LMFDB - Embedded newform 729.2.g.d.109.2

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			109.2
Character	$\chi$	$=$	729.109
Dual form			729.2.g.d.622.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.936951 - 0.993110i) q^{2} +(0.00789919 - 0.135624i) q^{4} +(3.78436 - 0.442328i) q^{5} +(1.56116 + 0.784043i) q^{7} +(-2.23391 + 1.87447i) q^{8} +O(q^{10})$	\(q+(-0.936951 - 0.993110i) q^{2} +(0.00789919 - 0.135624i) q^{4} +(3.78436 - 0.442328i) q^{5} +(1.56116 + 0.784043i) q^{7} +(-2.23391 + 1.87447i) q^{8} +(-3.98504 - 3.34385i) q^{10} +(-1.21227 - 2.81037i) q^{11} +(1.81780 + 0.430827i) q^{13} +(-0.684088 - 2.28501i) q^{14} +(3.68475 + 0.430686i) q^{16} +(1.21594 - 6.89593i) q^{17} +(0.858206 + 4.86713i) q^{19} +(-0.0300968 - 0.516743i) q^{20} +(-1.65516 + 3.83710i) q^{22} +(-1.70229 + 0.854924i) q^{23} +(9.26048 - 2.19477i) q^{25} +(-1.27533 - 2.20894i) q^{26} +(0.118667 - 0.205537i) q^{28} +(-0.0649657 + 0.217001i) q^{29} +(3.29127 + 2.16470i) q^{31} +(0.458106 + 0.615343i) q^{32} +(-7.98769 + 5.25359i) q^{34} +(6.25478 + 2.27656i) q^{35} +(0.346276 - 0.126034i) q^{37} +(4.02950 - 5.41256i) q^{38} +(-7.62478 + 8.08179i) q^{40} +(2.97164 - 3.14975i) q^{41} +(-1.93907 + 2.60463i) q^{43} +(-0.390729 + 0.142214i) q^{44} +(2.44400 + 0.889543i) q^{46} +(1.46028 - 0.960441i) q^{47} +(-2.35762 - 3.16683i) q^{49} +(-10.8563 - 7.14028i) q^{50} +(0.0727895 - 0.243134i) q^{52} +(-3.03142 + 5.25057i) q^{53} +(-5.83078 - 10.0992i) q^{55} +(-4.95715 + 1.17487i) q^{56} +(0.276375 - 0.138801i) q^{58} +(0.791355 - 1.83457i) q^{59} +(-0.743636 - 12.7677i) q^{61} +(-0.933972 - 5.29682i) q^{62} +(1.47029 - 8.33845i) q^{64} +(7.06978 + 0.826338i) q^{65} +(1.81970 + 6.07822i) q^{67} +(-0.925647 - 0.219382i) q^{68} +(-3.59956 - 8.34471i) q^{70} +(-10.6917 - 8.97137i) q^{71} +(2.42680 - 2.03633i) q^{73} +(-0.449609 - 0.225802i) q^{74} +(0.666878 - 0.0779468i) q^{76} +(0.310898 - 5.33790i) q^{77} +(1.79892 + 1.90674i) q^{79} +14.1349 q^{80} -5.91234 q^{82} +(-0.154287 - 0.163535i) q^{83} +(1.55128 - 26.6345i) q^{85} +(4.40350 - 0.514695i) q^{86} +(7.97607 + 4.00573i) q^{88} +(-5.45275 + 4.57540i) q^{89} +(2.50009 + 2.09782i) q^{91} +(0.102501 + 0.237625i) q^{92} +(-2.32203 - 0.550332i) q^{94} +(5.40063 + 18.0393i) q^{95} +(-15.4740 - 1.80865i) q^{97} +(-0.936040 + 5.30854i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

Coefficient data

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

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

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

$2$	−0.936951	−	0.993110i	−0.662525	−	0.702235i	0.305753	−	0.952111i	$-0.401092\pi$
$2$	−0.936951	−	0.993110i	−0.662525	−	0.702235i	−0.968278	+	0.249876i	$0.919610\pi$
$3$		0			0
$3$		0			0
$4$	0.00789919	−	0.135624i	0.00394959	−	0.0678119i
$5$	3.78436	−	0.442328i	1.69242	−	0.197815i	0.785423	−	0.618960i	$-0.212446\pi$
$5$	3.78436	−	0.442328i	1.69242	−	0.197815i	0.906993	+	0.421145i	$0.138372\pi$
$6$		0			0
$7$	1.56116	+	0.784043i	0.590062	+	0.296340i	0.718666	−	0.695356i	$-0.244753\pi$
$7$	1.56116	+	0.784043i	0.590062	+	0.296340i	−0.128604	+	0.991696i	$0.541049\pi$
$8$	−2.23391	+	1.87447i	−0.789806	+	0.662726i
$9$		0			0
$10$	−3.98504	−	3.34385i	−1.26018	−	1.05742i
$11$	−1.21227	−	2.81037i	−0.365515	−	0.847358i	−0.997384	−	0.0722832i	$-0.976971\pi$
$11$	−1.21227	−	2.81037i	−0.365515	−	0.847358i	0.631870	−	0.775075i	$-0.282288\pi$
$12$		0			0
$13$	1.81780	+	0.430827i	0.504167	+	0.119490i	0.474826	−	0.880080i	$-0.342511\pi$
$13$	1.81780	+	0.430827i	0.504167	+	0.119490i	0.0293412	+	0.999569i	$0.490659\pi$
$14$	−0.684088	−	2.28501i	−0.182830	−	0.610695i
$15$		0			0
$16$	3.68475	+	0.430686i	0.921188	+	0.107671i
$17$	1.21594	−	6.89593i	0.294908	−	1.67251i	−0.372667	−	0.927965i	$-0.621557\pi$
$17$	1.21594	−	6.89593i	0.294908	−	1.67251i	0.667575	−	0.744542i	$-0.267332\pi$
$18$		0			0
$19$	0.858206	+	4.86713i	0.196886	+	1.11660i	0.909707	+	0.415250i	$0.136306\pi$
$19$	0.858206	+	4.86713i	0.196886	+	1.11660i	−0.712821	+	0.701346i	$0.752583\pi$
$20$	−0.0300968	−	0.516743i	−0.00672986	−	0.115547i
$21$		0			0
$22$	−1.65516	+	3.83710i	−0.352882	+	0.818073i
$23$	−1.70229	+	0.854924i	−0.354953	+	0.178264i	−0.617336	−	0.786700i	$-0.711788\pi$
$23$	−1.70229	+	0.854924i	−0.354953	+	0.178264i	0.262383	+	0.964964i	$0.415492\pi$
$24$		0			0
$25$	9.26048	−	2.19477i	1.85210	−	0.438955i
$26$	−1.27533	−	2.20894i	−0.250113	−	0.433209i
$27$		0			0
$28$	0.118667	−	0.205537i	0.0224259	−	0.0388428i
$29$	−0.0649657	+	0.217001i	−0.0120638	+	0.0402960i	−0.963810	−	0.266592i	$-0.914102\pi$
$29$	−0.0649657	+	0.217001i	−0.0120638	+	0.0402960i	0.951746	+	0.306888i	$0.0992876\pi$
$30$		0			0
$31$	3.29127	+	2.16470i	0.591130	+	0.388792i	0.809540	−	0.587065i	$-0.199717\pi$
$31$	3.29127	+	2.16470i	0.591130	+	0.388792i	−0.218410	+	0.975857i	$0.570087\pi$
$32$	0.458106	+	0.615343i	0.0809825	+	0.108778i
$33$		0			0
$34$	−7.98769	+	5.25359i	−1.36988	+	0.900983i
$35$	6.25478	+	2.27656i	1.05725	+	0.384808i
$36$		0			0
$37$	0.346276	−	0.126034i	0.0569274	−	0.0207199i	−0.313400	−	0.949621i	$-0.601468\pi$
$37$	0.346276	−	0.126034i	0.0569274	−	0.0207199i	0.370327	+	0.928902i	$0.379246\pi$
$38$	4.02950	−	5.41256i	0.653671	−	0.878033i
$39$		0			0
$40$	−7.62478	+	8.08179i	−1.20558	+	1.27784i
$41$	2.97164	−	3.14975i	0.464092	−	0.491909i	−0.452482	−	0.891773i	$-0.649461\pi$
$41$	2.97164	−	3.14975i	0.464092	−	0.491909i	0.916574	+	0.399865i	$0.130943\pi$
$42$		0			0
$43$	−1.93907	+	2.60463i	−0.295706	+	0.397202i	−0.925001	−	0.379964i	$-0.875936\pi$
$43$	−1.93907	+	2.60463i	−0.295706	+	0.397202i	0.629295	+	0.777166i	$0.283344\pi$
$44$	−0.390729	+	0.142214i	−0.0589046	+	0.0214395i
$45$		0			0
$46$	2.44400	+	0.889543i	0.360348	+	0.131156i
$47$	1.46028	−	0.960441i	0.213004	−	0.140095i	−0.438524	−	0.898719i	$-0.644499\pi$
$47$	1.46028	−	0.960441i	0.213004	−	0.140095i	0.651528	+	0.758625i	$0.274128\pi$
$48$		0			0
$49$	−2.35762	−	3.16683i	−0.336803	−	0.452405i
$50$	−10.8563	−	7.14028i	−1.53531	−	1.00979i
$51$		0			0
$52$	0.0727895	−	0.243134i	0.0100941	−	0.0337166i
$53$	−3.03142	+	5.25057i	−0.416398	+	0.721222i	−0.995574	−	0.0939804i	$-0.970041\pi$
$53$	−3.03142	+	5.25057i	−0.416398	+	0.721222i	0.579176	+	0.815202i	$0.303374\pi$
$54$		0			0
$55$	−5.83078	−	10.0992i	−0.786223	−	1.36178i
$56$	−4.95715	+	1.17487i	−0.662427	+	0.156998i
$57$		0			0
$58$	0.276375	−	0.138801i	0.0362899	−	0.0182255i
$59$	0.791355	−	1.83457i	0.103026	−	0.238840i	−0.858904	−	0.512136i	$-0.828854\pi$
$59$	0.791355	−	1.83457i	0.103026	−	0.238840i	0.961930	+	0.273296i	$0.0881137\pi$
$60$		0			0
$61$	−0.743636	−	12.7677i	−0.0952129	−	1.63474i	−0.620777	−	0.783987i	$-0.713183\pi$
$61$	−0.743636	−	12.7677i	−0.0952129	−	1.63474i	0.525564	−	0.850754i	$-0.323854\pi$
$62$	−0.933972	−	5.29682i	−0.118615	−	0.672696i
$63$		0			0
$64$	1.47029	−	8.33845i	0.183787	−	1.04231i
$65$	7.06978	+	0.826338i	0.876898	+	0.102495i
$66$		0			0
$67$	1.81970	+	6.07822i	0.222312	+	0.742573i	0.994270	+	0.106899i	$0.0340922\pi$
$67$	1.81970	+	6.07822i	0.222312	+	0.742573i	−0.771958	+	0.635673i	$0.780723\pi$
$68$	−0.925647	−	0.219382i	−0.112251	−	0.0266040i
$69$		0			0
$70$	−3.59956	−	8.34471i	−0.430229	−	0.997384i
$71$	−10.6917	−	8.97137i	−1.26887	−	1.06471i	−0.994678	−	0.103030i	$-0.967146\pi$
$71$	−10.6917	−	8.97137i	−1.26887	−	1.06471i	−0.274189	−	0.961676i	$-0.588409\pi$
$72$		0			0
$73$	2.42680	−	2.03633i	0.284036	−	0.238334i	−0.489627	−	0.871932i	$-0.662867\pi$
$73$	2.42680	−	2.03633i	0.284036	−	0.238334i	0.773663	+	0.633598i	$0.218423\pi$
$74$	−0.449609	−	0.225802i	−0.0522660	−	0.0262490i
$75$		0			0
$76$	0.666878	−	0.0779468i	0.0764961	−	0.00894111i
$77$	0.310898	−	5.33790i	0.0354301	−	0.608311i
$78$		0			0
$79$	1.79892	+	1.90674i	0.202394	+	0.214525i	0.820619	−	0.571476i	$-0.193629\pi$
$79$	1.79892	+	1.90674i	0.202394	+	0.214525i	−0.618224	+	0.786002i	$0.712148\pi$
$80$	14.1349			1.58033
$81$		0			0
$82$	−5.91234			−0.652908
$83$	−0.154287	−	0.163535i	−0.0169352	−	0.0179503i	0.718851	−	0.695165i	$-0.244669\pi$
$83$	−0.154287	−	0.163535i	−0.0169352	−	0.0179503i	−0.735786	+	0.677214i	$0.763187\pi$
$84$		0			0
$85$	1.55128	−	26.6345i	0.168260	−	2.88892i
$86$	4.40350	−	0.514695i	0.474841	−	0.0555010i
$87$		0			0
$88$	7.97607	+	4.00573i	0.850252	+	0.427012i
$89$	−5.45275	+	4.57540i	−0.577990	+	0.484991i	−0.884286	−	0.466945i	$-0.845355\pi$
$89$	−5.45275	+	4.57540i	−0.577990	+	0.484991i	0.306296	+	0.951936i	$0.400910\pi$
$90$		0			0
$91$	2.50009	+	2.09782i	0.262080	+	0.219912i
$92$	0.102501	+	0.237625i	0.0106865	+	0.0247741i
$93$		0			0
$94$	−2.32203	−	0.550332i	−0.239500	−	0.0567624i
$95$	5.40063	+	18.0393i	0.554093	+	1.85080i
$96$		0			0
$97$	−15.4740	−	1.80865i	−1.57115	−	0.183641i	−0.714535	−	0.699600i	$-0.753362\pi$
$97$	−15.4740	−	1.80865i	−1.57115	−	0.183641i	−0.856613	+	0.515959i	$0.827436\pi$
$98$	−0.936040	+	5.30854i	−0.0945543	+	0.536244i
$99$		0			0
$100$	−0.224513	−	1.27328i	−0.0224513	−	0.127328i
$101$	0.499658	+	8.57880i	0.0497179	+	0.853623i	0.927328	+	0.374249i	$0.122099\pi$
$101$	0.499658	+	8.57880i	0.0497179	+	0.853623i	−0.877611	+	0.479374i	$0.840864\pi$
$102$		0			0
$103$	−0.457458	+	1.06051i	−0.0450747	+	0.104495i	−0.939266	−	0.343191i	$-0.888492\pi$
$103$	−0.457458	+	1.06051i	−0.0450747	+	0.104495i	0.894191	+	0.447686i	$0.147752\pi$
$104$	−4.86838	+	2.44499i	−0.477384	+	0.239751i
$105$		0			0
$106$	8.05469	−	1.90900i	0.782341	−	0.185418i
$107$	5.53177	+	9.58130i	0.534776	+	0.926259i	0.999174	+	0.0406326i	$0.0129373\pi$
$107$	5.53177	+	9.58130i	0.534776	+	0.926259i	−0.464398	+	0.885626i	$0.653729\pi$
$108$		0			0
$109$	−7.60162	+	13.1664i	−0.728103	+	1.26111i	0.229581	+	0.973290i	$0.426264\pi$
$109$	−7.60162	+	13.1664i	−0.728103	+	1.26111i	−0.957684	+	0.287822i	$0.907069\pi$
$110$	−4.56647	+	15.2531i	−0.435396	+	1.45432i
$111$		0			0
$112$	5.41480	+	3.56137i	0.511651	+	0.336518i
$113$	−1.26634	−	1.70099i	−0.119128	−	0.160016i	0.738559	−	0.674189i	$-0.235507\pi$
$113$	−1.26634	−	1.70099i	−0.119128	−	0.160016i	−0.857687	+	0.514173i	$0.828099\pi$
$114$		0			0
$115$	−6.06393	+	3.98831i	−0.565464	+	0.371912i
$116$	0.0289173	+	0.0105250i	0.00268490	+	0.000977224i
$117$		0			0
$118$	−2.56339	+	0.932997i	−0.235979	+	0.0858894i
$119$	7.30497	−	9.81228i	0.669646	−	0.899490i
$120$		0			0
$121$	1.12010	−	1.18723i	0.101827	−	0.107930i
$122$	−11.9830	+	12.7013i	−1.08489	+	1.14992i
$123$		0			0
$124$	0.319584	−	0.429275i	0.0286995	−	0.0385501i
$125$	16.1725	−	5.88629i	1.44651	−	0.526486i
$126$		0			0
$127$	10.6417	+	3.87328i	0.944302	+	0.343698i	0.767863	−	0.640614i	$-0.221320\pi$
$127$	10.6417	+	3.87328i	0.944302	+	0.343698i	0.176439	+	0.984312i	$0.443542\pi$
$128$	−8.37672	+	5.50945i	−0.740404	+	0.486971i
$129$		0			0
$130$	−5.80339	−	7.79531i	−0.508991	−	0.683694i
$131$	9.05051	+	5.95261i	0.790747	+	0.520082i	0.879459	−	0.475975i	$-0.157905\pi$
$131$	9.05051	+	5.95261i	0.790747	+	0.520082i	−0.0887122	+	0.996057i	$0.528275\pi$
$132$		0			0
$133$	−2.47624	+	8.27123i	−0.214718	+	0.717207i
$134$	4.33137	−	7.50216i	0.374174	−	0.648088i
$135$		0			0
$136$	10.2099	+	17.6841i	0.875494	+	1.51640i
$137$	−12.3269	+	2.92153i	−1.05316	+	0.249603i	−0.720507	−	0.693447i	$-0.756091\pi$
$137$	−12.3269	+	2.92153i	−1.05316	+	0.249603i	−0.332650	+	0.943050i	$0.607943\pi$
$138$		0			0
$139$	−8.67894	+	4.35873i	−0.736138	+	0.369703i	−0.777032	−	0.629461i	$-0.783276\pi$
$139$	−8.67894	+	4.35873i	−0.736138	+	0.369703i	0.0408939	+	0.999163i	$0.486979\pi$
$140$	0.358163	−	0.830314i	0.0302703	−	0.0701744i
$141$		0			0
$142$	1.10801	+	19.0237i	0.0929819	+	1.59644i
$143$	−0.992892	−	5.63097i	−0.0830298	−	0.470886i
$144$		0			0
$145$	−0.149868	+	0.849944i	−0.0124459	+	0.0705840i
$146$	−4.29610	−	0.502142i	−0.355547	−	0.0415575i
$147$		0			0
$148$	−0.0143579	−	0.0479588i	−0.00118021	−	0.00394219i
$149$	4.03952	+	0.957383i	0.330930	+	0.0784319i	0.392722	−	0.919657i	$-0.371533\pi$
$149$	4.03952	+	0.957383i	0.330930	+	0.0784319i	−0.0617920	+	0.998089i	$0.519682\pi$
$150$		0			0
$151$	−1.28290	−	2.97410i	−0.104401	−	0.242029i	0.858006	−	0.513639i	$-0.171703\pi$
$151$	−1.28290	−	2.97410i	−0.104401	−	0.242029i	−0.962407	+	0.271611i	$0.912444\pi$
$152$	−11.0405	−	9.26404i	−0.895499	−	0.751413i
$153$		0			0
$154$	−5.59242	+	4.69260i	−0.450650	+	0.378141i
$155$	13.4129	+	6.73619i	1.07735	+	0.541064i
$156$		0			0
$157$	7.42674	−	0.868061i	0.592718	−	0.0692788i	0.185554	−	0.982634i	$-0.440592\pi$
$157$	7.42674	−	0.868061i	0.592718	−	0.0692788i	0.407164	+	0.913355i	$0.366518\pi$
$158$	0.208107	−	3.57305i	0.0165561	−	0.284257i
$159$		0			0
$160$	2.00582	+	2.12605i	0.158574	+	0.168079i
$161$	−3.32785			−0.262271
$162$		0			0
$163$	−9.71856			−0.761216			−0.380608	−	0.924736i	$-0.624285\pi$
$163$	−9.71856			−0.761216			−0.380608	+	0.924736i	$0.624285\pi$
$164$	−0.403708	−	0.427906i	−0.0315243	−	0.0334138i
$165$		0			0
$166$	−0.0178486	+	0.306448i	−0.00138532	+	0.0237850i
$167$	0.715618	−	0.0836438i	0.0553762	−	0.00647255i	−0.0883597	−	0.996089i	$-0.528162\pi$
$167$	0.715618	−	0.0836438i	0.0553762	−	0.00647255i	0.143736	+	0.989616i	$0.454088\pi$
$168$		0			0
$169$	−8.49843	−	4.26807i	−0.653726	−	0.328313i
$170$	−27.9045	+	23.4146i	−2.14017	+	1.79582i
$171$		0			0
$172$	0.337932	+	0.283559i	0.0257671	+	0.0216212i
$173$	0.868881	+	2.01429i	0.0660598	+	0.153144i	0.948048	−	0.318128i	$-0.103054\pi$
$173$	0.868881	+	2.01429i	0.0660598	+	0.153144i	−0.881988	+	0.471272i	$0.843795\pi$
$174$		0			0
$175$	16.1779	+	3.83423i	1.22293	+	0.289840i
$176$	−3.25655	−	10.8776i	−0.245471	−	0.819931i
$177$		0			0
$178$	9.65284	+	1.12825i	0.723511	+	0.0845663i
$179$	−4.40985	+	25.0095i	−0.329608	+	1.86930i	0.145482	+	0.989361i	$0.453527\pi$
$179$	−4.40985	+	25.0095i	−0.329608	+	1.86930i	−0.475090	+	0.879937i	$0.657584\pi$
$180$		0			0
$181$	2.09357	+	11.8732i	0.155614	+	0.882531i	0.958222	+	0.286024i	$0.0923338\pi$
$181$	2.09357	+	11.8732i	0.155614	+	0.882531i	−0.802608	+	0.596506i	$0.796555\pi$
$182$	−0.259091	−	4.44842i	−0.0192051	−	0.329739i
$183$		0			0
$184$	2.20024	−	5.10072i	0.162204	−	0.376030i
$185$	1.25468	−	0.630125i	0.0922461	−	0.0463277i
$186$		0			0
$187$	−20.8541	+	4.94252i	−1.52501	+	0.361433i
$188$	−0.118724	−	0.205635i	−0.00865881	−	0.0149975i
$189$		0			0
$190$	12.8549	−	22.2654i	0.932596	−	1.61530i
$191$	4.19556	−	14.0141i	0.303580	−	1.01403i	−0.661033	−	0.750357i	$-0.729882\pi$
$191$	4.19556	−	14.0141i	0.303580	−	1.01403i	0.964613	−	0.263671i	$-0.0849332\pi$
$192$		0			0
$193$	17.7456	+	11.6714i	1.27735	+	0.840128i	0.992945	−	0.118575i	$-0.0378326\pi$
$193$	17.7456	+	11.6714i	1.27735	+	0.840128i	0.284408	+	0.958703i	$0.408203\pi$
$194$	12.7022	+	17.0620i	0.911965	+	1.22498i
$195$		0			0
$196$	−0.448121	+	0.294734i	−0.0320086	+	0.0210524i
$197$	16.9847	+	6.18193i	1.21011	+	0.440444i	0.866742	−	0.498756i	$-0.166210\pi$
$197$	16.9847	+	6.18193i	1.21011	+	0.440444i	0.343369	+	0.939201i	$0.388432\pi$
$198$		0			0
$199$	22.9288	−	8.34541i	1.62538	−	0.591590i	0.640985	−	0.767554i	$-0.278526\pi$
$199$	22.9288	−	8.34541i	1.62538	−	0.591590i	0.984397	+	0.175963i	$0.0563040\pi$
$200$	−16.5730	+	22.2614i	−1.17189	+	1.57412i
$201$		0			0
$202$	8.05155	−	8.53414i	0.566505	−	0.600460i
$203$	−0.271560	+	0.287836i	−0.0190597	+	0.0202021i
$204$		0			0
$205$	9.85252	−	13.2342i	0.688130	−	0.924319i
$206$	1.48182	−	0.539338i	0.103243	−	0.0375774i
$207$		0			0
$208$	6.51260	+	2.37039i	0.451567	+	0.164357i
$209$	12.6380	−	8.31217i	0.874192	−	0.574965i
$210$		0			0
$211$	−9.16549	−	12.3114i	−0.630979	−	0.847551i	0.365551	−	0.930791i	$-0.380881\pi$
$211$	−9.16549	−	12.3114i	−0.630979	−	0.847551i	−0.996530	+	0.0832399i	$0.973473\pi$
$212$	0.688157	+	0.452608i	0.0472628	+	0.0310852i
$213$		0			0
$214$	4.33229	−	14.4709i	0.296149	−	0.989208i
$215$	−6.18604	+	10.7145i	−0.421885	+	0.730726i
$216$		0			0
$217$	3.44097	+	5.95994i	0.233589	+	0.404587i
$218$	20.1980	−	4.78702i	1.36798	−	0.324218i
$219$		0			0
$220$	−1.41575	+	0.711017i	−0.0954500	+	0.0479368i
$221$	5.18128	−	12.0116i	0.348531	−	0.807985i
$222$		0			0
$223$	0.835212	+	14.3400i	0.0559299	+	0.960280i	0.903228	+	0.429162i	$0.141191\pi$
$223$	0.835212	+	14.3400i	0.0559299	+	0.960280i	−0.847298	+	0.531118i	$0.821772\pi$
$224$	0.232720	+	1.31982i	0.0155493	+	0.0881844i
$225$		0			0
$226$	−0.502773	+	2.85137i	−0.0334440	+	0.189670i
$227$	−11.1437	−	1.30251i	−0.739633	−	0.0864507i	−0.262071	−	0.965049i	$-0.584405\pi$
$227$	−11.1437	−	1.30251i	−0.739633	−	0.0864507i	−0.477562	+	0.878598i	$0.658479\pi$
$228$		0			0
$229$	−2.75304	−	9.19578i	−0.181926	−	0.607674i	−0.999493	−	0.0318410i	$-0.989863\pi$
$229$	−2.75304	−	9.19578i	−0.181926	−	0.607674i	0.817567	−	0.575833i	$-0.195322\pi$
$230$	9.64244	+	2.28530i	0.635804	+	0.150688i
$231$		0			0
$232$	−0.261634	−	0.606536i	−0.0171771	−	0.0398210i
$233$	13.4395	+	11.2771i	0.880451	+	0.738786i	0.966272	−	0.257524i	$-0.0829067\pi$
$233$	13.4395	+	11.2771i	0.880451	+	0.738786i	−0.0858206	+	0.996311i	$0.527351\pi$
$234$		0			0
$235$	5.10139	−	4.28057i	0.332778	−	0.279234i
$236$	−0.242560	−	0.121818i	−0.0157893	−	0.00792969i
$237$		0			0
$238$	−16.5891	+	1.93899i	−1.07531	+	0.125686i
$239$	−1.58767	+	27.2592i	−0.102698	+	1.76325i	0.417002	+	0.908905i	$0.363081\pi$
$239$	−1.58767	+	27.2592i	−0.102698	+	1.76325i	−0.519700	+	0.854349i	$0.673956\pi$
$240$		0			0
$241$	−3.56923	−	3.78316i	−0.229914	−	0.243695i	0.602138	−	0.798392i	$-0.294316\pi$
$241$	−3.56923	−	3.78316i	−0.229914	−	0.243695i	−0.832052	+	0.554697i	$0.812834\pi$
$242$	−2.22853			−0.143255
$243$		0			0
$244$	−1.73748			−0.111231
$245$	−10.3229	−	10.9416i	−0.659503	−	0.699032i
$246$		0			0
$247$	−0.536842	+	9.21721i	−0.0341584	+	0.586477i
$248$	−11.4101	+	1.33365i	−0.724541	+	0.0846866i
$249$		0			0
$250$	−20.9985	−	10.5459i	−1.32806	−	0.666979i
$251$	−3.65188	+	3.06429i	−0.230505	+	0.193416i	−0.750723	−	0.660617i	$-0.770295\pi$
$251$	−3.65188	+	3.06429i	−0.230505	+	0.193416i	0.520219	+	0.854033i	$0.325850\pi$
$252$		0			0
$253$	4.46630	+	3.74767i	0.280794	+	0.235614i
$254$	−6.12421	−	14.1975i	−0.384267	−	0.890831i
$255$		0			0
$256$	−3.15763	−	0.748372i	−0.197352	−	0.0467733i
$257$	−0.871576	−	2.91127i	−0.0543674	−	0.181600i	0.926493	−	0.376312i	$-0.122808\pi$
$257$	−0.871576	−	2.91127i	−0.0543674	−	0.181600i	−0.980860	+	0.194712i	$0.937623\pi$
$258$		0			0
$259$	0.639407	+	0.0747360i	0.0397308	+	0.00464387i
$260$	0.167917	−	0.952303i	0.0104137	−	0.0590593i
$261$		0			0
$262$	−2.56828	−	14.5655i	−0.158669	−	0.899857i
$263$	1.45254	+	24.9392i	0.0895675	+	1.53781i	0.681495	+	0.731823i	$0.261330\pi$
$263$	1.45254	+	24.9392i	0.0895675	+	1.53781i	−0.591927	+	0.805991i	$0.701633\pi$
$264$		0			0
$265$	−9.14950	+	21.2109i	−0.562049	+	1.30298i
$266$	10.5344	−	5.29056i	0.645903	−	0.324385i
$267$		0			0
$268$	0.838725	−	0.198781i	0.0512333	−	0.0121425i
$269$	−12.6465	−	21.9043i	−0.771069	−	1.33553i	−0.936977	−	0.349390i	$-0.886389\pi$
$269$	−12.6465	−	21.9043i	−0.771069	−	1.33553i	0.165908	−	0.986141i	$-0.446944\pi$
$270$		0			0
$271$	−11.3545	+	19.6666i	−0.689737	+	1.19466i	0.282186	+	0.959360i	$0.408941\pi$
$271$	−11.3545	+	19.6666i	−0.689737	+	1.19466i	−0.971923	+	0.235300i	$0.924393\pi$
$272$	7.45041	−	24.8861i	0.451747	−	1.50894i
$273$		0			0
$274$	14.4511	+	9.50464i	0.873023	+	0.574196i
$275$	−17.3944	−	23.3647i	−1.04892	−	1.40894i
$276$		0			0
$277$	24.0470	−	15.8160i	1.44485	−	0.950291i	0.446386	−	0.894841i	$-0.352711\pi$
$277$	24.0470	−	15.8160i	1.44485	−	0.950291i	0.998461	−	0.0554503i	$-0.0176594\pi$
$278$	12.4604	+	4.53523i	0.747328	+	0.272005i
$279$		0			0
$280$	−18.2400	+	6.63880i	−1.09005	+	0.396744i
$281$	−1.10177	+	1.47993i	−0.0657261	+	0.0882855i	−0.833771	−	0.552111i	$-0.813822\pi$
$281$	−1.10177	+	1.47993i	−0.0657261	+	0.0882855i	0.768045	+	0.640396i	$0.221230\pi$
$282$		0			0
$283$	−4.12133	+	4.36835i	−0.244988	+	0.259672i	−0.838186	−	0.545385i	$-0.816384\pi$
$283$	−4.12133	+	4.36835i	−0.244988	+	0.259672i	0.593198	+	0.805056i	$0.297865\pi$
$284$	−1.30119	+	1.37918i	−0.0772112	+	0.0818391i
$285$		0			0
$286$	−4.66189	+	6.26200i	−0.275663	+	0.370280i
$287$	7.10874	−	2.58737i	0.419616	−	0.152728i
$288$		0			0
$289$	−30.1005	−	10.9557i	−1.77062	−	0.644452i
$290$	0.984507	−	0.647521i	0.0578123	−	0.0380237i
$291$		0			0
$292$	−0.257005	−	0.345218i	−0.0150401	−	0.0202023i
$293$	−8.87378	−	5.83638i	−0.518412	−	0.340965i	0.263189	−	0.964744i	$-0.415226\pi$
$293$	−8.87378	−	5.83638i	−0.518412	−	0.340965i	−0.781600	+	0.623780i	$0.785596\pi$
$294$		0			0
$295$	2.18329	−	7.29270i	0.127116	−	0.424597i
$296$	−0.537301	+	0.930632i	−0.0312300	+	0.0540919i
$297$		0			0
$298$	−2.83404	−	4.90871i	−0.164172	−	0.284354i
$299$	−3.46276	+	0.820688i	−0.200256	+	0.0474616i
$300$		0			0
$301$	−5.06934	+	2.54592i	−0.292192	+	0.146744i
$302$	−1.75159	+	4.06065i	−0.100793	+	0.233664i
$303$		0			0
$304$	1.06607	+	18.3038i	0.0611435	+	1.04979i
$305$	−8.46171	−	47.9888i	−0.484516	−	2.74783i
$306$		0			0
$307$	0.293712	−	1.66572i	0.0167630	−	0.0950677i	−0.975278	−	0.220980i	$-0.929075\pi$
$307$	0.293712	−	1.66572i	0.0167630	−	0.0950677i	0.992041	+	0.125912i	$0.0401857\pi$
$308$	−0.721491	−	0.0843302i	−0.0411108	−	0.00480516i
$309$		0			0
$310$	−5.87741	−	19.6319i	−0.333815	−	1.11502i
$311$	−26.4251	−	6.26288i	−1.49843	−	0.355135i	−0.602065	−	0.798447i	$-0.705655\pi$
$311$	−26.4251	−	6.26288i	−1.49843	−	0.355135i	−0.896367	+	0.443312i	$0.853803\pi$
$312$		0			0
$313$	10.6694	+	24.7345i	0.603071	+	1.39808i	0.896906	+	0.442220i	$0.145809\pi$
$313$	10.6694	+	24.7345i	0.603071	+	1.39808i	−0.293835	+	0.955856i	$0.594932\pi$
$314$	−7.82057	−	6.56224i	−0.441340	−	0.370329i
$315$		0			0
$316$	0.272810	−	0.228915i	0.0153467	−	0.0128774i
$317$	4.75988	+	2.39050i	0.267342	+	0.134264i	0.577421	−	0.816447i	$-0.304059\pi$
$317$	4.75988	+	2.39050i	0.267342	+	0.134264i	−0.310079	+	0.950711i	$0.600356\pi$
$318$		0			0
$319$	0.688608	−	0.0804867i	0.0385546	−	0.00450639i
$320$	1.87579	−	32.2060i	0.104860	−	1.80037i
$321$		0			0
$322$	3.11803	+	3.30492i	0.173761	+	0.184176i
$323$	34.6069			1.92558
$324$		0			0
$325$	17.7793			0.986217
$326$	9.10582	+	9.65161i	0.504325	+	0.534553i
$327$		0			0
$328$	−0.734246	+	12.6065i	−0.0405420	+	0.696079i
$329$	3.03275	−	0.354478i	0.167201	−	0.0195430i
$330$		0			0
$331$	12.9227	+	6.49005i	0.710298	+	0.356725i	0.766983	−	0.641667i	$-0.221757\pi$
$331$	12.9227	+	6.49005i	0.710298	+	0.356725i	−0.0566852	+	0.998392i	$0.518053\pi$
$332$	−0.0233980	+	0.0196332i	−0.00128413	+	0.00107751i
$333$		0			0
$334$	−0.753567	−	0.632318i	−0.0412334	−	0.0345989i
$335$	9.57496	+	22.1972i	0.523136	+	1.21277i
$336$		0			0
$337$	14.0973	+	3.34111i	0.767927	+	0.182002i	0.595866	−	0.803084i	$-0.296809\pi$
$337$	14.0973	+	3.34111i	0.767927	+	0.182002i	0.172061	+	0.985086i	$0.444957\pi$
$338$	3.72395	+	12.4389i	0.202556	+	0.676585i
$339$		0			0
$340$	−3.60002	−	0.420782i	−0.195238	−	0.0228201i
$341$	2.09369	−	11.8739i	0.113380	−	0.643008i
$342$		0			0
$343$	−3.32120	−	18.8355i	−0.179328	−	1.01702i
$344$	−0.550588	−	9.45324i	−0.0296857	−	0.509684i
$345$		0			0
$346$	1.18632	−	2.75019i	0.0637767	−	0.147851i
$347$	−3.16541	+	1.58973i	−0.169928	+	0.0853411i	−0.531730	−	0.846914i	$-0.678458\pi$
$347$	−3.16541	+	1.58973i	−0.169928	+	0.0853411i	0.361802	+	0.932255i	$0.382162\pi$
$348$		0			0
$349$	−28.8257	+	6.83182i	−1.54301	+	0.365699i	−0.912037	−	0.410109i	$-0.865491\pi$
$349$	−28.8257	+	6.83182i	−1.54301	+	0.365699i	−0.630969	+	0.775808i	$0.717343\pi$
$350$	−11.3501	−	19.6589i	−0.606687	−	1.05081i
$351$		0			0
$352$	1.17399	−	2.03341i	0.0625739	−	0.108381i
$353$	−7.82072	+	26.1230i	−0.416255	+	1.39039i	0.451000	+	0.892524i	$0.351068\pi$
$353$	−7.82072	+	26.1230i	−0.416255	+	1.39039i	−0.867255	+	0.497865i	$0.834118\pi$
$354$		0			0
$355$	−44.4294	−	29.2217i	−2.35807	−	1.55092i
$356$	0.577461	+	0.775664i	0.0306054	+	0.0411101i
$357$		0			0
$358$	28.9690	−	19.0532i	1.53106	−	1.00699i
$359$	1.58829	+	0.578092i	0.0838270	+	0.0305105i	0.383593	−	0.923502i	$-0.374686\pi$
$359$	1.58829	+	0.578092i	0.0838270	+	0.0305105i	−0.299766	+	0.954013i	$0.596909\pi$
$360$		0			0
$361$	−5.09828	+	1.85562i	−0.268330	+	0.0976642i
$362$	9.82986	−	13.2038i	0.516646	−	0.693976i
$363$		0			0
$364$	0.304263	−	0.322500i	0.0159477	−	0.0169036i
$365$	8.28316	−	8.77964i	0.433561	−	0.459547i
$366$		0			0
$367$	3.25794	−	4.37617i	0.170063	−	0.228434i	−0.708918	−	0.705291i	$-0.750816\pi$
$367$	3.25794	−	4.37617i	0.170063	−	0.228434i	0.878981	+	0.476856i	$0.158224\pi$
$368$	−6.64073	+	2.41703i	−0.346172	+	0.125996i
$369$		0			0
$370$	−1.80136	−	0.655641i	−0.0936482	−	0.0340852i
$371$	−8.84920	+	5.82021i	−0.459428	+	0.302170i
$372$		0			0
$373$	12.5081	+	16.8013i	0.647643	+	0.869936i	0.997769	−	0.0667668i	$-0.0212683\pi$
$373$	12.5081	+	16.8013i	0.647643	+	0.869936i	−0.350125	+	0.936703i	$0.613861\pi$
$374$	24.4478	+	16.0796i	1.26416	+	0.831454i
$375$		0			0
$376$	−1.46181	+	4.88279i	−0.0753872	+	0.251811i
$377$	−0.211584	+	0.366475i	−0.0108972	+	0.0188744i
$378$		0			0
$379$	−17.0149	−	29.4707i	−0.873998	−	1.51381i	−0.857826	−	0.513940i	$-0.828185\pi$
$379$	−17.0149	−	29.4707i	−0.873998	−	1.51381i	−0.0161719	−	0.999869i	$-0.505148\pi$
$380$	2.48923	−	0.589957i	0.127695	−	0.0302642i
$381$		0			0
$382$	−17.8486	+	8.96391i	−0.913215	+	0.458634i
$383$	−3.94156	+	9.13755i	−0.201404	+	0.466907i	−0.988745	−	0.149611i	$-0.952198\pi$
$383$	−3.94156	+	9.13755i	−0.201404	+	0.466907i	0.787341	+	0.616518i	$0.211457\pi$
$384$		0			0
$385$	−1.18456	−	20.3381i	−0.0603706	−	1.03652i
$386$	−5.03570	−	28.5589i	−0.256310	−	1.45361i
$387$		0			0
$388$	−0.367528	+	2.08436i	−0.0186584	+	0.105817i
$389$	17.4378	+	2.03818i	0.884130	+	0.103340i	0.546026	−	0.837768i	$-0.316140\pi$
$389$	17.4378	+	2.03818i	0.884130	+	0.103340i	0.338105	+	0.941108i	$0.390214\pi$
$390$		0			0
$391$	3.82561	+	12.7784i	0.193469	+	0.646233i
$392$	11.2028	+	2.65512i	0.565829	+	0.134104i
$393$		0			0
$394$	−9.77451	−	22.6599i	−0.492433	−	1.14159i
$395$	7.65116	+	6.42008i	0.384972	+	0.323030i
$396$		0			0
$397$	−12.8659	+	10.7958i	−0.645721	+	0.541824i	−0.905769	−	0.423771i	$-0.860706\pi$
$397$	−12.8659	+	10.7958i	−0.645721	+	0.541824i	0.260048	+	0.965596i	$0.416262\pi$
$398$	−29.7711	−	14.9516i	−1.49229	−	0.749457i
$399$		0			0
$400$	35.0678	−	4.09884i	1.75339	−	0.204942i
$401$	0.152825	−	2.62391i	0.00763173	−	0.131032i	−0.992340	−	0.123535i	$-0.960577\pi$
$401$	0.152825	−	2.62391i	0.00763173	−	0.131032i	0.999972	−	0.00749640i	$-0.00238620\pi$
$402$		0			0
$403$	5.05027	+	5.35297i	0.251572	+	0.266650i
$404$	1.16744			0.0580822
$405$		0			0
$406$	0.540291			0.0268142
$407$	−0.773983	−	0.820374i	−0.0383649	−	0.0406644i
$408$		0			0
$409$	0.456729	−	7.84174i	0.0225838	−	0.387749i	−0.968010	−	0.250912i	$-0.919269\pi$
$409$	0.456729	−	7.84174i	0.0225838	−	0.387749i	0.990594	−	0.136837i	$-0.0436936\pi$
$410$	−22.3744	+	2.61519i	−1.10499	+	0.129155i
$411$		0			0
$412$	0.140217	+	0.0704194i	0.00690797	+	0.00346931i
$413$	2.67381	−	2.24359i	0.131570	−	0.110400i
$414$		0			0
$415$	−0.656214	−	0.550629i	−0.0322123	−	0.0270293i
$416$	0.567640	+	1.31594i	0.0278308	+	0.0645191i
$417$		0			0
$418$	−20.0961	−	4.76287i	−0.982934	−	0.232960i
$419$	−9.07933	−	30.3271i	−0.443554	−	1.48158i	−0.829213	−	0.558933i	$-0.811211\pi$
$419$	−9.07933	−	30.3271i	−0.443554	−	1.48158i	0.385658	−	0.922642i	$-0.373974\pi$
$420$		0			0
$421$	0.514644	+	0.0601533i	0.0250822	+	0.00293169i	0.128625	−	0.991693i	$-0.458944\pi$
$421$	0.514644	+	0.0601533i	0.0250822	+	0.00293169i	−0.103543	+	0.994625i	$0.533018\pi$
$422$	−3.63895	+	20.6375i	−0.177141	+	1.00462i
$423$		0			0
$424$	−3.07014	−	17.4116i	−0.149099	−	0.845583i
$425$	−3.87483	−	66.5283i	−0.187957	−	3.22710i
$426$		0			0
$427$	8.84952	−	20.5155i	0.428258	−	0.992815i
$428$	1.34315	−	0.674554i	0.0649235	−	0.0326058i
$429$		0			0
$430$	16.4367	−	3.89558i	0.792650	−	0.187862i
$431$	−5.66734	−	9.81613i	−0.272986	−	0.472826i	0.696639	−	0.717422i	$-0.254678\pi$
$431$	−5.66734	−	9.81613i	−0.272986	−	0.472826i	−0.969625	+	0.244596i	$0.921345\pi$
$432$		0			0
$433$	3.59806	−	6.23203i	0.172912	−	0.299492i	−0.766525	−	0.642215i	$-0.778016\pi$
$433$	3.59806	−	6.23203i	0.172912	−	0.299492i	0.939437	+	0.342723i	$0.111349\pi$
$434$	2.69486	−	9.00144i	0.129357	−	0.432083i
$435$		0			0
$436$	1.72563	+	1.13496i	0.0826426	+	0.0543549i
$437$	−5.62194	−	7.55158i	−0.268934	−	0.361241i
$438$		0			0
$439$	1.52694	−	1.00428i	0.0728767	−	0.0479317i	−0.512548	−	0.858659i	$-0.671298\pi$
$439$	1.52694	−	1.00428i	0.0728767	−	0.0479317i	0.585424	+	0.810727i	$0.300928\pi$
$440$	31.9561	+	11.6311i	1.52345	+	0.554490i
$441$		0			0
$442$	−16.7834	+	6.10867i	−0.798306	+	0.290560i
$443$	−9.44074	+	12.6811i	−0.448543	+	0.602498i	−0.967676	−	0.252196i	$-0.918847\pi$
$443$	−9.44074	+	12.6811i	−0.448543	+	0.602498i	0.519133	+	0.854693i	$0.326255\pi$
$444$		0			0
$445$	−18.6113	+	19.7268i	−0.882261	+	0.935142i
$446$	13.4587	−	14.2654i	0.637287	−	0.675485i
$447$		0			0
$448$	8.83306	−	11.8649i	0.417323	−	0.560562i
$449$	−9.12091	+	3.31974i	−0.430442	+	0.156668i	−0.548150	−	0.836380i	$-0.684668\pi$
$449$	−9.12091	+	3.31974i	−0.430442	+	0.156668i	0.117708	+	0.993048i	$0.462445\pi$
$450$		0			0
$451$	−12.4544	−	4.53304i	−0.586455	−	0.213452i
$452$	−0.240698	+	0.158310i	−0.0113215	+	0.00744627i
$453$		0			0
$454$	9.14756	+	12.2873i	0.429316	+	0.576672i
$455$	10.3892	+	6.83305i	0.487051	+	0.320339i
$456$		0			0
$457$	−0.736953	+	2.46159i	−0.0344732	+	0.115149i	−0.973494	−	0.228711i	$-0.926549\pi$
$457$	−0.736953	+	2.46159i	−0.0344732	+	0.115149i	0.939021	+	0.343859i	$0.111734\pi$
$458$	−6.55296	+	11.3501i	−0.306200	+	0.530354i
$459$		0			0
$460$	0.493010	+	0.853918i	0.0229867	+	0.0398141i
$461$	3.15508	−	0.747767i	0.146947	−	0.0348270i	−0.156484	−	0.987680i	$-0.550016\pi$
$461$	3.15508	−	0.747767i	0.146947	−	0.0348270i	0.303431	+	0.952853i	$0.401868\pi$
$462$		0			0
$463$	8.67454	−	4.35652i	0.403140	−	0.202465i	−0.235663	−	0.971835i	$-0.575726\pi$
$463$	8.67454	−	4.35652i	0.403140	−	0.202465i	0.638803	+	0.769370i	$0.279430\pi$
$464$	−0.332842	+	0.771614i	−0.0154518	+	0.0358213i
$465$		0			0
$466$	−1.39277	−	23.9130i	−0.0645190	−	1.10775i
$467$	0.550626	+	3.12276i	0.0254799	+	0.144504i	0.994894	−	0.100928i	$-0.0321812\pi$
$467$	0.550626	+	3.12276i	0.0254799	+	0.144504i	−0.969414	+	0.245432i	$0.921070\pi$
$468$		0			0
$469$	−1.92475	+	10.9158i	−0.0888765	+	0.504044i
$470$	−9.03084	−	1.05555i	−0.416561	−	0.0486890i
$471$		0			0
$472$	1.67103	+	5.58163i	0.0769154	+	0.256915i
$473$	9.67065	+	2.29199i	0.444657	+	0.105386i
$474$		0			0
$475$	18.6297	+	43.1884i	0.854787	+	1.98162i
$476$	−1.27308	−	1.06824i	−0.0583513	−	0.0489626i
$477$		0			0
$478$	28.5590	−	23.9639i	1.30626	−	1.09608i
$479$	−24.7479	−	12.4289i	−1.13076	−	0.567890i	−0.217824	−	0.975988i	$-0.569896\pi$
$479$	−24.7479	−	12.4289i	−1.13076	−	0.567890i	−0.912938	+	0.408098i	$0.866192\pi$
$480$		0			0
$481$	0.683759	−	0.0799200i	0.0311767	−	0.00364404i
$482$	−0.412903	+	7.08927i	−0.0188072	+	0.322908i
$483$		0			0
$484$	−0.152169	−	0.161290i	−0.00691679	−	0.00733137i
$485$	−59.3592			−2.69536
$486$		0			0
$487$	10.4889			0.475298			0.237649	−	0.971351i	$-0.423623\pi$
$487$	10.4889			0.475298			0.237649	+	0.971351i	$0.423623\pi$
$488$	25.5940	+	27.1280i	1.15859	+	1.22803i
$489$		0			0
$490$	−1.19419	+	20.5035i	−0.0539480	+	0.926252i
$491$	5.88746	−	0.688145i	0.265697	−	0.0310556i	0.0177989	−	0.999842i	$-0.494334\pi$
$491$	5.88746	−	0.688145i	0.265697	−	0.0310556i	0.247898	+	0.968786i	$0.420260\pi$
$492$		0			0
$493$	1.41743	+	0.711858i	0.0638376	+	0.0320605i
$494$	9.65671	−	8.10294i	0.434476	−	0.364568i
$495$		0			0
$496$	11.1952	+	9.39390i	0.502680	+	0.421798i
$497$	−9.65744	−	22.3885i	−0.433195	−	1.00426i
$498$		0			0
$499$	−37.0899	−	8.79048i	−1.66037	−	0.393516i	−0.709895	−	0.704307i	$-0.751258\pi$
$499$	−37.0899	−	8.79048i	−1.66037	−	0.393516i	−0.950478	+	0.310791i	$0.899406\pi$
$500$	−0.670572	−	2.23987i	−0.0299889	−	0.100170i
$501$		0			0
$502$	6.46481	+	0.755628i	0.288539	+	0.0337253i
$503$	−2.25782	+	12.8047i	−0.100671	+	0.570935i	0.892190	+	0.451660i	$0.149168\pi$
$503$	−2.25782	+	12.8047i	−0.100671	+	0.570935i	−0.992861	+	0.119275i	$0.961943\pi$
$504$		0			0
$505$	5.68553	+	32.2442i	0.253003	+	1.43485i
$506$	−0.462855	−	7.94691i	−0.0205764	−	0.353283i
$507$		0			0
$508$	0.609370	−	1.41268i	0.0270364	−	0.0626775i
$509$	24.3118	−	12.2098i	1.07760	−	0.541192i	0.180752	−	0.983529i	$-0.442147\pi$
$509$	24.3118	−	12.2098i	1.07760	−	0.541192i	0.896849	+	0.442337i	$0.145850\pi$
$510$		0			0
$511$	5.38519	−	1.27631i	0.238227	−	0.0564608i
$512$	12.2415	+	21.2028i	0.541002	+	0.937042i
$513$		0			0
$514$	−2.07458	+	3.59329i	−0.0915060	+	0.158493i
$515$	−1.26209	+	4.21569i	−0.0556145	+	0.185765i
$516$		0			0
$517$	−4.46945	−	2.93960i	−0.196566	−	0.129284i
$518$	−0.524872	−	0.705026i	−0.0230616	−	0.0309771i
$519$		0			0
$520$	−17.3422	+	11.4061i	−0.760505	+	0.500192i
$521$	8.60146	+	3.13068i	0.376837	+	0.137157i	0.523493	−	0.852030i	$-0.324629\pi$
$521$	8.60146	+	3.13068i	0.376837	+	0.137157i	−0.146656	+	0.989188i	$0.546851\pi$
$522$		0			0
$523$	24.5766	−	8.94516i	1.07466	−	0.391144i	0.256743	−	0.966480i	$-0.417351\pi$
$523$	24.5766	−	8.94516i	1.07466	−	0.391144i	0.817918	+	0.575335i	$0.195128\pi$
$524$	0.878807	−	1.18044i	0.0383909	−	0.0515679i
$525$		0			0
$526$	23.4064	−	24.8093i	1.02057	−	1.08174i
$527$	18.9296	−	20.0642i	0.824587	−	0.874011i
$528$		0			0
$529$	−11.5677	+	15.5382i	−0.502945	+	0.675573i
$530$	29.6374	−	10.7871i	1.28737	−	0.468564i
$531$		0			0
$532$	1.10222	+	0.401173i	0.0477871	+	0.0173931i
$533$	6.75885	−	4.44537i	0.292758	−	0.192550i
$534$		0			0
$535$	25.1723	+	33.8122i	1.08829	+	1.46183i
$536$	−15.4585	−	10.1672i	−0.667705	−	0.439157i
$537$		0			0
$538$	−9.90429	+	33.0826i	−0.427004	+	1.42629i
$539$	−6.04188	+	10.4648i	−0.260242	+	0.450753i
$540$		0			0
$541$	4.36966	+	7.56848i	0.187867	+	0.325394i	0.944539	−	0.328400i	$-0.106509\pi$
$541$	4.36966	+	7.56848i	0.187867	+	0.325394i	−0.756672	+	0.653794i	$0.773176\pi$
$542$	30.1697	−	7.15035i	1.29590	−	0.307134i
$543$		0			0
$544$	4.80039	−	2.41085i	0.205815	−	0.103364i
$545$	−22.9434	+	53.1887i	−0.982786	+	2.27835i
$546$		0			0
$547$	−1.76688	−	30.3361i	−0.0755461	−	1.29708i	−0.796731	−	0.604334i	$-0.793439\pi$
$547$	−1.76688	−	30.3361i	−0.0755461	−	1.29708i	0.721185	−	0.692743i	$-0.243598\pi$
$548$	0.298856	+	1.69490i	0.0127665	+	0.0724024i
$549$		0			0
$550$	−6.90604	+	39.1661i	−0.294475	+	1.67005i
$551$	−1.11192	−	0.129965i	−0.0473696	−	0.00553671i
$552$		0			0
$553$	1.31343	+	4.38716i	0.0558527	+	0.186561i
$554$	−38.2379	−	9.06256i	−1.62457	−	0.385031i
$555$		0			0
$556$	0.522591	+	1.21150i	0.0221628	+	0.0513791i
$557$	−19.9818	−	16.7668i	−0.846658	−	0.710430i	0.112393	−	0.993664i	$-0.464148\pi$
$557$	−19.9818	−	16.7668i	−0.846658	−	0.710430i	−0.959051	+	0.283234i	$0.908593\pi$
$558$		0			0
$559$	−4.64699	+	3.89929i	−0.196547	+	0.164922i
$560$	22.0668	+	11.0824i	0.932494	+	0.468316i
$561$		0			0
$562$	2.50204	−	0.292447i	0.105542	−	0.0123361i
$563$	−2.52063	+	43.2776i	−0.106232	+	1.82393i	0.353006	+	0.935621i	$0.385159\pi$
$563$	−2.52063	+	43.2776i	−0.106232	+	1.82393i	−0.459238	+	0.888313i	$0.651878\pi$
$564$		0			0
$565$	−5.54469	−	5.87703i	−0.233267	−	0.247249i
$566$	8.19974			0.344661
$567$		0			0
$568$	40.7008			1.70777
$569$	−4.50377	−	4.77371i	−0.188808	−	0.200124i	0.626054	−	0.779779i	$-0.284669\pi$
$569$	−4.50377	−	4.77371i	−0.188808	−	0.200124i	−0.814862	+	0.579655i	$0.803187\pi$
$570$		0			0
$571$	−1.39116	+	23.8854i	−0.0582184	+	0.999571i	0.835086	+	0.550119i	$0.185418\pi$
$571$	−1.39116	+	23.8854i	−0.0582184	+	0.999571i	−0.893304	+	0.449452i	$0.851619\pi$
$572$	−0.771537	+	0.0901797i	−0.0322596	+	0.00377060i
$573$		0			0
$574$	−9.23009	−	4.63553i	−0.385257	−	0.193483i
$575$	−13.8877	+	11.6532i	−0.579157	+	0.485970i
$576$		0			0
$577$	−24.0397	−	20.1717i	−1.00078	−	0.839758i	−0.0136918	−	0.999906i	$-0.504358\pi$
$577$	−24.0397	−	20.1717i	−1.00078	−	0.839758i	−0.987093	+	0.160148i	$0.948803\pi$
$578$	17.3225	+	40.1581i	0.720521	+	1.67036i
$579$		0			0
$580$	0.114089	+	0.0270395i	0.00473728	+	0.00112276i
$581$	−0.112648	−	0.376272i	−0.00467344	−	0.0156104i
$582$		0			0
$583$	18.4310	+	2.15427i	0.763332	+	0.0892208i
$584$	−1.60421	+	9.09795i	−0.0663828	+	0.376476i
$585$		0			0
$586$	2.51813	+	14.2810i	0.104023	+	0.589944i
$587$	2.58150	+	44.3226i	0.106550	+	1.82939i	0.453217	+	0.891400i	$0.350276\pi$
$587$	2.58150	+	44.3226i	0.106550	+	1.82939i	−0.346667	+	0.937988i	$0.612687\pi$
$588$		0			0
$589$	−7.71130	+	17.8768i	−0.317739	+	0.736601i
$590$	−9.28809	+	4.66465i	−0.382385	+	0.192041i
$591$		0			0
$592$	1.33022	−	0.315268i	0.0546717	−	0.0129574i
$593$	9.54772	+	16.5371i	0.392078	+	0.679099i	0.992723	−	0.120417i	$-0.0384230\pi$
$593$	9.54772	+	16.5371i	0.392078	+	0.679099i	−0.600646	+	0.799515i	$0.705090\pi$
$594$		0			0
$595$	23.3044	−	40.3644i	0.955387	−	1.65478i
$596$	0.161753	−	0.540292i	0.00662565	−	0.0221312i
$597$		0			0
$598$	4.05947	+	2.66995i	0.166004	+	0.109183i
$599$	0.526426	+	0.707113i	0.0215092	+	0.0288918i	0.812748	−	0.582616i	$-0.197971\pi$
$599$	0.526426	+	0.707113i	0.0215092	+	0.0288918i	−0.791239	+	0.611508i	$0.790563\pi$
$600$		0			0
$601$	−23.6223	+	15.5366i	−0.963575	+	0.633753i	−0.930730	−	0.365707i	$-0.880827\pi$
$601$	−23.6223	+	15.5366i	−0.963575	+	0.633753i	−0.0328449	+	0.999460i	$0.510457\pi$
$602$	7.27810	+	2.64901i	0.296633	+	0.107966i
$603$		0			0
$604$	−0.413492	+	0.150499i	−0.0168248	+	0.00612371i
$605$	3.71370	−	4.98837i	0.150983	−	0.202806i
$606$		0			0
$607$	25.6511	−	27.1886i	1.04115	−	1.10355i	0.0466354	−	0.998912i	$-0.485150\pi$
$607$	25.6511	−	27.1886i	1.04115	−	1.10355i	0.994510	−	0.104638i	$-0.0333684\pi$
$608$	−2.60181	+	2.75775i	−0.105517	+	0.111842i
$609$		0			0
$610$	−39.7299	+	53.3666i	−1.60862	+	2.16075i
$611$	3.06828	−	1.11676i	0.124129	−	0.0451794i
$612$		0			0
$613$	7.96120	+	2.89764i	0.321550	+	0.117035i	0.497752	−	0.867319i	$-0.334159\pi$
$613$	7.96120	+	2.89764i	0.321550	+	0.117035i	−0.176202	+	0.984354i	$0.556381\pi$
$614$	−1.92944	+	1.26901i	−0.0778658	+	0.0512131i
$615$		0			0
$616$	9.31124	+	12.5072i	0.375160	+	0.503928i
$617$	−31.0820	−	20.4430i	−1.25132	−	0.823003i	−0.261479	−	0.965209i	$-0.584210\pi$
$617$	−31.0820	−	20.4430i	−1.25132	−	0.823003i	−0.989837	+	0.142206i	$0.954580\pi$
$618$		0			0
$619$	11.0925	−	37.0515i	0.445845	−	1.48923i	−0.379817	−	0.925062i	$-0.624013\pi$
$619$	11.0925	−	37.0515i	0.445845	−	1.48923i	0.825662	−	0.564165i	$-0.190802\pi$
$620$	1.01954	−	1.76589i	0.0409456	−	0.0709199i
$621$		0			0
$622$	18.5394	+	32.1111i	0.743360	+	1.28754i
$623$	−12.0999	+	2.86773i	−0.484773	+	0.114893i
$624$		0			0
$625$	16.0751	−	8.07322i	0.643004	−	0.322929i
$626$	14.5674	−	33.7709i	0.582229	−	1.34976i
$627$		0			0
$628$	−0.0590645	−	1.01410i	−0.00235693	−	0.0404670i
$629$	−0.448072	−	2.54114i	−0.0178658	−	0.101322i
$630$		0			0
$631$	−0.0118315	+	0.0670997i	−0.000471004	+	0.00267120i	−0.985042	−	0.172312i	$-0.944876\pi$
$631$	−0.0118315	+	0.0670997i	−0.000471004	+	0.00267120i	0.984571	+	0.174984i	$0.0559872\pi$
$632$	−7.59276	−	0.887466i	−0.302024	−	0.0353015i
$633$		0			0
$634$	−2.08575	−	6.96688i	−0.0828355	−	0.276690i
$635$	41.9854	+	9.95073i	1.66614	+	0.394883i
$636$		0			0
$637$	−2.92133	−	6.77240i	−0.115747	−	0.268332i
$638$	−0.725124	−	0.608452i	−0.0287079	−	0.0240888i
$639$		0			0
$640$	−29.2635	+	24.5550i	−1.15674	+	0.970621i
$641$	−9.70187	−	4.87246i	−0.383201	−	0.192451i	0.246762	−	0.969076i	$-0.420633\pi$
$641$	−9.70187	−	4.87246i	−0.383201	−	0.192451i	−0.629963	+	0.776625i	$0.716930\pi$
$642$		0			0
$643$	−31.0638	+	3.63084i	−1.22504	+	0.143186i	−0.703908	−	0.710291i	$-0.748563\pi$
$643$	−31.0638	+	3.63084i	−1.22504	+	0.143186i	−0.521130	+	0.853477i	$0.674489\pi$
$644$	−0.0262873	+	0.451335i	−0.00103586	+	0.0177851i
$645$		0			0
$646$	−32.4250	−	34.3685i	−1.27574	−	1.35221i
$647$	−22.3771			−0.879735			−0.439868	−	0.898063i	$-0.644975\pi$
$647$	−22.3771			−0.879735			−0.439868	+	0.898063i	$0.644975\pi$
$648$		0			0
$649$	−6.11515			−0.240041
$650$	−16.6583	−	17.6568i	−0.653393	−	0.692556i
$651$		0			0
$652$	−0.0767687	+	1.31807i	−0.00300650	+	0.0516195i
$653$	37.2153	−	4.34984i	1.45635	−	0.170223i	0.649220	−	0.760601i	$-0.275095\pi$
$653$	37.2153	−	4.34984i	1.45635	−	0.170223i	0.807127	+	0.590378i	$0.201021\pi$
$654$		0			0
$655$	36.8834	+	18.5235i	1.44115	+	0.723774i
$656$	12.3063	−	10.3262i	0.480481	−	0.403171i
$657$		0			0
$658$	−3.19358	−	2.67973i	−0.124499	−	0.104467i
$659$	−1.83219	−	4.24750i	−0.0713722	−	0.165459i	0.878796	−	0.477199i	$-0.158348\pi$
$659$	−1.83219	−	4.24750i	−0.0713722	−	0.165459i	−0.950168	+	0.311739i	$0.899088\pi$
$660$		0			0
$661$	7.13756	+	1.69163i	0.277619	+	0.0657969i	0.367067	−	0.930195i	$-0.380362\pi$
$661$	7.13756	+	1.69163i	0.277619	+	0.0657969i	−0.0894479	+	0.995992i	$0.528510\pi$
$662$	−5.66265	−	18.9146i	−0.220085	−	0.735136i
$663$		0			0
$664$	0.651205	+	0.0761150i	0.0252717	+	0.00295383i
$665$	−5.71239	+	32.3966i	−0.221517	+	1.25629i
$666$		0			0
$667$	−0.0749283	−	0.424939i	−0.00290124	−	0.0164537i
$668$	−0.00569128	−	0.0977156i	−0.000220202	−	0.00378073i
$669$		0			0
$670$	13.0730	−	30.3067i	0.505056	−	1.17085i
$671$	−34.9806	+	17.5679i	−1.35041	+	0.678201i
$672$		0			0
$673$	12.0828	−	2.86368i	0.465759	−	0.110387i	0.00896566	−	0.999960i	$-0.497146\pi$
$673$	12.0828	−	2.86368i	0.465759	−	0.110387i	0.456793	+	0.889573i	$0.348998\pi$
$674$	−9.89036	−	17.1306i	−0.380962	−	0.659846i
$675$		0			0
$676$	−0.645983	+	1.11888i	−0.0248455	+	0.0430337i
$677$	7.09365	−	23.6945i	0.272631	−	0.910652i	−0.706550	−	0.707663i	$-0.749749\pi$
$677$	7.09365	−	23.6945i	0.272631	−	0.910652i	0.979181	−	0.202989i	$-0.0650654\pi$
$678$		0			0
$679$	−22.7393	−	14.9559i	−0.872655	−	0.573954i
$680$	46.4602	+	62.4069i	1.78167	+	2.39319i
$681$		0			0
$682$	−13.7538	+	9.04600i	−0.526659	+	0.346389i
$683$	−3.75317	−	1.36604i	−0.143611	−	0.0522702i	0.269215	−	0.963080i	$-0.413236\pi$
$683$	−3.75317	−	1.36604i	−0.143611	−	0.0522702i	−0.412826	+	0.910810i	$0.635458\pi$
$684$		0			0
$685$	−45.3571	+	16.5086i	−1.73301	+	0.630762i
$686$	−15.5939	+	20.9462i	−0.595378	+	0.799731i
$687$		0			0
$688$	−8.26678	+	8.76227i	−0.315168	+	0.334058i
$689$	−7.77261	+	8.23848i	−0.296113	+	0.313861i
$690$		0			0
$691$	3.18637	−	4.28004i	0.121215	−	0.162820i	−0.737374	−	0.675485i	$-0.763934\pi$
$691$	3.18637	−	4.28004i	0.121215	−	0.162820i	0.858589	+	0.512665i	$0.171342\pi$
$692$	0.280049	−	0.101930i	0.0106459	−	0.00387478i
$693$		0			0
$694$	4.54461	+	1.65410i	0.172511	+	0.0627889i
$695$	−30.9162	+	20.3339i	−1.17272	+	0.771310i
$696$		0			0
$697$	−18.1071	−	24.3221i	−0.685857	−	0.921266i
$698$	33.7931	+	22.2260i	1.27909	+	0.841268i
$699$		0			0
$700$	0.647804	−	2.16382i	0.0244847	−	0.0817846i
$701$	−9.39904	+	16.2796i	−0.354997	+	0.614873i	−0.987117	−	0.159997i	$-0.948851\pi$
$701$	−9.39904	+	16.2796i	−0.354997	+	0.614873i	0.632120	+	0.774870i	$0.282185\pi$
$702$		0			0
$703$	0.910600	+	1.57721i	0.0343439	+	0.0594854i
$704$	−25.2165	+	5.97642i	−0.950383	+	0.225245i
$705$		0			0
$706$	33.2707	−	16.7092i	1.25216	−	0.628858i
$707$	−5.94611	+	13.7846i	−0.223626	+	0.518424i
$708$		0			0
$709$	−1.06948	−	18.3623i	−0.0401653	−	0.689612i	−0.956954	−	0.290240i	$-0.906265\pi$
$709$	−1.06948	−	18.3623i	−0.0401653	−	0.689612i	0.916789	−	0.399373i	$-0.130772\pi$
$710$	12.6078	+	71.5025i	0.473163	+	2.68344i
$711$		0			0
$712$	3.60448	−	20.4420i	0.135084	−	0.766098i
$713$	−7.45337	−	0.871174i	−0.279131	−	0.0326257i
$714$		0			0
$715$	−6.24820	−	20.8704i	−0.233669	−	0.780510i
$716$	3.35705	+	0.795635i	0.125459	+	0.0297343i
$717$		0			0
$718$	−0.914046	−	2.11900i	−0.0341119	−	0.0790802i
$719$	−2.04229	−	1.71368i	−0.0761644	−	0.0639095i	0.603911	−	0.797052i	$-0.293608\pi$
$719$	−2.04229	−	1.71368i	−0.0761644	−	0.0639095i	−0.680075	+	0.733143i	$0.738053\pi$
$720$		0			0
$721$	−1.54565	+	1.29695i	−0.0575630	+	0.0483011i
$722$	6.61967	+	3.32452i	0.246359	+	0.123726i
$723$		0			0
$724$	1.62683	−	0.190149i	0.0604607	−	0.00706684i
$725$	−0.125346	+	2.15212i	−0.00465525	+	0.0799276i
$726$		0			0
$727$	0.291613	+	0.309092i	0.0108153	+	0.0114636i	0.732759	−	0.680489i	$-0.238232\pi$
$727$	0.291613	+	0.309092i	0.0108153	+	0.0114636i	−0.721943	+	0.691952i	$0.756751\pi$
$728$	−9.51728			−0.352734
$729$		0			0
$730$	−16.4801			−0.609955
$731$	15.6035	+	16.5388i	0.577117	+	0.611708i
$732$		0			0
$733$	1.38421	−	23.7660i	0.0511269	−	0.877816i	−0.871085	−	0.491132i	$-0.836583\pi$
$733$	1.38421	−	23.7660i	0.0511269	−	0.877816i	0.922212	−	0.386684i	$-0.126380\pi$
$734$	−7.39855	+	0.864767i	−0.273086	+	0.0319191i
$735$		0			0
$736$	−1.30590	−	0.655849i	−0.0481362	−	0.0241749i
$737$	14.8761	−	12.4825i	0.547967	−	0.459799i
$738$		0			0
$739$	19.6618	+	16.4982i	0.723271	+	0.606896i	0.928288	−	0.371862i	$-0.121281\pi$
$739$	19.6618	+	16.4982i	0.723271	+	0.606896i	−0.205017	+	0.978758i	$0.565725\pi$
$740$	−0.0755490	−	0.175142i	−0.00277724	−	0.00643836i
$741$		0			0
$742$	14.0714	+	3.33498i	0.516577	+	0.122431i
$743$	2.35323	+	7.86035i	0.0863318	+	0.288368i	0.990243	−	0.139352i	$-0.0445020\pi$
$743$	2.35323	+	7.86035i	0.0863318	+	0.288368i	−0.903911	+	0.427720i	$0.859317\pi$
$744$		0			0
$745$	15.7105	+	1.83629i	0.575587	+	0.0672764i
$746$	4.96605	−	28.1639i	0.181820	−	1.03115i
$747$		0			0
$748$	0.505593	+	2.86736i	0.0184863	+	0.104841i
$749$	1.12381	+	19.2951i	0.0410631	+	0.705026i
$750$		0			0
$751$	8.47798	−	19.6542i	0.309366	−	0.717190i	−0.690616	−	0.723222i	$-0.742661\pi$
$751$	8.47798	−	19.6542i	0.309366	−	0.717190i	0.999982	+	0.00603122i	$0.00191981\pi$
$752$	5.79441	−	2.91006i	0.211301	−	0.106119i
$753$		0			0
$754$	0.562195	−	0.133243i	0.0204739	−	0.00485241i
$755$	−6.17048	−	10.6876i	−0.224567	−	0.388961i
$756$		0			0
$757$	12.5431	−	21.7253i	0.455886	−	0.789618i	−0.542852	−	0.839828i	$-0.682656\pi$
$757$	12.5431	−	21.7253i	0.455886	−	0.789618i	0.998739	+	0.0502098i	$0.0159890\pi$
$758$	−13.3255	+	44.5103i	−0.484005	+	1.61669i
$759$		0			0
$760$	−45.8788	−	30.1749i	−1.66420	−	1.09456i
$761$	−28.0836	−	37.7228i	−1.01803	−	1.36745i	−0.928444	−	0.371472i	$-0.878853\pi$
$761$	−28.0836	−	37.7228i	−1.01803	−	1.36745i	−0.0895859	−	0.995979i	$-0.528554\pi$
$762$		0			0
$763$	−22.1903	+	14.5948i	−0.803344	+	0.528368i
$764$	−1.86751	−	0.679718i	−0.0675641	−	0.0245913i
$765$		0			0
$766$	12.7676	−	4.64704i	0.461314	−	0.167905i
$767$	2.22891	−	2.99394i	0.0804812	−	0.108105i
$768$		0			0
$769$	31.9385	−	33.8528i	1.15173	−	1.22076i	0.180258	−	0.983619i	$-0.442307\pi$
$769$	31.9385	−	33.8528i	1.15173	−	1.22076i	0.971474	−	0.237145i	$-0.0762118\pi$
$770$	−19.0881	+	20.2322i	−0.687886	+	0.729117i
$771$		0			0
$772$	1.72310	−	2.31452i	0.0620157	−	0.0833016i
$773$	37.5202	−	13.6562i	1.34951	−	0.491180i	0.436713	−	0.899601i	$-0.356142\pi$
$773$	37.5202	−	13.6562i	1.34951	−	0.491180i	0.912794	+	0.408420i	$0.133920\pi$
$774$		0			0
$775$	35.2298	+	12.8226i	1.26549	+	0.460601i
$776$	37.9578	−	24.9652i	1.36261	−	0.896200i
$777$		0			0
$778$	−14.3142	−	19.2273i	−0.513189	−	0.689333i
$779$	17.8805	+	11.7602i	0.640637	+	0.421354i
$780$		0			0
$781$	−12.2516	+	40.9233i	−0.438398	+	1.46435i
$782$	9.10598	−	15.7720i	0.325629	−	0.564006i
$783$		0			0
$784$	−7.32333	−	12.6844i	−0.261548	−	0.453014i
$785$	27.7215	−	6.57011i	0.989421	−	0.234497i
$786$		0			0
$787$	11.3969	−	5.72374i	0.406255	−	0.204029i	−0.233923	−	0.972255i	$-0.575157\pi$
$787$	11.3969	−	5.72374i	0.406255	−	0.204029i	0.640179	+	0.768226i	$0.278860\pi$
$788$	0.972582	−	2.25470i	0.0346468	−	0.0803203i
$789$		0			0
$790$	−0.792911	−	13.6138i	−0.0282105	−	0.484356i
$791$	−0.643309	−	3.64839i	−0.0228734	−	0.129722i
$792$		0			0
$793$	4.14890	−	23.5296i	0.147332	−	0.835560i
$794$	22.7761	+	2.66215i	0.808294	+	0.0944760i
$795$		0			0
$796$	−0.950717	−	3.17562i	−0.0336973	−	0.112557i
$797$	−15.2590	−	3.61644i	−0.540501	−	0.128101i	−0.0487076	−	0.998813i	$-0.515510\pi$
$797$	−15.2590	−	3.61644i	−0.540501	−	0.128101i	−0.491793	+	0.870712i	$0.663658\pi$
$798$		0			0
$799$	−4.84752	−	11.2378i	−0.171493	−	0.397565i
$800$	5.59282	+	4.69294i	0.197736	+	0.165920i
$801$		0			0
$802$	−2.74902	+	2.30670i	−0.0970713	+	0.0814525i
$803$	−8.66479	−	4.35162i	−0.305774	−	0.153565i
$804$		0			0
$805$	−12.5938	+	1.47200i	−0.443872	+	0.0518812i
$806$	0.584236	−	10.0309i	0.0205788	−	0.353325i
$807$		0			0
$808$	−17.1969	−	18.2277i	−0.604986	−	0.641247i
$809$	21.4680			0.754776			0.377388	−	0.926055i	$-0.376822\pi$
$809$	21.4680			0.754776			0.377388	+	0.926055i	$0.376822\pi$
$810$		0			0
$811$	−27.3610			−0.960774			−0.480387	−	0.877057i	$-0.659504\pi$
$811$	−27.3610			−0.960774			−0.480387	+	0.877057i	$0.659504\pi$
$812$	0.0368924	+	0.0391036i	0.00129467	+	0.00137227i
$813$		0			0
$814$	−0.0895376	+	1.53730i	−0.00313829	+	0.0538824i
$815$	−36.7785	+	4.29879i	−1.28829	+	0.150580i
$816$		0			0
$817$	−14.3412	−	7.20241i	−0.501734	−	0.251980i
$818$	−8.21565	+	6.89375i	−0.287253	+	0.241034i
$819$		0			0
$820$	−1.71705	−	1.44078i	−0.0599620	−	0.0503141i
$821$	−8.21544	−	19.0455i	−0.286721	−	0.664693i	0.712599	−	0.701572i	$-0.247518\pi$
$821$	−8.21544	−	19.0455i	−0.286721	−	0.664693i	−0.999320	+	0.0368782i	$0.988259\pi$
$822$		0			0
$823$	−38.0400	−	9.01565i	−1.32599	−	0.314266i	−0.494198	−	0.869350i	$-0.664538\pi$
$823$	−38.0400	−	9.01565i	−1.32599	−	0.314266i	−0.831794	+	0.555084i	$0.812686\pi$
$824$	−0.965972	−	3.22657i	−0.0336512	−	0.112403i
$825$		0			0
$826$	−4.73337	−	0.553251i	−0.164695	−	0.0192501i
$827$	5.22465	−	29.6305i	0.181679	−	1.03035i	−0.748470	−	0.663169i	$-0.769211\pi$
$827$	5.22465	−	29.6305i	0.181679	−	1.03035i	0.930149	−	0.367183i	$-0.119678\pi$
$828$		0			0
$829$	−4.90492	−	27.8172i	−0.170355	−	0.966132i	−0.943370	−	0.331743i	$-0.892363\pi$
$829$	−4.90492	−	27.8172i	−0.170355	−	0.966132i	0.773015	−	0.634388i	$-0.218748\pi$
$830$	0.0680053	+	1.16761i	0.00236050	+	0.0405282i
$831$		0			0
$832$	6.26513	−	14.5242i	0.217204	−	0.503536i
$833$	−24.7050	+	12.4073i	−0.855976	+	0.429887i
$834$		0			0
$835$	2.67116	−	0.633076i	0.0924392	−	0.0219085i
$836$	−1.02750	−	1.77968i	−0.0355368	−	0.0615515i
$837$		0			0
$838$	−21.6113	+	37.4318i	−0.746548	+	1.29306i
$839$	−5.67459	+	18.9545i	−0.195909	+	0.654380i	0.802429	+	0.596747i	$0.203541\pi$
$839$	−5.67459	+	18.9545i	−0.195909	+	0.654380i	−0.998338	+	0.0576331i	$0.981645\pi$
$840$		0			0
$841$	24.1863	+	15.9076i	0.834010	+	0.548537i
$842$	−0.422458	−	0.567459i	−0.0145589	−	0.0195559i
$843$		0			0
$844$	−1.74212	+	1.14581i	−0.0599662	+	0.0394404i
$845$	−34.0490	−	12.3928i	−1.17132	−	0.426326i
$846$		0			0
$847$	2.67949	−	0.975255i	0.0920684	−	0.0335102i
$848$	−13.4314	+	18.0415i	−0.461235	+	0.619547i
$849$		0			0
$850$	−62.4394	+	66.1819i	−2.14165	+	2.27002i
$851$	−0.481713	+	0.510586i	−0.0165129	+	0.0175027i
$852$		0			0
$853$	27.1775	−	36.5057i	0.930538	−	1.24993i	−0.0375433	−	0.999295i	$-0.511953\pi$
$853$	27.1775	−	36.5057i	0.930538	−	1.24993i	0.968082	−	0.250635i	$-0.0806394\pi$
$854$	−28.6657	+	10.4335i	−0.980921	+	0.357026i
$855$		0			0
$856$	−30.3173	−	11.0346i	−1.03623	−	0.377155i
$857$	−25.4122	+	16.7139i	−0.868066	+	0.570936i	−0.903573	−	0.428434i	$-0.859066\pi$
$857$	−25.4122	+	16.7139i	−0.868066	+	0.570936i	0.0355076	+	0.999369i	$0.488695\pi$
$858$		0			0
$859$	16.2513	+	21.8293i	0.554488	+	0.744807i	0.987679	−	0.156496i	$-0.0500197\pi$
$859$	16.2513	+	21.8293i	0.554488	+	0.744807i	−0.433191	+	0.901302i	$0.642612\pi$
$860$	1.40428	+	0.923611i	0.0478856	+	0.0314949i
$861$		0			0
$862$	−4.43847	+	14.8255i	−0.151175	+	0.504960i
$863$	5.22187	−	9.04454i	0.177754	−	0.307880i	−0.763357	−	0.645977i	$-0.776450\pi$
$863$	5.22187	−	9.04454i	0.177754	−	0.307880i	0.941111	+	0.338098i	$0.109783\pi$
$864$		0			0
$865$	4.17913	+	7.23847i	0.142095	+	0.246115i
$866$	−9.56030	+	2.26583i	−0.324872	+	0.0769962i
$867$		0			0
$868$	0.835491	−	0.419599i	0.0283584	−	0.0142421i
$869$	3.17787	−	7.36712i	0.107802	−	0.249912i
$870$		0			0
$871$	0.689192	+	11.8330i	0.0233524	+	0.400945i
$872$	−7.69871	−	43.6615i	−0.260711	−	1.47857i
$873$		0			0
$874$	−2.23207	+	12.6587i	−0.0755008	+	0.428186i
$875$	29.8629	+	3.49047i	1.00955	+	0.117999i
$876$		0			0
$877$	11.9386	+	39.8779i	0.403140	+	1.34658i	0.883057	+	0.469266i	$0.155481\pi$
$877$	11.9386	+	39.8779i	0.403140	+	1.34658i	−0.479917	+	0.877314i	$0.659333\pi$
$878$	−2.42803	−	0.575453i	−0.0819419	−	0.0194206i
$879$		0			0
$880$	−17.1354	−	39.7243i	−0.577634	−	1.33911i
$881$	35.1204	+	29.4695i	1.18324	+	0.992854i	0.999952	+	0.00979405i	$0.00311759\pi$
$881$	35.1204	+	29.4695i	1.18324	+	0.992854i	0.183285	+	0.983060i	$0.441327\pi$
$882$		0			0
$883$	4.08407	−	3.42694i	0.137440	−	0.115326i	−0.571476	−	0.820619i	$-0.693629\pi$
$883$	4.08407	−	3.42694i	0.137440	−	0.115326i	0.708916	+	0.705293i	$0.249185\pi$
$884$	−1.58813	−	0.797587i	−0.0534145	−	0.0268257i
$885$		0			0
$886$	21.4393	−	2.50589i	0.720266	−	0.0841870i
$887$	2.13539	−	36.6632i	0.0716993	−	1.23103i	−0.750128	−	0.661292i	$-0.770008\pi$
$887$	2.13539	−	36.6632i	0.0716993	−	1.23103i	0.821827	−	0.569737i	$-0.192955\pi$
$888$		0			0
$889$	13.5766	+	14.3904i	0.455346	+	0.482638i
$890$	37.0288			1.24121
$891$		0			0
$892$	1.95145			0.0653393
$893$	5.92781	+	6.28311i	0.198367	+	0.210256i
$894$		0			0
$895$	−5.62605	+	96.5955i	−0.188058	+	3.22883i
$896$	−17.3970	+	2.03342i	−0.581194	+	0.0679318i
$897$		0			0
$898$	11.8427	+	5.94764i	0.395197	+	0.198475i
$899$	−0.683562	+	0.573576i	−0.0227981	+	0.0191298i
$900$		0			0
$901$	32.5216	+	27.2888i	1.08345	+	0.909122i
$902$	7.16737	+	16.6158i	0.238647	+	0.553247i
$903$		0			0
$904$	6.01736	+	1.42614i	0.200135	+	0.0474327i
$905$	13.1747	+	44.0065i	0.437941	+	1.46283i
$906$		0			0
$907$	−45.7598	−	5.34855i	−1.51943	−	0.177596i	−0.684932	−	0.728607i	$-0.740168\pi$
$907$	−45.7598	−	5.34855i	−1.51943	−	0.177596i	−0.834498	+	0.551012i	$0.814242\pi$
$908$	−0.264678	+	1.50106i	−0.00878364	+	0.0498145i
$909$		0			0
$910$	−2.94815	−	16.7198i	−0.0977304	−	0.554257i
$911$	−1.49219	−	25.6200i	−0.0494385	−	0.848827i	−0.928319	−	0.371785i	$-0.878746\pi$
$911$	−1.49219	−	25.6200i	−0.0494385	−	0.848827i	0.878880	−	0.477042i	$-0.158291\pi$
$912$		0			0
$913$	−0.272555	+	0.631853i	−0.00902025	+	0.0209113i
$914$	3.13512	−	1.57452i	0.103701	−	0.0520804i
$915$		0			0
$916$	−1.26891	+	0.300738i	−0.0419261	+	0.00993666i
$917$	9.46217	+	16.3890i	0.312468	+	0.541211i
$918$		0			0
$919$	−4.49268	+	7.78154i	−0.148200	+	0.256689i	−0.930562	−	0.366134i	$-0.880681\pi$
$919$	−4.49268	+	7.78154i	−0.148200	+	0.256689i	0.782362	+	0.622823i	$0.214015\pi$
$920$	6.07029	−	20.2762i	0.200132	−	0.668486i
$921$		0			0
$922$	−3.69877	−	2.43272i	−0.121812	−	0.0801173i
$923$	−15.5702	−	20.9144i	−0.512500	−	0.688407i
$924$		0			0
$925$	2.93006	−	1.92713i	0.0963399	−	0.0633637i
$926$	−12.4541	−	4.53293i	−0.409268	−	0.148961i
$927$		0			0
$928$	−0.163291	+	0.0594331i	−0.00536029	+	0.00195099i
$929$	17.5007	−	23.5075i	0.574179	−	0.771256i	−0.416255	−	0.909248i	$-0.636658\pi$
$929$	17.5007	−	23.5075i	0.574179	−	0.771256i	0.990433	+	0.137992i	$0.0440649\pi$
$930$		0			0
$931$	13.3901	−	14.1926i	0.438842	−	0.465145i
$932$	1.63560	−	1.73364i	0.0535759	−	0.0567872i
$933$		0			0
$934$	2.58533	−	3.47270i	0.0845947	−	0.113630i
$935$	−76.7333	+	27.9286i	−2.50945	+	0.913364i
$936$		0			0
$937$	31.9986	+	11.6465i	1.04535	+	0.380476i	0.806905	−	0.590681i	$-0.201141\pi$
$937$	31.9986	+	11.6465i	1.04535	+	0.380476i	0.238443	+	0.971157i	$0.423363\pi$
$938$	12.6440	−	8.31607i	0.412840	−	0.271529i
$939$		0			0
$940$	−0.540251	−	0.725683i	−0.0176210	−	0.0236692i
$941$	−22.9598	−	15.1009i	−0.748467	−	0.492274i	0.117068	−	0.993124i	$-0.462651\pi$
$941$	−22.9598	−	15.1009i	−0.748467	−	0.492274i	−0.865534	+	0.500850i	$0.833021\pi$
$942$		0			0
$943$	−2.36580	+	7.90233i	−0.0770411	+	0.257335i
$944$	3.70607	−	6.41910i	0.120622	−	0.208924i
$945$		0			0
$946$	−6.78473	−	11.7515i	−0.220591	−	0.382074i
$947$	−17.1437	+	4.06313i	−0.557096	+	0.132034i	−0.499513	−	0.866307i	$-0.666488\pi$
$947$	−17.1437	+	4.06313i	−0.557096	+	0.132034i	−0.0575831	+	0.998341i	$0.518339\pi$
$948$		0			0
$949$	5.28875	−	2.65611i	0.171680	−	0.0862210i
$950$	25.4358	−	58.9667i	0.825245	−	1.91313i
$951$		0			0
$952$	2.07420	+	35.6127i	0.0672253	+	1.15421i
$953$	1.89789	+	10.7635i	0.0614788	+	0.348663i	0.999994	+	0.00342592i	$0.00109051\pi$
$953$	1.89789	+	10.7635i	0.0614788	+	0.348663i	−0.938515	+	0.345237i	$0.887798\pi$
$954$		0			0
$955$	9.67864	−	54.8903i	0.313194	−	1.77621i
$956$	3.68446	+	0.430652i	0.119164	+	0.0139283i
$957$		0			0
$958$	10.8444	+	36.2227i	0.350365	+	1.17030i
$959$	−21.5348	−	5.10385i	−0.695396	−	0.164812i
$960$		0			0
$961$	−6.13195	−	14.2154i	−0.197805	−	0.458563i
$962$	−0.720018	−	0.604167i	−0.0232143	−	0.0194791i
$963$		0			0
$964$	−0.541280	+	0.454188i	−0.0174335	+	0.0146284i
$965$	72.3181	+	36.3195i	2.32800	+	1.16917i
$966$		0			0
$967$	−30.1385	+	3.52268i	−0.969188	+	0.113282i	−0.585932	−	0.810360i	$-0.699271\pi$
$967$	−30.1385	+	3.52268i	−0.969188	+	0.113282i	−0.383256	+	0.923642i	$0.625197\pi$
$968$	−0.276759	+	4.75176i	−0.00889536	+	0.152728i
$969$		0			0
$970$	55.6167	+	58.9503i	1.78574	+	1.89278i
$971$	33.6807			1.08087			0.540433	−	0.841387i	$-0.318261\pi$
$971$	33.6807			1.08087			0.540433	+	0.841387i	$0.318261\pi$
$972$		0			0
$973$	−16.9666			−0.543925
$974$	−9.82761	−	10.4167i	−0.314897	−	0.333771i
$975$		0			0
$976$	2.75877	−	47.3662i	0.0883060	−	1.51616i
$977$	−6.11559	+	0.714810i	−0.195655	+	0.0228688i	−0.213356	−	0.976975i	$-0.568439\pi$
$977$	−6.11559	+	0.714810i	−0.195655	+	0.0228688i	0.0177008	+	0.999843i	$0.494365\pi$
$978$		0			0
$979$	19.4688	+	9.77759i	0.622225	+	0.312493i
$980$	−1.56548	+	1.31359i	−0.0500075	+	0.0419612i
$981$		0			0
$982$	−6.19967	−	5.20214i	−0.197839	−	0.166007i
$983$	−4.37124	−	10.1337i	−0.139421	−	0.323214i	0.834172	−	0.551504i	$-0.185946\pi$
$983$	−4.37124	−	10.1337i	−0.139421	−	0.323214i	−0.973593	+	0.228290i	$0.926687\pi$
$984$		0			0
$985$	67.0107	+	15.8818i	2.13514	+	0.506037i
$986$	−0.621105	−	2.07464i	−0.0197800	−	0.0660699i
$987$		0			0
$988$	1.24583	+	0.145617i	0.0396352	+	0.00463269i
$989$	1.07411	−	6.09160i	0.0341548	−	0.193702i
$990$		0			0
$991$	1.88340	+	10.6813i	0.0598283	+	0.339303i	0.999999	−	0.00140066i	$-0.000445845\pi$
$991$	1.88340	+	10.6813i	0.0598283	+	0.339303i	−0.940171	+	0.340704i	$0.889335\pi$
$992$	0.175716	+	3.01693i	0.00557899	+	0.0957875i
$993$		0			0
$994$	−13.1857	+	30.5678i	−0.418224	+	0.969551i
$995$	83.0795	−	41.7241i	2.63380	−	1.32274i
$996$		0			0
$997$	−18.8733	+	4.47306i	−0.597724	+	0.141663i	−0.518331	−	0.855180i	$-0.673446\pi$
$997$	−18.8733	+	4.47306i	−0.597724	+	0.141663i	−0.0793933	+	0.996843i	$0.525298\pi$
$998$	26.0216	+	45.0707i	0.823698	+	1.42669i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.109.2		144
3.2	odd	2		729.2.g.a.109.7		144
9.2	odd	6		729.2.g.b.352.7		144
9.4	even	3		81.2.g.a.76.7	yes	144
9.5	odd	6		243.2.g.a.118.2		144
9.7	even	3		729.2.g.c.352.2		144
81.11	odd	54		729.2.g.a.622.7		144
81.16	even	27		729.2.g.c.379.2		144
81.31	even	27		6561.2.a.c.1.53		72
81.38	odd	54		243.2.g.a.208.2		144
81.43	even	27		81.2.g.a.16.7	✓	144
81.50	odd	54		6561.2.a.d.1.20		72
81.65	odd	54		729.2.g.b.379.7		144
81.70	even	27	inner	729.2.g.d.622.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.7	✓	144	81.43	even	27
81.2.g.a.76.7	yes	144	9.4	even	3
243.2.g.a.118.2		144	9.5	odd	6
243.2.g.a.208.2		144	81.38	odd	54
729.2.g.a.109.7		144	3.2	odd	2
729.2.g.a.622.7		144	81.11	odd	54
729.2.g.b.352.7		144	9.2	odd	6
729.2.g.b.379.7		144	81.65	odd	54
729.2.g.c.352.2		144	9.7	even	3
729.2.g.c.379.2		144	81.16	even	27
729.2.g.d.109.2		144	1.1	even	1	trivial
729.2.g.d.622.2		144	81.70	even	27	inner
6561.2.a.c.1.53		72	81.31	even	27
6561.2.a.d.1.20		72	81.50	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.936951 - 0.993110i) q^{2} +(0.00789919 - 0.135624i) q^{4} +(3.78436 - 0.442328i) q^{5} +(1.56116 + 0.784043i) q^{7} +(-2.23391 + 1.87447i) q^{8} +O(q^{10})\)	\(q+(-0.936951 - 0.993110i) q^{2} +(0.00789919 - 0.135624i) q^{4} +(3.78436 - 0.442328i) q^{5} +(1.56116 + 0.784043i) q^{7} +(-2.23391 + 1.87447i) q^{8} +(-3.98504 - 3.34385i) q^{10} +(-1.21227 - 2.81037i) q^{11} +(1.81780 + 0.430827i) q^{13} +(-0.684088 - 2.28501i) q^{14} +(3.68475 + 0.430686i) q^{16} +(1.21594 - 6.89593i) q^{17} +(0.858206 + 4.86713i) q^{19} +(-0.0300968 - 0.516743i) q^{20} +(-1.65516 + 3.83710i) q^{22} +(-1.70229 + 0.854924i) q^{23} +(9.26048 - 2.19477i) q^{25} +(-1.27533 - 2.20894i) q^{26} +(0.118667 - 0.205537i) q^{28} +(-0.0649657 + 0.217001i) q^{29} +(3.29127 + 2.16470i) q^{31} +(0.458106 + 0.615343i) q^{32} +(-7.98769 + 5.25359i) q^{34} +(6.25478 + 2.27656i) q^{35} +(0.346276 - 0.126034i) q^{37} +(4.02950 - 5.41256i) q^{38} +(-7.62478 + 8.08179i) q^{40} +(2.97164 - 3.14975i) q^{41} +(-1.93907 + 2.60463i) q^{43} +(-0.390729 + 0.142214i) q^{44} +(2.44400 + 0.889543i) q^{46} +(1.46028 - 0.960441i) q^{47} +(-2.35762 - 3.16683i) q^{49} +(-10.8563 - 7.14028i) q^{50} +(0.0727895 - 0.243134i) q^{52} +(-3.03142 + 5.25057i) q^{53} +(-5.83078 - 10.0992i) q^{55} +(-4.95715 + 1.17487i) q^{56} +(0.276375 - 0.138801i) q^{58} +(0.791355 - 1.83457i) q^{59} +(-0.743636 - 12.7677i) q^{61} +(-0.933972 - 5.29682i) q^{62} +(1.47029 - 8.33845i) q^{64} +(7.06978 + 0.826338i) q^{65} +(1.81970 + 6.07822i) q^{67} +(-0.925647 - 0.219382i) q^{68} +(-3.59956 - 8.34471i) q^{70} +(-10.6917 - 8.97137i) q^{71} +(2.42680 - 2.03633i) q^{73} +(-0.449609 - 0.225802i) q^{74} +(0.666878 - 0.0779468i) q^{76} +(0.310898 - 5.33790i) q^{77} +(1.79892 + 1.90674i) q^{79} +14.1349 q^{80} -5.91234 q^{82} +(-0.154287 - 0.163535i) q^{83} +(1.55128 - 26.6345i) q^{85} +(4.40350 - 0.514695i) q^{86} +(7.97607 + 4.00573i) q^{88} +(-5.45275 + 4.57540i) q^{89} +(2.50009 + 2.09782i) q^{91} +(0.102501 + 0.237625i) q^{92} +(-2.32203 - 0.550332i) q^{94} +(5.40063 + 18.0393i) q^{95} +(-15.4740 - 1.80865i) q^{97} +(-0.936040 + 5.30854i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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