LMFDB - Embedded newform 729.2.g.c.28.6

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			28.6
Character	$\chi$	$=$	729.28
Dual form			729.2.g.c.703.6

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

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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	$-0.544958\pi$
$2$	1.00769	−	0.662771i	0.712548	−	0.468650i	0.853317	+	0.521392i	$0.174587\pi$
$3$		0			0
$3$		0			0
$4$	−0.215977	+	0.500690i	−0.107988	+	0.250345i
$5$	2.69736	−	2.85904i	1.20630	−	1.27860i	0.256208	−	0.966622i	$-0.417527\pi$
$5$	2.69736	−	2.85904i	1.20630	−	1.27860i	0.950089	−	0.311979i	$-0.100992\pi$
$6$		0			0
$7$	−1.84676	−	0.215855i	−0.698010	−	0.0815857i	−0.240315	−	0.970695i	$-0.577251\pi$
$7$	−1.84676	−	0.215855i	−0.698010	−	0.0815857i	−0.457695	+	0.889109i	$0.651325\pi$
$8$	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	−0.443983	−	0.896035i	$-0.646435\pi$
$11$	1.39079	−	4.64556i	0.419339	−	1.40069i	0.863322	−	0.504654i	$-0.168380\pi$
$12$		0			0
$13$	0.0180985	−	0.310740i	0.00501963	−	0.0861838i	−0.994868	−	0.101183i	$-0.967737\pi$
$13$	0.0180985	−	0.310740i	0.00501963	−	0.0861838i	0.999888	+	0.0149987i	$0.00477443\pi$
$14$	−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	$-0.476705\pi$
$17$	3.17561	−	1.15583i	0.770198	−	0.280329i	0.697079	+	0.716994i	$0.254483\pi$
$18$		0			0
$19$	1.05997	+	0.385798i	0.243174	+	0.0885081i	0.460732	−	0.887539i	$-0.347587\pi$
$19$	1.05997	+	0.385798i	0.243174	+	0.0885081i	−0.217558	+	0.976047i	$0.569809\pi$
$20$	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	$-0.613378\pi$
$23$	−2.26299	+	0.264506i	−0.471866	+	0.0551532i	−0.123163	+	0.992386i	$0.539304\pi$
$24$		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	$-0.266126\pi$
$29$	2.56086	+	1.28611i	0.475540	+	0.238825i	−0.194852	+	0.980833i	$0.562423\pi$
$30$		0			0
$31$	−2.90267	−	3.89896i	−0.521334	−	0.700273i	0.461002	−	0.887399i	$-0.347490\pi$
$31$	−2.90267	−	3.89896i	−0.521334	−	0.700273i	−0.982336	+	0.187126i	$0.940083\pi$
$32$	−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	0.945998	+	0.324173i	$0.105086\pi$
$37$	8.69541	+	7.29632i	1.42952	+	1.19951i	0.483519	+	0.875334i	$0.339358\pi$
$38$	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	$-0.350799\pi$
$41$	−1.20697	−	0.793835i	−0.188497	−	0.123976i	−0.640250	+	0.768167i	$0.721169\pi$
$42$		0			0
$43$	4.35354	−	1.03181i	0.663908	−	0.157349i	0.115173	−	0.993345i	$-0.463258\pi$
$43$	4.35354	−	1.03181i	0.663908	−	0.157349i	0.548735	+	0.835996i	$0.315110\pi$
$44$	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	$-0.888818\pi$
$47$	−2.34655	+	3.15196i	−0.342279	+	0.459760i	0.597337	+	0.801990i	$0.296225\pi$
$48$		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	$-0.868952\pi$
$53$	−0.812932	+	1.40804i	−0.111665	+	0.193409i	0.804777	+	0.593577i	$0.202285\pi$
$54$		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	0.914240	+	0.405173i	$0.132789\pi$
$59$	2.86545	+	9.57127i	0.373050	+	1.24607i	−0.541190	+	0.840900i	$0.682026\pi$
$60$		0			0
$61$	−0.302918	−	0.702244i	−0.0387847	−	0.0899131i	0.897723	−	0.440561i	$-0.145221\pi$
$61$	−0.302918	−	0.702244i	−0.0387847	−	0.0899131i	−0.936507	+	0.350648i	$0.885961\pi$
$62$	−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	−0.408120	−	0.912928i	$-0.633816\pi$
$67$	0.658500	−	0.330711i	0.0804486	−	0.0404028i	0.488569	+	0.872525i	$0.337519\pi$
$68$	−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	−0.831015	−	0.556250i	$-0.812240\pi$
$71$	1.18078	−	6.69652i	0.140133	−	0.794731i	0.971147	−	0.238481i	$-0.0766493\pi$
$72$		0			0
$73$	−0.692009	−	3.92458i	−0.0809935	−	0.459337i	−0.998149	−	0.0608086i	$-0.980632\pi$
$73$	−0.692009	−	3.92458i	−0.0809935	−	0.459337i	0.917156	−	0.398529i	$-0.130479\pi$
$74$	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	−0.976850	−	0.213923i	$-0.931376\pi$
$79$	−10.3755	+	6.82406i	−1.16733	+	0.767767i	−0.190483	+	0.981691i	$0.561005\pi$
$80$	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	$-0.818375\pi$
$83$	−6.18560	+	4.06833i	−0.678958	+	0.446558i	0.162623	+	0.986688i	$0.448004\pi$
$84$		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	0.993078	+	0.117458i	$0.0374744\pi$
$89$	0.943990	+	5.35363i	0.100063	+	0.567484i	−0.893015	+	0.450027i	$0.851414\pi$
$90$		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	0.546792	−	0.837268i	$-0.315849\pi$
$97$	−3.16003	−	3.34944i	−0.320852	−	0.340084i	−0.867645	+	0.497185i	$0.834367\pi$
$98$	−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	0.987740	+	0.156111i	$0.0498958\pi$
$101$	4.25575	+	9.86593i	0.423463	+	0.981697i	−0.564277	+	0.825586i	$0.690845\pi$
$102$		0			0
$103$	3.36931	+	11.2543i	0.331988	+	1.10892i	0.947223	+	0.320575i	$0.103876\pi$
$103$	3.36931	+	11.2543i	0.331988	+	1.10892i	−0.615235	+	0.788344i	$0.710939\pi$
$104$	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	$-0.0662363\pi$
$107$	3.20979	+	5.55953i	0.310302	+	0.537460i	−0.668125	+	0.744049i	$0.732903\pi$
$108$		0			0
$109$	−1.72147	+	2.98167i	−0.164887	+	0.285592i	−0.936615	−	0.350360i	$-0.886059\pi$
$109$	−1.72147	+	2.98167i	−0.164887	+	0.285592i	0.771728	+	0.635952i	$0.219393\pi$
$110$	−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	$-0.165823\pi$
$113$	15.0849	+	3.57519i	1.41907	+	0.336326i	0.551722	+	0.834028i	$0.313971\pi$
$114$		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	−0.948873	−	0.315659i	$-0.897775\pi$
$127$	−9.04687	+	7.59122i	−0.802780	+	0.673612i	0.146093	+	0.989271i	$0.453330\pi$
$128$	−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	−0.970566	−	0.240836i	$-0.922578\pi$
$131$	−10.5633	−	14.1890i	−0.922923	−	1.23970i	0.0476433	−	0.998864i	$-0.484829\pi$
$132$		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	0.970339	+	0.241750i	$0.0777213\pi$
$137$	0.405293	+	6.95861i	0.0346265	+	0.594514i	−0.935712	+	0.352765i	$0.885242\pi$
$138$		0			0
$139$	−6.26136	+	0.731848i	−0.531081	+	0.0620745i	−0.377408	−	0.926047i	$-0.623184\pi$
$139$	−6.26136	+	0.731848i	−0.531081	+	0.0620745i	−0.153674	+	0.988122i	$0.549110\pi$
$140$	−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	0.315688	+	0.948863i	$0.397765\pi$
$149$	−1.31857	+	22.6390i	−0.108022	+	1.85466i	−0.423710	+	0.905798i	$0.639272\pi$
$150$		0			0
$151$	−4.15613	+	13.8824i	−0.338221	+	1.12974i	0.604625	+	0.796510i	$0.293323\pi$
$151$	−4.15613	+	13.8824i	−0.338221	+	1.12974i	−0.942847	+	0.333227i	$0.891862\pi$
$152$	−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	−0.959602	−	0.281363i	$-0.909214\pi$
$157$	−7.80515	+	8.27298i	−0.622919	+	0.660256i	0.336682	+	0.941618i	$0.390695\pi$
$158$	−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	$-0.687155\pi$
$167$	3.98342	−	4.22218i	0.308246	−	0.326722i	0.862915	+	0.505349i	$0.168636\pi$
$168$		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	$-0.865206\pi$
$173$	0.997345	−	3.33136i	0.0758267	−	0.253279i	0.987496	+	0.157647i	$0.0503907\pi$
$174$		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	$-0.516759\pi$
$179$	7.34454	−	2.67320i	0.548957	−	0.199804i	0.601583	+	0.798810i	$0.294537\pi$
$180$		0			0
$181$	−10.9891	−	3.99971i	−0.816815	−	0.297296i	−0.100379	−	0.994949i	$-0.532006\pi$
$181$	−10.9891	−	3.99971i	−0.816815	−	0.297296i	−0.716436	+	0.697653i	$0.754228\pi$
$182$	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	$-0.175375\pi$
$191$	13.0036	+	6.53063i	0.940904	+	0.472540i	0.0888801	+	0.996042i	$0.471671\pi$
$192$		0			0
$193$	10.1622	+	13.6503i	0.731494	+	0.982568i	0.999815	+	0.0192379i	$0.00612399\pi$
$193$	10.1622	+	13.6503i	0.731494	+	0.982568i	−0.268320	+	0.963330i	$0.586469\pi$
$194$	−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	$-0.575940\pi$
$197$	9.53813	−	8.00344i	0.679563	−	0.570221i	0.915879	+	0.401455i	$0.131495\pi$
$198$		0			0
$199$	−16.5214	−	13.8631i	−1.17117	−	0.982731i	−0.171177	−	0.985240i	$-0.554757\pi$
$199$	−16.5214	−	13.8631i	−1.17117	−	0.982731i	−0.999997	+	0.00250896i	$0.999201\pi$
$200$	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	−0.217123	−	0.976144i	$-0.569667\pi$
$211$	−12.3360	−	2.92368i	−0.849244	−	0.201275i	−0.632121	+	0.774870i	$0.717815\pi$
$212$	−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	0.840336	−	0.542065i	$-0.182357\pi$
$223$	−1.95059	−	4.52199i	−0.130622	−	0.302815i	−0.970958	+	0.239251i	$0.923098\pi$
$224$	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	$-0.172328\pi$
$227$	4.41017	+	4.67451i	0.292713	+	0.310258i	−0.564282	+	0.825582i	$0.690847\pi$
$228$		0			0
$229$	26.5744	−	13.3462i	1.75608	−	0.881939i	0.794575	−	0.607166i	$-0.207694\pi$
$229$	26.5744	−	13.3462i	1.75608	−	0.881939i	0.961509	−	0.274773i	$-0.0886026\pi$
$230$	−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	−0.567786	−	0.823176i	$-0.692200\pi$
$233$	3.77489	−	21.4085i	0.247301	−	1.40252i	0.815087	−	0.579339i	$-0.196689\pi$
$234$		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	$-0.808751\pi$
$239$	2.35595	−	5.46170i	0.152394	−	0.353288i	0.977262	+	0.212037i	$0.0680099\pi$
$240$		0			0
$241$	0.990937	−	0.651749i	0.0638318	−	0.0419829i	−0.517192	−	0.855869i	$-0.673023\pi$
$241$	0.990937	−	0.651749i	0.0638318	−	0.0419829i	0.581024	+	0.813887i	$0.302652\pi$
$242$	−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	0.964854	+	0.262785i	$0.0846410\pi$
$251$	2.34580	+	13.3037i	0.148066	+	0.839722i	−0.816789	+	0.576937i	$0.804248\pi$
$252$		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	$-0.924659\pi$
$257$	−21.8753	+	10.9862i	−1.36454	+	0.685299i	−0.392423	+	0.919785i	$0.628363\pi$
$258$		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	−0.947557	−	0.319586i	$-0.896456\pi$
$263$	−8.59130	−	19.9169i	−0.529762	−	1.22813i	0.417795	−	0.908541i	$-0.362803\pi$
$264$		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	$-0.222666\pi$
$269$	−2.87056	−	4.97195i	−0.175021	−	0.303145i	−0.940169	+	0.340710i	$0.889333\pi$
$270$		0			0
$271$	7.23998	−	12.5400i	0.439798	−	0.761752i	−0.557876	−	0.829924i	$-0.688384\pi$
$271$	7.23998	−	12.5400i	0.439798	−	0.761752i	0.997674	+	0.0681726i	$0.0217169\pi$
$272$	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	−0.536921	−	0.843632i	$-0.680413\pi$
$277$	7.07774	−	9.50706i	0.425260	−	0.571224i	0.962182	+	0.272408i	$0.0878202\pi$
$278$	−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	$-0.723767\pi$
$281$	−14.7822	+	3.50346i	−0.881835	+	0.208999i	−0.235336	+	0.971914i	$0.575619\pi$
$282$		0			0
$283$	−20.8426	−	13.7084i	−1.23896	−	0.814880i	−0.250764	−	0.968048i	$-0.580682\pi$
$283$	−20.8426	−	13.7084i	−1.23896	−	0.814880i	−0.988200	+	0.153168i	$0.951052\pi$
$284$	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	$-0.284298\pi$
$293$	−5.12105	−	6.87876i	−0.299175	−	0.401862i	−0.926136	+	0.377189i	$0.876891\pi$
$294$		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	−0.290126	−	0.956989i	$-0.593697\pi$
$307$	1.80059	−	0.655362i	0.102765	−	0.0374035i	0.392891	+	0.919585i	$0.371475\pi$
$308$	−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	−0.874978	−	0.484162i	$-0.839124\pi$
$311$	0.886900	−	15.2275i	0.0502915	−	0.863472i	0.925270	−	0.379310i	$-0.123838\pi$
$312$		0			0
$313$	8.80754	−	29.4192i	0.497832	−	1.66287i	−0.226959	−	0.973904i	$-0.572878\pi$
$313$	8.80754	−	29.4192i	0.497832	−	1.66287i	0.724790	−	0.688969i	$-0.241937\pi$
$314$	−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	$-0.240001\pi$
$317$	22.7971	+	2.66460i	1.28042	+	0.149659i	0.551449	+	0.834209i	$0.314075\pi$
$318$		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	0.140654	−	0.990059i	$-0.455080\pi$
$331$	0.894983	+	0.104608i	0.0491927	+	0.00574980i	−0.0914610	+	0.995809i	$0.529154\pi$
$332$	−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	−0.231511	−	0.972832i	$-0.574367\pi$
$337$	2.04455	−	35.1035i	0.111374	−	1.91221i	0.342885	−	0.939377i	$-0.388596\pi$
$338$	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	$-0.403499\pi$
$347$	15.0726	−	1.76174i	0.809142	−	0.0945751i	0.510597	+	0.859820i	$0.329425\pi$
$348$		0			0
$349$	1.64660	+	28.2711i	0.0881406	+	1.51332i	0.695291	+	0.718728i	$0.255275\pi$
$349$	1.64660	+	28.2711i	0.0881406	+	1.51332i	−0.607151	+	0.794587i	$0.707688\pi$
$350$	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	$-0.497635\pi$
$353$	−14.8471	−	7.45651i	−0.790233	−	0.396870i	−0.797664	+	0.603102i	$0.793931\pi$
$354$		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	$-0.843085\pi$
$359$	−10.7593	+	9.02816i	−0.567856	+	0.476488i	0.313077	+	0.949728i	$0.398640\pi$
$360$		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	−0.0893336	−	0.996002i	$-0.528474\pi$
$367$	5.32264	−	1.26149i	0.277840	−	0.0658492i	0.367173	+	0.930153i	$0.380326\pi$
$368$	−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	0.869778	−	0.493443i	$-0.164262\pi$
$373$	27.5326	+	6.52534i	1.42558	+	0.337869i	0.555805	+	0.831313i	$0.312410\pi$
$374$	−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	0.578991	−	0.815334i	$-0.303447\pi$
$379$	−8.11043	−	14.0477i	−0.416605	−	0.721580i	−0.995595	+	0.0937537i	$0.970113\pi$
$380$	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	0.995280	+	0.0970408i	$0.0309377\pi$
$383$	4.24796	+	14.1892i	0.217061	+	0.725033i	−0.778220	+	0.627992i	$0.783877\pi$
$384$		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	$-0.180111\pi$
$389$	5.12493	+	5.43211i	0.259844	+	0.275419i	−0.584297	+	0.811540i	$0.698630\pi$
$390$		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	−0.779228	−	0.626741i	$-0.784388\pi$
$397$	−5.20739	−	29.5326i	−0.261351	−	1.48220i	0.517876	−	0.855455i	$-0.326723\pi$
$398$	−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	$-0.922679\pi$
$401$	−2.59509	+	6.01608i	−0.129592	+	0.300429i	0.841050	+	0.540958i	$0.181938\pi$
$402$		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	−0.899832	−	0.436237i	$-0.856311\pi$
$409$	0.707379	−	1.63989i	0.0349776	−	0.0810873i	0.934809	+	0.355150i	$0.115570\pi$
$410$	−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	$-0.479221\pi$
$419$	18.5168	−	9.29947i	0.904603	−	0.454309i	0.839370	+	0.543561i	$0.182924\pi$
$420$		0			0
$421$	−13.0106	−	13.7904i	−0.634097	−	0.672103i	0.328042	−	0.944663i	$-0.393611\pi$
$421$	−13.0106	−	13.7904i	−0.634097	−	0.672103i	−0.962139	+	0.272560i	$0.912130\pi$
$422$	−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	$-0.170566\pi$
$431$	−0.254281	−	0.440427i	−0.0122483	−	0.0212146i	−0.872085	+	0.489355i	$0.837232\pi$
$432$		0			0
$433$	10.9606	−	18.9844i	0.526734	−	0.912330i	−0.472781	−	0.881180i	$-0.656750\pi$
$433$	10.9606	−	18.9844i	0.526734	−	0.912330i	0.999515	−	0.0311498i	$-0.00991689\pi$
$434$	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	−0.00190618	+	0.999998i	$0.500607\pi$
$439$	−20.1006	+	26.9997i	−0.959347	+	1.28863i	−0.957441	+	0.288629i	$0.906801\pi$
$440$	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	$-0.668130\pi$
$443$	−11.9279	+	2.82696i	−0.566711	+	0.134313i	−0.0627341	+	0.998030i	$0.519982\pi$
$444$		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	$-0.0740328\pi$
$449$	19.3898	+	16.2699i	0.915060	+	0.767826i	−0.0580153	+	0.998316i	$0.518477\pi$
$450$		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	−0.285470	−	0.958388i	$-0.592150\pi$
$457$	−26.1808	−	13.1485i	−1.22469	−	0.615060i	−0.939216	+	0.343327i	$0.888446\pi$
$458$	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	−0.970152	−	0.242496i	$-0.922034\pi$
$461$	−0.745295	−	12.7962i	−0.0347119	−	0.595980i	0.935441	−	0.353484i	$-0.115003\pi$
$462$		0			0
$463$	−10.2547	+	1.19861i	−0.476578	+	0.0557040i	−0.350992	−	0.936379i	$-0.614155\pi$
$463$	−10.2547	+	1.19861i	−0.476578	+	0.0557040i	−0.125587	+	0.992083i	$0.540081\pi$
$464$	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	$-0.440446\pi$
$467$	−6.54957	−	2.38385i	−0.303078	−	0.110311i	−0.489083	+	0.872238i	$0.662668\pi$
$468$		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	$-0.186273\pi$
$479$	33.2090	+	3.88157i	1.51736	+	0.177354i	0.683752	+	0.729714i	$0.260347\pi$
$480$		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	$-0.877421\pi$
$491$	−11.0320	+	11.6932i	−0.497866	+	0.527707i	0.428897	+	0.903353i	$0.358902\pi$
$492$		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	0.973217	+	0.229889i	$0.0738365\pi$
$499$	−0.449179	+	7.71210i	−0.0201080	+	0.345241i	−0.993325	+	0.115351i	$0.963201\pi$
$500$	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	$-0.353107\pi$
$503$	30.5447	−	11.1174i	1.36192	−	0.495698i	0.916647	+	0.399697i	$0.130885\pi$
$504$		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	$-0.545852\pi$
$509$	−1.24093	+	0.145044i	−0.0550034	+	0.00642898i	0.0885467	+	0.996072i	$0.471778\pi$
$510$		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	$-0.893888\pi$
$521$	−17.9588	+	15.0692i	−0.786787	+	0.660193i	0.158161	+	0.987413i	$0.449444\pi$
$522$		0			0
$523$	26.2642	+	22.0383i	1.14845	+	0.963666i	0.999682	−	0.0252058i	$-0.00802411\pi$
$523$	26.2642	+	22.0383i	1.14845	+	0.963666i	0.148770	+	0.988872i	$0.452469\pi$
$524$	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	0.979250	−	0.202658i	$-0.0649580\pi$
$541$	7.30619	+	12.6547i	0.314118	+	0.544068i	−0.665132	+	0.746726i	$0.731625\pi$
$542$	−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	0.739996	−	0.672611i	$-0.234827\pi$
$547$	−6.01211	−	13.9376i	−0.257059	−	0.595931i	−0.997056	+	0.0766801i	$0.975568\pi$
$548$	−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	−0.888076	−	0.459697i	$-0.847958\pi$
$557$	2.44666	−	13.8757i	0.103668	−	0.587931i	0.991744	−	0.128234i	$-0.0409309\pi$
$558$		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	0.303418	+	0.952858i	$0.401872\pi$
$563$	−14.1864	+	32.8877i	−0.597884	+	1.38605i	−0.901302	+	0.433192i	$0.857387\pi$
$564$		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	$-0.885427\pi$
$569$	−23.4530	+	15.4253i	−0.983200	+	0.646661i	−0.0472828	+	0.998882i	$0.515056\pi$
$570$		0			0
$571$	−18.5275	+	42.9516i	−0.775353	+	1.79747i	−0.199536	+	0.979890i	$0.563943\pi$
$571$	−18.5275	+	42.9516i	−0.775353	+	1.79747i	−0.575817	+	0.817579i	$0.695316\pi$
$572$	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	−0.838372	−	0.545098i	$-0.816492\pi$
$577$	3.26382	−	18.5100i	0.135875	−	0.770583i	0.974247	−	0.225485i	$-0.0723966\pi$
$578$	−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	$-0.123208\pi$
$587$	0.387163	+	0.897546i	0.0159799	+	0.0370457i	−0.910039	+	0.414522i	$0.863949\pi$
$588$		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	−0.921964	−	0.387276i	$-0.873416\pi$
$593$	−19.3929	−	33.5896i	−0.796372	−	1.37936i	0.125592	−	0.992082i	$-0.459917\pi$
$594$		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	$-0.188004\pi$
$599$	32.3773	+	7.67356i	1.32290	+	0.313533i	0.492312	+	0.870419i	$0.336152\pi$
$600$		0			0
$601$	−12.1572	+	16.3299i	−0.495901	+	0.666111i	−0.977660	−	0.210193i	$-0.932591\pi$
$601$	−12.1572	+	16.3299i	−0.495901	+	0.666111i	0.481759	+	0.876304i	$0.339998\pi$
$602$	−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	0.576126	−	0.817361i	$-0.304564\pi$
$607$	1.32559	+	0.871857i	0.0538042	+	0.0353876i	−0.522322	+	0.852748i	$0.674934\pi$
$608$	−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	−0.742368	−	0.669992i	$-0.766297\pi$
$613$	−5.23563	+	4.39322i	−0.211465	+	0.177440i	0.530903	+	0.847433i	$0.321853\pi$
$614$	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	$-0.206311\pi$
$617$	−0.243038	−	0.326456i	−0.00978434	−	0.0131426i	−0.806988	+	0.590567i	$0.798904\pi$
$618$		0			0
$619$	8.95900	+	4.49938i	0.360093	+	0.180845i	0.619642	−	0.784885i	$-0.287278\pi$
$619$	8.95900	+	4.49938i	0.360093	+	0.180845i	−0.259550	+	0.965730i	$0.583574\pi$
$620$	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	−0.618937	−	0.785441i	$-0.712436\pi$
$631$	−14.7754	+	5.37779i	−0.588198	+	0.214086i	0.0307388	+	0.999527i	$0.490214\pi$
$632$	−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	$-0.513747\pi$
$641$	−7.99000	−	0.933897i	−0.315586	−	0.0368867i	−0.272412	+	0.962181i	$0.587821\pi$
$642$		0			0
$643$	6.55424	−	6.94709i	0.258474	−	0.273966i	−0.585121	−	0.810946i	$-0.698953\pi$
$643$	6.55424	−	6.94709i	0.258474	−	0.273966i	0.843595	+	0.536979i	$0.180435\pi$
$644$	−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	$-0.243873\pi$
$647$	36.6579			1.44117			0.720586	+	0.693365i	$0.243873\pi$
$648$		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	$-0.882677\pi$
$653$	−13.2604	+	14.0552i	−0.518918	+	0.550021i	0.413922	+	0.910312i	$0.364159\pi$
$654$		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	−0.593577	−	0.804777i	$-0.702285\pi$
$659$	8.84575	−	29.5469i	0.344582	−	1.15098i	0.938159	−	0.346205i	$-0.112530\pi$
$660$		0			0
$661$	−0.928413	+	15.9402i	−0.0361111	+	0.620003i	0.930901	+	0.365272i	$0.119024\pi$
$661$	−0.928413	+	15.9402i	−0.0361111	+	0.620003i	−0.967012	+	0.254731i	$0.918013\pi$
$662$	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	0.713399	+	0.700758i	$0.247155\pi$
$673$	2.23562	+	38.3841i	0.0861768	+	1.47960i	−0.627223	+	0.778840i	$0.715808\pi$
$674$	−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	$-0.271150\pi$
$677$	11.6642	+	5.85800i	0.448293	+	0.225141i	−0.210305	+	0.977636i	$0.567446\pi$
$678$		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	$-0.777947\pi$
$683$	−6.97390	+	5.85180i	−0.266849	+	0.223913i	0.499538	+	0.866292i	$0.333503\pi$
$684$		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	−0.00304009	−	0.999995i	$-0.500968\pi$
$691$	11.6461	−	2.76019i	0.443040	−	0.105002i	0.446080	+	0.894993i	$0.352820\pi$
$692$	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	$-0.828023\pi$
$701$	0.441721	−	0.765084i	0.0166836	−	0.0288968i	0.874247	+	0.485482i	$0.161356\pi$
$702$		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	0.998585	+	0.0531741i	$0.0169338\pi$
$709$	9.37251	+	21.7279i	0.351992	+	0.816009i	−0.646593	+	0.762835i	$0.723807\pi$
$710$	−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	−0.796792	−	0.604253i	$-0.793471\pi$
$719$	4.25311	−	24.1206i	0.158614	−	0.899547i	0.955407	−	0.295293i	$-0.0954174\pi$
$720$		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	−0.414952	−	0.909843i	$-0.636202\pi$
$727$	6.90593	−	4.54210i	0.256127	−	0.168457i	0.671079	+	0.741386i	$0.265831\pi$
$728$	−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	−0.992566	−	0.121710i	$-0.961162\pi$
$733$	−6.03471	+	13.9900i	−0.222897	+	0.516734i	0.769668	+	0.638444i	$0.220422\pi$
$734$	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	−0.745583	−	0.666413i	$-0.767829\pi$
$739$	4.97375	−	28.2075i	0.182962	−	1.03763i	0.928545	−	0.371219i	$-0.121060\pi$
$740$	−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	$-0.560901\pi$
$743$	13.1865	−	6.62253i	0.483767	−	0.242957i	0.673929	+	0.738796i	$0.264605\pi$
$744$		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	0.988057	−	0.154089i	$-0.0492443\pi$
$751$	2.13409	+	7.12836i	0.0778741	+	0.260118i	−0.910183	+	0.414207i	$0.864059\pi$
$752$	−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	−0.947425	−	0.319977i	$-0.896325\pi$
$757$	−5.40930	+	9.36918i	−0.196604	+	0.340529i	0.750821	+	0.660506i	$0.229658\pi$
$758$	−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	$-0.458853\pi$
$761$	−5.54356	−	1.31385i	−0.200954	−	0.0476270i	−0.329860	+	0.944030i	$0.607002\pi$
$762$		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	0.773132	−	0.634245i	$-0.218689\pi$
$769$	13.7817	+	9.06435i	0.496980	+	0.326869i	−0.276152	+	0.961114i	$0.589059\pi$
$770$	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	$-0.287241\pi$
$773$	−1.26612	−	1.06240i	−0.0455393	−	0.0382121i	−0.665273	+	0.746600i	$0.731685\pi$
$774$		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

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

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