LMFDB - Embedded newform 729.2.g.a.55.2

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			55.2
Character	$\chi$	$=$	729.55
Dual form			729.2.g.a.676.2

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

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	0.313683	+	0.949528i	$0.398437\pi$
$2$	−0.837555	+	1.94167i	−0.592241	+	1.37297i	−0.905924	+	0.423441i	$0.860822\pi$
$3$		0			0
$3$		0			0
$4$	−1.69610	−	1.79777i	−0.848052	−	0.898883i
$5$	−0.0261173	−	0.448416i	−0.0116800	−	0.200538i	−0.999100	−	0.0424181i	$-0.986494\pi$
$5$	−0.0261173	−	0.448416i	−0.0116800	−	0.200538i	0.987420	−	0.158120i	$-0.0505432\pi$
$6$		0			0
$7$	−2.37407	−	0.562666i	−0.897316	−	0.212668i	−0.244020	−	0.969770i	$-0.578466\pi$
$7$	−2.37407	−	0.562666i	−0.897316	−	0.212668i	−0.653296	+	0.757103i	$0.726614\pi$
$8$	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	0.902006	−	0.431723i	$-0.142094\pi$
$11$	2.86177	+	1.88222i	0.862857	+	0.567510i	−0.0391488	+	0.999233i	$0.512465\pi$
$12$		0			0
$13$	−3.02196	−	0.353216i	−0.838141	−	0.0979646i	−0.313817	−	0.949484i	$-0.601608\pi$
$13$	−3.02196	−	0.353216i	−0.838141	−	0.0979646i	−0.524324	+	0.851519i	$0.675682\pi$
$14$	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	−0.849570	−	0.527476i	$-0.823138\pi$
$17$	−1.96933	+	1.65247i	−0.477634	+	0.400782i	0.371936	+	0.928258i	$0.378694\pi$
$18$		0			0
$19$	−5.90790	−	4.95731i	−1.35536	−	1.13729i	−0.977384	−	0.211472i	$-0.932174\pi$
$19$	−5.90790	−	4.95731i	−1.35536	−	1.13729i	−0.377980	−	0.925814i	$-0.623381\pi$
$20$	−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	0.393836	−	0.919181i	$-0.371148\pi$
$23$	5.55505	−	1.31657i	1.15831	−	0.274524i	0.764472	+	0.644657i	$0.223000\pi$
$24$		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	0.593542	−	0.804803i	$-0.297729\pi$
$29$	−1.87232	−	2.51496i	−0.347680	−	0.467016i	−0.941223	+	0.337787i	$0.890322\pi$
$30$		0			0
$31$	2.39959	−	8.01520i	0.430980	−	1.43957i	−0.416691	−	0.909048i	$-0.636810\pi$
$31$	2.39959	−	8.01520i	0.430980	−	1.43957i	0.847670	−	0.530524i	$-0.178005\pi$
$32$	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	0.986703	−	0.162535i	$-0.0519672\pi$
$37$	0.0238144	+	0.135058i	0.00391506	+	0.0222034i	−0.982788	+	0.184739i	$0.940856\pi$
$38$	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	−0.675502	−	0.737358i	$-0.736073\pi$
$41$	−4.79132	−	11.1075i	−0.748279	−	1.73471i	−0.0727768	−	0.997348i	$-0.523186\pi$
$42$		0			0
$43$	4.05525	−	2.03662i	0.618420	−	0.310582i	−0.111867	−	0.993723i	$-0.535683\pi$
$43$	4.05525	−	2.03662i	0.618420	−	0.310582i	0.730286	+	0.683141i	$0.239387\pi$
$44$	−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	0.886263	−	0.463182i	$-0.153292\pi$
$47$	−0.745357	−	2.48967i	−0.108722	−	0.363155i	−0.994985	+	0.100027i	$0.968107\pi$
$48$		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	0.853067	−	0.521801i	$-0.174740\pi$
$53$	−0.184618	−	0.319767i	−0.0253592	−	0.0439234i	−0.878426	+	0.477877i	$0.841406\pi$
$54$		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	−0.973517	−	0.228617i	$-0.926580\pi$
$59$	−8.82708	+	5.80566i	−1.14919	+	0.755832i	−0.175671	+	0.984449i	$0.556209\pi$
$60$		0			0
$61$	1.55368	−	1.64680i	0.198928	−	0.210851i	−0.620229	−	0.784421i	$-0.712960\pi$
$61$	1.55368	−	1.64680i	0.198928	−	0.210851i	0.819157	+	0.573569i	$0.194442\pi$
$62$	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	−0.748418	−	0.663227i	$-0.769186\pi$
$67$	0.831589	−	1.11702i	0.101595	−	0.136465i	0.850013	+	0.526761i	$0.176594\pi$
$68$	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	0.135216	−	0.990816i	$-0.456827\pi$
$71$	−3.35434	−	1.22088i	−0.398087	−	0.144892i	−0.533303	+	0.845924i	$0.679049\pi$
$72$		0			0
$73$	4.75835	−	1.73190i	0.556922	−	0.202703i	−0.0481971	−	0.998838i	$-0.515348\pi$
$73$	4.75835	−	1.73190i	0.556922	−	0.202703i	0.605119	+	0.796135i	$0.293125\pi$
$74$	−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	0.520577	+	0.853815i	$0.325717\pi$
$79$	−4.06819	+	9.43112i	−0.457707	+	1.06108i	−0.978284	+	0.207269i	$0.933542\pi$
$80$	−1.27316			−0.142344
$81$		0			0
$82$	25.5802			2.82486
$83$	0.387605	−	0.898569i	0.0425452	−	0.0986308i	−0.895618	−	0.444823i	$-0.853266\pi$
$83$	0.387605	−	0.898569i	0.0425452	−	0.0986308i	0.938163	+	0.346193i	$0.112526\pi$
$84$		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	0.128058	−	0.991767i	$-0.459126\pi$
$89$	8.14767	−	2.96551i	0.863651	−	0.314343i	0.735593	+	0.677423i	$0.236903\pi$
$90$		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	−0.986147	−	0.165872i	$-0.946956\pi$
$97$	0.123983	−	2.12870i	0.0125886	−	0.216137i	0.998736	−	0.0502654i	$-0.0160067\pi$
$98$	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	−0.984981	−	0.172661i	$-0.944763\pi$
$101$	−7.59108	+	8.04607i	−0.755341	+	0.800614i	0.229641	+	0.973276i	$0.426245\pi$
$102$		0			0
$103$	2.85881	−	1.88027i	0.281686	−	0.185268i	−0.400802	−	0.916165i	$-0.631268\pi$
$103$	2.85881	−	1.88027i	0.281686	−	0.185268i	0.682488	+	0.730897i	$0.260898\pi$
$104$	−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	−0.113758	+	0.993508i	$0.536289\pi$
$107$	−9.48845	+	16.4345i	−0.917283	+	1.58878i	−0.803524	+	0.595272i	$0.797044\pi$
$108$		0			0
$109$	−6.75185	−	11.6945i	−0.646710	−	1.12013i	−0.983904	−	0.178699i	$-0.942811\pi$
$109$	−6.75185	−	11.6945i	−0.646710	−	1.12013i	0.337194	−	0.941435i	$-0.390522\pi$
$110$	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	0.250268	−	0.968177i	$-0.419481\pi$
$113$	−4.00629	−	2.01203i	−0.376880	−	0.189276i	−0.627148	+	0.778900i	$0.715778\pi$
$114$		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	0.493596	+	0.869691i	$0.335682\pi$
$127$	−3.01665	+	17.1083i	−0.267685	+	1.51811i	−0.761280	+	0.648423i	$0.775429\pi$
$128$	−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	−0.962229	−	0.272242i	$-0.912235\pi$
$131$	−0.0995656	+	0.332572i	−0.00869909	+	0.0290570i	0.953530	+	0.301299i	$0.0974201\pi$
$132$		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	−0.105572	−	0.994412i	$-0.533667\pi$
$137$	0.246145	−	0.0287702i	0.0210296	−	0.00245801i	0.126601	+	0.991954i	$0.459593\pi$
$138$		0			0
$139$	5.47744	−	1.29818i	0.464591	−	0.110110i	0.00834744	−	0.999965i	$-0.497343\pi$
$139$	5.47744	−	1.29818i	0.464591	−	0.110110i	0.456243	+	0.889855i	$0.349195\pi$
$140$	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	0.0347366	−	0.999397i	$-0.488941\pi$
$149$	−1.97673	−	0.231046i	−0.161940	−	0.0189280i	−0.196676	+	0.980468i	$0.563015\pi$
$150$		0			0
$151$	−9.65170	−	6.34802i	−0.785444	−	0.516595i	0.0922962	−	0.995732i	$-0.470579\pi$
$151$	−9.65170	−	6.34802i	−0.785444	−	0.516595i	−0.877740	+	0.479137i	$0.840950\pi$
$152$	−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	−0.409375	−	0.912366i	$-0.634253\pi$
$157$	−1.36185	−	23.3820i	−0.108687	−	1.86609i	0.300687	−	0.953723i	$-0.402784\pi$
$158$	−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	−0.988934	−	0.148356i	$-0.952602\pi$
$167$	−0.308984	−	5.30505i	−0.0239099	−	0.410517i	0.965024	−	0.262161i	$-0.0844351\pi$
$168$		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	0.482497	−	0.875898i	$-0.339730\pi$
$173$	−1.71855	−	1.13031i	−0.130659	−	0.0859359i	−0.613156	+	0.789962i	$0.710100\pi$
$174$		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	−0.371171	−	0.928565i	$-0.621043\pi$
$179$	6.40636	−	5.37558i	0.478834	−	0.401789i	0.850005	+	0.526775i	$0.176599\pi$
$180$		0			0
$181$	−9.88668	−	8.29591i	−0.734871	−	0.616630i	0.196584	−	0.980487i	$-0.437015\pi$
$181$	−9.88668	−	8.29591i	−0.734871	−	0.616630i	−0.931455	+	0.363857i	$0.881460\pi$
$182$	−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	0.767692	−	0.640819i	$-0.221405\pi$
$191$	−0.917423	−	1.23231i	−0.0663824	−	0.0891671i	−0.834074	+	0.551652i	$0.813998\pi$
$192$		0			0
$193$	0.485971	−	1.62326i	0.0349810	−	0.116845i	−0.938716	−	0.344692i	$-0.887983\pi$
$193$	0.485971	−	1.62326i	0.0349810	−	0.116845i	0.973697	+	0.227847i	$0.0731686\pi$
$194$	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	−0.705025	−	0.709182i	$-0.749064\pi$
$197$	2.80764	−	15.9229i	0.200036	−	1.13446i	0.905062	−	0.425280i	$-0.139825\pi$
$198$		0			0
$199$	−3.57558	−	20.2781i	−0.253466	−	1.43748i	−0.799980	−	0.600027i	$-0.795156\pi$
$199$	−3.57558	−	20.2781i	−0.253466	−	1.43748i	0.546513	−	0.837450i	$-0.315955\pi$
$200$	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	0.999167	−	0.0408081i	$-0.0129932\pi$
$211$	22.7053	+	11.4030i	1.56310	+	0.785016i	0.563928	+	0.825824i	$0.309290\pi$
$212$	−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	−0.515021	−	0.857178i	$-0.672216\pi$
$223$	5.53502	−	5.86678i	0.370652	−	0.392869i	0.885673	+	0.464309i	$0.153697\pi$
$224$	−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	0.226538	+	0.974002i	$0.427259\pi$
$227$	−1.68056	+	28.8542i	−0.111543	+	1.91512i	−0.338081	+	0.941117i	$0.609778\pi$
$228$		0			0
$229$	−3.88467	+	5.21802i	−0.256706	+	0.344817i	−0.911729	−	0.410793i	$-0.865252\pi$
$229$	−3.88467	+	5.21802i	−0.256706	+	0.344817i	0.655022	+	0.755610i	$0.272659\pi$
$230$	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	0.00615899	−	0.999981i	$-0.498040\pi$
$233$	−9.64551	−	3.51068i	−0.631898	−	0.229992i	−0.638057	+	0.769989i	$0.720262\pi$
$234$		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	0.935649	+	0.352931i	$0.114815\pi$
$239$	19.0707	+	20.2137i	1.23358	+	1.30752i	0.297931	+	0.954588i	$0.403704\pi$
$240$		0			0
$241$	2.63158	−	6.10070i	0.169515	−	0.392980i	−0.812189	−	0.583395i	$-0.801724\pi$
$241$	2.63158	−	6.10070i	0.169515	−	0.392980i	0.981704	+	0.190415i	$0.0609832\pi$
$242$	−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	−0.646546	−	0.762875i	$-0.723787\pi$
$251$	−10.3211	+	3.75657i	−0.651461	+	0.237113i	−0.00491575	+	0.999988i	$0.501565\pi$
$252$		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	0.218492	+	0.975839i	$0.429886\pi$
$257$	−12.4886	+	16.7751i	−0.779016	+	1.04640i	−0.997507	+	0.0705612i	$0.977521\pi$
$258$		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	−0.00246701	−	0.999997i	$-0.500785\pi$
$263$	16.1521	−	17.1202i	0.995982	−	1.05568i	0.998449	−	0.0556818i	$-0.0177332\pi$
$264$		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	−0.924777	−	0.380509i	$-0.875749\pi$
$269$	−2.17903	+	3.77420i	−0.132858	+	0.230117i	0.791919	+	0.610626i	$0.209082\pi$
$270$		0			0
$271$	−0.604369	−	1.04680i	−0.0367128	−	0.0635885i	0.847085	−	0.531457i	$-0.178355\pi$
$271$	−0.604369	−	1.04680i	−0.0367128	−	0.0635885i	−0.883798	+	0.467869i	$0.845022\pi$
$272$	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	0.997447	−	0.0714063i	$-0.0227487\pi$
$277$	2.07798	+	6.94094i	0.124854	+	0.417041i	−0.872593	+	0.488447i	$0.837564\pi$
$278$	−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	−0.376151	−	0.926559i	$-0.622752\pi$
$281$	2.38776	−	1.19918i	0.142442	−	0.0715371i	0.518593	+	0.855021i	$0.326456\pi$
$282$		0			0
$283$	10.2442	+	23.7487i	0.608954	+	1.41171i	0.891748	+	0.452533i	$0.149479\pi$
$283$	10.2442	+	23.7487i	0.608954	+	1.41171i	−0.282794	+	0.959181i	$0.591261\pi$
$284$	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	−0.657504	−	0.753451i	$-0.728388\pi$
$293$	5.23549	−	17.4878i	0.305861	−	1.02165i	0.963365	−	0.268195i	$-0.0864271\pi$
$294$		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	−0.614019	−	0.789291i	$-0.710448\pi$
$307$	0.992726	−	0.832996i	0.0566579	−	0.0475416i	0.670677	+	0.741750i	$0.266004\pi$
$308$	−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	−0.494104	−	0.869403i	$-0.664504\pi$
$311$	−20.7282	−	2.42278i	−1.17539	−	0.137383i	−0.681284	+	0.732020i	$0.738578\pi$
$312$		0			0
$313$	19.4581	+	12.7978i	1.09984	+	0.723375i	0.963613	−	0.267303i	$-0.0861324\pi$
$313$	19.4581	+	12.7978i	1.09984	+	0.723375i	0.136226	+	0.990678i	$0.456503\pi$
$314$	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	−0.286958	−	0.957943i	$-0.592644\pi$
$317$	−17.3294	−	4.10715i	−0.973317	−	0.230680i	−0.686359	+	0.727263i	$0.740792\pi$
$318$		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	0.520842	−	0.853653i	$-0.325618\pi$
$331$	10.9736	+	2.60079i	0.603164	+	0.142953i	0.0823225	+	0.996606i	$0.473766\pi$
$332$	−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	−0.500025	−	0.866011i	$-0.666676\pi$
$337$	−21.7773	−	2.54541i	−1.18629	−	0.138657i	−0.686263	+	0.727354i	$0.740750\pi$
$338$	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	−0.386153	−	0.922435i	$-0.626196\pi$
$347$	−5.90961	+	1.40060i	−0.317245	+	0.0751884i	0.0689086	+	0.997623i	$0.478048\pi$
$348$		0			0
$349$	9.10876	−	1.06466i	0.487581	−	0.0569900i	0.131249	−	0.991349i	$-0.458101\pi$
$349$	9.10876	−	1.06466i	0.487581	−	0.0569900i	0.356332	+	0.934359i	$0.384027\pi$
$350$	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	0.663535	−	0.748145i	$-0.269055\pi$
$353$	−4.57466	−	6.14483i	−0.243484	−	0.327056i	−0.907019	+	0.421089i	$0.861648\pi$
$354$		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	−0.755610	−	0.655021i	$-0.772660\pi$
$359$	3.38137	−	19.1767i	0.178462	−	1.01211i	0.934072	−	0.357085i	$-0.116229\pi$
$360$		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	−0.632905	−	0.774229i	$-0.718138\pi$
$367$	−7.46794	+	3.75054i	−0.389823	+	0.195777i	0.243082	+	0.970006i	$0.421842\pi$
$368$	−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	0.724203	−	0.689587i	$-0.242208\pi$
$373$	11.6562	+	5.85394i	0.603533	+	0.303106i	−0.120670	+	0.992693i	$0.538504\pi$
$374$	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	−0.795114	−	0.606460i	$-0.792589\pi$
$379$	2.48513	−	4.30437i	0.127653	−	0.221101i	0.922767	+	0.385359i	$0.125922\pi$
$380$	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	−0.468775	−	0.883317i	$-0.655305\pi$
$383$	3.06528	−	2.01606i	0.156628	−	0.103016i	0.625404	+	0.780301i	$0.284934\pi$
$384$		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	−0.980198	−	0.198022i	$-0.936548\pi$
$389$	0.322693	−	5.54043i	0.0163612	−	0.280911i	0.996559	−	0.0828890i	$-0.0264147\pi$
$390$		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	−0.0557747	−	0.998443i	$-0.517763\pi$
$397$	10.8249	−	3.93994i	0.543286	−	0.197740i	0.599061	+	0.800703i	$0.295541\pi$
$398$	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	0.993038	−	0.117794i	$-0.0375824\pi$
$401$	16.3745	+	17.3559i	0.817703	+	0.866714i	−0.175335	+	0.984509i	$0.556101\pi$
$402$		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	0.251795	−	0.967781i	$-0.418979\pi$
$409$	−14.7429	−	15.6266i	−0.728989	−	0.772683i	−0.980784	+	0.195097i	$0.937498\pi$
$410$	−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	−0.635128	−	0.772407i	$-0.719053\pi$
$419$	5.87447	−	7.89078i	0.286987	−	0.385490i	0.922115	+	0.386917i	$0.126460\pi$
$420$		0			0
$421$	0.660438	−	11.3393i	0.0321878	−	0.552643i	−0.943211	−	0.332195i	$-0.892211\pi$
$421$	0.660438	−	11.3393i	0.0321878	−	0.552643i	0.975399	−	0.220448i	$-0.0707520\pi$
$422$	−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	−0.677562	−	0.735465i	$-0.736964\pi$
$431$	6.18977	−	10.7210i	0.298151	−	0.516412i	0.975713	+	0.219053i	$0.0702969\pi$
$432$		0			0
$433$	0.835935	+	1.44788i	0.0401725	+	0.0695808i	0.885413	−	0.464806i	$-0.153876\pi$
$433$	0.835935	+	1.44788i	0.0401725	+	0.0695808i	−0.845240	+	0.534387i	$0.820543\pi$
$434$	−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	−0.988736	−	0.149668i	$-0.952180\pi$
$439$	−5.13129	−	17.1397i	−0.244903	−	0.818033i	0.743833	−	0.668365i	$-0.233006\pi$
$440$	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	−0.406468	−	0.913665i	$-0.633240\pi$
$443$	1.76123	−	0.884525i	0.0836788	−	0.0420251i	0.490146	+	0.871640i	$0.336943\pi$
$444$		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	−0.995313	−	0.0967089i	$-0.969168\pi$
$449$	−1.97278	−	11.1882i	−0.0931011	−	0.528003i	0.902212	−	0.431294i	$-0.141943\pi$
$450$		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	0.800394	−	0.599474i	$-0.204624\pi$
$457$	−0.0737908	−	0.0991182i	−0.00345179	−	0.00463655i	−0.803846	+	0.594838i	$0.797216\pi$
$458$	−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	0.573436	−	0.819250i	$-0.305610\pi$
$461$	28.3491	−	3.31353i	1.32035	−	0.154327i	0.746911	+	0.664924i	$0.231536\pi$
$462$		0			0
$463$	−23.7448	+	5.62762i	−1.10351	+	0.261537i	−0.741713	−	0.670718i	$-0.765986\pi$
$463$	−23.7448	+	5.62762i	−1.10351	+	0.261537i	−0.361801	+	0.932255i	$0.617838\pi$
$464$	−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	0.781102	−	0.624404i	$-0.214658\pi$
$467$	6.52240	+	5.47294i	0.301821	+	0.253258i	−0.479281	+	0.877662i	$0.659103\pi$
$468$		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	0.446677	−	0.894695i	$-0.352607\pi$
$479$	9.72408	+	2.30465i	0.444305	+	0.105302i	−0.00237286	+	0.999997i	$0.500755\pi$
$480$		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	0.980270	+	0.197664i	$0.0633355\pi$
$491$	0.655352	+	11.2520i	0.0295756	+	0.507794i	−0.950694	+	0.310130i	$0.899627\pi$
$492$		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	0.539680	−	0.841870i	$-0.318545\pi$
$499$	19.4492	+	2.27328i	0.870664	+	0.101766i	0.330984	+	0.943636i	$0.392619\pi$
$500$	−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	−0.944638	−	0.328114i	$-0.893587\pi$
$503$	−17.6179	+	14.7832i	−0.785544	+	0.659150i	0.159094	+	0.987263i	$0.449143\pi$
$504$		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	0.477219	−	0.878784i	$-0.341645\pi$
$509$	29.2859	−	6.94089i	1.29808	−	0.307650i	0.820856	+	0.571135i	$0.193497\pi$
$510$		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	0.730963	+	0.682418i	$0.239071\pi$
$521$	−4.32127	+	24.5071i	−0.189318	+	1.07368i	−0.920281	+	0.391259i	$0.872040\pi$
$522$		0			0
$523$	2.05500	+	11.6545i	0.0898590	+	0.509616i	0.996202	+	0.0870730i	$0.0277513\pi$
$523$	2.05500	+	11.6545i	0.0898590	+	0.509616i	−0.906343	+	0.422543i	$0.861138\pi$
$524$	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	−0.754017	−	0.656855i	$-0.771886\pi$
$541$	4.46220	−	7.72875i	0.191845	−	0.332285i	0.945862	+	0.324570i	$0.105220\pi$
$542$	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	−0.983460	−	0.181125i	$-0.942026\pi$
$547$	−17.4348	+	18.4798i	−0.745458	+	0.790139i	0.238002	+	0.971265i	$0.423507\pi$
$548$	−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	−0.615981	−	0.787761i	$-0.711240\pi$
$557$	−37.6248	−	13.6943i	−1.59421	−	0.580246i	−0.978232	+	0.207515i	$0.933462\pi$
$558$		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	0.540622	−	0.841266i	$-0.318189\pi$
$563$	−7.84566	−	8.31591i	−0.330655	−	0.350474i	−0.871277	+	0.490792i	$0.836708\pi$
$564$		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	−0.981340	−	0.192281i	$-0.938412\pi$
$569$	−4.00846	+	9.29267i	−0.168044	+	0.389569i	0.813296	+	0.581850i	$0.197671\pi$
$570$		0			0
$571$	−24.1948	−	25.6450i	−1.01252	−	1.07321i	−0.997308	−	0.0733255i	$-0.976639\pi$
$571$	−24.1948	−	25.6450i	−1.01252	−	1.07321i	−0.0152132	−	0.999884i	$-0.504843\pi$
$572$	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	0.316106	−	0.948724i	$-0.397624\pi$
$577$	−1.23876	−	0.450874i	−0.0515705	−	0.0187701i	−0.367677	+	0.929954i	$0.619847\pi$
$578$	−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	−0.880609	−	0.473844i	$-0.842866\pi$
$587$	−8.63402	+	9.15153i	−0.356364	+	0.377724i	0.524245	+	0.851568i	$0.324348\pi$
$588$		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	−0.999878	−	0.0156219i	$-0.995027\pi$
$593$	−11.8449	+	20.5159i	−0.486410	+	0.842487i	0.513468	+	0.858109i	$0.328361\pi$
$594$		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	0.411493	−	0.911413i	$-0.365007\pi$
$599$	−1.80734	−	0.907679i	−0.0738458	−	0.0370868i	−0.485339	+	0.874326i	$0.661304\pi$
$600$		0			0
$601$	−8.35262	−	27.8997i	−0.340710	−	1.13805i	−0.941039	−	0.338298i	$-0.890149\pi$
$601$	−8.35262	−	27.8997i	−0.340710	−	1.13805i	0.600329	−	0.799753i	$-0.295036\pi$
$602$	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	0.978677	+	0.205407i	$0.0658517\pi$
$607$	11.2464	+	26.0720i	0.456475	+	1.05823i	−0.522201	+	0.852822i	$0.674889\pi$
$608$	−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	−0.703769	−	0.710429i	$-0.748501\pi$
$613$	4.96510	−	28.1585i	0.200538	−	1.13731i	0.904308	−	0.426881i	$-0.140388\pi$
$614$	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	−0.727888	−	0.685696i	$-0.759498\pi$
$617$	6.38498	−	21.3273i	0.257050	−	0.858606i	0.984938	−	0.172910i	$-0.0553170\pi$
$618$		0			0
$619$	3.21871	+	4.32348i	0.129371	+	0.173775i	0.862089	−	0.506757i	$-0.169156\pi$
$619$	3.21871	+	4.32348i	0.129371	+	0.173775i	−0.732718	+	0.680532i	$0.761749\pi$
$620$	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	0.196576	−	0.980489i	$-0.437018\pi$
$631$	30.0508	−	25.2156i	1.19630	−	1.00382i	0.999728	−	0.0233298i	$-0.00742677\pi$
$632$	−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	0.895380	−	0.445303i	$-0.146904\pi$
$641$	37.8673	+	8.97472i	1.49567	+	0.354480i	0.600289	+	0.799783i	$0.295052\pi$
$642$		0			0
$643$	−1.72381	−	29.5966i	−0.0679803	−	1.16718i	−0.843956	−	0.536413i	$-0.819779\pi$
$643$	−1.72381	−	29.5966i	−0.0679803	−	1.16718i	0.775975	−	0.630763i	$-0.217258\pi$
$644$	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	−0.693239	−	0.720708i	$-0.743817\pi$
$653$	−2.25785	−	38.7658i	−0.0883565	−	1.51702i	0.604882	−	0.796315i	$-0.293220\pi$
$654$		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	0.947766	−	0.318965i	$-0.103335\pi$
$659$	26.4483	+	17.3953i	1.03028	+	0.677625i	0.0825118	+	0.996590i	$0.473706\pi$
$660$		0			0
$661$	0.614307	+	0.0718022i	0.0238938	+	0.00279278i	0.128031	−	0.991770i	$-0.459134\pi$
$661$	0.614307	+	0.0718022i	0.0238938	+	0.00279278i	−0.104138	+	0.994563i	$0.533208\pi$
$662$	−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	−0.112129	−	0.993694i	$-0.535767\pi$
$673$	0.205619	−	0.0240334i	0.00792602	−	0.000926419i	0.120055	+	0.992767i	$0.461693\pi$
$674$	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	−0.997260	−	0.0739735i	$-0.976432\pi$
$677$	−20.3499	−	27.3346i	−0.782109	−	1.05055i	0.215152	−	0.976581i	$-0.430975\pi$
$678$		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	0.429468	+	0.903082i	$0.358701\pi$
$683$	−7.39527	+	41.9406i	−0.282972	+	1.60481i	−0.712441	+	0.701732i	$0.752410\pi$
$684$		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	−0.236457	−	0.971642i	$-0.575986\pi$
$691$	10.5599	−	5.30337i	0.401717	−	0.201750i	0.638174	+	0.769892i	$0.279690\pi$
$692$	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	0.755174	−	0.655524i	$-0.227552\pi$
$701$	−5.03353	−	8.71832i	−0.190114	−	0.329286i	−0.945288	+	0.326238i	$0.894219\pi$
$702$		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	0.147591	−	0.989048i	$-0.452848\pi$
$709$	29.9923	−	31.7900i	1.12638	−	1.19390i	0.978793	−	0.204850i	$-0.0656705\pi$
$710$	−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	0.0862528	−	0.996273i	$-0.472511\pi$
$719$	−13.0871	−	4.76331i	−0.488066	−	0.177641i	−0.574319	+	0.818632i	$0.694733\pi$
$720$		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	−0.373879	−	0.927478i	$-0.621972\pi$
$727$	15.0269	−	34.8362i	0.557315	−	1.29200i	0.931194	−	0.364524i	$-0.118768\pi$
$728$	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	0.929840	−	0.367965i	$-0.119945\pi$
$733$	13.7653	+	14.5903i	0.508431	+	0.538906i	−0.421408	+	0.906871i	$0.638464\pi$
$734$	−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	−0.0551270	−	0.998479i	$-0.517556\pi$
$739$	−20.0939	−	7.31359i	−0.739167	−	0.269035i	−0.684040	+	0.729445i	$0.739779\pi$
$740$	−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	−0.623249	−	0.782023i	$-0.714188\pi$
$743$	8.30473	−	11.1552i	0.304671	−	0.409244i	0.927920	+	0.372779i	$0.121595\pi$
$744$		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	−0.547378	−	0.836885i	$-0.684374\pi$
$751$	0.116685	−	0.0767451i	0.00425791	−	0.00280047i	0.551636	+	0.834085i	$0.314004\pi$
$752$	−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	0.983409	+	0.181403i	$0.0580639\pi$
$757$	17.8510	+	30.9188i	0.648804	+	1.12376i	−0.334605	+	0.942359i	$0.608603\pi$
$758$	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	0.839325	−	0.543630i	$-0.182950\pi$
$761$	24.9511	+	12.5309i	0.904478	+	0.454246i	0.0651523	+	0.997875i	$0.479247\pi$
$762$		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	0.900428	−	0.435005i	$-0.143253\pi$
$769$	−0.939924	−	2.17899i	−0.0338945	−	0.0785764i	−0.934322	+	0.356429i	$0.883994\pi$
$770$	−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	0.923128	+	0.384492i	$0.125623\pi$
$773$	5.20402	+	29.5135i	0.187176	+	1.06153i	−0.735953	+	0.677033i	$0.763265\pi$
$774$		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
$783$

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more