LMFDB - Embedded newform 855.2.dl.b.298.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(127,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.dl (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0,0,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			298.13
Character	$\chi$	$=$	855.298
Dual form			855.2.dl.b.307.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.693370 + 0.0606620i) q^{2} +(-1.49253 - 0.263174i) q^{4} +(1.33943 - 1.79051i) q^{5} +(0.0498847 + 0.186172i) q^{7} +(-2.36352 - 0.633303i) q^{8} +(1.03734 - 1.16023i) q^{10} +(-1.69491 - 2.93568i) q^{11} +(-0.912547 + 1.95696i) q^{13} +(0.0232950 + 0.132112i) q^{14} +(1.24794 + 0.454214i) q^{16} +(0.604786 - 6.91273i) q^{17} +(-2.43830 + 3.61313i) q^{19} +(-2.47036 + 2.31989i) q^{20} +(-0.997118 - 2.13833i) q^{22} +(-4.28034 + 2.99713i) q^{23} +(-1.41184 - 4.79653i) q^{25} +(-0.751446 + 1.30154i) q^{26} +(-0.0254589 - 0.290997i) q^{28} +(-5.09429 - 4.27462i) q^{29} +(-1.89191 - 1.09230i) q^{31} +(5.27301 + 2.45884i) q^{32} +(0.838680 - 4.75639i) q^{34} +(0.400160 + 0.160046i) q^{35} +(-5.09701 - 5.09701i) q^{37} +(-1.90982 + 2.35732i) q^{38} +(-4.29971 + 3.38363i) q^{40} +(2.93503 - 8.06394i) q^{41} +(0.670512 - 0.957590i) q^{43} +(1.75712 + 4.82765i) q^{44} +(-3.14967 + 1.81846i) q^{46} +(-6.07749 + 0.531712i) q^{47} +(6.03001 - 3.48143i) q^{49} +(-0.687959 - 3.41142i) q^{50} +(1.87703 - 2.68067i) q^{52} +(6.81158 + 9.72794i) q^{53} +(-7.52658 - 0.897386i) q^{55} -0.471614i q^{56} +(-3.27292 - 3.27292i) q^{58} +(4.80729 - 4.03379i) q^{59} +(-1.65436 + 9.38236i) q^{61} +(-1.24553 - 0.872132i) q^{62} +(1.20677 + 0.696726i) q^{64} +(2.28166 + 4.25514i) q^{65} +(-0.768076 - 8.77915i) q^{67} +(-2.72191 + 10.1583i) q^{68} +(0.267750 + 0.135246i) q^{70} +(-2.15751 + 0.380428i) q^{71} +(-3.66082 - 7.85066i) q^{73} +(-3.22492 - 3.84331i) q^{74} +(4.59012 - 4.75102i) q^{76} +(0.461992 - 0.461992i) q^{77} +(7.22404 + 2.62934i) q^{79} +(2.48481 - 1.62606i) q^{80} +(2.52424 - 5.41325i) q^{82} +(-2.59137 + 0.694355i) q^{83} +(-11.5672 - 10.3420i) q^{85} +(0.523002 - 0.623290i) q^{86} +(2.14679 + 8.01192i) q^{88} +(-0.466220 + 0.169690i) q^{89} +(-0.409855 - 0.0722684i) q^{91} +(7.17732 - 3.34684i) q^{92} -4.24620 q^{94} +(3.20340 + 9.20534i) q^{95} +(2.57139 + 0.224967i) q^{97} +(4.39221 - 2.04812i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{7} - 36 q^{16} - 120 q^{20} + 24 q^{22} - 24 q^{23} - 24 q^{25} + 24 q^{26} - 72 q^{28} + 12 q^{32} + 132 q^{38} - 132 q^{40} + 72 q^{41} - 108 q^{43} - 24 q^{47} - 36 q^{53} - 144 q^{58}+ \cdots - 192 q^{98}+O(q^{100}) $ 240 * q - 12 * q^7 - 36 * q^16 - 120 * q^20 + 24 * q^22 - 24 * q^23 - 24 * q^25 + 24 * q^26 - 72 * q^28 + 12 * q^32 + 132 * q^38 - 132 * q^40 + 72 * q^41 - 108 * q^43 - 24 * q^47 - 36 * q^53 - 144 * q^58 + 24 * q^61 + 168 * q^62 - 144 * q^67 + 48 * q^68 - 48 * q^70 - 36 * q^73 - 48 * q^76 + 216 * q^77 - 24 * q^80 + 144 * q^82 + 12 * q^83 + 72 * q^85 - 96 * q^86 + 360 * q^88 + 72 * q^91 + 48 * q^92 - 24 * q^95 + 96 * q^97 - 192 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	0.693370	+	0.0606620i	0.490287	+	0.0428945i	0.329619	−	0.944114i	$-0.393080\pi$
$2$	0.693370	+	0.0606620i	0.490287	+	0.0428945i	0.160668	+	0.987009i	$0.448635\pi$
$3$		0			0
$3$		0			0
$4$	−1.49253	−	0.263174i	−0.746267	−	0.131587i
$5$	1.33943	−	1.79051i	0.599013	−	0.800740i
$5$	1.33943	−	1.79051i	0.599013	−	0.800740i
$6$		0			0
$7$	0.0498847	+	0.186172i	0.0188547	+	0.0703665i	0.974712	−	0.223464i	$-0.0717365\pi$
$7$	0.0498847	+	0.186172i	0.0188547	+	0.0703665i	−0.955858	+	0.293831i	$0.905070\pi$
$8$	−2.36352	−	0.633303i	−0.835630	−	0.223906i
$9$		0			0
$10$	1.03734	−	1.16023i	0.328035	−	0.366897i
$11$	−1.69491	−	2.93568i	−0.511036	−	0.885140i	−0.999918	−	0.0127903i	$-0.995929\pi$
$11$	−1.69491	−	2.93568i	−0.511036	−	0.885140i	0.488882	−	0.872350i	$-0.337405\pi$
$12$		0			0
$13$	−0.912547	+	1.95696i	−0.253095	+	0.542764i	−0.991270	−	0.131845i	$-0.957910\pi$
$13$	−0.912547	+	1.95696i	−0.253095	+	0.542764i	0.738175	+	0.674609i	$0.235688\pi$
$14$	0.0232950	+	0.132112i	0.00622585	+	0.0353085i
$15$		0			0
$16$	1.24794	+	0.454214i	0.311986	+	0.113554i
$17$	0.604786	−	6.91273i	0.146682	−	1.67658i	−0.464869	−	0.885379i	$-0.653899\pi$
$17$	0.604786	−	6.91273i	0.146682	−	1.67658i	0.611551	−	0.791205i	$-0.290546\pi$
$18$		0			0
$19$	−2.43830	+	3.61313i	−0.559384	+	0.828909i
$19$	−2.43830	+	3.61313i	−0.559384	+	0.828909i
$20$	−2.47036	+	2.31989i	−0.552390	+	0.518743i
$21$		0			0
$22$	−0.997118	−	2.13833i	−0.212586	−	0.455893i
$23$	−4.28034	+	2.99713i	−0.892513	+	0.624945i	−0.927246	−	0.374452i	$-0.877831\pi$
$23$	−4.28034	+	2.99713i	−0.892513	+	0.624945i	0.0347330	+	0.999397i	$0.488942\pi$
$24$		0			0
$25$	−1.41184	−	4.79653i	−0.282368	−	0.959306i
$26$	−0.751446	+	1.30154i	−0.147371	+	0.255253i
$27$		0			0
$28$	−0.0254589	−	0.290997i	−0.00481129	−	0.0549932i
$29$	−5.09429	−	4.27462i	−0.945986	−	0.793776i	0.0326312	−	0.999467i	$-0.489611\pi$
$29$	−5.09429	−	4.27462i	−0.945986	−	0.793776i	−0.978617	+	0.205691i	$0.934056\pi$
$30$		0			0
$31$	−1.89191	−	1.09230i	−0.339798	−	0.196182i	0.320385	−	0.947287i	$-0.396188\pi$
$31$	−1.89191	−	1.09230i	−0.339798	−	0.196182i	−0.660182	+	0.751105i	$0.729521\pi$
$32$	5.27301	+	2.45884i	0.932145	+	0.434666i
$33$		0			0
$34$	0.838680	−	4.75639i	0.143833	−	0.815715i
$35$	0.400160	+	0.160046i	0.0676395	+	0.0270528i
$36$		0			0
$37$	−5.09701	−	5.09701i	−0.837943	−	0.837943i	0.150645	−	0.988588i	$-0.451865\pi$
$37$	−5.09701	−	5.09701i	−0.837943	−	0.837943i	−0.988588	+	0.150645i	$0.951865\pi$
$38$	−1.90982	+	2.35732i	−0.309814	+	0.382408i
$39$		0			0
$40$	−4.29971	+	3.38363i	−0.679843	+	0.534999i
$41$	2.93503	−	8.06394i	0.458375	−	1.25938i	−0.468319	−	0.883560i	$-0.655140\pi$
$41$	2.93503	−	8.06394i	0.458375	−	1.25938i	0.926694	−	0.375816i	$-0.122638\pi$
$42$		0			0
$43$	0.670512	−	0.957590i	0.102252	−	0.146031i	−0.764765	−	0.644309i	$-0.777145\pi$
$43$	0.670512	−	0.957590i	0.102252	−	0.146031i	0.867017	+	0.498278i	$0.166034\pi$
$44$	1.75712	+	4.82765i	0.264896	+	0.727796i
$45$		0			0
$46$	−3.14967	+	1.81846i	−0.464394	+	0.268118i
$47$	−6.07749	+	0.531712i	−0.886493	+	0.0775581i	−0.521300	−	0.853374i	$-0.674553\pi$
$47$	−6.07749	+	0.531712i	−0.886493	+	0.0775581i	−0.365193	+	0.930932i	$0.618997\pi$
$48$		0			0
$49$	6.03001	−	3.48143i	0.861429	−	0.497347i
$50$	−0.687959	−	3.41142i	−0.0972921	−	0.482447i
$51$		0			0
$52$	1.87703	−	2.68067i	0.260297	−	0.371743i
$53$	6.81158	+	9.72794i	0.935642	+	1.33624i	0.941771	+	0.336254i	$0.109160\pi$
$53$	6.81158	+	9.72794i	0.935642	+	1.33624i	−0.00612942	+	0.999981i	$0.501951\pi$
$54$		0			0
$55$	−7.52658	−	0.897386i	−1.01488	−	0.121004i
$56$		−	0.471614i		−	0.0630220i
$57$		0			0
$58$	−3.27292	−	3.27292i	−0.429755	−	0.429755i
$59$	4.80729	−	4.03379i	0.625856	−	0.525155i	−0.273782	−	0.961792i	$-0.588275\pi$
$59$	4.80729	−	4.03379i	0.625856	−	0.525155i	0.899638	+	0.436636i	$0.143830\pi$
$60$		0			0
$61$	−1.65436	+	9.38236i	−0.211820	+	1.20129i	0.674521	+	0.738255i	$0.264350\pi$
$61$	−1.65436	+	9.38236i	−0.211820	+	1.20129i	−0.886341	+	0.463033i	$0.846761\pi$
$62$	−1.24553	−	0.872132i	−0.158183	−	0.110761i
$63$		0			0
$64$	1.20677	+	0.696726i	0.150846	+	0.0870908i
$65$	2.28166	+	4.25514i	0.283005	+	0.527785i
$66$		0			0
$67$	−0.768076	−	8.77915i	−0.0938355	−	1.07254i	−0.886451	−	0.462822i	$-0.846837\pi$
$67$	−0.768076	−	8.77915i	−0.0938355	−	1.07254i	0.792616	−	0.609722i	$-0.208719\pi$
$68$	−2.72191	+	10.1583i	−0.330081	+	1.23188i
$69$		0			0
$70$	0.267750	+	0.135246i	0.0320023	+	0.0161650i
$71$	−2.15751	+	0.380428i	−0.256050	+	0.0451485i	−0.300199	−	0.953876i	$-0.597053\pi$
$71$	−2.15751	+	0.380428i	−0.256050	+	0.0451485i	0.0441498	+	0.999025i	$0.485942\pi$
$72$		0			0
$73$	−3.66082	−	7.85066i	−0.428467	−	0.918850i	−0.995465	−	0.0951309i	$-0.969673\pi$
$73$	−3.66082	−	7.85066i	−0.428467	−	0.918850i	0.566998	−	0.823719i	$-0.308105\pi$
$74$	−3.22492	−	3.84331i	−0.374889	−	0.446775i
$75$		0			0
$76$	4.59012	−	4.75102i	0.526523	−	0.544980i
$77$	0.461992	−	0.461992i	0.0526488	−	0.0526488i
$78$		0			0
$79$	7.22404	+	2.62934i	0.812768	+	0.295823i	0.714767	−	0.699363i	$-0.246533\pi$
$79$	7.22404	+	2.62934i	0.812768	+	0.295823i	0.0980014	+	0.995186i	$0.468755\pi$
$80$	2.48481	−	1.62606i	0.277810	−	0.181799i
$81$		0			0
$82$	2.52424	−	5.41325i	0.278756	−	0.597793i
$83$	−2.59137	+	0.694355i	−0.284440	+	0.0762154i	−0.398218	−	0.917291i	$-0.630371\pi$
$83$	−2.59137	+	0.694355i	−0.284440	+	0.0762154i	0.113778	+	0.993506i	$0.463705\pi$
$84$		0			0
$85$	−11.5672	−	10.3420i	−1.25464	−	1.12175i
$86$	0.523002	−	0.623290i	0.0563968	−	0.0672111i
$87$		0			0
$88$	2.14679	+	8.01192i	0.228848	+	0.854073i
$89$	−0.466220	+	0.169690i	−0.0494192	+	0.0179871i	−0.366611	−	0.930374i	$-0.619482\pi$
$89$	−0.466220	+	0.169690i	−0.0494192	+	0.0179871i	0.317192	+	0.948361i	$0.397260\pi$
$90$		0			0
$91$	−0.409855	−	0.0722684i	−0.0429644	−	0.00757579i
$92$	7.17732	−	3.34684i	0.748288	−	0.348932i
$93$		0			0
$94$	−4.24620			−0.437963
$95$	3.20340	+	9.20534i	0.328662	+	0.944448i
$96$		0			0
$97$	2.57139	+	0.224967i	0.261085	+	0.0228420i	0.216947	−	0.976183i	$-0.430390\pi$
$97$	2.57139	+	0.224967i	0.261085	+	0.0228420i	0.0441382	+	0.999025i	$0.485946\pi$
$98$	4.39221	−	2.04812i	0.443681	−	0.206892i
$99$		0			0
$100$	0.844894	+	7.53054i	0.0844894	+	0.753054i
$101$	−12.7562	+	4.64289i	−1.26929	+	0.461985i	−0.886877	−	0.462005i	$-0.847130\pi$
$101$	−12.7562	+	4.64289i	−1.26929	+	0.461985i	−0.382416	+	0.923990i	$0.624908\pi$
$102$		0			0
$103$	11.4209	+	3.06022i	1.12533	+	0.301532i	0.773040	−	0.634357i	$-0.218735\pi$
$103$	11.4209	+	3.06022i	1.12533	+	0.301532i	0.352294	+	0.935890i	$0.385402\pi$
$104$	3.39617	−	4.04740i	0.333022	−	0.396880i
$105$		0			0
$106$	4.13283	+	7.15826i	0.401415	+	0.695272i
$107$	9.71954	−	2.60434i	0.939624	−	0.251771i	0.243670	−	0.969858i	$-0.421649\pi$
$107$	9.71954	−	2.60434i	0.939624	−	0.251771i	0.695954	+	0.718087i	$0.254982\pi$
$108$		0			0
$109$	−1.00018	−	5.67232i	−0.0958002	−	0.543310i	−0.994499	−	0.104744i	$-0.966598\pi$
$109$	−1.00018	−	5.67232i	−0.0958002	−	0.543310i	0.898699	−	0.438566i	$-0.144513\pi$
$110$	−5.16426	−	1.07880i	−0.492393	−	0.102859i
$111$		0			0
$112$	−0.0223088	+	0.254991i	−0.00210799	+	0.0240944i
$113$	2.77599	−	2.77599i	0.261143	−	0.261143i	−0.564375	−	0.825518i	$-0.690883\pi$
$113$	2.77599	−	2.77599i	0.261143	−	0.261143i	0.825518	+	0.564375i	$0.190883\pi$
$114$		0			0
$115$	−0.366851	+	11.6784i	−0.0342090	+	1.08902i
$116$	6.47843	+	7.72069i	0.601507	+	0.716848i
$117$		0			0
$118$	3.57793	−	2.50529i	0.329375	−	0.230631i
$119$	1.31713	−	0.232245i	0.120741	−	0.0212899i
$120$		0			0
$121$	−0.245467	+	0.425161i	−0.0223151	+	0.0386510i
$122$	−1.71624	+	6.40509i	−0.155381	+	0.579890i
$123$		0			0
$124$	2.53628	+	2.12819i	0.227765	+	0.191117i
$125$	−10.4793	−	3.89673i	−0.937296	−	0.348534i
$126$		0			0
$127$	17.0692	+	7.95952i	1.51465	+	0.706293i	0.989475	−	0.144701i	$-0.0462222\pi$
$127$	17.0692	+	7.95952i	1.51465	+	0.706293i	0.525175	+	0.850994i	$0.324000\pi$
$128$	−8.73738	−	6.11798i	−0.772283	−	0.540758i
$129$		0			0
$130$	1.32391	+	3.08880i	0.116115	+	0.270905i
$131$	10.7812	−	9.04652i	0.941959	−	0.790398i	−0.0359658	−	0.999353i	$-0.511451\pi$
$131$	10.7812	−	9.04652i	0.941959	−	0.790398i	0.977925	+	0.208955i	$0.0670063\pi$
$132$		0			0
$133$	−0.794299	−	0.273703i	−0.0688744	−	0.0237331i
$134$		−	6.13379i		−	0.529879i
$135$		0			0
$136$	−5.80727	+	15.9554i	−0.497970	+	1.36816i
$137$	4.11959	+	5.88338i	0.351960	+	0.502651i	0.955625	−	0.294587i	$-0.0951822\pi$
$137$	4.11959	+	5.88338i	0.351960	+	0.502651i	−0.603665	+	0.797238i	$0.706293\pi$
$138$		0			0
$139$	4.96460	+	13.6401i	0.421092	+	1.15694i	0.951082	+	0.308937i	$0.0999733\pi$
$139$	4.96460	+	13.6401i	0.421092	+	1.15694i	−0.529990	+	0.848004i	$0.677804\pi$
$140$	−0.555133	−	0.344186i	−0.0469173	−	0.0290891i
$141$		0			0
$142$	−1.51903	+	0.132898i	−0.127474	+	0.0111526i
$143$	7.29170	−	0.637941i	0.609762	−	0.0533473i
$144$		0			0
$145$	−14.4772	+	3.39580i	−1.20227	+	0.282006i
$146$	−2.06207	−	5.66548i	−0.170658	−	0.468879i
$147$		0			0
$148$	6.26606	+	8.94885i	0.515067	+	0.735591i
$149$	2.75049	−	7.55690i	0.225329	−	0.619086i	−0.774582	−	0.632474i	$-0.782040\pi$
$149$	2.75049	−	7.55690i	0.225329	−	0.619086i	0.999910	+	0.0133883i	$0.00426177\pi$
$150$		0			0
$151$		−	13.6744i		−	1.11281i	−0.830913	−	0.556403i	$-0.812181\pi$
$151$		−	13.6744i		−	1.11281i	0.830913	−	0.556403i	$-0.187819\pi$
$152$	8.05116	−	6.99552i	0.653035	−	0.567411i
$153$		0			0
$154$	0.348356	−	0.292306i	0.0280714	−	0.0235547i
$155$	−4.48986	+	1.92443i	−0.360634	+	0.154574i
$156$		0			0
$157$	12.3093	+	8.61903i	0.982386	+	0.687874i	0.950211	−	0.311608i	$-0.100868\pi$
$157$	12.3093	+	8.61903i	0.982386	+	0.687874i	0.0321750	+	0.999482i	$0.489757\pi$
$158$	4.84943	+	2.26133i	0.385800	+	0.179902i
$159$		0			0
$160$	11.4654	−	6.14791i	0.906421	−	0.486035i
$161$	−0.771506	−	0.647371i	−0.0608032	−	0.0510200i
$162$		0			0
$163$	−3.70896	+	13.8420i	−0.290508	+	1.08419i	0.654211	+	0.756312i	$0.273001\pi$
$163$	−3.70896	+	13.8420i	−0.290508	+	1.08419i	−0.944720	+	0.327880i	$0.893666\pi$
$164$	−6.50286	+	11.2633i	−0.507788	+	0.879514i
$165$		0			0
$166$	−1.83890	+	0.324247i	−0.142726	+	0.0251665i
$167$	−6.23499	+	4.36579i	−0.482478	+	0.337835i	−0.789378	−	0.613907i	$-0.789597\pi$
$167$	−6.23499	+	4.36579i	−0.482478	+	0.337835i	0.306900	+	0.951742i	$0.400708\pi$
$168$		0			0
$169$	5.35928	+	6.38694i	0.412252	+	0.491303i
$170$	−7.39300	−	7.87253i	−0.567018	−	0.603796i
$171$		0			0
$172$	−1.25277	+	1.25277i	−0.0955232	+	0.0955232i
$173$	−1.27326	+	14.5535i	−0.0968045	+	1.10648i	0.780047	+	0.625720i	$0.215195\pi$
$173$	−1.27326	+	14.5535i	−0.0968045	+	1.10648i	−0.876852	+	0.480760i	$0.840361\pi$
$174$		0			0
$175$	0.822553	−	0.502119i	0.0621791	−	0.0379566i
$176$	−0.781730	−	4.43341i	−0.0589251	−	0.334181i
$177$		0			0
$178$	−0.333556	+	0.0893761i	−0.0250011	+	0.00669903i
$179$	1.76075	+	3.04972i	0.131605	+	0.227946i	0.924295	−	0.381678i	$-0.124654\pi$
$179$	1.76075	+	3.04972i	0.131605	+	0.227946i	−0.792690	+	0.609624i	$0.791320\pi$
$180$		0			0
$181$	12.5411	−	14.9460i	0.932176	−	1.11092i	−0.0614406	−	0.998111i	$-0.519569\pi$
$181$	12.5411	−	14.9460i	0.932176	−	1.11092i	0.993616	−	0.112813i	$-0.0359861\pi$
$182$	−0.279797	−	0.0749713i	−0.0207399	−	0.00555724i
$183$		0			0
$184$	12.0148	−	4.37301i	0.885740	−	0.322383i
$185$	−15.9533	+	2.29913i	−1.17291	+	0.169036i
$186$		0			0
$187$	−21.3186	+	9.94103i	−1.55897	+	0.726960i
$188$	9.21079	+	0.805840i	0.671766	+	0.0587719i
$189$		0			0
$190$	1.66273	+	6.57703i	0.120627	+	0.477148i
$191$	−20.1484			−1.45789			−0.728943	−	0.684575i	$-0.759988\pi$
$191$	−20.1484			−1.45789			−0.728943	+	0.684575i	$0.759988\pi$
$192$		0			0
$193$	5.50289	−	2.56604i	0.396107	−	0.184708i	−0.214351	−	0.976757i	$-0.568764\pi$
$193$	5.50289	−	2.56604i	0.396107	−	0.184708i	0.610457	+	0.792049i	$0.290986\pi$
$194$	1.76928	+	0.311971i	0.127027	+	0.0223982i
$195$		0			0
$196$	−9.91621	+	3.60920i	−0.708301	+	0.257800i
$197$	4.33432	+	16.1759i	0.308808	+	1.15249i	0.929618	+	0.368525i	$0.120137\pi$
$197$	4.33432	+	16.1759i	0.308808	+	1.15249i	−0.620810	+	0.783961i	$0.713196\pi$
$198$		0			0
$199$	−6.31500	+	7.52592i	−0.447658	+	0.533498i	−0.941930	−	0.335809i	$-0.890990\pi$
$199$	−6.31500	+	7.52592i	−0.447658	+	0.533498i	0.494272	+	0.869307i	$0.335435\pi$
$200$	0.299248	+	12.2308i	0.0211600	+	0.864849i
$201$		0			0
$202$	−9.12644	+	2.44542i	−0.642134	+	0.172059i
$203$	0.541688	−	1.16165i	0.0380191	−	0.0815321i
$204$		0			0
$205$	−10.5073	−	16.0563i	−0.733859	−	1.12142i
$206$	7.73326	+	2.81468i	0.538802	+	0.196108i
$207$		0			0
$208$	−2.02769	+	2.02769i	−0.140595	+	0.140595i
$209$	14.7397	+	1.03411i	1.01957	+	0.0715307i
$210$		0			0
$211$	1.37685	+	1.64086i	0.0947859	+	0.112961i	0.811352	−	0.584557i	$-0.198732\pi$
$211$	1.37685	+	1.64086i	0.0947859	+	0.112961i	−0.716566	+	0.697519i	$0.754287\pi$
$212$	−7.60637	−	16.3119i	−0.522407	−	1.12031i
$213$		0			0
$214$	6.89722	−	1.21617i	0.471485	−	0.0831354i
$215$	−0.816467	−	2.48319i	−0.0556826	−	0.169352i
$216$		0			0
$217$	0.108978	−	0.406711i	0.00739790	−	0.0276093i
$218$	−0.349403	−	3.99369i	−0.0236645	−	0.270487i
$219$		0			0
$220$	10.9975	+	3.32018i	0.741451	+	0.223846i
$221$	12.9761	+	7.49173i	0.872865	+	0.503949i
$222$		0			0
$223$	−14.7242	−	10.3100i	−0.986008	−	0.690410i	−0.0349391	−	0.999389i	$-0.511124\pi$
$223$	−14.7242	−	10.3100i	−0.986008	−	0.690410i	−0.951069	+	0.308979i	$0.900013\pi$
$224$	−0.194726	+	1.10435i	−0.0130107	+	0.0737873i
$225$		0			0
$226$	2.09318	−	1.75639i	0.139237	−	0.116833i
$227$	4.14462	+	4.14462i	0.275088	+	0.275088i	0.831144	−	0.556057i	$-0.187686\pi$
$227$	4.14462	+	4.14462i	0.275088	+	0.275088i	−0.556057	+	0.831144i	$0.687686\pi$
$228$		0			0
$229$		−	22.4455i		−	1.48324i	−0.670821	−	0.741619i	$-0.734058\pi$
$229$		−	22.4455i		−	1.48324i	0.670821	−	0.741619i	$-0.265942\pi$
$230$	−0.962801	+	8.07523i	−0.0634852	+	0.532465i
$231$		0			0
$232$	9.33332	+	13.3294i	0.612762	+	0.875115i
$233$	2.04942	−	2.92687i	0.134262	−	0.191746i	−0.746391	−	0.665507i	$-0.768215\pi$
$233$	2.04942	−	2.92687i	0.134262	−	0.191746i	0.880653	+	0.473762i	$0.157104\pi$
$234$		0			0
$235$	−7.18836	+	11.5940i	−0.468917	+	0.756309i
$236$	−8.23663	+	4.75542i	−0.536159	+	0.309551i
$237$		0			0
$238$	0.927346	−	0.0811323i	0.0601109	−	0.00525903i
$239$	8.64517	−	4.99129i	0.559210	−	0.322860i	−0.193619	−	0.981077i	$-0.562022\pi$
$239$	8.64517	−	4.99129i	0.559210	−	0.322860i	0.752828	+	0.658217i	$0.228689\pi$
$240$		0			0
$241$	−10.2338	−	28.1170i	−0.659215	−	1.81118i	−0.580467	−	0.814284i	$-0.697130\pi$
$241$	−10.2338	−	28.1170i	−0.659215	−	1.81118i	−0.0787480	−	0.996895i	$-0.525092\pi$
$242$	−0.195990	+	0.279903i	−0.0125987	+	0.0179929i
$243$		0			0
$244$	4.93839	−	13.5681i	0.316148	−	0.868609i
$245$	1.84327	−	15.4599i	0.117762	−	0.987697i
$246$		0			0
$247$	−4.84570	−	8.06880i	−0.308325	−	0.513406i
$248$	3.77981	+	3.77981i	0.240018	+	0.240018i
$249$		0			0
$250$	−7.02964	−	3.33757i	−0.444594	−	0.211086i
$251$	4.56260	−	25.8758i	0.287989	−	1.63327i	−0.406420	−	0.913686i	$-0.633223\pi$
$251$	4.56260	−	25.8758i	0.287989	−	1.63327i	0.694409	−	0.719580i	$-0.255666\pi$
$252$		0			0
$253$	16.0534	+	7.48583i	1.00927	+	0.470630i
$254$	11.3525	+	6.55434i	0.712316	+	0.411256i
$255$		0			0
$256$	−7.82200	−	6.56344i	−0.488875	−	0.410215i
$257$	0.137726	+	1.57421i	0.00859109	+	0.0981966i	0.999280	−	0.0379515i	$-0.0120833\pi$
$257$	0.137726	+	1.57421i	0.00859109	+	0.0981966i	−0.990688	+	0.136148i	$0.956528\pi$
$258$		0			0
$259$	0.694659	−	1.20318i	0.0431640	−	0.0747623i
$260$	−2.28561	−	6.95142i	−0.141748	−	0.431109i
$261$		0			0
$262$	8.02415	−	5.61857i	0.495734	−	0.347116i
$263$	−2.57794	−	5.52841i	−0.158963	−	0.340896i	0.810654	−	0.585525i	$-0.199112\pi$
$263$	−2.57794	−	5.52841i	−0.158963	−	0.340896i	−0.969617	+	0.244629i	$0.921334\pi$
$264$		0			0
$265$	26.5416	+	0.833741i	1.63044	+	0.0512163i
$266$	−0.534139	−	0.237961i	−0.0327502	−	0.0145904i
$267$		0			0
$268$	−1.16406	+	13.3053i	−0.0711066	+	0.812752i
$269$	−15.1223	−	5.50406i	−0.922022	−	0.335588i	−0.162979	−	0.986630i	$-0.552110\pi$
$269$	−15.1223	−	5.50406i	−0.922022	−	0.335588i	−0.759042	+	0.651041i	$0.774333\pi$
$270$		0			0
$271$	−1.31423	−	7.45337i	−0.0798338	−	0.452760i	−0.998352	−	0.0573820i	$-0.981725\pi$
$271$	−1.31423	−	7.45337i	−0.0798338	−	0.452760i	0.918518	−	0.395378i	$-0.129386\pi$
$272$	3.89460	−	8.35200i	0.236145	−	0.506414i
$273$		0			0
$274$	2.49950	+	4.32926i	0.151000	+	0.261540i
$275$	−11.6881	+	12.2744i	−0.704820	+	0.740175i
$276$		0			0
$277$	13.1779	+	3.53100i	0.791782	+	0.212157i	0.631973	−	0.774990i	$-0.282245\pi$
$277$	13.1779	+	3.53100i	0.791782	+	0.212157i	0.159809	+	0.987148i	$0.448912\pi$
$278$	2.61487	+	9.75882i	0.156829	+	0.585295i
$279$		0			0
$280$	−0.844428	−	0.631695i	−0.0504642	−	0.0377510i
$281$	−26.3845	−	4.65230i	−1.57397	−	0.277533i	−0.682593	−	0.730799i	$-0.739148\pi$
$281$	−26.3845	−	4.65230i	−1.57397	−	0.277533i	−0.891376	+	0.453265i	$0.850259\pi$
$282$		0			0
$283$	−7.52421	−	0.658283i	−0.447268	−	0.0391309i	−0.138703	−	0.990334i	$-0.544293\pi$
$283$	−7.52421	−	0.658283i	−0.447268	−	0.0391309i	−0.308565	+	0.951203i	$0.599849\pi$
$284$	3.32028			0.197022
$285$		0			0
$286$	5.09454			0.301247
$287$	1.64770	+	0.144155i	0.0972604	+	0.00850919i
$288$		0			0
$289$	−30.6784	−	5.40943i	−1.80461	−	0.318202i
$290$	−10.2440	+	1.47633i	−0.601551	+	0.0866932i
$291$		0			0
$292$	3.39781	+	12.6808i	0.198842	+	0.742088i
$293$	11.7580	+	3.15055i	0.686911	+	0.184057i	0.585361	−	0.810773i	$-0.300953\pi$
$293$	11.7580	+	3.15055i	0.686911	+	0.184057i	0.101551	+	0.994830i	$0.467620\pi$
$294$		0			0
$295$	−0.783499	−	14.0105i	−0.0456171	−	0.815722i
$296$	8.81892	+	15.2748i	0.512589	+	0.887831i
$297$		0			0
$298$	2.36552	−	5.07288i	0.137031	−	0.293864i
$299$	−1.95926	−	11.1115i	−0.113307	−	0.642594i
$300$		0			0
$301$	0.211725	+	0.0770617i	0.0122036	+	0.00444176i
$302$	0.829515	−	9.48140i	0.0477332	−	0.545593i
$303$		0			0
$304$	−4.68399	+	3.40147i	−0.268645	+	0.195088i
$305$	14.5833	+	15.5292i	0.835037	+	0.889199i
$306$		0			0
$307$	12.1779	+	26.1155i	0.695027	+	1.49049i	0.863269	+	0.504744i	$0.168413\pi$
$307$	12.1779	+	26.1155i	0.695027	+	1.49049i	−0.168242	+	0.985746i	$0.553809\pi$
$308$	−0.811122	+	0.567954i	−0.0462180	+	0.0323622i
$309$		0			0
$310$	−3.22987	+	1.06198i	−0.183444	+	0.0603162i
$311$	−9.26325	+	16.0444i	−0.525271	+	0.909795i	0.474296	+	0.880365i	$0.342703\pi$
$311$	−9.26325	+	16.0444i	−0.525271	+	0.909795i	−0.999567	+	0.0294301i	$0.990631\pi$
$312$		0			0
$313$	−0.277135	−	3.16767i	−0.0156646	−	0.179047i	−0.999996	−	0.00272050i	$-0.999134\pi$
$313$	−0.277135	−	3.16767i	−0.0156646	−	0.179047i	0.984332	−	0.176327i	$-0.0564215\pi$
$314$	8.01202	+	6.72288i	0.452144	+	0.379394i
$315$		0			0
$316$	−10.0902	−	5.82555i	−0.567616	−	0.327713i
$317$	−4.76570	−	2.22228i	−0.267669	−	0.124816i	0.284151	−	0.958780i	$-0.408288\pi$
$317$	−4.76570	−	2.22228i	−0.267669	−	0.124816i	−0.551819	+	0.833964i	$0.686066\pi$
$318$		0			0
$319$	−3.91451	+	22.2003i	−0.219171	+	1.24298i
$320$	2.86388	−	1.22751i	0.160096	−	0.0686196i
$321$		0			0
$322$	−0.495668	−	0.495668i	−0.0276225	−	0.0276225i
$323$	23.5020	+	19.0405i	1.30768	+	1.05944i
$324$		0			0
$325$	10.6750	+	1.61414i	0.592142	+	0.0895366i
$326$	−3.41137	+	9.37265i	−0.188938	+	0.519103i
$327$		0			0
$328$	−12.0439	+	17.2005i	−0.665014	+	0.949739i
$329$	−0.402164	−	1.10494i	−0.0221720	−	0.0609171i
$330$		0			0
$331$	10.1471	−	5.85845i	0.557737	−	0.322010i	−0.194500	−	0.980903i	$-0.562308\pi$
$331$	10.1471	−	5.85845i	0.557737	−	0.322010i	0.752237	+	0.658893i	$0.228975\pi$
$332$	4.05044	−	0.354368i	0.222297	−	0.0194485i
$333$		0			0
$334$	−4.58799	+	2.64888i	−0.251044	+	0.144940i
$335$	−16.7479	−	10.3838i	−0.915037	−	0.567330i
$336$		0			0
$337$	7.24603	−	10.3484i	0.394716	−	0.563713i	−0.571776	−	0.820410i	$-0.693745\pi$
$337$	7.24603	−	10.3484i	0.394716	−	0.563713i	0.966492	+	0.256697i	$0.0826342\pi$
$338$	3.32852	+	4.75362i	0.181047	+	0.258563i
$339$		0			0
$340$	14.5427	+	18.4800i	0.788691	+	1.00222i
$341$			7.40539i			0.401024i
$342$		0			0
$343$	1.90296	+	1.90296i	0.102750	+	0.102750i
$344$	−2.19121	+	1.83864i	−0.118142	+	0.0991331i
$345$		0			0
$346$	−1.76569	+	10.0137i	−0.0949239	+	0.538340i
$347$	15.5150	+	10.8637i	0.832890	+	0.583196i	0.910369	−	0.413798i	$-0.135798\pi$
$347$	15.5150	+	10.8637i	0.832890	+	0.583196i	−0.0774785	+	0.996994i	$0.524687\pi$
$348$		0			0
$349$	−28.7967	−	16.6258i	−1.54145	−	0.889959i	−0.998747	−	0.0500357i	$-0.984066\pi$
$349$	−28.7967	−	16.6258i	−1.54145	−	0.889959i	−0.542706	−	0.839923i	$-0.682600\pi$
$350$	0.600793	−	0.298256i	0.0321137	−	0.0159425i
$351$		0			0
$352$	−1.71892	−	19.6474i	−0.0916189	−	1.04721i
$353$	−0.0162728	+	0.0607309i	−0.000866114	+	0.00323238i	−0.966358	−	0.257202i	$-0.917199\pi$
$353$	−0.0162728	+	0.0607309i	−0.000866114	+	0.00323238i	0.965491	+	0.260435i	$0.0838659\pi$
$354$		0			0
$355$	−2.20869	+	4.37260i	−0.117225	+	0.232074i
$356$	0.740506	−	0.130571i	0.0392468	−	0.00692026i
$357$		0			0
$358$	1.03585	+	2.22139i	0.0547465	+	0.117404i
$359$	−16.1846	−	19.2880i	−0.854190	−	1.01798i	−0.999591	−	0.0286106i	$-0.990892\pi$
$359$	−16.1846	−	19.2880i	−0.854190	−	1.01798i	0.145401	−	0.989373i	$-0.453553\pi$
$360$		0			0
$361$	−7.10942	−	17.6198i	−0.374180	−	0.927356i
$362$	9.60230	−	9.60230i	0.504686	−	0.504686i
$363$		0			0
$364$	0.592702	+	0.215726i	0.0310661	+	0.0113071i
$365$	−18.9601	−	3.96070i	−0.992417	−	0.207313i
$366$		0			0
$367$	5.40005	−	11.5804i	0.281880	−	0.604494i	−0.713484	−	0.700671i	$-0.752884\pi$
$367$	5.40005	−	11.5804i	0.281880	−	0.604494i	0.995364	+	0.0961775i	$0.0306617\pi$
$368$	−6.70297	+	1.79605i	−0.349416	+	0.0936258i
$369$		0			0
$370$	−11.2010	+	0.626388i	−0.582314	+	0.0325644i
$371$	−1.47128	+	1.75340i	−0.0763850	+	0.0910322i
$372$		0			0
$373$	−0.429109	−	1.60146i	−0.0222184	−	0.0829203i	0.953926	−	0.300041i	$-0.0970003\pi$
$373$	−0.429109	−	1.60146i	−0.0222184	−	0.0829203i	−0.976145	+	0.217120i	$0.930334\pi$
$374$	−15.3847	+	5.59958i	−0.795525	+	0.289548i
$375$		0			0
$376$	14.7010	+	2.59218i	0.758146	+	0.133682i
$377$	13.0140	−	6.06855i	0.670257	−	0.312546i
$378$		0			0
$379$	16.9664			0.871503			0.435752	−	0.900067i	$-0.356483\pi$
$379$	16.9664			0.871503			0.435752	+	0.900067i	$0.356483\pi$
$380$	−2.35858	−	14.5823i	−0.120993	−	0.748058i
$381$		0			0
$382$	−13.9703	−	1.22224i	−0.714781	−	0.0625353i
$383$	13.1219	−	6.11883i	0.670496	−	0.312658i	−0.0573936	−	0.998352i	$-0.518279\pi$
$383$	13.1219	−	6.11883i	0.670496	−	0.312658i	0.727890	+	0.685694i	$0.240501\pi$
$384$		0			0
$385$	−0.208393	−	1.44601i	−0.0106207	−	0.0736953i
$386$	3.97120	−	1.44540i	0.202129	−	0.0735688i
$387$		0			0
$388$	−3.77868	−	1.01249i	−0.191833	−	0.0514016i
$389$	19.9850	−	23.8172i	1.01328	−	1.20758i	0.0351924	−	0.999381i	$-0.488796\pi$
$389$	19.9850	−	23.8172i	1.01328	−	1.20758i	0.978087	−	0.208198i	$-0.0667600\pi$
$390$		0			0
$391$	18.1297	+	31.4015i	0.916856	+	1.58804i
$392$	−16.4568	+	4.40959i	−0.831195	+	0.222718i
$393$		0			0
$394$	2.02403	+	11.4788i	0.101969	+	0.578295i
$395$	14.3840	−	9.41289i	0.723736	−	0.473614i
$396$		0			0
$397$	2.67575	−	30.5840i	0.134292	−	1.53497i	−0.567971	−	0.823049i	$-0.692271\pi$
$397$	2.67575	−	30.5840i	0.134292	−	1.53497i	0.702263	−	0.711918i	$-0.252173\pi$
$398$	−4.83517	+	4.83517i	−0.242365	+	0.242365i
$399$		0			0
$400$	0.416759	−	6.62708i	0.0208380	−	0.331354i
$401$	11.4635	+	13.6616i	0.572458	+	0.682229i	0.972134	−	0.234428i	$-0.0753217\pi$
$401$	11.4635	+	13.6616i	0.572458	+	0.682229i	−0.399676	+	0.916657i	$0.630877\pi$
$402$		0			0
$403$	3.86404	−	2.70563i	0.192482	−	0.134777i
$404$	20.2610	−	3.57256i	1.00802	−	0.177742i
$405$		0			0
$406$	0.446059	−	0.772596i	0.0221375	−	0.0383433i
$407$	−6.32418	+	23.6022i	−0.313478	+	1.16992i
$408$		0			0
$409$	−19.0657	−	15.9980i	−0.942738	−	0.791051i	0.0353220	−	0.999376i	$-0.488754\pi$
$409$	−19.0657	−	15.9980i	−0.942738	−	0.791051i	−0.978060	+	0.208325i	$0.933199\pi$
$410$	−6.31141	−	11.7704i	−0.311699	−	0.581296i
$411$		0			0
$412$	−16.2407	−	7.57316i	−0.800121	−	0.373103i
$413$	0.990791	+	0.693759i	0.0487536	+	0.0341377i
$414$		0			0
$415$	−2.22772	+	5.56991i	−0.109354	+	0.273416i
$416$	−9.62373	+	8.07527i	−0.471842	+	0.395923i
$417$		0			0
$418$	10.1573	+	1.61116i	0.496811	+	0.0788043i
$419$			1.33645i			0.0652901i	0.999467	+	0.0326450i	$0.0103931\pi$
$419$			1.33645i			0.0652901i	−0.999467	+	0.0326450i	$0.989607\pi$
$420$		0			0
$421$	−4.21707	+	11.5863i	−0.205527	+	0.564681i	−0.999037	−	0.0438762i	$-0.986029\pi$
$421$	−4.21707	+	11.5863i	−0.205527	+	0.564681i	0.793510	+	0.608558i	$0.208252\pi$
$422$	0.855125	+	1.22125i	0.0416268	+	0.0594493i
$423$		0			0
$424$	−9.93855	−	27.3059i	−0.482659	−	1.32609i
$425$	−34.0110	+	6.85879i	−1.64978	+	0.332700i
$426$		0			0
$427$	−1.82926	+	0.160040i	−0.0885243	+	0.00774487i
$428$	−15.1921	+	1.32914i	−0.734340	+	0.0642464i
$429$		0			0
$430$	−0.415479	−	1.77129i	−0.0200362	−	0.0854194i
$431$	−2.50275	−	6.87626i	−0.120553	−	0.331218i	0.864708	−	0.502276i	$-0.167504\pi$
$431$	−2.50275	−	6.87626i	−0.120553	−	0.331218i	−0.985261	+	0.171058i	$0.945281\pi$
$432$		0			0
$433$	−7.55138	−	10.7845i	−0.362896	−	0.518270i	0.595636	−	0.803255i	$-0.296900\pi$
$433$	−7.55138	−	10.7845i	−0.362896	−	0.518270i	−0.958532	+	0.284985i	$0.908011\pi$
$434$	0.100234	−	0.275390i	0.00481138	−	0.0132192i
$435$		0			0
$436$			8.72935i			0.418060i
$437$	−0.392269	−	22.7733i	−0.0187648	−	1.08940i
$438$		0			0
$439$	−8.41002	+	7.05684i	−0.401388	+	0.336805i	−0.821030	−	0.570885i	$-0.806600\pi$
$439$	−8.41002	+	7.05684i	−0.401388	+	0.336805i	0.419642	+	0.907690i	$0.362156\pi$
$440$	17.2209	+	6.88759i	0.820973	+	0.328353i
$441$		0			0
$442$	8.54275	+	5.98170i	0.406337	+	0.284520i
$443$	−27.9554	−	13.0358i	−1.32820	−	0.619351i	−0.376513	−	0.926411i	$-0.622877\pi$
$443$	−27.9554	−	13.0358i	−1.32820	−	0.619351i	−0.951690	+	0.307060i	$0.900655\pi$
$444$		0			0
$445$	−0.320638	+	1.06206i	−0.0151997	+	0.0503464i
$446$	−9.58392	−	8.04186i	−0.453812	−	0.380793i
$447$		0			0
$448$	−0.0695120	+	0.259422i	−0.00328414	+	0.0122566i
$449$	1.99156	−	3.44949i	0.0939877	−	0.162791i	−0.815198	−	0.579182i	$-0.803372\pi$
$449$	1.99156	−	3.44949i	0.0939877	−	0.162791i	0.909186	+	0.416391i	$0.136705\pi$
$450$		0			0
$451$	−28.6478	+	5.05137i	−1.34897	+	0.237860i
$452$	−4.87383	+	3.41269i	−0.229245	+	0.160519i
$453$		0			0
$454$	2.62233	+	3.12517i	0.123072	+	0.146672i
$455$	−0.678370	+	0.637049i	−0.0318025	+	0.0298653i
$456$		0			0
$457$	−6.68640	+	6.68640i	−0.312777	+	0.312777i	−0.845984	−	0.533208i	$-0.820986\pi$
$457$	−6.68640	+	6.68640i	−0.312777	+	0.312777i	0.533208	+	0.845984i	$0.320986\pi$
$458$	1.36159	−	15.5630i	0.0636228	−	0.727212i
$459$		0			0
$460$	3.62100	−	17.3339i	0.168830	−	0.808198i
$461$	−1.82416	−	10.3453i	−0.0849594	−	0.481829i	−0.997365	−	0.0725423i	$-0.976889\pi$
$461$	−1.82416	−	10.3453i	−0.0849594	−	0.481829i	0.912406	−	0.409286i	$-0.134222\pi$
$462$		0			0
$463$	−6.18856	+	1.65822i	−0.287607	+	0.0770640i	−0.399738	−	0.916629i	$-0.630899\pi$
$463$	−6.18856	+	1.65822i	−0.287607	+	0.0770640i	0.112131	+	0.993693i	$0.464232\pi$
$464$	−4.41579	−	7.64838i	−0.204998	−	0.355067i
$465$		0			0
$466$	1.59855	−	1.90508i	0.0740516	−	0.0882512i
$467$	−26.8967	−	7.20694i	−1.24463	−	0.333497i	−0.424369	−	0.905489i	$-0.639504\pi$
$467$	−26.8967	−	7.20694i	−1.24463	−	0.333497i	−0.820259	+	0.571992i	$0.806171\pi$
$468$		0			0
$469$	1.59612	−	0.580940i	0.0737020	−	0.0268253i
$470$	−5.68751	+	7.60286i	−0.262345	+	0.350694i
$471$		0			0
$472$	−13.9167	+	6.48947i	−0.640569	+	0.298702i
$473$	−3.94764	−	0.345373i	−0.181513	−	0.0158803i
$474$		0			0
$475$	20.7730	+	6.59421i	0.953129	+	0.302563i
$476$	−2.02698			−0.0929065
$477$		0			0
$478$	6.29708	−	2.93638i	0.288022	−	0.134307i
$479$	10.9665	+	1.93369i	0.501073	+	0.0883527i	0.418471	−	0.908230i	$-0.362566\pi$
$479$	10.9665	+	1.93369i	0.501073	+	0.0883527i	0.0826015	+	0.996583i	$0.473677\pi$
$480$		0			0
$481$	14.6259	−	5.32340i	0.666884	−	0.242726i
$482$	−5.39015	−	20.1163i	−0.245515	−	0.916273i
$483$		0			0
$484$	0.478258	−	0.569966i	0.0217390	−	0.0259076i
$485$	3.84701	−	4.30276i	0.174684	−	0.195378i
$486$		0			0
$487$	−12.7948	+	3.42834i	−0.579786	+	0.155353i	−0.536781	−	0.843722i	$-0.680360\pi$
$487$	−12.7948	+	3.42834i	−0.579786	+	0.155353i	−0.0430050	+	0.999075i	$0.513693\pi$
$488$	9.85199	−	21.1277i	0.445979	−	0.956404i
$489$		0			0
$490$	2.21590	−	10.6076i	0.100104	−	0.479203i
$491$	−2.89857	−	1.05499i	−0.130810	−	0.0476111i	0.275785	−	0.961219i	$-0.411062\pi$
$491$	−2.89857	−	1.05499i	−0.130810	−	0.0476111i	−0.406596	+	0.913608i	$0.633284\pi$
$492$		0			0
$493$	−32.6302	+	32.6302i	−1.46959	+	1.46959i
$494$	−2.87039	−	5.88862i	−0.129145	−	0.264941i
$495$		0			0
$496$	−1.86486	−	2.22246i	−0.0837348	−	0.0997913i
$497$	−0.178452	−	0.382692i	−0.00800467	−	0.0171661i
$498$		0			0
$499$	−2.91253	+	0.513558i	−0.130383	+	0.0229900i	−0.238459	−	0.971153i	$-0.576642\pi$
$499$	−2.91253	+	0.513558i	−0.130383	+	0.0229900i	0.108076	+	0.994143i	$0.465531\pi$
$500$	14.6152	+	8.57387i	0.653611	+	0.383435i
$501$		0			0
$502$	4.73325	−	17.6647i	0.211255	−	0.788415i
$503$	1.52791	+	17.4641i	0.0681261	+	0.778684i	0.951024	+	0.309119i	$0.100034\pi$
$503$	1.52791	+	17.4641i	0.0681261	+	0.778684i	−0.882897	+	0.469566i	$0.844410\pi$
$504$		0			0
$505$	−8.77300	+	29.0590i	−0.390393	+	1.29311i
$506$	10.6768	+	6.16428i	0.474644	+	0.274036i
$507$		0			0
$508$	−23.3817	−	16.3720i	−1.03739	−	0.726391i
$509$	1.28121	−	7.26613i	0.0567888	−	0.322066i	−0.943158	−	0.332344i	$-0.892161\pi$
$509$	1.28121	−	7.26613i	0.0567888	−	0.322066i	0.999947	+	0.0102782i	$0.00327171\pi$
$510$		0			0
$511$	1.27896	−	1.07317i	0.0565777	−	0.0474743i
$512$	10.0591	+	10.0591i	0.444556	+	0.444556i
$513$		0			0
$514$			1.09987i			0.0485130i
$515$	20.7769	−	16.3502i	0.915538	−	0.720477i
$516$		0			0
$517$	11.8618	+	16.9403i	0.521680	+	0.745036i
$518$	0.554643	−	0.792113i	0.0243696	−	0.0348034i
$519$		0			0
$520$	−2.69796	−	11.5021i	−0.118313	−	0.504400i
$521$	25.0077	−	14.4382i	1.09561	−	0.632549i	0.160543	−	0.987029i	$-0.448675\pi$
$521$	25.0077	−	14.4382i	1.09561	−	0.632549i	0.935064	+	0.354480i	$0.115342\pi$
$522$		0			0
$523$	38.3013	−	3.35093i	1.67480	−	0.146526i	0.790190	−	0.612862i	$-0.209982\pi$
$523$	38.3013	−	3.35093i	1.67480	−	0.146526i	0.884608	+	0.466336i	$0.154426\pi$
$524$	−18.4721	+	10.6649i	−0.806959	+	0.465898i
$525$		0			0
$526$	−1.45210	−	3.98961i	−0.0633146	−	0.173955i
$527$	−8.69495	+	12.4177i	−0.378758	+	0.540923i
$528$		0			0
$529$	1.47210	−	4.04455i	0.0640041	−	0.175850i
$530$	18.3526	+	2.18816i	0.797185	+	0.0950475i
$531$		0			0
$532$	1.11349	+	0.617550i	0.0482757	+	0.0267742i
$533$	13.1025	+	13.1025i	0.567531	+	0.567531i
$534$		0			0
$535$	8.35558	−	20.8913i	0.361243	−	0.903208i
$536$	−3.74450	+	21.2361i	−0.161738	+	0.917260i
$537$		0			0
$538$	−10.1514	−	4.73370i	−0.437660	−	0.204084i
$539$	−20.4407	−	11.8014i	−0.880443	−	0.508324i
$540$		0			0
$541$	−19.1442	−	16.0639i	−0.823072	−	0.690639i	0.130617	−	0.991433i	$-0.458304\pi$
$541$	−19.1442	−	16.0639i	−0.823072	−	0.690639i	−0.953689	+	0.300793i	$0.902749\pi$
$542$	−0.459111	−	5.24767i	−0.0197205	−	0.225407i
$543$		0			0
$544$	20.1864	−	34.9638i	0.865484	−	1.49906i
$545$	−11.4960	−	5.80686i	−0.492435	−	0.248738i
$546$		0			0
$547$	−5.56779	+	3.89861i	−0.238062	+	0.166693i	−0.686519	−	0.727111i	$-0.740862\pi$
$547$	−5.56779	+	3.89861i	−0.238062	+	0.166693i	0.448458	+	0.893804i	$0.351973\pi$
$548$	−4.60027	−	9.86531i	−0.196514	−	0.421425i
$549$		0			0
$550$	−8.84878	+	7.80168i	−0.377313	+	0.332665i
$551$	27.8661	−	7.98355i	1.18714	−	0.340111i
$552$		0			0
$553$	−0.129140	+	1.47608i	−0.00549161	+	0.0627694i
$554$	8.92295	+	3.24769i	0.379100	+	0.137981i
$555$		0			0
$556$	−3.82011	−	21.6649i	−0.162009	−	0.918797i
$557$	11.5689	−	24.8095i	0.490188	−	1.05121i	−0.493236	−	0.869895i	$-0.664186\pi$
$557$	11.5689	−	24.8095i	0.490188	−	1.05121i	0.983425	−	0.181317i	$-0.0580360\pi$
$558$		0			0
$559$	1.26209	+	2.18601i	0.0533809	+	0.0924585i
$560$	0.426682	+	0.381488i	0.0180306	+	0.0161208i
$561$		0			0
$562$	−18.0120	−	4.82631i	−0.759791	−	0.203585i
$563$	−4.81614	−	17.9741i	−0.202976	−	0.757517i	−0.990057	−	0.140667i	$-0.955075\pi$
$563$	−4.81614	−	17.9741i	−0.202976	−	0.757517i	0.787081	−	0.616850i	$-0.211592\pi$
$564$		0			0
$565$	−1.25218	−	8.68868i	−0.0526796	−	0.365536i
$566$	−5.17713	−	0.912867i	−0.217611	−	0.0383707i
$567$		0			0
$568$	5.34025	+	0.467211i	0.224072	+	0.0196037i
$569$	−7.34466			−0.307904			−0.153952	−	0.988078i	$-0.549200\pi$
$569$	−7.34466			−0.307904			−0.153952	+	0.988078i	$0.549200\pi$
$570$		0			0
$571$	−20.8079			−0.870783			−0.435392	−	0.900241i	$-0.643390\pi$
$571$	−20.8079			−0.870783			−0.435392	+	0.900241i	$0.643390\pi$
$572$	−11.0510	−	0.966837i	−0.462065	−	0.0404255i
$573$		0			0
$574$	1.13372	+	0.199905i	0.0473205	+	0.00834388i
$575$	20.4190	+	16.2993i	0.851530	+	0.679730i
$576$		0			0
$577$	7.04295	+	26.2847i	0.293202	+	1.09424i	0.942635	+	0.333826i	$0.108340\pi$
$577$	7.04295	+	26.2847i	0.293202	+	1.09424i	−0.649433	+	0.760419i	$0.724994\pi$
$578$	−20.9433	−	5.61175i	−0.871127	−	0.233418i
$579$		0			0
$580$	22.5014	−	1.25833i	0.934319	−	0.0522493i
$581$	−0.258539	−	0.447804i	−0.0107260	−	0.0185780i
$582$		0			0
$583$	17.0131	−	36.4846i	0.704609	−	1.51104i
$584$	3.68057	+	20.8736i	0.152303	+	0.863755i
$585$		0			0
$586$	7.96154	+	2.89776i	0.328888	+	0.119706i
$587$	−3.63509	+	41.5493i	−0.150036	+	1.71492i	0.432096	+	0.901828i	$0.357774\pi$
$587$	−3.63509	+	41.5493i	−0.150036	+	1.71492i	−0.582132	+	0.813094i	$0.697781\pi$
$588$		0			0
$589$	8.55965	−	4.17238i	0.352694	−	0.171920i
$590$	0.306649	−	9.76198i	0.0126246	−	0.401894i
$591$		0			0
$592$	−4.04564	−	8.67591i	−0.166275	−	0.356578i
$593$	−27.3514	+	19.1517i	−1.12319	+	0.786465i	−0.979156	−	0.203108i	$-0.934896\pi$
$593$	−27.3514	+	19.1517i	−1.12319	+	0.786465i	−0.144032	+	0.989573i	$0.546007\pi$
$594$		0			0
$595$	1.34837	−	2.66941i	0.0552778	−	0.109435i
$596$	−6.09398	+	10.5551i	−0.249619	+	0.432353i
$597$		0			0
$598$	−0.684444	−	7.82323i	−0.0279890	−	0.319915i
$599$	17.9102	+	15.0284i	0.731790	+	0.614044i	0.930619	−	0.365990i	$-0.119269\pi$
$599$	17.9102	+	15.0284i	0.731790	+	0.614044i	−0.198829	+	0.980034i	$0.563714\pi$
$600$		0			0
$601$	29.9305	+	17.2804i	1.22089	+	0.704880i	0.965107	−	0.261854i	$-0.0843340\pi$
$601$	29.9305	+	17.2804i	1.22089	+	0.704880i	0.255781	+	0.966735i	$0.417667\pi$
$602$	0.142129	+	0.0662759i	0.00579275	+	0.00270120i
$603$		0			0
$604$	−3.59874	+	20.4095i	−0.146431	+	0.830450i
$605$	0.432467	+	1.00898i	0.0175823	+	0.0410210i
$606$		0			0
$607$	−21.4554	−	21.4554i	−0.870849	−	0.870849i	0.121716	−	0.992565i	$-0.461160\pi$
$607$	−21.4554	−	21.4554i	−0.870849	−	0.870849i	−0.992565	+	0.121716i	$0.961160\pi$
$608$	−21.7413	+	13.0567i	−0.881726	+	0.529518i
$609$		0			0
$610$	9.16958	+	11.6521i	0.371265	+	0.471781i
$611$	4.50545	−	12.3786i	0.182271	−	0.500786i
$612$		0			0
$613$	−5.38799	+	7.69485i	−0.217619	+	0.310792i	−0.913087	−	0.407765i	$-0.866308\pi$
$613$	−5.38799	+	7.69485i	−0.217619	+	0.310792i	0.695468	+	0.718557i	$0.255197\pi$
$614$	6.85954	+	18.8464i	0.276829	+	0.760580i
$615$		0			0
$616$	−1.38451	+	0.799345i	−0.0557833	+	0.0322065i
$617$	−5.01638	+	0.438877i	−0.201952	+	0.0176685i	−0.187683	−	0.982230i	$-0.560098\pi$
$617$	−5.01638	+	0.438877i	−0.201952	+	0.0176685i	−0.0142691	+	0.999898i	$0.504542\pi$
$618$		0			0
$619$	33.8862	−	19.5642i	1.36200	−	0.786352i	0.372112	−	0.928188i	$-0.378634\pi$
$619$	33.8862	−	19.5642i	1.36200	−	0.786352i	0.989890	+	0.141836i	$0.0453005\pi$
$620$	7.20772	−	1.69066i	0.289469	−	0.0678985i
$621$		0			0
$622$	−7.39614	+	10.5628i	−0.296558	+	0.423529i
$623$	−0.0548488	−	0.0783323i	−0.00219747	−	0.00313832i
$624$		0			0
$625$	−21.0134	+	13.5439i	−0.840537	+	0.541754i
$626$		−	2.21318i		−	0.0884564i
$627$		0			0
$628$	−16.1037	−	16.1037i	−0.642607	−	0.642607i
$629$	−38.3169	+	32.1517i	−1.52779	+	1.28197i
$630$		0			0
$631$	−8.00188	+	45.3809i	−0.318550	+	1.80659i	0.233037	+	0.972468i	$0.425134\pi$
$631$	−8.00188	+	45.3809i	−0.318550	+	1.80659i	−0.551587	+	0.834117i	$0.685978\pi$
$632$	−15.4090	−	10.7895i	−0.612937	−	0.429183i
$633$		0			0
$634$	−3.16959	−	1.82996i	−0.125880	−	0.0726771i
$635$	37.1147	−	19.9014i	1.47285	−	0.789762i
$636$		0			0
$637$	1.31036	+	14.9775i	0.0519183	+	0.593429i
$638$	−4.06092	+	15.1556i	−0.160773	+	0.600014i
$639$		0			0
$640$	−22.6574	+	7.44973i	−0.895614	+	0.294476i
$641$	−19.6668	+	3.46778i	−0.776790	+	0.136969i	−0.547968	−	0.836499i	$-0.684599\pi$
$641$	−19.6668	+	3.46778i	−0.776790	+	0.136969i	−0.228822	+	0.973468i	$0.573487\pi$
$642$		0			0
$643$	9.29147	+	19.9256i	0.366420	+	0.785790i	0.999927	+	0.0120533i	$0.00383678\pi$
$643$	9.29147	+	19.9256i	0.366420	+	0.785790i	−0.633508	+	0.773737i	$0.718385\pi$
$644$	0.981128	+	1.16926i	0.0386619	+	0.0460754i
$645$		0			0
$646$	15.1405	+	14.6278i	0.595696	+	0.575522i
$647$	−7.34110	+	7.34110i	−0.288608	+	0.288608i	−0.836530	−	0.547921i	$-0.815419\pi$
$647$	−7.34110	+	7.34110i	−0.288608	+	0.288608i	0.547921	+	0.836530i	$0.315419\pi$
$648$		0			0
$649$	−19.9899	−	7.27571i	−0.784670	−	0.285597i
$650$	7.30381	+	1.76677i	0.286479	+	0.0692983i
$651$		0			0
$652$	9.17861	−	19.6836i	0.359462	−	0.770869i
$653$	15.4299	−	4.13442i	0.603817	−	0.161792i	0.0560567	−	0.998428i	$-0.482147\pi$
$653$	15.4299	−	4.13442i	0.603817	−	0.161792i	0.547760	+	0.836635i	$0.315481\pi$
$654$		0			0
$655$	−1.75714	−	31.4211i	−0.0686571	−	1.22772i
$656$	7.32551	−	8.73021i	0.286013	−	0.340857i
$657$		0			0
$658$	−0.211821	−	0.790526i	−0.00825764	−	0.0308179i
$659$	−27.1741	+	9.89056i	−1.05855	+	0.385281i	−0.811884	−	0.583819i	$-0.801558\pi$
$659$	−27.1741	+	9.89056i	−1.05855	+	0.385281i	−0.246668	+	0.969100i	$0.579336\pi$
$660$		0			0
$661$	22.3546	+	3.94173i	0.869495	+	0.153315i	0.590559	−	0.806994i	$-0.298907\pi$
$661$	22.3546	+	3.94173i	0.869495	+	0.153315i	0.278936	+	0.960310i	$0.410018\pi$
$662$	7.39111	−	3.44653i	0.287263	−	0.133953i
$663$		0			0
$664$	6.56448			0.254751
$665$	−1.55398	+	1.05559i	−0.0602607	+	0.0409341i
$666$		0			0
$667$	34.6169	+	3.02858i	1.34037	+	0.117267i
$668$	10.4549	−	4.87520i	0.404512	−	0.188627i
$669$		0			0
$670$	−10.9826	−	8.21580i	−0.424295	−	0.317404i
$671$	30.3476	−	11.0456i	1.17156	−	0.426411i
$672$		0			0
$673$	−17.1565	−	4.59706i	−0.661333	−	0.177204i	−0.0874854	−	0.996166i	$-0.527883\pi$
$673$	−17.1565	−	4.59706i	−0.661333	−	0.177204i	−0.573848	+	0.818962i	$0.694550\pi$
$674$	5.65193	−	6.73571i	0.217704	−	0.259450i
$675$		0			0
$676$	−6.31803	−	10.9431i	−0.243001	−	0.420890i
$677$	−0.307337	+	0.0823506i	−0.0118119	+	0.00316499i	−0.264720	−	0.964325i	$-0.585280\pi$
$677$	−0.307337	+	0.0823506i	−0.0118119	+	0.00316499i	0.252908	+	0.967490i	$0.418613\pi$
$678$		0			0
$679$	0.0863903	+	0.489944i	0.00331536	+	0.0188023i
$680$	20.7897	+	31.7691i	0.797250	+	1.21829i
$681$		0			0
$682$	−0.449226	+	5.13468i	−0.0172017	+	0.196617i
$683$	17.2283	−	17.2283i	0.659224	−	0.659224i	−0.295973	−	0.955196i	$-0.595644\pi$
$683$	17.2283	−	17.2283i	0.659224	−	0.659224i	0.955196	+	0.295973i	$0.0956437\pi$
$684$		0			0
$685$	16.0521	+	0.504240i	0.613321	+	0.0192660i
$686$	1.20402	+	1.43490i	0.0459697	+	0.0547846i
$687$		0			0
$688$	1.27171	−	0.890463i	0.0484836	−	0.0339486i
$689$	−25.2531	+	4.45280i	−0.962066	+	0.169638i
$690$		0			0
$691$	−12.6992	+	21.9956i	−0.483099	+	0.836751i	−0.999812	−	0.0194073i	$-0.993822\pi$
$691$	−12.6992	+	21.9956i	−0.483099	+	0.836751i	0.516713	+	0.856159i	$0.327155\pi$
$692$	5.73049	−	21.3865i	0.217840	−	0.812992i
$693$		0			0
$694$	10.0986	+	8.47376i	0.383339	+	0.321660i
$695$	31.0725	+	9.38088i	1.17865	+	0.355837i
$696$		0			0
$697$	−53.9688	−	25.1661i	−2.04421	−	0.953233i
$698$	−18.9582	−	13.2747i	−0.717579	−	0.502455i
$699$		0			0
$700$	−1.35983	+	0.532955i	−0.0513968	+	0.0201438i
$701$	−11.7708	+	9.87690i	−0.444578	+	0.373045i	−0.837419	−	0.546561i	$-0.815937\pi$
$701$	−11.7708	+	9.87690i	−0.444578	+	0.373045i	0.392841	+	0.919606i	$0.371492\pi$
$702$		0			0
$703$	30.8442	−	5.98813i	1.16331	−	0.225847i
$704$		−	4.72357i		−	0.178026i
$705$		0			0
$706$	−0.0149671	+	0.0411219i	−0.000563296	+	0.00154764i
$707$	−1.50072	−	2.14325i	−0.0564404	−	0.0806052i
$708$		0			0
$709$	16.6116	+	45.6401i	0.623863	+	1.71405i	0.697329	+	0.716751i	$0.254372\pi$
$709$	16.6116	+	45.6401i	0.623863	+	1.71405i	−0.0734667	+	0.997298i	$0.523406\pi$
$710$	−1.79669	+	2.89785i	−0.0674284	+	0.108754i
$711$		0			0
$712$	1.20938	−	0.105807i	0.0453235	−	0.00396530i
$713$	11.3718	−	0.994902i	0.425877	−	0.0372594i
$714$		0			0
$715$	8.62450	−	13.9103i	0.322538	−	0.520217i
$716$	−1.82538	−	5.01519i	−0.0682176	−	0.187426i
$717$		0			0
$718$	−10.0519	−	14.3555i	−0.375132	−	0.535744i
$719$	−13.1205	+	36.0482i	−0.489311	+	1.34437i	0.411994	+	0.911187i	$0.364832\pi$
$719$	−13.1205	+	36.0482i	−0.489311	+	1.34437i	−0.901305	+	0.433185i	$0.857390\pi$
$720$		0			0
$721$			2.27891i			0.0848711i
$722$	−3.86061	−	12.6483i	−0.143677	−	0.470720i
$723$		0			0
$724$	−22.6515	+	19.0068i	−0.841835	+	0.706383i
$725$	−13.3110	+	30.4700i	−0.494359	+	1.13163i
$726$		0			0
$727$	18.6808	+	13.0804i	0.692831	+	0.485126i	0.866178	−	0.499735i	$-0.166569\pi$
$727$	18.6808	+	13.0804i	0.692831	+	0.485126i	−0.173347	+	0.984861i	$0.555458\pi$
$728$	0.922931	+	0.430370i	0.0342061	+	0.0159506i
$729$		0			0
$730$	−12.9061	−	3.89639i	−0.477676	−	0.144212i
$731$	−6.21405	−	5.21421i	−0.229835	−	0.192854i
$732$		0			0
$733$	−11.7454	+	43.8346i	−0.433828	+	1.61907i	0.310028	+	0.950727i	$0.399661\pi$
$733$	−11.7454	+	43.8346i	−0.433828	+	1.61907i	−0.743856	+	0.668340i	$0.767005\pi$
$734$	4.44672	−	7.70195i	0.164132	−	0.284284i
$735$		0			0
$736$	−29.9398	+	5.27919i	−1.10359	+	0.194593i
$737$	−24.4709	+	17.1347i	−0.901398	+	0.631166i
$738$		0			0
$739$	15.2269	+	18.1467i	0.560131	+	0.667538i	0.969574	−	0.244797i	$-0.0787214\pi$
$739$	15.2269	+	18.1467i	0.560131	+	0.667538i	−0.409443	+	0.912336i	$0.634277\pi$
$740$	24.4160	+	0.766969i	0.897548	+	0.0281944i
$741$		0			0
$742$	−1.12651	+	1.12651i	−0.0413553	+	0.0413553i
$743$	0.871715	−	9.96374i	0.0319801	−	0.365534i	−0.963295	−	0.268444i	$-0.913491\pi$
$743$	0.871715	−	9.96374i	0.0319801	−	0.365534i	0.995276	−	0.0970908i	$-0.0309537\pi$
$744$		0			0
$745$	−9.84660	−	15.0467i	−0.360752	−	0.551270i
$746$	−0.200384	−	1.13643i	−0.00733657	−	0.0416078i
$747$		0			0
$748$	34.4350	−	9.22682i	1.25907	−	0.337366i
$749$	0.969714	+	1.67959i	0.0354326	+	0.0613710i
$750$		0			0
$751$	−5.60626	+	6.68129i	−0.204576	+	0.243804i	−0.858571	−	0.512695i	$-0.828647\pi$
$751$	−5.60626	+	6.68129i	−0.204576	+	0.243804i	0.653995	+	0.756499i	$0.273092\pi$
$752$	−7.82588	−	2.09694i	−0.285380	−	0.0764675i
$753$		0			0
$754$	9.39167	−	3.41829i	0.342025	−	0.124487i
$755$	−24.4841	−	18.3159i	−0.891067	−	0.666584i
$756$		0			0
$757$	38.7126	−	18.0520i	1.40703	−	0.656111i	0.437085	−	0.899420i	$-0.356011\pi$
$757$	38.7126	−	18.0520i	1.40703	−	0.656111i	0.969949	+	0.243309i	$0.0782331\pi$
$758$	11.7640	+	1.02921i	0.427286	+	0.0373827i
$759$		0			0
$760$	−1.74154	−	23.7857i	−0.0631722	−	0.862798i
$761$	−27.7115			−1.00454			−0.502270	−	0.864711i	$-0.667502\pi$
$761$	−27.7115			−1.00454			−0.502270	+	0.864711i	$0.667502\pi$
$762$		0			0
$763$	1.00614	−	0.469169i	0.0364246	−	0.0169850i
$764$	30.0721	+	5.30253i	1.08797	+	0.191839i
$765$		0			0
$766$	9.46949	−	3.44661i	0.342147	−	0.124531i
$767$	3.50711	+	13.0887i	0.126634	+	0.472606i
$768$		0			0
$769$	7.06802	−	8.42334i	0.254879	−	0.303753i	−0.623398	−	0.781905i	$-0.714248\pi$
$769$	7.06802	−	8.42334i	0.254879	−	0.303753i	0.878278	+	0.478151i	$0.158693\pi$
$770$	−0.0567757	−	1.01526i	−0.00204605	−	0.0365874i
$771$		0			0
$772$	−8.88856	+	2.38168i	−0.319906	+	0.0857186i
$773$	5.67290	−	12.1656i	0.204040	−	0.437566i	−0.777484	−	0.628902i	$-0.783504\pi$
$773$	5.67290	−	12.1656i	0.204040	−	0.437566i	0.981524	+	0.191337i	$0.0612823\pi$
$774$		0			0
$775$	−2.56816	+	10.6168i	−0.0922510	+	0.381365i
$776$	−5.93505	−	2.16018i	−0.213056	−	0.0775460i
$777$		0			0
$778$	15.3018	−	15.3018i	0.548596	−	0.548596i
$779$	21.9796	+	30.2669i	0.787500	+	1.08443i
$780$		0			0
$781$	4.77361	+	5.68897i	0.170813	+	0.203567i
$782$	10.6657	+	22.8726i	0.381404	+	0.817924i
$783$		0			0
$784$	9.10642	−	1.60571i	0.325229	−	0.0573467i
$785$	31.9199	−	10.4952i	1.13927	−	0.374590i
$786$		0			0
$787$	−10.7805	+	40.2335i	−0.384284	+	1.43417i	0.455008	+	0.890487i	$0.349636\pi$
$787$	−10.7805	+	40.2335i	−0.384284	+	1.43417i	−0.839292	+	0.543681i	$0.817030\pi$
$788$	−2.21204	−	25.2838i	−0.0788008	−	0.900698i
$789$		0			0
$790$	10.5444	−	5.65405i	0.375153	−	0.201162i
$791$	0.655292	+	0.378333i	0.0232995	+	0.0134520i
$792$		0			0
$793$	−16.8512	−	11.7994i	−0.598405	−	0.419008i
$794$	3.71057	−	21.0437i	0.131683	−	0.746813i
$795$		0			0
$796$	11.4060	−	9.57075i	0.404274	−	0.339226i
$797$	33.9874	+	33.9874i	1.20389	+	1.20389i	0.972972	+	0.230923i	$0.0741744\pi$
$797$	33.9874	+	33.9874i	1.20389	+	1.20389i	0.230923	+	0.972972i	$0.425826\pi$
$798$		0			0
$799$			42.3337i			1.49766i
$800$	4.34929	−	28.7636i	0.153771	−	1.01695i
$801$		0			0
$802$	7.11968	+	10.1680i	0.251405	+	0.359043i
$803$	−16.8422	+	24.0532i	−0.594349	+	0.848818i
$804$		0			0
$805$	−2.19250	+	0.514279i	−0.0772756	+	0.0181259i
$806$	2.84334	−	1.64160i	0.100152	−	0.0578230i
$807$		0			0
$808$	33.0900	−	2.89500i	1.16410	−	0.101846i
$809$	32.3657	−	18.6864i	1.13792	−	0.656977i	0.192004	−	0.981394i	$-0.438501\pi$
$809$	32.3657	−	18.6864i	1.13792	−	0.656977i	0.945914	+	0.324417i	$0.105168\pi$
$810$		0			0
$811$	−3.85011	−	10.5781i	−0.135196	−	0.371447i	0.853559	−	0.520997i	$-0.174440\pi$
$811$	−3.85011	−	10.5781i	−0.135196	−	0.371447i	−0.988754	+	0.149550i	$0.952217\pi$
$812$	−1.11420	+	1.59125i	−0.0391009	+	0.0558419i
$813$		0			0
$814$	−5.81675	+	15.9814i	−0.203877	+	0.560147i
$815$	19.8164	+	25.1814i	0.694137	+	0.882066i
$816$		0			0
$817$	1.82499	+	4.75754i	0.0638484	+	0.166445i
$818$	−12.2491	−	12.2491i	−0.428280	−	0.428280i
$819$		0			0
$820$	11.4568	+	26.7298i	0.400090	+	0.933446i
$821$	−3.16955	+	17.9754i	−0.110618	+	0.627346i	0.878209	+	0.478277i	$0.158739\pi$
$821$	−3.16955	+	17.9754i	−0.110618	+	0.627346i	−0.988827	+	0.149069i	$0.952372\pi$
$822$		0			0
$823$	20.3408	+	9.48508i	0.709036	+	0.330629i	0.743462	−	0.668778i	$-0.233182\pi$
$823$	20.3408	+	9.48508i	0.709036	+	0.330629i	−0.0344257	+	0.999407i	$0.510960\pi$
$824$	−25.0554	−	14.4658i	−0.872847	−	0.503938i
$825$		0			0
$826$	0.644900	+	0.541135i	0.0224389	+	0.0188285i
$827$	−1.92661	−	22.0212i	−0.0669946	−	0.765752i	−0.953176	−	0.302415i	$-0.902207\pi$
$827$	−1.92661	−	22.0212i	−0.0669946	−	0.765752i	0.886182	−	0.463338i	$-0.153348\pi$
$828$		0			0
$829$	−5.19218	+	8.99311i	−0.180332	+	0.312344i	−0.941994	−	0.335631i	$-0.891050\pi$
$829$	−5.19218	+	8.99311i	−0.180332	+	0.312344i	0.761662	+	0.647975i	$0.224384\pi$
$830$	−1.88251	+	3.72687i	−0.0653430	+	0.129362i
$831$		0			0
$832$	−2.46470	+	1.72580i	−0.0854480	+	0.0598313i
$833$	−20.4193	−	43.7893i	−0.707487	−	1.51721i
$834$		0			0
$835$	−0.534375	+	17.0115i	−0.0184928	+	0.588706i
$836$	−21.7273	−	5.42254i	−0.751455	−	0.187543i
$837$		0			0
$838$	−0.0810720	+	0.926657i	−0.00280059	+	0.0320108i
$839$	−36.6781	−	13.3497i	−1.26627	−	0.460885i	−0.380402	−	0.924821i	$-0.624214\pi$
$839$	−36.6781	−	13.3497i	−1.26627	−	0.460885i	−0.885868	+	0.463937i	$0.846436\pi$
$840$		0			0
$841$	2.64364	+	14.9928i	0.0911601	+	0.516995i
$842$	−3.62683	+	7.77777i	−0.124989	+	0.268040i
$843$		0			0
$844$	−1.62316	−	2.81139i	−0.0558713	−	0.0967720i
$845$	18.6143	−	1.04095i	0.640350	−	0.0358099i
$846$		0			0
$847$	−0.0913982	−	0.0244901i	−0.00314048	−	0.000841489i
$848$	4.08189	+	15.2338i	0.140173	+	0.523132i
$849$		0			0
$850$	−23.9983	+	2.69250i	−0.823134	+	0.0923520i
$851$	37.0933	+	6.54055i	1.27154	+	0.224207i
$852$		0			0
$853$	23.2647	+	2.03539i	0.796567	+	0.0696906i	0.478170	−	0.878267i	$-0.341300\pi$
$853$	23.2647	+	2.03539i	0.796567	+	0.0696906i	0.318396	+	0.947958i	$0.396856\pi$
$854$	−1.27807			−0.0437345
$855$		0			0
$856$	−24.6217			−0.841551
$857$	−33.0886	−	2.89487i	−1.13028	−	0.0988870i	−0.493368	−	0.869821i	$-0.664234\pi$
$857$	−33.0886	−	2.89487i	−1.13028	−	0.0988870i	−0.636916	+	0.770934i	$0.719790\pi$
$858$		0			0
$859$	22.5330	+	3.97318i	0.768817	+	0.135563i	0.544282	−	0.838903i	$-0.316802\pi$
$859$	22.5330	+	3.97318i	0.768817	+	0.135563i	0.224536	+	0.974466i	$0.427913\pi$
$860$	0.565095	+	3.92111i	0.0192696	+	0.133709i
$861$		0			0
$862$	−1.31821	−	4.91961i	−0.0448983	−	0.167563i
$863$	−7.05432	−	1.89020i	−0.240132	−	0.0643431i	0.136746	−	0.990606i	$-0.456336\pi$
$863$	−7.05432	−	1.89020i	−0.240132	−	0.0643431i	−0.376878	+	0.926263i	$0.623002\pi$
$864$		0			0
$865$	24.3527	+	21.7732i	0.828016	+	0.740311i
$866$	−4.58169	−	7.93572i	−0.155692	−	0.269667i
$867$		0			0
$868$	−0.269689	+	0.578349i	−0.00915383	+	0.0196305i
$869$	−4.52525	−	25.6640i	−0.153509	−	0.870590i
$870$		0			0
$871$	17.8814	+	6.50829i	0.605887	+	0.220525i
$872$	−1.22834	+	14.0400i	−0.0415970	+	0.475456i
$873$		0			0
$874$	1.10949	−	15.8141i	0.0375290	−	0.534921i
$875$	0.202706	−	2.14534i	0.00685271	−	0.0725258i
$876$		0			0
$877$	−2.22531	−	4.77219i	−0.0751433	−	0.161145i	0.865148	−	0.501517i	$-0.167225\pi$
$877$	−2.22531	−	4.77219i	−0.0751433	−	0.161145i	−0.940291	+	0.340372i	$0.889447\pi$
$878$	−6.25934	+	4.38283i	−0.211242	+	0.147913i
$879$		0			0
$880$	−8.98514	−	4.53857i	−0.302889	−	0.152995i
$881$	22.9016	−	39.6667i	0.771574	−	1.33641i	−0.165126	−	0.986272i	$-0.552803\pi$
$881$	22.9016	−	39.6667i	0.771574	−	1.33641i	0.936700	−	0.350133i	$-0.113864\pi$
$882$		0			0
$883$	−4.29218	−	49.0599i	−0.144443	−	1.65100i	−0.629857	−	0.776711i	$-0.716886\pi$
$883$	−4.29218	−	49.0599i	−0.144443	−	1.65100i	0.485413	−	0.874285i	$-0.338669\pi$
$884$	−17.3956	−	14.5966i	−0.585077	−	0.490938i
$885$		0			0
$886$	−18.5927	−	10.7345i	−0.624633	−	0.360632i
$887$	48.6214	+	22.6726i	1.63255	+	0.761270i	0.999913	−	0.0131801i	$-0.00419547\pi$
$887$	48.6214	+	22.6726i	1.63255	+	0.761270i	0.632635	+	0.774450i	$0.281973\pi$
$888$		0			0
$889$	−0.630348	+	3.57488i	−0.0211412	+	0.119898i
$890$	−0.286748	+	0.716949i	−0.00961180	+	0.0240322i
$891$		0			0
$892$	19.2631	+	19.2631i	0.644976	+	0.644976i
$893$	12.8976	−	23.2552i	0.431601	−	0.778207i
$894$		0			0
$895$	7.81895	+	0.932245i	0.261359	+	0.0311615i
$896$	0.703137	−	1.93185i	0.0234902	−	0.0645387i
$897$		0			0
$898$	1.59014	−	2.27096i	0.0530637	−	0.0757829i
$899$	4.96880	+	13.6517i	0.165719	+	0.455309i
$900$		0			0
$901$	71.3662	−	41.2033i	2.37755	−	1.37268i
$902$	−20.1699	+	1.76464i	−0.671585	+	0.0587560i
$903$		0			0
$904$	−8.31914	+	4.80306i	−0.276691	+	0.159747i
$905$	−9.96282	−	42.4741i	−0.331175	−	1.41189i
$906$		0			0
$907$	−22.8022	+	32.5649i	−0.757135	+	1.08130i	0.236824	+	0.971553i	$0.423893\pi$
$907$	−22.8022	+	32.5649i	−0.757135	+	1.08130i	−0.993959	+	0.109749i	$0.964995\pi$
$908$	−5.09523	−	7.27674i	−0.169091	−	0.241487i
$909$		0			0
$910$	−0.509006	+	0.400559i	−0.0168734	+	0.0132784i
$911$		−	25.0202i		−	0.828956i	−0.910059	−	0.414478i	$-0.863964\pi$
$911$		−	25.0202i		−	0.828956i	0.910059	−	0.414478i	$-0.136036\pi$
$912$		0			0
$913$	6.43055	+	6.43055i	0.212820	+	0.212820i
$914$	−5.04176	+	4.23054i	−0.166767	+	0.139934i
$915$		0			0
$916$	−5.90706	+	33.5006i	−0.195175	+	1.10689i
$917$	2.22203	+	1.55588i	0.0733779	+	0.0513797i
$918$		0			0
$919$	−35.2152	−	20.3315i	−1.16164	−	0.670675i	−0.209946	−	0.977713i	$-0.567329\pi$
$919$	−35.2152	−	20.3315i	−1.16164	−	0.670675i	−0.951697	+	0.307038i	$0.900662\pi$
$920$	8.26305	−	27.3699i	0.272425	−	0.902358i
$921$		0			0
$922$	−0.637248	−	7.28378i	−0.0209866	−	0.239878i
$923$	1.22435	−	4.56933i	0.0402999	−	0.150401i
$924$		0			0
$925$	−17.2518	+	31.6441i	−0.567236	+	1.04045i
$926$	−4.39155	+	0.774349i	−0.144315	+	0.0254467i
$927$		0			0
$928$	−16.3516	−	35.0662i	−0.536768	−	1.15110i
$929$	7.31492	+	8.71758i	0.239995	+	0.286014i	0.872575	−	0.488480i	$-0.162449\pi$
$929$	7.31492	+	8.71758i	0.239995	+	0.286014i	−0.632580	+	0.774495i	$0.718004\pi$
$930$		0			0
$931$	−2.12410	+	30.2759i	−0.0696146	+	0.992254i
$932$	−3.82910	+	3.82910i	−0.125426	+	0.125426i
$933$		0			0
$934$	−18.2121	−	6.62868i	−0.595919	−	0.216897i
$935$	−10.7554	+	51.4865i	−0.351738	+	1.68379i
$936$		0			0
$937$	−15.0899	+	32.3604i	−0.492965	+	1.05717i	0.489719	+	0.871880i	$0.337099\pi$
$937$	−15.0899	+	32.3604i	−0.492965	+	1.05717i	−0.982684	+	0.185287i	$0.940678\pi$
$938$	1.14194	−	0.305983i	0.0372858	−	0.00999069i
$939$		0			0
$940$	13.7801	−	15.4126i	0.449457	−	0.502705i
$941$	33.0108	−	39.3407i	1.07612	−	1.28247i	0.118964	−	0.992899i	$-0.462043\pi$
$941$	33.0108	−	39.3407i	1.07612	−	1.28247i	0.957156	−	0.289572i	$-0.0935130\pi$
$942$		0			0
$943$	11.6057	+	43.3131i	0.377934	+	1.41047i
$944$	7.83143	−	2.85041i	0.254891	−	0.0927729i
$945$		0			0
$946$	−2.71622	−	0.478943i	−0.0883120	−	0.0155718i
$947$	5.20308	−	2.42624i	0.169077	−	0.0788421i	−0.336237	−	0.941777i	$-0.609154\pi$
$947$	5.20308	−	2.42624i	0.169077	−	0.0788421i	0.505314	+	0.862935i	$0.331377\pi$
$948$		0			0
$949$	18.7041			0.607161
$950$	14.0033	+	5.83236i	0.454328	+	0.189227i
$951$		0			0
$952$	−3.26014	−	0.285225i	−0.105662	−	0.00924421i
$953$	−12.4628	+	5.81151i	−0.403710	+	0.188253i	−0.613858	−	0.789416i	$-0.710383\pi$
$953$	−12.4628	+	5.81151i	−0.403710	+	0.188253i	0.210148	+	0.977670i	$0.432606\pi$
$954$		0			0
$955$	−26.9874	+	36.0758i	−0.873292	+	1.16739i
$956$	−14.2168	+	5.17449i	−0.459804	+	0.167355i
$957$		0			0
$958$	7.48655	+	2.00602i	0.241879	+	0.0648114i
$959$	−0.889818	+	1.06044i	−0.0287337	+	0.0342435i
$960$		0			0
$961$	−13.1138	−	22.7137i	−0.423025	−	0.732701i
$962$	10.4641	−	2.80385i	0.337376	−	0.0903996i
$963$		0			0
$964$	7.87457	+	44.6589i	0.253623	+	1.43837i
$965$	2.77624	−	13.2900i	0.0893702	−	0.427820i
$966$		0			0
$967$	4.82286	−	55.1255i	0.155093	−	1.77272i	−0.377175	−	0.926142i	$-0.623104\pi$
$967$	4.82286	−	55.1255i	0.155093	−	1.77272i	0.532268	−	0.846576i	$-0.321340\pi$
$968$	0.849420	−	0.849420i	0.0273014	−	0.0273014i
$969$		0			0
$970$	2.92841	−	2.75004i	0.0940257	−	0.0882984i
$971$	34.8261	+	41.5041i	1.11762	+	1.33193i	0.937380	+	0.348309i	$0.113244\pi$
$971$	34.8261	+	41.5041i	1.11762	+	1.33193i	0.180243	+	0.983622i	$0.442312\pi$
$972$		0			0
$973$	−2.29176	+	1.60471i	−0.0734704	+	0.0514445i
$974$	−9.07947	+	1.60096i	−0.290925	+	0.0512979i
$975$		0			0
$976$	−6.32616	+	10.9572i	−0.202495	+	0.350732i
$977$	−8.65086	+	32.2855i	−0.276766	+	1.03290i	0.677883	+	0.735170i	$0.262897\pi$
$977$	−8.65086	+	32.2855i	−0.276766	+	1.03290i	−0.954649	+	0.297734i	$0.903769\pi$
$978$		0			0
$979$	1.28836	+	1.08106i	0.0411761	+	0.0345508i
$980$	−6.81979	+	22.5893i	−0.217850	+	0.721590i
$981$		0			0
$982$	−1.94578	−	0.907332i	−0.0620923	−	0.0289541i
$983$	0.145200	+	0.101670i	0.00463116	+	0.00324277i	0.575890	−	0.817527i	$-0.304656\pi$
$983$	0.145200	+	0.101670i	0.00463116	+	0.00324277i	−0.571259	+	0.820770i	$0.693545\pi$
$984$		0			0
$985$	34.7687	+	13.9059i	1.10782	+	0.443079i
$986$	−24.6042	+	20.6454i	−0.783559	+	0.657484i
$987$		0			0
$988$	5.10887	+	13.3182i	0.162535	+	0.423709i
$989$			6.10843i			0.194237i
$990$		0			0
$991$	14.2937	−	39.2716i	0.454054	−	1.24750i	−0.475793	−	0.879557i	$-0.657839\pi$
$991$	14.2937	−	39.2716i	0.454054	−	1.24750i	0.929847	−	0.367946i	$-0.119939\pi$
$992$	−7.29029	−	10.4116i	−0.231467	−	0.330569i
$993$		0			0
$994$	−0.100518	−	0.276172i	−0.00318825	−	0.00875965i
$995$	5.01671	+	21.3875i	0.159040	+	0.678030i
$996$		0			0
$997$	−3.50226	+	0.306408i	−0.110918	+	0.00970404i	−0.142479	−	0.989798i	$-0.545507\pi$
$997$	−3.50226	+	0.306408i	−0.110918	+	0.00970404i	0.0315617	+	0.999502i	$0.489952\pi$
$998$	−2.05062	+	0.179406i	−0.0649111	+	0.00567899i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.dl.b.298.13		240
3.2	odd	2		285.2.bh.a.13.8	✓	240
5.2	odd	4	inner	855.2.dl.b.127.8		240
15.2	even	4		285.2.bh.a.127.13	yes	240
19.3	odd	18	inner	855.2.dl.b.478.8		240
57.41	even	18		285.2.bh.a.193.13	yes	240
95.22	even	36	inner	855.2.dl.b.307.13		240
285.212	odd	36		285.2.bh.a.22.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.bh.a.13.8	✓	240	3.2	odd	2
285.2.bh.a.22.8	yes	240	285.212	odd	36
285.2.bh.a.127.13	yes	240	15.2	even	4
285.2.bh.a.193.13	yes	240	57.41	even	18
855.2.dl.b.127.8		240	5.2	odd	4	inner
855.2.dl.b.298.13		240	1.1	even	1	trivial
855.2.dl.b.307.13		240	95.22	even	36	inner
855.2.dl.b.478.8		240	19.3	odd	18	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.693370 + 0.0606620i) q^{2} +(-1.49253 - 0.263174i) q^{4} +(1.33943 - 1.79051i) q^{5} +(0.0498847 + 0.186172i) q^{7} +(-2.36352 - 0.633303i) q^{8} +(1.03734 - 1.16023i) q^{10} +(-1.69491 - 2.93568i) q^{11} +(-0.912547 + 1.95696i) q^{13} +(0.0232950 + 0.132112i) q^{14} +(1.24794 + 0.454214i) q^{16} +(0.604786 - 6.91273i) q^{17} +(-2.43830 + 3.61313i) q^{19} +(-2.47036 + 2.31989i) q^{20} +(-0.997118 - 2.13833i) q^{22} +(-4.28034 + 2.99713i) q^{23} +(-1.41184 - 4.79653i) q^{25} +(-0.751446 + 1.30154i) q^{26} +(-0.0254589 - 0.290997i) q^{28} +(-5.09429 - 4.27462i) q^{29} +(-1.89191 - 1.09230i) q^{31} +(5.27301 + 2.45884i) q^{32} +(0.838680 - 4.75639i) q^{34} +(0.400160 + 0.160046i) q^{35} +(-5.09701 - 5.09701i) q^{37} +(-1.90982 + 2.35732i) q^{38} +(-4.29971 + 3.38363i) q^{40} +(2.93503 - 8.06394i) q^{41} +(0.670512 - 0.957590i) q^{43} +(1.75712 + 4.82765i) q^{44} +(-3.14967 + 1.81846i) q^{46} +(-6.07749 + 0.531712i) q^{47} +(6.03001 - 3.48143i) q^{49} +(-0.687959 - 3.41142i) q^{50} +(1.87703 - 2.68067i) q^{52} +(6.81158 + 9.72794i) q^{53} +(-7.52658 - 0.897386i) q^{55} -0.471614i q^{56} +(-3.27292 - 3.27292i) q^{58} +(4.80729 - 4.03379i) q^{59} +(-1.65436 + 9.38236i) q^{61} +(-1.24553 - 0.872132i) q^{62} +(1.20677 + 0.696726i) q^{64} +(2.28166 + 4.25514i) q^{65} +(-0.768076 - 8.77915i) q^{67} +(-2.72191 + 10.1583i) q^{68} +(0.267750 + 0.135246i) q^{70} +(-2.15751 + 0.380428i) q^{71} +(-3.66082 - 7.85066i) q^{73} +(-3.22492 - 3.84331i) q^{74} +(4.59012 - 4.75102i) q^{76} +(0.461992 - 0.461992i) q^{77} +(7.22404 + 2.62934i) q^{79} +(2.48481 - 1.62606i) q^{80} +(2.52424 - 5.41325i) q^{82} +(-2.59137 + 0.694355i) q^{83} +(-11.5672 - 10.3420i) q^{85} +(0.523002 - 0.623290i) q^{86} +(2.14679 + 8.01192i) q^{88} +(-0.466220 + 0.169690i) q^{89} +(-0.409855 - 0.0722684i) q^{91} +(7.17732 - 3.34684i) q^{92} -4.24620 q^{94} +(3.20340 + 9.20534i) q^{95} +(2.57139 + 0.224967i) q^{97} +(4.39221 - 2.04812i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{7} - 36 q^{16} - 120 q^{20} + 24 q^{22} - 24 q^{23} - 24 q^{25} + 24 q^{26} - 72 q^{28} + 12 q^{32} + 132 q^{38} - 132 q^{40} + 72 q^{41} - 108 q^{43} - 24 q^{47} - 36 q^{53} - 144 q^{58}+ \cdots - 192 q^{98}+O(q^{100}) \) 240 * q - 12 * q^7 - 36 * q^16 - 120 * q^20 + 24 * q^22 - 24 * q^23 - 24 * q^25 + 24 * q^26 - 72 * q^28 + 12 * q^32 + 132 * q^38 - 132 * q^40 + 72 * q^41 - 108 * q^43 - 24 * q^47 - 36 * q^53 - 144 * q^58 + 24 * q^61 + 168 * q^62 - 144 * q^67 + 48 * q^68 - 48 * q^70 - 36 * q^73 - 48 * q^76 + 216 * q^77 - 24 * q^80 + 144 * q^82 + 12 * q^83 + 72 * q^85 - 96 * q^86 + 360 * q^88 + 72 * q^91 + 48 * q^92 - 24 * q^95 + 96 * q^97 - 192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more