LMFDB - Embedded newform 729.2.g.d.55.1

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			55.1
Character	$\chi$	$=$	729.55
Dual form			729.2.g.d.676.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.971435 + 2.25204i) q^{2} +(-2.75551 - 2.92067i) q^{4} +(0.232513 + 3.99210i) q^{5} +(-1.28109 - 0.303625i) q^{7} +(4.64483 - 1.69058i) q^{8} +O(q^{10})$	\(q+(-0.971435 + 2.25204i) q^{2} +(-2.75551 - 2.92067i) q^{4} +(0.232513 + 3.99210i) q^{5} +(-1.28109 - 0.303625i) q^{7} +(4.64483 - 1.69058i) q^{8} +(-9.21624 - 3.35444i) q^{10} +(-2.04879 - 1.34751i) q^{11} +(-1.30311 - 0.152312i) q^{13} +(1.92827 - 2.59012i) q^{14} +(-0.237953 + 4.08549i) q^{16} +(0.206593 - 0.173352i) q^{17} +(1.02778 + 0.862409i) q^{19} +(11.0189 - 11.6794i) q^{20} +(5.02492 - 3.30494i) q^{22} +(-5.82111 + 1.37963i) q^{23} +(-10.9166 + 1.27597i) q^{25} +(1.60890 - 2.78670i) q^{26} +(2.64328 + 4.57830i) q^{28} +(-3.30965 - 4.44563i) q^{29} +(0.369677 - 1.23481i) q^{31} +(-0.135207 - 0.0679036i) q^{32} +(0.189704 + 0.633655i) q^{34} +(0.914230 - 5.18486i) q^{35} +(-0.00841562 - 0.0477273i) q^{37} +(-2.94060 + 1.47682i) q^{38} +(7.82896 + 18.1496i) q^{40} +(1.64212 + 3.80687i) q^{41} +(5.59352 - 2.80917i) q^{43} +(1.70983 + 9.69693i) q^{44} +(2.54785 - 14.4496i) q^{46} +(2.38036 + 7.95094i) q^{47} +(-4.70641 - 2.36365i) q^{49} +(7.73125 - 25.8242i) q^{50} +(3.14588 + 4.22565i) q^{52} +(-5.79529 - 10.0377i) q^{53} +(4.90304 - 8.49231i) q^{55} +(-6.46377 + 0.755507i) q^{56} +(13.2268 - 3.13482i) q^{58} +(8.15031 - 5.36055i) q^{59} +(2.93311 - 3.10891i) q^{61} +(2.42172 + 2.03206i) q^{62} +(-5.98568 + 5.02258i) q^{64} +(0.305054 - 5.23757i) q^{65} +(-0.791752 + 1.06351i) q^{67} +(-1.07557 - 0.125716i) q^{68} +(10.7884 + 7.09563i) q^{70} +(7.40721 + 2.69600i) q^{71} +(-8.12155 + 2.95600i) q^{73} +(0.115659 + 0.0274117i) q^{74} +(-0.313243 - 5.37818i) q^{76} +(2.21556 + 2.34836i) q^{77} +(2.07109 - 4.80133i) q^{79} -16.3650 q^{80} -10.1684 q^{82} +(-2.24944 + 5.21479i) q^{83} +(0.740074 + 0.784433i) q^{85} +(0.892623 + 15.3257i) q^{86} +(-11.7944 - 2.79532i) q^{88} +(-8.61170 + 3.13440i) q^{89} +(1.62316 + 0.590783i) q^{91} +(20.0696 + 13.2000i) q^{92} +(-20.2182 - 2.36317i) q^{94} +(-3.20385 + 4.30352i) q^{95} +(-0.721447 + 12.3868i) q^{97} +(9.89500 - 8.30289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.971435	+	2.25204i	−0.686908	+	1.59243i	0.113887	+	0.993494i	$0.463670\pi$
$2$	−0.971435	+	2.25204i	−0.686908	+	1.59243i	−0.800795	+	0.598938i	$0.795590\pi$
$3$		0			0
$3$		0			0
$4$	−2.75551	−	2.92067i	−1.37775	−	1.46033i
$5$	0.232513	+	3.99210i	0.103983	+	1.78532i	0.498954	+	0.866629i	$0.333718\pi$
$5$	0.232513	+	3.99210i	0.103983	+	1.78532i	−0.394971	+	0.918694i	$0.629245\pi$
$6$		0			0
$7$	−1.28109	−	0.303625i	−0.484208	−	0.114759i	−0.0187406	−	0.999824i	$-0.505966\pi$
$7$	−1.28109	−	0.303625i	−0.484208	−	0.114759i	−0.465468	+	0.885065i	$0.654114\pi$
$8$	4.64483	−	1.69058i	1.64220	−	0.597711i
$9$		0			0
$10$	−9.21624	−	3.35444i	−2.91443	−	1.06077i
$11$	−2.04879	−	1.34751i	−0.617734	−	0.406290i	0.201713	−	0.979445i	$-0.435349\pi$
$11$	−2.04879	−	1.34751i	−0.617734	−	0.406290i	−0.819447	+	0.573154i	$0.805720\pi$
$12$		0			0
$13$	−1.30311	−	0.152312i	−0.361418	−	0.0422437i	−0.0665537	−	0.997783i	$-0.521200\pi$
$13$	−1.30311	−	0.152312i	−0.361418	−	0.0422437i	−0.294864	+	0.955539i	$0.595274\pi$
$14$	1.92827	−	2.59012i	0.515353	−	0.692239i
$15$		0			0
$16$	−0.237953	+	4.08549i	−0.0594882	+	1.02137i
$17$	0.206593	−	0.173352i	0.0501061	−	0.0420440i	−0.617391	−	0.786657i	$-0.711810\pi$
$17$	0.206593	−	0.173352i	0.0501061	−	0.0420440i	0.667497	+	0.744613i	$0.267366\pi$
$18$		0			0
$19$	1.02778	+	0.862409i	0.235789	+	0.197850i	0.753024	−	0.657993i	$-0.228594\pi$
$19$	1.02778	+	0.862409i	0.235789	+	0.197850i	−0.517235	+	0.855843i	$0.673039\pi$
$20$	11.0189	−	11.6794i	2.46390	−	2.61159i
$21$		0			0
$22$	5.02492	−	3.30494i	1.07132	−	0.704616i
$23$	−5.82111	+	1.37963i	−1.21379	+	0.287673i	−0.787156	−	0.616754i	$-0.788447\pi$
$23$	−5.82111	+	1.37963i	−1.21379	+	0.287673i	−0.426630	+	0.904426i	$0.640299\pi$
$24$		0			0
$25$	−10.9166	+	1.27597i	−2.18333	+	0.255194i
$26$	1.60890	−	2.78670i	0.315531	−	0.546516i
$27$		0			0
$28$	2.64328	+	4.57830i	0.499533	+	0.865216i
$29$	−3.30965	−	4.44563i	−0.614587	−	0.825533i	0.380475	−	0.924791i	$-0.375760\pi$
$29$	−3.30965	−	4.44563i	−0.614587	−	0.825533i	−0.995062	+	0.0992581i	$0.968353\pi$
$30$		0			0
$31$	0.369677	−	1.23481i	0.0663960	−	0.221778i	−0.918352	−	0.395764i	$-0.870480\pi$
$31$	0.369677	−	1.23481i	0.0663960	−	0.221778i	0.984748	+	0.173986i	$0.0556649\pi$
$32$	−0.135207	−	0.0679036i	−0.0239015	−	0.0120038i
$33$		0			0
$34$	0.189704	+	0.633655i	0.0325339	+	0.108671i
$35$	0.914230	−	5.18486i	0.154533	−	0.876401i
$36$		0			0
$37$	−0.00841562	−	0.0477273i	−0.00138352	−	0.00784632i	0.984108	−	0.177570i	$-0.0568236\pi$
$37$	−0.00841562	−	0.0477273i	−0.00138352	−	0.00784632i	−0.985492	+	0.169724i	$0.945712\pi$
$38$	−2.94060	+	1.47682i	−0.477028	+	0.239572i
$39$		0			0
$40$	7.82896	+	18.1496i	1.23787	+	2.86970i
$41$	1.64212	+	3.80687i	0.256456	+	0.594533i	0.996994	−	0.0774824i	$-0.0246882\pi$
$41$	1.64212	+	3.80687i	0.256456	+	0.594533i	−0.740537	+	0.672015i	$0.765429\pi$
$42$		0			0
$43$	5.59352	−	2.80917i	0.853003	−	0.428394i	0.0321157	−	0.999484i	$-0.489775\pi$
$43$	5.59352	−	2.80917i	0.853003	−	0.428394i	0.820888	+	0.571090i	$0.193479\pi$
$44$	1.70983	+	9.69693i	0.257767	+	1.46187i
$45$		0			0
$46$	2.54785	−	14.4496i	0.375660	−	2.13048i
$47$	2.38036	+	7.95094i	0.347210	+	1.15976i	0.936154	+	0.351590i	$0.114359\pi$
$47$	2.38036	+	7.95094i	0.347210	+	1.15976i	−0.588944	+	0.808174i	$0.700456\pi$
$48$		0			0
$49$	−4.70641	−	2.36365i	−0.672345	−	0.337664i
$50$	7.73125	−	25.8242i	1.09336	−	3.65209i
$51$		0			0
$52$	3.14588	+	4.22565i	0.436256	+	0.585993i
$53$	−5.79529	−	10.0377i	−0.796044	−	1.37879i	−0.922174	−	0.386775i	$-0.873589\pi$
$53$	−5.79529	−	10.0377i	−0.796044	−	1.37879i	0.126130	−	0.992014i	$-0.459744\pi$
$54$		0			0
$55$	4.90304	−	8.49231i	0.661125	−	1.14510i
$56$	−6.46377	+	0.755507i	−0.863758	+	0.100959i
$57$		0			0
$58$	13.2268	−	3.13482i	1.73677	−	0.411622i
$59$	8.15031	−	5.36055i	1.06108	−	0.697884i	0.106041	−	0.994362i	$-0.466183\pi$
$59$	8.15031	−	5.36055i	1.06108	−	0.697884i	0.955040	+	0.296478i	$0.0958122\pi$
$60$		0			0
$61$	2.93311	−	3.10891i	0.375546	−	0.398055i	−0.511842	−	0.859080i	$-0.671037\pi$
$61$	2.93311	−	3.10891i	0.375546	−	0.398055i	0.887387	+	0.461025i	$0.152518\pi$
$62$	2.42172	+	2.03206i	0.307558	+	0.258072i
$63$		0			0
$64$	−5.98568	+	5.02258i	−0.748210	+	0.627823i
$65$	0.305054	−	5.23757i	0.0378372	−	0.649640i
$66$		0			0
$67$	−0.791752	+	1.06351i	−0.0967278	+	0.129928i	−0.847852	−	0.530233i	$-0.822105\pi$
$67$	−0.791752	+	1.06351i	−0.0967278	+	0.129928i	0.751124	+	0.660161i	$0.229512\pi$
$68$	−1.07557	−	0.125716i	−0.130432	−	0.0152453i
$69$		0			0
$70$	10.7884	+	7.09563i	1.28946	+	0.848090i
$71$	7.40721	+	2.69600i	0.879074	+	0.319957i	0.741836	−	0.670581i	$-0.233955\pi$
$71$	7.40721	+	2.69600i	0.879074	+	0.319957i	0.137238	+	0.990538i	$0.456177\pi$
$72$		0			0
$73$	−8.12155	+	2.95600i	−0.950556	+	0.345974i	−0.770326	−	0.637650i	$-0.779906\pi$
$73$	−8.12155	+	2.95600i	−0.950556	+	0.345974i	−0.180230	+	0.983624i	$0.557684\pi$
$74$	0.115659	+	0.0274117i	0.0134451	+	0.00318654i
$75$		0			0
$76$	−0.313243	−	5.37818i	−0.0359315	−	0.616919i
$77$	2.21556	+	2.34836i	0.252486	+	0.267620i
$78$		0			0
$79$	2.07109	−	4.80133i	0.233016	−	0.540192i	−0.761085	−	0.648653i	$-0.775333\pi$
$79$	2.07109	−	4.80133i	0.233016	−	0.540192i	0.994101	+	0.108460i	$0.0345921\pi$
$80$	−16.3650			−1.82967
$81$		0			0
$82$	−10.1684			−1.12291
$83$	−2.24944	+	5.21479i	−0.246908	+	0.572398i	−0.995928	−	0.0901496i	$-0.971265\pi$
$83$	−2.24944	+	5.21479i	−0.246908	+	0.572398i	0.749020	+	0.662548i	$0.230525\pi$
$84$		0			0
$85$	0.740074	+	0.784433i	0.0802723	+	0.0850837i
$86$	0.892623	+	15.3257i	0.0962540	+	1.65262i
$87$		0			0
$88$	−11.7944	−	2.79532i	−1.25729	−	0.297982i
$89$	−8.61170	+	3.13440i	−0.912838	+	0.332246i	−0.755385	−	0.655281i	$-0.772550\pi$
$89$	−8.61170	+	3.13440i	−0.912838	+	0.332246i	−0.157453	+	0.987527i	$0.550328\pi$
$90$		0			0
$91$	1.62316	+	0.590783i	0.170154	+	0.0619309i
$92$	20.0696	+	13.2000i	2.09240	+	1.37619i
$93$		0			0
$94$	−20.2182	−	2.36317i	−2.08535	−	0.243742i
$95$	−3.20385	+	4.30352i	−0.328708	+	0.441532i
$96$		0			0
$97$	−0.721447	+	12.3868i	−0.0732518	+	1.25769i	0.738729	+	0.674002i	$0.235426\pi$
$97$	−0.721447	+	12.3868i	−0.0732518	+	1.25769i	−0.811981	+	0.583684i	$0.801611\pi$
$98$	9.89500	−	8.30289i	0.999546	−	0.838719i
$99$		0			0
$100$	33.8076	+	28.3679i	3.38076	+	2.83679i
$101$	−8.54489	+	9.05705i	−0.850248	+	0.901211i	−0.996112	−	0.0880941i	$-0.971922\pi$
$101$	−8.54489	+	9.05705i	−0.850248	+	0.901211i	0.145864	+	0.989305i	$0.453404\pi$
$102$		0			0
$103$	5.22232	−	3.43478i	0.514571	−	0.338439i	−0.265519	−	0.964106i	$-0.585543\pi$
$103$	5.22232	−	3.43478i	0.514571	−	0.338439i	0.780090	+	0.625667i	$0.215173\pi$
$104$	−6.31023	+	1.49555i	−0.618769	+	0.146651i
$105$		0			0
$106$	28.2351	−	3.30021i	2.74244	−	0.320545i
$107$	−9.92075	+	17.1832i	−0.959075	+	1.66117i	−0.234320	+	0.972159i	$0.575286\pi$
$107$	−9.92075	+	17.1832i	−0.959075	+	1.66117i	−0.724755	+	0.689007i	$0.758047\pi$
$108$		0			0
$109$	−1.91684	−	3.32007i	−0.183600	−	0.318005i	0.759504	−	0.650503i	$-0.225442\pi$
$109$	−1.91684	−	3.32007i	−0.183600	−	0.318005i	−0.943104	+	0.332498i	$0.892109\pi$
$110$	14.3620	+	19.2915i	1.36937	+	1.83938i
$111$		0			0
$112$	1.54530	−	5.16165i	0.146017	−	0.487730i
$113$	−3.11864	−	1.56624i	−0.293377	−	0.147339i	0.296023	−	0.955181i	$-0.404339\pi$
$113$	−3.11864	−	1.56624i	−0.293377	−	0.147339i	−0.589400	+	0.807841i	$0.700636\pi$
$114$		0			0
$115$	−6.86111	−	22.9177i	−0.639802	−	2.13709i
$116$	−3.86445	+	21.9164i	−0.358805	+	2.03488i
$117$		0			0
$118$	4.15466	+	23.5622i	0.382467	+	2.16908i
$119$	−0.317299	+	0.159353i	−0.0290867	+	0.0146079i
$120$		0			0
$121$	−1.97511	−	4.57883i	−0.179556	−	0.416257i
$122$	4.15207	+	9.62557i	0.375910	+	0.871458i
$123$		0			0
$124$	−4.62511	+	2.32282i	−0.415347	+	0.208595i
$125$	−4.16009	−	23.5930i	−0.372090	−	2.11022i
$126$		0			0
$127$	2.28154	−	12.9392i	0.202454	−	1.14817i	−0.698943	−	0.715177i	$-0.746346\pi$
$127$	2.28154	−	12.9392i	0.202454	−	1.14817i	0.901397	−	0.432994i	$-0.142543\pi$
$128$	−5.58314	−	18.6490i	−0.493484	−	1.64835i
$129$		0			0
$130$	11.4989	+	5.77495i	1.00852	+	0.506496i
$131$	1.24215	−	4.14908i	0.108528	−	0.362507i	−0.886423	−	0.462877i	$-0.846817\pi$
$131$	1.24215	−	4.14908i	0.108528	−	0.362507i	0.994950	+	0.100369i	$0.0320025\pi$
$132$		0			0
$133$	−1.05483	−	1.41689i	−0.0914656	−	0.122860i
$134$	−1.62592	−	2.81618i	−0.140458	−	0.243281i
$135$		0			0
$136$	0.666523	−	1.15445i	0.0571539	−	0.0989935i
$137$	−22.2688	+	2.60285i	−1.90255	+	0.222376i	−0.984663	−	0.174465i	$-0.944180\pi$
$137$	−22.2688	+	2.60285i	−1.90255	+	0.222376i	−0.917887	+	0.396841i	$0.870106\pi$
$138$		0			0
$139$	−9.34045	+	2.21373i	−0.792247	+	0.187766i	−0.606765	−	0.794882i	$-0.707533\pi$
$139$	−9.34045	+	2.21373i	−0.792247	+	0.187766i	−0.185482	+	0.982648i	$0.559385\pi$
$140$	−17.6624	+	11.6168i	−1.49275	+	0.981795i
$141$		0			0
$142$	−13.2671	+	14.0623i	−1.11335	+	1.18008i
$143$	2.46456	+	2.06801i	0.206097	+	0.172936i
$144$		0			0
$145$	16.9779	−	14.2461i	1.40994	−	1.18308i
$146$	1.23252	−	21.1616i	0.102004	−	1.75135i
$147$		0			0
$148$	−0.116206	+	0.156092i	−0.00955211	+	0.0128307i
$149$	−16.5311	−	1.93221i	−1.35428	−	0.158293i	−0.592208	−	0.805785i	$-0.701743\pi$
$149$	−16.5311	−	1.93221i	−1.35428	−	0.158293i	−0.762071	+	0.647493i	$0.775818\pi$
$150$		0			0
$151$	1.53093	+	1.00691i	0.124585	+	0.0819412i	0.610272	−	0.792192i	$-0.291060\pi$
$151$	1.53093	+	1.00691i	0.124585	+	0.0819412i	−0.485687	+	0.874133i	$0.661430\pi$
$152$	6.23183	+	2.26820i	0.505468	+	0.183975i
$153$		0			0
$154$	−7.44086	+	2.70825i	−0.599601	+	0.218237i
$155$	5.01543	+	1.18868i	0.402849	+	0.0954770i
$156$		0			0
$157$	0.628412	+	10.7894i	0.0501528	+	0.861090i	0.925771	+	0.378085i	$0.123417\pi$
$157$	0.628412	+	10.7894i	0.0501528	+	0.861090i	−0.875618	+	0.483004i	$0.839546\pi$
$158$	8.80086	+	9.32836i	0.700159	+	0.742125i
$159$		0			0
$160$	0.239641	−	0.555549i	0.0189453	−	0.0439200i
$161$	7.87629			0.620738
$162$		0			0
$163$	3.76716			0.295067			0.147533	−	0.989057i	$-0.452867\pi$
$163$	3.76716			0.295067			0.147533	+	0.989057i	$0.452867\pi$
$164$	6.59372	−	15.2860i	0.514883	−	1.19363i
$165$		0			0
$166$	−9.55873	−	10.1317i	−0.741901	−	0.786369i
$167$	−0.688138	−	11.8149i	−0.0532498	−	0.914263i	−0.914121	−	0.405441i	$-0.867118\pi$
$167$	−0.688138	−	11.8149i	−0.0532498	−	0.914263i	0.860872	−	0.508822i	$-0.169919\pi$
$168$		0			0
$169$	−10.9747	−	2.60105i	−0.844206	−	0.200081i
$170$	−2.48551	+	0.904650i	−0.190630	+	0.0693835i
$171$		0			0
$172$	−23.6176	−	8.59612i	−1.80083	−	0.655448i
$173$	7.99384	+	5.25763i	0.607761	+	0.399730i	0.815753	−	0.578400i	$-0.196323\pi$
$173$	7.99384	+	5.25763i	0.607761	+	0.399730i	−0.207993	+	0.978130i	$0.566693\pi$
$174$		0			0
$175$	14.3726	+	1.67992i	1.08647	+	0.126990i
$176$	5.99277	−	8.04968i	0.451722	−	0.606768i
$177$		0			0
$178$	1.30691	−	22.4387i	0.0979569	−	1.68185i
$179$	−1.08723	+	0.912294i	−0.0812633	+	0.0681880i	−0.682514	−	0.730872i	$-0.739114\pi$
$179$	−1.08723	+	0.912294i	−0.0812633	+	0.0681880i	0.601251	+	0.799060i	$0.294669\pi$
$180$		0			0
$181$	−7.58350	−	6.36331i	−0.563677	−	0.472981i	0.315864	−	0.948804i	$-0.397706\pi$
$181$	−7.58350	−	6.36331i	−0.563677	−	0.472981i	−0.879541	+	0.475823i	$0.842150\pi$
$182$	−2.90726	+	3.08152i	−0.215501	+	0.228417i
$183$		0			0
$184$	−24.7057	+	16.2492i	−1.82133	+	1.19791i
$185$	0.188576	−	0.0446932i	0.0138644	−	0.00328591i
$186$		0			0
$187$	−0.656860	+	0.0767759i	−0.0480343	+	0.00561441i
$188$	16.6630	−	28.8611i	1.21527	−	2.10491i
$189$		0			0
$190$	−6.57936	−	11.3958i	−0.477317	−	0.826737i
$191$	−10.6439	−	14.2973i	−0.770166	−	1.03451i	−0.998147	−	0.0608474i	$-0.980620\pi$
$191$	−10.6439	−	14.2973i	−0.770166	−	1.03451i	0.227981	−	0.973666i	$-0.426788\pi$
$192$		0			0
$193$	−7.92466	+	26.4702i	−0.570430	+	1.90537i	−0.184533	+	0.982826i	$0.559077\pi$
$193$	−7.92466	+	26.4702i	−0.570430	+	1.90537i	−0.385897	+	0.922542i	$0.626108\pi$
$194$	−27.1946	−	13.6577i	−1.95246	−	0.980563i
$195$		0			0
$196$	6.06513	+	20.2589i	0.433223	+	1.44707i
$197$	−1.04040	+	5.90042i	−0.0741256	+	0.420387i	0.925052	+	0.379840i	$0.124021\pi$
$197$	−1.04040	+	5.90042i	−0.0741256	+	0.420387i	−0.999178	+	0.0405468i	$0.987090\pi$
$198$		0			0
$199$	2.78863	+	15.8151i	0.197681	+	1.12110i	0.908549	+	0.417779i	$0.137191\pi$
$199$	2.78863	+	15.8151i	0.197681	+	1.12110i	−0.710868	+	0.703326i	$0.751698\pi$
$200$	−48.5488	+	24.3821i	−3.43292	+	1.72408i
$201$		0			0
$202$	−12.0960	−	28.0418i	−0.851074	−	1.97301i
$203$	2.89017	+	6.70017i	0.202850	+	0.470260i
$204$		0			0
$205$	−14.8156	+	7.44067i	−1.03477	+	0.519679i
$206$	2.66210	+	15.0975i	0.185478	+	1.05190i
$207$		0			0
$208$	0.932348	−	5.28761i	0.0646467	−	0.366630i
$209$	−0.943600	−	3.15184i	−0.0652701	−	0.218017i
$210$		0			0
$211$	−9.00002	−	4.51998i	−0.619587	−	0.311168i	0.111175	−	0.993801i	$-0.464539\pi$
$211$	−9.00002	−	4.51998i	−0.619587	−	0.311168i	−0.730762	+	0.682633i	$0.760835\pi$
$212$	−13.3479	+	44.5852i	−0.916740	+	3.06212i
$213$		0			0
$214$	−29.0600	−	39.0343i	−1.98650	−	2.66833i
$215$	12.5151	+	21.6767i	0.853520	+	1.47834i
$216$		0			0
$217$	−0.848510	+	1.46966i	−0.0576006	+	0.0997672i
$218$	9.33901	−	1.09157i	0.632518	−	0.0739307i
$219$		0			0
$220$	−38.3136	+	9.08049i	−2.58310	+	0.612206i
$221$	−0.295617	+	0.194430i	−0.0198853	+	0.0130788i
$222$		0			0
$223$	8.95026	−	9.48672i	0.599354	−	0.635278i	−0.354676	−	0.934989i	$-0.615409\pi$
$223$	8.95026	−	9.48672i	0.599354	−	0.635278i	0.954030	+	0.299711i	$0.0968903\pi$
$224$	0.152596	+	0.128043i	0.0101957	+	0.00855525i
$225$		0			0
$226$	6.55678	−	5.50179i	0.436151	−	0.365974i
$227$	−0.947304	+	16.2646i	−0.0628748	+	1.07952i	0.808372	+	0.588673i	$0.200349\pi$
$227$	−0.947304	+	16.2646i	−0.0628748	+	1.07952i	−0.871246	+	0.490846i	$0.836688\pi$
$228$		0			0
$229$	−4.02339	+	5.40434i	−0.265873	+	0.357129i	−0.914931	−	0.403609i	$-0.867756\pi$
$229$	−4.02339	+	5.40434i	−0.265873	+	0.357129i	0.649059	+	0.760738i	$0.275163\pi$
$230$	58.2767	+	6.81156i	3.84265	+	0.449141i
$231$		0			0
$232$	−22.8885	−	15.0540i	−1.50270	−	0.988343i
$233$	−12.9692	−	4.72040i	−0.849641	−	0.309244i	−0.119747	−	0.992804i	$-0.538208\pi$
$233$	−12.9692	−	4.72040i	−0.849641	−	0.309244i	−0.729894	+	0.683560i	$0.760431\pi$
$234$		0			0
$235$	−31.1875	+	11.3513i	−2.03445	+	0.740479i
$236$	−38.1147	−	9.03334i	−2.48105	−	0.588020i
$237$		0			0
$238$	−0.0506351	−	0.869371i	−0.00328218	−	0.0563529i
$239$	−8.60415	−	9.11986i	−0.556556	−	0.589915i	0.386607	−	0.922244i	$-0.373647\pi$
$239$	−8.60415	−	9.11986i	−0.556556	−	0.589915i	−0.943163	+	0.332330i	$0.892165\pi$
$240$		0			0
$241$	5.42266	−	12.5711i	0.349304	−	0.809778i	−0.649475	−	0.760383i	$-0.725011\pi$
$241$	5.42266	−	12.5711i	0.349304	−	0.809778i	0.998779	−	0.0493949i	$-0.0157293\pi$
$242$	12.2304			0.786199
$243$		0			0
$244$	−17.1623			−1.09870
$245$	8.34163	−	19.3381i	0.532927	−	1.23546i
$246$		0			0
$247$	−1.20796	−	1.28036i	−0.0768604	−	0.0814672i
$248$	−0.370454	−	6.36044i	−0.0235238	−	0.403889i
$249$		0			0
$250$	57.1737	+	13.5504i	3.61598	+	0.857003i
$251$	−12.4879	+	4.54521i	−0.788226	+	0.286891i	−0.704599	−	0.709606i	$-0.748873\pi$
$251$	−12.4879	+	4.54521i	−0.788226	+	0.286891i	−0.0836277	+	0.996497i	$0.526651\pi$
$252$		0			0
$253$	13.7853	+	5.01745i	0.866676	+	0.315444i
$254$	26.9233	+	17.7077i	1.68932	+	1.11108i
$255$		0			0
$256$	31.9000	+	3.72858i	1.99375	+	0.233036i
$257$	−2.00787	+	2.69704i	−0.125248	+	0.168237i	−0.860324	−	0.509747i	$-0.829739\pi$
$257$	−2.00787	+	2.69704i	−0.125248	+	0.168237i	0.735076	+	0.677984i	$0.237146\pi$
$258$		0			0
$259$	−0.00371001	+	0.0636984i	−0.000230529	+	0.00395803i
$260$	−16.1378	+	13.5412i	−1.00082	+	0.839790i
$261$		0			0
$262$	8.13723	+	6.82794i	0.502720	+	0.421832i
$263$	16.7605	−	17.7651i	1.03350	−	1.09544i	0.0381328	−	0.999273i	$-0.487859\pi$
$263$	16.7605	−	17.7651i	1.03350	−	1.09544i	0.995365	−	0.0961708i	$-0.0306595\pi$
$264$		0			0
$265$	38.7242	−	25.4693i	2.37881	−	1.56457i
$266$	4.21558	−	0.999112i	0.258474	−	0.0612595i
$267$		0			0
$268$	5.28783	−	0.618059i	0.323006	−	0.0377539i
$269$	0.417322	−	0.722824i	0.0254446	−	0.0440713i	−0.853023	−	0.521874i	$-0.825233\pi$
$269$	0.417322	−	0.722824i	0.0254446	−	0.0440713i	0.878467	+	0.477802i	$0.158567\pi$
$270$		0			0
$271$	14.1085	+	24.4366i	0.857029	+	1.48442i	0.874750	+	0.484575i	$0.161026\pi$
$271$	14.1085	+	24.4366i	0.857029	+	1.48442i	−0.0177208	+	0.999843i	$0.505641\pi$
$272$	0.659069	+	0.885283i	0.0399619	+	0.0536782i
$273$		0			0
$274$	15.7710	−	52.6787i	0.952758	−	3.18243i
$275$	24.0853	+	12.0961i	1.45240	+	0.729422i
$276$		0			0
$277$	7.69228	+	25.6940i	0.462185	+	1.54380i	0.798465	+	0.602042i	$0.205646\pi$
$277$	7.69228	+	25.6940i	0.462185	+	1.54380i	−0.336280	+	0.941762i	$0.609169\pi$
$278$	4.08824	−	23.1856i	0.245196	−	1.39058i
$279$		0			0
$280$	−4.51897	−	25.6284i	−0.270060	−	1.53159i
$281$	13.0781	−	6.56809i	0.780177	−	0.391819i	−0.0136939	−	0.999906i	$-0.504359\pi$
$281$	13.0781	−	6.56809i	0.780177	−	0.391819i	0.793871	+	0.608087i	$0.208063\pi$
$282$		0			0
$283$	0.462413	+	1.07199i	0.0274876	+	0.0637234i	0.931407	−	0.363980i	$-0.118582\pi$
$283$	0.462413	+	1.07199i	0.0274876	+	0.0637234i	−0.903919	+	0.427703i	$0.859323\pi$
$284$	−12.5365	−	29.0629i	−0.743905	−	1.72456i
$285$		0			0
$286$	−7.05141	+	3.54135i	−0.416959	+	0.209405i
$287$	−0.947854	−	5.37555i	−0.0559500	−	0.317308i
$288$		0			0
$289$	−2.93939	+	16.6701i	−0.172905	+	0.980594i
$290$	15.5899	+	52.0740i	0.915473	+	3.05789i
$291$		0			0
$292$	31.0125	+	15.5751i	1.81487	+	0.911463i
$293$	−4.79954	+	16.0316i	−0.280392	+	0.936575i	0.695538	+	0.718490i	$0.255166\pi$
$293$	−4.79954	+	16.0316i	−0.280392	+	0.936575i	−0.975930	+	0.218085i	$0.930019\pi$
$294$		0			0
$295$	23.2949	+	31.2905i	1.35628	+	1.82180i
$296$	−0.119776	−	0.207458i	−0.00696184	−	0.0120583i
$297$		0			0
$298$	20.4103	−	35.3516i	1.18234	−	2.04786i
$299$	7.79569	−	0.911186i	0.450837	−	0.0526952i
$300$		0			0
$301$	−8.01876	+	1.90048i	−0.462194	+	0.109542i
$302$	−3.75480	+	2.46957i	−0.216064	+	0.142108i
$303$		0			0
$304$	−3.76793	+	3.99377i	−0.216105	+	0.229058i
$305$	13.0931	+	10.9864i	0.749707	+	0.629079i
$306$		0			0
$307$	−15.6362	+	13.1204i	−0.892407	+	0.748818i	−0.968691	−	0.248268i	$-0.920139\pi$
$307$	−15.6362	+	13.1204i	−0.892407	+	0.748818i	0.0762844	+	0.997086i	$0.475694\pi$
$308$	0.753776	−	12.9418i	0.0429504	−	0.737429i
$309$		0			0
$310$	−7.54912	+	10.1402i	−0.428761	+	0.575926i
$311$	−6.59097	−	0.770374i	−0.373740	−	0.0436839i	−0.0728501	−	0.997343i	$-0.523209\pi$
$311$	−6.59097	−	0.770374i	−0.373740	−	0.0436839i	−0.300889	+	0.953659i	$0.597284\pi$
$312$		0			0
$313$	7.66936	+	5.04422i	0.433498	+	0.285116i	0.747444	−	0.664325i	$-0.231281\pi$
$313$	7.66936	+	5.04422i	0.433498	+	0.285116i	−0.313946	+	0.949441i	$0.601651\pi$
$314$	−24.9087	−	9.06601i	−1.40568	−	0.511625i
$315$		0			0
$316$	−19.7300	+	7.18114i	−1.10990	+	0.403971i
$317$	0.0487426	+	0.0115522i	0.00273766	+	0.000648836i	0.231984	−	0.972719i	$-0.425478\pi$
$317$	0.0487426	+	0.0115522i	0.00273766	+	0.000648836i	−0.229247	+	0.973368i	$0.573626\pi$
$318$		0			0
$319$	0.790245	+	13.5680i	0.0442452	+	0.759661i
$320$	−21.4424	−	22.7276i	−1.19867	−	1.27051i
$321$		0			0
$322$	−7.65130	+	17.7377i	−0.426390	+	0.988483i
$323$	0.361832			0.0201329
$324$		0			0
$325$	14.4199			0.799874
$326$	−3.65955	+	8.48379i	−0.202684	+	0.469874i
$327$		0			0
$328$	14.0632	+	14.9061i	0.776510	+	0.823053i
$329$	−0.635356	−	10.9086i	−0.0350283	−	0.601413i
$330$		0			0
$331$	−18.0022	−	4.26660i	−0.989491	−	0.234514i	−0.296164	−	0.955137i	$-0.595708\pi$
$331$	−18.0022	−	4.26660i	−0.989491	−	0.234514i	−0.693327	+	0.720623i	$0.743856\pi$
$332$	21.4290	−	7.79954i	1.17607	−	0.428055i
$333$		0			0
$334$	27.2761	+	9.92767i	1.49248	+	0.543218i
$335$	−4.42972	−	2.91347i	−0.242022	−	0.159180i
$336$		0			0
$337$	3.62501	+	0.423702i	0.197467	+	0.0230805i	0.214251	−	0.976779i	$-0.431269\pi$
$337$	3.62501	+	0.423702i	0.197467	+	0.0230805i	−0.0167846	+	0.999859i	$0.505343\pi$
$338$	16.5188	−	22.1887i	0.898507	−	1.20690i
$339$		0			0
$340$	0.251787	−	4.32302i	0.0136551	−	0.234449i
$341$	−2.42131	+	2.03172i	−0.131121	+	0.110024i
$342$		0			0
$343$	12.3716	+	10.3810i	0.668005	+	0.560523i
$344$	21.2318	−	22.5044i	1.14474	−	1.21336i
$345$		0			0
$346$	−19.6059	+	12.8950i	−1.05402	+	0.693239i
$347$	3.98981	−	0.945603i	0.214184	−	0.0507626i	−0.122123	−	0.992515i	$-0.538970\pi$
$347$	3.98981	−	0.945603i	0.214184	−	0.0507626i	0.336307	+	0.941752i	$0.390822\pi$
$348$		0			0
$349$	−7.51393	+	0.878252i	−0.402211	+	0.0470118i	−0.314794	−	0.949160i	$-0.601935\pi$
$349$	−7.51393	+	0.878252i	−0.402211	+	0.0470118i	−0.0874174	+	0.996172i	$0.527861\pi$
$350$	−17.7453	+	30.7358i	−0.948528	+	1.64290i
$351$		0			0
$352$	0.185511	+	0.321314i	0.00988775	+	0.0171261i
$353$	1.22443	+	1.64470i	0.0651699	+	0.0875384i	0.833513	−	0.552500i	$-0.186326\pi$
$353$	1.22443	+	1.64470i	0.0651699	+	0.0875384i	−0.768343	+	0.640038i	$0.778919\pi$
$354$		0			0
$355$	−9.04045	+	30.1972i	−0.479817	+	1.60270i
$356$	32.8842	+	16.5150i	1.74286	+	0.875296i
$357$		0			0
$358$	−0.998349	−	3.33472i	−0.0527644	−	0.176245i
$359$	−1.74531	+	9.89817i	−0.0921141	+	0.522405i	0.903479	+	0.428631i	$0.141004\pi$
$359$	−1.74531	+	9.89817i	−0.0921141	+	0.522405i	−0.995594	+	0.0937737i	$0.970107\pi$
$360$		0			0
$361$	−2.98674	−	16.9386i	−0.157197	−	0.891506i
$362$	21.6973	−	10.8968i	1.14038	−	0.572722i
$363$		0			0
$364$	−2.74716	−	6.36863i	−0.143990	−	0.333807i
$365$	−13.6890	−	31.7348i	−0.716517	−	1.66107i
$366$		0			0
$367$	29.0225	−	14.5756i	1.51496	−	0.760842i	0.519363	−	0.854554i	$-0.326169\pi$
$367$	29.0225	−	14.5756i	1.51496	−	0.760842i	0.995599	+	0.0937115i	$0.0298731\pi$
$368$	−4.25131	−	24.1104i	−0.221615	−	1.25684i
$369$		0			0
$370$	−0.0825380	+	0.468096i	−0.00429095	+	0.0243352i
$371$	4.37661	+	14.6189i	0.227222	+	0.758975i
$372$		0			0
$373$	13.4959	+	6.77789i	0.698791	+	0.350946i	0.762469	−	0.647024i	$-0.223987\pi$
$373$	13.4959	+	6.77789i	0.698791	+	0.350946i	−0.0636783	+	0.997970i	$0.520283\pi$
$374$	0.465194	−	1.55386i	0.0240546	−	0.0803480i
$375$		0			0
$376$	24.4981	+	32.9066i	1.26339	+	1.69703i
$377$	3.63572	+	6.29725i	0.187249	+	0.324325i
$378$		0			0
$379$	1.32973	−	2.30316i	0.0683037	−	0.118305i	−0.829851	−	0.557985i	$-0.811575\pi$
$379$	1.32973	−	2.30316i	0.0683037	−	0.118305i	0.898155	+	0.439680i	$0.144908\pi$
$380$	21.3974	−	2.50100i	1.09766	−	0.128298i
$381$		0			0
$382$	42.5378	−	10.0817i	2.17643	−	0.515822i
$383$	1.29846	−	0.854009i	0.0663481	−	0.0436378i	−0.515902	−	0.856648i	$-0.672543\pi$
$383$	1.29846	−	0.854009i	0.0663481	−	0.0436378i	0.582250	+	0.813010i	$0.302173\pi$
$384$		0			0
$385$	−8.85973	+	9.39076i	−0.451534	+	0.478598i
$386$	−51.9137	−	43.5607i	−2.64234	−	2.21718i
$387$		0			0
$388$	38.1656	−	32.0247i	1.93757	−	1.62581i
$389$	0.213782	−	3.67050i	0.0108392	−	0.186102i	−0.988543	−	0.150943i	$-0.951769\pi$
$389$	0.213782	−	3.67050i	0.0108392	−	0.186102i	0.999382	−	0.0351591i	$-0.0111938\pi$
$390$		0			0
$391$	−0.963439	+	1.29412i	−0.0487232	+	0.0654466i
$392$	−25.8564	−	3.02218i	−1.30595	−	0.152643i
$393$		0			0
$394$	−12.2773	−	8.07490i	−0.618521	−	0.406807i
$395$	19.6490	+	7.15164i	0.988647	+	0.359838i
$396$		0			0
$397$	36.1674	−	13.1638i	1.81519	−	0.660674i	0.818965	−	0.573844i	$-0.194548\pi$
$397$	36.1674	−	13.1638i	1.81519	−	0.660674i	0.996223	−	0.0868301i	$-0.0276737\pi$
$398$	−38.3252	−	9.08325i	−1.92107	−	0.455302i
$399$		0			0
$400$	−2.61533	−	44.9034i	−0.130766	−	2.24517i
$401$	−12.2187	−	12.9510i	−0.610171	−	0.646743i	0.346454	−	0.938067i	$-0.387386\pi$
$401$	−12.2187	−	12.9510i	−0.610171	−	0.646743i	−0.956625	+	0.291324i	$0.905904\pi$
$402$		0			0
$403$	−0.669806	+	1.55279i	−0.0333654	+	0.0773498i
$404$	49.9982			2.48750
$405$		0			0
$406$	−17.8966			−0.888196
$407$	−0.0470713	+	0.109124i	−0.00233324	+	0.00540905i
$408$		0			0
$409$	12.5796	+	13.3336i	0.622022	+	0.659305i	0.959395	−	0.282066i	$-0.0910198\pi$
$409$	12.5796	+	13.3336i	0.622022	+	0.659305i	−0.337373	+	0.941371i	$0.609538\pi$
$410$	−2.36430	−	40.5934i	−0.116764	−	2.00477i
$411$		0			0
$412$	−24.4220	−	5.78812i	−1.20319	−	0.285160i
$413$	−12.0689	+	4.39273i	−0.593873	+	0.216152i
$414$		0			0
$415$	−21.3410	−	7.76749i	−1.04759	−	0.381291i
$416$	0.165848	+	0.109080i	0.00813134	+	0.00534807i
$417$		0			0
$418$	8.01472	+	0.936786i	0.392013	+	0.0458197i
$419$	−7.45896	+	10.0191i	−0.364394	+	0.489466i	−0.946074	−	0.323952i	$-0.894988\pi$
$419$	−7.45896	+	10.0191i	−0.364394	+	0.489466i	0.581680	+	0.813418i	$0.302396\pi$
$420$		0			0
$421$	−1.25709	+	21.5834i	−0.0612668	+	1.05191i	0.817889	+	0.575376i	$0.195144\pi$
$421$	−1.25709	+	21.5834i	−0.0612668	+	1.05191i	−0.879156	+	0.476534i	$0.841893\pi$
$422$	18.9221	−	15.8775i	0.921114	−	0.772906i
$423$		0			0
$424$	−43.8878	−	36.8262i	−2.13138	−	1.78844i
$425$	−2.03410	+	2.15602i	−0.0986685	+	0.104583i
$426$		0			0
$427$	−4.70153	+	3.09224i	−0.227523	+	0.149644i
$428$	77.5233	−	18.3734i	3.74723	−	0.888110i
$429$		0			0
$430$	−60.9744	+	7.12688i	−2.94045	+	0.343689i
$431$	15.5400	−	26.9162i	0.748538	−	1.29651i	−0.199986	−	0.979799i	$-0.564090\pi$
$431$	15.5400	−	26.9162i	0.748538	−	1.29651i	0.948524	−	0.316707i	$-0.102577\pi$
$432$		0			0
$433$	−6.64480	−	11.5091i	−0.319329	−	0.553093i	0.661019	−	0.750369i	$-0.270124\pi$
$433$	−6.64480	−	11.5091i	−0.319329	−	0.553093i	−0.980348	+	0.197275i	$0.936791\pi$
$434$	−2.48546	−	3.33856i	−0.119306	−	0.160256i
$435$		0			0
$436$	−4.41495	+	14.7469i	−0.211438	+	0.706251i
$437$	−7.17262	−	3.60223i	−0.343113	−	0.172318i
$438$		0			0
$439$	0.367842	+	1.22868i	0.0175562	+	0.0586417i	0.966319	−	0.257348i	$-0.0828487\pi$
$439$	0.367842	+	1.22868i	0.0175562	+	0.0586417i	−0.948763	+	0.315990i	$0.897663\pi$
$440$	8.41685	−	47.7343i	0.401258	−	2.27564i
$441$		0			0
$442$	−0.150692	−	0.854617i	−0.00716769	−	0.0406500i
$443$	−34.9439	+	17.5495i	−1.66023	+	0.833800i	−0.663939	+	0.747787i	$0.731116\pi$
$443$	−34.9439	+	17.5495i	−1.66023	+	0.833800i	−0.996294	+	0.0860134i	$0.972587\pi$
$444$		0			0
$445$	−14.5152	−	33.6500i	−0.688086	−	1.59516i
$446$	12.6699	+	29.3721i	0.599936	+	1.39081i
$447$		0			0
$448$	9.19320	−	4.61700i	0.434338	−	0.218133i
$449$	−2.78437	−	15.7909i	−0.131403	−	0.745221i	−0.977298	−	0.211871i	$-0.932044\pi$
$449$	−2.78437	−	15.7909i	−0.131403	−	0.745221i	0.845895	−	0.533349i	$-0.179067\pi$
$450$		0			0
$451$	1.76543	−	10.0123i	0.0831310	−	0.471459i
$452$	4.01897	+	13.4243i	0.189036	+	0.631426i
$453$		0			0
$454$	−35.7082	−	17.9333i	−1.67587	−	0.841654i
$455$	−1.98106	+	6.61720i	−0.0928735	+	0.310219i
$456$		0			0
$457$	−2.30852	−	3.10088i	−0.107988	−	0.145053i	0.744844	−	0.667239i	$-0.232524\pi$
$457$	−2.30852	−	3.10088i	−0.107988	−	0.145053i	−0.852832	+	0.522186i	$0.825117\pi$
$458$	−8.26234	−	14.3108i	−0.386074	−	0.668699i
$459$		0			0
$460$	−48.0292	+	83.1890i	−2.23937	+	3.87871i
$461$	21.0874	−	2.46477i	0.982140	−	0.114796i	0.390159	−	0.920748i	$-0.372420\pi$
$461$	21.0874	−	2.46477i	0.982140	−	0.114796i	0.591981	+	0.805952i	$0.298346\pi$
$462$		0			0
$463$	18.7929	−	4.45400i	0.873381	−	0.206995i	0.230603	−	0.973048i	$-0.425930\pi$
$463$	18.7929	−	4.45400i	0.873381	−	0.206995i	0.642778	+	0.766053i	$0.277782\pi$
$464$	18.9501	−	12.4637i	0.879738	−	0.578613i
$465$		0			0
$466$	23.2293	−	24.6216i	1.07607	−	1.14057i
$467$	−3.15564	−	2.64790i	−0.146026	−	0.122530i	0.566848	−	0.823822i	$-0.308162\pi$
$467$	−3.15564	−	2.64790i	−0.146026	−	0.122530i	−0.712874	+	0.701292i	$0.752607\pi$
$468$		0			0
$469$	1.33722	−	1.12206i	0.0617469	−	0.0518118i
$470$	4.73300	−	81.2625i	0.218317	−	3.74836i
$471$		0			0
$472$	28.7944	−	38.6776i	1.32537	−	1.78028i
$473$	−15.2453	−	1.78193i	−0.700982	−	0.0819330i
$474$		0			0
$475$	−12.3203	−	8.10318i	−0.565293	−	0.371799i
$476$	1.33974	+	0.487625i	0.0614068	+	0.0223503i
$477$		0			0
$478$	28.8966	−	10.5175i	1.32170	−	0.481060i
$479$	27.9772	+	6.63072i	1.27831	+	0.302966i	0.813043	−	0.582204i	$-0.197809\pi$
$479$	27.9772	+	6.63072i	1.27831	+	0.302966i	0.465269	+	0.885169i	$0.345958\pi$
$480$		0			0
$481$	0.00369705	+	0.0634758i	0.000168571	+	0.00289425i
$482$	23.0429	+	24.4241i	1.04958	+	1.11249i
$483$		0			0
$484$	−7.93080	+	18.3857i	−0.360491	+	0.835712i
$485$	−49.6170			−2.25299
$486$		0			0
$487$	8.88765			0.402738			0.201369	−	0.979515i	$-0.435461\pi$
$487$	8.88765			0.402738			0.201369	+	0.979515i	$0.435461\pi$
$488$	8.36792	−	19.3990i	0.378798	−	0.878153i
$489$		0			0
$490$	35.4467	+	37.5713i	1.60132	+	1.69730i
$491$	1.63971	+	28.1528i	0.0739991	+	1.27052i	0.807108	+	0.590404i	$0.201032\pi$
$491$	1.63971	+	28.1528i	0.0739991	+	1.27052i	−0.733108	+	0.680112i	$0.761931\pi$
$492$		0			0
$493$	−1.45441	−	0.344701i	−0.0655033	−	0.0155246i
$494$	4.05686	−	1.47658i	0.182527	−	0.0664344i
$495$		0			0
$496$	4.95683	+	1.80414i	0.222568	+	0.0810082i
$497$	−8.67076	−	5.70285i	−0.388937	−	0.255808i
$498$		0			0
$499$	−1.18198	−	0.138153i	−0.0529126	−	0.00618460i	0.0895954	−	0.995978i	$-0.471443\pi$
$499$	−1.18198	−	0.138153i	−0.0529126	−	0.00618460i	−0.142508	+	0.989794i	$0.545517\pi$
$500$	−57.4443	+	77.1611i	−2.56899	+	3.45075i
$501$		0			0
$502$	1.89515	−	32.5385i	0.0845848	−	1.45226i
$503$	4.59276	−	3.85379i	0.204781	−	0.171832i	−0.534629	−	0.845087i	$-0.679549\pi$
$503$	4.59276	−	3.85379i	0.204781	−	0.171832i	0.739411	+	0.673255i	$0.235104\pi$
$504$		0			0
$505$	−38.1435	−	32.0062i	−1.69736	−	1.42426i
$506$	−24.6910	+	26.1710i	−1.09765	+	1.16344i
$507$		0			0
$508$	−44.0780	+	28.9906i	−1.95565	+	1.28625i
$509$	24.4578	−	5.79659i	1.08407	−	0.256929i	0.350514	−	0.936558i	$-0.386007\pi$
$509$	24.4578	−	5.79659i	1.08407	−	0.256929i	0.733557	+	0.679628i	$0.237859\pi$
$510$		0			0
$511$	11.3020	−	1.32101i	0.499971	−	0.0584382i
$512$	−19.9189	+	34.5006i	−0.880300	+	1.52473i
$513$		0			0
$514$	−4.12333	−	7.14181i	−0.181872	−	0.315012i
$515$	14.9262	+	20.0494i	0.657729	+	0.883483i
$516$		0			0
$517$	5.83713	−	19.4974i	0.256717	−	0.857494i
$518$	−0.139847	−	0.0702339i	−0.00614454	−	0.00308590i
$519$		0			0
$520$	−7.43761	−	24.8433i	−0.326161	−	1.08945i
$521$	−5.84968	+	33.1752i	−0.256279	+	1.45343i	0.536488	+	0.843908i	$0.319750\pi$
$521$	−5.84968	+	33.1752i	−0.256279	+	1.45343i	−0.792768	+	0.609524i	$0.791361\pi$
$522$		0			0
$523$	4.18478	+	23.7331i	0.182988	+	1.03778i	0.928513	+	0.371299i	$0.121087\pi$
$523$	4.18478	+	23.7331i	0.182988	+	1.03778i	−0.745526	+	0.666477i	$0.767801\pi$
$524$	−15.5409	+	7.80492i	−0.678906	+	0.340960i
$525$		0			0
$526$	23.7260	+	55.0030i	1.03450	+	2.39824i
$527$	−0.137684	−	0.319187i	−0.00599759	−	0.0139040i
$528$		0			0
$529$	11.4284	−	5.73957i	0.496888	−	0.249547i
$530$	19.7398	+	111.950i	0.857443	+	4.86280i
$531$		0			0
$532$	−1.23166	+	6.98506i	−0.0533990	+	0.302841i
$533$	−1.56004	−	5.21089i	−0.0675727	−	0.225709i
$534$		0			0
$535$	−70.9040	−	35.6093i	−3.06545	−	1.53952i
$536$	−1.87961	+	6.27833i	−0.0811867	+	0.271183i
$537$		0			0
$538$	1.22243	+	1.64200i	0.0527025	+	0.0707918i
$539$	6.45742	+	11.1846i	0.278141	+	0.481754i
$540$		0			0
$541$	−11.3703	+	19.6940i	−0.488849	+	0.846712i	−0.999918	−	0.0128282i	$-0.995917\pi$
$541$	−11.3703	+	19.6940i	−0.488849	+	0.846712i	0.511068	+	0.859540i	$0.329250\pi$
$542$	−68.7376	+	8.03428i	−2.95253	+	0.345102i
$543$		0			0
$544$	−0.0397040	+	0.00941003i	−0.00170230	+	0.000403452i
$545$	12.8084	−	8.42419i	0.548650	−	0.360853i
$546$		0			0
$547$	−0.267245	+	0.283263i	−0.0114266	+	0.0121115i	−0.733062	−	0.680162i	$-0.761909\pi$
$547$	−0.267245	+	0.283263i	−0.0114266	+	0.0121115i	0.721635	+	0.692274i	$0.243391\pi$
$548$	68.9639	+	57.8676i	2.94599	+	2.47198i
$549$		0			0
$550$	−50.6382	+	42.4905i	−2.15922	+	1.81180i
$551$	0.432364	−	7.42340i	0.0184193	−	0.316247i
$552$		0			0
$553$	−4.11107	+	5.52213i	−0.174821	+	0.234825i
$554$	−65.3365	−	7.63674i	−2.77588	−	0.324454i
$555$		0			0
$556$	32.2033	+	21.1804i	1.36572	+	0.898250i
$557$	19.6611	+	7.15607i	0.833069	+	0.303212i	0.723118	−	0.690725i	$-0.242708\pi$
$557$	19.6611	+	7.15607i	0.833069	+	0.303212i	0.109951	+	0.993937i	$0.464931\pi$
$558$		0			0
$559$	−7.71685	+	2.80870i	−0.326388	+	0.118795i
$560$	20.9652	+	4.96883i	0.885939	+	0.209971i
$561$		0			0
$562$	2.08703	+	35.8330i	0.0880361	+	1.51152i
$563$	9.51661	+	10.0870i	0.401077	+	0.425117i	0.896162	−	0.443728i	$-0.146344\pi$
$563$	9.51661	+	10.0870i	0.401077	+	0.425117i	−0.495084	+	0.868845i	$0.664863\pi$
$564$		0			0
$565$	5.52746	−	12.8141i	0.232542	−	0.539093i
$566$	−2.86338			−0.120357
$567$		0			0
$568$	38.9631			1.63485
$569$	−3.68383	+	8.54007i	−0.154434	+	0.358019i	−0.977815	−	0.209471i	$-0.932826\pi$
$569$	−3.68383	+	8.54007i	−0.154434	+	0.358019i	0.823381	+	0.567489i	$0.192085\pi$
$570$		0			0
$571$	−24.7267	−	26.2088i	−1.03478	−	1.09680i	−0.995227	−	0.0975862i	$-0.968888\pi$
$571$	−24.7267	−	26.2088i	−1.03478	−	1.09680i	−0.0395538	−	0.999217i	$-0.512594\pi$
$572$	−0.751142	−	12.8966i	−0.0314068	−	0.539234i
$573$		0			0
$574$	13.0267	+	3.08739i	0.543725	+	0.128865i
$575$	61.7866	−	22.4885i	2.57668	−	0.937834i
$576$		0			0
$577$	8.15363	+	2.96768i	0.339440	+	0.123546i	0.506115	−	0.862466i	$-0.331081\pi$
$577$	8.15363	+	2.96768i	0.339440	+	0.123546i	−0.166675	+	0.986012i	$0.553303\pi$
$578$	−34.6863	−	22.8135i	−1.44276	−	0.948918i
$579$		0			0
$580$	−88.3909	−	10.3314i	−3.67023	−	0.428989i
$581$	4.46509	−	5.99766i	0.185243	−	0.248825i
$582$		0			0
$583$	−1.65262	+	28.3745i	−0.0684447	+	1.17515i
$584$	−32.7259	+	27.4603i	−1.35421	+	1.13631i
$585$		0			0
$586$	−31.4413	−	26.3824i	−1.29883	−	1.08985i
$587$	−6.35311	+	6.73390i	−0.262221	+	0.277938i	−0.845085	−	0.534632i	$-0.820450\pi$
$587$	−6.35311	+	6.73390i	−0.262221	+	0.277938i	0.582864	+	0.812569i	$0.301932\pi$
$588$		0			0
$589$	1.44486	−	0.950296i	0.0595342	−	0.0391563i
$590$	−93.0969	+	22.0644i	−3.83274	+	0.908375i
$591$		0			0
$592$	0.196992	−	0.0230251i	0.00809633	−	0.000946325i
$593$	18.3119	−	31.7171i	0.751979	−	1.30247i	−0.194884	−	0.980826i	$-0.562433\pi$
$593$	18.3119	−	31.7171i	0.751979	−	1.30247i	0.946862	−	0.321639i	$-0.104234\pi$
$594$		0			0
$595$	−0.709932	−	1.22964i	−0.0291044	−	0.0504102i
$596$	39.9082	+	53.6060i	1.63470	+	2.19579i
$597$		0			0
$598$	−5.52098	+	18.4414i	−0.225770	+	0.754123i
$599$	22.1250	+	11.1116i	0.904001	+	0.454007i	0.839157	−	0.543889i	$-0.183049\pi$
$599$	22.1250	+	11.1116i	0.904001	+	0.454007i	0.0648441	+	0.997895i	$0.479345\pi$
$600$		0			0
$601$	−6.33556	−	21.1622i	−0.258433	−	0.863226i	−0.984467	−	0.175568i	$-0.943824\pi$
$601$	−6.33556	−	21.1622i	−0.258433	−	0.863226i	0.726034	−	0.687658i	$-0.241361\pi$
$602$	3.50974	−	19.9047i	0.143046	−	0.811257i
$603$		0			0
$604$	−1.27765	−	7.24590i	−0.0519867	−	0.294831i
$605$	17.8199	−	8.94950i	0.724482	−	0.363849i
$606$		0			0
$607$	−3.79033	−	8.78698i	−0.153845	−	0.356653i	0.823811	−	0.566865i	$-0.191844\pi$
$607$	−3.79033	−	8.78698i	−0.153845	−	0.356653i	−0.977656	+	0.210212i	$0.932585\pi$
$608$	−0.0804024	−	0.186394i	−0.00326075	−	0.00755927i
$609$		0			0
$610$	−37.4609	+	18.8135i	−1.51675	+	0.761738i
$611$	−1.89085	−	10.7235i	−0.0764954	−	0.433827i
$612$		0			0
$613$	−2.38544	+	13.5285i	−0.0963469	+	0.546410i	0.897979	+	0.440037i	$0.145035\pi$
$613$	−2.38544	+	13.5285i	−0.0963469	+	0.546410i	−0.994326	+	0.106373i	$0.966076\pi$
$614$	−14.3580	−	47.9590i	−0.579441	−	1.93547i
$615$		0			0
$616$	14.2610	+	7.16214i	0.574592	+	0.288571i
$617$	3.90172	−	13.0327i	0.157077	−	0.524675i	−0.842831	−	0.538178i	$-0.819113\pi$
$617$	3.90172	−	13.0327i	0.157077	−	0.524675i	0.999909	+	0.0135025i	$0.00429810\pi$
$618$		0			0
$619$	−8.51625	−	11.4393i	−0.342297	−	0.459785i	0.597325	−	0.801999i	$-0.296230\pi$
$619$	−8.51625	−	11.4393i	−0.342297	−	0.459785i	−0.939622	+	0.342215i	$0.888823\pi$
$620$	−10.3483	−	17.9238i	−0.415599	−	0.719839i
$621$		0			0
$622$	8.13761	−	14.0947i	0.326288	−	0.565148i
$623$	11.9841	−	1.40074i	0.480132	−	0.0561194i
$624$		0			0
$625$	39.7451	−	9.41976i	1.58980	−	0.376790i
$626$	−18.8101	+	12.3716i	−0.751801	+	0.494467i
$627$		0			0
$628$	29.7807	−	31.5657i	1.18838	−	1.25961i
$629$	−0.0100122	−	0.00840126i	−0.000399214	−	0.000334980i
$630$		0			0
$631$	−6.09157	+	5.11144i	−0.242502	+	0.203483i	−0.755935	−	0.654646i	$-0.772818\pi$
$631$	−6.09157	+	5.11144i	−0.242502	+	0.203483i	0.513434	+	0.858129i	$0.328373\pi$
$632$	1.50284	−	25.8027i	0.0597797	−	1.02638i
$633$		0			0
$634$	−0.0733662	+	0.0985479i	−0.00291374	+	0.00391384i
$635$	52.1852	+	6.09958i	2.07091	+	0.242054i
$636$		0			0
$637$	5.77297	+	3.79694i	0.228733	+	0.150440i
$638$	−31.3233	−	11.4007i	−1.24010	−	0.451360i
$639$		0			0
$640$	73.1505	−	26.6246i	2.89153	−	1.05243i
$641$	4.09023	+	0.969403i	0.161555	+	0.0382891i	0.310597	−	0.950542i	$-0.399471\pi$
$641$	4.09023	+	0.969403i	0.161555	+	0.0382891i	−0.149043	+	0.988831i	$0.547619\pi$
$642$		0			0
$643$	−1.11571	−	19.1561i	−0.0439995	−	0.755442i	−0.946092	−	0.323899i	$-0.895006\pi$
$643$	−1.11571	−	19.1561i	−0.0439995	−	0.755442i	0.902092	−	0.431543i	$-0.142031\pi$
$644$	−21.7032	−	23.0040i	−0.855225	−	0.906486i
$645$		0			0
$646$	−0.351496	+	0.814859i	−0.0138294	+	0.0320602i
$647$	−33.3755			−1.31213			−0.656063	−	0.754706i	$-0.727779\pi$
$647$	−33.3755			−1.31213			−0.656063	+	0.754706i	$0.727779\pi$
$648$		0			0
$649$	−23.9217			−0.939009
$650$	−14.0080	+	32.4742i	−0.549440	+	1.27374i
$651$		0			0
$652$	−10.3804	−	11.0026i	−0.406530	−	0.430896i
$653$	−0.709166	−	12.1759i	−0.0277518	−	0.476480i	−0.983340	−	0.181775i	$-0.941816\pi$
$653$	−0.709166	−	12.1759i	−0.0277518	−	0.476480i	0.955588	−	0.294705i	$-0.0952214\pi$
$654$		0			0
$655$	16.8524	+	3.99409i	0.658477	+	0.156062i
$656$	−15.9437	+	5.80302i	−0.622496	+	0.226570i
$657$		0			0
$658$	25.1839	+	9.16619i	0.981770	+	0.357335i
$659$	19.5651	+	12.8682i	0.762148	+	0.501272i	0.870095	−	0.492884i	$-0.164057\pi$
$659$	19.5651	+	12.8682i	0.762148	+	0.501272i	−0.107947	+	0.994157i	$0.534428\pi$
$660$		0			0
$661$	33.4396	+	3.90853i	1.30065	+	0.152024i	0.738073	−	0.674721i	$-0.235736\pi$
$661$	33.4396	+	3.90853i	1.30065	+	0.152024i	0.562577	+	0.826745i	$0.309810\pi$
$662$	27.0965	−	36.3969i	1.05314	−	1.41461i
$663$		0			0
$664$	−1.63225	+	28.0247i	−0.0633437	+	1.08757i
$665$	5.41109	−	4.54045i	0.209833	−	0.176071i
$666$		0			0
$667$	25.3992	+	21.3124i	0.983460	+	0.825221i
$668$	−32.6112	+	34.5658i	−1.26176	+	1.33739i
$669$		0			0
$670$	10.8644	−	7.14565i	0.419730	−	0.276061i
$671$	−10.1986	+	2.41712i	−0.393713	+	0.0933118i
$672$		0			0
$673$	12.3262	−	1.44072i	0.475140	−	0.0555358i	0.124847	−	0.992176i	$-0.460156\pi$
$673$	12.3262	−	1.44072i	0.475140	−	0.0555358i	0.350293	+	0.936640i	$0.386082\pi$
$674$	−4.47565	+	7.75205i	−0.172396	+	0.298598i
$675$		0			0
$676$	22.6440	+	39.2206i	0.870925	+	1.50849i
$677$	−8.84021	−	11.8745i	−0.339757	−	0.456373i	0.599103	−	0.800672i	$-0.295524\pi$
$677$	−8.84021	−	11.8745i	−0.339757	−	0.456373i	−0.938860	+	0.344299i	$0.888117\pi$
$678$		0			0
$679$	4.68517	−	15.6496i	0.179800	−	0.600575i
$680$	4.76367	+	2.39240i	0.182678	+	0.0917445i
$681$		0			0
$682$	−2.22337	−	7.42657i	−0.0851372	−	0.284378i
$683$	6.94875	−	39.4083i	0.265887	−	1.50792i	−0.500612	−	0.865672i	$-0.666892\pi$
$683$	6.94875	−	39.4083i	0.265887	−	1.50792i	0.766499	−	0.642246i	$-0.221997\pi$
$684$		0			0
$685$	−15.5686	−	88.2941i	−0.594847	−	3.37354i
$686$	−35.3967	+	17.7769i	−1.35145	+	0.678725i
$687$		0			0
$688$	10.1458	+	23.5207i	0.386807	+	0.896719i
$689$	6.02304	+	13.9630i	0.229460	+	0.531947i
$690$		0			0
$691$	−35.1761	+	17.6661i	−1.33816	+	0.672050i	−0.966584	−	0.256351i	$-0.917480\pi$
$691$	−35.1761	+	17.6661i	−1.33816	+	0.672050i	−0.371578	+	0.928402i	$0.621183\pi$
$692$	−6.67130	−	37.8348i	−0.253605	−	1.43826i
$693$		0			0
$694$	−1.74631	+	9.90380i	−0.0662889	+	0.375943i
$695$	−11.0092	−	36.7733i	−0.417603	−	1.39489i
$696$		0			0
$697$	0.999178	+	0.501806i	0.0378466	+	0.0190073i
$698$	5.32143	−	17.7748i	0.201419	−	0.672787i
$699$		0			0
$700$	−34.6975	−	46.6068i	−1.31144	−	1.76157i
$701$	−2.37301	−	4.11018i	−0.0896274	−	0.155239i	0.817726	−	0.575607i	$-0.195234\pi$
$701$	−2.37301	−	4.11018i	−0.0896274	−	0.155239i	−0.907354	+	0.420368i	$0.861901\pi$
$702$		0			0
$703$	0.0325111	−	0.0563108i	0.00122618	−	0.00212380i
$704$	19.0314	−	2.22445i	0.717273	−	0.0838372i
$705$		0			0
$706$	−4.89337	+	1.15975i	−0.184165	+	0.0436478i
$707$	13.6968	−	9.00850i	0.515120	−	0.338800i
$708$		0			0
$709$	−0.249769	+	0.264740i	−0.00938029	+	0.00994253i	−0.732047	−	0.681254i	$-0.761435\pi$
$709$	−0.249769	+	0.264740i	−0.00938029	+	0.00994253i	0.722667	+	0.691197i	$0.242916\pi$
$710$	−59.2231	−	49.6940i	−2.22260	−	1.86498i
$711$		0			0
$712$	−34.7009	+	29.1175i	−1.30047	+	1.09123i
$713$	−0.448356	+	7.69797i	−0.0167911	+	0.288291i
$714$		0			0
$715$	−7.68268	+	10.3196i	−0.287316	+	0.385932i
$716$	5.66038	+	0.661604i	0.211538	+	0.0247253i
$717$		0			0
$718$	−20.5956	−	13.5459i	−0.768621	−	0.505530i
$719$	−15.2471	−	5.54950i	−0.568622	−	0.206961i	0.0416792	−	0.999131i	$-0.486729\pi$
$719$	−15.2471	−	5.54950i	−0.568622	−	0.206961i	−0.610301	+	0.792170i	$0.708951\pi$
$720$		0			0
$721$	−7.73318	+	2.81465i	−0.287998	+	0.104823i
$722$	41.0478	+	9.72852i	1.52764	+	0.362058i
$723$		0			0
$724$	2.31127	+	39.6830i	0.0858978	+	1.47481i
$725$	41.8027	+	44.3083i	1.55251	+	1.64557i
$726$		0			0
$727$	−6.27054	+	14.5368i	−0.232562	+	0.539138i	−0.994035	−	0.109057i	$-0.965217\pi$
$727$	−6.27054	+	14.5368i	−0.232562	+	0.539138i	0.761474	+	0.648196i	$0.224476\pi$
$728$	8.53809			0.316443
$729$		0			0
$730$	84.7659			3.13733
$731$	0.668605	−	1.55000i	0.0247293	−	0.0573289i
$732$		0			0
$733$	−31.3546	−	33.2339i	−1.15811	−	1.22752i	−0.969399	−	0.245491i	$-0.921051\pi$
$733$	−31.3546	−	33.2339i	−1.15811	−	1.22752i	−0.188710	−	0.982033i	$-0.560431\pi$
$734$	4.63146	+	79.5191i	0.170950	+	2.93510i
$735$		0			0
$736$	0.880738	+	0.208739i	0.0324644	+	0.00769421i
$737$	3.05522	−	1.11201i	0.112541	−	0.0409614i
$738$		0			0
$739$	−2.12852	−	0.774717i	−0.0782987	−	0.0284984i	0.302574	−	0.953126i	$-0.402154\pi$
$739$	−2.12852	−	0.774717i	−0.0782987	−	0.0284984i	−0.380873	+	0.924628i	$0.624376\pi$
$740$	−0.650156	−	0.427614i	−0.0239002	−	0.0157194i
$741$		0			0
$742$	−37.1739	−	4.34500i	−1.36470	−	0.159510i
$743$	−1.63022	+	2.18977i	−0.0598071	+	0.0803349i	−0.831020	−	0.556242i	$-0.812243\pi$
$743$	−1.63022	+	2.18977i	−0.0598071	+	0.0803349i	0.771213	+	0.636577i	$0.219650\pi$
$744$		0			0
$745$	3.86987	−	66.4430i	0.141781	−	2.43428i
$746$	−28.3745	+	23.8090i	−1.03886	+	0.871709i
$747$		0			0
$748$	2.03422	+	1.70691i	0.0743785	+	0.0624109i
$749$	17.9267	−	19.0012i	0.655027	−	0.694288i
$750$		0			0
$751$	36.0238	−	23.6932i	1.31453	−	0.864579i	0.318021	−	0.948084i	$-0.396982\pi$
$751$	36.0238	−	23.6932i	1.31453	−	0.864579i	0.996507	+	0.0835052i	$0.0266115\pi$
$752$	−33.0499	+	7.83297i	−1.20521	+	0.285639i
$753$		0			0
$754$	−17.7135	+	2.07041i	−0.645088	+	0.0754000i
$755$	−3.66372	+	6.34576i	−0.133337	+	0.230946i
$756$		0			0
$757$	19.3916	+	33.5873i	0.704800	+	1.22075i	0.966764	+	0.255672i	$0.0822968\pi$
$757$	19.3916	+	33.5873i	0.704800	+	1.22075i	−0.261963	+	0.965078i	$0.584370\pi$
$758$	3.89506	+	5.23198i	0.141475	+	0.190034i
$759$		0			0
$760$	−7.60591	+	25.4055i	−0.275895	+	0.921554i
$761$	−38.7081	−	19.4400i	−1.40317	−	0.704698i	−0.423608	−	0.905845i	$-0.639237\pi$
$761$	−38.7081	−	19.4400i	−1.40317	−	0.704698i	−0.979561	+	0.201147i	$0.935533\pi$
$762$		0			0
$763$	1.44760	+	4.83532i	0.0524067	+	0.175050i
$764$	−12.4282	+	70.4836i	−0.449635	+	2.55001i
$765$		0			0
$766$	0.661895	+	3.75379i	0.0239152	+	0.135630i
$767$	−11.4372	+	5.74400i	−0.412975	+	0.207404i
$768$		0			0
$769$	19.7676	+	45.8265i	0.712839	+	1.65255i	0.756912	+	0.653517i	$0.226707\pi$
$769$	19.7676	+	45.8265i	0.712839	+	1.65255i	−0.0440729	+	0.999028i	$0.514033\pi$
$770$	−12.5417	−	29.0750i	−0.451972	−	1.04779i
$771$		0			0
$772$	99.1473	−	49.7936i	3.56839	−	1.79211i
$773$	1.64610	+	9.33547i	0.0592059	+	0.335774i	0.999995	−	0.00321947i	$-0.00102479\pi$
$773$	1.64610	+	9.33547i	0.0592059	+	0.335774i	−0.940789	+	0.338993i	$0.889914\pi$
$774$		0			0
$775$	−2.46005	+	13.9516i	−0.0883676	+	0.501157i
$776$	17.5898	+	58.7541i	0.631438	+	2.10915i
$777$		0			0
$778$	8.05843	+	4.04710i	0.288909	+	0.145095i
$779$	−1.59534	+	5.32880i	−0.0571589	+	0.190924i
$780$		0			0
$781$	−11.5429	−	15.5049i	−0.413039	−	0.554808i
$782$	−1.97850	−	3.42686i	−0.0707509	−	0.122544i
$783$		0			0

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)

\(f(q)\)	\(=\)	\(q+(-0.971435 + 2.25204i) q^{2} +(-2.75551 - 2.92067i) q^{4} +(0.232513 + 3.99210i) q^{5} +(-1.28109 - 0.303625i) q^{7} +(4.64483 - 1.69058i) q^{8} +O(q^{10})\)	\(q+(-0.971435 + 2.25204i) q^{2} +(-2.75551 - 2.92067i) q^{4} +(0.232513 + 3.99210i) q^{5} +(-1.28109 - 0.303625i) q^{7} +(4.64483 - 1.69058i) q^{8} +(-9.21624 - 3.35444i) q^{10} +(-2.04879 - 1.34751i) q^{11} +(-1.30311 - 0.152312i) q^{13} +(1.92827 - 2.59012i) q^{14} +(-0.237953 + 4.08549i) q^{16} +(0.206593 - 0.173352i) q^{17} +(1.02778 + 0.862409i) q^{19} +(11.0189 - 11.6794i) q^{20} +(5.02492 - 3.30494i) q^{22} +(-5.82111 + 1.37963i) q^{23} +(-10.9166 + 1.27597i) q^{25} +(1.60890 - 2.78670i) q^{26} +(2.64328 + 4.57830i) q^{28} +(-3.30965 - 4.44563i) q^{29} +(0.369677 - 1.23481i) q^{31} +(-0.135207 - 0.0679036i) q^{32} +(0.189704 + 0.633655i) q^{34} +(0.914230 - 5.18486i) q^{35} +(-0.00841562 - 0.0477273i) q^{37} +(-2.94060 + 1.47682i) q^{38} +(7.82896 + 18.1496i) q^{40} +(1.64212 + 3.80687i) q^{41} +(5.59352 - 2.80917i) q^{43} +(1.70983 + 9.69693i) q^{44} +(2.54785 - 14.4496i) q^{46} +(2.38036 + 7.95094i) q^{47} +(-4.70641 - 2.36365i) q^{49} +(7.73125 - 25.8242i) q^{50} +(3.14588 + 4.22565i) q^{52} +(-5.79529 - 10.0377i) q^{53} +(4.90304 - 8.49231i) q^{55} +(-6.46377 + 0.755507i) q^{56} +(13.2268 - 3.13482i) q^{58} +(8.15031 - 5.36055i) q^{59} +(2.93311 - 3.10891i) q^{61} +(2.42172 + 2.03206i) q^{62} +(-5.98568 + 5.02258i) q^{64} +(0.305054 - 5.23757i) q^{65} +(-0.791752 + 1.06351i) q^{67} +(-1.07557 - 0.125716i) q^{68} +(10.7884 + 7.09563i) q^{70} +(7.40721 + 2.69600i) q^{71} +(-8.12155 + 2.95600i) q^{73} +(0.115659 + 0.0274117i) q^{74} +(-0.313243 - 5.37818i) q^{76} +(2.21556 + 2.34836i) q^{77} +(2.07109 - 4.80133i) q^{79} -16.3650 q^{80} -10.1684 q^{82} +(-2.24944 + 5.21479i) q^{83} +(0.740074 + 0.784433i) q^{85} +(0.892623 + 15.3257i) q^{86} +(-11.7944 - 2.79532i) q^{88} +(-8.61170 + 3.13440i) q^{89} +(1.62316 + 0.590783i) q^{91} +(20.0696 + 13.2000i) q^{92} +(-20.2182 - 2.36317i) q^{94} +(-3.20385 + 4.30352i) q^{95} +(-0.721447 + 12.3868i) q^{97} +(9.89500 - 8.30289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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

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