LMFDB - Embedded newform 161.2.g.a.45.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(45,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("161.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	161.g (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:	$1.28559147254$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.6
Character	$\chi$	$=$	161.45
Dual form			161.2.g.a.68.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.559952 - 0.969865i) q^{2} +(2.13402 + 1.23207i) q^{3} +(0.372908 - 0.645896i) q^{4} +(0.871219 + 1.50900i) q^{5} -2.75961i q^{6} +(0.785854 + 2.52635i) q^{7} -3.07505 q^{8} +(1.53601 + 2.66045i) q^{9} +(0.975681 - 1.68993i) q^{10} +(-4.42148 - 2.55274i) q^{11} +(1.59158 - 0.918902i) q^{12} +1.11431i q^{13} +(2.01018 - 2.17680i) q^{14} +4.29363i q^{15} +(0.976062 + 1.69059i) q^{16} +(1.62545 - 2.81536i) q^{17} +(1.72019 - 2.97945i) q^{18} +(-2.74008 - 4.74595i) q^{19} +1.29954 q^{20} +(-1.43562 + 6.35949i) q^{21} +5.71765i q^{22} +(2.81760 - 3.88086i) q^{23} +(-6.56220 - 3.78869i) q^{24} +(0.981954 - 1.70079i) q^{25} +(1.08073 - 0.623958i) q^{26} +0.177486i q^{27} +(1.92481 + 0.434516i) q^{28} -6.58548 q^{29} +(4.16424 - 2.40422i) q^{30} +(4.15841 + 2.40086i) q^{31} +(-1.98195 + 3.43285i) q^{32} +(-6.29034 - 10.8952i) q^{33} -3.64070 q^{34} +(-3.12760 + 3.38685i) q^{35} +2.29117 q^{36} +(-1.07366 + 0.619878i) q^{37} +(-3.06862 + 5.31501i) q^{38} +(-1.37291 + 2.37795i) q^{39} +(-2.67904 - 4.64024i) q^{40} +10.3638i q^{41} +(6.97173 - 2.16865i) q^{42} +7.76041i q^{43} +(-3.29761 + 1.90388i) q^{44} +(-2.67641 + 4.63568i) q^{45} +(-5.34163 - 0.559600i) q^{46} +(1.68406 - 0.972293i) q^{47} +4.81032i q^{48} +(-5.76487 + 3.97068i) q^{49} -2.19939 q^{50} +(6.93747 - 4.00535i) q^{51} +(0.719726 + 0.415534i) q^{52} +(-0.912184 - 0.526650i) q^{53} +(0.172137 - 0.0993835i) q^{54} -8.89600i q^{55} +(-2.41654 - 7.76864i) q^{56} -13.5039i q^{57} +(3.68755 + 6.38702i) q^{58} +(-6.93249 - 4.00248i) q^{59} +(2.77324 + 1.60113i) q^{60} +(3.59197 + 6.22148i) q^{61} -5.37746i q^{62} +(-5.51415 + 5.97123i) q^{63} +8.34344 q^{64} +(-1.68148 + 0.970805i) q^{65} +(-7.04457 + 12.2016i) q^{66} +(7.28297 + 4.20483i) q^{67} +(-1.21229 - 2.09975i) q^{68} +(10.7943 - 4.81032i) q^{69} +(5.03609 + 1.13687i) q^{70} +1.68123 q^{71} +(-4.72332 - 8.18103i) q^{72} +(5.01153 + 2.89341i) q^{73} +(1.20240 + 0.694204i) q^{74} +(4.19101 - 2.41968i) q^{75} -4.08719 q^{76} +(2.97448 - 13.1763i) q^{77} +3.07505 q^{78} +(9.52692 - 5.50037i) q^{79} +(-1.70073 + 2.94575i) q^{80} +(4.38937 - 7.60260i) q^{81} +(10.0515 - 5.80323i) q^{82} -11.4081 q^{83} +(3.57222 + 3.29877i) q^{84} +5.66450 q^{85} +(7.52655 - 4.34545i) q^{86} +(-14.0535 - 8.11380i) q^{87} +(13.5963 + 7.84981i) q^{88} +(5.34121 + 9.25124i) q^{89} +5.99464 q^{90} +(-2.81513 + 0.875682i) q^{91} +(-1.45593 - 3.26709i) q^{92} +(5.91608 + 10.2469i) q^{93} +(-1.88599 - 1.08887i) q^{94} +(4.77441 - 8.26953i) q^{95} +(-8.45904 + 4.88383i) q^{96} -12.4301 q^{97} +(7.07907 + 3.36775i) q^{98} -15.6842i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) $ 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.559952	−	0.969865i	−0.395946	−	0.685798i	0.597276	−	0.802036i	$-0.296250\pi$
$2$	−0.559952	−	0.969865i	−0.395946	−	0.685798i	−0.993221	+	0.116238i	$0.962916\pi$
$3$	2.13402	+	1.23207i	1.23207	+	0.711338i	0.967462	−	0.253017i	$-0.0814227\pi$
$3$	2.13402	+	1.23207i	1.23207	+	0.711338i	0.264612	+	0.964355i	$0.414756\pi$
$4$	0.372908	−	0.645896i	0.186454	−	0.322948i
$5$	0.871219	+	1.50900i	0.389621	+	0.674844i	0.992399	−	0.123066i	$-0.0392726\pi$
$5$	0.871219	+	1.50900i	0.389621	+	0.674844i	−0.602777	+	0.797909i	$0.705939\pi$
$6$		−	2.75961i		−	1.12661i
$7$	0.785854	+	2.52635i	0.297025	+	0.954870i
$7$	0.785854	+	2.52635i	0.297025	+	0.954870i
$8$	−3.07505			−1.08719
$9$	1.53601	+	2.66045i	0.512005	+	0.886818i
$10$	0.975681	−	1.68993i	0.308538	−	0.534403i
$11$	−4.42148	−	2.55274i	−1.33313	−	0.769681i	−0.347349	−	0.937736i	$-0.612918\pi$
$11$	−4.42148	−	2.55274i	−1.33313	−	0.769681i	−0.985778	+	0.168055i	$0.946251\pi$
$12$	1.59158	−	0.918902i	0.459451	−	0.265264i
$13$			1.11431i			0.309053i	0.987989	+	0.154527i	$0.0493852\pi$
$13$			1.11431i			0.309053i	−0.987989	+	0.154527i	$0.950615\pi$
$14$	2.01018	−	2.17680i	0.537242	−	0.581775i
$15$			4.29363i			1.10861i
$16$	0.976062	+	1.69059i	0.244016	+	0.422647i
$17$	1.62545	−	2.81536i	0.394230	−	0.682826i	−0.598773	−	0.800919i	$-0.704345\pi$
$17$	1.62545	−	2.81536i	0.394230	−	0.682826i	0.993003	+	0.118093i	$0.0376781\pi$
$18$	1.72019	−	2.97945i	0.405452	−	0.702263i
$19$	−2.74008	−	4.74595i	−0.628617	−	1.08880i	−0.987830	−	0.155540i	$-0.950288\pi$
$19$	−2.74008	−	4.74595i	−0.628617	−	1.08880i	0.359213	−	0.933256i	$-0.383045\pi$
$20$	1.29954			0.290586
$21$	−1.43562	+	6.35949i	−0.313279	+	1.38776i
$22$			5.71765i			1.21901i
$23$	2.81760	−	3.88086i	0.587511	−	0.809216i
$23$	2.81760	−	3.88086i	0.587511	−	0.809216i
$24$	−6.56220	−	3.78869i	−1.33950	−	0.773363i
$25$	0.981954	−	1.70079i	0.196391	−	0.340159i
$26$	1.08073	−	0.623958i	0.211948	−	0.122368i
$27$			0.177486i			0.0341572i
$28$	1.92481	+	0.434516i	0.363755	+	0.0821158i
$29$	−6.58548			−1.22289			−0.611446	−	0.791286i	$-0.709412\pi$
$29$	−6.58548			−1.22289			−0.611446	+	0.791286i	$0.709412\pi$
$30$	4.16424	−	2.40422i	0.760282	−	0.438949i
$31$	4.15841	+	2.40086i	0.746873	+	0.431207i	0.824563	−	0.565770i	$-0.191421\pi$
$31$	4.15841	+	2.40086i	0.746873	+	0.431207i	−0.0776899	+	0.996978i	$0.524754\pi$
$32$	−1.98195	+	3.43285i	−0.350363	+	0.606847i
$33$	−6.29034	−	10.8952i	−1.09501	−	1.89661i
$34$	−3.64070			−0.624374
$35$	−3.12760	+	3.38685i	−0.528661	+	0.572483i
$36$	2.29117			0.381862
$37$	−1.07366	+	0.619878i	−0.176509	+	0.101907i	−0.585651	−	0.810563i	$-0.699161\pi$
$37$	−1.07366	+	0.619878i	−0.176509	+	0.101907i	0.409143	+	0.912470i	$0.365828\pi$
$38$	−3.06862	+	5.31501i	−0.497796	+	0.862208i
$39$	−1.37291	+	2.37795i	−0.219841	+	0.380776i
$40$	−2.67904	−	4.64024i	−0.423594	−	0.733686i
$41$			10.3638i			1.61856i	0.587426	+	0.809278i	$0.300141\pi$
$41$			10.3638i			1.61856i	−0.587426	+	0.809278i	$0.699859\pi$
$42$	6.97173	−	2.16865i	1.07576	−	0.334630i
$43$			7.76041i			1.18345i	0.806139	+	0.591726i	$0.201553\pi$
$43$			7.76041i			1.18345i	−0.806139	+	0.591726i	$0.798447\pi$
$44$	−3.29761	+	1.90388i	−0.497134	+	0.287020i
$45$	−2.67641	+	4.63568i	−0.398976	+	0.691046i
$46$	−5.34163	−	0.559600i	−0.787581	−	0.0825085i
$47$	1.68406	−	0.972293i	0.245646	−	0.141824i	−0.372123	−	0.928183i	$-0.621370\pi$
$47$	1.68406	−	0.972293i	0.245646	−	0.141824i	0.617769	+	0.786360i	$0.288037\pi$
$48$			4.81032i			0.694310i
$49$	−5.76487	+	3.97068i	−0.823552	+	0.567240i
$50$	−2.19939			−0.311040
$51$	6.93747	−	4.00535i	0.971441	−	0.560862i
$52$	0.719726	+	0.415534i	0.0998081	+	0.0576242i
$53$	−0.912184	−	0.526650i	−0.125298	−	0.0723409i	0.436041	−	0.899927i	$-0.356380\pi$
$53$	−0.912184	−	0.526650i	−0.125298	−	0.0723409i	−0.561339	+	0.827586i	$0.689714\pi$
$54$	0.172137	−	0.0993835i	0.0234249	−	0.0135244i
$55$		−	8.89600i		−	1.19954i
$56$	−2.41654	−	7.76864i	−0.322924	−	1.03813i
$57$		−	13.5039i		−	1.78864i
$58$	3.68755	+	6.38702i	0.484199	+	0.838657i
$59$	−6.93249	−	4.00248i	−0.902534	−	0.521078i	−0.0245125	−	0.999700i	$-0.507803\pi$
$59$	−6.93249	−	4.00248i	−0.902534	−	0.521078i	−0.878021	+	0.478621i	$0.841137\pi$
$60$	2.77324	+	1.60113i	0.358023	+	0.206705i
$61$	3.59197	+	6.22148i	0.459905	+	0.796579i	0.998955	−	0.0456948i	$-0.0145502\pi$
$61$	3.59197	+	6.22148i	0.459905	+	0.796579i	−0.539051	+	0.842273i	$0.681217\pi$
$62$		−	5.37746i		−	0.682939i
$63$	−5.51415	+	5.97123i	−0.694717	+	0.752305i
$64$	8.34344			1.04293
$65$	−1.68148	+	0.970805i	−0.208562	+	0.120414i
$66$	−7.04457	+	12.2016i	−0.867127	+	1.50191i
$67$	7.28297	+	4.20483i	0.889757	+	0.513701i	0.873863	−	0.486172i	$-0.161607\pi$
$67$	7.28297	+	4.20483i	0.889757	+	0.513701i	0.0158939	+	0.999874i	$0.494941\pi$
$68$	−1.21229	−	2.09975i	−0.147012	−	0.254632i
$69$	10.7943	−	4.81032i	1.29948	−	0.579095i
$70$	5.03609	+	1.13687i	0.601928	+	0.135882i
$71$	1.68123			0.199525			0.0997627	−	0.995011i	$-0.468192\pi$
$71$	1.68123			0.199525			0.0997627	+	0.995011i	$0.468192\pi$
$72$	−4.72332	−	8.18103i	−0.556648	−	0.964143i
$73$	5.01153	+	2.89341i	0.586555	+	0.338648i	0.763734	−	0.645531i	$-0.223364\pi$
$73$	5.01153	+	2.89341i	0.586555	+	0.338648i	−0.177179	+	0.984179i	$0.556697\pi$
$74$	1.20240	+	0.694204i	0.139776	+	0.0806995i
$75$	4.19101	−	2.41968i	0.483936	−	0.279401i
$76$	−4.08719			−0.468833
$77$	2.97448	−	13.1763i	0.338973	−	1.50158i
$78$	3.07505			0.348181
$79$	9.52692	−	5.50037i	1.07186	−	0.618840i	0.143172	−	0.989698i	$-0.454270\pi$
$79$	9.52692	−	5.50037i	1.07186	−	0.618840i	0.928690	+	0.370858i	$0.120936\pi$
$80$	−1.70073	+	2.94575i	−0.190147	+	0.329345i
$81$	4.38937	−	7.60260i	0.487707	−	0.844734i
$82$	10.0515	−	5.80323i	1.11000	−	0.640860i
$83$	−11.4081			−1.25220			−0.626102	−	0.779741i	$-0.715351\pi$
$83$	−11.4081			−1.25220			−0.626102	+	0.779741i	$0.715351\pi$
$84$	3.57222	+	3.29877i	0.389761	+	0.359926i
$85$	5.66450			0.614401
$86$	7.52655	−	4.34545i	0.811608	−	0.468582i
$87$	−14.0535	−	8.11380i	−1.50669	−	0.869890i
$88$	13.5963	+	7.84981i	1.44937	+	0.836793i
$89$	5.34121	+	9.25124i	0.566167	+	0.980630i	0.996940	+	0.0781697i	$0.0249076\pi$
$89$	5.34121	+	9.25124i	0.566167	+	0.980630i	−0.430773	+	0.902460i	$0.641759\pi$
$90$	5.99464			0.631890
$91$	−2.81513	+	0.875682i	−0.295105	+	0.0917964i
$92$	−1.45593	−	3.26709i	−0.151791	−	0.340617i
$93$	5.91608	+	10.2469i	0.613469	+	1.06256i
$94$	−1.88599	−	1.08887i	−0.194525	−	0.112309i
$95$	4.77441	−	8.26953i	0.489845	−	0.848436i
$96$	−8.45904	+	4.88383i	−0.863347	+	0.498454i
$97$	−12.4301			−1.26209			−0.631044	−	0.775747i	$-0.717373\pi$
$97$	−12.4301			−1.26209			−0.631044	+	0.775747i	$0.717373\pi$
$98$	7.07907	+	3.36775i	0.715094	+	0.340194i
$99$		−	15.6842i		−	1.57632i
$100$	−0.732358	−	1.26848i	−0.0732358	−	0.126848i
$101$	4.50785	+	2.60261i	0.448547	+	0.258969i	0.707217	−	0.706997i	$-0.249951\pi$
$101$	4.50785	+	2.60261i	0.448547	+	0.258969i	−0.258669	+	0.965966i	$0.583284\pi$
$102$	−7.76930	−	4.48561i	−0.769275	−	0.444141i
$103$	−1.32618	−	2.29701i	−0.130673	−	0.226332i	0.793263	−	0.608879i	$-0.208380\pi$
$103$	−1.32618	−	2.29701i	−0.130673	−	0.226332i	−0.923936	+	0.382547i	$0.875047\pi$
$104$		−	3.42655i		−	0.336001i
$105$	−10.8472	+	3.37416i	−1.05858	+	0.329285i
$106$			1.17959i			0.114572i
$107$	4.81118	−	2.77774i	0.465115	−	0.268534i	−0.249078	−	0.968484i	$-0.580127\pi$
$107$	4.81118	−	2.77774i	0.465115	−	0.268534i	0.714192	+	0.699949i	$0.246794\pi$
$108$	0.114637	+	0.0661860i	0.0110310	+	0.00636875i
$109$	−6.72175	−	3.88081i	−0.643827	−	0.371714i	0.142260	−	0.989829i	$-0.454563\pi$
$109$	−6.72175	−	3.88081i	−0.643827	−	0.371714i	−0.786087	+	0.618116i	$0.787896\pi$
$110$	−8.62791	+	4.98133i	−0.822639	+	0.474951i
$111$	−3.05494			−0.289962
$112$	−3.50397	+	3.79443i	−0.331094	+	0.358540i
$113$			16.8846i			1.58837i	0.607678	+	0.794184i	$0.292101\pi$
$113$			16.8846i			1.58837i	−0.607678	+	0.794184i	$0.707899\pi$
$114$	−13.0970	+	7.56154i	−1.22664	+	0.708203i
$115$	8.31096	+	0.870671i	0.775001	+	0.0811905i
$116$	−2.45578	+	4.25354i	−0.228013	+	0.394931i
$117$	−2.96456	+	1.71159i	−0.274074	+	0.158237i
$118$			8.96478i			0.825274i
$119$	8.38996	+	1.89399i	0.769106	+	0.173622i
$120$		−	13.2031i		−	1.20527i
$121$	7.53299	+	13.0475i	0.684818	+	1.18614i
$122$	4.02266	−	6.96745i	0.364195	−	0.630804i
$123$	−12.7690	+	22.1165i	−1.15134	+	1.99418i
$124$	3.10141	−	1.79060i	0.278515	−	0.160801i
$125$	12.1342			1.08531
$126$	8.87894	+	2.00438i	0.790999	+	0.178564i
$127$	−15.5472			−1.37959			−0.689794	−	0.724006i	$-0.742299\pi$
$127$	−15.5472			−1.37959			−0.689794	+	0.724006i	$0.742299\pi$
$128$	−0.708016	−	1.22632i	−0.0625803	−	0.108392i
$129$	−9.56140	+	16.5608i	−0.841834	+	1.45810i
$130$	1.88310	+	1.08721i	0.165159	+	0.0953545i
$131$	1.30919	−	0.755860i	0.114384	−	0.0660398i	−0.441716	−	0.897155i	$-0.645630\pi$
$131$	1.30919	−	0.755860i	0.114384	−	0.0660398i	0.556101	+	0.831115i	$0.312297\pi$
$132$	−9.38288			−0.816675
$133$	9.83662	−	10.6520i	0.852943	−	0.923646i
$134$		−	9.41800i		−	0.813591i
$135$	−0.267825	+	0.154629i	−0.0230507	+	0.0133084i
$136$	−4.99834	+	8.65738i	−0.428604	+	0.742364i
$137$	2.70304	+	1.56060i	0.230936	+	0.133331i	0.611004	−	0.791628i	$-0.290766\pi$
$137$	2.70304	+	1.56060i	0.230936	+	0.133331i	−0.380068	+	0.924959i	$0.624099\pi$
$138$	−10.7097	−	7.77548i	−0.911667	−	0.661893i
$139$		−	6.54112i		−	0.554810i	−0.960753	−	0.277405i	$-0.910526\pi$
$139$		−	6.54112i		−	0.554810i	0.960753	−	0.277405i	$-0.0894744\pi$
$140$	1.02125	+	3.28309i	0.0863112	+	0.277472i
$141$	4.79175			0.403538
$142$	−0.941408	−	1.63057i	−0.0790012	−	0.136834i
$143$	2.84454	−	4.92688i	0.237872	−	0.412007i
$144$	−2.99849	+	5.19354i	−0.249874	+	0.432795i
$145$	−5.73740	−	9.93746i	−0.476465	−	0.825261i
$146$		−	6.48068i		−	0.536345i
$147$	−17.1945	+	1.37075i	−1.41818	+	0.113057i
$148$			0.924631i			0.0760042i
$149$	−7.14812	+	4.12697i	−0.585596	+	0.338094i	−0.763354	−	0.645980i	$-0.776449\pi$
$149$	−7.14812	+	4.12697i	−0.585596	+	0.338094i	0.177758	+	0.984074i	$0.443116\pi$
$150$	−4.69353	−	2.70981i	−0.383225	−	0.221255i
$151$	−2.81705	+	4.87927i	−0.229248	+	0.397069i	−0.957585	−	0.288150i	$-0.906960\pi$
$151$	−2.81705	+	4.87927i	−0.229248	+	0.397069i	0.728338	+	0.685219i	$0.240293\pi$
$152$	8.42587	+	14.5940i	0.683428	+	1.18373i
$153$	9.98686			0.807390
$154$	−14.4448	+	4.49324i	−1.16399	+	0.362075i
$155$			8.36671i			0.672030i
$156$	1.02394	+	1.77351i	0.0819807	+	0.141995i
$157$	8.67502	−	15.0256i	0.692342	−	1.19917i	−0.278726	−	0.960371i	$-0.589912\pi$
$157$	8.67502	−	15.0256i	0.692342	−	1.19917i	0.971068	−	0.238801i	$-0.0767544\pi$
$158$	−10.6692	−	6.15988i	−0.848798	−	0.490054i
$159$	−1.29774	−	2.24776i	−0.102918	−	0.178259i
$160$	−6.90687			−0.546036
$161$	12.0186	+	4.06846i	0.947201	+	0.320639i
$162$	−9.83133			−0.772422
$163$	−11.4852	−	19.8929i	−0.899587	−	1.55813i	−0.828022	−	0.560695i	$-0.810534\pi$
$163$	−11.4852	−	19.8929i	−0.899587	−	1.55813i	−0.0715650	−	0.997436i	$-0.522799\pi$
$164$	6.69395	+	3.86475i	0.522709	+	0.301786i
$165$	10.9605	−	18.9842i	0.853276	−	1.47792i
$166$	6.38800	+	11.0643i	0.495805	+	0.858760i
$167$		−	16.1670i		−	1.25104i	−0.780207	−	0.625521i	$-0.784886\pi$
$167$		−	16.1670i		−	1.25104i	0.780207	−	0.625521i	$-0.215114\pi$
$168$	4.41461	−	19.5558i	0.340595	−	1.50876i
$169$	11.7583			0.904486
$170$	−3.17184	−	5.49380i	−0.243269	−	0.421355i
$171$	8.41759	−	14.5797i	0.643709	−	1.11494i
$172$	5.01242	+	2.89392i	0.382193	+	0.220659i
$173$	8.90587	−	5.14180i	0.677101	−	0.390924i	−0.121661	−	0.992572i	$-0.538822\pi$
$173$	8.90587	−	5.14180i	0.677101	−	0.390924i	0.798762	+	0.601648i	$0.205489\pi$
$174$			18.1733i			1.37772i
$175$	5.06847	+	1.14418i	0.383140	+	0.0864920i
$176$		−	9.96654i		−	0.751256i
$177$	−9.86270	−	17.0827i	−0.741326	−	1.28401i
$178$	5.98164	−	10.3605i	0.448343	−	0.776552i
$179$	0.227097	−	0.393343i	0.0169740	−	0.0293998i	−0.857414	−	0.514628i	$-0.827930\pi$
$179$	0.227097	−	0.393343i	0.0169740	−	0.0293998i	0.874388	+	0.485228i	$0.161263\pi$
$180$	1.99611	+	3.45737i	0.148781	+	0.257697i
$181$	−6.05005			−0.449696			−0.224848	−	0.974394i	$-0.572189\pi$
$181$	−6.05005			−0.449696			−0.224848	+	0.974394i	$0.572189\pi$
$182$	2.42563	+	2.23995i	0.179799	+	0.166036i
$183$			17.7023i			1.30859i
$184$	−8.66427	+	11.9338i	−0.638739	+	0.879775i
$185$	−1.87079	−	1.08010i	−0.137543	−	0.0794105i
$186$	6.62543	−	11.4756i	0.485800	−	0.841431i
$187$	−14.3738	+	8.29872i	−1.05112	+	0.606862i
$188$		−	1.45031i		−	0.105774i
$189$	−0.448391	+	0.139478i	−0.0326157	+	0.0101455i
$190$	−10.6938			−0.775807
$191$	−11.7229	+	6.76822i	−0.848239	+	0.489731i	−0.860056	−	0.510199i	$-0.829572\pi$
$191$	−11.7229	+	6.76822i	−0.848239	+	0.489731i	0.0118173	+	0.999930i	$0.496238\pi$
$192$	17.8050	+	10.2797i	1.28497	+	0.741876i
$193$	−4.28615	+	7.42383i	−0.308524	+	0.534379i	−0.978040	−	0.208419i	$-0.933168\pi$
$193$	−4.28615	+	7.42383i	−0.308524	+	0.534379i	0.669516	+	0.742798i	$0.266502\pi$
$194$	6.96027	+	12.0555i	0.499718	+	0.865537i
$195$	−4.78442			−0.342619
$196$	0.414881	+	5.20421i	0.0296343	+	0.371729i
$197$	18.8569			1.34349			0.671747	−	0.740780i	$-0.265544\pi$
$197$	18.8569			1.34349			0.671747	+	0.740780i	$0.265544\pi$
$198$	−15.2115	+	8.78239i	−1.08104	+	0.624137i
$199$	7.08374	−	12.2694i	0.502153	−	0.869754i	−0.497844	−	0.867267i	$-0.665875\pi$
$199$	7.08374	−	12.2694i	0.502153	−	0.869754i	0.999997	−	0.00248759i	$-0.000791825\pi$
$200$	−3.01956	+	5.23003i	−0.213515	+	0.369819i
$201$	10.3613	+	17.9463i	0.730831	+	1.26584i
$202$		−	5.82933i		−	0.410151i
$203$	−5.17522	−	16.6372i	−0.363230	−	1.16770i
$204$		−	5.97452i		−	0.418300i
$205$	−15.6389	+	9.02915i	−1.09227	+	0.630623i
$206$	−1.48520	+	2.57243i	−0.103478	+	0.179230i
$207$	14.6527	+	1.53505i	1.01844	+	0.106693i
$208$	−1.88383	+	1.08763i	−0.130620	+	0.0754137i
$209$			27.9788i			1.93534i
$210$	9.34639	+	8.63094i	0.644962	+	0.595592i
$211$	−28.9365			−1.99207			−0.996035	−	0.0889590i	$-0.971646\pi$
$211$	−28.9365			−1.99207			−0.996035	+	0.0889590i	$0.971646\pi$
$212$	−0.680322	+	0.392784i	−0.0467247	+	0.0269765i
$213$	3.58777	+	2.07140i	0.245830	+	0.141930i
$214$	−5.38806	−	3.11080i	−0.368320	−	0.212650i
$215$	−11.7104	+	6.76102i	−0.798644	+	0.461098i
$216$		−	0.545778i		−	0.0371355i
$217$	−2.79750	+	12.3923i	−0.189907	+	0.841246i
$218$			8.69225i			0.588714i
$219$	7.12979	+	12.3492i	0.481787	+	0.834479i
$220$	−5.74589	−	3.31739i	−0.387388	−	0.223658i
$221$	3.13718	+	1.81125i	0.211029	+	0.121838i
$222$	1.71062	+	2.96288i	0.114809	+	0.198856i
$223$			12.3905i			0.829731i	0.909883	+	0.414865i	$0.136171\pi$
$223$			12.3905i			0.829731i	−0.909883	+	0.414865i	$0.863829\pi$
$224$	−10.2301	−	2.30939i	−0.683526	−	0.154303i
$225$	6.03318			0.402212
$226$	16.3758	−	9.45455i	1.08930	−	0.628907i
$227$	14.4100	−	24.9589i	0.956429	−	1.65658i	0.225364	−	0.974275i	$-0.427643\pi$
$227$	14.4100	−	24.9589i	0.956429	−	1.65658i	0.731065	−	0.682308i	$-0.239024\pi$
$228$	−8.72212	−	5.03572i	−0.577637	−	0.333499i
$229$	−4.19814	−	7.27140i	−0.277421	−	0.480508i	0.693322	−	0.720628i	$-0.256146\pi$
$229$	−4.19814	−	7.27140i	−0.277421	−	0.480508i	−0.970743	+	0.240120i	$0.922813\pi$
$230$	−3.80930	−	8.54804i	−0.251178	−	0.563641i
$231$	22.5817	−	24.4536i	1.48577	−	1.60893i
$232$	20.2507			1.32952
$233$	−9.57955	−	16.5923i	−0.627577	−	1.08700i	−0.988036	−	0.154221i	$-0.950713\pi$
$233$	−9.57955	−	16.5923i	−0.627577	−	1.08700i	0.360459	−	0.932775i	$-0.382620\pi$
$234$	3.32002	+	1.91682i	0.217037	+	0.125306i
$235$	2.93437	+	1.69416i	0.191417	+	0.110515i
$236$	−5.17037	+	2.98511i	−0.336562	+	0.194314i
$237$	27.1074			1.76082
$238$	−2.86106	−	9.19766i	−0.185455	−	0.596196i
$239$	7.74090			0.500717			0.250359	−	0.968153i	$-0.419451\pi$
$239$	7.74090			0.500717			0.250359	+	0.968153i	$0.419451\pi$
$240$	−7.25876	+	4.19085i	−0.468551	+	0.270518i
$241$	−4.55513	+	7.88971i	−0.293422	+	0.508221i	−0.974616	−	0.223881i	$-0.928127\pi$
$241$	−4.55513	+	7.88971i	−0.293422	+	0.508221i	0.681195	+	0.732102i	$0.261461\pi$
$242$	8.43622	−	14.6120i	0.542301	−	0.939293i
$243$	19.1951	−	11.0823i	1.23136	−	0.710928i
$244$	5.35790			0.343005
$245$	−11.0142	−	5.23983i	−0.703672	−	0.334760i
$246$	28.6001			1.82347
$247$	5.28844	−	3.05328i	0.336496	−	0.194276i
$248$	−12.7873	−	7.38277i	−0.811996	−	0.468806i
$249$	−24.3451	−	14.0557i	−1.54281	−	0.890741i
$250$	−6.79455	−	11.7685i	−0.429725	−	0.744306i
$251$	−5.33922			−0.337009			−0.168504	−	0.985701i	$-0.553894\pi$
$251$	−5.33922			−0.337009			−0.168504	+	0.985701i	$0.553894\pi$
$252$	1.80052	+	5.78829i	0.113422	+	0.364628i
$253$	−22.3648	+	9.96654i	−1.40606	+	0.626591i
$254$	8.70566	+	15.0786i	0.546241	+	0.946118i
$255$	12.0881	+	6.97908i	0.756988	+	0.437047i
$256$	7.55053	−	13.0779i	0.471908	−	0.817369i
$257$	−3.92276	+	2.26480i	−0.244695	+	0.141275i	−0.617333	−	0.786702i	$-0.711787\pi$
$257$	−3.92276	+	2.26480i	−0.244695	+	0.141275i	0.372638	+	0.927977i	$0.378453\pi$
$258$	21.4157			1.33328
$259$	−2.40977	−	2.22531i	−0.149736	−	0.138274i
$260$			1.44809i			0.0898065i
$261$	−10.1154	−	17.5204i	−0.626127	−	1.08448i
$262$	−1.46616	−	0.846490i	−0.0905799	−	0.0522963i
$263$	11.3886	+	6.57520i	0.702250	+	0.405444i	0.808185	−	0.588929i	$-0.200450\pi$
$263$	11.3886	+	6.57520i	0.702250	+	0.405444i	−0.105935	+	0.994373i	$0.533784\pi$
$264$	19.3431	+	33.5032i	1.19049	+	2.06198i
$265$		−	1.83531i		−	0.112742i
$266$	−15.8390	−	3.57558i	−0.971154	−	0.219233i
$267$			26.3231i			1.61095i
$268$	5.43176	−	3.13603i	0.331798	−	0.191564i
$269$	12.1418	+	7.01009i	0.740301	+	0.427413i	0.822179	−	0.569230i	$-0.192758\pi$
$269$	12.1418	+	7.01009i	0.740301	+	0.427413i	−0.0818780	+	0.996642i	$0.526092\pi$
$270$	0.299939	+	0.173170i	0.0182537	+	0.0105388i
$271$	0.187377	−	0.108182i	0.0113823	−	0.00657159i	−0.494298	−	0.869292i	$-0.664575\pi$
$271$	0.187377	−	0.108182i	0.0113823	−	0.00657159i	0.505680	+	0.862721i	$0.331242\pi$
$272$	6.34616			0.384793
$273$	−7.08643	−	1.59973i	−0.428890	−	0.0968198i
$274$		−	3.49545i		−	0.211168i
$275$	−8.68338	+	5.01335i	−0.523628	+	0.302317i
$276$	0.918324	−	8.76582i	0.0552766	−	0.527641i
$277$	−6.86808	+	11.8959i	−0.412663	+	0.714754i	−0.995180	−	0.0980651i	$-0.968735\pi$
$277$	−6.86808	+	11.8959i	−0.412663	+	0.714754i	0.582517	+	0.812819i	$0.302068\pi$
$278$	−6.34400	+	3.66271i	−0.380488	+	0.219675i
$279$			14.7510i			0.883121i
$280$	9.61752	−	10.4147i	0.574757	−	0.622400i
$281$			5.16656i			0.308211i	0.988054	+	0.154106i	$0.0492496\pi$
$281$			5.16656i			0.308211i	−0.988054	+	0.154106i	$0.950750\pi$
$282$	−2.68315	−	4.64735i	−0.159779	−	0.276746i
$283$	3.44769	−	5.97157i	0.204944	−	0.354973i	−0.745171	−	0.666873i	$-0.767632\pi$
$283$	3.44769	−	5.97157i	0.204944	−	0.354973i	0.950115	+	0.311900i	$0.100966\pi$
$284$	0.626945	−	1.08590i	0.0372023	−	0.0644363i
$285$	20.3773	−	11.7649i	1.20705	−	0.696890i
$286$	−6.37122			−0.376738
$287$	−26.1826	+	8.14444i	−1.54551	+	0.480751i
$288$	−12.1772			−0.717550
$289$	3.21582	+	5.56996i	0.189166	+	0.327645i
$290$	−6.42533	+	11.1290i	−0.377308	+	0.653517i
$291$	−26.5261	−	15.3148i	−1.55499	−	0.897771i
$292$	3.73768	−	2.15795i	0.218731	−	0.126285i
$293$	34.0179			1.98735			0.993674	−	0.112306i	$-0.0358237\pi$
$293$	34.0179			1.98735			0.993674	+	0.112306i	$0.0358237\pi$
$294$	10.9575	+	15.9088i	0.639056	+	0.927818i
$295$		−	13.9481i		−	0.812092i
$296$	3.30156	−	1.90616i	0.191899	−	0.110793i
$297$	0.453076	−	0.784750i	0.0262901	−	0.0455358i
$298$	8.00520	+	4.62180i	0.463729	+	0.267734i
$299$	4.32447	+	3.13968i	0.250091	+	0.181572i
$300$		−	3.60928i		−	0.208382i
$301$	−19.6055	+	6.09855i	−1.13004	+	0.351514i
$302$	6.30964			0.363079
$303$	6.41321	+	11.1080i	0.368429	+	0.638138i
$304$	5.34897	−	9.26469i	0.306784	−	0.531366i
$305$	−6.25879	+	10.8405i	−0.358377	+	0.620728i
$306$	−5.59216	−	9.68590i	−0.319682	−	0.553706i
$307$		−	16.4054i		−	0.936306i	−0.883647	−	0.468153i	$-0.844920\pi$
$307$		−	16.4054i		−	0.936306i	0.883647	−	0.468153i	$-0.155080\pi$
$308$	−7.40130	−	6.83475i	−0.421728	−	0.389446i
$309$		−	6.53582i		−	0.371810i
$310$	8.11457	−	4.68495i	0.460877	−	0.266087i
$311$	−2.83842	−	1.63876i	−0.160952	−	0.0929256i	0.417361	−	0.908741i	$-0.362955\pi$
$311$	−2.83842	−	1.63876i	−0.160952	−	0.0929256i	−0.578312	+	0.815815i	$0.696289\pi$
$312$	4.22176	−	7.31230i	0.239010	−	0.413978i
$313$	−5.63557	−	9.76109i	−0.318541	−	0.551729i	0.661643	−	0.749819i	$-0.269860\pi$
$313$	−5.63557	−	9.76109i	−0.318541	−	0.551729i	−0.980184	+	0.198090i	$0.936526\pi$
$314$	−19.4304			−1.09652
$315$	−13.8146	−	3.11858i	−0.778364	−	0.175712i
$316$		−	8.20453i		−	0.461541i
$317$	5.02084	+	8.69635i	0.281998	+	0.488435i	0.971877	−	0.235490i	$-0.0756694\pi$
$317$	5.02084	+	8.69635i	0.281998	+	0.488435i	−0.689878	+	0.723925i	$0.742336\pi$
$318$	−1.45335	+	2.51727i	−0.0814996	+	0.141161i
$319$	29.1176	+	16.8110i	1.63027	+	0.941237i
$320$	7.26897	+	12.5902i	0.406348	+	0.703815i
$321$	13.6895			0.764075
$322$	−2.78400	−	13.9346i	−0.155146	−	0.776544i
$323$	−17.8154			−0.991278
$324$	−3.27366	−	5.67015i	−0.181870	−	0.315008i
$325$	1.89521	+	1.09420i	0.105127	+	0.0606952i
$326$	−12.8623	+	22.2781i	−0.712375	+	1.23387i
$327$	−9.56288	−	16.5634i	−0.528828	−	0.915958i
$328$		−	31.8692i		−	1.75968i
$329$	3.77978	+	3.49044i	0.208386	+	0.192434i
$330$	−24.5495			−1.35140
$331$	4.61568	+	7.99459i	0.253701	+	0.439423i	0.964542	−	0.263930i	$-0.0850188\pi$
$331$	4.61568	+	7.99459i	0.253701	+	0.439423i	−0.710841	+	0.703353i	$0.751685\pi$
$332$	−4.25419	+	7.36847i	−0.233479	+	0.404397i
$333$	−3.29831	−	1.90428i	−0.180747	−	0.104354i
$334$	−15.6798	+	9.05275i	−0.857962	+	0.495345i
$335$			14.6533i			0.800596i
$336$	−12.1525	+	3.78021i	−0.662976	+	0.206227i
$337$		−	35.0958i		−	1.91179i	−0.293710	−	0.955895i	$-0.594890\pi$
$337$		−	35.0958i		−	1.91179i	0.293710	−	0.955895i	$-0.405110\pi$
$338$	−6.58409	−	11.4040i	−0.358127	−	0.620295i
$339$	−20.8031	+	36.0319i	−1.12987	+	1.95699i
$340$	2.11234	−	3.65868i	0.114558	−	0.198420i
$341$	−12.2576	−	21.2307i	−0.663784	−	1.14971i
$342$	−18.8538			−1.01950
$343$	−14.5617	−	11.4437i	−0.786256	−	0.617901i
$344$		−	23.8636i		−	1.28664i
$345$	16.6630	+	12.0977i	0.897105	+	0.651321i
$346$	−9.97371	−	5.75832i	−0.536190	−	0.309569i
$347$	0.869673	−	1.50632i	0.0466865	−	0.0808634i	−0.841738	−	0.539886i	$-0.818467\pi$
$347$	0.869673	−	1.50632i	0.0466865	−	0.0808634i	0.888424	+	0.459023i	$0.151800\pi$
$348$	−10.4813	+	6.05141i	−0.561859	+	0.324389i
$349$			7.83899i			0.419611i	0.977743	+	0.209806i	$0.0672831\pi$
$349$			7.83899i			0.419611i	−0.977743	+	0.209806i	$0.932717\pi$
$350$	−1.72840	−	5.55642i	−0.0923867	−	0.297003i
$351$	−0.197774			−0.0105564
$352$	17.5263	−	10.1188i	0.934157	−	0.539336i
$353$	5.91319	+	3.41398i	0.314728	+	0.181708i	0.649040	−	0.760754i	$-0.275171\pi$
$353$	5.91319	+	3.41398i	0.314728	+	0.181708i	−0.334312	+	0.942462i	$0.608504\pi$
$354$	−11.0453	+	19.1310i	−0.587049	+	1.01680i
$355$	1.46472	+	2.53697i	0.0777393	+	0.134648i
$356$	7.96713			0.422257
$357$	15.5708	+	14.3789i	0.824092	+	0.761010i
$358$	−0.508653			−0.0268831
$359$	−12.6483	+	7.30252i	−0.667554	+	0.385412i	−0.795149	−	0.606414i	$-0.792607\pi$
$359$	−12.6483	+	7.30252i	−0.667554	+	0.385412i	0.127595	+	0.991826i	$0.459274\pi$
$360$	8.23009	−	14.2549i	0.433764	−	0.751301i
$361$	−5.51603	+	9.55405i	−0.290318	+	0.502845i
$362$	3.38773	+	5.86773i	0.178055	+	0.308401i
$363$			37.1248i			1.94855i
$364$	−0.484184	+	2.14483i	−0.0253781	+	0.112420i
$365$			10.0832i			0.527777i
$366$	17.1688	−	9.91243i	0.897430	−	0.518131i
$367$	−9.49996	+	16.4544i	−0.495894	+	0.858913i	−0.999989	−	0.00473490i	$-0.998493\pi$
$367$	−9.49996	+	16.4544i	−0.495894	+	0.858913i	0.504095	+	0.863648i	$0.331826\pi$
$368$	9.31110	+	0.975448i	0.485375	+	0.0508488i
$369$	−27.5724	+	15.9190i	−1.43536	+	0.828708i
$370$			2.41921i			0.125769i
$371$	0.613657	−	2.71836i	0.0318595	−	0.141130i
$372$	8.82462			0.457535
$373$	−15.2065	+	8.77946i	−0.787361	+	0.454583i	−0.839033	−	0.544081i	$-0.816878\pi$
$373$	−15.2065	+	8.77946i	−0.787361	+	0.454583i	0.0516718	+	0.998664i	$0.483545\pi$
$374$	16.0973	+	9.29376i	0.832370	+	0.480569i
$375$	25.8945	+	14.9502i	1.33719	+	0.772026i
$376$	−5.17857	+	2.98985i	−0.267064	+	0.154190i
$377$		−	7.33824i		−	0.377939i
$378$	0.386352	+	0.356778i	0.0198718	+	0.0183507i
$379$			25.6105i			1.31552i	0.753227	+	0.657760i	$0.228496\pi$
$379$			25.6105i			1.31552i	−0.753227	+	0.657760i	$0.771504\pi$
$380$	−3.56084	−	6.16755i	−0.182667	−	0.316389i
$381$	−33.1779	−	19.1552i	−1.69975	−	0.981353i
$382$	13.1285	+	7.57975i	0.671713	+	0.387814i
$383$	−9.01017	−	15.6061i	−0.460398	−	0.797433i	0.538582	−	0.842573i	$-0.318960\pi$
$383$	−9.01017	−	15.6061i	−0.460398	−	0.797433i	−0.998981	+	0.0451395i	$0.985627\pi$
$384$		−	3.48931i		−	0.178063i
$385$	22.4744	−	6.99095i	1.14540	−	0.356292i
$386$	9.60014			0.488634
$387$	−20.6462	+	11.9201i	−1.04951	+	0.605932i
$388$	−4.63530	+	8.02857i	−0.235321	+	0.407589i
$389$	−17.2281	−	9.94664i	−0.873498	−	0.504314i	−0.00498905	−	0.999988i	$-0.501588\pi$
$389$	−17.2281	−	9.94664i	−0.873498	−	0.504314i	−0.868509	+	0.495673i	$0.834921\pi$
$390$	2.67904	+	4.64024i	0.135659	+	0.234968i
$391$	−6.34616	−	14.2407i	−0.320939	−	0.720185i
$392$	17.7272	−	12.2100i	0.895361	−	0.616700i
$393$	3.72510			0.187906
$394$	−10.5589	−	18.2886i	−0.531951	−	0.921366i
$395$	16.6001	+	9.58405i	0.835240	+	0.482226i
$396$	−10.1304	−	5.84877i	−0.509070	−	0.293912i
$397$	0.754078	−	0.435367i	0.0378461	−	0.0218505i	−0.480958	−	0.876744i	$-0.659711\pi$
$397$	0.754078	−	0.435367i	0.0378461	−	0.0218505i	0.518804	+	0.854893i	$0.326378\pi$
$398$	−15.8662			−0.795301
$399$	34.1156	−	10.6121i	1.70791	−	0.531269i
$400$	3.83379			0.191690
$401$	0.154507	−	0.0892046i	0.00771570	−	0.00445466i	−0.496137	−	0.868244i	$-0.665249\pi$
$401$	0.154507	−	0.0892046i	0.00771570	−	0.00445466i	0.503853	+	0.863789i	$0.331915\pi$
$402$	11.6037	−	20.0982i	0.578739	−	1.00240i
$403$	−2.67530	+	4.63375i	−0.133266	+	0.230823i
$404$	3.36203	−	1.94107i	0.167267	−	0.0965717i
$405$	15.2964			0.760084
$406$	−13.2380	+	14.3353i	−0.656989	+	0.711449i
$407$	6.32956			0.313745
$408$	−21.3331	+	12.3167i	−1.05614	+	0.609765i
$409$	−25.2313	−	14.5673i	−1.24761	−	0.720305i	−0.276974	−	0.960877i	$-0.589332\pi$
$409$	−25.2313	−	14.5673i	−1.24761	−	0.720305i	−0.970631	+	0.240572i	$0.922665\pi$
$410$	17.5141	+	10.1118i	0.864960	+	0.499385i
$411$	3.84555	+	6.66070i	0.189687	+	0.328548i
$412$	−1.97818			−0.0974578
$413$	4.66372	−	20.6593i	0.229487	−	1.01658i
$414$	−6.71604	−	15.0707i	−0.330075	−	0.740686i
$415$	−9.93898	−	17.2148i	−0.487885	−	0.845042i
$416$	−3.82524	−	2.20850i	−0.187548	−	0.108281i
$417$	8.05914	−	13.9588i	0.394658	−	0.683567i
$418$	27.1357	−	15.6668i	1.32725	−	0.766288i
$419$	4.16065			0.203261			0.101630	−	0.994822i	$-0.467594\pi$
$419$	4.16065			0.203261			0.101630	+	0.994822i	$0.467594\pi$
$420$	−1.86565	+	8.26442i	−0.0910344	+	0.403262i
$421$			12.3864i			0.603675i	0.953359	+	0.301838i	$0.0976000\pi$
$421$			12.3864i			0.603675i	−0.953359	+	0.301838i	$0.902400\pi$
$422$	16.2030	+	28.0645i	0.788752	+	1.36616i
$423$	5.17348	+	2.98691i	0.251543	+	0.145229i
$424$	2.80501	+	1.61947i	0.136223	+	0.0786486i
$425$	−3.19224	−	5.52912i	−0.154846	−	0.268202i
$426$		−	4.63954i		−	0.224786i
$427$	−12.8949	+	13.9637i	−0.624026	+	0.675753i
$428$		−	4.14337i		−	0.200277i
$429$	12.1406	−	7.00936i	0.586152	−	0.338415i
$430$	13.1145	+	7.57169i	0.632439	+	0.365139i
$431$	4.65239	+	2.68606i	0.224098	+	0.129383i	0.607846	−	0.794055i	$-0.292034\pi$
$431$	4.65239	+	2.68606i	0.224098	+	0.129383i	−0.383748	+	0.923438i	$0.625367\pi$
$432$	−0.300056	+	0.173237i	−0.0144364	+	0.00833488i
$433$	17.1216			0.822813			0.411406	−	0.911452i	$-0.365038\pi$
$433$	17.1216			0.822813			0.411406	+	0.911452i	$0.365038\pi$
$434$	13.5853	−	4.22590i	0.652117	−	0.202850i
$435$		−	28.2756i		−	1.35571i
$436$	−5.01320	+	2.89437i	−0.240088	+	0.138615i
$437$	−26.1388	−	2.73835i	−1.25039	−	0.130993i
$438$	7.98467	−	13.8299i	0.381522	−	0.660816i
$439$	33.1572	−	19.1433i	1.58251	−	0.913662i	0.588017	−	0.808849i	$-0.299909\pi$
$439$	33.1572	−	19.1433i	1.58251	−	0.913662i	0.994492	−	0.104813i	$-0.0334245\pi$
$440$			27.3556i			1.30413i
$441$	−19.4187	−	9.23814i	−0.924701	−	0.439912i
$442$		−	4.05685i		−	0.192965i
$443$	15.8658	+	27.4804i	0.753809	+	1.30564i	0.945964	+	0.324271i	$0.105119\pi$
$443$	15.8658	+	27.4804i	0.753809	+	1.30564i	−0.192156	+	0.981364i	$0.561548\pi$
$444$	−1.13921	+	1.97318i	−0.0540647	+	0.0936428i
$445$	−9.30673	+	16.1197i	−0.441181	+	0.764148i
$446$	12.0171	−	6.93809i	0.569028	−	0.328528i
$447$	−20.3389			−0.961998
$448$	6.55673	+	21.0784i	0.309776	+	0.995862i
$449$	−1.56348			−0.0737851			−0.0368925	−	0.999319i	$-0.511746\pi$
$449$	−1.56348			−0.0737851			−0.0368925	+	0.999319i	$0.511746\pi$
$450$	−3.37829	−	5.85137i	−0.159254	−	0.275836i
$451$	26.4561	−	45.8234i	1.24577	−	2.15774i
$452$	10.9057	+	6.29640i	0.512960	+	0.296158i
$453$	−12.0232	+	6.94162i	−0.564901	+	0.326146i
$454$	−32.2757			−1.51477
$455$	−3.77399	−	3.48510i	−0.176928	−	0.163384i
$456$			41.5252i			1.94459i
$457$	−13.4834	+	7.78465i	−0.630728	+	0.364151i	−0.781034	−	0.624489i	$-0.785307\pi$
$457$	−13.4834	+	7.78465i	−0.630728	+	0.364151i	0.150306	+	0.988639i	$0.451974\pi$
$458$	−4.70152	+	8.14326i	−0.219687	+	0.380510i
$459$	0.499687	+	0.288495i	0.0233234	+	0.0134658i
$460$	3.66159	−	5.04334i	0.170722	−	0.235147i
$461$			10.9673i			0.510796i	0.966836	+	0.255398i	$0.0822065\pi$
$461$			10.9673i			0.510796i	−0.966836	+	0.255398i	$0.917793\pi$
$462$	−36.3614	−	8.20839i	−1.69168	−	0.381889i
$463$	35.3939			1.64489			0.822447	−	0.568841i	$-0.192608\pi$
$463$	35.3939			1.64489			0.822447	+	0.568841i	$0.192608\pi$
$464$	−6.42784	−	11.1333i	−0.298405	−	0.516852i
$465$	−10.3084	+	17.8547i	−0.478041	+	0.827991i
$466$	−10.7282	+	18.5817i	−0.496973	+	0.860782i
$467$	13.9666	+	24.1908i	0.646296	+	1.11942i	0.984001	+	0.178165i	$0.0570161\pi$
$467$	13.9666	+	24.1908i	0.646296	+	1.11942i	−0.337705	+	0.941252i	$0.609651\pi$
$468$			2.55306i			0.118015i
$469$	−4.89950	+	21.7037i	−0.226238	+	1.00218i
$470$		−	3.79459i		−	0.175032i
$471$	37.0253	−	21.3765i	1.70603	−	0.984979i
$472$	21.3178	+	12.3078i	0.981230	+	0.566513i
$473$	19.8103	−	34.3125i	0.910880	−	1.57769i
$474$	−15.1789	−	26.2906i	−0.697188	−	1.20757i
$475$	−10.7625			−0.493818
$476$	4.35201	−	4.71276i	0.199474	−	0.216009i
$477$		−	3.23576i		−	0.148155i
$478$	−4.33453	−	7.50763i	−0.198257	−	0.343391i
$479$	−11.0589	+	19.1545i	−0.505292	+	0.875191i	0.494690	+	0.869070i	$0.335282\pi$
$479$	−11.0589	+	19.1545i	−0.505292	+	0.875191i	−0.999981	+	0.00612121i	$0.998052\pi$
$480$	−14.7394	−	8.50977i	−0.672757	−	0.388416i
$481$	−0.690734	−	1.19639i	−0.0314948	−	0.0545506i
$482$	10.2026			0.464716
$483$	20.6353	+	23.4900i	0.938939	+	1.06883i
$484$	11.2365			0.510748
$485$	−10.8294	−	18.7570i	−0.491736	−	0.851712i
$486$	−21.4966	−	12.4111i	−0.975106	−	0.562978i
$487$	−0.453618	+	0.785689i	−0.0205554	+	0.0356030i	−0.876120	−	0.482093i	$-0.839877\pi$
$487$	−0.453618	+	0.785689i	−0.0205554	+	0.0356030i	0.855565	+	0.517696i	$0.173210\pi$
$488$	−11.0455	−	19.1313i	−0.500006	−	0.866035i
$489$		−	56.6023i		−	2.55964i
$490$	1.08550	+	13.6163i	0.0490378	+	0.615123i
$491$	−7.81432			−0.352655			−0.176328	−	0.984332i	$-0.556422\pi$
$491$	−7.81432			−0.352655			−0.176328	+	0.984332i	$0.556422\pi$
$492$	9.52332	+	16.4949i	0.429344	+	0.743646i
$493$	−10.7044	+	18.5405i	−0.482101	+	0.835023i
$494$	−5.92255	−	3.41938i	−0.266468	−	0.153845i
$495$	23.6674	−	13.6644i	1.06377	−	0.614168i
$496$			9.37356i			0.420885i
$497$	1.32120	+	4.24737i	0.0592640	+	0.190521i
$498$			31.4820i			1.41074i
$499$	−16.7819	−	29.0671i	−0.751260	−	1.30122i	−0.947212	−	0.320607i	$-0.896113\pi$
$499$	−16.7819	−	29.0671i	−0.751260	−	1.30122i	0.195952	−	0.980613i	$-0.437220\pi$
$500$	4.52494	−	7.83742i	0.202361	−	0.350500i
$501$	19.9190	−	34.5007i	0.889914	−	1.54138i
$502$	2.98971	+	5.17832i	0.133437	+	0.231120i
$503$	19.2324			0.857532			0.428766	−	0.903416i	$-0.358948\pi$
$503$	19.2324			0.857532			0.428766	+	0.903416i	$0.358948\pi$
$504$	16.9563	−	18.3618i	0.755293	−	0.817901i
$505$			9.06976i			0.403599i
$506$	22.1894	+	16.1101i	0.986440	+	0.716180i
$507$	25.0924	+	14.4871i	1.11439	+	0.643396i
$508$	−5.79766	+	10.0418i	−0.257230	+	0.445535i
$509$	−22.0512	+	12.7313i	−0.977404	+	0.564304i	−0.901485	−	0.432810i	$-0.857522\pi$
$509$	−22.0512	+	12.7313i	−0.977404	+	0.564304i	−0.0759185	+	0.997114i	$0.524189\pi$
$510$		−	15.6318i		−	0.692187i
$511$	−3.37143	+	14.9347i	−0.149143	+	0.660671i
$512$	−19.7438			−0.872561
$513$	0.842339	−	0.486325i	0.0371902	−	0.0214718i
$514$	4.39311	+	2.53636i	0.193772	+	0.111874i
$515$	2.31079	−	4.00241i	0.101826	−	0.176367i
$516$	7.13105	+	12.3513i	0.313927	+	0.543738i
$517$	−9.92806			−0.436636
$518$	−0.808892	+	3.58321i	−0.0355407	+	0.157437i
$519$	25.3403			1.11232
$520$	5.17065	−	2.98527i	0.226748	−	0.130913i
$521$	−6.47025	+	11.2068i	−0.283467	+	0.490979i	−0.972236	−	0.234002i	$-0.924818\pi$
$521$	−6.47025	+	11.2068i	−0.283467	+	0.490979i	0.688770	+	0.724980i	$0.258151\pi$
$522$	−11.3283	+	19.6211i	−0.495824	+	0.858793i
$523$	−4.17553	−	7.23223i	−0.182583	−	0.316243i	0.760176	−	0.649717i	$-0.225113\pi$
$523$	−4.17553	−	7.23223i	−0.182583	−	0.316243i	−0.942759	+	0.333473i	$0.891779\pi$
$524$		−	1.12747i		−	0.0492536i
$525$	9.40648	+	8.68643i	0.410532	+	0.379107i
$526$		−	14.7272i		−	0.642135i
$527$	13.5186	−	7.80496i	0.588879	−	0.339990i
$528$	12.2795	−	21.2688i	0.534397	−	0.925604i
$529$	−7.12220	−	21.8695i	−0.309661	−	0.950847i
$530$	−1.78000	+	1.02768i	−0.0773183	+	0.0446397i
$531$		−	24.5914i		−	1.06718i
$532$	−3.21193	−	10.3257i	−0.139255	−	0.447674i
$533$	−11.5485			−0.500219
$534$	25.5298	−	14.7396i	1.10478	−	0.637847i
$535$	8.38319	+	4.84004i	0.362437	+	0.209253i
$536$	−22.3955	−	12.9300i	−0.967338	−	0.558493i
$537$	0.969256	−	0.559600i	0.0418265	−	0.0241485i
$538$		−	15.7012i		−	0.676929i
$539$	35.6254	−	2.84006i	1.53449	−	0.122330i
$540$			0.230650i			0.00992559i
$541$	2.42578	+	4.20158i	0.104293	+	0.180640i	0.913449	−	0.406953i	$-0.133409\pi$
$541$	2.42578	+	4.20158i	0.104293	+	0.180640i	−0.809156	+	0.587593i	$0.800076\pi$
$542$	−0.209844	−	0.121153i	−0.00901357	−	0.00520399i
$543$	−12.9109	−	7.45411i	−0.554059	−	0.319886i
$544$	6.44314	+	11.1598i	0.276247	+	0.478474i
$545$		−	13.5241i		−	0.579310i
$546$	2.41654	+	7.76864i	0.103418	+	0.332467i
$547$	5.70672			0.244002			0.122001	−	0.992530i	$-0.461069\pi$
$547$	5.70672			0.244002			0.122001	+	0.992530i	$0.461069\pi$
$548$	2.01597	−	1.16392i	0.0861181	−	0.0497203i
$549$	−11.0346	+	19.1125i	−0.470947	+	0.815704i
$550$	9.72455	+	5.61447i	0.414656	+	0.239402i
$551$	18.0447	+	31.2544i	0.768731	+	1.33148i
$552$	−33.1931	+	14.7920i	−1.41279	+	0.629588i
$553$	21.3826	+	19.7458i	0.909281	+	0.839678i
$554$	15.3832			0.653569
$555$	−2.66153	−	4.60990i	−0.112975	−	0.195679i
$556$	−4.22488	−	2.43924i	−0.179175	−	0.103447i
$557$	−39.9954	−	23.0913i	−1.69466	−	0.978411i	−0.950662	−	0.310228i	$-0.899595\pi$
$557$	−39.9954	−	23.0913i	−1.69466	−	0.978411i	−0.743996	−	0.668184i	$-0.767072\pi$
$558$	14.3065	−	8.25986i	0.605642	−	0.349668i
$559$	−8.64747			−0.365749
$560$	−8.77851	−	1.98170i	−0.370960	−	0.0837423i
$561$	−40.8985			−1.72674
$562$	5.01086	−	2.89302i	0.211370	−	0.122035i
$563$	−3.93900	+	6.82256i	−0.166009	+	0.287536i	−0.937013	−	0.349294i	$-0.886421\pi$
$563$	−3.93900	+	6.82256i	−0.166009	+	0.287536i	0.771004	+	0.636830i	$0.219755\pi$
$564$	1.78688	−	3.09497i	0.0752414	−	0.130322i
$565$	−25.4788	+	14.7102i	−1.07190	+	0.618861i
$566$	−7.72215			−0.324586
$567$	22.6562	+	5.11453i	0.951472	+	0.214790i
$568$	−5.16987			−0.216923
$569$	20.9228	−	12.0798i	0.877130	−	0.506411i	0.00741889	−	0.999972i	$-0.497638\pi$
$569$	20.9228	−	12.0798i	0.877130	−	0.506411i	0.869711	+	0.493561i	$0.164305\pi$
$570$	−22.8207	−	13.1755i	−0.955852	−	0.551861i
$571$	−8.73591	−	5.04368i	−0.365587	−	0.211071i	0.305942	−	0.952050i	$-0.401029\pi$
$571$	−8.73591	−	5.04368i	−0.365587	−	0.211071i	−0.671529	+	0.740979i	$0.734362\pi$
$572$	−2.12150	−	3.67455i	−0.0887045	−	0.153641i
$573$	−33.3558			−1.39346
$574$	22.5600	+	20.8331i	0.941636	+	0.869556i
$575$	−3.83379	−	8.60300i	−0.159880	−	0.358770i
$576$	12.8156	+	22.1973i	0.533985	+	0.924889i
$577$	9.51957	+	5.49612i	0.396305	+	0.228807i	0.684888	−	0.728648i	$-0.259851\pi$
$577$	9.51957	+	5.49612i	0.396305	+	0.228807i	−0.288584	+	0.957455i	$0.593184\pi$
$578$	3.60140	−	6.23781i	0.149799	−	0.259459i
$579$	−18.2934	+	10.5617i	−0.760248	+	0.438930i
$580$	−8.55809			−0.355355
$581$	−8.96512	−	28.8209i	−0.371936	−	1.19569i
$582$			34.3023i			1.42187i
$583$	2.68880	+	4.65714i	0.111359	+	0.192879i
$584$	−15.4107	−	8.89737i	−0.637700	−	0.368176i
$585$	−5.16557	−	2.98234i	−0.213570	−	0.123305i
$586$	−19.0484	−	32.9928i	−0.786881	−	1.36292i
$587$			16.5502i			0.683100i	0.939864	+	0.341550i	$0.110952\pi$
$587$			16.5502i			0.683100i	−0.939864	+	0.341550i	$0.889048\pi$
$588$	−5.52661	+	11.6170i	−0.227913	+	0.479078i
$589$		−	26.3142i		−	1.08426i
$590$	−13.5278	+	7.81029i	−0.556931	+	0.321544i
$591$	40.2408	+	23.2330i	1.65529	+	0.955680i
$592$	−2.09592	−	1.21008i	−0.0861417	−	0.0497339i
$593$	20.5149	−	11.8443i	0.842444	−	0.486385i	−0.0156500	−	0.999878i	$-0.504982\pi$
$593$	20.5149	−	11.8443i	0.842444	−	0.486385i	0.858094	+	0.513492i	$0.171648\pi$
$594$	−1.01480			−0.0416378
$595$	4.45147	+	14.3105i	0.182492	+	0.586673i
$596$			6.15592i			0.252156i
$597$	30.2336	−	17.4554i	1.23738	−	0.714401i
$598$	0.623565	−	5.95222i	0.0254995	−	0.243404i
$599$	17.2364	−	29.8543i	0.704260	−	1.21981i	−0.262698	−	0.964878i	$-0.584612\pi$
$599$	17.2364	−	29.8543i	0.704260	−	1.21981i	0.966958	−	0.254936i	$-0.0820545\pi$
$600$	−12.8876	+	7.44064i	−0.526132	+	0.303763i
$601$			46.8012i			1.90906i	0.298112	+	0.954531i	$0.403643\pi$
$601$			46.8012i			1.90906i	−0.298112	+	0.954531i	$0.596357\pi$
$602$	16.8929	+	15.5998i	0.688503	+	0.635800i
$603$			25.8347i			1.05207i
$604$	2.10100	+	3.63904i	0.0854884	+	0.148070i
$605$	−13.1258	+	22.7345i	−0.533639	+	0.924289i
$606$	7.18217	−	12.4399i	0.291756	−	0.505336i
$607$	6.92224	−	3.99656i	0.280965	−	0.162215i	−0.352895	−	0.935663i	$-0.614803\pi$
$607$	6.92224	−	3.99656i	0.280965	−	0.162215i	0.633860	+	0.773448i	$0.281469\pi$
$608$	21.7228			0.880977
$609$	9.45427	−	41.8803i	0.383106	−	1.69708i
$610$	14.0185			0.567592
$611$	1.08343	+	1.87656i	0.0438310	+	0.0759175i
$612$	3.72418	−	6.45048i	0.150541	−	0.260745i
$613$	19.7930	+	11.4275i	0.799430	+	0.461551i	0.843272	−	0.537487i	$-0.180626\pi$
$613$	19.7930	+	11.4275i	0.799430	+	0.461551i	−0.0438419	+	0.999038i	$0.513960\pi$
$614$	−15.9110	+	9.18624i	−0.642117	+	0.370726i
$615$	−44.4983			−1.79435
$616$	−9.14667	+	40.5177i	−0.368530	+	1.63251i
$617$		−	2.64708i		−	0.106568i	−0.998579	−	0.0532838i	$-0.983031\pi$
$617$		−	2.64708i		−	0.106568i	0.998579	−	0.0532838i	$-0.0169688\pi$
$618$	−6.33886	+	3.65974i	−0.254986	+	0.147216i
$619$	13.7975	−	23.8979i	0.554568	−	0.960539i	−0.443370	−	0.896339i	$-0.646217\pi$
$619$	13.7975	−	23.8979i	0.554568	−	0.960539i	0.997937	−	0.0642002i	$-0.0204496\pi$
$620$	5.40402	+	3.12001i	0.217031	+	0.125303i
$621$	0.688798	+	0.500085i	0.0276405	+	0.0200677i
$622$			3.67051i			0.147174i
$623$	−19.1745	+	20.7639i	−0.768208	+	0.831887i
$624$	−5.36017			−0.214579
$625$	5.66176	+	9.80646i	0.226470	+	0.392258i
$626$	−6.31129	+	10.9315i	−0.252250	+	0.436910i
$627$	−34.4720	+	59.7073i	−1.37668	+	2.38448i
$628$	−6.46998	−	11.2063i	−0.258180	−	0.447181i
$629$			4.03033i			0.160700i
$630$	4.71091	+	15.1445i	0.187687	+	0.603373i
$631$		−	31.7357i		−	1.26338i	−0.775222	−	0.631689i	$-0.782362\pi$
$631$		−	31.7357i		−	1.26338i	0.775222	−	0.631689i	$-0.217638\pi$
$632$	−29.2957	+	16.9139i	−1.16532	+	0.672799i
$633$	−61.7509	−	35.6519i	−2.45438	−	1.41704i
$634$	5.62285	−	9.73907i	0.223312	−	0.386788i
$635$	−13.5450	−	23.4606i	−0.537516	−	0.931005i
$636$	−1.93576			−0.0767577
$637$	−4.42456	−	6.42383i	−0.175307	−	0.254521i
$638$		−	37.6535i		−	1.49071i
$639$	2.58239	+	4.47284i	0.102158	+	0.176943i
$640$	1.23367	−	2.13679i	0.0487652	−	0.0844639i
$641$	−20.5145	−	11.8441i	−0.810276	−	0.467813i	0.0367759	−	0.999324i	$-0.488291\pi$
$641$	−20.5145	−	11.8441i	−0.810276	−	0.467813i	−0.847052	+	0.531511i	$0.821625\pi$
$642$	−7.66547	−	13.2770i	−0.302532	−	0.524001i
$643$	−31.2981			−1.23428			−0.617139	−	0.786854i	$-0.711708\pi$
$643$	−31.2981			−1.23428			−0.617139	+	0.786854i	$0.711708\pi$
$644$	7.10965	−	6.24563i	0.280160	−	0.246112i
$645$	−33.3203			−1.31199
$646$	9.97578	+	17.2786i	0.392492	+	0.679816i
$647$	−34.5148	−	19.9271i	−1.35692	−	0.783417i	−0.367710	−	0.929940i	$-0.619858\pi$
$647$	−34.5148	−	19.9271i	−1.35692	−	0.783417i	−0.989207	+	0.146524i	$0.953192\pi$
$648$	−13.4975	+	23.3784i	−0.530232	+	0.918389i
$649$	20.4346	+	35.3938i	0.802128	+	1.38933i
$650$		−	2.45079i		−	0.0961279i
$651$	−21.2382	+	22.9987i	−0.832390	+	0.901389i
$652$	−17.1317			−0.670927
$653$	5.56523	+	9.63926i	0.217784	+	0.377213i	0.954130	−	0.299392i	$-0.0967838\pi$
$653$	5.56523	+	9.63926i	0.217784	+	0.377213i	−0.736346	+	0.676605i	$0.763450\pi$
$654$	−10.7095	+	18.5494i	−0.418775	+	0.725339i
$655$	2.28118	+	1.31704i	0.0891330	+	0.0514610i
$656$	−17.5209	+	10.1157i	−0.684078	+	0.394953i
$657$			17.7773i			0.693557i
$658$	1.26877	−	5.62035i	0.0494617	−	0.219104i
$659$			38.9094i			1.51569i	0.652432	+	0.757847i	$0.273749\pi$
$659$			38.9094i			1.51569i	−0.652432	+	0.757847i	$0.726251\pi$
$660$	−8.17454	−	14.1587i	−0.318194	−	0.551128i
$661$	18.7348	−	32.4496i	0.728699	−	1.26214i	−0.228735	−	0.973489i	$-0.573459\pi$
$661$	18.7348	−	32.4496i	0.728699	−	1.26214i	0.957433	−	0.288654i	$-0.0932078\pi$
$662$	5.16912	−	8.95317i	0.200903	−	0.347975i
$663$	4.46319	+	7.73047i	0.173336	+	0.300227i
$664$	35.0806			1.36139
$665$	24.6437	+	5.56319i	0.955642	+	0.215731i
$666$			4.26522i			0.165274i
$667$	−18.5553	+	25.5573i	−0.718463	+	0.989584i
$668$	−10.4422	−	6.02882i	−0.404022	−	0.233262i
$669$	−15.2660	+	26.4416i	−0.590219	+	1.02229i
$670$	14.2117	−	8.20514i	0.549047	−	0.316992i
$671$		−	36.6775i		−	1.41592i
$672$	−18.9858	−	17.5325i	−0.732394	−	0.676331i
$673$	2.15130			0.0829266			0.0414633	−	0.999140i	$-0.486798\pi$
$673$	2.15130			0.0829266			0.0414633	+	0.999140i	$0.486798\pi$
$674$	−34.0382	+	19.6519i	−1.31110	+	0.756964i
$675$	0.301867	+	0.174283i	0.0116189	+	0.00670815i
$676$	4.38478	−	7.59465i	0.168645	−	0.292102i
$677$	−8.63767	−	14.9609i	−0.331973	−	0.574994i	0.650926	−	0.759141i	$-0.274381\pi$
$677$	−8.63767	−	14.9609i	−0.331973	−	0.574994i	−0.982899	+	0.184148i	$0.941048\pi$
$678$	46.5948			1.78946
$679$	−9.76826	−	31.4028i	−0.374871	−	1.20513i
$680$	−17.4186			−0.667973
$681$	61.5025	−	35.5085i	2.35678	−	1.36069i
$682$	−13.7273	+	23.7764i	−0.525645	+	0.910444i
$683$	−5.83323	+	10.1034i	−0.223202	+	0.386598i	−0.955779	−	0.294087i	$-0.904984\pi$
$683$	−5.83323	+	10.1034i	−0.223202	+	0.386598i	0.732576	+	0.680685i	$0.238318\pi$
$684$	−6.27798	−	10.8738i	−0.240044	−	0.415769i
$685$			5.43851i			0.207795i
$686$	−2.94500	+	20.5308i	−0.112441	+	0.783868i
$687$		−	20.6897i		−	0.789361i
$688$	−13.1197	+	7.57464i	−0.500182	+	0.288780i
$689$	0.586849	−	1.01645i	0.0223572	−	0.0387237i
$690$	2.40271	−	22.9350i	0.0914697	−	0.873120i
$691$	−34.2139	+	19.7534i	−1.30156	+	0.751454i	−0.980671	−	0.195664i	$-0.937314\pi$
$691$	−34.2139	+	19.7534i	−1.30156	+	0.751454i	−0.320886	+	0.947118i	$0.603981\pi$
$692$		−	7.66969i		−	0.291558i
$693$	39.6237	−	12.3255i	1.50518	−	0.468206i
$694$	−1.94790			−0.0739412
$695$	9.87052	−	5.69875i	0.374410	−	0.216166i
$696$	43.2152	+	24.9503i	1.63807	+	0.945740i
$697$	29.1779	+	16.8459i	1.10519	+	0.638083i
$698$	7.60276	−	4.38945i	0.287769	−	0.166143i
$699$		−	47.2109i		−	1.78568i
$700$	2.62910	−	2.84703i	0.0993705	−	0.107608i
$701$		−	2.90811i		−	0.109838i	−0.998491	−	0.0549190i	$-0.982510\pi$
$701$		−	2.90811i		−	0.109838i	0.998491	−	0.0549190i	$-0.0174901\pi$
$702$	0.110744	+	0.191814i	0.00417975	+	0.00723954i
$703$	5.88382	+	3.39703i	0.221913	+	0.128121i
$704$	−36.8904	−	21.2987i	−1.39036	−	0.802724i
$705$	4.17466	+	7.23073i	0.157227	+	0.272325i
$706$		−	7.64666i		−	0.287786i
$707$	−3.03258	+	13.4337i	−0.114052	+	0.505225i
$708$	−14.7115			−0.552893
$709$	−3.47529	+	2.00646i	−0.130517	+	0.0753543i	−0.563837	−	0.825886i	$-0.690675\pi$
$709$	−3.47529	+	2.00646i	−0.130517	+	0.0753543i	0.433320	+	0.901240i	$0.357342\pi$
$710$	1.64035	−	2.84116i	0.0615611	−	0.106627i
$711$	29.2669	+	16.8973i	1.09760	+	0.633698i
$712$	−16.4245	−	28.4480i	−0.615533	−	1.06614i
$713$	21.0342	−	9.37356i	0.787736	−	0.351042i
$714$	5.22667	−	23.1530i	0.195603	−	0.866479i
$715$	9.91287			0.370720
$716$	−0.169373	−	0.293362i	−0.00632975	−	0.0109634i
$717$	16.5192	+	9.53737i	0.616921	+	0.356180i
$718$	14.1649	+	8.17812i	0.528630	+	0.305205i
$719$	15.6262	−	9.02176i	0.582757	−	0.336455i	−0.179471	−	0.983763i	$-0.557439\pi$
$719$	15.6262	−	9.02176i	0.582757	−	0.336455i	0.762228	+	0.647308i	$0.224105\pi$
$720$	−10.4494			−0.389425
$721$	4.76087	−	5.15551i	0.177304	−	0.192001i
$722$	12.3549			0.459800
$723$	−19.4414	+	11.2245i	−0.723034	+	0.417444i
$724$	−2.25611	+	3.90770i	−0.0838478	+	0.145229i
$725$	−6.46664	+	11.2005i	−0.240165	+	0.415978i
$726$	36.0061	−	20.7881i	1.33631	−	0.771519i
$727$	30.0373			1.11402			0.557011	−	0.830505i	$-0.311948\pi$
$727$	30.0373			1.11402			0.557011	+	0.830505i	$0.311948\pi$
$728$	8.65665	−	2.69277i	0.320837	−	0.0998005i
$729$	28.2806			1.04743
$730$	9.77932	−	5.64609i	0.361949	−	0.208971i
$731$	21.8484	+	12.6142i	0.808091	+	0.466552i
$732$	11.4339	+	6.60134i	0.422607	+	0.243992i
$733$	4.26776	+	7.39198i	0.157633	+	0.273029i	0.934015	−	0.357234i	$-0.116280\pi$
$733$	4.26776	+	7.39198i	0.157633	+	0.273029i	−0.776381	+	0.630263i	$0.782947\pi$
$734$	21.2781			0.785388
$735$	−17.0486	−	24.7522i	−0.628848	−	0.912998i
$736$	7.73804	+	17.3641i	0.285228	+	0.640049i
$737$	−21.4677	−	37.1831i	−0.790772	−	1.36966i
$738$	30.8785	+	17.8277i	1.13665	+	0.656246i
$739$	21.3906	−	37.0496i	0.786866	−	1.36289i	−0.141013	−	0.990008i	$-0.545036\pi$
$739$	21.3906	−	37.0496i	0.786866	−	1.36289i	0.927878	−	0.372883i	$-0.121631\pi$
$740$	−1.39526	+	0.805556i	−0.0512909	+	0.0296128i
$741$	15.0475			0.552783
$742$	−2.98006	+	0.926988i	−0.109402	+	0.0340308i
$743$			25.3826i			0.931198i	0.884996	+	0.465599i	$0.154161\pi$
$743$			25.3826i			0.931198i	−0.884996	+	0.465599i	$0.845839\pi$
$744$	−18.1922	−	31.5099i	−0.666960	−	1.15521i
$745$	−12.4552	−	7.19099i	−0.456321	−	0.263457i
$746$	17.0298	+	9.83214i	0.623504	+	0.359980i
$747$	−17.5230	−	30.3508i	−0.641135	−	1.11048i
$748$			12.3786i			0.452608i
$749$	10.7984	+	9.97183i	0.394566	+	0.364363i
$750$		−	33.4856i		−	1.22272i
$751$	−39.2061	+	22.6357i	−1.43065	+	0.825987i	−0.997170	−	0.0751749i	$-0.976048\pi$
$751$	−39.2061	+	22.6357i	−1.43065	+	0.825987i	−0.433482	+	0.901162i	$0.642715\pi$
$752$	3.28750	+	1.89804i	0.119883	+	0.0692143i
$753$	−11.3940	−	6.57832i	−0.415220	−	0.239727i
$754$	−7.11710	+	4.10906i	−0.259190	+	0.149643i
$755$	−9.81706			−0.357279
$756$	−0.0771205	+	0.341627i	−0.00280484	+	0.0124248i
$757$		−	3.04735i		−	0.110758i	−0.998465	−	0.0553789i	$-0.982363\pi$
$757$		−	3.04735i		−	0.110758i	0.998465	−	0.0553789i	$-0.0176367\pi$
$758$	24.8387	−	14.3406i	0.902181	−	0.520875i
$759$	−60.0064	−	6.28638i	−2.17809	−	0.228181i
$760$	−14.6816	+	25.4292i	−0.532556	+	0.922414i
$761$	42.0317	−	24.2670i	1.52365	−	0.879679i	0.524040	−	0.851694i	$-0.324424\pi$
$761$	42.0317	−	24.2670i	1.52365	−	0.879679i	0.999608	−	0.0279851i	$-0.00890909\pi$
$762$			42.9041i			1.55425i
$763$	4.52195	−	20.0312i	0.163706	−	0.725179i
$764$			10.0957i			0.365250i
$765$	8.70075	+	15.0701i	0.314576	+	0.544862i
$766$	−10.0905	+	17.4773i	−0.364585	+	0.631481i
$767$	4.45999	−	7.72492i	0.161041	−	0.278931i
$768$	32.2259	−	18.6056i	1.16285	−	0.671373i
$769$	−49.5965			−1.78850			−0.894248	−	0.447573i	$-0.852289\pi$
$769$	−49.5965			−1.78850			−0.894248	+	0.447573i	$0.852289\pi$
$770$	−19.3648	−	17.8825i	−0.697860	−	0.644441i
$771$	−11.1616			−0.401976
$772$	3.19668	+	5.53681i	0.115051	+	0.199274i
$773$	−6.24463	+	10.8160i	−0.224604	+	0.389025i	−0.956200	−	0.292713i	$-0.905442\pi$
$773$	−6.24463	+	10.8160i	−0.224604	+	0.389025i	0.731597	+	0.681738i	$0.238775\pi$
$774$	23.1218	+	13.3494i	0.831094	+	0.479833i
$775$	8.16674	−	4.71507i	0.293358	−	0.169370i
$776$	38.2232			1.37213
$777$	−2.40074	−	7.71785i	−0.0861261	−	0.276876i
$778$			22.2785i			0.798724i
$779$	49.1861	−	28.3976i	1.76228	−	1.01745i
$780$	−1.78415	+	3.09024i	−0.0638828	+	0.110648i
$781$	−7.43353	−	4.29175i	−0.265993	−	0.153571i
$782$	−10.2580	+	14.1290i	−0.366827	+	0.505254i
$783$		−	1.16883i		−	0.0417706i
$784$	−12.3397	−	5.87039i	−0.440702	−	0.209657i
$785$	30.2314			1.07900
$786$	−2.08588	−	3.61284i	−0.0744007	−	0.128866i
$787$	5.59584	−	9.69228i	0.199470	−	0.345493i	−0.748887	−	0.662698i	$-0.769411\pi$
$787$	5.59584	−	9.69228i	0.199470	−	0.345493i	0.948357	+	0.317206i	$0.102745\pi$
$788$	7.03188	−	12.1796i	0.250500	−	0.433879i
$789$	16.2023	+	28.0632i	0.576816	+	0.999075i
$790$		−	21.4664i		−	0.763741i
$791$	−42.6563	+	13.2688i	−1.51668	+	0.471785i
$792$			48.2297i			1.71377i
$793$	−6.93263	+	4.00256i	−0.246185	+	0.142135i
$794$	−0.844495	−	0.487569i	−0.0299700	−	0.0173032i
$795$	2.26124	−	3.91658i	0.0801978	−	0.138907i
$796$	−5.28317	−	9.15072i	−0.187257	−	0.324339i
$797$	33.4971			1.18653			0.593265	−	0.805007i	$-0.297839\pi$
$797$	33.4971			1.18653			0.593265	+	0.805007i	$0.297839\pi$
$798$	−29.3954	−	27.1452i	−1.04058	−	0.960931i
$799$		−	6.32166i		−	0.223644i
$800$	3.89238	+	6.74179i	0.137616	+	0.238358i
$801$	−16.4083	+	28.4201i	−0.579760	+	1.00417i
$802$	−0.173033	−	0.0999005i	−0.00611000	−	0.00352761i
$803$	−14.7723	−	25.5863i	−0.521302	−	0.902921i
$804$	15.4553			0.545066
$805$	4.33158	+	21.6806i	0.152668	+	0.764141i
$806$	5.99214			0.211064
$807$	17.2739	+	29.9193i	0.608070	+	1.05321i
$808$	−13.8618	−	8.00314i	−0.487658	−	0.281550i
$809$	−4.07155	+	7.05212i	−0.143148	+	0.247939i	−0.928680	−	0.370881i	$-0.879056\pi$
$809$	−4.07155	+	7.05212i	−0.143148	+	0.247939i	0.785533	+	0.618820i	$0.212389\pi$
$810$	−8.56524	−	14.8354i	−0.300952	−	0.521264i
$811$		−	5.53741i		−	0.194445i	−0.995263	−	0.0972224i	$-0.969004\pi$
$811$		−	5.53741i		−	0.194445i	0.995263	−	0.0972224i	$-0.0309958\pi$
$812$	−12.6758	−	2.86150i	−0.444833	−	0.100419i
$813$	0.533153			0.0186985
$814$	−3.54425	−	6.13882i	−0.124226	−	0.215165i
$815$	20.0122	−	34.6621i	0.700996	−	1.21416i
$816$	13.5428	+	7.81895i	0.474093	+	0.273718i
$817$	36.8305	−	21.2641i	1.28854	−	0.743937i
$818$			32.6279i			1.14081i
$819$	−6.65378	−	6.14445i	−0.232502	−	0.214705i
$820$			13.4682i			0.470329i
$821$	−15.2878	−	26.4792i	−0.533547	−	0.924130i	−0.999232	−	0.0391795i	$-0.987526\pi$
$821$	−15.2878	−	26.4792i	−0.533547	−	0.924130i	0.465686	−	0.884950i	$-0.345808\pi$
$822$	4.30665	−	7.45933i	0.150212	−	0.260174i
$823$	−3.87292	+	6.70810i	−0.135002	+	0.233830i	−0.925598	−	0.378508i	$-0.876437\pi$
$823$	−3.87292	+	6.70810i	−0.135002	+	0.233830i	0.790596	+	0.612337i	$0.209771\pi$
$824$	4.07807	+	7.06343i	0.142066	+	0.246066i
$825$	−24.7073			−0.860197
$826$	−22.6481	+	7.04500i	−0.788030	+	0.245127i
$827$		−	37.1540i		−	1.29197i	−0.763349	−	0.645986i	$-0.776446\pi$
$827$		−	37.1540i		−	1.29197i	0.763349	−	0.645986i	$-0.223554\pi$
$828$	6.45561	−	8.89172i	0.224348	−	0.309008i
$829$	31.4232	+	18.1422i	1.09137	+	0.630104i	0.933941	−	0.357426i	$-0.116346\pi$
$829$	31.4232	+	18.1422i	1.09137	+	0.630104i	0.157430	+	0.987530i	$0.449679\pi$
$830$	−11.1307	+	19.2789i	−0.386352	+	0.669182i
$831$	−29.3132	+	16.9240i	−1.01686	+	0.587086i
$832$			9.29715i			0.322321i
$833$	1.80840	+	22.6843i	0.0626574	+	0.785966i
$834$	−18.0509			−0.625052
$835$	24.3960	−	14.0850i	0.844258	−	0.487432i
$836$	18.0714	+	10.4335i	0.625013	+	0.360852i
$837$	−0.426119	+	0.738060i	−0.0147288	+	0.0255111i
$838$	−2.32976	−	4.03527i	−0.0804803	−	0.139396i
$839$	−9.74112			−0.336301			−0.168150	−	0.985761i	$-0.553779\pi$
$839$	−9.74112			−0.336301			−0.168150	+	0.985761i	$0.553779\pi$
$840$	33.3557	−	10.3757i	1.15088	−	0.357996i
$841$	14.3685			0.495466
$842$	12.0131	−	6.93577i	0.413999	−	0.239022i
$843$	−6.36558	+	11.0255i	−0.219242	+	0.379739i
$844$	−10.7907	+	18.6900i	−0.371430	+	0.643335i
$845$	10.2441	+	17.7433i	0.352407	+	0.610387i
$846$		−	6.69010i		−	0.230011i
$847$	−27.0428	+	29.2844i	−0.929200	+	1.00622i
$848$		−	2.05617i		−	0.0706092i
$849$	14.7148	−	8.49561i	0.505012	−	0.291569i
$850$	−3.57500	+	6.19208i	−0.122621	+	0.212386i
$851$	−0.619488	+	5.91330i	−0.0212358	+	0.202705i
$852$	2.67582	−	1.54489i	0.0916721	−	0.0529269i
$853$		−	10.0341i		−	0.343560i	−0.985135	−	0.171780i	$-0.945048\pi$
$853$		−	10.0341i		−	0.343560i	0.985135	−	0.171780i	$-0.0549518\pi$
$854$	20.7634	+	4.68724i	0.710510	+	0.160394i
$855$	29.3343			1.00321
$856$	−14.7946	+	8.54168i	−0.505670	+	0.291949i
$857$	−6.04967	−	3.49278i	−0.206653	−	0.119311i	0.393102	−	0.919495i	$-0.371402\pi$
$857$	−6.04967	−	3.49278i	−0.206653	−	0.119311i	−0.599755	+	0.800184i	$0.704735\pi$
$858$	−13.5963	−	7.84981i	−0.464169	−	0.267988i
$859$	−39.3910	+	22.7424i	−1.34400	+	0.775962i	−0.987393	−	0.158291i	$-0.949402\pi$
$859$	−39.3910	+	22.7424i	−1.34400	+	0.775962i	−0.356612	+	0.934252i	$0.616068\pi$
$860$			10.0850i			0.343894i
$861$	−65.9086	−	14.8785i	−2.24616	−	0.507059i
$862$		−	6.01625i		−	0.204914i
$863$	20.7809	+	35.9936i	0.707391	+	1.22524i	0.965822	+	0.259207i	$0.0834612\pi$
$863$	20.7809	+	35.9936i	0.707391	+	1.22524i	−0.258431	+	0.966030i	$0.583205\pi$
$864$	−0.609282	−	0.351769i	−0.0207282	−	0.0119674i
$865$	15.5179	+	8.95928i	0.527625	+	0.304625i
$866$	−9.58728	−	16.6057i	−0.325789	−	0.564283i
$867$			15.8485i			0.538243i
$868$	6.96094	+	6.42810i	0.236270	+	0.218184i
$869$	−56.1641			−1.90524
$870$	−27.4235	+	15.8330i	−0.929744	+	0.536788i
$871$	−4.68547	+	8.11547i	−0.158761	+	0.274982i
$872$	20.6697	+	11.9337i	0.699965	+	0.404125i
$873$	−19.0928	−	33.0698i	−0.646195	−	1.11924i
$874$	11.9807	+	26.8845i	0.405252	+	0.909381i
$875$	9.53569	+	30.6552i	0.322365	+	1.03633i
$876$	10.6350			0.359324
$877$	17.4333	+	30.1954i	0.588682	+	1.01963i	0.994405	+	0.105631i	$0.0336862\pi$
$877$	17.4333	+	30.1954i	0.588682	+	1.01963i	−0.405724	+	0.913996i	$0.632980\pi$
$878$	−37.1329	−	21.4387i	−1.25317	−	0.723521i
$879$	72.5947	+	41.9126i	2.44856	+	1.41368i
$880$	15.0395	−	8.68304i	0.506980	−	0.292705i
$881$	−14.2407			−0.479782			−0.239891	−	0.970800i	$-0.577112\pi$
$881$	−14.2407			−0.479782			−0.239891	+	0.970800i	$0.577112\pi$
$882$	1.91380	+	24.0064i	0.0644410	+	0.808339i
$883$	34.0572			1.14612			0.573058	−	0.819515i	$-0.305757\pi$
$883$	34.0572			1.14612			0.573058	+	0.819515i	$0.305757\pi$
$884$	2.33976	−	1.35086i	0.0786947	−	0.0454344i
$885$	17.1851	−	29.7655i	0.577672	−	1.00056i
$886$	17.7682	−	30.7754i	0.596935	−	1.03392i
$887$	−15.1442	+	8.74352i	−0.508493	+	0.293579i	−0.732214	−	0.681074i	$-0.761513\pi$
$887$	−15.1442	+	8.74352i	−0.508493	+	0.293579i	0.223721	+	0.974653i	$0.428180\pi$
$888$	9.39410			0.315245
$889$	−12.2178	−	39.2775i	−0.409772	−	1.31733i
$890$	20.8453			0.698735
$891$	−38.8150	+	22.4098i	−1.30035	+	0.750758i
$892$	8.00299	+	4.62053i	0.267960	+	0.154707i
$893$	−9.22891	−	5.32832i	−0.308834	−	0.178305i
$894$	11.3888	+	19.7260i	0.380899	+	0.659736i
$895$	0.791404			0.0264537
$896$	2.54171	−	2.75240i	0.0849126	−	0.0919513i
$897$	5.36017	+	12.0282i	0.178971	+	0.401609i
$898$	0.875472	+	1.51636i	0.0292149	+	0.0506017i
$899$	−27.3851	−	15.8108i	−0.913346	−	0.527320i
$900$	2.24982	−	3.89681i	0.0749941	−	0.129894i
$901$	−2.96542	+	1.71209i	−0.0987925	+	0.0570379i
$902$	−59.2566			−1.97303
$903$	−49.3523	−	11.1410i	−1.64234	−	0.370750i
$904$		−	51.9209i		−	1.72686i
$905$	−5.27092	−	9.12950i	−0.175211	−	0.303475i
$906$	13.4649	+	7.77394i	0.447340	+	0.258272i
$907$	−40.0995	−	23.1515i	−1.33148	−	0.768732i	−0.345955	−	0.938251i	$-0.612445\pi$
$907$	−40.0995	−	23.1515i	−1.33148	−	0.768732i	−0.985527	+	0.169519i	$0.945778\pi$
$908$	−10.7473	−	18.6148i	−0.356660	−	0.617754i
$909$			15.9906i			0.530373i
$910$	−1.26682	+	5.61175i	−0.0419948	+	0.186028i
$911$			6.05621i			0.200651i	0.994955	+	0.100326i	$0.0319885\pi$
$911$			6.05621i			0.200651i	−0.994955	+	0.100326i	$0.968012\pi$
$912$	22.8296	−	13.1807i	0.755962	−	0.436455i
$913$	50.4408	+	29.1220i	1.66935	+	0.963798i
$914$	15.1001	+	8.71806i	0.499468	+	0.288368i
$915$	−26.7127	+	15.4226i	−0.883095	+	0.509855i
$916$	−6.26209			−0.206905
$917$	2.93839	+	2.71347i	0.0970343	+	0.0896066i
$918$		−	0.646172i		−	0.0213269i
$919$	1.87384	−	1.08186i	0.0618121	−	0.0356873i	−0.468775	−	0.883317i	$-0.655305\pi$
$919$	1.87384	−	1.08186i	0.0618121	−	0.0356873i	0.530588	+	0.847630i	$0.321971\pi$
$920$	−25.5566	−	2.67736i	−0.842576	−	0.0882699i
$921$	20.2127	−	35.0094i	0.666031	−	1.15360i
$922$	10.6368	−	6.14113i	0.350303	−	0.202247i
$923$			1.87341i			0.0616639i
$924$	−7.37357	−	23.7044i	−0.242573	−	0.779818i
$925$			2.43477i			0.0800547i
$926$	−19.8189	−	34.3273i	−0.651289	−	1.12807i
$927$	4.07407	−	7.05649i	0.133810	−	0.231766i
$928$	13.0521	−	22.6069i	0.428457	−	0.742109i
$929$	−4.73396	+	2.73315i	−0.155316	+	0.0896718i	−0.575644	−	0.817701i	$-0.695248\pi$
$929$	−4.73396	+	2.73315i	−0.155316	+	0.0896718i	0.420328	+	0.907372i	$0.361915\pi$
$930$	23.0888			0.757112
$931$	34.6408	+	16.4798i	1.13531	+	0.540104i
$932$	−14.2892			−0.468058
$933$	−4.03815	−	6.99428i	−0.132203	−	0.228982i
$934$	15.6412	−	27.0914i	0.511796	−	0.886457i
$935$	−25.0455	−	14.4600i	−0.819074	−	0.472893i
$936$	9.11617	−	5.26322i	0.297971	−	0.172034i
$937$	39.4755			1.28961			0.644805	−	0.764347i	$-0.276939\pi$
$937$	39.4755			1.28961			0.644805	+	0.764347i	$0.276939\pi$
$938$	23.7931	−	7.40117i	0.776874	−	0.241657i
$939$		−	27.7737i		−	0.906362i
$940$	2.18850	−	1.26353i	0.0713812	−	0.0412119i
$941$	11.4184	−	19.7773i	0.372229	−	0.644720i	−0.617679	−	0.786431i	$-0.711927\pi$
$941$	11.4184	−	19.7773i	0.372229	−	0.644720i	0.989908	+	0.141710i	$0.0452601\pi$
$942$	−41.4647	−	23.9397i	−1.35099	−	0.779996i
$943$	40.2205	+	29.2011i	1.30976	+	0.950919i
$944$		−	15.6267i		−	0.508605i
$945$	−0.601119	−	0.555104i	−0.0195544	−	0.0180575i
$946$	−44.3713			−1.44264
$947$	−9.18510	−	15.9091i	−0.298476	−	0.516975i	0.677312	−	0.735696i	$-0.263145\pi$
$947$	−9.18510	−	15.9091i	−0.298476	−	0.516975i	−0.975787	+	0.218721i	$0.929812\pi$
$948$	10.1086	−	17.5086i	0.328312	−	0.568653i
$949$	−3.22414	+	5.58438i	−0.104660	+	0.181277i
$950$	6.02649	+	10.4382i	0.195525	+	0.338659i
$951$			24.7442i			0.802385i
$952$	−25.7995	−	5.82411i	−0.836167	−	0.188761i
$953$			3.41341i			0.110571i	0.998471	+	0.0552856i	$0.0176069\pi$
$953$			3.41341i			0.110571i	−0.998471	+	0.0552856i	$0.982393\pi$
$954$	−3.13825	+	1.81187i	−0.101605	+	0.0586615i
$955$	−20.4264	−	11.7932i	−0.660984	−	0.381619i
$956$	2.88665	−	4.99982i	0.0933609	−	0.161706i
$957$	41.4249	+	71.7500i	1.33908	+	2.31935i
$958$	24.7697			0.800272
$959$	−1.81843	+	8.05523i	−0.0587201	+	0.260117i
$960$			35.8236i			1.15620i
$961$	−3.97173	−	6.87924i	−0.128120	−	0.221911i
$962$	−0.773556	+	1.33984i	−0.0249404	+	0.0431981i
$963$	14.7801	+	8.53329i	0.476282	+	0.274981i
$964$	3.39729	+	5.88428i	0.109419	+	0.189520i
$965$	−14.9367			−0.480829
$966$	11.2273	−	33.1667i	0.361234	−	1.06712i
$967$	−5.71094			−0.183651			−0.0918257	−	0.995775i	$-0.529270\pi$
$967$	−5.71094			−0.183651			−0.0918257	+	0.995775i	$0.529270\pi$
$968$	−23.1643	−	40.1218i	−0.744530	−	1.28956i
$969$	−38.0184	−	21.9499i	−1.22133	−	0.705134i
$970$	−12.1278	+	21.0060i	−0.389401	+	0.674463i
$971$	11.3971	+	19.7403i	0.365750	+	0.633497i	0.988896	−	0.148608i	$-0.0474793\pi$
$971$	11.3971	+	19.7403i	0.365750	+	0.633497i	−0.623146	+	0.782105i	$0.714146\pi$
$972$		−	16.5307i		−	0.530222i
$973$	16.5251	−	5.14036i	0.529772	−	0.164792i
$974$	1.01602			0.0325553
$975$	2.69627	+	4.67007i	0.0863496	+	0.149562i
$976$	−7.01197	+	12.1451i	−0.224448	+	0.388755i
$977$	−4.00002	−	2.30941i	−0.127972	−	0.0738847i	0.434647	−	0.900601i	$-0.356873\pi$
$977$	−4.00002	−	2.30941i	−0.127972	−	0.0738847i	−0.562619	+	0.826716i	$0.690206\pi$
$978$	−54.8966	+	31.6945i	−1.75540	+	1.01348i
$979$		−	54.5389i		−	1.74307i
$980$	−7.49167	+	5.16006i	−0.239313	+	0.164832i
$981$		−	23.8439i		−	0.761276i
$982$	4.37564	+	7.57883i	0.139632	+	0.241850i
$983$	−17.9493	+	31.0891i	−0.572494	+	0.991589i	0.423815	+	0.905749i	$0.360691\pi$
$983$	−17.9493	+	31.0891i	−0.572494	+	0.991589i	−0.996309	+	0.0858399i	$0.972643\pi$
$984$	39.2653	−	68.0094i	1.25173	−	2.16806i
$985$	16.4285	+	28.4549i	0.523454	+	0.906649i
$986$	23.9757			0.763543
$987$	3.76562	+	12.1056i	0.119861	+	0.385326i
$988$		−	4.55438i		−	0.144894i
$989$	30.1171	+	21.8658i	0.957668	+	0.695291i
$990$	−26.5052	−	15.3028i	−0.842390	−	0.486354i
$991$	−22.6483	+	39.2281i	−0.719448	+	1.24612i	0.241770	+	0.970334i	$0.422272\pi$
$991$	−22.6483	+	39.2281i	−0.719448	+	1.24612i	−0.961219	+	0.275788i	$0.911061\pi$
$992$	−16.4836	+	9.51679i	−0.523354	+	0.302158i
$993$			22.7474i			0.721868i
$994$	3.37957	−	3.65971i	0.107193	−	0.116079i
$995$	24.6860			0.782597
$996$	−18.1570	+	10.4829i	−0.575327	+	0.332165i
$997$	19.7511	+	11.4033i	0.625524	+	0.361146i	0.779016	−	0.627003i	$-0.215719\pi$
$997$	19.7511	+	11.4033i	0.625524	+	0.361146i	−0.153493	+	0.988150i	$0.549052\pi$
$998$	−18.7941	+	32.5523i	−0.594916	+	1.03043i
$999$	−0.110020	−	0.190560i	−0.00348087	−	0.00602904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.g.a.45.6	yes	28
7.3	odd	6		1127.2.c.c.1126.17		28
7.4	even	3		1127.2.c.c.1126.18		28
7.5	odd	6	inner	161.2.g.a.68.5	yes	28
23.22	odd	2	inner	161.2.g.a.45.5	✓	28
161.45	even	6		1127.2.c.c.1126.19		28
161.68	even	6	inner	161.2.g.a.68.6	yes	28
161.137	odd	6		1127.2.c.c.1126.20		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.g.a.45.5	✓	28	23.22	odd	2	inner
161.2.g.a.45.6	yes	28	1.1	even	1	trivial
161.2.g.a.68.5	yes	28	7.5	odd	6	inner
161.2.g.a.68.6	yes	28	161.68	even	6	inner
1127.2.c.c.1126.17		28	7.3	odd	6
1127.2.c.c.1126.18		28	7.4	even	3
1127.2.c.c.1126.19		28	161.45	even	6
1127.2.c.c.1126.20		28	161.137	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.559952 - 0.969865i) q^{2} +(2.13402 + 1.23207i) q^{3} +(0.372908 - 0.645896i) q^{4} +(0.871219 + 1.50900i) q^{5} -2.75961i q^{6} +(0.785854 + 2.52635i) q^{7} -3.07505 q^{8} +(1.53601 + 2.66045i) q^{9} +(0.975681 - 1.68993i) q^{10} +(-4.42148 - 2.55274i) q^{11} +(1.59158 - 0.918902i) q^{12} +1.11431i q^{13} +(2.01018 - 2.17680i) q^{14} +4.29363i q^{15} +(0.976062 + 1.69059i) q^{16} +(1.62545 - 2.81536i) q^{17} +(1.72019 - 2.97945i) q^{18} +(-2.74008 - 4.74595i) q^{19} +1.29954 q^{20} +(-1.43562 + 6.35949i) q^{21} +5.71765i q^{22} +(2.81760 - 3.88086i) q^{23} +(-6.56220 - 3.78869i) q^{24} +(0.981954 - 1.70079i) q^{25} +(1.08073 - 0.623958i) q^{26} +0.177486i q^{27} +(1.92481 + 0.434516i) q^{28} -6.58548 q^{29} +(4.16424 - 2.40422i) q^{30} +(4.15841 + 2.40086i) q^{31} +(-1.98195 + 3.43285i) q^{32} +(-6.29034 - 10.8952i) q^{33} -3.64070 q^{34} +(-3.12760 + 3.38685i) q^{35} +2.29117 q^{36} +(-1.07366 + 0.619878i) q^{37} +(-3.06862 + 5.31501i) q^{38} +(-1.37291 + 2.37795i) q^{39} +(-2.67904 - 4.64024i) q^{40} +10.3638i q^{41} +(6.97173 - 2.16865i) q^{42} +7.76041i q^{43} +(-3.29761 + 1.90388i) q^{44} +(-2.67641 + 4.63568i) q^{45} +(-5.34163 - 0.559600i) q^{46} +(1.68406 - 0.972293i) q^{47} +4.81032i q^{48} +(-5.76487 + 3.97068i) q^{49} -2.19939 q^{50} +(6.93747 - 4.00535i) q^{51} +(0.719726 + 0.415534i) q^{52} +(-0.912184 - 0.526650i) q^{53} +(0.172137 - 0.0993835i) q^{54} -8.89600i q^{55} +(-2.41654 - 7.76864i) q^{56} -13.5039i q^{57} +(3.68755 + 6.38702i) q^{58} +(-6.93249 - 4.00248i) q^{59} +(2.77324 + 1.60113i) q^{60} +(3.59197 + 6.22148i) q^{61} -5.37746i q^{62} +(-5.51415 + 5.97123i) q^{63} +8.34344 q^{64} +(-1.68148 + 0.970805i) q^{65} +(-7.04457 + 12.2016i) q^{66} +(7.28297 + 4.20483i) q^{67} +(-1.21229 - 2.09975i) q^{68} +(10.7943 - 4.81032i) q^{69} +(5.03609 + 1.13687i) q^{70} +1.68123 q^{71} +(-4.72332 - 8.18103i) q^{72} +(5.01153 + 2.89341i) q^{73} +(1.20240 + 0.694204i) q^{74} +(4.19101 - 2.41968i) q^{75} -4.08719 q^{76} +(2.97448 - 13.1763i) q^{77} +3.07505 q^{78} +(9.52692 - 5.50037i) q^{79} +(-1.70073 + 2.94575i) q^{80} +(4.38937 - 7.60260i) q^{81} +(10.0515 - 5.80323i) q^{82} -11.4081 q^{83} +(3.57222 + 3.29877i) q^{84} +5.66450 q^{85} +(7.52655 - 4.34545i) q^{86} +(-14.0535 - 8.11380i) q^{87} +(13.5963 + 7.84981i) q^{88} +(5.34121 + 9.25124i) q^{89} +5.99464 q^{90} +(-2.81513 + 0.875682i) q^{91} +(-1.45593 - 3.26709i) q^{92} +(5.91608 + 10.2469i) q^{93} +(-1.88599 - 1.08887i) q^{94} +(4.77441 - 8.26953i) q^{95} +(-8.45904 + 4.88383i) q^{96} -12.4301 q^{97} +(7.07907 + 3.36775i) q^{98} -15.6842i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) \) 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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