LMFDB - Embedded newform 855.2.dl.b.127.8

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			127.8
Character	$\chi$	$=$	855.127
Dual form			855.2.dl.b.478.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0606620 + 0.693370i) q^{2} +(1.49253 + 0.263174i) q^{4} +(-1.87105 - 1.22441i) q^{5} +(-0.186172 + 0.0498847i) q^{7} +(-0.633303 + 2.36352i) q^{8} +(0.962473 - 1.22305i) q^{10} +(-1.69491 - 2.93568i) q^{11} +(1.95696 + 0.912547i) q^{13} +(-0.0232950 - 0.132112i) q^{14} +(1.24794 + 0.454214i) q^{16} +(6.91273 + 0.604786i) q^{17} +(2.43830 - 3.61313i) q^{19} +(-2.47036 - 2.31989i) q^{20} +(2.13833 - 0.997118i) q^{22} +(2.99713 + 4.28034i) q^{23} +(2.00162 + 4.58187i) q^{25} +(-0.751446 + 1.30154i) q^{26} +(-0.290997 + 0.0254589i) q^{28} +(5.09429 + 4.27462i) q^{29} +(-1.89191 - 1.09230i) q^{31} +(-2.45884 + 5.27301i) q^{32} +(-0.838680 + 4.75639i) q^{34} +(0.409417 + 0.134615i) q^{35} +(5.09701 - 5.09701i) q^{37} +(2.35732 + 1.90982i) q^{38} +(4.07886 - 3.64682i) q^{40} +(2.93503 - 8.06394i) q^{41} +(-0.957590 - 0.670512i) q^{43} +(-1.75712 - 4.82765i) q^{44} +(-3.14967 + 1.81846i) q^{46} +(-0.531712 - 6.07749i) q^{47} +(-6.03001 + 3.48143i) q^{49} +(-3.29835 + 1.10992i) q^{50} +(2.68067 + 1.87703i) q^{52} +(9.72794 - 6.81158i) q^{53} +(-0.423224 + 7.56806i) q^{55} -0.471614i q^{56} +(-3.27292 + 3.27292i) q^{58} +(-4.80729 + 4.03379i) q^{59} +(-1.65436 + 9.38236i) q^{61} +(0.872132 - 1.24553i) q^{62} +(-1.20677 - 0.696726i) q^{64} +(-2.54423 - 4.10355i) q^{65} +(8.77915 - 0.768076i) q^{67} +(10.1583 + 2.72191i) q^{68} +(-0.118174 + 0.275711i) q^{70} +(-2.15751 + 0.380428i) q^{71} +(-7.85066 + 3.66082i) q^{73} +(3.22492 + 3.84331i) q^{74} +(4.59012 - 4.75102i) q^{76} +(0.461992 + 0.461992i) q^{77} +(-7.22404 - 2.62934i) q^{79} +(-1.77881 - 2.37786i) q^{80} +(5.41325 + 2.52424i) q^{82} +(0.694355 + 2.59137i) q^{83} +(-12.1935 - 9.59563i) q^{85} +(0.523002 - 0.623290i) q^{86} +(8.01192 - 2.14679i) q^{88} +(0.466220 - 0.169690i) q^{89} +(-0.409855 - 0.0722684i) q^{91} +(3.34684 + 7.17732i) q^{92} +4.24620 q^{94} +(-8.98613 + 3.77484i) q^{95} +(-0.224967 + 2.57139i) q^{97} +(-2.04812 - 4.39221i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.0606620	+	0.693370i	−0.0428945	+	0.490287i	0.944114	+	0.329619i	$0.106920\pi$
$2$	−0.0606620	+	0.693370i	−0.0428945	+	0.490287i	−0.987009	+	0.160668i	$0.948635\pi$
$3$		0			0
$3$		0			0
$4$	1.49253	+	0.263174i	0.746267	+	0.131587i
$5$	−1.87105	−	1.22441i	−0.836757	−	0.547575i
$5$	−1.87105	−	1.22441i	−0.836757	−	0.547575i
$6$		0			0
$7$	−0.186172	+	0.0498847i	−0.0703665	+	0.0188547i	−0.293831	−	0.955858i	$-0.594930\pi$
$7$	−0.186172	+	0.0498847i	−0.0703665	+	0.0188547i	0.223464	+	0.974712i	$0.428263\pi$
$8$	−0.633303	+	2.36352i	−0.223906	+	0.835630i
$9$		0			0
$10$	0.962473	−	1.22305i	0.304361	−	0.386763i
$11$	−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
$13$	1.95696	+	0.912547i	0.542764	+	0.253095i	0.674609	−	0.738175i	$-0.264312\pi$
$13$	1.95696	+	0.912547i	0.542764	+	0.253095i	−0.131845	+	0.991270i	$0.542090\pi$
$14$	−0.0232950	−	0.132112i	−0.00622585	−	0.0353085i
$15$		0			0
$16$	1.24794	+	0.454214i	0.311986	+	0.113554i
$17$	6.91273	+	0.604786i	1.67658	+	0.146682i	0.885379	−	0.464869i	$-0.153899\pi$
$17$	6.91273	+	0.604786i	1.67658	+	0.146682i	0.791205	+	0.611551i	$0.209454\pi$
$18$		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
$22$	2.13833	−	0.997118i	0.455893	−	0.212586i
$23$	2.99713	+	4.28034i	0.624945	+	0.892513i	0.999397	−	0.0347330i	$-0.0110581\pi$
$23$	2.99713	+	4.28034i	0.624945	+	0.892513i	−0.374452	+	0.927246i	$0.622169\pi$
$24$		0			0
$25$	2.00162	+	4.58187i	0.400324	+	0.916374i
$26$	−0.751446	+	1.30154i	−0.147371	+	0.255253i
$27$		0			0
$28$	−0.290997	+	0.0254589i	−0.0549932	+	0.00481129i
$29$	5.09429	+	4.27462i	0.945986	+	0.793776i	0.978617	−	0.205691i	$-0.0659442\pi$
$29$	5.09429	+	4.27462i	0.945986	+	0.793776i	−0.0326312	+	0.999467i	$0.510389\pi$
$30$		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	$0.729521\pi$
$32$	−2.45884	+	5.27301i	−0.434666	+	0.932145i
$33$		0			0
$34$	−0.838680	+	4.75639i	−0.143833	+	0.815715i
$35$	0.409417	+	0.134615i	0.0692040	+	0.0227542i
$36$		0			0
$37$	5.09701	−	5.09701i	0.837943	−	0.837943i	−0.150645	−	0.988588i	$-0.548135\pi$
$37$	5.09701	−	5.09701i	0.837943	−	0.837943i	0.988588	+	0.150645i	$0.0481351\pi$
$38$	2.35732	+	1.90982i	0.382408	+	0.309814i
$39$		0			0
$40$	4.07886	−	3.64682i	0.644925	−	0.576613i
$41$	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
$43$	−0.957590	−	0.670512i	−0.146031	−	0.102252i	0.498278	−	0.867017i	$-0.333966\pi$
$43$	−0.957590	−	0.670512i	−0.146031	−	0.102252i	−0.644309	+	0.764765i	$0.722855\pi$
$44$	−1.75712	−	4.82765i	−0.264896	−	0.727796i
$45$		0			0
$46$	−3.14967	+	1.81846i	−0.464394	+	0.268118i
$47$	−0.531712	−	6.07749i	−0.0775581	−	0.886493i	−0.930932	−	0.365193i	$-0.881003\pi$
$47$	−0.531712	−	6.07749i	−0.0775581	−	0.886493i	0.853374	−	0.521300i	$-0.174553\pi$
$48$		0			0
$49$	−6.03001	+	3.48143i	−0.861429	+	0.497347i
$50$	−3.29835	+	1.10992i	−0.466457	+	0.156966i
$51$		0			0
$52$	2.68067	+	1.87703i	0.371743	+	0.260297i
$53$	9.72794	−	6.81158i	1.33624	−	0.935642i	0.336254	−	0.941771i	$-0.390840\pi$
$53$	9.72794	−	6.81158i	1.33624	−	0.935642i	0.999981	+	0.00612942i	$0.00195107\pi$
$54$		0			0
$55$	−0.423224	+	7.56806i	−0.0570675	+	1.02048i
$56$		−	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	−0.899638	−	0.436636i	$-0.856170\pi$
$59$	−4.80729	+	4.03379i	−0.625856	+	0.525155i	0.273782	+	0.961792i	$0.411725\pi$
$60$		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	$0.846761\pi$
$62$	0.872132	−	1.24553i	0.110761	−	0.158183i
$63$		0			0
$64$	−1.20677	−	0.696726i	−0.150846	−	0.0870908i
$65$	−2.54423	−	4.10355i	−0.315573	−	0.508983i
$66$		0			0
$67$	8.77915	−	0.768076i	1.07254	−	0.0938355i	0.462822	−	0.886451i	$-0.346837\pi$
$67$	8.77915	−	0.768076i	1.07254	−	0.0938355i	0.609722	+	0.792616i	$0.291281\pi$
$68$	10.1583	+	2.72191i	1.23188	+	0.330081i
$69$		0			0
$70$	−0.118174	+	0.275711i	−0.0141245	+	0.0329538i
$71$	−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
$73$	−7.85066	+	3.66082i	−0.918850	+	0.428467i	−0.823719	−	0.566998i	$-0.808105\pi$
$73$	−7.85066	+	3.66082i	−0.918850	+	0.428467i	−0.0951309	+	0.995465i	$0.530327\pi$
$74$	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	−0.0980014	−	0.995186i	$-0.531245\pi$
$79$	−7.22404	−	2.62934i	−0.812768	−	0.295823i	−0.714767	+	0.699363i	$0.753467\pi$
$80$	−1.77881	−	2.37786i	−0.198877	−	0.265852i
$81$		0			0
$82$	5.41325	+	2.52424i	0.597793	+	0.278756i
$83$	0.694355	+	2.59137i	0.0762154	+	0.284440i	0.993506	−	0.113778i	$-0.0362954\pi$
$83$	0.694355	+	2.59137i	0.0762154	+	0.284440i	−0.917291	+	0.398218i	$0.869629\pi$
$84$		0			0
$85$	−12.1935	−	9.59563i	−1.32257	−	1.04079i
$86$	0.523002	−	0.623290i	0.0563968	−	0.0672111i
$87$		0			0
$88$	8.01192	−	2.14679i	0.854073	−	0.228848i
$89$	0.466220	−	0.169690i	0.0494192	−	0.0179871i	−0.317192	−	0.948361i	$-0.602740\pi$
$89$	0.466220	−	0.169690i	0.0494192	−	0.0179871i	0.366611	+	0.930374i	$0.380518\pi$
$90$		0			0
$91$	−0.409855	−	0.0722684i	−0.0429644	−	0.00757579i
$92$	3.34684	+	7.17732i	0.348932	+	0.748288i
$93$		0			0
$94$	4.24620			0.437963
$95$	−8.98613	+	3.77484i	−0.921958	+	0.387291i
$96$		0			0
$97$	−0.224967	+	2.57139i	−0.0228420	+	0.261085i	0.976183	+	0.216947i	$0.0696098\pi$
$97$	−0.224967	+	2.57139i	−0.0228420	+	0.261085i	−0.999025	+	0.0441382i	$0.985946\pi$
$98$	−2.04812	−	4.39221i	−0.206892	−	0.443681i
$99$		0			0
$100$	1.78166	+	7.36537i	0.178166	+	0.736537i
$101$	−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
$103$	3.06022	−	11.4209i	0.301532	−	1.12533i	−0.634357	−	0.773040i	$-0.718735\pi$
$103$	3.06022	−	11.4209i	0.301532	−	1.12533i	0.935890	−	0.352294i	$-0.114598\pi$
$104$	−3.39617	+	4.04740i	−0.333022	+	0.396880i
$105$		0			0
$106$	4.13283	+	7.15826i	0.401415	+	0.695272i
$107$	2.60434	+	9.71954i	0.251771	+	0.939624i	0.969858	+	0.243670i	$0.0783514\pi$
$107$	2.60434	+	9.71954i	0.251771	+	0.939624i	−0.718087	+	0.695954i	$0.754982\pi$
$108$		0			0
$109$	1.00018	+	5.67232i	0.0958002	+	0.543310i	0.994499	+	0.104744i	$0.0334023\pi$
$109$	1.00018	+	5.67232i	0.0958002	+	0.543310i	−0.898699	+	0.438566i	$0.855487\pi$
$110$	−5.22179	−	0.752544i	−0.497878	−	0.0717523i
$111$		0			0
$112$	−0.254991	−	0.0223088i	−0.0240944	−	0.00210799i
$113$	−2.77599	−	2.77599i	−0.261143	−	0.261143i	0.564375	−	0.825518i	$-0.309117\pi$
$113$	−2.77599	−	2.77599i	−0.261143	−	0.261143i	−0.825518	+	0.564375i	$0.809117\pi$
$114$		0			0
$115$	−0.366851	−	11.6784i	−0.0342090	−	1.08902i
$116$	6.47843	+	7.72069i	0.601507	+	0.716848i
$117$		0			0
$118$	−2.50529	−	3.57793i	−0.230631	−	0.329375i
$119$	−1.31713	+	0.232245i	−0.120741	+	0.0212899i
$120$		0			0
$121$	−0.245467	+	0.425161i	−0.0223151	+	0.0386510i
$122$	−6.40509	−	1.71624i	−0.579890	−	0.155381i
$123$		0			0
$124$	−2.53628	−	2.12819i	−0.227765	−	0.191117i
$125$	1.86498	−	11.0237i	0.166809	−	0.985989i
$126$		0			0
$127$	−7.95952	+	17.0692i	−0.706293	+	1.51465i	0.144701	+	0.989475i	$0.453778\pi$
$127$	−7.95952	+	17.0692i	−0.706293	+	1.51465i	−0.850994	+	0.525175i	$0.824000\pi$
$128$	−6.11798	+	8.73738i	−0.540758	+	0.772283i
$129$		0			0
$130$	2.99961	−	1.51516i	0.263084	−	0.132889i
$131$	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
$133$	−0.273703	+	0.794299i	−0.0237331	+	0.0688744i
$134$			6.13379i			0.529879i
$135$		0			0
$136$	−5.80727	+	15.9554i	−0.497970	+	1.36816i
$137$	−5.88338	+	4.11959i	−0.502651	+	0.351960i	−0.797238	−	0.603665i	$-0.793707\pi$
$137$	−5.88338	+	4.11959i	−0.502651	+	0.351960i	0.294587	+	0.955625i	$0.404818\pi$
$138$		0			0
$139$	−4.96460	−	13.6401i	−0.421092	−	1.15694i	−0.951082	−	0.308937i	$-0.900027\pi$
$139$	−4.96460	−	13.6401i	−0.421092	−	1.15694i	0.529990	−	0.848004i	$-0.322196\pi$
$140$	0.575641	+	0.308666i	0.0486505	+	0.0260870i
$141$		0			0
$142$	−0.132898	−	1.51903i	−0.0111526	−	0.127474i
$143$	−0.637941	−	7.29170i	−0.0533473	−	0.609762i
$144$		0			0
$145$	−4.29775	−	14.2355i	−0.356908	−	1.18220i
$146$	−2.06207	−	5.66548i	−0.170658	−	0.468879i
$147$		0			0
$148$	8.94885	−	6.26606i	0.735591	−	0.515067i
$149$	−2.75049	+	7.55690i	−0.225329	+	0.619086i	−0.999910	−	0.0133883i	$-0.995738\pi$
$149$	−2.75049	+	7.55690i	−0.225329	+	0.619086i	0.774582	+	0.632474i	$0.217960\pi$
$150$		0			0
$151$		−	13.6744i		−	1.11281i	−0.830913	−	0.556403i	$-0.812181\pi$
$151$		−	13.6744i		−	1.11281i	0.830913	−	0.556403i	$-0.187819\pi$
$152$	6.99552	+	8.05116i	0.567411	+	0.653035i
$153$		0			0
$154$	−0.348356	+	0.292306i	−0.0280714	+	0.0235547i
$155$	2.20243	+	4.36022i	0.176904	+	0.350221i
$156$		0			0
$157$	−8.61903	+	12.3093i	−0.687874	+	0.982386i	0.311608	+	0.950211i	$0.399132\pi$
$157$	−8.61903	+	12.3093i	−0.687874	+	0.982386i	−0.999482	+	0.0321750i	$0.989757\pi$
$158$	2.26133	−	4.84943i	0.179902	−	0.385800i
$159$		0			0
$160$	11.0570	−	6.85540i	0.874129	−	0.541967i
$161$	−0.771506	−	0.647371i	−0.0608032	−	0.0510200i
$162$		0			0
$163$	13.8420	+	3.70896i	1.08419	+	0.290508i	0.756312	−	0.654211i	$-0.226999\pi$
$163$	13.8420	+	3.70896i	1.08419	+	0.290508i	0.327880	+	0.944720i	$0.393666\pi$
$164$	6.50286	−	11.2633i	0.507788	−	0.879514i
$165$		0			0
$166$	−1.83890	+	0.324247i	−0.142726	+	0.0251665i
$167$	−4.36579	−	6.23499i	−0.337835	−	0.482478i	0.613907	−	0.789378i	$-0.289597\pi$
$167$	−4.36579	−	6.23499i	−0.337835	−	0.482478i	−0.951742	+	0.306900i	$0.900708\pi$
$168$		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
$173$	14.5535	+	1.27326i	1.10648	+	0.0968045i	0.625720	−	0.780047i	$-0.284805\pi$
$173$	14.5535	+	1.27326i	1.10648	+	0.0968045i	0.480760	+	0.876852i	$0.340361\pi$
$174$		0			0
$175$	−0.601212	−	0.753167i	−0.0454473	−	0.0569341i
$176$	−0.781730	−	4.43341i	−0.0589251	−	0.334181i
$177$		0			0
$178$	0.0893761	+	0.333556i	0.00669903	+	0.0250011i
$179$	−1.76075	−	3.04972i	−0.131605	−	0.227946i	0.792690	−	0.609624i	$-0.208680\pi$
$179$	−1.76075	−	3.04972i	−0.131605	−	0.227946i	−0.924295	+	0.381678i	$0.875346\pi$
$180$		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	$-0.0359861\pi$
$182$	0.0749713	−	0.279797i	0.00555724	−	0.0207399i
$183$		0			0
$184$	−12.0148	+	4.37301i	−0.885740	+	0.322383i
$185$	−15.7776	+	3.29588i	−1.15999	+	0.242318i
$186$		0			0
$187$	−9.94103	−	21.3186i	−0.726960	−	1.55897i
$188$	0.805840	−	9.21079i	0.0587719	−	0.671766i
$189$		0			0
$190$	−2.07225	−	6.45970i	−0.150337	−	0.468636i
$191$	−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
$193$	−2.56604	−	5.50289i	−0.184708	−	0.396107i	0.792049	−	0.610457i	$-0.209014\pi$
$193$	−2.56604	−	5.50289i	−0.184708	−	0.396107i	−0.976757	+	0.214351i	$0.931236\pi$
$194$	−1.76928	−	0.311971i	−0.127027	−	0.0223982i
$195$		0			0
$196$	−9.91621	+	3.60920i	−0.708301	+	0.257800i
$197$	−16.1759	+	4.33432i	−1.15249	+	0.308808i	−0.783961	−	0.620810i	$-0.786804\pi$
$197$	−16.1759	+	4.33432i	−1.15249	+	0.308808i	−0.368525	+	0.929618i	$0.620137\pi$
$198$		0			0
$199$	6.31500	−	7.52592i	0.447658	−	0.533498i	−0.494272	−	0.869307i	$-0.664565\pi$
$199$	6.31500	−	7.52592i	0.447658	−	0.533498i	0.941930	+	0.335809i	$0.109010\pi$
$200$	−12.0970	+	1.82916i	−0.855384	+	0.129341i
$201$		0			0
$202$	−2.44542	−	9.12644i	−0.172059	−	0.642134i
$203$	−1.16165	−	0.541688i	−0.0815321	−	0.0380191i
$204$		0			0
$205$	−15.3652	+	11.4943i	−1.07315	+	0.802797i
$206$	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	$0.754287\pi$
$212$	16.3119	−	7.60637i	1.12031	−	0.522407i
$213$		0			0
$214$	−6.89722	+	1.21617i	−0.471485	+	0.0831354i
$215$	0.970711	+	2.42705i	0.0662019	+	0.165523i
$216$		0			0
$217$	0.406711	+	0.108978i	0.0276093	+	0.00739790i
$218$	−3.99369	+	0.349403i	−0.270487	+	0.0236645i
$219$		0			0
$220$	−2.62339	+	11.1842i	−0.176869	+	0.754039i
$221$	12.9761	+	7.49173i	0.872865	+	0.503949i
$222$		0			0
$223$	−10.3100	+	14.7242i	−0.690410	+	0.986008i	0.308979	+	0.951069i	$0.400013\pi$
$223$	−10.3100	+	14.7242i	−0.690410	+	0.986008i	−0.999389	+	0.0349391i	$0.988876\pi$
$224$	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	$-0.812314\pi$
$227$	−4.14462	+	4.14462i	−0.275088	+	0.275088i	0.556057	+	0.831144i	$0.312314\pi$
$228$		0			0
$229$			22.4455i			1.48324i	0.670821	+	0.741619i	$0.265942\pi$
$229$			22.4455i			1.48324i	−0.670821	+	0.741619i	$0.734058\pi$
$230$	8.11973	+	0.454075i	0.535399	+	0.0299408i
$231$		0			0
$232$	−13.3294	+	9.33332i	−0.875115	+	0.612762i
$233$	−2.92687	−	2.04942i	−0.191746	−	0.134262i	0.473762	−	0.880653i	$-0.342896\pi$
$233$	−2.92687	−	2.04942i	−0.191746	−	0.134262i	−0.665507	+	0.746391i	$0.731785\pi$
$234$		0			0
$235$	−6.44651	+	12.0223i	−0.420524	+	0.784248i
$236$	−8.23663	+	4.75542i	−0.536159	+	0.309551i
$237$		0			0
$238$	−0.0811323	−	0.927346i	−0.00525903	−	0.0601109i
$239$	−8.64517	+	4.99129i	−0.559210	+	0.322860i	−0.752828	−	0.658217i	$-0.771311\pi$
$239$	−8.64517	+	4.99129i	−0.559210	+	0.322860i	0.193619	+	0.981077i	$0.437978\pi$
$240$		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	$-0.525092\pi$
$242$	−0.279903	−	0.195990i	−0.0179929	−	0.0125987i
$243$		0			0
$244$	−4.93839	+	13.5681i	−0.316148	+	0.868609i
$245$	15.5451	+	0.869320i	0.993141	+	0.0555388i
$246$		0			0
$247$	8.06880	−	4.84570i	0.513406	−	0.308325i
$248$	3.77981	−	3.77981i	0.240018	−	0.240018i
$249$		0			0
$250$	7.53036	+	1.96184i	0.476262	+	0.124078i
$251$	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
$253$	7.48583	−	16.0534i	0.470630	−	1.00927i
$254$	−11.3525	−	6.55434i	−0.712316	−	0.411256i
$255$		0			0
$256$	−7.82200	−	6.56344i	−0.488875	−	0.410215i
$257$	−1.57421	+	0.137726i	−0.0981966	+	0.00859109i	−0.136148	−	0.990688i	$-0.543472\pi$
$257$	−1.57421	+	0.137726i	−0.0981966	+	0.00859109i	0.0379515	+	0.999280i	$0.487917\pi$
$258$		0			0
$259$	−0.694659	+	1.20318i	−0.0431640	+	0.0747623i
$260$	−2.71740	−	6.79426i	−0.168526	−	0.421362i
$261$		0			0
$262$	5.61857	+	8.02415i	0.347116	+	0.495734i
$263$	−5.52841	+	2.57794i	−0.340896	+	0.158963i	−0.585525	−	0.810654i	$-0.699112\pi$
$263$	−5.52841	+	2.57794i	−0.340896	+	0.158963i	0.244629	+	0.969617i	$0.421334\pi$
$264$		0			0
$265$	−26.5416	+	0.833741i	−1.63044	+	0.0512163i
$266$	−0.534139	−	0.237961i	−0.0327502	−	0.0145904i
$267$		0			0
$268$	13.3053	+	1.16406i	0.812752	+	0.0711066i
$269$	15.1223	+	5.50406i	0.922022	+	0.335588i	0.759042	−	0.651041i	$-0.225667\pi$
$269$	15.1223	+	5.50406i	0.922022	+	0.335588i	0.162979	+	0.986630i	$0.447890\pi$
$270$		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	$-0.129386\pi$
$272$	8.35200	+	3.89460i	0.506414	+	0.236145i
$273$		0			0
$274$	−2.49950	−	4.32926i	−0.151000	−	0.261540i
$275$	10.0583	−	13.6420i	0.606539	−	0.822643i
$276$		0			0
$277$	−3.53100	+	13.1779i	−0.212157	+	0.791782i	0.774990	+	0.631973i	$0.217755\pi$
$277$	−3.53100	+	13.1779i	−0.212157	+	0.791782i	−0.987148	+	0.159809i	$0.948912\pi$
$278$	9.75882	−	2.61487i	0.585295	−	0.156829i
$279$		0			0
$280$	−0.577451	+	0.882411i	−0.0345093	+	0.0527341i
$281$	−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
$283$	−0.658283	+	7.52421i	−0.0391309	+	0.447268i	0.951203	+	0.308565i	$0.0998488\pi$
$283$	−0.658283	+	7.52421i	−0.0391309	+	0.447268i	−0.990334	+	0.138703i	$0.955707\pi$
$284$	−3.32028			−0.197022
$285$		0			0
$286$	5.09454			0.301247
$287$	−0.144155	+	1.64770i	−0.00850919	+	0.0972604i
$288$		0			0
$289$	30.6784	+	5.40943i	1.80461	+	0.318202i
$290$	10.1312	−	2.11637i	0.594924	−	0.124278i
$291$		0			0
$292$	−12.6808	+	3.39781i	−0.742088	+	0.198842i
$293$	3.15055	−	11.7580i	0.184057	−	0.686911i	−0.810773	−	0.585361i	$-0.800953\pi$
$293$	3.15055	−	11.7580i	0.184057	−	0.686911i	0.994830	−	0.101551i	$-0.0323804\pi$
$294$		0			0
$295$	13.9337	−	1.66130i	0.811251	−	0.0967246i
$296$	8.81892	+	15.2748i	0.512589	+	0.887831i
$297$		0			0
$298$	−5.07288	−	2.36552i	−0.293864	−	0.137031i
$299$	1.95926	+	11.1115i	0.113307	+	0.642594i
$300$		0			0
$301$	0.211725	+	0.0770617i	0.0122036	+	0.00444176i
$302$	9.48140	+	0.829515i	0.545593	+	0.0477332i
$303$		0			0
$304$	4.68399	−	3.40147i	0.268645	−	0.195088i
$305$	14.5833	−	15.5292i	0.835037	−	0.889199i
$306$		0			0
$307$	−26.1155	+	12.1779i	−1.49049	+	0.695027i	−0.985746	−	0.168242i	$-0.946191\pi$
$307$	−26.1155	+	12.1779i	−1.49049	+	0.695027i	−0.504744	+	0.863269i	$0.668413\pi$
$308$	0.567954	+	0.811122i	0.0323622	+	0.0462180i
$309$		0			0
$310$	−3.15685	+	1.26260i	−0.179297	+	0.0717108i
$311$	−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
$313$	−3.16767	+	0.277135i	−0.179047	+	0.0156646i	−0.176327	−	0.984332i	$-0.556422\pi$
$313$	−3.16767	+	0.277135i	−0.179047	+	0.0156646i	−0.00272050	+	0.999996i	$0.500866\pi$
$314$	−8.01202	−	6.72288i	−0.452144	−	0.379394i
$315$		0			0
$316$	−10.0902	−	5.82555i	−0.567616	−	0.327713i
$317$	2.22228	−	4.76570i	0.124816	−	0.267669i	−0.833964	−	0.551819i	$-0.813934\pi$
$317$	2.22228	−	4.76570i	0.124816	−	0.267669i	0.958780	+	0.284151i	$0.0917116\pi$
$318$		0			0
$319$	3.91451	−	22.2003i	0.219171	−	1.24298i
$320$	1.40483	+	2.78119i	0.0785325	+	0.155473i
$321$		0			0
$322$	0.495668	−	0.495668i	0.0276225	−	0.0276225i
$323$	19.0405	−	23.5020i	1.05944	−	1.30768i
$324$		0			0
$325$	−0.264072	+	10.7931i	−0.0146481	+	0.598694i
$326$	−3.41137	+	9.37265i	−0.188938	+	0.519103i
$327$		0			0
$328$	17.2005	+	12.0439i	0.949739	+	0.665014i
$329$	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	$0.228975\pi$
$332$	0.354368	+	4.05044i	0.0194485	+	0.222297i
$333$		0			0
$334$	4.58799	−	2.64888i	0.251044	−	0.144940i
$335$	−17.3666	−	9.31221i	−0.948841	−	0.508781i
$336$		0			0
$337$	10.3484	+	7.24603i	0.563713	+	0.394716i	0.820410	−	0.571776i	$-0.193745\pi$
$337$	10.3484	+	7.24603i	0.563713	+	0.394716i	−0.256697	+	0.966492i	$0.582634\pi$
$338$	4.75362	−	3.32852i	0.258563	−	0.181047i
$339$		0			0
$340$	−15.6739	−	17.5308i	−0.850038	−	0.950742i
$341$			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
$347$	−10.8637	+	15.5150i	−0.583196	+	0.832890i	−0.996994	−	0.0774785i	$-0.975313\pi$
$347$	−10.8637	+	15.5150i	−0.583196	+	0.832890i	0.413798	+	0.910369i	$0.364202\pi$
$348$		0			0
$349$	28.7967	+	16.6258i	1.54145	+	0.889959i	0.998747	+	0.0500357i	$0.0159335\pi$
$349$	28.7967	+	16.6258i	1.54145	+	0.889959i	0.542706	+	0.839923i	$0.317400\pi$
$350$	0.558694	−	0.371173i	0.0298635	−	0.0198401i
$351$		0			0
$352$	19.6474	−	1.71892i	1.04721	−	0.0916189i
$353$	0.0607309	+	0.0162728i	0.00323238	+	0.000866114i	0.260435	−	0.965491i	$-0.416134\pi$
$353$	0.0607309	+	0.0162728i	0.00323238	+	0.000866114i	−0.257202	+	0.966358i	$0.582801\pi$
$354$		0			0
$355$	4.50261	+	1.92989i	0.238973	+	0.102428i
$356$	0.740506	−	0.130571i	0.0392468	−	0.00692026i
$357$		0			0
$358$	2.22139	−	1.03585i	0.117404	−	0.0547465i
$359$	16.1846	+	19.2880i	0.854190	+	1.01798i	0.999591	+	0.0286106i	$0.00910829\pi$
$359$	16.1846	+	19.2880i	0.854190	+	1.01798i	−0.145401	+	0.989373i	$0.546447\pi$
$360$		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
$365$	19.1713	+	2.76289i	1.00347	+	0.144616i
$366$		0			0
$367$	11.5804	+	5.40005i	0.604494	+	0.281880i	0.700671	−	0.713484i	$-0.252884\pi$
$367$	11.5804	+	5.40005i	0.604494	+	0.281880i	−0.0961775	+	0.995364i	$0.530662\pi$
$368$	1.79605	+	6.70297i	0.0936258	+	0.349416i
$369$		0			0
$370$	−1.32817	−	11.1396i	−0.0690481	−	0.579122i
$371$	−1.47128	+	1.75340i	−0.0763850	+	0.0910322i
$372$		0			0
$373$	−1.60146	+	0.429109i	−0.0829203	+	0.0222184i	−0.300041	−	0.953926i	$-0.597000\pi$
$373$	−1.60146	+	0.429109i	−0.0829203	+	0.0222184i	0.217120	+	0.976145i	$0.430334\pi$
$374$	15.3847	−	5.59958i	0.795525	−	0.289548i
$375$		0			0
$376$	14.7010	+	2.59218i	0.758146	+	0.133682i
$377$	6.06855	+	13.0140i	0.312546	+	0.670257i
$378$		0			0
$379$	−16.9664			−0.871503			−0.435752	−	0.900067i	$-0.643517\pi$
$379$	−16.9664			−0.871503			−0.435752	+	0.900067i	$0.643517\pi$
$380$	−14.4055	+	3.26917i	−0.738989	+	0.167705i
$381$		0			0
$382$	1.22224	−	13.9703i	0.0625353	−	0.714781i
$383$	−6.11883	−	13.1219i	−0.312658	−	0.670496i	0.685694	−	0.727890i	$-0.259499\pi$
$383$	−6.11883	−	13.1219i	−0.312658	−	0.670496i	−0.998352	+	0.0573936i	$0.981721\pi$
$384$		0			0
$385$	−0.298738	−	1.43008i	−0.0152251	−	0.0728834i
$386$	3.97120	−	1.44540i	0.202129	−	0.0735688i
$387$		0			0
$388$	−1.01249	+	3.77868i	−0.0514016	+	0.191833i
$389$	−19.9850	+	23.8172i	−1.01328	+	1.20758i	−0.0351924	+	0.999381i	$0.511204\pi$
$389$	−19.9850	+	23.8172i	−1.01328	+	1.20758i	−0.978087	+	0.208198i	$0.933240\pi$
$390$		0			0
$391$	18.1297	+	31.4015i	0.916856	+	1.58804i
$392$	−4.40959	−	16.4568i	−0.222718	−	0.831195i
$393$		0			0
$394$	−2.02403	−	11.4788i	−0.101969	−	0.578295i
$395$	10.2971	+	13.7648i	0.518104	+	0.692584i
$396$		0			0
$397$	30.5840	+	2.67575i	1.53497	+	0.134292i	0.823049	−	0.567971i	$-0.192271\pi$
$397$	30.5840	+	2.67575i	1.53497	+	0.134292i	0.711918	+	0.702263i	$0.247827\pi$
$398$	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
$403$	−2.70563	−	3.86404i	−0.134777	−	0.192482i
$404$	−20.2610	+	3.57256i	−1.00802	+	0.177742i
$405$		0			0
$406$	0.446059	−	0.772596i	0.0221375	−	0.0383433i
$407$	−23.6022	−	6.32418i	−1.16992	−	0.313478i
$408$		0			0
$409$	19.0657	+	15.9980i	0.942738	+	0.791051i	0.978060	−	0.208325i	$-0.0668012\pi$
$409$	19.0657	+	15.9980i	0.942738	+	0.791051i	−0.0353220	+	0.999376i	$0.511246\pi$
$410$	−7.03772	−	11.3510i	−0.347568	−	0.560587i
$411$		0			0
$412$	7.57316	−	16.2407i	0.373103	−	0.800121i
$413$	0.693759	−	0.990791i	0.0341377	−	0.0487536i
$414$		0			0
$415$	1.87374	−	5.69875i	0.0919782	−	0.279740i
$416$	−9.62373	+	8.07527i	−0.471842	+	0.395923i
$417$		0			0
$418$	1.61116	−	10.1573i	0.0788043	−	0.496811i
$419$		−	1.33645i		−	0.0652901i	−0.999467	−	0.0326450i	$-0.989607\pi$
$419$		−	1.33645i		−	0.0652901i	0.999467	−	0.0326450i	$-0.0103931\pi$
$420$		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	$0.208252\pi$
$422$	−1.22125	+	0.855125i	−0.0594493	+	0.0416268i
$423$		0			0
$424$	9.93855	+	27.3059i	0.482659	+	1.32609i
$425$	11.0656	+	32.8838i	0.536761	+	1.59510i
$426$		0			0
$427$	−0.160040	−	1.82926i	−0.00774487	−	0.0885243i
$428$	1.32914	+	15.1921i	0.0642464	+	0.734340i
$429$		0			0
$430$	−1.74173	+	0.525832i	−0.0839935	+	0.0253579i
$431$	−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
$433$	−10.7845	+	7.55138i	−0.518270	+	0.362896i	−0.803255	−	0.595636i	$-0.796900\pi$
$433$	−10.7845	+	7.55138i	−0.518270	+	0.362896i	0.284985	+	0.958532i	$0.408011\pi$
$434$	−0.100234	+	0.275390i	−0.00481138	+	0.0132192i
$435$		0			0
$436$			8.72935i			0.418060i
$437$	22.7733	−	0.392269i	1.08940	−	0.0187648i
$438$		0			0
$439$	8.41002	−	7.05684i	0.401388	−	0.336805i	−0.419642	−	0.907690i	$-0.637844\pi$
$439$	8.41002	−	7.05684i	0.401388	−	0.336805i	0.821030	+	0.570885i	$0.193400\pi$
$440$	−17.6192	−	5.79317i	−0.839963	−	0.276179i
$441$		0			0
$442$	−5.98170	+	8.54275i	−0.284520	+	0.406337i
$443$	−13.0358	+	27.9554i	−0.619351	+	1.32820i	0.307060	+	0.951690i	$0.400655\pi$
$443$	−13.0358	+	27.9554i	−0.619351	+	1.32820i	−0.926411	+	0.376513i	$0.877123\pi$
$444$		0			0
$445$	−1.08009	−	0.253348i	−0.0512011	−	0.0120098i
$446$	−9.58392	−	8.04186i	−0.453812	−	0.380793i
$447$		0			0
$448$	0.259422	+	0.0695120i	0.0122566	+	0.00328414i
$449$	−1.99156	+	3.44949i	−0.0939877	+	0.162791i	−0.909186	−	0.416391i	$-0.863295\pi$
$449$	−1.99156	+	3.44949i	−0.0939877	+	0.162791i	0.815198	+	0.579182i	$0.196628\pi$
$450$		0			0
$451$	−28.6478	+	5.05137i	−1.34897	+	0.237860i
$452$	−3.41269	−	4.87383i	−0.160519	−	0.229245i
$453$		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	0.533208	−	0.845984i	$-0.320986\pi$
$457$	−6.68640	−	6.68640i	−0.312777	−	0.312777i	−0.845984	+	0.533208i	$0.820986\pi$
$458$	−15.5630	−	1.36159i	−0.727212	−	0.0636228i
$459$		0			0
$460$	2.52592	−	17.5270i	0.117772	−	0.817201i
$461$	−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
$463$	1.65822	+	6.18856i	0.0770640	+	0.287607i	0.993693	−	0.112131i	$-0.0357677\pi$
$463$	1.65822	+	6.18856i	0.0770640	+	0.287607i	−0.916629	+	0.399738i	$0.869101\pi$
$464$	4.41579	+	7.64838i	0.204998	+	0.355067i
$465$		0			0
$466$	1.59855	−	1.90508i	0.0740516	−	0.0882512i
$467$	7.20694	−	26.8967i	0.333497	−	1.24463i	−0.571992	−	0.820259i	$-0.693829\pi$
$467$	7.20694	−	26.8967i	0.333497	−	1.24463i	0.905489	−	0.424369i	$-0.139504\pi$
$468$		0			0
$469$	−1.59612	+	0.580940i	−0.0737020	+	0.0268253i
$470$	−7.94484	−	5.19911i	−0.366468	−	0.239817i
$471$		0			0
$472$	−6.48947	−	13.9167i	−0.298702	−	0.640569i
$473$	−0.345373	+	3.94764i	−0.0158803	+	0.181513i
$474$		0			0
$475$	21.4354	+	3.93984i	0.983525	+	0.180772i
$476$	−2.02698			−0.0929065
$477$		0			0
$478$	−2.93638	−	6.29708i	−0.134307	−	0.288022i
$479$	−10.9665	−	1.93369i	−0.501073	−	0.0883527i	−0.0826015	−	0.996583i	$-0.526323\pi$
$479$	−10.9665	−	1.93369i	−0.501073	−	0.0883527i	−0.418471	+	0.908230i	$0.637434\pi$
$480$		0			0
$481$	14.6259	−	5.32340i	0.666884	−	0.242726i
$482$	20.1163	−	5.39015i	0.916273	−	0.245515i
$483$		0			0
$484$	−0.478258	+	0.569966i	−0.0217390	+	0.0259076i
$485$	3.56937	−	4.53573i	0.162077	−	0.205957i
$486$		0			0
$487$	−3.42834	−	12.7948i	−0.155353	−	0.579786i	−0.999075	−	0.0430050i	$-0.986307\pi$
$487$	−3.42834	−	12.7948i	−0.155353	−	0.579786i	0.843722	−	0.536781i	$-0.180360\pi$
$488$	−21.1277	−	9.85199i	−0.956404	−	0.445979i
$489$		0			0
$490$	−1.54576	+	10.7258i	−0.0698302	+	0.484542i
$491$	−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
$497$	0.382692	−	0.178452i	0.0171661	−	0.00800467i
$498$		0			0
$499$	2.91253	−	0.513558i	0.130383	−	0.0229900i	−0.108076	−	0.994143i	$-0.534469\pi$
$499$	2.91253	−	0.513558i	0.130383	−	0.0229900i	0.238459	+	0.971153i	$0.423358\pi$
$500$	5.68470	−	15.9624i	0.254227	−	0.713861i
$501$		0			0
$502$	17.6647	+	4.73325i	0.788415	+	0.211255i
$503$	17.4641	−	1.52791i	0.778684	−	0.0681261i	0.309119	−	0.951024i	$-0.399966\pi$
$503$	17.4641	−	1.52791i	0.778684	−	0.0681261i	0.469566	+	0.882897i	$0.344410\pi$
$504$		0			0
$505$	29.5523	+	6.93186i	1.31506	+	0.308464i
$506$	10.6768	+	6.16428i	0.474644	+	0.274036i
$507$		0			0
$508$	−16.3720	+	23.3817i	−0.726391	+	1.03739i
$509$	−1.28121	+	7.26613i	−0.0567888	+	0.322066i	−0.999947	−	0.0102782i	$-0.996728\pi$
$509$	−1.28121	+	7.26613i	−0.0567888	+	0.322066i	0.943158	+	0.332344i	$0.107839\pi$
$510$		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
$515$	−19.7097	+	17.6220i	−0.868513	+	0.776519i
$516$		0			0
$517$	−16.9403	+	11.8618i	−0.745036	+	0.521680i
$518$	−0.792113	−	0.554643i	−0.0348034	−	0.0243696i
$519$		0			0
$520$	11.3101	−	3.41455i	0.495980	−	0.149738i
$521$	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
$523$	−3.35093	−	38.3013i	−0.146526	−	1.67480i	−0.612862	−	0.790190i	$-0.709982\pi$
$523$	−3.35093	−	38.3013i	−0.146526	−	1.67480i	0.466336	−	0.884608i	$-0.345574\pi$
$524$	18.4721	−	10.6649i	0.806959	−	0.465898i
$525$		0			0
$526$	−1.45210	−	3.98961i	−0.0633146	−	0.173955i
$527$	−12.4177	−	8.69495i	−0.540923	−	0.378758i
$528$		0			0
$529$	−1.47210	+	4.04455i	−0.0640041	+	0.175850i
$530$	1.03198	−	18.4537i	0.0448262	−	0.801579i
$531$		0			0
$532$	−0.617550	+	1.11349i	−0.0267742	+	0.0482757i
$533$	13.1025	−	13.1025i	0.567531	−	0.567531i
$534$		0			0
$535$	7.02790	−	21.3745i	0.303843	−	0.924100i
$536$	−3.74450	+	21.2361i	−0.161738	+	0.917260i
$537$		0			0
$538$	−4.73370	+	10.1514i	−0.204084	+	0.437660i
$539$	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	$0.902749\pi$
$542$	5.24767	−	0.459111i	0.225407	−	0.0197205i
$543$		0			0
$544$	−20.1864	+	34.9638i	−0.865484	+	1.49906i
$545$	5.07388	−	11.8378i	0.217341	−	0.507076i
$546$		0			0
$547$	−3.89861	−	5.56779i	−0.166693	−	0.238062i	0.727111	−	0.686519i	$-0.240862\pi$
$547$	−3.89861	−	5.56779i	−0.166693	−	0.238062i	−0.893804	+	0.448458i	$0.851973\pi$
$548$	−9.86531	+	4.60027i	−0.421425	+	0.196514i
$549$		0			0
$550$	8.84878	+	7.80168i	0.377313	+	0.332665i
$551$	27.8661	−	7.98355i	1.18714	−	0.340111i
$552$		0			0
$553$	1.47608	+	0.129140i	0.0627694	+	0.00549161i
$554$	−8.92295	−	3.24769i	−0.379100	−	0.137981i
$555$		0			0
$556$	−3.82011	−	21.6649i	−0.162009	−	0.918797i
$557$	24.8095	+	11.5689i	1.05121	+	0.490188i	0.869895	−	0.493236i	$-0.164186\pi$
$557$	24.8095	+	11.5689i	1.05121	+	0.490188i	0.181317	+	0.983425i	$0.441964\pi$
$558$		0			0
$559$	−1.26209	−	2.18601i	−0.0533809	−	0.0924585i
$560$	0.449784	+	0.353955i	0.0190069	+	0.0149573i
$561$		0			0
$562$	4.82631	−	18.0120i	0.203585	−	0.759791i
$563$	−17.9741	+	4.81614i	−0.757517	+	0.202976i	−0.616850	−	0.787081i	$-0.711592\pi$
$563$	−17.9741	+	4.81614i	−0.757517	+	0.202976i	−0.140667	+	0.990057i	$0.544925\pi$
$564$		0			0
$565$	1.79504	+	8.59296i	0.0755179	+	0.361509i
$566$	−5.17713	−	0.912867i	−0.217611	−	0.0383707i
$567$		0			0
$568$	0.467211	−	5.34025i	0.0196037	−	0.224072i
$569$	7.34466			0.307904			0.153952	−	0.988078i	$-0.450800\pi$
$569$	7.34466			0.307904			0.153952	+	0.988078i	$0.450800\pi$
$570$		0			0
$571$	−20.8079			−0.870783			−0.435392	−	0.900241i	$-0.643390\pi$
$571$	−20.8079			−0.870783			−0.435392	+	0.900241i	$0.643390\pi$
$572$	0.966837	−	11.0510i	0.0404255	−	0.462065i
$573$		0			0
$574$	−1.13372	−	0.199905i	−0.0473205	−	0.00834388i
$575$	−13.6129	+	22.3001i	−0.567695	+	0.929977i
$576$		0			0
$577$	−26.2847	+	7.04295i	−1.09424	+	0.293202i	−0.760419	−	0.649433i	$-0.775006\pi$
$577$	−26.2847	+	7.04295i	−1.09424	+	0.293202i	−0.333826	+	0.942635i	$0.608340\pi$
$578$	−5.61175	+	20.9433i	−0.233418	+	0.871127i
$579$		0			0
$580$	−2.66811	−	22.3780i	−0.110787	−	0.929198i
$581$	−0.258539	−	0.447804i	−0.0107260	−	0.0185780i
$582$		0			0
$583$	−36.4846	−	17.0131i	−1.51104	−	0.704609i
$584$	−3.68057	−	20.8736i	−0.152303	−	0.863755i
$585$		0			0
$586$	7.96154	+	2.89776i	0.328888	+	0.119706i
$587$	−41.5493	−	3.63509i	−1.71492	−	0.150036i	−0.813094	−	0.582132i	$-0.802219\pi$
$587$	−41.5493	−	3.63509i	−1.71492	−	0.150036i	−0.901828	+	0.432096i	$0.857774\pi$
$588$		0			0
$589$	−8.55965	+	4.17238i	−0.352694	+	0.171920i
$590$	0.306649	+	9.76198i	0.0126246	+	0.401894i
$591$		0			0
$592$	8.67591	−	4.04564i	0.356578	−	0.166275i
$593$	19.1517	+	27.3514i	0.786465	+	1.12319i	0.989573	+	0.144032i	$0.0460067\pi$
$593$	19.1517	+	27.3514i	0.786465	+	1.12319i	−0.203108	+	0.979156i	$0.565104\pi$
$594$		0			0
$595$	2.74877	+	1.17817i	0.112689	+	0.0483003i
$596$	−6.09398	+	10.5551i	−0.249619	+	0.432353i
$597$		0			0
$598$	−7.82323	+	0.684444i	−0.319915	+	0.0279890i
$599$	−17.9102	−	15.0284i	−0.731790	−	0.614044i	0.198829	−	0.980034i	$-0.436286\pi$
$599$	−17.9102	−	15.0284i	−0.731790	−	0.614044i	−0.930619	+	0.365990i	$0.880731\pi$
$600$		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	$0.417667\pi$
$602$	−0.0662759	+	0.142129i	−0.00270120	+	0.00579275i
$603$		0			0
$604$	3.59874	−	20.4095i	0.146431	−	0.830450i
$605$	0.979852	−	0.494942i	0.0398366	−	0.0201223i
$606$		0			0
$607$	21.4554	−	21.4554i	0.870849	−	0.870849i	−0.121716	−	0.992565i	$-0.538840\pi$
$607$	21.4554	−	21.4554i	0.870849	−	0.870849i	0.992565	+	0.121716i	$0.0388398\pi$
$608$	13.0567	+	21.7413i	0.529518	+	0.881726i
$609$		0			0
$610$	9.88283	+	11.0536i	0.400144	+	0.447549i
$611$	4.50545	−	12.3786i	0.182271	−	0.500786i
$612$		0			0
$613$	7.69485	+	5.38799i	0.310792	+	0.217619i	0.718557	−	0.695468i	$-0.244803\pi$
$613$	7.69485	+	5.38799i	0.310792	+	0.217619i	−0.407765	+	0.913087i	$0.633692\pi$
$614$	−6.85954	−	18.8464i	−0.276829	−	0.760580i
$615$		0			0
$616$	−1.38451	+	0.799345i	−0.0557833	+	0.0322065i
$617$	−0.438877	−	5.01638i	−0.0176685	−	0.201952i	−0.999898	−	0.0142691i	$-0.995458\pi$
$617$	−0.438877	−	5.01638i	−0.0176685	−	0.201952i	0.982230	−	0.187683i	$-0.0600977\pi$
$618$		0			0
$619$	−33.8862	+	19.5642i	−1.36200	+	0.786352i	−0.989890	−	0.141836i	$-0.954699\pi$
$619$	−33.8862	+	19.5642i	−1.36200	+	0.786352i	−0.372112	+	0.928188i	$0.621366\pi$
$620$	2.13971	+	7.08740i	0.0859327	+	0.284637i
$621$		0			0
$622$	−10.5628	−	7.39614i	−0.423529	−	0.296558i
$623$	−0.0783323	+	0.0548488i	−0.00313832	+	0.00219747i
$624$		0			0
$625$	−16.9870	+	18.3423i	−0.679481	+	0.733693i
$626$		−	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	$0.685978\pi$
$632$	10.7895	−	15.4090i	0.429183	−	0.612937i
$633$		0			0
$634$	3.16959	+	1.82996i	0.125880	+	0.0726771i
$635$	35.7924	−	22.1916i	1.42038	−	0.880646i
$636$		0			0
$637$	−14.9775	+	1.31036i	−0.593429	+	0.0519183i
$638$	15.1556	+	4.06092i	0.600014	+	0.160773i
$639$		0			0
$640$	22.1452	−	8.85710i	0.875366	−	0.350108i
$641$	−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
$643$	19.9256	−	9.29147i	0.785790	−	0.366420i	0.0120533	−	0.999927i	$-0.496163\pi$
$643$	19.9256	−	9.29147i	0.785790	−	0.366420i	0.773737	+	0.633508i	$0.218385\pi$
$644$	−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	0.547921	−	0.836530i	$-0.315419\pi$
$647$	−7.34110	−	7.34110i	−0.288608	−	0.288608i	−0.836530	+	0.547921i	$0.815419\pi$
$648$		0			0
$649$	19.9899	+	7.27571i	0.784670	+	0.285597i
$650$	−7.46760	−	0.837832i	−0.292903	−	0.0328625i
$651$		0			0
$652$	19.6836	+	9.17861i	0.770869	+	0.359462i
$653$	−4.13442	−	15.4299i	−0.161792	−	0.603817i	−0.998428	−	0.0560567i	$-0.982147\pi$
$653$	−4.13442	−	15.4299i	−0.161792	−	0.603817i	0.836635	−	0.547760i	$-0.184519\pi$
$654$		0			0
$655$	−31.2488	+	3.72577i	−1.22099	+	0.145578i
$656$	7.32551	−	8.73021i	0.286013	−	0.340857i
$657$		0			0
$658$	−0.790526	+	0.211821i	−0.0308179	+	0.00825764i
$659$	27.1741	−	9.89056i	1.05855	−	0.385281i	0.246668	−	0.969100i	$-0.420664\pi$
$659$	27.1741	−	9.89056i	1.05855	−	0.385281i	0.811884	+	0.583819i	$0.198442\pi$
$660$		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	$0.410018\pi$
$662$	3.44653	+	7.39111i	0.133953	+	0.287263i
$663$		0			0
$664$	−6.56448			−0.254751
$665$	1.48466	−	1.15104i	0.0575727	−	0.0446355i
$666$		0			0
$667$	−3.02858	+	34.6169i	−0.117267	+	1.34037i
$668$	−4.87520	−	10.4549i	−0.188627	−	0.404512i
$669$		0			0
$670$	7.51030	−	11.4766i	0.290148	−	0.443380i
$671$	30.3476	−	11.0456i	1.17156	−	0.426411i
$672$		0			0
$673$	−4.59706	+	17.1565i	−0.177204	+	0.661333i	0.818962	+	0.573848i	$0.194550\pi$
$673$	−4.59706	+	17.1565i	−0.177204	+	0.661333i	−0.996166	+	0.0874854i	$0.972117\pi$
$674$	−5.65193	+	6.73571i	−0.217704	+	0.259450i
$675$		0			0
$676$	−6.31803	−	10.9431i	−0.243001	−	0.420890i
$677$	−0.0823506	−	0.307337i	−0.00316499	−	0.0118119i	0.964325	−	0.264720i	$-0.0852796\pi$
$677$	−0.0823506	−	0.307337i	−0.00316499	−	0.0118119i	−0.967490	+	0.252908i	$0.918613\pi$
$678$		0			0
$679$	−0.0863903	−	0.489944i	−0.00331536	−	0.0188023i
$680$	30.4016	−	22.7427i	1.16585	−	0.872142i
$681$		0			0
$682$	−5.13468	−	0.449226i	−0.196617	−	0.0172017i
$683$	−17.2283	−	17.2283i	−0.659224	−	0.659224i	0.295973	−	0.955196i	$-0.404356\pi$
$683$	−17.2283	−	17.2283i	−0.659224	−	0.659224i	−0.955196	+	0.295973i	$0.904356\pi$
$684$		0			0
$685$	16.0521	−	0.504240i	0.613321	−	0.0192660i
$686$	1.20402	+	1.43490i	0.0459697	+	0.0547846i
$687$		0			0
$688$	−0.890463	−	1.27171i	−0.0339486	−	0.0484836i
$689$	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	$0.327155\pi$
$692$	21.3865	+	5.73049i	0.812992	+	0.217840i
$693$		0			0
$694$	−10.0986	−	8.47376i	−0.383339	−	0.321660i
$695$	−7.41218	+	31.6000i	−0.281160	+	1.19866i
$696$		0			0
$697$	25.1661	−	53.9688i	0.953233	−	2.04421i
$698$	−13.2747	+	18.9582i	−0.502455	+	0.717579i
$699$		0			0
$700$	−0.699115	−	1.28235i	−0.0264241	−	0.0484683i
$701$	−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
$703$	−5.98813	−	30.8442i	−0.225847	−	1.16331i
$704$			4.72357i			0.178026i
$705$		0			0
$706$	−0.0149671	+	0.0411219i	−0.000563296	+	0.00154764i
$707$	2.14325	−	1.50072i	0.0806052	−	0.0564404i
$708$		0			0
$709$	−16.6116	−	45.6401i	−0.623863	−	1.71405i	−0.697329	−	0.716751i	$-0.745628\pi$
$709$	−16.6116	−	45.6401i	−0.623863	−	1.71405i	0.0734667	−	0.997298i	$-0.476594\pi$
$710$	−1.61127	+	3.00490i	−0.0604697	+	0.112772i
$711$		0			0
$712$	0.105807	+	1.20938i	0.00396530	+	0.0453235i
$713$	−0.994902	−	11.3718i	−0.0372594	−	0.425877i
$714$		0			0
$715$	−7.73444	+	14.4242i	−0.289252	+	0.539434i
$716$	−1.82538	−	5.01519i	−0.0682176	−	0.187426i
$717$		0			0
$718$	−14.3555	+	10.0519i	−0.535744	+	0.375132i
$719$	13.1205	−	36.0482i	0.489311	−	1.34437i	−0.411994	−	0.911187i	$-0.635168\pi$
$719$	13.1205	−	36.0482i	0.489311	−	1.34437i	0.901305	−	0.433185i	$-0.142610\pi$
$720$		0			0
$721$			2.27891i			0.0848711i
$722$	12.6483	−	3.86061i	0.470720	−	0.143677i
$723$		0			0
$724$	22.6515	−	19.0068i	0.841835	−	0.706383i
$725$	−9.38890	+	31.8975i	−0.348695	+	1.18464i
$726$		0			0
$727$	−13.0804	+	18.6808i	−0.485126	+	0.692831i	−0.984861	−	0.173347i	$-0.944542\pi$
$727$	−13.0804	+	18.6808i	−0.485126	+	0.692831i	0.499735	+	0.866178i	$0.333431\pi$
$728$	0.430370	−	0.922931i	0.0159506	−	0.0342061i
$729$		0			0
$730$	−3.07868	+	13.1252i	−0.113947	+	0.485785i
$731$	−6.21405	−	5.21421i	−0.229835	−	0.192854i
$732$		0			0
$733$	43.8346	+	11.7454i	1.61907	+	0.433828i	0.950727	−	0.310028i	$-0.100339\pi$
$733$	43.8346	+	11.7454i	1.61907	+	0.433828i	0.668340	+	0.743856i	$0.267005\pi$
$734$	−4.44672	+	7.70195i	−0.164132	+	0.284284i
$735$		0			0
$736$	−29.9398	+	5.27919i	−1.10359	+	0.194593i
$737$	−17.1347	−	24.4709i	−0.631166	−	0.901398i
$738$		0			0
$739$	−15.2269	−	18.1467i	−0.560131	−	0.667538i	0.409443	−	0.912336i	$-0.365723\pi$
$739$	−15.2269	−	18.1467i	−0.560131	−	0.667538i	−0.969574	+	0.244797i	$0.921279\pi$
$740$	−24.4160	+	0.766969i	−0.897548	+	0.0281944i
$741$		0			0
$742$	−1.12651	−	1.12651i	−0.0413553	−	0.0413553i
$743$	−9.96374	−	0.871715i	−0.365534	−	0.0319801i	−0.0970908	−	0.995276i	$-0.530954\pi$
$743$	−9.96374	−	0.871715i	−0.365534	−	0.0319801i	−0.268444	+	0.963295i	$0.586509\pi$
$744$		0			0
$745$	14.3991	−	10.7716i	0.527541	−	0.394640i
$746$	−0.200384	−	1.13643i	−0.00733657	−	0.0416078i
$747$		0			0
$748$	−9.22682	−	34.4350i	−0.337366	−	1.25907i
$749$	−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	$0.273092\pi$
$752$	2.09694	−	7.82588i	0.0764675	−	0.285380i
$753$		0			0
$754$	−9.39167	+	3.41829i	−0.342025	+	0.124487i
$755$	−16.7431	+	25.5854i	−0.609344	+	0.931147i
$756$		0			0
$757$	18.0520	+	38.7126i	0.656111	+	1.40703i	0.899420	+	0.437085i	$0.143989\pi$
$757$	18.0520	+	38.7126i	0.656111	+	1.40703i	−0.243309	+	0.969949i	$0.578233\pi$
$758$	1.02921	−	11.7640i	0.0373827	−	0.427286i
$759$		0			0
$760$	−3.23097	−	23.6295i	−0.117200	−	0.857132i
$761$	−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
$763$	−0.469169	−	1.00614i	−0.0169850	−	0.0364246i
$764$	−30.0721	−	5.30253i	−1.08797	−	0.191839i
$765$		0			0
$766$	9.46949	−	3.44661i	0.342147	−	0.124531i
$767$	−13.0887	+	3.50711i	−0.472606	+	0.126634i
$768$		0			0
$769$	−7.06802	+	8.42334i	−0.254879	+	0.303753i	−0.878278	−	0.478151i	$-0.841307\pi$
$769$	−7.06802	+	8.42334i	−0.254879	+	0.303753i	0.623398	+	0.781905i	$0.285752\pi$
$770$	1.00969	−	0.120385i	0.0363868	−	0.00433837i
$771$		0			0
$772$	−2.38168	−	8.88856i	−0.0857186	−	0.319906i
$773$	−12.1656	−	5.67290i	−0.437566	−	0.204040i	0.191337	−	0.981524i	$-0.438718\pi$
$773$	−12.1656	−	5.67290i	−0.437566	−	0.204040i	−0.628902	+	0.777484i	$0.716496\pi$
$774$		0			0
$775$	1.21787	−	10.8549i	0.0437471	−	0.389918i
$776$	−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
$782$	−22.8726	+	10.6657i	−0.817924	+	0.381404i
$783$		0			0
$784$	−9.10642	+	1.60571i	−0.325229	+	0.0573467i
$785$	31.1982	−	12.4779i	1.11351	−	0.445356i
$786$		0			0
$787$	−40.2335	−	10.7805i	−1.43417	−	0.384284i	−0.543681	−	0.839292i	$-0.682970\pi$
$787$	−40.2335	−	10.7805i	−1.43417	−	0.384284i	−0.890487	+	0.455008i	$0.849636\pi$
$788$	−25.2838	+	2.21204i	−0.900698	+	0.0788008i
$789$		0			0
$790$	−10.1688	+	6.30471i	−0.361788	+	0.224311i
$791$	0.655292	+	0.378333i	0.0232995	+	0.0134520i
$792$		0			0
$793$	−11.7994	+	16.8512i	−0.419008	+	0.598405i
$794$	−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	−0.230923	+	0.972972i	$0.574174\pi$
$797$	−33.9874	+	33.9874i	−1.20389	+	1.20389i	−0.972972	+	0.230923i	$0.925826\pi$
$798$		0			0
$799$		−	42.3337i		−	1.49766i
$800$	−29.0819	−	0.711540i	−1.02820	−	0.0251567i
$801$		0			0
$802$	−10.1680	+	7.11968i	−0.359043	+	0.251405i
$803$	24.0532	+	16.8422i	0.848818	+	0.594349i
$804$		0			0
$805$	0.650873	+	2.15590i	0.0229403	+	0.0759856i
$806$	2.84334	−	1.64160i	0.100152	−	0.0578230i
$807$		0			0
$808$	−2.89500	−	33.0900i	−0.101846	−	1.16410i
$809$	−32.3657	+	18.6864i	−1.13792	+	0.656977i	−0.945914	−	0.324417i	$-0.894832\pi$
$809$	−32.3657	+	18.6864i	−1.13792	+	0.656977i	−0.192004	+	0.981394i	$0.561499\pi$
$810$		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	$0.952217\pi$
$812$	−1.59125	−	1.11420i	−0.0558419	−	0.0391009i
$813$		0			0
$814$	5.81675	−	15.9814i	0.203877	−	0.560147i
$815$	−21.3578	−	23.8880i	−0.748130	−	0.836760i
$816$		0			0
$817$	−4.75754	+	1.82499i	−0.166445	+	0.0638484i
$818$	−12.2491	+	12.2491i	−0.428280	+	0.428280i
$819$		0			0
$820$	−25.9581	+	13.1119i	−0.906494	+	0.457888i
$821$	−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
$823$	9.48508	−	20.3408i	0.330629	−	0.709036i	−0.668778	−	0.743462i	$-0.733182\pi$
$823$	9.48508	−	20.3408i	0.330629	−	0.709036i	0.999407	+	0.0344257i	$0.0109602\pi$
$824$	25.0554	+	14.4658i	0.872847	+	0.503938i
$825$		0			0
$826$	0.644900	+	0.541135i	0.0224389	+	0.0188285i
$827$	22.0212	−	1.92661i	0.765752	−	0.0669946i	0.302415	−	0.953176i	$-0.402207\pi$
$827$	22.0212	−	1.92661i	0.765752	−	0.0669946i	0.463338	+	0.886182i	$0.346652\pi$
$828$		0			0
$829$	5.19218	−	8.99311i	0.180332	−	0.312344i	−0.761662	−	0.647975i	$-0.775616\pi$
$829$	5.19218	−	8.99311i	0.180332	−	0.312344i	0.941994	+	0.335631i	$0.108950\pi$
$830$	3.83767	+	1.64489i	0.133208	+	0.0570950i
$831$		0			0
$832$	−1.72580	−	2.46470i	−0.0598313	−	0.0854480i
$833$	−43.7893	+	20.4193i	−1.51721	+	0.707487i
$834$		0			0
$835$	0.534375	+	17.0115i	0.0184928	+	0.588706i
$836$	−21.7273	−	5.42254i	−0.751455	−	0.187543i
$837$		0			0
$838$	0.926657	+	0.0810720i	0.0320108	+	0.00280059i
$839$	36.6781	+	13.3497i	1.26627	+	0.460885i	0.885868	−	0.463937i	$-0.153564\pi$
$839$	36.6781	+	13.3497i	1.26627	+	0.460885i	0.380402	+	0.924821i	$0.375786\pi$
$840$		0			0
$841$	2.64364	+	14.9928i	0.0911601	+	0.516995i
$842$	−7.77777	−	3.62683i	−0.268040	−	0.124989i
$843$		0			0
$844$	1.62316	+	2.81139i	0.0558713	+	0.0967720i
$845$	2.20719	+	18.5122i	0.0759298	+	0.636840i
$846$		0			0
$847$	0.0244901	−	0.0913982i	0.000841489	−	0.00314048i
$848$	15.2338	−	4.08189i	0.523132	−	0.140173i
$849$		0			0
$850$	−23.4719	+	5.67777i	−0.805079	+	0.194746i
$851$	37.0933	+	6.54055i	1.27154	+	0.224207i
$852$		0			0
$853$	2.03539	−	23.2647i	0.0696906	−	0.796567i	−0.878267	−	0.478170i	$-0.841300\pi$
$853$	2.03539	−	23.2647i	0.0696906	−	0.796567i	0.947958	−	0.318396i	$-0.103144\pi$
$854$	1.27807			0.0437345
$855$		0			0
$856$	−24.6217			−0.841551
$857$	2.89487	−	33.0886i	0.0988870	−	1.13028i	−0.770934	−	0.636916i	$-0.780210\pi$
$857$	2.89487	−	33.0886i	0.0988870	−	1.13028i	0.869821	−	0.493368i	$-0.164234\pi$
$858$		0			0
$859$	−22.5330	−	3.97318i	−0.768817	−	0.135563i	−0.224536	−	0.974466i	$-0.572087\pi$
$859$	−22.5330	−	3.97318i	−0.768817	−	0.135563i	−0.544282	+	0.838903i	$0.683198\pi$
$860$	0.810083	+	3.87791i	0.0276236	+	0.132236i
$861$		0			0
$862$	4.91961	−	1.31821i	0.167563	−	0.0448983i
$863$	−1.89020	+	7.05432i	−0.0643431	+	0.240132i	−0.990606	−	0.136746i	$-0.956336\pi$
$863$	−1.89020	+	7.05432i	−0.0643431	+	0.240132i	0.926263	+	0.376878i	$0.123002\pi$
$864$		0			0
$865$	−25.6712	−	20.2018i	−0.872848	−	0.686883i
$866$	−4.58169	−	7.93572i	−0.155692	−	0.269667i
$867$		0			0
$868$	0.578349	+	0.269689i	0.0196305	+	0.00915383i
$869$	4.52525	+	25.6640i	0.153509	+	0.870590i
$870$		0			0
$871$	17.8814	+	6.50829i	0.605887	+	0.220525i
$872$	−14.0400	−	1.22834i	−0.475456	−	0.0415970i
$873$		0			0
$874$	−1.10949	+	15.8141i	−0.0375290	+	0.534921i
$875$	0.202706	+	2.14534i	0.00685271	+	0.0725258i
$876$		0			0
$877$	4.77219	−	2.22531i	0.161145	−	0.0751433i	−0.340372	−	0.940291i	$-0.610553\pi$
$877$	4.77219	−	2.22531i	0.161145	−	0.0751433i	0.501517	+	0.865148i	$0.332775\pi$
$878$	4.38283	+	6.25934i	0.147913	+	0.211242i
$879$		0			0
$880$	−3.96568	+	9.25228i	−0.133683	+	0.311894i
$881$	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
$883$	−49.0599	+	4.29218i	−1.65100	+	0.144443i	−0.874285	−	0.485413i	$-0.838669\pi$
$883$	−49.0599	+	4.29218i	−1.65100	+	0.144443i	−0.776711	+	0.629857i	$0.783114\pi$
$884$	17.3956	+	14.5966i	0.585077	+	0.490938i
$885$		0			0
$886$	−18.5927	−	10.7345i	−0.624633	−	0.360632i
$887$	−22.6726	+	48.6214i	−0.761270	+	1.63255i	0.0131801	+	0.999913i	$0.495805\pi$
$887$	−22.6726	+	48.6214i	−0.761270	+	1.63255i	−0.774450	+	0.632635i	$0.781973\pi$
$888$		0			0
$889$	0.630348	−	3.57488i	0.0211412	−	0.119898i
$890$	0.241184	−	0.733532i	0.00808451	−	0.0245881i
$891$		0			0
$892$	−19.2631	+	19.2631i	−0.644976	+	0.644976i
$893$	−23.2552	−	12.8976i	−0.778207	−	0.431601i
$894$		0			0
$895$	−0.439664	+	7.86205i	−0.0146964	+	0.262799i
$896$	0.703137	−	1.93185i	0.0234902	−	0.0645387i
$897$		0			0
$898$	−2.27096	−	1.59014i	−0.0757829	−	0.0530637i
$899$	−4.96880	−	13.6517i	−0.165719	−	0.455309i
$900$		0			0
$901$	71.3662	−	41.2033i	2.37755	−	1.37268i
$902$	−1.76464	−	20.1699i	−0.0587560	−	0.671585i
$903$		0			0
$904$	8.31914	−	4.80306i	0.276691	−	0.159747i
$905$	−41.7651	+	12.6090i	−1.38832	+	0.419137i
$906$		0			0
$907$	−32.5649	−	22.8022i	−1.08130	−	0.757135i	−0.109749	−	0.993959i	$-0.535005\pi$
$907$	−32.5649	−	22.8022i	−1.08130	−	0.757135i	−0.971553	+	0.236824i	$0.923893\pi$
$908$	−7.27674	+	5.09523i	−0.241487	+	0.169091i
$909$		0			0
$910$	−0.482862	+	0.431717i	−0.0160067	+	0.0143113i
$911$		−	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
$917$	−1.55588	+	2.22203i	−0.0513797	+	0.0733779i
$918$		0			0
$919$	35.2152	+	20.3315i	1.16164	+	0.670675i	0.951697	−	0.307038i	$-0.0993377\pi$
$919$	35.2152	+	20.3315i	1.16164	+	0.670675i	0.209946	+	0.977713i	$0.432671\pi$
$920$	27.8345	+	6.52893i	0.917677	+	0.215252i
$921$		0			0
$922$	7.28378	−	0.637248i	0.239878	−	0.0209866i
$923$	−4.56933	−	1.22435i	−0.150401	−	0.0402999i
$924$		0			0
$925$	33.5561	+	13.1515i	1.10332	+	0.432420i
$926$	−4.39155	+	0.774349i	−0.144315	+	0.0254467i
$927$		0			0
$928$	−35.0662	+	16.3516i	−1.15110	+	0.536768i
$929$	−7.31492	−	8.71758i	−0.239995	−	0.286014i	0.632580	−	0.774495i	$-0.281996\pi$
$929$	−7.31492	−	8.71758i	−0.239995	−	0.286014i	−0.872575	+	0.488480i	$0.837551\pi$
$930$		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
$935$	−7.50269	+	52.0600i	−0.245364	+	1.70254i
$936$		0			0
$937$	−32.3604	−	15.0899i	−1.05717	−	0.492965i	−0.185287	−	0.982684i	$-0.559322\pi$
$937$	−32.3604	−	15.0899i	−1.05717	−	0.492965i	−0.871880	+	0.489719i	$0.837099\pi$
$938$	−0.305983	−	1.14194i	−0.00999069	−	0.0372858i
$939$		0			0
$940$	−12.7856	+	16.2471i	−0.417020	+	0.529923i
$941$	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
$943$	43.3131	−	11.6057i	1.41047	−	0.377934i
$944$	−7.83143	+	2.85041i	−0.254891	+	0.0927729i
$945$		0			0
$946$	−2.71622	−	0.478943i	−0.0883120	−	0.0155718i
$947$	2.42624	+	5.20308i	0.0788421	+	0.169077i	0.941777	−	0.336237i	$-0.109154\pi$
$947$	2.42624	+	5.20308i	0.0788421	+	0.169077i	−0.862935	+	0.505314i	$0.831377\pi$
$948$		0			0
$949$	−18.7041			−0.607161
$950$	−4.03208	+	14.6237i	−0.130818	+	0.474455i
$951$		0			0
$952$	0.285225	−	3.26014i	0.00924421	−	0.105662i
$953$	5.81151	+	12.4628i	0.188253	+	0.403710i	0.977670	−	0.210148i	$-0.0673945\pi$
$953$	5.81151	+	12.4628i	0.188253	+	0.403710i	−0.789416	+	0.613858i	$0.789617\pi$
$954$		0			0
$955$	37.6985	+	24.6700i	1.21990	+	0.798301i
$956$	−14.2168	+	5.17449i	−0.459804	+	0.167355i
$957$		0			0
$958$	2.00602	−	7.48655i	0.0648114	−	0.241879i
$959$	0.889818	−	1.06044i	0.0287337	−	0.0342435i
$960$		0			0
$961$	−13.1138	−	22.7137i	−0.423025	−	0.732701i
$962$	2.80385	+	10.4641i	0.0903996	+	0.337376i
$963$		0			0
$964$	−7.87457	−	44.6589i	−0.253623	−	1.43837i
$965$	−1.93664	+	13.4380i	−0.0623426	+	0.432586i
$966$		0			0
$967$	55.1255	+	4.82286i	1.77272	+	0.155093i	0.926142	−	0.377175i	$-0.123104\pi$
$967$	55.1255	+	4.82286i	1.77272	+	0.155093i	0.846576	+	0.532268i	$0.178660\pi$
$968$	−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
$973$	1.60471	+	2.29176i	0.0514445	+	0.0734704i
$974$	9.07947	−	1.60096i	0.290925	−	0.0512979i
$975$		0			0
$976$	−6.32616	+	10.9572i	−0.202495	+	0.350732i
$977$	−32.2855	−	8.65086i	−1.03290	−	0.276766i	−0.297734	−	0.954649i	$-0.596231\pi$
$977$	−32.2855	−	8.65086i	−1.03290	−	0.276766i	−0.735170	+	0.677883i	$0.762897\pi$
$978$		0			0
$979$	−1.28836	−	1.08106i	−0.0411761	−	0.0345508i
$980$	22.9728	+	5.38856i	0.733840	+	0.172131i
$981$		0			0
$982$	0.907332	−	1.94578i	0.0289541	−	0.0620923i
$983$	0.101670	−	0.145200i	0.00324277	−	0.00463116i	−0.817527	−	0.575890i	$-0.804656\pi$
$983$	0.101670	−	0.145200i	0.00324277	−	0.00463116i	0.820770	+	0.571259i	$0.193545\pi$
$984$		0			0
$985$	35.5729	+	11.6963i	1.13345	+	0.372675i
$986$	−24.6042	+	20.6454i	−0.783559	+	0.657484i
$987$		0			0
$988$	13.3182	−	5.10887i	0.423709	−	0.162535i
$989$		−	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	$-0.119939\pi$
$992$	10.4116	−	7.29029i	0.330569	−	0.231467i
$993$		0			0
$994$	0.100518	+	0.276172i	0.00318825	+	0.00875965i
$995$	−21.0305	+	6.34917i	−0.666711	+	0.201282i
$996$		0			0
$997$	−0.306408	−	3.50226i	−0.00970404	−	0.110918i	0.989798	−	0.142479i	$-0.0455075\pi$
$997$	−0.306408	−	3.50226i	−0.00970404	−	0.110918i	−0.999502	+	0.0315617i	$0.989952\pi$
$998$	0.179406	+	2.05062i	0.00567899	+	0.0649111i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.bh.a.13.8	✓	240	15.8	even	4
285.2.bh.a.22.8	yes	240	57.41	even	18
285.2.bh.a.127.13	yes	240	3.2	odd	2
285.2.bh.a.193.13	yes	240	285.98	odd	36
855.2.dl.b.127.8		240	1.1	even	1	trivial
855.2.dl.b.298.13		240	5.3	odd	4	inner
855.2.dl.b.307.13		240	19.3	odd	18	inner
855.2.dl.b.478.8		240	95.3	even	36	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)

\(f(q)\)	\(=\)	\(q+(-0.0606620 + 0.693370i) q^{2} +(1.49253 + 0.263174i) q^{4} +(-1.87105 - 1.22441i) q^{5} +(-0.186172 + 0.0498847i) q^{7} +(-0.633303 + 2.36352i) q^{8} +(0.962473 - 1.22305i) q^{10} +(-1.69491 - 2.93568i) q^{11} +(1.95696 + 0.912547i) q^{13} +(-0.0232950 - 0.132112i) q^{14} +(1.24794 + 0.454214i) q^{16} +(6.91273 + 0.604786i) q^{17} +(2.43830 - 3.61313i) q^{19} +(-2.47036 - 2.31989i) q^{20} +(2.13833 - 0.997118i) q^{22} +(2.99713 + 4.28034i) q^{23} +(2.00162 + 4.58187i) q^{25} +(-0.751446 + 1.30154i) q^{26} +(-0.290997 + 0.0254589i) q^{28} +(5.09429 + 4.27462i) q^{29} +(-1.89191 - 1.09230i) q^{31} +(-2.45884 + 5.27301i) q^{32} +(-0.838680 + 4.75639i) q^{34} +(0.409417 + 0.134615i) q^{35} +(5.09701 - 5.09701i) q^{37} +(2.35732 + 1.90982i) q^{38} +(4.07886 - 3.64682i) q^{40} +(2.93503 - 8.06394i) q^{41} +(-0.957590 - 0.670512i) q^{43} +(-1.75712 - 4.82765i) q^{44} +(-3.14967 + 1.81846i) q^{46} +(-0.531712 - 6.07749i) q^{47} +(-6.03001 + 3.48143i) q^{49} +(-3.29835 + 1.10992i) q^{50} +(2.68067 + 1.87703i) q^{52} +(9.72794 - 6.81158i) q^{53} +(-0.423224 + 7.56806i) q^{55} -0.471614i q^{56} +(-3.27292 + 3.27292i) q^{58} +(-4.80729 + 4.03379i) q^{59} +(-1.65436 + 9.38236i) q^{61} +(0.872132 - 1.24553i) q^{62} +(-1.20677 - 0.696726i) q^{64} +(-2.54423 - 4.10355i) q^{65} +(8.77915 - 0.768076i) q^{67} +(10.1583 + 2.72191i) q^{68} +(-0.118174 + 0.275711i) q^{70} +(-2.15751 + 0.380428i) q^{71} +(-7.85066 + 3.66082i) q^{73} +(3.22492 + 3.84331i) q^{74} +(4.59012 - 4.75102i) q^{76} +(0.461992 + 0.461992i) q^{77} +(-7.22404 - 2.62934i) q^{79} +(-1.77881 - 2.37786i) q^{80} +(5.41325 + 2.52424i) q^{82} +(0.694355 + 2.59137i) q^{83} +(-12.1935 - 9.59563i) q^{85} +(0.523002 - 0.623290i) q^{86} +(8.01192 - 2.14679i) q^{88} +(0.466220 - 0.169690i) q^{89} +(-0.409855 - 0.0722684i) q^{91} +(3.34684 + 7.17732i) q^{92} +4.24620 q^{94} +(-8.98613 + 3.77484i) q^{95} +(-0.224967 + 2.57139i) q^{97} +(-2.04812 - 4.39221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{7} - 36 q^{16} - 120 q^{20} + 24 q^{22} - 24 q^{23} - 24 q^{25} + 24 q^{26} - 72 q^{28} + 12 q^{32} + 132 q^{38} - 132 q^{40} + 72 q^{41} - 108 q^{43} - 24 q^{47} - 36 q^{53} - 144 q^{58}+ \cdots - 192 q^{98}+O(q^{100}) \) 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