LMFDB - Embedded newform 819.2.et.c.145.8

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			145.8
Character	$\chi$	$=$	819.145
Dual form			819.2.et.c.514.8

$q$-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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

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	−0.0726530	−	0.997357i	$-0.523147\pi$
$2$	1.30773	−	1.30773i	0.924704	−	0.924704i	0.997357	+	0.0726530i	$0.0231466\pi$
$3$		0			0
$3$		0			0
$4$		−	1.42031i		−	0.710156i
$5$	0.0744995	−	0.0199621i	0.0333172	−	0.00892732i	−0.242122	−	0.970246i	$-0.577843\pi$
$5$	0.0744995	−	0.0199621i	0.0333172	−	0.00892732i	0.275439	+	0.961319i	$0.411177\pi$
$6$		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	−0.358790	−	0.933418i	$-0.616811\pi$
$11$	−0.672618	+	0.180227i	−0.202802	+	0.0543406i	0.155988	+	0.987759i	$0.450144\pi$
$12$		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	0.570076	+	0.821592i	$0.306914\pi$
$19$	−1.45771	+	5.44023i	−0.334420	+	1.24807i	−0.904496	+	0.426482i	$0.859753\pi$
$20$	−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	$-0.721051\pi$
$23$		−	7.37027i		−	1.53681i	0.639965	−	0.768404i	$-0.278949\pi$
$24$		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	0.642365	−	0.766399i	$-0.277953\pi$
$29$	−1.84462	−	3.19498i	−0.342538	−	0.593293i	−0.984903	+	0.173105i	$0.944620\pi$
$30$		0			0
$31$	2.34941	−	8.76813i	0.421967	−	1.57480i	−0.348491	−	0.937312i	$-0.613306\pi$
$31$	2.34941	−	8.76813i	0.421967	−	1.57480i	0.770458	−	0.637491i	$-0.220028\pi$
$32$	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	0.922159	−	0.386811i	$-0.126423\pi$
$37$	3.25640	+	3.25640i	0.535348	+	0.535348i	−0.386811	+	0.922159i	$0.626423\pi$
$38$	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	−0.945457	−	0.325748i	$-0.894384\pi$
$41$	0.231836	−	0.865225i	0.0362067	−	0.135125i	0.981663	+	0.190622i	$0.0610506\pi$
$42$		0			0
$43$	−2.14988	−	1.24124i	−0.327854	−	0.189287i	0.327034	−	0.945013i	$-0.393951\pi$
$43$	−2.14988	−	1.24124i	−0.327854	−	0.189287i	−0.654888	+	0.755726i	$0.727284\pi$
$44$	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	0.957566	−	0.288213i	$-0.0930611\pi$
$47$	−0.108435	−	0.404685i	−0.0158169	−	0.0590293i	−0.973383	+	0.229184i	$0.926394\pi$
$48$		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	−0.925805	−	0.378001i	$-0.876612\pi$
$53$	−5.75319	−	9.96481i	−0.790261	−	1.36877i	0.135544	−	0.990771i	$-0.456722\pi$
$54$		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	−0.354193	+	0.935172i	$0.615244\pi$
$59$	−9.90380	+	9.90380i	−1.28937	+	1.28937i	−0.935172	+	0.354193i	$0.884756\pi$
$60$		0			0
$61$	5.63177	−	3.25150i	0.721074	−	0.416312i	−0.0940739	−	0.995565i	$-0.529989\pi$
$61$	5.63177	−	3.25150i	0.721074	−	0.416312i	0.815148	+	0.579253i	$0.196656\pi$
$62$	−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	0.925058	−	0.379826i	$-0.124016\pi$
$67$	−0.540059	−	2.01553i	−0.0659787	−	0.246236i	−0.991037	+	0.133590i	$0.957349\pi$
$68$		−	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	0.958483	−	0.285148i	$-0.0920428\pi$
$71$	−0.119329	−	0.445340i	−0.0141617	−	0.0528522i	−0.972645	+	0.232296i	$0.925376\pi$
$72$		0			0
$73$	−4.91231	−	1.31625i	−0.574942	−	0.154055i	−0.0403800	−	0.999184i	$-0.512857\pi$
$73$	−4.91231	−	1.31625i	−0.574942	−	0.154055i	−0.534562	+	0.845129i	$0.679524\pi$
$74$	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	−0.621908	−	0.783091i	$-0.713642\pi$
$79$	3.26395	−	5.65332i	0.367223	−	0.636048i	0.989130	+	0.147043i	$0.0469754\pi$
$80$	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	0.998819	+	0.0485904i	$0.0154729\pi$
$83$	9.54235	+	9.54235i	1.04741	+	1.04741i	0.0485904	+	0.998819i	$0.484527\pi$
$84$		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	−0.853936	−	0.520378i	$-0.825791\pi$
$89$	−3.14679	+	3.14679i	−0.333559	+	0.333559i	0.520378	+	0.853936i	$0.325791\pi$
$90$		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	−0.941815	−	0.336132i	$-0.890881\pi$
$97$	−15.6536	+	4.19437i	−1.58938	+	0.425874i	−0.647569	+	0.762007i	$0.724214\pi$
$98$	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	0.496134	+	0.868246i	$0.334752\pi$
$101$	−5.06369	+	8.77056i	−0.503856	+	0.872704i	−0.999990	+	0.00445781i	$0.998581\pi$
$102$		0			0
$103$	1.47339	−	2.55198i	0.145177	−	0.251454i	−0.784262	−	0.620430i	$-0.786958\pi$
$103$	1.47339	−	2.55198i	0.145177	−	0.251454i	0.929439	+	0.368976i	$0.120291\pi$
$104$	−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	−0.304061	−	0.952653i	$-0.598343\pi$
$109$	−10.8967	−	2.91975i	−1.04371	−	0.279662i	−0.739651	+	0.672991i	$0.765009\pi$
$110$	−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	−0.462946	−	0.886386i	$-0.653208\pi$
$113$	5.69946	−	9.87175i	0.536160	−	0.928656i	0.999106	−	0.0422699i	$-0.0134589\pi$
$114$		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	−0.925698	−	0.378263i	$-0.876522\pi$
$127$	−11.9564	+	6.90305i	−1.06096	+	0.612547i	−0.135264	+	0.990810i	$0.543188\pi$
$128$	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	0.931145	−	0.364648i	$-0.118811\pi$
$131$	12.3717	+	7.14282i	1.08092	+	0.624071i	0.149778	+	0.988720i	$0.452144\pi$
$132$		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	0.823111	−	0.567881i	$-0.192236\pi$
$137$	2.98739	+	2.98739i	0.255230	+	0.255230i	−0.567881	+	0.823111i	$0.692236\pi$
$138$		0			0
$139$	8.52594	+	4.92246i	0.723161	+	0.417517i	0.815915	−	0.578172i	$-0.196234\pi$
$139$	8.52594	+	4.92246i	0.723161	+	0.417517i	−0.0927539	+	0.995689i	$0.529567\pi$
$140$	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	0.117225	−	0.993105i	$-0.462600\pi$
$149$	−3.39107	−	0.908635i	−0.277807	−	0.0744383i	−0.395033	+	0.918667i	$0.629267\pi$
$150$		0			0
$151$	5.00350	−	18.6733i	0.407179	−	1.51961i	−0.392821	−	0.919615i	$-0.628501\pi$
$151$	5.00350	−	18.6733i	0.407179	−	1.51961i	0.800001	−	0.599999i	$-0.204832\pi$
$152$	−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	−0.409860	−	0.912148i	$-0.634423\pi$
$157$	2.19466	−	1.26709i	0.175153	−	0.101125i	0.585013	+	0.811024i	$0.301089\pi$
$158$	−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	−0.659611	−	0.751607i	$-0.729279\pi$
$163$	3.66969	−	13.6955i	0.287432	−	1.07271i	0.947044	−	0.321105i	$-0.104054\pi$
$164$	−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	0.377542	−	0.925993i	$-0.376770\pi$
$167$	3.12094	+	0.836254i	0.241506	+	0.0647113i	−0.136036	+	0.990704i	$0.543436\pi$
$168$		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	0.877904	−	0.478837i	$-0.158942\pi$
$173$	0.319180	+	0.552836i	0.0242668	+	0.0420314i	−0.853637	+	0.520868i	$0.825608\pi$
$174$		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	0.224791	−	0.974407i	$-0.427830\pi$
$179$	−6.77885	−	3.91377i	−0.506675	−	0.292529i	−0.731466	+	0.681878i	$0.761163\pi$
$180$		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	0.999935	−	0.0113800i	$-0.00362244\pi$
$191$	6.77349	+	11.7320i	0.490112	+	0.848899i	−0.509823	+	0.860279i	$0.670289\pi$
$192$		0			0
$193$	15.0008	−	4.01944i	1.07978	−	0.289326i	0.325273	−	0.945620i	$-0.394544\pi$
$193$	15.0008	−	4.01944i	1.07978	−	0.289326i	0.754505	+	0.656295i	$0.227877\pi$
$194$	−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	−0.234031	−	0.972229i	$-0.575192\pi$
$197$	−12.9524	−	3.47059i	−0.922822	−	0.247269i	−0.688791	+	0.724960i	$0.741858\pi$
$198$		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	0.562660	−	0.826689i	$-0.309778\pi$
$211$	−6.31298	−	10.9344i	−0.434604	−	0.752756i	−0.997263	+	0.0739331i	$0.976445\pi$
$212$	−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	−0.536726	−	0.843756i	$-0.680339\pi$
$223$	5.22617	−	19.5043i	0.349971	−	1.30611i	0.886697	−	0.462351i	$-0.152994\pi$
$224$	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	0.340648	−	0.940191i	$-0.389354\pi$
$227$	−9.03303	−	9.03303i	−0.599543	−	0.599543i	−0.940191	+	0.340648i	$0.889354\pi$
$228$		0			0
$229$	3.18409	+	11.8832i	0.210410	+	0.785262i	0.987732	+	0.156159i	$0.0499112\pi$
$229$	3.18409	+	11.8832i	0.210410	+	0.785262i	−0.777322	+	0.629104i	$0.783422\pi$
$230$	−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	0.501182	−	0.865342i	$-0.332899\pi$
$233$	0.0361142	+	0.0208505i	0.00236592	+	0.00136596i	−0.498817	+	0.866708i	$0.666232\pi$
$234$		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	−0.752510	−	0.658581i	$-0.771157\pi$
$239$	−1.45212	+	1.45212i	−0.0939296	+	0.0939296i	0.658581	+	0.752510i	$0.271157\pi$
$240$		0			0
$241$	−1.95322	+	1.95322i	−0.125818	+	0.125818i	−0.767212	−	0.641394i	$-0.778356\pi$
$241$	−1.95322	+	1.95322i	−0.125818	+	0.125818i	0.641394	+	0.767212i	$0.278356\pi$
$242$	−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	0.193353	+	0.981129i	$0.438064\pi$
$251$	−11.9299	+	20.6631i	−0.753006	+	1.30424i	−0.946359	+	0.323116i	$0.895270\pi$
$252$		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	−0.522850	−	0.852425i	$-0.675131\pi$
$263$	7.73235	−	13.3928i	0.476797	−	0.825836i	0.999646	+	0.0265886i	$0.00846440\pi$
$264$		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	$-0.996595\pi$
$269$		−	0.350892i		−	0.0213943i	0.999943	−	0.0106971i	$-0.00340507\pi$
$270$		0			0
$271$	7.06051	−	7.06051i	0.428895	−	0.428895i	−0.459357	−	0.888252i	$-0.651920\pi$
$271$	7.06051	−	7.06051i	0.428895	−	0.428895i	0.888252	+	0.459357i	$0.151920\pi$
$272$	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	$-0.905926\pi$
$277$		−	9.69499i		−	0.582516i	0.956645	−	0.291258i	$-0.0940738\pi$
$278$	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	0.917161	+	0.398518i	$0.130475\pi$
$281$	22.0548	+	22.0548i	1.31568	+	1.31568i	0.398518	+	0.917161i	$0.369525\pi$
$282$		0			0
$283$	2.07530	−	3.59453i	0.123364	−	0.213673i	−0.797728	−	0.603017i	$-0.793965\pi$
$283$	2.07530	−	3.59453i	0.123364	−	0.213673i	0.921092	+	0.389344i	$0.127298\pi$
$284$	−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	−0.975361	−	0.220617i	$-0.929193\pi$
$293$	−4.12495	−	15.3945i	−0.240982	−	0.899357i	0.734379	−	0.678740i	$-0.237474\pi$
$294$		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	−0.519221	−	0.854640i	$-0.673778\pi$
$307$	5.87701	−	5.87701i	0.335419	−	0.335419i	0.854640	+	0.519221i	$0.173778\pi$
$308$	−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	−0.957166	−	0.289539i	$-0.906498\pi$
$311$	−12.8619	−	22.2775i	−0.729331	−	1.26324i	0.227835	−	0.973700i	$-0.426835\pi$
$312$		0			0
$313$	−19.5449	−	11.2842i	−1.10474	−	0.637823i	−0.167280	−	0.985909i	$-0.553498\pi$
$313$	−19.5449	−	11.2842i	−1.10474	−	0.637823i	−0.937463	+	0.348086i	$0.886832\pi$
$314$	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	0.998826	+	0.0484339i	$0.0154230\pi$
$317$	2.81372	+	10.5010i	0.158034	+	0.589792i	−0.840792	+	0.541358i	$0.817910\pi$
$318$		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	0.782708	−	0.622389i	$-0.213838\pi$
$331$	20.9107	+	5.60302i	1.14936	+	0.307970i	0.366650	+	0.930359i	$0.380505\pi$
$332$	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	$0.140636\pi$
$337$			15.6989i			0.855172i	−0.903975	+	0.427586i	$0.859364\pi$
$338$	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	−0.395775	−	0.918348i	$-0.629524\pi$
$349$	−22.3749	−	5.99533i	−1.19770	−	0.320923i	−0.801925	+	0.597425i	$0.796191\pi$
$350$	−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	−0.572543	−	0.819875i	$-0.694043\pi$
$353$	−12.3710	+	3.31480i	−0.658442	+	0.176429i	−0.0858994	+	0.996304i	$0.527376\pi$
$354$		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	0.504163	−	0.863608i	$-0.331801\pi$
$359$	26.0068	−	6.96850i	1.37259	−	0.367783i	0.868423	+	0.495825i	$0.165134\pi$
$360$		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	−0.181062	−	0.983472i	$-0.557953\pi$
$367$	−21.5194	−	12.4242i	−1.12330	−	0.648540i	−0.942242	+	0.334932i	$0.891287\pi$
$368$		−	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	0.864918	+	0.501914i	$0.167371\pi$
$373$	16.7470	+	29.0067i	0.867129	+	1.50191i	0.00221133	+	0.999998i	$0.499296\pi$
$374$	−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	0.325946	−	0.945389i	$-0.394317\pi$
$379$	2.63846	+	0.706973i	0.135529	+	0.0363148i	−0.190417	+	0.981703i	$0.560984\pi$
$380$	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	0.681824	+	0.731516i	$0.261187\pi$
$383$	−5.37033	+	20.0424i	−0.274411	+	1.02412i	−0.956235	+	0.292600i	$0.905480\pi$
$384$		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	−0.999870	−	0.0161427i	$-0.994861\pi$
$389$	−29.3050	+	16.9193i	−1.48582	+	0.857841i	−0.485955	+	0.873984i	$0.661528\pi$
$390$		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	0.156356	−	0.987701i	$-0.450025\pi$
$397$	−4.02654	−	1.07891i	−0.202086	−	0.0541488i	−0.358442	+	0.933552i	$0.616692\pi$
$398$	−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	−0.891584	−	0.452856i	$-0.850405\pi$
$401$	−26.9224	−	26.9224i	−1.34444	−	1.34444i	−0.452856	−	0.891584i	$-0.649595\pi$
$402$		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	0.957298	−	0.289104i	$-0.0933573\pi$
$409$	13.5134	+	13.5134i	0.668194	+	0.668194i	−0.289104	+	0.957298i	$0.593357\pi$
$410$	−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	0.431043	−	0.902331i	$-0.358146\pi$
$419$	29.2306	−	16.8763i	1.42801	−	0.824460i	0.996963	+	0.0778716i	$0.0248124\pi$
$420$		0			0
$421$	20.2556	−	20.2556i	0.987197	−	0.987197i	−0.0127222	−	0.999919i	$-0.504050\pi$
$421$	20.2556	−	20.2556i	0.987197	−	0.987197i	0.999919	+	0.0127222i	$0.00404970\pi$
$422$	−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	−0.985041	−	0.172323i	$-0.944873\pi$
$431$	−4.52853	−	16.9007i	−0.218132	−	0.814079i	0.766909	−	0.641756i	$-0.221794\pi$
$432$		0			0
$433$	6.74582	−	11.6841i	0.324184	−	0.561502i	−0.657163	−	0.753748i	$-0.728244\pi$
$433$	6.74582	−	11.6841i	0.324184	−	0.561502i	0.981347	+	0.192246i	$0.0615771\pi$
$434$	−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	0.0232374	+	0.999730i	$0.492603\pi$
$443$	−17.9783	+	31.1393i	−0.854173	+	1.47947i	−0.877410	+	0.479741i	$0.840731\pi$
$444$		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	−0.835632	−	0.549290i	$-0.814898\pi$
$449$	−27.2216	+	7.29399i	−1.28466	+	0.344225i	−0.449033	+	0.893515i	$0.648231\pi$
$450$		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	−0.705037	−	0.709170i	$-0.749070\pi$
$457$	0.0883512	−	0.0883512i	0.00413290	−	0.00413290i	0.709170	+	0.705037i	$0.249070\pi$
$458$	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	0.154973	−	0.987919i	$-0.450471\pi$
$461$	16.8148	−	4.50551i	0.783143	−	0.209843i	0.628170	+	0.778076i	$0.283804\pi$
$462$		0			0
$463$	−1.07038	−	1.07038i	−0.0497447	−	0.0497447i	0.681797	−	0.731542i	$-0.261199\pi$
$463$	−1.07038	−	1.07038i	−0.0497447	−	0.0497447i	−0.731542	+	0.681797i	$0.761199\pi$
$464$	−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	−0.298782	−	0.954321i	$-0.596580\pi$
$467$	14.6317	−	25.3429i	0.677075	−	1.17273i	0.975858	−	0.218408i	$-0.0700862\pi$
$468$		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	0.983180	−	0.182638i	$-0.0584636\pi$
$479$	0.884245	+	3.30005i	0.0404022	+	0.150783i	−0.942778	+	0.333421i	$0.891797\pi$
$480$		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	−0.799251	−	0.600997i	$-0.794770\pi$
$487$	−4.37510	+	4.37510i	−0.198255	+	0.198255i	0.600997	+	0.799251i	$0.294770\pi$
$488$	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	0.494788	−	0.869014i	$-0.335246\pi$
$491$	33.1219	−	19.1229i	1.49477	−	0.863006i	0.999982	+	0.00600745i	$0.00191224\pi$
$492$		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	0.937785	−	0.347216i	$-0.112873\pi$
$499$	−1.07153	−	3.99901i	−0.0479684	−	0.179020i	−0.985754	+	0.168195i	$0.946206\pi$
$500$	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	0.888311	−	0.459241i	$-0.151879\pi$
$503$	20.9643	+	12.1038i	0.934752	+	0.539680i	0.0464410	+	0.998921i	$0.485212\pi$
$504$		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	0.970515	−	0.241039i	$-0.0774883\pi$
$509$	16.4577	+	16.4577i	0.729476	+	0.729476i	−0.241039	+	0.970515i	$0.577488\pi$
$510$		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	−0.978265	−	0.207360i	$-0.933513\pi$
$521$	−29.3950	+	16.9712i	−1.28782	+	0.743522i	−0.309553	+	0.950882i	$0.600179\pi$
$522$		0			0
$523$			7.59842i			0.332256i	0.986104	+	0.166128i	$0.0531264\pi$
$523$			7.59842i			0.332256i	−0.986104	+	0.166128i	$0.946874\pi$
$524$	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	−0.709420	−	0.704786i	$-0.751043\pi$
$541$	−22.5943	+	6.05411i	−0.971403	+	0.260287i	−0.261983	+	0.965073i	$0.584376\pi$
$542$		−	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	−0.00914829	−	0.999958i	$-0.502912\pi$
$557$	11.3970	−	3.05383i	0.482908	−	0.129395i	0.492056	+	0.870563i	$0.336245\pi$
$558$		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	$-0.908485\pi$
$569$		−	13.5278i		−	0.567116i	0.958955	−	0.283558i	$-0.0915149\pi$
$570$		0			0
$571$	−12.8299	+	7.40732i	−0.536913	+	0.309987i	−0.743827	−	0.668372i	$-0.766991\pi$
$571$	−12.8299	+	7.40732i	−0.536913	+	0.309987i	0.206914	+	0.978359i	$0.433658\pi$
$572$	−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	0.765198	+	0.643795i	$0.222641\pi$
$577$	−5.26970	+	19.6668i	−0.219381	+	0.818740i	−0.984578	+	0.174944i	$0.944025\pi$
$578$	−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	−0.608327	−	0.793686i	$-0.708159\pi$
$587$	7.64015	−	28.5134i	0.315343	−	1.17688i	0.923670	−	0.383189i	$-0.125174\pi$
$588$		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	0.845036	+	0.534710i	$0.179579\pi$
$593$	9.26744	+	34.5866i	0.380568	+	1.42030i	−0.464467	+	0.885590i	$0.653754\pi$
$594$		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	0.795427	−	0.606049i	$-0.207247\pi$
$599$	−3.11170	−	5.38963i	−0.127141	−	0.220214i	−0.922568	+	0.385835i	$0.873913\pi$
$600$		0			0
$601$	0.0256568	−	0.0148129i	0.00104656	−	0.000604232i	−0.499477	−	0.866327i	$-0.666474\pi$
$601$	0.0256568	−	0.0148129i	0.00104656	−	0.000604232i	0.500523	+	0.865723i	$0.333141\pi$
$602$	−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	0.0374913	−	0.999297i	$-0.488063\pi$
$607$	22.7071	−	13.1100i	0.921653	−	0.532117i	0.884162	+	0.467180i	$0.154730\pi$
$608$	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	0.949888	+	0.312591i	$0.101197\pi$
$613$	7.02053	+	26.2010i	0.283556	+	1.05825i	−0.666331	+	0.745656i	$0.732136\pi$
$614$		−	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	0.802488	+	0.596668i	$0.203509\pi$
$617$	10.0810	+	37.6229i	0.405847	+	1.51464i	−0.396641	+	0.917974i	$0.629824\pi$
$618$		0			0
$619$	28.5176	+	7.64126i	1.14622	+	0.307128i	0.781448	−	0.623970i	$-0.214481\pi$
$619$	28.5176	+	7.64126i	1.14622	+	0.307128i	0.364769	+	0.931098i	$0.381148\pi$
$620$	−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	0.556408	−	0.830909i	$-0.312179\pi$
$631$	36.5172	−	9.78475i	1.45373	−	0.389525i	0.897318	+	0.441384i	$0.145512\pi$
$632$	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	$-0.973900\pi$
$641$		−	4.14733i		−	0.163810i	0.996640	−	0.0819049i	$-0.0261004\pi$
$642$		0			0
$643$	39.3048	−	10.5317i	1.55003	−	0.415330i	0.620541	−	0.784174i	$-0.286913\pi$
$643$	39.3048	−	10.5317i	1.55003	−	0.415330i	0.929491	+	0.368845i	$0.120247\pi$
$644$	−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	0.266172	+	0.963926i	$0.414241\pi$
$647$	−17.8485	+	30.9146i	−0.701698	+	1.21538i	−0.967870	+	0.251451i	$0.919092\pi$
$648$		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	−0.845419	−	0.534104i	$-0.820649\pi$
$659$	1.02268	−	1.77133i	0.0398378	−	0.0690011i	0.885257	+	0.465103i	$0.153983\pi$
$660$		0			0
$661$	−5.33936	−	19.9268i	−0.207677	−	0.775061i	−0.988617	−	0.150455i	$-0.951926\pi$
$661$	−5.33936	−	19.9268i	−0.207677	−	0.775061i	0.780940	−	0.624606i	$-0.214740\pi$
$662$	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	−0.118199	−	0.992990i	$-0.537712\pi$
$673$	17.7096	−	10.2246i	0.682655	−	0.394131i	0.800855	+	0.598859i	$0.204379\pi$
$674$	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	0.999226	−	0.0393333i	$-0.0125234\pi$
$677$	38.1123	+	22.0042i	1.46478	+	0.845689i	0.465549	+	0.885022i	$0.345857\pi$
$678$		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	0.769687	−	0.638422i	$-0.220412\pi$
$683$	3.43053	+	3.43053i	0.131265	+	0.131265i	−0.638422	+	0.769687i	$0.720412\pi$
$684$		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	0.956872	+	0.290511i	$0.0938254\pi$
$691$	32.7898	+	32.7898i	1.24738	+	1.24738i	0.290511	+	0.956872i	$0.406175\pi$
$692$	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	$0.102715\pi$
$701$			16.7923i			0.634236i	−0.948386	+	0.317118i	$0.897285\pi$
$702$		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	−0.991252	−	0.131983i	$-0.957866\pi$
$709$	−1.77899	+	6.63927i	−0.0668113	+	0.249343i	0.924441	+	0.381326i	$0.124532\pi$
$710$	−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	−0.968437	−	0.249258i	$-0.919813\pi$
$719$	−18.7721	−	32.5143i	−0.700082	−	1.21258i	0.268355	−	0.963320i	$-0.413520\pi$
$720$		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	−0.567492	−	0.823379i	$-0.692086\pi$
$733$	−17.5240	+	4.69555i	−0.647265	+	0.173434i	−0.0797732	+	0.996813i	$0.525420\pi$
$734$	−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	−0.437177	−	0.899375i	$-0.644022\pi$
$739$	−9.95216	+	2.66667i	−0.366096	+	0.0980952i	0.0710811	+	0.997471i	$0.477355\pi$
$740$	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	0.872625	−	0.488390i	$-0.162416\pi$
$743$	37.7291	+	10.1095i	1.38415	+	0.370881i	0.511520	+	0.859271i	$0.329082\pi$
$744$		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	$0.198655\pi$
$751$			32.0282i			1.16872i	−0.811493	+	0.584362i	$0.801345\pi$
$752$	−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	0.916964	−	0.398969i	$-0.130632\pi$
$757$	3.10808	+	5.38335i	0.112965	+	0.195661i	−0.803999	+	0.594630i	$0.797299\pi$
$758$	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	−0.266479	−	0.963841i	$-0.585860\pi$
$761$	−27.0118	−	7.23779i	−0.979177	−	0.262370i	−0.712698	+	0.701471i	$0.752527\pi$
$762$		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	0.671539	+	0.740969i	$0.265634\pi$
$769$	−7.77893	+	29.0314i	−0.280515	+	1.04690i	−0.952054	+	0.305929i	$0.901033\pi$
$770$	−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	0.855202	−	0.518295i	$-0.173433\pi$
$773$	9.36696	+	9.36696i	0.336906	+	0.336906i	−0.518295	+	0.855202i	$0.673433\pi$
$774$		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	−0.982012	−	0.188820i	$-0.939534\pi$
$787$	−22.2518	+	22.2518i	−0.793192	+	0.793192i	0.188820	+	0.982012i	$0.439534\pi$
$788$	−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	−0.698808	−	0.715309i	$-0.746286\pi$
$797$	7.62445	−	13.2059i	0.270072	−	0.467778i	0.968880	+	0.247531i	$0.0796192\pi$
$798$		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	0.0832926	+	0.996525i	$0.473456\pi$
$809$	−23.3622	+	40.4644i	−0.821370	+	1.42265i	−0.904662	+	0.426129i	$0.859877\pi$
$810$		0			0
$811$	15.5284	+	15.5284i	0.545275	+	0.545275i	0.925070	−	0.379796i	$-0.124006\pi$
$811$	15.5284	+	15.5284i	0.545275	+	0.545275i	−0.379796	+	0.925070i	$0.624006\pi$
$812$	−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	−0.243302	−	0.969951i	$-0.578231\pi$
$821$	20.8207	−	20.8207i	0.726648	−	0.726648i	0.969951	+	0.243302i	$0.0782307\pi$
$822$		0			0
$823$		−	4.41442i		−	0.153877i	−0.997036	−	0.0769385i	$-0.975486\pi$
$823$		−	4.41442i		−	0.153877i	0.997036	−	0.0769385i	$-0.0245145\pi$
$824$	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	0.359568	−	0.933119i	$-0.382924\pi$
$827$	−16.4939	−	16.4939i	−0.573550	−	0.573550i	−0.933119	+	0.359568i	$0.882924\pi$
$828$		0			0
$829$	−20.8871	+	36.1775i	−0.725439	+	1.25650i	0.233354	+	0.972392i	$0.425030\pi$
$829$	−20.8871	+	36.1775i	−0.725439	+	1.25650i	−0.958793	+	0.284105i	$0.908303\pi$
$830$	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	−0.974262	−	0.225418i	$-0.927625\pi$
$839$	−7.04543	−	26.2939i	−0.243235	−	0.907766i	0.731027	−	0.682349i	$-0.239041\pi$
$840$		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	−0.0907640	−	0.995872i	$-0.528931\pi$
$853$	26.4347	−	26.4347i	0.905108	−	0.905108i	0.995872	+	0.0907640i	$0.0289309\pi$
$854$	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	0.812554	−	0.582887i	$-0.198077\pi$
$857$	−2.88406	−	4.99534i	−0.0985177	−	0.170638i	−0.911071	+	0.412249i	$0.864743\pi$
$858$		0			0
$859$	−30.2787	−	17.4814i	−1.03310	−	0.596459i	−0.115227	−	0.993339i	$-0.536760\pi$
$859$	−30.2787	−	17.4814i	−1.03310	−	0.596459i	−0.917870	+	0.396880i	$0.870093\pi$
$860$	−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	0.902194	+	0.431330i	$0.141956\pi$
$863$	9.88638	+	36.8965i	0.336536	+	1.25597i	−0.565658	+	0.824640i	$0.691378\pi$
$864$		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	0.324560	−	0.945865i	$-0.394784\pi$
$877$	3.92993	+	1.05302i	0.132704	+	0.0355580i	−0.191855	+	0.981423i	$0.561450\pi$
$878$	−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	0.743737	−	0.668472i	$-0.233051\pi$
$881$	−6.14545	−	10.6442i	−0.207045	−	0.358613i	−0.950782	+	0.309859i	$0.899718\pi$
$882$		0			0
$883$			23.2623i			0.782840i	0.920212	+	0.391420i	$0.128016\pi$
$883$			23.2623i			0.782840i	−0.920212	+	0.391420i	$0.871984\pi$
$884$	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	$0.110011\pi$
$887$			20.1789i			0.677540i	−0.940869	+	0.338770i	$0.889989\pi$
$888$		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	0.403041	−	0.915182i	$-0.367953\pi$
$907$	−5.66215	−	3.26904i	−0.188008	−	0.108547i	−0.591050	+	0.806635i	$0.701286\pi$
$908$	−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	0.785691	−	0.618619i	$-0.212308\pi$
$919$	−4.33185	−	7.50298i	−0.142894	−	0.247501i	−0.928585	+	0.371119i	$0.878974\pi$
$920$	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	−0.972553	−	0.232683i	$-0.925250\pi$
$929$	−0.425370	+	1.58750i	−0.0139559	+	0.0520842i	0.958597	+	0.284767i	$0.0919163\pi$
$930$		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	$0.460650\pi$
$937$			60.7537i			1.98474i	−0.123306	+	0.992369i	$0.539350\pi$
$938$	−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	−0.966512	−	0.256622i	$-0.917390\pi$
$941$	−0.0361077	+	0.134756i	−0.00117708	+	0.00439291i	0.965335	+	0.261015i	$0.0840572\pi$
$942$		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	0.903976	−	0.427583i	$-0.140635\pi$
$947$	14.6602	+	14.6602i	0.476393	+	0.476393i	−0.427583	+	0.903976i	$0.640635\pi$
$948$		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	0.472096	−	0.881547i	$-0.343498\pi$
$953$	−1.70711	−	0.985598i	−0.0552986	−	0.0319266i	−0.527394	+	0.849621i	$0.676831\pi$
$954$		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	−0.285641	−	0.958337i	$-0.592206\pi$
$967$	20.9186	−	20.9186i	0.672696	−	0.672696i	0.958337	+	0.285641i	$0.0922064\pi$
$968$	−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	−0.520115	+	0.854096i	$0.674111\pi$
$971$	−47.3596	+	27.3431i	−1.51984	+	0.877481i	−0.999727	+	0.0233852i	$0.992556\pi$
$972$		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	0.682632	+	0.730762i	$0.260835\pi$
$977$	14.2793	+	53.2912i	0.456836	+	1.70494i	−0.225796	+	0.974175i	$0.572498\pi$
$978$		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	0.542508	−	0.840051i	$-0.317475\pi$
$983$	18.5705	+	4.97596i	0.592308	+	0.158708i	0.0498003	+	0.998759i	$0.484142\pi$
$984$		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	−0.883008	−	0.469358i	$-0.844485\pi$
$991$	−1.10267	+	1.90988i	−0.0350275	+	0.0606695i	0.847980	+	0.530028i	$0.177819\pi$
$992$	−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	$0.00231951\pi$
$997$			0.460171i			0.0145738i	−0.999973	+	0.00728688i	$0.997680\pi$
$998$	−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.145.8		36
3.2	odd	2		273.2.bt.a.145.2	✓	36
7.3	odd	6		819.2.gh.c.262.8		36
13.7	odd	12		819.2.gh.c.397.8		36
21.17	even	6		273.2.cg.a.262.2	yes	36
39.20	even	12		273.2.cg.a.124.2	yes	36
91.59	even	12	inner	819.2.et.c.514.8		36
273.59	odd	12		273.2.bt.a.241.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.145.2	✓	36	3.2	odd	2
273.2.bt.a.241.2	yes	36	273.59	odd	12
273.2.cg.a.124.2	yes	36	39.20	even	12
273.2.cg.a.262.2	yes	36	21.17	even	6
819.2.et.c.145.8		36	1.1	even	1	trivial
819.2.et.c.514.8		36	91.59	even	12	inner
819.2.gh.c.262.8		36	7.3	odd	6
819.2.gh.c.397.8		36	13.7	odd	12

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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