LMFDB - Embedded newform 576.2.bd.a.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(37,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(16))

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

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

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

chi := DirichletCharacter("576.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			541.2
Character	$\chi$	$=$	576.541
Dual form			576.2.bd.a.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.468362 + 1.33441i) q^{2} +(-1.56127 - 1.24997i) q^{4} +(-0.914126 + 1.36809i) q^{5} +(2.65574 - 1.10004i) q^{7} +(2.39921 - 1.49793i) q^{8} +O(q^{10})$	\(q+(-0.468362 + 1.33441i) q^{2} +(-1.56127 - 1.24997i) q^{4} +(-0.914126 + 1.36809i) q^{5} +(2.65574 - 1.10004i) q^{7} +(2.39921 - 1.49793i) q^{8} +(-1.39744 - 1.86057i) q^{10} +(-0.246413 - 1.23880i) q^{11} +(0.319413 + 0.478036i) q^{13} +(0.224055 + 4.05906i) q^{14} +(0.875149 + 3.90309i) q^{16} +(3.38390 + 3.38390i) q^{17} +(4.19561 - 2.80342i) q^{19} +(3.13727 - 0.993326i) q^{20} +(1.76847 + 0.251393i) q^{22} +(-0.178010 + 0.429755i) q^{23} +(0.877384 + 2.11819i) q^{25} +(-0.787494 + 0.202333i) q^{26} +(-5.52137 - 1.60213i) q^{28} +(1.02242 - 5.14005i) q^{29} +10.0065i q^{31} +(-5.61819 - 0.660257i) q^{32} +(-6.10038 + 2.93060i) q^{34} +(-0.922728 + 4.63887i) q^{35} +(0.447703 + 0.299146i) q^{37} +(1.77583 + 6.91166i) q^{38} +(-0.143878 + 4.65162i) q^{40} +(-2.44115 + 5.89346i) q^{41} +(3.80641 - 0.757142i) q^{43} +(-1.16375 + 2.24212i) q^{44} +(-0.490094 - 0.438819i) q^{46} +(5.99084 + 5.99084i) q^{47} +(0.893127 - 0.893127i) q^{49} +(-3.23746 + 0.178704i) q^{50} +(0.0988389 - 1.14560i) q^{52} +(-0.810472 - 4.07452i) q^{53} +(1.92004 + 0.795307i) q^{55} +(4.72389 - 6.61736i) q^{56} +(6.38004 + 3.77172i) q^{58} +(1.03615 - 1.55070i) q^{59} +(-6.47490 - 1.28794i) q^{61} +(-13.3528 - 4.68668i) q^{62} +(3.51240 - 7.18770i) q^{64} -0.945978 q^{65} +(6.01983 + 1.19742i) q^{67} +(-1.05342 - 9.51296i) q^{68} +(-5.75795 - 3.40396i) q^{70} +(4.20400 - 1.74136i) q^{71} +(-0.911379 - 0.377506i) q^{73} +(-0.608868 + 0.457308i) q^{74} +(-10.0547 - 0.867487i) q^{76} +(-2.01715 - 3.01887i) q^{77} +(0.152459 - 0.152459i) q^{79} +(-6.13976 - 2.37064i) q^{80} +(-6.72092 - 6.01776i) q^{82} +(5.16472 - 3.45096i) q^{83} +(-7.72277 + 1.53615i) q^{85} +(-0.772445 + 5.43391i) q^{86} +(-2.44684 - 2.60303i) q^{88} +(-1.48745 - 3.59102i) q^{89} +(1.37414 + 0.918171i) q^{91} +(0.815104 - 0.448458i) q^{92} +(-10.8001 + 5.18832i) q^{94} +8.30263i q^{95} -13.7742i q^{97} +(0.773486 + 1.61010i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	−0.468362	+	1.33441i	−0.331182	+	0.943567i
$2$	−0.468362	+	1.33441i	−0.331182	+	0.943567i
$3$		0			0
$3$		0			0
$4$	−1.56127	−	1.24997i	−0.780637	−	0.624985i
$5$	−0.914126	+	1.36809i	−0.408810	+	0.611827i	−0.977553	−	0.210688i	$-0.932430\pi$
$5$	−0.914126	+	1.36809i	−0.408810	+	0.611827i	0.568744	+	0.822515i	$0.307430\pi$
$6$		0			0
$7$	2.65574	−	1.10004i	1.00378	−	0.415778i	0.180596	−	0.983557i	$-0.442197\pi$
$7$	2.65574	−	1.10004i	1.00378	−	0.415778i	0.823181	+	0.567779i	$0.192197\pi$
$8$	2.39921	−	1.49793i	0.848248	−	0.529599i
$9$		0			0
$10$	−1.39744	−	1.86057i	−0.441909	−	0.588365i
$11$	−0.246413	−	1.23880i	−0.0742963	−	0.373513i	0.925692	−	0.378277i	$-0.123483\pi$
$11$	−0.246413	−	1.23880i	−0.0742963	−	0.373513i	−0.999989	+	0.00476447i	$0.998483\pi$
$12$		0			0
$13$	0.319413	+	0.478036i	0.0885893	+	0.132583i	0.873117	−	0.487510i	$-0.162095\pi$
$13$	0.319413	+	0.478036i	0.0885893	+	0.132583i	−0.784528	+	0.620093i	$0.787095\pi$
$14$	0.224055	+	4.05906i	0.0598813	+	1.08483i
$15$		0			0
$16$	0.875149	+	3.90309i	0.218787	+	0.975773i
$17$	3.38390	+	3.38390i	0.820715	+	0.820715i	0.986211	−	0.165495i	$-0.0529223\pi$
$17$	3.38390	+	3.38390i	0.820715	+	0.820715i	−0.165495	+	0.986211i	$0.552922\pi$
$18$		0			0
$19$	4.19561	−	2.80342i	0.962539	−	0.643148i	0.0282261	−	0.999602i	$-0.491014\pi$
$19$	4.19561	−	2.80342i	0.962539	−	0.643148i	0.934313	+	0.356453i	$0.116014\pi$
$20$	3.13727	−	0.993326i	0.701514	−	0.222115i
$21$		0			0
$22$	1.76847	+	0.251393i	0.377040	+	0.0535972i
$23$	−0.178010	+	0.429755i	−0.0371177	+	0.0896101i	−0.941351	−	0.337428i	$-0.890443\pi$
$23$	−0.178010	+	0.429755i	−0.0371177	+	0.0896101i	0.904234	+	0.427038i	$0.140443\pi$
$24$		0			0
$25$	0.877384	+	2.11819i	0.175477	+	0.423638i
$26$	−0.787494	+	0.202333i	−0.154440	+	0.0396807i
$27$		0			0
$28$	−5.52137	−	1.60213i	−1.04344	−	0.302774i
$29$	1.02242	−	5.14005i	0.189858	−	0.954483i	−0.761914	−	0.647678i	$-0.775740\pi$
$29$	1.02242	−	5.14005i	0.189858	−	0.954483i	0.951773	−	0.306805i	$-0.0992598\pi$
$30$		0			0
$31$			10.0065i			1.79722i	0.438743	+	0.898612i	$0.355424\pi$
$31$			10.0065i			1.79722i	−0.438743	+	0.898612i	$0.644576\pi$
$32$	−5.61819	−	0.660257i	−0.993165	−	0.116718i
$33$		0			0
$34$	−6.10038	+	2.93060i	−1.04621	+	0.502593i
$35$	−0.922728	+	4.63887i	−0.155969	+	0.784111i
$36$		0			0
$37$	0.447703	+	0.299146i	0.0736019	+	0.0491792i	0.591827	−	0.806065i	$-0.298407\pi$
$37$	0.447703	+	0.299146i	0.0736019	+	0.0491792i	−0.518225	+	0.855244i	$0.673407\pi$
$38$	1.77583	+	6.91166i	0.288077	+	1.12122i
$39$		0			0
$40$	−0.143878	+	4.65162i	−0.0227491	+	0.735486i
$41$	−2.44115	+	5.89346i	−0.381244	+	0.920404i	0.610482	+	0.792030i	$0.290976\pi$
$41$	−2.44115	+	5.89346i	−0.381244	+	0.920404i	−0.991726	+	0.128374i	$0.959024\pi$
$42$		0			0
$43$	3.80641	−	0.757142i	0.580472	−	0.115463i	0.103883	−	0.994589i	$-0.466873\pi$
$43$	3.80641	−	0.757142i	0.580472	−	0.115463i	0.476589	+	0.879126i	$0.341873\pi$
$44$	−1.16375	+	2.24212i	−0.175441	+	0.338012i
$45$		0			0
$46$	−0.490094	−	0.438819i	−0.0722604	−	0.0647003i
$47$	5.99084	+	5.99084i	0.873854	+	0.873854i	0.992890	−	0.119036i	$-0.0379804\pi$
$47$	5.99084	+	5.99084i	0.873854	+	0.873854i	−0.119036	+	0.992890i	$0.537980\pi$
$48$		0			0
$49$	0.893127	−	0.893127i	0.127590	−	0.127590i
$50$	−3.23746	+	0.178704i	−0.457846	+	0.0252726i
$51$		0			0
$52$	0.0988389	−	1.14560i	0.0137065	−	0.158866i
$53$	−0.810472	−	4.07452i	−0.111327	−	0.559678i	−0.995679	−	0.0928581i	$-0.970400\pi$
$53$	−0.810472	−	4.07452i	−0.111327	−	0.559678i	0.884353	−	0.466820i	$-0.154600\pi$
$54$		0			0
$55$	1.92004	+	0.795307i	0.258898	+	0.107239i
$56$	4.72389	−	6.61736i	0.631256	−	0.884282i
$57$		0			0
$58$	6.38004	+	3.77172i	0.837740	+	0.495252i
$59$	1.03615	−	1.55070i	0.134895	−	0.201884i	−0.757872	−	0.652403i	$-0.773761\pi$
$59$	1.03615	−	1.55070i	0.134895	−	0.201884i	0.892767	+	0.450519i	$0.148761\pi$
$60$		0			0
$61$	−6.47490	−	1.28794i	−0.829026	−	0.164903i	−0.237702	−	0.971338i	$-0.576394\pi$
$61$	−6.47490	−	1.28794i	−0.829026	−	0.164903i	−0.591323	+	0.806435i	$0.701394\pi$
$62$	−13.3528	−	4.68668i	−1.69580	−	0.595209i
$63$		0			0
$64$	3.51240	−	7.18770i	0.439050	−	0.898463i
$65$	−0.945978			−0.117334
$66$		0			0
$67$	6.01983	+	1.19742i	0.735439	+	0.146288i	0.548579	−	0.836099i	$-0.315169\pi$
$67$	6.01983	+	1.19742i	0.735439	+	0.146288i	0.186860	+	0.982387i	$0.440169\pi$
$68$	−1.05342	−	9.51296i	−0.127746	−	1.15362i
$69$		0			0
$70$	−5.75795	−	3.40396i	−0.688207	−	0.406851i
$71$	4.20400	−	1.74136i	0.498924	−	0.206661i	−0.119007	−	0.992893i	$-0.537971\pi$
$71$	4.20400	−	1.74136i	0.498924	−	0.206661i	0.617931	+	0.786232i	$0.287971\pi$
$72$		0			0
$73$	−0.911379	−	0.377506i	−0.106669	−	0.0441837i	0.328711	−	0.944431i	$-0.393386\pi$
$73$	−0.911379	−	0.377506i	−0.106669	−	0.0441837i	−0.435380	+	0.900247i	$0.643386\pi$
$74$	−0.608868	+	0.457308i	−0.0707795	+	0.0531610i
$75$		0			0
$76$	−10.0547	−	0.867487i	−1.15335	−	0.0995076i
$77$	−2.01715	−	3.01887i	−0.229875	−	0.344033i
$78$		0			0
$79$	0.152459	−	0.152459i	0.0171530	−	0.0171530i	−0.698478	−	0.715631i	$-0.746139\pi$
$79$	0.152459	−	0.152459i	0.0171530	−	0.0171530i	0.715631	+	0.698478i	$0.246139\pi$
$80$	−6.13976	−	2.37064i	−0.686446	−	0.265045i
$81$		0			0
$82$	−6.72092	−	6.01776i	−0.742201	−	0.664550i
$83$	5.16472	−	3.45096i	0.566902	−	0.378792i	−0.238840	−	0.971059i	$-0.576767\pi$
$83$	5.16472	−	3.45096i	0.566902	−	0.378792i	0.805741	+	0.592267i	$0.201767\pi$
$84$		0			0
$85$	−7.72277	+	1.53615i	−0.837652	+	0.166619i
$86$	−0.772445	+	5.43391i	−0.0832949	+	0.585954i
$87$		0			0
$88$	−2.44684	−	2.60303i	−0.260834	−	0.277484i
$89$	−1.48745	−	3.59102i	−0.157669	−	0.380648i	0.825228	−	0.564799i	$-0.191046\pi$
$89$	−1.48745	−	3.59102i	−0.157669	−	0.380648i	−0.982898	+	0.184151i	$0.941046\pi$
$90$		0			0
$91$	1.37414	+	0.918171i	0.144049	+	0.0962505i
$92$	0.815104	−	0.448458i	0.0849805	−	0.0467549i
$93$		0			0
$94$	−10.8001	+	5.18832i	−1.11394	+	0.535135i
$95$			8.30263i			0.851832i
$96$		0			0
$97$		−	13.7742i		−	1.39856i	−0.714849	−	0.699279i	$-0.753505\pi$
$97$		−	13.7742i		−	1.39856i	0.714849	−	0.699279i	$-0.246495\pi$
$98$	0.773486	+	1.61010i	0.0781339	+	0.162645i
$99$		0			0
$100$	1.27784	−	4.40378i	0.127784	−	0.440378i
$101$	−3.34129	−	2.23258i	−0.332470	−	0.222150i	0.378118	−	0.925757i	$-0.376571\pi$
$101$	−3.34129	−	2.23258i	−0.332470	−	0.222150i	−0.710589	+	0.703608i	$0.751571\pi$
$102$		0			0
$103$	3.02140	+	7.29430i	0.297707	+	0.718728i	0.999977	+	0.00681740i	$0.00217006\pi$
$103$	3.02140	+	7.29430i	0.297707	+	0.718728i	−0.702270	+	0.711911i	$0.747830\pi$
$104$	1.48240	+	0.668448i	0.145362	+	0.0655467i
$105$		0			0
$106$	5.81665	+	0.826852i	0.564963	+	0.0803110i
$107$	5.40913	−	1.07594i	0.522920	−	0.104015i	0.0734296	−	0.997300i	$-0.476606\pi$
$107$	5.40913	−	1.07594i	0.522920	−	0.104015i	0.449490	+	0.893285i	$0.351606\pi$
$108$		0			0
$109$	−3.62995	+	2.42545i	−0.347686	+	0.232316i	−0.717134	−	0.696935i	$-0.754547\pi$
$109$	−3.62995	+	2.42545i	−0.347686	+	0.232316i	0.369448	+	0.929251i	$0.379547\pi$
$110$	−1.96054	+	2.18962i	−0.186930	+	0.208772i
$111$		0			0
$112$	6.61775	+	9.40290i	0.625318	+	0.888491i
$113$	11.6929	−	11.6929i	1.09998	−	1.09998i	0.105567	−	0.994412i	$-0.466334\pi$
$113$	11.6929	−	11.6929i	1.09998	−	1.09998i	0.994412	−	0.105567i	$-0.0336656\pi$
$114$		0			0
$115$	−0.425218	−	0.636384i	−0.0396518	−	0.0593431i
$116$	−8.02118	+	6.74702i	−0.744748	+	0.626445i
$117$		0			0
$118$	1.58397	+	2.10893i	0.145816	+	0.194142i
$119$	12.7092	+	5.26432i	1.16505	+	0.482580i
$120$		0			0
$121$	8.68876	−	3.59900i	0.789888	−	0.327182i
$122$	4.75123	−	8.03691i	0.430156	−	0.727628i
$123$		0			0
$124$	12.5079	−	15.6229i	1.12324	−	1.40298i
$125$	−11.7687	−	2.34095i	−1.05263	−	0.209381i
$126$		0			0
$127$	−21.9517			−1.94790			−0.973949	−	0.226767i	$-0.927185\pi$
$127$	−21.9517			−1.94790			−0.973949	+	0.226767i	$0.927185\pi$
$128$	7.94623	+	8.05341i	0.702354	+	0.711828i
$129$		0			0
$130$	0.443060	−	1.26232i	0.0388590	−	0.110713i
$131$	7.05871	+	1.40406i	0.616722	+	0.122674i	0.493558	−	0.869713i	$-0.335696\pi$
$131$	7.05871	+	1.40406i	0.616722	+	0.122674i	0.123164	+	0.992386i	$0.460696\pi$
$132$		0			0
$133$	8.05858	−	12.0605i	0.698768	−	1.04578i
$134$	−4.41730	+	7.47207i	−0.381597	+	0.645488i
$135$		0			0
$136$	13.1875	+	3.04982i	1.13082	+	0.261520i
$137$	−10.2318	−	4.23815i	−0.874161	−	0.362089i	−0.0999315	−	0.994994i	$-0.531862\pi$
$137$	−10.2318	−	4.23815i	−0.874161	−	0.362089i	−0.774229	+	0.632905i	$0.781862\pi$
$138$		0			0
$139$	−0.752410	−	3.78262i	−0.0638186	−	0.320838i	0.935668	−	0.352882i	$-0.114798\pi$
$139$	−0.752410	−	3.78262i	−0.0638186	−	0.320838i	−0.999486	+	0.0320443i	$0.989798\pi$
$140$	7.23907	−	6.08916i	0.611813	−	0.514628i
$141$		0			0
$142$	0.354676	+	6.42543i	0.0297638	+	0.539210i
$143$	0.513484	−	0.513484i	0.0429397	−	0.0429397i
$144$		0			0
$145$	6.09741	+	6.09741i	0.506362	+	0.506362i
$146$	0.930601	−	1.03934i	0.0770171	−	0.0860163i
$147$		0			0
$148$	−0.325064	−	1.02666i	−0.0267201	−	0.0843912i
$149$	−21.8201	+	4.34028i	−1.78757	+	0.355569i	−0.974114	−	0.226059i	$-0.927416\pi$
$149$	−21.8201	+	4.34028i	−1.78757	+	0.355569i	−0.813455	+	0.581628i	$0.802416\pi$
$150$		0			0
$151$	2.99065	−	7.22006i	0.243375	−	0.587560i	−0.754239	−	0.656600i	$-0.771994\pi$
$151$	2.99065	−	7.22006i	0.243375	−	0.587560i	0.997614	+	0.0690406i	$0.0219938\pi$
$152$	5.86681	−	13.0107i	0.475861	−	1.05531i
$153$		0			0
$154$	4.97316	−	1.27776i	0.400748	−	0.102965i
$155$	−13.6898	−	9.14722i	−1.09959	−	0.734723i
$156$		0			0
$157$	−4.09955	+	20.6098i	−0.327180	+	1.64484i	0.370790	+	0.928717i	$0.379087\pi$
$157$	−4.09955	+	20.6098i	−0.327180	+	1.64484i	−0.697970	+	0.716127i	$0.745913\pi$
$158$	0.132036	+	0.274849i	0.0105042	+	0.0218658i
$159$		0			0
$160$	6.03902	−	7.08261i	0.477427	−	0.559930i
$161$			1.33714i			0.105381i
$162$		0			0
$163$	3.99966	−	20.1077i	0.313278	−	1.57495i	−0.428015	−	0.903772i	$-0.640787\pi$
$163$	3.99966	−	20.1077i	0.313278	−	1.57495i	0.741293	−	0.671182i	$-0.234213\pi$
$164$	11.1780	−	6.14994i	0.872851	−	0.480229i
$165$		0			0
$166$	2.18601	+	8.50812i	0.169667	+	0.660359i
$167$	−5.57052	−	13.4484i	−0.431060	−	1.04067i	−0.978946	−	0.204118i	$-0.934567\pi$
$167$	−5.57052	−	13.4484i	−0.431060	−	1.04067i	0.547886	−	0.836553i	$-0.315433\pi$
$168$		0			0
$169$	4.84839	−	11.7051i	0.372953	−	0.900389i
$170$	1.56720	−	11.0248i	0.120199	−	0.845562i
$171$		0			0
$172$	−6.88925	−	3.57579i	−0.525301	−	0.272652i
$173$	15.4616	−	10.3311i	1.17552	−	0.785459i	0.194796	−	0.980844i	$-0.437595\pi$
$173$	15.4616	−	10.3311i	1.17552	−	0.785459i	0.980727	+	0.195384i	$0.0625954\pi$
$174$		0			0
$175$	4.66021	+	4.66021i	0.352279	+	0.352279i
$176$	4.61951	−	2.04591i	0.348208	−	0.154216i
$177$		0			0
$178$	5.48854	−	0.302961i	0.411384	−	0.0227079i
$179$	5.99376	+	8.97030i	0.447995	+	0.670472i	0.984891	−	0.173177i	$-0.0554032\pi$
$179$	5.99376	+	8.97030i	0.447995	+	0.670472i	−0.536896	+	0.843648i	$0.680403\pi$
$180$		0			0
$181$	0.698076	+	3.50946i	0.0518876	+	0.260856i	0.998018	−	0.0629294i	$-0.0200443\pi$
$181$	0.698076	+	3.50946i	0.0518876	+	0.260856i	−0.946130	+	0.323786i	$0.895044\pi$
$182$	−1.86881	+	1.40362i	−0.138525	+	0.104043i
$183$		0			0
$184$	0.216660	+	1.29772i	0.0159724	+	0.0956691i
$185$	−0.818514	+	0.339039i	−0.0601783	+	0.0249267i
$186$		0			0
$187$	3.35814	−	5.02581i	0.245572	−	0.367524i
$188$	−1.86497	−	16.8417i	−0.136017	−	1.22831i
$189$		0			0
$190$	−11.0791	−	3.88864i	−0.803761	−	0.282112i
$191$	0.722126			0.0522512			0.0261256	−	0.999659i	$-0.491683\pi$
$191$	0.722126			0.0522512			0.0261256	+	0.999659i	$0.491683\pi$
$192$		0			0
$193$	−5.30778			−0.382063			−0.191031	−	0.981584i	$-0.561183\pi$
$193$	−5.30778			−0.382063			−0.191031	+	0.981584i	$0.561183\pi$
$194$	18.3804	+	6.45131i	1.31963	+	0.463177i
$195$		0			0
$196$	−2.51080	+	0.278034i	−0.179343	+	0.0198595i
$197$	−8.28629	+	12.4013i	−0.590373	+	0.883556i	−0.999583	−	0.0288843i	$-0.990805\pi$
$197$	−8.28629	+	12.4013i	−0.590373	+	0.883556i	0.409209	+	0.912441i	$0.365805\pi$
$198$		0			0
$199$	−0.443861	+	0.183853i	−0.0314644	+	0.0130330i	−0.398360	−	0.917229i	$-0.630421\pi$
$199$	−0.443861	+	0.183853i	−0.0314644	+	0.0130330i	0.366896	+	0.930262i	$0.380421\pi$
$200$	5.27793	+	3.76772i	0.373206	+	0.266418i
$201$		0			0
$202$	4.54409	−	3.41297i	0.319721	−	0.240136i
$203$	−2.93900	−	14.7753i	−0.206277	−	1.03703i
$204$		0			0
$205$	−5.83124	−	8.72707i	−0.407272	−	0.609525i
$206$	−11.1487	+	0.615393i	−0.776764	+	0.0428765i
$207$		0			0
$208$	−1.58628	+	1.66505i	−0.109989	+	0.115451i
$209$	−4.50673	−	4.50673i	−0.311737	−	0.311737i
$210$		0			0
$211$	−12.2014	+	8.15273i	−0.839980	+	0.561257i	−0.899475	−	0.436972i	$-0.856051\pi$
$211$	−12.2014	+	8.15273i	−0.839980	+	0.561257i	0.0594948	+	0.998229i	$0.481051\pi$
$212$	−3.82766	+	7.37450i	−0.262884	+	0.506483i
$213$		0			0
$214$	−1.09769	+	7.72190i	−0.0750365	+	0.527858i
$215$	−2.44370	+	5.89962i	−0.166659	+	0.402351i
$216$		0			0
$217$	11.0076	+	26.5748i	0.747246	+	1.80401i
$218$	−1.53641	−	5.97982i	−0.104059	−	0.405004i
$219$		0			0
$220$	−2.00360	−	3.64168i	−0.135083	−	0.245522i
$221$	−0.536762	+	2.69848i	−0.0361065	+	0.181520i
$222$		0			0
$223$			20.5439i			1.37572i	0.725843	+	0.687860i	$0.241450\pi$
$223$			20.5439i			1.37572i	−0.725843	+	0.687860i	$0.758550\pi$
$224$	−15.6468	+	4.42679i	−1.04544	+	0.295777i
$225$		0			0
$226$	10.1266	+	21.0796i	0.673610	+	1.40220i
$227$	−3.83215	+	19.2655i	−0.254348	+	1.27870i	0.616582	+	0.787290i	$0.288517\pi$
$227$	−3.83215	+	19.2655i	−0.254348	+	1.27870i	−0.870931	+	0.491406i	$0.836483\pi$
$228$		0			0
$229$	−18.1422	−	12.1223i	−1.19887	−	0.801061i	−0.214425	−	0.976740i	$-0.568788\pi$
$229$	−18.1422	−	12.1223i	−1.19887	−	0.801061i	−0.984447	+	0.175680i	$0.943788\pi$
$230$	1.04835	−	0.269355i	0.0691261	−	0.0177607i
$231$		0			0
$232$	−5.24644	−	13.8636i	−0.344446	−	0.910187i
$233$	1.49754	−	3.61539i	0.0981074	−	0.236852i	−0.867204	−	0.497953i	$-0.834085\pi$
$233$	1.49754	−	3.61539i	0.0981074	−	0.236852i	0.965312	+	0.261100i	$0.0840854\pi$
$234$		0			0
$235$	−13.6724	+	2.71960i	−0.891887	+	0.177407i
$236$	−3.55604	+	1.12592i	−0.231478	+	0.0732910i
$237$		0			0
$238$	−12.9772	+	14.4936i	−0.841190	+	0.939481i
$239$	−4.87803	−	4.87803i	−0.315534	−	0.315534i	0.531515	−	0.847049i	$-0.321623\pi$
$239$	−4.87803	−	4.87803i	−0.315534	−	0.315534i	−0.847049	+	0.531515i	$0.821623\pi$
$240$		0			0
$241$	1.70539	−	1.70539i	0.109854	−	0.109854i	−0.650043	−	0.759897i	$-0.725249\pi$
$241$	1.70539	−	1.70539i	0.109854	−	0.109854i	0.759897	+	0.650043i	$0.225249\pi$
$242$	0.733039	+	13.2800i	0.0471215	+	0.853669i
$243$		0			0
$244$	8.49920	+	10.1042i	0.544106	+	0.646858i
$245$	0.405444	+	2.03831i	0.0259029	+	0.130223i
$246$		0			0
$247$	2.68027	+	1.11020i	0.170541	+	0.0706405i
$248$	14.9891	+	24.0077i	0.951808	+	1.52449i
$249$		0			0
$250$	8.63581	−	14.6079i	0.546177	−	0.923882i
$251$	0.380597	−	0.569604i	0.0240231	−	0.0359531i	−0.819264	−	0.573417i	$-0.805618\pi$
$251$	0.380597	−	0.569604i	0.0240231	−	0.0359531i	0.843287	+	0.537464i	$0.180618\pi$
$252$		0			0
$253$	0.576245	+	0.114622i	0.0362282	+	0.00720625i
$254$	10.2813	−	29.2925i	0.645109	−	1.83797i
$255$		0			0
$256$	−14.4682	+	6.83157i	−0.904264	+	0.426973i
$257$	−24.3404			−1.51831			−0.759156	−	0.650908i	$-0.774388\pi$
$257$	−24.3404			−1.51831			−0.759156	+	0.650908i	$0.774388\pi$
$258$		0			0
$259$	1.51806	+	0.301960i	0.0943275	+	0.0187629i
$260$	1.47693	+	1.18244i	0.0915953	+	0.0733321i
$261$		0			0
$262$	−5.17963	+	8.76157i	−0.319998	+	0.541291i
$263$	−9.60085	+	3.97680i	−0.592014	+	0.245220i	−0.658517	−	0.752566i	$-0.728816\pi$
$263$	−9.60085	+	3.97680i	−0.592014	+	0.245220i	0.0665030	+	0.997786i	$0.478816\pi$
$264$		0			0
$265$	6.31516	+	2.61583i	0.387937	+	0.160689i
$266$	12.3193	+	16.4021i	0.755344	+	1.00568i
$267$		0			0
$268$	−7.90186	−	9.39411i	−0.482683	−	0.573836i
$269$	17.3303	+	25.9367i	1.05665	+	1.58139i	0.785513	+	0.618845i	$0.212399\pi$
$269$	17.3303	+	25.9367i	1.05665	+	1.58139i	0.271136	+	0.962541i	$0.412601\pi$
$270$		0			0
$271$	11.8443	−	11.8443i	0.719491	−	0.719491i	−0.249010	−	0.968501i	$-0.580105\pi$
$271$	11.8443	−	11.8443i	0.719491	−	0.719491i	0.968501	+	0.249010i	$0.0801053\pi$
$272$	−10.2462	+	16.1691i	−0.621269	+	0.980394i
$273$		0			0
$274$	10.4476	−	11.6684i	0.631162	−	0.704912i
$275$	2.40782	−	1.60885i	0.145197	−	0.0970176i
$276$		0			0
$277$	−25.5130	+	5.07485i	−1.53293	+	0.304918i	−0.888187	−	0.459483i	$-0.848035\pi$
$277$	−25.5130	+	5.07485i	−1.53293	+	0.304918i	−0.644741	+	0.764401i	$0.723035\pi$
$278$	5.39995	+	0.767617i	0.323867	+	0.0460386i
$279$		0			0
$280$	4.73489	+	12.5118i	0.282964	+	0.747722i
$281$	9.37710	+	22.6383i	0.559391	+	1.35049i	0.910249	+	0.414061i	$0.135890\pi$
$281$	9.37710	+	22.6383i	0.559391	+	1.35049i	−0.350858	+	0.936429i	$0.614110\pi$
$282$		0			0
$283$	−19.3155	−	12.9062i	−1.14819	−	0.767195i	−0.172210	−	0.985060i	$-0.555091\pi$
$283$	−19.3155	−	12.9062i	−1.14819	−	0.767195i	−0.975979	+	0.217865i	$0.930091\pi$
$284$	−8.74024	−	2.53615i	−0.518638	−	0.150493i
$285$		0			0
$286$	0.444699	+	0.925692i	0.0262956	+	0.0547373i
$287$			18.3369i			1.08239i
$288$		0			0
$289$			5.90150i			0.347147i
$290$	−10.9922	+	5.28061i	−0.645484	+	0.310088i
$291$		0			0
$292$	0.951041	+	1.72859i	0.0556555	+	0.101158i
$293$	−23.5455	−	15.7326i	−1.37554	−	0.919109i	−0.375573	−	0.926793i	$-0.622554\pi$
$293$	−23.5455	−	15.7326i	−1.37554	−	0.919109i	−0.999970	+	0.00768446i	$0.997554\pi$
$294$		0			0
$295$	1.17433	+	2.83507i	0.0683719	+	0.165064i
$296$	1.52223	+	0.0470838i	0.0884779	+	0.00273669i
$297$		0			0
$298$	4.42800	−	31.1496i	0.256507	−	1.80445i
$299$	−0.262297	+	0.0521741i	−0.0151690	+	0.00301731i
$300$		0			0
$301$	9.27596	−	6.19800i	0.534657	−	0.357247i
$302$	8.23377	+	7.37234i	0.473800	+	0.424230i
$303$		0			0
$304$	14.6138	+	13.9224i	0.838158	+	0.798507i
$305$	7.68088	−	7.68088i	0.439806	−	0.439806i
$306$		0			0
$307$	−6.01712	−	9.00525i	−0.343415	−	0.513957i	0.619054	−	0.785348i	$-0.287516\pi$
$307$	−6.01712	−	9.00525i	−0.343415	−	0.513957i	−0.962469	+	0.271392i	$0.912516\pi$
$308$	−0.624184	+	7.23466i	−0.0355662	+	0.412233i
$309$		0			0
$310$	18.6179	−	13.9835i	1.05742	−	0.794210i
$311$	6.91332	+	2.86359i	0.392018	+	0.162379i	0.569981	−	0.821658i	$-0.306951\pi$
$311$	6.91332	+	2.86359i	0.392018	+	0.162379i	−0.177963	+	0.984037i	$0.556951\pi$
$312$		0			0
$313$	−20.9463	+	8.67625i	−1.18396	+	0.490411i	−0.885783	−	0.464101i	$-0.846378\pi$
$313$	−20.9463	+	8.67625i	−1.18396	+	0.490411i	−0.298174	+	0.954511i	$0.596378\pi$
$314$	−25.5818	−	15.1233i	−1.44366	−	0.853459i
$315$		0			0
$316$	−0.428600	+	0.0474611i	−0.0241106	+	0.00266989i
$317$	12.9479	+	2.57551i	0.727229	+	0.144655i	0.544802	−	0.838565i	$-0.316605\pi$
$317$	12.9479	+	2.57551i	0.727229	+	0.144655i	0.182427	+	0.983219i	$0.441605\pi$
$318$		0			0
$319$	−6.61944			−0.370617
$320$	6.62262	+	11.3757i	0.370216	+	0.635923i
$321$		0			0
$322$	−1.78428	−	0.626265i	−0.0994343	−	0.0349004i
$323$	23.6840	+	4.71104i	1.31781	+	0.262129i
$324$		0			0
$325$	−0.732323	+	1.09600i	−0.0406220	+	0.0607951i
$326$	24.9585	+	14.7548i	1.38232	+	0.817195i
$327$		0			0
$328$	2.97117	+	17.7963i	0.164056	+	0.982637i
$329$	22.5003	+	9.31994i	1.24048	+	0.513825i
$330$		0			0
$331$	0.994900	+	5.00170i	0.0546846	+	0.274918i	0.998447	−	0.0557056i	$-0.0177408\pi$
$331$	0.994900	+	5.00170i	0.0546846	+	0.274918i	−0.943763	+	0.330624i	$0.892741\pi$
$332$	−12.3771	−	1.06786i	−0.679283	−	0.0586064i
$333$		0			0
$334$	20.5547	−	1.13459i	1.12470	−	0.0620822i
$335$	−7.14106	+	7.14106i	−0.390158	+	0.390158i
$336$		0			0
$337$	−9.51763	−	9.51763i	−0.518459	−	0.518459i	0.398646	−	0.917105i	$-0.369480\pi$
$337$	−9.51763	−	9.51763i	−0.518459	−	0.518459i	−0.917105	+	0.398646i	$0.869480\pi$
$338$	13.3485	+	11.9519i	0.726061	+	0.650099i
$339$		0			0
$340$	13.9775	+	7.25487i	0.758036	+	0.393451i
$341$	12.3961	−	2.46574i	0.671286	−	0.133527i
$342$		0			0
$343$	−6.31088	+	15.2358i	−0.340755	+	0.822656i
$344$	7.99822	−	7.51829i	0.431235	−	0.405359i
$345$		0			0
$346$	6.54425	+	25.4707i	0.351821	+	1.36931i
$347$	−24.8873	−	16.6292i	−1.33602	−	0.892701i	−0.337210	−	0.941430i	$-0.609483\pi$
$347$	−24.8873	−	16.6292i	−1.33602	−	0.892701i	−0.998812	+	0.0487284i	$0.984483\pi$
$348$		0			0
$349$	2.77238	−	13.9377i	0.148402	−	0.746067i	−0.832874	−	0.553462i	$-0.813306\pi$
$349$	2.77238	−	13.9377i	0.148402	−	0.746067i	0.981276	−	0.192605i	$-0.0616936\pi$
$350$	−8.40128	+	4.03594i	−0.449067	+	0.215730i
$351$		0			0
$352$	0.566468	+	7.12252i	0.0301928	+	0.379632i
$353$		−	22.9803i		−	1.22312i	−0.791199	−	0.611558i	$-0.790543\pi$
$353$		−	22.9803i		−	1.22312i	0.791199	−	0.611558i	$-0.209457\pi$
$354$		0			0
$355$	−1.46066	+	7.34326i	−0.0775240	+	0.389740i
$356$	−2.16635	+	7.46584i	−0.114817	+	0.395689i
$357$		0			0
$358$	−14.7773	+	3.79676i	−0.781003	+	0.200665i
$359$	−2.63107	−	6.35196i	−0.138862	−	0.335244i	0.839115	−	0.543954i	$-0.183073\pi$
$359$	−2.63107	−	6.35196i	−0.138862	−	0.335244i	−0.977978	+	0.208710i	$0.933073\pi$
$360$		0			0
$361$	2.47302	−	5.97039i	0.130159	−	0.314231i
$362$	−5.01000	−	0.712185i	−0.263320	−	0.0374316i
$363$		0			0
$364$	−0.997722	−	3.15115i	−0.0522948	−	0.165165i
$365$	1.34958	−	0.901757i	0.0706400	−	0.0472001i
$366$		0			0
$367$	−2.41091	−	2.41091i	−0.125848	−	0.125848i	0.641377	−	0.767226i	$-0.278363\pi$
$367$	−2.41091	−	2.41091i	−0.125848	−	0.125848i	−0.767226	+	0.641377i	$0.778363\pi$
$368$	−1.83316	−	0.318691i	−0.0955600	−	0.0166129i
$369$		0			0
$370$	−0.0690550	−	1.25102i	−0.00359000	−	0.0650375i
$371$	−6.63456	−	9.92931i	−0.344449	−	0.515504i
$372$		0			0
$373$	2.78301	+	13.9911i	0.144099	+	0.724433i	0.983498	+	0.180918i	$0.0579068\pi$
$373$	2.78301	+	13.9911i	0.144099	+	0.724433i	−0.839400	+	0.543515i	$0.817093\pi$
$374$	5.13364	+	6.83502i	0.265454	+	0.353431i
$375$		0			0
$376$	23.3471	+	5.39940i	1.20404	+	0.278453i
$377$	2.78370	−	1.15305i	0.143368	−	0.0593849i
$378$		0			0
$379$	14.2902	−	21.3867i	0.734036	−	1.09856i	−0.257187	−	0.966362i	$-0.582796\pi$
$379$	14.2902	−	21.3867i	0.734036	−	1.09856i	0.991223	−	0.132201i	$-0.0422044\pi$
$380$	10.3780	−	12.9627i	0.532382	−	0.664972i
$381$		0			0
$382$	−0.338217	+	0.963608i	−0.0173047	+	0.0493025i
$383$	−21.5847			−1.10293			−0.551463	−	0.834199i	$-0.685930\pi$
$383$	−21.5847			−1.10293			−0.551463	+	0.834199i	$0.685930\pi$
$384$		0			0
$385$	5.97401			0.304464
$386$	2.48597	−	7.08273i	0.126532	−	0.360502i
$387$		0			0
$388$	−17.2173	+	21.5053i	−0.874077	+	1.09177i
$389$	−3.94394	+	5.90253i	−0.199966	+	0.299270i	−0.917877	−	0.396864i	$-0.870098\pi$
$389$	−3.94394	+	5.90253i	−0.199966	+	0.299270i	0.717911	+	0.696135i	$0.245098\pi$
$390$		0			0
$391$	−2.05662	+	0.851878i	−0.104007	+	0.0430813i
$392$	0.804954	−	3.48064i	0.0406563	−	0.175799i
$393$		0			0
$394$	−12.6674	−	16.8656i	−0.638173	−	0.849675i
$395$	0.0692105	+	0.347944i	0.00348236	+	0.0175070i
$396$		0			0
$397$	−7.40790	−	11.0867i	−0.371792	−	0.556426i	0.597647	−	0.801759i	$-0.296102\pi$
$397$	−7.40790	−	11.0867i	−0.371792	−	0.556426i	−0.969439	+	0.245334i	$0.921102\pi$
$398$	−0.0374469	−	0.678400i	−0.00187704	−	0.0340051i
$399$		0			0
$400$	−7.49965	+	5.27824i	−0.374983	+	0.263912i
$401$	8.50260	+	8.50260i	0.424600	+	0.424600i	0.886784	−	0.462184i	$-0.152934\pi$
$401$	8.50260	+	8.50260i	0.424600	+	0.424600i	−0.462184	+	0.886784i	$0.652934\pi$
$402$		0			0
$403$	−4.78347	+	3.19622i	−0.238282	+	0.159215i
$404$	2.42601	+	7.66217i	0.120698	+	0.381207i
$405$		0			0
$406$	21.0928	+	2.99840i	1.04682	+	0.148808i
$407$	0.260262	−	0.628329i	0.0129007	−	0.0311451i
$408$		0			0
$409$	10.8420	+	26.1750i	0.536104	+	1.29427i	0.927423	+	0.374014i	$0.122019\pi$
$409$	10.8420	+	26.1750i	0.536104	+	1.29427i	−0.391320	+	0.920255i	$0.627981\pi$
$410$	14.3766	−	3.69381i	0.710009	−	0.182424i
$411$		0			0
$412$	4.40043	−	15.1650i	0.216793	−	0.747128i
$413$	1.04590	−	5.25807i	0.0514651	−	0.258733i
$414$		0			0
$415$			10.2204i			0.501699i
$416$	−1.47890	−	2.89659i	−0.0725089	−	0.142017i
$417$		0			0
$418$	8.12459	−	3.90302i	0.397387	−	0.190903i
$419$	4.06419	−	20.4320i	0.198549	−	0.998171i	−0.745032	−	0.667028i	$-0.767566\pi$
$419$	4.06419	−	20.4320i	0.198549	−	0.998171i	0.943581	−	0.331142i	$-0.107434\pi$
$420$		0			0
$421$	−18.4939	−	12.3572i	−0.901337	−	0.602254i	0.0162157	−	0.999869i	$-0.494838\pi$
$421$	−18.4939	−	12.3572i	−0.901337	−	0.602254i	−0.917553	+	0.397614i	$0.869838\pi$
$422$	−5.16436	−	20.1001i	−0.251397	−	0.978456i
$423$		0			0
$424$	−8.04784	−	8.56158i	−0.390838	−	0.415787i
$425$	−4.19876	+	10.1367i	−0.203670	+	0.491703i
$426$		0			0
$427$	−18.6125	+	3.70225i	−0.900720	+	0.179164i
$428$	−9.79002	−	5.08141i	−0.473219	−	0.245619i
$429$		0			0
$430$	−6.72795	−	6.02405i	−0.324450	−	0.290505i
$431$	−9.16945	−	9.16945i	−0.441677	−	0.441677i	0.450898	−	0.892575i	$-0.351104\pi$
$431$	−9.16945	−	9.16945i	−0.441677	−	0.441677i	−0.892575	+	0.450898i	$0.851104\pi$
$432$		0			0
$433$	9.06306	−	9.06306i	0.435543	−	0.435543i	−0.454966	−	0.890509i	$-0.650349\pi$
$433$	9.06306	−	9.06306i	0.435543	−	0.435543i	0.890509	+	0.454966i	$0.150349\pi$
$434$	−40.6171	+	2.24201i	−1.94968	+	0.107620i
$435$		0			0
$436$	8.69909	+	0.750530i	0.416611	+	0.0359439i
$437$	0.457921	+	2.30212i	0.0219053	+	0.110125i
$438$		0			0
$439$	37.3964	+	15.4901i	1.78483	+	0.739301i	0.991436	+	0.130594i	$0.0416884\pi$
$439$	37.3964	+	15.4901i	1.78483	+	0.739301i	0.793395	+	0.608707i	$0.208312\pi$
$440$	5.79789	−	0.967984i	0.276404	−	0.0461468i
$441$		0			0
$442$	−3.34947	−	1.98013i	−0.159318	−	0.0941850i
$443$	0.953921	−	1.42764i	0.0453222	−	0.0678294i	−0.808117	−	0.589023i	$-0.799513\pi$
$443$	0.953921	−	1.42764i	0.0453222	−	0.0678294i	0.853439	+	0.521193i	$0.174513\pi$
$444$		0			0
$445$	6.27255	+	1.24769i	0.297347	+	0.0591460i
$446$	−27.4139	−	9.62198i	−1.29808	−	0.455614i
$447$		0			0
$448$	1.42123	−	22.9525i	0.0671470	−	1.08440i
$449$	24.6119			1.16151			0.580754	−	0.814079i	$-0.302758\pi$
$449$	24.6119			1.16151			0.580754	+	0.814079i	$0.302758\pi$
$450$		0			0
$451$	7.90236	+	1.57188i	0.372108	+	0.0740168i
$452$	−32.8717	+	3.64005i	−1.54615	+	0.171214i
$453$		0			0
$454$	−23.9131	−	14.1369i	−1.12230	−	0.663476i
$455$	−2.51227	+	1.04062i	−0.117777	+	0.0487849i
$456$		0			0
$457$	0.962960	+	0.398871i	0.0450454	+	0.0186584i	0.405092	−	0.914276i	$-0.367239\pi$
$457$	0.962960	+	0.398871i	0.0450454	+	0.0186584i	−0.360047	+	0.932934i	$0.617239\pi$
$458$	24.6731	−	18.5315i	1.15290	−	0.865919i
$459$		0			0
$460$	−0.131579	+	1.52508i	−0.00613491	+	0.0711072i
$461$	7.72794	+	11.5657i	0.359926	+	0.538667i	0.966602	−	0.256282i	$-0.0824975\pi$
$461$	7.72794	+	11.5657i	0.359926	+	0.538667i	−0.606676	+	0.794949i	$0.707498\pi$
$462$		0			0
$463$	8.29596	−	8.29596i	0.385546	−	0.385546i	−0.487549	−	0.873095i	$-0.662109\pi$
$463$	8.29596	−	8.29596i	0.385546	−	0.385546i	0.873095	+	0.487549i	$0.162109\pi$
$464$	20.9568	−	0.507716i	0.972896	−	0.0235701i
$465$		0			0
$466$	4.12300	+	3.69164i	0.190994	+	0.171012i
$467$	0.240041	−	0.160391i	0.0111078	−	0.00742199i	−0.550004	−	0.835162i	$-0.685374\pi$
$467$	0.240041	−	0.160391i	0.0111078	−	0.00742199i	0.561112	+	0.827740i	$0.310374\pi$
$468$		0			0
$469$	17.3043	−	3.44205i	0.799040	−	0.158939i
$470$	2.77457	−	19.5182i	0.127981	−	0.900309i
$471$		0			0
$472$	0.163083	−	5.27253i	0.00750651	−	0.242688i
$473$	−1.87590	−	4.52882i	−0.0862539	−	0.208235i
$474$		0			0
$475$	9.61934	+	6.42743i	0.441365	+	0.294911i
$476$	−13.2623	−	24.1052i	−0.607876	−	1.10486i
$477$		0			0
$478$	8.79395	−	4.22458i	0.402226	−	0.193228i
$479$		−	27.3994i		−	1.25191i	−0.779860	−	0.625954i	$-0.784710\pi$
$479$		−	27.3994i		−	1.25191i	0.779860	−	0.625954i	$-0.215290\pi$
$480$		0			0
$481$			0.309569i			0.0141151i
$482$	1.47694	+	3.07443i	0.0672730	+	0.140036i
$483$		0			0
$484$	−18.0642	−	5.24167i	−0.821099	−	0.238258i
$485$	18.8443	+	12.5913i	0.855675	+	0.571744i
$486$		0			0
$487$	−11.7477	−	28.3614i	−0.532338	−	1.28518i	−0.929971	−	0.367633i	$-0.880168\pi$
$487$	−11.7477	−	28.3614i	−0.532338	−	1.28518i	0.397633	−	0.917544i	$-0.369832\pi$
$488$	−17.4639	+	6.60893i	−0.790552	+	0.299172i
$489$		0			0
$490$	−2.90982	−	0.413639i	−0.131452	−	0.0186863i
$491$	−1.43618	+	0.285675i	−0.0648141	+	0.0128923i	−0.227391	−	0.973804i	$-0.573019\pi$
$491$	−1.43618	+	0.285675i	−0.0648141	+	0.0128923i	0.162577	+	0.986696i	$0.448019\pi$
$492$		0			0
$493$	20.8531	−	13.9336i	0.939178	−	0.627539i
$494$	−2.73680	+	3.05658i	−0.123134	+	0.137522i
$495$		0			0
$496$	−39.0564	+	8.75720i	−1.75368	+	0.393210i
$497$	9.24919	−	9.24919i	0.414883	−	0.414883i
$498$		0			0
$499$	8.33594	+	12.4756i	0.373168	+	0.558485i	0.969760	−	0.244059i	$-0.0784791\pi$
$499$	8.33594	+	12.4756i	0.373168	+	0.558485i	−0.596592	+	0.802544i	$0.703479\pi$
$500$	15.4481	+	18.3654i	0.690861	+	0.821328i
$501$		0			0
$502$	0.581825	+	0.774652i	0.0259681	+	0.0345744i
$503$	9.56425	+	3.96164i	0.426449	+	0.176641i	0.585577	−	0.810617i	$-0.300868\pi$
$503$	9.56425	+	3.96164i	0.426449	+	0.176641i	−0.159128	+	0.987258i	$0.550868\pi$
$504$		0			0
$505$	6.10871	−	2.53031i	0.271834	−	0.112597i
$506$	−0.422844	+	0.715260i	−0.0187977	+	0.0317972i
$507$		0			0
$508$	34.2726	+	27.4390i	1.52060	+	1.21741i
$509$	1.27790	+	0.254190i	0.0566419	+	0.0112668i	0.223330	−	0.974743i	$-0.428307\pi$
$509$	1.27790	+	0.254190i	0.0566419	+	0.0112668i	−0.166688	+	0.986010i	$0.553307\pi$
$510$		0			0
$511$	−2.83566			−0.125442
$512$	−2.33971	−	22.5061i	−0.103402	−	0.994640i
$513$		0			0
$514$	11.4001	−	32.4800i	0.502838	−	1.43263i
$515$	−12.7412	−	2.53437i	−0.561443	−	0.111678i
$516$		0			0
$517$	5.94524	−	8.89768i	0.261471	−	0.391320i
$518$	−1.11394	+	1.88428i	−0.0489436	+	0.0827904i
$519$		0			0
$520$	−2.26960	+	1.41701i	−0.0995284	+	0.0621400i
$521$	30.4733	+	12.6225i	1.33506	+	0.553001i	0.932095	−	0.362214i	$-0.117979\pi$
$521$	30.4733	+	12.6225i	1.33506	+	0.553001i	0.402967	+	0.915215i	$0.367979\pi$
$522$		0			0
$523$	0.709853	+	3.56867i	0.0310397	+	0.156047i	0.993197	−	0.116448i	$-0.0371510\pi$
$523$	0.709853	+	3.56867i	0.0310397	+	0.156047i	−0.962157	+	0.272496i	$0.912151\pi$
$524$	−9.26554	−	11.0153i	−0.404767	−	0.481206i
$525$		0			0
$526$	−0.809988	−	14.6740i	−0.0353172	−	0.639817i
$527$	−33.8610	+	33.8610i	−1.47501	+	1.47501i
$528$		0			0
$529$	16.1105	+	16.1105i	0.700455	+	0.700455i
$530$	−6.44835	+	7.20183i	−0.280099	+	0.312827i
$531$		0			0
$532$	−27.6569	+	8.75678i	−1.19908	+	0.379655i
$533$	−3.59702	+	0.715492i	−0.155804	+	0.0309914i
$534$		0			0
$535$	−3.47264	+	8.38370i	−0.150135	+	0.362459i
$536$	16.2365	−	6.14444i	0.701309	−	0.265399i
$537$		0			0
$538$	−42.7269	+	10.9779i	−1.84209	+	0.473292i
$539$	−1.32649	−	0.886330i	−0.0571358	−	0.0381769i
$540$		0			0
$541$	0.728776	−	3.66380i	0.0313325	−	0.157519i	−0.961952	−	0.273220i	$-0.911911\pi$
$541$	0.728776	−	3.66380i	0.0313325	−	0.157519i	0.993284	+	0.115701i	$0.0369113\pi$
$542$	10.2577	+	21.3525i	0.440605	+	0.917170i
$543$		0			0
$544$	−16.7771	−	21.2456i	−0.719314	−	0.910898i
$545$		−	7.18326i		−	0.307697i
$546$		0			0
$547$	2.21811	−	11.1512i	0.0948394	−	0.476790i	−0.903952	−	0.427635i	$-0.859347\pi$
$547$	2.21811	−	11.1512i	0.0948394	−	0.476790i	0.998791	−	0.0491555i	$-0.0156530\pi$
$548$	10.6771	+	19.4063i	0.456102	+	0.828998i
$549$		0			0
$550$	1.01913	+	3.96653i	0.0434559	+	0.169134i
$551$	−10.1200	−	24.4319i	−0.431128	−	1.04083i
$552$		0			0
$553$	0.237181	−	0.572605i	0.0100859	−	0.0243496i
$554$	5.17742	−	36.4215i	0.219968	−	1.54740i
$555$		0			0
$556$	−3.55344	+	6.84619i	−0.150700	+	0.290343i
$557$	15.2399	−	10.1830i	0.645734	−	0.431466i	−0.189107	−	0.981956i	$-0.560559\pi$
$557$	15.2399	−	10.1830i	0.645734	−	0.431466i	0.834841	+	0.550491i	$0.185559\pi$
$558$		0			0
$559$	1.57776	+	1.57776i	0.0667321	+	0.0667321i
$560$	−18.9134	+	0.458211i	−0.799239	+	0.0193630i
$561$		0			0
$562$	−34.6006	+	1.90991i	−1.45954	+	0.0805648i
$563$	−2.21898	−	3.32093i	−0.0935187	−	0.139961i	0.781760	−	0.623579i	$-0.214322\pi$
$563$	−2.21898	−	3.32093i	−0.0935187	−	0.139961i	−0.875279	+	0.483619i	$0.839322\pi$
$564$		0			0
$565$	5.30813	+	26.6858i	0.223315	+	1.12268i
$566$	26.2688	−	19.7300i	1.10416	−	0.829312i
$567$		0			0
$568$	7.47785	−	10.4752i	0.313764	−	0.439529i
$569$	−27.7449	+	11.4923i	−1.16313	+	0.481783i	−0.878915	−	0.476978i	$-0.841732\pi$
$569$	−27.7449	+	11.4923i	−1.16313	+	0.481783i	−0.284213	+	0.958761i	$0.591732\pi$
$570$		0			0
$571$	17.3752	−	26.0038i	0.727128	−	1.08822i	−0.265152	−	0.964207i	$-0.585422\pi$
$571$	17.3752	−	26.0038i	0.727128	−	1.08822i	0.992280	−	0.124017i	$-0.0395777\pi$
$572$	−1.44353	+	0.159849i	−0.0603569	+	0.00668363i
$573$		0			0
$574$	−24.4688	−	8.58831i	−1.02131	−	0.358469i
$575$	−1.06649			−0.0444756
$576$		0			0
$577$	−4.61192			−0.191997			−0.0959984	−	0.995381i	$-0.530604\pi$
$577$	−4.61192			−0.191997			−0.0959984	+	0.995381i	$0.530604\pi$
$578$	−7.87499	−	2.76404i	−0.327557	−	0.114969i
$579$		0			0
$580$	−1.89814	−	17.1413i	−0.0788161	−	0.711753i
$581$	9.91996	−	14.8463i	0.411549	−	0.615927i
$582$		0			0
$583$	−4.84781	+	2.00803i	−0.200776	+	0.0831640i
$584$	−2.75207	+	0.459470i	−0.113881	+	0.0190130i
$585$		0			0
$586$	32.0215	−	24.0507i	1.32280	−	0.993524i
$587$	4.06182	+	20.4202i	0.167649	+	0.842831i	0.969459	+	0.245252i	$0.0788706\pi$
$587$	4.06182	+	20.4202i	0.167649	+	0.842831i	−0.801810	+	0.597579i	$0.796129\pi$
$588$		0			0
$589$	28.0525	+	41.9835i	1.15588	+	1.72990i
$590$	−4.33314	+	0.239185i	−0.178393	+	0.00984707i
$591$		0			0
$592$	−0.775785	+	2.00922i	−0.0318846	+	0.0825785i
$593$	3.69463	+	3.69463i	0.151720	+	0.151720i	0.778886	−	0.627166i	$-0.215785\pi$
$593$	3.69463	+	3.69463i	0.151720	+	0.151720i	−0.627166	+	0.778886i	$0.715785\pi$
$594$		0			0
$595$	−18.8199	+	12.5750i	−0.771539	+	0.515526i
$596$	39.4923	+	20.4981i	1.61767	+	0.839633i
$597$		0			0
$598$	0.0532287	−	0.374447i	0.00217668	−	0.0153123i
$599$	4.44136	−	10.7224i	0.181469	−	0.438105i	−0.806801	−	0.590824i	$-0.798803\pi$
$599$	4.44136	−	10.7224i	0.181469	−	0.438105i	0.988270	+	0.152719i	$0.0488028\pi$
$600$		0			0
$601$	−4.16840	−	10.0634i	−0.170033	−	0.410495i	0.815776	−	0.578368i	$-0.196310\pi$
$601$	−4.16840	−	10.0634i	−0.170033	−	0.410495i	−0.985809	+	0.167873i	$0.946310\pi$
$602$	3.92613	+	15.2808i	0.160017	+	0.622799i
$603$		0			0
$604$	−13.6941	+	7.53427i	−0.557204	+	0.306565i
$605$	−3.01888	+	15.1769i	−0.122735	+	0.617030i
$606$		0			0
$607$		−	29.1457i		−	1.18299i	−0.806310	−	0.591493i	$-0.798539\pi$
$607$		−	29.1457i		−	1.18299i	0.806310	−	0.591493i	$-0.201461\pi$
$608$	−25.4227	+	12.9800i	−1.03103	+	0.526407i
$609$		0			0
$610$	6.65197	+	13.8468i	0.269330	+	0.560642i
$611$	−0.950281	+	4.77739i	−0.0384443	+	0.193272i
$612$		0			0
$613$	−5.29850	−	3.54035i	−0.214005	−	0.142993i	0.443948	−	0.896052i	$-0.353577\pi$
$613$	−5.29850	−	3.54035i	−0.214005	−	0.142993i	−0.657953	+	0.753059i	$0.728577\pi$
$614$	14.8348	−	3.81155i	0.598686	−	0.153822i
$615$		0			0
$616$	−9.36163	−	4.22136i	−0.377191	−	0.170083i
$617$	−3.88763	+	9.38556i	−0.156510	+	0.377849i	−0.982612	−	0.185673i	$-0.940554\pi$
$617$	−3.88763	+	9.38556i	−0.156510	+	0.377849i	0.826102	+	0.563521i	$0.190554\pi$
$618$		0			0
$619$	−3.09719	+	0.616070i	−0.124487	+	0.0247620i	−0.256940	−	0.966427i	$-0.582714\pi$
$619$	−3.09719	+	0.616070i	−0.124487	+	0.0247620i	0.132454	+	0.991189i	$0.457714\pi$
$620$	9.93975	+	31.3931i	0.399190	+	1.26078i
$621$		0			0
$622$	−7.05913	+	7.88397i	−0.283045	+	0.316118i
$623$	−7.90057	−	7.90057i	−0.316530	−	0.316530i
$624$		0			0
$625$	5.85477	−	5.85477i	0.234191	−	0.234191i
$626$	−1.76716	−	32.0145i	−0.0706301	−	1.27956i
$627$		0			0
$628$	32.1622	−	27.0533i	1.28341	−	1.07954i
$629$	0.502703	+	2.52726i	0.0200441	+	0.100768i
$630$		0			0
$631$	−29.9605	−	12.4100i	−1.19271	−	0.494036i	−0.304073	−	0.952649i	$-0.598347\pi$
$631$	−29.9605	−	12.4100i	−1.19271	−	0.494036i	−0.888636	+	0.458613i	$0.848347\pi$
$632$	0.137408	−	0.594155i	0.00546579	−	0.0236342i
$633$		0			0
$634$	−9.50110	+	16.0715i	−0.377337	+	0.638282i
$635$	20.0666	−	30.0318i	0.796319	−	1.19178i
$636$		0			0
$637$	0.712223	+	0.141670i	0.0282193	+	0.00561317i
$638$	3.10029	−	8.83301i	0.122742	−	0.349702i
$639$		0			0
$640$	−18.2816	+	3.50930i	−0.722644	+	0.138717i
$641$	−27.6811			−1.09334			−0.546668	−	0.837349i	$-0.684104\pi$
$641$	−27.6811			−1.09334			−0.546668	+	0.837349i	$0.684104\pi$
$642$		0			0
$643$	42.4514	+	8.44410i	1.67412	+	0.333003i	0.938733	−	0.344646i	$-0.112001\pi$
$643$	42.4514	+	8.44410i	1.67412	+	0.333003i	0.735386	+	0.677649i	$0.237001\pi$
$644$	1.67138	−	2.08764i	0.0658617	−	0.0822645i
$645$		0			0
$646$	−17.3791	+	29.3976i	−0.683772	+	1.15663i
$647$	35.3075	−	14.6248i	1.38808	−	0.574962i	0.441451	−	0.897285i	$-0.354464\pi$
$647$	35.3075	−	14.6248i	1.38808	−	0.574962i	0.946630	+	0.322324i	$0.104464\pi$
$648$		0			0
$649$	−2.17633	−	0.901466i	−0.0854285	−	0.0353856i
$650$	−1.11951	−	1.49054i	−0.0439109	−	0.0584638i
$651$		0			0
$652$	−31.3785	+	26.3941i	−1.22888	+	1.03367i
$653$	−13.3150	−	19.9272i	−0.521055	−	0.779813i	0.473853	−	0.880604i	$-0.342863\pi$
$653$	−13.3150	−	19.9272i	−0.521055	−	0.779813i	−0.994908	+	0.100791i	$0.967863\pi$
$654$		0			0
$655$	−8.37343	+	8.37343i	−0.327177	+	0.327177i
$656$	−25.1391	−	4.37037i	−0.981516	−	0.170634i
$657$		0			0
$658$	−22.9749	+	25.6594i	−0.895654	+	1.00031i
$659$	−17.2984	+	11.5584i	−0.673852	+	0.450253i	−0.844839	−	0.535020i	$-0.820304\pi$
$659$	−17.2984	+	11.5584i	−0.673852	+	0.450253i	0.170988	+	0.985273i	$0.445304\pi$
$660$		0			0
$661$	14.9381	−	2.97137i	0.581025	−	0.115573i	0.104177	−	0.994559i	$-0.466779\pi$
$661$	14.9381	−	2.97137i	0.581025	−	0.115573i	0.476848	+	0.878986i	$0.341779\pi$
$662$	−7.14027	−	1.01501i	−0.277514	−	0.0394494i
$663$		0			0
$664$	7.22194	−	16.0160i	0.280266	−	0.621540i
$665$	9.13327	+	22.0497i	0.354173	+	0.855049i
$666$		0			0
$667$	2.02696	+	1.35437i	0.0784842	+	0.0524415i
$668$	−8.11303	+	27.9597i	−0.313902	+	1.08179i
$669$		0			0
$670$	−6.18446	−	12.8737i	−0.238927	−	0.497353i
$671$			8.33848i			0.321903i
$672$		0			0
$673$		−	33.8371i		−	1.30432i	−0.758080	−	0.652162i	$-0.773862\pi$
$673$		−	33.8371i		−	1.30432i	0.758080	−	0.652162i	$-0.226138\pi$
$674$	17.1581	−	8.24268i	0.660905	−	0.317496i
$675$		0			0
$676$	−22.2006	+	12.2144i	−0.853870	+	0.469786i
$677$	−28.0419	−	18.7370i	−1.07774	−	0.720121i	−0.115768	−	0.993276i	$-0.536933\pi$
$677$	−28.0419	−	18.7370i	−1.07774	−	0.720121i	−0.961970	+	0.273155i	$0.911933\pi$
$678$		0			0
$679$	−15.1522	−	36.5807i	−0.581489	−	1.40384i
$680$	−16.2275	+	15.2537i	−0.622295	+	0.584954i
$681$		0			0
$682$	−2.51557	+	17.6963i	−0.0963263	+	0.677625i
$683$	−14.0115	+	2.78707i	−0.536137	+	0.106644i	−0.455730	−	0.890118i	$-0.650622\pi$
$683$	−14.0115	+	2.78707i	−0.536137	+	0.106644i	−0.0804066	+	0.996762i	$0.525622\pi$
$684$		0			0
$685$	15.1513	−	10.1238i	0.578901	−	0.386809i
$686$	−17.3750	−	15.5571i	−0.663379	−	0.593975i
$687$		0			0
$688$	6.28637	+	14.1942i	0.239666	+	0.541147i
$689$	1.68889	−	1.68889i	0.0643415	−	0.0643415i
$690$		0			0
$691$	10.9236	+	16.3483i	0.415552	+	0.621918i	0.978909	−	0.204296i	$-0.0654904\pi$
$691$	10.9236	+	16.3483i	0.415552	+	0.621918i	−0.563357	+	0.826214i	$0.690490\pi$
$692$	−37.0533	−	3.19685i	−1.40856	−	0.121526i
$693$		0			0
$694$	33.8463	−	25.4213i	1.28479	−	0.964979i
$695$	5.86275	+	2.42843i	0.222387	+	0.0921156i
$696$		0			0
$697$	−28.2035	+	11.6823i	−1.06828	+	0.442497i
$698$	17.3000	+	10.2274i	0.654816	+	0.387111i
$699$		0			0
$700$	−1.45074	−	13.1010i	−0.0548328	−	0.495171i
$701$	−11.0341	−	2.19482i	−0.416753	−	0.0828974i	−0.0177402	−	0.999843i	$-0.505647\pi$
$701$	−11.0341	−	2.19482i	−0.416753	−	0.0828974i	−0.399013	+	0.916945i	$0.630647\pi$
$702$		0			0
$703$	2.71702			0.102474
$704$	−9.76964	−	2.58002i	−0.368207	−	0.0972383i
$705$		0			0
$706$	30.6650	+	10.7631i	1.15409	+	0.405075i
$707$	−11.3295	−	2.25358i	−0.426091	−	0.0847548i
$708$		0			0
$709$	−23.4418	+	35.0831i	−0.880374	+	1.31757i	0.0671017	+	0.997746i	$0.478625\pi$
$709$	−23.4418	+	35.0831i	−0.880374	+	1.31757i	−0.947476	+	0.319827i	$0.896375\pi$
$710$	−9.11476	−	5.38842i	−0.342071	−	0.202224i
$711$		0			0
$712$	−8.94781	−	6.38751i	−0.335333	−	0.239382i
$713$	−4.30035	−	1.78127i	−0.161050	−	0.0667089i
$714$		0			0
$715$	0.233101	+	1.17188i	0.00871749	+	0.0438258i
$716$	1.85470	−	21.4971i	0.0693135	−	0.803385i
$717$		0			0
$718$	9.70838	−	0.535892i	0.362314	−	0.0199993i
$719$	9.10621	−	9.10621i	0.339604	−	0.339604i	−0.516614	−	0.856218i	$-0.672808\pi$
$719$	9.10621	−	9.10621i	0.339604	−	0.339604i	0.856218	+	0.516614i	$0.172808\pi$
$720$		0			0
$721$	16.0481	+	16.0481i	0.597663	+	0.597663i
$722$	6.80865	+	6.09631i	0.253392	+	0.226881i
$723$		0			0
$724$	3.29684	−	6.35181i	0.122526	−	0.236063i
$725$	11.7847	−	2.34411i	0.437671	−	0.0870582i
$726$		0			0
$727$	8.28934	−	20.0122i	0.307435	−	0.742213i	−0.692352	−	0.721560i	$-0.743426\pi$
$727$	8.28934	−	20.0122i	0.307435	−	0.742213i	0.999787	−	0.0206529i	$-0.00657449\pi$
$728$	4.67221	+	0.144515i	0.173163	+	0.00535607i
$729$		0			0
$730$	0.571219	+	2.22323i	0.0211418	+	0.0822854i
$731$	15.4426	+	10.3184i	0.571165	+	0.381640i
$732$		0			0
$733$	−1.86746	+	9.38837i	−0.0689763	+	0.346767i	−0.999826	−	0.0186340i	$-0.994068\pi$
$733$	−1.86746	+	9.38837i	−0.0689763	+	0.346767i	0.930850	+	0.365401i	$0.119068\pi$
$734$	4.34630	−	2.08795i	0.160425	−	0.0770676i
$735$		0			0
$736$	1.28384	−	2.29691i	0.0473232	−	0.0846653i
$737$		−	7.75244i		−	0.285565i
$738$		0			0
$739$	−3.72209	+	18.7122i	−0.136919	+	0.688340i	0.849956	+	0.526854i	$0.176629\pi$
$739$	−3.72209	+	18.7122i	−0.136919	+	0.688340i	−0.986875	+	0.161486i	$0.948371\pi$
$740$	1.70171	+	0.493784i	0.0625562	+	0.0181519i
$741$		0			0
$742$	16.3571	−	4.20267i	0.600488	−	0.154285i
$743$	2.74886	+	6.63633i	0.100846	+	0.243463i	0.966248	−	0.257615i	$-0.0829368\pi$
$743$	2.74886	+	6.63633i	0.100846	+	0.243463i	−0.865402	+	0.501079i	$0.832937\pi$
$744$		0			0
$745$	14.0084	−	33.8193i	0.513228	−	1.23904i
$746$	−19.9733	−	2.83926i	−0.731274	−	0.103953i
$747$		0			0
$748$	−11.5251	+	3.64909i	−0.421399	+	0.133424i
$749$	13.1817	−	8.80771i	0.481648	−	0.321827i
$750$		0			0
$751$	−1.88191	−	1.88191i	−0.0686719	−	0.0686719i	0.671937	−	0.740609i	$-0.265463\pi$
$751$	−1.88191	−	1.88191i	−0.0686719	−	0.0686719i	−0.740609	+	0.671937i	$0.765463\pi$
$752$	−18.1399	+	28.6257i	−0.661494	+	1.04387i
$753$		0			0
$754$	0.234850	+	4.25462i	0.00855275	+	0.154944i
$755$	7.14383	+	10.6915i	0.259991	+	0.389104i
$756$		0			0
$757$	7.70412	+	38.7312i	0.280011	+	1.40771i	0.823034	+	0.567992i	$0.192280\pi$
$757$	7.70412	+	38.7312i	0.280011	+	1.40771i	−0.543023	+	0.839718i	$0.682720\pi$
$758$	21.8456	+	29.0856i	0.793468	+	1.05644i
$759$		0			0
$760$	12.4368	+	19.9197i	0.451130	+	0.722565i
$761$	7.53878	−	3.12266i	0.273280	−	0.113196i	−0.241835	−	0.970317i	$-0.577749\pi$
$761$	7.53878	−	3.12266i	0.273280	−	0.113196i	0.515115	+	0.857121i	$0.327749\pi$
$762$		0			0
$763$	−6.97211	+	10.4345i	−0.252407	+	0.377754i
$764$	−1.12744	−	0.902636i	−0.0407892	−	0.0326562i
$765$		0			0
$766$	10.1095	−	28.8027i	0.365270	−	1.04068i
$767$	1.07225			0.0387167
$768$		0			0
$769$	3.77877			0.136266			0.0681330	−	0.997676i	$-0.478296\pi$
$769$	3.77877			0.136266			0.0681330	+	0.997676i	$0.478296\pi$
$770$	−2.79800	+	7.97175i	−0.100833	+	0.287282i
$771$		0			0
$772$	8.28690	+	6.63457i	0.298252	+	0.238783i
$773$	2.84091	−	4.25173i	0.102181	−	0.152924i	−0.776856	−	0.629678i	$-0.783187\pi$
$773$	2.84091	−	4.25173i	0.102181	−	0.152924i	0.879037	+	0.476754i	$0.158187\pi$
$774$		0			0
$775$	−21.1957	+	8.77956i	−0.761373	+	0.315371i
$776$	−20.6328	−	33.0472i	−0.740675	−	1.18632i
$777$		0			0
$778$	−6.02917	−	8.02734i	−0.216156	−	0.287794i
$779$	6.27971	+	31.5702i	0.224994	+	1.13112i
$780$		0			0
$781$	−3.19312	−	4.77884i	−0.114259	−	0.171000i
$782$	−0.173509	−	3.14335i	−0.00620467	−	0.112406i
$783$		0			0
$784$	4.26758	+	2.70434i	0.152413	+	0.0965835i
$785$	−24.4485	−	24.4485i	−0.872605	−	0.872605i
$786$		0			0
$787$	−25.7884	+	17.2312i	−0.919257	+	0.614228i	−0.922596	−	0.385767i	$-0.873937\pi$
$787$	−25.7884	+	17.2312i	−0.919257	+	0.614228i	0.00333965	+	0.999994i	$0.498937\pi$
$788$	28.4384	−	9.00422i	1.01308	−	0.320762i
$789$		0			0
$790$	−0.496714	−	0.0706093i	−0.0176723	−	0.00251217i
$791$	18.1907	−	43.9162i	0.646786	−	1.56148i
$792$		0			0
$793$	−1.45249	−	3.50662i	−0.0515793	−	0.124524i
$794$	18.2637	−	4.69254i	0.648156	−	0.166532i
$795$		0			0
$796$	0.922799	+	0.267768i	0.0327077	+	0.00949077i
$797$	−0.860359	+	4.32532i	−0.0304755	+	0.153211i	−0.993027	−	0.117889i	$-0.962387\pi$
$797$	−0.860359	+	4.32532i	−0.0304755	+	0.153211i	0.962551	+	0.271100i	$0.0873873\pi$
$798$		0			0
$799$			40.5448i			1.43437i
$800$	−3.53076	−	12.4797i	−0.124831	−	0.441224i
$801$		0			0
$802$	−15.3282	+	7.36362i	−0.541258	+	0.260018i
$803$	−0.243079	+	1.22204i	−0.00857807	+	0.0431249i
$804$		0			0
$805$	−1.82932	−	1.22231i	−0.0644751	−	0.0430809i
$806$	−2.02465	−	7.88008i	−0.0713151	−	0.277564i
$807$		0			0
$808$	−11.3607	−	0.351394i	−0.399668	−	0.0123620i
$809$	4.29079	−	10.3589i	0.150856	−	0.364199i	−0.830327	−	0.557276i	$-0.811847\pi$
$809$	4.29079	−	10.3589i	0.150856	−	0.364199i	0.981184	+	0.193077i	$0.0618466\pi$
$810$		0			0
$811$	3.92167	−	0.780069i	0.137709	−	0.0273919i	−0.125755	−	0.992061i	$-0.540135\pi$
$811$	3.92167	−	0.780069i	0.137709	−	0.0273919i	0.263463	+	0.964669i	$0.415135\pi$
$812$	−13.8802	+	26.7420i	−0.487098	+	0.938461i
$813$		0			0
$814$	0.716548	+	0.641581i	0.0251150	+	0.0224874i
$815$	23.8528	+	23.8528i	0.835528	+	0.835528i
$816$		0			0
$817$	13.8476	−	13.8476i	0.484467	−	0.484467i
$818$	−40.0060	+	2.20828i	−1.39878	+	0.0772109i
$819$		0			0
$820$	−1.80441	+	20.9142i	−0.0630129	+	0.730356i
$821$	7.39036	+	37.1538i	0.257925	+	1.29668i	0.864895	+	0.501953i	$0.167385\pi$
$821$	7.39036	+	37.1538i	0.257925	+	1.29668i	−0.606970	+	0.794725i	$0.707615\pi$
$822$		0			0
$823$	13.1154	+	5.43259i	0.457175	+	0.189368i	0.599373	−	0.800470i	$-0.295417\pi$
$823$	13.1154	+	5.43259i	0.457175	+	0.189368i	−0.142197	+	0.989838i	$0.545417\pi$
$824$	18.1753	+	12.9747i	0.633167	+	0.451995i
$825$		0			0
$826$	6.52654	+	3.85833i	0.227087	+	0.134248i
$827$	−13.3036	+	19.9102i	−0.462611	+	0.692347i	−0.987286	−	0.158956i	$-0.949187\pi$
$827$	−13.3036	+	19.9102i	−0.462611	+	0.692347i	0.524674	+	0.851303i	$0.324187\pi$
$828$		0			0
$829$	12.2166	+	2.43003i	0.424299	+	0.0843983i	0.402621	−	0.915367i	$-0.368099\pi$
$829$	12.2166	+	2.43003i	0.424299	+	0.0843983i	0.0216779	+	0.999765i	$0.493099\pi$
$830$	−13.6381	−	4.78685i	−0.473387	−	0.166154i
$831$		0			0
$832$	4.55788	−	0.616795i	0.158016	−	0.0213835i
$833$	6.04450			0.209430
$834$		0			0
$835$	23.4908	+	4.67260i	0.812932	+	0.161702i
$836$	1.40296	+	12.6695i	0.0485224	+	0.438185i
$837$		0			0
$838$	25.3611	+	14.9929i	0.876085	+	0.517920i
$839$	26.8826	−	11.1351i	0.928089	−	0.384427i	0.133136	−	0.991098i	$-0.457495\pi$
$839$	26.8826	−	11.1351i	0.928089	−	0.384427i	0.794953	+	0.606671i	$0.207495\pi$
$840$		0			0
$841$	1.41778	+	0.587262i	0.0488888	+	0.0202504i
$842$	25.1514	−	18.8907i	0.866774	−	0.651016i
$843$		0			0
$844$	29.2404	+	2.52277i	1.00650	+	0.0868374i
$845$	11.5815	+	17.3329i	0.398415	+	0.596270i
$846$		0			0
$847$	19.1161	−	19.1161i	0.656836	−	0.656836i
$848$	15.1939	−	6.72915i	0.521761	−	0.231080i
$849$		0			0
$850$	−11.5599	−	10.3505i	−0.396503	−	0.355019i
$851$	−0.208255	+	0.139152i	−0.00713889	+	0.00477006i
$852$		0			0
$853$	29.6923	−	5.90616i	1.01664	−	0.202223i	0.341479	−	0.939889i	$-0.389072\pi$
$853$	29.6923	−	5.90616i	1.01664	−	0.202223i	0.675165	+	0.737666i	$0.264072\pi$
$854$	3.77708	−	26.5705i	0.129249	−	0.909225i
$855$		0			0
$856$	11.3659	−	10.6839i	0.388480	−	0.365169i
$857$	0.425175	+	1.02646i	0.0145237	+	0.0350633i	0.930975	−	0.365083i	$-0.118959\pi$
$857$	0.425175	+	1.02646i	0.0145237	+	0.0350633i	−0.916451	+	0.400146i	$0.868959\pi$
$858$		0			0
$859$	−40.2028	−	26.8627i	−1.37170	−	0.916543i	−0.371773	−	0.928324i	$-0.621250\pi$
$859$	−40.2028	−	26.8627i	−1.37170	−	0.916543i	−0.999931	+	0.0117809i	$0.996250\pi$
$860$	11.1896	−	6.15637i	0.381564	−	0.209930i
$861$		0			0
$862$	16.5304	−	7.94114i	0.563027	−	0.270476i
$863$			54.0259i			1.83906i	0.393018	+	0.919531i	$0.371431\pi$
$863$			54.0259i			1.83906i	−0.393018	+	0.919531i	$0.628569\pi$
$864$		0			0
$865$			30.5967i			1.04032i
$866$	7.84900	+	16.3386i	0.266720	+	0.555208i
$867$		0			0
$868$	16.0317	−	55.2497i	0.544153	−	1.87530i
$869$	−0.226435	−	0.151299i	−0.00768127	−	0.00513246i
$870$		0			0
$871$	1.35040	+	3.26016i	0.0457567	+	0.110466i
$872$	−5.07584	+	11.2566i	−0.171890	+	0.381196i
$873$		0			0
$874$	−3.28644	−	0.467176i	−0.111165	−	0.0158025i
$875$	−33.8299	+	6.72919i	−1.14366	+	0.227488i
$876$		0			0
$877$	25.7807	−	17.2261i	0.870552	−	0.581684i	−0.0380835	−	0.999275i	$-0.512125\pi$
$877$	25.7807	−	17.2261i	0.870552	−	0.581684i	0.908635	+	0.417590i	$0.137125\pi$
$878$	−38.1851	+	42.6469i	−1.28868	+	1.43926i
$879$		0			0
$880$	−1.42383	+	8.19010i	−0.0479974	+	0.276088i
$881$	−24.7406	+	24.7406i	−0.833533	+	0.833533i	−0.987998	−	0.154465i	$-0.950635\pi$
$881$	−24.7406	+	24.7406i	−0.833533	+	0.833533i	0.154465	+	0.987998i	$0.450635\pi$
$882$		0			0
$883$	−17.5606	−	26.2813i	−0.590962	−	0.884436i	0.408639	−	0.912696i	$-0.366003\pi$
$883$	−17.5606	−	26.2813i	−0.590962	−	0.884436i	−0.999601	+	0.0282597i	$0.991003\pi$
$884$	4.21106	−	3.54213i	0.141633	−	0.119135i
$885$		0			0
$886$	1.45827	+	1.94157i	0.0489917	+	0.0652284i
$887$	15.7202	+	6.51152i	0.527833	+	0.218635i	0.630654	−	0.776064i	$-0.282787\pi$
$887$	15.7202	+	6.51152i	0.527833	+	0.218635i	−0.102821	+	0.994700i	$0.532787\pi$
$888$		0			0
$889$	−58.2981	+	24.1479i	−1.95525	+	0.809893i
$890$	−4.60274	+	7.78575i	−0.154284	+	0.260979i
$891$		0			0
$892$	25.6792	−	32.0746i	0.859805	−	1.07394i
$893$	41.9301	+	8.34041i	1.40314	+	0.279101i
$894$		0			0
$895$	−17.7512			−0.593357
$896$	29.9623	+	12.6466i	1.00097	+	0.422493i
$897$		0			0
$898$	−11.5273	+	32.8423i	−0.384671	+	1.09596i
$899$	51.4340	+	10.2309i	1.71542	+	0.341218i
$900$		0			0
$901$	11.0452	−	16.5303i	0.367968	−	0.550704i
$902$	−5.79869	+	9.80874i	−0.193075	+	0.326595i
$903$		0			0
$904$	10.5386	−	45.5690i	0.350507	−	1.51560i
$905$	−5.43938	−	2.25306i	−0.180811	−	0.0748944i
$906$		0			0
$907$	7.39593	+	37.1818i	0.245578	+	1.23460i	0.884943	+	0.465699i	$0.154197\pi$
$907$	7.39593	+	37.1818i	0.245578	+	1.23460i	−0.639365	+	0.768903i	$0.720803\pi$
$908$	30.0643	−	25.2886i	0.997720	−	0.839233i
$909$		0			0
$910$	−0.211951	−	3.83978i	−0.00702612	−	0.127287i
$911$	30.6254	−	30.6254i	1.01467	−	1.01467i	0.0147749	−	0.999891i	$-0.495297\pi$
$911$	30.6254	−	30.6254i	1.01467	−	1.01467i	0.999891	−	0.0147749i	$-0.00470317\pi$
$912$		0			0
$913$	−5.54770	−	5.54770i	−0.183602	−	0.183602i
$914$	−0.983270	+	1.09816i	−0.0325237	+	0.0363240i
$915$		0			0
$916$	13.1725	+	41.6034i	0.435233	+	1.37461i
$917$	20.2907	−	4.03606i	0.670057	−	0.133283i
$918$		0			0
$919$	3.89489	−	9.40310i	0.128481	−	0.310180i	−0.846529	−	0.532343i	$-0.821312\pi$
$919$	3.89489	−	9.40310i	0.128481	−	0.310180i	0.975010	+	0.222163i	$0.0713117\pi$
$920$	−1.97345	−	0.889869i	−0.0650626	−	0.0293381i
$921$		0			0
$922$	−19.0528	+	4.89527i	−0.627469	+	0.161217i
$923$	2.17524	+	1.45345i	0.0715990	+	0.0478409i
$924$		0			0
$925$	−0.240840	+	1.21079i	−0.00791878	+	0.0398104i
$926$	7.18465	+	14.9557i	0.236102	+	0.491474i
$927$		0			0
$928$	−9.13789	+	28.2027i	−0.299966	+	0.925799i
$929$		−	0.932872i		−	0.0306066i	−0.999883	−	0.0153033i	$-0.995129\pi$
$929$		−	0.932872i		−	0.0306066i	0.999883	−	0.0153033i	$-0.00487137\pi$
$930$		0			0
$931$	1.24341	−	6.25102i	0.0407510	−	0.204869i
$932$	−6.85721	+	3.77273i	−0.224615	+	0.123580i
$933$		0			0
$934$	0.101600	+	0.395433i	0.00332444	+	0.0129390i
$935$	3.80598	+	9.18845i	0.124469	+	0.300494i
$936$		0			0
$937$	9.77432	−	23.5973i	0.319313	−	0.770890i	−0.679978	−	0.733233i	$-0.738010\pi$
$937$	9.77432	−	23.5973i	0.319313	−	0.770890i	0.999291	−	0.0376573i	$-0.0119895\pi$
$938$	−3.51162	+	24.7031i	−0.114658	+	0.806586i
$939$		0			0
$940$	24.7457	+	12.8440i	0.807117	+	0.418925i
$941$	−14.0830	+	9.40994i	−0.459092	+	0.306755i	−0.763525	−	0.645778i	$-0.776533\pi$
$941$	−14.0830	+	9.40994i	−0.459092	+	0.306755i	0.304433	+	0.952534i	$0.401533\pi$
$942$		0			0
$943$	−2.09819	−	2.09819i	−0.0683266	−	0.0683266i
$944$	6.95931	+	2.68707i	0.226506	+	0.0874568i
$945$		0			0
$946$	6.92188	−	0.382080i	0.225050	−	0.0124225i
$947$	−13.0115	−	19.4731i	−0.422818	−	0.632791i	0.557510	−	0.830171i	$-0.311757\pi$
$947$	−13.0115	−	19.4731i	−0.422818	−	0.632791i	−0.980327	+	0.197379i	$0.936757\pi$
$948$		0			0
$949$	−0.110645	−	0.556252i	−0.00359170	−	0.0180567i
$950$	−13.0821	+	9.82572i	−0.424441	+	0.318789i
$951$		0			0
$952$	38.3776	−	6.40731i	1.24383	−	0.207662i
$953$	−44.5204	+	18.4410i	−1.44216	+	0.597361i	−0.960320	−	0.278899i	$-0.910030\pi$
$953$	−44.5204	+	18.4410i	−1.44216	+	0.597361i	−0.481838	+	0.876261i	$0.660030\pi$
$954$		0			0
$955$	−0.660114	+	0.987930i	−0.0213608	+	0.0319687i
$956$	1.51855	+	13.7133i	0.0491133	+	0.443521i
$957$		0			0
$958$	36.5618	+	12.8328i	1.18126	+	0.414610i
$959$	−31.8352			−1.02801
$960$		0			0
$961$	−69.1305			−2.23002
$962$	−0.413090	−	0.144990i	−0.0133186	−	0.00467468i
$963$		0			0
$964$	−4.79428	+	0.530895i	−0.154413	+	0.0170990i
$965$	4.85198	−	7.26150i	0.156191	−	0.233756i
$966$		0			0
$967$	25.4255	−	10.5316i	0.817629	−	0.338673i	0.0656353	−	0.997844i	$-0.479093\pi$
$967$	25.4255	−	10.5316i	0.817629	−	0.338673i	0.751993	+	0.659171i	$0.229093\pi$
$968$	15.4551	−	21.6499i	0.496745	−	0.695855i
$969$		0			0
$970$	−25.6279	+	19.2486i	−0.822863	+	0.618035i
$971$	−3.37327	−	16.9586i	−0.108254	−	0.544227i	−0.996408	−	0.0846822i	$-0.973012\pi$
$971$	−3.37327	−	16.9586i	−0.108254	−	0.544227i	0.888154	−	0.459545i	$-0.151988\pi$
$972$		0			0
$973$	−6.15926	−	9.21798i	−0.197457	−	0.295515i
$974$	43.3477	−	2.39275i	1.38895	−	0.0766685i
$975$		0			0
$976$	−0.639568	−	26.3992i	−0.0204721	−	0.845019i
$977$	26.1853	+	26.1853i	0.837743	+	0.837743i	0.988562	−	0.150818i	$-0.0481908\pi$
$977$	26.1853	+	26.1853i	0.837743	+	0.837743i	−0.150818	+	0.988562i	$0.548191\pi$
$978$		0			0
$979$	−4.08204	+	2.72753i	−0.130463	+	0.0871723i
$980$	1.91481	−	3.68915i	0.0611664	−	0.117845i
$981$		0			0
$982$	0.291449	−	2.05025i	0.00930050	−	0.0654261i
$983$	0.628339	−	1.51695i	0.0200409	−	0.0483831i	−0.913542	−	0.406744i	$-0.866664\pi$
$983$	0.628339	−	1.51695i	0.0200409	−	0.0483831i	0.933583	+	0.358361i	$0.116664\pi$
$984$		0			0
$985$	−9.39134	−	22.6727i	−0.299233	−	0.722412i
$986$	8.82627	+	34.3525i	0.281086	+	1.09401i
$987$		0			0
$988$	−2.79691	−	5.08358i	−0.0889815	−	0.161730i
$989$	−0.352195	+	1.77060i	−0.0111991	+	0.0563019i
$990$		0			0
$991$		−	0.482249i		−	0.0153191i	−0.999971	−	0.00765957i	$-0.997562\pi$
$991$		−	0.482249i		−	0.0153191i	0.999971	−	0.00765957i	$-0.00243814\pi$
$992$	6.60687	−	56.2186i	0.209768	−	1.78494i
$993$		0			0
$994$	8.01019	+	16.6741i	0.254068	+	0.528871i
$995$	0.154218	−	0.775305i	0.00488903	−	0.0245788i
$996$		0			0
$997$	−5.71075	−	3.81580i	−0.180861	−	0.120848i	0.461844	−	0.886961i	$-0.347188\pi$
$997$	−5.71075	−	3.81580i	−0.180861	−	0.120848i	−0.642705	+	0.766114i	$0.722188\pi$
$998$	−20.5518	+	5.28041i	−0.650555	+	0.167149i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.541.2		56
3.2	odd	2		64.2.i.a.29.6	✓	56
12.11	even	2		256.2.i.a.209.7		56
24.5	odd	2		512.2.i.b.161.7		56
24.11	even	2		512.2.i.a.161.1		56
64.53	even	16	inner	576.2.bd.a.181.2		56
192.11	even	16		256.2.i.a.49.7		56
192.53	odd	16		64.2.i.a.53.6	yes	56
192.107	even	16		512.2.i.a.353.1		56
192.149	odd	16		512.2.i.b.353.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.6	✓	56	3.2	odd	2
64.2.i.a.53.6	yes	56	192.53	odd	16
256.2.i.a.49.7		56	192.11	even	16
256.2.i.a.209.7		56	12.11	even	2
512.2.i.a.161.1		56	24.11	even	2
512.2.i.a.353.1		56	192.107	even	16
512.2.i.b.161.7		56	24.5	odd	2
512.2.i.b.353.7		56	192.149	odd	16
576.2.bd.a.181.2		56	64.53	even	16	inner
576.2.bd.a.541.2		56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.468362 + 1.33441i) q^{2} +(-1.56127 - 1.24997i) q^{4} +(-0.914126 + 1.36809i) q^{5} +(2.65574 - 1.10004i) q^{7} +(2.39921 - 1.49793i) q^{8} +O(q^{10})\)	\(q+(-0.468362 + 1.33441i) q^{2} +(-1.56127 - 1.24997i) q^{4} +(-0.914126 + 1.36809i) q^{5} +(2.65574 - 1.10004i) q^{7} +(2.39921 - 1.49793i) q^{8} +(-1.39744 - 1.86057i) q^{10} +(-0.246413 - 1.23880i) q^{11} +(0.319413 + 0.478036i) q^{13} +(0.224055 + 4.05906i) q^{14} +(0.875149 + 3.90309i) q^{16} +(3.38390 + 3.38390i) q^{17} +(4.19561 - 2.80342i) q^{19} +(3.13727 - 0.993326i) q^{20} +(1.76847 + 0.251393i) q^{22} +(-0.178010 + 0.429755i) q^{23} +(0.877384 + 2.11819i) q^{25} +(-0.787494 + 0.202333i) q^{26} +(-5.52137 - 1.60213i) q^{28} +(1.02242 - 5.14005i) q^{29} +10.0065i q^{31} +(-5.61819 - 0.660257i) q^{32} +(-6.10038 + 2.93060i) q^{34} +(-0.922728 + 4.63887i) q^{35} +(0.447703 + 0.299146i) q^{37} +(1.77583 + 6.91166i) q^{38} +(-0.143878 + 4.65162i) q^{40} +(-2.44115 + 5.89346i) q^{41} +(3.80641 - 0.757142i) q^{43} +(-1.16375 + 2.24212i) q^{44} +(-0.490094 - 0.438819i) q^{46} +(5.99084 + 5.99084i) q^{47} +(0.893127 - 0.893127i) q^{49} +(-3.23746 + 0.178704i) q^{50} +(0.0988389 - 1.14560i) q^{52} +(-0.810472 - 4.07452i) q^{53} +(1.92004 + 0.795307i) q^{55} +(4.72389 - 6.61736i) q^{56} +(6.38004 + 3.77172i) q^{58} +(1.03615 - 1.55070i) q^{59} +(-6.47490 - 1.28794i) q^{61} +(-13.3528 - 4.68668i) q^{62} +(3.51240 - 7.18770i) q^{64} -0.945978 q^{65} +(6.01983 + 1.19742i) q^{67} +(-1.05342 - 9.51296i) q^{68} +(-5.75795 - 3.40396i) q^{70} +(4.20400 - 1.74136i) q^{71} +(-0.911379 - 0.377506i) q^{73} +(-0.608868 + 0.457308i) q^{74} +(-10.0547 - 0.867487i) q^{76} +(-2.01715 - 3.01887i) q^{77} +(0.152459 - 0.152459i) q^{79} +(-6.13976 - 2.37064i) q^{80} +(-6.72092 - 6.01776i) q^{82} +(5.16472 - 3.45096i) q^{83} +(-7.72277 + 1.53615i) q^{85} +(-0.772445 + 5.43391i) q^{86} +(-2.44684 - 2.60303i) q^{88} +(-1.48745 - 3.59102i) q^{89} +(1.37414 + 0.918171i) q^{91} +(0.815104 - 0.448458i) q^{92} +(-10.8001 + 5.18832i) q^{94} +8.30263i q^{95} -13.7742i q^{97} +(0.773486 + 1.61010i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

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