LMFDB - Embedded newform 729.2.g.a.676.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$144$
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			676.2
Character	$\chi$	$=$	729.676
Dual form			729.2.g.a.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.837555 - 1.94167i) q^{2} +(-1.69610 + 1.79777i) q^{4} +(-0.0261173 + 0.448416i) q^{5} +(-2.37407 + 0.562666i) q^{7} +(0.937080 + 0.341069i) q^{8} +O(q^{10})$	\(q+(-0.837555 - 1.94167i) q^{2} +(-1.69610 + 1.79777i) q^{4} +(-0.0261173 + 0.448416i) q^{5} +(-2.37407 + 0.562666i) q^{7} +(0.937080 + 0.341069i) q^{8} +(0.892552 - 0.324862i) q^{10} +(2.86177 - 1.88222i) q^{11} +(-3.02196 + 0.353216i) q^{13} +(3.08093 + 4.13841i) q^{14} +(0.164808 + 2.82964i) q^{16} +(-1.96933 - 1.65247i) q^{17} +(-5.90790 + 4.95731i) q^{19} +(-0.761850 - 0.807514i) q^{20} +(-6.05154 - 3.98016i) q^{22} +(5.55505 + 1.31657i) q^{23} +(4.76580 + 0.557042i) q^{25} +(3.21689 + 5.57181i) q^{26} +(3.01514 - 5.22237i) q^{28} +(-1.87232 + 2.51496i) q^{29} +(2.39959 + 8.01520i) q^{31} +(7.13849 - 3.58509i) q^{32} +(-1.55912 + 5.20783i) q^{34} +(-0.190304 - 1.07927i) q^{35} +(0.0238144 - 0.135058i) q^{37} +(14.5737 + 7.31917i) q^{38} +(-0.177415 + 0.411294i) q^{40} +(-4.79132 + 11.1075i) q^{41} +(4.05525 + 2.03662i) q^{43} +(-1.47008 + 8.33724i) q^{44} +(-2.09631 - 11.8888i) q^{46} +(-0.745357 + 2.48967i) q^{47} +(-0.935796 + 0.469974i) q^{49} +(-2.91003 - 9.72016i) q^{50} +(4.49056 - 6.03187i) q^{52} +(-0.184618 + 0.319767i) q^{53} +(0.769276 + 1.33242i) q^{55} +(-2.41661 - 0.282461i) q^{56} +(6.45139 + 1.52901i) q^{58} +(-8.82708 - 5.80566i) q^{59} +(1.55368 + 1.64680i) q^{61} +(13.5531 - 11.3724i) q^{62} +(-8.59733 - 7.21402i) q^{64} +(-0.0794626 - 1.36432i) q^{65} +(0.831589 + 1.11702i) q^{67} +(6.31095 - 0.737644i) q^{68} +(-1.93619 + 1.27346i) q^{70} +(-3.35434 + 1.22088i) q^{71} +(4.75835 + 1.73190i) q^{73} +(-0.282184 + 0.0668789i) q^{74} +(1.10832 - 19.0291i) q^{76} +(-5.73500 + 6.07875i) q^{77} +(-4.06819 - 9.43112i) q^{79} -1.27316 q^{80} +25.5802 q^{82} +(0.387605 + 0.898569i) q^{83} +(0.792427 - 0.839924i) q^{85} +(0.557957 - 9.57975i) q^{86} +(3.32368 - 0.787727i) q^{88} +(8.14767 + 2.96551i) q^{89} +(6.97561 - 2.53891i) q^{91} +(-11.7888 + 7.75364i) q^{92} +(5.45839 - 0.637994i) q^{94} +(-2.06864 - 2.77867i) q^{95} +(0.123983 + 2.12870i) q^{97} +(1.69632 + 1.42338i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	−0.837555	−	1.94167i	−0.592241	−	1.37297i	−0.905924	−	0.423441i	$-0.860822\pi$
$2$	−0.837555	−	1.94167i	−0.592241	−	1.37297i	0.313683	−	0.949528i	$-0.398437\pi$
$3$		0			0
$3$		0			0
$4$	−1.69610	+	1.79777i	−0.848052	+	0.898883i
$5$	−0.0261173	+	0.448416i	−0.0116800	+	0.200538i	0.987420	+	0.158120i	$0.0505432\pi$
$5$	−0.0261173	+	0.448416i	−0.0116800	+	0.200538i	−0.999100	+	0.0424181i	$0.986494\pi$
$6$		0			0
$7$	−2.37407	+	0.562666i	−0.897316	+	0.212668i	−0.653296	−	0.757103i	$-0.726614\pi$
$7$	−2.37407	+	0.562666i	−0.897316	+	0.212668i	−0.244020	+	0.969770i	$0.578466\pi$
$8$	0.937080	+	0.341069i	0.331308	+	0.120586i
$9$		0			0
$10$	0.892552	−	0.324862i	0.282250	−	0.102730i
$11$	2.86177	−	1.88222i	0.862857	−	0.567510i	−0.0391488	−	0.999233i	$-0.512465\pi$
$11$	2.86177	−	1.88222i	0.862857	−	0.567510i	0.902006	+	0.431723i	$0.142094\pi$
$12$		0			0
$13$	−3.02196	+	0.353216i	−0.838141	+	0.0979646i	−0.524324	−	0.851519i	$-0.675682\pi$
$13$	−3.02196	+	0.353216i	−0.838141	+	0.0979646i	−0.313817	+	0.949484i	$0.601608\pi$
$14$	3.08093	+	4.13841i	0.823413	+	1.10604i
$15$		0			0
$16$	0.164808	+	2.82964i	0.0412020	+	0.707410i
$17$	−1.96933	−	1.65247i	−0.477634	−	0.400782i	0.371936	−	0.928258i	$-0.378694\pi$
$17$	−1.96933	−	1.65247i	−0.477634	−	0.400782i	−0.849570	+	0.527476i	$0.823138\pi$
$18$		0			0
$19$	−5.90790	+	4.95731i	−1.35536	+	1.13729i	−0.377980	+	0.925814i	$0.623381\pi$
$19$	−5.90790	+	4.95731i	−1.35536	+	1.13729i	−0.977384	+	0.211472i	$0.932174\pi$
$20$	−0.761850	−	0.807514i	−0.170355	−	0.180566i
$21$		0			0
$22$	−6.05154	−	3.98016i	−1.29019	−	0.848574i
$23$	5.55505	+	1.31657i	1.15831	+	0.274524i	0.764472	−	0.644657i	$-0.223000\pi$
$23$	5.55505	+	1.31657i	1.15831	+	0.274524i	0.393836	+	0.919181i	$0.371148\pi$
$24$		0			0
$25$	4.76580	+	0.557042i	0.953159	+	0.111408i
$26$	3.21689	+	5.57181i	0.630883	+	1.09272i
$27$		0			0
$28$	3.01514	−	5.22237i	0.569807	−	0.986935i
$29$	−1.87232	+	2.51496i	−0.347680	+	0.467016i	−0.941223	−	0.337787i	$-0.890322\pi$
$29$	−1.87232	+	2.51496i	−0.347680	+	0.467016i	0.593542	+	0.804803i	$0.297729\pi$
$30$		0			0
$31$	2.39959	+	8.01520i	0.430980	+	1.43957i	0.847670	+	0.530524i	$0.178005\pi$
$31$	2.39959	+	8.01520i	0.430980	+	1.43957i	−0.416691	+	0.909048i	$0.636810\pi$
$32$	7.13849	−	3.58509i	1.26192	−	0.633760i
$33$		0			0
$34$	−1.55912	+	5.20783i	−0.267387	+	0.893136i
$35$	−0.190304	−	1.07927i	−0.0321673	−	0.182430i
$36$		0			0
$37$	0.0238144	−	0.135058i	0.00391506	−	0.0222034i	−0.982788	−	0.184739i	$-0.940856\pi$
$37$	0.0238144	−	0.135058i	0.00391506	−	0.0222034i	0.986703	+	0.162535i	$0.0519672\pi$
$38$	14.5737	+	7.31917i	2.36416	+	1.18733i
$39$		0			0
$40$	−0.177415	+	0.411294i	−0.0280518	+	0.0650313i
$41$	−4.79132	+	11.1075i	−0.748279	+	1.73471i	−0.0727768	+	0.997348i	$0.523186\pi$
$41$	−4.79132	+	11.1075i	−0.748279	+	1.73471i	−0.675502	+	0.737358i	$0.736073\pi$
$42$		0			0
$43$	4.05525	+	2.03662i	0.618420	+	0.310582i	0.730286	−	0.683141i	$-0.239387\pi$
$43$	4.05525	+	2.03662i	0.618420	+	0.310582i	−0.111867	+	0.993723i	$0.535683\pi$
$44$	−1.47008	+	8.33724i	−0.221623	+	1.25689i
$45$		0			0
$46$	−2.09631	−	11.8888i	−0.309085	−	1.75291i
$47$	−0.745357	+	2.48967i	−0.108722	+	0.363155i	−0.994985	−	0.100027i	$-0.968107\pi$
$47$	−0.745357	+	2.48967i	−0.108722	+	0.363155i	0.886263	+	0.463182i	$0.153292\pi$
$48$		0			0
$49$	−0.935796	+	0.469974i	−0.133685	+	0.0671392i
$50$	−2.91003	−	9.72016i	−0.411540	−	1.37464i
$51$		0			0
$52$	4.49056	−	6.03187i	0.622728	−	0.836469i
$53$	−0.184618	+	0.319767i	−0.0253592	+	0.0439234i	−0.878426	−	0.477877i	$-0.841406\pi$
$53$	−0.184618	+	0.319767i	−0.0253592	+	0.0439234i	0.853067	+	0.521801i	$0.174740\pi$
$54$		0			0
$55$	0.769276	+	1.33242i	0.103729	+	0.179664i
$56$	−2.41661	−	0.282461i	−0.322933	−	0.0377454i
$57$		0			0
$58$	6.45139	+	1.52901i	0.847109	+	0.200768i
$59$	−8.82708	−	5.80566i	−1.14919	−	0.755832i	−0.175671	−	0.984449i	$-0.556209\pi$
$59$	−8.82708	−	5.80566i	−1.14919	−	0.755832i	−0.973517	+	0.228617i	$0.926580\pi$
$60$		0			0
$61$	1.55368	+	1.64680i	0.198928	+	0.210851i	0.819157	−	0.573569i	$-0.194442\pi$
$61$	1.55368	+	1.64680i	0.198928	+	0.210851i	−0.620229	+	0.784421i	$0.712960\pi$
$62$	13.5531	−	11.3724i	1.72124	−	1.44429i
$63$		0			0
$64$	−8.59733	−	7.21402i	−1.07467	−	0.901752i
$65$	−0.0794626	−	1.36432i	−0.00985613	−	0.169223i
$66$		0			0
$67$	0.831589	+	1.11702i	0.101595	+	0.136465i	0.850013	−	0.526761i	$-0.176594\pi$
$67$	0.831589	+	1.11702i	0.101595	+	0.136465i	−0.748418	+	0.663227i	$0.769186\pi$
$68$	6.31095	−	0.737644i	0.765315	−	0.0894525i
$69$		0			0
$70$	−1.93619	+	1.27346i	−0.231420	+	0.152207i
$71$	−3.35434	+	1.22088i	−0.398087	+	0.144892i	−0.533303	−	0.845924i	$-0.679049\pi$
$71$	−3.35434	+	1.22088i	−0.398087	+	0.144892i	0.135216	+	0.990816i	$0.456827\pi$
$72$		0			0
$73$	4.75835	+	1.73190i	0.556922	+	0.202703i	0.605119	−	0.796135i	$-0.293125\pi$
$73$	4.75835	+	1.73190i	0.556922	+	0.202703i	−0.0481971	+	0.998838i	$0.515348\pi$
$74$	−0.282184	+	0.0668789i	−0.0328033	+	0.00777451i
$75$		0			0
$76$	1.10832	−	19.0291i	0.127133	−	2.18279i
$77$	−5.73500	+	6.07875i	−0.653564	+	0.692738i
$78$		0			0
$79$	−4.06819	−	9.43112i	−0.457707	−	1.06108i	−0.978284	−	0.207269i	$-0.933542\pi$
$79$	−4.06819	−	9.43112i	−0.457707	−	1.06108i	0.520577	−	0.853815i	$-0.325717\pi$
$80$	−1.27316			−0.142344
$81$		0			0
$82$	25.5802			2.82486
$83$	0.387605	+	0.898569i	0.0425452	+	0.0986308i	0.938163	−	0.346193i	$-0.112526\pi$
$83$	0.387605	+	0.898569i	0.0425452	+	0.0986308i	−0.895618	+	0.444823i	$0.853266\pi$
$84$		0			0
$85$	0.792427	−	0.839924i	0.0859508	−	0.0911025i
$86$	0.557957	−	9.57975i	0.0601660	−	1.03301i
$87$		0			0
$88$	3.32368	−	0.787727i	0.354305	−	0.0839719i
$89$	8.14767	+	2.96551i	0.863651	+	0.314343i	0.735593	−	0.677423i	$-0.236903\pi$
$89$	8.14767	+	2.96551i	0.863651	+	0.314343i	0.128058	+	0.991767i	$0.459126\pi$
$90$		0			0
$91$	6.97561	−	2.53891i	0.731243	−	0.266151i
$92$	−11.7888	+	7.75364i	−1.22907	+	0.808373i
$93$		0			0
$94$	5.45839	−	0.637994i	0.562990	−	0.0658041i
$95$	−2.06864	−	2.77867i	−0.212238	−	0.285085i
$96$		0			0
$97$	0.123983	+	2.12870i	0.0125886	+	0.216137i	0.998736	+	0.0502654i	$0.0160067\pi$
$97$	0.123983	+	2.12870i	0.0125886	+	0.216137i	−0.986147	+	0.165872i	$0.946956\pi$
$98$	1.69632	+	1.42338i	0.171354	+	0.143783i
$99$		0			0
$100$	−9.08472	+	7.62299i	−0.908472	+	0.762299i
$101$	−7.59108	−	8.04607i	−0.755341	−	0.800614i	0.229641	−	0.973276i	$-0.426245\pi$
$101$	−7.59108	−	8.04607i	−0.755341	−	0.800614i	−0.984981	+	0.172661i	$0.944763\pi$
$102$		0			0
$103$	2.85881	+	1.88027i	0.281686	+	0.185268i	0.682488	−	0.730897i	$-0.260898\pi$
$103$	2.85881	+	1.88027i	0.281686	+	0.185268i	−0.400802	+	0.916165i	$0.631268\pi$
$104$	−2.95229	−	0.699705i	−0.289496	−	0.0686118i
$105$		0			0
$106$	0.775510	+	0.0906442i	0.0753242	+	0.00880414i
$107$	−9.48845	−	16.4345i	−0.917283	−	1.58878i	−0.803524	−	0.595272i	$-0.797044\pi$
$107$	−9.48845	−	16.4345i	−0.917283	−	1.58878i	−0.113758	−	0.993508i	$-0.536289\pi$
$108$		0			0
$109$	−6.75185	+	11.6945i	−0.646710	+	1.12013i	0.337194	+	0.941435i	$0.390522\pi$
$109$	−6.75185	+	11.6945i	−0.646710	+	1.12013i	−0.983904	+	0.178699i	$0.942811\pi$
$110$	1.94282	−	2.60966i	0.185241	−	0.248821i
$111$		0			0
$112$	−1.98341	−	6.62504i	−0.187414	−	0.626008i
$113$	−4.00629	+	2.01203i	−0.376880	+	0.189276i	−0.627148	−	0.778900i	$-0.715778\pi$
$113$	−4.00629	+	2.01203i	−0.376880	+	0.189276i	0.250268	+	0.968177i	$0.419481\pi$
$114$		0			0
$115$	−0.735455	+	2.45659i	−0.0685815	+	0.229078i
$116$	−1.34566	−	7.63162i	−0.124941	−	0.708578i
$117$		0			0
$118$	−3.87952	+	22.0018i	−0.357139	+	2.02543i
$119$	5.60513	+	2.81500i	0.513822	+	0.258051i
$120$		0			0
$121$	0.290128	−	0.672592i	0.0263753	−	0.0611447i
$122$	1.89626	−	4.39602i	0.171679	−	0.397997i
$123$		0			0
$124$	−18.4794	−	9.28071i	−1.65950	−	0.833432i
$125$	−0.764249	+	4.33427i	−0.0683565	+	0.387669i
$126$		0			0
$127$	−3.01665	−	17.1083i	−0.267685	−	1.51811i	−0.761280	−	0.648423i	$-0.775429\pi$
$127$	−3.01665	−	17.1083i	−0.267685	−	1.51811i	0.493596	−	0.869691i	$-0.335682\pi$
$128$	−2.22444	+	7.43015i	−0.196615	+	0.656739i
$129$		0			0
$130$	−2.58251	+	1.29698i	−0.226501	+	0.113753i
$131$	−0.0995656	−	0.332572i	−0.00869909	−	0.0290570i	0.953530	−	0.301299i	$-0.0974201\pi$
$131$	−0.0995656	−	0.332572i	−0.00869909	−	0.0290570i	−0.962229	+	0.272242i	$0.912235\pi$
$132$		0			0
$133$	11.2365	−	15.0932i	0.974325	−	1.30875i
$134$	1.47238	−	2.55024i	0.127194	−	0.220307i
$135$		0			0
$136$	−1.28182	−	2.22017i	−0.109915	−	0.190378i
$137$	0.246145	+	0.0287702i	0.0210296	+	0.00245801i	0.126601	−	0.991954i	$-0.459593\pi$
$137$	0.246145	+	0.0287702i	0.0210296	+	0.00245801i	−0.105572	+	0.994412i	$0.533667\pi$
$138$		0			0
$139$	5.47744	+	1.29818i	0.464591	+	0.110110i	0.456243	−	0.889855i	$-0.349195\pi$
$139$	5.47744	+	1.29818i	0.464591	+	0.110110i	0.00834744	+	0.999965i	$0.497343\pi$
$140$	2.26305	+	1.48843i	0.191263	+	0.125795i
$141$		0			0
$142$	5.17999	+	5.49047i	0.434695	+	0.460750i
$143$	−7.98333	+	6.69881i	−0.667600	+	0.560183i
$144$		0			0
$145$	−1.07885	−	0.905261i	−0.0895935	−	0.0751778i
$146$	−0.622604	−	10.6897i	−0.0515271	−	0.884686i
$147$		0			0
$148$	0.202411	+	0.271885i	0.0166381	+	0.0223488i
$149$	−1.97673	+	0.231046i	−0.161940	+	0.0189280i	−0.196676	−	0.980468i	$-0.563015\pi$
$149$	−1.97673	+	0.231046i	−0.161940	+	0.0189280i	0.0347366	+	0.999397i	$0.488941\pi$
$150$		0			0
$151$	−9.65170	+	6.34802i	−0.785444	+	0.516595i	−0.877740	−	0.479137i	$-0.840950\pi$
$151$	−9.65170	+	6.34802i	−0.785444	+	0.516595i	0.0922962	+	0.995732i	$0.470579\pi$
$152$	−7.22696	+	2.63040i	−0.586184	+	0.213354i
$153$		0			0
$154$	16.6063	+	6.04420i	1.33817	+	0.487056i
$155$	−3.65682	+	0.866681i	−0.293723	+	0.0696135i
$156$		0			0
$157$	−1.36185	+	23.3820i	−0.108687	+	1.86609i	0.300687	+	0.953723i	$0.402784\pi$
$157$	−1.36185	+	23.3820i	−0.108687	+	1.86609i	−0.409375	+	0.912366i	$0.634253\pi$
$158$	−14.9048	+	15.7982i	−1.18576	+	1.25684i
$159$		0			0
$160$	1.42117	+	3.29465i	0.112354	+	0.260465i
$161$	−13.9289			−1.09775
$162$		0			0
$163$	−12.2555			−0.959921			−0.479961	−	0.877290i	$-0.659349\pi$
$163$	−12.2555			−0.959921			−0.479961	+	0.877290i	$0.659349\pi$
$164$	−11.8422	−	27.4532i	−0.924718	−	2.14374i
$165$		0			0
$166$	1.42009	−	1.50520i	0.110220	−	0.116826i
$167$	−0.308984	+	5.30505i	−0.0239099	+	0.410517i	0.965024	+	0.262161i	$0.0844351\pi$
$167$	−0.308984	+	5.30505i	−0.0239099	+	0.410517i	−0.988934	+	0.148356i	$0.952602\pi$
$168$		0			0
$169$	−3.64211	+	0.863196i	−0.280162	+	0.0663997i
$170$	−2.29456	−	0.835150i	−0.175984	−	0.0640531i
$171$		0			0
$172$	−10.5395	+	3.83606i	−0.803629	+	0.292497i
$173$	−1.71855	+	1.13031i	−0.130659	+	0.0859359i	−0.613156	−	0.789962i	$-0.710100\pi$
$173$	−1.71855	+	1.13031i	−0.130659	+	0.0859359i	0.482497	+	0.875898i	$0.339730\pi$
$174$		0			0
$175$	−11.6278	+	1.35909i	−0.878978	+	0.102738i
$176$	5.79765	+	7.78759i	0.437014	+	0.587012i
$177$		0			0
$178$	−1.06608	−	18.3039i	−0.0799060	−	1.37193i
$179$	6.40636	+	5.37558i	0.478834	+	0.401789i	0.850005	−	0.526775i	$-0.176599\pi$
$179$	6.40636	+	5.37558i	0.478834	+	0.401789i	−0.371171	+	0.928565i	$0.621043\pi$
$180$		0			0
$181$	−9.88668	+	8.29591i	−0.734871	+	0.616630i	−0.931455	−	0.363857i	$-0.881460\pi$
$181$	−9.88668	+	8.29591i	−0.734871	+	0.616630i	0.196584	+	0.980487i	$0.437015\pi$
$182$	−10.7722	−	11.4179i	−0.798488	−	0.846348i
$183$		0			0
$184$	4.75649	+	3.12839i	0.350653	+	0.230628i
$185$	0.0599403	+	0.0142061i	0.00440690	+	0.00104445i
$186$		0			0
$187$	−8.74609	−	1.02227i	−0.639578	−	0.0747559i
$188$	−3.21163	−	5.56271i	−0.234232	−	0.405703i
$189$		0			0
$190$	−3.66266	+	6.34391i	−0.265717	+	0.460236i
$191$	−0.917423	+	1.23231i	−0.0663824	+	0.0891671i	−0.834074	−	0.551652i	$-0.813998\pi$
$191$	−0.917423	+	1.23231i	−0.0663824	+	0.0891671i	0.767692	+	0.640819i	$0.221405\pi$
$192$		0			0
$193$	0.485971	+	1.62326i	0.0349810	+	0.116845i	0.973697	−	0.227847i	$-0.0731686\pi$
$193$	0.485971	+	1.62326i	0.0349810	+	0.116845i	−0.938716	+	0.344692i	$0.887983\pi$
$194$	4.02940	−	2.02364i	0.289294	−	0.145289i
$195$		0			0
$196$	0.742304	−	2.47947i	0.0530217	−	0.177105i
$197$	2.80764	+	15.9229i	0.200036	+	1.13446i	0.905062	+	0.425280i	$0.139825\pi$
$197$	2.80764	+	15.9229i	0.200036	+	1.13446i	−0.705025	+	0.709182i	$0.749064\pi$
$198$		0			0
$199$	−3.57558	+	20.2781i	−0.253466	+	1.43748i	0.546513	+	0.837450i	$0.315955\pi$
$199$	−3.57558	+	20.2781i	−0.253466	+	1.43748i	−0.799980	+	0.600027i	$0.795156\pi$
$200$	4.27594	+	2.14746i	0.302355	+	0.151848i
$201$		0			0
$202$	−9.26488	+	21.4784i	−0.651875	+	1.51122i
$203$	3.02994	−	7.02418i	0.212660	−	0.493001i
$204$		0			0
$205$	−4.85567	−	2.43861i	−0.339134	−	0.170320i
$206$	1.25645	−	7.12569i	0.0875411	−	0.496470i
$207$		0			0
$208$	−1.49752	−	8.49285i	−0.103834	−	0.588873i
$209$	−7.57632	+	25.3067i	−0.524065	+	1.75050i
$210$		0			0
$211$	22.7053	−	11.4030i	1.56310	−	0.785016i	0.563928	−	0.825824i	$-0.309290\pi$
$211$	22.7053	−	11.4030i	1.56310	−	0.785016i	0.999167	+	0.0408081i	$0.0129932\pi$
$212$	−0.261736	−	0.874258i	−0.0179761	−	0.0600443i
$213$		0			0
$214$	−23.9632	+	32.1882i	−1.63809	+	2.20034i
$215$	−1.01917	+	1.76525i	−0.0695066	+	0.120389i
$216$		0			0
$217$	−10.2067	−	17.6785i	−0.692875	−	1.20009i
$218$	28.3620	+	3.31504i	1.92092	+	0.224523i
$219$		0			0
$220$	−3.70016	−	0.876954i	−0.249465	−	0.0591242i
$221$	6.53492	+	4.29809i	0.439587	+	0.289121i
$222$		0			0
$223$	5.53502	+	5.86678i	0.370652	+	0.392869i	0.885673	−	0.464309i	$-0.153697\pi$
$223$	5.53502	+	5.86678i	0.370652	+	0.392869i	−0.515021	+	0.857178i	$0.672216\pi$
$224$	−14.9301	+	12.5278i	−0.997560	+	0.837052i
$225$		0			0
$226$	7.26220	+	6.09371i	0.483074	+	0.405347i
$227$	−1.68056	−	28.8542i	−0.111543	−	1.91512i	−0.338081	−	0.941117i	$-0.609778\pi$
$227$	−1.68056	−	28.8542i	−0.111543	−	1.91512i	0.226538	−	0.974002i	$-0.427259\pi$
$228$		0			0
$229$	−3.88467	−	5.21802i	−0.256706	−	0.344817i	0.655022	−	0.755610i	$-0.272659\pi$
$229$	−3.88467	−	5.21802i	−0.256706	−	0.344817i	−0.911729	+	0.410793i	$0.865252\pi$
$230$	5.38588	−	0.629519i	0.355134	−	0.0415092i
$231$		0			0
$232$	−2.61229	+	1.71813i	−0.171505	+	0.112801i
$233$	−9.64551	+	3.51068i	−0.631898	+	0.229992i	−0.638057	−	0.769989i	$-0.720262\pi$
$233$	−9.64551	+	3.51068i	−0.631898	+	0.229992i	0.00615899	+	0.999981i	$0.498040\pi$
$234$		0			0
$235$	−1.09694	−	0.399254i	−0.0715565	−	0.0260444i
$236$	25.4089	−	6.02201i	1.65398	−	0.391999i
$237$		0			0
$238$	0.771203	−	13.2410i	0.0499897	−	0.858289i
$239$	19.0707	−	20.2137i	1.23358	−	1.30752i	0.297931	−	0.954588i	$-0.403704\pi$
$239$	19.0707	−	20.2137i	1.23358	−	1.30752i	0.935649	−	0.352931i	$-0.114815\pi$
$240$		0			0
$241$	2.63158	+	6.10070i	0.169515	+	0.392980i	0.981704	−	0.190415i	$-0.0609832\pi$
$241$	2.63158	+	6.10070i	0.169515	+	0.392980i	−0.812189	+	0.583395i	$0.801724\pi$
$242$	−1.54895			−0.0995703
$243$		0			0
$244$	−5.59577			−0.358232
$245$	−0.186304	−	0.431900i	−0.0119025	−	0.0275931i
$246$		0			0
$247$	16.1024	−	17.0676i	1.02457	−	1.08598i
$248$	−0.485127	+	8.32931i	−0.0308056	+	0.528912i
$249$		0			0
$250$	9.05584	−	2.14627i	0.572741	−	0.135742i
$251$	−10.3211	−	3.75657i	−0.651461	−	0.237113i	−0.00491575	−	0.999988i	$-0.501565\pi$
$251$	−10.3211	−	3.75657i	−0.651461	−	0.237113i	−0.646546	+	0.762875i	$0.723787\pi$
$252$		0			0
$253$	18.3754	−	6.68809i	1.15525	−	0.420477i
$254$	−30.6920	+	20.1865i	−1.92579	+	1.26661i
$255$		0			0
$256$	−6.00426	+	0.701797i	−0.375266	+	0.0438623i
$257$	−12.4886	−	16.7751i	−0.779016	−	1.04640i	−0.997507	−	0.0705612i	$-0.977521\pi$
$257$	−12.4886	−	16.7751i	−0.779016	−	1.04640i	0.218492	−	0.975839i	$-0.429886\pi$
$258$		0			0
$259$	0.0194555	+	0.334037i	0.00120890	+	0.0207561i
$260$	2.58751	+	2.17118i	0.160470	+	0.134651i
$261$		0			0
$262$	−0.562354	+	0.471871i	−0.0347424	+	0.0291523i
$263$	16.1521	+	17.1202i	0.995982	+	1.05568i	0.998449	+	0.0556818i	$0.0177332\pi$
$263$	16.1521	+	17.1202i	0.995982	+	1.05568i	−0.00246701	+	0.999997i	$0.500785\pi$
$264$		0			0
$265$	−0.138567	−	0.0911370i	−0.00851211	−	0.00559850i
$266$	−38.7172	−	9.17614i	−2.37390	−	0.562625i
$267$		0			0
$268$	−3.41860	−	0.399577i	−0.208824	−	0.0244081i
$269$	−2.17903	−	3.77420i	−0.132858	−	0.230117i	0.791919	−	0.610626i	$-0.209082\pi$
$269$	−2.17903	−	3.77420i	−0.132858	−	0.230117i	−0.924777	+	0.380509i	$0.875749\pi$
$270$		0			0
$271$	−0.604369	+	1.04680i	−0.0367128	+	0.0635885i	−0.883798	−	0.467869i	$-0.845022\pi$
$271$	−0.604369	+	1.04680i	−0.0367128	+	0.0635885i	0.847085	+	0.531457i	$0.178355\pi$
$272$	4.35133	−	5.84485i	0.263838	−	0.354396i
$273$		0			0
$274$	−0.150298	−	0.502029i	−0.00907982	−	0.0303287i
$275$	14.6871	−	7.37614i	0.885666	−	0.444798i
$276$		0			0
$277$	2.07798	−	6.94094i	0.124854	−	0.417041i	−0.872593	−	0.488447i	$-0.837564\pi$
$277$	2.07798	−	6.94094i	0.124854	−	0.417041i	0.997447	+	0.0714063i	$0.0227487\pi$
$278$	−2.06703	−	11.7227i	−0.123972	−	0.703080i
$279$		0			0
$280$	0.189775	−	1.07627i	0.0113412	−	0.0643193i
$281$	2.38776	+	1.19918i	0.142442	+	0.0715371i	0.518593	−	0.855021i	$-0.326456\pi$
$281$	2.38776	+	1.19918i	0.142442	+	0.0715371i	−0.376151	+	0.926559i	$0.622752\pi$
$282$		0			0
$283$	10.2442	−	23.7487i	0.608954	−	1.41171i	−0.282794	−	0.959181i	$-0.591261\pi$
$283$	10.2442	−	23.7487i	0.608954	−	1.41171i	0.891748	−	0.452533i	$-0.149479\pi$
$284$	3.49445	−	8.10105i	0.207358	−	0.480709i
$285$		0			0
$286$	19.6934	+	9.89038i	1.16449	+	0.584831i
$287$	5.12513	−	29.0660i	0.302527	−	1.71571i
$288$		0			0
$289$	−1.80439	−	10.2332i	−0.106141	−	0.601954i
$290$	−0.854124	+	2.85297i	−0.0501559	+	0.167532i
$291$		0			0
$292$	−11.1842	+	5.61692i	−0.654506	+	0.328705i
$293$	5.23549	+	17.4878i	0.305861	+	1.02165i	0.963365	+	0.268195i	$0.0864271\pi$
$293$	5.23549	+	17.4878i	0.305861	+	1.02165i	−0.657504	+	0.753451i	$0.728388\pi$
$294$		0			0
$295$	2.83389	−	3.80658i	0.164996	−	0.221627i
$296$	0.0683802	−	0.118438i	0.00397452	−	0.00688407i
$297$		0			0
$298$	2.10423	+	3.64464i	0.121895	+	0.211128i
$299$	−17.2522	−	2.01649i	−0.997719	−	0.116617i
$300$		0			0
$301$	−10.7734	−	2.55334i	−0.620969	−	0.147172i
$302$	20.4096	+	13.4236i	1.17444	+	0.772442i
$303$		0			0
$304$	−15.0011	−	15.9002i	−0.860371	−	0.911940i
$305$	−0.779031	+	0.653685i	−0.0446072	+	0.0374299i
$306$		0			0
$307$	0.992726	+	0.832996i	0.0566579	+	0.0475416i	0.670677	−	0.741750i	$-0.266004\pi$
$307$	0.992726	+	0.832996i	0.0566579	+	0.0475416i	−0.614019	+	0.789291i	$0.710448\pi$
$308$	−1.20100	−	20.6204i	−0.0684334	−	1.17496i
$309$		0			0
$310$	4.74560	+	6.37444i	0.269532	+	0.362044i
$311$	−20.7282	+	2.42278i	−1.17539	+	0.137383i	−0.681284	−	0.732020i	$-0.738578\pi$
$311$	−20.7282	+	2.42278i	−1.17539	+	0.137383i	−0.494104	+	0.869403i	$0.664504\pi$
$312$		0			0
$313$	19.4581	−	12.7978i	1.09984	−	0.723375i	0.136226	−	0.990678i	$-0.456503\pi$
$313$	19.4581	−	12.7978i	1.09984	−	0.723375i	0.963613	+	0.267303i	$0.0861324\pi$
$314$	46.5408	−	16.9395i	2.62645	−	0.955950i
$315$		0			0
$316$	23.8550	+	8.68252i	1.34195	+	0.488430i
$317$	−17.3294	+	4.10715i	−0.973317	+	0.230680i	−0.686359	−	0.727263i	$-0.740792\pi$
$317$	−17.3294	+	4.10715i	−0.973317	+	0.230680i	−0.286958	+	0.957943i	$0.592644\pi$
$318$		0			0
$319$	−0.624447	+	10.7213i	−0.0349623	+	0.600280i
$320$	3.45942	−	3.66677i	0.193388	−	0.204979i
$321$		0			0
$322$	11.6662	+	27.0453i	0.650133	+	1.50718i
$323$	19.8264			1.10317
$324$		0			0
$325$	−14.5988			−0.809796
$326$	10.2646	+	23.7961i	0.568505	+	1.31794i
$327$		0			0
$328$	−8.27830	+	8.77448i	−0.457093	+	0.484490i
$329$	0.368683	−	6.33004i	0.0203261	−	0.348986i
$330$		0			0
$331$	10.9736	−	2.60079i	0.603164	−	0.142953i	0.0823225	−	0.996606i	$-0.473766\pi$
$331$	10.9736	−	2.60079i	0.603164	−	0.142953i	0.520842	+	0.853653i	$0.325618\pi$
$332$	−2.27284	−	0.827245i	−0.124738	−	0.0454009i
$333$		0			0
$334$	10.5594	−	3.84332i	0.577787	−	0.210297i
$335$	−0.522608	+	0.343725i	−0.0285531	+	0.0187797i
$336$		0			0
$337$	−21.7773	+	2.54541i	−1.18629	+	0.138657i	−0.686263	−	0.727354i	$-0.740750\pi$
$337$	−21.7773	+	2.54541i	−1.18629	+	0.138657i	−0.500025	+	0.866011i	$0.666676\pi$
$338$	4.72651	+	6.34881i	0.257088	+	0.345330i
$339$		0			0
$340$	0.165947	+	2.84920i	0.00899973	+	0.154519i
$341$	21.9534	+	18.4211i	1.18885	+	0.997560i
$342$		0			0
$343$	15.0404	−	12.6204i	0.812105	−	0.681437i
$344$	3.10547	+	3.29160i	0.167435	+	0.177471i
$345$		0			0
$346$	3.63408	+	2.39017i	0.195369	+	0.128496i
$347$	−5.90961	−	1.40060i	−0.317245	−	0.0751884i	0.0689086	−	0.997623i	$-0.478048\pi$
$347$	−5.90961	−	1.40060i	−0.317245	−	0.0751884i	−0.386153	+	0.922435i	$0.626196\pi$
$348$		0			0
$349$	9.10876	+	1.06466i	0.487581	+	0.0569900i	0.356332	−	0.934359i	$-0.384027\pi$
$349$	9.10876	+	1.06466i	0.487581	+	0.0569900i	0.131249	+	0.991349i	$0.458101\pi$
$350$	12.3778	+	21.4390i	0.661622	+	1.14596i
$351$		0			0
$352$	13.6808	−	23.6959i	0.729191	−	1.26300i
$353$	−4.57466	+	6.14483i	−0.243484	+	0.327056i	−0.907019	−	0.421089i	$-0.861648\pi$
$353$	−4.57466	+	6.14483i	−0.243484	+	0.327056i	0.663535	+	0.748145i	$0.269055\pi$
$354$		0			0
$355$	−0.459856	−	1.53603i	−0.0244066	−	0.0815238i
$356$	−19.1506	+	9.61779i	−1.01498	+	0.509742i
$357$		0			0
$358$	5.07192	−	16.9414i	0.268059	−	0.895380i
$359$	3.38137	+	19.1767i	0.178462	+	1.01211i	0.934072	+	0.357085i	$0.116229\pi$
$359$	3.38137	+	19.1767i	0.178462	+	1.01211i	−0.755610	+	0.655021i	$0.772660\pi$
$360$		0			0
$361$	7.02896	−	39.8632i	0.369945	−	2.09806i
$362$	24.3886	+	12.2484i	1.28183	+	0.643761i
$363$		0			0
$364$	−7.26699	+	16.8468i	−0.380894	+	0.883011i
$365$	−0.900886	+	2.08849i	−0.0471545	+	0.109316i
$366$		0			0
$367$	−7.46794	−	3.75054i	−0.389823	−	0.195777i	0.243082	−	0.970006i	$-0.421842\pi$
$367$	−7.46794	−	3.75054i	−0.389823	−	0.195777i	−0.632905	+	0.774229i	$0.718138\pi$
$368$	−2.80991	+	15.9358i	−0.146477	+	0.830710i
$369$		0			0
$370$	−0.0226197	−	0.128283i	−0.00117594	−	0.00666910i
$371$	0.258374	−	0.863029i	0.0134141	−	0.0448062i
$372$		0			0
$373$	11.6562	−	5.85394i	0.603533	−	0.303106i	−0.120670	−	0.992693i	$-0.538504\pi$
$373$	11.6562	−	5.85394i	0.603533	−	0.303106i	0.724203	+	0.689587i	$0.242208\pi$
$374$	5.34042	+	17.8382i	0.276147	+	0.922394i
$375$		0			0
$376$	−1.54761	+	2.07880i	−0.0798118	+	0.107206i
$377$	4.76974	−	8.26143i	0.245654	−	0.425485i
$378$		0			0
$379$	2.48513	+	4.30437i	0.127653	+	0.221101i	0.922767	−	0.385359i	$-0.125922\pi$
$379$	2.48513	+	4.30437i	0.127653	+	0.221101i	−0.795114	+	0.606460i	$0.792589\pi$
$380$	8.50403	+	0.993978i	0.436247	+	0.0509900i
$381$		0			0
$382$	3.16114	+	0.749204i	0.161738	+	0.0383326i
$383$	3.06528	+	2.01606i	0.156628	+	0.103016i	0.625404	−	0.780301i	$-0.284934\pi$
$383$	3.06528	+	2.01606i	0.156628	+	0.103016i	−0.468775	+	0.883317i	$0.655305\pi$
$384$		0			0
$385$	−2.57603	−	2.73043i	−0.131287	−	0.139156i
$386$	2.74480	−	2.30316i	0.139707	−	0.117228i
$387$		0			0
$388$	−4.03720	−	3.38761i	−0.204958	−	0.171980i
$389$	0.322693	+	5.54043i	0.0163612	+	0.280911i	0.996559	+	0.0828890i	$0.0264147\pi$
$389$	0.322693	+	5.54043i	0.0163612	+	0.280911i	−0.980198	+	0.198022i	$0.936548\pi$
$390$		0			0
$391$	−8.76416	−	11.7723i	−0.443223	−	0.595351i
$392$	−1.03721	+	0.121232i	−0.0523870	+	0.00612316i
$393$		0			0
$394$	28.5656	−	18.7879i	1.43911	−	0.946519i
$395$	4.33532	−	1.57793i	0.218134	−	0.0793941i
$396$		0			0
$397$	10.8249	+	3.93994i	0.543286	+	0.197740i	0.599061	−	0.800703i	$-0.295541\pi$
$397$	10.8249	+	3.93994i	0.543286	+	0.197740i	−0.0557747	+	0.998443i	$0.517763\pi$
$398$	42.3682	−	10.0414i	2.12372	−	0.503332i
$399$		0			0
$400$	−0.790788	+	13.5773i	−0.0395394	+	0.678865i
$401$	16.3745	−	17.3559i	0.817703	−	0.866714i	−0.175335	−	0.984509i	$-0.556101\pi$
$401$	16.3745	−	17.3559i	0.817703	−	0.866714i	0.993038	+	0.117794i	$0.0375824\pi$
$402$		0			0
$403$	−10.0826	−	23.3740i	−0.502248	−	1.16434i
$404$	27.3402			1.36023
$405$		0			0
$406$	−16.1764			−0.802821
$407$	−0.186057	−	0.431330i	−0.00922253	−	0.0213802i
$408$		0			0
$409$	−14.7429	+	15.6266i	−0.728989	+	0.772683i	−0.980784	−	0.195097i	$-0.937498\pi$
$409$	−14.7429	+	15.6266i	−0.728989	+	0.772683i	0.251795	+	0.967781i	$0.418979\pi$
$410$	−0.668085	+	11.4706i	−0.0329944	+	0.566491i
$411$		0			0
$412$	−8.22911	+	1.95034i	−0.405419	+	0.0960861i
$413$	24.2228	+	8.81637i	1.19192	+	0.433825i
$414$		0			0
$415$	−0.413056	+	0.150340i	−0.0202761	+	0.00737991i
$416$	−20.3059	+	13.3554i	−0.995580	+	0.654803i
$417$		0			0
$418$	55.4828	−	6.48501i	2.71375	−	0.317192i
$419$	5.87447	+	7.89078i	0.286987	+	0.385490i	0.922115	−	0.386917i	$-0.126460\pi$
$419$	5.87447	+	7.89078i	0.286987	+	0.385490i	−0.635128	+	0.772407i	$0.719053\pi$
$420$		0			0
$421$	0.660438	+	11.3393i	0.0321878	+	0.552643i	0.975399	+	0.220448i	$0.0707520\pi$
$421$	0.660438	+	11.3393i	0.0321878	+	0.552643i	−0.943211	+	0.332195i	$0.892211\pi$
$422$	−41.1578	−	34.5355i	−2.00353	−	1.68116i
$423$		0			0
$424$	−0.282064	+	0.236680i	−0.0136983	+	0.0114942i
$425$	−8.46495	−	8.97232i	−0.410610	−	0.435222i
$426$		0			0
$427$	−4.61515	−	3.03543i	−0.223343	−	0.146895i
$428$	45.6387	+	10.8166i	2.20603	+	0.522839i
$429$		0			0
$430$	4.28114	+	0.500394i	0.206455	+	0.0241311i
$431$	6.18977	+	10.7210i	0.298151	+	0.516412i	0.975713	−	0.219053i	$-0.0702969\pi$
$431$	6.18977	+	10.7210i	0.298151	+	0.516412i	−0.677562	+	0.735465i	$0.736964\pi$
$432$		0			0
$433$	0.835935	−	1.44788i	0.0401725	−	0.0695808i	−0.845240	−	0.534387i	$-0.820543\pi$
$433$	0.835935	−	1.44788i	0.0401725	−	0.0695808i	0.885413	+	0.464806i	$0.153876\pi$
$434$	−25.7772	+	34.6247i	−1.23734	+	1.66204i
$435$		0			0
$436$	−9.57222	−	31.9734i	−0.458426	−	1.53125i
$437$	−39.3453	+	19.7600i	−1.88214	+	0.945247i
$438$		0			0
$439$	−5.13129	+	17.1397i	−0.244903	+	0.818033i	0.743833	+	0.668365i	$0.233006\pi$
$439$	−5.13129	+	17.1397i	−0.244903	+	0.818033i	−0.988736	+	0.149668i	$0.952180\pi$
$440$	0.266424	+	1.51097i	0.0127013	+	0.0720325i
$441$		0			0
$442$	2.87211	−	16.2886i	0.136612	−	0.774768i
$443$	1.76123	+	0.884525i	0.0836788	+	0.0420251i	0.490146	−	0.871640i	$-0.336943\pi$
$443$	1.76123	+	0.884525i	0.0836788	+	0.0420251i	−0.406468	+	0.913665i	$0.633240\pi$
$444$		0			0
$445$	−1.54258	+	3.57610i	−0.0731252	+	0.169523i
$446$	6.75547	−	15.6609i	0.319881	−	0.741567i
$447$		0			0
$448$	24.4698	+	12.2892i	1.15609	+	0.580609i
$449$	−1.97278	+	11.1882i	−0.0931011	+	0.528003i	0.902212	+	0.431294i	$0.141943\pi$
$449$	−1.97278	+	11.1882i	−0.0931011	+	0.528003i	−0.995313	+	0.0967089i	$0.969168\pi$
$450$		0			0
$451$	7.19513	+	40.8056i	0.338805	+	1.92146i
$452$	3.17792	−	10.6150i	0.149477	−	0.499287i
$453$		0			0
$454$	−54.6178	+	27.4301i	−2.56334	+	1.28736i
$455$	0.956307	+	3.19429i	0.0448323	+	0.149750i
$456$		0			0
$457$	−0.0737908	+	0.0991182i	−0.00345179	+	0.00463655i	−0.803846	−	0.594838i	$-0.797216\pi$
$457$	−0.0737908	+	0.0991182i	−0.00345179	+	0.00463655i	0.800394	+	0.599474i	$0.204624\pi$
$458$	−6.87805	+	11.9131i	−0.321390	+	0.556664i
$459$		0			0
$460$	−3.16897	−	5.48881i	−0.147754	−	0.255917i
$461$	28.3491	+	3.31353i	1.32035	+	0.154327i	0.746911	−	0.664924i	$-0.231536\pi$
$461$	28.3491	+	3.31353i	1.32035	+	0.154327i	0.573436	+	0.819250i	$0.305610\pi$
$462$		0			0
$463$	−23.7448	−	5.62762i	−1.10351	−	0.261537i	−0.361801	−	0.932255i	$-0.617838\pi$
$463$	−23.7448	−	5.62762i	−1.10351	−	0.261537i	−0.741713	+	0.670718i	$0.765986\pi$
$464$	−7.42500	−	4.88350i	−0.344697	−	0.226711i
$465$		0			0
$466$	14.8952	+	15.7880i	0.690008	+	0.731366i
$467$	6.52240	−	5.47294i	0.301821	−	0.253258i	−0.479281	−	0.877662i	$-0.659103\pi$
$467$	6.52240	−	5.47294i	0.301821	−	0.253258i	0.781102	+	0.624404i	$0.214658\pi$
$468$		0			0
$469$	−2.60276	−	2.18398i	−0.120184	−	0.100847i
$470$	0.143529	+	2.46429i	0.00662049	+	0.113669i
$471$		0			0
$472$	−6.29155	−	8.45101i	−0.289592	−	0.388989i
$473$	15.4386	−	1.80451i	0.709867	−	0.0829715i
$474$		0			0
$475$	−30.9173	+	20.3346i	−1.41858	+	0.933015i
$476$	−14.5676	+	5.30217i	−0.667705	+	0.243025i
$477$		0			0
$478$	−55.2212	−	20.0989i	−2.52576	−	0.919301i
$479$	9.72408	−	2.30465i	0.444305	−	0.105302i	−0.00237286	−	0.999997i	$-0.500755\pi$
$479$	9.72408	−	2.30465i	0.444305	−	0.105302i	0.446677	+	0.894695i	$0.352607\pi$
$480$		0			0
$481$	−0.0242614	+	0.416552i	−0.00110622	+	0.0189931i
$482$	9.64145	−	10.2193i	0.439156	−	0.465478i
$483$		0			0
$484$	0.717076	+	1.66237i	0.0325944	+	0.0755622i
$485$	−0.957783			−0.0434907
$486$		0			0
$487$	30.6747			1.39001			0.695003	−	0.719007i	$-0.255403\pi$
$487$	30.6747			1.39001			0.695003	+	0.719007i	$0.255403\pi$
$488$	0.894247	+	2.07310i	0.0404807	+	0.0938448i
$489$		0			0
$490$	−0.682569	+	0.723481i	−0.0308353	+	0.0326835i
$491$	0.655352	−	11.2520i	0.0295756	−	0.507794i	−0.950694	−	0.310130i	$-0.899627\pi$
$491$	0.655352	−	11.2520i	0.0295756	−	0.507794i	0.980270	−	0.197664i	$-0.0633355\pi$
$492$		0			0
$493$	7.84310	−	1.85885i	0.353235	−	0.0837183i
$494$	−46.6262	−	16.9706i	−2.09781	−	0.763542i
$495$		0			0
$496$	−22.2847	+	8.11095i	−1.00061	+	0.364193i
$497$	7.27650	−	4.78583i	0.326395	−	0.214674i
$498$		0			0
$499$	19.4492	−	2.27328i	0.870664	−	0.101766i	0.330984	−	0.943636i	$-0.392619\pi$
$499$	19.4492	−	2.27328i	0.870664	−	0.101766i	0.539680	+	0.841870i	$0.318545\pi$
$500$	−6.49576	−	8.72532i	−0.290499	−	0.390208i
$501$		0			0
$502$	1.35046	+	23.1865i	0.0602739	+	1.03486i
$503$	−17.6179	−	14.7832i	−0.785544	−	0.659150i	0.159094	−	0.987263i	$-0.449143\pi$
$503$	−17.6179	−	14.7832i	−0.785544	−	0.659150i	−0.944638	+	0.328114i	$0.893587\pi$
$504$		0			0
$505$	3.80625	−	3.19382i	0.169376	−	0.142123i
$506$	−28.3765	−	30.0773i	−1.26149	−	1.33710i
$507$		0			0
$508$	35.8732	+	23.5942i	1.59162	+	1.04682i
$509$	29.2859	+	6.94089i	1.29808	+	0.307650i	0.820856	−	0.571135i	$-0.193497\pi$
$509$	29.2859	+	6.94089i	1.29808	+	0.307650i	0.477219	+	0.878784i	$0.341645\pi$
$510$		0			0
$511$	−12.2711	−	1.43429i	−0.542843	−	0.0634493i
$512$	14.1475	+	24.5043i	0.625239	+	1.08295i
$513$		0			0
$514$	−22.1118	+	38.2988i	−0.975309	+	1.68929i
$515$	−0.917806	+	1.23283i	−0.0404434	+	0.0543249i
$516$		0			0
$517$	2.55305	+	8.52779i	0.112283	+	0.375052i
$518$	0.632296	−	0.317551i	0.0277815	−	0.0139524i
$519$		0			0
$520$	0.390865	−	1.30558i	0.0171406	−	0.0572535i
$521$	−4.32127	−	24.5071i	−0.189318	−	1.07368i	−0.920281	−	0.391259i	$-0.872040\pi$
$521$	−4.32127	−	24.5071i	−0.189318	−	1.07368i	0.730963	−	0.682418i	$-0.239071\pi$
$522$		0			0
$523$	2.05500	−	11.6545i	0.0898590	−	0.509616i	−0.906343	−	0.422543i	$-0.861138\pi$
$523$	2.05500	−	11.6545i	0.0898590	−	0.509616i	0.996202	−	0.0870730i	$-0.0277513\pi$
$524$	0.766761	+	0.385082i	0.0334961	+	0.0168224i
$525$		0			0
$526$	19.7136	−	45.7012i	0.859553	−	1.99267i
$527$	8.51925	−	19.7498i	0.371104	−	0.860317i
$528$		0			0
$529$	8.57170	+	4.30487i	0.372682	+	0.187168i
$530$	−0.0609005	+	0.345384i	−0.00264535	+	0.0150025i
$531$		0			0
$532$	8.07581	+	45.8002i	0.350131	+	1.98569i
$533$	10.5558	−	35.2589i	0.457223	−	1.52723i
$534$		0			0
$535$	7.61730	−	3.82555i	0.329325	−	0.165393i
$536$	0.398285	+	1.33037i	0.0172033	+	0.0574630i
$537$		0			0
$538$	−5.50319	+	7.39206i	−0.237259	+	0.318694i
$539$	−1.79344	+	3.10633i	−0.0772490	+	0.133799i
$540$		0			0
$541$	4.46220	+	7.72875i	0.191845	+	0.332285i	0.945862	−	0.324570i	$-0.105220\pi$
$541$	4.46220	+	7.72875i	0.191845	+	0.332285i	−0.754017	+	0.656855i	$0.771886\pi$
$542$	2.53873	+	0.296735i	0.109048	+	0.0127459i
$543$		0			0
$544$	−19.9823	−	4.73590i	−0.856735	−	0.203050i
$545$	−5.06769	−	3.33307i	−0.217076	−	0.142773i
$546$		0			0
$547$	−17.4348	−	18.4798i	−0.745458	−	0.790139i	0.238002	−	0.971265i	$-0.423507\pi$
$547$	−17.4348	−	18.4798i	−0.745458	−	0.790139i	−0.983460	+	0.181125i	$0.942026\pi$
$548$	−0.469210	+	0.393714i	−0.0200437	+	0.0168186i
$549$		0			0
$550$	−26.6233	−	22.3396i	−1.13522	−	0.952564i
$551$	−1.40598	−	24.1398i	−0.0598968	−	1.02839i
$552$		0			0
$553$	14.9648	+	20.1012i	0.636366	+	0.854788i
$554$	−15.2175	+	1.77867i	−0.646528	+	0.0755682i
$555$		0			0
$556$	−11.6241	+	7.64531i	−0.492973	+	0.324234i
$557$	−37.6248	+	13.6943i	−1.59421	+	0.580246i	−0.978232	−	0.207515i	$-0.933462\pi$
$557$	−37.6248	+	13.6943i	−1.59421	+	0.580246i	−0.615981	+	0.787761i	$0.711240\pi$
$558$		0			0
$559$	−12.9742	−	4.72221i	−0.548749	−	0.199728i
$560$	3.02258	−	0.716365i	0.127727	−	0.0302719i
$561$		0			0
$562$	0.328529	−	5.64063i	0.0138582	−	0.237936i
$563$	−7.84566	+	8.31591i	−0.330655	+	0.350474i	−0.871277	−	0.490792i	$-0.836708\pi$
$563$	−7.84566	+	8.31591i	−0.330655	+	0.350474i	0.540622	+	0.841266i	$0.318189\pi$
$564$		0			0
$565$	−0.797596	−	1.84903i	−0.0335551	−	0.0777895i
$566$	−54.6922			−2.29889
$567$		0			0
$568$	−3.55969			−0.149361
$569$	−4.00846	−	9.29267i	−0.168044	−	0.389569i	0.813296	−	0.581850i	$-0.197671\pi$
$569$	−4.00846	−	9.29267i	−0.168044	−	0.389569i	−0.981340	+	0.192281i	$0.938412\pi$
$570$		0			0
$571$	−24.1948	+	25.6450i	−1.01252	+	1.07321i	−0.0152132	+	0.999884i	$0.504843\pi$
$571$	−24.1948	+	25.6450i	−1.01252	+	1.07321i	−0.997308	+	0.0733255i	$0.976639\pi$
$572$	1.49767	−	25.7141i	0.0626209	−	1.07516i
$573$		0			0
$574$	−60.7292	+	14.3931i	−2.53479	+	0.600756i
$575$	25.7409	+	9.36891i	1.07347	+	0.390711i
$576$		0			0
$577$	−1.23876	+	0.450874i	−0.0515705	+	0.0187701i	−0.367677	−	0.929954i	$-0.619847\pi$
$577$	−1.23876	+	0.450874i	−0.0515705	+	0.0187701i	0.316106	+	0.948724i	$0.397624\pi$
$578$	−18.3583	+	12.0744i	−0.763603	+	0.502229i
$579$		0			0
$580$	3.45729	−	0.404099i	0.143556	−	0.0167793i
$581$	−1.42580	−	1.91518i	−0.0591520	−	0.0794550i
$582$		0			0
$583$	0.0735376	+	1.26259i	0.00304562	+	0.0522912i
$584$	3.86826	+	3.24585i	0.160070	+	0.134314i
$585$		0			0
$586$	29.5705	−	24.8126i	1.22154	−	1.02500i
$587$	−8.63402	−	9.15153i	−0.356364	−	0.377724i	0.524245	−	0.851568i	$-0.324348\pi$
$587$	−8.63402	−	9.15153i	−0.356364	−	0.377724i	−0.880609	+	0.473844i	$0.842866\pi$
$588$		0			0
$589$	−53.9104	−	35.4574i	−2.22134	−	1.46100i
$590$	−9.76466	−	2.31427i	−0.402005	−	0.0952769i
$591$		0			0
$592$	0.386091	+	0.0451275i	0.0158682	+	0.00185473i
$593$	−11.8449	−	20.5159i	−0.486410	−	0.842487i	0.513468	−	0.858109i	$-0.328361\pi$
$593$	−11.8449	−	20.5159i	−0.486410	−	0.842487i	−0.999878	+	0.0156219i	$0.995027\pi$
$594$		0			0
$595$	−1.40868	+	2.43991i	−0.0577504	+	0.100027i
$596$	2.93737	−	3.94557i	0.120319	−	0.161617i
$597$		0			0
$598$	10.5343	+	35.1870i	0.430779	+	1.43890i
$599$	−1.80734	+	0.907679i	−0.0738458	+	0.0370868i	−0.485339	−	0.874326i	$-0.661304\pi$
$599$	−1.80734	+	0.907679i	−0.0738458	+	0.0370868i	0.411493	+	0.911413i	$0.365007\pi$
$600$		0			0
$601$	−8.35262	+	27.8997i	−0.340710	+	1.13805i	0.600329	+	0.799753i	$0.295036\pi$
$601$	−8.35262	+	27.8997i	−0.340710	+	1.13805i	−0.941039	+	0.338298i	$0.890149\pi$
$602$	4.06557	+	23.0570i	0.165700	+	0.939732i
$603$		0			0
$604$	4.95803	−	28.1184i	0.201739	−	1.14412i
$605$	0.294024	+	0.147664i	0.0119538	+	0.00600341i
$606$		0			0
$607$	11.2464	−	26.0720i	0.456475	−	1.05823i	−0.522201	−	0.852822i	$-0.674889\pi$
$607$	11.2464	−	26.0720i	0.456475	−	1.05823i	0.978677	−	0.205407i	$-0.0658517\pi$
$608$	−24.4011	+	56.5681i	−0.989594	+	2.29414i
$609$		0			0
$610$	1.92172	+	0.965125i	0.0778082	+	0.0390768i
$611$	1.37305	−	7.78694i	0.0555476	−	0.315026i
$612$		0			0
$613$	4.96510	+	28.1585i	0.200538	+	1.13731i	0.904308	+	0.426881i	$0.140388\pi$
$613$	4.96510	+	28.1585i	0.200538	+	1.13731i	−0.703769	+	0.710429i	$0.748501\pi$
$614$	0.785942	−	2.62523i	0.0317180	−	0.105946i
$615$		0			0
$616$	−7.44743	+	3.74024i	−0.300066	+	0.150699i
$617$	6.38498	+	21.3273i	0.257050	+	0.858606i	0.984938	+	0.172910i	$0.0553170\pi$
$617$	6.38498	+	21.3273i	0.257050	+	0.858606i	−0.727888	+	0.685696i	$0.759498\pi$
$618$		0			0
$619$	3.21871	−	4.32348i	0.129371	−	0.173775i	−0.732718	−	0.680532i	$-0.761749\pi$
$619$	3.21871	−	4.32348i	0.129371	−	0.173775i	0.862089	+	0.506757i	$0.169156\pi$
$620$	4.64425	−	8.04408i	0.186518	−	0.323058i
$621$		0			0
$622$	22.0652	+	38.2181i	0.884735	+	1.53241i
$623$	−21.0118	−	2.45592i	−0.841818	−	0.0983944i
$624$		0			0
$625$	21.4209	+	5.07685i	0.856837	+	0.203074i
$626$	−41.1464	−	27.0624i	−1.64454	−	1.08163i
$627$		0			0
$628$	−39.7256	−	42.1067i	−1.58522	−	1.68024i
$629$	−0.270078	+	0.226622i	−0.0107687	+	0.00903601i
$630$		0			0
$631$	30.0508	+	25.2156i	1.19630	+	1.00382i	0.999728	+	0.0233298i	$0.00742677\pi$
$631$	30.0508	+	25.2156i	1.19630	+	1.00382i	0.196576	+	0.980489i	$0.437018\pi$
$632$	−0.595553	−	10.2253i	−0.0236898	−	0.406739i
$633$		0			0
$634$	22.4891	+	30.2081i	0.893155	+	1.19972i
$635$	7.75042	−	0.905894i	0.307566	−	0.0359493i
$636$		0			0
$637$	2.66193	−	1.75078i	0.105470	−	0.0693685i
$638$	21.3403	−	7.76725i	0.844872	−	0.307508i
$639$		0			0
$640$	−3.27371	−	1.19153i	−0.129405	−	0.0470994i
$641$	37.8673	−	8.97472i	1.49567	−	0.354480i	0.600289	−	0.799783i	$-0.295052\pi$
$641$	37.8673	−	8.97472i	1.49567	−	0.354480i	0.895380	+	0.445303i	$0.146904\pi$
$642$		0			0
$643$	−1.72381	+	29.5966i	−0.0679803	+	1.16718i	0.775975	+	0.630763i	$0.217258\pi$
$643$	−1.72381	+	29.5966i	−0.0679803	+	1.16718i	−0.843956	+	0.536413i	$0.819779\pi$
$644$	23.6249	−	25.0409i	0.930950	−	0.986749i
$645$		0			0
$646$	−16.6057	−	38.4964i	−0.653343	−	1.51462i
$647$	34.6188			1.36100			0.680502	−	0.732746i	$-0.261762\pi$
$647$	34.6188			1.36100			0.680502	+	0.732746i	$0.261762\pi$
$648$		0			0
$649$	−36.1886			−1.42053
$650$	12.2273	+	28.3461i	0.479594	+	1.11182i
$651$		0			0
$652$	20.7865	−	22.0324i	0.814063	−	0.862857i
$653$	−2.25785	+	38.7658i	−0.0883565	+	1.51702i	0.604882	+	0.796315i	$0.293220\pi$
$653$	−2.25785	+	38.7658i	−0.0883565	+	1.51702i	−0.693239	+	0.720708i	$0.743817\pi$
$654$		0			0
$655$	0.151731	−	0.0359610i	0.00592863	−	0.00140511i
$656$	−32.2200	−	11.7271i	−1.25798	−	0.457867i
$657$		0			0
$658$	−12.5996	+	4.58590i	−0.491185	+	0.178777i
$659$	26.4483	−	17.3953i	1.03028	−	0.677625i	0.0825118	−	0.996590i	$-0.473706\pi$
$659$	26.4483	−	17.3953i	1.03028	−	0.677625i	0.947766	+	0.318965i	$0.103335\pi$
$660$		0			0
$661$	0.614307	−	0.0718022i	0.0238938	−	0.00279278i	−0.104138	−	0.994563i	$-0.533208\pi$
$661$	0.614307	−	0.0718022i	0.0238938	−	0.00279278i	0.128031	+	0.991770i	$0.459134\pi$
$662$	−14.2409	−	19.1288i	−0.553488	−	0.743464i
$663$		0			0
$664$	0.0567425	+	0.974232i	0.00220204	+	0.0378075i
$665$	6.47457	+	5.43281i	0.251073	+	0.210675i
$666$		0			0
$667$	−13.7119	+	11.5057i	−0.530928	+	0.445502i
$668$	−9.01316	−	9.55340i	−0.348730	−	0.369632i
$669$		0			0
$670$	1.10511	+	0.726845i	0.0426943	+	0.0280805i
$671$	7.54592	+	1.78842i	0.291307	+	0.0690410i
$672$		0			0
$673$	0.205619	+	0.0240334i	0.00792602	+	0.000926419i	0.120055	−	0.992767i	$-0.461693\pi$
$673$	0.205619	+	0.0240334i	0.00792602	+	0.000926419i	−0.112129	+	0.993694i	$0.535767\pi$
$674$	23.1821	+	40.1525i	0.892940	+	1.54662i
$675$		0			0
$676$	4.62558	−	8.01174i	0.177907	−	0.308144i
$677$	−20.3499	+	27.3346i	−0.782109	+	1.05055i	0.215152	+	0.976581i	$0.430975\pi$
$677$	−20.3499	+	27.3346i	−0.782109	+	1.05055i	−0.997260	+	0.0739735i	$0.976432\pi$
$678$		0			0
$679$	−1.49209	−	4.98394i	−0.0572613	−	0.191266i
$680$	1.02904	−	0.516803i	0.0394619	−	0.0198185i
$681$		0			0
$682$	17.3805	−	58.0551i	0.665536	−	2.22304i
$683$	−7.39527	−	41.9406i	−0.282972	−	1.60481i	−0.712441	−	0.701732i	$-0.752410\pi$
$683$	−7.39527	−	41.9406i	−0.282972	−	1.60481i	0.429468	−	0.903082i	$-0.358701\pi$
$684$		0			0
$685$	−0.0193297	+	0.109624i	−0.000738549	+	0.00418852i
$686$	−37.1018	−	18.6332i	−1.41655	−	0.711420i
$687$		0			0
$688$	−5.09458	+	11.8106i	−0.194229	+	0.450273i
$689$	0.444960	−	1.03153i	0.0169516	−	0.0392983i
$690$		0			0
$691$	10.5599	+	5.30337i	0.401717	+	0.201750i	0.638174	−	0.769892i	$-0.279690\pi$
$691$	10.5599	+	5.30337i	0.401717	+	0.201750i	−0.236457	+	0.971642i	$0.575986\pi$
$692$	0.882813	−	5.00668i	0.0335595	−	0.190326i
$693$		0			0
$694$	2.23012	+	12.6476i	0.0846540	+	0.480097i
$695$	−0.725180	+	2.42227i	−0.0275076	+	0.0918819i
$696$		0			0
$697$	27.7906	−	13.9569i	1.05264	−	0.528657i
$698$	−5.56187	−	18.5779i	−0.210520	−	0.703185i
$699$		0			0
$700$	17.2786	−	23.2092i	0.653070	−	0.877225i
$701$	−5.03353	+	8.71832i	−0.190114	+	0.329286i	−0.945288	−	0.326238i	$-0.894219\pi$
$701$	−5.03353	+	8.71832i	−0.190114	+	0.329286i	0.755174	+	0.655524i	$0.227552\pi$
$702$		0			0
$703$	0.528832	+	0.915965i	0.0199453	+	0.0345463i
$704$	−38.1820	−	4.46283i	−1.43904	−	0.168199i
$705$		0			0
$706$	15.7628	+	3.73584i	0.593239	+	0.140600i
$707$	22.5490	+	14.8307i	0.848044	+	0.557767i
$708$		0			0
$709$	29.9923	+	31.7900i	1.12638	+	1.19390i	0.978793	+	0.204850i	$0.0656705\pi$
$709$	29.9923	+	31.7900i	1.12638	+	1.19390i	0.147591	+	0.989048i	$0.452848\pi$
$710$	−2.59730	+	2.17939i	−0.0974750	+	0.0817912i
$711$		0			0
$712$	6.62358	+	5.55784i	0.248229	+	0.208289i
$713$	2.77728	+	47.6841i	0.104010	+	1.78578i
$714$		0			0
$715$	−2.79535	−	3.75481i	−0.104540	−	0.140422i
$716$	−20.5299	+	2.39960i	−0.767238	+	0.0896773i
$717$		0			0
$718$	34.4027	−	22.6270i	1.28390	−	0.844433i
$719$	−13.0871	+	4.76331i	−0.488066	+	0.177641i	−0.574319	−	0.818632i	$-0.694733\pi$
$719$	−13.0871	+	4.76331i	−0.488066	+	0.177641i	0.0862528	+	0.996273i	$0.472511\pi$
$720$		0			0
$721$	−7.84497	−	2.85534i	−0.292162	−	0.106338i
$722$	−83.2884	+	19.7397i	−3.09967	+	0.734636i
$723$		0			0
$724$	1.85474	−	31.8447i	0.0689309	−	1.18350i
$725$	−10.3240	+	10.9428i	−0.383424	+	0.406406i
$726$		0			0
$727$	15.0269	+	34.8362i	0.557315	+	1.29200i	0.931194	+	0.364524i	$0.118768\pi$
$727$	15.0269	+	34.8362i	0.557315	+	1.29200i	−0.373879	+	0.927478i	$0.621972\pi$
$728$	7.40265			0.274361
$729$		0			0
$730$	4.80970			0.178015
$731$	−4.62069	−	10.7120i	−0.170902	−	0.396196i
$732$		0			0
$733$	13.7653	−	14.5903i	0.508431	−	0.538906i	−0.421408	−	0.906871i	$-0.638464\pi$
$733$	13.7653	−	14.5903i	0.508431	−	0.538906i	0.929840	+	0.367965i	$0.119945\pi$
$734$	−1.02750	+	17.6416i	−0.0379259	+	0.651162i
$735$		0			0
$736$	44.3747	−	10.5170i	1.63567	−	0.387662i
$737$	4.48229	+	1.63142i	0.165107	+	0.0600942i
$738$		0			0
$739$	−20.0939	+	7.31359i	−0.739167	+	0.269035i	−0.684040	−	0.729445i	$-0.739779\pi$
$739$	−20.0939	+	7.31359i	−0.739167	+	0.269035i	−0.0551270	+	0.998479i	$0.517556\pi$
$740$	−0.127204	+	0.0836636i	−0.00467612	+	0.00307553i
$741$		0			0
$742$	−1.89212	+	0.221157i	−0.0694619	+	0.00811894i
$743$	8.30473	+	11.1552i	0.304671	+	0.409244i	0.927920	−	0.372779i	$-0.121595\pi$
$743$	8.30473	+	11.1552i	0.304671	+	0.409244i	−0.623249	+	0.782023i	$0.714188\pi$
$744$		0			0
$745$	−0.0519782	−	0.892431i	−0.00190433	−	0.0326961i
$746$	−21.1291	−	17.7294i	−0.773592	−	0.649120i
$747$		0			0
$748$	16.6721	−	13.9896i	0.609592	−	0.511509i
$749$	31.7734	+	33.6778i	1.16097	+	1.23056i
$750$		0			0
$751$	0.116685	+	0.0767451i	0.00425791	+	0.00280047i	0.551636	−	0.834085i	$-0.314004\pi$
$751$	0.116685	+	0.0767451i	0.00425791	+	0.00280047i	−0.547378	+	0.836885i	$0.684374\pi$
$752$	−7.16770	−	1.69878i	−0.261379	−	0.0619480i
$753$		0			0
$754$	−20.0359	−	2.34186i	−0.729664	−	0.0852855i
$755$	−2.59448	−	4.49377i	−0.0944228	−	0.163545i
$756$		0			0
$757$	17.8510	−	30.9188i	0.648804	−	1.12376i	−0.334605	−	0.942359i	$-0.608603\pi$
$757$	17.8510	−	30.9188i	0.648804	−	1.12376i	0.983409	−	0.181403i	$-0.0580639\pi$
$758$	6.27624	−	8.43046i	0.227963	−	0.306208i
$759$		0			0
$760$	−0.990765	−	3.30939i	−0.0359388	−	0.120044i
$761$	24.9511	−	12.5309i	0.904478	−	0.454246i	0.0651523	−	0.997875i	$-0.479247\pi$
$761$	24.9511	−	12.5309i	0.904478	−	0.454246i	0.839325	+	0.543630i	$0.182950\pi$
$762$		0			0
$763$	9.44927	−	31.5628i	0.342086	−	1.14265i
$764$	−0.659365	−	3.73944i	−0.0238550	−	0.135288i
$765$		0			0
$766$	1.34719	−	7.64032i	0.0486761	−	0.276056i
$767$	28.7257	+	14.4266i	1.03723	+	0.520914i
$768$		0			0
$769$	−0.939924	+	2.17899i	−0.0338945	+	0.0785764i	−0.934322	−	0.356429i	$-0.883994\pi$
$769$	−0.939924	+	2.17899i	−0.0338945	+	0.0785764i	0.900428	+	0.435005i	$0.143253\pi$
$770$	−3.14403	+	7.28868i	−0.113303	+	0.262666i
$771$		0			0
$772$	−3.74249	−	1.87955i	−0.134695	−	0.0676465i
$773$	5.20402	−	29.5135i	0.187176	−	1.06153i	−0.735953	−	0.677033i	$-0.763265\pi$
$773$	5.20402	−	29.5135i	0.187176	−	1.06153i	0.923128	−	0.384492i	$-0.125623\pi$
$774$		0			0
$775$	6.97117	+	39.5355i	0.250412	+	1.42016i
$776$	−0.609854	+	2.03705i	−0.0218925	+	0.0731259i
$777$		0			0
$778$	10.4874	−	5.26698i	0.375992	−	0.188830i
$779$	−26.7569	−	89.3743i	−0.958665	−	3.20217i
$780$		0			0
$781$	−7.30139	+	9.80747i	−0.261264	+	0.350939i
$782$	−15.5175	+	26.8771i	−0.554904	+	0.961122i
$783$		0			0
$784$	−1.48408	−	2.57051i	−0.0530030	−	0.0918039i
$785$	−10.4493	−	1.22135i	−0.372952	−	0.0435918i
$786$		0			0
$787$	−9.04366	−	2.14339i	−0.322372	−	0.0764035i	0.0662440	−	0.997803i	$-0.478898\pi$
$787$	−9.04366	−	2.14339i	−0.322372	−	0.0764035i	−0.388616	+	0.921400i	$0.627047\pi$
$788$	−33.3878	−	21.9595i	−1.18939	−	0.782274i
$789$		0			0
$790$	−6.69489	−	7.09616i	−0.238193	−	0.252470i
$791$	8.37913	−	7.03092i	0.297927	−	0.249991i
$792$		0			0
$793$	−5.27683	−	4.42778i	−0.187386	−	0.157235i
$794$	−1.41638	−	24.3183i	−0.0502655	−	0.863025i
$795$		0			0
$796$	−30.3908	−	40.8219i	−1.07717	−	1.44689i
$797$	−18.5707	+	2.17060i	−0.657807	+	0.0768866i	−0.438446	−	0.898757i	$-0.644471\pi$
$797$	−18.5707	+	2.17060i	−0.657807	+	0.0768866i	−0.219360	+	0.975644i	$0.570397\pi$
$798$		0			0
$799$	5.58195	−	3.67131i	0.197475	−	0.129881i
$800$	36.0177	−	13.1094i	1.27342	−	0.463486i
$801$		0			0
$802$	−47.4141	−	17.2573i	−1.67425	−	0.609377i
$803$	16.8771	−	3.99995i	0.595581	−	0.141155i
$804$		0			0
$805$	0.363785	−	6.24594i	0.0128217	−	0.220141i
$806$	−36.9399	+	39.1541i	−1.30115	+	1.37914i
$807$		0			0
$808$	−4.36918	−	10.1289i	−0.153707	−	0.356334i
$809$	8.37322			0.294387			0.147193	−	0.989108i	$-0.452976\pi$
$809$	8.37322			0.294387			0.147193	+	0.989108i	$0.452976\pi$
$810$		0			0
$811$	12.9504			0.454748			0.227374	−	0.973807i	$-0.426986\pi$
$811$	12.9504			0.454748			0.227374	+	0.973807i	$0.426986\pi$
$812$	7.48875	+	17.3609i	0.262803	+	0.609247i
$813$		0			0
$814$	−0.681667	+	0.722525i	−0.0238924	+	0.0253245i
$815$	0.320079	−	5.49554i	0.0112119	−	0.192501i
$816$		0			0
$817$	−34.0542	+	8.07099i	−1.19140	+	0.282368i
$818$	42.6896	+	15.5377i	1.49261	+	0.543265i
$819$		0			0
$820$	12.6198	−	4.59322i	0.440701	−	0.160402i
$821$	−40.0431	+	26.3368i	−1.39751	+	0.919160i	−0.397516	+	0.917595i	$0.630128\pi$
$821$	−40.0431	+	26.3368i	−1.39751	+	0.919160i	−0.999999	+	0.00156423i	$0.999502\pi$
$822$		0			0
$823$	−27.3812	+	3.20040i	−0.954447	+	0.111559i	−0.579038	−	0.815300i	$-0.696572\pi$
$823$	−27.3812	+	3.20040i	−0.954447	+	0.111559i	−0.375409	+	0.926859i	$0.622498\pi$
$824$	2.03763	+	2.73701i	0.0709842	+	0.0953483i
$825$		0			0
$826$	−3.16942	−	54.4169i	−0.110278	−	1.89340i
$827$	2.70109	+	2.26648i	0.0939260	+	0.0788132i	0.688542	−	0.725197i	$-0.258251\pi$
$827$	2.70109	+	2.26648i	0.0939260	+	0.0788132i	−0.594616	+	0.804010i	$0.702696\pi$
$828$		0			0
$829$	27.6501	−	23.2012i	0.960326	−	0.805810i	−0.0206797	−	0.999786i	$-0.506583\pi$
$829$	27.6501	−	23.2012i	0.960326	−	0.805810i	0.981006	+	0.193977i	$0.0621386\pi$
$830$	0.637869	+	0.676101i	0.0221407	+	0.0234678i
$831$		0			0
$832$	28.5289	+	18.7637i	0.989061	+	0.650516i
$833$	2.61951	+	0.620835i	0.0907607	+	0.0215107i
$834$		0			0
$835$	−2.37080	−	0.277107i	−0.0820449	−	0.00958968i
$836$	−32.6452	−	56.5432i	−1.12906	−	1.95559i
$837$		0			0
$838$	10.4011	−	18.0153i	0.359300	−	0.622327i
$839$	30.8625	−	41.4556i	1.06549	−	1.43120i	0.170372	−	0.985380i	$-0.445503\pi$
$839$	30.8625	−	41.4556i	1.06549	−	1.43120i	0.895120	−	0.445825i	$-0.147090\pi$
$840$		0			0
$841$	5.49785	+	18.3641i	0.189581	+	0.633245i
$842$	21.4640	−	10.7796i	0.739699	−	0.371491i
$843$		0			0
$844$	−18.0106	+	60.1595i	−0.619949	+	2.07077i
$845$	−0.291949	−	1.65573i	−0.0100434	−	0.0569587i
$846$		0			0
$847$	−0.310340	+	1.76003i	−0.0106634	+	0.0604753i
$848$	−0.935253	−	0.469702i	−0.0321167	−	0.0161296i
$849$		0			0
$850$	−10.3314	+	23.9510i	−0.354365	+	0.821511i
$851$	0.310104	−	0.718901i	0.0106302	−	0.0246436i
$852$		0			0
$853$	−29.7345	−	14.9332i	−1.01809	−	0.511304i	−0.140178	−	0.990126i	$-0.544768\pi$
$853$	−29.7345	−	14.9332i	−1.01809	−	0.511304i	−0.877912	+	0.478822i	$0.841064\pi$
$854$	−2.02837	+	11.5034i	−0.0694092	+	0.393639i
$855$		0			0
$856$	−3.28614	−	18.6366i	−0.112318	−	0.636987i
$857$	−10.5852	+	35.3572i	−0.361585	+	1.20778i	0.562889	+	0.826532i	$0.309690\pi$
$857$	−10.5852	+	35.3572i	−0.361585	+	1.20778i	−0.924474	+	0.381245i	$0.875495\pi$
$858$		0			0
$859$	35.5190	−	17.8383i	1.21189	−	0.608635i	0.276080	−	0.961135i	$-0.410964\pi$
$859$	35.5190	−	17.8383i	1.21189	−	0.608635i	0.935812	+	0.352499i	$0.114668\pi$
$860$	−1.44489	−	4.82627i	−0.0492704	−	0.164575i
$861$		0			0
$862$	15.6324	−	20.9979i	0.532441	−	0.715192i
$863$	16.3832	−	28.3766i	0.557691	−	0.965950i	−0.439997	−	0.897999i	$-0.645021\pi$
$863$	16.3832	−	28.3766i	0.557691	−	0.965950i	0.997689	−	0.0679508i	$-0.0216461\pi$
$864$		0			0
$865$	−0.461966	−	0.800148i	−0.0157073	−	0.0272059i
$866$	−3.51145	−	0.410430i	−0.119324	−	0.0139470i
$867$		0			0
$868$	49.0934	+	11.6354i	1.66634	+	0.394930i
$869$	−29.3937	−	19.3325i	−0.997112	−	0.655811i
$870$		0			0
$871$	−2.90758	−	3.08185i	−0.0985195	−	0.104425i
$872$	−10.3157	+	8.65588i	−0.349333	+	0.293125i
$873$		0			0
$874$	71.3212	+	59.8456i	2.41248	+	2.02431i
$875$	−0.624363	−	10.7199i	−0.0211073	−	0.362399i
$876$		0			0
$877$	11.7706	+	15.8107i	0.397466	+	0.533889i	0.955134	−	0.296175i	$-0.0957112\pi$
$877$	11.7706	+	15.8107i	0.397466	+	0.533889i	−0.557668	+	0.830064i	$0.688304\pi$
$878$	37.5774	−	4.39217i	1.26818	−	0.148228i
$879$		0			0
$880$	−3.64350	+	2.39637i	−0.122822	+	0.0807816i
$881$	−33.9631	+	12.3616i	−1.14425	+	0.416472i	−0.843445	−	0.537215i	$-0.819476\pi$
$881$	−33.9631	+	12.3616i	−1.14425	+	0.416472i	−0.300802	+	0.953687i	$0.597254\pi$
$882$		0			0
$883$	1.27966	+	0.465760i	0.0430641	+	0.0156741i	0.363462	−	0.931609i	$-0.381595\pi$
$883$	1.27966	+	0.465760i	0.0430641	+	0.0156741i	−0.320398	+	0.947283i	$0.603817\pi$
$884$	−18.8109	+	4.45826i	−0.632678	+	0.149947i
$885$		0			0
$886$	0.242326	−	4.16058i	0.00814110	−	0.139777i
$887$	−31.9503	+	33.8653i	−1.07279	+	1.13709i	−0.0827062	+	0.996574i	$0.526356\pi$
$887$	−31.9503	+	33.8653i	−1.07279	+	1.13709i	−0.990079	+	0.140512i	$0.955125\pi$
$888$		0			0
$889$	16.7880	+	38.9190i	0.563051	+	1.30530i
$890$	8.23560			0.276058
$891$		0			0
$892$	−19.9351			−0.667476
$893$	−7.93856	−	18.4037i	−0.265654	−	0.615855i
$894$		0			0
$895$	−2.57781	+	2.73232i	−0.0861668	+	0.0913315i
$896$	1.10030	−	18.8914i	0.0367583	−	0.631116i
$897$		0			0
$898$	23.3761	−	5.54023i	0.780069	−	0.184880i
$899$	−24.6507	−	8.97211i	−0.822146	−	0.299237i
$900$		0			0
$901$	0.891979	−	0.324654i	0.0297161	−	0.0108158i
$902$	73.2047	−	48.1475i	2.43745	−	1.60314i
$903$		0			0
$904$	−4.44046	+	0.519015i	−0.147687	+	0.0172622i
$905$	−3.46181	−	4.65001i	−0.115074	−	0.154572i
$906$		0			0
$907$	−0.325964	−	5.59659i	−0.0108235	−	0.185832i	−0.999386	−	0.0350235i	$-0.988849\pi$
$907$	−0.325964	−	5.59659i	−0.0108235	−	0.185832i	0.988563	−	0.150808i	$-0.0481876\pi$
$908$	54.7235	+	45.9184i	1.81606	+	1.52386i
$909$		0			0
$910$	5.40129	−	4.53222i	0.179051	−	0.150242i
$911$	1.86462	+	1.97638i	0.0617776	+	0.0654804i	0.757525	−	0.652806i	$-0.226408\pi$
$911$	1.86462	+	1.97638i	0.0617776	+	0.0654804i	−0.695748	+	0.718286i	$0.744927\pi$
$912$		0			0
$913$	2.80054	+	1.84195i	0.0926844	+	0.0609595i
$914$	0.254259	+	0.0602604i	0.00841013	+	0.00199324i
$915$		0			0
$916$	15.9696	+	1.86658i	0.527650	+	0.0616735i
$917$	0.423503	+	0.733529i	0.0139853	+	0.0242233i
$918$		0			0
$919$	16.3650	−	28.3449i	0.539830	−	0.935013i	−0.459083	−	0.888393i	$-0.651822\pi$
$919$	16.3650	−	28.3449i	0.539830	−	0.935013i	0.998913	−	0.0466194i	$-0.0148448\pi$
$920$	−1.52705	+	2.05118i	−0.0503453	+	0.0676255i
$921$		0			0
$922$	−17.3101	−	57.8198i	−0.570079	−	1.90420i
$923$	9.70543	−	4.87425i	0.319458	−	0.160438i
$924$		0			0
$925$	0.188728	−	0.630394i	0.00620532	−	0.0207272i
$926$	8.96058	+	50.8180i	0.294463	+	1.66998i
$927$		0			0
$928$	−4.34918	+	24.6654i	−0.142769	+	0.809682i
$929$	−9.62615	−	4.83444i	−0.315824	−	0.158613i	0.283825	−	0.958876i	$-0.408397\pi$
$929$	−9.62615	−	4.83444i	−0.315824	−	0.158613i	−0.599649	+	0.800263i	$0.704693\pi$
$930$		0			0
$931$	3.19877	−	7.41559i	0.104836	−	0.243036i
$932$	10.0484	−	23.2948i	0.329147	−	0.763048i
$933$		0			0
$934$	−16.0895	−	8.08046i	−0.526465	−	0.264401i
$935$	0.686828	−	3.89519i	0.0224617	−	0.127386i
$936$		0			0
$937$	2.45640	+	13.9309i	0.0802470	+	0.455103i	0.998281	+	0.0586025i	$0.0186645\pi$
$937$	2.45640	+	13.9309i	0.0802470	+	0.455103i	−0.918034	+	0.396501i	$0.870224\pi$
$938$	−2.06061	+	6.88291i	−0.0672812	+	0.224735i
$939$		0			0
$940$	2.57829	−	1.29487i	0.0840946	−	0.0422339i
$941$	−1.90746	−	6.37136i	−0.0621814	−	0.207700i	0.921253	−	0.388963i	$-0.127167\pi$
$941$	−1.90746	−	6.37136i	−0.0621814	−	0.207700i	−0.983435	+	0.181263i	$0.941982\pi$
$942$		0			0
$943$	−41.2399	+	55.3948i	−1.34296	+	1.80390i
$944$	14.9732	−	25.9343i	0.487335	−	0.844089i
$945$		0			0
$946$	−16.4344	−	28.4653i	−0.534329	−	0.925486i
$947$	14.5295	+	1.69826i	0.472146	+	0.0551860i	0.348839	−	0.937183i	$-0.386576\pi$
$947$	14.5295	+	1.69826i	0.472146	+	0.0551860i	0.123307	+	0.992369i	$0.460650\pi$
$948$		0			0
$949$	−14.9913	−	3.55299i	−0.486637	−	0.115335i
$950$	65.3780	+	42.9998i	2.12114	+	1.39510i
$951$		0			0
$952$	4.29235	+	4.54962i	0.139116	+	0.147454i
$953$	−27.4790	+	23.0576i	−0.890133	+	0.746910i	−0.968237	−	0.250035i	$-0.919558\pi$
$953$	−27.4790	+	23.0576i	−0.890133	+	0.746910i	0.0781042	+	0.996945i	$0.475113\pi$
$954$		0			0
$955$	−0.528629	−	0.443572i	−0.0171060	−	0.0143537i
$956$	3.99370	+	68.5693i	0.129166	+	2.21769i
$957$		0			0
$958$	−12.6193	−	16.9507i	−0.407712	−	0.547652i
$959$	−0.600555	+	0.0701948i	−0.0193929	+	0.00226671i
$960$		0			0
$961$	−32.5852	+	21.4316i	−1.05114	+	0.691343i
$962$	0.829126	−	0.301777i	0.0267321	−	0.00972969i
$963$		0			0
$964$	−15.4311	−	5.61645i	−0.497001	−	0.180894i
$965$	−0.740587	+	0.175522i	−0.0238403	+	0.00565026i
$966$		0			0
$967$	0.741996	−	12.7396i	0.0238610	−	0.409677i	−0.965137	−	0.261746i	$-0.915702\pi$
$967$	0.741996	−	12.7396i	0.0238610	−	0.409677i	0.988998	−	0.147931i	$-0.0472613\pi$
$968$	0.501274	−	0.531319i	0.0161116	−	0.0170772i
$969$		0			0
$970$	0.802196	+	1.85970i	0.0257570	+	0.0597114i
$971$	1.62544			0.0521628			0.0260814	−	0.999660i	$-0.491697\pi$
$971$	1.62544			0.0521628			0.0260814	+	0.999660i	$0.491697\pi$
$972$		0			0
$973$	−13.7343			−0.440301
$974$	−25.6918	−	59.5603i	−0.823218	−	1.90843i
$975$		0			0
$976$	−4.40380	+	4.66776i	−0.140962	+	0.149411i
$977$	−1.99607	+	34.2712i	−0.0638600	+	1.09643i	0.802383	+	0.596810i	$0.203565\pi$
$977$	−1.99607	+	34.2712i	−0.0638600	+	1.09643i	−0.866243	+	0.499623i	$0.833472\pi$
$978$		0			0
$979$	28.8985	−	6.84908i	0.923601	−	0.218897i
$980$	1.09245	+	0.397618i	0.0348969	+	0.0127014i
$981$		0			0
$982$	−22.3965	+	8.15166i	−0.714701	+	0.260130i
$983$	12.0271	−	7.91037i	0.383606	−	0.252302i	−0.343030	−	0.939325i	$-0.611453\pi$
$983$	12.0271	−	7.91037i	0.383606	−	0.252302i	0.726636	+	0.687023i	$0.241083\pi$
$984$		0			0
$985$	−7.21344	+	0.843130i	−0.229839	+	0.0268643i
$986$	−10.1783	−	13.6718i	−0.324143	−	0.435400i
$987$		0			0
$988$	3.37210	+	57.8967i	0.107281	+	1.84194i
$989$	19.8458	+	16.6526i	0.631059	+	0.529521i
$990$		0			0
$991$	9.03189	−	7.57866i	0.286907	−	0.240744i	−0.487963	−	0.872865i	$-0.662260\pi$
$991$	9.03189	−	7.57866i	0.286907	−	0.240744i	0.774870	+	0.632121i	$0.217815\pi$
$992$	45.8646	+	48.6137i	1.45620	+	1.54349i
$993$		0			0
$994$	−15.3870	−	10.1202i	−0.488045	−	0.320992i
$995$	−8.99965	−	2.13296i	−0.285308	−	0.0676193i
$996$		0			0
$997$	24.7960	+	2.89823i	0.785297	+	0.0917880i	0.499285	−	0.866438i	$-0.333596\pi$
$997$	24.7960	+	2.89823i	0.785297	+	0.0917880i	0.286012	+	0.958226i	$0.407670\pi$
$998$	−20.7037	−	35.8599i	−0.655364	−	1.13512i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.676.2		144
3.2	odd	2		729.2.g.d.676.7		144
9.2	odd	6		729.2.g.c.190.7		144
9.4	even	3		243.2.g.a.64.7		144
9.5	odd	6		81.2.g.a.4.2	✓	144
9.7	even	3		729.2.g.b.190.2		144
81.7	even	27		243.2.g.a.19.7		144
81.14	odd	54		6561.2.a.c.1.63		72
81.20	odd	54		729.2.g.c.541.7		144
81.34	even	27	inner	729.2.g.a.55.2		144
81.47	odd	54		729.2.g.d.55.7		144
81.61	even	27		729.2.g.b.541.2		144
81.67	even	27		6561.2.a.d.1.10		72
81.74	odd	54		81.2.g.a.61.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.2	✓	144	9.5	odd	6
81.2.g.a.61.2	yes	144	81.74	odd	54
243.2.g.a.19.7		144	81.7	even	27
243.2.g.a.64.7		144	9.4	even	3
729.2.g.a.55.2		144	81.34	even	27	inner
729.2.g.a.676.2		144	1.1	even	1	trivial
729.2.g.b.190.2		144	9.7	even	3
729.2.g.b.541.2		144	81.61	even	27
729.2.g.c.190.7		144	9.2	odd	6
729.2.g.c.541.7		144	81.20	odd	54
729.2.g.d.55.7		144	81.47	odd	54
729.2.g.d.676.7		144	3.2	odd	2
6561.2.a.c.1.63		72	81.14	odd	54
6561.2.a.d.1.10		72	81.67	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.837555 - 1.94167i) q^{2} +(-1.69610 + 1.79777i) q^{4} +(-0.0261173 + 0.448416i) q^{5} +(-2.37407 + 0.562666i) q^{7} +(0.937080 + 0.341069i) q^{8} +O(q^{10})\)	\(q+(-0.837555 - 1.94167i) q^{2} +(-1.69610 + 1.79777i) q^{4} +(-0.0261173 + 0.448416i) q^{5} +(-2.37407 + 0.562666i) q^{7} +(0.937080 + 0.341069i) q^{8} +(0.892552 - 0.324862i) q^{10} +(2.86177 - 1.88222i) q^{11} +(-3.02196 + 0.353216i) q^{13} +(3.08093 + 4.13841i) q^{14} +(0.164808 + 2.82964i) q^{16} +(-1.96933 - 1.65247i) q^{17} +(-5.90790 + 4.95731i) q^{19} +(-0.761850 - 0.807514i) q^{20} +(-6.05154 - 3.98016i) q^{22} +(5.55505 + 1.31657i) q^{23} +(4.76580 + 0.557042i) q^{25} +(3.21689 + 5.57181i) q^{26} +(3.01514 - 5.22237i) q^{28} +(-1.87232 + 2.51496i) q^{29} +(2.39959 + 8.01520i) q^{31} +(7.13849 - 3.58509i) q^{32} +(-1.55912 + 5.20783i) q^{34} +(-0.190304 - 1.07927i) q^{35} +(0.0238144 - 0.135058i) q^{37} +(14.5737 + 7.31917i) q^{38} +(-0.177415 + 0.411294i) q^{40} +(-4.79132 + 11.1075i) q^{41} +(4.05525 + 2.03662i) q^{43} +(-1.47008 + 8.33724i) q^{44} +(-2.09631 - 11.8888i) q^{46} +(-0.745357 + 2.48967i) q^{47} +(-0.935796 + 0.469974i) q^{49} +(-2.91003 - 9.72016i) q^{50} +(4.49056 - 6.03187i) q^{52} +(-0.184618 + 0.319767i) q^{53} +(0.769276 + 1.33242i) q^{55} +(-2.41661 - 0.282461i) q^{56} +(6.45139 + 1.52901i) q^{58} +(-8.82708 - 5.80566i) q^{59} +(1.55368 + 1.64680i) q^{61} +(13.5531 - 11.3724i) q^{62} +(-8.59733 - 7.21402i) q^{64} +(-0.0794626 - 1.36432i) q^{65} +(0.831589 + 1.11702i) q^{67} +(6.31095 - 0.737644i) q^{68} +(-1.93619 + 1.27346i) q^{70} +(-3.35434 + 1.22088i) q^{71} +(4.75835 + 1.73190i) q^{73} +(-0.282184 + 0.0668789i) q^{74} +(1.10832 - 19.0291i) q^{76} +(-5.73500 + 6.07875i) q^{77} +(-4.06819 - 9.43112i) q^{79} -1.27316 q^{80} +25.5802 q^{82} +(0.387605 + 0.898569i) q^{83} +(0.792427 - 0.839924i) q^{85} +(0.557957 - 9.57975i) q^{86} +(3.32368 - 0.787727i) q^{88} +(8.14767 + 2.96551i) q^{89} +(6.97561 - 2.53891i) q^{91} +(-11.7888 + 7.75364i) q^{92} +(5.45839 - 0.637994i) q^{94} +(-2.06864 - 2.77867i) q^{95} +(0.123983 + 2.12870i) q^{97} +(1.69632 + 1.42338i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

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Database

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