LMFDB - Embedded newform 570.2.n.a.179.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(179,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("570.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.18
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.67546 - 0.439145i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.95241 + 1.09000i) q^{5} +(-1.67056 - 0.457417i) q^{6} +4.60944i q^{7} -1.00000i q^{8} +(2.61430 - 1.47153i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.67546 - 0.439145i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.95241 + 1.09000i) q^{5} +(-1.67056 - 0.457417i) q^{6} +4.60944i q^{7} -1.00000i q^{8} +(2.61430 - 1.47153i) q^{9} +(-1.14583 - 1.92017i) q^{10} -6.27586i q^{11} +(1.21804 + 1.23141i) q^{12} +(-1.27680 - 2.21149i) q^{13} +(2.30472 - 3.99190i) q^{14} +(3.74984 + 0.968866i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.20522 + 2.08749i) q^{17} +(-2.99982 - 0.0327655i) q^{18} +(2.80775 + 3.33415i) q^{19} +(0.0322312 + 2.23584i) q^{20} +(2.02421 + 7.72292i) q^{21} +(-3.13793 + 5.43505i) q^{22} +(1.74466 + 3.02184i) q^{23} +(-0.439145 - 1.67546i) q^{24} +(2.62378 + 4.25626i) q^{25} +2.55360i q^{26} +(3.73393 - 3.61355i) q^{27} +(-3.99190 + 2.30472i) q^{28} +(0.557163 + 0.965035i) q^{29} +(-2.76302 - 2.71398i) q^{30} +4.37073i q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.75601 - 10.5149i) q^{33} +(2.08749 - 1.20522i) q^{34} +(-5.02432 + 8.99951i) q^{35} +(2.58154 + 1.52829i) q^{36} +2.27739 q^{37} +(-0.764508 - 4.29133i) q^{38} +(-3.11039 - 3.14455i) q^{39} +(1.09000 - 1.95241i) q^{40} +(4.59916 - 7.96597i) q^{41} +(2.10844 - 7.70035i) q^{42} +(-5.05204 - 2.91679i) q^{43} +(5.43505 - 3.13793i) q^{44} +(6.70816 - 0.0234295i) q^{45} -3.48932i q^{46} +(-1.24051 - 2.14862i) q^{47} +(-0.457417 + 1.67056i) q^{48} -14.2470 q^{49} +(-0.144127 - 4.99792i) q^{50} +(-1.10257 + 4.02677i) q^{51} +(1.27680 - 2.21149i) q^{52} +(-0.0512773 + 0.0296049i) q^{53} +(-5.04046 + 1.26246i) q^{54} +(6.84072 - 12.2530i) q^{55} +4.60944 q^{56} +(6.16843 + 4.35321i) q^{57} -1.11433i q^{58} +(-4.22305 + 7.31454i) q^{59} +(1.03586 + 3.73189i) q^{60} +(-0.644175 - 1.11574i) q^{61} +(2.18537 - 3.78516i) q^{62} +(6.78296 + 12.0505i) q^{63} -1.00000 q^{64} +(-0.0823057 - 5.70944i) q^{65} +(-2.87069 + 10.4842i) q^{66} +(1.76268 + 3.05304i) q^{67} -2.41043 q^{68} +(4.25012 + 4.29680i) q^{69} +(8.85094 - 5.28164i) q^{70} +(1.26938 - 2.19862i) q^{71} +(-1.47153 - 2.61430i) q^{72} +(-10.9928 - 6.34671i) q^{73} +(-1.97227 - 1.13869i) q^{74} +(6.26514 + 5.97896i) q^{75} +(-1.48358 + 4.09866i) q^{76} +28.9282 q^{77} +(1.12140 + 4.27845i) q^{78} +(-8.43221 - 4.86834i) q^{79} +(-1.92017 + 1.14583i) q^{80} +(4.66917 - 7.69408i) q^{81} +(-7.96597 + 4.59916i) q^{82} -8.79050 q^{83} +(-5.67614 + 5.61448i) q^{84} +(-4.62845 + 2.76195i) q^{85} +(2.91679 + 5.05204i) q^{86} +(1.35729 + 1.37220i) q^{87} -6.27586 q^{88} +(-8.07900 - 13.9932i) q^{89} +(-5.82115 - 3.33379i) q^{90} +(10.1937 - 5.88535i) q^{91} +(-1.74466 + 3.02184i) q^{92} +(1.91938 + 7.32297i) q^{93} +2.48102i q^{94} +(1.84763 + 9.57007i) q^{95} +(1.23141 - 1.21804i) q^{96} +(3.17547 - 5.50008i) q^{97} +(12.3382 + 7.12349i) q^{98} +(-9.23514 - 16.4070i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 40 q^{4}+O(q^{10}) $ 80 * q + 40 * q^4	$ 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) $ 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.67546	−	0.439145i	0.967325	−	0.253540i
$3$	1.67546	−	0.439145i	0.967325	−	0.253540i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.95241	+	1.09000i	0.873143	+	0.487465i
$5$	1.95241	+	1.09000i	0.873143	+	0.487465i
$6$	−1.67056	−	0.457417i	−0.682003	−	0.186740i
$7$			4.60944i			1.74221i	0.491100	+	0.871103i	$0.336595\pi$
$7$			4.60944i			1.74221i	−0.491100	+	0.871103i	$0.663405\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.61430	−	1.47153i	0.871435	−	0.490512i
$10$	−1.14583	−	1.92017i	−0.362344	−	0.607213i
$11$		−	6.27586i		−	1.89224i	−0.323812	−	0.946121i	$-0.604965\pi$
$11$		−	6.27586i		−	1.89224i	0.323812	−	0.946121i	$-0.395035\pi$
$12$	1.21804	+	1.23141i	0.351617	+	0.355479i
$13$	−1.27680	−	2.21149i	−0.354121	−	0.613356i	0.632846	−	0.774278i	$-0.281887\pi$
$13$	−1.27680	−	2.21149i	−0.354121	−	0.613356i	−0.986967	+	0.160922i	$0.948553\pi$
$14$	2.30472	−	3.99190i	0.615963	−	1.06688i
$15$	3.74984	+	0.968866i	0.968204	+	0.250160i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.20522	+	2.08749i	−0.292308	+	0.506292i	−0.974355	−	0.225016i	$-0.927756\pi$
$17$	−1.20522	+	2.08749i	−0.292308	+	0.506292i	0.682047	+	0.731308i	$0.261090\pi$
$18$	−2.99982	−	0.0327655i	−0.707065	−	0.00772291i
$19$	2.80775	+	3.33415i	0.644142	+	0.764906i
$19$	2.80775	+	3.33415i	0.644142	+	0.764906i
$20$	0.0322312	+	2.23584i	0.00720712	+	0.499948i
$21$	2.02421	+	7.72292i	0.441719	+	1.68528i
$22$	−3.13793	+	5.43505i	−0.669009	+	1.15876i
$23$	1.74466	+	3.02184i	0.363786	+	0.630097i	0.988581	−	0.150693i	$-0.0481505\pi$
$23$	1.74466	+	3.02184i	0.363786	+	0.630097i	−0.624794	+	0.780789i	$0.714817\pi$
$24$	−0.439145	−	1.67546i	−0.0896400	−	0.342001i
$25$	2.62378	+	4.25626i	0.524756	+	0.851253i
$26$			2.55360i			0.500803i
$27$	3.73393	−	3.61355i	0.718596	−	0.695428i
$28$	−3.99190	+	2.30472i	−0.754397	+	0.435551i
$29$	0.557163	+	0.965035i	0.103463	+	0.179203i	0.913109	−	0.407715i	$-0.133674\pi$
$29$	0.557163	+	0.965035i	0.103463	+	0.179203i	−0.809646	+	0.586918i	$0.800341\pi$
$30$	−2.76302	−	2.71398i	−0.504457	−	0.495503i
$31$			4.37073i			0.785007i	0.919751	+	0.392503i	$0.128391\pi$
$31$			4.37073i			0.785007i	−0.919751	+	0.392503i	$0.871609\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−2.75601	−	10.5149i	−0.479760	−	1.83041i
$34$	2.08749	−	1.20522i	0.358002	−	0.206693i
$35$	−5.02432	+	8.99951i	−0.849264	+	1.52119i
$36$	2.58154	+	1.52829i	0.430256	+	0.254714i
$37$	2.27739			0.374400			0.187200	−	0.982322i	$-0.440059\pi$
$37$	2.27739			0.374400			0.187200	+	0.982322i	$0.440059\pi$
$38$	−0.764508	−	4.29133i	−0.124020	−	0.696146i
$39$	−3.11039	−	3.14455i	−0.498061	−	0.503530i
$40$	1.09000	−	1.95241i	0.172345	−	0.308703i
$41$	4.59916	−	7.96597i	0.718268	−	1.24408i	−0.243418	−	0.969921i	$-0.578269\pi$
$41$	4.59916	−	7.96597i	0.718268	−	1.24408i	0.961686	−	0.274154i	$-0.0883979\pi$
$42$	2.10844	−	7.70035i	0.325339	−	1.18819i
$43$	−5.05204	−	2.91679i	−0.770428	−	0.444807i	0.0625990	−	0.998039i	$-0.480061\pi$
$43$	−5.05204	−	2.91679i	−0.770428	−	0.444807i	−0.833027	+	0.553232i	$0.813394\pi$
$44$	5.43505	−	3.13793i	0.819365	−	0.473061i
$45$	6.70816	−	0.0234295i	0.999994	−	0.00349267i
$46$		−	3.48932i		−	0.514472i
$47$	−1.24051	−	2.14862i	−0.180947	−	0.313409i	0.761256	−	0.648451i	$-0.224583\pi$
$47$	−1.24051	−	2.14862i	−0.180947	−	0.313409i	−0.942203	+	0.335042i	$0.891250\pi$
$48$	−0.457417	+	1.67056i	−0.0660225	+	0.241125i
$49$	−14.2470			−2.03528
$50$	−0.144127	−	4.99792i	−0.0203827	−	0.706813i
$51$	−1.10257	+	4.02677i	−0.154391	+	0.563860i
$52$	1.27680	−	2.21149i	0.177061	−	0.306678i
$53$	−0.0512773	+	0.0296049i	−0.00704347	+	0.00406655i	−0.503518	−	0.863985i	$-0.667961\pi$
$53$	−0.0512773	+	0.0296049i	−0.00704347	+	0.00406655i	0.496474	+	0.868052i	$0.334628\pi$
$54$	−5.04046	+	1.26246i	−0.685919	+	0.171799i
$55$	6.84072	−	12.2530i	0.922402	−	1.65220i
$56$	4.60944			0.615963
$57$	6.16843	+	4.35321i	0.817029	+	0.576597i
$58$		−	1.11433i		−	0.146318i
$59$	−4.22305	+	7.31454i	−0.549795	+	0.952272i	0.448494	+	0.893786i	$0.351961\pi$
$59$	−4.22305	+	7.31454i	−0.549795	+	0.952272i	−0.998288	+	0.0584862i	$0.981373\pi$
$60$	1.03586	+	3.73189i	0.133729	+	0.481785i
$61$	−0.644175	−	1.11574i	−0.0824781	−	0.142856i	0.821836	−	0.569725i	$-0.192950\pi$
$61$	−0.644175	−	1.11574i	−0.0824781	−	0.142856i	−0.904314	+	0.426868i	$0.859617\pi$
$62$	2.18537	−	3.78516i	0.277542	−	0.480716i
$63$	6.78296	+	12.0505i	0.854572	+	1.51822i
$64$	−1.00000			−0.125000
$65$	−0.0823057	−	5.70944i	−0.0102088	−	0.708169i
$66$	−2.87069	+	10.4842i	−0.353357	+	1.29052i
$67$	1.76268	+	3.05304i	0.215345	+	0.372989i	0.953379	−	0.301775i	$-0.0975790\pi$
$67$	1.76268	+	3.05304i	0.215345	+	0.372989i	−0.738034	+	0.674763i	$0.764246\pi$
$68$	−2.41043			−0.292308
$69$	4.25012	+	4.29680i	0.511654	+	0.517274i
$70$	8.85094	−	5.28164i	1.05789	−	0.631277i
$71$	1.26938	−	2.19862i	0.150647	−	0.260929i	−0.780818	−	0.624758i	$-0.785198\pi$
$71$	1.26938	−	2.19862i	0.150647	−	0.260929i	0.931466	+	0.363829i	$0.118531\pi$
$72$	−1.47153	−	2.61430i	−0.173422	−	0.308099i
$73$	−10.9928	−	6.34671i	−1.28661	−	0.742827i	−0.308565	−	0.951203i	$-0.599849\pi$
$73$	−10.9928	−	6.34671i	−1.28661	−	0.742827i	−0.978049	+	0.208376i	$0.933182\pi$
$74$	−1.97227	−	1.13869i	−0.229272	−	0.132370i
$75$	6.26514	+	5.97896i	0.723436	+	0.690391i
$76$	−1.48358	+	4.09866i	−0.170179	+	0.470148i
$77$	28.9282			3.29668
$78$	1.12140	+	4.27845i	0.126974	+	0.484439i
$79$	−8.43221	−	4.86834i	−0.948698	−	0.547731i	−0.0560215	−	0.998430i	$-0.517842\pi$
$79$	−8.43221	−	4.86834i	−0.948698	−	0.547731i	−0.892676	+	0.450699i	$0.851175\pi$
$80$	−1.92017	+	1.14583i	−0.214682	+	0.128108i
$81$	4.66917	−	7.69408i	0.518797	−	0.854898i
$82$	−7.96597	+	4.59916i	−0.879695	+	0.507892i
$83$	−8.79050			−0.964883			−0.482442	−	0.875928i	$-0.660250\pi$
$83$	−8.79050			−0.964883			−0.482442	+	0.875928i	$0.660250\pi$
$84$	−5.67614	+	5.61448i	−0.619317	+	0.612590i
$85$	−4.62845	+	2.76195i	−0.502026	+	0.299575i
$86$	2.91679	+	5.05204i	0.314526	+	0.544775i
$87$	1.35729	+	1.37220i	0.145517	+	0.147115i
$88$	−6.27586			−0.669009
$89$	−8.07900	−	13.9932i	−0.856372	−	1.48328i	−0.875366	−	0.483460i	$-0.839380\pi$
$89$	−8.07900	−	13.9932i	−0.856372	−	1.48328i	0.0189945	−	0.999820i	$-0.493954\pi$
$90$	−5.82115	−	3.33379i	−0.613604	−	0.351412i
$91$	10.1937	−	5.88535i	1.06859	−	0.616952i
$92$	−1.74466	+	3.02184i	−0.181893	+	0.315048i
$93$	1.91938	+	7.32297i	0.199031	+	0.759356i
$94$			2.48102i			0.255897i
$95$	1.84763	+	9.57007i	0.189563	+	0.981869i
$96$	1.23141	−	1.21804i	0.125681	−	0.124316i
$97$	3.17547	−	5.50008i	0.322421	−	0.558449i	−0.658566	−	0.752523i	$-0.728837\pi$
$97$	3.17547	−	5.50008i	0.322421	−	0.558449i	0.980987	+	0.194074i	$0.0621701\pi$
$98$	12.3382	+	7.12349i	1.24635	+	0.719581i
$99$	−9.23514	−	16.4070i	−0.928167	−	1.64897i
$100$	−2.37414	+	4.40039i	−0.237414	+	0.440039i
$101$	−13.5746	+	7.83727i	−1.35072	+	0.779838i	−0.988350	−	0.152197i	$-0.951365\pi$
$101$	−13.5746	+	7.83727i	−1.35072	+	0.779838i	−0.362369	+	0.932035i	$0.618032\pi$
$102$	2.96824	−	2.93600i	0.293900	−	0.290707i
$103$	15.4529			1.52262			0.761311	−	0.648387i	$-0.224556\pi$
$103$	15.4529			1.52262			0.761311	+	0.648387i	$0.224556\pi$
$104$	−2.21149	+	1.27680i	−0.216854	+	0.125201i
$105$	−4.46593	+	17.2847i	−0.435831	+	1.68681i
$106$	0.0592099			0.00575097
$107$		−	4.71448i		−	0.455766i	−0.973689	−	0.227883i	$-0.926820\pi$
$107$		−	4.71448i		−	0.455766i	0.973689	−	0.227883i	$-0.0731804\pi$
$108$	4.99639	+	1.42691i	0.480778	+	0.137304i
$109$	6.86919	+	3.96593i	0.657949	+	0.379867i	0.791495	−	0.611176i	$-0.209303\pi$
$109$	6.86919	+	3.96593i	0.657949	+	0.379867i	−0.133546	+	0.991043i	$0.542636\pi$
$110$	−12.0507	+	7.19107i	−1.14899	+	0.685642i
$111$	3.81566	−	1.00010i	0.362166	−	0.0949255i
$112$	−3.99190	−	2.30472i	−0.377199	−	0.217776i
$113$		−	14.0526i		−	1.32196i	−0.750404	−	0.660979i	$-0.770141\pi$
$113$		−	14.0526i		−	1.32196i	0.750404	−	0.660979i	$-0.229859\pi$
$114$	−3.16541	−	6.85421i	−0.296468	−	0.641955i
$115$	0.112465	+	7.80154i	0.0104874	+	0.727497i
$116$	−0.557163	+	0.965035i	−0.0517313	+	0.0896013i
$117$	−6.59223	−	3.90264i	−0.609452	−	0.360799i
$118$	7.31454	−	4.22305i	0.673358	−	0.388764i
$119$	−9.62219	−	5.55537i	−0.882065	−	0.509260i
$120$	0.968866	−	3.74984i	0.0884450	−	0.342312i
$121$	−28.3864			−2.58058
$122$			1.28835i			0.116642i
$123$	4.20747	−	15.3663i	0.379375	−	1.38554i
$124$	−3.78516	+	2.18537i	−0.339918	+	0.196252i
$125$	0.483334	+	11.1699i	0.0432307	+	0.999065i
$126$	0.151031	−	13.8275i	0.0134549	−	1.23185i
$127$	−4.20396	−	7.28147i	−0.373041	−	0.646126i	0.616991	−	0.786970i	$-0.288352\pi$
$127$	−4.20396	−	7.28147i	−0.373041	−	0.646126i	−0.990032	+	0.140845i	$0.955018\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−9.74536	−	2.66839i	−0.858031	−	0.234938i
$130$	−2.78344	+	4.98567i	−0.244124	+	0.437272i
$131$	4.94573	+	2.85542i	0.432110	+	0.249479i	0.700245	−	0.713902i	$-0.253074\pi$
$131$	4.94573	+	2.85542i	0.432110	+	0.249479i	−0.268135	+	0.963381i	$0.586407\pi$
$132$	7.72819	−	7.64424i	0.672652	−	0.665345i
$133$	−15.3686	+	12.9422i	−1.33262	+	1.12223i
$134$		−	3.52535i		−	0.304544i
$135$	11.2289	−	2.98511i	0.966433	−	0.256917i
$136$	2.08749	+	1.20522i	0.179001	+	0.103346i
$137$	4.51364	+	7.81786i	0.385627	+	0.667925i	0.991856	−	0.127365i	$-0.0406520\pi$
$137$	4.51364	+	7.81786i	0.385627	+	0.667925i	−0.606229	+	0.795290i	$0.707319\pi$
$138$	−1.53231	−	5.84620i	−0.130439	−	0.497661i
$139$	7.12104	+	12.3340i	0.603999	+	1.04616i	0.992209	+	0.124586i	$0.0397603\pi$
$139$	7.12104	+	12.3340i	0.603999	+	1.04616i	−0.388210	+	0.921571i	$0.626906\pi$
$140$	−10.3060	+	0.148568i	−0.871012	+	0.0125563i
$141$	−3.02197	−	3.05516i	−0.254496	−	0.257291i
$142$	−2.19862	+	1.26938i	−0.184504	+	0.106524i
$143$	−13.8790	+	8.01303i	−1.16062	+	0.670083i
$144$	−0.0327655	+	2.99982i	−0.00273046	+	0.249985i
$145$	0.0359161	+	2.49145i	0.00298267	+	0.206904i
$146$	6.34671	+	10.9928i	0.525258	+	0.909773i
$147$	−23.8702	+	6.25648i	−1.96878	+	0.516026i
$148$	1.13869	+	1.97227i	0.0936000	+	0.162120i
$149$	−9.49064	−	5.47943i	−0.777504	−	0.448892i	0.0580411	−	0.998314i	$-0.481515\pi$
$149$	−9.49064	−	5.47943i	−0.777504	−	0.448892i	−0.835545	+	0.549422i	$0.814848\pi$
$150$	−2.43629	−	8.31050i	−0.198922	−	0.678550i
$151$		−	2.01053i		−	0.163615i	−0.996648	−	0.0818073i	$-0.973931\pi$
$151$		−	2.01053i		−	0.163615i	0.996648	−	0.0818073i	$-0.0260692\pi$
$152$	3.33415	−	2.80775i	0.270435	−	0.227739i
$153$	−0.0789790	+	7.23086i	−0.00638508	+	0.584581i
$154$	−25.0526	−	14.4641i	−2.01879	−	1.16555i
$155$	−4.76412	+	8.53344i	−0.382663	+	0.685423i
$156$	1.16806	−	4.26595i	0.0935199	−	0.341549i
$157$	−2.18249	−	1.26006i	−0.174182	−	0.100564i	0.410374	−	0.911917i	$-0.365398\pi$
$157$	−2.18249	−	1.26006i	−0.174182	−	0.100564i	−0.584556	+	0.811353i	$0.698731\pi$
$158$	4.86834	+	8.43221i	0.387304	+	0.670831i
$159$	−0.0729119	+	0.0721199i	−0.00578229	+	0.00571948i
$160$	2.23584	−	0.0322312i	0.176758	−	0.00254810i
$161$	−13.9290	+	8.04190i	−1.09776	+	0.633791i
$162$	−7.89066	+	4.32868i	−0.619949	+	0.340093i
$163$			4.47356i			0.350396i	0.984533	+	0.175198i	$0.0560566\pi$
$163$			4.47356i			0.350396i	−0.984533	+	0.175198i	$0.943943\pi$
$164$	9.19831			0.718268
$165$	6.08047	−	23.5335i	0.473364	−	1.83208i
$166$	7.61280	+	4.39525i	0.590868	+	0.341138i
$167$	−7.00410	+	4.04382i	−0.541993	+	0.312920i	−0.745886	−	0.666073i	$-0.767974\pi$
$167$	−7.00410	+	4.04382i	−0.541993	+	0.312920i	0.203893	+	0.978993i	$0.434641\pi$
$168$	7.72292	−	2.02421i	0.595836	−	0.156171i
$169$	3.23955	−	5.61107i	0.249196	−	0.431621i
$170$	5.38933	−	0.0776911i	0.413343	−	0.00595863i
$171$	12.2466	+	4.58478i	0.936523	+	0.350607i
$172$		−	5.83359i		−	0.444807i
$173$	−9.62554	−	5.55731i	−0.731816	−	0.422514i	0.0872698	−	0.996185i	$-0.472186\pi$
$173$	−9.62554	−	5.55731i	−0.731816	−	0.422514i	−0.819086	+	0.573670i	$0.805519\pi$
$174$	−0.489351	−	1.86700i	−0.0370976	−	0.141537i
$175$	−19.6190	+	12.0942i	−1.48306	+	0.914233i
$176$	5.43505	+	3.13793i	0.409683	+	0.236530i
$177$	−3.86340	+	14.1097i	−0.290391	+	1.06055i
$178$			16.1580i			1.21109i
$179$	−4.26112			−0.318491			−0.159245	−	0.987239i	$-0.550906\pi$
$179$	−4.26112			−0.318491			−0.159245	+	0.987239i	$0.550906\pi$
$180$	3.37437	+	5.79772i	0.251511	+	0.432137i
$181$	16.7578	−	9.67510i	1.24559	−	0.719145i	0.275367	−	0.961339i	$-0.411201\pi$
$181$	16.7578	−	9.67510i	1.24559	−	0.719145i	0.970228	+	0.242195i	$0.0778672\pi$
$182$	−11.7707			−0.872502
$183$	−1.56926	−	1.58649i	−0.116003	−	0.117277i
$184$	3.02184	−	1.74466i	0.222773	−	0.128618i
$185$	4.44638	+	2.48236i	0.326905	+	0.182507i
$186$	1.99925	−	7.30157i	0.146592	−	0.535377i
$187$	13.1008	+	7.56376i	0.958027	+	0.553117i
$188$	1.24051	−	2.14862i	0.0904734	−	0.156704i
$189$	16.6565	+	17.2114i	1.21158	+	1.25194i
$190$	3.18494	−	9.21174i	0.231060	−	0.668290i
$191$			3.83614i			0.277573i	0.990322	+	0.138786i	$0.0443202\pi$
$191$			3.83614i			0.277573i	−0.990322	+	0.138786i	$0.955680\pi$
$192$	−1.67546	+	0.439145i	−0.120916	+	0.0316925i
$193$	7.45236	−	12.9079i	0.536432	−	0.929128i	−0.462660	−	0.886536i	$-0.653105\pi$
$193$	7.45236	−	12.9079i	0.536432	−	0.929128i	0.999093	−	0.0425924i	$-0.0135617\pi$
$194$	−5.50008	+	3.17547i	−0.394883	+	0.227986i
$195$	−2.64517	−	9.52977i	−0.189424	−	0.682441i
$196$	−7.12349	−	12.3382i	−0.508820	−	0.881303i
$197$	−17.6150			−1.25502			−0.627508	−	0.778610i	$-0.715925\pi$
$197$	−17.6150			−1.25502			−0.627508	+	0.778610i	$0.715925\pi$
$198$	−0.205632	+	18.8265i	−0.0146136	+	1.33794i
$199$	−2.41926	−	4.19028i	−0.171497	−	0.297041i	0.767447	−	0.641113i	$-0.221527\pi$
$199$	−2.41926	−	4.19028i	−0.171497	−	0.297041i	−0.938943	+	0.344072i	$0.888194\pi$
$200$	4.25626	−	2.62378i	0.300963	−	0.185529i
$201$	4.29401	+	4.34117i	0.302876	+	0.306203i
$202$	15.6745			1.10286
$203$	−4.44828	+	2.56821i	−0.312208	+	0.180253i
$204$	−4.03857	+	1.05853i	−0.282757	+	0.0741118i
$205$	17.6624	−	10.5397i	1.23359	−	0.736125i
$206$	−13.3826	−	7.72646i	−0.932412	−	0.538328i
$207$	9.00780	+	5.33267i	0.626086	+	0.370647i
$208$	2.55360			0.177061
$209$	20.9246	−	17.6210i	1.44739	−	1.21887i
$210$	12.5100	−	12.7360i	0.863269	−	0.878868i
$211$	−4.49219	−	2.59357i	−0.309255	−	0.178548i	0.337338	−	0.941384i	$-0.390473\pi$
$211$	−4.49219	−	2.59357i	−0.309255	−	0.178548i	−0.646593	+	0.762835i	$0.723807\pi$
$212$	−0.0512773	−	0.0296049i	−0.00352174	−	0.00203328i
$213$	1.16127	−	4.24114i	0.0795689	−	0.290598i
$214$	−2.35724	+	4.08286i	−0.161138	+	0.279099i
$215$	−6.68431	−	11.2015i	−0.455866	−	0.763937i
$216$	−3.61355	−	3.73393i	−0.245871	−	0.254062i
$217$	−20.1466			−1.36764
$218$	−3.96593	−	6.86919i	−0.268607	−	0.465240i
$219$	−21.2051	−	5.80620i	−1.43291	−	0.392346i
$220$	14.0318	−	0.202278i	0.946023	−	0.0136376i
$221$	6.15529			0.414049
$222$	−3.80451	−	1.04172i	−0.255342	−	0.0699154i
$223$	−0.325555	+	0.563878i	−0.0218008	+	0.0377601i	−0.876720	−	0.481001i	$-0.840273\pi$
$223$	−0.325555	+	0.563878i	−0.0218008	+	0.0377601i	0.854919	+	0.518761i	$0.173607\pi$
$224$	2.30472	+	3.99190i	0.153991	+	0.266720i
$225$	13.1226	+	7.26619i	0.874840	+	0.484412i
$226$	−7.02630	+	12.1699i	−0.467383	+	0.809531i
$227$			8.15722i			0.541414i	0.962662	+	0.270707i	$0.0872575\pi$
$227$			8.15722i			0.541414i	−0.962662	+	0.270707i	$0.912743\pi$
$228$	−0.685774	+	7.51862i	−0.0454165	+	0.497933i
$229$	6.22202			0.411162			0.205581	−	0.978640i	$-0.434092\pi$
$229$	6.22202			0.411162			0.205581	+	0.978640i	$0.434092\pi$
$230$	3.80337	−	6.81256i	0.250787	−	0.449207i
$231$	48.4680	−	12.7037i	3.18896	−	0.835840i
$232$	0.965035	−	0.557163i	0.0633577	−	0.0365796i
$233$	13.8286	−	23.9519i	0.905942	−	1.56914i	0.0862948	−	0.996270i	$-0.472497\pi$
$233$	13.8286	−	23.9519i	0.905942	−	1.56914i	0.819647	−	0.572868i	$-0.194169\pi$
$234$	3.75772	+	6.67590i	0.245650	+	0.436417i
$235$	−0.0799662	−	5.54715i	−0.00521642	−	0.361856i
$236$	−8.44611			−0.549795
$237$	−16.2657	−	4.45373i	−1.05657	−	0.289301i
$238$	5.55537	+	9.62219i	0.360101	+	0.623714i
$239$			14.0092i			0.906177i	0.891465	+	0.453089i	$0.149678\pi$
$239$			14.0092i			0.906177i	−0.891465	+	0.453089i	$0.850322\pi$
$240$	−2.71398	+	2.76302i	−0.175187	+	0.178352i
$241$	−9.49382	+	5.48126i	−0.611551	+	0.353079i	−0.773572	−	0.633708i	$-0.781532\pi$
$241$	−9.49382	+	5.48126i	−0.611551	+	0.353079i	0.162021	+	0.986787i	$0.448199\pi$
$242$	24.5834	+	14.1932i	1.58028	+	0.912374i
$243$	4.44418	−	14.9415i	0.285094	−	0.958500i
$244$	0.644175	−	1.11574i	0.0412391	−	0.0714281i
$245$	−27.8159	−	15.5293i	−1.77709	−	0.992128i
$246$	−11.3269	+	11.2039i	−0.722179	+	0.714334i
$247$	3.78848	−	10.4663i	0.241055	−	0.665958i
$248$	4.37073			0.277542
$249$	−14.7281	+	3.86030i	−0.933355	+	0.244637i
$250$	5.16636	−	9.91507i	0.326750	−	0.627084i
$251$	−12.7805	+	7.37881i	−0.806697	+	0.465747i	−0.845807	−	0.533488i	$-0.820881\pi$
$251$	−12.7805	+	7.37881i	−0.806697	+	0.465747i	0.0391106	+	0.999235i	$0.487548\pi$
$252$	−7.04455	+	11.8995i	−0.443765	+	0.749595i
$253$	18.9646	−	10.9492i	1.19230	−	0.688372i
$254$			8.40792i			0.527560i
$255$	−6.54187	+	6.66008i	−0.409668	+	0.417070i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.44940	+	1.41416i	−0.152789	+	0.0882129i	−0.574445	−	0.818543i	$-0.694782\pi$
$257$	−2.44940	+	1.41416i	−0.152789	+	0.0882129i	0.421656	+	0.906756i	$0.361449\pi$
$258$	7.10554	+	7.18357i	0.442371	+	0.447230i
$259$			10.4975i			0.652282i
$260$	4.90337	−	2.92600i	0.304094	−	0.181463i
$261$	2.87668	+	1.70301i	0.178062	+	0.105414i
$262$	−2.85542	−	4.94573i	−0.176408	−	0.305548i
$263$	4.38223	−	7.59024i	0.270220	−	0.468034i	−0.698698	−	0.715417i	$-0.746237\pi$
$263$	4.38223	−	7.59024i	0.270220	−	0.468034i	0.968918	+	0.247382i	$0.0795703\pi$
$264$	−10.5149	+	2.75601i	−0.647149	+	0.169621i
$265$	−0.132384	+	0.00190841i	−0.00813226	+	0.000117232i
$266$	19.7807	−	3.52396i	1.21283	−	0.216068i
$267$	−19.6811	−	19.8972i	−1.20446	−	1.21769i
$268$	−1.76268	+	3.05304i	−0.107673	+	0.186494i
$269$	4.18520	−	7.24897i	0.255176	−	0.441978i	−0.709767	−	0.704436i	$-0.751200\pi$
$269$	4.18520	−	7.24897i	0.255176	−	0.441978i	0.964943	+	0.262458i	$0.0845333\pi$
$270$	−11.2171	−	3.02929i	−0.682651	−	0.184357i
$271$	−12.8353	+	22.2314i	−0.779690	+	1.35046i	0.152430	+	0.988314i	$0.451290\pi$
$271$	−12.8353	+	22.2314i	−0.779690	+	1.35046i	−0.932120	+	0.362149i	$0.882043\pi$
$272$	−1.20522	−	2.08749i	−0.0730769	−	0.126573i
$273$	14.4946	−	14.3372i	0.877254	−	0.867724i
$274$		−	9.02729i		−	0.545358i
$275$	26.7117	−	16.4665i	1.61078	−	0.992965i
$276$	−1.59607	+	5.82911i	−0.0960724	+	0.350871i
$277$		−	14.7374i		−	0.885482i	−0.896650	−	0.442741i	$-0.854006\pi$
$277$		−	14.7374i		−	0.885482i	0.896650	−	0.442741i	$-0.145994\pi$
$278$		−	14.2421i		−	0.854184i
$279$	6.43168	+	11.4264i	0.385055	+	0.684082i
$280$	8.99951	+	5.02432i	0.537823	+	0.300260i
$281$	−2.75553	−	4.77271i	−0.164381	−	0.284716i	0.772054	−	0.635557i	$-0.219229\pi$
$281$	−2.75553	−	4.77271i	−0.164381	−	0.284716i	−0.936435	+	0.350840i	$0.885896\pi$
$282$	1.08953	+	4.15683i	0.0648803	+	0.247536i
$283$	26.7533	+	15.4460i	1.59032	+	0.918172i	0.993251	+	0.115983i	$0.0370019\pi$
$283$	26.7533	+	15.4460i	1.59032	+	0.918172i	0.597070	+	0.802189i	$0.296331\pi$
$284$	2.53875			0.150647
$285$	7.29827	+	15.2229i	0.432312	+	0.901724i
$286$	16.0261			0.947641
$287$	36.7187	+	21.1996i	2.16744	+	1.25137i
$288$	1.52829	−	2.58154i	0.0900551	−	0.152119i
$289$	5.59491	+	9.69067i	0.329112	+	0.570039i
$290$	1.21462	−	2.17562i	0.0713250	−	0.127757i
$291$	2.90504	−	10.6096i	0.170296	−	0.621948i
$292$		−	12.6934i		−	0.742827i
$293$			26.7703i			1.56394i	0.623318	+	0.781968i	$0.285784\pi$
$293$			26.7703i			1.56394i	−0.623318	+	0.781968i	$0.714216\pi$
$294$	23.8004	+	6.51681i	1.38807	+	0.380068i
$295$	−16.2180	+	9.67781i	−0.944248	+	0.563464i
$296$		−	2.27739i		−	0.132370i
$297$	−22.6781	−	23.4336i	−1.31592	−	1.35976i
$298$	5.47943	+	9.49064i	0.317415	+	0.549778i
$299$	4.45517	−	7.71657i	0.257649	−	0.446261i
$300$	−2.04536	+	8.41525i	−0.118089	+	0.485855i
$301$	13.4448	−	23.2871i	0.774945	−	1.34224i
$302$	−1.00527	+	1.74117i	−0.0578465	+	0.100193i
$303$	−19.3019	+	19.0922i	−1.10886	+	1.09682i
$304$	−4.29133	+	0.764508i	−0.246125	+	0.0438475i
$305$	−0.0415250	−	2.88054i	−0.00237772	−	0.164939i
$306$	3.68383	−	6.22262i	0.210590	−	0.355724i
$307$	−14.0443	+	24.3254i	−0.801548	+	1.38832i	0.117048	+	0.993126i	$0.462657\pi$
$307$	−14.0443	+	24.3254i	−0.801548	+	1.38832i	−0.918597	+	0.395196i	$0.870677\pi$
$308$	14.4641	+	25.0526i	0.824169	+	1.42750i
$309$	25.8907	−	6.78607i	1.47287	−	0.386046i
$310$	8.39257	−	5.00812i	0.476666	−	0.284442i
$311$			19.3800i			1.09894i	0.835513	+	0.549470i	$0.185170\pi$
$311$			19.3800i			1.09894i	−0.835513	+	0.549470i	$0.814830\pi$
$312$	−3.14455	+	3.11039i	−0.178025	+	0.176091i
$313$	−21.0959	+	12.1797i	−1.19241	+	0.688439i	−0.958853	−	0.283904i	$-0.908370\pi$
$313$	−21.0959	+	12.1797i	−1.19241	+	0.688439i	−0.233558	+	0.972343i	$0.575037\pi$
$314$	1.26006	+	2.18249i	0.0711094	+	0.123165i
$315$	0.107997	+	30.9209i	0.00608494	+	1.74220i
$316$		−	9.73668i		−	0.547731i
$317$	22.7893	−	13.1574i	1.27997	−	0.738992i	0.303129	−	0.952949i	$-0.401969\pi$
$317$	22.7893	−	13.1574i	1.27997	−	0.738992i	0.976843	+	0.213957i	$0.0686352\pi$
$318$	0.0992035	−	0.0260017i	0.00556306	−	0.00145810i
$319$	6.05642	−	3.49668i	0.339095	−	0.195776i
$320$	−1.95241	−	1.09000i	−0.109143	−	0.0609331i
$321$	−2.07034	−	7.89890i	−0.115555	−	0.440874i
$322$	16.0838			0.896316
$323$	−10.3440	+	1.84279i	−0.575553	+	0.102536i
$324$	8.99785	+	0.196581i	0.499881	+	0.0109212i
$325$	6.06262	−	11.2369i	0.336294	−	0.623309i
$326$	2.23678	−	3.87421i	0.123884	−	0.214573i
$327$	13.2506	+	3.62817i	0.732762	+	0.200638i
$328$	−7.96597	−	4.59916i	−0.439847	−	0.253946i
$329$	9.90396	−	5.71805i	0.546023	−	0.315247i
$330$	−17.0326	+	17.3403i	−0.937612	+	0.954555i
$331$			23.9173i			1.31461i	0.753624	+	0.657306i	$0.228304\pi$
$331$			23.9173i			1.31461i	−0.753624	+	0.657306i	$0.771696\pi$
$332$	−4.39525	−	7.61280i	−0.241221	−	0.417807i
$333$	5.95378	−	3.35125i	0.326265	−	0.183648i
$334$	8.08764			0.442536
$335$	0.113626	+	7.88211i	0.00620807	+	0.430646i
$336$	−7.70035	−	2.10844i	−0.420089	−	0.115025i
$337$	−7.94689	+	13.7644i	−0.432895	+	0.749796i	−0.997121	−	0.0758243i	$-0.975841\pi$
$337$	−7.94689	+	13.7644i	−0.432895	+	0.749796i	0.564226	+	0.825620i	$0.309175\pi$
$338$	−5.61107	+	3.23955i	−0.305202	+	0.176208i
$339$	−6.17113	−	23.5445i	−0.335170	−	1.27876i
$340$	−4.70614	−	2.62738i	−0.255226	−	0.142490i
$341$	27.4301			1.48542
$342$	−8.31350	−	10.0938i	−0.449543	−	0.545813i
$343$		−	33.4045i		−	1.80367i
$344$	−2.91679	+	5.05204i	−0.157263	+	0.272388i
$345$	3.61443	+	13.0217i	0.194595	+	0.701067i
$346$	5.55731	+	9.62554i	0.298763	+	0.517472i
$347$	6.74308	−	11.6794i	0.361988	−	0.626981i	−0.626300	−	0.779582i	$-0.715432\pi$
$347$	6.74308	−	11.6794i	0.361988	−	0.626981i	0.988288	+	0.152601i	$0.0487649\pi$
$348$	−0.509712	+	1.86155i	−0.0273235	+	0.0997895i
$349$	−8.34194			−0.446534			−0.223267	−	0.974757i	$-0.571672\pi$
$349$	−8.34194			−0.446534			−0.223267	+	0.974757i	$0.571672\pi$
$350$	23.0376	−	0.664347i	1.23141	−	0.0355108i
$351$	−12.7588	−	3.64376i	−0.681015	−	0.194489i
$352$	−3.13793	−	5.43505i	−0.167252	−	0.289689i
$353$	8.00477			0.426051			0.213025	−	0.977047i	$-0.431668\pi$
$353$	8.00477			0.426051			0.213025	+	0.977047i	$0.431668\pi$
$354$	10.4007	−	10.2877i	0.552789	−	0.546784i
$355$	4.87485	−	2.90898i	0.258730	−	0.154393i
$356$	8.07900	−	13.9932i	0.428186	−	0.741640i
$357$	−18.5612	−	5.08225i	−0.982361	−	0.268981i
$358$	3.69023	+	2.13056i	0.195035	+	0.112603i
$359$	−7.33647	−	4.23571i	−0.387204	−	0.223552i	0.293744	−	0.955884i	$-0.405099\pi$
$359$	−7.33647	−	4.23571i	−0.387204	−	0.223552i	−0.680948	+	0.732332i	$0.738432\pi$
$360$	−0.0234295	−	6.70816i	−0.00123484	−	0.353551i
$361$	−3.23309	+	18.7229i	−0.170163	+	0.985416i
$362$	−19.3502			−1.01702
$363$	−47.5602	+	12.4657i	−2.49626	+	0.654282i
$364$	10.1937	+	5.88535i	0.534296	+	0.308476i
$365$	−14.5445	−	24.3736i	−0.761295	−	1.27577i
$366$	0.565772	+	2.15857i	0.0295734	+	0.112830i
$367$	21.8594	−	12.6205i	1.14105	−	0.658787i	0.194362	−	0.980930i	$-0.437736\pi$
$367$	21.8594	−	12.6205i	1.14105	−	0.658787i	0.946691	+	0.322143i	$0.104403\pi$
$368$	−3.48932			−0.181893
$369$	0.301388	−	27.5933i	0.0156896	−	1.43645i
$370$	−2.60950	−	4.37298i	−0.135661	−	0.227340i
$371$	−0.136462	−	0.236360i	−0.00708477	−	0.0122712i
$372$	−5.38218	+	5.32372i	−0.279053	+	0.276022i
$373$	27.8240			1.44067			0.720337	−	0.693624i	$-0.243987\pi$
$373$	27.8240			1.44067			0.720337	+	0.693624i	$0.243987\pi$
$374$	−7.56376	−	13.1008i	−0.391113	−	0.677427i
$375$	5.71500	+	18.5024i	0.295121	+	0.955460i
$376$	−2.14862	+	1.24051i	−0.110807	+	0.0639743i
$377$	1.42277	−	2.46432i	0.0732766	−	0.126919i
$378$	−5.81923	−	23.2337i	−0.299309	−	1.19501i
$379$			17.6962i			0.908995i	0.890748	+	0.454497i	$0.150181\pi$
$379$			17.6962i			0.908995i	−0.890748	+	0.454497i	$0.849819\pi$
$380$	−7.36411	+	6.38513i	−0.377771	+	0.327550i
$381$	−10.2412	−	10.3536i	−0.524671	−	0.530433i
$382$	1.91807	−	3.32219i	0.0981369	−	0.169978i
$383$	−19.2767	−	11.1294i	−0.984991	−	0.568685i	−0.0812179	−	0.996696i	$-0.525881\pi$
$383$	−19.2767	−	11.1294i	−0.984991	−	0.568685i	−0.903773	+	0.428011i	$0.859214\pi$
$384$	1.67056	+	0.457417i	0.0852504	+	0.0233425i
$385$	56.4796	+	31.5319i	2.87847	+	1.60701i
$386$	−12.9079	+	7.45236i	−0.656993	+	0.379315i
$387$	−17.4997	−	0.191141i	−0.889561	−	0.00971622i
$388$	6.35095			0.322421
$389$	8.70929	−	5.02831i	0.441579	−	0.254946i	−0.262688	−	0.964881i	$-0.584609\pi$
$389$	8.70929	−	5.02831i	0.441579	−	0.254946i	0.704267	+	0.709935i	$0.251276\pi$
$390$	−2.47410	+	9.57561i	−0.125281	+	0.484880i
$391$	−8.41076			−0.425350
$392$			14.2470i			0.719581i
$393$	9.54029	+	2.61223i	0.481244	+	0.131770i
$394$	15.2550	+	8.80750i	0.768538	+	0.443715i
$395$	−11.1566	−	18.6961i	−0.561349	−	0.940704i
$396$	9.59131	−	16.2014i	0.481981	−	0.814150i
$397$	−18.5066	−	10.6848i	−0.928819	−	0.536254i	−0.0423812	−	0.999102i	$-0.513494\pi$
$397$	−18.5066	−	10.6848i	−0.928819	−	0.536254i	−0.886438	+	0.462848i	$0.846828\pi$
$398$			4.83852i			0.242533i
$399$	−20.0659	+	28.4330i	−1.00455	+	1.42343i
$400$	−4.99792	+	0.144127i	−0.249896	+	0.00720637i
$401$	−7.33894	+	12.7114i	−0.366489	+	0.634778i	−0.989014	−	0.147822i	$-0.952774\pi$
$401$	−7.33894	+	12.7114i	−0.366489	+	0.634778i	0.622525	+	0.782600i	$0.286107\pi$
$402$	−1.54814	−	5.90657i	−0.0772142	−	0.294593i
$403$	9.66581	−	5.58056i	0.481488	−	0.277987i
$404$	−13.5746	−	7.83727i	−0.675359	−	0.389919i
$405$	17.5027	−	9.93255i	0.869716	−	0.493552i
$406$	5.13643			0.254917
$407$		−	14.2926i		−	0.708456i
$408$	4.02677	+	1.10257i	0.199355	+	0.0545855i
$409$	26.1399	−	15.0919i	1.29254	−	0.746246i	0.313432	−	0.949611i	$-0.398521\pi$
$409$	26.1399	−	15.0919i	1.29254	−	0.746246i	0.979103	+	0.203365i	$0.0651878\pi$
$410$	−20.5659	+	0.296473i	−1.01568	+	0.0146417i
$411$	10.9956	+	11.1163i	0.542372	+	0.548328i
$412$	7.72646	+	13.3826i	0.380655	+	0.659315i
$413$	−33.7160	−	19.4659i	−1.65905	−	0.957856i
$414$	−5.13465	−	9.12213i	−0.252354	−	0.448328i
$415$	−17.1626	−	9.58169i	−0.842481	−	0.470347i
$416$	−2.21149	−	1.27680i	−0.108427	−	0.0626004i
$417$	17.3474	+	17.5379i	0.849506	+	0.858836i
$418$	−26.9318	+	4.79794i	−1.31728	+	0.234675i
$419$			8.90336i			0.434958i	0.976065	+	0.217479i	$0.0697833\pi$
$419$			8.90336i			0.434958i	−0.976065	+	0.217479i	$0.930217\pi$
$420$	−17.2019	+	4.77473i	−0.839368	+	0.232983i
$421$	14.3115	+	8.26272i	0.697498	+	0.402701i	0.806415	−	0.591350i	$-0.201405\pi$
$421$	14.3115	+	8.26272i	0.697498	+	0.402701i	−0.108917	+	0.994051i	$0.534738\pi$
$422$	2.59357	+	4.49219i	0.126253	+	0.218676i
$423$	−6.40484	−	3.79170i	−0.311414	−	0.184359i
$424$	0.0296049	+	0.0512773i	0.00143774	+	0.00249024i
$425$	−12.0471	+	0.347409i	−0.584373	+	0.0168518i
$426$	−3.12626	+	3.09230i	−0.151468	+	0.149822i
$427$	5.14296	−	2.96929i	0.248885	−	0.143694i
$428$	4.08286	−	2.35724i	0.197352	−	0.113942i
$429$	−19.7347	+	19.5204i	−0.952802	+	0.942451i
$430$	0.188024	+	13.0429i	0.00906730	+	0.628987i
$431$	−8.40089	−	14.5508i	−0.404657	−	0.700886i	0.589625	−	0.807677i	$-0.299276\pi$
$431$	−8.40089	−	14.5508i	−0.404657	−	0.700886i	−0.994281	+	0.106791i	$0.965942\pi$
$432$	1.26246	+	5.04046i	0.0607400	+	0.242509i
$433$	−18.6240	−	32.2577i	−0.895013	−	1.55021i	−0.833789	−	0.552084i	$-0.813833\pi$
$433$	−18.6240	−	32.2577i	−0.895013	−	1.55021i	−0.0612243	−	0.998124i	$-0.519501\pi$
$434$	17.4475	+	10.0733i	0.837507	+	0.483535i
$435$	1.15428	+	4.15854i	0.0553436	+	0.199387i
$436$			7.93186i			0.379867i
$437$	−5.17669	+	14.3015i	−0.247635	+	0.684134i
$438$	15.4611	+	15.6309i	0.738759	+	0.746872i
$439$	−3.23579	−	1.86818i	−0.154436	−	0.0891635i	0.420791	−	0.907158i	$-0.361753\pi$
$439$	−3.23579	−	1.86818i	−0.154436	−	0.0891635i	−0.575226	+	0.817994i	$0.695086\pi$
$440$	−12.2530	−	6.84072i	−0.584140	−	0.326118i
$441$	−37.2459	+	20.9649i	−1.77361	+	0.998329i
$442$	−5.33063	−	3.07764i	−0.253552	−	0.146389i
$443$	−4.87764	−	8.44831i	−0.231744	−	0.401392i	0.726578	−	0.687084i	$-0.241110\pi$
$443$	−4.87764	−	8.44831i	−0.231744	−	0.401392i	−0.958321	+	0.285693i	$0.907776\pi$
$444$	2.77394	+	2.80441i	0.131646	+	0.133091i
$445$	−0.520792	−	36.1266i	−0.0246879	−	1.71257i
$446$	0.563878	−	0.325555i	0.0267004	−	0.0154155i
$447$	−18.3074	−	5.01277i	−0.865911	−	0.237096i
$448$		−	4.60944i		−	0.217776i
$449$	−20.1146			−0.949265			−0.474633	−	0.880184i	$-0.657419\pi$
$449$	−20.1146			−0.949265			−0.474633	+	0.880184i	$0.657419\pi$
$450$	−7.73141	−	12.8540i	−0.364462	−	0.605943i
$451$	−49.9933	−	28.8637i	−2.35409	−	1.35914i
$452$	12.1699	−	7.02630i	0.572425	−	0.330490i
$453$	−0.882913	−	3.36855i	−0.0414829	−	0.158268i
$454$	4.07861	−	7.06436i	0.191419	−	0.331547i
$455$	26.3173	−	0.379384i	1.23378	−	0.0177858i
$456$	4.35321	−	6.16843i	0.203858	−	0.288863i
$457$			10.7902i			0.504746i	0.967630	+	0.252373i	$0.0812110\pi$
$457$			10.7902i			0.504746i	−0.967630	+	0.252373i	$0.918789\pi$
$458$	−5.38842	−	3.11101i	−0.251784	−	0.145368i
$459$	3.04307	+	12.1497i	0.142038	+	0.567098i
$460$	−6.70010	+	3.99817i	−0.312394	+	0.186415i
$461$	3.84009	+	2.21708i	0.178851	+	0.103260i	0.586753	−	0.809766i	$-0.300406\pi$
$461$	3.84009	+	2.21708i	0.178851	+	0.103260i	−0.407902	+	0.913026i	$0.633739\pi$
$462$	−48.3263	−	13.2323i	−2.24834	−	0.615621i
$463$			33.5954i			1.56131i	0.624962	+	0.780655i	$0.285114\pi$
$463$			33.5954i			1.56131i	−0.624962	+	0.780655i	$0.714886\pi$
$464$	−1.11433			−0.0517313
$465$	−4.23465	+	16.3895i	−0.196377	+	0.760047i
$466$	−23.9519	+	13.8286i	−1.10955	+	0.640598i
$467$	18.3974			0.851330			0.425665	−	0.904881i	$-0.360040\pi$
$467$	18.3974			0.851330			0.425665	+	0.904881i	$0.360040\pi$
$468$	0.0836702	−	7.66035i	0.00386765	−	0.354100i
$469$	−14.0728	+	8.12496i	−0.649823	+	0.375176i
$470$	−2.70432	+	4.84395i	−0.124741	+	0.223435i
$471$	−4.21002	−	1.15275i	−0.193987	−	0.0531159i
$472$	7.31454	+	4.22305i	0.336679	+	0.194382i
$473$	−18.3054	+	31.7059i	−0.841683	+	1.45784i
$474$	11.8596	+	11.9899i	0.544732	+	0.550714i
$475$	−6.82410	+	20.6986i	−0.313111	+	0.949716i
$476$		−	11.1107i		−	0.509260i
$477$	−0.0904896	+	0.152853i	−0.00414324	+	0.00699864i
$478$	7.00458	−	12.1323i	0.320382	−	0.554918i
$479$	14.0729	−	8.12501i	0.643008	−	0.371241i	−0.142764	−	0.989757i	$-0.545599\pi$
$479$	14.0729	−	8.12501i	0.643008	−	0.371241i	0.785772	+	0.618516i	$0.212266\pi$
$480$	3.73189	−	1.03586i	0.170337	−	0.0472802i
$481$	−2.90777	−	5.03641i	−0.132583	−	0.229640i
$482$	10.9625			0.499329
$483$	−19.8058	+	19.5907i	−0.901197	+	0.891407i
$484$	−14.1932	−	24.5834i	−0.645146	−	1.11743i
$485$	12.1949	−	7.27711i	0.553743	−	0.330437i
$486$	−11.3195	+	10.7177i	−0.513464	+	0.486163i
$487$	15.7997			0.715951			0.357975	−	0.933731i	$-0.383467\pi$
$487$	15.7997			0.715951			0.357975	+	0.933731i	$0.383467\pi$
$488$	−1.11574	+	0.644175i	−0.0505073	+	0.0291604i
$489$	1.96454	+	7.49525i	0.0888395	+	0.338947i
$490$	16.3246	+	27.3567i	0.737471	+	1.23585i
$491$	−3.85305	−	2.22456i	−0.173886	−	0.100393i	0.410531	−	0.911847i	$-0.365343\pi$
$491$	−3.85305	−	2.22456i	−0.173886	−	0.100393i	−0.584417	+	0.811454i	$0.698677\pi$
$492$	15.4114	−	4.03939i	0.694798	−	0.182110i
$493$	−2.68601			−0.120972
$494$	−8.51409	+	7.16988i	−0.383067	+	0.322588i
$495$	−0.147040	−	42.0995i	−0.00660897	−	1.89223i
$496$	−3.78516	−	2.18537i	−0.169959	−	0.0981258i
$497$	10.1344	+	5.85112i	0.454591	+	0.262458i
$498$	14.6851	+	4.02093i	0.658053	+	0.180182i
$499$	16.6367	−	28.8156i	0.744762	−	1.28997i	−0.205544	−	0.978648i	$-0.565896\pi$
$499$	16.6367	−	28.8156i	0.744762	−	1.28997i	0.950306	−	0.311317i	$-0.100770\pi$
$500$	−9.43174	+	6.00352i	−0.421800	+	0.268486i
$501$	−9.95924	+	9.85105i	−0.444946	+	0.440112i
$502$	14.7576			0.658665
$503$	6.97093	+	12.0740i	0.310818	+	0.538353i	0.978540	−	0.206058i	$-0.0660636\pi$
$503$	6.97093	+	12.0740i	0.310818	+	0.538353i	−0.667721	+	0.744411i	$0.732730\pi$
$504$	12.0505	−	6.78296i	0.536771	−	0.302137i
$505$	−35.0457	+	0.505210i	−1.55951	+	0.0224815i
$506$	−21.8985			−0.973505
$507$	2.96366	−	10.8237i	0.131621	−	0.480699i
$508$	4.20396	−	7.28147i	0.186520	−	0.323063i
$509$	0.321137	+	0.556225i	0.0142341	+	0.0246542i	0.873055	−	0.487622i	$-0.162136\pi$
$509$	0.321137	+	0.556225i	0.0142341	+	0.0246542i	−0.858821	+	0.512276i	$0.828802\pi$
$510$	8.99546	−	2.49686i	0.398326	−	0.110563i
$511$	29.2548	−	50.6708i	1.29416	−	2.24155i
$512$			1.00000i			0.0441942i
$513$	22.5321	+	2.30355i	0.994815	+	0.101704i
$514$	2.82832			0.124752
$515$	30.1704	+	16.8438i	1.32947	+	0.742225i
$516$	−2.56179	−	9.77392i	−0.112776	−	0.430273i
$517$	−13.4845	+	7.78526i	−0.593046	+	0.342395i
$518$	5.24874	−	9.09109i	0.230617	−	0.399440i
$519$	−18.5676	−	5.08402i	−0.815029	−	0.223164i
$520$	−5.70944	+	0.0823057i	−0.250375	+	0.00360934i
$521$	15.7298			0.689135			0.344568	−	0.938761i	$-0.388026\pi$
$521$	15.7298			0.689135			0.344568	+	0.938761i	$0.388026\pi$
$522$	−1.63977	−	2.91319i	−0.0717708	−	0.127507i
$523$	−2.02261	−	3.50326i	−0.0884425	−	0.153187i	0.818410	−	0.574634i	$-0.194856\pi$
$523$	−2.02261	−	3.50326i	−0.0884425	−	0.153187i	−0.906853	+	0.421447i	$0.861522\pi$
$524$			5.71083i			0.249479i
$525$	−27.5597	+	28.8788i	−1.20280	+	1.26037i
$526$	−7.59024	+	4.38223i	−0.330950	+	0.191074i
$527$	−9.12388	−	5.26767i	−0.397442	−	0.229464i
$528$	10.4842	+	2.87069i	0.456266	+	0.124931i
$529$	5.41234	−	9.37444i	0.235319	−	0.407584i
$530$	0.115602	+	0.0645391i	0.00502142	+	0.00280340i
$531$	−0.276741	+	25.3368i	−0.0120095	+	1.09952i
$532$	−18.8925	−	6.83849i	−0.819095	−	0.296486i
$533$	−23.4888			−1.01741
$534$	7.09570	+	27.0720i	0.307061	+	1.17152i
$535$	5.13881	−	9.20458i	0.222170	−	0.397949i
$536$	3.05304	−	1.76268i	0.131871	−	0.0761360i
$537$	−7.13931	+	1.87125i	−0.308084	+	0.0807502i
$538$	−7.24897	+	4.18520i	−0.312525	+	0.180437i
$539$			89.4120i			3.85125i
$540$	8.19965	+	8.23199i	0.352857	+	0.354249i
$541$	3.58134	+	6.20307i	0.153974	+	0.266691i	0.932685	−	0.360692i	$-0.117459\pi$
$541$	3.58134	+	6.20307i	0.153974	+	0.266691i	−0.778711	+	0.627383i	$0.784126\pi$
$542$	22.2314	−	12.8353i	0.954922	−	0.551324i
$543$	23.8281	−	23.5693i	1.02256	−	1.01145i
$544$			2.41043i			0.103346i
$545$	9.08857	+	15.2306i	0.389311	+	0.652405i
$546$	−19.7213	+	5.16904i	−0.843993	+	0.221214i
$547$	12.4830	+	21.6212i	0.533736	+	0.924457i	0.999223	+	0.0394030i	$0.0125456\pi$
$547$	12.4830	+	21.6212i	0.533736	+	0.924457i	−0.465488	+	0.885054i	$0.654121\pi$
$548$	−4.51364	+	7.81786i	−0.192813	+	0.333962i
$549$	−3.32592	−	1.96897i	−0.141947	−	0.0840334i
$550$	−31.3663	+	0.904523i	−1.33746	+	0.0385690i
$551$	−1.65320	+	4.56724i	−0.0704285	+	0.194571i
$552$	4.29680	−	4.25012i	0.182884	−	0.180897i
$553$	22.4403	−	38.8678i	0.954260	−	1.65283i
$554$	−7.36868	+	12.7629i	−0.313065	+	0.542245i
$555$	8.53984	+	2.20648i	0.362496	+	0.0936600i
$556$	−7.12104	+	12.3340i	−0.302000	+	0.523079i
$557$	11.8399	+	20.5073i	0.501673	+	0.868924i	0.999998	+	0.00193347i	$0.000615443\pi$
$557$	11.8399	+	20.5073i	0.501673	+	0.868924i	−0.498325	+	0.866991i	$0.666051\pi$
$558$	0.143209	−	13.1114i	0.00606253	−	0.555050i
$559$			14.8967i			0.630062i
$560$	−5.28164	−	8.85094i	−0.223190	−	0.374020i
$561$	25.2714	+	6.91960i	1.06696	+	0.292146i
$562$			5.51105i			0.232470i
$563$			22.2752i			0.938786i	0.882989	+	0.469393i	$0.155527\pi$
$563$			22.2752i			0.938786i	−0.882989	+	0.469393i	$0.844473\pi$
$564$	1.13486	−	4.14469i	0.0477863	−	0.174523i
$565$	15.3174	−	27.4364i	0.644408	−	1.15426i
$566$	−15.4460	−	26.7533i	−0.649246	−	1.12453i
$567$	35.4654	+	21.5223i	1.48941	+	0.903851i
$568$	−2.19862	−	1.26938i	−0.0922522	−	0.0532618i
$569$	−1.70293			−0.0713903			−0.0356952	−	0.999363i	$-0.511365\pi$
$569$	−1.70293			−0.0713903			−0.0356952	+	0.999363i	$0.511365\pi$
$570$	1.29094	−	16.8325i	0.0540717	−	0.705036i
$571$	32.4721			1.35891			0.679457	−	0.733715i	$-0.262215\pi$
$571$	32.4721			1.35891			0.679457	+	0.733715i	$0.262215\pi$
$572$	−13.8790	−	8.01303i	−0.580309	−	0.335042i
$573$	1.68462	+	6.42727i	0.0703759	+	0.268503i
$574$	−21.1996	−	36.7187i	−0.884852	−	1.53261i
$575$	−8.28414	+	15.3544i	−0.345472	+	0.640321i
$576$	−2.61430	+	1.47153i	−0.108929	+	0.0613139i
$577$			10.4917i			0.436775i	0.975862	+	0.218388i	$0.0700797\pi$
$577$			10.4917i			0.436775i	−0.975862	+	0.218388i	$0.929920\pi$
$578$		−	11.1898i		−	0.465435i
$579$	6.81768	−	24.8992i	0.283333	−	1.03478i
$580$	−2.13970	+	1.27683i	−0.0888463	+	0.0530175i
$581$		−	40.5193i		−	1.68103i
$582$	−7.82065	+	7.73570i	−0.324177	+	0.320655i
$583$	0.185796	+	0.321809i	0.00769490	+	0.0133280i
$584$	−6.34671	+	10.9928i	−0.262629	+	0.454887i
$585$	−8.61681	−	14.8051i	−0.356261	−	0.612115i
$586$	13.3851	−	23.1837i	0.552935	−	0.957712i
$587$	−5.55634	+	9.62387i	−0.229335	+	0.397220i	−0.957611	−	0.288064i	$-0.906988\pi$
$587$	−5.55634	+	9.62387i	−0.229335	+	0.397220i	0.728276	+	0.685284i	$0.240322\pi$
$588$	−17.3534	−	17.5439i	−0.715640	−	0.723500i
$589$	−14.5727	+	12.2719i	−0.600456	+	0.505656i
$590$	18.8841	−	0.272228i	0.777446	−	0.0112075i
$591$	−29.5132	+	7.73553i	−1.21401	+	0.318197i
$592$	−1.13869	+	1.97227i	−0.0468000	+	0.0810600i
$593$	−6.57108	−	11.3814i	−0.269842	−	0.467380i	0.698979	−	0.715142i	$-0.253638\pi$
$593$	−6.57108	−	11.3814i	−0.269842	−	0.467380i	−0.968821	+	0.247762i	$0.920305\pi$
$594$	7.92301	+	31.6332i	0.325085	+	1.29793i
$595$	−12.7310	−	21.3346i	−0.521922	−	0.874632i
$596$		−	10.9589i		−	0.448892i
$597$	−5.89351	−	5.95823i	−0.241205	−	0.243854i
$598$	−7.71657	+	4.45517i	−0.315554	+	0.182185i
$599$	15.2831	+	26.4710i	0.624449	+	1.08158i	0.988647	+	0.150256i	$0.0480098\pi$
$599$	15.2831	+	26.4710i	0.624449	+	1.08158i	−0.364198	+	0.931322i	$0.618657\pi$
$600$	5.97896	−	6.26514i	0.244090	−	0.255773i
$601$			9.49333i			0.387241i	0.981076	+	0.193621i	$0.0620231\pi$
$601$			9.49333i			0.387241i	−0.981076	+	0.193621i	$0.937977\pi$
$602$	−23.2871	+	13.4448i	−0.949111	+	0.547969i
$603$	9.10083	+	5.38775i	0.370615	+	0.219406i
$604$	1.74117	−	1.00527i	0.0708472	−	0.0409037i
$605$	−55.4218	−	30.9413i	−2.25322	−	1.25794i
$606$	26.2620	−	6.88339i	1.06682	−	0.279619i
$607$	35.1509			1.42673			0.713365	−	0.700793i	$-0.247170\pi$
$607$	35.1509			1.42673			0.713365	+	0.700793i	$0.247170\pi$
$608$	4.09866	+	1.48358i	0.166222	+	0.0601672i
$609$	−6.32507	+	6.25636i	−0.256305	+	0.253521i
$610$	−1.40431	+	2.51538i	−0.0568587	+	0.101845i
$611$	−3.16777	+	5.48673i	−0.128154	+	0.221969i
$612$	−6.30160	+	3.54703i	−0.254727	+	0.143380i
$613$	−36.2692	−	20.9400i	−1.46490	−	0.845760i	−0.465668	−	0.884959i	$-0.654186\pi$
$613$	−36.2692	−	20.9400i	−1.46490	−	0.845760i	−0.999231	+	0.0391990i	$0.987519\pi$
$614$	24.3254	−	14.0443i	0.981692	−	0.566780i
$615$	24.9641	−	25.4152i	1.00665	−	1.02484i
$616$		−	28.9282i		−	1.16555i
$617$	16.1662	+	28.0007i	0.650826	+	1.12726i	0.982923	+	0.184018i	$0.0589106\pi$
$617$	16.1662	+	28.0007i	0.650826	+	1.12726i	−0.332097	+	0.943245i	$0.607756\pi$
$618$	−25.8150	−	7.06844i	−1.03843	−	0.284334i
$619$	11.1834			0.449497			0.224748	−	0.974417i	$-0.427844\pi$
$619$	11.1834			0.449497			0.224748	+	0.974417i	$0.427844\pi$
$620$	−9.77224	+	0.140874i	−0.392463	+	0.00565763i
$621$	17.4340	+	4.97893i	0.699602	+	0.199798i
$622$	9.69002	−	16.7836i	0.388534	−	0.672961i
$623$	64.5010	−	37.2397i	2.58418	−	1.49198i
$624$	4.27845	−	1.12140i	0.171275	−	0.0448920i
$625$	−11.2316	+	22.3350i	−0.449263	+	0.893400i
$626$	24.3594			0.973599
$627$	27.3201	−	38.7122i	1.09106	−	1.54602i
$628$		−	2.52012i		−	0.100564i
$629$	−2.74474	+	4.75403i	−0.109440	+	0.189556i
$630$	15.3669	−	26.8323i	0.612233	−	1.06902i
$631$	−16.0088	−	27.7280i	−0.637299	−	1.10383i	−0.986023	−	0.166609i	$-0.946718\pi$
$631$	−16.0088	−	27.7280i	−0.637299	−	1.10383i	0.348724	−	0.937225i	$-0.386615\pi$
$632$	−4.86834	+	8.43221i	−0.193652	+	0.335415i
$633$	−8.66541	−	2.37268i	−0.344419	−	0.0943057i
$634$	−26.3148			−1.04509
$635$	−0.270997	−	18.7987i	−0.0107542	−	0.746004i
$636$	−0.0989136	−	0.0270836i	−0.00392218	−	0.00107394i
$637$	18.1906	+	31.5070i	0.720736	+	1.24835i
$638$	−6.99336			−0.276870
$639$	0.0831835	−	7.61580i	0.00329069	−	0.301276i
$640$	1.14583	+	1.92017i	0.0452929	+	0.0759016i
$641$	21.2450	−	36.7975i	0.839128	−	1.45341i	−0.0514971	−	0.998673i	$-0.516399\pi$
$641$	21.2450	−	36.7975i	0.839128	−	1.45341i	0.890625	−	0.454739i	$-0.150267\pi$
$642$	−2.15649	+	7.87582i	−0.0851097	+	0.310834i
$643$	−29.2752	−	16.9020i	−1.15450	−	0.666552i	−0.204521	−	0.978862i	$-0.565564\pi$
$643$	−29.2752	−	16.9020i	−1.15450	−	0.666552i	−0.949980	+	0.312310i	$0.898897\pi$
$644$	−13.9290	−	8.04190i	−0.548879	−	0.316895i
$645$	−16.1183	−	15.8323i	−0.634659	−	0.623395i
$646$	9.87953	+	3.57607i	0.388705	+	0.140699i
$647$	0.964578			0.0379215			0.0189607	−	0.999820i	$-0.493964\pi$
$647$	0.964578			0.0379215			0.0189607	+	0.999820i	$0.493964\pi$
$648$	−7.69408	−	4.66917i	−0.302252	−	0.183422i
$649$	45.9050	+	26.5033i	1.80193	+	1.04034i
$650$	−10.8688	+	6.70009i	−0.426310	+	0.262799i
$651$	−33.7548	+	8.84729i	−1.32296	+	0.346753i
$652$	−3.87421	+	2.23678i	−0.151726	+	0.0875990i
$653$	44.6585			1.74762			0.873812	−	0.486264i	$-0.161641\pi$
$653$	44.6585			1.74762			0.873812	+	0.486264i	$0.161641\pi$
$654$	−9.66130	−	9.76741i	−0.377787	−	0.381936i
$655$	6.54365	+	10.9658i	0.255682	+	0.428469i
$656$	4.59916	+	7.96597i	0.179567	+	0.311019i
$657$	−38.0780	−	0.415907i	−1.48556	−	0.0162261i
$658$	−11.4361			−0.445826
$659$	7.39035	+	12.8005i	0.287887	+	0.498635i	0.973305	−	0.229514i	$-0.0737138\pi$
$659$	7.39035	+	12.8005i	0.287887	+	0.498635i	−0.685418	+	0.728150i	$0.740381\pi$
$660$	23.4208	−	6.50089i	0.911654	−	0.253047i
$661$	−38.0675	+	21.9783i	−1.48065	+	0.854856i	−0.999760	−	0.0219216i	$-0.993022\pi$
$661$	−38.0675	+	21.9783i	−1.48065	+	0.854856i	−0.480895	+	0.876778i	$0.659688\pi$
$662$	11.9586	−	20.7130i	0.464786	−	0.805032i
$663$	10.3129	−	2.70306i	0.400520	−	0.104978i
$664$			8.79050i			0.341138i
$665$	−44.1127	+	8.51654i	−1.71062	+	0.330257i
$666$	−6.83175	−	0.0746198i	−0.264725	−	0.00289146i
$667$	−1.94412	+	3.36731i	−0.0752766	+	0.130383i
$668$	−7.00410	−	4.04382i	−0.270997	−	0.156460i
$669$	−0.297829	+	1.08772i	−0.0115147	+	0.0420536i
$670$	3.84265	−	6.88292i	0.148455	−	0.265910i
$671$	−7.00225	+	4.04275i	−0.270319	+	0.156069i
$672$	5.61448	+	5.67614i	0.216583	+	0.218962i
$673$	14.4471			0.556893			0.278447	−	0.960452i	$-0.410180\pi$
$673$	14.4471			0.556893			0.278447	+	0.960452i	$0.410180\pi$
$674$	13.7644	−	7.94689i	0.530186	−	0.306103i
$675$	25.1772	+	6.41146i	0.969072	+	0.246777i
$676$	6.47911			0.249196
$677$			38.1292i			1.46542i	0.680539	+	0.732712i	$0.261746\pi$
$677$			38.1292i			1.46542i	−0.680539	+	0.732712i	$0.738254\pi$
$678$	−6.42791	+	23.4757i	−0.246862	+	0.901579i
$679$	25.3523	+	14.6372i	0.972933	+	0.561723i
$680$	2.76195	+	4.62845i	0.105916	+	0.177493i
$681$	3.58220	+	13.6671i	0.137270	+	0.523723i
$682$	−23.7552	−	13.7150i	−0.909632	−	0.525176i
$683$			33.2936i			1.27394i	0.770887	+	0.636972i	$0.219813\pi$
$683$			33.2936i			1.27394i	−0.770887	+	0.636972i	$0.780187\pi$
$684$	2.15278	+	12.8983i	0.0823136	+	0.493178i
$685$	0.290960	+	20.1835i	0.0111170	+	0.771173i
$686$	−16.7023	+	28.9292i	−0.637695	+	1.10452i
$687$	10.4247	−	2.73236i	0.397728	−	0.104246i
$688$	5.05204	−	2.91679i	0.192607	−	0.111202i
$689$	0.130942	+	0.0755993i	0.00498849	+	0.00288010i
$690$	3.38068	−	13.0844i	0.128700	−	0.498114i
$691$	7.32876			0.278799			0.139400	−	0.990236i	$-0.455483\pi$
$691$	7.32876			0.278799			0.139400	+	0.990236i	$0.455483\pi$
$692$		−	11.1146i		−	0.422514i
$693$	75.6272	−	42.5689i	2.87284	−	1.61706i
$694$	−11.6794	+	6.74308i	−0.443342	+	0.255964i
$695$	0.459040	+	31.8430i	0.0174124	+	1.20787i
$696$	1.37220	−	1.35729i	0.0520130	−	0.0514480i
$697$	11.0860	+	19.2014i	0.419910	+	0.727306i
$698$	7.22433	+	4.17097i	0.273445	+	0.157874i
$699$	12.6509	−	46.2030i	0.478501	−	1.74756i
$700$	−20.2834	−	10.9435i	−0.766639	−	0.413625i
$701$	−13.7046	−	7.91236i	−0.517616	−	0.298846i	0.218343	−	0.975872i	$-0.429935\pi$
$701$	−13.7046	−	7.91236i	−0.517616	−	0.298846i	−0.735959	+	0.677026i	$0.763268\pi$
$702$	9.22757	+	9.53499i	0.348272	+	0.359875i
$703$	6.39433	+	7.59314i	0.241167	+	0.286381i
$704$			6.27586i			0.236530i
$705$	−2.56998	−	9.25888i	−0.0967910	−	0.348710i
$706$	−6.93233	−	4.00239i	−0.260902	−	0.150632i
$707$	−36.1255	−	62.5712i	−1.35864	−	2.35323i
$708$	−14.1511	+	3.70906i	−0.531830	+	0.139395i
$709$	1.42321	+	2.46507i	0.0534498	+	0.0925778i	0.891512	−	0.452996i	$-0.149645\pi$
$709$	1.42321	+	2.46507i	0.0534498	+	0.0925778i	−0.838063	+	0.545574i	$0.816312\pi$
$710$	−5.67623	+	0.0818270i	−0.213025	+	0.00307091i
$711$	−29.2083	−	0.319027i	−1.09540	−	0.0119645i
$712$	−13.9932	+	8.07900i	−0.524419	+	0.302773i
$713$	−13.2076	+	7.62543i	−0.494630	+	0.285575i
$714$	13.5333	+	13.6819i	0.506472	+	0.512034i
$715$	−35.8316	+	0.516539i	−1.34003	+	0.0193175i
$716$	−2.13056	−	3.69023i	−0.0796227	−	0.137911i
$717$	6.15205	+	23.4717i	0.229752	+	0.876568i
$718$	4.23571	+	7.33647i	0.158075	+	0.273794i
$719$	−22.6148	−	13.0567i	−0.843389	−	0.486931i	0.0150255	−	0.999887i	$-0.495217\pi$
$719$	−22.6148	−	13.0567i	−0.843389	−	0.486931i	−0.858415	+	0.512956i	$0.828550\pi$
$720$	−3.33379	+	5.82115i	−0.124243	+	0.216942i
$721$			71.2294i			2.65272i
$722$	12.1614	−	14.5980i	0.452600	−	0.543280i
$723$	−13.4994	+	13.3528i	−0.502048	+	0.496595i
$724$	16.7578	+	9.67510i	0.622797	+	0.359572i
$725$	−2.64557	+	4.90347i	−0.0982540	+	0.182110i
$726$	47.4212	+	12.9844i	1.75997	+	0.481898i
$727$	−23.4044	−	13.5125i	−0.868022	−	0.501152i	−0.00133130	−	0.999999i	$-0.500424\pi$
$727$	−23.4044	−	13.5125i	−0.868022	−	0.501152i	−0.866690	+	0.498847i	$0.833757\pi$
$728$	−5.88535	−	10.1937i	−0.218125	−	0.377804i
$729$	0.884528	−	26.9855i	0.0327603	−	0.999463i
$730$	0.409124	+	28.3804i	0.0151424	+	1.05041i
$731$	12.1776	−	7.03073i	0.450404	−	0.260041i
$732$	0.589314	−	2.15226i	0.0217817	−	0.0795500i
$733$			30.6170i			1.13087i	0.824794	+	0.565433i	$0.191291\pi$
$733$			30.6170i			1.13087i	−0.824794	+	0.565433i	$0.808709\pi$
$734$	−25.2411			−0.931666
$735$	−53.4239	−	13.8034i	−1.97057	−	0.509146i
$736$	3.02184	+	1.74466i	0.111386	+	0.0643090i
$737$	19.1605	−	11.0623i	0.705785	−	0.407485i
$738$	−14.0577	+	23.7458i	−0.517469	+	0.874095i
$739$	10.0943	−	17.4838i	0.371324	−	0.643152i	−0.618446	−	0.785827i	$-0.712237\pi$
$739$	10.0943	−	17.4838i	0.371324	−	0.643152i	0.989769	+	0.142676i	$0.0455707\pi$
$740$	0.0734029	+	5.09186i	0.00269834	+	0.187181i
$741$	1.75120	−	19.1996i	0.0643318	−	0.705314i
$742$			0.272925i			0.0100194i
$743$	−15.4773	−	8.93584i	−0.567808	−	0.327824i	0.188465	−	0.982080i	$-0.439649\pi$
$743$	−15.4773	−	8.93584i	−0.567808	−	0.327824i	−0.756273	+	0.654256i	$0.772982\pi$
$744$	7.32297	−	1.91938i	0.268473	−	0.0703680i
$745$	−12.5570	−	21.0429i	−0.460053	−	0.770953i
$746$	−24.0963	−	13.9120i	−0.882229	−	0.509355i
$747$	−22.9811	+	12.9355i	−0.840833	+	0.473286i
$748$			15.1275i			0.553117i
$749$	21.7311			0.794038
$750$	4.30186	−	18.8810i	0.157082	−	0.689438i
$751$	5.47575	−	3.16143i	0.199813	−	0.115362i	−0.396755	−	0.917924i	$-0.629864\pi$
$751$	5.47575	−	3.16143i	0.199813	−	0.115362i	0.596568	+	0.802562i	$0.296530\pi$
$752$	2.48102			0.0904734
$753$	−18.1728	+	17.9754i	−0.662252	+	0.655058i
$754$	−2.46432	+	1.42277i	−0.0897451	+	0.0518144i
$755$	2.19149	−	3.92537i	0.0797564	−	0.142859i
$756$	−6.57725	+	23.0306i	−0.239212	+	0.837614i
$757$	−10.8515	−	6.26511i	−0.394404	−	0.227709i	0.289662	−	0.957129i	$-0.406457\pi$
$757$	−10.8515	−	6.26511i	−0.394404	−	0.227709i	−0.684067	+	0.729419i	$0.739790\pi$
$758$	8.84812	−	15.3254i	0.321378	−	0.556643i
$759$	26.9661	−	26.6732i	0.978807	−	0.968174i
$760$	9.57007	−	1.84763i	0.347143	−	0.0670205i
$761$			24.3793i			0.883747i	0.897077	+	0.441874i	$0.145686\pi$
$761$			24.3793i			0.883747i	−0.897077	+	0.441874i	$0.854314\pi$
$762$	3.69229	+	14.0871i	0.133758	+	0.510321i
$763$	−18.2807	+	31.6631i	−0.661807	+	1.14628i
$764$	−3.32219	+	1.91807i	−0.120193	+	0.0693932i
$765$	−8.03587	+	14.0315i	−0.290538	+	0.507310i
$766$	11.1294	+	19.2767i	0.402121	+	0.696494i
$767$	21.5680			0.778776
$768$	−1.21804	−	1.23141i	−0.0439522	−	0.0444349i
$769$	18.4689	+	31.9891i	0.666006	+	1.15356i	0.979011	+	0.203805i	$0.0653309\pi$
$769$	18.4689	+	31.9891i	0.666006	+	1.15356i	−0.313005	+	0.949751i	$0.601336\pi$
$770$	−33.1468	−	55.5472i	−1.19453	−	2.00178i
$771$	−3.48284	+	3.44500i	−0.125431	+	0.124069i
$772$	14.9047			0.536432
$773$	−14.1058	+	8.14398i	−0.507350	+	0.292919i	−0.731744	−	0.681580i	$-0.761293\pi$
$773$	−14.1058	+	8.14398i	−0.507350	+	0.292919i	0.224394	+	0.974499i	$0.427960\pi$
$774$	15.0596	+	8.91540i	0.541307	+	0.320457i
$775$	−18.6030	+	11.4678i	−0.668239	+	0.411937i
$776$	−5.50008	−	3.17547i	−0.197441	−	0.113993i
$777$	4.60991	+	17.5881i	0.165380	+	0.630969i
$778$	−10.0566			−0.360547
$779$	39.4730	−	7.03218i	1.41427	−	0.251954i
$780$	6.93044	−	7.05567i	0.248149	−	0.252633i
$781$	−13.7983	−	7.96642i	−0.493740	−	0.285061i
$782$	7.28393	+	4.20538i	0.260473	+	0.150384i
$783$	5.56761	+	1.59004i	0.198970	+	0.0568234i
$784$	7.12349	−	12.3382i	0.254410	−	0.440651i
$785$	−2.88764	−	4.83908i	−0.103064	−	0.172714i
$786$	−6.95601	−	7.03240i	−0.248113	−	0.250838i
$787$	−25.8536			−0.921581			−0.460790	−	0.887509i	$-0.652434\pi$
$787$	−25.8536			−0.921581			−0.460790	+	0.887509i	$0.652434\pi$
$788$	−8.80750	−	15.2550i	−0.313754	−	0.543438i
$789$	4.00902	−	14.6415i	0.142725	−	0.521253i
$790$	0.313825	+	21.7696i	0.0111654	+	0.774528i
$791$	64.7747			2.30312
$792$	−16.4070	+	9.23514i	−0.582997	+	0.328157i
$793$	−1.64497	+	2.84917i	−0.0584145	+	0.101177i
$794$	10.6848	+	18.5066i	0.379189	+	0.656774i
$795$	−0.220965	+	0.0613330i	−0.00783681	+	0.00217526i
$796$	2.41926	−	4.19028i	0.0857484	−	0.148521i
$797$		−	35.0865i		−	1.24283i	−0.783483	−	0.621413i	$-0.786559\pi$
$797$		−	35.0865i		−	1.24283i	0.783483	−	0.621413i	$-0.213441\pi$
$798$	31.5941	−	14.5908i	1.11842	−	0.516509i
$799$	5.98032			0.211569
$800$	4.40039	+	2.37414i	0.155577	+	0.0839386i
$801$	−41.7125	−	24.6940i	−1.47384	−	0.872521i
$802$	12.7114	−	7.33894i	0.448856	−	0.259147i
$803$	−39.8311	+	68.9895i	−1.40561	+	2.43459i
$804$	−1.61256	+	5.88931i	−0.0568705	+	0.207700i
$805$	−35.9608	+	0.518400i	−1.26745	+	0.0182712i
$806$	−11.1611			−0.393134
$807$	3.82876	−	13.9832i	0.134779	−	0.492233i
$808$	7.83727	+	13.5746i	0.275714	+	0.477551i
$809$		−	3.65833i		−	0.128620i	−0.997930	−	0.0643100i	$-0.979515\pi$
$809$		−	3.65833i		−	0.128620i	0.997930	−	0.0643100i	$-0.0204846\pi$
$810$	−20.1241	−	0.149512i	−0.707087	−	0.00525332i
$811$	34.6815	−	20.0234i	1.21783	−	0.703115i	0.253378	−	0.967367i	$-0.418458\pi$
$811$	34.6815	−	20.0234i	1.21783	−	0.703115i	0.964454	+	0.264252i	$0.0851250\pi$
$812$	−4.44828	−	2.56821i	−0.156104	−	0.0901266i
$813$	−11.7422	+	42.8843i	−0.411817	+	1.50402i
$814$	−7.14628	+	12.3777i	−0.250477	+	0.433839i
$815$	−4.87620	+	8.73420i	−0.170806	+	0.305946i
$816$	−2.93600	−	2.96824i	−0.102780	−	0.103909i
$817$	−4.45983	−	25.0339i	−0.156030	−	0.875824i
$818$	−30.1838			−1.05535
$819$	17.9890	−	30.3865i	0.628586	−	1.06179i
$820$	17.9588	+	10.0262i	0.627150	+	0.350130i
$821$	−3.34798	+	1.93296i	−0.116845	+	0.0674607i	−0.557284	−	0.830322i	$-0.688156\pi$
$821$	−3.34798	+	1.93296i	−0.116845	+	0.0674607i	0.440438	+	0.897783i	$0.354823\pi$
$822$	−3.96429	−	15.1248i	−0.138270	−	0.527539i
$823$	6.35250	−	3.66762i	0.221434	−	0.127845i	−0.385180	−	0.922841i	$-0.625861\pi$
$823$	6.35250	−	3.66762i	0.221434	−	0.127845i	0.606614	+	0.794996i	$0.292527\pi$
$824$		−	15.4529i		−	0.538328i
$825$	37.5231	−	39.3191i	1.30639	−	1.36892i
$826$	19.4659	+	33.7160i	0.677306	+	1.17313i
$827$	29.3460	−	16.9429i	1.02046	−	0.589163i	0.106223	−	0.994342i	$-0.466124\pi$
$827$	29.3460	−	16.9429i	1.02046	−	0.589163i	0.914237	+	0.405179i	$0.132791\pi$
$828$	−0.114329	+	10.4673i	−0.00397322	+	0.363765i
$829$		−	43.3738i		−	1.50643i	−0.657772	−	0.753217i	$-0.728501\pi$
$829$		−	43.3738i		−	1.50643i	0.657772	−	0.753217i	$-0.271499\pi$
$830$	10.0724	+	16.8793i	0.349619	+	0.585889i
$831$	−6.47183	−	24.6918i	−0.224505	−	0.856549i
$832$	1.27680	+	2.21149i	0.0442651	+	0.0766695i
$833$	17.1707	−	29.7405i	0.594929	−	1.03045i
$834$	−6.25434	−	23.8620i	−0.216570	−	0.826273i
$835$	−18.0826	+	0.260674i	−0.625775	+	0.00902100i
$836$	25.7226	+	9.31075i	0.889634	+	0.322019i
$837$	15.7939	+	16.3200i	0.545915	+	0.564103i
$838$	4.45168	−	7.71054i	0.153781	−	0.266356i
$839$	23.3709	−	40.4795i	0.806852	−	1.39751i	−0.108182	−	0.994131i	$-0.534503\pi$
$839$	23.3709	−	40.4795i	0.806852	−	1.39751i	0.915034	−	0.403377i	$-0.132164\pi$
$840$	17.2847	+	4.46593i	0.596378	+	0.154089i
$841$	13.8791	−	24.0394i	0.478591	−	0.828944i
$842$	−8.26272	−	14.3115i	−0.284752	−	0.493205i
$843$	−6.71268	−	6.78639i	−0.231197	−	0.233736i
$844$		−	5.18713i		−	0.178548i
$845$	12.4410	−	7.42396i	0.427984	−	0.255392i
$846$	3.65090	+	6.48613i	0.125521	+	0.222998i
$847$		−	130.846i		−	4.49591i
$848$		−	0.0592099i		−	0.00203328i
$849$	51.6071	+	14.1306i	1.77115	+	0.484960i
$850$	10.6068	+	5.72271i	0.363812	+	0.196287i
$851$	3.97326	+	6.88189i	0.136202	+	0.235908i
$852$	4.25357	−	1.11488i	0.145725	−	0.0381951i
$853$	44.2164	+	25.5284i	1.51394	+	0.874075i	0.999867	+	0.0163293i	$0.00519801\pi$
$853$	44.2164	+	25.5284i	1.51394	+	0.874075i	0.514075	+	0.857745i	$0.328135\pi$
$854$	−5.93857			−0.203214
$855$	18.9130	+	22.3002i	0.646809	+	0.762652i
$856$	−4.71448			−0.161138
$857$	−10.4943	−	6.05888i	−0.358478	−	0.206967i	0.309935	−	0.950758i	$-0.399693\pi$
$857$	−10.4943	−	6.05888i	−0.358478	−	0.206967i	−0.668413	+	0.743790i	$0.733026\pi$
$858$	26.8510	−	7.03776i	0.916676	−	0.240265i
$859$	4.51608	+	7.82208i	0.154087	+	0.266886i	0.932726	−	0.360586i	$-0.117423\pi$
$859$	4.51608	+	7.82208i	0.154087	+	0.266886i	−0.778639	+	0.627472i	$0.784090\pi$
$860$	6.35864	−	11.3895i	0.216828	−	0.388380i
$861$	70.8302	+	19.3941i	2.41389	+	0.660949i
$862$			16.8018i			0.572271i
$863$		−	42.4560i		−	1.44522i	−0.691256	−	0.722610i	$-0.742942\pi$
$863$		−	42.4560i		−	1.44522i	0.691256	−	0.722610i	$-0.257058\pi$
$864$	1.42691	−	4.99639i	0.0485444	−	0.169981i
$865$	−12.7355	−	21.3420i	−0.433019	−	0.725650i
$866$			37.2480i			1.26574i
$867$	13.6296	+	13.7793i	0.462887	+	0.467970i
$868$	−10.0733	−	17.4475i	−0.341911	−	0.592207i
$869$	−30.5530	+	52.9194i	−1.03644	+	1.79517i
$870$	1.07963	−	4.17855i	0.0366030	−	0.141666i
$871$	4.50118	−	7.79627i	0.152517	−	0.264166i
$872$	3.96593	−	6.86919i	0.134303	−	0.232620i
$873$	0.208092	−	19.0517i	0.00704285	−	0.644803i
$874$	11.6339	−	9.79713i	0.393522	−	0.331393i
$875$	−51.4870	+	2.22790i	−1.74058	+	0.0753168i
$876$	−5.57425	−	21.2673i	−0.188337	−	0.718555i
$877$	−23.7811	+	41.1901i	−0.803031	+	1.39089i	0.114581	+	0.993414i	$0.463447\pi$
$877$	−23.7811	+	41.1901i	−0.803031	+	1.39089i	−0.917612	+	0.397477i	$0.869886\pi$
$878$	1.86818	+	3.23579i	0.0630481	+	0.109202i
$879$	11.7560	+	44.8524i	0.396521	+	1.51283i
$880$	7.19107	+	12.0507i	0.242411	+	0.406231i
$881$		−	30.0492i		−	1.01238i	−0.862421	−	0.506192i	$-0.831053\pi$
$881$		−	30.0492i		−	1.01238i	0.862421	−	0.506192i	$-0.168947\pi$
$882$	42.7384	+	0.466809i	1.43908	+	0.0157183i
$883$	−40.7629	+	23.5345i	−1.37178	+	0.791998i	−0.991152	−	0.132730i	$-0.957626\pi$
$883$	−40.7629	+	23.5345i	−1.37178	+	0.791998i	−0.380629	+	0.924728i	$0.624292\pi$
$884$	3.07764	+	5.33063i	0.103512	+	0.179289i
$885$	−22.9226	+	23.3368i	−0.770534	+	0.784458i
$886$			9.75527i			0.327735i
$887$	6.34634	−	3.66406i	0.213089	−	0.123027i	−0.389657	−	0.920960i	$-0.627406\pi$
$887$	6.34634	−	3.66406i	0.213089	−	0.123027i	0.602746	+	0.797933i	$0.294073\pi$
$888$	−1.00010	−	3.81566i	−0.0335612	−	0.128045i
$889$	33.5635	−	19.3779i	1.12568	−	0.649914i
$890$	−17.6123	+	31.5470i	−0.590365	+	1.05746i
$891$	−48.2870	−	29.3031i	−1.61767	−	0.981689i
$892$	−0.651110			−0.0218008
$893$	3.68079	−	10.1688i	0.123173	−	0.340287i
$894$	13.3483	+	13.4949i	0.446434	+	0.451337i
$895$	−8.31943	−	4.64464i	−0.278088	−	0.155253i
$896$	−2.30472	+	3.99190i	−0.0769954	+	0.133360i
$897$	4.07574	−	14.8852i	0.136085	−	0.497004i
$898$	17.4197	+	10.0573i	0.581304	+	0.335616i
$899$	−4.21791	+	2.43521i	−0.140675	+	0.0812188i
$900$	0.268597	+	14.9976i	0.00895322	+	0.499920i
$901$		−	0.142721i		−	0.00475474i
$902$	28.8637	+	49.9933i	0.961055	+	1.66460i
$903$	12.2998	−	44.9207i	0.409311	−	1.49487i
$904$	−14.0526			−0.467383
$905$	43.2639	−	0.623680i	1.43814	−	0.0207318i
$906$	−0.919652	+	3.35871i	−0.0305534	+	0.111586i
$907$	−15.1568	+	26.2524i	−0.503274	+	0.871696i	0.496719	+	0.867912i	$0.334538\pi$
$907$	−15.1568	+	26.2524i	−0.503274	+	0.871696i	−0.999993	+	0.00378471i	$0.998795\pi$
$908$	−7.06436	+	4.07861i	−0.234439	+	0.135353i
$909$	−23.9552	+	40.4644i	−0.794544	+	1.34212i
$910$	−22.9812	−	12.8301i	−0.761818	−	0.425314i
$911$	−43.8965			−1.45435			−0.727177	−	0.686450i	$-0.759168\pi$
$911$	−43.8965			−1.45435			−0.727177	+	0.686450i	$0.759168\pi$
$912$	−6.85421	+	3.16541i	−0.226965	+	0.104817i
$913$			55.1680i			1.82579i
$914$	5.39512	−	9.34462i	0.178455	−	0.309093i
$915$	−1.33455	−	4.80798i	−0.0441187	−	0.158947i
$916$	3.11101	+	5.38842i	0.102791	+	0.178039i
$917$	−13.1619	+	22.7970i	−0.434644	+	0.752825i
$918$	3.43946	−	12.0435i	0.113519	−	0.397493i
$919$	39.7741			1.31203			0.656013	−	0.754749i	$-0.272242\pi$
$919$	39.7741			1.31203			0.656013	+	0.754749i	$0.272242\pi$
$920$	7.80154	−	0.112465i	0.257209	−	0.00370786i
$921$	−12.8482	+	46.9236i	−0.423362	+	1.54618i
$922$	−2.21708	−	3.84009i	−0.0730156	−	0.126467i
$923$	−6.48297			−0.213389
$924$	35.2357	+	35.6226i	1.15917	+	1.17190i
$925$	5.97536	+	9.69316i	0.196469	+	0.318709i
$926$	16.7977	−	29.0945i	0.552006	−	0.956103i
$927$	40.3986	−	22.7395i	1.32687	−	0.746864i
$928$	0.965035	+	0.557163i	0.0316788	+	0.0182898i
$929$	−3.78176	−	2.18340i	−0.124076	−	0.0716351i	0.436678	−	0.899618i	$-0.356155\pi$
$929$	−3.78176	−	2.18340i	−0.124076	−	0.0716351i	−0.560753	+	0.827983i	$0.689488\pi$
$930$	11.8621	−	12.0764i	0.388973	−	0.396002i
$931$	−40.0019	−	47.5015i	−1.31101	−	1.55680i
$932$	27.6572			0.905942
$933$	8.51064	+	32.4704i	0.278626	+	1.06303i
$934$	−15.9326	−	9.19870i	−0.521331	−	0.300991i
$935$	17.3336	+	29.0475i	0.566869	+	0.949955i
$936$	−3.90264	+	6.59223i	−0.127562	+	0.215474i
$937$	0.531492	−	0.306857i	0.0173631	−	0.0100246i	−0.491293	−	0.870994i	$-0.663476\pi$
$937$	0.531492	−	0.306857i	0.0173631	−	0.0100246i	0.508656	+	0.860970i	$0.330142\pi$
$938$	16.2499			0.530578
$939$	−29.9966	+	29.6707i	−0.978902	+	0.968268i
$940$	4.76399	−	2.84283i	0.155384	−	0.0927228i
$941$	21.5489	+	37.3238i	0.702473	+	1.21672i	0.967596	+	0.252505i	$0.0812543\pi$
$941$	21.5489	+	37.3238i	0.702473	+	1.21672i	−0.265122	+	0.964215i	$0.585412\pi$
$942$	3.06961	+	3.10332i	0.100013	+	0.101112i
$943$	32.0958			1.04518
$944$	−4.22305	−	7.31454i	−0.137449	−	0.238068i
$945$	13.7597	+	51.7592i	0.447603	+	1.68373i
$946$	31.7059	−	18.3054i	1.03085	−	0.595160i
$947$	−6.37824	+	11.0474i	−0.207265	+	0.358993i	−0.950852	−	0.309646i	$-0.899790\pi$
$947$	−6.37824	+	11.0474i	−0.207265	+	0.358993i	0.743587	+	0.668639i	$0.233123\pi$
$948$	−4.27581	−	16.3134i	−0.138872	−	0.529834i
$949$			32.4140i			1.05220i
$950$	16.2591	−	14.5135i	0.527516	−	0.470879i
$951$	32.4044	−	32.0524i	1.05078	−	1.03937i
$952$	−5.55537	+	9.62219i	−0.180051	+	0.311857i
$953$	13.9664	+	8.06352i	0.452417	+	0.261203i	0.708851	−	0.705359i	$-0.249214\pi$
$953$	13.9664	+	8.06352i	0.452417	+	0.261203i	−0.256433	+	0.966562i	$0.582547\pi$
$954$	0.154793	−	0.0871294i	0.00501160	−	0.00282092i
$955$	−4.18141	+	7.48969i	−0.135307	+	0.242361i
$956$	−12.1323	+	7.00458i	−0.392386	+	0.226544i
$957$	8.61172	−	8.51818i	0.278378	−	0.275354i
$958$	−16.2500			−0.525014
$959$	−36.0360	+	20.8054i	−1.16366	+	0.671841i
$960$	−3.74984	−	0.968866i	−0.121026	−	0.0312700i
$961$	11.8967			0.383765
$962$			5.81554i			0.187501i
$963$	−6.93752	−	12.3251i	−0.223559	−	0.397170i
$964$	−9.49382	−	5.48126i	−0.305775	−	0.176539i
$965$	28.6197	−	17.0783i	0.921299	−	0.549769i
$966$	26.9477	−	7.06312i	0.867028	−	0.227252i
$967$	−30.9453	−	17.8663i	−0.995135	−	0.574541i	−0.0883294	−	0.996091i	$-0.528153\pi$
$967$	−30.9453	−	17.8663i	−0.995135	−	0.574541i	−0.906805	+	0.421550i	$0.861486\pi$
$968$			28.3864i			0.912374i
$969$	−16.5216	+	7.63001i	−0.530750	+	0.245111i
$970$	−14.1997	+	0.204699i	−0.455924	+	0.00657248i
$971$	−6.45947	+	11.1881i	−0.207294	+	0.359044i	−0.950861	−	0.309617i	$-0.899799\pi$
$971$	−6.45947	+	11.1881i	−0.207294	+	0.359044i	0.743567	+	0.668662i	$0.233132\pi$
$972$	15.1618	−	3.62200i	0.486316	−	0.116176i
$973$	−56.8529	+	32.8241i	−1.82262	+	1.05229i
$974$	−13.6829	−	7.89983i	−0.438428	−	0.253127i
$975$	5.22305	−	21.4892i	0.167271	−	0.688206i
$976$	1.28835			0.0412391
$977$			22.9067i			0.732849i	0.930448	+	0.366425i	$0.119418\pi$
$977$			22.9067i			0.732849i	−0.930448	+	0.366425i	$0.880582\pi$
$978$	2.04628	−	7.47334i	0.0654329	−	0.238971i
$979$	−87.8196	+	50.7026i	−2.80673	+	1.62046i
$980$	−0.459197	−	31.8539i	−0.0146685	−	1.01754i
$981$	23.7941	+	0.259891i	0.759689	+	0.00829769i
$982$	2.22456	+	3.85305i	0.0709885	+	0.122956i
$983$	1.40908	+	0.813534i	0.0449428	+	0.0259477i	0.522303	−	0.852760i	$-0.325073\pi$
$983$	1.40908	+	0.813534i	0.0449428	+	0.0259477i	−0.477360	+	0.878708i	$0.658406\pi$
$984$	−15.3663	−	4.20747i	−0.489861	−	0.134129i
$985$	−34.3916	−	19.2004i	−1.09581	−	0.611777i
$986$	2.32615	+	1.34300i	0.0740797	+	0.0427700i
$987$	14.0826	−	13.9296i	0.448254	−	0.443385i
$988$	10.9584	−	1.95225i	0.348632	−	0.0621094i
$989$		−	20.3552i		−	0.647259i
$990$	−20.9224	+	36.5327i	−0.664958	+	1.16109i
$991$	−20.7104	−	11.9571i	−0.657886	−	0.379831i	0.133585	−	0.991037i	$-0.457351\pi$
$991$	−20.7104	−	11.9571i	−0.657886	−	0.379831i	−0.791471	+	0.611207i	$0.790684\pi$
$992$	2.18537	+	3.78516i	0.0693854	+	0.120179i
$993$	10.5031	+	40.0723i	0.333307	+	1.27166i
$994$	−5.85112	−	10.1344i	−0.185586	−	0.321445i
$995$	−0.155951	−	10.8181i	−0.00494399	−	0.342958i
$996$	−10.7072	−	10.8248i	−0.339270	−	0.342996i
$997$	23.4452	−	13.5361i	0.742517	−	0.428693i	−0.0804665	−	0.996757i	$-0.525641\pi$
$997$	23.4452	−	13.5361i	0.742517	−	0.428693i	0.822984	+	0.568065i	$0.192308\pi$
$998$	−28.8156	+	16.6367i	−0.912143	+	0.526626i
$999$	8.50361	−	8.22945i	0.269042	−	0.260368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.n.a.179.18	yes	80
3.2	odd	2	inner	570.2.n.a.179.29	yes	80
5.4	even	2	inner	570.2.n.a.179.23	yes	80
15.14	odd	2	inner	570.2.n.a.179.12	✓	80
19.12	odd	6	inner	570.2.n.a.449.12	yes	80
57.50	even	6	inner	570.2.n.a.449.23	yes	80
95.69	odd	6	inner	570.2.n.a.449.29	yes	80
285.164	even	6	inner	570.2.n.a.449.18	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.12	✓	80	15.14	odd	2	inner
570.2.n.a.179.18	yes	80	1.1	even	1	trivial
570.2.n.a.179.23	yes	80	5.4	even	2	inner
570.2.n.a.179.29	yes	80	3.2	odd	2	inner
570.2.n.a.449.12	yes	80	19.12	odd	6	inner
570.2.n.a.449.18	yes	80	285.164	even	6	inner
570.2.n.a.449.23	yes	80	57.50	even	6	inner
570.2.n.a.449.29	yes	80	95.69	odd	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.67546 - 0.439145i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.95241 + 1.09000i) q^{5} +(-1.67056 - 0.457417i) q^{6} +4.60944i q^{7} -1.00000i q^{8} +(2.61430 - 1.47153i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.67546 - 0.439145i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.95241 + 1.09000i) q^{5} +(-1.67056 - 0.457417i) q^{6} +4.60944i q^{7} -1.00000i q^{8} +(2.61430 - 1.47153i) q^{9} +(-1.14583 - 1.92017i) q^{10} -6.27586i q^{11} +(1.21804 + 1.23141i) q^{12} +(-1.27680 - 2.21149i) q^{13} +(2.30472 - 3.99190i) q^{14} +(3.74984 + 0.968866i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.20522 + 2.08749i) q^{17} +(-2.99982 - 0.0327655i) q^{18} +(2.80775 + 3.33415i) q^{19} +(0.0322312 + 2.23584i) q^{20} +(2.02421 + 7.72292i) q^{21} +(-3.13793 + 5.43505i) q^{22} +(1.74466 + 3.02184i) q^{23} +(-0.439145 - 1.67546i) q^{24} +(2.62378 + 4.25626i) q^{25} +2.55360i q^{26} +(3.73393 - 3.61355i) q^{27} +(-3.99190 + 2.30472i) q^{28} +(0.557163 + 0.965035i) q^{29} +(-2.76302 - 2.71398i) q^{30} +4.37073i q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.75601 - 10.5149i) q^{33} +(2.08749 - 1.20522i) q^{34} +(-5.02432 + 8.99951i) q^{35} +(2.58154 + 1.52829i) q^{36} +2.27739 q^{37} +(-0.764508 - 4.29133i) q^{38} +(-3.11039 - 3.14455i) q^{39} +(1.09000 - 1.95241i) q^{40} +(4.59916 - 7.96597i) q^{41} +(2.10844 - 7.70035i) q^{42} +(-5.05204 - 2.91679i) q^{43} +(5.43505 - 3.13793i) q^{44} +(6.70816 - 0.0234295i) q^{45} -3.48932i q^{46} +(-1.24051 - 2.14862i) q^{47} +(-0.457417 + 1.67056i) q^{48} -14.2470 q^{49} +(-0.144127 - 4.99792i) q^{50} +(-1.10257 + 4.02677i) q^{51} +(1.27680 - 2.21149i) q^{52} +(-0.0512773 + 0.0296049i) q^{53} +(-5.04046 + 1.26246i) q^{54} +(6.84072 - 12.2530i) q^{55} +4.60944 q^{56} +(6.16843 + 4.35321i) q^{57} -1.11433i q^{58} +(-4.22305 + 7.31454i) q^{59} +(1.03586 + 3.73189i) q^{60} +(-0.644175 - 1.11574i) q^{61} +(2.18537 - 3.78516i) q^{62} +(6.78296 + 12.0505i) q^{63} -1.00000 q^{64} +(-0.0823057 - 5.70944i) q^{65} +(-2.87069 + 10.4842i) q^{66} +(1.76268 + 3.05304i) q^{67} -2.41043 q^{68} +(4.25012 + 4.29680i) q^{69} +(8.85094 - 5.28164i) q^{70} +(1.26938 - 2.19862i) q^{71} +(-1.47153 - 2.61430i) q^{72} +(-10.9928 - 6.34671i) q^{73} +(-1.97227 - 1.13869i) q^{74} +(6.26514 + 5.97896i) q^{75} +(-1.48358 + 4.09866i) q^{76} +28.9282 q^{77} +(1.12140 + 4.27845i) q^{78} +(-8.43221 - 4.86834i) q^{79} +(-1.92017 + 1.14583i) q^{80} +(4.66917 - 7.69408i) q^{81} +(-7.96597 + 4.59916i) q^{82} -8.79050 q^{83} +(-5.67614 + 5.61448i) q^{84} +(-4.62845 + 2.76195i) q^{85} +(2.91679 + 5.05204i) q^{86} +(1.35729 + 1.37220i) q^{87} -6.27586 q^{88} +(-8.07900 - 13.9932i) q^{89} +(-5.82115 - 3.33379i) q^{90} +(10.1937 - 5.88535i) q^{91} +(-1.74466 + 3.02184i) q^{92} +(1.91938 + 7.32297i) q^{93} +2.48102i q^{94} +(1.84763 + 9.57007i) q^{95} +(1.23141 - 1.21804i) q^{96} +(3.17547 - 5.50008i) q^{97} +(12.3382 + 7.12349i) q^{98} +(-9.23514 - 16.4070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 40 q^{4}+O(q^{10}) \) 80 * q + 40 * q^4	\( 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) \) 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Introduction

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