LMFDB - Embedded newform 342.2.n.e.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(293,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("342.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.152695449.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 3x^{5} - 5x^{4} + 6x^{3} - 16x + 16 $ x^8 - 2x^7 + 3x^5 - 5x^4 + 6x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.1
Root			$1.05924 - 0.937022i$ of defining polynomial
Character	$\chi$	$=$	342.293
Dual form			342.2.n.e.335.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.37899 + 1.04804i) q^{3} +1.00000 q^{4} +(1.16085 - 0.670219i) q^{5} +(-1.37899 + 1.04804i) q^{6} +(1.55924 + 2.70068i) q^{7} +1.00000 q^{8} +(0.803221 - 2.89047i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.37899 + 1.04804i) q^{3} +1.00000 q^{4} +(1.16085 - 0.670219i) q^{5} +(-1.37899 + 1.04804i) q^{6} +(1.55924 + 2.70068i) q^{7} +1.00000 q^{8} +(0.803221 - 2.89047i) q^{9} +(1.16085 - 0.670219i) q^{10} +(-1.36246 + 0.786617i) q^{11} +(-1.37899 + 1.04804i) q^{12} +1.86329i q^{13} +(1.55924 + 2.70068i) q^{14} +(-0.898387 + 2.14085i) q^{15} +1.00000 q^{16} +(1.18474 + 0.684010i) q^{17} +(0.803221 - 2.89047i) q^{18} +(4.27933 + 0.829035i) q^{19} +(1.16085 - 0.670219i) q^{20} +(-4.98060 - 2.09007i) q^{21} +(-1.36246 + 0.786617i) q^{22} +2.31685i q^{23} +(-1.37899 + 1.04804i) q^{24} +(-1.60161 + 2.77408i) q^{25} +1.86329i q^{26} +(1.92170 + 4.82774i) q^{27} +(1.55924 + 2.70068i) q^{28} +(3.31526 - 5.74220i) q^{29} +(-0.898387 + 2.14085i) q^{30} +(-2.34559 - 1.35423i) q^{31} +1.00000 q^{32} +(1.05441 - 2.51265i) q^{33} +(1.18474 + 0.684010i) q^{34} +(3.62010 + 2.09007i) q^{35} +(0.803221 - 2.89047i) q^{36} -4.55619i q^{37} +(4.27933 + 0.829035i) q^{38} +(-1.95280 - 2.56945i) q^{39} +(1.16085 - 0.670219i) q^{40} +(-5.32171 - 9.21747i) q^{41} +(-4.98060 - 2.09007i) q^{42} -8.41611 q^{43} +(-1.36246 + 0.786617i) q^{44} +(-1.00483 - 3.89375i) q^{45} +2.31685i q^{46} +(3.82171 + 2.20646i) q^{47} +(-1.37899 + 1.04804i) q^{48} +(-1.36246 + 2.35985i) q^{49} +(-1.60161 + 2.77408i) q^{50} +(-2.35061 + 0.298414i) q^{51} +1.86329i q^{52} +(-4.02331 - 6.96859i) q^{53} +(1.92170 + 4.82774i) q^{54} +(-1.05441 + 1.82629i) q^{55} +(1.55924 + 2.70068i) q^{56} +(-6.77002 + 3.34169i) q^{57} +(3.31526 - 5.74220i) q^{58} +(-5.63697 - 9.76351i) q^{59} +(-0.898387 + 2.14085i) q^{60} +(-2.14881 + 3.72186i) q^{61} +(-2.34559 - 1.35423i) q^{62} +(9.05867 - 2.33770i) q^{63} +1.00000 q^{64} +(1.24881 + 2.16300i) q^{65} +(1.05441 - 2.51265i) q^{66} -4.79251i q^{67} +(1.18474 + 0.684010i) q^{68} +(-2.42815 - 3.19490i) q^{69} +(3.62010 + 2.09007i) q^{70} +(6.82171 - 11.8155i) q^{71} +(0.803221 - 2.89047i) q^{72} +(2.70805 - 4.69049i) q^{73} -4.55619i q^{74} +(-0.698737 - 5.50397i) q^{75} +(4.27933 + 0.829035i) q^{76} +(-4.24881 - 2.45305i) q^{77} +(-1.95280 - 2.56945i) q^{78} +9.76790i q^{79} +(1.16085 - 0.670219i) q^{80} +(-7.70967 - 4.64338i) q^{81} +(-5.32171 - 9.21747i) q^{82} +(3.32873 - 1.92184i) q^{83} +(-4.98060 - 2.09007i) q^{84} +1.83375 q^{85} -8.41611 q^{86} +(1.44635 + 11.3930i) q^{87} +(-1.36246 + 0.786617i) q^{88} +(3.19119 + 5.52730i) q^{89} +(-1.00483 - 3.89375i) q^{90} +(-5.03214 + 2.90531i) q^{91} +2.31685i q^{92} +(4.65383 - 0.590811i) q^{93} +(3.82171 + 2.20646i) q^{94} +(5.52331 - 1.90570i) q^{95} +(-1.37899 + 1.04804i) q^{96} +6.71422i q^{97} +(-1.36246 + 2.35985i) q^{98} +(1.17934 + 4.56999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} - 9 q^{5} + 4 q^{6} + 6 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 - 9 * q^5 + 4 * q^6 + 6 * q^7 + 8 * q^8 + 2 * q^9	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} - 9 q^{5} + 4 q^{6} + 6 q^{7} + 8 q^{8} + 2 q^{9} - 9 q^{10} + 4 q^{12} + 6 q^{14} - 19 q^{15} + 8 q^{16} + 18 q^{17} + 2 q^{18} + 3 q^{19} - 9 q^{20} - 13 q^{21} + 4 q^{24} - q^{25} - 2 q^{27} + 6 q^{28} + 18 q^{29} - 19 q^{30} - 9 q^{31} + 8 q^{32} - q^{33} + 18 q^{34} - 15 q^{35} + 2 q^{36} + 3 q^{38} - 18 q^{39} - 9 q^{40} - 6 q^{41} - 13 q^{42} - 26 q^{43} - 11 q^{45} - 6 q^{47} + 4 q^{48} - q^{50} + 23 q^{51} - 3 q^{53} - 2 q^{54} + q^{55} + 6 q^{56} - 20 q^{57} + 18 q^{58} - 19 q^{60} - 3 q^{61} - 9 q^{62} + 10 q^{63} + 8 q^{64} + 15 q^{65} - q^{66} + 18 q^{68} + 26 q^{69} - 15 q^{70} + 18 q^{71} + 2 q^{72} + q^{73} + 18 q^{75} + 3 q^{76} - 39 q^{77} - 18 q^{78} - 9 q^{80} - 10 q^{81} - 6 q^{82} + 18 q^{83} - 13 q^{84} - 26 q^{85} - 26 q^{86} + 42 q^{87} + 6 q^{89} - 11 q^{90} + 27 q^{91} - 9 q^{93} - 6 q^{94} + 15 q^{95} + 4 q^{96} - 41 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 - 9 * q^5 + 4 * q^6 + 6 * q^7 + 8 * q^8 + 2 * q^9 - 9 * q^10 + 4 * q^12 + 6 * q^14 - 19 * q^15 + 8 * q^16 + 18 * q^17 + 2 * q^18 + 3 * q^19 - 9 * q^20 - 13 * q^21 + 4 * q^24 - q^25 - 2 * q^27 + 6 * q^28 + 18 * q^29 - 19 * q^30 - 9 * q^31 + 8 * q^32 - q^33 + 18 * q^34 - 15 * q^35 + 2 * q^36 + 3 * q^38 - 18 * q^39 - 9 * q^40 - 6 * q^41 - 13 * q^42 - 26 * q^43 - 11 * q^45 - 6 * q^47 + 4 * q^48 - q^50 + 23 * q^51 - 3 * q^53 - 2 * q^54 + q^55 + 6 * q^56 - 20 * q^57 + 18 * q^58 - 19 * q^60 - 3 * q^61 - 9 * q^62 + 10 * q^63 + 8 * q^64 + 15 * q^65 - q^66 + 18 * q^68 + 26 * q^69 - 15 * q^70 + 18 * q^71 + 2 * q^72 + q^73 + 18 * q^75 + 3 * q^76 - 39 * q^77 - 18 * q^78 - 9 * q^80 - 10 * q^81 - 6 * q^82 + 18 * q^83 - 13 * q^84 - 26 * q^85 - 26 * q^86 + 42 * q^87 + 6 * q^89 - 11 * q^90 + 27 * q^91 - 9 * q^93 - 6 * q^94 + 15 * q^95 + 4 * q^96 - 41 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.37899	+	1.04804i	−0.796160	+	0.605087i
$3$	−1.37899	+	1.04804i	−0.796160	+	0.605087i
$4$	1.00000			0.500000
$5$	1.16085	−	0.670219i	0.519149	−	0.299731i	−0.217437	−	0.976074i	$-0.569770\pi$
$5$	1.16085	−	0.670219i	0.519149	−	0.299731i	0.736587	+	0.676343i	$0.236436\pi$
$6$	−1.37899	+	1.04804i	−0.562970	+	0.427861i
$7$	1.55924	+	2.70068i	0.589337	+	1.02076i	0.994319	+	0.106438i	$0.0339445\pi$
$7$	1.55924	+	2.70068i	0.589337	+	1.02076i	−0.404982	+	0.914325i	$0.632722\pi$
$8$	1.00000			0.353553
$9$	0.803221	−	2.89047i	0.267740	−	0.963491i
$10$	1.16085	−	0.670219i	0.367094	−	0.211942i
$11$	−1.36246	+	0.786617i	−0.410798	+	0.237174i	−0.691132	−	0.722728i	$-0.742888\pi$
$11$	−1.36246	+	0.786617i	−0.410798	+	0.237174i	0.280335	+	0.959902i	$0.409555\pi$
$12$	−1.37899	+	1.04804i	−0.398080	+	0.302543i
$13$			1.86329i			0.516782i	0.966040	+	0.258391i	$0.0831923\pi$
$13$			1.86329i			0.516782i	−0.966040	+	0.258391i	$0.916808\pi$
$14$	1.55924	+	2.70068i	0.416725	+	0.721788i
$15$	−0.898387	+	2.14085i	−0.231963	+	0.552764i
$16$	1.00000			0.250000
$17$	1.18474	+	0.684010i	0.287342	+	0.165897i	0.636742	−	0.771077i	$-0.280281\pi$
$17$	1.18474	+	0.684010i	0.287342	+	0.165897i	−0.349401	+	0.936973i	$0.613615\pi$
$18$	0.803221	−	2.89047i	0.189321	−	0.681291i
$19$	4.27933	+	0.829035i	0.981747	+	0.190194i
$19$	4.27933	+	0.829035i	0.981747	+	0.190194i
$20$	1.16085	−	0.670219i	0.259575	−	0.149866i
$21$	−4.98060	−	2.09007i	−1.08686	−	0.456090i
$22$	−1.36246	+	0.786617i	−0.290478	+	0.167707i
$23$			2.31685i			0.483096i	0.970389	+	0.241548i	$0.0776551\pi$
$23$			2.31685i			0.483096i	−0.970389	+	0.241548i	$0.922345\pi$
$24$	−1.37899	+	1.04804i	−0.281485	+	0.213930i
$25$	−1.60161	+	2.77408i	−0.320323	+	0.554815i
$26$			1.86329i			0.365420i
$27$	1.92170	+	4.82774i	0.369832	+	0.929099i
$28$	1.55924	+	2.70068i	0.294669	+	0.510381i
$29$	3.31526	−	5.74220i	0.615628	−	1.06630i	−0.374646	−	0.927168i	$-0.622236\pi$
$29$	3.31526	−	5.74220i	0.615628	−	1.06630i	0.990274	−	0.139131i	$-0.0444311\pi$
$30$	−0.898387	+	2.14085i	−0.164022	+	0.390863i
$31$	−2.34559	−	1.35423i	−0.421281	−	0.243227i	0.274344	−	0.961632i	$-0.411539\pi$
$31$	−2.34559	−	1.35423i	−0.421281	−	0.243227i	−0.695625	+	0.718405i	$0.744873\pi$
$32$	1.00000			0.176777
$33$	1.05441	−	2.51265i	0.183550	−	0.437396i
$34$	1.18474	+	0.684010i	0.203181	+	0.117307i
$35$	3.62010	+	2.09007i	0.611908	+	0.353285i
$36$	0.803221	−	2.89047i	0.133870	−	0.481746i
$37$		−	4.55619i		−	0.749034i	−0.927220	−	0.374517i	$-0.877809\pi$
$37$		−	4.55619i		−	0.749034i	0.927220	−	0.374517i	$-0.122191\pi$
$38$	4.27933	+	0.829035i	0.694200	+	0.134487i
$39$	−1.95280	−	2.56945i	−0.312698	−	0.411441i
$40$	1.16085	−	0.670219i	0.183547	−	0.105971i
$41$	−5.32171	−	9.21747i	−0.831111	−	1.43953i	−0.897158	−	0.441710i	$-0.854372\pi$
$41$	−5.32171	−	9.21747i	−0.831111	−	1.43953i	0.0660470	−	0.997817i	$-0.478961\pi$
$42$	−4.98060	−	2.09007i	−0.768524	−	0.322504i
$43$	−8.41611			−1.28344			−0.641722	−	0.766937i	$-0.721780\pi$
$43$	−8.41611			−1.28344			−0.641722	+	0.766937i	$0.721780\pi$
$44$	−1.36246	+	0.786617i	−0.205399	+	0.118587i
$45$	−1.00483	−	3.89375i	−0.149791	−	0.580446i
$46$			2.31685i			0.341600i
$47$	3.82171	+	2.20646i	0.557453	+	0.321846i	0.752123	−	0.659023i	$-0.229030\pi$
$47$	3.82171	+	2.20646i	0.557453	+	0.321846i	−0.194669	+	0.980869i	$0.562363\pi$
$48$	−1.37899	+	1.04804i	−0.199040	+	0.151272i
$49$	−1.36246	+	2.35985i	−0.194637	+	0.337122i
$50$	−1.60161	+	2.77408i	−0.226502	+	0.392313i
$51$	−2.35061	+	0.298414i	−0.329152	+	0.0417863i
$52$			1.86329i			0.258391i
$53$	−4.02331	−	6.96859i	−0.552645	−	0.957209i	−0.998083	−	0.0618959i	$-0.980285\pi$
$53$	−4.02331	−	6.96859i	−0.552645	−	0.957209i	0.445438	−	0.895313i	$-0.353048\pi$
$54$	1.92170	+	4.82774i	0.261510	+	0.656972i
$55$	−1.05441	+	1.82629i	−0.142177	+	0.246258i
$56$	1.55924	+	2.70068i	0.208362	+	0.360894i
$57$	−6.77002	+	3.34169i	−0.896711	+	0.442617i
$58$	3.31526	−	5.74220i	0.435315	−	0.753988i
$59$	−5.63697	−	9.76351i	−0.733871	−	1.27110i	−0.955217	−	0.295906i	$-0.904379\pi$
$59$	−5.63697	−	9.76351i	−0.733871	−	1.27110i	0.221347	−	0.975195i	$-0.428955\pi$
$60$	−0.898387	+	2.14085i	−0.115981	+	0.276382i
$61$	−2.14881	+	3.72186i	−0.275127	+	0.476535i	−0.970167	−	0.242437i	$-0.922053\pi$
$61$	−2.14881	+	3.72186i	−0.275127	+	0.476535i	0.695040	+	0.718971i	$0.255387\pi$
$62$	−2.34559	−	1.35423i	−0.297891	−	0.171987i
$63$	9.05867	−	2.33770i	1.14128	−	0.294522i
$64$	1.00000			0.125000
$65$	1.24881	+	2.16300i	0.154896	+	0.268287i
$66$	1.05441	−	2.51265i	0.129789	−	0.309286i
$67$		−	4.79251i		−	0.585498i	−0.956189	−	0.292749i	$-0.905430\pi$
$67$		−	4.79251i		−	0.585498i	0.956189	−	0.292749i	$-0.0945700\pi$
$68$	1.18474	+	0.684010i	0.143671	+	0.0829484i
$69$	−2.42815	−	3.19490i	−0.292315	−	0.384621i
$70$	3.62010	+	2.09007i	0.432685	+	0.249811i
$71$	6.82171	−	11.8155i	0.809588	−	1.40225i	−0.103562	−	0.994623i	$-0.533024\pi$
$71$	6.82171	−	11.8155i	0.809588	−	1.40225i	0.913150	−	0.407624i	$-0.133643\pi$
$72$	0.803221	−	2.89047i	0.0946605	−	0.340646i
$73$	2.70805	−	4.69049i	0.316954	−	0.548980i	−0.662897	−	0.748711i	$-0.730673\pi$
$73$	2.70805	−	4.69049i	0.316954	−	0.548980i	0.979851	+	0.199730i	$0.0640066\pi$
$74$		−	4.55619i		−	0.529647i
$75$	−0.698737	−	5.50397i	−0.0806832	−	0.635544i
$76$	4.27933	+	0.829035i	0.490873	+	0.0950969i
$77$	−4.24881	−	2.45305i	−0.484197	−	0.279551i
$78$	−1.95280	−	2.56945i	−0.221111	−	0.290933i
$79$			9.76790i			1.09897i	0.835502	+	0.549487i	$0.185177\pi$
$79$			9.76790i			1.09897i	−0.835502	+	0.549487i	$0.814823\pi$
$80$	1.16085	−	0.670219i	0.129787	−	0.0749328i
$81$	−7.70967	−	4.64338i	−0.856630	−	0.515931i
$82$	−5.32171	−	9.21747i	−0.587684	−	1.01790i
$83$	3.32873	−	1.92184i	0.365375	−	0.210949i	−0.306061	−	0.952012i	$-0.599011\pi$
$83$	3.32873	−	1.92184i	0.365375	−	0.210949i	0.671436	+	0.741063i	$0.265678\pi$
$84$	−4.98060	−	2.09007i	−0.543428	−	0.228045i
$85$	1.83375			0.198898
$86$	−8.41611			−0.907532
$87$	1.44635	+	11.3930i	0.155065	+	1.22145i
$88$	−1.36246	+	0.786617i	−0.145239	+	0.0838537i
$89$	3.19119	+	5.52730i	0.338265	+	0.585892i	0.984107	−	0.177579i	$-0.0568266\pi$
$89$	3.19119	+	5.52730i	0.338265	+	0.585892i	−0.645841	+	0.763472i	$0.723493\pi$
$90$	−1.00483	−	3.89375i	−0.105918	−	0.410437i
$91$	−5.03214	+	2.90531i	−0.527512	+	0.304559i
$92$			2.31685i			0.241548i
$93$	4.65383	−	0.590811i	0.482580	−	0.0612642i
$94$	3.82171	+	2.20646i	0.394179	+	0.227579i
$95$	5.52331	−	1.90570i	0.566680	−	0.195521i
$96$	−1.37899	+	1.04804i	−0.140742	+	0.106965i
$97$			6.71422i			0.681726i	0.940113	+	0.340863i	$0.110719\pi$
$97$			6.71422i			0.681726i	−0.940113	+	0.340863i	$0.889281\pi$
$98$	−1.36246	+	2.35985i	−0.137629	+	0.238381i
$99$	1.17934	+	4.56999i	0.118528	+	0.459301i
$100$	−1.60161	+	2.77408i	−0.160161	+	0.277408i
$101$	0.458673	+	0.264815i	0.0456397	+	0.0263501i	0.522646	−	0.852550i	$-0.324945\pi$
$101$	0.458673	+	0.264815i	0.0456397	+	0.0263501i	−0.477007	+	0.878900i	$0.658278\pi$
$102$	−2.35061	+	0.298414i	−0.232745	+	0.0295474i
$103$	17.0390	+	9.83749i	1.67891	+	0.969317i	0.962360	+	0.271777i	$0.0876114\pi$
$103$	17.0390	+	9.83749i	1.67891	+	0.969317i	0.716546	+	0.697540i	$0.245722\pi$
$104$			1.86329i			0.182710i
$105$	−7.18255	+	0.911835i	−0.700945	+	0.0889860i
$106$	−4.02331	−	6.96859i	−0.390779	−	0.676849i
$107$	−12.9860			−1.25540			−0.627700	−	0.778455i	$-0.716004\pi$
$107$	−12.9860			−1.25540			−0.627700	+	0.778455i	$0.716004\pi$
$108$	1.92170	+	4.82774i	0.184916	+	0.464549i
$109$	−10.0233	−	5.78696i	−0.960059	−	0.554291i	−0.0638681	−	0.997958i	$-0.520344\pi$
$109$	−10.0233	−	5.78696i	−0.960059	−	0.554291i	−0.896191	+	0.443668i	$0.853677\pi$
$110$	−1.05441	+	1.82629i	−0.100534	+	0.174130i
$111$	4.77508	+	6.28294i	0.453230	+	0.596350i
$112$	1.55924	+	2.70068i	0.147334	+	0.255191i
$113$	−2.79839	+	4.84696i	−0.263251	+	0.455963i	−0.967104	−	0.254382i	$-0.918128\pi$
$113$	−2.79839	+	4.84696i	−0.263251	+	0.455963i	0.703853	+	0.710345i	$0.251461\pi$
$114$	−6.77002	+	3.34169i	−0.634070	+	0.312978i
$115$	1.55279	+	2.68952i	0.144799	+	0.250799i
$116$	3.31526	−	5.74220i	0.307814	−	0.533150i
$117$	5.38578	+	1.49663i	0.497915	+	0.138363i
$118$	−5.63697	−	9.76351i	−0.518925	−	0.898804i
$119$			4.26614i			0.391077i
$120$	−0.898387	+	2.14085i	−0.0820111	+	0.195432i
$121$	−4.26247	+	7.38281i	−0.387497	+	0.671164i
$122$	−2.14881	+	3.72186i	−0.194544	+	0.336961i
$123$	16.9989	+	7.13342i	1.53274	+	0.643199i
$124$	−2.34559	−	1.35423i	−0.210641	−	0.121613i
$125$			10.9959i			0.983505i
$126$	9.05867	−	2.33770i	0.807010	−	0.208259i
$127$	−9.65441	+	5.57397i	−0.856690	+	0.494610i	−0.862902	−	0.505370i	$-0.831356\pi$
$127$	−9.65441	+	5.57397i	−0.856690	+	0.494610i	0.00621242	+	0.999981i	$0.498023\pi$
$128$	1.00000			0.0883883
$129$	11.6057	−	8.82043i	1.02183	−	0.776595i
$130$	1.24881	+	2.16300i	0.109528	+	0.189708i
$131$	11.1976	−	6.46496i	0.978342	−	0.564846i	0.0765727	−	0.997064i	$-0.475602\pi$
$131$	11.1976	−	6.46496i	0.978342	−	0.564846i	0.901769	+	0.432218i	$0.142269\pi$
$132$	1.05441	−	2.51265i	0.0917748	−	0.218698i
$133$	4.43355	+	12.8498i	0.384437	+	1.11422i
$134$		−	4.79251i		−	0.414009i
$135$	5.46646	+	4.31634i	0.470478	+	0.371491i
$136$	1.18474	+	0.684010i	0.101591	+	0.0586534i
$137$	−3.14341	−	1.81485i	−0.268560	−	0.155053i	0.359673	−	0.933078i	$-0.382888\pi$
$137$	−3.14341	−	1.81485i	−0.268560	−	0.155053i	−0.628233	+	0.778025i	$0.716222\pi$
$138$	−2.42815	−	3.19490i	−0.206698	−	0.271968i
$139$	1.59355			0.135163			0.0675815	−	0.997714i	$-0.478472\pi$
$139$	1.59355			0.135163			0.0675815	+	0.997714i	$0.478472\pi$
$140$	3.62010	+	2.09007i	0.305954	+	0.176643i
$141$	−7.58255	+	0.962616i	−0.638566	+	0.0810669i
$142$	6.82171	−	11.8155i	0.572465	−	0.991538i
$143$	−1.46569	−	2.53865i	−0.122567	−	0.212293i
$144$	0.803221	−	2.89047i	0.0669351	−	0.240873i
$145$		−	8.88780i		−	0.738092i
$146$	2.70805	−	4.69049i	0.224120	−	0.388188i
$147$	−0.594402	−	4.68212i	−0.0490255	−	0.386175i
$148$		−	4.55619i		−	0.374517i
$149$	5.26170	−	3.03785i	0.431055	−	0.248870i	−0.268741	−	0.963213i	$-0.586607\pi$
$149$	5.26170	−	3.03785i	0.431055	−	0.248870i	0.699796	+	0.714343i	$0.253274\pi$
$150$	−0.698737	−	5.50397i	−0.0570517	−	0.449398i
$151$	−14.7430	+	8.51189i	−1.19977	+	0.692688i	−0.960504	−	0.278266i	$-0.910240\pi$
$151$	−14.7430	+	8.51189i	−1.19977	+	0.692688i	−0.239267	+	0.970954i	$0.576907\pi$
$152$	4.27933	+	0.829035i	0.347100	+	0.0672436i
$153$	2.92872	−	2.87505i	0.236773	−	0.232434i
$154$	−4.24881	−	2.45305i	−0.342379	−	0.197672i
$155$	−3.63052			−0.291610
$156$	−1.95280	−	2.56945i	−0.156349	−	0.205721i
$157$	−5.71527	−	9.89913i	−0.456128	−	0.790037i	0.542624	−	0.839975i	$-0.317431\pi$
$157$	−5.71527	−	9.89913i	−0.456128	−	0.790037i	−0.998752	+	0.0499389i	$0.984097\pi$
$158$			9.76790i			0.777092i
$159$	12.8515	+	5.39300i	1.01919	+	0.427693i
$160$	1.16085	−	0.670219i	0.0917735	−	0.0529855i
$161$	−6.25707	+	3.61252i	−0.493126	+	0.284706i
$162$	−7.70967	−	4.64338i	−0.605729	−	0.364818i
$163$	5.20323			0.407548			0.203774	−	0.979018i	$-0.434679\pi$
$163$	5.20323			0.407548			0.203774	+	0.979018i	$0.434679\pi$
$164$	−5.32171	−	9.21747i	−0.415555	−	0.719763i
$165$	−0.460009	−	3.62351i	−0.0358117	−	0.282090i
$166$	3.32873	−	1.92184i	0.258359	−	0.149164i
$167$	2.44984			0.189575			0.0947873	−	0.995498i	$-0.469783\pi$
$167$	2.44984			0.189575			0.0947873	+	0.995498i	$0.469783\pi$
$168$	−4.98060	−	2.09007i	−0.384262	−	0.161252i
$169$	9.52817			0.732936
$170$	1.83375			0.140642
$171$	5.83355	−	11.7034i	0.446103	−	0.894982i
$172$	−8.41611			−0.641722
$173$	11.5221			0.876008			0.438004	−	0.898973i	$-0.355686\pi$
$173$	11.5221			0.876008			0.438004	+	0.898973i	$0.355686\pi$
$174$	1.44635	+	11.3930i	0.109648	+	0.863698i
$175$	−9.98920			−0.755112
$176$	−1.36246	+	0.786617i	−0.102699	+	0.0592935i
$177$	18.0059	+	7.55600i	1.35340	+	0.567944i
$178$	3.19119	+	5.52730i	0.239190	+	0.414288i
$179$	−22.7029			−1.69690			−0.848449	−	0.529278i	$-0.822463\pi$
$179$	−22.7029			−1.69690			−0.848449	+	0.529278i	$0.822463\pi$
$180$	−1.00483	−	3.89375i	−0.0748955	−	0.290223i
$181$	3.76806	−	2.17549i	0.280078	−	0.161703i	−0.353381	−	0.935480i	$-0.614968\pi$
$181$	3.76806	−	2.17549i	0.280078	−	0.161703i	0.633459	+	0.773777i	$0.281635\pi$
$182$	−5.03214	+	2.90531i	−0.373007	+	0.215356i
$183$	−0.937465	−	7.38444i	−0.0692994	−	0.545874i
$184$			2.31685i			0.170800i
$185$	−3.05365	−	5.28907i	−0.224509	−	0.388860i
$186$	4.65383	−	0.590811i	0.341236	−	0.0433204i
$187$	−2.15222			−0.157386
$188$	3.82171	+	2.20646i	0.278727	+	0.160923i
$189$	−10.0418	+	12.7175i	−0.730434	+	0.925063i
$190$	5.52331	−	1.90570i	0.400703	−	0.138254i
$191$	−14.8549	+	8.57646i	−1.07486	+	0.620571i	−0.929505	−	0.368808i	$-0.879766\pi$
$191$	−14.8549	+	8.57646i	−1.07486	+	0.620571i	−0.145355	+	0.989380i	$0.546433\pi$
$192$	−1.37899	+	1.04804i	−0.0995200	+	0.0756358i
$193$	11.6865	−	6.74723i	0.841216	−	0.485676i	−0.0164612	−	0.999865i	$-0.505240\pi$
$193$	11.6865	−	6.74723i	0.841216	−	0.485676i	0.857677	+	0.514188i	$0.171907\pi$
$194$			6.71422i			0.482053i
$195$	−3.98901	−	1.67395i	−0.285659	−	0.119874i
$196$	−1.36246	+	2.35985i	−0.0973187	+	0.168561i
$197$			9.03983i			0.644061i	0.946729	+	0.322031i	$0.104365\pi$
$197$			9.03983i			0.644061i	−0.946729	+	0.322031i	$0.895635\pi$
$198$	1.17934	+	4.56999i	0.0838120	+	0.324775i
$199$	−0.483132	−	0.836810i	−0.0342483	−	0.0593199i	0.848393	−	0.529367i	$-0.177570\pi$
$199$	−0.483132	−	0.836810i	−0.0342483	−	0.0593199i	−0.882642	+	0.470047i	$0.844237\pi$
$200$	−1.60161	+	2.77408i	−0.113251	+	0.196157i
$201$	5.02274	+	6.60881i	0.354277	+	0.466150i
$202$	0.458673	+	0.264815i	0.0322722	+	0.0186323i
$203$	20.6771			1.45125
$204$	−2.35061	+	0.298414i	−0.164576	+	0.0208931i
$205$	−12.3554	−	7.13342i	−0.862942	−	0.498220i
$206$	17.0390	+	9.83749i	1.18717	+	0.685411i
$207$	6.69678	+	1.86094i	0.465458	+	0.129344i
$208$			1.86329i			0.129196i
$209$	−6.48256	+	2.23667i	−0.448408	+	0.154714i
$210$	−7.18255	+	0.911835i	−0.495643	+	0.0629226i
$211$	12.8154	−	7.39895i	0.882245	−	0.509364i	0.0108471	−	0.999941i	$-0.496547\pi$
$211$	12.8154	−	7.39895i	0.882245	−	0.509364i	0.871398	+	0.490577i	$0.163214\pi$
$212$	−4.02331	−	6.96859i	−0.276322	−	0.478604i
$213$	2.97611	+	23.4429i	0.203920	+	1.60628i
$214$	−12.9860			−0.887702
$215$	−9.76987	+	5.64064i	−0.666300	+	0.384688i
$216$	1.92170	+	4.82774i	0.130755	+	0.328486i
$217$		−	8.44627i		−	0.573370i
$218$	−10.0233	−	5.78696i	−0.678865	−	0.391943i
$219$	1.18145	+	9.30628i	0.0798347	+	0.628860i
$220$	−1.05441	+	1.82629i	−0.0710884	+	0.123129i
$221$	−1.27451	+	2.20751i	−0.0857325	+	0.148493i
$222$	4.77508	+	6.28294i	0.320482	+	0.421683i
$223$		−	28.0299i		−	1.87702i	−0.345252	−	0.938510i	$-0.612206\pi$
$223$		−	28.0299i		−	1.87702i	0.345252	−	0.938510i	$-0.387794\pi$
$224$	1.55924	+	2.70068i	0.104181	+	0.180447i
$225$	6.73194	+	6.85761i	0.448796	+	0.457174i
$226$	−2.79839	+	4.84696i	−0.186146	+	0.322415i
$227$	6.29137	+	10.8970i	0.417573	+	0.723258i	0.995695	−	0.0926927i	$-0.0295474\pi$
$227$	6.29137	+	10.8970i	0.417573	+	0.723258i	−0.578122	+	0.815951i	$0.696214\pi$
$228$	−6.77002	+	3.34169i	−0.448355	+	0.221309i
$229$	10.4235	−	18.0541i	0.688805	−	1.19305i	−0.283420	−	0.958996i	$-0.591469\pi$
$229$	10.4235	−	18.0541i	0.688805	−	1.19305i	0.972225	−	0.234049i	$-0.0751977\pi$
$230$	1.55279	+	2.68952i	0.102388	+	0.177342i
$231$	8.42996	−	1.07020i	0.554651	−	0.0704137i
$232$	3.31526	−	5.74220i	0.217657	−	0.376994i
$233$	18.2017	+	10.5088i	1.19243	+	0.688452i	0.958858	−	0.283887i	$-0.0916241\pi$
$233$	18.2017	+	10.5088i	1.19243	+	0.688452i	0.233575	+	0.972339i	$0.424957\pi$
$234$	5.38578	+	1.49663i	0.352079	+	0.0978377i
$235$	5.91525			0.385869
$236$	−5.63697	−	9.76351i	−0.366935	−	0.635551i
$237$	−10.2372	−	13.4698i	−0.664975	−	0.874959i
$238$			4.26614i			0.276533i
$239$	−4.62407	−	2.66971i	−0.299106	−	0.172689i	0.342935	−	0.939359i	$-0.388579\pi$
$239$	−4.62407	−	2.66971i	−0.299106	−	0.172689i	−0.642041	+	0.766670i	$0.721912\pi$
$240$	−0.898387	+	2.14085i	−0.0579906	+	0.138191i
$241$	20.8012	+	12.0096i	1.33992	+	0.773606i	0.986796	−	0.161969i	$-0.0517845\pi$
$241$	20.8012	+	12.0096i	1.33992	+	0.773606i	0.353129	+	0.935575i	$0.385118\pi$
$242$	−4.26247	+	7.38281i	−0.274002	+	0.474585i
$243$	15.4980	−	1.67689i	0.994197	−	0.107572i
$244$	−2.14881	+	3.72186i	−0.137564	+	0.238267i
$245$			3.65259i			0.233355i
$246$	16.9989	+	7.13342i	1.08381	+	0.454810i
$247$	−1.54473	+	7.97362i	−0.0982887	+	0.507349i
$248$	−2.34559	−	1.35423i	−0.148945	−	0.0859936i
$249$	−2.57611	+	6.13884i	−0.163254	+	0.389033i
$250$			10.9959i			0.695443i
$251$	−16.9721	+	9.79887i	−1.07127	+	0.618499i	−0.928529	−	0.371261i	$-0.878926\pi$
$251$	−16.9721	+	9.79887i	−1.07127	+	0.618499i	−0.142743	+	0.989760i	$0.545592\pi$
$252$	9.05867	−	2.33770i	0.570642	−	0.147261i
$253$	−1.82247	−	3.15661i	−0.114578	−	0.198454i
$254$	−9.65441	+	5.57397i	−0.605771	+	0.349742i
$255$	−2.52872	+	1.92184i	−0.158354	+	0.120350i
$256$	1.00000			0.0625000
$257$	0.582747			0.0363507			0.0181754	−	0.999835i	$-0.494214\pi$
$257$	0.582747			0.0363507			0.0181754	+	0.999835i	$0.494214\pi$
$258$	11.6057	−	8.82043i	0.722541	−	0.549136i
$259$	12.3048	−	7.10420i	0.764585	−	0.441434i
$260$	1.24881	+	2.16300i	0.0774478	+	0.134144i
$261$	−13.9348	−	14.1949i	−0.862542	−	0.878644i
$262$	11.1976	−	6.46496i	0.691792	−	0.399406i
$263$		−	2.52349i		−	0.155605i	−0.996969	−	0.0778024i	$-0.975210\pi$
$263$		−	2.52349i		−	0.155605i	0.996969	−	0.0778024i	$-0.0247903\pi$
$264$	1.05441	−	2.51265i	0.0648946	−	0.154643i
$265$	−9.34096	−	5.39300i	−0.573810	−	0.331290i
$266$	4.43355	+	12.8498i	0.271838	+	0.787871i
$267$	−10.1934	−	4.27759i	−0.623829	−	0.261784i
$268$		−	4.79251i		−	0.292749i
$269$	−3.64399	+	6.31157i	−0.222178	+	0.384823i	−0.955469	−	0.295092i	$-0.904650\pi$
$269$	−3.64399	+	6.31157i	−0.222178	+	0.384823i	0.733291	+	0.679915i	$0.237983\pi$
$270$	5.46646	+	4.31634i	0.332678	+	0.262684i
$271$	−14.5699	+	25.2359i	−0.885061	+	1.53297i	−0.0394174	+	0.999223i	$0.512550\pi$
$271$	−14.5699	+	25.2359i	−0.885061	+	1.53297i	−0.845644	+	0.533748i	$0.820783\pi$
$272$	1.18474	+	0.684010i	0.0718354	+	0.0414742i
$273$	3.89439	−	9.28028i	0.235699	−	0.561668i
$274$	−3.14341	−	1.81485i	−0.189901	−	0.109639i
$275$		−	5.03943i		−	0.303889i
$276$	−2.42815	−	3.19490i	−0.146157	−	0.192311i
$277$	−7.83232	−	13.5660i	−0.470598	−	0.815100i	0.528836	−	0.848724i	$-0.322629\pi$
$277$	−7.83232	−	13.5660i	−0.470598	−	0.815100i	−0.999435	+	0.0336235i	$0.989295\pi$
$278$	1.59355			0.0955747
$279$	−5.79839	+	5.69213i	−0.347141	+	0.340779i
$280$	3.62010	+	2.09007i	0.216342	+	0.124905i
$281$	−12.9021	+	22.3470i	−0.769673	+	1.33311i	0.168067	+	0.985776i	$0.446247\pi$
$281$	−12.9021	+	22.3470i	−0.769673	+	1.33311i	−0.937740	+	0.347337i	$0.887086\pi$
$282$	−7.58255	+	0.962616i	−0.451535	+	0.0573230i
$283$	10.2978	+	17.8363i	0.612142	+	1.06026i	0.990879	+	0.134756i	$0.0430252\pi$
$283$	10.2978	+	17.8363i	0.612142	+	1.06026i	−0.378737	+	0.925504i	$0.623641\pi$
$284$	6.82171	−	11.8155i	0.404794	−	0.701123i
$285$	−5.61934	+	8.41660i	−0.332861	+	0.498556i
$286$	−1.46569	−	2.53865i	−0.0866682	−	0.150114i
$287$	16.5956	−	28.7445i	0.979610	−	1.69673i
$288$	0.803221	−	2.89047i	0.0473302	−	0.170323i
$289$	−7.56426	−	13.1017i	−0.444957	−	0.770687i
$290$		−	8.88780i		−	0.521910i
$291$	−7.03678	−	9.25884i	−0.412503	−	0.542763i
$292$	2.70805	−	4.69049i	0.158477	−	0.274490i
$293$	−9.98901	+	17.3015i	−0.583564	+	1.01076i	0.411489	+	0.911415i	$0.365009\pi$
$293$	−9.98901	+	17.3015i	−0.583564	+	1.01076i	−0.995053	+	0.0993477i	$0.968324\pi$
$294$	−0.594402	−	4.68212i	−0.0346663	−	0.273067i
$295$	−13.0874	−	7.55600i	−0.761977	−	0.439928i
$296$		−	4.55619i		−	0.264823i
$297$	−6.41583	−	5.06596i	−0.372284	−	0.293957i
$298$	5.26170	−	3.03785i	0.304802	−	0.175978i
$299$	−4.31694			−0.249655
$300$	−0.698737	−	5.50397i	−0.0403416	−	0.317772i
$301$	−13.1227	−	22.7292i	−0.756382	−	1.31009i
$302$	−14.7430	+	8.51189i	−0.848366	+	0.489804i
$303$	−0.910043	+	0.115531i	−0.0522806	+	0.00663710i
$304$	4.27933	+	0.829035i	0.245437	+	0.0475484i
$305$			5.76070i			0.329857i
$306$	2.92872	−	2.87505i	0.167424	−	0.164356i
$307$	−28.7886	−	16.6211i	−1.64305	−	0.948618i	−0.979739	−	0.200278i	$-0.935816\pi$
$307$	−28.7886	−	16.6211i	−1.64305	−	0.948618i	−0.663315	−	0.748340i	$-0.730851\pi$
$308$	−4.24881	−	2.45305i	−0.242098	−	0.139776i
$309$	−33.8067	+	4.29181i	−1.92320	+	0.244153i
$310$	−3.63052			−0.206200
$311$	14.0507	+	8.11217i	0.796742	+	0.459999i	0.842331	−	0.538961i	$-0.181183\pi$
$311$	14.0507	+	8.11217i	0.796742	+	0.459999i	−0.0455888	+	0.998960i	$0.514516\pi$
$312$	−1.95280	−	2.56945i	−0.110555	−	0.145466i
$313$	7.79061	−	13.4937i	0.440351	−	0.762711i	−0.557364	−	0.830268i	$-0.688187\pi$
$313$	7.79061	−	13.4937i	0.440351	−	0.762711i	0.997715	+	0.0675574i	$0.0215206\pi$
$314$	−5.71527	−	9.89913i	−0.322531	−	0.558640i
$315$	8.94902	−	8.78502i	0.504220	−	0.494980i
$316$			9.76790i			0.549487i
$317$	3.61705	−	6.26492i	0.203154	−	0.351873i	−0.746389	−	0.665510i	$-0.768214\pi$
$317$	3.61705	−	6.26492i	0.203154	−	0.351873i	0.949543	+	0.313637i	$0.101547\pi$
$318$	12.8515	+	5.39300i	0.720675	+	0.302425i
$319$			10.4314i			0.584044i
$320$	1.16085	−	0.670219i	0.0648937	−	0.0374664i
$321$	17.9075	−	13.6098i	0.999499	−	0.759626i
$322$	−6.25707	+	3.61252i	−0.348693	+	0.201318i
$323$	4.50283	+	3.90930i	0.250544	+	0.217519i
$324$	−7.70967	−	4.64338i	−0.428315	−	0.257965i
$325$	−5.16889	−	2.98426i	−0.286719	−	0.165537i
$326$	5.20323			0.288180
$327$	19.8870	−	2.52468i	1.09975	−	0.139615i
$328$	−5.32171	−	9.21747i	−0.293842	−	0.508949i
$329$			13.7616i			0.758703i
$330$	−0.460009	−	3.62351i	−0.0253227	−	0.199467i
$331$	−3.40445	+	1.96556i	−0.187126	+	0.108037i	−0.590636	−	0.806938i	$-0.701123\pi$
$331$	−3.40445	+	1.96556i	−0.187126	+	0.108037i	0.403511	+	0.914975i	$0.367790\pi$
$332$	3.32873	−	1.92184i	0.182688	−	0.105475i
$333$	−13.1696	−	3.65963i	−0.721687	−	0.200546i
$334$	2.44984			0.134050
$335$	−3.21203	−	5.56340i	−0.175492	−	0.303961i
$336$	−4.98060	−	2.09007i	−0.271714	−	0.114022i
$337$	4.44940	−	2.56886i	0.242374	−	0.139935i	−0.373893	−	0.927472i	$-0.621977\pi$
$337$	4.44940	−	2.56886i	0.242374	−	0.139935i	0.616267	+	0.787537i	$0.288644\pi$
$338$	9.52817			0.518264
$339$	−1.22086	−	9.61673i	−0.0663079	−	0.522309i
$340$	1.83375			0.0994488
$341$	4.26104			0.230748
$342$	5.83355	−	11.7034i	0.315442	−	0.632848i
$343$	13.3317			0.719847
$344$	−8.41611			−0.453766
$345$	−4.96001	−	2.08142i	−0.267038	−	0.112060i
$346$	11.5221			0.619431
$347$	−11.8953	+	6.86774i	−0.638571	+	0.368679i	−0.784064	−	0.620680i	$-0.786857\pi$
$347$	−11.8953	+	6.86774i	−0.638571	+	0.368679i	0.145493	+	0.989359i	$0.453523\pi$
$348$	1.44635	+	11.3930i	0.0775326	+	0.610727i
$349$	−7.49298	−	12.9782i	−0.401090	−	0.694708i	0.592768	−	0.805374i	$-0.298035\pi$
$349$	−7.49298	−	12.9782i	−0.401090	−	0.694708i	−0.993858	+	0.110665i	$0.964702\pi$
$350$	−9.98920			−0.533945
$351$	−8.99545	+	3.58068i	−0.480142	+	0.191122i
$352$	−1.36246	+	0.786617i	−0.0726194	+	0.0419268i
$353$	4.84321	−	2.79623i	0.257778	−	0.148828i	−0.365542	−	0.930795i	$-0.619117\pi$
$353$	4.84321	−	2.79623i	0.257778	−	0.148828i	0.623321	+	0.781966i	$0.285783\pi$
$354$	18.0059	+	7.55600i	0.957001	+	0.401597i
$355$		−	18.2881i		−	0.970634i
$356$	3.19119	+	5.52730i	0.169133	+	0.292946i
$357$	−4.47109	−	5.88297i	−0.236635	−	0.311360i
$358$	−22.7029			−1.19989
$359$	−25.4808	−	14.7113i	−1.34482	−	0.776434i	−0.357312	−	0.933985i	$-0.616307\pi$
$359$	−25.4808	−	14.7113i	−1.34482	−	0.776434i	−0.987511	+	0.157551i	$0.949640\pi$
$360$	−1.00483	−	3.89375i	−0.0529591	−	0.205219i
$361$	17.6254	+	7.09544i	0.927653	+	0.373444i
$362$	3.76806	−	2.17549i	0.198045	−	0.114341i
$363$	−1.85959	−	14.6480i	−0.0976032	−	0.768823i
$364$	−5.03214	+	2.90531i	−0.263756	+	0.152280i
$365$		−	7.25996i		−	0.380004i
$366$	−0.937465	−	7.38444i	−0.0490021	−	0.385991i
$367$	1.08275	−	1.87537i	0.0565189	−	0.0978936i	−0.836382	−	0.548148i	$-0.815333\pi$
$367$	1.08275	−	1.87537i	0.0565189	−	0.0978936i	0.892901	+	0.450254i	$0.148667\pi$
$368$			2.31685i			0.120774i
$369$	−30.9173	+	7.97859i	−1.60949	+	0.415349i
$370$	−3.05365	−	5.28907i	−0.158752	−	0.274966i
$371$	12.5466	−	21.7314i	0.651389	−	1.12824i
$372$	4.65383	−	0.590811i	0.241290	−	0.0306321i
$373$	27.1481	+	15.6739i	1.40567	+	0.811566i	0.994967	−	0.100202i	$-0.0319490\pi$
$373$	27.1481	+	15.6739i	1.40567	+	0.811566i	0.410706	+	0.911768i	$0.365282\pi$
$374$	−2.15222			−0.111288
$375$	−11.5242	−	15.1632i	−0.595106	−	0.783027i
$376$	3.82171	+	2.20646i	0.197089	+	0.113790i
$377$	10.6994	+	6.17727i	0.551045	+	0.318146i
$378$	−10.0418	+	12.7175i	−0.516494	+	0.654118i
$379$			10.4146i			0.534964i	0.963563	+	0.267482i	$0.0861916\pi$
$379$			10.4146i			0.534964i	−0.963563	+	0.267482i	$0.913808\pi$
$380$	5.52331	−	1.90570i	0.283340	−	0.0977605i
$381$	7.47157	−	17.8047i	0.382780	−	0.912160i
$382$	−14.8549	+	8.57646i	−0.760041	+	0.438810i
$383$	−3.19119	−	5.52730i	−0.163062	−	0.282432i	0.772903	−	0.634524i	$-0.218804\pi$
$383$	−3.19119	−	5.52730i	−0.163062	−	0.282432i	−0.935965	+	0.352092i	$0.885470\pi$
$384$	−1.37899	+	1.04804i	−0.0703712	+	0.0534826i
$385$	−6.57633			−0.335161
$386$	11.6865	−	6.74723i	0.594830	−	0.343425i
$387$	−6.75999	+	24.3265i	−0.343630	+	1.23659i
$388$			6.71422i			0.340863i
$389$	−5.45620	−	3.15014i	−0.276640	−	0.159718i	0.355261	−	0.934767i	$-0.384392\pi$
$389$	−5.45620	−	3.15014i	−0.276640	−	0.159718i	−0.631901	+	0.775049i	$0.717725\pi$
$390$	−3.98901	−	1.67395i	−0.201991	−	0.0847638i
$391$	−1.58475	+	2.74486i	−0.0801440	+	0.138813i
$392$	−1.36246	+	2.35985i	−0.0688147	+	0.119191i
$393$	−8.66587	+	20.6507i	−0.437136	+	1.04169i
$394$			9.03983i			0.455420i
$395$	6.54663	+	11.3391i	0.329397	+	0.570532i
$396$	1.17934	+	4.56999i	0.0592640	+	0.229650i
$397$	13.0601	−	22.6207i	0.655467	−	1.13530i	−0.326309	−	0.945263i	$-0.605805\pi$
$397$	13.0601	−	22.6207i	0.655467	−	1.13530i	0.981776	−	0.190040i	$-0.0608617\pi$
$398$	−0.483132	−	0.836810i	−0.0242172	−	0.0419455i
$399$	−19.5809	−	13.0732i	−0.980272	−	0.654478i
$400$	−1.60161	+	2.77408i	−0.0800806	+	0.138704i
$401$	−11.1900	−	19.3817i	−0.558804	−	0.967877i	−0.997597	−	0.0692887i	$-0.977927\pi$
$401$	−11.1900	−	19.3817i	−0.558804	−	0.967877i	0.438793	−	0.898588i	$-0.355406\pi$
$402$	5.02274	+	6.60881i	0.250512	+	0.329618i
$403$	2.52331	−	4.37051i	0.125695	−	0.217711i
$404$	0.458673	+	0.264815i	0.0228199	+	0.0131751i
$405$	−12.0619	−	0.223110i	−0.599360	−	0.0110864i
$406$	20.6771			1.02619
$407$	3.58398	+	6.20764i	0.177651	+	0.307701i
$408$	−2.35061	+	0.298414i	−0.116373	+	0.0147737i
$409$			28.9740i			1.43267i	0.697755	+	0.716337i	$0.254182\pi$
$409$			28.9740i			1.43267i	−0.697755	+	0.716337i	$0.745818\pi$
$410$	−12.3554	−	7.13342i	−0.610192	−	0.352294i
$411$	6.23677	−	0.791767i	0.307637	−	0.0390550i
$412$	17.0390	+	9.83749i	0.839453	+	0.484659i
$413$	17.5788	−	30.4473i	0.864995	−	1.49822i
$414$	6.69678	+	1.86094i	0.329129	+	0.0914601i
$415$	2.57611	−	4.46195i	0.126456	−	0.219029i
$416$			1.86329i			0.0913551i
$417$	−2.19749	+	1.67010i	−0.107611	+	0.0817853i
$418$	−6.48256	+	2.23667i	−0.317072	+	0.109399i
$419$	17.0286	+	9.83148i	0.831902	+	0.480299i	0.854504	−	0.519445i	$-0.173861\pi$
$419$	17.0286	+	9.83148i	0.831902	+	0.480299i	−0.0226012	+	0.999745i	$0.507195\pi$
$420$	−7.18255	+	0.911835i	−0.350473	+	0.0444930i
$421$		−	18.6819i		−	0.910498i	−0.890364	−	0.455249i	$-0.849550\pi$
$421$		−	18.6819i		−	0.910498i	0.890364	−	0.455249i	$-0.150450\pi$
$422$	12.8154	−	7.39895i	0.623842	−	0.360175i
$423$	9.44740	−	9.27426i	0.459348	−	0.450930i
$424$	−4.02331	−	6.96859i	−0.195389	−	0.338424i
$425$	−3.79499	+	2.19104i	−0.184084	+	0.106281i
$426$	2.97611	+	23.4429i	0.144193	+	1.13581i
$427$	−13.4021			−0.648572
$428$	−12.9860			−0.627700
$429$	4.68179	+	1.96467i	0.226039	+	0.0948551i
$430$	−9.76987	+	5.64064i	−0.471145	+	0.272016i
$431$	−20.5053	−	35.5162i	−0.987706	−	1.71076i	−0.629234	−	0.777216i	$-0.716631\pi$
$431$	−20.5053	−	35.5162i	−0.987706	−	1.71076i	−0.358471	−	0.933541i	$-0.616702\pi$
$432$	1.92170	+	4.82774i	0.0924579	+	0.232275i
$433$	−29.7693	+	17.1873i	−1.43062	+	0.825969i	−0.997168	−	0.0752083i	$-0.976038\pi$
$433$	−29.7693	+	17.1873i	−1.43062	+	0.825969i	−0.433452	+	0.901177i	$0.642705\pi$
$434$		−	8.44627i		−	0.405434i
$435$	9.31478	+	12.2562i	0.446609	+	0.587639i
$436$	−10.0233	−	5.78696i	−0.480030	−	0.277145i
$437$	−1.92075	+	9.91455i	−0.0918817	+	0.474277i
$438$	1.18145	+	9.30628i	0.0564517	+	0.444671i
$439$			33.2179i			1.58541i	0.609608	+	0.792703i	$0.291327\pi$
$439$			33.2179i			1.58541i	−0.609608	+	0.792703i	$0.708673\pi$
$440$	−1.05441	+	1.82629i	−0.0502671	+	0.0870652i
$441$	5.72673	+	5.83364i	0.272702	+	0.277792i
$442$	−1.27451	+	2.20751i	−0.0606220	+	0.105000i
$443$	−20.3759	−	11.7640i	−0.968090	−	0.558927i	−0.0694363	−	0.997586i	$-0.522120\pi$
$443$	−20.3759	−	11.7640i	−0.968090	−	0.558927i	−0.898653	+	0.438660i	$0.855453\pi$
$444$	4.77508	+	6.28294i	0.226615	+	0.298175i
$445$	7.40900	+	4.27759i	0.351220	+	0.202777i
$446$		−	28.0299i		−	1.32725i
$447$	−4.07204	+	9.70363i	−0.192601	+	0.458966i
$448$	1.55924	+	2.70068i	0.0736672	+	0.127595i
$449$	26.0258			1.22823			0.614116	−	0.789215i	$-0.289513\pi$
$449$	26.0258			1.22823			0.614116	+	0.789215i	$0.289513\pi$
$450$	6.73194	+	6.85761i	0.317347	+	0.323271i
$451$	14.5012	+	8.37229i	0.682837	+	0.394236i
$452$	−2.79839	+	4.84696i	−0.131625	+	0.227982i
$453$	11.4097	−	27.1891i	0.536073	−	1.27746i
$454$	6.29137	+	10.8970i	0.295269	+	0.511421i
$455$	−3.89439	+	6.74528i	−0.182572	+	0.316223i
$456$	−6.77002	+	3.34169i	−0.317035	+	0.156489i
$457$	17.8876	+	30.9822i	0.836746	+	1.44929i	0.892601	+	0.450848i	$0.148878\pi$
$457$	17.8876	+	30.9822i	0.836746	+	1.44929i	−0.0558550	+	0.998439i	$0.517788\pi$
$458$	10.4235	−	18.0541i	0.487059	−	0.843610i
$459$	−1.02550	+	7.03408i	−0.0478665	+	0.328323i
$460$	1.55279	+	2.68952i	0.0723994	+	0.125399i
$461$			31.5166i			1.46788i	0.679217	+	0.733938i	$0.262320\pi$
$461$			31.5166i			1.46788i	−0.679217	+	0.733938i	$0.737680\pi$
$462$	8.42996	−	1.07020i	0.392197	−	0.0497900i
$463$	−9.60721	+	16.6402i	−0.446485	+	0.773334i	−0.998154	−	0.0607285i	$-0.980658\pi$
$463$	−9.60721	+	16.6402i	−0.446485	+	0.773334i	0.551670	+	0.834063i	$0.313991\pi$
$464$	3.31526	−	5.74220i	0.153907	−	0.266575i
$465$	5.00645	−	3.80493i	0.232168	−	0.176450i
$466$	18.2017	+	10.5088i	0.843178	+	0.486809i
$467$			10.9865i			0.508396i	0.967152	+	0.254198i	$0.0818115\pi$
$467$			10.9865i			0.508396i	−0.967152	+	0.254198i	$0.918189\pi$
$468$	5.38578	+	1.49663i	0.248958	+	0.0691817i
$469$	12.9430	−	7.47267i	0.597654	−	0.345056i
$470$	5.91525			0.272850
$471$	18.2560	+	7.66096i	0.841191	+	0.352998i
$472$	−5.63697	−	9.76351i	−0.259462	−	0.449402i
$473$	11.4666	−	6.62026i	0.527236	−	0.304400i
$474$	−10.2372	−	13.4698i	−0.470208	−	0.618689i
$475$	−9.15364	+	10.5434i	−0.419998	+	0.483764i
$476$			4.26614i			0.195538i
$477$	−23.3741	+	6.03197i	−1.07023	+	0.276185i
$478$	−4.62407	−	2.66971i	−0.211500	−	0.122110i
$479$	−7.41668	−	4.28202i	−0.338877	−	0.195651i	0.320898	−	0.947114i	$-0.396015\pi$
$479$	−7.41668	−	4.28202i	−0.338877	−	0.195651i	−0.659775	+	0.751463i	$0.729349\pi$
$480$	−0.898387	+	2.14085i	−0.0410056	+	0.0977158i
$481$	8.48949			0.387087
$482$	20.8012	+	12.0096i	0.947470	+	0.547022i
$483$	4.84236	−	11.5393i	0.220335	−	0.525056i
$484$	−4.26247	+	7.38281i	−0.193748	+	0.335582i
$485$	4.50000	+	7.79423i	0.204334	+	0.353918i
$486$	15.4980	−	1.67689i	0.703004	−	0.0760651i
$487$			39.5989i			1.79440i	0.441628	+	0.897198i	$0.354401\pi$
$487$			39.5989i			1.79440i	−0.441628	+	0.897198i	$0.645599\pi$
$488$	−2.14881	+	3.72186i	−0.0972722	+	0.168480i
$489$	−7.17519	+	5.45319i	−0.324473	+	0.246602i
$490$			3.65259i			0.165007i
$491$	10.8270	−	6.25098i	0.488616	−	0.282103i	−0.235384	−	0.971902i	$-0.575635\pi$
$491$	10.8270	−	6.25098i	0.488616	−	0.282103i	0.724000	+	0.689800i	$0.242301\pi$
$492$	16.9989	+	7.13342i	0.766368	+	0.321599i
$493$	7.85544	−	4.53534i	0.353791	−	0.204262i
$494$	−1.54473	+	7.97362i	−0.0695006	+	0.358750i
$495$	4.43193	+	4.51467i	0.199200	+	0.202919i
$496$	−2.34559	−	1.35423i	−0.105320	−	0.0608067i
$497$	42.5467			1.90848
$498$	−2.57611	+	6.13884i	−0.115438	+	0.275088i
$499$	−7.58113	−	13.1309i	−0.339378	−	0.587820i	0.644938	−	0.764235i	$-0.276883\pi$
$499$	−7.58113	−	13.1309i	−0.339378	−	0.587820i	−0.984316	+	0.176415i	$0.943550\pi$
$500$			10.9959i			0.491752i
$501$	−3.37831	+	2.56754i	−0.150932	+	0.114709i
$502$	−16.9721	+	9.79887i	−0.757504	+	0.437345i
$503$	5.06362	−	2.92348i	0.225776	−	0.130352i	−0.382846	−	0.923812i	$-0.625056\pi$
$503$	5.06362	−	2.92348i	0.225776	−	0.130352i	0.608622	+	0.793460i	$0.291723\pi$
$504$	9.05867	−	2.33770i	0.403505	−	0.104129i
$505$	0.709937			0.0315918
$506$	−1.82247	−	3.15661i	−0.0810187	−	0.140329i
$507$	−13.1392	+	9.98591i	−0.583534	+	0.443490i
$508$	−9.65441	+	5.57397i	−0.428345	+	0.247305i
$509$	−12.7109			−0.563400			−0.281700	−	0.959503i	$-0.590898\pi$
$509$	−12.7109			−0.563400			−0.281700	+	0.959503i	$0.590898\pi$
$510$	−2.52872	+	1.92184i	−0.111973	+	0.0851005i
$511$	16.8900			0.747171
$512$	1.00000			0.0441942
$513$	4.22124	+	22.2527i	0.186372	+	0.982479i
$514$	0.582747			0.0257039
$515$	26.3731			1.16214
$516$	11.6057	−	8.82043i	0.510913	−	0.388298i
$517$	−6.94257			−0.305334
$518$	12.3048	−	7.10420i	0.540644	−	0.312141i
$519$	−15.8888	+	12.0756i	−0.697442	+	0.530060i
$520$	1.24881	+	2.16300i	0.0547639	+	0.0948539i
$521$	−41.6061			−1.82279			−0.911397	−	0.411527i	$-0.864995\pi$
$521$	−41.6061			−1.82279			−0.911397	+	0.411527i	$0.864995\pi$
$522$	−13.9348	−	14.1949i	−0.609909	−	0.621295i
$523$	18.7605	−	10.8314i	0.820338	−	0.473622i	−0.0301950	−	0.999544i	$-0.509613\pi$
$523$	18.7605	−	10.8314i	0.820338	−	0.473622i	0.850533	+	0.525922i	$0.176280\pi$
$524$	11.1976	−	6.46496i	0.489171	−	0.282423i
$525$	13.7750	−	10.4691i	0.601190	−	0.456908i
$526$		−	2.52349i		−	0.110029i
$527$	−1.85261	−	3.20882i	−0.0807011	−	0.139778i
$528$	1.05441	−	2.51265i	0.0458874	−	0.109349i
$529$	17.6322			0.766619
$530$	−9.34096	−	5.39300i	−0.405745	−	0.234257i
$531$	−32.7489	+	8.45125i	−1.42118	+	0.366753i
$532$	4.43355	+	12.8498i	0.192219	+	0.557109i
$533$	17.1748	−	9.91586i	0.743922	−	0.429503i
$534$	−10.1934	−	4.27759i	−0.441113	−	0.185109i
$535$	−15.0748	+	8.70344i	−0.651740	+	0.376282i
$536$		−	4.79251i		−	0.207005i
$537$	31.3071	−	23.7936i	1.35100	−	1.02677i
$538$	−3.64399	+	6.31157i	−0.157103	+	0.272111i
$539$		−	4.28694i		−	0.184652i
$540$	5.46646	+	4.31634i	0.235239	+	0.185746i
$541$	14.3410	+	24.8393i	0.616566	+	1.06792i	0.990108	+	0.140310i	$0.0448099\pi$
$541$	14.3410	+	24.8393i	0.616566	+	1.06792i	−0.373542	+	0.927613i	$0.621857\pi$
$542$	−14.5699	+	25.2359i	−0.625833	+	1.08397i
$543$	−2.91611	+	6.94906i	−0.125142	+	0.298213i
$544$	1.18474	+	0.684010i	0.0507953	+	0.0293267i
$545$	−15.5141			−0.664552
$546$	3.89439	−	9.28028i	0.166664	−	0.397159i
$547$	−20.7857	−	12.0006i	−0.888733	−	0.513110i	−0.0152052	−	0.999884i	$-0.504840\pi$
$547$	−20.7857	−	12.0006i	−0.888733	−	0.513110i	−0.873528	+	0.486774i	$0.838173\pi$
$548$	−3.14341	−	1.81485i	−0.134280	−	0.0775266i
$549$	9.03195	+	9.20056i	0.385474	+	0.392670i
$550$		−	5.03943i		−	0.214882i
$551$	18.9476	−	21.8243i	0.807194	−	0.929747i
$552$	−2.42815	−	3.19490i	−0.103349	−	0.135984i
$553$	−26.3800	+	15.2305i	−1.12179	+	0.647667i
$554$	−7.83232	−	13.5660i	−0.332763	−	0.576363i
$555$	9.75411	+	4.09323i	0.414039	+	0.173748i
$556$	1.59355			0.0675815
$557$	−1.35487	+	0.782235i	−0.0574077	+	0.0331443i	−0.528429	−	0.848977i	$-0.677219\pi$
$557$	−1.35487	+	0.782235i	−0.0574077	+	0.0331443i	0.471021	+	0.882122i	$0.343885\pi$
$558$	−5.79839	+	5.69213i	−0.245466	+	0.240967i
$559$		−	15.6816i		−	0.663261i
$560$	3.62010	+	2.09007i	0.152977	+	0.0883214i
$561$	2.96788	−	2.25561i	0.125304	−	0.0952320i
$562$	−12.9021	+	22.3470i	−0.544241	+	0.942653i
$563$	−2.73715	+	4.74089i	−0.115357	+	0.199805i	−0.917923	−	0.396760i	$-0.870135\pi$
$563$	−2.73715	+	4.74089i	−0.115357	+	0.199805i	0.802565	+	0.596564i	$0.203468\pi$
$564$	−7.58255	+	0.962616i	−0.319283	+	0.0405335i
$565$			7.50214i			0.315618i
$566$	10.2978	+	17.8363i	0.432850	+	0.749718i
$567$	0.519058	−	28.0615i	0.0217984	−	1.17847i
$568$	6.82171	−	11.8155i	0.286232	−	0.495769i
$569$	16.9645	+	29.3835i	0.711191	+	1.23182i	0.964410	+	0.264410i	$0.0851772\pi$
$569$	16.9645	+	29.3835i	0.711191	+	1.23182i	−0.253220	+	0.967409i	$0.581490\pi$
$570$	−5.61934	+	8.41660i	−0.235368	+	0.352533i
$571$	10.3019	−	17.8434i	0.431120	−	0.746723i	−0.565850	−	0.824508i	$-0.691452\pi$
$571$	10.3019	−	17.8434i	0.431120	−	0.746723i	0.996970	+	0.0777859i	$0.0247851\pi$
$572$	−1.46569	−	2.53865i	−0.0612837	−	0.106146i
$573$	11.4962	−	27.3954i	0.480261	−	1.14446i
$574$	16.5956	−	28.7445i	0.692689	−	1.19977i
$575$	−6.42710	−	3.71069i	−0.268029	−	0.154746i
$576$	0.803221	−	2.89047i	0.0334675	−	0.120436i
$577$	30.9865			1.28999			0.644993	−	0.764188i	$-0.276860\pi$
$577$	30.9865			1.28999			0.644993	+	0.764188i	$0.276860\pi$
$578$	−7.56426	−	13.1017i	−0.314632	−	0.544958i
$579$	−9.04425	+	21.5523i	−0.375866	+	0.895685i
$580$		−	8.88780i		−	0.369046i
$581$	10.3806	+	5.99322i	0.430658	+	0.248641i
$582$	−7.03678	−	9.25884i	−0.291684	−	0.383791i
$583$	10.9632	+	6.32962i	0.454050	+	0.262146i
$584$	2.70805	−	4.69049i	0.112060	−	0.194094i
$585$	7.25517	−	1.87228i	0.299964	−	0.0774093i
$586$	−9.98901	+	17.3015i	−0.412642	+	0.714717i
$587$			3.68629i			0.152150i	0.997102	+	0.0760748i	$0.0242388\pi$
$587$			3.68629i			0.152150i	−0.997102	+	0.0760748i	$0.975761\pi$
$588$	−0.594402	−	4.68212i	−0.0245127	−	0.193088i
$589$	−8.91487	−	7.73978i	−0.367331	−	0.318912i
$590$	−13.0874	−	7.55600i	−0.538799	−	0.311076i
$591$	−9.47411	−	12.4658i	−0.389713	−	0.512776i
$592$		−	4.55619i		−	0.187258i
$593$	13.9558	−	8.05741i	0.573098	−	0.330878i	−0.185288	−	0.982684i	$-0.559322\pi$
$593$	13.9558	−	8.05741i	0.573098	−	0.330878i	0.758386	+	0.651806i	$0.225988\pi$
$594$	−6.41583	−	5.06596i	−0.263245	−	0.207859i
$595$	2.85925	+	4.95237i	0.117218	+	0.203027i
$596$	5.26170	−	3.03785i	0.215528	−	0.124435i
$597$	1.54324	+	0.647609i	0.0631608	+	0.0265049i
$598$	−4.31694			−0.176533
$599$	41.3371			1.68899			0.844494	−	0.535566i	$-0.179902\pi$
$599$	41.3371			1.68899			0.844494	+	0.535566i	$0.179902\pi$
$600$	−0.698737	−	5.50397i	−0.0285258	−	0.224699i
$601$	32.2081	−	18.5954i	1.31380	−	0.758521i	0.331075	−	0.943604i	$-0.392589\pi$
$601$	32.2081	−	18.5954i	1.31380	−	0.758521i	0.982723	+	0.185083i	$0.0592554\pi$
$602$	−13.1227	−	22.7292i	−0.534843	−	0.926375i
$603$	−13.8526	−	3.84944i	−0.564122	−	0.156761i
$604$	−14.7430	+	8.51189i	−0.599885	+	0.346344i
$605$			11.4271i			0.464579i
$606$	−0.910043	+	0.115531i	−0.0369680	+	0.00469314i
$607$	−27.8067	−	16.0542i	−1.12864	−	0.651621i	−0.185048	−	0.982729i	$-0.559244\pi$
$607$	−27.8067	−	16.0542i	−1.12864	−	0.651621i	−0.943593	+	0.331108i	$0.892577\pi$
$608$	4.27933	+	0.829035i	0.173550	+	0.0336218i
$609$	−28.5136	+	21.6705i	−1.15543	+	0.878133i
$610$			5.76070i			0.233244i
$611$	−4.11127	+	7.12093i	−0.166324	+	0.288082i
$612$	2.92872	−	2.87505i	0.118387	−	0.116217i
$613$	−4.60047	+	7.96825i	−0.185811	+	0.321834i	−0.943850	−	0.330376i	$-0.892825\pi$
$613$	−4.60047	+	7.96825i	−0.185811	+	0.321834i	0.758038	+	0.652210i	$0.226158\pi$
$614$	−28.7886	−	16.6211i	−1.16181	−	0.670774i
$615$	24.5141	−	3.11210i	0.988505	−	0.125492i
$616$	−4.24881	−	2.45305i	−0.171189	−	0.0988362i
$617$			39.8393i			1.60387i	0.597413	+	0.801934i	$0.296196\pi$
$617$			39.8393i			1.60387i	−0.597413	+	0.801934i	$0.703804\pi$
$618$	−33.8067	+	4.29181i	−1.35991	+	0.172642i
$619$	−17.8989	−	31.0017i	−0.719416	−	1.24606i	−0.961231	−	0.275743i	$-0.911076\pi$
$619$	−17.8989	−	31.0017i	−0.719416	−	1.24606i	0.241816	−	0.970322i	$-0.422257\pi$
$620$	−3.63052			−0.145805
$621$	−11.1851	+	4.45228i	−0.448844	+	0.178664i
$622$	14.0507	+	8.11217i	0.563381	+	0.325268i
$623$	−9.95165	+	17.2368i	−0.398705	+	0.690577i
$624$	−1.95280	−	2.56945i	−0.0781745	−	0.102860i
$625$	−0.638393	−	1.10573i	−0.0255357	−	0.0442292i
$626$	7.79061	−	13.4937i	0.311375	−	0.539318i
$627$	6.59526	−	9.87833i	0.263389	−	0.394503i
$628$	−5.71527	−	9.89913i	−0.228064	−	0.395018i
$629$	3.11648	−	5.39791i	0.124262	−	0.215229i
$630$	8.94902	−	8.78502i	0.356537	−	0.350003i
$631$	−3.63535	−	6.29661i	−0.144721	−	0.250664i	0.784548	−	0.620068i	$-0.212895\pi$
$631$	−3.63535	−	6.29661i	−0.144721	−	0.250664i	−0.929269	+	0.369404i	$0.879562\pi$
$632$			9.76790i			0.388546i
$633$	−9.91783	+	23.6341i	−0.394198	+	0.939370i
$634$	3.61705	−	6.26492i	0.143652	−	0.248812i
$635$	−7.47157	+	12.9411i	−0.296500	+	0.513553i
$636$	12.8515	+	5.39300i	0.509594	+	0.213847i
$637$	−4.39708	−	2.53865i	−0.174219	−	0.100585i
$638$			10.4314i			0.412982i
$639$	−28.6732	−	29.2085i	−1.13429	−	1.15547i
$640$	1.16085	−	0.670219i	0.0458868	−	0.0264927i
$641$	−6.12610			−0.241966			−0.120983	−	0.992655i	$-0.538605\pi$
$641$	−6.12610			−0.241966			−0.120983	+	0.992655i	$0.538605\pi$
$642$	17.9075	−	13.6098i	0.706753	−	0.537137i
$643$	6.48958	+	11.2403i	0.255924	+	0.443273i	0.965146	−	0.261712i	$-0.0842870\pi$
$643$	6.48958	+	11.2403i	0.255924	+	0.443273i	−0.709222	+	0.704985i	$0.750954\pi$
$644$	−6.25707	+	3.61252i	−0.246563	+	0.142353i
$645$	7.56092	−	18.0176i	0.297711	−	0.709442i
$646$	4.50283	+	3.90930i	0.177161	+	0.153809i
$647$		−	8.95357i		−	0.352001i	−0.984390	−	0.176001i	$-0.943684\pi$
$647$		−	8.95357i		−	0.352001i	0.984390	−	0.176001i	$-0.0563161\pi$
$648$	−7.70967	−	4.64338i	−0.302865	−	0.182409i
$649$	15.3603	+	8.86827i	0.602944	+	0.348110i
$650$	−5.16889	−	2.98426i	−0.202741	−	0.117052i
$651$	8.85204	+	11.6473i	0.346939	+	0.456494i
$652$	5.20323			0.203774
$653$	−41.1032	−	23.7309i	−1.60849	−	0.928664i	−0.989708	−	0.143103i	$-0.954292\pi$
$653$	−41.1032	−	23.7309i	−1.60849	−	0.928664i	−0.618785	−	0.785561i	$-0.712375\pi$
$654$	19.8870	−	2.52468i	0.777644	−	0.0987230i
$655$	8.66587	−	15.0097i	0.338604	−	0.586479i
$656$	−5.32171	−	9.21747i	−0.207778	−	0.359882i
$657$	−11.3826	−	11.5951i	−0.444076	−	0.452366i
$658$			13.7616i			0.536484i
$659$	1.58977	−	2.75355i	0.0619285	−	0.107263i	−0.833399	−	0.552672i	$-0.813608\pi$
$659$	1.58977	−	2.75355i	0.0619285	−	0.107263i	0.895327	+	0.445409i	$0.146942\pi$
$660$	−0.460009	−	3.62351i	−0.0179058	−	0.141045i
$661$			21.3823i			0.831677i	0.909438	+	0.415838i	$0.136512\pi$
$661$			21.3823i			0.831677i	−0.909438	+	0.415838i	$0.863488\pi$
$662$	−3.40445	+	1.96556i	−0.132318	+	0.0763937i
$663$	−0.556030	−	4.37986i	−0.0215944	−	0.170100i
$664$	3.32873	−	1.92184i	0.129180	−	0.0745819i
$665$	13.7589	+	11.9453i	0.533546	+	0.463218i
$666$	−13.1696	−	3.65963i	−0.510310	−	0.141808i
$667$	13.3038	+	7.68094i	0.515125	+	0.297407i
$668$	2.44984			0.0947873
$669$	29.3765	+	38.6529i	1.13576	+	1.49441i
$670$	−3.21203	−	5.56340i	−0.124092	−	0.214933i
$671$		−	6.76118i		−	0.261012i
$672$	−4.98060	−	2.09007i	−0.192131	−	0.0806260i
$673$	18.9878	−	10.9626i	0.731925	−	0.422577i	−0.0872011	−	0.996191i	$-0.527792\pi$
$673$	18.9878	−	10.9626i	0.731925	−	0.422577i	0.819126	+	0.573614i	$0.194459\pi$
$674$	4.44940	−	2.56886i	0.171384	−	0.0989488i
$675$	−16.4703	−	2.40122i	−0.633943	−	0.0924232i
$676$	9.52817			0.366468
$677$	12.7482	+	22.0806i	0.489955	+	0.848626i	0.999933	−	0.0115609i	$-0.00368003\pi$
$677$	12.7482	+	22.0806i	0.489955	+	0.848626i	−0.509979	+	0.860187i	$0.670347\pi$
$678$	−1.22086	−	9.61673i	−0.0468868	−	0.369328i
$679$	−18.1330	+	10.4691i	−0.695880	+	0.401767i
$680$	1.83375			0.0703209
$681$	−20.0962	−	8.43320i	−0.770089	−	0.323161i
$682$	4.26104			0.163164
$683$	7.99277			0.305835			0.152917	−	0.988239i	$-0.451133\pi$
$683$	7.99277			0.305835			0.152917	+	0.988239i	$0.451133\pi$
$684$	5.83355	−	11.7034i	0.223052	−	0.447491i
$685$	−4.86539			−0.185897
$686$	13.3317			0.509008
$687$	4.54748	+	35.8206i	0.173497	+	1.36664i
$688$	−8.41611			−0.320861
$689$	12.9845	−	7.49658i	0.494669	−	0.285597i
$690$	−4.96001	−	2.08142i	−0.188824	−	0.0792384i
$691$	14.5886	+	25.2682i	0.554977	+	0.961249i	0.997905	+	0.0646917i	$0.0206064\pi$
$691$	14.5886	+	25.2682i	0.554977	+	0.961249i	−0.442928	+	0.896557i	$0.646060\pi$
$692$	11.5221			0.438004
$693$	−10.5032	+	10.3107i	−0.398984	+	0.391672i
$694$	−11.8953	+	6.86774i	−0.451538	+	0.260696i
$695$	1.84988	−	1.06803i	0.0701698	−	0.0405125i
$696$	1.44635	+	11.3930i	0.0548238	+	0.431849i
$697$		−	14.5604i		−	0.551515i
$698$	−7.49298	−	12.9782i	−0.283614	−	0.491233i
$699$	−36.1136	+	4.58467i	−1.36594	+	0.173408i
$700$	−9.98920			−0.377556
$701$	−37.3427	−	21.5598i	−1.41042	−	0.814304i	−0.414988	−	0.909827i	$-0.636214\pi$
$701$	−37.3427	−	21.5598i	−1.41042	−	0.814304i	−0.995427	+	0.0955229i	$0.969548\pi$
$702$	−8.99545	+	3.58068i	−0.339512	+	0.135144i
$703$	3.77725	−	19.4975i	0.142461	−	0.735361i
$704$	−1.36246	+	0.786617i	−0.0513497	+	0.0296468i
$705$	−8.15707	+	6.19943i	−0.307213	+	0.233484i
$706$	4.84321	−	2.79623i	0.182277	−	0.105237i
$707$			1.65164i			0.0621164i
$708$	18.0059	+	7.55600i	0.676702	+	0.283972i
$709$	1.08275	−	1.87537i	0.0406634	−	0.0704311i	−0.844977	−	0.534802i	$-0.820386\pi$
$709$	1.08275	−	1.87537i	0.0406634	−	0.0704311i	0.885641	+	0.464371i	$0.153720\pi$
$710$		−	18.2881i		−	0.686342i
$711$	28.2338	+	7.84578i	1.05885	+	0.294240i
$712$	3.19119	+	5.52730i	0.119595	+	0.207144i
$713$	3.13754	−	5.43438i	0.117502	−	0.203519i
$714$	−4.47109	−	5.88297i	−0.167326	−	0.220164i
$715$	−3.40291	−	1.96467i	−0.127262	−	0.0734745i
$716$	−22.7029			−0.848449
$717$	9.17451	−	1.16472i	0.342628	−	0.0434972i
$718$	−25.4808	−	14.7113i	−0.950933	−	0.549022i
$719$	20.9879	+	12.1173i	0.782715	+	0.451901i	0.837392	−	0.546603i	$-0.184079\pi$
$719$	20.9879	+	12.1173i	0.782715	+	0.451901i	−0.0546765	+	0.998504i	$0.517413\pi$
$720$	−1.00483	−	3.89375i	−0.0374478	−	0.145111i
$721$			61.3561i			2.28502i
$722$	17.6254	+	7.09544i	0.655950	+	0.264065i
$723$	−41.2712	+	5.23944i	−1.53489	+	0.194857i
$724$	3.76806	−	2.17549i	0.140039	−	0.0808514i
$725$	10.6195	+	18.3936i	0.394399	+	0.683120i
$726$	−1.85959	−	14.6480i	−0.0690159	−	0.543640i
$727$	−40.2844			−1.49406			−0.747032	−	0.664788i	$-0.768522\pi$
$727$	−40.2844			−1.49406			−0.747032	+	0.664788i	$0.768522\pi$
$728$	−5.03214	+	2.90531i	−0.186504	+	0.107678i
$729$	−19.6141	+	18.5549i	−0.726449	+	0.687220i
$730$		−	7.25996i		−	0.268703i
$731$	−9.97090	−	5.75670i	−0.368787	−	0.212919i
$732$	−0.937465	−	7.38444i	−0.0346497	−	0.272937i
$733$	7.49638	−	12.9841i	0.276885	−	0.479579i	−0.693724	−	0.720241i	$-0.744031\pi$
$733$	7.49638	−	12.9841i	0.276885	−	0.479579i	0.970609	+	0.240662i	$0.0773645\pi$
$734$	1.08275	−	1.87537i	0.0399649	−	0.0692213i
$735$	−3.82806	−	5.03688i	−0.141200	−	0.185788i
$736$			2.31685i			0.0854000i
$737$	3.76987	+	6.52960i	0.138865	+	0.240521i
$738$	−30.9173	+	7.97859i	−1.13808	+	0.293696i
$739$	2.78010	−	4.81527i	0.102268	−	0.177133i	−0.810351	−	0.585945i	$-0.800724\pi$
$739$	2.78010	−	4.81527i	0.102268	−	0.177133i	0.912619	+	0.408812i	$0.134057\pi$
$740$	−3.05365	−	5.28907i	−0.112254	−	0.194430i
$741$	−6.22651	−	12.6145i	−0.228737	−	0.463404i
$742$	12.5466	−	21.7314i	0.460601	−	0.797785i
$743$	−18.7635	−	32.4994i	−0.688367	−	1.19229i	−0.972366	−	0.233461i	$-0.924995\pi$
$743$	−18.7635	−	32.4994i	−0.688367	−	1.19229i	0.284000	−	0.958824i	$-0.408339\pi$
$744$	4.65383	−	0.590811i	0.170618	−	0.0216602i
$745$	4.07204	−	7.05299i	0.149188	−	0.258401i
$746$	27.1481	+	15.6739i	0.993961	+	0.573864i
$747$	−2.88133	−	11.1653i	−0.105422	−	0.408515i
$748$	−2.15222			−0.0786928
$749$	−20.2482	−	35.0710i	−0.739854	−	1.28147i
$750$	−11.5242	−	15.1632i	−0.420803	−	0.553683i
$751$		−	22.9911i		−	0.838958i	−0.907765	−	0.419479i	$-0.862213\pi$
$751$		−	22.9911i		−	0.838958i	0.907765	−	0.419479i	$-0.137787\pi$
$752$	3.82171	+	2.20646i	0.139363	+	0.0804614i
$753$	13.1348	−	31.3000i	0.478658	−	1.14064i
$754$	10.6994	+	6.17727i	0.389647	+	0.224963i
$755$	−11.4097	+	19.7621i	−0.415240	+	0.719217i
$756$	−10.0418	+	12.7175i	−0.365217	+	0.462531i
$757$	−4.27174	+	7.39888i	−0.155259	+	0.268917i	−0.933153	−	0.359479i	$-0.882955\pi$
$757$	−4.27174	+	7.39888i	−0.155259	+	0.268917i	0.777894	+	0.628395i	$0.216288\pi$
$758$			10.4146i			0.378277i
$759$	5.82142	+	2.44291i	0.211304	+	0.0886720i
$760$	5.52331	−	1.90570i	0.200352	−	0.0691271i
$761$	21.3234	+	12.3111i	0.772972	+	0.446276i	0.833934	−	0.551864i	$-0.186083\pi$
$761$	21.3234	+	12.3111i	0.772972	+	0.446276i	−0.0609616	+	0.998140i	$0.519417\pi$
$762$	7.47157	−	17.8047i	0.270666	−	0.644995i
$763$		−	36.0931i		−	1.30666i
$764$	−14.8549	+	8.57646i	−0.537430	+	0.310286i
$765$	1.47290	−	5.30039i	0.0532529	−	0.191636i
$766$	−3.19119	−	5.52730i	−0.115302	−	0.199709i
$767$	18.1922	−	10.5033i	0.656883	−	0.379251i
$768$	−1.37899	+	1.04804i	−0.0497600	+	0.0378179i
$769$	1.61139			0.0581081			0.0290540	−	0.999578i	$-0.490751\pi$
$769$	1.61139			0.0581081			0.0290540	+	0.999578i	$0.490751\pi$
$770$	−6.57633			−0.236994
$771$	−0.803601	+	0.610742i	−0.0289410	+	0.0219953i
$772$	11.6865	−	6.74723i	0.420608	−	0.242838i
$773$	−7.30144	−	12.6465i	−0.262614	−	0.454862i	0.704321	−	0.709881i	$-0.251251\pi$
$773$	−7.30144	−	12.6465i	−0.262614	−	0.454862i	−0.966936	+	0.255020i	$0.917918\pi$
$774$	−6.75999	+	24.3265i	−0.242983	+	0.874399i
$775$	7.51347	−	4.33790i	0.269892	−	0.155822i
$776$			6.71422i			0.241027i
$777$	−9.52274	+	22.6926i	−0.341626	+	0.814092i
$778$	−5.45620	−	3.15014i	−0.195614	−	0.112938i
$779$	−15.1318	−	43.8565i	−0.542151	−	1.57132i
$780$	−3.98901	−	1.67395i	−0.142829	−	0.0599371i
$781$			21.4643i			0.768053i
$782$	−1.58475	+	2.74486i	−0.0566704	+	0.0981560i
$783$	34.0928	+	4.97042i	1.21838	+	0.177628i
$784$	−1.36246	+	2.35985i	−0.0486593	+	0.0842804i
$785$	−13.2692	−	7.66096i	−0.473597	−	0.273431i
$786$	−8.66587	+	20.6507i	−0.309101	+	0.736585i
$787$	−17.1570	−	9.90558i	−0.611580	−	0.353096i	0.162004	−	0.986790i	$-0.448204\pi$
$787$	−17.1570	−	9.90558i	−0.611580	−	0.353096i	−0.773584	+	0.633694i	$0.781538\pi$
$788$			9.03983i			0.322031i
$789$	2.64472	+	3.47986i	0.0941544	+	0.123886i
$790$	6.54663	+	11.3391i	0.232919	+	0.403427i
$791$	−17.4535			−0.620574
$792$	1.17934	+	4.56999i	0.0419060	+	0.162387i
$793$	−6.93488	−	4.00385i	−0.246265	−	0.142181i
$794$	13.0601	−	22.6207i	0.463485	−	0.802780i
$795$	18.5332	−	2.35281i	0.657304	−	0.0834456i
$796$	−0.483132	−	0.836810i	−0.0171242	−	0.0296599i
$797$	1.12757	−	1.95300i	0.0399404	−	0.0691789i	−0.845364	−	0.534190i	$-0.820617\pi$
$797$	1.12757	−	1.95300i	0.0399404	−	0.0691789i	0.885305	+	0.465012i	$0.153950\pi$
$798$	−19.5809	−	13.0732i	−0.693157	−	0.462786i
$799$	3.01849	+	5.22817i	0.106786	+	0.184959i
$800$	−1.60161	+	2.77408i	−0.0566256	+	0.0980784i
$801$	18.5397	−	4.78440i	0.655069	−	0.169048i
$802$	−11.1900	−	19.3817i	−0.395134	−	0.684392i
$803$			8.52081i			0.300693i
$804$	5.02274	+	6.60881i	0.177138	+	0.233075i
$805$	−4.84236	+	8.38721i	−0.170671	+	0.295610i
$806$	2.52331	−	4.37051i	0.0888800	−	0.153945i
$807$	−1.58977	−	12.5226i	−0.0559624	−	0.440817i
$808$	0.458673	+	0.264815i	0.0161361	+	0.00931617i
$809$			29.5377i			1.03849i	0.854626	+	0.519244i	$0.173787\pi$
$809$			29.5377i			1.03849i	−0.854626	+	0.519244i	$0.826213\pi$
$810$	−12.0619	−	0.223110i	−0.423811	−	0.00783930i
$811$	−3.70272	+	2.13777i	−0.130020	+	0.0750671i	−0.563599	−	0.826048i	$-0.690584\pi$
$811$	−3.70272	+	2.13777i	−0.130020	+	0.0750671i	0.433579	+	0.901115i	$0.357250\pi$
$812$	20.6771			0.725626
$813$	−6.35645	−	50.0699i	−0.222930	−	1.75603i
$814$	3.58398	+	6.20764i	0.125618	+	0.217578i
$815$	6.04018	−	3.48730i	0.211578	−	0.122155i
$816$	−2.35061	+	0.298414i	−0.0822879	+	0.0104466i
$817$	−36.0153	−	6.97725i	−1.26002	−	0.244103i
$818$			28.9740i			1.01305i
$819$	4.35580	+	16.8789i	0.152204	+	0.589796i
$820$	−12.3554	−	7.13342i	−0.431471	−	0.249110i
$821$	−38.2537	−	22.0858i	−1.33506	−	0.770799i	−0.348992	−	0.937126i	$-0.613476\pi$
$821$	−38.2537	−	22.0858i	−1.33506	−	0.770799i	−0.986071	+	0.166327i	$0.946809\pi$
$822$	6.23677	−	0.791767i	0.217532	−	0.0276160i
$823$	36.4851			1.27179			0.635895	−	0.771775i	$-0.280631\pi$
$823$	36.4851			1.27179			0.635895	+	0.771775i	$0.280631\pi$
$824$	17.0390	+	9.83749i	0.593583	+	0.342705i
$825$	5.28152	+	6.94931i	0.183879	+	0.241944i
$826$	17.5788	−	30.4473i	0.611644	−	1.05940i
$827$	13.4855	+	23.3576i	0.468937	+	0.812223i	0.999370	−	0.0355041i	$-0.0113037\pi$
$827$	13.4855	+	23.3576i	0.468937	+	0.812223i	−0.530432	+	0.847727i	$0.677970\pi$
$828$	6.69678	+	1.86094i	0.232729	+	0.0646721i
$829$		−	17.9429i		−	0.623184i	−0.950216	−	0.311592i	$-0.899138\pi$
$829$		−	17.9429i		−	0.623184i	0.950216	−	0.311592i	$-0.100862\pi$
$830$	2.57611	−	4.46195i	0.0894180	−	0.154877i
$831$	25.0184	+	10.4987i	0.867878	+	0.364197i
$832$			1.86329i			0.0645978i
$833$	−3.22832	+	1.86387i	−0.111855	+	0.0645794i
$834$	−2.19749	+	1.67010i	−0.0760927	+	0.0578310i
$835$	2.84391	−	1.64193i	0.0984176	−	0.0568214i
$836$	−6.48256	+	2.23667i	−0.224204	+	0.0773569i
$837$	2.03033	−	13.9263i	0.0701786	−	0.481365i
$838$	17.0286	+	9.83148i	0.588244	+	0.339623i
$839$	−12.4953			−0.431387			−0.215693	−	0.976461i	$-0.569201\pi$
$839$	−12.4953			−0.431387			−0.215693	+	0.976461i	$0.569201\pi$
$840$	−7.18255	+	0.911835i	−0.247822	+	0.0314613i
$841$	−7.48190	−	12.9590i	−0.257996	−	0.446863i
$842$		−	18.6819i		−	0.643819i
$843$	−5.62880	−	44.3382i	−0.193866	−	1.52709i
$844$	12.8154	−	7.39895i	0.441123	−	0.254682i
$845$	11.0608	−	6.38596i	0.380503	−	0.219684i
$846$	9.44740	−	9.27426i	0.324808	−	0.318856i
$847$	−26.5848			−0.913466
$848$	−4.02331	−	6.96859i	−0.138161	−	0.239302i
$849$	−32.8938	−	13.8036i	−1.12891	−	0.473738i
$850$	−3.79499	+	2.19104i	−0.130167	+	0.0751520i
$851$	10.5560			0.361855
$852$	2.97611	+	23.4429i	0.101960	+	0.803142i
$853$	−5.90674			−0.202243			−0.101121	−	0.994874i	$-0.532243\pi$
$853$	−5.90674			−0.202243			−0.101121	+	0.994874i	$0.532243\pi$
$854$	−13.4021			−0.458609
$855$	−1.07194	−	17.4957i	−0.0366596	−	0.598340i
$856$	−12.9860			−0.443851
$857$	46.9567			1.60401			0.802006	−	0.597316i	$-0.203766\pi$
$857$	46.9567			1.60401			0.802006	+	0.597316i	$0.203766\pi$
$858$	4.68179	+	1.96467i	0.159834	+	0.0670727i
$859$	40.5249			1.38269			0.691346	−	0.722523i	$-0.257018\pi$
$859$	40.5249			1.38269			0.691346	+	0.722523i	$0.257018\pi$
$860$	−9.76987	+	5.64064i	−0.333150	+	0.192344i
$861$	7.24020	+	57.0312i	0.246745	+	1.94362i
$862$	−20.5053	−	35.5162i	−0.698413	−	1.20969i
$863$	−3.89951			−0.132741			−0.0663704	−	0.997795i	$-0.521142\pi$
$863$	−3.89951			−0.132741			−0.0663704	+	0.997795i	$0.521142\pi$
$864$	1.92170	+	4.82774i	0.0653776	+	0.164243i
$865$	13.3754	−	7.72232i	0.454779	−	0.262567i
$866$	−29.7693	+	17.1873i	−1.01160	+	0.584048i
$867$	24.1621	+	10.1394i	0.820589	+	0.344353i
$868$		−	8.44627i		−	0.286685i
$869$	−7.68360	−	13.3084i	−0.260648	−	0.451456i
$870$	9.31478	+	12.2562i	0.315801	+	0.415523i
$871$	8.92981			0.302575
$872$	−10.0233	−	5.78696i	−0.339432	−	0.195971i
$873$	19.4073	+	5.39300i	0.656837	+	0.182526i
$874$	−1.92075	+	9.91455i	−0.0649702	+	0.335365i
$875$	−29.6965	+	17.1453i	−1.00392	+	0.579616i
$876$	1.18145	+	9.30628i	0.0399174	+	0.314430i
$877$	0.162660	−	0.0939119i	0.00549264	−	0.00317118i	−0.497251	−	0.867607i	$-0.665657\pi$
$877$	0.162660	−	0.0939119i	0.00549264	−	0.00317118i	0.502744	+	0.864435i	$0.332324\pi$
$878$			33.2179i			1.12105i
$879$	−4.35791	−	34.3274i	−0.146989	−	1.15784i
$880$	−1.05441	+	1.82629i	−0.0355442	+	0.0615644i
$881$			43.6041i			1.46906i	0.678577	+	0.734529i	$0.262597\pi$
$881$			43.6041i			1.46906i	−0.678577	+	0.734529i	$0.737403\pi$
$882$	5.72673	+	5.83364i	0.192829	+	0.196429i
$883$	12.7475	+	22.0793i	0.428987	+	0.743027i	0.996783	−	0.0801421i	$-0.0255374\pi$
$883$	12.7475	+	22.0793i	0.428987	+	0.743027i	−0.567797	+	0.823169i	$0.692204\pi$
$884$	−1.27451	+	2.20751i	−0.0428663	+	0.0742465i
$885$	25.9664	−	3.29647i	0.872850	−	0.110809i
$886$	−20.3759	−	11.7640i	−0.684543	−	0.395221i
$887$	−20.6950			−0.694870			−0.347435	−	0.937704i	$-0.612947\pi$
$887$	−20.6950			−0.694870			−0.347435	+	0.937704i	$0.612947\pi$
$888$	4.77508	+	6.28294i	0.160241	+	0.210842i
$889$	−30.1071	−	17.3823i	−1.00976	−	0.582985i
$890$	7.40900	+	4.27759i	0.248350	+	0.143385i
$891$	14.1567	+	0.261858i	0.474267	+	0.00877258i
$892$		−	28.0299i		−	0.938510i
$893$	14.5251	+	12.6105i	0.486065	+	0.421995i
$894$	−4.07204	+	9.70363i	−0.136190	+	0.324538i
$895$	−26.3548	+	15.2159i	−0.880943	+	0.508613i
$896$	1.55924	+	2.70068i	0.0520906	+	0.0902235i
$897$	5.95302	−	4.52433i	0.198765	−	0.151063i
$898$	26.0258			0.868492
$899$	−15.5525	+	8.97924i	−0.518705	+	0.299474i
$900$	6.73194	+	6.85761i	0.224398	+	0.228587i
$901$		−	11.0079i		−	0.366728i
$902$	14.5012	+	8.37229i	0.482838	+	0.278767i
$903$	41.9173	+	17.5902i	1.39492	+	0.585366i
$904$	−2.79839	+	4.84696i	−0.0930731	+	0.161207i
$905$	2.91611	−	5.05085i	0.0969347	−	0.167896i
$906$	11.4097	−	27.1891i	0.379061	−	0.903297i
$907$			26.4564i			0.878471i	0.898372	+	0.439235i	$0.144751\pi$
$907$			26.4564i			0.878471i	−0.898372	+	0.439235i	$0.855249\pi$
$908$	6.29137	+	10.8970i	0.208787	+	0.361629i
$909$	1.13386	−	1.11308i	0.0376077	−	0.0369185i
$910$	−3.89439	+	6.74528i	−0.129098	+	0.223604i
$911$	−16.1131	−	27.9087i	−0.533850	−	0.924656i	−0.999218	−	0.0395383i	$-0.987411\pi$
$911$	−16.1131	−	27.9087i	−0.533850	−	0.924656i	0.465368	−	0.885117i	$-0.345922\pi$
$912$	−6.77002	+	3.34169i	−0.224178	+	0.110654i
$913$	−3.02351	+	5.23687i	−0.100063	+	0.173315i
$914$	17.8876	+	30.9822i	0.591669	+	1.02480i
$915$	−6.03745	−	7.94395i	−0.199592	−	0.262619i
$916$	10.4235	−	18.0541i	0.344403	−	0.596523i
$917$	34.9196	+	20.1608i	1.15315	+	0.665770i
$918$	−1.02550	+	7.03408i	−0.0338467	+	0.232159i
$919$	−15.4379			−0.509249			−0.254625	−	0.967040i	$-0.581952\pi$
$919$	−15.4379			−0.509249			−0.254625	+	0.967040i	$0.581952\pi$
$920$	1.55279	+	2.68952i	0.0511941	+	0.0886708i
$921$	57.1188	−	7.25132i	1.88213	−	0.238939i
$922$			31.5166i			1.03794i
$923$	22.0157	+	12.7108i	0.724656	+	0.418381i
$924$	8.42996	−	1.07020i	0.277325	−	0.0352068i
$925$	12.6392	+	7.29726i	0.415575	+	0.239932i
$926$	−9.60721	+	16.6402i	−0.315712	+	0.546830i
$927$	42.1211	−	41.3492i	1.38344	−	1.35809i
$928$	3.31526	−	5.74220i	0.108829	−	0.188497i
$929$		−	25.4656i		−	0.835500i	−0.908562	−	0.417750i	$-0.862819\pi$
$929$		−	25.4656i		−	0.835500i	0.908562	−	0.417750i	$-0.137181\pi$
$930$	5.00645	−	3.80493i	0.164168	−	0.124769i
$931$	−7.78683	+	8.96907i	−0.255203	+	0.293949i
$932$	18.2017	+	10.5088i	0.596217	+	0.344226i
$933$	−27.8776	+	3.53911i	−0.912673	+	0.115865i
$934$			10.9865i			0.359490i
$935$	−2.49841	+	1.44246i	−0.0817067	+	0.0471734i
$936$	5.38578	+	1.49663i	0.176040	+	0.0489189i
$937$	−25.6097	−	44.3573i	−0.836632	−	1.44909i	−0.892695	−	0.450661i	$-0.851188\pi$
$937$	−25.6097	−	44.3573i	−0.836632	−	1.44909i	0.0560633	−	0.998427i	$-0.482145\pi$
$938$	12.9430	−	7.47267i	0.422605	−	0.243991i
$939$	3.39882	+	26.7726i	0.110916	+	0.873690i
$940$	5.91525			0.192934
$941$	−29.7494			−0.969802			−0.484901	−	0.874569i	$-0.661144\pi$
$941$	−29.7494			−0.969802			−0.484901	+	0.874569i	$0.661144\pi$
$942$	18.2560	+	7.66096i	0.594812	+	0.249608i
$943$	21.3554	−	12.3296i	0.695429	−	0.401506i
$944$	−5.63697	−	9.76351i	−0.183468	−	0.317775i
$945$	−3.13354	+	21.4934i	−0.101934	+	0.699180i
$946$	11.4666	−	6.62026i	0.372812	−	0.215243i
$947$			56.8300i			1.84673i	0.383929	+	0.923363i	$0.374571\pi$
$947$			56.8300i			1.84673i	−0.383929	+	0.923363i	$0.625429\pi$
$948$	−10.2372	−	13.4698i	−0.332487	−	0.437479i
$949$	8.73972	+	5.04588i	0.283703	+	0.163796i
$950$	−9.15364	+	10.5434i	−0.296983	+	0.342073i
$951$	1.57802	+	12.4301i	0.0511707	+	0.403073i
$952$			4.26614i			0.138267i
$953$	−21.6382	+	37.4785i	−0.700930	+	1.21405i	0.267210	+	0.963638i	$0.413898\pi$
$953$	−21.6382	+	37.4785i	−0.700930	+	1.21405i	−0.968140	+	0.250408i	$0.919435\pi$
$954$	−23.3741	+	6.03197i	−0.756765	+	0.195292i
$955$	−11.4962	+	19.9120i	−0.372009	+	0.644338i
$956$	−4.62407	−	2.66971i	−0.149553	−	0.0863446i
$957$	−10.9325	−	14.3847i	−0.353397	−	0.464992i
$958$	−7.41668	−	4.28202i	−0.239622	−	0.138346i
$959$		−	11.3192i		−	0.365515i
$960$	−0.898387	+	2.14085i	−0.0289953	+	0.0690955i
$961$	−11.8321	−	20.4938i	−0.381682	−	0.661092i
$962$	8.48949			0.273712
$963$	−10.4306	+	37.5356i	−0.336121	+	1.20957i
$964$	20.8012	+	12.0096i	0.669962	+	0.386803i
$965$	9.04425	−	15.6651i	0.291145	−	0.504277i
$966$	4.84236	−	11.5393i	0.155800	−	0.371270i
$967$	−6.21231	−	10.7600i	−0.199774	−	0.346020i	0.748681	−	0.662931i	$-0.230688\pi$
$967$	−6.21231	−	10.7600i	−0.199774	−	0.346020i	−0.948455	+	0.316911i	$0.897354\pi$
$968$	−4.26247	+	7.38281i	−0.137001	+	0.237292i
$969$	−10.3065	−	0.671729i	−0.331091	−	0.0215790i
$970$	4.50000	+	7.79423i	0.144486	+	0.250258i
$971$	−3.91725	+	6.78488i	−0.125711	+	0.217737i	−0.922011	−	0.387165i	$-0.873454\pi$
$971$	−3.91725	+	6.78488i	−0.125711	+	0.217737i	0.796300	+	0.604902i	$0.206788\pi$
$972$	15.4980	−	1.67689i	0.497099	−	0.0537862i
$973$	2.48472	+	4.30367i	0.0796566	+	0.137969i
$974$			39.5989i			1.26883i
$975$	10.2555	−	1.30195i	0.328438	−	0.0416957i
$976$	−2.14881	+	3.72186i	−0.0687819	+	0.119134i
$977$	3.82294	−	6.62153i	0.122307	−	0.211841i	−0.798370	−	0.602167i	$-0.794304\pi$
$977$	3.82294	−	6.62153i	0.122307	−	0.211841i	0.920677	+	0.390325i	$0.127638\pi$
$978$	−7.17519	+	5.45319i	−0.229437	+	0.174374i
$979$	−8.69574	−	5.02049i	−0.277917	−	0.160455i
$980$			3.65259i			0.116678i
$981$	−24.7780	+	24.3239i	−0.791101	+	0.776603i
$982$	10.8270	−	6.25098i	0.345504	−	0.199477i
$983$	−60.1166			−1.91742			−0.958710	−	0.284384i	$-0.908211\pi$
$983$	−60.1166			−1.91742			−0.958710	+	0.284384i	$0.908211\pi$
$984$	16.9989	+	7.13342i	0.541904	+	0.227405i
$985$	6.05867	+	10.4939i	0.193045	+	0.334364i
$986$	7.85544	−	4.53534i	0.250168	−	0.144435i
$987$	−14.4227	−	18.9771i	−0.459081	−	0.604049i
$988$	−1.54473	+	7.97362i	−0.0491444	+	0.253675i
$989$		−	19.4988i		−	0.620026i
$990$	4.43193	+	4.51467i	0.140856	+	0.143486i
$991$	−42.4523	−	24.5099i	−1.34854	−	0.778581i	−0.360499	−	0.932760i	$-0.617394\pi$
$991$	−42.4523	−	24.5099i	−1.34854	−	0.778581i	−0.988043	+	0.154178i	$0.950727\pi$
$992$	−2.34559	−	1.35423i	−0.0744727	−	0.0429968i
$993$	2.63471	−	6.27849i	0.0836101	−	0.199242i
$994$	42.5467			1.34950
$995$	−1.12169	−	0.647609i	−0.0355600	−	0.0205306i
$996$	−2.57611	+	6.13884i	−0.0816271	+	0.194517i
$997$	−14.1173	+	24.4519i	−0.447101	+	0.774401i	−0.998196	−	0.0600414i	$-0.980877\pi$
$997$	−14.1173	+	24.4519i	−0.447101	+	0.774401i	0.551095	+	0.834442i	$0.314210\pi$
$998$	−7.58113	−	13.1309i	−0.239976	−	0.415651i
$999$	21.9961	−	8.75565i	0.695926	−	0.277016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.n.e.293.1	yes	8
3.2	odd	2		1026.2.n.e.179.1		8
9.2	odd	6		342.2.j.e.65.2	✓	8
9.7	even	3		1026.2.j.e.521.4		8
19.12	odd	6		342.2.j.e.221.2	yes	8
57.50	even	6		1026.2.j.e.449.1		8
171.88	odd	6		1026.2.n.e.791.1		8
171.164	even	6	inner	342.2.n.e.335.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.j.e.65.2	✓	8	9.2	odd	6
342.2.j.e.221.2	yes	8	19.12	odd	6
342.2.n.e.293.1	yes	8	1.1	even	1	trivial
342.2.n.e.335.1	yes	8	171.164	even	6	inner
1026.2.j.e.449.1		8	57.50	even	6
1026.2.j.e.521.4		8	9.7	even	3
1026.2.n.e.179.1		8	3.2	odd	2
1026.2.n.e.791.1		8	171.88	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.37899 + 1.04804i) q^{3} +1.00000 q^{4} +(1.16085 - 0.670219i) q^{5} +(-1.37899 + 1.04804i) q^{6} +(1.55924 + 2.70068i) q^{7} +1.00000 q^{8} +(0.803221 - 2.89047i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.37899 + 1.04804i) q^{3} +1.00000 q^{4} +(1.16085 - 0.670219i) q^{5} +(-1.37899 + 1.04804i) q^{6} +(1.55924 + 2.70068i) q^{7} +1.00000 q^{8} +(0.803221 - 2.89047i) q^{9} +(1.16085 - 0.670219i) q^{10} +(-1.36246 + 0.786617i) q^{11} +(-1.37899 + 1.04804i) q^{12} +1.86329i q^{13} +(1.55924 + 2.70068i) q^{14} +(-0.898387 + 2.14085i) q^{15} +1.00000 q^{16} +(1.18474 + 0.684010i) q^{17} +(0.803221 - 2.89047i) q^{18} +(4.27933 + 0.829035i) q^{19} +(1.16085 - 0.670219i) q^{20} +(-4.98060 - 2.09007i) q^{21} +(-1.36246 + 0.786617i) q^{22} +2.31685i q^{23} +(-1.37899 + 1.04804i) q^{24} +(-1.60161 + 2.77408i) q^{25} +1.86329i q^{26} +(1.92170 + 4.82774i) q^{27} +(1.55924 + 2.70068i) q^{28} +(3.31526 - 5.74220i) q^{29} +(-0.898387 + 2.14085i) q^{30} +(-2.34559 - 1.35423i) q^{31} +1.00000 q^{32} +(1.05441 - 2.51265i) q^{33} +(1.18474 + 0.684010i) q^{34} +(3.62010 + 2.09007i) q^{35} +(0.803221 - 2.89047i) q^{36} -4.55619i q^{37} +(4.27933 + 0.829035i) q^{38} +(-1.95280 - 2.56945i) q^{39} +(1.16085 - 0.670219i) q^{40} +(-5.32171 - 9.21747i) q^{41} +(-4.98060 - 2.09007i) q^{42} -8.41611 q^{43} +(-1.36246 + 0.786617i) q^{44} +(-1.00483 - 3.89375i) q^{45} +2.31685i q^{46} +(3.82171 + 2.20646i) q^{47} +(-1.37899 + 1.04804i) q^{48} +(-1.36246 + 2.35985i) q^{49} +(-1.60161 + 2.77408i) q^{50} +(-2.35061 + 0.298414i) q^{51} +1.86329i q^{52} +(-4.02331 - 6.96859i) q^{53} +(1.92170 + 4.82774i) q^{54} +(-1.05441 + 1.82629i) q^{55} +(1.55924 + 2.70068i) q^{56} +(-6.77002 + 3.34169i) q^{57} +(3.31526 - 5.74220i) q^{58} +(-5.63697 - 9.76351i) q^{59} +(-0.898387 + 2.14085i) q^{60} +(-2.14881 + 3.72186i) q^{61} +(-2.34559 - 1.35423i) q^{62} +(9.05867 - 2.33770i) q^{63} +1.00000 q^{64} +(1.24881 + 2.16300i) q^{65} +(1.05441 - 2.51265i) q^{66} -4.79251i q^{67} +(1.18474 + 0.684010i) q^{68} +(-2.42815 - 3.19490i) q^{69} +(3.62010 + 2.09007i) q^{70} +(6.82171 - 11.8155i) q^{71} +(0.803221 - 2.89047i) q^{72} +(2.70805 - 4.69049i) q^{73} -4.55619i q^{74} +(-0.698737 - 5.50397i) q^{75} +(4.27933 + 0.829035i) q^{76} +(-4.24881 - 2.45305i) q^{77} +(-1.95280 - 2.56945i) q^{78} +9.76790i q^{79} +(1.16085 - 0.670219i) q^{80} +(-7.70967 - 4.64338i) q^{81} +(-5.32171 - 9.21747i) q^{82} +(3.32873 - 1.92184i) q^{83} +(-4.98060 - 2.09007i) q^{84} +1.83375 q^{85} -8.41611 q^{86} +(1.44635 + 11.3930i) q^{87} +(-1.36246 + 0.786617i) q^{88} +(3.19119 + 5.52730i) q^{89} +(-1.00483 - 3.89375i) q^{90} +(-5.03214 + 2.90531i) q^{91} +2.31685i q^{92} +(4.65383 - 0.590811i) q^{93} +(3.82171 + 2.20646i) q^{94} +(5.52331 - 1.90570i) q^{95} +(-1.37899 + 1.04804i) q^{96} +6.71422i q^{97} +(-1.36246 + 2.35985i) q^{98} +(1.17934 + 4.56999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} - 9 q^{5} + 4 q^{6} + 6 q^{7} + 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 - 9 * q^5 + 4 * q^6 + 6 * q^7 + 8 * q^8 + 2 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} - 9 q^{5} + 4 q^{6} + 6 q^{7} + 8 q^{8} + 2 q^{9} - 9 q^{10} + 4 q^{12} + 6 q^{14} - 19 q^{15} + 8 q^{16} + 18 q^{17} + 2 q^{18} + 3 q^{19} - 9 q^{20} - 13 q^{21} + 4 q^{24} - q^{25} - 2 q^{27} + 6 q^{28} + 18 q^{29} - 19 q^{30} - 9 q^{31} + 8 q^{32} - q^{33} + 18 q^{34} - 15 q^{35} + 2 q^{36} + 3 q^{38} - 18 q^{39} - 9 q^{40} - 6 q^{41} - 13 q^{42} - 26 q^{43} - 11 q^{45} - 6 q^{47} + 4 q^{48} - q^{50} + 23 q^{51} - 3 q^{53} - 2 q^{54} + q^{55} + 6 q^{56} - 20 q^{57} + 18 q^{58} - 19 q^{60} - 3 q^{61} - 9 q^{62} + 10 q^{63} + 8 q^{64} + 15 q^{65} - q^{66} + 18 q^{68} + 26 q^{69} - 15 q^{70} + 18 q^{71} + 2 q^{72} + q^{73} + 18 q^{75} + 3 q^{76} - 39 q^{77} - 18 q^{78} - 9 q^{80} - 10 q^{81} - 6 q^{82} + 18 q^{83} - 13 q^{84} - 26 q^{85} - 26 q^{86} + 42 q^{87} + 6 q^{89} - 11 q^{90} + 27 q^{91} - 9 q^{93} - 6 q^{94} + 15 q^{95} + 4 q^{96} - 41 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 - 9 * q^5 + 4 * q^6 + 6 * q^7 + 8 * q^8 + 2 * q^9 - 9 * q^10 + 4 * q^12 + 6 * q^14 - 19 * q^15 + 8 * q^16 + 18 * q^17 + 2 * q^18 + 3 * q^19 - 9 * q^20 - 13 * q^21 + 4 * q^24 - q^25 - 2 * q^27 + 6 * q^28 + 18 * q^29 - 19 * q^30 - 9 * q^31 + 8 * q^32 - q^33 + 18 * q^34 - 15 * q^35 + 2 * q^36 + 3 * q^38 - 18 * q^39 - 9 * q^40 - 6 * q^41 - 13 * q^42 - 26 * q^43 - 11 * q^45 - 6 * q^47 + 4 * q^48 - q^50 + 23 * q^51 - 3 * q^53 - 2 * q^54 + q^55 + 6 * q^56 - 20 * q^57 + 18 * q^58 - 19 * q^60 - 3 * q^61 - 9 * q^62 + 10 * q^63 + 8 * q^64 + 15 * q^65 - q^66 + 18 * q^68 + 26 * q^69 - 15 * q^70 + 18 * q^71 + 2 * q^72 + q^73 + 18 * q^75 + 3 * q^76 - 39 * q^77 - 18 * q^78 - 9 * q^80 - 10 * q^81 - 6 * q^82 + 18 * q^83 - 13 * q^84 - 26 * q^85 - 26 * q^86 + 42 * q^87 + 6 * q^89 - 11 * q^90 + 27 * q^91 - 9 * q^93 - 6 * q^94 + 15 * q^95 + 4 * q^96 - 41 * q^99

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