LMFDB - Embedded newform 495.2.bj.a.73.4

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			73.4
Character	$\chi$	$=$	495.73
Dual form			495.2.bj.a.217.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.237790 + 1.50135i) q^{2} +(-0.295389 + 0.0959778i) q^{4} +(1.71486 - 1.43501i) q^{5} +(0.0869260 - 0.170602i) q^{7} +(1.16585 + 2.28811i) q^{8} +(2.56223 + 2.23337i) q^{10} +(-1.77694 - 2.80044i) q^{11} +(3.05749 - 0.484259i) q^{13} +(0.276803 + 0.0899388i) q^{14} +(-3.66057 + 2.65956i) q^{16} +(3.66088 + 0.579827i) q^{17} +(0.229844 - 0.707388i) q^{19} +(-0.368822 + 0.588475i) q^{20} +(3.78190 - 3.33373i) q^{22} +(1.14886 + 1.14886i) q^{23} +(0.881484 - 4.92169i) q^{25} +(1.45408 + 4.47521i) q^{26} +(-0.00930302 + 0.0587369i) q^{28} +(2.95025 + 9.07993i) q^{29} +(-0.283900 - 0.206266i) q^{31} +(-1.23166 - 1.23166i) q^{32} +5.63413i q^{34} +(-0.0957498 - 0.417298i) q^{35} +(-4.81621 - 2.45398i) q^{37} +(1.11669 + 0.176866i) q^{38} +(5.28274 + 2.25078i) q^{40} +(-6.36824 - 2.06917i) q^{41} +(-3.72708 + 3.72708i) q^{43} +(0.793670 + 0.656674i) q^{44} +(-1.45165 + 1.99802i) q^{46} +(-5.61318 - 11.0165i) q^{47} +(4.09295 + 5.63346i) q^{49} +(7.59877 + 0.153087i) q^{50} +(-0.856672 + 0.436496i) q^{52} +(1.41265 + 8.91914i) q^{53} +(-7.06587 - 2.25243i) q^{55} +0.491699 q^{56} +(-12.9306 + 6.58847i) q^{58} +(-9.15496 + 2.97463i) q^{59} +(-3.46383 - 4.76756i) q^{61} +(0.242168 - 0.475281i) q^{62} +(-3.76284 + 5.17911i) q^{64} +(4.54825 - 5.21797i) q^{65} +(4.13426 - 4.13426i) q^{67} +(-1.13704 + 0.180089i) q^{68} +(0.603742 - 0.242983i) q^{70} +(-9.27272 + 6.73702i) q^{71} +(2.14008 + 1.09042i) q^{73} +(2.53903 - 7.81434i) q^{74} +0.231015i q^{76} +(-0.632224 + 0.0597184i) q^{77} +(0.542434 + 0.394101i) q^{79} +(-2.46086 + 9.81373i) q^{80} +(1.59224 - 10.0530i) q^{82} +(2.60980 - 16.4776i) q^{83} +(7.10995 - 4.25908i) q^{85} +(-6.48191 - 4.70938i) q^{86} +(4.33608 - 7.33074i) q^{88} -7.92190i q^{89} +(0.183160 - 0.563709i) q^{91} +(-0.449625 - 0.229095i) q^{92} +(15.2048 - 11.0469i) q^{94} +(-0.620959 - 1.54290i) q^{95} +(-1.36201 + 0.215721i) q^{97} +(-7.48452 + 7.48452i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.237790	+	1.50135i	0.168143	+	1.06161i	0.917002	+	0.398884i	$0.130602\pi$
$2$	0.237790	+	1.50135i	0.168143	+	1.06161i	−0.748859	+	0.662730i	$0.769398\pi$
$3$		0			0
$3$		0			0
$4$	−0.295389	+	0.0959778i	−0.147695	+	0.0479889i
$5$	1.71486	−	1.43501i	0.766908	−	0.641757i
$5$	1.71486	−	1.43501i	0.766908	−	0.641757i
$6$		0			0
$7$	0.0869260	−	0.170602i	0.0328550	−	0.0644815i	−0.873996	−	0.485934i	$-0.838480\pi$
$7$	0.0869260	−	0.170602i	0.0328550	−	0.0644815i	0.906851	+	0.421452i	$0.138480\pi$
$8$	1.16585	+	2.28811i	0.412191	+	0.808970i
$9$		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
$13$	3.05749	−	0.484259i	0.847995	−	0.134309i	0.282711	−	0.959205i	$-0.408766\pi$
$13$	3.05749	−	0.484259i	0.847995	−	0.134309i	0.565285	+	0.824896i	$0.308766\pi$
$14$	0.276803	+	0.0899388i	0.0739787	+	0.0240372i
$15$		0			0
$16$	−3.66057	+	2.65956i	−0.915143	+	0.664890i
$17$	3.66088	+	0.579827i	0.887894	+	0.140629i	0.583688	−	0.811978i	$-0.301609\pi$
$17$	3.66088	+	0.579827i	0.887894	+	0.140629i	0.304206	+	0.952606i	$0.401609\pi$
$18$		0			0
$19$	0.229844	−	0.707388i	0.0527299	−	0.162286i	−0.921224	−	0.389033i	$-0.872809\pi$
$19$	0.229844	−	0.707388i	0.0527299	−	0.162286i	0.973954	+	0.226747i	$0.0728091\pi$
$20$	−0.368822	+	0.588475i	−0.0824710	+	0.131587i
$21$		0			0
$22$	3.78190	−	3.33373i	0.806304	−	0.710753i
$23$	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
$25$	0.881484	−	4.92169i	0.176297	−	0.984337i
$26$	1.45408	+	4.47521i	0.285169	+	0.877660i
$27$		0			0
$28$	−0.00930302	+	0.0587369i	−0.00175811	+	0.0111002i
$29$	2.95025	+	9.07993i	0.547847	+	1.68610i	0.714122	+	0.700021i	$0.246826\pi$
$29$	2.95025	+	9.07993i	0.547847	+	1.68610i	−0.166275	+	0.986079i	$0.553174\pi$
$30$		0			0
$31$	−0.283900	−	0.206266i	−0.0509900	−	0.0370464i	0.561998	−	0.827138i	$-0.310033\pi$
$31$	−0.283900	−	0.206266i	−0.0509900	−	0.0370464i	−0.612988	+	0.790092i	$0.710033\pi$
$32$	−1.23166	−	1.23166i	−0.217729	−	0.217729i
$33$		0			0
$34$			5.63413i			0.966246i
$35$	−0.0957498	−	0.417298i	−0.0161847	−	0.0705363i
$36$		0			0
$37$	−4.81621	−	2.45398i	−0.791780	−	0.403432i	0.0108264	−	0.999941i	$-0.496554\pi$
$37$	−4.81621	−	2.45398i	−0.791780	−	0.403432i	−0.802606	+	0.596510i	$0.796554\pi$
$38$	1.11669	+	0.176866i	0.181151	+	0.0286915i
$39$		0			0
$40$	5.28274	+	2.25078i	0.835274	+	0.355880i
$41$	−6.36824	−	2.06917i	−0.994552	−	0.323150i	−0.233866	−	0.972269i	$-0.575138\pi$
$41$	−6.36824	−	2.06917i	−0.994552	−	0.323150i	−0.760687	+	0.649119i	$0.775138\pi$
$42$		0			0
$43$	−3.72708	+	3.72708i	−0.568374	+	0.568374i	−0.931673	−	0.363299i	$-0.881650\pi$
$43$	−3.72708	+	3.72708i	−0.568374	+	0.568374i	0.363299	+	0.931673i	$0.381650\pi$
$44$	0.793670	+	0.656674i	0.119650	+	0.0989973i
$45$		0			0
$46$	−1.45165	+	1.99802i	−0.214034	+	0.294592i
$47$	−5.61318	−	11.0165i	−0.818766	−	1.60692i	−0.794539	−	0.607213i	$-0.792287\pi$
$47$	−5.61318	−	11.0165i	−0.818766	−	1.60692i	−0.0242272	−	0.999706i	$-0.507713\pi$
$48$		0			0
$49$	4.09295	+	5.63346i	0.584707	+	0.804780i
$50$	7.59877	+	0.153087i	1.07463	+	0.0216497i
$51$		0			0
$52$	−0.856672	+	0.436496i	−0.118799	+	0.0605311i
$53$	1.41265	+	8.91914i	0.194043	+	1.22514i	0.871804	+	0.489855i	$0.162950\pi$
$53$	1.41265	+	8.91914i	0.194043	+	1.22514i	−0.677761	+	0.735282i	$0.737050\pi$
$54$		0			0
$55$	−7.06587	−	2.25243i	−0.952762	−	0.303718i
$56$	0.491699			0.0657061
$57$		0			0
$58$	−12.9306	+	6.58847i	−1.69787	+	0.865108i
$59$	−9.15496	+	2.97463i	−1.19187	+	0.387263i	−0.836765	−	0.547562i	$-0.815556\pi$
$59$	−9.15496	+	2.97463i	−1.19187	+	0.387263i	−0.355108	+	0.934825i	$0.615556\pi$
$60$		0			0
$61$	−3.46383	−	4.76756i	−0.443498	−	0.610423i	0.527487	−	0.849563i	$-0.323134\pi$
$61$	−3.46383	−	4.76756i	−0.443498	−	0.610423i	−0.970985	+	0.239140i	$0.923134\pi$
$62$	0.242168	−	0.475281i	0.0307554	−	0.0603608i
$63$		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	$0.133750\pi$
$68$	−1.13704	+	0.180089i	−0.137886	+	0.0218390i
$69$		0			0
$70$	0.603742	−	0.242983i	0.0721609	−	0.0290421i
$71$	−9.27272	+	6.73702i	−1.10047	+	0.799538i	−0.981136	−	0.193317i	$-0.938075\pi$
$71$	−9.27272	+	6.73702i	−1.10047	+	0.799538i	−0.119333	+	0.992854i	$0.538075\pi$
$72$		0			0
$73$	2.14008	+	1.09042i	0.250477	+	0.127624i	0.574722	−	0.818349i	$-0.305110\pi$
$73$	2.14008	+	1.09042i	0.250477	+	0.127624i	−0.324245	+	0.945973i	$0.605110\pi$
$74$	2.53903	−	7.81434i	0.295156	−	0.908398i
$75$		0			0
$76$			0.231015i			0.0264992i
$77$	−0.632224	+	0.0597184i	−0.0720486	+	0.00680554i
$78$		0			0
$79$	0.542434	+	0.394101i	0.0610286	+	0.0443399i	0.617881	−	0.786271i	$-0.287991\pi$
$79$	0.542434	+	0.394101i	0.0610286	+	0.0443399i	−0.556853	+	0.830611i	$0.687991\pi$
$80$	−2.46086	+	9.81373i	−0.275133	+	1.09721i
$81$		0			0
$82$	1.59224	−	10.0530i	0.175833	−	1.11017i
$83$	2.60980	−	16.4776i	0.286463	−	1.80865i	−0.253909	−	0.967228i	$-0.581716\pi$
$83$	2.60980	−	16.4776i	0.286463	−	1.80865i	0.540372	−	0.841426i	$-0.318284\pi$
$84$		0			0
$85$	7.10995	−	4.25908i	0.771183	−	0.461963i
$86$	−6.48191	−	4.70938i	−0.698962	−	0.507826i
$87$		0			0
$88$	4.33608	−	7.33074i	0.462227	−	0.781460i
$89$		−	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
$92$	−0.449625	−	0.229095i	−0.0468766	−	0.0238848i
$93$		0			0
$94$	15.2048	−	11.0469i	1.56826	−	1.13941i
$95$	−0.620959	−	1.54290i	−0.0637090	−	0.158298i
$96$		0			0
$97$	−1.36201	+	0.215721i	−0.138291	+	0.0219032i	−0.225196	−	0.974313i	$-0.572302\pi$
$97$	−1.36201	+	0.215721i	−0.138291	+	0.0219032i	0.0869051	+	0.996217i	$0.472302\pi$
$98$	−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	−0.644244	−	0.764820i	$-0.722828\pi$
$101$	2.83633	−	3.90387i	0.282225	−	0.388449i	0.926469	+	0.376370i	$0.122828\pi$
$102$		0			0
$103$	−1.46972	+	2.88449i	−0.144816	+	0.284217i	−0.952009	−	0.306071i	$-0.900986\pi$
$103$	−1.46972	+	2.88449i	−0.144816	+	0.284217i	0.807193	+	0.590287i	$0.200986\pi$
$104$	4.67262	+	6.43131i	0.458188	+	0.630641i
$105$		0			0
$106$	−13.0548	+	4.24177i	−1.26800	+	0.411997i
$107$	9.85055	−	5.01911i	0.952289	−	0.485215i	0.0924142	−	0.995721i	$-0.470542\pi$
$107$	9.85055	−	5.01911i	0.952289	−	0.485215i	0.859875	+	0.510505i	$0.170542\pi$
$108$		0			0
$109$	−9.54212			−0.913969			−0.456985	−	0.889475i	$-0.651071\pi$
$109$	−9.54212			−0.913969			−0.456985	+	0.889475i	$0.651071\pi$
$110$	1.70149	−	11.1439i	0.162231	−	1.06253i
$111$		0			0
$112$	0.135527	+	0.855686i	0.0128061	+	0.0808547i
$113$	−3.69562	+	1.88301i	−0.347654	+	0.177139i	−0.619094	−	0.785317i	$-0.712500\pi$
$113$	−3.69562	+	1.88301i	−0.347654	+	0.177139i	0.271440	+	0.962455i	$0.412500\pi$
$114$		0			0
$115$	3.61875	+	0.321505i	0.337450	+	0.0299805i
$116$	−1.74294	−	2.39895i	−0.161828	−	0.222737i
$117$		0			0
$118$	−6.64291	−	13.0374i	−0.611529	−	1.20019i
$119$	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
$125$	−5.55105	−	9.70494i	−0.496501	−	0.868036i
$126$		0			0
$127$	14.3879	+	2.27881i	1.27672	+	0.202212i	0.757728	−	0.652570i	$-0.226309\pi$
$127$	14.3879	+	2.27881i	1.27672	+	0.202212i	0.518987	+	0.854782i	$0.326309\pi$
$128$	−11.7744	−	5.99935i	−1.04072	−	0.530273i
$129$		0			0
$130$	8.91552	+	5.58772i	0.781943	+	0.490076i
$131$			9.76926i			0.853544i	0.904359	+	0.426772i	$0.140349\pi$
$131$			9.76926i			0.853544i	−0.904359	+	0.426772i	$0.859651\pi$
$132$		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
$137$	−0.677380	+	4.27681i	−0.0578725	+	0.365392i	0.941708	+	0.336431i	$0.109220\pi$
$137$	−0.677380	+	4.27681i	−0.0578725	+	0.365392i	−0.999581	+	0.0289612i	$0.990780\pi$
$138$		0			0
$139$	−3.24794	−	9.99613i	−0.275487	−	0.847860i	−0.989090	−	0.147311i	$-0.952938\pi$
$139$	−3.24794	−	9.99613i	−0.275487	−	0.847860i	0.713604	−	0.700550i	$-0.247062\pi$
$140$	0.0683348	+	0.114076i	0.00577535	+	0.00964114i
$141$		0			0
$142$	−12.3196	−	12.3196i	−1.03384	−	1.03384i
$143$	−6.78912	−	7.70183i	−0.567735	−	0.644059i
$144$		0			0
$145$	18.0891	+	11.3372i	1.50221	+	0.941500i
$146$	−1.12822	+	3.47229i	−0.0933719	+	0.287369i
$147$		0			0
$148$	1.65818	+	0.262630i	0.136302	+	0.0215881i
$149$	4.66189	−	3.38706i	0.381917	−	0.277479i	−0.380218	−	0.924897i	$-0.624151\pi$
$149$	4.66189	−	3.38706i	0.381917	−	0.277479i	0.762135	+	0.647418i	$0.224151\pi$
$150$		0			0
$151$	−14.2318	−	4.62419i	−1.15817	−	0.376311i	−0.333953	−	0.942590i	$-0.608383\pi$
$151$	−14.2318	−	4.62419i	−1.15817	−	0.376311i	−0.824214	+	0.566278i	$0.808383\pi$
$152$	1.88655	−	0.298800i	0.153019	−	0.0242358i
$153$		0			0
$154$	−0.239995	−	0.934987i	−0.0193393	−	0.0753434i
$155$	−0.782843	+	0.0536836i	−0.0628795	+	0.00431197i
$156$		0			0
$157$	−2.24640	−	4.40881i	−0.179282	−	0.351861i	0.783824	−	0.620983i	$-0.213267\pi$
$157$	−2.24640	−	4.40881i	−0.179282	−	0.351861i	−0.963106	+	0.269122i	$0.913267\pi$
$158$	−0.462698	+	0.908095i	−0.0368103	+	0.0722442i
$159$		0			0
$160$	−3.87958	−	0.344678i	−0.306707	−	0.0272492i
$161$	0.295863	−	0.0961317i	0.0233173	−	0.00757624i
$162$		0			0
$163$	−1.56695	−	9.89335i	−0.122733	−	0.774907i	−0.969886	−	0.243558i	$-0.921685\pi$
$163$	−1.56695	−	9.89335i	−0.122733	−	0.774907i	0.847153	−	0.531349i	$-0.178315\pi$
$164$	2.07970			0.162398
$165$		0			0
$166$	25.3592			1.96826
$167$	1.88695	+	11.9137i	0.146017	+	0.921913i	0.946534	+	0.322604i	$0.104558\pi$
$167$	1.88695	+	11.9137i	0.146017	+	0.921913i	−0.800517	+	0.599310i	$0.795442\pi$
$168$		0			0
$169$	−3.24999	+	1.05599i	−0.250000	+	0.0812298i
$170$	8.08505	+	9.66175i	0.620095	+	0.741022i
$171$		0			0
$172$	0.743222	−	1.45866i	0.0566702	−	0.111221i
$173$	5.65903	+	11.1065i	0.430248	+	0.844410i	0.999749	+	0.0224186i	$0.00713665\pi$
$173$	5.65903	+	11.1065i	0.430248	+	0.844410i	−0.569501	+	0.821991i	$0.692863\pi$
$174$		0			0
$175$	−0.763025	−	0.578206i	−0.0576793	−	0.0437082i
$176$	13.9526	+	5.52533i	1.05171	+	0.416488i
$177$		0			0
$178$	11.8935	−	1.88375i	0.891458	−	0.141193i
$179$	−19.1909	−	6.23551i	−1.43440	−	0.466064i	−0.514252	−	0.857639i	$-0.671930\pi$
$179$	−19.1909	−	6.23551i	−1.43440	−	0.466064i	−0.920146	+	0.391575i	$0.871930\pi$
$180$		0			0
$181$	−3.72935	+	2.70953i	−0.277200	+	0.201398i	−0.717695	−	0.696357i	$-0.754803\pi$
$181$	−3.72935	+	2.70953i	−0.277200	+	0.201398i	0.440495	+	0.897755i	$0.354803\pi$
$182$	0.889877	+	0.140943i	0.0659620	+	0.0104474i
$183$		0			0
$184$	−1.28932	+	3.96811i	−0.0950497	+	0.292533i
$185$	−11.7806	+	2.70308i	−0.866127	+	0.198735i
$186$		0			0
$187$	−4.88140	−	11.2824i	−0.356963	−	0.825051i
$188$	2.71541	+	2.71541i	0.198042	+	0.198042i
$189$		0			0
$190$	2.16877	−	1.29916i	0.157339	−	0.0942511i
$191$	−1.95493	−	6.01667i	−0.141454	−	0.435351i	0.855084	−	0.518490i	$-0.173505\pi$
$191$	−1.95493	−	6.01667i	−0.141454	−	0.435351i	−0.996538	+	0.0831389i	$0.973505\pi$
$192$		0			0
$193$	−0.927951	+	5.85885i	−0.0667954	+	0.421729i	0.931519	+	0.363692i	$0.118484\pi$
$193$	−0.927951	+	5.85885i	−0.0667954	+	0.421729i	−0.998314	+	0.0580368i	$0.981516\pi$
$194$	−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	0.259918	−	0.965631i	$-0.416304\pi$
$197$	−9.90515	−	9.90515i	−0.705713	−	0.705713i	−0.965631	+	0.259918i	$0.916304\pi$
$198$		0			0
$199$			13.3828i			0.948680i	0.880342	+	0.474340i	$0.157313\pi$
$199$			13.3828i			0.948680i	−0.880342	+	0.474340i	$0.842687\pi$
$200$	12.2890	−	3.72102i	0.868967	−	0.263116i
$201$		0			0
$202$	6.53551	+	3.33001i	0.459837	+	0.234299i
$203$	1.80551	+	0.285964i	0.126722	+	0.0200708i
$204$		0			0
$205$	−13.8899	+	5.59017i	−0.970114	+	0.390434i
$206$	−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	−0.671944	−	0.740602i	$-0.734540\pi$
$211$	3.48696	−	4.79939i	0.240052	−	0.330404i	0.911996	+	0.410198i	$0.134540\pi$
$212$	−1.27332	−	2.49903i	−0.0874521	−	0.171634i
$213$		0			0
$214$	9.87779	+	13.5956i	0.675232	+	0.929377i
$215$	−1.04301	+	11.7398i	−0.0711330	+	0.800649i
$216$		0			0
$217$	−0.0598677	+	0.0305041i	−0.00406408	+	0.00207075i
$218$	−2.26902	−	14.3260i	−0.153678	−	0.970282i
$219$		0			0
$220$	2.30337	−	0.0128223i	0.155293	−	0.000864476i
$221$	11.4739			0.771818
$222$		0			0
$223$	−18.9389	+	9.64984i	−1.26824	+	0.646201i	−0.953046	−	0.302826i	$-0.902070\pi$
$223$	−18.9389	+	9.64984i	−1.26824	+	0.646201i	−0.315195	+	0.949027i	$0.602070\pi$
$224$	−0.317188	+	0.103060i	−0.0211930	+	0.00688602i
$225$		0			0
$226$	−3.70584	−	5.10065i	−0.246509	−	0.339290i
$227$	−5.93372	+	11.6456i	−0.393835	+	0.772944i	−0.999745	−	0.0225888i	$-0.992809\pi$
$227$	−5.93372	+	11.6456i	−0.393835	+	0.772944i	0.605910	+	0.795533i	$0.292809\pi$
$228$		0			0
$229$	9.65796	−	13.2930i	0.638216	−	0.878429i	−0.360303	−	0.932835i	$-0.617327\pi$
$229$	9.65796	−	13.2930i	0.638216	−	0.878429i	0.998519	+	0.0544066i	$0.0173267\pi$
$230$	0.377812	+	5.50946i	0.0249122	+	0.363283i
$231$		0			0
$232$	−17.3363	+	17.3363i	−1.13819	+	1.13819i
$233$	15.4510	−	2.44720i	1.01223	−	0.160321i	0.371779	−	0.928321i	$-0.378748\pi$
$233$	15.4510	−	2.44720i	1.01223	−	0.160321i	0.640450	+	0.768000i	$0.278748\pi$
$234$		0			0
$235$	−25.4346	−	10.8367i	−1.65917	−	0.706911i
$236$	2.41878	−	1.75734i	0.157449	−	0.114393i
$237$		0			0
$238$	0.961194	+	0.489753i	0.0623050	+	0.0317460i
$239$	1.63214	−	5.02322i	0.105575	−	0.324925i	−0.884290	−	0.466938i	$-0.845357\pi$
$239$	1.63214	−	5.02322i	0.105575	−	0.324925i	0.989865	+	0.142012i	$0.0453572\pi$
$240$		0			0
$241$			16.1676i			1.04144i	0.853726	+	0.520722i	$0.174337\pi$
$241$			16.1676i			1.04144i	−0.853726	+	0.520722i	$0.825663\pi$
$242$	−16.0561	−	4.66716i	−1.03213	−	0.300016i
$243$		0			0
$244$	1.48076	+	1.07583i	0.0947959	+	0.0688732i
$245$	15.1029	+	3.78716i	0.964889	+	0.241953i
$246$		0			0
$247$	0.360188	−	2.27413i	0.0229182	−	0.144700i
$248$	0.140973	−	0.890071i	0.00895182	−	0.0565196i
$249$		0			0
$250$	13.2505	−	10.6418i	0.838036	−	0.673047i
$251$	15.6486	+	11.3694i	0.987729	+	0.717627i	0.959423	−	0.281972i	$-0.0909886\pi$
$251$	15.6486	+	11.3694i	0.987729	+	0.717627i	0.0283063	+	0.999599i	$0.490989\pi$
$252$		0			0
$253$	1.17586	−	5.25876i	0.0739254	−	0.330615i
$254$			22.1431i			1.38938i
$255$		0			0
$256$	2.25079	−	6.92722i	0.140674	−	0.432951i
$257$	4.19318	+	2.13653i	0.261563	+	0.133273i	0.579855	−	0.814720i	$-0.303109\pi$
$257$	4.19318	+	2.13653i	0.261563	+	0.133273i	−0.318292	+	0.947993i	$0.603109\pi$
$258$		0			0
$259$	−0.837308	+	0.608340i	−0.0520278	+	0.0378004i
$260$	−0.842694	+	1.97786i	−0.0522617	+	0.122662i
$261$		0			0
$262$	−14.6671	+	2.32303i	−0.906134	+	0.143517i
$263$	−11.2218	+	11.2218i	−0.691964	+	0.691964i	−0.962664	−	0.270700i	$-0.912745\pi$
$263$	−11.2218	+	11.2218i	−0.691964	+	0.691964i	0.270700	+	0.962664i	$0.412745\pi$
$264$		0			0
$265$	15.2216	+	13.2679i	0.935053	+	0.815040i
$266$	0.127243	−	0.175135i	0.00780178	−	0.0107382i
$267$		0			0
$268$	−0.824419	+	1.61801i	−0.0503594	+	0.0988359i
$269$	6.64926	+	9.15192i	0.405412	+	0.558002i	0.962092	−	0.272725i	$-0.0879249\pi$
$269$	6.64926	+	9.15192i	0.405412	+	0.558002i	−0.556680	+	0.830727i	$0.687925\pi$
$270$		0			0
$271$	16.9556	−	5.50921i	1.02998	−	0.334661i	0.255198	−	0.966889i	$-0.417859\pi$
$271$	16.9556	−	5.50921i	1.02998	−	0.334661i	0.774782	+	0.632228i	$0.217859\pi$
$272$	−14.9430	+	7.61384i	−0.906052	+	0.461657i
$273$		0			0
$274$	−6.58205			−0.397636
$275$	−15.3492	+	6.27700i	−0.925594	+	0.378517i
$276$		0			0
$277$	0.732361	+	4.62395i	0.0440033	+	0.277826i	0.999873	−	0.0159666i	$-0.00508253\pi$
$277$	0.732361	+	4.62395i	0.0440033	+	0.277826i	−0.955869	+	0.293793i	$0.905083\pi$
$278$	14.2353	−	7.25327i	0.853779	−	0.435022i
$279$		0			0
$280$	0.843195	−	0.705594i	0.0503905	−	0.0421673i
$281$	7.75247	+	10.6704i	0.462474	+	0.636541i	0.975019	−	0.222119i	$-0.0712975\pi$
$281$	7.75247	+	10.6704i	0.462474	+	0.636541i	−0.512546	+	0.858660i	$0.671297\pi$
$282$		0			0
$283$	10.3449	+	20.3029i	0.614938	+	1.20688i	0.963022	+	0.269421i	$0.0868324\pi$
$283$	10.3449	+	20.3029i	0.614938	+	1.20688i	−0.348084	+	0.937463i	$0.613168\pi$
$284$	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
$290$	−12.7196	+	29.8538i	−0.746922	+	1.75308i
$291$		0			0
$292$	−0.736812	−	0.116700i	−0.0431187	−	0.00682933i
$293$	6.43996	+	3.28132i	0.376226	+	0.191697i	0.631870	−	0.775074i	$-0.282287\pi$
$293$	6.43996	+	3.28132i	0.376226	+	0.191697i	−0.255644	+	0.966771i	$0.582287\pi$
$294$		0			0
$295$	−11.4308	+	18.2385i	−0.665529	+	1.06189i
$296$		−	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
$302$	3.55834	−	22.4665i	0.204759	−	1.29280i
$303$		0			0
$304$	1.03998	+	3.20073i	0.0596469	+	0.183574i
$305$	−12.7815	−	3.20505i	−0.731866	−	0.183521i
$306$		0			0
$307$	20.1272	+	20.1272i	1.14872	+	1.14872i	0.986804	+	0.161918i	$0.0517681\pi$
$307$	20.1272	+	20.1272i	1.14872	+	1.14872i	0.161918	+	0.986804i	$0.448232\pi$
$308$	0.181020	−	0.0783196i	0.0103146	−	0.00446267i
$309$		0			0
$310$	−0.266750	−	1.16255i	−0.0151504	−	0.0660286i
$311$	2.32254	−	7.14803i	0.131699	−	0.405328i	−0.863363	−	0.504583i	$-0.831646\pi$
$311$	2.32254	−	7.14803i	0.131699	−	0.405328i	0.995062	+	0.0992557i	$0.0316462\pi$
$312$		0			0
$313$	−1.32951	−	0.210574i	−0.0751483	−	0.0119023i	0.118747	−	0.992925i	$-0.462112\pi$
$313$	−1.32951	−	0.210574i	−0.0751483	−	0.0119023i	−0.193895	+	0.981022i	$0.562112\pi$
$314$	6.08499	−	4.42100i	0.343396	−	0.249492i
$315$		0			0
$316$	−0.198054	−	0.0643517i	−0.0111414	−	0.00362006i
$317$	11.1924	−	1.77271i	0.628630	−	0.0995652i	0.166013	−	0.986124i	$-0.446911\pi$
$317$	11.1924	−	1.77271i	0.628630	−	0.0995652i	0.462617	+	0.886558i	$0.346911\pi$
$318$		0			0
$319$	20.1854	−	24.3965i	1.13017	−	1.36594i
$320$	0.979335	+	14.2812i	0.0547465	+	0.798342i
$321$		0			0
$322$	0.214680	+	0.421334i	0.0119637	+	0.0234800i
$323$	1.25159	−	2.45639i	0.0696406	−	0.136677i
$324$		0			0
$325$	0.311760	−	15.4749i	0.0172934	−	0.858391i
$326$	14.4808	−	4.70509i	0.802015	−	0.260591i
$327$		0			0
$328$	−2.68994	−	16.9836i	−0.148527	−	0.937762i
$329$	−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	$0.661753\pi$
$332$	0.810579	+	5.11780i	0.0444863	+	0.280876i
$333$		0			0
$334$	−17.4380	+	5.66594i	−0.954164	+	0.310027i
$335$	1.15696	−	13.0224i	0.0632117	−	0.711489i
$336$		0			0
$337$	3.45945	−	6.78954i	0.188448	−	0.369850i	−0.777381	−	0.629030i	$-0.783452\pi$
$337$	3.45945	−	6.78954i	0.188448	−	0.369850i	0.965829	+	0.259180i	$0.0834523\pi$
$338$	−2.35822	−	4.62827i	−0.128270	−	0.251745i
$339$		0			0
$340$	−1.69143	+	1.94049i	−0.0917305	+	0.105238i
$341$	−0.0731608	+	1.16157i	−0.00396188	+	0.0629025i
$342$		0			0
$343$	2.64066	−	0.418239i	0.142582	−	0.0225828i
$344$	−12.8732	−	4.18275i	−0.694076	−	0.225519i
$345$		0			0
$346$	−15.3290	+	11.1372i	−0.824093	+	0.598739i
$347$	9.21879	+	1.46011i	0.494891	+	0.0783830i	0.398891	−	0.916998i	$-0.369395\pi$
$347$	9.21879	+	1.46011i	0.494891	+	0.0783830i	0.0959998	+	0.995381i	$0.469395\pi$
$348$		0			0
$349$	0.464073	−	1.42827i	0.0248413	−	0.0764536i	−0.937867	−	0.346994i	$-0.887202\pi$
$349$	0.464073	−	1.42827i	0.0248413	−	0.0764536i	0.962709	+	0.270540i	$0.0872024\pi$
$350$	0.686648	−	1.28306i	0.0367029	−	0.0685823i
$351$		0			0
$352$	−1.26061	+	5.63779i	−0.0671906	+	0.300495i
$353$	−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
$355$	−6.23370	+	24.8595i	−0.330850	+	1.31941i
$356$	0.760327	+	2.34004i	0.0402972	+	0.124022i
$357$		0			0
$358$	4.79826	−	30.2950i	0.253596	−	1.60114i
$359$	−8.12845	−	25.0168i	−0.429003	−	1.32034i	−0.899108	−	0.437726i	$-0.855784\pi$
$359$	−8.12845	−	25.0168i	−0.429003	−	1.32034i	0.470105	−	0.882611i	$-0.344216\pi$
$360$		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
$365$	5.23470	−	1.20111i	0.273997	−	0.0628691i
$366$		0			0
$367$	7.27872	+	3.70869i	0.379946	+	0.193592i	0.633524	−	0.773723i	$-0.281608\pi$
$367$	7.27872	+	3.70869i	0.379946	+	0.193592i	−0.253579	+	0.967315i	$0.581608\pi$
$368$	−7.26093	−	1.15002i	−0.378502	−	0.0599488i
$369$		0			0
$370$	−6.85958	−	17.0440i	−0.356613	−	0.886077i
$371$	1.64442	+	0.534304i	0.0853740	+	0.0277397i
$372$		0			0
$373$	6.12473	−	6.12473i	0.317126	−	0.317126i	−0.530536	−	0.847662i	$-0.678009\pi$
$373$	6.12473	−	6.12473i	0.317126	−	0.317126i	0.847662	+	0.530536i	$0.178009\pi$
$374$	15.7781	−	10.0115i	0.815864	−	0.517684i
$375$		0			0
$376$	18.6628	−	25.6872i	0.962461	−	1.32471i
$377$	13.4174	+	26.3331i	0.691031	+	1.35622i
$378$		0			0
$379$	−0.363481	−	0.500288i	−0.0186708	−	0.0256981i	0.799580	−	0.600560i	$-0.205056\pi$
$379$	−0.363481	−	0.500288i	−0.0186708	−	0.0256981i	−0.818250	+	0.574862i	$0.805056\pi$
$380$	0.331509	+	0.396158i	0.0170060	+	0.0203225i
$381$		0			0
$382$	8.56825	−	4.36574i	0.438390	−	0.223371i
$383$	−1.62362	−	10.2511i	−0.0829629	−	0.523807i	−0.993813	−	0.111069i	$-0.964572\pi$
$383$	−1.62362	−	10.2511i	−0.0829629	−	0.523807i	0.910850	−	0.412738i	$-0.135428\pi$
$384$		0			0
$385$	−0.998478	+	1.00966i	−0.0508871	+	0.0514569i
$386$	−9.01683			−0.458945
$387$		0			0
$388$	0.381619	−	0.194444i	0.0193737	−	0.00987142i
$389$	21.0630	−	6.84378i	1.06794	−	0.346993i	0.278252	−	0.960508i	$-0.410245\pi$
$389$	21.0630	−	6.84378i	1.06794	−	0.346993i	0.789683	+	0.613515i	$0.210245\pi$
$390$		0			0
$391$	3.53969	+	4.87197i	0.179010	+	0.246386i
$392$	−8.11822	+	15.9329i	−0.410032	+	0.804733i
$393$		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	$0.125078\pi$
$398$	−20.0922	+	3.18229i	−1.00713	+	0.159514i
$399$		0			0
$400$	9.86278	+	20.3605i	0.493139	+	1.01803i
$401$	−3.46399	+	2.51673i	−0.172983	+	0.125680i	−0.670908	−	0.741540i	$-0.734096\pi$
$401$	−3.46399	+	2.51673i	−0.172983	+	0.125680i	0.497925	+	0.867220i	$0.334096\pi$
$402$		0			0
$403$	−0.967909	−	0.493174i	−0.0482150	−	0.0245668i
$404$	−0.463135	+	1.42538i	−0.0230418	+	0.0709155i
$405$		0			0
$406$			2.77869i			0.137904i
$407$	1.68589	+	17.8481i	0.0835664	+	0.884697i
$408$		0			0
$409$	3.47523	+	2.52490i	0.171839	+	0.124848i	0.670381	−	0.742017i	$-0.266131\pi$
$409$	3.47523	+	2.52490i	0.171839	+	0.124848i	−0.498541	+	0.866866i	$0.666131\pi$
$410$	−11.6957	−	19.5243i	−0.577608	−	0.964237i
$411$		0			0
$412$	0.157293	−	0.993106i	0.00774925	−	0.0489268i
$413$	−0.288327	+	1.82043i	−0.0141877	+	0.0895773i
$414$		0			0
$415$	−19.1701	−	32.0019i	−0.941025	−	1.57091i
$416$	−4.36224	−	3.16935i	−0.213876	−	0.155390i
$417$		0			0
$418$	−1.48899	−	3.44151i	−0.0728288	−	0.168330i
$419$			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	−0.379057	−	0.925373i	$-0.623752\pi$
$421$	9.67493	−	29.7764i	0.471527	−	1.45121i	0.850584	−	0.525839i	$-0.176248\pi$
$422$	8.03473	+	4.09390i	0.391124	+	0.199288i
$423$		0			0
$424$	−18.7610	+	13.6307i	−0.911117	+	0.661965i
$425$	6.08073	−	17.5066i	0.294959	−	0.849195i
$426$		0			0
$427$	−1.11445	+	0.176512i	−0.0539321	+	0.00854201i
$428$	−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	−0.645702	−	0.763590i	$-0.723435\pi$
$431$	5.81395	−	8.00222i	0.280048	−	0.385453i	0.925750	+	0.378137i	$0.123435\pi$
$432$		0			0
$433$	12.2497	−	24.0414i	0.588683	−	1.15536i	−0.384025	−	0.923323i	$-0.625462\pi$
$433$	12.2497	−	24.0414i	0.588683	−	1.15536i	0.972708	−	0.232033i	$-0.0745378\pi$
$434$	−0.0600332	−	0.0826286i	−0.00288169	−	0.00396630i
$435$		0			0
$436$	2.81864	−	0.915831i	0.134988	−	0.0438604i
$437$	1.07675	−	0.548629i	0.0515077	−	0.0262445i
$438$		0			0
$439$	−24.5862			−1.17344			−0.586718	−	0.809791i	$-0.699580\pi$
$439$	−24.5862			−1.17344			−0.586718	+	0.809791i	$0.699580\pi$
$440$	−3.08394	−	18.7935i	−0.147021	−	0.895945i
$441$		0			0
$442$	2.72838	+	17.2263i	0.129776	+	0.819372i
$443$	−27.4404	+	13.9816i	−1.30373	+	0.664286i	−0.961364	−	0.275279i	$-0.911230\pi$
$443$	−27.4404	+	13.9816i	−1.30373	+	0.664286i	−0.342370	+	0.939565i	$0.611230\pi$
$444$		0			0
$445$	−11.3680	−	13.5849i	−0.538896	−	0.643988i
$446$	−18.9912	−	26.1392i	−0.899262	−	1.23773i
$447$		0			0
$448$	0.556477	+	1.09215i	0.0262911	+	0.0515992i
$449$	4.30536	−	5.92582i	0.203182	−	0.279657i	−0.695250	−	0.718768i	$-0.744707\pi$
$449$	4.30536	−	5.92582i	0.203182	−	0.279657i	0.898433	+	0.439111i	$0.144707\pi$
$450$		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
$455$	−0.494835	−	1.22952i	−0.0231982	−	0.0576407i
$456$		0			0
$457$	−6.65265	−	1.05368i	−0.311198	−	0.0492889i	−0.00111791	−	0.999999i	$-0.500356\pi$
$457$	−6.65265	−	1.05368i	−0.311198	−	0.0492889i	−0.310080	+	0.950710i	$0.600356\pi$
$458$	22.2540	+	11.3390i	1.03986	+	0.529837i
$459$		0			0
$460$	−1.09980	+	0.252351i	−0.0512783	+	0.0117659i
$461$			29.0801i			1.35440i	0.735801	+	0.677198i	$0.236806\pi$
$461$			29.0801i			1.35440i	−0.735801	+	0.677198i	$0.763194\pi$
$462$		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
$467$	4.13890	−	26.1320i	0.191525	−	1.20924i	−0.685237	−	0.728320i	$-0.740302\pi$
$467$	4.13890	−	26.1320i	0.191525	−	1.20924i	0.876763	−	0.480923i	$-0.159698\pi$
$468$		0			0
$469$	−0.345938	−	1.06469i	−0.0159739	−	0.0491627i
$470$	10.2216	−	40.7631i	0.471489	−	1.88026i
$471$		0			0
$472$	−17.4796	−	17.4796i	−0.804563	−	0.804563i
$473$	17.0603	+	3.81467i	0.784432	+	0.175399i
$474$		0			0
$475$	−3.27894	−	1.75477i	−0.150448	−	0.0805145i
$476$	−0.0681145	+	0.209635i	−0.00312202	+	0.00960860i
$477$		0			0
$478$	7.92972	+	1.25594i	0.362697	+	0.0574455i
$479$	−21.2408	+	15.4324i	−0.970519	+	0.705123i	−0.955570	−	0.294765i	$-0.904759\pi$
$479$	−21.2408	+	15.4324i	−0.970519	+	0.705123i	−0.0149492	+	0.999888i	$0.504759\pi$
$480$		0			0
$481$	−15.9139	−	5.17073i	−0.725610	−	0.235765i
$482$	−24.2731	+	3.84449i	−1.10561	+	0.175112i
$483$		0			0
$484$	0.428672	−	3.38950i	0.0194851	−	0.154068i
$485$	−2.02609	+	2.32443i	−0.0920001	+	0.105547i
$486$		0			0
$487$	10.5939	+	20.7917i	0.480056	+	0.942163i	0.996318	+	0.0857326i	$0.0273231\pi$
$487$	10.5939	+	20.7917i	0.480056	+	0.942163i	−0.516262	+	0.856431i	$0.672677\pi$
$488$	6.87039	−	13.4839i	0.311008	−	0.610388i
$489$		0			0
$490$	−2.09453	+	23.5753i	−0.0946211	+	1.06502i
$491$	−17.4497	+	5.66974i	−0.787493	+	0.255872i	−0.675036	−	0.737785i	$-0.735872\pi$
$491$	−17.4497	+	5.66974i	−0.787493	+	0.255872i	−0.112457	+	0.993657i	$0.535872\pi$
$492$		0			0
$493$	5.53572	+	34.9512i	0.249316	+	1.57412i
$494$	3.49992			0.157469
$495$		0			0
$496$	1.58781			0.0712949
$497$	0.343309	+	2.16757i	0.0153995	+	0.0972286i
$498$		0			0
$499$	11.1824	−	3.63339i	0.500595	−	0.162653i	−0.0478260	−	0.998856i	$-0.515229\pi$
$499$	11.1824	−	3.63339i	0.500595	−	0.162653i	0.548421	+	0.836203i	$0.315229\pi$
$500$	2.57118	+	2.33396i	0.114987	+	0.104378i
$501$		0			0
$502$	−13.3483	+	26.1975i	−0.595763	+	1.16925i
$503$	2.42460	+	4.75855i	0.108108	+	0.212173i	0.938722	−	0.344674i	$-0.112011\pi$
$503$	2.42460	+	4.75855i	0.108108	+	0.212173i	−0.830615	+	0.556848i	$0.812011\pi$
$504$		0			0
$505$	−0.738195	−	10.7647i	−0.0328492	−	0.479025i
$506$	8.17484	+	0.514888i	0.363416	+	0.0228896i
$507$		0			0
$508$	−4.46873	+	0.707777i	−0.198268	+	0.0314025i
$509$	18.6283	+	6.05272i	0.825687	+	0.268282i	0.691228	−	0.722637i	$-0.257070\pi$
$509$	18.6283	+	6.05272i	0.825687	+	0.268282i	0.134459	+	0.990919i	$0.457070\pi$
$510$		0			0
$511$	0.372057	−	0.270315i	0.0164588	−	0.0119580i
$512$	−15.1686	−	2.40248i	−0.670365	−	0.106175i
$513$		0			0
$514$	−2.21058	+	6.80347i	−0.0975046	+	0.300088i
$515$	1.61891	+	7.05555i	0.0713376	+	0.310905i
$516$		0			0
$517$	−20.8767	+	35.2950i	−0.918158	+	1.55227i
$518$	−1.11243	−	1.11243i	−0.0488775	−	0.0488775i
$519$		0			0
$520$	17.2419	+	4.32353i	0.756106	+	0.189599i
$521$	−5.78913	−	17.8171i	−0.253626	−	0.780582i	−0.994097	−	0.108493i	$-0.965397\pi$
$521$	−5.78913	−	17.8171i	−0.253626	−	0.780582i	0.740471	−	0.672089i	$-0.234603\pi$
$522$		0			0
$523$	0.403961	−	2.55051i	0.0176640	−	0.111526i	−0.977281	−	0.211948i	$-0.932019\pi$
$523$	0.403961	−	2.55051i	0.0176640	−	0.111526i	0.994945	+	0.100422i	$0.0320193\pi$
$524$	−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
$530$	−16.3002	+	26.0078i	−0.708035	+	1.12971i
$531$		0			0
$532$	0.0394115	+	0.0200812i	0.00170871	+	0.000870630i
$533$	−20.4729	−	3.24258i	−0.886778	−	0.140452i
$534$		0			0
$535$	9.68984	−	22.7427i	0.418928	−	0.983253i
$536$	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	−0.676224	−	0.736696i	$-0.736385\pi$
$541$	5.42829	−	7.47139i	0.233380	−	0.321220i	0.909604	+	0.415476i	$0.136385\pi$
$542$	12.3031	+	24.1462i	0.528464	+	1.03717i
$543$		0			0
$544$	−3.79482	−	5.22312i	−0.162701	−	0.223939i
$545$	−16.3634	+	13.6931i	−0.700931	+	0.586546i
$546$		0			0
$547$	0.954295	−	0.486237i	0.0408027	−	0.0207900i	−0.433470	−	0.901168i	$-0.642711\pi$
$547$	0.954295	−	0.486237i	0.0408027	−	0.0207900i	0.474273	+	0.880378i	$0.342711\pi$
$548$	−0.210388	−	1.32834i	−0.00898732	−	0.0567437i
$549$		0			0
$550$	−13.0739	−	21.5519i	−0.557471	−	0.918978i
$551$	7.10113			0.302518
$552$		0			0
$553$	0.114386	−	0.0582826i	0.00486419	−	0.00247843i
$554$	−6.76800	+	2.19906i	−0.287545	+	0.0934290i
$555$		0			0
$556$	1.91881	+	2.64102i	0.0813758	+	0.112004i
$557$	19.5384	−	38.3462i	0.827868	−	1.62478i	0.0479915	−	0.998848i	$-0.484718\pi$
$557$	19.5384	−	38.3462i	0.827868	−	1.62478i	0.779876	−	0.625934i	$-0.215282\pi$
$558$		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
$563$	25.5439	−	4.04575i	1.07655	−	0.170508i	0.407111	−	0.913379i	$-0.366536\pi$
$563$	25.5439	−	4.04575i	1.07655	−	0.170508i	0.669435	+	0.742871i	$0.266536\pi$
$564$		0			0
$565$	−3.63532	+	8.53235i	−0.152939	+	0.358959i
$566$	−28.0219	+	20.3591i	−1.17785	+	0.855756i
$567$		0			0
$568$	−26.2257	−	13.3626i	−1.10040	−	0.560684i
$569$	−8.39651	+	25.8418i	−0.352000	+	1.08334i	0.605729	+	0.795671i	$0.292882\pi$
$569$	−8.39651	+	25.8418i	−0.352000	+	1.08334i	−0.957729	+	0.287673i	$0.907118\pi$
$570$		0			0
$571$		−	40.5475i		−	1.69686i	−0.529308	−	0.848430i	$-0.677549\pi$
$571$		−	40.5475i		−	1.69686i	0.529308	−	0.848430i	$-0.322451\pi$
$572$	2.74464	+	1.62343i	0.114759	+	0.0678791i
$573$		0			0
$574$	−1.57665	−	1.14550i	−0.0658081	−	0.0478124i
$575$	6.66701	−	4.64161i	0.278034	−	0.193569i
$576$		0			0
$577$	5.28872	−	33.3917i	0.220172	−	1.39011i	−0.591643	−	0.806200i	$-0.701521\pi$
$577$	5.28872	−	33.3917i	0.220172	−	1.39011i	0.811815	−	0.583914i	$-0.198479\pi$
$578$	0.775613	−	4.89703i	0.0322612	−	0.203689i
$579$		0			0
$580$	−6.43143	−	1.61273i	−0.267051	−	0.0669649i
$581$	−2.58426	−	1.87757i	−0.107213	−	0.0778948i
$582$		0			0
$583$	22.4673	−	19.8048i	0.930502	−	0.820233i
$584$			6.16801i			0.255234i
$585$		0			0
$586$	−3.39505	+	10.4489i	−0.140248	+	0.431640i
$587$	−8.62859	−	4.39649i	−0.356140	−	0.181462i	0.266762	−	0.963763i	$-0.414046\pi$
$587$	−8.62859	−	4.39649i	−0.356140	−	0.181462i	−0.622902	+	0.782300i	$0.714046\pi$
$588$		0			0
$589$	−0.211163	+	0.153419i	−0.00870081	+	0.00632151i
$590$	−30.1005	−	12.8247i	−1.23922	−	0.527986i
$591$		0			0
$592$	24.1566	−	3.82603i	0.992829	−	0.157249i
$593$	14.0452	−	14.0452i	0.576769	−	0.576769i	−0.357243	−	0.934012i	$-0.616283\pi$
$593$	14.0452	−	14.0452i	0.576769	−	0.576769i	0.934012	+	0.357243i	$0.116283\pi$
$594$		0			0
$595$	−0.108568	−	1.58320i	−0.00445086	−	0.0649048i
$596$	−1.05199	+	1.44794i	−0.0430912	+	0.0593099i
$597$		0			0
$598$	−3.47084	+	6.81191i	−0.141933	+	0.278560i
$599$	−2.65433	−	3.65338i	−0.108453	−	0.149273i	0.751340	−	0.659915i	$-0.229408\pi$
$599$	−2.65433	−	3.65338i	−0.108453	−	0.149273i	−0.859793	+	0.510642i	$0.829408\pi$
$600$		0			0
$601$	−7.96746	+	2.58878i	−0.324999	+	0.105599i	−0.466973	−	0.884272i	$-0.654655\pi$
$601$	−7.96746	+	2.58878i	−0.324999	+	0.105599i	0.141973	+	0.989871i	$0.454655\pi$
$602$	−1.36688	+	0.696458i	−0.0557097	+	0.0283855i
$603$		0			0
$604$	4.64774			0.189114
$605$	6.24783	+	23.7900i	0.254011	+	0.967201i
$606$		0			0
$607$	1.20123	+	7.58425i	0.0487563	+	0.307835i	1.00000		0.000605683i	$-0.000192795\pi$
$607$	1.20123	+	7.58425i	0.0487563	+	0.307835i	−0.951244	+	0.308441i	$0.900193\pi$
$608$	−1.15435	+	0.588172i	−0.0468152	+	0.0238535i
$609$		0			0
$610$	1.77258	−	19.9516i	0.0717698	−	0.807816i
$611$	−22.4971	−	30.9646i	−0.910134	−	1.25269i
$612$		0			0
$613$	19.4882	+	38.2477i	0.787120	+	1.54481i	0.837726	+	0.546091i	$0.183885\pi$
$613$	19.4882	+	38.2477i	0.787120	+	1.54481i	−0.0506058	+	0.998719i	$0.516115\pi$
$614$	−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	$-0.539389\pi$
$619$	−20.0674	−	6.52029i	−0.806576	−	0.262073i	−0.683147	+	0.730281i	$0.739389\pi$
$620$	0.226091	−	0.0909931i	0.00908003	−	0.00365437i
$621$		0			0
$622$	11.2840	+	1.78720i	0.452445	+	0.0716603i
$623$	−1.35149	−	0.688620i	−0.0541464	−	0.0275890i
$624$		0			0
$625$	−23.4460	−	8.67678i	−0.937839	−	0.347071i
$626$		−	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	−0.960420	−	0.278555i	$-0.910144\pi$
$631$	−8.72043	−	26.8387i	−0.347155	−	1.06843i	0.613265	−	0.789877i	$-0.289856\pi$
$632$	−0.269351	+	1.70061i	−0.0107142	+	0.0676467i
$633$		0			0
$634$	5.32290	+	16.3822i	0.211399	+	0.650621i
$635$	27.9433	−	16.7389i	1.10889	−	0.664263i
$636$		0			0
$637$	15.2422	+	15.2422i	0.603918	+	0.603918i
$638$	41.4275	+	24.5041i	1.64013	+	0.970125i
$639$		0			0
$640$	−28.8006	+	6.60834i	−1.13844	+	0.261218i
$641$	5.23436	−	16.1097i	0.206745	−	0.636295i	−0.792893	−	0.609362i	$-0.791426\pi$
$641$	5.23436	−	16.1097i	0.206745	−	0.636295i	0.999637	−	0.0269333i	$-0.00857417\pi$
$642$		0			0
$643$	6.19838	+	0.981726i	0.244440	+	0.0387155i	0.277452	−	0.960739i	$-0.410510\pi$
$643$	6.19838	+	0.981726i	0.244440	+	0.0387155i	−0.0330121	+	0.999455i	$0.510510\pi$
$644$	−0.0781682	+	0.0567925i	−0.00308026	+	0.00223794i
$645$		0			0
$646$	3.98552	+	1.29497i	0.156808	+	0.0509500i
$647$	42.9518	−	6.80289i	1.68861	−	0.267449i	0.763128	−	0.646247i	$-0.223662\pi$
$647$	42.9518	−	6.80289i	1.68861	−	0.267449i	0.925479	+	0.378798i	$0.123662\pi$
$648$		0			0
$649$	24.5981	+	20.3522i	0.965559	+	0.798893i
$650$	23.3073	−	3.21171i	0.914188	−	0.125974i
$651$		0			0
$652$	1.41240	+	2.77200i	0.0553140	+	0.108560i
$653$	4.41780	−	8.67042i	0.172882	−	0.339300i	−0.788266	−	0.615335i	$-0.789021\pi$
$653$	4.41780	−	8.67042i	0.172882	−	0.339300i	0.961147	+	0.276035i	$0.0890207\pi$
$654$		0			0
$655$	14.0190	+	16.7529i	0.547767	+	0.654590i
$656$	28.8145	−	9.36239i	1.12502	−	0.365540i
$657$		0			0
$658$	−0.562936	−	3.55424i	−0.0219455	−	0.138559i
$659$	3.37375			0.131423			0.0657113	−	0.997839i	$-0.479068\pi$
$659$	3.37375			0.131423			0.0657113	+	0.997839i	$0.479068\pi$
$660$		0			0
$661$	9.93056			0.386254			0.193127	−	0.981174i	$-0.438137\pi$
$661$	9.93056			0.386254			0.193127	+	0.981174i	$0.438137\pi$
$662$	−4.21003	−	26.5811i	−0.163628	−	1.03310i
$663$		0			0
$664$	40.7453	−	13.2389i	1.58122	−	0.513771i
$665$	−0.317199	−	0.0281813i	−0.0123005	−	0.00109282i
$666$		0			0
$667$	−7.04213	+	13.8210i	−0.272672	+	0.535150i
$668$	−1.70084	−	3.33809i	−0.0658075	−	0.129154i
$669$		0			0
$670$	19.8263	−	1.35959i	0.765955	−	0.0525256i
$671$	−7.19624	+	18.1719i	−0.277808	+	0.701520i
$672$		0			0
$673$	−37.7823	+	5.98412i	−1.45640	+	0.230671i	−0.833885	−	0.551938i	$-0.813889\pi$
$673$	−37.7823	+	5.98412i	−1.45640	+	0.230671i	−0.622514	+	0.782609i	$0.713889\pi$
$674$	11.0161	+	3.57935i	0.424324	+	0.137871i
$675$		0			0
$676$	0.858662	−	0.623855i	0.0330255	−	0.0239944i
$677$	31.7956	+	5.03592i	1.22200	+	0.193546i	0.733911	−	0.679246i	$-0.237693\pi$
$677$	31.7956	+	5.03592i	1.22200	+	0.193546i	0.488092	+	0.872792i	$0.337693\pi$
$678$		0			0
$679$	−0.0815917	+	0.251113i	−0.00313120	+	0.00963684i
$680$	18.0344	+	11.3029i	0.691588	+	0.433447i
$681$		0			0
$682$	−1.76132	+	0.166370i	−0.0674443	+	0.00637063i
$683$	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
$685$	4.97566	+	8.30617i	0.190110	+	0.317363i
$686$	1.25585	+	3.86510i	0.0479484	+	0.147570i
$687$		0			0
$688$	3.73084	−	23.5556i	0.142237	−	0.898050i
$689$	8.63834	+	26.5861i	0.329095	+	1.01285i
$690$		0			0
$691$	20.4397	+	14.8503i	0.777564	+	0.564933i	0.904247	−	0.427010i	$-0.140433\pi$
$691$	20.4397	+	14.8503i	0.777564	+	0.564933i	−0.126683	+	0.991943i	$0.540433\pi$
$692$	−2.73759	−	2.73759i	−0.104068	−	0.104068i
$693$		0			0
$694$			14.1878i			0.538562i
$695$	−19.9143	−	12.4811i	−0.755393	−	0.473436i
$696$		0			0
$697$	−22.1136	−	11.2675i	−0.837613	−	0.426785i
$698$	2.25468	+	0.357107i	0.0853410	+	0.0135167i
$699$		0			0
$700$	0.280884	+	0.0975622i	0.0106164	+	0.00368751i
$701$	−26.8458	−	8.72273i	−1.01395	−	0.329453i	−0.245525	−	0.969390i	$-0.578960\pi$
$701$	−26.8458	−	8.72273i	−1.01395	−	0.329453i	−0.768427	+	0.639937i	$0.778960\pi$
$702$		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
$707$	−0.419457	−	0.823230i	−0.0157753	−	0.0309608i
$708$		0			0
$709$	4.79615	+	6.60134i	0.180123	+	0.247918i	0.889526	−	0.456885i	$-0.151035\pi$
$709$	4.79615	+	6.60134i	0.180123	+	0.247918i	−0.709402	+	0.704804i	$0.751035\pi$
$710$	−38.8051	−	3.44761i	−1.45633	−	0.129386i
$711$		0			0
$712$	18.1262	−	9.23576i	0.679308	−	0.346125i
$713$	−0.0891912	−	0.563131i	−0.00334024	−	0.0210894i
$714$		0			0
$715$	−22.6946	−	3.46508i	−0.848730	−	0.129587i
$716$	6.26727			0.234219
$717$		0			0
$718$	35.6261	−	18.1524i	1.32955	−	0.677441i
$719$	−0.986856	+	0.320649i	−0.0368035	+	0.0119582i	−0.327361	−	0.944899i	$-0.606159\pi$
$719$	−0.986856	+	0.320649i	−0.0368035	+	0.0119582i	0.290557	+	0.956858i	$0.406159\pi$
$720$		0			0
$721$	0.364342	+	0.501474i	0.0135688	+	0.0186759i
$722$	−12.7300	+	24.9840i	−0.473762	+	0.929810i
$723$		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	$0.277406\pi$
$728$	1.50337	−	0.238110i	0.0557184	−	0.00882493i
$729$		0			0
$730$	3.04805	+	7.57350i	0.112813	+	0.280308i
$731$	−15.8055	+	11.4833i	−0.584586	+	0.424726i
$732$		0			0
$733$	40.6968	+	20.7361i	1.50317	+	0.765904i	0.995420	−	0.0956003i	$-0.0304771\pi$
$733$	40.6968	+	20.7361i	1.50317	+	0.765904i	0.507751	+	0.861504i	$0.330477\pi$
$734$	−3.83723	+	11.8098i	−0.141635	+	0.435907i
$735$		0			0
$736$		−	2.83001i		−	0.104315i
$737$	−18.9241	−	4.23142i	−0.697079	−	0.155866i
$738$		0			0
$739$	−3.07164	−	2.23167i	−0.112992	−	0.0820934i	0.529854	−	0.848089i	$-0.322247\pi$
$739$	−3.07164	−	2.23167i	−0.112992	−	0.0820934i	−0.642846	+	0.765995i	$0.722247\pi$
$740$	3.22043	−	1.92914i	0.118385	−	0.0709165i
$741$		0			0
$742$	−0.411150	+	2.59590i	−0.0150938	+	0.0952984i
$743$	−6.63736	+	41.9067i	−0.243501	+	1.53741i	0.498430	+	0.866930i	$0.333910\pi$
$743$	−6.63736	+	41.9067i	−0.243501	+	1.53741i	−0.741931	+	0.670476i	$0.766090\pi$
$744$		0			0
$745$	3.13401	−	12.4982i	0.114821	−	0.457899i
$746$	10.6517	+	7.73895i	0.389988	+	0.283343i
$747$		0			0
$748$	2.52477	+	2.86419i	0.0923149	+	0.104725i
$749$		−	2.11681i		−	0.0773467i
$750$		0			0
$751$	−3.08775	+	9.50312i	−0.112674	+	0.346774i	−0.991455	−	0.130451i	$-0.958357\pi$
$751$	−3.08775	+	9.50312i	−0.112674	+	0.346774i	0.878781	+	0.477225i	$0.158357\pi$
$752$	49.8464	+	25.3980i	1.81771	+	0.926171i
$753$		0			0
$754$	−36.3446	+	26.4059i	−1.32359	+	0.961647i
$755$	−31.0413	+	12.4930i	−1.12971	+	0.454665i
$756$		0			0
$757$	29.0217	−	4.59658i	1.05481	−	0.167065i	0.395140	−	0.918621i	$-0.370696\pi$
$757$	29.0217	−	4.59658i	1.05481	−	0.167065i	0.659670	+	0.751555i	$0.270696\pi$
$758$	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	−0.352238	−	0.935910i	$-0.614579\pi$
$761$	17.8404	−	24.5552i	0.646713	−	0.890124i	0.998951	+	0.0457864i	$0.0145794\pi$
$762$		0			0
$763$	−0.829459	+	1.62790i	−0.0300284	+	0.0589341i
$764$	1.15493	+	1.58963i	0.0417840	+	0.0575107i
$765$		0			0
$766$	15.0044	−	4.87523i	0.542131	−	0.176149i
$767$	−26.5507	+	13.5283i	−0.958690	+	0.488477i
$768$		0			0
$769$	37.6421			1.35741			0.678705	−	0.734411i	$-0.262542\pi$
$769$	37.6421			1.35741			0.678705	+	0.734411i	$0.262542\pi$
$770$	−1.75327	−	1.25898i	−0.0631836	−	0.0453704i
$771$		0			0
$772$	−0.288213	−	1.81970i	−0.0103730	−	0.0654926i
$773$	−22.9995	+	11.7188i	−0.827234	+	0.421497i	−0.815727	−	0.578437i	$-0.803663\pi$
$773$	−22.9995	+	11.7188i	−0.827234	+	0.421497i	−0.0115072	+	0.999934i	$0.503663\pi$
$774$		0			0
$775$	−1.26543	+	1.21545i	−0.0454555	+	0.0436602i
$776$	−2.08149	−	2.86493i	−0.0747213	−	0.102845i
$777$		0			0
$778$	15.2835	+	29.9955i	0.547939	+	1.07539i
$779$	−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
$785$	−10.1790	−	4.33688i	−0.363302	−	0.154790i
$786$		0			0
$787$	−17.0625	−	2.70244i	−0.608213	−	0.0963315i	−0.155272	−	0.987872i	$-0.549625\pi$
$787$	−17.0625	−	2.70244i	−0.608213	−	0.0963315i	−0.452942	+	0.891540i	$0.649625\pi$
$788$	3.87655	+	1.97520i	0.138096	+	0.0703636i
$789$		0			0
$790$	0.509666	+	2.22123i	0.0181331	+	0.0790279i
$791$			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
$797$	6.97213	−	44.0203i	0.246965	−	1.55928i	−0.482892	−	0.875680i	$-0.660414\pi$
$797$	6.97213	−	44.0203i	0.246965	−	1.55928i	0.729858	−	0.683599i	$-0.239586\pi$
$798$		0			0
$799$	−14.1615	−	43.5847i	−0.500999	−	1.54192i
$800$	−7.14755	+	4.97616i	−0.252704	+	0.175934i
$801$		0			0
$802$	−4.60219	−	4.60219i	−0.162509	−	0.162509i
$803$	−0.749124	−	7.93078i	−0.0264360	−	0.279871i
$804$		0			0
$805$	0.369413	−	0.589419i	0.0130201	−	0.0207743i
$806$	0.510267	−	1.57044i	0.0179734	−	0.0553164i
$807$		0			0
$808$	12.2392	+	1.93850i	0.430574	+	0.0681962i
$809$	−12.3255	+	8.95497i	−0.433340	+	0.314840i	−0.782983	−	0.622043i	$-0.786303\pi$
$809$	−12.3255	+	8.95497i	−0.433340	+	0.314840i	0.349643	+	0.936883i	$0.386303\pi$
$810$		0			0
$811$	−43.3276	−	14.0780i	−1.52144	−	0.494345i	−0.575253	−	0.817976i	$-0.695096\pi$
$811$	−43.3276	−	14.0780i	−1.52144	−	0.494345i	−0.946183	+	0.323631i	$0.895096\pi$
$812$	−0.560774	+	0.0888178i	−0.0196793	+	0.00311689i
$813$		0			0
$814$	−26.3953	+	6.77521i	−0.925155	+	0.237471i
$815$	−16.8842	−	14.7171i	−0.591427	−	0.515518i
$816$		0			0
$817$	1.77984	+	3.49314i	0.0622688	+	0.122209i
$818$	−2.96438	+	5.81793i	−0.103647	+	0.203419i
$819$		0			0
$820$	3.56640	−	2.98440i	0.124544	−	0.104220i
$821$	27.3071	−	8.87260i	0.953023	−	0.309656i	0.209079	−	0.977899i	$-0.432953\pi$
$821$	27.3071	−	8.87260i	0.953023	−	0.309656i	0.743943	+	0.668243i	$0.232953\pi$
$822$		0			0
$823$	−4.21701	−	26.6252i	−0.146996	−	0.928095i	−0.945386	−	0.325954i	$-0.894314\pi$
$823$	−4.21701	−	26.6252i	−0.146996	−	0.928095i	0.798390	−	0.602141i	$-0.205686\pi$
$824$	−8.31350			−0.289614
$825$		0			0
$826$	−2.80165			−0.0974820
$827$	6.20779	+	39.1944i	0.215866	+	1.36292i	0.822872	+	0.568227i	$0.192370\pi$
$827$	6.20779	+	39.1944i	0.215866	+	1.36292i	−0.607006	+	0.794697i	$0.707630\pi$
$828$		0			0
$829$	10.3353	−	3.35814i	0.358959	−	0.116633i	−0.123985	−	0.992284i	$-0.539567\pi$
$829$	10.3353	−	3.35814i	0.358959	−	0.116633i	0.482944	+	0.875651i	$0.339567\pi$
$830$	43.4875	−	36.3908i	1.50947	−	1.26314i
$831$		0			0
$832$	−8.99683	+	17.6573i	−0.311909	+	0.612156i
$833$	11.7174	+	22.9966i	0.405983	+	0.796786i
$834$		0			0
$835$	20.3322	+	17.7226i	0.703625	+	0.613316i
$836$	0.646943	−	0.410500i	0.0223750	−	0.0141974i
$837$		0			0
$838$	−1.80523	+	0.285920i	−0.0623606	+	0.00987695i
$839$	38.3426	+	12.4583i	1.32373	+	0.430107i	0.883775	−	0.467912i	$-0.154993\pi$
$839$	38.3426	+	12.4583i	1.32373	+	0.430107i	0.439958	+	0.898019i	$0.354993\pi$
$840$		0			0
$841$	−50.2797	+	36.5303i	−1.73378	+	1.25967i
$842$	47.0053	+	7.44491i	1.61991	+	0.256569i
$843$		0			0
$844$	−0.569376	+	1.75236i	−0.0195987	+	0.0603187i
$845$	−4.05793	+	6.47465i	−0.139597	+	0.222735i
$846$		0			0
$847$	1.29066	+	1.66439i	0.0443477	+	0.0571891i
$848$	−28.8921	−	28.8921i	−0.992159	−	0.992159i
$849$		0			0
$850$	27.7294	+	4.96640i	0.951112	+	0.170346i
$851$	−2.71386	−	8.35241i	−0.0930300	−	0.286317i
$852$		0			0
$853$	−2.18326	+	13.7845i	−0.0747533	+	0.471974i	0.921705	+	0.387890i	$0.126796\pi$
$853$	−2.18326	+	13.7845i	−0.0747533	+	0.471974i	−0.996459	+	0.0840831i	$0.973204\pi$
$854$	−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	0.0773373	−	0.997005i	$-0.475358\pi$
$857$	−26.9229	−	26.9229i	−0.919668	−	0.919668i	−0.997005	+	0.0773373i	$0.975358\pi$
$858$		0			0
$859$		−	18.3200i		−	0.625071i	−0.949906	−	0.312535i	$-0.898822\pi$
$859$		−	18.3200i		−	0.625071i	0.949906	−	0.312535i	$-0.101178\pi$
$860$	−0.818666	−	3.56792i	−0.0279163	−	0.121665i
$861$		0			0
$862$	13.3966	+	6.82592i	0.456291	+	0.232492i
$863$	12.0033	+	1.90114i	0.408597	+	0.0647154i	0.357350	−	0.933971i	$-0.383680\pi$
$863$	12.0033	+	1.90114i	0.408597	+	0.0647154i	0.0512472	+	0.998686i	$0.483680\pi$
$864$		0			0
$865$	25.6424	+	10.9253i	0.871866	+	0.371470i
$866$	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
$872$	−11.1247	−	21.8334i	−0.376730	−	0.739374i
$873$		0			0
$874$	1.07972	+	1.48611i	0.0365222	+	0.0502685i
$875$	−2.13821	+	0.103409i	−0.0722848	+	0.00349585i
$876$		0			0
$877$	−11.4361	+	5.82698i	−0.386169	+	0.196763i	−0.636287	−	0.771452i	$-0.719531\pi$
$877$	−11.4361	+	5.82698i	−0.386169	+	0.196763i	0.250118	+	0.968215i	$0.419531\pi$
$878$	−5.84636	−	36.9125i	−0.197305	−	1.24574i
$879$		0			0
$880$	31.8556	−	10.5469i	1.07385	−	0.355537i
$881$	−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
$883$	38.8377	−	19.7888i	1.30699	−	0.665947i	0.344893	−	0.938642i	$-0.387915\pi$
$883$	38.8377	−	19.7888i	1.30699	−	0.665947i	0.962100	+	0.272695i	$0.0879150\pi$
$884$	−3.38926	+	1.10124i	−0.113993	+	0.0370387i
$885$		0			0
$886$	−27.5163	−	37.8730i	−0.924429	−	1.27237i
$887$	4.72114	−	9.26576i	0.158520	−	0.311114i	−0.798062	−	0.602575i	$-0.794141\pi$
$887$	4.72114	−	9.26576i	0.158520	−	0.311114i	0.956583	+	0.291461i	$0.0941414\pi$
$888$		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
$893$	−9.08308	+	1.43862i	−0.303954	+	0.0481415i
$894$		0			0
$895$	−41.8578	+	16.8462i	−1.39915	+	0.563106i
$896$	−2.04700	+	1.48723i	−0.0683855	+	0.0496850i
$897$		0			0
$898$	9.92048	+	5.05474i	0.331051	+	0.168679i
$899$	1.03530	−	3.18633i	0.0345292	−	0.106270i
$900$		0			0
$901$			33.4710i			1.11508i
$902$	−30.9821	+	13.4046i	−1.03159	+	0.446324i
$903$		0			0
$904$	−8.61708	−	6.26067i	−0.286600	−	0.208227i
$905$	−2.50710	+	9.99811i	−0.0833388	+	0.332349i
$906$		0			0
$907$	2.55097	−	16.1062i	0.0847036	−	0.534798i	−0.908451	−	0.417991i	$-0.862734\pi$
$907$	2.55097	−	16.1062i	0.0847036	−	0.534798i	0.993155	−	0.116806i	$-0.0372657\pi$
$908$	0.635040	−	4.00948i	0.0210745	−	0.133059i
$909$		0			0
$910$	1.72827	−	1.03529i	0.0572915	−	0.0343194i
$911$	−14.3281	−	10.4099i	−0.474710	−	0.344897i	0.324564	−	0.945864i	$-0.394782\pi$
$911$	−14.3281	−	10.4099i	−0.474710	−	0.344897i	−0.799274	+	0.600967i	$0.794782\pi$
$912$		0			0
$913$	−50.7821	+	21.9712i	−1.68064	+	0.727140i
$914$		−	10.2385i		−	0.338659i
$915$		0			0
$916$	−1.57702	+	4.85357i	−0.0521062	+	0.160366i
$917$	1.66665	+	0.849203i	0.0550378	+	0.0280431i
$918$		0			0
$919$	−7.38632	+	5.36648i	−0.243652	+	0.177024i	−0.702909	−	0.711280i	$-0.748116\pi$
$919$	−7.38632	+	5.36648i	−0.243652	+	0.177024i	0.459257	+	0.888304i	$0.348116\pi$
$920$	3.48329	+	8.65494i	0.114841	+	0.285345i
$921$		0			0
$922$	−43.6594	+	6.91497i	−1.43785	+	0.227732i
$923$	−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
$928$	7.54970	−	14.8171i	0.247831	−	0.486396i
$929$	−1.06529	−	1.46625i	−0.0349511	−	0.0481061i	0.791184	−	0.611578i	$-0.209465\pi$
$929$	−1.06529	−	1.46625i	−0.0349511	−	0.0481061i	−0.826135	+	0.563472i	$0.809465\pi$
$930$		0			0
$931$	4.92578	−	1.60048i	0.161436	−	0.0524537i
$932$	−4.32918	+	2.20583i	−0.141807	+	0.0722543i
$933$		0			0
$934$	40.2174			1.31595
$935$	−24.5613	−	12.3429i	−0.803240	−	0.403655i
$936$		0			0
$937$	−2.37143	−	14.9726i	−0.0774711	−	0.489133i	−0.995666	−	0.0930039i	$-0.970353\pi$
$937$	−2.37143	−	14.9726i	−0.0774711	−	0.489133i	0.918195	−	0.396130i	$-0.129647\pi$
$938$	1.51621	−	0.772546i	0.0495059	−	0.0252245i
$939$		0			0
$940$	8.55319	+	0.759902i	0.278974	+	0.0247853i
$941$	12.8308	+	17.6600i	0.418271	+	0.575701i	0.965211	−	0.261471i	$-0.0842075\pi$
$941$	12.8308	+	17.6600i	0.418271	+	0.575701i	−0.546940	+	0.837172i	$0.684208\pi$
$942$		0			0
$943$	−4.93902	−	9.69338i	−0.160837	−	0.315660i
$944$	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
$950$	1.85483	−	5.34009i	0.0601785	−	0.173255i
$951$		0			0
$952$	1.80005	+	0.285100i	0.0583400	+	0.00924015i
$953$	11.6216	+	5.92153i	0.376462	+	0.191817i	0.631975	−	0.774989i	$-0.282244\pi$
$953$	11.6216	+	5.92153i	0.376462	+	0.191817i	−0.255513	+	0.966806i	$0.582244\pi$
$954$		0			0
$955$	−11.9864	−	7.51238i	−0.387871	−	0.243095i
$956$			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
$962$	3.97890	−	25.1218i	0.128285	−	0.809960i
$963$		0			0
$964$	−1.55173	−	4.77572i	−0.0499777	−	0.153816i
$965$	6.81621	+	11.3787i	0.219422	+	0.366294i
$966$		0			0
$967$	−13.6319	−	13.6319i	−0.438372	−	0.438372i	0.453092	−	0.891464i	$-0.350321\pi$
$967$	−13.6319	−	13.6319i	−0.438372	−	0.438372i	−0.891464	+	0.453092i	$0.850321\pi$
$968$	−28.2343	+	0.883368i	−0.907484	+	0.0283925i
$969$		0			0
$970$	−3.97156	−	2.48914i	−0.127519	−	0.0799216i
$971$	−1.26967	+	3.90765i	−0.0407457	+	0.125403i	−0.969360	−	0.245643i	$-0.921001\pi$
$971$	−1.26967	+	3.90765i	−0.0407457	+	0.125403i	0.928615	+	0.371046i	$0.121001\pi$
$972$		0			0
$973$	−1.98769	−	0.314819i	−0.0637224	−	0.0100926i
$974$	−28.6965	+	20.8492i	−0.919495	+	0.668052i
$975$		0			0
$976$	25.3592	+	8.23971i	0.811729	+	0.263747i
$977$	−30.3314	+	4.80402i	−0.970386	+	0.153694i	−0.621451	−	0.783453i	$-0.713457\pi$
$977$	−30.3314	+	4.80402i	−0.970386	+	0.153694i	−0.348935	+	0.937147i	$0.613457\pi$
$978$		0			0
$979$	−22.1848	+	14.0768i	−0.709030	+	0.449895i
$980$	−4.82472	+	0.330856i	−0.154120	+	0.0105688i
$981$		0			0
$982$	−12.6616	−	24.8498i	−0.404048	−	0.792990i
$983$	12.5871	−	24.7035i	0.401465	−	0.787919i	−0.598447	−	0.801162i	$-0.704215\pi$
$983$	12.5871	−	24.7035i	0.401465	−	0.787919i	0.999912	+	0.0132429i	$0.00421546\pi$
$984$		0			0
$985$	−31.1999	−	2.77194i	−0.994113	−	0.0883212i
$986$	−51.1575	+	16.6221i	−1.62919	+	0.529355i
$987$		0			0
$988$	0.111871	+	0.706325i	0.00355909	+	0.0224712i
$989$	−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	$0.453827\pi$
$992$	0.0956197	+	0.603719i	0.00303593	+	0.0191681i
$993$		0			0
$994$	−3.17264	+	1.03085i	−0.100630	+	0.0326966i
$995$	19.2044	+	22.9496i	0.608822	+	0.727551i
$996$		0			0
$997$	13.1070	−	25.7239i	0.415103	−	0.814685i	−0.584891	−	0.811112i	$-0.698863\pi$
$997$	13.1070	−	25.7239i	0.415103	−	0.814685i	0.999994	−	0.00357282i	$-0.00113727\pi$
$998$	8.11406	+	15.9247i	0.256846	+	0.504089i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.4	✓	32	15.2	even	4
55.2.l.a.8.4	yes	32	33.8	even	10
55.2.l.a.18.1	yes	32	3.2	odd	2
55.2.l.a.52.1	yes	32	165.107	odd	20
275.2.bm.b.7.1		32	15.8	even	4
275.2.bm.b.18.4		32	15.14	odd	2
275.2.bm.b.107.4		32	165.8	odd	20
275.2.bm.b.118.1		32	165.74	even	10
495.2.bj.a.73.4		32	1.1	even	1	trivial
495.2.bj.a.118.1		32	11.8	odd	10	inner
495.2.bj.a.172.1		32	5.2	odd	4	inner
495.2.bj.a.217.4		32	55.52	even	20	inner
605.2.e.b.362.3		32	165.137	even	20
605.2.e.b.362.14		32	165.17	odd	20
605.2.e.b.483.3		32	33.17	even	10
605.2.e.b.483.14		32	33.5	odd	10
605.2.m.c.112.4		32	165.92	even	20
605.2.m.c.233.4		32	33.26	odd	10
605.2.m.c.457.4		32	165.2	odd	20
605.2.m.c.578.4		32	33.2	even	10
605.2.m.d.112.1		32	165.62	odd	20
605.2.m.d.233.1		32	33.29	even	10
605.2.m.d.457.1		32	165.152	even	20
605.2.m.d.578.1		32	33.20	odd	10
605.2.m.e.118.1		32	33.14	odd	10
605.2.m.e.282.1		32	165.32	odd	4
605.2.m.e.403.4		32	33.32	even	2
605.2.m.e.602.4		32	165.47	even	20
880.2.cm.a.337.4		32	60.47	odd	4
880.2.cm.a.513.1		32	12.11	even	2
880.2.cm.a.657.1		32	660.107	even	20
880.2.cm.a.833.4		32	132.107	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.237790 + 1.50135i) q^{2} +(-0.295389 + 0.0959778i) q^{4} +(1.71486 - 1.43501i) q^{5} +(0.0869260 - 0.170602i) q^{7} +(1.16585 + 2.28811i) q^{8} +(2.56223 + 2.23337i) q^{10} +(-1.77694 - 2.80044i) q^{11} +(3.05749 - 0.484259i) q^{13} +(0.276803 + 0.0899388i) q^{14} +(-3.66057 + 2.65956i) q^{16} +(3.66088 + 0.579827i) q^{17} +(0.229844 - 0.707388i) q^{19} +(-0.368822 + 0.588475i) q^{20} +(3.78190 - 3.33373i) q^{22} +(1.14886 + 1.14886i) q^{23} +(0.881484 - 4.92169i) q^{25} +(1.45408 + 4.47521i) q^{26} +(-0.00930302 + 0.0587369i) q^{28} +(2.95025 + 9.07993i) q^{29} +(-0.283900 - 0.206266i) q^{31} +(-1.23166 - 1.23166i) q^{32} +5.63413i q^{34} +(-0.0957498 - 0.417298i) q^{35} +(-4.81621 - 2.45398i) q^{37} +(1.11669 + 0.176866i) q^{38} +(5.28274 + 2.25078i) q^{40} +(-6.36824 - 2.06917i) q^{41} +(-3.72708 + 3.72708i) q^{43} +(0.793670 + 0.656674i) q^{44} +(-1.45165 + 1.99802i) q^{46} +(-5.61318 - 11.0165i) q^{47} +(4.09295 + 5.63346i) q^{49} +(7.59877 + 0.153087i) q^{50} +(-0.856672 + 0.436496i) q^{52} +(1.41265 + 8.91914i) q^{53} +(-7.06587 - 2.25243i) q^{55} +0.491699 q^{56} +(-12.9306 + 6.58847i) q^{58} +(-9.15496 + 2.97463i) q^{59} +(-3.46383 - 4.76756i) q^{61} +(0.242168 - 0.475281i) q^{62} +(-3.76284 + 5.17911i) q^{64} +(4.54825 - 5.21797i) q^{65} +(4.13426 - 4.13426i) q^{67} +(-1.13704 + 0.180089i) q^{68} +(0.603742 - 0.242983i) q^{70} +(-9.27272 + 6.73702i) q^{71} +(2.14008 + 1.09042i) q^{73} +(2.53903 - 7.81434i) q^{74} +0.231015i q^{76} +(-0.632224 + 0.0597184i) q^{77} +(0.542434 + 0.394101i) q^{79} +(-2.46086 + 9.81373i) q^{80} +(1.59224 - 10.0530i) q^{82} +(2.60980 - 16.4776i) q^{83} +(7.10995 - 4.25908i) q^{85} +(-6.48191 - 4.70938i) q^{86} +(4.33608 - 7.33074i) q^{88} -7.92190i q^{89} +(0.183160 - 0.563709i) q^{91} +(-0.449625 - 0.229095i) q^{92} +(15.2048 - 11.0469i) q^{94} +(-0.620959 - 1.54290i) q^{95} +(-1.36201 + 0.215721i) q^{97} +(-7.48452 + 7.48452i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 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

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