LMFDB - Embedded newform 504.2.br.a.155.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(155,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("504.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.br (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.19
Character	$\chi$	$=$	504.155
Dual form			504.2.br.a.491.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.969566 - 1.02953i) q^{2} +(-0.139646 + 1.72641i) q^{3} +(-0.119883 + 1.99640i) q^{4} +(-0.851872 - 1.47549i) q^{5} +(1.91280 - 1.53010i) q^{6} +(0.866025 + 0.500000i) q^{7} +(2.17160 - 1.81222i) q^{8} +(-2.96100 - 0.482174i) q^{9} +O(q^{10})$	\(q+(-0.969566 - 1.02953i) q^{2} +(-0.139646 + 1.72641i) q^{3} +(-0.119883 + 1.99640i) q^{4} +(-0.851872 - 1.47549i) q^{5} +(1.91280 - 1.53010i) q^{6} +(0.866025 + 0.500000i) q^{7} +(2.17160 - 1.81222i) q^{8} +(-2.96100 - 0.482174i) q^{9} +(-0.693117 + 2.30761i) q^{10} +(-4.90588 - 2.83241i) q^{11} +(-3.42987 - 0.485758i) q^{12} +(4.57348 - 2.64050i) q^{13} +(-0.324902 - 1.37639i) q^{14} +(2.66626 - 1.26464i) q^{15} +(-3.97126 - 0.478670i) q^{16} -1.16410i q^{17} +(2.37447 + 3.51595i) q^{18} +3.95833 q^{19} +(3.04779 - 1.52380i) q^{20} +(-0.984143 + 1.42529i) q^{21} +(1.84051 + 7.79698i) q^{22} +(3.36087 + 5.82119i) q^{23} +(2.82539 + 4.00215i) q^{24} +(1.04863 - 1.81628i) q^{25} +(-7.15277 - 2.14841i) q^{26} +(1.24592 - 5.04457i) q^{27} +(-1.10202 + 1.66899i) q^{28} +(4.34900 - 7.53269i) q^{29} +(-3.88710 - 1.51886i) q^{30} +(-0.744902 + 0.430070i) q^{31} +(3.35759 + 4.55265i) q^{32} +(5.57499 - 8.07403i) q^{33} +(-1.19848 + 1.12867i) q^{34} -1.70374i q^{35} +(1.31759 - 5.85354i) q^{36} -4.19754i q^{37} +(-3.83786 - 4.07523i) q^{38} +(3.91992 + 8.26444i) q^{39} +(-4.52383 - 1.66039i) q^{40} +(-2.59340 + 1.49730i) q^{41} +(2.42158 - 0.368707i) q^{42} +(0.284152 - 0.492166i) q^{43} +(6.24276 - 9.45455i) q^{44} +(1.81095 + 4.77966i) q^{45} +(2.73454 - 9.10416i) q^{46} +(4.01807 - 6.95951i) q^{47} +(1.38095 - 6.78918i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.88663 + 0.681401i) q^{50} +(2.00972 + 0.162563i) q^{51} +(4.72322 + 9.44705i) q^{52} +6.85211 q^{53} +(-6.40156 + 3.60832i) q^{54} +9.65140i q^{55} +(2.78677 - 0.483629i) q^{56} +(-0.552766 + 6.83370i) q^{57} +(-11.9718 + 2.82599i) q^{58} +(5.05997 - 2.92137i) q^{59} +(2.20509 + 5.47454i) q^{60} +(-7.18677 - 4.14928i) q^{61} +(1.16500 + 0.349922i) q^{62} +(-2.32321 - 1.89807i) q^{63} +(1.43170 - 7.87085i) q^{64} +(-7.79203 - 4.49873i) q^{65} +(-13.7178 + 2.08866i) q^{66} +(-3.38279 - 5.85916i) q^{67} +(2.32402 + 0.139556i) q^{68} +(-10.5191 + 4.98933i) q^{69} +(-1.75406 + 1.65189i) q^{70} -4.48721 q^{71} +(-7.30391 + 4.31889i) q^{72} -14.9384 q^{73} +(-4.32151 + 4.06979i) q^{74} +(2.98920 + 2.06400i) q^{75} +(-0.474536 + 7.90242i) q^{76} +(-2.83241 - 4.90588i) q^{77} +(4.70791 - 12.0486i) q^{78} +(11.1068 + 6.41253i) q^{79} +(2.67673 + 6.26730i) q^{80} +(8.53502 + 2.85543i) q^{81} +(4.05600 + 1.21826i) q^{82} +(-5.68416 - 3.28175i) q^{83} +(-2.72748 - 2.13562i) q^{84} +(-1.71762 + 0.991666i) q^{85} +(-0.782206 + 0.184643i) q^{86} +(12.3972 + 8.56008i) q^{87} +(-15.7866 + 2.73967i) q^{88} -3.47260i q^{89} +(3.16499 - 6.49863i) q^{90} +5.28099 q^{91} +(-12.0244 + 6.01178i) q^{92} +(-0.638454 - 1.34607i) q^{93} +(-11.0608 + 2.61096i) q^{94} +(-3.37199 - 5.84046i) q^{95} +(-8.32862 + 5.16082i) q^{96} +(-3.36725 + 5.83224i) q^{97} +(0.406820 - 1.35444i) q^{98} +(13.1606 + 10.7522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{6}+O(q^{10}) $ 144 * q + 6 * q^6	$ 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) $ 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.969566	−	1.02953i	−0.685587	−	0.727991i
$2$	−0.969566	−	1.02953i	−0.685587	−	0.727991i
$3$	−0.139646	+	1.72641i	−0.0806248	+	0.996745i
$3$	−0.139646	+	1.72641i	−0.0806248	+	0.996745i
$4$	−0.119883	+	1.99640i	−0.0599415	+	0.998202i
$5$	−0.851872	−	1.47549i	−0.380969	−	0.659857i	0.610232	−	0.792223i	$-0.291076\pi$
$5$	−0.851872	−	1.47549i	−0.380969	−	0.659857i	−0.991201	+	0.132365i	$0.957743\pi$
$6$	1.91280	−	1.53010i	0.780896	−	0.624661i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	2.17160	−	1.81222i	0.767777	−	0.640717i
$9$	−2.96100	−	0.482174i	−0.986999	−	0.160725i
$10$	−0.693117	+	2.30761i	−0.219183	+	0.729731i
$11$	−4.90588	−	2.83241i	−1.47918	−	0.854004i	−0.479455	−	0.877566i	$-0.659166\pi$
$11$	−4.90588	−	2.83241i	−1.47918	−	0.854004i	−0.999722	+	0.0235628i	$0.992499\pi$
$12$	−3.42987	−	0.485758i	−0.990119	−	0.140226i
$13$	4.57348	−	2.64050i	1.26845	−	0.732342i	0.293758	−	0.955880i	$-0.405094\pi$
$13$	4.57348	−	2.64050i	1.26845	−	0.732342i	0.974695	+	0.223538i	$0.0717605\pi$
$14$	−0.324902	−	1.37639i	−0.0868336	−	0.367855i
$15$	2.66626	−	1.26464i	0.688425	−	0.326528i
$16$	−3.97126	−	0.478670i	−0.992814	−	0.119667i
$17$		−	1.16410i		−	0.282336i	−0.989986	−	0.141168i	$-0.954914\pi$
$17$		−	1.16410i		−	0.282336i	0.989986	−	0.141168i	$-0.0450858\pi$
$18$	2.37447	+	3.51595i	0.559668	+	0.828717i
$19$	3.95833			0.908102			0.454051	−	0.890976i	$-0.349978\pi$
$19$	3.95833			0.908102			0.454051	+	0.890976i	$0.349978\pi$
$20$	3.04779	−	1.52380i	0.681507	−	0.340731i
$21$	−0.984143	+	1.42529i	−0.214758	+	0.311025i
$22$	1.84051	+	7.79698i	0.392398	+	1.66232i
$23$	3.36087	+	5.82119i	0.700789	+	1.21380i	0.968190	+	0.250217i	$0.0805018\pi$
$23$	3.36087	+	5.82119i	0.700789	+	1.21380i	−0.267401	+	0.963585i	$0.586165\pi$
$24$	2.82539	+	4.00215i	0.576729	+	0.816935i
$25$	1.04863	−	1.81628i	0.209725	−	0.363255i
$26$	−7.15277	−	2.14841i	−1.40277	−	0.421339i
$27$	1.24592	−	5.04457i	0.239778	−	0.970828i
$28$	−1.10202	+	1.66899i	−0.208263	+	0.315410i
$29$	4.34900	−	7.53269i	0.807589	−	1.39879i	−0.106940	−	0.994265i	$-0.534105\pi$
$29$	4.34900	−	7.53269i	0.807589	−	1.39879i	0.914529	−	0.404520i	$-0.132561\pi$
$30$	−3.88710	−	1.51886i	−0.709684	−	0.277304i
$31$	−0.744902	+	0.430070i	−0.133788	+	0.0772428i	−0.565400	−	0.824817i	$-0.691278\pi$
$31$	−0.744902	+	0.430070i	−0.133788	+	0.0772428i	0.431612	+	0.902059i	$0.357945\pi$
$32$	3.35759	+	4.55265i	0.593543	+	0.804802i
$33$	5.57499	−	8.07403i	0.970482	−	1.40551i
$34$	−1.19848	+	1.12867i	−0.205538	+	0.193566i
$35$		−	1.70374i		−	0.287985i
$36$	1.31759	−	5.85354i	0.219598	−	0.975590i
$37$		−	4.19754i		−	0.690071i	−0.938590	−	0.345036i	$-0.887867\pi$
$37$		−	4.19754i		−	0.690071i	0.938590	−	0.345036i	$-0.112133\pi$
$38$	−3.83786	−	4.07523i	−0.622583	−	0.661090i
$39$	3.91992	+	8.26444i	0.627689	+	1.32337i
$40$	−4.52383	−	1.66039i	−0.715281	−	0.262530i
$41$	−2.59340	+	1.49730i	−0.405021	+	0.233839i	−0.688648	−	0.725096i	$-0.741796\pi$
$41$	−2.59340	+	1.49730i	−0.405021	+	0.233839i	0.283627	+	0.958935i	$0.408462\pi$
$42$	2.42158	−	0.368707i	0.373658	−	0.0568927i
$43$	0.284152	−	0.492166i	0.0433328	−	0.0750546i	−0.843546	−	0.537058i	$-0.819536\pi$
$43$	0.284152	−	0.492166i	0.0433328	−	0.0750546i	0.886878	+	0.462003i	$0.152869\pi$
$44$	6.24276	−	9.45455i	0.941132	−	1.42533i
$45$	1.81095	+	4.77966i	0.269961	+	0.712510i
$46$	2.73454	−	9.10416i	0.403185	−	1.34233i
$47$	4.01807	−	6.95951i	0.586096	−	1.01515i	−0.408642	−	0.912695i	$-0.633997\pi$
$47$	4.01807	−	6.95951i	0.586096	−	1.01515i	0.994738	−	0.102453i	$-0.0326693\pi$
$48$	1.38095	−	6.78918i	0.199323	−	0.979934i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−2.88663	+	0.681401i	−0.408231	+	0.0963647i
$51$	2.00972	+	0.162563i	0.281417	+	0.0227633i
$52$	4.72322	+	9.44705i	0.654992	+	1.31007i
$53$	6.85211			0.941210			0.470605	−	0.882344i	$-0.344036\pi$
$53$	6.85211			0.941210			0.470605	+	0.882344i	$0.344036\pi$
$54$	−6.40156	+	3.60832i	−0.871142	+	0.491030i
$55$			9.65140i			1.30140i
$56$	2.78677	−	0.483629i	0.372398	−	0.0646277i
$57$	−0.552766	+	6.83370i	−0.0732156	+	0.905146i
$58$	−11.9718	+	2.82599i	−1.57198	+	0.371071i
$59$	5.05997	−	2.92137i	0.658752	−	0.380330i	−0.133050	−	0.991109i	$-0.542477\pi$
$59$	5.05997	−	2.92137i	0.658752	−	0.380330i	0.791801	+	0.610779i	$0.209144\pi$
$60$	2.20509	+	5.47454i	0.284675	+	0.706760i
$61$	−7.18677	−	4.14928i	−0.920171	−	0.531261i	−0.0364815	−	0.999334i	$-0.511615\pi$
$61$	−7.18677	−	4.14928i	−0.920171	−	0.531261i	−0.883690	+	0.468073i	$0.844948\pi$
$62$	1.16500	+	0.349922i	0.147956	+	0.0444401i
$63$	−2.32321	−	1.89807i	−0.292697	−	0.239135i
$64$	1.43170	−	7.87085i	0.178963	−	0.983856i
$65$	−7.79203	−	4.49873i	−0.966483	−	0.557999i
$66$	−13.7178	+	2.08866i	−1.68855	+	0.257096i
$67$	−3.38279	−	5.85916i	−0.413273	−	0.715810i	0.581972	−	0.813209i	$-0.302281\pi$
$67$	−3.38279	−	5.85916i	−0.413273	−	0.715810i	−0.995245	+	0.0973986i	$0.968948\pi$
$68$	2.32402	+	0.139556i	0.281828	+	0.0169237i
$69$	−10.5191	+	4.98933i	−1.26635	+	0.600645i
$70$	−1.75406	+	1.65189i	−0.209651	+	0.197439i
$71$	−4.48721			−0.532534			−0.266267	−	0.963899i	$-0.585790\pi$
$71$	−4.48721			−0.532534			−0.266267	+	0.963899i	$0.585790\pi$
$72$	−7.30391	+	4.31889i	−0.860774	+	0.508987i
$73$	−14.9384			−1.74841			−0.874204	−	0.485558i	$-0.838616\pi$
$73$	−14.9384			−1.74841			−0.874204	+	0.485558i	$0.838616\pi$
$74$	−4.32151	+	4.06979i	−0.502366	+	0.473104i
$75$	2.98920	+	2.06400i	0.345164	+	0.238330i
$76$	−0.474536	+	7.90242i	−0.0544330	+	0.906470i
$77$	−2.83241	−	4.90588i	−0.322783	−	0.559077i
$78$	4.70791	−	12.0486i	0.533065	−	1.36424i
$79$	11.1068	+	6.41253i	1.24962	+	0.721466i	0.971033	−	0.238946i	$-0.0768018\pi$
$79$	11.1068	+	6.41253i	1.24962	+	0.721466i	0.278583	+	0.960412i	$0.410135\pi$
$80$	2.67673	+	6.26730i	0.299268	+	0.700705i
$81$	8.53502	+	2.85543i	0.948335	+	0.317270i
$82$	4.05600	+	1.21826i	0.447910	+	0.134535i
$83$	−5.68416	−	3.28175i	−0.623917	−	0.360219i	0.154475	−	0.987997i	$-0.450631\pi$
$83$	−5.68416	−	3.28175i	−0.623917	−	0.360219i	−0.778392	+	0.627778i	$0.783965\pi$
$84$	−2.72748	−	2.13562i	−0.297592	−	0.233015i
$85$	−1.71762	+	0.991666i	−0.186302	+	0.107561i
$86$	−0.782206	+	0.184643i	−0.0843474	+	0.0199106i
$87$	12.3972	+	8.56008i	1.32912	+	0.917737i
$88$	−15.7866	+	2.73967i	−1.68285	+	0.292050i
$89$		−	3.47260i		−	0.368095i	−0.982917	−	0.184047i	$-0.941080\pi$
$89$		−	3.47260i		−	0.368095i	0.982917	−	0.184047i	$-0.0589200\pi$
$90$	3.16499	−	6.49863i	0.333619	−	0.685016i
$91$	5.28099			0.553599
$92$	−12.0244	+	6.01178i	−1.25363	+	0.626772i
$93$	−0.638454	−	1.34607i	−0.0662046	−	0.139581i
$94$	−11.0608	+	2.61096i	−1.14084	+	0.269300i
$95$	−3.37199	−	5.84046i	−0.345959	−	0.599218i
$96$	−8.32862	+	5.16082i	−0.850036	+	0.526724i
$97$	−3.36725	+	5.83224i	−0.341892	+	0.592174i	−0.984784	−	0.173782i	$-0.944401\pi$
$97$	−3.36725	+	5.83224i	−0.341892	+	0.592174i	0.642892	+	0.765957i	$0.277734\pi$
$98$	0.406820	−	1.35444i	0.0410950	−	0.136819i
$99$	13.1606	+	10.7522i	1.32269	+	1.08064i
$100$	3.50031	+	2.31122i	0.350031	+	0.231122i
$101$	−4.55259	+	7.88532i	−0.453000	+	0.784619i	−0.998571	−	0.0534459i	$-0.982980\pi$
$101$	−4.55259	+	7.88532i	−0.453000	+	0.784619i	0.545571	+	0.838065i	$0.316313\pi$
$102$	−1.78119	−	2.22669i	−0.176364	−	0.220475i
$103$	8.09384	−	4.67298i	0.797510	−	0.460443i	−0.0450897	−	0.998983i	$-0.514357\pi$
$103$	8.09384	−	4.67298i	0.797510	−	0.460443i	0.842600	+	0.538540i	$0.181024\pi$
$104$	5.14660	−	14.0223i	0.504665	−	1.37500i
$105$	2.94137	+	0.237922i	0.287048	+	0.0232188i
$106$	−6.64357	−	7.05448i	−0.645281	−	0.685192i
$107$			16.8656i			1.63046i	0.579136	+	0.815231i	$0.303390\pi$
$107$			16.8656i			1.63046i	−0.579136	+	0.815231i	$0.696610\pi$
$108$	9.92163	+	3.09213i	0.954709	+	0.297540i
$109$		−	10.2479i		−	0.981573i	−0.871280	−	0.490787i	$-0.836709\pi$
$109$		−	10.2479i		−	0.981573i	0.871280	−	0.490787i	$-0.163291\pi$
$110$	9.93645	−	9.35767i	0.947404	−	0.892219i
$111$	7.24668	+	0.586171i	0.687825	+	0.0556369i
$112$	−3.19987	−	2.40017i	−0.302360	−	0.226795i
$113$	2.07846	−	1.20000i	0.195525	−	0.112887i	−0.399041	−	0.916933i	$-0.630657\pi$
$113$	2.07846	−	1.20000i	0.195525	−	0.112887i	0.594567	+	0.804046i	$0.297324\pi$
$114$	7.57148	−	6.05664i	0.709134	−	0.567256i
$115$	5.72606	−	9.91782i	0.533957	−	0.924842i
$116$	14.5169	+	9.58540i	1.34786	+	0.889982i
$117$	−14.8152	+	5.61329i	−1.36967	+	0.518949i
$118$	−7.91363	−	2.37695i	−0.728508	−	0.218816i
$119$	0.582051	−	1.00814i	0.0533565	−	0.0924162i
$120$	3.49825	−	7.57814i	0.319345	−	0.691786i
$121$	10.5451	+	18.2646i	0.958644	+	1.66042i
$122$	2.69622	+	11.4220i	0.244104	+	1.03410i
$123$	−2.22280	−	4.68637i	−0.200423	−	0.422556i
$124$	−0.769291	−	1.53868i	−0.0690844	−	0.138178i
$125$	−12.0919			−1.08153
$126$	0.298375	+	4.23214i	0.0265814	+	0.377029i
$127$		−	5.27253i		−	0.467862i	−0.972253	−	0.233931i	$-0.924841\pi$
$127$		−	5.27253i		−	0.467862i	0.972253	−	0.233931i	$-0.0751589\pi$
$128$	−9.49144	+	6.15732i	−0.838933	+	0.544235i
$129$	0.810000	+	0.559293i	0.0713165	+	0.0492430i
$130$	2.92329	+	12.3840i	0.256390	+	1.08615i
$131$	−5.51321	+	3.18305i	−0.481692	+	0.278105i	−0.721121	−	0.692809i	$-0.756373\pi$
$131$	−5.51321	+	3.18305i	−0.481692	+	0.278105i	0.239430	+	0.970914i	$0.423040\pi$
$132$	15.4507	+	12.0979i	1.34481	+	1.05299i
$133$	3.42801	+	1.97916i	0.297246	+	0.171615i
$134$	−2.75237	+	9.16354i	−0.237769	+	0.791609i
$135$	−8.50456	+	2.45898i	−0.731956	+	0.211636i
$136$	−2.10961	−	2.52796i	−0.180898	−	0.216771i
$137$	16.4380	+	9.49049i	1.40439	+	0.810827i	0.994840	−	0.101458i	$-0.0323508\pi$
$137$	16.4380	+	9.49049i	1.40439	+	0.810827i	0.409554	+	0.912286i	$0.365684\pi$
$138$	15.3357	+	5.99230i	1.30546	+	0.510098i
$139$	−1.26128	−	2.18460i	−0.106980	−	0.185295i	0.807565	−	0.589778i	$-0.200785\pi$
$139$	−1.26128	−	2.18460i	−0.106980	−	0.185295i	−0.914546	+	0.404483i	$0.867451\pi$
$140$	3.40136	+	0.204250i	0.287468	+	0.0172623i
$141$	11.4539	+	7.90872i	0.964590	+	0.666034i
$142$	4.35065	+	4.61974i	0.365098	+	0.387680i
$143$	−29.9159			−2.50169
$144$	11.5281	+	3.33218i	0.960673	+	0.277682i
$145$	−14.8192			−1.23067
$146$	14.4838	+	15.3796i	1.19869	+	1.27283i
$147$	−1.56494	+	0.742269i	−0.129074	+	0.0612213i
$148$	8.37998	+	0.503214i	0.688830	+	0.0413639i
$149$	5.40152	+	9.35570i	0.442510	+	0.766449i	0.997875	−	0.0651573i	$-0.0207549\pi$
$149$	5.40152	+	9.35570i	0.442510	+	0.766449i	−0.555365	+	0.831606i	$0.687422\pi$
$150$	−0.773272	−	5.07867i	−0.0631374	−	0.414672i
$151$	9.82270	+	5.67114i	0.799360	+	0.461510i	0.843247	−	0.537526i	$-0.180641\pi$
$151$	9.82270	+	5.67114i	0.799360	+	0.461510i	−0.0438876	+	0.999036i	$0.513974\pi$
$152$	8.59591	−	7.17337i	0.697220	−	0.581837i
$153$	−0.561300	+	3.44690i	−0.0453784	+	0.278666i
$154$	−2.30456	+	7.67264i	−0.185707	+	0.618279i
$155$	1.26912	+	0.732729i	0.101938	+	0.0588542i
$156$	−16.9691	+	6.83497i	−1.35861	+	0.547236i
$157$	−9.93248	+	5.73452i	−0.792699	+	0.457665i	−0.840912	−	0.541172i	$-0.817981\pi$
$157$	−9.93248	+	5.73452i	−0.792699	+	0.457665i	0.0482132	+	0.998837i	$0.484647\pi$
$158$	−4.16688	−	17.6522i	−0.331500	−	1.40434i
$159$	−0.956872	+	11.8296i	−0.0758849	+	0.938146i
$160$	3.85713	−	8.83235i	0.304933	−	0.698258i
$161$			6.72173i			0.529747i
$162$	−5.33549	−	11.5556i	−0.419196	−	0.907896i
$163$	−15.9182			−1.24681			−0.623406	−	0.781898i	$-0.714252\pi$
$163$	−15.9182			−1.24681			−0.623406	+	0.781898i	$0.714252\pi$
$164$	−2.67831	−	5.35698i	−0.209141	−	0.418310i
$165$	−16.6623	−	1.34778i	−1.29716	−	0.104925i
$166$	2.13249	+	9.03391i	0.165513	+	0.701167i
$167$	−7.70853	−	13.3516i	−0.596504	−	1.03318i	−0.993333	−	0.115283i	$-0.963223\pi$
$167$	−7.70853	−	13.3516i	−0.596504	−	1.03318i	0.396828	−	0.917893i	$-0.370111\pi$
$168$	0.445781	+	4.87866i	0.0343928	+	0.376396i
$169$	7.44445	−	12.8942i	0.572650	−	0.991859i
$170$	2.68630	+	0.806859i	0.206030	+	0.0618833i
$171$	−11.7206	−	1.90860i	−0.896296	−	0.145955i
$172$	0.948496	+	0.626284i	0.0723222	+	0.0477537i
$173$	9.87182	−	17.0985i	0.750541	−	1.29997i	−0.197020	−	0.980399i	$-0.563126\pi$
$173$	9.87182	−	17.0985i	0.750541	−	1.29997i	0.947561	−	0.319575i	$-0.103540\pi$
$174$	−3.20701	−	21.0629i	−0.243123	−	1.59678i
$175$	1.81628	−	1.04863i	0.137298	−	0.0792688i
$176$	18.1267	+	13.5965i	1.36635	+	1.02488i
$177$	4.33689	+	9.14355i	0.325981	+	0.687271i
$178$	−3.57516	+	3.36692i	−0.267970	+	0.252361i
$179$			9.31295i			0.696083i	0.937479	+	0.348041i	$0.113153\pi$
$179$			9.31295i			0.696083i	−0.937479	+	0.348041i	$0.886847\pi$
$180$	−9.75924	+	3.04239i	−0.727411	+	0.226766i
$181$		−	18.0744i		−	1.34346i	−0.740797	−	0.671729i	$-0.765552\pi$
$181$		−	18.0744i		−	1.34346i	0.740797	−	0.671729i	$-0.234448\pi$
$182$	−5.12027	−	5.43697i	−0.379540	−	0.403015i
$183$	8.16698	−	11.8279i	0.603720	−	0.874343i
$184$	17.8477	+	6.55067i	1.31575	+	0.482922i
$185$	−6.19341	+	3.57577i	−0.455349	+	0.262896i
$186$	−0.766798	+	1.96241i	−0.0562243	+	0.143891i
$187$	−3.29721	+	5.71094i	−0.241116	+	0.417625i
$188$	13.4123	+	8.85602i	0.978192	+	0.645892i
$189$	3.60129	−	3.74576i	0.261955	−	0.272464i
$190$	−2.74359	+	9.13429i	−0.199041	+	0.662671i
$191$	3.40321	−	5.89453i	0.246247	−	0.426513i	−0.716234	−	0.697860i	$-0.754136\pi$
$191$	3.40321	−	5.89453i	0.246247	−	0.426513i	0.962482	+	0.271347i	$0.0874691\pi$
$192$	13.3884	+	3.57085i	0.966224	+	0.257704i
$193$	−9.73475	−	16.8611i	−0.700722	−	1.21369i	−0.968213	−	0.250126i	$-0.919528\pi$
$193$	−9.73475	−	16.8611i	−0.700722	−	1.21369i	0.267491	−	0.963560i	$-0.413805\pi$
$194$	9.26926	−	2.18805i	0.665494	−	0.157093i
$195$	8.85479	−	12.8240i	0.634105	−	0.918348i
$196$	−1.78888	+	0.894380i	−0.127777	+	0.0638843i
$197$	−12.6388			−0.900476			−0.450238	−	0.892909i	$-0.648661\pi$
$197$	−12.6388			−0.900476			−0.450238	+	0.892909i	$0.648661\pi$
$198$	−1.69024	−	23.9743i	−0.120120	−	1.70378i
$199$			11.0711i			0.784810i	0.919793	+	0.392405i	$0.128357\pi$
$199$			11.0711i			0.784810i	−0.919793	+	0.392405i	$0.871643\pi$
$200$	−1.01429	−	5.84457i	−0.0717214	−	0.413274i
$201$	10.5877	−	5.02187i	0.746800	−	0.354216i
$202$	12.5323	−	2.95829i	0.881766	−	0.208144i
$203$	7.53269	−	4.34900i	0.528691	−	0.305240i
$204$	−0.565472	+	3.99272i	−0.0395909	+	0.279546i
$205$	4.41849	+	2.55102i	0.308601	+	0.178171i
$206$	−12.6585	−	3.80213i	−0.881960	−	0.264907i
$207$	−7.14469	−	18.8571i	−0.496590	−	1.31066i
$208$	−19.4264	+	8.29690i	−1.34698	+	0.575287i
$209$	−19.4191	−	11.2116i	−1.34324	−	0.775523i
$210$	−2.60690	−	3.25892i	−0.179893	−	0.224887i
$211$	11.3941	+	19.7351i	0.784401	+	1.35862i	0.929356	+	0.369184i	$0.120363\pi$
$211$	11.3941	+	19.7351i	0.784401	+	1.35862i	−0.144956	+	0.989438i	$0.546304\pi$
$212$	−0.821452	+	13.6796i	−0.0564175	+	0.939517i
$213$	0.626622	−	7.74677i	0.0429354	−	0.530800i
$214$	17.3637	−	16.3523i	1.18696	−	1.11782i
$215$	−0.968245			−0.0660338
$216$	−6.43623	−	13.2127i	−0.437930	−	0.899009i
$217$	−0.860139			−0.0583900
$218$	−10.5506	+	9.93604i	−0.714576	+	0.672954i
$219$	2.08609	−	25.7899i	0.140965	−	1.74272i
$220$	−19.2681	−	1.15704i	−1.29905	−	0.0780076i
$221$	−3.07381	−	5.32399i	−0.206767	−	0.358130i
$222$	−6.42266	−	8.02904i	−0.431060	−	0.538874i
$223$	−2.01149	−	1.16134i	−0.134700	−	0.0777688i	0.431136	−	0.902287i	$-0.358113\pi$
$223$	−2.01149	−	1.16134i	−0.134700	−	0.0777688i	−0.565835	+	0.824518i	$0.691446\pi$
$224$	0.631433	+	5.62150i	0.0421894	+	0.375602i
$225$	−3.98074	+	4.87237i	−0.265383	+	0.324825i
$226$	−3.25065	−	0.976369i	−0.216230	−	0.0649471i
$227$	−21.3050	−	12.3004i	−1.41406	−	0.816409i	−0.418294	−	0.908312i	$-0.637372\pi$
$227$	−21.3050	−	12.3004i	−1.41406	−	0.816409i	−0.995768	+	0.0919022i	$0.970705\pi$
$228$	−13.5766	−	1.92279i	−0.899130	−	0.127340i
$229$	−4.21893	+	2.43580i	−0.278794	+	0.160962i	−0.632878	−	0.774252i	$-0.718126\pi$
$229$	−4.21893	+	2.43580i	−0.278794	+	0.160962i	0.354083	+	0.935214i	$0.384793\pi$
$230$	−15.7625	+	3.72081i	−1.03935	+	0.245343i
$231$	8.86510	−	4.20482i	0.583281	−	0.276657i
$232$	−4.20661	−	24.2394i	−0.276177	−	1.59139i
$233$			14.4534i			0.946872i	0.880828	+	0.473436i	$0.156987\pi$
$233$			14.4534i			0.946872i	−0.880828	+	0.473436i	$0.843013\pi$
$234$	20.1434	+	9.81033i	1.31682	+	0.641321i
$235$	−13.6915			−0.893138
$236$	5.22564	+	10.4520i	0.340160	+	0.680365i
$237$	−12.6217	+	18.2795i	−0.819868	+	1.18738i
$238$	−1.60225	+	0.378218i	−0.103859	+	0.0245163i
$239$	2.78865	+	4.83008i	0.180383	+	0.312432i	0.942011	−	0.335582i	$-0.108933\pi$
$239$	2.78865	+	4.83008i	0.180383	+	0.312432i	−0.761628	+	0.648014i	$0.775600\pi$
$240$	−11.1937	+	3.74594i	−0.722553	+	0.241799i
$241$	8.57706	−	14.8559i	0.552497	−	0.956953i	−0.445596	−	0.895234i	$-0.647008\pi$
$241$	8.57706	−	14.8559i	0.552497	−	0.956953i	0.998094	−	0.0617192i	$-0.0196583\pi$
$242$	8.57990	−	28.5653i	0.551537	−	1.83625i
$243$	−6.12154	+	14.3362i	−0.392697	+	0.919668i
$244$	9.14521	−	13.8503i	0.585462	−	0.886672i
$245$	0.851872	−	1.47549i	0.0544241	−	0.0942653i
$246$	−2.66963	+	6.83220i	−0.170210	+	0.435605i
$247$	18.1033	−	10.4519i	1.15189	−	0.665042i
$248$	−0.838249	+	2.28387i	−0.0532289	+	0.145026i
$249$	6.45942	−	9.35491i	0.409349	−	0.592843i
$250$	11.7239	+	12.4490i	0.741485	+	0.787346i
$251$			18.1394i			1.14495i	0.819923	+	0.572474i	$0.194016\pi$
$251$			18.1394i			1.14495i	−0.819923	+	0.572474i	$0.805984\pi$
$252$	4.06784	−	4.41052i	0.256250	−	0.277837i
$253$		−	38.0774i		−	2.39390i
$254$	−5.42826	+	5.11207i	−0.340599	+	0.320760i
$255$	−1.47217	−	3.10379i	−0.0921906	−	0.194367i
$256$	15.5418	+	3.80184i	0.971359	+	0.237615i
$257$	5.96713	−	3.44512i	0.372219	−	0.214901i	−0.302208	−	0.953242i	$-0.597724\pi$
$257$	5.96713	−	3.44512i	0.372219	−	0.214901i	0.674428	+	0.738341i	$0.264390\pi$
$258$	−0.209538	−	1.37619i	−0.0130452	−	0.0856781i
$259$	2.09877	−	3.63518i	0.130411	−	0.225879i
$260$	9.91542	−	15.0167i	0.614928	−	0.931298i
$261$	−16.5095	+	20.2073i	−1.02191	+	1.25080i
$262$	8.62249	+	2.58986i	0.532699	+	0.160002i
$263$	−6.71018	+	11.6224i	−0.413767	+	0.716666i	−0.995298	−	0.0968585i	$-0.969121\pi$
$263$	−6.71018	+	11.6224i	−0.413767	+	0.716666i	0.581531	+	0.813524i	$0.302454\pi$
$264$	−2.52527	−	27.6367i	−0.155420	−	1.70092i
$265$	−5.83712	−	10.1102i	−0.358572	−	0.621064i
$266$	−1.28607	−	5.44819i	−0.0788538	−	0.334050i
$267$	5.99514	+	0.484936i	0.366897	+	0.0296776i
$268$	12.1028	−	6.05099i	0.739295	−	0.369623i
$269$	13.1518			0.801880			0.400940	−	0.916104i	$-0.368684\pi$
$269$	13.1518			0.801880			0.400940	+	0.916104i	$0.368684\pi$
$270$	10.7773	+	6.37159i	0.655888	+	0.387763i
$271$			25.3083i			1.53737i	0.639628	+	0.768684i	$0.279088\pi$
$271$			25.3083i			1.53737i	−0.639628	+	0.768684i	$0.720912\pi$
$272$	−0.557220	+	4.62295i	−0.0337865	+	0.280307i
$273$	−0.737471	+	9.11717i	−0.0446338	+	0.551796i
$274$	−6.16695	−	26.1252i	−0.372559	−	1.57828i
$275$	−10.2889	+	5.94028i	−0.620442	+	0.358213i
$276$	−8.69966	−	21.5985i	−0.523658	−	1.30008i
$277$	3.30042	+	1.90550i	0.198303	+	0.114490i	0.595864	−	0.803086i	$-0.296810\pi$
$277$	3.30042	+	1.90550i	0.198303	+	0.114490i	−0.397561	+	0.917576i	$0.630143\pi$
$278$	−1.02623	+	3.41664i	−0.0615490	+	0.204917i
$279$	2.41302	−	0.914262i	0.144464	−	0.0547354i
$280$	−3.08756	−	3.69985i	−0.184517	−	0.221109i
$281$	−10.2863	−	5.93880i	−0.613629	−	0.354279i	0.160755	−	0.986994i	$-0.448607\pi$
$281$	−10.2863	−	5.93880i	−0.613629	−	0.354279i	−0.774384	+	0.632715i	$0.781940\pi$
$282$	−2.96298	−	19.4602i	−0.176443	−	1.15884i
$283$	−3.98083	−	6.89499i	−0.236635	−	0.409865i	0.723111	−	0.690732i	$-0.242711\pi$
$283$	−3.98083	−	6.89499i	−0.236635	−	0.409865i	−0.959747	+	0.280867i	$0.909378\pi$
$284$	0.537940	−	8.95828i	0.0319209	−	0.531576i
$285$	10.5539	−	5.00584i	0.625160	−	0.296521i
$286$	29.0054	+	30.7994i	1.71513	+	1.82121i
$287$	−2.99460			−0.176766
$288$	−7.74664	−	15.0993i	−0.456475	−	0.889736i
$289$	15.6449			0.920286
$290$	14.3682	+	15.2569i	0.843728	+	0.895913i
$291$	−9.59863	−	6.62771i	−0.562682	−	0.388523i
$292$	1.79086	−	29.8231i	0.104802	−	1.74527i
$293$	13.5453	+	23.4611i	0.791323	+	1.37061i	0.925148	+	0.379607i	$0.123941\pi$
$293$	13.5453	+	23.4611i	0.791323	+	1.37061i	−0.133824	+	0.991005i	$0.542726\pi$
$294$	2.28150	+	0.891481i	0.133060	+	0.0519922i
$295$	−8.62089	−	4.97727i	−0.501928	−	0.289788i
$296$	−7.60687	−	9.11538i	−0.442141	−	0.529821i
$297$	−20.4006	+	21.2191i	−1.18376	+	1.23126i
$298$	4.39489	−	14.6320i	0.254589	−	0.847610i
$299$	30.7417	+	17.7487i	1.77784	+	1.02643i
$300$	−4.47893	+	5.72022i	−0.258591	+	0.330257i
$301$	0.492166	−	0.284152i	0.0283680	−	0.0163782i
$302$	−3.68512	−	15.6113i	−0.212055	−	0.898332i
$303$	−12.9776	−	8.96081i	−0.745541	−	0.514785i
$304$	−15.7195	−	1.89473i	−0.901577	−	0.108670i
$305$			14.1386i			0.809576i
$306$	4.09292	−	2.76412i	0.233977	−	0.158014i
$307$	13.4592			0.768156			0.384078	−	0.923301i	$-0.374519\pi$
$307$	13.4592			0.768156			0.384078	+	0.923301i	$0.374519\pi$
$308$	10.1337	−	5.06650i	0.577419	−	0.288691i
$309$	6.93722	+	14.6259i	0.394645	+	0.832037i
$310$	−0.476129	−	2.01703i	−0.0270423	−	0.114560i
$311$	−3.70154	−	6.41125i	−0.209895	−	0.363549i	0.741786	−	0.670636i	$-0.233979\pi$
$311$	−3.70154	−	6.41125i	−0.209895	−	0.363549i	−0.951681	+	0.307088i	$0.900646\pi$
$312$	23.4895	+	10.8433i	1.32983	+	0.613881i
$313$	2.95347	−	5.11556i	0.166940	−	0.289149i	−0.770402	−	0.637558i	$-0.779945\pi$
$313$	2.95347	−	5.11556i	0.166940	−	0.289149i	0.937343	+	0.348409i	$0.113278\pi$
$314$	15.5341	+	4.66584i	0.876639	+	0.263308i
$315$	−0.821502	+	5.04478i	−0.0462864	+	0.284241i
$316$	−14.1335	+	21.4050i	−0.795073	+	1.20412i
$317$	5.28844	−	9.15984i	0.297028	−	0.514468i	−0.678426	−	0.734668i	$-0.737338\pi$
$317$	5.28844	−	9.15984i	0.297028	−	0.514468i	0.975455	+	0.220200i	$0.0706711\pi$
$318$	13.1067	−	10.4844i	0.734987	−	0.587937i
$319$	−42.6713	+	24.6363i	−2.38914	+	1.37937i
$320$	−12.8330	+	4.59250i	−0.717384	+	0.256728i
$321$	−29.1170	−	2.35522i	−1.62515	−	0.131456i
$322$	6.92025	−	6.51716i	0.385651	−	0.363187i
$323$		−	4.60789i		−	0.256390i
$324$	−6.72380	+	16.6970i	−0.373545	+	0.927612i
$325$		−	11.0756i		−	0.614363i
$326$	15.4338	+	16.3884i	0.854798	+	0.907668i
$327$	17.6921	+	1.43109i	0.978378	+	0.0791392i
$328$	−2.91839	+	7.95136i	−0.161141	+	0.439040i
$329$	6.95951	−	4.01807i	0.383690	−	0.221524i
$330$	14.7676	+	18.4612i	0.812930	+	1.01625i
$331$	10.4218	−	18.0511i	0.572833	−	0.992176i	−0.423440	−	0.905924i	$-0.639178\pi$
$331$	10.4218	−	18.0511i	0.572833	−	0.992176i	0.996273	−	0.0862519i	$-0.0274890\pi$
$332$	7.23313	−	10.9544i	0.396970	−	0.601203i
$333$	−2.02395	+	12.4289i	−0.110912	+	0.681100i
$334$	−6.27197	+	20.8814i	−0.343187	+	1.14258i
$335$	−5.76340	+	9.98251i	−0.314888	+	0.545403i
$336$	4.59053	−	5.18913i	0.250434	−	0.283090i
$337$	1.05955	+	1.83519i	0.0577173	+	0.0999693i	0.893440	−	0.449182i	$-0.148284\pi$
$337$	1.05955	+	1.83519i	0.0577173	+	0.0999693i	−0.835723	+	0.549151i	$0.814951\pi$
$338$	−20.4929	+	4.83743i	−1.11467	+	0.263121i
$339$	1.78145	+	3.75586i	0.0967549	+	0.203990i
$340$	−1.77385	−	3.54794i	−0.0962007	−	0.192414i
$341$	4.87253			0.263862
$342$	9.39892	+	13.9173i	0.508235	+	0.752560i
$343$			1.00000i			0.0539949i
$344$	−0.274849	−	1.58373i	−0.0148188	−	0.0853892i
$345$	16.3226	+	11.2705i	0.878780	+	0.606784i
$346$	−27.1749	+	6.41474i	−1.46093	+	0.344859i
$347$	3.52647	−	2.03601i	0.189311	−	0.109299i	−0.402349	−	0.915486i	$-0.631806\pi$
$347$	3.52647	−	2.03601i	0.189311	−	0.109299i	0.591660	+	0.806188i	$0.298473\pi$
$348$	−18.5756	+	23.7236i	−0.995756	+	1.27172i
$349$	27.0631	+	15.6249i	1.44866	+	0.836382i	0.998402	−	0.0565176i	$-0.0179997\pi$
$349$	27.0631	+	15.6249i	1.44866	+	0.836382i	0.450255	+	0.892900i	$0.351333\pi$
$350$	−2.84060	−	0.853205i	−0.151836	−	0.0456057i
$351$	−7.62197	−	26.3611i	−0.406830	−	1.40705i
$352$	−3.57695	−	31.8448i	−0.190652	−	1.69733i
$353$	15.4224	+	8.90414i	0.820853	+	0.473920i	0.850710	−	0.525635i	$-0.176172\pi$
$353$	15.4224	+	8.90414i	0.820853	+	0.473920i	−0.0298577	+	0.999554i	$0.509505\pi$
$354$	5.20870	−	13.3303i	0.276839	−	0.708495i
$355$	3.82253	+	6.62081i	0.202879	+	0.351396i
$356$	6.93271	+	0.416306i	0.367433	+	0.0220642i
$357$	1.65919	+	1.14564i	0.0878135	+	0.0606338i
$358$	9.58801	−	9.02952i	0.506742	−	0.477225i
$359$	−24.0022			−1.26679			−0.633393	−	0.773830i	$-0.718338\pi$
$359$	−24.0022			−1.26679			−0.633393	+	0.773830i	$0.718338\pi$
$360$	12.5945	+	7.09768i	0.663787	+	0.374080i
$361$	−3.33165			−0.175350
$362$	−18.6082	+	17.5243i	−0.978025	+	0.921056i
$363$	−33.0049	+	15.6546i	−1.73231	+	0.821652i
$364$	−0.633102	+	10.5430i	−0.0331835	+	0.552603i
$365$	12.7256	+	22.0414i	0.666089	+	1.15370i
$366$	−20.0956	+	3.05974i	−1.05042	+	0.159935i
$367$	5.59603	+	3.23087i	0.292111	+	0.168650i	0.638893	−	0.769295i	$-0.279393\pi$
$367$	5.59603	+	3.23087i	0.292111	+	0.168650i	−0.346783	+	0.937946i	$0.612726\pi$
$368$	−10.5604	−	24.7262i	−0.550500	−	1.28894i
$369$	8.40102	−	3.18303i	0.437340	−	0.165702i
$370$	9.68630	+	2.90939i	0.503567	+	0.151252i
$371$	5.93410	+	3.42606i	0.308083	+	0.177872i
$372$	2.76383	−	1.11324i	0.143298	−	0.0577189i
$373$	22.3176	−	12.8850i	1.15556	−	0.667162i	0.205324	−	0.978694i	$-0.434175\pi$
$373$	22.3176	−	12.8850i	1.15556	−	0.667162i	0.950236	+	0.311532i	$0.100842\pi$
$374$	9.07647	−	2.14254i	0.469333	−	0.110788i
$375$	1.68859	−	20.8756i	0.0871984	−	1.07801i
$376$	−3.88652	−	22.3949i	−0.200432	−	1.15493i
$377$		−	45.9341i		−	2.36573i
$378$	−7.34808	−	0.0758841i	−0.377944	−	0.00390306i
$379$	19.1352			0.982908			0.491454	−	0.870903i	$-0.336466\pi$
$379$	19.1352			0.982908			0.491454	+	0.870903i	$0.336466\pi$
$380$	12.0642	−	6.03168i	0.618878	−	0.309419i
$381$	9.10257	+	0.736290i	0.466339	+	0.0377213i
$382$	−9.36826	+	2.21141i	−0.479322	+	0.113146i
$383$	−8.34120	−	14.4474i	−0.426216	−	0.738227i	0.570318	−	0.821424i	$-0.306820\pi$
$383$	−8.34120	−	14.4474i	−0.426216	−	0.738227i	−0.996533	+	0.0831973i	$0.973487\pi$
$384$	−9.30462	−	17.2460i	−0.474824	−	0.880081i
$385$	−4.82570	+	8.35836i	−0.245941	+	0.425982i
$386$	−7.92058	+	26.3702i	−0.403147	+	1.34221i
$387$	−1.07868	+	1.32029i	−0.0548325	+	0.0671142i
$388$	−11.2398	−	7.42157i	−0.570616	−	0.376773i
$389$	0.344370	−	0.596466i	0.0174602	−	0.0302420i	−0.857163	−	0.515045i	$-0.827775\pi$
$389$	0.344370	−	0.596466i	0.0174602	−	0.0302420i	0.874624	+	0.484803i	$0.161109\pi$
$390$	−21.7881	+	3.31743i	−1.10328	+	0.167984i
$391$	6.77646	−	3.91239i	0.342700	−	0.197858i
$392$	2.65523	+	0.974551i	0.134109	+	0.0492223i
$393$	−4.72536	−	9.96258i	−0.238363	−	0.502546i
$394$	12.2541	+	13.0121i	0.617354	+	0.655538i
$395$		−	21.8506i		−	1.09942i
$396$	−23.0436	+	24.9848i	−1.15798	+	1.25553i
$397$			30.8370i			1.54767i	0.633390	+	0.773833i	$0.281663\pi$
$397$			30.8370i			1.54767i	−0.633390	+	0.773833i	$0.718337\pi$
$398$	11.3981	−	10.7342i	0.571334	−	0.538055i
$399$	−3.89556	+	5.64178i	−0.195022	+	0.282442i
$400$	−5.03376	+	6.71095i	−0.251688	+	0.335548i
$401$	15.8956	−	9.17735i	0.793790	−	0.458295i	−0.0475049	−	0.998871i	$-0.515127\pi$
$401$	15.8956	−	9.17735i	0.793790	−	0.458295i	0.841295	+	0.540576i	$0.181794\pi$
$402$	−15.4357	−	6.03138i	−0.769862	−	0.300818i
$403$	−2.27119	+	3.93382i	−0.113136	+	0.195958i
$404$	−15.1965	−	10.0341i	−0.756054	−	0.499217i
$405$	−3.05759	−	15.0258i	−0.151933	−	0.746636i
$406$	−11.7809	−	3.53852i	−0.584676	−	0.175614i
$407$	−11.8892	+	20.5926i	−0.589323	+	1.02074i
$408$	4.65891	−	3.28904i	0.230650	−	0.162832i
$409$	9.38687	+	16.2585i	0.464151	+	0.803933i	0.999163	−	0.0409116i	$-0.0130262\pi$
$409$	9.38687	+	16.2585i	0.464151	+	0.803933i	−0.535012	+	0.844845i	$0.679693\pi$
$410$	−1.65766	−	7.02237i	−0.0818660	−	0.346810i
$411$	−18.6800	+	27.0535i	−0.921417	+	1.33445i
$412$	8.35885	+	16.7188i	0.411811	+	0.823676i
$413$	5.84275			0.287503
$414$	−12.4867	+	25.6389i	−0.613690	+	1.26008i
$415$			11.1825i			0.548928i
$416$	27.3771	+	11.9557i	1.34227	+	0.586177i
$417$	3.94765	−	1.87241i	0.193317	−	0.0916925i
$418$	7.28533	+	30.8630i	0.356337	+	1.50956i
$419$	26.0550	−	15.0429i	1.27287	−	0.734892i	0.297342	−	0.954771i	$-0.403900\pi$
$419$	26.0550	−	15.0429i	1.27287	−	0.734892i	0.975527	+	0.219879i	$0.0705664\pi$
$420$	−0.827608	+	5.84363i	−0.0403831	+	0.285140i
$421$	2.38556	+	1.37730i	0.116265	+	0.0671256i	0.557005	−	0.830509i	$-0.311951\pi$
$421$	2.38556	+	1.37730i	0.116265	+	0.0671256i	−0.440740	+	0.897635i	$0.645284\pi$
$422$	9.27068	−	30.8651i	0.451290	−	1.50249i
$423$	−15.2532	+	18.6697i	−0.741636	+	0.907751i
$424$	14.8801	−	12.4175i	0.722639	−	0.603049i
$425$	−2.11433	−	1.22071i	−0.102560	−	0.0592131i
$426$	−8.58312	+	6.86588i	−0.415854	+	0.332653i
$427$	−4.14928	−	7.18677i	−0.200798	−	0.347792i
$428$	−33.6706	−	2.02190i	−1.62753	−	0.0977324i
$429$	4.17764	−	51.6471i	0.201698	−	2.49355i
$430$	0.938777	+	0.996842i	0.0452719	+	0.0480720i
$431$	7.53249			0.362827			0.181414	−	0.983407i	$-0.441933\pi$
$431$	7.53249			0.362827			0.181414	+	0.983407i	$0.441933\pi$
$432$	−7.36257	+	19.4369i	−0.354232	+	0.935158i
$433$	6.89290			0.331252			0.165626	−	0.986189i	$-0.447036\pi$
$433$	6.89290			0.331252			0.165626	+	0.986189i	$0.447036\pi$
$434$	0.833962	+	0.885543i	0.0400314	+	0.0425074i
$435$	2.06944	−	25.5840i	0.0992222	−	1.22666i
$436$	20.4590	+	1.22855i	0.979808	+	0.0588370i
$437$	13.3034	+	23.0422i	0.636388	+	1.10226i
$438$	−28.5742	+	22.8573i	−1.36533	+	1.09216i
$439$	−2.92057	−	1.68619i	−0.139391	−	0.0804775i	0.428683	−	0.903455i	$-0.358978\pi$
$439$	−2.92057	−	1.68619i	−0.139391	−	0.0804775i	−0.568074	+	0.822978i	$0.692311\pi$
$440$	17.4905	+	20.9590i	0.833826	+	0.999181i
$441$	−1.06292	−	2.80539i	−0.0506154	−	0.133590i
$442$	−2.50097	+	8.32655i	−0.118959	+	0.396054i
$443$	12.9385	+	7.47004i	0.614726	+	0.354912i	0.774813	−	0.632191i	$-0.217844\pi$
$443$	12.9385	+	7.47004i	0.614726	+	0.354912i	−0.160087	+	0.987103i	$0.551177\pi$
$444$	−2.03899	+	14.3970i	−0.0967661	+	0.683253i
$445$	−5.12377	+	2.95821i	−0.242890	+	0.140233i
$446$	0.754640	+	3.19689i	0.0357332	+	0.151377i
$447$	−16.9061	+	8.01876i	−0.799631	+	0.379274i
$448$	5.17532	−	6.10050i	0.244511	−	0.288222i
$449$			19.3346i			0.912456i	0.889863	+	0.456228i	$0.150800\pi$
$449$			19.3346i			0.912456i	−0.889863	+	0.456228i	$0.849200\pi$
$450$	8.87587	−	0.625768i	0.418412	−	0.0294990i
$451$	16.9639			0.798798
$452$	2.14651	+	4.29331i	0.100964	+	0.201940i
$453$	−11.1624	+	16.1661i	−0.524456	+	0.759548i
$454$	7.99287	+	33.8603i	0.375124	+	1.58914i
$455$	−4.49873	−	7.79203i	−0.210904	−	0.365296i
$456$	11.1838	+	15.8418i	0.523729	+	0.741861i
$457$	−7.61383	+	13.1875i	−0.356160	+	0.616887i	−0.987316	−	0.158769i	$-0.949247\pi$
$457$	−7.61383	+	13.1875i	−0.356160	+	0.616887i	0.631156	+	0.775656i	$0.282581\pi$
$458$	6.59827	+	1.98186i	0.308317	+	0.0926064i
$459$	−5.87239	−	1.45038i	−0.274100	−	0.0676980i
$460$	19.1135	+	12.6205i	0.891172	+	0.588434i
$461$	2.20086	−	3.81200i	0.102504	−	0.177542i	−0.810212	−	0.586137i	$-0.800648\pi$
$461$	2.20086	−	3.81200i	0.102504	−	0.177542i	0.912716	+	0.408595i	$0.133981\pi$
$462$	−12.9243	−	5.05008i	−0.601293	−	0.234951i
$463$	21.8060	−	12.5897i	1.01341	−	0.585094i	0.101223	−	0.994864i	$-0.467724\pi$
$463$	21.8060	−	12.5897i	1.01341	−	0.585094i	0.912189	+	0.409770i	$0.134391\pi$
$464$	−20.8767	+	27.8325i	−0.969175	+	1.29209i
$465$	−1.44222	+	2.08871i	−0.0668813	+	0.0968615i
$466$	14.8803	−	14.0135i	0.689315	−	0.649163i
$467$			33.1032i			1.53183i	0.642940	+	0.765917i	$0.277715\pi$
$467$			33.1032i			1.53183i	−0.642940	+	0.765917i	$0.722285\pi$
$468$	−9.43031	−	30.2501i	−0.435916	−	1.39831i
$469$		−	6.76557i		−	0.312405i
$470$	13.2749	+	14.0959i	0.612323	+	0.650196i
$471$	−8.51311	−	17.9484i	−0.392264	−	0.827017i
$472$	5.69406	−	15.5138i	0.262090	−	0.714082i
$473$	−2.78803	+	1.60967i	−0.128194	+	0.0740127i
$474$	31.0569	−	4.72869i	1.42649	−	0.217196i
$475$	4.15081	−	7.18941i	0.190452	−	0.329873i
$476$	1.94288	+	1.28287i	0.0890517	+	0.0588001i
$477$	−20.2891	−	3.30391i	−0.928973	−	0.151276i
$478$	2.26896	−	7.55409i	0.103780	−	0.345516i
$479$	11.2889	−	19.5530i	0.515805	−	0.893400i	−0.484027	−	0.875053i	$-0.660826\pi$
$479$	11.2889	−	19.5530i	0.515805	−	0.893400i	0.999832	−	0.0183469i	$-0.00584034\pi$
$480$	14.7096	+	7.89240i	0.671400	+	0.360237i
$481$	−11.0836	−	19.1973i	−0.505368	−	0.875324i
$482$	−23.6107	+	5.57340i	−1.07544	+	0.253862i
$483$	−11.6045	−	0.938665i	−0.528022	−	0.0427107i
$484$	−37.7277	+	18.8626i	−1.71490	+	0.857392i
$485$	11.4739			0.521001
$486$	20.6949	−	7.59756i	0.938738	−	0.344632i
$487$			7.63430i			0.345943i	0.984927	+	0.172971i	$0.0553368\pi$
$487$			7.63430i			0.345943i	−0.984927	+	0.172971i	$0.944663\pi$
$488$	−23.1262	+	4.01343i	−1.04687	+	0.181679i
$489$	2.22292	−	27.4814i	0.100524	−	1.24275i
$490$	−2.34501	+	0.553549i	−0.105937	+	0.0250068i
$491$	−18.2180	+	10.5182i	−0.822167	+	0.474678i	−0.851163	−	0.524901i	$-0.824102\pi$
$491$	−18.2180	+	10.5182i	−0.822167	+	0.474678i	0.0289962	+	0.999580i	$0.490769\pi$
$492$	9.62237	−	3.87579i	0.433810	−	0.174734i
$493$	−8.76882	−	5.06268i	−0.394928	−	0.228012i
$494$	−28.3130	−	8.50413i	−1.27386	−	0.382619i
$495$	4.65366	−	28.5778i	0.209166	−	1.28448i
$496$	3.16406	−	1.35135i	0.142070	−	0.0606776i
$497$	−3.88604	−	2.24360i	−0.174313	−	0.100639i
$498$	−15.8940	+	2.42001i	−0.712229	+	0.108443i
$499$	0.704646	+	1.22048i	0.0315443	+	0.0546363i	0.881367	−	0.472433i	$-0.156624\pi$
$499$	0.704646	+	1.22048i	0.0315443	+	0.0546363i	−0.849822	+	0.527069i	$0.823291\pi$
$500$	1.44961	−	24.1403i	0.0648287	−	1.07959i
$501$	24.1268	−	11.4436i	1.07791	−	0.511263i
$502$	18.6751	−	17.5874i	0.833512	−	0.784962i
$503$	−7.32114			−0.326433			−0.163217	−	0.986590i	$-0.552187\pi$
$503$	−7.32114			−0.326433			−0.163217	+	0.986590i	$0.552187\pi$
$504$	−8.48482	+	0.0883155i	−0.377944	+	0.00393389i
$505$	15.5129			0.690315
$506$	−39.2020	+	36.9185i	−1.74274	+	1.64123i
$507$	21.2211	+	14.6528i	0.942460	+	0.650754i
$508$	10.5261	+	0.632087i	0.467020	+	0.0280443i
$509$	7.91414	+	13.7077i	0.350788	+	0.607583i	0.986388	−	0.164436i	$-0.0525805\pi$
$509$	7.91414	+	13.7077i	0.350788	+	0.607583i	−0.635600	+	0.772019i	$0.719247\pi$
$510$	−1.76810	+	4.52498i	−0.0782929	+	0.200369i
$511$	−12.9370	−	7.46921i	−0.572301	−	0.330418i
$512$	−11.1546	−	19.6869i	−0.492970	−	0.870047i
$513$	4.93177	−	19.9681i	0.217743	−	0.881611i
$514$	−9.33240	−	2.80309i	−0.411634	−	0.123639i
$515$	−13.7898	−	7.96157i	−0.607653	−	0.350829i
$516$	−1.21368	+	1.55004i	−0.0534292	+	0.0682366i
$517$	−39.4243	+	22.7617i	−1.73388	+	1.00106i
$518$	−5.77744	+	1.36379i	−0.253846	+	0.0599214i
$519$	28.1405	+	19.4306i	1.23523	+	0.852908i
$520$	−25.0739	+	4.35144i	−1.09956	+	0.190823i
$521$		−	9.79612i		−	0.429176i	−0.976705	−	0.214588i	$-0.931159\pi$
$521$		−	9.79612i		−	0.429176i	0.976705	−	0.214588i	$-0.0688409\pi$
$522$	36.8111	−	2.59527i	1.61118	−	0.113592i
$523$	−23.7884			−1.04019			−0.520096	−	0.854108i	$-0.674104\pi$
$523$	−23.7884			−1.04019			−0.520096	+	0.854108i	$0.674104\pi$
$524$	−5.69372	−	11.3882i	−0.248731	−	0.497495i
$525$	1.55673	+	3.28208i	0.0679411	+	0.143242i
$526$	18.4716	−	4.36029i	0.805399	−	0.190118i
$527$	0.500645	+	0.867142i	0.0218084	+	0.0377733i
$528$	−26.0045	+	29.3955i	−1.13170	+	1.27927i
$529$	−11.0908	+	19.2099i	−0.482210	+	0.835213i
$530$	−4.74932	+	15.8120i	−0.206297	+	0.686830i
$531$	−16.3912	+	6.21039i	−0.711316	+	0.269508i
$532$	−4.36217	+	6.60643i	−0.189124	+	0.286425i
$533$	−7.90724	+	13.6957i	−0.342501	+	0.593228i
$534$	−5.31343	−	6.64238i	−0.229934	−	0.287444i
$535$	24.8850	−	14.3674i	1.07587	−	0.621155i
$536$	−17.9642	−	6.59340i	−0.775933	−	0.284791i
$537$	−16.0780	−	1.30052i	−0.693817	−	0.0561216i
$538$	−12.7515	−	13.5402i	−0.549758	−	0.583761i
$539$		−	5.66482i		−	0.244001i
$540$	−3.88957	−	17.2733i	−0.167381	−	0.743325i
$541$		−	17.8232i		−	0.766280i	−0.923690	−	0.383140i	$-0.874843\pi$
$541$		−	17.8232i		−	0.766280i	0.923690	−	0.383140i	$-0.125157\pi$
$542$	26.0558	−	24.5381i	1.11919	−	1.05400i
$543$	31.2038	+	2.52402i	1.33908	+	0.108316i
$544$	5.29974	−	3.90857i	0.227225	−	0.167579i
$545$	−15.1207	+	8.72992i	−0.647698	+	0.373949i
$546$	10.1015	−	8.08045i	0.432303	−	0.345811i
$547$	−15.6493	+	27.1054i	−0.669117	+	1.15894i	0.309034	+	0.951051i	$0.399994\pi$
$547$	−15.6493	+	27.1054i	−0.669117	+	1.15894i	−0.978151	+	0.207894i	$0.933339\pi$
$548$	−20.9175	+	31.6792i	−0.893551	+	1.35327i
$549$	19.2793	+	15.7513i	0.822821	+	0.672249i
$550$	16.0915	+	4.83325i	0.686143	+	0.206091i
$551$	17.2148	−	29.8169i	0.733374	−	1.27024i
$552$	−13.8015	+	29.8978i	−0.587432	+	1.27253i
$553$	6.41253	+	11.1068i	0.272689	+	0.472311i
$554$	−1.23820	−	5.24541i	−0.0526061	−	0.222856i
$555$	−5.30836	−	11.1917i	−0.225327	−	0.475062i
$556$	4.51255	−	2.25612i	0.191375	−	0.0956810i
$557$	17.9847			0.762038			0.381019	−	0.924567i	$-0.375573\pi$
$557$	17.9847			0.762038			0.381019	+	0.924567i	$0.375573\pi$
$558$	−3.28085	−	1.59785i	−0.138889	−	0.0676425i
$559$		−	3.00121i		−	0.126938i
$560$	−0.815531	+	6.76601i	−0.0344625	+	0.285916i
$561$	−9.39899	−	6.48986i	−0.396826	−	0.274002i
$562$	3.85905	+	16.3482i	0.162784	+	0.689605i
$563$	0.575262	−	0.332128i	0.0242444	−	0.0139975i	−0.487829	−	0.872939i	$-0.662211\pi$
$563$	0.575262	−	0.332128i	0.0242444	−	0.0139975i	0.512073	+	0.858942i	$0.328878\pi$
$564$	−17.1621	+	21.9184i	−0.722656	+	0.922932i
$565$	−3.54117	−	2.04450i	−0.148978	−	0.0860126i
$566$	−3.23896	+	10.7835i	−0.136144	+	0.453266i
$567$	5.96382	+	6.74039i	0.250457	+	0.283070i
$568$	−9.74443	+	8.13182i	−0.408867	+	0.341203i
$569$	4.24738	+	2.45223i	0.178060	+	0.102803i	0.586381	−	0.810036i	$-0.300552\pi$
$569$	4.24738	+	2.45223i	0.178060	+	0.102803i	−0.408321	+	0.912838i	$0.633886\pi$
$570$	−15.3864	−	6.01213i	−0.644466	−	0.251820i
$571$	−18.9142	−	32.7604i	−0.791536	−	1.37098i	−0.925016	−	0.379929i	$-0.875948\pi$
$571$	−18.9142	−	32.7604i	−0.791536	−	1.37098i	0.133480	−	0.991052i	$-0.457385\pi$
$572$	3.58641	−	59.7242i	0.149955	−	2.49719i
$573$	9.70114	+	6.69849i	0.405271	+	0.279833i
$574$	2.90347	+	3.08305i	0.121188	+	0.128684i
$575$	14.0972			0.587893
$576$	−8.03439	+	22.6152i	−0.334766	+	0.942301i
$577$	8.65039			0.360120			0.180060	−	0.983656i	$-0.442371\pi$
$577$	8.65039			0.360120			0.180060	+	0.983656i	$0.442371\pi$
$578$	−15.1687	−	16.1069i	−0.630936	−	0.669960i
$579$	30.4686	−	14.4516i	1.26623	−	0.600588i
$580$	1.77657	−	29.5851i	0.0737680	−	1.22845i
$581$	−3.28175	−	5.68416i	−0.136150	−	0.235818i
$582$	2.48305	+	16.3081i	0.102926	+	0.675993i
$583$	−33.6156	−	19.4080i	−1.39222	−	0.803796i
$584$	−32.4403	+	27.0717i	−1.34239	+	1.12024i
$585$	20.9030	+	17.0779i	0.864234	+	0.706082i
$586$	11.0210	−	36.6924i	0.455272	−	1.51575i
$587$	−25.4369	−	14.6860i	−1.04989	−	0.606156i	−0.127273	−	0.991868i	$-0.540622\pi$
$587$	−25.4369	−	14.6860i	−1.04989	−	0.606156i	−0.922619	+	0.385712i	$0.873956\pi$
$588$	−1.29426	−	3.21324i	−0.0533743	−	0.132512i
$589$	−2.94857	+	1.70236i	−0.121494	+	0.0701443i
$590$	3.23425	+	13.7013i	0.133152	+	0.564074i
$591$	1.76496	−	21.8197i	0.0726007	−	0.897545i
$592$	−2.00924	+	16.6695i	−0.0825791	+	0.685112i
$593$		−	36.2741i		−	1.48960i	−0.667289	−	0.744799i	$-0.732545\pi$
$593$		−	36.2741i		−	1.48960i	0.667289	−	0.744799i	$-0.267455\pi$
$594$	41.6255	+	0.429870i	1.70792	+	0.0176378i
$595$	−1.98333			−0.0813087
$596$	−19.3253	+	9.66202i	−0.791596	+	0.395772i
$597$	−19.1133	−	1.54604i	−0.782255	−	0.0632752i
$598$	−11.5332	−	48.8582i	−0.471626	−	1.99796i
$599$	9.67739	+	16.7617i	0.395408	+	0.684866i	0.993153	−	0.116820i	$-0.0372700\pi$
$599$	9.67739	+	16.7617i	0.395408	+	0.684866i	−0.597746	+	0.801686i	$0.703937\pi$
$600$	10.2318	−	0.934916i	0.417711	−	0.0381678i
$601$	−8.09209	+	14.0159i	−0.330083	+	0.571721i	−0.982528	−	0.186116i	$-0.940410\pi$
$601$	−8.09209	+	14.0159i	−0.330083	+	0.571721i	0.652445	+	0.757836i	$0.273743\pi$
$602$	−0.769732	−	0.231197i	−0.0313719	−	0.00942291i
$603$	7.19129	+	18.9800i	0.292852	+	0.772927i
$604$	−12.4995	+	18.9302i	−0.508595	+	0.770259i
$605$	17.9661	−	31.1183i	0.730427	−	1.26514i
$606$	3.35714	+	22.0489i	0.136375	+	0.895677i
$607$	−18.2630	+	10.5441i	−0.741270	+	0.427973i	−0.822531	−	0.568720i	$-0.807439\pi$
$607$	−18.2630	+	10.5441i	−0.741270	+	0.427973i	0.0812606	+	0.996693i	$0.474105\pi$
$608$	13.2904	+	18.0209i	0.538998	+	0.730843i
$609$	6.45626	+	13.6119i	0.261621	+	0.551580i
$610$	14.5562	−	13.7083i	0.589364	−	0.555034i
$611$		−	42.4388i		−	1.71689i
$612$	−6.81412	−	1.53381i	−0.275444	−	0.0620004i
$613$			40.3653i			1.63034i	0.579222	+	0.815170i	$0.303356\pi$
$613$			40.3653i			1.63034i	−0.579222	+	0.815170i	$0.696644\pi$
$614$	−13.0496	−	13.8567i	−0.526638	−	0.559211i
$615$	−5.02114	+	7.27190i	−0.202472	+	0.293231i
$616$	−15.0414	−	5.52066i	−0.606035	−	0.222434i
$617$	20.8511	−	12.0384i	0.839434	−	0.484647i	−0.0176378	−	0.999844i	$-0.505615\pi$
$617$	20.8511	−	12.0384i	0.839434	−	0.484647i	0.857072	+	0.515197i	$0.172281\pi$
$618$	8.33175	−	21.3229i	0.335152	−	0.857731i
$619$	−19.2267	+	33.3016i	−0.772785	+	1.33850i	0.163246	+	0.986585i	$0.447804\pi$
$619$	−19.2267	+	33.3016i	−0.772785	+	1.33850i	−0.936031	+	0.351918i	$0.885530\pi$
$620$	−1.61497	+	2.44584i	−0.0648587	+	0.0982273i
$621$	33.5528	−	9.70136i	1.34643	−	0.389302i
$622$	−3.01172	+	10.0270i	−0.120759	+	0.402046i
$623$	1.73630	−	3.00736i	0.0695634	−	0.120487i
$624$	−11.6111	−	34.6965i	−0.464814	−	1.38897i
$625$	5.05762	+	8.76006i	0.202305	+	0.350403i
$626$	−8.13023	+	1.91917i	−0.324949	+	0.0767056i
$627$	22.0676	−	31.9596i	0.881297	−	1.27635i
$628$	−10.2577	−	20.5167i	−0.409326	−	0.818706i
$629$	−4.88636			−0.194832
$630$	5.99028	−	4.04549i	0.238658	−	0.161176i
$631$			23.3583i			0.929880i	0.885342	+	0.464940i	$0.153924\pi$
$631$			23.3583i			0.929880i	−0.885342	+	0.464940i	$0.846076\pi$
$632$	35.7405	−	6.20258i	1.42168	−	0.246725i
$633$	−35.6621	+	16.9149i	−1.41744	+	0.672308i
$634$	−14.5579	+	3.43644i	−0.578167	+	0.136479i
$635$	−7.77955	+	4.49153i	−0.308722	+	0.178241i
$636$	−23.5019	−	3.32847i	−0.931910	−	0.131982i
$637$	4.57348	+	2.64050i	0.181208	+	0.104620i
$638$	66.7366	+	20.0451i	2.64213	+	0.793593i
$639$	13.2866	+	2.16362i	0.525610	+	0.0855913i
$640$	17.1705	+	8.75924i	0.678725	+	0.346239i
$641$	9.60691	+	5.54655i	0.379450	+	0.219076i	0.677579	−	0.735450i	$-0.263029\pi$
$641$	9.60691	+	5.54655i	0.379450	+	0.219076i	−0.298129	+	0.954526i	$0.596363\pi$
$642$	25.8061	+	32.2605i	1.01849	+	1.27322i
$643$	−2.65686	−	4.60182i	−0.104776	−	0.181478i	0.808870	−	0.587987i	$-0.200079\pi$
$643$	−2.65686	−	4.60182i	−0.104776	−	0.181478i	−0.913647	+	0.406509i	$0.866746\pi$
$644$	−13.4193	−	0.805822i	−0.528794	−	0.0317538i
$645$	0.135212	−	1.67159i	0.00532396	−	0.0658188i
$646$	−4.74399	+	4.46766i	−0.186650	+	0.175778i
$647$	−24.1320			−0.948728			−0.474364	−	0.880329i	$-0.657322\pi$
$647$	−24.1320			−0.948728			−0.474364	+	0.880329i	$0.657322\pi$
$648$	23.7093	−	9.26648i	0.931390	−	0.364022i
$649$	−33.0981			−1.29921
$650$	−11.4027	+	10.7385i	−0.447251	+	0.421199i
$651$	0.120115	−	1.48495i	0.00470769	−	0.0582000i
$652$	1.90833	−	31.7792i	0.0747358	−	1.24457i
$653$	24.4665	+	42.3773i	0.957450	+	1.65835i	0.728660	+	0.684876i	$0.240143\pi$
$653$	24.4665	+	42.3773i	0.957450	+	1.65835i	0.228790	+	0.973476i	$0.426523\pi$
$654$	−15.6804	−	19.6022i	−0.613150	−	0.766507i
$655$	9.39311	+	5.42311i	0.367019	+	0.211899i
$656$	11.0158	−	4.70478i	0.430094	−	0.183691i
$657$	44.2326	+	7.20292i	1.72568	+	0.281013i
$658$	−10.8844	−	3.26927i	−0.424320	−	0.127449i
$659$	−23.9273	−	13.8145i	−0.932077	−	0.538135i	−0.0446091	−	0.999005i	$-0.514204\pi$
$659$	−23.9273	−	13.8145i	−0.932077	−	0.538135i	−0.887468	+	0.460870i	$0.847538\pi$
$660$	4.68825	−	33.1031i	0.182490	−	1.28854i
$661$	−36.5961	+	21.1287i	−1.42342	+	0.821813i	−0.996590	−	0.0825179i	$-0.973704\pi$
$661$	−36.5961	+	21.1287i	−1.42342	+	0.821813i	−0.426832	+	0.904331i	$0.640371\pi$
$662$	−28.6888	+	6.77211i	−1.11502	+	0.263205i
$663$	9.62065	−	4.56318i	0.373635	−	0.177219i
$664$	−18.2910	+	3.17430i	−0.709827	+	0.123187i
$665$		−	6.74398i		−	0.261520i
$666$	14.7583	−	9.96692i	0.571874	−	0.386210i
$667$	58.4656			2.26380
$668$	27.5793	−	13.7887i	1.06707	−	0.533502i
$669$	2.28584	−	3.31049i	0.0883758	−	0.127991i
$670$	15.8653	−	3.74508i	0.612931	−	0.144685i
$671$	23.5049	+	40.7117i	0.907398	+	1.57166i
$672$	−9.79321	+	0.305091i	−0.377781	+	0.0117691i
$673$	9.55212	−	16.5448i	0.368207	−	0.637753i	−0.621078	−	0.783749i	$-0.713305\pi$
$673$	9.55212	−	16.5448i	0.368207	−	0.637753i	0.989285	+	0.145995i	$0.0466384\pi$
$674$	0.862092	−	2.87018i	0.0332065	−	0.110555i
$675$	−7.85582	−	7.55281i	−0.302371	−	0.290708i
$676$	24.8495	+	16.4079i	0.955750	+	0.631074i
$677$	−10.3463	+	17.9203i	−0.397640	+	0.688733i	−0.993434	−	0.114404i	$-0.963504\pi$
$677$	−10.3463	+	17.9203i	−0.397640	+	0.688733i	0.595794	+	0.803137i	$0.296837\pi$
$678$	2.13956	−	5.47561i	0.0821692	−	0.210290i
$679$	−5.83224	+	3.36725i	−0.223821	+	0.129223i
$680$	−1.93286	+	5.26620i	−0.0741217	+	0.201950i
$681$	24.2108	−	35.0635i	0.927760	−	1.34364i
$682$	−4.72424	−	5.01644i	−0.180901	−	0.192089i
$683$			4.22115i			0.161518i	0.996734	+	0.0807588i	$0.0257344\pi$
$683$			4.22115i			0.161518i	−0.996734	+	0.0807588i	$0.974266\pi$
$684$	5.21544	−	23.1702i	0.199417	−	0.885936i
$685$		−	32.3387i		−	1.23560i
$686$	1.02953	−	0.969566i	0.0393078	−	0.0370182i
$687$	−3.61603	−	7.62376i	−0.137960	−	0.290864i
$688$	−1.36403	+	1.81850i	−0.0520030	+	0.0693297i
$689$	31.3380	−	18.0930i	1.19388	−	0.689288i
$690$	−4.22247	−	27.7322i	−0.160747	−	1.05575i
$691$	1.37058	−	2.37391i	0.0521392	−	0.0903077i	−0.838778	−	0.544474i	$-0.816729\pi$
$691$	1.37058	−	2.37391i	0.0521392	−	0.0903077i	0.890917	+	0.454166i	$0.150063\pi$
$692$	32.9520	+	21.7580i	1.25265	+	0.827114i
$693$	6.02127	+	15.8920i	0.228729	+	0.603687i
$694$	−5.51528	−	1.65658i	−0.209357	−	0.0628828i
$695$	−2.14890	+	3.72200i	−0.0815123	+	0.141183i
$696$	42.4346	−	3.87740i	1.60848	−	0.146973i
$697$	1.74301	+	3.01898i	0.0660212	+	0.114352i
$698$	−10.1531	−	43.0118i	−0.384301	−	1.62802i
$699$	−24.9525	−	2.01836i	−0.943790	−	0.0763414i
$700$	1.87574	+	3.75173i	0.0708964	+	0.141802i
$701$	33.4440			1.26316			0.631581	−	0.775310i	$-0.282406\pi$
$701$	33.4440			1.26316			0.631581	+	0.775310i	$0.282406\pi$
$702$	−19.7496	+	33.4059i	−0.745402	+	1.26082i
$703$		−	16.6152i		−	0.626655i
$704$	−29.3172	+	34.5582i	−1.10493	+	1.30246i
$705$	1.91197	−	23.6372i	0.0720091	−	0.890230i
$706$	−5.78594	−	24.5111i	−0.217757	−	0.922486i
$707$	−7.88532	+	4.55259i	−0.296558	+	0.171218i
$708$	−18.7741	+	7.56202i	−0.705575	+	0.284198i
$709$	−7.42273	−	4.28552i	−0.278766	−	0.160946i	0.354098	−	0.935208i	$-0.384788\pi$
$709$	−7.42273	−	4.28552i	−0.278766	−	0.160946i	−0.632865	+	0.774262i	$0.718121\pi$
$710$	3.11016	−	10.3547i	0.116722	−	0.388607i
$711$	−29.7954	−	24.3429i	−1.11741	−	0.912931i
$712$	−6.29312	−	7.54111i	−0.235845	−	0.282615i
$713$	−5.00703	−	2.89081i	−0.187515	−	0.108262i
$714$	−0.429212	−	2.81897i	−0.0160629	−	0.105497i
$715$	25.4845	+	44.1405i	0.953066	+	1.65076i
$716$	−18.5924	−	1.11647i	−0.694831	−	0.0417243i
$717$	−8.72813	+	4.13985i	−0.325958	+	0.154606i
$718$	23.2717	+	24.7111i	0.868492	+	0.922209i
$719$	−1.04023			−0.0387939			−0.0193970	−	0.999812i	$-0.506175\pi$
$719$	−1.04023			−0.0387939			−0.0193970	+	0.999812i	$0.506175\pi$
$720$	−4.90387	−	19.8481i	−0.182756	−	0.739695i
$721$	9.34597			0.348062
$722$	3.23026	+	3.43005i	0.120218	+	0.127653i
$723$	24.4497	+	16.8821i	0.909293	+	0.627853i
$724$	36.0837	+	2.16681i	1.34104	+	0.0805289i
$725$	−9.12096	−	15.7980i	−0.338744	−	0.586722i
$726$	48.1173	+	18.8015i	1.78580	+	0.697789i
$727$	−30.3021	−	17.4949i	−1.12384	−	0.648851i	−0.181464	−	0.983398i	$-0.558084\pi$
$727$	−30.3021	−	17.4949i	−1.12384	−	0.648851i	−0.942379	+	0.334547i	$0.891417\pi$
$728$	11.4682	−	9.57033i	0.425040	−	0.354700i
$729$	−23.8953	−	12.5703i	−0.885013	−	0.465567i
$730$	10.3541	−	34.4721i	0.383221	−	1.27587i
$731$	−0.572931	−	0.330782i	−0.0211906	−	0.0122344i
$732$	22.6342	+	17.7225i	0.836583	+	0.655044i
$733$	16.7966	−	9.69751i	0.620396	−	0.358186i	−0.156627	−	0.987658i	$-0.550062\pi$
$733$	16.7966	−	9.69751i	0.620396	−	0.358186i	0.777023	+	0.629472i	$0.216729\pi$
$734$	−2.09943	−	8.89385i	−0.0774914	−	0.328278i
$735$	2.42834	+	1.67673i	0.0895705	+	0.0618471i
$736$	−15.2174	+	34.8460i	−0.560922	+	1.28444i
$737$			38.3257i			1.41175i
$738$	−11.4224	−	5.56298i	−0.420464	−	0.204776i
$739$	−45.6788			−1.68032			−0.840162	−	0.542336i	$-0.817540\pi$
$739$	−45.6788			−1.68032			−0.840162	+	0.542336i	$0.817540\pi$
$740$	−6.39619	−	12.7932i	−0.235129	−	0.470288i
$741$	15.5163	+	32.7133i	0.570006	+	1.20175i
$742$	−2.22626	−	9.43115i	−0.0817286	−	0.346228i
$743$	2.91701	+	5.05241i	0.107015	+	0.185355i	0.914560	−	0.404451i	$-0.132537\pi$
$743$	2.91701	+	5.05241i	0.107015	+	0.185355i	−0.807545	+	0.589806i	$0.799204\pi$
$744$	−3.82584	−	1.76610i	−0.140262	−	0.0647483i
$745$	9.20281	−	15.9397i	0.337165	−	0.583987i
$746$	−34.9040	−	10.4838i	−1.27792	−	0.383839i
$747$	15.2484	+	12.4580i	0.557910	+	0.455814i
$748$	−11.0061	−	7.26721i	−0.402421	−	0.265716i
$749$	−8.43281	+	14.6061i	−0.308128	+	0.533694i
$750$	−23.1294	+	18.5018i	−0.844565	+	0.675591i
$751$	−3.35340	+	1.93609i	−0.122367	+	0.0706488i	−0.559934	−	0.828537i	$-0.689174\pi$
$751$	−3.35340	+	1.93609i	−0.122367	+	0.0706488i	0.437567	+	0.899186i	$0.355840\pi$
$752$	−19.2881	+	25.7147i	−0.703365	+	0.937717i
$753$	−31.3161	−	2.53310i	−1.14122	−	0.0923113i
$754$	−47.2907	+	44.5361i	−1.72223	+	1.62191i
$755$		−	19.3243i		−	0.703284i
$756$	7.04632	+	7.63867i	0.256272	+	0.277816i
$757$			14.2917i			0.519441i	0.965684	+	0.259721i	$0.0836305\pi$
$757$			14.2917i			0.519441i	−0.965684	+	0.259721i	$0.916370\pi$
$758$	−18.5528	−	19.7003i	−0.673869	−	0.715548i
$759$	65.7373	+	5.31737i	2.38611	+	0.193008i
$760$	−17.9068	−	6.57235i	−0.649548	−	0.238404i
$761$	5.95020	−	3.43535i	0.215695	−	0.124531i	−0.388261	−	0.921550i	$-0.626924\pi$
$761$	5.95020	−	3.43535i	0.215695	−	0.124531i	0.603955	+	0.797018i	$0.293591\pi$
$762$	−8.06750	−	10.0853i	−0.292255	−	0.365351i
$763$	5.12396	−	8.87496i	0.185500	−	0.321295i
$764$	11.3599	+	7.50083i	0.410986	+	0.271371i
$765$	5.56401	−	2.10813i	0.201167	−	0.0762196i
$766$	−6.78674	+	22.5953i	−0.245215	+	0.816400i
$767$	15.4278	−	26.7217i	0.557064	−	0.964863i
$768$	−8.73389	+	26.3006i	−0.315157	+	0.949039i
$769$	17.0525	+	29.5358i	0.614928	+	1.06509i	0.990397	+	0.138252i	$0.0441483\pi$
$769$	17.0525	+	29.5358i	0.614928	+	1.06509i	−0.375469	+	0.926835i	$0.622518\pi$
$770$	13.2841	−	3.13576i	0.478724	−	0.113005i
$771$	5.11442	+	10.7828i	0.184191	+	0.388334i
$772$	34.8285	−	17.4131i	1.25351	−	0.626712i
$773$	−33.6378			−1.20987			−0.604934	−	0.796275i	$-0.706801\pi$
$773$	−33.6378			−1.20987			−0.604934	+	0.796275i	$0.706801\pi$
$774$	2.40514	−	0.169568i	0.0864510	−	0.00609498i
$775$			1.80393i			0.0647991i
$776$	3.25700	+	18.7675i	0.116919	+	0.673714i
$777$	5.98273	+	4.13098i	0.214629	+	0.148198i
$778$	−0.947972	+	0.223773i	−0.0339864	+	0.00802264i
$779$	−10.2655	+	5.92681i	−0.367801	+	0.212350i
$780$	24.5404	+	19.2151i	0.878687	+	0.688012i
$781$	22.0137	+	12.7096i	0.787712	+	0.454786i
$782$	−10.5982	−	3.18328i	−0.378990	−	0.113834i
$783$	−32.5807	−	31.3240i	−1.16434	−	1.11943i
$784$	−1.57109	−	3.67854i	−0.0561103	−	0.131377i
$785$	16.9224	+	9.77016i	0.603987	+	0.348712i
$786$	−5.67527	+	14.5243i	−0.202430	+	0.518065i
$787$	−4.02277	−	6.96765i	−0.143396	−	0.248370i	0.785377	−	0.619018i	$-0.212469\pi$
$787$	−4.02277	−	6.96765i	−0.143396	−	0.248370i	−0.928774	+	0.370648i	$0.879136\pi$
$788$	1.51518	−	25.2321i	0.0539759	−	0.898857i
$789$	−19.1279	−	13.2075i	−0.680973	−	0.470201i
$790$	−22.4960	+	21.1856i	−0.800371	+	0.753751i
$791$	2.40000			0.0853342
$792$	48.0650	−	0.500291i	1.70791	−	0.0177771i
$793$	−43.8247			−1.55626
$794$	31.7478	−	29.8985i	1.12669	−	1.06106i
$795$	18.2695	−	8.66543i	0.647952	−	0.307331i
$796$	−22.1024	−	1.32724i	−0.783399	−	0.0470427i
$797$	−15.4450	−	26.7515i	−0.547090	−	0.947588i	−0.998472	−	0.0552571i	$-0.982402\pi$
$797$	−15.4450	−	26.7515i	−0.547090	−	0.947588i	0.451382	−	0.892331i	$-0.350931\pi$
$798$	9.58541	−	1.45946i	0.339320	−	0.0516644i
$799$	−8.10157	−	4.67745i	−0.286613	−	0.165476i
$800$	11.7897	−	1.32428i	0.416830	−	0.0468202i
$801$	−1.67440	+	10.2824i	−0.0591620	+	0.363309i
$802$	−24.8603	−	7.46706i	−0.877847	−	0.263671i
$803$	73.2860	+	42.3117i	2.58621	+	1.49315i
$804$	8.75640	+	21.7394i	0.308814	+	0.766689i
$805$	9.91782	−	5.72606i	0.349557	−	0.201817i
$806$	6.25208	−	1.47583i	0.220220	−	0.0519839i
$807$	−1.83660	+	22.7054i	−0.0646514	+	0.799269i
$808$	4.40353	+	25.3741i	0.154916	+	0.892657i
$809$			49.5678i			1.74271i	0.490651	+	0.871356i	$0.336759\pi$
$809$			49.5678i			1.74271i	−0.490651	+	0.871356i	$0.663241\pi$
$810$	−12.5050	+	17.7164i	−0.439381	+	0.622490i
$811$	42.7317			1.50051			0.750256	−	0.661148i	$-0.229930\pi$
$811$	42.7317			1.50051			0.750256	+	0.661148i	$0.229930\pi$
$812$	7.77932	+	15.5597i	0.273001	+	0.546037i
$813$	−43.6925	−	3.53421i	−1.53236	−	0.123950i
$814$	32.7281	−	7.72561i	1.14712	−	0.270782i
$815$	13.5603	+	23.4871i	0.474997	+	0.822719i
$816$	−7.90330	−	1.60757i	−0.276671	−	0.0562762i
$817$	1.12477	−	1.94815i	0.0393506	−	0.0681572i
$818$	7.63754	−	25.4278i	0.267040	−	0.889064i
$819$	−15.6370	−	2.54636i	−0.546401	−	0.0889770i
$820$	−5.62257	+	8.51528i	−0.196349	+	0.297366i
$821$	−4.55594	+	7.89112i	−0.159003	+	0.275402i	−0.934510	−	0.355938i	$-0.884161\pi$
$821$	−4.55594	+	7.89112i	−0.159003	+	0.275402i	0.775506	+	0.631340i	$0.217495\pi$
$822$	45.9640	−	6.99842i	1.60318	−	0.244098i
$823$	7.91708	−	4.57093i	0.275972	−	0.159332i	−0.355627	−	0.934628i	$-0.615732\pi$
$823$	7.91708	−	4.57093i	0.275972	−	0.159332i	0.631598	+	0.775296i	$0.282399\pi$
$824$	9.10812	−	24.8157i	0.317296	−	0.864496i
$825$	−8.81857	−	18.5924i	−0.307023	−	0.647303i
$826$	−5.66493	−	6.01531i	−0.197108	−	0.209299i
$827$		−	38.9274i		−	1.35364i	−0.736150	−	0.676819i	$-0.763358\pi$
$827$		−	38.9274i		−	1.35364i	0.736150	−	0.676819i	$-0.236642\pi$
$828$	38.5028	−	12.0030i	1.33807	−	0.417134i
$829$		−	39.1588i		−	1.36004i	−0.733193	−	0.680021i	$-0.761971\pi$
$829$		−	39.1588i		−	1.36004i	0.733193	−	0.680021i	$-0.238029\pi$
$830$	11.5128	−	10.8422i	0.399615	−	0.376338i
$831$	−3.75057	+	5.43180i	−0.130106	+	0.188427i
$832$	−14.2351	−	39.7775i	−0.493513	−	1.37904i
$833$	1.00814	−	0.582051i	0.0349300	−	0.0201669i
$834$	−5.75522	−	2.24881i	−0.199287	−	0.0778700i
$835$	−13.1334	+	22.7477i	−0.454499	+	0.787216i
$836$	24.7109	−	37.4242i	0.854644	−	1.29434i
$837$	1.24142	+	4.29354i	0.0429099	+	0.148407i
$838$	−40.7492	−	12.2395i	−1.40766	−	0.422805i
$839$	−13.9984	+	24.2459i	−0.483278	+	0.837062i	−0.999816	−	0.0192024i	$-0.993887\pi$
$839$	−13.9984	+	24.2459i	−0.483278	+	0.837062i	0.516538	+	0.856265i	$0.327221\pi$
$840$	6.81864	−	4.81373i	0.235265	−	0.166090i
$841$	−23.3276	−	40.4046i	−0.804401	−	1.39326i
$842$	−0.894976	−	3.79140i	−0.0308429	−	0.130660i
$843$	11.6893	−	16.9291i	0.402599	−	0.583068i
$844$	−40.7652	+	20.3813i	−1.40320	+	0.701552i
$845$	−25.3669			−0.872647
$846$	34.0101	−	2.39778i	1.16929	−	0.0824375i
$847$			21.0902i			0.724667i
$848$	−27.2115	−	3.27990i	−0.934446	−	0.112632i
$849$	12.4595	−	5.90968i	0.427609	−	0.202820i
$850$	0.793220	+	3.36033i	0.0272072	+	0.115258i
$851$	24.4347	−	14.1074i	0.837610	−	0.483594i
$852$	15.3906	+	2.17970i	0.527272	+	0.0746752i
$853$	−11.3703	−	6.56467i	−0.389313	−	0.224770i	0.292549	−	0.956250i	$-0.405496\pi$
$853$	−11.3703	−	6.56467i	−0.389313	−	0.224770i	−0.681862	+	0.731480i	$0.738830\pi$
$854$	−3.37602	+	11.2399i	−0.115525	+	0.384621i
$855$	7.16833	+	18.9195i	0.245152	+	0.647032i
$856$	30.5643	+	36.6254i	1.04466	+	1.25183i
$857$	−0.937309	−	0.541156i	−0.0320179	−	0.0184855i	0.483906	−	0.875120i	$-0.339218\pi$
$857$	−0.937309	−	0.541156i	−0.0320179	−	0.0184855i	−0.515924	+	0.856635i	$0.672551\pi$
$858$	−57.2230	+	45.7743i	−1.95356	+	1.56271i
$859$	−7.17010	−	12.4190i	−0.244641	−	0.423730i	0.717390	−	0.696672i	$-0.245337\pi$
$859$	−7.17010	−	12.4190i	−0.244641	−	0.423730i	−0.962031	+	0.272942i	$0.912003\pi$
$860$	0.116076	−	1.93301i	0.00395816	−	0.0659150i
$861$	0.418185	−	5.16992i	0.0142517	−	0.176190i
$862$	−7.30325	−	7.75496i	−0.248750	−	0.264135i
$863$	55.4445			1.88735			0.943676	−	0.330870i	$-0.107342\pi$
$863$	55.4445			1.88735			0.943676	+	0.330870i	$0.107342\pi$
$864$	27.1494	−	11.2653i	0.923643	−	0.383254i
$865$	−33.6381			−1.14373
$866$	−6.68312	−	7.09648i	−0.227102	−	0.241148i
$867$	−2.18475	+	27.0095i	−0.0741979	+	0.917290i
$868$	0.103116	−	1.71718i	0.00349999	−	0.0582850i
$869$	−36.3258	−	62.9182i	−1.23227	−	2.13435i
$870$	−28.3461	+	22.6748i	−0.961022	+	0.768748i
$871$	−30.9422	−	17.8645i	−1.04844	−	0.605315i
$872$	−18.5715	−	22.2544i	−0.628911	−	0.753629i
$873$	12.7826	−	15.6457i	0.432624	−	0.529525i
$874$	10.8242	−	36.0372i	0.366133	−	1.21898i
$875$	−10.4719	−	6.04595i	−0.354015	−	0.204391i
$876$	51.2369	+	7.25645i	1.73113	+	0.245173i
$877$	−19.2175	+	11.0952i	−0.648929	+	0.374659i	−0.788046	−	0.615617i	$-0.788907\pi$
$877$	−19.2175	+	11.0952i	−0.648929	+	0.374659i	0.139117	+	0.990276i	$0.455574\pi$
$878$	1.09569	+	4.64170i	0.0369778	+	0.156650i
$879$	−42.3951	+	20.1085i	−1.42995	+	0.678242i
$880$	4.61984	−	38.3282i	0.155735	−	1.29204i
$881$		−	9.25932i		−	0.311954i	−0.987761	−	0.155977i	$-0.950147\pi$
$881$		−	9.25932i		−	0.311954i	0.987761	−	0.155977i	$-0.0498526\pi$
$882$	−1.85767	+	3.81432i	−0.0625509	+	0.128435i
$883$	−37.3213			−1.25596			−0.627981	−	0.778229i	$-0.716118\pi$
$883$	−37.3213			−1.25596			−0.627981	+	0.778229i	$0.716118\pi$
$884$	10.9973	−	5.49830i	0.369880	−	0.184928i
$885$	9.79670	−	14.1882i	0.329313	−	0.476930i
$886$	−4.85405	−	20.5633i	−0.163075	−	0.690838i
$887$	23.8733	+	41.3498i	0.801588	+	1.38839i	0.918571	+	0.395257i	$0.129344\pi$
$887$	23.8733	+	41.3498i	0.801588	+	1.38839i	−0.116983	+	0.993134i	$0.537322\pi$
$888$	16.7992	−	11.8597i	0.563744	−	0.397984i
$889$	2.63627	−	4.56615i	0.0884176	−	0.153144i
$890$	8.01342	+	2.40692i	0.268610	+	0.0806802i
$891$	−33.7840	−	38.1831i	−1.13181	−	1.27918i
$892$	2.55964	−	3.87653i	0.0857031	−	0.129796i
$893$	15.9048	−	27.5480i	0.532235	−	0.921859i
$894$	24.6472	+	9.63070i	0.824325	+	0.322099i
$895$	13.7411	−	7.93345i	0.459315	−	0.265186i
$896$	−11.2985	+	0.586672i	−0.377456	+	0.0195993i
$897$	−34.9346	+	50.5942i	−1.16643	+	1.68929i
$898$	19.9056	−	18.7462i	0.664260	−	0.625568i
$899$			7.48149i			0.249522i
$900$	−9.24999	−	8.53129i	−0.308333	−	0.284376i
$901$		−	7.97655i		−	0.265737i
$902$	−16.4476	−	17.4649i	−0.547645	−	0.581518i
$903$	0.421834	+	0.889362i	0.0140378	+	0.0295961i
$904$	2.33892	−	6.37256i	0.0777915	−	0.211948i
$905$	−26.6685	+	15.3971i	−0.886490	+	0.511815i
$906$	27.4662	−	4.18197i	0.912504	−	0.138937i
$907$	2.84664	−	4.93053i	0.0945213	−	0.163716i	−0.814887	−	0.579619i	$-0.803201\pi$
$907$	2.84664	−	4.93053i	0.0945213	−	0.163716i	0.909409	+	0.415904i	$0.136535\pi$
$908$	27.1108	−	41.0588i	0.899702	−	1.36258i
$909$	17.2823	−	21.1533i	0.573218	−	0.701610i
$910$	−3.66035	+	12.1865i	−0.121339	+	0.403978i
$911$	9.80563	−	16.9838i	0.324875	−	0.562700i	−0.656612	−	0.754229i	$-0.728011\pi$
$911$	9.80563	−	16.9838i	0.324875	−	0.562700i	0.981487	+	0.191528i	$0.0613444\pi$
$912$	5.46626	−	26.8738i	0.181006	−	0.889880i
$913$	18.5905	+	32.1997i	0.615256	+	1.06565i
$914$	20.9591	−	4.94749i	0.693266	−	0.163648i
$915$	−24.4091	−	1.97441i	−0.806940	−	0.0652719i
$916$	−4.35706	−	8.71469i	−0.143961	−	0.287941i
$917$	−6.36611			−0.210227
$918$	4.20045	+	7.45207i	0.138636	+	0.245955i
$919$		−	5.91860i		−	0.195236i	−0.995224	−	0.0976182i	$-0.968878\pi$
$919$		−	5.91860i		−	0.195236i	0.995224	−	0.0976182i	$-0.0311224\pi$
$920$	−5.53858	−	31.9144i	−0.182602	−	1.05219i
$921$	−1.87953	+	23.2361i	−0.0619325	+	0.765656i
$922$	−6.05846	+	1.43012i	−0.199525	+	0.0470986i
$923$	−20.5221	+	11.8485i	−0.675494	+	0.389997i
$924$	7.33174	+	18.2024i	0.241197	+	0.598815i
$925$	−7.62389	−	4.40166i	−0.250672	−	0.144726i
$926$	−34.1039	−	10.2435i	−1.12072	−	0.336622i
$927$	−26.2190	+	9.93405i	−0.861146	+	0.326277i
$928$	48.8958	−	5.49220i	1.60508	−	0.180290i
$929$	−45.0441	−	26.0062i	−1.47785	−	0.853237i	−0.478162	−	0.878271i	$-0.658697\pi$
$929$	−45.0441	−	26.0062i	−1.47785	−	0.853237i	−0.999687	+	0.0250348i	$0.992030\pi$
$930$	3.54872	−	0.540324i	0.116367	−	0.0177179i
$931$	1.97916	+	3.42801i	0.0648645	+	0.112349i
$932$	−28.8548	−	1.73272i	−0.945170	−	0.0567570i
$933$	11.5854	−	5.49507i	0.379288	−	0.179901i
$934$	34.0809	−	32.0957i	1.11516	−	1.05020i
$935$	11.2352			0.367431
$936$	−22.0002	+	39.0383i	−0.719100	+	1.27601i
$937$	37.1230			1.21276			0.606378	−	0.795177i	$-0.292622\pi$
$937$	37.1230			1.21276			0.606378	+	0.795177i	$0.292622\pi$
$938$	−6.96539	+	6.55967i	−0.227428	+	0.214181i
$939$	8.41913	+	5.81328i	0.274748	+	0.189709i
$940$	1.64138	−	27.3338i	0.0535360	−	0.891532i
$941$	−18.0605	−	31.2817i	−0.588756	−	1.01975i	−0.994396	−	0.105722i	$-0.966285\pi$
$941$	−18.0605	−	31.2817i	−0.588756	−	1.01975i	0.405640	−	0.914033i	$-0.367049\pi$
$942$	−10.2244	+	26.1667i	−0.333130	+	0.852556i
$943$	−17.4322	−	10.0645i	−0.567669	−	0.327744i
$944$	−21.4928	+	9.17947i	−0.699531	+	0.298766i
$945$	−8.59466	−	2.12274i	−0.279584	−	0.0690526i
$946$	4.36039	+	1.30969i	0.141768	+	0.0425818i
$947$	−21.5117	−	12.4198i	−0.699037	−	0.403589i	0.107951	−	0.994156i	$-0.465571\pi$
$947$	−21.5117	−	12.4198i	−0.699037	−	0.403589i	−0.806989	+	0.590567i	$0.798904\pi$
$948$	−34.9801	−	27.3894i	−1.13610	−	0.889567i
$949$	−68.3205	+	39.4448i	−2.21778	+	1.28043i
$950$	−11.4262	+	2.69721i	−0.370716	+	0.0875090i
$951$	15.0752	+	10.4092i	0.488845	+	0.337540i
$952$	−0.562994	−	3.24409i	−0.0182467	−	0.105141i
$953$			2.05039i			0.0664186i	0.999448	+	0.0332093i	$0.0105728\pi$
$953$			2.05039i			0.0664186i	−0.999448	+	0.0332093i	$0.989427\pi$
$954$	16.2701	+	24.0917i	0.526764	+	0.779997i
$955$	−11.5964			−0.375250
$956$	−9.97710	+	4.98822i	−0.322682	+	0.161331i
$957$	−36.5735	−	77.1087i	−1.18225	−	2.49257i
$958$	−31.0759	+	7.33559i	−1.00402	+	0.237002i
$959$	9.49049	+	16.4380i	0.306464	+	0.530811i
$960$	−6.13646	−	22.7963i	−0.198054	−	0.735747i
$961$	−15.1301	+	26.2061i	−0.488067	+	0.845357i
$962$	−9.01806	+	30.0240i	−0.290754	+	0.968014i
$963$	8.13217	−	49.9391i	0.262056	−	1.60926i
$964$	28.6301	+	18.9043i	0.922115	+	0.608865i
$965$	−16.5855	+	28.7270i	−0.533907	+	0.924754i
$966$	10.2849	+	12.8573i	0.330912	+	0.413677i
$967$	18.3222	−	10.5784i	0.589204	−	0.340177i	−0.175579	−	0.984465i	$-0.556180\pi$
$967$	18.3222	−	10.5784i	0.589204	−	0.340177i	0.764783	+	0.644288i	$0.222846\pi$
$968$	55.9993	+	20.5534i	1.79988	+	0.660613i
$969$	7.95512	+	0.643475i	0.255555	+	0.0206714i
$970$	−11.1247	−	11.8127i	−0.357191	−	0.379284i
$971$			24.0825i			0.772844i	0.922322	+	0.386422i	$0.126289\pi$
$971$			24.0825i			0.772844i	−0.922322	+	0.386422i	$0.873711\pi$
$972$	−27.8870	−	13.9397i	−0.894475	−	0.447117i
$973$		−	2.52256i		−	0.0808694i
$974$	7.85977	−	7.40195i	0.251843	−	0.237174i
$975$	19.1210	+	1.54667i	0.612363	+	0.0495329i
$976$	26.5544	+	19.9179i	0.849984	+	0.637558i
$977$	−7.73938	+	4.46833i	−0.247605	+	0.142955i	−0.618667	−	0.785653i	$-0.712327\pi$
$977$	−7.73938	+	4.46833i	−0.247605	+	0.142955i	0.371062	+	0.928608i	$0.378994\pi$
$978$	−30.4484	+	24.3565i	−0.973631	+	0.778835i
$979$	−9.83583	+	17.0362i	−0.314354	+	0.544478i
$980$	2.84354	+	1.87757i	0.0908336	+	0.0599767i
$981$	−4.94129	+	30.3441i	−0.157763	+	0.968812i
$982$	28.4924	+	8.55800i	0.909228	+	0.273097i
$983$	−5.88551	+	10.1940i	−0.187719	+	0.325138i	−0.944489	−	0.328542i	$-0.893443\pi$
$983$	−5.88551	+	10.1940i	−0.187719	+	0.325138i	0.756771	+	0.653681i	$0.226776\pi$
$984$	−13.3198	−	6.14873i	−0.424619	−	0.196014i
$985$	10.7666	+	18.6483i	0.343053	+	0.594186i
$986$	3.28975	+	13.9364i	0.104767	+	0.443826i
$987$	5.96498	+	12.5761i	0.189867	+	0.400301i
$988$	18.6960	+	37.3945i	0.594800	+	1.18968i
$989$	3.81999			0.121469
$990$	−33.9338	+	22.9170i	−1.07849	+	0.728348i
$991$			50.8595i			1.61560i	0.589453	+	0.807802i	$0.299343\pi$
$991$			50.8595i			1.61560i	−0.589453	+	0.807802i	$0.700657\pi$
$992$	−4.45903	−	1.94728i	−0.141574	−	0.0618262i
$993$	29.7082	+	20.5131i	0.942761	+	0.650962i
$994$	1.45790	+	6.17613i	0.0462418	+	0.195895i
$995$	16.3353	−	9.43117i	0.517863	−	0.298988i
$996$	17.9018	+	14.0171i	0.567240	+	0.444149i
$997$	16.7851	+	9.69088i	0.531590	+	0.306913i	0.741664	−	0.670772i	$-0.234037\pi$
$997$	16.7851	+	9.69088i	0.531590	+	0.306913i	−0.210074	+	0.977686i	$0.567370\pi$
$998$	0.573329	−	1.90880i	0.0181484	−	0.0604219i
$999$	−21.1748	−	5.22982i	−0.669940	−	0.165464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.br.a.155.19	yes	144
8.3	odd	2	inner	504.2.br.a.155.6	✓	144
9.5	odd	6	inner	504.2.br.a.491.6	yes	144
72.59	even	6	inner	504.2.br.a.491.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.br.a.155.6	✓	144	8.3	odd	2	inner
504.2.br.a.155.19	yes	144	1.1	even	1	trivial
504.2.br.a.491.6	yes	144	9.5	odd	6	inner
504.2.br.a.491.19	yes	144	72.59	even	6	inner

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.br (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.969566 - 1.02953i) q^{2} +(-0.139646 + 1.72641i) q^{3} +(-0.119883 + 1.99640i) q^{4} +(-0.851872 - 1.47549i) q^{5} +(1.91280 - 1.53010i) q^{6} +(0.866025 + 0.500000i) q^{7} +(2.17160 - 1.81222i) q^{8} +(-2.96100 - 0.482174i) q^{9} +O(q^{10})\)	\(q+(-0.969566 - 1.02953i) q^{2} +(-0.139646 + 1.72641i) q^{3} +(-0.119883 + 1.99640i) q^{4} +(-0.851872 - 1.47549i) q^{5} +(1.91280 - 1.53010i) q^{6} +(0.866025 + 0.500000i) q^{7} +(2.17160 - 1.81222i) q^{8} +(-2.96100 - 0.482174i) q^{9} +(-0.693117 + 2.30761i) q^{10} +(-4.90588 - 2.83241i) q^{11} +(-3.42987 - 0.485758i) q^{12} +(4.57348 - 2.64050i) q^{13} +(-0.324902 - 1.37639i) q^{14} +(2.66626 - 1.26464i) q^{15} +(-3.97126 - 0.478670i) q^{16} -1.16410i q^{17} +(2.37447 + 3.51595i) q^{18} +3.95833 q^{19} +(3.04779 - 1.52380i) q^{20} +(-0.984143 + 1.42529i) q^{21} +(1.84051 + 7.79698i) q^{22} +(3.36087 + 5.82119i) q^{23} +(2.82539 + 4.00215i) q^{24} +(1.04863 - 1.81628i) q^{25} +(-7.15277 - 2.14841i) q^{26} +(1.24592 - 5.04457i) q^{27} +(-1.10202 + 1.66899i) q^{28} +(4.34900 - 7.53269i) q^{29} +(-3.88710 - 1.51886i) q^{30} +(-0.744902 + 0.430070i) q^{31} +(3.35759 + 4.55265i) q^{32} +(5.57499 - 8.07403i) q^{33} +(-1.19848 + 1.12867i) q^{34} -1.70374i q^{35} +(1.31759 - 5.85354i) q^{36} -4.19754i q^{37} +(-3.83786 - 4.07523i) q^{38} +(3.91992 + 8.26444i) q^{39} +(-4.52383 - 1.66039i) q^{40} +(-2.59340 + 1.49730i) q^{41} +(2.42158 - 0.368707i) q^{42} +(0.284152 - 0.492166i) q^{43} +(6.24276 - 9.45455i) q^{44} +(1.81095 + 4.77966i) q^{45} +(2.73454 - 9.10416i) q^{46} +(4.01807 - 6.95951i) q^{47} +(1.38095 - 6.78918i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.88663 + 0.681401i) q^{50} +(2.00972 + 0.162563i) q^{51} +(4.72322 + 9.44705i) q^{52} +6.85211 q^{53} +(-6.40156 + 3.60832i) q^{54} +9.65140i q^{55} +(2.78677 - 0.483629i) q^{56} +(-0.552766 + 6.83370i) q^{57} +(-11.9718 + 2.82599i) q^{58} +(5.05997 - 2.92137i) q^{59} +(2.20509 + 5.47454i) q^{60} +(-7.18677 - 4.14928i) q^{61} +(1.16500 + 0.349922i) q^{62} +(-2.32321 - 1.89807i) q^{63} +(1.43170 - 7.87085i) q^{64} +(-7.79203 - 4.49873i) q^{65} +(-13.7178 + 2.08866i) q^{66} +(-3.38279 - 5.85916i) q^{67} +(2.32402 + 0.139556i) q^{68} +(-10.5191 + 4.98933i) q^{69} +(-1.75406 + 1.65189i) q^{70} -4.48721 q^{71} +(-7.30391 + 4.31889i) q^{72} -14.9384 q^{73} +(-4.32151 + 4.06979i) q^{74} +(2.98920 + 2.06400i) q^{75} +(-0.474536 + 7.90242i) q^{76} +(-2.83241 - 4.90588i) q^{77} +(4.70791 - 12.0486i) q^{78} +(11.1068 + 6.41253i) q^{79} +(2.67673 + 6.26730i) q^{80} +(8.53502 + 2.85543i) q^{81} +(4.05600 + 1.21826i) q^{82} +(-5.68416 - 3.28175i) q^{83} +(-2.72748 - 2.13562i) q^{84} +(-1.71762 + 0.991666i) q^{85} +(-0.782206 + 0.184643i) q^{86} +(12.3972 + 8.56008i) q^{87} +(-15.7866 + 2.73967i) q^{88} -3.47260i q^{89} +(3.16499 - 6.49863i) q^{90} +5.28099 q^{91} +(-12.0244 + 6.01178i) q^{92} +(-0.638454 - 1.34607i) q^{93} +(-11.0608 + 2.61096i) q^{94} +(-3.37199 - 5.84046i) q^{95} +(-8.32862 + 5.16082i) q^{96} +(-3.36725 + 5.83224i) q^{97} +(0.406820 - 1.35444i) q^{98} +(13.1606 + 10.7522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{6}+O(q^{10}) \) 144 * q + 6 * q^6	\( 144 q + 6 q^{6} - 12 q^{12} + 34 q^{18} - 42 q^{20} - 30 q^{24} - 72 q^{25} + 24 q^{27} - 36 q^{30} - 30 q^{32} - 16 q^{33} + 12 q^{34} - 12 q^{36} + 12 q^{40} + 24 q^{41} - 20 q^{42} - 24 q^{46} - 24 q^{48} + 72 q^{49} - 78 q^{50} + 18 q^{52} + 10 q^{54} + 8 q^{57} - 18 q^{58} - 72 q^{59} + 88 q^{60} - 12 q^{64} + 2 q^{66} + 78 q^{68} + 42 q^{72} + 84 q^{74} - 112 q^{75} + 12 q^{76} + 112 q^{78} - 8 q^{81} - 36 q^{82} - 14 q^{84} + 30 q^{86} + 24 q^{88} + 104 q^{90} - 114 q^{92} - 42 q^{94} - 80 q^{96} - 64 q^{99}+O(q^{100}) \) 144 * q + 6 * q^6 - 12 * q^12 + 34 * q^18 - 42 * q^20 - 30 * q^24 - 72 * q^25 + 24 * q^27 - 36 * q^30 - 30 * q^32 - 16 * q^33 + 12 * q^34 - 12 * q^36 + 12 * q^40 + 24 * q^41 - 20 * q^42 - 24 * q^46 - 24 * q^48 + 72 * q^49 - 78 * q^50 + 18 * q^52 + 10 * q^54 + 8 * q^57 - 18 * q^58 - 72 * q^59 + 88 * q^60 - 12 * q^64 + 2 * q^66 + 78 * q^68 + 42 * q^72 + 84 * q^74 - 112 * q^75 + 12 * q^76 + 112 * q^78 - 8 * q^81 - 36 * q^82 - 14 * q^84 + 30 * q^86 + 24 * q^88 + 104 * q^90 - 114 * q^92 - 42 * q^94 - 80 * q^96 - 64 * q^99

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