LMFDB - Embedded newform 729.2.g.d.676.1

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			676.1
Character	$\chi$	$=$	729.676
Dual form			729.2.g.d.55.1

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.971435	−	2.25204i	−0.686908	−	1.59243i	−0.800795	−	0.598938i	$-0.795590\pi$
$2$	−0.971435	−	2.25204i	−0.686908	−	1.59243i	0.113887	−	0.993494i	$-0.463670\pi$
$3$		0			0
$3$		0			0
$4$	−2.75551	+	2.92067i	−1.37775	+	1.46033i
$5$	0.232513	−	3.99210i	0.103983	−	1.78532i	−0.394971	−	0.918694i	$-0.629245\pi$
$5$	0.232513	−	3.99210i	0.103983	−	1.78532i	0.498954	−	0.866629i	$-0.333718\pi$
$6$		0			0
$7$	−1.28109	+	0.303625i	−0.484208	+	0.114759i	−0.465468	−	0.885065i	$-0.654114\pi$
$7$	−1.28109	+	0.303625i	−0.484208	+	0.114759i	−0.0187406	+	0.999824i	$0.505966\pi$
$8$	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	−0.819447	−	0.573154i	$-0.805720\pi$
$11$	−2.04879	+	1.34751i	−0.617734	+	0.406290i	0.201713	+	0.979445i	$0.435349\pi$
$12$		0			0
$13$	−1.30311	+	0.152312i	−0.361418	+	0.0422437i	−0.294864	−	0.955539i	$-0.595274\pi$
$13$	−1.30311	+	0.152312i	−0.361418	+	0.0422437i	−0.0665537	+	0.997783i	$0.521200\pi$
$14$	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	0.667497	−	0.744613i	$-0.267366\pi$
$17$	0.206593	+	0.173352i	0.0501061	+	0.0420440i	−0.617391	+	0.786657i	$0.711810\pi$
$18$		0			0
$19$	1.02778	−	0.862409i	0.235789	−	0.197850i	−0.517235	−	0.855843i	$-0.673039\pi$
$19$	1.02778	−	0.862409i	0.235789	−	0.197850i	0.753024	+	0.657993i	$0.228594\pi$
$20$	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	−0.426630	−	0.904426i	$-0.640299\pi$
$23$	−5.82111	−	1.37963i	−1.21379	−	0.287673i	−0.787156	+	0.616754i	$0.788447\pi$
$24$		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	−0.995062	−	0.0992581i	$-0.968353\pi$
$29$	−3.30965	+	4.44563i	−0.614587	+	0.825533i	0.380475	+	0.924791i	$0.375760\pi$
$30$		0			0
$31$	0.369677	+	1.23481i	0.0663960	+	0.221778i	0.984748	−	0.173986i	$-0.0556649\pi$
$31$	0.369677	+	1.23481i	0.0663960	+	0.221778i	−0.918352	+	0.395764i	$0.870480\pi$
$32$	−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	−0.985492	−	0.169724i	$-0.945712\pi$
$37$	−0.00841562	+	0.0477273i	−0.00138352	+	0.00784632i	0.984108	+	0.177570i	$0.0568236\pi$
$38$	−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	−0.740537	−	0.672015i	$-0.765429\pi$
$41$	1.64212	−	3.80687i	0.256456	−	0.594533i	0.996994	+	0.0774824i	$0.0246882\pi$
$42$		0			0
$43$	5.59352	+	2.80917i	0.853003	+	0.428394i	0.820888	−	0.571090i	$-0.193479\pi$
$43$	5.59352	+	2.80917i	0.853003	+	0.428394i	0.0321157	+	0.999484i	$0.489775\pi$
$44$	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	−0.588944	−	0.808174i	$-0.700456\pi$
$47$	2.38036	−	7.95094i	0.347210	−	1.15976i	0.936154	−	0.351590i	$-0.114359\pi$
$48$		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	0.126130	+	0.992014i	$0.459744\pi$
$53$	−5.79529	+	10.0377i	−0.796044	+	1.37879i	−0.922174	+	0.386775i	$0.873589\pi$
$54$		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	0.955040	−	0.296478i	$-0.0958122\pi$
$59$	8.15031	+	5.36055i	1.06108	+	0.697884i	0.106041	+	0.994362i	$0.466183\pi$
$60$		0			0
$61$	2.93311	+	3.10891i	0.375546	+	0.398055i	0.887387	−	0.461025i	$-0.152518\pi$
$61$	2.93311	+	3.10891i	0.375546	+	0.398055i	−0.511842	+	0.859080i	$0.671037\pi$
$62$	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	0.751124	−	0.660161i	$-0.229512\pi$
$67$	−0.791752	−	1.06351i	−0.0967278	−	0.129928i	−0.847852	+	0.530233i	$0.822105\pi$
$68$	−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	0.137238	−	0.990538i	$-0.456177\pi$
$71$	7.40721	−	2.69600i	0.879074	−	0.319957i	0.741836	+	0.670581i	$0.233955\pi$
$72$		0			0
$73$	−8.12155	−	2.95600i	−0.950556	−	0.345974i	−0.180230	−	0.983624i	$-0.557684\pi$
$73$	−8.12155	−	2.95600i	−0.950556	−	0.345974i	−0.770326	+	0.637650i	$0.779906\pi$
$74$	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	0.994101	−	0.108460i	$-0.0345921\pi$
$79$	2.07109	+	4.80133i	0.233016	+	0.540192i	−0.761085	+	0.648653i	$0.775333\pi$
$80$	−16.3650			−1.82967
$81$		0			0
$82$	−10.1684			−1.12291
$83$	−2.24944	−	5.21479i	−0.246908	−	0.572398i	0.749020	−	0.662548i	$-0.230525\pi$
$83$	−2.24944	−	5.21479i	−0.246908	−	0.572398i	−0.995928	+	0.0901496i	$0.971265\pi$
$84$		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	−0.157453	−	0.987527i	$-0.550328\pi$
$89$	−8.61170	−	3.13440i	−0.912838	−	0.332246i	−0.755385	+	0.655281i	$0.772550\pi$
$90$		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	−0.811981	−	0.583684i	$-0.801611\pi$
$97$	−0.721447	−	12.3868i	−0.0732518	−	1.25769i	0.738729	−	0.674002i	$-0.235426\pi$
$98$	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	0.145864	−	0.989305i	$-0.453404\pi$
$101$	−8.54489	−	9.05705i	−0.850248	−	0.901211i	−0.996112	+	0.0880941i	$0.971922\pi$
$102$		0			0
$103$	5.22232	+	3.43478i	0.514571	+	0.338439i	0.780090	−	0.625667i	$-0.215173\pi$
$103$	5.22232	+	3.43478i	0.514571	+	0.338439i	−0.265519	+	0.964106i	$0.585543\pi$
$104$	−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	−0.724755	−	0.689007i	$-0.758047\pi$
$107$	−9.92075	−	17.1832i	−0.959075	−	1.66117i	−0.234320	−	0.972159i	$-0.575286\pi$
$108$		0			0
$109$	−1.91684	+	3.32007i	−0.183600	+	0.318005i	−0.943104	−	0.332498i	$-0.892109\pi$
$109$	−1.91684	+	3.32007i	−0.183600	+	0.318005i	0.759504	+	0.650503i	$0.225442\pi$
$110$	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	−0.589400	−	0.807841i	$-0.700636\pi$
$113$	−3.11864	+	1.56624i	−0.293377	+	0.147339i	0.296023	+	0.955181i	$0.404339\pi$
$114$		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	0.901397	+	0.432994i	$0.142543\pi$
$127$	2.28154	+	12.9392i	0.202454	+	1.14817i	−0.698943	+	0.715177i	$0.746346\pi$
$128$	−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	0.994950	−	0.100369i	$-0.0320025\pi$
$131$	1.24215	+	4.14908i	0.108528	+	0.362507i	−0.886423	+	0.462877i	$0.846817\pi$
$132$		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	−0.917887	−	0.396841i	$-0.870106\pi$
$137$	−22.2688	−	2.60285i	−1.90255	−	0.222376i	−0.984663	+	0.174465i	$0.944180\pi$
$138$		0			0
$139$	−9.34045	−	2.21373i	−0.792247	−	0.187766i	−0.185482	−	0.982648i	$-0.559385\pi$
$139$	−9.34045	−	2.21373i	−0.792247	−	0.187766i	−0.606765	+	0.794882i	$0.707533\pi$
$140$	−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	−0.762071	−	0.647493i	$-0.775818\pi$
$149$	−16.5311	+	1.93221i	−1.35428	+	0.158293i	−0.592208	+	0.805785i	$0.701743\pi$
$150$		0			0
$151$	1.53093	−	1.00691i	0.124585	−	0.0819412i	−0.485687	−	0.874133i	$-0.661430\pi$
$151$	1.53093	−	1.00691i	0.124585	−	0.0819412i	0.610272	+	0.792192i	$0.291060\pi$
$152$	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	−0.875618	−	0.483004i	$-0.839546\pi$
$157$	0.628412	−	10.7894i	0.0501528	−	0.861090i	0.925771	−	0.378085i	$-0.123417\pi$
$158$	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	0.860872	+	0.508822i	$0.169919\pi$
$167$	−0.688138	+	11.8149i	−0.0532498	+	0.914263i	−0.914121	+	0.405441i	$0.867118\pi$
$168$		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	−0.207993	−	0.978130i	$-0.566693\pi$
$173$	7.99384	−	5.25763i	0.607761	−	0.399730i	0.815753	+	0.578400i	$0.196323\pi$
$174$		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	0.601251	−	0.799060i	$-0.294669\pi$
$179$	−1.08723	−	0.912294i	−0.0812633	−	0.0681880i	−0.682514	+	0.730872i	$0.739114\pi$
$180$		0			0
$181$	−7.58350	+	6.36331i	−0.563677	+	0.472981i	−0.879541	−	0.475823i	$-0.842150\pi$
$181$	−7.58350	+	6.36331i	−0.563677	+	0.472981i	0.315864	+	0.948804i	$0.397706\pi$
$182$	−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	0.227981	+	0.973666i	$0.426788\pi$
$191$	−10.6439	+	14.2973i	−0.770166	+	1.03451i	−0.998147	+	0.0608474i	$0.980620\pi$
$192$		0			0
$193$	−7.92466	−	26.4702i	−0.570430	−	1.90537i	−0.385897	−	0.922542i	$-0.626108\pi$
$193$	−7.92466	−	26.4702i	−0.570430	−	1.90537i	−0.184533	−	0.982826i	$-0.559077\pi$
$194$	−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	−0.999178	−	0.0405468i	$-0.987090\pi$
$197$	−1.04040	−	5.90042i	−0.0741256	−	0.420387i	0.925052	−	0.379840i	$-0.124021\pi$
$198$		0			0
$199$	2.78863	−	15.8151i	0.197681	−	1.12110i	−0.710868	−	0.703326i	$-0.751698\pi$
$199$	2.78863	−	15.8151i	0.197681	−	1.12110i	0.908549	−	0.417779i	$-0.137191\pi$
$200$	−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	−0.730762	−	0.682633i	$-0.760835\pi$
$211$	−9.00002	+	4.51998i	−0.619587	+	0.311168i	0.111175	+	0.993801i	$0.464539\pi$
$212$	−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	0.954030	−	0.299711i	$-0.0968903\pi$
$223$	8.95026	+	9.48672i	0.599354	+	0.635278i	−0.354676	+	0.934989i	$0.615409\pi$
$224$	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	−0.871246	−	0.490846i	$-0.836688\pi$
$227$	−0.947304	−	16.2646i	−0.0628748	−	1.07952i	0.808372	−	0.588673i	$-0.200349\pi$
$228$		0			0
$229$	−4.02339	−	5.40434i	−0.265873	−	0.357129i	0.649059	−	0.760738i	$-0.275163\pi$
$229$	−4.02339	−	5.40434i	−0.265873	−	0.357129i	−0.914931	+	0.403609i	$0.867756\pi$
$230$	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	−0.729894	−	0.683560i	$-0.760431\pi$
$233$	−12.9692	+	4.72040i	−0.849641	+	0.309244i	−0.119747	+	0.992804i	$0.538208\pi$
$234$		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	−0.943163	−	0.332330i	$-0.892165\pi$
$239$	−8.60415	+	9.11986i	−0.556556	+	0.589915i	0.386607	+	0.922244i	$0.373647\pi$
$240$		0			0
$241$	5.42266	+	12.5711i	0.349304	+	0.809778i	0.998779	+	0.0493949i	$0.0157293\pi$
$241$	5.42266	+	12.5711i	0.349304	+	0.809778i	−0.649475	+	0.760383i	$0.725011\pi$
$242$	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	−0.0836277	−	0.996497i	$-0.526651\pi$
$251$	−12.4879	−	4.54521i	−0.788226	−	0.286891i	−0.704599	+	0.709606i	$0.748873\pi$
$252$		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	0.735076	−	0.677984i	$-0.237146\pi$
$257$	−2.00787	−	2.69704i	−0.125248	−	0.168237i	−0.860324	+	0.509747i	$0.829739\pi$
$258$		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	0.995365	+	0.0961708i	$0.0306595\pi$
$263$	16.7605	+	17.7651i	1.03350	+	1.09544i	0.0381328	+	0.999273i	$0.487859\pi$
$264$		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	0.878467	−	0.477802i	$-0.158567\pi$
$269$	0.417322	+	0.722824i	0.0254446	+	0.0440713i	−0.853023	+	0.521874i	$0.825233\pi$
$270$		0			0
$271$	14.1085	−	24.4366i	0.857029	−	1.48442i	−0.0177208	−	0.999843i	$-0.505641\pi$
$271$	14.1085	−	24.4366i	0.857029	−	1.48442i	0.874750	−	0.484575i	$-0.161026\pi$
$272$	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	−0.336280	−	0.941762i	$-0.609169\pi$
$277$	7.69228	−	25.6940i	0.462185	−	1.54380i	0.798465	−	0.602042i	$-0.205646\pi$
$278$	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	0.793871	−	0.608087i	$-0.208063\pi$
$281$	13.0781	+	6.56809i	0.780177	+	0.391819i	−0.0136939	+	0.999906i	$0.504359\pi$
$282$		0			0
$283$	0.462413	−	1.07199i	0.0274876	−	0.0637234i	−0.903919	−	0.427703i	$-0.859323\pi$
$283$	0.462413	−	1.07199i	0.0274876	−	0.0637234i	0.931407	+	0.363980i	$0.118582\pi$
$284$	−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	−0.975930	−	0.218085i	$-0.930019\pi$
$293$	−4.79954	−	16.0316i	−0.280392	−	0.936575i	0.695538	−	0.718490i	$-0.255166\pi$
$294$		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	0.0762844	−	0.997086i	$-0.475694\pi$
$307$	−15.6362	−	13.1204i	−0.892407	−	0.748818i	−0.968691	+	0.248268i	$0.920139\pi$
$308$	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	−0.300889	−	0.953659i	$-0.597284\pi$
$311$	−6.59097	+	0.770374i	−0.373740	+	0.0436839i	−0.0728501	+	0.997343i	$0.523209\pi$
$312$		0			0
$313$	7.66936	−	5.04422i	0.433498	−	0.285116i	−0.313946	−	0.949441i	$-0.601651\pi$
$313$	7.66936	−	5.04422i	0.433498	−	0.285116i	0.747444	+	0.664325i	$0.231281\pi$
$314$	−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	−0.229247	−	0.973368i	$-0.573626\pi$
$317$	0.0487426	−	0.0115522i	0.00273766	−	0.000648836i	0.231984	+	0.972719i	$0.425478\pi$
$318$		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	−0.693327	−	0.720623i	$-0.743856\pi$
$331$	−18.0022	+	4.26660i	−0.989491	+	0.234514i	−0.296164	+	0.955137i	$0.595708\pi$
$332$	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	−0.0167846	−	0.999859i	$-0.505343\pi$
$337$	3.62501	−	0.423702i	0.197467	−	0.0230805i	0.214251	+	0.976779i	$0.431269\pi$
$338$	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	0.336307	−	0.941752i	$-0.390822\pi$
$347$	3.98981	+	0.945603i	0.214184	+	0.0507626i	−0.122123	+	0.992515i	$0.538970\pi$
$348$		0			0
$349$	−7.51393	−	0.878252i	−0.402211	−	0.0470118i	−0.0874174	−	0.996172i	$-0.527861\pi$
$349$	−7.51393	−	0.878252i	−0.402211	−	0.0470118i	−0.314794	+	0.949160i	$0.601935\pi$
$350$	−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	−0.768343	−	0.640038i	$-0.778919\pi$
$353$	1.22443	−	1.64470i	0.0651699	−	0.0875384i	0.833513	+	0.552500i	$0.186326\pi$
$354$		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	−0.995594	−	0.0937737i	$-0.970107\pi$
$359$	−1.74531	−	9.89817i	−0.0921141	−	0.522405i	0.903479	−	0.428631i	$-0.141004\pi$
$360$		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	0.995599	−	0.0937115i	$-0.0298731\pi$
$367$	29.0225	+	14.5756i	1.51496	+	0.760842i	0.519363	+	0.854554i	$0.326169\pi$
$368$	−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	−0.0636783	−	0.997970i	$-0.520283\pi$
$373$	13.4959	−	6.77789i	0.698791	−	0.350946i	0.762469	+	0.647024i	$0.223987\pi$
$374$	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	0.898155	−	0.439680i	$-0.144908\pi$
$379$	1.32973	+	2.30316i	0.0683037	+	0.118305i	−0.829851	+	0.557985i	$0.811575\pi$
$380$	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	0.582250	−	0.813010i	$-0.302173\pi$
$383$	1.29846	+	0.854009i	0.0663481	+	0.0436378i	−0.515902	+	0.856648i	$0.672543\pi$
$384$		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	0.999382	+	0.0351591i	$0.0111938\pi$
$389$	0.213782	+	3.67050i	0.0108392	+	0.186102i	−0.988543	+	0.150943i	$0.951769\pi$
$390$		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	0.996223	+	0.0868301i	$0.0276737\pi$
$397$	36.1674	+	13.1638i	1.81519	+	0.660674i	0.818965	+	0.573844i	$0.194548\pi$
$398$	−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	−0.956625	−	0.291324i	$-0.905904\pi$
$401$	−12.2187	+	12.9510i	−0.610171	+	0.646743i	0.346454	+	0.938067i	$0.387386\pi$
$402$		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	−0.337373	−	0.941371i	$-0.609538\pi$
$409$	12.5796	−	13.3336i	0.622022	−	0.659305i	0.959395	+	0.282066i	$0.0910198\pi$
$410$	−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	0.581680	−	0.813418i	$-0.302396\pi$
$419$	−7.45896	−	10.0191i	−0.364394	−	0.489466i	−0.946074	+	0.323952i	$0.894988\pi$
$420$		0			0
$421$	−1.25709	−	21.5834i	−0.0612668	−	1.05191i	−0.879156	−	0.476534i	$-0.841893\pi$
$421$	−1.25709	−	21.5834i	−0.0612668	−	1.05191i	0.817889	−	0.575376i	$-0.195144\pi$
$422$	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	0.948524	+	0.316707i	$0.102577\pi$
$431$	15.5400	+	26.9162i	0.748538	+	1.29651i	−0.199986	+	0.979799i	$0.564090\pi$
$432$		0			0
$433$	−6.64480	+	11.5091i	−0.319329	+	0.553093i	−0.980348	−	0.197275i	$-0.936791\pi$
$433$	−6.64480	+	11.5091i	−0.319329	+	0.553093i	0.661019	+	0.750369i	$0.270124\pi$
$434$	−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	−0.948763	−	0.315990i	$-0.897663\pi$
$439$	0.367842	−	1.22868i	0.0175562	−	0.0586417i	0.966319	+	0.257348i	$0.0828487\pi$
$440$	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	−0.996294	−	0.0860134i	$-0.972587\pi$
$443$	−34.9439	−	17.5495i	−1.66023	−	0.833800i	−0.663939	−	0.747787i	$-0.731116\pi$
$444$		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	0.845895	+	0.533349i	$0.179067\pi$
$449$	−2.78437	+	15.7909i	−0.131403	+	0.745221i	−0.977298	+	0.211871i	$0.932044\pi$
$450$		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	−0.852832	−	0.522186i	$-0.825117\pi$
$457$	−2.30852	+	3.10088i	−0.107988	+	0.145053i	0.744844	+	0.667239i	$0.232524\pi$
$458$	−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	0.591981	−	0.805952i	$-0.298346\pi$
$461$	21.0874	+	2.46477i	0.982140	+	0.114796i	0.390159	+	0.920748i	$0.372420\pi$
$462$		0			0
$463$	18.7929	+	4.45400i	0.873381	+	0.206995i	0.642778	−	0.766053i	$-0.277782\pi$
$463$	18.7929	+	4.45400i	0.873381	+	0.206995i	0.230603	+	0.973048i	$0.425930\pi$
$464$	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	−0.712874	−	0.701292i	$-0.752607\pi$
$467$	−3.15564	+	2.64790i	−0.146026	+	0.122530i	0.566848	+	0.823822i	$0.308162\pi$
$468$		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	0.465269	−	0.885169i	$-0.345958\pi$
$479$	27.9772	−	6.63072i	1.27831	−	0.302966i	0.813043	+	0.582204i	$0.197809\pi$
$480$		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	−0.733108	−	0.680112i	$-0.761931\pi$
$491$	1.63971	−	28.1528i	0.0739991	−	1.27052i	0.807108	−	0.590404i	$-0.201032\pi$
$492$		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	−0.142508	−	0.989794i	$-0.545517\pi$
$499$	−1.18198	+	0.138153i	−0.0529126	+	0.00618460i	0.0895954	+	0.995978i	$0.471443\pi$
$500$	−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	0.739411	−	0.673255i	$-0.235104\pi$
$503$	4.59276	+	3.85379i	0.204781	+	0.171832i	−0.534629	+	0.845087i	$0.679549\pi$
$504$		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	0.733557	−	0.679628i	$-0.237859\pi$
$509$	24.4578	+	5.79659i	1.08407	+	0.256929i	0.350514	+	0.936558i	$0.386007\pi$
$510$		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	−0.792768	−	0.609524i	$-0.791361\pi$
$521$	−5.84968	−	33.1752i	−0.256279	−	1.45343i	0.536488	−	0.843908i	$-0.319750\pi$
$522$		0			0
$523$	4.18478	−	23.7331i	0.182988	−	1.03778i	−0.745526	−	0.666477i	$-0.767801\pi$
$523$	4.18478	−	23.7331i	0.182988	−	1.03778i	0.928513	−	0.371299i	$-0.121087\pi$
$524$	−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	0.511068	−	0.859540i	$-0.329250\pi$
$541$	−11.3703	−	19.6940i	−0.488849	−	0.846712i	−0.999918	+	0.0128282i	$0.995917\pi$
$542$	−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	0.721635	−	0.692274i	$-0.243391\pi$
$547$	−0.267245	−	0.283263i	−0.0114266	−	0.0121115i	−0.733062	+	0.680162i	$0.761909\pi$
$548$	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	0.109951	−	0.993937i	$-0.464931\pi$
$557$	19.6611	−	7.15607i	0.833069	−	0.303212i	0.723118	+	0.690725i	$0.242708\pi$
$558$		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	−0.495084	−	0.868845i	$-0.664863\pi$
$563$	9.51661	−	10.0870i	0.401077	−	0.425117i	0.896162	+	0.443728i	$0.146344\pi$
$564$		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	0.823381	−	0.567489i	$-0.192085\pi$
$569$	−3.68383	−	8.54007i	−0.154434	−	0.358019i	−0.977815	+	0.209471i	$0.932826\pi$
$570$		0			0
$571$	−24.7267	+	26.2088i	−1.03478	+	1.09680i	−0.0395538	+	0.999217i	$0.512594\pi$
$571$	−24.7267	+	26.2088i	−1.03478	+	1.09680i	−0.995227	+	0.0975862i	$0.968888\pi$
$572$	−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	−0.166675	−	0.986012i	$-0.553303\pi$
$577$	8.15363	−	2.96768i	0.339440	−	0.123546i	0.506115	+	0.862466i	$0.331081\pi$
$578$	−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	0.582864	−	0.812569i	$-0.301932\pi$
$587$	−6.35311	−	6.73390i	−0.262221	−	0.277938i	−0.845085	+	0.534632i	$0.820450\pi$
$588$		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	0.946862	+	0.321639i	$0.104234\pi$
$593$	18.3119	+	31.7171i	0.751979	+	1.30247i	−0.194884	+	0.980826i	$0.562433\pi$
$594$		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	0.0648441	−	0.997895i	$-0.479345\pi$
$599$	22.1250	−	11.1116i	0.904001	−	0.454007i	0.839157	+	0.543889i	$0.183049\pi$
$600$		0			0
$601$	−6.33556	+	21.1622i	−0.258433	+	0.863226i	0.726034	+	0.687658i	$0.241361\pi$
$601$	−6.33556	+	21.1622i	−0.258433	+	0.863226i	−0.984467	+	0.175568i	$0.943824\pi$
$602$	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	−0.977656	−	0.210212i	$-0.932585\pi$
$607$	−3.79033	+	8.78698i	−0.153845	+	0.356653i	0.823811	+	0.566865i	$0.191844\pi$
$608$	−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	−0.994326	−	0.106373i	$-0.966076\pi$
$613$	−2.38544	−	13.5285i	−0.0963469	−	0.546410i	0.897979	−	0.440037i	$-0.145035\pi$
$614$	−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	0.999909	−	0.0135025i	$-0.00429810\pi$
$617$	3.90172	+	13.0327i	0.157077	+	0.524675i	−0.842831	+	0.538178i	$0.819113\pi$
$618$		0			0
$619$	−8.51625	+	11.4393i	−0.342297	+	0.459785i	−0.939622	−	0.342215i	$-0.888823\pi$
$619$	−8.51625	+	11.4393i	−0.342297	+	0.459785i	0.597325	+	0.801999i	$0.296230\pi$
$620$	−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	0.513434	−	0.858129i	$-0.328373\pi$
$631$	−6.09157	−	5.11144i	−0.242502	−	0.203483i	−0.755935	+	0.654646i	$0.772818\pi$
$632$	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	−0.149043	−	0.988831i	$-0.547619\pi$
$641$	4.09023	−	0.969403i	0.161555	−	0.0382891i	0.310597	+	0.950542i	$0.399471\pi$
$642$		0			0
$643$	−1.11571	+	19.1561i	−0.0439995	+	0.755442i	0.902092	+	0.431543i	$0.142031\pi$
$643$	−1.11571	+	19.1561i	−0.0439995	+	0.755442i	−0.946092	+	0.323899i	$0.895006\pi$
$644$	−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	0.955588	+	0.294705i	$0.0952214\pi$
$653$	−0.709166	+	12.1759i	−0.0277518	+	0.476480i	−0.983340	+	0.181775i	$0.941816\pi$
$654$		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	−0.107947	−	0.994157i	$-0.534428\pi$
$659$	19.5651	−	12.8682i	0.762148	−	0.501272i	0.870095	+	0.492884i	$0.164057\pi$
$660$		0			0
$661$	33.4396	−	3.90853i	1.30065	−	0.152024i	0.562577	−	0.826745i	$-0.309810\pi$
$661$	33.4396	−	3.90853i	1.30065	−	0.152024i	0.738073	+	0.674721i	$0.235736\pi$
$662$	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	0.350293	−	0.936640i	$-0.386082\pi$
$673$	12.3262	+	1.44072i	0.475140	+	0.0555358i	0.124847	+	0.992176i	$0.460156\pi$
$674$	−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	−0.938860	−	0.344299i	$-0.888117\pi$
$677$	−8.84021	+	11.8745i	−0.339757	+	0.456373i	0.599103	+	0.800672i	$0.295524\pi$
$678$		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	0.766499	+	0.642246i	$0.221997\pi$
$683$	6.94875	+	39.4083i	0.265887	+	1.50792i	−0.500612	+	0.865672i	$0.666892\pi$
$684$		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	−0.371578	−	0.928402i	$-0.621183\pi$
$691$	−35.1761	−	17.6661i	−1.33816	−	0.672050i	−0.966584	+	0.256351i	$0.917480\pi$
$692$	−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	−0.907354	−	0.420368i	$-0.861901\pi$
$701$	−2.37301	+	4.11018i	−0.0896274	+	0.155239i	0.817726	+	0.575607i	$0.195234\pi$
$702$		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	0.722667	−	0.691197i	$-0.242916\pi$
$709$	−0.249769	−	0.264740i	−0.00938029	−	0.00994253i	−0.732047	+	0.681254i	$0.761435\pi$
$710$	−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	−0.610301	−	0.792170i	$-0.708951\pi$
$719$	−15.2471	+	5.54950i	−0.568622	+	0.206961i	0.0416792	+	0.999131i	$0.486729\pi$
$720$		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	0.761474	−	0.648196i	$-0.224476\pi$
$727$	−6.27054	−	14.5368i	−0.232562	−	0.539138i	−0.994035	+	0.109057i	$0.965217\pi$
$728$	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	−0.188710	+	0.982033i	$0.560431\pi$
$733$	−31.3546	+	33.2339i	−1.15811	+	1.22752i	−0.969399	+	0.245491i	$0.921051\pi$
$734$	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	−0.380873	−	0.924628i	$-0.624376\pi$
$739$	−2.12852	+	0.774717i	−0.0782987	+	0.0284984i	0.302574	+	0.953126i	$0.402154\pi$
$740$	−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	0.771213	−	0.636577i	$-0.219650\pi$
$743$	−1.63022	−	2.18977i	−0.0598071	−	0.0803349i	−0.831020	+	0.556242i	$0.812243\pi$
$744$		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	0.996507	−	0.0835052i	$-0.0266115\pi$
$751$	36.0238	+	23.6932i	1.31453	+	0.864579i	0.318021	+	0.948084i	$0.396982\pi$
$752$	−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	−0.261963	−	0.965078i	$-0.584370\pi$
$757$	19.3916	−	33.5873i	0.704800	−	1.22075i	0.966764	−	0.255672i	$-0.0822968\pi$
$758$	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	−0.979561	−	0.201147i	$-0.935533\pi$
$761$	−38.7081	+	19.4400i	−1.40317	+	0.704698i	−0.423608	+	0.905845i	$0.639237\pi$
$762$		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	−0.0440729	−	0.999028i	$-0.514033\pi$
$769$	19.7676	−	45.8265i	0.712839	−	1.65255i	0.756912	−	0.653517i	$-0.226707\pi$
$770$	−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	−0.940789	−	0.338993i	$-0.889914\pi$
$773$	1.64610	−	9.33547i	0.0592059	−	0.335774i	0.999995	+	0.00321947i	$0.00102479\pi$
$774$		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
$782$

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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