LMFDB - Embedded newform 729.2.e.m.568.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			568.1
Root			$0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.m.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 - 0.233956i) q^{2} +(-1.17365 - 0.984808i) q^{4} +(0.181985 - 1.03209i) q^{5} +(-0.0923963 + 0.0775297i) q^{7} +(1.20805 + 2.09240i) q^{8} +(-0.358441 + 0.620838i) q^{10} +(-0.943555 - 5.35117i) q^{11} +(4.29813 - 1.56439i) q^{13} +(0.0775297 - 0.0282185i) q^{14} +(0.245100 + 1.39003i) q^{16} +(-2.38917 + 4.13816i) q^{17} +(0.294263 + 0.509678i) q^{19} +(-1.23000 + 1.03209i) q^{20} +(-0.645430 + 3.66041i) q^{22} +(-5.97205 - 5.01114i) q^{23} +(3.66637 + 1.33445i) q^{25} -3.12879 q^{26} +0.184793 q^{28} +(-4.76400 - 1.73396i) q^{29} +(-6.70961 - 5.63003i) q^{31} +(1.00676 - 5.70961i) q^{32} +(2.50387 - 2.10100i) q^{34} +(0.0632028 + 0.109470i) q^{35} +(1.09240 - 1.89209i) q^{37} +(-0.0699065 - 0.396459i) q^{38} +(2.37939 - 0.866025i) q^{40} +(-7.10257 + 2.58512i) q^{41} +(-0.226682 - 1.28558i) q^{43} +(-4.16247 + 7.20961i) q^{44} +(2.66637 + 4.61830i) q^{46} +(1.85083 - 1.55303i) q^{47} +(-1.21301 + 6.87933i) q^{49} +(-2.04450 - 1.71554i) q^{50} +(-6.58512 - 2.39679i) q^{52} -3.04628 q^{53} -5.69459 q^{55} +(-0.273842 - 0.0996702i) q^{56} +(2.65657 + 2.22913i) q^{58} +(-0.00762319 + 0.0432332i) q^{59} +(-7.82295 + 6.56423i) q^{61} +(2.99568 + 5.18866i) q^{62} +(-0.571452 + 0.989783i) q^{64} +(-0.832396 - 4.72075i) q^{65} +(1.74763 - 0.636084i) q^{67} +(6.87933 - 2.50387i) q^{68} +(-0.0150147 - 0.0851529i) q^{70} +(3.25519 - 5.63816i) q^{71} +(-6.11721 - 10.5953i) q^{73} +(-1.14484 + 0.960637i) q^{74} +(0.156574 - 0.887975i) q^{76} +(0.502055 + 0.421274i) q^{77} +(-0.659978 - 0.240212i) q^{79} +1.47924 q^{80} +5.17024 q^{82} +(-6.36792 - 2.31773i) q^{83} +(3.83615 + 3.21891i) q^{85} +(-0.155059 + 0.879385i) q^{86} +(10.0569 - 8.43874i) q^{88} +(-3.42782 - 5.93717i) q^{89} +(-0.275845 + 0.477777i) q^{91} +(2.07407 + 11.7626i) q^{92} +(-1.55303 + 0.565258i) q^{94} +(0.579585 - 0.210952i) q^{95} +(-1.56758 - 8.89020i) q^{97} +(2.38917 - 4.13816i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55}+ \cdots - 66 q^{97}+O(q^{100}) $ 12 * q - 12 * q^4 + 6 * q^7 + 12 * q^10 + 24 * q^13 + 24 * q^19 + 24 * q^22 + 6 * q^25 - 12 * q^28 - 12 * q^31 - 18 * q^34 + 6 * q^37 + 6 * q^40 + 24 * q^43 - 6 * q^46 - 30 * q^49 - 36 * q^52 - 60 * q^55 - 12 * q^58 - 12 * q^61 - 6 * q^64 - 12 * q^67 + 60 * q^70 - 12 * q^73 - 42 * q^76 - 48 * q^79 - 24 * q^82 + 54 * q^85 + 48 * q^88 + 6 * q^94 - 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.642788	−	0.233956i	−0.454519	−	0.165432i	0.104608	−	0.994514i	$-0.466641\pi$
$2$	−0.642788	−	0.233956i	−0.454519	−	0.165432i	−0.559127	+	0.829082i	$0.688864\pi$
$3$		0			0
$3$		0			0
$4$	−1.17365	−	0.984808i	−0.586824	−	0.492404i
$5$	0.181985	−	1.03209i	0.0813862	−	0.461564i	−0.916692	−	0.399595i	$-0.869151\pi$
$5$	0.181985	−	1.03209i	0.0813862	−	0.461564i	0.998078	−	0.0619693i	$-0.0197381\pi$
$6$		0			0
$7$	−0.0923963	+	0.0775297i	−0.0349225	+	0.0293035i	−0.660082	−	0.751194i	$-0.729478\pi$
$7$	−0.0923963	+	0.0775297i	−0.0349225	+	0.0293035i	0.625159	+	0.780497i	$0.285034\pi$
$8$	1.20805	+	2.09240i	0.427109	+	0.739774i
$9$		0			0
$10$	−0.358441	+	0.620838i	−0.113349	+	0.196326i
$11$	−0.943555	−	5.35117i	−0.284493	−	1.61344i	−0.707092	−	0.707121i	$-0.749994\pi$
$11$	−0.943555	−	5.35117i	−0.284493	−	1.61344i	0.422600	−	0.906316i	$-0.361118\pi$
$12$		0			0
$13$	4.29813	−	1.56439i	1.19209	−	0.433884i	0.331632	−	0.943409i	$-0.392401\pi$
$13$	4.29813	−	1.56439i	1.19209	−	0.433884i	0.860456	+	0.509525i	$0.170179\pi$
$14$	0.0775297	−	0.0282185i	0.0207207	−	0.00754171i
$15$		0			0
$16$	0.245100	+	1.39003i	0.0612750	+	0.347508i
$17$	−2.38917	+	4.13816i	−0.579458	+	1.00365i	0.416084	+	0.909326i	$0.363402\pi$
$17$	−2.38917	+	4.13816i	−0.579458	+	1.00365i	−0.995542	+	0.0943239i	$0.969931\pi$
$18$		0			0
$19$	0.294263	+	0.509678i	0.0675085	+	0.116928i	0.897804	−	0.440395i	$-0.145162\pi$
$19$	0.294263	+	0.509678i	0.0675085	+	0.116928i	−0.830295	+	0.557323i	$0.811828\pi$
$20$	−1.23000	+	1.03209i	−0.275035	+	0.230782i
$21$		0			0
$22$	−0.645430	+	3.66041i	−0.137606	+	0.780403i
$23$	−5.97205	−	5.01114i	−1.24526	−	1.04490i	−0.997094	−	0.0761778i	$-0.975728\pi$
$23$	−5.97205	−	5.01114i	−1.24526	−	1.04490i	−0.248164	−	0.968718i	$-0.579827\pi$
$24$		0			0
$25$	3.66637	+	1.33445i	0.733275	+	0.266890i
$26$	−3.12879			−0.613605
$27$		0			0
$28$	0.184793			0.0349225
$29$	−4.76400	−	1.73396i	−0.884653	−	0.321987i	−0.140567	−	0.990071i	$-0.544893\pi$
$29$	−4.76400	−	1.73396i	−0.884653	−	0.321987i	−0.744086	+	0.668084i	$0.767115\pi$
$30$		0			0
$31$	−6.70961	−	5.63003i	−1.20508	−	1.01118i	−0.999470	−	0.0325493i	$-0.989637\pi$
$31$	−6.70961	−	5.63003i	−1.20508	−	1.01118i	−0.205611	−	0.978634i	$-0.565918\pi$
$32$	1.00676	−	5.70961i	0.177971	−	1.00933i
$33$		0			0
$34$	2.50387	−	2.10100i	0.429410	−	0.360318i
$35$	0.0632028	+	0.109470i	0.0106832	+	0.0185039i
$36$		0			0
$37$	1.09240	−	1.89209i	0.179589	−	0.311057i	−0.762151	−	0.647399i	$-0.775857\pi$
$37$	1.09240	−	1.89209i	0.179589	−	0.311057i	0.941740	+	0.336342i	$0.109190\pi$
$38$	−0.0699065	−	0.396459i	−0.0113403	−	0.0643142i
$39$		0			0
$40$	2.37939	−	0.866025i	0.376214	−	0.136931i
$41$	−7.10257	+	2.58512i	−1.10923	+	0.403728i	−0.830713	−	0.556702i	$-0.812067\pi$
$41$	−7.10257	+	2.58512i	−1.10923	+	0.403728i	−0.278522	+	0.960430i	$0.589844\pi$
$42$		0			0
$43$	−0.226682	−	1.28558i	−0.0345686	−	0.196048i	0.962633	−	0.270810i	$-0.0872915\pi$
$43$	−0.226682	−	1.28558i	−0.0345686	−	0.196048i	−0.997201	+	0.0747616i	$0.976180\pi$
$44$	−4.16247	+	7.20961i	−0.627516	+	1.08689i
$45$		0			0
$46$	2.66637	+	4.61830i	0.393135	+	0.680931i
$47$	1.85083	−	1.55303i	0.269972	−	0.226533i	−0.497744	−	0.867324i	$-0.665838\pi$
$47$	1.85083	−	1.55303i	0.269972	−	0.226533i	0.767715	+	0.640791i	$0.221393\pi$
$48$		0			0
$49$	−1.21301	+	6.87933i	−0.173287	+	0.982761i
$50$	−2.04450	−	1.71554i	−0.289136	−	0.242614i
$51$		0			0
$52$	−6.58512	−	2.39679i	−0.913192	−	0.332375i
$53$	−3.04628			−0.418439			−0.209219	−	0.977869i	$-0.567092\pi$
$53$	−3.04628			−0.418439			−0.209219	+	0.977869i	$0.567092\pi$
$54$		0			0
$55$	−5.69459			−0.767859
$56$	−0.273842	−	0.0996702i	−0.0365936	−	0.0133190i
$57$		0			0
$58$	2.65657	+	2.22913i	0.348825	+	0.292699i
$59$	−0.00762319	+	0.0432332i	−0.000992454	+	0.00562849i	−0.985300	−	0.170833i	$-0.945354\pi$
$59$	−0.00762319	+	0.0432332i	−0.000992454	+	0.00562849i	0.984308	+	0.176462i	$0.0564652\pi$
$60$		0			0
$61$	−7.82295	+	6.56423i	−1.00163	+	0.840464i	−0.987209	−	0.159432i	$-0.949034\pi$
$61$	−7.82295	+	6.56423i	−1.00163	+	0.840464i	−0.0144170	+	0.999896i	$0.504589\pi$
$62$	2.99568	+	5.18866i	0.380451	+	0.658961i
$63$		0			0
$64$	−0.571452	+	0.989783i	−0.0714315	+	0.123723i
$65$	−0.832396	−	4.72075i	−0.103246	−	0.585537i
$66$		0			0
$67$	1.74763	−	0.636084i	0.213507	−	0.0777100i	−0.233053	−	0.972464i	$-0.574871\pi$
$67$	1.74763	−	0.636084i	0.213507	−	0.0777100i	0.446559	+	0.894754i	$0.352649\pi$
$68$	6.87933	−	2.50387i	0.834241	−	0.303639i
$69$		0			0
$70$	−0.0150147	−	0.0851529i	−0.00179461	−	0.0101777i
$71$	3.25519	−	5.63816i	0.386320	−	0.669126i	−0.605631	−	0.795745i	$-0.707079\pi$
$71$	3.25519	−	5.63816i	0.386320	−	0.669126i	0.991951	+	0.126619i	$0.0404127\pi$
$72$		0			0
$73$	−6.11721	−	10.5953i	−0.715965	−	1.24009i	−0.962586	−	0.270976i	$-0.912653\pi$
$73$	−6.11721	−	10.5953i	−0.715965	−	1.24009i	0.246621	−	0.969112i	$-0.420680\pi$
$74$	−1.14484	+	0.960637i	−0.133085	+	0.111672i
$75$		0			0
$76$	0.156574	−	0.887975i	0.0179603	−	0.101858i
$77$	0.502055	+	0.421274i	0.0572145	+	0.0480087i
$78$		0			0
$79$	−0.659978	−	0.240212i	−0.0742533	−	0.0270260i	0.304626	−	0.952472i	$-0.401468\pi$
$79$	−0.659978	−	0.240212i	−0.0742533	−	0.0270260i	−0.378880	+	0.925446i	$0.623691\pi$
$80$	1.47924			0.165384
$81$		0			0
$82$	5.17024			0.570958
$83$	−6.36792	−	2.31773i	−0.698970	−	0.254404i	−0.0319990	−	0.999488i	$-0.510187\pi$
$83$	−6.36792	−	2.31773i	−0.698970	−	0.254404i	−0.666971	+	0.745084i	$0.732410\pi$
$84$		0			0
$85$	3.83615	+	3.21891i	0.416089	+	0.349140i
$86$	−0.155059	+	0.879385i	−0.0167205	+	0.0948265i
$87$		0			0
$88$	10.0569	−	8.43874i	1.07207	−	0.899573i
$89$	−3.42782	−	5.93717i	−0.363349	−	0.629338i	0.625161	−	0.780496i	$-0.285033\pi$
$89$	−3.42782	−	5.93717i	−0.363349	−	0.629338i	−0.988510	+	0.151157i	$0.951700\pi$
$90$		0			0
$91$	−0.275845	+	0.477777i	−0.0289164	+	0.0500846i
$92$	2.07407	+	11.7626i	0.216237	+	1.22634i
$93$		0			0
$94$	−1.55303	+	0.565258i	−0.160183	+	0.0583019i
$95$	0.579585	−	0.210952i	0.0594642	−	0.0216432i
$96$		0			0
$97$	−1.56758	−	8.89020i	−0.159164	−	0.902663i	−0.954880	−	0.296993i	$-0.904016\pi$
$97$	−1.56758	−	8.89020i	−0.159164	−	0.902663i	0.795716	−	0.605670i	$-0.207095\pi$
$98$	2.38917	−	4.13816i	0.241342	−	0.418017i
$99$		0			0
$100$	−2.98886	−	5.17685i	−0.298886	−	0.517685i
$101$	9.95253	−	8.35117i	0.990314	−	0.830972i	0.00470087	−	0.999989i	$-0.498504\pi$
$101$	9.95253	−	8.35117i	0.990314	−	0.830972i	0.985613	+	0.169017i	$0.0540592\pi$
$102$		0			0
$103$	1.57532	−	8.93410i	0.155221	−	0.880303i	−0.803362	−	0.595491i	$-0.796958\pi$
$103$	1.57532	−	8.93410i	0.155221	−	0.880303i	0.958583	−	0.284812i	$-0.0919312\pi$
$104$	8.46567	+	7.10354i	0.830127	+	0.696559i
$105$		0			0
$106$	1.95811	+	0.712694i	0.190189	+	0.0692230i
$107$	11.3865			1.10077			0.550386	−	0.834911i	$-0.314481\pi$
$107$	11.3865			1.10077			0.550386	+	0.834911i	$0.314481\pi$
$108$		0			0
$109$	2.89899			0.277672			0.138836	−	0.990315i	$-0.455664\pi$
$109$	2.89899			0.277672			0.138836	+	0.990315i	$0.455664\pi$
$110$	3.66041	+	1.33228i	0.349007	+	0.127028i
$111$		0			0
$112$	−0.130415	−	0.109431i	−0.0123231	−	0.0103403i
$113$	−2.01087	+	11.4042i	−0.189167	+	1.07282i	0.731318	+	0.682037i	$0.238906\pi$
$113$	−2.01087	+	11.4042i	−0.189167	+	1.07282i	−0.920484	+	0.390780i	$0.872205\pi$
$114$		0			0
$115$	−6.25877	+	5.25173i	−0.583633	+	0.489727i
$116$	3.88365	+	6.72668i	0.360588	+	0.624557i
$117$		0			0
$118$	0.0150147	−	0.0260063i	0.00138222	−	0.00239407i
$119$	−0.100080	−	0.567581i	−0.00917431	−	0.0520301i
$120$		0			0
$121$	−17.4081	+	6.33602i	−1.58255	+	0.576002i
$122$	6.56423	−	2.38919i	0.594298	−	0.216307i
$123$		0			0
$124$	2.33022	+	13.2153i	0.209260	+	1.18677i
$125$	4.66452	−	8.07919i	0.417208	−	0.722625i
$126$		0			0
$127$	7.70961	+	13.3534i	0.684117	+	1.18493i	0.973713	+	0.227777i	$0.0731456\pi$
$127$	7.70961	+	13.3534i	0.684117	+	1.18493i	−0.289596	+	0.957149i	$0.593521\pi$
$128$	−8.28368	+	6.95084i	−0.732181	+	0.614373i
$129$		0			0
$130$	−0.569392	+	3.22918i	−0.0499390	+	0.283218i
$131$	10.2314	+	8.58512i	0.893917	+	0.750086i	0.968992	−	0.247092i	$-0.0794751\pi$
$131$	10.2314	+	8.58512i	0.893917	+	0.750086i	−0.0750747	+	0.997178i	$0.523920\pi$
$132$		0			0
$133$	−0.0667040	−	0.0242783i	−0.00578397	−	0.00210519i
$134$	−1.27217			−0.109899
$135$		0			0
$136$	−11.5449			−0.989965
$137$	18.4402	+	6.71167i	1.57545	+	0.573416i	0.974208	−	0.225652i	$-0.0724511\pi$
$137$	18.4402	+	6.71167i	1.57545	+	0.573416i	0.601241	+	0.799068i	$0.294673\pi$
$138$		0			0
$139$	12.4914	+	10.4815i	1.05951	+	0.889030i	0.994061	−	0.108826i	$-0.0347091\pi$
$139$	12.4914	+	10.4815i	1.05951	+	0.889030i	0.0654443	+	0.997856i	$0.479154\pi$
$140$	0.0336295	−	0.190722i	0.00284221	−	0.0161190i
$141$		0			0
$142$	−3.41147	+	2.86257i	−0.286285	+	0.240221i
$143$	−12.4269	−	21.5239i	−1.03919	−	1.79992i
$144$		0			0
$145$	−2.65657	+	4.60132i	−0.220616	+	0.382119i
$146$	1.45323	+	8.24170i	0.120270	+	0.682088i
$147$		0			0
$148$	−3.14543	+	1.14484i	−0.258553	+	0.0941055i
$149$	−10.3814	+	3.77853i	−0.850480	+	0.309549i	−0.730236	−	0.683195i	$-0.760590\pi$
$149$	−10.3814	+	3.77853i	−0.850480	+	0.309549i	−0.120244	+	0.992744i	$0.538368\pi$
$150$		0			0
$151$	−1.18092	−	6.69734i	−0.0961021	−	0.545022i	−0.994404	−	0.105643i	$-0.966310\pi$
$151$	−1.18092	−	6.69734i	−0.0961021	−	0.545022i	0.898302	−	0.439379i	$-0.144801\pi$
$152$	−0.710966	+	1.23143i	−0.0576670	+	0.0998821i
$153$		0			0
$154$	−0.224155	−	0.388249i	−0.0180630	−	0.0312860i
$155$	−7.03174	+	5.90033i	−0.564803	+	0.473926i
$156$		0			0
$157$	2.93242	−	16.6306i	0.234032	−	1.32726i	−0.610609	−	0.791932i	$-0.709075\pi$
$157$	2.93242	−	16.6306i	0.234032	−	1.32726i	0.844642	−	0.535332i	$-0.179814\pi$
$158$	0.368026	+	0.308811i	0.0292786	+	0.0245677i
$159$		0			0
$160$	−5.70961	−	2.07813i	−0.451384	−	0.164290i
$161$	0.940307			0.0741066
$162$		0			0
$163$	8.41147			0.658838			0.329419	−	0.944184i	$-0.393147\pi$
$163$	8.41147			0.658838			0.329419	+	0.944184i	$0.393147\pi$
$164$	10.8818	+	3.96064i	0.849723	+	0.309274i
$165$		0			0
$166$	3.55097	+	2.97962i	0.275609	+	0.231263i
$167$	−0.455827	+	2.58512i	−0.0352729	+	0.200043i	−0.997352	−	0.0727289i	$-0.976829\pi$
$167$	−0.455827	+	2.58512i	−0.0352729	+	0.200043i	0.962079	+	0.272772i	$0.0879403\pi$
$168$		0			0
$169$	6.06805	−	5.09170i	0.466773	−	0.391669i
$170$	−1.71275	−	2.96657i	−0.131362	−	0.227525i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	2.27536	+	12.9042i	0.172992	+	0.981088i	0.940436	+	0.339971i	$0.110417\pi$
$173$	2.27536	+	12.9042i	0.172992	+	0.981088i	−0.767443	+	0.641117i	$0.778471\pi$
$174$		0			0
$175$	−0.442219	+	0.160954i	−0.0334286	+	0.0121670i
$176$	7.20702	−	2.62314i	0.543250	−	0.197727i
$177$		0			0
$178$	0.814330	+	4.61830i	0.0610366	+	0.346156i
$179$	11.0494	−	19.1382i	0.825872	−	1.43045i	−0.0753784	−	0.997155i	$-0.524016\pi$
$179$	11.0494	−	19.1382i	0.825872	−	1.43045i	0.901251	−	0.433298i	$-0.142650\pi$
$180$		0			0
$181$	1.02956	+	1.78325i	0.0765268	+	0.132548i	0.901749	−	0.432260i	$-0.142284\pi$
$181$	1.02956	+	1.78325i	0.0765268	+	0.132548i	−0.825222	+	0.564808i	$0.808950\pi$
$182$	0.289088	−	0.242574i	0.0214286	−	0.0179808i
$183$		0			0
$184$	3.27079	−	18.5496i	0.241126	−	1.36749i
$185$	−1.75400	−	1.47178i	−0.128957	−	0.108208i
$186$		0			0
$187$	24.3983	+	8.88024i	1.78418	+	0.649388i
$188$	−3.70167			−0.269972
$189$		0			0
$190$	−0.421903			−0.0306081
$191$	3.71102	+	1.35070i	0.268520	+	0.0977332i	0.472771	−	0.881185i	$-0.343254\pi$
$191$	3.71102	+	1.35070i	0.268520	+	0.0977332i	−0.204251	+	0.978918i	$0.565476\pi$
$192$		0			0
$193$	−6.47044	−	5.42934i	−0.465752	−	0.390813i	0.379490	−	0.925196i	$-0.376099\pi$
$193$	−6.47044	−	5.42934i	−0.465752	−	0.390813i	−0.845242	+	0.534383i	$0.820544\pi$
$194$	−1.07229	+	6.08125i	−0.0769858	+	0.436608i
$195$		0			0
$196$	8.19846	−	6.87933i	0.585605	−	0.491381i
$197$	1.14749	+	1.98751i	0.0817553	+	0.141604i	0.904004	−	0.427524i	$-0.140614\pi$
$197$	1.14749	+	1.98751i	0.0817553	+	0.141604i	−0.822249	+	0.569128i	$0.807281\pi$
$198$		0			0
$199$	11.7515	−	20.3542i	0.833042	−	1.44287i	−0.0625736	−	0.998040i	$-0.519931\pi$
$199$	11.7515	−	20.3542i	0.833042	−	1.44287i	0.895615	−	0.444830i	$-0.146736\pi$
$200$	1.63695	+	9.28359i	0.115750	+	0.656449i
$201$		0			0
$202$	−8.35117	+	3.03958i	−0.587586	+	0.213864i
$203$	0.574609	−	0.209141i	0.0403297	−	0.0146788i
$204$		0			0
$205$	1.37551	+	7.80093i	0.0960701	+	0.544841i
$206$	−3.10278	+	5.37417i	−0.216181	+	0.374436i
$207$		0			0
$208$	3.22803	+	5.59110i	0.223823	+	0.387673i
$209$	2.44972	−	2.05556i	0.169451	−	0.142186i
$210$		0			0
$211$	−0.289515	+	1.64192i	−0.0199310	+	0.113035i	−0.993150	−	0.116845i	$-0.962722\pi$
$211$	−0.289515	+	1.64192i	−0.0199310	+	0.113035i	0.973219	+	0.229879i	$0.0738331\pi$
$212$	3.57526	+	3.00000i	0.245550	+	0.206041i
$213$		0			0
$214$	−7.31908	−	2.66393i	−0.500322	−	0.182102i
$215$	−1.36808			−0.0933023
$216$		0			0
$217$	1.05644			0.0717156
$218$	−1.86343	−	0.678234i	−0.126208	−	0.0459358i
$219$		0			0
$220$	6.68345	+	5.60808i	0.450598	+	0.378097i
$221$	−3.79525	+	21.5239i	−0.255296	+	1.44786i
$222$		0			0
$223$	−7.50774	+	6.29974i	−0.502756	+	0.421862i	−0.858571	−	0.512694i	$-0.828647\pi$
$223$	−7.50774	+	6.29974i	−0.502756	+	0.421862i	0.355816	+	0.934556i	$0.384203\pi$
$224$	0.349643	+	0.605600i	0.0233615	+	0.0404634i
$225$		0			0
$226$	3.96064	−	6.86002i	0.263458	−	0.456322i
$227$	−2.68820	−	15.2456i	−0.178422	−	1.01188i	−0.934119	−	0.356962i	$-0.883813\pi$
$227$	−2.68820	−	15.2456i	−0.178422	−	1.01188i	0.755697	−	0.654922i	$-0.227299\pi$
$228$		0			0
$229$	10.5753	−	3.84910i	0.698837	−	0.254356i	0.0319227	−	0.999490i	$-0.489837\pi$
$229$	10.5753	−	3.84910i	0.698837	−	0.254356i	0.666914	+	0.745134i	$0.267615\pi$
$230$	5.25173	−	1.91147i	0.346289	−	0.126039i
$231$		0			0
$232$	−2.12701	−	12.0629i	−0.139645	−	0.791967i
$233$	2.61738	−	4.53343i	0.171470	−	0.296995i	−0.767464	−	0.641092i	$-0.778482\pi$
$233$	2.61738	−	4.53343i	0.171470	−	0.296995i	0.938934	+	0.344097i	$0.111815\pi$
$234$		0			0
$235$	−1.26604	−	2.19285i	−0.0825876	−	0.143046i
$236$	0.0515234	−	0.0432332i	0.00335389	−	0.00281424i
$237$		0			0
$238$	−0.0684587	+	0.388249i	−0.00443752	+	0.0251664i
$239$	7.89776	+	6.62701i	0.510864	+	0.428666i	0.861433	−	0.507871i	$-0.169567\pi$
$239$	7.89776	+	6.62701i	0.510864	+	0.428666i	−0.350569	+	0.936537i	$0.614012\pi$
$240$		0			0
$241$	−10.0963	−	3.67474i	−0.650358	−	0.236711i	−0.00428982	−	0.999991i	$-0.501365\pi$
$241$	−10.0963	−	3.67474i	−0.650358	−	0.236711i	−0.646068	+	0.763280i	$0.723588\pi$
$242$	12.6720			0.814590
$243$		0			0
$244$	15.6459			1.00163
$245$	6.87933	+	2.50387i	0.439504	+	0.159966i
$246$		0			0
$247$	2.06212	+	1.73032i	0.131209	+	0.110098i
$248$	3.67474	−	20.8405i	0.233346	−	1.32337i
$249$		0			0
$250$	−4.88847	+	4.10191i	−0.309174	+	0.259428i
$251$	7.53644	+	13.0535i	0.475696	+	0.823930i	0.999612	−	0.0278401i	$-0.00886291\pi$
$251$	7.53644	+	13.0535i	0.475696	+	0.823930i	−0.523916	+	0.851770i	$0.675530\pi$
$252$		0			0
$253$	−21.1805	+	36.6857i	−1.33161	+	2.30641i
$254$	−1.83153	−	10.3871i	−0.114920	−	0.651746i
$255$		0			0
$256$	9.09879	−	3.31169i	0.568675	−	0.206981i
$257$	−3.12208	+	1.13634i	−0.194750	+	0.0708832i	−0.437554	−	0.899192i	$-0.644155\pi$
$257$	−3.12208	+	1.13634i	−0.194750	+	0.0708832i	0.242804	+	0.970075i	$0.421933\pi$
$258$		0			0
$259$	0.0457595	+	0.259515i	0.00284335	+	0.0161255i
$260$	−3.67209	+	6.36025i	−0.227734	+	0.394446i
$261$		0			0
$262$	−4.56805	−	7.91209i	−0.282215	−	0.488811i
$263$	−6.77082	+	5.68139i	−0.417506	+	0.350329i	−0.827214	−	0.561888i	$-0.810075\pi$
$263$	−6.77082	+	5.68139i	−0.417506	+	0.350329i	0.409707	+	0.912217i	$0.365631\pi$
$264$		0			0
$265$	−0.554378	+	3.14403i	−0.0340551	+	0.193136i
$266$	0.0371965	+	0.0312115i	0.00228066	+	0.00191370i
$267$		0			0
$268$	−2.67752	−	0.974537i	−0.163555	−	0.0595293i
$269$	−8.09267			−0.493419			−0.246709	−	0.969090i	$-0.579349\pi$
$269$	−8.09267			−0.493419			−0.246709	+	0.969090i	$0.579349\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	−6.33775	−	2.30675i	−0.384282	−	0.139867i
$273$		0			0
$274$	−10.2829	−	8.62835i	−0.621211	−	0.521258i
$275$	3.68144	−	20.8785i	0.221999	−	1.25902i
$276$		0			0
$277$	−3.23989	+	2.71859i	−0.194666	+	0.163344i	−0.734911	−	0.678164i	$-0.762776\pi$
$277$	−3.23989	+	2.71859i	−0.194666	+	0.163344i	0.540245	+	0.841508i	$0.318332\pi$
$278$	−5.57710	−	9.65982i	−0.334492	−	0.579357i
$279$		0			0
$280$	−0.152704	+	0.264490i	−0.00912579	+	0.0158063i
$281$	−1.26800	−	7.19119i	−0.0756426	−	0.428990i	−0.998986	−	0.0450159i	$-0.985666\pi$
$281$	−1.26800	−	7.19119i	−0.0756426	−	0.428990i	0.923344	−	0.383975i	$-0.125445\pi$
$282$		0			0
$283$	−15.0544	+	5.47935i	−0.894890	+	0.325713i	−0.748203	−	0.663470i	$-0.769083\pi$
$283$	−15.0544	+	5.47935i	−0.894890	+	0.325713i	−0.146687	+	0.989183i	$0.546861\pi$
$284$	−9.37295	+	3.41147i	−0.556182	+	0.202434i
$285$		0			0
$286$	2.95218	+	16.7427i	0.174566	+	0.990014i
$287$	0.455827	−	0.789515i	0.0269066	−	0.0466036i
$288$		0			0
$289$	−2.91622	−	5.05104i	−0.171542	−	0.297120i
$290$	2.78412	−	2.33615i	0.163489	−	0.137184i
$291$		0			0
$292$	−3.25490	+	18.4595i	−0.190479	+	1.08026i
$293$	−13.7923	−	11.5731i	−0.805754	−	0.676108i	0.143836	−	0.989601i	$-0.454056\pi$
$293$	−13.7923	−	11.5731i	−0.805754	−	0.676108i	−0.949590	+	0.313494i	$0.898501\pi$
$294$		0			0
$295$	0.0432332	+	0.0157356i	0.00251714	+	0.000916163i
$296$	5.27866			0.306816
$297$		0			0
$298$	7.55707			0.437769
$299$	−33.5081	−	12.1959i	−1.93782	−	0.705309i
$300$		0			0
$301$	0.120615	+	0.101208i	0.00695212	+	0.00583352i
$302$	−0.807798	+	4.58125i	−0.0464836	+	0.263621i
$303$		0			0
$304$	−0.636345	+	0.533957i	−0.0364969	+	0.0306245i
$305$	5.35121	+	9.26857i	0.306409	+	0.530717i
$306$		0			0
$307$	6.75537	−	11.7006i	0.385549	−	0.667791i	−0.606296	−	0.795239i	$-0.707345\pi$
$307$	6.75537	−	11.7006i	0.385549	−	0.667791i	0.991845	+	0.127448i	$0.0406787\pi$
$308$	−0.174362	−	0.988856i	−0.00993519	−	0.0563453i
$309$		0			0
$310$	5.90033	−	2.14754i	0.335116	−	0.121972i
$311$	15.4319	−	5.61674i	0.875062	−	0.318496i	0.134846	−	0.990867i	$-0.456946\pi$
$311$	15.4319	−	5.61674i	0.875062	−	0.318496i	0.740215	+	0.672370i	$0.234724\pi$
$312$		0			0
$313$	−3.39739	−	19.2676i	−0.192032	−	1.08907i	−0.916582	−	0.399846i	$-0.869064\pi$
$313$	−3.39739	−	19.2676i	−0.192032	−	1.08907i	0.724550	−	0.689222i	$-0.242047\pi$
$314$	−5.77574	+	10.0039i	−0.325944	+	0.564551i
$315$		0			0
$316$	0.538019	+	0.931876i	0.0302659	+	0.0524221i
$317$	18.6751	−	15.6702i	1.04890	−	0.880129i	0.0559193	−	0.998435i	$-0.482191\pi$
$317$	18.6751	−	15.6702i	1.04890	−	0.880129i	0.992977	+	0.118307i	$0.0377466\pi$
$318$		0			0
$319$	−4.78359	+	27.1291i	−0.267829	+	1.51894i
$320$	0.917549	+	0.769915i	0.0512925	+	0.0430395i
$321$		0			0
$322$	−0.604418	−	0.219990i	−0.0336829	−	0.0122596i
$323$	−2.81217			−0.156473
$324$		0			0
$325$	17.8462			0.989927
$326$	−5.40679	−	1.96791i	−0.299454	−	0.108993i
$327$		0			0
$328$	−13.9893	−	11.7384i	−0.772431	−	0.648147i
$329$	−0.0506039	+	0.286989i	−0.00278988	+	0.0158222i
$330$		0			0
$331$	21.8314	−	18.3187i	1.19996	−	1.00689i	0.200331	−	0.979728i	$-0.435798\pi$
$331$	21.8314	−	18.3187i	1.19996	−	1.00689i	0.999631	−	0.0271599i	$-0.00864633\pi$
$332$	5.19118	+	8.99138i	0.284903	+	0.493466i
$333$		0			0
$334$	0.897804	−	1.55504i	0.0491256	−	0.0850881i
$335$	−0.338453	−	1.91946i	−0.0184917	−	0.104871i
$336$		0			0
$337$	16.3944	−	5.96707i	0.893060	−	0.325047i	0.145592	−	0.989345i	$-0.453491\pi$
$337$	16.3944	−	5.96707i	0.893060	−	0.325047i	0.747468	+	0.664298i	$0.231269\pi$
$338$	−5.09170	+	1.85323i	−0.276952	+	0.100802i
$339$		0			0
$340$	−1.33228	−	7.55574i	−0.0722531	−	0.409768i
$341$	−23.7963	+	41.2165i	−1.28864	+	2.23200i
$342$		0			0
$343$	−0.843426	−	1.46086i	−0.0455407	−	0.0788788i
$344$	2.41609	−	2.02734i	0.130267	−	0.109307i
$345$		0			0
$346$	1.55644	−	8.82699i	0.0836746	−	0.474542i
$347$	−19.2959	−	16.1912i	−1.03586	−	0.869189i	−0.0443222	−	0.999017i	$-0.514113\pi$
$347$	−19.2959	−	16.1912i	−1.03586	−	0.869189i	−0.991536	+	0.129829i	$0.958557\pi$
$348$		0			0
$349$	11.1373	+	4.05364i	0.596165	+	0.216986i	0.622439	−	0.782669i	$-0.286142\pi$
$349$	11.1373	+	4.05364i	0.596165	+	0.216986i	−0.0262739	+	0.999655i	$0.508364\pi$
$350$	0.321909			0.0172068
$351$		0			0
$352$	−31.5030			−1.67912
$353$	−7.89106	−	2.87211i	−0.419999	−	0.152867i	0.123371	−	0.992361i	$-0.460630\pi$
$353$	−7.89106	−	2.87211i	−0.419999	−	0.152867i	−0.543370	+	0.839494i	$0.682852\pi$
$354$		0			0
$355$	−5.22668	−	4.38571i	−0.277403	−	0.232769i
$356$	−1.82391	+	10.3439i	−0.0966669	+	0.548225i
$357$		0			0
$358$	−11.5799	+	9.71670i	−0.612017	+	0.513543i
$359$	1.32012	+	2.28652i	0.0696735	+	0.120678i	0.898758	−	0.438446i	$-0.144471\pi$
$359$	1.32012	+	2.28652i	0.0696735	+	0.120678i	−0.829084	+	0.559124i	$0.811138\pi$
$360$		0			0
$361$	9.32682	−	16.1545i	0.490885	−	0.850238i
$362$	−0.244588	−	1.38713i	−0.0128552	−	0.0729057i
$363$		0			0
$364$	0.794263	−	0.289088i	0.0416307	−	0.0151523i
$365$	−12.0486	+	4.38532i	−0.630650	+	0.229538i
$366$		0			0
$367$	1.59714	+	9.05785i	0.0833702	+	0.472816i	0.997696	+	0.0678375i	$0.0216099\pi$
$367$	1.59714	+	9.05785i	0.0833702	+	0.472816i	−0.914326	+	0.404979i	$0.867279\pi$
$368$	5.50190	−	9.52956i	0.286806	−	0.496763i
$369$		0			0
$370$	0.783119	+	1.35640i	0.0407124	+	0.0705159i
$371$	0.281465	−	0.236177i	0.0146129	−	0.0122617i
$372$		0			0
$373$	−4.65224	+	26.3841i	−0.240884	+	1.36612i	0.588978	+	0.808149i	$0.299531\pi$
$373$	−4.65224	+	26.3841i	−0.240884	+	1.36612i	−0.829861	+	0.557970i	$0.811580\pi$
$374$	−13.6053	−	11.4162i	−0.703515	−	0.590319i
$375$		0			0
$376$	5.48545	+	1.99654i	0.282891	+	0.102964i
$377$	−23.1889			−1.19429
$378$		0			0
$379$	−27.1242			−1.39328			−0.696639	−	0.717422i	$-0.745322\pi$
$379$	−27.1242			−1.39328			−0.696639	+	0.717422i	$0.745322\pi$
$380$	−0.887975	−	0.323197i	−0.0455522	−	0.0165796i
$381$		0			0
$382$	−2.06939	−	1.73643i	−0.105879	−	0.0888433i
$383$	5.97815	−	33.9038i	0.305469	−	1.73240i	−0.315818	−	0.948820i	$-0.602279\pi$
$383$	5.97815	−	33.9038i	0.305469	−	1.73240i	0.621287	−	0.783583i	$-0.286610\pi$
$384$		0			0
$385$	0.526159	−	0.441500i	0.0268156	−	0.0225009i
$386$	2.88889	+	5.00371i	0.147041	+	0.254682i
$387$		0			0
$388$	−6.91534	+	11.9777i	−0.351073	+	0.608077i
$389$	0.131381	+	0.745100i	0.00666129	+	0.0377781i	0.987957	−	0.154727i	$-0.0494499\pi$
$389$	0.131381	+	0.745100i	0.00666129	+	0.0377781i	−0.981296	+	0.192505i	$0.938339\pi$
$390$		0			0
$391$	35.0051	−	12.7408i	1.77028	−	0.644331i
$392$	−15.8597	+	5.77244i	−0.801033	+	0.291552i
$393$		0			0
$394$	−0.272603	−	1.54601i	−0.0137335	−	0.0778868i
$395$	−0.368026	+	0.637441i	−0.0185174	+	0.0320731i
$396$		0			0
$397$	−3.50387	−	6.06888i	−0.175854	−	0.304588i	0.764602	−	0.644502i	$-0.222935\pi$
$397$	−3.50387	−	6.06888i	−0.175854	−	0.304588i	−0.940457	+	0.339914i	$0.889602\pi$
$398$	−12.3157	+	10.3341i	−0.617330	+	0.518001i
$399$		0			0
$400$	−0.956300	+	5.42345i	−0.0478150	+	0.271172i
$401$	−7.23973	−	6.07486i	−0.361535	−	0.303364i	0.443867	−	0.896093i	$-0.353606\pi$
$401$	−7.23973	−	6.07486i	−0.361535	−	0.303364i	−0.805402	+	0.592729i	$0.798051\pi$
$402$		0			0
$403$	−37.6464	−	13.7022i	−1.87530	−	0.682553i
$404$	−19.9051			−0.990314
$405$		0			0
$406$	−0.418281			−0.0207590
$407$	−11.1556	−	4.06031i	−0.552963	−	0.201262i
$408$		0			0
$409$	4.22668	+	3.54661i	0.208996	+	0.175368i	0.741277	−	0.671199i	$-0.234221\pi$
$409$	4.22668	+	3.54661i	0.208996	+	0.175368i	−0.532281	+	0.846568i	$0.678665\pi$
$410$	0.940908	−	5.33615i	0.0464681	−	0.263534i
$411$		0			0
$412$	−10.6472	+	8.93410i	−0.524552	+	0.440151i
$413$	−0.00264750	−	0.00458561i	−0.000130275	−	0.000225643i
$414$		0			0
$415$	−3.55097	+	6.15047i	−0.174310	+	0.301915i
$416$	−4.60489	−	26.1156i	−0.225773	−	1.28042i
$417$		0			0
$418$	−2.05556	+	0.748163i	−0.100541	+	0.0365938i
$419$	0.438252	−	0.159511i	0.0214100	−	0.00779261i	−0.331293	−	0.943528i	$-0.607485\pi$
$419$	0.438252	−	0.159511i	0.0214100	−	0.00779261i	0.352703	+	0.935735i	$0.385263\pi$
$420$		0			0
$421$	−0.419215	−	2.37749i	−0.0204313	−	0.115872i	0.972886	−	0.231283i	$-0.0742924\pi$
$421$	−0.419215	−	2.37749i	−0.0204313	−	0.115872i	−0.993318	+	0.115412i	$0.963181\pi$
$422$	0.570234	−	0.987674i	0.0277585	−	0.0480792i
$423$		0			0
$424$	−3.68004	−	6.37402i	−0.178719	−	0.309550i
$425$	−14.2817	+	11.9838i	−0.692766	+	0.581300i
$426$		0			0
$427$	0.213888	−	1.21302i	0.0103508	−	0.0587022i
$428$	−13.3637	−	11.2135i	−0.645959	−	0.542024i
$429$		0			0
$430$	0.879385	+	0.320070i	0.0424077	+	0.0154351i
$431$	12.0992			0.582796			0.291398	−	0.956602i	$-0.405880\pi$
$431$	12.0992			0.582796			0.291398	+	0.956602i	$0.405880\pi$
$432$		0			0
$433$	33.3509			1.60274			0.801371	−	0.598167i	$-0.204104\pi$
$433$	33.3509			1.60274			0.801371	+	0.598167i	$0.204104\pi$
$434$	−0.679065	−	0.247159i	−0.0325961	−	0.0118640i
$435$		0			0
$436$	−3.40239	−	2.85494i	−0.162945	−	0.136727i
$437$	0.796719	−	4.51842i	0.0381122	−	0.216145i
$438$		0			0
$439$	−6.92855	+	5.81374i	−0.330682	+	0.277475i	−0.792977	−	0.609251i	$-0.791470\pi$
$439$	−6.92855	+	5.81374i	−0.330682	+	0.277475i	0.462296	+	0.886726i	$0.347026\pi$
$440$	−6.87933	−	11.9153i	−0.327959	−	0.568042i
$441$		0			0
$442$	7.47519	−	12.9474i	0.355558	−	0.615845i
$443$	0.812174	+	4.60607i	0.0385875	+	0.218841i	0.998004	−	0.0631526i	$-0.0201155\pi$
$443$	0.812174	+	4.60607i	0.0385875	+	0.218841i	−0.959416	+	0.281993i	$0.909004\pi$
$444$		0			0
$445$	−6.75150	+	2.45734i	−0.320052	+	0.116489i
$446$	6.29974	−	2.29292i	0.298301	−	0.108573i
$447$		0			0
$448$	−0.0239376	−	0.135757i	−0.00113094	−	0.00641390i
$449$	−13.3534	+	23.1288i	−0.630187	+	1.09152i	0.357326	+	0.933980i	$0.383689\pi$
$449$	−13.3534	+	23.1288i	−0.630187	+	1.09152i	−0.987513	+	0.157537i	$0.949645\pi$
$450$		0			0
$451$	20.5351	+	35.5678i	0.966959	+	1.67482i
$452$	13.5910	−	11.4042i	0.639267	−	0.536408i
$453$		0			0
$454$	−1.83884	+	10.4286i	−0.0863011	+	0.489438i
$455$	0.442909	+	0.371644i	0.0207639	+	0.0174230i
$456$		0			0
$457$	0.618089	+	0.224966i	0.0289130	+	0.0105235i	0.356436	−	0.934320i	$-0.383992\pi$
$457$	0.618089	+	0.224966i	0.0289130	+	0.0105235i	−0.327523	+	0.944843i	$0.606214\pi$
$458$	−7.69820			−0.359713
$459$		0			0
$460$	12.5175			0.583633
$461$	19.4551	+	7.08109i	0.906116	+	0.329799i	0.752701	−	0.658363i	$-0.228751\pi$
$461$	19.4551	+	7.08109i	0.906116	+	0.329799i	0.153415	+	0.988162i	$0.450973\pi$
$462$		0			0
$463$	−19.0162	−	15.9565i	−0.883758	−	0.741561i	0.0831906	−	0.996534i	$-0.473489\pi$
$463$	−19.0162	−	15.9565i	−0.883758	−	0.741561i	−0.966948	+	0.254973i	$0.917933\pi$
$464$	1.24259	−	7.04710i	0.0576860	−	0.327154i
$465$		0			0
$466$	−2.74304	+	2.30168i	−0.127069	+	0.106623i
$467$	13.3365	+	23.0994i	0.617138	+	1.06891i	0.990005	+	0.141029i	$0.0450412\pi$
$467$	13.3365	+	23.0994i	0.617138	+	1.06891i	−0.372868	+	0.927884i	$0.621625\pi$
$468$		0			0
$469$	−0.112159	+	0.194265i	−0.00517901	+	0.00897031i
$470$	0.300767	+	1.70574i	0.0138734	+	0.0786798i
$471$		0			0
$472$	−0.0996702	+	0.0362770i	−0.00458769	+	0.00166978i
$473$	−6.66544	+	2.42602i	−0.306477	+	0.111549i
$474$		0			0
$475$	0.398737	+	2.26135i	0.0182953	+	0.103758i
$476$	−0.441500	+	0.764700i	−0.0202361	+	0.0350500i
$477$		0			0
$478$	−3.52616	−	6.10749i	−0.161283	−	0.279350i
$479$	2.47167	−	2.07398i	0.112934	−	0.0947625i	−0.584572	−	0.811342i	$-0.698738\pi$
$479$	2.47167	−	2.07398i	0.112934	−	0.0947625i	0.697506	+	0.716579i	$0.254293\pi$
$480$		0			0
$481$	1.73530	−	9.84137i	0.0791229	−	0.448728i
$482$	5.63003	+	4.72416i	0.256441	+	0.215179i
$483$		0			0
$484$	26.6707	+	9.70735i	1.21231	+	0.441243i
$485$	−9.46075			−0.429590
$486$		0			0
$487$	−7.77930			−0.352514			−0.176257	−	0.984344i	$-0.556399\pi$
$487$	−7.77930			−0.352514			−0.176257	+	0.984344i	$0.556399\pi$
$488$	−23.1855	−	8.43882i	−1.04956	−	0.382007i
$489$		0			0
$490$	−3.83615	−	3.21891i	−0.173300	−	0.145416i
$491$	−2.96000	+	16.7870i	−0.133583	+	0.757586i	0.842253	+	0.539082i	$0.181229\pi$
$491$	−2.96000	+	16.7870i	−0.133583	+	0.757586i	−0.975836	+	0.218504i	$0.929882\pi$
$492$		0			0
$493$	18.5574	−	15.5715i	0.835782	−	0.701304i
$494$	−0.920686	−	1.59467i	−0.0414236	−	0.0717478i
$495$		0			0
$496$	6.18139	−	10.7065i	0.277553	−	0.480735i
$497$	0.136357	+	0.773318i	0.00611644	+	0.0346881i
$498$		0			0
$499$	−7.45249	+	2.71248i	−0.333619	+	0.121427i	−0.503398	−	0.864055i	$-0.667917\pi$
$499$	−7.45249	+	2.71248i	−0.333619	+	0.121427i	0.169779	+	0.985482i	$0.445695\pi$
$500$	−13.4310	+	4.88847i	−0.600651	+	0.218619i
$501$		0			0
$502$	−1.79039	−	10.1538i	−0.0799091	−	0.453187i
$503$	12.4748	−	21.6070i	0.556224	−	0.963409i	−0.441583	−	0.897220i	$-0.645583\pi$
$503$	12.4748	−	21.6070i	0.556224	−	0.963409i	0.997807	−	0.0661881i	$-0.0210837\pi$
$504$		0			0
$505$	−6.80793	−	11.7917i	−0.302949	−	0.524723i
$506$	22.1974	−	18.6258i	0.986795	−	0.828019i
$507$		0			0
$508$	4.10220	−	23.2647i	0.182006	−	1.03220i
$509$	31.0010	+	26.0130i	1.37410	+	1.15300i	0.971339	+	0.237697i	$0.0763926\pi$
$509$	31.0010	+	26.0130i	1.37410	+	1.15300i	0.402757	+	0.915307i	$0.368052\pi$
$510$		0			0
$511$	1.38666	+	0.504703i	0.0613422	+	0.0223267i
$512$	15.0038			0.663080
$513$		0			0
$514$	2.27269			0.100244
$515$	−8.93410	−	3.25174i	−0.393683	−	0.143289i
$516$		0			0
$517$	−10.0569	−	8.43874i	−0.442302	−	0.371136i
$518$	0.0313013	−	0.177519i	0.00137530	−	0.00779972i
$519$		0			0
$520$	8.87211	−	7.44459i	0.389068	−	0.326467i
$521$	12.6837	+	21.9688i	0.555684	+	0.962473i	0.997850	+	0.0655394i	$0.0208768\pi$
$521$	12.6837	+	21.9688i	0.555684	+	0.962473i	−0.442166	+	0.896933i	$0.645790\pi$
$522$		0			0
$523$	−6.36097	+	11.0175i	−0.278146	+	0.481762i	−0.970924	−	0.239388i	$-0.923053\pi$
$523$	−6.36097	+	11.0175i	−0.278146	+	0.481762i	0.692778	+	0.721151i	$0.256386\pi$
$524$	−3.55331	−	20.1518i	−0.155227	−	0.880337i
$525$		0			0
$526$	5.68139	−	2.06786i	0.247720	−	0.0901628i
$527$	39.3283	−	14.3143i	1.71317	−	0.623542i
$528$		0			0
$529$	6.55990	+	37.2030i	0.285213	+	1.61752i
$530$	1.09191	−	1.89124i	0.0474296	−	0.0821504i
$531$		0			0
$532$	0.0543776	+	0.0941848i	0.00235757	+	0.00408343i
$533$	−26.4836	+	22.2224i	−1.14713	+	0.962559i
$534$		0			0
$535$	2.07217	−	11.7518i	0.0895876	−	0.508076i
$536$	3.44215	+	2.88831i	0.148678	+	0.124756i
$537$		0			0
$538$	5.20187	+	1.89332i	0.224268	+	0.0816270i
$539$	37.9570			1.63492
$540$		0			0
$541$	2.09327			0.0899969			0.0449984	−	0.998987i	$-0.485672\pi$
$541$	2.09327			0.0899969			0.0449984	+	0.998987i	$0.485672\pi$
$542$	12.2130	+	4.44516i	0.524592	+	0.190936i
$543$		0			0
$544$	21.2219	+	17.8073i	0.909883	+	0.763482i
$545$	0.527572	−	2.99201i	0.0225987	−	0.128164i
$546$		0			0
$547$	2.64362	−	2.21826i	0.113033	−	0.0948459i	−0.584519	−	0.811380i	$-0.698717\pi$
$547$	2.64362	−	2.21826i	0.113033	−	0.0948459i	0.697552	+	0.716534i	$0.254272\pi$
$548$	−15.0326	−	26.0371i	−0.642159	−	1.11225i
$549$		0			0
$550$	−7.25103	+	12.5592i	−0.309185	+	0.535524i
$551$	−0.518110	−	2.93835i	−0.0220722	−	0.125178i
$552$		0			0
$553$	0.0796030	−	0.0289731i	0.00338507	−	0.00123206i
$554$	2.71859	−	0.989485i	0.115502	−	0.0420392i
$555$		0			0
$556$	−4.33821	−	24.6032i	−0.183981	−	1.04341i
$557$	−5.55017	+	9.61318i	−0.235168	+	0.407323i	−0.959322	−	0.282316i	$-0.908897\pi$
$557$	−5.55017	+	9.61318i	−0.235168	+	0.407323i	0.724153	+	0.689639i	$0.242231\pi$
$558$		0			0
$559$	−2.98545	−	5.17095i	−0.126271	−	0.218708i
$560$	−0.136676	+	0.114685i	−0.00577562	+	0.00484632i
$561$		0			0
$562$	−0.867364	+	4.91906i	−0.0365875	+	0.207498i
$563$	−18.6231	−	15.6266i	−0.784868	−	0.658583i	0.159601	−	0.987182i	$-0.448979\pi$
$563$	−18.6231	−	15.6266i	−0.784868	−	0.658583i	−0.944470	+	0.328599i	$0.893424\pi$
$564$		0			0
$565$	11.4042	+	4.15079i	0.479778	+	0.174625i
$566$	10.9587			0.460628
$567$		0			0
$568$	15.7297			0.660002
$569$	40.1850	+	14.6261i	1.68464	+	0.613159i	0.993934	−	0.109975i	$-0.0350771\pi$
$569$	40.1850	+	14.6261i	1.68464	+	0.613159i	0.690707	+	0.723134i	$0.257299\pi$
$570$		0			0
$571$	13.8105	+	11.5884i	0.577950	+	0.484957i	0.884273	−	0.466970i	$-0.154654\pi$
$571$	13.8105	+	11.5884i	0.577950	+	0.484957i	−0.306323	+	0.951928i	$0.599099\pi$
$572$	−6.61219	+	37.4996i	−0.276470	+	1.56794i
$573$		0			0
$574$	−0.477711	+	0.400847i	−0.0199393	+	0.0167310i
$575$	−15.2086	−	26.3421i	−0.634244	−	1.09854i
$576$		0			0
$577$	−12.6382	+	21.8899i	−0.526133	+	0.911290i	0.473403	+	0.880846i	$0.343025\pi$
$577$	−12.6382	+	21.8899i	−0.526133	+	0.911290i	−0.999536	+	0.0304438i	$0.990308\pi$
$578$	0.692791	+	3.92902i	0.0288163	+	0.163425i
$579$		0			0
$580$	7.64930	−	2.78412i	0.317620	−	0.115604i
$581$	0.768065	−	0.279553i	0.0318647	−	0.0115978i
$582$		0			0
$583$	2.87433	+	16.3012i	0.119043	+	0.675125i
$584$	14.7797	−	25.5993i	0.611590	−	1.05930i
$585$		0			0
$586$	6.15792	+	10.6658i	0.254381	+	0.440601i
$587$	−21.8823	+	18.3614i	−0.903179	+	0.757857i	−0.970809	−	0.239853i	$-0.922901\pi$
$587$	−21.8823	+	18.3614i	−0.903179	+	0.757857i	0.0676298	+	0.997710i	$0.478456\pi$
$588$		0			0
$589$	0.895115	−	5.07645i	0.0368826	−	0.209172i
$590$	−0.0241084	−	0.0202293i	−0.000992525	−	0.000832828i
$591$		0			0
$592$	2.89780	+	1.05471i	0.119099	+	0.0433485i
$593$	−20.6009			−0.845977			−0.422989	−	0.906135i	$-0.639019\pi$
$593$	−20.6009			−0.845977			−0.422989	+	0.906135i	$0.639019\pi$
$594$		0			0
$595$	−0.604007			−0.0247619
$596$	15.9053	+	5.78905i	0.651506	+	0.237129i
$597$		0			0
$598$	18.6853	+	15.6788i	0.764097	+	0.641154i
$599$	2.51352	−	14.2549i	0.102700	−	0.582439i	−0.889414	−	0.457102i	$-0.848887\pi$
$599$	2.51352	−	14.2549i	0.102700	−	0.582439i	0.992114	−	0.125338i	$-0.0400014\pi$
$600$		0			0
$601$	−10.2306	+	8.58445i	−0.417313	+	0.350167i	−0.827140	−	0.561996i	$-0.810034\pi$
$601$	−10.2306	+	8.58445i	−0.417313	+	0.350167i	0.409827	+	0.912163i	$0.365589\pi$
$602$	−0.0538515	−	0.0932736i	−0.00219483	−	0.00380155i
$603$		0			0
$604$	−5.20961	+	9.02330i	−0.211976	+	0.367153i
$605$	3.37133	+	19.1197i	0.137064	+	0.777328i
$606$		0			0
$607$	−29.3307	+	10.6755i	−1.19050	+	0.433305i	−0.859898	−	0.510466i	$-0.829473\pi$
$607$	−29.3307	+	10.6755i	−1.19050	+	0.433305i	−0.330598	+	0.943772i	$0.607251\pi$
$608$	3.20631	−	1.16700i	0.130033	−	0.0473282i
$609$		0			0
$610$	−1.27126	−	7.20967i	−0.0514718	−	0.291911i
$611$	5.52557	−	9.57057i	0.223541	−	0.387184i
$612$		0			0
$613$	−15.0326	−	26.0372i	−0.607159	−	1.05163i	−0.991706	−	0.128525i	$-0.958976\pi$
$613$	−15.0326	−	26.0372i	−0.607159	−	1.05163i	0.384547	−	0.923105i	$-0.374358\pi$
$614$	−7.07970	+	5.94057i	−0.285713	+	0.239742i
$615$		0			0
$616$	−0.274967	+	1.55942i	−0.0110787	+	0.0628307i
$617$	32.2916	+	27.0959i	1.30001	+	1.09084i	0.990143	+	0.140058i	$0.0447290\pi$
$617$	32.2916	+	27.0959i	1.30001	+	1.09084i	0.309867	+	0.950780i	$0.399715\pi$
$618$		0			0
$619$	−10.9106	−	3.97113i	−0.438534	−	0.159613i	0.113312	−	0.993559i	$-0.463854\pi$
$619$	−10.9106	−	3.97113i	−0.438534	−	0.159613i	−0.551846	+	0.833946i	$0.686076\pi$
$620$	14.0635			0.564803
$621$		0			0
$622$	−11.2335			−0.450422
$623$	0.777025	+	0.282814i	0.0311308	+	0.0113307i
$624$		0			0
$625$	7.45471	+	6.25524i	0.298188	+	0.250210i
$626$	−2.32395	+	13.1798i	−0.0928839	+	0.526771i
$627$		0			0
$628$	−19.8195	+	16.6306i	−0.790886	+	0.663632i
$629$	5.21983	+	9.04101i	0.208128	+	0.360489i
$630$		0			0
$631$	14.6552	−	25.3836i	0.583415	−	1.01051i	−0.411655	−	0.911340i	$-0.635049\pi$
$631$	14.6552	−	25.3836i	0.583415	−	1.01051i	0.995071	−	0.0991657i	$-0.0316174\pi$
$632$	−0.294664	−	1.67112i	−0.0117211	−	0.0664737i
$633$		0			0
$634$	−15.6702	+	5.70350i	−0.622345	+	0.226515i
$635$	15.1850	−	5.52687i	0.602597	−	0.219327i
$636$		0			0
$637$	5.54829	+	31.4659i	0.219831	+	1.24672i
$638$	9.42182	−	16.3191i	0.373014	−	0.646078i
$639$		0			0
$640$	5.66637	+	9.81445i	0.223983	+	0.387950i
$641$	23.8223	−	19.9893i	0.940926	−	0.789531i	−0.0368201	−	0.999322i	$-0.511723\pi$
$641$	23.8223	−	19.9893i	0.940926	−	0.789531i	0.977746	+	0.209791i	$0.0672784\pi$
$642$		0			0
$643$	7.30571	−	41.4328i	0.288109	−	1.63395i	−0.405854	−	0.913938i	$-0.633026\pi$
$643$	7.30571	−	41.4328i	0.288109	−	1.63395i	0.693963	−	0.720010i	$-0.255863\pi$
$644$	−1.10359	−	0.926022i	−0.0434875	−	0.0364904i
$645$		0			0
$646$	1.80763	+	0.657923i	0.0711202	+	0.0258856i
$647$	−4.66717			−0.183485			−0.0917427	−	0.995783i	$-0.529244\pi$
$647$	−4.66717			−0.183485			−0.0917427	+	0.995783i	$0.529244\pi$
$648$		0			0
$649$	0.238541			0.00936356
$650$	−11.4713	−	4.17521i	−0.449941	−	0.163765i
$651$		0			0
$652$	−9.87211	−	8.28368i	−0.386622	−	0.324414i
$653$	−0.542499	+	3.07667i	−0.0212296	+	0.120399i	−0.993581	−	0.113124i	$-0.963914\pi$
$653$	−0.542499	+	3.07667i	−0.0212296	+	0.120399i	0.972351	+	0.233523i	$0.0750254\pi$
$654$		0			0
$655$	10.7226	−	8.99730i	0.418965	−	0.351554i
$656$	−5.33424	−	9.23917i	−0.208267	−	0.360729i
$657$		0			0
$658$	0.0996702	−	0.172634i	0.00388555	−	0.00672997i
$659$	6.49951	+	36.8606i	0.253185	+	1.43588i	0.800689	+	0.599080i	$0.204467\pi$
$659$	6.49951	+	36.8606i	0.253185	+	1.43588i	−0.547504	+	0.836803i	$0.684422\pi$
$660$		0			0
$661$	−24.9021	+	9.06364i	−0.968581	+	0.352535i	−0.777391	−	0.629018i	$-0.783457\pi$
$661$	−24.9021	+	9.06364i	−0.968581	+	0.352535i	−0.191191	+	0.981553i	$0.561235\pi$
$662$	−18.3187	+	6.66747i	−0.711977	+	0.259139i
$663$		0			0
$664$	−2.84312	−	16.1241i	−0.110335	−	0.625738i
$665$	−0.0371965	+	0.0644262i	−0.00144242	+	0.00249834i
$666$		0			0
$667$	19.7618	+	34.2284i	0.765179	+	1.32533i
$668$	3.08083	−	2.58512i	0.119201	−	0.100021i
$669$		0			0
$670$	−0.231516	+	1.31299i	−0.00894423	+	0.0507252i
$671$	42.5077	+	35.6682i	1.64099	+	1.37696i
$672$		0			0
$673$	−1.61721	−	0.588617i	−0.0623389	−	0.0226895i	0.310662	−	0.950520i	$-0.399449\pi$
$673$	−1.61721	−	0.588617i	−0.0623389	−	0.0226895i	−0.373001	+	0.927831i	$0.621671\pi$
$674$	−11.9341			−0.459686
$675$		0			0
$676$	−12.1361			−0.466773
$677$	26.5738	+	9.67206i	1.02131	+	0.371727i	0.797767	−	0.602966i	$-0.206015\pi$
$677$	26.5738	+	9.67206i	1.02131	+	0.371727i	0.223546	+	0.974693i	$0.428237\pi$
$678$		0			0
$679$	0.834093	+	0.699887i	0.0320095	+	0.0268592i
$680$	−2.10100	+	11.9153i	−0.0805695	+	0.456933i
$681$		0			0
$682$	24.9388	−	20.9262i	0.954957	−	0.801304i
$683$	−12.3569	−	21.4029i	−0.472825	−	0.818958i	0.526691	−	0.850057i	$-0.323433\pi$
$683$	−12.3569	−	21.4029i	−0.472825	−	0.818958i	−0.999516	+	0.0310993i	$0.990099\pi$
$684$		0			0
$685$	10.2829	−	17.8105i	0.392888	−	0.680502i
$686$	0.200368	+	1.13634i	0.00765009	+	0.0433858i
$687$		0			0
$688$	1.73143	−	0.630189i	0.0660101	−	0.0240257i
$689$	−13.0933	+	4.76558i	−0.498816	+	0.181554i
$690$		0			0
$691$	−7.60101	−	43.1075i	−0.289156	−	1.63989i	−0.690050	−	0.723762i	$-0.742411\pi$
$691$	−7.60101	−	43.1075i	−0.289156	−	1.63989i	0.400894	−	0.916125i	$-0.368700\pi$
$692$	10.0377	−	17.3858i	0.381576	−	0.660908i
$693$		0			0
$694$	8.61515	+	14.9219i	0.327027	+	0.566427i
$695$	13.0911	−	10.9847i	0.496574	−	0.416675i
$696$		0			0
$697$	6.27156	−	35.5678i	0.237552	−	1.34723i
$698$	−6.21053	−	5.21126i	−0.235072	−	0.197249i
$699$		0			0
$700$	0.677519	+	0.246597i	0.0256078	+	0.00932048i
$701$	14.6504			0.553338			0.276669	−	0.960965i	$-0.410769\pi$
$701$	14.6504			0.553338			0.276669	+	0.960965i	$0.410769\pi$
$702$		0			0
$703$	1.28581			0.0484951
$704$	5.83569	+	2.12402i	0.219941	+	0.0800520i
$705$		0			0
$706$	4.40033	+	3.69232i	0.165609	+	0.138962i
$707$	−0.272114	+	1.54323i	−0.0102339	+	0.0580393i
$708$		0			0
$709$	3.88666	−	3.26129i	0.145967	−	0.122480i	−0.566880	−	0.823800i	$-0.691850\pi$
$709$	3.88666	−	3.26129i	0.145967	−	0.122480i	0.712847	+	0.701320i	$0.247405\pi$
$710$	2.33359	+	4.04189i	0.0875779	+	0.151689i
$711$		0			0
$712$	8.28194	−	14.3447i	0.310379	−	0.537592i
$713$	11.8572	+	67.2456i	0.444056	+	2.51837i
$714$		0			0
$715$	−24.4761	+	8.90858i	−0.915355	+	0.333162i
$716$	−31.8155	+	11.5799i	−1.18900	+	0.432761i
$717$		0			0
$718$	−0.313615	−	1.77860i	−0.0117040	−	0.0663767i
$719$	−2.66858	+	4.62212i	−0.0995213	+	0.172376i	−0.911487	−	0.411330i	$-0.865064\pi$
$719$	−2.66858	+	4.62212i	−0.0995213	+	0.172376i	0.811965	+	0.583706i	$0.198398\pi$
$720$		0			0
$721$	0.547104	+	0.947611i	0.0203752	+	0.0352909i
$722$	−9.77460	+	8.20187i	−0.363773	+	0.305242i
$723$		0			0
$724$	0.547819	−	3.10684i	0.0203595	−	0.115465i
$725$	−15.1527	−	12.7147i	−0.562759	−	0.472211i
$726$		0			0
$727$	−34.8812	−	12.6957i	−1.29367	−	0.470858i	−0.398741	−	0.917063i	$-0.630553\pi$
$727$	−34.8812	−	12.6957i	−1.29367	−	0.470858i	−0.894931	+	0.446205i	$0.852775\pi$
$728$	−1.33293			−0.0494017
$729$		0			0
$730$	8.77063			0.324616
$731$	5.86149	+	2.13341i	0.216795	+	0.0789069i
$732$		0			0
$733$	22.9402	+	19.2491i	0.847314	+	0.710981i	0.959196	−	0.282740i	$-0.0912435\pi$
$733$	22.9402	+	19.2491i	0.847314	+	0.710981i	−0.111882	+	0.993721i	$0.535688\pi$
$734$	1.09251	−	6.19594i	0.0403253	−	0.228696i
$735$		0			0
$736$	−34.6241	+	29.0530i	−1.27626	+	1.07091i
$737$	−5.05277	−	8.75166i	−0.186121	−	0.322371i
$738$		0			0
$739$	14.3050	−	24.7770i	0.526218	−	0.911436i	−0.473316	−	0.880893i	$-0.656943\pi$
$739$	14.3050	−	24.7770i	0.526218	−	0.911436i	0.999533	−	0.0305431i	$-0.00972368\pi$
$740$	0.609158	+	3.45471i	0.0223931	+	0.126998i
$741$		0			0
$742$	−0.236177	+	0.0859614i	−0.00867033	+	0.00315574i
$743$	46.6497	−	16.9791i	1.71141	−	0.622903i	0.714371	−	0.699767i	$-0.246713\pi$
$743$	46.6497	−	16.9791i	1.71141	−	0.622903i	0.997042	+	0.0768641i	$0.0244908\pi$
$744$		0			0
$745$	2.01052	+	11.4022i	0.0736596	+	0.417744i
$746$	9.16312	−	15.8710i	0.335486	−	0.581078i
$747$		0			0
$748$	−19.8897	−	34.4499i	−0.727238	−	1.25961i
$749$	−1.05207	+	0.882789i	−0.0384417	+	0.0322564i
$750$		0			0
$751$	−5.49138	+	31.1432i	−0.200383	+	1.13643i	0.704158	+	0.710044i	$0.251325\pi$
$751$	−5.49138	+	31.1432i	−0.200383	+	1.13643i	−0.904541	+	0.426387i	$0.859786\pi$
$752$	2.61240	+	2.19207i	0.0952645	+	0.0799364i
$753$		0			0
$754$	14.9055	+	5.42517i	0.542828	+	0.197573i
$755$	−7.12716			−0.259384
$756$		0			0
$757$	3.04189			0.110559			0.0552797	−	0.998471i	$-0.482395\pi$
$757$	3.04189			0.110559			0.0552797	+	0.998471i	$0.482395\pi$
$758$	17.4351	+	6.34587i	0.633272	+	0.230492i
$759$		0			0
$760$	1.14156	+	0.957882i	0.0414087	+	0.0347460i
$761$	−6.58618	+	37.3521i	−0.238749	+	1.35401i	0.595824	+	0.803115i	$0.296826\pi$
$761$	−6.58618	+	37.3521i	−0.238749	+	1.35401i	−0.834573	+	0.550898i	$0.814286\pi$
$762$		0			0
$763$	−0.267855	+	0.224757i	−0.00969702	+	0.00813676i
$764$	−3.02525	−	5.23989i	−0.109450	−	0.189572i
$765$		0			0
$766$	−11.7747	+	20.3943i	−0.425436	+	0.736877i
$767$	0.0348683	+	0.197748i	0.00125902	+	0.00714026i
$768$		0			0
$769$	19.1582	−	6.97302i	0.690863	−	0.251454i	0.0273584	−	0.999626i	$-0.491290\pi$
$769$	19.1582	−	6.97302i	0.690863	−	0.251454i	0.663505	+	0.748172i	$0.269068\pi$
$770$	−0.441500	+	0.160693i	−0.0159106	+	0.00579097i
$771$		0			0
$772$	2.24716	+	12.7443i	0.0808770	+	0.458676i
$773$	12.2332	−	21.1885i	0.439997	−	0.762097i	−0.557692	−	0.830048i	$-0.688313\pi$
$773$	12.2332	−	21.1885i	0.439997	−	0.762097i	0.997689	+	0.0679509i	$0.0216461\pi$
$774$		0			0
$775$	−17.0869	−	29.5954i	−0.613781	−	1.06310i
$776$	16.7081	−	14.0198i	0.599786	−	0.503280i
$777$		0			0
$778$	0.0898700	−	0.509678i	0.00322200	−	0.0182729i
$779$	−3.40760	−	2.85932i	−0.122090	−	0.102446i
$780$		0			0
$781$	−33.2422	−	12.0992i	−1.18950	−	0.432942i
$782$	−25.4816			−0.911221
$783$		0			0
$784$	−9.85978			−0.352135
$785$	−16.6306	−	6.05303i	−0.593571	−	0.216042i
$786$		0			0
$787$	28.7841	+	24.1527i	1.02604	+	0.860950i	0.990375	−	0.138413i	$-0.0442003\pi$
$787$	28.7841	+	24.1527i	1.02604	+	0.860950i	0.0356661	+	0.999364i	$0.488645\pi$
$788$	0.610567	−	3.46270i	0.0217505	−	0.123353i
$789$		0			0
$790$	0.385696	−	0.323637i	0.0137224	−	0.0115145i
$791$	−0.698367	−	1.20961i	−0.0248311	−	0.0430087i
$792$		0			0
$793$	−23.3550	+	40.4521i	−0.829362	+	1.43650i
$794$	0.832396	+	4.72075i	0.0295406	+	0.167533i
$795$		0			0
$796$	−33.8371	+	12.3157i	−1.19932	+	0.436518i
$797$	2.16593	−	0.788333i	0.0767211	−	0.0279242i	−0.303374	−	0.952871i	$-0.598113\pi$
$797$	2.16593	−	0.788333i	0.0767211	−	0.0279242i	0.380096	+	0.924947i	$0.375891\pi$
$798$		0			0
$799$	2.00475	+	11.3695i	0.0709229	+	0.402224i
$800$	11.3103	−	19.5901i	0.399881	−	0.692614i
$801$		0			0
$802$	3.23236	+	5.59862i	0.114139	+	0.197694i
$803$	−50.9254	+	42.7315i	−1.79712	+	1.50796i
$804$		0			0
$805$	0.171122	−	0.970481i	0.00603126	−	0.0342050i
$806$	20.9929	+	17.6152i	0.739444	+	0.620467i
$807$		0			0
$808$	29.4971	+	10.7361i	1.03770	+	0.377693i
$809$	28.8614			1.01471			0.507356	−	0.861736i	$-0.330623\pi$
$809$	28.8614			1.01471			0.507356	+	0.861736i	$0.330623\pi$
$810$		0			0
$811$	−51.8631			−1.82116			−0.910580	−	0.413334i	$-0.864364\pi$
$811$	−51.8631			−1.82116			−0.910580	+	0.413334i	$0.864364\pi$
$812$	−0.880352	−	0.320422i	−0.0308943	−	0.0112446i
$813$		0			0
$814$	6.22075	+	5.21983i	0.218037	+	0.182955i
$815$	1.53076	−	8.68139i	0.0536203	−	0.304096i
$816$		0			0
$817$	0.588526	−	0.493832i	0.0205899	−	0.0172770i
$818$	−1.88711	−	3.26857i	−0.0659813	−	0.114283i
$819$		0			0
$820$	6.06805	−	10.5102i	0.211905	−	0.367031i
$821$	−3.20226	−	18.1609i	−0.111760	−	0.633820i	−0.988304	−	0.152499i	$-0.951268\pi$
$821$	−3.20226	−	18.1609i	−0.111760	−	0.633820i	0.876544	−	0.481322i	$-0.159843\pi$
$822$		0			0
$823$	32.6698	−	11.8908i	1.13880	−	0.414489i	0.297319	−	0.954778i	$-0.403907\pi$
$823$	32.6698	−	11.8908i	1.13880	−	0.414489i	0.841479	+	0.540289i	$0.181685\pi$
$824$	20.5967	−	7.49660i	0.717521	−	0.261156i
$825$		0			0
$826$	0.000628954		0.00356697i	2.18841e−5		0.000124111i
$827$	−16.3886	+	28.3859i	−0.569889	+	0.987076i	0.426688	+	0.904399i	$0.359680\pi$
$827$	−16.3886	+	28.3859i	−0.569889	+	0.987076i	−0.996576	+	0.0826770i	$0.973653\pi$
$828$		0			0
$829$	−2.67634	−	4.63555i	−0.0929530	−	0.160999i	0.815799	−	0.578335i	$-0.196297\pi$
$829$	−2.67634	−	4.63555i	−0.0929530	−	0.160999i	−0.908752	+	0.417336i	$0.862964\pi$
$830$	3.72146	−	3.12267i	0.129174	−	0.108390i
$831$		0			0
$832$	−0.907766	+	5.14820i	−0.0314711	+	0.178482i
$833$	−25.5696	−	21.4555i	−0.885936	−	0.743388i
$834$		0			0
$835$	2.58512	+	0.940908i	0.0894618	+	0.0325614i
$836$	−4.89944			−0.169451
$837$		0			0
$838$	−0.319022			−0.0110204
$839$	5.11040	+	1.86003i	0.176431	+	0.0642155i	0.428725	−	0.903435i	$-0.358963\pi$
$839$	5.11040	+	1.86003i	0.176431	+	0.0642155i	−0.252294	+	0.967651i	$0.581185\pi$
$840$		0			0
$841$	−2.52616	−	2.11970i	−0.0871089	−	0.0730931i
$842$	−0.286760	+	1.62630i	−0.00988240	+	0.0560459i
$843$		0			0
$844$	1.95677	−	1.64192i	0.0673547	−	0.0565173i
$845$	−4.15079	−	7.18938i	−0.142791	−	0.247322i
$846$		0			0
$847$	1.11721	−	1.93507i	0.0383878	−	0.0664897i
$848$	−0.746643	−	4.23442i	−0.0256398	−	0.145411i
$849$		0			0
$850$	11.9838	−	4.36175i	0.411041	−	0.149607i
$851$	−16.0054	+	5.82547i	−0.548657	+	0.199695i
$852$		0			0
$853$	−8.18180	−	46.4013i	−0.280139	−	1.58875i	−0.722148	−	0.691739i	$-0.756845\pi$
$853$	−8.18180	−	46.4013i	−0.280139	−	1.58875i	0.442008	−	0.897011i	$-0.354266\pi$
$854$	−0.421278	+	0.729675i	−0.0144158	+	0.0249690i
$855$		0			0
$856$	13.7554	+	23.8250i	0.470149	+	0.814322i
$857$	35.9704	−	30.1827i	1.22872	−	1.03102i	0.230404	−	0.973095i	$-0.425995\pi$
$857$	35.9704	−	30.1827i	1.22872	−	1.03102i	0.998321	−	0.0579275i	$-0.0184492\pi$
$858$		0			0
$859$	1.24392	−	7.05461i	0.0424419	−	0.240700i	−0.956205	−	0.292697i	$-0.905447\pi$
$859$	1.24392	−	7.05461i	0.0424419	−	0.240700i	0.998647	+	0.0519966i	$0.0165585\pi$
$860$	1.60565	+	1.34730i	0.0547520	+	0.0459424i
$861$		0			0
$862$	−7.77719	−	2.83067i	−0.264892	−	0.0964128i
$863$	35.4309			1.20608			0.603041	−	0.797710i	$-0.293955\pi$
$863$	35.4309			1.20608			0.603041	+	0.797710i	$0.293955\pi$
$864$		0			0
$865$	13.7324			0.466914
$866$	−21.4376	−	7.80263i	−0.728478	−	0.265144i
$867$		0			0
$868$	−1.23989	−	1.04039i	−0.0420845	−	0.0353130i
$869$	−0.662690	+	3.75830i	−0.0224802	+	0.127492i
$870$		0			0
$871$	6.51645	−	5.46795i	0.220801	−	0.185274i
$872$	3.50211	+	6.06583i	0.118596	+	0.205415i
$873$		0			0
$874$	−1.56923	+	2.71799i	−0.0530800	+	0.0919373i
$875$	0.195393	+	1.10813i	0.00660547	+	0.0374615i
$876$		0			0
$877$	−7.68004	+	2.79531i	−0.259337	+	0.0943908i	−0.468417	−	0.883508i	$-0.655175\pi$
$877$	−7.68004	+	2.79531i	−0.259337	+	0.0943908i	0.209080	+	0.977899i	$0.432953\pi$
$878$	5.81374	−	2.11603i	0.196204	−	0.0714125i
$879$		0			0
$880$	−1.39574	−	7.91566i	−0.0470505	−	0.266837i
$881$	−16.6153	+	28.7786i	−0.559785	+	0.969575i	0.437729	+	0.899107i	$0.355783\pi$
$881$	−16.6153	+	28.7786i	−0.559785	+	0.969575i	−0.997514	+	0.0704686i	$0.977551\pi$
$882$		0			0
$883$	−16.5239	−	28.6203i	−0.556075	−	0.963150i	−0.997819	−	0.0660087i	$-0.978973\pi$
$883$	−16.5239	−	28.6203i	−0.556075	−	0.963150i	0.441744	−	0.897141i	$-0.354360\pi$
$884$	25.6512	−	21.5239i	0.862744	−	0.723928i
$885$		0			0
$886$	0.555560	−	3.15074i	0.0186644	−	0.105851i
$887$	38.1086	+	31.9769i	1.27956	+	1.07368i	0.993304	+	0.115526i	$0.0368553\pi$
$887$	38.1086	+	31.9769i	1.27956	+	1.07368i	0.286256	+	0.958153i	$0.407589\pi$
$888$		0			0
$889$	−1.74763	−	0.636084i	−0.0586135	−	0.0213336i
$890$	4.91469			0.164741
$891$		0			0
$892$	15.0155			0.502756
$893$	1.33618	+	0.486329i	0.0447135	+	0.0162744i
$894$		0			0
$895$	−17.7414	−	14.8868i	−0.593031	−	0.497612i
$896$	0.226485	−	1.28446i	0.00756635	−	0.0429109i
$897$		0			0
$898$	13.9945	−	11.7428i	0.467004	−	0.391863i
$899$	22.2024	+	38.4556i	0.740491	+	1.28257i
$900$		0			0
$901$	7.27807	−	12.6060i	0.242468	−	0.419966i
$902$	−4.87841	−	27.6668i	−0.162433	−	0.921205i
$903$		0			0
$904$	−26.2913	+	9.56926i	−0.874437	+	0.318269i
$905$	2.02784	−	0.738074i	0.0674078	−	0.0245344i
$906$		0			0
$907$	5.99928	+	34.0236i	0.199203	+	1.12974i	0.906305	+	0.422625i	$0.138891\pi$
$907$	5.99928	+	34.0236i	0.199203	+	1.12974i	−0.707102	+	0.707112i	$0.749998\pi$
$908$	−11.8589	+	20.5403i	−0.393553	+	0.681654i
$909$		0			0
$910$	−0.197748	−	0.342509i	−0.00655528	−	0.0113541i
$911$	10.4465	−	8.76563i	0.346107	−	0.290418i	−0.453117	−	0.891451i	$-0.649688\pi$
$911$	10.4465	−	8.76563i	0.346107	−	0.290418i	0.799225	+	0.601032i	$0.205244\pi$
$912$		0			0
$913$	−6.39410	+	36.2627i	−0.211614	+	1.20012i
$914$	−0.344668	−	0.289210i	−0.0114006	−	0.00956623i
$915$		0			0
$916$	−16.2023	−	5.89717i	−0.535340	−	0.194848i
$917$	−1.61094			−0.0531979
$918$		0			0
$919$	32.7701			1.08099			0.540493	−	0.841348i	$-0.318238\pi$
$919$	32.7701			1.08099			0.540493	+	0.841348i	$0.318238\pi$
$920$	−18.5496	−	6.75150i	−0.611562	−	0.222590i
$921$		0			0
$922$	−10.8489	−	9.10327i	−0.357288	−	0.299800i
$923$	5.17095	−	29.3259i	0.170204	−	0.965275i
$924$		0			0
$925$	6.53003	−	5.47935i	0.214706	−	0.180160i
$926$	8.49027	+	14.7056i	0.279008	+	0.483255i
$927$		0			0
$928$	−14.6964	+	25.4549i	−0.482433	+	0.835599i
$929$	−0.960529	−	5.44743i	−0.0315140	−	0.178724i	0.964988	−	0.262294i	$-0.0844790\pi$
$929$	−0.960529	−	5.44743i	−0.0315140	−	0.178724i	−0.996502	+	0.0835696i	$0.973368\pi$
$930$		0			0
$931$	−3.86319	+	1.40609i	−0.126611	+	0.0460826i
$932$	−7.53644	+	2.74304i	−0.246864	+	0.0898513i
$933$		0			0
$934$	−3.16827	−	17.9682i	−0.103669	−	0.587936i
$935$	13.6053	−	23.5651i	0.444942	−	0.770662i
$936$		0			0
$937$	0.497007	+	0.860841i	0.0162365	+	0.0281225i	0.874029	−	0.485873i	$-0.161498\pi$
$937$	0.497007	+	0.860841i	0.0162365	+	0.0281225i	−0.857793	+	0.513995i	$0.828165\pi$
$938$	0.117544	−	0.0986308i	0.00383793	−	0.00322041i
$939$		0			0
$940$	−0.673648	+	3.82045i	−0.0219720	+	0.124609i
$941$	−8.77671	−	7.36453i	−0.286113	−	0.240077i	0.488424	−	0.872607i	$-0.337572\pi$
$941$	−8.77671	−	7.36453i	−0.286113	−	0.240077i	−0.774536	+	0.632530i	$0.782017\pi$
$942$		0			0
$943$	55.3713	+	20.1535i	1.80314	+	0.656288i
$944$	−0.0619640			−0.00201676
$945$		0			0
$946$	4.85204			0.157754
$947$	−42.9299	−	15.6252i	−1.39503	−	0.507751i	−0.468333	−	0.883552i	$-0.655145\pi$
$947$	−42.9299	−	15.6252i	−1.39503	−	0.507751i	−0.926700	+	0.375801i	$0.877368\pi$
$948$		0			0
$949$	−42.8678	−	35.9704i	−1.39155	−	1.16765i
$950$	0.272752	−	1.54686i	0.00884925	−	0.0501866i
$951$		0			0
$952$	1.06670	−	0.895071i	0.0345721	−	0.0290094i
$953$	−7.25265	−	12.5620i	−0.234936	−	0.406922i	0.724318	−	0.689466i	$-0.242155\pi$
$953$	−7.25265	−	12.5620i	−0.234936	−	0.406922i	−0.959254	+	0.282545i	$0.908822\pi$
$954$		0			0
$955$	2.06939	−	3.58429i	0.0669640	−	0.115985i
$956$	−2.74286	−	15.5556i	−0.0887106	−	0.503103i
$957$		0			0
$958$	−2.07398	+	0.754866i	−0.0670072	+	0.0243886i
$959$	−2.22415	+	0.809526i	−0.0718217	+	0.0261410i
$960$		0			0
$961$	7.93851	+	45.0215i	0.256081	+	1.45231i
$962$	−3.41787	+	5.91993i	−0.110197	+	0.190866i
$963$		0			0
$964$	8.23055	+	14.2557i	0.265088	+	0.459146i
$965$	−6.78109	+	5.69001i	−0.218291	+	0.183168i
$966$		0			0
$967$	−4.34760	+	24.6565i	−0.139809	+	0.792899i	0.831580	+	0.555405i	$0.187437\pi$
$967$	−4.34760	+	24.6565i	−0.139809	+	0.792899i	−0.971389	+	0.237493i	$0.923674\pi$
$968$	−34.2872	−	28.7704i	−1.10203	−	0.924715i
$969$		0			0
$970$	6.08125	+	2.21339i	0.195257	+	0.0710678i
$971$	−27.0907			−0.869383			−0.434692	−	0.900579i	$-0.643143\pi$
$971$	−27.0907			−0.869383			−0.434692	+	0.900579i	$0.643143\pi$
$972$		0			0
$973$	−1.96679			−0.0630522
$974$	5.00044	+	1.82001i	0.160224	+	0.0583169i
$975$		0			0
$976$	−11.0419	−	9.26525i	−0.353442	−	0.296573i
$977$	0.429501	−	2.43582i	0.0137410	−	0.0779289i	−0.977166	−	0.212477i	$-0.931847\pi$
$977$	0.429501	−	2.43582i	0.0137410	−	0.0779289i	0.990907	+	0.134548i	$0.0429582\pi$
$978$		0			0
$979$	−28.5364	+	23.9449i	−0.912028	+	0.765282i
$980$	−5.60808	−	9.71348i	−0.179144	−	0.310286i
$981$		0			0
$982$	5.83006	−	10.0980i	0.186045	−	0.322239i
$983$	−3.31807	−	18.8177i	−0.105830	−	0.600192i	−0.990886	−	0.134707i	$-0.956991\pi$
$983$	−3.31807	−	18.8177i	−0.105830	−	0.600192i	0.885055	−	0.465486i	$-0.154120\pi$
$984$		0			0
$985$	2.26011	−	0.822614i	0.0720132	−	0.0262107i
$986$	−15.5715	+	5.66756i	−0.495897	+	0.180492i
$987$		0			0
$988$	−0.716166	−	4.06158i	−0.0227843	−	0.129216i
$989$	−5.08845	+	8.81345i	−0.161803	+	0.280251i
$990$		0			0
$991$	19.1582	+	33.1830i	0.608581	+	1.05409i	0.991475	+	0.130301i	$0.0415943\pi$
$991$	19.1582	+	33.1830i	0.608581	+	1.05409i	−0.382894	+	0.923792i	$0.625072\pi$
$992$	−38.9002	+	32.6411i	−1.23508	+	1.03636i
$993$		0			0
$994$	0.0932736	−	0.528981i	0.00295846	−	0.0167783i
$995$	−18.8687	−	15.8327i	−0.598179	−	0.501932i
$996$		0			0
$997$	−38.8794	−	14.1510i	−1.23132	−	0.448165i	−0.357273	−	0.934000i	$-0.616294\pi$
$997$	−38.8794	−	14.1510i	−1.23132	−	0.448165i	−0.874051	+	0.485834i	$0.838516\pi$
$998$	5.42497			0.171724
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.m.568.1		12
3.2	odd	2	inner	729.2.e.m.568.2		12
9.2	odd	6		729.2.e.q.82.1		12
9.4	even	3		729.2.e.r.325.2		12
9.5	odd	6		729.2.e.r.325.1		12
9.7	even	3		729.2.e.q.82.2		12
27.2	odd	18		729.2.e.r.406.1		12
27.4	even	9		729.2.c.c.244.3		12
27.5	odd	18		729.2.c.c.487.4		12
27.7	even	9	inner	729.2.e.m.163.1		12
27.11	odd	18		729.2.e.q.649.1		12
27.13	even	9		729.2.a.c.1.4	yes	6
27.14	odd	18		729.2.a.c.1.3	✓	6
27.16	even	9		729.2.e.q.649.2		12
27.20	odd	18	inner	729.2.e.m.163.2		12
27.22	even	9		729.2.c.c.487.3		12
27.23	odd	18		729.2.c.c.244.4		12
27.25	even	9		729.2.e.r.406.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.3	✓	6	27.14	odd	18
729.2.a.c.1.4	yes	6	27.13	even	9
729.2.c.c.244.3		12	27.4	even	9
729.2.c.c.244.4		12	27.23	odd	18
729.2.c.c.487.3		12	27.22	even	9
729.2.c.c.487.4		12	27.5	odd	18
729.2.e.m.163.1		12	27.7	even	9	inner
729.2.e.m.163.2		12	27.20	odd	18	inner
729.2.e.m.568.1		12	1.1	even	1	trivial
729.2.e.m.568.2		12	3.2	odd	2	inner
729.2.e.q.82.1		12	9.2	odd	6
729.2.e.q.82.2		12	9.7	even	3
729.2.e.q.649.1		12	27.11	odd	18
729.2.e.q.649.2		12	27.16	even	9
729.2.e.r.325.1		12	9.5	odd	6
729.2.e.r.325.2		12	9.4	even	3
729.2.e.r.406.1		12	27.2	odd	18
729.2.e.r.406.2		12	27.25	even	9

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.233956i) q^{2} +(-1.17365 - 0.984808i) q^{4} +(0.181985 - 1.03209i) q^{5} +(-0.0923963 + 0.0775297i) q^{7} +(1.20805 + 2.09240i) q^{8} +(-0.358441 + 0.620838i) q^{10} +(-0.943555 - 5.35117i) q^{11} +(4.29813 - 1.56439i) q^{13} +(0.0775297 - 0.0282185i) q^{14} +(0.245100 + 1.39003i) q^{16} +(-2.38917 + 4.13816i) q^{17} +(0.294263 + 0.509678i) q^{19} +(-1.23000 + 1.03209i) q^{20} +(-0.645430 + 3.66041i) q^{22} +(-5.97205 - 5.01114i) q^{23} +(3.66637 + 1.33445i) q^{25} -3.12879 q^{26} +0.184793 q^{28} +(-4.76400 - 1.73396i) q^{29} +(-6.70961 - 5.63003i) q^{31} +(1.00676 - 5.70961i) q^{32} +(2.50387 - 2.10100i) q^{34} +(0.0632028 + 0.109470i) q^{35} +(1.09240 - 1.89209i) q^{37} +(-0.0699065 - 0.396459i) q^{38} +(2.37939 - 0.866025i) q^{40} +(-7.10257 + 2.58512i) q^{41} +(-0.226682 - 1.28558i) q^{43} +(-4.16247 + 7.20961i) q^{44} +(2.66637 + 4.61830i) q^{46} +(1.85083 - 1.55303i) q^{47} +(-1.21301 + 6.87933i) q^{49} +(-2.04450 - 1.71554i) q^{50} +(-6.58512 - 2.39679i) q^{52} -3.04628 q^{53} -5.69459 q^{55} +(-0.273842 - 0.0996702i) q^{56} +(2.65657 + 2.22913i) q^{58} +(-0.00762319 + 0.0432332i) q^{59} +(-7.82295 + 6.56423i) q^{61} +(2.99568 + 5.18866i) q^{62} +(-0.571452 + 0.989783i) q^{64} +(-0.832396 - 4.72075i) q^{65} +(1.74763 - 0.636084i) q^{67} +(6.87933 - 2.50387i) q^{68} +(-0.0150147 - 0.0851529i) q^{70} +(3.25519 - 5.63816i) q^{71} +(-6.11721 - 10.5953i) q^{73} +(-1.14484 + 0.960637i) q^{74} +(0.156574 - 0.887975i) q^{76} +(0.502055 + 0.421274i) q^{77} +(-0.659978 - 0.240212i) q^{79} +1.47924 q^{80} +5.17024 q^{82} +(-6.36792 - 2.31773i) q^{83} +(3.83615 + 3.21891i) q^{85} +(-0.155059 + 0.879385i) q^{86} +(10.0569 - 8.43874i) q^{88} +(-3.42782 - 5.93717i) q^{89} +(-0.275845 + 0.477777i) q^{91} +(2.07407 + 11.7626i) q^{92} +(-1.55303 + 0.565258i) q^{94} +(0.579585 - 0.210952i) q^{95} +(-1.56758 - 8.89020i) q^{97} +(2.38917 - 4.13816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} + 6 q^{7} + 12 q^{10} + 24 q^{13} + 24 q^{19} + 24 q^{22} + 6 q^{25} - 12 q^{28} - 12 q^{31} - 18 q^{34} + 6 q^{37} + 6 q^{40} + 24 q^{43} - 6 q^{46} - 30 q^{49} - 36 q^{52} - 60 q^{55}+ \cdots - 66 q^{97}+O(q^{100}) \) 12 * q - 12 * q^4 + 6 * q^7 + 12 * q^10 + 24 * q^13 + 24 * q^19 + 24 * q^22 + 6 * q^25 - 12 * q^28 - 12 * q^31 - 18 * q^34 + 6 * q^37 + 6 * q^40 + 24 * q^43 - 6 * q^46 - 30 * q^49 - 36 * q^52 - 60 * q^55 - 12 * q^58 - 12 * q^61 - 6 * q^64 - 12 * q^67 + 60 * q^70 - 12 * q^73 - 42 * q^76 - 48 * q^79 - 24 * q^82 + 54 * q^85 + 48 * q^88 + 6 * q^94 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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