LMFDB - Embedded newform 333.2.br.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,2,Mod(17,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("333.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	333.br (of order $36$, degree $12$, 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:	$2.65901838731$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$12$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	333.17
Dual form			333.2.br.a.98.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669250 + 0.955789i) q^{2} +(0.218405 + 0.600062i) q^{4} +(1.25001 - 0.109362i) q^{5} +(1.89189 + 1.58748i) q^{7} +(-2.97379 - 0.796824i) q^{8} +O(q^{10})$	\(q+(-0.669250 + 0.955789i) q^{2} +(0.218405 + 0.600062i) q^{4} +(1.25001 - 0.109362i) q^{5} +(1.89189 + 1.58748i) q^{7} +(-2.97379 - 0.796824i) q^{8} +(-0.732043 + 1.26794i) q^{10} +(0.339581 + 0.588172i) q^{11} +(3.07624 + 1.43447i) q^{13} +(-2.78344 + 0.745821i) q^{14} +(1.77345 - 1.48811i) q^{16} +(-0.988466 + 0.460929i) q^{17} +(0.984890 - 0.689627i) q^{19} +(0.338632 + 0.726198i) q^{20} +(-0.789433 - 0.0690664i) q^{22} +(0.125785 + 0.469437i) q^{23} +(-3.37347 + 0.594834i) q^{25} +(-3.42983 + 1.98021i) q^{26} +(-0.539390 + 1.48196i) q^{28} +(-1.90766 + 7.11949i) q^{29} +(-0.0432614 + 0.0432614i) q^{31} +(-0.301223 - 3.44299i) q^{32} +(0.220980 - 1.25324i) q^{34} +(2.53849 + 1.77747i) q^{35} +(-1.52656 + 5.88809i) q^{37} +1.40288i q^{38} +(-3.80441 - 0.670820i) q^{40} +(5.83471 - 2.12366i) q^{41} +(-6.71091 - 6.71091i) q^{43} +(-0.278773 + 0.332229i) q^{44} +(-0.532865 - 0.193947i) q^{46} +(4.38105 + 2.52940i) q^{47} +(-0.156399 - 0.886981i) q^{49} +(1.68916 - 3.62242i) q^{50} +(-0.188908 + 2.15923i) q^{52} +(1.21046 + 1.44257i) q^{53} +(0.488804 + 0.698084i) q^{55} +(-4.36113 - 6.22834i) q^{56} +(-5.52802 - 6.58804i) q^{58} +(1.03749 - 11.8585i) q^{59} +(4.70712 - 10.0944i) q^{61} +(-0.0123960 - 0.0703015i) q^{62} +(7.50220 + 4.33140i) q^{64} +(4.00221 + 1.45668i) q^{65} +(5.52276 - 6.58177i) q^{67} +(-0.492472 - 0.492472i) q^{68} +(-3.39777 + 1.23669i) q^{70} +(2.34650 + 0.413752i) q^{71} +3.84166i q^{73} +(-4.60612 - 5.39967i) q^{74} +(0.628923 + 0.440377i) q^{76} +(-0.291263 + 1.65183i) q^{77} +(-0.501285 - 5.72971i) q^{79} +(2.05409 - 2.05409i) q^{80} +(-1.87511 + 6.99801i) q^{82} +(2.01658 - 5.54052i) q^{83} +(-1.18518 + 0.684267i) q^{85} +(10.9055 - 1.92293i) q^{86} +(-0.541173 - 2.01969i) q^{88} +(6.68423 + 0.584794i) q^{89} +(3.54270 + 7.59734i) q^{91} +(-0.254219 + 0.178006i) q^{92} +(-5.34959 + 2.49456i) q^{94} +(1.15570 - 0.969750i) q^{95} +(4.79559 - 1.28497i) q^{97} +(0.952436 + 0.444128i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q+O(q^{10}) $ 144 * q	$ 144 q + 24 q^{16} - 48 q^{28} - 48 q^{31} - 144 q^{34} - 12 q^{37} - 72 q^{40} - 48 q^{43} - 216 q^{46} + 108 q^{49} - 120 q^{52} + 132 q^{58} - 48 q^{67} + 48 q^{70} + 72 q^{82} + 144 q^{88} - 108 q^{91} + 144 q^{94} + 144 q^{97}+O(q^{100}) $ 144 * q + 24 * q^16 - 48 * q^28 - 48 * q^31 - 144 * q^34 - 12 * q^37 - 72 * q^40 - 48 * q^43 - 216 * q^46 + 108 * q^49 - 120 * q^52 + 132 * q^58 - 48 * q^67 + 48 * q^70 + 72 * q^82 + 144 * q^88 - 108 * q^91 + 144 * q^94 + 144 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$-1$	$e\left(\frac{7}{36}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.669250	+	0.955789i	−0.473231	+	0.675845i	−0.982819	−	0.184575i	$-0.940909\pi$
$2$	−0.669250	+	0.955789i	−0.473231	+	0.675845i	0.509587	+	0.860419i	$0.329798\pi$
$3$		0			0
$3$		0			0
$4$	0.218405	+	0.600062i	0.109202	+	0.300031i
$5$	1.25001	−	0.109362i	0.559021	−	0.0489080i	0.195856	−	0.980633i	$-0.437251\pi$
$5$	1.25001	−	0.109362i	0.559021	−	0.0489080i	0.363166	+	0.931725i	$0.381696\pi$
$6$		0			0
$7$	1.89189	+	1.58748i	0.715066	+	0.600012i	0.926016	−	0.377485i	$-0.123211\pi$
$7$	1.89189	+	1.58748i	0.715066	+	0.600012i	−0.210949	+	0.977497i	$0.567656\pi$
$8$	−2.97379	−	0.796824i	−1.05139	−	0.281720i
$9$		0			0
$10$	−0.732043	+	1.26794i	−0.231492	+	0.400956i
$11$	0.339581	+	0.588172i	0.102388	+	0.177341i	0.912668	−	0.408702i	$-0.134018\pi$
$11$	0.339581	+	0.588172i	0.102388	+	0.177341i	−0.810280	+	0.586043i	$0.800685\pi$
$12$		0			0
$13$	3.07624	+	1.43447i	0.853196	+	0.397852i	0.799471	−	0.600704i	$-0.205113\pi$
$13$	3.07624	+	1.43447i	0.853196	+	0.397852i	0.0537243	+	0.998556i	$0.482891\pi$
$14$	−2.78344	+	0.745821i	−0.743906	+	0.199329i
$15$		0			0
$16$	1.77345	−	1.48811i	0.443364	−	0.372026i
$17$	−0.988466	+	0.460929i	−0.239738	+	0.111792i	−0.538775	−	0.842450i	$-0.681113\pi$
$17$	−0.988466	+	0.460929i	−0.239738	+	0.111792i	0.299036	+	0.954242i	$0.403335\pi$
$18$		0			0
$19$	0.984890	−	0.689627i	0.225949	−	0.158211i	−0.455121	−	0.890430i	$-0.650404\pi$
$19$	0.984890	−	0.689627i	0.225949	−	0.158211i	0.681070	+	0.732218i	$0.261515\pi$
$20$	0.338632	+	0.726198i	0.0757204	+	0.162383i
$21$		0			0
$22$	−0.789433	−	0.0690664i	−0.168308	−	0.0147250i
$23$	0.125785	+	0.469437i	0.0262281	+	0.0978845i	0.977799	−	0.209544i	$-0.0671981\pi$
$23$	0.125785	+	0.469437i	0.0262281	+	0.0978845i	−0.951571	+	0.307429i	$0.900531\pi$
$24$		0			0
$25$	−3.37347	+	0.594834i	−0.674695	+	0.118967i
$26$	−3.42983	+	1.98021i	−0.672645	+	0.388352i
$27$		0			0
$28$	−0.539390	+	1.48196i	−0.101935	+	0.280065i
$29$	−1.90766	+	7.11949i	−0.354244	+	1.32206i	0.527190	+	0.849748i	$0.323246\pi$
$29$	−1.90766	+	7.11949i	−0.354244	+	1.32206i	−0.881434	+	0.472308i	$0.843421\pi$
$30$		0			0
$31$	−0.0432614	+	0.0432614i	−0.00776998	+	0.00776998i	−0.710981	−	0.703211i	$-0.751749\pi$
$31$	−0.0432614	+	0.0432614i	−0.00776998	+	0.00776998i	0.703211	+	0.710981i	$0.251749\pi$
$32$	−0.301223	−	3.44299i	−0.0532492	−	0.608641i
$33$		0			0
$34$	0.220980	−	1.25324i	0.0378978	−	0.214929i
$35$	2.53849	+	1.77747i	0.429083	+	0.300447i
$36$		0			0
$37$	−1.52656	+	5.88809i	−0.250965	+	0.967996i
$37$	−1.52656	+	5.88809i	−0.250965	+	0.967996i
$38$			1.40288i			0.227577i
$39$		0			0
$40$	−3.80441	−	0.670820i	−0.601530	−	0.106066i
$41$	5.83471	−	2.12366i	0.911229	−	0.331660i	0.156486	−	0.987680i	$-0.449984\pi$
$41$	5.83471	−	2.12366i	0.911229	−	0.331660i	0.754744	+	0.656020i	$0.227761\pi$
$42$		0			0
$43$	−6.71091	−	6.71091i	−1.02340	−	1.02340i	−0.999719	−	0.0236854i	$-0.992460\pi$
$43$	−6.71091	−	6.71091i	−1.02340	−	1.02340i	−0.0236854	−	0.999719i	$-0.507540\pi$
$44$	−0.278773	+	0.332229i	−0.0420267	+	0.0500854i
$45$		0			0
$46$	−0.532865	−	0.193947i	−0.0785666	−	0.0285959i
$47$	4.38105	+	2.52940i	0.639042	+	0.368951i	0.784245	−	0.620451i	$-0.213050\pi$
$47$	4.38105	+	2.52940i	0.639042	+	0.368951i	−0.145203	+	0.989402i	$0.546384\pi$
$48$		0			0
$49$	−0.156399	−	0.886981i	−0.0223427	−	0.126712i
$50$	1.68916	−	3.62242i	0.238884	−	0.512288i
$51$		0			0
$52$	−0.188908	+	2.15923i	−0.0261969	+	0.299431i
$53$	1.21046	+	1.44257i	0.166269	+	0.198152i	0.842745	−	0.538313i	$-0.180938\pi$
$53$	1.21046	+	1.44257i	0.166269	+	0.198152i	−0.676476	+	0.736465i	$0.736494\pi$
$54$		0			0
$55$	0.488804	+	0.698084i	0.0659103	+	0.0941296i
$56$	−4.36113	−	6.22834i	−0.582780	−	0.832297i
$57$		0			0
$58$	−5.52802	−	6.58804i	−0.725865	−	0.865052i
$59$	1.03749	−	11.8585i	0.135069	−	1.54385i	−0.562177	−	0.827017i	$-0.690036\pi$
$59$	1.03749	−	11.8585i	0.135069	−	1.54385i	0.697247	−	0.716831i	$-0.254408\pi$
$60$		0			0
$61$	4.70712	−	10.0944i	0.602684	−	1.29246i	−0.334095	−	0.942540i	$-0.608431\pi$
$61$	4.70712	−	10.0944i	0.602684	−	1.29246i	0.936779	−	0.349921i	$-0.113792\pi$
$62$	−0.0123960	−	0.0703015i	−0.00157430	−	0.00892830i
$63$		0			0
$64$	7.50220	+	4.33140i	0.937775	+	0.541425i
$65$	4.00221	+	1.45668i	0.496413	+	0.180680i
$66$		0			0
$67$	5.52276	−	6.58177i	0.674712	−	0.804091i	−0.314705	−	0.949190i	$-0.601906\pi$
$67$	5.52276	−	6.58177i	0.674712	−	0.804091i	0.989417	+	0.145099i	$0.0463500\pi$
$68$	−0.492472	−	0.492472i	−0.0597210	−	0.0597210i
$69$		0			0
$70$	−3.39777	+	1.23669i	−0.406111	+	0.147812i
$71$	2.34650	+	0.413752i	0.278479	+	0.0491033i	0.311143	−	0.950363i	$-0.399288\pi$
$71$	2.34650	+	0.413752i	0.278479	+	0.0491033i	−0.0326645	+	0.999466i	$0.510399\pi$
$72$		0			0
$73$			3.84166i			0.449632i	0.974401	+	0.224816i	$0.0721781\pi$
$73$			3.84166i			0.449632i	−0.974401	+	0.224816i	$0.927822\pi$
$74$	−4.60612	−	5.39967i	−0.535451	−	0.627699i
$75$		0			0
$76$	0.628923	+	0.440377i	0.0721425	+	0.0505147i
$77$	−0.291263	+	1.65183i	−0.0331925	+	0.188244i
$78$		0			0
$79$	−0.501285	−	5.72971i	−0.0563990	−	0.644643i	−0.970809	−	0.239854i	$-0.922900\pi$
$79$	−0.501285	−	5.72971i	−0.0563990	−	0.644643i	0.914410	−	0.404789i	$-0.132655\pi$
$80$	2.05409	−	2.05409i	0.229655	−	0.229655i
$81$		0			0
$82$	−1.87511	+	6.99801i	−0.207071	+	0.772801i
$83$	2.01658	−	5.54052i	0.221349	−	0.608151i	−0.778460	−	0.627694i	$-0.783999\pi$
$83$	2.01658	−	5.54052i	0.221349	−	0.608151i	0.999809	+	0.0195433i	$0.00622121\pi$
$84$		0			0
$85$	−1.18518	+	0.684267i	−0.128551	+	0.0742191i
$86$	10.9055	−	1.92293i	1.17597	−	0.207355i
$87$		0			0
$88$	−0.541173	−	2.01969i	−0.0576893	−	0.215299i
$89$	6.68423	+	0.584794i	0.708527	+	0.0619880i	0.435722	−	0.900081i	$-0.356493\pi$
$89$	6.68423	+	0.584794i	0.708527	+	0.0619880i	0.272805	+	0.962069i	$0.412049\pi$
$90$		0			0
$91$	3.54270	+	7.59734i	0.371376	+	0.796418i
$92$	−0.254219	+	0.178006i	−0.0265042	+	0.0185584i
$93$		0			0
$94$	−5.34959	+	2.49456i	−0.551768	+	0.257294i
$95$	1.15570	−	0.969750i	0.118573	−	0.0994943i
$96$		0			0
$97$	4.79559	−	1.28497i	0.486918	−	0.130469i	−0.00700404	−	0.999975i	$-0.502229\pi$
$97$	4.79559	−	1.28497i	0.486918	−	0.130469i	0.493922	+	0.869506i	$0.335563\pi$
$98$	0.952436	+	0.444128i	0.0962106	+	0.0448637i
$99$		0			0
$100$	−1.09372	−	1.89438i	−0.109372	−	0.189438i
$101$	6.13805	−	10.6314i	0.610758	−	1.05786i	−0.380354	−	0.924841i	$-0.624198\pi$
$101$	6.13805	−	10.6314i	0.610758	−	1.05786i	0.991113	−	0.133024i	$-0.0424687\pi$
$102$		0			0
$103$	−16.8999	−	4.52830i	−1.66519	−	0.446187i	−0.701384	−	0.712784i	$-0.747434\pi$
$103$	−16.8999	−	4.52830i	−1.66519	−	0.446187i	−0.963808	+	0.266597i	$0.914101\pi$
$104$	−8.00507	−	6.71705i	−0.784961	−	0.658661i
$105$		0			0
$106$	−2.18889	+	0.191503i	−0.212604	+	0.0186004i
$107$	2.15750	+	5.92769i	0.208574	+	0.573051i	0.999231	−	0.0392075i	$-0.0124833\pi$
$107$	2.15750	+	5.92769i	0.208574	+	0.573051i	−0.790658	+	0.612259i	$0.790261\pi$
$108$		0			0
$109$	2.07218	−	2.95938i	0.198479	−	0.283457i	−0.707559	−	0.706655i	$-0.750203\pi$
$109$	2.07218	−	2.95938i	0.198479	−	0.283457i	0.906037	+	0.423198i	$0.139092\pi$
$110$	−0.994352			−0.0948078
$111$		0			0
$112$	5.71752			0.540255
$113$	−1.15800	+	1.65380i	−0.108936	+	0.155577i	−0.869918	−	0.493196i	$-0.835829\pi$
$113$	−1.15800	+	1.65380i	−0.108936	+	0.155577i	0.760982	+	0.648773i	$0.224717\pi$
$114$		0			0
$115$	0.208571	+	0.573045i	0.0194494	+	0.0534368i
$116$	−4.68877	+	0.410215i	−0.435342	+	0.0380875i
$117$		0			0
$118$	10.6399	+	8.92794i	0.979482	+	0.821883i
$119$	−2.60178	−	0.697146i	−0.238505	−	0.0639072i
$120$		0			0
$121$	5.26937	−	9.12681i	0.479034	−	0.829710i
$122$	6.49791	+	11.2547i	0.588293	+	1.01895i
$123$		0			0
$124$	−0.0354080	−	0.0165110i	−0.00317973	−	0.00148273i
$125$	−10.2120	+	2.73629i	−0.913386	+	0.244741i
$126$		0			0
$127$	5.83402	−	4.89533i	0.517686	−	0.434390i	−0.346138	−	0.938183i	$-0.612507\pi$
$127$	5.83402	−	4.89533i	0.517686	−	0.434390i	0.863824	+	0.503794i	$0.168063\pi$
$128$	−2.89609	+	1.35047i	−0.255981	+	0.119366i
$129$		0			0
$130$	−4.07076	+	2.85038i	−0.357029	+	0.249995i
$131$	−2.25236	−	4.83020i	−0.196790	−	0.422016i	0.783007	−	0.622013i	$-0.213685\pi$
$131$	−2.25236	−	4.83020i	−0.196790	−	0.422016i	−0.979797	+	0.199996i	$0.935907\pi$
$132$		0			0
$133$	2.95807	+	0.258798i	0.256497	+	0.0224406i
$134$	2.59467	+	9.68344i	0.224145	+	0.836522i
$135$		0			0
$136$	3.30677	−	0.583073i	0.283553	−	0.0499981i
$137$	−13.3985	+	7.73564i	−1.14471	+	0.660900i	−0.947593	−	0.319479i	$-0.896492\pi$
$137$	−13.3985	+	7.73564i	−1.14471	+	0.660900i	−0.197120	+	0.980379i	$0.563159\pi$
$138$		0			0
$139$	0.235701	−	0.647583i	0.0199919	−	0.0549273i	−0.929295	−	0.369338i	$-0.879585\pi$
$139$	0.235701	−	0.647583i	0.0199919	−	0.0549273i	0.949287	+	0.314410i	$0.101807\pi$
$140$	−0.512173	+	1.91146i	−0.0432865	+	0.161548i
$141$		0			0
$142$	−1.96586	+	1.96586i	−0.164971	+	0.164971i
$143$	0.200916	+	2.29648i	0.0168014	+	0.192041i
$144$		0			0
$145$	−1.60600	+	9.10806i	−0.133371	+	0.756383i
$146$	−3.67181	−	2.57103i	−0.303881	−	0.212780i
$147$		0			0
$148$	−3.86663	+	0.369957i	−0.317835	+	0.0304103i
$149$			17.5389i			1.43684i	0.695609	+	0.718420i	$0.255135\pi$
$149$			17.5389i			1.43684i	−0.695609	+	0.718420i	$0.744865\pi$
$150$		0			0
$151$	−14.4578	−	2.54930i	−1.17656	−	0.207459i	−0.449018	−	0.893523i	$-0.648226\pi$
$151$	−14.4578	−	2.54930i	−1.17656	−	0.207459i	−0.727542	+	0.686063i	$0.759337\pi$
$152$	−3.47837	+	1.26602i	−0.282133	+	0.102688i
$153$		0			0
$154$	−1.38388	−	1.38388i	−0.111516	−	0.111516i
$155$	−0.0493461	+	0.0588084i	−0.00396357	+	0.00472360i
$156$		0			0
$157$	13.4993	+	4.91333i	1.07736	+	0.392126i	0.818924	−	0.573903i	$-0.194571\pi$
$157$	13.4993	+	4.91333i	1.07736	+	0.392126i	0.258434	+	0.966029i	$0.416793\pi$
$158$	5.81188	+	3.35549i	0.462368	+	0.266948i
$159$		0			0
$160$	−0.753063	−	4.27083i	−0.0595348	−	0.337639i
$161$	−0.507252	+	1.08780i	−0.0399770	+	0.0857310i
$162$		0			0
$163$	−1.54218	+	17.6272i	−0.120793	+	1.38067i	0.657827	+	0.753169i	$0.271476\pi$
$163$	−1.54218	+	17.6272i	−0.120793	+	1.38067i	−0.778619	+	0.627497i	$0.784080\pi$
$164$	2.54866	+	3.03737i	0.199017	+	0.237179i
$165$		0			0
$166$	3.94596	+	5.63542i	0.306266	+	0.437393i
$167$	−8.88376	−	12.6873i	−0.687446	−	0.981775i	−0.999497	−	0.0317094i	$-0.989905\pi$
$167$	−8.88376	−	12.6873i	−0.687446	−	0.981775i	0.312051	−	0.950065i	$-0.398984\pi$
$168$		0			0
$169$	−0.950697	−	1.13300i	−0.0731306	−	0.0871536i
$170$	0.139171	−	1.59073i	0.0106739	−	0.122004i
$171$		0			0
$172$	2.56127	−	5.49266i	0.195295	−	0.418811i
$173$	4.46874	+	25.3435i	0.339752	+	1.92683i	0.374024	+	0.927419i	$0.377978\pi$
$173$	4.46874	+	25.3435i	0.339752	+	1.92683i	−0.0342719	+	0.999413i	$0.510911\pi$
$174$		0			0
$175$	−7.32652	−	4.22997i	−0.553833	−	0.319756i
$176$	1.47749	+	0.537764i	0.111370	+	0.0405355i
$177$		0			0
$178$	−5.03236	+	5.99733i	−0.377191	+	0.449519i
$179$	−14.1682	−	14.1682i	−1.05898	−	1.05898i	−0.998148	−	0.0608325i	$-0.980624\pi$
$179$	−14.1682	−	14.1682i	−1.05898	−	1.05898i	−0.0608325	−	0.998148i	$-0.519376\pi$
$180$		0			0
$181$	−9.14115	+	3.32711i	−0.679456	+	0.247302i	−0.658614	−	0.752481i	$-0.728857\pi$
$181$	−9.14115	+	3.32711i	−0.679456	+	0.247302i	−0.0208423	+	0.999783i	$0.506635\pi$
$182$	−9.63240	−	1.69845i	−0.714001	−	0.125898i
$183$		0			0
$184$		−	1.49624i		−	0.110304i
$185$	−1.26428	+	7.52712i	−0.0929518	+	0.553405i
$186$		0			0
$187$	−0.606770	−	0.424865i	−0.0443714	−	0.0310692i
$188$	−0.560955	+	3.18133i	−0.0409118	+	0.232023i
$189$		0			0
$190$	0.153421	+	1.75361i	0.0111304	+	0.127220i
$191$	7.68086	−	7.68086i	0.555767	−	0.555767i	−0.372332	−	0.928100i	$-0.621442\pi$
$191$	7.68086	−	7.68086i	0.555767	−	0.555767i	0.928100	+	0.372332i	$0.121442\pi$
$192$		0			0
$193$	5.18230	−	19.3406i	0.373030	−	1.39217i	−0.483172	−	0.875525i	$-0.660515\pi$
$193$	5.18230	−	19.3406i	0.373030	−	1.39217i	0.856202	−	0.516641i	$-0.172818\pi$
$194$	−1.98128	+	5.44354i	−0.142248	+	0.390823i
$195$		0			0
$196$	0.498085	−	0.287570i	0.0355775	−	0.0205407i
$197$	−16.4707	+	2.90422i	−1.17349	+	0.206917i	−0.726207	−	0.687476i	$-0.758719\pi$
$197$	−16.4707	+	2.90422i	−1.17349	+	0.206917i	−0.447280	+	0.894394i	$0.647607\pi$
$198$		0			0
$199$	5.56230	+	20.7588i	0.394301	+	1.47155i	0.822967	+	0.568089i	$0.192317\pi$
$199$	5.56230	+	20.7588i	0.394301	+	1.47155i	−0.428666	+	0.903463i	$0.641016\pi$
$200$	10.5060	+	0.919154i	0.742885	+	0.0649940i
$201$		0			0
$202$	6.05349	+	12.9817i	0.425922	+	0.913393i
$203$	−14.9111	+	10.4409i	−1.04656	+	0.732807i
$204$		0			0
$205$	7.06120	−	3.29269i	0.493176	−	0.229972i
$206$	15.6383	−	13.1221i	1.08957	−	0.914261i
$207$		0			0
$208$	7.59022	−	2.03379i	0.526287	−	0.141018i
$209$	0.740070	+	0.345100i	0.0511917	+	0.0238711i
$210$		0			0
$211$	−0.219229	−	0.379716i	−0.0150924	−	0.0261407i	0.858381	−	0.513013i	$-0.171471\pi$
$211$	−0.219229	−	0.379716i	−0.0150924	−	0.0261407i	−0.873473	+	0.486873i	$0.838138\pi$
$212$	−0.601261	+	1.04141i	−0.0412948	+	0.0715246i
$213$		0			0
$214$	−7.10952	−	1.90499i	−0.485997	−	0.130223i
$215$	−9.12263	−	7.65479i	−0.622158	−	0.522053i
$216$		0			0
$217$	−0.150522	+	0.0131690i	−0.0102181	+	0.000893971i
$218$	1.44173	+	3.96113i	0.0976465	+	0.268282i
$219$		0			0
$220$	−0.312136	+	0.445777i	−0.0210442	+	0.0300543i
$221$	−3.70195			−0.249020
$222$		0			0
$223$	−17.8703			−1.19668			−0.598342	−	0.801241i	$-0.704174\pi$
$223$	−17.8703			−1.19668			−0.598342	+	0.801241i	$0.704174\pi$
$224$	4.89581	−	6.99194i	0.327115	−	0.467168i
$225$		0			0
$226$	−0.805690	−	2.21361i	−0.0535937	−	0.147247i
$227$	−8.85906	+	0.775067i	−0.587997	+	0.0514430i	−0.377272	−	0.926102i	$-0.623138\pi$
$227$	−8.85906	+	0.775067i	−0.587997	+	0.0514430i	−0.210724	+	0.977545i	$0.567582\pi$
$228$		0			0
$229$	19.2359	+	16.1408i	1.27114	+	1.06662i	0.994401	+	0.105673i	$0.0336997\pi$
$229$	19.2359	+	16.1408i	1.27114	+	1.06662i	0.276744	+	0.960944i	$0.410745\pi$
$230$	−0.687297	−	0.184161i	−0.0453190	−	0.0121432i
$231$		0			0
$232$	11.3460	−	19.6518i	0.744899	−	1.29020i
$233$	5.56538	+	9.63953i	0.364600	+	0.631507i	0.988712	−	0.149829i	$-0.0478722\pi$
$233$	5.56538	+	9.63953i	0.364600	+	0.631507i	−0.624111	+	0.781335i	$0.714539\pi$
$234$		0			0
$235$	5.75298	+	2.68266i	0.375283	+	0.174997i
$236$	7.34244	−	1.96740i	0.477952	−	0.128067i
$237$		0			0
$238$	2.40757	−	2.02019i	0.156059	−	0.130949i
$239$	13.3643	−	6.23185i	0.864462	−	0.403105i	0.0607704	−	0.998152i	$-0.480644\pi$
$239$	13.3643	−	6.23185i	0.864462	−	0.403105i	0.803691	+	0.595047i	$0.202866\pi$
$240$		0			0
$241$	5.39798	−	3.77970i	0.347714	−	0.243472i	−0.386652	−	0.922226i	$-0.626368\pi$
$241$	5.39798	−	3.77970i	0.347714	−	0.243472i	0.734366	+	0.678754i	$0.237480\pi$
$242$	5.19678	+	11.1445i	0.334062	+	0.716397i
$243$		0			0
$244$	7.08534	+	0.619887i	0.453593	+	0.0396842i
$245$	−0.292502	−	1.09163i	−0.0186872	−	0.0697417i
$246$		0			0
$247$	4.01901	−	0.708660i	0.255724	−	0.0450910i
$248$	0.163122	−	0.0941786i	0.0103583	−	0.00598034i
$249$		0			0
$250$	4.21905	−	11.5917i	0.266836	−	0.733126i
$251$	8.17612	−	30.5137i	0.516072	−	1.92601i	0.182953	−	0.983122i	$-0.441434\pi$
$251$	8.17612	−	30.5137i	0.516072	−	1.92601i	0.333118	−	0.942885i	$-0.391899\pi$
$252$		0			0
$253$	−0.233396	+	0.233396i	−0.0146735	+	0.0146735i
$254$	0.774475	+	8.85229i	0.0485949	+	0.555442i
$255$		0			0
$256$	−2.36111	+	13.3905i	−0.147569	+	0.836908i
$257$	−5.78539	−	4.05097i	−0.360883	−	0.252693i	0.379046	−	0.925378i	$-0.376252\pi$
$257$	−5.78539	−	4.05097i	−0.360883	−	0.252693i	−0.739929	+	0.672685i	$0.765141\pi$
$258$		0			0
$259$	−12.2353	+	8.71622i	−0.760265	+	0.541600i
$260$			2.71972i			0.168670i
$261$		0			0
$262$	6.12404	+	1.07983i	0.378344	+	0.0667123i
$263$	14.0689	−	5.12064i	0.867523	−	0.315752i	0.130359	−	0.991467i	$-0.458387\pi$
$263$	14.0689	−	5.12064i	0.867523	−	0.315752i	0.737164	+	0.675714i	$0.236165\pi$
$264$		0			0
$265$	1.67085	+	1.67085i	0.102639	+	0.102639i
$266$	−2.22705	+	2.65409i	−0.136549	+	0.162733i
$267$		0			0
$268$	5.15566	+	1.87651i	0.314932	+	0.114626i
$269$	3.88508	+	2.24305i	0.236877	+	0.136761i	0.613741	−	0.789508i	$-0.289664\pi$
$269$	3.88508	+	2.24305i	0.236877	+	0.136761i	−0.376863	+	0.926269i	$0.622997\pi$
$270$		0			0
$271$	−3.13564	−	17.7831i	−0.190476	−	1.08025i	−0.918715	−	0.394921i	$-0.870772\pi$
$271$	−3.13564	−	17.7831i	−0.190476	−	1.08025i	0.728239	−	0.685324i	$-0.240339\pi$
$272$	−1.06709	+	2.28838i	−0.0647018	+	0.138753i
$273$		0			0
$274$	1.57333	−	17.9832i	0.0950483	−	1.08641i
$275$	−1.49543	−	1.78219i	−0.0901780	−	0.107470i
$276$		0			0
$277$	4.21405	+	6.01828i	0.253198	+	0.361604i	0.925549	−	0.378629i	$-0.123604\pi$
$277$	4.21405	+	6.01828i	0.253198	+	0.361604i	−0.672351	+	0.740232i	$0.734715\pi$
$278$	0.461209	+	0.658675i	0.0276615	+	0.0395047i
$279$		0			0
$280$	−6.13260	−	7.30854i	−0.366493	−	0.436769i
$281$	2.54273	−	29.0636i	0.151687	−	1.73379i	−0.414971	−	0.909835i	$-0.636208\pi$
$281$	2.54273	−	29.0636i	0.151687	−	1.73379i	0.566657	−	0.823953i	$-0.308236\pi$
$282$		0			0
$283$	−5.97665	+	12.8170i	−0.355275	+	0.761889i	−0.999997	−	0.00252776i	$-0.999195\pi$
$283$	−5.97665	+	12.8170i	−0.355275	+	0.761889i	0.644722	+	0.764417i	$0.276973\pi$
$284$	0.264210	+	1.49841i	0.0156780	+	0.0889143i
$285$		0			0
$286$	−2.32941	−	1.34489i	−0.137741	−	0.0795248i
$287$	14.4099	+	5.24477i	0.850589	+	0.309589i
$288$		0			0
$289$	−10.1628	+	12.1115i	−0.597811	+	0.712443i
$290$	−7.63056	−	7.63056i	−0.448082	−	0.448082i
$291$		0			0
$292$	−2.30523	+	0.839036i	−0.134904	+	0.0491009i
$293$	−21.8930	−	3.86033i	−1.27900	−	0.225523i	−0.507447	−	0.861683i	$-0.669411\pi$
$293$	−21.8930	−	3.86033i	−1.27900	−	0.225523i	−0.771557	+	0.636160i	$0.780522\pi$
$294$		0			0
$295$		−	14.9367i		−	0.869650i
$296$	9.23143	−	16.2935i	0.536566	−	0.947043i
$297$		0			0
$298$	−16.7635	−	11.7379i	−0.971081	−	0.679958i
$299$	−0.286450	+	1.62454i	−0.0165658	+	0.0939495i
$300$		0			0
$301$	−2.04284	−	23.3497i	−0.117747	−	1.34586i
$302$	12.1125	−	12.1125i	0.696995	−	0.696995i
$303$		0			0
$304$	0.720420	−	2.68864i	0.0413189	−	0.154204i
$305$	4.78000	−	13.1329i	0.273702	−	0.751990i
$306$		0			0
$307$	−18.4306	+	10.6409i	−1.05189	+	0.607309i	−0.923178	−	0.384373i	$-0.874418\pi$
$307$	−18.4306	+	10.6409i	−1.05189	+	0.607309i	−0.128712	+	0.991682i	$0.541084\pi$
$308$	−1.05482	+	0.185992i	−0.0601037	+	0.0105979i
$309$		0			0
$310$	−0.0231835	−	0.0865219i	−0.00131673	−	0.00491411i
$311$	18.9694	+	1.65960i	1.07565	+	0.0941075i	0.611189	−	0.791484i	$-0.290691\pi$
$311$	18.9694	+	1.65960i	1.07565	+	0.0941075i	0.464464	+	0.885592i	$0.346247\pi$
$312$		0			0
$313$	7.73465	+	16.5870i	0.437188	+	0.937553i	0.994250	+	0.107082i	$0.0341508\pi$
$313$	7.73465	+	16.5870i	0.437188	+	0.937553i	−0.557062	+	0.830471i	$0.688071\pi$
$314$	−13.7305	+	9.61419i	−0.774856	+	0.542560i
$315$		0			0
$316$	3.32870	−	1.55220i	0.187254	−	0.0873179i
$317$	10.2990	−	8.64190i	0.578450	−	0.485377i	−0.305987	−	0.952036i	$-0.598987\pi$
$317$	10.2990	−	8.64190i	0.578450	−	0.485377i	0.884438	+	0.466658i	$0.154542\pi$
$318$		0			0
$319$	−4.83529	+	1.29561i	−0.270724	+	0.0725403i
$320$	9.85152	+	4.59384i	0.550717	+	0.256803i
$321$		0			0
$322$	−0.700233	−	1.21284i	−0.0390224	−	0.0675889i
$323$	−0.655661	+	1.13564i	−0.0364819	+	0.0631886i
$324$		0			0
$325$	−11.2309	−	3.00931i	−0.622978	−	0.166926i
$326$	−15.8157	−	13.2710i	−0.875953	−	0.735012i
$327$		0			0
$328$	−19.0434	+	1.66608i	−1.05150	+	0.0919939i
$329$	4.27308	+	11.7402i	0.235582	+	0.647257i
$330$		0			0
$331$	3.83346	−	5.47475i	0.210706	−	0.300920i	−0.699862	−	0.714278i	$-0.746755\pi$
$331$	3.83346	−	5.47475i	0.210706	−	0.300920i	0.910569	+	0.413358i	$0.135644\pi$
$332$	3.76508			0.206636
$333$		0			0
$334$	18.0719			0.988848
$335$	6.18371	−	8.83125i	0.337852	−	0.482503i
$336$		0			0
$337$	−6.42986	−	17.6659i	−0.350257	−	0.962322i	−0.982288	−	0.187379i	$-0.940001\pi$
$337$	−6.42986	−	17.6659i	−0.350257	−	0.962322i	0.632031	−	0.774943i	$-0.282221\pi$
$338$	1.71916	−	0.150407i	0.0935100	−	0.00818106i
$339$		0			0
$340$	−0.669452	−	0.561737i	−0.0363061	−	0.0304645i
$341$	−0.0401359	−	0.0107544i	−0.00217348	−	0.000582383i
$342$		0			0
$343$	9.75607	−	16.8980i	0.526778	−	0.912407i
$344$	14.6094	+	25.3043i	0.787687	+	1.36431i
$345$		0			0
$346$	−27.2137	−	12.6900i	−1.46302	−	0.682217i
$347$	−32.5835	+	8.73072i	−1.74917	+	0.468690i	−0.984450	−	0.175668i	$-0.943792\pi$
$347$	−32.5835	+	8.73072i	−1.74917	+	0.468690i	−0.764724	+	0.644357i	$0.777125\pi$
$348$		0			0
$349$	−14.4105	+	12.0918i	−0.771375	+	0.647261i	−0.941061	−	0.338238i	$-0.890169\pi$
$349$	−14.4105	+	12.0918i	−0.771375	+	0.647261i	0.169686	+	0.985498i	$0.445725\pi$
$350$	8.94623	−	4.17170i	0.478196	−	0.222987i
$351$		0			0
$352$	1.92278	−	1.34635i	0.102485	−	0.0717605i
$353$	11.1786	+	23.9725i	0.594975	+	1.27593i	0.941223	+	0.337785i	$0.109678\pi$
$353$	11.1786	+	23.9725i	0.594975	+	1.27593i	−0.346249	+	0.938143i	$0.612545\pi$
$354$		0			0
$355$	2.97840	+	0.260576i	0.158077	+	0.0138299i
$356$	1.10895	+	4.13867i	0.0587744	+	0.219349i
$357$		0			0
$358$	23.0239	−	4.05973i	1.21685	−	0.214563i
$359$	12.0660	−	6.96633i	0.636821	−	0.367669i	−0.146568	−	0.989201i	$-0.546823\pi$
$359$	12.0660	−	6.96633i	0.636821	−	0.367669i	0.783389	+	0.621532i	$0.213489\pi$
$360$		0			0
$361$	−6.00396	+	16.4957i	−0.315998	+	0.868197i
$362$	2.93771	−	10.9637i	0.154403	−	0.576238i
$363$		0			0
$364$	−3.78513	+	3.78513i	−0.198395	+	0.198395i
$365$	0.420130	+	4.80211i	0.0219906	+	0.251354i
$366$		0			0
$367$	−6.15023	+	34.8797i	−0.321040	+	1.82071i	0.215118	+	0.976588i	$0.430986\pi$
$367$	−6.15023	+	34.8797i	−0.321040	+	1.82071i	−0.536157	+	0.844118i	$0.680125\pi$
$368$	0.921647	+	0.645344i	0.0480442	+	0.0336409i
$369$		0			0
$370$	−6.34821	−	6.24591i	−0.330028	−	0.324710i
$371$			4.65076i			0.241456i
$372$		0			0
$373$	−11.2304	−	1.98022i	−0.581488	−	0.102532i	−0.124836	−	0.992177i	$-0.539840\pi$
$373$	−11.2304	−	1.98022i	−0.581488	−	0.102532i	−0.456652	+	0.889645i	$0.650952\pi$
$374$	0.812163	−	0.295603i	0.0419959	−	0.0152853i
$375$		0			0
$376$	−11.0128	−	11.0128i	−0.567943	−	0.567943i
$377$	−16.0811	+	19.1648i	−0.828221	+	0.987036i
$378$		0			0
$379$	2.86426	+	1.04250i	0.147127	+	0.0535498i	0.414534	−	0.910034i	$-0.363945\pi$
$379$	2.86426	+	1.04250i	0.147127	+	0.0535498i	−0.267407	+	0.963584i	$0.586167\pi$
$380$	0.834321	+	0.481695i	0.0427998	+	0.0247105i
$381$		0			0
$382$	2.20086	+	12.4817i	0.112606	+	0.638619i
$383$	3.27704	−	7.02764i	0.167449	−	0.359096i	−0.804620	−	0.593790i	$-0.797631\pi$
$383$	3.27704	−	7.02764i	0.167449	−	0.359096i	0.972069	+	0.234694i	$0.0754088\pi$
$384$		0			0
$385$	−0.183434	+	2.09666i	−0.00934867	+	0.106856i
$386$	15.0173	+	17.8969i	0.764359	+	0.910927i
$387$		0			0
$388$	1.81844	+	2.59700i	0.0923174	+	0.131843i
$389$	−6.92263	−	9.88655i	−0.350991	−	0.501268i	0.604371	−	0.796703i	$-0.293424\pi$
$389$	−6.92263	−	9.88655i	−0.350991	−	0.501268i	−0.955363	+	0.295435i	$0.904535\pi$
$390$		0			0
$391$	−0.340712	−	0.406045i	−0.0172305	−	0.0205346i
$392$	−0.241671	+	2.76232i	−0.0122062	+	0.139518i
$393$		0			0
$394$	8.24718	−	17.6861i	0.415487	−	0.891015i
$395$	−1.25322	−	7.10738i	−0.0630565	−	0.357611i
$396$		0			0
$397$	−6.10642	−	3.52554i	−0.306473	−	0.176942i	0.338874	−	0.940832i	$-0.389954\pi$
$397$	−6.10642	−	3.52554i	−0.306473	−	0.176942i	−0.645347	+	0.763890i	$0.723287\pi$
$398$	−23.5636	−	8.57645i	−1.18114	−	0.429898i
$399$		0			0
$400$	−5.09753	+	6.07500i	−0.254876	+	0.303750i
$401$	−6.81080	−	6.81080i	−0.340115	−	0.340115i	0.516295	−	0.856411i	$-0.327311\pi$
$401$	−6.81080	−	6.81080i	−0.340115	−	0.340115i	−0.856411	+	0.516295i	$0.827311\pi$
$402$		0			0
$403$	−0.195140	+	0.0710251i	−0.00972061	+	0.00353801i
$404$	7.72008	+	1.36126i	0.384088	+	0.0677251i
$405$		0			0
$406$		−	21.2395i		−	1.05410i
$407$	−3.98160	+	1.10161i	−0.197361	+	0.0546046i
$408$		0			0
$409$	2.69763	+	1.88890i	0.133389	+	0.0934002i	0.638367	−	0.769732i	$-0.279610\pi$
$409$	2.69763	+	1.88890i	0.133389	+	0.0934002i	−0.504977	+	0.863133i	$0.668499\pi$
$410$	−1.57859	+	8.95265i	−0.0779612	+	0.442140i
$411$		0			0
$412$	−0.973745	−	11.1300i	−0.0479730	−	0.548334i
$413$	20.7880	−	20.7880i	1.02291	−	1.02291i
$414$		0			0
$415$	1.91483	−	7.14624i	0.0939952	−	0.350795i
$416$	4.01225	−	11.0236i	0.196717	−	0.540475i
$417$		0			0
$418$	−0.825135	+	0.476392i	−0.0403587	+	0.0233011i
$419$	−38.6086	+	6.80774i	−1.88615	+	0.332580i	−0.993091	−	0.117351i	$-0.962560\pi$
$419$	−38.6086	+	6.80774i	−1.88615	+	0.332580i	−0.893064	+	0.449931i	$0.851449\pi$
$420$		0			0
$421$	7.57908	+	28.2855i	0.369382	+	1.37855i	0.861382	+	0.507957i	$0.169599\pi$
$421$	7.57908	+	28.2855i	0.369382	+	1.37855i	−0.492001	+	0.870595i	$0.663734\pi$
$422$	0.509648	+	0.0445884i	0.0248093	+	0.00217053i
$423$		0			0
$424$	−2.45018	−	5.25442i	−0.118991	−	0.255177i
$425$	3.06039	−	2.14291i	0.148451	−	0.103946i
$426$		0			0
$427$	24.9301	−	11.6251i	1.20645	−	0.562577i
$428$	−3.08577	+	2.58927i	−0.149156	+	0.125157i
$429$		0			0
$430$	13.4217	−	3.59633i	0.647251	−	0.173430i
$431$	−2.25930	−	1.05353i	−0.108827	−	0.0507467i	0.367443	−	0.930046i	$-0.380233\pi$
$431$	−2.25930	−	1.05353i	−0.108827	−	0.0507467i	−0.476269	+	0.879299i	$0.658011\pi$
$432$		0			0
$433$	2.41112	+	4.17618i	0.115871	+	0.200694i	0.918128	−	0.396285i	$-0.129701\pi$
$433$	2.41112	+	4.17618i	0.115871	+	0.200694i	−0.802257	+	0.596979i	$0.796367\pi$
$434$	0.0881504	−	0.152681i	0.00423136	−	0.00732892i
$435$		0			0
$436$	2.22838	+	0.597094i	0.106720	+	0.0285956i
$437$	0.447622	+	0.375599i	0.0214126	+	0.0179673i
$438$		0			0
$439$	−6.42476	+	0.562094i	−0.306637	+	0.0268273i	−0.239436	−	0.970912i	$-0.576963\pi$
$439$	−6.42476	+	0.562094i	−0.306637	+	0.0268273i	−0.0672013	+	0.997739i	$0.521407\pi$
$440$	−0.897348	−	2.46544i	−0.0427794	−	0.117535i
$441$		0			0
$442$	2.47753	−	3.53828i	0.117844	−	0.168299i
$443$	20.2546			0.962327			0.481163	−	0.876631i	$-0.340214\pi$
$443$	20.2546			0.962327			0.481163	+	0.876631i	$0.340214\pi$
$444$		0			0
$445$	8.41930			0.399113
$446$	11.9597	−	17.0802i	0.566309	−	0.808773i
$447$		0			0
$448$	7.31730	+	20.1041i	0.345710	+	0.949831i
$449$	−33.9648	+	2.97153i	−1.60290	+	0.140235i	−0.853213	−	0.521562i	$-0.825349\pi$
$449$	−33.9648	+	2.97153i	−1.60290	+	0.140235i	−0.749683	+	0.661797i	$0.769794\pi$
$450$		0			0
$451$	3.23044	+	2.71066i	0.152115	+	0.127640i
$452$	−1.24530	−	0.333676i	−0.0585738	−	0.0156948i
$453$		0			0
$454$	5.18813	−	8.98610i	0.243491	−	0.421739i
$455$	5.25927	+	9.10932i	0.246558	+	0.427051i
$456$		0			0
$457$	23.4479	+	10.9339i	1.09685	+	0.511467i	0.884884	−	0.465811i	$-0.154237\pi$
$457$	23.4479	+	10.9339i	1.09685	+	0.511467i	0.211961	+	0.977278i	$0.432015\pi$
$458$	−28.3009	+	7.58320i	−1.32241	+	0.354339i
$459$		0			0
$460$	−0.298310	+	0.250311i	−0.0139088	+	0.0116708i
$461$	−17.2517	+	8.04462i	−0.803494	+	0.374675i	−0.780575	−	0.625062i	$-0.785074\pi$
$461$	−17.2517	+	8.04462i	−0.803494	+	0.374675i	−0.0229187	+	0.999737i	$0.507296\pi$
$462$		0			0
$463$	12.7334	−	8.91605i	0.591773	−	0.414364i	−0.238964	−	0.971028i	$-0.576808\pi$
$463$	12.7334	−	8.91605i	0.591773	−	0.414364i	0.830738	+	0.556664i	$0.187919\pi$
$464$	7.21140	+	15.4649i	0.334781	+	0.717939i
$465$		0			0
$466$	−12.9380	−	1.13193i	−0.599341	−	0.0524355i
$467$	7.42105	+	27.6957i	0.343405	+	1.28161i	0.894464	+	0.447139i	$0.147557\pi$
$467$	7.42105	+	27.6957i	0.343405	+	1.28161i	−0.551059	+	0.834466i	$0.685776\pi$
$468$		0			0
$469$	20.8969	−	3.68468i	0.964928	−	0.170143i
$470$	−6.41423	+	3.70326i	−0.295867	+	0.170819i
$471$		0			0
$472$	−12.5344	+	34.4380i	−0.576944	+	1.58514i
$473$	1.66827	−	6.22607i	0.0767072	−	0.286275i
$474$		0			0
$475$	−2.91229	+	2.91229i	−0.133625	+	0.133625i
$476$	−0.149911	−	1.71349i	−0.00687116	−	0.0785377i
$477$		0			0
$478$	−2.98770	+	16.9441i	−0.136654	+	0.775004i
$479$	0.206065	+	0.144288i	0.00941533	+	0.00659269i	0.578275	−	0.815842i	$-0.303726\pi$
$479$	0.206065	+	0.144288i	0.00941533	+	0.00659269i	−0.568859	+	0.822435i	$0.692615\pi$
$480$		0			0
$481$	−13.1424	+	15.9234i	−0.599241	+	0.726044i
$482$			7.68889i			0.350220i
$483$		0			0
$484$	6.62751	+	1.16861i	0.301250	+	0.0531186i
$485$	5.85400	−	2.13068i	0.265817	−	0.0967493i
$486$		0			0
$487$	−9.81060	−	9.81060i	−0.444561	−	0.444561i	0.448981	−	0.893541i	$-0.351787\pi$
$487$	−9.81060	−	9.81060i	−0.444561	−	0.444561i	−0.893541	+	0.448981i	$0.851787\pi$
$488$	−22.0415	+	26.2680i	−0.997770	+	1.18910i
$489$		0			0
$490$	1.23913	+	0.451005i	0.0559780	+	0.0203743i
$491$	19.9970	+	11.5453i	0.902452	+	0.521031i	0.877995	−	0.478670i	$-0.158881\pi$
$491$	19.9970	+	11.5453i	0.902452	+	0.521031i	0.0244568	+	0.999701i	$0.492214\pi$
$492$		0			0
$493$	−1.39592	−	7.91667i	−0.0628692	−	0.356549i
$494$	−2.01240	+	4.31560i	−0.0905420	+	0.194168i
$495$		0			0
$496$	−0.0123446	+	0.141100i	−0.000554290	+	0.00633556i
$497$	3.78249	+	4.50780i	0.169668	+	0.202202i
$498$		0			0
$499$	14.8183	+	21.1627i	0.663357	+	0.947372i	0.999984	+	0.00573343i	$0.00182502\pi$
$499$	14.8183	+	21.1627i	0.663357	+	0.947372i	−0.336627	+	0.941638i	$0.609286\pi$
$500$	−3.87228	−	5.53019i	−0.173174	−	0.247318i
$501$		0			0
$502$	23.6928	+	28.2359i	1.05746	+	1.26023i
$503$	2.13712	−	24.4274i	0.0952894	−	1.08916i	−0.786523	−	0.617561i	$-0.788121\pi$
$503$	2.13712	−	24.4274i	0.0952894	−	1.08916i	0.881812	−	0.471601i	$-0.156324\pi$
$504$		0			0
$505$	6.50995	−	13.9606i	0.289689	−	0.621240i
$506$	−0.0668767	−	0.379277i	−0.00297303	−	0.0168609i
$507$		0			0
$508$	4.21167	+	2.43161i	0.186863	+	0.107885i
$509$	15.5013	+	5.64202i	0.687085	+	0.250078i	0.661886	−	0.749604i	$-0.269756\pi$
$509$	15.5013	+	5.64202i	0.687085	+	0.250078i	0.0251982	+	0.999682i	$0.491978\pi$
$510$		0			0
$511$	−6.09856	+	7.26798i	−0.269785	+	0.321517i
$512$	−15.7374	−	15.7374i	−0.695503	−	0.695503i
$513$		0			0
$514$	7.74374	−	2.81849i	0.341562	−	0.124318i
$515$	−21.6202	−	3.81223i	−0.952700	−	0.167987i
$516$		0			0
$517$			3.43575i			0.151104i
$518$	−0.142376	−	17.5277i	−0.00625566	−	0.770123i
$519$		0			0
$520$	−10.7410	−	7.52093i	−0.471024	−	0.329815i
$521$	0.0745386	−	0.422729i	0.00326559	−	0.0185201i	−0.983131	−	0.182901i	$-0.941451\pi$
$521$	0.0745386	−	0.422729i	0.00326559	−	0.0185201i	0.986397	+	0.164380i	$0.0525625\pi$
$522$		0			0
$523$	0.120380	+	1.37595i	0.00526387	+	0.0601663i	0.998372	−	0.0570329i	$-0.0181640\pi$
$523$	0.120380	+	1.37595i	0.00526387	+	0.0601663i	−0.993108	+	0.117199i	$0.962608\pi$
$524$	2.40649	−	2.40649i	0.105128	−	0.105128i
$525$		0			0
$526$	−4.52133	+	16.8738i	−0.197139	+	0.735734i
$527$	0.0228220	−	0.0627029i	0.000994142	−	0.00273138i
$528$		0			0
$529$	19.7140	−	11.3819i	0.857132	−	0.494865i
$530$	−2.71519	+	0.478762i	−0.117941	+	0.0207961i
$531$		0			0
$532$	0.490762	+	1.83155i	0.0212772	+	0.0794077i
$533$	20.9953	+	1.83685i	0.909408	+	0.0795629i
$534$		0			0
$535$	3.34516	+	7.17372i	0.144624	+	0.310147i
$536$	−21.6680	+	15.1721i	−0.935916	+	0.655335i
$537$		0			0
$538$	−4.74397	+	2.21215i	−0.204527	+	0.0953725i
$539$	0.468587	−	0.393191i	0.0201835	−	0.0169360i
$540$		0			0
$541$	0.451315	−	0.120930i	0.0194036	−	0.00519917i	−0.249104	−	0.968477i	$-0.580136\pi$
$541$	0.451315	−	0.120930i	0.0194036	−	0.00519917i	0.268508	+	0.963278i	$0.413470\pi$
$542$	19.0954	+	8.90433i	0.820217	+	0.382474i
$543$		0			0
$544$	1.88472	+	3.26444i	0.0808069	+	0.139962i
$545$	2.26660	−	3.92587i	0.0970906	−	0.168166i
$546$		0			0
$547$	−3.52944	−	0.945710i	−0.150908	−	0.0404356i	0.182574	−	0.983192i	$-0.441557\pi$
$547$	−3.52944	−	0.945710i	−0.150908	−	0.0404356i	−0.333482	+	0.942756i	$0.608224\pi$
$548$	−7.56816	−	6.35044i	−0.323296	−	0.271277i
$549$		0			0
$550$	2.70421	−	0.236588i	0.115308	−	0.0100882i
$551$	3.03096	+	8.32749i	0.129123	+	0.354763i
$552$		0			0
$553$	8.14744	−	11.6358i	0.346464	−	0.494802i
$554$	−8.57246			−0.364209
$555$		0			0
$556$	0.440068			0.0186630
$557$	−16.4773	+	23.5320i	−0.698166	+	0.997085i	0.300891	+	0.953659i	$0.402716\pi$
$557$	−16.4773	+	23.5320i	−0.698166	+	0.997085i	−0.999057	+	0.0434259i	$0.986173\pi$
$558$		0			0
$559$	−11.0178	−	30.2710i	−0.466001	−	1.28033i
$560$	7.14695	−	0.625277i	0.302014	−	0.0264228i
$561$		0			0
$562$	26.0769	+	21.8811i	1.09999	+	0.923000i
$563$	−33.1275	−	8.87648i	−1.39616	−	0.374099i	−0.519194	−	0.854657i	$-0.673768\pi$
$563$	−33.1275	−	8.87648i	−1.39616	−	0.374099i	−0.876963	+	0.480558i	$0.840434\pi$
$564$		0			0
$565$	−1.26665	+	2.19391i	−0.0532886	+	0.0922985i
$566$	−8.25043	−	14.2902i	−0.346792	−	0.600661i
$567$		0			0
$568$	−6.64831	−	3.10016i	−0.278957	−	0.130080i
$569$	−19.9963	+	5.35798i	−0.838286	+	0.224618i	−0.652325	−	0.757939i	$-0.726206\pi$
$569$	−19.9963	+	5.35798i	−0.838286	+	0.224618i	−0.185961	+	0.982557i	$0.559540\pi$
$570$		0			0
$571$	10.6443	−	8.93165i	0.445451	−	0.373778i	−0.392293	−	0.919840i	$-0.628318\pi$
$571$	10.6443	−	8.93165i	0.445451	−	0.373778i	0.837745	+	0.546062i	$0.183874\pi$
$572$	−1.33415	+	0.622124i	−0.0557836	+	0.0260123i
$573$		0			0
$574$	−14.6567	+	10.2627i	−0.611760	+	0.428359i
$575$	−0.703571	−	1.50881i	−0.0293409	−	0.0629219i
$576$		0			0
$577$	−15.2735	−	1.33626i	−0.635845	−	0.0556292i	−0.235324	−	0.971917i	$-0.575615\pi$
$577$	−15.2735	−	1.33626i	−0.635845	−	0.0556292i	−0.400521	+	0.916288i	$0.631171\pi$
$578$	−4.77462	−	17.8191i	−0.198598	−	0.741177i
$579$		0			0
$580$	−5.81615	+	1.02554i	−0.241503	+	0.0425834i
$581$	12.6106	−	7.28074i	0.523176	−	0.302056i
$582$		0			0
$583$	−0.437430	+	1.20183i	−0.0181165	+	0.0497746i
$584$	3.06113	−	11.4243i	0.126670	−	0.472740i
$585$		0			0
$586$	18.3416	−	18.3416i	0.757683	−	0.757683i
$587$	0.463599	+	5.29896i	0.0191348	+	0.218712i	0.999742	+	0.0227267i	$0.00723476\pi$
$587$	0.463599	+	5.29896i	0.0191348	+	0.218712i	−0.980607	+	0.195985i	$0.937210\pi$
$588$		0			0
$589$	−0.0127735	+	0.0724420i	−0.000526322	+	0.00298492i
$590$	14.2764	+	9.99641i	0.587748	+	0.411546i
$591$		0			0
$592$	6.05482	+	12.7139i	0.248851	+	0.522540i
$593$			5.76363i			0.236684i	0.992973	+	0.118342i	$0.0377579\pi$
$593$			5.76363i			0.236684i	−0.992973	+	0.118342i	$0.962242\pi$
$594$		0			0
$595$	−3.32850	−	0.586904i	−0.136455	−	0.0240607i
$596$	−10.5244	+	3.83057i	−0.431097	+	0.156906i
$597$		0			0
$598$	−1.36101	−	1.36101i	−0.0556558	−	0.0556558i
$599$	11.2750	−	13.4370i	0.460684	−	0.549022i	−0.484828	−	0.874610i	$-0.661118\pi$
$599$	11.2750	−	13.4370i	0.460684	−	0.549022i	0.945512	+	0.325588i	$0.105562\pi$
$600$		0			0
$601$	−4.11105	−	1.49630i	−0.167693	−	0.0610354i	0.256809	−	0.966462i	$-0.417329\pi$
$601$	−4.11105	−	1.49630i	−0.167693	−	0.0610354i	−0.424503	+	0.905427i	$0.639551\pi$
$602$	23.6846	+	13.6743i	0.965312	+	0.557323i
$603$		0			0
$604$	−1.62791	−	9.23236i	−0.0662389	−	0.375659i
$605$	5.58864	−	11.9849i	0.227211	−	0.487255i
$606$		0			0
$607$	3.23185	−	36.9402i	0.131177	−	1.49936i	−0.590449	−	0.807075i	$-0.701049\pi$
$607$	3.23185	−	36.9402i	0.131177	−	1.49936i	0.721626	−	0.692283i	$-0.243395\pi$
$608$	−2.67105	−	3.18324i	−0.108325	−	0.129097i
$609$		0			0
$610$	9.35329	+	13.3579i	0.378704	+	0.540845i
$611$	9.84881	+	14.0656i	0.398440	+	0.569031i
$612$		0			0
$613$	−26.9544	−	32.1230i	−1.08868	−	1.29744i	−0.951756	−	0.306855i	$-0.900723\pi$
$613$	−26.9544	−	32.1230i	−1.08868	−	1.29744i	−0.136922	−	0.990582i	$-0.543721\pi$
$614$	2.16422	−	24.7372i	0.0873410	−	0.998312i
$615$		0			0
$616$	2.18238	−	4.68012i	0.0879304	−	0.188567i
$617$	6.87765	+	39.0051i	0.276884	+	1.57029i	0.732913	+	0.680322i	$0.238160\pi$
$617$	6.87765	+	39.0051i	0.276884	+	1.57029i	−0.456029	+	0.889965i	$0.650729\pi$
$618$		0			0
$619$	−13.1229	−	7.57648i	−0.527452	−	0.304525i	0.212526	−	0.977155i	$-0.431831\pi$
$619$	−13.1229	−	7.57648i	−0.527452	−	0.304525i	−0.739978	+	0.672631i	$0.765164\pi$
$620$	−0.0460660	−	0.0167667i	−0.00185006	−	0.000673366i
$621$		0			0
$622$	−14.2815	+	17.0200i	−0.572635	+	0.682440i
$623$	11.7175	+	11.7175i	0.469450	+	0.469450i
$624$		0			0
$625$	3.62884	−	1.32079i	0.145153	−	0.0528315i
$626$	−21.0301	−	3.70817i	−0.840531	−	0.148208i
$627$		0			0
$628$			9.17348i			0.366062i
$629$	−1.20504	−	6.52381i	−0.0480482	−	0.260122i
$630$		0			0
$631$	−31.7313	−	22.2185i	−1.26320	−	0.884505i	−0.266358	−	0.963874i	$-0.585820\pi$
$631$	−31.7313	−	22.2185i	−1.26320	−	0.884505i	−0.996845	+	0.0793696i	$0.974709\pi$
$632$	−3.07486	+	17.4384i	−0.122311	+	0.693662i
$633$		0			0
$634$	1.36721	+	15.6273i	0.0542988	+	0.620638i
$635$	6.75723	−	6.75723i	0.268152	−	0.268152i
$636$		0			0
$637$	0.791232	−	2.95292i	0.0313497	−	0.116999i
$638$	1.99769	−	5.48860i	0.0790892	−	0.217296i
$639$		0			0
$640$	−3.47246	+	2.00482i	−0.137261	+	0.0792476i
$641$	13.6710	−	2.41057i	0.539972	−	0.0952116i	0.102991	−	0.994682i	$-0.467159\pi$
$641$	13.6710	−	2.41057i	0.539972	−	0.0952116i	0.436981	+	0.899471i	$0.356048\pi$
$642$		0			0
$643$	3.08733	+	11.5221i	0.121752	+	0.454386i	0.999703	−	0.0243651i	$-0.00775641\pi$
$643$	3.08733	+	11.5221i	0.121752	+	0.454386i	−0.877951	+	0.478751i	$0.841090\pi$
$644$	−0.763536	−	0.0668007i	−0.0300875	−	0.00263232i
$645$		0			0
$646$	−0.646628	−	1.38670i	−0.0254413	−	0.0545589i
$647$	−25.2423	+	17.6748i	−0.992375	+	0.694869i	−0.952564	−	0.304339i	$-0.901565\pi$
$647$	−25.2423	+	17.6748i	−0.992375	+	0.694869i	−0.0398113	+	0.999207i	$0.512676\pi$
$648$		0			0
$649$	7.32716	−	3.41671i	0.287616	−	0.134118i
$650$	10.3925	−	8.72038i	0.407629	−	0.342041i
$651$		0			0
$652$	−10.9142	+	2.92445i	−0.427433	+	0.114530i
$653$	35.1649	+	16.3977i	1.37611	+	0.641690i	0.963127	−	0.269049i	$-0.0867093\pi$
$653$	35.1649	+	16.3977i	1.37611	+	0.641690i	0.412983	+	0.910739i	$0.364487\pi$
$654$		0			0
$655$	−3.34371	−	5.79148i	−0.130650	−	0.226292i
$656$	7.18737	−	12.4489i	0.280620	−	0.486047i
$657$		0			0
$658$	−14.0809	−	3.77296i	−0.548930	−	0.147085i
$659$	−23.4017	−	19.6364i	−0.911601	−	0.764924i	0.0608216	−	0.998149i	$-0.480628\pi$
$659$	−23.4017	−	19.6364i	−0.911601	−	0.764924i	−0.972423	+	0.233224i	$0.925072\pi$
$660$		0			0
$661$	−0.562991	+	0.0492553i	−0.0218978	+	0.00191581i	−0.0980994	−	0.995177i	$-0.531276\pi$
$661$	−0.562991	+	0.0492553i	−0.0218978	+	0.00191581i	0.0762016	+	0.997092i	$0.475721\pi$
$662$	2.66716	+	7.32796i	0.103662	+	0.284809i
$663$		0			0
$664$	−10.4117	+	14.8695i	−0.404053	+	0.577047i
$665$	3.72592			0.144485
$666$		0			0
$667$	−3.58211			−0.138700
$668$	5.67292	−	8.10178i	0.219492	−	0.313467i
$669$		0			0
$670$	4.30236	+	11.8206i	0.166215	+	0.456671i
$671$	7.53572	−	0.659290i	0.290913	−	0.0254516i
$672$		0			0
$673$	10.6814	+	8.96279i	0.411739	+	0.345490i	0.825010	−	0.565118i	$-0.191169\pi$
$673$	10.6814	+	8.96279i	0.411739	+	0.345490i	−0.413271	+	0.910608i	$0.635614\pi$
$674$	21.1880	+	5.67732i	0.816132	+	0.218682i
$675$		0			0
$676$	0.472231	−	0.817929i	0.0181627	−	0.0314588i
$677$	−7.60765	−	13.1768i	−0.292386	−	0.506427i	0.681988	−	0.731364i	$-0.261116\pi$
$677$	−7.60765	−	13.1768i	−0.292386	−	0.506427i	−0.974373	+	0.224937i	$0.927782\pi$
$678$		0			0
$679$	11.1126	+	5.18188i	0.426462	+	0.198862i
$680$	4.06973	−	1.09048i	0.156067	−	0.0418180i
$681$		0			0
$682$	0.0371399	−	0.0311641i	0.00142216	−	0.00119333i
$683$	−21.7850	+	10.1585i	−0.833582	+	0.388705i	−0.792068	−	0.610433i	$-0.790996\pi$
$683$	−21.7850	+	10.1585i	−0.833582	+	0.388705i	−0.0415132	+	0.999138i	$0.513218\pi$
$684$		0			0
$685$	−15.9023	+	11.1349i	−0.607596	+	0.425443i
$686$	9.62167	+	20.6337i	0.367357	+	0.787800i
$687$		0			0
$688$	−21.8880	−	1.91496i	−0.834474	−	0.0730070i
$689$	1.65434	+	6.17407i	0.0630252	+	0.235213i
$690$		0			0
$691$	−6.88191	+	1.21347i	−0.261800	+	0.0461624i	−0.303007	−	0.952988i	$-0.597991\pi$
$691$	−6.88191	+	1.21347i	−0.261800	+	0.0461624i	0.0412072	+	0.999151i	$0.486880\pi$
$692$	−14.2317	+	8.21666i	−0.541007	+	0.312351i
$693$		0			0
$694$	13.4618	−	36.9860i	0.511003	−	1.40397i
$695$	0.223808	−	0.835262i	0.00848951	−	0.0316833i
$696$		0			0
$697$	−4.78856	+	4.78856i	−0.181380	+	0.181380i
$698$	−1.91301	−	21.8658i	−0.0724086	−	0.827634i
$699$		0			0
$700$	0.938096	−	5.32021i	0.0354567	−	0.201085i
$701$	23.3956	+	16.3818i	0.883641	+	0.618732i	0.924814	−	0.380420i	$-0.124221\pi$
$701$	23.3956	+	16.3818i	0.883641	+	0.618732i	−0.0411732	+	0.999152i	$0.513110\pi$
$702$		0			0
$703$	2.55710	+	6.85188i	0.0964427	+	0.258423i
$704$			5.88345i			0.221741i
$705$		0			0
$706$	−30.3939	−	5.35926i	−1.14389	−	0.201699i
$707$	28.4897	−	10.3694i	1.07146	−	0.389981i
$708$		0			0
$709$	−7.52752	−	7.52752i	−0.282702	−	0.282702i	0.551484	−	0.834186i	$-0.314062\pi$
$709$	−7.52752	−	7.52752i	−0.282702	−	0.282702i	−0.834186	+	0.551484i	$0.814062\pi$
$710$	−2.24235	+	2.67233i	−0.0841539	+	0.100291i
$711$		0			0
$712$	−19.4115	−	7.06521i	−0.727477	−	0.264780i
$713$	−0.0257502	−	0.0148669i	−0.000964352	−	0.000556769i
$714$		0			0
$715$	0.502294	+	2.84865i	0.0187847	+	0.106533i
$716$	5.40739	−	11.5962i	0.202084	−	0.433370i
$717$		0			0
$718$	−1.41686	+	16.1948i	−0.0528768	+	0.604385i
$719$	26.5739	+	31.6696i	0.991041	+	1.18108i	0.983464	+	0.181105i	$0.0579675\pi$
$719$	26.5739	+	31.6696i	0.991041	+	1.18108i	0.00757721	+	0.999971i	$0.497588\pi$
$720$		0			0
$721$	−24.7840	−	35.3952i	−0.923005	−	1.31819i
$722$	−11.7483	−	16.7783i	−0.437226	−	0.624424i
$723$		0			0
$724$	−3.99294	−	4.75860i	−0.148396	−	0.176852i
$725$	2.20053	−	25.1521i	0.0817255	−	0.934127i
$726$		0			0
$727$	5.73644	−	12.3018i	0.212753	−	0.456250i	−0.770751	−	0.637136i	$-0.780119\pi$
$727$	5.73644	−	12.3018i	0.212753	−	0.456250i	0.983504	+	0.180886i	$0.0578966\pi$
$728$	−4.48149	−	25.4158i	−0.166095	−	0.941972i
$729$		0			0
$730$	−4.87098	−	2.81226i	−0.180283	−	0.104086i
$731$	9.72677	+	3.54025i	0.359758	+	0.130941i
$732$		0			0
$733$	10.9000	−	12.9902i	0.402602	−	0.479803i	−0.526209	−	0.850355i	$-0.676387\pi$
$733$	10.9000	−	12.9902i	0.402602	−	0.479803i	0.928812	+	0.370552i	$0.120832\pi$
$734$	−29.2216	−	29.2216i	−1.07859	−	1.07859i
$735$		0			0
$736$	1.57838	−	0.574483i	0.0581798	−	0.0211757i
$737$	5.74664	+	1.01329i	0.211680	+	0.0373249i
$738$		0			0
$739$			31.3270i			1.15238i	0.817314	+	0.576192i	$0.195462\pi$
$739$			31.3270i			1.15238i	−0.817314	+	0.576192i	$0.804538\pi$
$740$	−4.79286	+	0.885311i	−0.176189	+	0.0325447i
$741$		0			0
$742$	−4.44515	−	3.11252i	−0.163186	−	0.114264i
$743$	8.19334	−	46.4667i	0.300584	−	1.70470i	−0.343009	−	0.939332i	$-0.611446\pi$
$743$	8.19334	−	46.4667i	0.300584	−	1.70470i	0.643594	−	0.765367i	$-0.277443\pi$
$744$		0			0
$745$	1.91808	+	21.9238i	0.0702731	+	0.803225i
$746$	9.40862	−	9.40862i	0.344474	−	0.344474i
$747$		0			0
$748$	0.122424	−	0.456892i	0.00447626	−	0.0167056i
$749$	−5.32835	+	14.6395i	−0.194694	+	0.534916i
$750$		0			0
$751$	43.4716	−	25.0984i	1.58630	−	0.915852i	0.592394	−	0.805648i	$-0.298183\pi$
$751$	43.4716	−	25.0984i	1.58630	−	0.915852i	0.993909	−	0.110204i	$-0.0351504\pi$
$752$	11.5336	−	2.03369i	0.420587	−	0.0741609i
$753$		0			0
$754$	−7.55515	−	28.1962i	−0.275142	−	1.02685i
$755$	−18.3512	−	1.60552i	−0.667869	−	0.0584309i
$756$		0			0
$757$	−14.3059	−	30.6791i	−0.519957	−	1.11505i	−0.974513	−	0.224333i	$-0.927980\pi$
$757$	−14.3059	−	30.6791i	−0.519957	−	1.11505i	0.454556	−	0.890718i	$-0.349798\pi$
$758$	−2.91332	+	2.03993i	−0.105816	+	0.0740935i
$759$		0			0
$760$	−4.20954	+	1.96294i	−0.152696	+	0.0712033i
$761$	27.2221	−	22.8421i	0.986801	−	0.828025i	0.00169985	−	0.999999i	$-0.499459\pi$
$761$	27.2221	−	22.8421i	0.986801	−	0.828025i	0.985102	+	0.171974i	$0.0550145\pi$
$762$		0			0
$763$	8.61829	−	2.30926i	0.312003	−	0.0836010i
$764$	6.28652	+	2.93145i	0.227438	+	0.106056i
$765$		0			0
$766$	4.52378	+	7.83541i	0.163451	+	0.283105i
$767$	20.2023	−	34.9914i	0.729463	−	1.26347i
$768$		0			0
$769$	−8.52249	−	2.28360i	−0.307329	−	0.0823486i	0.101858	−	0.994799i	$-0.467521\pi$
$769$	−8.52249	−	2.28360i	−0.307329	−	0.0823486i	−0.409187	+	0.912450i	$0.634188\pi$
$770$	−1.88120	−	1.57852i	−0.0677938	−	0.0568858i
$771$		0			0
$772$	12.7374	−	1.11438i	0.458429	−	0.0401073i
$773$	−3.52452	−	9.68354i	−0.126768	−	0.348293i	0.860031	−	0.510242i	$-0.170444\pi$
$773$	−3.52452	−	9.68354i	−0.126768	−	0.348293i	−0.986799	+	0.161949i	$0.948222\pi$
$774$		0			0
$775$	0.120208	−	0.171675i	0.00431799	−	0.00616674i
$776$	−15.2850			−0.548698
$777$		0			0
$778$	14.0824			0.504879
$779$	4.28201	−	6.11535i	0.153419	−	0.219105i
$780$		0			0
$781$	0.553471	+	1.52065i	0.0198048	+	0.0544131i
$782$	0.616115	−	0.0539030i	0.0220322	−	0.00192757i
$783$		0			0
$784$	−1.59729	−	1.34028i	−0.0570460	−	0.0478672i
$785$	17.4115	+	4.66541i	0.621444	+	0.166516i
$786$		0			0
$787$	5.42556	−	9.39734i	0.193400	−	0.334979i	−0.752975	−	0.658050i	$-0.771382\pi$
$787$	5.42556	−	9.39734i	0.193400	−	0.334979i	0.946375	+	0.323070i	$0.104715\pi$
$788$	−5.33999	−	9.24913i	−0.190229	−	0.329486i
$789$		0			0
$790$	7.63187	+	3.55880i	0.271530	+	0.126616i
$791$	−4.81619	+	1.29050i	−0.171244	+	0.0458847i
$792$		0			0
$793$	28.9604	−	24.3007i	1.02842	−	0.862943i
$794$	7.45640	−	3.47698i	0.264618	−	0.123393i
$795$		0			0
$796$	−11.2417	+	7.87154i	−0.398452	+	0.278999i
$797$	−16.2192	−	34.7823i	−0.574515	−	1.23205i	−0.952018	−	0.306043i	$-0.900995\pi$
$797$	−16.2192	−	34.7823i	−0.574515	−	1.23205i	0.377503	−	0.926008i	$-0.376783\pi$
$798$		0			0
$799$	−5.49640	−	0.480872i	−0.194448	−	0.0170120i
$800$	3.06418	+	11.4357i	0.108335	+	0.404312i
$801$		0			0
$802$	11.0678	−	1.95155i	0.390818	−	0.0689118i
$803$	−2.25956	+	1.30456i	−0.0797380	+	0.0460368i
$804$		0			0
$805$	−0.515105	+	1.41524i	−0.0181551	+	0.0498807i
$806$	0.0627125	−	0.234046i	0.00220895	−	0.00824392i
$807$		0			0
$808$	−26.7246	+	26.7246i	−0.940169	+	0.940169i
$809$	−4.16608	−	47.6185i	−0.146472	−	1.67418i	−0.613316	−	0.789838i	$-0.710165\pi$
$809$	−4.16608	−	47.6185i	−0.146472	−	1.67418i	0.466844	−	0.884339i	$-0.345391\pi$
$810$		0			0
$811$	−4.64945	+	26.3683i	−0.163264	+	0.925918i	0.787572	+	0.616223i	$0.211338\pi$
$811$	−4.64945	+	26.3683i	−0.163264	+	0.925918i	−0.950836	+	0.309695i	$0.899773\pi$
$812$	−9.52184	−	6.66726i	−0.334151	−	0.233975i
$813$		0			0
$814$	1.61178	−	4.54282i	0.0564930	−	0.159226i
$815$			22.2028i			0.777730i
$816$		0			0
$817$	−11.2375	−	1.98148i	−0.393152	−	0.0693233i
$818$	−3.61078	+	1.31422i	−0.126248	+	0.0459505i
$819$		0			0
$820$	3.51802	+	3.51802i	0.122855	+	0.122855i
$821$	−15.5913	+	18.5810i	−0.544141	+	0.648482i	−0.966111	−	0.258128i	$-0.916894\pi$
$821$	−15.5913	+	18.5810i	−0.544141	+	0.648482i	0.421970	+	0.906610i	$0.361339\pi$
$822$		0			0
$823$	36.4713	+	13.2745i	1.27131	+	0.462718i	0.887548	−	0.460714i	$-0.152407\pi$
$823$	36.4713	+	13.2745i	1.27131	+	0.462718i	0.383760	+	0.923433i	$0.374629\pi$
$824$	46.6483	+	26.9324i	1.62507	+	0.938235i
$825$		0			0
$826$	5.95655	+	33.7813i	0.207255	+	1.17540i
$827$	−16.0643	+	34.4499i	−0.558609	+	1.19794i	0.400864	+	0.916138i	$0.368710\pi$
$827$	−16.0643	+	34.4499i	−0.558609	+	1.19794i	−0.959472	+	0.281803i	$0.909068\pi$
$828$		0			0
$829$	−1.19578	+	13.6678i	−0.0415311	+	0.474703i	0.946741	+	0.321997i	$0.104354\pi$
$829$	−1.19578	+	13.6678i	−0.0415311	+	0.474703i	−0.988272	+	0.152706i	$0.951201\pi$
$830$	5.54879	+	6.61279i	0.192601	+	0.229533i
$831$		0			0
$832$	16.8653	+	24.0861i	0.584699	+	0.835037i
$833$	0.563430	+	0.804662i	0.0195217	+	0.0278799i
$834$		0			0
$835$	−12.4923	−	14.8877i	−0.432314	−	0.515212i
$836$	−0.0454468	+	0.519459i	−0.00157181	+	0.0179659i
$837$		0			0
$838$	19.3321	−	41.4577i	0.667815	−	1.43213i
$839$	9.17091	+	52.0108i	0.316615	+	1.79561i	0.563018	+	0.826445i	$0.309640\pi$
$839$	9.17091	+	52.0108i	0.316615	+	1.79561i	−0.246403	+	0.969167i	$0.579249\pi$
$840$		0			0
$841$	−21.9332	−	12.6631i	−0.756317	−	0.436660i
$842$	−32.1073	−	11.6861i	−1.10649	−	0.402729i
$843$		0			0
$844$	0.179973	−	0.214483i	0.00619491	−	0.00738281i
$845$	−1.31229	−	1.31229i	−0.0451441	−	0.0451441i
$846$		0			0
$847$	24.4577	−	8.90188i	0.840377	−	0.305872i
$848$	4.29339	+	0.757041i	0.147436	+	0.0259969i
$849$		0			0
$850$			4.35922i			0.149520i
$851$	−2.95611	+	0.0240123i	−0.101334	+	0.000823130i
$852$		0			0
$853$	32.0139	+	22.4164i	1.09614	+	0.767523i	0.974351	−	0.225034i	$-0.0722492\pi$
$853$	32.0139	+	22.4164i	1.09614	+	0.767523i	0.121785	+	0.992556i	$0.461138\pi$
$854$	−5.57334	+	31.6080i	−0.190716	+	1.08160i
$855$		0			0
$856$	−1.69263	−	19.3468i	−0.0578529	−	0.661261i
$857$	6.02125	−	6.02125i	0.205682	−	0.205682i	−0.596747	−	0.802429i	$-0.703540\pi$
$857$	6.02125	−	6.02125i	0.205682	−	0.205682i	0.802429	+	0.596747i	$0.203540\pi$
$858$		0			0
$859$	−11.1098	+	41.4623i	−0.379061	+	1.41467i	0.468259	+	0.883591i	$0.344881\pi$
$859$	−11.1098	+	41.4623i	−0.379061	+	1.41467i	−0.847320	+	0.531083i	$0.821785\pi$
$860$	2.60092	−	7.14598i	0.0886908	−	0.243676i
$861$		0			0
$862$	2.51899	−	1.45434i	0.0857971	−	0.0495350i
$863$	46.6462	−	8.22499i	1.58786	−	0.279982i	0.691185	−	0.722678i	$-0.257089\pi$
$863$	46.6462	−	8.22499i	1.58786	−	0.279982i	0.896672	+	0.442696i	$0.145978\pi$
$864$		0			0
$865$	8.35759	+	31.1909i	0.284166	+	1.06052i
$866$	−5.60519	−	0.490390i	−0.190472	−	0.0166641i
$867$		0			0
$868$	−0.0407770	−	0.0874466i	−0.00138406	−	0.00296813i
$869$	3.19983	−	2.24055i	0.108547	−	0.0760053i
$870$		0			0
$871$	26.4307	−	12.3248i	0.895570	−	0.417611i
$872$	−8.52033	+	7.14940i	−0.288535	+	0.242109i
$873$		0			0
$874$	−0.658564	+	0.176462i	−0.0222763	+	0.00596891i
$875$	−23.6637	−	11.0346i	−0.799979	−	0.373036i
$876$		0			0
$877$	−5.25820	−	9.10748i	−0.177557	−	0.307538i	0.763486	−	0.645824i	$-0.223486\pi$
$877$	−5.25820	−	9.10748i	−0.177557	−	0.307538i	−0.941043	+	0.338286i	$0.890153\pi$
$878$	3.76253	−	6.51690i	0.126979	−	0.219935i
$879$		0			0
$880$	1.90569	+	0.510629i	0.0642409	+	0.0172133i
$881$	−10.0246	−	8.41162i	−0.337736	−	0.283395i	0.458107	−	0.888897i	$-0.348528\pi$
$881$	−10.0246	−	8.41162i	−0.337736	−	0.283395i	−0.795843	+	0.605503i	$0.792972\pi$
$882$		0			0
$883$	25.7201	−	2.25022i	0.865550	−	0.0757258i	0.354273	−	0.935142i	$-0.384728\pi$
$883$	25.7201	−	2.25022i	0.865550	−	0.0757258i	0.511277	+	0.859416i	$0.329173\pi$
$884$	−0.808523	−	2.22140i	−0.0271936	−	0.0747138i
$885$		0			0
$886$	−13.5554	+	19.3591i	−0.455403	+	0.650383i
$887$	24.1397			0.810530			0.405265	−	0.914199i	$-0.367179\pi$
$887$	24.1397			0.810530			0.405265	+	0.914199i	$0.367179\pi$
$888$		0			0
$889$	18.8086			0.630819
$890$	−5.63462	+	8.04707i	−0.188873	+	0.269739i
$891$		0			0
$892$	−3.90296	−	10.7233i	−0.130681	−	0.359042i
$893$	6.05920	−	0.530111i	0.202763	−	0.0177395i
$894$		0			0
$895$	−19.2598	−	16.1609i	−0.643785	−	0.540200i
$896$	−7.62293	−	2.04256i	−0.254664	−	0.0682371i
$897$		0			0
$898$	19.8908	−	34.4518i	0.663764	−	1.14967i
$899$	−0.225471	−	0.390527i	−0.00751988	−	0.0130248i
$900$		0			0
$901$	−1.86142	−	0.867995i	−0.0620129	−	0.0289171i
$902$	−4.75279	+	1.27351i	−0.158251	+	0.0424031i
$903$		0			0
$904$	4.76145	−	3.99533i	0.158363	−	0.132883i
$905$	−11.0627	+	5.15861i	−0.367736	+	0.171478i
$906$		0			0
$907$	−34.0541	+	23.8449i	−1.13075	+	0.791758i	−0.980428	−	0.196880i	$-0.936919\pi$
$907$	−34.0541	+	23.8449i	−1.13075	+	0.791758i	−0.150319	+	0.988637i	$0.548030\pi$
$908$	−2.39995	−	5.14671i	−0.0796451	−	0.170799i
$909$		0			0
$910$	−12.2263	−	1.06967i	−0.405299	−	0.0354591i
$911$	3.40666	+	12.7138i	0.112868	+	0.421228i	0.999119	−	0.0419774i	$-0.0133657\pi$
$911$	3.40666	+	12.7138i	0.112868	+	0.421228i	−0.886251	+	0.463206i	$0.846699\pi$
$912$		0			0
$913$	3.94357	−	0.695358i	0.130513	−	0.0230130i
$914$	−26.1430	+	15.0937i	−0.864734	+	0.499254i
$915$		0			0
$916$	−5.48429	+	15.0680i	−0.181206	+	0.497860i
$917$	3.40664	−	12.7138i	0.112497	−	0.419846i
$918$		0			0
$919$	−15.0578	+	15.0578i	−0.496712	+	0.496712i	−0.910413	−	0.413701i	$-0.864236\pi$
$919$	−15.0578	+	15.0578i	−0.496712	+	0.496712i	0.413701	+	0.910413i	$0.364236\pi$
$920$	−0.163631	−	1.87031i	−0.00539475	−	0.0616623i
$921$		0			0
$922$	3.85678	−	21.8729i	0.127016	−	0.720345i
$923$	6.62489	+	4.63880i	0.218061	+	0.152688i
$924$		0			0
$925$	1.64736	−	20.7714i	0.0541650	−	0.682958i
$926$			18.1375i			0.596037i
$927$		0			0
$928$	25.0870	+	4.42351i	0.823520	+	0.145209i
$929$	−29.7735	+	10.8367i	−0.976837	+	0.355539i	−0.780609	−	0.625019i	$-0.785091\pi$
$929$	−29.7735	+	10.8367i	−0.976837	+	0.355539i	−0.196227	+	0.980558i	$0.562869\pi$
$930$		0			0
$931$	−0.765722	−	0.765722i	−0.0250955	−	0.0250955i
$932$	−4.56881	+	5.44489i	−0.149656	+	0.178353i
$933$		0			0
$934$	−31.4378	−	11.4424i	−1.02868	−	0.374407i
$935$	−0.804933	−	0.464728i	−0.0263241	−	0.0151982i
$936$		0			0
$937$	0.997733	+	5.65842i	0.0325945	+	0.184853i	0.996758	−	0.0804554i	$-0.0256375\pi$
$937$	0.997733	+	5.65842i	0.0325945	+	0.184853i	−0.964164	+	0.265308i	$0.914526\pi$
$938$	−10.4635	+	22.4390i	−0.341644	+	0.732658i
$939$		0			0
$940$	−0.353283	+	4.03805i	−0.0115228	+	0.131707i
$941$	−17.8109	−	21.2262i	−0.580619	−	0.691955i	0.393155	−	0.919472i	$-0.371384\pi$
$941$	−17.8109	−	21.2262i	−0.580619	−	0.691955i	−0.973774	+	0.227517i	$0.926939\pi$
$942$		0			0
$943$	1.73085	+	2.47191i	0.0563642	+	0.0804964i
$944$	−15.8068	−	22.5744i	−0.514467	−	0.734735i
$945$		0			0
$946$	4.83432	+	5.76132i	0.157177	+	0.187317i
$947$	−0.729383	+	8.33688i	−0.0237018	+	0.270912i	0.975092	+	0.221802i	$0.0711940\pi$
$947$	−0.729383	+	8.33688i	−0.0237018	+	0.270912i	−0.998793	+	0.0491099i	$0.984362\pi$
$948$		0			0
$949$	−5.51076	+	11.8179i	−0.178887	+	0.383624i
$950$	−0.834481	−	4.73258i	−0.0270741	−	0.153545i
$951$		0			0
$952$	7.18165	+	4.14633i	0.232759	+	0.134383i
$953$	41.8450	+	15.2303i	1.35549	+	0.493359i	0.914658	−	0.404229i	$-0.132460\pi$
$953$	41.8450	+	15.2303i	1.35549	+	0.493359i	0.440835	+	0.897588i	$0.354682\pi$
$954$		0			0
$955$	8.76116	−	10.4411i	0.283504	−	0.337867i
$956$	6.65831	+	6.65831i	0.215345	+	0.215345i
$957$		0			0
$958$	−0.275818	+	0.100389i	−0.00891126	+	0.00324343i
$959$	−37.6287	−	6.63495i	−1.21509	−	0.214254i
$960$		0			0
$961$			30.9963i			0.999879i
$962$	−6.42384	−	23.2181i	−0.207113	−	0.748580i
$963$		0			0
$964$	3.44700	+	2.41361i	0.111020	+	0.0777373i
$965$	4.36280	−	24.7427i	0.140444	−	0.796495i
$966$		0			0
$967$	2.20110	+	25.1587i	0.0707827	+	0.809049i	0.945756	+	0.324878i	$0.105323\pi$
$967$	2.20110	+	25.1587i	0.0707827	+	0.809049i	−0.874973	+	0.484171i	$0.839121\pi$
$968$	−22.9425	+	22.9425i	−0.737398	+	0.737398i
$969$		0			0
$970$	−1.88131	+	7.02115i	−0.0604053	+	0.225436i
$971$	−19.4113	+	53.3322i	−0.622939	+	1.71151i	0.0767377	+	0.997051i	$0.475550\pi$
$971$	−19.4113	+	53.3322i	−0.622939	+	1.71151i	−0.699677	+	0.714460i	$0.746673\pi$
$972$		0			0
$973$	1.47395	−	0.850983i	0.0472525	−	0.0272813i
$974$	15.9426	−	2.81111i	0.510834	−	0.0900738i
$975$		0			0
$976$	−6.67374	−	24.9067i	−0.213621	−	0.797245i
$977$	−18.0639	−	1.58038i	−0.577915	−	0.0505610i	−0.205548	−	0.978647i	$-0.565898\pi$
$977$	−18.0639	−	1.58038i	−0.577915	−	0.0505610i	−0.372366	+	0.928086i	$0.621453\pi$
$978$		0			0
$979$	1.92588	+	4.13006i	0.0615513	+	0.131997i
$980$	0.591162	−	0.413936i	0.0188840	−	0.0132227i
$981$		0			0
$982$	−24.4178	+	11.3862i	−0.779204	+	0.363349i
$983$	−13.6404	+	11.4456i	−0.435060	+	0.365059i	−0.833857	−	0.551980i	$-0.813872\pi$
$983$	−13.6404	+	11.4456i	−0.435060	+	0.365059i	0.398797	+	0.917039i	$0.369428\pi$
$984$		0			0
$985$	−20.2709	+	5.43157i	−0.645885	+	0.173064i
$986$	8.50088	+	3.96403i	0.270723	+	0.126240i
$987$		0			0
$988$	1.30301	+	2.25688i	0.0414543	+	0.0718009i
$989$	2.30622	−	3.99449i	0.0733335	−	0.127017i
$990$		0			0
$991$	−7.97943	−	2.13808i	−0.253475	−	0.0679184i	0.129844	−	0.991534i	$-0.458552\pi$
$991$	−7.97943	−	2.13808i	−0.253475	−	0.0679184i	−0.383319	+	0.923616i	$0.625219\pi$
$992$	0.161980	+	0.135917i	0.00514287	+	0.00431538i
$993$		0			0
$994$	−6.83994	+	0.598417i	−0.216950	+	0.0189806i
$995$	9.22315	+	25.3404i	0.292394	+	0.803345i
$996$		0			0
$997$	17.9026	−	25.5676i	0.566981	−	0.809733i	−0.428614	−	0.903488i	$-0.640998\pi$
$997$	17.9026	−	25.5676i	0.566981	−	0.809733i	0.995595	+	0.0937544i	$0.0298868\pi$
$998$	−30.1442			−0.954197
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.2.br.a.17.4	✓	144
3.2	odd	2	inner	333.2.br.a.17.9	yes	144
37.24	odd	36	inner	333.2.br.a.98.9	yes	144
111.98	even	36	inner	333.2.br.a.98.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
333.2.br.a.17.4	✓	144	1.1	even	1	trivial
333.2.br.a.17.9	yes	144	3.2	odd	2	inner
333.2.br.a.98.4	yes	144	111.98	even	36	inner
333.2.br.a.98.9	yes	144	37.24	odd	36	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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.br (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669250 + 0.955789i) q^{2} +(0.218405 + 0.600062i) q^{4} +(1.25001 - 0.109362i) q^{5} +(1.89189 + 1.58748i) q^{7} +(-2.97379 - 0.796824i) q^{8} +O(q^{10})\)	\(q+(-0.669250 + 0.955789i) q^{2} +(0.218405 + 0.600062i) q^{4} +(1.25001 - 0.109362i) q^{5} +(1.89189 + 1.58748i) q^{7} +(-2.97379 - 0.796824i) q^{8} +(-0.732043 + 1.26794i) q^{10} +(0.339581 + 0.588172i) q^{11} +(3.07624 + 1.43447i) q^{13} +(-2.78344 + 0.745821i) q^{14} +(1.77345 - 1.48811i) q^{16} +(-0.988466 + 0.460929i) q^{17} +(0.984890 - 0.689627i) q^{19} +(0.338632 + 0.726198i) q^{20} +(-0.789433 - 0.0690664i) q^{22} +(0.125785 + 0.469437i) q^{23} +(-3.37347 + 0.594834i) q^{25} +(-3.42983 + 1.98021i) q^{26} +(-0.539390 + 1.48196i) q^{28} +(-1.90766 + 7.11949i) q^{29} +(-0.0432614 + 0.0432614i) q^{31} +(-0.301223 - 3.44299i) q^{32} +(0.220980 - 1.25324i) q^{34} +(2.53849 + 1.77747i) q^{35} +(-1.52656 + 5.88809i) q^{37} +1.40288i q^{38} +(-3.80441 - 0.670820i) q^{40} +(5.83471 - 2.12366i) q^{41} +(-6.71091 - 6.71091i) q^{43} +(-0.278773 + 0.332229i) q^{44} +(-0.532865 - 0.193947i) q^{46} +(4.38105 + 2.52940i) q^{47} +(-0.156399 - 0.886981i) q^{49} +(1.68916 - 3.62242i) q^{50} +(-0.188908 + 2.15923i) q^{52} +(1.21046 + 1.44257i) q^{53} +(0.488804 + 0.698084i) q^{55} +(-4.36113 - 6.22834i) q^{56} +(-5.52802 - 6.58804i) q^{58} +(1.03749 - 11.8585i) q^{59} +(4.70712 - 10.0944i) q^{61} +(-0.0123960 - 0.0703015i) q^{62} +(7.50220 + 4.33140i) q^{64} +(4.00221 + 1.45668i) q^{65} +(5.52276 - 6.58177i) q^{67} +(-0.492472 - 0.492472i) q^{68} +(-3.39777 + 1.23669i) q^{70} +(2.34650 + 0.413752i) q^{71} +3.84166i q^{73} +(-4.60612 - 5.39967i) q^{74} +(0.628923 + 0.440377i) q^{76} +(-0.291263 + 1.65183i) q^{77} +(-0.501285 - 5.72971i) q^{79} +(2.05409 - 2.05409i) q^{80} +(-1.87511 + 6.99801i) q^{82} +(2.01658 - 5.54052i) q^{83} +(-1.18518 + 0.684267i) q^{85} +(10.9055 - 1.92293i) q^{86} +(-0.541173 - 2.01969i) q^{88} +(6.68423 + 0.584794i) q^{89} +(3.54270 + 7.59734i) q^{91} +(-0.254219 + 0.178006i) q^{92} +(-5.34959 + 2.49456i) q^{94} +(1.15570 - 0.969750i) q^{95} +(4.79559 - 1.28497i) q^{97} +(0.952436 + 0.444128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q+O(q^{10}) \) 144 * q	\( 144 q + 24 q^{16} - 48 q^{28} - 48 q^{31} - 144 q^{34} - 12 q^{37} - 72 q^{40} - 48 q^{43} - 216 q^{46} + 108 q^{49} - 120 q^{52} + 132 q^{58} - 48 q^{67} + 48 q^{70} + 72 q^{82} + 144 q^{88} - 108 q^{91} + 144 q^{94} + 144 q^{97}+O(q^{100}) \) 144 * q + 24 * q^16 - 48 * q^28 - 48 * q^31 - 144 * q^34 - 12 * q^37 - 72 * q^40 - 48 * q^43 - 216 * q^46 + 108 * q^49 - 120 * q^52 + 132 * q^58 - 48 * q^67 + 48 * q^70 + 72 * q^82 + 144 * q^88 - 108 * q^91 + 144 * q^94 + 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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