LMFDB - Embedded newform 63.2.g.b.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(4,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("63.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.g (of order $3$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.4
Root			$0.920620 - 1.59456i$ of defining polynomial
Character	$\chi$	$=$	63.4
Dual form			63.2.g.b.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.920620 - 1.59456i) q^{2} +(-1.58800 - 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} +1.33475 q^{5} +(-2.56469 + 1.89549i) q^{6} +(-2.54347 + 0.728536i) q^{7} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +(1.22880 - 2.12835i) q^{10} +1.51302 q^{11} +(0.271199 + 2.39252i) q^{12} +(-2.58800 + 4.48254i) q^{13} +(-1.17987 + 4.72642i) q^{14} +(-2.11958 - 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} +(0.774463 - 1.34141i) q^{17} +(5.38358 - 1.23637i) q^{18} +(-1.25211 - 2.16872i) q^{19} +(-0.927765 - 1.60694i) q^{20} +(4.54285 + 0.602068i) q^{21} +(1.39291 - 2.41260i) q^{22} -7.36079 q^{23} +(-1.78308 - 0.776526i) q^{24} -3.21843 q^{25} +(4.76513 + 8.25344i) q^{26} +(-1.72605 - 4.90110i) q^{27} +(2.64502 + 2.55574i) q^{28} +(-0.0309713 - 0.0536439i) q^{29} +(-3.42323 + 2.53001i) q^{30} +(1.92388 + 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(-2.40267 - 1.04635i) q^{33} +(-1.42597 - 2.46986i) q^{34} +(-3.39490 + 0.972416i) q^{35} +(1.22392 - 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} -4.61087 q^{38} +(7.20971 - 5.32849i) q^{39} +1.49873 q^{40} +(4.51188 - 7.81481i) q^{41} +(5.14228 - 6.68958i) q^{42} +(5.09988 + 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(2.72753 + 2.93167i) q^{45} +(-6.77649 + 11.7372i) q^{46} +(4.75925 - 8.24327i) q^{47} +(-6.75252 + 4.99060i) q^{48} +(5.93847 - 3.70602i) q^{49} +(-2.96296 + 5.13199i) q^{50} +(-2.15752 + 1.59456i) q^{51} +7.19550 q^{52} +(0.755374 - 1.30835i) q^{53} +(-9.40414 - 1.75975i) q^{54} +2.01950 q^{55} +(-2.85593 + 0.818036i) q^{56} +(0.488532 + 4.30983i) q^{57} -0.114051 q^{58} +(4.22166 + 7.31212i) q^{59} +(0.361984 + 3.19342i) q^{60} +(-1.61958 + 2.80520i) q^{61} +7.08467 q^{62} +(-6.79767 - 4.09777i) q^{63} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(-3.88042 + 2.86790i) q^{66} +(-3.46670 - 6.00449i) q^{67} -2.15327 q^{68} +(11.6889 + 5.09048i) q^{69} +(-1.57484 + 6.30861i) q^{70} -12.3304 q^{71} +(2.29451 + 2.46624i) q^{72} +(-1.37936 + 2.38912i) q^{73} -1.03702 q^{74} +(5.11086 + 2.22576i) q^{75} +(-1.74064 + 3.01488i) q^{76} +(-3.84831 + 1.10229i) q^{77} +(-1.85920 - 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} +(3.23529 - 5.60368i) q^{80} +(-0.648467 + 8.97661i) q^{81} +(-8.30746 - 14.3889i) q^{82} +(2.80111 + 4.85167i) q^{83} +(-2.43282 - 5.88772i) q^{84} +(1.03372 - 1.79045i) q^{85} +18.7802 q^{86} +(0.0120840 + 0.106605i) q^{87} +1.69889 q^{88} +(0.703287 + 1.21813i) q^{89} +(7.18575 - 1.65025i) q^{90} +(3.31680 - 13.2867i) q^{91} +(5.11636 + 8.86180i) q^{92} +(-0.750637 - 6.62212i) q^{93} +(-8.76293 - 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(1.30320 + 11.4968i) q^{96} +(-6.09713 - 10.5605i) q^{97} +(-0.442393 - 12.8811i) q^{98} +(3.09180 + 3.32321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} - 2 q^{6} - q^{7} - 6 q^{8} - 4 q^{9} - 7 q^{10} - 8 q^{11} + 22 q^{12} - 8 q^{13} + 16 q^{14} - 19 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + q^{19} + 5 q^{20}+ \cdots + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 - 2 * q^6 - q^7 - 6 * q^8 - 4 * q^9 - 7 * q^10 - 8 * q^11 + 22 * q^12 - 8 * q^13 + 16 * q^14 - 19 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 + q^19 + 5 * q^20 - 2 * q^21 - q^22 - 6 * q^23 + 3 * q^24 + 2 * q^25 + 11 * q^26 - 7 * q^27 - 2 * q^28 + 7 * q^29 - 26 * q^30 - 3 * q^31 - 2 * q^32 - q^33 + 3 * q^34 + 5 * q^35 + 34 * q^36 - 40 * q^38 + 20 * q^39 + 6 * q^40 + 5 * q^41 + 32 * q^42 - 7 * q^43 - 10 * q^44 - q^45 + 3 * q^46 + 27 * q^47 - 5 * q^48 + 25 * q^49 + 19 * q^50 + 24 * q^51 + 20 * q^52 - 21 * q^53 - 53 * q^54 + 4 * q^55 - 45 * q^56 - 4 * q^57 + 20 * q^58 + 30 * q^59 - 41 * q^60 - 14 * q^61 - 12 * q^62 - 35 * q^63 - 50 * q^64 - 11 * q^65 - 41 * q^66 - 2 * q^67 - 54 * q^68 + 15 * q^69 - 29 * q^70 - 6 * q^71 + 48 * q^72 + 15 * q^73 + 72 * q^74 + 31 * q^75 + 5 * q^76 - 31 * q^77 - 20 * q^78 - 4 * q^79 + 20 * q^80 + 8 * q^81 - 5 * q^82 + 9 * q^83 + 2 * q^84 - 6 * q^85 + 16 * q^86 + 32 * q^87 + 36 * q^88 + 28 * q^89 + 28 * q^90 - 4 * q^91 + 27 * q^92 - 12 * q^93 - 3 * q^94 - 14 * q^95 - q^96 - 12 * q^97 + 59 * q^98 + 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.920620	−	1.59456i	0.650977	−	1.12753i	−0.331909	−	0.943311i	$-0.607693\pi$
$2$	0.920620	−	1.59456i	0.650977	−	1.12753i	0.982886	−	0.184214i	$-0.0589739\pi$
$3$	−1.58800	−	0.691567i	−0.916831	−	0.399277i
$3$	−1.58800	−	0.691567i	−0.916831	−	0.399277i
$4$	−0.695084	−	1.20392i	−0.347542	−	0.601960i
$5$	1.33475			0.596920			0.298460	−	0.954422i	$-0.403527\pi$
$5$	1.33475			0.596920			0.298460	+	0.954422i	$0.403527\pi$
$6$	−2.56469	+	1.89549i	−1.04703	+	0.773830i
$7$	−2.54347	+	0.728536i	−0.961341	+	0.275361i
$7$	−2.54347	+	0.728536i	−0.961341	+	0.275361i
$8$	1.12285			0.396987
$9$	2.04347	+	2.19641i	0.681156	+	0.732138i
$10$	1.22880	−	2.12835i	0.388581	−	0.673042i
$11$	1.51302			0.456192			0.228096	−	0.973639i	$-0.426750\pi$
$11$	1.51302			0.456192			0.228096	+	0.973639i	$0.426750\pi$
$12$	0.271199	+	2.39252i	0.0782884	+	0.690661i
$13$	−2.58800	+	4.48254i	−0.717781	+	1.24323i	0.244096	+	0.969751i	$0.421509\pi$
$13$	−2.58800	+	4.48254i	−0.717781	+	1.24323i	−0.961877	+	0.273482i	$0.911824\pi$
$14$	−1.17987	+	4.72642i	−0.315335	+	1.26319i
$15$	−2.11958	−	0.923072i	−0.547274	−	0.238336i
$16$	2.42388	−	4.19829i	0.605971	−	1.04957i
$17$	0.774463	−	1.34141i	0.187835	−	0.325340i	−0.756693	−	0.653770i	$-0.773186\pi$
$17$	0.774463	−	1.34141i	0.187835	−	0.325340i	0.944528	+	0.328430i	$0.106520\pi$
$18$	5.38358	−	1.23637i	1.26892	−	0.291416i
$19$	−1.25211	−	2.16872i	−0.287254	−	0.497538i	0.685900	−	0.727696i	$-0.259409\pi$
$19$	−1.25211	−	2.16872i	−0.287254	−	0.497538i	−0.973153	+	0.230158i	$0.926076\pi$
$20$	−0.927765	−	1.60694i	−0.207455	−	0.359322i
$21$	4.54285	+	0.602068i	0.991332	+	0.131382i
$22$	1.39291	−	2.41260i	0.296970	−	0.514367i
$23$	−7.36079			−1.53483			−0.767415	−	0.641151i	$-0.778457\pi$
$23$	−7.36079			−1.53483			−0.767415	+	0.641151i	$0.778457\pi$
$24$	−1.78308	−	0.776526i	−0.363970	−	0.158508i
$25$	−3.21843			−0.643687
$26$	4.76513	+	8.25344i	0.934518	+	1.61863i
$27$	−1.72605	−	4.90110i	−0.332179	−	0.943216i
$28$	2.64502	+	2.55574i	0.499862	+	0.482990i
$29$	−0.0309713	−	0.0536439i	−0.00575123	−	0.00996143i	0.863135	−	0.504972i	$-0.168497\pi$
$29$	−0.0309713	−	0.0536439i	−0.00575123	−	0.00996143i	−0.868887	+	0.495011i	$0.835164\pi$
$30$	−3.42323	+	2.53001i	−0.624993	+	0.461914i
$31$	1.92388	+	3.33227i	0.345540	+	0.598493i	0.985452	−	0.169956i	$-0.0543625\pi$
$31$	1.92388	+	3.33227i	0.345540	+	0.598493i	−0.639912	+	0.768448i	$0.721029\pi$
$32$	−3.34011	−	5.78523i	−0.590453	−	1.02269i
$33$	−2.40267	−	1.04635i	−0.418250	−	0.182147i
$34$	−1.42597	−	2.46986i	−0.244552	−	0.423577i
$35$	−3.39490	+	0.972416i	−0.573844	+	0.164368i
$36$	1.22392	−	3.98687i	0.203987	−	0.664478i
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	0.841949	−	0.539557i	$-0.181408\pi$
$37$	−0.281608	−	0.487760i	−0.0462961	−	0.0801872i	−0.888245	+	0.459370i	$0.848075\pi$
$38$	−4.61087			−0.747982
$39$	7.20971	−	5.32849i	1.15448	−	0.853241i
$40$	1.49873			0.236969
$41$	4.51188	−	7.81481i	0.704638	−	1.22047i	−0.262185	−	0.965018i	$-0.584443\pi$
$41$	4.51188	−	7.81481i	0.704638	−	1.22047i	0.966822	−	0.255450i	$-0.0822237\pi$
$42$	5.14228	−	6.68958i	0.793471	−	1.03222i
$43$	5.09988	+	8.83325i	0.777724	+	1.34706i	0.933251	+	0.359226i	$0.116959\pi$
$43$	5.09988	+	8.83325i	0.777724	+	1.34706i	−0.155526	+	0.987832i	$0.549707\pi$
$44$	−1.05167	−	1.82155i	−0.158546	−	0.274609i
$45$	2.72753	+	2.93167i	0.406596	+	0.437028i
$46$	−6.77649	+	11.7372i	−0.999139	+	1.73056i
$47$	4.75925	−	8.24327i	0.694209	−	1.20240i	−0.276238	−	0.961089i	$-0.589088\pi$
$47$	4.75925	−	8.24327i	0.694209	−	1.20240i	0.970447	−	0.241315i	$-0.0775788\pi$
$48$	−6.75252	+	4.99060i	−0.974643	+	0.720330i
$49$	5.93847	−	3.70602i	0.848353	−	0.529431i
$50$	−2.96296	+	5.13199i	−0.419025	+	0.725773i
$51$	−2.15752	+	1.59456i	−0.302113	+	0.223283i
$52$	7.19550			0.997836
$53$	0.755374	−	1.30835i	0.103759	−	0.179715i	−0.809472	−	0.587159i	$-0.800246\pi$
$53$	0.755374	−	1.30835i	0.103759	−	0.179715i	0.913230	+	0.407444i	$0.133580\pi$
$54$	−9.40414	−	1.75975i	−1.27974	−	0.239471i
$55$	2.01950			0.272310
$56$	−2.85593	+	0.818036i	−0.381640	+	0.109315i
$57$	0.488532	+	4.30983i	0.0647077	+	0.570851i
$58$	−0.114051			−0.0149757
$59$	4.22166	+	7.31212i	0.549613	+	0.951957i	0.998301	+	0.0582689i	$0.0185581\pi$
$59$	4.22166	+	7.31212i	0.549613	+	0.951957i	−0.448688	+	0.893688i	$0.648109\pi$
$60$	0.361984	+	3.19342i	0.0467319	+	0.412269i
$61$	−1.61958	+	2.80520i	−0.207367	+	0.359169i	−0.950884	−	0.309547i	$-0.899823\pi$
$61$	−1.61958	+	2.80520i	−0.207367	+	0.359169i	0.743518	+	0.668716i	$0.233156\pi$
$62$	7.08467			0.899754
$63$	−6.79767	−	4.09777i	−0.856426	−	0.516271i
$64$	−2.60434			−0.325543
$65$	−3.45434	+	5.98309i	−0.428458	+	0.742111i
$66$	−3.88042	+	2.86790i	−0.477646	+	0.353014i
$67$	−3.46670	−	6.00449i	−0.423524	−	0.733566i	0.572757	−	0.819725i	$-0.305874\pi$
$67$	−3.46670	−	6.00449i	−0.423524	−	0.733566i	−0.996281	+	0.0861595i	$0.972541\pi$
$68$	−2.15327			−0.261122
$69$	11.6889	+	5.09048i	1.40718	+	0.612822i
$70$	−1.57484	+	6.30861i	−0.188230	+	0.754023i
$71$	−12.3304			−1.46335			−0.731673	−	0.681656i	$-0.761260\pi$
$71$	−12.3304			−1.46335			−0.731673	+	0.681656i	$0.761260\pi$
$72$	2.29451	+	2.46624i	0.270410	+	0.290649i
$73$	−1.37936	+	2.38912i	−0.161442	+	0.279625i	−0.935386	−	0.353629i	$-0.884948\pi$
$73$	−1.37936	+	2.38912i	−0.161442	+	0.279625i	0.773944	+	0.633254i	$0.218281\pi$
$74$	−1.03702			−0.120551
$75$	5.11086	+	2.22576i	0.590152	+	0.257009i
$76$	−1.74064	+	3.01488i	−0.199665	+	0.345830i
$77$	−3.84831	+	1.10229i	−0.438556	+	0.125617i
$78$	−1.85920	−	16.4018i	−0.210512	−	1.85714i
$79$	2.95969	−	5.12633i	0.332991	−	0.576758i	−0.650106	−	0.759844i	$-0.725275\pi$
$79$	2.95969	−	5.12633i	0.332991	−	0.576758i	0.983097	+	0.183086i	$0.0586087\pi$
$80$	3.23529	−	5.60368i	0.361716	−	0.626511i
$81$	−0.648467	+	8.97661i	−0.0720519	+	0.997401i
$82$	−8.30746	−	14.3889i	−0.917406	−	1.58899i
$83$	2.80111	+	4.85167i	0.307462	+	0.532540i	0.977806	−	0.209510i	$-0.0671870\pi$
$83$	2.80111	+	4.85167i	0.307462	+	0.532540i	−0.670344	+	0.742050i	$0.733854\pi$
$84$	−2.43282	−	5.88772i	−0.265443	−	0.642403i
$85$	1.03372	−	1.79045i	0.112122	−	0.194202i
$86$	18.7802			2.02512
$87$	0.0120840	+	0.106605i	0.00129554	+	0.0114293i
$88$	1.69889			0.181102
$89$	0.703287	+	1.21813i	0.0745483	+	0.129121i	0.900890	−	0.434048i	$-0.142915\pi$
$89$	0.703287	+	1.21813i	0.0745483	+	0.129121i	−0.826341	+	0.563169i	$0.809582\pi$
$90$	7.18575	−	1.65025i	0.757444	−	0.173952i
$91$	3.31680	−	13.2867i	0.347695	−	1.39282i
$92$	5.11636	+	8.86180i	0.533418	+	0.923906i
$93$	−0.750637	−	6.62212i	−0.0778374	−	0.686682i
$94$	−8.76293	−	15.1778i	−0.903827	−	1.56548i
$95$	−1.67126	−	2.89470i	−0.171467	−	0.296990i
$96$	1.30320	+	11.4968i	0.133007	+	1.17339i
$97$	−6.09713	−	10.5605i	−0.619070	−	1.07226i	−0.989656	−	0.143462i	$-0.954176\pi$
$97$	−6.09713	−	10.5605i	−0.619070	−	1.07226i	0.370586	−	0.928798i	$-0.379157\pi$
$98$	−0.442393	−	12.8811i	−0.0446885	−	1.30119i
$99$	3.09180	+	3.32321i	0.310738	+	0.333995i
$100$	2.23708	+	3.87474i	0.223708	+	0.387474i
$101$	1.11867			0.111312			0.0556560	−	0.998450i	$-0.482275\pi$
$101$	1.11867			0.111312			0.0556560	+	0.998450i	$0.482275\pi$
$102$	0.556368	+	4.90828i	0.0550886	+	0.485993i
$103$	1.93045			0.190213			0.0951063	−	0.995467i	$-0.469681\pi$
$103$	1.93045			0.190213			0.0951063	+	0.995467i	$0.469681\pi$
$104$	−2.90593	+	5.03322i	−0.284950	+	0.493548i
$105$	6.06359	+	0.803612i	0.591746	+	0.0784245i
$106$	−1.39082	−	2.40898i	−0.135089	−	0.233981i
$107$	2.88969	+	5.00509i	0.279357	+	0.483860i	0.971225	−	0.238163i	$-0.0765454\pi$
$107$	2.88969	+	5.00509i	0.279357	+	0.483860i	−0.691868	+	0.722024i	$0.743212\pi$
$108$	−4.70077	+	5.48470i	−0.452332	+	0.527766i
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	−0.993066	−	0.117557i	$-0.962494\pi$
$109$	−4.12106	+	7.13788i	−0.394726	+	0.683685i	0.598340	+	0.801242i	$0.295827\pi$
$110$	1.85920	−	3.22022i	0.177267	−	0.307036i
$111$	0.109874	+	0.969312i	0.0104288	+	0.0920030i
$112$	−3.10647	+	12.4441i	−0.293534	+	1.17586i
$113$	7.25105	−	12.5592i	0.682121	−	1.18147i	−0.292211	−	0.956354i	$-0.594391\pi$
$113$	7.25105	−	12.5592i	0.682121	−	1.18147i	0.974332	−	0.225115i	$-0.0722758\pi$
$114$	7.32205	+	3.18873i	0.685773	+	0.298652i
$115$	−9.82483			−0.916170
$116$	−0.0430553	+	0.0745740i	−0.00399759	+	0.00692403i
$117$	−15.1340	+	3.47562i	−1.39914	+	0.321322i
$118$	15.5462			1.43114
$119$	−0.992558	+	3.97606i	−0.0909877	+	0.364485i
$120$	−2.37997	−	1.03647i	−0.217261	−	0.0946164i
$121$	−8.71078			−0.791889
$122$	2.98204	+	5.16505i	0.269982	+	0.467622i
$123$	−12.5693	+	9.28962i	−1.13334	+	0.837617i
$124$	2.67452	−	4.63241i	0.240179	−	0.416002i
$125$	−10.9696			−0.981149
$126$	−12.7922	+	7.06681i	−1.13962	+	0.629561i
$127$	8.50004			0.754257			0.377128	−	0.926161i	$-0.376912\pi$
$127$	8.50004			0.754257			0.377128	+	0.926161i	$0.376912\pi$
$128$	4.28260	−	7.41769i	0.378532	−	0.655637i
$129$	−1.98981	−	17.5541i	−0.175193	−	1.54555i
$130$	6.36027	+	11.0163i	0.557832	+	0.966194i
$131$	−2.01346			−0.175917			−0.0879585	−	0.996124i	$-0.528034\pi$
$131$	−2.01346			−0.175917			−0.0879585	+	0.996124i	$0.528034\pi$
$132$	0.410328	+	3.61992i	0.0357145	+	0.315074i
$133$	4.76469	+	4.60386i	0.413151	+	0.399205i
$134$	−12.7660			−1.10282
$135$	−2.30386	−	6.54175i	−0.198285	−	0.563024i
$136$	0.869605	−	1.50620i	0.0745680	−	0.129156i
$137$	2.21740			0.189445			0.0947225	−	0.995504i	$-0.469804\pi$
$137$	2.21740			0.189445			0.0947225	+	0.995504i	$0.469804\pi$
$138$	18.8781	−	13.9523i	1.60701	−	1.18770i
$139$	0.377669	−	0.654143i	0.0320335	−	0.0554836i	−0.849564	−	0.527485i	$-0.823135\pi$
$139$	0.377669	−	0.654143i	0.0320335	−	0.0554836i	0.881598	+	0.472002i	$0.156468\pi$
$140$	3.53045	+	3.41128i	0.298378	+	0.288306i
$141$	−13.2585	+	9.79894i	−1.11656	+	0.825220i
$142$	−11.3516	+	19.6615i	−0.952604	+	1.64996i
$143$	−3.91568	+	6.78216i	−0.327446	+	0.567153i
$144$	14.1743	−	3.25523i	1.18119	−	0.271269i
$145$	−0.0413391	−	0.0716014i	−0.00343303	−	0.00594618i
$146$	2.53973	+	4.39894i	0.210189	+	0.364059i
$147$	−11.9932	+	1.77829i	−0.989185	+	0.146671i
$148$	−0.391482	+	0.678068i	−0.0321797	+	0.0557368i
$149$	6.58499			0.539463			0.269732	−	0.962936i	$-0.413065\pi$
$149$	6.58499			0.539463			0.269732	+	0.962936i	$0.413065\pi$
$150$	8.25428	−	6.10050i	0.673959	−	0.498104i
$151$	12.6671			1.03083			0.515417	−	0.856939i	$-0.327637\pi$
$151$	12.6671			1.03083			0.515417	+	0.856939i	$0.327637\pi$
$152$	−1.40593	−	2.43514i	−0.114036	−	0.197516i
$153$	4.52888	−	1.04009i	0.366138	−	0.0840861i
$154$	−1.78517	+	7.15115i	−0.143853	+	0.576256i
$155$	2.56791	+	4.44775i	0.206260	+	0.357252i
$156$	−11.4264	−	4.97617i	−0.914846	−	0.398413i
$157$	8.65372	+	14.9887i	0.690642	+	1.19623i	0.971628	+	0.236515i	$0.0760052\pi$
$157$	8.65372	+	14.9887i	0.690642	+	1.19623i	−0.280986	+	0.959712i	$0.590662\pi$
$158$	−5.44950	−	9.43882i	−0.433539	−	0.750912i
$159$	−2.10434	+	1.55526i	−0.166885	+	0.123340i
$160$	−4.45822	−	7.72186i	−0.352453	−	0.610467i
$161$	18.7219	−	5.36260i	1.47549	−	0.422632i
$162$	13.7168	+	9.29807i	1.07769	+	0.730525i
$163$	6.10963	+	10.5822i	0.478543	+	0.828861i	0.999697	−	0.0246014i	$-0.00783167\pi$
$163$	6.10963	+	10.5822i	0.478543	+	0.828861i	−0.521154	+	0.853463i	$0.674498\pi$
$164$	−12.5445			−0.979564
$165$	−3.20697	−	1.39662i	−0.249662	−	0.108727i
$166$	10.3150			0.800602
$167$	1.76248	−	3.05270i	0.136385	−	0.236225i	−0.789741	−	0.613440i	$-0.789785\pi$
$167$	1.76248	−	3.05270i	0.136385	−	0.236225i	0.926126	+	0.377215i	$0.123118\pi$
$168$	5.10094	+	0.676031i	0.393546	+	0.0521569i
$169$	−6.89546	−	11.9433i	−0.530420	−	0.918714i
$170$	−1.90332	−	3.29665i	−0.145978	−	0.252842i
$171$	2.20475	−	7.18186i	0.168602	−	0.549210i
$172$	7.08968	−	12.2797i	0.540583	−	0.936318i
$173$	−5.07046	+	8.78229i	−0.385500	+	0.667705i	−0.991838	−	0.127502i	$-0.959304\pi$
$173$	−5.07046	+	8.78229i	−0.385500	+	0.667705i	0.606339	+	0.795206i	$0.292638\pi$
$174$	0.181113	+	0.0788742i	0.0137302	+	0.00597944i
$175$	8.18599	−	2.34474i	0.618802	−	0.177246i
$176$	3.66738	−	6.35208i	0.276439	−	0.478806i
$177$	−1.64715	−	14.5312i	−0.123808	−	1.09223i
$178$	2.58984			0.194117
$179$	0.850579	−	1.47325i	0.0635752	−	0.110116i	−0.832486	−	0.554046i	$-0.813083\pi$
$179$	0.850579	−	1.47325i	0.0635752	−	0.110116i	0.896061	+	0.443931i	$0.146416\pi$
$180$	1.63364	−	5.32148i	0.121764	−	0.396640i
$181$	−16.9941			−1.26316			−0.631581	−	0.775310i	$-0.717594\pi$
$181$	−16.9941			−1.26316			−0.631581	+	0.775310i	$0.717594\pi$
$182$	−18.1329	−	17.5208i	−1.34410	−	1.29873i
$183$	4.51188	−	3.33460i	0.333528	−	0.246501i
$184$	−8.26505			−0.609308
$185$	−0.375877	−	0.651039i	−0.0276351	−	0.0478653i
$186$	−11.2504	−	4.89953i	−0.824922	−	0.359251i
$187$	1.17178	−	2.02957i	0.0856887	−	0.148417i
$188$	−13.2323			−0.965066
$189$	7.96079	+	11.2083i	0.579062	+	0.815283i
$190$	−6.15437			−0.446485
$191$	−11.3470	+	19.6535i	−0.821038	+	1.42208i	0.0838717	+	0.996477i	$0.473271\pi$
$191$	−11.3470	+	19.6535i	−0.821038	+	1.42208i	−0.904910	+	0.425603i	$0.860062\pi$
$192$	4.13568	+	1.80108i	0.298467	+	0.129982i
$193$	−3.09349	−	5.35808i	−0.222674	−	0.385683i	0.732945	−	0.680288i	$-0.238145\pi$
$193$	−3.09349	−	5.35808i	−0.222674	−	0.385683i	−0.955619	+	0.294605i	$0.904812\pi$
$194$	−22.4526			−1.61200
$195$	9.62319	−	7.11222i	0.689131	−	0.509317i
$196$	−8.58948	−	4.57345i	−0.613534	−	0.326675i
$197$	9.77010			0.696091			0.348045	−	0.937478i	$-0.386846\pi$
$197$	9.77010			0.696091			0.348045	+	0.937478i	$0.386846\pi$
$198$	8.14544	−	1.87065i	0.578871	−	0.132942i
$199$	−4.33973	+	7.51664i	−0.307636	+	0.532840i	−0.977845	−	0.209332i	$-0.932871\pi$
$199$	−4.33973	+	7.51664i	−0.307636	+	0.532840i	0.670209	+	0.742172i	$0.266204\pi$
$200$	−3.61381			−0.255535
$201$	1.35259	+	11.9326i	0.0954044	+	0.841659i
$202$	1.02987	−	1.78379i	0.0724615	−	0.125507i
$203$	0.117856	+	0.113878i	0.00827188	+	0.00799267i
$204$	3.41938	+	1.48913i	0.239405	+	0.104260i
$205$	6.02225	−	10.4308i	0.420612	−	0.728522i
$206$	1.77721	−	3.07822i	0.123824	−	0.214470i
$207$	−15.0415	−	16.1673i	−1.04546	−	1.12371i
$208$	12.5460	+	21.7303i	0.869909	+	1.50673i
$209$	−1.89446	−	3.28130i	−0.131043	−	0.226973i
$210$	6.86367	−	8.92894i	0.473638	−	0.616156i
$211$	−2.84219	+	4.92283i	−0.195665	+	0.338901i	−0.947118	−	0.320885i	$-0.896020\pi$
$211$	−2.84219	+	4.92283i	−0.195665	+	0.338901i	0.751453	+	0.659786i	$0.229353\pi$
$212$	−2.10019			−0.144242
$213$	19.5806	+	8.52728i	1.34164	+	0.584280i
$214$	10.6412			0.727420
$215$	6.80708	+	11.7902i	0.464239	+	0.804086i
$216$	−1.93810	−	5.50319i	−0.131871	−	0.374445i
$217$	−7.32102	−	7.07390i	−0.496983	−	0.480207i
$218$	7.58786	+	13.1426i	0.513915	+	0.890126i
$219$	3.84265	−	2.83999i	0.259662	−	0.191909i
$220$	−1.40372	−	2.43132i	−0.0946390	−	0.163920i
$221$	4.00862	+	6.94313i	0.269649	+	0.467045i
$222$	1.64678	+	0.717167i	0.110525	+	0.0481331i
$223$	5.86133	+	10.1521i	0.392503	+	0.679836i	0.992779	−	0.119957i	$-0.0382758\pi$
$223$	5.86133	+	10.1521i	0.392503	+	0.679836i	−0.600276	+	0.799793i	$0.704942\pi$
$224$	12.7102	+	12.2812i	0.849236	+	0.820571i
$225$	−6.57677	−	7.06901i	−0.438451	−	0.471267i
$226$	−13.3509	−	23.1245i	−0.888091	−	1.53822i
$227$	11.1831			0.742247			0.371123	−	0.928584i	$-0.378973\pi$
$227$	11.1831			0.742247			0.371123	+	0.928584i	$0.378973\pi$
$228$	4.84913	−	3.58385i	0.321141	−	0.237346i
$229$	−9.65647			−0.638118			−0.319059	−	0.947735i	$-0.603367\pi$
$229$	−9.65647			−0.638118			−0.319059	+	0.947735i	$0.603367\pi$
$230$	−9.04494	+	15.6663i	−0.596406	+	1.03301i
$231$	6.87341	+	0.910938i	0.452237	+	0.0599353i
$232$	−0.0347761	−	0.0602340i	−0.00228317	−	0.00395456i
$233$	−9.64492	−	16.7055i	−0.631860	−	1.09441i	−0.987171	−	0.159666i	$-0.948958\pi$
$233$	−9.64492	−	16.7055i	−0.631860	−	1.09441i	0.355311	−	0.934748i	$-0.384375\pi$
$234$	−8.39058	+	27.3318i	−0.548509	+	1.78674i
$235$	6.35243	−	11.0027i	0.414387	−	0.717739i
$236$	5.86881	−	10.1651i	0.382027	−	0.661690i
$237$	−8.24519	+	6.09378i	−0.535582	+	0.395833i
$238$	5.42630	+	5.24314i	0.351735	+	0.339862i
$239$	−0.194641	+	0.337128i	−0.0125903	+	0.0218070i	−0.872252	−	0.489057i	$-0.837341\pi$
$239$	−0.194641	+	0.337128i	−0.0125903	+	0.0218070i	0.859662	+	0.510864i	$0.170674\pi$
$240$	−9.01295	+	6.66121i	−0.581784	+	0.429979i
$241$	10.6361			0.685134			0.342567	−	0.939493i	$-0.388704\pi$
$241$	10.6361			0.685134			0.342567	+	0.939493i	$0.388704\pi$
$242$	−8.01932	+	13.8899i	−0.515502	+	0.892875i
$243$	7.23769	−	13.8064i	0.464298	−	0.885679i
$244$	4.50299			0.288274
$245$	7.92639	−	4.94662i	0.506399	−	0.316028i
$246$	3.24130	+	28.5948i	0.206658	+	1.82314i
$247$	12.9618			0.824741
$248$	2.16023	+	3.74163i	0.137175	+	0.237594i
$249$	−1.09290	−	9.64159i	−0.0692599	−	0.611011i
$250$	−10.0988	+	17.4917i	−0.638705	+	1.10627i
$251$	−3.26628			−0.206166			−0.103083	−	0.994673i	$-0.532871\pi$
$251$	−3.26628			−0.206166			−0.103083	+	0.994673i	$0.532871\pi$
$252$	−0.208441	+	11.0321i	−0.0131306	+	0.694960i
$253$	−11.1370			−0.700176
$254$	7.82531	−	13.5538i	0.491004	−	0.850443i
$255$	−2.87976	+	2.12835i	−0.180337	+	0.133282i
$256$	−10.4896	−	18.1686i	−0.655603	−	1.13554i
$257$	−4.69573			−0.292912			−0.146456	−	0.989217i	$-0.546787\pi$
$257$	−4.69573			−0.292912			−0.146456	+	0.989217i	$0.546787\pi$
$258$	−29.8229	−	12.9878i	−1.85669	−	0.808584i
$259$	1.07161	+	1.03544i	0.0665867	+	0.0643391i
$260$	9.60421			0.595628
$261$	0.0545353	−	0.177646i	0.00337565	−	0.0109960i
$262$	−1.85363	+	3.21059i	−0.114518	+	0.198351i
$263$	19.5498			1.20549			0.602747	−	0.797932i	$-0.294073\pi$
$263$	19.5498			1.20549			0.602747	+	0.797932i	$0.294073\pi$
$264$	−2.69783	−	1.17490i	−0.166040	−	0.0723098i
$265$	1.00824	−	1.74632i	0.0619355	−	0.107276i
$266$	11.7276	−	3.35918i	0.719066	−	0.205965i
$267$	−0.274400	−	2.42076i	−0.0167930	−	0.148148i
$268$	−4.81929	+	8.34725i	−0.294385	+	0.509890i
$269$	7.88365	−	13.6549i	0.480675	−	0.832553i	−0.519079	−	0.854726i	$-0.673725\pi$
$269$	7.88365	−	13.6549i	0.480675	−	0.832553i	0.999754	+	0.0221730i	$0.00705846\pi$
$270$	−12.5522	−	2.34883i	−0.763903	−	0.142945i
$271$	7.39882	+	12.8151i	0.449446	+	0.778464i	0.998350	−	0.0574218i	$-0.0182880\pi$
$271$	7.39882	+	12.8151i	0.449446	+	0.778464i	−0.548904	+	0.835886i	$0.684955\pi$
$272$	−3.75442	−	6.50285i	−0.227645	−	0.394293i
$273$	−14.4557	+	18.8054i	−0.874898	+	1.13815i
$274$	2.04138	−	3.53578i	0.123324	−	0.213604i
$275$	−4.86954			−0.293644
$276$	−1.99624	−	17.6108i	−0.120159	−	1.06005i
$277$	−7.45122			−0.447701			−0.223850	−	0.974624i	$-0.571863\pi$
$277$	−7.45122			−0.447701			−0.223850	+	0.974624i	$0.571863\pi$
$278$	−0.695380	−	1.20443i	−0.0417061	−	0.0722371i
$279$	−3.38764	+	11.0350i	−0.202812	+	0.660650i
$280$	−3.81196	+	1.09188i	−0.227808	+	0.0652521i
$281$	−12.9938	−	22.5060i	−0.775146	−	1.34259i	−0.934712	−	0.355406i	$-0.884343\pi$
$281$	−12.9938	−	22.5060i	−0.775146	−	1.34259i	0.159566	−	0.987187i	$-0.448991\pi$
$282$	3.41901	+	30.1625i	0.203599	+	1.79615i
$283$	−9.37768	−	16.2426i	−0.557445	−	0.965524i	−0.997709	−	0.0676550i	$-0.978448\pi$
$283$	−9.37768	−	16.2426i	−0.557445	−	0.965524i	0.440263	−	0.897869i	$-0.354885\pi$
$284$	8.57064	+	14.8448i	0.508574	+	0.880876i
$285$	0.652070	+	5.75257i	0.0386253	+	0.340753i
$286$	7.20971	+	12.4876i	0.426319	+	0.738406i
$287$	−5.78246	+	23.1638i	−0.341328	+	1.36732i
$288$	5.88136	−	19.1582i	0.346563	−	1.12891i
$289$	7.30041	+	12.6447i	0.429436	+	0.743805i
$290$	−0.152230			−0.00893928
$291$	2.37890	+	20.9867i	0.139454	+	1.23026i
$292$	3.83507			0.224431
$293$	−1.23089	+	2.13196i	−0.0719093	+	0.124551i	−0.899738	−	0.436430i	$-0.856243\pi$
$293$	−1.23089	+	2.13196i	−0.0719093	+	0.124551i	0.827829	+	0.560981i	$0.189576\pi$
$294$	−8.20562	+	20.7611i	−0.478562	+	1.21081i
$295$	5.63487	+	9.75988i	0.328075	+	0.568242i
$296$	−0.316203	−	0.547680i	−0.0183790	−	0.0318333i
$297$	−2.61155	−	7.41544i	−0.151537	−	0.430287i
$298$	6.06227	−	10.5002i	0.351178	−	0.608258i
$299$	19.0497	−	32.9950i	1.10167	−	1.90815i
$300$	−0.872835	−	7.70016i	−0.0503932	−	0.444569i
$301$	−19.4067	−	18.7517i	−1.11858	−	1.08083i
$302$	11.6616	−	20.1985i	0.671050	−	1.16229i
$303$	−1.77645	−	0.773637i	−0.102054	−	0.0444443i
$304$	−12.1399			−0.696270
$305$	−2.16175	+	3.74425i	−0.123781	+	0.214395i
$306$	2.51090	−	8.17911i	0.143538	−	0.467568i
$307$	−4.66277			−0.266118			−0.133059	−	0.991108i	$-0.542480\pi$
$307$	−4.66277			−0.266118			−0.133059	+	0.991108i	$0.542480\pi$
$308$	4.00196	+	3.86688i	0.228033	+	0.220336i
$309$	−3.06555	−	1.33503i	−0.174393	−	0.0759475i
$310$	9.45629			0.537081
$311$	−13.7410	−	23.8002i	−0.779183	−	1.34958i	−0.932413	−	0.361393i	$-0.882301\pi$
$311$	−13.7410	−	23.8002i	−0.779183	−	1.34958i	0.153231	−	0.988190i	$-0.451032\pi$
$312$	8.09542	−	5.98309i	0.458313	−	0.338726i
$313$	−2.74666	+	4.75735i	−0.155250	+	0.268901i	−0.933150	−	0.359487i	$-0.882952\pi$
$313$	−2.74666	+	4.75735i	−0.155250	+	0.268901i	0.777900	+	0.628388i	$0.216285\pi$
$314$	31.8671			1.79837
$315$	−9.07321	−	5.46951i	−0.511217	−	0.308172i
$316$	−8.22893			−0.462914
$317$	−4.93879	+	8.55424i	−0.277390	+	0.480454i	−0.970735	−	0.240152i	$-0.922803\pi$
$317$	−4.93879	+	8.55424i	−0.277390	+	0.480454i	0.693345	+	0.720606i	$0.256136\pi$
$318$	0.542654	+	4.78730i	0.0304305	+	0.268459i
$319$	−0.0468601	−	0.0811641i	−0.00262366	−	0.00454432i
$320$	−3.47615			−0.194323
$321$	−1.12746	−	9.94649i	−0.0629288	−	0.555159i
$322$	8.68480	−	34.7902i	0.483985	−	1.93878i
$323$	−3.87885			−0.215825
$324$	11.2579	−	5.45879i	0.625437	−	0.303266i
$325$	8.32930	−	14.4268i	0.462026	−	0.800253i
$326$	22.4986			1.24608
$327$	11.4806	−	8.48494i	0.634876	−	0.469218i
$328$	5.06616	−	8.77485i	0.279732	−	0.484510i
$329$	−6.09950	+	24.4338i	−0.336276	+	1.34708i
$330$	−5.17940	+	3.82794i	−0.285116	+	0.210721i
$331$	10.3471	−	17.9217i	0.568729	−	0.985067i	−0.427963	−	0.903796i	$-0.640769\pi$
$331$	10.3471	−	17.9217i	0.568729	−	0.985067i	0.996692	−	0.0812710i	$-0.0258979\pi$
$332$	3.89401	−	6.74463i	0.213712	−	0.370160i
$333$	0.495864	−	1.61525i	0.0271732	−	0.0885152i
$334$	−3.24514	−	5.62076i	−0.177566	−	0.307554i
$335$	−4.62718	−	8.01452i	−0.252810	−	0.437880i
$336$	13.5390	−	17.6129i	0.738613	−	0.960861i
$337$	0.748747	−	1.29687i	0.0407869	−	0.0706449i	−0.844911	−	0.534906i	$-0.820347\pi$
$337$	0.748747	−	1.29687i	0.0407869	−	0.0706449i	0.885698	+	0.464261i	$0.153680\pi$
$338$	−25.3924			−1.38116
$339$	−20.2002	+	14.9294i	−1.09712	+	0.810852i
$340$	−2.87408			−0.155869
$341$	2.91087	+	5.04177i	0.157632	+	0.273027i
$342$	−9.42217	−	10.1274i	−0.509493	−	0.547626i
$343$	−12.4044	+	13.7525i	−0.669772	+	0.742567i
$344$	5.72639	+	9.91840i	0.308746	+	0.534764i
$345$	15.6018	+	6.79453i	0.839973	+	0.365805i
$346$	9.33593	+	16.1703i	0.501903	+	0.869321i
$347$	14.7694	+	25.5813i	0.792862	+	1.37328i	0.924188	+	0.381938i	$0.124743\pi$
$347$	14.7694	+	25.5813i	0.792862	+	1.37328i	−0.131326	+	0.991339i	$0.541923\pi$
$348$	0.119945	−	0.0886477i	0.00642971	−	0.00475202i
$349$	18.0006	+	31.1780i	0.963551	+	1.66892i	0.713458	+	0.700698i	$0.247128\pi$
$349$	18.0006	+	31.1780i	0.963551	+	1.66892i	0.250094	+	0.968222i	$0.419539\pi$
$350$	3.79735	−	15.2117i	0.202977	−	0.813098i
$351$	26.4364	+	4.94691i	1.41107	+	0.264046i
$352$	−5.05363	−	8.75315i	−0.269360	−	0.466545i
$353$	−29.4930			−1.56975			−0.784877	−	0.619652i	$-0.787274\pi$
$353$	−29.4930			−1.56975			−0.784877	+	0.619652i	$0.787274\pi$
$354$	−24.6873	−	10.7512i	−1.31211	−	0.571421i
$355$	−16.4580			−0.873500
$356$	0.977687	−	1.69340i	0.0518173	−	0.0897502i
$357$	4.32589	−	5.62755i	0.228950	−	0.297841i
$358$	−1.56612	−	2.71260i	−0.0827720	−	0.143365i
$359$	2.70535	+	4.68580i	0.142783	+	0.247307i	0.928544	−	0.371224i	$-0.121062\pi$
$359$	2.70535	+	4.68580i	0.142783	+	0.247307i	−0.785761	+	0.618531i	$0.787728\pi$
$360$	3.06260	+	3.29182i	0.161413	+	0.173494i
$361$	6.36444	−	11.0235i	0.334971	−	0.580186i
$362$	−15.6451	+	27.0981i	−0.822289	+	1.42425i
$363$	13.8327	+	6.02409i	0.726028	+	0.316183i
$364$	−18.3015	+	5.24218i	−0.959261	+	0.274765i
$365$	−1.84110	+	3.18888i	−0.0963676	+	0.166914i
$366$	−1.16350	−	10.2644i	−0.0608169	−	0.536527i
$367$	−23.0843			−1.20499			−0.602496	−	0.798122i	$-0.705827\pi$
$367$	−23.0843			−1.20499			−0.602496	+	0.798122i	$0.705827\pi$
$368$	−17.8417	+	30.9027i	−0.930063	+	1.61092i
$369$	26.3844	−	6.05936i	1.37352	−	0.315438i
$370$	−1.38416			−0.0719591
$371$	−0.968093	+	3.87805i	−0.0502609	+	0.201339i
$372$	−7.45075	+	5.50664i	−0.386304	+	0.285506i
$373$	21.5030			1.11338			0.556692	−	0.830719i	$-0.312070\pi$
$373$	21.5030			1.11338			0.556692	+	0.830719i	$0.312070\pi$
$374$	−2.15752	−	3.73694i	−0.111563	−	0.193232i
$375$	17.4197	+	7.58620i	0.899548	+	0.391750i
$376$	5.34392	−	9.25595i	0.275592	−	0.477339i
$377$	0.320615			0.0165125
$378$	25.2012	−	2.37539i	1.29621	−	0.122177i
$379$	5.72168			0.293903			0.146952	−	0.989144i	$-0.453054\pi$
$379$	5.72168			0.293903			0.146952	+	0.989144i	$0.453054\pi$
$380$	−2.32333	+	4.02412i	−0.119184	+	0.206433i
$381$	−13.4980	−	5.87835i	−0.691526	−	0.301157i
$382$	20.8925	+	36.1869i	1.06895	+	1.85148i
$383$	−34.9209			−1.78437			−0.892187	−	0.451666i	$-0.850830\pi$
$383$	−34.9209			−1.78437			−0.892187	+	0.451666i	$0.850830\pi$
$384$	−11.9306	+	8.81756i	−0.608831	+	0.449969i
$385$	−5.13654	+	1.47128i	−0.261783	+	0.0749834i
$386$	−11.3917			−0.579823
$387$	−8.98003	+	29.2519i	−0.456480	+	1.48696i
$388$	−8.47603	+	14.6809i	−0.430305	+	0.745311i
$389$	−28.8822			−1.46438			−0.732192	−	0.681098i	$-0.761503\pi$
$389$	−28.8822			−1.46438			−0.732192	+	0.681098i	$0.761503\pi$
$390$	−2.48157	−	21.8924i	−0.125659	−	1.10857i
$391$	−5.70066	+	9.87383i	−0.288295	+	0.499341i
$392$	6.66801	−	4.16130i	0.336785	−	0.210177i
$393$	3.19737	+	1.39244i	0.161286	+	0.0702395i
$394$	8.99455	−	15.5790i	0.453139	−	0.784860i
$395$	3.95046	−	6.84239i	0.198769	−	0.344278i
$396$	1.85182	−	6.03219i	0.0930574	−	0.303129i
$397$	5.59226	+	9.68607i	0.280667	+	0.486130i	0.971549	−	0.236838i	$-0.0761109\pi$
$397$	5.59226	+	9.68607i	0.280667	+	0.486130i	−0.690882	+	0.722968i	$0.742778\pi$
$398$	7.99049	+	13.8399i	0.400527	+	0.693734i
$399$	−4.38243	−	10.6060i	−0.219396	−	0.530965i
$400$	−7.80111	+	13.5119i	−0.390056	+	0.675596i
$401$	−1.08212			−0.0540386			−0.0270193	−	0.999635i	$-0.508602\pi$
$401$	−1.08212			−0.0540386			−0.0270193	+	0.999635i	$0.508602\pi$
$402$	20.2724	+	8.82858i	1.01110	+	0.440330i
$403$	−19.9160			−0.992088
$404$	−0.777570	−	1.34679i	−0.0386856	−	0.0670054i
$405$	−0.865544	+	11.9816i	−0.0430092	+	0.595368i
$406$	0.290086	−	0.0830905i	0.0143967	−	0.00412371i
$407$	−0.426078	−	0.737988i	−0.0211199	−	0.0365807i
$408$	−2.42257	+	1.79045i	−0.119935	+	0.0886405i
$409$	10.8674	+	18.8229i	0.537360	+	0.930735i	0.999045	+	0.0436908i	$0.0139116\pi$
$409$	10.8674	+	18.8229i	0.537360	+	0.930735i	−0.461685	+	0.887044i	$0.652755\pi$
$410$	−11.0884	−	19.2057i	−0.547618	−	0.948501i
$411$	−3.52122	−	1.53348i	−0.173689	−	0.0756410i
$412$	−1.34182	−	2.32410i	−0.0661069	−	0.114500i
$413$	−16.0648	−	15.5225i	−0.790497	−	0.763814i
$414$	−39.6273	+	9.10068i	−1.94758	+	0.447274i
$415$	3.73879	+	6.47578i	0.183530	+	0.317884i
$416$	34.5767			1.69526
$417$	−1.05212	+	0.777593i	−0.0515226	+	0.0380789i
$418$	−6.97632			−0.341223
$419$	12.5906	−	21.8075i	0.615090	−	1.06537i	−0.375279	−	0.926912i	$-0.622453\pi$
$419$	12.5906	−	21.8075i	0.615090	−	1.06537i	0.990369	−	0.138455i	$-0.0442135\pi$
$420$	−3.24722	−	7.85865i	−0.158448	−	0.383463i
$421$	−14.8304	−	25.6869i	−0.722788	−	1.25191i	−0.959878	−	0.280418i	$-0.909527\pi$
$421$	−14.8304	−	25.6869i	−0.722788	−	1.25191i	0.237090	−	0.971488i	$-0.423806\pi$
$422$	5.23316	+	9.06411i	0.254746	+	0.441234i
$423$	27.8310	−	6.39158i	1.35319	−	0.310769i
$424$	0.848171	−	1.46907i	0.0411908	−	0.0713446i
$425$	−2.49256	+	4.31724i	−0.120907	+	0.209417i
$426$	31.6236	−	23.3721i	1.53217	−	1.13238i
$427$	2.07567	−	8.31487i	0.100449	−	0.402385i
$428$	4.01715	−	6.95791i	0.194176	−	0.336323i
$429$	10.9084	−	8.06209i	0.526663	−	0.389241i
$430$	25.0669			1.20884
$431$	2.44517	−	4.23516i	0.117780	−	0.204000i	−0.801108	−	0.598520i	$-0.795756\pi$
$431$	2.44517	−	4.23516i	0.117780	−	0.204000i	0.918887	+	0.394520i	$0.129089\pi$
$432$	−24.7600	−	4.63321i	−1.19127	−	0.222915i
$433$	9.71430			0.466839			0.233420	−	0.972376i	$-0.425008\pi$
$433$	9.71430			0.466839			0.233420	+	0.972376i	$0.425008\pi$
$434$	−18.0196	+	5.16144i	−0.864970	+	0.247757i
$435$	0.0161292	+	0.142292i	0.000773334	+	0.00682236i
$436$	11.4579			0.548735
$437$	9.21651	+	15.9635i	0.440885	+	0.763636i
$438$	−0.990919	−	8.74189i	−0.0473479	−	0.417704i
$439$	7.41176	−	12.8375i	0.353744	−	0.612703i	−0.633158	−	0.774022i	$-0.718242\pi$
$439$	7.41176	−	12.8375i	0.353744	−	0.612703i	0.986902	+	0.161320i	$0.0515751\pi$
$440$	2.26760			0.108103
$441$	20.2750	+	5.47021i	0.965478	+	0.260486i
$442$	14.7617			0.702141
$443$	10.9510	−	18.9676i	0.520297	−	0.901180i	−0.479425	−	0.877583i	$-0.659155\pi$
$443$	10.9510	−	18.9676i	0.520297	−	0.901180i	0.999722	−	0.0235972i	$-0.00751192\pi$
$444$	1.09060	−	0.806033i	0.0517577	−	0.0382526i
$445$	0.938715	+	1.62590i	0.0444994	+	0.0770751i
$446$	21.5842			1.02204
$447$	−10.4569	−	4.55396i	−0.494596	−	0.215395i
$448$	6.62406	−	1.89736i	0.312957	−	0.0896416i
$449$	21.4952			1.01442			0.507212	−	0.861822i	$-0.330676\pi$
$449$	21.4952			1.01442			0.507212	+	0.861822i	$0.330676\pi$
$450$	−17.3267	+	3.97919i	−0.816787	+	0.187581i
$451$	6.82655	−	11.8239i	0.321450	−	0.556767i
$452$	−20.1603			−0.948263
$453$	−20.1153	−	8.76016i	−0.945101	−	0.411588i
$454$	10.2954	−	17.8321i	0.483185	−	0.836902i
$455$	4.42711	−	17.7344i	0.207546	−	0.831402i
$456$	0.548548	+	4.83929i	0.0256881	+	0.226621i
$457$	−20.3128	+	35.1827i	−0.950190	+	1.64578i	−0.205181	+	0.978724i	$0.565778\pi$
$457$	−20.3128	+	35.1827i	−0.950190	+	1.64578i	−0.745009	+	0.667054i	$0.767555\pi$
$458$	−8.88995	+	15.3978i	−0.415400	+	0.719494i
$459$	−7.91114	−	1.48037i	−0.369261	−	0.0690978i
$460$	6.82908	+	11.8283i	0.318408	+	0.551498i
$461$	1.41541	+	2.45155i	0.0659220	+	0.114180i	0.897103	−	0.441822i	$-0.145668\pi$
$461$	1.41541	+	2.45155i	0.0659220	+	0.114180i	−0.831181	+	0.556003i	$0.812334\pi$
$462$	7.78035	−	10.1214i	0.361975	−	0.470892i
$463$	−13.9324	+	24.1317i	−0.647494	+	1.12149i	0.336225	+	0.941782i	$0.390850\pi$
$463$	−13.9324	+	24.1317i	−0.647494	+	1.12149i	−0.983719	+	0.179711i	$0.942484\pi$
$464$	−0.300284			−0.0139403
$465$	−1.00192	−	8.83890i	−0.0464627	−	0.409894i
$466$	−35.5173			−1.64531
$467$	−13.3219	−	23.0742i	−0.616464	−	1.06775i	−0.990126	−	0.140182i	$-0.955231\pi$
$467$	−13.3219	−	23.0742i	−0.616464	−	1.06775i	0.373661	−	0.927565i	$-0.378102\pi$
$468$	14.7038	+	15.8043i	0.679682	+	0.730554i
$469$	13.1919	+	12.7466i	0.609146	+	0.588585i
$470$	−11.6964	−	20.2587i	−0.539513	−	0.934463i
$471$	−3.37640	−	29.7866i	−0.155576	−	1.37249i
$472$	4.74028	+	8.21041i	0.218189	+	0.377915i
$473$	7.71620	+	13.3648i	0.354791	+	0.614516i
$474$	2.12622	+	18.7575i	0.0976604	+	0.861561i
$475$	4.02983	+	6.97987i	0.184901	+	0.320258i
$476$	5.47677	−	1.56873i	0.251027	−	0.0719027i
$477$	4.41725	−	1.01445i	0.202252	−	0.0464485i
$478$	0.358381	+	0.620734i	0.0163920	+	0.0283917i
$479$	−31.5791			−1.44289			−0.721443	−	0.692474i	$-0.756521\pi$
$479$	−31.5791			−1.44289			−0.721443	+	0.692474i	$0.756521\pi$
$480$	1.73945	+	15.3455i	0.0793947	+	0.700421i
$481$	2.91520			0.132922
$482$	9.79185	−	16.9600i	0.446007	−	0.772506i
$483$	−33.4390	−	4.43169i	−1.52153	−	0.201649i
$484$	6.05472	+	10.4871i	0.275215	+	0.476686i
$485$	−8.13817	−	14.0957i	−0.369535	−	0.640054i
$486$	−15.3519	−	24.2514i	−0.696378	−	1.10006i
$487$	−0.153087	+	0.265154i	−0.00693703	+	0.0120153i	−0.869473	−	0.493980i	$-0.835541\pi$
$487$	−0.153087	+	0.265154i	−0.00693703	+	0.0120153i	0.862536	+	0.505996i	$0.168875\pi$
$488$	−1.81855	+	3.14982i	−0.0823218	+	0.142586i
$489$	−2.38378	−	21.0297i	−0.107798	−	0.950996i
$490$	−0.590486	−	17.1931i	−0.0266754	−	0.776704i
$491$	−9.06981	+	15.7094i	−0.409315	+	0.708954i	−0.994813	−	0.101720i	$-0.967566\pi$
$491$	−9.06981	+	15.7094i	−0.409315	+	0.708954i	0.585498	+	0.810674i	$0.300899\pi$
$492$	19.9207	+	8.67539i	0.898094	+	0.391117i
$493$	−0.0959447			−0.00432113
$494$	11.9329	−	20.6684i	0.536887	−	0.929916i
$495$	4.12679	+	4.43567i	0.185486	+	0.199368i
$496$	18.6531			0.837549
$497$	31.3619	−	8.98311i	1.40677	−	0.402948i
$498$	−16.3803	−	7.13355i	−0.734017	−	0.319662i
$499$	−21.3091			−0.953928			−0.476964	−	0.878923i	$-0.658263\pi$
$499$	−21.3091			−0.953928			−0.476964	+	0.878923i	$0.658263\pi$
$500$	7.62478	+	13.2065i	0.340990	+	0.590613i
$501$	−4.90996	+	3.62881i	−0.219361	+	0.162123i
$502$	−3.00701	+	5.20829i	−0.134209	+	0.232457i
$503$	−17.0738			−0.761285			−0.380642	−	0.924722i	$-0.624297\pi$
$503$	−17.0738			−0.761285			−0.380642	+	0.924722i	$0.624297\pi$
$504$	−7.63275	−	4.60118i	−0.339990	−	0.204953i
$505$	1.49315			0.0664443
$506$	−10.2529	+	17.7586i	−0.455799	+	0.789466i
$507$	2.69038	+	23.7346i	0.119484	+	1.05409i
$508$	−5.90824	−	10.2334i	−0.262136	−	0.454032i
$509$	36.7735			1.62996			0.814979	−	0.579490i	$-0.196748\pi$
$509$	36.7735			1.62996			0.814979	+	0.579490i	$0.196748\pi$
$510$	0.742614	+	6.55135i	0.0328835	+	0.290099i
$511$	1.76780	−	7.08155i	0.0782027	−	0.313270i
$512$	−21.4975			−0.950065
$513$	−8.46788	+	9.88003i	−0.373866	+	0.436214i
$514$	−4.32299	+	7.48764i	−0.190679	+	0.330265i
$515$	2.57667			0.113542
$516$	−19.7506	+	14.5971i	−0.869473	+	0.642603i
$517$	7.20083	−	12.4722i	0.316692	−	0.548527i
$518$	2.63762	−	0.755504i	0.115890	−	0.0331949i
$519$	14.1254	−	10.4397i	0.620037	−	0.458251i
$520$	−3.87870	+	6.71810i	−0.170092	+	0.294608i
$521$	−9.57535	+	16.5850i	−0.419504	+	0.726602i	−0.995890	−	0.0905758i	$-0.971129\pi$
$521$	−9.57535	+	16.5850i	−0.419504	+	0.726602i	0.576386	+	0.817178i	$0.304463\pi$
$522$	−0.233061	−	0.250504i	−0.0102008	−	0.0109643i
$523$	−20.9715	−	36.3236i	−0.917018	−	1.58832i	−0.803920	−	0.594737i	$-0.797256\pi$
$523$	−20.9715	−	36.3236i	−0.917018	−	1.58832i	−0.113097	−	0.993584i	$-0.536077\pi$
$524$	1.39952	+	2.42405i	0.0611385	+	0.105895i
$525$	−14.6209	−	1.93771i	−0.638107	−	0.0845688i
$526$	17.9980	−	31.1734i	0.784749	−	1.35922i
$527$	5.95991			0.259618
$528$	−10.2167	+	7.55085i	−0.444624	+	0.328609i
$529$	31.1812			1.35570
$530$	−1.85641	−	3.21539i	−0.0806372	−	0.139668i
$531$	−7.43362	+	24.2146i	−0.322592	+	1.05082i
$532$	2.23082	−	8.93637i	0.0967183	−	0.387441i
$533$	23.3535	+	40.4494i	1.01155	+	1.75206i
$534$	−4.11266	−	1.79105i	−0.177972	−	0.0775063i
$535$	3.85702	+	6.68056i	0.166754	+	0.288826i
$536$	−3.89258	−	6.74214i	−0.168134	−	0.291216i
$537$	−2.36956	+	1.75128i	−0.102254	+	0.0755732i
$538$	−14.5157	−	25.1419i	−0.625816	−	1.08395i
$539$	8.98500	−	5.60726i	0.387011	−	0.241522i
$540$	−6.27438	+	7.32073i	−0.270006	+	0.315034i
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	0.833344	−	0.552754i	$-0.186423\pi$
$541$	−1.44272	−	2.49886i	−0.0620273	−	0.107434i	−0.895371	+	0.445320i	$0.853090\pi$
$542$	27.2460			1.17032
$543$	26.9866	+	11.7526i	1.15811	+	0.504351i
$544$	−10.3472			−0.443631
$545$	−5.50059	+	9.52731i	−0.235620	+	0.408105i
$546$	16.6781	+	40.3631i	0.713758	+	1.72738i
$547$	1.38738	+	2.40301i	0.0593201	+	0.102745i	0.894160	−	0.447747i	$-0.147773\pi$
$547$	1.38738	+	2.40301i	0.0593201	+	0.102745i	−0.834840	+	0.550492i	$0.814440\pi$
$548$	−1.54128	−	2.66957i	−0.0658401	−	0.114038i
$549$	−9.47096	+	2.17507i	−0.404211	+	0.0928296i
$550$	−4.48300	+	7.76478i	−0.191156	+	0.331091i
$551$	−0.0775590	+	0.134336i	−0.00330413	+	0.00572291i
$552$	13.1249	+	5.71584i	0.558632	+	0.243282i
$553$	−3.79316	+	15.1949i	−0.161302	+	0.646154i
$554$	−6.85975	+	11.8814i	−0.291443	+	0.504794i
$555$	0.146655	+	1.29379i	0.00622516	+	0.0549184i
$556$	−1.05005			−0.0445319
$557$	15.5344	−	26.9064i	0.658214	−	1.14006i	−0.322864	−	0.946445i	$-0.604646\pi$
$557$	15.5344	−	26.9064i	0.658214	−	1.14006i	0.981078	−	0.193614i	$-0.0620211\pi$
$558$	14.4773	+	15.5609i	0.612873	+	0.658744i
$559$	−52.7939			−2.23294
$560$	−4.14637	+	16.6098i	−0.175216	+	0.701893i
$561$	−3.26436	+	2.41260i	−0.137822	+	0.101860i
$562$	−47.8495			−2.01841
$563$	−0.144020	−	0.249451i	−0.00606973	−	0.0105131i	0.862975	−	0.505247i	$-0.168599\pi$
$563$	−0.144020	−	0.249451i	−0.00606973	−	0.0105131i	−0.869044	+	0.494734i	$0.835265\pi$
$564$	21.0129	+	9.15104i	0.884802	+	0.385328i
$565$	9.67836	−	16.7634i	0.407172	−	0.705242i
$566$	−34.5331			−1.45154
$567$	−4.89042	−	23.3042i	−0.205378	−	0.978683i
$568$	−13.8451			−0.580929
$569$	8.04004	−	13.9258i	0.337056	−	0.583798i	−0.646821	−	0.762641i	$-0.723902\pi$
$569$	8.04004	−	13.9258i	0.337056	−	0.583798i	0.983878	+	0.178843i	$0.0572354\pi$
$570$	9.77313	+	4.25616i	0.409351	+	0.178271i
$571$	7.64289	+	13.2379i	0.319845	+	0.553988i	0.980456	−	0.196741i	$-0.0630358\pi$
$571$	7.64289	+	13.2379i	0.319845	+	0.553988i	−0.660610	+	0.750729i	$0.729702\pi$
$572$	10.8869			0.455204
$573$	31.6107	−	23.3626i	1.32056	−	0.975985i
$574$	31.6126	+	30.5456i	1.31949	+	1.27495i
$575$	23.6902			0.987950
$576$	−5.32189	−	5.72021i	−0.221745	−	0.238342i
$577$	12.0812	−	20.9253i	0.502949	−	0.871133i	−0.497045	−	0.867725i	$-0.665582\pi$
$577$	12.0812	−	20.9253i	0.502949	−	0.871133i	0.999994	−	0.00340833i	$-0.00108491\pi$
$578$	26.8836			1.11821
$579$	1.20698	+	10.6480i	0.0501603	+	0.442515i
$580$	−0.0574683	+	0.0995380i	−0.00238624	+	0.00413309i
$581$	−10.6592	−	10.2994i	−0.442216	−	0.427289i
$582$	35.6546	+	15.5275i	1.47793	+	0.643634i
$583$	1.14289	−	1.97955i	0.0473338	−	0.0819845i
$584$	−1.54881	+	2.68262i	−0.0640902	+	0.111007i
$585$	−20.2002	+	4.63910i	−0.835174	+	0.191803i
$586$	2.26636	+	3.92546i	0.0936226	+	0.162159i
$587$	18.0145	+	31.2020i	0.743537	+	1.28784i	0.950875	+	0.309574i	$0.100186\pi$
$587$	18.0145	+	31.2020i	0.743537	+	1.28784i	−0.207339	+	0.978269i	$0.566480\pi$
$588$	10.4772	+	13.2028i	0.432073	+	0.544476i
$589$	4.81783	−	8.34472i	0.198515	−	0.343838i
$590$	20.7503			0.854276
$591$	−15.5149	−	6.75668i	−0.638197	−	0.277933i
$592$	−2.73034			−0.112216
$593$	12.4668	+	21.5932i	0.511951	+	0.886726i	0.999904	+	0.0138558i	$0.00441057\pi$
$593$	12.4668	+	21.5932i	0.511951	+	0.886726i	−0.487953	+	0.872870i	$0.662256\pi$
$594$	−14.2286	−	2.66253i	−0.583807	−	0.109245i
$595$	−1.32482	+	5.30706i	−0.0543124	+	0.217568i
$596$	−4.57712	−	7.92780i	−0.187486	−	0.324735i
$597$	12.0897	−	8.93518i	0.494800	−	0.365693i
$598$	−35.0751	−	60.7518i	−1.43433	−	2.48433i
$599$	−19.7642	−	34.2325i	−0.807542	−	1.39870i	−0.914561	−	0.404447i	$-0.867464\pi$
$599$	−19.7642	−	34.2325i	−0.807542	−	1.39870i	0.107019	−	0.994257i	$-0.465869\pi$
$600$	5.73873	+	2.49920i	0.234283	+	0.102029i
$601$	1.86447	+	3.22936i	0.0760534	+	0.131728i	0.901544	−	0.432688i	$-0.142435\pi$
$601$	1.86447	+	3.22936i	0.0760534	+	0.131728i	−0.825490	+	0.564416i	$0.809101\pi$
$602$	−47.7669	+	13.6821i	−1.94683	+	0.557639i
$603$	6.10427	−	19.8843i	0.248585	−	0.809751i
$604$	−8.80470	−	15.2502i	−0.358258	−	0.620521i
$605$	−11.6267			−0.472694
$606$	−2.86904	+	2.12043i	−0.116547	+	0.0861365i
$607$	23.6528			0.960036			0.480018	−	0.877259i	$-0.340630\pi$
$607$	23.6528			0.960036			0.480018	+	0.877259i	$0.340630\pi$
$608$	−8.36436	+	14.4875i	−0.339219	+	0.587545i
$609$	−0.108401	−	0.262343i	−0.00439263	−	0.0106307i
$610$	3.98029	+	6.89407i	0.161157	+	0.279133i
$611$	24.6339	+	42.6671i	0.996580	+	1.72613i
$612$	−4.40013	−	4.72947i	−0.177865	−	0.191177i
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	−0.825113	−	0.564968i	$-0.808888\pi$
$613$	1.89952	−	3.29006i	0.0767208	−	0.132884i	0.901833	+	0.432084i	$0.142222\pi$
$614$	−4.29264	+	7.43507i	−0.173237	+	0.300055i
$615$	−16.7769	+	12.3994i	−0.676512	+	0.499990i
$616$	−4.32107	+	1.23770i	−0.174101	+	0.0498684i
$617$	−17.5615	+	30.4174i	−0.706999	+	1.22456i	0.258966	+	0.965886i	$0.416618\pi$
$617$	−17.5615	+	30.4174i	−0.706999	+	1.22456i	−0.965965	+	0.258672i	$0.916715\pi$
$618$	−4.95100	+	3.65914i	−0.199158	+	0.147192i
$619$	−21.1632			−0.850622			−0.425311	−	0.905047i	$-0.639835\pi$
$619$	−21.1632			−0.850622			−0.425311	+	0.905047i	$0.639835\pi$
$620$	3.56983	−	6.18312i	0.143368	−	0.248320i
$621$	12.7051	+	36.0759i	0.509839	+	1.44768i
$622$	−50.6011			−2.02892
$623$	−2.67624	−	2.58590i	−0.107221	−	0.103602i
$624$	−4.89504	−	43.1841i	−0.195959	−	1.72875i
$625$	1.45048			0.0580192
$626$	5.05726	+	8.75943i	0.202129	+	0.350097i
$627$	0.739157	+	6.52085i	0.0295191	+	0.260418i
$628$	12.0301	−	20.8368i	0.480054	−	0.831477i
$629$	−0.872381			−0.0347841
$630$	−17.0745	+	9.43244i	−0.680263	+	0.375798i
$631$	4.74845			0.189033			0.0945164	−	0.995523i	$-0.469870\pi$
$631$	4.74845			0.189033			0.0945164	+	0.995523i	$0.469870\pi$
$632$	3.32329	−	5.75610i	0.132193	−	0.228965i
$633$	7.91786	−	5.85186i	0.314707	−	0.232591i
$634$	9.09350	+	15.7504i	0.361149	+	0.625529i
$635$	11.3455			0.450231
$636$	3.33510	+	1.45242i	0.132245	+	0.0575924i
$637$	1.24363	+	36.2106i	0.0492745	+	1.43472i
$638$	−0.172562			−0.00683178
$639$	−25.1967	−	27.0826i	−0.996767	−	1.07137i
$640$	5.71622	−	9.90078i	0.225953	−	0.391363i
$641$	−9.87469			−0.390027			−0.195013	−	0.980801i	$-0.562475\pi$
$641$	−9.87469			−0.390027			−0.195013	+	0.980801i	$0.562475\pi$
$642$	−16.8982	−	7.35913i	−0.666921	−	0.290442i
$643$	21.9748	−	38.0615i	0.866602	−	1.50100i	0.00115462	−	0.999999i	$-0.499632\pi$
$643$	21.9748	−	38.0615i	0.866602	−	1.50100i	0.865448	−	0.501000i	$-0.167034\pi$
$644$	−19.4694	−	18.8123i	−0.767204	−	0.741307i
$645$	−2.65590	−	23.4304i	−0.104576	−	0.922570i
$646$	−3.57095	+	6.18507i	−0.140497	+	0.243348i
$647$	22.1936	−	38.4404i	0.872521	−	1.51125i	0.0131398	−	0.999914i	$-0.495817\pi$
$647$	22.1936	−	38.4404i	0.872521	−	1.51125i	0.859381	−	0.511336i	$-0.170849\pi$
$648$	−0.728131	+	10.0794i	−0.0286037	+	0.395955i
$649$	6.38743	+	11.0634i	0.250729	+	0.434275i
$650$	−15.3362	−	26.5631i	−0.601537	−	1.04189i
$651$	6.73368	+	16.2963i	0.263914	+	0.638703i
$652$	8.49341	−	14.7110i	0.332628	−	0.576128i
$653$	41.9912			1.64324			0.821622	−	0.570033i	$-0.193070\pi$
$653$	41.9912			1.64324			0.821622	+	0.570033i	$0.193070\pi$
$654$	−2.96053	−	26.1179i	−0.115766	−	1.02129i
$655$	−2.68748			−0.105008
$656$	−21.8726	−	37.8844i	−0.853980	−	1.47914i
$657$	−8.06616	+	1.85245i	−0.314691	+	0.0722708i
$658$	33.3459	+	32.2203i	1.29996	+	1.25608i
$659$	−19.6365	−	34.0114i	−0.764928	−	1.32489i	−0.940284	−	0.340390i	$-0.889441\pi$
$659$	−19.6365	−	34.0114i	−0.764928	−	1.32489i	0.175356	−	0.984505i	$-0.443892\pi$
$660$	0.547687	+	4.83170i	0.0213187	+	0.188074i
$661$	0.0933694	+	0.161721i	0.00363165	+	0.00629020i	0.867836	−	0.496852i	$-0.165511\pi$
$661$	0.0933694	+	0.161721i	0.00363165	+	0.00629020i	−0.864204	+	0.503142i	$0.832177\pi$
$662$	−19.0515	−	32.9982i	−0.740459	−	1.28251i
$663$	−1.56403	−	13.7979i	−0.0607419	−	0.535866i
$664$	3.14522	+	5.44769i	0.122058	+	0.211411i
$665$	6.35969	+	6.14502i	0.246618	+	0.238293i
$666$	−2.11911	−	2.27772i	−0.0821139	−	0.0882598i
$667$	0.227973	+	0.394862i	0.00882717	+	0.0152891i
$668$	−4.90028			−0.189597
$669$	−2.28690	−	20.1750i	−0.0884166	−	0.780012i
$670$	−17.0395			−0.658294
$671$	−2.45046	+	4.24432i	−0.0945989	+	0.163850i
$672$	−11.6905	−	28.2924i	−0.450971	−	1.09140i
$673$	−5.43382	−	9.41166i	−0.209458	−	0.362793i	0.742086	−	0.670305i	$-0.233837\pi$
$673$	−5.43382	−	9.41166i	−0.209458	−	0.362793i	−0.951544	+	0.307512i	$0.900503\pi$
$674$	−1.37862	−	2.38785i	−0.0531026	−	0.0919764i
$675$	5.55519	+	15.7738i	0.213819	+	0.607136i
$676$	−9.58584	+	16.6032i	−0.368686	+	0.638583i
$677$	−14.1950	+	24.5865i	−0.545560	+	0.944937i	0.453012	+	0.891505i	$0.350350\pi$
$677$	−14.1950	+	24.5865i	−0.545560	+	0.944937i	−0.998571	+	0.0534326i	$0.982984\pi$
$678$	5.20910	+	45.9547i	0.200054	+	1.76488i
$679$	23.2016	+	22.4184i	0.890396	+	0.860341i
$680$	1.16071	−	2.01041i	0.0445111	−	0.0770956i
$681$	−17.7587	−	7.73385i	−0.680514	−	0.296362i
$682$	10.7192			0.410460
$683$	5.92034	−	10.2543i	0.226536	−	0.392371i	−0.730243	−	0.683187i	$-0.760593\pi$
$683$	5.92034	−	10.2543i	0.226536	−	0.392371i	0.956779	+	0.290816i	$0.0939267\pi$
$684$	−10.1789	+	2.33764i	−0.389199	+	0.0893821i
$685$	2.95968			0.113083
$686$	10.5095	+	32.4404i	0.401256	+	1.23858i
$687$	15.3345	+	6.67810i	0.585046	+	0.254786i
$688$	49.4461			1.88511
$689$	3.90981	+	6.77199i	0.148952	+	0.257992i
$690$	25.1976	−	18.6228i	0.959258	−	0.708960i
$691$	−5.95416	+	10.3129i	−0.226507	+	0.392321i	−0.956770	−	0.290844i	$-0.906064\pi$
$691$	−5.95416	+	10.3129i	−0.226507	+	0.392321i	0.730264	+	0.683165i	$0.239397\pi$
$692$	14.0976			0.535909
$693$	−10.2850	−	6.19999i	−0.390694	−	0.235518i
$694$	54.3880			2.06454
$695$	0.504096	−	0.873119i	0.0191214	−	0.0331193i
$696$	0.0135685	+	0.119702i	0.000514313	+	0.00453727i
$697$	−6.98857	−	12.1046i	−0.264711	−	0.458493i
$698$	66.2870			2.50900
$699$	3.76313	+	33.1984i	0.142335	+	1.25568i
$700$	−8.51283	−	8.22548i	−0.321755	−	0.310894i
$701$	−31.3902			−1.18559			−0.592795	−	0.805353i	$-0.701976\pi$
$701$	−31.3902			−1.18559			−0.592795	+	0.805353i	$0.701976\pi$
$702$	32.2260	−	37.6002i	1.21629	−	1.41913i
$703$	−0.705208	+	1.22146i	−0.0265974	+	0.0460681i
$704$	−3.94041			−0.148510
$705$	−17.6968	+	13.0792i	−0.666499	+	0.492590i
$706$	−27.1518	+	47.0284i	−1.02187	+	1.76994i
$707$	−2.84531	+	0.814992i	−0.107009	+	0.0306509i
$708$	−16.3495	+	12.0834i	−0.614451	+	0.454123i
$709$	−0.312609	+	0.541455i	−0.0117403	+	0.0203348i	−0.871836	−	0.489798i	$-0.837070\pi$
$709$	−0.312609	+	0.541455i	−0.0117403	+	0.0203348i	0.860096	+	0.510133i	$0.170404\pi$
$710$	−15.1516	+	26.2433i	−0.568628	+	0.984893i
$711$	17.3076	−	3.97480i	0.649085	−	0.149067i
$712$	0.789685	+	1.36777i	0.0295947	+	0.0512595i
$713$	−14.1613	−	24.5281i	−0.530345	−	0.918584i
$714$	−4.99097	−	12.0787i	−0.186782	−	0.452035i
$715$	−5.22647	+	9.05251i	−0.195459	+	0.338545i
$716$	−2.36489			−0.0883802
$717$	0.542236	−	0.400751i	0.0202502	−	0.0149663i
$718$	9.96239			0.371793
$719$	12.1969	+	21.1257i	0.454869	+	0.787857i	0.998681	−	0.0513506i	$-0.0163526\pi$
$719$	12.1969	+	21.1257i	0.454869	+	0.787857i	−0.543811	+	0.839208i	$0.683019\pi$
$720$	18.9192	−	4.34492i	0.705078	−	0.161926i
$721$	−4.91003	+	1.40640i	−0.182859	+	0.0523771i
$722$	−11.7185	−	20.2970i	−0.436116	−	0.755376i
$723$	−16.8902	−	7.35561i	−0.628152	−	0.273558i
$724$	11.8123	+	20.4595i	0.439002	+	0.760373i
$725$	0.0996792	+	0.172649i	0.00370199	+	0.00641204i
$726$	22.3404	−	16.5112i	0.829132	−	0.612787i
$727$	−18.9253	−	32.7796i	−0.701900	−	1.21573i	−0.967799	−	0.251726i	$-0.919002\pi$
$727$	−18.9253	−	32.7796i	−0.701900	−	1.21573i	0.265899	−	0.964001i	$-0.414331\pi$
$728$	3.72426	−	14.9189i	0.138030	−	0.552932i
$729$	−21.0415	+	16.9191i	−0.779314	+	0.626634i
$730$	3.38991	+	5.87150i	0.125466	+	0.217314i
$731$	15.7987			0.584335
$732$	−7.15073	−	3.11412i	−0.264299	−	0.115101i
$733$	2.40155			0.0887033			0.0443516	−	0.999016i	$-0.485878\pi$
$733$	2.40155			0.0887033			0.0443516	+	0.999016i	$0.485878\pi$
$734$	−21.2519	+	36.8093i	−0.784421	+	1.35866i
$735$	−16.0080	+	2.37358i	−0.590464	+	0.0875508i
$736$	24.5858	+	42.5839i	0.906245	+	1.56966i
$737$	−5.24517	−	9.08490i	−0.193208	−	0.334646i
$738$	14.6280	−	47.6500i	0.538465	−	1.75402i
$739$	−15.1940	+	26.3167i	−0.558920	+	0.968077i	0.438667	+	0.898650i	$0.355451\pi$
$739$	−15.1940	+	26.3167i	−0.558920	+	0.968077i	−0.997587	+	0.0694277i	$0.977883\pi$
$740$	−0.522533	+	0.905053i	−0.0192087	+	0.0332704i
$741$	−20.5833	−	8.96397i	−0.756148	−	0.329300i
$742$	5.29255	+	5.11390i	0.194296	+	0.187737i
$743$	−2.54785	+	4.41300i	−0.0934715	+	0.161897i	−0.908970	−	0.416862i	$-0.863130\pi$
$743$	−2.54785	+	4.41300i	−0.0934715	+	0.161897i	0.815498	+	0.578760i	$0.196463\pi$
$744$	−0.842852	−	7.43565i	−0.0309004	−	0.272604i
$745$	8.78934			0.322016
$746$	19.7961	−	34.2879i	0.724787	−	1.25537i
$747$	−4.93228	+	16.0666i	−0.180463	+	0.587847i
$748$	−3.25793			−0.119122
$749$	−10.9962	−	10.6251i	−0.401793	−	0.388231i
$750$	28.1336	−	20.7927i	1.02729	−	0.759242i
$751$	−0.975011			−0.0355787			−0.0177893	−	0.999842i	$-0.505663\pi$
$751$	−0.975011			−0.0355787			−0.0177893	+	0.999842i	$0.505663\pi$
$752$	−23.0718	−	39.9615i	−0.841341	−	1.45724i
$753$	5.18685	+	2.25885i	0.189019	+	0.0823172i
$754$	0.295165	−	0.511240i	0.0107493	−	0.0186183i
$755$	16.9075			0.615326
$756$	7.96047	−	17.3749i	0.289520	−	0.631917i
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$	5.26750	−	9.12357i	0.191324	−	0.331383i
$759$	17.6855	+	7.70198i	0.641943	+	0.279564i
$760$	−1.87657	−	3.25031i	−0.0680703	−	0.117901i
$761$	−54.1749			−1.96384			−0.981920	−	0.189298i	$-0.939379\pi$
$761$	−54.1749			−1.96384			−0.981920	+	0.189298i	$0.939379\pi$
$762$	−21.8000	+	16.1117i	−0.789729	+	0.583666i
$763$	5.28158	−	21.1573i	0.191206	−	0.765946i
$764$	31.5484			1.14138
$765$	6.04494	−	1.38826i	0.218555	−	0.0501927i
$766$	−32.1489	+	55.6835i	−1.16159	+	2.01193i
$767$	−43.7025			−1.57801
$768$	4.09272	+	36.1060i	0.147683	+	1.30286i
$769$	−10.4326	+	18.0698i	−0.376208	+	0.651612i	−0.990507	−	0.137462i	$-0.956106\pi$
$769$	−10.4326	+	18.0698i	−0.376208	+	0.651612i	0.614299	+	0.789074i	$0.289439\pi$
$770$	−2.38276	+	9.54503i	−0.0858687	+	0.343979i
$771$	7.45681	+	3.24742i	0.268551	+	0.116953i
$772$	−4.30047	+	7.44863i	−0.154777	+	0.268082i
$773$	−27.4972	+	47.6266i	−0.989007	+	1.71301i	−0.366447	+	0.930439i	$0.619426\pi$
$773$	−27.4972	+	47.6266i	−0.989007	+	1.71301i	−0.622561	+	0.782572i	$0.713908\pi$
$774$	38.3768	+	41.2491i	1.37942	+	1.48267i
$775$	−6.19189	−	10.7247i	−0.222419	−	0.385242i
$776$	−6.84616	−	11.8579i	−0.245763	−	0.425674i
$777$	−0.985640	−	2.38537i	−0.0353596	−	0.0855746i
$778$	−26.5895	+	46.0544i	−0.953281	+	1.65113i
$779$	−22.5975			−0.809639
$780$	−15.2515	−	6.64196i	−0.546090	−	0.237820i
$781$	−18.6560			−0.667566
$782$	10.4963	+	18.1801i	0.375346	+	0.650119i
$783$	−0.209456	+	0.244386i	−0.00748534	+	0.00873364i
$784$	−1.16477	−	33.9144i	−0.0415989	−	1.21123i
$785$	11.5506	+	20.0062i	0.412258	+	0.714051i
$786$	5.16390	−	3.81649i	0.184190	−	0.136130i
$787$	−4.59475	−	7.95833i	−0.163785	−	0.283684i	0.772438	−	0.635090i	$-0.219037\pi$
$787$	−4.59475	−	7.95833i	−0.163785	−	0.283684i	−0.936223	+	0.351406i	$0.885704\pi$
$788$	−6.79103	−	11.7624i	−0.241921	−	0.419019i
$789$	−31.0451	−	13.5200i	−1.10523	−	0.481325i
$790$	−7.27374	−	12.5985i	−0.258788	−	0.448234i
$791$	−9.29301	+	37.2266i	−0.330421	+	1.32362i
$792$	3.47163	+	3.73146i	0.123359	+	0.132592i
$793$	−8.38296	−	14.5197i	−0.297688	−	0.515610i
$794$	20.5934			0.730832
$795$	−2.80878	+	2.07588i	−0.0996170	+	0.0736241i
$796$	12.0659			0.427665
$797$	3.53774	−	6.12754i	0.125313	−	0.217049i	−0.796542	−	0.604583i	$-0.793340\pi$
$797$	3.53774	−	6.12754i	0.125313	−	0.217049i	0.921855	+	0.387534i	$0.126673\pi$
$798$	−20.9465	−	2.77605i	−0.741498	−	0.0982713i
$799$	−7.37174	−	12.7682i	−0.260793	−	0.451707i
$800$	10.7499	+	18.6194i	0.380067	+	0.658295i
$801$	−1.23837	+	4.03392i	−0.0437556	+	0.142532i
$802$	−0.996224	+	1.72551i	−0.0351779	+	0.0609299i
$803$	−2.08699	+	3.61477i	−0.0736483	+	0.127563i
$804$	13.4257	−	9.92255i	0.473488	−	0.349941i
$805$	24.9892	−	7.15774i	0.880752	−	0.252277i
$806$	−18.3351	+	31.7573i	−0.645827	+	1.11860i
$807$	−21.9625	+	16.2318i	−0.773116	+	0.571388i
$808$	1.25610			0.0441894
$809$	−2.97060	+	5.14522i	−0.104441	+	0.180896i	−0.913510	−	0.406817i	$-0.866639\pi$
$809$	−2.97060	+	5.14522i	−0.104441	+	0.180896i	0.809069	+	0.587714i	$0.199972\pi$
$810$	18.3085	+	12.4106i	0.643295	+	0.436065i
$811$	44.4139			1.55958			0.779791	−	0.626039i	$-0.215325\pi$
$811$	44.4139			1.55958			0.779791	+	0.626039i	$0.215325\pi$
$812$	0.0551801	−	0.221044i	0.00193644	−	0.00775713i
$813$	−2.88678	−	25.4672i	−0.101244	−	0.893173i
$814$	−1.56902			−0.0549942
$815$	8.15485	+	14.1246i	0.285652	+	0.494764i
$816$	1.46485	+	12.9229i	0.0512801	+	0.452393i
$817$	12.7712	−	22.1204i	0.446808	−	0.773894i
$818$	40.0191			1.39924
$819$	35.9608	−	19.8658i	1.25657	−	0.694168i
$820$	−16.7439			−0.584721
$821$	−3.17761	+	5.50378i	−0.110899	+	0.192083i	−0.916133	−	0.400874i	$-0.868706\pi$
$821$	−3.17761	+	5.50378i	−0.110899	+	0.192083i	0.805234	+	0.592958i	$0.202040\pi$
$822$	−5.68693	+	4.20305i	−0.198355	+	0.146598i
$823$	4.73216	+	8.19635i	0.164953	+	0.285707i	0.936639	−	0.350297i	$-0.113919\pi$
$823$	4.73216	+	8.19635i	0.164953	+	0.285707i	−0.771686	+	0.636004i	$0.780586\pi$
$824$	2.16760			0.0755120
$825$	7.73282	+	3.36762i	0.269222	+	0.117245i
$826$	−39.5412	+	11.3259i	−1.37581	+	0.394080i
$827$	−4.86261			−0.169090			−0.0845448	−	0.996420i	$-0.526944\pi$
$827$	−4.86261			−0.169090			−0.0845448	+	0.996420i	$0.526944\pi$
$828$	−9.00905	+	29.3465i	−0.313086	+	1.01986i
$829$	20.3926	−	35.3211i	0.708266	−	1.22675i	−0.257234	−	0.966349i	$-0.582811\pi$
$829$	20.3926	−	35.3211i	0.708266	−	1.22675i	0.965500	−	0.260403i	$-0.0838555\pi$
$830$	13.7680			0.477896
$831$	11.8325	+	5.15302i	0.410466	+	0.178756i
$832$	6.74003	−	11.6741i	0.233668	−	0.404725i
$833$	−0.372159	−	10.8361i	−0.0128946	−	0.375449i
$834$	0.271315	+	2.39354i	0.00939486	+	0.0828815i
$835$	2.35247	−	4.07460i	0.0814107	−	0.141007i
$836$	−2.63362	+	4.56156i	−0.0910856	+	0.157765i
$837$	13.0110	−	15.1808i	0.449727	−	0.524726i
$838$	−23.1823	−	40.1529i	−0.800818	−	1.38706i
$839$	9.60171	+	16.6307i	0.331488	+	0.574154i	0.982804	−	0.184653i	$-0.0591161\pi$
$839$	9.60171	+	16.6307i	0.331488	+	0.574154i	−0.651316	+	0.758807i	$0.725783\pi$
$840$	6.80849	+	0.902334i	0.234915	+	0.0311335i
$841$	14.4981	−	25.1114i	0.499934	−	0.865911i
$842$	−54.6126			−1.88207
$843$	5.06976	+	44.7255i	0.174612	+	1.54043i
$844$	7.90225			0.272007
$845$	−9.20374	−	15.9413i	−0.316618	−	0.548399i
$846$	15.4300	−	50.2625i	0.530496	−	1.72806i
$847$	22.1556	−	6.34612i	0.761276	−	0.218055i
$848$	−3.66188	−	6.34256i	−0.125749	−	0.217804i
$849$	3.65886	+	32.2785i	0.125572	+	1.10780i
$850$	4.58940	+	7.94907i	0.157415	+	0.272651i
$851$	2.07286	+	3.59029i	0.0710566	+	0.123074i
$852$	−3.34398	−	29.5006i	−0.114563	−	1.01068i
$853$	−6.95055	−	12.0387i	−0.237982	−	0.412198i	0.722153	−	0.691734i	$-0.243153\pi$
$853$	−6.95055	−	12.0387i	−0.237982	−	0.412198i	−0.960135	+	0.279536i	$0.909819\pi$
$854$	−11.3477	−	10.9646i	−0.388309	−	0.375202i
$855$	2.94280	−	9.58601i	0.100642	−	0.327835i
$856$	3.24469	+	5.61996i	0.110901	+	0.192086i
$857$	56.9838			1.94653			0.973265	−	0.229686i	$-0.0737700\pi$
$857$	56.9838			1.94653			0.973265	+	0.229686i	$0.0737700\pi$
$858$	−2.81299	−	24.8163i	−0.0960340	−	0.847213i
$859$	−20.1002			−0.685810			−0.342905	−	0.939370i	$-0.611411\pi$
$859$	−20.1002			−0.685810			−0.342905	+	0.939370i	$0.611411\pi$
$860$	9.46298	−	16.3904i	0.322685	−	0.558907i
$861$	25.2019	−	32.7851i	0.858877	−	1.11731i
$862$	−4.50214	−	7.79794i	−0.153344	−	0.265599i
$863$	−3.08893	−	5.35018i	−0.105148	−	0.182122i	0.808650	−	0.588289i	$-0.200198\pi$
$863$	−3.08893	−	5.35018i	−0.105148	−	0.182122i	−0.913799	+	0.406167i	$0.866865\pi$
$864$	−22.5888	+	26.3558i	−0.768486	+	0.896643i
$865$	−6.76781	+	11.7222i	−0.230112	+	0.398566i
$866$	8.94318	−	15.4900i	0.303902	−	0.526373i
$867$	−2.84838	−	25.1285i	−0.0967361	−	0.853407i
$868$	−3.42769	+	13.7309i	−0.116343	+	0.466056i
$869$	4.47806	−	7.75623i	0.151908	−	0.263112i
$870$	0.241742	+	0.105278i	0.00819581	+	0.00356925i
$871$	35.8872			1.21599
$872$	−4.62732	+	8.01476i	−0.156701	+	0.271414i
$873$	10.7360	−	34.9720i	0.363359	−	1.18362i
$874$	33.9396			1.14802
$875$	27.9008	−	7.99173i	0.943219	−	0.270170i
$876$	−6.09009	−	2.65221i	−0.205765	−	0.0896099i
$877$	−37.2574			−1.25809			−0.629046	−	0.777368i	$-0.716554\pi$
$877$	−37.2574			−1.25809			−0.629046	+	0.777368i	$0.716554\pi$
$878$	−13.6468	−	23.6370i	−0.460558	−	0.797710i
$879$	3.42905	−	2.53431i	0.115659	−	0.0854801i
$880$	4.89504	−	8.47846i	0.165012	−	0.285809i
$881$	−11.7848			−0.397041			−0.198520	−	0.980097i	$-0.563614\pi$
$881$	−11.7848			−0.397041			−0.198520	+	0.980097i	$0.563614\pi$
$882$	27.3882	−	27.2938i	0.922208	−	0.919030i
$883$	−29.2308			−0.983693			−0.491847	−	0.870682i	$-0.663678\pi$
$883$	−29.2308			−0.983693			−0.491847	+	0.870682i	$0.663678\pi$
$884$	5.57265	−	9.65211i	0.187428	−	0.324636i
$885$	−2.19854	−	19.3956i	−0.0739032	−	0.651974i
$886$	−20.1634	−	34.9240i	−0.677402	−	1.17329i
$887$	28.5161			0.957479			0.478739	−	0.877957i	$-0.341094\pi$
$887$	28.5161			0.957479			0.478739	+	0.877957i	$0.341094\pi$
$888$	0.123372	+	1.08839i	0.00414010	+	0.0365240i
$889$	−21.6196	+	6.19258i	−0.725098	+	0.207693i
$890$	3.45680			0.115872
$891$	−0.981141	+	13.5818i	−0.0328695	+	0.455006i
$892$	8.14822	−	14.1131i	0.272823	−	0.472543i
$893$	−23.8364			−0.797656
$894$	−16.8884	+	12.4818i	−0.564834	+	0.417453i
$895$	1.13531	−	1.96642i	0.0379493	−	0.0657301i
$896$	−5.48862	+	21.9867i	−0.183362	+	0.734524i
$897$	−53.0691	+	39.2219i	−1.77193	+	1.30958i
$898$	19.7890	−	34.2755i	0.660366	−	1.14379i
$899$	0.119171	−	0.206410i	0.00397456	−	0.00688414i
$900$	−3.93912	+	12.8315i	−0.131304	+	0.427715i
$901$	−1.17002	−	2.02653i	−0.0389790	−	0.0675135i
$902$	−12.5693	−	21.7707i	−0.418513	−	0.724885i
$903$	17.8498	+	43.1986i	0.594004	+	1.43756i
$904$	8.14183	−	14.1021i	0.270793	−	0.469028i
$905$	−22.6829			−0.754006
$906$	−32.4872	+	24.0104i	−1.07931	+	0.797690i
$907$	−7.89155			−0.262035			−0.131017	−	0.991380i	$-0.541824\pi$
$907$	−7.89155			−0.262035			−0.131017	+	0.991380i	$0.541824\pi$
$908$	−7.77317	−	13.4635i	−0.257962	−	0.446803i
$909$	2.28597	+	2.45707i	0.0758209	+	0.0814957i
$910$	−24.2029	−	23.3860i	−0.802319	−	0.775237i
$911$	−14.2206	−	24.6308i	−0.471150	−	0.816055i	0.528306	−	0.849054i	$-0.322827\pi$
$911$	−14.2206	−	24.6308i	−0.471150	−	0.816055i	−0.999455	+	0.0329991i	$0.989494\pi$
$912$	19.2781	+	8.39554i	0.638361	+	0.278004i
$913$	4.23813	+	7.34065i	0.140262	+	0.242940i
$914$	37.4007	+	64.7798i	1.23710	+	2.14273i
$915$	6.02225	−	4.45087i	0.199089	−	0.147141i
$916$	6.71206	+	11.6256i	0.221773	+	0.384121i
$917$	5.12118	−	1.46688i	0.169116	−	0.0484406i
$918$	−9.64370	+	11.2519i	−0.318290	+	0.371369i
$919$	3.99271	+	6.91558i	0.131707	+	0.228124i	0.924335	−	0.381582i	$-0.124621\pi$
$919$	3.99271	+	6.91558i	0.131707	+	0.228124i	−0.792627	+	0.609706i	$0.791287\pi$
$920$	−11.0318			−0.363708
$921$	7.40446	+	3.22462i	0.243985	+	0.106255i
$922$	5.21221			0.171655
$923$	31.9110	−	55.2714i	1.05036	−	1.81928i
$924$	−3.68090	−	8.90821i	−0.121093	−	0.293059i
$925$	0.906337	+	1.56982i	0.0298002	+	0.0516154i
$926$	25.6529	+	44.4322i	0.843008	+	1.46013i
$927$	3.94481	+	4.24006i	0.129565	+	0.139262i
$928$	−0.206895	+	0.358353i	−0.00679167	+	0.0117635i
$929$	−9.40031	+	16.2818i	−0.308414	+	0.534189i	−0.978016	−	0.208531i	$-0.933132\pi$
$929$	−9.40031	+	16.2818i	−0.308414	+	0.534189i	0.669601	+	0.742721i	$0.266465\pi$
$930$	−15.0166	−	6.53966i	−0.492412	−	0.214444i
$931$	−15.4729	−	8.23853i	−0.507104	−	0.270007i
$932$	−13.4081	+	23.2234i	−0.439196	+	0.760709i
$933$	5.36130	+	47.2974i	0.175521	+	1.54845i
$934$	−49.0577			−1.60522
$935$	1.56403	−	2.70898i	0.0511493	−	0.0885932i
$936$	−16.9932	+	3.90260i	−0.555440	+	0.127561i
$937$	48.5788			1.58700			0.793500	−	0.608570i	$-0.208256\pi$
$937$	48.5788			1.58700			0.793500	+	0.608570i	$0.208256\pi$
$938$	32.4700	−	9.30052i	1.06018	−	0.303673i
$939$	7.65172	−	5.65516i	0.249704	−	0.184549i
$940$	−17.6619			−0.576067
$941$	−10.2425	−	17.7406i	−0.333898	−	0.578328i	0.649375	−	0.760468i	$-0.275031\pi$
$941$	−10.2425	−	17.7406i	−0.333898	−	0.578328i	−0.983272	+	0.182141i	$0.941697\pi$
$942$	−50.6049	−	22.0383i	−1.64880	−	0.718046i
$943$	−33.2110	+	57.5231i	−1.08150	+	1.87321i
$944$	40.9312			1.33220
$945$	10.6257	+	14.9603i	0.345654	+	0.486659i
$946$	28.4148			0.923843
$947$	7.42524	−	12.8609i	0.241288	−	0.417923i	−0.719793	−	0.694188i	$-0.755764\pi$
$947$	7.42524	−	12.8609i	0.241288	−	0.417923i	0.961081	+	0.276265i	$0.0890969\pi$
$948$	13.0675	+	5.69086i	0.424413	+	0.184831i
$949$	−7.13954	−	12.3661i	−0.231759	−	0.401419i
$950$	14.8398			0.481466
$951$	13.7586	−	10.1686i	0.446154	−	0.329739i
$952$	−1.11449	+	4.46451i	−0.0361209	+	0.144696i
$953$	46.4678			1.50524			0.752620	−	0.658456i	$-0.228790\pi$
$953$	46.4678			1.50524			0.752620	+	0.658456i	$0.228790\pi$
$954$	2.44901	−	7.97750i	0.0792896	−	0.258281i
$955$	−15.1454	+	26.2326i	−0.490094	+	0.848868i
$956$	0.541167			0.0175026
$957$	0.0182833	+	0.161295i	0.000591015	+	0.00521394i
$958$	−29.0724	+	50.3548i	−0.939285	+	1.62689i
$959$	−5.63988	+	1.61545i	−0.182121	+	0.0521657i
$960$	5.52012	+	2.40399i	0.178161	+	0.0775886i
$961$	8.09733	−	14.0250i	0.261204	−	0.452419i
$962$	2.68380	−	4.64847i	0.0865291	−	0.149873i
$963$	−5.08826	+	16.5747i	−0.163967	+	0.534112i
$964$	−7.39301	−	12.8051i	−0.238113	−	0.412423i
$965$	−4.12905	−	7.15172i	−0.132919	−	0.230222i
$966$	−37.8512	+	49.2406i	−1.21784	+	1.58429i
$967$	0.863670	−	1.49592i	0.0277738	−	0.0481056i	−0.851804	−	0.523860i	$-0.824492\pi$
$967$	0.863670	−	1.49592i	0.0277738	−	0.0481056i	0.879578	+	0.475754i	$0.157825\pi$
$968$	−9.78089			−0.314370
$969$	6.15960	+	2.68249i	0.197875	+	0.0861739i
$970$	−29.9687			−0.962235
$971$	−3.78085	−	6.54863i	−0.121333	−	0.210156i	0.798960	−	0.601384i	$-0.205384\pi$
$971$	−3.78085	−	6.54863i	−0.121333	−	0.210156i	−0.920294	+	0.391228i	$0.872050\pi$
$972$	−21.6526	+	0.882976i	−0.694506	+	0.0283215i
$973$	−0.484024	+	1.93894i	−0.0155171	+	0.0621595i
$974$	0.281870	+	0.488213i	0.00903169	+	0.0156434i
$975$	−23.2040	+	17.1494i	−0.743122	+	0.549220i
$976$	7.85137	+	13.5990i	0.251316	+	0.435293i
$977$	28.3101	+	49.0345i	0.905721	+	1.56875i	0.819947	+	0.572440i	$0.194003\pi$
$977$	28.3101	+	49.0345i	0.905721	+	1.56875i	0.0857737	+	0.996315i	$0.472664\pi$
$978$	−35.7277	−	15.5593i	−1.14245	−	0.497531i
$979$	1.06408	+	1.84305i	0.0340083	+	0.0589041i
$980$	−11.4648	−	6.10443i	−0.366231	−	0.194999i
$981$	−24.0990	+	5.53449i	−0.769422	+	0.176703i
$982$	16.6997	+	28.9247i	0.532909	+	0.923025i
$983$	32.2972			1.03012			0.515061	−	0.857154i	$-0.327769\pi$
$983$	32.2972			1.03012			0.515061	+	0.857154i	$0.327769\pi$
$984$	−14.1134	+	10.4308i	−0.449920	+	0.332523i
$985$	13.0407			0.415510
$986$	−0.0883286	+	0.152990i	−0.00281296	+	0.00487218i
$987$	26.5836	−	34.5826i	0.846165	−	1.10078i
$988$	−9.00955	−	15.6050i	−0.286632	−	0.496461i
$989$	−37.5391	−	65.0197i	−1.19367	−	2.06750i
$990$	10.8721	−	2.49686i	0.345540	−	0.0793554i
$991$	−7.15502	+	12.3929i	−0.227287	+	0.393672i	−0.957003	−	0.290078i	$-0.906319\pi$
$991$	−7.15502	+	12.3929i	−0.227287	+	0.393672i	0.729716	+	0.683750i	$0.239652\pi$
$992$	12.8520	−	22.2602i	0.408050	−	0.706764i
$993$	−28.8253	+	21.3039i	−0.914742	+	0.676059i
$994$	14.5483	−	58.2785i	0.461444	−	1.84848i
$995$	−5.79247	+	10.0329i	−0.183634	+	0.318063i
$996$	−10.8480	+	8.01748i	−0.343734	+	0.254044i
$997$	56.2524			1.78153			0.890765	−	0.454463i	$-0.150169\pi$
$997$	56.2524			1.78153			0.890765	+	0.454463i	$0.150169\pi$
$998$	−19.6176	+	33.9787i	−0.620985	+	1.07558i
$999$	−1.90449	+	2.22209i	−0.0602553	+	0.0703038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.g.b.4.4	✓	10
3.2	odd	2		189.2.g.b.172.2		10
4.3	odd	2		1008.2.t.i.193.5		10
7.2	even	3		63.2.h.b.58.2	yes	10
7.3	odd	6		441.2.f.f.148.4		10
7.4	even	3		441.2.f.e.148.4		10
7.5	odd	6		441.2.h.f.373.2		10
7.6	odd	2		441.2.g.f.67.4		10
9.2	odd	6		189.2.h.b.46.4		10
9.4	even	3		567.2.e.f.487.4		10
9.5	odd	6		567.2.e.e.487.2		10
9.7	even	3		63.2.h.b.25.2	yes	10
12.11	even	2		3024.2.t.i.1873.2		10
21.2	odd	6		189.2.h.b.37.4		10
21.5	even	6		1323.2.h.f.226.4		10
21.11	odd	6		1323.2.f.e.442.2		10
21.17	even	6		1323.2.f.f.442.2		10
21.20	even	2		1323.2.g.f.361.2		10
28.23	odd	6		1008.2.q.i.625.2		10
36.7	odd	6		1008.2.q.i.529.2		10
36.11	even	6		3024.2.q.i.2881.4		10
63.2	odd	6		189.2.g.b.100.2		10
63.4	even	3		3969.2.a.z.1.2		5
63.11	odd	6		1323.2.f.e.883.2		10
63.16	even	3	inner	63.2.g.b.16.4	yes	10
63.20	even	6		1323.2.h.f.802.4		10
63.23	odd	6		567.2.e.e.163.2		10
63.25	even	3		441.2.f.e.295.4		10
63.31	odd	6		3969.2.a.ba.1.2		5
63.32	odd	6		3969.2.a.bc.1.4		5
63.34	odd	6		441.2.h.f.214.2		10
63.38	even	6		1323.2.f.f.883.2		10
63.47	even	6		1323.2.g.f.667.2		10
63.52	odd	6		441.2.f.f.295.4		10
63.58	even	3		567.2.e.f.163.4		10
63.59	even	6		3969.2.a.bb.1.4		5
63.61	odd	6		441.2.g.f.79.4		10
84.23	even	6		3024.2.q.i.2305.4		10
252.79	odd	6		1008.2.t.i.961.5		10
252.191	even	6		3024.2.t.i.289.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	1.1	even	1	trivial
63.2.g.b.16.4	yes	10	63.16	even	3	inner
63.2.h.b.25.2	yes	10	9.7	even	3
63.2.h.b.58.2	yes	10	7.2	even	3
189.2.g.b.100.2		10	63.2	odd	6
189.2.g.b.172.2		10	3.2	odd	2
189.2.h.b.37.4		10	21.2	odd	6
189.2.h.b.46.4		10	9.2	odd	6
441.2.f.e.148.4		10	7.4	even	3
441.2.f.e.295.4		10	63.25	even	3
441.2.f.f.148.4		10	7.3	odd	6
441.2.f.f.295.4		10	63.52	odd	6
441.2.g.f.67.4		10	7.6	odd	2
441.2.g.f.79.4		10	63.61	odd	6
441.2.h.f.214.2		10	63.34	odd	6
441.2.h.f.373.2		10	7.5	odd	6
567.2.e.e.163.2		10	63.23	odd	6
567.2.e.e.487.2		10	9.5	odd	6
567.2.e.f.163.4		10	63.58	even	3
567.2.e.f.487.4		10	9.4	even	3
1008.2.q.i.529.2		10	36.7	odd	6
1008.2.q.i.625.2		10	28.23	odd	6
1008.2.t.i.193.5		10	4.3	odd	2
1008.2.t.i.961.5		10	252.79	odd	6
1323.2.f.e.442.2		10	21.11	odd	6
1323.2.f.e.883.2		10	63.11	odd	6
1323.2.f.f.442.2		10	21.17	even	6
1323.2.f.f.883.2		10	63.38	even	6
1323.2.g.f.361.2		10	21.20	even	2
1323.2.g.f.667.2		10	63.47	even	6
1323.2.h.f.226.4		10	21.5	even	6
1323.2.h.f.802.4		10	63.20	even	6
3024.2.q.i.2305.4		10	84.23	even	6
3024.2.q.i.2881.4		10	36.11	even	6
3024.2.t.i.289.2		10	252.191	even	6
3024.2.t.i.1873.2		10	12.11	even	2
3969.2.a.z.1.2		5	63.4	even	3
3969.2.a.ba.1.2		5	63.31	odd	6
3969.2.a.bb.1.4		5	63.59	even	6
3969.2.a.bc.1.4		5	63.32	odd	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.920620 - 1.59456i) q^{2} +(-1.58800 - 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} +1.33475 q^{5} +(-2.56469 + 1.89549i) q^{6} +(-2.54347 + 0.728536i) q^{7} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +(1.22880 - 2.12835i) q^{10} +1.51302 q^{11} +(0.271199 + 2.39252i) q^{12} +(-2.58800 + 4.48254i) q^{13} +(-1.17987 + 4.72642i) q^{14} +(-2.11958 - 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} +(0.774463 - 1.34141i) q^{17} +(5.38358 - 1.23637i) q^{18} +(-1.25211 - 2.16872i) q^{19} +(-0.927765 - 1.60694i) q^{20} +(4.54285 + 0.602068i) q^{21} +(1.39291 - 2.41260i) q^{22} -7.36079 q^{23} +(-1.78308 - 0.776526i) q^{24} -3.21843 q^{25} +(4.76513 + 8.25344i) q^{26} +(-1.72605 - 4.90110i) q^{27} +(2.64502 + 2.55574i) q^{28} +(-0.0309713 - 0.0536439i) q^{29} +(-3.42323 + 2.53001i) q^{30} +(1.92388 + 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(-2.40267 - 1.04635i) q^{33} +(-1.42597 - 2.46986i) q^{34} +(-3.39490 + 0.972416i) q^{35} +(1.22392 - 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} -4.61087 q^{38} +(7.20971 - 5.32849i) q^{39} +1.49873 q^{40} +(4.51188 - 7.81481i) q^{41} +(5.14228 - 6.68958i) q^{42} +(5.09988 + 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(2.72753 + 2.93167i) q^{45} +(-6.77649 + 11.7372i) q^{46} +(4.75925 - 8.24327i) q^{47} +(-6.75252 + 4.99060i) q^{48} +(5.93847 - 3.70602i) q^{49} +(-2.96296 + 5.13199i) q^{50} +(-2.15752 + 1.59456i) q^{51} +7.19550 q^{52} +(0.755374 - 1.30835i) q^{53} +(-9.40414 - 1.75975i) q^{54} +2.01950 q^{55} +(-2.85593 + 0.818036i) q^{56} +(0.488532 + 4.30983i) q^{57} -0.114051 q^{58} +(4.22166 + 7.31212i) q^{59} +(0.361984 + 3.19342i) q^{60} +(-1.61958 + 2.80520i) q^{61} +7.08467 q^{62} +(-6.79767 - 4.09777i) q^{63} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(-3.88042 + 2.86790i) q^{66} +(-3.46670 - 6.00449i) q^{67} -2.15327 q^{68} +(11.6889 + 5.09048i) q^{69} +(-1.57484 + 6.30861i) q^{70} -12.3304 q^{71} +(2.29451 + 2.46624i) q^{72} +(-1.37936 + 2.38912i) q^{73} -1.03702 q^{74} +(5.11086 + 2.22576i) q^{75} +(-1.74064 + 3.01488i) q^{76} +(-3.84831 + 1.10229i) q^{77} +(-1.85920 - 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} +(3.23529 - 5.60368i) q^{80} +(-0.648467 + 8.97661i) q^{81} +(-8.30746 - 14.3889i) q^{82} +(2.80111 + 4.85167i) q^{83} +(-2.43282 - 5.88772i) q^{84} +(1.03372 - 1.79045i) q^{85} +18.7802 q^{86} +(0.0120840 + 0.106605i) q^{87} +1.69889 q^{88} +(0.703287 + 1.21813i) q^{89} +(7.18575 - 1.65025i) q^{90} +(3.31680 - 13.2867i) q^{91} +(5.11636 + 8.86180i) q^{92} +(-0.750637 - 6.62212i) q^{93} +(-8.76293 - 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(1.30320 + 11.4968i) q^{96} +(-6.09713 - 10.5605i) q^{97} +(-0.442393 - 12.8811i) q^{98} +(3.09180 + 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} - 2 q^{6} - q^{7} - 6 q^{8} - 4 q^{9} - 7 q^{10} - 8 q^{11} + 22 q^{12} - 8 q^{13} + 16 q^{14} - 19 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + q^{19} + 5 q^{20}+ \cdots + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 - 2 * q^6 - q^7 - 6 * q^8 - 4 * q^9 - 7 * q^10 - 8 * q^11 + 22 * q^12 - 8 * q^13 + 16 * q^14 - 19 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 + q^19 + 5 * q^20 - 2 * q^21 - q^22 - 6 * q^23 + 3 * q^24 + 2 * q^25 + 11 * q^26 - 7 * q^27 - 2 * q^28 + 7 * q^29 - 26 * q^30 - 3 * q^31 - 2 * q^32 - q^33 + 3 * q^34 + 5 * q^35 + 34 * q^36 - 40 * q^38 + 20 * q^39 + 6 * q^40 + 5 * q^41 + 32 * q^42 - 7 * q^43 - 10 * q^44 - q^45 + 3 * q^46 + 27 * q^47 - 5 * q^48 + 25 * q^49 + 19 * q^50 + 24 * q^51 + 20 * q^52 - 21 * q^53 - 53 * q^54 + 4 * q^55 - 45 * q^56 - 4 * q^57 + 20 * q^58 + 30 * q^59 - 41 * q^60 - 14 * q^61 - 12 * q^62 - 35 * q^63 - 50 * q^64 - 11 * q^65 - 41 * q^66 - 2 * q^67 - 54 * q^68 + 15 * q^69 - 29 * q^70 - 6 * q^71 + 48 * q^72 + 15 * q^73 + 72 * q^74 + 31 * q^75 + 5 * q^76 - 31 * q^77 - 20 * q^78 - 4 * q^79 + 20 * q^80 + 8 * q^81 - 5 * q^82 + 9 * q^83 + 2 * q^84 - 6 * q^85 + 16 * q^86 + 32 * q^87 + 36 * q^88 + 28 * q^89 + 28 * q^90 - 4 * q^91 + 27 * q^92 - 12 * q^93 - 3 * q^94 - 14 * q^95 - q^96 - 12 * q^97 + 59 * q^98 + 35 * q^99

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