LMFDB - Embedded newform 1805.2.b.k.1084.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1805,2,Mod(1084,1805)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1805, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1805.1084"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-18,-3,-12,0,0,-12,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1084.9
Character	$\chi$	$=$	1805.1084
Dual form			1805.2.b.k.1084.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.04740i q^{2} -0.531453i q^{3} +0.902948 q^{4} +(1.65192 - 1.50704i) q^{5} -0.556645 q^{6} -2.74033i q^{7} -3.04056i q^{8} +2.71756 q^{9} +(-1.57847 - 1.73023i) q^{10} +0.832835 q^{11} -0.479874i q^{12} -0.610831i q^{13} -2.87023 q^{14} +(-0.800919 - 0.877919i) q^{15} -1.37879 q^{16} +4.83841i q^{17} -2.84638i q^{18} +(1.49160 - 1.36077i) q^{20} -1.45636 q^{21} -0.872314i q^{22} -3.75094i q^{23} -1.61591 q^{24} +(0.457688 - 4.97901i) q^{25} -0.639786 q^{26} -3.03861i q^{27} -2.47437i q^{28} +3.97516 q^{29} +(-0.919534 + 0.838884i) q^{30} -6.92676 q^{31} -4.63696i q^{32} -0.442613i q^{33} +5.06777 q^{34} +(-4.12977 - 4.52681i) q^{35} +2.45381 q^{36} +4.33071i q^{37} -0.324628 q^{39} +(-4.58222 - 5.02276i) q^{40} +5.31691 q^{41} +1.52539i q^{42} +10.4585i q^{43} +0.752007 q^{44} +(4.48919 - 4.09546i) q^{45} -3.92874 q^{46} +3.40016i q^{47} +0.732762i q^{48} -0.509407 q^{49} +(-5.21503 - 0.479384i) q^{50} +2.57139 q^{51} -0.551549i q^{52} +13.6679i q^{53} -3.18265 q^{54} +(1.37578 - 1.25511i) q^{55} -8.33212 q^{56} -4.16359i q^{58} -10.0173 q^{59} +(-0.723188 - 0.792715i) q^{60} +9.07245 q^{61} +7.25511i q^{62} -7.44700i q^{63} -7.61435 q^{64} +(-0.920544 - 1.00905i) q^{65} -0.463594 q^{66} +10.9346i q^{67} +4.36883i q^{68} -1.99345 q^{69} +(-4.74139 + 4.32554i) q^{70} -0.677726 q^{71} -8.26288i q^{72} -7.01343i q^{73} +4.53600 q^{74} +(-2.64611 - 0.243240i) q^{75} -2.28224i q^{77} +0.340016i q^{78} -3.47957 q^{79} +(-2.27765 + 2.07788i) q^{80} +6.53779 q^{81} -5.56894i q^{82} +4.97485i q^{83} -1.31501 q^{84} +(7.29166 + 7.99268i) q^{85} +10.9542 q^{86} -2.11261i q^{87} -2.53228i q^{88} +5.88868 q^{89} +(-4.28959 - 4.70199i) q^{90} -1.67388 q^{91} -3.38690i q^{92} +3.68125i q^{93} +3.56134 q^{94} -2.46433 q^{96} -12.4387i q^{97} +0.533555i q^{98} +2.26328 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) $ 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times$.

$n$	$362$	$1446$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.04740i		−	0.740625i	−0.928907	−	0.370313i	$-0.879251\pi$
$2$		−	1.04740i		−	0.740625i	0.928907	−	0.370313i	$-0.120749\pi$
$3$		−	0.531453i		−	0.306835i	−0.988161	−	0.153417i	$-0.950972\pi$
$3$		−	0.531453i		−	0.306835i	0.988161	−	0.153417i	$-0.0490279\pi$
$4$	0.902948			0.451474
$5$	1.65192	−	1.50704i	0.738762	−	0.673967i
$5$	1.65192	−	1.50704i	0.738762	−	0.673967i
$6$	−0.556645			−0.227250
$7$		−	2.74033i		−	1.03575i	−0.855457	−	0.517874i	$-0.826724\pi$
$7$		−	2.74033i		−	1.03575i	0.855457	−	0.517874i	$-0.173276\pi$
$8$		−	3.04056i		−	1.07500i
$9$	2.71756			0.905853
$10$	−1.57847	−	1.73023i	−0.499157	−	0.547146i
$11$	0.832835			0.251109			0.125555	−	0.992087i	$-0.459929\pi$
$11$	0.832835			0.251109			0.125555	+	0.992087i	$0.459929\pi$
$12$		−	0.479874i		−	0.138528i
$13$		−	0.610831i		−	0.169414i	−0.996406	−	0.0847071i	$-0.973005\pi$
$13$		−	0.610831i		−	0.169414i	0.996406	−	0.0847071i	$-0.0269954\pi$
$14$	−2.87023			−0.767101
$15$	−0.800919	−	0.877919i	−0.206796	−	0.226678i
$16$	−1.37879			−0.344697
$17$			4.83841i			1.17349i	0.809773	+	0.586744i	$0.199590\pi$
$17$			4.83841i			1.17349i	−0.809773	+	0.586744i	$0.800410\pi$
$18$		−	2.84638i		−	0.670897i
$19$		0			0
$19$		0			0
$20$	1.49160	−	1.36077i	0.333532	−	0.304278i
$21$	−1.45636			−0.317803
$22$		−	0.872314i		−	0.185978i
$23$		−	3.75094i		−	0.782124i	−0.920364	−	0.391062i	$-0.872108\pi$
$23$		−	3.75094i		−	0.782124i	0.920364	−	0.391062i	$-0.127892\pi$
$24$	−1.61591			−0.329847
$25$	0.457688	−	4.97901i	0.0915377	−	0.995802i
$26$	−0.639786			−0.125472
$27$		−	3.03861i		−	0.584781i
$28$		−	2.47437i		−	0.467613i
$29$	3.97516			0.738168			0.369084	−	0.929396i	$-0.379671\pi$
$29$	3.97516			0.738168			0.369084	+	0.929396i	$0.379671\pi$
$30$	−0.919534	+	0.838884i	−0.167883	+	0.153159i
$31$	−6.92676			−1.24408			−0.622042	−	0.782984i	$-0.713697\pi$
$31$	−6.92676			−1.24408			−0.622042	+	0.782984i	$0.713697\pi$
$32$		−	4.63696i		−	0.819707i
$33$		−	0.442613i		−	0.0770490i
$34$	5.06777			0.869115
$35$	−4.12977	−	4.52681i	−0.698059	−	0.765170i
$36$	2.45381			0.408969
$37$			4.33071i			0.711965i	0.934493	+	0.355982i	$0.115854\pi$
$37$			4.33071i			0.711965i	−0.934493	+	0.355982i	$0.884146\pi$
$38$		0			0
$39$	−0.324628			−0.0519821
$40$	−4.58222	−	5.02276i	−0.724513	−	0.794168i
$41$	5.31691			0.830361			0.415181	−	0.909739i	$-0.363718\pi$
$41$	5.31691			0.830361			0.415181	+	0.909739i	$0.363718\pi$
$42$			1.52539i			0.235373i
$43$			10.4585i			1.59490i	0.603385	+	0.797450i	$0.293818\pi$
$43$			10.4585i			1.59490i	−0.603385	+	0.797450i	$0.706182\pi$
$44$	0.752007			0.113369
$45$	4.48919	−	4.09546i	0.669209	−	0.610514i
$46$	−3.92874			−0.579261
$47$			3.40016i			0.495965i	0.968765	+	0.247982i	$0.0797675\pi$
$47$			3.40016i			0.495965i	−0.968765	+	0.247982i	$0.920232\pi$
$48$			0.732762i			0.105765i
$49$	−0.509407			−0.0727725
$50$	−5.21503	−	0.479384i	−0.737516	−	0.0677951i
$51$	2.57139			0.360066
$52$		−	0.551549i		−	0.0764861i
$53$			13.6679i			1.87743i	0.344692	+	0.938716i	$0.387983\pi$
$53$			13.6679i			1.87743i	−0.344692	+	0.938716i	$0.612017\pi$
$54$	−3.18265			−0.433104
$55$	1.37578	−	1.25511i	0.185510	−	0.169239i
$56$	−8.33212			−1.11343
$57$		0			0
$58$		−	4.16359i		−	0.546706i
$59$	−10.0173			−1.30414			−0.652068	−	0.758160i	$-0.726098\pi$
$59$	−10.0173			−1.30414			−0.652068	+	0.758160i	$0.726098\pi$
$60$	−0.723188	−	0.792715i	−0.0933631	−	0.102339i
$61$	9.07245			1.16161			0.580804	−	0.814043i	$-0.302738\pi$
$61$	9.07245			1.16161			0.580804	+	0.814043i	$0.302738\pi$
$62$			7.25511i			0.921400i
$63$		−	7.44700i		−	0.938234i
$64$	−7.61435			−0.951793
$65$	−0.920544	−	1.00905i	−0.114179	−	0.125157i
$66$	−0.463594			−0.0570645
$67$			10.9346i			1.33587i	0.744220	+	0.667935i	$0.232821\pi$
$67$			10.9346i			1.33587i	−0.744220	+	0.667935i	$0.767179\pi$
$68$			4.36883i			0.529799i
$69$	−1.99345			−0.239983
$70$	−4.74139	+	4.32554i	−0.566705	+	0.517000i
$71$	−0.677726			−0.0804313			−0.0402157	−	0.999191i	$-0.512804\pi$
$71$	−0.677726			−0.0804313			−0.0402157	+	0.999191i	$0.512804\pi$
$72$		−	8.26288i		−	0.973790i
$73$		−	7.01343i		−	0.820859i	−0.911892	−	0.410430i	$-0.865379\pi$
$73$		−	7.01343i		−	0.820859i	0.911892	−	0.410430i	$-0.134621\pi$
$74$	4.53600			0.527299
$75$	−2.64611	−	0.243240i	−0.305546	−	0.0280869i
$76$		0			0
$77$		−	2.28224i		−	0.260086i
$78$			0.340016i			0.0384993i
$79$	−3.47957			−0.391482			−0.195741	−	0.980656i	$-0.562711\pi$
$79$	−3.47957			−0.391482			−0.195741	+	0.980656i	$0.562711\pi$
$80$	−2.27765	+	2.07788i	−0.254649	+	0.232315i
$81$	6.53779			0.726421
$82$		−	5.56894i		−	0.614987i
$83$			4.97485i			0.546060i	0.962005	+	0.273030i	$0.0880259\pi$
$83$			4.97485i			0.546060i	−0.962005	+	0.273030i	$0.911974\pi$
$84$	−1.31501			−0.143480
$85$	7.29166	+	7.99268i	0.790891	+	0.866927i
$86$	10.9542			1.18122
$87$		−	2.11261i		−	0.226495i
$88$		−	2.53228i		−	0.269942i
$89$	5.88868			0.624198			0.312099	−	0.950050i	$-0.398968\pi$
$89$	5.88868			0.624198			0.312099	+	0.950050i	$0.398968\pi$
$90$	−4.28959	−	4.70199i	−0.452163	−	0.495633i
$91$	−1.67388			−0.175470
$92$		−	3.38690i		−	0.353109i
$93$			3.68125i			0.381728i
$94$	3.56134			0.367324
$95$		0			0
$96$	−2.46433			−0.251514
$97$		−	12.4387i		−	1.26296i	−0.775391	−	0.631482i	$-0.782447\pi$
$97$		−	12.4387i		−	1.26296i	0.775391	−	0.631482i	$-0.217553\pi$
$98$			0.533555i			0.0538972i
$99$	2.26328			0.227468
$100$	0.413269	−	4.49578i	0.0413269	−	0.449578i
$101$	−17.7372			−1.76492			−0.882460	−	0.470387i	$-0.844114\pi$
$101$	−17.7372			−1.76492			−0.882460	+	0.470387i	$0.844114\pi$
$102$		−	2.69328i		−	0.266674i
$103$			5.21849i			0.514193i	0.966386	+	0.257097i	$0.0827659\pi$
$103$			5.21849i			0.514193i	−0.966386	+	0.257097i	$0.917234\pi$
$104$	−1.85727			−0.182120
$105$	−2.40579	+	2.19478i	−0.234781	+	0.214189i
$106$	14.3158			1.39047
$107$		−	15.1871i		−	1.46819i	−0.679044	−	0.734097i	$-0.737606\pi$
$107$		−	15.1871i		−	1.46819i	0.679044	−	0.734097i	$-0.262394\pi$
$108$		−	2.74371i		−	0.264014i
$109$	−3.92257			−0.375714			−0.187857	−	0.982196i	$-0.560154\pi$
$109$	−3.92257			−0.375714			−0.187857	+	0.982196i	$0.560154\pi$
$110$	−1.31461	−	1.44099i	−0.125343	−	0.137393i
$111$	2.30157			0.218455
$112$			3.77834i			0.357019i
$113$		−	3.97342i		−	0.373788i	−0.982380	−	0.186894i	$-0.940158\pi$
$113$		−	3.97342i		−	0.373788i	0.982380	−	0.186894i	$-0.0598421\pi$
$114$		0			0
$115$	−5.65279	−	6.19625i	−0.527126	−	0.577803i
$116$	3.58936			0.333264
$117$		−	1.65997i		−	0.153464i
$118$			10.4921i			0.965877i
$119$	13.2588			1.21544
$120$	−2.66936	+	2.43524i	−0.243678	+	0.222306i
$121$	−10.3064			−0.936944
$122$		−	9.50251i		−	0.860317i
$123$		−	2.82569i		−	0.254784i
$124$	−6.25451			−0.561671
$125$	−6.74748	−	8.91468i	−0.603513	−	0.797353i
$126$	−7.80001			−0.694880
$127$			9.18497i			0.815034i	0.913198	+	0.407517i	$0.133605\pi$
$127$			9.18497i			0.815034i	−0.913198	+	0.407517i	$0.866395\pi$
$128$		−	1.29864i		−	0.114785i
$129$	5.55818			0.489371
$130$	−1.05688	+	0.964181i	−0.0926942	+	0.0845642i
$131$	−3.73904			−0.326682			−0.163341	−	0.986570i	$-0.552227\pi$
$131$	−3.73904			−0.326682			−0.163341	+	0.986570i	$0.552227\pi$
$132$		−	0.399656i		−	0.0347856i
$133$		0			0
$134$	11.4529			0.989379
$135$	−4.57930	−	5.01955i	−0.394123	−	0.432014i
$136$	14.7115			1.26150
$137$			2.36335i			0.201914i	0.994891	+	0.100957i	$0.0321905\pi$
$137$			2.36335i			0.201914i	−0.994891	+	0.100957i	$0.967809\pi$
$138$			2.08794i			0.177737i
$139$	−2.44279			−0.207195			−0.103597	−	0.994619i	$-0.533035\pi$
$139$	−2.44279			−0.207195			−0.103597	+	0.994619i	$0.533035\pi$
$140$	−3.72897	−	4.08747i	−0.315156	−	0.345454i
$141$	1.80703			0.152179
$142$			0.709852i			0.0595695i
$143$		−	0.508722i		−	0.0425415i
$144$	−3.74694			−0.312245
$145$	6.56665	−	5.99070i	0.545330	−	0.497501i
$146$	−7.34588			−0.607949
$147$			0.270726i			0.0223291i
$148$			3.91041i			0.321433i
$149$	−14.2687			−1.16894			−0.584468	−	0.811417i	$-0.698697\pi$
$149$	−14.2687			−1.16894			−0.584468	+	0.811417i	$0.698697\pi$
$150$	−0.254770	+	2.77154i	−0.0208019	+	0.226295i
$151$	2.34319			0.190686			0.0953432	−	0.995444i	$-0.469605\pi$
$151$	2.34319			0.190686			0.0953432	+	0.995444i	$0.469605\pi$
$152$		0			0
$153$			13.1487i			1.06301i
$154$	−2.39043			−0.192626
$155$	−11.4425	+	10.4389i	−0.919081	+	0.838471i
$156$	−0.293122			−0.0234686
$157$		−	16.1747i		−	1.29088i	−0.763809	−	0.645442i	$-0.776673\pi$
$157$		−	16.1747i		−	1.29088i	0.763809	−	0.645442i	$-0.223327\pi$
$158$			3.64451i			0.289941i
$159$	7.26385			0.576061
$160$	−6.98807	−	7.65990i	−0.552455	−	0.605568i
$161$	−10.2788			−0.810083
$162$		−	6.84770i		−	0.538006i
$163$			16.0258i			1.25524i	0.778521	+	0.627618i	$0.215970\pi$
$163$			16.0258i			1.25524i	−0.778521	+	0.627618i	$0.784030\pi$
$164$	4.80089			0.374886
$165$	−0.667033	−	0.731162i	−0.0519285	−	0.0569209i
$166$	5.21067			0.404426
$167$			7.57646i			0.586284i	0.956069	+	0.293142i	$0.0947009\pi$
$167$			7.57646i			0.586284i	−0.956069	+	0.293142i	$0.905299\pi$
$168$			4.42813i			0.341638i
$169$	12.6269			0.971299
$170$	8.37155	−	7.63730i	0.642069	−	0.585754i
$171$		0			0
$172$			9.44344i			0.720056i
$173$			8.86205i			0.673769i	0.941546	+	0.336885i	$0.109373\pi$
$173$			8.86205i			0.673769i	−0.941546	+	0.336885i	$0.890627\pi$
$174$	−2.21275			−0.167748
$175$	−13.6441	−	1.25422i	−1.03140	−	0.0948099i
$176$	−1.14830			−0.0865567
$177$			5.32370i			0.400154i
$178$		−	6.16782i		−	0.462297i
$179$	−5.46546			−0.408508			−0.204254	−	0.978918i	$-0.565477\pi$
$179$	−5.46546			−0.408508			−0.204254	+	0.978918i	$0.565477\pi$
$180$	4.05351	−	3.69798i	0.302130	−	0.275631i
$181$	18.8164			1.39861			0.699306	−	0.714822i	$-0.253492\pi$
$181$	18.8164			1.39861			0.699306	+	0.714822i	$0.253492\pi$
$182$			1.75323i			0.129958i
$183$		−	4.82158i		−	0.356422i
$184$	−11.4049			−0.840782
$185$	6.52654	+	7.15399i	0.479840	+	0.525972i
$186$	3.85575			0.282717
$187$			4.02960i			0.294674i
$188$			3.07017i			0.223915i
$189$	−8.32680			−0.605686
$190$		0			0
$191$	−17.2606			−1.24893			−0.624465	−	0.781053i	$-0.714683\pi$
$191$	−17.2606			−1.24893			−0.624465	+	0.781053i	$0.714683\pi$
$192$			4.04667i			0.292043i
$193$		−	7.47422i		−	0.538006i	−0.963139	−	0.269003i	$-0.913306\pi$
$193$		−	7.47422i		−	0.538006i	0.963139	−	0.269003i	$-0.0866942\pi$
$194$	−13.0284			−0.935383
$195$	−0.536260	+	0.489226i	−0.0384024	+	0.0350342i
$196$	−0.459968			−0.0328549
$197$			12.2080i			0.869784i	0.900483	+	0.434892i	$0.143213\pi$
$197$			12.2080i			0.869784i	−0.900483	+	0.434892i	$0.856787\pi$
$198$		−	2.37056i		−	0.168469i
$199$	7.75788			0.549942			0.274971	−	0.961453i	$-0.411332\pi$
$199$	7.75788			0.549942			0.274971	+	0.961453i	$0.411332\pi$
$200$	−15.1389	−	1.39163i	−1.07049	−	0.0984029i
$201$	5.81121			0.409891
$202$			18.5780i			1.30715i
$203$		−	10.8932i		−	0.764556i
$204$	2.32183			0.162561
$205$	8.78311	−	8.01276i	0.613439	−	0.559636i
$206$	5.46586			0.380825
$207$		−	10.1934i		−	0.708489i
$208$			0.842208i			0.0583966i
$209$		0			0
$210$	2.29882	+	2.51983i	0.158634	+	0.173885i
$211$	10.0571			0.692359			0.346179	−	0.938168i	$-0.387479\pi$
$211$	10.0571			0.692359			0.346179	+	0.938168i	$0.387479\pi$
$212$			12.3414i			0.847612i
$213$			0.360180i			0.0246791i
$214$	−15.9070			−1.08738
$215$	15.7613	+	17.2766i	1.07491	+	1.17825i
$216$	−9.23907			−0.628639
$217$			18.9816i			1.28856i
$218$			4.10851i			0.278264i
$219$	−3.72731			−0.251868
$220$	1.24226	−	1.13330i	0.0837529	−	0.0764071i
$221$	2.95545			0.198805
$222$		−	2.41067i		−	0.161794i
$223$		−	28.3213i		−	1.89654i	−0.317470	−	0.948268i	$-0.602833\pi$
$223$		−	28.3213i		−	1.89654i	0.317470	−	0.948268i	$-0.397167\pi$
$224$	−12.7068			−0.849009
$225$	1.24379	−	13.5307i	0.0829196	−	0.902049i
$226$	−4.16177			−0.276837
$227$		−	15.8786i		−	1.05390i	−0.849897	−	0.526949i	$-0.823336\pi$
$227$		−	15.8786i		−	1.05390i	0.849897	−	0.526949i	$-0.176664\pi$
$228$		0			0
$229$	−11.3865			−0.752438			−0.376219	−	0.926531i	$-0.622776\pi$
$229$	−11.3865			−0.752438			−0.376219	+	0.926531i	$0.622776\pi$
$230$	−6.48997	+	5.92075i	−0.427936	+	0.390403i
$231$	−1.21291			−0.0798033
$232$		−	12.0867i		−	0.793530i
$233$			15.8642i			1.03930i	0.854379	+	0.519651i	$0.173938\pi$
$233$			15.8642i			1.03930i	−0.854379	+	0.519651i	$0.826062\pi$
$234$	−1.73866			−0.113660
$235$	5.12417	+	5.61680i	0.334264	+	0.366400i
$236$	−9.04506			−0.588783
$237$			1.84923i			0.120120i
$238$		−	13.8873i		−	0.900183i
$239$	−20.8648			−1.34963			−0.674817	−	0.737985i	$-0.735778\pi$
$239$	−20.8648			−1.34963			−0.674817	+	0.737985i	$0.735778\pi$
$240$	1.10430	+	1.21047i	0.0712822	+	0.0781352i
$241$	28.4290			1.83127			0.915636	−	0.402008i	$-0.131688\pi$
$241$	28.4290			1.83127			0.915636	+	0.402008i	$0.131688\pi$
$242$			10.7949i			0.693925i
$243$		−	12.5904i		−	0.807673i
$244$	8.19195			0.524436
$245$	−0.841501	+	0.767695i	−0.0537615	+	0.0490462i
$246$	−2.95963			−0.188699
$247$		0			0
$248$			21.0612i			1.33739i
$249$	2.64390			0.167550
$250$	−9.33726	+	7.06732i	−0.590540	+	0.446977i
$251$	24.8136			1.56622			0.783109	−	0.621884i	$-0.213632\pi$
$251$	24.8136			1.56622			0.783109	+	0.621884i	$0.213632\pi$
$252$		−	6.72426i		−	0.423588i
$253$		−	3.12391i		−	0.196399i
$254$	9.62036			0.603635
$255$	4.24773	−	3.87517i	0.266003	−	0.242673i
$256$	−16.5889			−1.03681
$257$		−	5.44223i		−	0.339477i	−0.985489	−	0.169739i	$-0.945708\pi$
$257$		−	5.44223i		−	0.339477i	0.985489	−	0.169739i	$-0.0542923\pi$
$258$		−	5.82165i		−	0.362440i
$259$	11.8676			0.737415
$260$	−0.831204	−	0.911115i	−0.0515491	−	0.0565050i
$261$	10.8027			0.668671
$262$			3.91628i			0.241949i
$263$			19.5197i			1.20363i	0.798634	+	0.601817i	$0.205556\pi$
$263$			19.5197i			1.20363i	−0.798634	+	0.601817i	$0.794444\pi$
$264$	−1.34579			−0.0828276
$265$	20.5980	+	22.5783i	1.26533	+	1.38697i
$266$		0			0
$267$		−	3.12956i		−	0.191526i
$268$			9.87334i			0.603110i
$269$	−18.5848			−1.13314			−0.566568	−	0.824015i	$-0.691729\pi$
$269$	−18.5848			−1.13314			−0.566568	+	0.824015i	$0.691729\pi$
$270$	−5.25749	+	4.79637i	−0.319961	+	0.291898i
$271$	1.89214			0.114939			0.0574696	−	0.998347i	$-0.481697\pi$
$271$	1.89214			0.114939			0.0574696	+	0.998347i	$0.481697\pi$
$272$		−	6.67115i		−	0.404498i
$273$			0.889588i			0.0538403i
$274$	2.47538			0.149543
$275$	0.381179	−	4.14669i	0.0229860	−	0.250055i
$276$	−1.79998			−0.108346
$277$		−	6.77887i		−	0.407303i	−0.979043	−	0.203652i	$-0.934719\pi$
$277$		−	6.77887i		−	0.407303i	0.979043	−	0.203652i	$-0.0652810\pi$
$278$			2.55859i			0.153454i
$279$	−18.8239			−1.12696
$280$	−13.7640	+	12.5568i	−0.822557	+	0.750413i
$281$	−12.2861			−0.732927			−0.366464	−	0.930432i	$-0.619432\pi$
$281$	−12.2861			−0.732927			−0.366464	+	0.930432i	$0.619432\pi$
$282$		−	1.89268i		−	0.112708i
$283$		−	25.6667i		−	1.52572i	−0.646561	−	0.762862i	$-0.723793\pi$
$283$		−	25.6667i		−	1.52572i	0.646561	−	0.762862i	$-0.276207\pi$
$284$	−0.611952			−0.0363126
$285$		0			0
$286$	−0.532837			−0.0315073
$287$		−	14.5701i		−	0.860044i
$288$		−	12.6012i		−	0.742534i
$289$	−6.41023			−0.377072
$290$	−6.27468	−	6.87792i	−0.368462	−	0.403885i
$291$	−6.61061			−0.387521
$292$		−	6.33276i		−	0.370597i
$293$			28.1121i			1.64232i	0.570695	+	0.821162i	$0.306674\pi$
$293$			28.1121i			1.64232i	−0.570695	+	0.821162i	$0.693326\pi$
$294$	0.283559			0.0165375
$295$	−16.5477	+	15.0964i	−0.963446	+	0.878944i
$296$	13.1678			0.765361
$297$		−	2.53067i		−	0.146844i
$298$			14.9451i			0.865744i
$299$	−2.29119			−0.132503
$300$	−2.38930	−	0.219633i	−0.137946	−	0.0126805i
$301$	28.6596			1.65191
$302$		−	2.45427i		−	0.141227i
$303$			9.42651i			0.541539i
$304$		0			0
$305$	14.9870	−	13.6725i	0.858152	−	0.782886i
$306$	13.7719			0.787290
$307$		−	2.57676i		−	0.147064i	−0.997293	−	0.0735319i	$-0.976573\pi$
$307$		−	2.57676i		−	0.147064i	0.997293	−	0.0735319i	$-0.0234271\pi$
$308$		−	2.06075i		−	0.117422i
$309$	2.77338			0.157772
$310$	10.9337	+	11.9849i	0.620993	+	0.680695i
$311$	14.6367			0.829974			0.414987	−	0.909827i	$-0.363786\pi$
$311$	14.6367			0.829974			0.414987	+	0.909827i	$0.363786\pi$
$312$			0.987050i			0.0558807i
$313$		−	1.49408i		−	0.0844507i	−0.999108	−	0.0422253i	$-0.986555\pi$
$313$		−	1.49408i		−	0.0844507i	0.999108	−	0.0422253i	$-0.0134447\pi$
$314$	−16.9415			−0.956062
$315$	−11.2229	−	12.3019i	−0.632339	−	0.693132i
$316$	−3.14187			−0.176744
$317$			5.64234i			0.316905i	0.987367	+	0.158453i	$0.0506505\pi$
$317$			5.64234i			0.316905i	−0.987367	+	0.158453i	$0.949349\pi$
$318$		−	7.60818i		−	0.426646i
$319$	3.31065			0.185361
$320$	−12.5783	+	11.4751i	−0.703148	+	0.641477i
$321$	−8.07124			−0.450493
$322$			10.7660i			0.599968i
$323$		0			0
$324$	5.90329			0.327960
$325$	−3.04133	−	0.279570i	−0.168703	−	0.0155078i
$326$	16.7854			0.929660
$327$			2.08466i			0.115282i
$328$		−	16.1663i		−	0.892637i
$329$	9.31757			0.513694
$330$	−0.765821	+	0.698653i	−0.0421570	+	0.0384596i
$331$	31.8920			1.75294			0.876472	−	0.481452i	$-0.159890\pi$
$331$	31.8920			1.75294			0.876472	+	0.481452i	$0.159890\pi$
$332$			4.49203i			0.246532i
$333$			11.7690i			0.644935i
$334$	7.93561			0.434217
$335$	16.4788	+	18.0630i	0.900331	+	0.986889i
$336$	2.00801			0.109546
$337$			15.3378i			0.835504i	0.908561	+	0.417752i	$0.137182\pi$
$337$			15.3378i			0.835504i	−0.908561	+	0.417752i	$0.862818\pi$
$338$		−	13.2254i		−	0.719369i
$339$	−2.11169			−0.114691
$340$	6.58399	+	7.21697i	0.357067	+	0.391395i
$341$	−5.76886			−0.312401
$342$		0			0
$343$		−	17.7864i		−	0.960373i
$344$	31.7995			1.71452
$345$	−3.29302	+	3.00419i	−0.177290	+	0.161740i
$346$	9.28214			0.499011
$347$		−	0.0826977i		−	0.00443945i	−0.999998	−	0.00221972i	$-0.999293\pi$
$347$		−	0.0826977i		−	0.00443945i	0.999998	−	0.00221972i	$-0.000706560\pi$
$348$		−	1.90758i		−	0.102257i
$349$	4.64333			0.248552			0.124276	−	0.992248i	$-0.460339\pi$
$349$	4.64333			0.248552			0.124276	+	0.992248i	$0.460339\pi$
$350$	−1.31367	+	14.2909i	−0.0702186	+	0.763880i
$351$	−1.85608			−0.0990702
$352$		−	3.86183i		−	0.205836i
$353$		−	3.99402i		−	0.212580i	−0.994335	−	0.106290i	$-0.966103\pi$
$353$		−	3.99402i		−	0.212580i	0.994335	−	0.106290i	$-0.0338972\pi$
$354$	5.57606			0.296364
$355$	−1.11955	+	1.02136i	−0.0594196	+	0.0542080i
$356$	5.31717			0.281809
$357$		−	7.04645i		−	0.372938i
$358$			5.72454i			0.302551i
$359$	−30.2198			−1.59494			−0.797471	−	0.603358i	$-0.793829\pi$
$359$	−30.2198			−1.59494			−0.797471	+	0.603358i	$0.793829\pi$
$360$	−12.4525	−	13.6496i	−0.656302	−	0.719399i
$361$		0			0
$362$		−	19.7084i		−	1.03585i
$363$			5.47736i			0.287487i
$364$	−1.51143			−0.0792202
$365$	−10.5695	−	11.5856i	−0.553232	−	0.606420i
$366$	−5.05014			−0.263975
$367$			18.1399i			0.946896i	0.880822	+	0.473448i	$0.156991\pi$
$367$			18.1399i			0.946896i	−0.880822	+	0.473448i	$0.843009\pi$
$368$			5.17175i			0.269596i
$369$	14.4490			0.752185
$370$	7.49311	−	6.83591i	0.389548	−	0.355382i
$371$	37.4546			1.94455
$372$			3.32398i			0.172340i
$373$			25.2151i			1.30559i	0.757536	+	0.652794i	$0.226403\pi$
$373$			25.2151i			1.30559i	−0.757536	+	0.652794i	$0.773597\pi$
$374$	4.22061			0.218243
$375$	−4.73774	+	3.58597i	−0.244656	+	0.185179i
$376$	10.3384			0.533161
$377$		−	2.42815i		−	0.125056i
$378$			8.72152i			0.448586i
$379$	27.5634			1.41584			0.707918	−	0.706294i	$-0.249634\pi$
$379$	27.5634			1.41584			0.707918	+	0.706294i	$0.249634\pi$
$380$		0			0
$381$	4.88138			0.250081
$382$			18.0788i			0.924990i
$383$		−	18.3237i		−	0.936296i	−0.883650	−	0.468148i	$-0.844921\pi$
$383$		−	18.3237i		−	0.936296i	0.883650	−	0.468148i	$-0.155079\pi$
$384$	−0.690166			−0.0352199
$385$	−3.43942	−	3.77009i	−0.175289	−	0.192141i
$386$	−7.82852			−0.398461
$387$			28.4215i			1.44474i
$388$		−	11.2315i		−	0.570195i
$389$	7.18503			0.364296			0.182148	−	0.983271i	$-0.441695\pi$
$389$	7.18503			0.364296			0.182148	+	0.983271i	$0.441695\pi$
$390$	0.512417	+	0.561680i	0.0259472	+	0.0284418i
$391$	18.1486			0.917813
$392$			1.54888i			0.0782303i
$393$			1.98713i			0.100237i
$394$	12.7867			0.644184
$395$	−5.74797	+	5.24383i	−0.289212	+	0.263846i
$396$	2.04362			0.102696
$397$		−	11.7242i		−	0.588423i	−0.955740	−	0.294211i	$-0.904943\pi$
$397$		−	11.7242i		−	0.588423i	0.955740	−	0.294211i	$-0.0950570\pi$
$398$		−	8.12562i		−	0.407301i
$399$		0			0
$400$	−0.631056	+	6.86500i	−0.0315528	+	0.343250i
$401$	39.2123			1.95817			0.979085	−	0.203451i	$-0.0652157\pi$
$401$	39.2123			1.95817			0.979085	+	0.203451i	$0.0652157\pi$
$402$		−	6.08667i		−	0.303576i
$403$			4.23108i			0.210765i
$404$	−16.0158			−0.796816
$405$	10.7999	−	9.85268i	0.536652	−	0.489584i
$406$	−11.4096			−0.566249
$407$			3.60677i			0.178781i
$408$		−	7.81845i		−	0.387071i
$409$	−8.87630			−0.438905			−0.219452	−	0.975623i	$-0.570427\pi$
$409$	−8.87630			−0.438905			−0.219452	+	0.975623i	$0.570427\pi$
$410$	−8.39259	−	9.19945i	−0.414481	−	0.454329i
$411$	1.25601			0.0619543
$412$			4.71203i			0.232145i
$413$			27.4506i			1.35076i
$414$	−10.6766			−0.524725
$415$	7.49727	+	8.21806i	0.368027	+	0.403409i
$416$	−2.83240			−0.138870
$417$			1.29823i			0.0635745i
$418$		0			0
$419$	7.80196			0.381151			0.190575	−	0.981673i	$-0.438965\pi$
$419$	7.80196			0.381151			0.190575	+	0.981673i	$0.438965\pi$
$420$	−2.17230	+	1.98177i	−0.105997	+	0.0967006i
$421$	34.5570			1.68421			0.842104	−	0.539316i	$-0.181317\pi$
$421$	34.5570			1.68421			0.842104	+	0.539316i	$0.181317\pi$
$422$		−	10.5338i		−	0.512779i
$423$			9.24014i			0.449271i
$424$	41.5580			2.01824
$425$	24.0905	+	2.21448i	1.16856	+	0.107418i
$426$	0.377253			0.0182780
$427$		−	24.8615i		−	1.20313i
$428$		−	13.7132i		−	0.662851i
$429$	−0.270362			−0.0130532
$430$	18.0955	−	16.5084i	0.872643	−	0.796105i
$431$	2.83951			0.136775			0.0683873	−	0.997659i	$-0.478215\pi$
$431$	2.83951			0.136775			0.0683873	+	0.997659i	$0.478215\pi$
$432$			4.18961i			0.201573i
$433$			21.8527i			1.05018i	0.851048	+	0.525088i	$0.175967\pi$
$433$			21.8527i			1.05018i	−0.851048	+	0.525088i	$0.824033\pi$
$434$	19.8814			0.954338
$435$	−3.18378	−	3.48986i	−0.152650	−	0.167326i
$436$	−3.54188			−0.169625
$437$		0			0
$438$			3.90399i			0.186540i
$439$	−32.5760			−1.55477			−0.777383	−	0.629027i	$-0.783453\pi$
$439$	−32.5760			−1.55477			−0.777383	+	0.629027i	$0.783453\pi$
$440$	−3.81624	−	4.18313i	−0.181932	−	0.199423i
$441$	−1.38434			−0.0659212
$442$		−	3.09555i		−	0.147240i
$443$		−	7.76173i		−	0.368771i	−0.982854	−	0.184385i	$-0.940971\pi$
$443$		−	7.76173i		−	0.368771i	0.982854	−	0.184385i	$-0.0590295\pi$
$444$	2.07820			0.0986269
$445$	9.72763	−	8.87444i	0.461134	−	0.420689i
$446$	−29.6638			−1.40462
$447$			7.58313i			0.358670i
$448$			20.8658i			0.985817i
$449$	−22.9821			−1.08459			−0.542296	−	0.840187i	$-0.682445\pi$
$449$	−22.9821			−1.08459			−0.542296	+	0.840187i	$0.682445\pi$
$450$	−14.1721	−	1.30275i	−0.668081	−	0.0614124i
$451$	4.42811			0.208511
$452$		−	3.58779i		−	0.168756i
$453$		−	1.24530i		−	0.0585092i
$454$	−16.6312			−0.780543
$455$	−2.76512	+	2.52260i	−0.129631	+	0.118261i
$456$		0			0
$457$			3.38866i			0.158515i	0.996854	+	0.0792573i	$0.0252549\pi$
$457$			3.38866i			0.158515i	−0.996854	+	0.0792573i	$0.974745\pi$
$458$			11.9262i			0.557275i
$459$	14.7021			0.686234
$460$	−5.10418	−	5.59489i	−0.237983	−	0.260863i
$461$	−10.8529			−0.505471			−0.252735	−	0.967535i	$-0.581330\pi$
$461$	−10.8529			−0.505471			−0.252735	+	0.967535i	$0.581330\pi$
$462$			1.27040i			0.0591044i
$463$		−	7.31171i		−	0.339804i	−0.985461	−	0.169902i	$-0.945655\pi$
$463$		−	7.31171i		−	0.339804i	0.985461	−	0.169902i	$-0.0543451\pi$
$464$	−5.48090			−0.254445
$465$	5.54777	+	6.08114i	0.257272	+	0.282006i
$466$	16.6163			0.769733
$467$		−	10.8418i		−	0.501699i	−0.968026	−	0.250850i	$-0.919290\pi$
$467$		−	10.8418i		−	0.501699i	0.968026	−	0.250850i	$-0.0807100\pi$
$468$		−	1.49887i		−	0.0692851i
$469$	29.9643			1.38362
$470$	5.88305	−	5.36706i	0.271365	−	0.247564i
$471$	−8.59612			−0.396088
$472$			30.4580i			1.40194i
$473$			8.71018i			0.400494i
$474$	1.93688			0.0889640
$475$		0			0
$476$	11.9720			0.548738
$477$			37.1433i			1.70068i
$478$			21.8539i			0.999574i
$479$	−3.44738			−0.157515			−0.0787574	−	0.996894i	$-0.525095\pi$
$479$	−3.44738			−0.157515			−0.0787574	+	0.996894i	$0.525095\pi$
$480$	−4.07088	+	3.71383i	−0.185809	+	0.169512i
$481$	2.64533			0.120617
$482$		−	29.7766i		−	1.35629i
$483$			5.46270i			0.248561i
$484$	−9.30613			−0.423006
$485$	−18.7456	−	20.5478i	−0.851195	−	0.933029i
$486$	−13.1872			−0.598183
$487$			26.9972i			1.22336i	0.791106	+	0.611680i	$0.209506\pi$
$487$			26.9972i			1.22336i	−0.791106	+	0.611680i	$0.790494\pi$
$488$		−	27.5853i		−	1.24873i
$489$	8.51695			0.385150
$490$	0.804086	+	0.881390i	0.0363249	+	0.0398172i
$491$	0.243979			0.0110106			0.00550530	−	0.999985i	$-0.498248\pi$
$491$	0.243979			0.0110106			0.00550530	+	0.999985i	$0.498248\pi$
$492$		−	2.55145i		−	0.115028i
$493$			19.2334i			0.866231i
$494$		0			0
$495$	3.73876	−	3.41084i	0.168045	−	0.153306i
$496$	9.55055			0.428832
$497$			1.85719i			0.0833065i
$498$		−	2.76923i		−	0.124092i
$499$	3.24868			0.145431			0.0727155	−	0.997353i	$-0.476833\pi$
$499$	3.24868			0.145431			0.0727155	+	0.997353i	$0.476833\pi$
$500$	−6.09262	−	8.04949i	−0.272470	−	0.359984i
$501$	4.02653			0.179892
$502$		−	25.9898i		−	1.15998i
$503$		−	7.12545i		−	0.317708i	−0.987302	−	0.158854i	$-0.949220\pi$
$503$		−	7.12545i		−	0.317708i	0.987302	−	0.158854i	$-0.0507799\pi$
$504$	−22.6430			−1.00860
$505$	−29.3005	+	26.7306i	−1.30386	+	1.18950i
$506$	−3.27199			−0.145458
$507$		−	6.71060i		−	0.298028i
$508$			8.29355i			0.367967i
$509$	−1.73022			−0.0766907			−0.0383453	−	0.999265i	$-0.512209\pi$
$509$	−1.73022			−0.0766907			−0.0383453	+	0.999265i	$0.512209\pi$
$510$	−4.05887	−	4.44909i	−0.179730	−	0.197009i
$511$	−19.2191			−0.850203
$512$			14.7780i			0.653100i
$513$		0			0
$514$	−5.70021			−0.251426
$515$	7.86445	+	8.62054i	0.346549	+	0.379866i
$516$	5.01875			0.220938
$517$			2.83178i			0.124541i
$518$		−	12.4301i		−	0.546149i
$519$	4.70977			0.206736
$520$	−3.06806	+	2.79897i	−0.134543	+	0.122743i
$521$	12.8033			0.560922			0.280461	−	0.959865i	$-0.409513\pi$
$521$	12.8033			0.560922			0.280461	+	0.959865i	$0.409513\pi$
$522$		−	11.3148i		−	0.495235i
$523$		−	8.71641i		−	0.381142i	−0.981673	−	0.190571i	$-0.938966\pi$
$523$		−	8.71641i		−	0.381142i	0.981673	−	0.190571i	$-0.0610340\pi$
$524$	−3.37616			−0.147488
$525$	−0.666558	+	7.25121i	−0.0290910	+	0.316469i
$526$	20.4449			0.891441
$527$		−	33.5145i		−	1.45992i
$528$			0.610270i			0.0265586i
$529$	8.93048			0.388282
$530$	23.6486	−	21.5744i	1.02723	−	0.937133i
$531$	−27.2225			−1.18136
$532$		0			0
$533$		−	3.24773i		−	0.140675i
$534$	−3.27790			−0.141849
$535$	−22.8875	−	25.0879i	−0.989514	−	1.08465i
$536$	33.2471			1.43606
$537$			2.90463i			0.125344i
$538$			19.4658i			0.839230i
$539$	−0.424253			−0.0182739
$540$	−4.13487	−	4.53239i	−0.177936	−	0.195043i
$541$	11.0154			0.473588			0.236794	−	0.971560i	$-0.423903\pi$
$541$	11.0154			0.473588			0.236794	+	0.971560i	$0.423903\pi$
$542$		−	1.98183i		−	0.0851268i
$543$		−	10.0000i		−	0.429143i
$544$	22.4355			0.961916
$545$	−6.47978	+	5.91146i	−0.277563	+	0.253219i
$546$	0.931757			0.0398755
$547$		−	18.3959i		−	0.786551i	−0.919421	−	0.393275i	$-0.871342\pi$
$547$		−	18.3959i		−	0.786551i	0.919421	−	0.393275i	$-0.128658\pi$
$548$			2.13398i			0.0911591i
$549$	24.6549			1.05225
$550$	−4.34326	−	0.399248i	−0.185197	−	0.0170240i
$551$		0			0
$552$			6.06118i			0.257981i
$553$			9.53516i			0.405476i
$554$	−7.10021			−0.301659
$555$	3.80201	−	3.46855i	0.161386	−	0.147232i
$556$	−2.20571			−0.0935431
$557$			0.202098i			0.00856316i	0.999991	+	0.00428158i	$0.00136287\pi$
$557$			0.202098i			0.00856316i	−0.999991	+	0.00428158i	$0.998637\pi$
$558$			19.7162i			0.834653i
$559$	6.38835			0.270199
$560$	5.69409	+	6.24152i	0.240619	+	0.263752i
$561$	2.14154			0.0904161
$562$			12.8685i			0.542824i
$563$			6.76375i			0.285058i	0.989791	+	0.142529i	$0.0455234\pi$
$563$			6.76375i			0.285058i	−0.989791	+	0.142529i	$0.954477\pi$
$564$	1.63165			0.0687049
$565$	−5.98809	−	6.56378i	−0.251921	−	0.276140i
$566$	−26.8833			−1.12999
$567$		−	17.9157i		−	0.752389i
$568$			2.06066i			0.0864636i
$569$	−7.15701			−0.300038			−0.150019	−	0.988683i	$-0.547933\pi$
$569$	−7.15701			−0.300038			−0.150019	+	0.988683i	$0.547933\pi$
$570$		0			0
$571$	−18.3153			−0.766471			−0.383236	−	0.923651i	$-0.625190\pi$
$571$	−18.3153			−0.766471			−0.383236	+	0.923651i	$0.625190\pi$
$572$		−	0.459349i		−	0.0192064i
$573$			9.17318i			0.383215i
$574$	−15.2607			−0.636971
$575$	−18.6759	−	1.71676i	−0.778841	−	0.0715938i
$576$	−20.6924			−0.862184
$577$		−	21.5794i		−	0.898364i	−0.893440	−	0.449182i	$-0.851716\pi$
$577$		−	21.5794i		−	0.898364i	0.893440	−	0.449182i	$-0.148284\pi$
$578$			6.71409i			0.279269i
$579$	−3.97220			−0.165079
$580$	5.92934	−	5.40929i	0.246202	−	0.224609i
$581$	13.6327			0.565581
$582$			6.92397i			0.287008i
$583$			11.3831i			0.471441i
$584$	−21.3247			−0.882423
$585$	−2.50163	−	2.74214i	−0.103430	−	0.113373i
$586$	29.4446			1.21635
$587$			28.9431i			1.19461i	0.802014	+	0.597305i	$0.203762\pi$
$587$			28.9431i			1.19461i	−0.802014	+	0.597305i	$0.796238\pi$
$588$			0.244452i			0.0100810i
$589$		0			0
$590$	15.8120	+	17.3321i	0.650969	+	0.713553i
$591$	6.48798			0.266880
$592$		−	5.97114i		−	0.245412i
$593$		−	17.8231i		−	0.731907i	−0.930633	−	0.365954i	$-0.880743\pi$
$593$		−	17.8231i		−	0.731907i	0.930633	−	0.365954i	$-0.119257\pi$
$594$	−2.65063			−0.108756
$595$	21.9026	−	19.9815i	0.897918	−	0.819164i
$596$	−12.8839			−0.527744
$597$		−	4.12295i		−	0.168741i
$598$			2.39980i			0.0981350i
$599$	8.55080			0.349376			0.174688	−	0.984624i	$-0.444108\pi$
$599$	8.55080			0.349376			0.174688	+	0.984624i	$0.444108\pi$
$600$	−0.739584	+	8.04564i	−0.0301934	+	0.328462i
$601$	−4.19029			−0.170925			−0.0854627	−	0.996341i	$-0.527237\pi$
$601$	−4.19029			−0.170925			−0.0854627	+	0.996341i	$0.527237\pi$
$602$		−	30.0182i		−	1.22345i
$603$			29.7153i			1.21010i
$604$	2.11578			0.0860899
$605$	−17.0253	+	15.5321i	−0.692178	+	0.631469i
$606$	9.87335			0.401077
$607$			7.59458i			0.308254i	0.988051	+	0.154127i	$0.0492566\pi$
$607$			7.59458i			0.308254i	−0.988051	+	0.154127i	$0.950743\pi$
$608$		0			0
$609$	−5.78925			−0.234592
$610$	−14.3206	−	15.6974i	−0.579825	−	0.635569i
$611$	2.07693			0.0840234
$612$			11.8726i			0.479920i
$613$		−	17.9449i		−	0.724788i	−0.932025	−	0.362394i	$-0.881959\pi$
$613$		−	17.9449i		−	0.724788i	0.932025	−	0.362394i	$-0.118041\pi$
$614$	−2.69891			−0.108919
$615$	−4.25841	−	4.66781i	−0.171716	−	0.188224i
$616$	−6.93929			−0.279592
$617$			40.5840i			1.63385i	0.576745	+	0.816924i	$0.304323\pi$
$617$			40.5840i			1.63385i	−0.576745	+	0.816924i	$0.695677\pi$
$618$		−	2.90485i		−	0.116850i
$619$	25.5608			1.02738			0.513688	−	0.857977i	$-0.328279\pi$
$619$	25.5608			1.02738			0.513688	+	0.857977i	$0.328279\pi$
$620$	−10.3320	+	9.42576i	−0.414941	+	0.378548i
$621$	−11.3976			−0.457372
$622$		−	15.3306i		−	0.614700i
$623$		−	16.1369i		−	0.646512i
$624$	0.447594			0.0179181
$625$	−24.5810	−	4.55767i	−0.983242	−	0.182307i
$626$	−1.56491			−0.0625463
$627$		0			0
$628$		−	14.6049i		−	0.582801i
$629$	−20.9538			−0.835481
$630$	−12.8850	+	11.7549i	−0.513351	+	0.468326i
$631$	4.63486			0.184511			0.0922555	−	0.995735i	$-0.470592\pi$
$631$	4.63486			0.184511			0.0922555	+	0.995735i	$0.470592\pi$
$632$			10.5798i			0.420842i
$633$		−	5.34487i		−	0.212440i
$634$	5.90980			0.234708
$635$	13.8421	+	15.1728i	0.549306	+	0.602116i
$636$	6.55888			0.260077
$637$			0.311162i			0.0123287i
$638$		−	3.46758i		−	0.137283i
$639$	−1.84176			−0.0728589
$640$	−1.95710	−	2.14525i	−0.0773610	−	0.0847985i
$641$	23.2079			0.916658			0.458329	−	0.888783i	$-0.348448\pi$
$641$	23.2079			0.916658			0.458329	+	0.888783i	$0.348448\pi$
$642$			8.45384i			0.333646i
$643$		−	15.2454i		−	0.601219i	−0.953747	−	0.300610i	$-0.902810\pi$
$643$		−	15.2454i		−	0.601219i	0.953747	−	0.300610i	$-0.0971902\pi$
$644$	−9.28122			−0.365731
$645$	9.18168	−	8.37638i	0.361528	−	0.329819i
$646$		0			0
$647$			17.6749i			0.694872i	0.937704	+	0.347436i	$0.112948\pi$
$647$			17.6749i			0.694872i	−0.937704	+	0.347436i	$0.887052\pi$
$648$		−	19.8785i		−	0.780902i
$649$	−8.34273			−0.327481
$650$	−0.292823	+	3.18550i	−0.0114855	+	0.124946i
$651$	10.0878			0.395374
$652$			14.4704i			0.566706i
$653$			6.86456i			0.268631i	0.990939	+	0.134315i	$0.0428835\pi$
$653$			6.86456i			0.268631i	−0.990939	+	0.134315i	$0.957116\pi$
$654$	2.18348			0.0853809
$655$	−6.17661	+	5.63487i	−0.241340	+	0.220173i
$656$	−7.33089			−0.286223
$657$		−	19.0594i		−	0.743578i
$658$		−	9.75924i		−	0.380455i
$659$	−27.3966			−1.06722			−0.533611	−	0.845730i	$-0.679165\pi$
$659$	−27.3966			−1.06722			−0.533611	+	0.845730i	$0.679165\pi$
$660$	−0.602296	−	0.660201i	−0.0234444	−	0.0256983i
$661$	28.5502			1.11048			0.555238	−	0.831692i	$-0.312627\pi$
$661$	28.5502			1.11048			0.555238	+	0.831692i	$0.312627\pi$
$662$		−	33.4038i		−	1.29828i
$663$		−	1.57068i		−	0.0610003i
$664$	15.1263			0.587014
$665$		0			0
$666$	12.3268			0.477655
$667$		−	14.9106i		−	0.577339i
$668$			6.84115i			0.264692i
$669$	−15.0515			−0.581923
$670$	18.9193	−	17.2599i	0.730915	−	0.666808i
$671$	7.55586			0.291691
$672$			6.75307i			0.260505i
$673$		−	45.1688i		−	1.74113i	−0.492054	−	0.870565i	$-0.663754\pi$
$673$		−	45.1688i		−	1.74113i	0.492054	−	0.870565i	$-0.336246\pi$
$674$	16.0649			0.618796
$675$	−15.1293	−	1.39074i	−0.582326	−	0.0535295i
$676$	11.4014			0.438516
$677$		−	46.9628i		−	1.80493i	−0.430767	−	0.902463i	$-0.641757\pi$
$677$		−	46.9628i		−	1.80493i	0.430767	−	0.902463i	$-0.358243\pi$
$678$			2.21179i			0.0849432i
$679$	−34.0863			−1.30811
$680$	24.3022	−	22.1707i	0.931946	−	0.850207i
$681$	−8.43871			−0.323372
$682$			6.04231i			0.231372i
$683$		−	19.4215i		−	0.743142i	−0.928405	−	0.371571i	$-0.878819\pi$
$683$		−	19.4215i		−	0.743142i	0.928405	−	0.371571i	$-0.121181\pi$
$684$		0			0
$685$	3.56165	+	3.90406i	0.136084	+	0.149167i
$686$	−18.6295			−0.711277
$687$			6.05137i			0.230874i
$688$		−	14.4200i		−	0.549758i
$689$	8.34879			0.318063
$690$	3.14660	+	3.44911i	0.119789	+	0.131306i
$691$	−17.8669			−0.679688			−0.339844	−	0.940482i	$-0.610374\pi$
$691$	−17.8669			−0.679688			−0.339844	+	0.940482i	$0.610374\pi$
$692$			8.00197i			0.304189i
$693$		−	6.20213i		−	0.235599i
$694$	−0.0866178			−0.00328797
$695$	−4.03530	+	3.68137i	−0.153068	+	0.139642i
$696$	−6.42350			−0.243482
$697$			25.7254i			0.974418i
$698$		−	4.86343i		−	0.184084i
$699$	8.43110			0.318894
$700$	−12.3199	−	1.13249i	−0.465650	−	0.0428042i
$701$	4.30484			0.162591			0.0812957	−	0.996690i	$-0.474094\pi$
$701$	4.30484			0.162591			0.0812957	+	0.996690i	$0.474094\pi$
$702$			1.94406i			0.0733739i
$703$		0			0
$704$	−6.34150			−0.239004
$705$	2.98507	−	2.72325i	0.112424	−	0.102564i
$706$	−4.18335			−0.157442
$707$			48.6059i			1.82801i
$708$			4.80703i			0.180659i
$709$	−35.1319			−1.31941			−0.659703	−	0.751526i	$-0.729318\pi$
$709$	−35.1319			−1.31941			−0.659703	+	0.751526i	$0.729318\pi$
$710$	1.06977	+	1.17262i	0.0401479	+	0.0440077i
$711$	−9.45592			−0.354625
$712$		−	17.9048i		−	0.671012i
$713$			25.9818i			0.973028i
$714$	−7.38047			−0.276207
$715$	−0.766662	−	0.840369i	−0.0286715	−	0.0314280i
$716$	−4.93502			−0.184431
$717$			11.0887i			0.414114i
$718$			31.6523i			1.18125i
$719$	−29.4030			−1.09655			−0.548273	−	0.836299i	$-0.684715\pi$
$719$	−29.4030			−1.09655			−0.548273	+	0.836299i	$0.684715\pi$
$720$	−6.18965	+	5.64677i	−0.230675	+	0.210443i
$721$	14.3004			0.532574
$722$		0			0
$723$		−	15.1087i		−	0.561898i
$724$	16.9902			0.631437
$725$	1.81938	−	19.7923i	0.0675702	−	0.735069i
$726$	5.73700			0.212920
$727$			22.5569i			0.836589i	0.908312	+	0.418294i	$0.137372\pi$
$727$			22.5569i			0.836589i	−0.908312	+	0.418294i	$0.862628\pi$
$728$			5.08952i			0.188630i
$729$	12.9222			0.478599
$730$	−12.1348	+	11.0705i	−0.449130	+	0.409738i
$731$	−50.6023			−1.87159
$732$		−	4.35364i		−	0.160915i
$733$		−	37.9002i		−	1.39988i	−0.714204	−	0.699938i	$-0.753211\pi$
$733$		−	37.9002i		−	1.39988i	0.714204	−	0.699938i	$-0.246789\pi$
$734$	18.9998			0.701295
$735$	0.407994	+	0.447218i	0.0150491	+	0.0164959i
$736$	−17.3929			−0.641113
$737$			9.10669i			0.335449i
$738$		−	15.1339i		−	0.557087i
$739$	26.0215			0.957218			0.478609	−	0.878028i	$-0.341141\pi$
$739$	26.0215			0.957218			0.478609	+	0.878028i	$0.341141\pi$
$740$	5.89312	+	6.45968i	0.216635	+	0.237463i
$741$		0			0
$742$		−	39.2300i		−	1.44018i
$743$		−	50.3874i		−	1.84854i	−0.381744	−	0.924268i	$-0.624677\pi$
$743$		−	50.3874i		−	1.84854i	0.381744	−	0.924268i	$-0.375323\pi$
$744$	11.1930			0.410357
$745$	−23.5707	+	21.5034i	−0.863565	+	0.787824i
$746$	26.4103			0.966951
$747$			13.5194i			0.494650i
$748$			3.63852i			0.133037i
$749$	−41.6177			−1.52068
$750$	3.75595	+	4.96232i	0.137148	+	0.181198i
$751$	27.1857			0.992021			0.496011	−	0.868316i	$-0.334798\pi$
$751$	27.1857			0.992021			0.496011	+	0.868316i	$0.334798\pi$
$752$		−	4.68811i		−	0.170958i
$753$		−	13.1873i		−	0.480570i
$754$	−2.54325			−0.0926197
$755$	3.87077	−	3.53128i	0.140872	−	0.128516i
$756$	−7.51867			−0.273451
$757$			32.8983i			1.19571i	0.801605	+	0.597855i	$0.203980\pi$
$757$			32.8983i			1.19571i	−0.801605	+	0.597855i	$0.796020\pi$
$758$		−	28.8700i		−	1.04860i
$759$	−1.66021			−0.0602619
$760$		0			0
$761$	3.47213			0.125865			0.0629323	−	0.998018i	$-0.479955\pi$
$761$	3.47213			0.125865			0.0629323	+	0.998018i	$0.479955\pi$
$762$		−	5.11277i		−	0.185216i
$763$			10.7491i			0.389145i
$764$	−15.5854			−0.563859
$765$	19.8155	+	21.7206i	0.716431	+	0.785308i
$766$	−19.1923			−0.693445
$767$			6.11886i			0.220939i
$768$			8.81622i			0.318128i
$769$	31.6735			1.14218			0.571089	−	0.820888i	$-0.306521\pi$
$769$	31.6735			1.14218			0.571089	+	0.820888i	$0.306521\pi$
$770$	−3.94880	+	3.60246i	−0.142305	+	0.129824i
$771$	−2.89229			−0.104163
$772$		−	6.74883i		−	0.242896i
$773$			35.0686i			1.26133i	0.776056	+	0.630665i	$0.217218\pi$
$773$			35.0686i			1.26133i	−0.776056	+	0.630665i	$0.782782\pi$
$774$	29.7687			1.07001
$775$	−3.17030	+	34.4884i	−0.113881	+	1.23886i
$776$	−37.8207			−1.35768
$777$		−	6.30706i		−	0.226265i
$778$		−	7.52562i		−	0.269807i
$779$		0			0
$780$	−0.484215	+	0.441746i	−0.0173377	+	0.0158170i
$781$	−0.564435			−0.0201971
$782$		−	19.0089i		−	0.679755i
$783$		−	12.0790i		−	0.431667i
$784$	0.702366			0.0250845
$785$	−24.3759	−	26.7194i	−0.870014	−	0.953656i
$786$	2.08132			0.0742383
$787$			42.1829i			1.50366i	0.659358	+	0.751829i	$0.270828\pi$
$787$			42.1829i			1.50366i	−0.659358	+	0.751829i	$0.729172\pi$
$788$			11.0232i			0.392685i
$789$	10.3738			0.369316
$790$	5.49240	+	6.02044i	0.195411	+	0.214198i
$791$	−10.8885			−0.387150
$792$		−	6.88162i		−	0.244528i
$793$		−	5.54174i		−	0.196793i
$794$	−12.2800			−0.435801
$795$	11.9993	−	10.9469i	0.425572	−	0.388246i
$796$	7.00496			0.248284
$797$		−	20.4194i		−	0.723291i	−0.932316	−	0.361646i	$-0.882215\pi$
$797$		−	20.4194i		−	0.723291i	0.932316	−	0.361646i	$-0.117785\pi$
$798$		0			0
$799$	−16.4514			−0.582008
$800$	−23.0875	−	2.12228i	−0.816265	−	0.0750341i
$801$	16.0028			0.565432
$802$		−	41.0711i		−	1.45027i
$803$		−	5.84103i		−	0.206125i
$804$	5.24722			0.185055
$805$	−16.9798	+	15.4905i	−0.598458	+	0.545969i
$806$	4.43165			0.156098
$807$			9.87696i			0.347685i
$808$			53.9310i			1.89729i
$809$	−28.5536			−1.00389			−0.501946	−	0.864899i	$-0.667382\pi$
$809$	−28.5536			−1.00389			−0.501946	+	0.864899i	$0.667382\pi$
$810$	−10.3197	−	11.3119i	−0.362598	−	0.397458i
$811$	−1.61158			−0.0565904			−0.0282952	−	0.999600i	$-0.509008\pi$
$811$	−1.61158			−0.0565904			−0.0282952	+	0.999600i	$0.509008\pi$
$812$		−	9.83603i		−	0.345177i
$813$		−	1.00558i		−	0.0352673i
$814$	3.77774			0.132410
$815$	24.1514	+	26.4733i	0.845987	+	0.927320i
$816$	−3.54540			−0.124114
$817$		0			0
$818$			9.29706i			0.325064i
$819$	−4.54886			−0.158950
$820$	7.93069	−	7.23511i	0.276952	−	0.252661i
$821$	−8.04886			−0.280907			−0.140454	−	0.990087i	$-0.544856\pi$
$821$	−8.04886			−0.280907			−0.140454	+	0.990087i	$0.544856\pi$
$822$		−	1.31555i		−	0.0458849i
$823$			37.3423i			1.30167i	0.759219	+	0.650835i	$0.225581\pi$
$823$			37.3423i			1.30167i	−0.759219	+	0.650835i	$0.774419\pi$
$824$	15.8671			0.552757
$825$	−2.20377	−	0.202579i	−0.0767255	−	0.00705289i
$826$	28.7518			1.00040
$827$		−	10.9302i		−	0.380082i	−0.981776	−	0.190041i	$-0.939138\pi$
$827$		−	10.9302i		−	0.380082i	0.981776	−	0.190041i	$-0.0608620\pi$
$828$		−	9.20409i		−	0.319864i
$829$	−33.6375			−1.16828			−0.584139	−	0.811654i	$-0.698568\pi$
$829$	−33.6375			−1.16828			−0.584139	+	0.811654i	$0.698568\pi$
$830$	8.60761	−	7.85266i	0.298775	−	0.272570i
$831$	−3.60265			−0.124975
$832$			4.65108i			0.161247i
$833$		−	2.46472i		−	0.0853976i
$834$	1.35977			0.0470849
$835$	11.4180	+	12.5157i	0.395136	+	0.433124i
$836$		0			0
$837$			21.0478i			0.727517i
$838$		−	8.17179i		−	0.282290i
$839$	−13.8735			−0.478965			−0.239483	−	0.970901i	$-0.576978\pi$
$839$	−13.8735			−0.478965			−0.239483	+	0.970901i	$0.576978\pi$
$840$	6.67335	+	7.31493i	0.230253	+	0.252389i
$841$	−13.1981			−0.455108
$842$		−	36.1951i		−	1.24737i
$843$			6.52948i			0.224887i
$844$	9.08103			0.312582
$845$	20.8586	−	19.0292i	0.717558	−	0.654623i
$846$	9.67815			0.332741
$847$			28.2429i			0.970437i
$848$		−	18.8452i		−	0.647146i
$849$	−13.6406			−0.468145
$850$	2.31946	−	25.2324i	0.0795567	−	0.865466i
$851$	16.2442			0.556845
$852$			0.325224i			0.0111420i
$853$			29.5477i			1.01169i	0.862624	+	0.505846i	$0.168820\pi$
$853$			29.5477i			1.01169i	−0.862624	+	0.505846i	$0.831180\pi$
$854$	−26.0400			−0.891071
$855$		0			0
$856$	−46.1773			−1.57831
$857$			4.28588i			0.146403i	0.997317	+	0.0732014i	$0.0233216\pi$
$857$			4.28588i			0.146403i	−0.997317	+	0.0732014i	$0.976678\pi$
$858$			0.283178i			0.00966753i
$859$	34.9764			1.19338			0.596689	−	0.802472i	$-0.296483\pi$
$859$	34.9764			1.19338			0.596689	+	0.802472i	$0.296483\pi$
$860$	14.2316	+	15.5998i	0.485294	+	0.531950i
$861$	−7.74331			−0.263891
$862$		−	2.97412i		−	0.101299i
$863$		−	20.0305i		−	0.681848i	−0.940091	−	0.340924i	$-0.889260\pi$
$863$		−	20.0305i		−	0.681848i	0.940091	−	0.340924i	$-0.110740\pi$
$864$	−14.0899			−0.479349
$865$	13.3554	+	14.6394i	0.454098	+	0.497755i
$866$	22.8886			0.777786
$867$			3.40674i			0.115699i
$868$			17.1394i			0.581750i
$869$	−2.89791			−0.0983047
$870$	−3.65529	+	3.33470i	−0.123926	+	0.113057i
$871$	6.67917			0.226315
$872$			11.9268i			0.403892i
$873$		−	33.8030i		−	1.14406i
$874$		0			0
$875$	−24.4292	+	18.4903i	−0.825857	+	0.625087i
$876$	−3.36556			−0.113712
$877$			45.5920i			1.53953i	0.638326	+	0.769766i	$0.279627\pi$
$877$			45.5920i			1.53953i	−0.638326	+	0.769766i	$0.720373\pi$
$878$			34.1202i			1.15150i
$879$	14.9402			0.503922
$880$	−1.89691	+	1.73054i	−0.0639448	+	0.0583364i
$881$	−17.2730			−0.581941			−0.290971	−	0.956732i	$-0.593978\pi$
$881$	−17.2730			−0.581941			−0.290971	+	0.956732i	$0.593978\pi$
$882$			1.44997i			0.0488229i
$883$			35.1932i			1.18434i	0.805812	+	0.592172i	$0.201729\pi$
$883$			35.1932i			1.18434i	−0.805812	+	0.592172i	$0.798271\pi$
$884$	2.66862			0.0897554
$885$	8.02301	+	8.79434i	0.269691	+	0.295619i
$886$	−8.12966			−0.273121
$887$			3.16110i			0.106139i	0.998591	+	0.0530697i	$0.0169005\pi$
$887$			3.16110i			0.106139i	−0.998591	+	0.0530697i	$0.983099\pi$
$888$		−	6.99805i		−	0.234839i
$889$	25.1698			0.844169
$890$	−9.29512	−	10.1887i	−0.311573	−	0.341528i
$891$	5.44491			0.182411
$892$		−	25.5727i		−	0.856237i
$893$		0			0
$894$	7.94259			0.265640
$895$	−9.02851	+	8.23664i	−0.301790	+	0.275321i
$896$	−3.55870			−0.118888
$897$			1.21766i			0.0406565i
$898$			24.0715i			0.803277i
$899$	−27.5350			−0.918343
$900$	1.12308	−	12.2176i	0.0374361	−	0.407252i
$901$	−66.1310			−2.20314
$902$		−	4.63801i		−	0.154429i
$903$		−	15.2312i		−	0.506864i
$904$	−12.0814			−0.401822
$905$	31.0832	−	28.3570i	1.03324	−	0.942619i
$906$	−1.30433			−0.0433334
$907$		−	15.9313i		−	0.528991i	−0.964387	−	0.264495i	$-0.914795\pi$
$907$		−	15.9313i		−	0.528991i	0.964387	−	0.264495i	$-0.0852054\pi$
$908$		−	14.3375i		−	0.475807i
$909$	−48.2019			−1.59876
$910$	2.64217	+	2.89619i	0.0875872	+	0.0960078i
$911$	0.0577380			0.00191294			0.000956472	−	1.00000i	$-0.499696\pi$
$911$	0.0577380			0.00191294			0.000956472		1.00000i	$0.499696\pi$
$912$		0			0
$913$			4.14323i			0.137121i
$914$	3.54929			0.117400
$915$	−7.26630	−	7.96488i	−0.240216	−	0.263311i
$916$	−10.2814			−0.339706
$917$			10.2462i			0.338360i
$918$		−	15.3990i		−	0.508242i
$919$	−50.0489			−1.65096			−0.825481	−	0.564430i	$-0.809096\pi$
$919$	−50.0489			−1.65096			−0.825481	+	0.564430i	$0.809096\pi$
$920$	−18.8400	+	17.1876i	−0.621138	+	0.566659i
$921$	−1.36943			−0.0451242
$922$			11.3674i			0.374365i
$923$			0.413977i			0.0136262i
$924$	−1.09519			−0.0360291
$925$	21.5626	+	1.98212i	0.708975	+	0.0651716i
$926$	−7.65831			−0.251668
$927$			14.1816i			0.465783i
$928$		−	18.4327i		−	0.605081i
$929$	16.9850			0.557259			0.278629	−	0.960399i	$-0.410120\pi$
$929$	16.9850			0.557259			0.278629	+	0.960399i	$0.410120\pi$
$930$	6.36940	−	5.81075i	0.208861	−	0.190542i
$931$		0			0
$932$			14.3246i			0.469218i
$933$		−	7.77874i		−	0.254665i
$934$	−11.3557			−0.371571
$935$	6.07275	+	6.65658i	0.198600	+	0.217694i
$936$	−5.04723			−0.164974
$937$		−	33.6925i		−	1.10069i	−0.834938	−	0.550344i	$-0.814497\pi$
$937$		−	33.6925i		−	1.10069i	0.834938	−	0.550344i	$-0.185503\pi$
$938$		−	31.3847i		−	1.02475i
$939$	−0.794036			−0.0259124
$940$	4.62685	+	5.07168i	0.150911	+	0.165420i
$941$	−27.1733			−0.885823			−0.442911	−	0.896565i	$-0.646054\pi$
$941$	−27.1733			−0.885823			−0.442911	+	0.896565i	$0.646054\pi$
$942$			9.00360i			0.293353i
$943$		−	19.9434i		−	0.649446i
$944$	13.8117			0.449532
$945$	−13.7552	+	12.5488i	−0.447458	+	0.408212i
$946$	9.12306			0.296616
$947$		−	33.2962i		−	1.08198i	−0.841028	−	0.540991i	$-0.818049\pi$
$947$		−	33.2962i		−	1.08198i	0.841028	−	0.540991i	$-0.181951\pi$
$948$			1.66975i			0.0542311i
$949$	−4.28402			−0.139065
$950$		0			0
$951$	2.99864			0.0972376
$952$		−	40.3142i		−	1.30659i
$953$			30.4086i			0.985030i	0.870304	+	0.492515i	$0.163922\pi$
$953$			30.4086i			0.985030i	−0.870304	+	0.492515i	$0.836078\pi$
$954$	38.9040			1.25956
$955$	−28.5131	+	26.0123i	−0.922662	+	0.841737i
$956$	−18.8399			−0.609325
$957$		−	1.75946i		−	0.0568751i
$958$			3.61079i			0.116659i
$959$	6.47635			0.209132
$960$	6.09847	+	6.68478i	0.196827	+	0.215750i
$961$	16.9801			0.547744
$962$		−	2.77073i		−	0.0893319i
$963$		−	41.2719i		−	1.32997i
$964$	25.6699			0.826772
$965$	−11.2639	−	12.3468i	−0.362598	−	0.397459i
$966$	5.72165			0.184091
$967$		−	58.9180i		−	1.89467i	−0.320239	−	0.947337i	$-0.603763\pi$
$967$		−	58.9180i		−	1.89467i	0.320239	−	0.947337i	$-0.396237\pi$
$968$			31.3371i			1.00721i
$969$		0			0
$970$	−21.5219	+	19.6342i	−0.691025	+	0.630417i
$971$	−40.8679			−1.31151			−0.655757	−	0.754972i	$-0.727651\pi$
$971$	−40.8679			−1.31151			−0.655757	+	0.754972i	$0.727651\pi$
$972$		−	11.3684i		−	0.364643i
$973$			6.69405i			0.214601i
$974$	28.2769			0.906051
$975$	−0.148579	+	1.61633i	−0.00475832	+	0.0517639i
$976$	−12.5090			−0.400403
$977$		−	35.9431i		−	1.14992i	−0.818181	−	0.574961i	$-0.805017\pi$
$977$		−	35.9431i		−	1.14992i	0.818181	−	0.574961i	$-0.194983\pi$
$978$		−	8.92068i		−	0.285252i
$979$	4.90430			0.156742
$980$	−0.759832	+	0.693189i	−0.0242719	+	0.0221431i
$981$	−10.6598			−0.340342
$982$		−	0.255544i		−	0.00815474i
$983$			10.0666i			0.321074i	0.987030	+	0.160537i	$0.0513226\pi$
$983$			10.0666i			0.321074i	−0.987030	+	0.160537i	$0.948677\pi$
$984$	−8.59165			−0.273892
$985$	18.3979	+	20.1667i	0.586205	+	0.642563i
$986$	20.1452			0.641553
$987$		−	4.95185i		−	0.157619i
$988$		0			0
$989$	39.2290			1.24741
$990$	−3.57252	−	3.91598i	−0.113542	−	0.124458i
$991$	−18.0301			−0.572745			−0.286372	−	0.958118i	$-0.592449\pi$
$991$	−18.0301			−0.572745			−0.286372	+	0.958118i	$0.592449\pi$
$992$			32.1191i			1.01978i
$993$		−	16.9491i		−	0.537864i
$994$	1.94523			0.0616989
$995$	12.8154	−	11.6914i	0.406276	−	0.370642i
$996$	2.38730			0.0756446
$997$			18.7246i			0.593014i	0.955031	+	0.296507i	$0.0958218\pi$
$997$			18.7246i			0.593014i	−0.955031	+	0.296507i	$0.904178\pi$
$998$		−	3.40268i		−	0.107710i
$999$	13.1594			0.416344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.b.k.1084.9		24
5.2	odd	4		9025.2.a.cu.1.16		24
5.3	odd	4		9025.2.a.cu.1.9		24
5.4	even	2	inner	1805.2.b.k.1084.16		24
19.9	even	9		95.2.p.a.24.6	yes	48
19.17	even	9		95.2.p.a.4.3	✓	48
19.18	odd	2		1805.2.b.l.1084.16		24
57.17	odd	18		855.2.da.b.289.6		48
57.47	odd	18		855.2.da.b.784.3		48
95.9	even	18		95.2.p.a.24.3	yes	48
95.17	odd	36		475.2.l.f.251.3		48
95.18	even	4		9025.2.a.ct.1.16		24
95.28	odd	36		475.2.l.f.176.6		48
95.37	even	4		9025.2.a.ct.1.9		24
95.47	odd	36		475.2.l.f.176.3		48
95.74	even	18		95.2.p.a.4.6	yes	48
95.93	odd	36		475.2.l.f.251.6		48
95.94	odd	2		1805.2.b.l.1084.9		24
285.74	odd	18		855.2.da.b.289.3		48
285.104	odd	18		855.2.da.b.784.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.3	✓	48	19.17	even	9
95.2.p.a.4.6	yes	48	95.74	even	18
95.2.p.a.24.3	yes	48	95.9	even	18
95.2.p.a.24.6	yes	48	19.9	even	9
475.2.l.f.176.3		48	95.47	odd	36
475.2.l.f.176.6		48	95.28	odd	36
475.2.l.f.251.3		48	95.17	odd	36
475.2.l.f.251.6		48	95.93	odd	36
855.2.da.b.289.3		48	285.74	odd	18
855.2.da.b.289.6		48	57.17	odd	18
855.2.da.b.784.3		48	57.47	odd	18
855.2.da.b.784.6		48	285.104	odd	18
1805.2.b.k.1084.9		24	1.1	even	1	trivial
1805.2.b.k.1084.16		24	5.4	even	2	inner
1805.2.b.l.1084.9		24	95.94	odd	2
1805.2.b.l.1084.16		24	19.18	odd	2
9025.2.a.ct.1.9		24	95.37	even	4
9025.2.a.ct.1.16		24	95.18	even	4
9025.2.a.cu.1.9		24	5.3	odd	4
9025.2.a.cu.1.16		24	5.2	odd	4

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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.04740i q^{2} -0.531453i q^{3} +0.902948 q^{4} +(1.65192 - 1.50704i) q^{5} -0.556645 q^{6} -2.74033i q^{7} -3.04056i q^{8} +2.71756 q^{9} +(-1.57847 - 1.73023i) q^{10} +0.832835 q^{11} -0.479874i q^{12} -0.610831i q^{13} -2.87023 q^{14} +(-0.800919 - 0.877919i) q^{15} -1.37879 q^{16} +4.83841i q^{17} -2.84638i q^{18} +(1.49160 - 1.36077i) q^{20} -1.45636 q^{21} -0.872314i q^{22} -3.75094i q^{23} -1.61591 q^{24} +(0.457688 - 4.97901i) q^{25} -0.639786 q^{26} -3.03861i q^{27} -2.47437i q^{28} +3.97516 q^{29} +(-0.919534 + 0.838884i) q^{30} -6.92676 q^{31} -4.63696i q^{32} -0.442613i q^{33} +5.06777 q^{34} +(-4.12977 - 4.52681i) q^{35} +2.45381 q^{36} +4.33071i q^{37} -0.324628 q^{39} +(-4.58222 - 5.02276i) q^{40} +5.31691 q^{41} +1.52539i q^{42} +10.4585i q^{43} +0.752007 q^{44} +(4.48919 - 4.09546i) q^{45} -3.92874 q^{46} +3.40016i q^{47} +0.732762i q^{48} -0.509407 q^{49} +(-5.21503 - 0.479384i) q^{50} +2.57139 q^{51} -0.551549i q^{52} +13.6679i q^{53} -3.18265 q^{54} +(1.37578 - 1.25511i) q^{55} -8.33212 q^{56} -4.16359i q^{58} -10.0173 q^{59} +(-0.723188 - 0.792715i) q^{60} +9.07245 q^{61} +7.25511i q^{62} -7.44700i q^{63} -7.61435 q^{64} +(-0.920544 - 1.00905i) q^{65} -0.463594 q^{66} +10.9346i q^{67} +4.36883i q^{68} -1.99345 q^{69} +(-4.74139 + 4.32554i) q^{70} -0.677726 q^{71} -8.26288i q^{72} -7.01343i q^{73} +4.53600 q^{74} +(-2.64611 - 0.243240i) q^{75} -2.28224i q^{77} +0.340016i q^{78} -3.47957 q^{79} +(-2.27765 + 2.07788i) q^{80} +6.53779 q^{81} -5.56894i q^{82} +4.97485i q^{83} -1.31501 q^{84} +(7.29166 + 7.99268i) q^{85} +10.9542 q^{86} -2.11261i q^{87} -2.53228i q^{88} +5.88868 q^{89} +(-4.28959 - 4.70199i) q^{90} -1.67388 q^{91} -3.38690i q^{92} +3.68125i q^{93} +3.56134 q^{94} -2.46433 q^{96} -12.4387i q^{97} +0.533555i q^{98} +2.26328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34}+ \cdots - 120 q^{96}+O(q^{100}) \) 24 * q - 18 * q^4 - 3 * q^5 - 12 * q^6 - 12 * q^9 - 6 * q^10 + 12 * q^11 - 24 * q^14 - 9 * q^15 + 6 * q^16 + 21 * q^20 + 6 * q^21 + 42 * q^24 - 3 * q^25 - 12 * q^26 - 36 * q^29 - 18 * q^30 + 42 * q^31 - 6 * q^34 + 27 * q^35 - 6 * q^36 - 24 * q^39 + 12 * q^40 + 60 * q^41 + 30 * q^44 + 9 * q^45 + 6 * q^46 - 12 * q^49 + 18 * q^50 + 30 * q^51 + 24 * q^54 + 33 * q^55 + 18 * q^56 - 60 * q^59 - 42 * q^60 + 30 * q^61 + 18 * q^65 + 36 * q^66 - 66 * q^69 + 9 * q^70 + 96 * q^71 - 24 * q^74 + 36 * q^75 - 72 * q^79 - 42 * q^80 - 96 * q^81 + 54 * q^84 - 27 * q^85 + 108 * q^86 - 84 * q^89 - 93 * q^90 + 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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