LMFDB - Embedded newform 324.3.j.a.199.5

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			199.5
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76188 + 0.946462i) q^{2} +(2.20842 - 3.33510i) q^{4} +(-1.82883 + 0.665640i) q^{5} +(-0.628756 + 0.110867i) q^{7} +(-0.734424 + 7.96622i) q^{8} +O(q^{10})$	\(q+(-1.76188 + 0.946462i) q^{2} +(2.20842 - 3.33510i) q^{4} +(-1.82883 + 0.665640i) q^{5} +(-0.628756 + 0.110867i) q^{7} +(-0.734424 + 7.96622i) q^{8} +(2.59217 - 2.90370i) q^{10} +(1.29839 - 3.56730i) q^{11} +(1.00493 + 0.843235i) q^{13} +(1.00286 - 0.790427i) q^{14} +(-6.24575 - 14.7306i) q^{16} +(-6.93411 + 12.0102i) q^{17} +(-11.8519 + 6.84271i) q^{19} +(-1.81885 + 7.56935i) q^{20} +(1.08871 + 7.51402i) q^{22} +(37.6484 + 6.63843i) q^{23} +(-16.2496 + 13.6350i) q^{25} +(-2.56865 - 0.534550i) q^{26} +(-1.01881 + 2.34180i) q^{28} +(-33.6135 + 28.2051i) q^{29} +(6.16725 + 1.08745i) q^{31} +(24.9462 + 20.0421i) q^{32} +(0.849827 - 27.7234i) q^{34} +(1.07609 - 0.621282i) q^{35} +(-16.9987 + 29.4426i) q^{37} +(14.4053 - 23.2734i) q^{38} +(-3.95950 - 15.0577i) q^{40} +(-17.2815 - 14.5009i) q^{41} +(-10.4038 + 28.5842i) q^{43} +(-9.02990 - 12.2084i) q^{44} +(-72.6148 + 23.9367i) q^{46} +(-52.0711 + 9.18154i) q^{47} +(-45.6619 + 16.6196i) q^{49} +(15.7247 - 39.4028i) q^{50} +(5.03157 - 1.48932i) q^{52} -69.0395 q^{53} +7.38825i q^{55} +(-0.421414 - 5.09023i) q^{56} +(32.5279 - 81.5079i) q^{58} +(30.6528 + 84.2178i) q^{59} +(0.993107 + 5.63219i) q^{61} +(-11.8952 + 3.92111i) q^{62} +(-62.9212 - 11.7012i) q^{64} +(-2.39914 - 0.873214i) q^{65} +(78.8696 - 93.9932i) q^{67} +(24.7419 + 49.6496i) q^{68} +(-1.30792 + 2.11310i) q^{70} +(-88.3661 - 51.0182i) q^{71} +(33.2465 + 57.5847i) q^{73} +(2.08332 - 67.9629i) q^{74} +(-3.35292 + 54.6389i) q^{76} +(-0.420876 + 2.38691i) q^{77} +(66.1314 + 78.8123i) q^{79} +(21.2277 + 22.7824i) q^{80} +(44.1725 + 9.19255i) q^{82} +(-3.87639 - 4.61971i) q^{83} +(4.68683 - 26.5803i) q^{85} +(-8.72362 - 60.2086i) q^{86} +(27.4643 + 12.9632i) q^{88} +(36.5192 + 63.2530i) q^{89} +(-0.725341 - 0.418776i) q^{91} +(105.283 - 110.901i) q^{92} +(83.0529 - 65.4601i) q^{94} +(17.1204 - 20.4033i) q^{95} +(123.655 + 45.0069i) q^{97} +(64.7209 - 72.4989i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.76188	+	0.946462i	−0.880938	+	0.473231i
$2$	−1.76188	+	0.946462i	−0.880938	+	0.473231i
$3$		0			0
$3$		0			0
$4$	2.20842	−	3.33510i	0.552105	−	0.833774i
$5$	−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	−0.218379	−	0.975864i	$-0.570077\pi$
$7$	−0.628756	+	0.110867i	−0.0898223	+	0.0158381i	0.128556	+	0.991702i	$0.458966\pi$
$8$	−0.734424	+	7.96622i	−0.0918030	+	0.995777i
$9$		0			0
$10$	2.59217	−	2.90370i	0.259217	−	0.290370i
$11$	1.29839	−	3.56730i	0.118035	−	0.324300i	−0.866579	−	0.499040i	$-0.833686\pi$
$11$	1.29839	−	3.56730i	0.118035	−	0.324300i	0.984615	+	0.174740i	$0.0559084\pi$
$12$		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	$0.706155\pi$
$14$	1.00286	−	0.790427i	0.0716328	−	0.0564590i
$15$		0			0
$16$	−6.24575	−	14.7306i	−0.390360	−	0.920662i
$17$	−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	−0.778341	−	0.627841i	$-0.783939\pi$
$19$	−11.8519	+	6.84271i	−0.623785	+	0.360143i	0.154556	+	0.987984i	$0.450605\pi$
$20$	−1.81885	+	7.56935i	−0.0909427	+	0.378467i
$21$		0			0
$22$	1.08871	+	7.51402i	0.0494867	+	0.341546i
$23$	37.6484	+	6.63843i	1.63689	+	0.288627i	0.915021	−	0.403406i	$-0.132174\pi$
$23$	37.6484	+	6.63843i	1.63689	+	0.288627i	0.721865	+	0.692034i	$0.243285\pi$
$24$		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	0.272232	−	0.962232i	$-0.412238\pi$
$31$	6.16725	+	1.08745i	0.198944	+	0.0350791i	−0.0732883	+	0.997311i	$0.523349\pi$
$32$	24.9462	+	20.0421i	0.779569	+	0.626317i
$33$		0			0
$34$	0.849827	−	27.7234i	0.0249949	−	0.815395i
$35$	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	$0.318611\pi$
$38$	14.4053	−	23.2734i	0.379086	−	0.612458i
$39$		0			0
$40$	−3.95950	−	15.0577i	−0.0989874	−	0.376443i
$41$	−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	$0.226189\pi$
$43$	−10.4038	+	28.5842i	−0.241948	+	0.664748i	−0.999922	+	0.0124630i	$0.996033\pi$
$44$	−9.02990	−	12.2084i	−0.205225	−	0.277463i
$45$		0			0
$46$	−72.6148	+	23.9367i	−1.57858	+	0.520362i
$47$	−52.0711	+	9.18154i	−1.10790	+	0.195352i	−0.697521	−	0.716565i	$-0.745714\pi$
$47$	−52.0711	+	9.18154i	−1.10790	+	0.195352i	−0.410376	+	0.911917i	$0.634602\pi$
$48$		0			0
$49$	−45.6619	+	16.6196i	−0.931875	+	0.339175i
$50$	15.7247	−	39.4028i	0.314494	−	0.788056i
$51$		0			0
$52$	5.03157	−	1.48932i	0.0967610	−	0.0286407i
$53$	−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
$56$	−0.421414	−	5.09023i	−0.00752525	−	0.0908969i
$57$		0			0
$58$	32.5279	−	81.5079i	0.560825	−	1.40531i
$59$	30.6528	+	84.2178i	0.519538	+	1.42742i	0.871030	+	0.491229i	$0.163452\pi$
$59$	30.6528	+	84.2178i	0.519538	+	1.42742i	−0.351492	+	0.936191i	$0.614326\pi$
$60$		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	$0.929517\pi$
$62$	−11.8952	+	3.92111i	−0.191858	+	0.0632437i
$63$		0			0
$64$	−62.9212	−	11.7012i	−0.983144	−	0.182831i
$65$	−2.39914	−	0.873214i	−0.0369098	−	0.0134341i
$66$		0			0
$67$	78.8696	−	93.9932i	1.17716	−	1.40288i	0.280677	−	0.959802i	$-0.409441\pi$
$67$	78.8696	−	93.9932i	1.17716	−	1.40288i	0.896482	−	0.443081i	$-0.146115\pi$
$68$	24.7419	+	49.6496i	0.363851	+	0.730141i
$69$		0			0
$70$	−1.30792	+	2.11310i	−0.0186846	+	0.0301872i
$71$	−88.3661	−	51.0182i	−1.24459	−	0.718566i	−0.274567	−	0.961568i	$-0.588535\pi$
$71$	−88.3661	−	51.0182i	−1.24459	−	0.718566i	−0.970026	+	0.243002i	$0.921868\pi$
$72$		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	$0.682818\pi$
$74$	2.08332	−	67.9629i	0.0281529	−	0.918417i
$75$		0			0
$76$	−3.35292	+	54.6389i	−0.0441174	+	0.718933i
$77$	−0.420876	+	2.38691i	−0.00546593	+	0.0309988i
$78$		0			0
$79$	66.1314	+	78.8123i	0.837106	+	0.997624i	0.999940	+	0.0109706i	$0.00349212\pi$
$79$	66.1314	+	78.8123i	0.837106	+	0.997624i	−0.162834	+	0.986654i	$0.552063\pi$
$80$	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	0.742187	−	0.670193i	$-0.233789\pi$
$83$	−3.87639	−	4.61971i	−0.0467035	−	0.0556591i	−0.788891	+	0.614534i	$0.789344\pi$
$84$		0			0
$85$	4.68683	−	26.5803i	0.0551391	−	0.312710i
$86$	−8.72362	−	60.2086i	−0.101437	−	0.700099i
$87$		0			0
$88$	27.4643	+	12.9632i	0.312094	+	0.147309i
$89$	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
$92$	105.283	−	110.901i	1.14438	−	1.20544i
$93$		0			0
$94$	83.0529	−	65.4601i	0.883542	−	0.696384i
$95$	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	$0.373826\pi$
$98$	64.7209	−	72.4989i	0.660417	−	0.739784i
$99$		0			0
$100$	9.58819	+	84.3057i	0.0958819	+	0.843057i
$101$	−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	$-0.925868\pi$
$103$	−38.7271	−	106.402i	−0.375991	−	1.03303i	0.597012	−	0.802232i	$-0.296355\pi$
$104$	−7.45543	+	7.38618i	−0.0716869	+	0.0710210i
$105$		0			0
$106$	121.639	−	65.3432i	1.14754	−	0.616446i
$107$		−	59.5984i		−	0.556994i	−0.960437	−	0.278497i	$-0.910164\pi$
$107$		−	59.5984i		−	0.556994i	0.960437	−	0.278497i	$-0.0898363\pi$
$108$		0			0
$109$	−4.29709			−0.0394229			−0.0197114	−	0.999806i	$-0.506275\pi$
$109$	−4.29709			−0.0394229			−0.0197114	+	0.999806i	$0.506275\pi$
$110$	−6.99269	−	13.0172i	−0.0635699	−	0.118338i
$111$		0			0
$112$	5.56019	+	8.56950i	0.0496445	+	0.0765134i
$113$	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
$116$	19.8340	+	174.393i	0.170982	+	1.50339i
$117$		0			0
$118$	−133.715	−	119.370i	−1.13318	−	1.01161i
$119$	3.02833	−	8.32027i	0.0254481	−	0.0699182i
$120$		0			0
$121$	81.6516	+	68.5138i	0.674806	+	0.566230i
$122$	−7.08038	−	8.98328i	−0.0580359	−	0.0736335i
$123$		0			0
$124$	17.2467	−	18.1668i	0.139086	−	0.146507i
$125$	44.9692	−	77.8890i	0.359754	−	0.623112i
$126$		0			0
$127$	127.194	−	73.4353i	1.00153	−	0.578231i	0.0928261	−	0.995682i	$-0.470410\pi$
$127$	127.194	−	73.4353i	1.00153	−	0.578231i	0.908699	+	0.417451i	$0.137077\pi$
$128$	121.934	−	38.9365i	0.952611	−	0.304192i
$129$		0			0
$130$	5.05344	−	0.732194i	0.0388726	−	0.00563226i
$131$	187.990	+	33.1476i	1.43504	+	0.253035i	0.836459	−	0.548030i	$-0.184622\pi$
$131$	187.990	+	33.1476i	1.43504	+	0.253035i	0.598577	+	0.801065i	$0.295733\pi$
$132$		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	−0.830631	−	0.556823i	$-0.812020\pi$
$139$	−250.424	−	44.1566i	−1.80161	−	0.317673i	−0.970983	+	0.239150i	$0.923131\pi$
$140$	0.304428	−	4.96092i	0.00217448	−	0.0354351i
$141$		0			0
$142$	203.977	+	6.25266i	1.43646	+	0.0440328i
$143$	4.31286	−	2.49003i	0.0301599	−	0.0174128i
$144$		0			0
$145$	42.6991	−	73.9569i	0.294476	−	0.510048i
$146$	−113.078	−	69.9906i	−0.774507	−	0.479388i
$147$		0			0
$148$	60.6537	+	121.714i	0.409822	+	0.822392i
$149$	−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	$0.388467\pi$
$151$	−79.0367	+	217.151i	−0.523422	+	1.43809i	−0.866688	+	0.498851i	$0.833756\pi$
$152$	−45.8062	−	99.4404i	−0.301356	−	0.654213i
$153$		0			0
$154$	−1.51758	−	4.60378i	−0.00985444	−	0.0298947i
$155$	−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	$0.559780\pi$
$158$	−191.108	−	76.2668i	−1.20955	−	0.482701i
$159$		0			0
$160$	−58.9632	−	20.0485i	−0.368520	−	0.125303i
$161$	−24.4076			−0.151600
$162$		0			0
$163$			5.93715i			0.0364242i	0.999834	+	0.0182121i	$0.00579741\pi$
$163$			5.93715i			0.0364242i	−0.999834	+	0.0182121i	$0.994203\pi$
$164$	−86.5269	+	25.6115i	−0.527603	+	0.156167i
$165$		0			0
$166$	11.2021	+	4.47050i	0.0674825	+	0.0269307i
$167$	2.28378	+	6.27464i	0.0136753	+	0.0375727i	0.946342	−	0.323165i	$-0.104747\pi$
$167$	2.28378	+	6.27464i	0.0136753	+	0.0375727i	−0.932667	+	0.360738i	$0.882525\pi$
$168$		0			0
$169$	−29.0477	−	164.738i	−0.171880	−	0.974779i
$170$	16.8996	+	51.2672i	0.0994096	+	0.301571i
$171$		0			0
$172$	72.3550	+	97.8235i	0.420669	+	0.568741i
$173$	−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
$176$	−60.6579	+	3.15440i	−0.344647	+	0.0179227i
$177$		0			0
$178$	−124.209	−	76.8801i	−0.697802	−	0.431911i
$179$	−126.375	−	72.9626i	−0.706005	−	0.407612i	0.103575	−	0.994622i	$-0.466972\pi$
$179$	−126.375	−	72.9626i	−0.706005	−	0.407612i	−0.809580	+	0.587009i	$0.800305\pi$
$180$		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	$-0.435719\pi$
$182$	1.67432	+	0.0513241i	0.00919954	+	0.000282000i
$183$		0			0
$184$	−80.5330	+	295.040i	−0.437679	+	1.60348i
$185$	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	0.657143	−	0.753766i	$-0.271765\pi$
$191$	−38.0631	−	45.3618i	−0.199283	−	0.237497i	−0.856426	+	0.516269i	$0.827320\pi$
$192$		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	$-0.0524624\pi$
$194$	−260.463	+	37.7385i	−1.34259	+	0.194528i
$195$		0			0
$196$	−45.4128	+	188.990i	−0.231698	+	0.964234i
$197$	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	0.983542	−	0.180680i	$-0.0578298\pi$
$199$	262.449	+	151.525i	1.31884	+	0.761432i	0.335298	+	0.942112i	$0.391163\pi$
$200$	−96.6853	−	139.461i	−0.483427	−	0.697307i
$201$		0			0
$202$	18.0064	+	22.8458i	0.0891408	+	0.113098i
$203$	18.0077	−	21.4607i	0.0887079	−	0.105718i
$204$		0			0
$205$	41.2574	+	15.0165i	0.201256	+	0.0732511i
$206$	168.937	+	150.813i	0.820085	+	0.732102i
$207$		0			0
$208$	6.14482	−	20.0698i	0.0295424	−	0.0964896i
$209$	9.02156	+	51.1638i	0.0431654	+	0.244803i
$210$		0			0
$211$	−36.9350	−	101.478i	−0.175047	−	0.480939i	0.820880	−	0.571101i	$-0.193484\pi$
$211$	−36.9350	−	101.478i	−0.175047	−	0.480939i	−0.995927	+	0.0901624i	$0.971261\pi$
$212$	−152.468	+	230.254i	−0.719190	+	1.08610i
$213$		0			0
$214$	56.4076	+	105.005i	0.263587	+	0.490678i
$215$		−	59.2008i		−	0.275353i
$216$		0			0
$217$	−3.99826			−0.0184252
$218$	7.57095	−	4.06703i	0.0347291	−	0.0186561i
$219$		0			0
$220$	24.6405	+	16.3164i	0.112002	+	0.0741653i
$221$	−17.0957	+	6.22234i	−0.0773562	+	0.0281554i
$222$		0			0
$223$	−185.399	+	32.6909i	−0.831388	+	0.146596i	−0.573114	−	0.819476i	$-0.694265\pi$
$223$	−185.399	+	32.6909i	−0.831388	+	0.146596i	−0.258274	+	0.966072i	$0.583154\pi$
$224$	−17.9071	−	9.83591i	−0.0799423	−	0.0439103i
$225$		0			0
$226$	−114.068	+	127.777i	−0.504726	+	0.565383i
$227$	−135.429	+	372.089i	−0.596605	+	1.63916i	0.161386	+	0.986891i	$0.448404\pi$
$227$	−135.429	+	372.089i	−0.596605	+	1.63916i	−0.757990	+	0.652266i	$0.773818\pi$
$228$		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	$0.837572\pi$
$230$	116.867	−	92.1115i	0.508118	−	0.400485i
$231$		0			0
$232$	−200.001	−	288.487i	−0.862075	−	1.24348i
$233$	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
$236$	348.569	+	83.7583i	1.47699	+	0.354908i
$237$		0			0
$238$	2.53927	+	17.5255i	0.0106692	+	0.0736365i
$239$	−28.9465	−	5.10405i	−0.121115	−	0.0213559i	0.112762	−	0.993622i	$-0.464030\pi$
$239$	−28.9465	−	5.10405i	−0.121115	−	0.0213559i	−0.233877	+	0.972266i	$0.575141\pi$
$240$		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
$248$	−13.1923	+	48.3310i	−0.0531946	+	0.194883i
$249$		0			0
$250$	−5.51131	+	179.792i	−0.0220453	+	0.719170i
$251$	288.384	−	166.498i	1.14894	−	0.663340i	0.200310	−	0.979733i	$-0.435805\pi$
$251$	288.384	−	166.498i	1.14894	−	0.663340i	0.948628	+	0.316393i	$0.102472\pi$
$252$		0			0
$253$	72.5635	−	125.684i	0.286812	−	0.496774i
$254$	−154.596	+	249.768i	−0.608646	+	0.983339i
$255$		0			0
$256$	−177.981	+	184.007i	−0.695239	+	0.718779i
$257$	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
$260$	−8.21055	+	6.07293i	−0.0315791	+	0.0233574i
$261$		0			0
$262$	−362.588	+	119.523i	−1.38392	+	0.456194i
$263$	−255.021	+	44.9671i	−0.969662	+	0.170978i	−0.635978	−	0.771707i	$-0.719403\pi$
$263$	−255.021	+	44.9671i	−0.969662	+	0.170978i	−0.333684	+	0.942685i	$0.608292\pi$
$264$		0			0
$265$	126.262	−	45.9555i	0.476459	−	0.173417i
$266$	−6.47715	+	16.2303i	−0.0243502	+	0.0610163i
$267$		0			0
$268$	−139.299	−	470.614i	−0.519773	−	1.75602i
$269$	−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	$-0.908169\pi$
$271$		−	154.204i		−	0.569018i	0.958673	−	0.284509i	$-0.0918306\pi$
$272$	220.227	+	27.1307i	0.809657	+	0.0997451i
$273$		0			0
$274$	−46.1581	+	115.662i	−0.168460	+	0.422126i
$275$	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	$-0.283315\pi$
$278$	483.009	−	159.219i	1.73744	−	0.572729i
$279$		0			0
$280$	4.15896	+	9.02866i	0.0148534	+	0.0322452i
$281$	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	−0.748638	−	0.662978i	$-0.769292\pi$
$283$	9.69771	−	11.5573i	0.0342675	−	0.0408384i	0.782906	+	0.622140i	$0.213737\pi$
$284$	−365.300	+	182.040i	−1.28627	+	0.640986i
$285$		0			0
$286$	−5.24201	+	8.46908i	−0.0183287	+	0.0296122i
$287$	12.4735	+	7.20160i	0.0434618	+	0.0250927i
$288$		0			0
$289$	48.3362	+	83.7208i	0.167253	+	0.289691i
$290$	−5.23309	+	170.716i	−0.0180451	+	0.588676i
$291$		0			0
$292$	265.473	+	16.2908i	0.909154	+	0.0557904i
$293$	−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
$302$	−66.2726	−	457.399i	−0.219446	−	1.51457i
$303$		0			0
$304$	174.821	+	131.848i	0.575070	+	0.433710i
$305$	−5.56524	−	9.63927i	−0.0182467	−	0.0316042i
$306$		0			0
$307$	13.9520	+	8.05517i	0.0454461	+	0.0262383i	0.522551	−	0.852608i	$-0.324980\pi$
$307$	13.9520	+	8.05517i	0.0454461	+	0.0262383i	−0.477105	+	0.878846i	$0.658314\pi$
$308$	7.03110	+	6.67496i	0.0228282	+	0.0216719i
$309$		0			0
$310$	19.1442	−	15.0890i	0.0617555	−	0.0486740i
$311$	120.014	−	143.028i	0.385899	−	0.459896i	−0.537768	−	0.843093i	$-0.680732\pi$
$311$	120.014	−	143.028i	0.385899	−	0.459896i	0.923667	+	0.383197i	$0.125177\pi$
$312$		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	$0.355462\pi$
$314$	213.898	−	239.604i	0.681205	−	0.763071i
$315$		0			0
$316$	408.893	−	46.5039i	1.29396	−	0.147164i
$317$	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
$320$	122.861	−	20.4835i	0.383941	−	0.0640108i
$321$		0			0
$322$	43.0032	−	23.1009i	0.133550	−	0.0717418i
$323$		−	189.792i		−	0.587593i
$324$		0			0
$325$	−27.8271			−0.0856220
$326$	−5.61928	−	10.4605i	−0.0172371	−	0.0320875i
$327$		0			0
$328$	128.210	−	127.019i	0.390883	−	0.387252i
$329$	31.7221	−	11.5459i	0.0964197	−	0.0350939i
$330$		0			0
$331$	−105.075	+	18.5275i	−0.317446	+	0.0559743i	−0.330101	−	0.943946i	$-0.607083\pi$
$331$	−105.075	+	18.5275i	−0.317446	+	0.0559743i	0.0126549	+	0.999920i	$0.495972\pi$
$332$	−23.9679	+	2.72590i	−0.0721924	+	0.00821053i
$333$		0			0
$334$	−9.96244	−	8.89362i	−0.0298277	−	0.0266276i
$335$	−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	$0.639740\pi$
$338$	207.096	+	262.755i	0.612711	+	0.777382i
$339$		0			0
$340$	−78.2975	−	74.3316i	−0.230287	−	0.218622i
$341$	11.8868	−	20.5885i	0.0348586	−	0.0603768i
$342$		0			0
$343$	53.9606	−	31.1542i	0.157320	−	0.0908285i
$344$	−220.067	−	103.872i	−0.639729	−	0.301953i
$345$		0			0
$346$	46.0899	−	6.67798i	0.133208	−	0.0193005i
$347$	−134.500	−	23.7159i	−0.387607	−	0.0683456i	−0.0235511	−	0.999723i	$-0.507497\pi$
$347$	−134.500	−	23.7159i	−0.387607	−	0.0683456i	−0.364056	+	0.931377i	$0.618608\pi$
$348$		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
$356$	291.605	+	17.8944i	0.819114	+	0.0502651i
$357$		0			0
$358$	291.713	+	8.94211i	0.814842	+	0.0249780i
$359$	350.781	−	202.523i	0.977106	−	0.564132i	0.0757107	−	0.997130i	$-0.475877\pi$
$359$	350.781	−	202.523i	0.977106	−	0.564132i	0.901395	+	0.432998i	$0.142544\pi$
$360$		0			0
$361$	−86.8547	+	150.437i	−0.240595	+	0.416722i
$362$	460.567	+	285.072i	1.27228	+	0.787491i
$363$		0			0
$364$	−2.99852	+	1.49425i	−0.00823768	+	0.00410508i
$365$	−99.1330	−	83.1825i	−0.271597	−	0.227897i
$366$		0			0
$367$	194.549	−	534.518i	0.530105	−	1.45645i	−0.328841	−	0.944385i	$-0.606658\pi$
$367$	194.549	−	534.518i	0.530105	−	1.45645i	0.858946	−	0.512066i	$-0.171120\pi$
$368$	−137.355	−	596.045i	−0.373246	−	1.61969i
$369$		0			0
$370$	41.4288	+	125.679i	0.111970	+	0.339674i
$371$	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	$0.235939\pi$
$374$	−97.7943	−	39.0274i	−0.261482	−	0.104351i
$375$		0			0
$376$	−34.8999	−	421.553i	−0.0928189	−	1.12115i
$377$	−57.5627			−0.152686
$378$		0			0
$379$			374.262i			0.987499i	0.869604	+	0.493750i	$0.164374\pi$
$379$			374.262i			0.987499i	−0.869604	+	0.493750i	$0.835626\pi$
$380$	−30.2379	−	102.157i	−0.0795734	−	0.268835i
$381$		0			0
$382$	109.996	+	43.8967i	0.287947	+	0.114913i
$383$	−86.4006	−	237.384i	−0.225589	−	0.619801i	0.774327	−	0.632786i	$-0.218089\pi$
$383$	−86.4006	−	237.384i	−0.225589	−	0.619801i	−0.999916	+	0.0129854i	$0.995866\pi$
$384$		0			0
$385$	−0.819110	−	4.64540i	−0.00212756	−	0.0120660i
$386$	80.4515	+	244.060i	0.208424	+	0.632279i
$387$		0			0
$388$	423.186	−	313.009i	1.09068	−	0.806723i
$389$	−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
$392$	−98.8599	−	375.958i	−0.252194	−	0.959078i
$393$		0			0
$394$	−400.051	−	247.615i	−1.01536	−	0.628464i
$395$	−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	$0.740121\pi$
$398$	−605.816	−	18.5705i	−1.52215	−	0.0466596i
$399$		0			0
$400$	302.343	+	154.205i	0.755856	+	0.385512i
$401$	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	$0.769854\pi$
$410$	−86.9030	+	12.5914i	−0.211959	+	0.0307107i
$411$		0			0
$412$	−440.386	−	105.821i	−1.06890	−	0.256848i
$413$	−28.6100	−	49.5540i	−0.0692737	−	0.119986i
$414$		0			0
$415$	10.1643	+	5.86838i	0.0244924	+	0.0141407i
$416$	8.16891	+	41.1764i	0.0196368	+	0.0989817i
$417$		0			0
$418$	−64.3195	−	81.6058i	−0.153874	−	0.195229i
$419$	−196.174	+	233.791i	−0.468195	+	0.557974i	−0.947533	−	0.319657i	$-0.896432\pi$
$419$	−196.174	+	233.791i	−0.468195	+	0.557974i	0.479338	+	0.877630i	$0.340877\pi$
$420$		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	$0.553960\pi$
$422$	161.120	+	143.834i	0.381801	+	0.340840i
$423$		0			0
$424$	50.7043	−	549.984i	0.119586	−	1.29713i
$425$	−51.0833	−	289.708i	−0.120196	−	0.681665i
$426$		0			0
$427$	−1.24884	−	3.43117i	−0.00292469	−	0.00803552i
$428$	−198.766	−	131.618i	−0.464408	−	0.307519i
$429$		0			0
$430$	56.0313	+	104.305i	0.130305	+	0.242569i
$431$			555.302i			1.28840i	0.764856	+	0.644202i	$0.222810\pi$
$431$			555.302i			1.28840i	−0.764856	+	0.644202i	$0.777190\pi$
$432$		0			0
$433$	388.469			0.897157			0.448579	−	0.893743i	$-0.351930\pi$
$433$	388.469			0.897157			0.448579	+	0.893743i	$0.351930\pi$
$434$	7.04444	−	3.78420i	0.0162314	−	0.00871935i
$435$		0			0
$436$	−9.48979	+	14.3312i	−0.0217656	+	0.0328698i
$437$	−491.630	+	178.939i	−1.12501	+	0.409471i
$438$		0			0
$439$	−153.154	+	27.0051i	−0.348870	+	0.0615151i	−0.345337	−	0.938479i	$-0.612236\pi$
$439$	−153.154	+	27.0051i	−0.348870	+	0.0615151i	−0.00353238	+	0.999994i	$0.501124\pi$
$440$	−58.8564	−	5.42611i	−0.133765	−	0.0123321i
$441$		0			0
$442$	24.2314	−	27.1434i	0.0548221	−	0.0614105i
$443$	178.524	−	490.491i	0.402989	−	1.10720i	−0.557813	−	0.829967i	$-0.688359\pi$
$443$	178.524	−	490.491i	0.402989	−	1.10720i	0.960802	−	0.277236i	$-0.0894184\pi$
$444$		0			0
$445$	−108.891	−	91.3705i	−0.244699	−	0.205327i
$446$	295.710	−	233.071i	0.663028	−	0.522580i
$447$		0			0
$448$	40.8594	+	0.381310i	0.0912039	+	0.000851138i
$449$	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
$452$	80.0384	−	333.088i	0.177076	−	0.736920i
$453$		0			0
$454$	−113.558	−	783.753i	−0.250128	−	1.72633i
$455$	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	0.323417	−	0.946257i	$-0.395168\pi$
$463$	140.609	+	24.7931i	0.303691	+	0.0535489i	−0.0197263	+	0.999805i	$0.506279\pi$
$464$	625.420	+	318.985i	1.34789	+	0.687469i
$465$		0			0
$466$	−20.6241	+	672.808i	−0.0442577	+	1.44379i
$467$	−287.772	+	166.145i	−0.616213	+	0.355771i	−0.775393	−	0.631479i	$-0.782448\pi$
$467$	−287.772	+	166.145i	−0.616213	+	0.355771i	0.159180	+	0.987250i	$0.449115\pi$
$468$		0			0
$469$	−39.1690	+	67.8428i	−0.0835161	+	0.144654i
$470$	−108.317	+	174.999i	−0.230462	+	0.372338i
$471$		0			0
$472$	−693.409	+	182.335i	−1.46909	+	0.386303i
$473$	88.4601	+	74.2268i	0.187019	+	0.156928i
$474$		0			0
$475$	99.2881	−	272.792i	0.209028	−	0.574299i
$476$	−21.0611	−	28.4744i	−0.0442460	−	0.0598202i
$477$		0			0
$478$	55.8310	−	18.4040i	0.116801	−	0.0385022i
$479$	140.813	−	24.8292i	0.293974	−	0.0518355i	−0.0247164	−	0.999695i	$-0.507868\pi$
$479$	140.813	−	24.8292i	0.293974	−	0.0518355i	0.318690	+	0.947859i	$0.396757\pi$
$480$		0			0
$481$	−41.9095	+	15.2538i	−0.0871299	+	0.0317127i
$482$	149.823	−	375.425i	0.310837	−	0.778890i
$483$		0			0
$484$	408.821	−	121.009i	0.844672	−	0.250018i
$485$	−256.103			−0.528048
$486$		0			0
$487$		−	238.167i		−	0.489050i	−0.969643	−	0.244525i	$-0.921368\pi$
$487$		−	238.167i		−	0.489050i	0.969643	−	0.244525i	$-0.0786320\pi$
$488$	−45.5966	+	3.77489i	−0.0934356	+	0.00773543i
$489$		0			0
$490$	−70.1054	+	175.669i	−0.143072	+	0.358508i
$491$	−13.1930	−	36.2476i	−0.0268697	−	0.0738240i	0.925533	−	0.378668i	$-0.123618\pi$
$491$	−13.1930	−	36.2476i	−0.0268697	−	0.0738240i	−0.952402	+	0.304844i	$0.901396\pi$
$492$		0			0
$493$	−105.670	−	599.284i	−0.214341	−	1.21559i
$494$	34.1012	−	11.2411i	0.0690307	−	0.0227552i
$495$		0			0
$496$	−22.5003	−	97.6393i	−0.0453635	−	0.196853i
$497$	61.2169	+	22.2811i	0.123173	+	0.0448313i
$498$		0			0
$499$	−56.0000	+	66.7382i	−0.112224	+	0.133744i	−0.819232	−	0.573462i	$-0.805600\pi$
$499$	−56.0000	+	66.7382i	−0.112224	+	0.133744i	0.707008	+	0.707206i	$0.250045\pi$
$500$	−160.456	−	321.988i	−0.320913	−	0.643977i
$501$		0			0
$502$	−350.512	+	566.293i	−0.698231	+	1.12807i
$503$	541.002	+	312.348i	1.07555	+	0.620970i	0.929693	−	0.368336i	$-0.120072\pi$
$503$	541.002	+	312.348i	1.07555	+	0.620970i	0.145858	+	0.989305i	$0.453406\pi$
$504$		0			0
$505$	14.1532	+	24.5141i	0.0280262	+	0.0485427i
$506$	−8.89320	+	290.118i	−0.0175755	+	0.573356i
$507$		0			0
$508$	35.9833	−	586.380i	0.0708332	−	1.15429i
$509$	−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
$518$	6.22492	+	42.9630i	0.0120172	+	0.0829402i
$519$		0			0
$520$	8.71819	−	18.4707i	0.0167658	−	0.0355206i
$521$	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	0.149588	−	0.988748i	$-0.452205\pi$
$523$	−330.483	−	190.805i	−0.631900	−	0.364827i	−0.781487	+	0.623921i	$0.785539\pi$
$524$	525.711	−	553.760i	1.00327	−	1.05679i
$525$		0			0
$526$	406.756	−	320.594i	0.773301	−	0.609495i
$527$	−55.8250	+	66.5296i	−0.105930	+	0.126242i
$528$		0			0
$529$	876.234	+	318.923i	1.65640	+	0.602880i
$530$	−178.962	+	200.470i	−0.337665	+	0.378245i
$531$		0			0
$532$	−3.94946	−	34.7262i	−0.00742379	−	0.0652749i
$533$	−5.13901	−	29.1448i	−0.00964167	−	0.0546806i
$534$		0			0
$535$	39.6711	+	108.995i	0.0741516	+	0.203730i
$536$	690.846	+	697.323i	1.28889	+	1.30098i
$537$		0			0
$538$	740.462	−	397.768i	1.37632	−	0.739347i
$539$			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	$0.799339\pi$
$542$	145.948	+	271.688i	0.269277	+	0.501270i
$543$		0			0
$544$	−413.690	+	160.635i	−0.760460	+	0.295285i
$545$	7.85866	−	2.86032i	0.0144196	−	0.00524829i
$546$		0			0
$547$	962.840	−	169.775i	1.76022	−	0.310374i	0.802196	−	0.597061i	$-0.203665\pi$
$547$	962.840	−	169.775i	1.76022	−	0.310374i	0.958024	+	0.286687i	$0.0925539\pi$
$548$	−28.1450	−	247.470i	−0.0513596	−	0.451587i
$549$		0			0
$550$	−120.145	−	107.255i	−0.218445	−	0.195009i
$551$	205.386	−	564.292i	0.372751	−	1.02412i
$552$		0			0
$553$	−50.3181	−	42.2219i	−0.0909912	−	0.0763507i
$554$	449.941	+	570.866i	0.812168	+	1.03044i
$555$		0			0
$556$	−700.309	+	737.673i	−1.25955	+	1.32675i
$557$	−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
$560$	−15.8729	−	11.9711i	−0.0283444	−	0.0213770i
$561$		0			0
$562$	−582.346	+	84.3762i	−1.03620	+	0.150136i
$563$	−791.225	−	139.514i	−1.40537	−	0.247805i	−0.581024	−	0.813887i	$-0.697348\pi$
$563$	−791.225	−	139.514i	−1.40537	−	0.247805i	−0.824349	+	0.566081i	$0.808459\pi$
$564$		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	0.711513	−	0.702673i	$-0.248010\pi$
$571$	650.819	+	114.757i	1.13979	+	0.200975i	0.428275	+	0.903648i	$0.359121\pi$
$572$	1.22011	−	19.8828i	0.00213307	−	0.0347602i
$573$		0			0
$574$	−28.7929	−	0.882609i	−0.0501618	−	0.00153765i
$575$	−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	$0.219483\pi$
$578$	−164.401	−	101.757i	−0.284431	−	0.176051i
$579$		0			0
$580$	−152.356	−	305.734i	−0.262683	−	0.527127i
$581$	2.94948	+	2.47490i	0.00507655	+	0.00425973i
$582$		0			0
$583$	−89.6402	+	246.285i	−0.153757	+	0.422443i
$584$	−483.149	+	222.558i	−0.827311	+	0.381092i
$585$		0			0
$586$	−52.7952	−	160.161i	−0.0900942	−	0.273312i
$587$	674.146	−	118.870i	1.14846	−	0.202505i	0.433157	−	0.901318i	$-0.357400\pi$
$587$	674.146	−	118.870i	1.14846	−	0.202505i	0.715304	+	0.698814i	$0.246288\pi$
$588$		0			0
$589$	−80.5349	+	29.3123i	−0.136732	+	0.0497662i
$590$	324.000	+	129.301i	0.549153	+	0.219154i
$591$		0			0
$592$	539.877	+	66.5097i	0.911954	+	0.112348i
$593$	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
$596$	−137.481	+	40.6934i	−0.230672	+	0.0682776i
$597$		0			0
$598$	−93.1569	−	37.1767i	−0.155781	−	0.0621684i
$599$	−57.9290	−	159.159i	−0.0967095	−	0.265707i	0.881899	−	0.471438i	$-0.156265\pi$
$599$	−57.9290	−	159.159i	−0.0967095	−	0.265707i	−0.978609	+	0.205731i	$0.934043\pi$
$600$		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	$-0.230920\pi$
$602$	12.1601	+	36.8893i	0.0201996	+	0.0612779i
$603$		0			0
$604$	549.675	+	743.157i	0.910058	+	1.23039i
$605$	−194.933	−	70.9496i	−0.322203	−	0.117272i
$606$		0			0
$607$	188.896	−	225.118i	0.311196	−	0.370869i	−0.587664	−	0.809105i	$-0.699952\pi$
$607$	188.896	−	225.118i	0.311196	−	0.370869i	0.898860	+	0.438236i	$0.144397\pi$
$608$	−432.803	−	66.8382i	−0.711847	−	0.109931i
$609$		0			0
$610$	18.9285	+	11.7159i	0.0310303	+	0.0192064i
$611$	−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	$0.858628\pi$
$614$	−32.2055	−	0.987220i	−0.0524520	−	0.00160785i
$615$		0			0
$616$	−18.7055	−	5.10579i	−0.0303661	−	0.00828863i
$617$	−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	$0.100173\pi$
$619$	675.081	+	804.530i	1.09060	+	1.29973i	0.139711	+	0.990192i	$0.455383\pi$
$620$	−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
$626$	−891.559	+	129.178i	−1.42422	+	0.206355i
$627$		0			0
$628$	−150.086	+	624.600i	−0.238991	+	0.994586i
$629$	−235.742	−	408.317i	−0.374788	−	0.649152i
$630$		0			0
$631$	−757.053	−	437.085i	−1.19977	−	0.692686i	−0.239264	−	0.970955i	$-0.576906\pi$
$631$	−757.053	−	437.085i	−1.19977	−	0.692686i	−0.960503	+	0.278269i	$0.910239\pi$
$632$	−676.404	+	468.935i	−1.07026	+	0.741986i
$633$		0			0
$634$	−300.246	−	380.939i	−0.473574	−	0.600850i
$635$	−183.734	+	218.966i	−0.289345	+	0.344829i
$636$		0			0
$637$	−59.9011	−	21.8022i	−0.0940363	−	0.0342264i
$638$	−248.529	−	221.866i	−0.389544	−	0.347752i
$639$		0			0
$640$	−197.079	+	152.373i	−0.307937	+	0.238082i
$641$	−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	0.859874	−	0.510506i	$-0.170542\pi$
$643$	−81.6449	−	224.318i	−0.126975	−	0.348861i	−0.986849	+	0.161646i	$0.948320\pi$
$644$	−53.9023	+	81.4018i	−0.0836992	+	0.126400i
$645$		0			0
$646$	179.631	+	334.391i	0.278067	+	0.517633i
$647$			980.601i			1.51561i	0.652480	+	0.757806i	$0.273729\pi$
$647$			980.601i			1.51561i	−0.652480	+	0.757806i	$0.726271\pi$
$648$		0			0
$649$	340.229			0.524236
$650$	49.0280	−	26.3373i	0.0754277	−	0.0405190i
$651$		0			0
$652$	19.8010	+	13.1117i	0.0303696	+	0.0201100i
$653$	−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
$656$	−105.671	+	345.137i	−0.161084	+	0.526123i
$657$		0			0
$658$	−44.9627	+	50.3662i	−0.0683323	+	0.0765444i
$659$	331.931	−	911.972i	0.503689	−	1.38387i	−0.383959	−	0.923350i	$-0.625440\pi$
$659$	331.931	−	911.972i	0.503689	−	1.38387i	0.887648	−	0.460523i	$-0.152338\pi$
$660$		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	$-0.607496\pi$
$662$	167.593	−	132.092i	0.253162	−	0.199535i
$663$		0			0
$664$	39.6485	−	27.4874i	0.0597116	−	0.0413966i
$665$	−8.50250	+	14.7268i	−0.0127857	+	0.0221455i
$666$		0			0
$667$	−1452.73	+	838.736i	−2.17801	+	1.25747i
$668$	25.9701	+	6.24040i	0.0388774	+	0.00934192i
$669$		0			0
$670$	−68.4837	−	472.660i	−0.102215	−	0.705463i
$671$	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
$680$	208.302	+	56.8575i	0.306327	+	0.0836140i
$681$		0			0
$682$	−1.45681	+	47.5248i	−0.00213609	+	0.0696844i
$683$	−410.870	+	237.216i	−0.601567	+	0.347315i	−0.769658	−	0.638457i	$-0.779573\pi$
$683$	−410.870	+	237.216i	−0.601567	+	0.347315i	0.168091	+	0.985772i	$0.446240\pi$
$684$		0			0
$685$	−60.5914	+	104.947i	−0.0884546	+	0.153208i
$686$	−65.5858	+	105.962i	−0.0956061	+	0.154463i
$687$		0			0
$688$	486.041	−	25.2757i	0.706455	−	0.0367379i
$689$	−69.3797	−	58.2165i	−0.100696	−	0.0844942i
$690$		0			0
$691$	69.6707	−	191.419i	0.100826	−	0.277017i	−0.879016	−	0.476793i	$-0.841799\pi$
$691$	69.6707	−	191.419i	0.100826	−	0.277017i	0.979842	+	0.199776i	$0.0640214\pi$
$692$	−74.8844	+	55.3881i	−0.108214	+	0.0800407i
$693$		0			0
$694$	259.418	−	85.5142i	0.373801	−	0.123219i
$695$	487.376	−	85.9376i	0.701261	−	0.123651i
$696$		0			0
$697$	293.992	−	107.004i	0.421796	−	0.153521i
$698$	441.525	−	1106.37i	0.632557	−	1.58505i
$699$		0			0
$700$	−15.3753	−	51.9447i	−0.0219647	−	0.0742067i
$701$	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
$704$	−123.438	+	209.266i	−0.175338	+	0.297253i
$705$		0			0
$706$	−114.381	+	286.615i	−0.162013	+	0.405970i
$707$	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	$-0.169028\pi$
$710$	−377.202	+	124.340i	−0.531270	+	0.175127i
$711$		0			0
$712$	−530.708	+	244.465i	−0.745376	+	0.343350i
$713$	224.968	+	81.8817i	0.315523	+	0.114841i
$714$		0			0
$715$	−6.23003	+	7.42466i	−0.00871333	+	0.0103841i
$716$	−522.426	+	260.341i	−0.729646	+	0.363604i
$717$		0			0
$718$	−426.352	+	688.822i	−0.593805	+	0.959362i
$719$	400.965	+	231.497i	0.557671	+	0.321971i	0.752210	−	0.658923i	$-0.228988\pi$
$719$	400.965	+	231.497i	0.557671	+	0.321971i	−0.194539	+	0.980895i	$0.562321\pi$
$720$		0			0
$721$	36.1463	+	62.6072i	0.0501335	+	0.0868338i
$722$	10.6447	−	347.256i	0.0147433	−	0.480964i
$723$		0			0
$724$	−1081.27	−	66.3524i	−1.49347	−	0.0916470i
$725$	161.629	−	916.641i	0.222936	−	1.26433i
$726$		0			0
$727$	−309.611	−	368.980i	−0.425875	−	0.507538i	0.509853	−	0.860262i	$-0.329700\pi$
$727$	−309.611	−	368.980i	−0.425875	−	0.507538i	−0.935727	+	0.352724i	$0.885256\pi$
$728$	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	$-8.15322e-5\pi$
$734$	163.130	+	1125.89i	0.222248	+	1.53391i
$735$		0			0
$736$	806.136	+	920.157i	1.09529	+	1.25021i
$737$	−232.898	−	403.391i	−0.316008	−	0.547342i
$738$		0			0
$739$	−392.033	−	226.340i	−0.530491	−	0.306279i	0.210725	−	0.977545i	$-0.432417\pi$
$739$	−392.033	−	226.340i	−0.530491	−	0.306279i	−0.741216	+	0.671266i	$0.765751\pi$
$740$	−191.943	−	182.221i	−0.259383	−	0.246244i
$741$		0			0
$742$	−69.2369	+	54.5707i	−0.0933112	+	0.0735454i
$743$	602.072	−	717.521i	0.810326	−	0.965709i	−0.189544	−	0.981872i	$-0.560701\pi$
$743$	602.072	−	717.521i	0.810326	−	0.965709i	0.999869	+	0.0161637i	$0.00514530\pi$
$744$		0			0
$745$	65.5529	+	23.8593i	0.0879905	+	0.0320259i
$746$	−459.272	+	514.467i	−0.615646	+	0.689633i
$747$		0			0
$748$	209.239	−	23.7971i	0.279732	−	0.0318143i
$749$	6.60747	+	37.4728i	0.00882172	+	0.0500305i
$750$		0			0
$751$	423.198	+	1162.73i	0.563513	+	1.54824i	0.814449	+	0.580234i	$0.197039\pi$
$751$	423.198	+	1162.73i	0.563513	+	1.54824i	−0.250937	+	0.968003i	$0.580739\pi$
$752$	460.473	+	709.693i	0.612331	+	0.943741i
$753$		0			0
$754$	101.418	−	54.4809i	0.134507	−	0.0722558i
$755$		−	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	$0.382894\pi$
$758$	−354.225	−	659.404i	−0.467315	−	0.869926i
$759$		0			0
$760$	149.963	+	151.369i	0.197320	+	0.199170i
$761$	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
$764$	−235.345	+	26.7661i	−0.308044	+	0.0350342i
$765$		0			0
$766$	376.902	+	336.466i	0.492039	+	0.439251i
$767$	−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	$0.452744\pi$
$770$	5.83987	+	7.40937i	0.00758424	+	0.00962256i
$771$		0			0
$772$	−372.739	−	353.859i	−0.482822	−	0.458366i
$773$	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
$776$	−449.350	+	952.012i	−0.579059	+	1.22682i
$777$		0			0
$778$	664.888	−	96.3357i	0.854612	−	0.123825i
$779$	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	0.303576	−	0.952807i	$-0.401819\pi$
$787$	206.953	+	36.4914i	0.262965	+	0.0463678i	−0.0406112	+	0.999175i	$0.512931\pi$
$788$	939.199	+	57.6341i	1.19188	+	0.0731397i
$789$		0			0
$790$	400.271	+	12.2698i	0.506672	+	0.0155314i
$791$	−47.3532	+	27.3394i	−0.0598650	+	0.0345631i
$792$		0			0
$793$	−3.75126	+	6.49737i	−0.00473046	+	0.00819340i
$794$	−389.783	−	241.259i	−0.490910	−	0.303853i
$795$		0			0
$796$	1084.95	−	540.662i	1.36300	−	0.679224i
$797$	−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
$800$	−678.639	+	14.4655i	−0.848299	+	0.0180818i
$801$		0			0
$802$	208.695	+	633.104i	0.260219	+	0.789406i
$803$	248.589	−	43.8329i	0.309575	−	0.0545865i
$804$		0			0
$805$	44.6374	−	16.2467i	0.0554502	−	0.0201822i
$806$	−15.2602	−	6.08999i	−0.0189333	−	0.00755582i
$807$		0			0
$808$	115.959	−	9.60010i	0.143513	−	0.0118813i
$809$	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	$0.0836778\pi$
$811$			421.500i			0.519728i	−0.965645	+	0.259864i	$0.916322\pi$
$812$	−31.8051	−	107.452i	−0.0391688	−	0.132330i
$813$		0			0
$814$	−239.739	−	95.6742i	−0.294520	−	0.117536i
$815$	−3.95200	−	10.8580i	−0.00484909	−	0.0133228i
$816$		0			0
$817$	−72.2883	−	409.967i	−0.0884801	−	0.501796i
$818$	−400.425	−	1214.74i	−0.489518	−	1.48501i
$819$		0			0
$820$	141.195	−	104.435i	0.172189	−	0.127360i
$821$	−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	−0.688296	−	0.725430i	$-0.741641\pi$
$823$	119.857	−	142.839i	0.145634	−	0.173559i	0.833930	+	0.551870i	$0.186086\pi$
$824$	876.061	−	230.364i	1.06318	−	0.279568i
$825$		0			0
$826$	97.3084	+	60.2298i	0.117807	+	0.0729175i
$827$	−86.7525	−	50.0866i	−0.104900	−	0.0605642i	0.446632	−	0.894718i	$-0.352623\pi$
$827$	−86.7525	−	50.0866i	−0.104900	−	0.0605642i	−0.551532	+	0.834154i	$0.685957\pi$
$828$		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	$0.906422\pi$
$830$	−23.4625	−	0.719214i	−0.0282681	−	0.000866522i
$831$		0			0
$832$	−53.3645	−	64.8162i	−0.0641400	−	0.0779041i
$833$	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	$-0.830015\pi$
$839$	−1017.34	−	1212.42i	−1.21256	−	1.44508i	−0.351798	−	0.936076i	$-0.614430\pi$
$840$		0			0
$841$	188.304	−	1067.92i	0.223905	−	1.26983i
$842$	−297.623	+	43.1227i	−0.353472	+	0.0512146i
$843$		0			0
$844$	−420.007	−	100.924i	−0.497639	−	0.119579i
$845$	162.779	+	281.942i	0.192638	+	0.333659i
$846$		0			0
$847$	−58.9348	−	34.0260i	−0.0695806	−	0.0401724i
$848$	431.204	+	1016.99i	0.508495	+	1.19928i
$849$		0			0
$850$	364.200	+	462.081i	0.428470	+	0.543625i
$851$	−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	$0.432657\pi$
$854$	5.44778	+	4.86331i	0.00637913	+	0.00569475i
$855$		0			0
$856$	474.774	+	43.7705i	0.554642	+	0.0511338i
$857$	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	$-0.942165\pi$
$859$	−297.432	−	817.186i	−0.346253	−	0.951323i	0.637286	−	0.770627i	$-0.280057\pi$
$860$	−197.440	−	130.740i	−0.229582	−	0.152024i
$861$		0			0
$862$	−525.572	−	978.374i	−0.609712	−	1.13500i
$863$		−	514.846i		−	0.596577i	−0.954476	−	0.298289i	$-0.903584\pi$
$863$		−	514.846i		−	0.596577i	0.954476	−	0.298289i	$-0.0964158\pi$
$864$		0			0
$865$	45.3185			0.0523913
$866$	−684.435	+	367.671i	−0.790340	+	0.424562i
$867$		0			0
$868$	−8.82984	+	13.3346i	−0.0101726	+	0.0153624i
$869$	367.011	−	133.581i	0.422338	−	0.153718i
$870$		0			0
$871$	158.517	−	27.9508i	0.181994	−	0.0320904i
$872$	3.15589	−	34.2316i	0.00361914	−	0.0392564i
$873$		0			0
$874$	696.833	−	780.577i	0.797292	−	0.893109i
$875$	−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	$0.655911\pi$
$878$	244.279	−	192.534i	0.278222	−	0.219287i
$879$		0			0
$880$	108.833	−	46.1452i	0.123674	−	0.0524377i
$881$	−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	−0.305086	−	0.952325i	$-0.598685\pi$
$883$	324.157	−	187.152i	0.367108	−	0.211950i	0.672194	+	0.740375i	$0.265352\pi$
$884$	−17.0025	+	70.7575i	−0.0192336	+	0.0800424i
$885$		0			0
$886$	149.693	+	1033.15i	0.168954	+	1.16608i
$887$	497.269	+	87.6819i	0.560619	+	0.0988522i	0.446775	−	0.894646i	$-0.352573\pi$
$887$	497.269	+	87.6819i	0.560619	+	0.0988522i	0.113844	+	0.993499i	$0.463684\pi$
$888$		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
$896$	−72.3501	+	38.0000i	−0.0807478	+	0.0424107i
$897$		0			0
$898$	−14.0236	+	457.484i	−0.0156165	+	0.509447i
$899$	−237.975	+	137.395i	−0.264711	+	0.152831i
$900$		0			0
$901$	478.728	−	829.181i	0.531329	−	0.920289i
$902$	90.1457	−	145.641i	0.0999398	−	0.161465i
$903$		0			0
$904$	174.237	+	662.613i	0.192740	+	0.732979i
$905$	403.769	+	338.802i	0.446154	+	0.374367i
$906$		0			0
$907$	224.910	−	617.936i	0.247972	−	0.681296i	−0.751789	−	0.659404i	$-0.770809\pi$
$907$	224.910	−	617.936i	0.247972	−	0.681296i	0.999760	−	0.0218922i	$-0.00696907\pi$
$908$	941.868	+	1273.40i	1.03730	+	1.40242i
$909$		0			0
$910$	−3.09621	+	1.02063i	−0.00340242	+	0.00112157i
$911$	−968.198	+	170.719i	−1.06279	+	0.187398i	−0.677592	−	0.735438i	$-0.736977\pi$
$911$	−968.198	+	170.719i	−1.06279	+	0.187398i	−0.385194	+	0.922836i	$0.625865\pi$
$912$		0			0
$913$	−21.5129	+	7.83007i	−0.0235629	+	0.00857620i
$914$	519.372	−	1301.43i	0.568241	−	1.42389i
$915$		0			0
$916$	−622.742	+	184.328i	−0.679850	+	0.201231i
$917$	−121.875			−0.132906
$918$		0			0
$919$			464.177i			0.505090i	0.967585	+	0.252545i	$0.0812675\pi$
$919$			464.177i			0.505090i	−0.967585	+	0.252545i	$0.918732\pi$
$920$	−49.1090	−	593.184i	−0.0533794	−	0.644765i
$921$		0			0
$922$	437.851	−	1097.16i	0.474893	−	1.18998i
$923$	−45.7813	−	125.783i	−0.0496005	−	0.136276i
$924$		0			0
$925$	−125.229	−	710.207i	−0.135382	−	0.767791i
$926$	−271.201	+	89.3984i	−0.292874	+	0.0965425i
$927$		0			0
$928$	−1403.82	+	29.9230i	−1.51274	+	0.0322446i
$929$	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
$932$	−600.449	−	1204.92i	−0.644259	−	1.29284i
$933$		0			0
$934$	349.768	−	565.092i	0.374484	−	0.605023i
$935$	−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	$0.637979\pi$
$938$	4.80046	−	156.603i	0.00511776	−	0.166954i
$939$		0			0
$940$	25.2115	−	410.844i	0.0268208	−	0.437068i
$941$	−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	$0.0519829\pi$
$947$	923.771	+	1100.91i	0.975471	+	1.16252i	−0.0112237	+	0.999937i	$0.503573\pi$
$948$		0			0
$949$	−15.1470	+	85.9031i	−0.0159611	+	0.0905196i
$950$	83.2536	+	574.598i	0.0876354	+	0.604840i
$951$		0			0
$952$	64.0570	+	30.2349i	0.0672867	+	0.0317594i
$953$	−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
$956$	−80.9486	+	85.2675i	−0.0846742	+	0.0891920i
$957$		0			0
$958$	−224.596	+	177.020i	−0.234442	+	0.184781i
$959$	−25.5535	+	30.4535i	−0.0266460	+	0.0317555i
$960$		0			0
$961$	−866.192	−	315.268i	−0.901345	−	0.328063i
$962$	59.4022	−	66.5411i	0.0617487	−	0.0691695i
$963$		0			0
$964$	91.3552	+	803.255i	0.0947668	+	0.833252i
$965$	43.4234	+	246.266i	0.0449983	+	0.255198i
$966$		0			0
$967$	504.202	+	1385.28i	0.521408	+	1.43256i	0.868953	+	0.494894i	$0.164793\pi$
$967$	504.202	+	1385.28i	0.521408	+	1.43256i	−0.347545	+	0.937663i	$0.612985\pi$
$968$	−605.763	+	600.136i	−0.625788	+	0.619975i
$969$		0			0
$970$	451.222	−	242.392i	0.465178	−	0.249889i
$971$		−	611.405i		−	0.629666i	−0.949147	−	0.314833i	$-0.898052\pi$
$971$		−	611.405i		−	0.629666i	0.949147	−	0.314833i	$-0.101948\pi$
$972$		0			0
$973$	162.351			0.166856
$974$	225.416	+	419.622i	0.231434	+	0.430823i
$975$		0			0
$976$	76.7628	−	49.8063i	0.0786504	−	0.0510311i
$977$	−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
$980$	−42.7469	−	375.859i	−0.0436193	−	0.383530i
$981$		0			0
$982$	57.5515	+	51.3771i	0.0586064	+	0.0523188i
$983$	−557.110	+	1530.65i	−0.566744	+	1.55712i	0.242811	+	0.970074i	$0.421930\pi$
$983$	−557.110	+	1530.65i	−0.566744	+	1.55712i	−0.809555	+	0.587043i	$0.800292\pi$
$984$		0			0
$985$	−350.716	−	294.286i	−0.356057	−	0.298767i
$986$	753.377	+	955.852i	0.764074	+	0.969424i
$987$		0			0
$988$	−49.4429	+	52.0808i	−0.0500434	+	0.0527134i
$989$	−581.439	+	1007.08i	−0.587906	+	1.01828i
$990$		0			0
$991$	880.472	−	508.341i	0.888468	−	0.512957i	0.0150271	−	0.999887i	$-0.495217\pi$
$991$	880.472	−	508.341i	0.888468	−	0.512957i	0.873441	+	0.486930i	$0.161883\pi$
$992$	132.055	+	150.733i	0.133120	+	0.151948i
$993$		0			0
$994$	−128.945	+	18.6828i	−0.129723	+	0.0187956i
$995$	−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.199.5		204
3.2	odd	2		108.3.j.a.103.30	yes	204
4.3	odd	2	inner	324.3.j.a.199.11		204
12.11	even	2		108.3.j.a.103.24	yes	204
27.11	odd	18		108.3.j.a.43.24	✓	204
27.16	even	9	inner	324.3.j.a.127.11		204
108.11	even	18		108.3.j.a.43.30	yes	204
108.43	odd	18	inner	324.3.j.a.127.5		204

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

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)

\(f(q)\)	\(=\)	\(q+(-1.76188 + 0.946462i) q^{2} +(2.20842 - 3.33510i) q^{4} +(-1.82883 + 0.665640i) q^{5} +(-0.628756 + 0.110867i) q^{7} +(-0.734424 + 7.96622i) q^{8} +O(q^{10})\)	\(q+(-1.76188 + 0.946462i) q^{2} +(2.20842 - 3.33510i) q^{4} +(-1.82883 + 0.665640i) q^{5} +(-0.628756 + 0.110867i) q^{7} +(-0.734424 + 7.96622i) q^{8} +(2.59217 - 2.90370i) q^{10} +(1.29839 - 3.56730i) q^{11} +(1.00493 + 0.843235i) q^{13} +(1.00286 - 0.790427i) q^{14} +(-6.24575 - 14.7306i) q^{16} +(-6.93411 + 12.0102i) q^{17} +(-11.8519 + 6.84271i) q^{19} +(-1.81885 + 7.56935i) q^{20} +(1.08871 + 7.51402i) q^{22} +(37.6484 + 6.63843i) q^{23} +(-16.2496 + 13.6350i) q^{25} +(-2.56865 - 0.534550i) q^{26} +(-1.01881 + 2.34180i) q^{28} +(-33.6135 + 28.2051i) q^{29} +(6.16725 + 1.08745i) q^{31} +(24.9462 + 20.0421i) q^{32} +(0.849827 - 27.7234i) q^{34} +(1.07609 - 0.621282i) q^{35} +(-16.9987 + 29.4426i) q^{37} +(14.4053 - 23.2734i) q^{38} +(-3.95950 - 15.0577i) q^{40} +(-17.2815 - 14.5009i) q^{41} +(-10.4038 + 28.5842i) q^{43} +(-9.02990 - 12.2084i) q^{44} +(-72.6148 + 23.9367i) q^{46} +(-52.0711 + 9.18154i) q^{47} +(-45.6619 + 16.6196i) q^{49} +(15.7247 - 39.4028i) q^{50} +(5.03157 - 1.48932i) q^{52} -69.0395 q^{53} +7.38825i q^{55} +(-0.421414 - 5.09023i) q^{56} +(32.5279 - 81.5079i) q^{58} +(30.6528 + 84.2178i) q^{59} +(0.993107 + 5.63219i) q^{61} +(-11.8952 + 3.92111i) q^{62} +(-62.9212 - 11.7012i) q^{64} +(-2.39914 - 0.873214i) q^{65} +(78.8696 - 93.9932i) q^{67} +(24.7419 + 49.6496i) q^{68} +(-1.30792 + 2.11310i) q^{70} +(-88.3661 - 51.0182i) q^{71} +(33.2465 + 57.5847i) q^{73} +(2.08332 - 67.9629i) q^{74} +(-3.35292 + 54.6389i) q^{76} +(-0.420876 + 2.38691i) q^{77} +(66.1314 + 78.8123i) q^{79} +(21.2277 + 22.7824i) q^{80} +(44.1725 + 9.19255i) q^{82} +(-3.87639 - 4.61971i) q^{83} +(4.68683 - 26.5803i) q^{85} +(-8.72362 - 60.2086i) q^{86} +(27.4643 + 12.9632i) q^{88} +(36.5192 + 63.2530i) q^{89} +(-0.725341 - 0.418776i) q^{91} +(105.283 - 110.901i) q^{92} +(83.0529 - 65.4601i) q^{94} +(17.1204 - 20.4033i) q^{95} +(123.655 + 45.0069i) q^{97} +(64.7209 - 72.4989i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 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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