LMFDB - Embedded newform 570.2.n.a.449.12

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			449.12
Character	$\chi$	$=$	570.449
Dual form			570.2.n.a.179.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.457417 - 1.67056i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.92017 + 1.14583i) q^{5} +(0.439145 + 1.67546i) q^{6} +4.60944i q^{7} +1.00000i q^{8} +(-2.58154 - 1.52829i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.457417 - 1.67056i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.92017 + 1.14583i) q^{5} +(0.439145 + 1.67546i) q^{6} +4.60944i q^{7} +1.00000i q^{8} +(-2.58154 - 1.52829i) q^{9} +(1.09000 - 1.95241i) q^{10} -6.27586i q^{11} +(-1.21804 - 1.23141i) q^{12} +(1.27680 - 2.21149i) q^{13} +(-2.30472 - 3.99190i) q^{14} +(1.03586 + 3.73189i) 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} +(7.70035 + 2.10844i) q^{21} +(3.13793 + 5.43505i) q^{22} +(1.74466 - 3.02184i) q^{23} +(1.67056 + 0.457417i) q^{24} +(2.37414 - 4.40039i) 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} +(-10.4842 - 2.87069i) q^{33} +(2.08749 + 1.20522i) q^{34} +(-5.28164 - 8.85094i) q^{35} +(-2.61430 + 1.47153i) q^{36} -2.27739 q^{37} +(-0.764508 + 4.29133i) q^{38} +(-3.11039 - 3.14455i) q^{39} +(-1.14583 - 1.92017i) q^{40} +(-4.59916 - 7.96597i) q^{41} +(-7.72292 + 2.02421i) 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} +(-1.67546 + 0.439145i) q^{48} -14.2470 q^{49} +(0.144127 + 4.99792i) q^{50} +(-4.03857 + 1.05853i) q^{51} +(-1.27680 - 2.21149i) q^{52} +(-0.0512773 - 0.0296049i) q^{53} +(1.42691 - 4.99639i) q^{54} +(7.19107 + 12.0507i) q^{55} -4.60944 q^{56} +(-4.28558 - 6.21561i) q^{57} -1.11433i q^{58} +(4.22305 + 7.31454i) q^{59} +(3.74984 + 0.968866i) q^{60} +(-0.644175 + 1.11574i) q^{61} +(2.18537 + 3.78516i) q^{62} +(7.04455 - 11.8995i) q^{63} -1.00000 q^{64} +(0.0823057 + 5.70944i) q^{65} +(10.5149 - 2.75601i) q^{66} +(-1.76268 + 3.05304i) q^{67} -2.41043 q^{68} +(-4.25012 - 4.29680i) q^{69} +(8.99951 + 5.02432i) q^{70} +(-1.26938 - 2.19862i) q^{71} +(1.52829 - 2.58154i) 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} +(4.26595 + 1.16806i) q^{78} +(-8.43221 + 4.86834i) q^{79} +(1.95241 + 1.09000i) q^{80} +(4.32868 + 7.89066i) q^{81} +(7.96597 + 4.59916i) q^{82} -8.79050 q^{83} +(5.67614 - 5.61448i) q^{84} +(4.70614 + 2.62738i) q^{85} +(-2.91679 + 5.05204i) q^{86} +(1.35729 + 1.37220i) q^{87} +6.27586 q^{88} +(8.07900 - 13.9932i) q^{89} +(-5.79772 + 3.37437i) q^{90} +(10.1937 + 5.88535i) q^{91} +(-1.74466 - 3.02184i) q^{92} +(-7.30157 - 1.99925i) q^{93} -2.48102i q^{94} +(-1.57100 + 9.61935i) q^{95} +(1.23141 - 1.21804i) q^{96} +(-3.17547 - 5.50008i) q^{97} +(12.3382 - 7.12349i) q^{98} +(-9.59131 + 16.2014i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	0.457417	−	1.67056i	0.264090	−	0.964498i
$3$	0.457417	−	1.67056i	0.264090	−	0.964498i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.92017	+	1.14583i	−0.858728	+	0.512431i
$5$	−1.92017	+	1.14583i	−0.858728	+	0.512431i
$6$	0.439145	+	1.67546i	0.179280	+	0.684002i
$7$			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
$9$	−2.58154	−	1.52829i	−0.860513	−	0.509429i
$10$	1.09000	−	1.95241i	0.344690	−	0.617405i
$11$		−	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	$-0.718113\pi$
$13$	1.27680	−	2.21149i	0.354121	−	0.613356i	0.986967	+	0.160922i	$0.0514467\pi$
$14$	−2.30472	−	3.99190i	−0.615963	−	1.06688i
$15$	1.03586	+	3.73189i	0.267457	+	0.963570i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.20522	−	2.08749i	−0.292308	−	0.506292i	0.682047	−	0.731308i	$-0.261090\pi$
$17$	−1.20522	−	2.08749i	−0.292308	−	0.506292i	−0.974355	+	0.225016i	$0.927756\pi$
$18$	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
$21$	7.70035	+	2.10844i	1.68035	+	0.460099i
$22$	3.13793	+	5.43505i	0.669009	+	1.15876i
$23$	1.74466	−	3.02184i	0.363786	−	0.630097i	−0.624794	−	0.780789i	$-0.714817\pi$
$23$	1.74466	−	3.02184i	0.363786	−	0.630097i	0.988581	+	0.150693i	$0.0481505\pi$
$24$	1.67056	+	0.457417i	0.341002	+	0.0933700i
$25$	2.37414	−	4.40039i	0.474829	−	0.880078i
$26$			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	$-0.866326\pi$
$29$	−0.557163	+	0.965035i	−0.103463	+	0.179203i	0.809646	+	0.586918i	$0.199659\pi$
$30$	−2.76302	−	2.71398i	−0.504457	−	0.495503i
$31$		−	4.37073i		−	0.785007i	−0.919751	−	0.392503i	$-0.871609\pi$
$31$		−	4.37073i		−	0.785007i	0.919751	−	0.392503i	$-0.128391\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−10.4842	−	2.87069i	−1.82506	−	0.499723i
$34$	2.08749	+	1.20522i	0.358002	+	0.206693i
$35$	−5.28164	−	8.85094i	−0.892761	−	1.49608i
$36$	−2.61430	+	1.47153i	−0.435717	+	0.245256i
$37$	−2.27739			−0.374400			−0.187200	−	0.982322i	$-0.559941\pi$
$37$	−2.27739			−0.374400			−0.187200	+	0.982322i	$0.559941\pi$
$38$	−0.764508	+	4.29133i	−0.124020	+	0.696146i
$39$	−3.11039	−	3.14455i	−0.498061	−	0.503530i
$40$	−1.14583	−	1.92017i	−0.181172	−	0.303606i
$41$	−4.59916	−	7.96597i	−0.718268	−	1.24408i	−0.961686	−	0.274154i	$-0.911602\pi$
$41$	−4.59916	−	7.96597i	−0.718268	−	1.24408i	0.243418	−	0.969921i	$-0.421731\pi$
$42$	−7.72292	+	2.02421i	−1.19167	+	0.312343i
$43$	5.05204	−	2.91679i	0.770428	−	0.444807i	−0.0625990	−	0.998039i	$-0.519939\pi$
$43$	5.05204	−	2.91679i	0.770428	−	0.444807i	0.833027	+	0.553232i	$0.186606\pi$
$44$	−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	−0.942203	−	0.335042i	$-0.891250\pi$
$47$	−1.24051	+	2.14862i	−0.180947	+	0.313409i	0.761256	+	0.648451i	$0.224583\pi$
$48$	−1.67546	+	0.439145i	−0.241831	+	0.0633851i
$49$	−14.2470			−2.03528
$50$	0.144127	+	4.99792i	0.0203827	+	0.706813i
$51$	−4.03857	+	1.05853i	−0.565513	+	0.148224i
$52$	−1.27680	−	2.21149i	−0.177061	−	0.306678i
$53$	−0.0512773	−	0.0296049i	−0.00704347	−	0.00406655i	0.496474	−	0.868052i	$-0.334628\pi$
$53$	−0.0512773	−	0.0296049i	−0.00704347	−	0.00406655i	−0.503518	+	0.863985i	$0.667961\pi$
$54$	1.42691	−	4.99639i	0.194177	−	0.679923i
$55$	7.19107	+	12.0507i	0.969644	+	1.62492i
$56$	−4.60944			−0.615963
$57$	−4.28558	−	6.21561i	−0.567639	−	0.823278i
$58$		−	1.11433i		−	0.146318i
$59$	4.22305	+	7.31454i	0.549795	+	0.952272i	0.998288	+	0.0584862i	$0.0186274\pi$
$59$	4.22305	+	7.31454i	0.549795	+	0.952272i	−0.448494	+	0.893786i	$0.648039\pi$
$60$	3.74984	+	0.968866i	0.484102	+	0.125080i
$61$	−0.644175	+	1.11574i	−0.0824781	+	0.142856i	−0.904314	−	0.426868i	$-0.859617\pi$
$61$	−0.644175	+	1.11574i	−0.0824781	+	0.142856i	0.821836	+	0.569725i	$0.192950\pi$
$62$	2.18537	+	3.78516i	0.277542	+	0.480716i
$63$	7.04455	−	11.8995i	0.887530	−	1.49919i
$64$	−1.00000			−0.125000
$65$	0.0823057	+	5.70944i	0.0102088	+	0.708169i
$66$	10.5149	−	2.75601i	1.29430	−	0.339241i
$67$	−1.76268	+	3.05304i	−0.215345	+	0.372989i	−0.953379	−	0.301775i	$-0.902421\pi$
$67$	−1.76268	+	3.05304i	−0.215345	+	0.372989i	0.738034	+	0.674763i	$0.235754\pi$
$68$	−2.41043			−0.292308
$69$	−4.25012	−	4.29680i	−0.511654	−	0.517274i
$70$	8.99951	+	5.02432i	1.07565	+	0.600521i
$71$	−1.26938	−	2.19862i	−0.150647	−	0.260929i	0.780818	−	0.624758i	$-0.214802\pi$
$71$	−1.26938	−	2.19862i	−0.150647	−	0.260929i	−0.931466	+	0.363829i	$0.881469\pi$
$72$	1.52829	−	2.58154i	0.180110	−	0.304237i
$73$	10.9928	−	6.34671i	1.28661	−	0.742827i	0.308565	−	0.951203i	$-0.400151\pi$
$73$	10.9928	−	6.34671i	1.28661	−	0.742827i	0.978049	+	0.208376i	$0.0668179\pi$
$74$	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
$78$	4.26595	+	1.16806i	0.483023	+	0.132257i
$79$	−8.43221	+	4.86834i	−0.948698	+	0.547731i	−0.892676	−	0.450699i	$-0.851175\pi$
$79$	−8.43221	+	4.86834i	−0.948698	+	0.547731i	−0.0560215	+	0.998430i	$0.517842\pi$
$80$	1.95241	+	1.09000i	0.218286	+	0.121866i
$81$	4.32868	+	7.89066i	0.480965	+	0.876740i
$82$	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
$85$	4.70614	+	2.62738i	0.510453	+	0.284980i
$86$	−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	−0.0189945	−	0.999820i	$-0.506046\pi$
$89$	8.07900	−	13.9932i	0.856372	−	1.48328i	0.875366	−	0.483460i	$-0.160620\pi$
$90$	−5.79772	+	3.37437i	−0.611134	+	0.355690i
$91$	10.1937	+	5.88535i	1.06859	+	0.616952i
$92$	−1.74466	−	3.02184i	−0.181893	−	0.315048i
$93$	−7.30157	−	1.99925i	−0.757137	−	0.207312i
$94$		−	2.48102i		−	0.255897i
$95$	−1.57100	+	9.61935i	−0.161181	+	0.986925i
$96$	1.23141	−	1.21804i	0.125681	−	0.124316i
$97$	−3.17547	−	5.50008i	−0.322421	−	0.558449i	0.658566	−	0.752523i	$-0.271163\pi$
$97$	−3.17547	−	5.50008i	−0.322421	−	0.558449i	−0.980987	+	0.194074i	$0.937830\pi$
$98$	12.3382	−	7.12349i	1.24635	−	0.719581i
$99$	−9.59131	+	16.2014i	−0.963963	+	1.62830i
$100$	−2.62378	−	4.25626i	−0.262378	−	0.425626i
$101$	13.5746	+	7.83727i	1.35072	+	0.779838i	0.988350	−	0.152197i	$-0.0486348\pi$
$101$	13.5746	+	7.83727i	1.35072	+	0.779838i	0.362369	+	0.932035i	$0.381968\pi$
$102$	2.96824	−	2.93600i	0.293900	−	0.290707i
$103$	−15.4529			−1.52262			−0.761311	−	0.648387i	$-0.775444\pi$
$103$	−15.4529			−1.52262			−0.761311	+	0.648387i	$0.775444\pi$
$104$	2.21149	+	1.27680i	0.216854	+	0.125201i
$105$	−17.2019	+	4.77473i	−1.67874	+	0.465965i
$106$	0.0592099			0.00575097
$107$			4.71448i			0.455766i	0.973689	+	0.227883i	$0.0731804\pi$
$107$			4.71448i			0.455766i	−0.973689	+	0.227883i	$0.926820\pi$
$108$	1.26246	+	5.04046i	0.121480	+	0.485018i
$109$	6.86919	−	3.96593i	0.657949	−	0.379867i	−0.133546	−	0.991043i	$-0.542636\pi$
$109$	6.86919	−	3.96593i	0.657949	−	0.379867i	0.791495	+	0.611176i	$0.209303\pi$
$110$	−12.2530	−	6.84072i	−1.16828	−	0.652237i
$111$	−1.04172	+	3.80451i	−0.0988754	+	0.361108i
$112$	3.99190	−	2.30472i	0.377199	−	0.217776i
$113$			14.0526i			1.32196i	0.750404	+	0.660979i	$0.229859\pi$
$113$			14.0526i			1.32196i	−0.750404	+	0.660979i	$0.770141\pi$
$114$	6.81923	+	3.24009i	0.638679	+	0.303462i
$115$	0.112465	+	7.80154i	0.0104874	+	0.727497i
$116$	0.557163	+	0.965035i	0.0517313	+	0.0896013i
$117$	−6.67590	+	3.75772i	−0.617187	+	0.347401i
$118$	−7.31454	−	4.22305i	−0.673358	−	0.388764i
$119$	9.62219	−	5.55537i	0.882065	−	0.509260i
$120$	−3.73189	+	1.03586i	−0.340673	+	0.0945604i
$121$	−28.3864			−2.58058
$122$		−	1.28835i		−	0.116642i
$123$	−15.4114	+	4.03939i	−1.38960	+	0.364219i
$124$	−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	$-0.711648\pi$
$127$	4.20396	−	7.28147i	0.373041	−	0.646126i	0.990032	+	0.140845i	$0.0449818\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.56179	−	9.77392i	−0.225553	−	0.860546i
$130$	−2.92600	−	4.90337i	−0.256627	−	0.430054i
$131$	−4.94573	+	2.85542i	−0.432110	+	0.249479i	−0.700245	−	0.713902i	$-0.746926\pi$
$131$	−4.94573	+	2.85542i	−0.432110	+	0.249479i	0.268135	+	0.963381i	$0.413593\pi$
$132$	−7.72819	+	7.64424i	−0.672652	+	0.665345i
$133$	15.3686	+	12.9422i	1.33262	+	1.12223i
$134$		−	3.52535i		−	0.304544i
$135$	3.02929	−	11.2171i	0.260720	−	0.965415i
$136$	2.08749	−	1.20522i	0.179001	−	0.103346i
$137$	4.51364	−	7.81786i	0.385627	−	0.667925i	−0.606229	−	0.795290i	$-0.707319\pi$
$137$	4.51364	−	7.81786i	0.385627	−	0.667925i	0.991856	+	0.127365i	$0.0406520\pi$
$138$	5.82911	+	1.59607i	0.496207	+	0.135867i
$139$	7.12104	−	12.3340i	0.603999	−	1.04616i	−0.388210	−	0.921571i	$-0.626906\pi$
$139$	7.12104	−	12.3340i	0.603999	−	1.04616i	0.992209	−	0.124586i	$-0.0397603\pi$
$140$	−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
$147$	−6.51681	+	23.8004i	−0.537498	+	1.96303i
$148$	−1.13869	+	1.97227i	−0.0936000	+	0.162120i
$149$	9.49064	−	5.47943i	0.777504	−	0.448892i	−0.0580411	−	0.998314i	$-0.518485\pi$
$149$	9.49064	−	5.47943i	0.777504	−	0.448892i	0.835545	+	0.549422i	$0.185152\pi$
$150$	8.41525	+	2.04536i	0.687103	+	0.167003i
$151$			2.01053i			0.163615i	0.996648	+	0.0818073i	$0.0260692\pi$
$151$			2.01053i			0.163615i	−0.996648	+	0.0818073i	$0.973931\pi$
$152$	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
$155$	5.00812	+	8.39257i	0.402262	+	0.674107i
$156$	−4.27845	+	1.12140i	−0.342550	+	0.0897840i
$157$	2.18249	−	1.26006i	0.174182	−	0.100564i	−0.410374	−	0.911917i	$-0.634602\pi$
$157$	2.18249	−	1.26006i	0.174182	−	0.100564i	0.584556	+	0.811353i	$0.301269\pi$
$158$	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
$162$	−7.69408	−	4.66917i	−0.604504	−	0.366845i
$163$			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
$165$	23.4208	−	6.50089i	1.82331	−	0.506094i
$166$	7.61280	−	4.39525i	0.590868	−	0.341138i
$167$	−7.00410	−	4.04382i	−0.541993	−	0.312920i	0.203893	−	0.978993i	$-0.434641\pi$
$167$	−7.00410	−	4.04382i	−0.541993	−	0.312920i	−0.745886	+	0.666073i	$0.767974\pi$
$168$	−2.10844	+	7.70035i	−0.162670	+	0.594095i
$169$	3.23955	+	5.61107i	0.249196	+	0.431621i
$170$	−5.38933	+	0.0776911i	−0.413343	+	0.00595863i
$171$	−12.3438	+	4.31619i	−0.943957	+	0.330067i
$172$		−	5.83359i		−	0.444807i
$173$	−9.62554	+	5.55731i	−0.731816	+	0.422514i	−0.819086	−	0.573670i	$-0.805519\pi$
$173$	−9.62554	+	5.55731i	−0.731816	+	0.422514i	0.0872698	+	0.996185i	$0.472186\pi$
$174$	−1.86155	−	0.509712i	−0.141124	−	0.0386412i
$175$	20.2834	+	10.9435i	1.53328	+	0.827249i
$176$	−5.43505	+	3.13793i	−0.409683	+	0.236530i
$177$	14.1511	−	3.70906i	1.06366	−	0.278790i
$178$			16.1580i			1.21109i
$179$	4.26112			0.318491			0.159245	−	0.987239i	$-0.449094\pi$
$179$	4.26112			0.318491			0.159245	+	0.987239i	$0.449094\pi$
$180$	3.33379	−	5.82115i	0.248486	−	0.433883i
$181$	16.7578	+	9.67510i	1.24559	+	0.719145i	0.970228	−	0.242195i	$-0.0778672\pi$
$181$	16.7578	+	9.67510i	1.24559	+	0.719145i	0.275367	+	0.961339i	$0.411201\pi$
$182$	−11.7707			−0.872502
$183$	1.56926	+	1.58649i	0.116003	+	0.117277i
$184$	3.02184	+	1.74466i	0.222773	+	0.128618i
$185$	4.37298	−	2.60950i	0.321508	−	0.191854i
$186$	7.32297	−	1.91938i	0.536946	−	0.140736i
$187$	−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
$190$	−3.44915	−	9.11610i	−0.250228	−	0.661352i
$191$			3.83614i			0.277573i	0.990322	+	0.138786i	$0.0443202\pi$
$191$			3.83614i			0.277573i	−0.990322	+	0.138786i	$0.955680\pi$
$192$	−0.457417	+	1.67056i	−0.0330113	+	0.120562i
$193$	−7.45236	−	12.9079i	−0.536432	−	0.929128i	−0.999093	−	0.0425924i	$-0.986438\pi$
$193$	−7.45236	−	12.9079i	−0.536432	−	0.929128i	0.462660	−	0.886536i	$-0.346895\pi$
$194$	5.50008	+	3.17547i	0.394883	+	0.227986i
$195$	9.57561	+	2.47410i	0.685723	+	0.177174i
$196$	−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	−0.938943	−	0.344072i	$-0.888194\pi$
$199$	−2.41926	+	4.19028i	−0.171497	+	0.297041i	0.767447	+	0.641113i	$0.221527\pi$
$200$	4.40039	+	2.37414i	0.311155	+	0.167877i
$201$	4.29401	+	4.34117i	0.302876	+	0.306203i
$202$	−15.6745			−1.10286
$203$	−4.44828	−	2.56821i	−0.312208	−	0.180253i
$204$	−1.10257	+	4.02677i	−0.0771956	+	0.281930i
$205$	17.9588	+	10.0262i	1.25430	+	0.700261i
$206$	13.3826	−	7.72646i	0.932412	−	0.538328i
$207$	−9.12213	+	5.13465i	−0.634032	+	0.356883i
$208$	−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	−0.646593	−	0.762835i	$-0.723807\pi$
$211$	−4.49219	+	2.59357i	−0.309255	+	0.178548i	0.337338	+	0.941384i	$0.390473\pi$
$212$	−0.0512773	+	0.0296049i	−0.00352174	+	0.00203328i
$213$	−4.25357	+	1.11488i	−0.291450	+	0.0763903i
$214$	−2.35724	−	4.08286i	−0.161138	−	0.279099i
$215$	−6.35864	+	11.3895i	−0.433656	+	0.776760i
$216$	−3.61355	−	3.73393i	−0.245871	−	0.254062i
$217$	20.1466			1.36764
$218$	−3.96593	+	6.86919i	−0.268607	+	0.465240i
$219$	−5.57425	−	21.2673i	−0.376673	−	1.43711i
$220$	14.0318	−	0.202278i	0.946023	−	0.0136376i
$221$	−6.15529			−0.414049
$222$	−1.00010	−	3.81566i	−0.0671225	−	0.256090i
$223$	0.325555	+	0.563878i	0.0218008	+	0.0377601i	0.876720	−	0.481001i	$-0.159727\pi$
$223$	0.325555	+	0.563878i	0.0218008	+	0.0377601i	−0.854919	+	0.518761i	$0.826393\pi$
$224$	−2.30472	+	3.99190i	−0.153991	+	0.266720i
$225$	−12.8540	+	7.73141i	−0.856933	+	0.515427i
$226$	−7.02630	−	12.1699i	−0.467383	−	0.809531i
$227$		−	8.15722i		−	0.541414i	−0.962662	−	0.270707i	$-0.912743\pi$
$227$		−	8.15722i		−	0.541414i	0.962662	−	0.270707i	$-0.0872575\pi$
$228$	−7.52567	+	0.603616i	−0.498399	+	0.0399754i
$229$	6.22202			0.411162			0.205581	−	0.978640i	$-0.434092\pi$
$229$	6.22202			0.411162			0.205581	+	0.978640i	$0.434092\pi$
$230$	−3.99817	−	6.70010i	−0.263631	−	0.441791i
$231$	13.2323	−	48.3263i	0.870620	−	3.17964i
$232$	−0.965035	−	0.557163i	−0.0633577	−	0.0365796i
$233$	13.8286	+	23.9519i	0.905942	+	1.56914i	0.819647	+	0.572868i	$0.194169\pi$
$233$	13.8286	+	23.9519i	0.905942	+	1.56914i	0.0862948	+	0.996270i	$0.472497\pi$
$234$	3.90264	−	6.59223i	0.255123	−	0.430947i
$235$	−0.0799662	−	5.54715i	−0.00521642	−	0.361856i
$236$	8.44611			0.549795
$237$	4.27581	+	16.3134i	0.277744	+	1.05967i
$238$	−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	0.162021	−	0.986787i	$-0.448199\pi$
$241$	−9.49382	−	5.48126i	−0.611551	−	0.353079i	−0.773572	+	0.633708i	$0.781532\pi$
$242$	24.5834	−	14.1932i	1.58028	−	0.912374i
$243$	15.1618	−	3.62200i	0.972632	−	0.232351i
$244$	0.644175	+	1.11574i	0.0412391	+	0.0714281i
$245$	27.3567	−	16.3246i	1.74775	−	1.04294i
$246$	11.3269	−	11.2039i	0.722179	−	0.714334i
$247$	−3.78848	−	10.4663i	−0.241055	−	0.665958i
$248$	4.37073			0.277542
$249$	−4.02093	+	14.6851i	−0.254816	+	0.930628i
$250$	−6.00352	−	9.43174i	−0.379696	−	0.596516i
$251$	12.7805	+	7.37881i	0.806697	+	0.465747i	0.845807	−	0.533488i	$-0.179119\pi$
$251$	12.7805	+	7.37881i	0.806697	+	0.465747i	−0.0391106	+	0.999235i	$0.512452\pi$
$252$	−6.78296	−	12.0505i	−0.427286	−	0.759109i
$253$	−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	0.421656	−	0.906756i	$-0.361449\pi$
$257$	−2.44940	−	1.41416i	−0.152789	−	0.0882129i	−0.574445	+	0.818543i	$0.694782\pi$
$258$	7.10554	+	7.18357i	0.442371	+	0.447230i
$259$		−	10.4975i		−	0.652282i
$260$	4.98567	+	2.78344i	0.309198	+	0.172622i
$261$	2.91319	−	1.63977i	0.180322	−	0.101499i
$262$	2.85542	−	4.94573i	0.176408	−	0.305548i
$263$	4.38223	+	7.59024i	0.270220	+	0.468034i	0.968918	−	0.247382i	$-0.0795703\pi$
$263$	4.38223	+	7.59024i	0.270220	+	0.468034i	−0.698698	+	0.715417i	$0.746237\pi$
$264$	2.87069	−	10.4842i	0.176679	−	0.645258i
$265$	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	$-0.248800\pi$
$269$	−4.18520	−	7.24897i	−0.255176	−	0.441978i	−0.964943	+	0.262458i	$0.915467\pi$
$270$	2.98511	+	11.2289i	0.181668	+	0.683372i
$271$	−12.8353	−	22.2314i	−0.779690	−	1.35046i	−0.932120	−	0.362149i	$-0.882043\pi$
$271$	−12.8353	−	22.2314i	−0.779690	−	1.35046i	0.152430	−	0.988314i	$-0.451290\pi$
$272$	−1.20522	+	2.08749i	−0.0730769	+	0.126573i
$273$	14.4946	−	14.3372i	0.877254	−	0.867724i
$274$			9.02729i			0.545358i
$275$	−27.6162	−	14.8998i	−1.66532	−	0.898491i
$276$	−5.84620	+	1.53231i	−0.351900	+	0.0922345i
$277$		−	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
$279$	−6.67973	+	11.2832i	−0.399905	+	0.675508i
$280$	8.85094	−	5.28164i	0.528945	−	0.315639i
$281$	2.75553	−	4.77271i	0.164381	−	0.284716i	−0.772054	−	0.635557i	$-0.780771\pi$
$281$	2.75553	−	4.77271i	0.164381	−	0.284716i	0.936435	+	0.350840i	$0.114104\pi$
$282$	−4.14469	−	1.13486i	−0.246813	−	0.0675800i
$283$	−26.7533	+	15.4460i	−1.59032	+	0.918172i	−0.597070	+	0.802189i	$0.703669\pi$
$283$	−26.7533	+	15.4460i	−1.59032	+	0.918172i	−0.993251	+	0.115983i	$0.962998\pi$
$284$	−2.53875			−0.150647
$285$	15.3511	+	7.02451i	0.909321	+	0.416096i
$286$	16.0261			0.947641
$287$	36.7187	−	21.1996i	2.16744	−	1.25137i
$288$	−1.47153	−	2.61430i	−0.0867110	−	0.154049i
$289$	5.59491	−	9.69067i	0.329112	−	0.570039i
$290$	1.27683	+	2.13970i	0.0749780	+	0.125648i
$291$	−10.6407	+	2.78898i	−0.623771	+	0.163493i
$292$		−	12.6934i		−	0.742827i
$293$		−	26.7703i		−	1.56394i	−0.623318	−	0.781968i	$-0.714216\pi$
$293$		−	26.7703i		−	1.56394i	0.623318	−	0.781968i	$-0.285784\pi$
$294$	−6.25648	−	23.8702i	−0.364885	−	1.39214i
$295$	−16.4902	−	9.20630i	−0.960098	−	0.536011i
$296$		−	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
$300$	−8.31050	+	2.43629i	−0.479807	+	0.140659i
$301$	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
$306$	−3.54703	−	6.30160i	−0.202770	−	0.360239i
$307$	14.0443	+	24.3254i	0.801548	+	1.38832i	0.918597	+	0.395196i	$0.129323\pi$
$307$	14.0443	+	24.3254i	0.801548	+	1.38832i	−0.117048	+	0.993126i	$0.537343\pi$
$308$	14.4641	−	25.0526i	0.824169	−	1.42750i
$309$	−7.06844	+	25.8150i	−0.402109	+	1.46857i
$310$	−8.53344	−	4.76412i	−0.484667	−	0.270584i
$311$			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	$-0.0916298\pi$
$313$	21.0959	+	12.1797i	1.19241	+	0.688439i	0.233558	+	0.972343i	$0.424963\pi$
$314$	−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	0.976843	−	0.213957i	$-0.0686352\pi$
$317$	22.7893	+	13.1574i	1.27997	+	0.738992i	0.303129	+	0.952949i	$0.401969\pi$
$318$	0.0270836	−	0.0989136i	0.00151877	−	0.00554680i
$319$	6.05642	+	3.49668i	0.339095	+	0.195776i
$320$	1.92017	−	1.14583i	0.107341	−	0.0640539i
$321$	7.87582	+	2.15649i	0.439585	+	0.120363i
$322$	−16.0838			−0.896316
$323$	−10.3440	−	1.84279i	−0.575553	−	0.102536i
$324$	8.99785	+	0.196581i	0.499881	+	0.0109212i
$325$	−6.70009	−	10.8688i	−0.371654	−	0.602893i
$326$	−2.23678	−	3.87421i	−0.123884	−	0.214573i
$327$	−3.48323	−	13.2895i	−0.192623	−	0.734910i
$328$	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	$-0.771696\pi$
$331$		−	23.9173i		−	1.31461i	0.753624	−	0.657306i	$-0.228304\pi$
$332$	−4.39525	+	7.61280i	−0.241221	+	0.417807i
$333$	5.87916	+	3.48050i	0.322176	+	0.190730i
$334$	8.08764			0.442536
$335$	−0.113626	−	7.88211i	−0.00620807	−	0.430646i
$336$	−2.02421	−	7.72292i	−0.110430	−	0.421320i
$337$	7.94689	+	13.7644i	0.432895	+	0.749796i	0.997121	−	0.0758243i	$-0.0241588\pi$
$337$	7.94689	+	13.7644i	0.432895	+	0.749796i	−0.564226	+	0.825620i	$0.690825\pi$
$338$	−5.61107	−	3.23955i	−0.305202	−	0.176208i
$339$	23.4757	+	6.42791i	1.27503	+	0.349116i
$340$	4.62845	−	2.76195i	0.251013	−	0.149788i
$341$	−27.4301			−1.48542
$342$	8.53199	−	9.90985i	0.461357	−	0.535863i
$343$		−	33.4045i		−	1.80367i
$344$	2.91679	+	5.05204i	0.157263	+	0.272388i
$345$	13.0844	+	3.38068i	0.704439	+	0.182010i
$346$	5.55731	−	9.62554i	0.298763	−	0.517472i
$347$	6.74308	+	11.6794i	0.361988	+	0.626981i	0.988288	−	0.152601i	$-0.0487649\pi$
$347$	6.74308	+	11.6794i	0.361988	+	0.626981i	−0.626300	+	0.779582i	$0.715432\pi$
$348$	1.86700	−	0.489351i	0.100082	−	0.0262319i
$349$	−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
$351$	3.22382	+	12.8713i	0.172075	+	0.687021i
$352$	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
$355$	4.95667	+	2.76725i	0.263073	+	0.146870i
$356$	−8.07900	−	13.9932i	−0.428186	−	0.741640i
$357$	−4.87922	−	18.6156i	−0.258236	−	0.985240i
$358$	−3.69023	+	2.13056i	−0.195035	+	0.112603i
$359$	7.33647	−	4.23571i	0.387204	−	0.223552i	−0.293744	−	0.955884i	$-0.594901\pi$
$359$	7.33647	−	4.23571i	0.387204	−	0.223552i	0.680948	+	0.732332i	$0.261568\pi$
$360$	0.0234295	+	6.70816i	0.00123484	+	0.353551i
$361$	−3.23309	−	18.7229i	−0.170163	−	0.985416i
$362$	−19.3502			−1.01702
$363$	−12.9844	+	47.4212i	−0.681506	+	2.48897i
$364$	10.1937	−	5.88535i	0.534296	−	0.308476i
$365$	−13.8359	+	24.7827i	−0.724204	+	1.29719i
$366$	−2.15226	−	0.589314i	−0.112501	−	0.0308039i
$367$	−21.8594	−	12.6205i	−1.14105	−	0.658787i	−0.194362	−	0.980930i	$-0.562264\pi$
$367$	−21.8594	−	12.6205i	−1.14105	−	0.658787i	−0.946691	+	0.322143i	$0.895597\pi$
$368$	−3.48932			−0.181893
$369$	−0.301388	+	27.5933i	−0.0156896	+	1.43645i
$370$	−2.48236	+	4.44638i	−0.129052	+	0.231156i
$371$	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	$-0.756013\pi$
$373$	−27.8240			−1.44067			−0.720337	+	0.693624i	$0.756013\pi$
$374$	7.56376	−	13.1008i	0.391113	−	0.677427i
$375$	18.8810	+	4.30186i	0.975013	+	0.222147i
$376$	−2.14862	−	1.24051i	−0.110807	−	0.0639743i
$377$	1.42277	+	2.46432i	0.0732766	+	0.126919i
$378$	23.0306	+	6.57725i	1.18457	+	0.338297i
$379$		−	17.6962i		−	0.908995i	−0.890748	−	0.454497i	$-0.849819\pi$
$379$		−	17.6962i		−	0.908995i	0.890748	−	0.454497i	$-0.150181\pi$
$380$	7.54510	+	6.17020i	0.387056	+	0.316525i
$381$	−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	−0.903773	−	0.428011i	$-0.859214\pi$
$383$	−19.2767	+	11.1294i	−0.984991	+	0.568685i	−0.0812179	+	0.996696i	$0.525881\pi$
$384$	−0.439145	−	1.67546i	−0.0224100	−	0.0855002i
$385$	−55.5472	+	33.1468i	−2.83095	+	1.68932i
$386$	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	$-0.415391\pi$
$389$	−8.70929	−	5.02831i	−0.441579	−	0.254946i	−0.704267	+	0.709935i	$0.748724\pi$
$390$	−9.52977	+	2.64517i	−0.482559	+	0.133943i
$391$	−8.41076			−0.425350
$392$		−	14.2470i		−	0.719581i
$393$	2.50788	+	9.56825i	0.126506	+	0.482654i
$394$	15.2550	−	8.80750i	0.768538	−	0.443715i
$395$	10.6130	−	19.0099i	0.533999	−	0.956494i
$396$	9.23514	+	16.4070i	0.464083	+	0.824483i
$397$	18.5066	−	10.6848i	0.928819	−	0.536254i	0.0423812	−	0.999102i	$-0.486506\pi$
$397$	18.5066	−	10.6848i	0.928819	−	0.536254i	0.886438	+	0.462848i	$0.153172\pi$
$398$		−	4.83852i		−	0.242533i
$399$	28.6505	−	19.7541i	1.43432	−	0.988944i
$400$	−4.99792	+	0.144127i	−0.249896	+	0.00720637i
$401$	7.33894	+	12.7114i	0.366489	+	0.634778i	0.989014	−	0.147822i	$-0.0472263\pi$
$401$	7.33894	+	12.7114i	0.366489	+	0.634778i	−0.622525	+	0.782600i	$0.713893\pi$
$402$	−5.88931	−	1.61256i	−0.293732	−	0.0804271i
$403$	−9.66581	−	5.58056i	−0.481488	−	0.277987i
$404$	13.5746	−	7.83727i	0.675359	−	0.389919i
$405$	−17.3532	−	10.1915i	−0.862287	−	0.506420i
$406$	5.13643			0.254917
$407$			14.2926i			0.708456i
$408$	−1.05853	−	4.03857i	−0.0524049	−	0.199939i
$409$	26.1399	+	15.0919i	1.29254	+	0.746246i	0.979103	−	0.203365i	$-0.0651878\pi$
$409$	26.1399	+	15.0919i	1.29254	+	0.746246i	0.313432	+	0.949611i	$0.398521\pi$
$410$	−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
$414$	5.33267	−	9.00780i	0.262087	−	0.442709i
$415$	16.8793	−	10.0724i	0.828573	−	0.494436i
$416$	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	$0.930217\pi$
$420$	−4.46593	+	17.2847i	−0.217915	+	0.843406i
$421$	14.3115	−	8.26272i	0.697498	−	0.402701i	−0.108917	−	0.994051i	$-0.534738\pi$
$421$	14.3115	−	8.26272i	0.697498	−	0.402701i	0.806415	+	0.591350i	$0.201405\pi$
$422$	2.59357	−	4.49219i	0.126253	−	0.218676i
$423$	6.48613	−	3.65090i	0.315367	−	0.177513i
$424$	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	$-0.700724\pi$
$431$	8.40089	−	14.5508i	0.404657	−	0.700886i	0.994281	+	0.106791i	$0.0340577\pi$
$432$	4.99639	+	1.42691i	0.240389	+	0.0686521i
$433$	18.6240	−	32.2577i	0.895013	−	1.55021i	0.0612243	−	0.998124i	$-0.480499\pi$
$433$	18.6240	−	32.2577i	0.895013	−	1.55021i	0.833789	−	0.552084i	$-0.186167\pi$
$434$	−17.4475	+	10.0733i	−0.837507	+	0.483535i
$435$	−4.17855	−	1.07963i	−0.200346	−	0.0517645i
$436$		−	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	−0.575226	−	0.817994i	$-0.695086\pi$
$439$	−3.23579	+	1.86818i	−0.154436	+	0.0891635i	0.420791	+	0.907158i	$0.361753\pi$
$440$	−12.0507	+	7.19107i	−0.574497	+	0.342821i
$441$	36.7791	+	21.7735i	1.75139	+	1.03683i
$442$	5.33063	−	3.07764i	0.253552	−	0.146389i
$443$	−4.87764	+	8.44831i	−0.231744	+	0.401392i	−0.958321	−	0.285693i	$-0.907776\pi$
$443$	−4.87764	+	8.44831i	−0.231744	+	0.401392i	0.726578	+	0.687084i	$0.241110\pi$
$444$	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
$447$	−4.81252	−	18.3611i	−0.227624	−	0.868449i
$448$		−	4.60944i		−	0.217776i
$449$	20.1146			0.949265			0.474633	−	0.880184i	$-0.342581\pi$
$449$	20.1146			0.949265			0.474633	+	0.880184i	$0.342581\pi$
$450$	7.26619	−	13.1226i	0.342531	−	0.618605i
$451$	−49.9933	+	28.8637i	−2.35409	+	1.35914i
$452$	12.1699	+	7.02630i	0.572425	+	0.330490i
$453$	3.35871	+	0.919652i	0.157806	+	0.0432090i
$454$	4.07861	+	7.06436i	0.191419	+	0.331547i
$455$	−26.3173	+	0.379384i	−1.23378	+	0.0177858i
$456$	6.21561	−	4.28558i	0.291073	−	0.200691i
$457$			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
$459$	12.0435	+	3.43946i	0.562141	+	0.160540i
$460$	6.81256	+	3.80337i	0.317637	+	0.177333i
$461$	−3.84009	+	2.21708i	−0.178851	+	0.103260i	−0.586753	−	0.809766i	$-0.699594\pi$
$461$	−3.84009	+	2.21708i	−0.178851	+	0.103260i	0.407902	+	0.913026i	$0.366261\pi$
$462$	12.7037	+	48.4680i	0.591028	+	2.25493i
$463$			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
$465$	16.3111	−	4.52745i	0.756409	−	0.209956i
$466$	−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
$470$	2.84283	+	4.76399i	0.131130	+	0.219746i
$471$	−1.10670	−	4.22236i	−0.0509940	−	0.194556i
$472$	−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
$475$	−8.00556	−	20.2709i	−0.367320	−	0.930095i
$476$		−	11.1107i		−	0.509260i
$477$	0.0871294	+	0.154793i	0.00398938	+	0.00708747i
$478$	−7.00458	−	12.1323i	−0.320382	−	0.554918i
$479$	−14.0729	−	8.12501i	−0.643008	−	0.371241i	0.142764	−	0.989757i	$-0.454401\pi$
$479$	−14.0729	−	8.12501i	−0.643008	−	0.371241i	−0.785772	+	0.618516i	$0.787734\pi$
$480$	−0.968866	+	3.74984i	−0.0442225	+	0.171156i
$481$	−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
$485$	12.3996	+	6.92256i	0.563038	+	0.314337i
$486$	−11.3195	+	10.7177i	−0.513464	+	0.486163i
$487$	−15.7997			−0.715951			−0.357975	−	0.933731i	$-0.616533\pi$
$487$	−15.7997			−0.715951			−0.357975	+	0.933731i	$0.616533\pi$
$488$	−1.11574	−	0.644175i	−0.0505073	−	0.0291604i
$489$	7.47334	+	2.04628i	0.337956	+	0.0925361i
$490$	−15.5293	+	27.8159i	−0.701541	+	1.25659i
$491$	3.85305	−	2.22456i	0.173886	−	0.100393i	−0.410531	−	0.911847i	$-0.634657\pi$
$491$	3.85305	−	2.22456i	0.173886	−	0.100393i	0.584417	+	0.811454i	$0.301323\pi$
$492$	−4.20747	+	15.3663i	−0.189687	+	0.692768i
$493$	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
$498$	−3.86030	−	14.7281i	−0.172984	−	0.659982i
$499$	16.6367	+	28.8156i	0.744762	+	1.28997i	0.950306	+	0.311317i	$0.100770\pi$
$499$	16.6367	+	28.8156i	0.744762	+	1.28997i	−0.205544	+	0.978648i	$0.565896\pi$
$500$	9.91507	+	5.16636i	0.443416	+	0.231047i
$501$	−9.95924	+	9.85105i	−0.444946	+	0.440112i
$502$	−14.7576			−0.658665
$503$	6.97093	−	12.0740i	0.310818	−	0.538353i	−0.667721	−	0.744411i	$-0.732730\pi$
$503$	6.97093	−	12.0740i	0.310818	−	0.538353i	0.978540	+	0.206058i	$0.0660636\pi$
$504$	11.8995	+	7.04455i	0.530044	+	0.313789i
$505$	−35.0457	+	0.505210i	−1.55951	+	0.0224815i
$506$	21.8985			0.973505
$507$	10.8555	−	2.84527i	0.482108	−	0.126363i
$508$	−4.20396	−	7.28147i	−0.186520	−	0.323063i
$509$	−0.321137	+	0.556225i	−0.0142341	+	0.0246542i	−0.873055	−	0.487622i	$-0.837864\pi$
$509$	−0.321137	+	0.556225i	−0.0142341	+	0.0246542i	0.858821	+	0.512276i	$0.171198\pi$
$510$	−2.33539	+	9.03873i	−0.103413	+	0.400242i
$511$	29.2548	+	50.6708i	1.29416	+	2.24155i
$512$		−	1.00000i		−	0.0441942i
$513$	1.56416	+	22.5954i	0.0690592	+	0.997613i
$514$	2.82832			0.124752
$515$	29.6723	−	17.7064i	1.30752	−	0.780239i
$516$	−9.74536	−	2.66839i	−0.429016	−	0.117469i
$517$	13.4845	+	7.78526i	0.593046	+	0.342395i
$518$	5.24874	+	9.09109i	0.230617	+	0.399440i
$519$	4.88093	+	18.6221i	0.214249	+	0.817417i
$520$	−5.70944	+	0.0823057i	−0.250375	+	0.00360934i
$521$	−15.7298			−0.689135			−0.344568	−	0.938761i	$-0.611974\pi$
$521$	−15.7298			−0.689135			−0.344568	+	0.938761i	$0.611974\pi$
$522$	−1.70301	+	2.87668i	−0.0745387	+	0.125909i
$523$	2.02261	−	3.50326i	0.0884425	−	0.153187i	−0.818410	−	0.574634i	$-0.805144\pi$
$523$	2.02261	−	3.50326i	0.0884425	−	0.153187i	0.906853	+	0.421447i	$0.138478\pi$
$524$			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
$528$	2.75601	+	10.5149i	0.119940	+	0.457603i
$529$	5.41234	+	9.37444i	0.235319	+	0.407584i
$530$	−0.113693	+	0.0678445i	−0.00493852	+	0.00294698i
$531$	0.276741	−	25.3368i	0.0120095	−	1.09952i
$532$	18.8925	−	6.83849i	0.819095	−	0.296486i
$533$	−23.4888			−1.01741
$534$	26.9929	+	7.39095i	1.16810	+	0.319838i
$535$	−5.40200	−	9.05263i	−0.233549	−	0.391379i
$536$	−3.05304	−	1.76268i	−0.131871	−	0.0761360i
$537$	1.94911	−	7.11845i	0.0841103	−	0.307184i
$538$	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	−0.778711	−	0.627383i	$-0.784126\pi$
$541$	3.58134	−	6.20307i	0.153974	−	0.266691i	0.932685	+	0.360692i	$0.117459\pi$
$542$	22.2314	+	12.8353i	0.954922	+	0.551324i
$543$	23.8281	−	23.5693i	1.02256	−	1.01145i
$544$		−	2.41043i		−	0.103346i
$545$	−8.64576	+	15.4862i	−0.370344	+	0.663356i
$546$	−5.38412	+	19.6636i	−0.230419	+	0.841526i
$547$	−12.4830	+	21.6212i	−0.533736	+	0.924457i	0.465488	+	0.885054i	$0.345879\pi$
$547$	−12.4830	+	21.6212i	−0.533736	+	0.924457i	−0.999223	+	0.0394030i	$0.987454\pi$
$548$	−4.51364	−	7.81786i	−0.192813	−	0.333962i
$549$	3.36814	−	1.89585i	0.143749	−	0.0809129i
$550$	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
$555$	−2.35905	−	8.49896i	−0.100136	−	0.360761i
$556$	−7.12104	−	12.3340i	−0.302000	−	0.523079i
$557$	11.8399	−	20.5073i	0.501673	−	0.868924i	−0.498325	−	0.866991i	$-0.666051\pi$
$557$	11.8399	−	20.5073i	0.501673	−	0.868924i	0.999998	−	0.00193347i	$-0.000615443\pi$
$558$	0.143209	−	13.1114i	0.00606253	−	0.555050i
$559$		−	14.8967i		−	0.630062i
$560$	−5.02432	+	8.99951i	−0.212316	+	0.380299i
$561$	6.64317	+	25.3455i	0.280475	+	1.07009i
$562$			5.51105i			0.232470i
$563$		−	22.2752i		−	0.938786i	−0.882989	−	0.469393i	$-0.844473\pi$
$563$		−	22.2752i		−	0.938786i	0.882989	−	0.469393i	$-0.155527\pi$
$564$	4.15683	−	1.08953i	0.175034	−	0.0458773i
$565$	−16.1019	−	26.9835i	−0.677412	−	1.13520i
$566$	15.4460	−	26.7533i	0.649246	−	1.12453i
$567$	−36.3716	+	19.9528i	−1.52746	+	0.837939i
$568$	2.19862	−	1.26938i	0.0922522	−	0.0532618i
$569$	1.70293			0.0713903			0.0356952	−	0.999363i	$-0.488635\pi$
$569$	1.70293			0.0713903			0.0356952	+	0.999363i	$0.488635\pi$
$570$	−16.8067	+	1.59215i	−0.703955	+	0.0666877i
$571$	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
$573$	6.40849	+	1.75472i	0.267719	+	0.0733043i
$574$	−21.1996	+	36.7187i	−0.884852	+	1.53261i
$575$	−9.15520	−	14.8515i	−0.381798	−	0.619348i
$576$	2.58154	+	1.52829i	0.107564	+	0.0636786i
$577$			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
$579$	−24.9722	+	6.54533i	−1.03781	+	0.272014i
$580$	−2.17562	−	1.21462i	−0.0903376	−	0.0504344i
$581$		−	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
$585$	8.51318	−	14.8649i	0.351977	−	0.614589i
$586$	13.3851	+	23.1837i	0.552935	+	0.957712i
$587$	−5.55634	−	9.62387i	−0.229335	−	0.397220i	0.728276	−	0.685284i	$-0.240322\pi$
$587$	−5.55634	−	9.62387i	−0.229335	−	0.397220i	−0.957611	+	0.288064i	$0.906988\pi$
$588$	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
$591$	−8.05741	+	29.4269i	−0.331438	+	1.21046i
$592$	1.13869	+	1.97227i	0.0468000	+	0.0810600i
$593$	−6.57108	+	11.3814i	−0.269842	+	0.467380i	−0.968821	−	0.247762i	$-0.920305\pi$
$593$	−6.57108	+	11.3814i	−0.269842	+	0.467380i	0.698979	+	0.715142i	$0.253638\pi$
$594$	−31.3567	−	8.95507i	−1.28658	−	0.367431i
$595$	−12.1108	+	21.6927i	−0.496493	+	0.889314i
$596$		−	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	0.364198	+	0.931322i	$0.381343\pi$
$599$	−15.2831	+	26.4710i	−0.624449	+	1.08158i	−0.988647	+	0.150256i	$0.951990\pi$
$600$	5.97896	−	6.26514i	0.244090	−	0.255773i
$601$		−	9.49333i		−	0.387241i	−0.981076	−	0.193621i	$-0.937977\pi$
$601$		−	9.49333i		−	0.387241i	0.981076	−	0.193621i	$-0.0620231\pi$
$602$	−23.2871	−	13.4448i	−0.949111	−	0.547969i
$603$	9.21634	−	5.18768i	0.375318	−	0.211259i
$604$	1.74117	+	1.00527i	0.0708472	+	0.0409037i
$605$	54.5069	−	32.5260i	2.21602	−	1.32237i
$606$	−7.16981	+	26.1853i	−0.291254	+	1.06370i
$607$	−35.1509			−1.42673			−0.713365	−	0.700793i	$-0.752830\pi$
$607$	−35.1509			−1.42673			−0.713365	+	0.700793i	$0.752830\pi$
$608$	4.09866	−	1.48358i	0.166222	−	0.0601672i
$609$	−6.32507	+	6.25636i	−0.256305	+	0.253521i
$610$	1.47623	+	2.47386i	0.0597708	+	0.100164i
$611$	3.16777	+	5.48673i	0.128154	+	0.221969i
$612$	6.22262	+	3.68383i	0.251535	+	0.148910i
$613$	36.2692	−	20.9400i	1.46490	−	0.845760i	0.465668	−	0.884959i	$-0.345814\pi$
$613$	36.2692	−	20.9400i	1.46490	−	0.845760i	0.999231	+	0.0391990i	$0.0124806\pi$
$614$	−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	−0.332097	−	0.943245i	$-0.607756\pi$
$617$	16.1662	−	28.0007i	0.650826	−	1.12726i	0.982923	−	0.184018i	$-0.0589106\pi$
$618$	−6.78607	−	25.8907i	−0.272976	−	1.04148i
$619$	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
$621$	4.40512	+	17.5877i	0.176771	+	0.705772i
$622$	−9.69002	−	16.7836i	−0.388534	−	0.672961i
$623$	64.5010	+	37.2397i	2.58418	+	1.49198i
$624$	−1.16806	+	4.26595i	−0.0467599	+	0.170775i
$625$	−13.7269	−	20.8943i	−0.549076	−	0.835773i
$626$	−24.3594			−0.973599
$627$	−39.0083	+	26.8957i	−1.55784	+	1.07411i
$628$		−	2.52012i		−	0.100564i
$629$	2.74474	+	4.75403i	0.109440	+	0.189556i
$630$	−15.5540	−	26.7243i	−0.619685	−	1.06472i
$631$	−16.0088	+	27.7280i	−0.637299	+	1.10383i	0.348724	+	0.937225i	$0.386615\pi$
$631$	−16.0088	+	27.7280i	−0.637299	+	1.10383i	−0.986023	+	0.166609i	$0.946718\pi$
$632$	−4.86834	−	8.43221i	−0.193652	−	0.335415i
$633$	2.27790	+	8.69081i	0.0905384	+	0.345429i
$634$	−26.3148			−1.04509
$635$	0.270997	+	18.7987i	0.0107542	+	0.746004i
$636$	0.0260017	+	0.0992035i	0.00103103	+	0.00393368i
$637$	−18.1906	+	31.5070i	−0.720736	+	1.24835i
$638$	−6.99336			−0.276870
$639$	−0.0831835	+	7.61580i	−0.00329069	+	0.301276i
$640$	−1.09000	+	1.95241i	−0.0430862	+	0.0771756i
$641$	−21.2450	−	36.7975i	−0.839128	−	1.45341i	−0.890625	−	0.454739i	$-0.849733\pi$
$641$	−21.2450	−	36.7975i	−0.839128	−	1.45341i	0.0514971	−	0.998673i	$-0.483601\pi$
$642$	−7.89890	+	2.07034i	−0.311745	+	0.0817098i
$643$	29.2752	−	16.9020i	1.15450	−	0.666552i	0.204521	−	0.978862i	$-0.434436\pi$
$643$	29.2752	−	16.9020i	1.15450	−	0.666552i	0.949980	+	0.312310i	$0.101103\pi$
$644$	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	$0.493964\pi$
$648$	−7.89066	+	4.32868i	−0.309974	+	0.170047i
$649$	45.9050	−	26.5033i	1.80193	−	1.04034i
$650$	11.2369	+	6.06262i	0.440746	+	0.237796i
$651$	9.21543	−	33.6562i	0.361181	−	1.31909i
$652$	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
$655$	6.22484	−	11.1499i	0.243224	−	0.435661i
$656$	−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	$-0.926286\pi$
$659$	−7.39035	+	12.8005i	−0.287887	+	0.498635i	0.685418	+	0.728150i	$0.259619\pi$
$660$	6.08047	−	23.5335i	0.236682	−	0.916039i
$661$	−38.0675	−	21.9783i	−1.48065	−	0.854856i	−0.480895	−	0.876778i	$-0.659688\pi$
$661$	−38.0675	−	21.9783i	−1.48065	−	0.854856i	−0.999760	+	0.0219216i	$0.993022\pi$
$662$	11.9586	+	20.7130i	0.464786	+	0.805032i
$663$	−2.81554	+	10.2828i	−0.109346	+	0.399350i
$664$		−	8.79050i		−	0.341138i
$665$	−44.3399	−	7.24143i	−1.71943	−	0.280811i
$666$	−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
$669$	1.09091	−	0.285932i	0.0421769	−	0.0110548i
$670$	4.03946	+	6.76929i	0.156058	+	0.261521i
$671$	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	$-0.589820\pi$
$673$	−14.4471			−0.556893			−0.278447	+	0.960452i	$0.589820\pi$
$674$	−13.7644	−	7.94689i	−0.530186	−	0.306103i
$675$	7.03613	+	25.0099i	0.270821	+	0.962630i
$676$	6.47911			0.249196
$677$		−	38.1292i		−	1.46542i	−0.680539	−	0.732712i	$-0.738254\pi$
$677$		−	38.1292i		−	1.46542i	0.680539	−	0.732712i	$-0.261746\pi$
$678$	−23.5445	+	6.17113i	−0.904222	+	0.237001i
$679$	25.3523	−	14.6372i	0.972933	−	0.561723i
$680$	−2.62738	+	4.70614i	−0.100755	+	0.180472i
$681$	−13.6271	−	3.73126i	−0.522193	−	0.142982i
$682$	23.7552	−	13.7150i	0.909632	−	0.525176i
$683$		−	33.2936i		−	1.27394i	−0.770887	−	0.636972i	$-0.780187\pi$
$683$		−	33.2936i		−	1.27394i	0.770887	−	0.636972i	$-0.219813\pi$
$684$	−2.43399	+	12.8482i	−0.0930661	+	0.491262i
$685$	0.290960	+	20.1835i	0.0111170	+	0.771173i
$686$	16.7023	+	28.9292i	0.637695	+	1.10452i
$687$	2.84606	−	10.3942i	0.108584	−	0.396565i
$688$	−5.05204	−	2.91679i	−0.192607	−	0.111202i
$689$	−0.130942	+	0.0755993i	−0.00498849	+	0.00288010i
$690$	−13.0217	+	3.61443i	−0.495729	+	0.137599i
$691$	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
$693$	−74.6793	−	44.2106i	−2.83683	−	1.67942i
$694$	−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
$699$	46.3384	−	12.1455i	1.75268	−	0.459386i
$700$	19.6190	−	12.0942i	0.741529	−	0.457116i
$701$	13.7046	−	7.91236i	0.517616	−	0.298846i	−0.218343	−	0.975872i	$-0.570065\pi$
$701$	13.7046	−	7.91236i	0.517616	−	0.298846i	0.735959	+	0.677026i	$0.236732\pi$
$702$	−9.22757	−	9.53499i	−0.348272	−	0.359875i
$703$	−6.39433	+	7.59314i	−0.241167	+	0.286381i
$704$			6.27586i			0.236530i
$705$	−9.30342	−	2.40377i	−0.350387	−	0.0905314i
$706$	−6.93233	+	4.00239i	−0.260902	+	0.150632i
$707$	−36.1255	+	62.5712i	−1.35864	+	2.35323i
$708$	3.86340	−	14.1097i	0.145195	−	0.530276i
$709$	1.42321	−	2.46507i	0.0534498	−	0.0925778i	−0.838063	−	0.545574i	$-0.816312\pi$
$709$	1.42321	−	2.46507i	0.0534498	−	0.0925778i	0.891512	+	0.452996i	$0.149645\pi$
$710$	−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
$717$	23.4031	+	6.40804i	0.874006	+	0.239312i
$718$	−4.23571	+	7.33647i	−0.158075	+	0.273794i
$719$	22.6148	−	13.0567i	0.843389	−	0.486931i	−0.0150255	−	0.999887i	$-0.504783\pi$
$719$	22.6148	−	13.0567i	0.843389	−	0.486931i	0.858415	+	0.512956i	$0.171450\pi$
$720$	−3.37437	−	5.79772i	−0.125755	−	0.216068i
$721$		−	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
$725$	2.92375	+	4.74287i	0.108585	+	0.176146i
$726$	−12.4657	−	47.5602i	−0.462647	−	1.76512i
$727$	23.4044	−	13.5125i	0.868022	−	0.501152i	0.00133130	−	0.999999i	$-0.499576\pi$
$727$	23.4044	−	13.5125i	0.868022	−	0.501152i	0.866690	+	0.498847i	$0.166243\pi$
$728$	−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
$732$	2.15857	−	0.565772i	0.0797831	−	0.0209115i
$733$			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
$735$	−14.7578	−	53.1681i	−0.544351	−	1.96114i
$736$	3.02184	−	1.74466i	0.111386	−	0.0643090i
$737$	19.1605	+	11.0623i	0.705785	+	0.407485i
$738$	−13.5356	−	24.0472i	−0.498254	−	0.885189i
$739$	10.0943	+	17.4838i	0.371324	+	0.643152i	0.989769	−	0.142676i	$-0.0455707\pi$
$739$	10.0943	+	17.4838i	0.371324	+	0.643152i	−0.618446	+	0.785827i	$0.712237\pi$
$740$	−0.0734029	−	5.09186i	−0.00269834	−	0.187181i
$741$	−19.2176	+	1.54140i	−0.705975	+	0.0566246i
$742$			0.272925i			0.0100194i
$743$	−15.4773	+	8.93584i	−0.567808	+	0.327824i	−0.756273	−	0.654256i	$-0.772982\pi$
$743$	−15.4773	+	8.93584i	−0.567808	+	0.327824i	0.188465	+	0.982080i	$0.439649\pi$
$744$	1.99925	−	7.30157i	0.0732960	−	0.267688i
$745$	−11.9452	+	21.3961i	−0.437638	+	0.783894i
$746$	24.0963	−	13.9120i	0.882229	−	0.509355i
$747$	22.6930	+	13.4344i	0.830294	+	0.491539i
$748$			15.1275i			0.553117i
$749$	−21.7311			−0.794038
$750$	−18.5024	+	5.71500i	−0.675612	+	0.208682i
$751$	5.47575	+	3.16143i	0.199813	+	0.115362i	0.596568	−	0.802562i	$-0.296530\pi$
$751$	5.47575	+	3.16143i	0.199813	+	0.115362i	−0.396755	+	0.917924i	$0.629864\pi$
$752$	2.48102			0.0904734
$753$	18.1728	−	17.9754i	0.662252	−	0.655058i
$754$	−2.46432	−	1.42277i	−0.0897451	−	0.0518144i
$755$	−2.30373	−	3.86057i	−0.0838412	−	0.140501i
$756$	−23.2337	+	5.81923i	−0.845001	+	0.211643i
$757$	10.8515	−	6.26511i	0.394404	−	0.227709i	−0.289662	−	0.957129i	$-0.593543\pi$
$757$	10.8515	−	6.26511i	0.394404	−	0.227709i	0.684067	+	0.729419i	$0.260210\pi$
$758$	8.84812	+	15.3254i	0.321378	+	0.556643i
$759$	−26.9661	+	26.6732i	−0.978807	+	0.968174i
$760$	−9.61935	−	1.57100i	−0.348931	−	0.0569861i
$761$			24.3793i			0.883747i	0.897077	+	0.441874i	$0.145686\pi$
$761$			24.3793i			0.883747i	−0.897077	+	0.441874i	$0.854314\pi$
$762$	14.0459	+	3.84593i	0.508830	+	0.139323i
$763$	18.2807	+	31.6631i	0.661807	+	1.14628i
$764$	3.32219	+	1.91807i	0.120193	+	0.0693932i
$765$	−8.13369	−	13.9750i	−0.294074	−	0.505268i
$766$	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	−0.313005	−	0.949751i	$-0.601336\pi$
$769$	18.4689	−	31.9891i	0.666006	−	1.15356i	0.979011	−	0.203805i	$-0.0653309\pi$
$770$	31.5319	−	56.4796i	1.13633	−	2.03538i
$771$	−3.48284	+	3.44500i	−0.125431	+	0.124069i
$772$	−14.9047			−0.536432
$773$	−14.1058	−	8.14398i	−0.507350	−	0.292919i	0.224394	−	0.974499i	$-0.427960\pi$
$773$	−14.1058	−	8.14398i	−0.507350	−	0.292919i	−0.731744	+	0.681580i	$0.761293\pi$
$774$	15.2508	−	8.58433i	0.548178	−	0.308557i
$775$	−19.2329	−	10.3767i	−0.690867	−	0.372744i
$776$	5.50008	−	3.17547i	0.197441	−	0.113993i
$777$	−17.5367	−	4.80173i	−0.629125	−	0.172261i
$778$	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
$783$	−1.40679	−	5.61671i	−0.0502746	−	0.200725i
$784$	7.12349	+	12.3382i	0.254410	+	0.440651i
$785$	−2.74695	+	4.92031i	−0.0980428	+	0.175613i
$786$	−6.95601	−	7.03240i	−0.248113	−	0.250838i
$787$	25.8536			0.921581			0.460790	−	0.887509i	$-0.347566\pi$
$787$	25.8536			0.921581			0.460790	+	0.887509i	$0.347566\pi$
$788$	−8.80750	+	15.2550i	−0.313754	+	0.543438i
$789$	14.6845	−	3.84886i	0.522781	−	0.137023i
$790$	0.313825	+	21.7696i	0.0111654	+	0.774528i
$791$	−64.7747			−2.30312
$792$	−16.2014	−	9.59131i	−0.575691	−	0.340812i
$793$	1.64497	+	2.84917i	0.0584145	+	0.101177i
$794$	−10.6848	+	18.5066i	−0.379189	+	0.656774i
$795$	0.0573665	−	0.222028i	0.00203458	−	0.00787451i
$796$	2.41926	+	4.19028i	0.0857484	+	0.148521i
$797$			35.0865i			1.24283i	0.783483	+	0.621413i	$0.213441\pi$
$797$			35.0865i			1.24283i	−0.783483	+	0.621413i	$0.786559\pi$
$798$	−14.9350	+	31.4328i	−0.528693	+	1.11271i
$799$	5.98032			0.211569
$800$	4.25626	−	2.62378i	0.150482	−	0.0927646i
$801$	−42.2419	+	23.7770i	−1.49254	+	0.840121i
$802$	−12.7114	−	7.33894i	−0.448856	−	0.259147i
$803$	−39.8311	−	68.9895i	−1.40561	−	2.43459i
$804$	5.90657	−	1.54814i	0.208309	−	0.0545987i
$805$	−35.9608	+	0.518400i	−1.26745	+	0.0182712i
$806$	11.1611			0.393134
$807$	−14.0242	+	3.67581i	−0.493676	+	0.129395i
$808$	−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	0.964454	−	0.264252i	$-0.0851250\pi$
$811$	34.6815	+	20.0234i	1.21783	+	0.703115i	0.253378	+	0.967367i	$0.418458\pi$
$812$	−4.44828	+	2.56821i	−0.156104	+	0.0901266i
$813$	−43.0100	+	11.2731i	−1.50843	+	0.395366i
$814$	−7.14628	−	12.3777i	−0.250477	−	0.433839i
$815$	−5.12594	−	8.59001i	−0.179554	−	0.300895i
$816$	2.93600	+	2.96824i	0.102780	+	0.103909i
$817$	4.45983	−	25.0339i	0.156030	−	0.875824i
$818$	−30.1838			−1.05535
$819$	−17.3210	−	30.7722i	−0.605244	−	1.07527i
$820$	17.6624	−	10.5397i	0.616797	−	0.368063i
$821$	3.34798	+	1.93296i	0.116845	+	0.0674607i	0.557284	−	0.830322i	$-0.311844\pi$
$821$	3.34798	+	1.93296i	0.116845	+	0.0674607i	−0.440438	+	0.897783i	$0.645177\pi$
$822$	15.0806	+	4.12924i	0.525997	+	0.144024i
$823$	−6.35250	−	3.66762i	−0.221434	−	0.127845i	0.385180	−	0.922841i	$-0.374139\pi$
$823$	−6.35250	−	3.66762i	−0.221434	−	0.127845i	−0.606614	+	0.794996i	$0.707473\pi$
$824$		−	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	0.914237	−	0.405179i	$-0.132791\pi$
$827$	29.3460	+	16.9429i	1.02046	+	0.589163i	0.106223	+	0.994342i	$0.466124\pi$
$828$	−0.114329	+	10.4673i	−0.00397322	+	0.363765i
$829$			43.3738i			1.50643i	0.657772	+	0.753217i	$0.271499\pi$
$829$			43.3738i			1.50643i	−0.657772	+	0.753217i	$0.728501\pi$
$830$	−9.58169	+	17.1626i	−0.332585	+	0.595724i
$831$	−24.6196	−	6.74112i	−0.854045	−	0.233847i
$832$	−1.27680	+	2.21149i	−0.0442651	+	0.0766695i
$833$	17.1707	+	29.7405i	0.594929	+	1.03045i
$834$	23.7923	+	6.51458i	0.823858	+	0.225581i
$835$	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	−0.915034	−	0.403377i	$-0.867836\pi$
$839$	−23.3709	−	40.4795i	−0.806852	−	1.39751i	0.108182	−	0.994131i	$-0.465497\pi$
$840$	−4.77473	−	17.2019i	−0.164744	−	0.593523i
$841$	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
$845$	−12.6498	−	7.06226i	−0.435168	−	0.242949i
$846$	−3.79170	+	6.40484i	−0.130361	+	0.220203i
$847$		−	130.846i		−	4.49591i
$848$			0.0592099i			0.00203328i
$849$	13.5661	+	51.7583i	0.465587	+	1.77634i
$850$	10.2594	−	6.32444i	0.351896	−	0.216926i
$851$	−3.97326	+	6.88189i	−0.136202	+	0.235908i
$852$	−1.16127	+	4.24114i	−0.0397844	+	0.145299i
$853$	−44.2164	+	25.5284i	−1.51394	+	0.874075i	−0.514075	+	0.857745i	$0.671865\pi$
$853$	−44.2164	+	25.5284i	−1.51394	+	0.874075i	−0.999867	+	0.0163293i	$0.994802\pi$
$854$	5.93857			0.203214
$855$	18.7567	−	22.4318i	0.641466	−	0.767151i
$856$	−4.71448			−0.161138
$857$	−10.4943	+	6.05888i	−0.358478	+	0.206967i	−0.668413	−	0.743790i	$-0.733026\pi$
$857$	−10.4943	+	6.05888i	−0.358478	+	0.206967i	0.309935	+	0.950758i	$0.399693\pi$
$858$	7.33060	−	26.7725i	0.250263	−	0.913998i
$859$	4.51608	−	7.82208i	0.154087	−	0.266886i	−0.778639	−	0.627472i	$-0.784090\pi$
$859$	4.51608	−	7.82208i	0.154087	−	0.266886i	0.932726	+	0.360586i	$0.117423\pi$
$860$	6.68431	+	11.2015i	0.227933	+	0.381968i
$861$	−18.6193	−	71.0378i	−0.634545	−	2.42096i
$862$			16.8018i			0.572271i
$863$			42.4560i			1.44522i	0.691256	+	0.722610i	$0.257058\pi$
$863$			42.4560i			1.44522i	−0.691256	+	0.722610i	$0.742942\pi$
$864$	−5.04046	+	1.26246i	−0.171480	+	0.0429497i
$865$	12.1150	−	21.7003i	0.411922	−	0.737831i
$866$			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
$870$	4.15854	−	1.15428i	0.140988	−	0.0391339i
$871$	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
$876$	−21.2051	−	5.80620i	−0.716455	−	0.196173i
$877$	23.7811	+	41.1901i	0.803031	+	1.39089i	0.917612	+	0.397477i	$0.130114\pi$
$877$	23.7811	+	41.1901i	0.803031	+	1.39089i	−0.114581	+	0.993414i	$0.536553\pi$
$878$	1.86818	−	3.23579i	0.0630481	−	0.109202i
$879$	−44.7214	−	12.2452i	−1.50841	−	0.413020i
$880$	6.84072	−	12.2530i	0.230601	−	0.413049i
$881$		−	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	$-0.0423742\pi$
$883$	40.7629	+	23.5345i	1.37178	+	0.791998i	0.380629	+	0.924728i	$0.375708\pi$
$884$	−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	0.602746	−	0.797933i	$-0.294073\pi$
$887$	6.34634	+	3.66406i	0.213089	+	0.123027i	−0.389657	+	0.920960i	$0.627406\pi$
$888$	−3.80451	−	1.04172i	−0.127671	−	0.0349577i
$889$	33.5635	+	19.3779i	1.12568	+	0.649914i
$890$	−18.5143	−	31.0262i	−0.620602	−	1.04000i
$891$	49.5207	−	27.1662i	1.65900	−	0.910102i
$892$	0.651110			0.0218008
$893$	3.68079	+	10.1688i	0.123173	+	0.340287i
$894$	13.3483	+	13.4949i	0.446434	+	0.451337i
$895$	−8.18209	+	4.88252i	−0.273497	+	0.163205i
$896$	2.30472	+	3.99190i	0.0769954	+	0.133360i
$897$	−14.9289	+	3.91292i	−0.498460	+	0.130649i
$898$	−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
$903$	45.0523	−	11.8084i	1.49925	−	0.392960i
$904$	−14.0526			−0.467383
$905$	−43.2639	+	0.623680i	−1.43814	+	0.0207318i
$906$	−3.36855	+	0.882913i	−0.111913	+	0.0293328i
$907$	15.1568	+	26.2524i	0.503274	+	0.871696i	0.999993	+	0.00378471i	$0.00120471\pi$
$907$	15.1568	+	26.2524i	0.503274	+	0.871696i	−0.496719	+	0.867912i	$0.665462\pi$
$908$	−7.06436	−	4.07861i	−0.234439	−	0.135353i
$909$	−23.0656	−	40.9780i	−0.765039	−	1.35916i
$910$	22.6018	−	13.4872i	0.749242	−	0.447097i
$911$	43.8965			1.45435			0.727177	−	0.686450i	$-0.240832\pi$
$911$	43.8965			1.45435			0.727177	+	0.686450i	$0.240832\pi$
$912$	−3.24009	+	6.81923i	−0.107290	+	0.225807i
$913$			55.1680i			1.82579i
$914$	−5.39512	−	9.34462i	−0.178455	−	0.309093i
$915$	−4.83110	−	1.24824i	−0.159711	−	0.0412655i
$916$	3.11101	−	5.38842i	0.102791	−	0.178039i
$917$	−13.1619	−	22.7970i	−0.434644	−	0.752825i
$918$	−12.1497	+	3.04307i	−0.400999	+	0.100436i
$919$	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
$921$	47.0611	−	12.3349i	1.55072	−	0.406450i
$922$	2.21708	−	3.84009i	0.0730156	−	0.126467i
$923$	−6.48297			−0.213389
$924$	−35.2357	−	35.6226i	−1.15917	−	1.17190i
$925$	−5.40684	+	10.0214i	−0.177776	+	0.329501i
$926$	−16.7977	−	29.0945i	−0.552006	−	0.956103i
$927$	39.8923	+	23.6165i	1.31024	+	0.775667i
$928$	−0.965035	+	0.557163i	−0.0316788	+	0.0182898i
$929$	3.78176	−	2.18340i	0.124076	−	0.0716351i	−0.436678	−	0.899618i	$-0.643845\pi$
$929$	3.78176	−	2.18340i	0.124076	−	0.0716351i	0.560753	+	0.827983i	$0.310512\pi$
$930$	−11.8621	+	12.0764i	−0.388973	+	0.396002i
$931$	−40.0019	+	47.5015i	−1.31101	+	1.55680i
$932$	27.6572			0.905942
$933$	32.3755	+	8.86477i	1.05993	+	0.290219i
$934$	−15.9326	+	9.19870i	−0.521331	+	0.300991i
$935$	16.4891	−	29.5351i	0.539250	−	0.965900i
$936$	−3.75772	−	6.67590i	−0.122825	−	0.218209i
$937$	−0.531492	−	0.306857i	−0.0173631	−	0.0100246i	0.491293	−	0.870994i	$-0.336524\pi$
$937$	−0.531492	−	0.306857i	−0.0173631	−	0.0100246i	−0.508656	+	0.860970i	$0.669858\pi$
$938$	16.2499			0.530578
$939$	29.9966	−	29.6707i	0.978902	−	0.968268i
$940$	−4.84395	−	2.70432i	−0.157992	−	0.0882052i
$941$	−21.5489	+	37.3238i	−0.702473	+	1.21672i	0.265122	+	0.964215i	$0.414588\pi$
$941$	−21.5489	+	37.3238i	−0.702473	+	1.21672i	−0.967596	+	0.252505i	$0.918746\pi$
$942$	3.06961	+	3.10332i	0.100013	+	0.101112i
$943$	−32.0958			−1.04518
$944$	4.22305	−	7.31454i	0.137449	−	0.238068i
$945$	51.7046	+	13.9633i	1.68195	+	0.454228i
$946$	31.7059	+	18.3054i	1.03085	+	0.595160i
$947$	−6.37824	−	11.0474i	−0.207265	−	0.358993i	0.743587	−	0.668639i	$-0.233123\pi$
$947$	−6.37824	−	11.0474i	−0.207265	−	0.358993i	−0.950852	+	0.309646i	$0.899790\pi$
$948$	16.2657	+	4.45373i	0.528285	+	0.144650i
$949$		−	32.4140i		−	1.05220i
$950$	17.0685	+	13.5524i	0.553775	+	0.439697i
$951$	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	−0.256433	−	0.966562i	$-0.582547\pi$
$953$	13.9664	−	8.06352i	0.452417	−	0.261203i	0.708851	+	0.705359i	$0.249214\pi$
$954$	−0.152853	−	0.0904896i	−0.00494879	−	0.00292971i
$955$	−4.39556	−	7.36605i	−0.142237	−	0.238360i
$956$	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
$960$	−1.03586	−	3.73189i	−0.0334321	−	0.120446i
$961$	11.8967			0.383765
$962$		−	5.81554i		−	0.187501i
$963$	7.20508	−	12.1706i	0.232180	−	0.392193i
$964$	−9.49382	+	5.48126i	−0.305775	+	0.176539i
$965$	29.1001	+	16.2462i	0.936764	+	0.522984i
$966$	−7.35701	+	26.8690i	−0.236708	+	0.864495i
$967$	30.9453	−	17.8663i	0.995135	−	0.574541i	0.0883294	−	0.996091i	$-0.471847\pi$
$967$	30.9453	−	17.8663i	0.995135	−	0.574541i	0.906805	+	0.421550i	$0.138514\pi$
$968$		−	28.3864i		−	0.912374i
$969$	−7.81001	+	16.4373i	−0.250894	+	0.528041i
$970$	−14.1997	+	0.204699i	−0.455924	+	0.00657248i
$971$	6.45947	+	11.1881i	0.207294	+	0.359044i	0.950861	−	0.309617i	$-0.100201\pi$
$971$	6.45947	+	11.1881i	0.207294	+	0.359044i	−0.743567	+	0.668662i	$0.766868\pi$
$972$	4.44418	−	14.9415i	0.142547	−	0.479250i
$973$	56.8529	+	32.8241i	1.82262	+	1.05229i
$974$	13.6829	−	7.89983i	0.438428	−	0.253127i
$975$	−21.2217	+	6.22132i	−0.679640	+	0.199242i
$976$	1.28835			0.0412391
$977$		−	22.9067i		−	0.732849i	−0.930448	−	0.366425i	$-0.880582\pi$
$977$		−	22.9067i		−	0.732849i	0.930448	−	0.366425i	$-0.119418\pi$
$978$	−7.49525	+	1.96454i	−0.239672	+	0.0628190i
$979$	−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	−0.477360	−	0.878708i	$-0.658406\pi$
$983$	1.40908	−	0.813534i	0.0449428	−	0.0259477i	0.522303	+	0.852760i	$0.325073\pi$
$984$	−4.03939	−	15.4114i	−0.128771	−	0.491296i
$985$	33.8239	−	20.1838i	1.07772	−	0.643110i
$986$	−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
$990$	21.1771	+	36.3857i	0.673052	+	1.15641i
$991$	−20.7104	+	11.9571i	−0.657886	+	0.379831i	−0.791471	−	0.611207i	$-0.790684\pi$
$991$	−20.7104	+	11.9571i	−0.657886	+	0.379831i	0.133585	+	0.991037i	$0.457351\pi$
$992$	2.18537	−	3.78516i	0.0693854	−	0.120179i
$993$	−39.9552	−	10.9402i	−1.26794	−	0.347176i
$994$	−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	$-0.474359\pi$
$997$	−23.4452	−	13.5361i	−0.742517	−	0.428693i	−0.822984	+	0.568065i	$0.807692\pi$
$998$	−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.449.12	yes	80
3.2	odd	2	inner	570.2.n.a.449.23	yes	80
5.4	even	2	inner	570.2.n.a.449.29	yes	80
15.14	odd	2	inner	570.2.n.a.449.18	yes	80
19.8	odd	6	inner	570.2.n.a.179.18	yes	80
57.8	even	6	inner	570.2.n.a.179.29	yes	80
95.84	odd	6	inner	570.2.n.a.179.23	yes	80
285.179	even	6	inner	570.2.n.a.179.12	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.12	✓	80	285.179	even	6	inner
570.2.n.a.179.18	yes	80	19.8	odd	6	inner
570.2.n.a.179.23	yes	80	95.84	odd	6	inner
570.2.n.a.179.29	yes	80	57.8	even	6	inner
570.2.n.a.449.12	yes	80	1.1	even	1	trivial
570.2.n.a.449.18	yes	80	15.14	odd	2	inner
570.2.n.a.449.23	yes	80	3.2	odd	2	inner
570.2.n.a.449.29	yes	80	5.4	even	2	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.457417 - 1.67056i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.92017 + 1.14583i) q^{5} +(0.439145 + 1.67546i) q^{6} +4.60944i q^{7} +1.00000i q^{8} +(-2.58154 - 1.52829i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.457417 - 1.67056i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.92017 + 1.14583i) q^{5} +(0.439145 + 1.67546i) q^{6} +4.60944i q^{7} +1.00000i q^{8} +(-2.58154 - 1.52829i) q^{9} +(1.09000 - 1.95241i) q^{10} -6.27586i q^{11} +(-1.21804 - 1.23141i) q^{12} +(1.27680 - 2.21149i) q^{13} +(-2.30472 - 3.99190i) q^{14} +(1.03586 + 3.73189i) 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} +(7.70035 + 2.10844i) q^{21} +(3.13793 + 5.43505i) q^{22} +(1.74466 - 3.02184i) q^{23} +(1.67056 + 0.457417i) q^{24} +(2.37414 - 4.40039i) 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} +(-10.4842 - 2.87069i) q^{33} +(2.08749 + 1.20522i) q^{34} +(-5.28164 - 8.85094i) q^{35} +(-2.61430 + 1.47153i) q^{36} -2.27739 q^{37} +(-0.764508 + 4.29133i) q^{38} +(-3.11039 - 3.14455i) q^{39} +(-1.14583 - 1.92017i) q^{40} +(-4.59916 - 7.96597i) q^{41} +(-7.72292 + 2.02421i) 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} +(-1.67546 + 0.439145i) q^{48} -14.2470 q^{49} +(0.144127 + 4.99792i) q^{50} +(-4.03857 + 1.05853i) q^{51} +(-1.27680 - 2.21149i) q^{52} +(-0.0512773 - 0.0296049i) q^{53} +(1.42691 - 4.99639i) q^{54} +(7.19107 + 12.0507i) q^{55} -4.60944 q^{56} +(-4.28558 - 6.21561i) q^{57} -1.11433i q^{58} +(4.22305 + 7.31454i) q^{59} +(3.74984 + 0.968866i) q^{60} +(-0.644175 + 1.11574i) q^{61} +(2.18537 + 3.78516i) q^{62} +(7.04455 - 11.8995i) q^{63} -1.00000 q^{64} +(0.0823057 + 5.70944i) q^{65} +(10.5149 - 2.75601i) q^{66} +(-1.76268 + 3.05304i) q^{67} -2.41043 q^{68} +(-4.25012 - 4.29680i) q^{69} +(8.99951 + 5.02432i) q^{70} +(-1.26938 - 2.19862i) q^{71} +(1.52829 - 2.58154i) 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} +(4.26595 + 1.16806i) q^{78} +(-8.43221 + 4.86834i) q^{79} +(1.95241 + 1.09000i) q^{80} +(4.32868 + 7.89066i) q^{81} +(7.96597 + 4.59916i) q^{82} -8.79050 q^{83} +(5.67614 - 5.61448i) q^{84} +(4.70614 + 2.62738i) q^{85} +(-2.91679 + 5.05204i) q^{86} +(1.35729 + 1.37220i) q^{87} +6.27586 q^{88} +(8.07900 - 13.9932i) q^{89} +(-5.79772 + 3.37437i) q^{90} +(10.1937 + 5.88535i) q^{91} +(-1.74466 - 3.02184i) q^{92} +(-7.30157 - 1.99925i) q^{93} -2.48102i q^{94} +(-1.57100 + 9.61935i) q^{95} +(1.23141 - 1.21804i) q^{96} +(-3.17547 - 5.50008i) q^{97} +(12.3382 - 7.12349i) q^{98} +(-9.59131 + 16.2014i) 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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