LMFDB - Embedded newform 507.2.p.a.25.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.13
Character	$\chi$	$=$	507.25
Dual form			507.2.p.a.142.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.15817 + 0.818487i) q^{2} +(0.568065 + 0.822984i) q^{3} +(2.49077 + 2.20663i) q^{4} +(-1.10490 - 0.134159i) q^{5} +(0.552380 + 2.24110i) q^{6} +(1.27631 + 2.43180i) q^{7} +(1.42410 + 2.71339i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-2.27476 - 1.19389i) q^{10} +(0.785015 - 0.297717i) q^{11} +(-0.401102 + 3.30337i) q^{12} +(-2.04354 - 2.97051i) q^{13} +(0.764095 + 6.29289i) q^{14} +(-0.517244 - 0.985527i) q^{15} +(0.0503695 + 0.414830i) q^{16} +(4.59452 - 2.41139i) q^{17} +(-1.53060 + 1.72769i) q^{18} +6.51566i q^{19} +(-2.45601 - 2.77227i) q^{20} +(-1.27631 + 2.43180i) q^{21} +1.93788 q^{22} -3.52525 q^{23} +(-1.42410 + 2.71339i) q^{24} +(-3.65190 - 0.900113i) q^{25} +(-1.97900 - 8.08349i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(-2.18709 + 8.87339i) q^{28} +(1.47554 - 3.89069i) q^{29} +(-0.309662 - 2.55030i) q^{30} +(-0.748705 - 3.03761i) q^{31} +(1.23589 - 5.01420i) q^{32} +(0.690956 + 0.476932i) q^{33} +(11.8895 - 1.44364i) q^{34} +(-1.08394 - 2.85813i) q^{35} +(-2.94647 + 1.54643i) q^{36} +(-0.134074 - 0.543960i) q^{37} +(-5.33299 + 14.0619i) q^{38} +(1.28382 - 3.36925i) q^{39} +(-1.20946 - 3.18908i) q^{40} +(7.70419 - 5.31781i) q^{41} +(-4.74489 + 4.20360i) q^{42} +(1.84209 + 0.454036i) q^{43} +(2.61224 + 0.990693i) q^{44} +(0.517244 - 0.985527i) q^{45} +(-7.60811 - 2.88538i) q^{46} +(5.92007 + 6.68238i) q^{47} +(-0.312785 + 0.277103i) q^{48} +(-0.308237 + 0.446559i) q^{49} +(-7.14471 - 4.93163i) q^{50} +(4.59452 + 2.41139i) q^{51} +(1.46482 - 11.9082i) q^{52} +(0.596204 - 0.312912i) q^{53} +(-2.29134 - 0.278219i) q^{54} +(-0.907305 + 0.223631i) q^{55} +(-4.78084 + 6.92624i) q^{56} +(-5.36229 + 3.70132i) q^{57} +(6.36896 - 7.18907i) q^{58} +(-0.111917 - 0.0135892i) q^{59} +(0.886356 - 3.59609i) q^{60} +(-11.6001 - 6.08820i) q^{61} +(0.870414 - 7.16850i) q^{62} +(-2.72636 + 0.331040i) q^{63} +(7.24609 - 10.4978i) q^{64} +(1.85939 + 3.55628i) q^{65} +(1.10084 + 1.59484i) q^{66} +(-6.95557 - 7.85121i) q^{67} +(16.7649 + 4.13218i) q^{68} +(-2.00257 - 2.90123i) q^{69} -7.05553i q^{70} +(-9.22342 + 6.36647i) q^{71} +(-3.04206 + 0.369372i) q^{72} +(9.93932 - 3.76949i) q^{73} +(0.155869 - 1.28370i) q^{74} +(-1.33374 - 3.51678i) q^{75} +(-14.3777 + 16.2290i) q^{76} +(1.72591 + 1.52902i) q^{77} +(5.52838 - 6.22063i) q^{78} +(-13.0909 + 11.5976i) q^{79} -0.465103i q^{80} +(-0.748511 - 0.663123i) q^{81} +(20.9795 - 5.17099i) q^{82} +(-2.71140 - 1.87154i) q^{83} +(-8.54507 + 3.24072i) q^{84} +(-5.40000 + 2.04795i) q^{85} +(3.60394 + 2.48762i) q^{86} +(4.04018 - 0.995815i) q^{87} +(1.92576 + 1.70607i) q^{88} +1.72303i q^{89} +(1.92294 - 1.70358i) q^{90} +(4.61550 - 8.76077i) q^{91} +(-8.78059 - 7.77893i) q^{92} +(2.07459 - 2.34173i) q^{93} +(7.30710 + 19.2672i) q^{94} +(0.874136 - 7.19916i) q^{95} +(4.82868 - 1.83127i) q^{96} +(-0.316426 + 0.0384210i) q^{97} +(-1.03073 + 0.711463i) q^{98} +0.839574i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

Coefficient data

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

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

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

$2$	2.15817	+	0.818487i	1.52606	+	0.578758i	0.967979	−	0.251030i	$-0.0807692\pi$
$2$	2.15817	+	0.818487i	1.52606	+	0.578758i	0.558080	+	0.829787i	$0.311538\pi$
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$3$	0.568065	+	0.822984i	0.327972	+	0.475150i
$4$	2.49077	+	2.20663i	1.24538	+	1.10331i
$5$	−1.10490	−	0.134159i	−0.494127	−	0.0599978i	−0.130319	−	0.991472i	$-0.541600\pi$
$5$	−1.10490	−	0.134159i	−0.494127	−	0.0599978i	−0.363807	+	0.931474i	$0.618523\pi$
$6$	0.552380	+	2.24110i	0.225508	+	0.914923i
$7$	1.27631	+	2.43180i	0.482399	+	0.919134i	0.998055	+	0.0623384i	$0.0198558\pi$
$7$	1.27631	+	2.43180i	0.482399	+	0.919134i	−0.515656	+	0.856795i	$0.672452\pi$
$8$	1.42410	+	2.71339i	0.503494	+	0.959328i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	−2.27476	−	1.19389i	−0.719342	−	0.377540i
$11$	0.785015	−	0.297717i	0.236691	−	0.0897650i	−0.233408	−	0.972379i	$-0.574988\pi$
$11$	0.785015	−	0.297717i	0.236691	−	0.0897650i	0.470099	+	0.882614i	$0.344218\pi$
$12$	−0.401102	+	3.30337i	−0.115788	+	0.953601i
$13$	−2.04354	−	2.97051i	−0.566777	−	0.823871i
$13$	−2.04354	−	2.97051i	−0.566777	−	0.823871i
$14$	0.764095	+	6.29289i	0.204213	+	1.68184i
$15$	−0.517244	−	0.985527i	−0.133552	−	0.254462i
$16$	0.0503695	+	0.414830i	0.0125924	+	0.103707i
$17$	4.59452	−	2.41139i	1.11433	−	0.584848i	0.195981	−	0.980608i	$-0.437211\pi$
$17$	4.59452	−	2.41139i	1.11433	−	0.584848i	0.918354	+	0.395760i	$0.129519\pi$
$18$	−1.53060	+	1.72769i	−0.360765	+	0.407220i
$19$			6.51566i			1.49480i	0.664377	+	0.747398i	$0.268697\pi$
$19$			6.51566i			1.49480i	−0.664377	+	0.747398i	$0.731303\pi$
$20$	−2.45601	−	2.77227i	−0.549181	−	0.619898i
$21$	−1.27631	+	2.43180i	−0.278513	+	0.530662i
$22$	1.93788			0.413157
$23$	−3.52525			−0.735066			−0.367533	−	0.930010i	$-0.619798\pi$
$23$	−3.52525			−0.735066			−0.367533	+	0.930010i	$0.619798\pi$
$24$	−1.42410	+	2.71339i	−0.290693	+	0.553868i
$25$	−3.65190	−	0.900113i	−0.730380	−	0.180023i
$26$	−1.97900	−	8.08349i	−0.388113	−	1.58530i
$27$	−0.970942	+	0.239316i	−0.186858	+	0.0460563i
$28$	−2.18709	+	8.87339i	−0.413322	+	1.67691i
$29$	1.47554	−	3.89069i	0.274002	−	0.722483i	−0.725414	−	0.688313i	$-0.758352\pi$
$29$	1.47554	−	3.89069i	0.274002	−	0.722483i	0.999416	−	0.0341706i	$-0.0108790\pi$
$30$	−0.309662	−	2.55030i	−0.0565363	−	0.465618i
$31$	−0.748705	−	3.03761i	−0.134471	−	0.545572i	−0.999070	−	0.0431092i	$-0.986274\pi$
$31$	−0.748705	−	3.03761i	−0.134471	−	0.545572i	0.864599	−	0.502462i	$-0.167572\pi$
$32$	1.23589	−	5.01420i	0.218477	−	0.886394i
$33$	0.690956	+	0.476932i	0.120280	+	0.0830233i
$34$	11.8895	−	1.44364i	2.03903	−	0.247583i
$35$	−1.08394	−	2.85813i	−0.183220	−	0.483111i
$36$	−2.94647	+	1.54643i	−0.491079	+	0.257738i
$37$	−0.134074	−	0.543960i	−0.0220416	−	0.0894265i	0.958891	−	0.283775i	$-0.0915869\pi$
$37$	−0.134074	−	0.543960i	−0.0220416	−	0.0894265i	−0.980933	+	0.194349i	$0.937741\pi$
$38$	−5.33299	+	14.0619i	−0.865125	+	2.28115i
$39$	1.28382	−	3.36925i	0.205575	−	0.539511i
$40$	−1.20946	−	3.18908i	−0.191232	−	0.504238i
$41$	7.70419	−	5.31781i	1.20319	−	0.830503i	0.213957	−	0.976843i	$-0.431365\pi$
$41$	7.70419	−	5.31781i	1.20319	−	0.830503i	0.989234	+	0.146340i	$0.0467493\pi$
$42$	−4.74489	+	4.20360i	−0.732152	+	0.648630i
$43$	1.84209	+	0.454036i	0.280917	+	0.0692398i	0.377257	−	0.926109i	$-0.376867\pi$
$43$	1.84209	+	0.454036i	0.280917	+	0.0692398i	−0.0963399	+	0.995348i	$0.530714\pi$
$44$	2.61224	+	0.990693i	0.393810	+	0.149353i
$45$	0.517244	−	0.985527i	0.0771062	−	0.146914i
$46$	−7.60811	−	2.88538i	−1.12175	−	0.425425i
$47$	5.92007	+	6.68238i	0.863531	+	0.974725i	0.999873	−	0.0159364i	$-0.00507293\pi$
$47$	5.92007	+	6.68238i	0.863531	+	0.974725i	−0.136342	+	0.990662i	$0.543534\pi$
$48$	−0.312785	+	0.277103i	−0.0451466	+	0.0399964i
$49$	−0.308237	+	0.446559i	−0.0440339	+	0.0637941i
$50$	−7.14471	−	4.93163i	−1.01041	−	0.697438i
$51$	4.59452	+	2.41139i	0.643361	+	0.337662i
$52$	1.46482	−	11.9082i	0.203133	−	1.65137i
$53$	0.596204	−	0.312912i	0.0818949	−	0.0429818i	−0.423279	−	0.906000i	$-0.639121\pi$
$53$	0.596204	−	0.312912i	0.0818949	−	0.0429818i	0.505173	+	0.863018i	$0.331429\pi$
$54$	−2.29134	−	0.278219i	−0.311812	−	0.0378608i
$55$	−0.907305	+	0.223631i	−0.122341	+	0.0301544i
$56$	−4.78084	+	6.92624i	−0.638866	+	0.925558i
$57$	−5.36229	+	3.70132i	−0.710252	+	0.490252i
$58$	6.36896	−	7.18907i	0.836286	−	0.943971i
$59$	−0.111917	−	0.0135892i	−0.0145703	−	0.00176916i	0.113248	−	0.993567i	$-0.463874\pi$
$59$	−0.111917	−	0.0135892i	−0.0145703	−	0.00176916i	−0.127819	+	0.991798i	$0.540798\pi$
$60$	0.886356	−	3.59609i	0.114428	−	0.464253i
$61$	−11.6001	−	6.08820i	−1.48524	−	0.779514i	−0.489524	−	0.871990i	$-0.662830\pi$
$61$	−11.6001	−	6.08820i	−1.48524	−	0.779514i	−0.995715	+	0.0924761i	$0.970522\pi$
$62$	0.870414	−	7.16850i	0.110543	−	0.910401i
$63$	−2.72636	+	0.331040i	−0.343489	+	0.0417071i
$64$	7.24609	−	10.4978i	0.905761	−	1.31222i
$65$	1.85939	+	3.55628i	0.230629	+	0.441102i
$66$	1.10084	+	1.59484i	0.135504	+	0.196311i
$67$	−6.95557	−	7.85121i	−0.849758	−	0.959178i	0.149806	−	0.988715i	$-0.452135\pi$
$67$	−6.95557	−	7.85121i	−0.849758	−	0.959178i	−0.999564	+	0.0295372i	$0.990597\pi$
$68$	16.7649	+	4.13218i	2.03305	+	0.501101i
$69$	−2.00257	−	2.90123i	−0.241081	−	0.349267i
$70$		−	7.05553i		−	0.843297i
$71$	−9.22342	+	6.36647i	−1.09462	+	0.755561i	−0.971549	−	0.236837i	$-0.923889\pi$
$71$	−9.22342	+	6.36647i	−1.09462	+	0.755561i	−0.123069	+	0.992398i	$0.539274\pi$
$72$	−3.04206	+	0.369372i	−0.358510	+	0.0435310i
$73$	9.93932	−	3.76949i	1.16331	−	0.441185i	0.304015	−	0.952667i	$-0.401673\pi$
$73$	9.93932	−	3.76949i	1.16331	−	0.441185i	0.859294	+	0.511482i	$0.170903\pi$
$74$	0.155869	−	1.28370i	0.0181194	−	0.149227i
$75$	−1.33374	−	3.51678i	−0.154007	−	0.406083i
$76$	−14.3777	+	16.2290i	−1.64923	+	1.86160i
$77$	1.72591	+	1.52902i	0.196686	+	0.174248i
$78$	5.52838	−	6.22063i	0.625966	−	0.704348i
$79$	−13.0909	+	11.5976i	−1.47285	+	1.30483i	−0.617731	+	0.786390i	$0.711948\pi$
$79$	−13.0909	+	11.5976i	−1.47285	+	1.30483i	−0.855115	+	0.518438i	$0.826514\pi$
$80$		−	0.465103i		−	0.0520001i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	20.9795	−	5.17099i	2.31680	−	0.571040i
$83$	−2.71140	−	1.87154i	−0.297615	−	0.205429i	0.409894	−	0.912133i	$-0.365566\pi$
$83$	−2.71140	−	1.87154i	−0.297615	−	0.205429i	−0.707509	+	0.706705i	$0.750181\pi$
$84$	−8.54507	+	3.24072i	−0.932343	+	0.353591i
$85$	−5.40000	+	2.04795i	−0.585712	+	0.222131i
$86$	3.60394	+	2.48762i	0.388623	+	0.268247i
$87$	4.04018	−	0.995815i	0.433153	−	0.106763i
$88$	1.92576	+	1.70607i	0.205287	+	0.181868i
$89$			1.72303i			0.182641i	0.995822	+	0.0913204i	$0.0291088\pi$
$89$			1.72303i			0.182641i	−0.995822	+	0.0913204i	$0.970891\pi$
$90$	1.92294	−	1.70358i	0.202696	−	0.179573i
$91$	4.61550	−	8.76077i	0.483835	−	0.918378i
$92$	−8.78059	−	7.77893i	−0.915440	−	0.811009i
$93$	2.07459	−	2.34173i	0.215125	−	0.242826i
$94$	7.30710	+	19.2672i	0.753670	+	1.98726i
$95$	0.874136	−	7.19916i	0.0896845	−	0.738618i
$96$	4.82868	−	1.83127i	0.492825	−	0.186904i
$97$	−0.316426	+	0.0384210i	−0.0321282	+	0.00390106i	−0.136585	−	0.990628i	$-0.543613\pi$
$97$	−0.316426	+	0.0384210i	−0.0321282	+	0.00390106i	0.104457	+	0.994529i	$0.466690\pi$
$98$	−1.03073	+	0.711463i	−0.104120	+	0.0718686i
$99$			0.839574i			0.0843803i
$100$	−7.10983	−	10.3004i	−0.710983	−	1.03004i
$101$	6.33619	+	1.56173i	0.630474	+	0.155398i	0.541588	−	0.840644i	$-0.317823\pi$
$101$	6.33619	+	1.56173i	0.630474	+	0.155398i	0.0888861	+	0.996042i	$0.471669\pi$
$102$	7.94208	+	8.96475i	0.786383	+	0.887643i
$103$	1.11289	+	1.61230i	0.109657	+	0.158865i	0.873970	−	0.485980i	$-0.161537\pi$
$103$	1.11289	+	1.61230i	0.109657	+	0.158865i	−0.764313	+	0.644845i	$0.776922\pi$
$104$	5.14995	−	9.77523i	0.504994	−	0.958540i
$105$	1.73644	−	2.51567i	0.169459	−	0.245504i
$106$	1.54283	−	0.187333i	0.149852	−	0.0181954i
$107$	−1.33630	+	11.0054i	−0.129185	+	1.06393i	0.773551	+	0.633735i	$0.218479\pi$
$107$	−1.33630	+	11.0054i	−0.129185	+	1.06393i	−0.902735	+	0.430197i	$0.858444\pi$
$108$	−2.94647	−	1.54643i	−0.283524	−	0.148805i
$109$	−1.35154	+	5.48343i	−0.129454	+	0.525217i	0.870027	+	0.493005i	$0.164101\pi$
$109$	−1.35154	+	5.48343i	−0.129454	+	0.525217i	−0.999481	+	0.0322125i	$0.989745\pi$
$110$	−2.14116	−	0.259984i	−0.204152	−	0.0247885i
$111$	0.371508	−	0.419345i	0.0352619	−	0.0398025i
$112$	−0.944496	+	0.651939i	−0.0892465	+	0.0616024i
$113$	1.63455	−	2.36805i	0.153765	−	0.222767i	−0.738529	−	0.674222i	$-0.764479\pi$
$113$	1.63455	−	2.36805i	0.153765	−	0.222767i	0.892294	+	0.451454i	$0.149095\pi$
$114$	−14.6022	+	3.59912i	−1.36762	+	0.337089i
$115$	3.89506	+	0.472945i	0.363216	+	0.0441024i
$116$	12.2606	−	6.43483i	1.13836	−	0.597459i
$117$	3.50213	−	0.857390i	0.323772	−	0.0792657i
$118$	−0.230414	−	0.120930i	−0.0212113	−	0.0111325i
$119$	11.7280	+	8.09528i	1.07511	+	0.742093i
$120$	1.93751	−	2.80697i	0.176870	−	0.256240i
$121$	−7.70600	+	6.82692i	−0.700546	+	0.620630i
$122$	−20.0519	−	22.6339i	−1.81541	−	2.04918i
$123$	8.75295	+	3.31956i	0.789227	+	0.299314i
$124$	4.83804	−	9.21811i	0.434469	−	0.827811i
$125$	9.11767	+	3.45788i	0.815509	+	0.309282i
$126$	−6.15490	−	1.51705i	−0.548322	−	0.135149i
$127$	−9.58624	+	8.49266i	−0.850641	+	0.753602i	−0.970988	−	0.239130i	$-0.923138\pi$
$127$	−9.58624	+	8.49266i	−0.850641	+	0.753602i	0.120347	+	0.992732i	$0.461599\pi$
$128$	15.7304	−	10.8579i	1.39038	−	0.959712i
$129$	0.672765	+	1.77394i	0.0592337	+	0.156186i
$130$	1.10212	+	9.19696i	0.0966625	+	0.806626i
$131$	0.189053	−	0.498492i	0.0165177	−	0.0435535i	−0.926504	−	0.376285i	$-0.877201\pi$
$131$	0.189053	−	0.498492i	0.0165177	−	0.0435535i	0.943021	+	0.332732i	$0.107970\pi$
$132$	0.668599	+	2.71261i	0.0581940	+	0.236103i
$133$	−15.8448	+	8.31599i	−1.37392	+	0.721087i
$134$	−8.58520	−	22.6373i	−0.741649	−	1.95557i
$135$	1.10490	−	0.134159i	0.0950947	−	0.0115466i
$136$	13.0861	+	9.03267i	1.12212	+	0.774545i
$137$	−2.10000	+	8.52004i	−0.179415	+	0.727916i	0.810438	+	0.585824i	$0.199229\pi$
$137$	−2.10000	+	8.52004i	−0.179415	+	0.727916i	−0.989853	+	0.142092i	$0.954617\pi$
$138$	−1.94728	−	7.90043i	−0.165764	−	0.672529i
$139$	−1.18731	−	9.77835i	−0.100706	−	0.829389i	−0.952295	−	0.305179i	$-0.901284\pi$
$139$	−1.18731	−	9.77835i	−0.100706	−	0.829389i	0.851589	−	0.524210i	$-0.175639\pi$
$140$	3.60697	−	9.51080i	0.304845	−	0.803809i
$141$	−2.13651	+	8.66815i	−0.179926	+	0.729990i
$142$	−25.1166	+	6.19069i	−2.10774	+	0.519511i
$143$	−2.48858	−	1.72350i	−0.208106	−	0.144126i
$144$	−0.405734	−	0.100004i	−0.0338112	−	0.00833370i
$145$	−2.15230	+	4.10087i	−0.178739	+	0.340559i
$146$	24.5361			2.03062
$147$	−0.542610			−0.0447537
$148$	0.866370	−	1.65073i	0.0712152	−	0.135689i
$149$	−14.3729	−	16.2237i	−1.17748	−	1.32910i	−0.933186	−	0.359395i	$-0.882983\pi$
$149$	−14.3729	−	16.2237i	−1.17748	−	1.32910i	−0.244291	−	0.969702i	$-0.578555\pi$
$150$		−	8.68147i		−	0.708839i
$151$	10.0663	−	11.3625i	0.819182	−	0.924666i	−0.179066	−	0.983837i	$-0.557307\pi$
$151$	10.0663	−	11.3625i	0.819182	−	0.924666i	0.998248	+	0.0591715i	$0.0188459\pi$
$152$	−17.6795	+	9.27894i	−1.43400	+	0.752621i
$153$	0.625450	+	5.15104i	0.0505646	+	0.416437i
$154$	2.47333	+	4.71253i	0.199306	+	0.379746i
$155$	0.419720	+	3.45671i	0.0337127	+	0.277649i
$156$	10.6324	−	5.55911i	0.851270	−	0.445085i
$157$	−0.856851	+	7.05680i	−0.0683841	+	0.563194i	0.917740	+	0.397182i	$0.130012\pi$
$157$	−0.856851	+	7.05680i	−0.0683841	+	0.563194i	−0.986124	+	0.166012i	$0.946911\pi$
$158$	−37.7450	+	14.3148i	−3.00283	+	1.13882i
$159$	0.596204	+	0.312912i	0.0472820	+	0.0248155i
$160$	−2.03824	+	5.37439i	−0.161137	+	0.424883i
$161$	−4.49931	−	8.57271i	−0.354595	−	0.675624i
$162$	−1.07266	−	2.04378i	−0.0842760	−	0.160575i
$163$	2.85959	+	11.6018i	0.223980	+	0.908725i	0.970060	+	0.242867i	$0.0780879\pi$
$163$	2.85959	+	11.6018i	0.223980	+	0.908725i	−0.746079	+	0.665857i	$0.768066\pi$
$164$	30.9238	+	3.75483i	2.41474	+	0.293203i
$165$	−0.699453	−	0.619661i	−0.0544523	−	0.0482405i
$166$	−4.31983	−	6.25836i	−0.335284	−	0.485743i
$167$	7.87862	+	2.98797i	0.609666	+	0.231216i	0.640063	−	0.768322i	$-0.278908\pi$
$167$	7.87862	+	2.98797i	0.609666	+	0.231216i	−0.0303974	+	0.999538i	$0.509677\pi$
$168$	−8.41601			−0.649309
$169$	−4.64786	+	12.1407i	−0.357527	+	0.933903i
$170$	−13.3304			−1.02239
$171$	−6.09225	−	2.31049i	−0.465886	−	0.176687i
$172$	3.58635	+	5.19572i	0.273456	+	0.396170i
$173$	−0.723800	−	0.641231i	−0.0550295	−	0.0487519i	0.635160	−	0.772381i	$-0.280934\pi$
$173$	−0.723800	−	0.641231i	−0.0550295	−	0.0487519i	−0.690189	+	0.723629i	$0.742473\pi$
$174$	9.53447	+	1.15769i	0.722806	+	0.0877646i
$175$	−2.47205	−	10.0295i	−0.186870	−	0.758160i
$176$	0.163043	+	0.310652i	0.0122898	+	0.0234163i
$177$	−0.0523924	−	0.0998253i	−0.00393805	−	0.00750333i
$178$	−1.41028	+	3.71860i	−0.105705	+	0.278721i
$179$	10.3865	+	5.45125i	0.776322	+	0.407445i	0.805851	−	0.592119i	$-0.201708\pi$
$179$	10.3865	+	5.45125i	0.776322	+	0.407445i	−0.0295286	+	0.999564i	$0.509401\pi$
$180$	3.46303	−	1.31335i	0.258119	−	0.0978916i
$181$	−1.29227	+	10.6428i	−0.0960536	+	0.791073i	0.862480	+	0.506092i	$0.168910\pi$
$181$	−1.29227	+	10.6428i	−0.0960536	+	0.791073i	−0.958533	+	0.284981i	$0.908013\pi$
$182$	17.1316	−	15.1295i	1.26988	−	1.12148i
$183$	−1.57911	−	13.0052i	−0.116731	−	0.961370i
$184$	−5.02030	−	9.56539i	−0.370102	−	0.705170i
$185$	0.0751613	+	0.619009i	0.00552597	+	0.0455105i
$186$	6.39401	−	3.35584i	0.468832	−	0.246062i
$187$	2.88886	−	3.26084i	0.211254	−	0.238457i
$188$			29.7077i			2.16665i
$189$	−1.82119	−	2.05570i	−0.132472	−	0.149530i
$190$	7.77896	−	14.8216i	0.564345	−	1.07527i
$191$	14.3292			1.03683			0.518414	−	0.855130i	$-0.326523\pi$
$191$	14.3292			1.03683			0.518414	+	0.855130i	$0.326523\pi$
$192$	12.7557			0.920567
$193$	−2.64167	+	5.03328i	−0.190151	+	0.362303i	−0.961803	−	0.273742i	$-0.911739\pi$
$193$	−2.64167	+	5.03328i	−0.190151	+	0.362303i	0.771652	+	0.636045i	$0.219431\pi$
$194$	−0.714349	−	0.176071i	−0.0512872	−	0.0126412i
$195$	−1.87051	+	3.55045i	−0.133950	+	0.254253i
$196$	−1.75314	+	0.432110i	−0.125224	+	0.0308650i
$197$	4.26889	−	17.3196i	0.304146	−	1.23397i	−0.597632	−	0.801770i	$-0.703892\pi$
$197$	4.26889	−	17.3196i	0.304146	−	1.23397i	0.901778	−	0.432199i	$-0.142262\pi$
$198$	−0.687180	+	1.81195i	−0.0488358	+	0.128769i
$199$	3.24854	+	26.7541i	0.230283	+	1.89655i	0.408821	+	0.912615i	$0.365940\pi$
$199$	3.24854	+	26.7541i	0.230283	+	1.89655i	−0.178538	+	0.983933i	$0.557137\pi$
$200$	−2.75831	−	11.1909i	−0.195042	−	0.791315i
$201$	2.51021	−	10.1843i	0.177056	−	0.718346i
$202$	12.3963	+	8.55658i	0.872203	+	0.602039i
$203$	11.3446	−	1.37749i	0.796237	−	0.0966807i
$204$	6.12285	+	16.1446i	0.428685	+	1.13035i
$205$	−9.22579	+	4.84207i	−0.644357	+	0.338185i
$206$	1.08217	+	4.39052i	0.0753980	+	0.305902i
$207$	1.25007	−	3.29617i	0.0868860	−	0.229100i
$208$	1.12932	−	0.997346i	0.0783045	−	0.0691535i
$209$	1.93982	+	5.11489i	0.134180	+	0.353805i
$210$	5.80658	−	4.00800i	0.400692	−	0.276578i
$211$	−16.7175	+	14.8104i	−1.15088	+	1.01959i	−0.151367	+	0.988478i	$0.548368\pi$
$211$	−16.7175	+	14.8104i	−1.15088	+	1.01959i	−0.999516	+	0.0311156i	$0.990094\pi$
$212$	2.17549	+	0.536209i	0.149413	+	0.0368270i
$213$	−10.4790	−	3.97416i	−0.718009	−	0.272305i
$214$	−11.8917	+	22.6578i	−0.812902	+	1.54886i
$215$	−1.97442	−	0.748798i	−0.134654	−	0.0510676i
$216$	−2.03207	−	2.29374i	−0.138265	−	0.156069i
$217$	6.43129	−	5.69763i	0.436585	−	0.386780i
$218$	−7.40498	+	10.7280i	−0.501529	+	0.726590i
$219$	8.74840	+	6.03859i	0.591162	+	0.408050i
$220$	−2.75336	−	1.44507i	−0.185631	−	0.0974269i
$221$	−16.5522	−	8.72028i	−1.11342	−	0.586590i
$222$	1.14501	−	0.600946i	0.0768478	−	0.0403328i
$223$	−23.5179	−	2.85559i	−1.57487	−	0.191224i	−0.714037	−	0.700108i	$-0.753135\pi$
$223$	−23.5179	−	2.85559i	−1.57487	−	0.191224i	−0.860835	+	0.508884i	$0.830058\pi$
$224$	13.7709	−	3.39423i	0.920108	−	0.226786i
$225$	2.13660	−	3.09540i	0.142440	−	0.206360i
$226$	5.46586	−	3.77281i	0.363583	−	0.250963i
$227$	−7.22237	+	8.15237i	−0.479365	+	0.541092i	−0.937589	−	0.347745i	$-0.886947\pi$
$227$	−7.22237	+	8.15237i	−0.479365	+	0.541092i	0.458224	+	0.888837i	$0.348486\pi$
$228$	−21.5237	−	2.61344i	−1.42544	−	0.173080i
$229$	−1.46369	+	5.93843i	−0.0967235	+	0.392423i	−0.999271	−	0.0381668i	$-0.987848\pi$
$229$	−1.46369	+	5.93843i	−0.0967235	+	0.392423i	0.902548	+	0.430590i	$0.141694\pi$
$230$	8.01911	+	4.20875i	0.528764	+	0.277517i
$231$	−0.277932	+	2.28898i	−0.0182866	+	0.150604i
$232$	12.6583	−	1.53699i	0.831057	−	0.100909i
$233$	−5.37991	+	7.79415i	−0.352450	+	0.510612i	−0.958607	−	0.284733i	$-0.908095\pi$
$233$	−5.37991	+	7.79415i	−0.352450	+	0.510612i	0.606157	+	0.795345i	$0.292710\pi$
$234$	8.25996	+	1.01605i	0.539970	+	0.0664212i
$235$	−5.64459	−	8.17760i	−0.368213	−	0.533448i
$236$	−0.248773	−	0.280807i	−0.0161937	−	0.0182790i
$237$	−16.9811	−	4.18547i	−1.10304	−	0.271875i
$238$	18.6853	+	27.0703i	1.21118	+	1.75470i
$239$		−	29.8282i		−	1.92943i	−0.263299	−	0.964714i	$-0.584811\pi$
$239$		−	29.8282i		−	1.92943i	0.263299	−	0.964714i	$-0.415189\pi$
$240$	0.382773	−	0.264209i	0.0247079	−	0.0170546i
$241$	22.6032	−	2.74452i	1.45600	−	0.176790i	0.646052	−	0.763293i	$-0.276419\pi$
$241$	22.6032	−	2.74452i	1.45600	−	0.176790i	0.809947	+	0.586503i	$0.199496\pi$
$242$	−22.2186	+	8.42642i	−1.42827	+	0.541671i
$243$	0.120537	−	0.992709i	0.00773243	−	0.0636823i
$244$	−15.4588	−	40.7614i	−0.989645	−	2.60948i
$245$	0.400482	−	0.452050i	0.0255858	−	0.0288804i
$246$	16.1734	+	14.3284i	1.03118	+	0.913543i
$247$	19.3548	−	13.3150i	1.23152	−	0.847216i
$248$	7.17600	−	6.35739i	0.455677	−	0.403694i
$249$		−	3.29460i		−	0.208787i
$250$	16.8473	+	14.9254i	1.06552	+	0.943965i
$251$	3.23410	−	0.797134i	0.204134	−	0.0503146i	−0.135922	−	0.990719i	$-0.543400\pi$
$251$	3.23410	−	0.797134i	0.204134	−	0.0503146i	0.340057	+	0.940405i	$0.389554\pi$
$252$	−7.52121	−	5.19151i	−0.473792	−	0.327035i
$253$	−2.76738	+	1.04953i	−0.173984	+	0.0659833i
$254$	−27.6399	+	10.4824i	−1.73428	+	0.657726i
$255$	−4.75298	−	3.28074i	−0.297643	−	0.205448i
$256$	18.0658	−	4.45282i	1.12911	−	0.278301i
$257$	−16.6722	−	14.7703i	−1.03999	−	0.921347i	−0.0430109	−	0.999075i	$-0.513695\pi$
$257$	−16.6722	−	14.7703i	−1.03999	−	0.921347i	−0.996975	+	0.0777279i	$0.975233\pi$
$258$			4.37911i			0.272632i
$259$	1.15168	−	1.02030i	0.0715621	−	0.0633984i
$260$	−3.21607	+	12.9609i	−0.199452	+	0.803798i
$261$	3.11462	+	2.75932i	0.192790	+	0.170797i
$262$	0.816019	−	0.921095i	0.0504138	−	0.0569054i
$263$	−0.859127	−	2.26533i	−0.0529760	−	0.139686i	0.905916	−	0.423457i	$-0.139184\pi$
$263$	−0.859127	−	2.26533i	−0.0529760	−	0.139686i	−0.958892	+	0.283771i	$0.908414\pi$
$264$	−0.310115	+	2.55403i	−0.0190863	+	0.157190i
$265$	−0.700726	+	0.265750i	−0.0430453	+	0.0163249i
$266$	−41.0023	+	4.97858i	−2.51401	+	0.305257i
$267$	−1.41803	+	0.978793i	−0.0867818	+	0.0599012i
$268$		−	34.9039i		−	2.13210i
$269$	3.03316	+	4.39429i	0.184935	+	0.267925i	0.904475	−	0.426526i	$-0.140263\pi$
$269$	3.03316	+	4.39429i	0.184935	+	0.267925i	−0.719540	+	0.694451i	$0.755647\pi$
$270$	2.49438	+	0.614808i	0.151803	+	0.0374160i
$271$	2.75150	+	3.10580i	0.167141	+	0.188664i	0.826114	−	0.563504i	$-0.190547\pi$
$271$	2.75150	+	3.10580i	0.167141	+	0.188664i	−0.658972	+	0.752167i	$0.729008\pi$
$272$	1.23174	+	1.78448i	0.0746852	+	0.108200i
$273$	9.83187	−	1.17821i	0.595052	−	0.0713084i
$274$	−11.5057	+	16.6689i	−0.695085	+	1.00700i
$275$	−3.13478	+	0.380631i	−0.189034	+	0.0229529i
$276$	1.41399	−	11.6452i	0.0851120	−	0.700960i
$277$	−26.0543	−	13.6744i	−1.56545	−	0.821613i	−0.565457	−	0.824778i	$-0.691300\pi$
$277$	−26.0543	−	13.6744i	−1.56545	−	0.821613i	−0.999995	+	0.00316537i	$0.998992\pi$
$278$	5.44104	−	22.0752i	0.326332	−	1.32398i
$279$	3.10571	+	0.377102i	0.185934	+	0.0225765i
$280$	6.21157	−	7.01141i	0.371212	−	0.419012i
$281$	−7.07397	+	4.88281i	−0.421998	+	0.291284i	−0.760076	−	0.649834i	$-0.774838\pi$
$281$	−7.07397	+	4.88281i	−0.421998	+	0.291284i	0.338078	+	0.941118i	$0.390223\pi$
$282$	−11.7057	+	16.9587i	−0.697066	+	1.00987i
$283$	7.51414	−	1.85207i	0.446669	−	0.110094i	−0.00956399	−	0.999954i	$-0.503044\pi$
$283$	7.51414	−	1.85207i	0.446669	−	0.110094i	0.456233	+	0.889860i	$0.349198\pi$
$284$	−37.0218	−	4.49527i	−2.19684	−	0.266745i
$285$	6.42136	−	3.37019i	0.380369	−	0.199633i
$286$	−3.96014	−	5.75648i	−0.234168	−	0.340388i
$287$	22.7648	+	11.9479i	1.34376	+	0.705261i
$288$	4.25011	+	2.93364i	0.250440	+	0.172866i
$289$	5.63771	−	8.16763i	0.331630	−	0.480449i
$290$	−8.00155	+	7.08876i	−0.469867	+	0.416266i
$291$	−0.211370	−	0.238588i	−0.0123907	−	0.0139863i
$292$	33.0744	+	12.5435i	1.93553	+	0.734051i
$293$	−11.3235	+	21.5752i	−0.661527	+	1.26044i	0.291216	+	0.956657i	$0.405940\pi$
$293$	−11.3235	+	21.5752i	−0.661527	+	1.26044i	−0.952743	+	0.303778i	$0.901752\pi$
$294$	−1.17105	−	0.444119i	−0.0682968	−	0.0259015i
$295$	0.121834	+	0.0300294i	0.00709345	+	0.00174838i
$296$	1.28504	−	1.13845i	0.0746915	−	0.0661709i
$297$	−0.690956	+	0.476932i	−0.0400933	+	0.0276744i
$298$	−17.7404	−	46.7776i	−1.02767	−	2.70975i
$299$	7.20401	+	10.4718i	0.416619	+	0.605600i
$300$	4.43819	−	11.7025i	0.256239	−	0.675647i
$301$	1.24695	+	5.05909i	0.0718733	+	0.291601i
$302$	31.0248	−	16.2831i	1.78528	−	0.936986i
$303$	2.31409	+	6.10175i	0.132941	+	0.350536i
$304$	−2.70289	+	0.328190i	−0.155021	+	0.0188230i
$305$	12.0002	+	8.28311i	0.687127	+	0.474290i
$306$	−2.86623	+	11.6288i	−0.163852	+	0.664772i
$307$	−3.78120	−	15.3409i	−0.215804	−	0.875553i	−0.974551	−	0.224167i	$-0.928034\pi$
$307$	−3.78120	−	15.3409i	−0.215804	−	0.875553i	0.758746	−	0.651386i	$-0.225812\pi$
$308$	0.924857	+	7.61688i	0.0526986	+	0.434012i
$309$	−0.694704	+	1.83179i	−0.0395204	+	0.104207i
$310$	−1.92344	+	7.80371i	−0.109244	+	0.443221i
$311$	27.3887	−	6.75072i	1.55307	−	0.382798i	0.632876	−	0.774254i	$-0.281874\pi$
$311$	27.3887	−	6.75072i	1.55307	−	0.382798i	0.920197	+	0.391456i	$0.128028\pi$
$312$	10.9704	−	1.31464i	0.621074	−	0.0744268i
$313$	−3.92412	−	0.967210i	−0.221805	−	0.0546699i	0.126847	−	0.991922i	$-0.459514\pi$
$313$	−3.92412	−	0.967210i	−0.221805	−	0.0546699i	−0.348652	+	0.937252i	$0.613360\pi$
$314$	−7.62513	+	14.5285i	−0.430311	+	0.819889i
$315$	3.05677			0.172229
$316$	−58.1980			−3.27389
$317$	−4.73726	+	9.02610i	−0.266071	+	0.506956i	−0.981435	−	0.191796i	$-0.938569\pi$
$317$	−4.73726	+	9.02610i	−0.266071	+	0.506956i	0.715364	+	0.698752i	$0.246261\pi$
$318$	1.03060	+	1.16330i	0.0577930	+	0.0652348i
$319$		−	3.49355i		−	0.195601i
$320$	−9.41458	+	10.6269i	−0.526291	+	0.594060i
$321$	−9.81636	+	5.15202i	−0.547896	+	0.287558i
$322$	−2.69363	−	22.1840i	−0.150110	−	1.23627i
$323$	15.7118	+	29.9363i	0.874228	+	1.66570i
$324$	−0.401102	−	3.30337i	−0.0222834	−	0.183521i
$325$	4.78903	+	12.6874i	0.265647	+	0.703772i
$326$	−3.32445	+	27.3793i	−0.184124	+	1.51640i
$327$	−5.28054	+	2.00264i	−0.292014	+	0.110746i
$328$	25.4008	+	13.3314i	1.40253	+	0.736102i
$329$	−8.69438	+	22.9252i	−0.479337	+	1.26391i
$330$	−1.00236	−	1.90983i	−0.0551779	−	0.105133i
$331$	−2.15597	−	4.10786i	−0.118503	−	0.225789i	0.818978	−	0.573825i	$-0.194541\pi$
$331$	−2.15597	−	4.10786i	−0.118503	−	0.225789i	−0.937481	+	0.348036i	$0.886849\pi$
$332$	−2.62367	−	10.6446i	−0.143992	−	0.584200i
$333$	0.556155	+	0.0675294i	0.0304771	+	0.00370059i
$334$	14.5578	+	12.8971i	0.796568	+	0.705698i
$335$	6.63190	+	9.60796i	0.362339	+	0.524939i
$336$	−1.07307	−	0.406962i	−0.0585408	−	0.0222016i
$337$	12.5912			0.685887			0.342943	−	0.939356i	$-0.388576\pi$
$337$	12.5912			0.685887			0.342943	+	0.939356i	$0.388576\pi$
$338$	−19.9679	+	22.3976i	−1.08611	+	1.21827i
$339$	2.87740			0.156279
$340$	−17.9692	−	6.81483i	−0.974518	−	0.369586i
$341$	−1.49209	−	2.16167i	−0.0808014	−	0.117061i
$342$	−11.2570	−	9.97286i	−0.608710	−	0.539270i
$343$	17.6052	+	2.13765i	0.950589	+	0.115422i
$344$	1.39135	+	5.64491i	0.0750164	+	0.304353i
$345$	1.82342	+	3.47423i	0.0981695	+	0.187046i
$346$	−1.03725	−	1.97631i	−0.0557627	−	0.106247i
$347$	1.18298	−	3.11926i	0.0635057	−	0.167451i	−0.899507	−	0.436906i	$-0.856074\pi$
$347$	1.18298	−	3.11926i	0.0635057	−	0.167451i	0.963013	+	0.269455i	$0.0868436\pi$
$348$	12.2606	+	6.43483i	0.657235	+	0.344943i
$349$	6.45315	−	2.44736i	0.345429	−	0.131004i	−0.175788	−	0.984428i	$-0.556247\pi$
$349$	6.45315	−	2.44736i	0.345429	−	0.131004i	0.521217	+	0.853424i	$0.325478\pi$
$350$	2.87391	−	23.6688i	0.153617	−	1.26515i
$351$	2.69505	+	2.39514i	0.143851	+	0.127843i
$352$	−0.522621	−	4.30417i	−0.0278558	−	0.229413i
$353$	6.36203	+	12.1218i	0.338617	+	0.645181i	0.993910	−	0.110194i	$-0.0351472\pi$
$353$	6.36203	+	12.1218i	0.338617	+	0.645181i	−0.655293	+	0.755375i	$0.727455\pi$
$354$	−0.0313661	−	0.258323i	−0.00166709	−	0.0137297i
$355$	11.0451	−	5.79691i	0.586212	−	0.307668i
$356$	−3.80209	+	4.29167i	−0.201510	+	0.227458i
$357$			14.2506i			0.754223i
$358$	17.9541	+	20.2659i	0.948901	+	1.07109i
$359$	1.76356	−	3.36019i	0.0930772	−	0.177344i	−0.834466	−	0.551059i	$-0.814224\pi$
$359$	1.76356	−	3.36019i	0.0930772	−	0.177344i	0.927544	+	0.373715i	$0.121916\pi$
$360$	3.41073			0.179761
$361$	−23.4539			−1.23441
$362$	−11.4999	+	21.9113i	−0.604423	+	1.15163i
$363$	−9.99596	−	2.46378i	−0.524652	−	0.129315i
$364$	30.8279	−	11.6364i	1.61582	−	0.609912i
$365$	−11.4877	+	2.83146i	−0.601292	+	0.148205i
$366$	7.23657	−	29.3599i	0.378261	−	1.53467i
$367$	10.6622	−	28.1140i	0.556564	−	1.46754i	−0.301233	−	0.953550i	$-0.597398\pi$
$367$	10.6622	−	28.1140i	0.556564	−	1.46754i	0.857797	−	0.513988i	$-0.171832\pi$
$368$	−0.177565	−	1.46238i	−0.00925622	−	0.0762319i
$369$	2.24030	+	9.08926i	0.116625	+	0.473168i
$370$	−0.344440	+	1.39745i	−0.0179066	+	0.0726499i
$371$	1.52188	+	1.05048i	0.0790120	+	0.0545380i
$372$	10.3347	−	1.25486i	0.535828	−	0.0650613i
$373$	−1.70458	−	4.49461i	−0.0882598	−	0.232722i	0.883618	−	0.468209i	$-0.155101\pi$
$373$	−1.70458	−	4.49461i	−0.0882598	−	0.232722i	−0.971877	+	0.235487i	$0.924331\pi$
$374$	8.90361	−	4.67298i	0.460395	−	0.241634i
$375$	2.33365	+	9.46799i	0.120509	+	0.488925i
$376$	−9.70115	+	25.5798i	−0.500299	+	1.31918i
$377$	−14.5727	+	3.56768i	−0.750531	+	0.183745i
$378$	−2.24788	−	5.92717i	−0.115618	−	0.304861i
$379$	−2.73891	+	1.89053i	−0.140688	+	0.0971101i	−0.636330	−	0.771417i	$-0.719548\pi$
$379$	−2.73891	+	1.89053i	−0.140688	+	0.0971101i	0.495642	+	0.868527i	$0.334933\pi$
$380$	18.0632	−	16.0026i	0.926620	−	0.820914i
$381$	−12.4349	−	3.06493i	−0.637061	−	0.157021i
$382$	30.9250	+	11.7283i	1.58226	+	0.600072i
$383$	−1.62487	+	3.09593i	−0.0830270	+	0.158195i	−0.923430	−	0.383768i	$-0.874626\pi$
$383$	−1.62487	+	3.09593i	−0.0830270	+	0.158195i	0.840403	+	0.541963i	$0.182319\pi$
$384$	17.8718	+	6.77786i	0.912014	+	0.345881i
$385$	−1.70183	−	1.92096i	−0.0867331	−	0.0979014i
$386$	−9.82085	+	8.70051i	−0.499868	+	0.442844i
$387$	−1.07775	+	1.56139i	−0.0547849	+	0.0793697i
$388$	−0.872924	−	0.602536i	−0.0443160	−	0.0305891i
$389$	−10.7439	−	5.63882i	−0.544736	−	0.285900i	0.169823	−	0.985475i	$-0.445680\pi$
$389$	−10.7439	−	5.63882i	−0.544736	−	0.285900i	−0.714559	+	0.699575i	$0.753373\pi$
$390$	−6.94287	+	6.13149i	−0.351566	+	0.310480i
$391$	−16.1968	+	8.50076i	−0.819110	+	0.429902i
$392$	−1.65065	−	0.200425i	−0.0833703	−	0.0101230i
$393$	0.517646	−	0.127588i	0.0261118	−	0.00643597i
$394$	23.3889	−	33.8846i	1.17831	−	1.70708i
$395$	16.0201	−	11.0579i	0.806059	−	0.556383i
$396$	−1.85263	+	2.09118i	−0.0930981	+	0.105086i
$397$	24.1567	+	2.93315i	1.21239	+	0.147211i	0.701647	−	0.712524i	$-0.252448\pi$
$397$	24.1567	+	2.93315i	1.21239	+	0.147211i	0.510740	+	0.859735i	$0.329371\pi$
$398$	−14.8870	+	60.3989i	−0.746217	+	3.02752i
$399$	−15.8448	−	8.31599i	−0.793232	−	0.416320i
$400$	0.189449	−	1.56026i	0.00947247	−	0.0780128i
$401$	37.9439	−	4.60723i	1.89483	−	0.230074i	0.911421	−	0.411476i	$-0.134986\pi$
$401$	37.9439	−	4.60723i	1.89483	−	0.230074i	0.983409	+	0.181402i	$0.0580634\pi$
$402$	13.7532	−	19.9249i	0.685947	−	0.993766i
$403$	−7.49325	+	8.43153i	−0.373265	+	0.420005i
$404$	12.3358	+	17.8715i	0.613730	+	0.889142i
$405$	0.738066	+	0.833104i	0.0366748	+	0.0413973i
$406$	25.6111	+	6.31258i	1.27106	+	0.313288i
$407$	−0.267196	−	0.387101i	−0.0132444	−	0.0191879i
$408$			15.9008i			0.787206i
$409$	17.7685	−	12.2647i	0.878597	−	0.606451i	−0.0410679	−	0.999156i	$-0.513076\pi$
$409$	17.7685	−	12.2647i	0.878597	−	0.606451i	0.919665	+	0.392705i	$0.128461\pi$
$410$	−23.8740	+	2.89883i	−1.17905	+	0.143163i
$411$	−8.20479	+	3.11167i	−0.404713	+	0.153487i
$412$	−0.785796	+	6.47162i	−0.0387134	+	0.318834i
$413$	−0.109794	−	0.289503i	−0.00540262	−	0.0142455i
$414$	5.39575	−	6.09054i	0.265186	−	0.299334i
$415$	2.74474	+	2.43163i	0.134734	+	0.119364i
$416$	−17.4203	+	6.57552i	−0.854102	+	0.322392i
$417$	7.37296	−	6.53187i	0.361055	−	0.319867i
$418$			12.6265i			0.617585i
$419$	−5.59502	−	4.95676i	−0.273335	−	0.242153i	0.515308	−	0.857005i	$-0.327677\pi$
$419$	−5.59502	−	4.95676i	−0.273335	−	0.242153i	−0.788643	+	0.614852i	$0.789216\pi$
$420$	9.87622	−	2.43427i	0.481910	−	0.118780i
$421$	12.1248	+	8.36915i	0.590927	+	0.407887i	0.825656	−	0.564173i	$-0.190805\pi$
$421$	12.1248	+	8.36915i	0.590927	+	0.407887i	−0.234729	+	0.972061i	$0.575420\pi$
$422$	−48.2015	+	18.2804i	−2.34641	+	0.889877i
$423$	−8.34742	+	3.16576i	−0.405866	+	0.153924i
$424$	1.69810	+	1.17212i	0.0824672	+	0.0569230i
$425$	−18.9493	+	4.67057i	−0.919174	+	0.226556i
$426$	−19.3627	−	17.1539i	−0.938126	−	0.831107i
$427$		−	35.9795i		−	1.74117i
$428$	−27.6132	+	24.4632i	−1.33474	+	1.18247i
$429$	0.00473353	−	3.02712i	0.000228537	−	0.146151i
$430$	−3.64826	−	3.23207i	−0.175935	−	0.155864i
$431$	20.9725	−	23.6730i	1.01021	−	1.14029i	0.0201255	−	0.999797i	$-0.493593\pi$
$431$	20.9725	−	23.6730i	1.01021	−	1.14029i	0.990082	−	0.140491i	$-0.0448681\pi$
$432$	−0.148181	−	0.390721i	−0.00712937	−	0.0187986i
$433$	−1.88845	+	15.5528i	−0.0907531	+	0.747419i	0.874304	+	0.485379i	$0.161318\pi$
$433$	−1.88845	+	15.5528i	−0.0907531	+	0.747419i	−0.965057	+	0.262040i	$0.915605\pi$
$434$	18.5433	−	7.03254i	0.890106	−	0.337573i
$435$	−4.59760	+	0.558249i	−0.220438	+	0.0267660i
$436$	−15.4663	+	10.6756i	−0.740700	+	0.511269i
$437$		−	22.9694i		−	1.09877i
$438$	13.9381	+	20.1928i	0.665987	+	0.964848i
$439$	0.682207	+	0.168149i	0.0325600	+	0.00802531i	0.255562	−	0.966793i	$-0.417740\pi$
$439$	0.682207	+	0.168149i	0.0325600	+	0.00802531i	−0.223002	+	0.974818i	$0.571586\pi$
$440$	−1.89889	−	2.14340i	−0.0905260	−	0.102183i
$441$	−0.308237	−	0.446559i	−0.0146780	−	0.0212647i
$442$	−28.5850	−	32.3676i	−1.35965	−	1.53957i
$443$	16.8893	−	24.4683i	0.802433	−	1.16252i	−0.181395	−	0.983410i	$-0.558061\pi$
$443$	16.8893	−	24.4683i	0.802433	−	1.16252i	0.983828	−	0.179114i	$-0.0573232\pi$
$444$	1.85068	−	0.224713i	0.0878294	−	0.0106644i
$445$	0.231160	−	1.90378i	0.0109581	−	0.0902477i
$446$	−48.4184	−	25.4119i	−2.29268	−	1.20329i
$447$	5.18708	−	21.0448i	0.245340	−	0.995385i
$448$	34.7767	+	4.22266i	1.64305	+	0.199502i
$449$	15.2775	−	17.2447i	0.720989	−	0.813829i	−0.267748	−	0.963489i	$-0.586279\pi$
$449$	15.2775	−	17.2447i	0.720989	−	0.813829i	0.988738	+	0.149660i	$0.0478179\pi$
$450$	7.14471	−	4.93163i	0.336805	−	0.232479i
$451$	4.46470	−	6.46823i	0.210234	−	0.304577i
$452$	9.29669	−	2.29143i	0.437280	−	0.107780i
$453$	15.0694	+	1.82976i	0.708024	+	0.0859697i
$454$	−22.2597	+	11.6828i	−1.04470	+	0.548301i
$455$	−6.27500	+	9.06057i	−0.294177	+	0.424766i
$456$	−17.6795	−	9.27894i	−0.827920	−	0.434526i
$457$	2.29646	+	1.58513i	0.107424	+	0.0741495i	0.620566	−	0.784155i	$-0.286903\pi$
$457$	2.29646	+	1.58513i	0.107424	+	0.0741495i	−0.513142	+	0.858304i	$0.671518\pi$
$458$	−8.01943	+	11.6182i	−0.374724	+	0.542881i
$459$	−3.88393	+	3.44086i	−0.181286	+	0.160606i
$460$	8.65807	+	9.77294i	0.403685	+	0.455666i
$461$	19.9673	+	7.57258i	0.929968	+	0.352690i	0.772632	−	0.634855i	$-0.218940\pi$
$461$	19.9673	+	7.57258i	0.929968	+	0.352690i	0.157336	+	0.987545i	$0.449709\pi$
$462$	−2.47333	+	4.71253i	−0.115069	+	0.219247i
$463$	11.2067	+	4.25014i	0.520819	+	0.197521i	0.600984	−	0.799261i	$-0.294776\pi$
$463$	11.2067	+	4.25014i	0.520819	+	0.197521i	−0.0801651	+	0.996782i	$0.525545\pi$
$464$	1.68830	+	0.416128i	0.0783772	+	0.0193183i
$465$	−2.60639	+	2.30906i	−0.120868	+	0.107080i
$466$	−17.9902	+	12.4177i	−0.833380	+	0.575240i
$467$	−7.71427	−	20.3409i	−0.356974	−	0.941262i	−0.986424	−	0.164221i	$-0.947489\pi$
$467$	−7.71427	−	20.3409i	−0.356974	−	0.941262i	0.629450	−	0.777041i	$-0.283280\pi$
$468$	10.6149	+	5.59233i	0.490675	+	0.258506i
$469$	10.2151	−	26.9351i	0.471691	−	1.24375i
$470$	−5.48874	−	22.2687i	−0.253177	−	1.02718i
$471$	−6.29438	+	3.30355i	−0.290030	+	0.152219i
$472$	−0.122508	−	0.323027i	−0.00563888	−	0.0148685i
$473$	1.58125	−	0.191998i	0.0727058	−	0.00882808i
$474$	−33.2224	−	22.9318i	−1.52596	−	1.05329i
$475$	5.86483	−	23.7946i	0.269097	−	1.09177i
$476$	11.3486	+	46.0429i	0.520160	+	2.11037i
$477$	0.0811609	+	0.668420i	0.00371610	+	0.0306049i
$478$	24.4140	−	64.3745i	1.11667	−	2.94442i
$479$	−3.64147	+	14.7740i	−0.166383	+	0.675042i	0.827197	+	0.561912i	$0.189934\pi$
$479$	−3.64147	+	14.7740i	−0.166383	+	0.675042i	−0.993580	+	0.113130i	$0.963912\pi$
$480$	−5.58089	+	1.37557i	−0.254732	+	0.0627857i
$481$	−1.34185	+	1.50987i	−0.0611832	+	0.0688444i
$482$	51.0279	+	12.5773i	2.32426	+	0.572878i
$483$	4.49931	−	8.57271i	0.204726	−	0.390072i
$484$	−34.2584			−1.55720
$485$	0.354774			0.0161094
$486$	1.07266	−	2.04378i	0.0486568	−	0.0927077i
$487$	−27.9134	−	31.5077i	−1.26488	−	1.42775i	−0.857496	−	0.514491i	$-0.827981\pi$
$487$	−27.9134	−	31.5077i	−1.26488	−	1.42775i	−0.407380	−	0.913259i	$-0.633558\pi$
$488$		−	40.1457i		−	1.81731i
$489$	−7.92368	+	8.94398i	−0.358321	+	0.404461i
$490$	1.23431	−	0.647814i	0.0557603	−	0.0292653i
$491$	−0.453069	−	3.73136i	−0.0204467	−	0.168394i	0.978908	−	0.204299i	$-0.0654916\pi$
$491$	−0.453069	−	3.73136i	−0.0204467	−	0.168394i	−0.999355	+	0.0359054i	$0.988568\pi$
$492$	14.4766	+	27.5828i	0.652653	+	1.24353i
$493$	−2.60255	−	21.4340i	−0.117213	−	0.965337i
$494$	52.6693	−	12.8945i	2.36970	−	0.580150i
$495$	0.112637	−	0.927646i	0.00506264	−	0.0416946i
$496$	1.22238	−	0.463588i	0.0548865	−	0.0208157i
$497$	−27.2539	−	14.3039i	−1.22250	−	0.641620i
$498$	2.69658	−	7.11031i	0.120837	−	0.318621i
$499$	15.2073	+	28.9751i	0.680773	+	1.29711i	0.943223	+	0.332160i	$0.107777\pi$
$499$	15.2073	+	28.9751i	0.680773	+	1.29711i	−0.262450	+	0.964946i	$0.584530\pi$
$500$	15.0798	+	28.7321i	0.674388	+	1.28494i
$501$	2.01652	+	8.18134i	0.0900914	+	0.365515i
$502$	7.63219	+	0.926715i	0.340641	+	0.0413613i
$503$	−3.82633	−	3.38983i	−0.170608	−	0.151145i	0.573498	−	0.819207i	$-0.305586\pi$
$503$	−3.82633	−	3.38983i	−0.170608	−	0.151145i	−0.744106	+	0.668061i	$0.767124\pi$
$504$	−4.78084	−	6.92624i	−0.212955	−	0.308519i
$505$	−6.79134	−	2.57562i	−0.302211	−	0.114613i
$506$	−6.83151			−0.303698
$507$	−12.6319	+	3.07161i	−0.561003	+	0.136415i
$508$	−42.6173			−1.89084
$509$	−26.2438	−	9.95294i	−1.16323	−	0.441156i	−0.303966	−	0.952683i	$-0.598311\pi$
$509$	−26.2438	−	9.95294i	−1.16323	−	0.441156i	−0.859268	+	0.511526i	$0.829080\pi$
$510$	−7.57250	−	10.9707i	−0.335316	−	0.485789i
$511$	21.8523	+	19.3594i	0.966687	+	0.856410i
$512$	4.68470	+	0.568826i	0.207036	+	0.0251388i
$513$	−1.55930	−	6.32633i	−0.0688448	−	0.279314i
$514$	−23.8923	−	45.5229i	−1.05384	−	2.00793i
$515$	−1.01333	−	1.93074i	−0.0446527	−	0.0850786i
$516$	−2.23872	+	5.90301i	−0.0985540	+	0.259865i
$517$	6.63681	+	3.48326i	0.291886	+	0.153194i
$518$	3.32063	−	1.25935i	0.145900	−	0.0553327i
$519$	0.116557	−	0.959937i	0.00511630	−	0.0421365i
$520$	−7.00162	+	10.1097i	−0.307041	+	0.443342i
$521$	−5.48900	−	45.2060i	−0.240478	−	1.98051i	−0.189988	−	0.981786i	$-0.560845\pi$
$521$	−5.48900	−	45.2060i	−0.240478	−	1.98051i	−0.0504900	−	0.998725i	$-0.516078\pi$
$522$	4.46343	+	8.50436i	0.195359	+	0.372226i
$523$	−1.42960	−	11.7738i	−0.0625119	−	0.514832i	−0.990009	−	0.141002i	$-0.954968\pi$
$523$	−1.42960	−	11.7738i	−0.0625119	−	0.514832i	0.927497	−	0.373830i	$-0.121956\pi$
$524$	1.57088	−	0.824459i	0.0686240	−	0.0360167i
$525$	6.84984	−	7.73187i	0.298952	−	0.337447i
$526$		−	5.59216i		−	0.243830i
$527$	−10.7648	−	12.1510i	−0.468922	−	0.529304i
$528$	−0.163043	+	0.310652i	−0.00709552	+	0.0135194i
$529$	−10.5726			−0.459678
$530$	−1.72980			−0.0751378
$531$	0.0523924	−	0.0998253i	0.00227364	−	0.00433205i
$532$	−57.8160	−	14.2504i	−2.50664	−	0.617832i
$533$	−31.5405	−	12.0182i	−1.36617	−	0.520565i
$534$	−3.86148	+	0.951768i	−0.167102	+	0.0411870i
$535$	2.95295	−	11.9806i	0.127667	−	0.517966i
$536$	11.3980	−	30.0541i	0.492319	−	1.29814i
$537$	1.41391	+	11.6446i	0.0610146	+	0.502500i
$538$	2.94942	+	11.9663i	0.127158	+	0.515902i
$539$	−0.109023	+	0.442323i	−0.00469595	+	0.0190522i
$540$	3.04809	+	2.10395i	0.131169	+	0.0905394i
$541$	−5.97034	+	0.724930i	−0.256685	+	0.0311672i	−0.247867	−	0.968794i	$-0.579730\pi$
$541$	−5.97034	+	0.724930i	−0.256685	+	0.0311672i	−0.00881735	+	0.999961i	$0.502807\pi$
$542$	3.39615	+	8.95491i	0.145877	+	0.384646i
$543$	−9.49294	+	4.98228i	−0.407381	+	0.213810i
$544$	−6.41288	−	26.0181i	−0.274950	−	1.11552i
$545$	2.22898	−	5.87732i	0.0954788	−	0.251757i
$546$	22.1832	+	5.50449i	0.949355	+	0.235570i
$547$	16.4040	+	43.2539i	0.701386	+	1.84940i	0.489191	+	0.872177i	$0.337292\pi$
$547$	16.4040	+	43.2539i	0.701386	+	1.84940i	0.212196	+	0.977227i	$0.431939\pi$
$548$	−24.0312	+	16.5875i	−1.02656	+	0.708584i
$549$	9.80601	−	8.68737i	0.418510	−	0.370768i
$550$	−7.07693	−	1.74431i	−0.301761	−	0.0743775i
$551$	25.3504	+	9.61415i	1.07996	+	0.409577i
$552$	5.02030	−	9.56539i	0.213678	−	0.407130i
$553$	−44.9110	−	17.0325i	−1.90981	−	0.724295i
$554$	−45.0374	−	50.8368i	−1.91346	−	2.15985i
$555$	−0.466738	+	0.413494i	−0.0198119	+	0.0175518i
$556$	18.6199	−	26.9756i	0.789659	−	1.14402i
$557$	−33.5563	−	23.1622i	−1.42182	−	0.981415i	−0.997101	−	0.0760921i	$-0.975756\pi$
$557$	−33.5563	−	23.1622i	−1.42182	−	0.981415i	−0.424724	−	0.905323i	$-0.639629\pi$
$558$	6.39401	+	3.35584i	0.270680	+	0.142064i
$559$	−2.41569	−	6.39980i	−0.102173	−	0.270683i
$560$	1.13104	−	0.593615i	0.0477951	−	0.0250848i
$561$	4.32468	+	0.525111i	0.182588	+	0.0221702i
$562$	−19.2634	+	4.74800i	−0.812576	+	0.200282i
$563$	−0.311551	+	0.451360i	−0.0131303	+	0.0190225i	−0.829494	−	0.558516i	$-0.811371\pi$
$563$	−0.311551	+	0.451360i	−0.0131303	+	0.0190225i	0.816364	+	0.577538i	$0.195987\pi$
$564$	−24.4489	+	16.8759i	−1.02949	+	0.710603i
$565$	−2.12371	+	2.39717i	−0.0893451	+	0.100850i
$566$	17.7327	+	2.15314i	0.745362	+	0.0905033i
$567$	0.657252	−	2.66658i	0.0276020	−	0.111986i
$568$	−30.4098	−	15.9603i	−1.27597	−	0.669678i
$569$	0.000623573	−	0.00513558i	2.61415e−5	−	0.000215295i	−0.992696	−	0.120644i	$-0.961504\pi$
$569$	0.000623573	−	0.00513558i	2.61415e−5	−	0.000215295i	0.992722	+	0.120429i	$0.0384270\pi$
$570$	16.6169	−	2.01765i	0.696004	−	0.0845102i
$571$	7.59677	−	11.0058i	0.317915	−	0.460579i	−0.631150	−	0.775661i	$-0.717417\pi$
$571$	7.59677	−	11.0058i	0.317915	−	0.460579i	0.949064	+	0.315082i	$0.102032\pi$
$572$	−2.39537	−	9.78422i	−0.100155	−	0.409099i
$573$	8.13994	+	11.7927i	0.340051	+	0.492649i
$574$	39.3511	+	44.4182i	1.64248	+	1.85398i
$575$	12.8739	+	3.17313i	0.536878	+	0.132329i
$576$	7.24609	+	10.4978i	0.301920	+	0.437407i
$577$			9.46018i			0.393832i	0.980420	+	0.196916i	$0.0630927\pi$
$577$			9.46018i			0.393832i	−0.980420	+	0.196916i	$0.936907\pi$
$578$	18.8523	−	13.0128i	0.784150	−	0.541260i
$579$	−5.64294	+	0.685177i	−0.234513	+	0.0284750i
$580$	−14.4100	+	5.46499i	−0.598342	+	0.226921i
$581$	1.09064	−	8.98224i	0.0452475	−	0.372646i
$582$	−0.260893	−	0.687917i	−0.0108143	−	0.0285151i
$583$	0.374870	−	0.423141i	0.0155255	−	0.0175247i
$584$	24.3826	+	21.6011i	1.00896	+	0.893862i
$585$	−3.98453	+	0.477488i	−0.164740	+	0.0197417i
$586$	−42.0971	+	37.2948i	−1.73902	+	1.54063i
$587$		−	19.2793i		−	0.795741i	−0.917442	−	0.397870i	$-0.869749\pi$
$587$		−	19.2793i		−	0.795741i	0.917442	−	0.397870i	$-0.130251\pi$
$588$	−1.35152	−	1.19734i	−0.0557355	−	0.0493774i
$589$	19.7921	−	4.87831i	0.815518	−	0.201007i
$590$	0.238360	+	0.164528i	0.00981313	+	0.00677352i
$591$	16.6787	−	6.32541i	0.686072	−	0.260193i
$592$	0.218898	−	0.0830169i	0.00899664	−	0.00341197i
$593$	30.2646	+	20.8901i	1.24282	+	0.857855i	0.993858	−	0.110659i	$-0.0352962\pi$
$593$	30.2646	+	20.8901i	1.24282	+	0.857855i	0.248959	+	0.968514i	$0.419912\pi$
$594$	−1.88157	+	0.463764i	−0.0772016	+	0.0190285i
$595$	−11.8723	−	10.5179i	−0.486715	−	0.431192i
$596$		−	72.1252i		−	2.95436i
$597$	−20.1728	+	17.8716i	−0.825618	+	0.731434i
$598$	6.97647	+	28.4964i	0.285289	+	1.16530i
$599$	22.8820	+	20.2717i	0.934932	+	0.828277i	0.985366	−	0.170450i	$-0.0545222\pi$
$599$	22.8820	+	20.2717i	0.934932	+	0.828277i	−0.0504345	+	0.998727i	$0.516061\pi$
$600$	7.64302	−	8.62719i	0.312025	−	0.352203i
$601$	6.12223	+	16.1430i	0.249731	+	0.658487i	0.999996	−	0.00265012i	$-0.000843562\pi$
$601$	6.12223	+	16.1430i	0.249731	+	0.658487i	−0.750265	+	0.661137i	$0.770074\pi$
$602$	−1.44966	+	11.9390i	−0.0590837	+	0.486598i
$603$	9.80749	−	3.71949i	0.399392	−	0.151469i
$604$	50.1456	−	6.08877i	2.04039	−	0.247749i
$605$	9.43027	−	6.50924i	0.383395	−	0.264638i
$606$			15.0627i			0.611879i
$607$	−15.6030	−	22.6048i	−0.633305	−	0.917500i	0.366613	−	0.930374i	$-0.380517\pi$
$607$	−15.6030	−	22.6048i	−0.633305	−	0.917500i	−0.999917	+	0.0128736i	$0.995902\pi$
$608$	32.6709	+	8.05265i	1.32498	+	0.326578i
$609$	7.57813	+	8.55394i	0.307081	+	0.346623i
$610$	19.1188	+	27.6984i	0.774098	+	1.12147i
$611$	7.75215	−	31.2414i	0.313618	−	1.26389i
$612$	−9.80859	+	14.2102i	−0.396489	+	0.574413i
$613$	11.5922	−	1.40755i	0.468206	−	0.0568504i	0.116966	−	0.993136i	$-0.462683\pi$
$613$	11.5922	−	1.40755i	0.468206	−	0.0568504i	0.351240	+	0.936286i	$0.385760\pi$
$614$	4.39587	−	36.2033i	0.177403	−	1.46104i
$615$	−9.22579	−	4.84207i	−0.372020	−	0.195251i
$616$	−1.69097	+	6.86054i	−0.0681312	+	0.276419i
$617$	20.2423	+	2.45786i	0.814923	+	0.0989496i	0.517377	−	0.855758i	$-0.326909\pi$
$617$	20.2423	+	2.45786i	0.814923	+	0.0989496i	0.297547	+	0.954707i	$0.403832\pi$
$618$	−2.99859	+	3.38470i	−0.120621	+	0.136153i
$619$	29.1339	−	20.1097i	1.17099	−	0.808277i	0.186284	−	0.982496i	$-0.440355\pi$
$619$	29.1339	−	20.1097i	1.17099	−	0.808277i	0.984707	+	0.174219i	$0.0557400\pi$
$620$	−6.58225	+	9.53603i	−0.264349	+	0.382976i
$621$	3.42282	−	0.843649i	0.137353	−	0.0338544i
$622$	64.6350	+	7.84811i	2.59163	+	0.314681i
$623$	−4.19007	+	2.19912i	−0.167871	+	0.0881057i
$624$	1.46233	+	0.362858i	0.0585400	+	0.0145260i
$625$	7.04165	+	3.69574i	0.281666	+	0.147830i
$626$	−7.67729	−	5.29925i	−0.306846	−	0.211801i
$627$	−3.10753	+	4.50203i	−0.124103	+	0.179794i
$628$	−17.7060	+	15.6861i	−0.706545	+	0.625944i
$629$	−1.92771	−	2.17593i	−0.0768627	−	0.0867600i
$630$	6.59703	+	2.50192i	0.262832	+	0.0996790i
$631$	3.35625	−	6.39480i	0.133610	−	0.254573i	−0.809454	−	0.587183i	$-0.800237\pi$
$631$	3.35625	−	6.39480i	0.133610	−	0.254573i	0.943064	+	0.332610i	$0.107929\pi$
$632$	−50.1115	−	19.0048i	−1.99333	−	0.755970i
$633$	−21.6854	−	5.34497i	−0.861917	−	0.212444i
$634$	−17.6116	+	15.6025i	−0.699445	+	0.619654i
$635$	11.7312	−	8.09747i	0.465539	−	0.321338i
$636$	0.794526	+	2.09499i	0.0315050	+	0.0830718i
$637$	1.95640	+	0.00305924i	0.0775156	+	0.000121212i
$638$	2.85942	−	7.53968i	0.113206	−	0.298499i
$639$	−2.68208	−	10.8816i	−0.106101	−	0.430471i
$640$	−18.8372	+	9.88653i	−0.744606	+	0.390799i
$641$	13.8496	+	36.5183i	0.547024	+	1.44238i	0.868606	+	0.495503i	$0.165016\pi$
$641$	13.8496	+	36.5183i	0.547024	+	1.44238i	−0.321582	+	0.946882i	$0.604215\pi$
$642$	−25.4023	+	3.08439i	−1.00255	+	0.121731i
$643$	26.3738	+	18.2045i	1.04008	+	0.717917i	0.960321	−	0.278898i	$-0.0899690\pi$
$643$	26.3738	+	18.2045i	1.04008	+	0.717917i	0.0797608	+	0.996814i	$0.474584\pi$
$644$	7.71006	−	31.2809i	0.303819	−	1.23264i
$645$	−0.505349	−	2.05028i	−0.0198981	−	0.0807297i
$646$	9.40628	+	77.4677i	0.370085	+	3.04793i
$647$	−14.0156	+	36.9561i	−0.551011	+	1.45290i	0.313162	+	0.949700i	$0.398612\pi$
$647$	−14.0156	+	36.9561i	−0.551011	+	1.45290i	−0.864172	+	0.503196i	$0.832157\pi$
$648$	0.733359	−	2.97535i	0.0288090	−	0.116883i
$649$	−0.0919022	+	0.0226519i	−0.00360748	+	0.000889163i
$650$	−0.0489463	+	31.3014i	−0.00191983	+	1.22774i
$651$	8.34245	+	2.05623i	0.326966	+	0.0805899i
$652$	−18.4783	+	35.2075i	−0.723667	+	1.37883i
$653$	−47.2525			−1.84913			−0.924566	−	0.381021i	$-0.875573\pi$
$653$	−47.2525			−1.84913			−0.924566	+	0.381021i	$0.875573\pi$
$654$	−13.0355			−0.509727
$655$	−0.275762	+	0.525421i	−0.0107749	+	0.0205299i
$656$	2.59404	+	2.92807i	0.101280	+	0.114322i
$657$			10.6301i			0.414720i
$658$	−37.5280	+	42.3603i	−1.46299	+	1.65138i
$659$	8.21660	−	4.31240i	0.320073	−	0.167987i	−0.297033	−	0.954867i	$-0.595997\pi$
$659$	8.21660	−	4.31240i	0.320073	−	0.167987i	0.617106	+	0.786880i	$0.288305\pi$
$660$	−0.374813	−	3.08687i	−0.0145896	−	0.120156i
$661$	7.02228	+	13.3798i	0.273135	+	0.520415i	0.982927	−	0.183996i	$-0.0589034\pi$
$661$	7.02228	+	13.3798i	0.273135	+	0.520415i	−0.709792	+	0.704411i	$0.751211\pi$
$662$	−1.29073	−	10.6301i	−0.0501657	−	0.413151i
$663$	−2.22605	−	18.5758i	−0.0864525	−	0.721426i
$664$	1.21693	−	10.0223i	0.0472262	−	0.388942i
$665$	18.6226	−	7.06262i	0.722153	−	0.273876i
$666$	1.14501	+	0.600946i	0.0443681	+	0.0232862i
$667$	−5.20167	+	13.7157i	−0.201409	+	0.531073i
$668$	13.0305	+	24.8275i	0.504165	+	0.960606i
$669$	−11.0096	−	20.9770i	−0.425654	−	0.811017i
$670$	6.44879	+	26.1638i	0.249139	+	1.01079i
$671$	−10.9188	−	1.32578i	−0.421516	−	0.0511813i
$672$	10.6162	+	9.40510i	0.409527	+	0.362810i
$673$	−4.89435	−	7.09069i	−0.188663	−	0.273326i	0.717226	−	0.696841i	$-0.245412\pi$
$673$	−4.89435	−	7.09069i	−0.188663	−	0.273326i	−0.905889	+	0.423515i	$0.860796\pi$
$674$	27.1740	+	10.3057i	1.04670	+	0.396962i
$675$	3.76120			0.144768
$676$	−38.3668	+	19.9837i	−1.47565	+	0.768603i
$677$	20.3085			0.780520			0.390260	−	0.920705i	$-0.372385\pi$
$677$	20.3085			0.780520			0.390260	+	0.920705i	$0.372385\pi$
$678$	6.20992	+	2.35511i	0.238491	+	0.0904475i
$679$	−0.497289	−	0.720447i	−0.0190842	−	0.0276482i
$680$	−13.2470	−	11.7358i	−0.508000	−	0.450048i
$681$	−10.8120	−	1.31282i	−0.414318	−	0.0503073i
$682$	−1.45090	−	5.88652i	−0.0555577	−	0.225407i
$683$	−11.6717	−	22.2386i	−0.446607	−	0.850938i	−0.999840	−	0.0179112i	$-0.994298\pi$
$683$	−11.6717	−	22.2386i	−0.446607	−	0.850938i	0.553233	−	0.833027i	$-0.313394\pi$
$684$	−10.0760	−	19.1982i	−0.385266	−	0.734062i
$685$	3.46334	−	9.13206i	0.132327	−	0.348918i
$686$	36.2453	+	19.0230i	1.38385	+	0.726302i
$687$	−5.71871	+	2.16882i	−0.218182	+	0.0827456i
$688$	−0.0955622	+	0.787025i	−0.00364327	+	0.0300051i
$689$	−2.14788	−	1.13158i	−0.0818276	−	0.0431098i
$690$	1.09164	+	8.99044i	0.0415579	+	0.342260i
$691$	10.4115	+	19.8375i	0.396072	+	0.754653i	0.999071	−	0.0430894i	$-0.0137200\pi$
$691$	10.4115	+	19.8375i	0.396072	+	0.754653i	−0.602999	+	0.797742i	$0.706028\pi$
$692$	−0.387860	−	3.19432i	−0.0147442	−	0.121430i
$693$	−2.04168	+	1.07155i	−0.0775568	+	0.0407050i
$694$	5.10615	−	5.76365i	0.193827	−	0.218785i
$695$			10.9634i			0.415865i
$696$	8.45564	+	9.54445i	0.320510	+	0.361781i
$697$	22.5737	−	43.0106i	0.855040	−	1.62914i
$698$	15.9301			0.602965
$699$	−9.47060			−0.358211
$700$	15.9741	−	30.4361i	0.603764	−	1.15038i
$701$	−12.1295	−	2.98964i	−0.458123	−	0.112917i	0.00349883	−	0.999994i	$-0.498886\pi$
$701$	−12.1295	−	2.98964i	−0.458123	−	0.112917i	−0.461622	+	0.887077i	$0.652732\pi$
$702$	3.85600	+	7.37499i	0.145535	+	0.278351i
$703$	3.54426	−	0.873582i	0.133674	−	0.0329478i
$704$	2.56292	−	10.3982i	0.0965939	−	0.391897i
$705$	3.52354	−	9.29081i	0.132704	−	0.349912i
$706$	3.80880	+	31.3683i	0.143346	+	1.18056i
$707$	4.28911	+	17.4016i	0.161308	+	0.654454i
$708$	0.0897802	−	0.364252i	0.00337415	−	0.0136894i
$709$	−11.7021	−	8.07734i	−0.439480	−	0.303351i	0.327702	−	0.944781i	$-0.393726\pi$
$709$	−11.7021	−	8.07734i	−0.439480	−	0.303351i	−0.767181	+	0.641430i	$0.778341\pi$
$710$	28.5819	−	3.47047i	1.07266	−	0.130244i
$711$	−6.20180	−	16.3528i	−0.232586	−	0.613278i
$712$	−4.67525	+	2.45376i	−0.175213	+	0.0919586i
$713$	2.63937	+	10.7084i	0.0988453	+	0.401031i
$714$	−11.6640	+	30.7553i	−0.436513	+	1.15099i
$715$	2.51842	+	2.23816i	0.0941834	+	0.0837025i
$716$	13.8415	+	36.4969i	0.517279	+	1.36395i
$717$	24.5482	−	16.9444i	0.916768	−	0.632799i
$718$	6.55634	−	5.80841i	0.244680	−	0.216768i
$719$	−33.6347	−	8.29020i	−1.25436	−	0.309172i	−0.444492	−	0.895783i	$-0.646616\pi$
$719$	−33.6347	−	8.29020i	−1.25436	−	0.309172i	−0.809869	+	0.586611i	$0.800462\pi$
$720$	0.434879	+	0.164928i	0.0162070	+	0.00614650i
$721$	−2.50041	+	4.76413i	−0.0931200	+	0.177425i
$722$	−50.6175	−	19.1967i	−1.88379	−	0.714427i
$723$	15.0988	+	17.0430i	0.561529	+	0.633836i
$724$	−26.7035	+	23.6572i	−0.992426	+	0.879213i
$725$	−8.89060	+	12.8803i	−0.330189	+	0.478361i
$726$	−19.5564	−	13.4988i	−0.725807	−	0.500989i
$727$	−24.6872	−	12.9568i	−0.915597	−	0.480542i	−0.0600079	−	0.998198i	$-0.519113\pi$
$727$	−24.6872	−	12.9568i	−0.915597	−	0.480542i	−0.855589	+	0.517656i	$0.826805\pi$
$728$	30.3443	+	0.0474496i	1.12463	+	0.00175860i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	−27.1099	−	3.29174i	−1.00338	−	0.121833i
$731$	9.55840	−	2.35593i	0.353530	−	0.0871374i
$732$	24.7644	−	35.8774i	0.915318	−	1.32607i
$733$	−27.2222	+	18.7901i	−1.00547	+	0.694029i	−0.952491	−	0.304567i	$-0.901488\pi$
$733$	−27.2222	+	18.7901i	−1.00547	+	0.694029i	−0.0529833	+	0.998595i	$0.516873\pi$
$734$	46.0219	−	51.9480i	1.69870	−	1.91743i
$735$	0.599530	+	0.0727961i	0.0221140	+	0.00268512i
$736$	−4.35683	+	17.6763i	−0.160595	+	0.651559i
$737$	−7.79766	−	4.09253i	−0.287231	−	0.150750i
$738$	−2.60448	+	21.4499i	−0.0958724	+	0.789580i
$739$	−48.4358	+	5.88117i	−1.78174	+	0.216342i	−0.944050	−	0.329803i	$-0.893018\pi$
$739$	−48.4358	+	5.88117i	−1.78174	+	0.216342i	−0.837690	+	0.546145i	$0.816095\pi$
$740$	−1.17871	+	1.70766i	−0.0433304	+	0.0627749i
$741$	21.9529	+	8.36491i	0.806459	+	0.307293i
$742$	2.42468	+	3.51275i	0.0890126	+	0.128957i
$743$	−0.0817854	−	0.0923166i	−0.00300041	−	0.00338677i	0.747009	−	0.664814i	$-0.231489\pi$
$743$	−0.0817854	−	0.0923166i	−0.00300041	−	0.00338677i	−0.750009	+	0.661428i	$0.769951\pi$
$744$	9.30846	+	2.29433i	0.341265	+	0.0841142i
$745$	13.7041	+	19.8538i	0.502080	+	0.727388i
$746$		−	11.0953i		−	0.406228i
$747$	2.71140	−	1.87154i	0.0992049	−	0.0684762i
$748$	14.3909	−	1.74738i	0.526185	−	0.0638904i
$749$	−28.4684	+	10.7967i	−1.04021	+	0.394501i
$750$	−2.71301	+	22.3436i	−0.0990651	+	0.815874i
$751$	15.6154	+	41.1744i	0.569814	+	1.50247i	0.841591	+	0.540115i	$0.181619\pi$
$751$	15.6154	+	41.1744i	0.569814	+	1.50247i	−0.271778	+	0.962360i	$0.587612\pi$
$752$	−2.47386	+	2.79241i	−0.0902124	+	0.101829i
$753$	2.49321	+	2.20879i	0.0908575	+	0.0804927i
$754$	−34.3705	−	4.22788i	−1.25170	−	0.153970i
$755$	−12.6466	+	11.2039i	−0.460258	+	0.407753i
$756$		−	9.13895i		−	0.332380i
$757$	−6.40108	−	5.67086i	−0.232651	−	0.206111i	0.538740	−	0.842472i	$-0.318900\pi$
$757$	−6.40108	−	5.67086i	−0.232651	−	0.206111i	−0.771391	+	0.636361i	$0.780439\pi$
$758$	−7.45841	+	1.83833i	−0.270902	+	0.0667713i
$759$	−2.43579	−	1.68131i	−0.0884137	−	0.0610276i
$760$	20.7790	−	7.88043i	0.753733	−	0.285853i
$761$	4.05989	−	1.53971i	0.147171	−	0.0558146i	−0.279920	−	0.960023i	$-0.590308\pi$
$761$	4.05989	−	1.53971i	0.147171	−	0.0558146i	0.427091	+	0.904209i	$0.359539\pi$
$762$	−24.3281	−	16.7925i	−0.881315	−	0.608328i
$763$	−15.0596	+	3.71186i	−0.545194	+	0.134378i
$764$	35.6908	+	31.6193i	1.29125	+	1.14395i
$765$		−	5.77530i		−	0.208806i
$766$	−6.04073	+	5.35162i	−0.218260	+	0.193362i
$767$	0.188340	+	0.360220i	0.00680058	+	0.0130068i
$768$	13.9271	+	12.3384i	0.502552	+	0.445222i
$769$	15.8188	−	17.8558i	0.570442	−	0.643895i	−0.390514	−	0.920597i	$-0.627703\pi$
$769$	15.8188	−	17.8558i	0.570442	−	0.643895i	0.960956	+	0.276701i	$0.0892413\pi$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.15817 + 0.818487i) q^{2} +(0.568065 + 0.822984i) q^{3} +(2.49077 + 2.20663i) q^{4} +(-1.10490 - 0.134159i) q^{5} +(0.552380 + 2.24110i) q^{6} +(1.27631 + 2.43180i) q^{7} +(1.42410 + 2.71339i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(-2.27476 - 1.19389i) q^{10} +(0.785015 - 0.297717i) q^{11} +(-0.401102 + 3.30337i) q^{12} +(-2.04354 - 2.97051i) q^{13} +(0.764095 + 6.29289i) q^{14} +(-0.517244 - 0.985527i) q^{15} +(0.0503695 + 0.414830i) q^{16} +(4.59452 - 2.41139i) q^{17} +(-1.53060 + 1.72769i) q^{18} +6.51566i q^{19} +(-2.45601 - 2.77227i) q^{20} +(-1.27631 + 2.43180i) q^{21} +1.93788 q^{22} -3.52525 q^{23} +(-1.42410 + 2.71339i) q^{24} +(-3.65190 - 0.900113i) q^{25} +(-1.97900 - 8.08349i) q^{26} +(-0.970942 + 0.239316i) q^{27} +(-2.18709 + 8.87339i) q^{28} +(1.47554 - 3.89069i) q^{29} +(-0.309662 - 2.55030i) q^{30} +(-0.748705 - 3.03761i) q^{31} +(1.23589 - 5.01420i) q^{32} +(0.690956 + 0.476932i) q^{33} +(11.8895 - 1.44364i) q^{34} +(-1.08394 - 2.85813i) q^{35} +(-2.94647 + 1.54643i) q^{36} +(-0.134074 - 0.543960i) q^{37} +(-5.33299 + 14.0619i) q^{38} +(1.28382 - 3.36925i) q^{39} +(-1.20946 - 3.18908i) q^{40} +(7.70419 - 5.31781i) q^{41} +(-4.74489 + 4.20360i) q^{42} +(1.84209 + 0.454036i) q^{43} +(2.61224 + 0.990693i) q^{44} +(0.517244 - 0.985527i) q^{45} +(-7.60811 - 2.88538i) q^{46} +(5.92007 + 6.68238i) q^{47} +(-0.312785 + 0.277103i) q^{48} +(-0.308237 + 0.446559i) q^{49} +(-7.14471 - 4.93163i) q^{50} +(4.59452 + 2.41139i) q^{51} +(1.46482 - 11.9082i) q^{52} +(0.596204 - 0.312912i) q^{53} +(-2.29134 - 0.278219i) q^{54} +(-0.907305 + 0.223631i) q^{55} +(-4.78084 + 6.92624i) q^{56} +(-5.36229 + 3.70132i) q^{57} +(6.36896 - 7.18907i) q^{58} +(-0.111917 - 0.0135892i) q^{59} +(0.886356 - 3.59609i) q^{60} +(-11.6001 - 6.08820i) q^{61} +(0.870414 - 7.16850i) q^{62} +(-2.72636 + 0.331040i) q^{63} +(7.24609 - 10.4978i) q^{64} +(1.85939 + 3.55628i) q^{65} +(1.10084 + 1.59484i) q^{66} +(-6.95557 - 7.85121i) q^{67} +(16.7649 + 4.13218i) q^{68} +(-2.00257 - 2.90123i) q^{69} -7.05553i q^{70} +(-9.22342 + 6.36647i) q^{71} +(-3.04206 + 0.369372i) q^{72} +(9.93932 - 3.76949i) q^{73} +(0.155869 - 1.28370i) q^{74} +(-1.33374 - 3.51678i) q^{75} +(-14.3777 + 16.2290i) q^{76} +(1.72591 + 1.52902i) q^{77} +(5.52838 - 6.22063i) q^{78} +(-13.0909 + 11.5976i) q^{79} -0.465103i q^{80} +(-0.748511 - 0.663123i) q^{81} +(20.9795 - 5.17099i) q^{82} +(-2.71140 - 1.87154i) q^{83} +(-8.54507 + 3.24072i) q^{84} +(-5.40000 + 2.04795i) q^{85} +(3.60394 + 2.48762i) q^{86} +(4.04018 - 0.995815i) q^{87} +(1.92576 + 1.70607i) q^{88} +1.72303i q^{89} +(1.92294 - 1.70358i) q^{90} +(4.61550 - 8.76077i) q^{91} +(-8.78059 - 7.77893i) q^{92} +(2.07459 - 2.34173i) q^{93} +(7.30710 + 19.2672i) q^{94} +(0.874136 - 7.19916i) q^{95} +(4.82868 - 1.83127i) q^{96} +(-0.316426 + 0.0384210i) q^{97} +(-1.03073 + 0.711463i) q^{98} +0.839574i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

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