LMFDB - Embedded newform 702.2.bb.a.71.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.12
Character	$\chi$	$=$	702.71
Dual form			702.2.bb.a.89.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.339151 + 0.0908752i) q^{5} +(2.97685 - 0.797644i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.304074 - 0.175557i) q^{10} +(2.35360 - 2.35360i) q^{11} +(2.60734 + 2.49034i) q^{13} +(2.66897 + 1.54093i) q^{14} -1.00000 q^{16} +(-3.87756 - 6.71613i) q^{17} +(3.67410 + 0.984473i) q^{19} +(-0.0908752 - 0.339151i) q^{20} +3.32849 q^{22} +(3.34250 + 5.78938i) q^{23} +(-4.22336 + 2.43836i) q^{25} +(0.0827293 + 3.60460i) q^{26} +(0.797644 + 2.97685i) q^{28} +5.68973i q^{29} +(0.293661 + 1.09596i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.00717 - 7.49087i) q^{34} +(-0.937115 + 0.541044i) q^{35} +(8.90068 - 2.38493i) q^{37} +(1.90186 + 3.29411i) q^{38} +(0.175557 - 0.304074i) q^{40} +(0.678577 - 2.53248i) q^{41} +(-3.68906 - 2.12988i) q^{43} +(2.35360 + 2.35360i) q^{44} +(-1.73021 + 6.45722i) q^{46} +(4.17527 + 1.11876i) q^{47} +(2.16322 - 1.24894i) q^{49} +(-4.71055 - 1.26219i) q^{50} +(-2.49034 + 2.60734i) q^{52} +5.65439i q^{53} +(-0.584342 + 1.01211i) q^{55} +(-1.54093 + 2.66897i) q^{56} +(-4.02325 + 4.02325i) q^{58} +(-7.75962 + 7.75962i) q^{59} +(5.01742 - 8.69042i) q^{61} +(-0.567309 + 0.982608i) q^{62} -1.00000i q^{64} +(-1.11059 - 0.607659i) q^{65} +(-13.3180 - 3.56856i) q^{67} +(6.71613 - 3.87756i) q^{68} +(-1.04522 - 0.280065i) q^{70} +(0.343507 - 1.28199i) q^{71} +(-2.19140 - 2.19140i) q^{73} +(7.98013 + 4.60733i) q^{74} +(-0.984473 + 3.67410i) q^{76} +(5.12898 - 8.88365i) q^{77} +(-6.22990 - 10.7905i) q^{79} +(0.339151 - 0.0908752i) q^{80} +(2.27056 - 1.31091i) q^{82} +(1.05166 - 3.92483i) q^{83} +(1.92541 + 1.92541i) q^{85} +(-1.10251 - 4.11462i) q^{86} +3.32849i q^{88} +(-1.43929 - 5.37149i) q^{89} +(9.74806 + 5.33364i) q^{91} +(-5.78938 + 3.34250i) q^{92} +(2.16128 + 3.74344i) q^{94} -1.33554 q^{95} +(-0.218799 - 0.816569i) q^{97} +(2.41276 + 0.646496i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−0.339151	+	0.0908752i	−0.151673	+	0.0406406i	−0.333857	−	0.942624i	$-0.608350\pi$
$5$	−0.339151	+	0.0908752i	−0.151673	+	0.0406406i	0.182184	+	0.983265i	$0.441683\pi$
$6$		0			0
$7$	2.97685	−	0.797644i	1.12514	−	0.301481i	0.352180	−	0.935932i	$-0.385440\pi$
$7$	2.97685	−	0.797644i	1.12514	−	0.301481i	0.772963	+	0.634451i	$0.218774\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−0.304074	−	0.175557i	−0.0961568	−	0.0555161i
$11$	2.35360	−	2.35360i	0.709637	−	0.709637i	−0.256821	−	0.966459i	$-0.582675\pi$
$11$	2.35360	−	2.35360i	0.709637	−	0.709637i	0.966459	+	0.256821i	$0.0826752\pi$
$12$		0			0
$13$	2.60734	+	2.49034i	0.723145	+	0.690696i
$13$	2.60734	+	2.49034i	0.723145	+	0.690696i
$14$	2.66897	+	1.54093i	0.713312	+	0.411831i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.87756	−	6.71613i	−0.940446	−	1.62890i	−0.764622	−	0.644479i	$-0.777074\pi$
$17$	−3.87756	−	6.71613i	−0.940446	−	1.62890i	−0.175824	−	0.984422i	$-0.556259\pi$
$18$		0			0
$19$	3.67410	+	0.984473i	0.842897	+	0.225854i	0.654332	−	0.756207i	$-0.272950\pi$
$19$	3.67410	+	0.984473i	0.842897	+	0.225854i	0.188565	+	0.982061i	$0.439616\pi$
$20$	−0.0908752	−	0.339151i	−0.0203203	−	0.0758364i
$21$		0			0
$22$	3.32849			0.709637
$23$	3.34250	+	5.78938i	0.696960	+	1.20717i	0.969515	+	0.245030i	$0.0787978\pi$
$23$	3.34250	+	5.78938i	0.696960	+	1.20717i	−0.272556	+	0.962140i	$0.587869\pi$
$24$		0			0
$25$	−4.22336	+	2.43836i	−0.844672	+	0.487672i
$26$	0.0827293	+	3.60460i	0.0162246	+	0.706921i
$27$		0			0
$28$	0.797644	+	2.97685i	0.150741	+	0.562572i
$29$			5.68973i			1.05656i	0.849071	+	0.528278i	$0.177162\pi$
$29$			5.68973i			1.05656i	−0.849071	+	0.528278i	$0.822838\pi$
$30$		0			0
$31$	0.293661	+	1.09596i	0.0527430	+	0.196840i	0.987270	−	0.159052i	$-0.0508438\pi$
$31$	0.293661	+	1.09596i	0.0527430	+	0.196840i	−0.934527	+	0.355892i	$0.884177\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	2.00717	−	7.49087i	0.344227	−	1.28467i
$35$	−0.937115	+	0.541044i	−0.158401	+	0.0914531i
$36$		0			0
$37$	8.90068	−	2.38493i	1.46326	−	0.392080i	0.562647	−	0.826697i	$-0.309783\pi$
$37$	8.90068	−	2.38493i	1.46326	−	0.392080i	0.900615	+	0.434617i	$0.143116\pi$
$38$	1.90186	+	3.29411i	0.308522	+	0.534375i
$39$		0			0
$40$	0.175557	−	0.304074i	0.0277581	−	0.0480784i
$41$	0.678577	−	2.53248i	0.105976	−	0.395508i	−0.892478	−	0.451091i	$-0.851035\pi$
$41$	0.678577	−	2.53248i	0.105976	−	0.395508i	0.998454	+	0.0555831i	$0.0177018\pi$
$42$		0			0
$43$	−3.68906	−	2.12988i	−0.562577	−	0.324804i	0.191602	−	0.981473i	$-0.438632\pi$
$43$	−3.68906	−	2.12988i	−0.562577	−	0.324804i	−0.754179	+	0.656669i	$0.771965\pi$
$44$	2.35360	+	2.35360i	0.354819	+	0.354819i
$45$		0			0
$46$	−1.73021	+	6.45722i	−0.255105	+	0.952065i
$47$	4.17527	+	1.11876i	0.609026	+	0.163188i	0.550134	−	0.835076i	$-0.314577\pi$
$47$	4.17527	+	1.11876i	0.609026	+	0.163188i	0.0588917	+	0.998264i	$0.481243\pi$
$48$		0			0
$49$	2.16322	−	1.24894i	0.309031	−	0.178419i
$50$	−4.71055	−	1.26219i	−0.666172	−	0.178500i
$51$		0			0
$52$	−2.49034	+	2.60734i	−0.345348	+	0.361573i
$53$			5.65439i			0.776690i	0.921514	+	0.388345i	$0.126953\pi$
$53$			5.65439i			0.776690i	−0.921514	+	0.388345i	$0.873047\pi$
$54$		0			0
$55$	−0.584342	+	1.01211i	−0.0787927	+	0.136473i
$56$	−1.54093	+	2.66897i	−0.205916	+	0.356656i
$57$		0			0
$58$	−4.02325	+	4.02325i	−0.528278	+	0.528278i
$59$	−7.75962	+	7.75962i	−1.01022	+	1.01022i	−0.0102689	+	0.999947i	$0.503269\pi$
$59$	−7.75962	+	7.75962i	−1.01022	+	1.01022i	−0.999947	+	0.0102689i	$0.996731\pi$
$60$		0			0
$61$	5.01742	−	8.69042i	0.642415	−	1.11269i	−0.342478	−	0.939526i	$-0.611266\pi$
$61$	5.01742	−	8.69042i	0.642415	−	1.11269i	0.984892	−	0.173169i	$-0.0554006\pi$
$62$	−0.567309	+	0.982608i	−0.0720483	+	0.124791i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−1.11059	−	0.607659i	−0.137752	−	0.0753708i
$66$		0			0
$67$	−13.3180	−	3.56856i	−1.62706	−	0.435969i	−0.673994	−	0.738737i	$-0.735423\pi$
$67$	−13.3180	−	3.56856i	−1.62706	−	0.435969i	−0.953064	+	0.302768i	$0.902089\pi$
$68$	6.71613	−	3.87756i	0.814450	−	0.470223i
$69$		0			0
$70$	−1.04522	−	0.280065i	−0.124927	−	0.0334741i
$71$	0.343507	−	1.28199i	0.0407668	−	0.152144i	−0.942542	−	0.334087i	$-0.891572\pi$
$71$	0.343507	−	1.28199i	0.0407668	−	0.152144i	0.983309	+	0.181943i	$0.0582387\pi$
$72$		0			0
$73$	−2.19140	−	2.19140i	−0.256484	−	0.256484i	0.567138	−	0.823622i	$-0.308050\pi$
$73$	−2.19140	−	2.19140i	−0.256484	−	0.256484i	−0.823622	+	0.567138i	$0.808050\pi$
$74$	7.98013	+	4.60733i	0.927671	+	0.535591i
$75$		0			0
$76$	−0.984473	+	3.67410i	−0.112927	+	0.421448i
$77$	5.12898	−	8.88365i	0.584502	−	1.01239i
$78$		0			0
$79$	−6.22990	−	10.7905i	−0.700919	−	1.21403i	−0.968144	−	0.250393i	$-0.919440\pi$
$79$	−6.22990	−	10.7905i	−0.700919	−	1.21403i	0.267225	−	0.963634i	$-0.413893\pi$
$80$	0.339151	−	0.0908752i	0.0379182	−	0.0101602i
$81$		0			0
$82$	2.27056	−	1.31091i	0.250742	−	0.144766i
$83$	1.05166	−	3.92483i	0.115434	−	0.430806i	−0.883885	−	0.467705i	$-0.845081\pi$
$83$	1.05166	−	3.92483i	0.115434	−	0.430806i	0.999319	+	0.0368984i	$0.0117478\pi$
$84$		0			0
$85$	1.92541	+	1.92541i	0.208840	+	0.208840i
$86$	−1.10251	−	4.11462i	−0.118887	−	0.443691i
$87$		0			0
$88$			3.32849i			0.354819i
$89$	−1.43929	−	5.37149i	−0.152564	−	0.569377i	−0.999302	−	0.0373662i	$-0.988103\pi$
$89$	−1.43929	−	5.37149i	−0.152564	−	0.569377i	0.846737	−	0.532011i	$-0.178563\pi$
$90$		0			0
$91$	9.74806	+	5.33364i	1.02187	+	0.559117i
$92$	−5.78938	+	3.34250i	−0.603585	+	0.348480i
$93$		0			0
$94$	2.16128	+	3.74344i	0.222919	+	0.386107i
$95$	−1.33554			−0.137023
$96$		0			0
$97$	−0.218799	−	0.816569i	−0.0222157	−	0.0829101i	0.953928	−	0.300036i	$-0.0969986\pi$
$97$	−0.218799	−	0.816569i	−0.0222157	−	0.0829101i	−0.976144	+	0.217126i	$0.930332\pi$
$98$	2.41276	+	0.646496i	0.243725	+	0.0653060i
$99$		0			0
$100$	−2.43836	−	4.22336i	−0.243836	−	0.422336i
$101$	−10.5139			−1.04617			−0.523087	−	0.852279i	$-0.675220\pi$
$101$	−10.5139			−1.04617			−0.523087	+	0.852279i	$0.675220\pi$
$102$		0			0
$103$	−1.30284	−	0.752193i	−0.128372	−	0.0741158i	0.434439	−	0.900701i	$-0.356947\pi$
$103$	−1.30284	−	0.752193i	−0.128372	−	0.0741158i	−0.562811	+	0.826586i	$0.690280\pi$
$104$	−3.60460	+	0.0827293i	−0.353460	+	0.00811228i
$105$		0			0
$106$	−3.99826	+	3.99826i	−0.388345	+	0.388345i
$107$	−4.75429	−	2.74489i	−0.459615	−	0.265359i	0.252267	−	0.967658i	$-0.418824\pi$
$107$	−4.75429	−	2.74489i	−0.459615	−	0.265359i	−0.711882	+	0.702299i	$0.752157\pi$
$108$		0			0
$109$	2.22967	−	2.22967i	0.213564	−	0.213564i	−0.592216	−	0.805780i	$-0.701747\pi$
$109$	2.22967	−	2.22967i	0.213564	−	0.213564i	0.805780	+	0.592216i	$0.201747\pi$
$110$	−1.12886	+	0.302478i	−0.107633	+	0.0288401i
$111$		0			0
$112$	−2.97685	+	0.797644i	−0.281286	+	0.0753703i
$113$			6.68745i			0.629102i	0.949241	+	0.314551i	$0.101854\pi$
$113$			6.68745i			0.629102i	−0.949241	+	0.314551i	$0.898146\pi$
$114$		0			0
$115$	−1.65972	−	1.65972i	−0.154770	−	0.154770i
$116$	−5.68973			−0.528278
$117$		0			0
$118$	−10.9738			−1.01022
$119$	−16.9000	−	16.9000i	−1.54922	−	1.54922i
$120$		0			0
$121$		−	0.0788774i		−	0.00717067i
$122$	9.69291	−	2.59721i	0.877555	−	0.235140i
$123$		0			0
$124$	−1.09596	+	0.293661i	−0.0984199	+	0.0263715i
$125$	2.45215	−	2.45215i	0.219327	−	0.219327i
$126$		0			0
$127$	−10.6922	−	6.17316i	−0.948782	−	0.547780i	−0.0560797	−	0.998426i	$-0.517860\pi$
$127$	−10.6922	−	6.17316i	−0.948782	−	0.547780i	−0.892702	+	0.450647i	$0.851193\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−0.355627	−	1.21499i	−0.0311905	−	0.106561i
$131$	−4.12094	−	2.37922i	−0.360048	−	0.207874i	0.309054	−	0.951045i	$-0.399988\pi$
$131$	−4.12094	−	2.37922i	−0.360048	−	0.207874i	−0.669102	+	0.743171i	$0.733321\pi$
$132$		0			0
$133$	11.7225			1.01647
$134$	−6.89393	−	11.9406i	−0.595545	−	1.03151i
$135$		0			0
$136$	7.49087	+	2.00717i	0.642337	+	0.172114i
$137$	1.27487	+	4.75789i	0.108920	+	0.406494i	0.998760	−	0.0497773i	$-0.0158512\pi$
$137$	1.27487	+	4.75789i	0.108920	+	0.406494i	−0.889840	+	0.456272i	$0.849185\pi$
$138$		0			0
$139$	4.10037			0.347789			0.173894	−	0.984764i	$-0.444365\pi$
$139$	4.10037			0.347789			0.173894	+	0.984764i	$0.444365\pi$
$140$	−0.541044	−	0.937115i	−0.0457265	−	0.0792007i
$141$		0			0
$142$	1.14940	−	0.663605i	0.0964553	−	0.0556885i
$143$	11.9979	−	0.275364i	1.00331	−	0.0230271i
$144$		0			0
$145$	−0.517055	−	1.92968i	−0.0429391	−	0.160251i
$146$		−	3.09911i		−	0.256484i
$147$		0			0
$148$	2.38493	+	8.90068i	0.196040	+	0.731631i
$149$	−5.36748	−	5.36748i	−0.439721	−	0.439721i	0.452197	−	0.891918i	$-0.350640\pi$
$149$	−5.36748	−	5.36748i	−0.439721	−	0.439721i	−0.891918	+	0.452197i	$0.850640\pi$
$150$		0			0
$151$	−3.77372	+	14.0837i	−0.307101	+	1.14612i	0.624021	+	0.781408i	$0.285498\pi$
$151$	−3.77372	+	14.0837i	−0.307101	+	1.14612i	−0.931122	+	0.364709i	$0.881169\pi$
$152$	−3.29411	+	1.90186i	−0.267188	+	0.154261i
$153$		0			0
$154$	9.90843	−	2.65496i	0.798444	−	0.213942i
$155$	−0.199191	−	0.345008i	−0.0159994	−	0.0277117i
$156$		0			0
$157$	−8.20325	+	14.2085i	−0.654691	+	1.13396i	0.327280	+	0.944927i	$0.393868\pi$
$157$	−8.20325	+	14.2085i	−0.654691	+	1.13396i	−0.981971	+	0.189031i	$0.939465\pi$
$158$	3.22484	−	12.0353i	0.256554	−	0.957473i
$159$		0			0
$160$	0.304074	+	0.175557i	0.0240392	+	0.0138790i
$161$	14.5680	+	14.5680i	1.14812	+	1.14812i
$162$		0			0
$163$	4.81720	−	17.9780i	0.377312	−	1.40815i	−0.472625	−	0.881263i	$-0.656694\pi$
$163$	4.81720	−	17.9780i	0.377312	−	1.40815i	0.849937	−	0.526884i	$-0.176640\pi$
$164$	2.53248	+	0.678577i	0.197754	+	0.0529880i
$165$		0			0
$166$	3.51891	−	2.03164i	0.273120	−	0.157686i
$167$	0.832317	+	0.223019i	0.0644066	+	0.0172577i	0.290878	−	0.956760i	$-0.406052\pi$
$167$	0.832317	+	0.223019i	0.0644066	+	0.0172577i	−0.226472	+	0.974018i	$0.572719\pi$
$168$		0			0
$169$	0.596413	+	12.9863i	0.0458779	+	0.998947i
$170$			2.72294i			0.208840i
$171$		0			0
$172$	2.12988	−	3.68906i	0.162402	−	0.281289i
$173$	11.9390	−	20.6789i	0.907702	−	1.57219i	0.0904542	−	0.995901i	$-0.471168\pi$
$173$	11.9390	−	20.6789i	0.907702	−	1.57219i	0.817248	−	0.576286i	$-0.195499\pi$
$174$		0			0
$175$	−10.6274	+	10.6274i	−0.803354	+	0.803354i
$176$	−2.35360	+	2.35360i	−0.177409	+	0.177409i
$177$		0			0
$178$	2.78049	−	4.81595i	0.208407	−	0.360971i
$179$	5.19785	−	9.00294i	0.388506	−	0.672912i	−0.603743	−	0.797179i	$-0.706325\pi$
$179$	5.19785	−	9.00294i	0.388506	−	0.672912i	0.992249	+	0.124267i	$0.0396581\pi$
$180$		0			0
$181$			0.635701i			0.0472513i	0.999721	+	0.0236256i	$0.00752097\pi$
$181$			0.635701i			0.0472513i	−0.999721	+	0.0236256i	$0.992479\pi$
$182$	3.12146	+	10.6644i	0.231378	+	0.790496i
$183$		0			0
$184$	−6.45722	−	1.73021i	−0.476033	−	0.127553i
$185$	−2.80194	+	1.61770i	−0.206003	+	0.118936i
$186$		0			0
$187$	−24.9333	−	6.68086i	−1.82330	−	0.488553i
$188$	−1.11876	+	4.17527i	−0.0815940	+	0.304513i
$189$		0			0
$190$	−0.944369	−	0.944369i	−0.0685117	−	0.0685117i
$191$	−0.129112	−	0.0745427i	−0.00934220	−	0.00539372i	0.495322	−	0.868710i	$-0.335050\pi$
$191$	−0.129112	−	0.0745427i	−0.00934220	−	0.00539372i	−0.504664	+	0.863316i	$0.668384\pi$
$192$		0			0
$193$	−1.10422	+	4.12101i	−0.0794837	+	0.296637i	−0.994213	−	0.107431i	$-0.965737\pi$
$193$	−1.10422	+	4.12101i	−0.0794837	+	0.296637i	0.914729	+	0.404068i	$0.132404\pi$
$194$	0.422687	−	0.732116i	0.0303472	−	0.0525629i
$195$		0			0
$196$	1.24894	+	2.16322i	0.0892097	+	0.154516i
$197$	−18.4733	+	4.94991i	−1.31617	+	0.352667i	−0.847542	−	0.530729i	$-0.821918\pi$
$197$	−18.4733	+	4.94991i	−1.31617	+	0.352667i	−0.468629	+	0.883395i	$0.655252\pi$
$198$		0			0
$199$	−4.55185	+	2.62801i	−0.322672	+	0.186295i	−0.652583	−	0.757717i	$-0.726315\pi$
$199$	−4.55185	+	2.62801i	−0.322672	+	0.186295i	0.329911	+	0.944012i	$0.392981\pi$
$200$	1.26219	−	4.71055i	0.0892501	−	0.333086i
$201$		0			0
$202$	−7.43446	−	7.43446i	−0.523087	−	0.523087i
$203$	4.53838	+	16.9375i	0.318532	+	1.18878i
$204$		0			0
$205$			0.920560i			0.0642947i
$206$	−0.389364	−	1.45313i	−0.0271283	−	0.101244i
$207$		0			0
$208$	−2.60734	−	2.49034i	−0.180786	−	0.172674i
$209$	10.9644	−	6.33032i	0.758425	−	0.437877i
$210$		0			0
$211$	−11.9338	−	20.6699i	−0.821556	−	1.42298i	−0.904523	−	0.426424i	$-0.859773\pi$
$211$	−11.9338	−	20.6699i	−0.821556	−	1.42298i	0.0829678	−	0.996552i	$-0.473560\pi$
$212$	−5.65439			−0.388345
$213$		0			0
$214$	−1.42086	−	5.30272i	−0.0971280	−	0.362487i
$215$	1.44470	+	0.387107i	0.0985279	+	0.0264005i
$216$		0			0
$217$	1.74837	+	3.02826i	0.118687	+	0.205572i
$218$	3.15324			0.213564
$219$		0			0
$220$	−1.01211	−	0.584342i	−0.0682364	−	0.0393963i
$221$	6.61534	−	27.1677i	0.444996	−	1.82749i
$222$		0			0
$223$	−15.6524	+	15.6524i	−1.04816	+	1.04816i	−0.0493797	+	0.998780i	$0.515724\pi$
$223$	−15.6524	+	15.6524i	−1.04816	+	1.04816i	−0.998780	+	0.0493797i	$0.984276\pi$
$224$	−2.66897	−	1.54093i	−0.178328	−	0.102958i
$225$		0			0
$226$	−4.72874	+	4.72874i	−0.314551	+	0.314551i
$227$	−21.5776	+	5.78170i	−1.43216	+	0.383745i	−0.889780	−	0.456390i	$-0.849142\pi$
$227$	−21.5776	+	5.78170i	−1.43216	+	0.383745i	−0.542377	+	0.840135i	$0.682475\pi$
$228$		0			0
$229$	8.99230	−	2.40948i	0.594228	−	0.159223i	0.0508431	−	0.998707i	$-0.483809\pi$
$229$	8.99230	−	2.40948i	0.594228	−	0.159223i	0.543385	+	0.839484i	$0.317142\pi$
$230$		−	2.34720i		−	0.154770i
$231$		0			0
$232$	−4.02325	−	4.02325i	−0.264139	−	0.264139i
$233$	28.4945			1.86674			0.933370	−	0.358917i	$-0.116854\pi$
$233$	28.4945			1.86674			0.933370	+	0.358917i	$0.116854\pi$
$234$		0			0
$235$	−1.51771			−0.0990047
$236$	−7.75962	−	7.75962i	−0.505108	−	0.505108i
$237$		0			0
$238$		−	23.9002i		−	1.54922i
$239$	−13.9526	+	3.73860i	−0.902521	+	0.241830i	−0.680099	−	0.733121i	$-0.738063\pi$
$239$	−13.9526	+	3.73860i	−0.902521	+	0.241830i	−0.222422	+	0.974950i	$0.571396\pi$
$240$		0			0
$241$	29.4794	−	7.89898i	1.89894	−	0.508818i	0.901893	−	0.431959i	$-0.142178\pi$
$241$	29.4794	−	7.89898i	1.89894	−	0.508818i	0.997042	−	0.0768587i	$-0.0244890\pi$
$242$	0.0557747	−	0.0557747i	0.00358534	−	0.00358534i
$243$		0			0
$244$	8.69042	+	5.01742i	0.556347	+	0.321207i
$245$	−0.620160	+	0.620160i	−0.0396206	+	0.0396206i
$246$		0			0
$247$	7.12795	+	11.7166i	0.453541	+	0.745511i
$248$	−0.982608	−	0.567309i	−0.0623957	−	0.0360242i
$249$		0			0
$250$	3.46786			0.219327
$251$	8.22674	+	14.2491i	0.519267	+	0.899397i	0.999749	+	0.0223928i	$0.00712844\pi$
$251$	8.22674	+	14.2491i	0.519267	+	0.899397i	−0.480482	+	0.877005i	$0.659538\pi$
$252$		0			0
$253$	21.4928	+	5.75898i	1.35124	+	0.362064i
$254$	−3.19546	−	11.9256i	−0.200501	−	0.748281i
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.07726	+	10.5261i	0.379089	+	0.656601i	0.990930	−	0.134380i	$-0.0429041\pi$
$257$	6.07726	+	10.5261i	0.379089	+	0.656601i	−0.611841	+	0.790981i	$0.709571\pi$
$258$		0			0
$259$	24.5936	−	14.1991i	1.52818	−	0.882292i
$260$	0.607659	−	1.11059i	0.0376854	−	0.0688759i
$261$		0			0
$262$	−1.23158	−	4.59631i	−0.0760871	−	0.283961i
$263$			8.30088i			0.511854i	0.966696	+	0.255927i	$0.0823808\pi$
$263$			8.30088i			0.511854i	−0.966696	+	0.255927i	$0.917619\pi$
$264$		0			0
$265$	−0.513844	−	1.91769i	−0.0315652	−	0.117803i
$266$	8.28907	+	8.28907i	0.508235	+	0.508235i
$267$		0			0
$268$	3.56856	−	13.3180i	0.217985	−	0.813529i
$269$	15.3432	−	8.85839i	0.935490	−	0.540105i	0.0469463	−	0.998897i	$-0.485051\pi$
$269$	15.3432	−	8.85839i	0.935490	−	0.540105i	0.888544	+	0.458792i	$0.151718\pi$
$270$		0			0
$271$	−6.44584	+	1.72716i	−0.391557	+	0.104917i	−0.449226	−	0.893418i	$-0.648300\pi$
$271$	−6.44584	+	1.72716i	−0.391557	+	0.104917i	0.0576685	+	0.998336i	$0.481633\pi$
$272$	3.87756	+	6.71613i	0.235112	+	0.407225i
$273$		0			0
$274$	−2.46287	+	4.26581i	−0.148787	+	0.257707i
$275$	−4.20118	+	15.6790i	−0.253341	+	0.945481i
$276$		0			0
$277$	−15.1301	−	8.73535i	−0.909077	−	0.524856i	−0.0289433	−	0.999581i	$-0.509214\pi$
$277$	−15.1301	−	8.73535i	−0.909077	−	0.524856i	−0.880134	+	0.474725i	$0.842548\pi$
$278$	2.89940	+	2.89940i	0.173894	+	0.173894i
$279$		0			0
$280$	0.280065	−	1.04522i	0.0167371	−	0.0624636i
$281$	−13.9665	−	3.74231i	−0.833172	−	0.223248i	−0.183075	−	0.983099i	$-0.558605\pi$
$281$	−13.9665	−	3.74231i	−0.833172	−	0.223248i	−0.650097	+	0.759851i	$0.725272\pi$
$282$		0			0
$283$	3.09306	−	1.78578i	0.183863	−	0.106154i	−0.405243	−	0.914209i	$-0.632813\pi$
$283$	3.09306	−	1.78578i	0.183863	−	0.106154i	0.589107	+	0.808055i	$0.299480\pi$
$284$	1.28199	+	0.343507i	0.0760719	+	0.0203834i
$285$		0			0
$286$	8.67851	+	8.28908i	0.513171	+	0.490144i
$287$		−	8.08009i		−	0.476953i
$288$		0			0
$289$	−21.5709	+	37.3619i	−1.26888	+	2.19776i
$290$	0.998874	−	1.73010i	0.0586559	−	0.101595i
$291$		0			0
$292$	2.19140	−	2.19140i	0.128242	−	0.128242i
$293$	4.84724	−	4.84724i	0.283179	−	0.283179i	−0.551197	−	0.834375i	$-0.685829\pi$
$293$	4.84724	−	4.84724i	0.283179	−	0.283179i	0.834375	+	0.551197i	$0.185829\pi$
$294$		0			0
$295$	1.92652	−	3.33684i	0.112167	−	0.194278i
$296$	−4.60733	+	7.98013i	−0.267796	+	0.463836i
$297$		0			0
$298$		−	7.59077i		−	0.439721i
$299$	−5.70251	+	23.4188i	−0.329784	+	1.35435i
$300$		0			0
$301$	−12.6807	−	3.39778i	−0.730902	−	0.195845i
$302$	−12.6271	+	7.29027i	−0.726609	+	0.419508i
$303$		0			0
$304$	−3.67410	−	0.984473i	−0.210724	−	0.0564634i
$305$	−0.911918	+	3.40332i	−0.0522163	+	0.194874i
$306$		0			0
$307$	2.89643	+	2.89643i	0.165308	+	0.165308i	0.784913	−	0.619605i	$-0.212707\pi$
$307$	2.89643	+	2.89643i	0.165308	+	0.165308i	−0.619605	+	0.784913i	$0.712707\pi$
$308$	8.88365	+	5.12898i	0.506193	+	0.292251i
$309$		0			0
$310$	0.103109	−	0.384807i	0.00585618	−	0.0218556i
$311$	−14.2341	+	24.6543i	−0.807144	+	1.39801i	0.107690	+	0.994185i	$0.465655\pi$
$311$	−14.2341	+	24.6543i	−0.807144	+	1.39801i	−0.914834	+	0.403830i	$0.867679\pi$
$312$		0			0
$313$	−2.79680	−	4.84421i	−0.158085	−	0.273811i	0.776093	−	0.630618i	$-0.217199\pi$
$313$	−2.79680	−	4.84421i	−0.158085	−	0.273811i	−0.934178	+	0.356807i	$0.883865\pi$
$314$	−15.8475	+	4.24632i	−0.894324	+	0.239634i
$315$		0			0
$316$	10.7905	−	6.22990i	0.607014	−	0.350459i
$317$	−0.535423	+	1.99822i	−0.0300723	+	0.112231i	−0.979331	−	0.202266i	$-0.935169\pi$
$317$	−0.535423	+	1.99822i	−0.0300723	+	0.112231i	0.949258	+	0.314498i	$0.101836\pi$
$318$		0			0
$319$	13.3914	+	13.3914i	0.749772	+	0.749772i
$320$	0.0908752	+	0.339151i	0.00508008	+	0.0189591i
$321$		0			0
$322$			20.6023i			1.14812i
$323$	−7.63470	−	28.4931i	−0.424806	−	1.58540i
$324$		0			0
$325$	−17.0841	−	4.15998i	−0.947654	−	0.230754i
$326$	16.1187	−	9.30611i	0.892730	−	0.515418i
$327$		0			0
$328$	1.31091	+	2.27056i	0.0723829	+	0.125371i
$329$	13.3215			0.734439
$330$		0			0
$331$	6.28560	+	23.4582i	0.345488	+	1.28938i	0.892042	+	0.451953i	$0.149273\pi$
$331$	6.28560	+	23.4582i	0.345488	+	1.28938i	−0.546554	+	0.837424i	$0.684061\pi$
$332$	3.92483	+	1.05166i	0.215403	+	0.0577171i
$333$		0			0
$334$	0.430839	+	0.746235i	0.0235745	+	0.0408322i
$335$	4.84112			0.264499
$336$		0			0
$337$	23.9772	+	13.8433i	1.30612	+	0.754090i	0.981447	−	0.191735i	$-0.0614113\pi$
$337$	23.9772	+	13.8433i	1.30612	+	0.754090i	0.324676	+	0.945825i	$0.394745\pi$
$338$	−8.76098	+	9.60444i	−0.476535	+	0.522412i
$339$		0			0
$340$	−1.92541	+	1.92541i	−0.104420	+	0.104420i
$341$	3.27061	+	1.88829i	0.177113	+	0.102256i
$342$		0			0
$343$	−9.81106	+	9.81106i	−0.529748	+	0.529748i
$344$	4.11462	−	1.10251i	0.221845	−	0.0594433i
$345$		0			0
$346$	23.0643	−	6.18006i	1.23994	−	0.332242i
$347$		−	2.18710i		−	0.117410i	−0.998275	−	0.0587049i	$-0.981303\pi$
$347$		−	2.18710i		−	0.117410i	0.998275	−	0.0587049i	$-0.0186971\pi$
$348$		0			0
$349$	−20.5657	−	20.5657i	−1.10086	−	1.10086i	−0.994307	−	0.106552i	$-0.966019\pi$
$349$	−20.5657	−	20.5657i	−1.10086	−	1.10086i	−0.106552	−	0.994307i	$-0.533981\pi$
$350$	−15.0294			−0.803354
$351$		0			0
$352$	−3.32849			−0.177409
$353$	5.13936	+	5.13936i	0.273541	+	0.273541i	0.830524	−	0.556983i	$-0.188041\pi$
$353$	5.13936	+	5.13936i	0.273541	+	0.273541i	−0.556983	+	0.830524i	$0.688041\pi$
$354$		0			0
$355$			0.466003i			0.0247329i
$356$	5.37149	−	1.43929i	0.284689	−	0.0762821i
$357$		0			0
$358$	10.0415	−	2.69061i	0.530709	−	0.142203i
$359$	−5.00179	+	5.00179i	−0.263985	+	0.263985i	−0.826671	−	0.562686i	$-0.809768\pi$
$359$	−5.00179	+	5.00179i	−0.263985	+	0.263985i	0.562686	+	0.826671i	$0.309768\pi$
$360$		0			0
$361$	−3.92464	−	2.26589i	−0.206560	−	0.119257i
$362$	−0.449508	+	0.449508i	−0.0236256	+	0.0236256i
$363$		0			0
$364$	−5.33364	+	9.74806i	−0.279559	+	0.510937i
$365$	0.942359	+	0.544071i	0.0493253	+	0.0284780i
$366$		0			0
$367$	17.5261			0.914857			0.457428	−	0.889246i	$-0.348771\pi$
$367$	17.5261			0.914857			0.457428	+	0.889246i	$0.348771\pi$
$368$	−3.34250	−	5.78938i	−0.174240	−	0.301793i
$369$		0			0
$370$	−3.12516	−	0.837384i	−0.162469	−	0.0435335i
$371$	4.51019	+	16.8323i	0.234157	+	0.873888i
$372$		0			0
$373$	12.1273			0.627927			0.313963	−	0.949435i	$-0.398343\pi$
$373$	12.1273			0.627927			0.313963	+	0.949435i	$0.398343\pi$
$374$	−12.9064	−	22.3546i	−0.667376	−	1.15593i
$375$		0			0
$376$	−3.74344	+	2.16128i	−0.193053	+	0.111459i
$377$	−14.1694	+	14.8350i	−0.729759	+	0.764044i
$378$		0			0
$379$	1.59520	+	5.95337i	0.0819399	+	0.305804i	0.994717	−	0.102654i	$-0.0327334\pi$
$379$	1.59520	+	5.95337i	0.0819399	+	0.305804i	−0.912777	+	0.408458i	$0.866067\pi$
$380$		−	1.33554i		−	0.0685117i
$381$		0			0
$382$	−0.0385862	−	0.144006i	−0.00197424	−	0.00736796i
$383$	10.3289	+	10.3289i	0.527785	+	0.527785i	0.919911	−	0.392127i	$-0.128260\pi$
$383$	10.3289	+	10.3289i	0.527785	+	0.527785i	−0.392127	+	0.919911i	$0.628260\pi$
$384$		0			0
$385$	−0.932194	+	3.47900i	−0.0475090	+	0.177306i
$386$	−3.69480	+	2.13319i	−0.188060	+	0.108577i
$387$		0			0
$388$	0.816569	−	0.218799i	0.0414550	−	0.0111078i
$389$	−2.49669	−	4.32440i	−0.126587	−	0.219256i	0.795765	−	0.605606i	$-0.207069\pi$
$389$	−2.49669	−	4.32440i	−0.126587	−	0.219256i	−0.922352	+	0.386350i	$0.873736\pi$
$390$		0			0
$391$	25.9215	−	44.8974i	1.31091	−	2.27056i
$392$	−0.646496	+	2.41276i	−0.0326530	+	0.121863i
$393$		0			0
$394$	−16.5627	−	9.56250i	−0.834419	−	0.481752i
$395$	3.09347	+	3.09347i	0.155649	+	0.155649i
$396$		0			0
$397$	−1.56112	+	5.82617i	−0.0783503	+	0.292407i	−0.993972	−	0.109634i	$-0.965032\pi$
$397$	−1.56112	+	5.82617i	−0.0783503	+	0.292407i	0.915622	+	0.402041i	$0.131699\pi$
$398$	−5.07693	−	1.36036i	−0.254483	−	0.0681886i
$399$		0			0
$400$	4.22336	−	2.43836i	0.211168	−	0.121918i
$401$	−7.37085	−	1.97501i	−0.368083	−	0.0986274i	0.0700364	−	0.997544i	$-0.477688\pi$
$401$	−7.37085	−	1.97501i	−0.368083	−	0.0986274i	−0.438119	+	0.898917i	$0.644355\pi$
$402$		0			0
$403$	−1.96363	+	3.58884i	−0.0978155	+	0.178773i
$404$		−	10.5139i		−	0.523087i
$405$		0			0
$406$	−8.76748	+	15.1857i	−0.435123	+	0.753655i
$407$	15.3355	−	26.5618i	0.760151	−	1.31662i
$408$		0			0
$409$	−3.33008	+	3.33008i	−0.164662	+	0.164662i	−0.784628	−	0.619966i	$-0.787146\pi$
$409$	−3.33008	+	3.33008i	−0.164662	+	0.164662i	0.619966	+	0.784628i	$0.287146\pi$
$410$	−0.650934	+	0.650934i	−0.0321474	+	0.0321474i
$411$		0			0
$412$	0.752193	−	1.30284i	0.0370579	−	0.0641862i
$413$	−16.9098	+	29.2886i	−0.832077	+	1.44120i
$414$		0			0
$415$			1.42668i			0.0700329i
$416$	−0.0827293	−	3.60460i	−0.00405614	−	0.176730i
$417$		0			0
$418$	12.2292	+	3.27681i	0.598151	+	0.160274i
$419$	12.1816	−	7.03305i	0.595110	−	0.343587i	−0.172005	−	0.985096i	$-0.555025\pi$
$419$	12.1816	−	7.03305i	0.595110	−	0.343587i	0.767116	+	0.641509i	$0.221691\pi$
$420$		0			0
$421$	29.6767	+	7.95186i	1.44636	+	0.387550i	0.894755	−	0.446558i	$-0.147350\pi$
$421$	29.6767	+	7.95186i	1.44636	+	0.387550i	0.551601	+	0.834108i	$0.314017\pi$
$422$	6.17738	−	23.0543i	0.300710	−	1.12227i
$423$		0			0
$424$	−3.99826	−	3.99826i	−0.194172	−	0.194172i
$425$	32.7527	+	18.9098i	1.58874	+	0.917258i
$426$		0			0
$427$	8.00423	−	29.8722i	0.387352	−	1.44562i
$428$	2.74489	−	4.75429i	0.132679	−	0.229807i
$429$		0			0
$430$	0.747833	+	1.29529i	0.0360637	+	0.0624642i
$431$	−37.7065	+	10.1034i	−1.81626	+	0.486665i	−0.996314	−	0.0857790i	$-0.972662\pi$
$431$	−37.7065	+	10.1034i	−1.81626	+	0.486665i	−0.819944	+	0.572444i	$0.805995\pi$
$432$		0			0
$433$	−1.12288	+	0.648297i	−0.0539623	+	0.0311552i	−0.526738	−	0.850027i	$-0.676585\pi$
$433$	−1.12288	+	0.648297i	−0.0539623	+	0.0311552i	0.472776	+	0.881183i	$0.343252\pi$
$434$	−0.905022	+	3.37759i	−0.0434424	+	0.162129i
$435$		0			0
$436$	2.22967	+	2.22967i	0.106782	+	0.106782i
$437$	6.58121	+	24.5614i	0.314822	+	1.17493i
$438$		0			0
$439$			18.8010i			0.897321i	0.893702	+	0.448660i	$0.148099\pi$
$439$			18.8010i			0.897321i	−0.893702	+	0.448660i	$0.851901\pi$
$440$	−0.302478	−	1.12886i	−0.0144201	−	0.0538164i
$441$		0			0
$442$	23.8882	−	14.5327i	1.13625	−	0.691249i
$443$	−18.8039	+	10.8564i	−0.893400	+	0.515805i	−0.875053	−	0.484027i	$-0.839174\pi$
$443$	−18.8039	+	10.8564i	−0.893400	+	0.515805i	−0.0183470	+	0.999832i	$0.505840\pi$
$444$		0			0
$445$	0.976271	+	1.69095i	0.0462797	+	0.0801588i
$446$	−22.1358			−1.04816
$447$		0			0
$448$	−0.797644	−	2.97685i	−0.0376852	−	0.140643i
$449$	21.9490	+	5.88123i	1.03584	+	0.277552i	0.736388	−	0.676559i	$-0.236530\pi$
$449$	21.9490	+	5.88123i	1.03584	+	0.277552i	0.299451	+	0.954112i	$0.403196\pi$
$450$		0			0
$451$	−4.36336	−	7.55756i	−0.205463	−	0.355872i
$452$	−6.68745			−0.314551
$453$		0			0
$454$	−19.3460	−	11.1694i	−0.907951	−	0.524206i
$455$	−3.79076	−	0.923052i	−0.177713	−	0.0432734i
$456$		0			0
$457$	−20.5331	+	20.5331i	−0.960498	+	0.960498i	−0.999249	−	0.0387513i	$-0.987662\pi$
$457$	−20.5331	+	20.5331i	−0.960498	+	0.960498i	0.0387513	+	0.999249i	$0.487662\pi$
$458$	8.06228	+	4.65476i	0.376725	+	0.217503i
$459$		0			0
$460$	1.65972	−	1.65972i	0.0773850	−	0.0773850i
$461$	−11.3082	+	3.03004i	−0.526678	+	0.141123i	−0.512354	−	0.858775i	$-0.671226\pi$
$461$	−11.3082	+	3.03004i	−0.526678	+	0.141123i	−0.0143239	+	0.999897i	$0.504560\pi$
$462$		0			0
$463$	−17.8104	+	4.77229i	−0.827722	+	0.221787i	−0.647720	−	0.761879i	$-0.724277\pi$
$463$	−17.8104	+	4.77229i	−0.827722	+	0.221787i	−0.180002	+	0.983666i	$0.557610\pi$
$464$		−	5.68973i		−	0.264139i
$465$		0			0
$466$	20.1487	+	20.1487i	0.933370	+	0.933370i
$467$	15.3781			0.711613			0.355807	−	0.934560i	$-0.384206\pi$
$467$	15.3781			0.711613			0.355807	+	0.934560i	$0.384206\pi$
$468$		0			0
$469$	−42.4923			−1.96211
$470$	−1.07319	−	1.07319i	−0.0495024	−	0.0495024i
$471$		0			0
$472$		−	10.9738i		−	0.505108i
$473$	−13.6955	+	3.66969i	−0.629719	+	0.168733i
$474$		0			0
$475$	−17.9176	+	4.80100i	−0.822114	+	0.220285i
$476$	16.9000	−	16.9000i	0.774610	−	0.774610i
$477$		0			0
$478$	−12.5096	−	7.22241i	−0.572175	−	0.330346i
$479$	10.9954	−	10.9954i	0.502391	−	0.502391i	−0.409789	−	0.912180i	$-0.634398\pi$
$479$	10.9954	−	10.9954i	0.502391	−	0.502391i	0.912180	+	0.409789i	$0.134398\pi$
$480$		0			0
$481$	29.1463	+	15.9474i	1.32896	+	0.727139i
$482$	26.4305	+	15.2597i	1.20388	+	0.695058i
$483$		0			0
$484$	0.0788774			0.00358534
$485$	0.148412	+	0.257057i	0.00673903	+	0.0116723i
$486$		0			0
$487$	16.7862	+	4.49786i	0.760656	+	0.203817i	0.618240	−	0.785990i	$-0.287846\pi$
$487$	16.7862	+	4.49786i	0.760656	+	0.203817i	0.142417	+	0.989807i	$0.454513\pi$
$488$	2.59721	+	9.69291i	0.117570	+	0.438777i
$489$		0			0
$490$	−0.877039			−0.0396206
$491$	−4.04041	−	6.99820i	−0.182341	−	0.315824i	0.760336	−	0.649530i	$-0.225034\pi$
$491$	−4.04041	−	6.99820i	−0.182341	−	0.315824i	−0.942677	+	0.333706i	$0.891701\pi$
$492$		0			0
$493$	38.2130	−	22.0623i	1.72103	−	0.993634i
$494$	−3.24468	+	13.3251i	−0.145985	+	0.599526i
$495$		0			0
$496$	−0.293661	−	1.09596i	−0.0131858	−	0.0492099i
$497$		−	4.09028i		−	0.183474i
$498$		0			0
$499$	3.39501	+	12.6704i	0.151982	+	0.567203i	0.999345	+	0.0361895i	$0.0115220\pi$
$499$	3.39501	+	12.6704i	0.151982	+	0.567203i	−0.847363	+	0.531014i	$0.821811\pi$
$500$	2.45215	+	2.45215i	0.109663	+	0.109663i
$501$		0			0
$502$	−4.25847	+	15.8928i	−0.190065	+	0.709332i
$503$	17.8854	−	10.3261i	0.797470	−	0.460419i	−0.0451158	−	0.998982i	$-0.514366\pi$
$503$	17.8854	−	10.3261i	0.797470	−	0.460419i	0.842586	+	0.538562i	$0.181032\pi$
$504$		0			0
$505$	3.56580	−	0.955455i	0.158676	−	0.0425172i
$506$	11.1255	+	19.2699i	0.494589	+	0.856653i
$507$		0			0
$508$	6.17316	−	10.6922i	0.273890	−	0.474391i
$509$	8.90280	−	33.2257i	0.394610	−	1.47270i	−0.427834	−	0.903857i	$-0.640723\pi$
$509$	8.90280	−	33.2257i	0.394610	−	1.47270i	0.822444	−	0.568846i	$-0.192610\pi$
$510$		0			0
$511$	−8.27143	−	4.77551i	−0.365906	−	0.211256i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−3.14582	+	11.7404i	−0.138756	+	0.517845i
$515$	0.510214	+	0.136711i	0.0224827	+	0.00602423i
$516$		0			0
$517$	12.4600	−	7.19380i	0.547992	−	0.316383i
$518$	27.4307	+	7.35002i	1.20523	+	0.322941i
$519$		0			0
$520$	1.21499	−	0.355627i	0.0532807	−	0.0155953i
$521$		−	10.8135i		−	0.473747i	−0.971540	−	0.236874i	$-0.923877\pi$
$521$		−	10.8135i		−	0.473747i	0.971540	−	0.236874i	$-0.0761227\pi$
$522$		0			0
$523$	12.9411	−	22.4147i	0.565876	−	0.980126i	−0.431091	−	0.902308i	$-0.641871\pi$
$523$	12.9411	−	22.4147i	0.565876	−	0.980126i	0.996968	−	0.0778180i	$-0.0247953\pi$
$524$	2.37922	−	4.12094i	0.103937	−	0.180024i
$525$		0			0
$526$	−5.86961	+	5.86961i	−0.255927	+	0.255927i
$527$	6.22190	−	6.22190i	0.271030	−	0.271030i
$528$		0			0
$529$	−10.8446	+	18.7835i	−0.471506	+	0.816673i
$530$	0.992670	−	1.71935i	0.0431188	−	0.0746840i
$531$		0			0
$532$			11.7225i			0.508235i
$533$	8.07603	−	4.91315i	0.349812	−	0.212812i
$534$		0			0
$535$	1.86187	+	0.498885i	0.0804954	+	0.0215687i
$536$	11.9406	−	6.89393i	0.515757	−	0.297772i
$537$		0			0
$538$	17.1131	+	4.58544i	0.737798	+	0.197692i
$539$	2.15186	−	8.03085i	0.0926872	−	0.345913i
$540$		0			0
$541$	−20.8711	−	20.8711i	−0.897318	−	0.897318i	0.0978806	−	0.995198i	$-0.468794\pi$
$541$	−20.8711	−	20.8711i	−0.897318	−	0.897318i	−0.995198	+	0.0978806i	$0.968794\pi$
$542$	−5.77918	−	3.33661i	−0.248237	−	0.143320i
$543$		0			0
$544$	−2.00717	+	7.49087i	−0.0860568	+	0.321168i
$545$	−0.553574	+	0.958818i	−0.0237125	+	0.0410713i
$546$		0			0
$547$	8.21466	+	14.2282i	0.351233	+	0.608354i	0.986466	−	0.163967i	$-0.0524291\pi$
$547$	8.21466	+	14.2282i	0.351233	+	0.608354i	−0.635233	+	0.772321i	$0.719096\pi$
$548$	−4.75789	+	1.27487i	−0.203247	+	0.0544599i
$549$		0			0
$550$	−14.0574	+	8.11607i	−0.599411	+	0.346070i
$551$	−5.60138	+	20.9047i	−0.238627	+	0.890568i
$552$		0			0
$553$	−27.1525	−	27.1525i	−1.15464	−	1.15464i
$554$	−4.52175	−	16.8754i	−0.192111	−	0.716967i
$555$		0			0
$556$			4.10037i			0.173894i
$557$	6.82819	+	25.4831i	0.289320	+	1.07976i	0.945625	+	0.325260i	$0.105452\pi$
$557$	6.82819	+	25.4831i	0.289320	+	1.07976i	−0.656305	+	0.754496i	$0.727882\pi$
$558$		0			0
$559$	−4.31450	−	14.7403i	−0.182484	−	0.623450i
$560$	0.937115	−	0.541044i	0.0396003	−	0.0228633i
$561$		0			0
$562$	−7.22960	−	12.5220i	−0.304962	−	0.528210i
$563$	27.8900			1.17542			0.587712	−	0.809070i	$-0.300029\pi$
$563$	27.8900			1.17542			0.587712	+	0.809070i	$0.300029\pi$
$564$		0			0
$565$	−0.607723	−	2.26805i	−0.0255671	−	0.0954177i
$566$	3.44986	+	0.924387i	0.145008	+	0.0388549i
$567$		0			0
$568$	0.663605	+	1.14940i	0.0278442	+	0.0482277i
$569$	0.402831			0.0168875			0.00844377	−	0.999964i	$-0.497312\pi$
$569$	0.402831			0.0168875			0.00844377	+	0.999964i	$0.497312\pi$
$570$		0			0
$571$	−30.8570	−	17.8153i	−1.29133	−	0.745548i	−0.312437	−	0.949938i	$-0.601145\pi$
$571$	−30.8570	−	17.8153i	−1.29133	−	0.745548i	−0.978889	+	0.204390i	$0.934479\pi$
$572$	0.275364	+	11.9979i	0.0115136	+	0.501657i
$573$		0			0
$574$	5.71349	−	5.71349i	0.238476	−	0.238476i
$575$	−28.2332	−	16.3004i	−1.17741	−	0.679775i
$576$		0			0
$577$	33.2996	−	33.2996i	1.38628	−	1.38628i	0.553294	−	0.832986i	$-0.313371\pi$
$577$	33.2996	−	33.2996i	1.38628	−	1.38628i	0.832986	−	0.553294i	$-0.186629\pi$
$578$	−41.6718	+	11.1659i	−1.73332	+	0.464442i
$579$		0			0
$580$	1.92968	−	0.517055i	0.0801255	−	0.0214696i
$581$		−	12.5225i		−	0.519520i
$582$		0			0
$583$	13.3082	+	13.3082i	0.551168	+	0.551168i
$584$	3.09911			0.128242
$585$		0			0
$586$	6.85503			0.283179
$587$	−4.31874	−	4.31874i	−0.178253	−	0.178253i	0.612341	−	0.790594i	$-0.290228\pi$
$587$	−4.31874	−	4.31874i	−0.178253	−	0.178253i	−0.790594	+	0.612341i	$0.790228\pi$
$588$		0			0
$589$			4.31576i			0.177828i
$590$	3.72176	−	0.997242i	0.153222	−	0.0410558i
$591$		0			0
$592$	−8.90068	+	2.38493i	−0.365816	+	0.0980200i
$593$	5.57423	−	5.57423i	0.228906	−	0.228906i	−0.583329	−	0.812236i	$-0.698250\pi$
$593$	5.57423	−	5.57423i	0.228906	−	0.228906i	0.812236	+	0.583329i	$0.198250\pi$
$594$		0			0
$595$	7.26744	+	4.19586i	0.297936	+	0.172013i
$596$	5.36748	−	5.36748i	0.219861	−	0.219861i
$597$		0			0
$598$	−20.5919	+	12.5273i	−0.842066	+	0.512281i
$599$	−12.2562	−	7.07612i	−0.500775	−	0.289122i	0.228259	−	0.973601i	$-0.426697\pi$
$599$	−12.2562	−	7.07612i	−0.500775	−	0.289122i	−0.729033	+	0.684478i	$0.760030\pi$
$600$		0			0
$601$	−39.6189			−1.61609			−0.808044	−	0.589121i	$-0.799474\pi$
$601$	−39.6189			−1.61609			−0.808044	+	0.589121i	$0.799474\pi$
$602$	−6.56400	−	11.3692i	−0.267529	−	0.463373i
$603$		0			0
$604$	−14.0837	−	3.77372i	−0.573058	−	0.153550i
$605$	0.00716800	+	0.0267513i	0.000291421	+	0.00108760i
$606$		0			0
$607$	−6.85360			−0.278179			−0.139090	−	0.990280i	$-0.544418\pi$
$607$	−6.85360			−0.278179			−0.139090	+	0.990280i	$0.544418\pi$
$608$	−1.90186	−	3.29411i	−0.0771304	−	0.133594i
$609$		0			0
$610$	−3.05134	+	1.76169i	−0.123545	+	0.0713288i
$611$	8.10024	+	13.3148i	0.327701	+	0.538660i
$612$		0			0
$613$	−5.58884	−	20.8578i	−0.225731	−	0.842440i	−0.982110	−	0.188307i	$-0.939700\pi$
$613$	−5.58884	−	20.8578i	−0.225731	−	0.842440i	0.756379	−	0.654134i	$-0.226967\pi$
$614$			4.09617i			0.165308i
$615$		0			0
$616$	2.65496	+	9.90843i	0.106971	+	0.399222i
$617$	−19.7634	−	19.7634i	−0.795644	−	0.795644i	0.186761	−	0.982405i	$-0.440201\pi$
$617$	−19.7634	−	19.7634i	−0.795644	−	0.795644i	−0.982405	+	0.186761i	$0.940201\pi$
$618$		0			0
$619$	4.70742	−	17.5683i	0.189207	−	0.706130i	−0.804484	−	0.593975i	$-0.797558\pi$
$619$	4.70742	−	17.5683i	0.189207	−	0.706130i	0.993691	−	0.112155i	$-0.0357754\pi$
$620$	0.345008	−	0.199191i	0.0138559	−	0.00799969i
$621$		0			0
$622$	−27.4983	+	7.36814i	−1.10258	+	0.295435i
$623$	−8.56908	−	14.8421i	−0.343313	−	0.594636i
$624$		0			0
$625$	11.5830	−	20.0623i	0.463319	−	0.802493i
$626$	1.44773	−	5.40301i	0.0578630	−	0.215948i
$627$		0			0
$628$	−14.2085	−	8.20325i	−0.566979	−	0.327345i
$629$	−50.5304	−	50.5304i	−2.01478	−	2.01478i
$630$		0			0
$631$	−2.24267	+	8.36975i	−0.0892792	+	0.333195i	−0.996090	−	0.0883431i	$-0.971843\pi$
$631$	−2.24267	+	8.36975i	−0.0892792	+	0.333195i	0.906811	+	0.421538i	$0.138509\pi$
$632$	12.0353	+	3.22484i	0.478737	+	0.128277i
$633$		0			0
$634$	−1.79156	+	1.03436i	−0.0711519	+	0.0410796i
$635$	4.18727	+	1.12197i	0.166167	+	0.0445242i
$636$		0			0
$637$	8.75051	+	2.13076i	0.346708	+	0.0844236i
$638$			18.9382i			0.749772i
$639$		0			0
$640$	−0.175557	+	0.304074i	−0.00693952	+	0.0120196i
$641$	13.2773	−	22.9970i	0.524424	−	0.908329i	−0.475172	−	0.879893i	$-0.657614\pi$
$641$	13.2773	−	22.9970i	0.524424	−	0.908329i	0.999596	−	0.0284355i	$-0.00905254\pi$
$642$		0			0
$643$	−23.6006	+	23.6006i	−0.930715	+	0.930715i	−0.997751	−	0.0670354i	$-0.978646\pi$
$643$	−23.6006	+	23.6006i	−0.930715	+	0.930715i	0.0670354	+	0.997751i	$0.478646\pi$
$644$	−14.5680	+	14.5680i	−0.574060	+	0.574060i
$645$		0			0
$646$	14.7491	−	25.5462i	0.580296	−	1.00510i
$647$	11.9267	−	20.6576i	0.468886	−	0.812134i	−0.530482	−	0.847696i	$-0.677989\pi$
$647$	11.9267	−	20.6576i	0.468886	−	0.812134i	0.999367	+	0.0355623i	$0.0113222\pi$
$648$		0			0
$649$			36.5261i			1.43377i
$650$	−9.13871	−	15.0218i	−0.358450	−	0.589204i
$651$		0			0
$652$	17.9780	+	4.81720i	0.704074	+	0.188656i
$653$	25.8931	−	14.9494i	1.01327	−	0.585014i	0.101126	−	0.994874i	$-0.467756\pi$
$653$	25.8931	−	14.9494i	1.01327	−	0.585014i	0.912149	+	0.409859i	$0.134422\pi$
$654$		0			0
$655$	1.61383	+	0.432425i	0.0630576	+	0.0168962i
$656$	−0.678577	+	2.53248i	−0.0264940	+	0.0988769i
$657$		0			0
$658$	9.41974	+	9.41974i	0.367220	+	0.367220i
$659$	−20.6263	−	11.9086i	−0.803487	−	0.463893i	0.0412023	−	0.999151i	$-0.486881\pi$
$659$	−20.6263	−	11.9086i	−0.803487	−	0.463893i	−0.844689	+	0.535258i	$0.820215\pi$
$660$		0			0
$661$	3.35543	−	12.5226i	0.130511	−	0.487074i	−0.869465	−	0.493995i	$-0.835536\pi$
$661$	3.35543	−	12.5226i	0.130511	−	0.487074i	0.999976	+	0.00692047i	$0.00220287\pi$
$662$	−12.1428	+	21.0320i	−0.471945	+	0.817432i
$663$		0			0
$664$	2.03164	+	3.51891i	0.0788430	+	0.136560i
$665$	−3.97570	+	1.06529i	−0.154171	+	0.0413100i
$666$		0			0
$667$	−32.9400	+	19.0179i	−1.27544	+	0.736377i
$668$	−0.223019	+	0.832317i	−0.00862885	+	0.0322033i
$669$		0			0
$670$	3.42319	+	3.42319i	0.132249	+	0.132249i
$671$	−8.64479	−	32.2628i	−0.333728	−	1.24549i
$672$		0			0
$673$			46.4053i			1.78879i	0.447276	+	0.894396i	$0.352394\pi$
$673$			46.4053i			1.78879i	−0.447276	+	0.894396i	$0.647606\pi$
$674$	7.16580	+	26.7431i	0.276016	+	1.03011i
$675$		0			0
$676$	−12.9863	+	0.596413i	−0.499474	+	0.0229389i
$677$	28.9400	−	16.7085i	1.11225	−	0.642159i	0.172841	−	0.984950i	$-0.444705\pi$
$677$	28.9400	−	16.7085i	1.11225	−	0.642159i	0.939412	+	0.342790i	$0.111372\pi$
$678$		0			0
$679$	−1.30266	−	2.25628i	−0.0499917	−	0.0865881i
$680$	−2.72294			−0.104420
$681$		0			0
$682$	0.977449	+	3.64789i	0.0374284	+	0.139685i
$683$	4.57669	+	1.22632i	0.175122	+	0.0469238i	0.345314	−	0.938487i	$-0.387772\pi$
$683$	4.57669	+	1.22632i	0.175122	+	0.0469238i	−0.170192	+	0.985411i	$0.554439\pi$
$684$		0			0
$685$	−0.864749	−	1.49779i	−0.0330404	−	0.0572276i
$686$	−13.8749			−0.529748
$687$		0			0
$688$	3.68906	+	2.12988i	0.140644	+	0.0812010i
$689$	−14.0813	+	14.7429i	−0.536457	+	0.561660i
$690$		0			0
$691$	3.43143	−	3.43143i	0.130538	−	0.130538i	−0.638819	−	0.769357i	$-0.720577\pi$
$691$	3.43143	−	3.43143i	0.130538	−	0.130538i	0.769357	+	0.638819i	$0.220577\pi$
$692$	20.6789	+	11.9390i	0.786093	+	0.453851i
$693$		0			0
$694$	1.54652	−	1.54652i	0.0587049	−	0.0587049i
$695$	−1.39064	+	0.372622i	−0.0527501	+	0.0141344i
$696$		0			0
$697$	−19.6397	+	5.26245i	−0.743907	+	0.199329i
$698$		−	29.0844i		−	1.10086i
$699$		0			0
$700$	−10.6274	−	10.6274i	−0.401677	−	0.401677i
$701$	−1.76335			−0.0666009			−0.0333004	−	0.999445i	$-0.510602\pi$
$701$	−1.76335			−0.0666009			−0.0333004	+	0.999445i	$0.510602\pi$
$702$		0			0
$703$	35.0499			1.32193
$704$	−2.35360	−	2.35360i	−0.0887047	−	0.0887047i
$705$		0			0
$706$			7.26816i			0.273541i
$707$	−31.2984	+	8.38637i	−1.17710	+	0.315402i
$708$		0			0
$709$	33.1400	−	8.87983i	1.24460	−	0.333489i	0.424350	−	0.905498i	$-0.360502\pi$
$709$	33.1400	−	8.87983i	1.24460	−	0.333489i	0.820247	+	0.572009i	$0.193836\pi$
$710$	−0.329514	+	0.329514i	−0.0123664	+	0.0123664i
$711$		0			0
$712$	4.81595	+	2.78049i	0.180485	+	0.104203i
$713$	−5.36335	+	5.36335i	−0.200859	+	0.200859i
$714$		0			0
$715$	−4.04407	+	1.18370i	−0.151240	+	0.0442679i
$716$	9.00294	+	5.19785i	0.336456	+	0.194253i
$717$		0			0
$718$	−7.07360			−0.263985
$719$	−15.1571	−	26.2528i	−0.565264	−	0.979065i	−0.997025	−	0.0770774i	$-0.975441\pi$
$719$	−15.1571	−	26.2528i	−0.565264	−	0.979065i	0.431762	−	0.901988i	$-0.357892\pi$
$720$		0			0
$721$	−4.47833	−	1.19997i	−0.166782	−	0.0446891i
$722$	−1.17291	−	4.37737i	−0.0436513	−	0.162909i
$723$		0			0
$724$	−0.635701			−0.0236256
$725$	−13.8736	−	24.0298i	−0.515253	−	0.892444i
$726$		0			0
$727$	19.2180	−	11.0955i	0.712758	−	0.411511i	−0.0993236	−	0.995055i	$-0.531668\pi$
$727$	19.2180	−	11.0955i	0.712758	−	0.411511i	0.812081	+	0.583544i	$0.198335\pi$
$728$	−10.6644	+	3.12146i	−0.395248	+	0.115689i
$729$		0			0
$730$	0.281632	+	1.05107i	0.0104237	+	0.0389017i
$731$			33.0350i			1.22184i
$732$		0			0
$733$	0.276984	+	1.03372i	0.0102306	+	0.0381813i	0.970852	−	0.239678i	$-0.0770418\pi$
$733$	0.276984	+	1.03372i	0.0102306	+	0.0381813i	−0.960622	+	0.277859i	$0.910375\pi$
$734$	12.3928	+	12.3928i	0.457428	+	0.457428i
$735$		0			0
$736$	1.73021	−	6.45722i	0.0637763	−	0.238016i
$737$	−39.7443	+	22.9464i	−1.46400	+	0.845242i
$738$		0			0
$739$	−44.6085	+	11.9528i	−1.64095	+	0.439691i	−0.957059	−	0.289894i	$-0.906380\pi$
$739$	−44.6085	+	11.9528i	−1.64095	+	0.439691i	−0.683890	+	0.729585i	$0.739713\pi$
$740$	−1.61770	−	2.80194i	−0.0594679	−	0.103001i
$741$		0			0
$742$	−8.71302	+	15.0914i	−0.319865	+	0.554022i
$743$	−0.837432	+	3.12534i	−0.0307224	+	0.114658i	−0.979584	−	0.201034i	$-0.935570\pi$
$743$	−0.837432	+	3.12534i	−0.0307224	+	0.114658i	0.948862	+	0.315692i	$0.102236\pi$
$744$		0			0
$745$	2.30816	+	1.33262i	0.0845643	+	0.0488232i
$746$	8.57528	+	8.57528i	0.313963	+	0.313963i
$747$		0			0
$748$	6.68086	−	24.9333i	0.244277	−	0.911652i
$749$	−16.3423	−	4.37890i	−0.597133	−	0.160001i
$750$		0			0
$751$	−19.1224	+	11.0403i	−0.697785	+	0.402866i	−0.806522	−	0.591204i	$-0.798653\pi$
$751$	−19.1224	+	11.0403i	−0.697785	+	0.402866i	0.108737	+	0.994071i	$0.465319\pi$
$752$	−4.17527	−	1.11876i	−0.152256	−	0.0407970i
$753$		0			0
$754$	−20.5092	+	0.470707i	−0.746901	+	0.0171422i
$755$		−	5.11944i		−	0.186316i
$756$		0			0
$757$	7.92964	−	13.7345i	0.288208	−	0.499190i	−0.685174	−	0.728379i	$-0.740274\pi$
$757$	7.92964	−	13.7345i	0.288208	−	0.499190i	0.973382	+	0.229189i	$0.0736074\pi$
$758$	−3.08169	+	5.33764i	−0.111932	+	0.193872i
$759$		0			0
$760$	0.944369	−	0.944369i	0.0342559	−	0.0342559i
$761$	9.46921	−	9.46921i	0.343259	−	0.343259i	−0.514332	−	0.857591i	$-0.671960\pi$
$761$	9.46921	−	9.46921i	0.343259	−	0.343259i	0.857591	+	0.514332i	$0.171960\pi$
$762$		0			0
$763$	4.85892	−	8.41589i	0.175905	−	0.304676i
$764$	0.0745427	−	0.129112i	0.00269686	−	0.00467110i
$765$		0			0
$766$			14.6073i			0.527785i
$767$	−39.5560	+	0.907851i	−1.42829	+	0.0327806i
$768$		0			0
$769$	−40.5584	−	10.8676i	−1.46257	−	0.391896i	−0.562196	−	0.827004i	$-0.690043\pi$
$769$	−40.5584	−	10.8676i	−1.46257	−	0.391896i	−0.900378	+	0.435109i	$0.856710\pi$
$770$	−3.11918	+	1.80086i	−0.112408	+	0.0648985i
$771$		0			0
$772$	−4.12101	−	1.10422i	−0.148319	−	0.0397418i
$773$	−7.14882	+	26.6797i	−0.257125	+	0.959604i	0.709771	+	0.704433i	$0.248798\pi$
$773$	−7.14882	+	26.6797i	−0.257125	+	0.959604i	−0.966896	+	0.255171i	$0.917868\pi$
$774$		0			0
$775$	−3.91257	−	3.91257i	−0.140544	−	0.140544i
$776$	0.732116	+	0.422687i	0.0262814	+	0.0151736i
$777$		0			0
$778$	1.29238	−	4.82324i	0.0463342	−	0.172922i
$779$	4.98632	−	8.63657i	0.178654	−	0.309437i
$780$		0			0
$781$	−2.20881	−	3.82576i	−0.0790373	−	0.136897i
$782$	50.0765	−	13.4180i	1.79073	−	0.479825i
$783$		0			0
$784$	−2.16322	+	1.24894i	−0.0772578	+	0.0446048i
$785$	1.49094	−	5.56428i	0.0532141	−	0.198598i
$786$		0			0
$787$	26.6056	+	26.6056i	0.948386	+	0.948386i	0.998732	−	0.0503460i	$-0.0160324\pi$
$787$	26.6056	+	26.6056i	0.948386	+	0.948386i	−0.0503460	+	0.998732i	$0.516032\pi$
$788$	−4.94991	−	18.4733i	−0.176333	−	0.658085i
$789$		0			0
$790$			4.37482i			0.155649i
$791$	5.33420	+	19.9075i	0.189662	+	0.707830i
$792$		0			0
$793$	34.7242	−	10.1638i	1.23309	−	0.360927i
$794$	−5.22360	+	3.01585i	−0.185379	+	0.107028i
$795$		0			0
$796$	−2.62801	−	4.55185i	−0.0931474	−	0.161336i
$797$	0.176961			0.00626828			0.00313414	−	0.999995i	$-0.499002\pi$
$797$	0.176961			0.00626828			0.00313414	+	0.999995i	$0.499002\pi$
$798$		0			0
$799$	−8.67612	−	32.3797i	−0.306939	−	1.14551i
$800$	4.71055	+	1.26219i	0.166543	+	0.0446251i
$801$		0			0
$802$	−3.81543	−	6.60852i	−0.134728	−	0.233355i
$803$	−10.3154			−0.364021
$804$		0			0
$805$	−6.26462	−	3.61688i	−0.220799	−	0.127478i
$806$	−3.92619	+	1.14920i	−0.138294	+	0.0404788i
$807$		0			0
$808$	7.43446	−	7.43446i	0.261544	−	0.261544i
$809$	−31.7825	−	18.3496i	−1.11741	−	0.645138i	−0.176673	−	0.984270i	$-0.556534\pi$
$809$	−31.7825	−	18.3496i	−1.11741	−	0.645138i	−0.940739	+	0.339131i	$0.889867\pi$
$810$		0			0
$811$	31.0646	−	31.0646i	1.09083	−	1.09083i	0.0953858	−	0.995440i	$-0.469592\pi$
$811$	31.0646	−	31.0646i	1.09083	−	1.09083i	0.995440	−	0.0953858i	$-0.0304085\pi$
$812$	−16.9375	+	4.53838i	−0.594389	+	0.159266i
$813$		0			0
$814$	29.6259	−	7.93822i	1.03839	−	0.278235i
$815$			6.53502i			0.228912i
$816$		0			0
$817$	−11.4572	−	11.4572i	−0.400836	−	0.400836i
$818$	−4.70945			−0.164662
$819$		0			0
$820$	−0.920560			−0.0321474
$821$	26.3396	+	26.3396i	0.919260	+	0.919260i	0.996976	−	0.0777160i	$-0.0247627\pi$
$821$	26.3396	+	26.3396i	0.919260	+	0.919260i	−0.0777160	+	0.996976i	$0.524763\pi$
$822$		0			0
$823$		−	0.0653619i		−	0.00227837i	−0.999999	−	0.00113919i	$-0.999637\pi$
$823$		−	0.0653619i		−	0.00227837i	0.999999	−	0.00113919i	$-0.000362614\pi$
$824$	1.45313	−	0.389364i	0.0506220	−	0.0135641i
$825$		0			0
$826$	−32.6672	+	8.75316i	−1.13664	+	0.304561i
$827$	18.7164	−	18.7164i	0.650834	−	0.650834i	−0.302360	−	0.953194i	$-0.597774\pi$
$827$	18.7164	−	18.7164i	0.650834	−	0.650834i	0.953194	+	0.302360i	$0.0977744\pi$
$828$		0			0
$829$	1.64039	+	0.947080i	0.0569731	+	0.0328934i	0.528216	−	0.849110i	$-0.322861\pi$
$829$	1.64039	+	0.947080i	0.0569731	+	0.0328934i	−0.471243	+	0.882003i	$0.656194\pi$
$830$	−1.00881	+	1.00881i	−0.0350165	+	0.0350165i
$831$		0			0
$832$	2.49034	−	2.60734i	0.0863370	−	0.0903931i
$833$	−16.7760	−	9.68564i	−0.581255	−	0.335588i
$834$		0			0
$835$	−0.302548			−0.0104701
$836$	6.33032	+	10.9644i	0.218939	+	0.379213i
$837$		0			0
$838$	13.5868	+	3.64058i	0.469349	+	0.125762i
$839$	−6.75646	−	25.2155i	−0.233259	−	0.870534i	−0.978926	−	0.204215i	$-0.934536\pi$
$839$	−6.75646	−	25.2155i	−0.233259	−	0.870534i	0.745667	−	0.666319i	$-0.232131\pi$
$840$		0			0
$841$	−3.37302			−0.116311
$842$	15.3618	+	26.6074i	0.529403	+	0.916953i
$843$		0			0
$844$	20.6699	−	11.9338i	0.711488	−	0.410778i
$845$	−1.38241	−	4.35012i	−0.0475563	−	0.149649i
$846$		0			0
$847$	−0.0629161	−	0.234806i	−0.00216182	−	0.00806803i
$848$		−	5.65439i		−	0.194172i
$849$		0			0
$850$	9.78841	+	36.5309i	0.335740	+	1.25300i
$851$	43.5578	+	43.5578i	1.49314	+	1.49314i
$852$		0			0
$853$	−7.70120	+	28.7413i	−0.263684	+	0.984083i	0.699367	+	0.714763i	$0.253466\pi$
$853$	−7.70120	+	28.7413i	−0.263684	+	0.984083i	−0.963051	+	0.269320i	$0.913201\pi$
$854$	26.7827	−	15.4630i	0.916485	−	0.529133i
$855$		0			0
$856$	5.30272	−	1.42086i	0.181243	−	0.0485640i
$857$	25.2245	+	43.6902i	0.861654	+	1.49243i	0.870332	+	0.492466i	$0.163904\pi$
$857$	25.2245	+	43.6902i	0.861654	+	1.49243i	−0.00867797	+	0.999962i	$0.502762\pi$
$858$		0			0
$859$	8.60940	−	14.9119i	0.293749	−	0.508788i	−0.680944	−	0.732335i	$-0.738430\pi$
$859$	8.60940	−	14.9119i	0.293749	−	0.508788i	0.974693	+	0.223547i	$0.0717637\pi$
$860$	−0.387107	+	1.44470i	−0.0132002	+	0.0492640i
$861$		0			0
$862$	−33.8067	−	19.5183i	−1.15146	−	0.664797i
$863$	31.1457	+	31.1457i	1.06021	+	1.06021i	0.998067	+	0.0621448i	$0.0197941\pi$
$863$	31.1457	+	31.1457i	1.06021	+	1.06021i	0.0621448	+	0.998067i	$0.480206\pi$
$864$		0			0
$865$	−2.16991	+	8.09822i	−0.0737792	+	0.275348i
$866$	−1.25241	−	0.335583i	−0.0425588	−	0.0114036i
$867$		0			0
$868$	−3.02826	+	1.74837i	−0.102786	+	0.0593435i
$869$	−40.0593	−	10.7338i	−1.35892	−	0.364121i
$870$		0			0
$871$	−25.8377	−	42.4709i	−0.875477	−	1.43907i
$872$			3.15324i			0.106782i
$873$		0			0
$874$	−12.7139	+	22.0211i	−0.430055	+	0.744876i
$875$	5.34374	−	9.25562i	0.180651	−	0.312897i
$876$		0			0
$877$	−10.5926	+	10.5926i	−0.357688	+	0.357688i	−0.862960	−	0.505272i	$-0.831392\pi$
$877$	−10.5926	+	10.5926i	−0.357688	+	0.357688i	0.505272	+	0.862960i	$0.331392\pi$
$878$	−13.2943	+	13.2943i	−0.448660	+	0.448660i
$879$		0			0
$880$	0.584342	−	1.01211i	0.0196982	−	0.0341182i
$881$	15.2576	−	26.4270i	0.514042	−	0.890347i	−0.485825	−	0.874056i	$-0.661481\pi$
$881$	15.2576	−	26.4270i	0.514042	−	0.890347i	0.999867	−	0.0162912i	$-0.00518587\pi$
$882$		0			0
$883$			43.4738i			1.46301i	0.681836	+	0.731506i	$0.261182\pi$
$883$			43.4738i			1.46301i	−0.681836	+	0.731506i	$0.738818\pi$
$884$	27.1677	+	6.61534i	0.913747	+	0.222498i
$885$		0			0
$886$	−20.9730	−	5.61970i	−0.704603	−	0.188798i
$887$	37.4910	−	21.6454i	1.25882	−	0.726783i	0.285979	−	0.958236i	$-0.407681\pi$
$887$	37.4910	−	21.6454i	1.25882	−	0.726783i	0.972846	+	0.231453i	$0.0743481\pi$
$888$		0			0
$889$	−36.7532	−	9.84798i	−1.23266	−	0.330291i
$890$	−0.505355	+	1.88601i	−0.0169395	+	0.0632192i
$891$		0			0
$892$	−15.6524	−	15.6524i	−0.524080	−	0.524080i
$893$	14.2390	+	8.22088i	0.476489	+	0.275101i
$894$		0			0
$895$	−0.944712	+	3.52571i	−0.0315782	+	0.117852i
$896$	1.54093	−	2.66897i	0.0514789	−	0.0891640i
$897$		0			0
$898$	11.3617	+	19.6790i	0.379144	+	0.656696i
$899$	−6.23570	+	1.67085i	−0.207972	+	0.0557260i
$900$		0			0
$901$	37.9756	−	21.9252i	1.26515	−	0.730435i
$902$	2.25864	−	8.42936i	0.0752045	−	0.280667i
$903$		0			0
$904$	−4.72874	−	4.72874i	−0.157275	−	0.157275i
$905$	−0.0577694	−	0.215598i	−0.00192032	−	0.00716674i
$906$		0			0
$907$			3.27990i			0.108907i	0.998516	+	0.0544536i	$0.0173417\pi$
$907$			3.27990i			0.108907i	−0.998516	+	0.0544536i	$0.982658\pi$
$908$	−5.78170	−	21.5776i	−0.191873	−	0.716078i
$909$		0			0
$910$	−2.02777	−	3.33317i	−0.0672201	−	0.110493i
$911$	28.5102	−	16.4604i	0.944585	−	0.545356i	0.0531903	−	0.998584i	$-0.483061\pi$
$911$	28.5102	−	16.4604i	0.944585	−	0.545356i	0.891395	+	0.453228i	$0.149728\pi$
$912$		0			0
$913$	−6.76231	−	11.7127i	−0.223800	−	0.387633i
$914$	−29.0382			−0.960498
$915$		0			0
$916$	2.40948	+	8.99230i	0.0796114	+	0.297114i
$917$	−14.1652	−	3.79555i	−0.467775	−	0.125340i
$918$		0			0
$919$	−7.23822	−	12.5370i	−0.238767	−	0.413556i	0.721594	−	0.692317i	$-0.243410\pi$
$919$	−7.23822	−	12.5370i	−0.238767	−	0.413556i	−0.960361	+	0.278760i	$0.910076\pi$
$920$	2.34720			0.0773850
$921$		0			0
$922$	−10.1387	−	5.85358i	−0.333900	−	0.192777i
$923$	4.08822	−	2.48712i	0.134565	−	0.0818646i
$924$		0			0
$925$	−31.7755	+	31.7755i	−1.04477	+	1.04477i
$926$	−15.9684	−	9.21937i	−0.524754	−	0.302967i
$927$		0			0
$928$	4.02325	−	4.02325i	0.132070	−	0.132070i
$929$	−7.39674	+	1.98195i	−0.242679	+	0.0650257i	−0.378108	−	0.925761i	$-0.623425\pi$
$929$	−7.39674	+	1.98195i	−0.242679	+	0.0650257i	0.135429	+	0.990787i	$0.456759\pi$
$930$		0			0
$931$	9.17743	−	2.45909i	0.300778	−	0.0805933i
$932$			28.4945i			0.933370i
$933$		0			0
$934$	10.8740	+	10.8740i	0.355807	+	0.355807i
$935$	9.06328			0.296401
$936$		0			0
$937$	5.37576			0.175618			0.0878092	−	0.996137i	$-0.472013\pi$
$937$	5.37576			0.175618			0.0878092	+	0.996137i	$0.472013\pi$
$938$	−30.0466	−	30.0466i	−0.981055	−	0.981055i
$939$		0			0
$940$		−	1.51771i		−	0.0495024i
$941$	10.0206	−	2.68502i	0.326663	−	0.0875292i	−0.0917603	−	0.995781i	$-0.529249\pi$
$941$	10.0206	−	2.68502i	0.326663	−	0.0875292i	0.418424	+	0.908252i	$0.362583\pi$
$942$		0			0
$943$	16.9297	−	4.53629i	0.551306	−	0.147722i
$944$	7.75962	−	7.75962i	0.252554	−	0.252554i
$945$		0			0
$946$	−12.2790	−	7.08930i	−0.399226	−	0.230493i
$947$	−7.93935	+	7.93935i	−0.257994	+	0.257994i	−0.824238	−	0.566244i	$-0.808396\pi$
$947$	−7.93935	+	7.93935i	−0.257994	+	0.257994i	0.566244	+	0.824238i	$0.308396\pi$
$948$		0			0
$949$	−0.256387	−	11.1710i	−0.00832268	−	0.362628i
$950$	−16.0644	−	9.27481i	−0.521200	−	0.300915i
$951$		0			0
$952$	23.9002			0.774610
$953$	26.5828	+	46.0427i	0.861100	+	1.49147i	0.870868	+	0.491517i	$0.163558\pi$
$953$	26.5828	+	46.0427i	0.861100	+	1.49147i	−0.00976733	+	0.999952i	$0.503109\pi$
$954$		0			0
$955$	0.0505625	+	0.0135482i	0.00163616	+	0.000438409i
$956$	−3.73860	−	13.9526i	−0.120915	−	0.451260i
$957$		0			0
$958$	15.5498			0.502391
$959$	7.59022	+	13.1466i	0.245101	+	0.424527i
$960$		0			0
$961$	25.7319	−	14.8563i	0.830061	−	0.479236i
$962$	9.33307	+	31.8861i	0.300910	+	1.02805i
$963$		0			0
$964$	7.89898	+	29.4794i	0.254409	+	0.949468i
$965$		−	1.49799i		−	0.0482221i
$966$		0			0
$967$	−3.34557	−	12.4858i	−0.107586	−	0.401517i	0.891039	−	0.453926i	$-0.149977\pi$
$967$	−3.34557	−	12.4858i	−0.107586	−	0.401517i	−0.998626	+	0.0524085i	$0.983310\pi$
$968$	0.0557747	+	0.0557747i	0.00179267	+	0.00179267i
$969$		0			0
$970$	−0.0768236	+	0.286710i	−0.00246666	+	0.00920569i
$971$	−2.94507	+	1.70033i	−0.0945117	+	0.0545663i	−0.546511	−	0.837452i	$-0.684044\pi$
$971$	−2.94507	+	1.70033i	−0.0945117	+	0.0545663i	0.451999	+	0.892018i	$0.350711\pi$
$972$		0			0
$973$	12.2062	−	3.27064i	0.391312	−	0.104852i
$974$	8.68919	+	15.0501i	0.278420	+	0.482237i
$975$		0			0
$976$	−5.01742	+	8.69042i	−0.160604	+	0.278174i
$977$	−13.0904	+	48.8539i	−0.418798	+	1.56297i	0.358307	+	0.933604i	$0.383354\pi$
$977$	−13.0904	+	48.8539i	−0.418798	+	1.56297i	−0.777105	+	0.629371i	$0.783313\pi$
$978$		0			0
$979$	−16.0299	−	9.25484i	−0.512317	−	0.295786i
$980$	−0.620160	−	0.620160i	−0.0198103	−	0.0198103i
$981$		0			0
$982$	2.09147	−	7.80547i	0.0667415	−	0.249083i
$983$	55.7899	+	14.9488i	1.77942	+	0.476794i	0.990478	−	0.137673i	$-0.0439624\pi$
$983$	55.7899	+	14.9488i	1.77942	+	0.476794i	0.788942	+	0.614467i	$0.210629\pi$
$984$		0			0
$985$	5.81542	−	3.35754i	0.185295	−	0.106980i
$986$	42.6210	+	11.4203i	1.35733	+	0.363695i
$987$		0			0
$988$	−11.7166	+	7.12795i	−0.372755	+	0.226770i
$989$		−	28.4766i		−	0.905502i
$990$		0			0
$991$	4.35876	−	7.54960i	0.138461	−	0.239821i	−0.788453	−	0.615094i	$-0.789118\pi$
$991$	4.35876	−	7.54960i	0.138461	−	0.239821i	0.926914	+	0.375274i	$0.122451\pi$
$992$	0.567309	−	0.982608i	0.0180121	−	0.0311978i
$993$		0			0
$994$	2.89226	−	2.89226i	0.0917370	−	0.0917370i
$995$	1.30494	−	1.30494i	0.0413695	−	0.0413695i
$996$		0			0
$997$	7.03892	−	12.1918i	0.222925	−	0.386117i	−0.732770	−	0.680476i	$-0.761773\pi$
$997$	7.03892	−	12.1918i	0.222925	−	0.386117i	0.955695	+	0.294359i	$0.0951062\pi$
$998$	−6.55866	+	11.3599i	−0.207611	+	0.359592i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.71.12		56
3.2	odd	2		234.2.y.a.149.4	yes	56
9.2	odd	6		702.2.bc.a.305.5		56
9.7	even	3		234.2.z.a.227.8	yes	56
13.11	odd	12		702.2.bc.a.557.5		56
39.11	even	12		234.2.z.a.167.8	yes	56
117.11	even	12	inner	702.2.bb.a.89.12		56
117.115	odd	12		234.2.y.a.11.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.4	✓	56	117.115	odd	12
234.2.y.a.149.4	yes	56	3.2	odd	2
234.2.z.a.167.8	yes	56	39.11	even	12
234.2.z.a.227.8	yes	56	9.7	even	3
702.2.bb.a.71.12		56	1.1	even	1	trivial
702.2.bb.a.89.12		56	117.11	even	12	inner
702.2.bc.a.305.5		56	9.2	odd	6
702.2.bc.a.557.5		56	13.11	odd	12

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.339151 + 0.0908752i) q^{5} +(2.97685 - 0.797644i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.304074 - 0.175557i) q^{10} +(2.35360 - 2.35360i) q^{11} +(2.60734 + 2.49034i) q^{13} +(2.66897 + 1.54093i) q^{14} -1.00000 q^{16} +(-3.87756 - 6.71613i) q^{17} +(3.67410 + 0.984473i) q^{19} +(-0.0908752 - 0.339151i) q^{20} +3.32849 q^{22} +(3.34250 + 5.78938i) q^{23} +(-4.22336 + 2.43836i) q^{25} +(0.0827293 + 3.60460i) q^{26} +(0.797644 + 2.97685i) q^{28} +5.68973i q^{29} +(0.293661 + 1.09596i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.00717 - 7.49087i) q^{34} +(-0.937115 + 0.541044i) q^{35} +(8.90068 - 2.38493i) q^{37} +(1.90186 + 3.29411i) q^{38} +(0.175557 - 0.304074i) q^{40} +(0.678577 - 2.53248i) q^{41} +(-3.68906 - 2.12988i) q^{43} +(2.35360 + 2.35360i) q^{44} +(-1.73021 + 6.45722i) q^{46} +(4.17527 + 1.11876i) q^{47} +(2.16322 - 1.24894i) q^{49} +(-4.71055 - 1.26219i) q^{50} +(-2.49034 + 2.60734i) q^{52} +5.65439i q^{53} +(-0.584342 + 1.01211i) q^{55} +(-1.54093 + 2.66897i) q^{56} +(-4.02325 + 4.02325i) q^{58} +(-7.75962 + 7.75962i) q^{59} +(5.01742 - 8.69042i) q^{61} +(-0.567309 + 0.982608i) q^{62} -1.00000i q^{64} +(-1.11059 - 0.607659i) q^{65} +(-13.3180 - 3.56856i) q^{67} +(6.71613 - 3.87756i) q^{68} +(-1.04522 - 0.280065i) q^{70} +(0.343507 - 1.28199i) q^{71} +(-2.19140 - 2.19140i) q^{73} +(7.98013 + 4.60733i) q^{74} +(-0.984473 + 3.67410i) q^{76} +(5.12898 - 8.88365i) q^{77} +(-6.22990 - 10.7905i) q^{79} +(0.339151 - 0.0908752i) q^{80} +(2.27056 - 1.31091i) q^{82} +(1.05166 - 3.92483i) q^{83} +(1.92541 + 1.92541i) q^{85} +(-1.10251 - 4.11462i) q^{86} +3.32849i q^{88} +(-1.43929 - 5.37149i) q^{89} +(9.74806 + 5.33364i) q^{91} +(-5.78938 + 3.34250i) q^{92} +(2.16128 + 3.74344i) q^{94} -1.33554 q^{95} +(-0.218799 - 0.816569i) q^{97} +(2.41276 + 0.646496i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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