LMFDB - Embedded newform 507.2.e.g.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(22,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("507.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.e (of order $3$, degree $2$, not 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:	$4.04841538248$
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:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$1.28078 - 2.21837i$ of defining polynomial
Character	$\chi$	$=$	507.22
Dual form			507.2.e.g.484.2

$q$-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} -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} +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} +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} +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} -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} +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} +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} - 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} + 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} - 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} + 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} - 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} + 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} + 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 - 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 + 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 - 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 + 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 - 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 + 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 + 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	$-0.472720\pi$
$2$	1.28078	−	2.21837i	0.905646	−	1.56862i	0.820048	−	0.572295i	$-0.193947\pi$
$3$	−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	$-0.540075\pi$
$5$	−0.561553			−0.251134			−0.125567	+	0.992085i	$0.540075\pi$
$6$	1.28078	+	2.21837i	0.522875	+	0.905646i
$7$	−1.78078	−	3.08440i	−0.673070	−	1.16579i	−0.977029	−	0.213107i	$-0.931642\pi$
$7$	−1.78078	−	3.08440i	−0.673070	−	1.16579i	0.303959	−	0.952685i	$-0.401692\pi$
$8$	−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	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	4.56155			1.31681
$13$		0			0
$13$		0			0
$14$	−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	0.794394	−	0.607403i	$-0.207789\pi$
$19$	−0.561553	−	0.972638i	−0.128829	−	0.223138i	−0.923223	+	0.384264i	$0.874455\pi$
$20$	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
$26$		0			0
$27$	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	$-0.455215\pi$
$31$	1.56155			0.280463			0.140232	+	0.990119i	$0.455215\pi$
$32$	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	−0.689395	−	0.724385i	$-0.742124\pi$
$37$	1.71922	−	2.97778i	0.282639	−	0.489544i	0.972034	+	0.234841i	$0.0754570\pi$
$38$	−2.87689			−0.466694
$39$		0			0
$40$	3.68466			0.582596
$41$	1.28078	−	2.21837i	0.200024	−	0.346451i	−0.748512	−	0.663121i	$-0.769231\pi$
$41$	1.28078	−	2.21837i	0.200024	−	0.346451i	0.948536	+	0.316670i	$0.102565\pi$
$42$	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	$-0.294603\pi$
$47$	8.24621			1.20283			0.601417	+	0.798935i	$0.294603\pi$
$48$	−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
$52$		0			0
$53$	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	$-0.908944\pi$
$59$	−5.56155	−	9.63289i	−0.724053	−	1.25410i	0.235310	−	0.971920i	$-0.424389\pi$
$60$	−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			0
$66$	−5.12311			−0.630611
$67$	0.219224	−	0.379706i	0.0267824	−	0.0463885i	−0.852324	−	0.523015i	$-0.824807\pi$
$67$	0.219224	−	0.379706i	0.0267824	−	0.0463885i	0.879106	+	0.476626i	$0.158141\pi$
$68$	−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	$0.145420\pi$
$71$	7.00000	+	12.1244i	0.830747	+	1.43890i	−0.0666994	+	0.997773i	$0.521247\pi$
$72$	3.28078	+	5.68247i	0.386643	+	0.669686i
$73$	1.87689			0.219674			0.109837	−	0.993950i	$-0.464967\pi$
$73$	1.87689			0.219674			0.109837	+	0.993950i	$0.464967\pi$
$74$	−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
$78$		0			0
$79$	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	$-0.333078\pi$
$83$	9.12311			1.00139			0.500695	+	0.865624i	$0.333078\pi$
$84$	−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	$-0.588506\pi$
$89$	6.56155	−	11.3649i	0.695523	−	1.20468i	0.970004	−	0.243089i	$-0.0781607\pi$
$90$	1.43845			0.151626
$91$		0			0
$92$	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	0.731090	−	0.682281i	$-0.239012\pi$
$97$	−2.21922	−	3.84381i	−0.225328	−	0.390280i	−0.956418	+	0.292002i	$0.905679\pi$
$98$	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	$0.621510\pi$
$104$		0			0
$105$	−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	$-0.825120\pi$
$109$	−17.8078			−1.70567			−0.852837	+	0.522177i	$0.825120\pi$
$110$	−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
$117$		0			0
$118$	−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
$130$		0			0
$131$	−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	0.833665	−	0.552270i	$-0.186238\pi$
$137$	−0.719224	−	1.24573i	−0.0614474	−	0.106430i	−0.895113	+	0.445840i	$0.852905\pi$
$138$	−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
$143$		0			0
$144$	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	0.699773	−	0.714365i	$-0.253284\pi$
$149$	−3.28078	−	5.68247i	−0.268772	−	0.465526i	−0.968545	+	0.248839i	$0.919951\pi$
$150$	−6.00000	−	10.3923i	−0.489898	−	0.848528i
$151$	−15.3693			−1.25074			−0.625369	−	0.780329i	$-0.715051\pi$
$151$	−15.3693			−1.25074			−0.625369	+	0.780329i	$0.715051\pi$
$152$	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
$156$		0			0
$157$	−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	$0.0458276\pi$
$163$	7.90388	+	13.6899i	0.619080	+	1.07228i	−0.370574	+	0.928803i	$0.620839\pi$
$164$	−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	−0.961191	−	0.275884i	$-0.911030\pi$
$167$	−3.12311	+	5.40938i	−0.241673	+	0.418590i	0.719518	+	0.694474i	$0.244363\pi$
$168$	−23.3693			−1.80298
$169$		0			0
$170$	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	$0.382801\pi$
$182$		0			0
$183$	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	$-0.585826\pi$
$193$	9.74621	−	16.8809i	0.701548	−	1.21512i	0.967923	−	0.251247i	$-0.0808406\pi$
$194$	−11.3693			−0.816269
$195$		0			0
$196$	25.9309			1.85220
$197$	−5.68466	+	9.84612i	−0.405015	+	0.701507i	−0.994323	−	0.106402i	$-0.966067\pi$
$197$	−5.68466	+	9.84612i	−0.405015	+	0.701507i	0.589308	+	0.807908i	$0.299400\pi$
$198$	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
$208$		0			0
$209$	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
$221$		0			0
$222$	8.80776			0.591138
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$	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	0.846788	−	0.531931i	$-0.178533\pi$
$227$	−0.561553	−	0.972638i	−0.0372716	−	0.0645563i	−0.884059	+	0.467374i	$0.845200\pi$
$228$	−2.56155	−	4.43674i	−0.169643	−	0.293830i
$229$	−0.246211			−0.0162701			−0.00813505	−	0.999967i	$-0.502589\pi$
$229$	−0.246211			−0.0162701			−0.00813505	+	0.999967i	$0.502589\pi$
$230$	−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	$0.175597\pi$
$234$		0			0
$235$	−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	$-0.493507\pi$
$239$	0.630683			0.0407955			0.0203977	+	0.999792i	$0.493507\pi$
$240$	2.15767	+	3.73720i	0.139277	+	0.241235i
$241$	1.40388	+	2.43160i	0.0904320	+	0.156633i	0.907693	−	0.419635i	$-0.137842\pi$
$241$	1.40388	+	2.43160i	0.0904320	+	0.156633i	−0.817261	+	0.576268i	$0.804509\pi$
$242$	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
$247$		0			0
$248$	−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
$260$		0			0
$261$	−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	−0.881805	−	0.471614i	$-0.843671\pi$
$271$	−0.534565	+	0.925894i	−0.0324725	+	0.0562441i	0.849332	+	0.527858i	$0.177005\pi$
$272$	19.6847			1.19356
$273$		0			0
$274$	−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	$-0.473311\pi$
$281$	2.80776			0.167497			0.0837486	+	0.996487i	$0.473311\pi$
$282$	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
$286$		0			0
$287$	−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	$0.0880244\pi$
$293$	12.2808	+	21.2709i	0.717451	+	1.24266i	−0.244556	+	0.969635i	$0.578642\pi$
$294$	−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
$299$		0			0
$300$	−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	$-0.593938\pi$
$307$	−10.1922			−0.581702			−0.290851	+	0.956768i	$0.593938\pi$
$308$	−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	$0.599789\pi$
$312$		0			0
$313$	−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	$-0.275848\pi$
$317$	23.0540			1.29484			0.647420	+	0.762133i	$0.275848\pi$
$318$	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
$325$		0			0
$326$	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	$-0.939631\pi$
$331$	−11.9039	−	20.6181i	−0.654297	−	1.13327i	0.327773	−	0.944756i	$-0.393702\pi$
$332$	−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	$0.481583\pi$
$338$		0			0
$339$	−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	−0.989496	−	0.144559i	$-0.953824\pi$
$349$	−6.90388	+	11.9579i	−0.369556	+	0.640090i	0.619940	+	0.784649i	$0.287157\pi$
$350$	42.7386			2.28448
$351$		0			0
$352$	−13.1231			−0.699464
$353$	8.84233	−	15.3154i	0.470630	−	0.815155i	−0.528806	−	0.848743i	$-0.677360\pi$
$353$	8.84233	−	15.3154i	0.470630	−	0.815155i	0.999436	+	0.0335881i	$0.0106934\pi$
$354$	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	$-0.632931\pi$
$359$	−15.3693			−0.811162			−0.405581	+	0.914059i	$0.632931\pi$
$360$	−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
$364$		0			0
$365$	−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
$377$		0			0
$378$	−9.12311			−0.469242
$379$	5.65767	−	9.79937i	0.290615	−	0.503360i	−0.683340	−	0.730100i	$-0.739473\pi$
$379$	5.65767	−	9.79937i	0.290615	−	0.503360i	0.973955	+	0.226740i	$0.0728068\pi$
$380$	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	$0.0727195\pi$
$383$	13.3693	+	23.1563i	0.683140	+	1.18323i	−0.290877	+	0.956760i	$0.593947\pi$
$384$	−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	$0.524669\pi$
$390$		0			0
$391$	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	0.674213	−	0.738537i	$-0.264483\pi$
$397$	−6.02699	−	10.4390i	−0.302486	−	0.523921i	−0.976698	+	0.214617i	$0.931150\pi$
$398$	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	−0.535671	−	0.844427i	$-0.679941\pi$
$401$	9.28078	−	16.0748i	0.463460	−	0.802736i	0.999131	+	0.0416909i	$0.0132745\pi$
$402$	1.12311			0.0560154
$403$		0			0
$404$	−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	0.544487	−	0.838769i	$-0.316724\pi$
$409$	−9.18466	−	15.9083i	−0.454152	−	0.786615i	−0.998639	+	0.0521548i	$0.983391\pi$
$410$	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
$416$		0			0
$417$	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	$-0.617062\pi$
$421$	−14.7538			−0.719056			−0.359528	+	0.933134i	$0.617062\pi$
$422$	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
$429$		0			0
$430$	0.630683			0.0304142
$431$	−1.43845	+	2.49146i	−0.0692876	+	0.120010i	−0.898588	−	0.438794i	$-0.855406\pi$
$431$	−1.43845	+	2.49146i	−0.0692876	+	0.120010i	0.829300	+	0.558803i	$0.188739\pi$
$432$	−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
$442$		0			0
$443$	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	0.946763	−	0.321931i	$-0.104332\pi$
$449$	4.12311	+	7.14143i	0.194581	+	0.337025i	−0.752182	+	0.658956i	$0.770998\pi$
$450$	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
$455$		0			0
$456$	−7.36932			−0.345100
$457$	−14.3078	+	24.7818i	−0.669289	+	1.15924i	0.308814	+	0.951122i	$0.400068\pi$
$457$	−14.3078	+	24.7818i	−0.669289	+	1.15924i	−0.978103	+	0.208120i	$0.933265\pi$
$458$	−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	$-0.838897\pi$
$461$	−18.4039	−	31.8765i	−0.857154	−	1.48463i	0.0174778	−	0.999847i	$-0.494436\pi$
$462$	9.12311	+	15.8017i	0.424445	+	0.735161i
$463$	26.6847			1.24014			0.620071	−	0.784546i	$-0.287104\pi$
$463$	26.6847			1.24014			0.620071	+	0.784546i	$0.287104\pi$
$464$	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	$0.705457\pi$
$468$		0			0
$469$	−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	−0.928512	−	0.371303i	$-0.878911\pi$
$479$	−3.12311	+	5.40938i	−0.142698	+	0.247161i	0.785814	+	0.618463i	$0.212245\pi$
$480$	3.68466			0.168181
$481$		0			0
$482$	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	0.853022	−	0.521875i	$-0.174767\pi$
$487$	−0.561553	−	0.972638i	−0.0254464	−	0.0440744i	−0.878468	+	0.477801i	$0.841434\pi$
$488$	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
$494$		0			0
$495$	−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	$-0.279866\pi$
$499$	28.4924			1.27550			0.637748	+	0.770245i	$0.279866\pi$
$500$	−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
$507$		0			0
$508$	43.6155			1.93513
$509$	3.40388	−	5.89570i	0.150874	−	0.261322i	−0.780675	−	0.624938i	$-0.785124\pi$
$509$	3.40388	−	5.89570i	0.150874	−	0.261322i	0.931549	+	0.363615i	$0.118458\pi$
$510$	−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
$520$		0			0
$521$	−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
$533$		0			0
$534$	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	$-0.279232\pi$
$541$	29.7386			1.27856			0.639282	+	0.768972i	$0.279232\pi$
$542$	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
$546$		0			0
$547$	−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	−0.975693	−	0.219142i	$-0.929674\pi$
$557$	−7.03457	+	12.1842i	−0.298064	+	0.516262i	0.677629	+	0.735404i	$0.263008\pi$
$558$	−4.00000			−0.169334
$559$		0			0
$560$	−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	$0.367170\pi$
$572$		0			0
$573$	−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	$-0.287986\pi$
$577$	29.6847			1.23579			0.617894	+	0.786261i	$0.287986\pi$
$578$	−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
$585$		0			0
$586$	62.9157			2.59902
$587$	7.31534	−	12.6705i	0.301936	−	0.522969i	−0.674638	−	0.738149i	$-0.735700\pi$
$587$	7.31534	−	12.6705i	0.301936	−	0.522969i	0.976575	+	0.215179i	$0.0690336\pi$
$588$	−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	$-0.865558\pi$
$593$	−44.4233			−1.82425			−0.912123	+	0.409917i	$0.865558\pi$
$594$	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
$598$		0			0
$599$	−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
$611$		0			0
$612$	11.6847			0.472324
$613$	11.4309	−	19.7988i	0.461688	−	0.799668i	−0.537357	−	0.843355i	$-0.680577\pi$
$613$	11.4309	−	19.7988i	0.461688	−	0.799668i	0.999045	+	0.0436871i	$0.0139105\pi$
$614$	−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	0.736507	−	0.676430i	$-0.236474\pi$
$617$	−5.40388	−	9.35980i	−0.217552	−	0.376811i	−0.954059	+	0.299619i	$0.903141\pi$
$618$	−9.68466	−	16.7743i	−0.389574	−	0.674762i
$619$	24.3002			0.976707			0.488353	−	0.872646i	$-0.337598\pi$
$619$	24.3002			0.976707			0.488353	+	0.872646i	$0.337598\pi$
$620$	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
$624$		0			0
$625$	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	0.685794	−	0.727796i	$-0.259455\pi$
$631$	−7.21922	−	12.5041i	−0.287393	−	0.497779i	−0.973187	+	0.230017i	$0.926122\pi$
$632$	−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
$637$		0			0
$638$	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	$0.108164\pi$
$643$	19.2732	+	33.3822i	0.760061	+	1.31646i	−0.182758	+	0.983158i	$0.558502\pi$
$644$	−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
$650$		0			0
$651$	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	$-0.632219\pi$
$661$	15.1847	−	26.3006i	0.590615	−	1.02297i	0.994150	−	0.108011i	$-0.0344480\pi$
$662$	−60.9848			−2.37024
$663$		0			0
$664$	−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
$676$		0			0
$677$	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	$0.0760819\pi$
$683$	18.0540	+	31.2704i	0.690816	+	1.19653i	−0.280755	+	0.959780i	$0.590585\pi$
$684$	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
$689$		0			0
$690$	2.87689			0.109521
$691$	1.15009	−	1.99202i	0.0437516	−	0.0757800i	−0.843320	−	0.537411i	$-0.819402\pi$
$691$	1.15009	−	1.99202i	0.0437516	−	0.0757800i	0.887072	+	0.461631i	$0.152736\pi$
$692$	−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	$0.380801\pi$
$702$		0			0
$703$	−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	0.999702	−	0.0244297i	$-0.00777700\pi$
$709$	12.7462	+	22.0771i	0.478694	+	0.829122i	−0.521008	+	0.853552i	$0.674444\pi$
$710$	−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
$715$		0			0
$716$	−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	$0.236886\pi$
$728$		0			0
$729$	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	$-0.950420\pi$
$733$	−53.4924			−1.97579			−0.987894	+	0.155131i	$0.950420\pi$
$734$	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	−0.917734	−	0.397196i	$-0.869983\pi$
$739$	−3.12311	+	5.40938i	−0.114885	+	0.198987i	0.802849	+	0.596183i	$0.203317\pi$
$740$	8.80776			0.323780
$741$		0			0
$742$	−106.600			−3.91342
$743$	−18.6847	+	32.3628i	−0.685474	+	1.18728i	0.287814	+	0.957686i	$0.407071\pi$
$743$	−18.6847	+	32.3628i	−0.685474	+	1.18728i	−0.973288	+	0.229589i	$0.926262\pi$
$744$	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
$754$		0			0
$755$	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	0.692461	−	0.721456i	$-0.256527\pi$
$761$	−7.68466	−	13.3102i	−0.278569	−	0.482495i	−0.971029	+	0.238961i	$0.923193\pi$
$762$	−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
$767$		0			0
$768$	−27.0540			−0.976226
$769$	−9.00000	+	15.5885i	−0.324548	+	0.562134i	−0.981421	−	0.191867i	$-0.938546\pi$
$769$	−9.00000	+	15.5885i	−0.324548	+	0.562134i	0.656873	+	0.754002i	$0.271879\pi$
$770$	−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	0.787843	−	0.615876i	$-0.211198\pi$
$773$	−3.87689	−	6.71498i	−0.139442	−	0.241521i	−0.927286	+	0.374355i	$0.877864\pi$
$774$	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
$780$		0			0
$781$	−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	0.855345	−	0.518058i	$-0.173345\pi$
$787$	−0.588540	−	1.01938i	−0.0209792	−	0.0363370i	−0.876324	+	0.481721i	$0.840012\pi$
$788$	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
$793$		0			0
$794$	−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
$806$		0			0
$807$	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	$-0.491272\pi$
$811$	1.56155			0.0548335			0.0274168	+	0.999624i	$0.491272\pi$
$812$	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
$819$		0			0
$820$	6.56155			0.229139
$821$	−13.2462	+	22.9431i	−0.462296	+	0.800720i	−0.999075	−	0.0430028i	$-0.986308\pi$
$821$	−13.2462	+	22.9431i	−0.462296	+	0.800720i	0.536779	+	0.843723i	$0.319641\pi$
$822$	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	$-0.706423\pi$
$827$	−34.7386			−1.20798			−0.603990	+	0.796992i	$0.706423\pi$
$828$	−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			0
$833$	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	0.645568	−	0.763703i	$-0.276621\pi$
$839$	−9.80776	−	16.9875i	−0.338602	−	0.586475i	−0.984170	+	0.177227i	$0.943287\pi$
$840$	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
$845$		0			0
$846$	−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	$-0.466572\pi$
$853$	6.12311			0.209651			0.104826	+	0.994491i	$0.466572\pi$
$854$	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	$0.319573\pi$
$858$		0			0
$859$	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	$-0.486493\pi$
$863$	2.49242			0.0848430			0.0424215	+	0.999100i	$0.486493\pi$
$864$	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
$871$		0			0
$872$	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	0.982154	−	0.188080i	$-0.0602264\pi$
$877$	9.71922	+	16.8342i	0.328195	+	0.568450i	−0.653959	+	0.756530i	$0.726893\pi$
$878$	−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	$0.563666\pi$
$884$		0			0
$885$	−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
$897$		0			0
$898$	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
$910$		0			0
$911$	−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
$923$		0			0
$924$	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	0.951747	−	0.306884i	$-0.0992862\pi$
$929$	6.40388	+	11.0918i	0.210105	+	0.363912i	−0.741643	+	0.670795i	$0.765953\pi$
$930$	−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
$936$		0			0
$937$	−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	$-0.487065\pi$
$941$	2.49242			0.0812507			0.0406253	+	0.999174i	$0.487065\pi$
$942$	−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	−0.765502	−	0.643434i	$-0.777509\pi$
$947$	5.36932	−	9.29993i	0.174479	−	0.302207i	0.939981	+	0.341227i	$0.110842\pi$
$948$	43.6155			1.41657
$949$		0			0
$950$	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
$962$		0			0
$963$	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	$-0.453138\pi$
$967$	9.12311			0.293379			0.146690	+	0.989183i	$0.453138\pi$
$968$	−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
$975$		0			0
$976$	93.1619			2.98204
$977$	7.91146	−	13.7030i	0.253110	−	0.438399i	−0.711270	−	0.702918i	$-0.751880\pi$
$977$	7.91146	−	13.7030i	0.253110	−	0.438399i	0.964380	+	0.264519i	$0.0852132\pi$
$978$	−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	$-0.354837\pi$
$983$	27.6155			0.880799			0.440399	+	0.897802i	$0.354837\pi$
$984$	−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
$988$		0			0
$989$	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	507.2.e.g.22.2		4
13.2	odd	12		507.2.j.g.361.4		8
13.3	even	3	inner	507.2.e.g.484.2		4
13.4	even	6		507.2.a.g.1.2		2
13.5	odd	4		507.2.j.g.316.1		8
13.6	odd	12		507.2.b.d.337.4		4
13.7	odd	12		507.2.b.d.337.1		4
13.8	odd	4		507.2.j.g.316.4		8
13.9	even	3		507.2.a.d.1.1		2
13.10	even	6		39.2.e.b.16.1	✓	4
13.11	odd	12		507.2.j.g.361.1		8
13.12	even	2		39.2.e.b.22.1	yes	4
39.17	odd	6		1521.2.a.g.1.1		2
39.20	even	12		1521.2.b.h.1351.4		4
39.23	odd	6		117.2.g.c.55.2		4
39.32	even	12		1521.2.b.h.1351.1		4
39.35	odd	6		1521.2.a.m.1.2		2
39.38	odd	2		117.2.g.c.100.2		4
52.23	odd	6		624.2.q.h.289.2		4
52.35	odd	6		8112.2.a.bo.1.1		2
52.43	odd	6		8112.2.a.bk.1.2		2
52.51	odd	2		624.2.q.h.529.2		4
65.12	odd	4		975.2.bb.i.724.1		8
65.23	odd	12		975.2.bb.i.874.1		8
65.38	odd	4		975.2.bb.i.724.4		8
65.49	even	6		975.2.i.k.601.2		4
65.62	odd	12		975.2.bb.i.874.4		8
65.64	even	2		975.2.i.k.451.2		4
156.23	even	6		1872.2.t.r.289.1		4
156.155	even	2		1872.2.t.r.1153.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.1	✓	4	13.10	even	6
39.2.e.b.22.1	yes	4	13.12	even	2
117.2.g.c.55.2		4	39.23	odd	6
117.2.g.c.100.2		4	39.38	odd	2
507.2.a.d.1.1		2	13.9	even	3
507.2.a.g.1.2		2	13.4	even	6
507.2.b.d.337.1		4	13.7	odd	12
507.2.b.d.337.4		4	13.6	odd	12
507.2.e.g.22.2		4	1.1	even	1	trivial
507.2.e.g.484.2		4	13.3	even	3	inner
507.2.j.g.316.1		8	13.5	odd	4
507.2.j.g.316.4		8	13.8	odd	4
507.2.j.g.361.1		8	13.11	odd	12
507.2.j.g.361.4		8	13.2	odd	12
624.2.q.h.289.2		4	52.23	odd	6
624.2.q.h.529.2		4	52.51	odd	2
975.2.i.k.451.2		4	65.64	even	2
975.2.i.k.601.2		4	65.49	even	6
975.2.bb.i.724.1		8	65.12	odd	4
975.2.bb.i.724.4		8	65.38	odd	4
975.2.bb.i.874.1		8	65.23	odd	12
975.2.bb.i.874.4		8	65.62	odd	12
1521.2.a.g.1.1		2	39.17	odd	6
1521.2.a.m.1.2		2	39.35	odd	6
1521.2.b.h.1351.1		4	39.32	even	12
1521.2.b.h.1351.4		4	39.20	even	12
1872.2.t.r.289.1		4	156.23	even	6
1872.2.t.r.1153.1		4	156.155	even	2
8112.2.a.bk.1.2		2	52.43	odd	6
8112.2.a.bo.1.1		2	52.35	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.e (of order \(3\), degree \(2\), not 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} -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} +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} +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} +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} -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} +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} +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	\( 4 q + q^{2} - 2 q^{3} - 5 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} - 2 q^{9} - 7 q^{10} - 4 q^{11} + 10 q^{12} - 20 q^{14} - 3 q^{15} - 3 q^{16} - q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} + 2 q^{22} - 4 q^{23} + 9 q^{24} + 6 q^{25} + 4 q^{27} - 16 q^{28} - q^{29} - 7 q^{30} - 2 q^{31} + 9 q^{32} - 4 q^{33} - 18 q^{34} + 4 q^{35} - 5 q^{36} + 11 q^{37} - 28 q^{38} - 10 q^{40} + q^{41} + 10 q^{42} - 5 q^{43} + 20 q^{44} - 3 q^{45} + 2 q^{46} - 3 q^{48} + q^{49} - 24 q^{50} + 2 q^{51} + 22 q^{53} + q^{54} - 6 q^{55} + 22 q^{56} - 12 q^{57} - 25 q^{58} - 14 q^{59} - 2 q^{60} - 16 q^{61} + 8 q^{62} - 3 q^{63} + 14 q^{64} - 4 q^{66} + 5 q^{67} - 11 q^{68} - 4 q^{69} + 4 q^{70} + 28 q^{71} + 9 q^{72} + 24 q^{73} + 3 q^{74} - 3 q^{75} - 2 q^{76} + 12 q^{77} + 30 q^{79} + 21 q^{80} - 2 q^{81} - 9 q^{82} + 20 q^{83} - 16 q^{84} + 7 q^{85} + 12 q^{86} - q^{87} + 18 q^{88} + 18 q^{89} + 14 q^{90} + 20 q^{92} + q^{93} + 34 q^{94} + 26 q^{95} - 18 q^{96} - 13 q^{97} + 25 q^{98} + 8 q^{99}+O(q^{100}) \) 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 - 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 + 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 - 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 + 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 - 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 + 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 + 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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