LMFDB - Embedded newform 729.2.k.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65153 - 0.0342818i) q^{2} +(0.952364 + 1.44672i) q^{3} +(5.03008 + 0.130090i) q^{4} +(-0.525411 - 0.161006i) q^{5} +(-2.47562 - 3.86867i) q^{6} +(-0.732244 + 1.82595i) q^{7} +(-8.03343 - 0.311734i) q^{8} +(-1.18601 + 2.75561i) q^{9} +O(q^{10})$	\(q+(-2.65153 - 0.0342818i) q^{2} +(0.952364 + 1.44672i) q^{3} +(5.03008 + 0.130090i) q^{4} +(-0.525411 - 0.161006i) q^{5} +(-2.47562 - 3.86867i) q^{6} +(-0.732244 + 1.82595i) q^{7} +(-8.03343 - 0.311734i) q^{8} +(-1.18601 + 2.75561i) q^{9} +(1.38762 + 0.444923i) q^{10} +(-1.49298 - 0.849151i) q^{11} +(4.60226 + 7.40102i) q^{12} +(0.0851078 + 0.190492i) q^{13} +(2.00416 - 4.81644i) q^{14} +(-0.267452 - 0.913459i) q^{15} +(11.2401 + 0.581782i) q^{16} +(-5.31943 - 2.41798i) q^{17} +(3.23920 - 7.26591i) q^{18} +(-2.03545 - 2.96775i) q^{19} +(-2.62192 - 0.878223i) q^{20} +(-3.33900 + 0.679611i) q^{21} +(3.92956 + 2.30273i) q^{22} +(0.731911 - 2.23293i) q^{23} +(-7.19975 - 11.9190i) q^{24} +(-3.89144 - 2.63213i) q^{25} +(-0.219135 - 0.508012i) q^{26} +(-5.11611 + 0.908520i) q^{27} +(-3.92078 + 9.08940i) q^{28} +(2.94839 - 1.88504i) q^{29} +(0.677840 + 2.43123i) q^{30} +(0.326466 + 1.20282i) q^{31} +(-13.7380 - 0.889291i) q^{32} +(-0.193373 - 2.96862i) q^{33} +(14.0217 + 6.59368i) q^{34} +(0.678716 - 0.841476i) q^{35} +(-6.32419 + 13.7067i) q^{36} +(-4.45653 - 0.875234i) q^{37} +(5.29530 + 7.93885i) q^{38} +(-0.194535 + 0.304545i) q^{39} +(4.17066 + 1.45722i) q^{40} +(-0.408447 + 0.154671i) q^{41} +(8.87673 - 1.68754i) q^{42} +(4.87607 - 2.14082i) q^{43} +(-7.39934 - 4.46552i) q^{44} +(1.06681 - 1.25687i) q^{45} +(-2.01723 + 5.89558i) q^{46} +(-2.53051 + 9.32335i) q^{47} +(9.86296 + 16.8153i) q^{48} +(2.26256 + 2.16243i) q^{49} +(10.2280 + 7.11257i) q^{50} +(-1.56789 - 9.99852i) q^{51} +(0.403318 + 0.969262i) q^{52} +(-0.702501 + 0.744607i) q^{53} +(13.5966 - 2.23358i) q^{54} +(0.647709 + 0.686531i) q^{55} +(6.45163 - 14.4403i) q^{56} +(2.35503 - 5.77110i) q^{57} +(-7.88235 + 4.89714i) q^{58} +(-0.114359 + 0.0194032i) q^{59} +(-1.22647 - 4.62957i) q^{60} +(6.91784 - 12.7313i) q^{61} +(-0.824397 - 3.20051i) q^{62} +(-4.16315 - 4.18336i) q^{63} +(13.9537 + 1.08457i) q^{64} +(-0.0140463 - 0.113789i) q^{65} +(0.410963 + 7.87801i) q^{66} +(-5.15688 + 2.67392i) q^{67} +(-26.4426 - 12.8546i) q^{68} +(3.92747 - 1.06769i) q^{69} +(-1.82848 + 2.20793i) q^{70} +(-0.537644 - 0.416706i) q^{71} +(10.3867 - 21.7673i) q^{72} +(-11.3675 + 3.64485i) q^{73} +(11.7866 + 2.47348i) q^{74} +(0.101902 - 8.13657i) q^{75} +(-9.85239 - 15.1928i) q^{76} +(2.64373 - 2.10431i) q^{77} +(0.526256 - 0.800840i) q^{78} +(0.466677 - 2.46023i) q^{79} +(-5.81199 - 2.11539i) q^{80} +(-6.18677 - 6.53635i) q^{81} +(1.08831 - 0.396113i) q^{82} +(-2.60006 - 15.9487i) q^{83} +(-16.8838 + 2.98413i) q^{84} +(2.40558 + 2.12689i) q^{85} +(-13.0024 + 5.50928i) q^{86} +(5.53506 + 2.47026i) q^{87} +(11.7290 + 7.28700i) q^{88} +(-11.0012 - 4.49450i) q^{89} +(-2.87176 + 3.29606i) q^{90} +(-0.410148 + 0.0159156i) q^{91} +(3.97205 - 11.1366i) q^{92} +(-1.42923 + 1.61783i) q^{93} +(7.02933 - 24.6344i) q^{94} +(0.591621 + 1.88701i) q^{95} +(-11.7971 - 20.7220i) q^{96} +(-2.70581 + 11.7548i) q^{97} +(-5.92511 - 5.81130i) q^{98} +(4.11061 - 3.10697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.65153	−	0.0342818i	−1.87491	−	0.0242409i	−0.932958	−	0.359984i	$-0.882782\pi$
$2$	−2.65153	−	0.0342818i	−1.87491	−	0.0242409i	−0.941953	+	0.335743i	$0.891012\pi$
$3$	0.952364	+	1.44672i	0.549847	+	0.835265i
$3$	0.952364	+	1.44672i	0.549847	+	0.835265i
$4$	5.03008	+	0.130090i	2.51504	+	0.0650452i
$5$	−0.525411	−	0.161006i	−0.234971	−	0.0720039i	0.173284	−	0.984872i	$-0.444562\pi$
$5$	−0.525411	−	0.161006i	−0.234971	−	0.0720039i	−0.408255	+	0.912868i	$0.633863\pi$
$6$	−2.47562	−	3.86867i	−1.01067	−	1.57938i
$7$	−0.732244	+	1.82595i	−0.276762	+	0.690143i	−1.00000		0.000456533i	$-0.999855\pi$
$7$	−0.732244	+	1.82595i	−0.276762	+	0.690143i	0.723238	+	0.690599i	$0.242653\pi$
$8$	−8.03343	−	0.311734i	−2.84024	−	0.110214i
$9$	−1.18601	+	2.75561i	−0.395336	+	0.918537i
$10$	1.38762	+	0.444923i	0.438804	+	0.140697i
$11$	−1.49298	−	0.849151i	−0.450150	−	0.256029i	0.252455	−	0.967609i	$-0.418762\pi$
$11$	−1.49298	−	0.849151i	−0.450150	−	0.256029i	−0.702605	+	0.711580i	$0.747980\pi$
$12$	4.60226	+	7.40102i	1.32856	+	2.13649i
$13$	0.0851078	+	0.190492i	0.0236046	+	0.0528330i	0.924439	−	0.381330i	$-0.124534\pi$
$13$	0.0851078	+	0.190492i	0.0236046	+	0.0528330i	−0.900834	+	0.434163i	$0.857044\pi$
$14$	2.00416	−	4.81644i	0.535634	−	1.28725i
$15$	−0.267452	−	0.913459i	−0.0690558	−	0.235854i
$16$	11.2401	+	0.581782i	2.81002	+	0.145445i
$17$	−5.31943	−	2.41798i	−1.29015	−	0.586445i	−0.353082	−	0.935592i	$-0.614866\pi$
$17$	−5.31943	−	2.41798i	−1.29015	−	0.586445i	−0.937068	+	0.349147i	$0.886471\pi$
$18$	3.23920	−	7.26591i	0.763486	−	1.71259i
$19$	−2.03545	−	2.96775i	−0.466963	−	0.680849i	0.517651	−	0.855592i	$-0.326807\pi$
$19$	−2.03545	−	2.96775i	−0.466963	−	0.680849i	−0.984614	+	0.174743i	$0.944091\pi$
$20$	−2.62192	−	0.878223i	−0.586278	−	0.196377i
$21$	−3.33900	+	0.679611i	−0.728629	+	0.148303i
$22$	3.92956	+	2.30273i	0.837785	+	0.490943i
$23$	0.731911	−	2.23293i	0.152614	−	0.465598i	−0.844990	−	0.534782i	$-0.820394\pi$
$23$	0.731911	−	2.23293i	0.152614	−	0.465598i	0.997604	+	0.0691845i	$0.0220397\pi$
$24$	−7.19975	−	11.9190i	−1.46964	−	2.43296i
$25$	−3.89144	−	2.63213i	−0.778287	−	0.526427i
$26$	−0.219135	−	0.508012i	−0.0429759	−	0.0996294i
$27$	−5.11611	+	0.908520i	−0.984596	+	0.174845i
$28$	−3.92078	+	9.08940i	−0.740958	+	1.71773i
$29$	2.94839	−	1.88504i	0.547502	−	0.350042i	−0.235684	−	0.971830i	$-0.575733\pi$
$29$	2.94839	−	1.88504i	0.547502	−	0.350042i	0.783186	+	0.621787i	$0.213593\pi$
$30$	0.677840	+	2.43123i	0.123756	+	0.443880i
$31$	0.326466	+	1.20282i	0.0586349	+	0.216033i	0.988338	−	0.152277i	$-0.0486606\pi$
$31$	0.326466	+	1.20282i	0.0586349	+	0.216033i	−0.929703	+	0.368310i	$0.879936\pi$
$32$	−13.7380	−	0.889291i	−2.42857	−	0.157206i
$33$	−0.193373	−	2.96862i	−0.0336619	−	0.516771i
$34$	14.0217	+	6.59368i	2.40470	+	1.13081i
$35$	0.678716	−	0.841476i	0.114724	−	0.142235i
$36$	−6.32419	+	13.7067i	−1.05403	+	2.28444i
$37$	−4.45653	−	0.875234i	−0.732649	−	0.143888i	−0.187545	−	0.982256i	$-0.560053\pi$
$37$	−4.45653	−	0.875234i	−0.732649	−	0.143888i	−0.545104	+	0.838368i	$0.683510\pi$
$38$	5.29530	+	7.93885i	0.859011	+	1.28785i
$39$	−0.194535	+	0.304545i	−0.0311506	+	0.0487662i
$40$	4.17066	+	1.45722i	0.659439	+	0.230406i
$41$	−0.408447	+	0.154671i	−0.0637888	+	0.0241556i	−0.385828	−	0.922571i	$-0.626084\pi$
$41$	−0.408447	+	0.154671i	−0.0637888	+	0.0241556i	0.322040	+	0.946726i	$0.395632\pi$
$42$	8.87673	−	1.68754i	1.36971	−	0.260393i
$43$	4.87607	−	2.14082i	0.743594	−	0.326472i	0.00442288	−	0.999990i	$-0.498592\pi$
$43$	4.87607	−	2.14082i	0.743594	−	0.326472i	0.739171	+	0.673518i	$0.235218\pi$
$44$	−7.39934	−	4.46552i	−1.11549	−	0.673203i
$45$	1.06681	−	1.25687i	0.159031	−	0.187364i
$46$	−2.01723	+	5.89558i	−0.297424	+	0.869255i
$47$	−2.53051	+	9.32335i	−0.369113	+	1.35995i	0.500295	+	0.865855i	$0.333225\pi$
$47$	−2.53051	+	9.32335i	−0.369113	+	1.35995i	−0.869408	+	0.494096i	$0.835499\pi$
$48$	9.86296	+	16.8153i	1.42360	+	2.42708i
$49$	2.26256	+	2.16243i	0.323223	+	0.308919i
$50$	10.2280	+	7.11257i	1.44646	+	1.00587i
$51$	−1.56789	−	9.99852i	−0.219548	−	1.40007i
$52$	0.403318	+	0.969262i	0.0559301	+	0.134412i
$53$	−0.702501	+	0.744607i	−0.0964959	+	0.102280i	−0.773822	−	0.633404i	$-0.781657\pi$
$53$	−0.702501	+	0.744607i	−0.0964959	+	0.102280i	0.677326	+	0.735683i	$0.263139\pi$
$54$	13.5966	−	2.23358i	1.85027	−	0.303951i
$55$	0.647709	+	0.686531i	0.0873371	+	0.0925719i
$56$	6.45163	−	14.4403i	0.862136	−	1.92967i
$57$	2.35503	−	5.77110i	0.311931	−	0.764402i
$58$	−7.88235	+	4.89714i	−1.03500	+	0.643026i
$59$	−0.114359	+	0.0194032i	−0.0148883	+	0.00252608i	−0.174718	−	0.984619i	$-0.555901\pi$
$59$	−0.114359	+	0.0194032i	−0.0148883	+	0.00252608i	0.159830	+	0.987145i	$0.448905\pi$
$60$	−1.22647	−	4.62957i	−0.158337	−	0.597675i
$61$	6.91784	−	12.7313i	0.885739	−	1.63007i	0.114593	−	0.993413i	$-0.463444\pi$
$61$	6.91784	−	12.7313i	0.885739	−	1.63007i	0.771146	−	0.636658i	$-0.219684\pi$
$62$	−0.824397	−	3.20051i	−0.104699	−	0.406465i
$63$	−4.16315	−	4.18336i	−0.524507	−	0.527054i
$64$	13.9537	+	1.08457i	1.74422	+	0.135571i
$65$	−0.0140463	−	0.113789i	−0.00174222	−	0.0141138i
$66$	0.410963	+	7.87801i	0.0505860	+	0.969716i
$67$	−5.15688	+	2.67392i	−0.630013	+	0.326671i	−0.745368	−	0.666653i	$-0.767726\pi$
$67$	−5.15688	+	2.67392i	−0.630013	+	0.326671i	0.115355	+	0.993324i	$0.463199\pi$
$68$	−26.4426	−	12.8546i	−3.20664	−	1.55885i
$69$	3.92747	−	1.06769i	0.472812	−	0.128535i
$70$	−1.82848	+	2.20793i	−0.218545	+	0.263898i
$71$	−0.537644	−	0.416706i	−0.0638066	−	0.0494539i	0.580198	−	0.814475i	$-0.302975\pi$
$71$	−0.537644	−	0.416706i	−0.0638066	−	0.0494539i	−0.644005	+	0.765022i	$0.722728\pi$
$72$	10.3867	−	21.7673i	1.22409	−	2.56530i
$73$	−11.3675	+	3.64485i	−1.33047	+	0.426598i	−0.883701	−	0.468052i	$-0.844956\pi$
$73$	−11.3675	+	3.64485i	−1.33047	+	0.426598i	−0.446768	+	0.894650i	$0.647425\pi$
$74$	11.7866	+	2.47348i	1.37016	+	0.287537i
$75$	0.101902	−	8.13657i	0.0117666	−	0.939530i
$76$	−9.85239	−	15.1928i	−1.13015	−	1.74274i
$77$	2.64373	−	2.10431i	0.301281	−	0.239808i
$78$	0.526256	−	0.800840i	0.0595867	−	0.0906772i
$79$	0.466677	−	2.46023i	0.0525053	−	0.276797i	−0.946431	−	0.322906i	$-0.895340\pi$
$79$	0.466677	−	2.46023i	0.0525053	−	0.276797i	0.998936	+	0.0461083i	$0.0146819\pi$
$80$	−5.81199	−	2.11539i	−0.649800	−	0.236508i
$81$	−6.18677	−	6.53635i	−0.687419	−	0.726261i
$82$	1.08831	−	0.396113i	0.120184	−	0.0437434i
$83$	−2.60006	−	15.9487i	−0.285394	−	1.75060i	−0.598721	−	0.800957i	$-0.704324\pi$
$83$	−2.60006	−	15.9487i	−0.285394	−	1.75060i	0.313327	−	0.949645i	$-0.398556\pi$
$84$	−16.8838	+	2.98413i	−1.84218	+	0.325595i
$85$	2.40558	+	2.12689i	0.260921	+	0.230694i
$86$	−13.0024	+	5.50928i	−1.40209	+	0.594081i
$87$	5.53506	+	2.47026i	0.593420	+	0.264839i
$88$	11.7290	+	7.28700i	1.25032	+	0.776797i
$89$	−11.0012	−	4.49450i	−1.16613	−	0.476416i	−0.289309	−	0.957236i	$-0.593425\pi$
$89$	−11.0012	−	4.49450i	−1.16613	−	0.476416i	−0.876819	+	0.480820i	$0.840339\pi$
$90$	−2.87176	+	3.29606i	−0.302710	+	0.347435i
$91$	−0.410148	+	0.0159156i	−0.0429952	+	0.00166841i
$92$	3.97205	−	11.1366i	0.414115	−	1.16107i
$93$	−1.42923	+	1.61783i	−0.148205	+	0.167761i
$94$	7.02933	−	24.6344i	0.725021	−	2.54084i
$95$	0.591621	+	1.88701i	0.0606990	+	0.193603i
$96$	−11.7971	−	20.7220i	−1.20403	−	2.11494i
$97$	−2.70581	+	11.7548i	−0.274734	+	1.19352i	0.633059	+	0.774104i	$0.281799\pi$
$97$	−2.70581	+	11.7548i	−0.274734	+	1.19352i	−0.907793	+	0.419419i	$0.862234\pi$
$98$	−5.92511	−	5.81130i	−0.598526	−	0.587030i
$99$	4.11061	−	3.10697i	0.413132	−	0.312262i
$100$	−19.2318	−	13.7461i	−1.92318	−	1.37461i
$101$	−0.414474	+	2.76719i	−0.0412417	+	0.275346i	−0.999959	−	0.00901396i	$-0.997131\pi$
$101$	−0.414474	+	2.76719i	−0.0412417	+	0.275346i	0.958718	+	0.284360i	$0.0917809\pi$
$102$	3.81453	+	26.5651i	0.377695	+	2.63034i
$103$	−4.04510	−	11.3414i	−0.398576	−	1.11750i	−0.957537	−	0.288309i	$-0.906907\pi$
$103$	−4.04510	−	11.3414i	−0.398576	−	1.11750i	0.558961	−	0.829194i	$-0.311200\pi$
$104$	−0.624324	−	1.55683i	−0.0612200	−	0.152660i
$105$	1.86377	+	0.180522i	0.181885	+	0.0176172i
$106$	1.88822	−	1.95026i	0.183401	−	0.189426i
$107$	0.989086	+	16.9819i	0.0956185	+	1.64171i	0.615981	+	0.787761i	$0.288760\pi$
$107$	0.989086	+	16.9819i	0.0956185	+	1.64171i	−0.520362	+	0.853946i	$0.674203\pi$
$108$	−25.8526	+	3.90437i	−2.48767	+	0.375699i
$109$	0.362402	−	6.22220i	0.0347118	−	0.595979i	−0.935441	−	0.353484i	$-0.884997\pi$
$109$	0.362402	−	6.22220i	0.0347118	−	0.595979i	0.970153	−	0.242495i	$-0.0779659\pi$
$110$	−1.69388	−	1.84256i	−0.161505	−	0.175681i
$111$	−2.97802	−	7.28090i	−0.282661	−	0.691072i
$112$	−9.29277	+	20.0978i	−0.878085	+	1.89906i
$113$	−1.87226	+	1.37513i	−0.176127	+	0.129361i	−0.676481	−	0.736460i	$-0.736496\pi$
$113$	−1.87226	+	1.37513i	−0.176127	+	0.129361i	0.500353	+	0.865821i	$0.333204\pi$
$114$	−6.44226	+	15.2215i	−0.603373	+	1.42562i
$115$	−0.744068	+	1.05536i	−0.0693847	+	0.0984131i
$116$	15.0759	−	9.09832i	1.39976	−	0.844758i
$117$	−0.625860	+	0.00859893i	−0.0578608	+	0.000794972i
$118$	0.303891	−	0.0475277i	0.0279754	−	0.00437528i
$119$	8.31021	−	7.94243i	0.761795	−	0.728082i
$120$	1.86380	+	7.42158i	0.170141	+	0.677495i
$121$	−4.11477	−	6.91885i	−0.374070	−	0.628986i
$122$	−18.7793	+	33.5201i	−1.70020	+	3.03477i
$123$	−0.612757	−	0.443606i	−0.0552504	−	0.0399986i
$124$	1.48567	+	6.09276i	0.133417	+	0.547146i
$125$	3.34581	+	4.14816i	0.299259	+	0.371022i
$126$	10.8953	+	11.2350i	0.970629	+	1.00089i
$127$	−0.334434	−	17.2433i	−0.0296762	−	1.53010i	−0.658519	−	0.752564i	$-0.728817\pi$
$127$	−0.334434	−	17.2433i	−0.0296762	−	1.53010i	0.628842	−	0.777533i	$-0.283529\pi$
$128$	−9.54057	−	0.865773i	−0.843275	−	0.0765242i
$129$	7.74096	+	5.01548i	0.681554	+	0.441588i
$130$	0.0333431	+	0.302197i	0.00292438	+	0.0265044i
$131$	16.8993	−	1.53355i	1.47649	−	0.133987i	0.677588	−	0.735442i	$-0.263025\pi$
$131$	16.8993	−	1.53355i	1.47649	−	0.133987i	0.798907	+	0.601455i	$0.205412\pi$
$132$	−0.586490	−	14.9576i	−0.0510474	−	1.30189i
$133$	6.90940	−	1.54350i	0.599121	−	0.133838i
$134$	13.7653	−	6.91318i	1.18914	−	0.597208i
$135$	2.83434	+	0.346377i	0.243941	+	0.0298113i
$136$	41.9795	+	21.0829i	3.59971	+	1.80784i
$137$	16.7220	+	4.19224i	1.42866	+	0.358167i	0.878840	−	0.477117i	$-0.158318\pi$
$137$	16.7220	+	4.19224i	1.42866	+	0.358167i	0.549818	+	0.835284i	$0.314697\pi$
$138$	−10.4504	+	2.69636i	−0.889597	+	0.229530i
$139$	−14.9438	−	2.13963i	−1.26752	−	0.181481i	−0.524881	−	0.851175i	$-0.675890\pi$
$139$	−14.9438	−	2.13963i	−1.26752	−	0.181481i	−0.742637	+	0.669694i	$0.766425\pi$
$140$	3.52347	−	4.14440i	0.297787	−	0.350266i
$141$	−15.8983	+	5.21828i	−1.33888	+	0.439458i
$142$	1.41129	+	1.12334i	0.118433	+	0.0942683i
$143$	0.0346925	−	0.356670i	0.00290113	−	0.0298262i
$144$	−14.9340	+	30.2833i	−1.24450	+	2.52361i
$145$	−1.85262	+	0.515711i	−0.153851	+	0.0428275i
$146$	30.2663	−	9.27472i	2.50485	−	0.767581i
$147$	−0.973654	+	5.33272i	−0.0803056	+	0.439835i
$148$	−22.3028	−	4.98225i	−1.83328	−	0.409538i
$149$	−11.7668	+	2.94997i	−0.963978	+	0.241671i	−0.693018	−	0.720920i	$-0.743720\pi$
$149$	−11.7668	+	2.94997i	−0.963978	+	0.241671i	−0.270959	+	0.962591i	$0.587341\pi$
$150$	−0.549132	+	21.5708i	−0.0448364	+	1.76125i
$151$	−3.51664	−	4.13637i	−0.286180	−	0.336613i	0.599960	−	0.800030i	$-0.295183\pi$
$151$	−3.51664	−	4.13637i	−0.286180	−	0.336613i	−0.886141	+	0.463416i	$0.846623\pi$
$152$	15.4265	+	24.4757i	1.25125	+	1.98525i
$153$	12.9719	−	11.7905i	1.04871	−	0.953208i
$154$	−7.08205	+	5.48900i	−0.570688	+	0.442316i
$155$	0.0221326	−	0.684539i	0.00177774	−	0.0549835i
$156$	−1.01815	+	1.50658i	−0.0815170	+	0.120623i
$157$	−2.74491	+	22.2367i	−0.219068	+	1.77468i	0.335010	+	0.942215i	$0.391260\pi$
$157$	−2.74491	+	22.2367i	−0.219068	+	1.77468i	−0.554078	+	0.832465i	$0.686929\pi$
$158$	−1.32175	+	6.50736i	−0.105153	+	0.517698i
$159$	−1.74628	−	0.307186i	−0.138489	−	0.0243614i
$160$	7.07494	+	2.67915i	0.559323	+	0.211805i
$161$	3.54127	+	2.97148i	0.279091	+	0.234185i
$162$	16.1803	+	17.5434i	1.27125	+	1.37834i
$163$	0.752587	−	0.631496i	0.0589472	−	0.0494626i	−0.612838	−	0.790209i	$-0.709972\pi$
$163$	0.752587	−	0.631496i	0.0589472	−	0.0494626i	0.671785	+	0.740746i	$0.265528\pi$
$164$	−2.07465	+	0.724875i	−0.162003	+	0.0566032i
$165$	−0.376365	+	1.59088i	−0.0293000	+	0.123850i
$166$	6.34739	+	42.3777i	0.492653	+	3.28914i
$167$	−0.467478	+	0.916013i	−0.0361745	+	0.0708832i	−0.908095	−	0.418765i	$-0.862463\pi$
$167$	−0.467478	+	0.916013i	−0.0361745	+	0.0708832i	0.871920	+	0.489648i	$0.162875\pi$
$168$	27.0354	−	4.41873i	2.08583	−	0.340912i
$169$	8.64465	−	9.65092i	0.664973	−	0.742378i
$170$	−6.30554	−	5.72197i	−0.483613	−	0.438855i
$171$	10.5920	−	2.08912i	0.809992	−	0.159759i
$172$	24.8055	−	10.1342i	1.89140	−	0.772723i
$173$	−19.3445	−	3.28216i	−1.47073	−	0.249538i	−0.623945	−	0.781468i	$-0.714471\pi$
$173$	−19.3445	−	3.28216i	−1.47073	−	0.249538i	−0.846788	+	0.531930i	$0.821467\pi$
$174$	−14.5917	−	6.73970i	−1.10619	−	0.510935i
$175$	7.65561	−	5.17819i	0.578710	−	0.391434i
$176$	−16.2872	−	10.4131i	−1.22769	−	0.784918i
$177$	−0.136982	−	0.146967i	−0.0102962	−	0.0110467i
$178$	29.0160	+	12.2944i	2.17484	+	0.921505i
$179$	5.87701	+	12.2907i	0.439269	+	0.918653i	0.996117	+	0.0880384i	$0.0280598\pi$
$179$	5.87701	+	12.2907i	0.439269	+	0.918653i	−0.556848	+	0.830614i	$0.687990\pi$
$180$	5.52965	−	6.18340i	0.412156	−	0.460883i
$181$	−8.94381	−	2.48968i	−0.664788	−	0.185056i	−0.0806897	−	0.996739i	$-0.525712\pi$
$181$	−8.94381	−	2.48968i	−0.664788	−	0.185056i	−0.584098	+	0.811683i	$0.698552\pi$
$182$	1.08806	−	0.0281400i	0.0806526	−	0.00208588i
$183$	25.0069	−	2.11660i	1.84856	−	0.156464i
$184$	−6.57583	+	17.7099i	−0.484777	+	1.30559i
$185$	2.20059	+	1.17738i	0.161791	+	0.0865630i
$186$	3.84511	−	4.24072i	0.281937	−	0.310944i
$187$	5.88856	+	8.12698i	0.430614	+	0.594304i
$188$	−13.9416	+	46.5680i	−1.01679	+	3.39632i
$189$	2.08733	−	10.0070i	0.151831	−	0.727902i
$190$	−1.50401	−	5.02373i	−0.109112	−	0.364460i
$191$	1.19519	−	1.56282i	0.0864807	−	0.113082i	−0.749081	−	0.662479i	$-0.769505\pi$
$191$	1.19519	−	1.56282i	0.0864807	−	0.113082i	0.835562	+	0.549397i	$0.185142\pi$
$192$	11.7200	+	21.2201i	0.845815	+	1.53143i
$193$	−15.9767	+	7.51302i	−1.15003	+	0.540799i	−0.903607	−	0.428363i	$-0.859090\pi$
$193$	−15.9767	+	7.51302i	−1.15003	+	0.540799i	−0.246422	+	0.969163i	$0.579255\pi$
$194$	7.57751	−	31.0755i	0.544034	−	2.23109i
$195$	0.151245	−	0.128690i	0.0108308	−	0.00921568i
$196$	11.0996	+	11.1715i	0.792826	+	0.797967i
$197$	−6.41968	+	1.26078i	−0.457383	+	0.0898271i	−0.416097	−	0.909320i	$-0.636602\pi$
$197$	−6.41968	+	1.26078i	−0.457383	+	0.0898271i	−0.0412861	+	0.999147i	$0.513146\pi$
$198$	−11.0059	+	8.09728i	−0.782156	+	0.575449i
$199$	−23.9790	+	13.2311i	−1.69983	+	0.937924i	−0.733843	+	0.679319i	$0.762275\pi$
$199$	−23.9790	+	13.2311i	−1.69983	+	0.937924i	−0.965983	+	0.258605i	$0.916737\pi$
$200$	30.4410	+	22.3581i	2.15251	+	1.58096i
$201$	−8.77964	−	4.91403i	−0.619268	−	0.346609i
$202$	1.19385	−	7.32306i	0.0839991	−	0.515249i
$203$	1.28303	+	6.76390i	0.0900513	+	0.474733i
$204$	−6.58590	−	50.4974i	−0.461105	−	3.53552i
$205$	0.239506	−	0.0155037i	0.0167278	−	0.00108282i
$206$	10.3369	+	30.2107i	0.720206	+	2.10488i
$207$	5.28503	+	4.66513i	0.367335	+	0.324249i
$208$	0.845793	+	2.19066i	0.0586452	+	0.151895i
$209$	0.518806	+	6.15919i	0.0358865	+	0.426040i
$210$	−4.93564	−	0.542553i	−0.340591	−	0.0374397i
$211$	5.42802	−	8.13783i	0.373680	−	0.560232i	−0.596501	−	0.802612i	$-0.703443\pi$
$211$	5.42802	−	8.13783i	0.373680	−	0.560232i	0.970181	+	0.242381i	$0.0779284\pi$
$212$	−3.63050	+	3.65405i	−0.249344	+	0.250961i
$213$	0.0908244	−	1.17468i	0.00622318	−	0.0804875i
$214$	−2.04041	−	45.0620i	−0.139480	−	3.08037i
$215$	−2.90662	+	0.339736i	−0.198230	+	0.0231698i
$216$	41.3831	−	5.70367i	2.81576	−	0.388085i
$217$	−2.43534	−	0.284650i	−0.165322	−	0.0193233i
$218$	−1.17423	+	16.4859i	−0.0795287	+	1.11657i
$219$	−16.0991	−	12.9744i	−1.08788	−	0.876731i
$220$	3.16872	+	3.53757i	0.213635	+	0.238503i
$221$	0.00788057	−	1.21910i	0.000530105	−	0.0820053i
$222$	7.64668	+	19.4076i	0.513212	+	1.30255i
$223$	−11.2089	+	9.91035i	−0.750604	+	0.663646i	−0.948572	−	0.316563i	$-0.897471\pi$
$223$	−11.2089	+	9.91035i	−0.750604	+	0.663646i	0.197968	+	0.980209i	$0.436566\pi$
$224$	11.6834	−	24.4337i	0.780629	−	1.63255i
$225$	11.8684	−	7.60155i	0.791227	−	0.506770i
$226$	5.01149	−	3.58200i	0.333359	−	0.238271i
$227$	2.73770	+	5.36446i	0.181707	+	0.356052i	0.963594	−	0.267369i	$-0.0861541\pi$
$227$	2.73770	+	5.36446i	0.181707	+	0.356052i	−0.781887	+	0.623420i	$0.785743\pi$
$228$	12.5968	−	28.7228i	0.834240	−	1.90221i
$229$	17.9718	+	23.4998i	1.18761	+	1.55291i	0.761396	+	0.648287i	$0.224514\pi$
$229$	17.9718	+	23.4998i	1.18761	+	1.55291i	0.426212	+	0.904623i	$0.359848\pi$
$230$	2.00910	−	2.77281i	0.132476	−	0.182834i
$231$	5.56214	+	1.82067i	0.365962	+	0.119791i
$232$	−24.2733	+	14.2242i	−1.59362	+	0.933863i
$233$	0.353158	+	1.63036i	0.0231361	+	0.106808i	0.987442	−	0.157983i	$-0.0504993\pi$
$233$	0.353158	+	1.63036i	0.0231361	+	0.106808i	−0.964306	+	0.264792i	$0.914697\pi$
$234$	1.65978	−	0.00134468i	0.108503	−	8.79042e-5i
$235$	2.83067	−	4.49117i	0.184653	−	0.292971i
$236$	−0.577759	+	0.0827227i	−0.0376089	+	0.00538479i
$237$	4.00371	−	1.66788i	0.260069	−	0.108340i
$238$	−22.3070	+	20.7747i	−1.44595	+	1.34662i
$239$	−8.57364	−	15.7785i	−0.554583	−	1.02063i	−0.992573	−	0.121648i	$-0.961182\pi$
$239$	−8.57364	−	15.7785i	−0.554583	−	1.02063i	0.437991	−	0.898979i	$-0.355690\pi$
$240$	−2.47474	−	10.4230i	−0.159744	−	0.672799i
$241$	−13.8128	+	23.2258i	−0.889761	+	1.49610i	−0.0216318	+	0.999766i	$0.506886\pi$
$241$	−13.8128	+	23.2258i	−0.889761	+	1.49610i	−0.868129	+	0.496338i	$0.834678\pi$
$242$	10.6732	+	18.4866i	0.686101	+	1.18836i
$243$	3.56422	−	15.1755i	0.228645	−	0.973510i
$244$	36.4535	−	63.1393i	2.33370	−	4.04208i
$245$	−0.840611	−	1.50045i	−0.0537047	−	0.0958602i
$246$	1.60953	+	1.19724i	0.102620	+	0.0763332i
$247$	0.392101	−	0.640315i	0.0249488	−	0.0407423i
$248$	−2.24768	−	9.76455i	−0.142728	−	0.620050i
$249$	20.5972	−	18.9506i	1.30529	−	1.20094i
$250$	−8.72930	−	11.1136i	−0.552089	−	0.702889i
$251$	−1.70867	−	3.24383i	−0.107850	−	0.204749i	0.824894	−	0.565288i	$-0.191235\pi$
$251$	−1.70867	−	3.24383i	−0.107850	−	0.204749i	−0.932744	+	0.360539i	$0.882593\pi$
$252$	−20.3968	−	21.5842i	−1.28487	−	1.35968i
$253$	−2.98882	+	2.71221i	−0.187906	+	0.170515i
$254$	0.295628	+	45.7326i	0.0185493	+	2.86952i
$255$	−0.786033	+	5.50577i	−0.0492233	+	0.344785i
$256$	−2.57465	−	0.267242i	−0.160916	−	0.0167026i
$257$	6.09142	−	0.791938i	0.379972	−	0.0493997i	0.0634504	−	0.997985i	$-0.479790\pi$
$257$	6.09142	−	0.791938i	0.379972	−	0.0493997i	0.316522	+	0.948585i	$0.397485\pi$
$258$	−20.3534	−	13.5640i	−1.26715	−	0.844460i
$259$	4.86139	−	7.49649i	0.302072	−	0.465810i
$260$	−0.0558509	−	0.574197i	−0.00346373	−	0.0356102i
$261$	1.69761	+	10.3603i	0.105080	+	0.641285i
$262$	−44.8614	+	3.48690i	−2.77155	+	0.215422i
$263$	2.38443	+	11.7393i	0.147030	+	0.723874i	0.984218	+	0.176959i	$0.0566260\pi$
$263$	2.38443	+	11.7393i	0.147030	+	0.723874i	−0.837188	+	0.546915i	$0.815802\pi$
$264$	0.628025	+	23.9085i	0.0386523	+	1.47147i
$265$	0.488988	−	0.278118i	0.0300383	−	0.0170847i
$266$	−18.3734	+	3.85575i	−1.12654	+	0.236411i
$267$	−3.97488	−	20.1961i	−0.243259	−	1.23598i
$268$	−26.2874	+	12.7792i	−1.60576	+	0.780612i
$269$	−8.71165	+	11.7018i	−0.531158	+	0.713470i	−0.984009	−	0.178117i	$-0.943000\pi$
$269$	−8.71165	+	11.7018i	−0.531158	+	0.713470i	0.452851	+	0.891586i	$0.350407\pi$
$270$	−7.50345	−	1.01559i	−0.456645	−	0.0618070i
$271$	13.2582	+	17.8089i	0.805381	+	1.08181i	0.994992	+	0.0999553i	$0.0318700\pi$
$271$	13.2582	+	17.8089i	0.805381	+	1.08181i	−0.189611	+	0.981859i	$0.560723\pi$
$272$	−58.3840	−	30.2730i	−3.54005	−	1.83557i
$273$	−0.413635	−	0.578212i	−0.0250343	−	0.0349950i
$274$	−44.1951	−	11.6891i	−2.66993	−	0.706163i
$275$	3.57475	+	7.23413i	0.215566	+	0.436235i
$276$	19.8944	−	4.85963i	1.19750	−	0.292516i
$277$	−15.5188	+	10.7918i	−0.932437	+	0.648418i	−0.936160	−	0.351575i	$-0.885646\pi$
$277$	−15.5188	+	10.7918i	−0.932437	+	0.648418i	0.00372304	+	0.999993i	$0.498815\pi$
$278$	39.5506	+	6.18560i	2.37209	+	0.370988i
$279$	−3.70170	−	0.526944i	−0.221615	−	0.0315473i
$280$	−5.71473	+	6.54836i	−0.341521	+	0.391339i
$281$	−12.7718	+	25.8461i	−0.761904	+	1.54185i	0.0766689	+	0.997057i	$0.475572\pi$
$281$	−12.7718	+	25.8461i	−0.761904	+	1.54185i	−0.838573	+	0.544790i	$0.816610\pi$
$282$	42.3335	−	13.2914i	2.52093	−	0.791490i
$283$	3.19849	−	2.75510i	0.190131	−	0.163773i	−0.552414	−	0.833570i	$-0.686293\pi$
$283$	3.19849	−	2.75510i	0.190131	−	0.163773i	0.742545	+	0.669796i	$0.233619\pi$
$284$	−2.65018	−	2.16601i	−0.157260	−	0.128529i
$285$	−2.16654	+	2.65303i	−0.128335	+	0.157152i
$286$	−0.104215	+	0.944530i	−0.00616238	+	0.0558512i
$287$	0.0166614	−	0.859060i	0.000983494	−	0.0507087i
$288$	18.7440	−	36.8020i	1.10450	−	2.16858i
$289$	11.2718	+	12.9161i	0.663049	+	0.759769i
$290$	4.92994	−	1.30391i	0.289496	−	0.0765682i
$291$	−19.5829	+	7.28031i	−1.14797	+	0.426780i
$292$	−57.6538	+	16.8551i	−3.37393	+	0.986370i
$293$	1.36915	−	16.2544i	0.0799867	−	0.949591i	−0.836091	−	0.548591i	$-0.815165\pi$
$293$	1.36915	−	16.2544i	0.0799867	−	0.949591i	0.916078	−	0.401001i	$-0.131337\pi$
$294$	2.76448	−	14.1065i	0.161228	−	0.822705i
$295$	0.0632095	+	0.00821779i	0.00368020	+	0.000478458i
$296$	35.5284	+	8.42038i	2.06504	+	0.489424i
$297$	8.40971	+	2.98795i	0.487981	+	0.173378i
$298$	31.3012	−	7.41853i	1.81323	−	0.429744i
$299$	0.487646	−	0.0506164i	0.0282013	−	0.00292722i
$300$	1.57107	−	40.9144i	0.0907055	−	2.36219i
$301$	0.338551	+	10.4710i	0.0195138	+	0.603541i
$302$	9.18267	+	11.0883i	0.528403	+	0.638058i
$303$	−4.39808	+	2.03574i	−0.252663	+	0.116950i
$304$	−21.1520	−	34.5420i	−1.21315	−	1.98112i
$305$	−5.68451	+	5.57533i	−0.325494	+	0.319243i
$306$	−34.7995	+	30.8182i	−1.98935	+	1.76176i
$307$	11.5728	−	16.8736i	0.660496	−	0.963026i	−0.339255	−	0.940694i	$-0.610175\pi$
$307$	11.5728	−	16.8736i	0.660496	−	0.963026i	0.999751	−	0.0223317i	$-0.00710898\pi$
$308$	13.5719	−	10.2409i	0.773332	−	0.583531i
$309$	12.5555	−	16.6533i	0.714255	−	0.947372i
$310$	−0.0821524	+	1.81431i	−0.00466595	+	0.103046i
$311$	−0.658449	−	9.24450i	−0.0373372	−	0.524207i	−0.981090	−	0.193554i	$-0.937998\pi$
$311$	−0.658449	−	9.24450i	−0.0373372	−	0.524207i	0.943752	−	0.330653i	$-0.107269\pi$
$312$	1.65772	−	2.38590i	0.0938501	−	0.135075i
$313$	−7.52646	−	20.2701i	−0.425421	−	1.14574i	−0.954774	−	0.297333i	$-0.903903\pi$
$313$	−7.52646	−	20.2701i	−0.425421	−	1.14574i	0.529353	−	0.848402i	$-0.322435\pi$
$314$	8.04052	−	58.8670i	0.453753	−	3.32206i
$315$	1.51382	+	2.86828i	0.0852940	+	0.161609i
$316$	2.66748	−	12.3144i	0.150057	−	0.692741i
$317$	−5.62651	−	17.1655i	−0.316016	−	0.964109i	−0.976914	−	0.213633i	$-0.931470\pi$
$317$	−5.62651	−	17.1655i	−0.316016	−	0.964109i	0.660898	−	0.750476i	$-0.270176\pi$
$318$	4.61976	+	0.874377i	0.259063	+	0.0490326i
$319$	−6.00256	+	0.310690i	−0.336079	+	0.0173953i
$320$	−7.15682	−	2.81647i	−0.400078	−	0.157446i
$321$	−23.6262	+	17.6039i	−1.31868	+	0.982555i
$322$	−9.28790	−	8.00035i	−0.517594	−	0.445842i
$323$	3.65145	+	20.7084i	0.203172	+	1.15225i
$324$	−30.2697	−	33.6832i	−1.68165	−	1.87129i
$325$	0.170209	−	0.965302i	0.00944149	−	0.0535453i
$326$	−2.01715	+	1.64863i	−0.111720	+	0.0913090i
$327$	9.34694	−	5.40151i	0.516887	−	0.298704i
$328$	3.32945	−	1.11521i	0.183838	−	0.0615774i
$329$	−15.1710	−	11.4475i	−0.836403	−	0.631123i
$330$	1.05248	−	4.20536i	0.0579372	−	0.231498i
$331$	5.56440	−	2.97712i	0.305847	−	0.163637i	−0.311680	−	0.950187i	$-0.600892\pi$
$331$	5.56440	−	2.97712i	0.305847	−	0.163637i	0.617527	+	0.786550i	$0.288135\pi$
$332$	−11.0038	−	80.5618i	−0.603910	−	4.42140i
$333$	7.69728	−	11.2424i	0.421808	−	0.616081i
$334$	1.27093	−	2.41281i	0.0695424	−	0.132023i
$335$	3.14000	−	0.574619i	0.171556	−	0.0313948i
$336$	−37.9260	+	5.69631i	−2.06903	+	0.310759i
$337$	22.7161	+	23.4624i	1.23743	+	1.27808i	0.947019	+	0.321177i	$0.104079\pi$
$337$	22.7161	+	23.4624i	1.23743	+	1.27808i	0.290406	+	0.956903i	$0.406209\pi$
$338$	−23.2523	+	25.2933i	−1.26476	+	1.37577i
$339$	−3.77250	−	1.39902i	−0.204894	−	0.0759843i
$340$	11.8236	+	11.0114i	0.641223	+	0.597175i
$341$	0.533972	−	2.07301i	0.0289162	−	0.112260i
$342$	−28.1566	+	5.17624i	−1.52254	+	0.279899i
$343$	−18.1419	+	8.24651i	−0.979571	+	0.445270i
$344$	−39.8389	+	15.6781i	−2.14797	+	0.845306i
$345$	−2.23544	−	0.0713702i	−0.120352	−	0.00384244i
$346$	51.1799	+	9.36591i	2.75145	+	0.503514i
$347$	2.83517	−	3.60957i	0.152200	−	0.193772i	−0.704325	−	0.709877i	$-0.748750\pi$
$347$	2.83517	−	3.60957i	0.152200	−	0.193772i	0.856525	+	0.516105i	$0.172619\pi$
$348$	27.5204	+	13.1457i	1.47525	+	0.704681i
$349$	−4.46081	−	15.6329i	−0.238782	−	0.836812i	−0.985211	−	0.171347i	$-0.945188\pi$
$349$	−4.46081	−	15.6329i	−0.238782	−	0.836812i	0.746429	−	0.665465i	$-0.231767\pi$
$350$	−20.4766	+	13.4676i	−1.09452	+	0.719876i
$351$	−0.608487	−	0.897256i	−0.0324786	−	0.0478920i
$352$	19.7554	+	12.9934i	1.05297	+	0.692549i
$353$	−2.98554	+	9.52256i	−0.158904	+	0.506835i	−0.999387	−	0.0350033i	$-0.988856\pi$
$353$	−2.98554	+	9.52256i	−0.158904	+	0.506835i	0.840483	+	0.541838i	$0.182271\pi$
$354$	0.358174	+	0.394382i	0.0190367	+	0.0209612i
$355$	0.215392	+	0.305505i	0.0114318	+	0.0162145i
$356$	−54.7524	−	24.0388i	−2.90187	−	1.27406i
$357$	19.4048	+	4.45847i	1.02701	+	0.235967i
$358$	−15.1617	−	32.7907i	−0.801321	−	1.73304i
$359$	−16.8749	−	9.31117i	−0.890623	−	0.491425i	−0.0293510	−	0.999569i	$-0.509344\pi$
$359$	−16.8749	−	9.31117i	−0.890623	−	0.491425i	−0.861272	+	0.508144i	$0.830332\pi$
$360$	−8.96195	+	9.76444i	−0.472336	+	0.514631i
$361$	2.17886	−	5.64338i	0.114677	−	0.297020i
$362$	23.6294	+	6.90806i	1.24193	+	0.363080i
$363$	6.09089	−	12.5422i	0.319689	−	0.658294i
$364$	−2.06515	+	0.0267005i	−0.108243	+	0.00139948i
$365$	6.55947	−	0.0848079i	0.343338	−	0.00443905i
$366$	−66.3790	+	4.75494i	−3.46968	+	0.248545i
$367$	12.6786	+	3.70658i	0.661816	+	0.193482i	0.594309	−	0.804237i	$-0.297426\pi$
$367$	12.6786	+	3.70658i	0.661816	+	0.193482i	0.0675069	+	0.997719i	$0.478496\pi$
$368$	9.52581	−	24.6725i	0.496567	−	1.28614i
$369$	0.0582075	−	1.30896i	0.00303016	−	0.0681419i
$370$	−5.79456	−	3.19730i	−0.301245	−	0.166220i
$371$	−0.845210	−	1.82796i	−0.0438811	−	0.0949030i
$372$	−7.39963	+	7.95188i	−0.383653	+	0.412286i
$373$	6.50788	+	2.85726i	0.336965	+	0.147943i	0.563625	−	0.826031i	$-0.309406\pi$
$373$	6.50788	+	2.85726i	0.336965	+	0.147943i	−0.226660	+	0.973974i	$0.572781\pi$
$374$	−15.3351	−	21.7508i	−0.792957	−	1.12471i
$375$	−2.81480	+	8.79101i	−0.145356	+	0.453966i
$376$	23.2351	−	74.1096i	1.19826	−	3.82191i
$377$	0.610015	+	0.401213i	0.0314174	+	0.0206635i
$378$	−5.87767	+	26.4623i	−0.302315	+	1.36107i
$379$	8.24540	−	5.42308i	0.423538	−	0.278565i	−0.319795	−	0.947487i	$-0.603614\pi$
$379$	8.24540	−	5.42308i	0.423538	−	0.278565i	0.743333	+	0.668922i	$0.233244\pi$
$380$	2.73042	+	9.56877i	0.140068	+	0.490868i
$381$	24.6278	−	16.9057i	1.26172	−	0.866107i
$382$	−3.22265	+	4.10289i	−0.164885	+	0.209922i
$383$	15.1942	+	2.78054i	0.776390	+	0.142079i	0.553595	−	0.832786i	$-0.313256\pi$
$383$	15.1942	+	2.78054i	0.776390	+	0.142079i	0.222795	+	0.974865i	$0.428482\pi$
$384$	−7.83356	−	14.6271i	−0.399755	−	0.746435i
$385$	−1.72785	+	0.679973i	−0.0880594	+	0.0346546i
$386$	42.6202	−	19.3733i	2.16931	−	0.986073i
$387$	0.116214	+	15.9756i	0.00590748	+	0.812084i
$388$	−15.1397	+	58.7758i	−0.768600	+	2.98389i
$389$	12.1656	+	11.3299i	0.616822	+	0.574451i	0.926455	−	0.376405i	$-0.122840\pi$
$389$	12.1656	+	11.3299i	0.616822	+	0.574451i	−0.309633	+	0.950856i	$0.600206\pi$
$390$	−0.405440	+	0.336040i	−0.0205303	+	0.0170160i
$391$	−9.29251	+	10.1082i	−0.469943	+	0.511191i
$392$	−17.5020	−	18.0770i	−0.883985	−	0.913028i
$393$	18.3129	+	22.9880i	0.923761	+	1.15959i
$394$	17.0652	−	3.12292i	0.859730	−	0.157331i
$395$	−0.641308	+	1.21749i	−0.0322677	+	0.0612587i
$396$	21.0809	−	15.0935i	1.05936	−	0.758479i
$397$	2.83916	+	20.7863i	0.142493	+	1.04324i	0.913624	+	0.406560i	$0.133272\pi$
$397$	2.83916	+	20.7863i	0.142493	+	1.04324i	−0.771131	+	0.636677i	$0.780309\pi$
$398$	64.0345	−	34.2604i	3.20976	−	1.71732i
$399$	8.81327	+	8.52601i	0.441215	+	0.426834i
$400$	−42.2087	−	31.8493i	−2.11043	−	1.59247i
$401$	25.7088	−	8.61127i	1.28383	−	0.430026i	0.408152	−	0.912914i	$-0.366173\pi$
$401$	25.7088	−	8.61127i	1.28383	−	0.430026i	0.875682	+	0.482888i	$0.160412\pi$
$402$	23.1110	+	13.3307i	1.15267	+	0.664873i
$403$	−0.201343	+	0.164559i	−0.0100296	+	0.00819725i
$404$	−2.44482	+	13.8653i	−0.121634	+	0.689823i
$405$	2.19821	+	4.43037i	0.109230	+	0.220147i
$406$	−3.17012	−	17.9786i	−0.157330	−	0.892265i
$407$	5.91029	+	5.09097i	0.292962	+	0.252350i
$408$	9.47865	+	80.8111i	0.469263	+	4.00075i
$409$	22.5635	+	8.87956i	1.11569	+	0.439066i	0.850946	−	0.525253i	$-0.176029\pi$
$409$	22.5635	+	8.87956i	1.11569	+	0.439066i	0.264745	+	0.964318i	$0.414712\pi$
$410$	−0.635587	+	0.0328977i	−0.0313894	+	0.00162470i
$411$	9.86044	+	28.1846i	0.486380	+	1.39025i
$412$	−18.8718	−	57.5745i	−0.929747	−	2.83649i
$413$	0.0483094	−	0.223021i	0.00237715	−	0.0109741i
$414$	−13.8535	−	12.5509i	−0.680860	−	0.616843i
$415$	−1.20174	+	8.79827i	−0.0589910	+	0.431890i
$416$	−0.999811	−	2.69267i	−0.0490198	−	0.132019i
$417$	−11.1365	−	23.6573i	−0.545357	−	1.15850i
$418$	−1.16448	−	16.3490i	−0.0569565	−	0.799658i
$419$	0.671953	−	14.8399i	0.0328270	−	0.724976i	−0.914477	−	0.404639i	$-0.867397\pi$
$419$	0.671953	−	14.8399i	0.0328270	−	0.724976i	0.947304	−	0.320337i	$-0.103796\pi$
$420$	9.35142	+	1.15050i	0.456302	+	0.0561387i
$421$	−12.1126	+	9.13975i	−0.590330	+	0.445444i	−0.854806	−	0.518948i	$-0.826324\pi$
$421$	−12.1126	+	9.13975i	−0.590330	+	0.445444i	0.264476	+	0.964392i	$0.414801\pi$
$422$	−14.6715	+	21.3916i	−0.714198	+	1.04133i
$423$	−22.6903	−	18.0307i	−1.10324	−	0.876681i
$424$	5.87561	−	5.76275i	0.285345	−	0.279864i
$425$	14.3358	+	23.4108i	0.695387	+	1.13559i
$426$	−0.281093	+	3.11157i	−0.0136190	+	0.150756i
$427$	18.1810	+	21.9540i	0.879842	+	1.06243i
$428$	2.76599	+	85.5493i	0.133699	+	4.13518i
$429$	0.549042	−	0.289489i	0.0265080	−	0.0139767i
$430$	7.71864	−	0.801174i	0.372226	−	0.0386360i
$431$	−10.2446	+	2.42802i	−0.493466	+	0.116954i	−0.469812	−	0.882767i	$-0.655678\pi$
$431$	−10.2446	+	2.42802i	−0.493466	+	0.116954i	−0.0236541	+	0.999720i	$0.507530\pi$
$432$	−58.0340	+	7.23538i	−2.79216	+	0.348112i
$433$	13.1890	+	3.12586i	0.633825	+	0.150219i	0.534954	−	0.844881i	$-0.320329\pi$
$433$	13.1890	+	3.12586i	0.633825	+	0.150219i	0.0988708	+	0.995100i	$0.468477\pi$
$434$	6.44761	+	0.838246i	0.309495	+	0.0402371i
$435$	−2.51045	−	2.18908i	−0.120367	−	0.104958i
$436$	2.63236	−	31.2510i	0.126067	−	1.49665i
$437$	−8.11655	+	2.37287i	−0.388267	+	0.113510i
$438$	42.2424	+	34.9539i	2.01842	+	1.67016i
$439$	16.2149	−	4.28865i	0.773896	−	0.204686i	0.152627	−	0.988284i	$-0.451227\pi$
$439$	16.2149	−	4.28865i	0.773896	−	0.204686i	0.621269	+	0.783598i	$0.286618\pi$
$440$	−4.98931	−	5.71711i	−0.237856	−	0.272553i
$441$	−8.64223	+	3.67008i	−0.411535	+	0.174766i
$442$	−0.0626884	+	3.23220i	−0.00298178	+	0.153740i
$443$	−3.38338	+	30.6644i	−0.160749	+	1.45691i	0.595883	+	0.803071i	$0.296802\pi$
$443$	−3.38338	+	30.6644i	−0.160749	+	1.45691i	−0.756633	+	0.653840i	$0.773157\pi$
$444$	−14.0325	−	37.0109i	−0.665953	−	1.75646i
$445$	5.05653	+	4.13272i	0.239702	+	0.195910i
$446$	30.0604	−	25.8933i	1.42340	−	1.22608i
$447$	−15.4741	−	14.2139i	−0.731900	−	0.672295i
$448$	−12.1979	+	24.6846i	−0.576296	+	1.16624i
$449$	−6.83737	+	7.83475i	−0.322675	+	0.369745i	−0.891740	−	0.452548i	$-0.850515\pi$
$449$	−6.83737	+	7.83475i	−0.322675	+	0.369745i	0.569065	+	0.822293i	$0.307305\pi$
$450$	−31.7300	+	19.7488i	−1.49577	+	0.930969i
$451$	0.741142	+	0.115913i	0.0348990	+	0.00545811i
$452$	−9.59651	+	6.67343i	−0.451382	+	0.313892i
$453$	2.63506	−	9.02694i	0.123806	−	0.424122i
$454$	−7.07517	−	14.3179i	−0.332054	−	0.671970i
$455$	0.218059	+	0.0576739i	0.0102227	+	0.00270379i
$456$	−20.7180	+	45.6276i	−0.970209	+	2.13671i
$457$	−0.214073	−	0.111000i	−0.0100139	−	0.00519235i	0.455300	−	0.890338i	$-0.349532\pi$
$457$	−0.214073	−	0.111000i	−0.0100139	−	0.00519235i	−0.465314	+	0.885146i	$0.654059\pi$
$458$	−46.8470	−	62.9264i	−2.18902	−	2.94036i
$459$	29.4116	+	7.53783i	1.37281	+	0.351836i
$460$	−3.88002	+	5.21177i	−0.180907	+	0.243000i
$461$	−10.0659	+	4.89337i	−0.468815	+	0.227907i	−0.656505	−	0.754322i	$-0.727966\pi$
$461$	−10.0659	+	4.89337i	−0.468815	+	0.227907i	0.187690	+	0.982228i	$0.439900\pi$
$462$	−14.6857	−	5.01823i	−0.683243	−	0.233469i
$463$	−0.944893	+	0.198291i	−0.0439129	+	0.00921537i	−0.227287	−	0.973828i	$-0.572985\pi$
$463$	−0.944893	+	0.198291i	−0.0439129	+	0.00921537i	0.183374	+	0.983043i	$0.441298\pi$
$464$	34.2368	−	19.4726i	1.58940	−	0.903994i
$465$	1.01142	−	0.619910i	0.0469033	−	0.0287476i
$466$	−0.880515	−	4.33504i	−0.0407891	−	0.200817i
$467$	4.44078	−	0.345165i	0.205495	−	0.0159723i	0.0256676	−	0.999671i	$-0.491829\pi$
$467$	4.44078	−	0.345165i	0.205495	−	0.0159723i	0.179827	+	0.983698i	$0.442446\pi$
$468$	−3.14925	−	0.0381651i	−0.145574	−	0.00176418i
$469$	−1.10634	−	11.3741i	−0.0510859	−	0.525209i
$470$	−7.65956	+	11.8114i	−0.353309	+	0.544819i
$471$	−34.7844	+	17.2063i	−1.60278	+	0.792823i
$472$	0.924743	−	0.120225i	0.0425647	−	0.00553379i
$473$	−9.09774	−	0.944321i	−0.418315	−	0.0434199i
$474$	−10.6731	+	4.28517i	−0.490233	+	0.196824i
$475$	0.109287	+	16.9064i	0.00501445	+	0.775718i
$476$	42.8343	−	38.8700i	1.96331	−	1.78160i
$477$	−1.21868	−	2.81893i	−0.0557993	−	0.129070i
$478$	22.1923	+	42.1311i	1.01505	+	1.92703i
$479$	−19.2520	−	24.5105i	−0.879645	−	1.11991i	−0.991999	−	0.126245i	$-0.959707\pi$
$479$	−19.2520	−	24.5105i	−0.879645	−	1.11991i	0.112354	−	0.993668i	$-0.464161\pi$
$480$	2.86193	+	12.7870i	0.130629	+	0.583643i
$481$	−0.212560	−	0.923422i	−0.00969191	−	0.0421044i
$482$	37.4212	−	61.1102i	1.70449	−	2.78349i
$483$	−0.926325	+	7.95316i	−0.0421493	+	0.361881i
$484$	−19.7976	−	35.3377i	−0.899889	−	1.60626i
$485$	3.31426	−	5.74047i	0.150493	−	0.260661i
$486$	−9.97086	+	40.1161i	−0.452287	+	1.81970i
$487$	−19.7478	−	34.2042i	−0.894858	−	1.54994i	−0.833980	−	0.551794i	$-0.813943\pi$
$487$	−19.7478	−	34.2042i	−0.894858	−	1.54994i	−0.0608779	−	0.998145i	$-0.519390\pi$
$488$	−59.5427	+	100.119i	−2.69537	+	4.53218i
$489$	1.63033	+	0.487371i	0.0737263	+	0.0220397i
$490$	2.17746	+	4.00730i	0.0983678	+	0.181031i
$491$	−0.649186	+	0.604592i	−0.0292974	+	0.0272848i	−0.696038	−	0.718005i	$-0.745055\pi$
$491$	−0.649186	+	0.604592i	−0.0292974	+	0.0272848i	0.666740	+	0.745290i	$0.267689\pi$
$492$	−3.02451	−	2.31109i	−0.136355	−	0.104192i
$493$	−20.2417	+	2.89818i	−0.911640	+	0.130527i
$494$	−1.06162	+	1.68437i	−0.0477644	+	0.0757834i
$495$	−2.66000	+	0.970602i	−0.119558	+	0.0436253i
$496$	2.96972	+	13.7097i	0.133344	+	0.615585i
$497$	1.15457	−	0.676579i	0.0517895	−	0.0303487i
$498$	−55.2636	+	49.5418i	−2.47642	+	2.22002i
$499$	−12.5056	+	17.2594i	−0.559828	+	0.772636i	−0.991599	−	0.129347i	$-0.958712\pi$
$499$	−12.5056	+	17.2594i	−0.559828	+	0.772636i	0.431771	+	0.901983i	$0.357889\pi$
$500$	16.2901	+	21.3008i	0.728514	+	0.952602i
$501$	−1.77043	+	0.196067i	−0.0790968	+	0.00875962i
$502$	4.41938	+	8.65968i	0.197247	+	0.386500i
$503$	16.2081	−	11.5848i	0.722682	−	0.516542i	−0.159648	−	0.987174i	$-0.551036\pi$
$503$	16.2081	−	11.5848i	0.722682	−	0.516542i	0.882330	+	0.470632i	$0.155974\pi$
$504$	32.1402	+	34.9045i	1.43164	+	1.55477i
$505$	0.663302	−	1.38718i	0.0295166	−	0.0617286i
$506$	8.01791	−	7.08903i	0.356440	−	0.315146i
$507$	22.1950	+	3.31521i	0.985716	+	0.147234i
$508$	0.560962	−	86.7788i	0.0248887	−	3.85019i
$509$	−20.9664	−	23.4070i	−0.929319	−	1.03750i	−0.999202	−	0.0399400i	$-0.987283\pi$
$509$	−20.9664	−	23.4070i	−0.929319	−	1.03750i	0.0698835	−	0.997555i	$-0.477737\pi$
$510$	2.27293	−	14.5718i	0.100647	−	0.645248i
$511$	1.66850	−	23.4254i	0.0738101	−	1.03628i
$512$	25.8476	+	3.02115i	1.14231	+	0.133517i
$513$	13.1098	+	13.3341i	0.578813	+	0.588715i
$514$	−16.1787	+	1.89102i	−0.713612	+	0.0834092i
$515$	0.299311	+	6.61019i	0.0131892	+	0.291280i
$516$	38.2852	+	26.2353i	1.68541	+	1.15494i
$517$	11.6949	−	11.7708i	0.514343	−	0.517678i
$518$	−13.1471	+	19.7105i	−0.577651	+	0.866029i
$519$	−13.6746	−	31.1119i	−0.600248	−	1.36566i
$520$	0.0773676	+	0.918498i	0.00339279	+	0.0402788i
$521$	14.3902	+	37.2716i	0.630447	+	1.63290i	0.766536	+	0.642201i	$0.221979\pi$
$521$	14.3902	+	37.2716i	0.630447	+	1.63290i	−0.136089	+	0.990697i	$0.543453\pi$
$522$	−4.14610	−	27.5287i	−0.181470	−	1.20490i
$523$	−5.33427	−	15.5900i	−0.233251	−	0.681703i	−0.999245	−	0.0388545i	$-0.987629\pi$
$523$	−5.33427	−	15.5900i	−0.233251	−	0.681703i	0.765994	−	0.642848i	$-0.222247\pi$
$524$	85.2041	−	5.51544i	3.72216	−	0.240943i
$525$	14.7823	+	6.14402i	0.645153	+	0.268147i
$526$	−5.91994	−	31.2087i	−0.258121	−	1.36076i
$527$	1.17179	−	7.18771i	0.0510438	−	0.313102i
$528$	−0.446431	−	33.4801i	−0.0194284	−	1.45703i
$529$	14.0870	+	10.3465i	0.612476	+	0.449848i
$530$	−1.30610	+	0.720674i	−0.0567332	+	0.0313041i
$531$	0.0821629	−	0.338141i	0.00356556	−	0.0146741i
$532$	34.9556	−	6.86506i	1.51552	−	0.297638i
$533$	−0.0642257	−	0.0646422i	−0.00278192	−	0.00279997i
$534$	9.84715	+	53.6868i	0.426128	+	2.32325i
$535$	2.21451	−	9.08175i	0.0957418	−	0.392638i
$536$	42.2610	−	19.8732i	1.82540	−	0.858390i
$537$	−12.1842	+	20.2077i	−0.525788	+	0.872025i
$538$	23.5003	−	30.7289i	1.01317	−	1.32482i
$539$	−1.54172	−	5.14972i	−0.0664068	−	0.221814i
$540$	14.2119	+	2.11102i	0.611582	+	0.0908440i
$541$	−4.18262	+	13.9709i	−0.179825	+	0.600657i	0.819784	+	0.572673i	$0.194094\pi$
$541$	−4.18262	+	13.9709i	−0.179825	+	0.600657i	−0.999608	+	0.0279832i	$0.991092\pi$
$542$	−34.5441	−	47.6753i	−1.48379	−	2.04783i
$543$	−4.91589	−	15.3103i	−0.210961	−	0.657027i
$544$	70.9282	+	37.9488i	3.04102	+	1.62704i
$545$	−1.19222	+	3.21087i	−0.0510691	+	0.137538i
$546$	1.07694	+	1.54732i	0.0460889	+	0.0662194i
$547$	−21.8917	+	0.566174i	−0.936021	+	0.0242078i	−0.490856	−	0.871241i	$-0.663316\pi$
$547$	−21.8917	+	0.566174i	−0.936021	+	0.0242078i	−0.445165	+	0.895449i	$0.646855\pi$
$548$	83.5677	+	23.2627i	3.56984	+	0.993732i
$549$	26.8778	+	34.1622i	1.14712	+	1.45801i
$550$	−9.23054	−	19.3040i	−0.393592	−	0.823127i
$551$	−11.5956	−	4.91320i	−0.493989	−	0.209309i
$552$	−31.8839	+	7.35287i	−1.35707	+	0.312959i
$553$	4.15052	+	2.65361i	0.176498	+	0.112843i
$554$	41.5186	−	28.0828i	1.76395	−	1.19312i
$555$	0.392416	+	4.30494i	0.0166571	+	0.182735i
$556$	−74.8903	−	12.7066i	−3.17606	−	0.538879i
$557$	−34.3661	+	14.0401i	−1.45614	+	0.594897i	−0.961648	−	0.274287i	$-0.911558\pi$
$557$	−34.3661	+	14.0401i	−1.45614	+	0.594897i	−0.494489	+	0.869184i	$0.664645\pi$
$558$	9.79709	+	1.52411i	0.414744	+	0.0645205i
$559$	0.822801	+	0.746652i	0.0348008	+	0.0315800i
$560$	8.11838	−	9.06339i	0.343064	−	0.382998i
$561$	−6.14943	+	16.2589i	−0.259629	+	0.686453i
$562$	34.7509	−	68.0936i	1.46588	−	2.87236i
$563$	3.52803	+	23.5545i	0.148689	+	0.992704i	0.929735	+	0.368230i	$0.120036\pi$
$563$	3.52803	+	23.5545i	0.148689	+	0.992704i	−0.781046	+	0.624474i	$0.785314\pi$
$564$	−80.6484	+	24.1802i	−3.39591	+	1.01817i
$565$	1.20511	−	0.421062i	0.0506993	−	0.0177142i
$566$	−8.57533	+	7.19556i	−0.360448	+	0.302452i
$567$	16.4652	−	6.51051i	0.691475	−	0.273416i
$568$	4.18922	+	3.51518i	0.175776	+	0.147493i
$569$	17.4390	+	6.60382i	0.731081	+	0.276847i	0.691507	−	0.722370i	$-0.256947\pi$
$569$	17.4390	+	6.60382i	0.731081	+	0.276847i	0.0395742	+	0.999217i	$0.487400\pi$
$570$	5.83558	−	6.96030i	0.244426	−	0.291535i
$571$	1.38597	−	6.82356i	0.0580011	−	0.285557i	−0.940532	−	0.339706i	$-0.889672\pi$
$571$	1.38597	−	6.82356i	0.0580011	−	0.285557i	0.998533	+	0.0541487i	$0.0172445\pi$
$572$	0.220905	−	1.78956i	0.00923651	−	0.0748255i
$573$	3.39922	+	0.240729i	0.142004	+	0.0100566i
$574$	−0.0736284	+	2.27725i	−0.00307319	+	0.0950505i
$575$	−8.72555	+	6.76281i	−0.363881	+	0.282029i
$576$	−19.5379	+	37.1647i	−0.814078	+	1.54853i
$577$	−9.47067	−	15.0262i	−0.394269	−	0.625550i	0.588909	−	0.808199i	$-0.299558\pi$
$577$	−9.47067	−	15.0262i	−0.394269	−	0.625550i	−0.983178	+	0.182649i	$0.941533\pi$
$578$	−29.4447	−	34.6337i	−1.22474	−	1.44057i
$579$	−26.0849	−	15.9587i	−1.08405	−	0.663222i
$580$	−9.38590	+	2.35306i	−0.389728	+	0.0977055i
$581$	31.0254	+	6.93079i	1.28715	+	0.287538i
$582$	52.1741	−	18.6326i	2.16269	−	0.772346i
$583$	1.68110	−	0.515153i	0.0696241	−	0.0213355i
$584$	92.4565	−	25.7370i	3.82588	−	1.06501i
$585$	0.330218	+	0.0962491i	0.0136528	+	0.00397941i
$586$	−4.18757	+	43.0520i	−0.172987	+	1.77846i
$587$	−26.5924	−	21.1666i	−1.09759	−	0.873639i	−0.104915	−	0.994481i	$-0.533457\pi$
$587$	−26.5924	−	21.1666i	−1.09759	−	0.873639i	−0.992672	+	0.120842i	$0.961441\pi$
$588$	−5.59129	+	26.6973i	−0.230581	+	1.10098i
$589$	2.90518	−	3.41715i	0.119706	−	0.140801i
$590$	−0.167320	−	0.0239566i	−0.00688845	−	0.000986278i
$591$	−7.93787	−	8.08676i	−0.326520	−	0.332645i
$592$	−49.5825	−	12.4304i	−2.03783	−	0.510887i
$593$	−10.1057	−	5.07525i	−0.414989	−	0.208416i	0.229039	−	0.973417i	$-0.426442\pi$
$593$	−10.1057	−	5.07525i	−0.414989	−	0.208416i	−0.644028	+	0.765002i	$0.722738\pi$
$594$	−22.1961	−	8.21093i	−0.910718	−	0.336898i
$595$	−5.64505	+	2.83505i	−0.231425	+	0.116226i
$596$	−59.5720	+	13.3078i	−2.44016	+	0.545110i
$597$	−41.9784	−	22.0902i	−1.71806	−	0.904090i
$598$	−1.29474	+	0.117493i	−0.0529459	+	0.00480465i
$599$	−3.75971	−	34.0753i	−0.153618	−	1.39228i	−0.786290	−	0.617858i	$-0.788001\pi$
$599$	−3.75971	−	34.0753i	−0.153618	−	1.39228i	0.632672	−	0.774420i	$-0.281958\pi$
$600$	−3.35506	+	65.3328i	−0.136970	+	2.66720i
$601$	8.41735	+	0.763845i	0.343351	+	0.0311579i	0.260698	−	0.965420i	$-0.416047\pi$
$601$	8.41735	+	0.763845i	0.343351	+	0.0311579i	0.0826533	+	0.996578i	$0.473661\pi$
$602$	−0.538712	−	27.7758i	−0.0219562	−	1.13206i
$603$	−1.25218	−	17.3816i	−0.0509927	−	0.707835i
$604$	−17.1509	−	21.2638i	−0.697860	−	0.865211i
$605$	1.04797	+	4.29774i	0.0426061	+	0.174728i
$606$	11.7314	−	5.24705i	0.476556	−	0.213147i
$607$	−10.6914	+	19.0836i	−0.433949	+	0.774579i	−0.998715	−	0.0506723i	$-0.983864\pi$
$607$	−10.6914	+	19.0836i	−0.433949	+	0.774579i	0.564766	+	0.825251i	$0.308966\pi$
$608$	25.3238	+	42.5812i	1.02702	+	1.72690i
$609$	−8.56356	+	8.29788i	−0.347013	+	0.336247i
$610$	15.2638	−	14.5883i	0.618012	−	0.590661i
$611$	−1.99139	+	0.311448i	−0.0805630	+	0.0125998i
$612$	66.7834	−	57.6198i	2.69956	−	2.32914i
$613$	−3.80645	+	2.29721i	−0.153741	+	0.0927833i	−0.591483	−	0.806317i	$-0.701457\pi$
$613$	−3.80645	+	2.29721i	−0.153741	+	0.0927833i	0.437742	+	0.899101i	$0.355778\pi$
$614$	−31.2641	+	44.3440i	−1.26172	+	1.78958i
$615$	0.250526	+	0.331733i	0.0101022	+	0.0133768i
$616$	−21.8942	+	16.0807i	−0.882141	+	0.647909i
$617$	8.80593	−	19.0448i	0.354513	−	0.766716i	−0.645482	−	0.763775i	$-0.723344\pi$
$617$	8.80593	−	19.0448i	0.354513	−	0.766716i	0.999996	−	0.00294125i	$-0.000936232\pi$
$618$	−33.8620	+	43.7262i	−1.36213	+	1.75893i
$619$	13.7593	+	14.9670i	0.553032	+	0.601574i	0.948450	−	0.316927i	$-0.102651\pi$
$619$	13.7593	+	14.9670i	0.553032	+	0.601574i	−0.395418	+	0.918501i	$0.629400\pi$
$620$	0.200381	−	3.44041i	0.00804749	−	0.138170i
$621$	−1.71588	+	12.0889i	−0.0688558	+	0.485109i
$622$	1.42898	+	24.5346i	0.0572968	+	0.983748i
$623$	16.2623	−	16.7966i	0.651535	−	0.672941i
$624$	−2.36377	+	3.30993i	−0.0946266	+	0.132503i
$625$	7.65315	+	19.0841i	0.306126	+	0.763366i
$626$	19.2617	+	54.0048i	0.769853	+	2.15846i
$627$	−8.41655	+	6.61636i	−0.336124	+	0.264232i
$628$	−16.6999	+	111.495i	−0.666399	+	4.44914i
$629$	21.5899	+	15.4315i	0.860845	+	0.615295i
$630$	−3.91560	−	7.65720i	−0.156001	−	0.305070i
$631$	−16.7055	−	16.3846i	−0.665035	−	0.652261i	0.287114	−	0.957896i	$-0.407304\pi$
$631$	−16.7055	−	16.3846i	−0.665035	−	0.652261i	−0.952149	+	0.305635i	$0.901131\pi$
$632$	−4.51595	+	19.6186i	−0.179635	+	0.780385i
$633$	16.9426	+	0.102658i	0.673409	+	0.00408031i
$634$	14.3304	+	45.7076i	0.569132	+	1.81528i
$635$	−2.60056	+	9.11367i	−0.103200	+	0.361665i
$636$	−8.74395	−	1.77235i	−0.346720	−	0.0702781i
$637$	−0.219364	+	0.615039i	−0.00869152	+	0.0243688i
$638$	15.9266	−	0.618024i	0.630540	−	0.0244678i
$639$	1.78593	−	0.987322i	0.0706502	−	0.0390578i
$640$	4.87333	+	1.99097i	0.192635	+	0.0787001i
$641$	24.2303	+	15.0538i	0.957038	+	0.594589i	0.914535	−	0.404508i	$-0.132557\pi$
$641$	24.2303	+	15.0538i	0.957038	+	0.594589i	0.0425037	+	0.999096i	$0.486467\pi$
$642$	63.2489	−	45.8673i	2.49624	−	1.81024i
$643$	42.2948	−	17.9208i	1.66794	−	0.706728i	0.668624	−	0.743601i	$-0.266884\pi$
$643$	42.2948	−	17.9208i	1.66794	−	0.706728i	0.999320	+	0.0368729i	$0.0117397\pi$
$644$	17.4263	+	15.4075i	0.686693	+	0.607139i
$645$	−3.25967	−	3.88153i	−0.128349	−	0.152835i
$646$	−8.97199	−	55.0341i	−0.352998	−	2.16529i
$647$	−20.2244	+	7.36107i	−0.795102	+	0.289393i	−0.707455	−	0.706758i	$-0.750157\pi$
$647$	−20.2244	+	7.36107i	−0.795102	+	0.289393i	−0.0876467	+	0.996152i	$0.527935\pi$
$648$	47.6634	+	54.4379i	1.87239	+	2.13852i
$649$	0.187212	+	0.0681395i	0.00734870	+	0.00267471i
$650$	−0.484405	+	2.55369i	−0.0189999	+	0.100164i
$651$	−1.90752	−	3.79435i	−0.0747616	−	0.148712i
$652$	3.86773	−	3.07857i	0.151472	−	0.120566i
$653$	−17.6267	−	27.1812i	−0.689785	−	1.06368i	−0.993818	−	0.111019i	$-0.964588\pi$
$653$	−17.6267	−	27.1812i	−0.689785	−	1.06368i	0.304033	−	0.952661i	$-0.401667\pi$
$654$	−24.9688	+	14.0018i	−0.976358	+	0.547514i
$655$	−9.12596	−	1.91513i	−0.356581	−	0.0748305i
$656$	−4.68096	+	1.50089i	−0.182761	+	0.0585999i
$657$	3.43818	−	35.6473i	0.134136	−	1.39073i
$658$	39.8338	+	30.8735i	1.55288	+	1.20358i
$659$	−0.736024	+	0.888764i	−0.0286714	+	0.0346213i	−0.784325	−	0.620351i	$-0.786990\pi$
$659$	−0.736024	+	0.888764i	−0.0286714	+	0.0346213i	0.755653	+	0.654972i	$0.227320\pi$
$660$	−2.10011	+	7.95331i	−0.0817466	+	0.309582i
$661$	16.7166	+	8.12651i	0.650201	+	0.316084i	0.732745	−	0.680503i	$-0.238239\pi$
$661$	16.7166	+	8.12651i	0.650201	+	0.316084i	−0.0825440	+	0.996587i	$0.526305\pi$
$662$	−14.8562	+	7.70316i	−0.577403	+	0.299392i
$663$	1.77120	−	1.14962i	0.0687877	−	0.0446476i
$664$	15.9157	+	128.934i	0.617648	+	5.00359i
$665$	−3.87879	−	0.301483i	−0.150413	−	0.0116910i
$666$	−20.7949	+	29.5457i	−0.805788	+	1.14487i
$667$	−2.05119	−	7.96322i	−0.0794225	−	0.308337i
$668$	−2.47062	+	4.54681i	−0.0955911	+	0.175921i
$669$	−25.0125	−	6.77792i	−0.967038	−	0.262049i
$670$	−8.34549	+	1.41597i	−0.322414	+	0.0547038i
$671$	−21.1389	+	13.1332i	−0.816060	+	0.507002i
$672$	46.4756	−	6.36719i	1.79284	−	0.245620i
$673$	−9.15119	+	20.4826i	−0.352753	+	0.789547i	0.646884	+	0.762588i	$0.276072\pi$
$673$	−9.15119	+	20.4826i	−0.352753	+	0.789547i	−0.999637	+	0.0269581i	$0.991418\pi$
$674$	−59.4280	−	62.9900i	−2.28908	−	2.42629i
$675$	22.3004	+	9.93084i	0.858341	+	0.382238i
$676$	44.7388	−	47.4203i	1.72072	−	1.82386i
$677$	−13.9410	−	33.5033i	−0.535796	−	1.28764i	−0.929644	−	0.368460i	$-0.879885\pi$
$677$	−13.9410	−	33.5033i	−0.535796	−	1.28764i	0.393848	−	0.919176i	$-0.371144\pi$
$678$	9.95491	+	3.83887i	0.382316	+	0.147431i
$679$	−19.4824	−	13.5481i	−0.747665	−	0.519927i
$680$	−18.6620	−	17.8361i	−0.715655	−	0.683983i
$681$	−5.15360	+	9.06960i	−0.197486	+	0.347548i
$682$	−1.48691	+	5.47832i	−0.0569366	+	0.209776i
$683$	4.12857	−	12.0662i	0.157975	−	0.461701i	−0.838566	−	0.544800i	$-0.816605\pi$
$683$	4.12857	−	12.0662i	0.157975	−	0.461701i	0.996541	+	0.0830997i	$0.0264820\pi$
$684$	53.5505	−	9.13052i	2.04756	−	0.349114i
$685$	−8.11096	−	4.89499i	−0.309904	−	0.187028i
$686$	48.3864	−	21.2439i	1.84740	−	0.811096i
$687$	−16.8820	+	48.3805i	−0.644089	+	1.84583i
$688$	56.0529	−	21.2262i	2.13700	−	0.809240i
$689$	−0.201630	−	0.0704489i	−0.00768149	−	0.00268389i
$690$	5.92488	+	0.265875i	0.225556	+	0.0101217i
$691$	−17.8481	−	26.7584i	−0.678975	−	1.01794i	−0.997544	−	0.0700384i	$-0.977688\pi$
$691$	−17.8481	−	26.7584i	−0.678975	−	1.01794i	0.318569	−	0.947900i	$-0.396798\pi$
$692$	−96.8773	−	19.0261i	−3.68272	−	0.723263i
$693$	2.66318	+	9.78081i	0.101166	+	0.371542i
$694$	−7.64126	+	9.47367i	−0.290058	+	0.359616i
$695$	7.50716	+	3.53023i	0.284763	+	0.133909i
$696$	−43.6954	−	21.5701i	−1.65627	−	0.817612i
$697$	2.54670	+	0.164853i	0.0964631	+	0.00624425i
$698$	11.2920	+	41.6041i	0.427409	+	1.57474i
$699$	−2.02234	+	2.06361i	−0.0764919	+	0.0780531i
$700$	39.1820	−	25.0508i	1.48094	−	0.946831i
$701$	−14.7605	+	34.2188i	−0.557498	+	1.29243i	0.373577	+	0.927599i	$0.378131\pi$
$701$	−14.7605	+	34.2188i	−0.557498	+	1.29243i	−0.931075	+	0.364827i	$0.881128\pi$
$702$	1.58266	+	2.39996i	0.0597336	+	0.0905806i
$703$	6.47355	+	15.0074i	0.244154	+	0.566014i
$704$	−19.9116	−	13.4681i	−0.750448	−	0.507597i
$705$	9.19329	−	0.182029i	0.346240	−	0.00685562i
$706$	8.24269	−	25.1470i	0.310218	−	0.946419i
$707$	−4.74924	−	2.78306i	−0.178614	−	0.104668i
$708$	−0.669913	−	0.757074i	−0.0251769	−	0.0284526i
$709$	43.4963	+	14.5693i	1.63354	+	0.547162i	0.978109	−	0.208094i	$-0.0667260\pi$
$709$	43.4963	+	14.5693i	1.63354	+	0.547162i	0.655430	+	0.755256i	$0.272487\pi$
$710$	−0.560644	−	0.817440i	−0.0210406	−	0.0306780i
$711$	6.22595	+	4.20383i	0.233491	+	0.157656i
$712$	86.9765	+	39.5356i	3.25958	+	1.48166i
$713$	2.92476	+	0.151384i	0.109533	+	0.00566939i
$714$	−51.2996	−	12.4870i	−1.91984	−	0.467314i
$715$	−0.0756537	+	0.181813i	−0.00282929	+	0.00679940i
$716$	27.9630	+	62.5879i	1.04502	+	2.33902i
$717$	14.6619	−	27.4306i	0.547559	−	1.02441i
$718$	44.4250	+	25.2673i	1.65793	+	0.942968i
$719$	−38.7801	−	12.4343i	−1.44625	−	0.463722i	−0.524470	−	0.851429i	$-0.675736\pi$
$719$	−38.7801	−	12.4343i	−1.44625	−	0.463722i	−0.921783	+	0.387707i	$0.873267\pi$
$720$	12.7223	−	13.5067i	0.474130	−	0.503365i
$721$	23.6708	+	0.918535i	0.881547	+	0.0342080i
$722$	−5.97076	+	14.8889i	−0.222209	+	0.554107i
$723$	−46.7561	+	2.13610i	−1.73888	+	0.0794425i
$724$	−44.6642	−	13.6868i	−1.65993	−	0.508666i
$725$	−16.4351	−	0.425053i	−0.610385	−	0.0157861i
$726$	−16.5801	+	33.0471i	−0.615346	+	1.22649i
$727$	8.02218	+	0.103719i	0.297526	+	0.00384674i	0.161547	−	0.986865i	$-0.448352\pi$
$727$	8.02218	+	0.103719i	0.297526	+	0.00384674i	0.135979	+	0.990712i	$0.456582\pi$
$728$	3.29985			0.122301
$729$	25.3492	−	9.29618i	0.938859	−	0.344303i
$730$	−17.3955			−0.643837
$731$	−31.1143	−	0.402280i	−1.15081	−	0.0148789i
$732$	126.062	−	7.39352i	4.65939	−	0.273272i
$733$	3.79653	+	0.0981876i	0.140228	+	0.00362664i	0.0959041	−	0.995391i	$-0.469426\pi$
$733$	3.79653	+	0.0981876i	0.140228	+	0.00362664i	0.0443238	+	0.999017i	$0.485887\pi$
$734$	−33.4905	−	10.2627i	−1.23616	−	0.378805i
$735$	1.37017	−	2.64510i	0.0505393	−	0.0975661i
$736$	−12.0407	+	30.0252i	−0.443828	+	1.10674i
$737$	9.96967	+	0.386869i	0.367238	+	0.0142505i
$738$	−0.199212	+	3.46875i	−0.00733311	+	0.127687i
$739$	−42.3262	−	13.5713i	−1.55699	−	0.499230i	−0.602666	−	0.797994i	$-0.705895\pi$
$739$	−42.3262	−	13.5713i	−1.55699	−	0.499230i	−0.954327	+	0.298764i	$0.903426\pi$
$740$	10.9160	+	6.20861i	0.401280	+	0.228233i
$741$	1.29978	−	0.0425518i	0.0477486	−	0.00156318i
$742$	2.17843	+	4.87586i	0.0799727	+	0.178999i
$743$	9.89398	−	23.7774i	0.362975	−	0.872309i	−0.632256	−	0.774760i	$-0.717871\pi$
$743$	9.89398	−	23.7774i	0.362975	−	0.872309i	0.995231	−	0.0975494i	$-0.0311004\pi$
$744$	11.9860	−	12.5512i	0.439427	−	0.460148i
$745$	6.65739	+	0.344584i	0.243908	+	0.0126246i
$746$	−17.1579	−	7.79920i	−0.628194	−	0.285549i
$747$	47.0322	+	11.7506i	1.72082	+	0.429931i
$748$	28.5627	+	41.6454i	1.04436	+	1.52271i
$749$	−31.7324	−	10.6289i	−1.15948	−	0.388372i
$750$	7.76488	−	23.2131i	0.283533	−	0.847623i
$751$	4.06380	+	2.38139i	0.148290	+	0.0868982i	0.577862	−	0.816134i	$-0.303887\pi$
$751$	4.06380	+	2.38139i	0.148290	+	0.0868982i	−0.429572	+	0.903033i	$0.641336\pi$
$752$	−33.8673	+	103.323i	−1.23501	+	3.76780i
$753$	3.06565	−	5.56128i	0.111718	−	0.202664i
$754$	−1.60372	−	1.08474i	−0.0584039	−	0.0395039i
$755$	1.18170	+	2.73950i	0.0430066	+	0.0997005i
$756$	11.8013	−	50.0645i	0.429208	−	1.82083i
$757$	3.01498	−	6.98952i	0.109581	−	0.254038i	−0.854598	−	0.519291i	$-0.826196\pi$
$757$	3.01498	−	6.98952i	0.109581	−	0.254038i	0.964179	+	0.265253i	$0.0854554\pi$
$758$	−22.0488	+	14.0968i	−0.800848	+	0.512018i
$759$	−6.77026	−	1.74098i	−0.245745	−	0.0631936i
$760$	−4.16450	−	15.3436i	−0.151062	−	0.556570i
$761$	0.894577	+	0.0579077i	0.0324284	+	0.00209915i	0.0808025	−	0.996730i	$-0.474252\pi$
$761$	0.894577	+	0.0579077i	0.0324284	+	0.00209915i	−0.0483741	+	0.998829i	$0.515404\pi$
$762$	−65.8808	+	43.9817i	−2.38661	+	1.59329i
$763$	11.0960	+	5.21790i	0.401704	+	0.188900i
$764$	6.21520	−	7.70564i	0.224858	−	0.278780i
$765$	−8.71391	+	4.10633i	−0.315052	+	0.148465i
$766$	−40.1926	−	7.89357i	−1.45222	−	0.285206i
$767$	−0.0134290	−	0.0201331i	−0.000484893	−	0.000726964i
$768$	−2.06538	−	3.97931i	−0.0745279	−	0.143591i
$769$	12.8360	+	4.48488i	0.462880	+	0.161729i	0.551217	−	0.834362i	$-0.314164\pi$
$769$	12.8360	+	4.48488i	0.462880	+	0.161729i	−0.0883374	+	0.996091i	$0.528155\pi$
$770$	4.60475	−	1.74373i	0.165944	−	0.0628397i
$771$	6.94696	+	8.05837i	0.250189	+	0.290215i
$772$	−81.3415	+	35.7127i	−2.92755	+	1.28533i
$773$	−22.9682	−	13.8614i	−0.826109	−	0.498559i	0.0395360	−	0.999218i	$-0.487412\pi$
$773$	−22.9682	−	13.8614i	−0.826109	−	0.498559i	−0.865645	+	0.500659i	$0.833091\pi$
$774$	0.239528	−	42.3636i	0.00860965	−	1.52273i
$775$	1.89557	−	5.54001i	0.0680908	−	0.199003i
$776$	25.4013	−	93.5881i	0.911855	−	3.35962i
$777$	15.4752	−	0.106305i	0.555168	−	0.00381365i
$778$	−31.8691	−	30.4587i	−1.14256	−	1.09200i
$779$	1.29040	+	0.897346i	0.0462334	+	0.0321508i
$780$	0.777514	−	0.627645i	0.0278395	−	0.0224733i
$781$	0.448845	+	1.07867i	0.0160609	+	0.0385980i
$782$	24.9859	−	26.4835i	0.893493	−	0.947047i
$783$	−13.3717	+	12.3227i	−0.477865	+	0.440378i
$784$	24.1733	+	25.6222i	0.863332	+	0.915078i
$785$	5.02244	−	11.2414i	0.179259	−	0.401224i
$786$	−47.7689	−	61.5811i	−1.70386	−	2.19653i
$787$	9.62972	−	5.98275i	0.343262	−	0.213262i	−0.345208	−	0.938526i	$-0.612192\pi$
$787$	9.62972	−	5.98275i	0.343262	−	0.213262i	0.688471	+	0.725264i	$0.258282\pi$
$788$	−32.4555	+	5.50671i	−1.15618	+	0.196168i
$789$	−14.7126	+	14.6297i	−0.523783	+	0.520830i
$790$	1.74218	−	3.20623i	0.0619841	−	0.114073i
$791$	−1.13995	−	4.42557i	−0.0405321	−	0.157355i
$792$	−33.9908	+	23.6782i	−1.20781	+	0.841367i
$793$	3.01397	+	0.234264i	0.107029	+	0.00831896i
$794$	−6.81552	−	55.2128i	−0.241874	−	1.95943i
$795$	0.868053	+	0.442559i	0.0307867	+	0.0156960i
$796$	−122.338	+	63.4338i	−4.33614	+	2.24835i
$797$	25.8942	+	12.5880i	0.917220	+	0.445891i	0.834704	−	0.550698i	$-0.185639\pi$
$797$	25.8942	+	12.5880i	0.917220	+	0.445891i	0.0825161	+	0.996590i	$0.473704\pi$
$798$	−23.0763	−	22.9091i	−0.816893	−	0.810972i
$799$	36.0045	−	43.4762i	1.27375	−	1.53808i
$800$	51.1200	+	39.6210i	1.80736	+	1.40081i
$801$	25.4326	−	24.9846i	0.898617	−	0.882787i
$802$	−68.4627	+	21.9517i	−2.41750	+	0.775140i
$803$	20.0665	+	4.21107i	0.708132	+	0.148605i
$804$	−43.5231	−	25.8601i	−1.53494	−	0.912016i
$805$	−1.38220	−	2.13141i	−0.0487160	−	0.0751224i
$806$	0.539508	−	0.429429i	0.0190034	−	0.0151260i
$807$	−25.2259	−	1.45899i	−0.887992	−	0.0513587i
$808$	4.19227	−	22.1008i	0.147483	−	0.777503i
$809$	−45.1947	−	16.4495i	−1.58896	−	0.578335i	−0.611834	−	0.790986i	$-0.709568\pi$
$809$	−45.1947	−	16.4495i	−1.58896	−	0.578335i	−0.977128	+	0.212652i	$0.931790\pi$
$810$	−5.67673	−	11.8226i	−0.199460	−	0.415404i
$811$	−8.07131	+	2.93772i	−0.283422	+	0.103157i	−0.479820	−	0.877367i	$-0.659298\pi$
$811$	−8.07131	+	2.93772i	−0.283422	+	0.103157i	0.196398	+	0.980524i	$0.437076\pi$
$812$	5.57385	+	34.1899i	0.195604	+	1.19983i
$813$	−13.1379	+	36.1416i	−0.460765	+	1.26754i
$814$	−15.4968	−	13.7015i	−0.543162	−	0.480236i
$815$	−0.497092	+	0.210624i	−0.0174124	+	0.00737783i
$816$	−11.8062	−	113.296i	−0.413301	−	3.96616i
$817$	−16.2784	−	10.1134i	−0.569509	−	0.353825i
$818$	−59.5232	−	24.3179i	−2.08118	−	0.850255i
$819$	0.442581	−	1.14908i	0.0154650	−	0.0401522i
$820$	1.20675	−	0.0468274i	0.0421416	−	0.00163528i
$821$	12.9688	−	36.3610i	0.452613	−	1.26901i	−0.469790	−	0.882778i	$-0.655670\pi$
$821$	12.9688	−	36.3610i	0.452613	−	1.26901i	0.922403	−	0.386230i	$-0.126223\pi$
$822$	−25.1790	−	75.0703i	−0.878218	−	2.61838i
$823$	10.0992	−	35.3926i	0.352034	−	1.23371i	−0.561682	−	0.827353i	$-0.689845\pi$
$823$	10.0992	−	35.3926i	0.352034	−	1.23371i	0.913716	−	0.406354i	$-0.133200\pi$
$824$	28.9606	+	92.3714i	1.00889	+	3.21791i
$825$	−7.06132	+	12.0612i	−0.245843	+	0.419917i
$826$	−0.135739	+	0.589690i	−0.00472297	+	0.0205179i
$827$	6.11790	+	6.00040i	0.212740	+	0.208654i	0.798772	−	0.601634i	$-0.205483\pi$
$827$	6.11790	+	6.00040i	0.212740	+	0.208654i	−0.586032	+	0.810288i	$0.699311\pi$
$828$	25.9772	+	24.1535i	0.902771	+	0.839393i
$829$	26.7802	+	19.1413i	0.930113	+	0.664805i	0.942175	−	0.335122i	$-0.108778\pi$
$829$	26.7802	+	19.1413i	0.930113	+	0.664805i	−0.0120615	+	0.999927i	$0.503839\pi$
$830$	3.48806	−	23.2876i	0.121072	−	0.808326i
$831$	−30.3923	−	12.1737i	−1.05430	−	0.422301i
$832$	0.980969	+	2.75038i	0.0340090	+	0.0953522i
$833$	−6.80682	−	16.9737i	−0.235842	−	0.588104i
$834$	28.7177	+	63.1096i	0.994412	+	2.18531i
$835$	0.393102	−	0.406017i	0.0136038	−	0.0140508i
$836$	1.80838	+	31.0487i	0.0625442	+	1.07384i
$837$	−2.76302	−	5.85717i	−0.0955040	−	0.202453i
$838$	−2.29044	+	39.3253i	−0.0791219	+	1.35847i
$839$	6.74486	+	7.33689i	0.232859	+	0.253297i	0.841638	−	0.540042i	$-0.181592\pi$
$839$	6.74486	+	7.33689i	0.232859	+	0.253297i	−0.608780	+	0.793339i	$0.708341\pi$
$840$	−14.9162	−	2.03121i	−0.514656	−	0.0700835i
$841$	−7.03129	+	15.2068i	−0.242458	+	0.524372i
$842$	32.4301	−	23.8190i	1.11761	−	0.820859i
$843$	−49.5555	+	6.13755i	−1.70678	+	0.211388i
$844$	28.3620	−	40.2278i	0.976262	−	1.38470i
$845$	−6.09584	+	3.67886i	−0.209703	+	0.126557i
$846$	59.5458	+	48.5866i	2.04723	+	1.67044i
$847$	15.6465	−	2.44706i	0.537619	−	0.0840820i
$848$	−8.32936	+	7.96074i	−0.286031	+	0.273373i
$849$	7.03198	+	2.00347i	0.241337	+	0.0687590i
$850$	−37.2091	−	62.5659i	−1.27626	−	2.14599i
$851$	−5.21612	+	9.31052i	−0.178806	+	0.319160i
$852$	0.609668	−	5.89690i	0.0208869	−	0.202025i
$853$	−2.76736	−	11.3490i	−0.0947525	−	0.388581i	0.904532	−	0.426406i	$-0.140220\pi$
$853$	−2.76736	−	11.3490i	−0.0947525	−	0.388581i	−0.999284	+	0.0378249i	$0.987957\pi$
$854$	−47.4549	−	58.8348i	−1.62387	−	2.01329i
$855$	−5.90153	−	0.607730i	−0.201828	−	0.0207839i
$856$	−2.65191	−	136.732i	−0.0906403	−	4.67339i
$857$	−5.28015	−	0.479155i	−0.180366	−	0.0163676i	−0.000179428	−	1.00000i	$-0.500057\pi$
$857$	−5.28015	−	0.479155i	−0.180366	−	0.0163676i	−0.180187	+	0.983632i	$0.557670\pi$
$858$	−1.46572	+	0.748765i	−0.0500389	+	0.0255624i
$859$	2.86597	+	25.9750i	0.0977856	+	0.886256i	0.938617	+	0.344960i	$0.112107\pi$
$859$	2.86597	+	25.9750i	0.0977856	+	0.886256i	−0.840832	+	0.541296i	$0.817934\pi$
$860$	−14.6648	+	1.33077i	−0.500064	+	0.0453790i
$861$	1.25869	−	0.794033i	0.0428960	−	0.0270606i
$862$	27.2471	−	6.08675i	0.928040	−	0.207316i
$863$	36.6452	−	18.4039i	1.24742	−	0.626476i	0.302302	−	0.953212i	$-0.402245\pi$
$863$	36.6452	−	18.4039i	1.24742	−	0.626476i	0.945116	+	0.326736i	$0.105949\pi$
$864$	71.0933	−	7.93158i	2.41864	−	0.269838i
$865$	9.63535	+	4.83906i	0.327612	+	0.164533i
$866$	−34.8639	−	8.74045i	−1.18472	−	0.297012i
$867$	−7.95110	+	28.6080i	−0.270033	+	0.971579i
$868$	−12.2129	−	1.74863i	−0.414534	−	0.0593523i
$869$	−2.78584	+	3.27679i	−0.0945033	+	0.111157i
$870$	6.58149	+	5.89045i	0.223133	+	0.199705i
$871$	−0.948251	−	0.754773i	−0.0321303	−	0.0255745i
$872$	−4.85100	+	49.8726i	−0.164276	+	1.68890i
$873$	−29.1826	−	21.3975i	−0.987682	−	0.724195i
$874$	21.6026	−	6.01349i	0.730718	−	0.203409i
$875$	−10.0243	+	3.07181i	−0.338882	+	0.103846i
$876$	−79.2920	−	67.3568i	−2.67903	−	2.27578i
$877$	44.2839	+	9.89262i	1.49536	+	0.334050i	0.887803	−	0.460224i	$-0.152231\pi$
$877$	44.2839	+	9.89262i	1.49536	+	0.334050i	0.607559	+	0.794274i	$0.292149\pi$
$878$	−43.1413	+	10.8156i	−1.45595	+	0.365009i
$879$	24.8195	−	13.4993i	0.837141	−	0.455320i
$880$	6.88088	+	8.09349i	0.231955	+	0.272831i
$881$	−15.2017	−	24.1191i	−0.512157	−	0.812592i	0.485957	−	0.873983i	$-0.338471\pi$
$881$	−15.2017	−	24.1191i	−0.512157	−	0.812592i	−0.998114	+	0.0613906i	$0.980446\pi$
$882$	23.0409	−	9.43504i	0.775828	−	0.317694i
$883$	−29.9807	+	23.2368i	−1.00893	+	0.781980i	−0.976065	−	0.217480i	$-0.930216\pi$
$883$	−29.9807	+	23.2368i	−1.00893	+	0.781980i	−0.0328654	+	0.999460i	$0.510463\pi$
$884$	0.198233	−	6.13113i	0.00666729	−	0.206212i
$885$	0.0483095	+	0.0992728i	0.00162391	+	0.00333702i
$886$	10.0223	−	81.1916i	0.336707	−	2.72768i
$887$	6.63325	−	32.6575i	0.222723	−	1.09653i	−0.700910	−	0.713250i	$-0.747222\pi$
$887$	6.63325	−	32.6575i	0.222723	−	1.09653i	0.923632	−	0.383280i	$-0.125206\pi$
$888$	21.6540	+	59.4189i	0.726660	+	1.99397i
$889$	31.7302	+	12.0157i	1.06420	+	0.402992i
$890$	−13.2658	−	11.1314i	−0.444672	−	0.373124i
$891$	3.68637	+	15.0121i	0.123498	+	0.502925i
$892$	−57.6710	+	48.3917i	−1.93097	+	1.62027i
$893$	32.8201	−	11.4673i	1.09828	−	0.383737i
$894$	40.5427	+	38.2190i	1.35595	+	1.27824i
$895$	−1.10897	−	7.40392i	−0.0370688	−	0.247486i
$896$	8.56688	−	16.7866i	0.286199	−	0.560801i
$897$	0.537644	+	0.657283i	0.0179514	+	0.0219461i
$898$	18.3980	−	20.5396i	0.613951	−	0.685417i
$899$	3.22991	+	2.93099i	0.107723	+	0.0977538i
$900$	60.6879	−	36.6925i	2.02293	−	1.22308i
$901$	5.53734	−	2.26225i	0.184476	−	0.0753666i
$902$	−1.96118	−	0.332753i	−0.0653003	−	0.0110795i
$903$	−14.8263	+	10.4620i	−0.493387	+	0.348154i
$904$	15.4693	−	10.4633i	0.514503	−	0.348005i
$905$	4.29832	+	2.74811i	0.142881	+	0.0913503i
$906$	−7.29639	+	23.8448i	−0.242406	+	0.792191i
$907$	25.2091	+	10.6814i	0.837056	+	0.354671i	0.766031	−	0.642804i	$-0.222229\pi$
$907$	25.2091	+	10.6814i	0.837056	+	0.354671i	0.0710248	+	0.997475i	$0.477373\pi$
$908$	13.0730	+	27.3398i	0.433842	+	0.907304i
$909$	−7.13372	−	4.42403i	−0.236611	−	0.146736i
$910$	−0.576211	−	0.160399i	−0.0191012	−	0.00531718i
$911$	32.1866	−	0.832426i	1.06639	−	0.0275795i	0.511326	−	0.859387i	$-0.329154\pi$
$911$	32.1866	−	0.832426i	1.06639	−	0.0275795i	0.555064	+	0.831807i	$0.312694\pi$
$912$	29.8282	−	63.4975i	0.987711	−	2.10261i
$913$	−9.66106	+	26.0190i	−0.319734	+	0.861102i
$914$	0.563814	+	0.301658i	0.0186493	+	0.00997795i
$915$	−13.4797	−	2.91417i	−0.445624	−	0.0963394i
$916$	87.3424	+	120.544i	2.88587	+	3.98288i
$917$	−9.57420	+	31.9800i	−0.316168	+	1.05607i
$918$	−77.7271	−	20.9950i	−2.56538	−	0.692939i
$919$	5.88654	+	19.6624i	0.194179	+	0.648603i	0.998518	+	0.0544316i	$0.0173347\pi$
$919$	5.88654	+	19.6624i	0.194179	+	0.648603i	−0.804339	+	0.594171i	$0.797480\pi$
$920$	6.30641	−	8.24623i	0.207916	−	0.271870i
$921$	35.4329	+	0.672862i	1.16755	+	0.0221716i
$922$	26.8577	−	12.6298i	0.884512	−	0.415941i
$923$	0.0336214	−	0.137882i	0.00110666	−	0.00453843i
$924$	27.7412	+	9.88169i	0.912618	+	0.325084i
$925$	15.0386	+	15.1361i	0.494465	+	0.497672i
$926$	2.51221	−	0.493381i	0.0825562	−	0.0162135i
$927$	36.0500	+	2.30426i	1.18404	+	0.0756820i
$928$	−42.1814	+	23.2747i	−1.38467	+	0.764030i
$929$	−44.5430	−	32.7157i	−1.46141	−	1.07337i	−0.980483	−	0.196604i	$-0.937009\pi$
$929$	−44.5430	−	32.7157i	−1.46141	−	1.07337i	−0.480925	−	0.876762i	$-0.659699\pi$
$930$	−2.70305	+	1.60903i	−0.0886363	+	0.0527623i
$931$	1.81224	−	11.1162i	0.0593937	−	0.364320i
$932$	1.56432	+	8.24678i	0.0512410	+	0.270132i
$933$	12.7471	−	9.75672i	0.417322	−	0.319421i
$934$	−11.7867	+	0.762975i	−0.385672	+	0.0249653i
$935$	−1.78542	−	5.21810i	−0.0583896	−	0.170650i
$936$	5.03048	+	0.126023i	0.164426	+	0.00411918i
$937$	−11.0257	−	28.5574i	−0.360195	−	0.932930i	−0.987985	−	0.154547i	$-0.950608\pi$
$937$	−11.0257	−	28.5574i	−0.360195	−	0.932930i	0.627790	−	0.778383i	$-0.283960\pi$
$938$	2.54356	+	30.1968i	0.0830500	+	0.985959i
$939$	22.1573	−	30.1932i	0.723076	−	0.985319i
$940$	14.8228	−	22.2227i	0.483465	−	0.724824i
$941$	−30.0094	+	30.2040i	−0.978278	+	0.984622i	−0.999885	−	0.0151441i	$-0.995179\pi$
$941$	−30.0094	+	30.2040i	−0.978278	+	0.984622i	0.0216072	+	0.999767i	$0.493122\pi$
$942$	92.8217	−	44.4304i	3.02429	−	1.44762i
$943$	0.0464230	+	1.02524i	0.00151174	+	0.0333864i
$944$	−1.29669	+	0.151561i	−0.0422037	+	0.00493291i
$945$	−2.70789	+	4.92171i	−0.0880877	+	0.160103i
$946$	24.0905	+	2.81578i	0.783251	+	0.0915489i
$947$	2.05681	−	28.8771i	0.0668372	−	0.938381i	−0.846816	−	0.531886i	$-0.821483\pi$
$947$	2.05681	−	28.8771i	0.0668372	−	0.938381i	0.913653	−	0.406495i	$-0.133249\pi$
$948$	20.3560	−	7.86873i	0.661131	−	0.255564i
$949$	−1.66178	−	1.85522i	−0.0539437	−	0.0602230i
$950$	0.289803	−	44.8315i	0.00940245	−	1.45452i
$951$	19.4752	−	24.4878i	0.631526	−	0.794070i
$952$	−69.2354	+	61.2144i	−2.24393	+	1.98397i
$953$	24.8765	−	52.0249i	0.805830	−	1.68525i	0.0805987	−	0.996747i	$-0.474317\pi$
$953$	24.8765	−	52.0249i	0.805830	−	1.68525i	0.725232	−	0.688505i	$-0.241733\pi$
$954$	3.13471	+	7.51624i	0.101490	+	0.243347i
$955$	−0.879588	+	0.628691i	−0.0284628	+	0.0203440i
$956$	−41.0735	−	80.4826i	−1.32841	−	2.60299i
$957$	−6.16610	−	8.38814i	−0.199322	−	0.271150i
$958$	50.2068	+	65.6502i	1.62211	+	2.12106i
$959$	−19.8994	+	27.4637i	−0.642585	+	0.886851i
$960$	−2.74124	−	13.0362i	−0.0884731	−	0.420743i
$961$	25.4058	−	14.8879i	0.819543	−	0.480253i
$962$	0.531952	+	2.45577i	0.0171508	+	0.0791770i
$963$	−47.9687	−	17.4152i	−1.54577	−	0.561196i
$964$	−72.5010	+	115.031i	−2.33510	+	3.70489i
$965$	9.60398	−	1.37508i	0.309163	−	0.0442655i
$966$	2.72882	−	21.0562i	0.0877985	−	0.677473i
$967$	−24.9622	+	23.2475i	−0.802731	+	0.747589i	−0.971238	−	0.238111i	$-0.923472\pi$
$967$	−24.9622	+	23.2475i	−0.802731	+	0.747589i	0.168507	+	0.985700i	$0.446105\pi$
$968$	30.8989	+	56.8648i	0.993127	+	1.82770i
$969$	−26.4818	+	25.0046i	−0.850718	+	0.803262i
$970$	−8.98464	+	15.1074i	−0.288479	+	0.485069i
$971$	28.2349	+	48.9042i	0.906100	+	1.56941i	0.819434	+	0.573174i	$0.194288\pi$
$971$	28.2349	+	48.9042i	0.906100	+	1.56941i	0.0866661	+	0.996237i	$0.472379\pi$
$972$	19.9025	−	75.8704i	0.638373	−	2.43355i
$973$	14.8494	−	25.7199i	0.476049	−	0.824541i
$974$	51.1892	+	91.3703i	1.64021	+	2.92769i
$975$	1.55862	−	0.673074i	0.0499159	−	0.0215556i
$976$	85.1638	−	139.076i	2.72603	−	4.45170i
$977$	12.4798	+	54.2156i	0.399263	+	1.73451i	0.644095	+	0.764946i	$0.277234\pi$
$977$	12.4798	+	54.2156i	0.399263	+	1.73451i	−0.244832	+	0.969566i	$0.578733\pi$
$978$	−4.30617	−	1.34817i	−0.137696	−	0.0431096i
$979$	12.6081	+	16.0519i	0.402956	+	0.513021i
$980$	−4.03315	−	7.65674i	−0.128834	−	0.244586i
$981$	16.7162	+	8.37822i	0.533706	+	0.267496i
$982$	1.74206	−	1.58084i	0.0555914	−	0.0504465i
$983$	−0.0150980	−	2.33560i	−0.000481550	−	0.0744941i	−0.999526	−	0.0307874i	$-0.990199\pi$
$983$	−0.0150980	−	2.33560i	−0.000481550	−	0.0744941i	0.999044	−	0.0437067i	$-0.0139167\pi$
$984$	4.78425	+	3.75470i	0.152516	+	0.119695i
$985$	3.57596	+	0.371175i	0.113940	+	0.0118266i
$986$	53.7707	−	6.99067i	1.71241	−	0.222628i
$987$	2.11311	−	32.8504i	0.0672611	−	1.04564i
$988$	2.05560	−	3.16983i	0.0653973	−	0.100846i
$989$	−1.21145	−	12.4548i	−0.0385219	−	0.396040i
$990$	7.08633	−	2.48239i	0.225218	−	0.0788954i
$991$	−6.66742	+	0.518233i	−0.211798	+	0.0164622i	−0.182953	−	0.983122i	$-0.558566\pi$
$991$	−6.66742	+	0.518233i	−0.211798	+	0.0164622i	−0.0288448	+	0.999584i	$0.509183\pi$
$992$	−3.41534	−	16.8147i	−0.108437	−	0.533868i
$993$	9.60640	+	5.21483i	0.304850	+	0.165488i
$994$	−3.08456	+	1.75439i	−0.0978363	+	0.0556457i
$995$	14.7291	−	3.09098i	0.466944	−	0.0979908i
$996$	106.071	−	92.6435i	3.36098	−	2.93552i
$997$	−41.9206	+	20.3790i	−1.32764	+	0.645410i	−0.958800	−	0.284083i	$-0.908311\pi$
$997$	−41.9206	+	20.3790i	−1.32764	+	0.645410i	−0.368840	+	0.929493i	$0.620245\pi$
$998$	33.7506	−	45.3350i	1.06836	−	1.43505i
$999$	23.5953	+	0.428946i	0.746521	+	0.0135712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.k.a.4.3	✓	12960
729.547	even	243	inner	729.2.k.a.547.3	yes	12960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.k.a.4.3	✓	12960	1.1	even	1	trivial
729.2.k.a.547.3	yes	12960	729.547	even	243	inner

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.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65153 - 0.0342818i) q^{2} +(0.952364 + 1.44672i) q^{3} +(5.03008 + 0.130090i) q^{4} +(-0.525411 - 0.161006i) q^{5} +(-2.47562 - 3.86867i) q^{6} +(-0.732244 + 1.82595i) q^{7} +(-8.03343 - 0.311734i) q^{8} +(-1.18601 + 2.75561i) q^{9} +O(q^{10})\)	\(q+(-2.65153 - 0.0342818i) q^{2} +(0.952364 + 1.44672i) q^{3} +(5.03008 + 0.130090i) q^{4} +(-0.525411 - 0.161006i) q^{5} +(-2.47562 - 3.86867i) q^{6} +(-0.732244 + 1.82595i) q^{7} +(-8.03343 - 0.311734i) q^{8} +(-1.18601 + 2.75561i) q^{9} +(1.38762 + 0.444923i) q^{10} +(-1.49298 - 0.849151i) q^{11} +(4.60226 + 7.40102i) q^{12} +(0.0851078 + 0.190492i) q^{13} +(2.00416 - 4.81644i) q^{14} +(-0.267452 - 0.913459i) q^{15} +(11.2401 + 0.581782i) q^{16} +(-5.31943 - 2.41798i) q^{17} +(3.23920 - 7.26591i) q^{18} +(-2.03545 - 2.96775i) q^{19} +(-2.62192 - 0.878223i) q^{20} +(-3.33900 + 0.679611i) q^{21} +(3.92956 + 2.30273i) q^{22} +(0.731911 - 2.23293i) q^{23} +(-7.19975 - 11.9190i) q^{24} +(-3.89144 - 2.63213i) q^{25} +(-0.219135 - 0.508012i) q^{26} +(-5.11611 + 0.908520i) q^{27} +(-3.92078 + 9.08940i) q^{28} +(2.94839 - 1.88504i) q^{29} +(0.677840 + 2.43123i) q^{30} +(0.326466 + 1.20282i) q^{31} +(-13.7380 - 0.889291i) q^{32} +(-0.193373 - 2.96862i) q^{33} +(14.0217 + 6.59368i) q^{34} +(0.678716 - 0.841476i) q^{35} +(-6.32419 + 13.7067i) q^{36} +(-4.45653 - 0.875234i) q^{37} +(5.29530 + 7.93885i) q^{38} +(-0.194535 + 0.304545i) q^{39} +(4.17066 + 1.45722i) q^{40} +(-0.408447 + 0.154671i) q^{41} +(8.87673 - 1.68754i) q^{42} +(4.87607 - 2.14082i) q^{43} +(-7.39934 - 4.46552i) q^{44} +(1.06681 - 1.25687i) q^{45} +(-2.01723 + 5.89558i) q^{46} +(-2.53051 + 9.32335i) q^{47} +(9.86296 + 16.8153i) q^{48} +(2.26256 + 2.16243i) q^{49} +(10.2280 + 7.11257i) q^{50} +(-1.56789 - 9.99852i) q^{51} +(0.403318 + 0.969262i) q^{52} +(-0.702501 + 0.744607i) q^{53} +(13.5966 - 2.23358i) q^{54} +(0.647709 + 0.686531i) q^{55} +(6.45163 - 14.4403i) q^{56} +(2.35503 - 5.77110i) q^{57} +(-7.88235 + 4.89714i) q^{58} +(-0.114359 + 0.0194032i) q^{59} +(-1.22647 - 4.62957i) q^{60} +(6.91784 - 12.7313i) q^{61} +(-0.824397 - 3.20051i) q^{62} +(-4.16315 - 4.18336i) q^{63} +(13.9537 + 1.08457i) q^{64} +(-0.0140463 - 0.113789i) q^{65} +(0.410963 + 7.87801i) q^{66} +(-5.15688 + 2.67392i) q^{67} +(-26.4426 - 12.8546i) q^{68} +(3.92747 - 1.06769i) q^{69} +(-1.82848 + 2.20793i) q^{70} +(-0.537644 - 0.416706i) q^{71} +(10.3867 - 21.7673i) q^{72} +(-11.3675 + 3.64485i) q^{73} +(11.7866 + 2.47348i) q^{74} +(0.101902 - 8.13657i) q^{75} +(-9.85239 - 15.1928i) q^{76} +(2.64373 - 2.10431i) q^{77} +(0.526256 - 0.800840i) q^{78} +(0.466677 - 2.46023i) q^{79} +(-5.81199 - 2.11539i) q^{80} +(-6.18677 - 6.53635i) q^{81} +(1.08831 - 0.396113i) q^{82} +(-2.60006 - 15.9487i) q^{83} +(-16.8838 + 2.98413i) q^{84} +(2.40558 + 2.12689i) q^{85} +(-13.0024 + 5.50928i) q^{86} +(5.53506 + 2.47026i) q^{87} +(11.7290 + 7.28700i) q^{88} +(-11.0012 - 4.49450i) q^{89} +(-2.87176 + 3.29606i) q^{90} +(-0.410148 + 0.0159156i) q^{91} +(3.97205 - 11.1366i) q^{92} +(-1.42923 + 1.61783i) q^{93} +(7.02933 - 24.6344i) q^{94} +(0.591621 + 1.88701i) q^{95} +(-11.7971 - 20.7220i) q^{96} +(-2.70581 + 11.7548i) q^{97} +(-5.92511 - 5.81130i) q^{98} +(4.11061 - 3.10697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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