LMFDB - Embedded newform 819.2.dt.a.337.58

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(337,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 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("819.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dt (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			337.58
Character	$\chi$	$=$	819.337
Dual form			819.2.dt.a.610.58

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13423 - 0.654848i) q^{2} +(1.11529 + 1.32519i) q^{3} +(-0.142347 + 0.246553i) q^{4} +(-2.61566 - 1.51015i) q^{5} +(2.13279 + 0.772730i) q^{6} +(-0.866025 + 0.500000i) q^{7} +2.99226i q^{8} +(-0.512271 + 2.95594i) q^{9} +O(q^{10})$	\(q+(1.13423 - 0.654848i) q^{2} +(1.11529 + 1.32519i) q^{3} +(-0.142347 + 0.246553i) q^{4} +(-2.61566 - 1.51015i) q^{5} +(2.13279 + 0.772730i) q^{6} +(-0.866025 + 0.500000i) q^{7} +2.99226i q^{8} +(-0.512271 + 2.95594i) q^{9} -3.95568 q^{10} +(-1.63540 + 0.944199i) q^{11} +(-0.485488 + 0.0863394i) q^{12} +(-3.17619 - 1.70640i) q^{13} +(-0.654848 + 1.13423i) q^{14} +(-0.915969 - 5.15051i) q^{15} +(1.67478 + 2.90080i) q^{16} +3.51910 q^{17} +(1.35466 + 3.68818i) q^{18} +4.33503i q^{19} +(0.744664 - 0.429932i) q^{20} +(-1.62846 - 0.590007i) q^{21} +(-1.23661 + 2.14188i) q^{22} +(-3.51048 + 6.08034i) q^{23} +(-3.96532 + 3.33722i) q^{24} +(2.06112 + 3.56997i) q^{25} +(-4.71997 + 0.144467i) q^{26} +(-4.48852 + 2.61786i) q^{27} -0.284694i q^{28} +(0.999993 + 1.73204i) q^{29} +(-4.41172 - 5.24204i) q^{30} +(-6.79795 - 3.92480i) q^{31} +(-1.38357 - 0.798803i) q^{32} +(-3.07519 - 1.11417i) q^{33} +(3.99147 - 2.30447i) q^{34} +3.02031 q^{35} +(-0.655874 - 0.547071i) q^{36} +6.98344i q^{37} +(2.83879 + 4.91693i) q^{38} +(-1.28105 - 6.11219i) q^{39} +(4.51877 - 7.82673i) q^{40} +(5.12886 + 2.96115i) q^{41} +(-2.23342 + 0.397192i) q^{42} +(-5.34074 - 9.25043i) q^{43} -0.537617i q^{44} +(5.80385 - 6.95813i) q^{45} +9.19534i q^{46} +(3.56956 - 2.06088i) q^{47} +(-1.97626 + 5.45463i) q^{48} +(0.500000 - 0.866025i) q^{49} +(4.67558 + 2.69945i) q^{50} +(3.92480 + 4.66348i) q^{51} +(0.872840 - 0.540196i) q^{52} +9.36950 q^{53} +(-3.37671 + 5.90856i) q^{54} +5.70354 q^{55} +(-1.49613 - 2.59137i) q^{56} +(-5.74475 + 4.83480i) q^{57} +(2.26844 + 1.30969i) q^{58} +(11.3123 + 6.53119i) q^{59} +(1.40026 + 0.507326i) q^{60} +(-6.03436 - 10.4518i) q^{61} -10.2806 q^{62} +(-1.03433 - 2.81605i) q^{63} -8.79150 q^{64} +(5.73091 + 9.25991i) q^{65} +(-4.21758 + 0.750057i) q^{66} +(7.24215 + 4.18125i) q^{67} +(-0.500934 + 0.867642i) q^{68} +(-11.9728 + 2.12925i) q^{69} +(3.42572 - 1.97784i) q^{70} -15.2021i q^{71} +(-8.84493 - 1.53285i) q^{72} +4.55944i q^{73} +(4.57309 + 7.92083i) q^{74} +(-2.43215 + 6.71293i) q^{75} +(-1.06881 - 0.617080i) q^{76} +(0.944199 - 1.63540i) q^{77} +(-5.45556 - 6.09375i) q^{78} +(5.45812 + 9.45374i) q^{79} -10.1167i q^{80} +(-8.47516 - 3.02848i) q^{81} +7.75641 q^{82} +(9.69751 - 5.59886i) q^{83} +(0.377275 - 0.317516i) q^{84} +(-9.20476 - 5.31437i) q^{85} +(-12.1153 - 6.99475i) q^{86} +(-1.18001 + 3.25690i) q^{87} +(-2.82529 - 4.89354i) q^{88} +7.11905i q^{89} +(2.02638 - 11.6928i) q^{90} +(3.60386 - 0.110306i) q^{91} +(-0.999415 - 1.73104i) q^{92} +(-2.38055 - 13.3859i) q^{93} +(2.69913 - 4.67504i) q^{94} +(6.54656 - 11.3390i) q^{95} +(-0.484507 - 2.72439i) q^{96} +(2.47342 - 1.42803i) q^{97} -1.30970i q^{98} +(-1.95323 - 5.31783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 8 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 8 * q^9	$ 168 q + 84 q^{4} - 8 q^{9} - 24 q^{12} + 8 q^{14} - 84 q^{16} - 32 q^{23} + 84 q^{25} - 8 q^{26} + 48 q^{27} + 4 q^{29} + 80 q^{30} - 32 q^{35} + 4 q^{36} + 24 q^{38} + 24 q^{39} + 4 q^{48} + 84 q^{49} + 64 q^{51} + 18 q^{52} - 48 q^{53} - 24 q^{56} + 24 q^{62} - 240 q^{64} - 22 q^{65} - 132 q^{66} - 156 q^{68} - 52 q^{69} + 84 q^{74} - 60 q^{75} - 16 q^{77} - 148 q^{78} + 12 q^{79} - 8 q^{81} - 24 q^{82} + 88 q^{87} + 24 q^{88} - 164 q^{90} + 12 q^{91} + 128 q^{92} - 60 q^{94} - 96 q^{95}+O(q^{100}) $ 168 * q + 84 * q^4 - 8 * q^9 - 24 * q^12 + 8 * q^14 - 84 * q^16 - 32 * q^23 + 84 * q^25 - 8 * q^26 + 48 * q^27 + 4 * q^29 + 80 * q^30 - 32 * q^35 + 4 * q^36 + 24 * q^38 + 24 * q^39 + 4 * q^48 + 84 * q^49 + 64 * q^51 + 18 * q^52 - 48 * q^53 - 24 * q^56 + 24 * q^62 - 240 * q^64 - 22 * q^65 - 132 * q^66 - 156 * q^68 - 52 * q^69 + 84 * q^74 - 60 * q^75 - 16 * q^77 - 148 * q^78 + 12 * q^79 - 8 * q^81 - 24 * q^82 + 88 * q^87 + 24 * q^88 - 164 * q^90 + 12 * q^91 + 128 * q^92 - 60 * q^94 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.13423	−	0.654848i	0.802022	−	0.463048i	−0.0421556	−	0.999111i	$-0.513423\pi$
$2$	1.13423	−	0.654848i	0.802022	−	0.463048i	0.844178	+	0.536063i	$0.180089\pi$
$3$	1.11529	+	1.32519i	0.643911	+	0.765100i
$3$	1.11529	+	1.32519i	0.643911	+	0.765100i
$4$	−0.142347	+	0.246553i	−0.0711736	+	0.123276i
$5$	−2.61566	−	1.51015i	−1.16976	−	0.675361i	−0.216136	−	0.976363i	$-0.569345\pi$
$5$	−2.61566	−	1.51015i	−1.16976	−	0.675361i	−0.953623	+	0.301002i	$0.902679\pi$
$6$	2.13279	+	0.772730i	0.870709	+	0.315466i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			2.99226i			1.05792i
$9$	−0.512271	+	2.95594i	−0.170757	+	0.985313i
$10$	−3.95568			−1.25090
$11$	−1.63540	+	0.944199i	−0.493092	+	0.284687i	−0.725856	−	0.687846i	$-0.758556\pi$
$11$	−1.63540	+	0.944199i	−0.493092	+	0.284687i	0.232764	+	0.972533i	$0.425223\pi$
$12$	−0.485488	+	0.0863394i	−0.140148	+	0.0249240i
$13$	−3.17619	−	1.70640i	−0.880917	−	0.473271i
$13$	−3.17619	−	1.70640i	−0.880917	−	0.473271i
$14$	−0.654848	+	1.13423i	−0.175016	+	0.303136i
$15$	−0.915969	−	5.15051i	−0.236502	−	1.32986i
$16$	1.67478	+	2.90080i	0.418695	+	0.725201i
$17$	3.51910			0.853506			0.426753	−	0.904368i	$-0.359657\pi$
$17$	3.51910			0.853506			0.426753	+	0.904368i	$0.359657\pi$
$18$	1.35466	+	3.68818i	0.319296	+	0.869312i
$19$			4.33503i			0.994524i	0.867600	+	0.497262i	$0.165661\pi$
$19$			4.33503i			0.994524i	−0.867600	+	0.497262i	$0.834339\pi$
$20$	0.744664	−	0.429932i	0.166512	−	0.0961357i
$21$	−1.62846	−	0.590007i	−0.355360	−	0.128750i
$22$	−1.23661	+	2.14188i	−0.263647	+	0.456650i
$23$	−3.51048	+	6.08034i	−0.731987	+	1.26784i	0.224046	+	0.974579i	$0.428073\pi$
$23$	−3.51048	+	6.08034i	−0.731987	+	1.26784i	−0.956033	+	0.293260i	$0.905260\pi$
$24$	−3.96532	+	3.33722i	−0.809417	+	0.681208i
$25$	2.06112	+	3.56997i	0.412225	+	0.713994i
$26$	−4.71997	+	0.144467i	−0.925662	+	0.0283323i
$27$	−4.48852	+	2.61786i	−0.863816	+	0.503808i
$28$		−	0.284694i		−	0.0538022i
$29$	0.999993	+	1.73204i	0.185694	+	0.321631i	0.943810	−	0.330488i	$-0.107213\pi$
$29$	0.999993	+	1.73204i	0.185694	+	0.321631i	−0.758116	+	0.652120i	$0.773880\pi$
$30$	−4.41172	−	5.24204i	−0.805467	−	0.957062i
$31$	−6.79795	−	3.92480i	−1.22095	−	0.704914i	−0.255827	−	0.966723i	$-0.582348\pi$
$31$	−6.79795	−	3.92480i	−1.22095	−	0.704914i	−0.965120	+	0.261808i	$0.915681\pi$
$32$	−1.38357	−	0.798803i	−0.244582	−	0.141210i
$33$	−3.07519	−	1.11417i	−0.535321	−	0.193952i
$34$	3.99147	−	2.30447i	0.684531	−	0.395214i
$35$	3.02031			0.510525
$36$	−0.655874	−	0.547071i	−0.109312	−	0.0911786i
$37$			6.98344i			1.14807i	0.818831	+	0.574035i	$0.194623\pi$
$37$			6.98344i			1.14807i	−0.818831	+	0.574035i	$0.805377\pi$
$38$	2.83879	+	4.91693i	0.460512	+	0.797631i
$39$	−1.28105	−	6.11219i	−0.205132	−	0.978734i
$40$	4.51877	−	7.82673i	0.714480	−	1.23751i
$41$	5.12886	+	2.96115i	0.800993	+	0.462454i	0.843818	−	0.536629i	$-0.180303\pi$
$41$	5.12886	+	2.96115i	0.800993	+	0.462454i	−0.0428252	+	0.999083i	$0.513636\pi$
$42$	−2.23342	+	0.397192i	−0.344624	+	0.0612881i
$43$	−5.34074	−	9.25043i	−0.814455	−	1.41068i	−0.909719	−	0.415225i	$-0.863703\pi$
$43$	−5.34074	−	9.25043i	−0.814455	−	1.41068i	0.0952639	−	0.995452i	$-0.469631\pi$
$44$		−	0.537617i		−	0.0810487i
$45$	5.80385	−	6.95813i	0.865186	−	1.03726i
$46$			9.19534i			1.35578i
$47$	3.56956	−	2.06088i	0.520673	−	0.300611i	−0.216537	−	0.976274i	$-0.569476\pi$
$47$	3.56956	−	2.06088i	0.520673	−	0.300611i	0.737210	+	0.675664i	$0.236143\pi$
$48$	−1.97626	+	5.45463i	−0.285249	+	0.787309i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	4.67558	+	2.69945i	0.661227	+	0.381759i
$51$	3.92480	+	4.66348i	0.549582	+	0.653018i
$52$	0.872840	−	0.540196i	0.121041	−	0.0749117i
$53$	9.36950			1.28700			0.643500	−	0.765446i	$-0.277482\pi$
$53$	9.36950			1.28700			0.643500	+	0.765446i	$0.277482\pi$
$54$	−3.37671	+	5.90856i	−0.459512	+	0.804053i
$55$	5.70354			0.769065
$56$	−1.49613	−	2.59137i	−0.199929	−	0.346286i
$57$	−5.74475	+	4.83480i	−0.760911	+	0.640385i
$58$	2.26844	+	1.30969i	0.297861	+	0.171970i
$59$	11.3123	+	6.53119i	1.47274	+	0.850288i	0.999530	−	0.0306603i	$-0.00976099\pi$
$59$	11.3123	+	6.53119i	1.47274	+	0.850288i	0.473212	+	0.880948i	$0.343094\pi$
$60$	1.40026	+	0.507326i	0.180772	+	0.0654955i
$61$	−6.03436	−	10.4518i	−0.772620	−	1.33822i	−0.936122	−	0.351674i	$-0.885613\pi$
$61$	−6.03436	−	10.4518i	−0.772620	−	1.33822i	0.163502	−	0.986543i	$-0.447721\pi$
$62$	−10.2806			−1.30564
$63$	−1.03433	−	2.81605i	−0.130313	−	0.354789i
$64$	−8.79150			−1.09894
$65$	5.73091	+	9.25991i	0.710831	+	1.14855i
$66$	−4.21758	+	0.750057i	−0.519149	+	0.0923257i
$67$	7.24215	+	4.18125i	0.884769	+	0.510822i	0.872228	−	0.489100i	$-0.162675\pi$
$67$	7.24215	+	4.18125i	0.884769	+	0.510822i	0.0125411	+	0.999921i	$0.496008\pi$
$68$	−0.500934	+	0.867642i	−0.0607471	+	0.105217i
$69$	−11.9728	+	2.12925i	−1.44136	+	0.256332i
$70$	3.42572	−	1.97784i	0.409452	−	0.236397i
$71$		−	15.2021i		−	1.80415i	−0.431577	−	0.902076i	$-0.642043\pi$
$71$		−	15.2021i		−	1.80415i	0.431577	−	0.902076i	$-0.357957\pi$
$72$	−8.84493	−	1.53285i	−1.04239	−	0.180648i
$73$			4.55944i			0.533642i	0.963746	+	0.266821i	$0.0859733\pi$
$73$			4.55944i			0.533642i	−0.963746	+	0.266821i	$0.914027\pi$
$74$	4.57309	+	7.92083i	0.531611	+	0.920778i
$75$	−2.43215	+	6.71293i	−0.280841	+	0.775142i
$76$	−1.06881	−	0.617080i	−0.122601	−	0.0707839i
$77$	0.944199	−	1.63540i	0.107601	−	0.186371i
$78$	−5.45556	−	6.09375i	−0.617721	−	0.689981i
$79$	5.45812	+	9.45374i	0.614086	+	1.06363i	0.990544	+	0.137195i	$0.0438086\pi$
$79$	5.45812	+	9.45374i	0.614086	+	1.06363i	−0.376458	+	0.926434i	$0.622858\pi$
$80$		−	10.1167i		−	1.13108i
$81$	−8.47516	−	3.02848i	−0.941684	−	0.336498i
$82$	7.75641			0.856552
$83$	9.69751	−	5.59886i	1.06444	−	0.614555i	0.137783	−	0.990462i	$-0.456002\pi$
$83$	9.69751	−	5.59886i	1.06444	−	0.614555i	0.926657	+	0.375908i	$0.122669\pi$
$84$	0.377275	−	0.317516i	0.0411641	−	0.0346438i
$85$	−9.20476	−	5.31437i	−0.998397	−	0.576425i
$86$	−12.1153	−	6.99475i	−1.30642	−	0.754263i
$87$	−1.18001	+	3.25690i	−0.126510	+	0.349177i
$88$	−2.82529	−	4.89354i	−0.301177	−	0.521653i
$89$			7.11905i			0.754618i	0.926087	+	0.377309i	$0.123151\pi$
$89$			7.11905i			0.754618i	−0.926087	+	0.377309i	$0.876849\pi$
$90$	2.02638	−	11.6928i	0.213599	−	1.23253i
$91$	3.60386	−	0.110306i	0.377788	−	0.0115632i
$92$	−0.999415	−	1.73104i	−0.104196	−	0.180473i
$93$	−2.38055	−	13.3859i	−0.246851	−	1.38805i
$94$	2.69913	−	4.67504i	0.278394	−	0.482193i
$95$	6.54656	−	11.3390i	0.671663	−	1.16335i
$96$	−0.484507	−	2.72439i	−0.0494497	−	0.278057i
$97$	2.47342	−	1.42803i	0.251138	−	0.144995i	−0.369147	−	0.929371i	$-0.620350\pi$
$97$	2.47342	−	1.42803i	0.251138	−	0.144995i	0.620285	+	0.784376i	$0.287017\pi$
$98$		−	1.30970i		−	0.132299i
$99$	−1.95323	−	5.31783i	−0.196307	−	0.534462i
$100$	−1.17358			−0.117358
$101$	5.62849	+	9.74883i	0.560056	+	0.970045i	0.997491	+	0.0707950i	$0.0225536\pi$
$101$	5.62849	+	9.74883i	0.560056	+	0.970045i	−0.437435	+	0.899250i	$0.644113\pi$
$102$	7.50550	+	2.71931i	0.743156	+	0.269252i
$103$	3.81692	−	6.61109i	0.376092	−	0.651410i	−0.614398	−	0.788996i	$-0.710601\pi$
$103$	3.81692	−	6.61109i	0.376092	−	0.651410i	0.990490	+	0.137586i	$0.0439344\pi$
$104$	5.10600	−	9.50398i	0.500685	−	0.931942i
$105$	3.36851	+	4.00249i	0.328733	+	0.390603i
$106$	10.6272	−	6.13560i	1.03220	−	0.595942i
$107$	−4.47612			−0.432723			−0.216362	−	0.976313i	$-0.569419\pi$
$107$	−4.47612			−0.432723			−0.216362	+	0.976313i	$0.569419\pi$
$108$	−0.00651299	−	1.47930i	−0.000626713	−	0.142346i
$109$			14.2326i			1.36324i	0.731708	+	0.681618i	$0.238723\pi$
$109$			14.2326i			1.36324i	−0.731708	+	0.681618i	$0.761277\pi$
$110$	6.46913	−	3.73495i	0.616807	−	0.356114i
$111$	−9.25440	+	7.78854i	−0.878389	+	0.739255i
$112$	−2.90080	−	1.67478i	−0.274100	−	0.158252i
$113$	−8.95947	+	15.5183i	−0.842836	+	1.45983i	0.0446517	+	0.999003i	$0.485782\pi$
$113$	−8.95947	+	15.5183i	−0.842836	+	1.45983i	−0.887487	+	0.460832i	$0.847551\pi$
$114$	−3.34981	+	9.24572i	−0.313738	+	0.865941i
$115$	18.3645	−	10.6027i	1.71250	−	0.988710i
$116$	−0.569385			−0.0528660
$117$	6.67110	−	8.51449i	0.616743	−	0.787164i
$118$	17.1077			1.57490
$119$	−3.04763	+	1.75955i	−0.279375	+	0.161298i
$120$	15.4116	−	2.74082i	1.40688	−	0.250201i
$121$	−3.71698	+	6.43799i	−0.337907	+	0.585272i
$122$	−13.6887	−	7.90318i	−1.23932	−	0.715520i
$123$	1.79606	+	10.0993i	0.161945	+	0.910619i
$124$	1.93534	−	1.11737i	0.173798	−	0.100343i
$125$			2.65108i			0.237120i
$126$	−3.01726	−	2.51673i	−0.268799	−	0.224208i
$127$	−6.06656			−0.538320			−0.269160	−	0.963095i	$-0.586746\pi$
$127$	−6.06656			−0.538320			−0.269160	+	0.963095i	$0.586746\pi$
$128$	−7.20445	+	4.15949i	−0.636790	+	0.367651i
$129$	6.30215	−	17.3944i	0.554873	−	1.53149i
$130$	12.5640	+	6.75000i	1.10194	+	0.592014i
$131$	5.83400	−	10.1048i	0.509719	−	0.882858i	−0.490218	−	0.871600i	$-0.663083\pi$
$131$	5.83400	−	10.1048i	0.509719	−	0.882858i	0.999937	−	0.0112586i	$-0.00358379\pi$
$132$	0.712445	−	0.599597i	0.0620104	−	0.0521882i
$133$	−2.16752	−	3.75425i	−0.187947	−	0.325535i
$134$	10.9524			0.946139
$135$	15.6938	−	0.0690959i	1.35071	−	0.00594683i
$136$			10.5300i			0.902943i
$137$	−9.52812	+	5.50106i	−0.814042	+	0.469987i	−0.848358	−	0.529424i	$-0.822408\pi$
$137$	−9.52812	+	5.50106i	−0.814042	+	0.469987i	0.0343155	+	0.999411i	$0.489075\pi$
$138$	−12.1856	+	10.2554i	−1.03731	+	0.873001i
$139$	−3.08301	+	5.33993i	−0.261497	+	0.452927i	−0.966640	−	0.256139i	$-0.917550\pi$
$139$	−3.08301	+	5.33993i	−0.261497	+	0.452927i	0.705143	+	0.709065i	$0.250883\pi$
$140$	−0.429932	+	0.744664i	−0.0363359	+	0.0629356i
$141$	6.71215	+	2.43187i	0.565265	+	0.204801i
$142$	−9.95504	−	17.2426i	−0.835409	−	1.44697i
$143$	6.80553	−	0.208301i	0.569107	−	0.0174190i
$144$	−9.43254	+	3.46455i	−0.786045	+	0.288713i
$145$		−	6.04057i		−	0.501642i
$146$	2.98574	+	5.17146i	0.247102	+	0.427993i
$147$	1.70529	−	0.303270i	0.140650	−	0.0250133i
$148$	−1.72178	−	0.994073i	−0.141530	−	0.0817123i
$149$	3.85933	+	2.22818i	0.316168	+	0.182540i	0.649683	−	0.760205i	$-0.274901\pi$
$149$	3.85933	+	2.22818i	0.316168	+	0.182540i	−0.333515	+	0.942745i	$0.608235\pi$
$150$	1.63732	+	9.20670i	0.133687	+	0.751724i
$151$	−10.5260	+	6.07720i	−0.856595	+	0.494556i	−0.862871	−	0.505425i	$-0.831336\pi$
$151$	−10.5260	+	6.07720i	−0.856595	+	0.494556i	0.00627531	+	0.999980i	$0.498002\pi$
$152$	−12.9715			−1.05213
$153$	−1.80273	+	10.4022i	−0.145742	+	0.840971i
$154$		−	2.47323i		−	0.199299i
$155$	11.8541	+	20.5319i	0.952143	+	1.64916i
$156$	1.68933	+	0.554208i	0.135255	+	0.0443721i
$157$	7.71149	−	13.3567i	0.615444	−	1.06598i	−0.374862	−	0.927081i	$-0.622310\pi$
$157$	7.71149	−	13.3567i	0.615444	−	1.06598i	0.990306	−	0.138900i	$-0.0443567\pi$
$158$	12.3815	+	7.14848i	0.985021	+	0.568702i
$159$	10.4497	+	12.4164i	0.828713	+	0.984683i
$160$	2.41263	+	4.17880i	0.190735	+	0.330363i
$161$		−	7.02097i		−	0.553330i
$162$	−11.5960	+	2.11495i	−0.911066	+	0.166166i
$163$		−	4.82826i		−	0.378179i	−0.981960	−	0.189089i	$-0.939446\pi$
$163$		−	4.82826i		−	0.378179i	0.981960	−	0.189089i	$-0.0605536\pi$
$164$	−1.46016	+	0.843022i	−0.114019	+	0.0658290i
$165$	6.36108	+	7.55829i	0.495210	+	0.588412i
$166$	7.33281	−	12.7008i	0.569136	−	0.985773i
$167$	1.88602	+	1.08889i	0.145944	+	0.0842610i	0.571194	−	0.820815i	$-0.306480\pi$
$167$	1.88602	+	1.08889i	0.145944	+	0.0842610i	−0.425250	+	0.905076i	$0.639814\pi$
$168$	1.76545	−	4.87278i	0.136208	−	0.375943i
$169$	7.17637	+	10.8397i	0.552028	+	0.833825i
$170$	−13.9204			−1.06765
$171$	−12.8141	−	2.22071i	−0.979918	−	0.169822i
$172$	3.04096			0.231871
$173$	0.861049	+	1.49138i	0.0654644	+	0.113388i	0.896900	−	0.442234i	$-0.145814\pi$
$173$	0.861049	+	1.49138i	0.0654644	+	0.113388i	−0.831436	+	0.555621i	$0.812480\pi$
$174$	0.794379	+	4.46680i	0.0602217	+	0.338627i
$175$	−3.56997	−	2.06112i	−0.269864	−	0.155806i
$176$	−5.47787	−	3.16265i	−0.412910	−	0.238394i
$177$	3.96143	+	22.2752i	0.297759	+	1.67431i
$178$	4.66190	+	8.07465i	0.349424	+	0.605220i
$179$	−4.88694			−0.365267			−0.182634	−	0.983181i	$-0.558462\pi$
$179$	−4.88694			−0.365267			−0.182634	+	0.983181i	$0.558462\pi$
$180$	0.889384	+	2.42142i	0.0662908	+	0.180482i
$181$	8.47033			0.629595			0.314797	−	0.949159i	$-0.398063\pi$
$181$	8.47033			0.629595			0.314797	+	0.949159i	$0.398063\pi$
$182$	4.01538	−	2.48510i	0.297640	−	0.184208i
$183$	7.12062	−	19.6534i	0.526372	−	1.45282i
$184$	−18.1939	−	10.5043i	−1.34127	−	0.774385i
$185$	10.5461	−	18.2663i	0.775362	−	1.34297i
$186$	−11.4658	−	13.6238i	−0.840713	−	0.998942i
$187$	−5.75513	+	3.32273i	−0.420857	+	0.242982i
$188$			1.17344i			0.0855823i
$189$	2.57824	−	4.51139i	0.187539	−	0.328156i
$190$		−	17.1480i		−	1.24405i
$191$	−1.91855	−	3.32303i	−0.138822	−	0.240446i	0.788229	−	0.615382i	$-0.210998\pi$
$191$	−1.91855	−	3.32303i	−0.138822	−	0.240446i	−0.927051	+	0.374936i	$0.877665\pi$
$192$	−9.80504	−	11.6504i	−0.707618	−	0.840797i
$193$	−7.06639	−	4.07978i	−0.508650	−	0.293669i	0.223629	−	0.974674i	$-0.428210\pi$
$193$	−7.06639	−	4.07978i	−0.508650	−	0.293669i	−0.732279	+	0.681005i	$0.761543\pi$
$194$	1.87029	−	3.23944i	0.134279	−	0.232578i
$195$	−5.87956	+	17.9220i	−0.421044	+	1.28342i
$196$	0.142347	+	0.246553i	0.0101677	+	0.0176109i
$197$			7.84458i			0.558903i	0.960160	+	0.279452i	$0.0901526\pi$
$197$			7.84458i			0.558903i	−0.960160	+	0.279452i	$0.909847\pi$
$198$	−5.69778	−	4.75258i	−0.404924	−	0.337751i
$199$	−16.0999			−1.14130			−0.570648	−	0.821195i	$-0.693308\pi$
$199$	−16.0999			−1.14130			−0.570648	+	0.821195i	$0.693308\pi$
$200$	−10.6823	+	6.16741i	−0.755350	+	0.436102i
$201$	2.53610	+	14.2605i	0.178883	+	1.00586i
$202$	12.7680	+	7.37161i	0.898354	+	0.518665i
$203$	−1.73204	−	0.999993i	−0.121565	−	0.0701857i
$204$	−1.70848	+	0.303837i	−0.119617	+	0.0212728i
$205$	−8.94357	−	15.4907i	−0.624646	−	1.08192i
$206$		−	9.99800i		−	0.696594i
$207$	−16.1748	−	13.4916i	−1.12423	−	0.937728i
$208$	−0.369475	−	12.0714i	−0.0256185	−	0.836998i
$209$	−4.09313	−	7.08951i	−0.283128	−	0.490392i
$210$	6.44169	+	2.33388i	0.444519	+	0.161053i
$211$	12.5822	−	21.7930i	0.866193	−	1.50029i	0.000336143	−	1.00000i	$-0.499893\pi$
$211$	12.5822	−	21.7930i	0.866193	−	1.50029i	0.865857	−	0.500291i	$-0.166774\pi$
$212$	−1.33372	+	2.31007i	−0.0916004	+	0.158657i
$213$	20.1457	−	16.9547i	1.38036	−	1.16171i
$214$	−5.07696	+	2.93118i	−0.347054	+	0.200372i
$215$			32.2613i			2.20020i
$216$	−7.83332	−	13.4308i	−0.532990	−	0.913850i
$217$	7.84959			0.532865
$218$	9.32020	+	16.1431i	0.631244	+	1.09335i
$219$	−6.04214	+	5.08509i	−0.408290	+	0.343618i
$220$	−0.811883	+	1.40622i	−0.0547372	+	0.0948075i
$221$	−11.1773	−	6.00500i	−0.751868	−	0.403940i
$222$	−5.39631	+	14.8942i	−0.362177	+	0.999635i
$223$	−0.374076	+	0.215973i	−0.0250500	+	0.0144626i	−0.512473	−	0.858704i	$-0.671270\pi$
$223$	−0.374076	+	0.215973i	−0.0250500	+	0.0144626i	0.487423	+	0.873166i	$0.337937\pi$
$224$	1.59761			0.106745
$225$	−11.6085	+	4.26377i	−0.773898	+	0.284251i
$226$			23.4684i			1.56109i
$227$	−3.02871	+	1.74863i	−0.201023	+	0.116060i	−0.597132	−	0.802143i	$-0.703693\pi$
$227$	−3.02871	+	1.74863i	−0.201023	+	0.116060i	0.396110	+	0.918203i	$0.370360\pi$
$228$	−0.374284	−	2.10460i	−0.0247876	−	0.139381i
$229$	−7.20899	−	4.16211i	−0.476384	−	0.275040i	0.242525	−	0.970145i	$-0.422024\pi$
$229$	−7.20899	−	4.16211i	−0.476384	−	0.275040i	−0.718908	+	0.695105i	$0.755358\pi$
$230$	13.8864	−	24.0519i	0.915640	−	1.58594i
$231$	3.22027	−	0.572695i	0.211878	−	0.0376806i
$232$	−5.18270	+	2.99224i	−0.340261	+	0.196450i
$233$	25.8487			1.69340			0.846701	−	0.532069i	$-0.178585\pi$
$233$	25.8487			1.69340			0.846701	+	0.532069i	$0.178585\pi$
$234$	1.99087	−	14.0259i	0.130147	−	0.916905i
$235$	−12.4490			−0.812083
$236$	−3.22056	+	1.85939i	−0.209641	+	0.121036i
$237$	−6.44066	+	17.7767i	−0.418366	+	1.15472i
$238$	−2.30447	+	3.99147i	−0.149377	+	0.258728i
$239$	9.19257	+	5.30733i	0.594618	+	0.343303i	0.766921	−	0.641741i	$-0.221788\pi$
$239$	9.19257	+	5.30733i	0.594618	+	0.343303i	−0.172304	+	0.985044i	$0.555121\pi$
$240$	13.4066	−	11.2830i	0.865390	−	0.728316i
$241$	−15.4576	+	8.92447i	−0.995713	+	0.574875i	−0.906977	−	0.421180i	$-0.861616\pi$
$241$	−15.4576	+	8.92447i	−0.995713	+	0.574875i	−0.0887363	+	0.996055i	$0.528283\pi$
$242$			9.73622i			0.625868i
$243$	−5.43891	−	14.6088i	−0.348906	−	0.937158i
$244$	3.43589			0.219961
$245$	−2.61566	+	1.51015i	−0.167108	+	0.0964801i
$246$	8.65062	+	10.2787i	0.551544	+	0.655348i
$247$	7.39732	−	13.7689i	0.470680	−	0.876093i
$248$	11.7440	−	20.3412i	0.745745	−	1.29167i
$249$	18.2351	+	6.60673i	1.15560	+	0.418685i
$250$	1.73606	+	3.00694i	0.109798	+	0.190176i
$251$	7.05441			0.445270			0.222635	−	0.974902i	$-0.428534\pi$
$251$	7.05441			0.445270			0.222635	+	0.974902i	$0.428534\pi$
$252$	0.841540	+	0.145841i	0.0530120	+	0.00918709i
$253$		−	13.2584i		−	0.833548i
$254$	−6.88088	+	3.97268i	−0.431745	+	0.249268i
$255$	−3.22338	−	18.1251i	−0.201856	−	1.13504i
$256$	3.34382	−	5.79167i	0.208989	−	0.361980i
$257$	−10.8263	+	18.7517i	−0.675326	+	1.16970i	0.301048	+	0.953609i	$0.402664\pi$
$257$	−10.8263	+	18.7517i	−0.675326	+	1.16970i	−0.976374	+	0.216089i	$0.930670\pi$
$258$	−4.24260	−	23.8562i	−0.264133	−	1.48522i
$259$	−3.49172	−	6.04783i	−0.216965	−	0.375794i
$260$	−3.09883	+	0.0948478i	−0.192181	+	0.00588221i
$261$	−5.63207	+	2.06865i	−0.348616	+	0.128046i
$262$		−	15.2815i		−	0.944096i
$263$	−1.49410	−	2.58786i	−0.0921303	−	0.159574i	0.816277	−	0.577661i	$-0.196034\pi$
$263$	−1.49410	−	2.58786i	−0.0921303	−	0.159574i	−0.908407	+	0.418086i	$0.862701\pi$
$264$	3.33388	−	9.20175i	0.205186	−	0.566329i
$265$	−24.5074	−	14.1494i	−1.50548	−	0.869189i
$266$	−4.91693	−	2.83879i	−0.301476	−	0.174057i
$267$	−9.43412	+	7.93979i	−0.577358	+	0.485907i
$268$	−2.06180	+	1.19038i	−0.125944	+	0.0727140i
$269$	−24.9871			−1.52349			−0.761745	−	0.647877i	$-0.775657\pi$
$269$	−24.9871			−1.52349			−0.761745	+	0.647877i	$0.775657\pi$
$270$	17.7552	−	10.3554i	1.08054	−	0.630212i
$271$		−	13.0467i		−	0.792532i	−0.918136	−	0.396266i	$-0.870306\pi$
$271$		−	13.0467i		−	0.792532i	0.918136	−	0.396266i	$-0.129694\pi$
$272$	5.89371	+	10.2082i	0.357359	+	0.618964i
$273$	4.16552	+	4.65279i	0.252109	+	0.281600i
$274$	−7.20472	+	12.4789i	−0.435253	+	0.753881i
$275$	−6.74153	−	3.89222i	−0.406529	−	0.234710i
$276$	1.17932	−	3.25502i	0.0709870	−	0.195929i
$277$	8.75940	+	15.1717i	0.526301	+	0.911580i	0.999530	+	0.0306410i	$0.00975485\pi$
$277$	8.75940	+	15.1717i	0.526301	+	0.911580i	−0.473229	+	0.880939i	$0.656912\pi$
$278$			8.07561i			0.484343i
$279$	15.0838	−	18.0838i	0.903046	−	1.08265i
$280$			9.03753i			0.540096i
$281$	−7.67467	+	4.43097i	−0.457832	+	0.264330i	−0.711132	−	0.703058i	$-0.751817\pi$
$281$	−7.67467	+	4.43097i	−0.457832	+	0.264330i	0.253300	+	0.967388i	$0.418484\pi$
$282$	9.20563	−	1.63713i	0.548187	−	0.0974900i
$283$	5.09186	−	8.81935i	0.302679	−	0.524256i	−0.674063	−	0.738674i	$-0.735452\pi$
$283$	5.09186	−	8.81935i	0.302679	−	0.524256i	0.976742	+	0.214418i	$0.0687855\pi$
$284$	3.74811	+	2.16397i	0.222409	+	0.128408i
$285$	22.3276	−	3.97076i	1.32257	−	0.235207i
$286$	7.58264	−	4.69285i	0.448371	−	0.277494i
$287$	−5.92230			−0.349582
$288$	3.06997	−	3.68054i	0.180900	−	0.216878i
$289$	−4.61596			−0.271527
$290$	−3.95566	−	6.85140i	−0.232284	−	0.402328i
$291$	4.65100	+	1.68510i	0.272646	+	0.0987822i
$292$	−1.12414	−	0.649024i	−0.0657855	−	0.0379813i
$293$	−24.4520	−	14.1174i	−1.42850	−	0.824745i	−0.431497	−	0.902114i	$-0.642015\pi$
$293$	−24.4520	−	14.1174i	−1.42850	−	0.824745i	−0.997002	+	0.0773695i	$0.975348\pi$
$294$	1.73560	−	1.46069i	0.101222	−	0.0851890i
$295$	−19.7262	−	34.1667i	−1.14850	−	1.98927i
$296$	−20.8962			−1.21457
$297$	4.86874	−	8.51931i	0.282513	−	0.494341i
$298$	5.83649			0.338099
$299$	21.5255	−	13.3220i	1.24485	−	0.770431i
$300$	−1.30888	−	1.55522i	−0.0755682	−	0.0897907i
$301$	9.25043	+	5.34074i	0.533186	+	0.307835i
$302$	−7.95929	+	13.7859i	−0.458006	+	0.793289i
$303$	−6.64170	+	18.3316i	−0.381556	+	1.05312i
$304$	−12.5751	+	7.26022i	−0.721230	+	0.416402i
$305$			36.4512i			2.08719i
$306$	4.76718	+	12.9790i	0.272521	+	0.741963i
$307$		−	13.5435i		−	0.772967i	−0.922296	−	0.386483i	$-0.873690\pi$
$307$		−	13.5435i		−	0.772967i	0.922296	−	0.386483i	$-0.126310\pi$
$308$	0.268808	+	0.465590i	0.0153168	+	0.0265294i
$309$	13.0179	−	2.31511i	0.740564	−	0.131702i
$310$	26.8905	+	15.5253i	1.52728	+	0.881775i
$311$	−8.11884	+	14.0622i	−0.460377	+	0.797396i	−0.998980	−	0.0451635i	$-0.985619\pi$
$311$	−8.11884	+	14.0622i	−0.460377	+	0.797396i	0.538603	+	0.842560i	$0.318952\pi$
$312$	18.2893	−	3.83323i	1.03543	−	0.217014i
$313$	11.8911	+	20.5961i	0.672127	+	1.16416i	0.977300	+	0.211861i	$0.0679523\pi$
$313$	11.8911	+	20.5961i	0.672127	+	1.16416i	−0.305173	+	0.952297i	$0.598714\pi$
$314$		−	20.1994i		−	1.13992i
$315$	−1.54721	+	8.92784i	−0.0871756	+	0.503027i
$316$	−3.10779			−0.174827
$317$	−6.07891	+	3.50966i	−0.341425	+	0.197122i	−0.660902	−	0.750472i	$-0.729826\pi$
$317$	−6.07891	+	3.50966i	−0.341425	+	0.197122i	0.319477	+	0.947594i	$0.396493\pi$
$318$	19.9832	+	7.24009i	1.12060	+	0.406004i
$319$	−3.27078	−	1.88838i	−0.183128	−	0.105729i
$320$	22.9956	+	13.2765i	1.28549	+	0.742179i
$321$	−4.99216	−	5.93173i	−0.278635	−	0.331077i
$322$	−4.59767	−	7.96340i	−0.256218	−	0.443783i
$323$			15.2554i			0.848833i
$324$	1.95310	−	1.65848i	0.108505	−	0.0921376i
$325$	−0.454706	−	14.8560i	−0.0252226	−	0.824063i
$326$	−3.16178	−	5.47637i	−0.175115	−	0.303308i
$327$	−18.8609	+	15.8734i	−1.04301	+	0.877803i
$328$	−8.86051	+	15.3469i	−0.489240	+	0.847389i
$329$	−2.06088	+	3.56956i	−0.113620	+	0.196796i
$330$	12.1645	+	4.40730i	0.669632	+	0.242614i
$331$	−1.63426	+	0.943543i	−0.0898273	+	0.0518618i	−0.544241	−	0.838929i	$-0.683182\pi$
$331$	−1.63426	+	0.943543i	−0.0898273	+	0.0518618i	0.454413	+	0.890791i	$0.349849\pi$
$332$			3.18793i			0.174960i
$333$	−20.6426	−	3.57741i	−1.13121	−	0.196041i
$334$	2.85224			0.156067
$335$	−12.6287	−	21.8735i	−0.689978	−	1.19508i
$336$	−1.01582	−	5.71198i	−0.0554177	−	0.311614i
$337$	−16.4807	+	28.5455i	−0.897762	+	1.55497i	−0.0674142	+	0.997725i	$0.521475\pi$
$337$	−16.4807	+	28.5455i	−0.897762	+	1.55497i	−0.830348	+	0.557245i	$0.811858\pi$
$338$	15.2380	+	7.59532i	0.828840	+	0.413131i
$339$	−30.5570	+	5.43428i	−1.65963	+	0.295150i
$340$	2.62055	−	1.51297i	0.142119	−	0.0820525i
$341$	14.8232			0.802719
$342$	−15.9884	+	5.87249i	−0.864552	+	0.317548i
$343$			1.00000i			0.0539949i
$344$	27.6797	−	15.9809i	1.49239	−	0.861630i
$345$	34.5323	+	12.5114i	1.85916	+	0.673590i
$346$	1.95326	+	1.12771i	0.105008	+	0.0606262i
$347$	7.97520	−	13.8135i	0.428131	−	0.741545i	−0.568576	−	0.822631i	$-0.692505\pi$
$347$	7.97520	−	13.8135i	0.428131	−	0.741545i	0.996707	+	0.0810857i	$0.0258388\pi$
$348$	−0.635027	−	0.754544i	−0.0340410	−	0.0404478i
$349$	13.3854	−	7.72807i	0.716505	−	0.413674i	−0.0969601	−	0.995288i	$-0.530912\pi$
$349$	13.3854	−	7.72807i	0.716505	−	0.413674i	0.813465	+	0.581614i	$0.197579\pi$
$350$	−5.39889			−0.288583
$351$	18.7235	−	0.655605i	0.999388	−	0.0349936i
$352$	3.01692			0.160802
$353$	−23.9967	+	13.8545i	−1.27722	+	0.737400i	−0.976335	−	0.216262i	$-0.930614\pi$
$353$	−23.9967	+	13.8545i	−1.27722	+	0.737400i	−0.300880	+	0.953662i	$0.597280\pi$
$354$	19.0800	+	22.6711i	1.01409	+	1.20495i
$355$	−22.9574	+	39.7634i	−1.21845	+	2.11042i
$356$	−1.75522	−	1.01338i	−0.0930265	−	0.0537089i
$357$	−5.73072	−	2.07629i	−0.303302	−	0.109889i
$358$	−5.54292	+	3.20021i	−0.292953	+	0.169136i
$359$			9.30615i			0.491160i	0.969376	+	0.245580i	$0.0789784\pi$
$359$			9.30615i			0.491160i	−0.969376	+	0.245580i	$0.921022\pi$
$360$	20.8205	+	17.3666i	1.09734	+	0.915300i
$361$	0.207504			0.0109213
$362$	9.60731	−	5.54678i	0.504949	−	0.291532i
$363$	−12.6771	+	2.25450i	−0.665374	+	0.118330i
$364$	−0.485804	+	0.904244i	−0.0254630	+	0.0473952i
$365$	6.88546	−	11.9260i	0.360401	−	0.624233i
$366$	−4.79360	−	26.9545i	−0.250565	−	1.40893i
$367$	5.20081	+	9.00807i	0.271480	+	0.470218i	0.969241	−	0.246113i	$-0.0791535\pi$
$367$	5.20081	+	9.00807i	0.271480	+	0.470218i	−0.697761	+	0.716331i	$0.745820\pi$
$368$	−23.5172			−1.22592
$369$	−11.3803	+	13.6437i	−0.592437	+	0.710262i
$370$		−	27.6243i		−	1.43612i
$371$	−8.11422	+	4.68475i	−0.421269	+	0.243220i
$372$	3.63918	+	1.31851i	0.188683	+	0.0683615i
$373$	2.59409	−	4.49310i	0.134317	−	0.232644i	−0.791019	−	0.611791i	$-0.790449\pi$
$373$	2.59409	−	4.49310i	0.134317	−	0.232644i	0.925336	+	0.379147i	$0.123783\pi$
$374$	−4.35177	+	7.53748i	−0.225024	+	0.389754i
$375$	−3.51320	+	2.95672i	−0.181421	+	0.152684i
$376$	6.16670	+	10.6810i	0.318023	+	0.550832i
$377$	−0.220609	−	7.20768i	−0.0113620	−	0.371214i
$378$	−0.0299621	−	6.80532i	−0.00154108	−	0.350028i
$379$			21.4336i			1.10097i	0.834845	+	0.550484i	$0.185557\pi$
$379$			21.4336i			1.10097i	−0.834845	+	0.550484i	$0.814443\pi$
$380$	1.86377	+	3.22814i	0.0956093	+	0.165600i
$381$	−6.76596	−	8.03936i	−0.346630	−	0.411869i
$382$	−4.35217	−	2.51273i	−0.222676	−	0.128562i
$383$	−1.16397	−	0.672020i	−0.0594762	−	0.0343386i	0.469967	−	0.882684i	$-0.344266\pi$
$383$	−1.16397	−	0.672020i	−0.0594762	−	0.0343386i	−0.529443	+	0.848345i	$0.677599\pi$
$384$	−13.5472	−	4.90826i	−0.691326	−	0.250474i
$385$	−4.93941	+	2.85177i	−0.251736	+	0.145340i
$386$	−10.6866			−0.543931
$387$	30.0796	−	11.0482i	1.52903	−	0.561610i
$388$			0.813106i			0.0412792i
$389$	1.16644	+	2.02033i	0.0591406	+	0.102435i	0.894080	−	0.447908i	$-0.147831\pi$
$389$	1.16644	+	2.02033i	0.0591406	+	0.102435i	−0.834939	+	0.550342i	$0.814497\pi$
$390$	5.06742	+	24.1779i	0.256599	+	1.22430i
$391$	−12.3537	+	21.3973i	−0.624755	+	1.08211i
$392$	2.59137	+	1.49613i	0.130884	+	0.0755659i
$393$	19.8974	−	3.53856i	1.00369	−	0.178497i
$394$	5.13701	+	8.89756i	0.258799	+	0.448253i
$395$		−	32.9704i		−	1.65892i
$396$	1.58916	+	0.275405i	0.0798584	+	0.0138396i
$397$		−	13.4118i		−	0.673117i	−0.941663	−	0.336558i	$-0.890737\pi$
$397$		−	13.4118i		−	0.673117i	0.941663	−	0.336558i	$-0.109263\pi$
$398$	−18.2611	+	10.5430i	−0.915344	+	0.528474i
$399$	2.55770	−	7.05944i	0.128045	−	0.353414i
$400$	−6.90386	+	11.9578i	−0.345193	+	0.597892i
$401$	26.3759	+	15.2281i	1.31715	+	0.760456i	0.983269	−	0.182160i	$-0.0583090\pi$
$401$	26.3759	+	15.2281i	1.31715	+	0.760456i	0.333879	+	0.942616i	$0.391642\pi$
$402$	12.2150	+	14.5140i	0.609230	+	0.723891i
$403$	14.8943	+	24.0659i	0.741937	+	1.19881i
$404$	−3.20480			−0.159445
$405$	17.5947	+	20.7203i	0.874286	+	1.02960i
$406$	−2.61937			−0.129997
$407$	−6.59376	−	11.4207i	−0.326840	−	0.566104i
$408$	−13.9543	+	11.7440i	−0.690842	+	0.581415i
$409$	12.1508	+	7.01529i	0.600820	+	0.346884i	0.769364	−	0.638810i	$-0.220573\pi$
$409$	12.1508	+	7.01529i	0.600820	+	0.346884i	−0.168544	+	0.985694i	$0.553907\pi$
$410$	−20.2881	−	11.7134i	−1.00196	−	0.578482i
$411$	−17.9165	−	6.49133i	−0.883758	−	0.320194i
$412$	1.08665	+	1.88214i	0.0535356	+	0.0927264i
$413$	−13.0624			−0.642757
$414$	−27.1809	−	4.71050i	−1.33587	−	0.231509i
$415$	−33.8205			−1.66018
$416$	3.03139	+	4.89807i	0.148626	+	0.240148i
$417$	−10.5149	+	1.86997i	−0.514915	+	0.0915728i
$418$	−9.28511	−	5.36076i	−0.454150	−	0.262204i
$419$	6.85652	−	11.8758i	0.334963	−	0.580173i	−0.648515	−	0.761202i	$-0.724609\pi$
$419$	6.85652	−	11.8758i	0.334963	−	0.580173i	0.983478	+	0.181029i	$0.0579428\pi$
$420$	−1.46632	+	0.260771i	−0.0715491	+	0.0127243i
$421$	11.1258	−	6.42349i	0.542239	−	0.313062i	−0.203747	−	0.979024i	$-0.565312\pi$
$421$	11.1258	−	6.42349i	0.542239	−	0.313062i	0.745986	+	0.665962i	$0.231979\pi$
$422$		−	32.9577i		−	1.60436i
$423$	4.26327	+	11.6071i	0.207287	+	0.564358i
$424$			28.0359i			1.36155i
$425$	7.25329	+	12.5631i	0.351836	+	0.609398i
$426$	11.7471	−	32.4228i	0.569148	−	1.57089i
$427$	10.4518	+	6.03436i	0.505799	+	0.292023i
$428$	0.637164	−	1.10360i	0.0307985	−	0.0533445i
$429$	7.86616	+	8.78632i	0.379782	+	0.424208i
$430$	21.1263	+	36.5918i	1.01880	+	1.76461i
$431$		−	17.4792i		−	0.841943i	−0.907074	−	0.420971i	$-0.861689\pi$
$431$		−	17.4792i		−	0.841943i	0.907074	−	0.420971i	$-0.138311\pi$
$432$	−15.1112	−	8.63597i	−0.727037	−	0.415498i
$433$	31.2594			1.50223			0.751116	−	0.660170i	$-0.229516\pi$
$433$	31.2594			1.50223			0.751116	+	0.660170i	$0.229516\pi$
$434$	8.90325	−	5.14029i	0.427370	−	0.246742i
$435$	8.00492	−	6.73697i	0.383806	−	0.323013i
$436$	−3.50909	−	2.02597i	−0.168055	−	0.0970265i
$437$	−26.3585	−	15.2181i	−1.26090	−	0.727979i
$438$	−3.52322	+	9.72435i	−0.168346	+	0.464647i
$439$	−10.5910	−	18.3442i	−0.505482	−	0.875521i	−0.999980	−	0.00634217i	$-0.997981\pi$
$439$	−10.5910	−	18.3442i	−0.505482	−	0.875521i	0.494497	−	0.869179i	$-0.335352\pi$
$440$			17.0665i			0.813612i
$441$	2.30378	+	1.92161i	0.109704	+	0.0915052i
$442$	−16.6100	+	0.508392i	−0.790058	+	0.0241818i
$443$	9.02172	+	15.6261i	0.428635	+	0.742418i	0.996752	−	0.0805300i	$-0.0256613\pi$
$443$	9.02172	+	15.6261i	0.428635	+	0.742418i	−0.568117	+	0.822948i	$0.692328\pi$
$444$	−0.602946	−	3.39037i	−0.0286145	−	0.160900i
$445$	10.7509	−	18.6210i	0.509640	−	0.882722i
$446$	−0.282859	+	0.489926i	−0.0133937	+	0.0231986i
$447$	1.35148	+	7.59942i	0.0639230	+	0.359440i
$448$	7.61366	−	4.39575i	0.359712	−	0.207680i
$449$		−	10.0135i		−	0.472564i	−0.971685	−	0.236282i	$-0.924071\pi$
$449$		−	10.0135i		−	0.472564i	0.971685	−	0.236282i	$-0.0759289\pi$
$450$	−10.3746	+	12.4379i	−0.489062	+	0.586327i
$451$	−11.1837			−0.526618
$452$	−2.55071	−	4.41796i	−0.119975	−	0.207803i
$453$	−19.7930	−	7.17118i	−0.929956	−	0.336932i
$454$	−2.29017	+	3.96669i	−0.107483	+	0.186166i
$455$	−9.59307	−	5.15386i	−0.449730	−	0.241617i
$456$	−14.4670	−	17.1898i	−0.677478	−	0.804985i
$457$	22.9801	−	13.2676i	1.07496	−	0.620630i	0.145430	−	0.989369i	$-0.453543\pi$
$457$	22.9801	−	13.2676i	1.07496	−	0.620630i	0.929533	+	0.368738i	$0.120210\pi$
$458$	−10.9022			−0.509427
$459$	−15.7955	+	9.21251i	−0.737272	+	0.430003i
$460$			6.03708i			0.281480i
$461$	17.0601	−	9.84968i	0.794570	−	0.458745i	−0.0469990	−	0.998895i	$-0.514966\pi$
$461$	17.0601	−	9.84968i	0.794570	−	0.458745i	0.841569	+	0.540150i	$0.181632\pi$
$462$	3.27751	−	2.75836i	0.152483	−	0.128331i
$463$	8.67319	+	5.00747i	0.403077	+	0.232717i	0.687811	−	0.725890i	$-0.258572\pi$
$463$	8.67319	+	5.00747i	0.403077	+	0.232717i	−0.284734	+	0.958607i	$0.591905\pi$
$464$	−3.34954	+	5.80157i	−0.155498	+	0.269331i
$465$	−13.9880	+	38.6079i	−0.648677	+	1.79040i
$466$	29.3183	−	16.9270i	1.35815	−	0.784126i
$467$	23.0584			1.06702			0.533508	−	0.845795i	$-0.320873\pi$
$467$	23.0584			1.06702			0.533508	+	0.845795i	$0.320873\pi$
$468$	1.14966	+	2.85679i	0.0531429	+	0.132055i
$469$	−8.36251			−0.386145
$470$	−14.1200	+	8.15221i	−0.651309	+	0.376033i
$471$	26.3007	−	4.67734i	1.21187	−	0.215520i
$472$	−19.5430	+	33.8495i	−0.899539	+	1.55805i
$473$	17.4685	+	10.0854i	0.803202	+	0.463729i
$474$	4.33584	+	24.3805i	0.199152	+	1.11983i
$475$	−15.4759	+	8.93503i	−0.710085	+	0.409967i
$476$		−	1.00187i		−	0.0459205i
$477$	−4.79972	+	27.6957i	−0.219764	+	1.26810i
$478$	13.9020			0.635862
$479$	3.16872	−	1.82946i	0.144783	−	0.0835902i	−0.425859	−	0.904790i	$-0.640028\pi$
$479$	3.16872	−	1.82946i	0.144783	−	0.0835902i	0.570641	+	0.821199i	$0.306695\pi$
$480$	−2.84694	+	7.85775i	−0.129944	+	0.358656i
$481$	11.9166	−	22.1807i	0.543349	−	1.01135i
$482$	−11.6883	+	20.2448i	−0.532390	+	0.922126i
$483$	9.30414	−	7.83039i	0.423353	−	0.356295i
$484$	−1.05820	−	1.83286i	−0.0481001	−	0.0833118i
$485$	−8.62619			−0.391695
$486$	−15.7356	−	13.0081i	−0.713779	−	0.590061i
$487$			10.0842i			0.456960i	0.973549	+	0.228480i	$0.0733756\pi$
$487$			10.0842i			0.456960i	−0.973549	+	0.228480i	$0.926624\pi$
$488$	31.2745	−	18.0563i	1.41573	−	0.817372i
$489$	6.39838	−	5.38490i	0.289345	−	0.243514i
$490$	−1.97784	+	3.42572i	−0.0893498	+	0.154758i
$491$	8.88053	−	15.3815i	0.400773	−	0.694158i	−0.593047	−	0.805168i	$-0.702075\pi$
$491$	8.88053	−	15.3815i	0.400773	−	0.694158i	0.993819	+	0.111010i	$0.0354084\pi$
$492$	−2.74566	−	0.994778i	−0.123784	−	0.0448481i
$493$	3.51907	+	6.09521i	0.158491	+	0.274514i
$494$	−0.626268	−	20.4612i	−0.0281771	−	0.920593i
$495$	−2.92176	+	16.8593i	−0.131323	+	0.757770i
$496$		−	26.2927i		−	1.18058i
$497$	7.60103	+	13.1654i	0.340953	+	0.590547i
$498$	25.0092	−	4.44765i	1.12069	−	0.199304i
$499$	36.6211	+	21.1432i	1.63938	+	0.946499i	0.981046	+	0.193776i	$0.0620736\pi$
$499$	36.6211	+	21.1432i	1.63938	+	0.946499i	0.658338	+	0.752722i	$0.271260\pi$
$500$	−0.653632	−	0.377374i	−0.0292313	−	0.0168767i
$501$	0.660458	+	3.71376i	0.0295071	+	0.165919i
$502$	8.00133	−	4.61957i	0.357117	−	0.206181i
$503$	−10.0497			−0.448096			−0.224048	−	0.974578i	$-0.571927\pi$
$503$	−10.0497			−0.448096			−0.224048	+	0.974578i	$0.571927\pi$
$504$	8.42636	−	3.09498i	0.375340	−	0.137861i
$505$		−	33.9995i		−	1.51296i
$506$	−8.68223	−	15.0381i	−0.385972	−	0.668524i
$507$	−6.36102	+	21.5995i	−0.282503	+	0.959266i
$508$	0.863558	−	1.49573i	0.0383142	−	0.0663621i
$509$	19.4956	+	11.2558i	0.864126	+	0.498903i	0.865392	−	0.501096i	$-0.167070\pi$
$509$	19.4956	+	11.2558i	0.864126	+	0.498903i	−0.00126603	+	0.999999i	$0.500403\pi$
$510$	−15.5253	−	18.4473i	−0.687471	−	0.816858i
$511$	−2.27972	−	3.94859i	−0.100849	−	0.174675i
$512$		−	25.3968i		−	1.12239i
$513$	−11.3485	−	19.4579i	−0.501049	−	0.859086i
$514$			28.3583i			1.25083i
$515$	−19.9675	+	11.5283i	−0.879874	+	0.507995i
$516$	3.39154	+	4.02985i	0.149304	+	0.177404i
$517$	−3.89177	+	6.74075i	−0.171160	+	0.296458i
$518$	−7.92083	−	4.57309i	−0.348021	−	0.200930i
$519$	−1.01605	+	2.80437i	−0.0445997	+	0.123098i
$520$	−27.7080	+	17.1483i	−1.21508	+	0.752005i
$521$	8.91816			0.390712			0.195356	−	0.980732i	$-0.437414\pi$
$521$	8.91816			0.390712			0.195356	+	0.980732i	$0.437414\pi$
$522$	−5.03341	+	6.03447i	−0.220307	+	0.264122i
$523$	−24.0282			−1.05068			−0.525341	−	0.850892i	$-0.676062\pi$
$523$	−24.0282			−1.05068			−0.525341	+	0.850892i	$0.676062\pi$
$524$	1.66091	+	2.87677i	0.0725570	+	0.125672i
$525$	−1.25016	−	7.02964i	−0.0545613	−	0.306799i
$526$	−3.38931	−	1.95682i	−0.147781	−	0.0853215i
$527$	−23.9226	−	13.8117i	−1.04209	−	0.601649i
$528$	−1.91828	−	10.7865i	−0.0834823	−	0.469422i
$529$	−13.1470	−	22.7713i	−0.571609	−	0.990056i
$530$	−37.0628			−1.60990
$531$	−25.1008	+	30.0929i	−1.08928	+	1.30592i
$532$	1.23416			0.0535076
$533$	−11.2373	−	18.1571i	−0.486742	−	0.786470i
$534$	−5.50111	+	15.1835i	−0.238056	+	0.657053i
$535$	11.7080	+	6.75963i	0.506182	+	0.292244i
$536$	−12.5114	+	21.6704i	−0.540410	+	0.936017i
$537$	−5.45035	−	6.47614i	−0.235200	−	0.279466i
$538$	−28.3411	+	16.3628i	−1.22187	+	0.705449i
$539$			1.88840i			0.0813391i
$540$	−2.21694	+	3.87919i	−0.0954017	+	0.166934i
$541$			20.7477i			0.892013i	0.895030	+	0.446007i	$0.147154\pi$
$541$			20.7477i			0.892013i	−0.895030	+	0.446007i	$0.852846\pi$
$542$	−8.54363	−	14.7980i	−0.366980	−	0.635628i
$543$	9.44685	+	11.2248i	0.405403	+	0.481703i
$544$	−4.86891	−	2.81106i	−0.208753	−	0.120523i
$545$	21.4934	−	37.2277i	0.920677	−	1.59466i
$546$	7.77153	+	2.54956i	0.332591	+	0.109111i
$547$	−10.4194	−	18.0470i	−0.445503	−	0.771634i	0.552584	−	0.833457i	$-0.313642\pi$
$547$	−10.4194	−	18.0470i	−0.445503	−	0.771634i	−0.998087	+	0.0618229i	$0.980309\pi$
$548$		−	3.13224i		−	0.133803i
$549$	33.9861	−	12.4830i	1.45049	−	0.532763i
$550$	−10.1953			−0.434727
$551$	−7.50844	+	4.33500i	−0.319870	+	0.184677i
$552$	−6.37127	−	35.8257i	−0.271179	−	1.52484i
$553$	−9.45374	−	5.45812i	−0.402014	−	0.232103i
$554$	19.8704	+	11.4722i	0.844210	+	0.487405i
$555$	35.9683	−	6.39662i	1.52677	−	0.271521i
$556$	−0.877715	−	1.52025i	−0.0372234	−	0.0644728i
$557$		−	17.4470i		−	0.739253i	−0.929180	−	0.369627i	$-0.879486\pi$
$557$		−	17.4470i		−	0.739253i	0.929180	−	0.369627i	$-0.120514\pi$
$558$	5.26644	−	30.3888i	0.222946	−	1.28646i
$559$	1.17823	+	38.4946i	0.0498336	+	1.62815i
$560$	5.05835	+	8.76132i	0.213754	+	0.370233i
$561$	−10.8219	−	3.92087i	−0.456900	−	0.165539i
$562$	−5.80323	+	10.0515i	−0.244794	+	0.423996i
$563$	−4.91301	+	8.50958i	−0.207059	+	0.358636i	−0.950787	−	0.309846i	$-0.899722\pi$
$563$	−4.91301	+	8.50958i	−0.207059	+	0.358636i	0.743728	+	0.668482i	$0.233056\pi$
$564$	−1.55504	+	1.30873i	−0.0654790	+	0.0551074i
$565$	46.8699	−	27.0603i	1.97183	−	1.13844i
$566$		−	13.3376i		−	0.560620i
$567$	8.85394	−	1.61484i	0.371831	−	0.0678168i
$568$	45.4885			1.90865
$569$	1.67533	+	2.90176i	0.0702335	+	0.121648i	0.899004	−	0.437941i	$-0.144292\pi$
$569$	1.67533	+	2.90176i	0.0702335	+	0.121648i	−0.828770	+	0.559589i	$0.810959\pi$
$570$	22.7244	−	19.1250i	0.951821	−	0.801056i
$571$	−21.7967	+	37.7530i	−0.912163	+	1.57991i	−0.101160	+	0.994870i	$0.532255\pi$
$571$	−21.7967	+	37.7530i	−0.912163	+	1.57991i	−0.811003	+	0.585042i	$0.801078\pi$
$572$	−0.917391	+	1.70757i	−0.0383581	+	0.0713972i
$573$	2.26392	−	6.24859i	0.0945767	−	0.261039i
$574$	−6.71725	+	3.87821i	−0.280373	+	0.161873i
$575$	−28.9422			−1.20697
$576$	4.50363	−	25.9871i	0.187651	−	1.08280i
$577$		−	2.77777i		−	0.115640i	−0.998327	−	0.0578200i	$-0.981585\pi$
$577$		−	2.77777i		−	0.115640i	0.998327	−	0.0578200i	$-0.0184150\pi$
$578$	−5.23556	+	3.02275i	−0.217771	+	0.125730i
$579$	−2.47455	−	13.9145i	−0.102839	−	0.578265i
$580$	1.48932	+	0.859858i	0.0618406	+	0.0357037i
$581$	−5.59886	+	9.69751i	−0.232280	+	0.402320i
$582$	6.37879	−	1.13441i	0.264409	−	0.0470227i
$583$	−15.3229	+	8.84667i	−0.634609	+	0.366392i
$584$	−13.6430			−0.564552
$585$	−30.3075	+	12.1966i	−1.25306	+	0.504269i
$586$	−36.9789			−1.52758
$587$	7.01172	−	4.04822i	0.289404	−	0.167088i	−0.348269	−	0.937395i	$-0.613230\pi$
$587$	7.01172	−	4.04822i	0.289404	−	0.167088i	0.637673	+	0.770307i	$0.279897\pi$
$588$	−0.167972	+	0.463614i	−0.00692704	+	0.0191191i
$589$	17.0141	−	29.4693i	0.701054	−	1.21426i
$590$	−44.7481	−	25.8353i	−1.84225	−	1.06362i
$591$	−10.3956	+	8.74895i	−0.427617	+	0.359884i
$592$	−20.2576	+	11.6957i	−0.832582	+	0.480691i
$593$			12.7831i			0.524940i	0.964940	+	0.262470i	$0.0845371\pi$
$593$			12.7831i			0.524940i	−0.964940	+	0.262470i	$0.915463\pi$
$594$	−0.0565804	−	12.8512i	−0.00232152	−	0.527289i
$595$	10.6287			0.435736
$596$	−1.09873	+	0.634352i	−0.0450057	+	0.0259841i
$597$	−17.9561	−	21.3355i	−0.734893	−	0.873205i
$598$	15.6910	−	29.2062i	0.641651	−	1.19433i
$599$	20.0043	−	34.6484i	0.817352	−	1.41570i	−0.0902740	−	0.995917i	$-0.528774\pi$
$599$	20.0043	−	34.6484i	0.817352	−	1.41570i	0.907626	−	0.419779i	$-0.137892\pi$
$600$	−20.0868	−	7.27763i	−0.820040	−	0.297108i
$601$	−6.46099	−	11.1908i	−0.263549	−	0.456481i	0.703633	−	0.710563i	$-0.251560\pi$
$601$	−6.46099	−	11.1908i	−0.263549	−	0.456481i	−0.967183	+	0.254082i	$0.918227\pi$
$602$	13.9895			0.570169
$603$	−16.0695	+	19.2654i	−0.654400	+	0.784548i
$604$		−	3.46029i		−	0.140797i
$605$	19.4447	−	11.2264i	0.790539	−	0.456418i
$606$	4.47119	+	25.1415i	0.181630	+	1.02131i
$607$	−12.0115	+	20.8045i	−0.487531	+	0.844428i	−0.999897	−	0.0143391i	$-0.995436\pi$
$607$	−12.0115	+	20.8045i	−0.487531	+	0.844428i	0.512367	+	0.858767i	$0.328769\pi$
$608$	3.46284	−	5.99781i	0.140437	−	0.243243i
$609$	−0.606537	−	3.41056i	−0.0245781	−	0.138203i
$610$	23.8700	+	41.3441i	0.966468	+	1.67397i
$611$	−14.8543	+	0.454654i	−0.600940	+	0.0183933i
$612$	−2.30808	−	1.92520i	−0.0932988	−	0.0778215i
$613$			33.8640i			1.36775i	0.729597	+	0.683877i	$0.239707\pi$
$613$			33.8640i			1.36775i	−0.729597	+	0.683877i	$0.760293\pi$
$614$	−8.86892	−	15.3614i	−0.357921	−	0.619937i
$615$	10.5535	−	29.1285i	0.425560	−	1.17458i
$616$	4.89354	+	2.82529i	0.197166	+	0.113834i
$617$	23.7029	+	13.6849i	0.954242	+	0.550932i	0.894396	−	0.447276i	$-0.147606\pi$
$617$	23.7029	+	13.6849i	0.954242	+	0.550932i	0.0598458	+	0.998208i	$0.480939\pi$
$618$	13.2493	−	11.1506i	0.532964	−	0.448545i
$619$	−16.7742	+	9.68457i	−0.674211	+	0.389256i	−0.797670	−	0.603094i	$-0.793934\pi$
$619$	−16.7742	+	9.68457i	−0.674211	+	0.389256i	0.123460	+	0.992350i	$0.460601\pi$
$620$	−6.74958			−0.271070
$621$	−0.160620	−	36.4817i	−0.00644544	−	1.46396i
$622$			21.2664i			0.852706i
$623$	−3.55953	−	6.16528i	−0.142609	−	0.247007i
$624$	15.5848	−	13.9527i	0.623891	−	0.558553i
$625$	14.3092	−	24.7842i	0.572366	−	0.991368i
$626$	26.9746	+	15.5738i	1.07812	+	0.622454i
$627$	4.82995	−	13.3310i	0.192890	−	0.532390i
$628$	2.19542	+	3.80258i	0.0876068	+	0.151739i
$629$			24.5754i			0.979885i
$630$	4.09148	+	11.1394i	0.163009	+	0.443805i
$631$			21.4613i			0.854363i	0.904166	+	0.427181i	$0.140493\pi$
$631$			21.4613i			0.854363i	−0.904166	+	0.427181i	$0.859507\pi$
$632$	−28.2880	+	16.3321i	−1.12524	+	0.649656i
$633$	42.9126	−	7.63161i	1.70562	−	0.303329i
$634$	−4.59659	+	7.96152i	−0.182554	+	0.316193i
$635$	15.8681	+	9.16144i	0.629705	+	0.363560i
$636$	−4.54877	+	0.808957i	−0.180371	+	0.0320772i
$637$	−3.06588	+	1.89746i	−0.121475	+	0.0751801i
$638$	−4.94642			−0.195831
$639$	44.9364	+	7.78757i	1.77766	+	0.308071i
$640$	25.1259			0.993188
$641$	5.73063	+	9.92574i	0.226346	+	0.392043i	0.956722	−	0.291002i	$-0.0939886\pi$
$641$	5.73063	+	9.92574i	0.226346	+	0.392043i	−0.730376	+	0.683045i	$0.760655\pi$
$642$	−9.54665	−	3.45884i	−0.376776	−	0.136509i
$643$	−30.4561	−	17.5838i	−1.20107	−	0.693439i	−0.240278	−	0.970704i	$-0.577238\pi$
$643$	−30.4561	−	17.5838i	−1.20107	−	0.693439i	−0.960793	+	0.277266i	$0.910572\pi$
$644$	1.73104	+	0.999415i	0.0682125	+	0.0393825i
$645$	−42.7525	+	35.9806i	−1.68338	+	1.41674i
$646$	9.98997	+	17.3031i	0.393050	+	0.680783i
$647$	28.7880			1.13177			0.565886	−	0.824483i	$-0.308534\pi$
$647$	28.7880			1.13177			0.565886	+	0.824483i	$0.308534\pi$
$648$	9.06200	−	25.3598i	0.355989	−	0.996229i
$649$	−24.6670			−0.968263
$650$	−10.2442	−	16.5524i	−0.401810	−	0.649238i
$651$	8.75455	+	10.4022i	0.343118	+	0.407695i
$652$	1.19042	+	0.687290i	0.0466205	+	0.0269164i
$653$	12.8325	−	22.2265i	0.502173	−	0.869789i	−0.497824	−	0.867278i	$-0.665868\pi$
$653$	12.8325	−	22.2265i	0.502173	−	0.869789i	0.999997	−	0.00251063i	$-0.000799158\pi$
$654$	−10.9980	+	30.3552i	−0.430054	+	1.18698i
$655$	−30.5195	+	17.6204i	−1.19250	+	0.688488i
$656$			19.8371i			0.774508i
$657$	−13.4774	−	2.33567i	−0.525805	−	0.0911231i
$658$			5.39827i			0.210446i
$659$	−10.2143	−	17.6918i	−0.397894	−	0.689173i	0.595572	−	0.803302i	$-0.296926\pi$
$659$	−10.2143	−	17.6918i	−0.397894	−	0.689173i	−0.993466	+	0.114129i	$0.963592\pi$
$660$	−2.76900	+	0.492440i	−0.107783	+	0.0191682i
$661$	−6.62407	−	3.82441i	−0.257646	−	0.148752i	0.365614	−	0.930767i	$-0.380859\pi$
$661$	−6.62407	−	3.82441i	−0.257646	−	0.148752i	−0.623260	+	0.782014i	$0.714192\pi$
$662$	−1.23575	+	2.14039i	−0.0480290	+	0.0831886i
$663$	−4.50813	−	21.5094i	−0.175081	−	0.835356i
$664$	16.7532	+	29.0174i	0.650151	+	1.12609i
$665$			13.0931i			0.507729i
$666$	−25.7562	+	9.46018i	−0.998031	+	0.366574i
$667$	−14.0418			−0.543702
$668$	−0.536938	+	0.310002i	−0.0207748	+	0.0119943i
$669$	−0.703407	−	0.254851i	−0.0271953	−	0.00985310i
$670$	−28.6476	−	16.5397i	−1.10676	−	0.638985i
$671$	19.7372	+	11.3953i	0.761945	+	0.439909i
$672$	1.78179	+	2.11714i	0.0687340	+	0.0816703i
$673$	−3.78167	−	6.55004i	−0.145773	−	0.252486i	0.783888	−	0.620902i	$-0.213233\pi$
$673$	−3.78167	−	6.55004i	−0.145773	−	0.252486i	−0.929661	+	0.368416i	$0.879900\pi$
$674$			43.1695i			1.66283i
$675$	−18.5971	−	10.6281i	−0.715802	−	0.409077i
$676$	−3.69410	+	0.226347i	−0.142081	+	0.00870565i
$677$	20.3581	+	35.2613i	0.782426	+	1.35520i	0.930525	+	0.366229i	$0.119351\pi$
$677$	20.3581	+	35.2613i	0.782426	+	1.35520i	−0.148099	+	0.988973i	$0.547315\pi$
$678$	−31.1001	+	26.1740i	−1.19439	+	1.00521i
$679$	−1.42803	+	2.47342i	−0.0548028	+	0.0949213i
$680$	15.9020	−	27.5430i	0.609813	−	1.05623i
$681$	−5.69515	−	2.06340i	−0.218239	−	0.0790698i
$682$	16.8129	−	9.70692i	0.643798	−	0.371697i
$683$		−	44.4956i		−	1.70258i	−0.524697	−	0.851289i	$-0.675821\pi$
$683$		−	44.4956i		−	1.70258i	0.524697	−	0.851289i	$-0.324179\pi$
$684$	2.37157	−	2.84324i	0.0906793	−	0.108714i
$685$	33.2298			1.26964
$686$	0.654848	+	1.13423i	0.0250022	+	0.0433051i
$687$	−2.52449	−	14.1953i	−0.0963154	−	0.541583i
$688$	17.8891	−	30.9849i	0.682016	−	1.18129i
$689$	−29.7593	−	15.9881i	−1.13374	−	0.609100i
$690$	47.3607	−	8.42265i	1.80299	−	0.320645i
$691$	−24.6685	+	14.2424i	−0.938436	+	0.541806i	−0.889470	−	0.456994i	$-0.848926\pi$
$691$	−24.6685	+	14.2424i	−0.938436	+	0.541806i	−0.0489661	+	0.998800i	$0.515593\pi$
$692$	−0.490272			−0.0186373
$693$	4.35046	+	3.62876i	0.165260	+	0.137845i
$694$		−	20.8902i		−	0.792981i
$695$	16.1282	−	9.31162i	0.611778	−	0.353210i
$696$	−9.74549	−	3.53088i	−0.369402	−	0.133838i
$697$	18.0489	+	10.4206i	0.683653	+	0.394707i
$698$	10.1214	−	17.5308i	0.383102	−	0.663552i
$699$	28.8287	+	34.2545i	1.09040	+	1.29562i
$700$	1.01635	−	0.586790i	0.0384144	−	0.0221786i
$701$	−26.1955			−0.989390			−0.494695	−	0.869067i	$-0.664720\pi$
$701$	−26.1955			−0.989390			−0.494695	+	0.869067i	$0.664720\pi$
$702$	20.8075	−	13.0047i	0.785327	−	0.490830i
$703$	−30.2734			−1.14178
$704$	14.3776	−	8.30093i	0.541877	−	0.312853i
$705$	−13.8842	−	16.4973i	−0.522910	−	0.621325i
$706$	−18.1452	+	31.4284i	−0.682903	+	1.18282i
$707$	−9.74883	−	5.62849i	−0.366643	−	0.211681i
$708$	−6.05590	−	2.19411i	−0.227595	−	0.0824597i
$709$	−9.12875	+	5.27049i	−0.342837	+	0.197937i	−0.661526	−	0.749922i	$-0.730091\pi$
$709$	−9.12875	+	5.27049i	−0.342837	+	0.197937i	0.318689	+	0.947859i	$0.396758\pi$
$710$			60.1345i			2.25681i
$711$	−30.7407	+	11.2910i	−1.15287	+	0.423445i
$712$	−21.3020			−0.798327
$713$	47.7282	−	27.5559i	1.78743	−	1.03198i
$714$	−7.85961	+	1.39776i	−0.294139	+	0.0523098i
$715$	−18.1155	−	9.73255i	−0.677482	−	0.363977i
$716$	0.695643	−	1.20489i	0.0259974	−	0.0450288i
$717$	3.21911	+	18.1011i	0.120220	+	0.675999i
$718$	6.09412	+	10.5553i	0.227430	+	0.393921i
$719$	9.95929			0.371419			0.185709	−	0.982605i	$-0.440542\pi$
$719$	9.95929			0.371419			0.185709	+	0.982605i	$0.440542\pi$
$720$	29.9043	+	5.18249i	1.11447	+	0.193140i
$721$			7.63383i			0.284299i
$722$	0.235357	−	0.135884i	0.00875910	−	0.00505707i
$723$	−29.0663	−	10.5310i	−1.08099	−	0.391652i
$724$	−1.20573	+	2.08838i	−0.0448105	+	0.0776141i
$725$	−4.12222	+	7.13989i	−0.153095	+	0.265169i
$726$	−12.9024	+	10.8587i	−0.478852	+	0.403003i
$727$	−4.85790	−	8.41412i	−0.180169	−	0.312063i	0.761769	−	0.647849i	$-0.224331\pi$
$727$	−4.85790	−	8.41412i	−0.180169	−	0.312063i	−0.941938	+	0.335787i	$0.890998\pi$
$728$	0.330062	+	10.7837i	0.0122329	+	0.399670i
$729$	13.2936	−	23.5007i	0.492355	−	0.870394i
$730$		−	18.0357i		−	0.667532i
$731$	−18.7946	−	32.5531i	−0.695142	−	1.20402i
$732$	3.83201	+	4.55322i	0.141635	+	0.168292i
$733$	−23.2205	−	13.4064i	−0.857670	−	0.495176i	0.00556152	−	0.999985i	$-0.498230\pi$
$733$	−23.2205	−	13.4064i	−0.857670	−	0.495176i	−0.863231	+	0.504809i	$0.831563\pi$
$734$	11.7978	+	6.81149i	0.435466	+	0.251417i
$735$	−4.91846	−	1.78200i	−0.181420	−	0.0657301i
$736$	9.71398	−	5.60837i	0.358062	−	0.206727i
$737$	−15.7918			−0.581697
$738$	−3.97338	+	22.9275i	−0.146262	+	0.843972i
$739$		−	23.8147i		−	0.876037i	−0.898966	−	0.438019i	$-0.855680\pi$
$739$		−	23.8147i		−	0.876037i	0.898966	−	0.438019i	$-0.144320\pi$
$740$	3.00240	+	5.20032i	0.110371	+	0.191167i
$741$	26.4966	−	5.55339i	0.973375	−	0.204009i
$742$	−6.13560	+	10.6272i	−0.225245	+	0.390136i
$743$	35.8758	+	20.7129i	1.31615	+	0.759882i	0.983108	−	0.183029i	$-0.0585902\pi$
$743$	35.8758	+	20.7129i	1.31615	+	0.759882i	0.333046	+	0.942911i	$0.391923\pi$
$744$	40.0539	−	7.12321i	1.46845	−	0.261150i
$745$	−6.72980	−	11.6564i	−0.246561	−	0.427056i
$746$		−	6.79495i		−	0.248781i
$747$	11.5821	+	31.5334i	0.423768	+	1.15375i
$748$		−	1.89192i		−	0.0691756i
$749$	3.87644	−	2.23806i	0.141642	−	0.0817770i
$750$	−2.04857	+	5.65421i	−0.0748033	+	0.206463i
$751$	−6.39054	+	11.0687i	−0.233194	+	0.403904i	−0.958746	−	0.284263i	$-0.908251\pi$
$751$	−6.39054	+	11.0687i	−0.233194	+	0.403904i	0.725552	+	0.688167i	$0.241584\pi$
$752$	11.9564	+	6.90306i	0.436007	+	0.251729i
$753$	7.86769	+	9.34845i	0.286715	+	0.340676i
$754$	−4.97016	−	8.03070i	−0.181002	−	0.292461i
$755$	36.7100			1.33601
$756$	0.745291	+	1.27786i	0.0271060	+	0.0464752i
$757$	5.14705			0.187073			0.0935363	−	0.995616i	$-0.470183\pi$
$757$	5.14705			0.187073			0.0935363	+	0.995616i	$0.470183\pi$
$758$	14.0357	+	24.3106i	0.509801	+	0.883001i
$759$	17.5699	−	14.7869i	0.637748	−	0.536731i
$760$	33.9291	+	19.5890i	1.23074	+	0.710567i
$761$	−11.1083	−	6.41338i	−0.402676	−	0.232485i	0.284962	−	0.958539i	$-0.408019\pi$
$761$	−11.1083	−	6.41338i	−0.402676	−	0.232485i	−0.687638	+	0.726054i	$0.741352\pi$
$762$	−12.9387	−	4.68782i	−0.468720	−	0.169822i
$763$	−7.11630	−	12.3258i	−0.257627	−	0.446224i
$764$	1.09240			0.0395218
$765$	20.4243	−	24.4863i	0.738442	−	0.885305i
$766$	−1.76028			−0.0636017
$767$	−24.7853	−	40.0477i	−0.894946	−	1.44604i
$768$	11.4044	−	2.02817i	0.411521	−	0.0731851i
$769$	−0.271695	−	0.156863i	−0.00979758	−	0.00565663i	0.495093	−	0.868840i	$-0.335134\pi$
$769$	−0.271695	−	0.156863i	−0.00979758	−	0.00565663i	−0.504891	+	0.863183i	$0.668467\pi$
$770$	−3.73495	+	6.46913i	−0.134598	+	0.233131i
$771$	−36.9240	+	6.56659i	−1.32979	+	0.236490i
$772$	2.01176	−	1.16149i	0.0724049	−	0.0418030i
$773$		−	10.5961i		−	0.381115i	−0.981676	−	0.190557i	$-0.938970\pi$
$773$		−	10.5961i		−	0.381115i	0.981676	−	0.190557i	$-0.0610295\pi$
$774$	26.8823	−	32.2288i	0.966266	−	1.15844i
$775$		−	32.3580i		−	1.16233i
$776$	4.27304	+	7.40112i	0.153393	+	0.265685i
$777$	4.12028	−	11.3723i	0.147814	−	0.407978i
$778$	2.64601	+	1.52768i	0.0948642	+	0.0547699i
$779$	−12.8367	+	22.2338i	−0.459921	+	0.796607i
$780$	−3.58178	−	4.00077i	−0.128248	−	0.143250i
$781$	14.3538	+	24.8615i	0.513618	+	0.889613i
$782$			32.3593i			1.15717i
$783$	−9.02272	−	5.15644i	−0.322446	−	0.184276i
$784$	3.34956			0.119627
$785$	−40.3413	+	23.2911i	−1.43984	+	0.831294i
$786$	20.2510	−	17.0433i	0.722328	−	0.607914i
$787$	22.8107	+	13.1698i	0.813113	+	0.469451i	0.848036	−	0.529939i	$-0.177785\pi$
$787$	22.8107	+	13.1698i	0.813113	+	0.469451i	−0.0349226	+	0.999390i	$0.511118\pi$
$788$	−1.93410	−	1.11665i	−0.0688995	−	0.0397791i
$789$	1.76306	−	4.86618i	0.0627667	−	0.173241i
$790$	−21.5906	−	37.3960i	−0.768159	−	1.33049i
$791$		−	17.9189i		−	0.637124i
$792$	15.9123	−	5.84456i	0.565420	−	0.207677i
$793$	1.33125	+	43.4940i	0.0472739	+	1.54452i
$794$	−8.78267	−	15.2120i	−0.311685	−	0.539855i
$795$	−8.58217	−	48.2577i	−0.304378	−	1.71152i
$796$	2.29178	−	3.96948i	0.0812301	−	0.140695i
$797$	15.8502	−	27.4534i	0.561443	−	0.972448i	−0.435928	−	0.899982i	$-0.643580\pi$
$797$	15.8502	−	27.4534i	0.561443	−	0.972448i	0.997371	−	0.0724663i	$-0.0230870\pi$
$798$	−1.72184	−	9.68194i	−0.0609525	−	0.342737i
$799$	12.5616	−	7.25245i	0.444398	−	0.256573i
$800$		−	6.58572i		−	0.232841i
$801$	−21.0435	−	3.64688i	−0.743535	−	0.128856i
$802$	39.8884			1.40851
$803$	−4.30502	−	7.45652i	−0.151921	−	0.263135i
$804$	−3.87698	−	1.40467i	−0.136731	−	0.0495387i
$805$	−10.6027	+	18.3645i	−0.373697	+	0.647263i
$806$	32.6531	+	17.5428i	1.15016	+	0.617920i
$807$	−27.8678	−	33.1127i	−0.980992	−	1.16562i
$808$	−29.1710	+	16.8419i	−1.02623	+	0.592496i
$809$	2.65591			0.0933768			0.0466884	−	0.998910i	$-0.485133\pi$
$809$	2.65591			0.0933768			0.0466884	+	0.998910i	$0.485133\pi$
$810$	33.5251	+	11.9797i	1.17795	+	0.420924i
$811$		−	31.5051i		−	1.10629i	−0.833084	−	0.553147i	$-0.813427\pi$
$811$		−	31.5051i		−	1.10629i	0.833084	−	0.553147i	$-0.186573\pi$
$812$	0.493102	−	0.284692i	0.0173045	−	0.00999074i
$813$	17.2894	−	14.5508i	0.606366	−	0.510320i
$814$	−14.9577	−	8.63582i	−0.524266	−	0.302685i
$815$	−7.29142	+	12.6291i	−0.255407	+	0.442378i
$816$	−6.95466	+	19.1954i	−0.243462	+	0.671973i
$817$	40.1009	−	23.1523i	1.40295	−	0.809995i
$818$	18.3758			0.642495
$819$	−1.52010	+	10.7093i	−0.0531165	+	0.374214i
$820$	5.09237			0.177833
$821$	8.70836	−	5.02777i	0.303924	−	0.175470i	−0.340280	−	0.940324i	$-0.610522\pi$
$821$	8.70836	−	5.02777i	0.303924	−	0.175470i	0.644204	+	0.764854i	$0.277189\pi$
$822$	−24.5723	+	4.36996i	−0.857059	+	0.152420i
$823$	14.0512	−	24.3374i	0.489793	−	0.848347i	−0.510138	−	0.860093i	$-0.670406\pi$
$823$	14.0512	−	24.3374i	0.489793	−	0.848347i	0.999931	+	0.0117458i	$0.00373890\pi$
$824$	19.7821	+	11.4212i	0.689141	+	0.397876i
$825$	−2.36079	−	13.2748i	−0.0821922	−	0.462168i
$826$	−14.8157	+	8.55387i	−0.515506	+	0.297627i
$827$		−	22.3099i		−	0.775791i	−0.921703	−	0.387895i	$-0.873202\pi$
$827$		−	22.3099i		−	0.775791i	0.921703	−	0.387895i	$-0.126798\pi$
$828$	5.62882	−	2.06745i	0.195615	−	0.0718489i
$829$	29.2861			1.01715			0.508575	−	0.861018i	$-0.330173\pi$
$829$	29.2861			1.01715			0.508575	+	0.861018i	$0.330173\pi$
$830$	−38.3603	+	22.1473i	−1.33150	+	0.768745i
$831$	−10.3362	+	28.5287i	−0.358559	+	0.989650i
$832$	27.9235	+	15.0019i	0.968072	+	0.520096i
$833$	1.75955	−	3.04763i	0.0609647	−	0.105594i
$834$	−10.7017	+	9.00662i	−0.370571	+	0.311874i
$835$	−3.28879	−	5.69635i	−0.113813	−	0.197130i
$836$	2.33058			0.0806050
$837$	40.7873	−	0.179576i	1.40981	−	0.00620706i
$838$		−	17.9599i		−	0.620416i
$839$	12.4266	−	7.17449i	0.429013	−	0.247691i	−0.269913	−	0.962885i	$-0.586995\pi$
$839$	12.4266	−	7.17449i	0.429013	−	0.247691i	0.698926	+	0.715194i	$0.253662\pi$
$840$	−11.9765	+	10.0794i	−0.413227	+	0.347774i
$841$	12.5000	−	21.6507i	0.431035	−	0.746575i
$842$	8.41282	−	14.5714i	0.289925	−	0.502165i
$843$	−14.4313	−	5.22861i	−0.497042	−	0.180083i
$844$	3.58208	+	6.20434i	0.123300	+	0.213562i
$845$	−2.40130	−	39.1905i	−0.0826072	−	1.34819i
$846$	12.4364	+	10.3734i	0.427574	+	0.356643i
$847$		−	7.43395i		−	0.255434i
$848$	15.6918	+	27.1791i	0.538860	+	0.933333i
$849$	17.3662	−	3.08842i	0.596007	−	0.105994i
$850$	16.4538	+	9.49961i	0.564361	+	0.325834i
$851$	−42.4617	−	24.5153i	−1.45557	−	0.840372i
$852$	1.31254	+	7.38041i	0.0449668	+	0.252849i
$853$	37.1460	−	21.4463i	1.27186	−	0.734307i	0.296519	−	0.955027i	$-0.404174\pi$
$853$	37.1460	−	21.4463i	1.27186	−	0.734307i	0.975337	+	0.220720i	$0.0708407\pi$
$854$	15.8064			0.540882
$855$	30.1637	+	25.1599i	1.03158	+	0.860449i
$856$		−	13.3937i		−	0.457788i
$857$	−5.79098	−	10.0303i	−0.197816	−	0.342627i	0.750004	−	0.661433i	$-0.230052\pi$
$857$	−5.79098	−	10.0303i	−0.197816	−	0.342627i	−0.947820	+	0.318806i	$0.896718\pi$
$858$	14.6757	+	4.81458i	0.501022	+	0.164367i
$859$	−1.63193	+	2.82659i	−0.0556808	+	0.0964420i	−0.892522	−	0.451003i	$-0.851066\pi$
$859$	−1.63193	+	2.82659i	−0.0556808	+	0.0964420i	0.836841	+	0.547445i	$0.184400\pi$
$860$	−7.95411	−	4.59231i	−0.271233	−	0.156596i
$861$	−6.60506	−	7.84818i	−0.225100	−	0.267465i
$862$	−11.4462	−	19.8254i	−0.389860	−	0.675257i
$863$		−	12.6320i		−	0.429999i	−0.976614	−	0.215000i	$-0.931025\pi$
$863$		−	12.6320i		−	0.429999i	0.976614	−	0.215000i	$-0.0689751\pi$
$864$	8.30132	−	0.0365486i	0.282417	−	0.00124341i
$865$		−	5.20126i		−	0.176848i
$866$	35.4554	−	20.4702i	1.20482	−	0.695605i
$867$	−5.14812	−	6.11704i	−0.174839	−	0.207745i
$868$	−1.11737	+	1.93534i	−0.0379259	+	0.0656896i
$869$	−17.8524	−	10.3071i	−0.605602	−	0.349644i
$870$	4.66773	−	12.8833i	0.158251	−	0.436784i
$871$	−15.8675	−	25.6385i	−0.537650	−	0.868727i
$872$	−42.5876			−1.44220
$873$	2.95411	+	8.04283i	0.0999816	+	0.272209i
$874$	−39.8621			−1.34836
$875$	−1.32554	−	2.29591i	−0.0448115	−	0.0776158i
$876$	−0.393660	−	2.21355i	−0.0133005	−	0.0747890i
$877$	−2.13194	−	1.23087i	−0.0719904	−	0.0415637i	0.463573	−	0.886059i	$-0.346567\pi$
$877$	−2.13194	−	1.23087i	−0.0719904	−	0.0415637i	−0.535563	+	0.844495i	$0.679901\pi$
$878$	−24.0253	−	13.8710i	−0.810816	−	0.468125i
$879$	−8.56275	−	48.1485i	−0.288815	−	1.62401i
$880$	9.55218	+	16.5449i	0.322004	+	0.557727i
$881$	−15.7643			−0.531112			−0.265556	−	0.964095i	$-0.585555\pi$
$881$	−15.7643			−0.531112			−0.265556	+	0.964095i	$0.585555\pi$
$882$	3.87138	+	0.670919i	0.130356	+	0.0225910i
$883$	57.9852			1.95136			0.975679	−	0.219202i	$-0.0703454\pi$
$883$	57.9852			1.95136			0.975679	+	0.219202i	$0.0703454\pi$
$884$	3.07161	−	1.90100i	0.103309	−	0.0639376i
$885$	23.2772	−	64.2467i	0.782454	−	2.15963i
$886$	20.4654	+	11.8157i	0.687550	+	0.396957i
$887$	−8.19845	+	14.2001i	−0.275277	+	0.476794i	−0.970205	−	0.242286i	$-0.922103\pi$
$887$	−8.19845	+	14.2001i	−0.275277	+	0.476794i	0.694928	+	0.719079i	$0.255436\pi$
$888$	−23.3053	−	27.6915i	−0.782075	−	0.929267i
$889$	5.25380	−	3.03328i	0.176207	−	0.101733i
$890$		−	28.1607i		−	0.943950i
$891$	16.7198	−	3.04945i	0.560133	−	0.102161i
$892$		−	0.122972i		−	0.00411742i
$893$	8.93400	+	15.4741i	0.298965	+	0.517822i
$894$	6.50936	+	7.73447i	0.217706	+	0.258680i
$895$	12.7826	+	7.38003i	0.427275	+	0.246687i
$896$	4.15949	−	7.20445i	0.138959	−	0.240684i
$897$	41.6613	+	13.6676i	1.39103	+	0.456346i
$898$	−6.55729	−	11.3576i	−0.218820	−	0.379007i
$899$		−	15.6991i		−	0.523593i
$900$	0.601191	−	3.46903i	0.0200397	−	0.115634i
$901$	32.9722			1.09846
$902$	−12.6848	+	7.32360i	−0.422359	+	0.243849i
$903$	3.23938	+	18.2151i	0.107800	+	0.606159i
$904$	−46.4346	−	26.8090i	−1.54439	−	0.891655i
$905$	−22.1555	−	12.7915i	−0.736474	−	0.425204i
$906$	−27.1459	+	4.82763i	−0.901861	+	0.160387i
$907$	14.8455	+	25.7132i	0.492938	+	0.853794i	0.999967	−	0.00813497i	$-0.00258947\pi$
$907$	14.8455	+	25.7132i	0.492938	+	0.853794i	−0.507029	+	0.861929i	$0.669256\pi$
$908$		−	0.995649i		−	0.0330418i
$909$	−31.7003	+	11.6434i	−1.05143	+	0.386188i
$910$	−14.2557	+	0.436334i	−0.472573	+	0.0144643i
$911$	−11.4768	−	19.8784i	−0.380243	−	0.658601i	0.610853	−	0.791744i	$-0.290826\pi$
$911$	−11.4768	−	19.8784i	−0.380243	−	0.658601i	−0.991097	+	0.133143i	$0.957493\pi$
$912$	−23.6460	−	8.56717i	−0.782998	−	0.283687i
$913$	−10.5729	+	18.3128i	−0.349911	+	0.606064i
$914$	17.3765	−	30.0970i	0.574763	−	0.995519i
$915$	−48.3049	+	40.6535i	−1.59691	+	1.34396i
$916$	2.05236	−	1.18493i	0.0678119	−	0.0391512i
$917$			11.6680i			0.385311i
$918$	−11.8830	+	20.7928i	−0.392196	+	0.686264i
$919$	−45.4542			−1.49940			−0.749698	−	0.661780i	$-0.769801\pi$
$919$	−45.4542			−1.49940			−0.749698	+	0.661780i	$0.769801\pi$
$920$	31.7261	+	54.9512i	1.04598	+	1.81169i
$921$	17.9477	−	15.1049i	0.591397	−	0.497722i
$922$	12.9001	−	22.3436i	0.424842	−	0.735848i
$923$	−25.9409	+	48.2846i	−0.853854	+	1.58931i
$924$	−0.317198	+	0.875489i	−0.0104350	+	0.0288015i
$925$	−24.9307	+	14.3937i	−0.819715	+	0.473263i
$926$	13.1165			0.431036
$927$	17.5867	+	14.6692i	0.577623	+	0.481801i
$928$		−	3.19519i		−	0.104887i
$929$	28.4332	−	16.4159i	0.932864	−	0.538589i	0.0451479	−	0.998980i	$-0.485624\pi$
$929$	28.4332	−	16.4159i	0.932864	−	0.538589i	0.887716	+	0.460391i	$0.152291\pi$
$930$	9.41670	+	52.9502i	0.308786	+	1.73631i
$931$	3.75425	+	2.16752i	0.123040	+	0.0710375i
$932$	−3.67949	+	6.37306i	−0.120526	+	0.208756i
$933$	−27.6900	+	4.92441i	−0.906530	+	0.161218i
$934$	26.1536	−	15.0998i	0.855770	−	0.494079i
$935$	20.0713			0.656402
$936$	25.4775	+	19.9616i	0.832759	+	0.652467i
$937$	−16.0842			−0.525449			−0.262724	−	0.964871i	$-0.584621\pi$
$937$	−16.0842			−0.525449			−0.262724	+	0.964871i	$0.584621\pi$
$938$	−9.48502	+	5.47618i	−0.309697	+	0.178803i
$939$	−14.0317	+	38.7286i	−0.457907	+	1.26386i
$940$	1.77208	−	3.06933i	0.0577989	−	0.100111i
$941$	28.3815	+	16.3861i	0.925211	+	0.534171i	0.885294	−	0.465032i	$-0.153957\pi$
$941$	28.3815	+	16.3861i	0.925211	+	0.534171i	0.0399175	+	0.999203i	$0.487290\pi$
$942$	26.7681	−	22.5282i	0.872153	−	0.734007i
$943$	−36.0096	+	20.7901i	−1.17263	+	0.677020i
$944$			43.7532i			1.42405i
$945$	−13.5567	+	7.90675i	−0.440999	+	0.257207i
$946$	26.4177			0.858915
$947$	2.41051	−	1.39171i	0.0783309	−	0.0452244i	−0.460323	−	0.887752i	$-0.652266\pi$
$947$	2.41051	−	1.39171i	0.0783309	−	0.0452244i	0.538654	+	0.842527i	$0.318933\pi$
$948$	−3.46608	−	4.11842i	−0.112573	−	0.133760i
$949$	7.78025	−	14.4817i	0.252558	−	0.470094i
$950$	−11.7022	+	20.2688i	−0.379669	+	0.657606i
$951$	−11.4307	−	4.14145i	−0.370666	−	0.134296i
$952$	−5.26502	−	9.11928i	−0.170640	−	0.295558i
$953$	22.9158			0.742315			0.371157	−	0.928570i	$-0.378961\pi$
$953$	22.9158			0.742315			0.371157	+	0.928570i	$0.378961\pi$
$954$	12.6925	+	34.5564i	0.410934	+	1.11880i
$955$			11.5892i			0.375019i
$956$	−2.61707	+	1.51097i	−0.0846422	+	0.0488682i
$957$	−1.14538	−	6.44050i	−0.0370250	−	0.208192i
$958$	2.39604	−	4.15006i	0.0774125	−	0.134082i
$959$	5.50106	−	9.52812i	0.177639	−	0.307679i
$960$	8.05274	+	45.2807i	0.259901	+	1.46143i
$961$	15.3080	+	26.5143i	0.493808	+	0.855300i
$962$	−1.00887	−	32.9616i	−0.0325274	−	1.06272i
$963$	2.29299	−	13.2312i	0.0738905	−	0.426368i
$964$		−	5.08149i		−	0.163664i
$965$	12.3222	+	21.3427i	0.396665	+	0.687045i
$966$	5.42532	−	14.9743i	0.174557	−	0.481789i
$967$	12.5200	+	7.22845i	0.402617	+	0.232451i	0.687613	−	0.726078i	$-0.258659\pi$
$967$	12.5200	+	7.22845i	0.402617	+	0.232451i	−0.284995	+	0.958529i	$0.591992\pi$
$968$	−19.2641	−	11.1221i	−0.619172	−	0.357479i
$969$	−20.2163	+	17.0141i	−0.649442	+	0.546573i
$970$	−9.78409	+	5.64885i	−0.314148	+	0.181373i
$971$	−16.7954			−0.538991			−0.269496	−	0.963002i	$-0.586857\pi$
$971$	−16.7954			−0.538991			−0.269496	+	0.963002i	$0.586857\pi$
$972$	4.37606	+	0.738551i	0.140362	+	0.0236890i
$973$		−	6.16601i		−	0.197673i
$974$	6.60365	+	11.4379i	0.211595	+	0.366492i
$975$	19.1800	−	17.1713i	0.614250	−	0.549921i
$976$	20.2124	−	35.0090i	0.646984	−	1.12061i
$977$	−27.9341	−	16.1278i	−0.893691	−	0.515973i	−0.0185429	−	0.999828i	$-0.505903\pi$
$977$	−27.9341	−	16.1278i	−0.893691	−	0.515973i	−0.875148	+	0.483855i	$0.839236\pi$
$978$	3.73095	−	10.2977i	0.119303	−	0.329284i
$979$	−6.72180	−	11.6425i	−0.214830	−	0.372096i
$980$		−	0.859864i		−	0.0274674i
$981$	−42.0707	−	7.29095i	−1.34321	−	0.232782i
$982$		−	23.2616i		−	0.742307i
$983$	−10.5013	+	6.06291i	−0.334938	+	0.193377i	−0.658031	−	0.752990i	$-0.728611\pi$
$983$	−10.5013	+	6.06291i	−0.334938	+	0.193377i	0.323093	+	0.946367i	$0.395277\pi$
$984$	−30.2196	+	5.37426i	−0.963364	+	0.171325i
$985$	11.8465	−	20.5188i	0.377461	−	0.653782i
$986$	7.98288	+	4.60892i	0.254227	+	0.146778i
$987$	−7.02883	+	1.25001i	−0.223730	+	0.0397883i
$988$	2.34177	+	3.78379i	0.0745015	+	0.120378i
$989$	74.9943			2.38468
$990$	7.72635	+	21.0357i	0.245560	+	0.668557i
$991$	−35.7042			−1.13418			−0.567091	−	0.823655i	$-0.691931\pi$
$991$	−35.7042			−1.13418			−0.567091	+	0.823655i	$0.691931\pi$
$992$	6.27028	+	10.8604i	0.199081	+	0.344819i
$993$	−3.07305	−	1.11339i	−0.0975203	−	0.0353325i
$994$	17.2426	+	9.95504i	0.546903	+	0.315755i
$995$	42.1120	+	24.3134i	1.33504	+	0.770786i
$996$	−4.22462	+	3.55545i	−0.133862	+	0.112659i
$997$	−14.9390	−	25.8752i	−0.473124	−	0.819476i	0.526402	−	0.850236i	$-0.323541\pi$
$997$	−14.9390	−	25.8752i	−0.473124	−	0.819476i	−0.999527	+	0.0307600i	$0.990207\pi$
$998$	55.3823			1.75310
$999$	−18.2817	−	31.3453i	−0.578407	−	0.991721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dt.a.337.58	yes	168
9.7	even	3	inner	819.2.dt.a.610.27	yes	168
13.12	even	2	inner	819.2.dt.a.337.27	✓	168
117.25	even	6	inner	819.2.dt.a.610.58	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dt.a.337.27	✓	168	13.12	even	2	inner
819.2.dt.a.337.58	yes	168	1.1	even	1	trivial
819.2.dt.a.610.27	yes	168	9.7	even	3	inner
819.2.dt.a.610.58	yes	168	117.25	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13423 - 0.654848i) q^{2} +(1.11529 + 1.32519i) q^{3} +(-0.142347 + 0.246553i) q^{4} +(-2.61566 - 1.51015i) q^{5} +(2.13279 + 0.772730i) q^{6} +(-0.866025 + 0.500000i) q^{7} +2.99226i q^{8} +(-0.512271 + 2.95594i) q^{9} +O(q^{10})\)	\(q+(1.13423 - 0.654848i) q^{2} +(1.11529 + 1.32519i) q^{3} +(-0.142347 + 0.246553i) q^{4} +(-2.61566 - 1.51015i) q^{5} +(2.13279 + 0.772730i) q^{6} +(-0.866025 + 0.500000i) q^{7} +2.99226i q^{8} +(-0.512271 + 2.95594i) q^{9} -3.95568 q^{10} +(-1.63540 + 0.944199i) q^{11} +(-0.485488 + 0.0863394i) q^{12} +(-3.17619 - 1.70640i) q^{13} +(-0.654848 + 1.13423i) q^{14} +(-0.915969 - 5.15051i) q^{15} +(1.67478 + 2.90080i) q^{16} +3.51910 q^{17} +(1.35466 + 3.68818i) q^{18} +4.33503i q^{19} +(0.744664 - 0.429932i) q^{20} +(-1.62846 - 0.590007i) q^{21} +(-1.23661 + 2.14188i) q^{22} +(-3.51048 + 6.08034i) q^{23} +(-3.96532 + 3.33722i) q^{24} +(2.06112 + 3.56997i) q^{25} +(-4.71997 + 0.144467i) q^{26} +(-4.48852 + 2.61786i) q^{27} -0.284694i q^{28} +(0.999993 + 1.73204i) q^{29} +(-4.41172 - 5.24204i) q^{30} +(-6.79795 - 3.92480i) q^{31} +(-1.38357 - 0.798803i) q^{32} +(-3.07519 - 1.11417i) q^{33} +(3.99147 - 2.30447i) q^{34} +3.02031 q^{35} +(-0.655874 - 0.547071i) q^{36} +6.98344i q^{37} +(2.83879 + 4.91693i) q^{38} +(-1.28105 - 6.11219i) q^{39} +(4.51877 - 7.82673i) q^{40} +(5.12886 + 2.96115i) q^{41} +(-2.23342 + 0.397192i) q^{42} +(-5.34074 - 9.25043i) q^{43} -0.537617i q^{44} +(5.80385 - 6.95813i) q^{45} +9.19534i q^{46} +(3.56956 - 2.06088i) q^{47} +(-1.97626 + 5.45463i) q^{48} +(0.500000 - 0.866025i) q^{49} +(4.67558 + 2.69945i) q^{50} +(3.92480 + 4.66348i) q^{51} +(0.872840 - 0.540196i) q^{52} +9.36950 q^{53} +(-3.37671 + 5.90856i) q^{54} +5.70354 q^{55} +(-1.49613 - 2.59137i) q^{56} +(-5.74475 + 4.83480i) q^{57} +(2.26844 + 1.30969i) q^{58} +(11.3123 + 6.53119i) q^{59} +(1.40026 + 0.507326i) q^{60} +(-6.03436 - 10.4518i) q^{61} -10.2806 q^{62} +(-1.03433 - 2.81605i) q^{63} -8.79150 q^{64} +(5.73091 + 9.25991i) q^{65} +(-4.21758 + 0.750057i) q^{66} +(7.24215 + 4.18125i) q^{67} +(-0.500934 + 0.867642i) q^{68} +(-11.9728 + 2.12925i) q^{69} +(3.42572 - 1.97784i) q^{70} -15.2021i q^{71} +(-8.84493 - 1.53285i) q^{72} +4.55944i q^{73} +(4.57309 + 7.92083i) q^{74} +(-2.43215 + 6.71293i) q^{75} +(-1.06881 - 0.617080i) q^{76} +(0.944199 - 1.63540i) q^{77} +(-5.45556 - 6.09375i) q^{78} +(5.45812 + 9.45374i) q^{79} -10.1167i q^{80} +(-8.47516 - 3.02848i) q^{81} +7.75641 q^{82} +(9.69751 - 5.59886i) q^{83} +(0.377275 - 0.317516i) q^{84} +(-9.20476 - 5.31437i) q^{85} +(-12.1153 - 6.99475i) q^{86} +(-1.18001 + 3.25690i) q^{87} +(-2.82529 - 4.89354i) q^{88} +7.11905i q^{89} +(2.02638 - 11.6928i) q^{90} +(3.60386 - 0.110306i) q^{91} +(-0.999415 - 1.73104i) q^{92} +(-2.38055 - 13.3859i) q^{93} +(2.69913 - 4.67504i) q^{94} +(6.54656 - 11.3390i) q^{95} +(-0.484507 - 2.72439i) q^{96} +(2.47342 - 1.42803i) q^{97} -1.30970i q^{98} +(-1.95323 - 5.31783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 8 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 8 * q^9	\( 168 q + 84 q^{4} - 8 q^{9} - 24 q^{12} + 8 q^{14} - 84 q^{16} - 32 q^{23} + 84 q^{25} - 8 q^{26} + 48 q^{27} + 4 q^{29} + 80 q^{30} - 32 q^{35} + 4 q^{36} + 24 q^{38} + 24 q^{39} + 4 q^{48} + 84 q^{49} + 64 q^{51} + 18 q^{52} - 48 q^{53} - 24 q^{56} + 24 q^{62} - 240 q^{64} - 22 q^{65} - 132 q^{66} - 156 q^{68} - 52 q^{69} + 84 q^{74} - 60 q^{75} - 16 q^{77} - 148 q^{78} + 12 q^{79} - 8 q^{81} - 24 q^{82} + 88 q^{87} + 24 q^{88} - 164 q^{90} + 12 q^{91} + 128 q^{92} - 60 q^{94} - 96 q^{95}+O(q^{100}) \) 168 * q + 84 * q^4 - 8 * q^9 - 24 * q^12 + 8 * q^14 - 84 * q^16 - 32 * q^23 + 84 * q^25 - 8 * q^26 + 48 * q^27 + 4 * q^29 + 80 * q^30 - 32 * q^35 + 4 * q^36 + 24 * q^38 + 24 * q^39 + 4 * q^48 + 84 * q^49 + 64 * q^51 + 18 * q^52 - 48 * q^53 - 24 * q^56 + 24 * q^62 - 240 * q^64 - 22 * q^65 - 132 * q^66 - 156 * q^68 - 52 * q^69 + 84 * q^74 - 60 * q^75 - 16 * q^77 - 148 * q^78 + 12 * q^79 - 8 * q^81 - 24 * q^82 + 88 * q^87 + 24 * q^88 - 164 * q^90 + 12 * q^91 + 128 * q^92 - 60 * q^94 - 96 * q^95

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