LMFDB - Embedded newform 418.2.h.b.65.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(65,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("418.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.h (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 $ x^20 + 41x^18 + 707x^16 + 6667x^14 + 37400x^12 + 126976x^10 + 253280x^8 + 273276x^6 + 137476x^4 + 30336*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.8
Root			$-2.01980i$ of defining polynomial
Character	$\chi$	$=$	418.65
Dual form			418.2.h.b.373.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.74919 + 1.00990i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.0648685 - 0.112356i) q^{5} +(1.74919 - 1.00990i) q^{6} -4.47991i q^{7} -1.00000 q^{8} +(0.539789 + 0.934941i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.74919 + 1.00990i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.0648685 - 0.112356i) q^{5} +(1.74919 - 1.00990i) q^{6} -4.47991i q^{7} -1.00000 q^{8} +(0.539789 + 0.934941i) q^{9} +(-0.0648685 - 0.112356i) q^{10} +(0.0670646 - 3.31595i) q^{11} -2.01980i q^{12} +(1.96561 + 3.40453i) q^{13} +(-3.87972 - 2.23996i) q^{14} +(0.226935 - 0.131021i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.48638 + 1.43551i) q^{17} +1.07958 q^{18} +(-4.32001 - 0.580935i) q^{19} -0.129737 q^{20} +(4.52426 - 7.83624i) q^{21} +(-2.83816 - 1.71605i) q^{22} +(2.80144 + 4.85224i) q^{23} +(-1.74919 - 1.00990i) q^{24} +(2.49158 + 4.31555i) q^{25} +3.93122 q^{26} -3.87886i q^{27} +(-3.87972 + 2.23996i) q^{28} +(1.99288 + 3.45178i) q^{29} -0.262042i q^{30} +6.05829i q^{31} +(0.500000 + 0.866025i) q^{32} +(3.46608 - 5.73251i) q^{33} +(2.48638 - 1.43551i) q^{34} +(-0.503343 - 0.290605i) q^{35} +(0.539789 - 0.934941i) q^{36} -4.74193i q^{37} +(-2.66311 + 3.45077i) q^{38} +7.94026i q^{39} +(-0.0648685 + 0.112356i) q^{40} +(-2.41415 + 4.18143i) q^{41} +(-4.52426 - 7.83624i) q^{42} +(-0.219263 - 0.126591i) q^{43} +(-2.90523 + 1.59989i) q^{44} +0.140061 q^{45} +5.60288 q^{46} +(-1.82197 - 3.15574i) q^{47} +(-1.74919 + 1.00990i) q^{48} -13.0696 q^{49} +4.98317 q^{50} +(2.89944 + 5.02198i) q^{51} +(1.96561 - 3.40453i) q^{52} +(-0.112462 + 0.0649300i) q^{53} +(-3.35919 - 1.93943i) q^{54} +(-0.368215 - 0.222636i) q^{55} +4.47991i q^{56} +(-6.96986 - 5.37894i) q^{57} +3.98577 q^{58} +(5.17436 + 2.98742i) q^{59} +(-0.226935 - 0.131021i) q^{60} +(-11.3345 + 6.54398i) q^{61} +(5.24664 + 3.02915i) q^{62} +(4.18846 - 2.41821i) q^{63} +1.00000 q^{64} +0.510025 q^{65} +(-3.23146 - 5.86797i) q^{66} +(3.51727 - 2.03070i) q^{67} -2.87102i q^{68} +11.3167i q^{69} +(-0.503343 + 0.290605i) q^{70} +(-12.5132 - 7.22450i) q^{71} +(-0.539789 - 0.934941i) q^{72} +(-6.68675 - 3.86060i) q^{73} +(-4.10663 - 2.37096i) q^{74} +10.0650i q^{75} +(1.65690 + 4.03171i) q^{76} +(-14.8552 - 0.300444i) q^{77} +(6.87647 + 3.97013i) q^{78} +(2.26364 - 3.92074i) q^{79} +(0.0648685 + 0.112356i) q^{80} +(5.53662 - 9.58971i) q^{81} +(2.41415 + 4.18143i) q^{82} +4.50822i q^{83} -9.04852 q^{84} +(0.322575 - 0.186239i) q^{85} +(-0.219263 + 0.126591i) q^{86} +8.05044i q^{87} +(-0.0670646 + 3.31595i) q^{88} +(14.4364 - 8.33488i) q^{89} +(0.0700306 - 0.121297i) q^{90} +(15.2520 - 8.80576i) q^{91} +(2.80144 - 4.85224i) q^{92} +(-6.11826 + 10.5971i) q^{93} -3.64393 q^{94} +(-0.345504 + 0.447693i) q^{95} +2.01980i q^{96} +(11.7545 + 6.78649i) q^{97} +(-6.53482 + 11.3186i) q^{98} +(3.13642 - 1.72721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.74919	+	1.00990i	1.00990	+	0.583065i	0.911162	−	0.412049i	$-0.135187\pi$
$3$	1.74919	+	1.00990i	1.00990	+	0.583065i	0.0987363	+	0.995114i	$0.468520\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.0648685	−	0.112356i	0.0290101	−	0.0502469i	−0.851156	−	0.524913i	$-0.824098\pi$
$5$	0.0648685	−	0.112356i	0.0290101	−	0.0502469i	0.880166	+	0.474666i	$0.157431\pi$
$6$	1.74919	−	1.00990i	0.714106	−	0.412289i
$7$		−	4.47991i		−	1.69325i	−0.532191	−	0.846624i	$-0.678631\pi$
$7$		−	4.47991i		−	1.69325i	0.532191	−	0.846624i	$-0.321369\pi$
$8$	−1.00000			−0.353553
$9$	0.539789	+	0.934941i	0.179930	+	0.311647i
$10$	−0.0648685	−	0.112356i	−0.0205132	−	0.0355300i
$11$	0.0670646	−	3.31595i	0.0202207	−	0.999796i
$11$	0.0670646	−	3.31595i	0.0202207	−	0.999796i
$12$		−	2.01980i		−	0.583065i
$13$	1.96561	+	3.40453i	0.545162	+	0.944248i	0.998597	+	0.0529585i	$0.0168651\pi$
$13$	1.96561	+	3.40453i	0.545162	+	0.944248i	−0.453435	+	0.891289i	$0.649802\pi$
$14$	−3.87972	−	2.23996i	−1.03690	−	0.598654i
$15$	0.226935	−	0.131021i	0.0585945	−	0.0338295i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.48638	+	1.43551i	0.603035	+	0.348163i	0.770235	−	0.637761i	$-0.220139\pi$
$17$	2.48638	+	1.43551i	0.603035	+	0.348163i	−0.167199	+	0.985923i	$0.553472\pi$
$18$	1.07958			0.254459
$19$	−4.32001	−	0.580935i	−0.991079	−	0.133276i
$19$	−4.32001	−	0.580935i	−0.991079	−	0.133276i
$20$	−0.129737			−0.0290101
$21$	4.52426	−	7.83624i	0.987274	−	1.71001i
$22$	−2.83816	−	1.71605i	−0.605098	−	0.365864i
$23$	2.80144	+	4.85224i	0.584141	+	1.01176i	0.994982	+	0.100054i	$0.0319017\pi$
$23$	2.80144	+	4.85224i	0.584141	+	1.01176i	−0.410841	+	0.911707i	$0.634765\pi$
$24$	−1.74919	−	1.00990i	−0.357053	−	0.206145i
$25$	2.49158	+	4.31555i	0.498317	+	0.863110i
$26$	3.93122			0.770975
$27$		−	3.87886i		−	0.746487i
$28$	−3.87972	+	2.23996i	−0.733198	+	0.423312i
$29$	1.99288	+	3.45178i	0.370069	+	0.640979i	0.989576	−	0.144013i	$-0.0460006\pi$
$29$	1.99288	+	3.45178i	0.370069	+	0.640979i	−0.619506	+	0.784992i	$0.712667\pi$
$30$		−	0.262042i		−	0.0478422i
$31$			6.05829i			1.08810i	0.839052	+	0.544051i	$0.183110\pi$
$31$			6.05829i			1.08810i	−0.839052	+	0.544051i	$0.816890\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.46608	−	5.73251i	0.603367	−	0.997902i
$34$	2.48638	−	1.43551i	0.426410	−	0.246188i
$35$	−0.503343	−	0.290605i	−0.0850806	−	0.0491213i
$36$	0.539789	−	0.934941i	0.0899648	−	0.155824i
$37$		−	4.74193i		−	0.779568i	−0.920906	−	0.389784i	$-0.872550\pi$
$37$		−	4.74193i		−	0.779568i	0.920906	−	0.389784i	$-0.127450\pi$
$38$	−2.66311	+	3.45077i	−0.432014	+	0.559789i
$39$			7.94026i			1.27146i
$40$	−0.0648685	+	0.112356i	−0.0102566	+	0.0177650i
$41$	−2.41415	+	4.18143i	−0.377027	+	0.653030i	−0.990628	−	0.136586i	$-0.956387\pi$
$41$	−2.41415	+	4.18143i	−0.377027	+	0.653030i	0.613601	+	0.789616i	$0.289720\pi$
$42$	−4.52426	−	7.83624i	−0.698108	−	1.20916i
$43$	−0.219263	−	0.126591i	−0.0334372	−	0.0193050i	0.483188	−	0.875517i	$-0.339479\pi$
$43$	−0.219263	−	0.126591i	−0.0334372	−	0.0193050i	−0.516625	+	0.856212i	$0.672812\pi$
$44$	−2.90523	+	1.59989i	−0.437979	+	0.241193i
$45$	0.140061			0.0208791
$46$	5.60288			0.826100
$47$	−1.82197	−	3.15574i	−0.265761	−	0.460312i	0.702002	−	0.712175i	$-0.252290\pi$
$47$	−1.82197	−	3.15574i	−0.265761	−	0.460312i	−0.967763	+	0.251864i	$0.918957\pi$
$48$	−1.74919	+	1.00990i	−0.252475	+	0.145766i
$49$	−13.0696			−1.86709
$50$	4.98317			0.704726
$51$	2.89944	+	5.02198i	0.406003	+	0.703217i
$52$	1.96561	−	3.40453i	0.272581	−	0.472124i
$53$	−0.112462	+	0.0649300i	−0.0154479	+	0.00891882i	−0.507704	−	0.861532i	$-0.669506\pi$
$53$	−0.112462	+	0.0649300i	−0.0154479	+	0.00891882i	0.492256	+	0.870450i	$0.336172\pi$
$54$	−3.35919	−	1.93943i	−0.457128	−	0.263923i
$55$	−0.368215	−	0.222636i	−0.0496501	−	0.0300202i
$56$			4.47991i			0.598654i
$57$	−6.96986	−	5.37894i	−0.923181	−	0.712458i
$58$	3.98577			0.523357
$59$	5.17436	+	2.98742i	0.673645	+	0.388929i	0.797456	−	0.603377i	$-0.206178\pi$
$59$	5.17436	+	2.98742i	0.673645	+	0.388929i	−0.123812	+	0.992306i	$0.539512\pi$
$60$	−0.226935	−	0.131021i	−0.0292972	−	0.0169148i
$61$	−11.3345	+	6.54398i	−1.45123	+	0.837870i	−0.998552	−	0.0538016i	$-0.982866\pi$
$61$	−11.3345	+	6.54398i	−1.45123	+	0.837870i	−0.452682	+	0.891672i	$0.649533\pi$
$62$	5.24664	+	3.02915i	0.666324	+	0.384702i
$63$	4.18846	−	2.41821i	0.527696	−	0.304665i
$64$	1.00000			0.125000
$65$	0.510025			0.0632608
$66$	−3.23146	−	5.86797i	−0.397765	−	0.722297i
$67$	3.51727	−	2.03070i	0.429703	−	0.248089i	−0.269517	−	0.962996i	$-0.586864\pi$
$67$	3.51727	−	2.03070i	0.429703	−	0.248089i	0.699220	+	0.714906i	$0.253531\pi$
$68$		−	2.87102i		−	0.348163i
$69$			11.3167i			1.36237i
$70$	−0.503343	+	0.290605i	−0.0601610	+	0.0347340i
$71$	−12.5132	−	7.22450i	−1.48504	−	0.857390i	−0.485188	−	0.874410i	$-0.661249\pi$
$71$	−12.5132	−	7.22450i	−1.48504	−	0.857390i	−0.999855	+	0.0170198i	$0.994582\pi$
$72$	−0.539789	−	0.934941i	−0.0636147	−	0.110184i
$73$	−6.68675	−	3.86060i	−0.782625	−	0.451849i	0.0547346	−	0.998501i	$-0.482569\pi$
$73$	−6.68675	−	3.86060i	−0.782625	−	0.451849i	−0.837360	+	0.546652i	$0.815902\pi$
$74$	−4.10663	−	2.37096i	−0.477386	−	0.275619i
$75$			10.0650i			1.16220i
$76$	1.65690	+	4.03171i	0.190060	+	0.462469i
$77$	−14.8552	−	0.300444i	−1.69290	−	0.0342387i
$78$	6.87647	+	3.97013i	0.778606	+	0.449529i
$79$	2.26364	−	3.92074i	0.254680	−	0.441118i	−0.710129	−	0.704072i	$-0.751363\pi$
$79$	2.26364	−	3.92074i	0.254680	−	0.441118i	0.964808	+	0.262954i	$0.0846966\pi$
$80$	0.0648685	+	0.112356i	0.00725252	+	0.0125617i
$81$	5.53662	−	9.58971i	0.615180	−	1.06552i
$82$	2.41415	+	4.18143i	0.266598	+	0.461762i
$83$			4.50822i			0.494842i	0.968908	+	0.247421i	$0.0795830\pi$
$83$			4.50822i			0.494842i	−0.968908	+	0.247421i	$0.920417\pi$
$84$	−9.04852			−0.987274
$85$	0.322575	−	0.186239i	0.0349882	−	0.0202005i
$86$	−0.219263	+	0.126591i	−0.0236437	+	0.0136507i
$87$			8.05044i			0.863098i
$88$	−0.0670646	+	3.31595i	−0.00714911	+	0.353481i
$89$	14.4364	−	8.33488i	1.53026	−	0.883496i	0.530911	−	0.847428i	$-0.321850\pi$
$89$	14.4364	−	8.33488i	1.53026	−	0.883496i	0.999349	−	0.0360682i	$-0.0114834\pi$
$90$	0.0700306	−	0.121297i	0.00738187	−	0.0127858i
$91$	15.2520	−	8.80576i	1.59885	−	0.923094i
$92$	2.80144	−	4.85224i	0.292070	−	0.505881i
$93$	−6.11826	+	10.5971i	−0.634434	+	1.09887i
$94$	−3.64393			−0.375843
$95$	−0.345504	+	0.447693i	−0.0354480	+	0.0459324i
$96$			2.01980i			0.206145i
$97$	11.7545	+	6.78649i	1.19349	+	0.689063i	0.959097	−	0.283078i	$-0.0913554\pi$
$97$	11.7545	+	6.78649i	1.19349	+	0.689063i	0.234396	+	0.972141i	$0.424689\pi$
$98$	−6.53482	+	11.3186i	−0.660116	+	1.14335i
$99$	3.13642	−	1.72721i	0.315222	−	0.173591i
$100$	2.49158	−	4.31555i	0.249158	−	0.431555i
$101$	0.321471	−	0.185601i	0.0319876	−	0.0184680i	−0.483921	−	0.875112i	$-0.660788\pi$
$101$	0.321471	−	0.185601i	0.0319876	−	0.0184680i	0.515909	+	0.856644i	$0.327454\pi$
$102$	5.79888			0.574175
$103$			9.00448i			0.887238i	0.896215	+	0.443619i	$0.146306\pi$
$103$			9.00448i			0.887238i	−0.896215	+	0.443619i	$0.853694\pi$
$104$	−1.96561	−	3.40453i	−0.192744	−	0.333842i
$105$	−0.586964	−	1.01665i	−0.0572818	−	0.0992150i
$106$			0.129860i			0.0126131i
$107$	10.5908			1.02385			0.511924	−	0.859031i	$-0.328933\pi$
$107$	10.5908			1.02385			0.511924	+	0.859031i	$0.328933\pi$
$108$	−3.35919	+	1.93943i	−0.323239	+	0.186622i
$109$	−9.29222	+	16.0946i	−0.890033	+	1.54158i	−0.0501996	+	0.998739i	$0.515986\pi$
$109$	−9.29222	+	16.0946i	−0.890033	+	1.54158i	−0.839834	+	0.542844i	$0.817348\pi$
$110$	−0.376916	+	0.207566i	−0.0359375	+	0.0197906i
$111$	4.78886	−	8.29456i	0.454539	−	0.787284i
$112$	3.87972	+	2.23996i	0.366599	+	0.211656i
$113$		−	6.76377i		−	0.636282i	−0.948043	−	0.318141i	$-0.896942\pi$
$113$		−	6.76377i		−	0.636282i	0.948043	−	0.318141i	$-0.103058\pi$
$114$	−8.14323	+	3.34661i	−0.762683	+	0.313438i
$115$	0.726901			0.0677839
$116$	1.99288	−	3.45178i	0.185035	−	0.320490i
$117$	−2.12203	+	3.67546i	−0.196181	+	0.339796i
$118$	5.17436	−	2.98742i	0.476339	−	0.275014i
$119$	6.43097	−	11.1388i	0.589526	−	1.02109i
$120$	−0.226935	+	0.131021i	−0.0207163	+	0.0119605i
$121$	−10.9910	−	0.444765i	−0.999182	−	0.0404332i
$122$			13.0880i			1.18493i
$123$	−8.44564	+	4.87609i	−0.761518	+	0.439663i
$124$	5.24664	−	3.02915i	0.471162	−	0.272025i
$125$	1.29519			0.115845
$126$		−	4.83641i		−	0.430862i
$127$	−3.50584	−	6.07229i	−0.311093	−	0.538828i	0.667507	−	0.744604i	$-0.267362\pi$
$127$	−3.50584	−	6.07229i	−0.311093	−	0.538828i	−0.978599	+	0.205776i	$0.934028\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.255689	−	0.442866i	−0.0225121	−	0.0389922i
$130$	0.255012	−	0.441694i	0.0223661	−	0.0387392i
$131$	6.86539	+	3.96374i	0.599832	+	0.346313i	0.768976	−	0.639278i	$-0.220767\pi$
$131$	6.86539	+	3.96374i	0.599832	+	0.346313i	−0.169143	+	0.985591i	$0.554100\pi$
$132$	−6.69754	−	0.135457i	−0.582946	−	0.0117900i
$133$	−2.60254	+	19.3533i	−0.225669	+	1.67814i
$134$		−	4.06140i		−	0.350851i
$135$	−0.435812	−	0.251616i	−0.0375087	−	0.0216557i
$136$	−2.48638	−	1.43551i	−0.213205	−	0.123094i
$137$	−2.45790	−	4.25721i	−0.209992	−	0.363718i	0.741719	−	0.670710i	$-0.234011\pi$
$137$	−2.45790	−	4.25721i	−0.209992	−	0.363718i	−0.951712	+	0.306993i	$0.900677\pi$
$138$	9.80053	+	5.65834i	0.834277	+	0.481670i
$139$	−11.3003	+	6.52424i	−0.958481	+	0.553379i	−0.895705	−	0.444649i	$-0.853329\pi$
$139$	−11.3003	+	6.52424i	−0.958481	+	0.553379i	−0.0627756	+	0.998028i	$0.519995\pi$
$140$			0.581211i			0.0491213i
$141$		−	7.36000i		−	0.619824i
$142$	−12.5132	+	7.22450i	−1.05008	+	0.606266i
$143$	11.4211	−	6.28953i	0.955078	−	0.525957i
$144$	−1.07958			−0.0899648
$145$	0.517102			0.0429430
$146$	−6.68675	+	3.86060i	−0.553400	+	0.319505i
$147$	−22.8613	−	13.1990i	−1.88557	−	1.08864i
$148$	−4.10663	+	2.37096i	−0.337563	+	0.194892i
$149$	17.4584	+	10.0796i	1.43025	+	0.825754i	0.997139	−	0.0755879i	$-0.0240834\pi$
$149$	17.4584	+	10.0796i	1.43025	+	0.825754i	0.433109	+	0.901342i	$0.357417\pi$
$150$	8.71653	+	5.03249i	0.711702	+	0.410901i
$151$	−9.71609			−0.790684			−0.395342	−	0.918534i	$-0.629374\pi$
$151$	−9.71609			−0.790684			−0.395342	+	0.918534i	$0.629374\pi$
$152$	4.32001	+	0.580935i	0.350399	+	0.0471200i
$153$			3.09949i			0.250579i
$154$	−7.68777	+	12.7147i	−0.619498	+	1.02458i
$155$	0.680683	+	0.392993i	0.0546738	+	0.0315659i
$156$	6.87647	−	3.97013i	0.550558	−	0.317865i
$157$	−12.3175	+	21.3346i	−0.983046	+	1.70269i	−0.332731	+	0.943022i	$0.607970\pi$
$157$	−12.3175	+	21.3346i	−0.983046	+	1.70269i	−0.650315	+	0.759665i	$0.725363\pi$
$158$	−2.26364	−	3.92074i	−0.180086	−	0.311918i
$159$	−0.262291			−0.0208010
$160$	0.129737			0.0102566
$161$	21.7376	−	12.5502i	1.71316	−	0.989095i
$162$	−5.53662	−	9.58971i	−0.434998	−	0.753439i
$163$	8.78657			0.688217			0.344109	−	0.938930i	$-0.388181\pi$
$163$	8.78657			0.688217			0.344109	+	0.938930i	$0.388181\pi$
$164$	4.82830			0.377027
$165$	−0.419240	−	0.761293i	−0.0326378	−	0.0592666i
$166$	3.90423	+	2.25411i	0.303027	+	0.174953i
$167$	1.15915	+	2.00771i	0.0896979	+	0.155361i	0.907383	−	0.420304i	$-0.138077\pi$
$167$	1.15915	+	2.00771i	0.0896979	+	0.155361i	−0.817686	+	0.575665i	$0.804743\pi$
$168$	−4.52426	+	7.83624i	−0.349054	+	0.604579i
$169$	−1.22724	+	2.12563i	−0.0944028	+	0.163510i
$170$		−	0.372478i		−	0.0285678i
$171$	−1.78875	−	4.35254i	−0.136789	−	0.332847i
$172$			0.253183i			0.0193050i
$173$	3.62502	−	6.27873i	0.275605	−	0.477363i	−0.694682	−	0.719317i	$-0.744455\pi$
$173$	3.62502	−	6.27873i	0.275605	−	0.477363i	0.970288	+	0.241954i	$0.0777883\pi$
$174$	6.97189	+	4.02522i	0.528537	+	0.305151i
$175$	19.3333	−	11.1621i	1.46146	−	0.843774i
$176$	2.83816	+	1.71605i	0.213934	+	0.129352i
$177$	6.03398	+	10.4512i	0.453542	+	0.785557i
$178$		−	16.6698i		−	1.24945i
$179$		−	16.2846i		−	1.21717i	−0.793489	−	0.608584i	$-0.791738\pi$
$179$		−	16.2846i		−	1.21717i	0.793489	−	0.608584i	$-0.208262\pi$
$180$	−0.0700306	−	0.121297i	−0.00521977	−	0.00904091i
$181$	5.80563	−	3.35188i	0.431529	−	0.249143i	−0.268469	−	0.963288i	$-0.586518\pi$
$181$	5.80563	−	3.35188i	0.431529	−	0.249143i	0.699998	+	0.714145i	$0.253184\pi$
$182$		−	17.6115i		−	1.30545i
$183$	−26.4350			−1.95413
$184$	−2.80144	−	4.85224i	−0.206525	−	0.357712i
$185$	−0.532782	−	0.307602i	−0.0391709	−	0.0226153i
$186$	6.11826	+	10.5971i	0.448613	+	0.777020i
$187$	4.92683	−	8.14842i	0.360285	−	0.595872i
$188$	−1.82197	+	3.15574i	−0.132881	+	0.230156i
$189$	−17.3770			−1.26399
$190$	0.214962	+	0.523062i	0.0155950	+	0.0379469i
$191$	−14.4067			−1.04243			−0.521216	−	0.853425i	$-0.674521\pi$
$191$	−14.4067			−1.04243			−0.521216	+	0.853425i	$0.674521\pi$
$192$	1.74919	+	1.00990i	0.126237	+	0.0728831i
$193$	−1.09475	+	1.89617i	−0.0788021	+	0.136489i	−0.902733	−	0.430201i	$-0.858443\pi$
$193$	−1.09475	+	1.89617i	−0.0788021	+	0.136489i	0.823931	+	0.566690i	$0.191776\pi$
$194$	11.7545	−	6.78649i	0.843927	−	0.487241i
$195$	0.892132	+	0.515073i	0.0638869	+	0.0368851i
$196$	6.53482	+	11.3186i	0.466773	+	0.808474i
$197$		−	23.1367i		−	1.64842i	−0.566284	−	0.824210i	$-0.691619\pi$
$197$		−	23.1367i		−	1.64842i	0.566284	−	0.824210i	$-0.308381\pi$
$198$	0.0724014	−	3.57982i	0.00514535	−	0.254407i
$199$	−0.412771	−	0.714940i	−0.0292606	−	0.0506808i	0.851024	−	0.525126i	$-0.175982\pi$
$199$	−0.412771	−	0.714940i	−0.0292606	−	0.0506808i	−0.880285	+	0.474446i	$0.842649\pi$
$200$	−2.49158	−	4.31555i	−0.176182	−	0.305155i
$201$	8.20319			0.578609
$202$		−	0.371203i		−	0.0261177i
$203$	15.4637	−	8.92795i	1.08534	−	0.626619i
$204$	2.89944	−	5.02198i	0.203001	−	0.351609i
$205$	0.313205	+	0.542487i	0.0218752	+	0.0378889i
$206$	7.79811	+	4.50224i	0.543320	+	0.313686i
$207$	−3.02437	+	5.23837i	−0.210208	+	0.364092i
$208$	−3.93122			−0.272581
$209$	−2.21607	+	14.2860i	−0.153289	+	0.988181i
$210$	−1.17393			−0.0810087
$211$	10.8046	−	18.7142i	0.743822	−	1.28834i	−0.206920	−	0.978358i	$-0.566344\pi$
$211$	10.8046	−	18.7142i	0.743822	−	1.28834i	0.950743	−	0.309981i	$-0.100323\pi$
$212$	0.112462	+	0.0649300i	0.00772393	+	0.00445941i
$213$	−14.5920	−	25.2741i	−0.999828	−	1.73175i
$214$	5.29538	−	9.17187i	0.361985	−	0.626976i
$215$	−0.0284465	+	0.0164236i	−0.00194003	+	0.00112008i
$216$			3.87886i			0.263923i
$217$	27.1406			1.84243
$218$	9.29222	+	16.0946i	0.629349	+	1.09006i
$219$	−7.79762	−	13.5059i	−0.526915	−	0.912643i
$220$	−0.00870076	+	0.430201i	−0.000586605	+	0.0290042i
$221$			11.2866i			0.759220i
$222$	−4.78886	−	8.29456i	−0.321408	−	0.556694i
$223$	−21.3131	−	12.3051i	−1.42723	−	0.824011i	−0.430328	−	0.902672i	$-0.641602\pi$
$223$	−21.3131	−	12.3051i	−1.42723	−	0.824011i	−0.996901	+	0.0786610i	$0.974936\pi$
$224$	3.87972	−	2.23996i	0.259225	−	0.149663i
$225$	−2.68986	+	4.65897i	−0.179324	+	0.310598i
$226$	−5.85759	−	3.38188i	−0.389641	−	0.224959i
$227$	9.38555			0.622941			0.311470	−	0.950256i	$-0.399179\pi$
$227$	9.38555			0.622941			0.311470	+	0.950256i	$0.399179\pi$
$228$	−1.17337	+	8.72555i	−0.0777083	+	0.577863i
$229$	−24.5509			−1.62237			−0.811184	−	0.584791i	$-0.801176\pi$
$229$	−24.5509			−1.62237			−0.811184	+	0.584791i	$0.801176\pi$
$230$	0.363451	−	0.629515i	0.0239652	−	0.0415090i
$231$	−25.6811	−	15.5277i	−1.68970	−	1.02165i
$232$	−1.99288	−	3.45178i	−0.130839	−	0.226620i
$233$	−23.7955	−	13.7383i	−1.55889	−	0.900027i	−0.997363	−	0.0725695i	$-0.976880\pi$
$233$	−23.7955	−	13.7383i	−1.55889	−	0.900027i	−0.561529	−	0.827457i	$-0.689787\pi$
$234$	2.12203	+	3.67546i	0.138721	+	0.240272i
$235$	−0.472753			−0.0308390
$236$		−	5.97484i		−	0.388929i
$237$	7.91911	−	4.57210i	0.514401	−	0.296990i
$238$	−6.43097	−	11.1388i	−0.416858	−	0.722019i
$239$		−	15.3803i		−	0.994870i	−0.867501	−	0.497435i	$-0.834275\pi$
$239$		−	15.3803i		−	0.994870i	0.867501	−	0.497435i	$-0.165725\pi$
$240$			0.262042i			0.0169148i
$241$	−5.04394	−	8.73636i	−0.324909	−	0.562758i	0.656585	−	0.754252i	$-0.272000\pi$
$241$	−5.04394	−	8.73636i	−0.324909	−	0.562758i	−0.981494	+	0.191493i	$0.938667\pi$
$242$	−5.88068	+	9.29611i	−0.378024	+	0.597576i
$243$	9.29168	−	5.36456i	0.596062	−	0.344136i
$244$	11.3345	+	6.54398i	0.725617	+	0.418935i
$245$	−0.847808	+	1.46845i	−0.0541645	+	0.0938156i
$246$			9.75219i			0.621777i
$247$	−6.51364	−	15.8495i	−0.414453	−	1.00848i
$248$		−	6.05829i		−	0.384702i
$249$	−4.55284	+	7.88576i	−0.288525	+	0.499740i
$250$	0.647593	−	1.12166i	0.0409574	−	0.0709403i
$251$	−4.38439	−	7.59399i	−0.276740	−	0.479328i	0.693832	−	0.720137i	$-0.255921\pi$
$251$	−4.38439	−	7.59399i	−0.276740	−	0.479328i	−0.970573	+	0.240808i	$0.922588\pi$
$252$	−4.18846	−	2.41821i	−0.263848	−	0.152333i
$253$	16.2776	−	8.96401i	1.02337	−	0.563563i
$254$	−7.01167			−0.439951
$255$	0.752330			0.0471127
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−27.4704	+	15.8601i	−1.71356	+	0.989324i	−0.783912	+	0.620872i	$0.786779\pi$
$257$	−27.4704	+	15.8601i	−1.71356	+	0.989324i	−0.929647	+	0.368452i	$0.879888\pi$
$258$	−0.511377			−0.0318370
$259$	−21.2434			−1.32000
$260$	−0.255012	−	0.441694i	−0.0158152	−	0.0273927i
$261$	−2.15147	+	3.72646i	−0.133173	+	0.230662i
$262$	6.86539	−	3.96374i	0.424145	−	0.244880i
$263$	25.6515	+	14.8099i	1.58174	+	0.913217i	0.994606	+	0.103727i	$0.0330769\pi$
$263$	25.6515	+	14.8099i	1.58174	+	0.913217i	0.587133	+	0.809490i	$0.300256\pi$
$264$	−3.46608	+	5.73251i	−0.213322	+	0.352812i
$265$			0.0168477i			0.00103494i
$266$	15.4592	+	11.9305i	0.947863	+	0.731506i
$267$	33.6695			2.06054
$268$	−3.51727	−	2.03070i	−0.214852	−	0.124045i
$269$	12.2618	+	7.07936i	0.747616	+	0.431636i	0.824832	−	0.565378i	$-0.191270\pi$
$269$	12.2618	+	7.07936i	0.747616	+	0.431636i	−0.0772161	+	0.997014i	$0.524603\pi$
$270$	−0.435812	+	0.251616i	−0.0265227	+	0.0153129i
$271$	5.10308	+	2.94627i	0.309990	+	0.178973i	0.646922	−	0.762556i	$-0.276056\pi$
$271$	5.10308	+	2.94627i	0.309990	+	0.178973i	−0.336932	+	0.941529i	$0.609389\pi$
$272$	−2.48638	+	1.43551i	−0.150759	+	0.0870406i
$273$	35.5717			2.15290
$274$	−4.91580			−0.296974
$275$	14.4772	−	7.97254i	0.873010	−	0.480762i
$276$	9.80053	−	5.65834i	0.589923	−	0.340592i
$277$			19.5231i			1.17303i	0.809939	+	0.586514i	$0.199500\pi$
$277$			19.5231i			1.17303i	−0.809939	+	0.586514i	$0.800500\pi$
$278$			13.0485i			0.782596i
$279$	−5.66415	+	3.27020i	−0.339104	+	0.195782i
$280$	0.503343	+	0.290605i	0.0300805	+	0.0173670i
$281$	5.67340	+	9.82662i	0.338447	+	0.586207i	0.984141	−	0.177389i	$-0.0567651\pi$
$281$	5.67340	+	9.82662i	0.338447	+	0.586207i	−0.645694	+	0.763596i	$0.723432\pi$
$282$	−6.37395	−	3.68000i	−0.379563	−	0.219141i
$283$	8.52486	+	4.92183i	0.506750	+	0.292572i	0.731497	−	0.681845i	$-0.238822\pi$
$283$	8.52486	+	4.92183i	0.506750	+	0.292572i	−0.224747	+	0.974417i	$0.572155\pi$
$284$			14.4490i			0.857390i
$285$	−1.05648	+	0.434179i	−0.0625804	+	0.0257185i
$286$	0.263646	−	13.0357i	0.0155897	−	0.770818i
$287$	18.7325	+	10.8152i	1.10574	+	0.638401i
$288$	−0.539789	+	0.934941i	−0.0318074	+	0.0550920i
$289$	−4.37862	−	7.58399i	−0.257566	−	0.446117i
$290$	0.258551	−	0.447823i	0.0151826	−	0.0262971i
$291$	13.7073	+	23.7418i	0.803538	+	1.39177i
$292$			7.72120i			0.451849i
$293$	2.93837			0.171661			0.0858307	−	0.996310i	$-0.472646\pi$
$293$	2.93837			0.171661			0.0858307	+	0.996310i	$0.472646\pi$
$294$	−22.8613	+	13.1990i	−1.33330	+	0.769781i
$295$	0.671307	−	0.387579i	0.0390850	−	0.0225657i
$296$			4.74193i			0.275619i
$297$	−12.8621	−	0.260134i	−0.746335	−	0.0150945i
$298$	17.4584	−	10.0796i	1.01134	−	0.583896i
$299$	−11.0131	+	19.0752i	−0.636902	+	1.10315i
$300$	8.71653	−	5.03249i	0.503249	−	0.290551i
$301$	−0.567118	+	0.982278i	−0.0326881	+	0.0566175i
$302$	−4.85804	+	8.41438i	−0.279549	+	0.484193i
$303$	0.749754			0.0430723
$304$	2.66311	−	3.45077i	0.152740	−	0.197915i
$305$			1.69799i			0.0972268i
$306$	2.68424	+	1.54975i	0.153448	+	0.0885930i
$307$	5.95515	−	10.3146i	0.339879	−	0.588687i	−0.644531	−	0.764578i	$-0.722947\pi$
$307$	5.95515	−	10.3146i	0.339879	−	0.588687i	0.984410	+	0.175891i	$0.0562807\pi$
$308$	7.16739	+	13.0152i	0.408400	+	0.741608i
$309$	−9.09361	+	15.7506i	−0.517317	+	0.896020i
$310$	0.680683	−	0.392993i	0.0386602	−	0.0223205i
$311$	−6.31922			−0.358330			−0.179165	−	0.983819i	$-0.557340\pi$
$311$	−6.31922			−0.358330			−0.179165	+	0.983819i	$0.557340\pi$
$312$		−	7.94026i		−	0.449529i
$313$	−7.21873	−	12.5032i	−0.408027	−	0.706723i	0.586642	−	0.809847i	$-0.300450\pi$
$313$	−7.21873	−	12.5032i	−0.408027	−	0.706723i	−0.994669	+	0.103123i	$0.967116\pi$
$314$	12.3175	+	21.3346i	0.695119	+	1.20398i
$315$		−	0.627462i		−	0.0353535i
$316$	−4.52729			−0.254680
$317$	−3.32252	+	1.91826i	−0.186611	+	0.107740i	−0.590395	−	0.807114i	$-0.701028\pi$
$317$	−3.32252	+	1.91826i	−0.186611	+	0.107740i	0.403784	+	0.914854i	$0.367695\pi$
$318$	−0.131145	+	0.227150i	−0.00735427	+	0.0127380i
$319$	11.5796	−	6.37681i	0.648331	−	0.357033i
$320$	0.0648685	−	0.112356i	0.00362626	−	0.00628087i
$321$	18.5253	+	10.6956i	1.03398	+	0.596970i
$322$		−	25.1004i		−	1.39879i
$323$	−9.90725	−	7.64585i	−0.551254	−	0.425426i
$324$	−11.0732			−0.615180
$325$	−9.79496	+	16.9654i	−0.543327	+	0.941069i
$326$	4.39329	−	7.60939i	0.243322	−	0.421445i
$327$	−32.5078	+	18.7684i	−1.79769	+	1.03789i
$328$	2.41415	−	4.18143i	0.133299	−	0.230881i
$329$	−14.1374	+	8.16225i	−0.779422	+	0.450000i
$330$	−0.868919	−	0.0175738i	−0.0478324	−	0.000967404i
$331$			0.387307i			0.0212883i	0.999943	+	0.0106442i	$0.00338820\pi$
$331$			0.387307i			0.0212883i	−0.999943	+	0.0106442i	$0.996612\pi$
$332$	3.90423	−	2.25411i	0.214273	−	0.123710i
$333$	4.43342	−	2.55964i	0.242950	−	0.140267i
$334$	2.31830			0.126852
$335$		−	0.526914i		−	0.0287884i
$336$	4.52426	+	7.83624i	0.246818	+	0.427502i
$337$	−0.176938	+	0.306466i	−0.00963844	+	0.0166943i	−0.870804	−	0.491630i	$-0.836401\pi$
$337$	−0.176938	+	0.306466i	−0.00963844	+	0.0166943i	0.861166	+	0.508324i	$0.169735\pi$
$338$	1.22724	+	2.12563i	0.0667528	+	0.115619i
$339$	6.83071	−	11.8311i	0.370993	−	0.642580i
$340$	−0.322575	−	0.186239i	−0.0174941	−	0.0101002i
$341$	20.0890	+	0.406297i	1.08788	+	0.0220022i
$342$	−4.66379	−	0.627164i	−0.252189	−	0.0339131i
$343$			27.1914i			1.46820i
$344$	0.219263	+	0.126591i	0.0118218	+	0.00682535i
$345$	1.27149	+	0.734096i	0.0684548	+	0.0395224i
$346$	−3.62502	−	6.27873i	−0.194882	−	0.337546i
$347$	−16.9725	−	9.79909i	−0.911133	−	0.526043i	−0.0303372	−	0.999540i	$-0.509658\pi$
$347$	−16.9725	−	9.79909i	−0.911133	−	0.526043i	−0.880795	+	0.473497i	$0.842991\pi$
$348$	6.97189	−	4.02522i	0.373732	−	0.215775i
$349$			2.72211i			0.145711i	0.997342	+	0.0728557i	$0.0232112\pi$
$349$			2.72211i			0.145711i	−0.997342	+	0.0728557i	$0.976789\pi$
$350$		−	22.3242i		−	1.19328i
$351$	13.2057	−	7.62433i	0.704869	−	0.406956i
$352$	2.90523	−	1.59989i	0.154849	−	0.0852746i
$353$	18.9919			1.01084			0.505418	−	0.862875i	$-0.331338\pi$
$353$	18.9919			1.01084			0.505418	+	0.862875i	$0.331338\pi$
$354$	12.0680			0.641405
$355$	−1.62343	+	0.937285i	−0.0861625	+	0.0497459i
$356$	−14.4364	−	8.33488i	−0.765130	−	0.441748i
$357$	22.4980	−	12.9892i	1.19072	−	0.687464i
$358$	−14.1029	−	8.14230i	−0.745360	−	0.430334i
$359$	−22.2856	−	12.8666i	−1.17619	−	0.679072i	−0.221058	−	0.975261i	$-0.570951\pi$
$359$	−22.2856	−	12.8666i	−1.17619	−	0.679072i	−0.955129	+	0.296189i	$0.904284\pi$
$360$	−0.140061			−0.00738187
$361$	18.3250	+	5.01929i	0.964475	+	0.264173i
$362$		−	6.70377i		−	0.352342i
$363$	−18.7762	−	11.8778i	−0.985497	−	0.623422i
$364$	−15.2520	−	8.80576i	−0.799423	−	0.461547i
$365$	−0.867520	+	0.500863i	−0.0454081	+	0.0262164i
$366$	−13.2175	+	22.8934i	−0.690890	+	1.19666i
$367$	−1.47625	−	2.55694i	−0.0770596	−	0.133471i	0.824920	−	0.565249i	$-0.191220\pi$
$367$	−1.47625	−	2.55694i	−0.0770596	−	0.133471i	−0.901980	+	0.431778i	$0.857887\pi$
$368$	−5.60288			−0.292070
$369$	−5.21253			−0.271353
$370$	−0.532782	+	0.307602i	−0.0276980	+	0.0159915i
$371$	0.290881	+	0.503820i	0.0151018	+	0.0261571i
$372$	12.2365			0.634434
$373$	−18.1589			−0.940233			−0.470117	−	0.882604i	$-0.655788\pi$
$373$	−18.1589			−0.940233			−0.470117	+	0.882604i	$0.655788\pi$
$374$	−4.59333	−	8.34097i	−0.237515	−	0.431301i
$375$	2.26553	+	1.30801i	0.116992	+	0.0675452i
$376$	1.82197	+	3.15574i	0.0939608	+	0.162745i
$377$	−7.83446	+	13.5697i	−0.403495	+	0.698875i
$378$	−8.68849	+	15.0489i	−0.446888	+	0.774032i
$379$			19.8897i			1.02166i	0.859681	+	0.510832i	$0.170662\pi$
$379$			19.8897i			1.02166i	−0.859681	+	0.510832i	$0.829338\pi$
$380$	0.560466	+	0.0753687i	0.0287513	+	0.00386633i
$381$		−	14.1621i		−	0.725549i
$382$	−7.20335	+	12.4766i	−0.368555	+	0.638356i
$383$	7.90191	+	4.56217i	0.403769	+	0.233116i	0.688109	−	0.725607i	$-0.258441\pi$
$383$	7.90191	+	4.56217i	0.403769	+	0.233116i	−0.284340	+	0.958723i	$0.591774\pi$
$384$	1.74919	−	1.00990i	0.0892632	−	0.0515362i
$385$	−0.997389	+	1.64957i	−0.0508316	+	0.0840699i
$386$	1.09475	+	1.89617i	0.0557215	+	0.0965124i
$387$		−	0.273330i		−	0.0138942i
$388$		−	13.5730i		−	0.689063i
$389$	9.99429	+	17.3106i	0.506730	+	0.877683i	0.999970	+	0.00778918i	$0.00247940\pi$
$389$	9.99429	+	17.3106i	0.506730	+	0.877683i	−0.493239	+	0.869894i	$0.664187\pi$
$390$	0.892132	−	0.515073i	0.0451749	−	0.0260817i
$391$			16.0860i			0.813504i
$392$	13.0696			0.660116
$393$	8.00594	+	13.8667i	0.403846	+	0.699482i
$394$	−20.0370	−	11.5683i	−1.00945	−	0.582805i
$395$	−0.293678	−	0.508666i	−0.0147766	−	0.0255938i
$396$	−3.06402	−	1.85261i	−0.153973	−	0.0930973i
$397$	−10.7075	+	18.5458i	−0.537392	+	0.930789i	0.461652	+	0.887061i	$0.347257\pi$
$397$	−10.7075	+	18.5458i	−0.537392	+	0.930789i	−0.999043	+	0.0437283i	$0.986076\pi$
$398$	−0.825542			−0.0413807
$399$	−24.0972	+	31.2244i	−1.20637	+	1.56317i
$400$	−4.98317			−0.249158
$401$	0.706399	+	0.407840i	0.0352759	+	0.0203665i	0.517534	−	0.855663i	$-0.326850\pi$
$401$	0.706399	+	0.407840i	0.0352759	+	0.0203665i	−0.482258	+	0.876029i	$0.660183\pi$
$402$	4.10160	−	7.10417i	0.204569	−	0.354324i
$403$	−20.6257	+	11.9082i	−1.02744	+	0.593192i
$404$	−0.321471	−	0.185601i	−0.0159938	−	0.00923402i
$405$	−0.718305	−	1.24414i	−0.0356929	−	0.0618219i
$406$		−	17.8559i		−	0.886174i
$407$	−15.7240	−	0.318015i	−0.779409	−	0.0157634i
$408$	−2.89944	−	5.02198i	−0.143544	−	0.248625i
$409$	4.40138	+	7.62341i	0.217634	+	0.376953i	0.954084	−	0.299539i	$-0.0968327\pi$
$409$	4.40138	+	7.62341i	0.217634	+	0.376953i	−0.736450	+	0.676492i	$0.763499\pi$
$410$	0.626410			0.0309362
$411$		−	9.92891i		−	0.489757i
$412$	7.79811	−	4.50224i	0.384185	−	0.221809i
$413$	13.3834	−	23.1807i	0.658553	−	1.14065i
$414$	3.02437	+	5.23837i	0.148640	+	0.257452i
$415$	0.506524	+	0.292442i	0.0248643	+	0.0143554i
$416$	−1.96561	+	3.40453i	−0.0963719	+	0.166921i
$417$	−26.3553			−1.29062
$418$	11.2640	+	9.06216i	0.550939	+	0.443245i
$419$	12.3145			0.601601			0.300801	−	0.953687i	$-0.402746\pi$
$419$	12.3145			0.601601			0.300801	+	0.953687i	$0.402746\pi$
$420$	−0.586964	+	1.01665i	−0.0286409	+	0.0496075i
$421$	−29.0645	−	16.7804i	−1.41652	−	0.817828i	−0.420528	−	0.907279i	$-0.638155\pi$
$421$	−29.0645	−	16.7804i	−1.41652	−	0.817828i	−0.995991	+	0.0894517i	$0.971489\pi$
$422$	−10.8046	−	18.7142i	−0.525962	−	0.910993i
$423$	1.96695	−	3.40686i	0.0956366	−	0.165647i
$424$	0.112462	−	0.0649300i	0.00546164	−	0.00315328i
$425$			14.3068i			0.693981i
$426$	−29.1840			−1.41397
$427$	29.3165	+	50.7776i	1.41872	+	2.45730i
$428$	−5.29538	−	9.17187i	−0.255962	−	0.443339i
$429$	26.3295	+	0.532510i	1.27120	+	0.0257098i
$430$			0.0328472i			0.00158403i
$431$	9.43169	+	16.3362i	0.454308	+	0.786885i	0.998648	−	0.0519795i	$-0.0165531\pi$
$431$	9.43169	+	16.3362i	0.454308	+	0.786885i	−0.544340	+	0.838865i	$0.683220\pi$
$432$	3.35919	+	1.93943i	0.161619	+	0.0933109i
$433$	−8.89336	+	5.13458i	−0.427387	+	0.246752i	−0.698233	−	0.715871i	$-0.746030\pi$
$433$	−8.89336	+	5.13458i	−0.427387	+	0.246752i	0.270846	+	0.962623i	$0.412697\pi$
$434$	13.5703	−	23.5045i	0.651396	−	1.12825i
$435$	0.904512	+	0.522220i	0.0433680	+	0.0250386i
$436$	18.5844			0.890033
$437$	−9.28343	−	22.5892i	−0.444087	−	1.08059i
$438$	−15.5952			−0.745170
$439$	15.8473	−	27.4484i	0.756352	−	1.31004i	−0.188347	−	0.982103i	$-0.560313\pi$
$439$	15.8473	−	27.4484i	0.756352	−	1.31004i	0.944699	−	0.327938i	$-0.106354\pi$
$440$	0.368215	+	0.222636i	0.0175540	+	0.0106137i
$441$	−7.05484	−	12.2193i	−0.335945	−	0.581873i
$442$	9.77449	+	5.64331i	0.464925	+	0.268425i
$443$	5.62125	+	9.73630i	0.267074	+	0.462585i	0.968105	−	0.250545i	$-0.0806099\pi$
$443$	5.62125	+	9.73630i	0.267074	+	0.462585i	−0.701031	+	0.713131i	$0.747277\pi$
$444$	−9.57773			−0.454539
$445$		−	2.16269i		−	0.102521i
$446$	−21.3131	+	12.3051i	−1.00920	+	0.582664i
$447$	20.3588	+	35.2624i	0.962936	+	1.66785i
$448$		−	4.47991i		−	0.211656i
$449$		−	39.2910i		−	1.85426i	−0.374743	−	0.927129i	$-0.622269\pi$
$449$		−	39.2910i		−	1.85426i	0.374743	−	0.927129i	$-0.377731\pi$
$450$	2.68986	+	4.65897i	0.126801	+	0.219626i
$451$	13.7035	+	8.28562i	0.645273	+	0.390155i
$452$	−5.85759	+	3.38188i	−0.275518	+	0.159070i
$453$	−16.9953	−	9.81226i	−0.798510	−	0.461020i
$454$	4.69277	−	8.12812i	0.220243	−	0.381472i
$455$		−	2.28487i		−	0.107116i
$456$	6.96986	+	5.37894i	0.326394	+	0.251892i
$457$		−	17.9324i		−	0.838842i	−0.907792	−	0.419421i	$-0.862233\pi$
$457$		−	17.9324i		−	0.838842i	0.907792	−	0.419421i	$-0.137767\pi$
$458$	−12.2754	+	21.2617i	−0.573594	+	0.993493i
$459$	5.56815	−	9.64432i	0.259899	−	0.450158i
$460$	−0.363451	−	0.629515i	−0.0169460	−	0.0293513i
$461$	−6.80571	−	3.92928i	−0.316973	−	0.183005i	0.333069	−	0.942902i	$-0.391916\pi$
$461$	−6.80571	−	3.92928i	−0.316973	−	0.183005i	−0.650043	+	0.759898i	$0.725249\pi$
$462$	−26.2880	+	14.4767i	−1.22303	+	0.673515i
$463$	5.56513			0.258634			0.129317	−	0.991603i	$-0.458722\pi$
$463$	5.56513			0.258634			0.129317	+	0.991603i	$0.458722\pi$
$464$	−3.98577			−0.185035
$465$	0.793765	+	1.37484i	0.0368100	+	0.0637568i
$466$	−23.7955	+	13.7383i	−1.10230	+	0.636415i
$467$	11.6657			0.539826			0.269913	−	0.962885i	$-0.413005\pi$
$467$	11.6657			0.539826			0.269913	+	0.962885i	$0.413005\pi$
$468$	4.24405			0.196181
$469$	−9.09735	−	15.7571i	−0.420077	−	0.727594i
$470$	−0.236377	+	0.409416i	−0.0109032	+	0.0188850i
$471$	−43.0915	+	24.8789i	−1.98555	+	1.14636i
$472$	−5.17436	−	2.98742i	−0.238169	−	0.137507i
$473$	−0.434475	+	0.718573i	−0.0199772	+	0.0330400i
$474$		−	9.14420i		−	0.420007i
$475$	−8.25662	−	20.0907i	−0.378840	−	0.921824i
$476$	−12.8619			−0.589526
$477$	−0.121411	−	0.0700970i	−0.00555905	−	0.00320952i
$478$	−13.3197	−	7.69016i	−0.609231	−	0.351740i
$479$	27.3906	−	15.8140i	1.25151	−	0.722560i	0.280101	−	0.959971i	$-0.409632\pi$
$479$	27.3906	−	15.8140i	1.25151	−	0.722560i	0.971409	+	0.237411i	$0.0762989\pi$
$480$	0.226935	+	0.131021i	0.0103581	+	0.00598027i
$481$	16.1441	−	9.32077i	0.736106	−	0.424991i
$482$	−10.0879			−0.459490
$483$	50.6978			2.30683
$484$	5.11032	+	9.74087i	0.232287	+	0.442767i
$485$	1.52500	−	0.880459i	0.0692467	−	0.0399796i
$486$		−	10.7291i		−	0.486682i
$487$		−	18.6345i		−	0.844410i	−0.906500	−	0.422205i	$-0.861256\pi$
$487$		−	18.6345i		−	0.844410i	0.906500	−	0.422205i	$-0.138744\pi$
$488$	11.3345	−	6.54398i	0.513089	−	0.296232i
$489$	15.3694	+	8.87354i	0.695030	+	0.401275i
$490$	0.847808	+	1.46845i	0.0383001	+	0.0663376i
$491$	13.4139	+	7.74450i	0.605360	+	0.349504i	0.771147	−	0.636657i	$-0.219683\pi$
$491$	13.4139	+	7.74450i	0.605360	+	0.349504i	−0.165788	+	0.986161i	$0.553017\pi$
$492$	8.44564	+	4.87609i	0.380759	+	0.219831i
$493$			11.4432i			0.515377i
$494$	−16.9829	−	2.28378i	−0.764097	−	0.102752i
$495$	0.00939315	−	0.464435i	0.000422191	−	0.0208748i
$496$	−5.24664	−	3.02915i	−0.235581	−	0.136013i
$497$	−32.3651	+	56.0580i	−1.45177	+	2.51455i
$498$	4.55284	+	7.88576i	0.204018	+	0.353369i
$499$	−7.05643	+	12.2221i	−0.315889	+	0.547136i	−0.979626	−	0.200830i	$-0.935636\pi$
$499$	−7.05643	+	12.2221i	−0.315889	+	0.547136i	0.663737	+	0.747966i	$0.268970\pi$
$500$	−0.647593	−	1.12166i	−0.0289613	−	0.0501624i
$501$			4.68250i			0.209199i
$502$	−8.76878			−0.391370
$503$	−3.02208	+	1.74480i	−0.134748	+	0.0777968i	−0.565859	−	0.824502i	$-0.691455\pi$
$503$	−3.02208	+	1.74480i	−0.134748	+	0.0777968i	0.431111	+	0.902299i	$0.358122\pi$
$504$	−4.18846	+	2.41821i	−0.186569	+	0.107716i
$505$		−	0.0481588i		−	0.00214304i
$506$	0.375755	−	18.5789i	0.0167043	−	0.825931i
$507$	−4.29335	+	2.47877i	−0.190674	+	0.110086i
$508$	−3.50584	+	6.07229i	−0.155546	+	0.269414i
$509$	26.1640	−	15.1058i	1.15970	−	0.669552i	0.208467	−	0.978029i	$-0.433153\pi$
$509$	26.1640	−	15.1058i	1.15970	−	0.669552i	0.951232	+	0.308477i	$0.0998194\pi$
$510$	0.376165	−	0.651537i	0.0166569	−	0.0288505i
$511$	−17.2952	+	29.9561i	−0.765092	+	1.32518i
$512$	−1.00000			−0.0441942
$513$	−2.25337	+	16.7567i	−0.0994885	+	0.739828i
$514$			31.7201i			1.39911i
$515$	1.01170	+	0.584107i	0.0445810	+	0.0257389i
$516$	−0.255689	+	0.442866i	−0.0112561	+	0.0194961i
$517$	−10.5865	+	5.82991i	−0.465592	+	0.256399i
$518$	−10.6217	+	18.3974i	−0.466691	+	0.808333i
$519$	12.6817	−	7.32181i	0.556667	−	0.321392i
$520$	−0.510025			−0.0223661
$521$		−	26.0601i		−	1.14171i	−0.821050	−	0.570856i	$-0.806611\pi$
$521$		−	26.0601i		−	1.14171i	0.821050	−	0.570856i	$-0.193389\pi$
$522$	2.15147	+	3.72646i	0.0941674	+	0.163103i
$523$	−1.77172	−	3.06870i	−0.0774718	−	0.134185i	0.824687	−	0.565590i	$-0.191351\pi$
$523$	−1.77172	−	3.06870i	−0.0774718	−	0.134185i	−0.902158	+	0.431405i	$0.858018\pi$
$524$		−	7.92747i		−	0.346313i
$525$	45.0903			1.96790
$526$	25.6515	−	14.8099i	1.11846	−	0.645742i
$527$	−8.69675	+	15.0632i	−0.378836	+	0.656164i
$528$	3.23146	+	5.86797i	0.140631	+	0.255370i
$529$	−4.19614	+	7.26792i	−0.182441	+	0.315997i
$530$	0.0145905	+	0.00842383i	0.000633771	+	0.000365908i
$531$			6.45030i			0.279919i
$532$	18.0617	−	7.42278i	0.783074	−	0.321818i
$533$	−18.9811			−0.822163
$534$	16.8348	−	29.1587i	0.728512	−	1.26182i
$535$	0.687007	−	1.18993i	0.0297019	−	0.0514452i
$536$	−3.51727	+	2.03070i	−0.151923	+	0.0877128i
$537$	16.4458	−	28.4849i	0.709688	−	1.22922i
$538$	12.2618	−	7.07936i	0.528644	−	0.305213i
$539$	−0.876510	+	43.3382i	−0.0377539	+	1.86671i
$540$			0.503232i			0.0216557i
$541$	0.827614	−	0.477823i	0.0355819	−	0.0205432i	−0.482104	−	0.876114i	$-0.660127\pi$
$541$	0.827614	−	0.477823i	0.0355819	−	0.0205432i	0.517685	+	0.855571i	$0.326794\pi$
$542$	5.10308	−	2.94627i	0.219196	−	0.126553i
$543$	13.5402			0.581067
$544$			2.87102i			0.123094i
$545$	1.20555	+	2.08807i	0.0516399	+	0.0894429i
$546$	17.7858	−	30.8060i	0.761164	−	1.31837i
$547$	−5.38930	−	9.33454i	−0.230430	−	0.399116i	0.727505	−	0.686102i	$-0.240680\pi$
$547$	−5.38930	−	9.33454i	−0.230430	−	0.399116i	−0.957935	+	0.286986i	$0.907347\pi$
$548$	−2.45790	+	4.25721i	−0.104996	+	0.181859i
$549$	−12.2365	−	7.06473i	−0.522240	−	0.301515i
$550$	0.334194	−	16.5239i	0.0142501	−	0.704582i
$551$	−6.60403	−	16.0695i	−0.281341	−	0.684582i
$552$		−	11.3167i		−	0.481670i
$553$	−17.5646	−	10.1409i	−0.746923	−	0.431236i
$554$	16.9075	+	9.76153i	0.718330	+	0.414728i
$555$	−0.621293	−	1.07611i	−0.0263724	−	0.0456784i
$556$	11.3003	+	6.52424i	0.479240	+	0.276690i
$557$	−11.4752	+	6.62520i	−0.486219	+	0.280719i	−0.723005	−	0.690843i	$-0.757240\pi$
$557$	−11.4752	+	6.62520i	−0.486219	+	0.280719i	0.236785	+	0.971562i	$0.423906\pi$
$558$			6.54040i			0.276877i
$559$		−	0.995316i		−	0.0420974i
$560$	0.503343	−	0.290605i	0.0212701	−	0.0122803i
$561$	16.8471	−	9.27759i	0.711283	−	0.391700i
$562$	11.3468			0.478636
$563$	−24.6625			−1.03940			−0.519701	−	0.854348i	$-0.673957\pi$
$563$	−24.6625			−1.03940			−0.519701	+	0.854348i	$0.673957\pi$
$564$	−6.37395	+	3.68000i	−0.268392	+	0.154956i
$565$	−0.759947	−	0.438756i	−0.0319712	−	0.0184586i
$566$	8.52486	−	4.92183i	0.358326	−	0.206880i
$567$	−42.9611	−	24.8036i	−1.80420	−	1.04165i
$568$	12.5132	+	7.22450i	0.525042	+	0.303133i
$569$	1.60056			0.0670990			0.0335495	−	0.999437i	$-0.489319\pi$
$569$	1.60056			0.0670990			0.0335495	+	0.999437i	$0.489319\pi$
$570$	−0.152230	+	1.13203i	−0.00637619	+	0.0474154i
$571$			41.6813i			1.74431i	0.489231	+	0.872154i	$0.337277\pi$
$571$			41.6813i			1.74431i	−0.489231	+	0.872154i	$0.662723\pi$
$572$	−11.1574	−	6.74618i	−0.466516	−	0.282072i
$573$	−25.2001	−	14.5493i	−1.05275	−	0.607805i
$574$	18.7325	−	10.8152i	0.781878	−	0.451417i
$575$	−13.9600	+	24.1795i	−0.582174	+	1.00836i
$576$	0.539789	+	0.934941i	0.0224912	+	0.0389559i
$577$	−25.1475			−1.04690			−0.523452	−	0.852055i	$-0.675356\pi$
$577$	−25.1475			−1.04690			−0.523452	+	0.852055i	$0.675356\pi$
$578$	−8.75723			−0.364253
$579$	−3.82987	+	2.21118i	−0.159164	+	0.0918935i
$580$	−0.258551	−	0.447823i	−0.0107357	−	0.0185949i
$581$	20.1964			0.837890
$582$	27.4146			1.13637
$583$	0.207762	+	0.377273i	0.00860463	+	0.0156250i
$584$	6.68675	+	3.86060i	0.276700	+	0.159753i
$585$	0.275306	+	0.476843i	0.0113825	+	0.0197150i
$586$	1.46919	−	2.54470i	0.0606915	−	0.105121i
$587$	−6.80724	+	11.7905i	−0.280965	+	0.486645i	−0.971623	−	0.236536i	$-0.923988\pi$
$587$	−6.80724	+	11.7905i	−0.280965	+	0.486645i	0.690658	+	0.723182i	$0.257321\pi$
$588$			26.3980i			1.08864i
$589$	3.51947	−	26.1719i	0.145017	−	1.07839i
$590$		−	0.775158i		−	0.0319128i
$591$	23.3657	−	40.4706i	0.961136	−	1.66474i
$592$	4.10663	+	2.37096i	0.168781	+	0.0974460i
$593$	−6.91328	+	3.99138i	−0.283894	+	0.163906i	−0.635185	−	0.772360i	$-0.719076\pi$
$593$	−6.91328	+	3.99138i	−0.283894	+	0.163906i	0.351291	+	0.936266i	$0.385743\pi$
$594$	−6.65633	+	11.0088i	−0.273113	+	0.451698i
$595$	−0.834335	−	1.44511i	−0.0342044	−	0.0592437i
$596$		−	20.1592i		−	0.825754i
$597$		−	1.66743i		−	0.0682432i
$598$	11.0131	+	19.0752i	0.450358	+	0.780043i
$599$	−27.4903	+	15.8715i	−1.12322	+	0.648493i	−0.942222	−	0.334990i	$-0.891267\pi$
$599$	−27.4903	+	15.8715i	−1.12322	+	0.648493i	−0.181001	+	0.983483i	$0.557934\pi$
$600$		−	10.0650i		−	0.410901i
$601$	29.9977			1.22363			0.611815	−	0.791001i	$-0.290440\pi$
$601$	29.9977			1.22363			0.611815	+	0.791001i	$0.290440\pi$
$602$	0.567118	+	0.982278i	0.0231140	+	0.0400346i
$603$	3.79717	+	2.19230i	0.154633	+	0.0892772i
$604$	4.85804	+	8.41438i	0.197671	+	0.342376i
$605$	−0.762942	+	1.20605i	−0.0310180	+	0.0490329i
$606$	0.374877	−	0.649306i	0.0152283	−	0.0263763i
$607$	−15.1457			−0.614745			−0.307373	−	0.951589i	$-0.599450\pi$
$607$	−15.1457			−0.614745			−0.307373	+	0.951589i	$0.599450\pi$
$608$	−1.65690	−	4.03171i	−0.0671963	−	0.163507i
$609$	36.0653			1.46144
$610$	1.47050	+	0.848996i	0.0595390	+	0.0343749i
$611$	7.16255	−	12.4059i	0.289766	−	0.501889i
$612$	2.68424	−	1.54975i	0.108504	−	0.0626447i
$613$	13.3958	+	7.73407i	0.541051	+	0.312376i	0.745505	−	0.666500i	$-0.232208\pi$
$613$	13.3958	+	7.73407i	0.541051	+	0.312376i	−0.204454	+	0.978876i	$0.565542\pi$
$614$	−5.95515	−	10.3146i	−0.240330	−	0.416265i
$615$			1.26522i			0.0510186i
$616$	14.8552	+	0.300444i	0.598531	+	0.0121052i
$617$	−11.6427	−	20.1657i	−0.468717	−	0.811842i	0.530643	−	0.847595i	$-0.321950\pi$
$617$	−11.6427	−	20.1657i	−0.468717	−	0.811842i	−0.999361	+	0.0357531i	$0.988617\pi$
$618$	9.09361	+	15.7506i	0.365799	+	0.633582i
$619$	41.2500			1.65798			0.828990	−	0.559264i	$-0.188916\pi$
$619$	41.2500			1.65798			0.828990	+	0.559264i	$0.188916\pi$
$620$		−	0.785985i		−	0.0315659i
$621$	18.8212	−	10.8664i	0.755267	−	0.436054i
$622$	−3.15961	+	5.47260i	−0.126689	+	0.219431i
$623$	−37.3396	−	64.6740i	−1.49598	−	2.59111i
$624$	−6.87647	−	3.97013i	−0.275279	−	0.158932i
$625$	−12.3739	+	21.4322i	−0.494956	+	0.857289i
$626$	−14.4375			−0.577037
$627$	−18.3037	+	22.7510i	−0.730980	+	0.908585i
$628$	24.6351			0.983046
$629$	6.80709	−	11.7902i	0.271416	−	0.470107i
$630$	−0.543398	−	0.313731i	−0.0216495	−	0.0124993i
$631$	0.244717	+	0.423863i	0.00974204	+	0.0168737i	0.870855	−	0.491539i	$-0.163566\pi$
$631$	0.244717	+	0.423863i	0.00974204	+	0.0168737i	−0.861113	+	0.508413i	$0.830232\pi$
$632$	−2.26364	+	3.92074i	−0.0900429	+	0.155959i
$633$	37.7989	−	21.8232i	1.50237	−	0.867394i
$634$			3.83651i			0.152367i
$635$	−0.909674			−0.0360993
$636$	0.131145	+	0.227150i	0.00520025	+	0.00900710i
$637$	−25.6898	−	44.4960i	−1.01787	−	1.76300i
$638$	0.267304	−	13.2166i	0.0105827	−	0.523250i
$639$		−	15.5988i		−	0.617079i
$640$	−0.0648685	−	0.112356i	−0.00256415	−	0.00444124i
$641$	22.5012	+	12.9911i	0.888744	+	0.513116i	0.873531	−	0.486768i	$-0.161824\pi$
$641$	22.5012	+	12.9911i	0.888744	+	0.513116i	0.0152123	+	0.999884i	$0.495158\pi$
$642$	18.5253	−	10.6956i	0.731135	−	0.422121i
$643$	22.5233	−	39.0116i	0.888234	−	1.53847i	0.0462721	−	0.998929i	$-0.485266\pi$
$643$	22.5233	−	39.0116i	0.888234	−	1.53847i	0.841962	−	0.539537i	$-0.181401\pi$
$644$	−21.7376	−	12.5502i	−0.856582	−	0.494548i
$645$	−0.0663446			−0.00261232
$646$	−11.5751	+	4.75700i	−0.455417	+	0.187162i
$647$	−37.9571			−1.49225			−0.746125	−	0.665806i	$-0.768088\pi$
$647$	−37.9571			−1.49225			−0.746125	+	0.665806i	$0.768088\pi$
$648$	−5.53662	+	9.58971i	−0.217499	+	0.376719i
$649$	10.2531	−	16.9576i	0.402471	−	0.665643i
$650$	9.79496	+	16.9654i	0.384190	+	0.665436i
$651$	47.4743	+	27.4093i	1.86066	+	1.07425i
$652$	−4.39329	−	7.60939i	−0.172054	−	0.298007i
$653$	31.8364			1.24586			0.622928	−	0.782279i	$-0.285943\pi$
$653$	31.8364			1.24586			0.622928	+	0.782279i	$0.285943\pi$
$654$			37.5368i			1.46780i
$655$	0.890696	−	0.514244i	0.0348024	−	0.0200932i
$656$	−2.41415	−	4.18143i	−0.0942568	−	0.163258i
$657$		−	8.33563i		−	0.325204i
$658$			16.3245i			0.636396i
$659$	10.1845	+	17.6401i	0.396732	+	0.687159i	0.993321	−	0.115388i	$-0.0368111\pi$
$659$	10.1845	+	17.6401i	0.396732	+	0.687159i	−0.596589	+	0.802547i	$0.703478\pi$
$660$	−0.449679	+	0.743719i	−0.0175037	+	0.0289492i
$661$	43.3159	−	25.0084i	1.68479	−	0.972715i	0.726396	−	0.687277i	$-0.241194\pi$
$661$	43.3159	−	25.0084i	1.68479	−	0.972715i	0.958397	−	0.285439i	$-0.0921393\pi$
$662$	0.335417	+	0.193653i	0.0130364	+	0.00752655i
$663$	−11.3983	+	19.7425i	−0.442674	+	0.766735i
$664$		−	4.50822i		−	0.174953i
$665$	2.00563	+	1.54783i	0.0777749	+	0.0600222i
$666$		−	5.11928i		−	0.198368i
$667$	−11.1659	+	19.3399i	−0.432345	+	0.748844i
$668$	1.15915	−	2.00771i	0.0448489	−	0.0776806i
$669$	−24.8538	−	43.0481i	−0.960904	−	1.66434i
$670$	−0.456321	−	0.263457i	−0.0176292	−	0.0101782i
$671$	20.9393	+	38.0235i	0.808354	+	1.46788i
$672$	9.04852			0.349054
$673$	−31.7420			−1.22356			−0.611782	−	0.791026i	$-0.709547\pi$
$673$	−31.7420			−1.22356			−0.611782	+	0.791026i	$0.709547\pi$
$674$	0.176938	+	0.306466i	0.00681541	+	0.0118046i
$675$	16.7394	−	9.66451i	0.644301	−	0.371987i
$676$	2.45447			0.0944028
$677$	23.7389			0.912360			0.456180	−	0.889887i	$-0.349217\pi$
$677$	23.7389			0.912360			0.456180	+	0.889887i	$0.349217\pi$
$678$	−6.83071	−	11.8311i	−0.262332	−	0.454372i
$679$	30.4029	−	52.6593i	1.16676	−	2.02088i
$680$	−0.322575	+	0.186239i	−0.0123702	+	0.00714194i
$681$	16.4172	+	9.47845i	0.629107	+	0.363215i
$682$	10.3964	−	17.1944i	0.398097	−	0.658408i
$683$			14.0384i			0.537166i	0.963257	+	0.268583i	$0.0865553\pi$
$683$			14.0384i			0.537166i	−0.963257	+	0.268583i	$0.913445\pi$
$684$	−2.87503	+	3.72538i	−0.109930	+	0.142443i
$685$	−0.637761			−0.0243676
$686$	23.5485	+	13.5957i	0.899085	+	0.519087i
$687$	−42.9443	−	24.7939i	−1.63843	−	0.945946i
$688$	0.219263	−	0.126591i	0.00835931	−	0.00482625i
$689$	−0.442113	−	0.255254i	−0.0168432	−	0.00972440i
$690$	1.27149	−	0.734096i	0.0484049	−	0.0279466i
$691$	−25.7327			−0.978919			−0.489460	−	0.872026i	$-0.662806\pi$
$691$	−25.7327			−0.978919			−0.489460	+	0.872026i	$0.662806\pi$
$692$	−7.25005			−0.275605
$693$	−7.73775	−	14.0509i	−0.293933	−	0.533749i
$694$	−16.9725	+	9.79909i	−0.644268	+	0.371968i
$695$			1.69287i			0.0642143i
$696$		−	8.05044i		−	0.305151i
$697$	−12.0050	+	6.93108i	−0.454721	+	0.262533i
$698$	2.35742	+	1.36106i	0.0892296	+	0.0515167i
$699$	−27.7486	−	48.0620i	−1.04955	−	1.81787i
$700$	−19.3333	−	11.1621i	−0.730730	−	0.421887i
$701$	−13.3777	−	7.72362i	−0.505269	−	0.291717i	0.225618	−	0.974216i	$-0.427560\pi$
$701$	−13.3777	−	7.72362i	−0.505269	−	0.291717i	−0.730887	+	0.682499i	$0.760893\pi$
$702$		−	15.2487i		−	0.575523i
$703$	−2.75475	+	20.4852i	−0.103897	+	0.772614i
$704$	0.0670646	−	3.31595i	0.00252759	−	0.124974i
$705$	−0.826937	−	0.477433i	−0.0311443	−	0.0179812i
$706$	9.49593	−	16.4474i	0.357384	−	0.619008i
$707$	−0.831479	−	1.44016i	−0.0312710	−	0.0541629i
$708$	6.03398	−	10.4512i	0.226771	−	0.392779i
$709$	−19.5140	−	33.7992i	−0.732863	−	1.26936i	−0.955655	−	0.294490i	$-0.904850\pi$
$709$	−19.5140	−	33.7992i	−0.732863	−	1.26936i	0.222791	−	0.974866i	$-0.428483\pi$
$710$			1.87457i			0.0703514i
$711$	4.88756			0.183298
$712$	−14.4364	+	8.33488i	−0.541029	+	0.312363i
$713$	−29.3963	+	16.9720i	−1.10090	+	0.635605i
$714$		−	25.9785i		−	0.972220i
$715$	0.0342046	−	1.69121i	0.00127918	−	0.0632478i
$716$	−14.1029	+	8.14230i	−0.527049	+	0.304292i
$717$	15.5326	−	26.9032i	0.580074	−	1.00472i
$718$	−22.2856	+	12.8666i	−0.831690	+	0.480176i
$719$	−3.76361	+	6.51877i	−0.140359	+	0.243109i	−0.927632	−	0.373496i	$-0.878159\pi$
$719$	−3.76361	+	6.51877i	−0.140359	+	0.243109i	0.787273	+	0.616605i	$0.211492\pi$
$720$	−0.0700306	+	0.121297i	−0.00260989	+	0.00452046i
$721$	40.3393			1.50231
$722$	13.5093	−	13.3603i	0.502766	−	0.497219i
$723$		−	20.3755i		−	0.757772i
$724$	−5.80563	−	3.35188i	−0.215765	−	0.124572i
$725$	−9.93088	+	17.2008i	−0.368824	+	0.638821i
$726$	−19.6746	+	10.3218i	−0.730192	+	0.383078i
$727$	−11.1300	+	19.2777i	−0.412787	+	0.714969i	−0.995193	−	0.0979293i	$-0.968778\pi$
$727$	−11.1300	+	19.2777i	−0.412787	+	0.714969i	0.582406	+	0.812898i	$0.302111\pi$
$728$	−15.2520	+	8.80576i	−0.565278	+	0.326363i
$729$	−11.5491			−0.427745
$730$			1.00173i			0.0370755i
$731$	−0.363446	−	0.629508i	−0.0134425	−	0.0232832i
$732$	13.2175	+	22.8934i	0.488533	+	0.846164i
$733$			43.1218i			1.59274i	0.604811	+	0.796369i	$0.293249\pi$
$733$			43.1218i			1.59274i	−0.604811	+	0.796369i	$0.706751\pi$
$734$	−2.95250			−0.108979
$735$	−2.96596	+	1.71240i	−0.109401	+	0.0631628i
$736$	−2.80144	+	4.85224i	−0.103262	+	0.178856i
$737$	−6.49780	−	11.7993i	−0.239350	−	0.434632i
$738$	−2.60626	+	4.51418i	−0.0959379	+	0.166169i
$739$	−17.2620	−	9.96623i	−0.634993	−	0.366614i	0.147690	−	0.989034i	$-0.452816\pi$
$739$	−17.2620	−	9.96623i	−0.634993	−	0.366614i	−0.782683	+	0.622420i	$0.786150\pi$
$740$			0.615204i			0.0226153i
$741$	4.61277	−	34.3020i	0.169454	−	1.26012i
$742$	0.581762			0.0213571
$743$	−8.67725	+	15.0294i	−0.318338	+	0.551377i	−0.980141	−	0.198300i	$-0.936458\pi$
$743$	−8.67725	+	15.0294i	−0.318338	+	0.551377i	0.661804	+	0.749677i	$0.269791\pi$
$744$	6.11826	−	10.5971i	0.224306	−	0.388510i
$745$	2.26500	−	1.30770i	0.0829832	−	0.0479104i
$746$	−9.07946	+	15.7261i	−0.332423	+	0.575773i
$747$	−4.21492	+	2.43349i	−0.154216	+	0.0890366i
$748$	−9.52016	−	0.192544i	−0.348091	−	0.00704010i
$749$		−	47.4457i		−	1.73363i
$750$	2.26553	−	1.30801i	0.0827256	−	0.0477617i
$751$	30.4579	−	17.5849i	1.11142	−	0.641680i	0.172225	−	0.985058i	$-0.444904\pi$
$751$	30.4579	−	17.5849i	1.11142	−	0.641680i	0.939198	+	0.343377i	$0.111571\pi$
$752$	3.64393			0.132881
$753$		−	17.7112i		−	0.645431i
$754$	7.83446	+	13.5697i	0.285314	+	0.494179i
$755$	−0.630268	+	1.09166i	−0.0229378	+	0.0397295i
$756$	8.68849	+	15.0489i	0.315997	+	0.547323i
$757$	−5.34556	+	9.25878i	−0.194288	+	0.336516i	−0.946667	−	0.322214i	$-0.895573\pi$
$757$	−5.34556	+	9.25878i	−0.194288	+	0.336516i	0.752379	+	0.658730i	$0.228906\pi$
$758$	17.2250	+	9.94483i	0.625638	+	0.361213i
$759$	37.5255	+	0.758948i	1.36209	+	0.0275481i
$760$	0.345504	−	0.447693i	0.0125328	−	0.0162395i
$761$		−	23.8022i		−	0.862828i	−0.902154	−	0.431414i	$-0.858015\pi$
$761$		−	23.8022i		−	0.862828i	0.902154	−	0.431414i	$-0.141985\pi$
$762$	−12.2648	−	7.08107i	−0.444306	−	0.256520i
$763$	72.1024	+	41.6284i	2.61028	+	1.50705i
$764$	7.20335	+	12.4766i	0.260608	+	0.451386i
$765$	0.348245	+	0.201059i	0.0125908	+	0.00726932i
$766$	7.90191	−	4.56217i	0.285508	−	0.164838i
$767$			23.4884i			0.848117i
$768$		−	2.01980i		−	0.0728831i
$769$	12.9558	−	7.48002i	0.467197	−	0.269736i	−0.247868	−	0.968794i	$-0.579730\pi$
$769$	12.9558	−	7.48002i	0.467197	−	0.269736i	0.715066	+	0.699057i	$0.246397\pi$
$770$	0.929876	+	1.68855i	0.0335104	+	0.0608511i
$771$	−64.0682			−2.30736
$772$	2.18951			0.0788021
$773$	24.5501	−	14.1740i	0.883004	−	0.509803i	0.0113563	−	0.999936i	$-0.496385\pi$
$773$	24.5501	−	14.1740i	0.883004	−	0.509803i	0.871648	+	0.490133i	$0.163052\pi$
$774$	−0.236711	−	0.136665i	−0.00850840	−	0.00491233i
$775$	−26.1449	+	15.0948i	−0.939152	+	0.542219i
$776$	−11.7545	−	6.78649i	−0.421963	−	0.243621i
$777$	−37.1589	−	21.4537i	−1.33307	−	0.769647i
$778$	19.9886			0.716625
$779$	12.8583	−	16.6614i	0.460697	−	0.596956i
$780$		−	1.03015i		−	0.0368851i
$781$	−24.7952	+	41.0086i	−0.887243	+	1.46740i
$782$	13.9309	+	8.04300i	0.498167	+	0.287617i
$783$	13.3890	−	7.73013i	0.478483	−	0.276252i
$784$	6.53482	−	11.3186i	0.233386	−	0.404237i
$785$	1.59804	+	2.76789i	0.0570365	+	0.0987902i
$786$	16.0119			0.571125
$787$	−17.8108			−0.634887			−0.317444	−	0.948277i	$-0.602824\pi$
$787$	−17.8108			−0.634887			−0.317444	+	0.948277i	$0.602824\pi$
$788$	−20.0370	+	11.5683i	−0.713787	+	0.412105i
$789$	29.9130	+	51.8108i	1.06493	+	1.84451i
$790$	−0.587357			−0.0208972
$791$	−30.3011			−1.07738
$792$	−3.13642	+	1.72721i	−0.111448	+	0.0613737i
$793$	−44.5584	−	25.7258i	−1.58231	−	0.913550i
$794$	10.7075	+	18.5458i	0.379993	+	0.658168i
$795$	−0.0170144	+	0.0294698i	−0.000603439	+	0.00104519i
$796$	−0.412771	+	0.714940i	−0.0146303	+	0.0253404i
$797$			21.4014i			0.758075i	0.925381	+	0.379038i	$0.123745\pi$
$797$			21.4014i			0.758075i	−0.925381	+	0.379038i	$0.876255\pi$
$798$	14.9925	+	36.4810i	0.530729	+	1.29141i
$799$		−	10.4618i		−	0.370112i
$800$	−2.49158	+	4.31555i	−0.0880908	+	0.152578i
$801$	15.5853	+	8.99815i	0.550678	+	0.317934i
$802$	0.706399	−	0.407840i	0.0249438	−	0.0144013i
$803$	−13.2500	+	21.9140i	−0.467582	+	0.773329i
$804$	−4.10160	−	7.10417i	−0.144652	−	0.250545i
$805$		−	3.25646i		−	0.114775i
$806$			23.8165i			0.838900i
$807$	14.2989	+	24.7664i	0.503344	+	0.871817i
$808$	−0.321471	+	0.185601i	−0.0113093	+	0.00652944i
$809$			32.9671i			1.15906i	0.814950	+	0.579531i	$0.196764\pi$
$809$			32.9671i			1.15906i	−0.814950	+	0.579531i	$0.803236\pi$
$810$	−1.43661			−0.0504773
$811$	9.10086	+	15.7632i	0.319574	+	0.553519i	0.980399	−	0.197021i	$-0.0631267\pi$
$811$	9.10086	+	15.7632i	0.319574	+	0.553519i	−0.660825	+	0.750540i	$0.729793\pi$
$812$	−15.4637	−	8.92795i	−0.542668	−	0.313310i
$813$	5.95086	+	10.3072i	0.208706	+	0.361489i
$814$	−8.13740	+	13.4584i	−0.285216	+	0.471715i
$815$	0.569972	−	0.987220i	0.0199652	−	0.0345808i
$816$	−5.79888			−0.203001
$817$	0.873676	+	0.674253i	0.0305661	+	0.0235891i
$818$	8.80275			0.307781
$819$	16.4657	+	9.50650i	0.575359	+	0.332184i
$820$	0.313205	−	0.542487i	0.0109376	−	0.0189445i
$821$	−19.4920	+	11.2537i	−0.680276	+	0.392758i	−0.799959	−	0.600055i	$-0.795146\pi$
$821$	−19.4920	+	11.2537i	−0.680276	+	0.392758i	0.119683	+	0.992812i	$0.461812\pi$
$822$	−8.59869	−	4.96445i	−0.299914	−	0.173155i
$823$	−12.4961	−	21.6439i	−0.435587	−	0.754459i	0.561756	−	0.827303i	$-0.310126\pi$
$823$	−12.4961	−	21.6439i	−0.435587	−	0.754459i	−0.997343	+	0.0728437i	$0.976793\pi$
$824$		−	9.00448i		−	0.313686i
$825$	33.3750	+	0.675004i	1.16197	+	0.0235006i
$826$	−13.3834	−	23.1807i	−0.465668	−	0.806560i
$827$	−19.1720	−	33.2068i	−0.666674	−	1.15471i	−0.978828	−	0.204683i	$-0.934384\pi$
$827$	−19.1720	−	33.2068i	−0.666674	−	1.15471i	0.312154	−	0.950032i	$-0.398950\pi$
$828$	6.04874			0.210208
$829$			38.5814i			1.33999i	0.742366	+	0.669994i	$0.233703\pi$
$829$			38.5814i			1.33999i	−0.742366	+	0.669994i	$0.766297\pi$
$830$	0.506524	−	0.292442i	0.0175817	−	0.0101508i
$831$	−19.7163	+	34.1496i	−0.683951	+	1.18464i
$832$	1.96561	+	3.40453i	0.0681452	+	0.118031i
$833$	−32.4960	−	18.7616i	−1.12592	−	0.650051i
$834$	−13.1776	+	22.8243i	−0.456304	+	0.790343i
$835$	0.300770			0.0104086
$836$	13.4801	−	5.22382i	0.466217	−	0.180669i
$837$	23.4993			0.812254
$838$	6.15724	−	10.6646i	0.212698	−	0.368404i
$839$	−29.1071	−	16.8050i	−1.00489	−	0.580173i	−0.0951975	−	0.995458i	$-0.530348\pi$
$839$	−29.1071	−	16.8050i	−1.00489	−	0.580173i	−0.909691	+	0.415286i	$0.863682\pi$
$840$	0.586964	+	1.01665i	0.0202522	+	0.0350778i
$841$	6.55682	−	11.3567i	0.226097	−	0.391612i
$842$	−29.0645	+	16.7804i	−1.00163	+	0.578292i
$843$			22.9182i			0.789346i
$844$	−21.6093			−0.743822
$845$	0.159218	+	0.275774i	0.00547726	+	0.00948690i
$846$	−1.96695	−	3.40686i	−0.0676253	−	0.117130i
$847$	−1.99251	+	49.2388i	−0.0684635	+	1.69186i
$848$		−	0.129860i		−	0.00445941i
$849$	9.94109	+	17.2185i	0.341177	+	0.590936i
$850$	12.3900	+	7.15339i	0.424975	+	0.245359i
$851$	23.0090	−	13.2842i	0.788737	−	0.455377i
$852$	−14.5920	+	25.2741i	−0.499914	+	0.865877i
$853$	4.36144	+	2.51808i	0.149333	+	0.0862173i	0.572805	−	0.819692i	$-0.305855\pi$
$853$	4.36144	+	2.51808i	0.149333	+	0.0862173i	−0.423472	+	0.905909i	$0.639189\pi$
$854$	58.6329			2.00638
$855$	−0.605066	−	0.0813664i	−0.0206928	−	0.00278267i
$856$	−10.5908			−0.361985
$857$	−18.6540	+	32.3096i	−0.637207	+	1.10367i	0.348836	+	0.937184i	$0.386577\pi$
$857$	−18.6540	+	32.3096i	−0.637207	+	1.10367i	−0.986043	+	0.166491i	$0.946756\pi$
$858$	13.6259	−	22.5357i	0.465181	−	0.769357i
$859$	−8.20513	−	14.2117i	−0.279955	−	0.484897i	0.691418	−	0.722455i	$-0.256986\pi$
$859$	−8.20513	−	14.2117i	−0.279955	−	0.484897i	−0.971373	+	0.237558i	$0.923653\pi$
$860$	0.0284465	+	0.0164236i	0.000970017	+	0.000560040i
$861$	21.8445	+	37.8358i	0.744458	+	1.28944i
$862$	18.8634			0.642489
$863$			33.2130i			1.13058i	0.824891	+	0.565292i	$0.191237\pi$
$863$			33.2130i			1.13058i	−0.824891	+	0.565292i	$0.808763\pi$
$864$	3.35919	−	1.93943i	0.114282	−	0.0659808i
$865$	−0.470300	−	0.814583i	−0.0159907	−	0.0276967i
$866$			10.2692i			0.348960i
$867$		−	17.6878i		−	0.600710i
$868$	−13.5703	−	23.5045i	−0.460607	−	0.797794i
$869$	−12.8492	−	7.76906i	−0.435878	−	0.263547i
$870$	0.904512	−	0.522220i	0.0306658	−	0.0177049i
$871$	13.8272	+	7.98312i	0.468516	+	0.270498i
$872$	9.29222	−	16.0946i	0.314674	−	0.545032i
$873$			14.6531i			0.495932i
$874$	−24.2045	−	3.25491i	−0.818730	−	0.110099i
$875$		−	5.80233i		−	0.196154i
$876$	−7.79762	+	13.5059i	−0.263457	+	0.456321i
$877$	−18.7099	+	32.4064i	−0.631787	+	1.09429i	0.355399	+	0.934715i	$0.384345\pi$
$877$	−18.7099	+	32.4064i	−0.631787	+	1.09429i	−0.987186	+	0.159573i	$0.948988\pi$
$878$	−15.8473	−	27.4484i	−0.534822	−	0.926339i
$879$	5.13978	+	2.96745i	0.173361	+	0.100090i
$880$	0.376916	−	0.207566i	0.0127058	−	0.00699703i
$881$	−28.4239			−0.957627			−0.478813	−	0.877917i	$-0.658933\pi$
$881$	−28.4239			−0.957627			−0.478813	+	0.877917i	$0.658933\pi$
$882$	−14.1097			−0.475098
$883$	−13.6042	−	23.5631i	−0.457817	−	0.792963i	0.541028	−	0.841005i	$-0.318035\pi$
$883$	−13.6042	−	23.5631i	−0.457817	−	0.792963i	−0.998845	+	0.0480416i	$0.984702\pi$
$884$	9.77449	−	5.64331i	0.328752	−	0.189805i
$885$	1.56566			0.0526291
$886$	11.2425			0.377699
$887$	4.78008	+	8.27934i	0.160499	+	0.277993i	0.935048	−	0.354521i	$-0.115356\pi$
$887$	4.78008	+	8.27934i	0.160499	+	0.277993i	−0.774548	+	0.632515i	$0.782023\pi$
$888$	−4.78886	+	8.29456i	−0.160704	+	0.278347i
$889$	−27.2033	+	15.7058i	−0.912370	+	0.526757i
$890$	−1.87294	−	1.08134i	−0.0627812	−	0.0362467i
$891$	−31.4277	−	19.0023i	−1.05287	−	0.636600i
$892$			24.6102i			0.824011i
$893$	6.03764	+	14.6913i	0.202042	+	0.491625i
$894$	40.7175			1.36180
$895$	−1.82967	−	1.05636i	−0.0611590	−	0.0353102i
$896$	−3.87972	−	2.23996i	−0.129612	−	0.0748317i
$897$	−38.5280	+	22.2442i	−1.28641	+	0.742711i
$898$	−34.0270	−	19.6455i	−1.13550	−	0.655579i
$899$	−20.9119	+	12.0735i	−0.697450	+	0.402673i
$900$	5.37972			0.179324
$901$	−0.372831			−0.0124208
$902$	14.0273	−	7.72477i	0.467058	−	0.257207i
$903$	−1.98400	+	1.14546i	−0.0660234	+	0.0381186i
$904$			6.76377i			0.224959i
$905$		−	0.869727i		−	0.0289107i
$906$	−16.9953	+	9.81226i	−0.564632	+	0.325990i
$907$	0.627538	+	0.362309i	0.0208371	+	0.0120303i	0.510382	−	0.859948i	$-0.329504\pi$
$907$	0.627538	+	0.362309i	0.0208371	+	0.0120303i	−0.489545	+	0.871978i	$0.662837\pi$
$908$	−4.69277	−	8.12812i	−0.155735	−	0.269741i
$909$	0.347053	+	0.200371i	0.0115110	+	0.00664589i
$910$	−1.97875	−	1.14243i	−0.0655950	−	0.0378713i
$911$		−	33.6066i		−	1.11344i	−0.830702	−	0.556718i	$-0.812060\pi$
$911$		−	33.6066i		−	1.11344i	0.830702	−	0.556718i	$-0.187940\pi$
$912$	8.14323	−	3.34661i	0.269649	−	0.110817i
$913$	14.9490	+	0.302342i	0.494740	+	0.0100061i
$914$	−15.5299	−	8.96620i	−0.513684	−	0.296576i
$915$	−1.71480	+	2.97012i	−0.0566895	+	0.0981891i
$916$	12.2754	+	21.2617i	0.405592	+	0.702506i
$917$	17.7572	−	30.7564i	0.586394	−	1.01566i
$918$	−5.56815	−	9.64432i	−0.183776	−	0.318310i
$919$			35.4628i			1.16981i	0.811102	+	0.584904i	$0.198868\pi$
$919$			35.4628i			1.16981i	−0.811102	+	0.584904i	$0.801132\pi$
$920$	−0.726901			−0.0239652
$921$	20.8335	−	12.0282i	0.686486	−	0.396343i
$922$	−6.80571	+	3.92928i	−0.224134	+	0.129404i
$923$		−	56.8021i		−	1.86967i
$924$	−0.606835	+	30.0044i	−0.0199634	+	0.987072i
$925$	20.4640	−	11.8149i	0.672853	−	0.388472i
$926$	2.78257	−	4.81955i	0.0914408	−	0.158380i
$927$	−8.41866	+	4.86052i	−0.276505	+	0.159640i
$928$	−1.99288	+	3.45178i	−0.0654196	+	0.113310i
$929$	6.04455	−	10.4695i	0.198315	−	0.343492i	−0.749667	−	0.661815i	$-0.769786\pi$
$929$	6.04455	−	10.4695i	0.198315	−	0.343492i	0.947982	+	0.318323i	$0.103120\pi$
$930$	1.58753			0.0520572
$931$	56.4610	+	7.59260i	1.85043	+	0.248837i
$932$			27.4766i			0.900027i
$933$	−11.0535	−	6.38177i	−0.361877	−	0.208930i
$934$	5.83287	−	10.1028i	0.190857	−	0.330575i
$935$	−0.595925	−	1.08213i	−0.0194888	−	0.0353895i
$936$	2.12203	−	3.67546i	0.0693606	−	0.120136i
$937$	6.31515	−	3.64605i	0.206307	−	0.119111i	−0.393287	−	0.919416i	$-0.628662\pi$
$937$	6.31515	−	3.64605i	0.206307	−	0.119111i	0.599594	+	0.800304i	$0.295329\pi$
$938$	−18.1947			−0.594078
$939$		−	29.1607i		−	0.951625i
$940$	0.236377	+	0.409416i	0.00770975	+	0.0133537i
$941$	0.960244	+	1.66319i	0.0313031	+	0.0542185i	0.881253	−	0.472646i	$-0.156701\pi$
$941$	0.960244	+	1.66319i	0.0313031	+	0.0542185i	−0.849949	+	0.526864i	$0.823368\pi$
$942$			49.7578i			1.62120i
$943$	−27.0524			−0.880947
$944$	−5.17436	+	2.98742i	−0.168411	+	0.0972322i
$945$	−1.12722	+	1.95240i	−0.0366684	+	0.0635116i
$946$	0.405065	+	0.735553i	0.0131698	+	0.0239149i
$947$	−21.1607	+	36.6513i	−0.687629	+	1.19101i	0.284974	+	0.958535i	$0.408015\pi$
$947$	−21.1607	+	36.6513i	−0.687629	+	1.19101i	−0.972603	+	0.232473i	$0.925318\pi$
$948$	−7.91911	−	4.57210i	−0.257201	−	0.148495i
$949$		−	30.3537i		−	0.985323i
$950$	−21.5274	−	2.89489i	−0.698440	−	0.0939228i
$951$	−7.74897			−0.251278
$952$	−6.43097	+	11.1388i	−0.208429	+	0.361009i
$953$	14.4815	−	25.0828i	0.469103	−	0.812511i	−0.530273	−	0.847827i	$-0.677911\pi$
$953$	14.4815	−	25.0828i	0.469103	−	0.812511i	0.999376	+	0.0353162i	$0.0112438\pi$
$954$	−0.121411	+	0.0700970i	−0.00393084	+	0.00226947i
$955$	−0.934541	+	1.61867i	−0.0302410	+	0.0523790i
$956$	−13.3197	+	7.69016i	−0.430791	+	0.248717i
$957$	26.6948	+	0.539900i	0.862922	+	0.0174525i
$958$		−	31.6280i		−	1.02185i
$959$	−19.0719	+	11.0112i	−0.615864	+	0.355569i
$960$	0.226935	−	0.131021i	0.00732431	−	0.00422869i
$961$	−5.70293			−0.183966
$962$		−	18.6415i		−	0.601028i
$963$	5.71677	+	9.90174i	0.184220	+	0.319079i
$964$	−5.04394	+	8.73636i	−0.162454	+	0.281379i
$965$	0.142030	+	0.246003i	0.00457211	+	0.00791913i
$966$	25.3489	−	43.9055i	0.815587	−	1.41264i
$967$	50.6423	+	29.2384i	1.62855	+	0.940242i	0.984527	+	0.175234i	$0.0560682\pi$
$967$	50.6423	+	29.2384i	1.62855	+	0.940242i	0.644021	+	0.765008i	$0.277265\pi$
$968$	10.9910	+	0.444765i	0.353264	+	0.0142953i
$969$	−9.60818	−	23.3794i	−0.308659	−	0.751054i
$970$		−	1.76092i		−	0.0565397i
$971$	−2.18314	−	1.26044i	−0.0700603	−	0.0404493i	0.464561	−	0.885541i	$-0.346212\pi$
$971$	−2.18314	−	1.26044i	−0.0700603	−	0.0404493i	−0.534621	+	0.845092i	$0.679546\pi$
$972$	−9.29168	−	5.36456i	−0.298031	−	0.172068i
$973$	29.2281	+	50.6245i	0.937008	+	1.62295i
$974$	−16.1380	−	9.31725i	−0.517094	−	0.298544i
$975$	−34.2666	+	19.7838i	−1.09741	+	0.633589i
$976$		−	13.0880i		−	0.418935i
$977$			36.1199i			1.15558i	0.816186	+	0.577789i	$0.196084\pi$
$977$			36.1199i			1.15558i	−0.816186	+	0.577789i	$0.803916\pi$
$978$	15.3694	−	8.87354i	0.491460	−	0.283745i
$979$	−26.6699	−	48.4295i	−0.852372	−	1.54781i
$980$	1.69562			0.0541645
$981$	−20.0633			−0.640573
$982$	13.4139	−	7.74450i	0.428054	−	0.247137i
$983$	−12.7193	−	7.34349i	−0.405682	−	0.234221i	0.283250	−	0.959046i	$-0.408587\pi$
$983$	−12.7193	−	7.34349i	−0.405682	−	0.234221i	−0.688933	+	0.724825i	$0.741921\pi$
$984$	8.44564	−	4.87609i	0.269237	−	0.155444i
$985$	−2.59954	−	1.50084i	−0.0828281	−	0.0478208i
$986$	9.91013	+	5.72162i	0.315603	+	0.182213i
$987$	−32.9722			−1.04952
$988$	−10.4693	+	13.5657i	−0.333072	+	0.431584i
$989$		−	1.41855i		−	0.0451073i
$990$	−0.397516	−	0.240352i	−0.0126339	−	0.00763890i
$991$	0.982105	+	0.567019i	0.0311976	+	0.0180119i	0.515518	−	0.856879i	$-0.327600\pi$
$991$	0.982105	+	0.567019i	0.0311976	+	0.0180119i	−0.484320	+	0.874891i	$0.660933\pi$
$992$	−5.24664	+	3.02915i	−0.166581	+	0.0961755i
$993$	−0.391140	+	0.677475i	−0.0124125	+	0.0214990i
$994$	32.3651	+	56.0580i	1.02656	+	1.77805i
$995$	−0.107103			−0.00339540
$996$	9.10569			0.288525
$997$	43.6376	−	25.1942i	1.38202	−	0.797907i	0.389618	−	0.920977i	$-0.372607\pi$
$997$	43.6376	−	25.1942i	1.38202	−	0.797907i	0.992398	+	0.123069i	$0.0392738\pi$
$998$	7.05643	+	12.2221i	0.223368	+	0.386884i
$999$	−18.3933			−0.581938

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.h.b.65.8	yes	20
11.10	odd	2		418.2.h.a.65.8	✓	20
19.12	odd	6		418.2.h.a.373.8	yes	20
209.164	even	6	inner	418.2.h.b.373.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.h.a.65.8	✓	20	11.10	odd	2
418.2.h.a.373.8	yes	20	19.12	odd	6
418.2.h.b.65.8	yes	20	1.1	even	1	trivial
418.2.h.b.373.8	yes	20	209.164	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.74919 + 1.00990i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.0648685 - 0.112356i) q^{5} +(1.74919 - 1.00990i) q^{6} -4.47991i q^{7} -1.00000 q^{8} +(0.539789 + 0.934941i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.74919 + 1.00990i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.0648685 - 0.112356i) q^{5} +(1.74919 - 1.00990i) q^{6} -4.47991i q^{7} -1.00000 q^{8} +(0.539789 + 0.934941i) q^{9} +(-0.0648685 - 0.112356i) q^{10} +(0.0670646 - 3.31595i) q^{11} -2.01980i q^{12} +(1.96561 + 3.40453i) q^{13} +(-3.87972 - 2.23996i) q^{14} +(0.226935 - 0.131021i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.48638 + 1.43551i) q^{17} +1.07958 q^{18} +(-4.32001 - 0.580935i) q^{19} -0.129737 q^{20} +(4.52426 - 7.83624i) q^{21} +(-2.83816 - 1.71605i) q^{22} +(2.80144 + 4.85224i) q^{23} +(-1.74919 - 1.00990i) q^{24} +(2.49158 + 4.31555i) q^{25} +3.93122 q^{26} -3.87886i q^{27} +(-3.87972 + 2.23996i) q^{28} +(1.99288 + 3.45178i) q^{29} -0.262042i q^{30} +6.05829i q^{31} +(0.500000 + 0.866025i) q^{32} +(3.46608 - 5.73251i) q^{33} +(2.48638 - 1.43551i) q^{34} +(-0.503343 - 0.290605i) q^{35} +(0.539789 - 0.934941i) q^{36} -4.74193i q^{37} +(-2.66311 + 3.45077i) q^{38} +7.94026i q^{39} +(-0.0648685 + 0.112356i) q^{40} +(-2.41415 + 4.18143i) q^{41} +(-4.52426 - 7.83624i) q^{42} +(-0.219263 - 0.126591i) q^{43} +(-2.90523 + 1.59989i) q^{44} +0.140061 q^{45} +5.60288 q^{46} +(-1.82197 - 3.15574i) q^{47} +(-1.74919 + 1.00990i) q^{48} -13.0696 q^{49} +4.98317 q^{50} +(2.89944 + 5.02198i) q^{51} +(1.96561 - 3.40453i) q^{52} +(-0.112462 + 0.0649300i) q^{53} +(-3.35919 - 1.93943i) q^{54} +(-0.368215 - 0.222636i) q^{55} +4.47991i q^{56} +(-6.96986 - 5.37894i) q^{57} +3.98577 q^{58} +(5.17436 + 2.98742i) q^{59} +(-0.226935 - 0.131021i) q^{60} +(-11.3345 + 6.54398i) q^{61} +(5.24664 + 3.02915i) q^{62} +(4.18846 - 2.41821i) q^{63} +1.00000 q^{64} +0.510025 q^{65} +(-3.23146 - 5.86797i) q^{66} +(3.51727 - 2.03070i) q^{67} -2.87102i q^{68} +11.3167i q^{69} +(-0.503343 + 0.290605i) q^{70} +(-12.5132 - 7.22450i) q^{71} +(-0.539789 - 0.934941i) q^{72} +(-6.68675 - 3.86060i) q^{73} +(-4.10663 - 2.37096i) q^{74} +10.0650i q^{75} +(1.65690 + 4.03171i) q^{76} +(-14.8552 - 0.300444i) q^{77} +(6.87647 + 3.97013i) q^{78} +(2.26364 - 3.92074i) q^{79} +(0.0648685 + 0.112356i) q^{80} +(5.53662 - 9.58971i) q^{81} +(2.41415 + 4.18143i) q^{82} +4.50822i q^{83} -9.04852 q^{84} +(0.322575 - 0.186239i) q^{85} +(-0.219263 + 0.126591i) q^{86} +8.05044i q^{87} +(-0.0670646 + 3.31595i) q^{88} +(14.4364 - 8.33488i) q^{89} +(0.0700306 - 0.121297i) q^{90} +(15.2520 - 8.80576i) q^{91} +(2.80144 - 4.85224i) q^{92} +(-6.11826 + 10.5971i) q^{93} -3.64393 q^{94} +(-0.345504 + 0.447693i) q^{95} +2.01980i q^{96} +(11.7545 + 6.78649i) q^{97} +(-6.53482 + 11.3186i) q^{98} +(3.13642 - 1.72721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

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