LMFDB - Embedded newform 819.2.et.c.514.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			514.8
Character	$\chi$	$=$	819.514
Dual form			819.2.et.c.145.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30773 + 1.30773i) q^{2} +1.42031i q^{4} +(0.0744995 + 0.0199621i) q^{5} +(2.55141 - 0.700217i) q^{7} +(0.758075 - 0.758075i) q^{8} +O(q^{10})$	\(q+(1.30773 + 1.30773i) q^{2} +1.42031i q^{4} +(0.0744995 + 0.0199621i) q^{5} +(2.55141 - 0.700217i) q^{7} +(0.758075 - 0.758075i) q^{8} +(0.0713202 + 0.123530i) q^{10} +(-0.672618 - 0.180227i) q^{11} +(2.39818 - 2.69235i) q^{13} +(4.25225 + 2.42086i) q^{14} +4.82334 q^{16} +1.23731 q^{17} +(-1.45771 - 5.44023i) q^{19} +(-0.0283524 + 0.105813i) q^{20} +(-0.643914 - 1.11529i) q^{22} +7.37027i q^{23} +(-4.32498 - 2.49703i) q^{25} +(6.65703 - 0.384694i) q^{26} +(0.994527 + 3.62380i) q^{28} +(-1.84462 + 3.19498i) q^{29} +(2.34941 + 8.76813i) q^{31} +(4.79147 + 4.79147i) q^{32} +(1.61806 + 1.61806i) q^{34} +(0.204057 - 0.00123434i) q^{35} +(3.25640 - 3.25640i) q^{37} +(5.20806 - 9.02063i) q^{38} +(0.0716090 - 0.0413434i) q^{40} +(0.231836 + 0.865225i) q^{41} +(-2.14988 + 1.24124i) q^{43} +(0.255979 - 0.955327i) q^{44} +(-9.63832 + 9.63832i) q^{46} +(-0.108435 + 0.404685i) q^{47} +(6.01939 - 3.57308i) q^{49} +(-2.39046 - 8.92133i) q^{50} +(3.82397 + 3.40616i) q^{52} +(-5.75319 + 9.96481i) q^{53} +(-0.0465120 - 0.0268537i) q^{55} +(1.40334 - 2.46498i) q^{56} +(-6.59044 + 1.76590i) q^{58} +(-9.90380 - 9.90380i) q^{59} +(5.63177 + 3.25150i) q^{61} +(-8.39395 + 14.5387i) q^{62} +2.88522i q^{64} +(0.232408 - 0.152706i) q^{65} +(-0.540059 + 2.01553i) q^{67} +1.75736i q^{68} +(0.268465 + 0.265237i) q^{70} +(-0.119329 + 0.445340i) q^{71} +(-4.91231 + 1.31625i) q^{73} +8.51697 q^{74} +(7.72682 - 2.07040i) q^{76} +(-1.84232 + 0.0111443i) q^{77} +(3.26395 + 5.65332i) q^{79} +(0.359336 + 0.0962839i) q^{80} +(-0.828301 + 1.43466i) q^{82} +(9.54235 - 9.54235i) q^{83} +(0.0921787 + 0.0246992i) q^{85} +(-4.43466 - 1.18826i) q^{86} +(-0.646521 + 0.373269i) q^{88} +(-3.14679 - 3.14679i) q^{89} +(4.23351 - 8.54853i) q^{91} -10.4681 q^{92} +(-0.671022 + 0.387414i) q^{94} -0.434393i q^{95} +(-15.6536 - 4.19437i) q^{97} +(12.5444 + 3.19911i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.30773	+	1.30773i	0.924704	+	0.924704i	0.997357	−	0.0726530i	$-0.0231466\pi$
$2$	1.30773	+	1.30773i	0.924704	+	0.924704i	−0.0726530	+	0.997357i	$0.523147\pi$
$3$		0			0
$3$		0			0
$4$			1.42031i			0.710156i
$5$	0.0744995	+	0.0199621i	0.0333172	+	0.00892732i	0.275439	−	0.961319i	$-0.411177\pi$
$5$	0.0744995	+	0.0199621i	0.0333172	+	0.00892732i	−0.242122	+	0.970246i	$0.577843\pi$
$6$		0			0
$7$	2.55141	−	0.700217i	0.964343	−	0.264657i
$7$	2.55141	−	0.700217i	0.964343	−	0.264657i
$8$	0.758075	−	0.758075i	0.268020	−	0.268020i
$9$		0			0
$10$	0.0713202	+	0.123530i	0.0225534	+	0.0390637i
$11$	−0.672618	−	0.180227i	−0.202802	−	0.0543406i	0.155988	−	0.987759i	$-0.450144\pi$
$11$	−0.672618	−	0.180227i	−0.202802	−	0.0543406i	−0.358790	+	0.933418i	$0.616811\pi$
$12$		0			0
$13$	2.39818	−	2.69235i	0.665135	−	0.746723i
$13$	2.39818	−	2.69235i	0.665135	−	0.746723i
$14$	4.25225	+	2.42086i	1.13646	+	0.647002i
$15$		0			0
$16$	4.82334			1.20583
$17$	1.23731			0.300091			0.150045	−	0.988679i	$-0.452058\pi$
$17$	1.23731			0.300091			0.150045	+	0.988679i	$0.452058\pi$
$18$		0			0
$19$	−1.45771	−	5.44023i	−0.334420	−	1.24807i	−0.904496	−	0.426482i	$-0.859753\pi$
$19$	−1.45771	−	5.44023i	−0.334420	−	1.24807i	0.570076	−	0.821592i	$-0.306914\pi$
$20$	−0.0283524	+	0.105813i	−0.00633979	+	0.0236604i
$21$		0			0
$22$	−0.643914	−	1.11529i	−0.137283	−	0.237781i
$23$			7.37027i			1.53681i	0.639965	+	0.768404i	$0.278949\pi$
$23$			7.37027i			1.53681i	−0.639965	+	0.768404i	$0.721051\pi$
$24$		0			0
$25$	−4.32498	−	2.49703i	−0.864995	−	0.499405i
$26$	6.65703	−	0.384694i	1.30555	−	0.0754446i
$27$		0			0
$28$	0.994527	+	3.62380i	0.187948	+	0.684834i
$29$	−1.84462	+	3.19498i	−0.342538	+	0.593293i	−0.984903	−	0.173105i	$-0.944620\pi$
$29$	−1.84462	+	3.19498i	−0.342538	+	0.593293i	0.642365	+	0.766399i	$0.277953\pi$
$30$		0			0
$31$	2.34941	+	8.76813i	0.421967	+	1.57480i	0.770458	+	0.637491i	$0.220028\pi$
$31$	2.34941	+	8.76813i	0.421967	+	1.57480i	−0.348491	+	0.937312i	$0.613306\pi$
$32$	4.79147	+	4.79147i	0.847020	+	0.847020i
$33$		0			0
$34$	1.61806	+	1.61806i	0.277495	+	0.277495i
$35$	0.204057	−	0.00123434i	0.0344919	−	0.000208642i
$36$		0			0
$37$	3.25640	−	3.25640i	0.535348	−	0.535348i	−0.386811	−	0.922159i	$-0.626423\pi$
$37$	3.25640	−	3.25640i	0.535348	−	0.535348i	0.922159	+	0.386811i	$0.126423\pi$
$38$	5.20806	−	9.02063i	0.844860	−	1.46334i
$39$		0			0
$40$	0.0716090	−	0.0413434i	0.0113224	−	0.00653697i
$41$	0.231836	+	0.865225i	0.0362067	+	0.135125i	0.981663	−	0.190622i	$-0.0610506\pi$
$41$	0.231836	+	0.865225i	0.0362067	+	0.135125i	−0.945457	+	0.325748i	$0.894384\pi$
$42$		0			0
$43$	−2.14988	+	1.24124i	−0.327854	+	0.189287i	−0.654888	−	0.755726i	$-0.727284\pi$
$43$	−2.14988	+	1.24124i	−0.327854	+	0.189287i	0.327034	+	0.945013i	$0.393951\pi$
$44$	0.255979	−	0.955327i	0.0385903	−	0.144021i
$45$		0			0
$46$	−9.63832	+	9.63832i	−1.42109	+	1.42109i
$47$	−0.108435	+	0.404685i	−0.0158169	+	0.0590293i	−0.973383	−	0.229184i	$-0.926394\pi$
$47$	−0.108435	+	0.404685i	−0.0158169	+	0.0590293i	0.957566	+	0.288213i	$0.0930611\pi$
$48$		0			0
$49$	6.01939	−	3.57308i	0.859913	−	0.510440i
$50$	−2.39046	−	8.92133i	−0.338063	−	1.26167i
$51$		0			0
$52$	3.82397	+	3.40616i	0.530290	+	0.472350i
$53$	−5.75319	+	9.96481i	−0.790261	+	1.36877i	0.135544	+	0.990771i	$0.456722\pi$
$53$	−5.75319	+	9.96481i	−0.790261	+	1.36877i	−0.925805	+	0.378001i	$0.876612\pi$
$54$		0			0
$55$	−0.0465120	−	0.0268537i	−0.00627168	−	0.00362095i
$56$	1.40334	−	2.46498i	0.187530	−	0.329396i
$57$		0			0
$58$	−6.59044	+	1.76590i	−0.865367	+	0.231875i
$59$	−9.90380	−	9.90380i	−1.28937	−	1.28937i	−0.935172	−	0.354193i	$-0.884756\pi$
$59$	−9.90380	−	9.90380i	−1.28937	−	1.28937i	−0.354193	−	0.935172i	$-0.615244\pi$
$60$		0			0
$61$	5.63177	+	3.25150i	0.721074	+	0.416312i	0.815148	−	0.579253i	$-0.196656\pi$
$61$	5.63177	+	3.25150i	0.721074	+	0.416312i	−0.0940739	+	0.995565i	$0.529989\pi$
$62$	−8.39395	+	14.5387i	−1.06603	+	1.84642i
$63$		0			0
$64$			2.88522i			0.360652i
$65$	0.232408	−	0.152706i	0.0288267	−	0.0189408i
$66$		0			0
$67$	−0.540059	+	2.01553i	−0.0659787	+	0.246236i	−0.991037	−	0.133590i	$-0.957349\pi$
$67$	−0.540059	+	2.01553i	−0.0659787	+	0.246236i	0.925058	+	0.379826i	$0.124016\pi$
$68$			1.75736i			0.213111i
$69$		0			0
$70$	0.268465	+	0.265237i	0.0320877	+	0.0317018i
$71$	−0.119329	+	0.445340i	−0.0141617	+	0.0528522i	−0.972645	−	0.232296i	$-0.925376\pi$
$71$	−0.119329	+	0.445340i	−0.0141617	+	0.0528522i	0.958483	+	0.285148i	$0.0920428\pi$
$72$		0			0
$73$	−4.91231	+	1.31625i	−0.574942	+	0.154055i	−0.534562	−	0.845129i	$-0.679524\pi$
$73$	−4.91231	+	1.31625i	−0.574942	+	0.154055i	−0.0403800	+	0.999184i	$0.512857\pi$
$74$	8.51697			0.990078
$75$		0			0
$76$	7.72682	−	2.07040i	0.886328	−	0.237491i
$77$	−1.84232	+	0.0111443i	−0.209952	+	0.00127001i
$78$		0			0
$79$	3.26395	+	5.65332i	0.367223	+	0.636048i	0.989130	−	0.147043i	$-0.0469754\pi$
$79$	3.26395	+	5.65332i	0.367223	+	0.636048i	−0.621908	+	0.783091i	$0.713642\pi$
$80$	0.359336	+	0.0962839i	0.0401750	+	0.0107649i
$81$		0			0
$82$	−0.828301	+	1.43466i	−0.0914705	+	0.158432i
$83$	9.54235	−	9.54235i	1.04741	−	1.04741i	0.0485904	−	0.998819i	$-0.484527\pi$
$83$	9.54235	−	9.54235i	1.04741	−	1.04741i	0.998819	−	0.0485904i	$-0.0154729\pi$
$84$		0			0
$85$	0.0921787	+	0.0246992i	0.00999818	+	0.00267900i
$86$	−4.43466	−	1.18826i	−0.478202	−	0.128134i
$87$		0			0
$88$	−0.646521	+	0.373269i	−0.0689193	+	0.0397906i
$89$	−3.14679	−	3.14679i	−0.333559	−	0.333559i	0.520378	−	0.853936i	$-0.325791\pi$
$89$	−3.14679	−	3.14679i	−0.333559	−	0.333559i	−0.853936	+	0.520378i	$0.825791\pi$
$90$		0			0
$91$	4.23351	−	8.54853i	0.443793	−	0.896130i
$92$	−10.4681			−1.09137
$93$		0			0
$94$	−0.671022	+	0.387414i	−0.0692106	+	0.0399588i
$95$		−	0.434393i		−	0.0445678i
$96$		0			0
$97$	−15.6536	−	4.19437i	−1.58938	−	0.425874i	−0.647569	−	0.762007i	$-0.724214\pi$
$97$	−15.6536	−	4.19437i	−1.58938	−	0.425874i	−0.941815	+	0.336132i	$0.890881\pi$
$98$	12.5444	+	3.19911i	1.26717	+	0.323159i
$99$		0			0
$100$	3.54656	−	6.14282i	0.354656	−	0.614282i
$101$	−5.06369	−	8.77056i	−0.503856	−	0.872704i	−0.999990	−	0.00445781i	$-0.998581\pi$
$101$	−5.06369	−	8.77056i	−0.503856	−	0.872704i	0.496134	−	0.868246i	$-0.334752\pi$
$102$		0			0
$103$	1.47339	+	2.55198i	0.145177	+	0.251454i	0.929439	−	0.368976i	$-0.120291\pi$
$103$	1.47339	+	2.55198i	0.145177	+	0.251454i	−0.784262	+	0.620430i	$0.786958\pi$
$104$	−0.223002	−	3.85900i	−0.0218672	−	0.378406i
$105$		0			0
$106$	−20.5549	+	5.50767i	−1.99647	+	0.534952i
$107$	−16.8417			−1.62815			−0.814075	−	0.580760i	$-0.802755\pi$
$107$	−16.8417			−1.62815			−0.814075	+	0.580760i	$0.802755\pi$
$108$		0			0
$109$	−10.8967	+	2.91975i	−1.04371	+	0.279662i	−0.739651	−	0.672991i	$-0.765009\pi$
$109$	−10.8967	+	2.91975i	−1.04371	+	0.279662i	−0.304061	+	0.952653i	$0.598343\pi$
$110$	−0.0257077	−	0.0959425i	−0.00245113	−	0.00914776i
$111$		0			0
$112$	12.3063	−	3.37738i	1.16284	−	0.319133i
$113$	5.69946	+	9.87175i	0.536160	+	0.928656i	0.999106	+	0.0422699i	$0.0134589\pi$
$113$	5.69946	+	9.87175i	0.536160	+	0.928656i	−0.462946	+	0.886386i	$0.653208\pi$
$114$		0			0
$115$	−0.147126	+	0.549082i	−0.0137196	+	0.0512021i
$116$	−4.53787	−	2.61994i	−0.421331	−	0.243256i
$117$		0			0
$118$		−	25.9030i		−	2.38456i
$119$	3.15688	−	0.866382i	0.289390	−	0.0794211i
$120$		0			0
$121$	−9.10635	−	5.25755i	−0.827850	−	0.477959i
$122$	3.11274	+	11.6169i	0.281814	+	1.05175i
$123$		0			0
$124$	−12.4535	+	3.33690i	−1.11836	+	0.299663i
$125$	−0.545050	−	0.545050i	−0.0487507	−	0.0487507i
$126$		0			0
$127$	−11.9564	−	6.90305i	−1.06096	−	0.612547i	−0.135264	−	0.990810i	$-0.543188\pi$
$127$	−11.9564	−	6.90305i	−1.06096	−	0.612547i	−0.925698	+	0.378263i	$0.876522\pi$
$128$	5.80986	−	5.80986i	0.513524	−	0.513524i
$129$		0			0
$130$	0.503625	+	0.104229i	0.0441708	+	0.00914147i
$131$	12.3717	−	7.14282i	1.08092	−	0.624071i	0.149778	−	0.988720i	$-0.452144\pi$
$131$	12.3717	−	7.14282i	1.08092	−	0.624071i	0.931145	+	0.364648i	$0.118811\pi$
$132$		0			0
$133$	−7.52855	−	12.8596i	−0.652808	−	1.11506i
$134$	−3.34201	+	1.92951i	−0.288706	+	0.166685i
$135$		0			0
$136$	0.937970	−	0.937970i	0.0804303	−	0.0804303i
$137$	2.98739	−	2.98739i	0.255230	−	0.255230i	−0.567881	−	0.823111i	$-0.692236\pi$
$137$	2.98739	−	2.98739i	0.255230	−	0.255230i	0.823111	+	0.567881i	$0.192236\pi$
$138$		0			0
$139$	8.52594	−	4.92246i	0.723161	−	0.417517i	−0.0927539	−	0.995689i	$-0.529567\pi$
$139$	8.52594	−	4.92246i	0.723161	−	0.417517i	0.815915	+	0.578172i	$0.196234\pi$
$140$	0.00175315	+	0.289824i	0.000148169	+	0.0244946i
$141$		0			0
$142$	−0.738434	+	0.426335i	−0.0619680	+	0.0357772i
$143$	−2.09829	+	1.37870i	−0.175468	+	0.115293i
$144$		0			0
$145$	−0.201202	+	0.201202i	−0.0167089	+	0.0167089i
$146$	−8.14527	−	4.70267i	−0.674107	−	0.389196i
$147$		0			0
$148$	4.62510	+	4.62510i	0.380181	+	0.380181i
$149$	−3.39107	+	0.908635i	−0.277807	+	0.0744383i	−0.395033	−	0.918667i	$-0.629267\pi$
$149$	−3.39107	+	0.908635i	−0.277807	+	0.0744383i	0.117225	+	0.993105i	$0.462600\pi$
$150$		0			0
$151$	5.00350	+	18.6733i	0.407179	+	1.51961i	0.800001	+	0.599999i	$0.204832\pi$
$151$	5.00350	+	18.6733i	0.407179	+	1.51961i	−0.392821	+	0.919615i	$0.628501\pi$
$152$	−5.22915	−	3.01905i	−0.424140	−	0.244877i
$153$		0			0
$154$	−2.42383	−	2.39469i	−0.195318	−	0.192969i
$155$			0.700121i			0.0562351i
$156$		0			0
$157$	2.19466	+	1.26709i	0.175153	+	0.101125i	0.585013	−	0.811024i	$-0.301089\pi$
$157$	2.19466	+	1.26709i	0.175153	+	0.101125i	−0.409860	+	0.912148i	$0.634423\pi$
$158$	−3.12465	+	11.6614i	−0.248584	+	0.927729i
$159$		0			0
$160$	0.261314	+	0.452610i	0.0206587	+	0.0357820i
$161$	5.16079	+	18.8046i	0.406727	+	1.48201i
$162$		0			0
$163$	3.66969	+	13.6955i	0.287432	+	1.07271i	0.947044	+	0.321105i	$0.104054\pi$
$163$	3.66969	+	13.6955i	0.287432	+	1.07271i	−0.659611	+	0.751607i	$0.729279\pi$
$164$	−1.22889	+	0.329280i	−0.0959601	+	0.0257124i
$165$		0			0
$166$	24.9576			1.93709
$167$	3.12094	−	0.836254i	0.241506	−	0.0647113i	−0.136036	−	0.990704i	$-0.543436\pi$
$167$	3.12094	−	0.836254i	0.241506	−	0.0647113i	0.377542	+	0.925993i	$0.376770\pi$
$168$		0			0
$169$	−1.49748	−	12.9135i	−0.115190	−	0.993343i
$170$	0.0882449	+	0.152845i	0.00676807	+	0.0117226i
$171$		0			0
$172$	−1.76294	−	3.05350i	−0.134423	−	0.232828i
$173$	0.319180	−	0.552836i	0.0242668	−	0.0420314i	−0.853637	−	0.520868i	$-0.825608\pi$
$173$	0.319180	−	0.552836i	0.0242668	−	0.0420314i	0.877904	+	0.478837i	$0.158942\pi$
$174$		0			0
$175$	−12.7832	−	3.34252i	−0.966323	−	0.252671i
$176$	−3.24426	−	0.869298i	−0.244546	−	0.0655258i
$177$		0			0
$178$		−	8.23029i		−	0.616886i
$179$	−6.77885	+	3.91377i	−0.506675	+	0.292529i	−0.731466	−	0.681878i	$-0.761163\pi$
$179$	−6.77885	+	3.91377i	−0.506675	+	0.292529i	0.224791	+	0.974407i	$0.427830\pi$
$180$		0			0
$181$	7.74072			0.575363			0.287682	−	0.957726i	$-0.407115\pi$
$181$	7.74072			0.575363			0.287682	+	0.957726i	$0.407115\pi$
$182$	16.7155	−	5.64288i	1.23903	−	0.418278i
$183$		0			0
$184$	5.58722	+	5.58722i	0.411895	+	0.411895i
$185$	0.307604	−	0.177595i	0.0226155	−	0.0130571i
$186$		0			0
$187$	−0.832234	−	0.222996i	−0.0608590	−	0.0163071i
$188$	−0.574779	−	0.154011i	−0.0419200	−	0.0112324i
$189$		0			0
$190$	0.568069	−	0.568069i	0.0412120	−	0.0412120i
$191$	6.77349	−	11.7320i	0.490112	−	0.848899i	−0.509823	−	0.860279i	$-0.670289\pi$
$191$	6.77349	−	11.7320i	0.490112	−	0.848899i	0.999935	+	0.0113800i	$0.00362244\pi$
$192$		0			0
$193$	15.0008	+	4.01944i	1.07978	+	0.289326i	0.754505	−	0.656295i	$-0.227877\pi$
$193$	15.0008	+	4.01944i	1.07978	+	0.289326i	0.325273	+	0.945620i	$0.394544\pi$
$194$	−14.9856	−	25.9558i	−1.07590	−	1.86352i
$195$		0			0
$196$	5.07489	+	8.54942i	0.362492	+	0.610673i
$197$	−12.9524	+	3.47059i	−0.922822	+	0.247269i	−0.688791	−	0.724960i	$-0.741858\pi$
$197$	−12.9524	+	3.47059i	−0.922822	+	0.247269i	−0.234031	+	0.972229i	$0.575192\pi$
$198$		0			0
$199$	−3.28625			−0.232956			−0.116478	−	0.993193i	$-0.537160\pi$
$199$	−3.28625			−0.232956			−0.116478	+	0.993193i	$0.537160\pi$
$200$	−5.17159	+	1.38572i	−0.365686	+	0.0979854i
$201$		0			0
$202$	4.84759	−	18.0915i	0.341075	−	1.27291i
$203$	−2.46921	+	9.44335i	−0.173305	+	0.662793i
$204$		0			0
$205$			0.0690867i			0.00482523i
$206$	−1.41051	+	5.26409i	−0.0982748	+	0.366767i
$207$		0			0
$208$	11.5672	−	12.9861i	0.802043	−	0.900424i
$209$			3.92191i			0.271285i
$210$		0			0
$211$	−6.31298	+	10.9344i	−0.434604	+	0.752756i	−0.997263	−	0.0739331i	$-0.976445\pi$
$211$	−6.31298	+	10.9344i	−0.434604	+	0.752756i	0.562660	+	0.826689i	$0.309778\pi$
$212$	−14.1531	−	8.17132i	−0.972042	−	0.561209i
$213$		0			0
$214$	−22.0244	−	22.0244i	−1.50556	−	1.50556i
$215$	−0.184943	+	0.0495553i	−0.0126130	+	0.00337964i
$216$		0			0
$217$	12.1339	+	20.7260i	0.823704	+	1.40697i
$218$	−18.0681	−	10.4316i	−1.22373	−	0.706520i
$219$		0			0
$220$	0.0381407	−	0.0660616i	0.00257144	−	0.00445387i
$221$	2.96728	−	3.33126i	0.199601	−	0.224085i
$222$		0			0
$223$	5.22617	+	19.5043i	0.349971	+	1.30611i	0.886697	+	0.462351i	$0.152994\pi$
$223$	5.22617	+	19.5043i	0.349971	+	1.30611i	−0.536726	+	0.843756i	$0.680339\pi$
$224$	15.5801	+	8.86994i	1.04099	+	0.592648i
$225$		0			0
$226$	−5.45623	+	20.3629i	−0.362943	+	1.35452i
$227$	−9.03303	+	9.03303i	−0.599543	+	0.599543i	−0.940191	−	0.340648i	$-0.889354\pi$
$227$	−9.03303	+	9.03303i	−0.599543	+	0.599543i	0.340648	+	0.940191i	$0.389354\pi$
$228$		0			0
$229$	3.18409	−	11.8832i	0.210410	−	0.785262i	−0.777322	−	0.629104i	$-0.783422\pi$
$229$	3.18409	−	11.8832i	0.210410	−	0.785262i	0.987732	−	0.156159i	$-0.0499112\pi$
$230$	−0.910452	+	0.525649i	−0.0600334	+	0.0346603i
$231$		0			0
$232$	1.02367	+	3.82040i	0.0672074	+	0.250821i
$233$	0.0361142	−	0.0208505i	0.00236592	−	0.00136596i	−0.498817	−	0.866708i	$-0.666232\pi$
$233$	0.0361142	−	0.0208505i	0.00236592	−	0.00136596i	0.501182	+	0.865342i	$0.332899\pi$
$234$		0			0
$235$	−0.0161567	+	0.0279842i	−0.00105395	+	0.00182549i
$236$	14.0665	−	14.0665i	0.915651	−	0.915651i
$237$		0			0
$238$	5.26133	+	2.99534i	0.341042	+	0.194159i
$239$	−1.45212	−	1.45212i	−0.0939296	−	0.0939296i	0.658581	−	0.752510i	$-0.271157\pi$
$239$	−1.45212	−	1.45212i	−0.0939296	−	0.0939296i	−0.752510	+	0.658581i	$0.771157\pi$
$240$		0			0
$241$	−1.95322	−	1.95322i	−0.125818	−	0.125818i	0.641394	−	0.767212i	$-0.278356\pi$
$241$	−1.95322	−	1.95322i	−0.125818	−	0.125818i	−0.767212	+	0.641394i	$0.778356\pi$
$242$	−5.03318	−	18.7841i	−0.323545	−	1.20749i
$243$		0			0
$244$	−4.61815	+	7.99887i	−0.295647	+	0.512075i
$245$	0.519768	−	0.146033i	0.0332068	−	0.00932972i
$246$		0			0
$247$	−18.1428	−	9.12199i	−1.15440	−	0.580419i
$248$	8.42793	+	4.86587i	0.535174	+	0.308983i
$249$		0			0
$250$		−	1.42556i		−	0.0901600i
$251$	−11.9299	−	20.6631i	−0.753006	−	1.30424i	−0.946359	−	0.323116i	$-0.895270\pi$
$251$	−11.9299	−	20.6631i	−0.753006	−	1.30424i	0.193353	−	0.981129i	$-0.438064\pi$
$252$		0			0
$253$	1.32833	−	4.95738i	0.0835111	−	0.311668i
$254$	−6.60846	−	24.6631i	−0.414652	−	1.54750i
$255$		0			0
$256$	20.9659			1.31037
$257$	−6.71724			−0.419010			−0.209505	−	0.977808i	$-0.567185\pi$
$257$	−6.71724			−0.419010			−0.209505	+	0.977808i	$0.567185\pi$
$258$		0			0
$259$	6.02822	−	10.5886i	0.374575	−	0.657943i
$260$	0.216890	+	0.330092i	0.0134510	+	0.0204714i
$261$		0			0
$262$	25.5198	+	6.83800i	1.57662	+	0.422453i
$263$	7.73235	+	13.3928i	0.476797	+	0.825836i	0.999646	−	0.0265886i	$-0.00846440\pi$
$263$	7.73235	+	13.3928i	0.476797	+	0.825836i	−0.522850	+	0.852425i	$0.675131\pi$
$264$		0			0
$265$	−0.627528	+	0.627528i	−0.0385487	+	0.0385487i
$266$	6.97151	−	26.6621i	0.427451	−	1.63476i
$267$		0			0
$268$	−2.86268	−	0.767052i	−0.174866	−	0.0468552i
$269$			0.350892i			0.0213943i	0.999943	+	0.0106971i	$0.00340507\pi$
$269$			0.350892i			0.0213943i	−0.999943	+	0.0106971i	$0.996595\pi$
$270$		0			0
$271$	7.06051	+	7.06051i	0.428895	+	0.428895i	0.888252	−	0.459357i	$-0.151920\pi$
$271$	7.06051	+	7.06051i	0.428895	+	0.428895i	−0.459357	+	0.888252i	$0.651920\pi$
$272$	5.96794			0.361860
$273$		0			0
$274$	7.81340			0.472025
$275$	2.45902	+	2.45902i	0.148285	+	0.148285i
$276$		0			0
$277$			9.69499i			0.582516i	0.956645	+	0.291258i	$0.0940738\pi$
$277$			9.69499i			0.582516i	−0.956645	+	0.291258i	$0.905926\pi$
$278$	17.5869	+	4.71239i	1.05479	+	0.282630i
$279$		0			0
$280$	0.153754	−	0.155626i	0.00918859	−	0.00930043i
$281$	22.0548	−	22.0548i	1.31568	−	1.31568i	0.398518	−	0.917161i	$-0.369525\pi$
$281$	22.0548	−	22.0548i	1.31568	−	1.31568i	0.917161	−	0.398518i	$-0.130475\pi$
$282$		0			0
$283$	2.07530	+	3.59453i	0.123364	+	0.213673i	0.921092	−	0.389344i	$-0.127298\pi$
$283$	2.07530	+	3.59453i	0.123364	+	0.213673i	−0.797728	+	0.603017i	$0.793965\pi$
$284$	−0.632522	−	0.169484i	−0.0375333	−	0.0100570i
$285$		0			0
$286$	−4.54697	−	0.941028i	−0.268868	−	0.0556441i
$287$	1.19735	+	2.04521i	0.0706776	+	0.120725i
$288$		0			0
$289$	−15.4691			−0.909946
$290$	−0.526236			−0.0309016
$291$		0			0
$292$	−1.86949	−	6.97701i	−0.109403	−	0.408299i
$293$	−4.12495	+	15.3945i	−0.240982	+	0.899357i	0.734379	+	0.678740i	$0.237474\pi$
$293$	−4.12495	+	15.3945i	−0.240982	+	0.899357i	−0.975361	+	0.220617i	$0.929193\pi$
$294$		0			0
$295$	−0.540128	−	0.935529i	−0.0314475	−	0.0544686i
$296$		−	4.93718i		−	0.286968i
$297$		0			0
$298$	−5.62285	−	3.24635i	−0.325723	−	0.188056i
$299$	19.8433	+	17.6752i	1.14757	+	1.02219i
$300$		0			0
$301$	−4.61610	+	4.67228i	−0.266068	+	0.269306i
$302$	−17.8764	+	30.9629i	−1.02867	+	1.78171i
$303$		0			0
$304$	−7.03100	−	26.2401i	−0.403256	−	1.50497i
$305$	0.354657	+	0.354657i	0.0203076	+	0.0203076i
$306$		0			0
$307$	5.87701	+	5.87701i	0.335419	+	0.335419i	0.854640	−	0.519221i	$-0.173778\pi$
$307$	5.87701	+	5.87701i	0.335419	+	0.335419i	−0.519221	+	0.854640i	$0.673778\pi$
$308$	−0.0158283	−	2.61667i	−0.000901902	−	0.149099i
$309$		0			0
$310$	−0.915569	+	0.915569i	−0.0520008	+	0.0520008i
$311$	−12.8619	+	22.2775i	−0.729331	+	1.26324i	0.227835	+	0.973700i	$0.426835\pi$
$311$	−12.8619	+	22.2775i	−0.729331	+	1.26324i	−0.957166	+	0.289539i	$0.906498\pi$
$312$		0			0
$313$	−19.5449	+	11.2842i	−1.10474	+	0.637823i	−0.937463	−	0.348086i	$-0.886832\pi$
$313$	−19.5449	+	11.2842i	−1.10474	+	0.637823i	−0.167280	+	0.985909i	$0.553498\pi$
$314$	1.21301	+	4.52703i	0.0684543	+	0.255475i
$315$		0			0
$316$	−8.02948	+	4.63582i	−0.451693	+	0.260785i
$317$	2.81372	−	10.5010i	0.158034	−	0.589792i	−0.840792	−	0.541358i	$-0.817910\pi$
$317$	2.81372	−	10.5010i	0.158034	−	0.589792i	0.998826	−	0.0484339i	$-0.0154230\pi$
$318$		0			0
$319$	1.81655	−	1.81655i	0.101707	−	0.101707i
$320$	−0.0575950	+	0.214947i	−0.00321966	+	0.0120159i
$321$		0			0
$322$	−17.8424	+	31.3402i	−0.994318	+	1.74652i
$323$	−1.80363	−	6.73123i	−0.100356	−	0.374536i
$324$		0			0
$325$	−17.0949	+	5.65602i	−0.948256	+	0.313740i
$326$	−13.1110	+	22.7089i	−0.726152	+	1.25773i
$327$		0			0
$328$	0.831654	+	0.480156i	0.0459204	+	0.0265122i
$329$	0.00670501	+	1.10844i	0.000369659	+	0.0611105i
$330$		0			0
$331$	20.9107	−	5.60302i	1.14936	−	0.307970i	0.366650	−	0.930359i	$-0.380505\pi$
$331$	20.9107	−	5.60302i	1.14936	−	0.307970i	0.782708	+	0.622389i	$0.213838\pi$
$332$	13.5531	+	13.5531i	0.743824	+	0.743824i
$333$		0			0
$334$	5.17494	+	2.98775i	0.283160	+	0.163483i
$335$	−0.0804682	+	0.139375i	−0.00439645	+	0.00761487i
$336$		0			0
$337$		−	15.6989i		−	0.855172i	−0.903975	−	0.427586i	$-0.859364\pi$
$337$		−	15.6989i		−	0.855172i	0.903975	−	0.427586i	$-0.140636\pi$
$338$	14.9290	−	18.8456i	0.812032	−	1.02507i
$339$		0			0
$340$	−0.0350806	+	0.130923i	−0.00190251	+	0.00710027i
$341$		−	6.32103i		−	0.342303i
$342$		0			0
$343$	12.8560	−	13.3313i	0.694159	−	0.719821i
$344$	−0.688822	+	2.57072i	−0.0371388	+	0.138604i
$345$		0			0
$346$	1.14036	−	0.305559i	0.0613062	−	0.0164270i
$347$	20.2272			1.08585			0.542927	−	0.839780i	$-0.317316\pi$
$347$	20.2272			1.08585			0.542927	+	0.839780i	$0.317316\pi$
$348$		0			0
$349$	−22.3749	+	5.99533i	−1.19770	+	0.320923i	−0.801925	−	0.597425i	$-0.796191\pi$
$349$	−22.3749	+	5.99533i	−1.19770	+	0.320923i	−0.395775	+	0.918348i	$0.629524\pi$
$350$	−12.3459	−	21.0881i	−0.659917	−	1.12721i
$351$		0			0
$352$	−2.35927	−	4.08638i	−0.125750	−	0.217805i
$353$	−12.3710	−	3.31480i	−0.658442	−	0.176429i	−0.0858994	−	0.996304i	$-0.527376\pi$
$353$	−12.3710	−	3.31480i	−0.658442	−	0.176429i	−0.572543	+	0.819875i	$0.694043\pi$
$354$		0			0
$355$	−0.0177798	+	0.0307956i	−0.000943656	+	0.00163446i
$356$	4.46942	−	4.46942i	0.236879	−	0.236879i
$357$		0			0
$358$	−13.9830	−	3.74675i	−0.739027	−	0.198022i
$359$	26.0068	+	6.96850i	1.37259	+	0.367783i	0.868423	−	0.495825i	$-0.165134\pi$
$359$	26.0068	+	6.96850i	1.37259	+	0.367783i	0.504163	+	0.863608i	$0.331801\pi$
$360$		0			0
$361$	−11.0167	+	6.36050i	−0.579827	+	0.334763i
$362$	10.1228	+	10.1228i	0.532041	+	0.532041i
$363$		0			0
$364$	12.1416	+	6.01291i	0.636392	+	0.315162i
$365$	−0.392240			−0.0205308
$366$		0			0
$367$	−21.5194	+	12.4242i	−1.12330	+	0.648540i	−0.942242	−	0.334932i	$-0.891287\pi$
$367$	−21.5194	+	12.4242i	−1.12330	+	0.648540i	−0.181062	+	0.983472i	$0.557953\pi$
$368$			35.5493i			1.85314i
$369$		0			0
$370$	0.634510	+	0.170016i	0.0329866	+	0.00883874i
$371$	−7.70121	+	29.4528i	−0.399827	+	1.52911i
$372$		0			0
$373$	16.7470	−	29.0067i	0.867129	−	1.50191i	0.00221133	−	0.999998i	$-0.499296\pi$
$373$	16.7470	−	29.0067i	0.867129	−	1.50191i	0.864918	−	0.501914i	$-0.167371\pi$
$374$	−0.796718	−	1.37996i	−0.0411973	−	0.0713558i
$375$		0			0
$376$	0.224579	+	0.388983i	0.0115818	+	0.0200603i
$377$	4.17827	+	12.6285i	0.215192	+	0.650401i
$378$		0			0
$379$	2.63846	−	0.706973i	0.135529	−	0.0363148i	−0.190417	−	0.981703i	$-0.560984\pi$
$379$	2.63846	−	0.706973i	0.135529	−	0.0363148i	0.325946	+	0.945389i	$0.394317\pi$
$380$	0.616974			0.0316501
$381$		0			0
$382$	24.2002	−	6.48442i	1.23819	−	0.331772i
$383$	−5.37033	−	20.0424i	−0.274411	−	1.02412i	−0.956235	−	0.292600i	$-0.905480\pi$
$383$	−5.37033	−	20.0424i	−0.274411	−	1.02412i	0.681824	−	0.731516i	$-0.261187\pi$
$384$		0			0
$385$	−0.137475	−	0.0359464i	−0.00700636	−	0.00183200i
$386$	14.3606	+	24.8733i	0.730935	+	1.26602i
$387$		0			0
$388$	5.95732	−	22.2330i	0.302437	−	1.12871i
$389$	−29.3050	−	16.9193i	−1.48582	−	0.857841i	−0.485955	−	0.873984i	$-0.661528\pi$
$389$	−29.3050	−	16.9193i	−1.48582	−	0.857841i	−0.999870	+	0.0161427i	$0.994861\pi$
$390$		0			0
$391$			9.11928i			0.461182i
$392$	1.85449	−	7.27181i	0.0936657	−	0.367282i
$393$		0			0
$394$	−21.4769	−	12.3997i	−1.08199	−	0.624686i
$395$	0.130310	+	0.486325i	0.00655662	+	0.0244697i
$396$		0			0
$397$	−4.02654	+	1.07891i	−0.202086	+	0.0541488i	−0.358442	−	0.933552i	$-0.616692\pi$
$397$	−4.02654	+	1.07891i	−0.202086	+	0.0541488i	0.156356	+	0.987701i	$0.450025\pi$
$398$	−4.29752	−	4.29752i	−0.215415	−	0.215415i
$399$		0			0
$400$	−20.8608	−	12.0440i	−1.04304	−	0.602200i
$401$	−26.9224	+	26.9224i	−1.34444	+	1.34444i	−0.452856	+	0.891584i	$0.649595\pi$
$401$	−26.9224	+	26.9224i	−1.34444	+	1.34444i	−0.891584	+	0.452856i	$0.850405\pi$
$402$		0			0
$403$	29.2412	+	14.7021i	1.45661	+	0.732364i
$404$	12.4569	−	7.19202i	0.619756	−	0.357816i
$405$		0			0
$406$	−15.5784	+	9.12028i	−0.773143	+	0.452632i
$407$	−2.77720	+	1.60342i	−0.137661	+	0.0794785i
$408$		0			0
$409$	13.5134	−	13.5134i	0.668194	−	0.668194i	−0.289104	−	0.957298i	$-0.593357\pi$
$409$	13.5134	−	13.5134i	0.668194	−	0.668194i	0.957298	+	0.289104i	$0.0933573\pi$
$410$	−0.0903468	+	0.0903468i	−0.00446191	+	0.00446191i
$411$		0			0
$412$	−3.62461	+	2.09267i	−0.178572	+	0.103098i
$413$	−32.2035	−	18.3339i	−1.58463	−	0.902150i
$414$		0			0
$415$	0.901386	−	0.520415i	0.0442473	−	0.0255462i
$416$	24.3911	−	1.40950i	1.19587	−	0.0691066i
$417$		0			0
$418$	−5.12880	+	5.12880i	−0.250858	+	0.250858i
$419$	29.2306	+	16.8763i	1.42801	+	0.824460i	0.996963	−	0.0778716i	$-0.0248124\pi$
$419$	29.2306	+	16.8763i	1.42801	+	0.824460i	0.431043	+	0.902331i	$0.358146\pi$
$420$		0			0
$421$	20.2556	+	20.2556i	0.987197	+	0.987197i	0.999919	−	0.0127222i	$-0.00404970\pi$
$421$	20.2556	+	20.2556i	0.987197	+	0.987197i	−0.0127222	+	0.999919i	$0.504050\pi$
$422$	−22.5549	+	6.04357i	−1.09796	+	0.294196i
$423$		0			0
$424$	3.19273	+	11.9154i	0.155053	+	0.578664i
$425$	−5.35132	−	3.08958i	−0.259577	−	0.149867i
$426$		0			0
$427$	16.6457	+	4.35246i	0.805542	+	0.210630i
$428$		−	23.9205i		−	1.15624i
$429$		0			0
$430$	−0.306660	−	0.177050i	−0.0147885	−	0.00853812i
$431$	−4.52853	+	16.9007i	−0.218132	+	0.814079i	0.766909	+	0.641756i	$0.221794\pi$
$431$	−4.52853	+	16.9007i	−0.218132	+	0.814079i	−0.985041	+	0.172323i	$0.944873\pi$
$432$		0			0
$433$	6.74582	+	11.6841i	0.324184	+	0.561502i	0.981347	−	0.192246i	$-0.0615771\pi$
$433$	6.74582	+	11.6841i	0.324184	+	0.561502i	−0.657163	+	0.753748i	$0.728244\pi$
$434$	−11.2361	+	42.9719i	−0.539352	+	2.06272i
$435$		0			0
$436$	−4.14696	−	15.4767i	−0.198603	−	0.741198i
$437$	40.0960	−	10.7437i	1.91805	−	0.513940i
$438$		0			0
$439$	−23.7377			−1.13294			−0.566470	−	0.824082i	$-0.691691\pi$
$439$	−23.7377			−1.13294			−0.566470	+	0.824082i	$0.691691\pi$
$440$	−0.0556167	+	0.0149024i	−0.00265142	+	0.000710446i
$441$		0			0
$442$	8.23678	−	0.475984i	0.391784	−	0.0226402i
$443$	−17.9783	−	31.1393i	−0.854173	−	1.47947i	−0.877410	−	0.479741i	$-0.840731\pi$
$443$	−17.9783	−	31.1393i	−0.854173	−	1.47947i	0.0232374	−	0.999730i	$-0.492603\pi$
$444$		0			0
$445$	−0.171618	−	0.297250i	−0.00813545	−	0.0140910i
$446$	−18.6720	+	32.3408i	−0.884144	+	1.53138i
$447$		0			0
$448$	2.02028	+	7.36138i	0.0954492	+	0.347792i
$449$	−27.2216	−	7.29399i	−1.28466	−	0.344225i	−0.449033	−	0.893515i	$-0.648231\pi$
$449$	−27.2216	−	7.29399i	−1.28466	−	0.344225i	−0.835632	+	0.549290i	$0.814898\pi$
$450$		0			0
$451$		−	0.623749i		−	0.0293712i
$452$	−14.0210	+	8.09501i	−0.659491	+	0.380757i
$453$		0			0
$454$	−23.6255			−1.10880
$455$	0.486041	−	0.552352i	0.0227860	−	0.0258946i
$456$		0			0
$457$	0.0883512	+	0.0883512i	0.00413290	+	0.00413290i	0.709170	−	0.705037i	$-0.249070\pi$
$457$	0.0883512	+	0.0883512i	0.00413290	+	0.00413290i	−0.705037	+	0.709170i	$0.749070\pi$
$458$	19.7039	−	11.3761i	0.920703	−	0.531568i
$459$		0			0
$460$	−0.779868	−	0.208965i	−0.0363615	−	0.00974304i
$461$	16.8148	+	4.50551i	0.783143	+	0.209843i	0.628170	−	0.778076i	$-0.283804\pi$
$461$	16.8148	+	4.50551i	0.783143	+	0.209843i	0.154973	+	0.987919i	$0.450471\pi$
$462$		0			0
$463$	−1.07038	+	1.07038i	−0.0497447	+	0.0497447i	−0.731542	−	0.681797i	$-0.761199\pi$
$463$	−1.07038	+	1.07038i	−0.0497447	+	0.0497447i	0.681797	+	0.731542i	$0.261199\pi$
$464$	−8.89725	+	15.4105i	−0.413044	+	0.715414i
$465$		0			0
$466$	0.0744944	+	0.0199607i	0.00345089	+	0.000924663i
$467$	14.6317	+	25.3429i	0.677075	+	1.17273i	0.975858	+	0.218408i	$0.0700862\pi$
$467$	14.6317	+	25.3429i	0.677075	+	1.17273i	−0.298782	+	0.954321i	$0.596580\pi$
$468$		0			0
$469$	0.0333942	+	5.52059i	0.00154200	+	0.254917i
$470$	−0.0577244	+	0.0154672i	−0.00266263	+	0.000713449i
$471$		0			0
$472$	−15.0156			−0.691151
$473$	1.66975	−	0.447409i	0.0767754	−	0.0205719i
$474$		0			0
$475$	−7.27985	+	27.1688i	−0.334023	+	1.24659i
$476$	1.23053	+	4.48375i	0.0564014	+	0.205512i
$477$		0			0
$478$		−	3.79795i		−	0.173714i
$479$	0.884245	−	3.30005i	0.0404022	−	0.150783i	−0.942778	−	0.333421i	$-0.891797\pi$
$479$	0.884245	−	3.30005i	0.0404022	−	0.150783i	0.983180	+	0.182638i	$0.0584636\pi$
$480$		0			0
$481$	−0.957931	−	16.5768i	−0.0436779	−	0.755836i
$482$		−	5.10857i		−	0.232689i
$483$		0			0
$484$	7.46736	−	12.9339i	0.339426	−	0.587903i
$485$	−1.08246	−	0.624958i	−0.0491519	−	0.0283779i
$486$		0			0
$487$	−4.37510	−	4.37510i	−0.198255	−	0.198255i	0.600997	−	0.799251i	$-0.294770\pi$
$487$	−4.37510	−	4.37510i	−0.198255	−	0.198255i	−0.799251	+	0.600997i	$0.794770\pi$
$488$	6.73418	−	1.80442i	0.304842	−	0.0816822i
$489$		0			0
$490$	0.870688	+	0.488744i	0.0393337	+	0.0220792i
$491$	33.1219	+	19.1229i	1.49477	+	0.863006i	0.999982	−	0.00600745i	$-0.00191224\pi$
$491$	33.1219	+	19.1229i	1.49477	+	0.863006i	0.494788	+	0.869014i	$0.335246\pi$
$492$		0			0
$493$	−2.28236	+	3.95317i	−0.102793	+	0.178042i
$494$	−11.7968	−	35.6550i	−0.530764	−	1.60419i
$495$		0			0
$496$	11.3320	+	42.2917i	0.508823	+	1.89895i
$497$	0.00737861	+	1.21980i	0.000330976	+	0.0547156i
$498$		0			0
$499$	−1.07153	+	3.99901i	−0.0479684	+	0.179020i	−0.985754	−	0.168195i	$-0.946206\pi$
$499$	−1.07153	+	3.99901i	−0.0479684	+	0.179020i	0.937785	+	0.347216i	$0.112873\pi$
$500$	0.774141	−	0.774141i	0.0346206	−	0.0346206i
$501$		0			0
$502$	11.4207	−	42.6228i	0.509733	−	1.90235i
$503$	20.9643	−	12.1038i	0.934752	−	0.539680i	0.0464410	−	0.998921i	$-0.485212\pi$
$503$	20.9643	−	12.1038i	0.934752	−	0.539680i	0.888311	+	0.459241i	$0.151879\pi$
$504$		0			0
$505$	−0.202163	−	0.754484i	−0.00899616	−	0.0335741i
$506$	8.22000	−	4.74582i	0.365424	−	0.210977i
$507$		0			0
$508$	9.80449	−	16.9819i	0.435004	−	0.753449i
$509$	16.4577	−	16.4577i	0.729476	−	0.729476i	−0.241039	−	0.970515i	$-0.577488\pi$
$509$	16.4577	−	16.4577i	0.729476	−	0.729476i	0.970515	+	0.241039i	$0.0774883\pi$
$510$		0			0
$511$	−11.6117	+	6.79797i	−0.513670	+	0.300725i
$512$	15.7980	+	15.7980i	0.698179	+	0.698179i
$513$		0			0
$514$	−8.78434	−	8.78434i	−0.387460	−	0.387460i
$515$	0.0588237	+	0.219533i	0.00259208	+	0.00967379i
$516$		0			0
$517$	0.145871	−	0.252655i	0.00641538	−	0.0111118i
$518$	21.7303	−	5.96373i	0.954774	−	0.262031i
$519$		0			0
$520$	0.0604201	−	0.291945i	0.00264960	−	0.0128026i
$521$	−29.3950	−	16.9712i	−1.28782	−	0.743522i	−0.309553	−	0.950882i	$-0.600179\pi$
$521$	−29.3950	−	16.9712i	−1.28782	−	0.743522i	−0.978265	+	0.207360i	$0.933513\pi$
$522$		0			0
$523$		−	7.59842i		−	0.332256i	−0.986104	−	0.166128i	$-0.946874\pi$
$523$		−	7.59842i		−	0.332256i	0.986104	−	0.166128i	$-0.0531264\pi$
$524$	10.1450	+	17.5717i	0.443188	+	0.767624i
$525$		0			0
$526$	−7.40236	+	27.6260i	−0.322758	+	1.20455i
$527$	2.90694	+	10.8489i	0.126628	+	0.472584i
$528$		0			0
$529$	−31.3209			−1.36178
$530$	−1.64127			−0.0712924
$531$		0			0
$532$	18.2646	−	10.6929i	0.791870	−	0.463595i
$533$	2.88547	+	1.45078i	0.124984	+	0.0628402i
$534$		0			0
$535$	−1.25470	−	0.336196i	−0.0542454	−	0.0145350i
$536$	1.11851	+	1.93732i	0.0483125	+	0.0836797i
$537$		0			0
$538$	−0.458872	+	0.458872i	−0.0197834	+	0.0197834i
$539$	−4.69272	+	1.31846i	−0.202130	+	0.0567901i
$540$		0			0
$541$	−22.5943	−	6.05411i	−0.971403	−	0.260287i	−0.261983	−	0.965073i	$-0.584376\pi$
$541$	−22.5943	−	6.05411i	−0.971403	−	0.260287i	−0.709420	+	0.704786i	$0.751043\pi$
$542$			18.4665i			0.793203i
$543$		0			0
$544$	5.92851	+	5.92851i	0.254183	+	0.254183i
$545$	−0.870081			−0.0372702
$546$		0			0
$547$	39.6600			1.69574			0.847870	−	0.530204i	$-0.177885\pi$
$547$	39.6600			1.69574			0.847870	+	0.530204i	$0.177885\pi$
$548$	4.24303	+	4.24303i	0.181253	+	0.181253i
$549$		0			0
$550$			6.43147i			0.274239i
$551$	20.0704	+	5.37784i	0.855026	+	0.229104i
$552$		0			0
$553$	12.2862	+	12.1385i	0.522463	+	0.516180i
$554$	−12.6784	+	12.6784i	−0.538655	+	0.538655i
$555$		0			0
$556$	6.99142	+	12.1095i	0.296502	+	0.513557i
$557$	11.3970	+	3.05383i	0.482908	+	0.129395i	0.492056	−	0.870563i	$-0.336245\pi$
$557$	11.3970	+	3.05383i	0.482908	+	0.129395i	−0.00914829	+	0.999958i	$0.502912\pi$
$558$		0			0
$559$	−1.81397	+	8.76494i	−0.0767226	+	0.370717i
$560$	0.984234	−	0.00595366i	0.0415915	−	0.000251588i
$561$		0			0
$562$	57.6834			2.43323
$563$	−18.3834			−0.774770			−0.387385	−	0.921918i	$-0.626622\pi$
$563$	−18.3834			−0.774770			−0.387385	+	0.921918i	$0.626622\pi$
$564$		0			0
$565$	0.227546	+	0.849214i	0.00957294	+	0.0357267i
$566$	−1.98674	+	7.41460i	−0.0835088	+	0.311659i
$567$		0			0
$568$	0.247141	+	0.428061i	0.0103698	+	0.0179610i
$569$			13.5278i			0.567116i	0.958955	+	0.283558i	$0.0915149\pi$
$569$			13.5278i			0.567116i	−0.958955	+	0.283558i	$0.908485\pi$
$570$		0			0
$571$	−12.8299	−	7.40732i	−0.536913	−	0.309987i	0.206914	−	0.978359i	$-0.433658\pi$
$571$	−12.8299	−	7.40732i	−0.536913	−	0.309987i	−0.743827	+	0.668372i	$0.766991\pi$
$572$	−1.95819	−	2.98023i	−0.0818760	−	0.124610i
$573$		0			0
$574$	−1.10876	+	4.24039i	−0.0462789	+	0.176991i
$575$	18.4038	−	31.8763i	0.767490	−	1.32933i
$576$		0			0
$577$	−5.26970	−	19.6668i	−0.219381	−	0.818740i	−0.984578	−	0.174944i	$-0.944025\pi$
$577$	−5.26970	−	19.6668i	−0.219381	−	0.818740i	0.765198	−	0.643795i	$-0.222641\pi$
$578$	−20.2294	−	20.2294i	−0.841431	−	0.841431i
$579$		0			0
$580$	−0.285770	−	0.285770i	−0.0118659	−	0.0118659i
$581$	17.6647	−	31.0282i	0.732857	−	1.28727i
$582$		0			0
$583$	5.66563	−	5.66563i	0.234646	−	0.234646i
$584$	−2.72608	+	4.72171i	−0.112806	+	0.195386i
$585$		0			0
$586$	−25.5262	+	14.7375i	−1.05448	+	0.608802i
$587$	7.64015	+	28.5134i	0.315343	+	1.17688i	0.923670	+	0.383189i	$0.125174\pi$
$587$	7.64015	+	28.5134i	0.315343	+	1.17688i	−0.608327	+	0.793686i	$0.708159\pi$
$588$		0			0
$589$	44.2759	−	25.5627i	1.82436	−	1.05329i
$590$	0.517078	−	1.92976i	0.0212877	−	0.0794470i
$591$		0			0
$592$	15.7067	−	15.7067i	0.645541	−	0.645541i
$593$	9.26744	−	34.5866i	0.380568	−	1.42030i	−0.464467	−	0.885590i	$-0.653754\pi$
$593$	9.26744	−	34.5866i	0.380568	−	1.42030i	0.845036	−	0.534710i	$-0.179579\pi$
$594$		0			0
$595$	0.252480	−	0.00152726i	0.0103507	−	6.26116e-5i
$596$	−1.29055	−	4.81638i	−0.0528628	−	0.197287i
$597$		0			0
$598$	2.83530	+	49.0641i	0.115944	+	2.00638i
$599$	−3.11170	+	5.38963i	−0.127141	+	0.220214i	−0.922568	−	0.385835i	$-0.873913\pi$
$599$	−3.11170	+	5.38963i	−0.127141	+	0.220214i	0.795427	+	0.606049i	$0.207247\pi$
$600$		0			0
$601$	0.0256568	+	0.0148129i	0.00104656	+	0.000604232i	0.500523	−	0.865723i	$-0.333141\pi$
$601$	0.0256568	+	0.0148129i	0.00104656	+	0.000604232i	−0.499477	+	0.866327i	$0.666474\pi$
$602$	−12.1467	+	0.0734756i	−0.495062	+	0.00299464i
$603$		0			0
$604$	−26.5220	+	7.10654i	−1.07916	+	0.289161i
$605$	−0.573467	−	0.573467i	−0.0233147	−	0.0233147i
$606$		0			0
$607$	22.7071	+	13.1100i	0.921653	+	0.532117i	0.884162	−	0.467180i	$-0.154730\pi$
$607$	22.7071	+	13.1100i	0.921653	+	0.532117i	0.0374913	+	0.999297i	$0.488063\pi$
$608$	19.0822	−	33.0513i	0.773883	−	1.34041i
$609$		0			0
$610$			0.927591i			0.0375571i
$611$	0.829506	+	1.26245i	0.0335582	+	0.0510733i
$612$		0			0
$613$	7.02053	−	26.2010i	0.283556	−	1.05825i	−0.666331	−	0.745656i	$-0.732136\pi$
$613$	7.02053	−	26.2010i	0.283556	−	1.05825i	0.949888	−	0.312591i	$-0.101197\pi$
$614$			15.3711i			0.620326i
$615$		0			0
$616$	−1.38817	+	1.40507i	−0.0559310	+	0.0566117i
$617$	10.0810	−	37.6229i	0.405847	−	1.51464i	−0.396641	−	0.917974i	$-0.629824\pi$
$617$	10.0810	−	37.6229i	0.405847	−	1.51464i	0.802488	−	0.596668i	$-0.203509\pi$
$618$		0			0
$619$	28.5176	−	7.64126i	1.14622	−	0.307128i	0.364769	−	0.931098i	$-0.381148\pi$
$619$	28.5176	−	7.64126i	1.14622	−	0.307128i	0.781448	+	0.623970i	$0.214481\pi$
$620$	−0.994390			−0.0399357
$621$		0			0
$622$	−45.9528	+	12.3130i	−1.84254	+	0.493707i
$623$	−10.2322	−	5.82531i	−0.409943	−	0.233386i
$624$		0			0
$625$	12.4554	+	21.5734i	0.498216	+	0.862936i
$626$	−40.3162	−	10.8027i	−1.61136	−	0.431762i
$627$		0			0
$628$	−1.79966	+	3.11710i	−0.0718142	+	0.124386i
$629$	4.02916	−	4.02916i	0.160653	−	0.160653i
$630$		0			0
$631$	36.5172	+	9.78475i	1.45373	+	0.389525i	0.897318	−	0.441384i	$-0.145512\pi$
$631$	36.5172	+	9.78475i	1.45373	+	0.389525i	0.556408	+	0.830909i	$0.312179\pi$
$632$	6.75995	+	1.81132i	0.268896	+	0.0720506i
$633$		0			0
$634$	17.4120	−	10.0528i	0.691518	−	0.399248i
$635$	−0.752949	−	0.752949i	−0.0298799	−	0.0298799i
$636$		0			0
$637$	4.81560	−	24.7752i	0.190801	−	0.981629i
$638$	4.75111			0.188098
$639$		0			0
$640$	0.548808	−	0.316855i	0.0216936	−	0.0125248i
$641$			4.14733i			0.163810i	0.996640	+	0.0819049i	$0.0261004\pi$
$641$			4.14733i			0.163810i	−0.996640	+	0.0819049i	$0.973900\pi$
$642$		0			0
$643$	39.3048	+	10.5317i	1.55003	+	0.415330i	0.929491	−	0.368845i	$-0.120247\pi$
$643$	39.3048	+	10.5317i	1.55003	+	0.415330i	0.620541	+	0.784174i	$0.286913\pi$
$644$	−26.7084	+	7.32993i	−1.05246	+	0.288840i
$645$		0			0
$646$	6.44397	−	11.1613i	0.253535	−	0.439135i
$647$	−17.8485	−	30.9146i	−0.701698	−	1.21538i	−0.967870	−	0.251451i	$-0.919092\pi$
$647$	−17.8485	−	30.9146i	−0.701698	−	1.21538i	0.266172	−	0.963926i	$-0.414241\pi$
$648$		0			0
$649$	4.87654	+	8.44641i	0.191421	+	0.331551i
$650$	−29.7521	−	14.9590i	−1.16697	−	0.586740i
$651$		0			0
$652$	−19.4518	+	5.21211i	−0.761793	+	0.204122i
$653$	−35.3648			−1.38393			−0.691966	−	0.721930i	$-0.743255\pi$
$653$	−35.3648			−1.38393			−0.691966	+	0.721930i	$0.743255\pi$
$654$		0			0
$655$	1.06427	−	0.285171i	0.0415846	−	0.0111426i
$656$	1.11822	+	4.17327i	0.0436593	+	0.162939i
$657$		0			0
$658$	−1.44078	+	1.45831i	−0.0561674	+	0.0568510i
$659$	1.02268	+	1.77133i	0.0398378	+	0.0690011i	0.885257	−	0.465103i	$-0.153983\pi$
$659$	1.02268	+	1.77133i	0.0398378	+	0.0690011i	−0.845419	+	0.534104i	$0.820649\pi$
$660$		0			0
$661$	−5.33936	+	19.9268i	−0.207677	+	0.775061i	0.780940	+	0.624606i	$0.214740\pi$
$661$	−5.33936	+	19.9268i	−0.207677	+	0.775061i	−0.988617	+	0.150455i	$0.951926\pi$
$662$	34.6728	+	20.0184i	1.34760	+	0.778036i
$663$		0			0
$664$		−	14.4676i		−	0.561453i
$665$	−0.304170	−	1.10832i	−0.0117952	−	0.0429786i
$666$		0			0
$667$	−23.5479	−	13.5954i	−0.911778	−	0.526415i
$668$	1.18774	+	4.43271i	0.0459551	+	0.171507i
$669$		0			0
$670$	−0.287496	+	0.0770342i	−0.0111069	+	0.00297609i
$671$	−3.20202	−	3.20202i	−0.123613	−	0.123613i
$672$		0			0
$673$	17.7096	+	10.2246i	0.682655	+	0.394131i	0.800855	−	0.598859i	$-0.204379\pi$
$673$	17.7096	+	10.2246i	0.682655	+	0.394131i	−0.118199	+	0.992990i	$0.537712\pi$
$674$	20.5299	−	20.5299i	0.790781	−	0.790781i
$675$		0			0
$676$	18.3412	−	2.12688i	0.705429	−	0.0818032i
$677$	38.1123	−	22.0042i	1.46478	−	0.845689i	0.465549	−	0.885022i	$-0.345857\pi$
$677$	38.1123	−	22.0042i	1.46478	−	0.845689i	0.999226	+	0.0393333i	$0.0125234\pi$
$678$		0			0
$679$	−42.8758	+	0.259357i	−1.64542	+	0.00995319i
$680$	0.0886022	−	0.0511545i	0.00339774	−	0.00196169i
$681$		0			0
$682$	8.26620	−	8.26620i	0.316529	−	0.316529i
$683$	3.43053	−	3.43053i	0.131265	−	0.131265i	−0.638422	−	0.769687i	$-0.720412\pi$
$683$	3.43053	−	3.43053i	0.131265	−	0.131265i	0.769687	+	0.638422i	$0.220412\pi$
$684$		0			0
$685$	0.282194	−	0.162925i	0.0107821	−	0.00622504i
$686$	34.2459	−	0.621523i	1.30751	−	0.0237299i
$687$		0			0
$688$	−10.3696	+	5.98690i	−0.395338	+	0.228248i
$689$	13.0316	+	39.3870i	0.496463	+	1.50052i
$690$		0			0
$691$	32.7898	−	32.7898i	1.24738	−	1.24738i	0.290511	−	0.956872i	$-0.406175\pi$
$691$	32.7898	−	32.7898i	1.24738	−	1.24738i	0.956872	−	0.290511i	$-0.0938254\pi$
$692$	0.785200	+	0.453336i	0.0298488	+	0.0172332i
$693$		0			0
$694$	26.4517	+	26.4517i	1.00409	+	1.00409i
$695$	0.733441	−	0.196525i	0.0278210	−	0.00745462i
$696$		0			0
$697$	0.286852	+	1.07055i	0.0108653	+	0.0405499i
$698$	−37.1006	−	21.4200i	−1.40428	−	0.810760i
$699$		0			0
$700$	4.74742	−	18.1562i	0.179436	−	0.686240i
$701$		−	16.7923i		−	0.634236i	−0.948386	−	0.317118i	$-0.897285\pi$
$701$		−	16.7923i		−	0.634236i	0.948386	−	0.317118i	$-0.102715\pi$
$702$		0			0
$703$	−22.4624	−	12.9687i	−0.847186	−	0.489123i
$704$	0.519996	−	1.94065i	0.0195981	−	0.0731410i
$705$		0			0
$706$	−11.8431	−	20.5128i	−0.445720	−	0.772009i
$707$	−19.0608	−	18.8316i	−0.716857	−	0.708236i
$708$		0			0
$709$	−1.77899	−	6.63927i	−0.0668113	−	0.249343i	0.924441	−	0.381326i	$-0.124532\pi$
$709$	−1.77899	−	6.63927i	−0.0668113	−	0.249343i	−0.991252	+	0.131983i	$0.957866\pi$
$710$	−0.0635235	+	0.0170211i	−0.00238399	+	0.000638789i
$711$		0			0
$712$	−4.77100			−0.178801
$713$	−64.6235	+	17.3158i	−2.42017	+	0.648483i
$714$		0			0
$715$	−0.183844	+	0.0608265i	−0.00687536	+	0.00227478i
$716$	−5.55877	−	9.62808i	−0.207741	−	0.359818i
$717$		0			0
$718$	24.8969	+	43.1228i	0.929145	+	1.60933i
$719$	−18.7721	+	32.5143i	−0.700082	+	1.21258i	0.268355	+	0.963320i	$0.413520\pi$
$719$	−18.7721	+	32.5143i	−0.700082	+	1.21258i	−0.968437	+	0.249258i	$0.919813\pi$
$720$		0			0
$721$	5.54615	+	5.47946i	0.206550	+	0.204066i
$722$	−22.7247	−	6.08906i	−0.845725	−	0.226611i
$723$		0			0
$724$			10.9942i			0.408598i
$725$	15.9559	−	9.21215i	0.592588	−	0.342131i
$726$		0			0
$727$	−23.0678			−0.855536			−0.427768	−	0.903888i	$-0.640700\pi$
$727$	−23.0678			−0.855536			−0.427768	+	0.903888i	$0.640700\pi$
$728$	−3.27111	−	9.68974i	−0.121235	−	0.359126i
$729$		0			0
$730$	−0.512943	−	0.512943i	−0.0189849	−	0.0189849i
$731$	−2.66006	+	1.53579i	−0.0983859	+	0.0568032i
$732$		0			0
$733$	−17.5240	−	4.69555i	−0.647265	−	0.173434i	−0.0797732	−	0.996813i	$-0.525420\pi$
$733$	−17.5240	−	4.69555i	−0.647265	−	0.173434i	−0.567492	+	0.823379i	$0.692086\pi$
$734$	−44.3891	−	11.8940i	−1.63843	−	0.439017i
$735$		0			0
$736$	−35.3145	+	35.3145i	−1.30171	+	1.30171i
$737$	0.726506	−	1.25835i	0.0267612	−	0.0463518i
$738$		0			0
$739$	−9.95216	−	2.66667i	−0.366096	−	0.0980952i	0.0710811	−	0.997471i	$-0.477355\pi$
$739$	−9.95216	−	2.66667i	−0.366096	−	0.0980952i	−0.437177	+	0.899375i	$0.644022\pi$
$740$	0.252241	+	0.436894i	0.00927256	+	0.0160606i
$741$		0			0
$742$	−48.5874	+	28.4452i	−1.78370	+	1.04426i
$743$	37.7291	−	10.1095i	1.38415	−	0.370881i	0.511520	−	0.859271i	$-0.329082\pi$
$743$	37.7291	−	10.1095i	1.38415	−	0.370881i	0.872625	+	0.488390i	$0.162416\pi$
$744$		0			0
$745$	−0.270771			−0.00992030
$746$	59.8335	−	16.0324i	2.19066	−	0.586986i
$747$		0			0
$748$	0.316725	−	1.18203i	0.0115806	−	0.0432194i
$749$	−42.9701	+	11.7928i	−1.57009	+	0.430901i
$750$		0			0
$751$		−	32.0282i		−	1.16872i	−0.811493	−	0.584362i	$-0.801345\pi$
$751$		−	32.0282i		−	1.16872i	0.811493	−	0.584362i	$-0.198655\pi$
$752$	−0.523018	+	1.95193i	−0.0190725	+	0.0711796i
$753$		0			0
$754$	−11.0506	+	21.9787i	−0.402440	+	0.800418i
$755$			1.49103i			0.0542643i
$756$		0			0
$757$	3.10808	−	5.38335i	0.112965	−	0.195661i	−0.803999	−	0.594630i	$-0.797299\pi$
$757$	3.10808	−	5.38335i	0.112965	−	0.195661i	0.916964	+	0.398969i	$0.130632\pi$
$758$	4.37492	+	2.52586i	0.158904	+	0.0917435i
$759$		0			0
$760$	−0.329303	−	0.329303i	−0.0119451	−	0.0119451i
$761$	−27.0118	+	7.23779i	−0.979177	+	0.262370i	−0.712698	−	0.701471i	$-0.752527\pi$
$761$	−27.0118	+	7.23779i	−0.979177	+	0.262370i	−0.266479	+	0.963841i	$0.585860\pi$
$762$		0			0
$763$	−25.7574	+	15.0795i	−0.932481	+	0.545915i
$764$	16.6631	+	9.62047i	0.602851	+	0.348056i
$765$		0			0
$766$	19.1870	−	33.2329i	0.693256	−	1.20075i
$767$	−50.4156	+	2.91339i	−1.82040	+	0.105197i
$768$		0			0
$769$	−7.77893	−	29.0314i	−0.280515	−	1.04690i	−0.952054	−	0.305929i	$-0.901033\pi$
$769$	−7.77893	−	29.0314i	−0.280515	−	1.04690i	0.671539	−	0.740969i	$-0.265634\pi$
$770$	−0.132771	−	0.226788i	−0.00478475	−	0.00817286i
$771$		0			0
$772$	−5.70886	+	21.3058i	−0.205466	+	0.766811i
$773$	9.36696	−	9.36696i	0.336906	−	0.336906i	−0.518295	−	0.855202i	$-0.673433\pi$
$773$	9.36696	−	9.36696i	0.336906	−	0.336906i	0.855202	+	0.518295i	$0.173433\pi$
$774$		0			0
$775$	11.7331	−	43.7885i	0.421465	−	1.57293i
$776$	−15.0463	+	8.68696i	−0.540129	+	0.311844i
$777$		0			0
$778$	−16.1972	−	60.4489i	−0.580699	−	2.16720i
$779$	4.36907	−	2.52248i	0.156538	−	0.0903774i
$780$		0			0
$781$	0.160525	−	0.278038i	0.00574404	−	0.00994897i
$782$	−11.9256	+	11.9256i	−0.426457	+	0.426457i
$783$		0			0
$784$	29.0336	−	17.2342i	1.03691	−	0.615506i
$785$	0.138207	+	0.138207i	0.00493283	+	0.00493283i
$786$		0			0
$787$	−22.2518	−	22.2518i	−0.793192	−	0.793192i	0.188820	−	0.982012i	$-0.439534\pi$
$787$	−22.2518	−	22.2518i	−0.793192	−	0.793192i	−0.982012	+	0.188820i	$0.939534\pi$
$788$	−4.92932	−	18.3965i	−0.175600	−	0.655347i
$789$		0			0
$790$	−0.465570	+	0.806392i	−0.0165643	+	0.0286901i
$791$	21.4540	+	21.1960i	0.762817	+	0.753644i
$792$		0			0
$793$	22.2602	−	7.36499i	0.790481	−	0.261539i
$794$	−6.67654	−	3.85470i	−0.236942	−	0.136798i
$795$		0			0
$796$		−	4.66750i		−	0.165435i
$797$	7.62445	+	13.2059i	0.270072	+	0.467778i	0.968880	−	0.247531i	$-0.0796192\pi$
$797$	7.62445	+	13.2059i	0.270072	+	0.467778i	−0.698808	+	0.715309i	$0.746286\pi$
$798$		0			0
$799$	−0.134167	+	0.500719i	−0.00474649	+	0.0177142i
$800$	−8.75857	−	32.6874i	−0.309662	−	1.15567i
$801$		0			0
$802$	−70.4144			−2.48642
$803$	3.54133			0.124971
$804$		0			0
$805$	0.00909745	+	1.50395i	0.000320643	+	0.0530074i
$806$	19.0132	+	57.4659i	0.669710	+	2.02415i
$807$		0			0
$808$	−10.4874	−	2.81009i	−0.368945	−	0.0988586i
$809$	−23.3622	−	40.4644i	−0.821370	−	1.42265i	−0.904662	−	0.426129i	$-0.859877\pi$
$809$	−23.3622	−	40.4644i	−0.821370	−	1.42265i	0.0832926	−	0.996525i	$-0.473456\pi$
$810$		0			0
$811$	15.5284	−	15.5284i	0.545275	−	0.545275i	−0.379796	−	0.925070i	$-0.624006\pi$
$811$	15.5284	−	15.5284i	0.545275	−	0.545275i	0.925070	+	0.379796i	$0.124006\pi$
$812$	−13.4125	−	3.50705i	−0.470687	−	0.123073i
$813$		0			0
$814$	−5.72867	−	1.53499i	−0.200790	−	0.0538014i
$815$			1.09356i			0.0383058i
$816$		0			0
$817$	9.88650	+	9.88650i	0.345885	+	0.345885i
$818$	35.3437			1.23576
$819$		0			0
$820$	−0.0981247			−0.00342666
$821$	20.8207	+	20.8207i	0.726648	+	0.726648i	0.969951	−	0.243302i	$-0.0782307\pi$
$821$	20.8207	+	20.8207i	0.726648	+	0.726648i	−0.243302	+	0.969951i	$0.578231\pi$
$822$		0			0
$823$			4.41442i			0.153877i	0.997036	+	0.0769385i	$0.0245145\pi$
$823$			4.41442i			0.153877i	−0.997036	+	0.0769385i	$0.975486\pi$
$824$	3.05153	+	0.817655i	0.106305	+	0.0284844i
$825$		0			0
$826$	−18.1377	−	66.0892i	−0.631092	−	2.29954i
$827$	−16.4939	+	16.4939i	−0.573550	+	0.573550i	−0.933119	−	0.359568i	$-0.882924\pi$
$827$	−16.4939	+	16.4939i	−0.573550	+	0.573550i	0.359568	+	0.933119i	$0.382924\pi$
$828$		0			0
$829$	−20.8871	−	36.1775i	−0.725439	−	1.25650i	−0.958793	−	0.284105i	$-0.908303\pi$
$829$	−20.8871	−	36.1775i	−0.725439	−	1.25650i	0.233354	−	0.972392i	$-0.425030\pi$
$830$	1.85933	+	0.498206i	0.0645383	+	0.0172930i
$831$		0			0
$832$	7.76801	+	6.91927i	0.269307	+	0.239883i
$833$	7.44783	−	4.42099i	0.258052	−	0.153178i
$834$		0			0
$835$	0.249202			0.00862399
$836$	−5.57034			−0.192654
$837$		0			0
$838$	16.1561	+	60.2953i	0.558102	+	2.08287i
$839$	−7.04543	+	26.2939i	−0.243235	+	0.907766i	0.731027	+	0.682349i	$0.239041\pi$
$839$	−7.04543	+	26.2939i	−0.243235	+	0.907766i	−0.974262	+	0.225418i	$0.927625\pi$
$840$		0			0
$841$	7.69472	+	13.3277i	0.265335	+	0.459574i
$842$			52.9777i			1.82573i
$843$		0			0
$844$	−15.5303	−	8.96641i	−0.534574	−	0.308636i
$845$	0.146218	−	0.991940i	0.00503007	−	0.0341238i
$846$		0			0
$847$	−26.9155	−	7.03776i	−0.924826	−	0.241820i
$848$	−27.7496	+	48.0637i	−0.952924	+	1.65051i
$849$		0			0
$850$	−2.95773	−	11.0384i	−0.101449	−	0.378615i
$851$	24.0005	+	24.0005i	0.822728	+	0.822728i
$852$		0			0
$853$	26.4347	+	26.4347i	0.905108	+	0.905108i	0.995872	−	0.0907640i	$-0.0289309\pi$
$853$	26.4347	+	26.4347i	0.905108	+	0.905108i	−0.0907640	+	0.995872i	$0.528931\pi$
$854$	16.0762	+	27.4599i	0.550118	+	0.939659i
$855$		0			0
$856$	−12.7673	+	12.7673i	−0.436376	+	0.436376i
$857$	−2.88406	+	4.99534i	−0.0985177	+	0.170638i	−0.911071	−	0.412249i	$-0.864743\pi$
$857$	−2.88406	+	4.99534i	−0.0985177	+	0.170638i	0.812554	+	0.582887i	$0.198077\pi$
$858$		0			0
$859$	−30.2787	+	17.4814i	−1.03310	+	0.596459i	−0.917870	−	0.396880i	$-0.870093\pi$
$859$	−30.2787	+	17.4814i	−1.03310	+	0.596459i	−0.115227	+	0.993339i	$0.536760\pi$
$860$	−0.0703840	−	0.262677i	−0.00240007	−	0.00895720i
$861$		0			0
$862$	−28.0237	+	16.1795i	−0.954490	+	0.551075i
$863$	9.88638	−	36.8965i	0.336536	−	1.25597i	−0.565658	−	0.824640i	$-0.691378\pi$
$863$	9.88638	−	36.8965i	0.336536	−	1.25597i	0.902194	−	0.431330i	$-0.141956\pi$
$864$		0			0
$865$	0.0348145	−	0.0348145i	0.00118373	−	0.00118373i
$866$	−6.45794	+	24.1014i	−0.219450	+	0.818998i
$867$		0			0
$868$	−29.4374	+	17.2339i	−0.999171	+	0.584958i
$869$	−1.17651	−	4.39078i	−0.0399102	−	0.148947i
$870$		0			0
$871$	4.13134	+	6.28762i	0.139985	+	0.213048i
$872$	−6.04710	+	10.4739i	−0.204781	+	0.354690i
$873$		0			0
$874$	66.4845	+	38.3849i	2.24887	+	1.29839i
$875$	−1.77230	−	1.00899i	−0.0599146	−	0.0341102i
$876$		0			0
$877$	3.92993	−	1.05302i	0.132704	−	0.0355580i	−0.191855	−	0.981423i	$-0.561450\pi$
$877$	3.92993	−	1.05302i	0.132704	−	0.0355580i	0.324560	+	0.945865i	$0.394784\pi$
$878$	−31.0425	−	31.0425i	−1.04763	−	1.04763i
$879$		0			0
$880$	−0.224343	−	0.129525i	−0.00756260	−	0.00436627i
$881$	−6.14545	+	10.6442i	−0.207045	+	0.358613i	−0.950782	−	0.309859i	$-0.899718\pi$
$881$	−6.14545	+	10.6442i	−0.207045	+	0.358613i	0.743737	+	0.668472i	$0.233051\pi$
$882$		0			0
$883$		−	23.2623i		−	0.782840i	−0.920212	−	0.391420i	$-0.871984\pi$
$883$		−	23.2623i		−	0.782840i	0.920212	−	0.391420i	$-0.128016\pi$
$884$	4.73143	+	4.21447i	0.159135	+	0.141748i
$885$		0			0
$886$	17.2110	−	64.2324i	0.578216	−	2.15793i
$887$		−	20.1789i		−	0.677540i	−0.940869	−	0.338770i	$-0.889989\pi$
$887$		−	20.1789i		−	0.677540i	0.940869	−	0.338770i	$-0.110011\pi$
$888$		0			0
$889$	−35.3394	−	9.24042i	−1.18525	−	0.309914i
$890$	0.164294	−	0.613152i	0.00550714	−	0.0205529i
$891$		0			0
$892$	−27.7023	+	7.42280i	−0.927540	+	0.248534i
$893$	2.35964			0.0789625
$894$		0			0
$895$	−0.583148	+	0.156254i	−0.0194925	+	0.00522299i
$896$	10.7552	−	18.8915i	0.359305	−	0.631120i
$897$		0			0
$898$	−26.0599	−	45.1370i	−0.869629	−	1.50624i
$899$	−32.3478	−	8.66757i	−1.07886	−	0.289080i
$900$		0			0
$901$	−7.11845	+	12.3295i	−0.237150	+	0.410756i
$902$	0.815695	−	0.815695i	0.0271597	−	0.0271597i
$903$		0			0
$904$	11.8041	+	3.16291i	0.392600	+	0.105197i
$905$	0.576680	+	0.154521i	0.0191695	+	0.00513645i
$906$		0			0
$907$	−5.66215	+	3.26904i	−0.188008	+	0.108547i	−0.591050	−	0.806635i	$-0.701286\pi$
$907$	−5.66215	+	3.26904i	−0.188008	+	0.108547i	0.403041	+	0.915182i	$0.367953\pi$
$908$	−12.8297	−	12.8297i	−0.425769	−	0.425769i
$909$		0			0
$910$	1.35794	−	0.0867164i	0.0450152	−	0.00287462i
$911$	58.2713			1.93061			0.965307	−	0.261119i	$-0.0840913\pi$
$911$	58.2713			1.93061			0.965307	+	0.261119i	$0.0840913\pi$
$912$		0			0
$913$	−8.13815	+	4.69856i	−0.269333	+	0.155500i
$914$			0.231079i			0.00764341i
$915$		0			0
$916$	16.8778	+	4.52240i	0.557659	+	0.149424i
$917$	26.5638	−	26.8872i	0.877216	−	0.887893i
$918$		0			0
$919$	−4.33185	+	7.50298i	−0.142894	+	0.247501i	−0.928585	−	0.371119i	$-0.878974\pi$
$919$	−4.33185	+	7.50298i	−0.142894	+	0.247501i	0.785691	+	0.618619i	$0.212308\pi$
$920$	0.304713	+	0.527778i	0.0100461	+	0.0174003i
$921$		0			0
$922$	16.0972	+	27.8812i	0.530134	+	0.918218i
$923$	0.912840	+	1.38928i	0.0300465	+	0.0457287i
$924$		0			0
$925$	−22.2151	+	5.95253i	−0.730429	+	0.195718i
$926$	−2.79953			−0.0919982
$927$		0			0
$928$	−24.1471	+	6.47020i	−0.792668	+	0.212395i
$929$	−0.425370	−	1.58750i	−0.0139559	−	0.0520842i	0.958597	−	0.284767i	$-0.0919163\pi$
$929$	−0.425370	−	1.58750i	−0.0139559	−	0.0520842i	−0.972553	+	0.232683i	$0.925250\pi$
$930$		0			0
$931$	−28.2129	−	27.5384i	−0.924640	−	0.902534i
$932$	0.0296143	+	0.0512934i	0.000970048	+	0.00168017i
$933$		0			0
$934$	−14.0073	+	52.2760i	−0.458333	+	1.71052i
$935$	−0.0575496	−	0.0332263i	−0.00188207	−	0.00108661i
$936$		0			0
$937$		−	60.7537i		−	1.98474i	−0.123306	−	0.992369i	$-0.539350\pi$
$937$		−	60.7537i		−	1.98474i	0.123306	−	0.992369i	$-0.460650\pi$
$938$	−7.17577	+	7.26311i	−0.234297	+	0.237149i
$939$		0			0
$940$	−0.0397463	−	0.0229476i	−0.00129638	−	0.000748467i
$941$	−0.0361077	−	0.134756i	−0.00117708	−	0.00439291i	0.965335	−	0.261015i	$-0.0840572\pi$
$941$	−0.0361077	−	0.134756i	−0.00117708	−	0.00439291i	−0.966512	+	0.256622i	$0.917390\pi$
$942$		0			0
$943$	−6.37694	+	1.70870i	−0.207662	+	0.0556428i
$944$	−47.7694	−	47.7694i	−1.55476	−	1.55476i
$945$		0			0
$946$	2.76868	+	1.59850i	0.0900174	+	0.0519716i
$947$	14.6602	−	14.6602i	0.476393	−	0.476393i	−0.427583	−	0.903976i	$-0.640635\pi$
$947$	14.6602	−	14.6602i	0.476393	−	0.476393i	0.903976	+	0.427583i	$0.140635\pi$
$948$		0			0
$949$	−8.23680	+	16.3822i	−0.267378	+	0.531790i
$950$	−45.0495	+	26.0093i	−1.46160	+	0.843854i
$951$		0			0
$952$	1.73636	−	3.04993i	0.0562759	−	0.0988488i
$953$	−1.70711	+	0.985598i	−0.0552986	+	0.0319266i	−0.527394	−	0.849621i	$-0.676831\pi$
$953$	−1.70711	+	0.985598i	−0.0552986	+	0.0319266i	0.472096	+	0.881547i	$0.343498\pi$
$954$		0			0
$955$	0.738817	−	0.738817i	0.0239076	−	0.0239076i
$956$	2.06246	−	2.06246i	0.0667047	−	0.0667047i
$957$		0			0
$958$	5.47192	−	3.15922i	0.176790	−	0.102070i
$959$	5.53024	−	9.71389i	0.178581	−	0.313678i
$960$		0			0
$961$	−44.5136	+	25.7000i	−1.43592	+	0.829031i
$962$	20.4252	−	22.9306i	0.658535	−	0.739314i
$963$		0			0
$964$	2.77418	−	2.77418i	0.0893504	−	0.0893504i
$965$	1.03731	+	0.598893i	0.0333923	+	0.0192790i
$966$		0			0
$967$	20.9186	+	20.9186i	0.672696	+	0.672696i	0.958337	−	0.285641i	$-0.0922064\pi$
$967$	20.9186	+	20.9186i	0.672696	+	0.672696i	−0.285641	+	0.958337i	$0.592206\pi$
$968$	−10.8889	+	2.91767i	−0.349983	+	0.0937776i
$969$		0			0
$970$	−0.598287	−	2.23284i	−0.0192098	−	0.0716921i
$971$	−47.3596	−	27.3431i	−1.51984	−	0.877481i	−0.999727	−	0.0233852i	$-0.992556\pi$
$971$	−47.3596	−	27.3431i	−1.51984	−	0.877481i	−0.520115	−	0.854096i	$-0.674111\pi$
$972$		0			0
$973$	18.3064	−	18.5292i	0.586876	−	0.594019i
$974$		−	11.4429i		−	0.366654i
$975$		0			0
$976$	27.1639	+	15.6831i	0.869496	+	0.502004i
$977$	14.2793	−	53.2912i	0.456836	−	1.70494i	−0.225796	−	0.974175i	$-0.572498\pi$
$977$	14.2793	−	53.2912i	0.456836	−	1.70494i	0.682632	−	0.730762i	$-0.260835\pi$
$978$		0			0
$979$	1.54945	+	2.68372i	0.0495206	+	0.0857721i
$980$	0.207413	+	0.738233i	0.00662556	+	0.0235820i
$981$		0			0
$982$	18.3069	+	68.3221i	0.584195	+	2.18025i
$983$	18.5705	−	4.97596i	0.592308	−	0.158708i	0.0498003	−	0.998759i	$-0.484142\pi$
$983$	18.5705	−	4.97596i	0.592308	−	0.158708i	0.542508	+	0.840051i	$0.317475\pi$
$984$		0			0
$985$	−1.03423			−0.0329533
$986$	−8.15439	+	2.18496i	−0.259689	+	0.0695834i
$987$		0			0
$988$	12.9561	−	25.7685i	0.412188	−	0.819805i
$989$	−9.14824	−	15.8452i	−0.290897	−	0.503849i
$990$		0			0
$991$	−1.10267	−	1.90988i	−0.0350275	−	0.0606695i	0.847980	−	0.530028i	$-0.177819\pi$
$991$	−1.10267	−	1.90988i	−0.0350275	−	0.0606695i	−0.883008	+	0.469358i	$0.844485\pi$
$992$	−30.7551	+	53.2694i	−0.976476	+	1.69131i
$993$		0			0
$994$	−1.58552	+	1.60482i	−0.0502897	+	0.0509018i
$995$	−0.244824	−	0.0656003i	−0.00776143	−	0.00207967i
$996$		0			0
$997$		−	0.460171i		−	0.0145738i	−0.999973	−	0.00728688i	$-0.997680\pi$
$997$		−	0.460171i		−	0.0145738i	0.999973	−	0.00728688i	$-0.00231951\pi$
$998$	−6.63090	+	3.82835i	−0.209897	+	0.121184i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.514.8		36
3.2	odd	2		273.2.bt.a.241.2	yes	36
7.5	odd	6		819.2.gh.c.397.8		36
13.2	odd	12		819.2.gh.c.262.8		36
21.5	even	6		273.2.cg.a.124.2	yes	36
39.2	even	12		273.2.cg.a.262.2	yes	36
91.54	even	12	inner	819.2.et.c.145.8		36
273.236	odd	12		273.2.bt.a.145.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.2	✓	36	273.236	odd	12
273.2.bt.a.241.2	yes	36	3.2	odd	2
273.2.cg.a.124.2	yes	36	21.5	even	6
273.2.cg.a.262.2	yes	36	39.2	even	12
819.2.et.c.145.8		36	91.54	even	12	inner
819.2.et.c.514.8		36	1.1	even	1	trivial
819.2.gh.c.262.8		36	13.2	odd	12
819.2.gh.c.397.8		36	7.5	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30773 + 1.30773i) q^{2} +1.42031i q^{4} +(0.0744995 + 0.0199621i) q^{5} +(2.55141 - 0.700217i) q^{7} +(0.758075 - 0.758075i) q^{8} +O(q^{10})\)	\(q+(1.30773 + 1.30773i) q^{2} +1.42031i q^{4} +(0.0744995 + 0.0199621i) q^{5} +(2.55141 - 0.700217i) q^{7} +(0.758075 - 0.758075i) q^{8} +(0.0713202 + 0.123530i) q^{10} +(-0.672618 - 0.180227i) q^{11} +(2.39818 - 2.69235i) q^{13} +(4.25225 + 2.42086i) q^{14} +4.82334 q^{16} +1.23731 q^{17} +(-1.45771 - 5.44023i) q^{19} +(-0.0283524 + 0.105813i) q^{20} +(-0.643914 - 1.11529i) q^{22} +7.37027i q^{23} +(-4.32498 - 2.49703i) q^{25} +(6.65703 - 0.384694i) q^{26} +(0.994527 + 3.62380i) q^{28} +(-1.84462 + 3.19498i) q^{29} +(2.34941 + 8.76813i) q^{31} +(4.79147 + 4.79147i) q^{32} +(1.61806 + 1.61806i) q^{34} +(0.204057 - 0.00123434i) q^{35} +(3.25640 - 3.25640i) q^{37} +(5.20806 - 9.02063i) q^{38} +(0.0716090 - 0.0413434i) q^{40} +(0.231836 + 0.865225i) q^{41} +(-2.14988 + 1.24124i) q^{43} +(0.255979 - 0.955327i) q^{44} +(-9.63832 + 9.63832i) q^{46} +(-0.108435 + 0.404685i) q^{47} +(6.01939 - 3.57308i) q^{49} +(-2.39046 - 8.92133i) q^{50} +(3.82397 + 3.40616i) q^{52} +(-5.75319 + 9.96481i) q^{53} +(-0.0465120 - 0.0268537i) q^{55} +(1.40334 - 2.46498i) q^{56} +(-6.59044 + 1.76590i) q^{58} +(-9.90380 - 9.90380i) q^{59} +(5.63177 + 3.25150i) q^{61} +(-8.39395 + 14.5387i) q^{62} +2.88522i q^{64} +(0.232408 - 0.152706i) q^{65} +(-0.540059 + 2.01553i) q^{67} +1.75736i q^{68} +(0.268465 + 0.265237i) q^{70} +(-0.119329 + 0.445340i) q^{71} +(-4.91231 + 1.31625i) q^{73} +8.51697 q^{74} +(7.72682 - 2.07040i) q^{76} +(-1.84232 + 0.0111443i) q^{77} +(3.26395 + 5.65332i) q^{79} +(0.359336 + 0.0962839i) q^{80} +(-0.828301 + 1.43466i) q^{82} +(9.54235 - 9.54235i) q^{83} +(0.0921787 + 0.0246992i) q^{85} +(-4.43466 - 1.18826i) q^{86} +(-0.646521 + 0.373269i) q^{88} +(-3.14679 - 3.14679i) q^{89} +(4.23351 - 8.54853i) q^{91} -10.4681 q^{92} +(-0.671022 + 0.387414i) q^{94} -0.434393i q^{95} +(-15.6536 - 4.19437i) q^{97} +(12.5444 + 3.19911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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