LMFDB - Embedded newform 153.2.s.a.113.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			113.6
Character	$\chi$	$=$	153.113
Dual form			153.2.s.a.65.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06433 + 0.140121i) q^{2} +(-1.69215 + 0.369645i) q^{3} +(-0.818692 + 0.219368i) q^{4} +(-0.828848 - 1.68074i) q^{5} +(1.74920 - 0.630530i) q^{6} +(2.57290 + 1.26881i) q^{7} +(2.82421 - 1.16983i) q^{8} +(2.72672 - 1.25099i) q^{9} +O(q^{10})$	\(q+(-1.06433 + 0.140121i) q^{2} +(-1.69215 + 0.369645i) q^{3} +(-0.818692 + 0.219368i) q^{4} +(-0.828848 - 1.68074i) q^{5} +(1.74920 - 0.630530i) q^{6} +(2.57290 + 1.26881i) q^{7} +(2.82421 - 1.16983i) q^{8} +(2.72672 - 1.25099i) q^{9} +(1.11767 + 1.67272i) q^{10} +(2.97662 - 1.01042i) q^{11} +(1.30426 - 0.673829i) q^{12} +(0.326499 + 1.21851i) q^{13} +(-2.91620 - 0.989916i) q^{14} +(2.02381 + 2.53768i) q^{15} +(-1.37393 + 0.793237i) q^{16} +(-3.15306 - 2.65672i) q^{17} +(-2.72684 + 1.71353i) q^{18} +(3.20325 + 1.32683i) q^{19} +(1.04727 + 1.19418i) q^{20} +(-4.82274 - 1.19596i) q^{21} +(-3.02651 + 1.49251i) q^{22} +(4.17115 - 4.75629i) q^{23} +(-4.34656 + 3.02347i) q^{24} +(0.905918 - 1.18061i) q^{25} +(-0.518241 - 1.25114i) q^{26} +(-4.15160 + 3.12478i) q^{27} +(-2.38475 - 0.474357i) q^{28} +(-0.202920 + 3.09596i) q^{29} +(-2.50958 - 2.41734i) q^{30} +(3.39423 - 9.99909i) q^{31} +(-3.49925 + 2.68507i) q^{32} +(-4.66337 + 2.81008i) q^{33} +(3.72816 + 2.38581i) q^{34} -5.37603i q^{35} +(-1.95792 + 1.62233i) q^{36} +(2.17970 + 10.9581i) q^{37} +(-3.59522 - 0.963337i) q^{38} +(-1.00290 - 1.94121i) q^{39} +(-4.30701 - 3.77715i) q^{40} +(2.20154 - 0.144297i) q^{41} +(5.30055 + 0.597125i) q^{42} +(0.443342 + 0.340188i) q^{43} +(-2.21528 + 1.48020i) q^{44} +(-4.36262 - 3.54603i) q^{45} +(-3.77301 + 5.64671i) q^{46} +(-0.911896 + 3.40324i) q^{47} +(2.03167 - 1.85014i) q^{48} +(0.748601 + 0.975596i) q^{49} +(-0.798764 + 1.38350i) q^{50} +(6.31750 + 3.33005i) q^{51} +(-0.534604 - 0.925961i) q^{52} +(-2.19448 + 5.29795i) q^{53} +(3.98081 - 3.90751i) q^{54} +(-4.16542 - 4.16542i) q^{55} +(8.75070 + 0.573551i) q^{56} +(-5.91083 - 1.06113i) q^{57} +(-0.217837 - 3.32354i) q^{58} +(0.121049 - 0.919458i) q^{59} +(-2.21356 - 1.63362i) q^{60} +(5.16405 - 10.4717i) q^{61} +(-2.21149 + 11.1179i) q^{62} +(8.60287 + 0.241039i) q^{63} +(5.59173 - 5.59173i) q^{64} +(1.77738 - 1.55872i) q^{65} +(4.56960 - 3.64428i) q^{66} +(-0.933364 - 0.538878i) q^{67} +(3.16419 + 1.48336i) q^{68} +(-5.30006 + 9.59018i) q^{69} +(0.753296 + 5.72185i) q^{70} +(6.90345 - 1.37318i) q^{71} +(6.23740 - 6.72285i) q^{72} +(-7.27098 - 4.85831i) q^{73} +(-3.85538 - 11.3576i) q^{74} +(-1.09654 + 2.33264i) q^{75} +(-2.91354 - 0.383575i) q^{76} +(8.94058 + 1.17705i) q^{77} +(1.33942 + 1.92556i) q^{78} +(-0.886594 - 2.61182i) q^{79} +(2.47200 + 1.65174i) q^{80} +(5.87006 - 6.82220i) q^{81} +(-2.32295 + 0.462063i) q^{82} +(1.28987 + 9.79756i) q^{83} +(4.21070 - 0.0788306i) q^{84} +(-1.85184 + 7.50149i) q^{85} +(-0.519529 - 0.299950i) q^{86} +(-0.801035 - 5.31382i) q^{87} +(7.22457 - 6.33577i) q^{88} +(-8.37709 + 8.37709i) q^{89} +(5.14013 + 3.16284i) q^{90} +(-0.706014 + 3.54937i) q^{91} +(-2.37151 + 4.80895i) q^{92} +(-2.04743 + 18.1746i) q^{93} +(0.493689 - 3.74994i) q^{94} +(-0.424955 - 6.48356i) q^{95} +(4.92872 - 5.83701i) q^{96} +(1.70996 + 0.112076i) q^{97} +(-0.933458 - 0.933458i) q^{98} +(6.85238 - 6.47886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.06433	+	0.140121i	−0.752593	+	0.0990808i	−0.497056	−	0.867718i	$-0.665586\pi$
$2$	−1.06433	+	0.140121i	−0.752593	+	0.0990808i	−0.255537	+	0.966799i	$0.582252\pi$
$3$	−1.69215	+	0.369645i	−0.976962	+	0.213415i
$3$	−1.69215	+	0.369645i	−0.976962	+	0.213415i
$4$	−0.818692	+	0.219368i	−0.409346	+	0.109684i
$5$	−0.828848	−	1.68074i	−0.370672	−	0.751649i	0.628996	−	0.777408i	$-0.283466\pi$
$5$	−0.828848	−	1.68074i	−0.370672	−	0.751649i	−0.999668	+	0.0257598i	$0.991799\pi$
$6$	1.74920	−	0.630530i	0.714109	−	0.257413i
$7$	2.57290	+	1.26881i	0.972465	+	0.479567i	0.857882	−	0.513847i	$-0.171780\pi$
$7$	2.57290	+	1.26881i	0.972465	+	0.479567i	0.114583	+	0.993414i	$0.463447\pi$
$8$	2.82421	−	1.16983i	0.998509	−	0.413596i
$9$	2.72672	−	1.25099i	0.908908	−	0.416996i
$10$	1.11767	+	1.67272i	0.353439	+	0.528959i
$11$	2.97662	−	1.01042i	0.897483	−	0.304655i	0.165687	−	0.986178i	$-0.447016\pi$
$11$	2.97662	−	1.01042i	0.897483	−	0.304655i	0.731796	+	0.681524i	$0.238682\pi$
$12$	1.30426	−	0.673829i	0.376507	−	0.194518i
$13$	0.326499	+	1.21851i	0.0905545	+	0.337954i	0.996308	−	0.0858510i	$-0.0273609\pi$
$13$	0.326499	+	1.21851i	0.0905545	+	0.337954i	−0.905754	+	0.423805i	$0.860694\pi$
$14$	−2.91620	−	0.989916i	−0.779387	−	0.264566i
$15$	2.02381	+	2.53768i	0.522545	+	0.655225i
$16$	−1.37393	+	0.793237i	−0.343482	+	0.198309i
$17$	−3.15306	−	2.65672i	−0.764731	−	0.644350i
$17$	−3.15306	−	2.65672i	−0.764731	−	0.644350i
$18$	−2.72684	+	1.71353i	−0.642722	+	0.403884i
$19$	3.20325	+	1.32683i	0.734876	+	0.304396i	0.718554	−	0.695471i	$-0.244804\pi$
$19$	3.20325	+	1.32683i	0.734876	+	0.304396i	0.0163219	+	0.999867i	$0.494804\pi$
$20$	1.04727	+	1.19418i	0.234177	+	0.267028i
$21$	−4.82274	−	1.19596i	−1.05241	−	0.260980i
$22$	−3.02651	+	1.49251i	−0.645255	+	0.318204i
$23$	4.17115	−	4.75629i	0.869745	−	0.991754i	−0.130255	−	0.991481i	$-0.541580\pi$
$23$	4.17115	−	4.75629i	0.869745	−	0.991754i	1.00000		0.000273557i	$-8.70760e-5\pi$
$24$	−4.34656	+	3.02347i	−0.887237	+	0.617164i
$25$	0.905918	−	1.18061i	0.181184	−	0.236123i
$26$	−0.518241	−	1.25114i	−0.101635	−	0.245370i
$27$	−4.15160	+	3.12478i	−0.798976	+	0.601364i
$28$	−2.38475	−	0.474357i	−0.450676	−	0.0896450i
$29$	−0.202920	+	3.09596i	−0.0376812	+	0.574905i	0.936719	+	0.350083i	$0.113847\pi$
$29$	−0.202920	+	3.09596i	−0.0376812	+	0.574905i	−0.974400	+	0.224822i	$0.927820\pi$
$30$	−2.50958	−	2.41734i	−0.458184	−	0.441344i
$31$	3.39423	−	9.99909i	0.609622	−	1.79589i	0.00419222	−	0.999991i	$-0.498666\pi$
$31$	3.39423	−	9.99909i	0.609622	−	1.79589i	0.605430	−	0.795898i	$-0.293001\pi$
$32$	−3.49925	+	2.68507i	−0.618586	+	0.474657i
$33$	−4.66337	+	2.81008i	−0.811789	+	0.489172i
$34$	3.72816	+	2.38581i	0.639374	+	0.409164i
$35$		−	5.37603i		−	0.908714i
$36$	−1.95792	+	1.62233i	−0.326320	+	0.270388i
$37$	2.17970	+	10.9581i	0.358340	+	1.80150i	0.567230	+	0.823559i	$0.308015\pi$
$37$	2.17970	+	10.9581i	0.358340	+	1.80150i	−0.208890	+	0.977939i	$0.566985\pi$
$38$	−3.59522	−	0.963337i	−0.583222	−	0.156274i
$39$	−1.00290	−	1.94121i	−0.160593	−	0.310842i
$40$	−4.30701	−	3.77715i	−0.680998	−	0.597219i
$41$	2.20154	−	0.144297i	0.343824	−	0.0225354i	0.107487	−	0.994207i	$-0.465720\pi$
$41$	2.20154	−	0.144297i	0.343824	−	0.0225354i	0.236337	+	0.971671i	$0.424053\pi$
$42$	5.30055	+	0.597125i	0.817893	+	0.0921384i
$43$	0.443342	+	0.340188i	0.0676090	+	0.0518782i	0.642013	−	0.766694i	$-0.278099\pi$
$43$	0.443342	+	0.340188i	0.0676090	+	0.0518782i	−0.574404	+	0.818572i	$0.694766\pi$
$44$	−2.21528	+	1.48020i	−0.333966	+	0.223149i
$45$	−4.36262	−	3.54603i	−0.650341	−	0.528611i
$46$	−3.77301	+	5.64671i	−0.556300	+	0.832562i
$47$	−0.911896	+	3.40324i	−0.133014	+	0.496414i	−0.999998	−	0.00192122i	$-0.999388\pi$
$47$	−0.911896	+	3.40324i	−0.133014	+	0.496414i	0.866984	+	0.498335i	$0.166055\pi$
$48$	2.03167	−	1.85014i	0.293247	−	0.267045i
$49$	0.748601	+	0.975596i	0.106943	+	0.139371i
$50$	−0.798764	+	1.38350i	−0.112962	+	0.195656i
$51$	6.31750	+	3.33005i	0.884626	+	0.466301i
$52$	−0.534604	−	0.925961i	−0.0741362	−	0.128408i
$53$	−2.19448	+	5.29795i	−0.301435	+	0.727729i	0.698491	+	0.715618i	$0.253855\pi$
$53$	−2.19448	+	5.29795i	−0.301435	+	0.727729i	−0.999927	+	0.0121106i	$0.996145\pi$
$54$	3.98081	−	3.90751i	0.541720	−	0.531745i
$55$	−4.16542	−	4.16542i	−0.561665	−	0.561665i
$56$	8.75070	+	0.573551i	1.16936	+	0.0766440i
$57$	−5.91083	−	1.06113i	−0.782908	−	0.140549i
$58$	−0.217837	−	3.32354i	−0.0286033	−	0.436403i
$59$	0.121049	−	0.919458i	0.0157592	−	0.119703i	−0.981757	−	0.190140i	$-0.939106\pi$
$59$	0.121049	−	0.919458i	0.0157592	−	0.119703i	0.997516	+	0.0704365i	$0.0224392\pi$
$60$	−2.21356	−	1.63362i	−0.285770	−	0.210899i
$61$	5.16405	−	10.4717i	0.661189	−	1.34076i	−0.265201	−	0.964193i	$-0.585438\pi$
$61$	5.16405	−	10.4717i	0.661189	−	1.34076i	0.926390	−	0.376566i	$-0.122895\pi$
$62$	−2.21149	+	11.1179i	−0.280860	+	1.41198i
$63$	8.60287	+	0.241039i	1.08386	+	0.0303681i
$64$	5.59173	−	5.59173i	0.698966	−	0.698966i
$65$	1.77738	−	1.55872i	0.220457	−	0.193335i
$66$	4.56960	−	3.64428i	0.562479	−	0.448580i
$67$	−0.933364	−	0.538878i	−0.114029	−	0.0658344i	0.441901	−	0.897064i	$-0.354304\pi$
$67$	−0.933364	−	0.538878i	−0.114029	−	0.0658344i	−0.555930	+	0.831229i	$0.687638\pi$
$68$	3.16419	+	1.48336i	0.383714	+	0.179884i
$69$	−5.30006	+	9.59018i	−0.638053	+	1.15452i
$70$	0.753296	+	5.72185i	0.0900361	+	0.683892i
$71$	6.90345	−	1.37318i	0.819288	−	0.162967i	0.232385	−	0.972624i	$-0.425347\pi$
$71$	6.90345	−	1.37318i	0.819288	−	0.162967i	0.586903	+	0.809657i	$0.300347\pi$
$72$	6.23740	−	6.72285i	0.735085	−	0.792295i
$73$	−7.27098	−	4.85831i	−0.851004	−	0.568623i	0.0518086	−	0.998657i	$-0.483501\pi$
$73$	−7.27098	−	4.85831i	−0.851004	−	0.568623i	−0.902812	+	0.430034i	$0.858501\pi$
$74$	−3.85538	−	11.3576i	−0.448178	−	1.32029i
$75$	−1.09654	+	2.33264i	−0.126617	+	0.269350i
$76$	−2.91354	−	0.383575i	−0.334206	−	0.0439991i
$77$	8.94058	+	1.17705i	1.01887	+	0.134137i
$78$	1.33942	+	1.92556i	0.151659	+	0.218026i
$79$	−0.886594	−	2.61182i	−0.0997496	−	0.293853i	0.885587	−	0.464473i	$-0.153756\pi$
$79$	−0.886594	−	2.61182i	−0.0997496	−	0.293853i	−0.985337	+	0.170620i	$0.945423\pi$
$80$	2.47200	+	1.65174i	0.276378	+	0.184670i
$81$	5.87006	−	6.82220i	0.652229	−	0.758022i
$82$	−2.32295	+	0.462063i	−0.256526	+	0.0510263i
$83$	1.28987	+	9.79756i	0.141582	+	1.07542i	0.903755	+	0.428049i	$0.140799\pi$
$83$	1.28987	+	9.79756i	0.141582	+	1.07542i	−0.762173	+	0.647373i	$0.775868\pi$
$84$	4.21070	−	0.0788306i	0.459425	−	0.00860113i
$85$	−1.85184	+	7.50149i	−0.200861	+	0.813651i
$86$	−0.519529	−	0.299950i	−0.0560222	−	0.0323444i
$87$	−0.801035	−	5.31382i	−0.0858800	−	0.569701i
$88$	7.22457	−	6.33577i	0.770141	−	0.675396i
$89$	−8.37709	+	8.37709i	−0.887969	+	0.887969i	−0.994328	−	0.106359i	$-0.966081\pi$
$89$	−8.37709	+	8.37709i	−0.887969	+	0.887969i	0.106359	+	0.994328i	$0.466081\pi$
$90$	5.14013	+	3.16284i	0.541818	+	0.333393i
$91$	−0.706014	+	3.54937i	−0.0740104	+	0.372075i
$92$	−2.37151	+	4.80895i	−0.247247	+	0.501368i
$93$	−2.04743	+	18.1746i	−0.212308	+	1.88462i
$94$	0.493689	−	3.74994i	0.0509202	−	0.386777i
$95$	−0.424955	−	6.48356i	−0.0435995	−	0.665199i
$96$	4.92872	−	5.83701i	0.503035	−	0.595737i
$97$	1.70996	+	0.112076i	0.173620	+	0.0113796i	0.151965	−	0.988386i	$-0.451440\pi$
$97$	1.70996	+	0.112076i	0.173620	+	0.0113796i	0.0216547	+	0.999766i	$0.493107\pi$
$98$	−0.933458	−	0.933458i	−0.0942935	−	0.0942935i
$99$	6.85238	−	6.47886i	0.688690	−	0.651150i
$100$	−0.482679	+	1.16529i	−0.0482679	+	0.116529i
$101$	−4.33753	−	7.51282i	−0.431600	−	0.747553i	0.565411	−	0.824809i	$-0.308717\pi$
$101$	−4.33753	−	7.51282i	−0.431600	−	0.747553i	−0.997011	+	0.0772560i	$0.975384\pi$
$102$	−7.19050	−	2.65905i	−0.711965	−	0.263285i
$103$	−4.37962	+	7.58572i	−0.431537	+	0.747443i	−0.997006	−	0.0773260i	$-0.975362\pi$
$103$	−4.37962	+	7.58572i	−0.431537	+	0.747443i	0.565469	+	0.824769i	$0.308695\pi$
$104$	2.34755	+	3.05938i	0.230196	+	0.299997i
$105$	1.98722	+	9.09703i	0.193933	+	0.887779i
$106$	1.59329	−	5.94625i	0.154754	−	0.577550i
$107$	3.96430	−	5.93299i	0.383243	−	0.573564i	−0.588826	−	0.808260i	$-0.700410\pi$
$107$	3.96430	−	5.93299i	0.383243	−	0.573564i	0.972069	+	0.234696i	$0.0754096\pi$
$108$	2.71341	−	3.46896i	0.261098	−	0.333801i
$109$	−2.53655	+	1.69487i	−0.242958	+	0.162339i	−0.671088	−	0.741378i	$-0.734173\pi$
$109$	−2.53655	+	1.69487i	−0.242958	+	0.162339i	0.428130	+	0.903717i	$0.359173\pi$
$110$	5.01704	+	3.84971i	0.478356	+	0.367055i
$111$	−7.73898	−	17.7370i	−0.734551	−	1.68352i
$112$	−4.54145	+	0.297662i	−0.429127	+	0.0281265i
$113$	−0.355037	−	0.311359i	−0.0333991	−	0.0292902i	0.642484	−	0.766299i	$-0.277904\pi$
$113$	−0.355037	−	0.311359i	−0.0333991	−	0.0292902i	−0.675883	+	0.737009i	$0.736237\pi$
$114$	6.43974	+	0.301152i	0.603137	+	0.0282054i
$115$	−11.4513	−	3.06837i	−1.06784	−	0.286127i
$116$	−0.513025	−	2.57915i	−0.0476331	−	0.239468i
$117$	2.41461	+	2.91410i	0.223231	+	0.269408i
$118$			0.995566i			0.0916492i
$119$	−4.74163	−	10.8361i	−0.434665	−	0.993348i
$120$	8.68430	+	4.79942i	0.792765	+	0.438125i
$121$	−0.887605	+	0.681083i	−0.0806913	+	0.0619166i
$122$	−4.02894	+	11.8689i	−0.364763	+	1.07456i
$123$	−3.67200	+	1.05796i	−0.331093	+	0.0953932i
$124$	−0.585353	+	8.93077i	−0.0525663	+	0.802006i
$125$	−11.9251	−	2.37205i	−1.06662	−	0.212163i
$126$	−9.19004	+	0.948901i	−0.818714	+	0.0845348i
$127$	−1.98315	−	4.78775i	−0.175976	−	0.424844i	0.811140	−	0.584853i	$-0.198848\pi$
$127$	−1.98315	−	4.78775i	−0.175976	−	0.424844i	−0.987116	+	0.160009i	$0.948848\pi$
$128$	0.202228	−	0.263548i	0.0178746	−	0.0232946i
$129$	−0.875949	−	0.411769i	−0.0771230	−	0.0362543i
$130$	−1.67330	+	1.90804i	−0.146758	+	0.167346i
$131$	−12.8394	+	6.33168i	−1.12178	+	0.553202i	−0.906016	−	0.423243i	$-0.860891\pi$
$131$	−12.8394	+	6.33168i	−1.12178	+	0.553202i	−0.215766	+	0.976445i	$0.569225\pi$
$132$	3.20143	−	3.32359i	0.278648	−	0.289281i
$133$	6.55814	+	7.47813i	0.568663	+	0.648436i
$134$	1.06891	+	0.442758i	0.0923401	+	0.0382485i
$135$	8.69297	+	4.38778i	0.748172	+	0.377640i
$136$	−12.0128	−	3.81461i	−1.03009	−	0.327100i
$137$	−7.52164	+	4.34262i	−0.642617	+	0.371015i	−0.785622	−	0.618707i	$-0.787657\pi$
$137$	−7.52164	+	4.34262i	−0.642617	+	0.371015i	0.143005	+	0.989722i	$0.454324\pi$
$138$	4.29721	−	10.9497i	0.365803	−	0.932104i
$139$	20.1552	+	6.84178i	1.70954	+	0.580312i	0.993093	−	0.117326i	$-0.0374323\pi$
$139$	20.1552	+	6.84178i	1.70954	+	0.580312i	0.716450	+	0.697638i	$0.245766\pi$
$140$	1.17933	+	4.40131i	0.0996714	+	0.371979i
$141$	0.285071	−	6.09587i	0.0240073	−	0.513365i
$142$	−7.15512	+	2.42884i	−0.600444	+	0.203823i
$143$	2.20307	+	3.29713i	0.184230	+	0.275720i
$144$	−2.75399	+	3.88171i	−0.229499	+	0.323476i
$145$	5.37168	−	2.22502i	0.446094	−	0.184778i
$146$	8.41946	+	4.15202i	0.696799	+	0.343623i
$147$	−1.62737	−	1.37413i	−0.134223	−	0.113337i
$148$	−4.18836	−	8.49315i	−0.344281	−	0.698132i
$149$	−14.5039	+	3.88631i	−1.18821	+	0.318379i	−0.798177	−	0.602423i	$-0.794202\pi$
$149$	−14.5039	+	3.88631i	−1.18821	+	0.318379i	−0.390030	+	0.920802i	$0.627535\pi$
$150$	0.840222	−	2.63634i	0.0686038	−	0.215257i
$151$	−10.3681	+	1.36499i	−0.843746	+	0.111081i	−0.539993	−	0.841669i	$-0.681573\pi$
$151$	−10.3681	+	1.36499i	−0.843746	+	0.111081i	−0.303753	+	0.952751i	$0.598240\pi$
$152$	10.5988			0.859677
$153$	−11.9211	−	3.29971i	−0.963761	−	0.266766i
$154$	−9.68064			−0.780088
$155$	−19.6192	+	2.58291i	−1.57585	+	0.207464i
$156$	1.24691	+	1.36925i	0.0998324	+	0.109628i
$157$	−23.7458	+	6.36268i	−1.89513	+	0.507797i	−0.897335	+	0.441350i	$0.854500\pi$
$157$	−23.7458	+	6.36268i	−1.89513	+	0.507797i	−0.997790	+	0.0664473i	$0.978834\pi$
$158$	1.30960	+	2.65560i	0.104186	+	0.211268i
$159$	1.75503	−	9.77609i	0.139183	−	0.775294i
$160$	7.41324	+	3.65580i	0.586068	+	0.289017i
$161$	16.7668	−	6.94504i	1.32141	−	0.547346i
$162$	−5.29173	+	8.08358i	−0.415757	+	0.635106i
$163$	4.54314	+	6.79929i	0.355846	+	0.532562i	0.965601	−	0.260029i	$-0.0837320\pi$
$163$	4.54314	+	6.79929i	0.355846	+	0.532562i	−0.609755	+	0.792590i	$0.708732\pi$
$164$	−1.77073	+	0.601083i	−0.138271	+	0.0469367i
$165$	8.58823	+	5.50878i	0.668593	+	0.428858i
$166$	−2.74570	−	10.2471i	−0.213107	−	0.795328i
$167$	7.66199	+	2.60089i	0.592902	+	0.201263i	0.601732	−	0.798698i	$-0.294477\pi$
$167$	7.66199	+	2.60089i	0.592902	+	0.201263i	−0.00883008	+	0.999961i	$0.502811\pi$
$168$	−15.0195	+	2.26412i	−1.15878	+	0.174681i
$169$	9.88017	−	5.70432i	0.760013	−	0.438794i
$170$	0.919849	−	8.24353i	0.0705492	−	0.632250i
$171$	10.3942	−	0.389328i	0.794867	−	0.0297727i
$172$	−0.437587	−	0.181255i	−0.0333657	−	0.0138205i
$173$	−15.2704	−	17.4126i	−1.16099	−	1.32385i	−0.937027	−	0.349256i	$-0.886434\pi$
$173$	−15.2704	−	17.4126i	−1.16099	−	1.32385i	−0.223962	−	0.974598i	$-0.571899\pi$
$174$	1.59714	+	5.54340i	0.121079	+	0.420244i
$175$	3.82882	−	1.88816i	0.289431	−	0.142732i
$176$	−3.28815	+	3.74941i	−0.247853	+	0.282623i
$177$	0.135040	+	1.60060i	0.0101503	+	0.120309i
$178$	7.74215	−	10.0898i	0.580299	−	0.756260i
$179$	5.56258	+	13.4292i	0.415767	+	1.00375i	0.983561	+	0.180579i	$0.0577970\pi$
$179$	5.56258	+	13.4292i	0.415767	+	1.00375i	−0.567794	+	0.823171i	$0.692203\pi$
$180$	4.34953	+	1.94609i	0.324195	+	0.145053i
$181$	23.1232	+	4.59949i	1.71873	+	0.341877i	0.953389	−	0.301745i	$-0.0975691\pi$
$181$	23.1232	+	4.59949i	1.71873	+	0.341877i	0.765344	+	0.643622i	$0.222569\pi$
$182$	0.254087	−	3.87662i	0.0188342	−	0.287354i
$183$	−4.86754	+	19.6285i	−0.359819	+	1.45098i
$184$	6.21618	−	18.3123i	0.458263	−	1.35000i
$185$	16.6110	−	12.7461i	1.22127	−	0.937111i
$186$	−0.367515	−	19.6306i	−0.0269475	−	1.43939i
$187$	−12.0699	−	4.72211i	−0.882637	−	0.345315i
$188$		−	2.98625i		−	0.217795i
$189$	−14.6464	+	2.77213i	−1.06537	+	0.201643i
$190$	1.36078	+	6.84109i	0.0987211	+	0.496305i
$191$	21.3121	+	5.71057i	1.54209	+	0.413202i	0.926941	−	0.375206i	$-0.122428\pi$
$191$	21.3121	+	5.71057i	1.54209	+	0.413202i	0.615151	+	0.788409i	$0.289095\pi$
$192$	−7.39507	+	11.5290i	−0.533693	+	0.832032i
$193$	18.7044	+	16.4033i	1.34637	+	1.18073i	0.966789	+	0.255575i	$0.0822649\pi$
$193$	18.7044	+	16.4033i	1.34637	+	1.18073i	0.379580	+	0.925159i	$0.376068\pi$
$194$	−1.83566	+	0.120315i	−0.131793	+	0.00863814i
$195$	−2.43141	+	3.29458i	−0.174117	+	0.235930i
$196$	−0.826888	−	0.634494i	−0.0590634	−	0.0453210i
$197$	3.89996	−	2.60587i	0.277861	−	0.185661i	−0.408829	−	0.912611i	$-0.634063\pi$
$197$	3.89996	−	2.60587i	0.277861	−	0.185661i	0.686690	+	0.726950i	$0.259063\pi$
$198$	−6.38535	+	7.85580i	−0.453787	+	0.558287i
$199$	−7.99870	+	11.9709i	−0.567013	+	0.848595i	−0.998568	−	0.0534914i	$-0.982965\pi$
$199$	−7.99870	+	11.9709i	−0.567013	+	0.848595i	0.431555	+	0.902087i	$0.357965\pi$
$200$	1.17739	−	4.39407i	0.0832539	−	0.310708i
$201$	1.77858	+	0.566847i	0.125452	+	0.0399823i
$202$	5.66925	+	7.38832i	0.398887	+	0.519840i
$203$	−4.45029	+	7.70812i	−0.312349	+	0.541004i
$204$	−5.90259	−	1.34043i	−0.413264	−	0.0938491i
$205$	−2.06727	−	3.58062i	−0.144384	−	0.250081i
$206$	3.59843	−	8.68737i	0.250714	−	0.605278i
$207$	5.42352	−	18.1871i	0.376961	−	1.26409i
$208$	−1.41515	−	1.41515i	−0.0981232	−	0.0981232i
$209$	10.8755	+	0.712818i	0.752274	+	0.0493067i
$210$	−3.38974	−	9.40377i	−0.233915	−	0.648921i
$211$	−1.37034	−	20.9074i	−0.0943383	−	1.43932i	−0.738406	−	0.674356i	$-0.764421\pi$
$211$	−1.37034	−	20.9074i	−0.0943383	−	1.43932i	0.644068	−	0.764969i	$-0.277246\pi$
$212$	0.634405	−	4.81879i	0.0435711	−	0.330956i
$213$	−11.1741	+	4.87545i	−0.765634	+	0.334060i
$214$	−3.38797	+	6.87013i	−0.231597	+	0.469632i
$215$	0.204304	−	1.02711i	0.0139334	−	0.0700480i
$216$	−8.06954	+	13.6817i	−0.549063	+	0.930920i
$217$	21.4200	−	21.4200i	1.45409	−	1.45409i
$218$	2.46224	−	2.15932i	0.166764	−	0.146248i
$219$	14.0994	+	5.53330i	0.952751	+	0.373906i
$220$	4.32396	+	2.49644i	0.291521	+	0.168310i
$221$	2.20777	−	4.70946i	0.148511	−	0.316792i
$222$	10.7221	+	17.7936i	0.719623	+	1.19423i
$223$	−0.512254	−	3.89096i	−0.0343031	−	0.260558i	−1.00000		0.000884490i	$-0.999718\pi$
$223$	−0.512254	−	3.89096i	−0.0343031	−	0.260558i	0.965697	−	0.259673i	$-0.0836149\pi$
$224$	−12.4101	+	2.46852i	−0.829183	+	0.164935i
$225$	0.993253	−	4.35250i	0.0662169	−	0.290167i
$226$	0.421504	+	0.281640i	0.0280380	+	0.0187344i
$227$	−0.866488	−	2.55259i	−0.0575108	−	0.169421i	0.914378	−	0.404861i	$-0.132680\pi$
$227$	−0.866488	−	2.55259i	−0.0575108	−	0.169421i	−0.971889	+	0.235440i	$0.924347\pi$
$228$	5.07193	−	0.427911i	0.335896	−	0.0283391i
$229$	−4.60430	−	0.606168i	−0.304261	−	0.0400567i	−0.0231500	−	0.999732i	$-0.507370\pi$
$229$	−4.60430	−	0.606168i	−0.304261	−	0.0400567i	−0.281111	+	0.959675i	$0.590703\pi$
$230$	12.6179	+	1.66118i	0.832000	+	0.109535i
$231$	−15.5639	+	1.31310i	−1.02403	+	0.0863957i
$232$	3.04864	+	8.98101i	0.200153	+	0.589632i
$233$	−12.4529	−	8.32078i	−0.815818	−	0.545112i	0.0762099	−	0.997092i	$-0.475718\pi$
$233$	−12.4529	−	8.32078i	−0.815818	−	0.545112i	−0.892028	+	0.451979i	$0.850718\pi$
$234$	−2.97827	−	2.76321i	−0.194695	−	0.180637i
$235$	6.47578	−	1.28811i	0.422433	−	0.0840272i
$236$	0.102598	+	0.779307i	0.00667854	+	0.0507286i
$237$	2.46570	+	4.09186i	0.160164	+	0.265795i
$238$	6.56503	+	10.8688i	0.425548	+	0.704520i
$239$	−6.88744	−	3.97647i	−0.445512	−	0.257216i	0.260421	−	0.965495i	$-0.416139\pi$
$239$	−6.88744	−	3.97647i	−0.445512	−	0.257216i	−0.705933	+	0.708279i	$0.749472\pi$
$240$	−4.79355	−	1.88122i	−0.309422	−	0.121432i
$241$	−15.3731	+	13.4818i	−0.990269	+	0.868442i	−0.991309	−	0.131557i	$-0.958002\pi$
$241$	−15.3731	+	13.4818i	−0.990269	+	0.868442i	0.00104001	+	0.999999i	$0.499669\pi$
$242$	0.849268	−	0.849268i	0.0545930	−	0.0545930i
$243$	−7.41121	+	13.7140i	−0.475429	+	0.879754i
$244$	−1.93062	+	9.70590i	−0.123595	+	0.621356i
$245$	1.01924	−	2.06682i	0.0651171	−	0.132044i
$246$	3.75997	−	1.64054i	0.239727	−	0.104597i
$247$	−0.570898	+	4.33640i	−0.0363254	+	0.275919i
$248$	−2.11117	−	32.2102i	−0.134059	−	2.04535i
$249$	−5.80428	−	16.1021i	−0.367831	−	1.02043i
$250$	13.0246	+	0.853678i	0.823749	+	0.0539913i
$251$	7.88000	+	7.88000i	0.497381	+	0.497381i	0.910622	−	0.413241i	$-0.135603\pi$
$251$	7.88000	+	7.88000i	0.497381	+	0.497381i	−0.413241	+	0.910622i	$0.635603\pi$
$252$	−7.09598	+	1.68986i	−0.447005	+	0.106451i
$253$	7.61004	−	18.3723i	0.478439	−	1.15505i
$254$	2.78159	+	4.81785i	0.174532	+	0.302299i
$255$	0.360702	−	13.3782i	0.0225880	−	0.837773i
$256$	−8.08620	+	14.0057i	−0.505388	+	0.875357i
$257$	3.20583	+	4.17792i	0.199974	+	0.260612i	0.882566	−	0.470188i	$-0.155814\pi$
$257$	3.20583	+	4.17792i	0.199974	+	0.260612i	−0.682592	+	0.730800i	$0.739147\pi$
$258$	0.989994	+	0.315518i	0.0616343	+	0.0196433i
$259$	−8.29563	+	30.9597i	−0.515465	+	1.92374i
$260$	−1.11319	+	1.66601i	−0.0690373	+	0.103322i
$261$	3.31970	+	8.69567i	0.205484	+	0.538248i
$262$	12.7781	−	8.53806i	0.789434	−	0.527483i
$263$	16.2252	+	12.4500i	1.00049	+	0.767701i	0.972736	−	0.231914i	$-0.0744988\pi$
$263$	16.2252	+	12.4500i	1.00049	+	0.767701i	0.0277508	+	0.999615i	$0.491166\pi$
$264$	−9.88304	+	13.3916i	−0.608259	+	0.824195i
$265$	10.7234	−	0.702845i	0.658730	−	0.0431755i
$266$	−8.02786	−	7.04024i	−0.492220	−	0.431665i
$267$	11.0787	−	17.2718i	0.678006	−	1.05702i
$268$	0.882351	+	0.236425i	0.0538981	+	0.0144420i
$269$	−1.55591	−	7.82207i	−0.0948653	−	0.476920i	−0.998788	−	0.0492238i	$-0.984325\pi$
$269$	−1.55591	−	7.82207i	−0.0948653	−	0.476920i	0.903922	−	0.427696i	$-0.140675\pi$
$270$	−9.86699	−	3.45197i	−0.600486	−	0.210080i
$271$		−	8.85289i		−	0.537775i	−0.963172	−	0.268887i	$-0.913344\pi$
$271$		−	8.85289i		−	0.537775i	0.963172	−	0.268887i	$-0.0866560\pi$
$272$	6.43950	+	1.14902i	0.390452	+	0.0696694i
$273$	−0.117328	−	6.26703i	−0.00710104	−	0.379298i
$274$	7.39700	−	5.67592i	0.446869	−	0.342895i
$275$	1.50365	−	4.42960i	0.0906733	−	0.267115i
$276$	2.23534	−	9.01407i	0.134552	−	0.542583i
$277$	0.787303	−	12.0119i	0.0473045	−	0.721727i	−0.906670	−	0.421840i	$-0.861384\pi$
$277$	0.787303	−	12.0119i	0.0473045	−	0.721727i	0.953975	−	0.299887i	$-0.0969489\pi$
$278$	−22.4104	−	4.45771i	−1.34409	−	0.267356i
$279$	−3.25360	−	31.5109i	−0.194788	−	1.88651i
$280$	−6.28901	−	15.1830i	−0.375841	−	0.907359i
$281$	−9.55167	+	12.4480i	−0.569805	+	0.742584i	−0.986010	−	0.166687i	$-0.946693\pi$
$281$	−9.55167	+	12.4480i	−0.569805	+	0.742584i	0.416205	+	0.909271i	$0.363360\pi$
$282$	0.550753	+	6.52794i	0.0327969	+	0.388733i
$283$	−4.75961	+	5.42730i	−0.282930	+	0.322619i	−0.875796	−	0.482681i	$-0.839663\pi$
$283$	−4.75961	+	5.42730i	−0.282930	+	0.322619i	0.592866	+	0.805301i	$0.297996\pi$
$284$	−5.35057	+	2.63861i	−0.317498	+	0.156573i
$285$	3.11570	+	10.8141i	0.184558	+	0.640570i
$286$	−2.80679	−	3.20053i	−0.165969	−	0.189251i
$287$	5.84744	+	2.42209i	0.345164	+	0.142971i
$288$	−6.18250	+	11.6990i	−0.364307	+	0.689368i
$289$	2.88364	+	16.7536i	0.169626	+	0.985509i
$290$	−5.40545	+	3.12084i	−0.317419	+	0.183262i
$291$	−2.93493	+	0.442427i	−0.172048	+	0.0259355i
$292$	7.01845	+	2.38244i	0.410724	+	0.139422i
$293$	−1.69264	−	6.31704i	−0.0988854	−	0.369045i	0.898694	−	0.438575i	$-0.144517\pi$
$293$	−1.69264	−	6.31704i	−0.0988854	−	0.369045i	−0.997580	+	0.0695300i	$0.977850\pi$
$294$	1.92460	+	1.23450i	0.112245	+	0.0719975i
$295$	−1.64570	+	0.558639i	−0.0958162	+	0.0325252i
$296$	18.9750	+	28.3981i	1.10290	+	1.65060i
$297$	−9.20036	+	13.4961i	−0.533859	+	0.783125i
$298$	14.8924	−	6.16862i	0.862691	−	0.357339i
$299$	7.15746	+	3.52967i	0.413926	+	0.204126i
$300$	0.386020	−	2.15026i	0.0222869	−	0.124145i
$301$	0.709039	+	1.43779i	0.0408683	+	0.0828728i
$302$	10.8438	−	2.90559i	0.623992	−	0.167198i
$303$	10.1168	+	11.1094i	0.581195	+	0.638221i
$304$	−5.45352	+	0.717970i	−0.312781	+	0.0411784i
$305$	−21.8803			−1.25286
$306$	13.1503	+	1.84157i	0.751752	+	0.105276i
$307$	−11.5622			−0.659891			−0.329946	−	0.944000i	$-0.607030\pi$
$307$	−11.5622			−0.659891			−0.329946	+	0.944000i	$0.607030\pi$
$308$	−7.57779	+	0.997635i	−0.431785	+	0.0568455i
$309$	4.60693	−	14.4551i	0.262079	−	0.822320i
$310$	20.5193	−	5.49813i	1.16542	−	0.312273i
$311$	−1.45524	−	2.95094i	−0.0825194	−	0.167333i	0.851702	−	0.524026i	$-0.175571\pi$
$311$	−1.45524	−	2.95094i	−0.0825194	−	0.167333i	−0.934221	+	0.356694i	$0.883904\pi$
$312$	−5.10328	−	4.30916i	−0.288916	−	0.243958i
$313$	−13.3388	−	6.57796i	−0.753952	−	0.371808i	0.0243453	−	0.999704i	$-0.492250\pi$
$313$	−13.3388	−	6.57796i	−0.753952	−	0.371808i	−0.778298	+	0.627895i	$0.783917\pi$
$314$	24.3818	−	10.0993i	1.37595	−	0.569935i
$315$	−6.72534	−	14.6589i	−0.378930	−	0.825938i
$316$	1.29880	+	1.94379i	0.0730631	+	0.109347i
$317$	13.4529	−	4.56665i	0.755591	−	0.256489i	0.0830471	−	0.996546i	$-0.473535\pi$
$317$	13.4529	−	4.56665i	0.755591	−	0.256489i	0.672544	+	0.740057i	$0.265201\pi$
$318$	−0.498083	+	10.6509i	−0.0279311	+	0.597271i
$319$	2.52422	+	9.42050i	0.141329	+	0.527447i
$320$	−14.0329	−	4.76353i	−0.784464	−	0.266290i
$321$	−4.51507	+	11.5049i	−0.252007	+	0.642139i
$322$	−16.8722	+	9.74118i	−0.940252	+	0.542855i
$323$	−6.57503	−	12.6937i	−0.365845	−	0.706298i
$324$	−3.30920	+	6.87299i	−0.183844	+	0.381833i
$325$	1.73437	+	0.718400i	0.0962056	+	0.0398497i
$326$	−5.78812	−	6.60008i	−0.320574	−	0.365545i
$327$	3.66572	−	3.80560i	0.202715	−	0.210450i
$328$	6.04882	−	2.98295i	0.333990	−	0.164706i
$329$	−6.66430	+	7.59918i	−0.367415	+	0.418956i
$330$	−9.91259	−	4.65975i	−0.545670	−	0.256511i
$331$	−11.4302	+	14.8961i	−0.628260	+	0.818765i	−0.993700	−	0.112070i	$-0.964252\pi$
$331$	−11.4302	+	14.8961i	−0.628260	+	0.818765i	0.365440	+	0.930835i	$0.380919\pi$
$332$	−3.20528	−	7.73823i	−0.175913	−	0.424691i
$333$	19.6519	+	27.1529i	1.07692	+	1.48797i
$334$	−8.51930	−	1.69459i	−0.466156	−	0.0927241i
$335$	−0.132095	+	2.01539i	−0.00721715	+	0.110112i
$336$	7.57478	−	2.18241i	0.413238	−	0.119060i
$337$	−7.68241	+	22.6316i	−0.418487	+	1.23282i	0.509584	+	0.860421i	$0.329799\pi$
$337$	−7.68241	+	22.6316i	−0.418487	+	1.23282i	−0.928071	+	0.372403i	$0.878534\pi$
$338$	−9.71644	+	7.45568i	−0.528504	+	0.405536i
$339$	0.715868	+	0.395628i	0.0388806	+	0.0214876i
$340$	−0.129497	−	6.54765i	−0.00702297	−	0.355096i
$341$		−	33.1931i		−	1.79751i
$342$	−11.0083	+	1.87083i	−0.595261	+	0.101163i
$343$	−3.22943	−	16.2354i	−0.174373	−	0.876631i
$344$	1.65005	+	0.442130i	0.0889648	+	0.0238381i
$345$	20.5115	+	0.959212i	1.10430	+	0.0516423i
$346$	18.6926	+	16.3930i	1.00492	+	0.881292i
$347$	−17.5944	+	1.15320i	−0.944519	+	0.0619070i	−0.529874	−	0.848076i	$-0.677761\pi$
$347$	−17.5944	+	1.15320i	−0.944519	+	0.0619070i	−0.414645	+	0.909983i	$0.636094\pi$
$348$	1.82148	+	4.17466i	0.0976418	+	0.223785i
$349$	3.01940	+	2.31686i	0.161625	+	0.124019i	0.686407	−	0.727217i	$-0.259187\pi$
$349$	3.01940	+	2.31686i	0.161625	+	0.124019i	−0.524783	+	0.851236i	$0.675853\pi$
$350$	−3.81054	+	2.54612i	−0.203682	+	0.136096i
$351$	−5.16306	−	4.03853i	−0.275584	−	0.215561i
$352$	−7.70286	+	11.5281i	−0.410564	+	0.614452i
$353$	1.73089	−	6.45975i	0.0921257	−	0.343818i	−0.904442	−	0.426596i	$-0.859713\pi$
$353$	1.73089	−	6.45975i	0.0921257	−	0.343818i	0.996568	+	0.0827781i	$0.0263793\pi$
$354$	−0.368006	−	1.68464i	−0.0195593	−	0.0895378i
$355$	−8.02987	−	10.4647i	−0.426181	−	0.555410i
$356$	5.02059	−	8.69592i	0.266091	−	0.460883i
$357$	12.0291	+	16.5836i	0.636646	+	0.877699i
$358$	−7.80213	−	13.5137i	−0.412355	−	0.714220i
$359$	−11.3116	+	27.3086i	−0.597004	+	1.44130i	0.279616	+	0.960112i	$0.409793\pi$
$359$	−11.3116	+	27.3086i	−0.597004	+	1.44130i	−0.876620	+	0.481183i	$0.840207\pi$
$360$	−16.4692	−	4.91122i	−0.868003	−	0.258844i
$361$	−4.93470	−	4.93470i	−0.259721	−	0.259721i
$362$	−25.2551	−	1.65531i	−1.32738	−	0.0870011i
$363$	1.25020	−	1.48059i	0.0656184	−	0.0777109i
$364$	−0.200610	−	3.06072i	−0.0105148	−	0.160425i
$365$	−2.13901	+	16.2474i	−0.111961	+	0.850428i
$366$	2.43029	−	21.5732i	0.127033	−	1.12765i
$367$	2.87380	−	5.82748i	0.150011	−	0.304192i	−0.808877	−	0.587978i	$-0.799924\pi$
$367$	2.87380	−	5.82748i	0.150011	−	0.304192i	0.958888	+	0.283786i	$0.0915906\pi$
$368$	−1.95799	+	9.84350i	−0.102068	+	0.513128i
$369$	5.82249	−	3.14756i	0.303107	−	0.163856i
$370$	−15.8936	+	15.8936i	−0.826268	+	0.826268i
$371$	−12.3683	+	10.8467i	−0.642130	+	0.563133i
$372$	−2.31071	−	15.3285i	−0.119805	−	0.794748i
$373$	−8.00286	−	4.62045i	−0.414372	−	0.239238i	0.278294	−	0.960496i	$-0.410231\pi$
$373$	−8.00286	−	4.62045i	−0.414372	−	0.239238i	−0.692667	+	0.721258i	$0.743564\pi$
$374$	13.5080	+	3.33462i	0.698481	+	0.172429i
$375$	21.0559	−	0.394198i	1.08732	−	0.0203563i
$376$	1.40582	+	10.6782i	0.0724994	+	0.550688i
$377$	−3.83871	+	0.763566i	−0.197703	+	0.0393256i
$378$	15.2001	−	5.00273i	0.781811	−	0.257313i
$379$	−24.2598	−	16.2099i	−1.24614	−	0.832646i	−0.255195	−	0.966890i	$-0.582140\pi$
$379$	−24.2598	−	16.2099i	−1.24614	−	0.832646i	−0.990948	+	0.134244i	$0.957140\pi$
$380$	1.77019	+	5.21482i	0.0908090	+	0.267515i
$381$	5.12555	+	7.36851i	0.262590	+	0.377500i
$382$	−23.4833	−	3.09163i	−1.20151	−	0.158182i
$383$	19.3328	+	2.54521i	0.987861	+	0.130054i	0.607105	−	0.794621i	$-0.292331\pi$
$383$	19.3328	+	2.54521i	0.987861	+	0.130054i	0.380755	+	0.924676i	$0.375664\pi$
$384$	−0.244780	+	0.520715i	−0.0124914	+	0.0265726i
$385$	−5.43207	−	16.0024i	−0.276844	−	0.815556i
$386$	−22.2060	−	14.8376i	−1.13026	−	0.755213i
$387$	1.63444	+	0.372984i	0.0830834	+	0.0189599i
$388$	−1.42451	+	0.283354i	−0.0723188	+	0.0143851i
$389$	−2.34720	−	17.8288i	−0.119008	−	0.903954i	−0.941932	−	0.335803i	$-0.890992\pi$
$389$	−2.34720	−	17.8288i	−0.119008	−	0.903954i	0.822924	−	0.568151i	$-0.192341\pi$
$390$	2.12618	−	3.84721i	0.107663	−	0.194811i
$391$	−25.7880	+	3.91528i	−1.30416	+	0.198004i
$392$	3.25548	+	1.87955i	0.164427	+	0.0949318i
$393$	19.3856	−	15.4602i	0.977877	−	0.779862i
$394$	−3.78570	+	3.31997i	−0.190721	+	0.167258i
$395$	−3.65494	+	3.65494i	−0.183900	+	0.183900i
$396$	−4.18874	+	6.80739i	−0.210492	+	0.342084i
$397$	−0.141599	+	0.711868i	−0.00710666	+	0.0357276i	−0.984176	−	0.177194i	$-0.943298\pi$
$397$	−0.141599	+	0.711868i	−0.00710666	+	0.0357276i	0.977069	+	0.212922i	$0.0682979\pi$
$398$	6.83586	−	13.8618i	0.342651	−	0.694827i
$399$	−13.8616	−	10.2299i	−0.693948	−	0.512136i
$400$	−0.308157	+	2.34069i	−0.0154079	+	0.117034i
$401$	0.885597	+	13.5116i	0.0442246	+	0.674737i	0.961210	+	0.275817i	$0.0889483\pi$
$401$	0.885597	+	13.5116i	0.0442246	+	0.674737i	−0.916986	+	0.398920i	$0.869385\pi$
$402$	−1.97242	−	0.354094i	−0.0983755	−	0.0176606i
$403$	13.2922	+	0.871217i	0.662132	+	0.0433984i
$404$	5.19917	+	5.19917i	0.258668	+	0.258668i
$405$	−16.3317	−	4.21146i	−0.811529	−	0.209269i
$406$	3.65649	−	8.82755i	0.181469	−	0.438104i
$407$	17.5604	+	30.4156i	0.870439	+	1.50764i
$408$	21.7375	+	2.01440i	1.07617	+	0.0997276i
$409$	−4.62685	+	8.01393i	−0.228783	+	0.396264i	−0.957448	−	0.288607i	$-0.906808\pi$
$409$	−4.62685	+	8.01393i	−0.228783	+	0.396264i	0.728665	+	0.684870i	$0.240141\pi$
$410$	2.70198	+	3.52128i	0.133441	+	0.173904i
$411$	11.1225	−	10.1287i	0.548633	−	0.499612i
$412$	1.92150	−	7.17112i	0.0946653	−	0.353296i
$413$	1.47807	−	2.21208i	0.0727310	−	0.108850i
$414$	−3.22400	+	20.1170i	−0.158451	+	0.988698i
$415$	15.3980	−	10.2886i	0.755859	−	0.505049i
$416$	−4.41428	−	3.38720i	−0.216428	−	0.166071i
$417$	−36.6346	−	4.12701i	−1.79401	−	0.202101i
$418$	−11.6750	+	0.765219i	−0.571042	+	0.0374281i
$419$	14.6375	+	12.8367i	0.715088	+	0.627116i	0.937560	−	0.347824i	$-0.113079\pi$
$419$	14.6375	+	12.8367i	0.715088	+	0.627116i	−0.222472	+	0.974939i	$0.571413\pi$
$420$	−3.62252	−	7.01174i	−0.176761	−	0.342138i
$421$	−3.12390	−	0.837045i	−0.152249	−	0.0407951i	0.181889	−	0.983319i	$-0.441779\pi$
$421$	−3.12390	−	0.837045i	−0.152249	−	0.0407951i	−0.334139	+	0.942524i	$0.608445\pi$
$422$	4.38807	+	22.0603i	0.213608	+	1.07388i
$423$	1.77093	+	10.4205i	0.0861054	+	0.506661i
$424$			17.5297i			0.851316i
$425$	−5.99298	+	1.31578i	−0.290702	+	0.0638248i
$426$	11.2097	−	6.75480i	0.543112	−	0.327271i
$427$	26.5732	−	20.3903i	1.28597	−	0.986757i
$428$	−1.94403	+	5.72693i	−0.0939683	+	0.276822i
$429$	−4.94669	−	4.76488i	−0.238829	−	0.230051i
$430$	−0.0735270	+	1.12180i	−0.00354578	+	0.0540982i
$431$	35.6591	+	7.09305i	1.71764	+	0.341660i	0.953040	−	0.302844i	$-0.0979363\pi$
$431$	35.6591	+	7.09305i	1.71764	+	0.341660i	0.764601	+	0.644504i	$0.222936\pi$
$432$	3.22531	−	7.58642i	0.155178	−	0.365002i
$433$	−14.2266	−	34.3461i	−0.683688	−	1.65057i	−0.757125	−	0.653270i	$-0.773397\pi$
$433$	−14.2266	−	34.3461i	−0.683688	−	1.65057i	0.0734367	−	0.997300i	$-0.476603\pi$
$434$	−19.7965	+	25.7993i	−0.950263	+	1.23841i
$435$	−8.26720	+	5.75068i	−0.396382	+	0.275724i
$436$	1.70486	−	1.94402i	0.0816478	−	0.0931015i
$437$	19.6720	−	9.70116i	0.941040	−	0.464070i
$438$	−15.7817	−	3.91361i	−0.754081	−	0.187000i
$439$	0.0313818	+	0.0357840i	0.00149777	+	0.00170788i	0.752588	−	0.658491i	$-0.228805\pi$
$439$	0.0313818	+	0.0357840i	0.00149777	+	0.00170788i	−0.751090	+	0.660199i	$0.770472\pi$
$440$	−16.6368	−	6.89120i	−0.793130	−	0.328525i
$441$	3.26169	+	1.72369i	0.155318	+	0.0820805i
$442$	−1.68990	+	5.32176i	−0.0803802	+	0.253130i
$443$	20.7944	−	12.0057i	0.987974	−	0.570407i	0.0833059	−	0.996524i	$-0.473452\pi$
$443$	20.7944	−	12.0057i	0.987974	−	0.570407i	0.904668	+	0.426117i	$0.140119\pi$
$444$	10.2268	+	12.8234i	0.485341	+	0.608574i
$445$	21.0230	+	7.13635i	0.996586	+	0.338296i
$446$	1.09041	+	4.06948i	0.0516325	+	0.192695i
$447$	23.1062	−	11.9375i	1.09289	−	0.564625i
$448$	21.4818	−	7.29210i	1.01492	−	0.344519i
$449$	18.0163	+	26.9633i	0.850242	+	1.27248i	0.960417	+	0.278565i	$0.0898587\pi$
$449$	18.0163	+	26.9633i	0.850242	+	1.27248i	−0.110175	+	0.993912i	$0.535141\pi$
$450$	−0.447268	+	4.77167i	−0.0210844	+	0.224938i
$451$	6.40735	−	2.65401i	0.301710	−	0.124973i
$452$	0.358969	+	0.177024i	0.0168845	+	0.00832650i
$453$	17.0398	−	6.14229i	0.800601	−	0.288590i
$454$	1.27990	+	2.59538i	0.0600687	+	0.121807i
$455$	6.55074	−	1.75527i	0.307103	−	0.0822881i
$456$	−17.9347	+	3.91780i	−0.839871	+	0.183468i
$457$	19.0027	−	2.50175i	0.888908	−	0.117027i	0.327778	−	0.944755i	$-0.393700\pi$
$457$	19.0027	−	2.50175i	0.888908	−	0.117027i	0.561130	+	0.827728i	$0.310367\pi$
$458$	4.98542			0.232953
$459$	21.3919	+	1.17703i	0.998490	+	0.0549390i
$460$	10.0482			0.468500
$461$	7.29858	−	0.960876i	0.339929	−	0.0447525i	0.0413705	−	0.999144i	$-0.486828\pi$
$461$	7.29858	−	0.960876i	0.339929	−	0.0447525i	0.298558	+	0.954391i	$0.403494\pi$
$462$	16.3811	−	3.57840i	0.762116	−	0.166482i
$463$	21.1729	−	5.67325i	0.983987	−	0.263658i	0.269264	−	0.963066i	$-0.413220\pi$
$463$	21.1729	−	5.67325i	0.983987	−	0.263658i	0.714723	+	0.699408i	$0.246553\pi$
$464$	−2.17703	−	4.41458i	−0.101066	−	0.204942i
$465$	32.2437	−	11.6228i	1.49527	−	0.538994i
$466$	14.4199	+	7.11112i	0.667990	+	0.329416i
$467$	−19.9408	+	8.25973i	−0.922748	+	0.382215i	−0.792923	−	0.609322i	$-0.791442\pi$
$467$	−19.9408	+	8.25973i	−0.922748	+	0.382215i	−0.129825	+	0.991537i	$0.541442\pi$
$468$	−2.61608	−	1.85606i	−0.120929	−	0.0857964i
$469$	−1.71772	−	2.57075i	−0.0793168	−	0.118706i
$470$	−6.71186	+	2.27837i	−0.309595	+	0.105093i
$471$	37.8295	−	19.5441i	1.74309	−	0.900546i
$472$	−0.733738	−	2.73835i	−0.0337730	−	0.126043i
$473$	1.66339	+	0.564646i	0.0764829	+	0.0259624i
$474$	−3.19767	−	4.00959i	−0.146874	−	0.184166i
$475$	4.46835	−	2.57981i	0.205022	−	0.118370i
$476$	6.25904	+	7.83131i	0.286883	+	0.358947i
$477$	0.643921	+	17.1913i	0.0294831	+	0.787136i
$478$	7.88768	+	3.26719i	0.360774	+	0.149438i
$479$	−24.3132	−	27.7239i	−1.11090	−	1.26674i	−0.960552	−	0.278102i	$-0.910295\pi$
$479$	−24.3132	−	27.7239i	−1.11090	−	1.26674i	−0.150345	−	0.988634i	$-0.548039\pi$
$480$	−13.8956	−	3.44589i	−0.634246	−	0.157283i
$481$	−12.6409	+	6.23379i	−0.576374	+	0.284236i
$482$	14.4729	−	16.5032i	0.659224	−	0.751700i
$483$	−25.8047	+	17.9498i	−1.17415	+	0.816744i
$484$	0.577267	−	0.752310i	0.0262394	−	0.0341959i
$485$	−1.22892	−	2.96688i	−0.0558025	−	0.134719i
$486$	5.96633	−	15.6347i	0.270638	−	0.709203i
$487$	−4.63471	−	0.921901i	−0.210019	−	0.0417753i	0.0889596	−	0.996035i	$-0.471646\pi$
$487$	−4.63471	−	0.921901i	−0.210019	−	0.0417753i	−0.298978	+	0.954260i	$0.596646\pi$
$488$	2.33434	−	35.6152i	0.105671	−	1.61222i
$489$	−10.2010	−	9.82605i	−0.461305	−	0.444349i
$490$	−0.795203	+	2.34259i	−0.0359236	+	0.105828i
$491$	−18.7070	+	14.3544i	−0.844236	+	0.647805i	−0.937557	−	0.347831i	$-0.886918\pi$
$491$	−18.7070	+	14.3544i	−0.844236	+	0.647805i	0.0933209	+	0.995636i	$0.470252\pi$
$492$	2.77416	−	1.67166i	0.125069	−	0.0753645i
$493$	8.86492	−	9.22265i	0.399256	−	0.415367i
$494$		−	4.69534i		−	0.211254i
$495$	−16.5688	−	6.14707i	−0.744714	−	0.276290i
$496$	3.26822	+	16.4305i	0.146747	+	0.737749i
$497$	19.5042	+	5.22613i	0.874883	+	0.234424i
$498$	8.43391	+	16.3246i	0.377932	+	0.731524i
$499$	−15.8470	−	13.8975i	−0.709411	−	0.622137i	0.226649	−	0.973976i	$-0.427223\pi$
$499$	−15.8470	−	13.8975i	−0.709411	−	0.622137i	−0.936060	+	0.351840i	$0.885556\pi$
$500$	10.2834	−	0.674007i	0.459886	−	0.0301425i
$501$	−13.9266	−	1.56888i	−0.622195	−	0.0700924i
$502$	−9.49106	−	7.28275i	−0.423607	−	0.325045i
$503$	−20.7471	+	13.8628i	−0.925070	+	0.618112i	−0.924209	−	0.381888i	$-0.875274\pi$
$503$	−20.7471	+	13.8628i	−0.925070	+	0.618112i	−0.000860885		1.00000i	$0.500274\pi$
$504$	24.5783	−	9.38311i	1.09480	−	0.417957i
$505$	−9.03192	+	13.5172i	−0.401915	+	0.601509i
$506$	−5.52523	+	20.6204i	−0.245626	+	0.916690i
$507$	−14.6101	+	13.3047i	−0.648858	+	0.590882i
$508$	2.67387	+	3.48465i	0.118634	+	0.154606i
$509$	7.06911	−	12.2441i	0.313333	−	0.542708i	−0.665749	−	0.746176i	$-0.731888\pi$
$509$	7.06911	−	12.2441i	0.313333	−	0.542708i	0.979082	+	0.203468i	$0.0652211\pi$
$510$	1.49066	+	14.2893i	0.0660076	+	0.632740i
$511$	−12.5432	−	21.7255i	−0.554879	−	0.961079i
$512$	6.38962	−	15.4259i	0.282384	−	0.681735i
$513$	−17.4447	+	4.50098i	−0.770200	+	0.198723i
$514$	−3.99747	−	3.99747i	−0.176321	−	0.176321i
$515$	16.3796	+	1.07358i	0.721773	+	0.0473075i
$516$	0.807462	+	0.144957i	0.0355465	+	0.00638139i
$517$	0.724357	+	11.0515i	0.0318572	+	0.486047i
$518$	4.49115	−	34.1137i	0.197330	−	1.49887i
$519$	32.2763	+	23.8200i	1.41677	+	1.04558i
$520$	3.19626	−	6.48137i	0.140165	−	0.284227i
$521$	−5.85003	+	29.4101i	−0.256295	+	1.28848i	0.611376	+	0.791340i	$0.290616\pi$
$521$	−5.85003	+	29.4101i	−0.256295	+	1.28848i	−0.867671	+	0.497140i	$0.834384\pi$
$522$	−4.75169	−	8.78988i	−0.207976	−	0.384723i
$523$	−4.96667	+	4.96667i	−0.217177	+	0.217177i	−0.807308	−	0.590130i	$-0.799076\pi$
$523$	−4.96667	+	4.96667i	−0.217177	+	0.217177i	0.590130	+	0.807308i	$0.299076\pi$
$524$	9.12254	−	8.00025i	0.398520	−	0.349493i
$525$	−5.78097	+	4.61036i	−0.252302	+	0.201212i
$526$	−19.0134	−	10.9774i	−0.829024	−	0.478637i
$527$	−37.2671	+	22.5102i	−1.62338	+	0.980561i
$528$	4.17808	−	7.56001i	0.181827	−	0.329007i
$529$	−2.22165	−	16.8751i	−0.0965936	−	0.733701i
$530$	−11.3147	+	2.25063i	−0.491478	+	0.0977611i
$531$	−0.820163	−	2.65854i	−0.0355921	−	0.115371i
$532$	−7.00957	−	4.68364i	−0.303903	−	0.203062i
$533$	0.894629	+	2.63549i	0.0387507	+	0.114156i
$534$	−9.37123	+	19.9352i	−0.405533	+	0.862682i
$535$	−13.2576	−	1.74540i	−0.573176	−	0.0754600i
$536$	−3.26641	−	0.430031i	−0.141087	−	0.0185745i
$537$	−14.3768	−	20.6681i	−0.620403	−	0.891894i
$538$	2.75203	+	8.10723i	0.118649	+	0.349528i
$539$	3.21406	+	2.14757i	0.138439	+	0.0925023i
$540$	−8.07941	−	1.68528i	−0.347682	−	0.0725231i
$541$	−17.1179	+	3.40496i	−0.735956	+	0.146391i	−0.548817	−	0.835943i	$-0.684922\pi$
$541$	−17.1179	+	3.40496i	−0.735956	+	0.146391i	−0.187139	+	0.982333i	$0.559922\pi$
$542$	1.24048	+	9.42238i	0.0532832	+	0.404726i
$543$	−40.8280	+	0.764362i	−1.75210	+	0.0328019i
$544$	18.1668	+	0.830344i	0.778897	+	0.0356007i
$545$	4.95105	+	2.85849i	0.212080	+	0.122444i
$546$	1.00302	+	6.65374i	0.0429254	+	0.284754i
$547$	−19.9334	+	17.4811i	−0.852292	+	0.747440i	−0.969350	−	0.245685i	$-0.920987\pi$
$547$	−19.9334	+	17.4811i	−0.852292	+	0.747440i	0.117058	+	0.993125i	$0.462654\pi$
$548$	5.20528	−	5.20528i	0.222359	−	0.222359i
$549$	0.981026	−	35.0135i	0.0418692	−	1.49434i
$550$	−0.979690	+	4.92524i	−0.0417741	+	0.210013i
$551$	−4.75781	+	9.64788i	−0.202689	+	0.411013i
$552$	−3.74965	+	33.2848i	−0.159596	+	1.41670i
$553$	1.03280	−	7.84488i	0.0439191	−	0.333598i
$554$	0.845179	+	12.8949i	0.0359082	+	0.547854i
$555$	−23.3968	+	27.7084i	−0.993138	+	1.17616i
$556$	−18.0018	−	1.17990i	−0.763446	−	0.0500389i
$557$	−8.34593	−	8.34593i	−0.353628	−	0.353628i	0.507829	−	0.861458i	$-0.330448\pi$
$557$	−8.34593	−	8.34593i	−0.353628	−	0.353628i	−0.861458	+	0.507829i	$0.830448\pi$
$558$	7.87825	+	33.0820i	0.333513	+	1.40047i
$559$	−0.269772	+	0.651288i	−0.0114101	+	0.0275465i
$560$	4.26447	+	7.38627i	0.180207	+	0.312127i
$561$	22.1695	+	3.52893i	0.935998	+	0.148992i
$562$	8.42188	−	14.5871i	0.355255	−	0.615320i
$563$	20.4239	+	26.6170i	0.860766	+	1.12177i	0.991468	+	0.130350i	$0.0416101\pi$
$563$	20.4239	+	26.6170i	0.860766	+	1.12177i	−0.130702	+	0.991422i	$0.541723\pi$
$564$	1.10385	+	5.05318i	0.0464806	+	0.212777i
$565$	−0.229041	+	0.854794i	−0.00963584	+	0.0359615i
$566$	4.30531	−	6.44335i	0.180966	−	0.270834i
$567$	23.7592	−	10.1048i	0.997792	−	0.424363i
$568$	17.8904	−	11.9540i	0.750664	−	0.501578i
$569$	5.87635	+	4.50908i	0.246350	+	0.189031i	0.724554	−	0.689218i	$-0.242046\pi$
$569$	5.87635	+	4.50908i	0.246350	+	0.189031i	−0.478205	+	0.878248i	$0.658712\pi$
$570$	−4.83141	−	11.0731i	−0.202366	−	0.463802i
$571$	−38.1319	+	2.49930i	−1.59577	+	0.104592i	−0.837163	−	0.546954i	$-0.815787\pi$
$571$	−38.1319	+	2.49930i	−1.59577	+	0.104592i	−0.758609	+	0.651546i	$0.774121\pi$
$572$	−2.52693	−	2.21605i	−0.105656	−	0.0926579i
$573$	−38.1742	−	1.78520i	−1.59475	−	0.0745777i
$574$	−6.56298	−	1.75855i	−0.273934	−	0.0734003i
$575$	−1.83662	−	9.23332i	−0.0765924	−	0.385056i
$576$	8.25192	−	22.2423i	0.343830	−	0.926762i
$577$			23.3028i			0.970109i	0.874484	+	0.485055i	$0.161200\pi$
$577$			23.3028i			0.970109i	−0.874484	+	0.485055i	$0.838800\pi$
$578$	−5.41668	−	17.4273i	−0.225304	−	0.724880i
$579$	−37.7139	−	20.8428i	−1.56734	−	0.866197i
$580$	−3.90965	+	2.99998i	−0.162340	+	0.124568i
$581$	−9.11257	+	26.8448i	−0.378053	+	1.11371i
$582$	3.06173	−	0.882133i	0.126913	−	0.0365656i
$583$	−1.17895	+	17.9873i	−0.0488271	+	0.744958i
$584$	−26.2182	−	5.21512i	−1.08491	−	0.215803i
$585$	2.89648	−	6.47367i	0.119755	−	0.267653i
$586$	2.68668	+	6.48622i	0.110986	+	0.267943i
$587$	−5.27043	+	6.86855i	−0.217534	+	0.283496i	−0.889355	−	0.457218i	$-0.848846\pi$
$587$	−5.27043	+	6.86855i	−0.217534	+	0.283496i	0.671821	+	0.740714i	$0.265513\pi$
$588$	1.63375	+	0.768001i	0.0673749	+	0.0316718i
$589$	24.1397	−	27.5260i	0.994658	−	1.13419i
$590$	1.67328	−	0.825173i	0.0688880	−	0.0339718i
$591$	−5.63606	+	5.85112i	−0.231837	+	0.240683i
$592$	−11.6871	−	13.3266i	−0.480337	−	0.547720i
$593$	32.2794	+	13.3706i	1.32556	+	0.549063i	0.929385	−	0.369113i	$-0.120338\pi$
$593$	32.2794	+	13.3706i	1.32556	+	0.549063i	0.396172	+	0.918176i	$0.370338\pi$
$594$	7.90110	−	15.6535i	0.324186	−	0.642270i
$595$	−14.2826	+	16.9510i	−0.585530	+	0.694922i
$596$	11.0217	−	6.36339i	0.451467	−	0.260655i
$597$	9.11000	−	23.2132i	0.372847	−	0.950054i
$598$	−8.11246	−	2.75381i	−0.331743	−	0.112612i
$599$	−8.95462	−	33.4191i	−0.365876	−	1.36547i	−0.866230	−	0.499646i	$-0.833463\pi$
$599$	−8.95462	−	33.4191i	−0.365876	−	1.36547i	0.500354	−	0.865821i	$-0.333203\pi$
$600$	−0.368066	+	7.87063i	−0.0150262	+	0.321317i
$601$	−16.7087	+	5.67185i	−0.681564	+	0.231360i	−0.640684	−	0.767804i	$-0.721349\pi$
$601$	−16.7087	+	5.67185i	−0.681564	+	0.231360i	−0.0408795	+	0.999164i	$0.513016\pi$
$602$	−0.956115	−	1.43093i	−0.0389683	−	0.0583203i
$603$	−3.21916	−	0.301745i	−0.131094	−	0.0122880i
$604$	8.18887	−	3.39194i	0.333201	−	0.138016i
$605$	1.88041	+	0.927316i	0.0764496	+	0.0377008i
$606$	−12.3243	−	10.4065i	−0.500639	−	0.422735i
$607$	−4.82679	−	9.78776i	−0.195913	−	0.397273i	0.776643	−	0.629941i	$-0.216921\pi$
$607$	−4.82679	−	9.78776i	−0.195913	−	0.397273i	−0.972556	+	0.232668i	$0.925254\pi$
$608$	−14.7716	+	3.95804i	−0.599067	+	0.160520i
$609$	4.68127	−	14.6883i	0.189695	−	0.595200i
$610$	23.2878	−	3.06590i	0.942897	−	0.124135i
$611$	−4.44462			−0.179810
$612$	10.4835	+	0.0863456i	0.423772	+	0.00349031i
$613$	26.5318			1.07161			0.535804	−	0.844342i	$-0.320009\pi$
$613$	26.5318			1.07161			0.535804	+	0.844342i	$0.320009\pi$
$614$	12.3060	−	1.62012i	0.496630	−	0.0653825i
$615$	4.82169	+	5.29478i	0.194429	+	0.213506i
$616$	26.6270	−	7.13469i	1.07283	−	0.287465i
$617$	−10.1166	−	20.5145i	−0.407280	−	0.825882i	−0.999794	−	0.0203212i	$-0.993531\pi$
$617$	−10.1166	−	20.5145i	−0.407280	−	0.825882i	0.592514	−	0.805560i	$-0.298136\pi$
$618$	−2.87782	+	16.0305i	−0.115763	+	0.644839i
$619$	−3.86869	−	1.90782i	−0.155496	−	0.0766819i	0.362876	−	0.931837i	$-0.381795\pi$
$619$	−3.86869	−	1.90782i	−0.155496	−	0.0766819i	−0.518372	+	0.855156i	$0.673462\pi$
$620$	15.4954	−	6.41842i	0.622312	−	0.257770i
$621$	−2.45461	+	32.7801i	−0.0985002	+	1.31542i
$622$	1.96235	+	2.93686i	0.0786830	+	0.117757i
$623$	−32.1824	+	10.9244i	−1.28936	+	0.437679i
$624$	2.91775	+	1.87154i	0.116804	+	0.0749217i
$625$	3.97153	+	14.8219i	0.158861	+	0.592878i
$626$	15.1185	+	5.13205i	0.604259	+	0.205118i
$627$	−18.6664	+	2.81388i	−0.745466	+	0.112376i
$628$	18.0448	−	10.4182i	0.720065	−	0.415730i
$629$	22.2399	−	40.3424i	0.886762	−	1.60856i
$630$	9.21200	+	14.6596i	0.367015	+	0.584051i
$631$	15.4851	+	6.41414i	0.616453	+	0.255343i	0.668985	−	0.743276i	$-0.266729\pi$
$631$	15.4851	+	6.41414i	0.616453	+	0.255343i	−0.0525320	+	0.998619i	$0.516729\pi$
$632$	−5.55931	−	6.33917i	−0.221137	−	0.252159i
$633$	10.0471	+	34.8719i	0.399338	+	1.38603i
$634$	−13.6784	+	6.74546i	−0.543240	+	0.267896i
$635$	−6.40322	+	7.30147i	−0.254104	+	0.289750i
$636$	0.707734	+	8.38860i	0.0280635	+	0.332630i
$637$	−0.944356	+	1.23071i	−0.0374167	+	0.0487624i
$638$	−4.00661	−	9.67281i	−0.158623	−	0.382950i
$639$	17.1060	−	12.3804i	0.676702	−	0.489762i
$640$	−0.610571	−	0.121450i	−0.0241350	−	0.00480074i
$641$	−0.0816239	+	1.24534i	−0.00322395	+	0.0491880i	−0.999168	−	0.0407893i	$-0.987013\pi$
$641$	−0.0816239	+	1.24534i	−0.00322395	+	0.0491880i	0.995944	+	0.0899773i	$0.0286794\pi$
$642$	3.19344	−	12.8776i	0.126035	−	0.508239i
$643$	−14.0217	+	41.3066i	−0.552962	+	1.62897i	0.206517	+	0.978443i	$0.433787\pi$
$643$	−14.0217	+	41.3066i	−0.552962	+	1.62897i	−0.759479	+	0.650532i	$0.774546\pi$
$644$	−12.2033	+	9.36395i	−0.480879	+	0.368991i
$645$	0.0339521	+	1.81353i	0.00133686	+	0.0714078i
$646$	8.77665	+	12.5890i	0.345313	+	0.495307i
$647$		−	33.6904i		−	1.32451i	−0.749279	−	0.662254i	$-0.769600\pi$
$647$		−	33.6904i		−	1.32451i	0.749279	−	0.662254i	$-0.230400\pi$
$648$	8.59749	−	26.1343i	0.337741	−	1.02665i
$649$	−0.568727	−	2.85918i	−0.0223245	−	0.112233i
$650$	−1.94660	−	0.521591i	−0.0763520	−	0.0204585i
$651$	−28.3280	+	44.1636i	−1.11026	+	1.73091i
$652$	−5.21098	−	4.56991i	−0.204078	−	0.178971i
$653$	−48.3203	+	3.16708i	−1.89092	+	0.123937i	−0.966375	−	0.257138i	$-0.917220\pi$
$653$	−48.3203	+	3.16708i	−1.89092	+	0.123937i	−0.924544	+	0.381076i	$0.875554\pi$
$654$	−3.36828	+	4.56405i	−0.131710	+	0.178468i
$655$	21.2838	+	16.3316i	0.831627	+	0.638130i
$656$	−2.91030	+	1.94460i	−0.113628	+	0.0759239i
$657$	−25.9037	−	4.15138i	−1.01060	−	0.161961i
$658$	6.02819	−	9.02183i	0.235003	−	0.351708i
$659$	−3.53019	+	13.1748i	−0.137517	+	0.513219i	0.862458	+	0.506128i	$0.168924\pi$
$659$	−3.53019	+	13.1748i	−0.137517	+	0.513219i	−0.999975	+	0.00709055i	$0.997743\pi$
$660$	−8.23957	−	2.62601i	−0.320725	−	0.102217i
$661$	−4.08238	−	5.32026i	−0.158786	−	0.206934i	0.707184	−	0.707029i	$-0.249965\pi$
$661$	−4.08238	−	5.32026i	−0.158786	−	0.206934i	−0.865971	+	0.500095i	$0.833298\pi$
$662$	10.0782	−	17.4560i	0.391701	−	0.678445i
$663$	−1.99505	+	8.78519i	−0.0774813	+	0.341188i
$664$	15.1043	+	26.1614i	0.586161	+	1.01526i
$665$	7.13307	−	17.2208i	0.276609	−	0.667792i
$666$	−24.7207	−	26.1459i	−0.957909	−	1.01313i
$667$	13.8788	+	13.8788i	0.537391	+	0.537391i
$668$	−6.84336	−	0.448538i	−0.264778	−	0.0173544i
$669$	2.30508	+	6.39472i	0.0891197	+	0.247234i
$670$	−0.141806	−	2.16354i	−0.00547845	−	0.0835849i
$671$	4.79057	−	36.3880i	0.184938	−	1.40474i
$672$	20.0872	−	8.76442i	0.774880	−	0.338095i
$673$	9.34756	−	18.9550i	0.360322	−	0.730661i	−0.638933	−	0.769263i	$-0.720624\pi$
$673$	9.34756	−	18.9550i	0.360322	−	0.730661i	0.999255	+	0.0386020i	$0.0122904\pi$
$674$	5.00542	−	25.1640i	0.192802	−	0.969279i
$675$	−0.0718487	+	7.73223i	−0.00276546	+	0.297614i
$676$	−6.83747	+	6.83747i	−0.262980	+	0.262980i
$677$	−20.7436	+	18.1916i	−0.797241	+	0.699162i	−0.957665	−	0.287886i	$-0.907047\pi$
$677$	−20.7436	+	18.1916i	−0.797241	+	0.699162i	0.160423	+	0.987048i	$0.448714\pi$
$678$	−0.817354	−	0.320770i	−0.0313903	−	0.0123191i
$679$	4.25734	+	2.45798i	0.163382	+	0.0943286i
$680$	3.54545	+	23.3521i	0.135962	+	0.895513i
$681$	2.40978	+	3.99907i	0.0923429	+	0.153245i
$682$	4.65106	+	35.3283i	0.178098	+	1.35279i
$683$	13.5491	−	2.69509i	0.518444	−	0.103125i	0.0710689	−	0.997471i	$-0.477359\pi$
$683$	13.5491	−	2.69509i	0.518444	−	0.103125i	0.447375	+	0.894347i	$0.352359\pi$
$684$	−8.42427	+	2.59890i	−0.322110	+	0.0993715i
$685$	13.5331	+	9.04254i	0.517074	+	0.345498i
$686$	5.71210	+	16.8273i	0.218089	+	0.642469i
$687$	8.01522	−	0.676232i	0.305800	−	0.0257999i
$688$	−0.878970	−	0.115719i	−0.0335104	−	0.00441173i
$689$	−7.17210	−	0.944224i	−0.273235	−	0.0359721i
$690$	−21.9654	+	1.85319i	−0.836208	+	0.0705496i
$691$	1.54926	+	4.56399i	0.0589368	+	0.173622i	0.972411	−	0.233275i	$-0.0749441\pi$
$691$	1.54926	+	4.56399i	0.0589368	+	0.173622i	−0.913474	+	0.406897i	$0.866611\pi$
$692$	16.3215	+	10.9057i	0.620452	+	0.414573i
$693$	25.8510	−	7.97507i	0.981997	−	0.302948i
$694$	18.5647	−	3.69274i	0.704705	−	0.140174i
$695$	−5.20639	−	39.5464i	−0.197490	−	1.50008i
$696$	−8.47854	−	14.0703i	−0.321378	−	0.533332i
$697$	−7.32497	−	5.39392i	−0.277453	−	0.204309i
$698$	−3.53827	−	2.04282i	−0.133925	−	0.0773219i
$699$	24.1479	+	9.47682i	0.913358	+	0.358446i
$700$	−2.72042	+	2.38575i	−0.102822	+	0.0901727i
$701$	−5.44428	+	5.44428i	−0.205628	+	0.205628i	−0.802406	−	0.596778i	$-0.796447\pi$
$701$	−5.44428	+	5.44428i	−0.205628	+	0.205628i	0.596778	+	0.802406i	$0.296447\pi$
$702$	6.06107	+	3.57486i	0.228761	+	0.134924i
$703$	−7.55739	+	37.9936i	−0.285032	+	1.43295i
$704$	10.9944	−	22.2944i	0.414367	−	0.840253i
$705$	−10.4818	+	4.57342i	−0.394769	+	0.172245i
$706$	−0.937080	+	7.11783i	−0.0352675	+	0.267883i
$707$	−1.62766	−	24.8332i	−0.0612143	−	0.933950i
$708$	−0.461678	−	1.28078i	−0.0173509	−	0.0481346i
$709$	30.4069	+	1.99297i	1.14195	+	0.0748477i	0.624615	−	0.780933i	$-0.285256\pi$
$709$	30.4069	+	1.99297i	1.14195	+	0.0748477i	0.517340	+	0.855780i	$0.326922\pi$
$710$	10.0127	+	10.0127i	0.375771	+	0.375771i
$711$	−5.68486	−	6.01260i	−0.213199	−	0.225490i
$712$	−13.8589	+	33.4584i	−0.519385	+	1.25391i
$713$	−33.4007	−	57.8517i	−1.25086	−	2.16656i
$714$	−15.1266	−	15.9649i	−0.566099	−	0.597471i
$715$	3.71560	−	6.43561i	0.138956	−	0.240678i
$716$	−7.49999	−	9.77417i	−0.280288	−	0.365278i
$717$	13.1245	+	4.18286i	0.490142	+	0.156212i
$718$	8.21274	−	30.6503i	0.306497	−	1.14386i
$719$	9.28833	−	13.9010i	0.346396	−	0.518418i	−0.616835	−	0.787092i	$-0.711585\pi$
$719$	9.28833	−	13.9010i	0.346396	−	0.518418i	0.963231	+	0.268674i	$0.0865854\pi$
$720$	8.80677	+	1.41139i	0.328209	+	0.0525995i
$721$	−20.8932	+	13.9604i	−0.778103	+	0.519912i
$722$	5.94359	+	4.56068i	0.221198	+	0.169731i
$723$	21.0301	−	28.4959i	0.782116	−	1.05977i
$724$	−19.9397	+	1.30692i	−0.741055	+	0.0485713i
$725$	3.47130	+	3.04425i	0.128921	+	0.113061i
$726$	−1.12316	+	1.75101i	−0.0416843	+	0.0649862i
$727$	29.4309	+	7.88599i	1.09153	+	0.292475i	0.759312	−	0.650727i	$-0.225536\pi$
$727$	29.4309	+	7.88599i	1.09153	+	0.292475i	0.332220	+	0.943202i	$0.392202\pi$
$728$	2.15822	+	10.8501i	0.0799888	+	0.402131i
$729$	7.47154	−	25.9456i	0.276724	−	0.960950i
$730$		−	17.5923i		−	0.651120i
$731$	−0.494100	−	2.25047i	−0.0182749	−	0.0832367i
$732$	−0.320839	−	17.1375i	−0.0118586	−	0.633419i
$733$	13.7352	−	10.5394i	0.507320	−	0.389280i	−0.323147	−	0.946349i	$-0.604741\pi$
$733$	13.7352	−	10.5394i	0.507320	−	0.389280i	0.830466	+	0.557069i	$0.188074\pi$
$734$	−2.24211	+	6.60503i	−0.0827577	+	0.243796i
$735$	−0.960720	+	3.87413i	−0.0354367	+	0.142899i
$736$	−1.82494	+	27.8432i	−0.0672683	+	1.02632i
$737$	−3.32276	−	0.660938i	−0.122395	−	0.0243460i
$738$	−5.75600	+	4.16590i	−0.211881	+	0.153349i
$739$	−3.31457	−	8.00209i	−0.121929	−	0.294362i	0.851116	−	0.524977i	$-0.175926\pi$
$739$	−3.31457	−	8.00209i	−0.121929	−	0.294362i	−0.973045	+	0.230615i	$0.925926\pi$
$740$	−10.8032	+	14.0791i	−0.397135	+	0.517556i
$741$	−0.636886	−	7.54886i	−0.0233966	−	0.277314i
$742$	11.6441	−	13.2775i	0.427467	−	0.487433i
$743$	−14.7457	+	7.27176i	−0.540966	+	0.266775i	−0.692179	−	0.721726i	$-0.743349\pi$
$743$	−14.7457	+	7.27176i	−0.540966	+	0.266775i	0.151212	+	0.988501i	$0.451682\pi$
$744$	15.4787	+	53.7240i	0.567478	+	1.96962i
$745$	18.5534	+	21.1561i	0.679745	+	0.775100i
$746$	9.16509	+	3.79630i	0.335558	+	0.138993i
$747$	15.7738	+	25.1016i	0.577132	+	0.918421i
$748$	10.9174	+	1.21821i	0.399180	+	0.0445422i
$749$	17.7276	−	10.2350i	0.647753	−	0.373980i
$750$	−22.3551	+	3.36993i	−0.816293	+	0.123053i
$751$	−11.8886	−	4.03565i	−0.433823	−	0.147263i	0.0959812	−	0.995383i	$-0.469401\pi$
$751$	−11.8886	−	4.03565i	−0.433823	−	0.147263i	−0.529804	+	0.848120i	$0.677734\pi$
$752$	−1.44670	−	5.39916i	−0.0527557	−	0.196887i
$753$	−16.2469	−	10.4213i	−0.592071	−	0.379774i
$754$	3.97865	−	1.35057i	0.144894	−	0.0491848i
$755$	10.8878	+	16.2947i	0.396247	+	0.593026i
$756$	11.3828	−	5.48248i	0.413988	−	0.199396i
$757$	41.4764	−	17.1801i	1.50749	−	0.624421i	0.532448	−	0.846463i	$-0.321272\pi$
$757$	41.4764	−	17.1801i	1.50749	−	0.624421i	0.975037	+	0.222042i	$0.0712721\pi$
$758$	28.0917	+	13.8533i	1.02034	+	0.503175i
$759$	−6.08609	+	33.9016i	−0.220911	+	1.23055i
$760$	−8.78480	−	17.8138i	−0.318658	−	0.646175i
$761$	33.5760	−	8.99666i	1.21713	−	0.326129i	0.407573	−	0.913172i	$-0.366375\pi$
$761$	33.5760	−	8.99666i	1.21713	−	0.326129i	0.809555	+	0.587044i	$0.199708\pi$
$762$	−6.48775	−	7.12431i	−0.235026	−	0.258087i
$763$	−8.67678	+	1.14232i	−0.314120	+	0.0413547i
$764$	−18.7008			−0.676571
$765$	4.33481	+	22.7711i	0.156725	+	0.823293i
$766$	−20.9331			−0.756343
$767$	1.15989	−	0.152702i	0.0418812	−	0.00551377i
$768$	8.50590	−	26.6888i	0.306930	−	0.963047i
$769$	−18.5146	+	4.96098i	−0.667654	+	0.178897i	−0.576698	−	0.816958i	$-0.695659\pi$
$769$	−18.5146	+	4.96098i	−0.667654	+	0.178897i	−0.0909562	+	0.995855i	$0.528992\pi$
$770$	8.02378	+	16.2706i	0.289157	+	0.586352i
$771$	−6.96909	−	5.88464i	−0.250986	−	0.211930i
$772$	−18.9115	−	9.32611i	−0.680639	−	0.335654i
$773$	−6.81384	+	2.82238i	−0.245077	+	0.101514i	−0.501841	−	0.864960i	$-0.667344\pi$
$773$	−6.81384	+	2.82238i	−0.245077	+	0.101514i	0.256764	+	0.966474i	$0.417344\pi$
$774$	−1.79185	−	0.167957i	−0.0644066	−	0.00603709i
$775$	−8.73018	−	13.0656i	−0.313597	−	0.469331i
$776$	4.96039	−	1.68382i	0.178067	−	0.0604458i
$777$	2.59332	−	55.4548i	0.0930349	−	1.98943i
$778$	4.99638	+	18.6468i	0.179129	+	0.668518i
$779$	7.24356	+	2.45886i	0.259527	+	0.0880976i
$780$	1.26785	−	3.23062i	0.0453964	−	0.115675i
$781$	19.1614	−	11.0628i	0.685649	−	0.395860i
$782$	26.8983	−	7.78060i	0.961882	−	0.278234i
$783$	−8.83173	−	13.4872i	−0.315620	−	0.481995i
$784$	−1.80240	−	0.746579i	−0.0643715	−	0.0266636i
$785$	30.3757	+	34.6368i	1.08416	+	1.23624i
$786$	−18.4664	+	19.1710i	−0.658674	+	0.683807i
$787$	25.5465	−	12.5981i	0.910635	−	0.449075i	0.0742633	−	0.997239i	$-0.476339\pi$
$787$	25.5465	−	12.5981i	0.910635	−	0.449075i	0.836371	+	0.548163i	$0.184673\pi$
$788$	−2.62123	+	2.98894i	−0.0933773	+	0.106476i
$789$	−32.0575	−	15.0697i	−1.14128	−	0.536496i
$790$	3.37791	−	4.40218i	0.120181	−	0.156623i
$791$	−0.518419	−	1.25157i	−0.0184328	−	0.0445008i
$792$	11.7734	−	26.3138i	0.418350	−	0.935019i
$793$	14.4459	+	2.87346i	0.512988	+	0.102040i
$794$	0.0509601	−	0.777502i	0.00180851	−	0.0275925i
$795$	−17.8857	+	5.15315i	−0.634340	+	0.182763i
$796$	3.92245	−	11.5552i	0.139027	−	0.409561i
$797$	−1.71676	+	1.31732i	−0.0608109	+	0.0466618i	−0.638720	−	0.769440i	$-0.720536\pi$
$797$	−1.71676	+	1.31732i	−0.0608109	+	0.0466618i	0.577909	+	0.816101i	$0.303869\pi$
$798$	16.1867	+	8.94567i	0.573003	+	0.316673i
$799$	11.9167	−	8.30799i	0.421584	−	0.293916i
$800$			6.56371i			0.232062i
$801$	−12.3624	+	33.3216i	−0.436803	+	1.17736i
$802$	−2.83583	−	14.2567i	−0.100137	−	0.503421i
$803$	−26.5519	−	7.11455i	−0.936995	−	0.251067i
$804$	−1.58046	−	0.0739095i	−0.0557385	−	0.00260659i
$805$	−25.5699	−	22.4242i	−0.901221	−	0.790350i
$806$	−14.2693	+	0.935262i	−0.502616	+	0.0329432i
$807$	5.52422	+	12.6610i	0.194462	+	0.445687i
$808$	−21.0388	−	16.1436i	−0.740141	−	0.567930i
$809$	−5.71841	+	3.82092i	−0.201049	+	0.134336i	−0.652019	−	0.758202i	$-0.726078\pi$
$809$	−5.71841	+	3.82092i	−0.201049	+	0.134336i	0.450971	+	0.892539i	$0.351078\pi$
$810$	17.9724	+	2.19395i	0.631486	+	0.0770875i
$811$	−16.0336	+	23.9960i	−0.563015	+	0.842612i	−0.998336	−	0.0576636i	$-0.981635\pi$
$811$	−16.0336	+	23.9960i	−0.563015	+	0.842612i	0.435321	+	0.900275i	$0.356635\pi$
$812$	1.95250	−	7.28683i	0.0685193	−	0.255718i
$813$	3.27243	+	14.9804i	0.114769	+	0.525386i
$814$	−22.9519	−	29.9116i	−0.804465	−	1.04840i
$815$	7.66225	−	13.2714i	0.268397	−	0.464877i
$816$	−11.3213	+	0.436022i	−0.396325	+	0.0152638i
$817$	0.968763	+	1.67795i	0.0338927	+	0.0587039i
$818$	3.80156	−	9.17777i	0.132918	−	0.320893i
$819$	2.51512	+	10.5614i	0.0878853	+	0.369044i
$820$	2.47793	+	2.47793i	0.0865332	+	0.0865332i
$821$	13.3504	+	0.875032i	0.465933	+	0.0305388i	0.296562	−	0.955014i	$-0.404160\pi$
$821$	13.3504	+	0.875032i	0.465933	+	0.0305388i	0.169371	+	0.985552i	$0.445827\pi$
$822$	−10.4187	+	12.3388i	−0.363395	+	0.430363i
$823$	0.273683	+	4.17559i	0.00953998	+	0.145552i	0.999972	+	0.00754706i	$0.00240233\pi$
$823$	0.273683	+	4.17559i	0.00953998	+	0.145552i	−0.990432	+	0.138005i	$0.955931\pi$
$824$	−3.49499	+	26.5471i	−0.121754	+	0.924811i
$825$	−0.907011	+	8.05135i	−0.0315781	+	0.280312i
$826$	−1.26319	+	2.56149i	−0.0439519	+	0.0891257i
$827$	5.72886	−	28.8009i	0.199212	−	1.00151i	−0.743713	−	0.668500i	$-0.766937\pi$
$827$	5.72886	−	28.8009i	0.199212	−	1.00151i	0.942925	−	0.333007i	$-0.108063\pi$
$828$	−0.450521	+	16.0794i	−0.0156567	+	0.558799i
$829$	−1.81936	+	1.81936i	−0.0631889	+	0.0631889i	−0.737995	−	0.674806i	$-0.764227\pi$
$829$	−1.81936	+	1.81936i	−0.0631889	+	0.0631889i	0.674806	+	0.737995i	$0.264227\pi$
$830$	−14.9469	+	13.1081i	−0.518814	+	0.454988i
$831$	3.10792	+	20.6170i	0.107812	+	0.715195i
$832$	8.63926	+	4.98788i	0.299513	+	0.172924i
$833$	0.231501	−	5.06494i	0.00802104	−	0.175490i
$834$	39.5695	−	0.740802i	1.37018	−	0.0256519i
$835$	−1.97920	−	15.0335i	−0.0684931	−	0.520257i
$836$	−9.06006	+	1.80216i	−0.313349	+	0.0623290i
$837$	17.1534	+	52.1184i	0.592909	+	1.80148i
$838$	−17.3778	−	11.6115i	−0.600306	−	0.401111i
$839$	5.41377	+	15.9485i	0.186904	+	0.550602i	0.999480	−	0.0322541i	$-0.0102686\pi$
$839$	5.41377	+	15.9485i	0.186904	+	0.550602i	−0.812576	+	0.582856i	$0.801935\pi$
$840$	16.2543	+	23.3672i	0.560826	+	0.806245i
$841$	19.2081	+	2.52880i	0.662350	+	0.0872000i
$842$	3.44214	+	0.453166i	0.118624	+	0.0156171i
$843$	11.5615	−	24.5945i	0.398199	−	0.847081i
$844$	5.70830	+	16.8161i	0.196488	+	0.578835i
$845$	−17.7766	−	11.8780i	−0.611534	−	0.408614i
$846$	−3.34498	−	10.8427i	−0.115003	−	0.372778i
$847$	−3.14789	+	0.626154i	−0.108163	+	0.0215149i
$848$	−1.18747	−	9.01974i	−0.0407779	−	0.309739i
$849$	6.04779	−	10.9432i	0.207560	−	0.375568i
$850$	6.19413	−	2.24017i	0.212457	−	0.0768371i
$851$	61.2116	+	35.3406i	2.09831	+	1.21146i
$852$	8.07860	−	6.44272i	0.276768	−	0.220724i
$853$	−3.30555	+	2.89889i	−0.113180	+	0.0992560i	−0.714065	−	0.700079i	$-0.753148\pi$
$853$	−3.30555	+	2.89889i	−0.113180	+	0.0992560i	0.600886	+	0.799335i	$0.294815\pi$
$854$	−25.4255	+	25.4255i	−0.870041	+	0.870041i
$855$	−9.26959	−	17.1473i	−0.317013	−	0.586424i
$856$	4.25544	−	21.3935i	0.145448	−	0.731216i
$857$	16.5620	−	33.5844i	0.565747	−	1.14722i	−0.406583	−	0.913614i	$-0.633280\pi$
$857$	16.5620	−	33.5844i	0.565747	−	1.14722i	0.972331	−	0.233608i	$-0.0750534\pi$
$858$	5.93257	+	4.37825i	0.202534	+	0.149471i
$859$	4.10148	−	31.1538i	0.139941	−	1.06296i	−0.766985	−	0.641665i	$-0.778244\pi$
$859$	4.10148	−	31.1538i	0.139941	−	1.06296i	0.906926	−	0.421290i	$-0.138423\pi$
$860$	0.0580519	+	0.885702i	0.00197955	+	0.0302022i
$861$	−10.7900	−	1.93705i	−0.367724	−	0.0660146i
$862$	−38.9469	−	2.55271i	−1.32654	−	0.0869458i
$863$	2.99484	+	2.99484i	0.101946	+	0.101946i	0.756240	−	0.654294i	$-0.227034\pi$
$863$	2.99484	+	2.99484i	0.101946	+	0.101946i	−0.654294	+	0.756240i	$0.727034\pi$
$864$	6.13724	−	22.0817i	0.208793	−	0.751234i
$865$	−16.6091	+	40.0980i	−0.564727	+	1.36337i
$866$	19.9544	+	34.5621i	0.678079	+	1.17447i
$867$	−11.0724	−	27.2837i	−0.376040	−	0.926604i
$868$	−12.8375	+	22.2353i	−0.435735	+	0.754714i
$869$	−5.27810	−	6.87855i	−0.179047	−	0.233339i
$870$	7.99322	−	7.27902i	0.270995	−	0.246782i
$871$	0.351886	−	1.31326i	0.0119232	−	0.0444980i
$872$	−5.18105	+	7.75400i	−0.175453	+	0.262583i
$873$	4.80279	−	1.83353i	0.162550	−	0.0620557i
$874$	−19.5781	+	13.0817i	−0.662240	+	0.442495i
$875$	−27.6725	−	21.2338i	−0.935500	−	0.717834i
$876$	−12.7569	−	1.43711i	−0.431016	−	0.0485554i
$877$	20.2492	−	1.32720i	0.683766	−	0.0448164i	0.280439	−	0.959872i	$-0.409520\pi$
$877$	20.2492	−	1.32720i	0.683766	−	0.0448164i	0.403328	+	0.915056i	$0.367853\pi$
$878$	−0.0384146	−	0.0336887i	−0.00129643	−	0.00113694i
$879$	5.19927	+	10.0637i	0.175367	+	0.339439i
$880$	9.02715	+	2.41882i	0.304305	+	0.0815384i
$881$	6.70063	+	33.6863i	0.225750	+	1.13492i	0.912830	+	0.408340i	$0.133892\pi$
$881$	6.70063	+	33.6863i	0.225750	+	1.13492i	−0.687080	+	0.726582i	$0.741108\pi$
$882$	−3.71303	−	1.37754i	−0.125024	−	0.0463841i
$883$			12.0173i			0.404415i	0.979343	+	0.202207i	$0.0648115\pi$
$883$			12.0173i			0.404415i	−0.979343	+	0.202207i	$0.935189\pi$
$884$	−0.774383	+	4.33991i	−0.0260453	+	0.145967i
$885$	2.57827	−	1.55362i	0.0866674	−	0.0522245i
$886$	−20.4498	+	15.6917i	−0.687026	+	0.527174i
$887$	0.628663	−	1.85198i	0.0211084	−	0.0621834i	−0.935865	−	0.352358i	$-0.885380\pi$
$887$	0.628663	−	1.85198i	0.0211084	−	0.0621834i	0.956974	+	0.290174i	$0.0937133\pi$
$888$	−42.6057	−	41.0397i	−1.42975	−	1.37720i
$889$	0.972314	−	14.8346i	0.0326104	−	0.497538i
$890$	−23.3753	−	4.64964i	−0.783543	−	0.155856i
$891$	10.5796	−	26.2383i	0.354429	−	0.879017i
$892$	1.27293	+	3.07313i	0.0426209	+	0.102896i
$893$	−7.43655	+	9.69151i	−0.248855	+	0.324314i
$894$	−22.9199	+	15.9431i	−0.766555	+	0.533217i
$895$	17.9605	−	20.4800i	0.600354	−	0.684572i
$896$	0.854706	−	0.421494i	0.0285537	−	0.0140811i
$897$	−13.4162	−	3.32700i	−0.447954	−	0.111085i
$898$	−22.9534	−	26.1733i	−0.765964	−	0.873415i
$899$	30.2680	+	12.5374i	1.00949	+	0.418146i
$900$	0.141631	+	3.78125i	0.00472104	+	0.126042i
$901$	20.9945	−	10.8746i	0.699429	−	0.362287i
$902$	−6.44764	+	3.72255i	−0.214683	+	0.123947i
$903$	−1.73127	−	2.17086i	−0.0576131	−	0.0722417i
$904$	−1.36694	−	0.464012i	−0.0454636	−	0.0154328i
$905$	−11.4351	−	42.6763i	−0.380115	−	1.41861i
$906$	−17.2753	+	8.92506i	−0.573934	+	0.296515i
$907$	0.923546	−	0.313502i	0.0306658	−	0.0104096i	−0.306064	−	0.952011i	$-0.599012\pi$
$907$	0.923546	−	0.313502i	0.0306658	−	0.0104096i	0.336730	+	0.941601i	$0.390679\pi$
$908$	1.26934	+	1.89971i	0.0421246	+	0.0630440i
$909$	−21.2257	−	15.0592i	−0.704011	−	0.499482i
$910$	−6.72618	+	2.78608i	−0.222971	+	0.0923575i
$911$	−2.67472	−	1.31902i	−0.0886173	−	0.0437012i	0.397440	−	0.917628i	$-0.369899\pi$
$911$	−2.67472	−	1.31902i	−0.0886173	−	0.0437012i	−0.486057	+	0.873927i	$0.661565\pi$
$912$	8.96277	−	3.23078i	0.296787	−	0.106982i
$913$	13.7392	+	27.8603i	0.454700	+	0.922040i
$914$	−19.8745	+	5.32536i	−0.657391	+	0.176147i
$915$	37.0247	−	8.08796i	1.22400	−	0.267380i
$916$	3.90248	−	0.513771i	0.128942	−	0.0169755i
$917$	−41.0682			−1.35619
$918$	−22.9329	+	1.74472i	−0.756900	+	0.0575845i
$919$	−17.2397			−0.568685			−0.284342	−	0.958723i	$-0.591775\pi$
$919$	−17.2397			−0.568685			−0.284342	+	0.958723i	$0.591775\pi$
$920$	−35.9304	+	4.73032i	−1.18459	+	0.155954i
$921$	19.5650	−	4.27392i	0.644689	−	0.140831i
$922$	−7.63344	+	2.04537i	−0.251394	+	0.0673608i
$923$	3.92720	+	7.96358i	0.129265	+	0.262124i
$924$	12.4540	−	4.48924i	0.409705	−	0.147685i
$925$	14.9119	+	7.35374i	0.490300	+	0.241789i
$926$	−21.7399	+	9.00497i	−0.714418	+	0.295922i
$927$	−2.45237	+	26.1630i	−0.0805463	+	0.859307i
$928$	−7.60278	−	11.3784i	−0.249574	−	0.373513i
$929$	−7.87236	+	2.67231i	−0.258284	+	0.0876755i	−0.447578	−	0.894245i	$-0.647713\pi$
$929$	−7.87236	+	2.67231i	−0.258284	+	0.0876755i	0.189294	+	0.981920i	$0.439380\pi$
$930$	−32.6893	+	16.8885i	−1.07192	+	0.553795i
$931$	1.10351	+	4.11834i	0.0361660	+	0.134973i
$932$	12.0204	+	4.08039i	0.393742	+	0.133658i
$933$	3.55329	+	4.45551i	0.116330	+	0.145867i
$934$	20.0661	−	11.5852i	0.656584	−	0.379079i
$935$	2.06747	+	24.2002i	0.0676135	+	0.791432i
$936$	10.2284	+	5.40534i	0.334324	+	0.176679i
$937$	−41.1014	−	17.0247i	−1.34272	−	0.556174i	−0.408466	−	0.912773i	$-0.633936\pi$
$937$	−41.1014	−	17.0247i	−1.34272	−	0.556174i	−0.934257	+	0.356599i	$0.883936\pi$
$938$	2.18843	+	2.49543i	0.0714548	+	0.0814786i
$939$	25.0027	+	6.20026i	0.815932	+	0.202338i
$940$	−5.01910	+	2.47515i	−0.163705	+	0.0807304i
$941$	10.9401	−	12.4748i	0.356636	−	0.406666i	−0.545504	−	0.838108i	$-0.683662\pi$
$941$	10.9401	−	12.4748i	0.356636	−	0.406666i	0.902141	+	0.431442i	$0.141995\pi$
$942$	−37.5245	+	26.1021i	−1.22261	+	0.850452i
$943$	8.49666	−	11.0731i	0.276689	−	0.360588i
$944$	0.563036	+	1.35929i	0.0183253	+	0.0442411i
$945$	16.7989	+	22.3191i	0.546468	+	0.726040i
$946$	−1.84951	−	0.367891i	−0.0601329	−	0.0119612i
$947$	−1.39017	+	21.2098i	−0.0451744	+	0.689227i	0.913876	+	0.405993i	$0.133074\pi$
$947$	−1.39017	+	21.2098i	−0.0451744	+	0.689227i	−0.959051	+	0.283235i	$0.908592\pi$
$948$	−2.91627	−	2.80908i	−0.0947160	−	0.0912348i
$949$	3.54594	−	10.4460i	0.115106	−	0.339091i
$950$	−4.39431	+	3.37187i	−0.142570	+	0.109398i
$951$	−21.0763	+	12.7003i	−0.683445	+	0.411834i
$952$	−26.0678	−	25.0567i	−0.844861	−	0.812091i
$953$			48.0757i			1.55732i	0.627443	+	0.778662i	$0.284101\pi$
$953$			48.0757i			1.55732i	−0.627443	+	0.778662i	$0.715899\pi$
$954$	−3.09421	−	18.2070i	−0.100179	−	0.589472i
$955$	−8.06656	−	40.5533i	−0.261028	−	1.31227i
$956$	6.51101	+	1.74462i	0.210581	+	0.0564250i
$957$	−7.75359	−	15.0078i	−0.250638	−	0.485134i
$958$	29.7619	+	26.1005i	0.961563	+	0.843268i
$959$	−24.8624	+	1.62957i	−0.802850	+	0.0526216i
$960$	25.5066	+	2.87340i	0.823221	+	0.0927386i
$961$	−63.8670	−	49.0069i	−2.06023	−	1.58087i
$962$	12.5805	−	8.40605i	0.405613	−	0.271022i
$963$	3.38745	−	21.1369i	0.109159	−	0.681128i
$964$	9.62836	−	14.4099i	0.310108	−	0.464110i
$965$	12.0665	−	45.0330i	0.388436	−	1.44966i
$966$	24.9495	−	22.7202i	0.802737	−	0.731012i
$967$	−14.2392	−	18.5569i	−0.457902	−	0.596750i	0.506155	−	0.862442i	$-0.331066\pi$
$967$	−14.2392	−	18.5569i	−0.457902	−	0.596750i	−0.964058	+	0.265692i	$0.914400\pi$
$968$	−1.71003	+	2.96186i	−0.0549625	+	0.0951979i
$969$	15.8181	+	19.0492i	0.508151	+	0.611949i
$970$	1.72370	+	2.98554i	0.0553447	+	0.0958598i
$971$	3.93166	−	9.49188i	0.126173	−	0.304609i	−0.848153	−	0.529752i	$-0.822285\pi$
$971$	3.93166	−	9.49188i	0.126173	−	0.304609i	0.974326	+	0.225143i	$0.0722850\pi$
$972$	3.05909	−	12.8533i	0.0981203	−	0.412271i
$973$	43.1765	+	43.1765i	1.38417	+	1.38417i
$974$	5.06203	+	0.331783i	0.162198	+	0.0106310i
$975$	−3.20037	−	0.574537i	−0.102494	−	0.0183999i
$976$	1.21148	+	18.4836i	0.0387786	+	0.591646i
$977$	−6.24428	+	47.4300i	−0.199772	+	1.51742i	0.538331	+	0.842734i	$0.319055\pi$
$977$	−6.24428	+	47.4300i	−0.199772	+	1.51742i	−0.738103	+	0.674688i	$0.764278\pi$
$978$	12.2340	+	9.02876i	0.391201	+	0.288708i
$979$	−16.4709	+	33.3998i	−0.526414	+	1.06746i
$980$	−0.381053	+	1.91568i	−0.0121723	+	0.0611942i
$981$	−4.79622	+	7.79464i	−0.153132	+	0.248864i
$982$	17.8990	−	17.8990i	0.571182	−	0.571182i
$983$	46.4012	−	40.6928i	1.47997	−	1.29790i	0.623354	−	0.781940i	$-0.285770\pi$
$983$	46.4012	−	40.6928i	1.47997	−	1.29790i	0.856614	−	0.515958i	$-0.172564\pi$
$984$	−9.13287	+	7.28351i	−0.291145	+	0.232190i
$985$	−7.61226	−	4.39494i	−0.242547	−	0.140035i
$986$	−8.14289	+	11.0581i	−0.259322	+	0.352161i
$987$	8.46798	−	15.3224i	0.269539	−	0.487716i
$988$	−0.483877	−	3.67541i	−0.0153942	−	0.116931i
$989$	3.46728	−	0.689685i	0.110253	−	0.0219307i
$990$	18.4960	+	4.22084i	0.587842	+	0.134147i
$991$	32.4346	+	21.6721i	1.03032	+	0.688437i	0.951246	−	0.308432i	$-0.0998043\pi$
$991$	32.4346	+	21.6721i	1.03032	+	0.688437i	0.0790719	+	0.996869i	$0.474804\pi$
$992$	14.9710	+	44.1030i	0.475329	+	1.40027i
$993$	13.8353	−	29.4315i	0.439050	−	0.933982i
$994$	−21.4912	−	2.82936i	−0.681658	−	0.0897420i
$995$	26.7497	+	3.52166i	0.848021	+	0.111644i
$996$	8.28421	+	11.9094i	0.262495	+	0.377364i
$997$	9.67936	+	28.5145i	0.306549	+	0.903063i	0.985618	+	0.168989i	$0.0540502\pi$
$997$	9.67936	+	28.5145i	0.306549	+	0.903063i	−0.679069	+	0.734074i	$0.737616\pi$
$998$	18.8138	+	12.5710i	0.595540	+	0.397927i
$999$	−43.2908	−	38.6825i	−1.36966	−	1.22386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.113.6	yes	256
3.2	odd	2		459.2.y.a.368.11		256
9.2	odd	6	inner	153.2.s.a.11.6	✓	256
9.7	even	3		459.2.y.a.62.11		256
17.14	odd	16	inner	153.2.s.a.14.6	yes	256
51.14	even	16		459.2.y.a.422.11		256
153.65	even	48	inner	153.2.s.a.65.6	yes	256
153.133	odd	48		459.2.y.a.116.11		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.6	✓	256	9.2	odd	6	inner
153.2.s.a.14.6	yes	256	17.14	odd	16	inner
153.2.s.a.65.6	yes	256	153.65	even	48	inner
153.2.s.a.113.6	yes	256	1.1	even	1	trivial
459.2.y.a.62.11		256	9.7	even	3
459.2.y.a.116.11		256	153.133	odd	48
459.2.y.a.368.11		256	3.2	odd	2
459.2.y.a.422.11		256	51.14	even	16

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06433 + 0.140121i) q^{2} +(-1.69215 + 0.369645i) q^{3} +(-0.818692 + 0.219368i) q^{4} +(-0.828848 - 1.68074i) q^{5} +(1.74920 - 0.630530i) q^{6} +(2.57290 + 1.26881i) q^{7} +(2.82421 - 1.16983i) q^{8} +(2.72672 - 1.25099i) q^{9} +O(q^{10})\)	\(q+(-1.06433 + 0.140121i) q^{2} +(-1.69215 + 0.369645i) q^{3} +(-0.818692 + 0.219368i) q^{4} +(-0.828848 - 1.68074i) q^{5} +(1.74920 - 0.630530i) q^{6} +(2.57290 + 1.26881i) q^{7} +(2.82421 - 1.16983i) q^{8} +(2.72672 - 1.25099i) q^{9} +(1.11767 + 1.67272i) q^{10} +(2.97662 - 1.01042i) q^{11} +(1.30426 - 0.673829i) q^{12} +(0.326499 + 1.21851i) q^{13} +(-2.91620 - 0.989916i) q^{14} +(2.02381 + 2.53768i) q^{15} +(-1.37393 + 0.793237i) q^{16} +(-3.15306 - 2.65672i) q^{17} +(-2.72684 + 1.71353i) q^{18} +(3.20325 + 1.32683i) q^{19} +(1.04727 + 1.19418i) q^{20} +(-4.82274 - 1.19596i) q^{21} +(-3.02651 + 1.49251i) q^{22} +(4.17115 - 4.75629i) q^{23} +(-4.34656 + 3.02347i) q^{24} +(0.905918 - 1.18061i) q^{25} +(-0.518241 - 1.25114i) q^{26} +(-4.15160 + 3.12478i) q^{27} +(-2.38475 - 0.474357i) q^{28} +(-0.202920 + 3.09596i) q^{29} +(-2.50958 - 2.41734i) q^{30} +(3.39423 - 9.99909i) q^{31} +(-3.49925 + 2.68507i) q^{32} +(-4.66337 + 2.81008i) q^{33} +(3.72816 + 2.38581i) q^{34} -5.37603i q^{35} +(-1.95792 + 1.62233i) q^{36} +(2.17970 + 10.9581i) q^{37} +(-3.59522 - 0.963337i) q^{38} +(-1.00290 - 1.94121i) q^{39} +(-4.30701 - 3.77715i) q^{40} +(2.20154 - 0.144297i) q^{41} +(5.30055 + 0.597125i) q^{42} +(0.443342 + 0.340188i) q^{43} +(-2.21528 + 1.48020i) q^{44} +(-4.36262 - 3.54603i) q^{45} +(-3.77301 + 5.64671i) q^{46} +(-0.911896 + 3.40324i) q^{47} +(2.03167 - 1.85014i) q^{48} +(0.748601 + 0.975596i) q^{49} +(-0.798764 + 1.38350i) q^{50} +(6.31750 + 3.33005i) q^{51} +(-0.534604 - 0.925961i) q^{52} +(-2.19448 + 5.29795i) q^{53} +(3.98081 - 3.90751i) q^{54} +(-4.16542 - 4.16542i) q^{55} +(8.75070 + 0.573551i) q^{56} +(-5.91083 - 1.06113i) q^{57} +(-0.217837 - 3.32354i) q^{58} +(0.121049 - 0.919458i) q^{59} +(-2.21356 - 1.63362i) q^{60} +(5.16405 - 10.4717i) q^{61} +(-2.21149 + 11.1179i) q^{62} +(8.60287 + 0.241039i) q^{63} +(5.59173 - 5.59173i) q^{64} +(1.77738 - 1.55872i) q^{65} +(4.56960 - 3.64428i) q^{66} +(-0.933364 - 0.538878i) q^{67} +(3.16419 + 1.48336i) q^{68} +(-5.30006 + 9.59018i) q^{69} +(0.753296 + 5.72185i) q^{70} +(6.90345 - 1.37318i) q^{71} +(6.23740 - 6.72285i) q^{72} +(-7.27098 - 4.85831i) q^{73} +(-3.85538 - 11.3576i) q^{74} +(-1.09654 + 2.33264i) q^{75} +(-2.91354 - 0.383575i) q^{76} +(8.94058 + 1.17705i) q^{77} +(1.33942 + 1.92556i) q^{78} +(-0.886594 - 2.61182i) q^{79} +(2.47200 + 1.65174i) q^{80} +(5.87006 - 6.82220i) q^{81} +(-2.32295 + 0.462063i) q^{82} +(1.28987 + 9.79756i) q^{83} +(4.21070 - 0.0788306i) q^{84} +(-1.85184 + 7.50149i) q^{85} +(-0.519529 - 0.299950i) q^{86} +(-0.801035 - 5.31382i) q^{87} +(7.22457 - 6.33577i) q^{88} +(-8.37709 + 8.37709i) q^{89} +(5.14013 + 3.16284i) q^{90} +(-0.706014 + 3.54937i) q^{91} +(-2.37151 + 4.80895i) q^{92} +(-2.04743 + 18.1746i) q^{93} +(0.493689 - 3.74994i) q^{94} +(-0.424955 - 6.48356i) q^{95} +(4.92872 - 5.83701i) q^{96} +(1.70996 + 0.112076i) q^{97} +(-0.933458 - 0.933458i) q^{98} +(6.85238 - 6.47886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

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