LMFDB - Embedded newform 729.2.g.b.703.3

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			703.3
Character	$\chi$	$=$	729.703
Dual form			729.2.g.b.28.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00769 - 0.662771i) q^{2} +(-0.215977 - 0.500690i) q^{4} +(-2.69736 - 2.85904i) q^{5} +(-1.84676 + 0.215855i) q^{7} +(-0.533084 + 3.02327i) q^{8} +O(q^{10})$	\(q+(-1.00769 - 0.662771i) q^{2} +(-0.215977 - 0.500690i) q^{4} +(-2.69736 - 2.85904i) q^{5} +(-1.84676 + 0.215855i) q^{7} +(-0.533084 + 3.02327i) q^{8} +(0.823230 + 4.66877i) q^{10} +(-1.39079 - 4.64556i) q^{11} +(0.0180985 + 0.310740i) q^{13} +(2.00403 + 1.00646i) q^{14} +(1.79253 - 1.89997i) q^{16} +(-3.17561 - 1.15583i) q^{17} +(1.05997 - 0.385798i) q^{19} +(-0.848924 + 1.96803i) q^{20} +(-1.67745 + 5.60308i) q^{22} +(2.26299 + 0.264506i) q^{23} +(-0.607605 + 10.4322i) q^{25} +(0.187712 - 0.325126i) q^{26} +(0.506934 + 0.878035i) q^{28} +(-2.56086 + 1.28611i) q^{29} +(-2.90267 + 3.89896i) q^{31} +(2.90875 - 0.689387i) q^{32} +(2.43399 + 3.26942i) q^{34} +(5.59852 + 4.69772i) q^{35} +(8.69541 - 7.29632i) q^{37} +(-1.32382 - 0.313752i) q^{38} +(10.0816 - 6.63075i) q^{40} +(1.20697 - 0.793835i) q^{41} +(4.35354 + 1.03181i) q^{43} +(-2.02561 + 1.69969i) q^{44} +(-2.10510 - 1.76639i) q^{46} +(2.34655 + 3.15196i) q^{47} +(-3.44738 + 0.817044i) q^{49} +(7.52643 - 10.1097i) q^{50} +(0.151676 - 0.0761743i) q^{52} +(0.812932 + 1.40804i) q^{53} +(-9.53037 + 16.5071i) q^{55} +(0.331890 - 5.69833i) q^{56} +(3.43296 + 0.401256i) q^{58} +(-2.86545 + 9.57127i) q^{59} +(-0.302918 + 0.702244i) q^{61} +(5.50912 - 2.00515i) q^{62} +(-8.29717 - 3.01992i) q^{64} +(0.839599 - 0.889923i) q^{65} +(0.658500 + 0.330711i) q^{67} +(0.107146 + 1.83963i) q^{68} +(-2.52809 - 8.44441i) q^{70} +(-1.18078 - 6.69652i) q^{71} +(-0.692009 + 3.92458i) q^{73} +(-13.5981 + 1.58939i) q^{74} +(-0.422094 - 0.447393i) q^{76} +(3.57123 + 8.27903i) q^{77} +(-10.3755 - 6.82406i) q^{79} -10.2672 q^{80} -1.74239 q^{82} +(6.18560 + 4.06833i) q^{83} +(5.26121 + 12.1969i) q^{85} +(-3.70318 - 3.92515i) q^{86} +(14.7862 - 1.72826i) q^{88} +(-0.943990 + 5.35363i) q^{89} +(-0.100499 - 0.569956i) q^{91} +(-0.356318 - 1.19018i) q^{92} +(-0.275575 - 4.73143i) q^{94} +(-3.96214 - 1.98986i) q^{95} +(-3.16003 + 3.34944i) q^{97} +(4.01542 + 1.46149i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 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 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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 $

$2$	−1.00769	−	0.662771i	−0.712548	−	0.468650i	0.140769	−	0.990042i	$-0.455042\pi$
$2$	−1.00769	−	0.662771i	−0.712548	−	0.468650i	−0.853317	+	0.521392i	$0.825413\pi$
$3$		0			0
$3$		0			0
$4$	−0.215977	−	0.500690i	−0.107988	−	0.250345i
$5$	−2.69736	−	2.85904i	−1.20630	−	1.27860i	−0.950089	−	0.311979i	$-0.899008\pi$
$5$	−2.69736	−	2.85904i	−1.20630	−	1.27860i	−0.256208	−	0.966622i	$-0.582473\pi$
$6$		0			0
$7$	−1.84676	+	0.215855i	−0.698010	+	0.0815857i	−0.457695	−	0.889109i	$-0.651325\pi$
$7$	−1.84676	+	0.215855i	−0.698010	+	0.0815857i	−0.240315	+	0.970695i	$0.577251\pi$
$8$	−0.533084	+	3.02327i	−0.188474	+	1.06889i
$9$		0			0
$10$	0.823230	+	4.66877i	0.260328	+	1.47640i
$11$	−1.39079	−	4.64556i	−0.419339	−	1.40069i	−0.863322	−	0.504654i	$-0.831620\pi$
$11$	−1.39079	−	4.64556i	−0.419339	−	1.40069i	0.443983	−	0.896035i	$-0.353565\pi$
$12$		0			0
$13$	0.0180985	+	0.310740i	0.00501963	+	0.0861838i	0.999888	−	0.0149987i	$-0.00477443\pi$
$13$	0.0180985	+	0.310740i	0.00501963	+	0.0861838i	−0.994868	+	0.101183i	$0.967737\pi$
$14$	2.00403	+	1.00646i	0.535601	+	0.268989i
$15$		0			0
$16$	1.79253	−	1.89997i	0.448132	−	0.474992i
$17$	−3.17561	−	1.15583i	−0.770198	−	0.280329i	−0.0731188	−	0.997323i	$-0.523295\pi$
$17$	−3.17561	−	1.15583i	−0.770198	−	0.280329i	−0.697079	+	0.716994i	$0.745517\pi$
$18$		0			0
$19$	1.05997	−	0.385798i	0.243174	−	0.0885081i	−0.217558	−	0.976047i	$-0.569809\pi$
$19$	1.05997	−	0.385798i	0.243174	−	0.0885081i	0.460732	+	0.887539i	$0.347587\pi$
$20$	−0.848924	+	1.96803i	−0.189825	+	0.440064i
$21$		0			0
$22$	−1.67745	+	5.60308i	−0.357634	+	1.19458i
$23$	2.26299	+	0.264506i	0.471866	+	0.0551532i	0.348703	−	0.937233i	$-0.386622\pi$
$23$	2.26299	+	0.264506i	0.471866	+	0.0551532i	0.123163	+	0.992386i	$0.460696\pi$
$24$		0			0
$25$	−0.607605	+	10.4322i	−0.121521	+	2.08644i
$26$	0.187712	−	0.325126i	0.0368133	−	0.0637625i
$27$		0			0
$28$	0.506934	+	0.878035i	0.0958015	+	0.165933i
$29$	−2.56086	+	1.28611i	−0.475540	+	0.238825i	−0.670391	−	0.742008i	$-0.733874\pi$
$29$	−2.56086	+	1.28611i	−0.475540	+	0.238825i	0.194852	+	0.980833i	$0.437577\pi$
$30$		0			0
$31$	−2.90267	+	3.89896i	−0.521334	+	0.700273i	−0.982336	−	0.187126i	$-0.940083\pi$
$31$	−2.90267	+	3.89896i	−0.521334	+	0.700273i	0.461002	+	0.887399i	$0.347490\pi$
$32$	2.90875	−	0.689387i	0.514200	−	0.121868i
$33$		0			0
$34$	2.43399	+	3.26942i	0.417427	+	0.560701i
$35$	5.59852	+	4.69772i	0.946323	+	0.794059i
$36$		0			0
$37$	8.69541	−	7.29632i	1.42952	−	1.19951i	0.483519	−	0.875334i	$-0.339358\pi$
$37$	8.69541	−	7.29632i	1.42952	−	1.19951i	0.945998	−	0.324173i	$-0.105086\pi$
$38$	−1.32382	−	0.313752i	−0.214752	−	0.0508973i
$39$		0			0
$40$	10.0816	−	6.63075i	1.59403	−	1.04841i
$41$	1.20697	−	0.793835i	0.188497	−	0.123976i	−0.451753	−	0.892143i	$-0.649201\pi$
$41$	1.20697	−	0.793835i	0.188497	−	0.123976i	0.640250	+	0.768167i	$0.278831\pi$
$42$		0			0
$43$	4.35354	+	1.03181i	0.663908	+	0.157349i	0.548735	−	0.835996i	$-0.315110\pi$
$43$	4.35354	+	1.03181i	0.663908	+	0.157349i	0.115173	+	0.993345i	$0.463258\pi$
$44$	−2.02561	+	1.69969i	−0.305372	+	0.256237i
$45$		0			0
$46$	−2.10510	−	1.76639i	−0.310380	−	0.260439i
$47$	2.34655	+	3.15196i	0.342279	+	0.459760i	0.939616	−	0.342230i	$-0.111182\pi$
$47$	2.34655	+	3.15196i	0.342279	+	0.459760i	−0.597337	+	0.801990i	$0.703775\pi$
$48$		0			0
$49$	−3.44738	+	0.817044i	−0.492483	+	0.116721i
$50$	7.52643	−	10.1097i	1.06440	−	1.42973i
$51$		0			0
$52$	0.151676	−	0.0761743i	0.0210336	−	0.0105635i
$53$	0.812932	+	1.40804i	0.111665	+	0.193409i	0.916442	−	0.400168i	$-0.131048\pi$
$53$	0.812932	+	1.40804i	0.111665	+	0.193409i	−0.804777	+	0.593577i	$0.797715\pi$
$54$		0			0
$55$	−9.53037	+	16.5071i	−1.28507	+	2.22581i
$56$	0.331890	−	5.69833i	0.0443506	−	0.761471i
$57$		0			0
$58$	3.43296	+	0.401256i	0.450770	+	0.0526875i
$59$	−2.86545	+	9.57127i	−0.373050	+	1.24607i	0.541190	+	0.840900i	$0.317974\pi$
$59$	−2.86545	+	9.57127i	−0.373050	+	1.24607i	−0.914240	+	0.405173i	$0.867211\pi$
$60$		0			0
$61$	−0.302918	+	0.702244i	−0.0387847	+	0.0899131i	−0.936507	−	0.350648i	$-0.885961\pi$
$61$	−0.302918	+	0.702244i	−0.0387847	+	0.0899131i	0.897723	+	0.440561i	$0.145221\pi$
$62$	5.50912	−	2.00515i	0.699659	−	0.254655i
$63$		0			0
$64$	−8.29717	−	3.01992i	−1.03715	−	0.377490i
$65$	0.839599	−	0.889923i	0.104139	−	0.110381i
$66$		0			0
$67$	0.658500	+	0.330711i	0.0804486	+	0.0404028i	0.488569	−	0.872525i	$-0.337519\pi$
$67$	0.658500	+	0.330711i	0.0804486	+	0.0404028i	−0.408120	+	0.912928i	$0.633816\pi$
$68$	0.107146	+	1.83963i	0.0129934	+	0.223088i
$69$		0			0
$70$	−2.52809	−	8.44441i	−0.302164	−	1.00930i
$71$	−1.18078	−	6.69652i	−0.140133	−	0.794731i	−0.971147	−	0.238481i	$-0.923351\pi$
$71$	−1.18078	−	6.69652i	−0.140133	−	0.794731i	0.831015	−	0.556250i	$-0.187760\pi$
$72$		0			0
$73$	−0.692009	+	3.92458i	−0.0809935	+	0.459337i	0.917156	+	0.398529i	$0.130479\pi$
$73$	−0.692009	+	3.92458i	−0.0809935	+	0.459337i	−0.998149	+	0.0608086i	$0.980632\pi$
$74$	−13.5981	+	1.58939i	−1.58075	+	0.184763i
$75$		0			0
$76$	−0.422094	−	0.447393i	−0.0484175	−	0.0513196i
$77$	3.57123	+	8.27903i	0.406979	+	0.943483i
$78$		0			0
$79$	−10.3755	−	6.82406i	−1.16733	−	0.767767i	−0.190483	−	0.981691i	$-0.561005\pi$
$79$	−10.3755	−	6.82406i	−1.16733	−	0.767767i	−0.976850	+	0.213923i	$0.931376\pi$
$80$	−10.2672			−1.14790
$81$		0			0
$82$	−1.74239			−0.192414
$83$	6.18560	+	4.06833i	0.678958	+	0.446558i	0.841581	−	0.540131i	$-0.181625\pi$
$83$	6.18560	+	4.06833i	0.678958	+	0.446558i	−0.162623	+	0.986688i	$0.551996\pi$
$84$		0			0
$85$	5.26121	+	12.1969i	0.570659	+	1.32294i
$86$	−3.70318	−	3.92515i	−0.399325	−	0.423259i
$87$		0			0
$88$	14.7862	−	1.72826i	1.57621	−	0.184233i
$89$	−0.943990	+	5.35363i	−0.100063	+	0.567484i	0.893015	+	0.450027i	$0.148586\pi$
$89$	−0.943990	+	5.35363i	−0.100063	+	0.567484i	−0.993078	+	0.117458i	$0.962526\pi$
$90$		0			0
$91$	−0.100499	−	0.569956i	−0.0105351	−	0.0597476i
$92$	−0.356318	−	1.19018i	−0.0371487	−	0.124085i
$93$		0			0
$94$	−0.275575	−	4.73143i	−0.0284234	−	0.488010i
$95$	−3.96214	−	1.98986i	−0.406507	−	0.204155i
$96$		0			0
$97$	−3.16003	+	3.34944i	−0.320852	+	0.340084i	−0.867645	−	0.497185i	$-0.834367\pi$
$97$	−3.16003	+	3.34944i	−0.320852	+	0.340084i	0.546792	+	0.837268i	$0.315849\pi$
$98$	4.01542	+	1.46149i	0.405619	+	0.147633i
$99$		0			0
$100$	5.35452	−	1.94888i	0.535452	−	0.194888i
$101$	−4.25575	+	9.86593i	−0.423463	+	0.981697i	0.564277	+	0.825586i	$0.309155\pi$
$101$	−4.25575	+	9.86593i	−0.423463	+	0.981697i	−0.987740	+	0.156111i	$0.950104\pi$
$102$		0			0
$103$	3.36931	−	11.2543i	0.331988	−	1.10892i	−0.615235	−	0.788344i	$-0.710939\pi$
$103$	3.36931	−	11.2543i	0.331988	−	1.10892i	0.947223	−	0.320575i	$-0.103876\pi$
$104$	−0.949099	−	0.110934i	−0.0930668	−	0.0108779i
$105$		0			0
$106$	0.114021	−	1.95766i	0.0110747	−	0.190145i
$107$	−3.20979	+	5.55953i	−0.310302	+	0.537460i	−0.978428	−	0.206589i	$-0.933764\pi$
$107$	−3.20979	+	5.55953i	−0.310302	+	0.537460i	0.668125	+	0.744049i	$0.267097\pi$
$108$		0			0
$109$	−1.72147	−	2.98167i	−0.164887	−	0.285592i	0.771728	−	0.635952i	$-0.219393\pi$
$109$	−1.72147	−	2.98167i	−0.164887	−	0.285592i	−0.936615	+	0.350360i	$0.886059\pi$
$110$	20.5441	−	10.3176i	1.95881	−	0.983749i
$111$		0			0
$112$	−2.90025	+	3.89571i	−0.274048	+	0.368110i
$113$	−15.0849	+	3.57519i	−1.41907	+	0.336326i	−0.867348	−	0.497702i	$-0.834177\pi$
$113$	−15.0849	+	3.57519i	−1.41907	+	0.336326i	−0.551722	+	0.834028i	$0.686029\pi$
$114$		0			0
$115$	−5.34788	−	7.18344i	−0.498692	−	0.669859i
$116$	1.19703	+	1.00443i	0.111141	+	0.0932587i
$117$		0			0
$118$	9.23106	−	7.74578i	0.849788	−	0.713057i
$119$	6.11408	+	1.44906i	0.560477	+	0.132835i
$120$		0			0
$121$	−10.4566	+	6.87740i	−0.950598	+	0.625218i
$122$	0.770676	−	0.506882i	0.0697738	−	0.0458909i
$123$		0			0
$124$	2.57908	+	0.611252i	0.231608	+	0.0548921i
$125$	16.4097	−	13.7694i	1.46773	−	1.23157i
$126$		0			0
$127$	−9.04687	−	7.59122i	−0.802780	−	0.673612i	0.146093	−	0.989271i	$-0.453330\pi$
$127$	−9.04687	−	7.59122i	−0.802780	−	0.673612i	−0.948873	+	0.315659i	$0.897775\pi$
$128$	2.78929	+	3.74666i	0.246540	+	0.331161i
$129$		0			0
$130$	−1.43587	+	0.340309i	−0.125935	+	0.0298470i
$131$	10.5633	−	14.1890i	0.922923	−	1.23970i	−0.0476433	−	0.998864i	$-0.515171\pi$
$131$	10.5633	−	14.1890i	0.922923	−	1.23970i	0.970566	−	0.240836i	$-0.0774215\pi$
$132$		0			0
$133$	−1.87424	+	0.941277i	−0.162517	+	0.0816191i
$134$	−0.444381	−	0.769691i	−0.0383887	−	0.0664911i
$135$		0			0
$136$	5.18724	−	8.98457i	0.444802	−	0.770420i
$137$	−0.405293	+	6.95861i	−0.0346265	+	0.594514i	0.935712	+	0.352765i	$0.114758\pi$
$137$	−0.405293	+	6.95861i	−0.0346265	+	0.594514i	−0.970339	+	0.241750i	$0.922279\pi$
$138$		0			0
$139$	−6.26136	−	0.731848i	−0.531081	−	0.0620745i	−0.153674	−	0.988122i	$-0.549110\pi$
$139$	−6.26136	−	0.731848i	−0.531081	−	0.0620745i	−0.377408	+	0.926047i	$0.623184\pi$
$140$	1.14295	−	3.81772i	0.0965970	−	0.322656i
$141$		0			0
$142$	−3.24840	+	7.53064i	−0.272600	+	0.631957i
$143$	1.41839	−	0.516252i	0.118612	−	0.0431712i
$144$		0			0
$145$	10.5846	+	3.85248i	0.879004	+	0.319931i
$146$	3.29843	−	3.49613i	0.272980	−	0.289342i
$147$		0			0
$148$	−5.53120	−	2.77787i	−0.454662	−	0.228340i
$149$	1.31857	+	22.6390i	0.108022	+	1.85466i	0.423710	+	0.905798i	$0.360728\pi$
$149$	1.31857	+	22.6390i	0.108022	+	1.85466i	−0.315688	+	0.948863i	$0.602235\pi$
$150$		0			0
$151$	−4.15613	−	13.8824i	−0.338221	−	1.12974i	−0.942847	−	0.333227i	$-0.891862\pi$
$151$	−4.15613	−	13.8824i	−0.338221	−	1.12974i	0.604625	−	0.796510i	$-0.293323\pi$
$152$	0.601317	+	3.41024i	0.0487733	+	0.276607i
$153$		0			0
$154$	1.88840	−	10.7096i	0.152172	−	0.863008i
$155$	18.9768	−	2.21807i	1.52425	−	0.178160i
$156$		0			0
$157$	−7.80515	−	8.27298i	−0.622919	−	0.660256i	0.336682	−	0.941618i	$-0.390695\pi$
$157$	−7.80515	−	8.27298i	−0.622919	−	0.660256i	−0.959602	+	0.281363i	$0.909214\pi$
$158$	5.93253	+	13.7531i	0.471967	+	1.09414i
$159$		0			0
$160$	−9.81695	−	6.45671i	−0.776098	−	0.510448i
$161$	−4.23630			−0.333867
$162$		0			0
$163$	−0.789620			−0.0618478			−0.0309239	−	0.999522i	$-0.509845\pi$
$163$	−0.789620			−0.0618478			−0.0309239	+	0.999522i	$0.509845\pi$
$164$	−0.658142	−	0.432867i	−0.0513923	−	0.0338012i
$165$		0			0
$166$	−3.53682	−	8.19928i	−0.274511	−	0.636387i
$167$	−3.98342	−	4.22218i	−0.308246	−	0.326722i	0.554668	−	0.832071i	$-0.312845\pi$
$167$	−3.98342	−	4.22218i	−0.308246	−	0.326722i	−0.862915	+	0.505349i	$0.831364\pi$
$168$		0			0
$169$	12.8159	−	1.49796i	0.985836	−	0.115228i
$170$	2.78203	−	15.7777i	0.213372	−	1.21009i
$171$		0			0
$172$	−0.423646	−	2.40262i	−0.0323027	−	0.183198i
$173$	−0.997345	−	3.33136i	−0.0758267	−	0.253279i	0.911669	−	0.410926i	$-0.134794\pi$
$173$	−0.997345	−	3.33136i	−0.0758267	−	0.253279i	−0.987496	+	0.157647i	$0.949609\pi$
$174$		0			0
$175$	−1.12974	−	19.3969i	−0.0854004	−	1.46627i
$176$	−11.3194	−	5.68484i	−0.853235	−	0.428511i
$177$		0			0
$178$	4.49949	−	4.76918i	0.337251	−	0.357465i
$179$	−7.34454	−	2.67320i	−0.548957	−	0.199804i	0.0526260	−	0.998614i	$-0.483241\pi$
$179$	−7.34454	−	2.67320i	−0.548957	−	0.199804i	−0.601583	+	0.798810i	$0.705463\pi$
$180$		0			0
$181$	−10.9891	+	3.99971i	−0.816815	+	0.297296i	−0.716436	−	0.697653i	$-0.754228\pi$
$181$	−10.9891	+	3.99971i	−0.816815	+	0.297296i	−0.100379	+	0.994949i	$0.532006\pi$
$182$	−0.276478	+	0.640949i	−0.0204939	+	0.0475103i
$183$		0			0
$184$	−2.00604	+	6.70063i	−0.147887	+	0.493977i
$185$	−44.3151	−	5.17969i	−3.25811	−	0.380819i
$186$		0			0
$187$	−0.952861	+	16.3600i	−0.0696801	+	1.19636i
$188$	1.07135	−	1.85564i	0.0781366	−	0.135337i
$189$		0			0
$190$	2.67380	+	4.63116i	0.193978	+	0.335980i
$191$	−13.0036	+	6.53063i	−0.940904	+	0.472540i	−0.852024	−	0.523502i	$-0.824625\pi$
$191$	−13.0036	+	6.53063i	−0.940904	+	0.472540i	−0.0888801	+	0.996042i	$0.528329\pi$
$192$		0			0
$193$	10.1622	−	13.6503i	0.731494	−	0.982568i	−0.268320	−	0.963330i	$-0.586469\pi$
$193$	10.1622	−	13.6503i	0.731494	−	0.982568i	0.999815	−	0.0192379i	$-0.00612399\pi$
$194$	5.40425	−	1.28083i	0.388003	−	0.0919584i
$195$		0			0
$196$	1.15364	+	1.54961i	0.0824028	+	0.110686i
$197$	−9.53813	−	8.00344i	−0.679563	−	0.570221i	0.236315	−	0.971676i	$-0.424060\pi$
$197$	−9.53813	−	8.00344i	−0.679563	−	0.570221i	−0.915879	+	0.401455i	$0.868505\pi$
$198$		0			0
$199$	−16.5214	+	13.8631i	−1.17117	+	0.982731i	−0.999997	−	0.00250896i	$-0.999201\pi$
$199$	−16.5214	+	13.8631i	−1.17117	+	0.982731i	−0.171177	+	0.985240i	$0.554757\pi$
$200$	−31.2154	−	7.39818i	−2.20726	−	0.523131i
$201$		0			0
$202$	10.8273	−	7.12126i	0.761809	−	0.501050i
$203$	4.45168	−	2.92792i	0.312447	−	0.205499i
$204$		0			0
$205$	−5.52524	−	1.30950i	−0.385899	−	0.0914598i
$206$	−10.8543	+	9.10781i	−0.756252	+	0.634571i
$207$		0			0
$208$	0.622838	+	0.522623i	0.0431860	+	0.0362374i
$209$	−3.26644	−	4.38760i	−0.225945	−	0.303496i
$210$		0			0
$211$	−12.3360	+	2.92368i	−0.849244	+	0.201275i	−0.632121	−	0.774870i	$-0.717815\pi$
$211$	−12.3360	+	2.92368i	−0.849244	+	0.201275i	−0.217123	+	0.976144i	$0.569667\pi$
$212$	0.529417	−	0.711130i	0.0363605	−	0.0488406i
$213$		0			0
$214$	6.91919	−	3.47495i	0.472986	−	0.237542i
$215$	−8.79309	−	15.2301i	−0.599684	−	1.03868i
$216$		0			0
$217$	4.51892	−	7.82700i	0.306764	−	0.531331i
$218$	−0.241451	+	4.14555i	−0.0163531	+	0.280772i
$219$		0			0
$220$	10.3233	+	1.20662i	0.695995	+	0.0813501i
$221$	0.301688	−	1.00771i	0.0202937	−	0.0677857i
$222$		0			0
$223$	−1.95059	+	4.52199i	−0.130622	+	0.302815i	−0.970958	−	0.239251i	$-0.923098\pi$
$223$	−1.95059	+	4.52199i	−0.130622	+	0.302815i	0.840336	+	0.542065i	$0.182357\pi$
$224$	−5.22297	+	1.90100i	−0.348974	+	0.127016i
$225$		0			0
$226$	17.5705	+	6.39515i	1.16877	+	0.425399i
$227$	−4.41017	+	4.67451i	−0.292713	+	0.310258i	−0.856995	−	0.515324i	$-0.827672\pi$
$227$	−4.41017	+	4.67451i	−0.292713	+	0.310258i	0.564282	+	0.825582i	$0.309153\pi$
$228$		0			0
$229$	26.5744	+	13.3462i	1.75608	+	0.881939i	0.961509	+	0.274773i	$0.0886026\pi$
$229$	26.5744	+	13.3462i	1.75608	+	0.881939i	0.794575	+	0.607166i	$0.207694\pi$
$230$	0.628046	+	10.7831i	0.0414121	+	0.711019i
$231$		0			0
$232$	−2.52311	−	8.42777i	−0.165650	−	0.553310i
$233$	−3.77489	−	21.4085i	−0.247301	−	1.40252i	−0.815087	−	0.579339i	$-0.803311\pi$
$233$	−3.77489	−	21.4085i	−0.247301	−	1.40252i	0.567786	−	0.823176i	$-0.307800\pi$
$234$		0			0
$235$	2.68208	−	15.2108i	0.174960	−	0.992245i
$236$	5.41111	−	0.632468i	0.352233	−	0.0411702i
$237$		0			0
$238$	−5.20073	−	5.51245i	−0.337113	−	0.357319i
$239$	−2.35595	−	5.46170i	−0.152394	−	0.353288i	0.824868	−	0.565325i	$-0.191249\pi$
$239$	−2.35595	−	5.46170i	−0.152394	−	0.353288i	−0.977262	+	0.212037i	$0.931990\pi$
$240$		0			0
$241$	0.990937	+	0.651749i	0.0638318	+	0.0419829i	0.581024	−	0.813887i	$-0.302652\pi$
$241$	0.990937	+	0.651749i	0.0638318	+	0.0419829i	−0.517192	+	0.855869i	$0.673023\pi$
$242$	15.0952			0.970355
$243$		0			0
$244$	0.417030			0.0266976
$245$	11.6348	+	7.65233i	0.743320	+	0.488889i
$246$		0			0
$247$	0.139067	+	0.322393i	0.00884861	+	0.0205134i
$248$	−10.2402	−	10.8540i	−0.650255	−	0.689230i
$249$		0			0
$250$	−25.6620	+	2.99945i	−1.62301	+	0.189702i
$251$	−2.34580	+	13.3037i	−0.148066	+	0.839722i	0.816789	+	0.576937i	$0.195752\pi$
$251$	−2.34580	+	13.3037i	−0.148066	+	0.839722i	−0.964854	+	0.262785i	$0.915359\pi$
$252$		0			0
$253$	−1.91857	−	10.8807i	−0.120619	−	0.684066i
$254$	4.08524	+	13.6456i	0.256331	+	0.856204i
$255$		0			0
$256$	0.699229	+	12.0053i	0.0437018	+	0.750331i
$257$	21.8753	+	10.9862i	1.36454	+	0.685299i	0.972120	−	0.234486i	$-0.0753406\pi$
$257$	21.8753	+	10.9862i	1.36454	+	0.685299i	0.392423	+	0.919785i	$0.371637\pi$
$258$		0			0
$259$	−14.4834	+	15.3515i	−0.899955	+	0.953896i
$260$	−0.626909	−	0.228176i	−0.0388793	−	0.0141509i
$261$		0			0
$262$	−20.0487	+	7.29712i	−1.23861	+	0.450818i
$263$	8.59130	−	19.9169i	0.529762	−	1.22813i	−0.417795	−	0.908541i	$-0.637197\pi$
$263$	8.59130	−	19.9169i	0.529762	−	1.22813i	0.947557	−	0.319586i	$-0.103544\pi$
$264$		0			0
$265$	1.83286	−	6.12219i	0.112592	−	0.376083i
$266$	2.51251	+	0.293670i	0.154052	+	0.0180061i
$267$		0			0
$268$	0.0233632	−	0.401130i	0.00142713	−	0.0245029i
$269$	2.87056	−	4.97195i	0.175021	−	0.303145i	−0.765148	−	0.643855i	$-0.777334\pi$
$269$	2.87056	−	4.97195i	0.175021	−	0.303145i	0.940169	+	0.340710i	$0.110667\pi$
$270$		0			0
$271$	7.23998	+	12.5400i	0.439798	+	0.761752i	0.997674	−	0.0681726i	$-0.0217169\pi$
$271$	7.23998	+	12.5400i	0.439798	+	0.761752i	−0.557876	+	0.829924i	$0.688384\pi$
$272$	−7.88839	+	3.96170i	−0.478304	+	0.240213i
$273$		0			0
$274$	5.02038	−	6.74354i	0.303292	−	0.407392i
$275$	49.3084	−	11.6863i	2.97341	−	0.704711i
$276$		0			0
$277$	7.07774	+	9.50706i	0.425260	+	0.571224i	0.962182	−	0.272408i	$-0.0878202\pi$
$277$	7.07774	+	9.50706i	0.425260	+	0.571224i	−0.536921	+	0.843632i	$0.680413\pi$
$278$	5.82449	+	4.88733i	0.349330	+	0.293122i
$279$		0			0
$280$	−17.1870	+	14.4216i	−1.02712	+	0.861853i
$281$	14.7822	+	3.50346i	0.881835	+	0.208999i	0.646498	−	0.762915i	$-0.276233\pi$
$281$	14.7822	+	3.50346i	0.881835	+	0.208999i	0.235336	+	0.971914i	$0.424381\pi$
$282$		0			0
$283$	−20.8426	+	13.7084i	−1.23896	+	0.814880i	−0.988200	−	0.153168i	$-0.951052\pi$
$283$	−20.8426	+	13.7084i	−1.23896	+	0.814880i	−0.250764	+	0.968048i	$0.580682\pi$
$284$	−3.09786	+	2.03750i	−0.183824	+	0.120903i
$285$		0			0
$286$	−1.77146	−	0.419844i	−0.104749	−	0.0248259i
$287$	−2.05763	+	1.72655i	−0.121458	+	0.101915i
$288$		0			0
$289$	−4.27421	−	3.58648i	−0.251424	−	0.210970i
$290$	−8.11274	−	10.8973i	−0.476396	−	0.639912i
$291$		0			0
$292$	2.11446	−	0.501135i	0.123739	−	0.0293267i
$293$	5.12105	−	6.87876i	0.299175	−	0.401862i	−0.626962	−	0.779050i	$-0.715702\pi$
$293$	5.12105	−	6.87876i	0.299175	−	0.401862i	0.926136	+	0.377189i	$0.123109\pi$
$294$		0			0
$295$	35.0938	−	17.6248i	2.04324	−	1.02615i
$296$	17.4233	+	30.1781i	1.01271	+	1.75407i
$297$		0			0
$298$	13.6758	−	23.6871i	0.792216	−	1.37216i
$299$	−0.0412357	+	0.707989i	−0.00238472	+	0.0409441i
$300$		0			0
$301$	−8.26266	−	0.965767i	−0.476252	−	0.0556659i
$302$	−5.01277	+	16.7438i	−0.288453	+	0.963499i
$303$		0			0
$304$	1.16702	−	2.70546i	0.0669333	−	0.155169i
$305$	2.82482	−	1.02815i	0.161749	−	0.0588718i
$306$		0			0
$307$	1.80059	+	0.655362i	0.102765	+	0.0374035i	0.392891	−	0.919585i	$-0.371475\pi$
$307$	1.80059	+	0.655362i	0.102765	+	0.0374035i	−0.290126	+	0.956989i	$0.593697\pi$
$308$	3.37393	−	3.57615i	0.192247	−	0.203770i
$309$		0			0
$310$	−20.5929	−	10.3421i	−1.16960	−	0.587394i
$311$	−0.886900	−	15.2275i	−0.0502915	−	0.863472i	−0.925270	−	0.379310i	$-0.876162\pi$
$311$	−0.886900	−	15.2275i	−0.0502915	−	0.863472i	0.874978	−	0.484162i	$-0.160876\pi$
$312$		0			0
$313$	8.80754	+	29.4192i	0.497832	+	1.66287i	0.724790	+	0.688969i	$0.241937\pi$
$313$	8.80754	+	29.4192i	0.497832	+	1.66287i	−0.226959	+	0.973904i	$0.572878\pi$
$314$	2.38212	+	13.5097i	0.134431	+	0.762395i
$315$		0			0
$316$	−1.17588	+	6.66874i	−0.0661484	+	0.375146i
$317$	−22.7971	+	2.66460i	−1.28042	+	0.149659i	−0.728966	−	0.684549i	$-0.759999\pi$
$317$	−22.7971	+	2.66460i	−1.28042	+	0.149659i	−0.551449	+	0.834209i	$0.685925\pi$
$318$		0			0
$319$	9.53633	+	10.1079i	0.533932	+	0.565935i
$320$	13.7464	+	31.8677i	0.768447	+	1.78146i
$321$		0			0
$322$	4.26890	+	2.80770i	0.237896	+	0.156467i
$323$	−3.81197			−0.212104
$324$		0			0
$325$	−3.25269			−0.180427
$326$	0.795696	+	0.523337i	0.0440695	+	0.0289850i
$327$		0			0
$328$	1.75656	+	4.07217i	0.0969900	+	0.224848i
$329$	−5.01388	−	5.31440i	−0.276424	−	0.292992i
$330$		0			0
$331$	0.894983	−	0.104608i	0.0491927	−	0.00574980i	−0.0914610	−	0.995809i	$-0.529154\pi$
$331$	0.894983	−	0.104608i	0.0491927	−	0.00574980i	0.140654	+	0.990059i	$0.455080\pi$
$332$	0.701029	−	3.97573i	0.0384740	−	0.218197i
$333$		0			0
$334$	1.21573	+	6.89476i	0.0665219	+	0.377265i
$335$	−0.830698	−	2.77472i	−0.0453859	−	0.151599i
$336$		0			0
$337$	2.04455	+	35.1035i	0.111374	+	1.91221i	0.342885	+	0.939377i	$0.388596\pi$
$337$	2.04455	+	35.1035i	0.111374	+	1.91221i	−0.231511	+	0.972832i	$0.574367\pi$
$338$	−13.9073	−	6.98450i	−0.756457	−	0.379907i
$339$		0			0
$340$	4.97055	−	5.26848i	0.269566	−	0.285723i
$341$	22.1498	+	8.06188i	1.19948	+	0.436575i
$342$		0			0
$343$	18.4205	−	6.70453i	0.994616	−	0.362010i
$344$	−5.44023	+	12.6119i	−0.293318	+	0.679987i
$345$		0			0
$346$	−1.20291	+	4.01801i	−0.0646690	+	0.216010i
$347$	−15.0726	−	1.76174i	−0.809142	−	0.0945751i	−0.298545	−	0.954396i	$-0.596501\pi$
$347$	−15.0726	−	1.76174i	−0.809142	−	0.0945751i	−0.510597	+	0.859820i	$0.670575\pi$
$348$		0			0
$349$	1.64660	−	28.2711i	0.0881406	−	1.51332i	−0.607151	−	0.794587i	$-0.707688\pi$
$349$	1.64660	−	28.2711i	0.0881406	−	1.51332i	0.695291	−	0.718728i	$-0.255275\pi$
$350$	−11.7173	+	20.2949i	−0.626315	+	1.08481i
$351$		0			0
$352$	−7.24806	−	12.5540i	−0.386323	−	0.669131i
$353$	14.8471	−	7.45651i	0.790233	−	0.396870i	−0.00743042	−	0.999972i	$-0.502365\pi$
$353$	14.8471	−	7.45651i	0.790233	−	0.396870i	0.797664	+	0.603102i	$0.206069\pi$
$354$		0			0
$355$	−15.9606	+	21.4388i	−0.847102	+	1.13786i
$356$	2.88439	−	0.683613i	0.152872	−	0.0362314i
$357$		0			0
$358$	5.62934	+	7.56152i	0.297520	+	0.399639i
$359$	10.7593	+	9.02816i	0.567856	+	0.476488i	0.880934	−	0.473239i	$-0.156915\pi$
$359$	10.7593	+	9.02816i	0.567856	+	0.476488i	−0.313077	+	0.949728i	$0.601360\pi$
$360$		0			0
$361$	−13.5801	+	11.3951i	−0.714745	+	0.599742i
$362$	13.7246	+	3.25278i	0.721348	+	0.170963i
$363$		0			0
$364$	−0.263666	+	0.173416i	−0.0138198	+	0.00908946i
$365$	13.0871	−	8.60753i	0.685011	−	0.450539i
$366$		0			0
$367$	5.32264	+	1.26149i	0.277840	+	0.0658492i	0.367173	−	0.930153i	$-0.380326\pi$
$367$	5.32264	+	1.26149i	0.277840	+	0.0658492i	−0.0893336	+	0.996002i	$0.528474\pi$
$368$	4.55902	−	3.82547i	0.237656	−	0.199417i
$369$		0			0
$370$	41.2232	+	34.5903i	2.14309	+	1.79827i
$371$	−1.80522	−	2.42484i	−0.0937225	−	0.125891i
$372$		0			0
$373$	27.5326	−	6.52534i	1.42558	−	0.337869i	0.555805	−	0.831313i	$-0.312410\pi$
$373$	27.5326	−	6.52534i	1.42558	−	0.337869i	0.869778	+	0.493443i	$0.164262\pi$
$374$	11.8031	−	15.8544i	0.610325	−	0.819809i
$375$		0			0
$376$	−10.7801	+	5.41398i	−0.555942	+	0.279205i
$377$	−0.445994	−	0.772485i	−0.0229699	−	0.0397850i
$378$		0			0
$379$	−8.11043	+	14.0477i	−0.416605	+	0.721580i	−0.995595	−	0.0937537i	$-0.970113\pi$
$379$	−8.11043	+	14.0477i	−0.416605	+	0.721580i	0.578991	+	0.815334i	$0.303447\pi$
$380$	−0.140574	+	2.41356i	−0.00721130	+	0.123813i
$381$		0			0
$382$	17.4319	+	2.03750i	0.891895	+	0.104248i
$383$	−4.24796	+	14.1892i	−0.217061	+	0.725033i	0.778220	+	0.627992i	$0.216123\pi$
$383$	−4.24796	+	14.1892i	−0.217061	+	0.725033i	−0.995280	+	0.0970408i	$0.969062\pi$
$384$		0			0
$385$	14.0372	−	32.5418i	0.715401	−	1.65848i
$386$	−19.2874	+	7.02006i	−0.981705	+	0.357311i
$387$		0			0
$388$	2.35952	+	0.858795i	0.119787	+	0.0435987i
$389$	−5.12493	+	5.43211i	−0.259844	+	0.275419i	−0.844141	−	0.536121i	$-0.819889\pi$
$389$	−5.12493	+	5.43211i	−0.259844	+	0.275419i	0.584297	+	0.811540i	$0.301370\pi$
$390$		0			0
$391$	−6.88065	−	3.45559i	−0.347969	−	0.174757i
$392$	−0.632402	−	10.8579i	−0.0319411	−	0.548408i
$393$		0			0
$394$	4.30707	+	14.3866i	0.216987	+	0.724787i
$395$	8.47619	+	48.0709i	0.426484	+	2.41871i
$396$		0			0
$397$	−5.20739	+	29.5326i	−0.261351	+	1.48220i	0.517876	+	0.855455i	$0.326723\pi$
$397$	−5.20739	+	29.5326i	−0.261351	+	1.48220i	−0.779228	+	0.626741i	$0.784388\pi$
$398$	25.8367	−	3.01987i	1.29507	−	0.151372i
$399$		0			0
$400$	18.7317	+	19.8544i	0.936583	+	0.992720i
$401$	2.59509	+	6.01608i	0.129592	+	0.300429i	0.970642	−	0.240529i	$-0.0773210\pi$
$401$	2.59509	+	6.01608i	0.129592	+	0.300429i	−0.841050	+	0.540958i	$0.818062\pi$
$402$		0			0
$403$	−1.26410	−	0.831409i	−0.0629691	−	0.0414154i
$404$	5.85891			0.291492
$405$		0			0
$406$	−6.42647			−0.318941
$407$	−45.9890	−	30.2474i	−2.27959	−	1.49931i
$408$		0			0
$409$	0.707379	+	1.63989i	0.0349776	+	0.0810873i	0.934809	−	0.355150i	$-0.115570\pi$
$409$	0.707379	+	1.63989i	0.0349776	+	0.0810873i	−0.899832	+	0.436237i	$0.856311\pi$
$410$	4.69985	+	4.98155i	0.232109	+	0.246021i
$411$		0			0
$412$	−6.36261	+	0.743682i	−0.313463	+	0.0366386i
$413$	3.22579	−	18.2944i	0.158731	−	0.900207i
$414$		0			0
$415$	−5.05329	−	28.6586i	−0.248056	−	1.40680i
$416$	0.266864	+	0.891389i	0.0130841	+	0.0437040i
$417$		0			0
$418$	0.383606	+	6.58626i	0.0187628	+	0.322145i
$419$	−18.5168	−	9.29947i	−0.904603	−	0.454309i	−0.0652339	−	0.997870i	$-0.520779\pi$
$419$	−18.5168	−	9.29947i	−0.904603	−	0.454309i	−0.839370	+	0.543561i	$0.817076\pi$
$420$		0			0
$421$	−13.0106	+	13.7904i	−0.634097	+	0.672103i	−0.962139	−	0.272560i	$-0.912130\pi$
$421$	−13.0106	+	13.7904i	−0.634097	+	0.672103i	0.328042	+	0.944663i	$0.393611\pi$
$422$	14.3686	+	5.22976i	0.699454	+	0.254581i
$423$		0			0
$424$	−4.69024	+	1.70711i	−0.227778	+	0.0829045i
$425$	13.9873	−	32.4262i	0.678484	−	1.57290i
$426$		0			0
$427$	0.407835	−	1.36226i	0.0197365	−	0.0659245i
$428$	3.47684	+	0.406384i	0.168059	+	0.0196433i
$429$		0			0
$430$	−1.23331	+	21.1751i	−0.0594754	+	1.02115i
$431$	0.254281	−	0.440427i	0.0122483	−	0.0212146i	−0.859836	−	0.510570i	$-0.829434\pi$
$431$	0.254281	−	0.440427i	0.0122483	−	0.0212146i	0.872085	+	0.489355i	$0.162768\pi$
$432$		0			0
$433$	10.9606	+	18.9844i	0.526734	+	0.912330i	0.999515	+	0.0311498i	$0.00991689\pi$
$433$	10.9606	+	18.9844i	0.526734	+	0.912330i	−0.472781	+	0.881180i	$0.656750\pi$
$434$	−9.74120	+	4.89221i	−0.467593	+	0.234834i
$435$		0			0
$436$	−1.12110	+	1.50589i	−0.0536908	+	0.0721192i
$437$	2.50075	−	0.592689i	0.119627	−	0.0283521i
$438$		0			0
$439$	−20.1006	−	26.9997i	−0.959347	−	1.28863i	−0.957441	−	0.288629i	$-0.906801\pi$
$439$	−20.1006	−	26.9997i	−0.959347	−	1.28863i	−0.00190618	−	0.999998i	$-0.500607\pi$
$440$	−44.8249	−	37.6125i	−2.13694	−	1.79311i
$441$		0			0
$442$	−0.971889	+	0.815511i	−0.0462280	+	0.0387899i
$443$	11.9279	+	2.82696i	0.566711	+	0.134313i	0.503976	−	0.863717i	$-0.331870\pi$
$443$	11.9279	+	2.82696i	0.566711	+	0.134313i	0.0627341	+	0.998030i	$0.480018\pi$
$444$		0			0
$445$	17.8525	−	11.7418i	0.846291	−	0.556614i
$446$	4.96265	−	3.26398i	0.234988	−	0.154554i
$447$		0			0
$448$	15.9748	+	3.78609i	0.754736	+	0.178876i
$449$	−19.3898	+	16.2699i	−0.915060	+	0.767826i	−0.973075	−	0.230490i	$-0.925967\pi$
$449$	−19.3898	+	16.2699i	−0.915060	+	0.767826i	0.0580153	+	0.998316i	$0.481523\pi$
$450$		0			0
$451$	−5.36645	−	4.50299i	−0.252696	−	0.212037i
$452$	5.04805	+	6.78071i	0.237440	+	0.318938i
$453$		0			0
$454$	7.54224	−	1.78754i	0.353975	−	0.0838935i
$455$	−1.35844	+	1.82471i	−0.0636848	+	0.0855436i
$456$		0			0
$457$	−26.1808	+	13.1485i	−1.22469	+	0.615060i	−0.939216	−	0.343327i	$-0.888446\pi$
$457$	−26.1808	+	13.1485i	−1.22469	+	0.615060i	−0.285470	+	0.958388i	$0.592150\pi$
$458$	−17.9334	−	31.0616i	−0.837973	−	1.45141i
$459$		0			0
$460$	−2.44166	+	4.22908i	−0.113843	+	0.197182i
$461$	0.745295	−	12.7962i	0.0347119	−	0.595980i	−0.935441	−	0.353484i	$-0.884997\pi$
$461$	0.745295	−	12.7962i	0.0347119	−	0.595980i	0.970152	−	0.242496i	$-0.0779661\pi$
$462$		0			0
$463$	−10.2547	−	1.19861i	−0.476578	−	0.0557040i	−0.125587	−	0.992083i	$-0.540081\pi$
$463$	−10.2547	−	1.19861i	−0.476578	−	0.0557040i	−0.350992	+	0.936379i	$0.614155\pi$
$464$	−2.14684	+	7.17094i	−0.0996645	+	0.332902i
$465$		0			0
$466$	−10.3850	+	24.0751i	−0.481075	+	1.11526i
$467$	6.54957	−	2.38385i	0.303078	−	0.110311i	−0.186005	−	0.982549i	$-0.559554\pi$
$467$	6.54957	−	2.38385i	0.303078	−	0.110311i	0.489083	+	0.872238i	$0.337332\pi$
$468$		0			0
$469$	−1.28748	−	0.468604i	−0.0594502	−	0.0216381i
$470$	−12.7840	+	13.5503i	−0.589683	+	0.625027i
$471$		0			0
$472$	−27.4090	−	13.7653i	−1.26160	−	0.633600i
$473$	−1.26153	−	21.6596i	−0.0580053	−	0.995912i
$474$		0			0
$475$	3.38067	+	11.2922i	0.155116	+	0.518123i
$476$	−0.594967	−	3.37422i	−0.0272702	−	0.154657i
$477$		0			0
$478$	−1.24578	+	7.06518i	−0.0569807	+	0.323154i
$479$	−33.2090	+	3.88157i	−1.51736	+	0.177354i	−0.833605	−	0.552361i	$-0.813727\pi$
$479$	−33.2090	+	3.88157i	−1.51736	+	0.177354i	−0.683752	+	0.729714i	$0.739653\pi$
$480$		0			0
$481$	2.42463	+	2.56996i	0.110554	+	0.117180i
$482$	−0.566601	−	1.31353i	−0.0258080	−	0.0598296i
$483$		0			0
$484$	5.70182	+	3.75015i	0.259174	+	0.170461i
$485$	18.0999			0.821874
$486$		0			0
$487$	−8.67546			−0.393122			−0.196561	−	0.980492i	$-0.562977\pi$
$487$	−8.67546			−0.393122			−0.196561	+	0.980492i	$0.562977\pi$
$488$	−1.96159	−	1.29016i	−0.0887971	−	0.0584028i
$489$		0			0
$490$	−6.65258	−	15.4224i	−0.300533	−	0.696714i
$491$	11.0320	+	11.6932i	0.497866	+	0.527707i	0.926763	−	0.375646i	$-0.122579\pi$
$491$	11.0320	+	11.6932i	0.497866	+	0.527707i	−0.428897	+	0.903353i	$0.641098\pi$
$492$		0			0
$493$	9.61881	−	1.12428i	0.433209	−	0.0506349i
$494$	0.0735360	−	0.417043i	0.00330854	−	0.0187637i
$495$		0			0
$496$	2.20478	+	12.5040i	0.0989977	+	0.561444i
$497$	3.62609	+	12.1120i	0.162653	+	0.543297i
$498$		0			0
$499$	−0.449179	−	7.71210i	−0.0201080	−	0.345241i	−0.993325	−	0.115351i	$-0.963201\pi$
$499$	−0.449179	−	7.71210i	−0.0201080	−	0.345241i	0.973217	−	0.229889i	$-0.0738365\pi$
$500$	−10.4383	−	5.24232i	−0.466816	−	0.234444i
$501$		0			0
$502$	11.1812	−	11.8513i	0.499040	−	0.528951i
$503$	−30.5447	−	11.1174i	−1.36192	−	0.495698i	−0.445272	−	0.895395i	$-0.646893\pi$
$503$	−30.5447	−	11.1174i	−1.36192	−	0.495698i	−0.916647	+	0.399697i	$0.869115\pi$
$504$		0			0
$505$	39.6864	−	14.4447i	1.76602	−	0.642778i
$506$	−5.27811	+	12.2360i	−0.234641	+	0.543958i
$507$		0			0
$508$	−1.84694	+	6.16920i	−0.0819446	+	0.273714i
$509$	1.24093	+	0.145044i	0.0550034	+	0.00642898i	0.143550	−	0.989643i	$-0.454148\pi$
$509$	1.24093	+	0.145044i	0.0550034	+	0.00642898i	−0.0885467	+	0.996072i	$0.528222\pi$
$510$		0			0
$511$	0.430834	−	7.39713i	0.0190590	−	0.327230i
$512$	11.9231	−	20.6514i	0.526931	−	0.912671i
$513$		0			0
$514$	−14.7623	−	25.5690i	−0.651136	−	1.12780i
$515$	−41.2647	+	20.7239i	−1.81834	+	0.913205i
$516$		0			0
$517$	11.3791	−	15.2847i	0.500451	−	0.672222i
$518$	24.7694	−	5.87045i	1.08830	−	0.257933i
$519$		0			0
$520$	2.24290	+	3.01274i	0.0983577	+	0.132117i
$521$	17.9588	+	15.0692i	0.786787	+	0.660193i	0.944948	−	0.327220i	$-0.106112\pi$
$521$	17.9588	+	15.0692i	0.786787	+	0.660193i	−0.158161	+	0.987413i	$0.550556\pi$
$522$		0			0
$523$	26.2642	−	22.0383i	1.14845	−	0.963666i	0.148770	−	0.988872i	$-0.452469\pi$
$523$	26.2642	−	22.0383i	1.14845	−	0.963666i	0.999682	+	0.0252058i	$0.00802411\pi$
$524$	−9.38573	−	2.22446i	−0.410018	−	0.0971760i
$525$		0			0
$526$	−21.8577	+	14.3761i	−0.953043	+	0.626826i
$527$	13.7242	−	9.02658i	0.597838	−	0.393204i
$528$		0			0
$529$	−17.3289	−	4.10702i	−0.753429	−	0.178566i
$530$	−5.90458	+	4.95453i	−0.256479	+	0.215211i
$531$		0			0
$532$	0.876079	+	0.735118i	0.0379828	+	0.0318714i
$533$	0.268521	+	0.360686i	0.0116309	+	0.0156230i
$534$		0			0
$535$	24.5529	−	5.81914i	1.06151	−	0.251583i
$536$	−1.35086	+	1.81453i	−0.0583485	+	0.0783756i
$537$		0			0
$538$	−6.18791	+	3.10769i	−0.266780	+	0.133982i
$539$	8.59021	+	14.8787i	0.370007	+	0.640870i
$540$		0			0
$541$	7.30619	−	12.6547i	0.314118	−	0.544068i	−0.665132	−	0.746726i	$-0.731625\pi$
$541$	7.30619	−	12.6547i	0.314118	−	0.544068i	0.979250	+	0.202658i	$0.0649580\pi$
$542$	1.01547	−	17.4350i	0.0436182	−	0.748896i
$543$		0			0
$544$	−10.0339	−	1.17279i	−0.430199	−	0.0502830i
$545$	−3.88128	+	12.9644i	−0.166256	+	0.555334i
$546$		0			0
$547$	−6.01211	+	13.9376i	−0.257059	+	0.595931i	−0.997056	−	0.0766801i	$-0.975568\pi$
$547$	−6.01211	+	13.9376i	−0.257059	+	0.595931i	0.739996	+	0.672611i	$0.234827\pi$
$548$	3.57164	−	1.29997i	0.152573	−	0.0555320i
$549$		0			0
$550$	−57.4331	−	20.9040i	−2.44896	−	0.891348i
$551$	−2.21826	+	2.35121i	−0.0945009	+	0.100165i
$552$		0			0
$553$	20.6341	+	10.3628i	0.877449	+	0.440672i
$554$	−0.831199	−	14.2711i	−0.0353143	−	0.606323i
$555$		0			0
$556$	0.985878	+	3.29306i	0.0418105	+	0.139657i
$557$	−2.44666	−	13.8757i	−0.103668	−	0.587931i	−0.991744	−	0.128234i	$-0.959069\pi$
$557$	−2.44666	−	13.8757i	−0.103668	−	0.587931i	0.888076	−	0.459697i	$-0.152042\pi$
$558$		0			0
$559$	−0.241831	+	1.37149i	−0.0102284	+	0.0580079i
$560$	18.9610	−	2.21622i	0.801249	−	0.0936526i
$561$		0			0
$562$	−12.5740	−	13.3277i	−0.530402	−	0.562193i
$563$	14.1864	+	32.8877i	0.597884	+	1.38605i	0.901302	+	0.433192i	$0.142613\pi$
$563$	14.1864	+	32.8877i	0.597884	+	1.38605i	−0.303418	+	0.952858i	$0.598128\pi$
$564$		0			0
$565$	50.9111	+	33.4848i	2.14185	+	1.40871i
$566$	30.0885			1.26471
$567$		0			0
$568$	20.8748			0.875889
$569$	23.4530	+	15.4253i	0.983200	+	0.646661i	0.935917	−	0.352221i	$-0.114573\pi$
$569$	23.4530	+	15.4253i	0.983200	+	0.646661i	0.0472828	+	0.998882i	$0.484944\pi$
$570$		0			0
$571$	−18.5275	−	42.9516i	−0.775353	−	1.79747i	−0.575817	−	0.817579i	$-0.695316\pi$
$571$	−18.5275	−	42.9516i	−0.775353	−	1.79747i	−0.199536	−	0.979890i	$-0.563943\pi$
$572$	−0.564821	−	0.598676i	−0.0236164	−	0.0250319i
$573$		0			0
$574$	3.21777	−	0.376104i	0.134307	−	0.0156983i
$575$	−4.13438	+	23.4472i	−0.172415	+	0.977816i
$576$		0			0
$577$	3.26382	+	18.5100i	0.135875	+	0.770583i	0.974247	+	0.225485i	$0.0723966\pi$
$577$	3.26382	+	18.5100i	0.135875	+	0.770583i	−0.838372	+	0.545098i	$0.816492\pi$
$578$	1.93008	+	6.44690i	0.0802806	+	0.268156i
$579$		0			0
$580$	−0.357128	−	6.13165i	−0.0148289	−	0.254603i
$581$	−12.3015	−	6.17804i	−0.510352	−	0.256308i
$582$		0			0
$583$	5.41051	−	5.73481i	0.224081	−	0.237512i
$584$	−11.4962	−	4.18426i	−0.475714	−	0.173146i
$585$		0			0
$586$	−9.71950	+	3.53761i	−0.401509	+	0.146137i
$587$	−0.387163	+	0.897546i	−0.0159799	+	0.0370457i	−0.926019	−	0.377476i	$-0.876792\pi$
$587$	−0.387163	+	0.897546i	−0.0159799	+	0.0370457i	0.910039	+	0.414522i	$0.136051\pi$
$588$		0			0
$589$	−1.57253	+	5.25262i	−0.0647950	+	0.216431i
$590$	−47.0450	−	5.49877i	−1.93681	−	0.226381i
$591$		0			0
$592$	1.72399	−	29.5998i	0.0708557	−	1.21655i
$593$	19.3929	−	33.5896i	0.796372	−	1.37936i	−0.125592	−	0.992082i	$-0.540083\pi$
$593$	19.3929	−	33.5896i	0.796372	−	1.37936i	0.921964	−	0.387276i	$-0.126584\pi$
$594$		0			0
$595$	−12.3490	−	21.3890i	−0.506258	−	0.876865i
$596$	11.0504	−	5.54970i	0.452640	−	0.227324i
$597$		0			0
$598$	0.510788	−	0.686107i	0.0208877	−	0.0280570i
$599$	−32.3773	+	7.67356i	−1.32290	+	0.313533i	−0.830589	−	0.556886i	$-0.811996\pi$
$599$	−32.3773	+	7.67356i	−1.32290	+	0.313533i	−0.492312	+	0.870419i	$0.663848\pi$
$600$		0			0
$601$	−12.1572	−	16.3299i	−0.495901	−	0.666111i	0.481759	−	0.876304i	$-0.339998\pi$
$601$	−12.1572	−	16.3299i	−0.495901	−	0.666111i	−0.977660	+	0.210193i	$0.932591\pi$
$602$	7.68616	+	6.44945i	0.313264	+	0.262860i
$603$		0			0
$604$	−6.05317	+	5.07922i	−0.246300	+	0.206670i
$605$	47.8679	+	11.3449i	1.94611	+	0.461236i
$606$		0			0
$607$	1.32559	−	0.871857i	0.0538042	−	0.0353876i	−0.522322	−	0.852748i	$-0.674934\pi$
$607$	1.32559	−	0.871857i	0.0538042	−	0.0353876i	0.576126	+	0.817361i	$0.304564\pi$
$608$	2.81723	−	1.85292i	0.114254	−	0.0751459i
$609$		0			0
$610$	−3.52799	−	0.836148i	−0.142844	−	0.0338547i
$611$	−0.936970	+	0.786211i	−0.0379058	+	0.0318067i
$612$		0			0
$613$	−5.23563	−	4.39322i	−0.211465	−	0.177440i	0.530903	−	0.847433i	$-0.321853\pi$
$613$	−5.23563	−	4.39322i	−0.211465	−	0.177440i	−0.742368	+	0.669992i	$0.766297\pi$
$614$	−1.38009	−	1.85379i	−0.0556960	−	0.0748127i
$615$		0			0
$616$	−26.9335	+	6.38336i	−1.08518	+	0.257193i
$617$	0.243038	−	0.326456i	0.00978434	−	0.0131426i	−0.797204	−	0.603710i	$-0.793689\pi$
$617$	0.243038	−	0.326456i	0.00978434	−	0.0131426i	0.806988	+	0.590567i	$0.201096\pi$
$618$		0			0
$619$	8.95900	−	4.49938i	0.360093	−	0.180845i	−0.259550	−	0.965730i	$-0.583574\pi$
$619$	8.95900	−	4.49938i	0.360093	−	0.180845i	0.619642	+	0.784885i	$0.287278\pi$
$620$	−5.20911	−	9.02245i	−0.209203	−	0.362350i
$621$		0			0
$622$	−9.19862	+	15.9325i	−0.368831	+	0.638834i
$623$	0.587713	−	10.0906i	0.0235462	−	0.404273i
$624$		0			0
$625$	−31.7342	−	3.70920i	−1.26937	−	0.148368i
$626$	10.6229	−	35.4830i	0.424577	−	1.41819i
$627$		0			0
$628$	−2.45647	+	5.69473i	−0.0980237	+	0.227245i
$629$	−36.0465	+	13.1199i	−1.43727	+	0.523123i
$630$		0			0
$631$	−14.7754	−	5.37779i	−0.588198	−	0.214086i	0.0307388	−	0.999527i	$-0.490214\pi$
$631$	−14.7754	−	5.37779i	−0.588198	−	0.214086i	−0.618937	+	0.785441i	$0.712436\pi$
$632$	26.1620	−	27.7301i	1.04067	−	1.10304i
$633$		0			0
$634$	24.7386	+	12.4242i	0.982495	+	0.493428i
$635$	2.69909	+	46.3416i	0.107110	+	1.83901i
$636$		0			0
$637$	−0.316281	−	1.05645i	−0.0125315	−	0.0418581i
$638$	−2.91047	−	16.5061i	−0.115227	−	0.653483i
$639$		0			0
$640$	3.18813	−	18.0808i	0.126022	−	0.714706i
$641$	7.99000	−	0.933897i	0.315586	−	0.0368867i	0.0431744	−	0.999068i	$-0.486253\pi$
$641$	7.99000	−	0.933897i	0.315586	−	0.0368867i	0.272412	+	0.962181i	$0.412179\pi$
$642$		0			0
$643$	6.55424	+	6.94709i	0.258474	+	0.273966i	0.843595	−	0.536979i	$-0.180435\pi$
$643$	6.55424	+	6.94709i	0.258474	+	0.273966i	−0.585121	+	0.810946i	$0.698953\pi$
$644$	0.914941	+	2.12107i	0.0360537	+	0.0835820i
$645$		0			0
$646$	3.84130	+	2.52646i	0.151134	+	0.0994023i
$647$	−36.6579			−1.44117			−0.720586	−	0.693365i	$-0.756127\pi$
$647$	−36.6579			−1.44117			−0.720586	+	0.693365i	$0.756127\pi$
$648$		0			0
$649$	48.4492			1.90180
$650$	3.27772	+	2.15579i	0.128563	+	0.0845571i
$651$		0			0
$652$	0.170539	+	0.395355i	0.00667884	+	0.0154833i
$653$	13.2604	+	14.0552i	0.518918	+	0.550021i	0.932840	−	0.360292i	$-0.117323\pi$
$653$	13.2604	+	14.0552i	0.518918	+	0.550021i	−0.413922	+	0.910312i	$0.635841\pi$
$654$		0			0
$655$	−69.0601	+	8.07196i	−2.69840	+	0.315398i
$656$	0.655261	−	3.71617i	0.0255836	−	0.145092i
$657$		0			0
$658$	1.53023	+	8.67834i	0.0596544	+	0.338317i
$659$	−8.84575	−	29.5469i	−0.344582	−	1.15098i	−0.938159	−	0.346205i	$-0.887470\pi$
$659$	−8.84575	−	29.5469i	−0.344582	−	1.15098i	0.593577	−	0.804777i	$-0.297715\pi$
$660$		0			0
$661$	−0.928413	−	15.9402i	−0.0361111	−	0.620003i	−0.967012	−	0.254731i	$-0.918013\pi$
$661$	−0.928413	−	15.9402i	−0.0361111	−	0.620003i	0.930901	−	0.365272i	$-0.119024\pi$
$662$	−0.971201	−	0.487755i	−0.0377468	−	0.0189572i
$663$		0			0
$664$	−15.5971	+	16.5320i	−0.605285	+	0.641565i
$665$	7.74664	+	2.81955i	0.300402	+	0.109337i
$666$		0			0
$667$	−6.13538	+	2.23310i	−0.237563	+	0.0864659i
$668$	−1.25368	+	2.90635i	−0.0485062	+	0.112450i
$669$		0			0
$670$	−1.00192	+	3.34664i	−0.0387074	+	0.129292i
$671$	3.68361	+	0.430553i	0.142204	+	0.0166213i
$672$		0			0
$673$	2.23562	−	38.3841i	0.0861768	−	1.47960i	−0.627223	−	0.778840i	$-0.715808\pi$
$673$	2.23562	−	38.3841i	0.0861768	−	1.47960i	0.713399	−	0.700758i	$-0.247155\pi$
$674$	21.2053	−	36.7287i	0.816798	−	1.41474i
$675$		0			0
$676$	−3.51794	−	6.09325i	−0.135305	−	0.234356i
$677$	−11.6642	+	5.85800i	−0.448293	+	0.225141i	−0.658599	−	0.752494i	$-0.728850\pi$
$677$	−11.6642	+	5.85800i	−0.448293	+	0.225141i	0.210305	+	0.977636i	$0.432554\pi$
$678$		0			0
$679$	5.11283	−	6.86772i	0.196212	−	0.263559i
$680$	−39.6791	+	9.40411i	−1.52162	+	0.360631i
$681$		0			0
$682$	−16.9771	−	22.8042i	−0.650087	−	0.873218i
$683$	6.97390	+	5.85180i	0.266849	+	0.223913i	0.766387	−	0.642379i	$-0.222053\pi$
$683$	6.97390	+	5.85180i	0.266849	+	0.223913i	−0.499538	+	0.866292i	$0.666497\pi$
$684$		0			0
$685$	20.9882	−	17.6112i	0.801916	−	0.672888i
$686$	−23.0058	−	5.45249i	−0.878367	−	0.208177i
$687$		0			0
$688$	9.76423	−	6.42203i	0.372258	−	0.244838i
$689$	−0.422821	+	0.278094i	−0.0161082	+	0.0105945i
$690$		0			0
$691$	11.6461	+	2.76019i	0.443040	+	0.105002i	0.446080	−	0.894993i	$-0.352820\pi$
$691$	11.6461	+	2.76019i	0.443040	+	0.105002i	−0.00304009	+	0.999995i	$0.500968\pi$
$692$	−1.45258	+	1.21886i	−0.0552187	+	0.0463340i
$693$		0			0
$694$	14.0210	+	11.7650i	0.532229	+	0.446594i
$695$	14.7968	+	19.8755i	0.561273	+	0.753921i
$696$		0			0
$697$	−4.75039	+	1.12586i	−0.179934	+	0.0426451i
$698$	−20.3965	+	27.3973i	−0.772020	+	1.03700i
$699$		0			0
$700$	−9.46784	+	4.75493i	−0.357851	+	0.179719i
$701$	−0.441721	−	0.765084i	−0.0166836	−	0.0288968i	0.857563	−	0.514379i	$-0.171977\pi$
$701$	−0.441721	−	0.765084i	−0.0166836	−	0.0288968i	−0.874247	+	0.485482i	$0.838644\pi$
$702$		0			0
$703$	6.40198	−	11.0886i	0.241455	−	0.418213i
$704$	−2.48962	+	42.7451i	−0.0938310	+	1.61102i
$705$		0			0
$706$	−19.9033	−	2.32637i	−0.749072	−	0.0875540i
$707$	5.72973	−	19.1386i	0.215489	−	0.719783i
$708$		0			0
$709$	9.37251	−	21.7279i	0.351992	−	0.816009i	−0.646593	−	0.762835i	$-0.723807\pi$
$709$	9.37251	−	21.7279i	0.351992	−	0.816009i	0.998585	−	0.0531741i	$-0.0169338\pi$
$710$	30.2925	−	11.0256i	1.13686	−	0.413782i
$711$		0			0
$712$	−15.6823	−	5.70787i	−0.587717	−	0.213912i
$713$	−7.60000	+	8.05553i	−0.284622	+	0.301682i
$714$		0			0
$715$	−5.30190	−	2.66271i	−0.198280	−	0.0995798i
$716$	0.247807	+	4.25469i	0.00926100	+	0.159005i
$717$		0			0
$718$	−4.85853	−	16.2286i	−0.181319	−	0.605647i
$719$	−4.25311	−	24.1206i	−0.158614	−	0.899547i	−0.955407	−	0.295293i	$-0.904583\pi$
$719$	−4.25311	−	24.1206i	−0.158614	−	0.899547i	0.796792	−	0.604253i	$-0.206529\pi$
$720$		0			0
$721$	−3.79302	+	21.5113i	−0.141259	+	0.801122i
$722$	21.2370	−	2.48225i	0.790359	−	0.0923797i
$723$		0			0
$724$	4.37601	+	4.63830i	0.162633	+	0.172381i
$725$	−11.8610	−	27.4968i	−0.440505	−	1.02121i
$726$		0			0
$727$	6.90593	+	4.54210i	0.256127	+	0.168457i	0.671079	−	0.741386i	$-0.265831\pi$
$727$	6.90593	+	4.54210i	0.256127	+	0.168457i	−0.414952	+	0.909843i	$0.636202\pi$
$728$	1.77670			0.0658490
$729$		0			0
$730$	−18.8926			−0.699248
$731$	−12.6325	−	8.30855i	−0.467231	−	0.307303i
$732$		0			0
$733$	−6.03471	−	13.9900i	−0.222897	−	0.516734i	0.769668	−	0.638444i	$-0.220422\pi$
$733$	−6.03471	−	13.9900i	−0.222897	−	0.516734i	−0.992566	+	0.121710i	$0.961162\pi$
$734$	−4.52752	−	4.79889i	−0.167114	−	0.177130i
$735$		0			0
$736$	6.76483	−	0.790695i	0.249355	−	0.0291454i
$737$	0.620504	−	3.51905i	0.0228565	−	0.129626i
$738$		0			0
$739$	4.97375	+	28.2075i	0.182962	+	1.03763i	0.928545	+	0.371219i	$0.121060\pi$
$739$	4.97375	+	28.2075i	0.182962	+	1.03763i	−0.745583	+	0.666413i	$0.767829\pi$
$740$	6.97761	+	23.3068i	0.256502	+	0.856776i
$741$		0			0
$742$	0.212003	+	3.63994i	0.00778286	+	0.133627i
$743$	−13.1865	−	6.62253i	−0.483767	−	0.242957i	0.190162	−	0.981753i	$-0.439099\pi$
$743$	−13.1865	−	6.62253i	−0.483767	−	0.242957i	−0.673929	+	0.738796i	$0.735395\pi$
$744$		0			0
$745$	61.1691	−	64.8355i	2.24106	−	2.37539i
$746$	−32.0692	−	11.6723i	−1.17414	−	0.427352i
$747$		0			0
$748$	8.39708	−	3.05629i	0.307028	−	0.111749i
$749$	4.72767	−	10.9600i	0.172745	−	0.400468i
$750$		0			0
$751$	2.13409	−	7.12836i	0.0778741	−	0.260118i	−0.910183	−	0.414207i	$-0.864059\pi$
$751$	2.13409	−	7.12836i	0.0778741	−	0.260118i	0.988057	+	0.154089i	$0.0492443\pi$
$752$	10.1949	+	1.19161i	0.371768	+	0.0434535i
$753$		0			0
$754$	−0.0625546	+	1.07402i	−0.00227810	+	0.0391135i
$755$	−28.4798	+	49.3285i	−1.03649	+	1.79525i
$756$		0			0
$757$	−5.40930	−	9.36918i	−0.196604	−	0.340529i	0.750821	−	0.660506i	$-0.229658\pi$
$757$	−5.40930	−	9.36918i	−0.196604	−	0.340529i	−0.947425	+	0.319977i	$0.896325\pi$
$758$	17.4832	−	8.78041i	0.635019	−	0.318919i
$759$		0			0
$760$	8.12803	−	10.9178i	0.294835	−	0.396032i
$761$	5.54356	−	1.31385i	0.200954	−	0.0476270i	−0.128906	−	0.991657i	$-0.541147\pi$
$761$	5.54356	−	1.31385i	0.200954	−	0.0476270i	0.329860	+	0.944030i	$0.392998\pi$
$762$		0			0
$763$	3.82275	+	5.13485i	0.138393	+	0.185894i
$764$	6.07829	+	5.10029i	0.219905	+	0.184522i
$765$		0			0
$766$	13.6848	−	11.4829i	0.494453	−	0.414895i
$767$	−3.02604	−	0.717184i	−0.109264	−	0.0258960i
$768$		0			0
$769$	13.7817	−	9.06435i	0.496980	−	0.326869i	−0.276152	−	0.961114i	$-0.589059\pi$
$769$	13.7817	−	9.06435i	0.496980	−	0.326869i	0.773132	+	0.634245i	$0.218689\pi$
$770$	−35.7130	+	23.4888i	−1.28701	+	0.846477i
$771$		0			0
$772$	−9.02936	−	2.14000i	−0.324974	−	0.0770202i
$773$	1.26612	−	1.06240i	0.0455393	−	0.0382121i	−0.619734	−	0.784812i	$-0.712759\pi$
$773$	1.26612	−	1.06240i	0.0455393	−	0.0382121i	0.665273	+	0.746600i	$0.268315\pi$
$774$		0			0
$775$	−38.9109	−	32.6502i	−1.39772	−	1.17283i
$776$	−8.44168	−	11.3391i	−0.303039	−	0.407052i
$777$		0			0
$778$	8.76461	−	2.07725i	0.314226	−	0.0744730i
$779$	0.973091	−	1.30709i	0.0348646	−	0.0468313i
$780$		0			0
$781$	−29.4669	+	14.7988i	−1.05441	+	0.529544i
$782$	4.64333	+	8.04248i	0.166045	+	0.287598i
$783$		0			0
$784$	−4.62716	+	8.01448i	−0.165256	+	0.286232i
$785$	−2.59943	+	44.6304i	−0.0927776	+	1.59293i
$786$		0			0
$787$	41.3885	+	4.83762i	1.47534	+	0.172443i	0.815410	−	0.578884i	$-0.196512\pi$
$787$	41.3885	+	4.83762i	1.47534	+	0.172443i	0.659931	+	0.751326i	$0.270586\pi$
$788$	−1.94723	+	6.50420i	−0.0693672	+	0.231703i
$789$		0			0
$790$	23.3186	−	54.0585i	0.829638	−	1.92332i
$791$	27.0865	−	9.85869i	0.963086	−	0.350535i
$792$		0			0
$793$	−0.223698	−	0.0814193i	−0.00794374	−	0.00289128i
$794$	24.8208	−	26.3085i	0.880857	−	0.933653i
$795$		0			0
$796$	10.5094	+	5.27801i	0.372495	+	0.187074i
$797$	−2.70404	−	46.4266i	−0.0957820	−	1.64451i	−0.614029	−	0.789283i	$-0.710452\pi$
$797$	−2.70404	−	46.4266i	−0.0957820	−	1.64451i	0.518247	−	0.855231i	$-0.326585\pi$
$798$		0			0
$799$	−3.80859	−	12.7216i	−0.134738	−	0.450057i
$800$	5.42444	+	30.7635i	0.191783	+	1.08765i
$801$		0			0
$802$	1.37223	−	7.78232i	0.0484553	−	0.274803i
$803$	19.1943	−	2.24349i	0.677353	−	0.0791712i
$804$		0			0
$805$	11.4268	+	12.1117i	0.402743	+	0.426883i
$806$	0.722789	+	1.67561i	0.0254592	+	0.0590209i
$807$		0			0
$808$	−27.5587	−	18.1256i	−0.969511	−	0.637658i
$809$	25.7135			0.904038			0.452019	−	0.892008i	$-0.350704\pi$
$809$	25.7135			0.904038			0.452019	+	0.892008i	$0.350704\pi$
$810$		0			0
$811$	−33.1951			−1.16564			−0.582818	−	0.812602i	$-0.698050\pi$
$811$	−33.1951			−1.16564			−0.582818	+	0.812602i	$0.698050\pi$
$812$	−2.42744	−	1.59655i	−0.0851864	−	0.0560280i
$813$		0			0
$814$	26.2957	+	60.9603i	0.921665	+	2.13666i
$815$	2.12989	+	2.25755i	0.0746068	+	0.0790786i
$816$		0			0
$817$	5.01269	−	0.585899i	0.175372	−	0.0204980i
$818$	0.374049	−	2.12134i	0.0130783	−	0.0741708i
$819$		0			0
$820$	0.537666	+	3.04925i	0.0187761	+	0.106485i
$821$	0.0625495	+	0.208930i	0.00218299	+	0.00729170i	0.959074	−	0.283155i	$-0.0913812\pi$
$821$	0.0625495	+	0.208930i	0.00218299	+	0.00729170i	−0.956891	+	0.290447i	$0.906196\pi$
$822$		0			0
$823$	−0.900993	−	15.4695i	−0.0314066	−	0.539231i	−0.976914	−	0.213631i	$-0.931471\pi$
$823$	−0.900993	−	15.4695i	−0.0314066	−	0.539231i	0.945508	−	0.325600i	$-0.105566\pi$
$824$	32.2286	+	16.1858i	1.12274	+	0.563860i
$825$		0			0
$826$	−15.3756	+	16.2972i	−0.534986	+	0.567052i
$827$	43.9974	+	16.0138i	1.52994	+	0.556853i	0.963607	−	0.267323i	$-0.0861391\pi$
$827$	43.9974	+	16.0138i	1.52994	+	0.556853i	0.566334	+	0.824176i	$0.308361\pi$
$828$		0			0
$829$	−12.5795	+	4.57858i	−0.436905	+	0.159021i	−0.551103	−	0.834438i	$-0.685793\pi$
$829$	−12.5795	+	4.57858i	−0.436905	+	0.159021i	0.114197	+	0.993458i	$0.463570\pi$
$830$	−13.9019	+	32.2283i	−0.482544	+	1.11866i
$831$		0			0
$832$	0.788244	−	2.63292i	0.0273274	−	0.0912800i
$833$	11.8919	+	1.38996i	0.412030	+	0.0481594i
$834$		0			0
$835$	−1.32664	+	22.7775i	−0.0459102	+	0.788248i
$836$	−1.49135	+	2.58309i	−0.0515794	+	0.0893382i
$837$		0			0
$838$	12.4958	+	21.6434i	0.431661	+	0.747659i
$839$	21.1461	−	10.6200i	0.730045	−	0.366642i	−0.0446286	−	0.999004i	$-0.514210\pi$
$839$	21.1461	−	10.6200i	0.730045	−	0.366642i	0.774674	+	0.632361i	$0.217914\pi$
$840$		0			0
$841$	−12.4137	+	16.6745i	−0.428058	+	0.574982i
$842$	22.2506	−	5.27348i	0.766806	−	0.181736i
$843$		0			0
$844$	4.12814	+	5.54506i	0.142097	+	0.190869i
$845$	−38.8518	−	32.6005i	−1.33654	−	1.12149i
$846$		0			0
$847$	17.8263	−	14.9580i	0.612518	−	0.513964i
$848$	4.13243	+	0.979404i	0.141908	+	0.0336329i
$849$		0			0
$850$	−35.5861	+	23.4054i	−1.22059	+	0.802797i
$851$	21.6076	−	14.2115i	0.740697	−	0.487164i
$852$		0			0
$853$	−29.2236	−	6.92612i	−1.00060	−	0.237146i	−0.302501	−	0.953149i	$-0.597821\pi$
$853$	−29.2236	−	6.92612i	−1.00060	−	0.237146i	−0.698097	+	0.716003i	$0.745970\pi$
$854$	−1.31384	+	1.10244i	−0.0449587	+	0.0377249i
$855$		0			0
$856$	−15.0969	−	12.6678i	−0.516000	−	0.432975i
$857$	7.39525	+	9.93354i	0.252617	+	0.339323i	0.910283	−	0.413986i	$-0.135864\pi$
$857$	7.39525	+	9.93354i	0.252617	+	0.339323i	−0.657666	+	0.753309i	$0.728456\pi$
$858$		0			0
$859$	−37.1696	+	8.80936i	−1.26821	+	0.300571i	−0.809028	−	0.587771i	$-0.800006\pi$
$859$	−37.1696	+	8.80936i	−1.26821	+	0.300571i	−0.459183	+	0.888342i	$0.651858\pi$
$860$	−5.72645	+	7.69195i	−0.195270	+	0.262293i
$861$		0			0
$862$	−0.548139	+	0.275286i	−0.0186697	+	0.00937628i
$863$	−1.57263	−	2.72387i	−0.0535329	−	0.0927217i	0.838017	−	0.545644i	$-0.183715\pi$
$863$	−1.57263	−	2.72387i	−0.0535329	−	0.0927217i	−0.891550	+	0.452922i	$0.850382\pi$
$864$		0			0
$865$	−6.83429	+	11.8373i	−0.232373	+	0.402482i
$866$	1.53732	−	26.3948i	0.0522404	−	0.896932i
$867$		0			0
$868$	−4.89488	−	0.572130i	−0.166143	−	0.0194193i
$869$	−17.2715	+	57.6908i	−0.585895	+	1.95703i
$870$		0			0
$871$	−0.0908473	+	0.210608i	−0.00307824	+	0.00713617i
$872$	9.93208	−	3.61498i	0.336343	−	0.122419i
$873$		0			0
$874$	−2.91281	−	1.06018i	−0.0985272	−	0.0358610i
$875$	−27.3327	+	28.9709i	−0.924013	+	0.979396i
$876$		0			0
$877$	−33.5229	−	16.8358i	−1.13199	−	0.568505i	−0.218688	−	0.975795i	$-0.570178\pi$
$877$	−33.5229	−	16.8358i	−1.13199	−	0.568505i	−0.913299	+	0.407289i	$0.866474\pi$
$878$	2.36058	+	40.5296i	0.0796657	+	1.36781i
$879$		0			0
$880$	14.2795	+	47.6968i	0.481361	+	1.60786i
$881$	4.15332	+	23.5546i	0.139929	+	0.793576i	0.971300	+	0.237858i	$0.0764453\pi$
$881$	4.15332	+	23.5546i	0.139929	+	0.793576i	−0.831371	+	0.555718i	$0.812444\pi$
$882$		0			0
$883$	2.98131	−	16.9078i	0.100329	−	0.568994i	−0.892655	−	0.450742i	$-0.851160\pi$
$883$	2.98131	−	16.9078i	0.100329	−	0.568994i	0.992984	−	0.118253i	$-0.0377293\pi$
$884$	−0.569706	+	0.0665891i	−0.0191613	+	0.00223963i
$885$		0			0
$886$	−10.1460	−	10.7542i	−0.340863	−	0.361293i
$887$	−1.90630	−	4.41930i	−0.0640072	−	0.148385i	0.883210	−	0.468977i	$-0.155377\pi$
$887$	−1.90630	−	4.41930i	−0.0640072	−	0.148385i	−0.947217	+	0.320592i	$0.896118\pi$
$888$		0			0
$889$	18.3460	+	12.0664i	0.615305	+	0.404693i
$890$	−25.7720			−0.863880
$891$		0			0
$892$	2.68540			0.0899137
$893$	3.70329	+	2.43569i	0.123926	+	0.0815073i
$894$		0			0
$895$	12.1681	+	28.2089i	0.406736	+	0.942920i
$896$	−5.95988	−	6.31711i	−0.199106	−	0.211040i
$897$		0			0
$898$	30.3222	−	3.54416i	1.01187	−	0.118270i
$899$	2.41882	−	13.7178i	0.0806723	−	0.457515i
$900$		0			0
$901$	−0.954103	−	5.41099i	−0.0317858	−	0.180266i
$902$	2.42329	+	8.09436i	0.0806868	+	0.269513i
$903$		0			0
$904$	−2.76724	−	47.5117i	−0.0920370	−	1.58021i
$905$	41.0770	+	20.6296i	1.36544	+	0.685752i
$906$		0			0
$907$	−14.4151	+	15.2791i	−0.478646	+	0.507335i	−0.921030	−	0.389491i	$-0.872651\pi$
$907$	−14.4151	+	15.2791i	−0.478646	+	0.507335i	0.442385	+	0.896825i	$0.354133\pi$
$908$	3.29297	+	1.19854i	0.109281	+	0.0397751i
$909$		0			0
$910$	2.57826	−	0.938410i	0.0854685	−	0.0311080i
$911$	10.0239	−	23.2381i	0.332108	−	0.769913i	−0.667570	−	0.744547i	$-0.732666\pi$
$911$	10.0239	−	23.2381i	0.332108	−	0.769913i	0.999678	−	0.0253663i	$-0.00807520\pi$
$912$		0			0
$913$	10.2968	−	34.3938i	0.340775	−	1.13827i
$914$	35.0967	+	4.10222i	1.16090	+	0.135689i
$915$		0			0
$916$	0.942843	−	16.1880i	0.0311524	−	0.534866i
$917$	−16.4452	+	28.4839i	−0.543067	+	0.940620i
$918$		0			0
$919$	−20.2378	−	35.0529i	−0.667583	−	1.15629i	−0.978578	−	0.205876i	$-0.933996\pi$
$919$	−20.2378	−	35.0529i	−0.667583	−	1.15629i	0.310995	−	0.950411i	$-0.399338\pi$
$920$	24.5683	−	12.3387i	0.809994	−	0.406795i
$921$		0			0
$922$	−9.23200	+	12.4007i	−0.304040	+	0.408396i
$923$	2.05951	−	0.488112i	0.0677895	−	0.0160664i
$924$		0			0
$925$	70.8331	+	95.1454i	2.32898	+	3.12836i
$926$	9.53925	+	8.00438i	0.313479	+	0.263040i
$927$		0			0
$928$	−6.56228	+	5.50641i	−0.215417	+	0.180757i
$929$	−14.6660	−	3.47591i	−0.481177	−	0.114041i	−0.0171330	−	0.999853i	$-0.505454\pi$
$929$	−14.6660	−	3.47591i	−0.481177	−	0.114041i	−0.464044	+	0.885812i	$0.653602\pi$
$930$		0			0
$931$	−3.33891	+	2.19604i	−0.109428	+	0.0719721i
$932$	−9.90372	+	6.51378i	−0.324407	+	0.213366i
$933$		0			0
$934$	−8.17992	−	1.93868i	−0.267655	−	0.0634354i
$935$	49.3440	−	41.4046i	1.61372	−	1.35407i
$936$		0			0
$937$	10.3708	+	8.70215i	0.338800	+	0.284287i	0.796274	−	0.604936i	$-0.206801\pi$
$937$	10.3708	+	8.70215i	0.338800	+	0.284287i	−0.457474	+	0.889223i	$0.651246\pi$
$938$	0.986808	+	1.32551i	0.0322204	+	0.0432795i
$939$		0			0
$940$	−8.19518	+	1.94229i	−0.267297	+	0.0633506i
$941$	18.4024	−	24.7187i	0.599900	−	0.805806i	−0.393643	−	0.919264i	$-0.628785\pi$
$941$	18.4024	−	24.7187i	0.599900	−	0.805806i	0.993543	+	0.113458i	$0.0361927\pi$
$942$		0			0
$943$	2.94133	−	1.47719i	0.0957829	−	0.0481040i
$944$	13.0487	+	22.6010i	0.424699	+	0.735601i
$945$		0			0
$946$	−13.0842	+	22.6624i	−0.425403	+	0.736819i
$947$	2.88862	−	49.5957i	0.0938676	−	1.61164i	−0.542362	−	0.840145i	$-0.682470\pi$
$947$	2.88862	−	49.5957i	0.0938676	−	1.61164i	0.636230	−	0.771499i	$-0.280493\pi$
$948$		0			0
$949$	−1.23205	−	0.144006i	−0.0399940	−	0.00467462i
$950$	4.07748	−	13.6197i	0.132291	−	0.441882i
$951$		0			0
$952$	−7.64023	+	17.7120i	−0.247621	+	0.574051i
$953$	−21.4128	+	7.79362i	−0.693629	+	0.252460i	−0.664688	−	0.747121i	$-0.731436\pi$
$953$	−21.4128	+	7.79362i	−0.693629	+	0.252460i	−0.0289406	+	0.999581i	$0.509213\pi$
$954$		0			0
$955$	53.7466	+	19.5622i	1.73920	+	0.633017i
$956$	−2.22579	+	2.35920i	−0.0719872	+	0.0763019i
$957$		0			0
$958$	36.0371	+	18.0985i	1.16431	+	0.584737i
$959$	−0.753575	−	12.9384i	−0.0243342	−	0.417802i
$960$		0			0
$961$	2.11450	+	7.06294i	0.0682098	+	0.227837i
$962$	−0.739993	−	4.19671i	−0.0238583	−	0.135307i
$963$		0			0
$964$	0.112305	−	0.636915i	0.00361711	−	0.0205136i
$965$	−66.4379	+	7.76547i	−2.13871	+	0.249979i
$966$		0			0
$967$	−39.1298	−	41.4751i	−1.25833	−	1.33375i	−0.919595	−	0.392867i	$-0.871483\pi$
$967$	−39.1298	−	41.4751i	−1.25833	−	1.33375i	−0.338733	−	0.940883i	$-0.609998\pi$
$968$	−15.2180	−	35.2793i	−0.489125	−	1.13392i
$969$		0			0
$970$	−18.2392	−	11.9961i	−0.585625	−	0.385171i
$971$	−38.8020			−1.24521			−0.622607	−	0.782535i	$-0.713926\pi$
$971$	−38.8020			−1.24521			−0.622607	+	0.782535i	$0.713926\pi$
$972$		0			0
$973$	11.7212			0.375765
$974$	8.74221	+	5.74984i	0.280119	+	0.184237i
$975$		0			0
$976$	0.791251	+	1.83433i	0.0253273	+	0.0587153i
$977$	−29.9675	−	31.7637i	−0.958747	−	1.01621i	−0.999855	−	0.0170572i	$-0.994570\pi$
$977$	−29.9675	−	31.7637i	−0.958747	−	1.01621i	0.0411080	−	0.999155i	$-0.486911\pi$
$978$		0			0
$979$	26.1835	−	3.06042i	0.836829	−	0.0978113i
$980$	1.31860	−	7.47815i	0.0421211	−	0.238881i
$981$		0			0
$982$	−3.36694	−	19.0949i	−0.107443	−	0.609342i
$983$	10.0516	+	33.5745i	0.320595	+	1.07086i	0.954689	+	0.297605i	$0.0961880\pi$
$983$	10.0516	+	33.5745i	0.320595	+	1.07086i	−0.634094	+	0.773256i	$0.718627\pi$
$984$		0			0
$985$	2.84566	+	48.8580i	0.0906702	+	1.55675i
$986$	−10.4380	−	5.24214i	−0.332412	−	0.166944i
$987$		0			0
$988$	0.131384	−	0.139259i	0.00417987	−	0.00443041i
$989$	9.57909	+	3.48651i	0.304597	+	0.110864i
$990$		0			0
$991$	−0.299988	+	0.109187i	−0.00952943	+	0.00346843i	−0.346780	−	0.937946i	$-0.612725\pi$
$991$	−0.299988	+	0.109187i	−0.00952943	+	0.00346843i	0.337251	+	0.941415i	$0.390503\pi$
$992$	−5.75525	+	13.3422i	−0.182729	+	0.423614i
$993$		0			0
$994$	4.37349	−	14.6085i	0.138719	−	0.463353i
$995$	84.1995	+	9.84151i	2.66930	+	0.311997i
$996$		0			0
$997$	−0.625507	+	10.7395i	−0.0198100	+	0.340125i	0.973811	+	0.227357i	$0.0730085\pi$
$997$	−0.625507	+	10.7395i	−0.0198100	+	0.340125i	−0.993621	+	0.112767i	$0.964029\pi$
$998$	−4.65872	+	8.06914i	−0.147469	+	0.255424i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.b.703.3		144
3.2	odd	2		729.2.g.c.703.6		144
9.2	odd	6		729.2.g.d.217.6		144
9.4	even	3		243.2.g.a.73.6		144
9.5	odd	6		81.2.g.a.25.3	yes	144
9.7	even	3		729.2.g.a.217.3		144
81.13	even	27		729.2.g.a.514.3		144
81.14	odd	54		729.2.g.c.28.6		144
81.38	odd	54		6561.2.a.c.1.24		72
81.40	even	27		243.2.g.a.10.6		144
81.41	odd	54		81.2.g.a.13.3	✓	144
81.43	even	27		6561.2.a.d.1.49		72
81.67	even	27	inner	729.2.g.b.28.3		144
81.68	odd	54		729.2.g.d.514.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.3	✓	144	81.41	odd	54
81.2.g.a.25.3	yes	144	9.5	odd	6
243.2.g.a.10.6		144	81.40	even	27
243.2.g.a.73.6		144	9.4	even	3
729.2.g.a.217.3		144	9.7	even	3
729.2.g.a.514.3		144	81.13	even	27
729.2.g.b.28.3		144	81.67	even	27	inner
729.2.g.b.703.3		144	1.1	even	1	trivial
729.2.g.c.28.6		144	81.14	odd	54
729.2.g.c.703.6		144	3.2	odd	2
729.2.g.d.217.6		144	9.2	odd	6
729.2.g.d.514.6		144	81.68	odd	54
6561.2.a.c.1.24		72	81.38	odd	54
6561.2.a.d.1.49		72	81.43	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.00769 - 0.662771i) q^{2} +(-0.215977 - 0.500690i) q^{4} +(-2.69736 - 2.85904i) q^{5} +(-1.84676 + 0.215855i) q^{7} +(-0.533084 + 3.02327i) q^{8} +O(q^{10})\)	\(q+(-1.00769 - 0.662771i) q^{2} +(-0.215977 - 0.500690i) q^{4} +(-2.69736 - 2.85904i) q^{5} +(-1.84676 + 0.215855i) q^{7} +(-0.533084 + 3.02327i) q^{8} +(0.823230 + 4.66877i) q^{10} +(-1.39079 - 4.64556i) q^{11} +(0.0180985 + 0.310740i) q^{13} +(2.00403 + 1.00646i) q^{14} +(1.79253 - 1.89997i) q^{16} +(-3.17561 - 1.15583i) q^{17} +(1.05997 - 0.385798i) q^{19} +(-0.848924 + 1.96803i) q^{20} +(-1.67745 + 5.60308i) q^{22} +(2.26299 + 0.264506i) q^{23} +(-0.607605 + 10.4322i) q^{25} +(0.187712 - 0.325126i) q^{26} +(0.506934 + 0.878035i) q^{28} +(-2.56086 + 1.28611i) q^{29} +(-2.90267 + 3.89896i) q^{31} +(2.90875 - 0.689387i) q^{32} +(2.43399 + 3.26942i) q^{34} +(5.59852 + 4.69772i) q^{35} +(8.69541 - 7.29632i) q^{37} +(-1.32382 - 0.313752i) q^{38} +(10.0816 - 6.63075i) q^{40} +(1.20697 - 0.793835i) q^{41} +(4.35354 + 1.03181i) q^{43} +(-2.02561 + 1.69969i) q^{44} +(-2.10510 - 1.76639i) q^{46} +(2.34655 + 3.15196i) q^{47} +(-3.44738 + 0.817044i) q^{49} +(7.52643 - 10.1097i) q^{50} +(0.151676 - 0.0761743i) q^{52} +(0.812932 + 1.40804i) q^{53} +(-9.53037 + 16.5071i) q^{55} +(0.331890 - 5.69833i) q^{56} +(3.43296 + 0.401256i) q^{58} +(-2.86545 + 9.57127i) q^{59} +(-0.302918 + 0.702244i) q^{61} +(5.50912 - 2.00515i) q^{62} +(-8.29717 - 3.01992i) q^{64} +(0.839599 - 0.889923i) q^{65} +(0.658500 + 0.330711i) q^{67} +(0.107146 + 1.83963i) q^{68} +(-2.52809 - 8.44441i) q^{70} +(-1.18078 - 6.69652i) q^{71} +(-0.692009 + 3.92458i) q^{73} +(-13.5981 + 1.58939i) q^{74} +(-0.422094 - 0.447393i) q^{76} +(3.57123 + 8.27903i) q^{77} +(-10.3755 - 6.82406i) q^{79} -10.2672 q^{80} -1.74239 q^{82} +(6.18560 + 4.06833i) q^{83} +(5.26121 + 12.1969i) q^{85} +(-3.70318 - 3.92515i) q^{86} +(14.7862 - 1.72826i) q^{88} +(-0.943990 + 5.35363i) q^{89} +(-0.100499 - 0.569956i) q^{91} +(-0.356318 - 1.19018i) q^{92} +(-0.275575 - 4.73143i) q^{94} +(-3.96214 - 1.98986i) q^{95} +(-3.16003 + 3.34944i) q^{97} +(4.01542 + 1.46149i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 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 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

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Database

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