LMFDB - Embedded newform 950.2.l.i.351.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} + \cdots + 64 $ x^18 + 24x^16 - 12x^15 + 393x^14 - 222x^13 + 3518x^12 - 2478x^11 + 22809x^10 - 12862x^9 + 77397x^8 - 24822x^7 + 178501x^6 - 39408x^5 + 132588x^4 + 45584x^3 + 50640x^2 + 1824x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.1
Root			$-1.71449 - 2.96958i$ of defining polynomial
Character	$\chi$	$=$	950.351
Dual form			950.2.l.i.701.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-2.62675 + 2.20410i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-2.62675 - 2.20410i) q^{6} +(0.933500 - 1.61687i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.52078 - 8.62480i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-2.62675 + 2.20410i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-2.62675 - 2.20410i) q^{6} +(0.933500 - 1.61687i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.52078 - 8.62480i) q^{9} +(1.80254 + 3.12210i) q^{11} +(1.71449 - 2.96958i) q^{12} +(2.17319 + 1.82353i) q^{13} +(1.75441 + 0.638551i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-1.03994 - 5.89781i) q^{17} +8.75785 q^{18} +(4.32047 + 0.577506i) q^{19} +(1.11168 + 6.30463i) q^{21} +(-2.76166 + 2.31731i) q^{22} +(4.78092 - 1.74011i) q^{23} +(3.22218 + 1.17278i) q^{24} +(-1.41845 + 2.45683i) q^{26} +(9.87176 + 17.0984i) q^{27} +(-0.324201 + 1.83864i) q^{28} +(0.204642 - 1.16058i) q^{29} +(2.59932 - 4.50215i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-11.6162 - 4.22797i) q^{33} +(5.62762 - 2.04829i) q^{34} +(1.52078 + 8.62480i) q^{36} -3.35231 q^{37} +(0.181510 + 4.35512i) q^{38} -9.72766 q^{39} +(-2.85406 + 2.39484i) q^{41} +(-6.01581 + 2.18958i) q^{42} +(0.631247 + 0.229755i) q^{43} +(-2.76166 - 2.31731i) q^{44} +(2.54388 + 4.40612i) q^{46} +(1.09789 - 6.22647i) q^{47} +(-0.595435 + 3.37688i) q^{48} +(1.75716 + 3.04348i) q^{49} +(15.7310 + 13.1999i) q^{51} +(-2.66582 - 0.970278i) q^{52} +(2.40711 - 0.876116i) q^{53} +(-15.1244 + 12.6909i) q^{54} -1.86700 q^{56} +(-12.6217 + 8.00580i) q^{57} +1.17848 q^{58} +(-0.827999 - 4.69581i) q^{59} +(-7.73966 + 2.81701i) q^{61} +(4.88512 + 1.77804i) q^{62} +(-12.5255 - 10.5102i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.14660 - 12.1739i) q^{66} +(-1.38291 + 7.84286i) q^{67} +(2.99439 + 5.18644i) q^{68} +(-8.72288 + 15.1085i) q^{69} +(1.81077 + 0.659065i) q^{71} +(-8.22969 + 2.99536i) q^{72} +(3.83942 - 3.22165i) q^{73} +(-0.582122 - 3.30138i) q^{74} +(-4.25744 + 0.935010i) q^{76} +6.73070 q^{77} +(-1.68919 - 9.57988i) q^{78} +(-0.460535 + 0.386434i) q^{79} +(-38.9281 - 14.1687i) q^{81} +(-2.85406 - 2.39484i) q^{82} +(-0.951408 + 1.64789i) q^{83} +(-3.20094 - 5.54420i) q^{84} +(-0.116650 + 0.661553i) q^{86} +(2.02049 + 3.49960i) q^{87} +(1.80254 - 3.12210i) q^{88} +(0.755257 + 0.633736i) q^{89} +(4.97708 - 1.81151i) q^{91} +(-3.89744 + 3.27034i) q^{92} +(3.09545 + 17.5552i) q^{93} +6.32252 q^{94} -3.42897 q^{96} +(0.0325697 + 0.184712i) q^{97} +(-2.69212 + 2.25896i) q^{98} +(29.6688 - 10.7985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 9 * q^8 - 18 * q^9	$ 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) $ 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−2.62675	+	2.20410i	−1.51655	+	1.27254i	−0.666966	+	0.745088i	$0.732407\pi$
$3$	−2.62675	+	2.20410i	−1.51655	+	1.27254i	−0.849586	+	0.527450i	$0.823148\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	−2.62675	−	2.20410i	−1.07236	−	0.899820i
$7$	0.933500	−	1.61687i	0.352830	−	0.611119i	−0.633914	−	0.773403i	$-0.718553\pi$
$7$	0.933500	−	1.61687i	0.352830	−	0.611119i	0.986744	+	0.162284i	$0.0518861\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	1.52078	−	8.62480i	0.506928	−	2.87493i
$10$		0			0
$11$	1.80254	+	3.12210i	0.543488	+	0.941348i	0.998700	+	0.0509654i	$0.0162298\pi$
$11$	1.80254	+	3.12210i	0.543488	+	0.941348i	−0.455213	+	0.890383i	$0.650437\pi$
$12$	1.71449	−	2.96958i	0.494930	−	0.857243i
$13$	2.17319	+	1.82353i	0.602736	+	0.505755i	0.892324	−	0.451396i	$-0.149074\pi$
$13$	2.17319	+	1.82353i	0.602736	+	0.505755i	−0.289588	+	0.957151i	$0.593518\pi$
$14$	1.75441	+	0.638551i	0.468885	+	0.170660i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.03994	−	5.89781i	−0.252223	−	1.43043i	−0.803101	−	0.595842i	$-0.796818\pi$
$17$	−1.03994	−	5.89781i	−0.252223	−	1.43043i	0.550878	−	0.834586i	$-0.314293\pi$
$18$	8.75785			2.06425
$19$	4.32047	+	0.577506i	0.991184	+	0.132489i
$19$	4.32047	+	0.577506i	0.991184	+	0.132489i
$20$		0			0
$21$	1.11168	+	6.30463i	0.242588	+	1.37578i
$22$	−2.76166	+	2.31731i	−0.588787	+	0.494051i
$23$	4.78092	−	1.74011i	0.996892	−	0.362839i	0.208507	−	0.978021i	$-0.433140\pi$
$23$	4.78092	−	1.74011i	0.996892	−	0.362839i	0.788385	+	0.615182i	$0.210918\pi$
$24$	3.22218	+	1.17278i	0.657725	+	0.239392i
$25$		0			0
$26$	−1.41845	+	2.45683i	−0.278181	+	0.481824i
$27$	9.87176	+	17.0984i	1.89982	+	3.29059i
$28$	−0.324201	+	1.83864i	−0.0612682	+	0.347469i
$29$	0.204642	−	1.16058i	0.0380010	−	0.215514i	−0.959894	−	0.280363i	$-0.909545\pi$
$29$	0.204642	−	1.16058i	0.0380010	−	0.215514i	0.997895	+	0.0648484i	$0.0206564\pi$
$30$		0			0
$31$	2.59932	−	4.50215i	0.466851	−	0.808610i	−0.532432	−	0.846473i	$-0.678722\pi$
$31$	2.59932	−	4.50215i	0.466851	−	0.808610i	0.999283	+	0.0378630i	$0.0120550\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−11.6162	−	4.22797i	−2.02213	−	0.735995i
$34$	5.62762	−	2.04829i	0.965129	−	0.351278i
$35$		0			0
$36$	1.52078	+	8.62480i	0.253464	+	1.43747i
$37$	−3.35231			−0.551116			−0.275558	−	0.961285i	$-0.588863\pi$
$37$	−3.35231			−0.551116			−0.275558	+	0.961285i	$0.588863\pi$
$38$	0.181510	+	4.35512i	0.0294447	+	0.706493i
$39$	−9.72766			−1.55767
$40$		0			0
$41$	−2.85406	+	2.39484i	−0.445730	+	0.374012i	−0.837848	−	0.545903i	$-0.816187\pi$
$41$	−2.85406	+	2.39484i	−0.445730	+	0.374012i	0.392119	+	0.919915i	$0.371742\pi$
$42$	−6.01581	+	2.18958i	−0.928259	+	0.337859i
$43$	0.631247	+	0.229755i	0.0962642	+	0.0350373i	0.389703	−	0.920940i	$-0.372578\pi$
$43$	0.631247	+	0.229755i	0.0962642	+	0.0350373i	−0.293439	+	0.955978i	$0.594800\pi$
$44$	−2.76166	−	2.31731i	−0.416336	−	0.349347i
$45$		0			0
$46$	2.54388	+	4.40612i	0.375074	+	0.649647i
$47$	1.09789	−	6.22647i	0.160144	−	0.908223i	−0.793786	−	0.608197i	$-0.791893\pi$
$47$	1.09789	−	6.22647i	0.160144	−	0.908223i	0.953931	−	0.300027i	$-0.0969956\pi$
$48$	−0.595435	+	3.37688i	−0.0859436	+	0.487410i
$49$	1.75716	+	3.04348i	0.251022	+	0.434783i
$50$		0			0
$51$	15.7310	+	13.1999i	2.20278	+	1.84836i
$52$	−2.66582	−	0.970278i	−0.369682	−	0.134553i
$53$	2.40711	−	0.876116i	0.330642	−	0.120344i	−0.171365	−	0.985208i	$-0.554818\pi$
$53$	2.40711	−	0.876116i	0.330642	−	0.120344i	0.502006	+	0.864864i	$0.332595\pi$
$54$	−15.1244	+	12.6909i	−2.05817	+	1.72701i
$55$		0			0
$56$	−1.86700			−0.249488
$57$	−12.6217	+	8.00580i	−1.67178	+	1.06039i
$58$	1.17848			0.154743
$59$	−0.827999	−	4.69581i	−0.107796	−	0.611343i	−0.990067	−	0.140600i	$-0.955097\pi$
$59$	−0.827999	−	4.69581i	−0.107796	−	0.611343i	0.882270	−	0.470743i	$-0.156014\pi$
$60$		0			0
$61$	−7.73966	+	2.81701i	−0.990962	+	0.360681i	−0.786093	−	0.618109i	$-0.787899\pi$
$61$	−7.73966	+	2.81701i	−0.990962	+	0.360681i	−0.204869	+	0.978789i	$0.565677\pi$
$62$	4.88512	+	1.77804i	0.620411	+	0.225811i
$63$	−12.5255	−	10.5102i	−1.57807	−	1.32416i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	2.14660	−	12.1739i	0.264228	−	1.49851i
$67$	−1.38291	+	7.84286i	−0.168949	+	0.958158i	0.775949	+	0.630795i	$0.217271\pi$
$67$	−1.38291	+	7.84286i	−0.168949	+	0.958158i	−0.944899	+	0.327363i	$0.893840\pi$
$68$	2.99439	+	5.18644i	0.363124	+	0.628949i
$69$	−8.72288	+	15.1085i	−1.05011	+	1.81885i
$70$		0			0
$71$	1.81077	+	0.659065i	0.214898	+	0.0782166i	0.447226	−	0.894421i	$-0.352412\pi$
$71$	1.81077	+	0.659065i	0.214898	+	0.0782166i	−0.232328	+	0.972638i	$0.574634\pi$
$72$	−8.22969	+	2.99536i	−0.969878	+	0.353007i
$73$	3.83942	−	3.22165i	0.449370	−	0.377066i	−0.389832	−	0.920886i	$-0.627467\pi$
$73$	3.83942	−	3.22165i	0.449370	−	0.377066i	0.839202	+	0.543820i	$0.183022\pi$
$74$	−0.582122	−	3.30138i	−0.0676703	−	0.383777i
$75$		0			0
$76$	−4.25744	+	0.935010i	−0.488361	+	0.107253i
$77$	6.73070			0.767034
$78$	−1.68919	−	9.57988i	−0.191263	−	1.08471i
$79$	−0.460535	+	0.386434i	−0.0518142	+	0.0434773i	−0.668327	−	0.743868i	$-0.732989\pi$
$79$	−0.460535	+	0.386434i	−0.0518142	+	0.0434773i	0.616513	+	0.787345i	$0.288545\pi$
$80$		0			0
$81$	−38.9281	−	14.1687i	−4.32534	−	1.57430i
$82$	−2.85406	−	2.39484i	−0.315179	−	0.264466i
$83$	−0.951408	+	1.64789i	−0.104431	+	0.180879i	−0.913505	−	0.406827i	$-0.866635\pi$
$83$	−0.951408	+	1.64789i	−0.104431	+	0.180879i	0.809075	+	0.587706i	$0.199969\pi$
$84$	−3.20094	−	5.54420i	−0.349252	−	0.604922i
$85$		0			0
$86$	−0.116650	+	0.661553i	−0.0125787	+	0.0713371i
$87$	2.02049	+	3.49960i	0.216620	+	0.375196i
$88$	1.80254	−	3.12210i	0.192152	−	0.332817i
$89$	0.755257	+	0.633736i	0.0800571	+	0.0671759i	0.681938	−	0.731410i	$-0.261137\pi$
$89$	0.755257	+	0.633736i	0.0800571	+	0.0671759i	−0.601881	+	0.798586i	$0.705582\pi$
$90$		0			0
$91$	4.97708	−	1.81151i	0.521740	−	0.189898i
$92$	−3.89744	+	3.27034i	−0.406337	+	0.340957i
$93$	3.09545	+	17.5552i	0.320983	+	1.82039i
$94$	6.32252			0.652118
$95$		0			0
$96$	−3.42897			−0.349968
$97$	0.0325697	+	0.184712i	0.00330695	+	0.0187547i	0.986417	−	0.164263i	$-0.0525246\pi$
$97$	0.0325697	+	0.184712i	0.00330695	+	0.0187547i	−0.983110	+	0.183018i	$0.941413\pi$
$98$	−2.69212	+	2.25896i	−0.271945	+	0.228189i
$99$	29.6688	−	10.7985i	2.98182	−	1.08529i
$100$		0			0
$101$	−1.50168	−	1.26006i	−0.149423	−	0.125380i	0.565012	−	0.825083i	$-0.308872\pi$
$101$	−1.50168	−	1.26006i	−0.149423	−	0.125380i	−0.714435	+	0.699702i	$0.753316\pi$
$102$	−10.2677	+	17.7842i	−1.01665	+	1.76090i
$103$	8.75199	+	15.1589i	0.862359	+	1.49365i	0.869646	+	0.493676i	$0.164347\pi$
$103$	8.75199	+	15.1589i	0.862359	+	1.49365i	−0.00728653	+	0.999973i	$0.502319\pi$
$104$	0.492623	−	2.79380i	0.0483057	−	0.273955i
$105$		0			0
$106$	1.28080	+	2.21840i	0.124402	+	0.215470i
$107$	5.29485	−	9.17096i	0.511873	−	0.886590i	−0.488032	−	0.872826i	$-0.662285\pi$
$107$	5.29485	−	9.17096i	0.511873	−	0.886590i	0.999905	−	0.0137643i	$-0.00438146\pi$
$108$	−15.1244	−	12.6909i	−1.45535	−	1.22118i
$109$	13.0386	+	4.74565i	1.24887	+	0.454551i	0.880019	−	0.474939i	$-0.157530\pi$
$109$	13.0386	+	4.74565i	1.24887	+	0.454551i	0.368849	+	0.929489i	$0.379752\pi$
$110$		0			0
$111$	8.80565	−	7.38882i	0.835796	−	0.701316i
$112$	−0.324201	−	1.83864i	−0.0306341	−	0.173735i
$113$	15.9357			1.49911			0.749553	−	0.661944i	$-0.230268\pi$
$113$	15.9357			1.49911			0.749553	+	0.661944i	$0.230268\pi$
$114$	−10.0759	−	11.0397i	−0.943694	−	1.03396i
$115$		0			0
$116$	0.204642	+	1.16058i	0.0190005	+	0.107757i
$117$	19.0325	−	15.9702i	1.75956	−	1.47644i
$118$	4.48069	−	1.63084i	0.412481	−	0.150131i
$119$	−10.5068	−	3.82415i	−0.963154	−	0.350559i
$120$		0			0
$121$	−0.998331	+	1.72916i	−0.0907574	+	0.157196i
$122$	−4.11819	−	7.13291i	−0.372843	−	0.645783i
$123$	2.21842	−	12.5813i	0.200028	−	1.13442i
$124$	−0.902733	+	5.11966i	−0.0810679	+	0.459759i
$125$		0			0
$126$	8.17545	−	14.1603i	0.728327	−	1.26150i
$127$	12.8803	+	10.8078i	1.14294	+	0.959041i	0.999531	−	0.0306225i	$-0.00974897\pi$
$127$	12.8803	+	10.8078i	1.14294	+	0.959041i	0.143409	+	0.989663i	$0.454193\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−2.16453	+	0.787824i	−0.190576	+	0.0693640i
$130$		0			0
$131$	1.13110	+	6.41481i	0.0988249	+	0.560464i	0.993508	+	0.113763i	$0.0362903\pi$
$131$	1.13110	+	6.41481i	0.0988249	+	0.560464i	−0.894683	+	0.446702i	$0.852599\pi$
$132$	12.3617			1.07595
$133$	4.96691	−	6.44654i	0.430686	−	0.558986i
$134$	−7.96385			−0.687972
$135$		0			0
$136$	−4.58768	+	3.84952i	−0.393390	+	0.330094i
$137$	19.0252	−	6.92459i	1.62543	−	0.591608i	0.641023	−	0.767521i	$-0.278510\pi$
$137$	19.0252	−	6.92459i	1.62543	−	0.591608i	0.984406	+	0.175914i	$0.0562880\pi$
$138$	−16.3937	−	5.96680i	−1.39552	−	0.507928i
$139$	3.05535	+	2.56374i	0.259151	+	0.217454i	0.763101	−	0.646279i	$-0.223676\pi$
$139$	3.05535	+	2.56374i	0.259151	+	0.217454i	−0.503950	+	0.863733i	$0.668120\pi$
$140$		0			0
$141$	10.8399	+	18.7752i	0.912882	+	1.58116i
$142$	−0.334616	+	1.89770i	−0.0280803	+	0.159252i
$143$	−1.77595	+	10.0719i	−0.148512	+	0.842256i
$144$	−4.37893	−	7.58452i	−0.364910	−	0.632043i
$145$		0			0
$146$	3.83942	+	3.22165i	0.317753	+	0.266626i
$147$	−11.3237	−	4.12151i	−0.933967	−	0.339936i
$148$	3.15014	−	1.14656i	0.258940	−	0.0942463i
$149$	4.31479	−	3.62054i	0.353481	−	0.296606i	−0.448705	−	0.893680i	$-0.648115\pi$
$149$	4.31479	−	3.62054i	0.353481	−	0.296606i	0.802186	+	0.597074i	$0.203670\pi$
$150$		0			0
$151$	−1.23848			−0.100786			−0.0503932	−	0.998729i	$-0.516047\pi$
$151$	−1.23848			−0.100786			−0.0503932	+	0.998729i	$0.516047\pi$
$152$	−1.66010	−	4.03039i	−0.134652	−	0.326908i
$153$	−52.4489			−4.24024
$154$	1.16877	+	6.62844i	0.0941825	+	0.534135i
$155$		0			0
$156$	9.14101	−	3.32706i	0.731867	−	0.266378i
$157$	−20.2103	−	7.35594i	−1.61296	−	0.587068i	−0.630934	−	0.775837i	$-0.717328\pi$
$157$	−20.2103	−	7.35594i	−1.61296	−	0.587068i	−0.982021	+	0.188769i	$0.939550\pi$
$158$	−0.460535	−	0.386434i	−0.0366382	−	0.0307431i
$159$	−4.39181	+	7.60685i	−0.348294	+	0.603262i
$160$		0			0
$161$	1.64946	−	9.35452i	0.129995	−	0.737240i
$162$	7.19362	−	40.7970i	0.565184	−	3.20532i
$163$	9.01050	+	15.6067i	0.705757	+	1.22241i	0.966418	+	0.256977i	$0.0827263\pi$
$163$	9.01050	+	15.6067i	0.705757	+	1.22241i	−0.260660	+	0.965431i	$0.583940\pi$
$164$	1.86286	−	3.22656i	0.145465	−	0.251952i
$165$		0			0
$166$	−1.78806	−	0.650801i	−0.138781	−	0.0505120i
$167$	−10.2510	+	3.73105i	−0.793244	+	0.288717i	−0.706684	−	0.707530i	$-0.749810\pi$
$167$	−10.2510	+	3.73105i	−0.793244	+	0.288717i	−0.0865598	+	0.996247i	$0.527587\pi$
$168$	4.90413	−	4.11506i	0.378362	−	0.317483i
$169$	−0.859902	−	4.87675i	−0.0661463	−	0.375134i
$170$		0			0
$171$	11.5514	−	36.3850i	0.883357	−	2.78243i
$172$	−0.671759			−0.0512211
$173$	−0.0253357	−	0.143686i	−0.00192623	−	0.0109242i	0.983829	−	0.179108i	$-0.0573210\pi$
$173$	−0.0253357	−	0.143686i	−0.00192623	−	0.0109242i	−0.985756	+	0.168183i	$0.946210\pi$
$174$	−3.09558	+	2.59750i	−0.234675	+	0.196916i
$175$		0			0
$176$	3.38767	+	1.23301i	0.255356	+	0.0929418i
$177$	12.5250	+	10.5097i	0.941436	+	0.789958i
$178$	−0.492959	+	0.853830i	−0.0369488	+	0.0639973i
$179$	−2.84974	−	4.93590i	−0.213000	−	0.368927i	0.739652	−	0.672989i	$-0.234990\pi$
$179$	−2.84974	−	4.93590i	−0.213000	−	0.368927i	−0.952652	+	0.304063i	$0.901657\pi$
$180$		0			0
$181$	−3.21271	+	18.2202i	−0.238799	+	1.35430i	0.595665	+	0.803233i	$0.296889\pi$
$181$	−3.21271	+	18.2202i	−0.238799	+	1.35430i	−0.834464	+	0.551063i	$0.814223\pi$
$182$	2.64825	+	4.58690i	0.196301	+	0.340004i
$183$	14.1212	−	24.4586i	1.04387	−	1.80803i
$184$	−3.89744	−	3.27034i	−0.287323	−	0.241093i
$185$		0			0
$186$	−16.7509	+	6.09684i	−1.22824	+	0.447042i
$187$	16.5390	−	13.8779i	1.20945	−	1.01485i
$188$	1.09789	+	6.22647i	0.0800721	+	0.454112i
$189$	36.8611			2.68125
$190$		0			0
$191$	18.8820			1.36626			0.683128	−	0.730298i	$-0.260619\pi$
$191$	18.8820			1.36626			0.683128	+	0.730298i	$0.260619\pi$
$192$	−0.595435	−	3.37688i	−0.0429718	−	0.243705i
$193$	−3.74110	+	3.13916i	−0.269290	+	0.225961i	−0.767426	−	0.641138i	$-0.778463\pi$
$193$	−3.74110	+	3.13916i	−0.269290	+	0.225961i	0.498135	+	0.867099i	$0.334018\pi$
$194$	−0.176250	+	0.0641498i	−0.0126540	+	0.00460568i
$195$		0			0
$196$	−2.69212	−	2.25896i	−0.192294	−	0.161354i
$197$	−1.75874	+	3.04622i	−0.125305	+	0.217034i	−0.921852	−	0.387542i	$-0.873324\pi$
$197$	−1.75874	+	3.04622i	−0.125305	+	0.217034i	0.796547	+	0.604576i	$0.206658\pi$
$198$	15.7864	+	27.3429i	1.12189	+	1.94317i
$199$	−0.145954	+	0.827747i	−0.0103464	+	0.0586774i	−0.989544	−	0.144232i	$-0.953929\pi$
$199$	−0.145954	+	0.827747i	−0.0103464	+	0.0586774i	0.979197	+	0.202910i	$0.0650398\pi$
$200$		0			0
$201$	−13.6539	−	23.6493i	−0.963073	−	1.66809i
$202$	0.980151	−	1.69767i	0.0689632	−	0.119448i
$203$	−1.68547	−	1.41428i	−0.118297	−	0.0992630i
$204$	−19.2970	−	7.02352i	−1.35106	−	0.491745i
$205$		0			0
$206$	−13.4088	+	11.2513i	−0.934237	+	0.783918i
$207$	−7.73738	−	43.8809i	−0.537785	−	3.04993i
$208$	2.83690			0.196704
$209$	5.98481	+	14.5299i	0.413978	+	1.00506i
$210$		0			0
$211$	−4.75961	−	26.9931i	−0.327665	−	1.85828i	−0.490244	−	0.871585i	$-0.663092\pi$
$211$	−4.75961	−	26.9931i	−0.327665	−	1.85828i	0.162579	−	0.986695i	$-0.448019\pi$
$212$	−1.96229	+	1.64656i	−0.134771	+	0.113086i
$213$	−6.20906	+	2.25991i	−0.425438	+	0.154847i
$214$	9.95107	+	3.62189i	0.680241	+	0.247588i
$215$		0			0
$216$	9.87176	−	17.0984i	0.671688	−	1.16340i
$217$	−4.85292	−	8.40551i	−0.329438	−	0.570603i
$218$	−2.40943	+	13.6646i	−0.163187	+	0.925480i
$219$	−2.98432	+	16.9249i	−0.201662	+	1.14368i
$220$		0			0
$221$	8.49481	−	14.7134i	0.571423	−	0.989733i
$222$	8.80565	+	7.38882i	0.590997	+	0.495905i
$223$	−10.7455	−	3.91105i	−0.719574	−	0.261903i	−0.0438288	−	0.999039i	$-0.513956\pi$
$223$	−10.7455	−	3.91105i	−0.719574	−	0.261903i	−0.675745	+	0.737136i	$0.736178\pi$
$224$	1.75441	−	0.638551i	0.117221	−	0.0426650i
$225$		0			0
$226$	2.76721	+	15.6936i	0.184072	+	1.04392i
$227$	−15.6154			−1.03643			−0.518214	−	0.855251i	$-0.673403\pi$
$227$	−15.6154			−1.03643			−0.518214	+	0.855251i	$0.673403\pi$
$228$	9.12234	−	11.8399i	0.604142	−	0.784113i
$229$	5.50003			0.363452			0.181726	−	0.983349i	$-0.441832\pi$
$229$	5.50003			0.363452			0.181726	+	0.983349i	$0.441832\pi$
$230$		0			0
$231$	−17.6798	+	14.8351i	−1.16325	+	0.976080i
$232$	−1.10741	+	0.403065i	−0.0727052	+	0.0264625i
$233$	−10.6454	−	3.87461i	−0.697404	−	0.253834i	−0.0311019	−	0.999516i	$-0.509902\pi$
$233$	−10.6454	−	3.87461i	−0.697404	−	0.253834i	−0.666302	+	0.745682i	$0.732124\pi$
$234$	19.0325	+	15.9702i	1.24419	+	1.04400i
$235$		0			0
$236$	2.38413	+	4.12943i	0.155193	+	0.268803i
$237$	0.357967	−	2.03013i	0.0232524	−	0.131871i
$238$	1.94157	−	11.0112i	0.125853	−	0.713750i
$239$	−0.741670	−	1.28461i	−0.0479747	−	0.0830946i	0.841041	−	0.540972i	$-0.181943\pi$
$239$	−0.741670	−	1.28461i	−0.0479747	−	0.0830946i	−0.889016	+	0.457877i	$0.848610\pi$
$240$		0			0
$241$	−6.44943	−	5.41172i	−0.415444	−	0.348599i	0.410983	−	0.911643i	$-0.365186\pi$
$241$	−6.44943	−	5.41172i	−0.415444	−	0.348599i	−0.826427	+	0.563044i	$0.809630\pi$
$242$	−1.87625	−	0.682899i	−0.120610	−	0.0438984i
$243$	77.8248	−	28.3259i	4.99247	−	1.81711i
$244$	6.30943	−	5.29424i	0.403920	−	0.338929i
$245$		0			0
$246$	12.7754			0.814528
$247$	8.33613	+	9.13353i	0.530415	+	0.581153i
$248$	−5.19863			−0.330114
$249$	−1.13300	−	6.42558i	−0.0718011	−	0.407204i
$250$		0			0
$251$	−10.4219	+	3.79327i	−0.657826	+	0.239429i	−0.649298	−	0.760535i	$-0.724937\pi$
$251$	−10.4219	+	3.79327i	−0.657826	+	0.239429i	−0.00852858	+	0.999964i	$0.502715\pi$
$252$	15.3648	+	5.59234i	0.967893	+	0.352284i
$253$	14.0506	+	11.7899i	0.883356	+	0.741223i
$254$	−8.40701	+	14.5614i	−0.527503	+	0.913661i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.99428	+	11.3101i	−0.124400	+	0.705506i	0.857263	+	0.514879i	$0.172163\pi$
$257$	−1.99428	+	11.3101i	−0.124400	+	0.705506i	−0.981663	+	0.190627i	$0.938948\pi$
$258$	−1.15172	−	1.99484i	−0.0717030	−	0.124193i
$259$	−3.12938	+	5.42024i	−0.194450	+	0.336797i
$260$		0			0
$261$	−9.69856	−	3.52999i	−0.600326	−	0.218501i
$262$	−6.12094	+	2.22784i	−0.378153	+	0.137636i
$263$	−24.3129	+	20.4010i	−1.49920	+	1.25798i	−0.617126	+	0.786864i	$0.711703\pi$
$263$	−24.3129	+	20.4010i	−1.49920	+	1.25798i	−0.882073	+	0.471113i	$0.843852\pi$
$264$	2.14660	+	12.1739i	0.132114	+	0.749255i
$265$		0			0
$266$	7.21109	+	3.77202i	0.442141	+	0.231278i
$267$	−3.38069			−0.206895
$268$	−1.38291	−	7.84286i	−0.0844746	−	0.479079i
$269$	−17.8932	+	15.0142i	−1.09097	+	0.915431i	−0.996785	−	0.0801240i	$-0.974468\pi$
$269$	−17.8932	+	15.0142i	−1.09097	+	0.915431i	−0.0941831	+	0.995555i	$0.530024\pi$
$270$		0			0
$271$	20.7560	+	7.55458i	1.26084	+	0.458908i	0.884050	−	0.467392i	$-0.154806\pi$
$271$	20.7560	+	7.55458i	1.26084	+	0.458908i	0.376788	+	0.926299i	$0.377028\pi$
$272$	−4.58768	−	3.84952i	−0.278169	−	0.233411i
$273$	−9.08077	+	15.7284i	−0.549593	+	0.951924i
$274$	10.1231	+	17.5337i	0.611557	+	1.05925i
$275$		0			0
$276$	3.02943	−	17.1807i	0.182350	−	1.03416i
$277$	−9.90622	−	17.1581i	−0.595207	−	1.03093i	−0.993518	−	0.113679i	$-0.963737\pi$
$277$	−9.90622	−	17.1581i	−0.595207	−	1.03093i	0.398310	−	0.917251i	$-0.369597\pi$
$278$	−1.99424	+	3.45412i	−0.119606	+	0.207164i
$279$	−34.8771	−	29.2654i	−2.08804	−	1.75207i
$280$		0			0
$281$	19.8856	−	7.23776i	1.18627	−	0.431769i	0.327860	−	0.944726i	$-0.393672\pi$
$281$	19.8856	−	7.23776i	1.18627	−	0.431769i	0.858414	+	0.512958i	$0.171450\pi$
$282$	−16.6076	+	13.9355i	−0.988971	+	0.829845i
$283$	3.23851	+	18.3665i	0.192510	+	1.09178i	0.915921	+	0.401359i	$0.131462\pi$
$283$	3.23851	+	18.3665i	0.192510	+	1.09178i	−0.723411	+	0.690418i	$0.757427\pi$
$284$	−1.92698			−0.114345
$285$		0			0
$286$	−10.2273			−0.604752
$287$	1.20788	+	6.85023i	0.0712989	+	0.404356i
$288$	6.70890	−	5.62944i	0.395326	−	0.331718i
$289$	−17.7279	+	6.45241i	−1.04282	+	0.379554i
$290$		0			0
$291$	−0.492676	−	0.413404i	−0.0288812	−	0.0242342i
$292$	−2.50600	+	4.34052i	−0.146653	+	0.254010i
$293$	−14.8653	−	25.7475i	−0.868442	−	1.50419i	−0.863589	−	0.504197i	$-0.831788\pi$
$293$	−14.8653	−	25.7475i	−0.868442	−	1.50419i	−0.00485332	−	0.999988i	$-0.501545\pi$
$294$	2.09254	−	11.8674i	0.122040	−	0.692121i
$295$		0			0
$296$	1.67615	+	2.90318i	0.0974244	+	0.168744i
$297$	−35.5886	+	61.6412i	−2.06506	+	3.57678i
$298$	4.31479	+	3.62054i	0.249949	+	0.209732i
$299$	13.5630	+	4.93654i	0.784370	+	0.285487i
$300$		0			0
$301$	0.960753	−	0.806167i	0.0553769	−	0.0464667i
$302$	−0.215061	−	1.21967i	−0.0123753	−	0.0701841i
$303$	6.72182			0.386159
$304$	3.68089	−	2.33475i	0.211113	−	0.133907i
$305$		0			0
$306$	−9.10766	−	51.6521i	−0.520650	−	2.95275i
$307$	3.95389	−	3.31770i	0.225660	−	0.189351i	−0.522947	−	0.852365i	$-0.675167\pi$
$307$	3.95389	−	3.31770i	0.225660	−	0.189351i	0.748607	+	0.663014i	$0.230723\pi$
$308$	−6.32479	+	2.30203i	−0.360388	+	0.131171i
$309$	−56.4010	−	20.5283i	−3.20854	−	1.16781i
$310$		0			0
$311$	13.0187	−	22.5490i	0.738223	−	1.27864i	−0.215072	−	0.976598i	$-0.568999\pi$
$311$	13.0187	−	22.5490i	0.738223	−	1.27864i	0.953295	−	0.302041i	$-0.0976680\pi$
$312$	4.86383	+	8.42440i	0.275360	+	0.476938i
$313$	0.0481224	−	0.272916i	0.00272004	−	0.0154261i	−0.983418	−	0.181356i	$-0.941951\pi$
$313$	0.0481224	−	0.272916i	0.00272004	−	0.0154261i	0.986138	+	0.165930i	$0.0530625\pi$
$314$	3.73471	−	21.1806i	0.210762	−	1.19529i
$315$		0			0
$316$	0.300593	−	0.520642i	0.0169097	−	0.0292884i
$317$	−19.0958	−	16.0233i	−1.07253	−	0.899958i	−0.0772492	−	0.997012i	$-0.524614\pi$
$317$	−19.0958	−	16.0233i	−1.07253	−	0.899958i	−0.995279	+	0.0970537i	$0.969058\pi$
$318$	−8.25391	−	3.00418i	−0.462856	−	0.168466i
$319$	3.99232	−	1.45309i	0.223527	−	0.0813572i
$320$		0			0
$321$	6.30548	+	35.7602i	0.351938	+	1.99594i
$322$	9.49883			0.529349
$323$	−1.08702	−	26.0819i	−0.0604835	−	1.45123i
$324$	41.4264			2.30147
$325$		0			0
$326$	−13.8049	+	11.5837i	−0.764582	+	0.641561i
$327$	−44.7089	+	16.2727i	−2.47241	+	0.899882i
$328$	3.50103	+	1.27427i	0.193312	+	0.0703598i
$329$	−9.04250	−	7.58755i	−0.498529	−	0.418315i
$330$		0			0
$331$	5.34847	+	9.26381i	0.293978	+	0.509185i	0.974747	−	0.223313i	$-0.0716873\pi$
$331$	5.34847	+	9.26381i	0.293978	+	0.509185i	−0.680768	+	0.732499i	$0.738354\pi$
$332$	0.330420	−	1.87391i	0.0181342	−	0.102844i
$333$	−5.09814	+	28.9130i	−0.279376	+	1.58442i
$334$	−5.45442	−	9.44734i	−0.298453	−	0.516935i
$335$		0			0
$336$	4.90413	+	4.11506i	0.267542	+	0.224495i
$337$	−4.28303	−	1.55890i	−0.233312	−	0.0849184i	0.222719	−	0.974883i	$-0.428507\pi$
$337$	−4.28303	−	1.55890i	−0.233312	−	0.0849184i	−0.456030	+	0.889964i	$0.650729\pi$
$338$	4.65334	−	1.69368i	0.253108	−	0.0921238i
$339$	−41.8591	+	35.1239i	−2.27347	+	1.90767i
$340$		0			0
$341$	18.7415			1.01491
$342$	37.8381	+	5.05771i	2.04605	+	0.273490i
$343$	19.6302			1.05993
$344$	−0.116650	−	0.661553i	−0.00628933	−	0.0356686i
$345$		0			0
$346$	0.137103	−	0.0499015i	0.00737072	−	0.00268272i
$347$	19.6329	+	7.14578i	1.05395	+	0.383606i	0.810151	−	0.586221i	$-0.199385\pi$
$347$	19.6329	+	7.14578i	1.05395	+	0.383606i	0.243796	+	0.969826i	$0.421607\pi$
$348$	−3.09558	−	2.59750i	−0.165940	−	0.139240i
$349$	5.64218	−	9.77255i	0.302019	−	0.523112i	−0.674574	−	0.738207i	$-0.735673\pi$
$349$	5.64218	−	9.77255i	0.302019	−	0.523112i	0.976593	+	0.215095i	$0.0690060\pi$
$350$		0			0
$351$	−9.72611	+	55.1595i	−0.519141	+	2.94420i
$352$	−0.626017	+	3.55032i	−0.0333668	+	0.189233i
$353$	−4.10792	−	7.11512i	−0.218642	−	0.378700i	0.735751	−	0.677252i	$-0.236829\pi$
$353$	−4.10792	−	7.11512i	−0.218642	−	0.378700i	−0.954393	+	0.298553i	$0.903496\pi$
$354$	−8.17511	+	14.1597i	−0.434502	+	0.752580i
$355$		0			0
$356$	−0.926460	−	0.337204i	−0.0491023	−	0.0178718i
$357$	36.0274	−	13.1129i	1.90677	−	0.694009i
$358$	4.36606	−	3.66356i	0.230753	−	0.193625i
$359$	−1.86656	−	10.5858i	−0.0985131	−	0.558696i	−0.993614	−	0.112832i	$-0.964008\pi$
$359$	−1.86656	−	10.5858i	−0.0985131	−	0.558696i	0.895101	−	0.445864i	$-0.147103\pi$
$360$		0			0
$361$	18.3330	+	4.99020i	0.964893	+	0.262642i
$362$	−18.5013			−0.972405
$363$	−1.18888	−	6.74248i	−0.0624001	−	0.353889i
$364$	−4.05735	+	3.40452i	−0.212663	+	0.178446i
$365$		0			0
$366$	26.5391	+	9.65944i	1.38722	+	0.504907i
$367$	11.4507	+	9.60825i	0.597720	+	0.501547i	0.890712	−	0.454568i	$-0.150206\pi$
$367$	11.4507	+	9.60825i	0.597720	+	0.501547i	−0.292992	+	0.956115i	$0.594651\pi$
$368$	2.54388	−	4.40612i	0.132609	−	0.229685i
$369$	16.3146	+	28.2578i	0.849306	+	1.47104i
$370$		0			0
$371$	0.830471	−	4.70983i	0.0431159	−	0.244522i
$372$	−8.91299	−	15.4377i	−0.462117	−	0.800410i
$373$	4.36113	−	7.55370i	0.225811	−	0.391116i	−0.730752	−	0.682644i	$-0.760830\pi$
$373$	4.36113	−	7.55370i	0.225811	−	0.391116i	0.956562	+	0.291528i	$0.0941635\pi$
$374$	16.5390	+	13.8779i	0.855211	+	0.717607i
$375$		0			0
$376$	−5.94122	+	2.16243i	−0.306395	+	0.111519i
$377$	2.56107	−	2.14900i	0.131902	−	0.110679i
$378$	6.40087	+	36.3011i	0.329225	+	1.86713i
$379$	15.9169			0.817597			0.408799	−	0.912625i	$-0.365948\pi$
$379$	15.9169			0.817597			0.408799	+	0.912625i	$0.365948\pi$
$380$		0			0
$381$	−57.6548			−2.95375
$382$	3.27883	+	18.5952i	0.167760	+	0.951412i
$383$	1.33589	−	1.12094i	0.0682607	−	0.0572776i	−0.608019	−	0.793923i	$-0.708036\pi$
$383$	1.33589	−	1.12094i	0.0682607	−	0.0572776i	0.676280	+	0.736645i	$0.263591\pi$
$384$	3.22218	−	1.17278i	0.164431	−	0.0598481i
$385$		0			0
$386$	−3.74110	−	3.13916i	−0.190417	−	0.159779i
$387$	2.94158	−	5.09497i	0.149529	−	0.258992i
$388$	−0.0937807	−	0.162433i	−0.00476099	−	0.00824628i
$389$	5.63929	−	31.9820i	0.285924	−	1.62155i	−0.416044	−	0.909344i	$-0.636584\pi$
$389$	5.63929	−	31.9820i	0.285924	−	1.62155i	0.701968	−	0.712209i	$-0.252305\pi$
$390$		0			0
$391$	−15.2347	−	26.3873i	−0.770454	−	1.33447i
$392$	1.75716	−	3.04348i	0.0887498	−	0.153719i
$393$	−17.1100	−	14.3570i	−0.863085	−	0.724214i
$394$	−3.30534	−	1.20305i	−0.166521	−	0.0606086i
$395$		0			0
$396$	−24.1862	+	20.2946i	−1.21540	+	1.01984i
$397$	0.712877	+	4.04292i	0.0357783	+	0.202909i	0.997457	−	0.0712700i	$-0.0227052\pi$
$397$	0.712877	+	4.04292i	0.0357783	+	0.202909i	−0.961679	+	0.274179i	$0.911594\pi$
$398$	−0.840516			−0.0421313
$399$	1.16200	+	27.8810i	0.0581730	+	1.39580i
$400$		0			0
$401$	5.41766	+	30.7251i	0.270545	+	1.53434i	0.752766	+	0.658288i	$0.228719\pi$
$401$	5.41766	+	30.7251i	0.270545	+	1.53434i	−0.482221	+	0.876049i	$0.660170\pi$
$402$	20.9190	−	17.5531i	1.04335	−	0.875471i
$403$	13.8586	−	5.04412i	0.690347	−	0.251266i
$404$	1.84208	+	0.670463i	0.0916470	+	0.0333568i
$405$		0			0
$406$	1.10011	−	1.90545i	0.0545978	−	0.0945661i
$407$	−6.04268	−	10.4662i	−0.299524	−	0.518792i
$408$	3.56593	−	20.2234i	0.176540	−	1.00121i
$409$	1.52348	−	8.64010i	0.0753313	−	0.427225i	−0.923696	−	0.383127i	$-0.874847\pi$
$409$	1.52348	−	8.64010i	0.0753313	−	0.427225i	0.999027	−	0.0440987i	$-0.0140416\pi$
$410$		0			0
$411$	−34.7117	+	60.1225i	−1.71220	+	2.96562i
$412$	−13.4088	−	11.2513i	−0.660605	−	0.554314i
$413$	−8.36545	−	3.04478i	−0.411637	−	0.149824i
$414$	41.8706	−	15.2397i	2.05783	−	0.748988i
$415$		0			0
$416$	0.492623	+	2.79380i	0.0241528	+	0.136978i
$417$	−13.6764			−0.669734
$418$	−13.2699	+	8.41698i	−0.649053	+	0.411688i
$419$	−6.13252			−0.299593			−0.149797	−	0.988717i	$-0.547862\pi$
$419$	−6.13252			−0.299593			−0.149797	+	0.988717i	$0.547862\pi$
$420$		0			0
$421$	−2.93864	+	2.46581i	−0.143220	+	0.120176i	−0.711583	−	0.702602i	$-0.752021\pi$
$421$	−2.93864	+	2.46581i	−0.143220	+	0.120176i	0.568363	+	0.822778i	$0.307577\pi$
$422$	25.7565	−	9.37460i	1.25381	−	0.456348i
$423$	−52.0324	−	18.9382i	−2.52990	−	0.920808i
$424$	−1.96229	−	1.64656i	−0.0952974	−	0.0799640i
$425$		0			0
$426$	−3.30377	−	5.72230i	−0.160068	−	0.277247i
$427$	−2.67024	+	15.1437i	−0.129222	+	0.732855i
$428$	−1.83888	+	10.4288i	−0.0888858	+	0.504096i
$429$	−17.5345	−	30.3707i	−0.846576	−	1.46631i
$430$		0			0
$431$	−19.5996	−	16.4460i	−0.944081	−	0.792178i	0.0342100	−	0.999415i	$-0.489108\pi$
$431$	−19.5996	−	16.4460i	−0.944081	−	0.792178i	−0.978291	+	0.207237i	$0.933553\pi$
$432$	18.5528	+	6.75268i	0.892624	+	0.324888i
$433$	26.7471	−	9.73513i	1.28538	−	0.467841i	0.393173	−	0.919464i	$-0.371377\pi$
$433$	26.7471	−	9.73513i	1.28538	−	0.467841i	0.892208	+	0.451624i	$0.149155\pi$
$434$	7.43511	−	6.23880i	0.356897	−	0.299472i
$435$		0			0
$436$	−13.8754			−0.664509
$437$	21.6608	−	4.75710i	1.03618	−	0.227563i
$438$	−17.1860			−0.821180
$439$	6.61684	+	37.5260i	0.315805	+	1.79102i	0.567671	+	0.823256i	$0.307845\pi$
$439$	6.61684	+	37.5260i	0.315805	+	1.79102i	−0.251866	+	0.967762i	$0.581044\pi$
$440$		0			0
$441$	28.9217	−	10.5266i	1.37722	−	0.501268i
$442$	15.9650	+	5.81079i	0.759379	+	0.276391i
$443$	−17.4493	−	14.6417i	−0.829042	−	0.695649i	0.126029	−	0.992027i	$-0.459777\pi$
$443$	−17.4493	−	14.6417i	−0.829042	−	0.695649i	−0.955071	+	0.296377i	$0.904221\pi$
$444$	−5.74748	+	9.95493i	−0.272763	+	0.472440i
$445$		0			0
$446$	1.98569	−	11.2614i	0.0940253	−	0.533244i
$447$	−3.35382	+	19.0205i	−0.158630	+	0.899637i
$448$	0.933500	+	1.61687i	0.0441037	+	0.0763899i
$449$	15.5911	−	27.0045i	0.735787	−	1.27442i	−0.218590	−	0.975817i	$-0.570146\pi$
$449$	15.5911	−	27.0045i	0.735787	−	1.27442i	0.954377	−	0.298604i	$-0.0965211\pi$
$450$		0			0
$451$	−12.6215	−	4.59385i	−0.594324	−	0.216316i
$452$	−14.9747	+	5.45034i	−0.704350	+	0.256362i
$453$	3.25318	−	2.72975i	0.152848	−	0.128255i
$454$	−2.71158	−	15.3781i	−0.127261	−	0.721731i
$455$		0			0
$456$	13.2441	+	6.92778i	0.620210	+	0.324423i
$457$	13.0810			0.611902			0.305951	−	0.952047i	$-0.401026\pi$
$457$	13.0810			0.611902			0.305951	+	0.952047i	$0.401026\pi$
$458$	0.955070	+	5.41647i	0.0446275	+	0.253095i
$459$	90.5769	−	76.0030i	4.22777	−	3.54752i
$460$		0			0
$461$	−17.1219	−	6.23187i	−0.797448	−	0.290247i	−0.0890194	−	0.996030i	$-0.528373\pi$
$461$	−17.1219	−	6.23187i	−0.797448	−	0.290247i	−0.708429	+	0.705783i	$0.750596\pi$
$462$	−17.6798	−	14.8351i	−0.822540	−	0.690193i
$463$	−11.5040	+	19.9255i	−0.534636	+	0.926017i	0.464545	+	0.885550i	$0.346218\pi$
$463$	−11.5040	+	19.9255i	−0.534636	+	0.926017i	−0.999181	+	0.0404670i	$0.987115\pi$
$464$	−0.589242	−	1.02060i	−0.0273549	−	0.0473800i
$465$		0			0
$466$	1.96719	−	11.1565i	0.0911284	−	0.516815i
$467$	−12.5265	−	21.6966i	−0.579658	−	1.00400i	−0.995518	−	0.0945691i	$-0.969853\pi$
$467$	−12.5265	−	21.6966i	−0.579658	−	1.00400i	0.415860	−	0.909429i	$-0.363481\pi$
$468$	−12.4226	+	21.5166i	−0.574234	+	0.994603i
$469$	11.3899	+	9.55729i	0.525938	+	0.441315i
$470$		0			0
$471$	69.3005	−	25.2233i	3.19320	−	1.16223i
$472$	−3.65269	+	3.06497i	−0.168129	+	0.141077i
$473$	0.420532	+	2.38496i	0.0193361	+	0.109660i
$474$	2.06145			0.0946854
$475$		0			0
$476$	11.1811			0.512483
$477$	−3.89563	−	22.0932i	−0.178369	−	1.01158i
$478$	1.13631	−	0.953473i	0.0519734	−	0.0436108i
$479$	−20.3567	+	7.40924i	−0.930122	+	0.338537i	−0.762258	−	0.647274i	$-0.775909\pi$
$479$	−20.3567	+	7.40924i	−0.930122	+	0.338537i	−0.167864	+	0.985810i	$0.553687\pi$
$480$		0			0
$481$	−7.28521	−	6.11302i	−0.332177	−	0.278730i
$482$	4.20957	−	7.29118i	0.191741	−	0.332104i
$483$	16.2856	+	28.2075i	0.741021	+	1.28349i
$484$	0.346717	−	1.96633i	0.0157598	−	0.0893785i
$485$		0			0
$486$	41.4097	+	71.7238i	1.87838	+	3.25346i
$487$	−1.66266	+	2.87982i	−0.0753425	+	0.130497i	−0.901235	−	0.433330i	$-0.857338\pi$
$487$	−1.66266	+	2.87982i	−0.0753425	+	0.130497i	0.825893	+	0.563827i	$0.190672\pi$
$488$	6.30943	+	5.29424i	0.285614	+	0.239659i
$489$	−58.0669	−	21.1346i	−2.62588	−	0.955741i
$490$		0			0
$491$	−3.86014	+	3.23904i	−0.174206	+	0.146176i	−0.725722	−	0.687988i	$-0.758494\pi$
$491$	−3.86014	+	3.23904i	−0.174206	+	0.146176i	0.551516	+	0.834164i	$0.314050\pi$
$492$	2.21842	+	12.5813i	0.100014	+	0.567208i
$493$	−7.05769			−0.317862
$494$	−7.54722	+	9.79551i	−0.339565	+	0.440721i
$495$		0			0
$496$	−0.902733	−	5.11966i	−0.0405339	−	0.229879i
$497$	2.75597	−	2.31253i	0.123622	−	0.103731i
$498$	6.13121	−	2.23158i	0.274746	−	0.0999995i
$499$	9.62114	+	3.50181i	0.430701	+	0.156762i	0.548268	−	0.836302i	$-0.315287\pi$
$499$	9.62114	+	3.50181i	0.430701	+	0.156762i	−0.117567	+	0.993065i	$0.537509\pi$
$500$		0			0
$501$	18.7031	−	32.3947i	0.835592	−	1.44729i
$502$	−5.54539	−	9.60490i	−0.247503	−	0.428688i
$503$	−1.16399	+	6.60132i	−0.0518998	+	0.294338i	−0.999699	−	0.0245291i	$-0.992191\pi$
$503$	−1.16399	+	6.60132i	−0.0518998	+	0.294338i	0.947799	+	0.318867i	$0.103302\pi$
$504$	−2.83930	+	16.1025i	−0.126473	+	0.717262i
$505$		0			0
$506$	−9.17090	+	15.8845i	−0.407696	+	0.706151i
$507$	13.0076	+	10.9147i	0.577687	+	0.484737i
$508$	−15.8000	−	5.75073i	−0.701012	−	0.255148i
$509$	−22.6049	+	8.22751i	−1.00195	+	0.364678i	−0.790334	−	0.612676i	$-0.790093\pi$
$509$	−22.6049	+	8.22751i	−1.00195	+	0.364678i	−0.211611	+	0.977354i	$0.567871\pi$
$510$		0			0
$511$	−1.62490	−	9.21525i	−0.0718812	−	0.407659i
$512$	1.00000			0.0441942
$513$	32.7762	+	79.5741i	1.44711	+	3.51328i
$514$	−11.4846			−0.506564
$515$		0			0
$516$	1.76454	−	1.48062i	0.0776795	−	0.0651808i
$517$	21.4186	−	7.79575i	0.941991	−	0.342857i
$518$	−5.88130	−	2.14062i	−0.258410	−	0.0940534i
$519$	0.383248	+	0.321583i	0.0168227	+	0.0141159i
$520$		0			0
$521$	−13.2375	−	22.9280i	−0.579945	−	1.00449i	−0.995485	−	0.0949192i	$-0.969741\pi$
$521$	−13.2375	−	22.9280i	−0.579945	−	1.00449i	0.415540	−	0.909575i	$-0.363593\pi$
$522$	1.79222	−	10.1642i	0.0784434	−	0.444874i
$523$	2.71298	−	15.3861i	0.118631	−	0.672787i	−0.866258	−	0.499597i	$-0.833481\pi$
$523$	2.71298	−	15.3861i	0.118631	−	0.672787i	0.984888	−	0.173190i	$-0.0554075\pi$
$524$	−3.25688	−	5.64108i	−0.142278	−	0.246432i
$525$		0			0
$526$	−24.3129	−	20.4010i	−1.06009	−	0.889524i
$527$	−29.2559	−	10.6483i	−1.27441	−	0.463847i
$528$	−11.6162	+	4.22797i	−0.505532	+	0.183999i
$529$	2.21022	−	1.85459i	0.0960963	−	0.0806344i
$530$		0			0
$531$	−41.7597			−1.81222
$532$	−2.46253	+	7.75655i	−0.106764	+	0.336289i
$533$	−10.5695			−0.457816
$534$	−0.587050	−	3.32933i	−0.0254041	−	0.144074i
$535$		0			0
$536$	7.48357	−	2.72380i	0.323241	−	0.117650i
$537$	18.3648	+	6.68423i	0.792498	+	0.288446i
$538$	−17.8932	−	15.0142i	−0.771431	−	0.647307i
$539$	−6.33470	+	10.9720i	−0.272855	+	0.472599i
$540$		0			0
$541$	−2.57421	+	14.5991i	−0.110674	+	0.627664i	0.878127	+	0.478427i	$0.158793\pi$
$541$	−2.57421	+	14.5991i	−0.110674	+	0.627664i	−0.988801	+	0.149237i	$0.952318\pi$
$542$	−3.83556	+	21.7525i	−0.164751	+	0.934351i
$543$	−31.7202	−	54.9409i	−1.36124	−	2.35774i
$544$	2.99439	−	5.18644i	0.128384	−	0.222367i
$545$		0			0
$546$	−17.0663	−	6.21161i	−0.730369	−	0.265833i
$547$	−18.2130	+	6.62897i	−0.778730	+	0.283434i	−0.700643	−	0.713512i	$-0.747103\pi$
$547$	−18.2130	+	6.62897i	−0.778730	+	0.283434i	−0.0780869	+	0.996947i	$0.524881\pi$
$548$	−15.5095	+	13.0140i	−0.662531	+	0.555929i
$549$	12.5258	+	71.0371i	0.534586	+	3.03179i
$550$		0			0
$551$	1.55439	−	4.89607i	0.0662193	−	0.208580i
$552$	17.4458			0.742541
$553$	0.194905	+	1.10536i	0.00828820	+	0.0470047i
$554$	15.1772	−	12.7352i	0.644818	−	0.541067i
$555$		0			0
$556$	−3.74794	−	1.36414i	−0.158948	−	0.0578523i
$557$	29.2047	+	24.5056i	1.23744	+	1.03834i	0.997720	+	0.0674946i	$0.0215005\pi$
$557$	29.2047	+	24.5056i	1.23744	+	1.03834i	0.239721	+	0.970842i	$0.422944\pi$
$558$	22.7644	−	39.4292i	0.963695	−	1.66917i
$559$	0.952858	+	1.65040i	0.0403016	+	0.0698044i
$560$		0			0
$561$	−12.8555	+	72.9072i	−0.542760	+	3.07814i
$562$	10.5809	+	18.3267i	0.446328	+	0.773063i
$563$	6.16458	−	10.6774i	0.259806	−	0.449998i	−0.706384	−	0.707829i	$-0.749675\pi$
$563$	6.16458	−	10.6774i	0.259806	−	0.449998i	0.966190	+	0.257832i	$0.0830080\pi$
$564$	−16.6076	−	13.9355i	−0.699308	−	0.586789i
$565$		0			0
$566$	−17.5251	+	6.37863i	−0.736636	+	0.268114i
$567$	−59.2482	+	49.7152i	−2.48819	+	2.08784i
$568$	−0.334616	−	1.89770i	−0.0140402	−	0.0796258i
$569$	−3.18778			−0.133639			−0.0668194	−	0.997765i	$-0.521285\pi$
$569$	−3.18778			−0.133639			−0.0668194	+	0.997765i	$0.521285\pi$
$570$		0			0
$571$	3.67370			0.153740			0.0768698	−	0.997041i	$-0.475507\pi$
$571$	3.67370			0.153740			0.0768698	+	0.997041i	$0.475507\pi$
$572$	−1.77595	−	10.0719i	−0.0742562	−	0.421128i
$573$	−49.5983	+	41.6179i	−2.07200	+	1.73861i
$574$	−6.53641	+	2.37906i	−0.272825	+	0.0993001i
$575$		0			0
$576$	6.70890	+	5.62944i	0.279538	+	0.234560i
$577$	−1.07552	+	1.86286i	−0.0447746	+	0.0775519i	−0.887544	−	0.460723i	$-0.847590\pi$
$577$	−1.07552	+	1.86286i	−0.0447746	+	0.0775519i	0.842770	+	0.538274i	$0.180924\pi$
$578$	−9.43280	−	16.3381i	−0.392353	−	0.679575i
$579$	2.90790	−	16.4915i	0.120848	−	0.685364i
$580$		0			0
$581$	1.77628	+	3.07660i	0.0736924	+	0.127639i
$582$	0.321571	−	0.556978i	0.0133296	−	0.0230875i
$583$	7.07424	+	5.93599i	0.292985	+	0.245844i
$584$	−4.70974	−	1.71421i	−0.194891	−	0.0709344i
$585$		0			0
$586$	22.7750	−	19.1105i	0.940827	−	0.789447i
$587$	4.95317	+	28.0908i	0.204439	+	1.15943i	0.898320	+	0.439342i	$0.144788\pi$
$587$	4.95317	+	28.0908i	0.204439	+	1.15943i	−0.693880	+	0.720090i	$0.744100\pi$
$588$	12.0505			0.496953
$589$	13.8303	−	17.9503i	0.569868	−	0.739629i
$590$		0			0
$591$	−2.09442	−	11.8781i	−0.0861531	−	0.488599i
$592$	−2.56801	+	2.15482i	−0.105545	+	0.0885626i
$593$	9.48294	−	3.45151i	0.389418	−	0.141737i	−0.139889	−	0.990167i	$-0.544674\pi$
$593$	9.48294	−	3.45151i	0.389418	−	0.141737i	0.529306	+	0.848431i	$0.322452\pi$
$594$	−66.8846	−	24.3440i	−2.74431	−	0.998847i
$595$		0			0
$596$	−2.81628	+	4.87794i	−0.115359	+	0.199808i
$597$	−1.44105	−	2.49598i	−0.0589784	−	0.102154i
$598$	−2.50635	+	14.2142i	−0.102492	+	0.581261i
$599$	0.479831	−	2.72126i	0.0196054	−	0.111188i	−0.973435	−	0.228965i	$-0.926466\pi$
$599$	0.479831	−	2.72126i	0.0196054	−	0.111188i	0.993040	+	0.117778i	$0.0375770\pi$
$600$		0			0
$601$	−8.51074	+	14.7410i	−0.347160	+	0.601299i	−0.985744	−	0.168253i	$-0.946187\pi$
$601$	−8.51074	+	14.7410i	−0.347160	+	0.601299i	0.638583	+	0.769553i	$0.279521\pi$
$602$	0.960753	+	0.806167i	0.0391574	+	0.0328569i
$603$	65.5400	+	23.8546i	2.66900	+	0.971435i
$604$	1.16380	−	0.423587i	0.0473542	−	0.0172355i
$605$		0			0
$606$	1.16723	+	6.61970i	0.0474156	+	0.268907i
$607$	45.0807			1.82977			0.914884	−	0.403717i	$-0.132282\pi$
$607$	45.0807			1.82977			0.914884	+	0.403717i	$0.132282\pi$
$608$	2.93846	+	3.21954i	0.119170	+	0.130570i
$609$	7.54452			0.305720
$610$		0			0
$611$	13.7401	−	11.5293i	0.555863	−	0.466425i
$612$	49.2859	−	17.9386i	1.99226	−	0.725124i
$613$	−1.15435	−	0.420147i	−0.0466236	−	0.0169696i	0.318603	−	0.947888i	$-0.396786\pi$
$613$	−1.15435	−	0.420147i	−0.0466236	−	0.0169696i	−0.365227	+	0.930919i	$0.619009\pi$
$614$	3.95389	+	3.31770i	0.159566	+	0.133892i
$615$		0			0
$616$	−3.36535	−	5.82896i	−0.135594	−	0.234855i
$617$	−4.11879	+	23.3588i	−0.165816	+	0.940392i	0.782402	+	0.622773i	$0.213994\pi$
$617$	−4.11879	+	23.3588i	−0.165816	+	0.940392i	−0.948219	+	0.317618i	$0.897117\pi$
$618$	10.4225	−	59.1088i	0.419254	−	2.37771i
$619$	−6.32545	−	10.9560i	−0.254241	−	0.440359i	0.710448	−	0.703750i	$-0.248492\pi$
$619$	−6.32545	−	10.9560i	−0.254241	−	0.440359i	−0.964689	+	0.263391i	$0.915159\pi$
$620$		0			0
$621$	76.9493	+	64.5681i	3.08787	+	2.59103i
$622$	24.4672	+	8.90531i	0.981043	+	0.357071i
$623$	1.72970	−	0.629559i	0.0692990	−	0.0252228i
$624$	−7.45182	+	6.25282i	−0.298312	+	0.250313i
$625$		0			0
$626$	0.277126			0.0110762
$627$	−47.7460	−	24.9753i	−1.90679	−	0.997416i
$628$	21.5073			0.858235
$629$	3.48620	+	19.7712i	0.139004	+	0.788331i
$630$		0			0
$631$	−35.9350	+	13.0793i	−1.43055	+	0.520677i	−0.937089	−	0.349091i	$-0.886490\pi$
$631$	−35.9350	+	13.0793i	−1.43055	+	0.520677i	−0.493460	+	0.869769i	$0.664268\pi$
$632$	0.564929	+	0.205617i	0.0224717	+	0.00817902i
$633$	71.9978	+	60.4133i	2.86165	+	2.40121i
$634$	12.4639	−	21.5881i	0.495005	−	0.857374i
$635$		0			0
$636$	1.52526	−	8.65019i	0.0604805	−	0.343002i
$637$	−1.73123	+	9.81830i	−0.0685939	+	0.389015i
$638$	2.12427	+	3.67934i	0.0841006	+	0.145667i
$639$	8.43809	−	14.6152i	0.333806	−	0.578168i
$640$		0			0
$641$	−9.64318	−	3.50983i	−0.380883	−	0.138630i	0.144481	−	0.989508i	$-0.453849\pi$
$641$	−9.64318	−	3.50983i	−0.380883	−	0.138630i	−0.525364	+	0.850878i	$0.676071\pi$
$642$	−34.1219	+	12.4194i	−1.34669	+	0.490154i
$643$	11.1597	−	9.36407i	0.440094	−	0.369283i	−0.395650	−	0.918401i	$-0.629481\pi$
$643$	11.1597	−	9.36407i	0.440094	−	0.369283i	0.835745	+	0.549118i	$0.185036\pi$
$644$	1.64946	+	9.35452i	0.0649976	+	0.368620i
$645$		0			0
$646$	25.4969	−	5.59958i	1.00316	−	0.220313i
$647$	−4.44223			−0.174642			−0.0873211	−	0.996180i	$-0.527831\pi$
$647$	−4.44223			−0.174642			−0.0873211	+	0.996180i	$0.527831\pi$
$648$	7.19362	+	40.7970i	0.282592	+	1.60266i
$649$	13.1683	−	11.0495i	0.516900	−	0.433731i
$650$		0			0
$651$	31.2740	+	11.3828i	1.22572	+	0.446127i
$652$	−13.8049	−	11.5837i	−0.540641	−	0.453652i
$653$	9.72417	−	16.8427i	0.380536	−	0.659108i	−0.610603	−	0.791937i	$-0.709073\pi$
$653$	9.72417	−	16.8427i	0.380536	−	0.659108i	0.991139	+	0.132829i	$0.0424062\pi$
$654$	−23.7891	−	41.2039i	−0.930227	−	1.61120i
$655$		0			0
$656$	−0.646964	+	3.66911i	−0.0252597	+	0.143255i
$657$	−21.9472	−	38.0137i	−0.856242	−	1.48305i
$658$	5.90207	−	10.2227i	0.230087	−	0.398522i
$659$	9.54535	+	8.00950i	0.371834	+	0.312006i	0.809487	−	0.587138i	$-0.199746\pi$
$659$	9.54535	+	8.00950i	0.371834	+	0.312006i	−0.437652	+	0.899144i	$0.644190\pi$
$660$		0			0
$661$	−7.75350	+	2.82204i	−0.301576	+	0.109765i	−0.488376	−	0.872633i	$-0.662411\pi$
$661$	−7.75350	+	2.82204i	−0.301576	+	0.109765i	0.186800	+	0.982398i	$0.440188\pi$
$662$	−8.19432	+	6.87585i	−0.318481	+	0.267238i
$663$	10.1162	+	57.3719i	0.392881	+	2.22814i
$664$	1.90282			0.0738436
$665$		0			0
$666$	−29.3590			−1.13764
$667$	−1.04117	−	5.90475i	−0.0403141	−	0.228633i
$668$	8.35666	−	7.01207i	0.323329	−	0.271305i
$669$	36.8461	−	13.4109i	1.42455	−	0.518495i
$670$		0			0
$671$	−22.7461	−	19.0862i	−0.878102	−	0.736815i
$672$	−3.20094	+	5.54420i	−0.123479	+	0.213872i
$673$	−0.616571	−	1.06793i	−0.0237671	−	0.0411658i	0.853897	−	0.520442i	$-0.174233\pi$
$673$	−0.616571	−	1.06793i	−0.0237671	−	0.0411658i	−0.877664	+	0.479276i	$0.840899\pi$
$674$	0.791472	−	4.48866i	0.0304864	−	0.172897i
$675$		0			0
$676$	2.47599	+	4.28854i	0.0952303	+	0.164944i
$677$	−8.92630	+	15.4608i	−0.343065	+	0.594207i	−0.985000	−	0.172552i	$-0.944799\pi$
$677$	−8.92630	+	15.4608i	−0.343065	+	0.594207i	0.641935	+	0.766759i	$0.278132\pi$
$678$	−41.8591	−	35.1239i	−1.60759	−	1.34893i
$679$	0.329059	+	0.119768i	0.0126281	+	0.00459626i
$680$		0			0
$681$	41.0176	−	34.4178i	1.57180	−	1.31889i
$682$	3.25443	+	18.4568i	0.124619	+	0.706748i
$683$	−27.7712			−1.06264			−0.531318	−	0.847173i	$-0.678303\pi$
$683$	−27.7712			−1.06264			−0.531318	+	0.847173i	$0.678303\pi$
$684$	1.58963	+	38.1415i	0.0607812	+	1.45838i
$685$		0			0
$686$	3.40875	+	19.3320i	0.130147	+	0.738099i
$687$	−14.4472	+	12.1226i	−0.551194	+	0.462507i
$688$	0.631247	−	0.229755i	0.0240661	−	0.00875933i
$689$	6.82874	+	2.48546i	0.260154	+	0.0946884i
$690$		0			0
$691$	−21.3398	+	36.9617i	−0.811805	+	1.40609i	0.0997945	+	0.995008i	$0.468181\pi$
$691$	−21.3398	+	36.9617i	−0.811805	+	1.40609i	−0.911600	+	0.411079i	$0.865152\pi$
$692$	0.0729511	+	0.126355i	0.00277319	+	0.00480330i
$693$	10.2359	−	58.0509i	0.388831	−	2.20517i
$694$	−3.62801	+	20.5755i	−0.137717	+	0.781033i
$695$		0			0
$696$	2.02049	−	3.49960i	0.0765866	−	0.132652i
$697$	17.0924	+	14.3422i	0.647420	+	0.543250i
$698$	10.6038	+	3.85948i	0.401361	+	0.146083i
$699$	36.5028	−	13.2859i	1.38066	−	0.502520i
$700$		0			0
$701$	−6.91944	−	39.2421i	−0.261344	−	1.48215i	−0.779249	−	0.626715i	$-0.784399\pi$
$701$	−6.91944	−	39.2421i	−0.261344	−	1.48215i	0.517905	−	0.855438i	$-0.326712\pi$
$702$	−56.0104			−2.11398
$703$	−14.4835	−	1.93598i	−0.546257	−	0.0730168i
$704$	−3.60509			−0.135872
$705$		0			0
$706$	6.29370	−	5.28104i	0.236866	−	0.198754i
$707$	−3.43916	+	1.25175i	−0.129343	+	0.0470770i
$708$	−15.3642	−	5.59210i	−0.577421	−	0.210164i
$709$	36.8093	+	30.8866i	1.38240	+	1.15997i	0.968314	+	0.249734i	$0.0803433\pi$
$709$	36.8093	+	30.8866i	1.38240	+	1.15997i	0.414086	+	0.910238i	$0.364101\pi$
$710$		0			0
$711$	2.63255	+	4.55970i	0.0987282	+	0.171002i
$712$	0.171203	−	0.970940i	0.00641610	−	0.0363875i
$713$	4.59288	−	26.0475i	0.172005	−	0.975488i
$714$	19.1698	+	33.2030i	0.717411	+	1.24259i
$715$		0			0
$716$	4.36606	+	3.66356i	0.163167	+	0.136914i
$717$	4.77959	+	1.73963i	0.178497	+	0.0649676i
$718$	10.1008	−	3.67640i	0.376960	−	0.137202i
$719$	−23.2680	+	19.5242i	−0.867749	+	0.728128i	−0.963623	−	0.267266i	$-0.913880\pi$
$719$	−23.2680	+	19.5242i	−0.867749	+	0.728128i	0.0958738	+	0.995393i	$0.469435\pi$
$720$		0			0
$721$	32.6799			1.21706
$722$	−1.73090	+	18.9210i	−0.0644175	+	0.704166i
$723$	28.8690			1.07365
$724$	−3.21271	−	18.2202i	−0.119399	−	0.677148i
$725$		0			0
$726$	6.43360	−	2.34164i	0.238773	−	0.0869064i
$727$	−28.7236	−	10.4545i	−1.06530	−	0.387737i	−0.250883	−	0.968018i	$-0.580721\pi$
$727$	−28.7236	−	10.4545i	−1.06530	−	0.387737i	−0.814417	+	0.580280i	$0.802943\pi$
$728$	−4.05735	−	3.40452i	−0.150376	−	0.126180i
$729$	−79.8532	+	138.310i	−2.95753	+	5.12259i
$730$		0			0
$731$	0.698590	−	3.96190i	0.0258383	−	0.146536i
$732$	−4.90422	+	27.8132i	−0.181265	+	1.02801i
$733$	−21.9999	−	38.1050i	−0.812586	−	1.40744i	−0.911049	−	0.412299i	$-0.864726\pi$
$733$	−21.9999	−	38.1050i	−0.812586	−	1.40744i	0.0984629	−	0.995141i	$-0.468607\pi$
$734$	−7.47389	+	12.9452i	−0.275866	+	0.477815i
$735$		0			0
$736$	4.78092	+	1.74011i	0.176227	+	0.0641415i
$737$	−26.9789	+	9.81953i	−0.993782	+	0.361707i
$738$	−24.9955	+	20.9737i	−0.920096	+	0.772052i
$739$	5.08815	+	28.8563i	0.187171	+	1.06150i	0.923135	+	0.384476i	$0.125618\pi$
$739$	5.08815	+	28.8563i	0.187171	+	1.06150i	−0.735964	+	0.677020i	$0.763271\pi$
$740$		0			0
$741$	−42.0281	−	5.61779i	−1.54394	−	0.206375i
$742$	4.78249			0.175571
$743$	−2.27875	−	12.9235i	−0.0835994	−	0.474116i	−0.997650	−	0.0685156i	$-0.978174\pi$
$743$	−2.27875	−	12.9235i	−0.0835994	−	0.474116i	0.914051	−	0.405600i	$-0.132937\pi$
$744$	13.6555	−	11.4583i	0.500635	−	0.420082i
$745$		0			0
$746$	8.19625	+	2.98319i	0.300086	+	0.109222i
$747$	12.7658	+	10.7118i	0.467076	+	0.391924i
$748$	−10.7951	+	18.6976i	−0.394706	+	0.683651i
$749$	−9.88549	−	17.1222i	−0.361208	−	0.625631i
$750$		0			0
$751$	3.47466	−	19.7058i	0.126792	−	0.719074i	−0.853435	−	0.521199i	$-0.825485\pi$
$751$	3.47466	−	19.7058i	0.126792	−	0.719074i	0.980227	−	0.197875i	$-0.0634040\pi$
$752$	−3.16126	−	5.47546i	−0.115279	−	0.199670i
$753$	19.0150	−	32.9349i	0.692945	−	1.20022i
$754$	2.56107	+	2.14900i	0.0932688	+	0.0782618i
$755$		0			0
$756$	−34.6381	+	12.6072i	−1.25978	+	0.458521i
$757$	27.9516	−	23.4542i	1.01592	−	0.852458i	0.0268104	−	0.999641i	$-0.491465\pi$
$757$	27.9516	−	23.4542i	1.01592	−	0.852458i	0.989109	+	0.147183i	$0.0470205\pi$
$758$	2.76394	+	15.6751i	0.100391	+	0.569345i
$759$	−62.8935			−2.28289
$760$		0			0
$761$	3.91470			0.141908			0.0709540	−	0.997480i	$-0.477396\pi$
$761$	3.91470			0.141908			0.0709540	+	0.997480i	$0.477396\pi$
$762$	−10.0117	−	56.7789i	−0.362684	−	2.05688i
$763$	19.8446	−	16.6516i	0.718422	−	0.602828i
$764$	−17.7433	+	6.45804i	−0.641931	+	0.233644i
$765$		0			0
$766$	1.33589	+	1.12094i	0.0482676	+	0.0405013i
$767$	6.76354	−	11.7148i	0.244217	−	0.422997i
$768$	1.71449	+	2.96958i	0.0618662	+	0.107155i
$769$	−3.94857	+	22.3935i	−0.142389	+	0.807530i	0.827037	+	0.562147i	$0.190025\pi$
$769$	−3.94857	+	22.3935i	−0.142389	+	0.807530i	−0.969426	+	0.245382i	$0.921087\pi$
$770$		0			0
$771$	−19.6902	−	34.1044i	−0.709125	−	1.22824i
$772$	2.44183	−	4.22937i	0.0878834	−	0.152218i
$773$	−16.7478	−	14.0531i	−0.602377	−	0.505454i	0.289832	−	0.957078i	$-0.406401\pi$
$773$	−16.7478	−	14.0531i	−0.602377	−	0.505454i	−0.892209	+	0.451623i	$0.850845\pi$
$774$	5.52837	+	2.01216i	0.198713	+	0.0723256i
$775$		0			0
$776$	0.143680	−	0.120562i	0.00515782	−	0.00432793i
$777$	−3.72668	−	21.1350i	−0.133694	−	0.758216i
$778$	32.4754			1.16430
$779$	−13.7139	+	8.69862i	−0.491353	+	0.311660i
$780$		0			0
$781$	1.20632	+	6.84138i	0.0431655	+	0.244804i
$782$	23.3410	−	19.5854i	0.834672	−	0.700373i
$783$	21.8642	−	7.95792i	0.781363	−	0.284393i
$784$	3.30237	+	1.20197i	0.117942	+	0.0429273i
$785$		0			0
$786$	11.1678	−	19.3431i	0.398341	−	0.689946i
$787$	−15.0675	−	26.0977i	−0.537098	−	0.930282i	−0.999059	−	0.0433810i	$-0.986187\pi$
$787$	−15.0675	−	26.0977i	−0.537098	−	0.930282i	0.461960	−	0.886901i	$-0.347146\pi$
$788$	0.610802	−	3.46403i	0.0217589	−	0.123401i
$789$	18.8981	−	107.176i	0.672789	−	3.81558i
$790$		0			0
$791$	14.8760	−	25.7660i	0.528929	−	0.916133i
$792$	−24.1862	−	20.2946i	−0.859419	−	0.721138i
$793$	−21.9567	−	7.99158i	−0.779704	−	0.283789i
$794$	−3.85771	+	1.40409i	−0.136905	+	0.0498294i
$795$		0			0
$796$	−0.145954	−	0.827747i	−0.00517321	−	0.0293387i
$797$	19.4641			0.689456			0.344728	−	0.938703i	$-0.387971\pi$
$797$	19.4641			0.689456			0.344728	+	0.938703i	$0.387971\pi$
$798$	−27.2556	+	5.98583i	−0.964839	+	0.211896i
$799$	−37.8642			−1.33954
$800$		0			0
$801$	6.61443	−	5.55016i	0.233709	−	0.196105i
$802$	−29.3175	+	10.6707i	−1.03524	+	0.376796i
$803$	16.9790	+	6.17987i	0.599177	+	0.218083i
$804$	20.9190	+	17.5531i	0.737757	+	0.619051i
$805$		0			0
$806$	7.37401	+	12.7722i	0.259739	+	0.449880i
$807$	13.9081	−	78.8769i	0.489589	−	2.77660i
$808$	−0.340403	+	1.93052i	−0.0119753	+	0.0679155i
$809$	20.1616	+	34.9209i	0.708844	+	1.22775i	0.965286	+	0.261194i	$0.0841162\pi$
$809$	20.1616	+	34.9209i	0.708844	+	1.22775i	−0.256443	+	0.966559i	$0.582550\pi$
$810$		0			0
$811$	−14.7737	−	12.3966i	−0.518775	−	0.435304i	0.345430	−	0.938445i	$-0.387733\pi$
$811$	−14.7737	−	12.3966i	−0.518775	−	0.435304i	−0.864204	+	0.503141i	$0.832178\pi$
$812$	2.06754	+	0.752523i	0.0725564	+	0.0264084i
$813$	−71.1718	+	25.9044i	−2.49611	+	0.908508i
$814$	9.25792	−	7.76832i	0.324490	−	0.272279i
$815$		0			0
$816$	20.5354			0.718883
$817$	2.59460	+	1.35720i	0.0907736	+	0.0474824i
$818$	8.77338			0.306754
$819$	−8.05483	−	45.6812i	−0.281459	−	1.59623i
$820$		0			0
$821$	−39.3911	+	14.3372i	−1.37476	+	0.500372i	−0.920586	−	0.390541i	$-0.872288\pi$
$821$	−39.3911	+	14.3372i	−1.37476	+	0.500372i	−0.454175	+	0.890913i	$0.650066\pi$
$822$	−65.2367	−	23.7442i	−2.27539	−	0.828175i
$823$	−18.3273	−	15.3785i	−0.638851	−	0.536059i	0.264814	−	0.964299i	$-0.414689\pi$
$823$	−18.3273	−	15.3785i	−0.638851	−	0.536059i	−0.903665	+	0.428240i	$0.859134\pi$
$824$	8.75199	−	15.1589i	0.304890	−	0.528085i
$825$		0			0
$826$	1.54587	−	8.76708i	0.0537878	−	0.305046i
$827$	−4.27216	+	24.2286i	−0.148557	+	0.842511i	0.815884	+	0.578215i	$0.196251\pi$
$827$	−4.27216	+	24.2286i	−0.148557	+	0.842511i	−0.964442	+	0.264296i	$0.914861\pi$
$828$	22.2789	+	38.5882i	0.774245	+	1.34103i
$829$	17.5981	−	30.4809i	0.611209	−	1.05865i	−0.379828	−	0.925057i	$-0.624017\pi$
$829$	17.5981	−	30.4809i	0.611209	−	1.05865i	0.991037	−	0.133588i	$-0.0426498\pi$
$830$		0			0
$831$	63.8393	+	23.2356i	2.21456	+	0.806034i
$832$	−2.66582	+	0.970278i	−0.0924206	+	0.0336383i
$833$	16.1225	−	13.5284i	0.558613	−	0.468732i
$834$	−2.37487	−	13.4686i	−0.0822352	−	0.466379i
$835$		0			0
$836$	−10.5934	−	11.6067i	−0.366381	−	0.401427i
$837$	102.639			3.54773
$838$	−1.06490	−	6.03935i	−0.0367864	−	0.208626i
$839$	−18.3065	+	15.3610i	−0.632010	+	0.530319i	−0.901553	−	0.432669i	$-0.857572\pi$
$839$	−18.3065	+	15.3610i	−0.632010	+	0.530319i	0.269543	+	0.962988i	$0.413127\pi$
$840$		0			0
$841$	25.9460	+	9.44358i	0.894690	+	0.325641i
$842$	−2.93864	−	2.46581i	−0.101272	−	0.0849774i
$843$	−36.2816	+	62.8416i	−1.24960	+	2.16438i
$844$	13.7047	+	23.7373i	0.471737	+	0.817072i
$845$		0			0
$846$	9.61519	−	54.5305i	0.330577	−	1.87480i
$847$	1.86388	+	3.22834i	0.0640438	+	0.110927i
$848$	1.28080	−	2.21840i	0.0439827	−	0.0761803i
$849$	−48.9884	−	41.1062i	−1.68128	−	1.41076i
$850$		0			0
$851$	−16.0271	+	5.83339i	−0.549403	+	0.199966i
$852$	5.06168	−	4.24725i	0.173410	−	0.145508i
$853$	−4.53551	−	25.7222i	−0.155293	−	0.880710i	−0.958517	−	0.285034i	$-0.907995\pi$
$853$	−4.53551	−	25.7222i	−0.155293	−	0.880710i	0.803225	−	0.595676i	$-0.203116\pi$
$854$	−15.3773			−0.526201
$855$		0			0
$856$	−10.5897			−0.361949
$857$	8.53842	+	48.4238i	0.291667	+	1.65412i	0.680449	+	0.732795i	$0.261785\pi$
$857$	8.53842	+	48.4238i	0.291667	+	1.65412i	−0.388783	+	0.921329i	$0.627104\pi$
$858$	26.8645	−	22.5420i	0.917138	−	0.769570i
$859$	13.6388	−	4.96410i	0.465348	−	0.169373i	−0.0986958	−	0.995118i	$-0.531467\pi$
$859$	13.6388	−	4.96410i	0.465348	−	0.169373i	0.564044	+	0.825745i	$0.309245\pi$
$860$		0			0
$861$	−18.2714	−	15.3315i	−0.622688	−	0.522497i
$862$	12.7927	−	22.1577i	0.435723	−	0.754694i
$863$	−5.45178	−	9.44276i	−0.185581	−	0.321435i	0.758191	−	0.652032i	$-0.226083\pi$
$863$	−5.45178	−	9.44276i	−0.185581	−	0.321435i	−0.943772	+	0.330597i	$0.892750\pi$
$864$	−3.42843	+	19.4436i	−0.116637	+	0.661484i
$865$		0			0
$866$	14.2318	+	24.6502i	0.483617	+	0.837649i
$867$	32.3448	−	56.0228i	1.09849	−	1.90264i
$868$	7.43511	+	6.23880i	0.252364	+	0.211759i
$869$	−2.03662	−	0.741269i	−0.0690876	−	0.0251458i
$870$		0			0
$871$	−17.3070	+	14.5223i	−0.586425	+	0.492069i
$872$	−2.40943	−	13.6646i	−0.0815936	−	0.462740i
$873$	1.64263			0.0555948
$874$	8.44619	+	20.5056i	0.285696	+	0.693614i
$875$		0			0
$876$	−2.98432	−	16.9249i	−0.100831	−	0.571840i
$877$	−8.61676	+	7.23032i	−0.290967	+	0.244150i	−0.776573	−	0.630028i	$-0.783044\pi$
$877$	−8.61676	+	7.23032i	−0.290967	+	0.244150i	0.485606	+	0.874178i	$0.338599\pi$
$878$	−35.8069	+	13.0326i	−1.20842	+	0.439830i
$879$	95.7975	+	34.8675i	3.23117	+	1.17605i
$880$		0			0
$881$	4.90996	−	8.50431i	0.165421	−	0.286517i	−0.771384	−	0.636370i	$-0.780435\pi$
$881$	4.90996	−	8.50431i	0.165421	−	0.286517i	0.936805	+	0.349853i	$0.113768\pi$
$882$	15.3889	+	26.6544i	0.518172	+	0.897500i
$883$	−5.28801	+	29.9898i	−0.177956	+	1.00924i	0.756721	+	0.653738i	$0.226800\pi$
$883$	−5.28801	+	29.9898i	−0.177956	+	1.00924i	−0.934677	+	0.355499i	$0.884311\pi$
$884$	−2.95022	+	16.7315i	−0.0992265	+	0.562742i
$885$		0			0
$886$	11.3892	−	19.7267i	0.382629	−	0.662733i
$887$	−9.42994	−	7.91266i	−0.316627	−	0.265681i	0.470598	−	0.882348i	$-0.344038\pi$
$887$	−9.42994	−	7.91266i	−0.316627	−	0.265681i	−0.787224	+	0.616667i	$0.788483\pi$
$888$	−10.8017	−	3.93151i	−0.362482	−	0.131933i
$889$	29.4986	−	10.7366i	0.989352	−	0.360095i
$890$		0			0
$891$	−25.9336	−	147.077i	−0.868810	−	4.92726i
$892$	11.4351			0.382877
$893$	8.33924	−	26.2672i	0.279062	−	0.879000i
$894$	−19.3139			−0.645953
$895$		0			0
$896$	−1.43020	+	1.20008i	−0.0477798	+	0.0400920i
$897$	−46.5072	+	16.9272i	−1.55283	+	0.565184i
$898$	29.3016	+	10.6649i	0.977807	+	0.355893i
$899$	−4.69318	−	3.93804i	−0.156526	−	0.131341i
$900$		0			0
$901$	−7.67042	−	13.2856i	−0.255539	−	0.442606i
$902$	2.33236	−	13.2275i	0.0776591	−	0.440427i
$903$	−0.746778	+	4.23519i	−0.0248512	+	0.140938i
$904$	−7.96786	−	13.8007i	−0.265007	−	0.459006i
$905$		0			0
$906$	3.25318	+	2.72975i	0.108080	+	0.0906897i
$907$	−38.3564	−	13.9606i	−1.27360	−	0.463554i	−0.385292	−	0.922795i	$-0.625899\pi$
$907$	−38.3564	−	13.9606i	−1.27360	−	0.463554i	−0.888312	+	0.459241i	$0.848121\pi$
$908$	14.6736	−	5.34077i	0.486962	−	0.177240i
$909$	−13.1515	+	11.0354i	−0.436207	+	0.366021i
$910$		0			0
$911$	1.58058			0.0523671			0.0261836	−	0.999657i	$-0.491665\pi$
$911$	1.58058			0.0523671			0.0261836	+	0.999657i	$0.491665\pi$
$912$	−4.52273	+	14.2458i	−0.149763	+	0.471727i
$913$	−6.85982			−0.227027
$914$	2.27149	+	12.8822i	0.0751341	+	0.426107i
$915$		0			0
$916$	−5.16834	+	1.88112i	−0.170767	+	0.0621540i
$917$	11.4278	+	4.15937i	0.377379	+	0.137355i
$918$	90.5769	+	76.0030i	2.98948	+	2.50847i
$919$	23.8891	−	41.3772i	0.788029	−	1.36491i	−0.139143	−	0.990272i	$-0.544435\pi$
$919$	23.8891	−	41.3772i	0.788029	−	1.36491i	0.927172	−	0.374635i	$-0.122232\pi$
$920$		0			0
$921$	−3.07330	+	17.4295i	−0.101269	+	0.574322i
$922$	3.16401	−	17.9440i	0.104201	−	0.590953i
$923$	2.73332	+	4.73425i	0.0899684	+	0.155830i
$924$	11.5397	−	19.9873i	0.379628	−	0.657535i
$925$		0			0
$926$	−21.6204	−	7.86919i	−0.710492	−	0.258598i
$927$	144.052	−	52.4307i	4.73130	−	1.72205i
$928$	0.902771	−	0.757515i	0.0296349	−	0.0248666i
$929$	−8.32760	−	47.2282i	−0.273220	−	1.54951i	−0.744561	−	0.667555i	$-0.767341\pi$
$929$	−8.32760	−	47.2282i	−0.273220	−	1.54951i	0.471341	−	0.881951i	$-0.343770\pi$
$930$		0			0
$931$	5.83411	+	14.1641i	0.191205	+	0.464208i
$932$	11.3286			0.371081
$933$	15.5036	+	87.9251i	0.507564	+	2.87854i
$934$	19.1917	−	16.1038i	0.627973	−	0.526932i
$935$		0			0
$936$	−23.3468	−	8.49755i	−0.763115	−	0.277751i
$937$	−29.1684	−	24.4752i	−0.952890	−	0.799570i	0.0268915	−	0.999638i	$-0.491439\pi$
$937$	−29.1684	−	24.4752i	−0.952890	−	0.799570i	−0.979782	+	0.200068i	$0.935884\pi$
$938$	−7.43425	+	12.8765i	−0.242737	+	0.420433i
$939$	0.475128	+	0.822946i	0.0155052	+	0.0268558i
$940$		0			0
$941$	−6.81969	+	38.6764i	−0.222315	+	1.26081i	0.645436	+	0.763815i	$0.276676\pi$
$941$	−6.81969	+	38.6764i	−0.222315	+	1.26081i	−0.867751	+	0.496999i	$0.834435\pi$
$942$	36.8740	+	63.8676i	1.20142	+	2.08092i
$943$	−9.47776	+	16.4160i	−0.308638	+	0.534577i
$944$	−3.65269	−	3.06497i	−0.118885	−	0.0997564i
$945$		0			0
$946$	−2.27570	+	0.828287i	−0.0739894	+	0.0269299i
$947$	5.48561	−	4.60297i	0.178258	−	0.149577i	−0.549293	−	0.835630i	$-0.685103\pi$
$947$	5.48561	−	4.60297i	0.178258	−	0.149577i	0.727551	+	0.686053i	$0.240658\pi$
$948$	0.357967	+	2.03013i	0.0116262	+	0.0659355i
$949$	14.2186			0.461555
$950$		0			0
$951$	85.4768			2.77178
$952$	1.94157	+	11.0112i	0.0629267	+	0.356875i
$953$	25.4580	−	21.3618i	0.824667	−	0.691977i	−0.129393	−	0.991593i	$-0.541303\pi$
$953$	25.4580	−	21.3618i	0.824667	−	0.691977i	0.954060	+	0.299616i	$0.0968586\pi$
$954$	21.0811	−	7.67290i	0.682526	−	0.248419i
$955$		0			0
$956$	1.13631	+	0.953473i	0.0367507	+	0.0308375i
$957$	−7.28406	+	12.6164i	−0.235460	+	0.407829i
$958$	−10.8316	−	18.7608i	−0.349952	−	0.606135i
$959$	6.56382	−	37.2253i	0.211957	−	1.20207i
$960$		0			0
$961$	1.98710	+	3.44176i	0.0641000	+	0.111024i
$962$	4.75508	−	8.23605i	0.153310	−	0.265541i
$963$	−71.0453	−	59.6141i	−2.28940	−	1.92104i
$964$	7.91140	+	2.87951i	0.254809	+	0.0927429i
$965$		0			0
$966$	−24.9510	+	20.9364i	−0.802786	+	0.673617i
$967$	4.38031	+	24.8420i	0.140861	+	0.798864i	0.970597	+	0.240708i	$0.0773798\pi$
$967$	4.38031	+	24.8420i	0.140861	+	0.798864i	−0.829736	+	0.558156i	$0.811509\pi$
$968$	1.99666			0.0641751
$969$	60.3424	+	66.1146i	1.93848	+	2.12391i
$970$		0			0
$971$	7.59334	+	43.0640i	0.243682	+	1.38199i	0.823534	+	0.567267i	$0.191999\pi$
$971$	7.59334	+	43.0640i	0.243682	+	1.38199i	−0.579852	+	0.814722i	$0.696890\pi$
$972$	−63.4434	+	53.2353i	−2.03495	+	1.70752i
$973$	6.99739	−	2.54684i	0.224326	−	0.0816481i
$974$	−3.12479	−	1.13733i	−0.100125	−	0.0364424i
$975$		0			0
$976$	−4.11819	+	7.13291i	−0.131820	+	0.228319i
$977$	−0.00239184	−	0.00414279i	−7.65217e−5	−	0.000132539i	0.865987	−	0.500066i	$-0.166691\pi$
$977$	−0.00239184	−	0.00414279i	−7.65217e−5	−	0.000132539i	−0.866064	+	0.499934i	$0.833358\pi$
$978$	10.7303	−	60.8548i	0.343118	−	1.94592i
$979$	−0.617201	+	3.50032i	−0.0197258	+	0.111871i
$980$		0			0
$981$	60.7591	−	105.238i	1.93989	−	3.35999i
$982$	−3.86014	−	3.23904i	−0.123182	−	0.103362i
$983$	34.7535	+	12.6492i	1.10846	+	0.403448i	0.830430	−	0.557123i	$-0.188095\pi$
$983$	34.7535	+	12.6492i	1.10846	+	0.403448i	0.278034	+	0.960571i	$0.410317\pi$
$984$	−12.0049	+	4.36943i	−0.382703	+	0.139292i
$985$		0			0
$986$	−1.22556	−	6.95047i	−0.0390296	−	0.221348i
$987$	40.4761			1.28837
$988$	−10.9573	−	5.73159i	−0.348597	−	0.182346i
$989$	3.41774			0.108678
$990$		0			0
$991$	−4.48081	+	3.75985i	−0.142338	+	0.119435i	−0.711176	−	0.703014i	$-0.751837\pi$
$991$	−4.48081	+	3.75985i	−0.142338	+	0.119435i	0.568839	+	0.822449i	$0.307393\pi$
$992$	4.88512	−	1.77804i	0.155103	−	0.0564528i
$993$	−34.4674	−	12.5451i	−1.09379	−	0.398107i
$994$	2.75597	+	2.31253i	0.0874141	+	0.0733491i
$995$		0			0
$996$	3.26235	+	5.65056i	0.103372	+	0.179045i
$997$	10.0610	−	57.0588i	0.318635	−	1.80707i	−0.232437	−	0.972612i	$-0.574670\pi$
$997$	10.0610	−	57.0588i	0.318635	−	1.80707i	0.551072	−	0.834458i	$-0.314219\pi$
$998$	−1.77791	+	10.0831i	−0.0562789	+	0.319174i
$999$	−33.0931	−	57.3190i	−1.04702	−	1.81349i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.i.351.1		18
5.2	odd	4		950.2.u.g.199.3		36
5.3	odd	4		950.2.u.g.199.4		36
5.4	even	2		190.2.k.d.161.3	yes	18
19.17	even	9	inner	950.2.l.i.701.1		18
95.17	odd	36		950.2.u.g.549.4		36
95.44	even	18		3610.2.a.bi.1.9		9
95.74	even	18		190.2.k.d.131.3	✓	18
95.89	odd	18		3610.2.a.bj.1.1		9
95.93	odd	36		950.2.u.g.549.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.d.131.3	✓	18	95.74	even	18
190.2.k.d.161.3	yes	18	5.4	even	2
950.2.l.i.351.1		18	1.1	even	1	trivial
950.2.l.i.701.1		18	19.17	even	9	inner
950.2.u.g.199.3		36	5.2	odd	4
950.2.u.g.199.4		36	5.3	odd	4
950.2.u.g.549.3		36	95.93	odd	36
950.2.u.g.549.4		36	95.17	odd	36
3610.2.a.bi.1.9		9	95.44	even	18
3610.2.a.bj.1.1		9	95.89	odd	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-2.62675 + 2.20410i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-2.62675 - 2.20410i) q^{6} +(0.933500 - 1.61687i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.52078 - 8.62480i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-2.62675 + 2.20410i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-2.62675 - 2.20410i) q^{6} +(0.933500 - 1.61687i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.52078 - 8.62480i) q^{9} +(1.80254 + 3.12210i) q^{11} +(1.71449 - 2.96958i) q^{12} +(2.17319 + 1.82353i) q^{13} +(1.75441 + 0.638551i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-1.03994 - 5.89781i) q^{17} +8.75785 q^{18} +(4.32047 + 0.577506i) q^{19} +(1.11168 + 6.30463i) q^{21} +(-2.76166 + 2.31731i) q^{22} +(4.78092 - 1.74011i) q^{23} +(3.22218 + 1.17278i) q^{24} +(-1.41845 + 2.45683i) q^{26} +(9.87176 + 17.0984i) q^{27} +(-0.324201 + 1.83864i) q^{28} +(0.204642 - 1.16058i) q^{29} +(2.59932 - 4.50215i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-11.6162 - 4.22797i) q^{33} +(5.62762 - 2.04829i) q^{34} +(1.52078 + 8.62480i) q^{36} -3.35231 q^{37} +(0.181510 + 4.35512i) q^{38} -9.72766 q^{39} +(-2.85406 + 2.39484i) q^{41} +(-6.01581 + 2.18958i) q^{42} +(0.631247 + 0.229755i) q^{43} +(-2.76166 - 2.31731i) q^{44} +(2.54388 + 4.40612i) q^{46} +(1.09789 - 6.22647i) q^{47} +(-0.595435 + 3.37688i) q^{48} +(1.75716 + 3.04348i) q^{49} +(15.7310 + 13.1999i) q^{51} +(-2.66582 - 0.970278i) q^{52} +(2.40711 - 0.876116i) q^{53} +(-15.1244 + 12.6909i) q^{54} -1.86700 q^{56} +(-12.6217 + 8.00580i) q^{57} +1.17848 q^{58} +(-0.827999 - 4.69581i) q^{59} +(-7.73966 + 2.81701i) q^{61} +(4.88512 + 1.77804i) q^{62} +(-12.5255 - 10.5102i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.14660 - 12.1739i) q^{66} +(-1.38291 + 7.84286i) q^{67} +(2.99439 + 5.18644i) q^{68} +(-8.72288 + 15.1085i) q^{69} +(1.81077 + 0.659065i) q^{71} +(-8.22969 + 2.99536i) q^{72} +(3.83942 - 3.22165i) q^{73} +(-0.582122 - 3.30138i) q^{74} +(-4.25744 + 0.935010i) q^{76} +6.73070 q^{77} +(-1.68919 - 9.57988i) q^{78} +(-0.460535 + 0.386434i) q^{79} +(-38.9281 - 14.1687i) q^{81} +(-2.85406 - 2.39484i) q^{82} +(-0.951408 + 1.64789i) q^{83} +(-3.20094 - 5.54420i) q^{84} +(-0.116650 + 0.661553i) q^{86} +(2.02049 + 3.49960i) q^{87} +(1.80254 - 3.12210i) q^{88} +(0.755257 + 0.633736i) q^{89} +(4.97708 - 1.81151i) q^{91} +(-3.89744 + 3.27034i) q^{92} +(3.09545 + 17.5552i) q^{93} +6.32252 q^{94} -3.42897 q^{96} +(0.0325697 + 0.184712i) q^{97} +(-2.69212 + 2.25896i) q^{98} +(29.6688 - 10.7985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 9 * q^8 - 18 * q^9	\( 18 q - 9 q^{8} - 18 q^{9} - 12 q^{11} + 6 q^{13} + 6 q^{14} + 42 q^{18} + 12 q^{21} + 3 q^{22} - 9 q^{23} - 9 q^{26} + 18 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{31} - 66 q^{33} + 18 q^{34} - 18 q^{36} + 12 q^{37} + 6 q^{38} + 48 q^{39} - 21 q^{41} - 42 q^{42} - 18 q^{43} + 3 q^{44} + 18 q^{46} + 54 q^{47} - 39 q^{49} + 42 q^{51} - 12 q^{52} + 24 q^{53} - 54 q^{54} + 18 q^{57} - 30 q^{59} + 48 q^{61} + 30 q^{62} + 57 q^{63} - 9 q^{64} + 24 q^{66} + 6 q^{67} + 6 q^{68} - 30 q^{69} + 30 q^{71} - 6 q^{73} - 3 q^{74} - 21 q^{76} - 30 q^{77} + 24 q^{78} + 30 q^{79} + 18 q^{81} - 21 q^{82} - 6 q^{83} + 6 q^{84} + 36 q^{86} - 24 q^{87} - 12 q^{88} + 30 q^{89} - 60 q^{91} + 18 q^{92} + 12 q^{93} + 6 q^{94} + 12 q^{97} + 18 q^{98} + 171 q^{99}+O(q^{100}) \) 18 * q - 9 * q^8 - 18 * q^9 - 12 * q^11 + 6 * q^13 + 6 * q^14 + 42 * q^18 + 12 * q^21 + 3 * q^22 - 9 * q^23 - 9 * q^26 + 18 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^31 - 66 * q^33 + 18 * q^34 - 18 * q^36 + 12 * q^37 + 6 * q^38 + 48 * q^39 - 21 * q^41 - 42 * q^42 - 18 * q^43 + 3 * q^44 + 18 * q^46 + 54 * q^47 - 39 * q^49 + 42 * q^51 - 12 * q^52 + 24 * q^53 - 54 * q^54 + 18 * q^57 - 30 * q^59 + 48 * q^61 + 30 * q^62 + 57 * q^63 - 9 * q^64 + 24 * q^66 + 6 * q^67 + 6 * q^68 - 30 * q^69 + 30 * q^71 - 6 * q^73 - 3 * q^74 - 21 * q^76 - 30 * q^77 + 24 * q^78 + 30 * q^79 + 18 * q^81 - 21 * q^82 - 6 * q^83 + 6 * q^84 + 36 * q^86 - 24 * q^87 - 12 * q^88 + 30 * q^89 - 60 * q^91 + 18 * q^92 + 12 * q^93 + 6 * q^94 + 12 * q^97 + 18 * q^98 + 171 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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