LMFDB - Embedded newform 39.2.e.b.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,2,Mod(16,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("39.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	39.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.311416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	39.22
Dual form			39.2.e.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28078 + 2.21837i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} +0.561553 q^{5} +(-1.28078 - 2.21837i) q^{6} +(1.78078 + 3.08440i) q^{7} +6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.28078 + 2.21837i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} +0.561553 q^{5} +(-1.28078 - 2.21837i) q^{6} +(1.78078 + 3.08440i) q^{7} +6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.719224 + 1.24573i) q^{10} +(1.00000 - 1.73205i) q^{11} +4.56155 q^{12} +(0.500000 - 3.57071i) q^{13} -9.12311 q^{14} +(-0.280776 + 0.486319i) q^{15} +(-3.84233 + 6.65511i) q^{16} +(-1.28078 - 2.21837i) q^{17} +2.56155 q^{18} +(0.561553 + 0.972638i) q^{19} +(-1.28078 - 2.21837i) q^{20} -3.56155 q^{21} +(2.56155 + 4.43674i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(-3.28078 + 5.68247i) q^{24} -4.68466 q^{25} +(7.28078 + 5.68247i) q^{26} +1.00000 q^{27} +(8.12311 - 14.0696i) q^{28} +(2.84233 - 4.92306i) q^{29} +(-0.719224 - 1.24573i) q^{30} -1.56155 q^{31} +(-3.28078 - 5.68247i) q^{32} +(1.00000 + 1.73205i) q^{33} +6.56155 q^{34} +(1.00000 + 1.73205i) q^{35} +(-2.28078 + 3.95042i) q^{36} +(-1.71922 + 2.97778i) q^{37} -2.87689 q^{38} +(2.84233 + 2.21837i) q^{39} +3.68466 q^{40} +(-1.28078 + 2.21837i) q^{41} +(4.56155 - 7.90084i) q^{42} +(-0.219224 - 0.379706i) q^{43} -9.12311 q^{44} +(-0.280776 - 0.486319i) q^{45} +(-2.56155 - 4.43674i) q^{46} -8.24621 q^{47} +(-3.84233 - 6.65511i) q^{48} +(-2.84233 + 4.92306i) q^{49} +(6.00000 - 10.3923i) q^{50} +2.56155 q^{51} +(-15.2462 + 6.16879i) q^{52} +11.6847 q^{53} +(-1.28078 + 2.21837i) q^{54} +(0.561553 - 0.972638i) q^{55} +(11.6847 + 20.2384i) q^{56} -1.12311 q^{57} +(7.28078 + 12.6107i) q^{58} +(5.56155 + 9.63289i) q^{59} +2.56155 q^{60} +(-6.06155 - 10.4989i) q^{61} +(2.00000 - 3.46410i) q^{62} +(1.78078 - 3.08440i) q^{63} +1.43845 q^{64} +(0.280776 - 2.00514i) q^{65} -5.12311 q^{66} +(-0.219224 + 0.379706i) q^{67} +(-5.84233 + 10.1192i) q^{68} +(-1.00000 - 1.73205i) q^{69} -5.12311 q^{70} +(-7.00000 - 12.1244i) q^{71} +(-3.28078 - 5.68247i) q^{72} -1.87689 q^{73} +(-4.40388 - 7.62775i) q^{74} +(2.34233 - 4.05703i) q^{75} +(2.56155 - 4.43674i) q^{76} +7.12311 q^{77} +(-8.56155 + 3.46410i) q^{78} +9.56155 q^{79} +(-2.15767 + 3.73720i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.28078 - 5.68247i) q^{82} -9.12311 q^{83} +(8.12311 + 14.0696i) q^{84} +(-0.719224 - 1.24573i) q^{85} +1.12311 q^{86} +(2.84233 + 4.92306i) q^{87} +(6.56155 - 11.3649i) q^{88} +(-6.56155 + 11.3649i) q^{89} +1.43845 q^{90} +(11.9039 - 4.81645i) q^{91} +9.12311 q^{92} +(0.780776 - 1.35234i) q^{93} +(10.5616 - 18.2931i) q^{94} +(0.315342 + 0.546188i) q^{95} +6.56155 q^{96} +(2.21922 + 3.84381i) q^{97} +(-7.28078 - 12.6107i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 2 q^{3} - 5 q^{4} - 6 q^{5} - q^{6} + 3 q^{7} + 18 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - q^2 - 2 * q^3 - 5 * q^4 - 6 * q^5 - q^6 + 3 * q^7 + 18 * q^8 - 2 * q^9	\( 4 q - q^{2} - 2 q^{3} - 5 q^{4} - 6 q^{5} - q^{6} + 3 q^{7} + 18 q^{8} - 2 q^{9} - 7 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 20 q^{14} + 3 q^{15} - 3 q^{16} - q^{17} + 2 q^{18} - 6 q^{19} - q^{20} - 6 q^{21} + 2 q^{22} - 4 q^{23} - 9 q^{24} + 6 q^{25} + 25 q^{26} + 4 q^{27} + 16 q^{28} - q^{29} - 7 q^{30} + 2 q^{31} - 9 q^{32} + 4 q^{33} + 18 q^{34} + 4 q^{35} - 5 q^{36} - 11 q^{37} - 28 q^{38} - q^{39} - 10 q^{40} - q^{41} + 10 q^{42} - 5 q^{43} - 20 q^{44} + 3 q^{45} - 2 q^{46} - 3 q^{48} + q^{49} + 24 q^{50} + 2 q^{51} - 28 q^{52} + 22 q^{53} - q^{54} - 6 q^{55} + 22 q^{56} + 12 q^{57} + 25 q^{58} + 14 q^{59} + 2 q^{60} - 16 q^{61} + 8 q^{62} + 3 q^{63} + 14 q^{64} - 3 q^{65} - 4 q^{66} - 5 q^{67} - 11 q^{68} - 4 q^{69} - 4 q^{70} - 28 q^{71} - 9 q^{72} - 24 q^{73} + 3 q^{74} - 3 q^{75} + 2 q^{76} + 12 q^{77} - 26 q^{78} + 30 q^{79} - 21 q^{80} - 2 q^{81} - 9 q^{82} - 20 q^{83} + 16 q^{84} - 7 q^{85} - 12 q^{86} - q^{87} + 18 q^{88} - 18 q^{89} + 14 q^{90} + 27 q^{91} + 20 q^{92} - q^{93} + 34 q^{94} + 26 q^{95} + 18 q^{96} + 13 q^{97} - 25 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 - 5 * q^4 - 6 * q^5 - q^6 + 3 * q^7 + 18 * q^8 - 2 * q^9 - 7 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 20 * q^14 + 3 * q^15 - 3 * q^16 - q^17 + 2 * q^18 - 6 * q^19 - q^20 - 6 * q^21 + 2 * q^22 - 4 * q^23 - 9 * q^24 + 6 * q^25 + 25 * q^26 + 4 * q^27 + 16 * q^28 - q^29 - 7 * q^30 + 2 * q^31 - 9 * q^32 + 4 * q^33 + 18 * q^34 + 4 * q^35 - 5 * q^36 - 11 * q^37 - 28 * q^38 - q^39 - 10 * q^40 - q^41 + 10 * q^42 - 5 * q^43 - 20 * q^44 + 3 * q^45 - 2 * q^46 - 3 * q^48 + q^49 + 24 * q^50 + 2 * q^51 - 28 * q^52 + 22 * q^53 - q^54 - 6 * q^55 + 22 * q^56 + 12 * q^57 + 25 * q^58 + 14 * q^59 + 2 * q^60 - 16 * q^61 + 8 * q^62 + 3 * q^63 + 14 * q^64 - 3 * q^65 - 4 * q^66 - 5 * q^67 - 11 * q^68 - 4 * q^69 - 4 * q^70 - 28 * q^71 - 9 * q^72 - 24 * q^73 + 3 * q^74 - 3 * q^75 + 2 * q^76 + 12 * q^77 - 26 * q^78 + 30 * q^79 - 21 * q^80 - 2 * q^81 - 9 * q^82 - 20 * q^83 + 16 * q^84 - 7 * q^85 - 12 * q^86 - q^87 + 18 * q^88 - 18 * q^89 + 14 * q^90 + 27 * q^91 + 20 * q^92 - q^93 + 34 * q^94 + 26 * q^95 + 18 * q^96 + 13 * q^97 - 25 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.28078	+	2.21837i	−0.905646	+	1.56862i	−0.0855975	+	0.996330i	$0.527280\pi$
$2$	−1.28078	+	2.21837i	−0.905646	+	1.56862i	−0.820048	+	0.572295i	$0.806053\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−2.28078	−	3.95042i	−1.14039	−	1.97521i
$5$	0.561553			0.251134			0.125567	−	0.992085i	$-0.459925\pi$
$5$	0.561553			0.251134			0.125567	+	0.992085i	$0.459925\pi$
$6$	−1.28078	−	2.21837i	−0.522875	−	0.905646i
$7$	1.78078	+	3.08440i	0.673070	+	1.16579i	0.977029	+	0.213107i	$0.0683582\pi$
$7$	1.78078	+	3.08440i	0.673070	+	1.16579i	−0.303959	+	0.952685i	$0.598308\pi$
$8$	6.56155			2.31986
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.719224	+	1.24573i	−0.227438	+	0.393935i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	4.56155			1.31681
$13$	0.500000	−	3.57071i	0.138675	−	0.990338i
$13$	0.500000	−	3.57071i	0.138675	−	0.990338i
$14$	−9.12311			−2.43825
$15$	−0.280776	+	0.486319i	−0.0724962	+	0.125567i
$16$	−3.84233	+	6.65511i	−0.960582	+	1.66378i
$17$	−1.28078	−	2.21837i	−0.310634	−	0.538034i	0.667866	−	0.744282i	$-0.267208\pi$
$17$	−1.28078	−	2.21837i	−0.310634	−	0.538034i	−0.978500	+	0.206248i	$0.933875\pi$
$18$	2.56155			0.603764
$19$	0.561553	+	0.972638i	0.128829	+	0.223138i	0.923223	−	0.384264i	$-0.125545\pi$
$19$	0.561553	+	0.972638i	0.128829	+	0.223138i	−0.794394	+	0.607403i	$0.792211\pi$
$20$	−1.28078	−	2.21837i	−0.286390	−	0.496043i
$21$	−3.56155			−0.777195
$22$	2.56155	+	4.43674i	0.546125	+	0.945916i
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$	−3.28078	+	5.68247i	−0.669686	+	1.15993i
$25$	−4.68466			−0.936932
$26$	7.28078	+	5.68247i	1.42788	+	1.11442i
$27$	1.00000			0.192450
$28$	8.12311	−	14.0696i	1.53512	−	2.65891i
$29$	2.84233	−	4.92306i	0.527807	−	0.914189i	−0.471667	−	0.881777i	$-0.656348\pi$
$29$	2.84233	−	4.92306i	0.527807	−	0.914189i	0.999475	−	0.0324124i	$-0.0103190\pi$
$30$	−0.719224	−	1.24573i	−0.131312	−	0.227438i
$31$	−1.56155			−0.280463			−0.140232	−	0.990119i	$-0.544785\pi$
$31$	−1.56155			−0.280463			−0.140232	+	0.990119i	$0.544785\pi$
$32$	−3.28078	−	5.68247i	−0.579965	−	1.00453i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	6.56155			1.12530
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	−2.28078	+	3.95042i	−0.380129	+	0.658403i
$37$	−1.71922	+	2.97778i	−0.282639	+	0.489544i	−0.972034	−	0.234841i	$-0.924543\pi$
$37$	−1.71922	+	2.97778i	−0.282639	+	0.489544i	0.689395	+	0.724385i	$0.257876\pi$
$38$	−2.87689			−0.466694
$39$	2.84233	+	2.21837i	0.455137	+	0.355223i
$40$	3.68466			0.582596
$41$	−1.28078	+	2.21837i	−0.200024	+	0.346451i	−0.948536	−	0.316670i	$-0.897435\pi$
$41$	−1.28078	+	2.21837i	−0.200024	+	0.346451i	0.748512	+	0.663121i	$0.230769\pi$
$42$	4.56155	−	7.90084i	0.703863	−	1.21913i
$43$	−0.219224	−	0.379706i	−0.0334313	−	0.0579047i	0.848826	−	0.528673i	$-0.177310\pi$
$43$	−0.219224	−	0.379706i	−0.0334313	−	0.0579047i	−0.882257	+	0.470768i	$0.843977\pi$
$44$	−9.12311			−1.37536
$45$	−0.280776	−	0.486319i	−0.0418557	−	0.0724962i
$46$	−2.56155	−	4.43674i	−0.377680	−	0.654162i
$47$	−8.24621			−1.20283			−0.601417	−	0.798935i	$-0.705397\pi$
$47$	−8.24621			−1.20283			−0.601417	+	0.798935i	$0.705397\pi$
$48$	−3.84233	−	6.65511i	−0.554592	−	0.960582i
$49$	−2.84233	+	4.92306i	−0.406047	+	0.703294i
$50$	6.00000	−	10.3923i	0.848528	−	1.46969i
$51$	2.56155			0.358689
$52$	−15.2462	+	6.16879i	−2.11427	+	0.855457i
$53$	11.6847			1.60501			0.802506	−	0.596645i	$-0.203500\pi$
$53$	11.6847			1.60501			0.802506	+	0.596645i	$0.203500\pi$
$54$	−1.28078	+	2.21837i	−0.174292	+	0.301882i
$55$	0.561553	−	0.972638i	0.0757198	−	0.131150i
$56$	11.6847	+	20.2384i	1.56143	+	2.70447i
$57$	−1.12311			−0.148759
$58$	7.28078	+	12.6107i	0.956013	+	1.65586i
$59$	5.56155	+	9.63289i	0.724053	+	1.25410i	0.959363	+	0.282175i	$0.0910560\pi$
$59$	5.56155	+	9.63289i	0.724053	+	1.25410i	−0.235310	+	0.971920i	$0.575611\pi$
$60$	2.56155			0.330695
$61$	−6.06155	−	10.4989i	−0.776102	−	1.34425i	−0.934173	−	0.356821i	$-0.883861\pi$
$61$	−6.06155	−	10.4989i	−0.776102	−	1.34425i	0.158071	−	0.987428i	$-0.449473\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$	1.78078	−	3.08440i	0.224357	−	0.388597i
$64$	1.43845			0.179806
$65$	0.280776	−	2.00514i	0.0348260	−	0.248708i
$66$	−5.12311			−0.630611
$67$	−0.219224	+	0.379706i	−0.0267824	+	0.0463885i	−0.879106	−	0.476626i	$-0.841859\pi$
$67$	−0.219224	+	0.379706i	−0.0267824	+	0.0463885i	0.852324	+	0.523015i	$0.175193\pi$
$68$	−5.84233	+	10.1192i	−0.708486	+	1.22713i
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$	−5.12311			−0.612328
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	−0.897447	−	0.441123i	$-0.854580\pi$
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	0.0666994	−	0.997773i	$-0.478753\pi$
$72$	−3.28078	−	5.68247i	−0.386643	−	0.669686i
$73$	−1.87689			−0.219674			−0.109837	−	0.993950i	$-0.535033\pi$
$73$	−1.87689			−0.219674			−0.109837	+	0.993950i	$0.535033\pi$
$74$	−4.40388	−	7.62775i	−0.511941	−	0.886708i
$75$	2.34233	−	4.05703i	0.270469	−	0.468466i
$76$	2.56155	−	4.43674i	0.293830	−	0.508929i
$77$	7.12311			0.811753
$78$	−8.56155	+	3.46410i	−0.969405	+	0.392232i
$79$	9.56155			1.07576			0.537879	−	0.843022i	$-0.319226\pi$
$79$	9.56155			1.07576			0.537879	+	0.843022i	$0.319226\pi$
$80$	−2.15767	+	3.73720i	−0.241235	+	0.417831i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.28078	−	5.68247i	−0.362301	−	0.627524i
$83$	−9.12311			−1.00139			−0.500695	−	0.865624i	$-0.666922\pi$
$83$	−9.12311			−1.00139			−0.500695	+	0.865624i	$0.666922\pi$
$84$	8.12311	+	14.0696i	0.886303	+	1.53512i
$85$	−0.719224	−	1.24573i	−0.0780108	−	0.135119i
$86$	1.12311			0.121108
$87$	2.84233	+	4.92306i	0.304730	+	0.527807i
$88$	6.56155	−	11.3649i	0.699464	−	1.21151i
$89$	−6.56155	+	11.3649i	−0.695523	+	1.20468i	0.274481	+	0.961593i	$0.411494\pi$
$89$	−6.56155	+	11.3649i	−0.695523	+	1.20468i	−0.970004	+	0.243089i	$0.921839\pi$
$90$	1.43845			0.151626
$91$	11.9039	−	4.81645i	1.24787	−	0.504901i
$92$	9.12311			0.951150
$93$	0.780776	−	1.35234i	0.0809627	−	0.140232i
$94$	10.5616	−	18.2931i	1.08934	−	1.88679i
$95$	0.315342	+	0.546188i	0.0323534	+	0.0560377i
$96$	6.56155			0.669686
$97$	2.21922	+	3.84381i	0.225328	+	0.390280i	0.956418	−	0.292002i	$-0.0943213\pi$
$97$	2.21922	+	3.84381i	0.225328	+	0.390280i	−0.731090	+	0.682281i	$0.760988\pi$
$98$	−7.28078	−	12.6107i	−0.735469	−	1.27387i
$99$	−2.00000			−0.201008
$100$	10.6847	+	18.5064i	1.06847	+	1.85064i
$101$	1.71922	−	2.97778i	0.171069	−	0.296300i	−0.767725	−	0.640780i	$-0.778611\pi$
$101$	1.71922	−	2.97778i	0.171069	−	0.296300i	0.938794	+	0.344479i	$0.111945\pi$
$102$	−3.28078	+	5.68247i	−0.324845	+	0.562649i
$103$	−7.56155			−0.745062			−0.372531	−	0.928020i	$-0.621510\pi$
$103$	−7.56155			−0.745062			−0.372531	+	0.928020i	$0.621510\pi$
$104$	3.28078	−	23.4294i	0.321707	−	2.29744i
$105$	−2.00000			−0.195180
$106$	−14.9654	+	25.9209i	−1.45357	+	2.51766i
$107$	−4.12311	+	7.14143i	−0.398596	+	0.690388i	−0.993553	−	0.113369i	$-0.963836\pi$
$107$	−4.12311	+	7.14143i	−0.398596	+	0.690388i	0.594957	+	0.803757i	$0.297169\pi$
$108$	−2.28078	−	3.95042i	−0.219468	−	0.380129i
$109$	17.8078			1.70567			0.852837	−	0.522177i	$-0.174880\pi$
$109$	17.8078			1.70567			0.852837	+	0.522177i	$0.174880\pi$
$110$	1.43845	+	2.49146i	0.137151	+	0.237552i
$111$	−1.71922	−	2.97778i	−0.163181	−	0.282639i
$112$	−27.3693			−2.58616
$113$	7.40388	+	12.8239i	0.696499	+	1.20637i	0.969673	+	0.244406i	$0.0785931\pi$
$113$	7.40388	+	12.8239i	0.696499	+	1.20637i	−0.273174	+	0.961965i	$0.588074\pi$
$114$	1.43845	−	2.49146i	0.134723	−	0.233347i
$115$	−0.561553	+	0.972638i	−0.0523651	+	0.0906990i
$116$	−25.9309			−2.40762
$117$	−3.34233	+	1.35234i	−0.308998	+	0.125024i
$118$	−28.4924			−2.62294
$119$	4.56155	−	7.90084i	0.418157	−	0.724269i
$120$	−1.84233	+	3.19101i	−0.168181	+	0.291298i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	31.0540			2.81149
$123$	−1.28078	−	2.21837i	−0.115484	−	0.200024i
$124$	3.56155	+	6.16879i	0.319837	+	0.553974i
$125$	−5.43845			−0.486430
$126$	4.56155	+	7.90084i	0.406375	+	0.703863i
$127$	−4.78078	+	8.28055i	−0.424225	+	0.734780i	−0.996348	−	0.0853884i	$-0.972787\pi$
$127$	−4.78078	+	8.28055i	−0.424225	+	0.734780i	0.572122	+	0.820168i	$0.306120\pi$
$128$	4.71922	−	8.17394i	0.417124	−	0.722481i
$129$	0.438447			0.0386031
$130$	4.08854	+	3.19101i	0.358589	+	0.279870i
$131$	−17.3693			−1.51756			−0.758782	−	0.651345i	$-0.774205\pi$
$131$	−17.3693			−1.51756			−0.758782	+	0.651345i	$0.774205\pi$
$132$	4.56155	−	7.90084i	0.397032	−	0.687680i
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$	−0.561553	−	0.972638i	−0.0485108	−	0.0840231i
$135$	0.561553			0.0483308
$136$	−8.40388	−	14.5560i	−0.720627	−	1.24816i
$137$	0.719224	+	1.24573i	0.0614474	+	0.106430i	0.895113	−	0.445840i	$-0.147095\pi$
$137$	0.719224	+	1.24573i	0.0614474	+	0.106430i	−0.833665	+	0.552270i	$0.813762\pi$
$138$	5.12311			0.436108
$139$	−5.46543	−	9.46641i	−0.463572	−	0.802930i	0.535564	−	0.844495i	$-0.320099\pi$
$139$	−5.46543	−	9.46641i	−0.463572	−	0.802930i	−0.999136	+	0.0415643i	$0.986766\pi$
$140$	4.56155	−	7.90084i	0.385522	−	0.667743i
$141$	4.12311	−	7.14143i	0.347228	−	0.601417i
$142$	35.8617			3.00945
$143$	−5.68466	−	4.43674i	−0.475375	−	0.371019i
$144$	7.68466			0.640388
$145$	1.59612	−	2.76456i	0.132550	−	0.229584i
$146$	2.40388	−	4.16365i	0.198947	−	0.344586i
$147$	−2.84233	−	4.92306i	−0.234431	−	0.406047i
$148$	15.6847			1.28927
$149$	3.28078	+	5.68247i	0.268772	+	0.465526i	0.968545	−	0.248839i	$-0.0800490\pi$
$149$	3.28078	+	5.68247i	0.268772	+	0.465526i	−0.699773	+	0.714365i	$0.746716\pi$
$150$	6.00000	+	10.3923i	0.489898	+	0.848528i
$151$	15.3693			1.25074			0.625369	−	0.780329i	$-0.284949\pi$
$151$	15.3693			1.25074			0.625369	+	0.780329i	$0.284949\pi$
$152$	3.68466	+	6.38202i	0.298865	+	0.517650i
$153$	−1.28078	+	2.21837i	−0.103545	+	0.179345i
$154$	−9.12311	+	15.8017i	−0.735161	+	1.27334i
$155$	−0.876894			−0.0704339
$156$	2.28078	−	16.2880i	0.182608	−	1.30408i
$157$	−4.36932			−0.348709			−0.174355	−	0.984683i	$-0.555784\pi$
$157$	−4.36932			−0.348709			−0.174355	+	0.984683i	$0.555784\pi$
$158$	−12.2462	+	21.2111i	−0.974256	+	1.68746i
$159$	−5.84233	+	10.1192i	−0.463327	+	0.802506i
$160$	−1.84233	−	3.19101i	−0.145649	−	0.252271i
$161$	−7.12311			−0.561379
$162$	−1.28078	−	2.21837i	−0.100627	−	0.174292i
$163$	−7.90388	−	13.6899i	−0.619080	−	1.07228i	−0.989654	−	0.143475i	$-0.954172\pi$
$163$	−7.90388	−	13.6899i	−0.619080	−	1.07228i	0.370574	−	0.928803i	$-0.379161\pi$
$164$	11.6847			0.912419
$165$	0.561553	+	0.972638i	0.0437168	+	0.0757198i
$166$	11.6847	−	20.2384i	0.906905	−	1.57081i
$167$	3.12311	−	5.40938i	0.241673	−	0.418590i	−0.719518	−	0.694474i	$-0.755637\pi$
$167$	3.12311	−	5.40938i	0.241673	−	0.418590i	0.961191	+	0.275884i	$0.0889705\pi$
$168$	−23.3693			−1.80298
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$	3.68466			0.282600
$171$	0.561553	−	0.972638i	0.0429430	−	0.0743795i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−1.87689	−	3.25088i	−0.142698	−	0.247160i	0.785814	−	0.618463i	$-0.212244\pi$
$173$	−1.87689	−	3.25088i	−0.142698	−	0.247160i	−0.928512	+	0.371303i	$0.878911\pi$
$174$	−14.5616			−1.10391
$175$	−8.34233	−	14.4493i	−0.630621	−	1.09227i
$176$	7.68466	+	13.3102i	0.579253	+	1.00330i
$177$	−11.1231			−0.836064
$178$	−16.8078	−	29.1119i	−1.25980	−	2.18203i
$179$	6.56155	−	11.3649i	0.490433	−	0.849456i	−0.509506	−	0.860467i	$-0.670172\pi$
$179$	6.56155	−	11.3649i	0.490433	−	0.849456i	0.999939	+	0.0110115i	$0.00350513\pi$
$180$	−1.28078	+	2.21837i	−0.0954634	+	0.165348i
$181$	9.68466			0.719855			0.359927	−	0.932980i	$-0.382801\pi$
$181$	9.68466			0.719855			0.359927	+	0.932980i	$0.382801\pi$
$182$	−4.56155	+	32.5760i	−0.338125	+	2.41469i
$183$	12.1231			0.896166
$184$	−6.56155	+	11.3649i	−0.483724	+	0.837835i
$185$	−0.965435	+	1.67218i	−0.0709802	+	0.122941i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−5.12311			−0.374639
$188$	18.8078	+	32.5760i	1.37170	+	2.37585i
$189$	1.78078	+	3.08440i	0.129532	+	0.224357i
$190$	−1.61553			−0.117203
$191$	0.438447	+	0.759413i	0.0317249	+	0.0549492i	0.881452	−	0.472274i	$-0.156567\pi$
$191$	0.438447	+	0.759413i	0.0317249	+	0.0549492i	−0.849727	+	0.527223i	$0.823233\pi$
$192$	−0.719224	+	1.24573i	−0.0519055	+	0.0899029i
$193$	−9.74621	+	16.8809i	−0.701548	+	1.21512i	0.266375	+	0.963869i	$0.414174\pi$
$193$	−9.74621	+	16.8809i	−0.701548	+	1.21512i	−0.967923	+	0.251247i	$0.919159\pi$
$194$	−11.3693			−0.816269
$195$	1.59612	+	1.24573i	0.114300	+	0.0892087i
$196$	25.9309			1.85220
$197$	5.68466	−	9.84612i	0.405015	−	0.701507i	−0.589308	−	0.807908i	$-0.700600\pi$
$197$	5.68466	−	9.84612i	0.405015	−	0.701507i	0.994323	+	0.106402i	$0.0339329\pi$
$198$	2.56155	−	4.43674i	0.182042	−	0.315305i
$199$	11.5885	+	20.0719i	0.821490	+	1.42286i	0.904573	+	0.426320i	$0.140190\pi$
$199$	11.5885	+	20.0719i	0.821490	+	1.42286i	−0.0830828	+	0.996543i	$0.526477\pi$
$200$	−30.7386			−2.17355
$201$	−0.219224	−	0.379706i	−0.0154628	−	0.0267824i
$202$	4.40388	+	7.62775i	0.309856	+	0.536686i
$203$	20.2462			1.42101
$204$	−5.84233	−	10.1192i	−0.409045	−	0.708486i
$205$	−0.719224	+	1.24573i	−0.0502328	+	0.0870057i
$206$	9.68466	−	16.7743i	0.674762	−	1.16872i
$207$	2.00000			0.139010
$208$	21.8423	+	17.0474i	1.51449	+	1.18203i
$209$	2.24621			0.155374
$210$	2.56155	−	4.43674i	0.176764	−	0.306164i
$211$	−3.65767	+	6.33527i	−0.251804	+	0.436138i	−0.964023	−	0.265820i	$-0.914357\pi$
$211$	−3.65767	+	6.33527i	−0.251804	+	0.436138i	0.712218	+	0.701958i	$0.247691\pi$
$212$	−26.6501	−	46.1593i	−1.83034	−	3.17023i
$213$	14.0000			0.959264
$214$	−10.5616	−	18.2931i	−0.721973	−	1.25049i
$215$	−0.123106	−	0.213225i	−0.00839573	−	0.0145418i
$216$	6.56155			0.446457
$217$	−2.78078	−	4.81645i	−0.188771	−	0.326962i
$218$	−22.8078	+	39.5042i	−1.54474	+	2.67556i
$219$	0.938447	−	1.62544i	0.0634144	−	0.109837i
$220$	−5.12311			−0.345400
$221$	−8.56155	+	3.46410i	−0.575912	+	0.233021i
$222$	8.80776			0.591138
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	−0.968309	−	0.249756i	$-0.919650\pi$
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	0.700449	+	0.713702i	$0.252983\pi$
$224$	11.6847	−	20.2384i	0.780714	−	1.35224i
$225$	2.34233	+	4.05703i	0.156155	+	0.270469i
$226$	−37.9309			−2.52312
$227$	0.561553	+	0.972638i	0.0372716	+	0.0645563i	0.884059	−	0.467374i	$-0.154800\pi$
$227$	0.561553	+	0.972638i	0.0372716	+	0.0645563i	−0.846788	+	0.531931i	$0.821467\pi$
$228$	2.56155	+	4.43674i	0.169643	+	0.293830i
$229$	0.246211			0.0162701			0.00813505	−	0.999967i	$-0.497411\pi$
$229$	0.246211			0.0162701			0.00813505	+	0.999967i	$0.497411\pi$
$230$	−1.43845	−	2.49146i	−0.0948484	−	0.164282i
$231$	−3.56155	+	6.16879i	−0.234333	+	0.405877i
$232$	18.6501	−	32.3029i	1.22444	−	2.12079i
$233$	26.0000			1.70332			0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000			1.70332			0.851658	+	0.524097i	$0.175597\pi$
$234$	1.28078	−	9.14657i	0.0837270	−	0.597930i
$235$	−4.63068			−0.302072
$236$	25.3693	−	43.9409i	1.65140	−	2.86031i
$237$	−4.78078	+	8.28055i	−0.310545	+	0.537879i
$238$	11.6847	+	20.2384i	0.757404	+	1.31186i
$239$	−0.630683			−0.0407955			−0.0203977	−	0.999792i	$-0.506493\pi$
$239$	−0.630683			−0.0407955			−0.0203977	+	0.999792i	$0.506493\pi$
$240$	−2.15767	−	3.73720i	−0.139277	−	0.241235i
$241$	−1.40388	−	2.43160i	−0.0904320	−	0.156633i	0.817261	−	0.576268i	$-0.195491\pi$
$241$	−1.40388	−	2.43160i	−0.0904320	−	0.156633i	−0.907693	+	0.419635i	$0.862158\pi$
$242$	−17.9309			−1.15264
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−27.6501	+	47.8914i	−1.77012	+	3.06593i
$245$	−1.59612	+	2.76456i	−0.101972	+	0.176621i
$246$	6.56155			0.418349
$247$	3.75379	−	1.51883i	0.238848	−	0.0966406i
$248$	−10.2462			−0.650635
$249$	4.56155	−	7.90084i	0.289077	−	0.500695i
$250$	6.96543	−	12.0645i	0.440533	−	0.763025i
$251$	15.3693	+	26.6204i	0.970103	+	1.68027i	0.695231	+	0.718786i	$0.255302\pi$
$251$	15.3693	+	26.6204i	0.970103	+	1.68027i	0.274871	+	0.961481i	$0.411365\pi$
$252$	−16.2462			−1.02342
$253$	2.00000	+	3.46410i	0.125739	+	0.217786i
$254$	−12.2462	−	21.2111i	−0.768396	−	1.33090i
$255$	1.43845			0.0900791
$256$	13.5270	+	23.4294i	0.845437	+	1.46434i
$257$	8.08854	−	14.0098i	0.504549	−	0.873905i	−0.495437	−	0.868644i	$-0.664992\pi$
$257$	8.08854	−	14.0098i	0.504549	−	0.873905i	0.999986	−	0.00526106i	$-0.00167466\pi$
$258$	−0.561553	+	0.972638i	−0.0349608	+	0.0605538i
$259$	−12.2462			−0.760943
$260$	−8.56155	+	3.46410i	−0.530965	+	0.214834i
$261$	−5.68466			−0.351872
$262$	22.2462	−	38.5316i	1.37438	−	2.38049i
$263$	7.68466	−	13.3102i	0.473856	−	0.820743i	−0.525696	−	0.850673i	$-0.676195\pi$
$263$	7.68466	−	13.3102i	0.473856	−	0.820743i	0.999552	+	0.0299295i	$0.00952826\pi$
$264$	6.56155	+	11.3649i	0.403836	+	0.699464i
$265$	6.56155			0.403073
$266$	−5.12311	−	8.87348i	−0.314118	−	0.544068i
$267$	−6.56155	−	11.3649i	−0.401561	−	0.695523i
$268$	2.00000			0.122169
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	0.810087	−	0.586310i	$-0.199420\pi$
$269$	−1.68466	−	2.91791i	−0.102715	−	0.177908i	−0.912803	+	0.408401i	$0.866086\pi$
$270$	−0.719224	+	1.24573i	−0.0437706	+	0.0758128i
$271$	0.534565	−	0.925894i	0.0324725	−	0.0562441i	−0.849332	−	0.527858i	$-0.822995\pi$
$271$	0.534565	−	0.925894i	0.0324725	−	0.0562441i	0.881805	+	0.471614i	$0.156329\pi$
$272$	19.6847			1.19356
$273$	−1.78078	+	12.7173i	−0.107777	+	0.769685i
$274$	−3.68466			−0.222598
$275$	−4.68466	+	8.11407i	−0.282496	+	0.489297i
$276$	−4.56155	+	7.90084i	−0.274573	+	0.475575i
$277$	−8.84233	−	15.3154i	−0.531284	−	0.920211i	−0.999333	−	0.0365086i	$-0.988376\pi$
$277$	−8.84233	−	15.3154i	−0.531284	−	0.920211i	0.468049	−	0.883702i	$-0.344957\pi$
$278$	28.0000			1.67933
$279$	0.780776	+	1.35234i	0.0467439	+	0.0809627i
$280$	6.56155	+	11.3649i	0.392128	+	0.679185i
$281$	−2.80776			−0.167497			−0.0837486	−	0.996487i	$-0.526689\pi$
$281$	−2.80776			−0.167497			−0.0837486	+	0.996487i	$0.526689\pi$
$282$	10.5616	+	18.2931i	0.628931	+	1.08934i
$283$	0.657671	−	1.13912i	0.0390945	−	0.0677136i	−0.845816	−	0.533475i	$-0.820886\pi$
$283$	0.657671	−	1.13912i	0.0390945	−	0.0677136i	0.884911	+	0.465761i	$0.154219\pi$
$284$	−31.9309	+	55.3059i	−1.89475	+	3.28180i
$285$	−0.630683			−0.0373584
$286$	17.1231	−	6.92820i	1.01251	−	0.409673i
$287$	−9.12311			−0.538520
$288$	−3.28078	+	5.68247i	−0.193322	+	0.334843i
$289$	5.21922	−	9.03996i	0.307013	−	0.531762i
$290$	4.08854	+	7.08156i	0.240087	+	0.415844i
$291$	−4.43845			−0.260186
$292$	4.28078	+	7.41452i	0.250513	+	0.433902i
$293$	−12.2808	−	21.2709i	−0.717451	−	1.24266i	−0.962007	−	0.273026i	$-0.911976\pi$
$293$	−12.2808	−	21.2709i	−0.717451	−	1.24266i	0.244556	−	0.969635i	$-0.421358\pi$
$294$	14.5616			0.849247
$295$	3.12311	+	5.40938i	0.181834	+	0.314946i
$296$	−11.2808	+	19.5389i	−0.655682	+	1.13567i
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$	−16.8078			−0.973648
$299$	5.68466	+	4.43674i	0.328752	+	0.256583i
$300$	−21.3693			−1.23376
$301$	0.780776	−	1.35234i	0.0450032	−	0.0779478i
$302$	−19.6847	+	34.0948i	−1.13272	+	1.96194i
$303$	1.71922	+	2.97778i	0.0987668	+	0.171069i
$304$	−8.63068			−0.495004
$305$	−3.40388	−	5.89570i	−0.194906	−	0.337587i
$306$	−3.28078	−	5.68247i	−0.187550	−	0.324845i
$307$	10.1922			0.581702			0.290851	−	0.956768i	$-0.406062\pi$
$307$	10.1922			0.581702			0.290851	+	0.956768i	$0.406062\pi$
$308$	−16.2462	−	28.1393i	−0.925714	−	1.60338i
$309$	3.78078	−	6.54850i	0.215081	−	0.372531i
$310$	1.12311	−	1.94528i	0.0637881	−	0.110484i
$311$	−10.8769			−0.616772			−0.308386	−	0.951261i	$-0.599789\pi$
$311$	−10.8769			−0.616772			−0.308386	+	0.951261i	$0.599789\pi$
$312$	18.6501	+	14.5560i	1.05585	+	0.824068i
$313$	−1.31534			−0.0743475			−0.0371738	−	0.999309i	$-0.511835\pi$
$313$	−1.31534			−0.0743475			−0.0371738	+	0.999309i	$0.511835\pi$
$314$	5.59612	−	9.69276i	0.315807	−	0.546994i
$315$	1.00000	−	1.73205i	0.0563436	−	0.0975900i
$316$	−21.8078	−	37.7722i	−1.22678	−	2.12485i
$317$	−23.0540			−1.29484			−0.647420	−	0.762133i	$-0.724152\pi$
$317$	−23.0540			−1.29484			−0.647420	+	0.762133i	$0.724152\pi$
$318$	−14.9654	−	25.9209i	−0.839220	−	1.45357i
$319$	−5.68466	−	9.84612i	−0.318280	−	0.551277i
$320$	0.807764			0.0451554
$321$	−4.12311	−	7.14143i	−0.230129	−	0.398596i
$322$	9.12311	−	15.8017i	0.508411	−	0.880593i
$323$	1.43845	−	2.49146i	0.0800373	−	0.138629i
$324$	4.56155			0.253420
$325$	−2.34233	+	16.7276i	−0.129929	+	0.927879i
$326$	40.4924			2.24267
$327$	−8.90388	+	15.4220i	−0.492386	+	0.852837i
$328$	−8.40388	+	14.5560i	−0.464027	+	0.803718i
$329$	−14.6847	−	25.4346i	−0.809591	−	1.40225i
$330$	−2.87689			−0.158368
$331$	11.9039	+	20.6181i	0.654297	+	1.13327i	0.982070	+	0.188518i	$0.0603685\pi$
$331$	11.9039	+	20.6181i	0.654297	+	1.13327i	−0.327773	+	0.944756i	$0.606298\pi$
$332$	20.8078	+	36.0401i	1.14197	+	1.97796i
$333$	3.43845			0.188426
$334$	8.00000	+	13.8564i	0.437741	+	0.758189i
$335$	−0.123106	+	0.213225i	−0.00672598	+	0.0116497i
$336$	13.6847	−	23.7025i	0.746559	−	1.29308i
$337$	2.12311			0.115653			0.0578265	−	0.998327i	$-0.481583\pi$
$337$	2.12311			0.115653			0.0578265	+	0.998327i	$0.481583\pi$
$338$	23.9309	−	23.1563i	1.30167	−	1.25954i
$339$	−14.8078			−0.804247
$340$	−3.28078	+	5.68247i	−0.177925	+	0.308175i
$341$	−1.56155	+	2.70469i	−0.0845628	+	0.146467i
$342$	1.43845	+	2.49146i	0.0777823	+	0.134723i
$343$	4.68466			0.252948
$344$	−1.43845	−	2.49146i	−0.0775559	−	0.134331i
$345$	−0.561553	−	0.972638i	−0.0302330	−	0.0523651i
$346$	9.61553			0.516934
$347$	6.80776	+	11.7914i	0.365460	+	0.632995i	0.988850	−	0.148916i	$-0.0475784\pi$
$347$	6.80776	+	11.7914i	0.365460	+	0.632995i	−0.623390	+	0.781911i	$0.714245\pi$
$348$	12.9654	−	22.4568i	0.695020	−	1.20381i
$349$	6.90388	−	11.9579i	0.369556	−	0.640090i	−0.619940	−	0.784649i	$-0.712843\pi$
$349$	6.90388	−	11.9579i	0.369556	−	0.640090i	0.989496	+	0.144559i	$0.0461763\pi$
$350$	42.7386			2.28448
$351$	0.500000	−	3.57071i	0.0266880	−	0.190591i
$352$	−13.1231			−0.699464
$353$	−8.84233	+	15.3154i	−0.470630	+	0.815155i	−0.999436	−	0.0335881i	$-0.989307\pi$
$353$	−8.84233	+	15.3154i	−0.470630	+	0.815155i	0.528806	+	0.848743i	$0.322640\pi$
$354$	14.2462	−	24.6752i	0.757178	−	1.31147i
$355$	−3.93087	−	6.80847i	−0.208629	−	0.361356i
$356$	59.8617			3.17267
$357$	4.56155	+	7.90084i	0.241423	+	0.418157i
$358$	16.8078	+	29.1119i	0.888318	+	1.53861i
$359$	15.3693			0.811162			0.405581	−	0.914059i	$-0.367069\pi$
$359$	15.3693			0.811162			0.405581	+	0.914059i	$0.367069\pi$
$360$	−1.84233	−	3.19101i	−0.0970993	−	0.168181i
$361$	8.86932	−	15.3621i	0.466806	−	0.808532i
$362$	−12.4039	+	21.4842i	−0.651934	+	1.12918i
$363$	−7.00000			−0.367405
$364$	−46.1771	−	36.0401i	−2.42034	−	1.88901i
$365$	−1.05398			−0.0551676
$366$	−15.5270	+	26.8935i	−0.811609	+	1.40575i
$367$	−10.0270	+	17.3673i	−0.523404	+	0.906563i	0.476224	+	0.879324i	$0.342005\pi$
$367$	−10.0270	+	17.3673i	−0.523404	+	0.906563i	−0.999629	+	0.0272394i	$0.991328\pi$
$368$	−7.68466	−	13.3102i	−0.400591	−	0.693843i
$369$	2.56155			0.133349
$370$	−2.47301	−	4.28338i	−0.128566	−	0.222682i
$371$	20.8078	+	36.0401i	1.08029	+	1.87111i
$372$	−7.12311			−0.369316
$373$	−1.81534	−	3.14426i	−0.0939948	−	0.162804i	0.815194	−	0.579188i	$-0.196630\pi$
$373$	−1.81534	−	3.14426i	−0.0939948	−	0.162804i	−0.909189	+	0.416384i	$0.863297\pi$
$374$	6.56155	−	11.3649i	0.339290	−	0.587667i
$375$	2.71922	−	4.70983i	0.140420	−	0.243215i
$376$	−54.1080			−2.79040
$377$	−16.1577	−	12.6107i	−0.832162	−	0.649483i
$378$	−9.12311			−0.469242
$379$	−5.65767	+	9.79937i	−0.290615	+	0.503360i	−0.973955	−	0.226740i	$-0.927193\pi$
$379$	−5.65767	+	9.79937i	−0.290615	+	0.503360i	0.683340	+	0.730100i	$0.260527\pi$
$380$	1.43845	−	2.49146i	0.0737908	−	0.127809i
$381$	−4.78078	−	8.28055i	−0.244927	−	0.424225i
$382$	−2.24621			−0.114926
$383$	−13.3693	−	23.1563i	−0.683140	−	1.18323i	−0.974017	−	0.226473i	$-0.927280\pi$
$383$	−13.3693	−	23.1563i	−0.683140	−	1.18323i	0.290877	−	0.956760i	$-0.406053\pi$
$384$	4.71922	+	8.17394i	0.240827	+	0.417124i
$385$	4.00000			0.203859
$386$	−24.9654	−	43.2414i	−1.27071	−	2.20093i
$387$	−0.219224	+	0.379706i	−0.0111438	+	0.0193016i
$388$	10.1231	−	17.5337i	0.513923	−	0.890140i
$389$	−3.05398			−0.154843			−0.0774213	−	0.996998i	$-0.524669\pi$
$389$	−3.05398			−0.154843			−0.0774213	+	0.996998i	$0.524669\pi$
$390$	−4.80776	+	1.94528i	−0.243451	+	0.0985029i
$391$	5.12311			0.259087
$392$	−18.6501	+	32.3029i	−0.941972	+	1.63154i
$393$	8.68466	−	15.0423i	0.438083	−	0.758782i
$394$	14.5616	+	25.2213i	0.733600	+	1.27063i
$395$	5.36932			0.270160
$396$	4.56155	+	7.90084i	0.229227	+	0.397032i
$397$	6.02699	+	10.4390i	0.302486	+	0.523921i	0.976698	−	0.214617i	$-0.0688502\pi$
$397$	6.02699	+	10.4390i	0.302486	+	0.523921i	−0.674213	+	0.738537i	$0.735517\pi$
$398$	−59.3693			−2.97591
$399$	−2.00000	−	3.46410i	−0.100125	−	0.173422i
$400$	18.0000	−	31.1769i	0.900000	−	1.55885i
$401$	−9.28078	+	16.0748i	−0.463460	+	0.802736i	−0.999131	−	0.0416909i	$-0.986726\pi$
$401$	−9.28078	+	16.0748i	−0.463460	+	0.802736i	0.535671	+	0.844427i	$0.320059\pi$
$402$	1.12311			0.0560154
$403$	−0.780776	+	5.57586i	−0.0388932	+	0.277753i
$404$	−15.6847			−0.780341
$405$	−0.280776	+	0.486319i	−0.0139519	+	0.0241654i
$406$	−25.9309	+	44.9136i	−1.28693	+	2.22902i
$407$	3.43845	+	5.95557i	0.170437	+	0.295206i
$408$	16.8078			0.832108
$409$	9.18466	+	15.9083i	0.454152	+	0.786615i	0.998639	−	0.0521548i	$-0.0166089\pi$
$409$	9.18466	+	15.9083i	0.454152	+	0.786615i	−0.544487	+	0.838769i	$0.683276\pi$
$410$	−1.84233	−	3.19101i	−0.0909862	−	0.157593i
$411$	−1.43845			−0.0709534
$412$	17.2462	+	29.8713i	0.849660	+	1.47165i
$413$	−19.8078	+	34.3081i	−0.974676	+	1.68819i
$414$	−2.56155	+	4.43674i	−0.125893	+	0.218054i
$415$	−5.12311			−0.251483
$416$	−21.9309	+	8.87348i	−1.07525	+	0.435058i
$417$	10.9309			0.535287
$418$	−2.87689	+	4.98293i	−0.140714	+	0.243723i
$419$	8.87689	−	15.3752i	0.433665	−	0.751129i	−0.563521	−	0.826102i	$-0.690554\pi$
$419$	8.87689	−	15.3752i	0.433665	−	0.751129i	0.997186	+	0.0749725i	$0.0238869\pi$
$420$	4.56155	+	7.90084i	0.222581	+	0.385522i
$421$	14.7538			0.719056			0.359528	−	0.933134i	$-0.382938\pi$
$421$	14.7538			0.719056			0.359528	+	0.933134i	$0.382938\pi$
$422$	−9.36932	−	16.2281i	−0.456091	−	0.789973i
$423$	4.12311	+	7.14143i	0.200472	+	0.347228i
$424$	76.6695			3.72340
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	−17.9309	+	31.0572i	−0.868753	+	1.50473i
$427$	21.5885	−	37.3924i	1.04474	−	1.80955i
$428$	37.6155			1.81822
$429$	6.68466	−	2.70469i	0.322738	−	0.130584i
$430$	0.630683			0.0304142
$431$	1.43845	−	2.49146i	0.0692876	−	0.120010i	−0.829300	−	0.558803i	$-0.811261\pi$
$431$	1.43845	−	2.49146i	0.0692876	−	0.120010i	0.898588	+	0.438794i	$0.144594\pi$
$432$	−3.84233	+	6.65511i	−0.184864	+	0.320194i
$433$	−12.6231	−	21.8639i	−0.606628	−	1.05071i	−0.991792	−	0.127862i	$-0.959189\pi$
$433$	−12.6231	−	21.8639i	−0.606628	−	1.05071i	0.385164	−	0.922848i	$-0.374145\pi$
$434$	14.2462			0.683840
$435$	1.59612	+	2.76456i	0.0765280	+	0.132550i
$436$	−40.6155	−	70.3482i	−1.94513	−	3.36907i
$437$	−2.24621			−0.107451
$438$	2.40388	+	4.16365i	0.114862	+	0.198947i
$439$	0.657671	−	1.13912i	0.0313889	−	0.0543672i	−0.849904	−	0.526937i	$-0.823340\pi$
$439$	0.657671	−	1.13912i	0.0313889	−	0.0543672i	0.881293	+	0.472570i	$0.156674\pi$
$440$	3.68466	−	6.38202i	0.175659	−	0.304251i
$441$	5.68466			0.270698
$442$	3.28078	−	23.4294i	0.156051	−	1.11442i
$443$	14.7386			0.700254			0.350127	−	0.936702i	$-0.386138\pi$
$443$	14.7386			0.700254			0.350127	+	0.936702i	$0.386138\pi$
$444$	−7.84233	+	13.5833i	−0.372180	+	0.644635i
$445$	−3.68466	+	6.38202i	−0.174670	+	0.302537i
$446$	−10.2462	−	17.7470i	−0.485172	−	0.840343i
$447$	−6.56155			−0.310351
$448$	2.56155	+	4.43674i	0.121022	+	0.209616i
$449$	−4.12311	−	7.14143i	−0.194581	−	0.337025i	0.752182	−	0.658956i	$-0.229002\pi$
$449$	−4.12311	−	7.14143i	−0.194581	−	0.337025i	−0.946763	+	0.321931i	$0.895668\pi$
$450$	−12.0000			−0.565685
$451$	2.56155	+	4.43674i	0.120619	+	0.208918i
$452$	33.7732	−	58.4969i	1.58856	−	2.75146i
$453$	−7.68466	+	13.3102i	−0.361057	+	0.625369i
$454$	−2.87689			−0.135019
$455$	6.68466	−	2.70469i	0.313382	−	0.126798i
$456$	−7.36932			−0.345100
$457$	14.3078	−	24.7818i	0.669289	−	1.15924i	−0.308814	−	0.951122i	$-0.599932\pi$
$457$	14.3078	−	24.7818i	0.669289	−	1.15924i	0.978103	−	0.208120i	$-0.0667345\pi$
$458$	−0.315342	+	0.546188i	−0.0147349	+	0.0255217i
$459$	−1.28078	−	2.21837i	−0.0597815	−	0.103545i
$460$	5.12311			0.238866
$461$	18.4039	+	31.8765i	0.857154	+	1.48463i	0.874632	+	0.484787i	$0.161103\pi$
$461$	18.4039	+	31.8765i	0.857154	+	1.48463i	−0.0174778	+	0.999847i	$0.505564\pi$
$462$	−9.12311	−	15.8017i	−0.424445	−	0.735161i
$463$	−26.6847			−1.24014			−0.620071	−	0.784546i	$-0.712896\pi$
$463$	−26.6847			−1.24014			−0.620071	+	0.784546i	$0.712896\pi$
$464$	21.8423	+	37.8320i	1.01400	+	1.75631i
$465$	0.438447	−	0.759413i	0.0203325	−	0.0352169i
$466$	−33.3002	+	57.6776i	−1.54260	+	2.67186i
$467$	−26.0000			−1.20314			−0.601568	−	0.798821i	$-0.705457\pi$
$467$	−26.0000			−1.20314			−0.601568	+	0.798821i	$0.705457\pi$
$468$	12.9654	+	10.1192i	0.599327	+	0.467761i
$469$	−1.56155			−0.0721058
$470$	5.93087	−	10.2726i	0.273571	−	0.473838i
$471$	2.18466	−	3.78394i	0.100664	−	0.174355i
$472$	36.4924	+	63.2067i	1.67970	+	2.90933i
$473$	−0.876894			−0.0403196
$474$	−12.2462	−	21.2111i	−0.562487	−	0.974256i
$475$	−2.63068	−	4.55648i	−0.120704	−	0.209065i
$476$	−41.6155			−1.90744
$477$	−5.84233	−	10.1192i	−0.267502	−	0.463327i
$478$	0.807764	−	1.39909i	0.0369463	−	0.0639928i
$479$	3.12311	−	5.40938i	0.142698	−	0.247161i	−0.785814	−	0.618463i	$-0.787755\pi$
$479$	3.12311	−	5.40938i	0.142698	−	0.247161i	0.928512	+	0.371303i	$0.121089\pi$
$480$	3.68466			0.168181
$481$	9.77320	+	7.62775i	0.445620	+	0.347795i
$482$	7.19224			0.327597
$483$	3.56155	−	6.16879i	0.162056	−	0.280690i
$484$	15.9654	−	27.6529i	0.725702	−	1.25695i
$485$	1.24621	+	2.15850i	0.0565875	+	0.0980125i
$486$	2.56155			0.116194
$487$	0.561553	+	0.972638i	0.0254464	+	0.0440744i	0.878468	−	0.477801i	$-0.158566\pi$
$487$	0.561553	+	0.972638i	0.0254464	+	0.0440744i	−0.853022	+	0.521875i	$0.825233\pi$
$488$	−39.7732	−	68.8892i	−1.80045	−	3.11847i
$489$	15.8078			0.714852
$490$	−4.08854	−	7.08156i	−0.184701	−	0.319912i
$491$	9.87689	−	17.1073i	0.445738	−	0.772041i	−0.552365	−	0.833602i	$-0.686275\pi$
$491$	9.87689	−	17.1073i	0.445738	−	0.772041i	0.998103	+	0.0615613i	$0.0196080\pi$
$492$	−5.84233	+	10.1192i	−0.263393	+	0.456209i
$493$	−14.5616			−0.655819
$494$	−1.43845	+	10.2726i	−0.0647188	+	0.462185i
$495$	−1.12311			−0.0504798
$496$	6.00000	−	10.3923i	0.269408	−	0.466628i
$497$	24.9309	−	43.1815i	1.11830	−	1.93696i
$498$	11.6847	+	20.2384i	0.523602	+	0.906905i
$499$	−28.4924			−1.27550			−0.637748	−	0.770245i	$-0.720134\pi$
$499$	−28.4924			−1.27550			−0.637748	+	0.770245i	$0.720134\pi$
$500$	12.4039	+	21.4842i	0.554718	+	0.960801i
$501$	3.12311	+	5.40938i	0.139530	+	0.241673i
$502$	−78.7386			−3.51428
$503$	5.87689	+	10.1791i	0.262038	+	0.453863i	0.966783	−	0.255597i	$-0.0822722\pi$
$503$	5.87689	+	10.1791i	0.262038	+	0.453863i	−0.704746	+	0.709460i	$0.748939\pi$
$504$	11.6847	−	20.2384i	0.520476	−	0.901491i
$505$	0.965435	−	1.67218i	0.0429613	−	0.0744111i
$506$	−10.2462			−0.455500
$507$	9.34233	−	9.03996i	0.414907	−	0.401479i
$508$	43.6155			1.93513
$509$	−3.40388	+	5.89570i	−0.150874	+	0.261322i	−0.931549	−	0.363615i	$-0.881542\pi$
$509$	−3.40388	+	5.89570i	−0.150874	+	0.261322i	0.780675	+	0.624938i	$0.214876\pi$
$510$	−1.84233	+	3.19101i	−0.0815797	+	0.141300i
$511$	−3.34233	−	5.78908i	−0.147856	−	0.256094i
$512$	−50.4233			−2.22842
$513$	0.561553	+	0.972638i	0.0247932	+	0.0429430i
$514$	20.7192	+	35.8867i	0.913886	+	1.58290i
$515$	−4.24621			−0.187110
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	−8.24621	+	14.2829i	−0.362668	+	0.628159i
$518$	15.6847	−	27.1666i	0.689144	−	1.19363i
$519$	3.75379			0.164773
$520$	1.84233	−	13.1569i	0.0807915	−	0.576967i
$521$	−37.9309			−1.66178			−0.830891	−	0.556436i	$-0.812169\pi$
$521$	−37.9309			−1.66178			−0.830891	+	0.556436i	$0.812169\pi$
$522$	7.28078	−	12.6107i	0.318671	−	0.551954i
$523$	11.9309	−	20.6649i	0.521701	−	0.903612i	−0.477981	−	0.878370i	$-0.658631\pi$
$523$	11.9309	−	20.6649i	0.521701	−	0.903612i	0.999681	−	0.0252415i	$-0.00803549\pi$
$524$	39.6155	+	68.6161i	1.73061	+	2.99751i
$525$	16.6847			0.728178
$526$	19.6847	+	34.0948i	0.858292	+	1.48661i
$527$	2.00000	+	3.46410i	0.0871214	+	0.150899i
$528$	−15.3693			−0.668864
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$	−8.40388	+	14.5560i	−0.365041	+	0.632270i
$531$	5.56155	−	9.63289i	0.241351	−	0.418032i
$532$	18.2462			0.791074
$533$	7.28078	+	5.68247i	0.315365	+	0.246135i
$534$	33.6155			1.45469
$535$	−2.31534	+	4.01029i	−0.100101	+	0.173380i
$536$	−1.43845	+	2.49146i	−0.0621315	+	0.107615i
$537$	6.56155	+	11.3649i	0.283152	+	0.490433i
$538$	8.63068			0.372095
$539$	5.68466	+	9.84612i	0.244856	+	0.424102i
$540$	−1.28078	−	2.21837i	−0.0551158	−	0.0954634i
$541$	−29.7386			−1.27856			−0.639282	−	0.768972i	$-0.720768\pi$
$541$	−29.7386			−1.27856			−0.639282	+	0.768972i	$0.720768\pi$
$542$	1.36932	+	2.37173i	0.0588172	+	0.101874i
$543$	−4.84233	+	8.38716i	−0.207804	+	0.359927i
$544$	−8.40388	+	14.5560i	−0.360313	+	0.624081i
$545$	10.0000			0.428353
$546$	−25.9309	−	20.2384i	−1.10974	−	0.866125i
$547$	−24.9309			−1.06597			−0.532984	−	0.846126i	$-0.678929\pi$
$547$	−24.9309			−1.06597			−0.532984	+	0.846126i	$0.678929\pi$
$548$	3.28078	−	5.68247i	0.140148	−	0.242743i
$549$	−6.06155	+	10.4989i	−0.258701	+	0.448083i
$550$	−12.0000	−	20.7846i	−0.511682	−	0.886259i
$551$	6.38447			0.271988
$552$	−6.56155	−	11.3649i	−0.279278	−	0.483724i
$553$	17.0270	+	29.4916i	0.724061	+	1.25411i
$554$	45.3002			1.92462
$555$	−0.965435	−	1.67218i	−0.0409804	−	0.0709802i
$556$	−24.9309	+	43.1815i	−1.05730	+	1.83130i
$557$	7.03457	−	12.1842i	0.298064	−	0.516262i	−0.677629	−	0.735404i	$-0.736992\pi$
$557$	7.03457	−	12.1842i	0.298064	−	0.516262i	0.975693	+	0.219142i	$0.0703257\pi$
$558$	−4.00000			−0.169334
$559$	−1.46543	+	0.592932i	−0.0619813	+	0.0250783i
$560$	−15.3693			−0.649472
$561$	2.56155	−	4.43674i	0.108149	−	0.187319i
$562$	3.59612	−	6.22866i	0.151693	−	0.262740i
$563$	−0.684658	−	1.18586i	−0.0288549	−	0.0499782i	0.851237	−	0.524781i	$-0.175853\pi$
$563$	−0.684658	−	1.18586i	−0.0288549	−	0.0499782i	−0.880092	+	0.474803i	$0.842519\pi$
$564$	−37.6155			−1.58390
$565$	4.15767	+	7.20130i	0.174915	+	0.302961i
$566$	1.68466	+	2.91791i	0.0708115	+	0.122649i
$567$	−3.56155			−0.149571
$568$	−45.9309	−	79.5546i	−1.92722	−	3.33804i
$569$	−20.3693	+	35.2807i	−0.853926	+	1.47904i	0.0237115	+	0.999719i	$0.492452\pi$
$569$	−20.3693	+	35.2807i	−0.853926	+	1.47904i	−0.877638	+	0.479325i	$0.840882\pi$
$570$	0.807764	−	1.39909i	0.0338335	−	0.0586014i
$571$	19.3693			0.810581			0.405290	−	0.914188i	$-0.367170\pi$
$571$	19.3693			0.810581			0.405290	+	0.914188i	$0.367170\pi$
$572$	−4.56155	+	32.5760i	−0.190728	+	1.36207i
$573$	−0.876894			−0.0366328
$574$	11.6847	−	20.2384i	0.487708	−	0.844735i
$575$	4.68466	−	8.11407i	0.195364	−	0.338380i
$576$	−0.719224	−	1.24573i	−0.0299676	−	0.0519055i
$577$	−29.6847			−1.23579			−0.617894	−	0.786261i	$-0.712014\pi$
$577$	−29.6847			−1.23579			−0.617894	+	0.786261i	$0.712014\pi$
$578$	13.3693	+	23.1563i	0.556090	+	0.963177i
$579$	−9.74621	−	16.8809i	−0.405039	−	0.701548i
$580$	−14.5616			−0.604636
$581$	−16.2462	−	28.1393i	−0.674006	−	1.16741i
$582$	5.68466	−	9.84612i	0.235637	−	0.408135i
$583$	11.6847	−	20.2384i	0.483929	−	0.838190i
$584$	−12.3153			−0.509612
$585$	−1.87689	+	0.759413i	−0.0776000	+	0.0313979i
$586$	62.9157			2.59902
$587$	−7.31534	+	12.6705i	−0.301936	+	0.522969i	−0.976575	−	0.215179i	$-0.930966\pi$
$587$	−7.31534	+	12.6705i	−0.301936	+	0.522969i	0.674638	+	0.738149i	$0.264300\pi$
$588$	−12.9654	+	22.4568i	−0.534686	+	0.926102i
$589$	−0.876894	−	1.51883i	−0.0361318	−	0.0625821i
$590$	−16.0000			−0.658710
$591$	5.68466	+	9.84612i	0.233836	+	0.405015i
$592$	−13.2116	−	22.8832i	−0.542995	−	0.940495i
$593$	44.4233			1.82425			0.912123	−	0.409917i	$-0.134442\pi$
$593$	44.4233			1.82425			0.912123	+	0.409917i	$0.134442\pi$
$594$	2.56155	+	4.43674i	0.105102	+	0.182042i
$595$	2.56155	−	4.43674i	0.105013	−	0.181889i
$596$	14.9654	−	25.9209i	0.613008	−	1.06176i
$597$	−23.1771			−0.948575
$598$	−17.1231	+	6.92820i	−0.700216	+	0.283315i
$599$	−0.384472			−0.0157091			−0.00785455	−	0.999969i	$-0.502500\pi$
$599$	−0.384472			−0.0157091			−0.00785455	+	0.999969i	$0.502500\pi$
$600$	15.3693	−	26.6204i	0.627450	−	1.08677i
$601$	17.9654	−	31.1170i	0.732825	−	1.26929i	−0.222846	−	0.974854i	$-0.571535\pi$
$601$	17.9654	−	31.1170i	0.732825	−	1.26929i	0.955671	−	0.294437i	$-0.0951321\pi$
$602$	2.00000	+	3.46410i	0.0815139	+	0.141186i
$603$	0.438447			0.0178549
$604$	−35.0540	−	60.7153i	−1.42633	−	2.47047i
$605$	1.96543	+	3.40423i	0.0799063	+	0.138402i
$606$	−8.80776			−0.357791
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	3.68466	−	6.38202i	0.149433	−	0.258825i
$609$	−10.1231	+	17.5337i	−0.410209	+	0.710503i
$610$	17.4384			0.706062
$611$	−4.12311	+	29.4449i	−0.166803	+	1.19121i
$612$	11.6847			0.472324
$613$	−11.4309	+	19.7988i	−0.461688	+	0.799668i	−0.999045	−	0.0436871i	$-0.986090\pi$
$613$	−11.4309	+	19.7988i	−0.461688	+	0.799668i	0.537357	+	0.843355i	$0.319423\pi$
$614$	−13.0540	+	22.6101i	−0.526816	+	0.912471i
$615$	−0.719224	−	1.24573i	−0.0290019	−	0.0502328i
$616$	46.7386			1.88315
$617$	5.40388	+	9.35980i	0.217552	+	0.376811i	0.954059	−	0.299619i	$-0.0968595\pi$
$617$	5.40388	+	9.35980i	0.217552	+	0.376811i	−0.736507	+	0.676430i	$0.763526\pi$
$618$	9.68466	+	16.7743i	0.389574	+	0.674762i
$619$	−24.3002			−0.976707			−0.488353	−	0.872646i	$-0.662402\pi$
$619$	−24.3002			−0.976707			−0.488353	+	0.872646i	$0.662402\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$	13.9309	−	24.1290i	0.558577	−	0.967484i
$623$	−46.7386			−1.87254
$624$	−25.6847	+	10.3923i	−1.02821	+	0.416025i
$625$	20.3693			0.814773
$626$	1.68466	−	2.91791i	0.0673325	−	0.116623i
$627$	−1.12311	+	1.94528i	−0.0448525	+	0.0776868i
$628$	9.96543	+	17.2606i	0.397664	+	0.688774i
$629$	8.80776			0.351189
$630$	2.56155	+	4.43674i	0.102055	+	0.176764i
$631$	7.21922	+	12.5041i	0.287393	+	0.497779i	0.973187	−	0.230017i	$-0.0738782\pi$
$631$	7.21922	+	12.5041i	0.287393	+	0.497779i	−0.685794	+	0.727796i	$0.740545\pi$
$632$	62.7386			2.49561
$633$	−3.65767	−	6.33527i	−0.145379	−	0.251804i
$634$	29.5270	−	51.1422i	1.17267	−	2.03112i
$635$	−2.68466	+	4.64996i	−0.106537	+	0.184528i
$636$	53.3002			2.11349
$637$	16.1577	+	12.6107i	0.640190	+	0.499653i
$638$	29.1231			1.15299
$639$	−7.00000	+	12.1244i	−0.276916	+	0.479632i
$640$	2.65009	−	4.59010i	0.104754	−	0.181439i
$641$	−13.0885	−	22.6700i	−0.516966	−	0.895412i	−0.999806	−	0.0197030i	$-0.993728\pi$
$641$	−13.0885	−	22.6700i	−0.516966	−	0.895412i	0.482840	−	0.875709i	$-0.339605\pi$
$642$	21.1231			0.833662
$643$	−19.2732	−	33.3822i	−0.760061	−	1.31646i	−0.942819	−	0.333306i	$-0.891836\pi$
$643$	−19.2732	−	33.3822i	−0.760061	−	1.31646i	0.182758	−	0.983158i	$-0.441498\pi$
$644$	16.2462	+	28.1393i	0.640190	+	1.10884i
$645$	0.246211			0.00969456
$646$	3.68466	+	6.38202i	0.144971	+	0.251097i
$647$	23.8078	−	41.2363i	0.935980	−	1.62116i	0.163102	−	0.986609i	$-0.447850\pi$
$647$	23.8078	−	41.2363i	0.935980	−	1.62116i	0.772877	−	0.634555i	$-0.218817\pi$
$648$	−3.28078	+	5.68247i	−0.128881	+	0.223229i
$649$	22.2462			0.873240
$650$	−34.1080	−	26.6204i	−1.33782	−	1.04414i
$651$	5.56155			0.217974
$652$	−36.0540	+	62.4473i	−1.41198	+	2.44563i
$653$	−7.43845	+	12.8838i	−0.291089	+	0.504181i	−0.974068	−	0.226258i	$-0.927351\pi$
$653$	−7.43845	+	12.8838i	−0.291089	+	0.504181i	0.682979	+	0.730438i	$0.260684\pi$
$654$	−22.8078	−	39.5042i	−0.891854	−	1.54474i
$655$	−9.75379			−0.381112
$656$	−9.84233	−	17.0474i	−0.384278	−	0.665590i
$657$	0.938447	+	1.62544i	0.0366123	+	0.0634144i
$658$	75.2311			2.93281
$659$	−7.12311	−	12.3376i	−0.277477	−	0.480604i	0.693280	−	0.720668i	$-0.256165\pi$
$659$	−7.12311	−	12.3376i	−0.277477	−	0.480604i	−0.970757	+	0.240064i	$0.922831\pi$
$660$	2.56155	−	4.43674i	0.0997083	−	0.172700i
$661$	−15.1847	+	26.3006i	−0.590615	+	1.02297i	0.403535	+	0.914964i	$0.367781\pi$
$661$	−15.1847	+	26.3006i	−0.590615	+	1.02297i	−0.994150	+	0.108011i	$0.965552\pi$
$662$	−60.9848			−2.37024
$663$	1.28078	−	9.14657i	0.0497412	−	0.355223i
$664$	−59.8617			−2.32309
$665$	−1.12311	+	1.94528i	−0.0435522	+	0.0754346i
$666$	−4.40388	+	7.62775i	−0.170647	+	0.295569i
$667$	5.68466	+	9.84612i	0.220111	+	0.381243i
$668$	−28.4924			−1.10240
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$	−0.315342	−	0.546188i	−0.0121827	−	0.0211011i
$671$	−24.2462			−0.936015
$672$	11.6847	+	20.2384i	0.450745	+	0.780714i
$673$	3.37689	−	5.84895i	0.130170	−	0.225461i	−0.793572	−	0.608476i	$-0.791781\pi$
$673$	3.37689	−	5.84895i	0.130170	−	0.225461i	0.923742	+	0.383016i	$0.125114\pi$
$674$	−2.71922	+	4.70983i	−0.104741	+	0.181416i
$675$	−4.68466			−0.180313
$676$	14.4039	+	57.5243i	0.553995	+	2.21247i
$677$	25.6155			0.984485			0.492242	−	0.870458i	$-0.336177\pi$
$677$	25.6155			0.984485			0.492242	+	0.870458i	$0.336177\pi$
$678$	18.9654	−	32.8491i	0.728363	−	1.26156i
$679$	−7.90388	+	13.6899i	−0.303323	+	0.525371i
$680$	−4.71922	−	8.17394i	−0.180974	−	0.313456i
$681$	−1.12311			−0.0430375
$682$	−4.00000	−	6.92820i	−0.153168	−	0.265295i
$683$	−18.0540	−	31.2704i	−0.690816	−	1.19653i	−0.971571	−	0.236749i	$-0.923918\pi$
$683$	−18.0540	−	31.2704i	−0.690816	−	1.19653i	0.280755	−	0.959780i	$-0.409415\pi$
$684$	−5.12311			−0.195887
$685$	0.403882	+	0.699544i	0.0154315	+	0.0267282i
$686$	−6.00000	+	10.3923i	−0.229081	+	0.396780i
$687$	−0.123106	+	0.213225i	−0.00469677	+	0.00813505i
$688$	3.36932			0.128454
$689$	5.84233	−	41.7226i	0.222575	−	1.58950i
$690$	2.87689			0.109521
$691$	−1.15009	+	1.99202i	−0.0437516	+	0.0757800i	−0.887072	−	0.461631i	$-0.847264\pi$
$691$	−1.15009	+	1.99202i	−0.0437516	+	0.0757800i	0.843320	+	0.537411i	$0.180598\pi$
$692$	−8.56155	+	14.8290i	−0.325461	+	0.563716i
$693$	−3.56155	−	6.16879i	−0.135292	−	0.234333i
$694$	−34.8769			−1.32391
$695$	−3.06913	−	5.31589i	−0.116419	−	0.201643i
$696$	18.6501	+	32.3029i	0.706930	+	1.22444i
$697$	6.56155			0.248537
$698$	17.6847	+	30.6307i	0.669374	+	1.15939i
$699$	−13.0000	+	22.5167i	−0.491705	+	0.851658i
$700$	−38.0540	+	65.9114i	−1.43831	+	2.49122i
$701$	19.3693			0.731569			0.365785	−	0.930700i	$-0.380801\pi$
$701$	19.3693			0.731569			0.365785	+	0.930700i	$0.380801\pi$
$702$	7.28078	+	5.68247i	0.274795	+	0.214471i
$703$	−3.86174			−0.145648
$704$	1.43845	−	2.49146i	0.0542135	−	0.0939006i
$705$	2.31534	−	4.01029i	0.0872008	−	0.151036i
$706$	−22.6501	−	39.2311i	−0.852448	−	1.47648i
$707$	12.2462			0.460566
$708$	25.3693	+	43.9409i	0.953437	+	1.65140i
$709$	−12.7462	−	22.0771i	−0.478694	−	0.829122i	0.521008	−	0.853552i	$-0.325556\pi$
$709$	−12.7462	−	22.0771i	−0.478694	−	0.829122i	−0.999702	+	0.0244297i	$0.992223\pi$
$710$	20.1383			0.755775
$711$	−4.78078	−	8.28055i	−0.179293	−	0.310545i
$712$	−43.0540	+	74.5717i	−1.61352	+	2.79469i
$713$	1.56155	−	2.70469i	0.0584806	−	0.101291i
$714$	−23.3693			−0.874575
$715$	−3.19224	−	2.49146i	−0.119383	−	0.0931755i
$716$	−59.8617			−2.23714
$717$	0.315342	−	0.546188i	0.0117766	−	0.0203977i
$718$	−19.6847	+	34.0948i	−0.734625	+	1.27241i
$719$	−0.684658	−	1.18586i	−0.0255335	−	0.0442252i	0.852976	−	0.521950i	$-0.174795\pi$
$719$	−0.684658	−	1.18586i	−0.0255335	−	0.0442252i	−0.878510	+	0.477724i	$0.841462\pi$
$720$	4.31534			0.160823
$721$	−13.4654	−	23.3228i	−0.501479	−	0.868587i
$722$	22.7192	+	39.3508i	0.845522	+	1.46449i
$723$	2.80776			0.104422
$724$	−22.0885	−	38.2585i	−0.820914	−	1.42187i
$725$	−13.3153	+	23.0628i	−0.494519	+	0.856533i
$726$	8.96543	−	15.5286i	0.332738	−	0.576320i
$727$	39.6695			1.47126			0.735630	−	0.677383i	$-0.236886\pi$
$727$	39.6695			1.47126			0.735630	+	0.677383i	$0.236886\pi$
$728$	78.1080	−	31.6034i	2.89487	−	1.17130i
$729$	1.00000			0.0370370
$730$	1.34991	−	2.33811i	0.0499623	−	0.0865372i
$731$	−0.561553	+	0.972638i	−0.0207698	+	0.0359743i
$732$	−27.6501	−	47.8914i	−1.02198	−	1.77012i
$733$	53.4924			1.97579			0.987894	−	0.155131i	$-0.0495801\pi$
$733$	53.4924			1.97579			0.987894	+	0.155131i	$0.0495801\pi$
$734$	−25.6847	−	44.4871i	−0.948038	−	1.64205i
$735$	−1.59612	−	2.76456i	−0.0588737	−	0.101972i
$736$	13.1231			0.483724
$737$	0.438447	+	0.759413i	0.0161504	+	0.0279733i
$738$	−3.28078	+	5.68247i	−0.120767	+	0.209175i
$739$	3.12311	−	5.40938i	0.114885	−	0.198987i	−0.802849	−	0.596183i	$-0.796683\pi$
$739$	3.12311	−	5.40938i	0.114885	−	0.198987i	0.917734	+	0.397196i	$0.130017\pi$
$740$	8.80776			0.323780
$741$	−0.561553	+	4.01029i	−0.0206292	+	0.147322i
$742$	−106.600			−3.91342
$743$	18.6847	−	32.3628i	0.685474	−	1.18728i	−0.287814	−	0.957686i	$-0.592929\pi$
$743$	18.6847	−	32.3628i	0.685474	−	1.18728i	0.973288	−	0.229589i	$-0.0737382\pi$
$744$	5.12311	−	8.87348i	0.187822	−	0.325318i
$745$	1.84233	+	3.19101i	0.0674977	+	0.116909i
$746$	9.30019			0.340504
$747$	4.56155	+	7.90084i	0.166898	+	0.289077i
$748$	11.6847	+	20.2384i	0.427233	+	0.739990i
$749$	−29.3693			−1.07313
$750$	6.96543	+	12.0645i	0.254342	+	0.440533i
$751$	15.0540	−	26.0743i	0.549327	−	0.951463i	−0.448993	−	0.893535i	$-0.648217\pi$
$751$	15.0540	−	26.0743i	0.549327	−	0.951463i	0.998321	−	0.0579278i	$-0.0184493\pi$
$752$	31.6847	−	54.8794i	1.15542	−	2.00125i
$753$	−30.7386			−1.12018
$754$	48.6695	−	19.6922i	1.77244	−	0.717149i
$755$	8.63068			0.314103
$756$	8.12311	−	14.0696i	0.295434	−	0.511708i
$757$	−15.0000	+	25.9808i	−0.545184	+	0.944287i	0.453411	+	0.891302i	$0.350207\pi$
$757$	−15.0000	+	25.9808i	−0.545184	+	0.944287i	−0.998595	+	0.0529853i	$0.983126\pi$
$758$	−14.4924	−	25.1016i	−0.526388	−	0.911732i
$759$	−4.00000			−0.145191
$760$	2.06913	+	3.58384i	0.0750552	+	0.129999i
$761$	7.68466	+	13.3102i	0.278569	+	0.482495i	0.971029	−	0.238961i	$-0.0768067\pi$
$761$	7.68466	+	13.3102i	0.278569	+	0.482495i	−0.692461	+	0.721456i	$0.743473\pi$
$762$	24.4924			0.887267
$763$	31.7116	+	54.9262i	1.14804	+	1.98846i
$764$	2.00000	−	3.46410i	0.0723575	−	0.125327i
$765$	−0.719224	+	1.24573i	−0.0260036	+	0.0450395i
$766$	68.4924			2.47473
$767$	37.1771	−	15.0423i	1.34239	−	0.543145i
$768$	−27.0540			−0.976226
$769$	9.00000	−	15.5885i	0.324548	−	0.562134i	−0.656873	−	0.754002i	$-0.728121\pi$
$769$	9.00000	−	15.5885i	0.324548	−	0.562134i	0.981421	+	0.191867i	$0.0614544\pi$
$770$	−5.12311	+	8.87348i	−0.184624	+	0.319778i
$771$	8.08854	+	14.0098i	0.291302	+	0.504549i
$772$	88.9157			3.20015
$773$	3.87689	+	6.71498i	0.139442	+	0.241521i	0.927286	−	0.374355i	$-0.122136\pi$
$773$	3.87689	+	6.71498i	0.139442	+	0.241521i	−0.787843	+	0.615876i	$0.788802\pi$
$774$	−0.561553	−	0.972638i	−0.0201846	−	0.0349608i
$775$	7.31534			0.262775
$776$	14.5616	+	25.2213i	0.522729	+	0.905394i
$777$	6.12311	−	10.6055i	0.219665	−	0.380471i
$778$	3.91146	−	6.77485i	0.140233	−	0.242890i
$779$	−2.87689			−0.103075
$780$	1.28078	−	9.14657i	0.0458592	−	0.327500i
$781$	−28.0000			−1.00192
$782$	−6.56155	+	11.3649i	−0.234641	+	0.406410i
$783$	2.84233	−	4.92306i	0.101577	−	0.175936i
$784$	−21.8423	−	37.8320i	−0.780083	−	1.35114i
$785$	−2.45360			−0.0875728
$786$	22.2462	+	38.5316i	0.793496	+	1.37438i
$787$	0.588540	+	1.01938i	0.0209792	+	0.0363370i	0.876324	−	0.481721i	$-0.159988\pi$
$787$	0.588540	+	1.01938i	0.0209792	+	0.0363370i	−0.855345	+	0.518058i	$0.826655\pi$
$788$	−51.8617			−1.84750
$789$	7.68466	+	13.3102i	0.273581	+	0.473856i
$790$	−6.87689	+	11.9111i	−0.244669	+	0.423779i
$791$	−26.3693	+	45.6730i	−0.937585	+	1.62394i
$792$	−13.1231			−0.466309
$793$	−40.5194	+	16.3946i	−1.43889	+	0.582190i
$794$	−30.8769			−1.09578
$795$	−3.28078	+	5.68247i	−0.116357	+	0.201536i
$796$	52.8617	−	91.5592i	1.87363	−	3.24523i
$797$	20.8078	+	36.0401i	0.737049	+	1.27661i	0.953819	+	0.300383i	$0.0971146\pi$
$797$	20.8078	+	36.0401i	0.737049	+	1.27661i	−0.216770	+	0.976223i	$0.569552\pi$
$798$	10.2462			0.362712
$799$	10.5616	+	18.2931i	0.373641	+	0.647165i
$800$	15.3693	+	26.6204i	0.543387	+	0.941175i
$801$	13.1231			0.463682
$802$	−23.7732	−	41.1764i	−0.839461	−	1.45399i
$803$	−1.87689	+	3.25088i	−0.0662342	+	0.114721i
$804$	−1.00000	+	1.73205i	−0.0352673	+	0.0610847i
$805$	−4.00000			−0.140981
$806$	−11.3693	−	8.87348i	−0.400467	−	0.312555i
$807$	3.36932			0.118606
$808$	11.2808	−	19.5389i	0.396856	−	0.687375i
$809$	−18.6501	+	32.3029i	−0.655702	+	1.13571i	0.326015	+	0.945365i	$0.394294\pi$
$809$	−18.6501	+	32.3029i	−0.655702	+	1.13571i	−0.981717	+	0.190345i	$0.939039\pi$
$810$	−0.719224	−	1.24573i	−0.0252709	−	0.0437706i
$811$	−1.56155			−0.0548335			−0.0274168	−	0.999624i	$-0.508728\pi$
$811$	−1.56155			−0.0548335			−0.0274168	+	0.999624i	$0.508728\pi$
$812$	−46.1771	−	79.9811i	−1.62050	−	2.80678i
$813$	0.534565	+	0.925894i	0.0187480	+	0.0324725i
$814$	−17.6155			−0.617424
$815$	−4.43845	−	7.68762i	−0.155472	−	0.269285i
$816$	−9.84233	+	17.0474i	−0.344550	+	0.596779i
$817$	0.246211	−	0.426450i	0.00861384	−	0.0149196i
$818$	−47.0540			−1.64520
$819$	−10.1231	−	7.90084i	−0.353730	−	0.276078i
$820$	6.56155			0.229139
$821$	13.2462	−	22.9431i	0.462296	−	0.800720i	−0.536779	−	0.843723i	$-0.680359\pi$
$821$	13.2462	−	22.9431i	0.462296	−	0.800720i	0.999075	+	0.0430028i	$0.0136924\pi$
$822$	1.84233	−	3.19101i	0.0642586	−	0.111299i
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$	−49.6155			−1.72844
$825$	−4.68466	−	8.11407i	−0.163099	−	0.282496i
$826$	−50.7386	−	87.8819i	−1.76542	−	3.05780i
$827$	34.7386			1.20798			0.603990	−	0.796992i	$-0.293577\pi$
$827$	34.7386			1.20798			0.603990	+	0.796992i	$0.293577\pi$
$828$	−4.56155	−	7.90084i	−0.158525	−	0.274573i
$829$	9.74621	−	16.8809i	0.338500	−	0.586299i	−0.645651	−	0.763633i	$-0.723414\pi$
$829$	9.74621	−	16.8809i	0.338500	−	0.586299i	0.984151	+	0.177334i	$0.0567472\pi$
$830$	6.56155	−	11.3649i	0.227755	−	0.394483i
$831$	17.6847			0.613474
$832$	0.719224	−	5.13628i	0.0249346	−	0.178069i
$833$	14.5616			0.504528
$834$	−14.0000	+	24.2487i	−0.484780	+	0.839664i
$835$	1.75379	−	3.03765i	0.0606924	−	0.105122i
$836$	−5.12311	−	8.87348i	−0.177186	−	0.306896i
$837$	−1.56155			−0.0539752
$838$	22.7386	+	39.3845i	0.785493	+	1.36051i
$839$	9.80776	+	16.9875i	0.338602	+	0.586475i	0.984170	−	0.177227i	$-0.0567128\pi$
$839$	9.80776	+	16.9875i	0.338602	+	0.586475i	−0.645568	+	0.763703i	$0.723379\pi$
$840$	−13.1231			−0.452790
$841$	−1.65767	−	2.87117i	−0.0571611	−	0.0990059i
$842$	−18.8963	+	32.7294i	−0.651210	+	1.12793i
$843$	1.40388	−	2.43160i	0.0483523	−	0.0837486i
$844$	33.3693			1.14862
$845$	−7.01941	−	2.00514i	−0.241475	−	0.0689791i
$846$	−21.1231			−0.726227
$847$	−12.4654	+	21.5908i	−0.428317	+	0.741868i
$848$	−44.8963	+	77.7627i	−1.54175	+	2.67038i
$849$	0.657671	+	1.13912i	0.0225712	+	0.0390945i
$850$	−30.7386			−1.05433
$851$	−3.43845	−	5.95557i	−0.117868	−	0.204154i
$852$	−31.9309	−	55.3059i	−1.09393	−	1.89475i
$853$	−6.12311			−0.209651			−0.104826	−	0.994491i	$-0.533428\pi$
$853$	−6.12311			−0.209651			−0.104826	+	0.994491i	$0.533428\pi$
$854$	55.3002	+	95.7827i	1.89233	+	3.27762i
$855$	0.315342	−	0.546188i	0.0107845	−	0.0186792i
$856$	−27.0540	+	46.8589i	−0.924686	+	1.60160i
$857$	31.4384			1.07392			0.536958	−	0.843609i	$-0.319573\pi$
$857$	31.4384			1.07392			0.536958	+	0.843609i	$0.319573\pi$
$858$	−2.56155	+	18.2931i	−0.0874500	+	0.624518i
$859$	20.4384			0.697351			0.348675	−	0.937244i	$-0.386632\pi$
$859$	20.4384			0.697351			0.348675	+	0.937244i	$0.386632\pi$
$860$	−0.561553	+	0.972638i	−0.0191488	+	0.0331667i
$861$	4.56155	−	7.90084i	0.155457	−	0.269260i
$862$	3.68466	+	6.38202i	0.125500	+	0.217372i
$863$	−2.49242			−0.0848430			−0.0424215	−	0.999100i	$-0.513507\pi$
$863$	−2.49242			−0.0848430			−0.0424215	+	0.999100i	$0.513507\pi$
$864$	−3.28078	−	5.68247i	−0.111614	−	0.193322i
$865$	−1.05398	−	1.82554i	−0.0358362	−	0.0620702i
$866$	64.6695			2.19756
$867$	5.21922	+	9.03996i	0.177254	+	0.307013i
$868$	−12.6847	+	21.9705i	−0.430545	+	0.745726i
$869$	9.56155	−	16.5611i	0.324353	−	0.561797i
$870$	−8.17708			−0.277229
$871$	1.24621	+	0.972638i	0.0422263	+	0.0329566i
$872$	116.847			3.95692
$873$	2.21922	−	3.84381i	0.0751093	−	0.130093i
$874$	2.87689	−	4.98293i	0.0973124	−	0.168550i
$875$	−9.68466	−	16.7743i	−0.327401	−	0.567076i
$876$	−8.56155			−0.289268
$877$	−9.71922	−	16.8342i	−0.328195	−	0.568450i	0.653959	−	0.756530i	$-0.273107\pi$
$877$	−9.71922	−	16.8342i	−0.328195	−	0.568450i	−0.982154	+	0.188080i	$0.939774\pi$
$878$	1.68466	+	2.91791i	0.0568545	+	0.0984748i
$879$	24.5616			0.828441
$880$	4.31534	+	7.47439i	0.145470	+	0.251962i
$881$	18.9654	−	32.8491i	0.638962	−	1.10671i	−0.346699	−	0.937976i	$-0.612698\pi$
$881$	18.9654	−	32.8491i	0.638962	−	1.10671i	0.985661	−	0.168738i	$-0.0539691\pi$
$882$	−7.28078	+	12.6107i	−0.245156	+	0.424624i
$883$	−11.8078			−0.397363			−0.198681	−	0.980064i	$-0.563666\pi$
$883$	−11.8078			−0.397363			−0.198681	+	0.980064i	$0.563666\pi$
$884$	33.2116	+	25.9209i	1.11703	+	0.871814i
$885$	−6.24621			−0.209964
$886$	−18.8769	+	32.6957i	−0.634182	+	1.09843i
$887$	−24.6847	+	42.7551i	−0.828830	+	1.43558i	0.0701272	+	0.997538i	$0.477659\pi$
$887$	−24.6847	+	42.7551i	−0.828830	+	1.43558i	−0.898957	+	0.438037i	$0.855674\pi$
$888$	−11.2808	−	19.5389i	−0.378558	−	0.655682i
$889$	−34.0540			−1.14213
$890$	−9.43845	−	16.3479i	−0.316377	−	0.547982i
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	36.4924			1.22186
$893$	−4.63068	−	8.02058i	−0.154960	−	0.268398i
$894$	8.40388	−	14.5560i	0.281068	−	0.486824i
$895$	3.68466	−	6.38202i	0.123165	−	0.213327i
$896$	33.6155			1.12302
$897$	−6.68466	+	2.70469i	−0.223194	+	0.0903069i
$898$	21.1231			0.704887
$899$	−4.43845	+	7.68762i	−0.148031	+	0.256396i
$900$	10.6847	−	18.5064i	0.356155	−	0.616879i
$901$	−14.9654	−	25.9209i	−0.498571	−	0.863550i
$902$	−13.1231			−0.436952
$903$	0.780776	+	1.35234i	0.0259826	+	0.0450032i
$904$	48.5810	+	84.1447i	1.61578	+	2.79861i
$905$	5.43845			0.180780
$906$	−19.6847	−	34.0948i	−0.653979	−	1.13272i
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$	2.56155	−	4.43674i	0.0850081	−	0.147238i
$909$	−3.43845			−0.114046
$910$	−2.56155	+	18.2931i	−0.0849146	+	0.606412i
$911$	−10.7386			−0.355787			−0.177893	−	0.984050i	$-0.556928\pi$
$911$	−10.7386			−0.355787			−0.177893	+	0.984050i	$0.556928\pi$
$912$	4.31534	−	7.47439i	0.142895	−	0.247502i
$913$	−9.12311	+	15.8017i	−0.301931	+	0.522959i
$914$	36.6501	+	63.4798i	1.21228	+	2.09973i
$915$	6.80776			0.225058
$916$	−0.561553	−	0.972638i	−0.0185542	−	0.0321369i
$917$	−30.9309	−	53.5738i	−1.02143	−	1.76916i
$918$	6.56155			0.216564
$919$	−22.2462	−	38.5316i	−0.733835	−	1.27104i	−0.955233	−	0.295856i	$-0.904395\pi$
$919$	−22.2462	−	38.5316i	−0.733835	−	1.27104i	0.221398	−	0.975184i	$-0.428938\pi$
$920$	−3.68466	+	6.38202i	−0.121480	+	0.210409i
$921$	−5.09612	+	8.82674i	−0.167923	+	0.290851i
$922$	−94.2850			−3.10511
$923$	−46.7926	+	18.9328i	−1.54020	+	0.623181i
$924$	32.4924			1.06892
$925$	8.05398	−	13.9499i	0.264813	−	0.458670i
$926$	34.1771	−	59.1964i	1.12313	−	1.94532i
$927$	3.78078	+	6.54850i	0.124177	+	0.215081i
$928$	−37.3002			−1.22444
$929$	−6.40388	−	11.0918i	−0.210105	−	0.363912i	0.741643	−	0.670795i	$-0.234047\pi$
$929$	−6.40388	−	11.0918i	−0.210105	−	0.363912i	−0.951747	+	0.306884i	$0.900714\pi$
$930$	1.12311	+	1.94528i	0.0368281	+	0.0637881i
$931$	−6.38447			−0.209243
$932$	−59.3002	−	102.711i	−1.94244	−	3.36441i
$933$	5.43845	−	9.41967i	0.178047	−	0.308386i
$934$	33.3002	−	57.6776i	1.08962	−	1.88727i
$935$	−2.87689			−0.0940845
$936$	−21.9309	+	8.87348i	−0.716833	+	0.290039i
$937$	−3.43845			−0.112329			−0.0561646	−	0.998422i	$-0.517887\pi$
$937$	−3.43845			−0.112329			−0.0561646	+	0.998422i	$0.517887\pi$
$938$	2.00000	−	3.46410i	0.0653023	−	0.113107i
$939$	0.657671	−	1.13912i	0.0214623	−	0.0371738i
$940$	10.5616	+	18.2931i	0.344480	+	0.596657i
$941$	−2.49242			−0.0812507			−0.0406253	−	0.999174i	$-0.512935\pi$
$941$	−2.49242			−0.0812507			−0.0406253	+	0.999174i	$0.512935\pi$
$942$	5.59612	+	9.69276i	0.182331	+	0.315807i
$943$	−2.56155	−	4.43674i	−0.0834156	−	0.144480i
$944$	−85.4773			−2.78205
$945$	1.00000	+	1.73205i	0.0325300	+	0.0563436i
$946$	1.12311	−	1.94528i	0.0365153	−	0.0632464i
$947$	−5.36932	+	9.29993i	−0.174479	+	0.302207i	−0.939981	−	0.341227i	$-0.889158\pi$
$947$	−5.36932	+	9.29993i	−0.174479	+	0.302207i	0.765502	+	0.643434i	$0.222491\pi$
$948$	43.6155			1.41657
$949$	−0.938447	+	6.70185i	−0.0304633	+	0.217551i
$950$	13.4773			0.437260
$951$	11.5270	−	19.9653i	0.373788	−	0.647420i
$952$	29.9309	−	51.8418i	0.970065	−	1.68020i
$953$	17.4924	+	30.2978i	0.566635	+	0.981441i	0.996896	+	0.0787360i	$0.0250884\pi$
$953$	17.4924	+	30.2978i	0.566635	+	0.981441i	−0.430260	+	0.902705i	$0.641578\pi$
$954$	29.9309			0.969048
$955$	0.246211	+	0.426450i	0.00796721	+	0.0137996i
$956$	1.43845	+	2.49146i	0.0465227	+	0.0805797i
$957$	11.3693			0.367518
$958$	8.00000	+	13.8564i	0.258468	+	0.447680i
$959$	−2.56155	+	4.43674i	−0.0827169	+	0.143270i
$960$	−0.403882	+	0.699544i	−0.0130352	+	0.0225777i
$961$	−28.5616			−0.921340
$962$	−29.4384	+	11.9111i	−0.949134	+	0.384030i
$963$	8.24621			0.265730
$964$	−6.40388	+	11.0918i	−0.206255	+	0.357244i
$965$	−5.47301	+	9.47954i	−0.176183	+	0.305157i
$966$	9.12311	+	15.8017i	0.293531	+	0.508411i
$967$	−9.12311			−0.293379			−0.146690	−	0.989183i	$-0.546862\pi$
$967$	−9.12311			−0.293379			−0.146690	+	0.989183i	$0.546862\pi$
$968$	22.9654	+	39.7773i	0.738137	+	1.27849i
$969$	1.43845	+	2.49146i	0.0462096	+	0.0800373i
$970$	−6.38447			−0.204993
$971$	−26.4924	−	45.8862i	−0.850182	−	1.47256i	−0.881043	−	0.473035i	$-0.843158\pi$
$971$	−26.4924	−	45.8862i	−0.850182	−	1.47256i	0.0308612	−	0.999524i	$-0.490175\pi$
$972$	−2.28078	+	3.95042i	−0.0731559	+	0.126710i
$973$	19.4654	−	33.7151i	0.624033	−	1.08086i
$974$	−2.87689			−0.0921816
$975$	−13.3153	−	10.3923i	−0.426432	−	0.332820i
$976$	93.1619			2.98204
$977$	−7.91146	+	13.7030i	−0.253110	+	0.438399i	−0.964380	−	0.264519i	$-0.914787\pi$
$977$	−7.91146	+	13.7030i	−0.253110	+	0.438399i	0.711270	+	0.702918i	$0.248120\pi$
$978$	−20.2462	+	35.0675i	−0.647402	+	1.12133i
$979$	13.1231	+	22.7299i	0.419416	+	0.726450i
$980$	14.5616			0.465152
$981$	−8.90388	−	15.4220i	−0.284279	−	0.492386i
$982$	25.3002	+	43.8212i	0.807361	+	1.39839i
$983$	−27.6155			−0.880799			−0.440399	−	0.897802i	$-0.645163\pi$
$983$	−27.6155			−0.880799			−0.440399	+	0.897802i	$0.645163\pi$
$984$	−8.40388	−	14.5560i	−0.267906	−	0.464027i
$985$	3.19224	−	5.52911i	0.101713	−	0.176172i
$986$	18.6501	−	32.3029i	0.593940	−	1.02873i
$987$	29.3693			0.934836
$988$	−14.5616	−	11.3649i	−0.463265	−	0.361567i
$989$	0.876894			0.0278836
$990$	1.43845	−	2.49146i	0.0457169	−	0.0791839i
$991$	−20.1771	+	34.9477i	−0.640946	+	1.11015i	0.344276	+	0.938869i	$0.388124\pi$
$991$	−20.1771	+	34.9477i	−0.640946	+	1.11015i	−0.985222	+	0.171283i	$0.945209\pi$
$992$	5.12311	+	8.87348i	0.162659	+	0.281733i
$993$	−23.8078			−0.755517
$994$	63.8617	+	110.612i	2.02557	+	3.50839i
$995$	6.50758	+	11.2715i	0.206304	+	0.357329i
$996$	−41.6155			−1.31864
$997$	−10.3078	−	17.8536i	−0.326450	−	0.565428i	0.655355	−	0.755321i	$-0.272519\pi$
$997$	−10.3078	−	17.8536i	−0.326450	−	0.565428i	−0.981805	+	0.189893i	$0.939186\pi$
$998$	36.4924	−	63.2067i	1.15515	−	2.00077i
$999$	−1.71922	+	2.97778i	−0.0543938	+	0.0942129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.2.e.b.22.1	yes	4
3.2	odd	2		117.2.g.c.100.2		4
4.3	odd	2		624.2.q.h.529.2		4
5.2	odd	4		975.2.bb.i.724.1		8
5.3	odd	4		975.2.bb.i.724.4		8
5.4	even	2		975.2.i.k.451.2		4
12.11	even	2		1872.2.t.r.1153.1		4
13.2	odd	12		507.2.j.g.361.1		8
13.3	even	3	inner	39.2.e.b.16.1	✓	4
13.4	even	6		507.2.a.d.1.1		2
13.5	odd	4		507.2.j.g.316.4		8
13.6	odd	12		507.2.b.d.337.1		4
13.7	odd	12		507.2.b.d.337.4		4
13.8	odd	4		507.2.j.g.316.1		8
13.9	even	3		507.2.a.g.1.2		2
13.10	even	6		507.2.e.g.484.2		4
13.11	odd	12		507.2.j.g.361.4		8
13.12	even	2		507.2.e.g.22.2		4
39.17	odd	6		1521.2.a.m.1.2		2
39.20	even	12		1521.2.b.h.1351.1		4
39.29	odd	6		117.2.g.c.55.2		4
39.32	even	12		1521.2.b.h.1351.4		4
39.35	odd	6		1521.2.a.g.1.1		2
52.3	odd	6		624.2.q.h.289.2		4
52.35	odd	6		8112.2.a.bk.1.2		2
52.43	odd	6		8112.2.a.bo.1.1		2
65.3	odd	12		975.2.bb.i.874.1		8
65.29	even	6		975.2.i.k.601.2		4
65.42	odd	12		975.2.bb.i.874.4		8
156.107	even	6		1872.2.t.r.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.1	✓	4	13.3	even	3	inner
39.2.e.b.22.1	yes	4	1.1	even	1	trivial
117.2.g.c.55.2		4	39.29	odd	6
117.2.g.c.100.2		4	3.2	odd	2
507.2.a.d.1.1		2	13.4	even	6
507.2.a.g.1.2		2	13.9	even	3
507.2.b.d.337.1		4	13.6	odd	12
507.2.b.d.337.4		4	13.7	odd	12
507.2.e.g.22.2		4	13.12	even	2
507.2.e.g.484.2		4	13.10	even	6
507.2.j.g.316.1		8	13.8	odd	4
507.2.j.g.316.4		8	13.5	odd	4
507.2.j.g.361.1		8	13.2	odd	12
507.2.j.g.361.4		8	13.11	odd	12
624.2.q.h.289.2		4	52.3	odd	6
624.2.q.h.529.2		4	4.3	odd	2
975.2.i.k.451.2		4	5.4	even	2
975.2.i.k.601.2		4	65.29	even	6
975.2.bb.i.724.1		8	5.2	odd	4
975.2.bb.i.724.4		8	5.3	odd	4
975.2.bb.i.874.1		8	65.3	odd	12
975.2.bb.i.874.4		8	65.42	odd	12
1521.2.a.g.1.1		2	39.35	odd	6
1521.2.a.m.1.2		2	39.17	odd	6
1521.2.b.h.1351.1		4	39.20	even	12
1521.2.b.h.1351.4		4	39.32	even	12
1872.2.t.r.289.1		4	156.107	even	6
1872.2.t.r.1153.1		4	12.11	even	2
8112.2.a.bk.1.2		2	52.35	odd	6
8112.2.a.bo.1.1		2	52.43	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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	39.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28078 + 2.21837i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} +0.561553 q^{5} +(-1.28078 - 2.21837i) q^{6} +(1.78078 + 3.08440i) q^{7} +6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.28078 + 2.21837i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.28078 - 3.95042i) q^{4} +0.561553 q^{5} +(-1.28078 - 2.21837i) q^{6} +(1.78078 + 3.08440i) q^{7} +6.56155 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.719224 + 1.24573i) q^{10} +(1.00000 - 1.73205i) q^{11} +4.56155 q^{12} +(0.500000 - 3.57071i) q^{13} -9.12311 q^{14} +(-0.280776 + 0.486319i) q^{15} +(-3.84233 + 6.65511i) q^{16} +(-1.28078 - 2.21837i) q^{17} +2.56155 q^{18} +(0.561553 + 0.972638i) q^{19} +(-1.28078 - 2.21837i) q^{20} -3.56155 q^{21} +(2.56155 + 4.43674i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(-3.28078 + 5.68247i) q^{24} -4.68466 q^{25} +(7.28078 + 5.68247i) q^{26} +1.00000 q^{27} +(8.12311 - 14.0696i) q^{28} +(2.84233 - 4.92306i) q^{29} +(-0.719224 - 1.24573i) q^{30} -1.56155 q^{31} +(-3.28078 - 5.68247i) q^{32} +(1.00000 + 1.73205i) q^{33} +6.56155 q^{34} +(1.00000 + 1.73205i) q^{35} +(-2.28078 + 3.95042i) q^{36} +(-1.71922 + 2.97778i) q^{37} -2.87689 q^{38} +(2.84233 + 2.21837i) q^{39} +3.68466 q^{40} +(-1.28078 + 2.21837i) q^{41} +(4.56155 - 7.90084i) q^{42} +(-0.219224 - 0.379706i) q^{43} -9.12311 q^{44} +(-0.280776 - 0.486319i) q^{45} +(-2.56155 - 4.43674i) q^{46} -8.24621 q^{47} +(-3.84233 - 6.65511i) q^{48} +(-2.84233 + 4.92306i) q^{49} +(6.00000 - 10.3923i) q^{50} +2.56155 q^{51} +(-15.2462 + 6.16879i) q^{52} +11.6847 q^{53} +(-1.28078 + 2.21837i) q^{54} +(0.561553 - 0.972638i) q^{55} +(11.6847 + 20.2384i) q^{56} -1.12311 q^{57} +(7.28078 + 12.6107i) q^{58} +(5.56155 + 9.63289i) q^{59} +2.56155 q^{60} +(-6.06155 - 10.4989i) q^{61} +(2.00000 - 3.46410i) q^{62} +(1.78078 - 3.08440i) q^{63} +1.43845 q^{64} +(0.280776 - 2.00514i) q^{65} -5.12311 q^{66} +(-0.219224 + 0.379706i) q^{67} +(-5.84233 + 10.1192i) q^{68} +(-1.00000 - 1.73205i) q^{69} -5.12311 q^{70} +(-7.00000 - 12.1244i) q^{71} +(-3.28078 - 5.68247i) q^{72} -1.87689 q^{73} +(-4.40388 - 7.62775i) q^{74} +(2.34233 - 4.05703i) q^{75} +(2.56155 - 4.43674i) q^{76} +7.12311 q^{77} +(-8.56155 + 3.46410i) q^{78} +9.56155 q^{79} +(-2.15767 + 3.73720i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.28078 - 5.68247i) q^{82} -9.12311 q^{83} +(8.12311 + 14.0696i) q^{84} +(-0.719224 - 1.24573i) q^{85} +1.12311 q^{86} +(2.84233 + 4.92306i) q^{87} +(6.56155 - 11.3649i) q^{88} +(-6.56155 + 11.3649i) q^{89} +1.43845 q^{90} +(11.9039 - 4.81645i) q^{91} +9.12311 q^{92} +(0.780776 - 1.35234i) q^{93} +(10.5616 - 18.2931i) q^{94} +(0.315342 + 0.546188i) q^{95} +6.56155 q^{96} +(2.21922 + 3.84381i) q^{97} +(-7.28078 - 12.6107i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 2 q^{3} - 5 q^{4} - 6 q^{5} - q^{6} + 3 q^{7} + 18 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - q^2 - 2 * q^3 - 5 * q^4 - 6 * q^5 - q^6 + 3 * q^7 + 18 * q^8 - 2 * q^9	\( 4 q - q^{2} - 2 q^{3} - 5 q^{4} - 6 q^{5} - q^{6} + 3 q^{7} + 18 q^{8} - 2 q^{9} - 7 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 20 q^{14} + 3 q^{15} - 3 q^{16} - q^{17} + 2 q^{18} - 6 q^{19} - q^{20} - 6 q^{21} + 2 q^{22} - 4 q^{23} - 9 q^{24} + 6 q^{25} + 25 q^{26} + 4 q^{27} + 16 q^{28} - q^{29} - 7 q^{30} + 2 q^{31} - 9 q^{32} + 4 q^{33} + 18 q^{34} + 4 q^{35} - 5 q^{36} - 11 q^{37} - 28 q^{38} - q^{39} - 10 q^{40} - q^{41} + 10 q^{42} - 5 q^{43} - 20 q^{44} + 3 q^{45} - 2 q^{46} - 3 q^{48} + q^{49} + 24 q^{50} + 2 q^{51} - 28 q^{52} + 22 q^{53} - q^{54} - 6 q^{55} + 22 q^{56} + 12 q^{57} + 25 q^{58} + 14 q^{59} + 2 q^{60} - 16 q^{61} + 8 q^{62} + 3 q^{63} + 14 q^{64} - 3 q^{65} - 4 q^{66} - 5 q^{67} - 11 q^{68} - 4 q^{69} - 4 q^{70} - 28 q^{71} - 9 q^{72} - 24 q^{73} + 3 q^{74} - 3 q^{75} + 2 q^{76} + 12 q^{77} - 26 q^{78} + 30 q^{79} - 21 q^{80} - 2 q^{81} - 9 q^{82} - 20 q^{83} + 16 q^{84} - 7 q^{85} - 12 q^{86} - q^{87} + 18 q^{88} - 18 q^{89} + 14 q^{90} + 27 q^{91} + 20 q^{92} - q^{93} + 34 q^{94} + 26 q^{95} + 18 q^{96} + 13 q^{97} - 25 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 - 5 * q^4 - 6 * q^5 - q^6 + 3 * q^7 + 18 * q^8 - 2 * q^9 - 7 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 20 * q^14 + 3 * q^15 - 3 * q^16 - q^17 + 2 * q^18 - 6 * q^19 - q^20 - 6 * q^21 + 2 * q^22 - 4 * q^23 - 9 * q^24 + 6 * q^25 + 25 * q^26 + 4 * q^27 + 16 * q^28 - q^29 - 7 * q^30 + 2 * q^31 - 9 * q^32 + 4 * q^33 + 18 * q^34 + 4 * q^35 - 5 * q^36 - 11 * q^37 - 28 * q^38 - q^39 - 10 * q^40 - q^41 + 10 * q^42 - 5 * q^43 - 20 * q^44 + 3 * q^45 - 2 * q^46 - 3 * q^48 + q^49 + 24 * q^50 + 2 * q^51 - 28 * q^52 + 22 * q^53 - q^54 - 6 * q^55 + 22 * q^56 + 12 * q^57 + 25 * q^58 + 14 * q^59 + 2 * q^60 - 16 * q^61 + 8 * q^62 + 3 * q^63 + 14 * q^64 - 3 * q^65 - 4 * q^66 - 5 * q^67 - 11 * q^68 - 4 * q^69 - 4 * q^70 - 28 * q^71 - 9 * q^72 - 24 * q^73 + 3 * q^74 - 3 * q^75 + 2 * q^76 + 12 * q^77 - 26 * q^78 + 30 * q^79 - 21 * q^80 - 2 * q^81 - 9 * q^82 - 20 * q^83 + 16 * q^84 - 7 * q^85 - 12 * q^86 - q^87 + 18 * q^88 - 18 * q^89 + 14 * q^90 + 27 * q^91 + 20 * q^92 - q^93 + 34 * q^94 + 26 * q^95 + 18 * q^96 + 13 * q^97 - 25 * q^98 - 8 * q^99

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