LMFDB - Embedded newform 495.2.bj.a.28.4

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			28.4
Character	$\chi$	$=$	495.28
Dual form			495.2.bj.a.442.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.15100 - 2.25897i) q^{2} +(-2.60258 - 3.58214i) q^{4} +(-1.91314 + 1.15755i) q^{5} +(-1.78576 - 0.282837i) q^{7} +(-6.07934 + 0.962874i) q^{8} +(0.412838 + 5.65406i) q^{10} +(-1.72268 - 2.83415i) q^{11} +(-2.00993 - 1.02411i) q^{13} +(-2.69434 + 3.70844i) q^{14} +(-2.08573 + 6.41923i) q^{16} +(-2.99738 + 1.52724i) q^{17} +(-1.05647 - 0.767569i) q^{19} +(9.12557 + 3.84051i) q^{20} +(-8.38507 + 0.629367i) q^{22} +(3.16488 + 3.16488i) q^{23} +(2.32018 - 4.42908i) q^{25} +(-4.62687 + 3.36162i) q^{26} +(3.63442 + 7.13295i) q^{28} +(2.37569 - 1.72604i) q^{29} +(-1.23925 - 3.81401i) q^{31} +(3.39552 + 3.39552i) q^{32} +8.52886i q^{34} +(3.74380 - 1.52600i) q^{35} +(0.501987 - 3.16942i) q^{37} +(-2.94992 + 1.50306i) q^{38} +(10.5160 - 8.87923i) q^{40} +(-0.766287 + 1.05470i) q^{41} +(4.55431 - 4.55431i) q^{43} +(-5.66890 + 13.5469i) q^{44} +(10.7922 - 3.50658i) q^{46} +(7.62854 - 1.20824i) q^{47} +(-3.54845 - 1.15296i) q^{49} +(-7.33465 - 10.3391i) q^{50} +(1.56249 + 9.86517i) q^{52} +(2.89146 - 5.67482i) q^{53} +(6.57637 + 3.42803i) q^{55} +11.1286 q^{56} +(-1.16465 - 7.35329i) q^{58} +(-7.28135 - 10.0219i) q^{59} +(-8.85435 - 2.87695i) q^{61} +(-10.0421 - 1.59052i) q^{62} +(-1.25983 + 0.409344i) q^{64} +(5.03072 - 0.367324i) q^{65} +(-2.46236 + 2.46236i) q^{67} +(13.2717 + 6.76227i) q^{68} +(0.861947 - 10.2136i) q^{70} +(2.09243 - 6.43984i) q^{71} +(-1.47735 + 9.32763i) q^{73} +(-6.58185 - 4.78199i) q^{74} +5.78207i q^{76} +(2.27469 + 5.54835i) q^{77} +(0.353860 + 1.08907i) q^{79} +(-3.44026 - 14.6952i) q^{80} +(1.50055 + 2.94499i) q^{82} +(4.75092 + 9.32422i) q^{83} +(3.96654 - 6.39143i) q^{85} +(-5.04603 - 15.5301i) q^{86} +(13.2017 + 15.5710i) q^{88} +3.85743i q^{89} +(3.29960 + 2.39730i) q^{91} +(3.10019 - 19.5739i) q^{92} +(6.05109 - 18.6233i) q^{94} +(2.90966 + 0.245553i) q^{95} +(-0.693249 - 0.353228i) q^{97} +(-6.68878 + 6.68878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.15100	−	2.25897i	0.813883	−	1.59733i	0.0119437	−	0.999929i	$-0.496198\pi$
$2$	1.15100	−	2.25897i	0.813883	−	1.59733i	0.801939	−	0.597406i	$-0.203802\pi$
$3$		0			0
$3$		0			0
$4$	−2.60258	−	3.58214i	−1.30129	−	1.79107i
$5$	−1.91314	+	1.15755i	−0.855580	+	0.517670i
$5$	−1.91314	+	1.15755i	−0.855580	+	0.517670i
$6$		0			0
$7$	−1.78576	−	0.282837i	−0.674955	−	0.106902i	−0.190458	−	0.981695i	$-0.560997\pi$
$7$	−1.78576	−	0.282837i	−0.674955	−	0.106902i	−0.484497	+	0.874793i	$0.660997\pi$
$8$	−6.07934	+	0.962874i	−2.14937	+	0.340427i
$9$		0			0
$10$	0.412838	+	5.65406i	0.130551	+	1.78797i
$11$	−1.72268	−	2.83415i	−0.519407	−	0.854527i
$11$	−1.72268	−	2.83415i	−0.519407	−	0.854527i
$12$		0			0
$13$	−2.00993	−	1.02411i	−0.557454	−	0.284037i	0.152478	−	0.988307i	$-0.451275\pi$
$13$	−2.00993	−	1.02411i	−0.557454	−	0.284037i	−0.709933	+	0.704270i	$0.751275\pi$
$14$	−2.69434	+	3.70844i	−0.720093	+	0.991122i
$15$		0			0
$16$	−2.08573	+	6.41923i	−0.521434	+	1.60481i
$17$	−2.99738	+	1.52724i	−0.726972	+	0.370411i	−0.777981	−	0.628288i	$-0.783756\pi$
$17$	−2.99738	+	1.52724i	−0.726972	+	0.370411i	0.0510094	+	0.998698i	$0.483756\pi$
$18$		0			0
$19$	−1.05647	−	0.767569i	−0.242370	−	0.176092i	0.459968	−	0.887935i	$-0.347861\pi$
$19$	−1.05647	−	0.767569i	−0.242370	−	0.176092i	−0.702339	+	0.711843i	$0.747861\pi$
$20$	9.12557	+	3.84051i	2.04054	+	0.858765i
$21$		0			0
$22$	−8.38507	+	0.629367i	−1.78770	+	0.134181i
$23$	3.16488	+	3.16488i	0.659922	+	0.659922i	0.955362	−	0.295439i	$-0.0954660\pi$
$23$	3.16488	+	3.16488i	0.659922	+	0.659922i	−0.295439	+	0.955362i	$0.595466\pi$
$24$		0			0
$25$	2.32018	−	4.42908i	0.464035	−	0.885817i
$26$	−4.62687	+	3.36162i	−0.907405	+	0.659268i
$27$		0			0
$28$	3.63442	+	7.13295i	0.686841	+	1.34800i
$29$	2.37569	−	1.72604i	0.441154	−	0.320517i	−0.344939	−	0.938625i	$-0.612100\pi$
$29$	2.37569	−	1.72604i	0.441154	−	0.320517i	0.786093	+	0.618108i	$0.212100\pi$
$30$		0			0
$31$	−1.23925	−	3.81401i	−0.222575	−	0.685016i	−0.998529	−	0.0542261i	$-0.982731\pi$
$31$	−1.23925	−	3.81401i	−0.222575	−	0.685016i	0.775953	−	0.630790i	$-0.217269\pi$
$32$	3.39552	+	3.39552i	0.600248	+	0.600248i
$33$		0			0
$34$			8.52886i			1.46269i
$35$	3.74380	−	1.52600i	0.632818	−	0.257940i
$36$		0			0
$37$	0.501987	−	3.16942i	0.0825262	−	0.521050i	−0.911446	−	0.411419i	$-0.865033\pi$
$37$	0.501987	−	3.16942i	0.0825262	−	0.521050i	0.993972	−	0.109631i	$-0.0349668\pi$
$38$	−2.94992	+	1.50306i	−0.478539	+	0.243828i
$39$		0			0
$40$	10.5160	−	8.87923i	1.66273	−	1.40393i
$41$	−0.766287	+	1.05470i	−0.119674	+	0.164717i	−0.864651	−	0.502373i	$-0.832460\pi$
$41$	−0.766287	+	1.05470i	−0.119674	+	0.164717i	0.744977	+	0.667090i	$0.232460\pi$
$42$		0			0
$43$	4.55431	−	4.55431i	0.694526	−	0.694526i	−0.268698	−	0.963224i	$-0.586593\pi$
$43$	4.55431	−	4.55431i	0.694526	−	0.694526i	0.963224	+	0.268698i	$0.0865935\pi$
$44$	−5.66890	+	13.5469i	−0.854620	+	2.04228i
$45$		0			0
$46$	10.7922	−	3.50658i	1.59122	−	0.517017i
$47$	7.62854	−	1.20824i	1.11274	−	0.176240i	0.427114	−	0.904198i	$-0.359530\pi$
$47$	7.62854	−	1.20824i	1.11274	−	0.176240i	0.685622	+	0.727957i	$0.259530\pi$
$48$		0			0
$49$	−3.54845	−	1.15296i	−0.506921	−	0.164709i
$50$	−7.33465	−	10.3391i	−1.03728	−	1.46217i
$51$		0			0
$52$	1.56249	+	9.86517i	0.216678	+	1.36805i
$53$	2.89146	−	5.67482i	0.397173	−	0.779496i	−0.602656	−	0.798001i	$-0.705891\pi$
$53$	2.89146	−	5.67482i	0.397173	−	0.779496i	0.999829	+	0.0185052i	$0.00589073\pi$
$54$		0			0
$55$	6.57637	+	3.42803i	0.886757	+	0.462235i
$56$	11.1286			1.48712
$57$		0			0
$58$	−1.16465	−	7.35329i	−0.152926	−	0.965535i
$59$	−7.28135	−	10.0219i	−0.947952	−	1.30474i	−0.952431	−	0.304753i	$-0.901426\pi$
$59$	−7.28135	−	10.0219i	−0.947952	−	1.30474i	0.00447977	−	0.999990i	$-0.498574\pi$
$60$		0			0
$61$	−8.85435	−	2.87695i	−1.13368	−	0.368356i	−0.318709	−	0.947853i	$-0.603249\pi$
$61$	−8.85435	−	2.87695i	−1.13368	−	0.368356i	−0.814975	+	0.579496i	$0.803249\pi$
$62$	−10.0421	−	1.59052i	−1.27535	−	0.201996i
$63$		0			0
$64$	−1.25983	+	0.409344i	−0.157479	+	0.0511679i
$65$	5.03072	−	0.367324i	0.623984	−	0.0455609i
$66$		0			0
$67$	−2.46236	+	2.46236i	−0.300825	+	0.300825i	−0.841336	−	0.540512i	$-0.818231\pi$
$67$	−2.46236	+	2.46236i	−0.300825	+	0.300825i	0.540512	+	0.841336i	$0.318231\pi$
$68$	13.2717	+	6.76227i	1.60943	+	0.820046i
$69$		0			0
$70$	0.861947	−	10.2136i	0.103022	−	1.22076i
$71$	2.09243	−	6.43984i	0.248326	−	0.764268i	−0.746746	−	0.665110i	$-0.768385\pi$
$71$	2.09243	−	6.43984i	0.248326	−	0.764268i	0.995072	−	0.0991588i	$-0.0316152\pi$
$72$		0			0
$73$	−1.47735	+	9.32763i	−0.172911	+	1.09172i	0.736689	+	0.676232i	$0.236388\pi$
$73$	−1.47735	+	9.32763i	−0.172911	+	1.09172i	−0.909600	+	0.415485i	$0.863612\pi$
$74$	−6.58185	−	4.78199i	−0.765125	−	0.555896i
$75$		0			0
$76$			5.78207i			0.663249i
$77$	2.27469	+	5.54835i	0.259225	+	0.632293i
$78$		0			0
$79$	0.353860	+	1.08907i	0.0398123	+	0.122530i	0.968987	−	0.247110i	$-0.0794810\pi$
$79$	0.353860	+	1.08907i	0.0398123	+	0.122530i	−0.929175	+	0.369640i	$0.879481\pi$
$80$	−3.44026	−	14.6952i	−0.384633	−	1.64297i
$81$		0			0
$82$	1.50055	+	2.94499i	0.165708	+	0.325220i
$83$	4.75092	+	9.32422i	0.521482	+	1.02347i	0.990139	+	0.140086i	$0.0447378\pi$
$83$	4.75092	+	9.32422i	0.521482	+	1.02347i	−0.468658	+	0.883380i	$0.655262\pi$
$84$		0			0
$85$	3.96654	−	6.39143i	0.430232	−	0.693248i
$86$	−5.04603	−	15.5301i	−0.544128	−	1.67465i
$87$		0			0
$88$	13.2017	+	15.5710i	1.40730	+	1.65988i
$89$			3.85743i			0.408887i	0.978878	+	0.204443i	$0.0655384\pi$
$89$			3.85743i			0.408887i	−0.978878	+	0.204443i	$0.934462\pi$
$90$		0			0
$91$	3.29960	+	2.39730i	0.345892	+	0.251305i
$92$	3.10019	−	19.5739i	0.323218	−	2.04072i
$93$		0			0
$94$	6.05109	−	18.6233i	0.624123	−	1.92085i
$95$	2.90966	+	0.245553i	0.298525	+	0.0251932i
$96$		0			0
$97$	−0.693249	−	0.353228i	−0.0703888	−	0.0358649i	0.418442	−	0.908244i	$-0.362576\pi$
$97$	−0.693249	−	0.353228i	−0.0703888	−	0.0358649i	−0.488831	+	0.872379i	$0.662576\pi$
$98$	−6.68878	+	6.68878i	−0.675669	+	0.675669i
$99$		0			0
$100$	−21.9040	+	3.21584i	−2.19040	+	0.321584i
$101$	−9.28960	+	3.01837i	−0.924350	+	0.300339i	−0.732250	−	0.681036i	$-0.761530\pi$
$101$	−9.28960	+	3.01837i	−0.924350	+	0.300339i	−0.192100	+	0.981375i	$0.561530\pi$
$102$		0			0
$103$	4.61435	+	0.730841i	0.454665	+	0.0720119i	0.379567	−	0.925164i	$-0.376073\pi$
$103$	4.61435	+	0.730841i	0.454665	+	0.0720119i	0.0750982	+	0.997176i	$0.476073\pi$
$104$	13.2051	+	4.29061i	1.29487	+	0.420729i
$105$		0			0
$106$	−9.49117	−	13.0635i	−0.921864	−	1.26884i
$107$	2.39372	+	15.1133i	0.231410	+	1.46106i	0.780424	+	0.625250i	$0.215003\pi$
$107$	2.39372	+	15.1133i	0.231410	+	1.46106i	−0.549015	+	0.835813i	$0.684997\pi$
$108$		0			0
$109$	17.8837			1.71295			0.856476	−	0.516187i	$-0.172649\pi$
$109$	17.8837			1.71295			0.856476	+	0.516187i	$0.172649\pi$
$110$	15.3132	−	10.9102i	1.46006	−	1.04024i
$111$		0			0
$112$	5.54022	−	10.8733i	0.523502	−	1.02743i
$113$	−1.16850	−	7.37759i	−0.109923	−	0.694025i	−0.979683	−	0.200551i	$-0.935727\pi$
$113$	−1.16850	−	7.37759i	−0.109923	−	0.694025i	0.869760	−	0.493474i	$-0.164273\pi$
$114$		0			0
$115$	−9.71833	−	2.39135i	−0.906239	−	0.222994i
$116$	−12.3658	−	4.01790i	−1.14814	−	0.373053i
$117$		0			0
$118$	−31.0201	+	4.91310i	−2.85563	+	0.452288i
$119$	5.78457	−	1.87952i	0.530271	−	0.172295i
$120$		0			0
$121$	−5.06477	+	9.76464i	−0.460433	+	0.887694i
$122$	−16.6904	+	16.6904i	−1.51107	+	1.51107i
$123$		0			0
$124$	−10.4371	+	14.3654i	−0.937277	+	1.29005i
$125$	0.688059	+	11.1591i	0.0615419	+	0.998105i
$126$		0			0
$127$	−0.183716	+	0.0936079i	−0.0163021	+	0.00830635i	−0.462123	−	0.886816i	$-0.652912\pi$
$127$	−0.183716	+	0.0936079i	−0.0163021	+	0.00830635i	0.445820	+	0.895122i	$0.352912\pi$
$128$	−2.02777	+	12.8028i	−0.179231	+	1.13162i
$129$		0			0
$130$	4.96061	−	11.7871i	0.435074	−	1.03379i
$131$			0.551708i			0.0482029i	0.999710	+	0.0241015i	$0.00767248\pi$
$131$			0.551708i			0.0482029i	−0.999710	+	0.0241015i	$0.992328\pi$
$132$		0			0
$133$	1.66950	+	1.66950i	0.144764	+	0.144764i
$134$	2.72821	+	8.39658i	0.235682	+	0.725354i
$135$		0			0
$136$	16.7516	−	12.1707i	1.43644	−	1.04363i
$137$	−7.02615	−	13.7896i	−0.600284	−	1.17812i	−0.968647	−	0.248442i	$-0.920081\pi$
$137$	−7.02615	−	13.7896i	−0.600284	−	1.17812i	0.368362	−	0.929682i	$-0.379919\pi$
$138$		0			0
$139$	1.15101	−	0.836256i	0.0976272	−	0.0709303i	−0.537901	−	0.843008i	$-0.680782\pi$
$139$	1.15101	−	0.836256i	0.0976272	−	0.0709303i	0.635528	+	0.772078i	$0.280782\pi$
$140$	−15.2099	−	9.43929i	−1.28547	−	0.797766i
$141$		0			0
$142$	−12.1390	−	12.1390i	−1.01868	−	1.01868i
$143$	0.559982	+	7.46065i	0.0468280	+	0.623891i
$144$		0			0
$145$	−2.54705	+	6.05212i	−0.211521	+	0.502601i
$146$	19.3704	+	14.0734i	1.60311	+	1.16473i
$147$		0			0
$148$	−12.6598	+	6.45048i	−1.04063	+	0.530226i
$149$	7.35615	−	22.6399i	0.602639	−	1.85473i	0.0903702	−	0.995908i	$-0.471195\pi$
$149$	7.35615	−	22.6399i	0.602639	−	1.85473i	0.512269	−	0.858825i	$-0.328805\pi$
$150$		0			0
$151$	−8.45592	+	11.6386i	−0.688133	+	0.947134i	−0.999996	−	0.00299311i	$-0.999047\pi$
$151$	−8.45592	+	11.6386i	−0.688133	+	0.947134i	0.311862	+	0.950127i	$0.399047\pi$
$152$	7.16170	+	3.64907i	0.580891	+	0.295979i
$153$		0			0
$154$	15.1517	+	1.24771i	1.22096	+	0.100543i
$155$	6.78574	+	5.86223i	0.545044	+	0.470866i
$156$		0			0
$157$	13.3277	−	2.11091i	1.06367	−	0.168469i	0.400016	−	0.916508i	$-0.369005\pi$
$157$	13.3277	−	2.11091i	1.06367	−	0.168469i	0.663654	+	0.748040i	$0.269005\pi$
$158$	2.86747	+	0.454163i	0.228124	+	0.0361312i
$159$		0			0
$160$	−10.4266	−	2.56562i	−0.824291	−	0.202830i
$161$	−4.75657	−	6.54686i	−0.374870	−	0.515965i
$162$		0			0
$163$	−0.487228	+	0.956239i	−0.0381626	+	0.0748984i	−0.909300	−	0.416140i	$-0.863383\pi$
$163$	−0.487228	+	0.956239i	−0.0381626	+	0.0748984i	0.871138	+	0.491039i	$0.163383\pi$
$164$	5.77242			0.450750
$165$		0			0
$166$	26.5315			2.05924
$167$	0.858874	−	1.68563i	0.0664616	−	0.130438i	−0.855386	−	0.517992i	$-0.826680\pi$
$167$	0.858874	−	1.68563i	0.0664616	−	0.130438i	0.921847	+	0.387554i	$0.126680\pi$
$168$		0			0
$169$	−4.65019	−	6.40044i	−0.357707	−	0.492342i
$170$	−9.87255	−	16.3169i	−0.757190	−	1.25145i
$171$		0			0
$172$	−28.1671	−	4.46123i	−2.14772	−	0.340166i
$173$	−18.7140	+	2.96401i	−1.42280	+	0.225350i	−0.819919	−	0.572480i	$-0.805981\pi$
$173$	−18.7140	+	2.96401i	−1.42280	+	0.225350i	−0.602883	+	0.797830i	$0.705981\pi$
$174$		0			0
$175$	−5.39599	+	7.25306i	−0.407898	+	0.548280i
$176$	21.7861	−	5.14699i	1.64219	−	0.387969i
$177$		0			0
$178$	8.71383	+	4.43992i	0.653129	+	0.332786i
$179$	9.62961	−	13.2540i	0.719751	−	0.990652i	−0.279781	−	0.960064i	$-0.590262\pi$
$179$	9.62961	−	13.2540i	0.719751	−	0.990652i	0.999532	−	0.0305880i	$-0.00973800\pi$
$180$		0			0
$181$	4.59306	−	14.1360i	0.341400	−	1.05072i	−0.622084	−	0.782951i	$-0.713714\pi$
$181$	4.59306	−	14.1360i	0.341400	−	1.05072i	0.963483	−	0.267769i	$-0.0862864\pi$
$182$	9.21329	−	4.69440i	0.682934	−	0.347972i
$183$		0			0
$184$	−22.2878	−	16.1930i	−1.64307	−	1.19376i
$185$	2.70838	+	6.64461i	0.199124	+	0.488522i
$186$		0			0
$187$	9.49195	+	5.86407i	0.694120	+	0.428823i
$188$	−24.1819	−	24.1819i	−1.76365	−	1.76365i
$189$		0			0
$190$	3.90373	−	6.29021i	0.283206	−	0.456340i
$191$	−1.54488	+	1.12242i	−0.111784	+	0.0812156i	−0.642273	−	0.766476i	$-0.722008\pi$
$191$	−1.54488	+	1.12242i	−0.111784	+	0.0812156i	0.530489	+	0.847692i	$0.322008\pi$
$192$		0			0
$193$	5.16774	+	10.1423i	0.371982	+	0.730056i	0.998793	−	0.0491153i	$-0.0156402\pi$
$193$	5.16774	+	10.1423i	0.371982	+	0.730056i	−0.626811	+	0.779171i	$0.715640\pi$
$194$	−1.59586	+	1.15946i	−0.114576	+	0.0832446i
$195$		0			0
$196$	5.10504	+	15.7117i	0.364646	+	1.12226i
$197$	−13.8092	−	13.8092i	−0.983863	−	0.983863i	0.0160086	−	0.999872i	$-0.494904\pi$
$197$	−13.8092	−	13.8092i	−0.983863	−	0.983863i	−0.999872	+	0.0160086i	$0.994904\pi$
$198$		0			0
$199$		−	22.3508i		−	1.58441i	−0.610258	−	0.792203i	$-0.708934\pi$
$199$		−	22.3508i		−	1.58441i	0.610258	−	0.792203i	$-0.291066\pi$
$200$	−9.84050	+	29.1600i	−0.695828	+	2.06192i
$201$		0			0
$202$	−3.87394	+	24.4591i	−0.272570	+	1.72094i
$203$	−4.73060	+	2.41036i	−0.332023	+	0.169174i
$204$		0			0
$205$	0.245143	−	2.90480i	0.0171215	−	0.202880i
$206$	6.96208	−	9.58248i	0.485071	−	0.667643i
$207$		0			0
$208$	10.7662	−	10.7662i	0.746501	−	0.746501i
$209$	−0.355449	+	4.31646i	−0.0245869	+	0.298576i
$210$		0			0
$211$	−0.358113	+	0.116358i	−0.0246535	+	0.00801042i	−0.321318	−	0.946971i	$-0.604126\pi$
$211$	−0.358113	+	0.116358i	−0.0246535	+	0.00801042i	0.296664	+	0.954982i	$0.404126\pi$
$212$	−27.8532	+	4.41152i	−1.91297	+	0.302984i
$213$		0			0
$214$	36.8958	+	11.9882i	2.52215	+	0.819495i
$215$	−3.44119	+	13.9848i	−0.234687	+	0.953758i
$216$		0			0
$217$	1.13426	+	7.16142i	0.0769984	+	0.486149i
$218$	20.5843	−	40.3989i	1.39414	−	2.73616i
$219$		0			0
$220$	−4.83583	−	32.4792i	−0.326032	−	2.18974i
$221$	7.58859			0.510464
$222$		0			0
$223$	1.19037	+	7.51570i	0.0797131	+	0.503289i	0.994950	+	0.100372i	$0.0320034\pi$
$223$	1.19037	+	7.51570i	0.0797131	+	0.503289i	−0.915237	+	0.402916i	$0.867997\pi$
$224$	−5.10321	−	7.02396i	−0.340972	−	0.469308i
$225$		0			0
$226$	−18.0107	−	5.85204i	−1.19806	−	0.389272i
$227$	8.10167	+	1.28318i	0.537727	+	0.0851676i	0.419390	−	0.907806i	$-0.362244\pi$
$227$	8.10167	+	1.28318i	0.537727	+	0.0851676i	0.118336	+	0.992974i	$0.462244\pi$
$228$		0			0
$229$	7.21772	−	2.34518i	0.476960	−	0.154974i	−0.0606641	−	0.998158i	$-0.519322\pi$
$229$	7.21772	−	2.34518i	0.476960	−	0.154974i	0.537624	+	0.843184i	$0.319322\pi$
$230$	−16.5878	+	19.2010i	−1.09377	+	1.26608i
$231$		0			0
$232$	−12.7807	+	12.7807i	−0.839092	+	0.839092i
$233$	23.3597	+	11.9023i	1.53034	+	0.779749i	0.997777	−	0.0666396i	$-0.0212278\pi$
$233$	23.3597	+	11.9023i	1.53034	+	0.779749i	0.532566	+	0.846388i	$0.321228\pi$
$234$		0			0
$235$	−13.1958	+	11.1419i	−0.860801	+	0.726818i
$236$	−16.9496	+	52.1656i	−1.10333	+	3.39569i
$237$		0			0
$238$	2.41228	−	15.2305i	0.156365	−	0.987248i
$239$	1.84133	+	1.33781i	0.119106	+	0.0865356i	0.645744	−	0.763554i	$-0.276548\pi$
$239$	1.84133	+	1.33781i	0.119106	+	0.0865356i	−0.526638	+	0.850090i	$0.676548\pi$
$240$		0			0
$241$			6.29531i			0.405517i	0.979229	+	0.202758i	$0.0649906\pi$
$241$			6.29531i			0.405517i	−0.979229	+	0.202758i	$0.935009\pi$
$242$	16.2285	+	22.6803i	1.04321	+	1.45795i
$243$		0			0
$244$	12.7385	+	39.2050i	0.815498	+	2.50984i
$245$	8.12326	−	1.90172i	0.518976	−	0.121496i
$246$		0			0
$247$	1.33735	+	2.62470i	0.0850936	+	0.167006i
$248$	11.2062	+	21.9934i	0.711596	+	1.39658i
$249$		0			0
$250$	26.0002	+	11.2899i	1.64439	+	0.714037i
$251$	8.21826	+	25.2932i	0.518732	+	1.59649i	0.776387	+	0.630256i	$0.217050\pi$
$251$	8.21826	+	25.2932i	0.518732	+	1.59649i	−0.257655	+	0.966237i	$0.582950\pi$
$252$		0			0
$253$	3.51766	−	14.4218i	0.221153	−	0.906690i
$254$			0.522752i			0.0328004i
$255$		0			0
$256$	24.4439	+	17.7595i	1.52774	+	1.10997i
$257$	−3.09337	+	19.5307i	−0.192959	+	1.21829i	0.680996	+	0.732287i	$0.261547\pi$
$257$	−3.09337	+	19.5307i	−0.192959	+	1.21829i	−0.873955	+	0.486007i	$0.838453\pi$
$258$		0			0
$259$	−1.79286	+	5.51786i	−0.111403	+	0.342863i
$260$	−14.4086	−	17.0648i	−0.893586	−	1.05831i
$261$		0			0
$262$	1.24629	+	0.635018i	0.0769962	+	0.0392315i
$263$	5.91748	−	5.91748i	0.364888	−	0.364888i	−0.500721	−	0.865609i	$-0.666932\pi$
$263$	5.91748	−	5.91748i	0.364888	−	0.364888i	0.865609	+	0.500721i	$0.166932\pi$
$264$		0			0
$265$	1.03710	+	14.2037i	0.0637085	+	0.872526i
$266$	5.69297	−	1.84976i	0.349058	−	0.113416i
$267$		0			0
$268$	15.2290	+	2.41203i	0.930258	+	0.147338i
$269$	9.23539	+	3.00076i	0.563092	+	0.182960i	0.576712	−	0.816948i	$-0.304336\pi$
$269$	9.23539	+	3.00076i	0.563092	+	0.182960i	−0.0136201	+	0.999907i	$0.504336\pi$
$270$		0			0
$271$	1.79360	+	2.46868i	0.108954	+	0.149962i	0.860012	−	0.510274i	$-0.170456\pi$
$271$	1.79360	+	2.46868i	0.108954	+	0.149962i	−0.751058	+	0.660236i	$0.770456\pi$
$272$	−3.55198	−	22.4263i	−0.215370	−	1.35979i
$273$		0			0
$274$	−39.2374			−2.37042
$275$	−16.5496	+	1.05417i	−0.997977	+	0.0635687i
$276$		0			0
$277$	−1.08057	+	2.12073i	−0.0649249	+	0.127422i	−0.921188	−	0.389117i	$-0.872780\pi$
$277$	−1.08057	+	2.12073i	−0.0649249	+	0.127422i	0.856263	+	0.516540i	$0.172780\pi$
$278$	−0.564265	−	3.56263i	−0.0338424	−	0.213672i
$279$		0			0
$280$	−21.2905	+	12.8819i	−1.27235	+	0.769839i
$281$	−26.8503	−	8.72419i	−1.60175	−	0.520442i	−0.634214	−	0.773157i	$-0.718676\pi$
$281$	−26.8503	−	8.72419i	−1.60175	−	0.520442i	−0.967541	+	0.252716i	$0.918676\pi$
$282$		0			0
$283$	16.8040	−	2.66149i	0.998893	−	0.158209i	0.364486	−	0.931209i	$-0.381245\pi$
$283$	16.8040	−	2.66149i	0.998893	−	0.158209i	0.634406	+	0.773000i	$0.281245\pi$
$284$	−28.5141	+	9.26479i	−1.69200	+	0.549764i
$285$		0			0
$286$	17.4979	+	7.32225i	1.03467	+	0.432974i
$287$	1.66672	−	1.66672i	0.0983831	−	0.0983831i
$288$		0			0
$289$	−3.34052	+	4.59783i	−0.196501	+	0.270461i
$290$	10.7399	+	12.7197i	0.630669	+	0.746927i
$291$		0			0
$292$	37.2578	−	18.9838i	2.18035	−	1.11094i
$293$	1.67148	−	10.5533i	0.0976492	−	0.616533i	−0.889525	−	0.456886i	$-0.848965\pi$
$293$	1.67148	−	10.5533i	0.0976492	−	0.616533i	0.987174	−	0.159646i	$-0.0510354\pi$
$294$		0			0
$295$	25.5311	+	10.7448i	1.48648	+	0.625586i
$296$			19.7514i			1.14803i
$297$		0			0
$298$	−42.6760	−	42.6760i	−2.47215	−	2.47215i
$299$	−3.12000	−	9.60236i	−0.180434	−	0.555319i
$300$		0			0
$301$	−9.42104	+	6.84479i	−0.543020	+	0.394527i
$302$	16.5584	+	32.4977i	0.952831	+	1.87004i
$303$		0			0
$304$	7.13071	−	5.18077i	0.408975	−	0.297137i
$305$	20.2698	−	4.74532i	1.16064	−	0.271716i
$306$		0			0
$307$	−22.9923	−	22.9923i	−1.31224	−	1.31224i	−0.919763	−	0.392474i	$-0.871619\pi$
$307$	−22.9923	−	22.9923i	−1.31224	−	1.31224i	−0.392474	−	0.919763i	$-0.628381\pi$
$308$	13.9549	−	22.5882i	0.795154	−	1.28708i
$309$		0			0
$310$	21.0530	−	8.58134i	1.19573	−	0.487388i
$311$	11.2361	+	8.16354i	0.637143	+	0.462912i	0.858868	−	0.512198i	$-0.171168\pi$
$311$	11.2361	+	8.16354i	0.637143	+	0.462912i	−0.221724	+	0.975109i	$0.571168\pi$
$312$		0			0
$313$	−15.4928	+	7.89399i	−0.875707	+	0.446195i	−0.833245	−	0.552903i	$-0.813520\pi$
$313$	−15.4928	+	7.89399i	−0.875707	+	0.446195i	−0.0424612	+	0.999098i	$0.513520\pi$
$314$	10.5718	−	32.5367i	0.596601	−	1.83615i
$315$		0			0
$316$	2.98025	−	4.10196i	0.167652	−	0.230753i
$317$	−14.3960	−	7.33513i	−0.808560	−	0.411982i	0.000287853	−	1.00000i	$-0.499908\pi$
$317$	−14.3960	−	7.33513i	−0.808560	−	0.411982i	−0.808848	+	0.588018i	$0.799908\pi$
$318$		0			0
$319$	−8.98439	−	3.75964i	−0.503029	−	0.210500i
$320$	1.93639	−	2.24144i	0.108248	−	0.125300i
$321$		0			0
$322$	−20.2640	+	3.20950i	−1.12927	+	0.178859i
$323$	4.33890	+	0.687214i	0.241423	+	0.0382376i
$324$		0			0
$325$	−9.19926	+	6.52603i	−0.510283	+	0.361999i
$326$	1.59932	+	2.20127i	0.0885779	+	0.121917i
$327$		0			0
$328$	3.64298	−	7.14975i	0.201150	−	0.394779i
$329$	−13.9645			−0.769887
$330$		0			0
$331$	14.6837			0.807090			0.403545	−	0.914960i	$-0.367778\pi$
$331$	14.6837			0.807090			0.403545	+	0.914960i	$0.367778\pi$
$332$	21.0360	−	41.2854i	1.15450	−	2.26583i
$333$		0			0
$334$	−2.81924	−	3.88034i	−0.154262	−	0.212323i
$335$	1.86053	−	7.56111i	0.101652	−	0.413108i
$336$		0			0
$337$	−13.3250	−	2.11047i	−0.725859	−	0.114965i	−0.217439	−	0.976074i	$-0.569770\pi$
$337$	−13.3250	−	2.11047i	−0.725859	−	0.114965i	−0.508420	+	0.861109i	$0.669770\pi$
$338$	−19.8108	+	3.13772i	−1.07757	+	0.170670i
$339$		0			0
$340$	−33.2182	+	2.42547i	−1.80151	+	0.131539i
$341$	−8.67464	+	10.0825i	−0.469758	+	0.545999i
$342$		0			0
$343$	17.2873	+	8.80832i	0.933426	+	0.475604i
$344$	−23.3020	+	32.0725i	−1.25636	+	1.72923i
$345$		0			0
$346$	−14.8443	+	45.6861i	−0.798035	+	2.45610i
$347$	−10.9022	+	5.55495i	−0.585261	+	0.298205i	−0.721438	−	0.692479i	$-0.756518\pi$
$347$	−10.9022	+	5.55495i	−0.585261	+	0.298205i	0.136177	+	0.990685i	$0.456518\pi$
$348$		0			0
$349$	−16.4807	−	11.9739i	−0.882193	−	0.640951i	0.0516378	−	0.998666i	$-0.483556\pi$
$349$	−16.4807	−	11.9739i	−0.882193	−	0.640951i	−0.933831	+	0.357715i	$0.883556\pi$
$350$	10.1737	+	20.5377i	0.543805	+	1.09779i
$351$		0			0
$352$	3.77401	−	15.4728i	0.201156	−	0.824702i
$353$	−13.7886	−	13.7886i	−0.733893	−	0.733893i	0.237495	−	0.971389i	$-0.423674\pi$
$353$	−13.7886	−	13.7886i	−0.733893	−	0.733893i	−0.971389	+	0.237495i	$0.923674\pi$
$354$		0			0
$355$	3.45131	+	14.7424i	0.183176	+	0.782444i
$356$	13.8179	−	10.0393i	0.732345	−	0.532079i
$357$		0			0
$358$	−18.8567	−	37.0084i	−0.996610	−	1.95596i
$359$	−13.3648	+	9.71011i	−0.705368	+	0.512480i	−0.881676	−	0.471855i	$-0.843585\pi$
$359$	−13.3648	+	9.71011i	−0.705368	+	0.512480i	0.176308	+	0.984335i	$0.443585\pi$
$360$		0			0
$361$	−5.34436	−	16.4483i	−0.281282	−	0.865697i
$362$	−26.6462	−	26.6462i	−1.40049	−	1.40049i
$363$		0			0
$364$		−	18.0588i		−	0.946537i
$365$	−7.97079	−	19.5551i	−0.417210	−	1.02356i
$366$		0			0
$367$	−1.00765	+	6.36207i	−0.0525990	+	0.332097i	0.947331	+	0.320256i	$0.103769\pi$
$367$	−1.00765	+	6.36207i	−0.0525990	+	0.332097i	−0.999930	+	0.0118406i	$0.996231\pi$
$368$	−26.9172	+	13.7150i	−1.40315	+	0.714943i
$369$		0			0
$370$	18.1274	+	1.52981i	0.942396	+	0.0795310i
$371$	−6.76851	+	9.31606i	−0.351404	+	0.483666i
$372$		0			0
$373$	9.69631	−	9.69631i	0.502056	−	0.502056i	−0.410021	−	0.912076i	$-0.634478\pi$
$373$	9.69631	−	9.69631i	0.502056	−	0.502056i	0.912076	+	0.410021i	$0.134478\pi$
$374$	24.1720	−	14.6925i	1.24991	−	0.759730i
$375$		0			0
$376$	−45.2131	+	14.6906i	−2.33169	+	0.757612i
$377$	−6.54262	+	1.03625i	−0.336962	+	0.0533696i
$378$		0			0
$379$	20.4487	+	6.64419i	1.05038	+	0.341289i	0.782818	−	0.622251i	$-0.213782\pi$
$379$	20.4487	+	6.64419i	1.05038	+	0.341289i	0.267563	+	0.963540i	$0.413782\pi$
$380$	−6.69301	−	11.0619i	−0.343344	−	0.567463i
$381$		0			0
$382$	0.757356	+	4.78176i	0.0387497	+	0.244656i
$383$	0.137756	−	0.270362i	0.00703902	−	0.0138148i	−0.887460	−	0.460884i	$-0.847532\pi$
$383$	0.137756	−	0.270362i	0.00703902	−	0.0138148i	0.894499	+	0.447069i	$0.147532\pi$
$384$		0			0
$385$	−10.7743	−	7.98168i	−0.549107	−	0.406784i
$386$	28.8592			1.46889
$387$		0			0
$388$	0.538921	+	3.40262i	0.0273596	+	0.172742i
$389$	−2.11680	−	2.91353i	−0.107326	−	0.147722i	0.751975	−	0.659191i	$-0.229101\pi$
$389$	−2.11680	−	2.91353i	−0.107326	−	0.147722i	−0.859301	+	0.511470i	$0.829101\pi$
$390$		0			0
$391$	−14.3199	−	4.65281i	−0.724187	−	0.235303i
$392$	22.6824	+	3.59254i	1.14563	+	0.181451i
$393$		0			0
$394$	−47.0890	+	15.3001i	−2.37231	+	0.770810i
$395$	−1.93763	−	1.67393i	−0.0974927	−	0.0842244i
$396$		0			0
$397$	22.1781	−	22.1781i	1.11309	−	1.11309i	0.120357	−	0.992731i	$-0.461596\pi$
$397$	22.1781	−	22.1781i	1.11309	−	1.11309i	0.992731	−	0.120357i	$-0.0384039\pi$
$398$	−50.4898	−	25.7259i	−2.53083	−	1.28952i
$399$		0			0
$400$	23.5920	+	24.1316i	1.17960	+	1.20658i
$401$	3.08934	−	9.50802i	0.154274	−	0.474808i	−0.843812	−	0.536639i	$-0.819694\pi$
$401$	3.08934	−	9.50802i	0.154274	−	0.474808i	0.998087	+	0.0618306i	$0.0196939\pi$
$402$		0			0
$403$	−1.41517	+	8.93502i	−0.0704945	+	0.445085i
$404$	34.9891	+	25.4211i	1.74077	+	1.26475i
$405$		0			0
$406$			13.4606i			0.668040i
$407$	−9.84737	+	4.03719i	−0.488116	+	0.200116i
$408$		0			0
$409$	−9.39140	−	28.9037i	−0.464375	−	1.42920i	−0.859767	−	0.510686i	$-0.829391\pi$
$409$	−9.39140	−	28.9037i	−0.464375	−	1.42920i	0.395393	−	0.918512i	$-0.370609\pi$
$410$	−6.27971	−	3.89721i	−0.310133	−	0.192470i
$411$		0			0
$412$	−9.39122	−	18.4313i	−0.462672	−	0.908045i
$413$	10.1682	+	19.9562i	0.500344	+	0.981981i
$414$		0			0
$415$	−19.8824	−	12.3391i	−0.975987	−	0.605701i
$416$	−3.34737	−	10.3021i	−0.164118	−	0.505104i
$417$		0			0
$418$	9.34163	+	5.77121i	0.456914	+	0.282279i
$419$		−	7.48185i		−	0.365512i	−0.983158	−	0.182756i	$-0.941498\pi$
$419$		−	7.48185i		−	0.365512i	0.983158	−	0.182756i	$-0.0585019\pi$
$420$		0			0
$421$	−16.5226	−	12.0043i	−0.805260	−	0.585056i	0.107192	−	0.994238i	$-0.465814\pi$
$421$	−16.5226	−	12.0043i	−0.805260	−	0.585056i	−0.912453	+	0.409182i	$0.865814\pi$
$422$	−0.149340	+	0.942896i	−0.00726976	+	0.0458995i
$423$		0			0
$424$	−12.1141	+	37.2833i	−0.588311	+	1.81064i
$425$	−0.190165	+	16.8191i	−0.00922437	+	0.815847i
$426$		0			0
$427$	14.9981	+	7.64189i	0.725807	+	0.369817i
$428$	47.9083	−	47.9083i	2.31573	−	2.31573i
$429$		0			0
$430$	27.6305	+	23.8702i	1.33246	+	1.15112i
$431$	32.0182	−	10.4034i	1.54226	−	0.501112i	0.590264	−	0.807210i	$-0.299024\pi$
$431$	32.0182	−	10.4034i	1.54226	−	0.501112i	0.952000	+	0.306098i	$0.0990236\pi$
$432$		0			0
$433$	11.4564	+	1.81451i	0.550557	+	0.0871997i	0.425514	−	0.904952i	$-0.360093\pi$
$433$	11.4564	+	1.81451i	0.550557	+	0.0871997i	0.125043	+	0.992151i	$0.460093\pi$
$434$	17.4830	+	5.68056i	0.839210	+	0.272676i
$435$		0			0
$436$	−46.5438	−	64.0620i	−2.22904	−	3.06801i
$437$	−0.914330	−	5.77285i	−0.0437383	−	0.276153i
$438$		0			0
$439$	−10.7242			−0.511837			−0.255918	−	0.966698i	$-0.582378\pi$
$439$	−10.7242			−0.511837			−0.255918	+	0.966698i	$0.582378\pi$
$440$	−43.2808	−	14.5079i	−2.06333	−	0.691639i
$441$		0			0
$442$	8.73450	−	17.1424i	0.415458	−	0.815382i
$443$	6.30958	+	39.8371i	0.299777	+	1.89272i	0.432612	+	0.901580i	$0.357592\pi$
$443$	6.30958	+	39.8371i	0.299777	+	1.89272i	−0.132835	+	0.991138i	$0.542408\pi$
$444$		0			0
$445$	−4.46515	−	7.37979i	−0.211669	−	0.349836i
$446$	18.3479	+	5.96159i	0.868797	+	0.282289i
$447$		0			0
$448$	2.36553	−	0.374664i	0.111761	−	0.0177012i
$449$	−3.46337	+	1.12532i	−0.163447	+	0.0531070i	−0.389597	−	0.920985i	$-0.627386\pi$
$449$	−3.46337	+	1.12532i	−0.163447	+	0.0531070i	0.226151	+	0.974092i	$0.427386\pi$
$450$		0			0
$451$	4.30925	+	0.354856i	0.202915	+	0.0167095i
$452$	−23.3865	+	23.3865i	−1.10001	+	1.10001i
$453$		0			0
$454$	12.2237	−	16.8245i	0.573688	−	0.789613i
$455$	−9.08757	−	0.766921i	−0.426032	−	0.0359538i
$456$		0			0
$457$	−16.1207	+	8.21391i	−0.754094	+	0.384230i	−0.788385	−	0.615182i	$-0.789083\pi$
$457$	−16.1207	+	8.21391i	−0.754094	+	0.384230i	0.0342910	+	0.999412i	$0.489083\pi$
$458$	3.00993	−	19.0039i	0.140645	−	0.887996i
$459$		0			0
$460$	16.7265	+	41.0361i	0.779879	+	1.91332i
$461$		−	35.5884i		−	1.65751i	−0.559608	−	0.828757i	$-0.689048\pi$
$461$		−	35.5884i		−	1.65751i	0.559608	−	0.828757i	$-0.310952\pi$
$462$		0			0
$463$	−4.46802	−	4.46802i	−0.207647	−	0.207647i	0.595620	−	0.803266i	$-0.296907\pi$
$463$	−4.46802	−	4.46802i	−0.207647	−	0.207647i	−0.803266	+	0.595620i	$0.796907\pi$
$464$	6.12479	+	18.8502i	0.284336	+	0.875097i
$465$		0			0
$466$	53.7742	−	39.0692i	2.49104	−	1.80985i
$467$	−3.92827	−	7.70967i	−0.181779	−	0.356761i	0.782079	−	0.623180i	$-0.214160\pi$
$467$	−3.92827	−	7.70967i	−0.181779	−	0.356761i	−0.963857	+	0.266419i	$0.914160\pi$
$468$		0			0
$469$	5.09363	−	3.70074i	0.235202	−	0.170884i
$470$	9.98082	+	42.6334i	0.460381	+	1.96653i
$471$		0			0
$472$	53.9157	+	53.9157i	2.48167	+	2.48167i
$473$	−20.7532	−	5.06198i	−0.954233	−	0.232750i
$474$		0			0
$475$	−5.85082	+	2.89829i	−0.268454	+	0.132983i
$476$	−21.7875	−	15.8295i	−0.998628	−	0.725545i
$477$		0			0
$478$	5.14145	−	2.61970i	0.235165	−	0.119822i
$479$	−4.75378	+	14.6306i	−0.217206	+	0.668490i	0.781784	+	0.623549i	$0.214310\pi$
$479$	−4.75378	+	14.6306i	−0.217206	+	0.668490i	−0.998990	+	0.0449410i	$0.985690\pi$
$480$		0			0
$481$	−4.25480	+	5.85623i	−0.194002	+	0.267021i
$482$	14.2209	+	7.24593i	0.647746	+	0.330043i
$483$		0			0
$484$	48.1597	−	7.27051i	2.18908	−	0.330478i
$485$	1.73516	−	0.126694i	0.0787894	−	0.00575290i
$486$		0			0
$487$	−5.87316	+	0.930218i	−0.266138	+	0.0421522i	−0.288077	−	0.957607i	$-0.593016\pi$
$487$	−5.87316	+	0.930218i	−0.266138	+	0.0421522i	0.0219390	+	0.999759i	$0.493016\pi$
$488$	56.5988	+	8.96437i	2.56211	+	0.405798i
$489$		0			0
$490$	5.05397	−	20.5391i	0.228315	−	0.927863i
$491$	−24.0702	−	33.1298i	−1.08627	−	1.49513i	−0.852422	−	0.522855i	$-0.824867\pi$
$491$	−24.0702	−	33.1298i	−1.08627	−	1.49513i	−0.233851	−	0.972272i	$-0.575133\pi$
$492$		0			0
$493$	−4.48477	+	8.80185i	−0.201984	+	0.396415i
$494$	7.46842			0.336020
$495$		0			0
$496$	27.0678			1.21538
$497$	−5.55801	+	10.9082i	−0.249311	+	0.489300i
$498$		0			0
$499$	13.6289	+	18.7585i	0.610111	+	0.839746i	0.996587	−	0.0825534i	$-0.0263075\pi$
$499$	13.6289	+	18.7585i	0.610111	+	0.839746i	−0.386475	+	0.922300i	$0.626308\pi$
$500$	38.1829	−	31.5072i	1.70759	−	1.40905i
$501$		0			0
$502$	66.5959	+	10.5478i	2.97232	+	0.470769i
$503$	3.30226	−	0.523026i	0.147240	−	0.0233206i	−0.0823791	−	0.996601i	$-0.526252\pi$
$503$	3.30226	−	0.523026i	0.147240	−	0.0233206i	0.229619	+	0.973280i	$0.426252\pi$
$504$		0			0
$505$	14.2784	−	16.5277i	0.635379	−	0.735473i
$506$	−28.5296	−	24.5458i	−1.26829	−	1.09120i
$507$		0			0
$508$	0.813450	+	0.414474i	0.0360910	+	0.0183893i
$509$	13.0172	−	17.9166i	0.576977	−	0.794141i	−0.416383	−	0.909189i	$-0.636702\pi$
$509$	13.0172	−	17.9166i	0.576977	−	0.794141i	0.993360	+	0.115049i	$0.0367024\pi$
$510$		0			0
$511$	5.27640	−	16.2391i	0.233414	−	0.718375i
$512$	45.1541	−	23.0072i	1.99555	−	1.01678i
$513$		0			0
$514$	40.5589	+	29.4678i	1.78898	+	1.29977i
$515$	−9.67385	+	3.94312i	−0.426281	+	0.173755i
$516$		0			0
$517$	−16.5658	−	19.5390i	−0.728565	−	0.859323i
$518$	10.4011	+	10.4011i	0.456998	+	0.456998i
$519$		0			0
$520$	−30.2298	+	7.07704i	−1.32567	+	0.310349i
$521$	−8.59679	+	6.24594i	−0.376632	+	0.273639i	−0.759956	−	0.649975i	$-0.774779\pi$
$521$	−8.59679	+	6.24594i	−0.376632	+	0.273639i	0.383323	+	0.923614i	$0.374779\pi$
$522$		0			0
$523$	19.6244	+	38.5151i	0.858116	+	1.68415i	0.720269	+	0.693694i	$0.244018\pi$
$523$	19.6244	+	38.5151i	0.858116	+	1.68415i	0.137847	+	0.990454i	$0.455982\pi$
$524$	1.97629	−	1.43586i	0.0863348	−	0.0627259i
$525$		0			0
$526$	−6.55638	−	20.1785i	−0.285872	−	0.879823i
$527$	9.53941	+	9.53941i	0.415543	+	0.415543i
$528$		0			0
$529$		−	2.96712i		−	0.129005i
$530$	33.2795	+	14.0057i	1.44557	+	0.608370i
$531$		0			0
$532$	1.63538	−	10.3254i	0.0709028	−	0.447663i
$533$	2.62032	−	1.33512i	0.113499	−	0.0578304i
$534$		0			0
$535$	−22.0739	−	26.1430i	−0.954338	−	1.13026i
$536$	12.5986	−	17.3405i	0.544176	−	0.748994i
$537$		0			0
$538$	17.4086	−	17.4086i	0.750538	−	0.750538i
$539$	2.84517	+	12.0430i	0.122550	+	0.518728i
$540$		0			0
$541$	−20.0780	+	6.52373i	−0.863220	+	0.280477i	−0.706973	−	0.707241i	$-0.749940\pi$
$541$	−20.0780	+	6.52373i	−0.863220	+	0.280477i	−0.156247	+	0.987718i	$0.549940\pi$
$542$	7.64114	−	1.21024i	0.328215	−	0.0519841i
$543$		0			0
$544$	−15.3634	−	4.99188i	−0.658702	−	0.214025i
$545$	−34.2140	+	20.7012i	−1.46557	+	0.886744i
$546$		0			0
$547$	0.218056	+	1.37675i	0.00932342	+	0.0588658i	0.991911	−	0.126932i	$-0.0405130\pi$
$547$	0.218056	+	1.37675i	0.00932342	+	0.0588658i	−0.982588	+	0.185798i	$0.940513\pi$
$548$	−31.1101	+	61.0571i	−1.32896	+	2.60823i
$549$		0			0
$550$	−16.6673	+	38.5984i	−0.710696	+	1.64584i
$551$	−3.83469			−0.163363
$552$		0			0
$553$	−0.323881	−	2.04490i	−0.0137728	−	0.0869581i
$554$	3.54693	+	4.88193i	0.150695	+	0.207414i
$555$		0			0
$556$	−5.99117	−	1.94665i	−0.254082	−	0.0825563i
$557$	3.78516	+	0.599510i	0.160382	+	0.0254021i	0.236109	−	0.971727i	$-0.424128\pi$
$557$	3.78516	+	0.599510i	0.160382	+	0.0254021i	−0.0757269	+	0.997129i	$0.524128\pi$
$558$		0			0
$559$	−13.8180	+	4.48973i	−0.584438	+	0.189895i
$560$	1.98715	+	27.2152i	0.0839722	+	1.15005i
$561$		0			0
$562$	−50.6125	+	50.6125i	−2.13496	+	2.13496i
$563$	2.17596	+	1.10871i	0.0917058	+	0.0467264i	0.499242	−	0.866463i	$-0.333612\pi$
$563$	2.17596	+	1.10871i	0.0917058	+	0.0467264i	−0.407536	+	0.913189i	$0.633612\pi$
$564$		0			0
$565$	10.7754	+	12.7617i	0.453324	+	0.536891i
$566$	13.3292	−	41.0231i	0.560269	−	1.72433i
$567$		0			0
$568$	−6.51986	+	41.1648i	−0.273567	+	1.72723i
$569$	5.21403	+	3.78822i	0.218584	+	0.158810i	0.691689	−	0.722196i	$-0.256867\pi$
$569$	5.21403	+	3.78822i	0.218584	+	0.158810i	−0.473105	+	0.881006i	$0.656867\pi$
$570$		0			0
$571$			13.2864i			0.556019i	0.960578	+	0.278009i	$0.0896747\pi$
$571$			13.2864i			0.556019i	−0.960578	+	0.278009i	$0.910325\pi$
$572$	25.2677	−	21.4228i	1.05649	−	0.895733i
$573$		0			0
$574$	−1.84667	−	5.68346i	−0.0770785	−	0.237223i
$575$	21.3606	−	6.67444i	0.890797	−	0.278343i
$576$		0			0
$577$	−8.50263	−	16.6874i	−0.353969	−	0.694704i	0.643527	−	0.765423i	$-0.277470\pi$
$577$	−8.50263	−	16.6874i	−0.353969	−	0.694704i	−0.997496	+	0.0707197i	$0.977470\pi$
$578$	6.54143	+	12.8383i	0.272088	+	0.534002i
$579$		0			0
$580$	28.3084	−	6.62722i	1.17544	−	0.275180i
$581$	−5.84679	−	17.9946i	−0.242566	−	0.746540i
$582$		0			0
$583$	−21.0643	+	1.58105i	−0.872395	+	0.0654803i
$584$		−	58.1284i		−	2.40537i
$585$		0			0
$586$	−21.9158	−	15.9228i	−0.905334	−	0.657764i
$587$	1.31860	−	8.32531i	0.0544244	−	0.343622i	−0.945418	−	0.325861i	$-0.894346\pi$
$587$	1.31860	−	8.32531i	0.0544244	−	0.343622i	0.999842	−	0.0177617i	$-0.00565403\pi$
$588$		0			0
$589$	−1.61829	+	4.98059i	−0.0666805	+	0.205221i
$590$	53.6585	−	45.3066i	2.20909	−	1.86524i
$591$		0			0
$592$	19.2983	+	9.83295i	0.793153	+	0.404132i
$593$	−4.37233	+	4.37233i	−0.179550	+	0.179550i	−0.791160	−	0.611610i	$-0.790522\pi$
$593$	−4.37233	+	4.37233i	−0.179550	+	0.179550i	0.611610	+	0.791160i	$0.290522\pi$
$594$		0			0
$595$	−8.89103	+	10.2917i	−0.364497	+	0.421918i
$596$	−100.244	+	32.5713i	−4.10616	+	1.33417i
$597$		0			0
$598$	−25.2826	−	4.00437i	−1.03388	−	0.163751i
$599$	−34.7989	−	11.3068i	−1.42184	−	0.461985i	−0.505656	−	0.862735i	$-0.668750\pi$
$599$	−34.7989	−	11.3068i	−1.42184	−	0.461985i	−0.916187	+	0.400750i	$0.868750\pi$
$600$		0			0
$601$	6.33088	+	8.71371i	0.258242	+	0.355440i	0.918376	−	0.395708i	$-0.129501\pi$
$601$	6.33088	+	8.71371i	0.258242	+	0.355440i	−0.660134	+	0.751147i	$0.729501\pi$
$602$	4.61853	+	29.1603i	0.188237	+	1.18848i
$603$		0			0
$604$	63.6982			2.59184
$605$	−1.61343	−	24.5438i	−0.0655952	−	0.997846i
$606$		0			0
$607$	15.0249	−	29.4880i	0.609842	−	1.19688i	−0.355201	−	0.934790i	$-0.615588\pi$
$607$	15.0249	−	29.4880i	0.609842	−	1.19688i	0.965043	−	0.262092i	$-0.0844124\pi$
$608$	−0.980962	−	6.19355i	−0.0397833	−	0.251182i
$609$		0			0
$610$	12.6111	−	51.2508i	0.510607	−	2.07508i
$611$	−16.5702	−	5.38398i	−0.670359	−	0.217813i
$612$		0			0
$613$	−21.3721	+	3.38501i	−0.863213	+	0.136719i	−0.572314	−	0.820034i	$-0.693954\pi$
$613$	−21.3721	+	3.38501i	−0.863213	+	0.136719i	−0.290898	+	0.956754i	$0.593954\pi$
$614$	−78.4030	+	25.4747i	−3.16409	+	1.02807i
$615$		0			0
$616$	−19.1710	−	31.5401i	−0.772421	−	1.27079i
$617$	23.2611	−	23.2611i	0.936455	−	0.936455i	−0.0616431	−	0.998098i	$-0.519634\pi$
$617$	23.2611	−	23.2611i	0.936455	−	0.936455i	0.998098	+	0.0616431i	$0.0196341\pi$
$618$		0			0
$619$	24.3484	−	33.5126i	0.978643	−	1.34699i	0.0410856	−	0.999156i	$-0.486918\pi$
$619$	24.3484	−	33.5126i	0.978643	−	1.34699i	0.937557	−	0.347831i	$-0.113082\pi$
$620$	3.33893	−	39.5644i	0.134095	−	1.58894i
$621$		0			0
$622$	31.3741	−	15.9859i	1.25798	−	0.640975i
$623$	1.09102	−	6.88845i	0.0437109	−	0.275980i
$624$		0			0
$625$	−14.2336	−	20.5525i	−0.569343	−	0.822100i
$626$			44.0839i			1.76195i
$627$		0			0
$628$	−42.2480	−	42.2480i	−1.68588	−	1.68588i
$629$	3.33583	+	10.2666i	0.133008	+	0.409357i
$630$		0			0
$631$	25.4513	−	18.4915i	1.01320	−	0.736134i	0.0483238	−	0.998832i	$-0.484612\pi$
$631$	25.4513	−	18.4915i	1.01320	−	0.736134i	0.964878	+	0.262697i	$0.0846121\pi$
$632$	−3.19987	−	6.28010i	−0.127284	−	0.249809i
$633$		0			0
$634$	−33.1397	+	24.0774i	−1.31615	+	0.956236i
$635$	0.243118	−	0.391744i	0.00964783	−	0.0155459i
$636$		0			0
$637$	5.95137	+	5.95137i	0.235802	+	0.235802i
$638$	−18.8340	+	15.9681i	−0.745645	+	0.632184i
$639$		0			0
$640$	−10.9404	−	26.8407i	−0.432459	−	1.06097i
$641$	16.6022	+	12.0622i	0.655749	+	0.476430i	0.865225	−	0.501384i	$-0.167176\pi$
$641$	16.6022	+	12.0622i	0.655749	+	0.476430i	−0.209476	+	0.977814i	$0.567176\pi$
$642$		0			0
$643$	15.7020	−	8.00058i	0.619228	−	0.315512i	−0.116086	−	0.993239i	$-0.537035\pi$
$643$	15.7020	−	8.00058i	0.619228	−	0.315512i	0.735314	+	0.677727i	$0.237035\pi$
$644$	−11.0724	+	34.0774i	−0.436314	+	1.34284i
$645$		0			0
$646$	6.54649	−	9.01047i	0.257568	−	0.354512i
$647$	−5.13354	−	2.61567i	−0.201820	−	0.102833i	0.350159	−	0.936690i	$-0.386127\pi$
$647$	−5.13354	−	2.61567i	−0.201820	−	0.102833i	−0.551980	+	0.833857i	$0.686127\pi$
$648$		0			0
$649$	−15.8602	+	37.9010i	−0.622566	+	1.48774i
$650$	4.15374	+	28.2924i	0.162923	+	1.10972i
$651$		0			0
$652$	4.69343	−	0.743366i	0.183809	−	0.0291125i
$653$	−5.76236	−	0.912669i	−0.225499	−	0.0357155i	0.0426625	−	0.999090i	$-0.486416\pi$
$653$	−5.76236	−	0.912669i	−0.225499	−	0.0357155i	−0.268161	+	0.963374i	$0.586416\pi$
$654$		0			0
$655$	−0.638627	−	1.05549i	−0.0249532	−	0.0412415i
$656$	−5.17212	−	7.11881i	−0.201937	−	0.277943i
$657$		0			0
$658$	−16.0732	+	31.5454i	−0.626598	+	1.22977i
$659$	5.21347			0.203088			0.101544	−	0.994831i	$-0.467622\pi$
$659$	5.21347			0.203088			0.101544	+	0.994831i	$0.467622\pi$
$660$		0			0
$661$	4.56016			0.177369			0.0886847	−	0.996060i	$-0.471734\pi$
$661$	4.56016			0.177369			0.0886847	+	0.996060i	$0.471734\pi$
$662$	16.9010	−	33.1701i	0.656877	−	1.28919i
$663$		0			0
$664$	−37.8606	−	52.1106i	−1.46927	−	2.02228i
$665$	−5.12651	−	1.26146i	−0.198798	−	0.0489173i
$666$		0			0
$667$	12.9815	+	2.05606i	0.502644	+	0.0796110i
$668$	−8.27346	+	1.31039i	−0.320110	+	0.0507004i
$669$		0			0
$670$	−14.9389	−	12.9058i	−0.577139	−	0.498593i
$671$	7.09949	+	30.0506i	0.274073	+	1.16009i
$672$		0			0
$673$	−0.498417	−	0.253956i	−0.0192126	−	0.00978930i	0.444358	−	0.895849i	$-0.353432\pi$
$673$	−0.498417	−	0.253956i	−0.0192126	−	0.00978930i	−0.463570	+	0.886060i	$0.653432\pi$
$674$	−20.1046	+	27.6716i	−0.774401	+	1.06587i
$675$		0			0
$676$	−10.8248	+	33.3153i	−0.416338	+	1.28136i
$677$	25.9390	−	13.2166i	0.996918	−	0.507955i	0.122157	−	0.992511i	$-0.461019\pi$
$677$	25.9390	−	13.2166i	0.996918	−	0.507955i	0.874760	+	0.484556i	$0.161019\pi$
$678$		0			0
$679$	1.13807	+	0.826858i	0.0436752	+	0.0317319i
$680$	−17.9599	+	42.6750i	−0.688729	+	1.63651i
$681$		0			0
$682$	12.7916	+	31.2008i	0.489815	+	1.19474i
$683$	−5.43554	−	5.43554i	−0.207985	−	0.207985i	0.595425	−	0.803411i	$-0.296984\pi$
$683$	−5.43554	−	5.43554i	−0.207985	−	0.207985i	−0.803411	+	0.595425i	$0.796984\pi$
$684$		0			0
$685$	29.4041	+	18.2483i	1.12347	+	0.697231i
$686$	39.7955	−	28.9131i	1.51940	−	1.10391i
$687$		0			0
$688$	19.7361	+	38.7343i	0.752432	+	1.47673i
$689$	−11.6233	+	8.44481i	−0.442812	+	0.321722i
$690$		0			0
$691$	−2.91716	−	8.97809i	−0.110974	−	0.341542i	0.880112	−	0.474766i	$-0.157467\pi$
$691$	−2.91716	−	8.97809i	−0.110974	−	0.341542i	−0.991086	+	0.133223i	$0.957467\pi$
$692$	59.3222	+	59.3222i	2.25509	+	2.25509i
$693$		0			0
$694$			31.0215i			1.17756i
$695$	−1.23403	+	2.93222i	−0.0468094	+	0.111225i
$696$		0			0
$697$	0.686067	−	4.33166i	0.0259866	−	0.164073i
$698$	−46.0182	+	23.4474i	−1.74181	+	0.887499i
$699$		0			0
$700$	40.0249	+	0.452542i	1.51280	+	0.0171045i
$701$	11.5843	−	15.9445i	0.437535	−	0.602215i	−0.532127	−	0.846664i	$-0.678607\pi$
$701$	11.5843	−	15.9445i	0.437535	−	0.602215i	0.969662	+	0.244449i	$0.0786072\pi$
$702$		0			0
$703$	−2.96308	+	2.96308i	−0.111755	+	0.111755i
$704$	3.33042	+	2.86537i	0.125520	+	0.107993i
$705$		0			0
$706$	−47.0188	+	15.2773i	−1.76958	+	0.574970i
$707$	17.4427	−	2.76266i	0.656001	−	0.103900i
$708$		0			0
$709$	−42.2836	−	13.7388i	−1.58799	−	0.515970i	−0.623893	−	0.781510i	$-0.714450\pi$
$709$	−42.2836	−	13.7388i	−1.58799	−	0.515970i	−0.964100	+	0.265540i	$0.914450\pi$
$710$	37.2751	+	9.17212i	1.39891	+	0.344224i
$711$		0			0
$712$	−3.71422	−	23.4507i	−0.139196	−	0.878850i
$713$	8.14881	−	15.9929i	0.305175	−	0.598940i
$714$		0			0
$715$	−9.70736	−	13.6250i	−0.363035	−	0.509547i
$716$	−72.5395			−2.71093
$717$		0			0
$718$	6.55191	+	41.3671i	0.244515	+	1.54381i
$719$	14.1002	+	19.4073i	0.525850	+	0.723770i	0.986491	−	0.163816i	$-0.0523804\pi$
$719$	14.1002	+	19.4073i	0.525850	+	0.723770i	−0.460641	+	0.887587i	$0.652380\pi$
$720$		0			0
$721$	−8.03342	−	2.61022i	−0.299180	−	0.0972095i
$722$	−43.3075	−	6.85924i	−1.61174	−	0.255274i
$723$		0			0
$724$	−62.5908	+	20.3370i	−2.32617	+	0.755819i
$725$	−2.13276	−	14.5268i	−0.0792087	−	0.539513i
$726$		0			0
$727$	−17.6187	+	17.6187i	−0.653441	+	0.653441i	−0.953820	−	0.300379i	$-0.902887\pi$
$727$	−17.6187	+	17.6187i	−0.653441	+	0.653441i	0.300379	+	0.953820i	$0.402887\pi$
$728$	−22.3677	−	11.3969i	−0.829002	−	0.422398i
$729$		0			0
$730$	−53.3489	−	4.50224i	−1.97453	−	0.166635i
$731$	−6.69547	+	20.6065i	−0.247641	+	0.762161i
$732$		0			0
$733$	−0.00846331	+	0.0534353i	−0.000312600	+	0.00197368i	−0.987844	−	0.155448i	$-0.950318\pi$
$733$	−0.00846331	+	0.0534353i	−0.000312600	+	0.00197368i	0.987532	+	0.157421i	$0.0503180\pi$
$734$	13.2119	+	9.59902i	0.487661	+	0.354306i
$735$		0			0
$736$			21.4928i			0.792235i
$737$	11.2205	+	2.73683i	0.413313	+	0.100813i
$738$		0			0
$739$	−5.95011	−	18.3126i	−0.218878	−	0.673638i	−0.998855	−	0.0478303i	$-0.984769\pi$
$739$	−5.95011	−	18.3126i	−0.218878	−	0.673638i	0.779977	−	0.625808i	$-0.215231\pi$
$740$	16.7531	−	26.9949i	0.615858	−	0.992352i
$741$		0			0
$742$	13.2541	+	26.0127i	0.486575	+	0.954957i
$743$	3.38155	+	6.63666i	0.124057	+	0.243475i	0.944679	−	0.327995i	$-0.106373\pi$
$743$	3.38155	+	6.63666i	0.124057	+	0.243475i	−0.820622	+	0.571471i	$0.806373\pi$
$744$		0			0
$745$	12.1334	+	51.8283i	0.444534	+	1.89884i
$746$	−10.7432	−	33.0642i	−0.393337	−	1.21057i
$747$		0			0
$748$	−3.69760	−	49.2632i	−0.135198	−	1.80124i
$749$		−	27.6659i		−	1.01089i
$750$		0			0
$751$	24.3907	+	17.7209i	0.890031	+	0.646645i	0.935886	−	0.352303i	$-0.114601\pi$
$751$	24.3907	+	17.7209i	0.890031	+	0.646645i	−0.0458552	+	0.998948i	$0.514601\pi$
$752$	−8.15512	+	51.4894i	−0.297387	+	1.87763i
$753$		0			0
$754$	−5.18973	+	15.9723i	−0.188999	+	0.581678i
$755$	2.70514	−	32.0543i	0.0984500	−	1.16658i
$756$		0			0
$757$	39.6521	+	20.2037i	1.44118	+	0.734318i	0.987614	−	0.156905i	$-0.0501516\pi$
$757$	39.6521	+	20.2037i	1.44118	+	0.734318i	0.453566	+	0.891223i	$0.350152\pi$
$758$	38.5456	−	38.5456i	1.40004	−	1.40004i
$759$		0			0
$760$	−17.9253	+	1.30883i	−0.650218	+	0.0474764i
$761$	−44.8060	+	14.5584i	−1.62422	+	0.527740i	−0.972932	−	0.231093i	$-0.925770\pi$
$761$	−44.8060	+	14.5584i	−1.62422	+	0.527740i	−0.651285	+	0.758833i	$0.725770\pi$
$762$		0			0
$763$	−31.9361	−	5.05818i	−1.15616	−	0.183118i
$764$	8.04134	+	2.61279i	0.290926	+	0.0945274i
$765$		0			0
$766$	−0.452182	−	0.622375i	−0.0163380	−	0.0224873i
$767$	4.37145	+	27.6003i	0.157844	+	0.996588i
$768$		0			0
$769$	29.7849			1.07407			0.537036	−	0.843559i	$-0.319544\pi$
$769$	29.7849			1.07407			0.537036	+	0.843559i	$0.319544\pi$
$770$	−30.4316	+	15.1518i	−1.09668	+	0.546033i
$771$		0			0
$772$	22.8815	−	44.9076i	0.823525	−	1.61626i
$773$	1.11434	+	7.03566i	0.0400800	+	0.253055i	0.999590	−	0.0286180i	$-0.00911063\pi$
$773$	1.11434	+	7.03566i	0.0400800	+	0.253055i	−0.959510	+	0.281673i	$0.909111\pi$
$774$		0			0
$775$	−19.7678	−	3.36044i	−0.710082	−	0.120711i
$776$	4.55461	+	1.47988i	0.163501	+	0.0531247i
$777$		0			0
$778$	−9.01803	+	1.42832i	−0.323312	+	0.0512076i
$779$	1.61912	−	0.526083i	0.0580108	−	0.0188489i
$780$		0			0
$781$	−21.8560	+	5.16351i	−0.782070	+	0.184765i
$782$	−26.9928	+	26.9928i	−0.965260	+	0.965260i
$783$		0			0
$784$	14.8022	−	20.3735i	0.528651	−	0.727626i
$785$	−23.0543	+	19.4659i	−0.822844	+	0.694769i
$786$		0			0
$787$	−25.7117	+	13.1008i	−0.916524	+	0.466992i	−0.847604	−	0.530630i	$-0.821955\pi$
$787$	−25.7117	+	13.1008i	−0.916524	+	0.466992i	−0.0689202	+	0.997622i	$0.521955\pi$
$788$	−13.5270	+	85.4058i	−0.481878	+	3.04246i
$789$		0			0
$790$	−6.01157	+	2.45035i	−0.213882	+	0.0871796i
$791$			13.5051i			0.480187i
$792$		0			0
$793$	14.8503	+	14.8503i	0.527350	+	0.527350i
$794$	−24.5726	−	75.6268i	−0.872051	−	2.68390i
$795$		0			0
$796$	−80.0636	+	58.1696i	−2.83778	+	2.06177i
$797$	−14.0459	−	27.5666i	−0.497531	−	0.976460i	−0.994100	−	0.108463i	$-0.965407\pi$
$797$	−14.0459	−	27.5666i	−0.497531	−	0.976460i	0.496569	−	0.867997i	$-0.334593\pi$
$798$		0			0
$799$	−21.0204	+	15.2722i	−0.743647	+	0.540291i
$800$	22.9172	−	7.16084i	0.810246	−	0.253174i
$801$		0			0
$802$	−17.9225	−	17.9225i	−0.632866	−	0.632866i
$803$	28.9809	−	11.8815i	1.02271	−	0.419288i
$804$		0			0
$805$	16.6783	+	7.01908i	0.587831	+	0.247390i
$806$	18.5551	+	13.4811i	0.653575	+	0.474850i
$807$		0			0
$808$	53.5684	−	27.2945i	1.88453	−	0.960215i
$809$	−6.07857	+	18.7079i	−0.213711	+	0.657735i	0.785531	+	0.618822i	$0.212390\pi$
$809$	−6.07857	+	18.7079i	−0.213711	+	0.657735i	−0.999243	+	0.0389136i	$0.987610\pi$
$810$		0			0
$811$	24.8398	−	34.1891i	0.872243	−	1.20054i	−0.106266	−	0.994338i	$-0.533890\pi$
$811$	24.8398	−	34.1891i	0.872243	−	1.20054i	0.978509	−	0.206202i	$-0.0661105\pi$
$812$	20.9460	+	10.6725i	0.735061	+	0.374532i
$813$		0			0
$814$	−2.21447	+	26.8918i	−0.0776170	+	0.942556i
$815$	−0.174757	−	2.39340i	−0.00612147	−	0.0838373i
$816$		0			0
$817$	−8.30723	+	1.31574i	−0.290633	+	0.0460318i
$818$	−76.1023	−	12.0534i	−2.66085	−	0.421438i
$819$		0			0
$820$	−11.0434	+	6.68184i	−0.385653	+	0.233340i
$821$	31.2544	+	43.0180i	1.09079	+	1.50134i	0.847061	+	0.531496i	$0.178370\pi$
$821$	31.2544	+	43.0180i	1.09079	+	1.50134i	0.243726	+	0.969844i	$0.421630\pi$
$822$		0			0
$823$	0.635792	−	1.24781i	0.0221623	−	0.0434960i	−0.879660	−	0.475603i	$-0.842230\pi$
$823$	0.635792	−	1.24781i	0.0221623	−	0.0434960i	0.901822	+	0.432107i	$0.142230\pi$
$824$	−28.7559			−1.00176
$825$		0			0
$826$	56.7841			1.97577
$827$	7.84783	−	15.4022i	0.272896	−	0.535588i	−0.713363	−	0.700794i	$-0.752829\pi$
$827$	7.84783	−	15.4022i	0.272896	−	0.535588i	0.986259	+	0.165206i	$0.0528290\pi$
$828$		0			0
$829$	21.0969	+	29.0374i	0.732727	+	1.00851i	0.999004	+	0.0446158i	$0.0142064\pi$
$829$	21.0969	+	29.0374i	0.732727	+	1.00851i	−0.266277	+	0.963897i	$0.585794\pi$
$830$	−50.7583	+	30.7114i	−1.76185	+	1.06601i
$831$		0			0
$832$	2.95138	+	0.467453i	0.102321	+	0.0162060i
$833$	12.3969	−	1.96348i	0.429527	−	0.0680304i
$834$		0			0
$835$	0.308058	+	4.21903i	0.0106608	+	0.146006i
$836$	16.3872	−	9.96064i	0.566764	−	0.344496i
$837$		0			0
$838$	−16.9013	−	8.61164i	−0.583845	−	0.297484i
$839$	−2.91587	+	4.01335i	−0.100667	+	0.138556i	−0.856379	−	0.516348i	$-0.827291\pi$
$839$	−2.91587	+	4.01335i	−0.100667	+	0.138556i	0.755712	+	0.654904i	$0.227291\pi$
$840$		0			0
$841$	−6.29681	+	19.3796i	−0.217131	+	0.668261i
$842$	−46.1350	+	23.5070i	−1.58992	+	0.810103i
$843$		0			0
$844$	1.34883	+	0.979980i	0.0464285	+	0.0337323i
$845$	16.3053	+	6.86210i	0.560918	+	0.236063i
$846$		0			0
$847$	11.8063	−	16.0048i	0.405668	−	0.549932i
$848$	30.3971	+	30.3971i	1.04384	+	1.04384i
$849$		0			0
$850$	37.7751	+	19.7885i	1.29567	+	0.678738i
$851$	11.6196	−	8.44211i	0.398313	−	0.289392i
$852$		0			0
$853$	−12.0658	−	23.6804i	−0.413125	−	0.810803i	−0.999999	−	0.00112492i	$-0.999642\pi$
$853$	−12.0658	−	23.6804i	−0.413125	−	0.810803i	0.586875	−	0.809678i	$-0.300358\pi$
$854$	34.5257	−	25.0844i	1.18144	−	0.858369i
$855$		0			0
$856$	−29.1045	−	89.5744i	−0.994771	−	3.06159i
$857$	1.04396	+	1.04396i	0.0356609	+	0.0356609i	0.724712	−	0.689051i	$-0.241973\pi$
$857$	1.04396	+	1.04396i	0.0356609	+	0.0356609i	−0.689051	+	0.724712i	$0.741973\pi$
$858$		0			0
$859$		−	13.9402i		−	0.475633i	−0.971310	−	0.237816i	$-0.923568\pi$
$859$		−	13.9402i		−	0.475633i	0.971310	−	0.237816i	$-0.0764316\pi$
$860$	59.0516	−	24.0698i	2.01364	−	0.820773i
$861$		0			0
$862$	13.3522	−	84.3026i	0.454778	−	2.87136i
$863$	45.7166	−	23.2938i	1.55621	−	0.792929i	0.556919	−	0.830567i	$-0.311983\pi$
$863$	45.7166	−	23.2938i	1.55621	−	0.792929i	0.999291	+	0.0376382i	$0.0119834\pi$
$864$		0			0
$865$	32.3715	−	27.3329i	1.10066	−	0.929347i
$866$	17.2852	−	23.7911i	0.587376	−	0.808454i
$867$		0			0
$868$	22.7012	−	22.7012i	0.770529	−	0.770529i
$869$	2.47699	−	2.87900i	0.0840262	−	0.0976635i
$870$		0			0
$871$	7.47089	−	2.42744i	0.253141	−	0.0822507i
$872$	−108.721	+	17.2198i	−3.68177	+	0.583135i
$873$		0			0
$874$	−14.0931	−	4.57913i	−0.476706	−	0.154891i
$875$	1.92751	−	20.1222i	0.0651617	−	0.680254i
$876$		0			0
$877$	1.04392	+	6.59105i	0.0352507	+	0.222564i	0.999025	−	0.0441563i	$-0.0140600\pi$
$877$	1.04392	+	6.59105i	0.0352507	+	0.222564i	−0.963774	+	0.266720i	$0.914060\pi$
$878$	−12.3436	+	24.2256i	−0.416575	+	0.817574i
$879$		0			0
$880$	−35.7219	+	35.0653i	−1.20418	+	1.18205i
$881$	14.4573			0.487080			0.243540	−	0.969891i	$-0.421691\pi$
$881$	14.4573			0.487080			0.243540	+	0.969891i	$0.421691\pi$
$882$		0			0
$883$	−1.63650	−	10.3324i	−0.0550725	−	0.347714i	−0.999803	−	0.0198651i	$-0.993676\pi$
$883$	−1.63650	−	10.3324i	−0.0550725	−	0.347714i	0.944730	−	0.327849i	$-0.106324\pi$
$884$	−19.7499	−	27.1834i	−0.664260	−	0.914276i
$885$		0			0
$886$	97.2533	+	31.5995i	3.26729	+	1.06161i
$887$	−9.76140	−	1.54605i	−0.327756	−	0.0519114i	−0.00961170	−	0.999954i	$-0.503060\pi$
$887$	−9.76140	−	1.54605i	−0.327756	−	0.0519114i	−0.318144	+	0.948042i	$0.603060\pi$
$888$		0			0
$889$	0.354548	−	0.115200i	0.0118912	−	0.00386368i
$890$	−21.8101	+	1.59249i	−0.731078	+	0.0533805i
$891$		0			0
$892$	23.8243	−	23.8243i	0.797695	−	0.797695i
$893$	−8.98671	−	4.57896i	−0.300729	−	0.153229i
$894$		0			0
$895$	−3.08061	+	36.5034i	−0.102973	+	1.22018i
$896$	7.24221	−	22.2892i	0.241945	−	0.744631i
$897$		0			0
$898$	−1.44429	+	9.11891i	−0.0481967	+	0.304302i
$899$	−9.52719	−	6.92191i	−0.317750	−	0.230859i
$900$		0			0
$901$			21.4256i			0.713789i
$902$	5.76157	−	9.32604i	0.191839	−	0.310523i
$903$		0			0
$904$	14.2074	+	43.7258i	0.472530	+	1.45430i
$905$	7.57591	+	32.3607i	0.251832	+	1.07571i
$906$		0			0
$907$	5.25319	+	10.3100i	0.174429	+	0.342337i	0.961625	−	0.274366i	$-0.0884680\pi$
$907$	5.25319	+	10.3100i	0.174429	+	0.342337i	−0.787196	+	0.616703i	$0.788468\pi$
$908$	−16.4887	−	32.3609i	−0.547196	−	1.07393i
$909$		0			0
$910$	−12.1923	+	19.6458i	−0.404170	+	0.651253i
$911$	2.69510	+	8.29465i	0.0892925	+	0.274814i	0.985724	−	0.168368i	$-0.0538496\pi$
$911$	2.69510	+	8.29465i	0.0892925	+	0.274814i	−0.896432	+	0.443182i	$0.853850\pi$
$912$		0			0
$913$	18.2419	−	29.5274i	0.603718	−	0.977215i
$914$			45.8704i			1.51726i
$915$		0			0
$916$	−27.1854	−	19.7514i	−0.898231	−	0.652603i
$917$	0.156043	−	0.985219i	0.00515301	−	0.0325348i
$918$		0			0
$919$	1.78507	−	5.49388i	0.0588840	−	0.181226i	−0.917288	−	0.398224i	$-0.869627\pi$
$919$	1.78507	−	5.49388i	0.0588840	−	0.181226i	0.976172	+	0.216998i	$0.0696265\pi$
$920$	61.3836	+	5.18031i	2.02376	+	0.170790i
$921$		0			0
$922$	−80.3931	−	40.9623i	−2.64761	−	1.34902i
$923$	−10.8007	+	10.8007i	−0.355511	+	0.355511i
$924$		0			0
$925$	−12.8729	−	9.57696i	−0.423260	−	0.314889i
$926$	−15.2359	+	4.95043i	−0.500681	+	0.162681i
$927$		0			0
$928$	13.9275	+	2.20590i	0.457192	+	0.0724121i
$929$	17.2514	+	5.60532i	0.566000	+	0.183905i	0.578019	−	0.816023i	$-0.303826\pi$
$929$	17.2514	+	5.60532i	0.566000	+	0.183905i	−0.0120191	+	0.999928i	$0.503826\pi$
$930$		0			0
$931$	2.86384	+	3.94174i	0.0938587	+	0.129185i
$932$	−18.1595	−	114.654i	−0.594833	−	3.75563i
$933$		0			0
$934$	−21.9374			−0.717813
$935$	−24.9473	−	0.231399i	−0.815864	−	0.00756755i
$936$		0			0
$937$	−14.5907	+	28.6359i	−0.476659	+	0.935496i	0.520027	+	0.854150i	$0.325922\pi$
$937$	−14.5907	+	28.6359i	−0.476659	+	0.935496i	−0.996686	+	0.0813459i	$0.974078\pi$
$938$	−2.49708	−	15.7659i	−0.0815325	−	0.514776i
$939$		0			0
$940$	74.2550	+	18.2716i	2.42193	+	0.595955i
$941$	4.95612	+	1.61034i	0.161565	+	0.0524956i	0.388683	−	0.921372i	$-0.372930\pi$
$941$	4.95612	+	1.61034i	0.161565	+	0.0524956i	−0.227118	+	0.973867i	$0.572930\pi$
$942$		0			0
$943$	−5.76321	+	0.912803i	−0.187676	+	0.0297250i
$944$	79.5200	−	25.8376i	2.58816	−	0.840943i
$945$		0			0
$946$	−35.3219	+	41.0545i	−1.14841	+	1.33480i
$947$	0.545091	−	0.545091i	0.0177131	−	0.0177131i	−0.698195	−	0.715908i	$-0.746013\pi$
$947$	0.545091	−	0.545091i	0.0177131	−	0.0177131i	0.715908	+	0.698195i	$0.246013\pi$
$948$		0			0
$949$	12.5219	−	17.2349i	0.406478	−	0.559469i
$950$	−0.187154	+	16.5528i	−0.00607207	+	0.537043i
$951$		0			0
$952$	−33.3567	+	16.9961i	−1.08110	+	0.550846i
$953$	−2.12456	+	13.4139i	−0.0688211	+	0.434519i	0.929086	+	0.369863i	$0.120595\pi$
$953$	−2.12456	+	13.4139i	−0.0688211	+	0.434519i	−0.997908	+	0.0646568i	$0.979405\pi$
$954$		0			0
$955$	1.65631	−	3.93562i	0.0535970	−	0.127354i
$956$		−	10.0777i		−	0.325935i
$957$		0			0
$958$	27.5786	+	27.5786i	0.891023	+	0.891023i
$959$	8.64682	+	26.6122i	0.279221	+	0.859352i
$960$		0			0
$961$	12.0686	−	8.76834i	0.389309	−	0.282850i
$962$	8.33177	+	16.3520i	0.268627	+	0.527210i
$963$		0			0
$964$	22.5507	−	16.3840i	0.726309	−	0.527694i
$965$	−21.6267	−	13.4216i	−0.696189	−	0.432057i
$966$		0			0
$967$	28.7882	+	28.7882i	0.925767	+	0.925767i	0.997429	−	0.0716619i	$-0.0228303\pi$
$967$	28.7882	+	28.7882i	0.925767	+	0.925767i	−0.0716619	+	0.997429i	$0.522830\pi$
$968$	21.3884	−	64.2393i	0.687448	−	2.06473i
$969$		0			0
$970$	1.71097	−	4.06550i	0.0549360	−	0.130535i
$971$	−23.7651	−	17.2663i	−0.762657	−	0.554103i	0.137067	−	0.990562i	$-0.456232\pi$
$971$	−23.7651	−	17.2663i	−0.762657	−	0.554103i	−0.899724	+	0.436459i	$0.856232\pi$
$972$		0			0
$973$	−2.29195	+	1.16781i	−0.0734765	+	0.0374382i
$974$	−4.65870	+	14.3380i	−0.149274	+	0.459419i
$975$		0			0
$976$	36.9357	−	50.8376i	1.18228	−	1.62727i
$977$	20.8453	+	10.6212i	0.666901	+	0.339803i	0.754450	−	0.656357i	$-0.227904\pi$
$977$	20.8453	+	10.6212i	0.666901	+	0.339803i	−0.0875496	+	0.996160i	$0.527904\pi$
$978$		0			0
$979$	10.9325	−	6.64511i	0.349405	−	0.212379i
$980$	−27.9536	−	24.1493i	−0.892946	−	0.771420i
$981$		0			0
$982$	−102.544	+	16.2414i	−3.27232	+	0.518284i
$983$	20.6008	+	3.26285i	0.657064	+	0.104069i	0.476059	−	0.879413i	$-0.342065\pi$
$983$	20.6008	+	3.26285i	0.657064	+	0.104069i	0.181005	+	0.983482i	$0.442065\pi$
$984$		0			0
$985$	42.4036	+	10.4341i	1.35109	+	0.332457i
$986$	14.7212	+	20.2619i	0.468817	+	0.645271i
$987$		0			0
$988$	5.92148	−	11.6216i	0.188387	−	0.369731i
$989$	28.8277			0.916666
$990$		0			0
$991$	−6.50787			−0.206729			−0.103365	−	0.994644i	$-0.532961\pi$
$991$	−6.50787			−0.206729			−0.103365	+	0.994644i	$0.532961\pi$
$992$	8.74265	−	17.1584i	0.277579	−	0.544780i
$993$		0			0
$994$	18.2440	+	25.1108i	0.578666	+	0.796465i
$995$	25.8721	+	42.7601i	0.820200	+	1.35559i
$996$		0			0
$997$	26.0805	+	4.13075i	0.825978	+	0.130822i	0.555092	−	0.831789i	$-0.312683\pi$
$997$	26.0805	+	4.13075i	0.825978	+	0.130822i	0.270886	+	0.962611i	$0.412683\pi$
$998$	58.0618	−	9.19609i	1.83792	−	0.291097i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.a.28.4		32
3.2	odd	2		55.2.l.a.28.1	yes	32
5.2	odd	4	inner	495.2.bj.a.127.4		32
11.2	odd	10	inner	495.2.bj.a.343.4		32
12.11	even	2		880.2.cm.a.193.1		32
15.2	even	4		55.2.l.a.17.1	yes	32
15.8	even	4		275.2.bm.b.182.4		32
15.14	odd	2		275.2.bm.b.193.4		32
33.2	even	10		55.2.l.a.13.1	yes	32
33.5	odd	10		605.2.m.c.403.1		32
33.8	even	10		605.2.e.b.483.1		32
33.14	odd	10		605.2.e.b.483.16		32
33.17	even	10		605.2.m.d.403.4		32
33.20	odd	10		605.2.m.e.233.4		32
33.26	odd	10		605.2.m.d.118.1		32
33.29	even	10		605.2.m.c.118.4		32
33.32	even	2		605.2.m.e.578.4		32
55.2	even	20	inner	495.2.bj.a.442.4		32
60.47	odd	4		880.2.cm.a.17.1		32
132.35	odd	10		880.2.cm.a.673.1		32
165.2	odd	20		55.2.l.a.2.1	✓	32
165.17	odd	20		605.2.m.d.282.1		32
165.32	odd	4		605.2.m.e.457.4		32
165.47	even	20		605.2.e.b.362.1		32
165.62	odd	20		605.2.m.c.602.1		32
165.68	odd	20		275.2.bm.b.57.4		32
165.92	even	20		605.2.m.d.602.4		32
165.107	odd	20		605.2.e.b.362.16		32
165.134	even	10		275.2.bm.b.68.4		32
165.137	even	20		605.2.m.c.282.4		32
165.152	even	20		605.2.m.e.112.4		32
660.167	even	20		880.2.cm.a.497.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.1	✓	32	165.2	odd	20
55.2.l.a.13.1	yes	32	33.2	even	10
55.2.l.a.17.1	yes	32	15.2	even	4
55.2.l.a.28.1	yes	32	3.2	odd	2
275.2.bm.b.57.4		32	165.68	odd	20
275.2.bm.b.68.4		32	165.134	even	10
275.2.bm.b.182.4		32	15.8	even	4
275.2.bm.b.193.4		32	15.14	odd	2
495.2.bj.a.28.4		32	1.1	even	1	trivial
495.2.bj.a.127.4		32	5.2	odd	4	inner
495.2.bj.a.343.4		32	11.2	odd	10	inner
495.2.bj.a.442.4		32	55.2	even	20	inner
605.2.e.b.362.1		32	165.47	even	20
605.2.e.b.362.16		32	165.107	odd	20
605.2.e.b.483.1		32	33.8	even	10
605.2.e.b.483.16		32	33.14	odd	10
605.2.m.c.118.4		32	33.29	even	10
605.2.m.c.282.4		32	165.137	even	20
605.2.m.c.403.1		32	33.5	odd	10
605.2.m.c.602.1		32	165.62	odd	20
605.2.m.d.118.1		32	33.26	odd	10
605.2.m.d.282.1		32	165.17	odd	20
605.2.m.d.403.4		32	33.17	even	10
605.2.m.d.602.4		32	165.92	even	20
605.2.m.e.112.4		32	165.152	even	20
605.2.m.e.233.4		32	33.20	odd	10
605.2.m.e.457.4		32	165.32	odd	4
605.2.m.e.578.4		32	33.32	even	2
880.2.cm.a.17.1		32	60.47	odd	4
880.2.cm.a.193.1		32	12.11	even	2
880.2.cm.a.497.1		32	660.167	even	20
880.2.cm.a.673.1		32	132.35	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)

\(f(q)\)	\(=\)	\(q+(1.15100 - 2.25897i) q^{2} +(-2.60258 - 3.58214i) q^{4} +(-1.91314 + 1.15755i) q^{5} +(-1.78576 - 0.282837i) q^{7} +(-6.07934 + 0.962874i) q^{8} +(0.412838 + 5.65406i) q^{10} +(-1.72268 - 2.83415i) q^{11} +(-2.00993 - 1.02411i) q^{13} +(-2.69434 + 3.70844i) q^{14} +(-2.08573 + 6.41923i) q^{16} +(-2.99738 + 1.52724i) q^{17} +(-1.05647 - 0.767569i) q^{19} +(9.12557 + 3.84051i) q^{20} +(-8.38507 + 0.629367i) q^{22} +(3.16488 + 3.16488i) q^{23} +(2.32018 - 4.42908i) q^{25} +(-4.62687 + 3.36162i) q^{26} +(3.63442 + 7.13295i) q^{28} +(2.37569 - 1.72604i) q^{29} +(-1.23925 - 3.81401i) q^{31} +(3.39552 + 3.39552i) q^{32} +8.52886i q^{34} +(3.74380 - 1.52600i) q^{35} +(0.501987 - 3.16942i) q^{37} +(-2.94992 + 1.50306i) q^{38} +(10.5160 - 8.87923i) q^{40} +(-0.766287 + 1.05470i) q^{41} +(4.55431 - 4.55431i) q^{43} +(-5.66890 + 13.5469i) q^{44} +(10.7922 - 3.50658i) q^{46} +(7.62854 - 1.20824i) q^{47} +(-3.54845 - 1.15296i) q^{49} +(-7.33465 - 10.3391i) q^{50} +(1.56249 + 9.86517i) q^{52} +(2.89146 - 5.67482i) q^{53} +(6.57637 + 3.42803i) q^{55} +11.1286 q^{56} +(-1.16465 - 7.35329i) q^{58} +(-7.28135 - 10.0219i) q^{59} +(-8.85435 - 2.87695i) q^{61} +(-10.0421 - 1.59052i) q^{62} +(-1.25983 + 0.409344i) q^{64} +(5.03072 - 0.367324i) q^{65} +(-2.46236 + 2.46236i) q^{67} +(13.2717 + 6.76227i) q^{68} +(0.861947 - 10.2136i) q^{70} +(2.09243 - 6.43984i) q^{71} +(-1.47735 + 9.32763i) q^{73} +(-6.58185 - 4.78199i) q^{74} +5.78207i q^{76} +(2.27469 + 5.54835i) q^{77} +(0.353860 + 1.08907i) q^{79} +(-3.44026 - 14.6952i) q^{80} +(1.50055 + 2.94499i) q^{82} +(4.75092 + 9.32422i) q^{83} +(3.96654 - 6.39143i) q^{85} +(-5.04603 - 15.5301i) q^{86} +(13.2017 + 15.5710i) q^{88} +3.85743i q^{89} +(3.29960 + 2.39730i) q^{91} +(3.10019 - 19.5739i) q^{92} +(6.05109 - 18.6233i) q^{94} +(2.90966 + 0.245553i) q^{95} +(-0.693249 - 0.353228i) q^{97} +(-6.68878 + 6.68878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 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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