	0.745617i
$210$		0			0
$211$	20.2858	+	5.95646i	1.39654	+	0.410060i	0.891493	−	0.453035i	$-0.149659\pi$
$211$	20.2858	+	5.95646i	1.39654	+	0.410060i	0.505042	+	0.863095i	$0.331477\pi$
$212$	−1.46060	−	1.68562i	−0.100314	−	0.115769i
$213$		0			0
$214$	12.5045	+	8.03615i	0.854790	+	0.549340i
$215$	−1.29166	+	2.82835i	−0.0880908	+	0.192892i
$216$		0			0
$217$	−11.2236	+	7.21298i	−0.761909	+	0.489649i
$218$	1.74805	+	12.1580i	0.118393	+	0.823442i
$219$		0			0
$220$	1.48118	−	0.951895i	0.0998610	−	0.0641768i
$221$	14.0666	−	16.2337i	0.946223	−	1.09200i
$222$		0			0
$223$	−2.14678	−	1.37965i	−0.143759	−	0.0923885i	0.466784	−	0.884371i	$-0.345413\pi$
$223$	−2.14678	−	1.37965i	−0.143759	−	0.0923885i	−0.610543	+	0.791983i	$0.709049\pi$
$224$	4.24593	−	1.24672i	0.283693	−	0.0832998i
$225$		0			0
$226$	2.89251	+	0.849316i	0.192407	+	0.0564957i
$227$	8.19315	+	17.9405i	0.543798	+	1.19075i	0.959618	+	0.281305i	$0.0907673\pi$
$227$	8.19315	+	17.9405i	0.543798	+	1.19075i	−0.415820	+	0.909447i	$0.636505\pi$
$228$		0			0
$229$	−11.2054			−0.740473			−0.370237	−	0.928937i	$-0.620723\pi$
$229$	−11.2054			−0.740473			−0.370237	+	0.928937i	$0.620723\pi$
$230$	−4.48285	+	2.47072i	−0.295590	+	0.162915i
$231$		0			0
$232$	0.910738	−	6.33432i	0.0597929	−	0.415869i
$233$	−7.48542	−	16.3908i	−0.490386	−	1.07380i	−0.979476	−	0.201562i	$-0.935398\pi$
$233$	−7.48542	−	16.3908i	−0.490386	−	1.07380i	0.489090	−	0.872234i	$-0.337329\pi$
$234$		0			0
$235$	−6.72593	−	7.76213i	−0.438751	−	0.506346i
$236$	9.35706	−	2.74748i	0.609092	−	0.178846i
$237$		0			0
$238$	7.21735	−	15.8038i	0.467831	−	1.02441i
$239$	17.8436	−	20.5926i	1.15421	−	1.33203i	0.219914	−	0.975519i	$-0.429422\pi$
$239$	17.8436	−	20.5926i	1.15421	−	1.33203i	0.934293	−	0.356506i	$-0.116032\pi$
$240$		0			0
$241$	3.17028	+	22.0498i	0.204216	+	1.42035i	0.791599	+	0.611041i	$0.209249\pi$
$241$	3.17028	+	22.0498i	0.204216	+	1.42035i	−0.587383	+	0.809309i	$0.699842\pi$
$242$	−1.17818	−	8.19441i	−0.0757362	−	0.526757i
$243$		0			0
$244$	1.02123	−	1.17856i	0.0653773	−	0.0754494i
$245$	5.57866	−	12.2156i	0.356408	−	0.780424i
$246$		0			0
$247$	−34.6545	+	10.1755i	−2.20502	+	0.647451i
$248$	−1.97435	−	2.27852i	−0.125371	−	0.144686i
$249$		0			0
$250$	3.92869	+	8.60263i	0.248472	+	0.544078i
$251$	−1.45152	+	10.0956i	−0.0916192	+	0.637226i	0.891331	+	0.453353i	$0.149772\pi$
$251$	−1.45152	+	10.0956i	−0.0916192	+	0.637226i	−0.982950	+	0.183872i	$0.941137\pi$
$252$		0			0
$253$	−0.595379	−	7.88898i	−0.0374311	−	0.495976i
$254$	5.45241			0.342115
$255$		0			0
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	26.7109	+	7.84303i	1.66618	+	0.489235i	0.972860	−	0.231395i	$-0.0743288\pi$
$257$	26.7109	+	7.84303i	1.66618	+	0.489235i	0.693321	+	0.720629i	$0.256147\pi$
$258$		0			0
$259$	9.38672	−	2.75619i	0.583263	−	0.171261i
$260$	4.91239	+	3.15700i	0.304654	+	0.195789i
$261$		0			0
$262$	5.68255	−	6.55801i	0.351069	−	0.405155i
$263$	−6.35034	+	4.08112i	−0.391579	+	0.251652i	−0.721584	−	0.692327i	$-0.756586\pi$
$263$	−6.35034	+	4.08112i	−0.391579	+	0.251652i	0.330006	+	0.943979i	$0.392949\pi$
$264$		0			0
$265$	−0.338784	−	2.35629i	−0.0208113	−	0.144746i
$266$	−24.5754	+	15.7936i	−1.50681	+	0.968370i
$267$		0			0
$268$	5.00380	−	10.9568i	0.305656	−	0.669293i
$269$	−4.94396	−	3.17729i	−0.301439	−	0.193723i	0.381174	−	0.924503i	$-0.375520\pi$
$269$	−4.94396	−	3.17729i	−0.301439	−	0.193723i	−0.682612	+	0.730781i	$0.739156\pi$
$270$		0			0
$271$	−13.8865	−	16.0259i	−0.843545	−	0.973503i	0.156354	−	0.987701i	$-0.450026\pi$
$271$	−13.8865	−	16.0259i	−0.843545	−	0.973503i	−0.999899	+	0.0141978i	$0.995481\pi$
$272$	3.76709	+	1.10612i	0.228414	+	0.0670683i
$273$		0			0
$274$	−1.27824	+	8.89033i	−0.0772211	+	0.537085i
$275$	−6.36903			−0.384067
$276$		0			0
$277$	3.17305			0.190650			0.0953251	−	0.995446i	$-0.469611\pi$
$277$	3.17305			0.190650			0.0953251	+	0.995446i	$0.469611\pi$
$278$	0.435892	−	3.03169i	0.0261430	−	0.181829i
$279$		0			0
$280$	4.53172	+	1.33063i	0.270822	+	0.0795205i
$281$	−11.9648	−	13.8081i	−0.713759	−	0.823722i	0.276783	−	0.960932i	$-0.410732\pi$
$281$	−11.9648	−	13.8081i	−0.713759	−	0.823722i	−0.990542	+	0.137211i	$0.956186\pi$
$282$		0			0
$283$	18.9284	+	12.1645i	1.12518	+	0.723107i	0.964548	−	0.263908i	$-0.0850116\pi$
$283$	18.9284	+	12.1645i	1.12518	+	0.723107i	0.160628	+	0.987015i	$0.448648\pi$
$284$	2.18681	−	4.78845i	0.129763	−	0.284142i
$285$		0			0
$286$	−7.59265	+	4.87950i	−0.448963	+	0.288531i
$287$	2.57687	+	17.9225i	0.152108	+	1.05793i
$288$		0			0
$289$	−1.33382	+	0.857197i	−0.0784603	+	0.0504234i
$290$	4.47283	−	5.16192i	0.262654	−	0.303118i
$291$		0			0
$292$	6.04488	+	3.88481i	0.353750	+	0.227341i
$293$	−9.98040	+	2.93051i	−0.583061	+	0.171202i	−0.559944	−	0.828530i	$-0.689177\pi$
$293$	−9.98040	+	2.93051i	−0.583061	+	0.171202i	−0.0231175	+	0.999733i	$0.507359\pi$
$294$		0			0
$295$	9.98687	+	2.93241i	0.581458	+	0.170731i
$296$	0.918382	+	2.01098i	0.0533799	+	0.116886i
$297$		0			0
$298$	−20.4130			−1.18249
$299$	22.9795	−	12.6651i	1.32894	−	0.732444i
$300$		0			0
$301$	1.83467	−	12.7604i	0.105749	−	0.735499i
$302$	5.28173	+	11.5654i	0.303929	+	0.665513i
$303$		0			0
$304$	−4.32306	−	4.98908i	−0.247944	−	0.286143i
$305$	1.59700	−	0.468921i	0.0914439	−	0.0268504i
$306$		0			0
$307$	2.13196	−	4.66834i	0.121677	−	0.266436i	−0.838985	−	0.544154i	$-0.816851\pi$
$307$	2.13196	−	4.66834i	0.121677	−	0.266436i	0.960663	+	0.277718i	$0.0895780\pi$
$308$	−4.78047	+	5.51695i	−0.272392	+	0.314357i
$309$		0			0
$310$	−0.457947	−	3.18509i	−0.0260096	−	0.180901i
$311$	3.04140	+	21.1534i	0.172462	+	1.19950i	0.873661	+	0.486534i	$0.161739\pi$
$311$	3.04140	+	21.1534i	0.172462	+	1.19950i	−0.701199	+	0.712965i	$0.747352\pi$
$312$		0			0
$313$	−10.4550	+	12.0658i	−0.590953	+	0.681997i	−0.969923	−	0.243413i	$-0.921733\pi$
$313$	−10.4550	+	12.0658i	−0.590953	+	0.681997i	0.378969	+	0.925409i	$0.376279\pi$
$314$	0.475566	−	1.04134i	0.0268377	−	0.0587664i
$315$		0			0
$316$	−2.58469	+	0.758933i	−0.145400	+	0.0426933i
$317$	7.12740	+	8.22545i	0.400314	+	0.461987i	0.919740	−	0.392528i	$-0.128399\pi$
$317$	7.12740	+	8.22545i	0.400314	+	0.461987i	−0.519426	+	0.854516i	$0.673854\pi$
$318$		0			0
$319$	4.38547	+	9.60283i	0.245539	+	0.537655i
$320$	−0.151894	+	1.05645i	−0.00849113	+	0.0590571i
$321$		0			0
$322$	14.9475	−	15.0653i	0.832990	−	0.839558i
$323$	−25.9183			−1.44213
$324$		0			0
$325$	−8.77489	−	19.2143i	−0.486743	−	1.06582i
$326$	4.60881	+	1.35327i	0.255258	+	0.0749506i
$327$		0			0
$328$	−3.92603	+	1.15279i	−0.216779	+	0.0636519i
$329$	35.8238	+	23.0225i	1.97503	+	1.26927i
$330$		0			0
$331$	8.84577	−	10.2086i	0.486208	−	0.561113i	−0.458641	−	0.888622i	$-0.651664\pi$
$331$	8.84577	−	10.2086i	0.486208	−	0.561113i	0.944848	+	0.327508i	$0.106209\pi$
$332$	−4.65922	+	2.99430i	−0.255708	+	0.164334i
$333$		0			0
$334$	−1.67190	−	11.6283i	−0.0914821	−	0.636272i
$335$	10.8152	−	6.95051i	0.590898	−	0.379747i
$336$		0			0
$337$	−0.791811	+	1.73382i	−0.0431327	+	0.0944474i	−0.929972	−	0.367631i	$-0.880169\pi$
$337$	−0.791811	+	1.73382i	−0.0431327	+	0.0944474i	0.886839	+	0.462079i	$0.152896\pi$
$338$	−14.2451	−	9.15475i	−0.774830	−	0.497953i
$339$		0			0
$340$	2.74412	+	3.16689i	0.148821	+	0.171749i
$341$	4.77207	+	1.40121i	0.258422	+	0.0758796i
$342$		0			0
$343$	−3.51551	+	24.4509i	−0.189820	+	1.32023i
$344$	2.91325			0.157072
$345$		0			0
$346$	−5.11919			−0.275209
$347$	1.37041	−	9.53143i	0.0735676	−	0.511674i	−0.919403	−	0.393316i	$-0.871328\pi$
$347$	1.37041	−	9.53143i	0.0735676	−	0.511674i	0.992971	−	0.118358i	$-0.0377630\pi$
$348$		0			0
$349$	30.4262	+	8.93395i	1.62868	+	0.478223i	0.963332	−	0.268311i	$-0.0864655\pi$
$349$	30.4262	+	8.93395i	1.62868	+	0.478223i	0.665347	+	0.746534i	$0.268284\pi$
$350$	−11.1883	−	12.9120i	−0.598038	−	0.690173i
$351$		0			0
$352$	−1.38777	−	0.891865i	−0.0739683	−	0.0475366i
$353$	−3.21155	+	7.03232i	−0.170934	+	0.374292i	−0.975639	−	0.219382i	$-0.929596\pi$
$353$	−3.21155	+	7.03232i	−0.170934	+	0.374292i	0.804705	+	0.593674i	$0.202323\pi$
$354$		0			0
$355$	4.72657	−	3.03758i	0.250860	−	0.161218i
$356$	1.61187	+	11.2108i	0.0854291	+	0.594173i
$357$		0			0
$358$	−15.7713	+	10.1356i	−0.833538	+	0.535682i
$359$	−24.2538	+	27.9904i	−1.28007	+	1.47728i	−0.480128	+	0.877198i	$0.659410\pi$
$359$	−24.2538	+	27.9904i	−1.28007	+	1.47728i	−0.799940	+	0.600080i	$0.795136\pi$
$360$		0			0
$361$	20.6778	+	13.2888i	1.08830	+	0.699410i
$362$	−6.97137	+	2.04698i	−0.366407	+	0.107587i
$363$		0			0
$364$	−23.2300	−	6.82094i	−1.21758	−	0.357514i
$365$	3.18591	+	6.97616i	0.166758	+	0.365149i
$366$		0			0
$367$	−12.1890			−0.636260			−0.318130	−	0.948047i	$-0.603055\pi$
$367$	−12.1890			−0.636260			−0.318130	+	0.948047i	$0.603055\pi$
$368$	3.85052	+	2.85894i	0.200722	+	0.149032i
$369$		0			0
$370$	−0.335801	+	2.33554i	−0.0174574	+	0.121419i
$371$	4.10011	+	8.97798i	0.212867	+	0.466114i
$372$		0			0
$373$	−3.63198	−	4.19152i	−0.188057	−	0.217029i	0.653890	−	0.756589i	$-0.273136\pi$
$373$	−3.63198	−	4.19152i	−0.188057	−	0.217029i	−0.841947	+	0.539561i	$0.818590\pi$
$374$	−6.21436	+	1.82470i	−0.321337	+	0.0943530i
$375$		0			0
$376$	−3.99756	+	8.75344i	−0.206159	+	0.451424i
$377$	−22.9281	+	26.4605i	−1.18086	+	1.36278i
$378$		0			0
$379$	1.45629	+	10.1287i	0.0748044	+	0.520276i	0.992428	+	0.122826i	$0.0391957\pi$
$379$	1.45629	+	10.1287i	0.0748044	+	0.520276i	−0.917624	+	0.397450i	$0.869895\pi$
$380$	−1.00273	−	6.97412i	−0.0514388	−	0.357765i
$381$		0			0
$382$	−16.4905	+	19.0310i	−0.843726	+	0.973711i
$383$	1.86555	−	4.08499i	0.0953253	−	0.208733i	−0.855962	−	0.517038i	$-0.827034\pi$
$383$	1.86555	−	4.08499i	0.0953253	−	0.208733i	0.951288	+	0.308305i	$0.0997617\pi$
$384$		0			0
$385$	−7.47572	+	2.19507i	−0.380998	+	0.111871i
$386$	11.0715	+	12.7772i	0.563527	+	0.650345i
$387$		0			0
$388$	4.97643	+	10.8969i	0.252640	+	0.553204i
$389$	0.486473	−	3.38350i	0.0246652	−	0.171550i	−0.973765	−	0.227555i	$-0.926927\pi$
$389$	0.486473	−	3.38350i	0.0246652	−	0.171550i	0.998431	+	0.0560044i	$0.0178361\pi$
$390$		0			0
$391$	18.3829	−	4.07462i	0.929662	−	0.206063i
$392$	−12.5822			−0.635499
$393$		0			0
$394$	−5.33474	−	11.6815i	−0.268760	−	0.588503i
$395$	−2.75866	−	0.810016i	−0.138803	−	0.0407563i
$396$		0			0
$397$	24.0355	−	7.05746i	1.20631	−	0.354204i	0.384046	−	0.923314i	$-0.374531\pi$
$397$	24.0355	−	7.05746i	1.20631	−	0.354204i	0.822261	+	0.569111i	$0.192712\pi$
$398$	−11.4449	−	7.35518i	−0.573680	−	0.368682i
$399$		0			0
$400$	2.52832	−	2.91784i	0.126416	−	0.145892i
$401$	7.53498	−	4.84244i	0.376279	−	0.241820i	−0.338808	−	0.940856i	$-0.610024\pi$
$401$	7.53498	−	4.84244i	0.376279	−	0.241820i	0.715087	+	0.699036i	$0.246387\pi$
$402$		0			0
$403$	2.34748	+	16.3271i	0.116936	+	0.813309i
$404$	15.5303	−	9.98075i	0.772663	−	0.496561i
$405$		0			0
$406$	−11.7640	+	25.7597i	−0.583840	+	1.27843i
$407$	−3.06802	−	1.97170i	−0.152076	−	0.0977334i
$408$		0			0
$409$	15.2462	+	17.5950i	0.753874	+	0.870017i	0.994938	−	0.100492i	$-0.0320418\pi$
$409$	15.2462	+	17.5950i	0.753874	+	0.870017i	−0.241064	+	0.970509i	$0.577496\pi$
$410$	−4.19028	−	1.23038i	−0.206943	−	0.0607640i
$411$		0			0
$412$	1.62633	−	11.3114i	0.0801237	−	0.557273i
$413$	−43.1547			−2.12351
$414$		0			0
$415$	−5.91121			−0.290170
$416$	0.778622	−	5.41543i	0.0381751	−	0.265513i
$417$		0			0
$418$	10.4490	+	3.06810i	0.511077	+	0.150066i
$419$	−1.47320	−	1.70016i	−0.0719705	−	0.0830584i	0.718622	−	0.695400i	$-0.244773\pi$
$419$	−1.47320	−	1.70016i	−0.0719705	−	0.0830584i	−0.790593	+	0.612342i	$0.790228\pi$
$420$		0			0
$421$	−15.6993	−	10.0893i	−0.765138	−	0.491724i	0.0989332	−	0.995094i	$-0.468457\pi$
$421$	−15.6993	−	10.0893i	−0.765138	−	0.491724i	−0.864071	+	0.503370i	$0.832093\pi$
$422$	8.78281	−	19.2317i	0.427540	−	0.936183i
$423$		0			0
$424$	−1.87633	+	1.20584i	−0.0911226	+	0.0585609i
$425$	−2.15724	−	15.0039i	−0.104641	−	0.727796i
$426$		0			0
$427$	−5.80538	+	3.73089i	−0.280942	+	0.180551i
$428$	9.73393	−	11.2336i	0.470507	−	0.542994i
$429$		0			0
$430$	2.61574	+	1.68103i	0.126142	+	0.0810666i
$431$	4.62210	−	1.35717i	0.222639	−	0.0653726i	−0.168511	−	0.985700i	$-0.553896\pi$
$431$	4.62210	−	1.35717i	0.222639	−	0.0653726i	0.391149	+	0.920327i	$0.372078\pi$
$432$		0			0
$433$	6.00189	+	1.76231i	0.288433	+	0.0846914i	0.422748	−	0.906247i	$-0.361065\pi$
$433$	6.00189	+	1.76231i	0.288433	+	0.0846914i	−0.134316	+	0.990939i	$0.542884\pi$
$434$	5.54228	+	12.1359i	0.266038	+	0.582541i
$435$		0			0
$436$	12.2830			0.588249
$437$	−29.7067	−	10.9473i	−1.42107	−	0.523682i
$438$		0			0
$439$	1.92771	−	13.4075i	0.0920045	−	0.639905i	−0.890682	−	0.454627i	$-0.849772\pi$
$439$	1.92771	−	13.4075i	0.0920045	−	0.639905i	0.982686	−	0.185278i	$-0.0593185\pi$
$440$	−0.731413	−	1.60157i	−0.0348687	−	0.0763519i
$441$		0			0
$442$	−14.0666	−	16.2337i	−0.669081	−	0.772160i
$443$	5.31546	−	1.56076i	0.252545	−	0.0741540i	−0.153010	−	0.988225i	$-0.548897\pi$
$443$	5.31546	−	1.56076i	0.252545	−	0.0741540i	0.405555	+	0.914071i	$0.367078\pi$
$444$		0			0
$445$	−5.02173	+	10.9960i	−0.238053	+	0.521263i
$446$	−1.67113	+	1.92859i	−0.0791304	+	0.0913213i
$447$		0			0
$448$	−0.629769	−	4.38014i	−0.0297538	−	0.206942i
$449$	−1.92795	−	13.4092i	−0.0909858	−	0.632820i	−0.983379	−	0.181562i	$-0.941885\pi$
$449$	−1.92795	−	13.4092i	−0.0909858	−	0.632820i	0.892394	−	0.451258i	$-0.149024\pi$
$450$		0			0
$451$	4.42029	−	5.10128i	0.208143	−	0.240210i
$452$	1.25232	−	2.74219i	0.0589041	−	0.128982i
$453$		0			0
$454$	18.9239	−	5.55655i	0.888142	−	0.260782i
$455$	−16.9218	−	19.5288i	−0.793306	−	0.915524i
$456$		0			0
$457$	−4.61680	−	10.1094i	−0.215965	−	0.472897i	0.770381	−	0.637584i	$-0.220066\pi$
$457$	−4.61680	−	10.1094i	−0.215965	−	0.472897i	−0.986346	+	0.164687i	$0.947339\pi$
$458$	−1.59469	+	11.0913i	−0.0745151	+	0.518264i
$459$		0			0
$460$	1.80760	+	4.78884i	0.0842797	+	0.223281i
$461$	33.3324			1.55245			0.776223	−	0.630459i	$-0.217133\pi$
$461$	33.3324			1.55245			0.776223	+	0.630459i	$0.217133\pi$
$462$		0			0
$463$	−8.07365	−	17.6788i	−0.375214	−	0.821605i	−0.999193	−	0.0401636i	$-0.987212\pi$
$463$	−8.07365	−	17.6788i	−0.375214	−	0.821605i	0.623979	−	0.781441i	$-0.285515\pi$
$464$	−6.14024	−	1.80294i	−0.285053	−	0.0836992i
$465$		0			0
$466$	−17.2892	+	5.07658i	−0.800908	+	0.235168i
$467$	28.2030	+	18.1250i	1.30508	+	0.838724i	0.993756	−	0.111579i	$-0.0355908\pi$
$467$	28.2030	+	18.1250i	1.30508	+	0.838724i	0.311325	+	0.950303i	$0.399227\pi$
$468$		0			0
$469$	−34.9058	+	40.2835i	−1.61180	+	1.86012i
$470$	−8.64033	+	5.55280i	−0.398549	+	0.256132i
$471$		0			0
$472$	−1.38787	−	9.65282i	−0.0638817	−	0.444307i
$473$	−4.04291	+	2.59822i	−0.185893	+	0.119466i
$474$		0			0
$475$	−10.5878	+	23.1841i	−0.485804	+	1.06376i
$476$	−14.6158	−	9.39300i	−0.669914	−	0.430527i
$477$		0			0
$478$	−17.8436	−	20.5926i	−0.816147	−	0.941884i
$479$	−1.58866	−	0.466472i	−0.0725876	−	0.0213137i	0.245237	−	0.969463i	$-0.421134\pi$
$479$	−1.58866	−	0.466472i	−0.0725876	−	0.0213137i	−0.317825	+	0.948149i	$0.602952\pi$
$480$		0			0
$481$	1.72134	−	11.9722i	0.0784865	−	0.545886i
$482$	22.2765			1.01467
$483$		0			0
$484$	−8.27868			−0.376303
$485$	−1.81960	+	12.6556i	−0.0826238	+	0.574661i
$486$		0			0
$487$	20.1450	+	5.91510i	0.912856	+	0.268039i	0.704243	−	0.709959i	$-0.251287\pi$
$487$	20.1450	+	5.91510i	0.912856	+	0.268039i	0.208614	+	0.977998i	$0.433105\pi$
$488$	−1.02123	−	1.17856i	−0.0462287	−	0.0533508i
$489$		0			0
$490$	−11.2973	−	7.26033i	−0.510360	−	0.327988i
$491$	−10.7230	+	23.4802i	−0.483924	+	1.05965i	0.497442	+	0.867497i	$0.334273\pi$
$491$	−10.7230	+	23.4802i	−0.483924	+	1.05965i	−0.981366	+	0.192148i	$0.938455\pi$
$492$		0			0
$493$	−21.1366	+	13.5837i	−0.951944	+	0.611777i
$494$	5.14006	+	35.7499i	0.231262	+	1.60847i
$495$		0			0
$496$	−2.53631	+	1.62999i	−0.113884	+	0.0731885i
$497$	−15.2549	+	17.6051i	−0.684275	+	0.789695i
$498$		0			0
$499$	−5.41570	−	3.48046i	−0.242440	−	0.155807i	0.413779	−	0.910378i	$-0.364209\pi$
$499$	−5.41570	−	3.48046i	−0.242440	−	0.155807i	−0.656219	+	0.754571i	$0.727845\pi$
$500$	9.07418	−	2.66442i	0.405810	−	0.119156i
$501$		0			0
$502$	9.78622	+	2.87349i	0.436781	+	0.128250i
$503$	−4.22191	−	9.24470i	−0.188246	−	0.412201i	0.791853	−	0.610712i	$-0.209117\pi$
$503$	−4.22191	−	9.24470i	−0.188246	−	0.412201i	−0.980099	+	0.198511i	$0.936389\pi$
$504$		0			0
$505$	19.7035			0.876796
$506$	−7.89341	−	0.533400i	−0.350905	−	0.0237125i
$507$		0			0
$508$	0.775959	−	5.39691i	0.0344276	−	0.239449i
$509$	10.8955	+	23.8578i	0.482933	+	1.05748i	0.981647	+	0.190709i	$0.0610788\pi$
$509$	10.8955	+	23.8578i	0.482933	+	1.05748i	−0.498713	+	0.866767i	$0.666194\pi$
$510$		0			0
$511$	−20.8229	−	24.0309i	−0.921150	−	1.06306i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$		0			0
$514$	11.5646	−	25.3228i	0.510091	−	1.11694i
$515$	7.98727	−	9.21780i	0.351961	−	0.406185i
$516$		0			0
$517$	−2.25919	−	15.7130i	−0.0993592	−	0.691059i
$518$	−1.39227	−	9.68343i	−0.0611727	−	0.425465i
$519$		0			0
$520$	3.82398	−	4.41311i	0.167693	−	0.193527i
$521$	−6.39845	+	14.0106i	−0.280321	+	0.613818i	−0.996453	−	0.0841470i	$-0.973183\pi$
$521$	−6.39845	+	14.0106i	−0.280321	+	0.613818i	0.716132	+	0.697965i	$0.245911\pi$
$522$		0			0
$523$	25.1618	−	7.38818i	1.10025	−	0.323062i	0.319298	−	0.947654i	$-0.396553\pi$
$523$	25.1618	−	7.38818i	1.10025	−	0.323062i	0.780951	+	0.624592i	$0.214735\pi$
$524$	−5.68255	−	6.55801i	−0.248243	−	0.286488i
$525$		0			0
$526$	3.13583	+	6.86651i	0.136729	+	0.299394i
$527$	−1.68457	+	11.7165i	−0.0733811	+	0.510377i
$528$		0			0
$529$	22.7909	+	3.09434i	0.990909	+	0.134536i
$530$	−2.38052			−0.103403
$531$		0			0
$532$	12.1354	+	26.5729i	0.526138	+	1.15208i
$533$	21.4798	+	6.30703i	0.930392	+	0.273188i
$534$		0			0
$535$	15.2220	−	4.46958i	0.658104	−	0.193237i
$536$	−10.1332	−	6.51219i	−0.437686	−	0.281284i
$537$		0			0
$538$	−3.84855	+	4.44146i	−0.165923	+	0.191485i
$539$	17.4612	−	11.2216i	0.752108	−	0.483351i
$540$		0			0
$541$	−0.141885	−	0.986830i	−0.00610010	−	0.0424271i	0.986544	−	0.163496i	$-0.0522770\pi$
$541$	−0.141885	−	0.986830i	−0.00610010	−	0.0424271i	−0.992644	+	0.121069i	$0.961368\pi$
$542$	−17.8390	+	11.4644i	−0.766252	+	0.492440i
$543$		0			0
$544$	1.63097	−	3.57133i	0.0699274	−	0.153120i
$545$	11.0286	+	7.08767i	0.472414	+	0.303602i
$546$		0			0
$547$	−3.81944	−	4.40787i	−0.163307	−	0.188467i	0.668198	−	0.743984i	$-0.267066\pi$
$547$	−3.81944	−	4.40787i	−0.163307	−	0.188467i	−0.831505	+	0.555517i	$0.812520\pi$
$548$	8.61793	+	2.53045i	0.368140	+	0.108096i
$549$		0			0
$550$	−0.906407	+	6.30420i	−0.0386493	+	0.268812i
$551$	42.2460			1.79974
$552$		0			0
$553$	11.9206			0.506914
$554$	0.451573	−	3.14076i	0.0191855	−	0.133438i
$555$		0			0
$556$	−2.93880	−	0.862910i	−0.124633	−	0.0365955i
$557$	−21.5121	−	24.8262i	−0.911495	−	1.05192i	−0.998447	−	0.0557089i	$-0.982258\pi$
$557$	−21.5121	−	24.8262i	−0.911495	−	1.05192i	0.0869520	−	0.996213i	$-0.472287\pi$
$558$		0			0
$559$	−13.4085	−	8.61713i	−0.567120	−	0.364466i
$560$	1.96202	−	4.29622i	0.0829105	−	0.181549i
$561$		0			0
$562$	−15.3703	+	9.87790i	−0.648357	+	0.416674i
$563$	−1.71395	−	11.9208i	−0.0722344	−	0.502402i	−0.993533	−	0.113545i	$-0.963779\pi$
$563$	−1.71395	−	11.9208i	−0.0722344	−	0.502402i	0.921298	−	0.388856i	$-0.127130\pi$
$564$		0			0
$565$	2.70676	−	1.73953i	0.113874	−	0.0731825i
$566$	14.7345	−	17.0045i	0.619338	−	0.714754i
$567$		0			0
$568$	−4.42849	−	2.84602i	−0.185815	−	0.119416i
$569$	−12.3983	+	3.64048i	−0.519765	+	0.152617i	−0.531084	−	0.847319i	$-0.678215\pi$
$569$	−12.3983	+	3.64048i	−0.519765	+	0.152617i	0.0113189	+	0.999936i	$0.496397\pi$
$570$		0			0
$571$	−32.5250	−	9.55020i	−1.36113	−	0.399663i	−0.481968	−	0.876189i	$-0.660078\pi$
$571$	−32.5250	−	9.55020i	−1.36113	−	0.399663i	−0.879161	+	0.476525i	$0.841896\pi$
$572$	3.74929	+	8.20979i	0.156766	+	0.343269i
$573$		0			0
$574$	18.1068			0.755764
$575$	3.86478	−	18.1082i	0.161172	−	0.755163i
$576$		0			0
$577$	3.19552	−	22.2254i	0.133031	−	0.925254i	−0.808540	−	0.588441i	$-0.799742\pi$
$577$	3.19552	−	22.2254i	0.133031	−	0.925254i	0.941572	−	0.336813i	$-0.109349\pi$
$578$	0.658649	+	1.44224i	0.0273962	+	0.0599893i
$579$		0			0
$580$	−4.47283	−	5.16192i	−0.185724	−	0.214337i
$581$	23.5158	−	6.90486i	0.975599	−	0.286462i
$582$		0			0
$583$	1.52846	−	3.34686i	0.0633024	−	0.138613i
$584$	4.70554	−	5.43048i	0.194717	−	0.224715i
$585$		0			0
$586$	1.48032	+	10.2959i	0.0611516	+	0.425319i
$587$	−0.163758	−	1.13896i	−0.00675903	−	0.0470101i	0.986163	−	0.165780i	$-0.0530141\pi$
$587$	−0.163758	−	1.13896i	−0.00675903	−	0.0470101i	−0.992922	+	0.118770i	$0.962105\pi$
$588$		0			0
$589$	13.0336	−	15.0416i	0.537042	−	0.619780i
$590$	4.32384	−	9.46789i	0.178010	−	0.389787i
$591$		0			0
$592$	2.12121	−	0.622842i	0.0871810	−	0.0255987i
$593$	−2.14872	−	2.47976i	−0.0882376	−	0.101832i	0.709914	−	0.704289i	$-0.248734\pi$
$593$	−2.14872	−	2.47976i	−0.0882376	−	0.101832i	−0.798151	+	0.602457i	$0.794188\pi$
$594$		0			0
$595$	−7.70314	−	16.8675i	−0.315798	−	0.691501i
$596$	−2.90507	+	20.2052i	−0.118996	+	0.827639i
$597$		0			0
$598$	−9.26591	−	24.5480i	−0.378911	−	1.00384i
$599$	−3.76746			−0.153934			−0.0769671	−	0.997034i	$-0.524524\pi$
$599$	−3.76746			−0.153934			−0.0769671	+	0.997034i	$0.524524\pi$
$600$		0			0
$601$	8.17680	+	17.9047i	0.333538	+	0.730347i	0.999883	−	0.0152967i	$-0.00486927\pi$
$601$	8.17680	+	17.9047i	0.333538	+	0.730347i	−0.666345	+	0.745644i	$0.732142\pi$
$602$	−12.3694	−	3.63200i	−0.504141	−	0.148029i
$603$		0			0
$604$	12.1993	−	3.58205i	0.496384	−	0.145751i
$605$	−7.43324	−	4.77705i	−0.302204	−	0.194215i
$606$		0			0
$607$	−28.1237	+	32.4564i	−1.14150	+	1.31737i	−0.200221	+	0.979751i	$0.564166\pi$
$607$	−28.1237	+	32.4564i	−1.14150	+	1.31737i	−0.941284	+	0.337616i	$0.890380\pi$
$608$	−5.55353	+	3.56904i	−0.225225	+	0.144744i
$609$		0			0
$610$	−0.236872	−	1.64748i	−0.00959066	−	0.0667045i
$611$	44.2911	−	28.4641i	1.79183	−	1.15154i
$612$		0			0
$613$	9.71463	−	21.2721i	0.392370	−	0.859171i	−0.605617	−	0.795756i	$-0.707074\pi$
$613$	9.71463	−	21.2721i	0.392370	−	0.859171i	0.997987	−	0.0634149i	$-0.0201991\pi$
$614$	−4.31741	−	2.77463i	−0.174237	−	0.111975i
$615$		0			0
$616$	4.78047	+	5.51695i	0.192610	+	0.222284i
$617$	7.16091	+	2.10263i	0.288287	+	0.0846488i	0.422679	−	0.906280i	$-0.361090\pi$
$617$	7.16091	+	2.10263i	0.288287	+	0.0846488i	−0.134392	+	0.990928i	$0.542908\pi$
$618$		0			0
$619$	−4.63655	+	32.2479i	−0.186359	+	1.29615i	0.654980	+	0.755646i	$0.272677\pi$
$619$	−4.63655	+	32.2479i	−0.186359	+	1.29615i	−0.841339	+	0.540508i	$0.818232\pi$
$620$	−3.21784			−0.129232
$621$		0			0
$622$	21.3709			0.856896
$623$	7.13283	−	49.6099i	0.285771	−	1.98758i
$624$		0			0
$625$	−8.83735	−	2.59488i	−0.353494	−	0.103795i
$626$	10.4550	+	12.0658i	0.417867	+	0.482244i
$627$		0			0
$628$	−0.963064	−	0.618924i	−0.0384304	−	0.0246977i
$629$	3.60568	−	7.89535i	0.143768	−	0.314808i
$630$		0			0
$631$	−14.5045	+	9.32146i	−0.577414	+	0.371082i	−0.796513	−	0.604621i	$-0.793325\pi$
$631$	−14.5045	+	9.32146i	−0.577414	+	0.371082i	0.219099	+	0.975703i	$0.429688\pi$
$632$	0.383368	+	2.66639i	0.0152496	+	0.106063i
$633$		0			0
$634$	9.15606	−	5.88425i	0.363634	−	0.233693i
$635$	3.81090	−	4.39802i	0.151231	−	0.174530i
$636$		0			0
$637$	57.9110	+	37.2171i	2.29452	+	1.47460i
$638$	10.1292	−	2.97420i	0.401019	−	0.117750i
$639$		0			0
$640$	1.02408	+	0.300696i	0.0404801	+	0.0118860i
$641$	−16.8914	−	36.9870i	−0.667170	−	1.46090i	−0.875686	−	0.482880i	$-0.839591\pi$
$641$	−16.8914	−	36.9870i	−0.667170	−	1.46090i	0.208516	−	0.978019i	$-0.433137\pi$
$642$		0			0
$643$	−11.4111			−0.450008			−0.225004	−	0.974358i	$-0.572240\pi$
$643$	−11.4111			−0.450008			−0.225004	+	0.974358i	$0.572240\pi$
$644$	−12.7847	−	16.9393i	−0.503790	−	0.667504i
$645$		0			0
$646$	−3.68856	+	25.6545i	−0.145124	+	1.00936i
$647$	−14.3578	−	31.4391i	−0.564462	−	1.23600i	−0.949694	−	0.313180i	$-0.898606\pi$
$647$	−14.3578	−	31.4391i	−0.564462	−	1.23600i	0.385232	−	0.922820i	$-0.374122\pi$
$648$		0			0
$649$	10.5350	+	12.1581i	0.413537	+	0.477247i
$650$	−20.2675	+	5.95109i	−0.794959	+	0.233421i
$651$		0			0
$652$	1.99540	−	4.36931i	0.0781457	−	0.171115i
$653$	5.61473	−	6.47974i	0.219721	−	0.253572i	−0.635178	−	0.772366i	$-0.719073\pi$
$653$	5.61473	−	6.47974i	0.219721	−	0.253572i	0.854899	+	0.518794i	$0.173619\pi$
$654$		0			0
$655$	−1.31806	−	9.16729i	−0.0515008	−	0.358196i
$656$	0.582320	+	4.05012i	0.0227358	+	0.158131i
$657$		0			0
$658$	27.8864	−	32.1827i	1.08713	−	1.25461i
$659$	1.75450	−	3.84181i	0.0683454	−	0.149656i	−0.872376	−	0.488835i	$-0.837422\pi$
$659$	1.75450	−	3.84181i	0.0683454	−	0.149656i	0.940722	+	0.339179i	$0.110149\pi$
$660$		0			0
$661$	22.1777	−	6.51196i	0.862612	−	0.253286i	0.179642	−	0.983732i	$-0.442506\pi$
$661$	22.1777	−	6.51196i	0.862612	−	0.253286i	0.682970	+	0.730446i	$0.260688\pi$
$662$	−8.84577	−	10.2086i	−0.343801	−	0.396767i
$663$		0			0
$664$	2.30075	+	5.03793i	0.0892863	+	0.195510i
$665$	−4.43725	+	30.8617i	−0.172069	+	1.19677i
$666$		0			0
$667$	−29.9635	+	6.64150i	−1.16019	+	0.257160i
$668$	−11.7479			−0.454539
$669$		0			0
$670$	−5.34060	−	11.6943i	−0.206325	−	0.451790i
$671$	2.46834	+	0.724770i	0.0952892	+	0.0279794i
$672$		0			0
$673$	43.1923	−	12.6824i	1.66494	−	0.488871i	0.692384	−	0.721529i	$-0.256561\pi$
$673$	43.1923	−	12.6824i	1.66494	−	0.488871i	0.972559	+	0.232658i	$0.0747423\pi$
$674$	1.60349	+	1.03050i	0.0617641	+	0.0396934i
$675$		0			0
$676$	−11.0889	+	12.7972i	−0.426495	+	0.492201i
$677$	26.1110	−	16.7805i	1.00353	−	0.644928i	0.0678176	−	0.997698i	$-0.478396\pi$
$677$	26.1110	−	16.7805i	1.00353	−	0.644928i	0.935710	+	0.352770i	$0.114760\pi$
$678$		0			0
$679$	−7.54427	−	52.4715i	−0.289522	−	2.01367i
$680$	3.52518	−	2.26550i	0.135185	−	0.0868778i
$681$		0			0
$682$	2.06608	−	4.52408i	0.0791143	−	0.173236i
$683$	21.8572	+	14.0468i	0.836344	+	0.537485i	0.887288	−	0.461216i	$-0.152587\pi$
$683$	21.8572	+	14.0468i	0.836344	+	0.537485i	−0.0509442	+	0.998701i	$0.516223\pi$
$684$		0			0
$685$	6.27770	+	7.24485i	0.239858	+	0.276811i
$686$	23.7018	+	6.95946i	0.904937	+	0.265714i
$687$		0			0
$688$	0.414598	−	2.88359i	0.0158064	−	0.109936i
$689$	12.2028			0.464888
$690$		0			0
$691$	33.5110			1.27482			0.637410	−	0.770525i	$-0.280006\pi$
$691$	33.5110			1.27482			0.637410	+	0.770525i	$0.280006\pi$
$692$	−0.728537	+	5.06708i	−0.0276948	+	0.192622i
$693$		0			0
$694$	−9.23938	−	2.71293i	−0.350722	−	0.102981i
$695$	−2.14076	−	2.47057i	−0.0812036	−	0.0937139i
$696$		0			0
$697$	13.5146	+	8.68530i	0.511901	+	0.328979i
$698$	13.1731	−	28.8451i	0.498610	−	1.09180i
$699$		0			0
$700$	−14.3728	+	9.23683i	−0.543240	+	0.349119i
$701$	−0.833884	−	5.79979i	−0.0314954	−	0.219055i	0.967995	−	0.250968i	$-0.0807490\pi$
$701$	−0.833884	−	5.79979i	−0.0314954	−	0.219055i	−0.999491	+	0.0319133i	$0.989840\pi$
$702$		0			0
$703$	−12.2775	+	7.89027i	−0.463055	+	0.297587i
$704$	−1.08029	+	1.24672i	−0.0407148	+	0.0469874i
$705$		0			0
$706$	6.50369	+	4.17967i	0.244769	+	0.157304i
$707$	−78.3839	+	23.0156i	−2.94793	+	0.865591i
$708$		0			0
$709$	−43.2693	−	12.7050i	−1.62501	−	0.477147i	−0.662653	−	0.748926i	$-0.730570\pi$
$709$	−43.2693	−	12.7050i	−1.62501	−	0.477147i	−0.962360	+	0.271779i	$0.912388\pi$
$710$	−2.33400	−	5.11075i	−0.0875935	−	0.191803i
$711$		0			0
$712$	11.3261			0.424464
$713$	−6.87958	+	12.7175i	−0.257642	+	0.476274i
$714$		0			0
$715$	−1.37090	+	9.53484i	−0.0512689	+	0.356583i
$716$	7.78793	+	17.0532i	0.291049	+	0.637308i
$717$		0			0
$718$	24.2538	+	27.9904i	0.905145	+	1.04459i
$719$	−31.5875	+	9.27493i	−1.17802	+	0.345897i	−0.811409	−	0.584479i	$-0.801299\pi$
$719$	−31.5875	+	9.27493i	−1.17802	+	0.345897i	−0.366607	+	0.930376i	$0.619481\pi$
$720$		0			0
$721$	−21.0074	+	45.9998i	−0.782357	+	1.71312i
$722$	16.0963	−	18.5761i	0.599042	−	0.691331i
$723$		0			0
$724$	1.03401	+	7.19172i	0.0384288	+	0.267278i
$725$	3.51622	+	24.4559i	0.130589	+	0.908269i
$726$		0			0
$727$	1.64107	−	1.89390i	0.0608641	−	0.0702409i	−0.724501	−	0.689274i	$-0.757930\pi$
$727$	1.64107	−	1.89390i	0.0608641	−	0.0702409i	0.785365	+	0.619033i	$0.212475\pi$
$728$	−10.0575	+	22.0228i	−0.372755	+	0.816220i
$729$		0			0
$730$	7.35855	−	2.16067i	0.272352	−	0.0799699i
$731$	−7.49015	−	8.64410i	−0.277033	−	0.319714i
$732$		0			0
$733$	−4.60963	−	10.0937i	−0.170261	−	0.372818i	0.805197	−	0.593008i	$-0.202060\pi$
$733$	−4.60963	−	10.0937i	−0.170261	−	0.372818i	−0.975457	+	0.220189i	$0.929332\pi$
$734$	−1.73467	+	12.0649i	−0.0640279	+	0.445324i
$735$		0			0
$736$	3.37782	−	3.40446i	0.124508	−	0.125490i
$737$	19.8705			0.731938
$738$		0			0
$739$	−15.0167	−	32.8820i	−0.552399	−	1.20958i	−0.955653	−	0.294496i	$-0.904848\pi$
$739$	−15.0167	−	32.8820i	−0.552399	−	1.20958i	0.403254	−	0.915088i	$-0.367879\pi$
$740$	2.26398	+	0.664765i	0.0832256	+	0.0244373i
$741$		0			0
$742$	9.47011	−	2.78067i	0.347659	−	0.102082i
$743$	−22.3469	−	14.3615i	−0.819830	−	0.526873i	0.0622013	−	0.998064i	$-0.480188\pi$
$743$	−22.3469	−	14.3615i	−0.819830	−	0.526873i	−0.882031	+	0.471191i	$0.843824\pi$
$744$		0			0
$745$	−14.2674	+	16.4655i	−0.522719	+	0.603249i
$746$	−4.66574	+	2.99849i	−0.170825	+	0.109783i
$747$		0			0
$748$	0.921732	+	6.41079i	0.0337019	+	0.234402i
$749$	−55.3347	+	35.5614i	−2.02188	+	1.29939i
$750$		0			0
$751$	5.72851	−	12.5437i	0.209036	−	0.457725i	−0.775852	−	0.630914i	$-0.782680\pi$
$751$	5.72851	−	12.5437i	0.209036	−	0.457725i	0.984889	+	0.173189i	$0.0554072\pi$
$752$	8.09543	+	5.20262i	0.295210	+	0.189720i
$753$		0			0
$754$	22.9281	+	26.4605i	0.834993	+	0.963633i
$755$	13.0204	+	3.82315i	0.473863	+	0.139139i
$756$		0			0
$757$	5.42275	−	37.7160i	0.197093	−	1.37081i	−0.615571	−	0.788081i	$-0.711075\pi$
$757$	5.42275	−	37.7160i	0.197093	−	1.37081i	0.812664	−	0.582732i	$-0.198016\pi$
$758$	10.2328			0.371674
$759$		0			0
$760$	−7.04583			−0.255579
$761$	6.16173	−	42.8558i	0.223363	−	1.55352i	−0.501825	−	0.864969i	$-0.667338\pi$
$761$	6.16173	−	42.8558i	0.223363	−	1.55352i	0.725187	−	0.688551i	$-0.241753\pi$
$762$		0			0
$763$	−52.1527	−	15.3134i	−1.88806	−	0.554383i
$764$	16.4905	+	19.0310i	0.596604	+	0.688518i
$765$		0			0
$766$	−3.77792	−	2.42792i	−0.136502	−	0.0877243i
$767$	−22.1644	+	48.5333i	−0.800310	+	1.75243i
$768$		0			0
$769$	−29.5055	+	18.9620i	−1.06400	+	0.683789i	−0.950807	−	0.309785i	$-0.899743\pi$
$769$	−29.5055	+	18.9620i	−1.06400	+	0.683789i	−0.113189	+	0.993573i	$0.536107\pi$
$770$	1.10882	+	7.71202i	0.0399591	+	0.277922i
$771$		0			0
$772$	14.2228	−	9.14046i	0.511891	−	0.328973i
$773$	−9.74424	+	11.2455i	−0.350476	+	0.404471i	−0.903426	−	0.428743i	$-0.858956\pi$
$773$	−9.74424	+	11.2455i	−0.350476	+	0.404471i	0.552950	+	0.833214i	$0.313502\pi$
$774$		0			0
$775$	9.79230	+	6.29313i	0.351750	+	0.226056i
$776$	11.4942	−	3.37499i	0.412617	−	0.121155i
$777$		0			0
$778$	−3.27983	−	0.963044i	−0.117587	−	0.0345268i
$779$	−11.2211	−	24.5708i	−0.402038	−	0.880340i
$780$		0			0
$781$	8.68398			0.310737
$782$	−1.41699	−	18.7757i	−0.0506716	−	0.671416i
$783$		0			0
$784$	−1.79064	+	12.4542i	−0.0639513	+	0.444791i
$785$	−0.507575	−	1.11143i	−0.0181161	−	0.0396688i
$786$		0			0
$787$	−23.9230	−	27.6087i	−0.852764	−	0.984142i	0.147224	−	0.989103i	$-0.452966\pi$
$787$	−23.9230	−	27.6087i	−0.852764	−	0.984142i	−0.999988	+	0.00496096i	$0.998421\pi$
$788$	−12.3218	+	3.61800i	−0.438945	+	0.128886i
$789$		0			0
$790$	−1.19437	+	2.61530i	−0.0424937	+	0.0930483i
$791$	−8.73599	+	10.0819i	−0.310616	+	0.358470i
$792$		0			0
$793$	1.21423	+	8.44512i	0.0431184	+	0.299895i
$794$	−3.56501	−	24.7952i	−0.126518	−	0.879950i
$795$		0			0
$796$	−8.90909	+	10.2816i	−0.315774	+	0.364423i
$797$	18.9378	−	41.4680i	0.670811	−	1.46887i	−0.201282	−	0.979533i	$-0.564511\pi$
$797$	18.9378	−	41.4680i	0.670811	−	1.46887i	0.872094	−	0.489339i	$-0.162762\pi$
$798$		0			0
$799$	36.2509	−	10.6442i	1.28247	−	0.376566i
$800$	−2.52832	−	2.91784i	−0.0893896	−	0.103161i
$801$		0			0
$802$	−3.72081	−	8.14744i	−0.131386	−	0.287696i
$803$	−1.68695	+	11.7330i	−0.0595310	+	0.414047i
$804$		0			0
$805$	−1.70461	−	22.5866i	−0.0600795	−	0.796075i
$806$	16.4950			0.581010
$807$		0			0
$808$	−7.66896	−	16.7927i	−0.269793	−	0.590764i
$809$	−20.9411	−	6.14886i	−0.736250	−	0.216182i	−0.107953	−	0.994156i	$-0.534430\pi$
$809$	−20.9411	−	6.14886i	−0.736250	−	0.216182i	−0.628297	+	0.777974i	$0.716248\pi$
$810$		0			0
$811$	−29.1306	+	8.55353i	−1.02292	+	0.300355i	−0.749827	−	0.661634i	$-0.769863\pi$
$811$	−29.1306	+	8.55353i	−1.02292	+	0.300355i	−0.273088	+	0.961989i	$0.588045\pi$
$812$	23.8233	+	15.3103i	0.836033	+	0.537286i
$813$		0			0
$814$	−2.38825	+	2.75619i	−0.0837082	+	0.0966044i
$815$	4.31285	−	2.77170i	0.151072	−	0.0970883i
$816$		0			0
$817$	2.73697	+	19.0360i	0.0957544	+	0.665986i
$818$	19.5857	−	12.5869i	0.684797	−	0.440092i
$819$		0			0
$820$	−1.81419	+	3.97253i	−0.0633544	+	0.138727i
$821$	28.6045	+	18.3830i	0.998305	+	0.641572i	0.934341	−	0.356381i	$-0.115989\pi$
$821$	28.6045	+	18.3830i	0.998305	+	0.641572i	0.0639641	+	0.997952i	$0.479626\pi$
$822$		0			0
$823$	−34.2879	−	39.5703i	−1.19520	−	1.37933i	−0.906657	−	0.421868i	$-0.861375\pi$
$823$	−34.2879	−	39.5703i	−1.19520	−	1.37933i	−0.288543	−	0.957467i	$-0.593171\pi$
$824$	−10.9648	−	3.21956i	−0.381977	−	0.112159i
$825$		0			0
$826$	−6.14156	+	42.7155i	−0.213692	+	1.48626i
$827$	20.0689			0.697864			0.348932	−	0.937148i	$-0.386544\pi$
$827$	20.0689			0.697864			0.348932	+	0.937148i	$0.386544\pi$
$828$		0			0
$829$	−30.6227			−1.06357			−0.531785	−	0.846879i	$-0.678479\pi$
$829$	−30.6227			−1.06357			−0.531785	+	0.846879i	$0.678479\pi$
$830$	−0.841254	+	5.85105i	−0.0292003	+	0.203093i
$831$		0			0
$832$	−5.24950	−	1.54139i	−0.181994	−	0.0534382i
$833$	32.3498	+	37.3336i	1.12085	+	1.29353i
$834$		0			0
$835$	−10.5481	−	6.77888i	−0.365034	−	0.234593i
$836$	4.52392	−	9.90599i	0.156463	−	0.342606i
$837$		0			0
$838$	−1.89252	+	1.21625i	−0.0653759	+	0.0420145i
$839$	5.68452	+	39.5367i	0.196251	+	1.36496i	0.815042	+	0.579402i	$0.196714\pi$
$839$	5.68452	+	39.5367i	0.196251	+	1.36496i	−0.618791	+	0.785556i	$0.712377\pi$
$840$		0			0
$841$	10.0556	−	6.46233i	0.346744	−	0.222839i
$842$	−12.2209	+	14.1037i	−0.421160	+	0.486044i
$843$		0			0
$844$	−17.7860	−	11.4304i	−0.612219	−	0.393449i
$845$	−17.3408	+	5.09173i	−0.596543	+	0.175161i
$846$		0			0
$847$	35.1507	+	10.3212i	1.20779	+	0.354640i
$848$	0.926540	+	2.02884i	0.0318175	+	0.0696706i
$849$		0			0
$850$	−15.1582			−0.519922
$851$	7.46754	−	7.52643i	0.255984	−	0.258003i
$852$		0			0
$853$	0.551160	−	3.83340i	0.0188714	−	0.131253i	−0.978208	−	0.207628i	$-0.933426\pi$
$853$	0.551160	−	3.83340i	0.0188714	−	0.131253i	0.997079	+	0.0763751i	$0.0243346\pi$
$854$	2.86673	+	6.27725i	0.0980973	+	0.214803i
$855$		0			0
$856$	−9.73393	−	11.2336i	−0.332699	−	0.383955i
$857$	6.91320	−	2.02990i	0.236150	−	0.0693400i	−0.161516	−	0.986870i	$-0.551638\pi$
$857$	6.91320	−	2.02990i	0.236150	−	0.0693400i	0.397666	+	0.917530i	$0.369820\pi$
$858$		0			0
$859$	4.25641	−	9.32025i	0.145227	−	0.318003i	−0.823014	−	0.568021i	$-0.807709\pi$
$859$	4.25641	−	9.32025i	0.145227	−	0.318003i	0.968241	+	0.250018i	$0.0804366\pi$
$860$	2.03618	−	2.34988i	0.0694332	−	0.0801302i
$861$		0			0
$862$	−0.685564	−	4.76820i	−0.0233504	−	0.162405i
$863$	5.28585	+	36.7639i	0.179933	+	1.25146i	0.856914	+	0.515459i	$0.172378\pi$
$863$	5.28585	+	36.7639i	0.179933	+	1.25146i	−0.676982	+	0.736000i	$0.736712\pi$
$864$		0			0
$865$	−3.57800	+	4.12923i	−0.121656	+	0.140398i
$866$	2.59854	−	5.69000i	0.0883018	−	0.193354i
$867$		0			0
$868$	12.8011	−	3.75875i	0.434498	−	0.127580i
$869$	−2.91008	−	3.35841i	−0.0987178	−	0.113926i
$870$		0			0
$871$	27.3764	+	59.9460i	0.927614	+	2.03119i
$872$	1.74805	−	12.1580i	0.0591965	−	0.411721i
$873$		0			0
$874$	−15.0636	+	27.8464i	−0.509534	+	0.941918i
$875$	−41.8501			−1.41479
$876$		0			0
$877$	−0.594109	−	1.30092i	−0.0200616	−	0.0439289i	0.899336	−	0.437258i	$-0.144050\pi$
$877$	−0.594109	−	1.30092i	−0.0200616	−	0.0439289i	−0.919398	+	0.393329i	$0.871323\pi$
$878$	−12.9967	−	3.81617i	−0.438617	−	0.128790i
$879$		0			0
$880$	−1.68936	+	0.496041i	−0.0569483	+	0.0167215i
$881$	16.7233	+	10.7474i	0.563421	+	0.362089i	0.791137	−	0.611639i	$-0.209489\pi$
$881$	16.7233	+	10.7474i	0.563421	+	0.362089i	−0.227716	+	0.973728i	$0.573126\pi$
$882$		0			0
$883$	−10.6666	+	12.3099i	−0.358960	+	0.414262i	−0.906291	−	0.422654i	$-0.861098\pi$
$883$	−10.6666	+	12.3099i	−0.358960	+	0.414262i	0.547331	+	0.836916i	$0.315644\pi$
$884$	−18.0704	+	11.6131i	−0.607773	+	0.390592i
$885$		0			0
$886$	−0.788405	−	5.48348i	−0.0264870	−	0.184221i
$887$	18.4832	−	11.8784i	0.620604	−	0.398838i	−0.192216	−	0.981353i	$-0.561567\pi$
$887$	18.4832	−	11.8784i	0.620604	−	0.398838i	0.812820	+	0.582515i	$0.197931\pi$
$888$		0			0
$889$	−10.0231	+	21.9475i	−0.336164	+	0.736096i
$890$	10.1695	+	6.53551i	0.340881	+	0.219071i
$891$		0			0
$892$	1.67113	+	1.92859i	0.0559536	+	0.0645739i
$893$	−60.9533	−	17.8975i	−2.03972	−	0.598917i
$894$		0			0
$895$	−2.84761	+	19.8056i	−0.0951851	+	0.662027i
$896$	−4.42518			−0.147835
$897$		0			0
$898$	−13.5471			−0.452073
$899$	2.74580	−	19.0974i	0.0915774	−	0.636935i
$900$		0			0
$901$	8.40211	+	2.46708i	0.279915	+	0.0821904i
$902$	−4.42029	−	5.10128i	−0.147179	−	0.169854i
$903$		0			0
$904$	−2.53606	−	1.62983i	−0.0843480	−	0.0542072i
$905$	−3.22143	+	7.05394i	−0.107084	+	0.234481i
$906$		0			0
$907$	39.5458	−	25.4146i	1.31310	−	0.843877i	0.318524	−	0.947915i	$-0.396813\pi$
$907$	39.5458	−	25.4146i	1.31310	−	0.843877i	0.994573	+	0.104038i	$0.0331763\pi$
$908$	−2.80685	−	19.5220i	−0.0931485	−	0.647862i
$909$		0			0
$910$	−21.7382	+	13.9703i	−0.720616	+	0.463111i
$911$	−7.57632	+	8.74354i	−0.251015	+	0.289686i	−0.867247	−	0.497878i	$-0.834113\pi$
$911$	−7.57632	+	8.74354i	−0.251015	+	0.289686i	0.616232	+	0.787564i	$0.288658\pi$
$912$		0			0
$913$	−7.68606	−	4.93953i	−0.254371	−	0.163475i
$914$	−10.6635	+	3.13109i	−0.352718	+	0.103567i
$915$		0			0
$916$	10.7515	+	3.15692i	0.355239	+	0.104308i
$917$	15.9517	+	34.9294i	0.526772	+	1.15347i
$918$		0			0
$919$	35.1441			1.15930			0.579648	−	0.814867i	$-0.303190\pi$
$919$	35.1441			1.15930			0.579648	+	0.814867i	$0.303190\pi$
$920$	4.99735	−	1.10768i	0.164758	−	0.0365190i
$921$		0			0
$922$	4.74370	−	32.9931i	0.156225	−	1.08657i
$923$	11.9643	+	26.1982i	0.393810	+	0.862323i
$924$		0			0
$925$	−5.58950	−	6.45063i	−0.183782	−	0.212095i
$926$	−18.6479	+	5.47551i	−0.612808	+	0.179937i
$927$		0			0
$928$	−2.65843	+	5.82115i	−0.0872673	+	0.191089i
$929$	−23.4261	+	27.0352i	−0.768586	+	0.886995i	−0.996230	−	0.0867489i	$-0.972352\pi$
$929$	−23.4261	+	27.0352i	−0.768586	+	0.886995i	0.227644	+	0.973744i	$0.426898\pi$
$930$		0			0
$931$	−11.8209	−	82.2160i	−0.387414	−	2.69452i
$932$	2.56439	+	17.8357i	0.0839994	+	0.584229i
$933$		0			0
$934$	21.9542	−	25.3365i	0.718364	−	0.829036i
$935$	−2.87162	+	6.28797i	−0.0939120	+	0.205639i
$936$		0			0
$937$	−16.9547	+	4.97835i	−0.553886	+	0.162636i	−0.546685	−	0.837338i	$-0.684110\pi$
$937$	−16.9547	+	4.97835i	−0.553886	+	0.162636i	−0.00720126	+	0.999974i	$0.502292\pi$
$938$	34.9058	+	40.2835i	1.13972	+	1.31530i
$939$		0			0
$940$	4.26663	+	9.34263i	0.139162	+	0.304723i
$941$	−2.26593	+	15.7599i	−0.0738673	+	0.513758i	0.918974	+	0.394318i	$0.129019\pi$
$941$	−2.26593	+	15.7599i	−0.0738673	+	0.513758i	−0.992841	+	0.119440i	$0.961890\pi$
$942$		0			0
$943$	11.8215	+	15.6631i	0.384961	+	0.510060i
$944$	−9.75208			−0.317403
$945$		0			0
$946$	1.99641	+	4.37153i	0.0649089	+	0.142131i
$947$	−18.5903	−	5.45860i	−0.604103	−	0.177381i	−0.0346429	−	0.999400i	$-0.511029\pi$
$947$	−18.5903	−	5.45860i	−0.604103	−	0.177381i	−0.569460	+	0.822019i	$0.692848\pi$
$948$		0			0
$949$	−37.7206	+	11.0758i	−1.22446	+	0.359535i
$950$	21.4414	+	13.7795i	0.695649	+	0.447067i
$951$		0			0
$952$	−11.3774	+	13.1303i	−0.368745	+	0.425554i
$953$	24.8293	−	15.9568i	0.804300	−	0.516892i	−0.0727163	−	0.997353i	$-0.523167\pi$
$953$	24.8293	−	15.9568i	0.804300	−	0.516892i	0.877016	+	0.480460i	$0.159530\pi$
$954$		0			0
$955$	3.82494	+	26.6030i	0.123772	+	0.860854i
$956$	−22.9224	+	14.7313i	−0.741364	+	0.476446i
$957$		0			0
$958$	−0.687814	+	1.50610i	−0.0222222	+	0.0486599i
$959$	−33.4364	−	21.4883i	−1.07972	−	0.693892i
$960$		0			0
$961$	14.3482	+	16.5587i	0.462845	+	0.534152i
$962$	−11.6054	−	3.40765i	−0.374172	−	0.109867i
$963$		0			0
$964$	3.17028	−	22.0498i	0.102108	−	0.710175i
$965$	18.0447			0.580879
$966$		0			0
$967$	5.25882			0.169112			0.0845562	−	0.996419i	$-0.473053\pi$
$967$	5.25882			0.169112			0.0845562	+	0.996419i	$0.473053\pi$
$968$	−1.17818	+	8.19441i	−0.0378681	+	0.263378i
$969$		0			0
$970$	12.2678	+	3.60216i	0.393896	+	0.115658i
$971$	13.4313	+	15.5006i	0.431032	+	0.497437i	0.929166	−	0.369663i	$-0.120527\pi$
$971$	13.4313	+	15.5006i	0.431032	+	0.497437i	−0.498134	+	0.867100i	$0.665981\pi$
$972$		0			0
$973$	11.4021	+	7.32771i	0.365536	+	0.234916i
$974$	8.72182	−	19.0981i	0.279465	−	0.611943i
$975$		0			0
$976$	−1.31190	+	0.843105i	−0.0419928	+	0.0269871i
$977$	0.247958	+	1.72459i	0.00793289	+	0.0551744i	0.993403	−	0.114672i	$-0.0365818\pi$
$977$	0.247958	+	1.72459i	0.00793289	+	0.0551744i	−0.985470	+	0.169847i	$0.945673\pi$
$978$		0			0
$979$	−15.7180	+	10.1014i	−0.502350	+	0.322841i
$980$	−8.79421	+	10.1491i	−0.280921	+	0.324200i
$981$		0			0
$982$	21.7151	+	13.9555i	0.692958	+	0.445337i
$983$	0.0225550	−	0.00662274i	0.000719392	−	0.000211233i	−0.281373	−	0.959599i	$-0.590790\pi$
$983$	0.0225550	−	0.00662274i	0.000719392	−	0.000211233i	0.282092	+	0.959387i	$0.408972\pi$
$984$		0			0
$985$	−13.1511	−	3.86152i	−0.419030	−	0.123038i
$986$	10.4373	+	22.8546i	0.332393	+	0.727838i
$987$		0			0
$988$	36.1176			1.14905
$989$	−4.93389	−	13.0713i	−0.156889	−	0.415642i
$990$		0			0
$991$	2.25098	−	15.6559i	0.0715048	−	0.497327i	−0.922325	−	0.386414i	$-0.873714\pi$
$991$	2.25098	−	15.6559i	0.0715048	−	0.497327i	0.993830	−	0.110913i	$-0.0353773\pi$
$992$	1.25244	+	2.74246i	0.0397650	+	0.0870732i
$993$		0			0
$994$	15.2549	+	17.6051i	0.483855	+	0.558399i
$995$	−13.9321	+	4.09083i	−0.441677	+	0.129688i
$996$		0			0
$997$	−4.06792	+	8.90750i	−0.128832	+	0.282103i	−0.963046	−	0.269339i	$-0.913195\pi$
$997$	−4.06792	+	8.90750i	−0.128832	+	0.282103i	0.834213	+	0.551442i	$0.185922\pi$
$998$	−4.21577	+	4.86526i	−0.133448	+	0.154007i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.e.307.1		10
3.2	odd	2		138.2.e.b.31.1	✓	10
23.3	even	11	inner	414.2.i.e.325.1		10
23.7	odd	22		9522.2.a.br.1.2		5
23.16	even	11		9522.2.a.bs.1.4		5
69.26	odd	22		138.2.e.b.49.1	yes	10
69.53	even	22		3174.2.a.bb.1.4		5
69.62	odd	22		3174.2.a.ba.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.31.1	✓	10	3.2	odd	2
138.2.e.b.49.1	yes	10	69.26	odd	22
414.2.i.e.307.1		10	1.1	even	1	trivial
414.2.i.e.325.1		10	23.3	even	11	inner
3174.2.a.ba.1.2		5	69.62	odd	22
3174.2.a.bb.1.4		5	69.53	even	22
9522.2.a.br.1.2		5	23.7	odd	22
9522.2.a.bs.1.4		5	23.16	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(-0.698939 - 0.806618i) q^{5} +(3.72270 + 2.39243i) q^{7} +(-0.415415 + 0.909632i) q^{8} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.959493 - 0.281733i) q^{4} +(-0.698939 - 0.806618i) q^{5} +(3.72270 + 2.39243i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.897877 + 0.577031i) q^{10} +(-0.234769 - 1.63285i) q^{11} +(4.60260 - 2.95791i) q^{13} +(2.89788 - 3.34433i) q^{14} +(0.841254 + 0.540641i) q^{16} +(3.76709 - 1.10612i) q^{17} +(-6.33409 - 1.85986i) q^{19} +(0.443376 + 0.970858i) q^{20} -1.64964 q^{22} +(4.78492 + 0.323343i) q^{23} +(0.549456 - 3.82155i) q^{25} +(-2.27279 - 4.97671i) q^{26} +(-2.89788 - 3.34433i) q^{28} +(-6.14024 + 1.80294i) q^{29} +(-1.25244 + 2.74246i) q^{31} +(0.654861 - 0.755750i) q^{32} +(-0.558746 - 3.88617i) q^{34} +(-0.672158 - 4.67496i) q^{35} +(1.44774 - 1.67078i) q^{37} +(-2.74236 + 6.00493i) q^{38} +(1.02408 - 0.300696i) q^{40} +(2.67954 + 3.09235i) q^{41} +(-1.21021 - 2.64998i) q^{43} +(-0.234769 + 1.63285i) q^{44} +(1.00102 - 4.69020i) q^{46} +9.62306 q^{47} +(5.22685 + 11.4452i) q^{49} +(-3.70446 - 1.08773i) q^{50} +(-5.24950 + 1.54139i) q^{52} +(1.87633 + 1.20584i) q^{53} +(-1.15300 + 1.33063i) q^{55} +(-3.72270 + 2.39243i) q^{56} +(0.910738 + 6.33432i) q^{58} +(-8.20397 + 5.27237i) q^{59} +(-0.647821 + 1.41853i) q^{61} +(2.53631 + 1.62999i) q^{62} +(-0.654861 - 0.755750i) q^{64} +(-5.60284 - 1.64514i) q^{65} +(-1.71423 + 11.9227i) q^{67} -3.92613 q^{68} -4.72304 q^{70} +(-0.749168 + 5.21058i) q^{71} +(-6.89449 - 2.02441i) q^{73} +(-1.44774 - 1.67078i) q^{74} +(5.55353 + 3.56904i) q^{76} +(3.03252 - 6.64029i) q^{77} +(2.26617 - 1.45638i) q^{79} +(-0.151894 - 1.05645i) q^{80} +(3.44222 - 2.21218i) q^{82} +(3.62690 - 4.18567i) q^{83} +(-3.52518 - 2.26550i) q^{85} +(-2.79524 + 0.820757i) q^{86} +(1.58282 + 0.464758i) q^{88} +(-4.70504 - 10.3026i) q^{89} +24.2107 q^{91} +(-4.50000 - 1.65831i) q^{92} +(1.36950 - 9.52511i) q^{94} +(2.92694 + 6.40911i) q^{95} +(-7.84485 - 9.05344i) q^{97} +(12.0726 - 3.54482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{4} + 2 q^{5} + q^{8}+O(q^{10}) \) 10 * q + q^2 - q^4 + 2 * q^5 + q^8	\( 10 q + q^{2} - q^{4} + 2 q^{5} + q^{8} + 9 q^{10} - 11 q^{11} + 13 q^{13} + 11 q^{14} - q^{16} + 24 q^{17} - 14 q^{19} + 13 q^{20} + 22 q^{22} + 10 q^{23} - 43 q^{25} + 9 q^{26} - 11 q^{28} - 13 q^{29} + 8 q^{31} + q^{32} + 9 q^{34} - 13 q^{37} + 3 q^{38} + 9 q^{40} + 10 q^{41} - 8 q^{43} - 11 q^{44} + q^{46} + 8 q^{47} + 29 q^{49} - 23 q^{50} + 2 q^{52} + 35 q^{53} - 11 q^{55} + 13 q^{58} - 37 q^{59} - 2 q^{61} - 8 q^{62} - q^{64} - 37 q^{65} + 14 q^{67} + 2 q^{68} - 22 q^{70} - 44 q^{71} - 49 q^{73} + 13 q^{74} + 8 q^{76} - 44 q^{77} - 8 q^{79} + 2 q^{80} + 12 q^{82} + 17 q^{83} - 37 q^{85} - 14 q^{86} - 59 q^{89} + 66 q^{91} - 45 q^{92} - 19 q^{94} + 28 q^{95} - 21 q^{97} + 26 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^4 + 2 * q^5 + q^8 + 9 * q^10 - 11 * q^11 + 13 * q^13 + 11 * q^14 - q^16 + 24 * q^17 - 14 * q^19 + 13 * q^20 + 22 * q^22 + 10 * q^23 - 43 * q^25 + 9 * q^26 - 11 * q^28 - 13 * q^29 + 8 * q^31 + q^32 + 9 * q^34 - 13 * q^37 + 3 * q^38 + 9 * q^40 + 10 * q^41 - 8 * q^43 - 11 * q^44 + q^46 + 8 * q^47 + 29 * q^49 - 23 * q^50 + 2 * q^52 + 35 * q^53 - 11 * q^55 + 13 * q^58 - 37 * q^59 - 2 * q^61 - 8 * q^62 - q^64 - 37 * q^65 + 14 * q^67 + 2 * q^68 - 22 * q^70 - 44 * q^71 - 49 * q^73 + 13 * q^74 + 8 * q^76 - 44 * q^77 - 8 * q^79 + 2 * q^80 + 12 * q^82 + 17 * q^83 - 37 * q^85 - 14 * q^86 - 59 * q^89 + 66 * q^91 - 45 * q^92 - 19 * q^94 + 28 * q^95 - 21 * q^97 + 26 * q^98

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