LMFDB - Embedded newform 891.2.f.d.163.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(82,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.6
Character	$\chi$	$=$	891.163
Dual form			891.2.f.d.82.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.858580 - 2.64244i) q^{2} +(-4.62728 - 3.36192i) q^{4} +(-0.818647 - 2.51954i) q^{5} +(0.0646331 + 0.0469587i) q^{7} +(-8.36097 + 6.07460i) q^{8} -7.36059 q^{10} +(0.163962 - 3.31257i) q^{11} +(-1.08956 + 3.35332i) q^{13} +(0.179578 - 0.130471i) q^{14} +(5.33826 + 16.4295i) q^{16} +(-1.52123 - 4.68186i) q^{17} +(1.85373 - 1.34682i) q^{19} +(-4.68236 + 14.4108i) q^{20} +(-8.61249 - 3.27736i) q^{22} -1.44749 q^{23} +(-1.63279 + 1.18629i) q^{25} +(7.92547 + 5.75819i) q^{26} +(-0.141204 - 0.434582i) q^{28} +(6.85282 + 4.97886i) q^{29} +(-1.59261 + 4.90156i) q^{31} +27.3278 q^{32} -13.6776 q^{34} +(0.0654024 - 0.201288i) q^{35} +(-3.25547 - 2.36524i) q^{37} +(-1.96730 - 6.05472i) q^{38} +(22.1499 + 16.0928i) q^{40} +(-3.95702 + 2.87494i) q^{41} -4.53962 q^{43} +(-11.8953 + 14.7770i) q^{44} +(-1.24279 + 3.82491i) q^{46} +(5.78899 - 4.20595i) q^{47} +(-2.16115 - 6.65133i) q^{49} +(1.73282 + 5.33309i) q^{50} +(16.3153 - 11.8538i) q^{52} +(1.00902 - 3.10546i) q^{53} +(-8.48036 + 2.29872i) q^{55} -0.825651 q^{56} +(19.0400 - 13.8334i) q^{58} +(-10.7153 - 7.78513i) q^{59} +(-2.98234 - 9.17870i) q^{61} +(11.5847 + 8.41676i) q^{62} +(12.7866 - 39.3530i) q^{64} +9.34078 q^{65} +0.419065 q^{67} +(-8.70087 + 26.7785i) q^{68} +(-0.475738 - 0.345644i) q^{70} +(1.83547 + 5.64900i) q^{71} +(3.22213 + 2.34101i) q^{73} +(-9.04508 + 6.57164i) q^{74} -13.1056 q^{76} +(0.166151 - 0.206402i) q^{77} +(-1.88291 + 5.79499i) q^{79} +(37.0245 - 26.8999i) q^{80} +(4.19944 + 12.9246i) q^{82} +(-1.10637 - 3.40505i) q^{83} +(-10.5508 + 7.66557i) q^{85} +(-3.89762 + 11.9957i) q^{86} +(18.7517 + 28.6923i) q^{88} +0.516913 q^{89} +(-0.227889 + 0.165571i) q^{91} +(6.69796 + 4.86635i) q^{92} +(-6.14365 - 18.9082i) q^{94} +(-4.91090 - 3.56798i) q^{95} +(0.646394 - 1.98940i) q^{97} -19.4312 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 8 q^{4} - 4 q^{5} + 7 q^{7} - 10 q^{8} - 16 q^{10} - 5 q^{11} + 7 q^{13} - 13 q^{14} + 2 q^{16} + 5 q^{17} + 4 q^{19} - 27 q^{20} - 2 q^{22} - 6 q^{23} - 2 q^{25} + 34 q^{26} - 9 q^{28}+ \cdots - 68 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 - 8 * q^4 - 4 * q^5 + 7 * q^7 - 10 * q^8 - 16 * q^10 - 5 * q^11 + 7 * q^13 - 13 * q^14 + 2 * q^16 + 5 * q^17 + 4 * q^19 - 27 * q^20 - 2 * q^22 - 6 * q^23 - 2 * q^25 + 34 * q^26 - 9 * q^28 - 22 * q^29 + 2 * q^31 - 18 * q^32 - 42 * q^34 + 6 * q^37 + 5 * q^38 + 53 * q^40 - 10 * q^41 - 30 * q^43 - 59 * q^44 + 31 * q^46 - 4 * q^47 - 3 * q^49 - 9 * q^50 - 26 * q^52 - 17 * q^53 + 12 * q^55 + 48 * q^56 + 53 * q^58 - 11 * q^59 + 3 * q^61 + 2 * q^62 + 38 * q^64 + 68 * q^65 - 14 * q^67 - 22 * q^68 - 20 * q^70 + 36 * q^71 + 35 * q^73 - 3 * q^74 - 102 * q^76 + 88 * q^77 - 9 * q^79 + 37 * q^80 - 6 * q^82 - 32 * q^83 - 45 * q^85 + 110 * q^86 + 54 * q^88 - 34 * q^89 + 13 * q^91 + q^92 - 25 * q^94 + 84 * q^95 + 15 * q^97 - 68 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.858580	−	2.64244i	0.607108	−	1.86849i	0.125513	−	0.992092i	$-0.459942\pi$
$2$	0.858580	−	2.64244i	0.607108	−	1.86849i	0.481595	−	0.876394i	$-0.340058\pi$
$3$		0			0
$3$		0			0
$4$	−4.62728	−	3.36192i	−2.31364	−	1.68096i
$5$	−0.818647	−	2.51954i	−0.366110	−	1.12677i	−0.949283	−	0.314423i	$-0.898189\pi$
$5$	−0.818647	−	2.51954i	−0.366110	−	1.12677i	0.583173	−	0.812348i	$-0.301811\pi$
$6$		0			0
$7$	0.0646331	+	0.0469587i	0.0244290	+	0.0177487i	0.599933	−	0.800050i	$-0.295194\pi$
$7$	0.0646331	+	0.0469587i	0.0244290	+	0.0177487i	−0.575504	+	0.817799i	$0.695194\pi$
$8$	−8.36097	+	6.07460i	−2.95605	+	2.14770i
$9$		0			0
$10$	−7.36059			−2.32762
$11$	0.163962	−	3.31257i	0.0494363	−	0.998777i
$11$	0.163962	−	3.31257i	0.0494363	−	0.998777i
$12$		0			0
$13$	−1.08956	+	3.35332i	−0.302190	+	0.930044i	0.678521	+	0.734581i	$0.262621\pi$
$13$	−1.08956	+	3.35332i	−0.302190	+	0.930044i	−0.980711	+	0.195463i	$0.937379\pi$
$14$	0.179578	−	0.130471i	0.0479942	−	0.0348699i
$15$		0			0
$16$	5.33826	+	16.4295i	1.33457	+	4.10737i
$17$	−1.52123	−	4.68186i	−0.368952	−	1.13552i	−0.947469	−	0.319847i	$-0.896369\pi$
$17$	−1.52123	−	4.68186i	−0.368952	−	1.13552i	0.578517	−	0.815670i	$-0.303631\pi$
$18$		0			0
$19$	1.85373	−	1.34682i	0.425275	−	0.308981i	−0.354482	−	0.935063i	$-0.615343\pi$
$19$	1.85373	−	1.34682i	0.425275	−	0.308981i	0.779757	+	0.626082i	$0.215343\pi$
$20$	−4.68236	+	14.4108i	−1.04701	+	3.22236i
$21$		0			0
$22$	−8.61249	−	3.27736i	−1.83619	−	0.698736i
$23$	−1.44749			−0.301823			−0.150911	−	0.988547i	$-0.548221\pi$
$23$	−1.44749			−0.301823			−0.150911	+	0.988547i	$0.548221\pi$
$24$		0			0
$25$	−1.63279	+	1.18629i	−0.326559	+	0.237259i
$26$	7.92547	+	5.75819i	1.55431	+	1.12927i
$27$		0			0
$28$	−0.141204	−	0.434582i	−0.0266851	−	0.0821283i
$29$	6.85282	+	4.97886i	1.27254	+	0.924552i	0.999301	−	0.0373955i	$-0.0119061\pi$
$29$	6.85282	+	4.97886i	1.27254	+	0.924552i	0.273236	+	0.961947i	$0.411906\pi$
$30$		0			0
$31$	−1.59261	+	4.90156i	−0.286042	+	0.880346i	0.700043	+	0.714101i	$0.253164\pi$
$31$	−1.59261	+	4.90156i	−0.286042	+	0.880346i	−0.986084	+	0.166245i	$0.946836\pi$
$32$	27.3278			4.83091
$33$		0			0
$34$	−13.6776			−2.34569
$35$	0.0654024	−	0.201288i	0.0110550	−	0.0340239i
$36$		0			0
$37$	−3.25547	−	2.36524i	−0.535197	−	0.388843i	0.287101	−	0.957900i	$-0.407308\pi$
$37$	−3.25547	−	2.36524i	−0.535197	−	0.388843i	−0.822298	+	0.569057i	$0.807308\pi$
$38$	−1.96730	−	6.05472i	−0.319138	−	0.982206i
$39$		0			0
$40$	22.1499	+	16.0928i	3.50220	+	2.54450i
$41$	−3.95702	+	2.87494i	−0.617983	+	0.448991i	−0.852216	−	0.523190i	$-0.824742\pi$
$41$	−3.95702	+	2.87494i	−0.617983	+	0.448991i	0.234233	+	0.972180i	$0.424742\pi$
$42$		0			0
$43$	−4.53962			−0.692285			−0.346142	−	0.938182i	$-0.612509\pi$
$43$	−4.53962			−0.692285			−0.346142	+	0.938182i	$0.612509\pi$
$44$	−11.8953	+	14.7770i	−1.79328	+	2.22771i
$45$		0			0
$46$	−1.24279	+	3.82491i	−0.183239	+	0.563952i
$47$	5.78899	−	4.20595i	0.844411	−	0.613501i	−0.0791880	−	0.996860i	$-0.525233\pi$
$47$	5.78899	−	4.20595i	0.844411	−	0.613501i	0.923599	+	0.383359i	$0.125233\pi$
$48$		0			0
$49$	−2.16115	−	6.65133i	−0.308735	−	0.950189i
$50$	1.73282	+	5.33309i	0.245058	+	0.754212i
$51$		0			0
$52$	16.3153	−	11.8538i	2.26253	−	1.64382i
$53$	1.00902	−	3.10546i	0.138600	−	0.426567i	−0.857533	−	0.514430i	$-0.828004\pi$
$53$	1.00902	−	3.10546i	0.138600	−	0.426567i	0.996133	+	0.0878625i	$0.0280036\pi$
$54$		0			0
$55$	−8.48036	+	2.29872i	−1.14349	+	0.309959i
$56$	−0.825651			−0.110332
$57$		0			0
$58$	19.0400	−	13.8334i	2.50008	−	1.81641i
$59$	−10.7153	−	7.78513i	−1.39502	−	1.01354i	−0.995294	−	0.0969011i	$-0.969107\pi$
$59$	−10.7153	−	7.78513i	−1.39502	−	1.01354i	−0.399721	−	0.916637i	$-0.630893\pi$
$60$		0			0
$61$	−2.98234	−	9.17870i	−0.381850	−	1.17521i	−0.938740	−	0.344626i	$-0.888006\pi$
$61$	−2.98234	−	9.17870i	−0.381850	−	1.17521i	0.556890	−	0.830586i	$-0.311994\pi$
$62$	11.5847	+	8.41676i	1.47126	+	1.06893i
$63$		0			0
$64$	12.7866	−	39.3530i	1.59832	−	4.91912i
$65$	9.34078			1.15858
$66$		0			0
$67$	0.419065			0.0511970			0.0255985	−	0.999672i	$-0.491851\pi$
$67$	0.419065			0.0511970			0.0255985	+	0.999672i	$0.491851\pi$
$68$	−8.70087	+	26.7785i	−1.05514	+	3.24737i
$69$		0			0
$70$	−0.475738	−	0.345644i	−0.0568615	−	0.0413123i
$71$	1.83547	+	5.64900i	0.217830	+	0.670413i	0.998941	+	0.0460199i	$0.0146538\pi$
$71$	1.83547	+	5.64900i	0.217830	+	0.670413i	−0.781110	+	0.624393i	$0.785346\pi$
$72$		0			0
$73$	3.22213	+	2.34101i	0.377122	+	0.273995i	0.760158	−	0.649738i	$-0.225122\pi$
$73$	3.22213	+	2.34101i	0.377122	+	0.273995i	−0.383036	+	0.923733i	$0.625122\pi$
$74$	−9.04508	+	6.57164i	−1.05147	+	0.763937i
$75$		0			0
$76$	−13.1056			−1.50332
$77$	0.166151	−	0.206402i	0.0189347	−	0.0235217i
$78$		0			0
$79$	−1.88291	+	5.79499i	−0.211843	+	0.651987i	0.787519	+	0.616290i	$0.211365\pi$
$79$	−1.88291	+	5.79499i	−0.211843	+	0.651987i	−0.999363	+	0.0356969i	$0.988635\pi$
$80$	37.0245	−	26.8999i	4.13947	−	3.00750i
$81$		0			0
$82$	4.19944	+	12.9246i	0.463751	+	1.42728i
$83$	−1.10637	−	3.40505i	−0.121440	−	0.373752i	0.871796	−	0.489869i	$-0.162955\pi$
$83$	−1.10637	−	3.40505i	−0.121440	−	0.373752i	−0.993236	+	0.116117i	$0.962955\pi$
$84$		0			0
$85$	−10.5508	+	7.66557i	−1.14439	+	0.831448i
$86$	−3.89762	+	11.9957i	−0.420292	+	1.29352i
$87$		0			0
$88$	18.7517	+	28.6923i	1.99893	+	3.05861i
$89$	0.516913			0.0547927			0.0273963	−	0.999625i	$-0.491278\pi$
$89$	0.516913			0.0547927			0.0273963	+	0.999625i	$0.491278\pi$
$90$		0			0
$91$	−0.227889	+	0.165571i	−0.0238893	+	0.0173566i
$92$	6.69796	+	4.86635i	0.698310	+	0.507352i
$93$		0			0
$94$	−6.14365	−	18.9082i	−0.633669	−	1.95023i
$95$	−4.91090	−	3.56798i	−0.503848	−	0.366067i
$96$		0			0
$97$	0.646394	−	1.98940i	0.0656314	−	0.201993i	−0.912863	−	0.408266i	$-0.866134\pi$
$97$	0.646394	−	1.98940i	0.0656314	−	0.201993i	0.978494	+	0.206273i	$0.0661336\pi$
$98$	−19.4312			−1.96285
$99$		0			0
$100$	11.5436			1.15436
$101$	−2.09768	+	6.45598i	−0.208727	+	0.642394i	0.790813	+	0.612058i	$0.209658\pi$
$101$	−2.09768	+	6.45598i	−0.208727	+	0.642394i	−0.999540	+	0.0303367i	$0.990342\pi$
$102$		0			0
$103$	4.94578	+	3.59332i	0.487322	+	0.354060i	0.804153	−	0.594422i	$-0.202619\pi$
$103$	4.94578	+	3.59332i	0.487322	+	0.354060i	−0.316832	+	0.948482i	$0.602619\pi$
$104$	−11.2603	−	34.6557i	−1.10416	−	3.39827i
$105$		0			0
$106$	−7.33965	−	5.33257i	−0.712890	−	0.517945i
$107$	10.0160	−	7.27708i	0.968288	−	0.703502i	0.0132270	−	0.999913i	$-0.495790\pi$
$107$	10.0160	−	7.27708i	0.968288	−	0.703502i	0.955061	+	0.296410i	$0.0957896\pi$
$108$		0			0
$109$	−3.19748			−0.306263			−0.153132	−	0.988206i	$-0.548936\pi$
$109$	−3.19748			−0.306263			−0.153132	+	0.988206i	$0.548936\pi$
$110$	−1.20685	+	24.3825i	−0.115069	+	2.32478i
$111$		0			0
$112$	−0.426479	+	1.31257i	−0.0402984	+	0.124026i
$113$	−11.3001	+	8.21004i	−1.06303	+	0.772336i	−0.974646	−	0.223751i	$-0.928170\pi$
$113$	−11.3001	+	8.21004i	−1.06303	+	0.772336i	−0.0883824	+	0.996087i	$0.528170\pi$
$114$		0			0
$115$	1.18498	+	3.64701i	0.110500	+	0.340085i
$116$	−14.9714	−	46.0772i	−1.39006	−	4.27816i
$117$		0			0
$118$	−29.7717	+	21.6304i	−2.74071	+	1.99124i
$119$	0.121532	−	0.374038i	0.0111408	−	0.0342880i
$120$		0			0
$121$	−10.9462	−	1.08627i	−0.995112	−	0.0987516i
$122$	−26.8147			−2.42769
$123$		0			0
$124$	23.8481	−	17.3267i	2.14162	−	1.55598i
$125$	−6.39063	−	4.64307i	−0.571596	−	0.415289i
$126$		0			0
$127$	−3.22466	−	9.92448i	−0.286142	−	0.880655i	−0.986054	−	0.166426i	$-0.946777\pi$
$127$	−3.22466	−	9.92448i	−0.286142	−	0.880655i	0.699912	−	0.714229i	$-0.253223\pi$
$128$	−48.7922	−	35.4496i	−4.31266	−	3.13333i
$129$		0			0
$130$	8.01981	−	24.6824i	0.703384	−	2.16479i
$131$	7.93307			0.693116			0.346558	−	0.938029i	$-0.387350\pi$
$131$	7.93307			0.693116			0.346558	+	0.938029i	$0.387350\pi$
$132$		0			0
$133$	0.183057			0.0158731
$134$	0.359801	−	1.10735i	0.0310821	−	0.0956608i
$135$		0			0
$136$	41.1594	+	29.9040i	3.52939	+	2.56425i
$137$	−6.77332	−	20.8461i	−0.578684	−	1.78100i	−0.623279	−	0.782000i	$-0.714200\pi$
$137$	−6.77332	−	20.8461i	−0.578684	−	1.78100i	0.0445953	−	0.999005i	$-0.485800\pi$
$138$		0			0
$139$	−4.39737	−	3.19488i	−0.372980	−	0.270986i	0.385466	−	0.922722i	$-0.374041\pi$
$139$	−4.39737	−	3.19488i	−0.372980	−	0.270986i	−0.758446	+	0.651736i	$0.774041\pi$
$140$	−0.979349	+	0.711539i	−0.0827701	+	0.0601360i
$141$		0			0
$142$	16.5030			1.38490
$143$	10.9295	+	4.15906i	0.913968	+	0.347798i
$144$		0			0
$145$	6.93439	−	21.3419i	0.575870	−	1.77234i
$146$	8.95244	−	6.50433i	0.740909	−	0.538302i
$147$		0			0
$148$	7.11226	+	21.8893i	0.584624	+	1.79929i
$149$	−0.507435	−	1.56172i	−0.0415707	−	0.127941i	0.928117	−	0.372288i	$-0.121427\pi$
$149$	−0.507435	−	1.56172i	−0.0415707	−	0.127941i	−0.969688	+	0.244346i	$0.921427\pi$
$150$		0			0
$151$	−13.5217	+	9.82407i	−1.10038	+	0.799471i	−0.981122	−	0.193392i	$-0.938051\pi$
$151$	−13.5217	+	9.82407i	−1.10038	+	0.799471i	−0.119256	+	0.992864i	$0.538051\pi$
$152$	−7.31764	+	22.5214i	−0.593539	+	1.82672i
$153$		0			0
$154$	−0.402751	−	0.616257i	−0.0324546	−	0.0496594i
$155$	13.6534			1.09667
$156$		0			0
$157$	−0.495106	+	0.359716i	−0.0395138	+	0.0287085i	−0.607367	−	0.794421i	$-0.707774\pi$
$157$	−0.495106	+	0.359716i	−0.0395138	+	0.0287085i	0.567853	+	0.823130i	$0.307774\pi$
$158$	13.6963	+	9.95092i	1.08962	+	0.791653i
$159$		0			0
$160$	−22.3718	−	68.8533i	−1.76865	−	5.44333i
$161$	−0.0935558	−	0.0679723i	−0.00737323	−	0.00535697i
$162$		0			0
$163$	0.430987	−	1.32644i	0.0337575	−	0.103895i	−0.932758	−	0.360503i	$-0.882605\pi$
$163$	0.430987	−	1.32644i	0.0337575	−	0.103895i	0.966516	+	0.256608i	$0.0826050\pi$
$164$	27.9756			2.18453
$165$		0			0
$166$	−9.94753			−0.772078
$167$	5.66647	−	17.4396i	0.438485	−	1.34952i	−0.450989	−	0.892530i	$-0.648928\pi$
$167$	5.66647	−	17.4396i	0.438485	−	1.34952i	0.889473	−	0.456987i	$-0.151072\pi$
$168$		0			0
$169$	0.459594	+	0.333914i	0.0353534	+	0.0256857i
$170$	11.1971	+	34.4612i	0.858781	+	2.64306i
$171$		0			0
$172$	21.0061	+	15.2618i	1.60170	+	1.16370i
$173$	−2.67960	+	1.94684i	−0.203726	+	0.148016i	−0.684971	−	0.728571i	$-0.740185\pi$
$173$	−2.67960	+	1.94684i	−0.203726	+	0.148016i	0.481244	+	0.876586i	$0.340185\pi$
$174$		0			0
$175$	−0.161239			−0.0121885
$176$	55.2991	−	14.9896i	4.16833	−	1.12988i
$177$		0			0
$178$	0.443811	−	1.36591i	0.0332651	−	0.102379i
$179$	−4.08829	+	2.97032i	−0.305574	+	0.222012i	−0.729995	−	0.683453i	$-0.760478\pi$
$179$	−4.08829	+	2.97032i	−0.305574	+	0.222012i	0.424421	+	0.905465i	$0.360478\pi$
$180$		0			0
$181$	−6.38384	−	19.6474i	−0.474507	−	1.46038i	−0.846622	−	0.532195i	$-0.821367\pi$
$181$	−6.38384	−	19.6474i	−0.474507	−	1.46038i	0.372115	−	0.928187i	$-0.378633\pi$
$182$	0.241850	+	0.744339i	0.0179271	+	0.0551741i
$183$		0			0
$184$	12.1024	−	8.79294i	0.892204	−	0.648224i
$185$	−3.29422	+	10.1386i	−0.242196	+	0.745403i
$186$		0			0
$187$	−15.7584	+	4.27153i	−1.15237	+	0.312365i
$188$	−40.9274			−2.98494
$189$		0			0
$190$	−13.6446	+	9.91336i	−0.989881	+	0.719191i
$191$	−3.73258	−	2.71188i	−0.270080	−	0.196225i	0.444499	−	0.895779i	$-0.353382\pi$
$191$	−3.73258	−	2.71188i	−0.270080	−	0.196225i	−0.714579	+	0.699555i	$0.753382\pi$
$192$		0			0
$193$	5.82758	+	17.9355i	0.419479	+	1.29102i	0.908183	+	0.418573i	$0.137470\pi$
$193$	5.82758	+	17.9355i	0.419479	+	1.29102i	−0.488704	+	0.872449i	$0.662530\pi$
$194$	−4.70188	−	3.41611i	−0.337575	−	0.245263i
$195$		0			0
$196$	−12.3610	+	38.0432i	−0.882927	+	2.71737i
$197$	−3.33764			−0.237797			−0.118899	−	0.992906i	$-0.537936\pi$
$197$	−3.33764			−0.237797			−0.118899	+	0.992906i	$0.537936\pi$
$198$		0			0
$199$	13.1083			0.929224			0.464612	−	0.885514i	$-0.346194\pi$
$199$	13.1083			0.929224			0.464612	+	0.885514i	$0.346194\pi$
$200$	6.44548	−	19.8372i	0.455764	−	1.40270i
$201$		0			0
$202$	15.2585	+	11.0860i	1.07359	+	0.780005i
$203$	0.209118	+	0.643598i	0.0146772	+	0.0451717i
$204$		0			0
$205$	10.4829	+	7.61629i	0.732160	+	0.531945i
$206$	13.7415	−	9.98375i	0.957413	−	0.695601i
$207$		0			0
$208$	−60.9097			−4.22333
$209$	−4.15748	−	6.36144i	−0.287579	−	0.440030i
$210$		0			0
$211$	−2.13975	+	6.58547i	−0.147306	+	0.453363i	−0.997300	−	0.0734299i	$-0.976605\pi$
$211$	−2.13975	+	6.58547i	−0.147306	+	0.453363i	0.849994	+	0.526792i	$0.176605\pi$
$212$	−15.1093	+	10.9776i	−1.03771	+	0.753943i
$213$		0			0
$214$	−10.6297	−	32.7147i	−0.726629	−	2.23633i
$215$	3.71634	+	11.4377i	0.253452	+	0.780046i
$216$		0			0
$217$	−0.333106	+	0.242016i	−0.0226127	+	0.0164291i
$218$	−2.74530	+	8.44915i	−0.185935	+	0.572249i
$219$		0			0
$220$	46.9692	+	17.8735i	3.16666	+	1.20503i
$221$	17.3572			1.16757
$222$		0			0
$223$	21.5011	−	15.6215i	1.43982	−	1.04609i	0.451744	−	0.892148i	$-0.350802\pi$
$223$	21.5011	−	15.6215i	1.43982	−	1.04609i	0.988079	−	0.153945i	$-0.0491980\pi$
$224$	1.76628	+	1.28328i	0.118014	+	0.0857425i
$225$		0			0
$226$	11.9924	+	36.9089i	0.797725	+	2.45514i
$227$	2.77035	+	2.01278i	0.183874	+	0.133593i	0.675915	−	0.736980i	$-0.263749\pi$
$227$	2.77035	+	2.01278i	0.183874	+	0.133593i	−0.492040	+	0.870572i	$0.663749\pi$
$228$		0			0
$229$	−2.83684	+	8.73090i	−0.187464	+	0.576954i	−0.999982	−	0.00598163i	$-0.998096\pi$
$229$	−2.83684	+	8.73090i	−0.187464	+	0.576954i	0.812518	+	0.582935i	$0.198096\pi$
$230$	10.6544			0.702530
$231$		0			0
$232$	−87.5408			−5.74734
$233$	6.44958	−	19.8498i	0.422526	−	1.30040i	−0.482817	−	0.875721i	$-0.660386\pi$
$233$	6.44958	−	19.8498i	0.422526	−	1.30040i	0.905343	−	0.424681i	$-0.139614\pi$
$234$		0			0
$235$	−15.3362	−	11.1424i	−1.00042	−	0.726849i
$236$	23.4098	+	72.0480i	1.52385	+	4.68993i
$237$		0			0
$238$	−0.884026	−	0.642282i	−0.0573029	−	0.0416330i
$239$	18.1627	−	13.1960i	1.17485	−	0.853575i	0.183264	−	0.983064i	$-0.441334\pi$
$239$	18.1627	−	13.1960i	1.17485	−	0.853575i	0.991581	+	0.129489i	$0.0413335\pi$
$240$		0			0
$241$	3.84131			0.247441			0.123720	−	0.992317i	$-0.460517\pi$
$241$	3.84131			0.247441			0.123720	+	0.992317i	$0.460517\pi$
$242$	−12.2686	+	27.9921i	−0.788656	+	1.79940i
$243$		0			0
$244$	−17.0579	+	52.4989i	−1.09202	+	3.36089i
$245$	−14.9890	+	10.8902i	−0.957615	+	0.695748i
$246$		0			0
$247$	2.49655	+	7.68360i	0.158852	+	0.488896i
$248$	−16.4592	−	50.6563i	−1.04516	−	3.21668i
$249$		0			0
$250$	−17.7559	+	12.9004i	−1.12298	+	0.815893i
$251$	4.12982	−	12.7103i	0.260672	−	0.802265i	−0.731987	−	0.681318i	$-0.761407\pi$
$251$	4.12982	−	12.7103i	0.260672	−	0.802265i	0.992659	−	0.120947i	$-0.0385930\pi$
$252$		0			0
$253$	−0.237333	+	4.79492i	−0.0149210	+	0.301454i
$254$	−28.9935			−1.81921
$255$		0			0
$256$	−68.6142	+	49.8511i	−4.28839	+	3.11570i
$257$	2.44345	+	1.77527i	0.152418	+	0.110738i	0.661381	−	0.750051i	$-0.269971\pi$
$257$	2.44345	+	1.77527i	0.152418	+	0.110738i	−0.508963	+	0.860789i	$0.669971\pi$
$258$		0			0
$259$	−0.0993427	−	0.305745i	−0.00617285	−	0.0189981i
$260$	−43.2225	−	31.4030i	−2.68054	−	1.94753i
$261$		0			0
$262$	6.81118	−	20.9627i	0.420796	−	1.29508i
$263$	11.1810			0.689447			0.344724	−	0.938704i	$-0.387973\pi$
$263$	11.1810			0.689447			0.344724	+	0.938704i	$0.387973\pi$
$264$		0			0
$265$	−8.65034			−0.531386
$266$	0.157169	−	0.483717i	0.00963666	−	0.0296586i
$267$		0			0
$268$	−1.93913	−	1.40886i	−0.118451	−	0.0860601i
$269$	1.46263	+	4.50151i	0.0891782	+	0.274462i	0.985693	−	0.168552i	$-0.0539091\pi$
$269$	1.46263	+	4.50151i	0.0891782	+	0.274462i	−0.896515	+	0.443014i	$0.853909\pi$
$270$		0			0
$271$	22.9084	+	16.6439i	1.39158	+	1.01105i	0.995689	+	0.0927500i	$0.0295657\pi$
$271$	22.9084	+	16.6439i	1.39158	+	1.01105i	0.395895	+	0.918296i	$0.370434\pi$
$272$	68.7998	−	49.9860i	4.17160	−	3.03084i
$273$		0			0
$274$	−60.9000			−3.67911
$275$	3.66197	+	5.60325i	0.220825	+	0.337889i
$276$		0			0
$277$	4.11016	−	12.6498i	0.246956	−	0.760051i	−0.748353	−	0.663301i	$-0.769155\pi$
$277$	4.11016	−	12.6498i	0.246956	−	0.760051i	0.995309	−	0.0967507i	$-0.0308450\pi$
$278$	−12.2178	+	8.87672i	−0.732772	+	0.532390i
$279$		0			0
$280$	0.675916	+	2.08026i	0.0403937	+	0.124319i
$281$	−3.13606	−	9.65180i	−0.187082	−	0.575778i	0.812896	−	0.582408i	$-0.197890\pi$
$281$	−3.13606	−	9.65180i	−0.187082	−	0.575778i	−0.999978	+	0.00663019i	$0.997890\pi$
$282$		0			0
$283$	18.6321	−	13.5370i	1.10756	−	0.804691i	0.125284	−	0.992121i	$-0.460016\pi$
$283$	18.6321	−	13.5370i	1.10756	−	0.804691i	0.982278	+	0.187430i	$0.0600159\pi$
$284$	10.4982	−	32.3103i	0.622956	−	1.91726i
$285$		0			0
$286$	20.3739	−	25.3096i	1.20473	−	1.49659i
$287$	−0.390758			−0.0230657
$288$		0			0
$289$	−5.85236	+	4.25199i	−0.344256	+	0.250117i
$290$	−50.4408	−	36.6474i	−2.96199	−	2.15201i
$291$		0			0
$292$	−7.03941	−	21.6651i	−0.411950	−	1.26785i
$293$	−1.21048	−	0.879465i	−0.0707170	−	0.0513789i	0.551865	−	0.833933i	$-0.313916\pi$
$293$	−1.21048	−	0.879465i	−0.0707170	−	0.0513789i	−0.622582	+	0.782555i	$0.713916\pi$
$294$		0			0
$295$	−10.8429	+	33.3709i	−0.631296	+	1.94293i
$296$	41.5868			2.41718
$297$		0			0
$298$	−4.56243			−0.264295
$299$	1.57713	−	4.85391i	0.0912077	−	0.280709i
$300$		0			0
$301$	−0.293409	−	0.213174i	−0.0169118	−	0.0122872i
$302$	14.3501	+	44.1649i	0.825753	+	2.54141i
$303$		0			0
$304$	32.0232	+	23.2662i	1.83666	+	1.33441i
$305$	−20.6846	+	15.0282i	−1.18440	+	0.860514i
$306$		0			0
$307$	17.3347			0.989343			0.494672	−	0.869080i	$-0.335288\pi$
$307$	17.3347			0.989343			0.494672	+	0.869080i	$0.335288\pi$
$308$	−1.46274	+	0.396494i	−0.0833471	+	0.0225924i
$309$		0			0
$310$	11.7226	−	36.0784i	0.665798	−	2.04911i
$311$	−3.76162	+	2.73298i	−0.213302	+	0.154973i	−0.689306	−	0.724470i	$-0.742085\pi$
$311$	−3.76162	+	2.73298i	−0.213302	+	0.154973i	0.476004	+	0.879443i	$0.342085\pi$
$312$		0			0
$313$	0.751865	+	2.31400i	0.0424979	+	0.130795i	0.970054	−	0.242888i	$-0.0780947\pi$
$313$	0.751865	+	2.31400i	0.0424979	+	0.130795i	−0.927556	+	0.373683i	$0.878095\pi$
$314$	0.525438	+	1.61713i	0.0296522	+	0.0912601i
$315$		0			0
$316$	28.1950	−	20.4849i	1.58609	−	1.15236i
$317$	−6.02187	+	18.5334i	−0.338222	+	1.04094i	0.626892	+	0.779106i	$0.284327\pi$
$317$	−6.02187	+	18.5334i	−0.338222	+	1.04094i	−0.965113	+	0.261833i	$0.915673\pi$
$318$		0			0
$319$	17.6164	−	21.8841i	0.986331	−	1.22527i
$320$	−109.619			−6.12788
$321$		0			0
$322$	−0.259938	+	0.188856i	−0.0144858	+	0.0105245i
$323$	−9.12554	−	6.63010i	−0.507759	−	0.368908i
$324$		0			0
$325$	−2.19900	−	6.76782i	−0.121979	−	0.375411i
$326$	−3.13500	−	2.27771i	−0.173632	−	0.126151i
$327$		0			0
$328$	15.6204	−	48.0747i	0.862493	−	2.65448i
$329$	0.571666			0.0315170
$330$		0			0
$331$	18.4167			1.01227			0.506136	−	0.862454i	$-0.331074\pi$
$331$	18.4167			1.01227			0.506136	+	0.862454i	$0.331074\pi$
$332$	−6.32802	+	19.4756i	−0.347295	+	1.06886i
$333$		0			0
$334$	−41.2180	−	29.9466i	−2.25535	−	1.63860i
$335$	−0.343067	−	1.05585i	−0.0187437	−	0.0576873i
$336$		0			0
$337$	−13.5488	−	9.84376i	−0.738049	−	0.536224i	0.154051	−	0.988063i	$-0.450768\pi$
$337$	−13.5488	−	9.84376i	−0.738049	−	0.536224i	−0.892099	+	0.451839i	$0.850768\pi$
$338$	1.27695	−	0.927755i	0.0694567	−	0.0504632i
$339$		0			0
$340$	74.5924			4.04534
$341$	15.9756	+	6.07931i	0.865129	+	0.329213i
$342$		0			0
$343$	0.345469	−	1.06325i	0.0186536	−	0.0574098i
$344$	37.9556	−	27.5764i	2.04643	−	1.48682i
$345$		0			0
$346$	2.84376	+	8.75219i	0.152881	+	0.470521i
$347$	3.27060	+	10.0659i	0.175575	+	0.540365i	0.999659	−	0.0261025i	$-0.00830964\pi$
$347$	3.27060	+	10.0659i	0.175575	+	0.540365i	−0.824084	+	0.566468i	$0.808310\pi$
$348$		0			0
$349$	21.2064	−	15.4073i	1.13515	−	0.824736i	0.148716	−	0.988880i	$-0.452486\pi$
$349$	21.2064	−	15.4073i	1.13515	−	0.824736i	0.986436	+	0.164144i	$0.0524860\pi$
$350$	−0.138437	+	0.426065i	−0.00739976	+	0.0227741i
$351$		0			0
$352$	4.48070	−	90.5251i	0.238822	−	4.82501i
$353$	−22.3235			−1.18816			−0.594079	−	0.804407i	$-0.702483\pi$
$353$	−22.3235			−1.18816			−0.594079	+	0.804407i	$0.702483\pi$
$354$		0			0
$355$	12.7303	−	9.24908i	0.675652	−	0.490890i
$356$	−2.39190	−	1.73782i	−0.126771	−	0.0921043i
$357$		0			0
$358$	4.33876	+	13.3533i	0.229310	+	0.705745i
$359$	−16.4544	−	11.9548i	−0.868428	−	0.630950i	0.0617363	−	0.998092i	$-0.480336\pi$
$359$	−16.4544	−	11.9548i	−0.868428	−	0.630950i	−0.930165	+	0.367142i	$0.880336\pi$
$360$		0			0
$361$	−4.24891	+	13.0768i	−0.223627	+	0.688253i
$362$	−57.3982			−3.01678
$363$		0			0
$364$	1.61114			0.0844469
$365$	3.26048	−	10.0347i	0.170661	−	0.525242i
$366$		0			0
$367$	6.10614	+	4.43637i	0.318738	+	0.231577i	0.735637	−	0.677376i	$-0.236883\pi$
$367$	6.10614	+	4.43637i	0.318738	+	0.231577i	−0.416899	+	0.908953i	$0.636883\pi$
$368$	−7.72709	−	23.7815i	−0.402803	−	1.23970i
$369$		0			0
$370$	23.9622	+	17.4096i	1.24574	+	0.905080i
$371$	0.211044	−	0.153333i	0.0109569	−	0.00796064i
$372$		0			0
$373$	20.6599			1.06973			0.534865	−	0.844937i	$-0.320362\pi$
$373$	20.6599			1.06973			0.534865	+	0.844937i	$0.320362\pi$
$374$	−2.24260	+	45.3080i	−0.115962	+	2.34282i
$375$		0			0
$376$	−22.8521	+	70.3317i	−1.17851	+	3.62708i
$377$	−24.1623	+	17.5549i	−1.24442	+	0.904125i
$378$		0			0
$379$	1.72879	+	5.32066i	0.0888019	+	0.273304i	0.985589	−	0.169158i	$-0.0541050\pi$
$379$	1.72879	+	5.32066i	0.0888019	+	0.273304i	−0.896787	+	0.442463i	$0.854105\pi$
$380$	10.7289	+	33.0201i	0.550380	+	1.69390i
$381$		0			0
$382$	−10.3707	+	7.53475i	−0.530611	+	0.385511i
$383$	−0.595916	+	1.83404i	−0.0304499	+	0.0937151i	−0.965126	−	0.261784i	$-0.915689\pi$
$383$	−0.595916	+	1.83404i	−0.0304499	+	0.0937151i	0.934677	+	0.355499i	$0.115689\pi$
$384$		0			0
$385$	−0.656057	−	0.249653i	−0.0334357	−	0.0127235i
$386$	52.3968			2.66693
$387$		0			0
$388$	−9.67924	+	7.03238i	−0.491389	+	0.357015i
$389$	5.18643	+	3.76816i	0.262963	+	0.191054i	0.711452	−	0.702735i	$-0.248038\pi$
$389$	5.18643	+	3.76816i	0.262963	+	0.191054i	−0.448489	+	0.893788i	$0.648038\pi$
$390$		0			0
$391$	2.20196	+	6.77695i	0.111358	+	0.342725i
$392$	58.4734	+	42.4834i	2.95336	+	2.14574i
$393$		0			0
$394$	−2.86563	+	8.81951i	−0.144368	+	0.444320i
$395$	16.1421			0.812198
$396$		0			0
$397$	31.8131			1.59666			0.798328	−	0.602223i	$-0.205718\pi$
$397$	31.8131			1.59666			0.798328	+	0.602223i	$0.205718\pi$
$398$	11.2545	−	34.6379i	0.564139	−	1.73624i
$399$		0			0
$400$	−28.2065	−	20.4932i	−1.41032	−	1.02466i
$401$	−3.44310	−	10.5968i	−0.171940	−	0.529178i	0.827540	−	0.561406i	$-0.189740\pi$
$401$	−3.44310	−	10.5968i	−0.171940	−	0.529178i	−0.999481	+	0.0322287i	$0.989740\pi$
$402$		0			0
$403$	−14.7013	−	10.6811i	−0.732322	−	0.532063i
$404$	31.4110	−	22.8215i	1.56276	−	1.13541i
$405$		0			0
$406$	1.88021			0.0933134
$407$	−8.36879	+	10.3962i	−0.414826	+	0.515319i
$408$		0			0
$409$	−12.2987	+	37.8515i	−0.608132	+	1.87164i	−0.134505	+	0.990913i	$0.542944\pi$
$409$	−12.2987	+	37.8515i	−0.608132	+	1.87164i	−0.473628	+	0.880725i	$0.657056\pi$
$410$	29.1260	−	21.1613i	1.43843	−	1.04508i
$411$		0			0
$412$	−10.8051	−	33.2546i	−0.532328	−	1.63834i
$413$	−0.326984	−	1.00635i	−0.0160898	−	0.0495194i
$414$		0			0
$415$	−7.67341	+	5.57506i	−0.376673	+	0.273669i
$416$	−29.7753	+	91.6388i	−1.45985	+	4.49296i
$417$		0			0
$418$	−20.3792	+	5.52407i	−0.996782	+	0.270191i
$419$	35.7850			1.74821			0.874105	−	0.485737i	$-0.161449\pi$
$419$	35.7850			1.74821			0.874105	+	0.485737i	$0.161449\pi$
$420$		0			0
$421$	11.5988	−	8.42702i	0.565291	−	0.410708i	−0.268101	−	0.963391i	$-0.586396\pi$
$421$	11.5988	−	8.42702i	0.565291	−	0.410708i	0.833392	+	0.552683i	$0.186396\pi$
$422$	15.5646	+	11.3083i	0.757671	+	0.550480i
$423$		0			0
$424$	10.4280	+	32.0941i	0.506428	+	1.55863i
$425$	8.03791	+	5.83988i	0.389896	+	0.283276i
$426$		0			0
$427$	0.238262	−	0.733294i	0.0115303	−	0.0354866i
$428$	−70.8121			−3.42283
$429$		0			0
$430$	33.4143			1.61138
$431$	5.34463	−	16.4491i	0.257442	−	0.792324i	−0.735897	−	0.677093i	$-0.763239\pi$
$431$	5.34463	−	16.4491i	0.257442	−	0.792324i	0.993339	−	0.115231i	$-0.0367607\pi$
$432$		0			0
$433$	15.0864	+	10.9609i	0.725004	+	0.526746i	0.887979	−	0.459884i	$-0.152109\pi$
$433$	15.0864	+	10.9609i	0.725004	+	0.526746i	−0.162975	+	0.986630i	$0.552109\pi$
$434$	0.353513	+	1.08800i	0.0169692	+	0.0522258i
$435$		0			0
$436$	14.7957	+	10.7497i	0.708584	+	0.514816i
$437$	−2.68326	+	1.94950i	−0.128358	+	0.0932574i
$438$		0			0
$439$	−15.9892			−0.763125			−0.381562	−	0.924343i	$-0.624614\pi$
$439$	−15.9892			−0.763125			−0.381562	+	0.924343i	$0.624614\pi$
$440$	56.9403	−	70.7344i	2.71452	−	3.37213i
$441$		0			0
$442$	14.9026	−	45.8654i	0.708844	−	2.18160i
$443$	−25.7908	+	18.7381i	−1.22536	+	0.890276i	−0.996534	−	0.0831910i	$-0.973489\pi$
$443$	−25.7908	+	18.7381i	−1.22536	+	0.890276i	−0.228826	+	0.973467i	$0.573489\pi$
$444$		0			0
$445$	−0.423169	−	1.30238i	−0.0200601	−	0.0617388i
$446$	−22.8184	−	70.2278i	−1.08048	−	3.32538i
$447$		0			0
$448$	2.67440	−	1.94306i	0.126353	−	0.0918011i
$449$	−5.70480	+	17.5576i	−0.269226	+	0.828593i	0.721463	+	0.692453i	$0.243470\pi$
$449$	−5.70480	+	17.5576i	−0.269226	+	0.828593i	−0.990690	+	0.136141i	$0.956530\pi$
$450$		0			0
$451$	8.87465	+	13.5793i	0.417891	+	0.639424i
$452$	79.8905			3.75773
$453$		0			0
$454$	7.69720	−	5.59234i	0.361248	−	0.262462i
$455$	0.603723	+	0.438631i	0.0283030	+	0.0205633i
$456$		0			0
$457$	4.37874	+	13.4764i	0.204829	+	0.630398i	0.999720	+	0.0236469i	$0.00752773\pi$
$457$	4.37874	+	13.4764i	0.204829	+	0.630398i	−0.794891	+	0.606752i	$0.792472\pi$
$458$	20.6352	+	14.9923i	0.964219	+	0.700546i
$459$		0			0
$460$	6.77768	−	20.8596i	0.316011	−	0.972582i
$461$	−9.59329			−0.446804			−0.223402	−	0.974726i	$-0.571716\pi$
$461$	−9.59329			−0.446804			−0.223402	+	0.974726i	$0.571716\pi$
$462$		0			0
$463$	21.9634			1.02073			0.510363	−	0.859959i	$-0.329511\pi$
$463$	21.9634			1.02073			0.510363	+	0.859959i	$0.329511\pi$
$464$	−45.2180	+	139.167i	−2.09919	+	6.46065i
$465$		0			0
$466$	−46.9143	−	34.0852i	−2.17326	−	1.57897i
$467$	−10.5199	−	32.3768i	−0.486802	−	1.49822i	−0.829354	−	0.558723i	$-0.811291\pi$
$467$	−10.5199	−	32.3768i	−0.486802	−	1.49822i	0.342553	−	0.939499i	$-0.388709\pi$
$468$		0			0
$469$	0.0270855	+	0.0196787i	0.00125069	+	0.000908680i
$470$	−42.6104	+	30.9583i	−1.96547	+	1.42800i
$471$		0			0
$472$	136.882			6.30051
$473$	−0.744322	+	15.0378i	−0.0342240	+	0.691439i
$474$		0			0
$475$	−1.42904	+	4.39814i	−0.0655690	+	0.201801i
$476$	−1.81985	+	1.32220i	−0.0834126	+	0.0606028i
$477$		0			0
$478$	−19.2754	−	59.3235i	−0.881635	−	2.71339i
$479$	−10.9849	−	33.8079i	−0.501911	−	1.54472i	−0.805903	−	0.592048i	$-0.798319\pi$
$479$	−10.9849	−	33.8079i	−0.501911	−	1.54472i	0.303992	−	0.952675i	$-0.401681\pi$
$480$		0			0
$481$	11.4784	−	8.33958i	0.523372	−	0.380252i
$482$	3.29807	−	10.1504i	0.150223	−	0.462339i
$483$		0			0
$484$	46.9994	+	41.8268i	2.13634	+	1.90122i
$485$	−5.54153			−0.251628
$486$		0			0
$487$	−28.4135	+	20.6436i	−1.28754	+	0.935453i	−0.999753	−	0.0222417i	$-0.992920\pi$
$487$	−28.4135	+	20.6436i	−1.28754	+	0.935453i	−0.287787	+	0.957694i	$0.592920\pi$
$488$	80.6922	+	58.6263i	3.65277	+	2.65389i
$489$		0			0
$490$	15.9073	+	48.9577i	0.718619	+	2.21168i
$491$	7.74669	+	5.62830i	0.349603	+	0.254002i	0.748703	−	0.662906i	$-0.230677\pi$
$491$	7.74669	+	5.62830i	0.349603	+	0.254002i	−0.399099	+	0.916908i	$0.630677\pi$
$492$		0			0
$493$	12.8856	−	39.6579i	0.580340	−	1.78610i
$494$	22.4469			1.00993
$495$		0			0
$496$	−89.0319			−3.99765
$497$	−0.146637	+	0.451304i	−0.00657759	+	0.0202437i
$498$		0			0
$499$	29.4923	+	21.4274i	1.32026	+	0.959223i	0.999929	+	0.0119164i	$0.00379319\pi$
$499$	29.4923	+	21.4274i	1.32026	+	0.959223i	0.320328	+	0.947307i	$0.396207\pi$
$500$	13.9617	+	42.9696i	0.624385	+	1.92166i
$501$		0			0
$502$	−30.0403	−	21.8256i	−1.34076	−	0.974122i
$503$	16.7217	−	12.1490i	0.745582	−	0.541697i	−0.148873	−	0.988856i	$-0.547564\pi$
$503$	16.7217	−	12.1490i	0.745582	−	0.541697i	0.894454	+	0.447160i	$0.147564\pi$
$504$		0			0
$505$	17.9833			0.800248
$506$	12.4665	+	4.74396i	0.554203	+	0.210895i
$507$		0			0
$508$	−18.4439	+	56.7644i	−0.818315	+	2.51851i
$509$	16.4921	−	11.9822i	0.731000	−	0.531103i	−0.158880	−	0.987298i	$-0.550788\pi$
$509$	16.4921	−	11.9822i	0.731000	−	0.531103i	0.889880	+	0.456195i	$0.150788\pi$
$510$		0			0
$511$	0.0983252	+	0.302614i	0.00434965	+	0.0133868i
$512$	35.5438	+	109.393i	1.57083	+	4.83451i
$513$		0			0
$514$	6.78893	−	4.93244i	0.299447	−	0.217561i
$515$	5.00465	−	15.4027i	0.220531	−	0.678725i
$516$		0			0
$517$	−12.9833	−	19.8661i	−0.571006	−	0.873708i
$518$	−0.893207			−0.0392453
$519$		0			0
$520$	−78.0980	+	56.7415i	−3.42482	+	2.48828i
$521$	−19.5996	−	14.2399i	−0.858673	−	0.623863i	0.0688503	−	0.997627i	$-0.478067\pi$
$521$	−19.5996	−	14.2399i	−0.858673	−	0.623863i	−0.927524	+	0.373764i	$0.878067\pi$
$522$		0			0
$523$	−7.54257	−	23.2136i	−0.329814	−	1.01506i	−0.969221	−	0.246193i	$-0.920820\pi$
$523$	−7.54257	−	23.2136i	−0.329814	−	1.01506i	0.639407	−	0.768868i	$-0.279180\pi$
$524$	−36.7086	−	26.6704i	−1.60362	−	1.16510i
$525$		0			0
$526$	9.59975	−	29.5450i	0.418569	−	1.28822i
$527$	25.3711			1.10518
$528$		0			0
$529$	−20.9048			−0.908903
$530$	−7.42701	+	22.8580i	−0.322609	+	0.992888i
$531$		0			0
$532$	−0.847057	−	0.615423i	−0.0367246	−	0.0266820i
$533$	−5.32920	−	16.4016i	−0.230833	−	0.710432i
$534$		0			0
$535$	−26.5345	−	19.2784i	−1.14719	−	0.833479i
$536$	−3.50379	+	2.54566i	−0.151341	+	0.109956i
$537$		0			0
$538$	13.1508			0.566969
$539$	−22.3873	+	6.06839i	−0.964290	+	0.261384i
$540$		0			0
$541$	9.10611	−	28.0257i	0.391502	−	1.20492i	−0.540150	−	0.841569i	$-0.681633\pi$
$541$	9.10611	−	28.0257i	0.391502	−	1.20492i	0.931652	−	0.363351i	$-0.118367\pi$
$542$	63.6492	−	46.2438i	2.73397	−	1.98634i
$543$		0			0
$544$	−41.5718	−	127.945i	−1.78237	−	5.48558i
$545$	2.61761	+	8.05617i	0.112126	+	0.345089i
$546$		0			0
$547$	20.3345	−	14.7739i	0.869441	−	0.631686i	−0.0609956	−	0.998138i	$-0.519428\pi$
$547$	20.3345	−	14.7739i	0.869441	−	0.631686i	0.930437	+	0.366452i	$0.119428\pi$
$548$	−38.7409	+	119.232i	−1.65493	+	5.09335i
$549$		0			0
$550$	17.9503	−	4.86568i	0.765405	−	0.207473i
$551$	19.4089			0.826847
$552$		0			0
$553$	−0.393823	+	0.286129i	−0.0167470	+	0.0121674i
$554$	−29.8973	−	21.7217i	−1.27022	−	0.922866i
$555$		0			0
$556$	9.60697	+	29.5672i	0.407426	+	1.25393i
$557$	34.5124	+	25.0747i	1.46234	+	1.06245i	0.982747	+	0.184957i	$0.0592146\pi$
$557$	34.5124	+	25.0747i	1.46234	+	1.06245i	0.479590	+	0.877493i	$0.340785\pi$
$558$		0			0
$559$	4.94619	−	15.2228i	0.209201	−	0.643856i
$560$	3.65619			0.154502
$561$		0			0
$562$	−28.1968			−1.18941
$563$	9.81557	−	30.2092i	0.413677	−	1.27317i	−0.499752	−	0.866168i	$-0.666576\pi$
$563$	9.81557	−	30.2092i	0.413677	−	1.27317i	0.913429	−	0.406998i	$-0.133424\pi$
$564$		0			0
$565$	29.9363	+	21.7500i	1.25943	+	0.915030i
$566$	−19.7735	−	60.8567i	−0.831144	−	2.55800i
$567$		0			0
$568$	−49.6618	−	36.0814i	−2.08376	−	1.51394i
$569$	1.91761	−	1.39323i	0.0803904	−	0.0584071i	−0.546864	−	0.837221i	$-0.684179\pi$
$569$	1.91761	−	1.39323i	0.0803904	−	0.0584071i	0.627255	+	0.778814i	$0.284179\pi$
$570$		0			0
$571$	8.99511			0.376434			0.188217	−	0.982128i	$-0.439729\pi$
$571$	8.99511			0.376434			0.188217	+	0.982128i	$0.439729\pi$
$572$	−36.5913	−	55.9891i	−1.52996	−	2.34102i
$573$		0			0
$574$	−0.335497	+	1.03255i	−0.0140034	+	0.0430980i
$575$	2.36346	−	1.71715i	0.0985629	−	0.0716101i
$576$		0			0
$577$	10.2358	+	31.5025i	0.426122	+	1.31147i	0.901916	+	0.431911i	$0.142161\pi$
$577$	10.2358	+	31.5025i	0.426122	+	1.31147i	−0.475795	+	0.879556i	$0.657839\pi$
$578$	6.21089	+	19.1152i	0.258339	+	0.795086i
$579$		0			0
$580$	−103.837	+	75.4420i	−4.31160	+	3.13256i
$581$	0.0883886	−	0.272032i	0.00366698	−	0.0112858i
$582$		0			0
$583$	−10.1216	−	3.85164i	−0.419194	−	0.159519i
$584$	−41.1609			−1.70325
$585$		0			0
$586$	−3.36322	+	2.44353i	−0.138934	+	0.100941i
$587$	−17.4214	−	12.6574i	−0.719060	−	0.522427i	0.167024	−	0.985953i	$-0.446584\pi$
$587$	−17.4214	−	12.6574i	−0.719060	−	0.522427i	−0.886084	+	0.463526i	$0.846584\pi$
$588$		0			0
$589$	3.64922	+	11.2311i	0.150363	+	0.462771i
$590$	78.8711	+	57.3032i	3.24707	+	2.35913i
$591$		0			0
$592$	21.4811	−	66.1120i	0.882868	−	2.71719i
$593$	21.7365			0.892613			0.446306	−	0.894880i	$-0.352739\pi$
$593$	21.7365			0.892613			0.446306	+	0.894880i	$0.352739\pi$
$594$		0			0
$595$	−1.04189			−0.0427134
$596$	−2.90234	+	8.93250i	−0.118885	+	0.365889i
$597$		0			0
$598$	−11.4721	−	8.33493i	−0.469127	−	0.340841i
$599$	6.33154	+	19.4865i	0.258700	+	0.796196i	0.993078	+	0.117456i	$0.0374739\pi$
$599$	6.33154	+	19.4865i	0.258700	+	0.796196i	−0.734378	+	0.678740i	$0.762526\pi$
$600$		0			0
$601$	−8.84162	−	6.42382i	−0.360657	−	0.262033i	0.392669	−	0.919680i	$-0.371552\pi$
$601$	−8.84162	−	6.42382i	−0.360657	−	0.262033i	−0.753326	+	0.657647i	$0.771552\pi$
$602$	−0.815215	+	0.592289i	−0.0332257	+	0.0241399i
$603$		0			0
$604$	95.5963			3.88976
$605$	6.22421	+	28.4687i	0.253050	+	1.15742i
$606$		0			0
$607$	4.88443	−	15.0327i	0.198253	−	0.610159i	−0.801671	−	0.597766i	$-0.796055\pi$
$607$	4.88443	−	15.0327i	0.198253	−	0.610159i	0.999923	−	0.0123929i	$-0.00394488\pi$
$608$	50.6584	−	36.8055i	2.05447	−	1.49266i
$609$		0			0
$610$	21.9518	+	67.5607i	0.888802	+	2.73545i
$611$	7.79645	+	23.9950i	0.315410	+	0.970734i
$612$		0			0
$613$	12.7199	−	9.24157i	0.513753	−	0.373264i	−0.300492	−	0.953784i	$-0.597151\pi$
$613$	12.7199	−	9.24157i	0.513753	−	0.373264i	0.814246	+	0.580521i	$0.197151\pi$
$614$	14.8832	−	45.8059i	0.600638	−	1.84857i
$615$		0			0
$616$	−0.135375	+	2.73502i	−0.00545441	+	0.110197i
$617$	−36.9248			−1.48654			−0.743268	−	0.668993i	$-0.766725\pi$
$617$	−36.9248			−1.48654			−0.743268	+	0.668993i	$0.766725\pi$
$618$		0			0
$619$	−33.0593	+	24.0190i	−1.32877	+	0.965405i	−0.328988	+	0.944334i	$0.606708\pi$
$619$	−33.0593	+	24.0190i	−1.32877	+	0.965405i	−0.999778	+	0.0210710i	$0.993292\pi$
$620$	−63.1784	−	45.9018i	−2.53730	−	1.84346i
$621$		0			0
$622$	3.99207	+	12.2863i	0.160067	+	0.492637i
$623$	0.0334097	+	0.0242735i	0.00133853	+	0.000972499i
$624$		0			0
$625$	−9.58506	+	29.4998i	−0.383402	+	1.17999i
$626$	6.76015			0.270190
$627$		0			0
$628$	3.50033			0.139679
$629$	−6.12140	+	18.8397i	−0.244076	+	0.751189i
$630$		0			0
$631$	−20.1222	−	14.6196i	−0.801051	−	0.581997i	0.110172	−	0.993913i	$-0.464860\pi$
$631$	−20.1222	−	14.6196i	−0.801051	−	0.581997i	−0.911222	+	0.411915i	$0.864860\pi$
$632$	−19.4593	−	59.8896i	−0.774050	−	2.38228i
$633$		0			0
$634$	43.8031	+	31.8248i	1.73964	+	1.26392i
$635$	−22.3652	+	16.2493i	−0.887537	+	0.644833i
$636$		0			0
$637$	24.6587			0.977015
$638$	−42.7022	−	65.3396i	−1.69060	−	2.58682i
$639$		0			0
$640$	−49.3730	+	151.954i	−1.95164	+	6.00653i
$641$	−38.3138	+	27.8366i	−1.51330	+	1.09948i	−0.548620	+	0.836072i	$0.684847\pi$
$641$	−38.3138	+	27.8366i	−1.51330	+	1.09948i	−0.964684	+	0.263409i	$0.915153\pi$
$642$		0			0
$643$	−13.0891	−	40.2841i	−0.516184	−	1.58865i	−0.781117	−	0.624385i	$-0.785350\pi$
$643$	−13.0891	−	40.2841i	−0.516184	−	1.58865i	0.264933	−	0.964267i	$-0.414650\pi$
$644$	0.204392	+	0.629054i	0.00805418	+	0.0247882i
$645$		0			0
$646$	−25.3546	+	18.4212i	−0.997565	+	0.724773i
$647$	−3.00628	+	9.25236i	−0.118189	+	0.363748i	−0.992599	−	0.121440i	$-0.961249\pi$
$647$	−3.00628	+	9.25236i	−0.118189	+	0.363748i	0.874410	+	0.485188i	$0.161249\pi$
$648$		0			0
$649$	−27.5457	+	34.2188i	−1.08126	+	1.34320i
$650$	−19.7716			−0.775505
$651$		0			0
$652$	−6.45369	+	4.68888i	−0.252746	+	0.183631i
$653$	−23.3761	−	16.9837i	−0.914777	−	0.664624i	0.0274414	−	0.999623i	$-0.491264\pi$
$653$	−23.3761	−	16.9837i	−0.914777	−	0.664624i	−0.942218	+	0.334999i	$0.891264\pi$
$654$		0			0
$655$	−6.49439	−	19.9877i	−0.253757	−	0.780983i
$656$	−68.3575	−	49.6646i	−2.66891	−	1.93908i
$657$		0			0
$658$	0.490821	−	1.51059i	0.0191342	−	0.0588890i
$659$	29.3783			1.14441			0.572207	−	0.820109i	$-0.306087\pi$
$659$	29.3783			1.14441			0.572207	+	0.820109i	$0.306087\pi$
$660$		0			0
$661$	−40.1300			−1.56088			−0.780439	−	0.625233i	$-0.785004\pi$
$661$	−40.1300			−1.56088			−0.780439	+	0.625233i	$0.785004\pi$
$662$	15.8122	−	48.6649i	0.614558	−	1.89141i
$663$		0			0
$664$	29.9346	+	21.7488i	1.16169	+	0.844016i
$665$	−0.149859	−	0.461219i	−0.00581129	−	0.0178853i
$666$		0			0
$667$	−9.91939	−	7.20686i	−0.384080	−	0.279051i
$668$	−84.8509	+	61.6478i	−3.28298	+	2.38522i
$669$		0			0
$670$	−3.08457			−0.119167
$671$	−30.8941	+	8.37426i	−1.19265	+	0.323285i
$672$		0			0
$673$	−5.62675	+	17.3174i	−0.216895	+	0.667535i	0.782118	+	0.623130i	$0.214139\pi$
$673$	−5.62675	+	17.3174i	−0.216895	+	0.667535i	−0.999014	+	0.0444052i	$0.985861\pi$
$674$	−37.6442	+	27.3501i	−1.45000	+	1.05349i
$675$		0			0
$676$	−1.00408	−	3.09023i	−0.0386184	−	0.118855i
$677$	0.335152	+	1.03149i	0.0128809	+	0.0396435i	0.957290	−	0.289128i	$-0.0933654\pi$
$677$	0.335152	+	1.03149i	0.0128809	+	0.0396435i	−0.944409	+	0.328772i	$0.893365\pi$
$678$		0			0
$679$	0.135198	−	0.0982270i	0.00518842	−	0.00376961i
$680$	41.6493	−	128.183i	1.59718	−	4.91561i
$681$		0			0
$682$	29.7806	−	36.9950i	1.14036	−	1.41661i
$683$	31.3775			1.20063			0.600313	−	0.799765i	$-0.295043\pi$
$683$	31.3775			1.20063			0.600313	+	0.799765i	$0.295043\pi$
$684$		0			0
$685$	−46.9776	+	34.1312i	−1.79492	+	1.30409i
$686$	−2.51295	−	1.82576i	−0.0959447	−	0.0697079i
$687$		0			0
$688$	−24.2337	−	74.5836i	−0.923900	−	2.84347i
$689$	9.31420	+	6.76716i	0.354843	+	0.257808i
$690$		0			0
$691$	0.299803	−	0.922700i	0.0114051	−	0.0351012i	−0.945192	−	0.326515i	$-0.894126\pi$
$691$	0.299803	−	0.922700i	0.0114051	−	0.0351012i	0.956597	+	0.291414i	$0.0941256\pi$
$692$	18.9444			0.720158
$693$		0			0
$694$	29.4066			1.11626
$695$	−4.44971	+	13.6948i	−0.168787	+	0.519474i
$696$		0			0
$697$	19.4796	+	14.1528i	0.737843	+	0.536074i
$698$	−22.5056	−	69.2650i	−0.851848	−	2.62172i
$699$		0			0
$700$	0.746100	+	0.542073i	0.0281999	+	0.0204885i
$701$	−33.0112	+	23.9841i	−1.24682	+	0.905865i	−0.998033	−	0.0626935i	$-0.980031\pi$
$701$	−33.0112	+	23.9841i	−1.24682	+	0.905865i	−0.248784	+	0.968559i	$0.580031\pi$
$702$		0			0
$703$	−9.22032			−0.347751
$704$	−128.263	−	48.8087i	−4.83409	−	1.83955i
$705$		0			0
$706$	−19.1665	+	58.9884i	−0.721340	+	2.22006i
$707$	−0.438744	+	0.318766i	−0.0165006	+	0.0119884i
$708$		0			0
$709$	2.92572	+	9.00443i	0.109878	+	0.338169i	0.990844	−	0.135010i	$-0.0431066\pi$
$709$	2.92572	+	9.00443i	0.109878	+	0.338169i	−0.880967	+	0.473178i	$0.843107\pi$
$710$	−13.5102	−	41.5800i	−0.507027	−	1.56047i
$711$		0			0
$712$	−4.32190	+	3.14004i	−0.161970	+	0.117678i
$713$	2.30529	−	7.09497i	0.0863339	−	0.265709i
$714$		0			0
$715$	1.53153	−	30.9420i	0.0572759	−	1.15716i
$716$	28.9037			1.08018
$717$		0			0
$718$	−45.7172	+	33.2155i	−1.70615	+	1.23959i
$719$	−16.1880	−	11.7613i	−0.603710	−	0.438621i	0.243484	−	0.969905i	$-0.421710\pi$
$719$	−16.1880	−	11.7613i	−0.603710	−	0.438621i	−0.847194	+	0.531284i	$0.821710\pi$
$720$		0			0
$721$	0.150923	+	0.464494i	0.00562068	+	0.0172987i
$722$	30.9066	+	22.4550i	1.15022	+	0.835687i
$723$		0			0
$724$	−36.5132	+	112.376i	−1.35700	+	4.17643i
$725$	−17.0956			−0.634916
$726$		0			0
$727$	−15.0966			−0.559904			−0.279952	−	0.960014i	$-0.590318\pi$
$727$	−15.0966			−0.559904			−0.279952	+	0.960014i	$0.590318\pi$
$728$	0.899596	−	2.76867i	0.0333413	−	0.102614i
$729$		0			0
$730$	−23.7168	−	17.2312i	−0.877797	−	0.637757i
$731$	6.90579	+	21.2538i	0.255420	+	0.786101i
$732$		0			0
$733$	−34.7686	−	25.2609i	−1.28421	−	0.933032i	−0.284537	−	0.958665i	$-0.591840\pi$
$733$	−34.7686	−	25.2609i	−1.28421	−	0.933032i	−0.999671	+	0.0256328i	$0.991840\pi$
$734$	16.9654	−	12.3261i	0.626206	−	0.454965i
$735$		0			0
$736$	−39.5567			−1.45808
$737$	0.0687106	−	1.38818i	0.00253099	−	0.0511344i
$738$		0			0
$739$	−9.45629	+	29.1035i	−0.347855	+	1.07059i	0.612182	+	0.790717i	$0.290292\pi$
$739$	−9.45629	+	29.1035i	−0.347855	+	1.07059i	−0.960037	+	0.279871i	$0.909708\pi$
$740$	49.3284	−	35.8392i	1.81335	−	1.31747i
$741$		0			0
$742$	−0.223974	−	0.689320i	−0.00822233	−	0.0253057i
$743$	2.02214	+	6.22352i	0.0741853	+	0.228319i	0.981273	−	0.192623i	$-0.0616996\pi$
$743$	2.02214	+	6.22352i	0.0741853	+	0.228319i	−0.907088	+	0.420942i	$0.861700\pi$
$744$		0			0
$745$	−3.51941	+	2.55700i	−0.128941	+	0.0936813i
$746$	17.7382	−	54.5926i	0.649442	−	1.99878i
$747$		0			0
$748$	87.2791	+	33.2129i	3.19124	+	1.21438i
$749$	0.989090			0.0361406
$750$		0			0
$751$	31.6106	−	22.9665i	1.15349	−	0.838058i	0.164547	−	0.986369i	$-0.447384\pi$
$751$	31.6106	−	22.9665i	1.15349	−	0.838058i	0.988941	+	0.148312i	$0.0473838\pi$
$752$	100.005	+	72.6577i	3.64680	+	2.64955i
$753$		0			0
$754$	25.6426	+	78.9197i	0.933847	+	2.87408i
$755$	35.8216	+	26.0259i	1.30368	+	0.947179i
$756$		0			0
$757$	−13.5885	+	41.8212i	−0.493884	+	1.52002i	0.324804	+	0.945781i	$0.394702\pi$
$757$	−13.5885	+	41.8212i	−0.493884	+	1.52002i	−0.818689	+	0.574238i	$0.805298\pi$
$758$	15.5438			0.564577
$759$		0			0
$760$	62.7340			2.27560
$761$	−9.30633	+	28.6419i	−0.337354	+	1.03827i	0.628196	+	0.778055i	$0.283793\pi$
$761$	−9.30633	+	28.6419i	−0.337354	+	1.03827i	−0.965551	+	0.260215i	$0.916207\pi$
$762$		0			0
$763$	−0.206663	−	0.150150i	−0.00748171	−	0.00543578i
$764$	8.15460	+	25.0973i	0.295023	+	0.907988i
$765$		0			0
$766$	4.33470	+	3.14934i	0.156619	+	0.113790i
$767$	37.7810	−	27.4495i	1.36419	−	0.991145i
$768$		0			0
$769$	−24.6918			−0.890410			−0.445205	−	0.895429i	$-0.646869\pi$
$769$	−24.6918			−0.890410			−0.445205	+	0.895429i	$0.646869\pi$
$770$	−1.22297	+	1.51924i	−0.0440728	+	0.0547497i
$771$		0			0
$772$	33.3317	−	102.584i	1.19963	−	3.69209i
$773$	−11.0104	+	7.99955i	−0.396018	+	0.287724i	−0.767917	−	0.640549i	$-0.778707\pi$
$773$	−11.0104	+	7.99955i	−0.396018	+	0.287724i	0.371899	+	0.928273i	$0.378707\pi$
$774$		0			0
$775$	−3.21428	−	9.89255i	−0.115460	−	0.355351i
$776$	6.68031	+	20.5599i	0.239809	+	0.738057i
$777$		0			0
$778$	14.4101	−	10.4696i	0.516627	−	0.375352i
$779$	−3.46324	+	10.6588i	−0.124083	+	0.381889i
$780$		0			0
$781$	19.0137	−	5.15391i	0.680362	−	0.184421i
$782$	19.7982			0.707983
$783$		0			0
$784$	97.7411	−	71.0131i	3.49075	−	2.53618i
$785$	1.31163	+	0.952958i	0.0468142	+	0.0340125i
$786$		0			0
$787$	−8.12309	−	25.0003i	−0.289557	−	0.891165i	−0.984996	−	0.172579i	$-0.944790\pi$
$787$	−8.12309	−	25.0003i	−0.289557	−	0.891165i	0.695439	−	0.718586i	$-0.255210\pi$
$788$	15.4442	+	11.2209i	0.550177	+	0.399727i
$789$		0			0
$790$	13.8593	−	42.6545i	0.493092	−	1.51758i
$791$	−1.11590			−0.0396767
$792$		0			0
$793$	34.0286			1.20839
$794$	27.3141	−	84.0642i	0.969342	−	2.98333i
$795$		0			0
$796$	−60.6559	−	44.0691i	−2.14989	−	1.56199i
$797$	−0.377842	−	1.16288i	−0.0133839	−	0.0411913i	0.944142	−	0.329540i	$-0.106894\pi$
$797$	−0.377842	−	1.16288i	−0.0133839	−	0.0411913i	−0.957525	+	0.288349i	$0.906894\pi$
$798$		0			0
$799$	−28.4980	−	20.7050i	−1.00819	−	0.732491i
$800$	−44.6206	+	32.4188i	−1.57758	+	1.14618i
$801$		0			0
$802$	−30.9575			−1.09315
$803$	8.28308	−	10.2897i	0.292303	−	0.363115i
$804$		0			0
$805$	−0.0946694	+	0.291363i	−0.00333666	+	0.0102692i
$806$	−40.8463	+	29.6766i	−1.43875	+	1.04531i
$807$		0			0
$808$	−21.6789	−	66.7208i	−0.762662	−	2.34723i
$809$	2.92510	+	9.00253i	0.102841	+	0.316512i	0.989218	−	0.146453i	$-0.0467856\pi$
$809$	2.92510	+	9.00253i	0.102841	+	0.316512i	−0.886377	+	0.462965i	$0.846786\pi$
$810$		0			0
$811$	1.87016	−	1.35875i	0.0656701	−	0.0477121i	−0.554466	−	0.832206i	$-0.687077\pi$
$811$	1.87016	−	1.35875i	0.0656701	−	0.0477121i	0.620136	+	0.784494i	$0.287077\pi$
$812$	1.19608	−	3.68115i	0.0419741	−	0.129183i
$813$		0			0
$814$	20.2860	+	31.0400i	0.711023	+	1.08795i
$815$	−3.69484			−0.129425
$816$		0			0
$817$	−8.41523	+	6.11402i	−0.294412	+	0.213903i
$818$	89.4609	+	64.9972i	3.12793	+	2.27257i
$819$		0			0
$820$	−22.9021	−	70.4855i	−0.799777	−	2.46146i
$821$	33.1728	+	24.1014i	1.15774	+	0.841146i	0.989490	−	0.144599i	$-0.0461893\pi$
$821$	33.1728	+	24.1014i	1.15774	+	0.841146i	0.168247	+	0.985745i	$0.446189\pi$
$822$		0			0
$823$	12.7588	−	39.2676i	0.444744	−	1.36878i	−0.438020	−	0.898965i	$-0.644320\pi$
$823$	12.7588	−	39.2676i	0.444744	−	1.36878i	0.882764	−	0.469816i	$-0.155680\pi$
$824$	−63.1795			−2.20096
$825$		0			0
$826$	−2.93997			−0.102295
$827$	3.23676	−	9.96172i	0.112553	−	0.346403i	−0.878876	−	0.477051i	$-0.841706\pi$
$827$	3.23676	−	9.96172i	0.112553	−	0.346403i	0.991429	+	0.130648i	$0.0417057\pi$
$828$		0			0
$829$	−32.8312	−	23.8533i	−1.14027	−	0.828458i	−0.153117	−	0.988208i	$-0.548931\pi$
$829$	−32.8312	−	23.8533i	−1.14027	−	0.828458i	−0.987157	+	0.159750i	$0.948931\pi$
$830$	8.14351	+	25.0632i	0.282665	+	0.869955i
$831$		0			0
$832$	118.031	+	85.7548i	4.09200	+	2.97301i
$833$	−27.8530	+	20.2364i	−0.965048	+	0.701148i
$834$		0			0
$835$	−48.5785			−1.68113
$836$	−2.14882	+	43.4133i	−0.0743185	+	1.50148i
$837$		0			0
$838$	30.7243	−	94.5595i	1.06135	−	3.26650i
$839$	−34.5140	+	25.0759i	−1.19156	+	0.865716i	−0.993428	−	0.114460i	$-0.963486\pi$
$839$	−34.5140	+	25.0759i	−1.19156	+	0.865716i	−0.198128	+	0.980176i	$0.563486\pi$
$840$		0			0
$841$	13.2105	+	40.6578i	0.455536	+	1.40199i
$842$	−12.3094	−	37.8844i	−0.424209	−	1.30558i
$843$		0			0
$844$	32.0410	−	23.2792i	1.10290	−	0.801303i
$845$	0.465064	−	1.43132i	0.0159987	−	0.0492389i
$846$		0			0
$847$	−0.656479	−	0.584229i	−0.0225569	−	0.0200744i
$848$	56.4075			1.93704
$849$		0			0
$850$	22.3327	−	16.2257i	0.766006	−	0.556536i
$851$	4.71227	+	3.42366i	0.161535	+	0.117362i
$852$		0			0
$853$	−10.8987	−	33.5428i	−0.373165	−	1.14849i	−0.944708	−	0.327913i	$-0.893655\pi$
$853$	−10.8987	−	33.5428i	−0.373165	−	1.14849i	0.571543	−	0.820572i	$-0.306345\pi$
$854$	−1.73312	−	1.25918i	−0.0593061	−	0.0430884i
$855$		0			0
$856$	−39.5385	+	121.687i	−1.35140	+	4.15918i
$857$	−19.7097			−0.673272			−0.336636	−	0.941635i	$-0.609289\pi$
$857$	−19.7097			−0.673272			−0.336636	+	0.941635i	$0.609289\pi$
$858$		0			0
$859$	4.52292			0.154320			0.0771601	−	0.997019i	$-0.475415\pi$
$859$	4.52292			0.154320			0.0771601	+	0.997019i	$0.475415\pi$
$860$	21.2561	−	65.4197i	0.724828	−	2.23079i
$861$		0			0
$862$	−38.8769	−	28.2457i	−1.32415	−	0.962052i
$863$	−9.40646	−	28.9501i	−0.320200	−	0.985473i	−0.973561	−	0.228427i	$-0.926642\pi$
$863$	−9.40646	−	28.9501i	−0.320200	−	0.985473i	0.653361	−	0.757046i	$-0.273358\pi$
$864$		0			0
$865$	7.09878	+	5.15757i	0.241366	+	0.175363i
$866$	41.9163	−	30.4540i	1.42437	−	1.03487i
$867$		0			0
$868$	2.35501			0.0799344
$869$	18.8876	+	7.18741i	0.640717	+	0.243816i
$870$		0			0
$871$	−0.456597	+	1.40526i	−0.0154712	+	0.0476155i
$872$	26.7341	−	19.4234i	0.905330	−	0.657761i
$873$		0			0
$874$	2.84765	+	8.76416i	0.0963231	+	0.296452i
$875$	−0.195014	−	0.600191i	−0.00659268	−	0.0202902i
$876$		0			0
$877$	18.4844	−	13.4297i	0.624173	−	0.453488i	−0.230204	−	0.973142i	$-0.573939\pi$
$877$	18.4844	−	13.4297i	0.624173	−	0.453488i	0.854377	+	0.519654i	$0.173939\pi$
$878$	−13.7280	+	42.2506i	−0.463299	+	1.42589i
$879$		0			0
$880$	−83.0372	−	127.057i	−2.79918	−	4.28309i
$881$	−23.1357			−0.779461			−0.389731	−	0.920929i	$-0.627432\pi$
$881$	−23.1357			−0.779461			−0.389731	+	0.920929i	$0.627432\pi$
$882$		0			0
$883$	−27.1834	+	19.7499i	−0.914793	+	0.664636i	−0.942223	−	0.334988i	$-0.891268\pi$
$883$	−27.1834	+	19.7499i	−0.914793	+	0.664636i	0.0274293	+	0.999624i	$0.491268\pi$
$884$	−80.3169	−	58.3536i	−2.70135	−	1.96265i
$885$		0			0
$886$	27.3709	+	84.2389i	0.919543	+	2.83006i
$887$	0.318107	+	0.231118i	0.0106810	+	0.00776018i	0.593113	−	0.805119i	$-0.297899\pi$
$887$	0.318107	+	0.231118i	0.0106810	+	0.00776018i	−0.582432	+	0.812879i	$0.697899\pi$
$888$		0			0
$889$	0.257621	−	0.792875i	0.00864032	−	0.0265922i
$890$	−3.80479			−0.127537
$891$		0			0
$892$	−152.010			−5.08968
$893$	5.06661	−	15.5934i	0.169548	−	0.521814i
$894$		0			0
$895$	10.8307	+	7.86896i	0.362030	+	0.263030i
$896$	−1.48892	−	4.58243i	−0.0497414	−	0.153088i
$897$		0			0
$898$	41.4968	+	30.1492i	1.38477	+	1.00609i
$899$	−35.3181	+	25.6601i	−1.17792	+	0.855812i
$900$		0			0
$901$	−16.0743			−0.535511
$902$	43.5020	−	11.7918i	1.44846	−	0.392624i
$903$		0			0
$904$	44.6075	−	137.288i	1.48362	−	4.56613i
$905$	−44.2763	+	32.1686i	−1.47179	+	1.06932i
$906$		0			0
$907$	9.52958	+	29.3290i	0.316425	+	0.973855i	0.975164	+	0.221484i	$0.0710899\pi$
$907$	9.52958	+	29.3290i	0.316425	+	0.973855i	−0.658740	+	0.752371i	$0.728910\pi$
$908$	−6.05240	−	18.6274i	−0.200856	−	0.618171i
$909$		0			0
$910$	1.67740	−	1.21870i	0.0556052	−	0.0403996i
$911$	−5.80004	+	17.8507i	−0.192164	+	0.591420i	0.807834	+	0.589410i	$0.200640\pi$
$911$	−5.80004	+	17.8507i	−0.192164	+	0.591420i	−0.999998	+	0.00200989i	$0.999360\pi$
$912$		0			0
$913$	−11.4609	+	3.10662i	−0.379299	+	0.102814i
$914$	39.3700			1.30224
$915$		0			0
$916$	42.4794	−	30.8631i	1.40356	−	1.01975i
$917$	0.512739	+	0.372527i	0.0169321	+	0.0123019i
$918$		0			0
$919$	3.34672	+	10.3002i	0.110398	+	0.339771i	0.990959	−	0.134162i	$-0.0428341\pi$
$919$	3.34672	+	10.3002i	0.110398	+	0.339771i	−0.880561	+	0.473932i	$0.842834\pi$
$920$	−32.0617	−	23.2942i	−1.05704	−	0.767988i
$921$		0			0
$922$	−8.23661	+	25.3497i	−0.271258	+	0.834847i
$923$	−20.9428			−0.689340
$924$		0			0
$925$	8.12139			0.267030
$926$	18.8573	−	58.0370i	0.619691	−	1.90721i
$927$		0			0
$928$	187.272	+	136.061i	6.14751	+	4.46643i
$929$	14.4711	+	44.5375i	0.474782	+	1.46123i	0.846252	+	0.532784i	$0.178854\pi$
$929$	14.4711	+	44.5375i	0.474782	+	1.46123i	−0.371470	+	0.928445i	$0.621146\pi$
$930$		0			0
$931$	−12.9643	−	9.41911i	−0.424888	−	0.308699i
$932$	−96.5774	+	70.1676i	−3.16350	+	2.29842i
$933$		0			0
$934$	−94.5860			−3.09495
$935$	23.6628	+	36.2070i	0.773857	+	1.18409i
$936$		0			0
$937$	15.2404	−	46.9051i	0.497882	−	1.53232i	−0.314534	−	0.949246i	$-0.601848\pi$
$937$	15.2404	−	46.9051i	0.497882	−	1.53232i	0.812417	−	0.583077i	$-0.198152\pi$
$938$	0.0752549	−	0.0546759i	0.00245716	−	0.00178523i
$939$		0			0
$940$	33.5051	+	103.118i	1.09282	+	3.36334i
$941$	−6.27193	−	19.3030i	−0.204459	−	0.629260i	−0.999735	−	0.0230126i	$-0.992674\pi$
$941$	−6.27193	−	19.3030i	−0.204459	−	0.629260i	0.795276	−	0.606247i	$-0.207326\pi$
$942$		0			0
$943$	5.72775	−	4.16146i	0.186521	−	0.135516i
$944$	70.7046	−	217.606i	2.30124	−	7.08248i
$945$		0			0
$946$	39.0974	+	14.8780i	1.27117	+	0.483725i
$947$	38.8652			1.26295			0.631475	−	0.775396i	$-0.282450\pi$
$947$	38.8652			1.26295			0.631475	+	0.775396i	$0.282450\pi$
$948$		0			0
$949$	−11.3609	+	8.25416i	−0.368790	+	0.267941i
$950$	10.3949	+	7.55232i	0.337254	+	0.245030i
$951$		0			0
$952$	1.25600	+	3.86558i	0.0407073	+	0.125284i
$953$	14.0214	+	10.1871i	0.454198	+	0.329994i	0.791251	−	0.611492i	$-0.209430\pi$
$953$	14.0214	+	10.1871i	0.454198	+	0.329994i	−0.337053	+	0.941486i	$0.609430\pi$
$954$		0			0
$955$	−3.77701	+	11.6244i	−0.122221	+	0.376158i
$956$	−128.408			−4.15300
$957$		0			0
$958$	−98.7667			−3.19101
$959$	0.541126	−	1.66541i	0.0174739	−	0.0537791i
$960$		0			0
$961$	3.59066	+	2.60877i	0.115828	+	0.0841538i
$962$	−12.1817	−	37.4913i	−0.392752	−	1.20877i
$963$		0			0
$964$	−17.7748	−	12.9142i	−0.572489	−	0.415938i
$965$	40.4183	−	29.3656i	1.30111	−	0.945313i
$966$		0			0
$967$	−34.3964			−1.10611			−0.553057	−	0.833144i	$-0.686539\pi$
$967$	−34.3964			−1.10611			−0.553057	+	0.833144i	$0.686539\pi$
$968$	98.1198	−	57.4118i	3.15369	−	1.84528i
$969$		0			0
$970$	−4.75784	+	14.6431i	−0.152765	+	0.470163i
$971$	44.7417	−	32.5067i	1.43583	−	1.04319i	0.446935	−	0.894566i	$-0.352516\pi$
$971$	44.7417	−	32.5067i	1.43583	−	1.04319i	0.988894	−	0.148624i	$-0.0474845\pi$
$972$		0			0
$973$	−0.134188	−	0.412989i	−0.00430188	−	0.0132398i
$974$	30.1542	+	92.8052i	0.966204	+	2.97367i
$975$		0			0
$976$	134.881	−	97.9967i	4.31743	−	3.13680i
$977$	−2.38102	+	7.32803i	−0.0761756	+	0.234444i	−0.981893	−	0.189439i	$-0.939333\pi$
$977$	−2.38102	+	7.32803i	−0.0761756	+	0.234444i	0.905717	+	0.423883i	$0.139333\pi$
$978$		0			0
$979$	0.0847539	−	1.71231i	0.00270874	−	0.0547257i
$980$	105.970			3.38510
$981$		0			0
$982$	21.5236	−	15.6378i	0.686846	−	0.499023i
$983$	28.9470	+	21.0313i	0.923267	+	0.670793i	0.944335	−	0.328985i	$-0.106707\pi$
$983$	28.9470	+	21.0313i	0.923267	+	0.670793i	−0.0210677	+	0.999778i	$0.506707\pi$
$984$		0			0
$985$	2.73235	+	8.40931i	0.0870599	+	0.267943i
$986$	−93.7302	−	68.0990i	−2.98498	−	2.16871i
$987$		0			0
$988$	14.2794	−	43.9474i	0.454288	−	1.39815i
$989$	6.57106			0.208947
$990$		0			0
$991$	5.90515			0.187583			0.0937917	−	0.995592i	$-0.470101\pi$
$991$	5.90515			0.187583			0.0937917	+	0.995592i	$0.470101\pi$
$992$	−43.5226	+	133.949i	−1.38184	+	4.25287i
$993$		0			0
$994$	1.06664	+	0.774961i	0.0338318	+	0.0245803i
$995$	−10.7311	−	33.0269i	−0.340198	−	1.04702i
$996$		0			0
$997$	36.8792	+	26.7943i	1.16798	+	0.848585i	0.990765	−	0.135587i	$-0.0432921\pi$
$997$	36.8792	+	26.7943i	1.16798	+	0.848585i	0.177212	+	0.984173i	$0.443292\pi$
$998$	81.9421	−	59.5344i	2.59383	−	1.88453i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.d.163.6	yes	24
3.2	odd	2		891.2.f.c.163.1	yes	24
9.2	odd	6		891.2.n.k.757.6		48
9.4	even	3		891.2.n.j.460.6		48
9.5	odd	6		891.2.n.k.460.1		48
9.7	even	3		891.2.n.j.757.1		48
11.4	even	5		9801.2.a.ck.1.12		12
11.5	even	5	inner	891.2.f.d.82.6	yes	24
11.7	odd	10		9801.2.a.cf.1.1		12
33.5	odd	10		891.2.f.c.82.1	✓	24
33.26	odd	10		9801.2.a.cg.1.1		12
33.29	even	10		9801.2.a.cl.1.12		12
99.5	odd	30		891.2.n.k.379.6		48
99.16	even	15		891.2.n.j.676.6		48
99.38	odd	30		891.2.n.k.676.1		48
99.49	even	15		891.2.n.j.379.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.c.82.1	✓	24	33.5	odd	10
891.2.f.c.163.1	yes	24	3.2	odd	2
891.2.f.d.82.6	yes	24	11.5	even	5	inner
891.2.f.d.163.6	yes	24	1.1	even	1	trivial
891.2.n.j.379.1		48	99.49	even	15
891.2.n.j.460.6		48	9.4	even	3
891.2.n.j.676.6		48	99.16	even	15
891.2.n.j.757.1		48	9.7	even	3
891.2.n.k.379.6		48	99.5	odd	30
891.2.n.k.460.1		48	9.5	odd	6
891.2.n.k.676.1		48	99.38	odd	30
891.2.n.k.757.6		48	9.2	odd	6
9801.2.a.cf.1.1		12	11.7	odd	10
9801.2.a.cg.1.1		12	33.26	odd	10
9801.2.a.ck.1.12		12	11.4	even	5
9801.2.a.cl.1.12		12	33.29	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.858580 - 2.64244i) q^{2} +(-4.62728 - 3.36192i) q^{4} +(-0.818647 - 2.51954i) q^{5} +(0.0646331 + 0.0469587i) q^{7} +(-8.36097 + 6.07460i) q^{8} -7.36059 q^{10} +(0.163962 - 3.31257i) q^{11} +(-1.08956 + 3.35332i) q^{13} +(0.179578 - 0.130471i) q^{14} +(5.33826 + 16.4295i) q^{16} +(-1.52123 - 4.68186i) q^{17} +(1.85373 - 1.34682i) q^{19} +(-4.68236 + 14.4108i) q^{20} +(-8.61249 - 3.27736i) q^{22} -1.44749 q^{23} +(-1.63279 + 1.18629i) q^{25} +(7.92547 + 5.75819i) q^{26} +(-0.141204 - 0.434582i) q^{28} +(6.85282 + 4.97886i) q^{29} +(-1.59261 + 4.90156i) q^{31} +27.3278 q^{32} -13.6776 q^{34} +(0.0654024 - 0.201288i) q^{35} +(-3.25547 - 2.36524i) q^{37} +(-1.96730 - 6.05472i) q^{38} +(22.1499 + 16.0928i) q^{40} +(-3.95702 + 2.87494i) q^{41} -4.53962 q^{43} +(-11.8953 + 14.7770i) q^{44} +(-1.24279 + 3.82491i) q^{46} +(5.78899 - 4.20595i) q^{47} +(-2.16115 - 6.65133i) q^{49} +(1.73282 + 5.33309i) q^{50} +(16.3153 - 11.8538i) q^{52} +(1.00902 - 3.10546i) q^{53} +(-8.48036 + 2.29872i) q^{55} -0.825651 q^{56} +(19.0400 - 13.8334i) q^{58} +(-10.7153 - 7.78513i) q^{59} +(-2.98234 - 9.17870i) q^{61} +(11.5847 + 8.41676i) q^{62} +(12.7866 - 39.3530i) q^{64} +9.34078 q^{65} +0.419065 q^{67} +(-8.70087 + 26.7785i) q^{68} +(-0.475738 - 0.345644i) q^{70} +(1.83547 + 5.64900i) q^{71} +(3.22213 + 2.34101i) q^{73} +(-9.04508 + 6.57164i) q^{74} -13.1056 q^{76} +(0.166151 - 0.206402i) q^{77} +(-1.88291 + 5.79499i) q^{79} +(37.0245 - 26.8999i) q^{80} +(4.19944 + 12.9246i) q^{82} +(-1.10637 - 3.40505i) q^{83} +(-10.5508 + 7.66557i) q^{85} +(-3.89762 + 11.9957i) q^{86} +(18.7517 + 28.6923i) q^{88} +0.516913 q^{89} +(-0.227889 + 0.165571i) q^{91} +(6.69796 + 4.86635i) q^{92} +(-6.14365 - 18.9082i) q^{94} +(-4.91090 - 3.56798i) q^{95} +(0.646394 - 1.98940i) q^{97} -19.4312 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 8 q^{4} - 4 q^{5} + 7 q^{7} - 10 q^{8} - 16 q^{10} - 5 q^{11} + 7 q^{13} - 13 q^{14} + 2 q^{16} + 5 q^{17} + 4 q^{19} - 27 q^{20} - 2 q^{22} - 6 q^{23} - 2 q^{25} + 34 q^{26} - 9 q^{28}+ \cdots - 68 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 - 8 * q^4 - 4 * q^5 + 7 * q^7 - 10 * q^8 - 16 * q^10 - 5 * q^11 + 7 * q^13 - 13 * q^14 + 2 * q^16 + 5 * q^17 + 4 * q^19 - 27 * q^20 - 2 * q^22 - 6 * q^23 - 2 * q^25 + 34 * q^26 - 9 * q^28 - 22 * q^29 + 2 * q^31 - 18 * q^32 - 42 * q^34 + 6 * q^37 + 5 * q^38 + 53 * q^40 - 10 * q^41 - 30 * q^43 - 59 * q^44 + 31 * q^46 - 4 * q^47 - 3 * q^49 - 9 * q^50 - 26 * q^52 - 17 * q^53 + 12 * q^55 + 48 * q^56 + 53 * q^58 - 11 * q^59 + 3 * q^61 + 2 * q^62 + 38 * q^64 + 68 * q^65 - 14 * q^67 - 22 * q^68 - 20 * q^70 + 36 * q^71 + 35 * q^73 - 3 * q^74 - 102 * q^76 + 88 * q^77 - 9 * q^79 + 37 * q^80 - 6 * q^82 - 32 * q^83 - 45 * q^85 + 110 * q^86 + 54 * q^88 - 34 * q^89 + 13 * q^91 + q^92 - 25 * q^94 + 84 * q^95 + 15 * q^97 - 68 * q^98

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