LMFDB - Embedded newform 225.2.m.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (of order $10$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Root			$-1.53655i$ of defining polynomial
Character	$\chi$	$=$	225.19
Dual form			225.2.m.b.154.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46134 + 0.474819i) q^{2} +(0.292036 - 0.212177i) q^{4} +(2.06122 + 0.866816i) q^{5} -1.49550i q^{7} +(1.48030 - 2.03746i) q^{8} +O(q^{10})$	\(q+(-1.46134 + 0.474819i) q^{2} +(0.292036 - 0.212177i) q^{4} +(2.06122 + 0.866816i) q^{5} -1.49550i q^{7} +(1.48030 - 2.03746i) q^{8} +(-3.42373 - 0.288008i) q^{10} +(0.728123 + 2.24093i) q^{11} +(1.28346 + 0.417020i) q^{13} +(0.710090 + 2.18543i) q^{14} +(-1.41890 + 4.36692i) q^{16} +(-1.28963 + 1.77502i) q^{17} +(4.62004 + 3.35666i) q^{19} +(0.785869 - 0.184201i) q^{20} +(-2.12807 - 2.92904i) q^{22} +(8.36455 - 2.71781i) q^{23} +(3.49726 + 3.57340i) q^{25} -2.07358 q^{26} +(-0.317309 - 0.436739i) q^{28} +(-6.39137 + 4.64360i) q^{29} +(2.99107 + 2.17314i) q^{31} -2.01841i q^{32} +(1.04178 - 3.20626i) q^{34} +(1.29632 - 3.08255i) q^{35} +(-9.27372 - 3.01321i) q^{37} +(-8.34527 - 2.71154i) q^{38} +(4.81733 - 2.91650i) q^{40} +(-0.573380 + 1.76468i) q^{41} -8.01874i q^{43} +(0.688111 + 0.499942i) q^{44} +(-10.9330 + 7.94330i) q^{46} +(-3.91640 - 5.39046i) q^{47} +4.76349 q^{49} +(-6.80741 - 3.56139i) q^{50} +(0.463298 - 0.150535i) q^{52} +(2.45196 + 3.37484i) q^{53} +(-0.441653 + 5.25020i) q^{55} +(-3.04701 - 2.21378i) q^{56} +(7.13511 - 9.82064i) q^{58} +(3.41917 - 10.5231i) q^{59} +(-3.78151 - 11.6383i) q^{61} +(-5.40283 - 1.75549i) q^{62} +(-1.87942 - 5.78425i) q^{64} +(2.28401 + 1.97209i) q^{65} +(-2.53546 + 3.48976i) q^{67} +0.792000i q^{68} +(-0.430715 + 5.12018i) q^{70} +(4.67410 - 3.39593i) q^{71} +(-6.58781 + 2.14051i) q^{73} +14.9828 q^{74} +2.06142 q^{76} +(3.35130 - 1.08890i) q^{77} +(-8.63118 + 6.27092i) q^{79} +(-6.70997 + 7.77126i) q^{80} -2.85106i q^{82} +(-0.131666 + 0.181222i) q^{83} +(-4.19683 + 2.54084i) q^{85} +(3.80745 + 11.7181i) q^{86} +(5.64364 + 1.83373i) q^{88} +(0.132620 + 0.408162i) q^{89} +(0.623652 - 1.91940i) q^{91} +(1.86610 - 2.56846i) q^{92} +(8.28270 + 6.01773i) q^{94} +(6.61332 + 10.9235i) q^{95} +(7.34411 + 10.1083i) q^{97} +(-6.96109 + 2.26180i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) $ 16 * q + 2 * q^4 + 30 * q^8	$ 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.46134	+	0.474819i	−1.03333	+	0.335748i	−0.776104	−	0.630605i	$-0.782807\pi$
$2$	−1.46134	+	0.474819i	−1.03333	+	0.335748i	−0.257221	+	0.966353i	$0.582807\pi$
$3$		0			0
$3$		0			0
$4$	0.292036	−	0.212177i	0.146018	−	0.106088i
$5$	2.06122	+	0.866816i	0.921806	+	0.387652i
$5$	2.06122	+	0.866816i	0.921806	+	0.387652i
$6$		0			0
$7$		−	1.49550i		−	0.565244i	−0.959231	−	0.282622i	$-0.908796\pi$
$7$		−	1.49550i		−	0.565244i	0.959231	−	0.282622i	$-0.0912043\pi$
$8$	1.48030	−	2.03746i	0.523365	−	0.720350i
$9$		0			0
$10$	−3.42373	−	0.288008i	−1.08268	−	0.0910762i
$11$	0.728123	+	2.24093i	0.219537	+	0.675666i	0.998800	+	0.0489693i	$0.0155936\pi$
$11$	0.728123	+	2.24093i	0.219537	+	0.675666i	−0.779263	+	0.626697i	$0.784406\pi$
$12$		0			0
$13$	1.28346	+	0.417020i	0.355967	+	0.115661i	0.481541	−	0.876424i	$-0.340077\pi$
$13$	1.28346	+	0.417020i	0.355967	+	0.115661i	−0.125574	+	0.992084i	$0.540077\pi$
$14$	0.710090	+	2.18543i	0.189780	+	0.584081i
$15$		0			0
$16$	−1.41890	+	4.36692i	−0.354724	+	1.09173i
$17$	−1.28963	+	1.77502i	−0.312781	+	0.430507i	−0.936246	−	0.351345i	$-0.885724\pi$
$17$	−1.28963	+	1.77502i	−0.312781	+	0.430507i	0.623465	+	0.781851i	$0.285724\pi$
$18$		0			0
$19$	4.62004	+	3.35666i	1.05991	+	0.770070i	0.974072	−	0.226239i	$-0.0726431\pi$
$19$	4.62004	+	3.35666i	1.05991	+	0.770070i	0.0858386	+	0.996309i	$0.472643\pi$
$20$	0.785869	−	0.184201i	0.175726	−	0.0411887i
$21$		0			0
$22$	−2.12807	−	2.92904i	−0.453707	−	0.624474i
$23$	8.36455	−	2.71781i	1.74413	−	0.566702i	0.748762	−	0.662840i	$-0.230649\pi$
$23$	8.36455	−	2.71781i	1.74413	−	0.566702i	0.995368	+	0.0961375i	$0.0306488\pi$
$24$		0			0
$25$	3.49726	+	3.57340i	0.699452	+	0.714679i
$26$	−2.07358			−0.406662
$27$		0			0
$28$	−0.317309	−	0.436739i	−0.0599658	−	0.0825359i
$29$	−6.39137	+	4.64360i	−1.18685	+	0.862296i	−0.992928	−	0.118722i	$-0.962120\pi$
$29$	−6.39137	+	4.64360i	−1.18685	+	0.862296i	−0.193920	+	0.981017i	$0.562120\pi$
$30$		0			0
$31$	2.99107	+	2.17314i	0.537213	+	0.390308i	0.823049	−	0.567971i	$-0.192271\pi$
$31$	2.99107	+	2.17314i	0.537213	+	0.390308i	−0.285836	+	0.958279i	$0.592271\pi$
$32$		−	2.01841i		−	0.356808i
$33$		0			0
$34$	1.04178	−	3.20626i	0.178663	−	0.549869i
$35$	1.29632	−	3.08255i	0.219118	−	0.521046i
$36$		0			0
$37$	−9.27372	−	3.01321i	−1.52459	−	0.495369i	−0.577515	−	0.816380i	$-0.695977\pi$
$37$	−9.27372	−	3.01321i	−1.52459	−	0.495369i	−0.947076	+	0.321011i	$0.895977\pi$
$38$	−8.34527	−	2.71154i	−1.35378	−	0.439870i
$39$		0			0
$40$	4.81733	−	2.91650i	0.761686	−	0.461140i
$41$	−0.573380	+	1.76468i	−0.0895468	+	0.275597i	−0.985794	−	0.167958i	$-0.946283\pi$
$41$	−0.573380	+	1.76468i	−0.0895468	+	0.275597i	0.896247	+	0.443555i	$0.146283\pi$
$42$		0			0
$43$		−	8.01874i		−	1.22285i	−0.791304	−	0.611423i	$-0.790597\pi$
$43$		−	8.01874i		−	1.22285i	0.791304	−	0.611423i	$-0.209403\pi$
$44$	0.688111	+	0.499942i	0.103737	+	0.0753691i
$45$		0			0
$46$	−10.9330	+	7.94330i	−1.61198	+	1.17118i
$47$	−3.91640	−	5.39046i	−0.571266	−	0.786280i	0.421438	−	0.906857i	$-0.361525\pi$
$47$	−3.91640	−	5.39046i	−0.571266	−	0.786280i	−0.992704	+	0.120577i	$0.961525\pi$
$48$		0			0
$49$	4.76349			0.680499
$50$	−6.80741	−	3.56139i	−0.962714	−	0.503657i
$51$		0			0
$52$	0.463298	−	0.150535i	0.0642478	−	0.0208754i
$53$	2.45196	+	3.37484i	0.336803	+	0.463569i	0.943504	−	0.331360i	$-0.107508\pi$
$53$	2.45196	+	3.37484i	0.336803	+	0.463569i	−0.606701	+	0.794930i	$0.707508\pi$
$54$		0			0
$55$	−0.441653	+	5.25020i	−0.0595525	+	0.707937i
$56$	−3.04701	−	2.21378i	−0.407174	−	0.295829i
$57$		0			0
$58$	7.13511	−	9.82064i	0.936886	−	1.28951i
$59$	3.41917	−	10.5231i	0.445138	−	1.36999i	−0.437195	−	0.899367i	$-0.644028\pi$
$59$	3.41917	−	10.5231i	0.445138	−	1.36999i	0.882332	−	0.470627i	$-0.155972\pi$
$60$		0			0
$61$	−3.78151	−	11.6383i	−0.484173	−	1.49013i	−0.833175	−	0.553009i	$-0.813480\pi$
$61$	−3.78151	−	11.6383i	−0.484173	−	1.49013i	0.349003	−	0.937122i	$-0.386520\pi$
$62$	−5.40283	−	1.75549i	−0.686161	−	0.222947i
$63$		0			0
$64$	−1.87942	−	5.78425i	−0.234927	−	0.723031i
$65$	2.28401	+	1.97209i	0.283296	+	0.244608i
$66$		0			0
$67$	−2.53546	+	3.48976i	−0.309756	+	0.426342i	−0.935305	−	0.353842i	$-0.884875\pi$
$67$	−2.53546	+	3.48976i	−0.309756	+	0.426342i	0.625549	+	0.780185i	$0.284875\pi$
$68$			0.792000i			0.0960442i
$69$		0			0
$70$	−0.430715	+	5.12018i	−0.0514803	+	0.611978i
$71$	4.67410	−	3.39593i	0.554713	−	0.403023i	−0.274807	−	0.961499i	$-0.588614\pi$
$71$	4.67410	−	3.39593i	0.554713	−	0.403023i	0.829520	+	0.558477i	$0.188614\pi$
$72$		0			0
$73$	−6.58781	+	2.14051i	−0.771045	+	0.250528i	−0.668012	−	0.744150i	$-0.732855\pi$
$73$	−6.58781	+	2.14051i	−0.771045	+	0.250528i	−0.103033	+	0.994678i	$0.532855\pi$
$74$	14.9828			1.74172
$75$		0			0
$76$	2.06142			0.236461
$77$	3.35130	−	1.08890i	0.381917	−	0.124092i
$78$		0			0
$79$	−8.63118	+	6.27092i	−0.971084	+	0.705534i	−0.955698	−	0.294348i	$-0.904898\pi$
$79$	−8.63118	+	6.27092i	−0.971084	+	0.705534i	−0.0153858	+	0.999882i	$0.504898\pi$
$80$	−6.70997	+	7.77126i	−0.750198	+	0.868853i
$81$		0			0
$82$		−	2.85106i		−	0.314846i
$83$	−0.131666	+	0.181222i	−0.0144522	+	0.0198917i	−0.816182	−	0.577795i	$-0.803913\pi$
$83$	−0.131666	+	0.181222i	−0.0144522	+	0.0198917i	0.801730	+	0.597687i	$0.203913\pi$
$84$		0			0
$85$	−4.19683	+	2.54084i	−0.455210	+	0.275593i
$86$	3.80745	+	11.7181i	0.410568	+	1.26360i
$87$		0			0
$88$	5.64364	+	1.83373i	0.601615	+	0.195476i
$89$	0.132620	+	0.408162i	0.0140577	+	0.0432651i	0.957839	−	0.287304i	$-0.0927592\pi$
$89$	0.132620	+	0.408162i	0.0140577	+	0.0432651i	−0.943782	+	0.330570i	$0.892759\pi$
$90$		0			0
$91$	0.623652	−	1.91940i	0.0653765	−	0.201208i
$92$	1.86610	−	2.56846i	0.194554	−	0.267780i
$93$		0			0
$94$	8.28270	+	6.01773i	0.854295	+	0.620682i
$95$	6.61332	+	10.9235i	0.678513	+	1.12073i
$96$		0			0
$97$	7.34411	+	10.1083i	0.745682	+	1.02634i	0.998272	+	0.0587692i	$0.0187176\pi$
$97$	7.34411	+	10.1083i	0.745682	+	1.02634i	−0.252590	+	0.967573i	$0.581282\pi$
$98$	−6.96109	+	2.26180i	−0.703177	+	0.228476i
$99$		0			0
$100$	1.77952	+	0.301524i	0.177952	+	0.0301524i
$101$	−8.19767			−0.815698			−0.407849	−	0.913049i	$-0.633721\pi$
$101$	−8.19767			−0.815698			−0.407849	+	0.913049i	$0.633721\pi$
$102$		0			0
$103$	−1.46949	−	2.02258i	−0.144794	−	0.199291i	0.730460	−	0.682955i	$-0.239306\pi$
$103$	−1.46949	−	2.02258i	−0.144794	−	0.199291i	−0.875254	+	0.483664i	$0.839306\pi$
$104$	2.74956	−	1.99767i	0.269617	−	0.195888i
$105$		0			0
$106$	−5.18559	−	3.76755i	−0.503669	−	0.365937i
$107$		−	1.81004i		−	0.174983i	−0.996165	−	0.0874914i	$-0.972115\pi$
$107$		−	1.81004i		−	0.174983i	0.996165	−	0.0874914i	$-0.0278850\pi$
$108$		0			0
$109$	0.910913	−	2.80350i	0.0872496	−	0.268527i	−0.897907	−	0.440186i	$-0.854913\pi$
$109$	0.910913	−	2.80350i	0.0872496	−	0.268527i	0.985156	+	0.171659i	$0.0549127\pi$
$110$	−1.84749	−	7.88205i	−0.176151	−	0.751524i
$111$		0			0
$112$	6.53071	+	2.12196i	0.617094	+	0.200506i
$113$	−13.1593	−	4.27571i	−1.23792	−	0.402225i	−0.384342	−	0.923191i	$-0.625572\pi$
$113$	−13.1593	−	4.27571i	−1.23792	−	0.402225i	−0.853577	+	0.520966i	$0.825572\pi$
$114$		0			0
$115$	19.5970	+	1.64852i	1.82743	+	0.153726i
$116$	−0.881247	+	2.71220i	−0.0818217	+	0.251821i
$117$		0			0
$118$			17.0014i			1.56510i
$119$	2.65454	+	1.92864i	0.243341	+	0.176798i
$120$		0			0
$121$	4.40757	−	3.20229i	0.400689	−	0.291117i
$122$	11.0522	+	15.2120i	1.00062	+	1.37723i
$123$		0			0
$124$	1.33459			0.119850
$125$	4.11115	+	10.3970i	0.367712	+	0.929940i
$126$		0			0
$127$	5.45902	−	1.77374i	0.484410	−	0.157394i	−0.0566233	−	0.998396i	$-0.518033\pi$
$127$	5.45902	−	1.77374i	0.484410	−	0.157394i	0.541033	+	0.841001i	$0.318033\pi$
$128$	7.86572	+	10.8262i	0.695238	+	0.956914i
$129$		0			0
$130$	−4.27411	−	1.79741i	−0.374864	−	0.157643i
$131$	−3.52534	−	2.56131i	−0.308010	−	0.223783i	0.423032	−	0.906115i	$-0.360966\pi$
$131$	−3.52534	−	2.56131i	−0.308010	−	0.223783i	−0.731042	+	0.682332i	$0.760966\pi$
$132$		0			0
$133$	5.01987	−	6.90926i	0.435278	−	0.599108i
$134$	2.04817	−	6.30363i	0.176935	−	0.544550i
$135$		0			0
$136$	1.70750	+	5.25514i	0.146417	+	0.450624i
$137$	1.87796	+	0.610187i	0.160445	+	0.0521318i	0.388138	−	0.921601i	$-0.373118\pi$
$137$	1.87796	+	0.610187i	0.160445	+	0.0521318i	−0.227693	+	0.973733i	$0.573118\pi$
$138$		0			0
$139$	−0.518869	−	1.59692i	−0.0440099	−	0.135449i	0.926637	−	0.375957i	$-0.122686\pi$
$139$	−0.518869	−	1.59692i	−0.0440099	−	0.135449i	−0.970647	+	0.240508i	$0.922686\pi$
$140$	−0.275472	−	1.17526i	−0.0232817	−	0.0993279i
$141$		0			0
$142$	−5.21801	+	7.18197i	−0.437885	+	0.602698i
$143$			3.17978i			0.265907i
$144$		0			0
$145$	−17.1992	+	4.03135i	−1.42831	+	0.334785i
$146$	8.61070	−	6.25604i	0.712627	−	0.517754i
$147$		0			0
$148$	−3.34759	+	1.08770i	−0.275171	+	0.0894083i
$149$	−7.38524			−0.605023			−0.302511	−	0.953146i	$-0.597825\pi$
$149$	−7.38524			−0.605023			−0.302511	+	0.953146i	$0.597825\pi$
$150$		0			0
$151$	−4.26137			−0.346785			−0.173393	−	0.984853i	$-0.555473\pi$
$151$	−4.26137			−0.346785			−0.173393	+	0.984853i	$0.555473\pi$
$152$	13.6781	−	4.44428i	1.10944	−	0.360479i
$153$		0			0
$154$	−4.38037	+	3.18253i	−0.352980	+	0.256455i
$155$	4.28155	+	7.07204i	0.343902	+	0.568040i
$156$		0			0
$157$		−	16.0573i		−	1.28152i	−0.767743	−	0.640758i	$-0.778620\pi$
$157$		−	16.0573i		−	1.28152i	0.767743	−	0.640758i	$-0.221380\pi$
$158$	9.63557	−	13.2622i	0.766565	−	1.05509i
$159$		0			0
$160$	1.74959	−	4.16039i	0.138317	−	0.328908i
$161$	−4.06447	−	12.5092i	−0.320325	−	0.985859i
$162$		0			0
$163$	−21.2026	−	6.88916i	−1.66072	−	0.539600i	−0.679697	−	0.733493i	$-0.737889\pi$
$163$	−21.2026	−	6.88916i	−1.66072	−	0.539600i	−0.981023	+	0.193893i	$0.937889\pi$
$164$	0.206976	+	0.637008i	0.0161621	+	0.0497420i
$165$		0			0
$166$	0.106361	−	0.327345i	0.00825520	−	0.0254069i
$167$	−3.80062	+	5.23111i	−0.294101	+	0.404795i	−0.930341	−	0.366696i	$-0.880489\pi$
$167$	−3.80062	+	5.23111i	−0.294101	+	0.404795i	0.636240	+	0.771491i	$0.280489\pi$
$168$		0			0
$169$	−9.04387	−	6.57075i	−0.695682	−	0.505443i
$170$	4.92657	−	5.70578i	0.377851	−	0.437613i
$171$		0			0
$172$	−1.70139	−	2.34176i	−0.129730	−	0.178558i
$173$	−11.2396	+	3.65198i	−0.854533	+	0.277655i	−0.703344	−	0.710850i	$-0.748310\pi$
$173$	−11.2396	+	3.65198i	−0.854533	+	0.277655i	−0.151190	+	0.988505i	$0.548310\pi$
$174$		0			0
$175$	5.34400	−	5.23014i	0.403969	−	0.395361i
$176$	−10.8191			−0.815520
$177$		0			0
$178$	−0.387606	−	0.533494i	−0.0290523	−	0.0399871i
$179$	−12.6001	+	9.15450i	−0.941775	+	0.684240i	−0.948847	−	0.315735i	$-0.897749\pi$
$179$	−12.6001	+	9.15450i	−0.941775	+	0.684240i	0.00707213	+	0.999975i	$0.497749\pi$
$180$		0			0
$181$	11.7952	+	8.56974i	0.876733	+	0.636984i	0.932385	−	0.361466i	$-0.117724\pi$
$181$	11.7952	+	8.56974i	0.876733	+	0.636984i	−0.0556522	+	0.998450i	$0.517724\pi$
$182$			3.10103i			0.229864i
$183$		0			0
$184$	6.84463	−	21.0656i	0.504593	−	1.55298i
$185$	−16.5033	−	14.2495i	−1.21335	−	1.04764i
$186$		0			0
$187$	−4.91672	−	1.59754i	−0.359546	−	0.116824i
$188$	−2.28746	−	0.743241i	−0.166830	−	0.0542064i
$189$		0			0
$190$	−14.8510	−	12.8229i	−1.07741	−	0.930271i
$191$	6.48577	−	19.9611i	0.469294	−	1.44434i	−0.384207	−	0.923247i	$-0.625525\pi$
$191$	6.48577	−	19.9611i	0.469294	−	1.44434i	0.853501	−	0.521091i	$-0.174475\pi$
$192$		0			0
$193$			22.7094i			1.63466i	0.576173	+	0.817328i	$0.304546\pi$
$193$			22.7094i			1.63466i	−0.576173	+	0.817328i	$0.695454\pi$
$194$	−15.5319	−	11.2846i	−1.11512	−	0.810185i
$195$		0			0
$196$	1.39111	−	1.01070i	0.0993651	−	0.0721930i
$197$	−0.795517	−	1.09494i	−0.0566782	−	0.0780109i	0.779737	−	0.626107i	$-0.215353\pi$
$197$	−0.795517	−	1.09494i	−0.0566782	−	0.0780109i	−0.836415	+	0.548096i	$0.815353\pi$
$198$		0			0
$199$	8.96061			0.635201			0.317600	−	0.948225i	$-0.397123\pi$
$199$	8.96061			0.635201			0.317600	+	0.948225i	$0.397123\pi$
$200$	12.4576	−	1.83582i	0.880888	−	0.129812i
$201$		0			0
$202$	11.9796	−	3.89241i	0.842882	−	0.273869i
$203$	6.94449	+	9.55827i	0.487408	+	0.670859i
$204$		0			0
$205$	−2.71151	+	3.14038i	−0.189380	+	0.219334i
$206$	3.10780	+	2.25795i	0.216530	+	0.157319i
$207$		0			0
$208$	−3.64219	+	5.01304i	−0.252540	+	0.347592i
$209$	−4.15808	+	12.7973i	−0.287621	+	0.885205i
$210$		0			0
$211$	1.80461	+	5.55401i	0.124234	+	0.382354i	0.993761	−	0.111532i	$-0.0355759\pi$
$211$	1.80461	+	5.55401i	0.124234	+	0.382354i	−0.869527	+	0.493886i	$0.835576\pi$
$212$	1.43212	+	0.465325i	0.0983586	+	0.0319586i
$213$		0			0
$214$	0.859440	+	2.64508i	0.0587501	+	0.180814i
$215$	6.95077	−	16.5284i	0.474039	−	1.12723i
$216$		0			0
$217$	3.24993	−	4.47314i	0.220619	−	0.303656i
$218$			4.52939i			0.306769i
$219$		0			0
$220$	0.984992	+	1.62696i	0.0664081	+	0.109689i
$221$	−2.39541	+	1.74036i	−0.161132	+	0.117070i
$222$		0			0
$223$	7.43818	−	2.41681i	0.498098	−	0.161842i	−0.0491848	−	0.998790i	$-0.515662\pi$
$223$	7.43818	−	2.41681i	0.498098	−	0.161842i	0.547283	+	0.836948i	$0.315662\pi$
$224$	−3.01853			−0.201684
$225$		0			0
$226$	21.2604			1.41422
$227$	−15.5107	+	5.03975i	−1.02948	+	0.334500i	−0.774586	−	0.632468i	$-0.782042\pi$
$227$	−15.5107	+	5.03975i	−1.02948	+	0.334500i	−0.254898	+	0.966968i	$0.582042\pi$
$228$		0			0
$229$	−17.5628	+	12.7601i	−1.16058	+	0.843211i	−0.989851	−	0.142107i	$-0.954612\pi$
$229$	−17.5628	+	12.7601i	−1.16058	+	0.843211i	−0.170729	+	0.985318i	$0.554612\pi$
$230$	−29.4207	+	6.89598i	−1.93995	+	0.454708i
$231$		0			0
$232$			19.8961i			1.30624i
$233$	7.95512	−	10.9493i	0.521157	−	0.717312i	−0.464593	−	0.885524i	$-0.653799\pi$
$233$	7.95512	−	10.9493i	0.521157	−	0.717312i	0.985751	+	0.168213i	$0.0537995\pi$
$234$		0			0
$235$	−3.40003	−	14.5057i	−0.221793	−	0.946249i
$236$	−1.23424	−	3.79860i	−0.0803421	−	0.247268i
$237$		0			0
$238$	−4.79495	−	1.55797i	−0.310810	−	0.100988i
$239$	−3.25514	−	10.0183i	−0.210557	−	0.648028i	−0.999439	−	0.0334838i	$-0.989340\pi$
$239$	−3.25514	−	10.0183i	−0.210557	−	0.648028i	0.788882	−	0.614545i	$-0.210660\pi$
$240$		0			0
$241$	6.02082	−	18.5302i	0.387835	−	1.19363i	−0.546567	−	0.837415i	$-0.684066\pi$
$241$	6.02082	−	18.5302i	0.387835	−	1.19363i	0.934403	−	0.356219i	$-0.115934\pi$
$242$	−4.92047	+	6.77244i	−0.316300	+	0.435349i
$243$		0			0
$244$	−3.57371	−	2.59645i	−0.228783	−	0.166221i
$245$	9.81861	+	4.12907i	0.627288	+	0.263797i
$246$		0			0
$247$	4.52983	+	6.23478i	0.288226	+	0.396709i
$248$	8.85537	−	2.87728i	0.562317	−	0.182708i
$249$		0			0
$250$	−10.9445	−	13.2416i	−0.692192	−	0.837472i
$251$	20.9446			1.32201			0.661007	−	0.750380i	$-0.270129\pi$
$251$	20.9446			1.32201			0.661007	+	0.750380i	$0.270129\pi$
$252$		0			0
$253$	12.1808	+	16.7655i	0.765803	+	1.05404i
$254$	−7.13529	+	5.18409i	−0.447708	+	0.325279i
$255$		0			0
$256$	−6.79428	−	4.93633i	−0.424643	−	0.308521i
$257$		−	1.67121i		−	0.104247i	−0.998641	−	0.0521237i	$-0.983401\pi$
$257$		−	1.67121i		−	0.104247i	0.998641	−	0.0521237i	$-0.0165990\pi$
$258$		0			0
$259$	−4.50625	+	13.8688i	−0.280005	+	0.861766i
$260$	1.08544	+	0.0913088i	0.0673164	+	0.00566273i
$261$		0			0
$262$	6.36789	+	2.06905i	0.393409	+	0.127826i
$263$	−7.18682	−	2.33514i	−0.443158	−	0.143991i	0.0789341	−	0.996880i	$-0.474848\pi$
$263$	−7.18682	−	2.33514i	−0.443158	−	0.143991i	−0.522092	+	0.852889i	$0.674848\pi$
$264$		0			0
$265$	2.12867	+	9.08168i	0.130763	+	0.557883i
$266$	−4.05510	+	12.4803i	−0.248634	+	0.765218i
$267$		0			0
$268$			1.55710i			0.0951151i
$269$	9.12904	+	6.63264i	0.556608	+	0.404399i	0.830216	−	0.557442i	$-0.188217\pi$
$269$	9.12904	+	6.63264i	0.556608	+	0.404399i	−0.273608	+	0.961841i	$0.588217\pi$
$270$		0			0
$271$	8.87912	−	6.45106i	0.539368	−	0.391874i	−0.284482	−	0.958681i	$-0.591822\pi$
$271$	8.87912	−	6.45106i	0.539368	−	0.391874i	0.823850	+	0.566808i	$0.191822\pi$
$272$	−5.92153	−	8.15029i	−0.359045	−	0.494184i
$273$		0			0
$274$	−3.03407			−0.183295
$275$	−5.46130	+	10.4390i	−0.329329	+	0.629495i
$276$		0			0
$277$	−5.46964	+	1.77719i	−0.328639	+	0.106781i	−0.468689	−	0.883363i	$-0.655274\pi$
$277$	−5.46964	+	1.77719i	−0.328639	+	0.106781i	0.140050	+	0.990144i	$0.455274\pi$
$278$	1.51649	+	2.08727i	0.0909531	+	0.125186i
$279$		0			0
$280$	−4.36162	−	7.20429i	−0.260657	−	0.430539i
$281$	6.87633	+	4.99595i	0.410208	+	0.298033i	0.773686	−	0.633569i	$-0.218411\pi$
$281$	6.87633	+	4.99595i	0.410208	+	0.298033i	−0.363478	+	0.931603i	$0.618411\pi$
$282$		0			0
$283$	−10.1245	+	13.9352i	−0.601839	+	0.828360i	−0.995875	−	0.0907350i	$-0.971078\pi$
$283$	−10.1245	+	13.9352i	−0.601839	+	0.828360i	0.394036	+	0.919095i	$0.371078\pi$
$284$	0.644468	−	1.98347i	0.0382421	−	0.117697i
$285$		0			0
$286$	−1.50982	−	4.64675i	−0.0892776	−	0.274768i
$287$	2.63907	+	0.857487i	0.155780	+	0.0506158i
$288$		0			0
$289$	3.76573	+	11.5897i	0.221513	+	0.681748i
$290$	23.2197	−	14.0577i	1.36351	−	0.825496i
$291$		0			0
$292$	−1.46971	+	2.02289i	−0.0860084	+	0.118380i
$293$		−	9.38764i		−	0.548432i	−0.961668	−	0.274216i	$-0.911582\pi$
$293$		−	9.38764i		−	0.548432i	0.961668	−	0.274216i	$-0.0884183\pi$
$294$		0			0
$295$	16.1693	−	18.7267i	0.941411	−	1.09031i
$296$	−19.8672	+	14.4344i	−1.15476	+	0.838980i
$297$		0			0
$298$	10.7924	−	3.50665i	0.625185	−	0.203135i
$299$	11.8689			0.686397
$300$		0			0
$301$	−11.9920			−0.691207
$302$	6.22732	−	2.02338i	0.358342	−	0.116432i
$303$		0			0
$304$	−21.2136	+	15.4126i	−1.21668	+	0.883973i
$305$	2.29373	−	27.2670i	0.131338	−	1.56130i
$306$		0			0
$307$		−	10.6465i		−	0.607627i	−0.952731	−	0.303814i	$-0.901740\pi$
$307$		−	10.6465i		−	0.607627i	0.952731	−	0.303814i	$-0.0982600\pi$
$308$	0.747662	−	1.02907i	0.0426020	−	0.0586366i
$309$		0			0
$310$	−9.61475	−	8.30171i	−0.546081	−	0.471505i
$311$	8.45383	+	26.0182i	0.479373	+	1.47536i	0.839969	+	0.542635i	$0.182573\pi$
$311$	8.45383	+	26.0182i	0.479373	+	1.47536i	−0.360596	+	0.932722i	$0.617427\pi$
$312$		0			0
$313$	−1.89744	−	0.616517i	−0.107250	−	0.0348476i	0.254900	−	0.966967i	$-0.417957\pi$
$313$	−1.89744	−	0.616517i	−0.107250	−	0.0348476i	−0.362150	+	0.932120i	$0.617957\pi$
$314$	7.62433	+	23.4653i	0.430266	+	1.32422i
$315$		0			0
$316$	−1.19007	+	3.66267i	−0.0669469	+	0.206041i
$317$	5.08361	−	6.99699i	0.285524	−	0.392990i	−0.642030	−	0.766680i	$-0.721907\pi$
$317$	5.08361	−	6.99699i	0.285524	−	0.392990i	0.927554	+	0.373690i	$0.121907\pi$
$318$		0			0
$319$	−15.0597	−	10.9415i	−0.843182	−	0.612607i
$320$	1.13999	−	13.5517i	0.0637271	−	0.757564i
$321$		0			0
$322$	11.8792	+	16.3503i	0.662000	+	0.911165i
$323$	−11.9163	+	3.87184i	−0.663040	+	0.215435i
$324$		0			0
$325$	2.99840	+	6.04473i	0.166322	+	0.335301i
$326$	34.2554			1.89723
$327$		0			0
$328$	2.74669	+	3.78049i	0.151661	+	0.208743i
$329$	−8.06141	+	5.85696i	−0.444440	+	0.322905i
$330$		0			0
$331$	3.19020	+	2.31782i	0.175349	+	0.127399i	0.671998	−	0.740553i	$-0.265436\pi$
$331$	3.19020	+	2.31782i	0.175349	+	0.127399i	−0.496649	+	0.867952i	$0.665436\pi$
$332$			0.0808598i			0.00443776i
$333$		0			0
$334$	3.07018	−	9.44905i	0.167993	−	0.517029i
$335$	−8.25113	+	4.99539i	−0.450807	+	0.272927i
$336$		0			0
$337$	−3.76115	−	1.22207i	−0.204883	−	0.0665706i	0.204778	−	0.978809i	$-0.434353\pi$
$337$	−3.76115	−	1.22207i	−0.204883	−	0.0665706i	−0.409661	+	0.912238i	$0.634353\pi$
$338$	16.3361	+	5.30792i	0.888567	+	0.288713i
$339$		0			0
$340$	−0.686518	+	1.63249i	−0.0372317	+	0.0885341i
$341$	−2.69199	+	8.28511i	−0.145780	+	0.448664i
$342$		0			0
$343$		−	17.5923i		−	0.949893i
$344$	−16.3379	−	11.8701i	−0.880878	−	0.639995i
$345$		0			0
$346$	14.6909	−	10.6736i	0.789789	−	0.573815i
$347$	5.87548	+	8.08690i	0.315412	+	0.434127i	0.937060	−	0.349170i	$-0.113536\pi$
$347$	5.87548	+	8.08690i	0.315412	+	0.434127i	−0.621647	+	0.783297i	$0.713536\pi$
$348$		0			0
$349$	−18.4534			−0.987789			−0.493895	−	0.869522i	$-0.664427\pi$
$349$	−18.4534			−0.987789			−0.493895	+	0.869522i	$0.664427\pi$
$350$	−5.32605	+	10.1805i	−0.284689	+	0.544169i
$351$		0			0
$352$	4.52312	−	1.46965i	0.241083	−	0.0783327i
$353$	5.48050	+	7.54326i	0.291697	+	0.401487i	0.929565	−	0.368659i	$-0.120183\pi$
$353$	5.48050	+	7.54326i	0.291697	+	0.401487i	−0.637867	+	0.770146i	$0.720183\pi$
$354$		0			0
$355$	12.5780	−	2.94818i	0.667571	−	0.156473i
$356$	0.125332	+	0.0910592i	0.00664260	+	0.00482613i
$357$		0			0
$358$	14.0663	−	19.3606i	0.743428	−	1.02324i
$359$	8.94412	−	27.5272i	0.472052	−	1.45283i	−0.377839	−	0.925871i	$-0.623333\pi$
$359$	8.94412	−	27.5272i	0.472052	−	1.45283i	0.849892	−	0.526957i	$-0.176667\pi$
$360$		0			0
$361$	4.20632	+	12.9457i	0.221385	+	0.681354i
$362$	−21.3060	−	6.92273i	−1.11982	−	0.363850i
$363$		0			0
$364$	−0.225124	−	0.692860i	−0.0117997	−	0.0363157i
$365$	−15.4344	−	1.29836i	−0.807872	−	0.0679591i
$366$		0			0
$367$	2.35037	−	3.23501i	0.122688	−	0.168866i	−0.743255	−	0.669008i	$-0.766719\pi$
$367$	2.35037	−	3.23501i	0.122688	−	0.168866i	0.865943	+	0.500142i	$0.166719\pi$
$368$			40.3836i			2.10514i
$369$		0			0
$370$	30.8829	+	12.9873i	1.60553	+	0.675180i
$371$	5.04705	−	3.66690i	0.262030	−	0.190376i
$372$		0			0
$373$	3.01732	−	0.980386i	0.156231	−	0.0507625i	−0.229857	−	0.973224i	$-0.573826\pi$
$373$	3.01732	−	0.980386i	0.156231	−	0.0507625i	0.386088	+	0.922462i	$0.373826\pi$
$374$	7.94355			0.410751
$375$		0			0
$376$	−16.7803			−0.865377
$377$	−10.1395	+	3.29453i	−0.522212	+	0.169677i
$378$		0			0
$379$	23.0736	−	16.7640i	1.18521	−	0.861107i	0.192462	−	0.981304i	$-0.438353\pi$
$379$	23.0736	−	16.7640i	1.18521	−	0.861107i	0.992750	+	0.120198i	$0.0383528\pi$
$380$	4.24905	+	1.78687i	0.217972	+	0.0916647i
$381$		0			0
$382$			32.2497i			1.65004i
$383$	6.73667	−	9.27224i	0.344228	−	0.473789i	−0.601442	−	0.798916i	$-0.705407\pi$
$383$	6.73667	−	9.27224i	0.344228	−	0.473789i	0.945670	+	0.325127i	$0.105407\pi$
$384$		0			0
$385$	7.85166	+	0.660490i	0.400158	+	0.0336617i
$386$	−10.7828	−	33.1862i	−0.548832	−	1.68913i
$387$		0			0
$388$	4.28949	+	1.39374i	0.217766	+	0.0707564i
$389$	10.5827	+	32.5702i	0.536564	+	1.65137i	0.740245	+	0.672337i	$0.234709\pi$
$389$	10.5827	+	32.5702i	0.536564	+	1.65137i	−0.203681	+	0.979037i	$0.565291\pi$
$390$		0			0
$391$	−5.96301	+	18.3522i	−0.301562	+	0.928113i
$392$	7.05140	−	9.70541i	0.356149	−	0.490197i
$393$		0			0
$394$	1.68242	+	1.22235i	0.0847591	+	0.0615811i
$395$	−23.2265	+	5.44411i	−1.16865	+	0.273923i
$396$		0			0
$397$	−11.7753	−	16.2073i	−0.590986	−	0.813422i	0.403860	−	0.914821i	$-0.367668\pi$
$397$	−11.7753	−	16.2073i	−0.590986	−	0.813422i	−0.994846	+	0.101399i	$0.967668\pi$
$398$	−13.0945	+	4.25467i	−0.656369	+	0.213267i
$399$		0			0
$400$	−20.5670	+	10.2020i	−1.02835	+	0.510098i
$401$	−4.98200			−0.248789			−0.124395	−	0.992233i	$-0.539699\pi$
$401$	−4.98200			−0.248789			−0.124395	+	0.992233i	$0.539699\pi$
$402$		0			0
$403$	2.93267	+	4.03647i	0.146087	+	0.201071i
$404$	−2.39401	+	1.73935i	−0.119107	+	0.0865361i
$405$		0			0
$406$	−14.6867	−	10.6705i	−0.728890	−	0.529570i
$407$		−	22.9758i		−	1.13887i
$408$		0			0
$409$	−7.37286	+	22.6913i	−0.364565	+	1.12201i	0.585689	+	0.810536i	$0.300824\pi$
$409$	−7.37286	+	22.6913i	−0.364565	+	1.12201i	−0.950253	+	0.311478i	$0.899176\pi$
$410$	2.47134	−	5.87665i	0.122051	−	0.290227i
$411$		0			0
$412$	−0.858290	−	0.278875i	−0.0422849	−	0.0137392i
$413$	−15.7373	−	5.11335i	−0.774381	−	0.251612i
$414$		0			0
$415$	−0.428478	+	0.259409i	−0.0210332	+	0.0127339i
$416$	0.841718	−	2.59054i	0.0412686	−	0.127012i
$417$		0			0
$418$		−	20.6755i		−	1.01127i
$419$	−0.390391	−	0.283636i	−0.0190719	−	0.0138565i	0.578208	−	0.815889i	$-0.303752\pi$
$419$	−0.390391	−	0.283636i	−0.0190719	−	0.0138565i	−0.597280	+	0.802033i	$0.703752\pi$
$420$		0			0
$421$	14.3344	−	10.4146i	0.698616	−	0.507575i	−0.180865	−	0.983508i	$-0.557890\pi$
$421$	14.3344	−	10.4146i	0.698616	−	0.507575i	0.879481	+	0.475933i	$0.157890\pi$
$422$	−5.27430	−	7.25945i	−0.256749	−	0.353385i
$423$		0			0
$424$	10.5057			0.510203
$425$	−10.8530	+	1.59936i	−0.526450	+	0.0775804i
$426$		0			0
$427$	−17.4050	+	5.65523i	−0.842288	+	0.273676i
$428$	−0.384047	−	0.528596i	−0.0185636	−	0.0255506i
$429$		0			0
$430$	−2.30946	+	27.4540i	−0.111372	+	1.32395i
$431$	21.6866	+	15.7562i	1.04461	+	0.758952i	0.971180	−	0.238349i	$-0.0766061\pi$
$431$	21.6866	+	15.7562i	1.04461	+	0.758952i	0.0734279	+	0.997301i	$0.476606\pi$
$432$		0			0
$433$	−5.42593	+	7.46816i	−0.260754	+	0.358897i	−0.919241	−	0.393695i	$-0.871197\pi$
$433$	−5.42593	+	7.46816i	−0.260754	+	0.358897i	0.658487	+	0.752592i	$0.271197\pi$
$434$	−2.62532	+	8.07992i	−0.126020	+	0.387848i
$435$		0			0
$436$	−0.328818	−	1.01200i	−0.0157475	−	0.0484659i
$437$	47.7673	+	15.5205i	2.28502	+	0.742448i
$438$		0			0
$439$	−0.309760	−	0.953343i	−0.0147840	−	0.0455006i	0.943392	−	0.331679i	$-0.107615\pi$
$439$	−0.309760	−	0.953343i	−0.0147840	−	0.0455006i	−0.958176	+	0.286178i	$0.907615\pi$
$440$	10.0433	+	8.67173i	0.478795	+	0.413408i
$441$		0			0
$442$	2.67415	−	3.68065i	0.127196	−	0.175071i
$443$			26.2872i			1.24894i	0.781048	+	0.624471i	$0.214685\pi$
$443$			26.2872i			1.24894i	−0.781048	+	0.624471i	$0.785315\pi$
$444$		0			0
$445$	−0.0804425	+	0.956269i	−0.00381334	+	0.0453315i
$446$	−9.72219	+	7.06358i	−0.460359	+	0.334470i
$447$		0			0
$448$	−8.65032	+	2.81066i	−0.408689	+	0.132791i
$449$	4.75449			0.224378			0.112189	−	0.993687i	$-0.464214\pi$
$449$	4.75449			0.224378			0.112189	+	0.993687i	$0.464214\pi$
$450$		0			0
$451$	−4.37202			−0.205870
$452$	−4.75019	+	1.54343i	−0.223430	+	0.0725968i
$453$		0			0
$454$	20.2736	−	14.7296i	0.951485	−	0.691294i
$455$	2.94926	−	3.41572i	0.138263	−	0.160132i
$456$		0			0
$457$		−	15.9703i		−	0.747059i	−0.927618	−	0.373529i	$-0.878148\pi$
$457$		−	15.9703i		−	0.747059i	0.927618	−	0.373529i	$-0.121852\pi$
$458$	19.6065	−	26.9860i	0.916151	−	1.26097i
$459$		0			0
$460$	6.07282	−	3.67660i	0.283146	−	0.171422i
$461$	−12.2852	−	37.8100i	−0.572180	−	1.76099i	−0.645588	−	0.763686i	$-0.723387\pi$
$461$	−12.2852	−	37.8100i	−0.572180	−	1.76099i	0.0734077	−	0.997302i	$-0.476613\pi$
$462$		0			0
$463$	−24.8425	−	8.07181i	−1.15453	−	0.375129i	−0.331681	−	0.943392i	$-0.607616\pi$
$463$	−24.8425	−	8.07181i	−1.15453	−	0.375129i	−0.822847	+	0.568263i	$0.807616\pi$
$464$	−11.2095	−	34.4994i	−0.520389	−	1.60159i
$465$		0			0
$466$	−6.42623	+	19.7779i	−0.297689	+	0.916194i
$467$	2.26417	−	3.11637i	0.104773	−	0.144208i	−0.753411	−	0.657550i	$-0.771593\pi$
$467$	2.26417	−	3.11637i	0.104773	−	0.144208i	0.858184	+	0.513342i	$0.171593\pi$
$468$		0			0
$469$	5.21893	+	3.79177i	0.240988	+	0.175088i
$470$	11.8562	+	19.5834i	0.546886	+	0.903317i
$471$		0			0
$472$	−16.3790	−	22.5438i	−0.753906	−	1.03766i
$473$	17.9695	−	5.83863i	0.826236	−	0.268460i
$474$		0			0
$475$	4.16283	+	28.2484i	0.191004	+	1.29612i
$476$	1.18443			0.0542884
$477$		0			0
$478$	9.51374	+	13.0945i	0.435148	+	0.598930i
$479$	11.5445	−	8.38758i	0.527483	−	0.383239i	−0.291933	−	0.956439i	$-0.594298\pi$
$479$	11.5445	−	8.38758i	0.527483	−	0.383239i	0.819415	+	0.573200i	$0.194298\pi$
$480$		0			0
$481$	−10.6458	−	7.73466i	−0.485409	−	0.352670i
$482$			29.9377i			1.36363i
$483$		0			0
$484$	0.607720	−	1.87037i	0.0276236	−	0.0850167i
$485$	6.37580	+	27.2014i	0.289510	+	1.23515i
$486$		0			0
$487$	23.6073	+	7.67049i	1.06975	+	0.347583i	0.790390	−	0.612604i	$-0.209878\pi$
$487$	23.6073	+	7.67049i	1.06975	+	0.347583i	0.279360	+	0.960186i	$0.409878\pi$
$488$	−29.3103	−	9.52349i	−1.32681	−	0.431108i
$489$		0			0
$490$	−16.3089	−	1.37192i	−0.736762	−	0.0619772i
$491$	−3.55040	+	10.9270i	−0.160227	+	0.493129i	−0.998653	−	0.0518868i	$-0.983476\pi$
$491$	−3.55040	+	10.9270i	−0.160227	+	0.493129i	0.838426	+	0.545016i	$0.183476\pi$
$492$		0			0
$493$		−	17.3334i		−	0.780656i
$494$	−9.58003	−	6.96030i	−0.431026	−	0.313159i
$495$		0			0
$496$	−13.7340	+	9.97831i	−0.616673	+	0.448039i
$497$	−5.07860	−	6.99010i	−0.227806	−	0.313549i
$498$		0			0
$499$	4.17487			0.186893			0.0934465	−	0.995624i	$-0.470212\pi$
$499$	4.17487			0.186893			0.0934465	+	0.995624i	$0.470212\pi$
$500$	3.40661	+	2.16402i	0.152348	+	0.0967779i
$501$		0			0
$502$	−30.6073	+	9.94491i	−1.36607	+	0.443863i
$503$	−22.7569	−	31.3221i	−1.01468	−	1.39658i	−0.915869	−	0.401478i	$-0.868497\pi$
$503$	−22.7569	−	31.3221i	−1.01468	−	1.39658i	−0.0988094	−	0.995106i	$-0.531503\pi$
$504$		0			0
$505$	−16.8972	−	7.10587i	−0.751916	−	0.316207i
$506$	−25.7610	−	18.7164i	−1.14521	−	0.832047i
$507$		0			0
$508$	1.21788	−	1.67627i	0.0540349	−	0.0743726i
$509$	9.32603	−	28.7026i	0.413369	−	1.27222i	−0.500333	−	0.865833i	$-0.666789\pi$
$509$	9.32603	−	28.7026i	0.413369	−	1.27222i	0.913702	−	0.406385i	$-0.133211\pi$
$510$		0			0
$511$	3.20112	+	9.85205i	0.141609	+	0.435829i
$512$	−13.1814	−	4.28289i	−0.582540	−	0.189279i
$513$		0			0
$514$	0.793523	+	2.44221i	0.0350008	+	0.107721i
$515$	−1.27574	−	5.44277i	−0.0562159	−	0.239837i
$516$		0			0
$517$	9.22804	−	12.7013i	0.405849	−	0.558603i
$518$		−	22.4067i		−	0.984496i
$519$		0			0
$520$	7.39907	−	1.73428i	0.324471	−	0.0760533i
$521$	−20.6183	+	14.9801i	−0.903304	+	0.656288i	−0.939312	−	0.343063i	$-0.888536\pi$
$521$	−20.6183	+	14.9801i	−0.903304	+	0.656288i	0.0360088	+	0.999351i	$0.488536\pi$
$522$		0			0
$523$	−3.70132	+	1.20263i	−0.161847	+	0.0525874i	−0.388820	−	0.921314i	$-0.627117\pi$
$523$	−3.70132	+	1.20263i	−0.161847	+	0.0525874i	0.226973	+	0.973901i	$0.427117\pi$
$524$	−1.57298			−0.0687158
$525$		0			0
$526$	11.6112			0.506271
$527$	−7.71476	+	2.50668i	−0.336060	+	0.109193i
$528$		0			0
$529$	43.9719	−	31.9474i	1.91182	−	1.38902i
$530$	−7.42288	−	12.2607i	−0.322429	−	0.532571i
$531$		0			0
$532$		−	3.08285i		−	0.133659i
$533$	−1.47182	+	2.02578i	−0.0637514	+	0.0877463i
$534$		0			0
$535$	1.56897	−	3.73088i	0.0678324	−	0.161300i
$536$	3.35700	+	10.3318i	0.145000	+	0.446265i
$537$		0			0
$538$	−16.4900	−	5.35792i	−0.710933	−	0.230996i
$539$	3.46841	+	10.6747i	0.149395	+	0.459790i
$540$		0			0
$541$	12.4270	−	38.2465i	0.534280	−	1.64435i	−0.210919	−	0.977504i	$-0.567646\pi$
$541$	12.4270	−	38.2465i	0.534280	−	1.64435i	0.745199	−	0.666842i	$-0.232354\pi$
$542$	−9.91235	+	13.6432i	−0.425772	+	0.586025i
$543$		0			0
$544$	3.58273	+	2.60300i	0.153608	+	0.111603i
$545$	4.30771	−	4.98904i	0.184522	−	0.213707i
$546$		0			0
$547$	4.33740	+	5.96992i	0.185454	+	0.255255i	0.891613	−	0.452797i	$-0.149574\pi$
$547$	4.33740	+	5.96992i	0.185454	+	0.255255i	−0.706160	+	0.708053i	$0.749574\pi$
$548$	0.677900	−	0.220263i	0.0289584	−	0.00940917i
$549$		0			0
$550$	3.02420	−	17.8481i	0.128952	−	0.761045i
$551$	−45.1154			−1.92198
$552$		0			0
$553$	9.37814	+	12.9079i	0.398799	+	0.548900i
$554$	7.14917	−	5.19418i	0.303739	−	0.220679i
$555$		0			0
$556$	−0.490357	−	0.356265i	−0.0207958	−	0.0151090i
$557$			1.52499i			0.0646160i	0.999478	+	0.0323080i	$0.0102857\pi$
$557$			1.52499i			0.0646160i	−0.999478	+	0.0323080i	$0.989714\pi$
$558$		0			0
$559$	3.34398	−	10.2917i	0.141435	−	0.435293i
$560$	11.6219	+	10.0347i	0.491114	+	0.424045i
$561$		0			0
$562$	−12.4209	−	4.03578i	−0.523942	−	0.170239i
$563$	−13.1203	−	4.26305i	−0.552955	−	0.179666i	0.0191938	−	0.999816i	$-0.493890\pi$
$563$	−13.1203	−	4.26305i	−0.552955	−	0.179666i	−0.572149	+	0.820150i	$0.693890\pi$
$564$		0			0
$565$	−23.4179	−	20.2198i	−0.985199	−	0.850655i
$566$	8.17867	−	25.1714i	0.343775	−	1.05803i
$567$		0			0
$568$		−	14.5503i		−	0.610516i
$569$	6.87586	+	4.99561i	0.288251	+	0.209427i	0.722508	−	0.691362i	$-0.242989\pi$
$569$	6.87586	+	4.99561i	0.288251	+	0.209427i	−0.434257	+	0.900789i	$0.642989\pi$
$570$		0			0
$571$	−31.8130	+	23.1135i	−1.33133	+	0.967269i	−0.331617	+	0.943414i	$0.607594\pi$
$571$	−31.8130	+	23.1135i	−1.33133	+	0.967269i	−0.999715	+	0.0238553i	$0.992406\pi$
$572$	0.674675	+	0.928611i	0.0282096	+	0.0388272i
$573$		0			0
$574$	−4.26374			−0.177965
$575$	38.9648	+	20.3850i	1.62495	+	0.850112i
$576$		0			0
$577$	23.3800	−	7.59664i	0.973324	−	0.316252i	0.221167	−	0.975236i	$-0.429013\pi$
$577$	23.3800	−	7.59664i	0.973324	−	0.316252i	0.752157	+	0.658984i	$0.229013\pi$
$578$	−11.0060	−	15.1485i	−0.457791	−	0.630095i
$579$		0			0
$580$	−4.16742	+	4.82656i	−0.173043	+	0.200412i
$581$	0.271017	+	0.196905i	0.0112437	+	0.00816901i
$582$		0			0
$583$	−5.77745	+	7.95197i	−0.239277	+	0.329337i
$584$	−5.39074	+	16.5910i	−0.223070	+	0.686540i
$585$		0			0
$586$	4.45743	+	13.7186i	0.184135	+	0.566708i
$587$	−8.79033	−	2.85615i	−0.362816	−	0.117886i	0.121936	−	0.992538i	$-0.461090\pi$
$587$	−8.79033	−	2.85615i	−0.362816	−	0.117886i	−0.484751	+	0.874652i	$0.661090\pi$
$588$		0			0
$589$	6.52439	+	20.0800i	0.268833	+	0.827383i
$590$	−14.7371	+	35.0436i	−0.606715	+	1.44272i
$591$		0			0
$592$	26.3169	−	36.2221i	1.08162	−	1.48872i
$593$			6.07888i			0.249630i	0.992180	+	0.124815i	$0.0398337\pi$
$593$			6.07888i			0.249630i	−0.992180	+	0.124815i	$0.960166\pi$
$594$		0			0
$595$	3.79982	+	6.27634i	0.155778	+	0.257305i
$596$	−2.15676	+	1.56698i	−0.0883442	+	0.0641858i
$597$		0			0
$598$	−17.3446	+	5.63559i	−0.709272	+	0.230456i
$599$	6.40129			0.261550			0.130775	−	0.991412i	$-0.458254\pi$
$599$	6.40129			0.261550			0.130775	+	0.991412i	$0.458254\pi$
$600$		0			0
$601$	−38.4675			−1.56912			−0.784560	−	0.620052i	$-0.787111\pi$
$601$	−38.4675			−1.56912			−0.784560	+	0.620052i	$0.787111\pi$
$602$	17.5244	−	5.69403i	0.714242	−	0.232071i
$603$		0			0
$604$	−1.24447	+	0.904162i	−0.0506369	+	0.0367898i
$605$	11.8608	−	2.78007i	0.482209	−	0.113026i
$606$		0			0
$607$		−	5.22464i		−	0.212062i	−0.994363	−	0.106031i	$-0.966186\pi$
$607$		−	5.22464i		−	0.212062i	0.994363	−	0.106031i	$-0.0338142\pi$
$608$	6.77511	−	9.32514i	0.274767	−	0.378184i
$609$		0			0
$610$	9.59495	+	40.9355i	0.388488	+	1.65743i
$611$	−2.77860	−	8.55164i	−0.112410	−	0.345962i
$612$		0			0
$613$	28.3560	+	9.21343i	1.14529	+	0.372127i	0.819367	−	0.573270i	$-0.194325\pi$
$613$	28.3560	+	9.21343i	1.14529	+	0.372127i	0.325922	+	0.945397i	$0.394325\pi$
$614$	5.05516	+	15.5582i	0.204010	+	0.627877i
$615$		0			0
$616$	2.74234	−	8.44005i	0.110492	−	0.340059i
$617$	13.6969	−	18.8521i	0.551415	−	0.758958i	−0.438788	−	0.898591i	$-0.644592\pi$
$617$	13.6969	−	18.8521i	0.551415	−	0.758958i	0.990203	+	0.139633i	$0.0445921\pi$
$618$		0			0
$619$	−0.191326	−	0.139007i	−0.00769006	−	0.00558715i	0.583934	−	0.811801i	$-0.301513\pi$
$619$	−0.191326	−	0.139007i	−0.00769006	−	0.00558715i	−0.591624	+	0.806214i	$0.701513\pi$
$620$	2.75089	+	1.15684i	0.110478	+	0.0464600i
$621$		0			0
$622$	−24.7079	−	34.0075i	−0.990696	−	1.36358i
$623$	0.610405	−	0.198333i	0.0244554	−	0.00794603i
$624$		0			0
$625$	−0.538331	+	24.9942i	−0.0215332	+	0.999768i
$626$	3.06555			0.122524
$627$		0			0
$628$	−3.40699	−	4.68932i	−0.135954	−	0.187124i
$629$	17.3082	−	12.5751i	0.690123	−	0.501404i
$630$		0			0
$631$	14.4643	+	10.5090i	0.575816	+	0.418355i	0.837213	−	0.546876i	$-0.184183\pi$
$631$	14.4643	+	10.5090i	0.575816	+	0.418355i	−0.261397	+	0.965231i	$0.584183\pi$
$632$			26.8685i			1.06877i
$633$		0			0
$634$	−4.10659	+	12.6388i	−0.163094	+	0.501951i
$635$	12.7898	+	1.07589i	0.507546	+	0.0426953i
$636$		0			0
$637$	6.11374	+	1.98647i	0.242235	+	0.0787069i
$638$	27.2026	+	8.83867i	1.07696	+	0.349926i
$639$		0			0
$640$	6.82864	+	29.1334i	0.269926	+	1.15160i
$641$	−3.35839	+	10.3361i	−0.132648	+	0.408250i	−0.995217	−	0.0976905i	$-0.968854\pi$
$641$	−3.35839	+	10.3361i	−0.132648	+	0.408250i	0.862568	+	0.505940i	$0.168854\pi$
$642$		0			0
$643$			3.09039i			0.121873i	0.998142	+	0.0609366i	$0.0194088\pi$
$643$			3.09039i			0.121873i	−0.998142	+	0.0609366i	$0.980591\pi$
$644$	−3.84112	−	2.79074i	−0.151361	−	0.109970i
$645$		0			0
$646$	15.5754	−	11.3162i	0.612805	−	0.445229i
$647$	3.25460	+	4.47957i	0.127951	+	0.176110i	0.868186	−	0.496238i	$-0.165286\pi$
$647$	3.25460	+	4.47957i	0.127951	+	0.176110i	−0.740235	+	0.672348i	$0.765286\pi$
$648$		0			0
$649$	26.0712			1.02338
$650$	−7.25185	−	7.40972i	−0.284441	−	0.290633i
$651$		0			0
$652$	−7.65366	+	2.48682i	−0.299740	+	0.0973915i
$653$	22.8504	+	31.4509i	0.894206	+	1.23077i	0.972280	+	0.233821i	$0.0751230\pi$
$653$	22.8504	+	31.4509i	0.894206	+	1.23077i	−0.0780738	+	0.996948i	$0.524877\pi$
$654$		0			0
$655$	−5.04632	−	8.33524i	−0.197176	−	0.325685i
$656$	−6.89265	−	5.00780i	−0.269113	−	0.195522i
$657$		0			0
$658$	8.99949	−	12.3867i	0.350837	−	0.482885i
$659$	−6.34687	+	19.5337i	−0.247239	+	0.760923i	0.748021	+	0.663675i	$0.231004\pi$
$659$	−6.34687	+	19.5337i	−0.247239	+	0.760923i	−0.995260	+	0.0972484i	$0.968996\pi$
$660$		0			0
$661$	11.8741	+	36.5447i	0.461848	+	1.42142i	0.862903	+	0.505369i	$0.168644\pi$
$661$	11.8741	+	36.5447i	0.461848	+	1.42142i	−0.401055	+	0.916054i	$0.631356\pi$
$662$	−5.76252	−	1.87236i	−0.223967	−	0.0727712i
$663$		0			0
$664$	0.174328	+	0.536526i	0.00676524	+	0.0208213i
$665$	16.3361	−	9.89020i	0.633487	−	0.383525i
$666$		0			0
$667$	−40.8405	+	56.2122i	−1.58135	+	2.17654i
$668$			2.33408i			0.0903081i
$669$		0			0
$670$	9.68582	−	11.2178i	0.374196	−	0.433380i
$671$	23.3272	−	16.9482i	0.900537	−	0.654278i
$672$		0			0
$673$	12.3466	−	4.01164i	0.475925	−	0.154637i	−0.0612254	−	0.998124i	$-0.519501\pi$
$673$	12.3466	−	4.01164i	0.475925	−	0.154637i	0.537150	+	0.843487i	$0.319501\pi$
$674$	6.07660			0.234062
$675$		0			0
$676$	−4.03529			−0.155204
$677$	−6.88524	+	2.23715i	−0.264621	+	0.0859807i	−0.438323	−	0.898818i	$-0.644427\pi$
$677$	−6.88524	+	2.23715i	−0.264621	+	0.0859807i	0.173701	+	0.984798i	$0.444427\pi$
$678$		0			0
$679$	15.1169	−	10.9831i	0.580134	−	0.421492i
$680$	−1.03571	+	12.3121i	−0.0397175	+	0.472147i
$681$		0			0
$682$		−	13.3856i		−	0.512561i
$683$	−14.6241	+	20.1283i	−0.559575	+	0.770188i	−0.991272	−	0.131830i	$-0.957915\pi$
$683$	−14.6241	+	20.1283i	−0.559575	+	0.770188i	0.431698	+	0.902018i	$0.357915\pi$
$684$		0			0
$685$	3.34197	+	2.88558i	0.127690	+	0.110252i
$686$	8.35314	+	25.7083i	0.318924	+	0.981548i
$687$		0			0
$688$	35.0172	+	11.3778i	1.33502	+	0.433774i
$689$	1.73961	+	5.35397i	0.0662739	+	0.203970i
$690$		0			0
$691$	−10.2812	+	31.6422i	−0.391114	+	1.20373i	0.540832	+	0.841130i	$0.318109\pi$
$691$	−10.2812	+	31.6422i	−0.391114	+	1.20373i	−0.931947	+	0.362595i	$0.881891\pi$
$692$	−2.50751	+	3.45130i	−0.0953213	+	0.131199i
$693$		0			0
$694$	−12.4259	−	9.02794i	−0.471681	−	0.342696i
$695$	0.314727	−	3.74136i	0.0119383	−	0.141918i
$696$		0			0
$697$	−2.39290	−	3.29355i	−0.0906377	−	0.124752i
$698$	26.9668	−	8.76204i	1.02071	−	0.331648i
$699$		0			0
$700$	0.450928	−	2.66126i	0.0170435	−	0.100586i
$701$	13.2163			0.499173			0.249586	−	0.968353i	$-0.419705\pi$
$701$	13.2163			0.499173			0.249586	+	0.968353i	$0.419705\pi$
$702$		0			0
$703$	−32.7307	−	45.0499i	−1.23446	−	1.69909i
$704$	11.5937	−	8.42328i	0.436952	−	0.317464i
$705$		0			0
$706$	−11.5906	−	8.42104i	−0.436217	−	0.316930i
$707$			12.2596i			0.461069i
$708$		0			0
$709$	−1.93157	+	5.94475i	−0.0725415	+	0.223260i	−0.980753	−	0.195251i	$-0.937448\pi$
$709$	−1.93157	+	5.94475i	−0.0725415	+	0.223260i	0.908212	+	0.418511i	$0.137448\pi$
$710$	−16.9809	+	10.2806i	−0.637282	+	0.385823i
$711$		0			0
$712$	1.02793	+	0.333995i	0.0385233	+	0.0125170i
$713$	30.9252	+	10.0482i	1.15816	+	0.376308i
$714$		0			0
$715$	−2.75628	+	6.55423i	−0.103079	+	0.245114i
$716$	−1.73731	+	5.34689i	−0.0649263	+	0.199823i
$717$		0			0
$718$			44.4735i			1.65973i
$719$	−22.2492	−	16.1650i	−0.829757	−	0.602854i	0.0897336	−	0.995966i	$-0.471398\pi$
$719$	−22.2492	−	16.1650i	−0.829757	−	0.602854i	−0.919491	+	0.393112i	$0.871398\pi$
$720$		0			0
$721$	−3.02477	+	2.19762i	−0.112648	+	0.0818437i
$722$	−12.2938	−	16.9209i	−0.457526	−	0.629731i
$723$		0			0
$724$	5.26293			0.195595
$725$	−38.9457	−	6.59902i	−1.44641	−	0.245081i
$726$		0			0
$727$	−20.9610	+	6.81063i	−0.777399	+	0.252592i	−0.670729	−	0.741702i	$-0.734019\pi$
$727$	−20.9610	+	6.81063i	−0.777399	+	0.252592i	−0.106670	+	0.994295i	$0.534019\pi$
$728$	−2.98751	−	4.11196i	−0.110725	−	0.152399i
$729$		0			0
$730$	23.1714	−	5.43119i	0.857611	−	0.201017i
$731$	14.2335	+	10.3412i	0.526443	+	0.382484i
$732$		0			0
$733$	20.4041	−	28.0838i	0.753641	−	1.03730i	−0.244076	−	0.969756i	$-0.578485\pi$
$733$	20.4041	−	28.0838i	0.753641	−	1.03730i	0.997716	−	0.0675414i	$-0.0215155\pi$
$734$	−1.89865	+	5.84345i	−0.0700806	+	0.215686i
$735$		0			0
$736$	−5.48565	−	16.8831i	−0.202204	−	0.622319i
$737$	−9.66645	−	3.14082i	−0.356068	−	0.115694i
$738$		0			0
$739$	2.34418	+	7.21465i	0.0862321	+	0.265395i	0.984870	−	0.173297i	$-0.0554420\pi$
$739$	2.34418	+	7.21465i	0.0862321	+	0.265395i	−0.898638	+	0.438692i	$0.855442\pi$
$740$	−7.84297	−	0.659759i	−0.288313	−	0.0242532i
$741$		0			0
$742$	−5.63436	+	7.75503i	−0.206844	+	0.284696i
$743$		−	27.5328i		−	1.01008i	−0.863096	−	0.505040i	$-0.831478\pi$
$743$		−	27.5328i		−	1.01008i	0.863096	−	0.505040i	$-0.168522\pi$
$744$		0			0
$745$	−15.2226	−	6.40164i	−0.557713	−	0.234538i
$746$	−3.94383	+	2.86536i	−0.144394	+	0.104908i
$747$		0			0
$748$	−1.77482	+	0.576674i	−0.0648938	+	0.0210853i
$749$	−2.70690			−0.0989081
$750$		0			0
$751$	4.24930			0.155059			0.0775296	−	0.996990i	$-0.475297\pi$
$751$	4.24930			0.155059			0.0775296	+	0.996990i	$0.475297\pi$
$752$	29.0967	−	9.45408i	1.06105	−	0.344755i
$753$		0			0
$754$	13.2530	−	9.62888i	0.482646	−	0.350663i
$755$	−8.78362	−	3.69382i	−0.319669	−	0.134432i
$756$		0			0
$757$			45.6609i			1.65957i	0.558081	+	0.829787i	$0.311538\pi$
$757$			45.6609i			1.65957i	−0.558081	+	0.829787i	$0.688462\pi$
$758$	−25.7586	+	35.4537i	−0.935595	+	1.28774i
$759$		0			0
$760$	32.0459	+	2.69574i	1.16243	+	0.0977848i
$761$	12.3999	+	38.1628i	0.449495	+	1.38340i	0.877479	+	0.479616i	$0.159224\pi$
$761$	12.3999	+	38.1628i	0.449495	+	1.38340i	−0.427984	+	0.903786i	$0.640776\pi$
$762$		0			0
$763$	−4.19262	−	1.36227i	−0.151783	−	0.0493173i
$764$	−2.34121	−	7.20550i	−0.0847020	−	0.260686i
$765$		0			0
$766$	−5.44196	+	16.7486i	−0.196626	+	0.605152i
$767$	8.77671	−	12.0801i	0.316909	−	0.436187i
$768$		0			0
$769$	−30.6092	−	22.2389i	−1.10380	−	0.801954i	−0.122120	−	0.992515i	$-0.538969\pi$
$769$	−30.6092	−	22.2389i	−1.10380	−	0.801954i	−0.981675	+	0.190561i	$0.938969\pi$
$770$	−11.7876	+	2.76291i	−0.424795	+	0.0995685i
$771$		0			0
$772$	4.81840	+	6.63195i	0.173418	+	0.238689i
$773$	−24.9318	+	8.10082i	−0.896733	+	0.291366i	−0.720888	−	0.693052i	$-0.756266\pi$
$773$	−24.9318	+	8.10082i	−0.896733	+	0.291366i	−0.175845	+	0.984418i	$0.556266\pi$
$774$		0			0
$775$	2.69507	+	18.2883i	0.0968096	+	0.656937i
$776$	31.4667			1.12959
$777$		0			0
$778$	−30.9299	−	42.5713i	−1.10889	−	1.52626i
$779$	−8.57247	+	6.22826i	−0.307140	+	0.223151i
$780$		0			0
$781$	11.0134	+	8.00168i	0.394089	+	0.286323i
$782$		−	29.6503i		−	1.06029i
$783$		0			0
$784$	−6.75891	+	20.8018i	−0.241390	+	0.742921i
$785$	13.9188	−	33.0977i	0.496782	−	1.18131i
$786$		0			0
$787$	2.29446	+	0.745515i	0.0817887	+	0.0265747i	0.349626	−	0.936890i	$-0.386309\pi$
$787$	2.29446	+	0.745515i	0.0817887	+	0.0265747i	−0.267837	+	0.963464i	$0.586309\pi$
$788$	−0.464639	−	0.150970i	−0.0165521	−	0.00537810i
$789$		0			0
$790$	31.3569	−	18.9841i	1.11563	−	0.675424i
$791$	−6.39430	+	19.6796i	−0.227355	+	0.699727i
$792$		0			0
$793$		−	16.5142i		−	0.586437i
$794$	24.9033	+	18.0933i	0.883785	+	0.642108i
$795$		0			0
$796$	2.61682	−	1.90123i	0.0927508	−	0.0673874i
$797$	−4.76829	−	6.56299i	−0.168902	−	0.232473i	0.716172	−	0.697923i	$-0.245892\pi$
$797$	−4.76829	−	6.56299i	−0.168902	−	0.232473i	−0.885074	+	0.465450i	$0.845892\pi$
$798$		0			0
$799$	14.6189			0.517180
$800$	7.21258	−	7.05891i	0.255003	−	0.249570i
$801$		0			0
$802$	7.28041	−	2.36555i	0.257080	−	0.0835304i
$803$	−9.59348	−	13.2043i	−0.338546	−	0.465969i
$804$		0			0
$805$	2.46536	−	29.3073i	0.0868926	−	1.03295i
$806$	−6.20223	−	4.50618i	−0.218464	−	0.158724i
$807$		0			0
$808$	−12.1350	+	16.7024i	−0.426908	+	0.587589i
$809$	−12.5798	+	38.7166i	−0.442282	+	1.36120i	0.443155	+	0.896445i	$0.353859\pi$
$809$	−12.5798	+	38.7166i	−0.442282	+	1.36120i	−0.885437	+	0.464759i	$0.846141\pi$
$810$		0			0
$811$	−15.2960	−	47.0763i	−0.537116	−	1.65307i	−0.739032	−	0.673671i	$-0.764717\pi$
$811$	−15.2960	−	47.0763i	−0.537116	−	1.65307i	0.201915	−	0.979403i	$-0.435283\pi$
$812$	4.05608	+	1.31790i	0.142341	+	0.0462493i
$813$		0			0
$814$	10.9093	+	33.5755i	0.382372	+	1.17682i
$815$	−37.7317	−	32.5789i	−1.32168	−	1.14119i
$816$		0			0
$817$	26.9162	−	37.0469i	0.941678	−	1.29611i
$818$		−	36.6606i		−	1.28181i
$819$		0			0
$820$	−0.125544	+	1.49242i	−0.00438420	+	0.0521177i
$821$	34.1498	−	24.8113i	1.19183	−	0.865919i	0.198378	−	0.980126i	$-0.436433\pi$
$821$	34.1498	−	24.8113i	1.19183	−	0.865919i	0.993457	+	0.114207i	$0.0364327\pi$
$822$		0			0
$823$	46.8252	−	15.2144i	1.63222	−	0.530342i	0.657443	−	0.753504i	$-0.271638\pi$
$823$	46.8252	−	15.2144i	1.63222	−	0.530342i	0.974781	+	0.223162i	$0.0716380\pi$
$824$	−6.29622			−0.219339
$825$		0			0
$826$	25.4255			0.884666
$827$	−48.5050	+	15.7602i	−1.68668	+	0.548036i	−0.986189	−	0.165623i	$-0.947037\pi$
$827$	−48.5050	+	15.7602i	−1.68668	+	0.548036i	−0.700493	+	0.713659i	$0.747037\pi$
$828$		0			0
$829$	−30.9321	+	22.4735i	−1.07432	+	0.780537i	−0.976683	−	0.214686i	$-0.931127\pi$
$829$	−30.9321	+	22.4735i	−1.07432	+	0.780537i	−0.0976336	+	0.995222i	$0.531127\pi$
$830$	0.502981	−	0.582535i	0.0174587	−	0.0202201i
$831$		0			0
$832$		−	8.20758i		−	0.284547i
$833$	−6.14314	+	8.45531i	−0.212847	+	0.292959i
$834$		0			0
$835$	−12.3683	+	7.48803i	−0.428024	+	0.259134i
$836$	1.50097	+	4.61951i	0.0519121	+	0.159769i
$837$		0			0
$838$	0.705171	+	0.229124i	0.0243597	+	0.00791496i
$839$	−5.16324	−	15.8908i	−0.178255	−	0.548612i	0.821512	−	0.570191i	$-0.193131\pi$
$839$	−5.16324	−	15.8908i	−0.178255	−	0.548612i	−0.999767	+	0.0215787i	$0.993131\pi$
$840$		0			0
$841$	10.3251	−	31.7774i	0.356038	−	1.09577i
$842$	−16.0025	+	22.0255i	−0.551481	+	0.759049i
$843$		0			0
$844$	1.70544	+	1.23908i	0.0587037	+	0.0426507i
$845$	−12.9458	−	21.3831i	−0.445348	−	0.735602i
$846$		0			0
$847$	−4.78901	−	6.59151i	−0.164552	−	0.226487i
$848$	−18.2167	+	5.91897i	−0.625564	+	0.203258i
$849$		0			0
$850$	15.1006	−	7.49044i	0.517946	−	0.256920i
$851$	−85.7599			−2.93981
$852$		0			0
$853$	10.7355	+	14.7762i	0.367578	+	0.505928i	0.952241	−	0.305349i	$-0.0987731\pi$
$853$	10.7355	+	14.7762i	0.367578	+	0.505928i	−0.584662	+	0.811277i	$0.698773\pi$
$854$	22.7495	−	16.5285i	0.778471	−	0.565593i
$855$		0			0
$856$	−3.68787	−	2.67940i	−0.126049	−	0.0915799i
$857$		−	53.4773i		−	1.82675i	−0.407119	−	0.913375i	$-0.633466\pi$
$857$		−	53.4773i		−	1.82675i	0.407119	−	0.913375i	$-0.366534\pi$
$858$		0			0
$859$	5.79639	−	17.8395i	0.197770	−	0.608674i	−0.802163	−	0.597105i	$-0.796317\pi$
$859$	5.79639	−	17.8395i	0.197770	−	0.608674i	0.999933	−	0.0115690i	$-0.00368259\pi$
$860$	−1.47706	−	6.30168i	−0.0503674	−	0.214885i
$861$		0			0
$862$	−39.1730	−	12.7281i	−1.33424	−	0.433520i
$863$	48.7286	+	15.8329i	1.65874	+	0.538957i	0.980607	−	0.195982i	$-0.0627894\pi$
$863$	48.7286	+	15.8329i	1.65874	+	0.538957i	0.678133	+	0.734939i	$0.262789\pi$
$864$		0			0
$865$	−26.3329	−	2.21516i	−0.895347	−	0.0753176i
$866$	4.38313	−	13.4899i	0.148945	−	0.458405i
$867$		0			0
$868$		−	1.99588i		−	0.0677444i
$869$	−20.3373	−	14.7759i	−0.689895	−	0.501238i
$870$		0			0
$871$	−4.70946	+	3.42162i	−0.159574	+	0.115937i
$872$	−4.36359	−	6.00597i	−0.147770	−	0.203388i
$873$		0			0
$874$	−77.1739			−2.61045
$875$	15.5487	−	6.14821i	0.525643	−	0.207847i
$876$		0			0
$877$	−5.76631	+	1.87359i	−0.194715	+	0.0632666i	−0.404751	−	0.914427i	$-0.632642\pi$
$877$	−5.76631	+	1.87359i	−0.194715	+	0.0632666i	0.210036	+	0.977694i	$0.432642\pi$
$878$	0.905331	+	1.24608i	0.0305534	+	0.0420532i
$879$		0			0
$880$	−22.3005	−	9.37816i	−0.751751	−	0.316138i
$881$	18.3403	+	13.3250i	0.617899	+	0.448930i	0.852187	−	0.523237i	$-0.175276\pi$
$881$	18.3403	+	13.3250i	0.617899	+	0.448930i	−0.234288	+	0.972167i	$0.575276\pi$
$882$		0			0
$883$	−3.25574	+	4.48114i	−0.109564	+	0.150802i	−0.860278	−	0.509826i	$-0.829710\pi$
$883$	−3.25574	+	4.48114i	−0.109564	+	0.150802i	0.750713	+	0.660628i	$0.229710\pi$
$884$	−0.330280	+	1.01650i	−0.0111085	+	0.0341885i
$885$		0			0
$886$	−12.4817	−	38.4146i	−0.419329	−	1.29056i
$887$	−10.4346	−	3.39041i	−0.350360	−	0.113839i	0.128550	−	0.991703i	$-0.458968\pi$
$887$	−10.4346	−	3.39041i	−0.350360	−	0.113839i	−0.478909	+	0.877864i	$0.658968\pi$
$888$		0			0
$889$	−2.65263	−	8.16394i	−0.0889662	−	0.273810i
$890$	−0.336501	−	1.43563i	−0.0112795	−	0.0481225i
$891$		0			0
$892$	1.65943	−	2.28401i	0.0555617	−	0.0764742i
$893$		−	38.0502i		−	1.27330i
$894$		0			0
$895$	−33.9068	+	7.94749i	−1.13338	+	0.265655i
$896$	16.1906	−	11.7632i	0.540890	−	0.392980i
$897$		0			0
$898$	−6.94794	+	2.25752i	−0.231856	+	0.0753345i
$899$	−29.2083			−0.974151
$900$		0			0
$901$	−9.15254			−0.304915
$902$	6.38902	−	2.07592i	0.212731	−	0.0691205i
$903$		0			0
$904$	−28.1912	+	20.4821i	−0.937627	+	0.681226i
$905$	16.8842	+	27.8884i	0.561250	+	0.927042i
$906$		0			0
$907$			19.3907i			0.643856i	0.946764	+	0.321928i	$0.104331\pi$
$907$			19.3907i			0.643856i	−0.946764	+	0.321928i	$0.895669\pi$
$908$	−3.46038	+	4.76281i	−0.114837	+	0.158059i
$909$		0			0
$910$	−2.68802	+	6.39191i	−0.0891071	+	0.211890i
$911$	4.23940	+	13.0475i	0.140458	+	0.432284i	0.996399	−	0.0847888i	$-0.0270216\pi$
$911$	4.23940	+	13.0475i	0.140458	+	0.432284i	−0.855941	+	0.517073i	$0.827022\pi$
$912$		0			0
$913$	−0.501975	−	0.163102i	−0.0166130	−	0.00539788i
$914$	7.58300	+	23.3381i	0.250823	+	0.771955i
$915$		0			0
$916$	−2.42157	+	7.45282i	−0.0800108	+	0.246248i
$917$	−3.83043	+	5.27213i	−0.126492	+	0.174101i
$918$		0			0
$919$	−26.2209	−	19.0506i	−0.864947	−	0.628421i	0.0642792	−	0.997932i	$-0.479525\pi$
$919$	−26.2209	−	19.0506i	−0.864947	−	0.628421i	−0.929226	+	0.369511i	$0.879525\pi$
$920$	32.3683	−	37.4878i	1.06715	−	1.23594i
$921$		0			0
$922$	35.9058	+	49.4202i	1.18250	+	1.62757i
$923$	7.41518	−	2.40934i	0.244073	−	0.0793043i
$924$		0			0
$925$	−21.6652	−	43.6767i	−0.712348	−	1.43608i
$926$	40.1360			1.31895
$927$		0			0
$928$	9.37270	+	12.9004i	0.307674	+	0.423477i
$929$	3.50664	−	2.54772i	0.115049	−	0.0835880i	−0.528773	−	0.848763i	$-0.677348\pi$
$929$	3.50664	−	2.54772i	0.115049	−	0.0835880i	0.643822	+	0.765175i	$0.277348\pi$
$930$		0			0
$931$	22.0075	+	15.9894i	0.721268	+	0.524032i
$932$		−	4.88548i		−	0.160029i
$933$		0			0
$934$	−1.82902	+	5.62915i	−0.0598474	+	0.184192i
$935$	−8.74967	−	7.55477i	−0.286145	−	0.247067i
$936$		0			0
$937$	51.9206	+	16.8700i	1.69617	+	0.551120i	0.987937	−	0.154857i	$-0.0494918\pi$
$937$	51.9206	+	16.8700i	1.69617	+	0.551120i	0.708235	+	0.705977i	$0.249492\pi$
$938$	−9.42705	−	3.06303i	−0.307804	−	0.100012i
$939$		0			0
$940$	−4.07071	−	3.51479i	−0.132772	−	0.114640i
$941$	−1.30978	+	4.03108i	−0.0426975	+	0.131409i	−0.970133	−	0.242574i	$-0.922008\pi$
$941$	−1.30978	+	4.03108i	−0.0426975	+	0.131409i	0.927435	+	0.373983i	$0.122008\pi$
$942$		0			0
$943$			16.3191i			0.531423i
$944$	41.1022	+	29.8625i	1.33776	+	0.971940i
$945$		0			0
$946$	−23.4872	+	17.0645i	−0.763636	+	0.554814i
$947$	7.41018	+	10.1992i	0.240798	+	0.331431i	0.912262	−	0.409607i	$-0.134334\pi$
$947$	7.41018	+	10.1992i	0.240798	+	0.331431i	−0.671464	+	0.741037i	$0.734334\pi$
$948$		0			0
$949$	−9.34781			−0.303443
$950$	−19.4962	−	39.3039i	−0.632539	−	1.27519i
$951$		0			0
$952$	7.85903	−	2.55356i	0.254713	−	0.0827612i
$953$	18.3174	+	25.2118i	0.593360	+	0.816690i	0.995080	−	0.0990725i	$-0.0315876\pi$
$953$	18.3174	+	25.2118i	0.593360	+	0.816690i	−0.401720	+	0.915762i	$0.631588\pi$
$954$		0			0
$955$	30.6712	−	35.5224i	0.992498	−	1.14948i
$956$	−3.07626	−	2.23503i	−0.0994934	−	0.0722862i
$957$		0			0
$958$	−12.8879	+	17.7387i	−0.416390	+	0.573111i
$959$	0.912532	−	2.80848i	0.0294672	−	0.0906907i
$960$		0			0
$961$	−5.35555	−	16.4827i	−0.172760	−	0.531700i
$962$	19.2298	+	6.24814i	0.619994	+	0.201448i
$963$		0			0
$964$	−2.17337	−	6.68896i	−0.0699997	−	0.215437i
$965$	−19.6848	+	46.8090i	−0.633677	+	1.50684i
$966$		0			0
$967$	0.912880	−	1.25647i	0.0293562	−	0.0404054i	−0.794087	−	0.607805i	$-0.792050\pi$
$967$	0.912880	−	1.25647i	0.0293562	−	0.0404054i	0.823443	+	0.567399i	$0.192050\pi$
$968$		−	13.7206i		−	0.440997i
$969$		0			0
$970$	−22.2330	−	36.7233i	−0.713858	−	1.17911i
$971$	−30.9548	+	22.4900i	−0.993388	+	0.721739i	−0.960660	−	0.277725i	$-0.910419\pi$
$971$	−30.9548	+	22.4900i	−0.993388	+	0.721739i	−0.0327278	+	0.999464i	$0.510419\pi$
$972$		0			0
$973$	−2.38818	+	0.775967i	−0.0765616	+	0.0248764i
$974$	−38.1405			−1.22210
$975$		0			0
$976$	56.1890			1.79857
$977$	−19.3693	+	6.29348i	−0.619680	+	0.201346i	−0.601998	−	0.798497i	$-0.705629\pi$
$977$	−19.3693	+	6.29348i	−0.619680	+	0.201346i	−0.0176817	+	0.999844i	$0.505629\pi$
$978$		0			0
$979$	−0.818100	+	0.594384i	−0.0261466	+	0.0189966i
$980$	3.74348	−	0.877442i	0.119581	−	0.0280288i
$981$		0			0
$982$		−	17.6539i		−	0.563359i
$983$	−7.79150	+	10.7241i	−0.248510	+	0.342045i	−0.914989	−	0.403479i	$-0.867801\pi$
$983$	−7.79150	+	10.7241i	−0.248510	+	0.342045i	0.666479	+	0.745524i	$0.267801\pi$
$984$		0			0
$985$	−0.690629	−	2.94647i	−0.0220053	−	0.0938823i
$986$	8.23022	+	25.3300i	0.262103	+	0.806671i
$987$		0			0
$988$	2.64575	+	0.859655i	0.0841724	+	0.0273493i
$989$	−21.7934	−	67.0732i	−0.692990	−	2.13280i
$990$		0			0
$991$	−0.692448	+	2.13113i	−0.0219963	+	0.0676977i	−0.961452	−	0.274972i	$-0.911331\pi$
$991$	−0.692448	+	2.13113i	−0.0219963	+	0.0676977i	0.939456	+	0.342670i	$0.111331\pi$
$992$	4.38629	−	6.03721i	0.139265	−	0.191682i
$993$		0			0
$994$	10.7406	+	7.80351i	0.340671	+	0.247512i
$995$	18.4698	+	7.76720i	0.585532	+	0.246237i
$996$		0			0
$997$	8.25272	+	11.3589i	0.261366	+	0.359740i	0.919451	−	0.393204i	$-0.128633\pi$
$997$	8.25272	+	11.3589i	0.261366	+	0.359740i	−0.658085	+	0.752943i	$0.728633\pi$
$998$	−6.10092	+	1.98231i	−0.193121	+	0.0627489i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.b.19.1		16
3.2	odd	2		75.2.i.a.19.4	yes	16
15.2	even	4		375.2.g.d.151.3		16
15.8	even	4		375.2.g.e.151.2		16
15.14	odd	2		375.2.i.c.349.1		16
25.2	odd	20		5625.2.a.t.1.3		8
25.4	even	10	inner	225.2.m.b.154.1		16
25.23	odd	20		5625.2.a.bd.1.6		8
75.2	even	20		1875.2.a.p.1.6		8
75.11	odd	10		1875.2.b.h.1249.4		16
75.14	odd	10		1875.2.b.h.1249.13		16
75.23	even	20		1875.2.a.m.1.3		8
75.29	odd	10		75.2.i.a.4.4	✓	16
75.47	even	20		375.2.g.d.226.3		16
75.53	even	20		375.2.g.e.226.2		16
75.71	odd	10		375.2.i.c.274.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.4	✓	16	75.29	odd	10
75.2.i.a.19.4	yes	16	3.2	odd	2
225.2.m.b.19.1		16	1.1	even	1	trivial
225.2.m.b.154.1		16	25.4	even	10	inner
375.2.g.d.151.3		16	15.2	even	4
375.2.g.d.226.3		16	75.47	even	20
375.2.g.e.151.2		16	15.8	even	4
375.2.g.e.226.2		16	75.53	even	20
375.2.i.c.274.1		16	75.71	odd	10
375.2.i.c.349.1		16	15.14	odd	2
1875.2.a.m.1.3		8	75.23	even	20
1875.2.a.p.1.6		8	75.2	even	20
1875.2.b.h.1249.4		16	75.11	odd	10
1875.2.b.h.1249.13		16	75.14	odd	10
5625.2.a.t.1.3		8	25.2	odd	20
5625.2.a.bd.1.6		8	25.23	odd	20

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46134 + 0.474819i) q^{2} +(0.292036 - 0.212177i) q^{4} +(2.06122 + 0.866816i) q^{5} -1.49550i q^{7} +(1.48030 - 2.03746i) q^{8} +O(q^{10})\)	\(q+(-1.46134 + 0.474819i) q^{2} +(0.292036 - 0.212177i) q^{4} +(2.06122 + 0.866816i) q^{5} -1.49550i q^{7} +(1.48030 - 2.03746i) q^{8} +(-3.42373 - 0.288008i) q^{10} +(0.728123 + 2.24093i) q^{11} +(1.28346 + 0.417020i) q^{13} +(0.710090 + 2.18543i) q^{14} +(-1.41890 + 4.36692i) q^{16} +(-1.28963 + 1.77502i) q^{17} +(4.62004 + 3.35666i) q^{19} +(0.785869 - 0.184201i) q^{20} +(-2.12807 - 2.92904i) q^{22} +(8.36455 - 2.71781i) q^{23} +(3.49726 + 3.57340i) q^{25} -2.07358 q^{26} +(-0.317309 - 0.436739i) q^{28} +(-6.39137 + 4.64360i) q^{29} +(2.99107 + 2.17314i) q^{31} -2.01841i q^{32} +(1.04178 - 3.20626i) q^{34} +(1.29632 - 3.08255i) q^{35} +(-9.27372 - 3.01321i) q^{37} +(-8.34527 - 2.71154i) q^{38} +(4.81733 - 2.91650i) q^{40} +(-0.573380 + 1.76468i) q^{41} -8.01874i q^{43} +(0.688111 + 0.499942i) q^{44} +(-10.9330 + 7.94330i) q^{46} +(-3.91640 - 5.39046i) q^{47} +4.76349 q^{49} +(-6.80741 - 3.56139i) q^{50} +(0.463298 - 0.150535i) q^{52} +(2.45196 + 3.37484i) q^{53} +(-0.441653 + 5.25020i) q^{55} +(-3.04701 - 2.21378i) q^{56} +(7.13511 - 9.82064i) q^{58} +(3.41917 - 10.5231i) q^{59} +(-3.78151 - 11.6383i) q^{61} +(-5.40283 - 1.75549i) q^{62} +(-1.87942 - 5.78425i) q^{64} +(2.28401 + 1.97209i) q^{65} +(-2.53546 + 3.48976i) q^{67} +0.792000i q^{68} +(-0.430715 + 5.12018i) q^{70} +(4.67410 - 3.39593i) q^{71} +(-6.58781 + 2.14051i) q^{73} +14.9828 q^{74} +2.06142 q^{76} +(3.35130 - 1.08890i) q^{77} +(-8.63118 + 6.27092i) q^{79} +(-6.70997 + 7.77126i) q^{80} -2.85106i q^{82} +(-0.131666 + 0.181222i) q^{83} +(-4.19683 + 2.54084i) q^{85} +(3.80745 + 11.7181i) q^{86} +(5.64364 + 1.83373i) q^{88} +(0.132620 + 0.408162i) q^{89} +(0.623652 - 1.91940i) q^{91} +(1.86610 - 2.56846i) q^{92} +(8.28270 + 6.01773i) q^{94} +(6.61332 + 10.9235i) q^{95} +(7.34411 + 10.1083i) q^{97} +(-6.96109 + 2.26180i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) \) 16 * q + 2 * q^4 + 30 * q^8	\( 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

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