LMFDB - Embedded newform 495.2.bj.a.118.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,2,Mod(28,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 15, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.28"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,10,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.1
Character	$\chi$	$=$	495.118
Dual form			495.2.bj.a.172.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50135 - 0.237790i) q^{2} +(0.295389 + 0.0959778i) q^{4} +(1.89470 + 1.18749i) q^{5} +(0.170602 - 0.0869260i) q^{7} +(2.28811 + 1.16585i) q^{8} +(-2.56223 - 2.23337i) q^{10} +(-1.77694 + 2.80044i) q^{11} +(-0.484259 + 3.05749i) q^{13} +(-0.276803 + 0.0899388i) q^{14} +(-3.66057 - 2.65956i) q^{16} +(-0.579827 - 3.66088i) q^{17} +(-0.229844 - 0.707388i) q^{19} +(0.445701 + 0.532619i) q^{20} +(3.33373 - 3.78190i) q^{22} +(1.14886 + 1.14886i) q^{23} +(2.17976 + 4.49985i) q^{25} +(1.45408 - 4.47521i) q^{26} +(0.0587369 - 0.00930302i) q^{28} +(-2.95025 + 9.07993i) q^{29} +(-0.283900 + 0.206266i) q^{31} +(1.23166 + 1.23166i) q^{32} +5.63413i q^{34} +(0.426463 + 0.0378887i) q^{35} +(2.45398 + 4.81621i) q^{37} +(0.176866 + 1.11669i) q^{38} +(2.95085 + 4.92603i) q^{40} +(-6.36824 + 2.06917i) q^{41} +(3.72708 - 3.72708i) q^{43} +(-0.793670 + 0.656674i) q^{44} +(-1.45165 - 1.99802i) q^{46} +(11.0165 + 5.61318i) q^{47} +(-4.09295 + 5.63346i) q^{49} +(-2.20256 - 7.27417i) q^{50} +(-0.436496 + 0.856672i) q^{52} +(8.91914 + 1.41265i) q^{53} +(-6.69225 + 3.19590i) q^{55} +0.491699 q^{56} +(6.58847 - 12.9306i) q^{58} +(9.15496 + 2.97463i) q^{59} +(-3.46383 + 4.76756i) q^{61} +(0.475281 - 0.242168i) q^{62} +(3.76284 + 5.17911i) q^{64} +(-4.54825 + 5.21797i) q^{65} +(4.13426 - 4.13426i) q^{67} +(0.180089 - 1.13704i) q^{68} +(-0.631259 - 0.158293i) q^{70} +(-9.27272 - 6.73702i) q^{71} +(1.09042 + 2.14008i) q^{73} +(-2.53903 - 7.81434i) q^{74} -0.231015i q^{76} +(-0.0597184 + 0.632224i) q^{77} +(-0.542434 + 0.394101i) q^{79} +(-3.77749 - 9.38594i) q^{80} +(10.0530 - 1.59224i) q^{82} +(-16.4776 + 2.60980i) q^{83} +(3.24865 - 7.62480i) q^{85} +(-6.48191 + 4.70938i) q^{86} +(-7.33074 + 4.33608i) q^{88} -7.92190i q^{89} +(0.183160 + 0.563709i) q^{91} +(0.229095 + 0.449625i) q^{92} +(-15.2048 - 11.0469i) q^{94} +(0.404527 - 1.61322i) q^{95} +(-0.215721 + 1.36201i) q^{97} +(7.48452 - 7.48452i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.50135	−	0.237790i	−1.06161	−	0.168143i	−0.398884	−	0.917002i	$-0.630602\pi$
$2$	−1.50135	−	0.237790i	−1.06161	−	0.168143i	−0.662730	+	0.748859i	$0.730602\pi$
$3$		0			0
$3$		0			0
$4$	0.295389	+	0.0959778i	0.147695	+	0.0479889i
$5$	1.89470	+	1.18749i	0.847335	+	0.531060i
$5$	1.89470	+	1.18749i	0.847335	+	0.531060i
$6$		0			0
$7$	0.170602	−	0.0869260i	0.0644815	−	0.0328550i	−0.421452	−	0.906851i	$-0.638480\pi$
$7$	0.170602	−	0.0869260i	0.0644815	−	0.0328550i	0.485934	+	0.873996i	$0.338480\pi$
$8$	2.28811	+	1.16585i	0.808970	+	0.412191i
$9$		0			0
$10$	−2.56223	−	2.23337i	−0.810248	−	0.706253i
$11$	−1.77694	+	2.80044i	−0.535768	+	0.844365i
$11$	−1.77694	+	2.80044i	−0.535768	+	0.844365i
$12$		0			0
$13$	−0.484259	+	3.05749i	−0.134309	+	0.847995i	0.824896	+	0.565285i	$0.191234\pi$
$13$	−0.484259	+	3.05749i	−0.134309	+	0.847995i	−0.959205	+	0.282711i	$0.908766\pi$
$14$	−0.276803	+	0.0899388i	−0.0739787	+	0.0240372i
$15$		0			0
$16$	−3.66057	−	2.65956i	−0.915143	−	0.664890i
$17$	−0.579827	−	3.66088i	−0.140629	−	0.887894i	−0.952606	−	0.304206i	$-0.901609\pi$
$17$	−0.579827	−	3.66088i	−0.140629	−	0.887894i	0.811978	−	0.583688i	$-0.198391\pi$
$18$		0			0
$19$	−0.229844	−	0.707388i	−0.0527299	−	0.162286i	0.921224	−	0.389033i	$-0.127191\pi$
$19$	−0.229844	−	0.707388i	−0.0527299	−	0.162286i	−0.973954	+	0.226747i	$0.927191\pi$
$20$	0.445701	+	0.532619i	0.0996618	+	0.119097i
$21$		0			0
$22$	3.33373	−	3.78190i	0.710753	−	0.806304i
$23$	1.14886	+	1.14886i	0.239553	+	0.239553i	0.816665	−	0.577112i	$-0.195820\pi$
$23$	1.14886	+	1.14886i	0.239553	+	0.239553i	−0.577112	+	0.816665i	$0.695820\pi$
$24$		0			0
$25$	2.17976	+	4.49985i	0.435952	+	0.899970i
$26$	1.45408	−	4.47521i	0.285169	−	0.877660i
$27$		0			0
$28$	0.0587369	−	0.00930302i	0.0111002	−	0.00175811i
$29$	−2.95025	+	9.07993i	−0.547847	+	1.68610i	0.166275	+	0.986079i	$0.446826\pi$
$29$	−2.95025	+	9.07993i	−0.547847	+	1.68610i	−0.714122	+	0.700021i	$0.753174\pi$
$30$		0			0
$31$	−0.283900	+	0.206266i	−0.0509900	+	0.0370464i	−0.612988	−	0.790092i	$-0.710033\pi$
$31$	−0.283900	+	0.206266i	−0.0509900	+	0.0370464i	0.561998	+	0.827138i	$0.310033\pi$
$32$	1.23166	+	1.23166i	0.217729	+	0.217729i
$33$		0			0
$34$			5.63413i			0.966246i
$35$	0.426463	+	0.0378887i	0.0720853	+	0.00640437i
$36$		0			0
$37$	2.45398	+	4.81621i	0.403432	+	0.791780i	0.999941	−	0.0108264i	$-0.00344622\pi$
$37$	2.45398	+	4.81621i	0.403432	+	0.791780i	−0.596510	+	0.802606i	$0.703446\pi$
$38$	0.176866	+	1.11669i	0.0286915	+	0.181151i
$39$		0			0
$40$	2.95085	+	4.92603i	0.466570	+	0.778874i
$41$	−6.36824	+	2.06917i	−0.994552	+	0.323150i	−0.760687	−	0.649119i	$-0.775138\pi$
$41$	−6.36824	+	2.06917i	−0.994552	+	0.323150i	−0.233866	+	0.972269i	$0.575138\pi$
$42$		0			0
$43$	3.72708	−	3.72708i	0.568374	−	0.568374i	−0.363299	−	0.931673i	$-0.618350\pi$
$43$	3.72708	−	3.72708i	0.568374	−	0.568374i	0.931673	+	0.363299i	$0.118350\pi$
$44$	−0.793670	+	0.656674i	−0.119650	+	0.0989973i
$45$		0			0
$46$	−1.45165	−	1.99802i	−0.214034	−	0.294592i
$47$	11.0165	+	5.61318i	1.60692	+	0.818766i	0.999706	+	0.0242272i	$0.00771250\pi$
$47$	11.0165	+	5.61318i	1.60692	+	0.818766i	0.607213	+	0.794539i	$0.292287\pi$
$48$		0			0
$49$	−4.09295	+	5.63346i	−0.584707	+	0.804780i
$50$	−2.20256	−	7.27417i	−0.311488	−	1.02872i
$51$		0			0
$52$	−0.436496	+	0.856672i	−0.0605311	+	0.118799i
$53$	8.91914	+	1.41265i	1.22514	+	0.194043i	0.735282	−	0.677761i	$-0.237050\pi$
$53$	8.91914	+	1.41265i	1.22514	+	0.194043i	0.489855	+	0.871804i	$0.337050\pi$
$54$		0			0
$55$	−6.69225	+	3.19590i	−0.902383	+	0.430935i
$56$	0.491699			0.0657061
$57$		0			0
$58$	6.58847	−	12.9306i	0.865108	−	1.69787i
$59$	9.15496	+	2.97463i	1.19187	+	0.387263i	0.836765	−	0.547562i	$-0.184444\pi$
$59$	9.15496	+	2.97463i	1.19187	+	0.387263i	0.355108	+	0.934825i	$0.384444\pi$
$60$		0			0
$61$	−3.46383	+	4.76756i	−0.443498	+	0.610423i	−0.970985	−	0.239140i	$-0.923134\pi$
$61$	−3.46383	+	4.76756i	−0.443498	+	0.610423i	0.527487	+	0.849563i	$0.323134\pi$
$62$	0.475281	−	0.242168i	0.0603608	−	0.0307554i
$63$		0			0
$64$	3.76284	+	5.17911i	0.470356	+	0.647389i
$65$	−4.54825	+	5.21797i	−0.564141	+	0.647209i
$66$		0			0
$67$	4.13426	−	4.13426i	0.505081	−	0.505081i	−0.407932	−	0.913012i	$-0.633750\pi$
$67$	4.13426	−	4.13426i	0.505081	−	0.505081i	0.913012	+	0.407932i	$0.133750\pi$
$68$	0.180089	−	1.13704i	0.0218390	−	0.137886i
$69$		0			0
$70$	−0.631259	−	0.158293i	−0.0754499	−	0.0189196i
$71$	−9.27272	−	6.73702i	−1.10047	−	0.799538i	−0.119333	−	0.992854i	$-0.538075\pi$
$71$	−9.27272	−	6.73702i	−1.10047	−	0.799538i	−0.981136	+	0.193317i	$0.938075\pi$
$72$		0			0
$73$	1.09042	+	2.14008i	0.127624	+	0.250477i	0.945973	−	0.324245i	$-0.105110\pi$
$73$	1.09042	+	2.14008i	0.127624	+	0.250477i	−0.818349	+	0.574722i	$0.805110\pi$
$74$	−2.53903	−	7.81434i	−0.295156	−	0.908398i
$75$		0			0
$76$		−	0.231015i		−	0.0264992i
$77$	−0.0597184	+	0.632224i	−0.00680554	+	0.0720486i
$78$		0			0
$79$	−0.542434	+	0.394101i	−0.0610286	+	0.0443399i	−0.617881	−	0.786271i	$-0.712009\pi$
$79$	−0.542434	+	0.394101i	−0.0610286	+	0.0443399i	0.556853	+	0.830611i	$0.312009\pi$
$80$	−3.77749	−	9.38594i	−0.422336	−	1.04938i
$81$		0			0
$82$	10.0530	−	1.59224i	1.11017	−	0.175833i
$83$	−16.4776	+	2.60980i	−1.80865	+	0.286463i	−0.967228	−	0.253909i	$-0.918284\pi$
$83$	−16.4776	+	2.60980i	−1.80865	+	0.286463i	−0.841426	+	0.540372i	$0.818284\pi$
$84$		0			0
$85$	3.24865	−	7.62480i	0.352365	−	0.827025i
$86$	−6.48191	+	4.70938i	−0.698962	+	0.507826i
$87$		0			0
$88$	−7.33074	+	4.33608i	−0.781460	+	0.462227i
$89$		−	7.92190i		−	0.839720i	−0.907589	−	0.419860i	$-0.862079\pi$
$89$		−	7.92190i		−	0.839720i	0.907589	−	0.419860i	$-0.137921\pi$
$90$		0			0
$91$	0.183160	+	0.563709i	0.0192004	+	0.0590927i
$92$	0.229095	+	0.449625i	0.0238848	+	0.0468766i
$93$		0			0
$94$	−15.2048	−	11.0469i	−1.56826	−	1.13941i
$95$	0.404527	−	1.61322i	0.0415036	−	0.165513i
$96$		0			0
$97$	−0.215721	+	1.36201i	−0.0219032	+	0.138291i	−0.996217	−	0.0869051i	$-0.972302\pi$
$97$	−0.215721	+	1.36201i	−0.0219032	+	0.138291i	0.974313	+	0.225196i	$0.0723023\pi$
$98$	7.48452	−	7.48452i	0.756051	−	0.756051i
$99$		0			0
$100$	0.211991	+	1.53842i	0.0211991	+	0.153842i
$101$	2.83633	+	3.90387i	0.282225	+	0.388449i	0.926469	−	0.376370i	$-0.122828\pi$
$101$	2.83633	+	3.90387i	0.282225	+	0.388449i	−0.644244	+	0.764820i	$0.722828\pi$
$102$		0			0
$103$	2.88449	−	1.46972i	0.284217	−	0.144816i	−0.306071	−	0.952009i	$-0.599014\pi$
$103$	2.88449	−	1.46972i	0.284217	−	0.144816i	0.590287	+	0.807193i	$0.299014\pi$
$104$	−4.67262	+	6.43131i	−0.458188	+	0.630641i
$105$		0			0
$106$	−13.0548	−	4.24177i	−1.26800	−	0.411997i
$107$	5.01911	−	9.85055i	0.485215	−	0.952289i	−0.510505	−	0.859875i	$-0.670542\pi$
$107$	5.01911	−	9.85055i	0.485215	−	0.952289i	0.995721	−	0.0924142i	$-0.0294584\pi$
$108$		0			0
$109$	9.54212			0.913969			0.456985	−	0.889475i	$-0.348929\pi$
$109$	9.54212			0.913969			0.456985	+	0.889475i	$0.348929\pi$
$110$	10.8074	−	3.20681i	1.03044	−	0.305757i
$111$		0			0
$112$	−0.855686	−	0.135527i	−0.0808547	−	0.0128061i
$113$	1.88301	−	3.69562i	0.177139	−	0.347654i	−0.785317	−	0.619094i	$-0.787500\pi$
$113$	1.88301	−	3.69562i	0.177139	−	0.347654i	0.962455	+	0.271440i	$0.0874999\pi$
$114$		0			0
$115$	0.812486	+	3.54099i	0.0757647	+	0.330199i
$116$	−1.74294	+	2.39895i	−0.161828	+	0.222737i
$117$		0			0
$118$	−13.0374	−	6.64291i	−1.20019	−	0.611529i
$119$	−0.417145	−	0.574151i	−0.0382397	−	0.0526324i
$120$		0			0
$121$	−4.68496	−	9.95245i	−0.425905	−	0.904768i
$122$	6.33410	−	6.33410i	0.573462	−	0.573462i
$123$		0			0
$124$	−0.103658	+	0.0336805i	−0.00930877	+	0.00302460i
$125$	−1.21352	+	11.1143i	−0.108541	+	0.994092i
$126$		0			0
$127$	−2.27881	−	14.3879i	−0.202212	−	1.27672i	−0.854782	−	0.518987i	$-0.826309\pi$
$127$	−2.27881	−	14.3879i	−0.202212	−	1.27672i	0.652570	−	0.757728i	$-0.273691\pi$
$128$	−5.99935	−	11.7744i	−0.530273	−	1.04072i
$129$		0			0
$130$	8.06929	−	6.75246i	0.707723	−	0.592230i
$131$		−	9.76926i		−	0.853544i	−0.904359	−	0.426772i	$-0.859651\pi$
$131$		−	9.76926i		−	0.853544i	0.904359	−	0.426772i	$-0.140349\pi$
$132$		0			0
$133$	−0.100702	−	0.100702i	−0.00873200	−	0.00873200i
$134$	−7.19006	+	5.22388i	−0.621126	+	0.451275i
$135$		0			0
$136$	2.94133	−	9.05250i	0.252217	−	0.776245i
$137$	−4.27681	+	0.677380i	−0.365392	+	0.0578725i	−0.336431	−	0.941708i	$-0.609220\pi$
$137$	−4.27681	+	0.677380i	−0.365392	+	0.0578725i	−0.0289612	+	0.999581i	$0.509220\pi$
$138$		0			0
$139$	3.24794	−	9.99613i	0.275487	−	0.847860i	−0.713604	−	0.700550i	$-0.752938\pi$
$139$	3.24794	−	9.99613i	0.275487	−	0.847860i	0.989090	−	0.147311i	$-0.0470618\pi$
$140$	0.122336	+	0.0521228i	0.0103393	+	0.00440518i
$141$		0			0
$142$	12.3196	+	12.3196i	1.03384	+	1.03384i
$143$	−7.70183	−	6.78912i	−0.644059	−	0.567735i
$144$		0			0
$145$	−16.3721	+	13.7003i	−1.35963	+	1.13775i
$146$	−1.12822	−	3.47229i	−0.0933719	−	0.287369i
$147$		0			0
$148$	0.262630	+	1.65818i	0.0215881	+	0.136302i
$149$	−4.66189	−	3.38706i	−0.381917	−	0.277479i	0.380218	−	0.924897i	$-0.375849\pi$
$149$	−4.66189	−	3.38706i	−0.381917	−	0.277479i	−0.762135	+	0.647418i	$0.775849\pi$
$150$		0			0
$151$	−14.2318	+	4.62419i	−1.15817	+	0.376311i	−0.824214	−	0.566278i	$-0.808383\pi$
$151$	−14.2318	+	4.62419i	−1.15817	+	0.376311i	−0.333953	+	0.942590i	$0.608383\pi$
$152$	0.298800	−	1.88655i	0.0242358	−	0.153019i
$153$		0			0
$154$	0.239995	−	0.934987i	0.0193393	−	0.0753434i
$155$	−0.782843	+	0.0536836i	−0.0628795	+	0.00431197i
$156$		0			0
$157$	4.40881	+	2.24640i	0.351861	+	0.179282i	0.620983	−	0.783824i	$-0.286733\pi$
$157$	4.40881	+	2.24640i	0.351861	+	0.179282i	−0.269122	+	0.963106i	$0.586733\pi$
$158$	0.908095	−	0.462698i	0.0722442	−	0.0368103i
$159$		0			0
$160$	0.871047	+	3.79621i	0.0688623	+	0.300117i
$161$	0.295863	+	0.0961317i	0.0233173	+	0.00757624i
$162$		0			0
$163$	−9.89335	−	1.56695i	−0.774907	−	0.122733i	−0.243558	−	0.969886i	$-0.578315\pi$
$163$	−9.89335	−	1.56695i	−0.774907	−	0.122733i	−0.531349	+	0.847153i	$0.678315\pi$
$164$	−2.07970			−0.162398
$165$		0			0
$166$	25.3592			1.96826
$167$	−11.9137	−	1.88695i	−0.921913	−	0.146017i	−0.322604	−	0.946534i	$-0.604558\pi$
$167$	−11.9137	−	1.88695i	−0.921913	−	0.146017i	−0.599310	+	0.800517i	$0.704558\pi$
$168$		0			0
$169$	3.24999	+	1.05599i	0.250000	+	0.0812298i
$170$	−6.69045	+	10.6750i	−0.513134	+	0.818734i
$171$		0			0
$172$	1.45866	−	0.743222i	0.111221	−	0.0566702i
$173$	11.1065	+	5.65903i	0.844410	+	0.430248i	0.821991	−	0.569501i	$-0.192863\pi$
$173$	11.1065	+	5.65903i	0.844410	+	0.430248i	0.0224186	+	0.999749i	$0.492863\pi$
$174$		0			0
$175$	0.763025	+	0.578206i	0.0576793	+	0.0437082i
$176$	13.9526	−	5.52533i	1.05171	−	0.416488i
$177$		0			0
$178$	−1.88375	+	11.8935i	−0.141193	+	0.891458i
$179$	19.1909	−	6.23551i	1.43440	−	0.466064i	0.514252	−	0.857639i	$-0.328070\pi$
$179$	19.1909	−	6.23551i	1.43440	−	0.466064i	0.920146	+	0.391575i	$0.128070\pi$
$180$		0			0
$181$	−3.72935	−	2.70953i	−0.277200	−	0.201398i	0.440495	−	0.897755i	$-0.354803\pi$
$181$	−3.72935	−	2.70953i	−0.277200	−	0.201398i	−0.717695	+	0.696357i	$0.754803\pi$
$182$	−0.140943	−	0.889877i	−0.0104474	−	0.0659620i
$183$		0			0
$184$	1.28932	+	3.96811i	0.0950497	+	0.292533i
$185$	−1.06962	+	12.0393i	−0.0786403	+	0.885148i
$186$		0			0
$187$	11.2824	+	4.88140i	0.825051	+	0.356963i
$188$	2.71541	+	2.71541i	0.198042	+	0.198042i
$189$		0			0
$190$	−0.990944	+	2.32582i	−0.0718907	+	0.168732i
$191$	−1.95493	+	6.01667i	−0.141454	+	0.435351i	−0.996538	−	0.0831389i	$-0.973505\pi$
$191$	−1.95493	+	6.01667i	−0.141454	+	0.435351i	0.855084	+	0.518490i	$0.173505\pi$
$192$		0			0
$193$	5.85885	−	0.927951i	0.421729	−	0.0667954i	0.0580368	−	0.998314i	$-0.481516\pi$
$193$	5.85885	−	0.927951i	0.421729	−	0.0667954i	0.363692	+	0.931519i	$0.381516\pi$
$194$	0.647745	−	1.99355i	0.0465054	−	0.143129i
$195$		0			0
$196$	−1.74970	+	1.27123i	−0.124979	+	0.0908022i
$197$	9.90515	+	9.90515i	0.705713	+	0.705713i	0.965631	−	0.259918i	$-0.0836955\pi$
$197$	9.90515	+	9.90515i	0.705713	+	0.705713i	−0.259918	+	0.965631i	$0.583696\pi$
$198$		0			0
$199$			13.3828i			0.948680i	0.880342	+	0.474340i	$0.157313\pi$
$199$			13.3828i			0.948680i	−0.880342	+	0.474340i	$0.842687\pi$
$200$	−0.258626	+	12.8374i	−0.0182876	+	0.907744i
$201$		0			0
$202$	−3.33001	−	6.53551i	−0.234299	−	0.459837i
$203$	0.285964	+	1.80551i	0.0200708	+	0.126722i
$204$		0			0
$205$	−14.5230	−	3.64175i	−1.01433	−	0.254351i
$206$	−4.68010	+	1.52066i	−0.326078	+	0.105949i
$207$		0			0
$208$	9.90424	−	9.90424i	0.686736	−	0.686736i
$209$	2.38942	+	0.613321i	0.165280	+	0.0424243i
$210$		0			0
$211$	3.48696	+	4.79939i	0.240052	+	0.330404i	0.911996	−	0.410198i	$-0.134540\pi$
$211$	3.48696	+	4.79939i	0.240052	+	0.330404i	−0.671944	+	0.740602i	$0.734540\pi$
$212$	2.49903	+	1.27332i	0.171634	+	0.0874521i
$213$		0			0
$214$	−9.87779	+	13.5956i	−0.675232	+	0.929377i
$215$	11.4875	−	2.63584i	0.783444	−	0.179763i
$216$		0			0
$217$	−0.0305041	+	0.0598677i	−0.00207075	+	0.00406408i
$218$	−14.3260	−	2.26902i	−0.970282	−	0.153678i
$219$		0			0
$220$	−2.28355	+	0.301727i	−0.153957	+	0.0203424i
$221$	11.4739			0.771818
$222$		0			0
$223$	9.64984	−	18.9389i	0.646201	−	1.26824i	−0.302826	−	0.953046i	$-0.597930\pi$
$223$	9.64984	−	18.9389i	0.646201	−	1.26824i	0.949027	−	0.315195i	$-0.102070\pi$
$224$	0.317188	+	0.103060i	0.0211930	+	0.00688602i
$225$		0			0
$226$	−3.70584	+	5.10065i	−0.246509	+	0.339290i
$227$	−11.6456	+	5.93372i	−0.772944	+	0.393835i	−0.795533	−	0.605910i	$-0.792809\pi$
$227$	−11.6456	+	5.93372i	−0.772944	+	0.393835i	0.0225888	+	0.999745i	$0.492809\pi$
$228$		0			0
$229$	−9.65796	−	13.2930i	−0.638216	−	0.878429i	0.360303	−	0.932835i	$-0.382673\pi$
$229$	−9.65796	−	13.2930i	−0.638216	−	0.878429i	−0.998519	+	0.0544066i	$0.982673\pi$
$230$	−0.377812	−	5.50946i	−0.0249122	−	0.363283i
$231$		0			0
$232$	−17.3363	+	17.3363i	−1.13819	+	1.13819i
$233$	−2.44720	+	15.4510i	−0.160321	+	1.01223i	0.768000	+	0.640450i	$0.221252\pi$
$233$	−2.44720	+	15.4510i	−0.160321	+	1.01223i	−0.928321	+	0.371779i	$0.878748\pi$
$234$		0			0
$235$	14.2073	+	23.7172i	0.926785	+	1.54714i
$236$	2.41878	+	1.75734i	0.157449	+	0.114393i
$237$		0			0
$238$	0.489753	+	0.961194i	0.0317460	+	0.0623050i
$239$	−1.63214	−	5.02322i	−0.105575	−	0.324925i	0.884290	−	0.466938i	$-0.154643\pi$
$239$	−1.63214	−	5.02322i	−0.105575	−	0.324925i	−0.989865	+	0.142012i	$0.954643\pi$
$240$		0			0
$241$		−	16.1676i		−	1.04144i	−0.853726	−	0.520722i	$-0.825663\pi$
$241$		−	16.1676i		−	1.04144i	0.853726	−	0.520722i	$-0.174337\pi$
$242$	4.66716	+	16.0561i	0.300016	+	1.03213i
$243$		0			0
$244$	−1.48076	+	1.07583i	−0.0947959	+	0.0688732i
$245$	−14.4445	+	5.81339i	−0.922828	+	0.371404i
$246$		0			0
$247$	2.27413	−	0.360188i	0.144700	−	0.0229182i
$248$	−0.890071	+	0.140973i	−0.0565196	+	0.00895182i
$249$		0			0
$250$	4.46479	−	16.3978i	0.282378	−	1.03709i
$251$	15.6486	−	11.3694i	0.987729	−	0.717627i	0.0283063	−	0.999599i	$-0.490989\pi$
$251$	15.6486	−	11.3694i	0.987729	−	0.717627i	0.959423	+	0.281972i	$0.0909886\pi$
$252$		0			0
$253$	−5.25876	+	1.17586i	−0.330615	+	0.0739254i
$254$			22.1431i			1.38938i
$255$		0			0
$256$	2.25079	+	6.92722i	0.140674	+	0.432951i
$257$	−2.13653	−	4.19318i	−0.133273	−	0.261563i	0.814720	−	0.579855i	$-0.196891\pi$
$257$	−2.13653	−	4.19318i	−0.133273	−	0.261563i	−0.947993	+	0.318292i	$0.896891\pi$
$258$		0			0
$259$	0.837308	+	0.608340i	0.0520278	+	0.0378004i
$260$	−1.84431	+	1.10480i	−0.114379	+	0.0685169i
$261$		0			0
$262$	−2.32303	+	14.6671i	−0.143517	+	0.906134i
$263$	11.2218	−	11.2218i	0.691964	−	0.691964i	−0.270700	−	0.962664i	$-0.587255\pi$
$263$	11.2218	−	11.2218i	0.691964	−	0.691964i	0.962664	+	0.270700i	$0.0872550\pi$
$264$		0			0
$265$	15.2216	+	13.2679i	0.935053	+	0.815040i
$266$	0.127243	+	0.175135i	0.00780178	+	0.0107382i
$267$		0			0
$268$	1.61801	−	0.824419i	0.0988359	−	0.0503594i
$269$	−6.64926	+	9.15192i	−0.405412	+	0.558002i	−0.962092	−	0.272725i	$-0.912075\pi$
$269$	−6.64926	+	9.15192i	−0.405412	+	0.558002i	0.556680	+	0.830727i	$0.312075\pi$
$270$		0			0
$271$	16.9556	+	5.50921i	1.02998	+	0.334661i	0.774782	−	0.632228i	$-0.217859\pi$
$271$	16.9556	+	5.50921i	1.02998	+	0.334661i	0.255198	+	0.966889i	$0.417859\pi$
$272$	−7.61384	+	14.9430i	−0.461657	+	0.906052i
$273$		0			0
$274$	6.58205			0.397636
$275$	−16.4749	−	1.89169i	−0.993472	−	0.114073i
$276$		0			0
$277$	−4.62395	−	0.732361i	−0.277826	−	0.0440033i	0.0159666	−	0.999873i	$-0.494917\pi$
$277$	−4.62395	−	0.732361i	−0.277826	−	0.0440033i	−0.293793	+	0.955869i	$0.594917\pi$
$278$	−7.25327	+	14.2353i	−0.435022	+	0.853779i
$279$		0			0
$280$	0.931621	+	0.583886i	0.0556750	+	0.0348938i
$281$	7.75247	−	10.6704i	0.462474	−	0.636541i	−0.512546	−	0.858660i	$-0.671297\pi$
$281$	7.75247	−	10.6704i	0.462474	−	0.636541i	0.975019	+	0.222119i	$0.0712975\pi$
$282$		0			0
$283$	20.3029	+	10.3449i	1.20688	+	0.614938i	0.937463	−	0.348084i	$-0.113168\pi$
$283$	20.3029	+	10.3449i	1.20688	+	0.614938i	0.269421	+	0.963022i	$0.413168\pi$
$284$	−2.09246	−	2.88002i	−0.124164	−	0.170898i
$285$		0			0
$286$	9.94874	+	12.0243i	0.588281	+	0.711009i
$287$	−0.906570	+	0.906570i	−0.0535131	+	0.0535131i
$288$		0			0
$289$	3.10211	−	1.00794i	0.182477	−	0.0592904i
$290$	27.8380	−	16.6759i	1.63471	−	0.979240i
$291$		0			0
$292$	0.116700	+	0.736812i	0.00682933	+	0.0431187i
$293$	3.28132	+	6.43996i	0.191697	+	0.376226i	0.966771	−	0.255644i	$-0.0822875\pi$
$293$	3.28132	+	6.43996i	0.191697	+	0.376226i	−0.775074	+	0.631870i	$0.782287\pi$
$294$		0			0
$295$	13.8135	+	16.5074i	0.804256	+	0.961097i
$296$			13.8810i			0.806817i
$297$		0			0
$298$	6.19371	+	6.19371i	0.358792	+	0.358792i
$299$	−4.06896	+	2.95628i	−0.235314	+	0.170966i
$300$		0			0
$301$	0.311867	−	0.959827i	0.0179757	−	0.0553235i
$302$	22.4665	−	3.55834i	1.29280	−	0.204759i
$303$		0			0
$304$	−1.03998	+	3.20073i	−0.0596469	+	0.183574i
$305$	−12.2243	+	4.91983i	−0.699963	+	0.281709i
$306$		0			0
$307$	−20.1272	−	20.1272i	−1.14872	−	1.14872i	−0.986804	−	0.161918i	$-0.948232\pi$
$307$	−20.1272	−	20.1272i	−1.14872	−	1.14872i	−0.161918	−	0.986804i	$-0.551768\pi$
$308$	−0.0783196	+	0.181020i	−0.00446267	+	0.0103146i
$309$		0			0
$310$	1.18809	+	0.105555i	0.0674787	+	0.00599509i
$311$	2.32254	+	7.14803i	0.131699	+	0.405328i	0.995062	−	0.0992557i	$-0.0316462\pi$
$311$	2.32254	+	7.14803i	0.131699	+	0.405328i	−0.863363	+	0.504583i	$0.831646\pi$
$312$		0			0
$313$	−0.210574	−	1.32951i	−0.0119023	−	0.0751483i	0.981022	−	0.193895i	$-0.0621122\pi$
$313$	−0.210574	−	1.32951i	−0.0119023	−	0.0751483i	−0.992925	+	0.118747i	$0.962112\pi$
$314$	−6.08499	−	4.42100i	−0.343396	−	0.249492i
$315$		0			0
$316$	−0.198054	+	0.0643517i	−0.0111414	+	0.00362006i
$317$	1.77271	−	11.1924i	0.0995652	−	0.628630i	−0.886558	−	0.462617i	$-0.846911\pi$
$317$	1.77271	−	11.1924i	0.0995652	−	0.628630i	0.986124	−	0.166013i	$-0.0530894\pi$
$318$		0			0
$319$	−20.1854	−	24.3965i	−1.13017	−	1.36594i
$320$	0.979335	+	14.2812i	0.0547465	+	0.798342i
$321$		0			0
$322$	−0.421334	−	0.214680i	−0.0234800	−	0.0119637i
$323$	−2.45639	+	1.25159i	−0.136677	+	0.0696406i
$324$		0			0
$325$	−14.8138	+	4.48550i	−0.821723	+	0.248811i
$326$	14.4808	+	4.70509i	0.802015	+	0.260591i
$327$		0			0
$328$	−16.9836	−	2.68994i	−0.937762	−	0.148527i
$329$	2.36737			0.130517
$330$		0			0
$331$	−17.7048			−0.973145			−0.486572	−	0.873640i	$-0.661753\pi$
$331$	−17.7048			−0.973145			−0.486572	+	0.873640i	$0.661753\pi$
$332$	−5.11780	−	0.810579i	−0.280876	−	0.0444863i
$333$		0			0
$334$	17.4380	+	5.66594i	0.954164	+	0.310027i
$335$	12.7426	−	2.92380i	0.696200	−	0.159744i
$336$		0			0
$337$	6.78954	−	3.45945i	0.369850	−	0.188448i	−0.259180	−	0.965829i	$-0.583452\pi$
$337$	6.78954	−	3.45945i	0.369850	−	0.188448i	0.629030	+	0.777381i	$0.283452\pi$
$338$	−4.62827	−	2.35822i	−0.251745	−	0.128270i
$339$		0			0
$340$	1.69143	−	1.94049i	0.0917305	−	0.105238i
$341$	−0.0731608	−	1.16157i	−0.00396188	−	0.0629025i
$342$		0			0
$343$	−0.418239	+	2.64066i	−0.0225828	+	0.142582i
$344$	12.8732	−	4.18275i	0.694076	−	0.225519i
$345$		0			0
$346$	−15.3290	−	11.1372i	−0.824093	−	0.598739i
$347$	−1.46011	−	9.21879i	−0.0783830	−	0.494891i	−0.995381	−	0.0959998i	$-0.969395\pi$
$347$	−1.46011	−	9.21879i	−0.0783830	−	0.494891i	0.916998	−	0.398891i	$-0.130605\pi$
$348$		0			0
$349$	−0.464073	−	1.42827i	−0.0248413	−	0.0764536i	0.937867	−	0.346994i	$-0.112798\pi$
$349$	−0.464073	−	1.42827i	−0.0248413	−	0.0764536i	−0.962709	+	0.270540i	$0.912798\pi$
$350$	−1.00807	−	1.04953i	−0.0538839	−	0.0560996i
$351$		0			0
$352$	−5.63779	+	1.26061i	−0.300495	+	0.0671906i
$353$	−4.40229	−	4.40229i	−0.234310	−	0.234310i	0.580179	−	0.814489i	$-0.302983\pi$
$353$	−4.40229	−	4.40229i	−0.234310	−	0.234310i	−0.814489	+	0.580179i	$0.802983\pi$
$354$		0			0
$355$	−9.56888	−	23.7758i	−0.507863	−	1.26189i
$356$	0.760327	−	2.34004i	0.0402972	−	0.124022i
$357$		0			0
$358$	−30.2950	+	4.79826i	−1.60114	+	0.253596i
$359$	8.12845	−	25.0168i	0.429003	−	1.32034i	−0.470105	−	0.882611i	$-0.655784\pi$
$359$	8.12845	−	25.0168i	0.429003	−	1.32034i	0.899108	−	0.437726i	$-0.144216\pi$
$360$		0			0
$361$	14.9238	−	10.8427i	0.785461	−	0.570671i
$362$	4.95475	+	4.95475i	0.260416	+	0.260416i
$363$		0			0
$364$			0.184093i			0.00964908i
$365$	−0.475287	+	5.34966i	−0.0248776	+	0.280014i
$366$		0			0
$367$	−3.70869	−	7.27872i	−0.193592	−	0.379946i	0.773723	−	0.633524i	$-0.218392\pi$
$367$	−3.70869	−	7.27872i	−0.193592	−	0.379946i	−0.967315	+	0.253579i	$0.918392\pi$
$368$	−1.15002	−	7.26093i	−0.0599488	−	0.378502i
$369$		0			0
$370$	4.46871	−	17.8209i	0.232317	−	0.926463i
$371$	1.64442	−	0.534304i	0.0853740	−	0.0277397i
$372$		0			0
$373$	−6.12473	+	6.12473i	−0.317126	+	0.317126i	−0.847662	−	0.530536i	$-0.821991\pi$
$373$	−6.12473	+	6.12473i	−0.317126	+	0.317126i	0.530536	+	0.847662i	$0.321991\pi$
$374$	−15.7781	−	10.0115i	−0.815864	−	0.517684i
$375$		0			0
$376$	18.6628	+	25.6872i	0.962461	+	1.32471i
$377$	−26.3331	−	13.4174i	−1.35622	−	0.691031i
$378$		0			0
$379$	0.363481	−	0.500288i	0.0186708	−	0.0256981i	−0.799580	−	0.600560i	$-0.794944\pi$
$379$	0.363481	−	0.500288i	0.0186708	−	0.0256981i	0.818250	+	0.574862i	$0.194944\pi$
$380$	0.274326	−	0.437703i	0.0140726	−	0.0224537i
$381$		0			0
$382$	4.36574	−	8.56825i	0.223371	−	0.438390i
$383$	−10.2511	−	1.62362i	−0.523807	−	0.0829629i	−0.111069	−	0.993813i	$-0.535428\pi$
$383$	−10.2511	−	1.62362i	−0.523807	−	0.0829629i	−0.412738	+	0.910850i	$0.635428\pi$
$384$		0			0
$385$	−0.863904	+	1.12696i	−0.0440286	+	0.0574351i
$386$	−9.01683			−0.458945
$387$		0			0
$388$	−0.194444	+	0.381619i	−0.00987142	+	0.0193737i
$389$	−21.0630	−	6.84378i	−1.06794	−	0.346993i	−0.278252	−	0.960508i	$-0.589755\pi$
$389$	−21.0630	−	6.84378i	−1.06794	−	0.346993i	−0.789683	+	0.613515i	$0.789755\pi$
$390$		0			0
$391$	3.53969	−	4.87197i	0.179010	−	0.246386i
$392$	−15.9329	+	8.11822i	−0.804733	+	0.410032i
$393$		0			0
$394$	−12.5157	−	17.2264i	−0.630534	−	0.867855i
$395$	−1.49574	+	0.102571i	−0.0752587	+	0.00516089i
$396$		0			0
$397$	10.7769	−	10.7769i	0.540876	−	0.540876i	−0.382910	−	0.923786i	$-0.625078\pi$
$397$	10.7769	−	10.7769i	0.540876	−	0.540876i	0.923786	+	0.382910i	$0.125078\pi$
$398$	3.18229	−	20.0922i	0.159514	−	1.00713i
$399$		0			0
$400$	3.98847	−	22.2692i	0.199423	−	1.11346i
$401$	−3.46399	−	2.51673i	−0.172983	−	0.125680i	0.497925	−	0.867220i	$-0.334096\pi$
$401$	−3.46399	−	2.51673i	−0.172983	−	0.125680i	−0.670908	+	0.741540i	$0.734096\pi$
$402$		0			0
$403$	−0.493174	−	0.967909i	−0.0245668	−	0.0482150i
$404$	0.463135	+	1.42538i	0.0230418	+	0.0709155i
$405$		0			0
$406$		−	2.77869i		−	0.137904i
$407$	−17.8481	−	1.68589i	−0.884697	−	0.0835664i
$408$		0			0
$409$	−3.47523	+	2.52490i	−0.171839	+	0.124848i	−0.670381	−	0.742017i	$-0.733869\pi$
$409$	−3.47523	+	2.52490i	−0.171839	+	0.124848i	0.498541	+	0.866866i	$0.333869\pi$
$410$	20.9381	+	8.92096i	1.03406	+	0.440575i
$411$		0			0
$412$	0.993106	−	0.157293i	0.0489268	−	0.00774925i
$413$	1.82043	−	0.288327i	0.0895773	−	0.0141877i
$414$		0			0
$415$	−34.3192	−	14.6222i	−1.68466	−	0.717773i
$416$	−4.36224	+	3.16935i	−0.213876	+	0.155390i
$417$		0			0
$418$	−3.44151	−	1.48899i	−0.168330	−	0.0728288i
$419$			1.20241i			0.0587414i	0.999569	+	0.0293707i	$0.00935032\pi$
$419$			1.20241i			0.0587414i	−0.999569	+	0.0293707i	$0.990650\pi$
$420$		0			0
$421$	9.67493	+	29.7764i	0.471527	+	1.45121i	0.850584	+	0.525839i	$0.176248\pi$
$421$	9.67493	+	29.7764i	0.471527	+	1.45121i	−0.379057	+	0.925373i	$0.623752\pi$
$422$	−4.09390	−	8.03473i	−0.199288	−	0.391124i
$423$		0			0
$424$	18.7610	+	13.6307i	0.911117	+	0.661965i
$425$	15.2095	−	10.5890i	0.737771	−	0.513640i
$426$		0			0
$427$	−0.176512	+	1.11445i	−0.00854201	+	0.0539321i
$428$	2.42802	−	2.42802i	0.117363	−	0.117363i
$429$		0			0
$430$	−17.8736	+	1.22568i	−0.861940	+	0.0591078i
$431$	5.81395	+	8.00222i	0.280048	+	0.385453i	0.925750	−	0.378137i	$-0.123435\pi$
$431$	5.81395	+	8.00222i	0.280048	+	0.385453i	−0.645702	+	0.763590i	$0.723435\pi$
$432$		0			0
$433$	−24.0414	+	12.2497i	−1.15536	+	0.588683i	−0.923323	−	0.384025i	$-0.874538\pi$
$433$	−24.0414	+	12.2497i	−1.15536	+	0.588683i	−0.232033	+	0.972708i	$0.574538\pi$
$434$	0.0600332	−	0.0826286i	0.00288169	−	0.00396630i
$435$		0			0
$436$	2.81864	+	0.915831i	0.134988	+	0.0438604i
$437$	0.548629	−	1.07675i	0.0262445	−	0.0515077i
$438$		0			0
$439$	24.5862			1.17344			0.586718	−	0.809791i	$-0.300420\pi$
$439$	24.5862			1.17344			0.586718	+	0.809791i	$0.300420\pi$
$440$	−19.0386	−	0.489593i	−0.907628	−	0.0233404i
$441$		0			0
$442$	−17.2263	−	2.72838i	−0.819372	−	0.129776i
$443$	13.9816	−	27.4404i	0.664286	−	1.30373i	−0.275279	−	0.961364i	$-0.588770\pi$
$443$	13.9816	−	27.4404i	0.664286	−	1.30373i	0.939565	−	0.342370i	$-0.111230\pi$
$444$		0			0
$445$	9.40714	−	15.0096i	0.445941	−	0.711524i
$446$	−18.9912	+	26.1392i	−0.899262	+	1.23773i
$447$		0			0
$448$	1.09215	+	0.556477i	0.0515992	+	0.0262911i
$449$	−4.30536	−	5.92582i	−0.203182	−	0.279657i	0.695250	−	0.718768i	$-0.255293\pi$
$449$	−4.30536	−	5.92582i	−0.203182	−	0.279657i	−0.898433	+	0.439111i	$0.855293\pi$
$450$		0			0
$451$	5.52141	−	21.5107i	0.259993	−	1.01290i
$452$	0.910918	−	0.910918i	0.0428460	−	0.0428460i
$453$		0			0
$454$	18.8951	−	6.13938i	0.886789	−	0.288135i
$455$	−0.322363	+	1.28556i	−0.0151126	+	0.0602678i
$456$		0			0
$457$	1.05368	+	6.65265i	0.0492889	+	0.311198i	0.999999	+	0.00111791i	$0.000355842\pi$
$457$	1.05368	+	6.65265i	0.0492889	+	0.311198i	−0.950710	+	0.310080i	$0.899644\pi$
$458$	11.3390	+	22.2540i	0.529837	+	1.03986i
$459$		0			0
$460$	−0.0998565	+	1.12395i	−0.00465583	+	0.0524044i
$461$		−	29.0801i		−	1.35440i	−0.735801	−	0.677198i	$-0.763194\pi$
$461$		−	29.0801i		−	1.35440i	0.735801	−	0.677198i	$-0.236806\pi$
$462$		0			0
$463$	17.5146	+	17.5146i	0.813970	+	0.813970i	0.985227	−	0.171256i	$-0.0547826\pi$
$463$	17.5146	+	17.5146i	0.813970	+	0.813970i	−0.171256	+	0.985227i	$0.554783\pi$
$464$	34.9482	−	25.3914i	1.62243	−	1.17876i
$465$		0			0
$466$	7.34819	−	22.6154i	0.340398	−	1.04764i
$467$	26.1320	−	4.13890i	1.20924	−	0.191525i	0.480923	−	0.876763i	$-0.340302\pi$
$467$	26.1320	−	4.13890i	1.20924	−	0.191525i	0.728320	+	0.685237i	$0.240302\pi$
$468$		0			0
$469$	0.345938	−	1.06469i	0.0159739	−	0.0491627i
$470$	−15.6904	−	38.9861i	−0.723746	−	1.79830i
$471$		0			0
$472$	17.4796	+	17.4796i	0.804563	+	0.804563i
$473$	3.81467	+	17.0603i	0.175399	+	0.784432i
$474$		0			0
$475$	2.68213	−	2.57620i	0.123065	−	0.118204i
$476$	−0.0681145	−	0.209635i	−0.00312202	−	0.00960860i
$477$		0			0
$478$	1.25594	+	7.92972i	0.0574455	+	0.362697i
$479$	21.2408	+	15.4324i	0.970519	+	0.705123i	0.955570	−	0.294765i	$-0.0952413\pi$
$479$	21.2408	+	15.4324i	0.970519	+	0.705123i	0.0149492	+	0.999888i	$0.495241\pi$
$480$		0			0
$481$	−15.9139	+	5.17073i	−0.725610	+	0.235765i
$482$	−3.84449	+	24.2731i	−0.175112	+	1.10561i
$483$		0			0
$484$	−0.428672	−	3.38950i	−0.0194851	−	0.154068i
$485$	−2.02609	+	2.32443i	−0.0920001	+	0.105547i
$486$		0			0
$487$	−20.7917	−	10.5939i	−0.942163	−	0.480056i	−0.0857326	−	0.996318i	$-0.527323\pi$
$487$	−20.7917	−	10.5939i	−0.942163	−	0.480056i	−0.856431	+	0.516262i	$0.827323\pi$
$488$	−13.4839	+	6.87039i	−0.610388	+	0.311008i
$489$		0			0
$490$	23.0687	−	5.29315i	1.04214	−	0.239120i
$491$	−17.4497	−	5.66974i	−0.787493	−	0.255872i	−0.112457	−	0.993657i	$-0.535872\pi$
$491$	−17.4497	−	5.66974i	−0.787493	−	0.255872i	−0.675036	+	0.737785i	$0.735872\pi$
$492$		0			0
$493$	34.9512	+	5.53572i	1.57412	+	0.249316i
$494$	−3.49992			−0.157469
$495$		0			0
$496$	1.58781			0.0712949
$497$	−2.16757	−	0.343309i	−0.0972286	−	0.0153995i
$498$		0			0
$499$	−11.1824	−	3.63339i	−0.500595	−	0.162653i	0.0478260	−	0.998856i	$-0.484771\pi$
$499$	−11.1824	−	3.63339i	−0.500595	−	0.162653i	−0.548421	+	0.836203i	$0.684771\pi$
$500$	−1.42519	+	3.16657i	−0.0637363	+	0.141613i
$501$		0			0
$502$	−26.1975	+	13.3483i	−1.16925	+	0.595763i
$503$	4.75855	+	2.42460i	0.212173	+	0.108108i	0.556848	−	0.830615i	$-0.312011\pi$
$503$	4.75855	+	2.42460i	0.212173	+	0.108108i	−0.344674	+	0.938722i	$0.612011\pi$
$504$		0			0
$505$	0.738195	+	10.7647i	0.0328492	+	0.479025i
$506$	8.17484	−	0.514888i	0.363416	−	0.0228896i
$507$		0			0
$508$	0.707777	−	4.46873i	0.0314025	−	0.198268i
$509$	−18.6283	+	6.05272i	−0.825687	+	0.268282i	−0.691228	−	0.722637i	$-0.742930\pi$
$509$	−18.6283	+	6.05272i	−0.825687	+	0.268282i	−0.134459	+	0.990919i	$0.542930\pi$
$510$		0			0
$511$	0.372057	+	0.270315i	0.0164588	+	0.0119580i
$512$	2.40248	+	15.1686i	0.106175	+	0.670365i
$513$		0			0
$514$	2.21058	+	6.80347i	0.0975046	+	0.300088i
$515$	7.21050	+	0.640611i	0.317732	+	0.0282287i
$516$		0			0
$517$	−35.2950	+	20.8767i	−1.55227	+	0.918158i
$518$	−1.11243	−	1.11243i	−0.0488775	−	0.0488775i
$519$		0			0
$520$	−16.4903	+	6.63672i	−0.723147	+	0.291039i
$521$	−5.78913	+	17.8171i	−0.253626	+	0.780582i	0.740471	+	0.672089i	$0.234603\pi$
$521$	−5.78913	+	17.8171i	−0.253626	+	0.780582i	−0.994097	+	0.108493i	$0.965397\pi$
$522$		0			0
$523$	−2.55051	+	0.403961i	−0.111526	+	0.0176640i	−0.211948	−	0.977281i	$-0.567981\pi$
$523$	−2.55051	+	0.403961i	−0.111526	+	0.0176640i	0.100422	+	0.994945i	$0.467981\pi$
$524$	0.937631	−	2.88573i	0.0409606	−	0.126064i
$525$		0			0
$526$	−19.5162	+	14.1794i	−0.850948	+	0.618250i
$527$	0.919727	+	0.919727i	0.0400639	+	0.0400639i
$528$		0			0
$529$		−	20.3603i		−	0.885228i
$530$	−19.6979	−	23.5393i	−0.855622	−	1.02248i
$531$		0			0
$532$	−0.0200812	−	0.0394115i	−0.000870630	−	0.00170871i
$533$	−3.24258	−	20.4729i	−0.140452	−	0.886778i
$534$		0			0
$535$	21.2071	−	12.7037i	0.916862	−	0.549229i
$536$	14.2796	−	4.63972i	0.616784	−	0.200405i
$537$		0			0
$538$	12.1591	−	12.1591i	0.524216	−	0.524216i
$539$	−8.50325	−	21.4724i	−0.366261	−	0.924881i
$540$		0			0
$541$	5.42829	+	7.47139i	0.233380	+	0.321220i	0.909604	−	0.415476i	$-0.136385\pi$
$541$	5.42829	+	7.47139i	0.233380	+	0.321220i	−0.676224	+	0.736696i	$0.736385\pi$
$542$	−24.1462	−	12.3031i	−1.03717	−	0.528464i
$543$		0			0
$544$	3.79482	−	5.22312i	0.162701	−	0.223939i
$545$	18.0794	+	11.3311i	0.774438	+	0.485372i
$546$		0			0
$547$	0.486237	−	0.954295i	0.0207900	−	0.0408027i	−0.880378	−	0.474273i	$-0.842711\pi$
$547$	0.486237	−	0.954295i	0.0207900	−	0.0408027i	0.901168	+	0.433470i	$0.142711\pi$
$548$	−1.32834	−	0.210388i	−0.0567437	−	0.00898732i
$549$		0			0
$550$	24.2847	+	6.75764i	1.03550	+	0.288147i
$551$	7.10113			0.302518
$552$		0			0
$553$	−0.0582826	+	0.114386i	−0.00247843	+	0.00486419i
$554$	6.76800	+	2.19906i	0.287545	+	0.0934290i
$555$		0			0
$556$	1.91881	−	2.64102i	0.0813758	−	0.112004i
$557$	38.3462	−	19.5384i	1.62478	−	0.827868i	0.625934	−	0.779876i	$-0.284718\pi$
$557$	38.3462	−	19.5384i	1.62478	−	0.827868i	0.998848	−	0.0479915i	$-0.0152820\pi$
$558$		0			0
$559$	9.59064	+	13.2004i	0.405641	+	0.558316i
$560$	−1.46033	−	1.27290i	−0.0617102	−	0.0537897i
$561$		0			0
$562$	−14.1765	+	14.1765i	−0.597998	+	0.597998i
$563$	−4.04575	+	25.5439i	−0.170508	+	1.07655i	0.742871	+	0.669435i	$0.233464\pi$
$563$	−4.04575	+	25.5439i	−0.170508	+	1.07655i	−0.913379	+	0.407111i	$0.866536\pi$
$564$		0			0
$565$	7.95622	−	4.76603i	0.334721	−	0.200508i
$566$	−28.0219	−	20.3591i	−1.17785	−	0.855756i
$567$		0			0
$568$	−13.3626	−	26.2257i	−0.560684	−	1.10040i
$569$	8.39651	+	25.8418i	0.352000	+	1.08334i	0.957729	+	0.287673i	$0.0928816\pi$
$569$	8.39651	+	25.8418i	0.352000	+	1.08334i	−0.605729	+	0.795671i	$0.707118\pi$
$570$		0			0
$571$			40.5475i			1.69686i	0.529308	+	0.848430i	$0.322451\pi$
$571$			40.5475i			1.69686i	−0.529308	+	0.848430i	$0.677549\pi$
$572$	−1.62343	−	2.74464i	−0.0678791	−	0.114759i
$573$		0			0
$574$	1.57665	−	1.14550i	0.0658081	−	0.0478124i
$575$	−2.66546	+	7.67392i	−0.111157	+	0.320024i
$576$		0			0
$577$	33.3917	−	5.28872i	1.39011	−	0.220172i	0.583914	−	0.811815i	$-0.301521\pi$
$577$	33.3917	−	5.28872i	1.39011	−	0.220172i	0.806200	+	0.591643i	$0.201521\pi$
$578$	−4.89703	+	0.775613i	−0.203689	+	0.0322612i
$579$		0			0
$580$	−6.15107	+	2.47558i	−0.255409	+	0.102793i
$581$	−2.58426	+	1.87757i	−0.107213	+	0.0778948i
$582$		0			0
$583$	−19.8048	+	22.4673i	−0.820233	+	0.930502i
$584$			6.16801i			0.255234i
$585$		0			0
$586$	−3.39505	−	10.4489i	−0.140248	−	0.431640i
$587$	4.39649	+	8.62859i	0.181462	+	0.356140i	0.963763	−	0.266762i	$-0.0859536\pi$
$587$	4.39649	+	8.62859i	0.181462	+	0.356140i	−0.782300	+	0.622902i	$0.785954\pi$
$588$		0			0
$589$	0.211163	+	0.153419i	0.00870081	+	0.00632151i
$590$	−16.8137	−	28.0681i	−0.692207	−	1.15554i
$591$		0			0
$592$	3.82603	−	24.1566i	0.157249	−	0.992829i
$593$	−14.0452	+	14.0452i	−0.576769	+	0.576769i	−0.934012	−	0.357243i	$-0.883717\pi$
$593$	−14.0452	+	14.0452i	−0.576769	+	0.576769i	0.357243	+	0.934012i	$0.383717\pi$
$594$		0			0
$595$	−0.108568	−	1.58320i	−0.00445086	−	0.0649048i
$596$	−1.05199	−	1.44794i	−0.0430912	−	0.0593099i
$597$		0			0
$598$	6.81191	−	3.47084i	0.278560	−	0.141933i
$599$	2.65433	−	3.65338i	0.108453	−	0.149273i	−0.751340	−	0.659915i	$-0.770592\pi$
$599$	2.65433	−	3.65338i	0.108453	−	0.149273i	0.859793	+	0.510642i	$0.170592\pi$
$600$		0			0
$601$	−7.96746	−	2.58878i	−0.324999	−	0.105599i	0.141973	−	0.989871i	$-0.454655\pi$
$601$	−7.96746	−	2.58878i	−0.324999	−	0.105599i	−0.466973	+	0.884272i	$0.654655\pi$
$602$	−0.696458	+	1.36688i	−0.0283855	+	0.0557097i
$603$		0			0
$604$	−4.64774			−0.189114
$605$	2.94181	−	24.4202i	0.119601	−	0.992822i
$606$		0			0
$607$	−7.58425	−	1.20123i	−0.307835	−	0.0487563i	0.000605683	−	1.00000i	$-0.499807\pi$
$607$	−7.58425	−	1.20123i	−0.307835	−	0.0487563i	−0.308441	+	0.951244i	$0.599807\pi$
$608$	0.588172	−	1.15435i	0.0238535	−	0.0468152i
$609$		0			0
$610$	19.5229	−	4.47955i	0.790457	−	0.181372i
$611$	−22.4971	+	30.9646i	−0.910134	+	1.25269i
$612$		0			0
$613$	38.2477	+	19.4882i	1.54481	+	0.787120i	0.998719	−	0.0506058i	$-0.0161152\pi$
$613$	38.2477	+	19.4882i	1.54481	+	0.787120i	0.546091	+	0.837726i	$0.316115\pi$
$614$	25.4319	+	35.0041i	1.02635	+	1.41265i
$615$		0			0
$616$	−0.873721	+	1.37698i	−0.0352032	+	0.0554799i
$617$	−33.4407	+	33.4407i	−1.34627	+	1.34627i	−0.456601	+	0.889671i	$0.650933\pi$
$617$	−33.4407	+	33.4407i	−1.34627	+	1.34627i	−0.889671	+	0.456601i	$0.849067\pi$
$618$		0			0
$619$	20.0674	−	6.52029i	0.806576	−	0.262073i	0.123429	−	0.992353i	$-0.460611\pi$
$619$	20.0674	−	6.52029i	0.806576	−	0.262073i	0.683147	+	0.730281i	$0.260611\pi$
$620$	−0.236396	−	0.0592779i	−0.00949388	−	0.00238066i
$621$		0			0
$622$	−1.78720	−	11.2840i	−0.0716603	−	0.452445i
$623$	−0.688620	−	1.35149i	−0.0275890	−	0.0541464i
$624$		0			0
$625$	−15.4973	+	19.6172i	−0.619892	+	0.784687i
$626$			2.04613i			0.0817798i
$627$		0			0
$628$	1.08671	+	1.08671i	0.0433645	+	0.0433645i
$629$	16.2087	−	11.7763i	0.646282	−	0.469552i
$630$		0			0
$631$	−8.72043	+	26.8387i	−0.347155	+	1.06843i	0.613265	+	0.789877i	$0.289856\pi$
$631$	−8.72043	+	26.8387i	−0.347155	+	1.06843i	−0.960420	+	0.278555i	$0.910144\pi$
$632$	−1.70061	+	0.269351i	−0.0676467	+	0.0107142i
$633$		0			0
$634$	−5.32290	+	16.3822i	−0.211399	+	0.650621i
$635$	12.7677	−	29.9667i	0.506671	−	1.18919i
$636$		0			0
$637$	−15.2422	−	15.2422i	−0.603918	−	0.603918i
$638$	24.5041	+	41.4275i	0.970125	+	1.64013i
$639$		0			0
$640$	2.61496	−	29.4330i	0.103365	−	1.16344i
$641$	5.23436	+	16.1097i	0.206745	+	0.636295i	0.999637	+	0.0269333i	$0.00857417\pi$
$641$	5.23436	+	16.1097i	0.206745	+	0.636295i	−0.792893	+	0.609362i	$0.791426\pi$
$642$		0			0
$643$	0.981726	+	6.19838i	0.0387155	+	0.244440i	0.999455	−	0.0330121i	$-0.0105100\pi$
$643$	0.981726	+	6.19838i	0.0387155	+	0.244440i	−0.960739	+	0.277452i	$0.910510\pi$
$644$	0.0781682	+	0.0567925i	0.00308026	+	0.00223794i
$645$		0			0
$646$	3.98552	−	1.29497i	0.156808	−	0.0509500i
$647$	6.80289	−	42.9518i	0.267449	−	1.68861i	−0.378798	−	0.925479i	$-0.623662\pi$
$647$	6.80289	−	42.9518i	0.267449	−	1.68861i	0.646247	−	0.763128i	$-0.276338\pi$
$648$		0			0
$649$	−24.5981	+	20.3522i	−0.965559	+	0.798893i
$650$	23.3073	−	3.21171i	0.914188	−	0.125974i
$651$		0			0
$652$	−2.77200	−	1.41240i	−0.108560	−	0.0553140i
$653$	−8.67042	+	4.41780i	−0.339300	+	0.172882i	−0.615335	−	0.788266i	$-0.710979\pi$
$653$	−8.67042	+	4.41780i	−0.339300	+	0.172882i	0.276035	+	0.961147i	$0.410979\pi$
$654$		0			0
$655$	11.6008	−	18.5098i	0.453283	−	0.723237i
$656$	28.8145	+	9.36239i	1.12502	+	0.365540i
$657$		0			0
$658$	−3.55424	−	0.562936i	−0.138559	−	0.0219455i
$659$	−3.37375			−0.131423			−0.0657113	−	0.997839i	$-0.520932\pi$
$659$	−3.37375			−0.131423			−0.0657113	+	0.997839i	$0.520932\pi$
$660$		0			0
$661$	9.93056			0.386254			0.193127	−	0.981174i	$-0.438137\pi$
$661$	9.93056			0.386254			0.193127	+	0.981174i	$0.438137\pi$
$662$	26.5811	+	4.21003i	1.03310	+	0.163628i
$663$		0			0
$664$	−40.7453	−	13.2389i	−1.58122	−	0.513771i
$665$	−0.0712179	−	0.310383i	−0.00276171	−	0.0120361i
$666$		0			0
$667$	−13.8210	+	7.04213i	−0.535150	+	0.272672i
$668$	−3.33809	−	1.70084i	−0.129154	−	0.0658075i
$669$		0			0
$670$	−19.8263	+	1.35959i	−0.765955	+	0.0525256i
$671$	−7.19624	−	18.1719i	−0.277808	−	0.701520i
$672$		0			0
$673$	5.98412	−	37.7823i	0.230671	−	1.45640i	−0.551938	−	0.833885i	$-0.686111\pi$
$673$	5.98412	−	37.7823i	0.230671	−	1.45640i	0.782609	−	0.622514i	$-0.213889\pi$
$674$	−11.0161	+	3.57935i	−0.424324	+	0.137871i
$675$		0			0
$676$	0.858662	+	0.623855i	0.0330255	+	0.0239944i
$677$	−5.03592	−	31.7956i	−0.193546	−	1.22200i	−0.872792	−	0.488092i	$-0.837693\pi$
$677$	−5.03592	−	31.7956i	−0.193546	−	1.22200i	0.679246	−	0.733911i	$-0.262307\pi$
$678$		0			0
$679$	0.0815917	+	0.251113i	0.00313120	+	0.00963684i
$680$	16.3226	−	13.6590i	0.625945	−	0.523797i
$681$		0			0
$682$	−0.166370	+	1.76132i	−0.00637063	+	0.0674443i
$683$	28.7223	+	28.7223i	1.09903	+	1.09903i	0.994524	+	0.104505i	$0.0333260\pi$
$683$	28.7223	+	28.7223i	1.09903	+	1.09903i	0.104505	+	0.994524i	$0.466674\pi$
$684$		0			0
$685$	−8.90764	−	3.79522i	−0.340343	−	0.145008i
$686$	1.25585	−	3.86510i	0.0479484	−	0.147570i
$687$		0			0
$688$	−23.5556	+	3.73084i	−0.898050	+	0.142237i
$689$	−8.63834	+	26.5861i	−0.329095	+	1.01285i
$690$		0			0
$691$	20.4397	−	14.8503i	0.777564	−	0.564933i	−0.126683	−	0.991943i	$-0.540433\pi$
$691$	20.4397	−	14.8503i	0.777564	−	0.564933i	0.904247	+	0.427010i	$0.140433\pi$
$692$	2.73759	+	2.73759i	0.104068	+	0.104068i
$693$		0			0
$694$			14.1878i			0.538562i
$695$	18.0241	−	15.0828i	0.683694	−	0.572122i
$696$		0			0
$697$	11.2675	+	22.1136i	0.426785	+	0.837613i
$698$	0.357107	+	2.25468i	0.0135167	+	0.0853410i
$699$		0			0
$700$	0.169895	+	0.244029i	0.00642141	+	0.00922344i
$701$	−26.8458	+	8.72273i	−1.01395	+	0.329453i	−0.768427	−	0.639937i	$-0.778960\pi$
$701$	−26.8458	+	8.72273i	−1.01395	+	0.329453i	−0.245525	+	0.969390i	$0.578960\pi$
$702$		0			0
$703$	2.84289	−	2.84289i	0.107222	−	0.107222i
$704$	−21.1902	+	1.33465i	−0.798634	+	0.0503015i
$705$		0			0
$706$	5.56255	+	7.65620i	0.209349	+	0.288145i
$707$	0.823230	+	0.419457i	0.0309608	+	0.0157753i
$708$		0			0
$709$	−4.79615	+	6.60134i	−0.180123	+	0.247918i	−0.889526	−	0.456885i	$-0.848965\pi$
$709$	−4.79615	+	6.60134i	−0.180123	+	0.247918i	0.709402	+	0.704804i	$0.248965\pi$
$710$	8.71256	+	37.9712i	0.326977	+	1.42503i
$711$		0			0
$712$	9.23576	−	18.1262i	0.346125	−	0.679308i
$713$	−0.563131	−	0.0891912i	−0.0210894	−	0.00334024i
$714$		0			0
$715$	−6.53065	−	22.0091i	−0.244232	−	0.823095i
$716$	6.26727			0.234219
$717$		0			0
$718$	−18.1524	+	35.6261i	−0.677441	+	1.32955i
$719$	0.986856	+	0.320649i	0.0368035	+	0.0119582i	0.327361	−	0.944899i	$-0.393841\pi$
$719$	0.986856	+	0.320649i	0.0368035	+	0.0119582i	−0.290557	+	0.956858i	$0.593841\pi$
$720$		0			0
$721$	0.364342	−	0.501474i	0.0135688	−	0.0186759i
$722$	−24.9840	+	12.7300i	−0.929810	+	0.473762i
$723$		0			0
$724$	−0.841554	−	1.15830i	−0.0312761	−	0.0430479i
$725$	−47.2892	+	6.51637i	−1.75627	+	0.242012i
$726$		0			0
$727$	−3.27903	+	3.27903i	−0.121612	+	0.121612i	−0.765294	−	0.643681i	$-0.777406\pi$
$727$	−3.27903	+	3.27903i	−0.121612	+	0.121612i	0.643681	+	0.765294i	$0.277406\pi$
$728$	−0.238110	+	1.50337i	−0.00882493	+	0.0557184i
$729$		0			0
$730$	1.98567	−	7.91869i	0.0734929	−	0.293084i
$731$	−15.8055	−	11.4833i	−0.584586	−	0.424726i
$732$		0			0
$733$	20.7361	+	40.6968i	0.765904	+	1.50317i	0.861504	+	0.507751i	$0.169523\pi$
$733$	20.7361	+	40.6968i	0.765904	+	1.50317i	−0.0956003	+	0.995420i	$0.530477\pi$
$734$	3.83723	+	11.8098i	0.141635	+	0.435907i
$735$		0			0
$736$			2.83001i			0.104315i
$737$	4.23142	+	18.9241i	0.155866	+	0.697079i
$738$		0			0
$739$	3.07164	−	2.23167i	0.112992	−	0.0820934i	−0.529854	−	0.848089i	$-0.677753\pi$
$739$	3.07164	−	2.23167i	0.112992	−	0.0820934i	0.642846	+	0.765995i	$0.277753\pi$
$740$	−1.47146	+	3.45363i	−0.0540920	+	0.126958i
$741$		0			0
$742$	−2.59590	+	0.411150i	−0.0952984	+	0.0150938i
$743$	41.9067	−	6.63736i	1.53741	−	0.243501i	0.670476	−	0.741931i	$-0.266090\pi$
$743$	41.9067	−	6.63736i	1.53741	−	0.243501i	0.866930	+	0.498430i	$0.166090\pi$
$744$		0			0
$745$	−4.81079	−	11.9534i	−0.176254	−	0.437938i
$746$	10.6517	−	7.73895i	0.389988	−	0.283343i
$747$		0			0
$748$	2.86419	+	2.52477i	0.104725	+	0.0923149i
$749$		−	2.11681i		−	0.0773467i
$750$		0			0
$751$	−3.08775	−	9.50312i	−0.112674	−	0.346774i	0.878781	−	0.477225i	$-0.158357\pi$
$751$	−3.08775	−	9.50312i	−0.112674	−	0.346774i	−0.991455	+	0.130451i	$0.958357\pi$
$752$	−25.3980	−	49.8464i	−0.926171	−	1.81771i
$753$		0			0
$754$	36.3446	+	26.4059i	1.32359	+	0.961647i
$755$	−32.4561	−	8.13861i	−1.18120	−	0.296194i
$756$		0			0
$757$	4.59658	−	29.0217i	0.167065	−	1.05481i	−0.751555	−	0.659670i	$-0.770696\pi$
$757$	4.59658	−	29.0217i	0.167065	−	1.05481i	0.918621	−	0.395140i	$-0.129304\pi$
$758$	−0.664675	+	0.664675i	−0.0241421	+	0.0241421i
$759$		0			0
$760$	2.80638	−	3.21961i	0.101798	−	0.116788i
$761$	17.8404	+	24.5552i	0.646713	+	0.890124i	0.998951	−	0.0457864i	$-0.0145794\pi$
$761$	17.8404	+	24.5552i	0.646713	+	0.890124i	−0.352238	+	0.935910i	$0.614579\pi$
$762$		0			0
$763$	1.62790	−	0.829459i	0.0589341	−	0.0300284i
$764$	−1.15493	+	1.58963i	−0.0417840	+	0.0575107i
$765$		0			0
$766$	15.0044	+	4.87523i	0.542131	+	0.176149i
$767$	−13.5283	+	26.5507i	−0.488477	+	0.958690i
$768$		0			0
$769$	−37.6421			−1.35741			−0.678705	−	0.734411i	$-0.737458\pi$
$769$	−37.6421			−1.35741			−0.678705	+	0.734411i	$0.737458\pi$
$770$	1.56500	−	1.48653i	0.0563987	−	0.0535707i
$771$		0			0
$772$	1.81970	+	0.288213i	0.0654926	+	0.0103730i
$773$	11.7188	−	22.9995i	0.421497	−	0.827234i	−0.578437	−	0.815727i	$-0.696337\pi$
$773$	11.7188	−	22.9995i	0.421497	−	0.827234i	0.999934	−	0.0115072i	$-0.00366294\pi$
$774$		0			0
$775$	−1.54700	−	0.827900i	−0.0555698	−	0.0297390i
$776$	−2.08149	+	2.86493i	−0.0747213	+	0.102845i
$777$		0			0
$778$	29.9955	+	15.2835i	1.07539	+	0.547939i
$779$	2.92741	+	4.02923i	0.104885	+	0.144362i
$780$		0			0
$781$	35.3437	−	13.9964i	1.26470	−	0.500831i
$782$	−6.47282	+	6.47282i	−0.231467	+	0.231467i
$783$		0			0
$784$	29.9651	−	9.73624i	1.07018	−	0.347723i
$785$	5.68579	+	9.49165i	0.202935	+	0.338771i
$786$		0			0
$787$	2.70244	+	17.0625i	0.0963315	+	0.608213i	0.987872	+	0.155272i	$0.0496254\pi$
$787$	2.70244	+	17.0625i	0.0963315	+	0.608213i	−0.891540	+	0.452942i	$0.850375\pi$
$788$	1.97520	+	3.87655i	0.0703636	+	0.138096i
$789$		0			0
$790$	2.27001	+	0.201678i	0.0807634	+	0.00717537i
$791$		−	0.794162i		−	0.0282372i
$792$		0			0
$793$	−12.8994	−	12.8994i	−0.458070	−	0.458070i
$794$	−18.7425	+	13.6172i	−0.665145	+	0.483256i
$795$		0			0
$796$	−1.28445	+	3.95313i	−0.0455261	+	0.140115i
$797$	44.0203	−	6.97213i	1.55928	−	0.246965i	0.683599	−	0.729858i	$-0.260414\pi$
$797$	44.0203	−	6.97213i	1.55928	−	0.246965i	0.875680	+	0.482892i	$0.160414\pi$
$798$		0			0
$799$	14.1615	−	43.5847i	0.500999	−	1.54192i
$800$	−2.85757	+	8.22702i	−0.101030	+	0.290869i
$801$		0			0
$802$	4.60219	+	4.60219i	0.162509	+	0.162509i
$803$	−7.93078	−	0.749124i	−0.279871	−	0.0264360i
$804$		0			0
$805$	0.446416	+	0.533473i	0.0157341	+	0.0188025i
$806$	0.510267	+	1.57044i	0.0179734	+	0.0553164i
$807$		0			0
$808$	1.93850	+	12.2392i	0.0681962	+	0.430574i
$809$	12.3255	+	8.95497i	0.433340	+	0.314840i	0.782983	−	0.622043i	$-0.213697\pi$
$809$	12.3255	+	8.95497i	0.433340	+	0.314840i	−0.349643	+	0.936883i	$0.613697\pi$
$810$		0			0
$811$	−43.3276	+	14.0780i	−1.52144	+	0.494345i	−0.946183	−	0.323631i	$-0.895096\pi$
$811$	−43.3276	+	14.0780i	−1.52144	+	0.494345i	−0.575253	+	0.817976i	$0.695096\pi$
$812$	−0.0888178	+	0.560774i	−0.00311689	+	0.0196793i
$813$		0			0
$814$	26.3953	+	6.77521i	0.925155	+	0.237471i
$815$	−16.8842	−	14.7171i	−0.591427	−	0.515518i
$816$		0			0
$817$	−3.49314	−	1.77984i	−0.122209	−	0.0622688i
$818$	5.81793	−	2.96438i	0.203419	−	0.103647i
$819$		0			0
$820$	−3.94041	−	2.46962i	−0.137605	−	0.0862428i
$821$	27.3071	+	8.87260i	0.953023	+	0.309656i	0.743943	−	0.668243i	$-0.232953\pi$
$821$	27.3071	+	8.87260i	0.953023	+	0.309656i	0.209079	+	0.977899i	$0.432953\pi$
$822$		0			0
$823$	−26.6252	−	4.21701i	−0.928095	−	0.146996i	−0.325954	−	0.945386i	$-0.605686\pi$
$823$	−26.6252	−	4.21701i	−0.928095	−	0.146996i	−0.602141	+	0.798390i	$0.705686\pi$
$824$	8.31350			0.289614
$825$		0			0
$826$	−2.80165			−0.0974820
$827$	−39.1944	−	6.20779i	−1.36292	−	0.215866i	−0.568227	−	0.822872i	$-0.692370\pi$
$827$	−39.1944	−	6.20779i	−1.36292	−	0.215866i	−0.794697	+	0.607006i	$0.792370\pi$
$828$		0			0
$829$	−10.3353	−	3.35814i	−0.358959	−	0.116633i	0.123985	−	0.992284i	$-0.460433\pi$
$829$	−10.3353	−	3.35814i	−0.358959	−	0.116633i	−0.482944	+	0.875651i	$0.660433\pi$
$830$	48.0481	+	30.1137i	1.66777	+	1.04526i
$831$		0			0
$832$	−17.6573	+	8.99683i	−0.612156	+	0.311909i
$833$	22.9966	+	11.7174i	0.796786	+	0.405983i
$834$		0			0
$835$	−20.3322	−	17.7226i	−0.703625	−	0.613316i
$836$	0.646943	+	0.410500i	0.0223750	+	0.0141974i
$837$		0			0
$838$	0.285920	−	1.80523i	0.00987695	−	0.0623606i
$839$	−38.3426	+	12.4583i	−1.32373	+	0.430107i	−0.883775	−	0.467912i	$-0.845007\pi$
$839$	−38.3426	+	12.4583i	−1.32373	+	0.430107i	−0.439958	+	0.898019i	$0.645007\pi$
$840$		0			0
$841$	−50.2797	−	36.5303i	−1.73378	−	1.25967i
$842$	−7.44491	−	47.0053i	−0.256569	−	1.61991i
$843$		0			0
$844$	0.569376	+	1.75236i	0.0195987	+	0.0603187i
$845$	4.90379	+	5.86010i	0.168695	+	0.201593i
$846$		0			0
$847$	−1.66439	−	1.29066i	−0.0571891	−	0.0443477i
$848$	−28.8921	−	28.8921i	−0.992159	−	0.992159i
$849$		0			0
$850$	−25.3528	+	12.2810i	−0.869593	+	0.421237i
$851$	−2.71386	+	8.35241i	−0.0930300	+	0.286317i
$852$		0			0
$853$	13.7845	−	2.18326i	0.471974	−	0.0747533i	0.0840831	−	0.996459i	$-0.473204\pi$
$853$	13.7845	−	2.18326i	0.471974	−	0.0747533i	0.387890	+	0.921705i	$0.373204\pi$
$854$	0.530012	−	1.63121i	0.0181366	−	0.0558188i
$855$		0			0
$856$	22.9686	−	16.6876i	0.785049	−	0.570372i
$857$	26.9229	+	26.9229i	0.919668	+	0.919668i	0.997005	−	0.0773373i	$-0.0246418\pi$
$857$	26.9229	+	26.9229i	0.919668	+	0.919668i	−0.0773373	+	0.997005i	$0.524642\pi$
$858$		0			0
$859$		−	18.3200i		−	0.625071i	−0.949906	−	0.312535i	$-0.898822\pi$
$859$		−	18.3200i		−	0.625071i	0.949906	−	0.312535i	$-0.101178\pi$
$860$	3.64628	+	0.323951i	0.124337	+	0.0110466i
$861$		0			0
$862$	−6.82592	−	13.3966i	−0.232492	−	0.456291i
$863$	1.90114	+	12.0033i	0.0647154	+	0.408597i	0.998686	+	0.0512472i	$0.0163196\pi$
$863$	1.90114	+	12.0033i	0.0647154	+	0.408597i	−0.933971	+	0.357350i	$0.883680\pi$
$864$		0			0
$865$	14.3234	+	23.9109i	0.487010	+	0.812996i
$866$	39.0074	−	12.6743i	1.32552	−	0.430689i
$867$		0			0
$868$	−0.0147565	+	0.0147565i	−0.000500870	+	0.000500870i
$869$	−0.139785	−	2.21935i	−0.00474187	−	0.0752863i
$870$		0			0
$871$	10.6384	+	14.6425i	0.360469	+	0.496143i
$872$	21.8334	+	11.1247i	0.739374	+	0.376730i
$873$		0			0
$874$	−1.07972	+	1.48611i	−0.0365222	+	0.0502685i
$875$	0.759091	+	2.00161i	0.0256620	+	0.0676666i
$876$		0			0
$877$	−5.82698	+	11.4361i	−0.196763	+	0.386169i	−0.968215	−	0.250118i	$-0.919531\pi$
$877$	−5.82698	+	11.4361i	−0.196763	+	0.386169i	0.771452	+	0.636287i	$0.219531\pi$
$878$	−36.9125	−	5.84636i	−1.24574	−	0.197305i
$879$		0			0
$880$	32.9971	+	6.09963i	1.11233	+	0.205618i
$881$	−13.8380			−0.466216			−0.233108	−	0.972451i	$-0.574890\pi$
$881$	−13.8380			−0.466216			−0.233108	+	0.972451i	$0.574890\pi$
$882$		0			0
$883$	−19.7888	+	38.8377i	−0.665947	+	1.30699i	0.272695	+	0.962100i	$0.412085\pi$
$883$	−19.7888	+	38.8377i	−0.665947	+	1.30699i	−0.938642	+	0.344893i	$0.887915\pi$
$884$	3.38926	+	1.10124i	0.113993	+	0.0370387i
$885$		0			0
$886$	−27.5163	+	37.8730i	−0.924429	+	1.27237i
$887$	9.26576	−	4.72114i	0.311114	−	0.158520i	−0.291461	−	0.956583i	$-0.594141\pi$
$887$	9.26576	−	4.72114i	0.311114	−	0.158520i	0.602575	+	0.798062i	$0.294141\pi$
$888$		0			0
$889$	−1.63945	−	2.25651i	−0.0549853	−	0.0756808i
$890$	−17.6925	+	20.2977i	−0.593055	+	0.680381i
$891$		0			0
$892$	4.66817	−	4.66817i	0.156302	−	0.156302i
$893$	1.43862	−	9.08308i	0.0481415	−	0.303954i
$894$		0			0
$895$	43.7656	+	10.9745i	1.46292	+	0.366838i
$896$	−2.04700	−	1.48723i	−0.0683855	−	0.0496850i
$897$		0			0
$898$	5.05474	+	9.92048i	0.168679	+	0.331051i
$899$	−1.03530	−	3.18633i	−0.0345292	−	0.106270i
$900$		0			0
$901$		−	33.4710i		−	1.11508i
$902$	−13.4046	+	30.9821i	−0.446324	+	1.03159i
$903$		0			0
$904$	8.61708	−	6.26067i	0.286600	−	0.208227i
$905$	−3.84846	−	9.56228i	−0.127927	−	0.317861i
$906$		0			0
$907$	16.1062	−	2.55097i	0.534798	−	0.0847036i	0.116806	−	0.993155i	$-0.462734\pi$
$907$	16.1062	−	2.55097i	0.534798	−	0.0847036i	0.417991	+	0.908451i	$0.362734\pi$
$908$	−4.00948	+	0.635040i	−0.133059	+	0.0210745i
$909$		0			0
$910$	0.789672	−	1.85341i	0.0261774	−	0.0614401i
$911$	−14.3281	+	10.4099i	−0.474710	+	0.344897i	−0.799274	−	0.600967i	$-0.794782\pi$
$911$	−14.3281	+	10.4099i	−0.474710	+	0.344897i	0.324564	+	0.945864i	$0.394782\pi$
$912$		0			0
$913$	21.9712	−	50.7821i	0.727140	−	1.68064i
$914$		−	10.2385i		−	0.338659i
$915$		0			0
$916$	−1.57702	−	4.85357i	−0.0521062	−	0.160366i
$917$	−0.849203	−	1.66665i	−0.0280431	−	0.0550378i
$918$		0			0
$919$	7.38632	+	5.36648i	0.243652	+	0.177024i	0.702909	−	0.711280i	$-0.251884\pi$
$919$	7.38632	+	5.36648i	0.243652	+	0.177024i	−0.459257	+	0.888304i	$0.651884\pi$
$920$	−2.26921	+	9.04942i	−0.0748135	+	0.298350i
$921$		0			0
$922$	−6.91497	+	43.6594i	−0.227732	+	1.43785i
$923$	25.0888	−	25.0888i	0.825807	−	0.825807i
$924$		0			0
$925$	−16.3231	+	21.5407i	−0.536701	+	0.708254i
$926$	−22.1307	−	30.4602i	−0.727259	−	1.00099i
$927$		0			0
$928$	−14.8171	+	7.54970i	−0.486396	+	0.247831i
$929$	1.06529	−	1.46625i	0.0349511	−	0.0481061i	−0.791184	−	0.611578i	$-0.790535\pi$
$929$	1.06529	−	1.46625i	0.0349511	−	0.0481061i	0.826135	+	0.563472i	$0.190535\pi$
$930$		0			0
$931$	4.92578	+	1.60048i	0.161436	+	0.0524537i
$932$	−2.20583	+	4.32918i	−0.0722543	+	0.141807i
$933$		0			0
$934$	−40.2174			−1.31595
$935$	15.5802	+	22.6465i	0.509525	+	0.740619i
$936$		0			0
$937$	14.9726	+	2.37143i	0.489133	+	0.0774711i	0.396130	−	0.918195i	$-0.370353\pi$
$937$	14.9726	+	2.37143i	0.489133	+	0.0774711i	0.0930039	+	0.995666i	$0.470353\pi$
$938$	−0.772546	+	1.51621i	−0.0252245	+	0.0495059i
$939$		0			0
$940$	1.92037	+	8.36939i	0.0626356	+	0.272979i
$941$	12.8308	−	17.6600i	0.418271	−	0.575701i	−0.546940	−	0.837172i	$-0.684208\pi$
$941$	12.8308	−	17.6600i	0.418271	−	0.575701i	0.965211	+	0.261471i	$0.0842075\pi$
$942$		0			0
$943$	−9.69338	−	4.93902i	−0.315660	−	0.160837i
$944$	−25.6012	−	35.2370i	−0.833247	−	1.14687i
$945$		0			0
$946$	−1.67038	−	26.5205i	−0.0543087	−	0.862256i
$947$	−6.90662	+	6.90662i	−0.224435	+	0.224435i	−0.810363	−	0.585928i	$-0.800730\pi$
$947$	−6.90662	+	6.90662i	−0.224435	+	0.224435i	0.585928	+	0.810363i	$0.300730\pi$
$948$		0			0
$949$	−7.07131	+	2.29761i	−0.229545	+	0.0745835i
$950$	−4.63941	+	3.22999i	−0.150522	+	0.104795i
$951$		0			0
$952$	−0.285100	−	1.80005i	−0.00924015	−	0.0583400i
$953$	5.92153	+	11.6216i	0.191817	+	0.376462i	0.966806	−	0.255513i	$-0.0822444\pi$
$953$	5.92153	+	11.6216i	0.191817	+	0.376462i	−0.774989	+	0.631975i	$0.782244\pi$
$954$		0			0
$955$	−10.8487	+	9.07831i	−0.351056	+	0.293767i
$956$		−	1.64046i		−	0.0530561i
$957$		0			0
$958$	−28.2202	−	28.2202i	−0.911755	−	0.911755i
$959$	−0.670750	+	0.487328i	−0.0216596	+	0.0157367i
$960$		0			0
$961$	−9.54147	+	29.3656i	−0.307789	+	0.947279i
$962$	25.1218	−	3.97890i	0.809960	−	0.128285i
$963$		0			0
$964$	1.55173	−	4.77572i	0.0499777	−	0.153816i
$965$	12.2027	+	5.19911i	0.392818	+	0.167365i
$966$		0			0
$967$	13.6319	+	13.6319i	0.438372	+	0.438372i	0.891464	−	0.453092i	$-0.149679\pi$
$967$	13.6319	+	13.6319i	0.438372	+	0.438372i	−0.453092	+	0.891464i	$0.649679\pi$
$968$	0.883368	−	28.2343i	0.0283925	−	0.907484i
$969$		0			0
$970$	3.59460	−	3.00800i	0.115416	−	0.0965809i
$971$	−1.26967	−	3.90765i	−0.0407457	−	0.125403i	0.928615	−	0.371046i	$-0.121001\pi$
$971$	−1.26967	−	3.90765i	−0.0407457	−	0.125403i	−0.969360	+	0.245643i	$0.921001\pi$
$972$		0			0
$973$	−0.314819	−	1.98769i	−0.0100926	−	0.0637224i
$974$	28.6965	+	20.8492i	0.919495	+	0.668052i
$975$		0			0
$976$	25.3592	−	8.23971i	0.811729	−	0.263747i
$977$	−4.80402	+	30.3314i	−0.153694	+	0.970386i	0.783453	+	0.621451i	$0.213457\pi$
$977$	−4.80402	+	30.3314i	−0.153694	+	0.970386i	−0.937147	+	0.348935i	$0.886543\pi$
$978$		0			0
$979$	22.1848	+	14.0768i	0.709030	+	0.449895i
$980$	−4.82472	+	0.330856i	−0.154120	+	0.0105688i
$981$		0			0
$982$	24.8498	+	12.6616i	0.792990	+	0.404048i
$983$	−24.7035	+	12.5871i	−0.787919	+	0.401465i	−0.801162	−	0.598447i	$-0.795785\pi$
$983$	−24.7035	+	12.5871i	−0.787919	+	0.401465i	0.0132429	+	0.999912i	$0.495785\pi$
$984$		0			0
$985$	7.00505	+	30.5295i	0.223199	+	0.972750i
$986$	−51.1575	−	16.6221i	−1.62919	−	0.529355i
$987$		0			0
$988$	0.706325	+	0.111871i	0.0224712	+	0.00355909i
$989$	8.56376			0.272312
$990$		0			0
$991$	9.10087			0.289099			0.144549	−	0.989498i	$-0.453827\pi$
$991$	9.10087			0.289099			0.144549	+	0.989498i	$0.453827\pi$
$992$	−0.603719	−	0.0956197i	−0.0191681	−	0.00303593i
$993$		0			0
$994$	3.17264	+	1.03085i	0.100630	+	0.0326966i
$995$	−15.8919	+	25.3563i	−0.503806	+	0.803849i
$996$		0			0
$997$	25.7239	−	13.1070i	0.814685	−	0.415103i	0.00357282	−	0.999994i	$-0.498863\pi$
$997$	25.7239	−	13.1070i	0.814685	−	0.415103i	0.811112	+	0.584891i	$0.198863\pi$
$998$	15.9247	+	8.11406i	0.504089	+	0.256846i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.a.118.1		32
3.2	odd	2		55.2.l.a.8.4	yes	32
5.2	odd	4	inner	495.2.bj.a.217.4		32
11.7	odd	10	inner	495.2.bj.a.73.4		32
12.11	even	2		880.2.cm.a.833.4		32
15.2	even	4		55.2.l.a.52.1	yes	32
15.8	even	4		275.2.bm.b.107.4		32
15.14	odd	2		275.2.bm.b.118.1		32
33.2	even	10		605.2.e.b.483.14		32
33.5	odd	10		605.2.m.d.233.1		32
33.8	even	10		605.2.m.d.578.1		32
33.14	odd	10		605.2.m.c.578.4		32
33.17	even	10		605.2.m.c.233.4		32
33.20	odd	10		605.2.e.b.483.3		32
33.26	odd	10		605.2.m.e.403.4		32
33.29	even	10		55.2.l.a.18.1	yes	32
33.32	even	2		605.2.m.e.118.1		32
55.7	even	20	inner	495.2.bj.a.172.1		32
60.47	odd	4		880.2.cm.a.657.1		32
132.95	odd	10		880.2.cm.a.513.1		32
165.2	odd	20		605.2.e.b.362.3		32
165.17	odd	20		605.2.m.c.112.4		32
165.29	even	10		275.2.bm.b.18.4		32
165.32	odd	4		605.2.m.e.602.4		32
165.47	even	20		605.2.m.c.457.4		32
165.62	odd	20		55.2.l.a.7.4	✓	32
165.92	even	20		605.2.m.e.282.1		32
165.107	odd	20		605.2.m.d.457.1		32
165.128	odd	20		275.2.bm.b.7.1		32
165.137	even	20		605.2.m.d.112.1		32
165.152	even	20		605.2.e.b.362.14		32
660.227	even	20		880.2.cm.a.337.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	165.62	odd	20
55.2.l.a.8.4	yes	32	3.2	odd	2
55.2.l.a.18.1	yes	32	33.29	even	10
55.2.l.a.52.1	yes	32	15.2	even	4
275.2.bm.b.7.1		32	165.128	odd	20
275.2.bm.b.18.4		32	165.29	even	10
275.2.bm.b.107.4		32	15.8	even	4
275.2.bm.b.118.1		32	15.14	odd	2
495.2.bj.a.73.4		32	11.7	odd	10	inner
495.2.bj.a.118.1		32	1.1	even	1	trivial
495.2.bj.a.172.1		32	55.7	even	20	inner
495.2.bj.a.217.4		32	5.2	odd	4	inner
605.2.e.b.362.3		32	165.2	odd	20
605.2.e.b.362.14		32	165.152	even	20
605.2.e.b.483.3		32	33.20	odd	10
605.2.e.b.483.14		32	33.2	even	10
605.2.m.c.112.4		32	165.17	odd	20
605.2.m.c.233.4		32	33.17	even	10
605.2.m.c.457.4		32	165.47	even	20
605.2.m.c.578.4		32	33.14	odd	10
605.2.m.d.112.1		32	165.137	even	20
605.2.m.d.233.1		32	33.5	odd	10
605.2.m.d.457.1		32	165.107	odd	20
605.2.m.d.578.1		32	33.8	even	10
605.2.m.e.118.1		32	33.32	even	2
605.2.m.e.282.1		32	165.92	even	20
605.2.m.e.403.4		32	33.26	odd	10
605.2.m.e.602.4		32	165.32	odd	4
880.2.cm.a.337.4		32	660.227	even	20
880.2.cm.a.513.1		32	132.95	odd	10
880.2.cm.a.657.1		32	60.47	odd	4
880.2.cm.a.833.4		32	12.11	even	2

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50135 - 0.237790i) q^{2} +(0.295389 + 0.0959778i) q^{4} +(1.89470 + 1.18749i) q^{5} +(0.170602 - 0.0869260i) q^{7} +(2.28811 + 1.16585i) q^{8} +(-2.56223 - 2.23337i) q^{10} +(-1.77694 + 2.80044i) q^{11} +(-0.484259 + 3.05749i) q^{13} +(-0.276803 + 0.0899388i) q^{14} +(-3.66057 - 2.65956i) q^{16} +(-0.579827 - 3.66088i) q^{17} +(-0.229844 - 0.707388i) q^{19} +(0.445701 + 0.532619i) q^{20} +(3.33373 - 3.78190i) q^{22} +(1.14886 + 1.14886i) q^{23} +(2.17976 + 4.49985i) q^{25} +(1.45408 - 4.47521i) q^{26} +(0.0587369 - 0.00930302i) q^{28} +(-2.95025 + 9.07993i) q^{29} +(-0.283900 + 0.206266i) q^{31} +(1.23166 + 1.23166i) q^{32} +5.63413i q^{34} +(0.426463 + 0.0378887i) q^{35} +(2.45398 + 4.81621i) q^{37} +(0.176866 + 1.11669i) q^{38} +(2.95085 + 4.92603i) q^{40} +(-6.36824 + 2.06917i) q^{41} +(3.72708 - 3.72708i) q^{43} +(-0.793670 + 0.656674i) q^{44} +(-1.45165 - 1.99802i) q^{46} +(11.0165 + 5.61318i) q^{47} +(-4.09295 + 5.63346i) q^{49} +(-2.20256 - 7.27417i) q^{50} +(-0.436496 + 0.856672i) q^{52} +(8.91914 + 1.41265i) q^{53} +(-6.69225 + 3.19590i) q^{55} +0.491699 q^{56} +(6.58847 - 12.9306i) q^{58} +(9.15496 + 2.97463i) q^{59} +(-3.46383 + 4.76756i) q^{61} +(0.475281 - 0.242168i) q^{62} +(3.76284 + 5.17911i) q^{64} +(-4.54825 + 5.21797i) q^{65} +(4.13426 - 4.13426i) q^{67} +(0.180089 - 1.13704i) q^{68} +(-0.631259 - 0.158293i) q^{70} +(-9.27272 - 6.73702i) q^{71} +(1.09042 + 2.14008i) q^{73} +(-2.53903 - 7.81434i) q^{74} -0.231015i q^{76} +(-0.0597184 + 0.632224i) q^{77} +(-0.542434 + 0.394101i) q^{79} +(-3.77749 - 9.38594i) q^{80} +(10.0530 - 1.59224i) q^{82} +(-16.4776 + 2.60980i) q^{83} +(3.24865 - 7.62480i) q^{85} +(-6.48191 + 4.70938i) q^{86} +(-7.33074 + 4.33608i) q^{88} -7.92190i q^{89} +(0.183160 + 0.563709i) q^{91} +(0.229095 + 0.449625i) q^{92} +(-15.2048 - 11.0469i) q^{94} +(0.404527 - 1.61322i) q^{95} +(-0.215721 + 1.36201i) q^{97} +(7.48452 - 7.48452i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more