LMFDB - Embedded newform 243.2.g.a.73.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(10,243)] 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("243.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	243.73
Dual form			243.2.g.a.10.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.744407 + 0.373855i) q^{2} +(-0.779943 + 1.04765i) q^{4} +(-0.345929 + 1.15548i) q^{5} +(-0.520803 + 1.20736i) q^{7} +(0.478230 - 2.71217i) q^{8} +(-0.174471 - 0.989477i) q^{10} +(-2.11479 - 0.501215i) q^{11} +(-3.80561 + 2.50299i) q^{13} +(-0.0636874 - 1.09347i) q^{14} +(-0.0912185 - 0.304691i) q^{16} +(-3.54217 - 1.28924i) q^{17} +(-2.50517 + 0.911807i) q^{19} +(-0.940731 - 1.26362i) q^{20} +(1.76165 - 0.417519i) q^{22} +(2.38967 + 5.53988i) q^{23} +(2.96197 + 1.94812i) q^{25} +(1.89717 - 3.28599i) q^{26} +(-0.858686 - 1.48729i) q^{28} +(-0.241756 + 4.15079i) q^{29} +(-7.40674 - 0.865723i) q^{31} +(3.96165 + 4.19911i) q^{32} +(3.11881 - 0.364536i) q^{34} +(-1.21492 - 1.01944i) q^{35} +(7.47819 - 6.27494i) q^{37} +(1.52398 - 1.61533i) q^{38} +(2.96844 + 1.49081i) q^{40} +(-5.17242 - 2.59769i) q^{41} +(3.46904 - 3.67697i) q^{43} +(2.17451 - 1.82463i) q^{44} +(-3.85000 - 3.23053i) q^{46} +(-2.97767 + 0.348040i) q^{47} +(3.61722 + 3.83402i) q^{49} +(-2.93322 - 0.342844i) q^{50} +(0.345914 - 5.93911i) q^{52} +(6.22987 + 10.7905i) q^{53} +(1.31071 - 2.27022i) q^{55} +(3.02550 + 1.98990i) q^{56} +(-1.37183 - 3.18026i) q^{58} +(10.6138 - 2.51552i) q^{59} +(7.04237 + 9.45955i) q^{61} +(5.83728 - 2.12460i) q^{62} +(-3.92120 - 1.42720i) q^{64} +(-1.57569 - 5.26317i) q^{65} +(0.0482665 + 0.828703i) q^{67} +(4.11336 - 2.70540i) q^{68} +(1.28552 + 0.304673i) q^{70} +(-1.25916 - 7.14107i) q^{71} +(-1.41006 + 7.99685i) q^{73} +(-3.22089 + 7.46687i) q^{74} +(0.998639 - 3.33569i) q^{76} +(1.70654 - 2.29228i) q^{77} +(-10.2764 + 5.16099i) q^{79} +0.383620 q^{80} +4.82155 q^{82} +(4.26695 - 2.14294i) q^{83} +(2.71504 - 3.64693i) q^{85} +(-1.20772 + 4.03408i) q^{86} +(-2.37074 + 5.49599i) q^{88} +(-0.578632 + 3.28158i) q^{89} +(-1.04003 - 5.89829i) q^{91} +(-7.66763 - 1.81726i) q^{92} +(2.08648 - 1.37230i) q^{94} +(-0.186967 - 3.21010i) q^{95} +(-0.390985 - 1.30598i) q^{97} +(-4.12605 - 1.50176i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	−0.744407	+	0.373855i	−0.526375	+	0.264356i	−0.692081	−	0.721820i	$-0.743306\pi$
$2$	−0.744407	+	0.373855i	−0.526375	+	0.264356i	0.165706	+	0.986175i	$0.447010\pi$
$3$		0			0
$3$		0			0
$4$	−0.779943	+	1.04765i	−0.389972	+	0.523823i
$5$	−0.345929	+	1.15548i	−0.154704	+	0.516747i	−0.999842	−	0.0178015i	$-0.994333\pi$
$5$	−0.345929	+	1.15548i	−0.154704	+	0.516747i	0.845137	+	0.534549i	$0.179518\pi$
$6$		0			0
$7$	−0.520803	+	1.20736i	−0.196845	+	0.456338i	−0.987838	−	0.155487i	$-0.950305\pi$
$7$	−0.520803	+	1.20736i	−0.196845	+	0.456338i	0.790993	+	0.611825i	$0.209565\pi$
$8$	0.478230	−	2.71217i	0.169080	−	0.958899i
$9$		0			0
$10$	−0.174471	−	0.989477i	−0.0551727	−	0.312900i
$11$	−2.11479	−	0.501215i	−0.637634	−	0.151122i	−0.100931	−	0.994893i	$-0.532182\pi$
$11$	−2.11479	−	0.501215i	−0.637634	−	0.151122i	−0.536703	+	0.843771i	$0.680330\pi$
$12$		0			0
$13$	−3.80561	+	2.50299i	−1.05549	+	0.694204i	−0.953748	−	0.300607i	$-0.902811\pi$
$13$	−3.80561	+	2.50299i	−1.05549	+	0.694204i	−0.101738	+	0.994811i	$0.532440\pi$
$14$	−0.0636874	−	1.09347i	−0.0170212	−	0.292242i
$15$		0			0
$16$	−0.0912185	−	0.304691i	−0.0228046	−	0.0761727i
$17$	−3.54217	−	1.28924i	−0.859102	−	0.312688i	−0.125356	−	0.992112i	$-0.540007\pi$
$17$	−3.54217	−	1.28924i	−0.859102	−	0.312688i	−0.733746	+	0.679424i	$0.762230\pi$
$18$		0			0
$19$	−2.50517	+	0.911807i	−0.574725	+	0.209183i	−0.612998	−	0.790084i	$-0.710037\pi$
$19$	−2.50517	+	0.911807i	−0.574725	+	0.209183i	0.0382728	+	0.999267i	$0.487814\pi$
$20$	−0.940731	−	1.26362i	−0.210354	−	0.282554i
$21$		0			0
$22$	1.76165	−	0.417519i	0.375585	−	0.0890153i
$23$	2.38967	+	5.53988i	0.498281	+	1.15514i	0.962955	+	0.269663i	$0.0869122\pi$
$23$	2.38967	+	5.53988i	0.498281	+	1.15514i	−0.464674	+	0.885482i	$0.653829\pi$
$24$		0			0
$25$	2.96197	+	1.94812i	0.592393	+	0.389623i
$26$	1.89717	−	3.28599i	0.372065	−	0.644435i
$27$		0			0
$28$	−0.858686	−	1.48729i	−0.162276	−	0.281071i
$29$	−0.241756	+	4.15079i	−0.0448929	+	0.770782i	0.898473	+	0.439028i	$0.144677\pi$
$29$	−0.241756	+	4.15079i	−0.0448929	+	0.770782i	−0.943366	+	0.331753i	$0.892360\pi$
$30$		0			0
$31$	−7.40674	−	0.865723i	−1.33029	−	0.155488i	−0.578927	−	0.815379i	$-0.696529\pi$
$31$	−7.40674	−	0.865723i	−1.33029	−	0.155488i	−0.751362	+	0.659891i	$0.770603\pi$
$32$	3.96165	+	4.19911i	0.700328	+	0.742304i
$33$		0			0
$34$	3.11881	−	0.364536i	0.534871	−	0.0625174i
$35$	−1.21492	−	1.01944i	−0.205359	−	0.172317i
$36$		0			0
$37$	7.47819	−	6.27494i	1.22941	−	1.03159i	0.231129	−	0.972923i	$-0.425758\pi$
$37$	7.47819	−	6.27494i	1.22941	−	1.03159i	0.998277	−	0.0586711i	$-0.0186863\pi$
$38$	1.52398	−	1.61533i	0.247222	−	0.262040i
$39$		0			0
$40$	2.96844	+	1.49081i	0.469351	+	0.235717i
$41$	−5.17242	−	2.59769i	−0.807797	−	0.405691i	−0.00355548	−	0.999994i	$-0.501132\pi$
$41$	−5.17242	−	2.59769i	−0.807797	−	0.405691i	−0.804241	+	0.594303i	$0.797428\pi$
$42$		0			0
$43$	3.46904	−	3.67697i	0.529024	−	0.560732i	−0.406657	−	0.913581i	$-0.633305\pi$
$43$	3.46904	−	3.67697i	0.529024	−	0.560732i	0.935680	+	0.352849i	$0.114787\pi$
$44$	2.17451	−	1.82463i	0.327820	−	0.275074i
$45$		0			0
$46$	−3.85000	−	3.23053i	−0.567652	−	0.476316i
$47$	−2.97767	+	0.348040i	−0.434338	+	0.0507669i	−0.330453	−	0.943822i	$-0.607202\pi$
$47$	−2.97767	+	0.348040i	−0.434338	+	0.0507669i	−0.103885	+	0.994589i	$0.533127\pi$
$48$		0			0
$49$	3.61722	+	3.83402i	0.516745	+	0.547718i
$50$	−2.93322	−	0.342844i	−0.414820	−	0.0484855i
$51$		0			0
$52$	0.345914	−	5.93911i	0.0479696	−	0.823607i
$53$	6.22987	+	10.7905i	0.855739	+	1.48218i	0.875958	+	0.482388i	$0.160230\pi$
$53$	6.22987	+	10.7905i	0.855739	+	1.48218i	−0.0202187	+	0.999796i	$0.506436\pi$
$54$		0			0
$55$	1.31071	−	2.27022i	0.176737	−	0.306117i
$56$	3.02550	+	1.98990i	0.404300	+	0.265912i
$57$		0			0
$58$	−1.37183	−	3.18026i	−0.180130	−	0.417588i
$59$	10.6138	−	2.51552i	1.38180	−	0.327493i	0.528510	−	0.848927i	$-0.322751\pi$
$59$	10.6138	−	2.51552i	1.38180	−	0.327493i	0.853292	+	0.521434i	$0.174603\pi$
$60$		0			0
$61$	7.04237	+	9.45955i	0.901684	+	1.21117i	0.976834	+	0.213999i	$0.0686490\pi$
$61$	7.04237	+	9.45955i	0.901684	+	1.21117i	−0.0751502	+	0.997172i	$0.523944\pi$
$62$	5.83728	−	2.12460i	0.741336	−	0.269824i
$63$		0			0
$64$	−3.92120	−	1.42720i	−0.490150	−	0.178400i
$65$	−1.57569	−	5.26317i	−0.195440	−	0.652816i
$66$		0			0
$67$	0.0482665	+	0.828703i	0.00589669	+	0.101242i	0.999972	−	0.00744893i	$-0.00237109\pi$
$67$	0.0482665	+	0.828703i	0.00589669	+	0.101242i	−0.994076	+	0.108691i	$0.965334\pi$
$68$	4.11336	−	2.70540i	0.498818	−	0.328078i
$69$		0			0
$70$	1.28552	+	0.304673i	0.153649	+	0.0364154i
$71$	−1.25916	−	7.14107i	−0.149435	−	0.847489i	−0.963698	−	0.266993i	$-0.913970\pi$
$71$	−1.25916	−	7.14107i	−0.149435	−	0.847489i	0.814263	−	0.580496i	$-0.197141\pi$
$72$		0			0
$73$	−1.41006	+	7.99685i	−0.165035	+	0.935960i	0.783993	+	0.620769i	$0.213180\pi$
$73$	−1.41006	+	7.99685i	−0.165035	+	0.935960i	−0.949028	+	0.315191i	$0.897931\pi$
$74$	−3.22089	+	7.46687i	−0.374421	+	0.868006i
$75$		0			0
$76$	0.998639	−	3.33569i	0.114552	−	0.382629i
$77$	1.70654	−	2.29228i	0.194478	−	0.261229i
$78$		0			0
$79$	−10.2764	+	5.16099i	−1.15618	+	0.580657i	−0.920334	−	0.391133i	$-0.872083\pi$
$79$	−10.2764	+	5.16099i	−1.15618	+	0.580657i	−0.235849	+	0.971790i	$0.575787\pi$
$80$	0.383620			0.0428900
$81$		0			0
$82$	4.82155			0.532451
$83$	4.26695	−	2.14294i	0.468358	−	0.235218i	−0.198936	−	0.980012i	$-0.563749\pi$
$83$	4.26695	−	2.14294i	0.468358	−	0.235218i	0.667294	+	0.744794i	$0.267452\pi$
$84$		0			0
$85$	2.71504	−	3.64693i	0.294487	−	0.395565i
$86$	−1.20772	+	4.03408i	−0.130232	+	0.435006i
$87$		0			0
$88$	−2.37074	+	5.49599i	−0.252722	+	0.585875i
$89$	−0.578632	+	3.28158i	−0.0613348	+	0.347847i	0.938661	+	0.344842i	$0.112068\pi$
$89$	−0.578632	+	3.28158i	−0.0613348	+	0.347847i	−0.999995	+	0.00300484i	$0.999044\pi$
$90$		0			0
$91$	−1.04003	−	5.89829i	−0.109025	−	0.618309i
$92$	−7.66763	−	1.81726i	−0.799406	−	0.189463i
$93$		0			0
$94$	2.08648	−	1.37230i	0.215204	−	0.141542i
$95$	−0.186967	−	3.21010i	−0.0191824	−	0.329349i
$96$		0			0
$97$	−0.390985	−	1.30598i	−0.0396985	−	0.132602i	0.935843	−	0.352417i	$-0.114640\pi$
$97$	−0.390985	−	1.30598i	−0.0396985	−	0.132602i	−0.975542	+	0.219814i	$0.929455\pi$
$98$	−4.12605	−	1.50176i	−0.416794	−	0.151701i
$99$		0			0
$100$	−4.35110	+	1.58367i	−0.435110	+	0.158367i
$101$	−1.38233	−	1.85679i	−0.137547	−	0.184757i	0.728013	−	0.685564i	$-0.240444\pi$
$101$	−1.38233	−	1.85679i	−0.137547	−	0.184757i	−0.865559	+	0.500807i	$0.833037\pi$
$102$		0			0
$103$	4.42692	−	1.04920i	0.436198	−	0.103381i	−0.00664935	−	0.999978i	$-0.502117\pi$
$103$	4.42692	−	1.04920i	0.436198	−	0.103381i	0.442847	+	0.896597i	$0.353968\pi$
$104$	4.96858	+	11.5185i	0.487210	+	1.12948i
$105$		0			0
$106$	−8.67163	−	5.70342i	−0.842263	−	0.553965i
$107$	−6.14665	+	10.6463i	−0.594219	+	1.02922i	0.399438	+	0.916760i	$0.369205\pi$
$107$	−6.14665	+	10.6463i	−0.594219	+	1.02922i	−0.993657	+	0.112457i	$0.964128\pi$
$108$		0			0
$109$	4.45327	+	7.71330i	0.426546	+	0.738800i	0.996563	−	0.0828329i	$-0.0263968\pi$
$109$	4.45327	+	7.71330i	0.426546	+	0.738800i	−0.570017	+	0.821633i	$0.693063\pi$
$110$	−0.126970	+	2.17999i	−0.0121061	+	0.207854i
$111$		0			0
$112$	0.415378	+	0.0485507i	0.0392495	+	0.00458761i
$113$	−11.9342	−	12.6496i	−1.12268	−	1.18997i	−0.979747	−	0.200238i	$-0.935828\pi$
$113$	−11.9342	−	12.6496i	−1.12268	−	1.18997i	−0.142932	−	0.989733i	$-0.545653\pi$
$114$		0			0
$115$	−7.22789	+	0.844819i	−0.674004	+	0.0787798i
$116$	−4.16000	−	3.49065i	−0.386246	−	0.324099i
$117$		0			0
$118$	−6.96056	+	5.84061i	−0.640772	+	0.537671i
$119$	3.40135	−	3.60522i	0.311801	−	0.330490i
$120$		0			0
$121$	−5.60882	−	2.81686i	−0.509893	−	0.256078i
$122$	−8.77890	−	4.40893i	−0.794804	−	0.399166i
$123$		0			0
$124$	6.68380	−	7.08442i	0.600223	−	0.636199i
$125$	−7.89548	+	6.62509i	−0.706193	+	0.592566i
$126$		0			0
$127$	4.35255	+	3.65222i	0.386226	+	0.324082i	0.815141	−	0.579263i	$-0.196660\pi$
$127$	4.35255	+	3.65222i	0.386226	+	0.324082i	−0.428915	+	0.903345i	$0.641104\pi$
$128$	−8.01534	+	0.936859i	−0.708462	+	0.0828074i
$129$		0			0
$130$	3.14062	+	3.32886i	0.275450	+	0.291960i
$131$	−19.3865	−	2.26596i	−1.69381	−	0.197978i	−0.786250	−	0.617909i	$-0.787980\pi$
$131$	−19.3865	−	2.26596i	−1.69381	−	0.197978i	−0.907556	+	0.419931i	$0.862054\pi$
$132$		0			0
$133$	0.203823	−	3.49951i	0.0176737	−	0.303446i
$134$	−0.345745	−	0.598848i	−0.0298678	−	0.0517326i
$135$		0			0
$136$	−5.19062	+	8.99042i	−0.445092	+	0.770922i
$137$	13.2460	+	8.71204i	1.13168	+	0.744320i	0.970140	−	0.242546i	$-0.0779825\pi$
$137$	13.2460	+	8.71204i	1.13168	+	0.744320i	0.161543	+	0.986866i	$0.448353\pi$
$138$		0			0
$139$	−4.13477	−	9.58547i	−0.350707	−	0.813029i	−0.998680	−	0.0513663i	$-0.983642\pi$
$139$	−4.13477	−	9.58547i	−0.350707	−	0.813029i	0.647973	−	0.761663i	$-0.275617\pi$
$140$	2.01558	−	0.477701i	0.170347	−	0.0403731i
$141$		0			0
$142$	3.60706	+	4.84512i	0.302697	+	0.406593i
$143$	9.30261	−	3.38587i	0.777923	−	0.283141i
$144$		0			0
$145$	−4.71253	−	1.71522i	−0.391354	−	0.142441i
$146$	−1.94001	−	6.48007i	−0.160556	−	0.536294i
$147$		0			0
$148$	0.741356	+	12.7286i	0.0609391	+	1.04628i
$149$	−2.43554	+	1.60188i	−0.199527	+	0.131231i	−0.645341	−	0.763895i	$-0.723285\pi$
$149$	−2.43554	+	1.60188i	−0.199527	+	0.131231i	0.445814	+	0.895126i	$0.352914\pi$
$150$		0			0
$151$	−12.4159	−	2.94262i	−1.01039	−	0.239467i	−0.308098	−	0.951355i	$-0.599692\pi$
$151$	−12.4159	−	2.94262i	−1.01039	−	0.239467i	−0.702293	+	0.711888i	$0.747840\pi$
$152$	1.27493	+	7.23051i	0.103411	+	0.586472i
$153$		0			0
$154$	−0.413378	+	2.34439i	−0.0333110	+	0.188916i
$155$	3.56253	−	8.25887i	0.286149	−	0.663369i
$156$		0			0
$157$	0.364422	−	1.21726i	0.0290841	−	0.0971476i	−0.942215	−	0.335008i	$-0.891261\pi$
$157$	0.364422	−	1.21726i	0.0290841	−	0.0971476i	0.971299	+	0.237861i	$0.0764461\pi$
$158$	5.72035	−	7.68376i	0.455086	−	0.611287i
$159$		0			0
$160$	−6.22244	+	3.12503i	−0.491927	+	0.247055i
$161$	−7.93316			−0.625221
$162$		0			0
$163$	12.3636			0.968391			0.484195	−	0.874960i	$-0.339112\pi$
$163$	12.3636			0.968391			0.484195	+	0.874960i	$0.339112\pi$
$164$	6.75565	−	3.39282i	0.527528	−	0.264934i
$165$		0			0
$166$	−2.37520	+	3.19044i	−0.184351	+	0.247626i
$167$	1.09374	−	3.65334i	0.0846359	−	0.282704i	−0.905186	−	0.425016i	$-0.860269\pi$
$167$	1.09374	−	3.65334i	0.0846359	−	0.282704i	0.989822	+	0.142312i	$0.0454537\pi$
$168$		0			0
$169$	3.06867	−	7.11397i	0.236051	−	0.547228i
$170$	−0.657669	+	3.72983i	−0.0504409	+	0.286065i
$171$		0			0
$172$	1.14650	+	6.50215i	0.0874201	+	0.495784i
$173$	23.4213	+	5.55096i	1.78069	+	0.422031i	0.983383	−	0.181542i	$-0.0581089\pi$
$173$	23.4213	+	5.55096i	1.78069	+	0.422031i	0.797307	+	0.603574i	$0.206257\pi$
$174$		0			0
$175$	−3.89467	+	2.56157i	−0.294410	+	0.193636i
$176$	0.0401925	+	0.690078i	0.00302962	+	0.0520166i
$177$		0			0
$178$	−0.796100	−	2.65916i	−0.0596702	−	0.199312i
$179$	−5.95691	−	2.16814i	−0.445240	−	0.162054i	0.109664	−	0.993969i	$-0.465023\pi$
$179$	−5.95691	−	2.16814i	−0.445240	−	0.162054i	−0.554904	+	0.831915i	$0.687245\pi$
$180$		0			0
$181$	−5.82014	+	2.11836i	−0.432608	+	0.157456i	−0.549140	−	0.835731i	$-0.685045\pi$
$181$	−5.82014	+	2.11836i	−0.432608	+	0.157456i	0.116532	+	0.993187i	$0.462822\pi$
$182$	2.97931	+	4.00191i	0.220841	+	0.296641i
$183$		0			0
$184$	16.1679	−	3.83187i	1.19192	−	0.282489i
$185$	4.66367	+	10.8116i	0.342880	+	0.794884i
$186$		0			0
$187$	6.84476	+	4.50187i	0.500539	+	0.329210i
$188$	1.95779	−	3.39100i	0.142787	−	0.247314i
$189$		0			0
$190$	1.33929	+	2.31972i	0.0971625	+	0.168290i
$191$	0.392632	−	6.74123i	0.0284098	−	0.487778i	−0.953854	−	0.300272i	$-0.902923\pi$
$191$	0.392632	−	6.74123i	0.0284098	−	0.487778i	0.982263	−	0.187506i	$-0.0600404\pi$
$192$		0			0
$193$	15.8040	+	1.84722i	1.13759	+	0.132966i	0.663969	−	0.747761i	$-0.268871\pi$
$193$	15.8040	+	1.84722i	1.13759	+	0.132966i	0.473626	+	0.880726i	$0.342945\pi$
$194$	0.779300	+	0.826010i	0.0559505	+	0.0593041i
$195$		0			0
$196$	−6.83792	+	0.799238i	−0.488423	+	0.0570884i
$197$	8.88023	+	7.45140i	0.632690	+	0.530890i	0.901764	−	0.432229i	$-0.142273\pi$
$197$	8.88023	+	7.45140i	0.632690	+	0.530890i	−0.269073	+	0.963120i	$0.586717\pi$
$198$		0			0
$199$	3.29385	−	2.76387i	0.233495	−	0.195925i	−0.518531	−	0.855059i	$-0.673521\pi$
$199$	3.29385	−	2.76387i	0.233495	−	0.195925i	0.752026	+	0.659133i	$0.229077\pi$
$200$	6.70013	−	7.10172i	0.473771	−	0.502168i
$201$		0			0
$202$	1.72318	+	0.865416i	0.121243	+	0.0608904i
$203$	−4.88558	−	2.45363i	−0.342900	−	0.172211i
$204$		0			0
$205$	4.79087	−	5.07803i	0.334609	−	0.354665i
$206$	−2.90318	+	2.43606i	−0.202274	+	0.169728i
$207$		0			0
$208$	1.10978	+	0.931215i	0.0769493	+	0.0645682i
$209$	5.75493	−	0.672654i	0.398077	−	0.0465285i
$210$		0			0
$211$	−9.80038	−	10.3878i	−0.674686	−	0.715126i	0.296077	−	0.955164i	$-0.404321\pi$
$211$	−9.80038	−	10.3878i	−0.674686	−	0.715126i	−0.970763	+	0.240038i	$0.922840\pi$
$212$	−16.1635	−	1.88924i	−1.11012	−	0.129754i
$213$		0			0
$214$	0.595430	−	10.2231i	0.0407028	−	0.698840i
$215$	3.04863	+	5.28038i	0.207915	+	0.360119i
$216$		0			0
$217$	4.90269	−	8.49171i	0.332816	−	0.576455i
$218$	−6.19871	−	4.07695i	−0.419829	−	0.276126i
$219$		0			0
$220$	1.35611	+	3.14381i	0.0914286	+	0.211955i
$221$	16.7071	−	3.95965i	1.12384	−	0.266355i
$222$		0			0
$223$	−12.0568	−	16.1950i	−0.807381	−	1.08450i	−0.994762	−	0.102214i	$-0.967408\pi$
$223$	−12.0568	−	16.1950i	−0.807381	−	1.08450i	0.187382	−	0.982287i	$-0.440000\pi$
$224$	−7.13306	+	2.59622i	−0.476598	+	0.173467i
$225$		0			0
$226$	13.6130	+	4.95474i	0.905526	+	0.329585i
$227$	0.781091	+	2.60903i	0.0518428	+	0.173167i	0.979990	−	0.199046i	$-0.0637843\pi$
$227$	0.781091	+	2.60903i	0.0518428	+	0.173167i	−0.928147	+	0.372213i	$0.878599\pi$
$228$		0			0
$229$	−0.0887613	−	1.52397i	−0.00586551	−	0.100707i	0.994105	−	0.108424i	$-0.0345805\pi$
$229$	−0.0887613	−	1.52397i	−0.00586551	−	0.100707i	−0.999970	+	0.00771732i	$0.997543\pi$
$230$	5.06465	−	3.33107i	0.333953	−	0.219645i
$231$		0			0
$232$	11.1420	+	2.64071i	0.731511	+	0.173371i
$233$	1.13347	+	6.42825i	0.0742563	+	0.421128i	0.999162	+	0.0409317i	$0.0130326\pi$
$233$	1.13347	+	6.42825i	0.0742563	+	0.421128i	−0.924906	+	0.380197i	$0.875856\pi$
$234$		0			0
$235$	0.627909	−	3.56105i	0.0409602	−	0.232297i
$236$	−5.64280	+	13.0815i	−0.367315	+	0.851532i
$237$		0			0
$238$	−1.18416	+	3.95536i	−0.0767576	+	0.256388i
$239$	10.0905	−	13.5539i	0.652702	−	0.876731i	−0.345391	−	0.938459i	$-0.612254\pi$
$239$	10.0905	−	13.5539i	0.652702	−	0.876731i	0.998093	+	0.0617275i	$0.0196610\pi$
$240$		0			0
$241$	−11.2588	+	5.65439i	−0.725244	+	0.364231i	−0.772811	−	0.634637i	$-0.781150\pi$
$241$	−11.2588	+	5.65439i	−0.725244	+	0.364231i	0.0475663	+	0.998868i	$0.484853\pi$
$242$	5.22835			0.336091
$243$		0			0
$244$	−15.4029			−0.986070
$245$	−5.68145	+	2.85333i	−0.362974	+	0.182293i
$246$		0			0
$247$	7.25145	−	9.74038i	0.461399	−	0.619766i
$248$	−5.89011	+	19.6743i	−0.374023	+	1.24932i
$249$		0			0
$250$	3.40062	−	7.88353i	0.215074	−	0.498598i
$251$	4.48052	−	25.4103i	0.282808	−	1.60388i	−0.430204	−	0.902732i	$-0.641558\pi$
$251$	4.48052	−	25.4103i	0.282808	−	1.60388i	0.713012	−	0.701152i	$-0.247331\pi$
$252$		0			0
$253$	−2.27699	−	12.9134i	−0.143153	−	0.811861i
$254$	−4.60547	−	1.09152i	−0.288973	−	0.0684878i
$255$		0			0
$256$	12.5892	−	8.28002i	0.786822	−	0.517501i
$257$	0.841489	+	14.4478i	0.0524906	+	0.901229i	0.917068	+	0.398730i	$0.130549\pi$
$257$	0.841489	+	14.4478i	0.0524906	+	0.901229i	−0.864578	+	0.502499i	$0.832414\pi$
$258$		0			0
$259$	3.68144	+	12.2969i	0.228753	+	0.764089i
$260$	6.74288	+	2.45421i	0.418176	+	0.152204i
$261$		0			0
$262$	15.2786	−	5.56095i	0.943914	−	0.343557i
$263$	6.24306	+	8.38588i	0.384963	+	0.517096i	0.951794	−	0.306739i	$-0.0992379\pi$
$263$	6.24306	+	8.38588i	0.384963	+	0.517096i	−0.566830	+	0.823835i	$0.691830\pi$
$264$		0			0
$265$	−14.6233	+	3.46578i	−0.898301	+	0.212901i
$266$	1.15658	+	2.68126i	0.0709146	+	0.164398i
$267$		0			0
$268$	−0.905832	−	0.595775i	−0.0553325	−	0.0363928i
$269$	−0.105374	+	0.182513i	−0.00642476	+	0.0111280i	−0.869220	−	0.494426i	$-0.835378\pi$
$269$	−0.105374	+	0.182513i	−0.00642476	+	0.0111280i	0.862795	+	0.505554i	$0.168712\pi$
$270$		0			0
$271$	5.70846	+	9.88735i	0.346765	+	0.600614i	0.985673	−	0.168669i	$-0.0539470\pi$
$271$	5.70846	+	9.88735i	0.346765	+	0.600614i	−0.638908	+	0.769283i	$0.720614\pi$
$272$	−0.0697097	+	1.19687i	−0.00422677	+	0.0725708i
$273$		0			0
$274$	−13.1175	−	1.53321i	−0.792455	−	0.0926247i
$275$	−5.28752	−	5.60444i	−0.318850	−	0.337961i
$276$		0			0
$277$	11.0740	−	1.29437i	0.665375	−	0.0777712i	0.223301	−	0.974750i	$-0.428317\pi$
$277$	11.0740	−	1.29437i	0.665375	−	0.0777712i	0.442074	+	0.896978i	$0.354243\pi$
$278$	6.66153	+	5.58969i	0.399532	+	0.335247i
$279$		0			0
$280$	−3.34591	+	2.80755i	−0.199956	+	0.167783i
$281$	−14.8936	+	15.7863i	−0.888478	+	0.941732i	−0.998638	−	0.0521821i	$-0.983382\pi$
$281$	−14.8936	+	15.7863i	−0.888478	+	0.941732i	0.110159	+	0.993914i	$0.464864\pi$
$282$		0			0
$283$	−0.264982	−	0.133079i	−0.0157515	−	0.00791072i	0.440906	−	0.897553i	$-0.354657\pi$
$283$	−0.264982	−	0.133079i	−0.0157515	−	0.00791072i	−0.456658	+	0.889643i	$0.650954\pi$
$284$	8.46338	+	4.25047i	0.502209	+	0.252219i
$285$		0			0
$286$	−5.65910	+	5.99830i	−0.334630	+	0.354687i
$287$	5.83015	−	4.89208i	0.344143	−	0.288770i
$288$		0			0
$289$	−2.13795	−	1.79396i	−0.125762	−	0.105527i
$290$	4.14929	−	0.484982i	0.243654	−	0.0284791i
$291$		0			0
$292$	−7.27809	−	7.71433i	−0.425918	−	0.451447i
$293$	−14.4085	−	1.68412i	−0.841755	−	0.0983871i	−0.315723	−	0.948852i	$-0.602247\pi$
$293$	−14.4085	−	1.68412i	−0.841755	−	0.0983871i	−0.526032	+	0.850464i	$0.676321\pi$
$294$		0			0
$295$	−0.764985	+	13.1343i	−0.0445391	+	0.764707i
$296$	−13.4425	−	23.2830i	−0.781327	−	1.35330i
$297$		0			0
$298$	1.21416	−	2.10299i	0.0703346	−	0.121823i
$299$	−22.9604	−	15.1013i	−1.32783	−	0.873330i
$300$		0			0
$301$	2.63273	+	6.10335i	0.151748	+	0.351791i
$302$	10.3426	−	2.45124i	0.595149	−	0.141053i
$303$		0			0
$304$	0.506337	+	0.680128i	0.0290404	+	0.0390080i
$305$	−13.3665	+	4.86501i	−0.765364	+	0.278570i
$306$		0			0
$307$	−3.56052	−	1.29592i	−0.203210	−	0.0739622i	0.238410	−	0.971165i	$-0.423374\pi$
$307$	−3.56052	−	1.29592i	−0.203210	−	0.0739622i	−0.441620	+	0.897202i	$0.645596\pi$
$308$	1.07049	+	3.57569i	0.0609969	+	0.203744i
$309$		0			0
$310$	0.435651	+	7.47984i	0.0247433	+	0.424826i
$311$	10.3012	−	6.77519i	0.584126	−	0.384186i	−0.222777	−	0.974869i	$-0.571512\pi$
$311$	10.3012	−	6.77519i	0.584126	−	0.384186i	0.806903	+	0.590684i	$0.201142\pi$
$312$		0			0
$313$	6.62237	+	1.56953i	0.374319	+	0.0887151i	0.413469	−	0.910518i	$-0.364317\pi$
$313$	6.62237	+	1.56953i	0.374319	+	0.0887151i	−0.0391504	+	0.999233i	$0.512465\pi$
$314$	0.183799	+	1.04238i	0.0103724	+	0.0588246i
$315$		0			0
$316$	2.60810	−	14.7913i	0.146717	−	0.832074i
$317$	5.91605	−	13.7150i	0.332279	−	0.770309i	−0.667394	−	0.744705i	$-0.732590\pi$
$317$	5.91605	−	13.7150i	0.332279	−	0.770309i	0.999672	−	0.0256033i	$-0.00815067\pi$
$318$		0			0
$319$	2.59170	−	8.65688i	0.145107	−	0.484692i
$320$	3.00556	−	4.03717i	0.168016	−	0.225684i
$321$		0			0
$322$	5.90550	−	2.96585i	0.329101	−	0.165281i
$323$	10.0493			0.559156
$324$		0			0
$325$	−16.1482			−0.895740
$326$	−9.20354	+	4.62219i	−0.509737	+	0.256000i
$327$		0			0
$328$	−9.51899	+	12.7862i	−0.525598	+	0.706001i
$329$	1.13057	−	3.77638i	0.0623305	−	0.208198i
$330$		0			0
$331$	−1.46304	+	3.39172i	−0.0804162	+	0.186426i	−0.953681	−	0.300821i	$-0.902739\pi$
$331$	−1.46304	+	3.39172i	−0.0804162	+	0.186426i	0.873265	+	0.487246i	$0.161999\pi$
$332$	−1.08293	+	6.14162i	−0.0594337	+	0.337065i
$333$		0			0
$334$	0.551633	+	3.12847i	0.0301840	+	0.171182i
$335$	−0.974249	−	0.230901i	−0.0532289	−	0.0126155i
$336$		0			0
$337$	−15.4103	+	10.1355i	−0.839450	+	0.552115i	−0.894859	−	0.446349i	$-0.852724\pi$
$337$	−15.4103	+	10.1355i	−0.839450	+	0.552115i	0.0554092	+	0.998464i	$0.482354\pi$
$338$	0.375258	+	6.44292i	0.0204113	+	0.350449i
$339$		0			0
$340$	1.70311	+	5.68879i	0.0923642	+	0.308518i
$341$	15.2298	+	5.54319i	0.824740	+	0.300181i
$342$		0			0
$343$	−15.1621	+	5.51854i	−0.818675	+	0.297973i
$344$	−8.31358	−	11.1671i	−0.448238	−	0.602089i
$345$		0			0
$346$	−19.5103	+	4.62402i	−1.04888	+	0.248589i
$347$	13.3067	+	30.8484i	0.714341	+	1.65603i	0.754049	+	0.656818i	$0.228098\pi$
$347$	13.3067	+	30.8484i	0.714341	+	1.65603i	−0.0397080	+	0.999211i	$0.512643\pi$
$348$		0			0
$349$	27.5190	+	18.0995i	1.47306	+	0.968844i	0.995941	+	0.0900033i	$0.0286878\pi$
$349$	27.5190	+	18.0995i	1.47306	+	0.968844i	0.477115	+	0.878841i	$0.341683\pi$
$350$	1.94157	−	3.36289i	0.103781	−	0.179754i
$351$		0			0
$352$	−6.27342	−	10.8659i	−0.334374	−	0.579154i
$353$	0.775734	−	13.3188i	0.0412881	−	0.708890i	−0.912623	−	0.408802i	$-0.865947\pi$
$353$	0.775734	−	13.3188i	0.0412881	−	0.708890i	0.953911	−	0.300088i	$-0.0970162\pi$
$354$		0			0
$355$	8.68696	+	1.01536i	0.461056	+	0.0538897i
$356$	−2.98664	−	3.16565i	−0.158291	−	0.167779i
$357$		0			0
$358$	5.24493	−	0.613045i	0.277203	−	0.0324004i
$359$	−6.91454	−	5.80199i	−0.364936	−	0.306217i	0.441819	−	0.897104i	$-0.354333\pi$
$359$	−6.91454	−	5.80199i	−0.364936	−	0.306217i	−0.806754	+	0.590887i	$0.798778\pi$
$360$		0			0
$361$	−9.11037	+	7.64450i	−0.479493	+	0.402342i
$362$	3.54060	−	3.75281i	0.186090	−	0.197243i
$363$		0			0
$364$	6.99048	+	3.51075i	0.366401	+	0.184013i
$365$	−8.75244	−	4.39564i	−0.458124	−	0.230078i
$366$		0			0
$367$	−17.5705	+	18.6236i	−0.917171	+	0.972145i	−0.999701	−	0.0244437i	$-0.992219\pi$
$367$	−17.5705	+	18.6236i	−0.917171	+	0.972145i	0.0825298	+	0.996589i	$0.473700\pi$
$368$	1.46997	−	1.23345i	0.0766274	−	0.0642980i
$369$		0			0
$370$	−7.51364	−	6.30469i	−0.390616	−	0.327765i
$371$	−16.2725	+	1.90198i	−0.844825	+	0.0987459i
$372$		0			0
$373$	15.0065	+	15.9060i	0.777008	+	0.823580i	0.988088	−	0.153888i	$-0.0491796\pi$
$373$	15.0065	+	15.9060i	0.777008	+	0.823580i	−0.211080	+	0.977469i	$0.567698\pi$
$374$	−6.77834	−	0.792274i	−0.350500	−	0.0409675i
$375$		0			0
$376$	−0.480066	+	8.24241i	−0.0247575	+	0.425070i
$377$	−9.46934	−	16.4014i	−0.487696	−	0.844714i
$378$		0			0
$379$	−5.26717	+	9.12300i	−0.270556	+	0.468617i	−0.969004	−	0.247043i	$-0.920541\pi$
$379$	−5.26717	+	9.12300i	−0.270556	+	0.468617i	0.698448	+	0.715661i	$0.253874\pi$
$380$	3.50887	+	2.30782i	0.180001	+	0.118389i
$381$		0			0
$382$	2.22797	+	5.16500i	0.113993	+	0.264265i
$383$	−21.2791	+	5.04324i	−1.08731	+	0.257698i	−0.734919	−	0.678154i	$-0.762780\pi$
$383$	−21.2791	+	5.04324i	−1.08731	+	0.257698i	−0.352393	+	0.935852i	$0.614632\pi$
$384$		0			0
$385$	2.05835	+	2.76484i	0.104903	+	0.140909i
$386$	−12.4552	+	4.53331i	−0.633952	+	0.230740i
$387$		0			0
$388$	1.67315	+	0.608977i	0.0849414	+	0.0309161i
$389$	6.99531	+	23.3660i	0.354676	+	1.18470i	0.930242	+	0.366946i	$0.119597\pi$
$389$	6.99531	+	23.3660i	0.354676	+	1.18470i	−0.575566	+	0.817755i	$0.695218\pi$
$390$		0			0
$391$	−1.32236	−	22.7040i	−0.0668746	−	1.14819i
$392$	12.1284	−	7.97698i	0.612577	−	0.402898i
$393$		0			0
$394$	−9.39625	−	2.22695i	−0.473376	−	0.112192i
$395$	−2.40854	−	13.6595i	−0.121187	−	0.687285i
$396$		0			0
$397$	4.16728	−	23.6338i	0.209150	−	1.18615i	−0.681625	−	0.731702i	$-0.738726\pi$
$397$	4.16728	−	23.6338i	0.209150	−	1.18615i	0.890775	−	0.454445i	$-0.150163\pi$
$398$	−1.41868	+	3.28887i	−0.0711119	+	0.164856i
$399$		0			0
$400$	0.323387	−	1.08019i	0.0161694	−	0.0540094i
$401$	22.0434	−	29.6094i	1.10079	−	1.47862i	0.239235	−	0.970962i	$-0.423103\pi$
$401$	22.0434	−	29.6094i	1.10079	−	1.47862i	0.861558	−	0.507660i	$-0.169489\pi$
$402$		0			0
$403$	30.3540	−	15.2444i	1.51204	−	0.759376i
$404$	3.02339			0.150419
$405$		0			0
$406$	4.55416			0.226019
$407$	−18.9599	+	9.52203i	−0.939808	+	0.471989i
$408$		0			0
$409$	−1.70501	+	2.29023i	−0.0843075	+	0.113245i	−0.842276	−	0.539047i	$-0.818785\pi$
$409$	−1.70501	+	2.29023i	−0.0843075	+	0.113245i	0.757968	+	0.652291i	$0.226192\pi$
$410$	−1.66791	+	5.57121i	−0.0823723	+	0.275143i
$411$		0			0
$412$	−2.35356	+	5.45616i	−0.115952	+	0.268806i
$413$	−2.49058	+	14.1248i	−0.122553	+	0.695035i
$414$		0			0
$415$	1.00007	+	5.67169i	0.0490916	+	0.278412i
$416$	−25.5868	−	6.06418i	−1.25450	−	0.297321i
$417$		0			0
$418$	−4.03253	+	2.65224i	−0.197238	+	0.129725i
$419$	1.99872	+	34.3166i	0.0976437	+	1.67648i	0.591016	+	0.806660i	$0.298727\pi$
$419$	1.99872	+	34.3166i	0.0976437	+	1.67648i	−0.493372	+	0.869818i	$0.664236\pi$
$420$		0			0
$421$	−1.79299	−	5.98899i	−0.0873849	−	0.291886i	0.903115	−	0.429398i	$-0.141274\pi$
$421$	−1.79299	−	5.98899i	−0.0873849	−	0.291886i	−0.990500	+	0.137513i	$0.956089\pi$
$422$	11.1790	+	4.06883i	0.544186	+	0.198067i
$423$		0			0
$424$	32.2449	−	11.7362i	1.56595	−	0.569960i
$425$	−7.98018	−	10.7192i	−0.387096	−	0.519960i
$426$		0			0
$427$	−15.0887	+	3.57610i	−0.730196	+	0.173060i
$428$	−6.35952	−	14.7430i	−0.307399	−	0.712631i
$429$		0			0
$430$	−4.24352	−	2.79101i	−0.204641	−	0.134594i
$431$	1.50862	−	2.61301i	0.0726679	−	0.125864i	−0.827402	−	0.561610i	$-0.810182\pi$
$431$	1.50862	−	2.61301i	0.0726679	−	0.125864i	0.900070	+	0.435746i	$0.143515\pi$
$432$		0			0
$433$	−15.3659	−	26.6146i	−0.738439	−	1.27901i	−0.953198	−	0.302347i	$-0.902230\pi$
$433$	−15.3659	−	26.6146i	−0.738439	−	1.27901i	0.214759	−	0.976667i	$-0.431104\pi$
$434$	−0.474927	+	8.15418i	−0.0227972	+	0.391413i
$435$		0			0
$436$	−11.5541	−	1.35048i	−0.553341	−	0.0646763i
$437$	−11.0378	−	11.6994i	−0.528011	−	0.559659i
$438$		0			0
$439$	−0.454536	+	0.0531276i	−0.0216938	+	0.00253564i	−0.126933	−	0.991911i	$-0.540513\pi$
$439$	−0.454536	+	0.0531276i	−0.0216938	+	0.00253564i	0.105239	+	0.994447i	$0.466439\pi$
$440$	−5.53042	−	4.64057i	−0.263652	−	0.221231i
$441$		0			0
$442$	−10.9565	+	9.19361i	−0.521148	+	0.437296i
$443$	−23.9557	+	25.3916i	−1.13817	+	1.20639i	−0.162602	+	0.986692i	$0.551989\pi$
$443$	−23.9557	+	25.3916i	−1.13817	+	1.20639i	−0.975568	+	0.219698i	$0.929493\pi$
$444$		0			0
$445$	−3.59165	−	1.80379i	−0.170260	−	0.0855080i
$446$	15.0297	+	7.54822i	0.711679	+	0.357419i
$447$		0			0
$448$	3.76531	−	3.99100i	0.177894	−	0.188557i
$449$	5.48196	−	4.59991i	0.258710	−	0.217083i	−0.504202	−	0.863586i	$-0.668213\pi$
$449$	5.48196	−	4.59991i	0.258710	−	0.217083i	0.762912	+	0.646502i	$0.223769\pi$
$450$		0			0
$451$	9.63661	+	8.08607i	0.453770	+	0.380758i
$452$	22.5603	−	2.63692i	1.06115	−	0.124030i
$453$		0			0
$454$	−1.55685	−	1.65016i	−0.0730665	−	0.0774459i
$455$	7.17515	+	0.838655i	0.336376	+	0.0393167i
$456$		0			0
$457$	0.737417	−	12.6610i	0.0344949	−	0.592255i	−0.936130	−	0.351655i	$-0.885619\pi$
$457$	0.737417	−	12.6610i	0.0344949	−	0.592255i	0.970625	−	0.240599i	$-0.0773440\pi$
$458$	0.635820	+	1.10127i	0.0297099	+	0.0514591i
$459$		0			0
$460$	4.75227	−	8.23117i	0.221576	−	0.383780i
$461$	0.385841	+	0.253772i	0.0179704	+	0.0118193i	0.558462	−	0.829530i	$-0.311392\pi$
$461$	0.385841	+	0.253772i	0.0179704	+	0.0118193i	−0.540492	+	0.841349i	$0.681762\pi$
$462$		0			0
$463$	14.6949	+	34.0667i	0.682931	+	1.58321i	0.806740	+	0.590906i	$0.201230\pi$
$463$	14.6949	+	34.0667i	0.682931	+	1.58321i	−0.123809	+	0.992306i	$0.539511\pi$
$464$	1.28676	−	0.304968i	0.0597363	−	0.0141578i
$465$		0			0
$466$	−3.24700	−	4.36148i	−0.150414	−	0.202042i
$467$	25.8480	−	9.40792i	1.19611	−	0.435347i	0.334242	−	0.942487i	$-0.391520\pi$
$467$	25.8480	−	9.40792i	1.19611	−	0.435347i	0.861863	+	0.507141i	$0.169298\pi$
$468$		0			0
$469$	−1.02568	−	0.373316i	−0.0473614	−	0.0172381i
$470$	0.863897	+	2.88562i	0.0398486	+	0.133104i
$471$		0			0
$472$	−1.74669	−	29.9895i	−0.0803980	−	1.38038i
$473$	−9.17926	+	6.03729i	−0.422063	+	0.277595i
$474$		0			0
$475$	−9.19653	−	2.17962i	−0.421966	−	0.100008i
$476$	1.12413	+	6.37527i	0.0515245	+	0.292210i
$477$		0			0
$478$	−2.44425	+	13.8620i	−0.111798	+	0.634035i
$479$	5.64829	−	13.0942i	0.258077	−	0.598290i	−0.739082	−	0.673616i	$-0.764740\pi$
$479$	5.64829	−	13.0942i	0.258077	−	0.598290i	0.997159	+	0.0753257i	$0.0239996\pi$
$480$		0			0
$481$	−12.7529	+	42.5978i	−0.581484	+	1.94229i
$482$	6.26722	−	8.41834i	0.285464	−	0.383445i
$483$		0			0
$484$	7.32563	−	3.67907i	0.332983	−	0.167230i
$485$	1.64429			0.0746634
$486$		0			0
$487$	9.07752			0.411342			0.205671	−	0.978621i	$-0.434062\pi$
$487$	9.07752			0.411342			0.205671	+	0.978621i	$0.434062\pi$
$488$	29.0238	−	14.5763i	1.31385	−	0.659839i
$489$		0			0
$490$	3.16258	−	4.24808i	0.142871	−	0.191909i
$491$	−7.99691	+	26.7115i	−0.360896	+	1.20548i	0.564167	+	0.825661i	$0.309197\pi$
$491$	−7.99691	+	26.7115i	−0.360896	+	1.20548i	−0.925063	+	0.379815i	$0.875988\pi$
$492$		0			0
$493$	6.20771	−	14.3911i	0.279581	−	0.648142i
$494$	−1.75653	+	9.96180i	−0.0790302	+	0.448203i
$495$		0			0
$496$	0.411853	+	2.33573i	0.0184927	+	0.104878i
$497$	9.27760	+	2.19883i	0.416157	+	0.0986310i
$498$		0			0
$499$	19.8773	−	13.0735i	0.889828	−	0.585249i	−0.0202000	−	0.999796i	$-0.506430\pi$
$499$	19.8773	−	13.0735i	0.889828	−	0.585249i	0.910028	+	0.414547i	$0.136060\pi$
$500$	−0.782724	−	13.4389i	−0.0350045	−	0.601004i
$501$		0			0
$502$	6.16444	+	20.5907i	0.275133	+	0.919007i
$503$	−7.57016	−	2.75531i	−0.337537	−	0.122853i	0.167690	−	0.985840i	$-0.446369\pi$
$503$	−7.57016	−	2.75531i	−0.337537	−	0.122853i	−0.505227	+	0.862986i	$0.668591\pi$
$504$		0			0
$505$	2.62367	−	0.954939i	0.116752	−	0.0424942i
$506$	6.52276	+	8.76159i	0.289972	+	0.389500i
$507$		0			0
$508$	−7.22097	+	1.71140i	−0.320379	+	0.0759311i
$509$	7.64624	+	17.7260i	0.338914	+	0.785690i	0.999393	+	0.0348457i	$0.0110940\pi$
$509$	7.64624	+	17.7260i	0.338914	+	0.785690i	−0.660479	+	0.750844i	$0.729647\pi$
$510$		0			0
$511$	−8.92069	−	5.86723i	−0.394628	−	0.259551i
$512$	1.79397	−	3.10725i	0.0792832	−	0.137323i
$513$		0			0
$514$	−6.02780	−	10.4405i	−0.265875	−	0.460509i
$515$	−0.319068	+	5.47818i	−0.0140598	+	0.241398i
$516$		0			0
$517$	6.47161	+	0.756422i	0.284621	+	0.0332674i
$518$	−7.33773	−	7.77754i	−0.322401	−	0.341725i
$519$		0			0
$520$	−15.0282	+	1.75654i	−0.659029	+	0.0770294i
$521$	−2.04454	−	1.71557i	−0.0895727	−	0.0751604i	0.596902	−	0.802314i	$-0.296398\pi$
$521$	−2.04454	−	1.71557i	−0.0895727	−	0.0751604i	−0.686474	+	0.727154i	$0.740843\pi$
$522$		0			0
$523$	11.7693	−	9.87562i	0.514636	−	0.431831i	−0.348121	−	0.937450i	$-0.613180\pi$
$523$	11.7693	−	9.87562i	0.514636	−	0.431831i	0.862757	+	0.505619i	$0.168736\pi$
$524$	17.4943	−	18.5429i	0.764241	−	0.810048i
$525$		0			0
$526$	−7.78248	−	3.90851i	−0.339332	−	0.170419i
$527$	25.1198	+	12.6156i	1.09423	+	0.549545i
$528$		0			0
$529$	−9.19617	+	9.74738i	−0.399834	+	0.423799i
$530$	9.58997	−	8.04694i	0.416562	−	0.349537i
$531$		0			0
$532$	3.50727	+	2.94295i	0.152059	+	0.127593i
$533$	26.1862	−	3.06073i	1.13425	−	0.132575i
$534$		0			0
$535$	−10.1753	−	10.7852i	−0.439917	−	0.466285i
$536$	2.27067	+	0.265403i	0.0980780	+	0.0114637i
$537$		0			0
$538$	0.0102077	−	0.175259i	0.000440083	−	0.00755594i
$539$	−5.72799	−	9.92117i	−0.246722	−	0.427335i
$540$		0			0
$541$	9.39421	−	16.2713i	0.403889	−	0.699556i	−0.590303	−	0.807182i	$-0.700992\pi$
$541$	9.39421	−	16.2713i	0.403889	−	0.699556i	0.994191	+	0.107626i	$0.0343250\pi$
$542$	−7.94586	−	5.22607i	−0.341304	−	0.224479i
$543$		0			0
$544$	−8.61917	−	19.9815i	−0.369544	−	0.856699i
$545$	−10.4531	+	2.47743i	−0.447761	+	0.106121i
$546$		0			0
$547$	−6.84395	−	9.19302i	−0.292626	−	0.393065i	0.631361	−	0.775489i	$-0.282497\pi$
$547$	−6.84395	−	9.19302i	−0.292626	−	0.393065i	−0.923987	+	0.382424i	$0.875089\pi$
$548$	−19.4583	+	7.08223i	−0.831216	+	0.302538i
$549$		0			0
$550$	6.03132	+	2.19522i	0.257176	+	0.0936045i
$551$	−3.17908	−	10.6189i	−0.135433	−	0.452378i
$552$		0			0
$553$	−0.879191	−	15.0951i	−0.0373870	−	0.641910i
$554$	−7.75969	+	5.10363i	−0.329678	+	0.216832i
$555$		0			0
$556$	13.2671	+	3.14435i	0.562649	+	0.133350i
$557$	−4.33665	−	24.5943i	−0.183750	−	1.04210i	−0.927551	−	0.373695i	$-0.878091\pi$
$557$	−4.33665	−	24.5943i	−0.183750	−	1.04210i	0.743802	−	0.668400i	$-0.233021\pi$
$558$		0			0
$559$	−3.99840	+	22.6761i	−0.169114	+	0.959095i
$560$	−0.199791	+	0.463167i	−0.00844269	+	0.0195724i
$561$		0			0
$562$	5.18511	−	17.3195i	0.218721	−	0.730579i
$563$	10.4988	−	14.1023i	0.442471	−	0.594341i	−0.523809	−	0.851836i	$-0.675489\pi$
$563$	10.4988	−	14.1023i	0.442471	−	0.594341i	0.966280	+	0.257494i	$0.0828969\pi$
$564$		0			0
$565$	18.7447	−	9.41396i	0.788597	−	0.396048i
$566$	0.247007			0.0103825
$567$		0			0
$568$	−19.9700			−0.837922
$569$	−14.2884	+	7.17589i	−0.599000	+	0.300829i	−0.722343	−	0.691535i	$-0.756935\pi$
$569$	−14.2884	+	7.17589i	−0.599000	+	0.300829i	0.123343	+	0.992364i	$0.460638\pi$
$570$		0			0
$571$	6.16873	−	8.28604i	0.258153	−	0.346760i	−0.654084	−	0.756422i	$-0.726946\pi$
$571$	6.16873	−	8.28604i	0.258153	−	0.346760i	0.912238	+	0.409662i	$0.134353\pi$
$572$	−3.70831	+	12.3866i	−0.155052	+	0.517911i
$573$		0			0
$574$	−2.51108	+	5.82133i	−0.104810	+	0.242978i
$575$	−3.71420	+	21.0643i	−0.154893	+	0.878441i
$576$		0			0
$577$	6.79785	+	38.5525i	0.282998	+	1.60496i	0.712349	+	0.701825i	$0.247631\pi$
$577$	6.79785	+	38.5525i	0.282998	+	1.60496i	−0.429351	+	0.903138i	$0.641258\pi$
$578$	2.26219	+	0.536148i	0.0940946	+	0.0223008i
$579$		0			0
$580$	5.47245	−	3.59929i	0.227231	−	0.149452i
$581$	0.365057	+	6.26778i	0.0151451	+	0.260031i
$582$		0			0
$583$	−7.76656	−	25.9421i	−0.321658	−	1.07441i
$584$	21.0145	+	7.64866i	0.869587	+	0.316504i
$585$		0			0
$586$	11.3554	−	4.13304i	0.469088	−	0.170734i
$587$	10.6305	+	14.2792i	0.438766	+	0.589365i	0.965415	−	0.260718i	$-0.0839592\pi$
$587$	10.6305	+	14.2792i	0.438766	+	0.589365i	−0.526649	+	0.850083i	$0.676552\pi$
$588$		0			0
$589$	19.3445	−	4.58473i	0.797076	−	0.188910i
$590$	−4.34086	−	10.0632i	−0.178710	−	0.414297i
$591$		0			0
$592$	−2.59407	−	1.70614i	−0.106615	−	0.0701221i
$593$	−6.92687	+	11.9977i	−0.284452	+	0.492686i	−0.972476	−	0.233002i	$-0.925145\pi$
$593$	−6.92687	+	11.9977i	−0.284452	+	0.492686i	0.688024	+	0.725688i	$0.258478\pi$
$594$		0			0
$595$	2.98914	+	5.17735i	0.122543	+	0.212251i
$596$	0.221381	−	3.80096i	0.00906811	−	0.155693i
$597$		0			0
$598$	22.7376	+	2.65764i	0.929809	+	0.108679i
$599$	2.48356	+	2.63242i	0.101475	+	0.107558i	0.776121	−	0.630585i	$-0.217185\pi$
$599$	2.48356	+	2.63242i	0.101475	+	0.107558i	−0.674645	+	0.738142i	$0.735703\pi$
$600$		0			0
$601$	10.3128	−	1.20539i	0.420667	−	0.0491689i	0.0968736	−	0.995297i	$-0.469116\pi$
$601$	10.3128	−	1.20539i	0.420667	−	0.0491689i	0.323794	+	0.946128i	$0.395042\pi$
$602$	−4.24159	−	3.55912i	−0.172874	−	0.145059i
$603$		0			0
$604$	12.7665	−	10.7124i	0.519462	−	0.435880i
$605$	5.19508	−	5.50647i	0.211210	−	0.223870i
$606$		0			0
$607$	12.0040	+	6.02866i	0.487229	+	0.244696i	0.675415	−	0.737438i	$-0.263964\pi$
$607$	12.0040	+	6.02866i	0.487229	+	0.244696i	−0.188186	+	0.982133i	$0.560261\pi$
$608$	−13.7534	−	6.90721i	−0.557773	−	0.280124i
$609$		0			0
$610$	8.13131	−	8.61869i	0.329227	−	0.348960i
$611$	10.4607	−	8.77758i	0.423195	−	0.355103i
$612$		0			0
$613$	22.2652	+	18.6827i	0.899281	+	0.754587i	0.970050	−	0.242906i	$-0.0781007\pi$
$613$	22.2652	+	18.6827i	0.899281	+	0.754587i	−0.0707686	+	0.997493i	$0.522545\pi$
$614$	3.13496	−	0.366425i	0.126517	−	0.0147877i
$615$		0			0
$616$	−5.40094	−	5.72466i	−0.217610	−	0.230653i
$617$	12.3463	+	1.44308i	0.497044	+	0.0580961i	0.360922	−	0.932596i	$-0.382462\pi$
$617$	12.3463	+	1.44308i	0.497044	+	0.0580961i	0.136122	+	0.990692i	$0.456536\pi$
$618$		0			0
$619$	−2.00980	+	34.5070i	−0.0807807	+	1.38695i	0.677739	+	0.735302i	$0.262960\pi$
$619$	−2.00980	+	34.5070i	−0.0807807	+	1.38695i	−0.758520	+	0.651650i	$0.774077\pi$
$620$	5.87380	+	10.1737i	0.235898	+	0.408586i
$621$		0			0
$622$	−5.13533	+	8.89464i	−0.205908	+	0.356643i
$623$	−3.66069	−	2.40767i	−0.146662	−	0.0964614i
$624$		0			0
$625$	2.09699	+	4.86137i	0.0838796	+	0.194455i
$626$	−5.51652	+	1.30744i	−0.220484	+	0.0522558i
$627$		0			0
$628$	0.991023	+	1.33118i	0.0395461	+	0.0531197i
$629$	−34.5789	+	12.5857i	−1.37875	+	0.501825i
$630$		0			0
$631$	12.4258	+	4.52262i	0.494663	+	0.180042i	0.577292	−	0.816538i	$-0.304109\pi$
$631$	12.4258	+	4.52262i	0.494663	+	0.180042i	−0.0826292	+	0.996580i	$0.526332\pi$
$632$	9.08304	+	30.3395i	0.361304	+	1.20684i
$633$		0			0
$634$	0.723456	+	12.4213i	0.0287321	+	0.493311i
$635$	−5.72575	+	3.76588i	−0.227219	+	0.149445i
$636$		0			0
$637$	−23.3622	−	5.53695i	−0.925645	−	0.219382i
$638$	1.30714	+	7.41317i	0.0517502	+	0.293490i
$639$		0			0
$640$	1.69021	−	9.58567i	0.0668115	−	0.378907i
$641$	2.08848	−	4.84165i	0.0824901	−	0.191234i	−0.871979	−	0.489543i	$-0.837164\pi$
$641$	2.08848	−	4.84165i	0.0824901	−	0.191234i	0.954469	+	0.298310i	$0.0964228\pi$
$642$		0			0
$643$	−1.25523	+	4.19275i	−0.0495013	+	0.165346i	−0.979166	−	0.203060i	$-0.934911\pi$
$643$	−1.25523	+	4.19275i	−0.0495013	+	0.165346i	0.929665	+	0.368406i	$0.120096\pi$
$644$	6.18741	−	8.31114i	0.243818	−	0.327505i
$645$		0			0
$646$	−7.48075	+	3.75697i	−0.294326	+	0.147816i
$647$	−5.42624			−0.213327			−0.106664	−	0.994295i	$-0.534017\pi$
$647$	−5.42624			−0.213327			−0.106664	+	0.994295i	$0.534017\pi$
$648$		0			0
$649$	−23.7069			−0.930576
$650$	12.0208	−	6.03709i	0.471496	−	0.236794i
$651$		0			0
$652$	−9.64289	+	12.9527i	−0.377645	+	0.507265i
$653$	3.18380	−	10.6346i	0.124592	−	0.416166i	−0.872822	−	0.488039i	$-0.837712\pi$
$653$	3.18380	−	10.6346i	0.124592	−	0.416166i	0.997414	+	0.0718731i	$0.0228977\pi$
$654$		0			0
$655$	9.32462	−	21.6169i	0.364343	−	0.844642i
$656$	−0.319672	+	1.81295i	−0.0124811	+	0.0707837i
$657$		0			0
$658$	0.570212	+	3.23383i	0.0222292	+	0.126068i
$659$	7.23488	+	1.71470i	0.281831	+	0.0667951i	0.369100	−	0.929390i	$-0.379666\pi$
$659$	7.23488	+	1.71470i	0.281831	+	0.0667951i	−0.0872694	+	0.996185i	$0.527814\pi$
$660$		0			0
$661$	3.20127	−	2.10551i	0.124515	−	0.0818948i	−0.485724	−	0.874112i	$-0.661444\pi$
$661$	3.20127	−	2.10551i	0.124515	−	0.0818948i	0.610239	+	0.792218i	$0.291074\pi$
$662$	−0.178911	−	3.07178i	−0.00695358	−	0.119388i
$663$		0			0
$664$	−3.77145	−	12.5975i	−0.146361	−	0.488879i
$665$	3.97311	+	1.44609i	0.154071	+	0.0560771i
$666$		0			0
$667$	−23.5726	+	8.57971i	−0.912733	+	0.332208i
$668$	2.97435	+	3.99524i	0.115081	+	0.154581i
$669$		0			0
$670$	0.811561	−	0.192344i	0.0313533	−	0.00743088i
$671$	−10.1519	−	23.5347i	−0.391910	−	0.908549i
$672$		0			0
$673$	−35.1668	−	23.1295i	−1.35558	−	0.891578i	−0.356492	−	0.934298i	$-0.616027\pi$
$673$	−35.1668	−	23.1295i	−1.35558	−	0.891578i	−0.999087	+	0.0427202i	$0.986398\pi$
$674$	7.68230	−	13.3061i	0.295911	−	0.512533i
$675$		0			0
$676$	5.05953	+	8.76336i	0.194597	+	0.337052i
$677$	−0.144919	+	2.48817i	−0.00556970	+	0.0956281i	−0.999947	−	0.0102640i	$-0.996733\pi$
$677$	−0.144919	+	2.48817i	−0.00556970	+	0.0956281i	0.994378	+	0.105892i	$0.0337698\pi$
$678$		0			0
$679$	1.78041	+	0.208100i	0.0683260	+	0.00798616i
$680$	−8.59269	−	9.10772i	−0.329515	−	0.349265i
$681$		0			0
$682$	−13.4095	+	1.56735i	−0.513477	+	0.0600169i
$683$	11.7411	+	9.85194i	0.449260	+	0.376974i	0.839161	−	0.543883i	$-0.183046\pi$
$683$	11.7411	+	9.85194i	0.449260	+	0.376974i	−0.389901	+	0.920857i	$0.627491\pi$
$684$		0			0
$685$	−14.6488	+	12.2918i	−0.559701	+	0.469645i
$686$	9.22362	−	9.77646i	0.352159	−	0.373267i
$687$		0			0
$688$	−1.43678	−	0.721578i	−0.0547767	−	0.0275099i
$689$	−50.7168	−	25.4710i	−1.93216	−	0.970366i
$690$		0			0
$691$	−25.4658	+	26.9922i	−0.968765	+	1.02683i	0.0308620	+	0.999524i	$0.490175\pi$
$691$	−25.4658	+	26.9922i	−0.968765	+	1.02683i	−0.999627	+	0.0273073i	$0.991307\pi$
$692$	−24.0827	+	20.2078i	−0.915488	+	0.768186i
$693$		0			0
$694$	−21.4384	−	17.9890i	−0.813792	−	0.682853i
$695$	12.5062	−	1.46176i	0.474387	−	0.0554478i
$696$		0			0
$697$	14.9725	+	15.8700i	0.567125	+	0.601118i
$698$	−27.2519	−	3.18529i	−1.03150	−	0.120565i
$699$		0			0
$700$	0.354010	−	6.07811i	0.0133803	−	0.229731i
$701$	3.35489	+	5.81083i	0.126712	+	0.219472i	0.922401	−	0.386234i	$-0.126224\pi$
$701$	3.35489	+	5.81083i	0.126712	+	0.219472i	−0.795689	+	0.605706i	$0.792891\pi$
$702$		0			0
$703$	−13.0126	+	22.5385i	−0.490779	+	0.850054i
$704$	7.57719	+	4.98360i	0.285576	+	0.187826i
$705$		0			0
$706$	4.40186	+	10.2046i	0.165666	+	0.384057i
$707$	2.96173	−	0.701942i	0.111387	−	0.0263993i
$708$		0			0
$709$	−14.2011	−	19.0753i	−0.533332	−	0.716389i	0.451037	−	0.892505i	$-0.351054\pi$
$709$	−14.2011	−	19.0753i	−0.533332	−	0.716389i	−0.984369	+	0.176116i	$0.943647\pi$
$710$	−6.84623	+	2.49182i	−0.256934	+	0.0935165i
$711$		0			0
$712$	8.62351	+	3.13870i	0.323180	+	0.117628i
$713$	−12.9037	−	43.1012i	−0.483246	−	1.61415i
$714$		0			0
$715$	0.694277	+	11.9203i	0.0259645	+	0.445793i
$716$	6.91748	−	4.54970i	0.258519	−	0.170030i
$717$		0			0
$718$	7.31634	+	1.73400i	0.273043	+	0.0647125i
$719$	7.41202	+	42.0356i	0.276422	+	1.56766i	0.734410	+	0.678706i	$0.237459\pi$
$719$	7.41202	+	42.0356i	0.276422	+	1.56766i	−0.457988	+	0.888958i	$0.651430\pi$
$720$		0			0
$721$	−1.03880	+	5.89131i	−0.0386868	+	0.219404i
$722$	3.92388	−	9.09658i	0.146032	−	0.338540i
$723$		0			0
$724$	2.32009	−	7.74965i	0.0862255	−	0.288013i
$725$	−8.80228	+	11.8235i	−0.326909	+	0.439114i
$726$		0			0
$727$	17.0289	−	8.55222i	0.631565	−	0.317184i	−0.104062	−	0.994571i	$-0.533184\pi$
$727$	17.0289	−	8.55222i	0.631565	−	0.317184i	0.735627	+	0.677387i	$0.236888\pi$
$728$	−16.4946			−0.611329
$729$		0			0
$730$	8.15871			0.301967
$731$	−17.0284	+	8.55200i	−0.629819	+	0.316307i
$732$		0			0
$733$	−10.7269	+	14.4087i	−0.396207	+	0.532199i	−0.954802	−	0.297242i	$-0.903933\pi$
$733$	−10.7269	+	14.4087i	−0.396207	+	0.532199i	0.558595	+	0.829441i	$0.311341\pi$
$734$	6.11705	−	20.4324i	0.225784	−	0.754173i
$735$		0			0
$736$	−13.7955	+	31.9816i	−0.508509	+	1.17886i
$737$	0.313285	−	1.77673i	0.0115400	−	0.0654466i
$738$		0			0
$739$	2.16602	+	12.2841i	0.0796782	+	0.451878i	0.998379	+	0.0569224i	$0.0181288\pi$
$739$	2.16602	+	12.2841i	0.0796782	+	0.451878i	−0.918700	+	0.394955i	$0.870760\pi$
$740$	−14.9641	−	3.54656i	−0.550092	−	0.130374i
$741$		0			0
$742$	11.4023	−	7.49940i	0.418591	−	0.275312i
$743$	−1.50694	−	25.8731i	−0.0552842	−	0.949193i	−0.905923	−	0.423443i	$-0.860821\pi$
$743$	−1.50694	−	25.8731i	−0.0552842	−	0.949193i	0.850639	−	0.525751i	$-0.176216\pi$
$744$		0			0
$745$	−1.00842	−	3.36836i	−0.0369457	−	0.123407i
$746$	−17.1175	−	6.23026i	−0.626716	−	0.228106i
$747$		0			0
$748$	−10.0549	+	3.65968i	−0.367643	+	0.133811i
$749$	−9.65270	−	12.9658i	−0.352702	−	0.473761i
$750$		0			0
$751$	10.2130	−	2.42053i	0.372679	−	0.0883265i	−0.0400083	−	0.999199i	$-0.512738\pi$
$751$	10.2130	−	2.42053i	0.372679	−	0.0883265i	0.412687	+	0.910873i	$0.364590\pi$
$752$	0.377663	+	0.875522i	0.0137720	+	0.0319270i
$753$		0			0
$754$	13.1808	+	8.66914i	0.480016	+	0.315711i
$755$	7.69516	−	13.3284i	0.280056	−	0.485070i
$756$		0			0
$757$	−0.0864170	−	0.149679i	−0.00314088	−	0.00544016i	0.864451	−	0.502718i	$-0.167666\pi$
$757$	−0.0864170	−	0.149679i	−0.00314088	−	0.00544016i	−0.867592	+	0.497277i	$0.834333\pi$
$758$	0.510234	−	8.76039i	0.0185326	−	0.318192i
$759$		0			0
$760$	−8.79576	−	1.02808i	−0.319056	−	0.0372923i
$761$	1.28543	+	1.36248i	0.0465968	+	0.0493897i	0.750253	−	0.661151i	$-0.229932\pi$
$761$	1.28543	+	1.36248i	0.0465968	+	0.0493897i	−0.703656	+	0.710541i	$0.748450\pi$
$762$		0			0
$763$	−11.6320	+	1.35958i	−0.421106	+	0.0492203i
$764$	6.75618	+	5.66911i	0.244430	+	0.205101i
$765$		0			0
$766$	13.9549	−	11.7095i	0.504211	−	0.423083i
$767$	−34.0957	+	36.1394i	−1.23113	+	1.30492i
$768$		0			0
$769$	−24.9413	−	12.5260i	−0.899405	−	0.451698i	−0.0618716	−	0.998084i	$-0.519707\pi$
$769$	−24.9413	−	12.5260i	−0.899405	−	0.451698i	−0.837534	+	0.546386i	$0.816003\pi$
$770$	−2.56590	−	1.28864i	−0.0924685	−	0.0464394i
$771$		0			0
$772$	−14.2614	+	15.1162i	−0.513280	+	0.544045i
$773$	−0.0418155	+	0.0350873i	−0.00150400	+	0.00126200i	−0.643539	−	0.765413i	$-0.722535\pi$
$773$	−0.0418155	+	0.0350873i	−0.00150400	+	0.00126200i	0.642035	+	0.766675i	$0.278090\pi$
$774$		0			0
$775$	−20.2520	−	16.9934i	−0.727472	−	0.610422i
$776$	−3.72903	+	0.435861i	−0.133864	+	0.0156465i
$777$		0			0
$778$	−13.9429	−	14.7786i	−0.499875	−	0.529837i
$779$	15.3264	+	1.79140i	0.549125	+	0.0641835i
$780$		0			0
$781$	−0.916342	+	15.7330i	−0.0327893	+	0.562971i
$782$	9.47240	+	16.4067i	0.338732	+	0.586702i
$783$		0			0
$784$	0.838235	−	1.45187i	0.0299370	−	0.0518524i
$785$	1.28045	+	0.842167i	0.0457013	+	0.0300582i
$786$		0			0
$787$	−13.4349	−	31.1455i	−0.478901	−	1.11022i	−0.970871	−	0.239604i	$-0.922982\pi$
$787$	−13.4349	−	31.1455i	−0.478901	−	1.11022i	0.491970	−	0.870612i	$-0.336277\pi$
$788$	−14.7325	+	3.49167i	−0.524824	+	0.124385i
$789$		0			0
$790$	6.89962	+	9.26779i	0.245477	+	0.329733i
$791$	21.4879	−	7.82097i	0.764023	−	0.278082i
$792$		0			0
$793$	−50.4776	−	18.3724i	−1.79251	−	0.652422i
$794$	5.73347	+	19.1511i	0.203473	+	0.679648i
$795$		0			0
$796$	0.326538	+	5.60645i	0.0115738	+	0.198715i
$797$	12.1670	−	8.00239i	0.430979	−	0.283459i	−0.315428	−	0.948950i	$-0.602148\pi$
$797$	12.1670	−	8.00239i	0.430979	−	0.283459i	0.746406	+	0.665491i	$0.231778\pi$
$798$		0			0
$799$	10.9961	+	2.60613i	0.389015	+	0.0921982i
$800$	3.55394	+	20.1554i	0.125651	+	0.712600i
$801$		0			0
$802$	−5.33961	+	30.2825i	−0.188548	+	1.06931i
$803$	6.99013	−	16.2049i	0.246676	−	0.571860i
$804$		0			0
$805$	2.74431	−	9.16663i	0.0967242	−	0.323081i
$806$	−16.8966	+	22.6960i	−0.595156	+	0.799433i
$807$		0			0
$808$	−5.69700	+	2.86114i	−0.200420	+	0.100655i
$809$	−28.0189			−0.985092			−0.492546	−	0.870286i	$-0.663934\pi$
$809$	−28.0189			−0.985092			−0.492546	+	0.870286i	$0.663934\pi$
$810$		0			0
$811$	29.1924			1.02508			0.512542	−	0.858662i	$-0.328704\pi$
$811$	29.1924			1.02508			0.512542	+	0.858662i	$0.328704\pi$
$812$	6.38100	−	3.20466i	0.223929	−	0.112462i
$813$		0			0
$814$	10.5540	−	14.1765i	0.369919	−	0.496887i
$815$	−4.27692	+	14.2859i	−0.149814	+	0.500413i
$816$		0			0
$817$	−5.33785	+	12.3745i	−0.186748	+	0.432930i
$818$	0.413009	−	2.34229i	0.0144405	−	0.0818964i
$819$		0			0
$820$	1.58337	+	8.97971i	0.0552935	+	0.313585i
$821$	29.0511	+	6.88525i	1.01389	+	0.240297i	0.703791	−	0.710407i	$-0.251489\pi$
$821$	29.0511	+	6.88525i	1.01389	+	0.240297i	0.310101	+	0.950704i	$0.399637\pi$
$822$		0			0
$823$	33.5799	−	22.0858i	1.17052	−	0.769864i	0.193103	−	0.981178i	$-0.438145\pi$
$823$	33.5799	−	22.0858i	1.17052	−	0.769864i	0.977418	+	0.211315i	$0.0677745\pi$
$824$	−0.728528	−	12.5084i	−0.0253795	−	0.435749i
$825$		0			0
$826$	−3.42662	−	11.4457i	−0.119227	−	0.398247i
$827$	−39.9498	−	14.5405i	−1.38919	−	0.505623i	−0.464238	−	0.885710i	$-0.653672\pi$
$827$	−39.9498	−	14.5405i	−1.38919	−	0.505623i	−0.924951	+	0.380087i	$0.875894\pi$
$828$		0			0
$829$	5.90599	−	2.14960i	0.205124	−	0.0746589i	−0.237415	−	0.971408i	$-0.576300\pi$
$829$	5.90599	−	2.14960i	0.205124	−	0.0746589i	0.442539	+	0.896749i	$0.354078\pi$
$830$	−2.86485	−	3.84816i	−0.0994404	−	0.133572i
$831$		0			0
$832$	18.4948	−	4.38335i	0.641192	−	0.151965i
$833$	−7.86979	−	18.2442i	−0.272672	−	0.632125i
$834$		0			0
$835$	3.84301	+	2.52759i	0.132993	+	0.0874708i
$836$	−3.78381	+	6.55375i	−0.130866	+	0.226666i
$837$		0			0
$838$	−14.3173	−	24.7983i	−0.494584	−	0.856644i
$839$	0.963006	−	16.5342i	0.0332466	−	0.570823i	−0.940016	−	0.341129i	$-0.889191\pi$
$839$	0.963006	−	16.5342i	0.0332466	−	0.570823i	0.973263	−	0.229694i	$-0.0737724\pi$
$840$		0			0
$841$	11.6333	+	1.35974i	0.401149	+	0.0468876i
$842$	3.57373	+	3.78793i	0.123159	+	0.130541i
$843$		0			0
$844$	18.5265	−	2.16543i	0.637707	−	0.0745373i
$845$	7.15852	+	6.00671i	0.246261	+	0.206637i
$846$		0			0
$847$	6.32205	−	5.30483i	0.217228	−	0.182276i
$848$	2.71947	−	2.88247i	0.0933871	−	0.0989846i
$849$		0			0
$850$	9.94795	+	4.99605i	0.341212	+	0.171363i
$851$	52.6328	+	26.4332i	1.80423	+	0.906118i
$852$		0			0
$853$	35.7674	−	37.9112i	1.22465	−	1.29806i	0.283943	−	0.958841i	$-0.408357\pi$
$853$	35.7674	−	37.9112i	1.22465	−	1.29806i	0.940709	−	0.339214i	$-0.110161\pi$
$854$	9.89523	−	8.30308i	0.338608	−	0.284126i
$855$		0			0
$856$	25.9351	+	21.7622i	0.886445	+	0.743815i
$857$	−38.6194	+	4.51396i	−1.31921	+	0.154194i	−0.746404	−	0.665493i	$-0.768221\pi$
$857$	−38.6194	+	4.51396i	−1.31921	+	0.154194i	−0.572811	+	0.819687i	$0.694147\pi$
$858$		0			0
$859$	14.8940	+	15.7867i	0.508177	+	0.538637i	0.929766	−	0.368151i	$-0.120009\pi$
$859$	14.8940	+	15.7867i	0.508177	+	0.538637i	−0.421589	+	0.906787i	$0.638527\pi$
$860$	−7.90973	−	0.924515i	−0.269720	−	0.0315257i
$861$		0			0
$862$	−0.146142	+	2.50915i	−0.00497760	+	0.0854621i
$863$	21.9404	+	38.0020i	0.746861	+	1.29360i	0.949320	+	0.314311i	$0.101773\pi$
$863$	21.9404	+	38.0020i	0.746861	+	1.29360i	−0.202459	+	0.979291i	$0.564893\pi$
$864$		0			0
$865$	−14.5161	+	25.1427i	−0.493564	+	0.854877i
$866$	21.3885	+	14.0674i	0.726811	+	0.478031i
$867$		0			0
$868$	5.07248	+	11.7593i	0.172171	+	0.399138i
$869$	24.3192	−	5.76375i	0.824972	−	0.195522i
$870$		0			0
$871$	−2.25792	−	3.03291i	−0.0765066	−	0.102766i
$872$	23.0495	−	8.38933i	0.780554	−	0.284099i
$873$		0			0
$874$	12.5905	+	4.58258i	0.425881	+	0.155008i
$875$	−3.88687	−	12.9830i	−0.131400	−	0.438907i
$876$		0			0
$877$	1.46065	+	25.0784i	0.0493226	+	0.846837i	0.928728	+	0.370763i	$0.120904\pi$
$877$	1.46065	+	25.0784i	0.0493226	+	0.846837i	−0.879405	+	0.476074i	$0.842059\pi$
$878$	0.318498	−	0.209479i	0.0107488	−	0.00706958i
$879$		0			0
$880$	−0.811277	−	0.192276i	−0.0273481	−	0.00648163i
$881$	−0.463850	−	2.63063i	−0.0156275	−	0.0886281i	0.975996	−	0.217786i	$-0.0698836\pi$
$881$	−0.463850	−	2.63063i	−0.0156275	−	0.0886281i	−0.991624	+	0.129158i	$0.958772\pi$
$882$		0			0
$883$	6.82642	−	38.7145i	0.229727	−	1.30285i	−0.623711	−	0.781655i	$-0.714376\pi$
$883$	6.82642	−	38.7145i	0.229727	−	1.30285i	0.853439	−	0.521193i	$-0.174513\pi$
$884$	−8.88225	+	20.5914i	−0.298742	+	0.692563i
$885$		0			0
$886$	8.34003	−	27.8576i	0.280189	−	0.935895i
$887$	−19.9569	+	26.8067i	−0.670086	+	0.900081i	−0.999020	−	0.0442716i	$-0.985903\pi$
$887$	−19.9569	+	26.8067i	−0.670086	+	0.900081i	0.328934	+	0.944353i	$0.393311\pi$
$888$		0			0
$889$	−6.67635	+	3.35299i	−0.223918	+	0.112456i
$890$	3.34800			0.112225
$891$		0			0
$892$	26.3703			0.882942
$893$	7.14223	−	3.58696i	0.239006	−	0.120033i
$894$		0			0
$895$	4.56591	−	6.13308i	0.152621	−	0.205006i
$896$	3.04329	−	10.1653i	0.101669	−	0.339599i
$897$		0			0
$898$	−2.36111	+	5.47367i	−0.0787912	+	0.182659i
$899$	5.38405	−	30.5345i	0.179568	−	1.01838i
$900$		0			0
$901$	−8.15573	−	46.2534i	−0.271707	−	1.54093i
$902$	−10.1966	−	2.41663i	−0.339509	−	0.0804651i
$903$		0			0
$904$	−40.0151	+	26.3184i	−1.33088	+	0.875336i
$905$	−0.434372	−	7.45788i	−0.0144390	−	0.247908i
$906$		0			0
$907$	3.52864	+	11.7865i	0.117167	+	0.391364i	0.996375	−	0.0850742i	$-0.0271127\pi$
$907$	3.52864	+	11.7865i	0.117167	+	0.391364i	−0.879208	+	0.476438i	$0.841928\pi$
$908$	−3.34254	−	1.21658i	−0.110926	−	0.0403738i
$909$		0			0
$910$	−5.65477	+	2.05817i	−0.187454	+	0.0682276i
$911$	13.0498	+	17.5289i	0.432359	+	0.580759i	0.963897	−	0.266276i	$-0.0857931\pi$
$911$	13.0498	+	17.5289i	0.432359	+	0.580759i	−0.531538	+	0.847034i	$0.678386\pi$
$912$		0			0
$913$	−10.0978	+	2.39322i	−0.334188	+	0.0792040i
$914$	4.18443	+	9.70059i	0.138409	+	0.320867i
$915$		0			0
$916$	1.66581	+	1.09562i	0.0550400	+	0.0362004i
$917$	12.8324	−	22.2263i	0.423762	−	0.733977i
$918$		0			0
$919$	27.9349	+	48.3846i	0.921487	+	1.59606i	0.797116	+	0.603826i	$0.206358\pi$
$919$	27.9349	+	48.3846i	0.921487	+	1.59606i	0.124370	+	0.992236i	$0.460309\pi$
$920$	−1.16529	+	20.0073i	−0.0384186	+	0.659622i
$921$		0			0
$922$	−0.382097	−	0.0446607i	−0.0125837	−	0.00147082i
$923$	22.6659	+	24.0244i	0.746056	+	0.790774i
$924$		0			0
$925$	34.3744	−	4.01780i	1.13022	−	0.132104i
$926$	−23.6750	−	19.8657i	−0.778009	−	0.652827i
$927$		0			0
$928$	−18.3873	+	15.4288i	−0.603594	+	0.506476i
$929$	29.4428	−	31.2075i	0.965986	−	1.02389i	−0.0337151	−	0.999431i	$-0.510734\pi$
$929$	29.4428	−	31.2075i	0.965986	−	1.02389i	0.999701	−	0.0244537i	$-0.00778463\pi$
$930$		0			0
$931$	−12.5576	−	6.30668i	−0.411560	−	0.206693i
$932$	−7.61857	−	3.82619i	−0.249554	−	0.125331i
$933$		0			0
$934$	−15.7243	+	16.6668i	−0.514514	+	0.545353i
$935$	−7.56964	+	6.35168i	−0.247554	+	0.207722i
$936$		0			0
$937$	−10.4519	−	8.77015i	−0.341447	−	0.286508i	0.455898	−	0.890032i	$-0.349318\pi$
$937$	−10.4519	−	8.77015i	−0.341447	−	0.286508i	−0.797345	+	0.603524i	$0.793763\pi$
$938$	0.903088	−	0.105556i	0.0294869	−	0.00344652i
$939$		0			0
$940$	3.24098	+	3.43524i	0.105709	+	0.112045i
$941$	44.1544	+	5.16091i	1.43939	+	0.168241i	0.799704	−	0.600395i	$-0.204990\pi$
$941$	44.1544	+	5.16091i	1.43939	+	0.168241i	0.639687	+	0.768635i	$0.279064\pi$
$942$		0			0
$943$	2.03049	−	34.8622i	0.0661219	−	1.13527i
$944$	−1.73463	−	3.00447i	−0.0564575	−	0.0977873i
$945$		0			0
$946$	4.57603	−	7.92592i	0.148780	−	0.257694i
$947$	−3.62204	−	2.38225i	−0.117700	−	0.0774128i	0.489294	−	0.872119i	$-0.337255\pi$
$947$	−3.62204	−	2.38225i	−0.117700	−	0.0774128i	−0.606994	+	0.794706i	$0.707625\pi$
$948$		0			0
$949$	−14.6499	−	33.9622i	−0.475555	−	1.10246i
$950$	7.66082	−	1.81565i	0.248550	−	0.0589074i
$951$		0			0
$952$	−8.15136	−	10.9492i	−0.264187	−	0.354865i
$953$	34.6339	−	12.6057i	1.12190	−	0.408339i	0.286556	−	0.958063i	$-0.407489\pi$
$953$	34.6339	−	12.6057i	1.12190	−	0.408339i	0.835346	+	0.549724i	$0.185267\pi$
$954$		0			0
$955$	7.65355	+	2.78566i	0.247663	+	0.0901419i
$956$	6.32968	+	21.1426i	0.204716	+	0.683801i
$957$		0			0
$958$	0.690712	+	11.8591i	0.0223159	+	0.383149i
$959$	−17.4171	+	11.4554i	−0.562428	+	0.369915i
$960$		0			0
$961$	23.9459	+	5.67527i	0.772447	+	0.183073i
$962$	−6.43203	−	36.4778i	−0.207377	−	1.17609i
$963$		0			0
$964$	2.85744	−	16.2054i	0.0920320	−	0.521939i
$965$	−7.60147	+	17.6222i	−0.244700	+	0.567279i
$966$		0			0
$967$	2.93507	−	9.80383i	0.0943856	−	0.315270i	−0.897738	−	0.440529i	$-0.854791\pi$
$967$	2.93507	−	9.80383i	0.0943856	−	0.315270i	0.992124	+	0.125259i	$0.0399761\pi$
$968$	−10.3221	+	13.8650i	−0.331765	+	0.445638i
$969$		0			0
$970$	−1.22402	+	0.614727i	−0.0393010	+	0.0197377i
$971$	43.9486			1.41038			0.705188	−	0.709020i	$-0.250862\pi$
$971$	43.9486			1.41038			0.705188	+	0.709020i	$0.250862\pi$
$972$		0			0
$973$	13.7265			0.440051
$974$	−6.75737	+	3.39368i	−0.216520	+	0.108740i
$975$		0			0
$976$	2.23984	−	3.00863i	0.0716957	−	0.0963040i
$977$	16.9236	−	56.5287i	0.541433	−	1.80851i	−0.0456115	−	0.998959i	$-0.514524\pi$
$977$	16.9236	−	56.5287i	0.541433	−	1.80851i	0.587045	−	0.809554i	$-0.300291\pi$
$978$		0			0
$979$	2.86847	−	6.64985i	0.0916766	−	0.212530i
$980$	1.44193	−	8.17758i	0.0460607	−	0.261223i
$981$		0			0
$982$	−4.03329	−	22.8740i	−0.128708	−	0.729937i
$983$	26.0666	+	6.17791i	0.831397	+	0.197045i	0.624210	−	0.781257i	$-0.285421\pi$
$983$	26.0666	+	6.17791i	0.831397	+	0.197045i	0.207187	+	0.978301i	$0.433569\pi$
$984$		0			0
$985$	−11.6819	+	7.68330i	−0.372216	+	0.244810i
$986$	0.759122	+	13.0336i	0.0241754	+	0.415075i
$987$		0			0
$988$	4.54875	+	15.1939i	0.144715	+	0.483382i
$989$	28.6598	+	10.4313i	0.911329	+	0.331697i
$990$		0			0
$991$	8.60252	−	3.13106i	0.273268	−	0.0994614i	−0.201751	−	0.979437i	$-0.564663\pi$
$991$	8.60252	−	3.13106i	0.273268	−	0.0994614i	0.475019	+	0.879975i	$0.342441\pi$
$992$	−25.7076	−	34.5314i	−0.816219	−	1.09637i
$993$		0			0
$994$	−7.72835	+	1.83165i	−0.245128	+	0.0580965i
$995$	2.05416	+	4.76209i	0.0651214	+	0.150968i
$996$		0			0
$997$	−35.3642	−	23.2594i	−1.12000	−	0.736633i	−0.152195	−	0.988350i	$-0.548634\pi$
$997$	−35.3642	−	23.2594i	−1.12000	−	0.736633i	−0.967801	+	0.251718i	$0.919005\pi$
$998$	−9.90918	+	17.1632i	−0.313670	+	0.543292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.73.3		144
3.2	odd	2		81.2.g.a.25.6	yes	144
9.2	odd	6		729.2.g.c.703.3		144
9.4	even	3		729.2.g.a.217.6		144
9.5	odd	6		729.2.g.d.217.3		144
9.7	even	3		729.2.g.b.703.6		144
81.13	even	27	inner	243.2.g.a.10.3		144
81.14	odd	54		729.2.g.d.514.3		144
81.16	even	27		6561.2.a.d.1.24		72
81.40	even	27		729.2.g.b.28.6		144
81.41	odd	54		729.2.g.c.28.3		144
81.65	odd	54		6561.2.a.c.1.49		72
81.67	even	27		729.2.g.a.514.6		144
81.68	odd	54		81.2.g.a.13.6	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.6	✓	144	81.68	odd	54
81.2.g.a.25.6	yes	144	3.2	odd	2
243.2.g.a.10.3		144	81.13	even	27	inner
243.2.g.a.73.3		144	1.1	even	1	trivial
729.2.g.a.217.6		144	9.4	even	3
729.2.g.a.514.6		144	81.67	even	27
729.2.g.b.28.6		144	81.40	even	27
729.2.g.b.703.6		144	9.7	even	3
729.2.g.c.28.3		144	81.41	odd	54
729.2.g.c.703.3		144	9.2	odd	6
729.2.g.d.217.3		144	9.5	odd	6
729.2.g.d.514.3		144	81.14	odd	54
6561.2.a.c.1.49		72	81.65	odd	54
6561.2.a.d.1.24		72	81.16	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.744407 + 0.373855i) q^{2} +(-0.779943 + 1.04765i) q^{4} +(-0.345929 + 1.15548i) q^{5} +(-0.520803 + 1.20736i) q^{7} +(0.478230 - 2.71217i) q^{8} +(-0.174471 - 0.989477i) q^{10} +(-2.11479 - 0.501215i) q^{11} +(-3.80561 + 2.50299i) q^{13} +(-0.0636874 - 1.09347i) q^{14} +(-0.0912185 - 0.304691i) q^{16} +(-3.54217 - 1.28924i) q^{17} +(-2.50517 + 0.911807i) q^{19} +(-0.940731 - 1.26362i) q^{20} +(1.76165 - 0.417519i) q^{22} +(2.38967 + 5.53988i) q^{23} +(2.96197 + 1.94812i) q^{25} +(1.89717 - 3.28599i) q^{26} +(-0.858686 - 1.48729i) q^{28} +(-0.241756 + 4.15079i) q^{29} +(-7.40674 - 0.865723i) q^{31} +(3.96165 + 4.19911i) q^{32} +(3.11881 - 0.364536i) q^{34} +(-1.21492 - 1.01944i) q^{35} +(7.47819 - 6.27494i) q^{37} +(1.52398 - 1.61533i) q^{38} +(2.96844 + 1.49081i) q^{40} +(-5.17242 - 2.59769i) q^{41} +(3.46904 - 3.67697i) q^{43} +(2.17451 - 1.82463i) q^{44} +(-3.85000 - 3.23053i) q^{46} +(-2.97767 + 0.348040i) q^{47} +(3.61722 + 3.83402i) q^{49} +(-2.93322 - 0.342844i) q^{50} +(0.345914 - 5.93911i) q^{52} +(6.22987 + 10.7905i) q^{53} +(1.31071 - 2.27022i) q^{55} +(3.02550 + 1.98990i) q^{56} +(-1.37183 - 3.18026i) q^{58} +(10.6138 - 2.51552i) q^{59} +(7.04237 + 9.45955i) q^{61} +(5.83728 - 2.12460i) q^{62} +(-3.92120 - 1.42720i) q^{64} +(-1.57569 - 5.26317i) q^{65} +(0.0482665 + 0.828703i) q^{67} +(4.11336 - 2.70540i) q^{68} +(1.28552 + 0.304673i) q^{70} +(-1.25916 - 7.14107i) q^{71} +(-1.41006 + 7.99685i) q^{73} +(-3.22089 + 7.46687i) q^{74} +(0.998639 - 3.33569i) q^{76} +(1.70654 - 2.29228i) q^{77} +(-10.2764 + 5.16099i) q^{79} +0.383620 q^{80} +4.82155 q^{82} +(4.26695 - 2.14294i) q^{83} +(2.71504 - 3.64693i) q^{85} +(-1.20772 + 4.03408i) q^{86} +(-2.37074 + 5.49599i) q^{88} +(-0.578632 + 3.28158i) q^{89} +(-1.04003 - 5.89829i) q^{91} +(-7.66763 - 1.81726i) q^{92} +(2.08648 - 1.37230i) q^{94} +(-0.186967 - 3.21010i) q^{95} +(-0.390985 - 1.30598i) q^{97} +(-4.12605 - 1.50176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more