LMFDB - Embedded newform 117.2.g.c.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(55,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, 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("117.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.g (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:	$0.934249703649$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.2
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	117.55
Dual form			117.2.g.c.100.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.28078	+	2.21837i	0.905646	+	1.56862i	0.820048	+	0.572295i	$0.193947\pi$
$2$	1.28078	+	2.21837i	0.905646	+	1.56862i	0.0855975	+	0.996330i	$0.472720\pi$
$3$		0			0
$3$		0			0
$4$	−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	$0.540075\pi$
$6$		0			0
$7$	1.78078	−	3.08440i	0.673070	−	1.16579i	−0.303959	−	0.952685i	$-0.598308\pi$
$7$	1.78078	−	3.08440i	0.673070	−	1.16579i	0.977029	−	0.213107i	$-0.0683582\pi$
$8$	−6.56155			−2.31986
$9$		0			0
$10$	−0.719224	−	1.24573i	−0.227438	−	0.393935i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	0.500000	+	3.57071i	0.138675	+	0.990338i
$13$	0.500000	+	3.57071i	0.138675	+	0.990338i
$14$	9.12311			2.43825
$15$		0			0
$16$	−3.84233	−	6.65511i	−0.960582	−	1.66378i
$17$	1.28078	−	2.21837i	0.310634	−	0.538034i	−0.667866	−	0.744282i	$-0.732792\pi$
$17$	1.28078	−	2.21837i	0.310634	−	0.538034i	0.978500	+	0.206248i	$0.0661254\pi$
$18$		0			0
$19$	0.561553	−	0.972638i	0.128829	−	0.223138i	−0.794394	−	0.607403i	$-0.792211\pi$
$19$	0.561553	−	0.972638i	0.128829	−	0.223138i	0.923223	+	0.384264i	$0.125545\pi$
$20$	1.28078	−	2.21837i	0.286390	−	0.496043i
$21$		0			0
$22$	2.56155	−	4.43674i	0.546125	−	0.945916i
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	0.951247	−	0.308431i	$-0.0998038\pi$
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	−0.742732	+	0.669588i	$0.766471\pi$
$24$		0			0
$25$	−4.68466			−0.936932
$26$	−7.28078	+	5.68247i	−1.42788	+	1.11442i
$27$		0			0
$28$	8.12311	+	14.0696i	1.53512	+	2.65891i
$29$	−2.84233	−	4.92306i	−0.527807	−	0.914189i	−0.999475	−	0.0324124i	$-0.989681\pi$
$29$	−2.84233	−	4.92306i	−0.527807	−	0.914189i	0.471667	−	0.881777i	$-0.343652\pi$
$30$		0			0
$31$	−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
$33$		0			0
$34$	6.56155			1.12530
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$		0			0
$37$	−1.71922	−	2.97778i	−0.282639	−	0.489544i	0.689395	−	0.724385i	$-0.257876\pi$
$37$	−1.71922	−	2.97778i	−0.282639	−	0.489544i	−0.972034	+	0.234841i	$0.924543\pi$
$38$	2.87689			0.466694
$39$		0			0
$40$	3.68466			0.582596
$41$	1.28078	+	2.21837i	0.200024	+	0.346451i	0.948536	−	0.316670i	$-0.102565\pi$
$41$	1.28078	+	2.21837i	0.200024	+	0.346451i	−0.748512	+	0.663121i	$0.769231\pi$
$42$		0			0
$43$	−0.219224	+	0.379706i	−0.0334313	+	0.0579047i	−0.882257	−	0.470768i	$-0.843977\pi$
$43$	−0.219224	+	0.379706i	−0.0334313	+	0.0579047i	0.848826	+	0.528673i	$0.177310\pi$
$44$	9.12311			1.37536
$45$		0			0
$46$	−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	$0.294603\pi$
$48$		0			0
$49$	−2.84233	−	4.92306i	−0.406047	−	0.703294i
$50$	−6.00000	−	10.3923i	−0.848528	−	1.46969i
$51$		0			0
$52$	−15.2462	−	6.16879i	−2.11427	−	0.855457i
$53$	−11.6847			−1.60501			−0.802506	−	0.596645i	$-0.796500\pi$
$53$	−11.6847			−1.60501			−0.802506	+	0.596645i	$0.796500\pi$
$54$		0			0
$55$	0.561553	+	0.972638i	0.0757198	+	0.131150i
$56$	−11.6847	+	20.2384i	−1.56143	+	2.70447i
$57$		0			0
$58$	7.28078	−	12.6107i	0.956013	−	1.65586i
$59$	−5.56155	+	9.63289i	−0.724053	+	1.25410i	0.235310	+	0.971920i	$0.424389\pi$
$59$	−5.56155	+	9.63289i	−0.724053	+	1.25410i	−0.959363	+	0.282175i	$0.908944\pi$
$60$		0			0
$61$	−6.06155	+	10.4989i	−0.776102	+	1.34425i	0.158071	+	0.987428i	$0.449473\pi$
$61$	−6.06155	+	10.4989i	−0.776102	+	1.34425i	−0.934173	+	0.356821i	$0.883861\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$		0			0
$64$	1.43845			0.179806
$65$	−0.280776	−	2.00514i	−0.0348260	−	0.248708i
$66$		0			0
$67$	−0.219224	−	0.379706i	−0.0267824	−	0.0463885i	0.852324	−	0.523015i	$-0.175193\pi$
$67$	−0.219224	−	0.379706i	−0.0267824	−	0.0463885i	−0.879106	+	0.476626i	$0.841859\pi$
$68$	5.84233	+	10.1192i	0.708486	+	1.22713i
$69$		0			0
$70$	−5.12311			−0.612328
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	−0.0666994	−	0.997773i	$-0.521247\pi$
$71$	7.00000	−	12.1244i	0.830747	−	1.43890i	0.897447	−	0.441123i	$-0.145420\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	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			0
$82$	−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	$0.333078\pi$
$84$		0			0
$85$	−0.719224	+	1.24573i	−0.0780108	+	0.135119i
$86$	−1.12311			−0.121108
$87$		0			0
$88$	6.56155	+	11.3649i	0.699464	+	1.21151i
$89$	6.56155	+	11.3649i	0.695523	+	1.20468i	0.970004	+	0.243089i	$0.0781607\pi$
$89$	6.56155	+	11.3649i	0.695523	+	1.20468i	−0.274481	+	0.961593i	$0.588506\pi$
$90$		0			0
$91$	11.9039	+	4.81645i	1.24787	+	0.504901i
$92$	−9.12311			−0.951150
$93$		0			0
$94$	10.5616	+	18.2931i	1.08934	+	1.88679i
$95$	−0.315342	+	0.546188i	−0.0323534	+	0.0560377i
$96$		0			0
$97$	2.21922	−	3.84381i	0.225328	−	0.390280i	−0.731090	−	0.682281i	$-0.760988\pi$
$97$	2.21922	−	3.84381i	0.225328	−	0.390280i	0.956418	+	0.292002i	$0.0943213\pi$
$98$	7.28078	−	12.6107i	0.735469	−	1.27387i
$99$		0			0
$100$	10.6847	−	18.5064i	1.06847	−	1.85064i
$101$	−1.71922	−	2.97778i	−0.171069	−	0.296300i	0.767725	−	0.640780i	$-0.221389\pi$
$101$	−1.71922	−	2.97778i	−0.171069	−	0.296300i	−0.938794	+	0.344479i	$0.888055\pi$
$102$		0			0
$103$	−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
$105$		0			0
$106$	−14.9654	−	25.9209i	−1.45357	−	2.51766i
$107$	4.12311	+	7.14143i	0.398596	+	0.690388i	0.993553	−	0.113369i	$-0.0361644\pi$
$107$	4.12311	+	7.14143i	0.398596	+	0.690388i	−0.594957	+	0.803757i	$0.702831\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−27.3693			−2.58616
$113$	−7.40388	+	12.8239i	−0.696499	+	1.20637i	0.273174	+	0.961965i	$0.411926\pi$
$113$	−7.40388	+	12.8239i	−0.696499	+	1.20637i	−0.969673	+	0.244406i	$0.921407\pi$
$114$		0			0
$115$	−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
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−31.0540			−2.81149
$123$		0			0
$124$	3.56155	−	6.16879i	0.319837	−	0.553974i
$125$	5.43845			0.486430
$126$		0			0
$127$	−4.78078	−	8.28055i	−0.424225	−	0.734780i	0.572122	−	0.820168i	$-0.306120\pi$
$127$	−4.78078	−	8.28055i	−0.424225	−	0.734780i	−0.996348	+	0.0853884i	$0.972787\pi$
$128$	−4.71922	−	8.17394i	−0.417124	−	0.722481i
$129$		0			0
$130$	4.08854	−	3.19101i	0.358589	−	0.279870i
$131$	17.3693			1.51756			0.758782	−	0.651345i	$-0.225795\pi$
$131$	17.3693			1.51756			0.758782	+	0.651345i	$0.225795\pi$
$132$		0			0
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	0.561553	−	0.972638i	0.0485108	−	0.0840231i
$135$		0			0
$136$	−8.40388	+	14.5560i	−0.720627	+	1.24816i
$137$	−0.719224	+	1.24573i	−0.0614474	+	0.106430i	−0.895113	−	0.445840i	$-0.852905\pi$
$137$	−0.719224	+	1.24573i	−0.0614474	+	0.106430i	0.833665	+	0.552270i	$0.186238\pi$
$138$		0			0
$139$	−5.46543	+	9.46641i	−0.463572	+	0.802930i	−0.999136	−	0.0415643i	$-0.986766\pi$
$139$	−5.46543	+	9.46641i	−0.463572	+	0.802930i	0.535564	+	0.844495i	$0.320099\pi$
$140$	−4.56155	−	7.90084i	−0.385522	−	0.667743i
$141$		0			0
$142$	35.8617			3.00945
$143$	5.68466	−	4.43674i	0.475375	−	0.371019i
$144$		0			0
$145$	1.59612	+	2.76456i	0.132550	+	0.229584i
$146$	−2.40388	−	4.16365i	−0.198947	−	0.344586i
$147$		0			0
$148$	15.6847			1.28927
$149$	−3.28078	+	5.68247i	−0.268772	+	0.465526i	−0.968545	−	0.248839i	$-0.919951\pi$
$149$	−3.28078	+	5.68247i	−0.268772	+	0.465526i	0.699773	+	0.714365i	$0.253284\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−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
$159$		0			0
$160$	−1.84233	+	3.19101i	−0.145649	+	0.252271i
$161$	7.12311			0.561379
$162$		0			0
$163$	−7.90388	+	13.6899i	−0.619080	+	1.07228i	0.370574	+	0.928803i	$0.379161\pi$
$163$	−7.90388	+	13.6899i	−0.619080	+	1.07228i	−0.989654	+	0.143475i	$0.954172\pi$
$164$	−11.6847			−0.912419
$165$		0			0
$166$	11.6847	+	20.2384i	0.906905	+	1.57081i
$167$	−3.12311	−	5.40938i	−0.241673	−	0.418590i	0.719518	−	0.694474i	$-0.244363\pi$
$167$	−3.12311	−	5.40938i	−0.241673	−	0.418590i	−0.961191	+	0.275884i	$0.911030\pi$
$168$		0			0
$169$	−12.5000	+	3.57071i	−0.961538	+	0.274670i
$170$	−3.68466			−0.282600
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	1.87689	−	3.25088i	0.142698	−	0.247160i	−0.785814	−	0.618463i	$-0.787756\pi$
$173$	1.87689	−	3.25088i	0.142698	−	0.247160i	0.928512	+	0.371303i	$0.121089\pi$
$174$		0			0
$175$	−8.34233	+	14.4493i	−0.630621	+	1.09227i
$176$	−7.68466	+	13.3102i	−0.579253	+	1.00330i
$177$		0			0
$178$	−16.8078	+	29.1119i	−1.25980	+	2.18203i
$179$	−6.56155	−	11.3649i	−0.490433	−	0.849456i	0.509506	−	0.860467i	$-0.329828\pi$
$179$	−6.56155	−	11.3649i	−0.490433	−	0.849456i	−0.999939	+	0.0110115i	$0.996495\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−6.56155	−	11.3649i	−0.483724	−	0.837835i
$185$	0.965435	+	1.67218i	0.0709802	+	0.122941i
$186$		0			0
$187$	−5.12311			−0.374639
$188$	−18.8078	+	32.5760i	−1.37170	+	2.37585i
$189$		0			0
$190$	−1.61553			−0.117203
$191$	−0.438447	+	0.759413i	−0.0317249	+	0.0549492i	−0.881452	−	0.472274i	$-0.843433\pi$
$191$	−0.438447	+	0.759413i	−0.0317249	+	0.0549492i	0.849727	+	0.527223i	$0.176767\pi$
$192$		0			0
$193$	−9.74621	−	16.8809i	−0.701548	−	1.21512i	−0.967923	−	0.251247i	$-0.919159\pi$
$193$	−9.74621	−	16.8809i	−0.701548	−	1.21512i	0.266375	−	0.963869i	$-0.414174\pi$
$194$	11.3693			0.816269
$195$		0			0
$196$	25.9309			1.85220
$197$	−5.68466	−	9.84612i	−0.405015	−	0.701507i	0.589308	−	0.807908i	$-0.299400\pi$
$197$	−5.68466	−	9.84612i	−0.405015	−	0.701507i	−0.994323	+	0.106402i	$0.966067\pi$
$198$		0			0
$199$	11.5885	−	20.0719i	0.821490	−	1.42286i	−0.0830828	−	0.996543i	$-0.526477\pi$
$199$	11.5885	−	20.0719i	0.821490	−	1.42286i	0.904573	−	0.426320i	$-0.140190\pi$
$200$	30.7386			2.17355
$201$		0			0
$202$	4.40388	−	7.62775i	0.309856	−	0.536686i
$203$	−20.2462			−1.42101
$204$		0			0
$205$	−0.719224	−	1.24573i	−0.0502328	−	0.0870057i
$206$	−9.68466	−	16.7743i	−0.674762	−	1.16872i
$207$		0			0
$208$	21.8423	−	17.0474i	1.51449	−	1.18203i
$209$	−2.24621			−0.155374
$210$		0			0
$211$	−3.65767	−	6.33527i	−0.251804	−	0.436138i	0.712218	−	0.701958i	$-0.247691\pi$
$211$	−3.65767	−	6.33527i	−0.251804	−	0.436138i	−0.964023	+	0.265820i	$0.914357\pi$
$212$	26.6501	−	46.1593i	1.83034	−	3.17023i
$213$		0			0
$214$	−10.5616	+	18.2931i	−0.721973	+	1.25049i
$215$	0.123106	−	0.213225i	0.00839573	−	0.0145418i
$216$		0			0
$217$	−2.78078	+	4.81645i	−0.188771	+	0.326962i
$218$	22.8078	+	39.5042i	1.54474	+	2.67556i
$219$		0			0
$220$	−5.12311			−0.345400
$221$	8.56155	+	3.46410i	0.575912	+	0.233021i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	−11.6847	−	20.2384i	−0.780714	−	1.35224i
$225$		0			0
$226$	−37.9309			−2.52312
$227$	−0.561553	+	0.972638i	−0.0372716	+	0.0645563i	−0.884059	−	0.467374i	$-0.845200\pi$
$227$	−0.561553	+	0.972638i	−0.0372716	+	0.0645563i	0.846788	+	0.531931i	$0.178533\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	18.6501	+	32.3029i	1.22444	+	2.12079i
$233$	−26.0000			−1.70332			−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000			−1.70332			−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	−4.63068			−0.302072
$236$	−25.3693	−	43.9409i	−1.65140	−	2.86031i
$237$		0			0
$238$	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	$0.493507\pi$
$240$		0			0
$241$	−1.40388	+	2.43160i	−0.0904320	+	0.156633i	−0.907693	−	0.419635i	$-0.862158\pi$
$241$	−1.40388	+	2.43160i	−0.0904320	+	0.156633i	0.817261	+	0.576268i	$0.195491\pi$
$242$	17.9309			1.15264
$243$		0			0
$244$	−27.6501	−	47.8914i	−1.77012	−	3.06593i
$245$	1.59612	+	2.76456i	0.101972	+	0.176621i
$246$		0			0
$247$	3.75379	+	1.51883i	0.238848	+	0.0966406i
$248$	10.2462			0.650635
$249$		0			0
$250$	6.96543	+	12.0645i	0.440533	+	0.763025i
$251$	−15.3693	+	26.6204i	−0.970103	+	1.68027i	−0.274871	+	0.961481i	$0.588635\pi$
$251$	−15.3693	+	26.6204i	−0.970103	+	1.68027i	−0.695231	+	0.718786i	$0.744698\pi$
$252$		0			0
$253$	2.00000	−	3.46410i	0.125739	−	0.217786i
$254$	12.2462	−	21.2111i	0.768396	−	1.33090i
$255$		0			0
$256$	13.5270	−	23.4294i	0.845437	−	1.46434i
$257$	−8.08854	−	14.0098i	−0.504549	−	0.873905i	−0.999986	−	0.00526106i	$-0.998325\pi$
$257$	−8.08854	−	14.0098i	−0.504549	−	0.873905i	0.495437	−	0.868644i	$-0.335008\pi$
$258$		0			0
$259$	−12.2462			−0.760943
$260$	8.56155	+	3.46410i	0.530965	+	0.214834i
$261$		0			0
$262$	22.2462	+	38.5316i	1.37438	+	2.38049i
$263$	−7.68466	−	13.3102i	−0.473856	−	0.820743i	0.525696	−	0.850673i	$-0.323805\pi$
$263$	−7.68466	−	13.3102i	−0.473856	−	0.820743i	−0.999552	+	0.0299295i	$0.990472\pi$
$264$		0			0
$265$	6.56155			0.403073
$266$	5.12311	−	8.87348i	0.314118	−	0.544068i
$267$		0			0
$268$	2.00000			0.122169
$269$	1.68466	−	2.91791i	0.102715	−	0.177908i	−0.810087	−	0.586310i	$-0.800580\pi$
$269$	1.68466	−	2.91791i	0.102715	−	0.177908i	0.912803	+	0.408401i	$0.133914\pi$
$270$		0			0
$271$	0.534565	+	0.925894i	0.0324725	+	0.0562441i	0.881805	−	0.471614i	$-0.156329\pi$
$271$	0.534565	+	0.925894i	0.0324725	+	0.0562441i	−0.849332	+	0.527858i	$0.822995\pi$
$272$	−19.6847			−1.19356
$273$		0			0
$274$	−3.68466			−0.222598
$275$	4.68466	+	8.11407i	0.282496	+	0.489297i
$276$		0			0
$277$	−8.84233	+	15.3154i	−0.531284	+	0.920211i	0.468049	+	0.883702i	$0.344957\pi$
$277$	−8.84233	+	15.3154i	−0.531284	+	0.920211i	−0.999333	+	0.0365086i	$0.988376\pi$
$278$	−28.0000			−1.67933
$279$		0			0
$280$	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	$0.473311\pi$
$282$		0			0
$283$	0.657671	+	1.13912i	0.0390945	+	0.0677136i	0.884911	−	0.465761i	$-0.154219\pi$
$283$	0.657671	+	1.13912i	0.0390945	+	0.0677136i	−0.845816	+	0.533475i	$0.820886\pi$
$284$	31.9309	+	55.3059i	1.89475	+	3.28180i
$285$		0			0
$286$	17.1231	+	6.92820i	1.01251	+	0.409673i
$287$	9.12311			0.538520
$288$		0			0
$289$	5.21922	+	9.03996i	0.307013	+	0.531762i
$290$	−4.08854	+	7.08156i	−0.240087	+	0.415844i
$291$		0			0
$292$	4.28078	−	7.41452i	0.250513	−	0.433902i
$293$	12.2808	−	21.2709i	0.717451	−	1.24266i	−0.244556	−	0.969635i	$-0.578642\pi$
$293$	12.2808	−	21.2709i	0.717451	−	1.24266i	0.962007	−	0.273026i	$-0.0880244\pi$
$294$		0			0
$295$	3.12311	−	5.40938i	0.181834	−	0.314946i
$296$	11.2808	+	19.5389i	0.655682	+	1.13567i
$297$		0			0
$298$	−16.8078			−0.973648
$299$	−5.68466	+	4.43674i	−0.328752	+	0.256583i
$300$		0			0
$301$	0.780776	+	1.35234i	0.0450032	+	0.0779478i
$302$	19.6847	+	34.0948i	1.13272	+	1.96194i
$303$		0			0
$304$	−8.63068			−0.495004
$305$	3.40388	−	5.89570i	0.194906	−	0.337587i
$306$		0			0
$307$	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
$309$		0			0
$310$	1.12311	+	1.94528i	0.0637881	+	0.110484i
$311$	10.8769			0.616772			0.308386	−	0.951261i	$-0.400211\pi$
$311$	10.8769			0.616772			0.308386	+	0.951261i	$0.400211\pi$
$312$		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
$315$		0			0
$316$	−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	$0.275848\pi$
$318$		0			0
$319$	−5.68466	+	9.84612i	−0.318280	+	0.551277i
$320$	−0.807764			−0.0451554
$321$		0			0
$322$	9.12311	+	15.8017i	0.508411	+	0.880593i
$323$	−1.43845	−	2.49146i	−0.0800373	−	0.138629i
$324$		0			0
$325$	−2.34233	−	16.7276i	−0.129929	−	0.927879i
$326$	−40.4924			−2.24267
$327$		0			0
$328$	−8.40388	−	14.5560i	−0.464027	−	0.803718i
$329$	14.6847	−	25.4346i	0.809591	−	1.40225i
$330$		0			0
$331$	11.9039	−	20.6181i	0.654297	−	1.13327i	−0.327773	−	0.944756i	$-0.606298\pi$
$331$	11.9039	−	20.6181i	0.654297	−	1.13327i	0.982070	−	0.188518i	$-0.0603685\pi$
$332$	−20.8078	+	36.0401i	−1.14197	+	1.97796i
$333$		0			0
$334$	8.00000	−	13.8564i	0.437741	−	0.758189i
$335$	0.123106	+	0.213225i	0.00672598	+	0.0116497i
$336$		0			0
$337$	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
$339$		0			0
$340$	−3.28078	−	5.68247i	−0.177925	−	0.308175i
$341$	1.56155	+	2.70469i	0.0845628	+	0.146467i
$342$		0			0
$343$	4.68466			0.252948
$344$	1.43845	−	2.49146i	0.0775559	−	0.134331i
$345$		0			0
$346$	9.61553			0.516934
$347$	−6.80776	+	11.7914i	−0.365460	+	0.632995i	−0.988850	−	0.148916i	$-0.952422\pi$
$347$	−6.80776	+	11.7914i	−0.365460	+	0.632995i	0.623390	+	0.781911i	$0.285755\pi$
$348$		0			0
$349$	6.90388	+	11.9579i	0.369556	+	0.640090i	0.989496	−	0.144559i	$-0.0461763\pi$
$349$	6.90388	+	11.9579i	0.369556	+	0.640090i	−0.619940	+	0.784649i	$0.712843\pi$
$350$	−42.7386			−2.28448
$351$		0			0
$352$	−13.1231			−0.699464
$353$	8.84233	+	15.3154i	0.470630	+	0.815155i	0.999436	−	0.0335881i	$-0.0106934\pi$
$353$	8.84233	+	15.3154i	0.470630	+	0.815155i	−0.528806	+	0.848743i	$0.677360\pi$
$354$		0			0
$355$	−3.93087	+	6.80847i	−0.208629	+	0.361356i
$356$	−59.8617			−3.17267
$357$		0			0
$358$	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	$0.632931\pi$
$360$		0			0
$361$	8.86932	+	15.3621i	0.466806	+	0.808532i
$362$	12.4039	+	21.4842i	0.651934	+	1.12918i
$363$		0			0
$364$	−46.1771	+	36.0401i	−2.42034	+	1.88901i
$365$	1.05398			0.0551676
$366$		0			0
$367$	−10.0270	−	17.3673i	−0.523404	−	0.906563i	−0.999629	−	0.0272394i	$-0.991328\pi$
$367$	−10.0270	−	17.3673i	−0.523404	−	0.906563i	0.476224	−	0.879324i	$-0.342005\pi$
$368$	7.68466	−	13.3102i	0.400591	−	0.693843i
$369$		0			0
$370$	−2.47301	+	4.28338i	−0.128566	+	0.222682i
$371$	−20.8078	+	36.0401i	−1.08029	+	1.87111i
$372$		0			0
$373$	−1.81534	+	3.14426i	−0.0939948	+	0.162804i	−0.909189	−	0.416384i	$-0.863297\pi$
$373$	−1.81534	+	3.14426i	−0.0939948	+	0.162804i	0.815194	+	0.579188i	$0.196630\pi$
$374$	−6.56155	−	11.3649i	−0.339290	−	0.587667i
$375$		0			0
$376$	−54.1080			−2.79040
$377$	16.1577	−	12.6107i	0.832162	−	0.649483i
$378$		0			0
$379$	−5.65767	−	9.79937i	−0.290615	−	0.503360i	0.683340	−	0.730100i	$-0.260527\pi$
$379$	−5.65767	−	9.79937i	−0.290615	−	0.503360i	−0.973955	+	0.226740i	$0.927193\pi$
$380$	−1.43845	−	2.49146i	−0.0737908	−	0.127809i
$381$		0			0
$382$	−2.24621			−0.114926
$383$	13.3693	−	23.1563i	0.683140	−	1.18323i	−0.290877	−	0.956760i	$-0.593947\pi$
$383$	13.3693	−	23.1563i	0.683140	−	1.18323i	0.974017	−	0.226473i	$-0.0727195\pi$
$384$		0			0
$385$	4.00000			0.203859
$386$	24.9654	−	43.2414i	1.27071	−	2.20093i
$387$		0			0
$388$	10.1231	+	17.5337i	0.513923	+	0.890140i
$389$	3.05398			0.154843			0.0774213	−	0.996998i	$-0.475331\pi$
$389$	3.05398			0.154843			0.0774213	+	0.996998i	$0.475331\pi$
$390$		0			0
$391$	5.12311			0.259087
$392$	18.6501	+	32.3029i	0.941972	+	1.63154i
$393$		0			0
$394$	14.5616	−	25.2213i	0.733600	−	1.27063i
$395$	−5.36932			−0.270160
$396$		0			0
$397$	6.02699	−	10.4390i	0.302486	−	0.523921i	−0.674213	−	0.738537i	$-0.735517\pi$
$397$	6.02699	−	10.4390i	0.302486	−	0.523921i	0.976698	+	0.214617i	$0.0688502\pi$
$398$	59.3693			2.97591
$399$		0			0
$400$	18.0000	+	31.1769i	0.900000	+	1.55885i
$401$	9.28078	+	16.0748i	0.463460	+	0.802736i	0.999131	−	0.0416909i	$-0.0132745\pi$
$401$	9.28078	+	16.0748i	0.463460	+	0.802736i	−0.535671	+	0.844427i	$0.679941\pi$
$402$		0			0
$403$	−0.780776	−	5.57586i	−0.0388932	−	0.277753i
$404$	15.6847			0.780341
$405$		0			0
$406$	−25.9309	−	44.9136i	−1.28693	−	2.22902i
$407$	−3.43845	+	5.95557i	−0.170437	+	0.295206i
$408$		0			0
$409$	9.18466	−	15.9083i	0.454152	−	0.786615i	−0.544487	−	0.838769i	$-0.683276\pi$
$409$	9.18466	−	15.9083i	0.454152	−	0.786615i	0.998639	+	0.0521548i	$0.0166089\pi$
$410$	1.84233	−	3.19101i	0.0909862	−	0.157593i
$411$		0			0
$412$	17.2462	−	29.8713i	0.849660	−	1.47165i
$413$	19.8078	+	34.3081i	0.974676	+	1.68819i
$414$		0			0
$415$	−5.12311			−0.251483
$416$	21.9309	+	8.87348i	1.07525	+	0.435058i
$417$		0			0
$418$	−2.87689	−	4.98293i	−0.140714	−	0.243723i
$419$	−8.87689	−	15.3752i	−0.433665	−	0.751129i	0.563521	−	0.826102i	$-0.309446\pi$
$419$	−8.87689	−	15.3752i	−0.433665	−	0.751129i	−0.997186	+	0.0749725i	$0.976113\pi$
$420$		0			0
$421$	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
$423$		0			0
$424$	76.6695			3.72340
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	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	0.829300	−	0.558803i	$-0.188739\pi$
$431$	−1.43845	−	2.49146i	−0.0692876	−	0.120010i	−0.898588	+	0.438794i	$0.855406\pi$
$432$		0			0
$433$	−12.6231	+	21.8639i	−0.606628	+	1.05071i	0.385164	+	0.922848i	$0.374145\pi$
$433$	−12.6231	+	21.8639i	−0.606628	+	1.05071i	−0.991792	+	0.127862i	$0.959189\pi$
$434$	−14.2462			−0.683840
$435$		0			0
$436$	−40.6155	+	70.3482i	−1.94513	+	3.36907i
$437$	2.24621			0.107451
$438$		0			0
$439$	0.657671	+	1.13912i	0.0313889	+	0.0543672i	0.881293	−	0.472570i	$-0.156674\pi$
$439$	0.657671	+	1.13912i	0.0313889	+	0.0543672i	−0.849904	+	0.526937i	$0.823340\pi$
$440$	−3.68466	−	6.38202i	−0.175659	−	0.304251i
$441$		0			0
$442$	3.28078	+	23.4294i	0.156051	+	1.11442i
$443$	−14.7386			−0.700254			−0.350127	−	0.936702i	$-0.613862\pi$
$443$	−14.7386			−0.700254			−0.350127	+	0.936702i	$0.613862\pi$
$444$		0			0
$445$	−3.68466	−	6.38202i	−0.174670	−	0.302537i
$446$	10.2462	−	17.7470i	0.485172	−	0.840343i
$447$		0			0
$448$	2.56155	−	4.43674i	0.121022	−	0.209616i
$449$	4.12311	−	7.14143i	0.194581	−	0.337025i	−0.752182	−	0.658956i	$-0.770998\pi$
$449$	4.12311	−	7.14143i	0.194581	−	0.337025i	0.946763	+	0.321931i	$0.104332\pi$
$450$		0			0
$451$	2.56155	−	4.43674i	0.120619	−	0.208918i
$452$	−33.7732	−	58.4969i	−1.58856	−	2.75146i
$453$		0			0
$454$	−2.87689			−0.135019
$455$	−6.68466	−	2.70469i	−0.313382	−	0.126798i
$456$		0			0
$457$	14.3078	+	24.7818i	0.669289	+	1.15924i	0.978103	+	0.208120i	$0.0667345\pi$
$457$	14.3078	+	24.7818i	0.669289	+	1.15924i	−0.308814	+	0.951122i	$0.599932\pi$
$458$	0.315342	+	0.546188i	0.0147349	+	0.0255217i
$459$		0			0
$460$	5.12311			0.238866
$461$	−18.4039	+	31.8765i	−0.857154	+	1.48463i	0.0174778	+	0.999847i	$0.494436\pi$
$461$	−18.4039	+	31.8765i	−0.857154	+	1.48463i	−0.874632	+	0.484787i	$0.838897\pi$
$462$		0			0
$463$	−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			0
$466$	−33.3002	−	57.6776i	−1.54260	−	2.67186i
$467$	26.0000			1.20314			0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000			1.20314			0.601568	+	0.798821i	$0.294543\pi$
$468$		0			0
$469$	−1.56155			−0.0721058
$470$	−5.93087	−	10.2726i	−0.273571	−	0.473838i
$471$		0			0
$472$	36.4924	−	63.2067i	1.67970	−	2.90933i
$473$	0.876894			0.0403196
$474$		0			0
$475$	−2.63068	+	4.55648i	−0.120704	+	0.209065i
$476$	41.6155			1.90744
$477$		0			0
$478$	0.807764	+	1.39909i	0.0369463	+	0.0639928i
$479$	−3.12311	−	5.40938i	−0.142698	−	0.247161i	0.785814	−	0.618463i	$-0.212245\pi$
$479$	−3.12311	−	5.40938i	−0.142698	−	0.247161i	−0.928512	+	0.371303i	$0.878911\pi$
$480$		0			0
$481$	9.77320	−	7.62775i	0.445620	−	0.347795i
$482$	−7.19224			−0.327597
$483$		0			0
$484$	15.9654	+	27.6529i	0.725702	+	1.25695i
$485$	−1.24621	+	2.15850i	−0.0565875	+	0.0980125i
$486$		0			0
$487$	0.561553	−	0.972638i	0.0254464	−	0.0440744i	−0.853022	−	0.521875i	$-0.825233\pi$
$487$	0.561553	−	0.972638i	0.0254464	−	0.0440744i	0.878468	+	0.477801i	$0.158566\pi$
$488$	39.7732	−	68.8892i	1.80045	−	3.11847i
$489$		0			0
$490$	−4.08854	+	7.08156i	−0.184701	+	0.319912i
$491$	−9.87689	−	17.1073i	−0.445738	−	0.772041i	0.552365	−	0.833602i	$-0.313725\pi$
$491$	−9.87689	−	17.1073i	−0.445738	−	0.772041i	−0.998103	+	0.0615613i	$0.980392\pi$
$492$		0			0
$493$	−14.5616			−0.655819
$494$	1.43845	+	10.2726i	0.0647188	+	0.462185i
$495$		0			0
$496$	6.00000	+	10.3923i	0.269408	+	0.466628i
$497$	−24.9309	−	43.1815i	−1.11830	−	1.93696i
$498$		0			0
$499$	−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
$501$		0			0
$502$	−78.7386			−3.51428
$503$	−5.87689	+	10.1791i	−0.262038	+	0.453863i	−0.966783	−	0.255597i	$-0.917728\pi$
$503$	−5.87689	+	10.1791i	−0.262038	+	0.453863i	0.704746	+	0.709460i	$0.251061\pi$
$504$		0			0
$505$	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	0.931549	−	0.363615i	$-0.118458\pi$
$509$	3.40388	+	5.89570i	0.150874	+	0.261322i	−0.780675	+	0.624938i	$0.785124\pi$
$510$		0			0
$511$	−3.34233	+	5.78908i	−0.147856	+	0.256094i
$512$	50.4233			2.22842
$513$		0			0
$514$	20.7192	−	35.8867i	0.913886	−	1.58290i
$515$	4.24621			0.187110
$516$		0			0
$517$	−8.24621	−	14.2829i	−0.362668	−	0.628159i
$518$	−15.6847	−	27.1666i	−0.689144	−	1.19363i
$519$		0			0
$520$	1.84233	+	13.1569i	0.0807915	+	0.576967i
$521$	37.9309			1.66178			0.830891	−	0.556436i	$-0.187831\pi$
$521$	37.9309			1.66178			0.830891	+	0.556436i	$0.187831\pi$
$522$		0			0
$523$	11.9309	+	20.6649i	0.521701	+	0.903612i	0.999681	+	0.0252415i	$0.00803549\pi$
$523$	11.9309	+	20.6649i	0.521701	+	0.903612i	−0.477981	+	0.878370i	$0.658631\pi$
$524$	−39.6155	+	68.6161i	−1.73061	+	2.99751i
$525$		0			0
$526$	19.6847	−	34.0948i	0.858292	−	1.48661i
$527$	−2.00000	+	3.46410i	−0.0871214	+	0.150899i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	8.40388	+	14.5560i	0.365041	+	0.632270i
$531$		0			0
$532$	18.2462			0.791074
$533$	−7.28078	+	5.68247i	−0.315365	+	0.246135i
$534$		0			0
$535$	−2.31534	−	4.01029i	−0.100101	−	0.173380i
$536$	1.43845	+	2.49146i	0.0621315	+	0.107615i
$537$		0			0
$538$	8.63068			0.372095
$539$	−5.68466	+	9.84612i	−0.244856	+	0.424102i
$540$		0			0
$541$	−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
$543$		0			0
$544$	−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
$549$		0			0
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$	−6.38447			−0.271988
$552$		0			0
$553$	17.0270	−	29.4916i	0.724061	−	1.25411i
$554$	−45.3002			−1.92462
$555$		0			0
$556$	−24.9309	−	43.1815i	−1.05730	−	1.83130i
$557$	−7.03457	−	12.1842i	−0.298064	−	0.516262i	0.677629	−	0.735404i	$-0.263008\pi$
$557$	−7.03457	−	12.1842i	−0.298064	−	0.516262i	−0.975693	+	0.219142i	$0.929674\pi$
$558$		0			0
$559$	−1.46543	−	0.592932i	−0.0619813	−	0.0250783i
$560$	15.3693			0.649472
$561$		0			0
$562$	3.59612	+	6.22866i	0.151693	+	0.262740i
$563$	0.684658	−	1.18586i	0.0288549	−	0.0499782i	−0.851237	−	0.524781i	$-0.824147\pi$
$563$	0.684658	−	1.18586i	0.0288549	−	0.0499782i	0.880092	+	0.474803i	$0.157481\pi$
$564$		0			0
$565$	4.15767	−	7.20130i	0.174915	−	0.302961i
$566$	−1.68466	+	2.91791i	−0.0708115	+	0.122649i
$567$		0			0
$568$	−45.9309	+	79.5546i	−1.92722	+	3.33804i
$569$	20.3693	+	35.2807i	0.853926	+	1.47904i	0.877638	+	0.479325i	$0.159118\pi$
$569$	20.3693	+	35.2807i	0.853926	+	1.47904i	−0.0237115	+	0.999719i	$0.507548\pi$
$570$		0			0
$571$	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			0
$574$	11.6847	+	20.2384i	0.487708	+	0.844735i
$575$	−4.68466	−	8.11407i	−0.195364	−	0.338380i
$576$		0			0
$577$	−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
$579$		0			0
$580$	−14.5616			−0.604636
$581$	16.2462	−	28.1393i	0.674006	−	1.16741i
$582$		0			0
$583$	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	0.976575	−	0.215179i	$-0.0690336\pi$
$587$	7.31534	+	12.6705i	0.301936	+	0.522969i	−0.674638	+	0.738149i	$0.735700\pi$
$588$		0			0
$589$	−0.876894	+	1.51883i	−0.0361318	+	0.0625821i
$590$	16.0000			0.658710
$591$		0			0
$592$	−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	$0.865558\pi$
$594$		0			0
$595$	2.56155	+	4.43674i	0.105013	+	0.181889i
$596$	−14.9654	−	25.9209i	−0.613008	−	1.06176i
$597$		0			0
$598$	−17.1231	−	6.92820i	−0.700216	−	0.283315i
$599$	0.384472			0.0157091			0.00785455	−	0.999969i	$-0.497500\pi$
$599$	0.384472			0.0157091			0.00785455	+	0.999969i	$0.497500\pi$
$600$		0			0
$601$	17.9654	+	31.1170i	0.732825	+	1.26929i	0.955671	+	0.294437i	$0.0951321\pi$
$601$	17.9654	+	31.1170i	0.732825	+	1.26929i	−0.222846	+	0.974854i	$0.571535\pi$
$602$	−2.00000	+	3.46410i	−0.0815139	+	0.141186i
$603$		0			0
$604$	−35.0540	+	60.7153i	−1.42633	+	2.47047i
$605$	−1.96543	+	3.40423i	−0.0799063	+	0.138402i
$606$		0			0
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	−3.68466	−	6.38202i	−0.149433	−	0.258825i
$609$		0			0
$610$	17.4384			0.706062
$611$	4.12311	+	29.4449i	0.166803	+	1.19121i
$612$		0			0
$613$	−11.4309	−	19.7988i	−0.461688	−	0.799668i	0.537357	−	0.843355i	$-0.319423\pi$
$613$	−11.4309	−	19.7988i	−0.461688	−	0.799668i	−0.999045	+	0.0436871i	$0.986090\pi$
$614$	13.0540	+	22.6101i	0.526816	+	0.912471i
$615$		0			0
$616$	46.7386			1.88315
$617$	−5.40388	+	9.35980i	−0.217552	+	0.376811i	−0.954059	−	0.299619i	$-0.903141\pi$
$617$	−5.40388	+	9.35980i	−0.217552	+	0.376811i	0.736507	+	0.676430i	$0.236474\pi$
$618$		0			0
$619$	−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
$621$		0			0
$622$	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
$627$		0			0
$628$	9.96543	−	17.2606i	0.397664	−	0.688774i
$629$	−8.80776			−0.351189
$630$		0			0
$631$	7.21922	−	12.5041i	0.287393	−	0.497779i	−0.685794	−	0.727796i	$-0.740545\pi$
$631$	7.21922	−	12.5041i	0.287393	−	0.497779i	0.973187	+	0.230017i	$0.0738782\pi$
$632$	−62.7386			−2.49561
$633$		0			0
$634$	29.5270	+	51.1422i	1.17267	+	2.03112i
$635$	2.68466	+	4.64996i	0.106537	+	0.184528i
$636$		0			0
$637$	16.1577	−	12.6107i	0.640190	−	0.499653i
$638$	−29.1231			−1.15299
$639$		0			0
$640$	2.65009	+	4.59010i	0.104754	+	0.181439i
$641$	13.0885	−	22.6700i	0.516966	−	0.895412i	−0.482840	−	0.875709i	$-0.660395\pi$
$641$	13.0885	−	22.6700i	0.516966	−	0.895412i	0.999806	−	0.0197030i	$-0.00627208\pi$
$642$		0			0
$643$	−19.2732	+	33.3822i	−0.760061	+	1.31646i	0.182758	+	0.983158i	$0.441498\pi$
$643$	−19.2732	+	33.3822i	−0.760061	+	1.31646i	−0.942819	+	0.333306i	$0.891836\pi$
$644$	−16.2462	+	28.1393i	−0.640190	+	1.10884i
$645$		0			0
$646$	3.68466	−	6.38202i	0.144971	−	0.251097i
$647$	−23.8078	−	41.2363i	−0.935980	−	1.62116i	−0.772877	−	0.634555i	$-0.781183\pi$
$647$	−23.8078	−	41.2363i	−0.935980	−	1.62116i	−0.163102	−	0.986609i	$-0.552150\pi$
$648$		0			0
$649$	22.2462			0.873240
$650$	34.1080	−	26.6204i	1.33782	−	1.04414i
$651$		0			0
$652$	−36.0540	−	62.4473i	−1.41198	−	2.44563i
$653$	7.43845	+	12.8838i	0.291089	+	0.504181i	0.974068	−	0.226258i	$-0.0726491\pi$
$653$	7.43845	+	12.8838i	0.291089	+	0.504181i	−0.682979	+	0.730438i	$0.739316\pi$
$654$		0			0
$655$	−9.75379			−0.381112
$656$	9.84233	−	17.0474i	0.384278	−	0.665590i
$657$		0			0
$658$	75.2311			2.93281
$659$	7.12311	−	12.3376i	0.277477	−	0.480604i	−0.693280	−	0.720668i	$-0.743835\pi$
$659$	7.12311	−	12.3376i	0.277477	−	0.480604i	0.970757	+	0.240064i	$0.0771685\pi$
$660$		0			0
$661$	−15.1847	−	26.3006i	−0.590615	−	1.02297i	−0.994150	−	0.108011i	$-0.965552\pi$
$661$	−15.1847	−	26.3006i	−0.590615	−	1.02297i	0.403535	−	0.914964i	$-0.367781\pi$
$662$	60.9848			2.37024
$663$		0			0
$664$	−59.8617			−2.32309
$665$	1.12311	+	1.94528i	0.0435522	+	0.0754346i
$666$		0			0
$667$	5.68466	−	9.84612i	0.220111	−	0.381243i
$668$	28.4924			1.10240
$669$		0			0
$670$	−0.315342	+	0.546188i	−0.0121827	+	0.0211011i
$671$	24.2462			0.936015
$672$		0			0
$673$	3.37689	+	5.84895i	0.130170	+	0.225461i	0.923742	−	0.383016i	$-0.125114\pi$
$673$	3.37689	+	5.84895i	0.130170	+	0.225461i	−0.793572	+	0.608476i	$0.791781\pi$
$674$	2.71922	+	4.70983i	0.104741	+	0.181416i
$675$		0			0
$676$	14.4039	−	57.5243i	0.553995	−	2.21247i
$677$	−25.6155			−0.984485			−0.492242	−	0.870458i	$-0.663823\pi$
$677$	−25.6155			−0.984485			−0.492242	+	0.870458i	$0.663823\pi$
$678$		0			0
$679$	−7.90388	−	13.6899i	−0.303323	−	0.525371i
$680$	4.71922	−	8.17394i	0.180974	−	0.313456i
$681$		0			0
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	18.0540	−	31.2704i	0.690816	−	1.19653i	−0.280755	−	0.959780i	$-0.590585\pi$
$683$	18.0540	−	31.2704i	0.690816	−	1.19653i	0.971571	−	0.236749i	$-0.0760819\pi$
$684$		0			0
$685$	0.403882	−	0.699544i	0.0154315	−	0.0267282i
$686$	6.00000	+	10.3923i	0.229081	+	0.396780i
$687$		0			0
$688$	3.36932			0.128454
$689$	−5.84233	−	41.7226i	−0.222575	−	1.58950i
$690$		0			0
$691$	−1.15009	−	1.99202i	−0.0437516	−	0.0757800i	0.843320	−	0.537411i	$-0.180598\pi$
$691$	−1.15009	−	1.99202i	−0.0437516	−	0.0757800i	−0.887072	+	0.461631i	$0.847264\pi$
$692$	8.56155	+	14.8290i	0.325461	+	0.563716i
$693$		0			0
$694$	−34.8769			−1.32391
$695$	3.06913	−	5.31589i	0.116419	−	0.201643i
$696$		0			0
$697$	6.56155			0.248537
$698$	−17.6847	+	30.6307i	−0.669374	+	1.15939i
$699$		0			0
$700$	−38.0540	−	65.9114i	−1.43831	−	2.49122i
$701$	−19.3693			−0.731569			−0.365785	−	0.930700i	$-0.619199\pi$
$701$	−19.3693			−0.731569			−0.365785	+	0.930700i	$0.619199\pi$
$702$		0			0
$703$	−3.86174			−0.145648
$704$	−1.43845	−	2.49146i	−0.0542135	−	0.0939006i
$705$		0			0
$706$	−22.6501	+	39.2311i	−0.852448	+	1.47648i
$707$	−12.2462			−0.460566
$708$		0			0
$709$	−12.7462	+	22.0771i	−0.478694	+	0.829122i	−0.999702	−	0.0244297i	$-0.992223\pi$
$709$	−12.7462	+	22.0771i	−0.478694	+	0.829122i	0.521008	+	0.853552i	$0.325556\pi$
$710$	−20.1383			−0.755775
$711$		0			0
$712$	−43.0540	−	74.5717i	−1.61352	−	2.79469i
$713$	−1.56155	−	2.70469i	−0.0584806	−	0.101291i
$714$		0			0
$715$	−3.19224	+	2.49146i	−0.119383	+	0.0931755i
$716$	59.8617			2.23714
$717$		0			0
$718$	−19.6847	−	34.0948i	−0.734625	−	1.27241i
$719$	0.684658	−	1.18586i	0.0255335	−	0.0442252i	−0.852976	−	0.521950i	$-0.825205\pi$
$719$	0.684658	−	1.18586i	0.0255335	−	0.0442252i	0.878510	+	0.477724i	$0.158538\pi$
$720$		0			0
$721$	−13.4654	+	23.3228i	−0.501479	+	0.868587i
$722$	−22.7192	+	39.3508i	−0.845522	+	1.46449i
$723$		0			0
$724$	−22.0885	+	38.2585i	−0.820914	+	1.42187i
$725$	13.3153	+	23.0628i	0.494519	+	0.856533i
$726$		0			0
$727$	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
$729$		0			0
$730$	1.34991	+	2.33811i	0.0499623	+	0.0865372i
$731$	0.561553	+	0.972638i	0.0207698	+	0.0359743i
$732$		0			0
$733$	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
$735$		0			0
$736$	13.1231			0.483724
$737$	−0.438447	+	0.759413i	−0.0161504	+	0.0279733i
$738$		0			0
$739$	3.12311	+	5.40938i	0.114885	+	0.198987i	0.917734	−	0.397196i	$-0.130017\pi$
$739$	3.12311	+	5.40938i	0.114885	+	0.198987i	−0.802849	+	0.596183i	$0.796683\pi$
$740$	−8.80776			−0.323780
$741$		0			0
$742$	−106.600			−3.91342
$743$	−18.6847	−	32.3628i	−0.685474	−	1.18728i	−0.973288	−	0.229589i	$-0.926262\pi$
$743$	−18.6847	−	32.3628i	−0.685474	−	1.18728i	0.287814	−	0.957686i	$-0.407071\pi$
$744$		0			0
$745$	1.84233	−	3.19101i	0.0674977	−	0.116909i
$746$	−9.30019			−0.340504
$747$		0			0
$748$	11.6847	−	20.2384i	0.427233	−	0.739990i
$749$	29.3693			1.07313
$750$		0			0
$751$	15.0540	+	26.0743i	0.549327	+	0.951463i	0.998321	+	0.0579278i	$0.0184493\pi$
$751$	15.0540	+	26.0743i	0.549327	+	0.951463i	−0.448993	+	0.893535i	$0.648217\pi$
$752$	−31.6847	−	54.8794i	−1.15542	−	2.00125i
$753$		0			0
$754$	48.6695	+	19.6922i	1.77244	+	0.717149i
$755$	−8.63068			−0.314103
$756$		0			0
$757$	−15.0000	−	25.9808i	−0.545184	−	0.944287i	−0.998595	−	0.0529853i	$-0.983126\pi$
$757$	−15.0000	−	25.9808i	−0.545184	−	0.944287i	0.453411	−	0.891302i	$-0.350207\pi$
$758$	14.4924	−	25.1016i	0.526388	−	0.911732i
$759$		0			0
$760$	2.06913	−	3.58384i	0.0750552	−	0.129999i
$761$	−7.68466	+	13.3102i	−0.278569	+	0.482495i	−0.971029	−	0.238961i	$-0.923193\pi$
$761$	−7.68466	+	13.3102i	−0.278569	+	0.482495i	0.692461	+	0.721456i	$0.256527\pi$
$762$		0			0
$763$	31.7116	−	54.9262i	1.14804	−	1.98846i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$		0			0
$766$	68.4924			2.47473
$767$	−37.1771	−	15.0423i	−1.34239	−	0.543145i
$768$		0			0
$769$	9.00000	+	15.5885i	0.324548	+	0.562134i	0.981421	−	0.191867i	$-0.0614544\pi$
$769$	9.00000	+	15.5885i	0.324548	+	0.562134i	−0.656873	+	0.754002i	$0.728121\pi$
$770$	5.12311	+	8.87348i	0.184624	+	0.319778i
$771$		0			0
$772$	88.9157			3.20015
$773$	−3.87689	+	6.71498i	−0.139442	+	0.241521i	−0.927286	−	0.374355i	$-0.877864\pi$
$773$	−3.87689	+	6.71498i	−0.139442	+	0.241521i	0.787843	+	0.615876i	$0.211198\pi$
$774$		0			0
$775$	7.31534			0.262775
$776$	−14.5616	+	25.2213i	−0.522729	+	0.905394i
$777$		0			0
$778$	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
$783$		0			0
$784$	−21.8423	+	37.8320i	−0.780083	+	1.35114i
$785$	2.45360			0.0875728
$786$		0			0
$787$	0.588540	−	1.01938i	0.0209792	−	0.0363370i	−0.855345	−	0.518058i	$-0.826655\pi$
$787$	0.588540	−	1.01938i	0.0209792	−	0.0363370i	0.876324	+	0.481721i	$0.159988\pi$
$788$	51.8617			1.84750
$789$		0			0
$790$	−6.87689	−	11.9111i	−0.244669	−	0.423779i
$791$	26.3693	+	45.6730i	0.937585	+	1.62394i
$792$		0			0
$793$	−40.5194	−	16.3946i	−1.43889	−	0.582190i
$794$	30.8769			1.09578
$795$		0			0
$796$	52.8617	+	91.5592i	1.87363	+	3.24523i
$797$	−20.8078	+	36.0401i	−0.737049	+	1.27661i	0.216770	+	0.976223i	$0.430448\pi$
$797$	−20.8078	+	36.0401i	−0.737049	+	1.27661i	−0.953819	+	0.300383i	$0.902885\pi$
$798$		0			0
$799$	10.5616	−	18.2931i	0.373641	−	0.647165i
$800$	−15.3693	+	26.6204i	−0.543387	+	0.941175i
$801$		0			0
$802$	−23.7732	+	41.1764i	−0.839461	+	1.45399i
$803$	1.87689	+	3.25088i	0.0662342	+	0.114721i
$804$		0			0
$805$	−4.00000			−0.140981
$806$	11.3693	−	8.87348i	0.400467	−	0.312555i
$807$		0			0
$808$	11.2808	+	19.5389i	0.396856	+	0.687375i
$809$	18.6501	+	32.3029i	0.655702	+	1.13571i	0.981717	+	0.190345i	$0.0609607\pi$
$809$	18.6501	+	32.3029i	0.655702	+	1.13571i	−0.326015	+	0.945365i	$0.605706\pi$
$810$		0			0
$811$	−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			0
$814$	−17.6155			−0.617424
$815$	4.43845	−	7.68762i	0.155472	−	0.269285i
$816$		0			0
$817$	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	0.536779	−	0.843723i	$-0.319641\pi$
$821$	−13.2462	−	22.9431i	−0.462296	−	0.800720i	−0.999075	+	0.0430028i	$0.986308\pi$
$822$		0			0
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	−0.927281	−	0.374365i	$-0.877861\pi$
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	0.787850	+	0.615867i	$0.211194\pi$
$824$	49.6155			1.72844
$825$		0			0
$826$	−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	$0.706423\pi$
$828$		0			0
$829$	9.74621	+	16.8809i	0.338500	+	0.586299i	0.984151	−	0.177334i	$-0.0567472\pi$
$829$	9.74621	+	16.8809i	0.338500	+	0.586299i	−0.645651	+	0.763633i	$0.723414\pi$
$830$	−6.56155	−	11.3649i	−0.227755	−	0.394483i
$831$		0			0
$832$	0.719224	+	5.13628i	0.0249346	+	0.178069i
$833$	−14.5616			−0.504528
$834$		0			0
$835$	1.75379	+	3.03765i	0.0606924	+	0.105122i
$836$	5.12311	−	8.87348i	0.177186	−	0.306896i
$837$		0			0
$838$	22.7386	−	39.3845i	0.785493	−	1.36051i
$839$	−9.80776	+	16.9875i	−0.338602	+	0.586475i	−0.984170	−	0.177227i	$-0.943287\pi$
$839$	−9.80776	+	16.9875i	−0.338602	+	0.586475i	0.645568	+	0.763703i	$0.276621\pi$
$840$		0			0
$841$	−1.65767	+	2.87117i	−0.0571611	+	0.0990059i
$842$	18.8963	+	32.7294i	0.651210	+	1.12793i
$843$		0			0
$844$	33.3693			1.14862
$845$	7.01941	−	2.00514i	0.241475	−	0.0689791i
$846$		0			0
$847$	−12.4654	−	21.5908i	−0.428317	−	0.741868i
$848$	44.8963	+	77.7627i	1.54175	+	2.67038i
$849$		0			0
$850$	−30.7386			−1.05433
$851$	3.43845	−	5.95557i	0.117868	−	0.204154i
$852$		0			0
$853$	−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			0
$856$	−27.0540	−	46.8589i	−0.924686	−	1.60160i
$857$	−31.4384			−1.07392			−0.536958	−	0.843609i	$-0.680427\pi$
$857$	−31.4384			−1.07392			−0.536958	+	0.843609i	$0.680427\pi$
$858$		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
$861$		0			0
$862$	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	$0.486493\pi$
$864$		0			0
$865$	−1.05398	+	1.82554i	−0.0358362	+	0.0620702i
$866$	−64.6695			−2.19756
$867$		0			0
$868$	−12.6847	−	21.9705i	−0.430545	−	0.745726i
$869$	−9.56155	−	16.5611i	−0.324353	−	0.561797i
$870$		0			0
$871$	1.24621	−	0.972638i	0.0422263	−	0.0329566i
$872$	−116.847			−3.95692
$873$		0			0
$874$	2.87689	+	4.98293i	0.0973124	+	0.168550i
$875$	9.68466	−	16.7743i	0.327401	−	0.567076i
$876$		0			0
$877$	−9.71922	+	16.8342i	−0.328195	+	0.568450i	−0.982154	−	0.188080i	$-0.939774\pi$
$877$	−9.71922	+	16.8342i	−0.328195	+	0.568450i	0.653959	+	0.756530i	$0.273107\pi$
$878$	−1.68466	+	2.91791i	−0.0568545	+	0.0984748i
$879$		0			0
$880$	4.31534	−	7.47439i	0.145470	−	0.251962i
$881$	−18.9654	−	32.8491i	−0.638962	−	1.10671i	−0.985661	−	0.168738i	$-0.946031\pi$
$881$	−18.9654	−	32.8491i	−0.638962	−	1.10671i	0.346699	−	0.937976i	$-0.387302\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	−18.8769	−	32.6957i	−0.634182	−	1.09843i
$887$	24.6847	+	42.7551i	0.828830	+	1.43558i	0.898957	+	0.438037i	$0.144326\pi$
$887$	24.6847	+	42.7551i	0.828830	+	1.43558i	−0.0701272	+	0.997538i	$0.522341\pi$
$888$		0			0
$889$	−34.0540			−1.14213
$890$	9.43845	−	16.3479i	0.316377	−	0.547982i
$891$		0			0
$892$	36.4924			1.22186
$893$	4.63068	−	8.02058i	0.154960	−	0.268398i
$894$		0			0
$895$	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
$900$		0			0
$901$	−14.9654	+	25.9209i	−0.498571	+	0.863550i
$902$	13.1231			0.436952
$903$		0			0
$904$	48.5810	−	84.1447i	1.61578	−	2.79861i
$905$	−5.43845			−0.180780
$906$		0			0
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	−2.56155	−	4.43674i	−0.0850081	−	0.147238i
$909$		0			0
$910$	−2.56155	−	18.2931i	−0.0849146	−	0.606412i
$911$	10.7386			0.355787			0.177893	−	0.984050i	$-0.443072\pi$
$911$	10.7386			0.355787			0.177893	+	0.984050i	$0.443072\pi$
$912$		0			0
$913$	−9.12311	−	15.8017i	−0.301931	−	0.522959i
$914$	−36.6501	+	63.4798i	−1.21228	+	2.09973i
$915$		0			0
$916$	−0.561553	+	0.972638i	−0.0185542	+	0.0321369i
$917$	30.9309	−	53.5738i	1.02143	−	1.76916i
$918$		0			0
$919$	−22.2462	+	38.5316i	−0.733835	+	1.27104i	0.221398	+	0.975184i	$0.428938\pi$
$919$	−22.2462	+	38.5316i	−0.733835	+	1.27104i	−0.955233	+	0.295856i	$0.904395\pi$
$920$	3.68466	+	6.38202i	0.121480	+	0.210409i
$921$		0			0
$922$	−94.2850			−3.10511
$923$	46.7926	+	18.9328i	1.54020	+	0.623181i
$924$		0			0
$925$	8.05398	+	13.9499i	0.264813	+	0.458670i
$926$	−34.1771	−	59.1964i	−1.12313	−	1.94532i
$927$		0			0
$928$	−37.3002			−1.22444
$929$	6.40388	−	11.0918i	0.210105	−	0.363912i	−0.741643	−	0.670795i	$-0.765953\pi$
$929$	6.40388	−	11.0918i	0.210105	−	0.363912i	0.951747	+	0.306884i	$0.0992862\pi$
$930$		0			0
$931$	−6.38447			−0.209243
$932$	59.3002	−	102.711i	1.94244	−	3.36441i
$933$		0			0
$934$	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			0
$940$	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	$0.487065\pi$
$942$		0			0
$943$	−2.56155	+	4.43674i	−0.0834156	+	0.144480i
$944$	85.4773			2.78205
$945$		0			0
$946$	1.12311	+	1.94528i	0.0365153	+	0.0632464i
$947$	5.36932	+	9.29993i	0.174479	+	0.302207i	0.939981	−	0.341227i	$-0.110842\pi$
$947$	5.36932	+	9.29993i	0.174479	+	0.302207i	−0.765502	+	0.643434i	$0.777509\pi$
$948$		0			0
$949$	−0.938447	−	6.70185i	−0.0304633	−	0.217551i
$950$	−13.4773			−0.437260
$951$		0			0
$952$	29.9309	+	51.8418i	0.970065	+	1.68020i
$953$	−17.4924	+	30.2978i	−0.566635	+	0.981441i	0.430260	+	0.902705i	$0.358422\pi$
$953$	−17.4924	+	30.2978i	−0.566635	+	0.981441i	−0.996896	+	0.0787360i	$0.974912\pi$
$954$		0			0
$955$	0.246211	−	0.426450i	0.00796721	−	0.0137996i
$956$	−1.43845	+	2.49146i	−0.0465227	+	0.0805797i
$957$		0			0
$958$	8.00000	−	13.8564i	0.258468	−	0.447680i
$959$	2.56155	+	4.43674i	0.0827169	+	0.143270i
$960$		0			0
$961$	−28.5616			−0.921340
$962$	29.4384	+	11.9111i	0.949134	+	0.384030i
$963$		0			0
$964$	−6.40388	−	11.0918i	−0.206255	−	0.357244i
$965$	5.47301	+	9.47954i	0.176183	+	0.305157i
$966$		0			0
$967$	−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
$969$		0			0
$970$	−6.38447			−0.204993
$971$	26.4924	−	45.8862i	0.850182	−	1.47256i	−0.0308612	−	0.999524i	$-0.509825\pi$
$971$	26.4924	−	45.8862i	0.850182	−	1.47256i	0.881043	−	0.473035i	$-0.156842\pi$
$972$		0			0
$973$	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	0.964380	−	0.264519i	$-0.0852132\pi$
$977$	7.91146	+	13.7030i	0.253110	+	0.438399i	−0.711270	+	0.702918i	$0.751880\pi$
$978$		0			0
$979$	13.1231	−	22.7299i	0.419416	−	0.726450i
$980$	−14.5616			−0.465152
$981$		0			0
$982$	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	$0.354837\pi$
$984$		0			0
$985$	3.19224	+	5.52911i	0.101713	+	0.176172i
$986$	−18.6501	−	32.3029i	−0.593940	−	1.02873i
$987$		0			0
$988$	−14.5616	+	11.3649i	−0.463265	+	0.361567i
$989$	−0.876894			−0.0278836
$990$		0			0
$991$	−20.1771	−	34.9477i	−0.640946	−	1.11015i	−0.985222	−	0.171283i	$-0.945209\pi$
$991$	−20.1771	−	34.9477i	−0.640946	−	1.11015i	0.344276	−	0.938869i	$-0.388124\pi$
$992$	−5.12311	+	8.87348i	−0.162659	+	0.281733i
$993$		0			0
$994$	63.8617	−	110.612i	2.02557	−	3.50839i
$995$	−6.50758	+	11.2715i	−0.206304	+	0.357329i
$996$		0			0
$997$	−10.3078	+	17.8536i	−0.326450	+	0.565428i	−0.981805	−	0.189893i	$-0.939186\pi$
$997$	−10.3078	+	17.8536i	−0.326450	+	0.565428i	0.655355	+	0.755321i	$0.272519\pi$
$998$	−36.4924	−	63.2067i	−1.15515	−	2.00077i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.g.c.55.2		4
3.2	odd	2		39.2.e.b.16.1	✓	4
4.3	odd	2		1872.2.t.r.289.1		4
12.11	even	2		624.2.q.h.289.2		4
13.2	odd	12		1521.2.b.h.1351.4		4
13.3	even	3		1521.2.a.g.1.1		2
13.9	even	3	inner	117.2.g.c.100.2		4
13.10	even	6		1521.2.a.m.1.2		2
13.11	odd	12		1521.2.b.h.1351.1		4
15.2	even	4		975.2.bb.i.874.4		8
15.8	even	4		975.2.bb.i.874.1		8
15.14	odd	2		975.2.i.k.601.2		4
39.2	even	12		507.2.b.d.337.1		4
39.5	even	4		507.2.j.g.361.1		8
39.8	even	4		507.2.j.g.361.4		8
39.11	even	12		507.2.b.d.337.4		4
39.17	odd	6		507.2.e.g.22.2		4
39.20	even	12		507.2.j.g.316.1		8
39.23	odd	6		507.2.a.d.1.1		2
39.29	odd	6		507.2.a.g.1.2		2
39.32	even	12		507.2.j.g.316.4		8
39.35	odd	6		39.2.e.b.22.1	yes	4
39.38	odd	2		507.2.e.g.484.2		4
52.35	odd	6		1872.2.t.r.1153.1		4
156.23	even	6		8112.2.a.bo.1.1		2
156.35	even	6		624.2.q.h.529.2		4
156.107	even	6		8112.2.a.bk.1.2		2
195.74	odd	6		975.2.i.k.451.2		4
195.113	even	12		975.2.bb.i.724.4		8
195.152	even	12		975.2.bb.i.724.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.1	✓	4	3.2	odd	2
39.2.e.b.22.1	yes	4	39.35	odd	6
117.2.g.c.55.2		4	1.1	even	1	trivial
117.2.g.c.100.2		4	13.9	even	3	inner
507.2.a.d.1.1		2	39.23	odd	6
507.2.a.g.1.2		2	39.29	odd	6
507.2.b.d.337.1		4	39.2	even	12
507.2.b.d.337.4		4	39.11	even	12
507.2.e.g.22.2		4	39.17	odd	6
507.2.e.g.484.2		4	39.38	odd	2
507.2.j.g.316.1		8	39.20	even	12
507.2.j.g.316.4		8	39.32	even	12
507.2.j.g.361.1		8	39.5	even	4
507.2.j.g.361.4		8	39.8	even	4
624.2.q.h.289.2		4	12.11	even	2
624.2.q.h.529.2		4	156.35	even	6
975.2.i.k.451.2		4	195.74	odd	6
975.2.i.k.601.2		4	15.14	odd	2
975.2.bb.i.724.1		8	195.152	even	12
975.2.bb.i.724.4		8	195.113	even	12
975.2.bb.i.874.1		8	15.8	even	4
975.2.bb.i.874.4		8	15.2	even	4
1521.2.a.g.1.1		2	13.3	even	3
1521.2.a.m.1.2		2	13.10	even	6
1521.2.b.h.1351.1		4	13.11	odd	12
1521.2.b.h.1351.4		4	13.2	odd	12
1872.2.t.r.289.1		4	4.3	odd	2
1872.2.t.r.1153.1		4	52.35	odd	6
8112.2.a.bk.1.2		2	156.107	even	6
8112.2.a.bo.1.1		2	156.23	even	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

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

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