LMFDB - Embedded newform 324.3.j.a.199.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, not 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.11
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23803 + 1.57076i) q^{2} +(-0.934566 - 3.88929i) q^{4} +(-1.82883 + 0.665640i) q^{5} +(0.628756 - 0.110867i) q^{7} +(7.26616 + 3.34708i) q^{8} +O(q^{10})$	\(q+(-1.23803 + 1.57076i) q^{2} +(-0.934566 - 3.88929i) q^{4} +(-1.82883 + 0.665640i) q^{5} +(0.628756 - 0.110867i) q^{7} +(7.26616 + 3.34708i) q^{8} +(1.21859 - 3.69674i) q^{10} +(-1.29839 + 3.56730i) q^{11} +(1.00493 + 0.843235i) q^{13} +(-0.604274 + 1.12488i) q^{14} +(-14.2532 + 7.26960i) q^{16} +(-6.93411 + 12.0102i) q^{17} +(11.8519 - 6.84271i) q^{19} +(4.29803 + 6.49077i) q^{20} +(-3.99592 - 6.45588i) q^{22} +(-37.6484 - 6.63843i) q^{23} +(-16.2496 + 13.6350i) q^{25} +(-2.56865 + 0.534550i) q^{26} +(-1.01881 - 2.34180i) q^{28} +(-33.6135 + 28.2051i) q^{29} +(-6.16725 - 1.08745i) q^{31} +(6.22706 - 31.3883i) q^{32} +(-10.2805 - 25.7608i) q^{34} +(-1.07609 + 0.621282i) q^{35} +(-16.9987 + 29.4426i) q^{37} +(-3.92478 + 27.0880i) q^{38} +(-15.5165 - 1.28460i) q^{40} +(-17.2815 - 14.5009i) q^{41} +(10.4038 - 28.5842i) q^{43} +(15.0877 + 1.71594i) q^{44} +(57.0372 - 50.9180i) q^{46} +(52.0711 - 9.18154i) q^{47} +(-45.6619 + 16.6196i) q^{49} +(-1.29986 - 42.4047i) q^{50} +(2.34041 - 4.69652i) q^{52} -69.0395 q^{53} -7.38825i q^{55} +(4.93972 + 1.29892i) q^{56} +(-2.68887 - 87.7175i) q^{58} +(-30.6528 - 84.2178i) q^{59} +(0.993107 + 5.63219i) q^{61} +(9.34337 - 8.34097i) q^{62} +(41.5941 + 48.6408i) q^{64} +(-2.39914 - 0.873214i) q^{65} +(-78.8696 + 93.9932i) q^{67} +(53.1917 + 15.7444i) q^{68} +(0.356349 - 2.45944i) q^{70} +(88.3661 + 51.0182i) q^{71} +(33.2465 + 57.5847i) q^{73} +(-25.2024 - 63.1517i) q^{74} +(-37.6897 - 39.7006i) q^{76} +(-0.420876 + 2.38691i) q^{77} +(-66.1314 - 78.8123i) q^{79} +(21.2277 - 22.7824i) q^{80} +(44.1725 - 9.19255i) q^{82} +(3.87639 + 4.61971i) q^{83} +(4.68683 - 26.5803i) q^{85} +(32.0186 + 51.7299i) q^{86} +(-21.3743 + 21.5747i) q^{88} +(36.5192 + 63.2530i) q^{89} +(0.725341 + 0.418776i) q^{91} +(9.36614 + 152.630i) q^{92} +(-50.0436 + 93.1582i) q^{94} +(-17.1204 + 20.4033i) q^{95} +(123.655 + 45.0069i) q^{97} +(30.4254 - 92.2993i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.23803	+	1.57076i	−0.619015	+	0.785379i
$2$	−1.23803	+	1.57076i	−0.619015	+	0.785379i
$3$		0			0
$3$		0			0
$4$	−0.934566	−	3.88929i	−0.233642	−	0.972323i
$5$	−1.82883	+	0.665640i	−0.365766	+	0.133128i	−0.518363	−	0.855160i	$-0.673459\pi$
$5$	−1.82883	+	0.665640i	−0.365766	+	0.133128i	0.152597	+	0.988288i	$0.451236\pi$
$6$		0			0
$7$	0.628756	−	0.110867i	0.0898223	−	0.0158381i	−0.128556	−	0.991702i	$-0.541034\pi$
$7$	0.628756	−	0.110867i	0.0898223	−	0.0158381i	0.218379	+	0.975864i	$0.429923\pi$
$8$	7.26616	+	3.34708i	0.908270	+	0.418385i
$9$		0			0
$10$	1.21859	−	3.69674i	0.121859	−	0.369674i
$11$	−1.29839	+	3.56730i	−0.118035	+	0.324300i	−0.984615	−	0.174740i	$-0.944092\pi$
$11$	−1.29839	+	3.56730i	−0.118035	+	0.324300i	0.866579	+	0.499040i	$0.166314\pi$
$12$		0			0
$13$	1.00493	+	0.843235i	0.0773022	+	0.0648642i	0.680620	−	0.732637i	$-0.261711\pi$
$13$	1.00493	+	0.843235i	0.0773022	+	0.0648642i	−0.603318	+	0.797501i	$0.706155\pi$
$14$	−0.604274	+	1.12488i	−0.0431624	+	0.0803486i
$15$		0			0
$16$	−14.2532	+	7.26960i	−0.890823	+	0.454350i
$17$	−6.93411	+	12.0102i	−0.407889	+	0.706484i	−0.994653	−	0.103274i	$-0.967068\pi$
$17$	−6.93411	+	12.0102i	−0.407889	+	0.706484i	0.586764	+	0.809758i	$0.300402\pi$
$18$		0			0
$19$	11.8519	−	6.84271i	0.623785	−	0.360143i	−0.154556	−	0.987984i	$-0.549395\pi$
$19$	11.8519	−	6.84271i	0.623785	−	0.360143i	0.778341	+	0.627841i	$0.216061\pi$
$20$	4.29803	+	6.49077i	0.214902	+	0.324539i
$21$		0			0
$22$	−3.99592	−	6.45588i	−0.181633	−	0.293449i
$23$	−37.6484	−	6.63843i	−1.63689	−	0.288627i	−0.721865	−	0.692034i	$-0.756715\pi$
$23$	−37.6484	−	6.63843i	−1.63689	−	0.288627i	−0.915021	+	0.403406i	$0.867826\pi$
$24$		0			0
$25$	−16.2496	+	13.6350i	−0.649983	+	0.545400i
$26$	−2.56865	+	0.534550i	−0.0987942	+	0.0205596i
$27$		0			0
$28$	−1.01881	−	2.34180i	−0.0363859	−	0.0836358i
$29$	−33.6135	+	28.2051i	−1.15909	+	0.972590i	−0.999893	−	0.0146571i	$-0.995334\pi$
$29$	−33.6135	+	28.2051i	−1.15909	+	0.972590i	−0.159195	+	0.987247i	$0.550890\pi$
$30$		0			0
$31$	−6.16725	−	1.08745i	−0.198944	−	0.0350791i	0.0732883	−	0.997311i	$-0.476651\pi$
$31$	−6.16725	−	1.08745i	−0.198944	−	0.0350791i	−0.272232	+	0.962232i	$0.587762\pi$
$32$	6.22706	−	31.3883i	0.194596	−	0.980884i
$33$		0			0
$34$	−10.2805	−	25.7608i	−0.302369	−	0.757672i
$35$	−1.07609	+	0.621282i	−0.0307455	+	0.0177509i
$36$		0			0
$37$	−16.9987	+	29.4426i	−0.459424	+	0.795746i	−0.998931	−	0.0462353i	$-0.985278\pi$
$37$	−16.9987	+	29.4426i	−0.459424	+	0.795746i	0.539506	+	0.841982i	$0.318611\pi$
$38$	−3.92478	+	27.0880i	−0.103284	+	0.712842i
$39$		0			0
$40$	−15.5165	−	1.28460i	−0.387913	−	0.0321149i
$41$	−17.2815	−	14.5009i	−0.421501	−	0.353681i	0.407233	−	0.913324i	$-0.366494\pi$
$41$	−17.2815	−	14.5009i	−0.421501	−	0.353681i	−0.828734	+	0.559643i	$0.810938\pi$
$42$		0			0
$43$	10.4038	−	28.5842i	0.241948	−	0.664748i	−0.757974	−	0.652285i	$-0.773811\pi$
$43$	10.4038	−	28.5842i	0.241948	−	0.664748i	0.999922	−	0.0124630i	$-0.00396720\pi$
$44$	15.0877	+	1.71594i	0.342902	+	0.0389987i
$45$		0			0
$46$	57.0372	−	50.9180i	1.23994	−	1.10691i
$47$	52.0711	−	9.18154i	1.10790	−	0.195352i	0.410376	−	0.911917i	$-0.365398\pi$
$47$	52.0711	−	9.18154i	1.10790	−	0.195352i	0.697521	+	0.716565i	$0.254286\pi$
$48$		0			0
$49$	−45.6619	+	16.6196i	−0.931875	+	0.339175i
$50$	−1.29986	−	42.4047i	−0.0259972	−	0.848094i
$51$		0			0
$52$	2.34041	−	4.69652i	0.0450080	−	0.0903176i
$53$	−69.0395			−1.30263			−0.651316	−	0.758807i	$-0.725783\pi$
$53$	−69.0395			−1.30263			−0.651316	+	0.758807i	$0.725783\pi$
$54$		0			0
$55$		−	7.38825i		−	0.134332i
$56$	4.93972	+	1.29892i	0.0882093	+	0.0231950i
$57$		0			0
$58$	−2.68887	−	87.7175i	−0.0463598	−	1.51237i
$59$	−30.6528	−	84.2178i	−0.519538	−	1.42742i	−0.871030	−	0.491229i	$-0.836548\pi$
$59$	−30.6528	−	84.2178i	−0.519538	−	1.42742i	0.351492	−	0.936191i	$-0.385674\pi$
$60$		0			0
$61$	0.993107	+	5.63219i	0.0162804	+	0.0923309i	0.991865	−	0.127292i	$-0.0406285\pi$
$61$	0.993107	+	5.63219i	0.0162804	+	0.0923309i	−0.975585	+	0.219623i	$0.929517\pi$
$62$	9.34337	−	8.34097i	0.150699	−	0.134532i
$63$		0			0
$64$	41.5941	+	48.6408i	0.649908	+	0.760013i
$65$	−2.39914	−	0.873214i	−0.0369098	−	0.0134341i
$66$		0			0
$67$	−78.8696	+	93.9932i	−1.17716	+	1.40288i	−0.280677	+	0.959802i	$0.590559\pi$
$67$	−78.8696	+	93.9932i	−1.17716	+	1.40288i	−0.896482	+	0.443081i	$0.853885\pi$
$68$	53.1917	+	15.7444i	0.782231	+	0.231536i
$69$		0			0
$70$	0.356349	−	2.45944i	0.00509070	−	0.0351349i
$71$	88.3661	+	51.0182i	1.24459	+	0.718566i	0.970026	−	0.243002i	$-0.0781321\pi$
$71$	88.3661	+	51.0182i	1.24459	+	0.718566i	0.274567	+	0.961568i	$0.411465\pi$
$72$		0			0
$73$	33.2465	+	57.5847i	0.455432	+	0.788832i	0.998713	−	0.0507194i	$-0.0161514\pi$
$73$	33.2465	+	57.5847i	0.455432	+	0.788832i	−0.543281	+	0.839551i	$0.682818\pi$
$74$	−25.2024	−	63.1517i	−0.340572	−	0.853401i
$75$		0			0
$76$	−37.6897	−	39.7006i	−0.495917	−	0.522376i
$77$	−0.420876	+	2.38691i	−0.00546593	+	0.0309988i
$78$		0			0
$79$	−66.1314	−	78.8123i	−0.837106	−	0.997624i	−0.999940	−	0.0109706i	$-0.996508\pi$
$79$	−66.1314	−	78.8123i	−0.837106	−	0.997624i	0.162834	−	0.986654i	$-0.447937\pi$
$80$	21.2277	−	22.7824i	0.265346	−	0.284780i
$81$		0			0
$82$	44.1725	−	9.19255i	0.538689	−	0.112104i
$83$	3.87639	+	4.61971i	0.0467035	+	0.0556591i	0.788891	−	0.614534i	$-0.210656\pi$
$83$	3.87639	+	4.61971i	0.0467035	+	0.0556591i	−0.742187	+	0.670193i	$0.766211\pi$
$84$		0			0
$85$	4.68683	−	26.5803i	0.0551391	−	0.312710i
$86$	32.0186	+	51.7299i	0.372310	+	0.601510i
$87$		0			0
$88$	−21.3743	+	21.5747i	−0.242890	+	0.245168i
$89$	36.5192	+	63.2530i	0.410328	+	0.710708i	0.994925	−	0.100615i	$-0.0320810\pi$
$89$	36.5192	+	63.2530i	0.410328	+	0.710708i	−0.584598	+	0.811323i	$0.698748\pi$
$90$		0			0
$91$	0.725341	+	0.418776i	0.00797078	+	0.00460193i
$92$	9.36614	+	152.630i	0.101806	+	1.65902i
$93$		0			0
$94$	−50.0436	+	93.1582i	−0.532379	+	0.991045i
$95$	−17.1204	+	20.4033i	−0.180215	+	0.214771i
$96$		0			0
$97$	123.655	+	45.0069i	1.27480	+	0.463988i	0.888708	−	0.458473i	$-0.151603\pi$
$97$	123.655	+	45.0069i	1.27480	+	0.463988i	0.386089	+	0.922461i	$0.373826\pi$
$98$	30.4254	−	92.2993i	0.310464	−	0.941830i
$99$		0			0
$100$	68.2168	+	50.4565i	0.682168	+	0.504565i
$101$	−2.52562	−	14.3235i	−0.0250061	−	0.141817i	0.969749	−	0.244106i	$-0.0784944\pi$
$101$	−2.52562	−	14.3235i	−0.0250061	−	0.141817i	−0.994755	+	0.102289i	$0.967383\pi$
$102$		0			0
$103$	38.7271	+	106.402i	0.375991	+	1.03303i	0.973003	+	0.230794i	$0.0741323\pi$
$103$	38.7271	+	106.402i	0.375991	+	1.03303i	−0.597012	+	0.802232i	$0.703645\pi$
$104$	4.47959	+	9.49065i	0.0430730	+	0.0912563i
$105$		0			0
$106$	85.4729	−	108.444i	0.806349	−	1.02306i
$107$			59.5984i			0.556994i	0.960437	+	0.278497i	$0.0898363\pi$
$107$			59.5984i			0.556994i	−0.960437	+	0.278497i	$0.910164\pi$
$108$		0			0
$109$	−4.29709			−0.0394229			−0.0197114	−	0.999806i	$-0.506275\pi$
$109$	−4.29709			−0.0394229			−0.0197114	+	0.999806i	$0.506275\pi$
$110$	11.6052	+	9.14687i	0.105501	+	0.0831534i
$111$		0			0
$112$	−8.15581	+	6.15100i	−0.0728197	+	0.0549197i
$113$	80.4774	−	29.2914i	0.712190	−	0.259216i	0.0395834	−	0.999216i	$-0.487397\pi$
$113$	80.4774	−	29.2914i	0.712190	−	0.259216i	0.672606	+	0.740000i	$0.265175\pi$
$114$		0			0
$115$	73.2714	−	12.9197i	0.637142	−	0.112345i
$116$	141.112	+	104.373i	1.21648	+	0.899770i
$117$		0			0
$118$	170.235	+	56.1160i	1.44267	+	0.475559i
$119$	−3.02833	+	8.32027i	−0.0254481	+	0.0699182i
$120$		0			0
$121$	81.6516	+	68.5138i	0.674806	+	0.566230i
$122$	−10.0763	−	5.41288i	−0.0825927	−	0.0443679i
$123$		0			0
$124$	1.53428	+	25.0025i	0.0123733	+	0.201633i
$125$	44.9692	−	77.8890i	0.359754	−	0.623112i
$126$		0			0
$127$	−127.194	+	73.4353i	−1.00153	+	0.578231i	−0.908699	−	0.417451i	$-0.862923\pi$
$127$	−127.194	+	73.4353i	−1.00153	+	0.578231i	−0.0928261	+	0.995682i	$0.529590\pi$
$128$	−127.898	+	5.11558i	−0.999201	+	0.0399655i
$129$		0			0
$130$	4.34181	−	2.68740i	0.0333985	−	0.0206723i
$131$	−187.990	−	33.1476i	−1.43504	−	0.253035i	−0.598577	−	0.801065i	$-0.704267\pi$
$131$	−187.990	−	33.1476i	−1.43504	−	0.253035i	−0.836459	+	0.548030i	$0.815378\pi$
$132$		0			0
$133$	6.69333	−	5.61637i	0.0503258	−	0.0422284i
$134$	−49.9977	−	240.251i	−0.373117	−	1.79292i
$135$		0			0
$136$	−90.5835	+	64.0592i	−0.666056	+	0.471024i
$137$	47.6987	−	40.0240i	0.348166	−	0.292146i	−0.451887	−	0.892075i	$-0.649249\pi$
$137$	47.6987	−	40.0240i	0.348166	−	0.292146i	0.800053	+	0.599929i	$0.204805\pi$
$138$		0			0
$139$	250.424	+	44.1566i	1.80161	+	0.317673i	0.970983	−	0.239150i	$-0.0768689\pi$
$139$	250.424	+	44.1566i	1.80161	+	0.317673i	0.830631	+	0.556823i	$0.187980\pi$
$140$	3.42202	+	3.60460i	0.0244430	+	0.0257472i
$141$		0			0
$142$	−189.537	+	75.6398i	−1.33477	+	0.532675i
$143$	−4.31286	+	2.49003i	−0.0301599	+	0.0174128i
$144$		0			0
$145$	42.6991	−	73.9569i	0.294476	−	0.510048i
$146$	−131.612	−	19.0693i	−0.901451	−	0.130611i
$147$		0			0
$148$	130.397	+	38.5968i	0.881063	+	0.260789i
$149$	−27.4582	−	23.0402i	−0.184283	−	0.154632i	0.545979	−	0.837799i	$-0.316158\pi$
$149$	−27.4582	−	23.0402i	−0.184283	−	0.154632i	−0.730262	+	0.683167i	$0.760602\pi$
$150$		0			0
$151$	79.0367	−	217.151i	0.523422	−	1.43809i	−0.343266	−	0.939238i	$-0.611533\pi$
$151$	79.0367	−	217.151i	0.523422	−	1.43809i	0.866688	−	0.498851i	$-0.166244\pi$
$152$	109.021	−	10.0509i	0.717243	−	0.0661243i
$153$		0			0
$154$	−3.22820	−	3.61616i	−0.0209623	−	0.0234815i
$155$	12.0027	−	2.11640i	0.0774369	−	0.0136542i
$156$		0			0
$157$	−150.910	+	54.9267i	−0.961209	+	0.349851i	−0.774507	−	0.632565i	$-0.782002\pi$
$157$	−150.910	+	54.9267i	−0.961209	+	0.349851i	−0.186702	+	0.982417i	$0.559780\pi$
$158$	205.668	−	6.30449i	1.30169	−	0.0399018i
$159$		0			0
$160$	9.50506	+	61.5488i	0.0594066	+	0.384680i
$161$	−24.4076			−0.151600
$162$		0			0
$163$		−	5.93715i		−	0.0364242i	−0.999834	−	0.0182121i	$-0.994203\pi$
$163$		−	5.93715i		−	0.0364242i	0.999834	−	0.0182121i	$-0.00579741\pi$
$164$	−40.2476	+	80.7650i	−0.245412	+	0.492470i
$165$		0			0
$166$	−12.0555	+	0.369547i	−0.0726237	+	0.00222619i
$167$	−2.28378	−	6.27464i	−0.0136753	−	0.0375727i	0.932667	−	0.360738i	$-0.117475\pi$
$167$	−2.28378	−	6.27464i	−0.0136753	−	0.0375727i	−0.946342	+	0.323165i	$0.895253\pi$
$168$		0			0
$169$	−29.0477	−	164.738i	−0.171880	−	0.974779i
$170$	35.9488	+	40.2691i	0.211464	+	0.236877i
$171$		0			0
$172$	−120.895	−	13.7496i	−0.702879	−	0.0799393i
$173$	−21.8813	−	7.96415i	−0.126482	−	0.0460355i	0.278004	−	0.960580i	$-0.410327\pi$
$173$	−21.8813	−	7.96415i	−0.126482	−	0.0460355i	−0.404486	+	0.914544i	$0.632549\pi$
$174$		0			0
$175$	−8.70534	+	10.3746i	−0.0497448	+	0.0592835i
$176$	−7.42665	−	60.2841i	−0.0421969	−	0.342523i
$177$		0			0
$178$	−144.567	−	20.9463i	−0.812175	−	0.117676i
$179$	126.375	+	72.9626i	0.706005	+	0.407612i	0.809580	−	0.587009i	$-0.199695\pi$
$179$	126.375	+	72.9626i	0.706005	+	0.407612i	−0.103575	+	0.994622i	$0.533028\pi$
$180$		0			0
$181$	−135.413	−	234.543i	−0.748140	−	1.29582i	−0.948713	−	0.316137i	$-0.897614\pi$
$181$	−135.413	−	234.543i	−0.748140	−	1.29582i	0.200574	−	0.979679i	$-0.435719\pi$
$182$	−1.55579	+	0.620879i	−0.00854829	+	0.00341142i
$183$		0			0
$184$	−251.340	−	174.248i	−1.36598	−	0.947000i
$185$	11.4896	−	65.1606i	0.0621058	−	0.352219i
$186$		0			0
$187$	−33.8409	−	40.3300i	−0.180967	−	0.215669i
$188$	−84.3736	−	193.939i	−0.448796	−	1.03159i
$189$		0			0
$190$	−10.8531	−	52.1518i	−0.0571215	−	0.274483i
$191$	38.0631	+	45.3618i	0.199283	+	0.237497i	0.856426	−	0.516269i	$-0.172680\pi$
$191$	38.0631	+	45.3618i	0.199283	+	0.237497i	−0.657143	+	0.753766i	$0.728235\pi$
$192$		0			0
$193$	22.3119	−	126.537i	0.115605	−	0.655631i	−0.870843	−	0.491561i	$-0.836427\pi$
$193$	22.3119	−	126.537i	0.115605	−	0.655631i	0.986449	−	0.164070i	$-0.0524624\pi$
$194$	−223.784	+	138.513i	−1.15353	+	0.713984i
$195$		0			0
$196$	107.312	+	162.060i	0.547512	+	0.826838i
$197$	117.621	+	203.725i	0.597059	+	1.03414i	0.993253	+	0.115970i	$0.0369977\pi$
$197$	117.621	+	203.725i	0.597059	+	1.03414i	−0.396193	+	0.918167i	$0.629669\pi$
$198$		0			0
$199$	−262.449	−	151.525i	−1.31884	−	0.761432i	−0.335298	−	0.942112i	$-0.608837\pi$
$199$	−262.449	−	151.525i	−1.31884	−	0.761432i	−0.983542	+	0.180680i	$0.942170\pi$
$200$	−163.709	+	44.6855i	−0.818547	+	0.223428i
$201$		0			0
$202$	25.6255	+	13.7658i	0.126859	+	0.0681473i
$203$	−18.0077	+	21.4607i	−0.0887079	+	0.105718i
$204$		0			0
$205$	41.2574	+	15.0165i	0.201256	+	0.0732511i
$206$	−215.077	−	70.8976i	−1.04406	−	0.344163i
$207$		0			0
$208$	−20.4534	−	4.71334i	−0.0983336	−	0.0226603i
$209$	9.02156	+	51.1638i	0.0431654	+	0.244803i
$210$		0			0
$211$	36.9350	+	101.478i	0.175047	+	0.480939i	0.995927	−	0.0901624i	$-0.0287386\pi$
$211$	36.9350	+	101.478i	0.175047	+	0.480939i	−0.820880	+	0.571101i	$0.806516\pi$
$212$	64.5220	+	268.515i	0.304349	+	1.26658i
$213$		0			0
$214$	−93.6147	−	73.7846i	−0.437452	−	0.344788i
$215$			59.2008i			0.275353i
$216$		0			0
$217$	−3.99826			−0.0184252
$218$	5.31993	−	6.74970i	0.0244033	−	0.0309619i
$219$		0			0
$220$	−28.7351	+	6.90481i	−0.130614	+	0.0313855i
$221$	−17.0957	+	6.22234i	−0.0773562	+	0.0281554i
$222$		0			0
$223$	185.399	−	32.6909i	0.831388	−	0.146596i	0.258274	−	0.966072i	$-0.416846\pi$
$223$	185.399	−	32.6909i	0.831388	−	0.146596i	0.573114	+	0.819476i	$0.305735\pi$
$224$	0.435387	−	20.4259i	0.00194369	−	0.0911872i
$225$		0			0
$226$	−53.6237	+	162.674i	−0.237273	+	0.719798i
$227$	135.429	−	372.089i	0.596605	−	1.63916i	−0.161386	−	0.986891i	$-0.551596\pi$
$227$	135.429	−	372.089i	0.596605	−	1.63916i	0.757990	−	0.652266i	$-0.226182\pi$
$228$		0			0
$229$	−124.377	−	104.365i	−0.543130	−	0.455740i	0.329476	−	0.944164i	$-0.393128\pi$
$229$	−124.377	−	104.365i	−0.543130	−	0.455740i	−0.872607	+	0.488423i	$0.837572\pi$
$230$	−70.4183	+	131.087i	−0.306167	+	0.569942i
$231$		0			0
$232$	−338.646	+	92.4356i	−1.45968	+	0.398429i
$233$	168.281	−	291.471i	0.722236	−	1.25095i	−0.237866	−	0.971298i	$-0.576448\pi$
$233$	168.281	−	291.471i	0.722236	−	1.25095i	0.960102	−	0.279651i	$-0.0902187\pi$
$234$		0			0
$235$	−89.1177	+	51.4521i	−0.379224	+	0.218945i
$236$	−298.900	+	197.925i	−1.26653	+	0.838664i
$237$		0			0
$238$	−9.31997	−	15.0575i	−0.0391595	−	0.0632668i
$239$	28.9465	+	5.10405i	0.121115	+	0.0213559i	0.233877	−	0.972266i	$-0.424859\pi$
$239$	28.9465	+	5.10405i	0.121115	+	0.0213559i	−0.112762	+	0.993622i	$0.535970\pi$
$240$		0			0
$241$	−154.824	+	129.913i	−0.642423	+	0.539057i	−0.904761	−	0.425919i	$-0.859951\pi$
$241$	−154.824	+	129.913i	−0.642423	+	0.539057i	0.262338	+	0.964976i	$0.415506\pi$
$242$	−208.706	+	43.4328i	−0.862420	+	0.179474i
$243$		0			0
$244$	20.9771	−	9.12613i	0.0859717	−	0.0374022i
$245$	72.4453	−	60.7888i	0.295695	−	0.248118i
$246$		0			0
$247$	17.6803	+	3.11752i	0.0715803	+	0.0126215i
$248$	−41.1724	−	28.5439i	−0.166018	−	0.115096i
$249$		0			0
$250$	66.6716	+	167.065i	0.266686	+	0.668259i
$251$	−288.384	+	166.498i	−1.14894	+	0.663340i	−0.948628	−	0.316393i	$-0.897528\pi$
$251$	−288.384	+	166.498i	−1.14894	+	0.663340i	−0.200310	+	0.979733i	$0.564195\pi$
$252$		0			0
$253$	72.5635	−	125.684i	0.286812	−	0.496774i
$254$	42.1204	−	290.706i	0.165828	−	1.14451i
$255$		0			0
$256$	150.306	−	207.230i	0.587132	−	0.809491i
$257$	116.593	+	97.8335i	0.453671	+	0.380675i	0.840796	−	0.541352i	$-0.182087\pi$
$257$	116.593	+	97.8335i	0.453671	+	0.380675i	−0.387125	+	0.922027i	$0.626532\pi$
$258$		0			0
$259$	−7.42383	+	20.3968i	−0.0286634	+	0.0787521i
$260$	−1.15403	+	10.1470i	−0.00443858	+	0.0390270i
$261$		0			0
$262$	284.804	−	254.249i	1.08704	−	0.970415i
$263$	255.021	−	44.9671i	0.969662	−	0.170978i	0.333684	−	0.942685i	$-0.391708\pi$
$263$	255.021	−	44.9671i	0.969662	−	0.170978i	0.635978	+	0.771707i	$0.280597\pi$
$264$		0			0
$265$	126.262	−	45.9555i	0.476459	−	0.173417i
$266$	0.535424	+	17.4669i	0.00201287	+	0.0656649i
$267$		0			0
$268$	439.276	+	218.904i	1.63909	+	0.816806i
$269$	−420.269			−1.56234			−0.781169	−	0.624320i	$-0.785376\pi$
$269$	−420.269			−1.56234			−0.781169	+	0.624320i	$0.785376\pi$
$270$		0			0
$271$			154.204i			0.569018i	0.958673	+	0.284509i	$0.0918306\pi$
$271$			154.204i			0.569018i	−0.958673	+	0.284509i	$0.908169\pi$
$272$	11.5235	−	221.592i	0.0423657	−	0.814677i
$273$		0			0
$274$	3.81560	+	124.474i	0.0139255	+	0.454285i
$275$	−27.5418	−	75.6706i	−0.100152	−	0.275166i
$276$		0			0
$277$	−63.1095	−	357.912i	−0.227832	−	1.29210i	−0.857196	−	0.514990i	$-0.827796\pi$
$277$	−63.1095	−	357.912i	−0.227832	−	1.29210i	0.629364	−	0.777111i	$-0.283315\pi$
$278$	−379.392	+	338.689i	−1.36472	+	1.21831i
$279$		0			0
$280$	−9.89853	+	0.912568i	−0.0353519	+	0.00325917i
$281$	276.470	+	100.627i	0.983880	+	0.358103i	0.783347	−	0.621584i	$-0.213511\pi$
$281$	276.470	+	100.627i	0.983880	+	0.358103i	0.200532	+	0.979687i	$0.435733\pi$
$282$		0			0
$283$	−9.69771	+	11.5573i	−0.0342675	+	0.0408384i	−0.782906	−	0.622140i	$-0.786263\pi$
$283$	−9.69771	+	11.5573i	−0.0342675	+	0.0408384i	0.748638	+	0.662978i	$0.230708\pi$
$284$	115.841	−	391.361i	0.407890	−	1.37803i
$285$		0			0
$286$	1.42821	−	9.85719i	0.00499374	−	0.0344657i
$287$	−12.4735	−	7.20160i	−0.0434618	−	0.0250927i
$288$		0			0
$289$	48.3362	+	83.7208i	0.167253	+	0.289691i
$290$	63.3058	+	158.631i	0.218296	+	0.547003i
$291$		0			0
$292$	192.893	−	183.122i	0.660591	−	0.627131i
$293$	−14.6418	+	83.0380i	−0.0499722	+	0.283406i	−0.999546	−	0.0301380i	$-0.990405\pi$
$293$	−14.6418	+	83.0380i	−0.0499722	+	0.283406i	0.949574	+	0.313544i	$0.101516\pi$
$294$		0			0
$295$	112.117	+	133.616i	0.380059	+	0.452937i
$296$	−222.062	+	157.039i	−0.750209	+	0.530536i
$297$		0			0
$298$	70.1847	−	14.6058i	0.235519	−	0.0490128i
$299$	−32.2362	−	38.4176i	−0.107813	−	0.128487i
$300$		0			0
$301$	3.37241	−	19.1259i	0.0112040	−	0.0635412i
$302$	243.243	+	392.987i	0.805440	+	1.30128i
$303$		0			0
$304$	−119.184	+	183.689i	−0.392052	+	0.604240i
$305$	−5.56524	−	9.63927i	−0.0182467	−	0.0316042i
$306$		0			0
$307$	−13.9520	−	8.05517i	−0.0454461	−	0.0262383i	0.477105	−	0.878846i	$-0.341686\pi$
$307$	−13.9520	−	8.05517i	−0.0454461	−	0.0262383i	−0.522551	+	0.852608i	$0.675020\pi$
$308$	9.67672	−	0.593813i	0.0314179	−	0.00192796i
$309$		0			0
$310$	−11.5354	+	21.4735i	−0.0372108	+	0.0692695i
$311$	−120.014	+	143.028i	−0.385899	+	0.459896i	−0.923667	−	0.383197i	$-0.874823\pi$
$311$	−120.014	+	143.028i	−0.385899	+	0.459896i	0.537768	+	0.843093i	$0.319268\pi$
$312$		0			0
$313$	423.270	+	154.058i	1.35230	+	0.492197i	0.913665	−	0.406468i	$-0.133240\pi$
$313$	423.270	+	154.058i	1.35230	+	0.492197i	0.438635	+	0.898665i	$0.355462\pi$
$314$	100.554	−	305.044i	0.320236	−	0.971477i
$315$		0			0
$316$	−244.720	+	330.859i	−0.774430	+	1.04702i
$317$	42.1130	+	238.835i	0.132849	+	0.753422i	0.976334	+	0.216269i	$0.0693889\pi$
$317$	42.1130	+	238.835i	0.132849	+	0.753422i	−0.843485	+	0.537152i	$0.819500\pi$
$318$		0			0
$319$	−56.9725	−	156.531i	−0.178597	−	0.490692i
$320$	−108.446	−	61.2691i	−0.338894	−	0.191466i
$321$		0			0
$322$	30.2174	−	38.3385i	0.0938427	−	0.119064i
$323$			189.792i			0.587593i
$324$		0			0
$325$	−27.8271			−0.0856220
$326$	9.32583	+	7.35036i	0.0286068	+	0.0225471i
$327$		0			0
$328$	−77.0346	−	163.209i	−0.234862	−	0.497588i
$329$	31.7221	−	11.5459i	0.0964197	−	0.0350939i
$330$		0			0
$331$	105.075	−	18.5275i	0.317446	−	0.0559743i	−0.0126549	−	0.999920i	$-0.504028\pi$
$331$	105.075	−	18.5275i	0.317446	−	0.0559743i	0.330101	+	0.943946i	$0.392917\pi$
$332$	14.3446	−	19.3938i	0.0432067	−	0.0584152i
$333$		0			0
$334$	12.6833	+	4.18091i	0.0379740	+	0.0125177i
$335$	81.6736	−	224.396i	0.243802	−	0.669840i
$336$		0			0
$337$	132.298	+	111.012i	0.392577	+	0.329411i	0.817616	−	0.575764i	$-0.195295\pi$
$337$	132.298	+	111.012i	0.392577	+	0.329411i	−0.425039	+	0.905175i	$0.639740\pi$
$338$	294.725	+	158.323i	0.871968	+	0.468412i
$339$		0			0
$340$	−107.759	+	6.61263i	−0.316937	+	0.0194489i
$341$	11.8868	−	20.5885i	0.0348586	−	0.0603768i
$342$		0			0
$343$	−53.9606	+	31.1542i	−0.157320	+	0.0908285i
$344$	171.269	−	172.875i	0.497875	−	0.502543i
$345$		0			0
$346$	39.5995	−	24.5104i	0.114449	−	0.0708394i
$347$	134.500	+	23.7159i	0.387607	+	0.0683456i	0.364056	−	0.931377i	$-0.381392\pi$
$347$	134.500	+	23.7159i	0.387607	+	0.0683456i	0.0235511	+	0.999723i	$0.492503\pi$
$348$		0			0
$349$	−456.261	+	382.849i	−1.30734	+	1.09699i	−0.318512	+	0.947919i	$0.603183\pi$
$349$	−456.261	+	382.849i	−1.30734	+	1.09699i	−0.988827	+	0.149068i	$0.952373\pi$
$350$	−5.51856	−	26.5181i	−0.0157673	−	0.0757659i
$351$		0			0
$352$	103.886	+	62.9680i	0.295131	+	0.178886i
$353$	118.199	−	99.1807i	0.334841	−	0.280965i	−0.459828	−	0.888008i	$-0.652089\pi$
$353$	118.199	−	99.1807i	0.334841	−	0.280965i	0.794669	+	0.607043i	$0.207644\pi$
$354$		0			0
$355$	−195.566	−	34.4836i	−0.550891	−	0.0971370i
$356$	211.880	−	201.148i	0.595168	−	0.565022i
$357$		0			0
$358$	−271.063	+	108.175i	−0.757158	+	0.302164i
$359$	−350.781	+	202.523i	−0.977106	+	0.564132i	−0.901395	−	0.432998i	$-0.857456\pi$
$359$	−350.781	+	202.523i	−0.977106	+	0.564132i	−0.0757107	+	0.997130i	$0.524123\pi$
$360$		0			0
$361$	−86.8547	+	150.437i	−0.240595	+	0.416722i
$362$	536.056	+	77.6691i	1.48082	+	0.214556i
$363$		0			0
$364$	0.950862	−	3.21244i	0.00261226	−	0.00882537i
$365$	−99.1330	−	83.1825i	−0.271597	−	0.227897i
$366$		0			0
$367$	−194.549	+	534.518i	−0.530105	+	1.45645i	0.328841	+	0.944385i	$0.393342\pi$
$367$	−194.549	+	534.518i	−0.530105	+	1.45645i	−0.858946	+	0.512066i	$0.828880\pi$
$368$	584.868	−	179.070i	1.58931	−	0.486603i
$369$		0			0
$370$	88.1272	+	98.7181i	0.238182	+	0.266806i
$371$	−43.4090	+	7.65418i	−0.117005	+	0.0206312i
$372$		0			0
$373$	324.026	−	117.936i	0.868702	−	0.316182i	0.131061	−	0.991374i	$-0.458162\pi$
$373$	324.026	−	117.936i	0.868702	−	0.316182i	0.737642	+	0.675192i	$0.235939\pi$
$374$	105.245	−	3.22615i	0.281403	−	0.00862606i
$375$		0			0
$376$	409.088	+	107.572i	1.08800	+	0.286095i
$377$	−57.5627			−0.152686
$378$		0			0
$379$		−	374.262i		−	0.987499i	−0.869604	−	0.493750i	$-0.835626\pi$
$379$		−	374.262i		−	0.987499i	0.869604	−	0.493750i	$-0.164374\pi$
$380$	95.3544	+	47.5179i	0.250933	+	0.125047i
$381$		0			0
$382$	−118.376	+	3.62866i	−0.309884	+	0.00949911i
$383$	86.4006	+	237.384i	0.225589	+	0.619801i	0.999916	−	0.0129854i	$-0.00413351\pi$
$383$	86.4006	+	237.384i	0.225589	+	0.619801i	−0.774327	+	0.632786i	$0.781911\pi$
$384$		0			0
$385$	−0.819110	−	4.64540i	−0.00212756	−	0.0120660i
$386$	171.136	+	191.703i	0.443358	+	0.496639i
$387$		0			0
$388$	59.4807	−	522.994i	0.153301	−	1.34792i
$389$	−315.657	−	114.890i	−0.811459	−	0.295347i	−0.0972324	−	0.995262i	$-0.530999\pi$
$389$	−315.657	−	114.890i	−0.811459	−	0.295347i	−0.714226	+	0.699915i	$0.753221\pi$
$390$		0			0
$391$	340.787	−	406.134i	0.871578	−	1.03871i
$392$	−387.414	−	32.0735i	−0.988300	−	0.0818202i
$393$		0			0
$394$	−465.621	−	67.4638i	−1.18178	−	0.171228i
$395$	173.404	+	100.115i	0.438997	+	0.253455i
$396$		0			0
$397$	114.602	+	198.496i	0.288669	+	0.499990i	0.973492	−	0.228720i	$-0.0734539\pi$
$397$	114.602	+	198.496i	0.288669	+	0.499990i	−0.684823	+	0.728709i	$0.740121\pi$
$398$	562.929	−	224.652i	1.41439	−	0.564452i
$399$		0			0
$400$	132.487	−	312.470i	0.331217	−	0.781175i
$401$	57.8781	−	328.243i	0.144335	−	0.818562i	−0.823565	−	0.567223i	$-0.808018\pi$
$401$	57.8781	−	328.243i	0.144335	−	0.818562i	0.967899	−	0.251339i	$-0.0808709\pi$
$402$		0			0
$403$	−5.28067	−	6.29325i	−0.0131034	−	0.0156160i
$404$	−53.3478	+	23.2091i	−0.132049	+	0.0574483i
$405$		0			0
$406$	−11.4156	−	54.8548i	−0.0281172	−	0.135110i
$407$	−82.9596	−	98.8674i	−0.203832	−	0.242918i
$408$		0			0
$409$	−111.051	+	629.803i	−0.271519	+	1.53986i	0.478288	+	0.878203i	$0.341257\pi$
$409$	−111.051	+	629.803i	−0.271519	+	1.53986i	−0.749807	+	0.661657i	$0.769854\pi$
$410$	−74.6652	+	46.2146i	−0.182110	+	0.112719i
$411$		0			0
$412$	377.634	−	250.060i	0.916588	−	0.606942i
$413$	−28.6100	−	49.5540i	−0.0692737	−	0.119986i
$414$		0			0
$415$	−10.1643	−	5.86838i	−0.0244924	−	0.0141407i
$416$	32.7254	−	26.2921i	0.0786669	−	0.0632021i
$417$		0			0
$418$	−91.5350	−	49.1716i	−0.218983	−	0.117635i
$419$	196.174	−	233.791i	0.468195	−	0.557974i	−0.479338	−	0.877630i	$-0.659123\pi$
$419$	196.174	−	233.791i	0.468195	−	0.557974i	0.947533	+	0.319657i	$0.103568\pi$
$420$		0			0
$421$	141.297	+	51.4281i	0.335623	+	0.122157i	0.504334	−	0.863509i	$-0.331738\pi$
$421$	141.297	+	51.4281i	0.335623	+	0.122157i	−0.168710	+	0.985666i	$0.553960\pi$
$422$	−205.124	−	67.6169i	−0.486076	−	0.160230i
$423$		0			0
$424$	−501.652	−	231.081i	−1.18314	−	0.545002i
$425$	−51.0833	−	289.708i	−0.120196	−	0.681665i
$426$		0			0
$427$	1.24884	+	3.43117i	0.00292469	+	0.00803552i
$428$	231.795	−	55.6986i	0.541578	−	0.130137i
$429$		0			0
$430$	−92.9902	−	73.2923i	−0.216256	−	0.170447i
$431$		−	555.302i		−	1.28840i	−0.764856	−	0.644202i	$-0.777190\pi$
$431$		−	555.302i		−	1.28840i	0.764856	−	0.644202i	$-0.222810\pi$
$432$		0			0
$433$	388.469			0.897157			0.448579	−	0.893743i	$-0.351930\pi$
$433$	388.469			0.897157			0.448579	+	0.893743i	$0.351930\pi$
$434$	4.94996	−	6.28030i	0.0114054	−	0.0144707i
$435$		0			0
$436$	4.01592	+	16.7127i	0.00921082	+	0.0383318i
$437$	−491.630	+	178.939i	−1.12501	+	0.409471i
$438$		0			0
$439$	153.154	−	27.0051i	0.348870	−	0.0615151i	0.00353238	−	0.999994i	$-0.498876\pi$
$439$	153.154	−	27.0051i	0.348870	−	0.0615151i	0.345337	+	0.938479i	$0.387764\pi$
$440$	24.7291	−	53.6842i	0.0562024	−	0.122010i
$441$		0			0
$442$	11.3912	−	34.5567i	0.0257720	−	0.0781826i
$443$	−178.524	+	490.491i	−0.402989	+	1.10720i	0.557813	+	0.829967i	$0.311641\pi$
$443$	−178.524	+	490.491i	−0.402989	+	1.10720i	−0.960802	+	0.277236i	$0.910582\pi$
$444$		0			0
$445$	−108.891	−	91.3705i	−0.244699	−	0.205327i
$446$	−178.180	+	331.690i	−0.399508	+	0.743700i
$447$		0			0
$448$	31.5452	+	25.9718i	0.0704134	+	0.0579728i
$449$	114.425	−	198.189i	0.254843	−	0.441402i	−0.710010	−	0.704192i	$-0.751309\pi$
$449$	114.425	−	198.189i	0.254843	−	0.441402i	0.964853	+	0.262790i	$0.0846428\pi$
$450$		0			0
$451$	74.1673	−	42.8205i	0.164451	−	0.0949457i
$452$	−189.134	−	285.625i	−0.418439	−	0.631915i
$453$		0			0
$454$	416.796	+	673.383i	0.918054	+	1.48322i
$455$	−1.60528	−	0.283054i	−0.00352809	−	0.000622097i
$456$		0			0
$457$	−536.707	+	450.351i	−1.17441	+	0.985450i	−0.174414	+	0.984672i	$0.555803\pi$
$457$	−536.707	+	450.351i	−1.17441	+	0.985450i	−1.00000		0.000777552i	$0.999752\pi$
$458$	317.914	−	66.1596i	0.694135	−	0.144453i
$459$		0			0
$460$	−118.725	−	272.899i	−0.258099	−	0.593259i
$461$	−452.465	+	379.663i	−0.981486	+	0.823564i	−0.984313	−	0.176432i	$-0.943545\pi$
$461$	−452.465	+	379.663i	−0.981486	+	0.823564i	0.00282725	+	0.999996i	$0.499100\pi$
$462$		0			0
$463$	−140.609	−	24.7931i	−0.303691	−	0.0535489i	0.0197263	−	0.999805i	$-0.493721\pi$
$463$	−140.609	−	24.7931i	−0.303691	−	0.0535489i	−0.323417	+	0.946257i	$0.604832\pi$
$464$	274.060	−	646.369i	0.590646	−	1.39304i
$465$		0			0
$466$	249.494	+	625.178i	0.535395	+	1.34158i
$467$	287.772	−	166.145i	0.616213	−	0.355771i	−0.159180	−	0.987250i	$-0.550885\pi$
$467$	287.772	−	166.145i	0.616213	−	0.355771i	0.775393	+	0.631479i	$0.217552\pi$
$468$		0			0
$469$	−39.1690	+	67.8428i	−0.0835161	+	0.144654i
$470$	29.5115	−	203.682i	0.0627903	−	0.433365i
$471$		0			0
$472$	59.1557	−	714.537i	0.125330	−	1.51385i
$473$	88.4601	+	74.2268i	0.187019	+	0.156928i
$474$		0			0
$475$	−99.2881	+	272.792i	−0.209028	+	0.574299i
$476$	35.1901	+	4.00221i	0.0739288	+	0.00840801i
$477$		0			0
$478$	−43.8538	+	39.1490i	−0.0917445	+	0.0819017i
$479$	−140.813	+	24.8292i	−0.293974	+	0.0518355i	−0.318690	−	0.947859i	$-0.603243\pi$
$479$	−140.813	+	24.8292i	−0.293974	+	0.0518355i	0.0247164	+	0.999695i	$0.492132\pi$
$480$		0			0
$481$	−41.9095	+	15.2538i	−0.0871299	+	0.0317127i
$482$	−12.3849	−	404.027i	−0.0256949	−	0.838230i
$483$		0			0
$484$	190.161	−	381.597i	0.392895	−	0.788424i
$485$	−256.103			−0.528048
$486$		0			0
$487$			238.167i			0.489050i	0.969643	+	0.244525i	$0.0786320\pi$
$487$			238.167i			0.489050i	−0.969643	+	0.244525i	$0.921368\pi$
$488$	−11.6353	+	44.2484i	−0.0238428	+	0.0906729i
$489$		0			0
$490$	5.79516	+	189.052i	0.0118269	+	0.385821i
$491$	13.1930	+	36.2476i	0.0268697	+	0.0738240i	0.952402	−	0.304844i	$-0.0986044\pi$
$491$	13.1930	+	36.2476i	0.0268697	+	0.0738240i	−0.925533	+	0.378668i	$0.876382\pi$
$492$		0			0
$493$	−105.670	−	599.284i	−0.214341	−	1.21559i
$494$	−26.7856	+	23.9120i	−0.0542220	+	0.0484048i
$495$		0			0
$496$	95.8083	−	29.3338i	0.193162	−	0.0591407i
$497$	61.2169	+	22.2811i	0.123173	+	0.0448313i
$498$		0			0
$499$	56.0000	−	66.7382i	0.112224	−	0.133744i	−0.707008	−	0.707206i	$-0.749955\pi$
$499$	56.0000	−	66.7382i	0.112224	−	0.133744i	0.819232	+	0.573462i	$0.194400\pi$
$500$	−344.960	−	102.106i	−0.689919	−	0.204212i
$501$		0			0
$502$	95.4986	−	659.111i	0.190236	−	1.31297i
$503$	−541.002	−	312.348i	−1.07555	−	0.620970i	−0.145858	−	0.989305i	$-0.546594\pi$
$503$	−541.002	−	312.348i	−1.07555	−	0.620970i	−0.929693	+	0.368336i	$0.879928\pi$
$504$		0			0
$505$	14.1532	+	24.5141i	0.0280262	+	0.0485427i
$506$	107.583	+	269.580i	0.212615	+	0.532767i
$507$		0			0
$508$	404.482	+	426.063i	0.796225	+	0.838707i
$509$	−78.2751	+	443.920i	−0.153782	+	0.872142i	0.806109	+	0.591768i	$0.201570\pi$
$509$	−78.2751	+	443.920i	−0.153782	+	0.872142i	−0.959891	+	0.280374i	$0.909541\pi$
$510$		0			0
$511$	27.2882	+	32.5208i	0.0534015	+	0.0636415i
$512$	139.425	+	492.651i	0.272314	+	0.962208i
$513$		0			0
$514$	−298.019	+	62.0194i	−0.579803	+	0.120660i
$515$	−141.651	−	168.813i	−0.275050	−	0.327791i
$516$		0			0
$517$	−34.8553	+	197.674i	−0.0674185	+	0.382349i
$518$	−22.8475	−	36.9129i	−0.0441072	−	0.0712604i
$519$		0			0
$520$	−14.5098	−	14.3750i	−0.0279034	−	0.0276442i
$521$	292.333	+	506.336i	0.561101	+	0.971855i	0.997401	+	0.0720536i	$0.0229553\pi$
$521$	292.333	+	506.336i	0.561101	+	0.971855i	−0.436300	+	0.899801i	$0.643711\pi$
$522$		0			0
$523$	330.483	+	190.805i	0.631900	+	0.364827i	0.781487	−	0.623921i	$-0.214461\pi$
$523$	330.483	+	190.805i	0.631900	+	0.364827i	−0.149588	+	0.988748i	$0.547795\pi$
$524$	46.7679	+	762.125i	0.0892518	+	1.45444i
$525$		0			0
$526$	−245.091	+	456.247i	−0.465953	+	0.867390i
$527$	55.8250	−	66.5296i	0.105930	−	0.126242i
$528$		0			0
$529$	876.234	+	318.923i	1.65640	+	0.602880i
$530$	−84.1307	+	255.221i	−0.158737	+	0.481549i
$531$		0			0
$532$	−28.0991	−	20.7835i	−0.0528178	−	0.0390666i
$533$	−5.13901	−	29.1448i	−0.00964167	−	0.0546806i
$534$		0			0
$535$	−39.6711	−	108.995i	−0.0741516	−	0.203730i
$536$	−887.682	+	418.986i	−1.65612	+	0.781691i
$537$		0			0
$538$	520.305	−	660.141i	0.967110	−	1.22703i
$539$		−	184.468i		−	0.342242i
$540$		0			0
$541$	−874.033			−1.61559			−0.807794	−	0.589465i	$-0.799339\pi$
$541$	−874.033			−1.61559			−0.807794	+	0.589465i	$0.799339\pi$
$542$	−242.217	−	190.909i	−0.446895	−	0.352231i
$543$		0			0
$544$	333.801	+	292.438i	0.613605	+	0.537570i
$545$	7.85866	−	2.86032i	0.0144196	−	0.00524829i
$546$		0			0
$547$	−962.840	+	169.775i	−1.76022	+	0.310374i	−0.958024	−	0.286687i	$-0.907446\pi$
$547$	−962.840	+	169.775i	−1.76022	+	0.310374i	−0.802196	+	0.597061i	$0.796335\pi$
$548$	−200.243	−	148.109i	−0.365406	−	0.270272i
$549$		0			0
$550$	152.958	+	50.4208i	0.278105	+	0.0916742i
$551$	−205.386	+	564.292i	−0.372751	+	1.02412i
$552$		0			0
$553$	−50.3181	−	42.2219i	−0.0909912	−	0.0763507i
$554$	640.325	+	343.976i	1.15582	+	0.620895i
$555$		0			0
$556$	−62.3004	−	1015.24i	−0.112051	−	1.82597i
$557$	−291.019	+	504.060i	−0.522476	+	0.904955i	0.477182	+	0.878804i	$0.341658\pi$
$557$	−291.019	+	504.060i	−0.522476	+	0.904955i	−0.999658	+	0.0261504i	$0.991675\pi$
$558$		0			0
$559$	34.5582	−	19.9522i	0.0618215	−	0.0356927i
$560$	10.8212	−	16.6780i	0.0193237	−	0.0297821i
$561$		0			0
$562$	−500.339	+	309.689i	−0.890283	+	0.551048i
$563$	791.225	+	139.514i	1.40537	+	0.247805i	0.824349	−	0.566081i	$-0.191541\pi$
$563$	791.225	+	139.514i	1.40537	+	0.247805i	0.581024	+	0.813887i	$0.302652\pi$
$564$		0			0
$565$	−127.682	+	107.138i	−0.225986	+	0.189625i
$566$	−6.14765	−	29.5410i	−0.0108616	−	0.0521926i
$567$		0			0
$568$	471.320	+	666.475i	0.829789	+	1.17337i
$569$	−200.968	+	168.632i	−0.353195	+	0.296366i	−0.802071	−	0.597228i	$-0.796269\pi$
$569$	−200.968	+	168.632i	−0.353195	+	0.296366i	0.448877	+	0.893594i	$0.351824\pi$
$570$		0			0
$571$	−650.819	−	114.757i	−1.13979	−	0.200975i	−0.428275	−	0.903648i	$-0.640879\pi$
$571$	−650.819	−	114.757i	−1.13979	−	0.200975i	−0.711513	+	0.702673i	$0.751990\pi$
$572$	13.7151	+	14.4469i	0.0239775	+	0.0252568i
$573$		0			0
$574$	26.7546	−	10.6771i	0.0466108	−	0.0186013i
$575$	702.285	−	405.464i	1.22136	−	0.705155i
$576$		0			0
$577$	−95.3011	+	165.066i	−0.165167	+	0.286077i	−0.936714	−	0.350094i	$-0.886150\pi$
$577$	−95.3011	+	165.066i	−0.165167	+	0.286077i	0.771548	+	0.636171i	$0.219483\pi$
$578$	−191.347	−	27.7242i	−0.331050	−	0.0479658i
$579$		0			0
$580$	−327.545	−	96.9514i	−0.564733	−	0.167158i
$581$	2.94948	+	2.47490i	0.00507655	+	0.00425973i
$582$		0			0
$583$	89.6402	−	246.285i	0.153757	−	0.422443i
$584$	48.8341	+	529.698i	0.0836201	+	0.907018i
$585$		0			0
$586$	−112.306	−	125.802i	−0.191648	−	0.214680i
$587$	−674.146	+	118.870i	−1.14846	+	0.202505i	−0.715304	−	0.698814i	$-0.753712\pi$
$587$	−674.146	+	118.870i	−1.14846	+	0.202505i	−0.433157	+	0.901318i	$0.642600\pi$
$588$		0			0
$589$	−80.5349	+	29.3123i	−0.136732	+	0.0497662i
$590$	−348.684	+	10.6885i	−0.590990	+	0.0181160i
$591$		0			0
$592$	28.2494	−	543.224i	0.0477185	−	0.917609i
$593$	368.375			0.621205			0.310603	−	0.950540i	$-0.399469\pi$
$593$	368.375			0.621205			0.310603	+	0.950540i	$0.399469\pi$
$594$		0			0
$595$		−	17.2321i		−	0.0289616i
$596$	−63.9485	+	128.326i	−0.107296	+	0.215311i
$597$		0			0
$598$	100.254	−	3.07316i	0.167649	−	0.00513907i
$599$	57.9290	+	159.159i	0.0967095	+	0.265707i	0.978609	−	0.205731i	$-0.0659572\pi$
$599$	57.9290	+	159.159i	0.0967095	+	0.265707i	−0.881899	+	0.471438i	$0.843735\pi$
$600$		0			0
$601$	−109.262	−	619.657i	−0.181801	−	1.03104i	−0.929998	−	0.367566i	$-0.880191\pi$
$601$	−109.262	−	619.657i	−0.181801	−	1.03104i	0.748197	−	0.663477i	$-0.230920\pi$
$602$	25.8670	+	28.9757i	0.0429685	+	0.0481323i
$603$		0			0
$604$	−918.430	−	104.454i	−1.52058	−	0.172937i
$605$	−194.933	−	70.9496i	−0.322203	−	0.117272i
$606$		0			0
$607$	−188.896	+	225.118i	−0.311196	+	0.370869i	−0.898860	−	0.438236i	$-0.855603\pi$
$607$	−188.896	+	225.118i	−0.311196	+	0.370869i	0.587664	+	0.809105i	$0.300048\pi$
$608$	−140.978	−	414.621i	−0.231872	−	0.681943i
$609$		0			0
$610$	22.0309	+	3.19206i	0.0361162	+	0.00523288i
$611$	60.0699	+	34.6814i	0.0983141	+	0.0567617i
$612$		0			0
$613$	−48.6612	−	84.2836i	−0.0793820	−	0.137494i	0.823601	−	0.567169i	$-0.191961\pi$
$613$	−48.6612	−	84.2836i	−0.0793820	−	0.137494i	−0.902983	+	0.429675i	$0.858628\pi$
$614$	29.9257	−	11.9426i	0.0487389	−	0.0194505i
$615$		0			0
$616$	−11.0473	+	15.9349i	−0.0179340	+	0.0258684i
$617$	−103.769	+	588.505i	−0.168184	+	0.953817i	0.777537	+	0.628837i	$0.216469\pi$
$617$	−103.769	+	588.505i	−0.168184	+	0.953817i	−0.945721	+	0.324980i	$0.894642\pi$
$618$		0			0
$619$	−675.081	−	804.530i	−1.09060	−	1.29973i	−0.950889	−	0.309533i	$-0.899827\pi$
$619$	−675.081	−	804.530i	−1.09060	−	1.29973i	−0.139711	−	0.990192i	$-0.544617\pi$
$620$	−19.4486	−	44.7041i	−0.0313688	−	0.0721035i
$621$		0			0
$622$	−76.0805	−	365.586i	−0.122316	−	0.587759i
$623$	29.9743	+	35.7220i	0.0481128	+	0.0573386i
$624$		0			0
$625$	61.6918	−	349.872i	0.0987069	−	0.559795i
$626$	−766.008	+	474.127i	−1.22366	+	0.757392i
$627$		0			0
$628$	354.661	+	535.599i	0.564747	+	0.852865i
$629$	−235.742	−	408.317i	−0.374788	−	0.649152i
$630$		0			0
$631$	757.053	+	437.085i	1.19977	+	0.692686i	0.960503	−	0.278269i	$-0.0897605\pi$
$631$	757.053	+	437.085i	1.19977	+	0.692686i	0.239264	+	0.970955i	$0.423094\pi$
$632$	−216.730	−	794.010i	−0.342927	−	1.25634i
$633$		0			0
$634$	−427.289	−	229.535i	−0.673957	−	0.362043i
$635$	183.734	−	218.966i	0.289345	−	0.344829i
$636$		0			0
$637$	−59.9011	−	21.8022i	−0.0940363	−	0.0342264i
$638$	316.406	+	104.300i	0.495934	+	0.163479i
$639$		0			0
$640$	230.498	−	94.4894i	0.360154	−	0.147640i
$641$	−115.831	−	656.912i	−0.180704	−	1.02482i	−0.931352	−	0.364121i	$-0.881370\pi$
$641$	−115.831	−	656.912i	−0.180704	−	1.02482i	0.750648	−	0.660702i	$-0.229742\pi$
$642$		0			0
$643$	81.6449	+	224.318i	0.126975	+	0.348861i	0.986849	−	0.161646i	$-0.0516802\pi$
$643$	81.6449	+	224.318i	0.126975	+	0.348861i	−0.859874	+	0.510506i	$0.829458\pi$
$644$	22.8105	+	94.9283i	0.0354201	+	0.147404i
$645$		0			0
$646$	−298.118	−	234.969i	−0.461483	−	0.363728i
$647$		−	980.601i		−	1.51561i	−0.652480	−	0.757806i	$-0.726271\pi$
$647$		−	980.601i		−	1.51561i	0.652480	−	0.757806i	$-0.273729\pi$
$648$		0			0
$649$	340.229			0.524236
$650$	34.4508	−	43.7097i	0.0530013	−	0.0672458i
$651$		0			0
$652$	−23.0913	+	5.54866i	−0.0354161	+	0.00851021i
$653$	−57.2426	+	20.8346i	−0.0876609	+	0.0319060i	−0.385478	−	0.922717i	$-0.625964\pi$
$653$	−57.2426	+	20.8346i	−0.0876609	+	0.0319060i	0.297817	+	0.954623i	$0.403741\pi$
$654$		0			0
$655$	365.866	−	64.5120i	0.558574	−	0.0984916i
$656$	351.733	+	81.0544i	0.536178	+	0.123559i
$657$		0			0
$658$	−21.1371	+	64.1219i	−0.0321232	+	0.0974497i
$659$	−331.931	+	911.972i	−0.503689	+	1.38387i	0.383959	+	0.923350i	$0.374560\pi$
$659$	−331.931	+	911.972i	−0.503689	+	1.38387i	−0.887648	+	0.460523i	$0.847662\pi$
$660$		0			0
$661$	−871.226	−	731.045i	−1.31804	−	1.10597i	−0.986716	−	0.162452i	$-0.948060\pi$
$661$	−871.226	−	731.045i	−1.31804	−	1.10597i	−0.331326	−	0.943516i	$-0.607496\pi$
$662$	−100.983	+	187.985i	−0.152543	+	0.283965i
$663$		0			0
$664$	12.7040	+	46.5421i	0.0191325	+	0.0700935i
$665$	−8.50250	+	14.7268i	−0.0127857	+	0.0221455i
$666$		0			0
$667$	1452.73	−	838.736i	2.17801	−	1.25747i
$668$	−22.2695	+	14.7463i	−0.0333376	+	0.0220754i
$669$		0			0
$670$	251.358	+	406.099i	0.375162	+	0.606118i
$671$	−21.3811	−	3.77007i	−0.0318646	−	0.00561859i
$672$		0			0
$673$	235.218	−	197.371i	0.349506	−	0.293271i	−0.451085	−	0.892481i	$-0.648963\pi$
$673$	235.218	−	197.371i	0.349506	−	0.293271i	0.800592	+	0.599210i	$0.204519\pi$
$674$	−338.162	+	70.3733i	−0.501724	+	0.104411i
$675$		0			0
$676$	−613.566	+	266.933i	−0.907642	+	0.394872i
$677$	394.447	−	330.980i	0.582639	−	0.488893i	−0.303173	−	0.952935i	$-0.598046\pi$
$677$	394.447	−	330.980i	0.582639	−	0.488893i	0.885813	+	0.464043i	$0.153602\pi$
$678$		0			0
$679$	82.7388	+	14.5891i	0.121854	+	0.0214861i
$680$	123.022	−	177.450i	0.180914	−	0.260955i
$681$		0			0
$682$	17.6234	+	44.1604i	0.0258407	+	0.0647513i
$683$	410.870	−	237.216i	0.601567	−	0.347315i	−0.168091	−	0.985772i	$-0.553760\pi$
$683$	410.870	−	237.216i	0.601567	−	0.347315i	0.769658	+	0.638457i	$0.220427\pi$
$684$		0			0
$685$	−60.5914	+	104.947i	−0.0884546	+	0.153208i
$686$	17.8691	−	123.329i	0.0260483	−	0.179780i
$687$		0			0
$688$	59.5085	+	483.046i	0.0864949	+	0.702102i
$689$	−69.3797	−	58.2165i	−0.100696	−	0.0844942i
$690$		0			0
$691$	−69.6707	+	191.419i	−0.100826	+	0.277017i	−0.979842	−	0.199776i	$-0.935979\pi$
$691$	−69.6707	+	191.419i	−0.100826	+	0.277017i	0.879016	+	0.476793i	$0.158201\pi$
$692$	−10.5253	+	92.5458i	−0.0152100	+	0.133737i
$693$		0			0
$694$	−203.767	+	181.906i	−0.293612	+	0.262112i
$695$	−487.376	+	85.9376i	−0.701261	+	0.123651i
$696$		0			0
$697$	293.992	−	107.004i	0.421796	−	0.153521i
$698$	−36.4980	−	1190.65i	−0.0522894	−	1.70581i
$699$		0			0
$700$	48.4856	+	24.1618i	0.0692652	+	0.0345169i
$701$	1158.25			1.65228			0.826138	−	0.563468i	$-0.190533\pi$
$701$	1158.25			1.65228			0.826138	+	0.563468i	$0.190533\pi$
$702$		0			0
$703$			465.269i			0.661833i
$704$	−227.522	+	85.2239i	−0.323184	+	0.121057i
$705$		0			0
$706$	9.45516	+	308.451i	0.0133926	+	0.436899i
$707$	−3.17599	−	8.72597i	−0.00449221	−	0.0123422i
$708$		0			0
$709$	−85.9306	−	487.337i	−0.121200	−	0.687358i	−0.983493	−	0.180948i	$-0.942083\pi$
$709$	−85.9306	−	487.337i	−0.121200	−	0.687358i	0.862293	−	0.506410i	$-0.169028\pi$
$710$	296.283	−	264.496i	0.417299	−	0.372530i
$711$		0			0
$712$	53.6411	+	581.839i	0.0753386	+	0.817190i
$713$	224.968	+	81.8817i	0.315523	+	0.114841i
$714$		0			0
$715$	6.23003	−	7.42466i	0.00871333	−	0.0103841i
$716$	165.667	−	559.697i	0.231379	−	0.781700i
$717$		0			0
$718$	116.162	−	801.722i	0.161785	−	1.11660i
$719$	−400.965	−	231.497i	−0.557671	−	0.321971i	0.194539	−	0.980895i	$-0.437679\pi$
$719$	−400.965	−	231.497i	−0.557671	−	0.321971i	−0.752210	+	0.658923i	$0.771012\pi$
$720$		0			0
$721$	36.1463	+	62.6072i	0.0501335	+	0.0868338i
$722$	−128.771	−	322.673i	−0.178353	−	0.446915i
$723$		0			0
$724$	−785.652	+	745.857i	−1.08515	+	1.03019i
$725$	161.629	−	916.641i	0.222936	−	1.26433i
$726$		0			0
$727$	309.611	+	368.980i	0.425875	+	0.507538i	0.935727	−	0.352724i	$-0.114744\pi$
$727$	309.611	+	368.980i	0.425875	+	0.507538i	−0.509853	+	0.860262i	$0.670300\pi$
$728$	3.86877	+	5.47066i	0.00531424	+	0.00751465i
$729$		0			0
$730$	253.389	−	52.7317i	0.347109	−	0.0722352i
$731$	271.161	+	323.158i	0.370946	+	0.442076i
$732$		0			0
$733$	44.2695	−	251.065i	0.0603950	−	0.342517i	−0.939605	−	0.342261i	$-0.888807\pi$
$733$	44.2695	−	251.065i	0.0603950	−	0.342517i	1.00000		0.000256141i	$-8.15322e-5\pi$
$734$	−598.742	−	967.337i	−0.815724	−	1.31790i
$735$		0			0
$736$	−442.807	+	1140.38i	−0.601640	+	1.54943i
$737$	−232.898	−	403.391i	−0.316008	−	0.547342i
$738$		0			0
$739$	392.033	+	226.340i	0.530491	+	0.306279i	0.741216	−	0.671266i	$-0.234249\pi$
$739$	392.033	+	226.340i	0.530491	+	0.306279i	−0.210725	+	0.977545i	$0.567583\pi$
$740$	−264.166	+	16.2106i	−0.356982	+	0.0219062i
$741$		0			0
$742$	41.7187	−	77.6612i	0.0562247	−	0.104665i
$743$	−602.072	+	717.521i	−0.810326	+	0.965709i	−0.999869	−	0.0161637i	$-0.994855\pi$
$743$	−602.072	+	717.521i	−0.810326	+	0.965709i	0.189544	+	0.981872i	$0.439299\pi$
$744$		0			0
$745$	65.5529	+	23.8593i	0.0879905	+	0.0320259i
$746$	−215.905	+	654.975i	−0.289417	+	0.877982i
$747$		0			0
$748$	−125.229	+	169.308i	−0.167418	+	0.226348i
$749$	6.60747	+	37.4728i	0.00882172	+	0.0500305i
$750$		0			0
$751$	−423.198	−	1162.73i	−0.563513	−	1.54824i	−0.814449	−	0.580234i	$-0.802961\pi$
$751$	−423.198	−	1162.73i	−0.563513	−	1.54824i	0.250937	−	0.968003i	$-0.419261\pi$
$752$	−675.433	+	509.402i	−0.898182	+	0.677397i
$753$		0			0
$754$	71.2643	−	90.4171i	0.0945150	−	0.119917i
$755$			449.743i			0.595687i
$756$		0			0
$757$	544.520			0.719313			0.359656	−	0.933085i	$-0.382894\pi$
$757$	544.520			0.719313			0.359656	+	0.933085i	$0.382894\pi$
$758$	587.876	+	463.348i	0.775562	+	0.611277i
$759$		0			0
$760$	−192.691	+	90.9502i	−0.253540	+	0.119671i
$761$	1334.15	−	485.590i	1.75315	−	0.638095i	0.753343	−	0.657628i	$-0.228440\pi$
$761$	1334.15	−	485.590i	1.75315	−	0.638095i	0.999809	+	0.0195333i	$0.00621803\pi$
$762$		0			0
$763$	−2.70182	+	0.476404i	−0.00354105	+	0.000624383i
$764$	140.853	−	190.432i	0.184362	−	0.249257i
$765$		0			0
$766$	−479.839	−	158.173i	−0.626421	−	0.206493i
$767$	40.2115	−	110.480i	0.0524270	−	0.144042i
$768$		0			0
$769$	882.484	+	740.492i	1.14757	+	0.962928i	0.999660	−	0.0260723i	$-0.00830000\pi$
$769$	882.484	+	740.492i	1.14757	+	0.962928i	0.147913	+	0.989000i	$0.452744\pi$
$770$	8.31089	+	4.46452i	0.0107934	+	0.00579808i
$771$		0			0
$772$	−512.990	+	31.4797i	−0.664495	+	0.0407769i
$773$	35.0856	−	60.7701i	0.0453889	−	0.0786159i	−0.842438	−	0.538793i	$-0.818881\pi$
$773$	35.0856	−	60.7701i	0.0453889	−	0.0786159i	0.887827	+	0.460177i	$0.152214\pi$
$774$		0			0
$775$	115.043	−	66.4199i	0.148442	−	0.0857030i
$776$	747.858	+	740.912i	0.963735	+	0.954783i
$777$		0			0
$778$	571.257	−	353.585i	0.734264	−	0.454479i
$779$	−304.045	−	53.6113i	−0.390302	−	0.0688207i
$780$		0			0
$781$	−296.731	+	248.987i	−0.379937	+	0.318805i
$782$	216.034	+	1038.10i	0.276259	+	1.32749i
$783$		0			0
$784$	530.009	−	568.825i	0.676032	−	0.725543i
$785$	239.427	−	200.903i	0.305003	−	0.255928i
$786$		0			0
$787$	−206.953	−	36.4914i	−0.262965	−	0.0463678i	0.0406112	−	0.999175i	$-0.487069\pi$
$787$	−206.953	−	36.4914i	−0.262965	−	0.0463678i	−0.303576	+	0.952807i	$0.598181\pi$
$788$	682.422	−	647.856i	0.866017	−	0.822152i
$789$		0			0
$790$	−371.935	+	148.431i	−0.470804	+	0.187887i
$791$	47.3532	−	27.3394i	0.0598650	−	0.0345631i
$792$		0			0
$793$	−3.75126	+	6.49737i	−0.00473046	+	0.00819340i
$794$	−453.670	−	65.7322i	−0.571372	−	0.0827862i
$795$		0			0
$796$	−344.049	+	1162.35i	−0.432222	+	1.46024i
$797$	−94.9924	−	79.7081i	−0.119187	−	0.100010i	0.581246	−	0.813728i	$-0.302565\pi$
$797$	−94.9924	−	79.7081i	−0.119187	−	0.100010i	−0.700433	+	0.713718i	$0.747010\pi$
$798$		0			0
$799$	−250.794	+	689.052i	−0.313885	+	0.862393i
$800$	326.792	+	594.952i	0.408490	+	0.743690i
$801$		0			0
$802$	443.936	+	497.287i	0.553536	+	0.620059i
$803$	−248.589	+	43.8329i	−0.309575	+	0.0545865i
$804$		0			0
$805$	44.6374	−	16.2467i	0.0554502	−	0.0201822i
$806$	16.4228	−	0.503420i	0.0203757	−	0.000624591i
$807$		0			0
$808$	29.5903	−	112.530i	0.0366216	−	0.139270i
$809$	634.664			0.784504			0.392252	−	0.919858i	$-0.371696\pi$
$809$	634.664			0.784504			0.392252	+	0.919858i	$0.371696\pi$
$810$		0			0
$811$		−	421.500i		−	0.519728i	−0.965645	−	0.259864i	$-0.916322\pi$
$811$		−	421.500i		−	0.519728i	0.965645	−	0.259864i	$-0.0836778\pi$
$812$	100.296	+	49.9807i	0.123518	+	0.0615526i
$813$		0			0
$814$	258.003	−	7.90877i	0.316957	−	0.00971593i
$815$	3.95200	+	10.8580i	0.00484909	+	0.0133228i
$816$		0			0
$817$	−72.2883	−	409.967i	−0.0884801	−	0.501796i
$818$	−851.783	−	954.149i	−1.04130	−	1.16644i
$819$		0			0
$820$	19.8456	−	174.496i	0.0242020	−	0.212800i
$821$	−455.794	−	165.895i	−0.555169	−	0.202065i	0.0491727	−	0.998790i	$-0.484342\pi$
$821$	−455.794	−	165.895i	−0.555169	−	0.202065i	−0.604342	+	0.796725i	$0.706564\pi$
$822$		0			0
$823$	−119.857	+	142.839i	−0.145634	+	0.173559i	−0.833930	−	0.551870i	$-0.813914\pi$
$823$	−119.857	+	142.839i	−0.145634	+	0.173559i	0.688296	+	0.725430i	$0.258359\pi$
$824$	−74.7380	+	902.754i	−0.0907014	+	1.09558i
$825$		0			0
$826$	113.258	+	16.4099i	0.137116	+	0.0198667i
$827$	86.7525	+	50.0866i	0.104900	+	0.0605642i	0.551532	−	0.834154i	$-0.314043\pi$
$827$	86.7525	+	50.0866i	0.104900	+	0.0605642i	−0.446632	+	0.894718i	$0.647377\pi$
$828$		0			0
$829$	−188.683	−	326.808i	−0.227603	−	0.394220i	0.729494	−	0.683987i	$-0.239756\pi$
$829$	−188.683	−	326.808i	−0.227603	−	0.394220i	−0.957097	+	0.289767i	$0.906422\pi$
$830$	21.8016	−	8.70049i	0.0262669	−	0.0104825i
$831$		0			0
$832$	0.783481	+	83.9541i	0.000941684	+	0.100906i
$833$	117.020	−	663.652i	0.140480	−	0.796701i
$834$		0			0
$835$	8.35330	+	9.95507i	0.0100040	+	0.0119222i
$836$	190.560	−	82.9035i	0.227942	−	0.0991668i
$837$		0			0
$838$	124.360	+	597.582i	0.148401	+	0.713105i
$839$	1017.34	+	1212.42i	1.21256	+	1.44508i	0.860766	+	0.509001i	$0.169985\pi$
$839$	1017.34	+	1212.42i	1.21256	+	1.44508i	0.351798	+	0.936076i	$0.385570\pi$
$840$		0			0
$841$	188.304	−	1067.92i	0.223905	−	1.26983i
$842$	−255.712	+	158.275i	−0.303695	+	0.187975i
$843$		0			0
$844$	360.160	−	238.489i	0.426729	−	0.282570i
$845$	162.779	+	281.942i	0.192638	+	0.333659i
$846$		0			0
$847$	58.9348	+	34.0260i	0.0695806	+	0.0401724i
$848$	984.032	−	501.890i	1.16042	−	0.591851i
$849$		0			0
$850$	518.303	+	278.427i	0.609769	+	0.327561i
$851$	835.426	−	995.622i	0.981699	−	1.16994i
$852$		0			0
$853$	852.409	+	310.251i	0.999307	+	0.363718i	0.789317	−	0.613986i	$-0.210435\pi$
$853$	852.409	+	310.251i	0.999307	+	0.363718i	0.209990	+	0.977704i	$0.432657\pi$
$854$	−6.93564	−	2.28626i	−0.00812136	−	0.00267712i
$855$		0			0
$856$	−199.481	+	433.051i	−0.233038	+	0.505901i
$857$	223.028	+	1264.85i	0.260242	+	1.47591i	0.782249	+	0.622966i	$0.214072\pi$
$857$	223.028	+	1264.85i	0.260242	+	1.47591i	−0.522007	+	0.852941i	$0.674816\pi$
$858$		0			0
$859$	297.432	+	817.186i	0.346253	+	0.951323i	0.983539	+	0.180695i	$0.0578348\pi$
$859$	297.432	+	817.186i	0.346253	+	0.951323i	−0.637286	+	0.770627i	$0.719943\pi$
$860$	230.249	−	55.3271i	0.267732	−	0.0643338i
$861$		0			0
$862$	872.245	+	687.480i	1.01189	+	0.797541i
$863$			514.846i			0.596577i	0.954476	+	0.298289i	$0.0964158\pi$
$863$			514.846i			0.596577i	−0.954476	+	0.298289i	$0.903584\pi$
$864$		0			0
$865$	45.3185			0.0523913
$866$	−480.936	+	610.191i	−0.555353	+	0.704609i
$867$		0			0
$868$	3.73664	+	15.5504i	0.00430488	+	0.0179152i
$869$	367.011	−	133.581i	0.422338	−	0.153718i
$870$		0			0
$871$	−158.517	+	27.9508i	−0.181994	+	0.0320904i
$872$	−31.2234	−	14.3827i	−0.0358066	−	0.0164939i
$873$		0			0
$874$	327.583	−	993.764i	0.374809	−	1.13703i
$875$	19.6394	−	53.9587i	0.0224450	−	0.0616671i
$876$		0			0
$877$	277.892	+	233.179i	0.316867	+	0.265883i	0.787323	−	0.616540i	$-0.211466\pi$
$877$	277.892	+	233.179i	0.316867	+	0.265883i	−0.470456	+	0.882423i	$0.655911\pi$
$878$	−147.190	+	274.001i	−0.167643	+	0.312074i
$879$		0			0
$880$	53.7096	+	105.306i	0.0610337	+	0.119666i
$881$	−69.9962	+	121.237i	−0.0794508	+	0.137613i	−0.903013	−	0.429613i	$-0.858650\pi$
$881$	−69.9962	+	121.237i	−0.0794508	+	0.137613i	0.823562	+	0.567226i	$0.191983\pi$
$882$		0			0
$883$	−324.157	+	187.152i	−0.367108	+	0.211950i	−0.672194	−	0.740375i	$-0.734648\pi$
$883$	−324.157	+	187.152i	−0.367108	+	0.211950i	0.305086	+	0.952325i	$0.401315\pi$
$884$	40.1776	+	60.6751i	0.0454497	+	0.0686370i
$885$		0			0
$886$	−549.425	−	887.660i	−0.620118	−	1.00187i
$887$	−497.269	−	87.6819i	−0.560619	−	0.0988522i	−0.113844	−	0.993499i	$-0.536316\pi$
$887$	−497.269	−	87.6819i	−0.560619	−	0.0988522i	−0.446775	+	0.894646i	$0.647427\pi$
$888$		0			0
$889$	−71.8323	+	60.2744i	−0.0808012	+	0.0678003i
$890$	278.332	−	57.9223i	0.312732	−	0.0650813i
$891$		0			0
$892$	−300.413	−	690.521i	−0.336785	−	0.774126i
$893$	554.316	−	465.126i	0.620735	−	0.520858i
$894$		0			0
$895$	−279.685	−	49.3161i	−0.312498	−	0.0551018i
$896$	−79.8493	+	17.3960i	−0.0891175	+	0.0194152i
$897$		0			0
$898$	169.647	+	425.098i	0.188916	+	0.473383i
$899$	237.975	−	137.395i	0.264711	−	0.152831i
$900$		0			0
$901$	478.728	−	829.181i	0.531329	−	0.920289i
$902$	−24.5606	+	169.512i	−0.0272291	+	0.187929i
$903$		0			0
$904$	682.803	+	56.5284i	0.755313	+	0.0625315i
$905$	403.769	+	338.802i	0.446154	+	0.374367i
$906$		0			0
$907$	−224.910	+	617.936i	−0.247972	+	0.681296i	0.751789	+	0.659404i	$0.229191\pi$
$907$	−224.910	+	617.936i	−0.247972	+	0.681296i	−0.999760	+	0.0218922i	$0.993031\pi$
$908$	−1573.73	−	178.982i	−1.73318	−	0.197117i
$909$		0			0
$910$	2.43199	−	2.17108i	0.00267252	−	0.00238580i
$911$	968.198	−	170.719i	1.06279	−	0.187398i	0.385194	−	0.922836i	$-0.374135\pi$
$911$	968.198	−	170.719i	1.06279	−	0.187398i	0.677592	+	0.735438i	$0.263023\pi$
$912$		0			0
$913$	−21.5129	+	7.83007i	−0.0235629	+	0.00857620i
$914$	−42.9332	−	1400.58i	−0.0469728	−	1.53237i
$915$		0			0
$916$	−289.666	+	581.273i	−0.316229	+	0.634578i
$917$	−121.875			−0.132906
$918$		0			0
$919$		−	464.177i		−	0.505090i	−0.967585	−	0.252545i	$-0.918732\pi$
$919$		−	464.177i		−	0.505090i	0.967585	−	0.252545i	$-0.0812675\pi$
$920$	575.645	+	151.368i	0.625701	+	0.164531i
$921$		0			0
$922$	−36.1943	−	1180.75i	−0.0392563	−	1.28064i
$923$	45.7813	+	125.783i	0.0496005	+	0.136276i
$924$		0			0
$925$	−125.229	−	710.207i	−0.135382	−	0.767791i
$926$	213.022	−	190.168i	0.230045	−	0.205365i
$927$		0			0
$928$	675.996	+	1230.71i	0.728444	+	1.32619i
$929$	199.079	+	72.4587i	0.214293	+	0.0779964i	0.446936	−	0.894566i	$-0.352515\pi$
$929$	199.079	+	72.4587i	0.214293	+	0.0779964i	−0.232643	+	0.972562i	$0.574737\pi$
$930$		0			0
$931$	−427.458	+	509.425i	−0.459139	+	0.547180i
$932$	−1290.89	−	382.094i	−1.38507	−	0.409973i
$933$		0			0
$934$	−95.2960	+	657.712i	−0.102030	+	0.704189i
$935$	88.7346	+	51.2309i	0.0949033	+	0.0547924i
$936$		0			0
$937$	539.632	+	934.670i	0.575914	+	0.997513i	0.995942	+	0.0900016i	$0.0286872\pi$
$937$	539.632	+	934.670i	0.575914	+	0.997513i	−0.420027	+	0.907512i	$0.637979\pi$
$938$	−58.0722	−	145.516i	−0.0619107	−	0.155135i
$939$		0			0
$940$	283.399	+	298.519i	0.301488	+	0.317574i
$941$	−196.302	+	1113.28i	−0.208610	+	1.18308i	0.683048	+	0.730373i	$0.260654\pi$
$941$	−196.302	+	1113.28i	−0.208610	+	1.18308i	−0.891658	+	0.452710i	$0.850457\pi$
$942$		0			0
$943$	554.359	+	660.659i	0.587867	+	0.700593i
$944$	1049.13	+	977.537i	1.11137	+	1.03553i
$945$		0			0
$946$	−226.109	+	47.0544i	−0.239015	+	0.0497404i
$947$	−923.771	−	1100.91i	−0.975471	−	1.16252i	−0.986695	−	0.162584i	$-0.948017\pi$
$947$	−923.771	−	1100.91i	−0.975471	−	1.16252i	0.0112237	−	0.999937i	$-0.496427\pi$
$948$		0			0
$949$	−15.1470	+	85.9031i	−0.0159611	+	0.0905196i
$950$	−305.569	−	493.682i	−0.321651	−	0.519665i
$951$		0			0
$952$	−49.8529	+	50.3203i	−0.0523665	+	0.0528575i
$953$	−604.893	−	1047.71i	−0.634725	−	1.09938i	−0.986573	−	0.163319i	$-0.947780\pi$
$953$	−604.893	−	1047.71i	−0.634725	−	1.09938i	0.351848	−	0.936057i	$-0.385553\pi$
$954$		0			0
$955$	−99.8057	−	57.6228i	−0.104509	−	0.0603380i
$956$	−7.20129	−	117.351i	−0.00753273	−	0.122753i
$957$		0			0
$958$	135.330	−	251.923i	0.141263	−	0.262968i
$959$	25.5535	−	30.4535i	0.0266460	−	0.0317555i
$960$		0			0
$961$	−866.192	−	315.268i	−0.901345	−	0.328063i
$962$	27.9251	−	84.7144i	0.0290282	−	0.0880607i
$963$		0			0
$964$	649.962	+	480.743i	0.674234	+	0.498697i
$965$	43.4234	+	246.266i	0.0449983	+	0.255198i
$966$		0			0
$967$	−504.202	−	1385.28i	−0.521408	−	1.43256i	−0.868953	−	0.494894i	$-0.835207\pi$
$967$	−504.202	−	1385.28i	−0.521408	−	1.43256i	0.347545	−	0.937663i	$-0.387015\pi$
$968$	363.972	+	771.126i	0.376004	+	0.796618i
$969$		0			0
$970$	317.063	−	402.276i	0.326869	−	0.414718i
$971$			611.405i			0.629666i	0.949147	+	0.314833i	$0.101948\pi$
$971$			611.405i			0.629666i	−0.949147	+	0.314833i	$0.898052\pi$
$972$		0			0
$973$	162.351			0.166856
$974$	−374.103	−	294.858i	−0.384090	−	0.302729i
$975$		0			0
$976$	−55.0987	−	73.0571i	−0.0564536	−	0.0748535i
$977$	−1049.66	+	382.044i	−1.07437	+	0.391038i	−0.817808	−	0.575491i	$-0.804811\pi$
$977$	−1049.66	+	382.044i	−1.07437	+	0.391038i	−0.256559	+	0.966528i	$0.582589\pi$
$978$		0			0
$979$	−273.059	+	48.1476i	−0.278916	+	0.0491804i
$980$	−304.130	−	224.950i	−0.310337	−	0.229540i
$981$		0			0
$982$	−73.2696	−	24.1525i	−0.0746126	−	0.0245952i
$983$	557.110	−	1530.65i	0.566744	−	1.55712i	−0.242811	−	0.970074i	$-0.578070\pi$
$983$	557.110	−	1530.65i	0.566744	−	1.55712i	0.809555	−	0.587043i	$-0.199708\pi$
$984$		0			0
$985$	−350.716	−	294.286i	−0.356057	−	0.298767i
$986$	1072.15	+	575.949i	1.08738	+	0.584127i
$987$		0			0
$988$	−4.39850	−	71.6775i	−0.00445192	−	0.0725481i
$989$	−581.439	+	1007.08i	−0.587906	+	1.01828i
$990$		0			0
$991$	−880.472	+	508.341i	−0.888468	+	0.512957i	−0.873441	−	0.486930i	$-0.838117\pi$
$991$	−880.472	+	508.341i	−0.888468	+	0.512957i	−0.0150271	+	0.999887i	$0.504783\pi$
$992$	−72.5371	+	186.808i	−0.0731221	+	0.188314i
$993$		0			0
$994$	−110.787	+	68.5723i	−0.111455	+	0.0689862i
$995$	580.836	+	102.417i	0.583755	+	0.102932i
$996$		0			0
$997$	−781.216	+	655.518i	−0.783567	+	0.657491i	−0.944144	−	0.329532i	$-0.893109\pi$
$997$	−781.216	+	655.518i	−0.783567	+	0.657491i	0.160577	+	0.987023i	$0.448664\pi$
$998$	35.4999	+	170.586i	0.0355711	+	0.170928i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.11		204
3.2	odd	2		108.3.j.a.103.24	yes	204
4.3	odd	2	inner	324.3.j.a.199.5		204
12.11	even	2		108.3.j.a.103.30	yes	204
27.11	odd	18		108.3.j.a.43.30	yes	204
27.16	even	9	inner	324.3.j.a.127.5		204
108.11	even	18		108.3.j.a.43.24	✓	204
108.43	odd	18	inner	324.3.j.a.127.11		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.24	✓	204	108.11	even	18
108.3.j.a.43.30	yes	204	27.11	odd	18
108.3.j.a.103.24	yes	204	3.2	odd	2
108.3.j.a.103.30	yes	204	12.11	even	2
324.3.j.a.127.5		204	27.16	even	9	inner
324.3.j.a.127.11		204	108.43	odd	18	inner
324.3.j.a.199.5		204	4.3	odd	2	inner
324.3.j.a.199.11		204	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23803 + 1.57076i) q^{2} +(-0.934566 - 3.88929i) q^{4} +(-1.82883 + 0.665640i) q^{5} +(0.628756 - 0.110867i) q^{7} +(7.26616 + 3.34708i) q^{8} +O(q^{10})\)	\(q+(-1.23803 + 1.57076i) q^{2} +(-0.934566 - 3.88929i) q^{4} +(-1.82883 + 0.665640i) q^{5} +(0.628756 - 0.110867i) q^{7} +(7.26616 + 3.34708i) q^{8} +(1.21859 - 3.69674i) q^{10} +(-1.29839 + 3.56730i) q^{11} +(1.00493 + 0.843235i) q^{13} +(-0.604274 + 1.12488i) q^{14} +(-14.2532 + 7.26960i) q^{16} +(-6.93411 + 12.0102i) q^{17} +(11.8519 - 6.84271i) q^{19} +(4.29803 + 6.49077i) q^{20} +(-3.99592 - 6.45588i) q^{22} +(-37.6484 - 6.63843i) q^{23} +(-16.2496 + 13.6350i) q^{25} +(-2.56865 + 0.534550i) q^{26} +(-1.01881 - 2.34180i) q^{28} +(-33.6135 + 28.2051i) q^{29} +(-6.16725 - 1.08745i) q^{31} +(6.22706 - 31.3883i) q^{32} +(-10.2805 - 25.7608i) q^{34} +(-1.07609 + 0.621282i) q^{35} +(-16.9987 + 29.4426i) q^{37} +(-3.92478 + 27.0880i) q^{38} +(-15.5165 - 1.28460i) q^{40} +(-17.2815 - 14.5009i) q^{41} +(10.4038 - 28.5842i) q^{43} +(15.0877 + 1.71594i) q^{44} +(57.0372 - 50.9180i) q^{46} +(52.0711 - 9.18154i) q^{47} +(-45.6619 + 16.6196i) q^{49} +(-1.29986 - 42.4047i) q^{50} +(2.34041 - 4.69652i) q^{52} -69.0395 q^{53} -7.38825i q^{55} +(4.93972 + 1.29892i) q^{56} +(-2.68887 - 87.7175i) q^{58} +(-30.6528 - 84.2178i) q^{59} +(0.993107 + 5.63219i) q^{61} +(9.34337 - 8.34097i) q^{62} +(41.5941 + 48.6408i) q^{64} +(-2.39914 - 0.873214i) q^{65} +(-78.8696 + 93.9932i) q^{67} +(53.1917 + 15.7444i) q^{68} +(0.356349 - 2.45944i) q^{70} +(88.3661 + 51.0182i) q^{71} +(33.2465 + 57.5847i) q^{73} +(-25.2024 - 63.1517i) q^{74} +(-37.6897 - 39.7006i) q^{76} +(-0.420876 + 2.38691i) q^{77} +(-66.1314 - 78.8123i) q^{79} +(21.2277 - 22.7824i) q^{80} +(44.1725 - 9.19255i) q^{82} +(3.87639 + 4.61971i) q^{83} +(4.68683 - 26.5803i) q^{85} +(32.0186 + 51.7299i) q^{86} +(-21.3743 + 21.5747i) q^{88} +(36.5192 + 63.2530i) q^{89} +(0.725341 + 0.418776i) q^{91} +(9.36614 + 152.630i) q^{92} +(-50.0436 + 93.1582i) q^{94} +(-17.1204 + 20.4033i) q^{95} +(123.655 + 45.0069i) q^{97} +(30.4254 - 92.2993i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

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