LMFDB - Embedded newform 117.2.g.c.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(55,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			55.1
Root			$-0.780776 - 1.35234i$ of defining polynomial
Character	$\chi$	$=$	117.55
Dual form			117.2.g.c.100.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.780776 - 1.35234i) q^{2} +(-0.219224 + 0.379706i) q^{4} +3.56155 q^{5} +(-0.280776 + 0.486319i) q^{7} -2.43845 q^{8} +(-2.78078 - 4.81645i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 3.57071i) q^{13} +0.876894 q^{14} +(2.34233 + 4.05703i) q^{16} +(-0.780776 + 1.35234i) q^{17} +(-3.56155 + 6.16879i) q^{19} +(-0.780776 + 1.35234i) q^{20} +(-1.56155 + 2.70469i) q^{22} +(1.00000 + 1.73205i) q^{23} +7.68466 q^{25} +(-5.21922 + 2.11176i) q^{26} +(-0.123106 - 0.213225i) q^{28} +(3.34233 + 5.78908i) q^{29} +2.56155 q^{31} +(1.21922 - 2.11176i) q^{32} +2.43845 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-3.78078 - 6.54850i) q^{37} +11.1231 q^{38} -8.68466 q^{40} +(-0.780776 - 1.35234i) q^{41} +(-2.28078 + 3.95042i) q^{43} +0.876894 q^{44} +(1.56155 - 2.70469i) q^{46} -8.24621 q^{47} +(3.34233 + 5.78908i) q^{49} +(-6.00000 - 10.3923i) q^{50} +(1.24621 + 0.972638i) q^{52} +0.684658 q^{53} +(-3.56155 - 6.16879i) q^{55} +(0.684658 - 1.18586i) q^{56} +(5.21922 - 9.03996i) q^{58} +(-1.43845 + 2.49146i) q^{59} +(-1.93845 + 3.35749i) q^{61} +(-2.00000 - 3.46410i) q^{62} +5.56155 q^{64} +(1.78078 - 12.7173i) q^{65} +(-2.28078 - 3.95042i) q^{67} +(-0.342329 - 0.592932i) q^{68} +3.12311 q^{70} +(7.00000 - 12.1244i) q^{71} -10.1231 q^{73} +(-5.90388 + 10.2258i) q^{74} +(-1.56155 - 2.70469i) q^{76} +1.12311 q^{77} +5.43845 q^{79} +(8.34233 + 14.4493i) q^{80} +(-1.21922 + 2.11176i) q^{82} +0.876894 q^{83} +(-2.78078 + 4.81645i) q^{85} +7.12311 q^{86} +(2.43845 + 4.22351i) q^{88} +(2.43845 + 4.22351i) q^{89} +(1.59612 + 1.24573i) q^{91} -0.876894 q^{92} +(6.43845 + 11.1517i) q^{94} +(-12.6847 + 21.9705i) q^{95} +(4.28078 - 7.41452i) q^{97} +(5.21922 - 9.03996i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 5 q^{4} + 6 q^{5} + 3 q^{7} - 18 q^{8} - 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}+ \cdots + 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

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 $

$2$	−0.780776	−	1.35234i	−0.552092	−	0.956252i	−0.998123	−	0.0612344i	$-0.980496\pi$
$2$	−0.780776	−	1.35234i	−0.552092	−	0.956252i	0.446031	−	0.895017i	$-0.352837\pi$
$3$		0			0
$3$		0			0
$4$	−0.219224	+	0.379706i	−0.109612	+	0.189853i
$5$	3.56155			1.59277			0.796387	−	0.604787i	$-0.206742\pi$
$5$	3.56155			1.59277			0.796387	+	0.604787i	$0.206742\pi$
$6$		0			0
$7$	−0.280776	+	0.486319i	−0.106124	+	0.183811i	−0.914197	−	0.405271i	$-0.867177\pi$
$7$	−0.280776	+	0.486319i	−0.106124	+	0.183811i	0.808073	+	0.589082i	$0.200511\pi$
$8$	−2.43845			−0.862121
$9$		0			0
$10$	−2.78078	−	4.81645i	−0.879359	−	1.52309i
$11$	−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
$14$	0.876894			0.234360
$15$		0			0
$16$	2.34233	+	4.05703i	0.585582	+	1.01426i
$17$	−0.780776	+	1.35234i	−0.189366	+	0.327992i	−0.945039	−	0.326957i	$-0.893977\pi$
$17$	−0.780776	+	1.35234i	−0.189366	+	0.327992i	0.755673	+	0.654949i	$0.227310\pi$
$18$		0			0
$19$	−3.56155	+	6.16879i	−0.817076	+	1.41522i	0.0907512	+	0.995874i	$0.471073\pi$
$19$	−3.56155	+	6.16879i	−0.817076	+	1.41522i	−0.907827	+	0.419344i	$0.862260\pi$
$20$	−0.780776	+	1.35234i	−0.174587	+	0.302393i
$21$		0			0
$22$	−1.56155	+	2.70469i	−0.332924	+	0.576642i
$23$	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
$25$	7.68466			1.53693
$26$	−5.21922	+	2.11176i	−1.02357	+	0.414150i
$27$		0			0
$28$	−0.123106	−	0.213225i	−0.0232648	−	0.0402958i
$29$	3.34233	+	5.78908i	0.620655	+	1.07501i	0.989364	+	0.145461i	$0.0464665\pi$
$29$	3.34233	+	5.78908i	0.620655	+	1.07501i	−0.368709	+	0.929545i	$0.620200\pi$
$30$		0			0
$31$	2.56155			0.460068			0.230034	−	0.973183i	$-0.426116\pi$
$31$	2.56155			0.460068			0.230034	+	0.973183i	$0.426116\pi$
$32$	1.21922	−	2.11176i	0.215530	−	0.373309i
$33$		0			0
$34$	2.43845			0.418190
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$		0			0
$37$	−3.78078	−	6.54850i	−0.621556	−	1.07657i	−0.989196	−	0.146598i	$-0.953168\pi$
$37$	−3.78078	−	6.54850i	−0.621556	−	1.07657i	0.367640	−	0.929968i	$-0.380166\pi$
$38$	11.1231			1.80441
$39$		0			0
$40$	−8.68466			−1.37317
$41$	−0.780776	−	1.35234i	−0.121937	−	0.211201i	0.798595	−	0.601869i	$-0.205577\pi$
$41$	−0.780776	−	1.35234i	−0.121937	−	0.211201i	−0.920531	+	0.390669i	$0.872244\pi$
$42$		0			0
$43$	−2.28078	+	3.95042i	−0.347815	+	0.602433i	−0.985861	−	0.167565i	$-0.946410\pi$
$43$	−2.28078	+	3.95042i	−0.347815	+	0.602433i	0.638046	+	0.769998i	$0.279743\pi$
$44$	0.876894			0.132197
$45$		0			0
$46$	1.56155	−	2.70469i	0.230238	−	0.398785i
$47$	−8.24621			−1.20283			−0.601417	−	0.798935i	$-0.705397\pi$
$47$	−8.24621			−1.20283			−0.601417	+	0.798935i	$0.705397\pi$
$48$		0			0
$49$	3.34233	+	5.78908i	0.477476	+	0.827012i
$50$	−6.00000	−	10.3923i	−0.848528	−	1.46969i
$51$		0			0
$52$	1.24621	+	0.972638i	0.172818	+	0.134881i
$53$	0.684658			0.0940451			0.0470225	−	0.998894i	$-0.485027\pi$
$53$	0.684658			0.0940451			0.0470225	+	0.998894i	$0.485027\pi$
$54$		0			0
$55$	−3.56155	−	6.16879i	−0.480240	−	0.831800i
$56$	0.684658	−	1.18586i	0.0914913	−	0.158468i
$57$		0			0
$58$	5.21922	−	9.03996i	0.685318	−	1.18700i
$59$	−1.43845	+	2.49146i	−0.187270	+	0.324361i	−0.944339	−	0.328974i	$-0.893297\pi$
$59$	−1.43845	+	2.49146i	−0.187270	+	0.324361i	0.757069	+	0.653335i	$0.226631\pi$
$60$		0			0
$61$	−1.93845	+	3.35749i	−0.248193	+	0.429882i	−0.963024	−	0.269414i	$-0.913170\pi$
$61$	−1.93845	+	3.35749i	−0.248193	+	0.429882i	0.714832	+	0.699297i	$0.246503\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$		0			0
$64$	5.56155			0.695194
$65$	1.78078	−	12.7173i	0.220878	−	1.57739i
$66$		0			0
$67$	−2.28078	−	3.95042i	−0.278641	−	0.482621i	0.692406	−	0.721508i	$-0.256551\pi$
$67$	−2.28078	−	3.95042i	−0.278641	−	0.482621i	−0.971047	+	0.238887i	$0.923217\pi$
$68$	−0.342329	−	0.592932i	−0.0415135	−	0.0719035i
$69$		0			0
$70$	3.12311			0.373283
$71$	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
$73$	−10.1231			−1.18482			−0.592410	−	0.805637i	$-0.701823\pi$
$73$	−10.1231			−1.18482			−0.592410	+	0.805637i	$0.701823\pi$
$74$	−5.90388	+	10.2258i	−0.686312	+	1.18873i
$75$		0			0
$76$	−1.56155	−	2.70469i	−0.179122	−	0.310249i
$77$	1.12311			0.127990
$78$		0			0
$79$	5.43845			0.611873			0.305937	−	0.952052i	$-0.401030\pi$
$79$	5.43845			0.611873			0.305937	+	0.952052i	$0.401030\pi$
$80$	8.34233	+	14.4493i	0.932701	+	1.61549i
$81$		0			0
$82$	−1.21922	+	2.11176i	−0.134641	+	0.233205i
$83$	0.876894			0.0962517			0.0481258	−	0.998841i	$-0.484675\pi$
$83$	0.876894			0.0962517			0.0481258	+	0.998841i	$0.484675\pi$
$84$		0			0
$85$	−2.78078	+	4.81645i	−0.301618	+	0.522417i
$86$	7.12311			0.768104
$87$		0			0
$88$	2.43845	+	4.22351i	0.259939	+	0.450228i
$89$	2.43845	+	4.22351i	0.258475	+	0.447692i	0.965834	−	0.259163i	$-0.0834467\pi$
$89$	2.43845	+	4.22351i	0.258475	+	0.447692i	−0.707359	+	0.706855i	$0.750113\pi$
$90$		0			0
$91$	1.59612	+	1.24573i	0.167319	+	0.130588i
$92$	−0.876894			−0.0914226
$93$		0			0
$94$	6.43845	+	11.1517i	0.664075	+	1.15021i
$95$	−12.6847	+	21.9705i	−1.30142	+	2.25412i
$96$		0			0
$97$	4.28078	−	7.41452i	0.434647	−	0.752831i	−0.562620	−	0.826716i	$-0.690206\pi$
$97$	4.28078	−	7.41452i	0.434647	−	0.752831i	0.997267	+	0.0738851i	$0.0235398\pi$
$98$	5.21922	−	9.03996i	0.527221	−	0.913174i
$99$		0			0
$100$	−1.68466	+	2.91791i	−0.168466	+	0.291791i
$101$	−3.78078	−	6.54850i	−0.376201	−	0.651600i	0.614305	−	0.789069i	$-0.289437\pi$
$101$	−3.78078	−	6.54850i	−0.376201	−	0.651600i	−0.990506	+	0.137469i	$0.956103\pi$
$102$		0			0
$103$	−3.43845			−0.338800			−0.169400	−	0.985547i	$-0.554183\pi$
$103$	−3.43845			−0.338800			−0.169400	+	0.985547i	$0.554183\pi$
$104$	−1.21922	+	8.70700i	−0.119555	+	0.853791i
$105$		0			0
$106$	−0.534565	−	0.925894i	−0.0519216	−	0.0899308i
$107$	−4.12311	−	7.14143i	−0.398596	−	0.690388i	0.594957	−	0.803757i	$-0.297169\pi$
$107$	−4.12311	−	7.14143i	−0.398596	−	0.690388i	−0.993553	+	0.113369i	$0.963836\pi$
$108$		0			0
$109$	−2.80776			−0.268935			−0.134468	−	0.990918i	$-0.542932\pi$
$109$	−2.80776			−0.268935			−0.134468	+	0.990918i	$0.542932\pi$
$110$	−5.56155	+	9.63289i	−0.530273	+	0.918460i
$111$		0			0
$112$	−2.63068			−0.248576
$113$	2.90388	−	5.02967i	0.273174	−	0.473152i	−0.696499	−	0.717558i	$-0.745260\pi$
$113$	2.90388	−	5.02967i	0.273174	−	0.473152i	0.969673	+	0.244406i	$0.0785931\pi$
$114$		0			0
$115$	3.56155	+	6.16879i	0.332117	+	0.575243i
$116$	−2.93087			−0.272124
$117$		0			0
$118$	4.49242			0.413561
$119$	−0.438447	−	0.759413i	−0.0401924	−	0.0696153i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	6.05398			0.548101
$123$		0			0
$124$	−0.561553	+	0.972638i	−0.0504289	+	0.0873455i
$125$	9.56155			0.855211
$126$		0			0
$127$	−2.71922	−	4.70983i	−0.241292	−	0.417930i	0.719791	−	0.694191i	$-0.244238\pi$
$127$	−2.71922	−	4.70983i	−0.241292	−	0.417930i	−0.961083	+	0.276261i	$0.910905\pi$
$128$	−6.78078	−	11.7446i	−0.599342	−	1.03809i
$129$		0			0
$130$	−18.5885	+	7.52113i	−1.63032	+	0.659647i
$131$	−7.36932			−0.643860			−0.321930	−	0.946763i	$-0.604332\pi$
$131$	−7.36932			−0.643860			−0.321930	+	0.946763i	$0.604332\pi$
$132$		0			0
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	−3.56155	+	6.16879i	−0.307671	+	0.532902i
$135$		0			0
$136$	1.90388	−	3.29762i	0.163257	−	0.282769i
$137$	−2.78078	+	4.81645i	−0.237578	+	0.411497i	−0.960019	−	0.279936i	$-0.909687\pi$
$137$	−2.78078	+	4.81645i	−0.237578	+	0.411497i	0.722441	+	0.691433i	$0.243020\pi$
$138$		0			0
$139$	8.96543	−	15.5286i	0.760438	−	1.31712i	−0.182187	−	0.983264i	$-0.558318\pi$
$139$	8.96543	−	15.5286i	0.760438	−	1.31712i	0.942625	−	0.333854i	$-0.108349\pi$
$140$	−0.438447	−	0.759413i	−0.0370556	−	0.0641821i
$141$		0			0
$142$	−21.8617			−1.83460
$143$	−6.68466	+	2.70469i	−0.558999	+	0.226177i
$144$		0			0
$145$	11.9039	+	20.6181i	0.988564	+	1.71224i
$146$	7.90388	+	13.6899i	0.654130	+	1.13299i
$147$		0			0
$148$	3.31534			0.272519
$149$	−1.21922	+	2.11176i	−0.0998827	+	0.173002i	−0.911636	−	0.410999i	$-0.865180\pi$
$149$	−1.21922	+	2.11176i	−0.0998827	+	0.173002i	0.811753	+	0.584001i	$0.198513\pi$
$150$		0			0
$151$	−9.36932			−0.762464			−0.381232	−	0.924479i	$-0.624500\pi$
$151$	−9.36932			−0.762464			−0.381232	+	0.924479i	$0.624500\pi$
$152$	8.68466	−	15.0423i	0.704419	−	1.22009i
$153$		0			0
$154$	−0.876894	−	1.51883i	−0.0706622	−	0.122390i
$155$	9.12311			0.732785
$156$		0			0
$157$	20.3693			1.62565			0.812824	−	0.582509i	$-0.197929\pi$
$157$	20.3693			1.62565			0.812824	+	0.582509i	$0.197929\pi$
$158$	−4.24621	−	7.35465i	−0.337810	−	0.585105i
$159$		0			0
$160$	4.34233	−	7.52113i	0.343291	−	0.594598i
$161$	−1.12311			−0.0885131
$162$		0			0
$163$	2.40388	−	4.16365i	0.188287	−	0.326122i	−0.756393	−	0.654118i	$-0.773040\pi$
$163$	2.40388	−	4.16365i	0.188287	−	0.326122i	0.944679	+	0.327996i	$0.106373\pi$
$164$	0.684658			0.0534628
$165$		0			0
$166$	−0.684658	−	1.18586i	−0.0531398	−	0.0920408i
$167$	5.12311	+	8.87348i	0.396438	+	0.686650i	0.993284	−	0.115706i	$-0.0369129\pi$
$167$	5.12311	+	8.87348i	0.396438	+	0.686650i	−0.596846	+	0.802356i	$0.703580\pi$
$168$		0			0
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$	8.68466			0.666083
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	10.1231	−	17.5337i	0.769645	−	1.33307i	−0.168110	−	0.985768i	$-0.553766\pi$
$173$	10.1231	−	17.5337i	0.769645	−	1.33307i	0.937755	−	0.347297i	$-0.112900\pi$
$174$		0			0
$175$	−2.15767	+	3.73720i	−0.163105	+	0.282505i
$176$	4.68466	−	8.11407i	0.353119	−	0.611621i
$177$		0			0
$178$	3.80776	−	6.59524i	0.285404	−	0.494334i
$179$	−2.43845	−	4.22351i	−0.182258	−	0.315680i	0.760391	−	0.649466i	$-0.225007\pi$
$179$	−2.43845	−	4.22351i	−0.182258	−	0.315680i	−0.942649	+	0.333785i	$0.891674\pi$
$180$		0			0
$181$	−2.68466			−0.199549			−0.0997745	−	0.995010i	$-0.531812\pi$
$181$	−2.68466			−0.199549			−0.0997745	+	0.995010i	$0.531812\pi$
$182$	0.438447	−	3.13114i	0.0324999	−	0.232095i
$183$		0			0
$184$	−2.43845	−	4.22351i	−0.179765	−	0.311362i
$185$	−13.4654	−	23.3228i	−0.989998	−	1.71473i
$186$		0			0
$187$	3.12311			0.228384
$188$	1.80776	−	3.13114i	0.131845	−	0.228362i
$189$		0			0
$190$	39.6155			2.87401
$191$	−4.56155	+	7.90084i	−0.330062	+	0.571685i	−0.982524	−	0.186137i	$-0.940403\pi$
$191$	−4.56155	+	7.90084i	−0.330062	+	0.571685i	0.652461	+	0.757822i	$0.273736\pi$
$192$		0			0
$193$	6.74621	+	11.6848i	0.485603	+	0.841089i	0.999863	−	0.0165453i	$-0.00526677\pi$
$193$	6.74621	+	11.6848i	0.485603	+	0.841089i	−0.514260	+	0.857634i	$0.671933\pi$
$194$	−13.3693			−0.959861
$195$		0			0
$196$	−2.93087			−0.209348
$197$	6.68466	+	11.5782i	0.476262	+	0.824910i	0.999630	−	0.0271965i	$-0.00865798\pi$
$197$	6.68466	+	11.5782i	0.476262	+	0.824910i	−0.523368	+	0.852107i	$0.675325\pi$
$198$		0			0
$199$	−11.0885	+	19.2059i	−0.786046	+	1.36147i	0.142327	+	0.989820i	$0.454542\pi$
$199$	−11.0885	+	19.2059i	−0.786046	+	1.36147i	−0.928372	+	0.371651i	$0.878792\pi$
$200$	−18.7386			−1.32502
$201$		0			0
$202$	−5.90388	+	10.2258i	−0.415396	+	0.719486i
$203$	−3.75379			−0.263464
$204$		0			0
$205$	−2.78078	−	4.81645i	−0.194218	−	0.336395i
$206$	2.68466	+	4.64996i	0.187049	+	0.323978i
$207$		0			0
$208$	15.6577	−	6.33527i	1.08566	−	0.439272i
$209$	14.2462			0.985431
$210$		0			0
$211$	−9.84233	−	17.0474i	−0.677574	−	1.17359i	−0.975709	−	0.219069i	$-0.929698\pi$
$211$	−9.84233	−	17.0474i	−0.677574	−	1.17359i	0.298136	−	0.954524i	$-0.403635\pi$
$212$	−0.150093	+	0.259969i	−0.0103084	+	0.0178548i
$213$		0			0
$214$	−6.43845	+	11.1517i	−0.440123	+	0.762316i
$215$	−8.12311	+	14.0696i	−0.553991	+	0.959541i
$216$		0			0
$217$	−0.719224	+	1.24573i	−0.0488241	+	0.0845658i
$218$	2.19224	+	3.79706i	0.148477	+	0.257170i
$219$		0			0
$220$	3.12311			0.210560
$221$	4.43845	+	3.46410i	0.298562	+	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	$0.919650\pi$
$224$	0.684658	+	1.18586i	0.0457457	+	0.0792338i
$225$		0			0
$226$	−9.06913			−0.603270
$227$	3.56155	−	6.16879i	0.236389	−	0.409437i	−0.723287	−	0.690548i	$-0.757370\pi$
$227$	3.56155	−	6.16879i	0.236389	−	0.409437i	0.959675	+	0.281111i	$0.0907028\pi$
$228$		0			0
$229$	−16.2462			−1.07358			−0.536790	−	0.843716i	$-0.680363\pi$
$229$	−16.2462			−1.07358			−0.536790	+	0.843716i	$0.680363\pi$
$230$	5.56155	−	9.63289i	0.366718	−	0.635174i
$231$		0			0
$232$	−8.15009	−	14.1164i	−0.535080	−	0.926785i
$233$	−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
$235$	−29.3693			−1.91584
$236$	−0.630683	−	1.09238i	−0.0410540	−	0.0711076i
$237$		0			0
$238$	−0.684658	+	1.18586i	−0.0443798	+	0.0768681i
$239$	25.3693			1.64100			0.820502	−	0.571643i	$-0.193694\pi$
$239$	25.3693			1.64100			0.820502	+	0.571643i	$0.193694\pi$
$240$		0			0
$241$	8.90388	−	15.4220i	0.573549	−	0.993417i	−0.422648	−	0.906294i	$-0.638899\pi$
$241$	8.90388	−	15.4220i	0.573549	−	0.993417i	0.996198	−	0.0871229i	$-0.0277673\pi$
$242$	−10.9309			−0.702663
$243$		0			0
$244$	−0.849907	−	1.47208i	−0.0544097	−	0.0942404i
$245$	11.9039	+	20.6181i	0.760511	+	1.31724i
$246$		0			0
$247$	20.2462	+	15.8017i	1.28824	+	1.00544i
$248$	−6.24621			−0.396635
$249$		0			0
$250$	−7.46543	−	12.9305i	−0.472156	−	0.817797i
$251$	9.36932	−	16.2281i	0.591386	−	1.02431i	−0.402660	−	0.915350i	$-0.631914\pi$
$251$	9.36932	−	16.2281i	0.591386	−	1.02431i	0.994046	−	0.108961i	$-0.0347524\pi$
$252$		0			0
$253$	2.00000	−	3.46410i	0.125739	−	0.217786i
$254$	−4.24621	+	7.35465i	−0.266431	+	0.461472i
$255$		0			0
$256$	−5.02699	+	8.70700i	−0.314187	+	0.544187i
$257$	14.5885	+	25.2681i	0.910008	+	1.57618i	0.814050	+	0.580795i	$0.197258\pi$
$257$	14.5885	+	25.2681i	0.910008	+	1.57618i	0.0959583	+	0.995385i	$0.469408\pi$
$258$		0			0
$259$	4.24621			0.263847
$260$	4.43845	+	3.46410i	0.275261	+	0.214834i
$261$		0			0
$262$	5.75379	+	9.96585i	0.355470	+	0.615693i
$263$	4.68466	+	8.11407i	0.288868	+	0.500335i	0.973540	−	0.228517i	$-0.0733877\pi$
$263$	4.68466	+	8.11407i	0.288868	+	0.500335i	−0.684672	+	0.728852i	$0.740054\pi$
$264$		0			0
$265$	2.43845			0.149793
$266$	−3.12311	+	5.40938i	−0.191490	+	0.331670i
$267$		0			0
$268$	2.00000			0.122169
$269$	−10.6847	+	18.5064i	−0.651455	+	1.12835i	0.331315	+	0.943520i	$0.392508\pi$
$269$	−10.6847	+	18.5064i	−0.651455	+	1.12835i	−0.982770	+	0.184833i	$0.940826\pi$
$270$		0			0
$271$	14.9654	+	25.9209i	0.909085	+	1.57458i	0.815337	+	0.578986i	$0.196551\pi$
$271$	14.9654	+	25.9209i	0.909085	+	1.57458i	0.0937481	+	0.995596i	$0.470115\pi$
$272$	−7.31534			−0.443558
$273$		0			0
$274$	8.68466			0.524659
$275$	−7.68466	−	13.3102i	−0.463402	−	0.802636i
$276$		0			0
$277$	−2.65767	+	4.60322i	−0.159684	+	0.276581i	−0.934755	−	0.355294i	$-0.884381\pi$
$277$	−2.65767	+	4.60322i	−0.159684	+	0.276581i	0.775071	+	0.631874i	$0.217714\pi$
$278$	−28.0000			−1.67933
$279$		0			0
$280$	2.43845	−	4.22351i	0.145725	−	0.252403i
$281$	−17.8078			−1.06232			−0.531161	−	0.847271i	$-0.678244\pi$
$281$	−17.8078			−1.06232			−0.531161	+	0.847271i	$0.678244\pi$
$282$		0			0
$283$	6.84233	+	11.8513i	0.406734	+	0.704484i	0.994522	−	0.104531i	$-0.0333342\pi$
$283$	6.84233	+	11.8513i	0.406734	+	0.704484i	−0.587787	+	0.809015i	$0.700001\pi$
$284$	3.06913	+	5.31589i	0.182119	+	0.315440i
$285$		0			0
$286$	8.87689	+	6.92820i	0.524902	+	0.409673i
$287$	0.876894			0.0517614
$288$		0			0
$289$	7.28078	+	12.6107i	0.428281	+	0.741804i
$290$	18.5885	−	32.1963i	1.09156	−	1.89063i
$291$		0			0
$292$	2.21922	−	3.84381i	0.129870	−	0.224942i
$293$	10.2192	−	17.7002i	0.597013	−	1.03406i	−0.396246	−	0.918144i	$-0.629687\pi$
$293$	10.2192	−	17.7002i	0.597013	−	1.03406i	0.993259	−	0.115913i	$-0.0369794\pi$
$294$		0			0
$295$	−5.12311	+	8.87348i	−0.298279	+	0.516634i
$296$	9.21922	+	15.9682i	0.535856	+	0.928131i
$297$		0			0
$298$	3.80776			0.220578
$299$	6.68466	−	2.70469i	0.386584	−	0.156416i
$300$		0			0
$301$	−1.28078	−	2.21837i	−0.0738227	−	0.127865i
$302$	7.31534	+	12.6705i	0.420951	+	0.729108i
$303$		0			0
$304$	−33.3693			−1.91386
$305$	−6.90388	+	11.9579i	−0.395315	+	0.684706i
$306$		0			0
$307$	30.8078			1.75829			0.879146	−	0.476553i	$-0.158114\pi$
$307$	30.8078			1.75829			0.879146	+	0.476553i	$0.158114\pi$
$308$	−0.246211	+	0.426450i	−0.0140292	+	0.0242993i
$309$		0			0
$310$	−7.12311	−	12.3376i	−0.404565	−	0.700728i
$311$	19.1231			1.08437			0.542186	−	0.840259i	$-0.317597\pi$
$311$	19.1231			1.08437			0.542186	+	0.840259i	$0.317597\pi$
$312$		0			0
$313$	−13.6847			−0.773503			−0.386751	−	0.922184i	$-0.626403\pi$
$313$	−13.6847			−0.773503			−0.386751	+	0.922184i	$0.626403\pi$
$314$	−15.9039	−	27.5463i	−0.897508	−	1.55453i
$315$		0			0
$316$	−1.19224	+	2.06501i	−0.0670685	+	0.116166i
$317$	−14.0540			−0.789350			−0.394675	−	0.918821i	$-0.629143\pi$
$317$	−14.0540			−0.789350			−0.394675	+	0.918821i	$0.629143\pi$
$318$		0			0
$319$	6.68466	−	11.5782i	0.374269	−	0.648253i
$320$	19.8078			1.10729
$321$		0			0
$322$	0.876894	+	1.51883i	0.0488674	+	0.0846408i
$323$	−5.56155	−	9.63289i	−0.309453	−	0.535988i
$324$		0			0
$325$	3.84233	−	27.4397i	0.213134	−	1.52208i
$326$	−7.50758			−0.415806
$327$		0			0
$328$	1.90388	+	3.29762i	0.105124	+	0.182081i
$329$	2.31534	−	4.01029i	0.127649	−	0.221094i
$330$		0			0
$331$	1.59612	−	2.76456i	0.0877306	−	0.151954i	−0.818821	−	0.574049i	$-0.805372\pi$
$331$	1.59612	−	2.76456i	0.0877306	−	0.151954i	0.906552	+	0.422095i	$0.138705\pi$
$332$	−0.192236	+	0.332962i	−0.0105503	+	0.0182737i
$333$		0			0
$334$	8.00000	−	13.8564i	0.437741	−	0.758189i
$335$	−8.12311	−	14.0696i	−0.443813	−	0.768706i
$336$		0			0
$337$	−6.12311			−0.333547			−0.166773	−	0.985995i	$-0.553335\pi$
$337$	−6.12311			−0.333547			−0.166773	+	0.985995i	$0.553335\pi$
$338$	4.93087	+	19.6922i	0.268204	+	1.07112i
$339$		0			0
$340$	−1.21922	−	2.11176i	−0.0661217	−	0.114526i
$341$	−2.56155	−	4.43674i	−0.138716	−	0.240263i
$342$		0			0
$343$	−7.68466			−0.414933
$344$	5.56155	−	9.63289i	0.299859	−	0.519371i
$345$		0			0
$346$	−31.6155			−1.69966
$347$	13.8078	−	23.9157i	0.741240	−	1.28386i	−0.210692	−	0.977553i	$-0.567572\pi$
$347$	13.8078	−	23.9157i	0.741240	−	1.28386i	0.951931	−	0.306312i	$-0.0990951\pi$
$348$		0			0
$349$	−3.40388	−	5.89570i	−0.182206	−	0.315589i	0.760426	−	0.649425i	$-0.224990\pi$
$349$	−3.40388	−	5.89570i	−0.182206	−	0.315589i	−0.942631	+	0.333836i	$0.891657\pi$
$350$	6.73863			0.360195
$351$		0			0
$352$	−4.87689			−0.259939
$353$	2.65767	+	4.60322i	0.141454	+	0.245005i	0.928044	−	0.372470i	$-0.121489\pi$
$353$	2.65767	+	4.60322i	0.141454	+	0.245005i	−0.786591	+	0.617475i	$0.788156\pi$
$354$		0			0
$355$	24.9309	−	43.1815i	1.32319	−	2.29184i
$356$	−2.13826			−0.113328
$357$		0			0
$358$	−3.80776	+	6.59524i	−0.201247	+	0.348569i
$359$	9.36932			0.494494			0.247247	−	0.968953i	$-0.420474\pi$
$359$	9.36932			0.494494			0.247247	+	0.968953i	$0.420474\pi$
$360$		0			0
$361$	−15.8693	−	27.4865i	−0.835227	−	1.44666i
$362$	2.09612	+	3.63058i	0.110170	+	0.190819i
$363$		0			0
$364$	−0.822919	+	0.332962i	−0.0431327	+	0.0174520i
$365$	−36.0540			−1.88715
$366$		0			0
$367$	8.52699	+	14.7692i	0.445105	+	0.770945i	0.998060	−	0.0622668i	$-0.0198330\pi$
$367$	8.52699	+	14.7692i	0.445105	+	0.770945i	−0.552954	+	0.833212i	$0.686500\pi$
$368$	−4.68466	+	8.11407i	−0.244205	+	0.422975i
$369$		0			0
$370$	−21.0270	+	36.4198i	−1.09314	+	1.89338i
$371$	−0.192236	+	0.332962i	−0.00998039	+	0.0172865i
$372$		0			0
$373$	−14.1847	+	24.5685i	−0.734454	+	1.27211i	0.220509	+	0.975385i	$0.429228\pi$
$373$	−14.1847	+	24.5685i	−0.734454	+	1.27211i	−0.954963	+	0.296726i	$0.904105\pi$
$374$	−2.43845	−	4.22351i	−0.126089	−	0.218393i
$375$		0			0
$376$	20.1080			1.03699
$377$	22.3423	−	9.03996i	1.15069	−	0.465582i
$378$		0			0
$379$	−11.8423	−	20.5115i	−0.608300	−	1.05361i	−0.991521	−	0.129949i	$-0.958519\pi$
$379$	−11.8423	−	20.5115i	−0.608300	−	1.05361i	0.383221	−	0.923657i	$-0.374815\pi$
$380$	−5.56155	−	9.63289i	−0.285302	−	0.494157i
$381$		0			0
$382$	14.2462			0.728900
$383$	−11.3693	+	19.6922i	−0.580945	+	1.00623i	0.414423	+	0.910085i	$0.363984\pi$
$383$	−11.3693	+	19.6922i	−0.580945	+	1.00623i	−0.995368	+	0.0961417i	$0.969350\pi$
$384$		0			0
$385$	4.00000			0.203859
$386$	10.5346	−	18.2464i	0.536195	−	0.928717i
$387$		0			0
$388$	1.87689	+	3.25088i	0.0952849	+	0.165038i
$389$	−34.0540			−1.72661			−0.863303	−	0.504687i	$-0.831608\pi$
$389$	−34.0540			−1.72661			−0.863303	+	0.504687i	$0.831608\pi$
$390$		0			0
$391$	−3.12311			−0.157942
$392$	−8.15009	−	14.1164i	−0.411642	−	0.712985i
$393$		0			0
$394$	10.4384	−	18.0799i	0.525881	−	0.910853i
$395$	19.3693			0.974576
$396$		0			0
$397$	−12.5270	+	21.6974i	−0.628711	+	1.08896i	0.359099	+	0.933299i	$0.383084\pi$
$397$	−12.5270	+	21.6974i	−0.628711	+	1.08896i	−0.987811	+	0.155661i	$0.950249\pi$
$398$	34.6307			1.73588
$399$		0			0
$400$	18.0000	+	31.1769i	0.900000	+	1.55885i
$401$	7.21922	+	12.5041i	0.360511	+	0.624423i	0.988045	−	0.154166i	$-0.0492691\pi$
$401$	7.21922	+	12.5041i	0.360511	+	0.624423i	−0.627534	+	0.778589i	$0.715936\pi$
$402$		0			0
$403$	1.28078	−	9.14657i	0.0638000	−	0.455623i
$404$	3.31534			0.164944
$405$		0			0
$406$	2.93087	+	5.07642i	0.145457	+	0.251938i
$407$	−7.56155	+	13.0970i	−0.374812	+	0.649194i
$408$		0			0
$409$	−3.18466	+	5.51599i	−0.157471	+	0.272748i	−0.933956	−	0.357388i	$-0.883667\pi$
$409$	−3.18466	+	5.51599i	−0.157471	+	0.272748i	0.776485	+	0.630136i	$0.217001\pi$
$410$	−4.34233	+	7.52113i	−0.214452	+	0.371442i
$411$		0			0
$412$	0.753789	−	1.30560i	0.0371365	−	0.0643223i
$413$	−0.807764	−	1.39909i	−0.0397475	−	0.0688446i
$414$		0			0
$415$	3.12311			0.153307
$416$	−6.93087	−	5.40938i	−0.339814	−	0.265217i
$417$		0			0
$418$	−11.1231	−	19.2658i	−0.544049	−	0.942320i
$419$	−17.1231	−	29.6581i	−0.836518	−	1.44889i	−0.892788	−	0.450477i	$-0.851254\pi$
$419$	−17.1231	−	29.6581i	−0.836518	−	1.44889i	0.0562697	−	0.998416i	$-0.482079\pi$
$420$		0			0
$421$	31.2462			1.52285			0.761424	−	0.648255i	$-0.224501\pi$
$421$	31.2462			1.52285			0.761424	+	0.648255i	$0.224501\pi$
$422$	−15.3693	+	26.6204i	−0.748167	+	1.29586i
$423$		0			0
$424$	−1.66950			−0.0810783
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	−1.08854	−	1.88541i	−0.0526782	−	0.0912413i
$428$	3.61553			0.174763
$429$		0			0
$430$	25.3693			1.22342
$431$	−5.56155	−	9.63289i	−0.267891	−	0.464000i	0.700426	−	0.713725i	$-0.252993\pi$
$431$	−5.56155	−	9.63289i	−0.267891	−	0.464000i	−0.968317	+	0.249725i	$0.919660\pi$
$432$		0			0
$433$	−4.37689	+	7.58100i	−0.210340	+	0.364320i	−0.951821	−	0.306654i	$-0.900790\pi$
$433$	−4.37689	+	7.58100i	−0.210340	+	0.364320i	0.741481	+	0.670974i	$0.234124\pi$
$434$	2.24621			0.107822
$435$		0			0
$436$	0.615528	−	1.06613i	0.0294785	−	0.0510582i
$437$	−14.2462			−0.681489
$438$		0			0
$439$	6.84233	+	11.8513i	0.326567	+	0.565630i	0.981828	−	0.189772i	$-0.0607749\pi$
$439$	6.84233	+	11.8513i	0.326567	+	0.565630i	−0.655262	+	0.755402i	$0.727442\pi$
$440$	8.68466	+	15.0423i	0.414025	+	0.717112i
$441$		0			0
$442$	1.21922	−	8.70700i	0.0579926	−	0.414150i
$443$	34.7386			1.65048			0.825241	−	0.564781i	$-0.191039\pi$
$443$	34.7386			1.65048			0.825241	+	0.564781i	$0.191039\pi$
$444$		0			0
$445$	8.68466	+	15.0423i	0.411692	+	0.713072i
$446$	−6.24621	+	10.8188i	−0.295767	+	0.512283i
$447$		0			0
$448$	−1.56155	+	2.70469i	−0.0737764	+	0.127785i
$449$	−4.12311	+	7.14143i	−0.194581	+	0.337025i	−0.946763	−	0.321931i	$-0.895668\pi$
$449$	−4.12311	+	7.14143i	−0.194581	+	0.337025i	0.752182	+	0.658956i	$0.229002\pi$
$450$		0			0
$451$	−1.56155	+	2.70469i	−0.0735307	+	0.127359i
$452$	1.27320	+	2.20525i	0.0598862	+	0.103726i
$453$		0			0
$454$	−11.1231			−0.522033
$455$	5.68466	+	4.43674i	0.266501	+	0.207998i
$456$		0			0
$457$	−6.30776	−	10.9254i	−0.295065	−	0.511067i	0.679935	−	0.733272i	$-0.262008\pi$
$457$	−6.30776	−	10.9254i	−0.295065	−	0.511067i	−0.975000	+	0.222205i	$0.928675\pi$
$458$	12.6847	+	21.9705i	0.592715	+	1.02661i
$459$		0			0
$460$	−3.12311			−0.145616
$461$	−8.09612	+	14.0229i	−0.377074	+	0.653111i	−0.990635	−	0.136536i	$-0.956403\pi$
$461$	−8.09612	+	14.0229i	−0.377074	+	0.653111i	0.613561	+	0.789647i	$0.289736\pi$
$462$		0			0
$463$	−14.3153			−0.665290			−0.332645	−	0.943052i	$-0.607941\pi$
$463$	−14.3153			−0.665290			−0.332645	+	0.943052i	$0.607941\pi$
$464$	−15.6577	+	27.1199i	−0.726889	+	1.25901i
$465$		0			0
$466$	20.3002	+	35.1610i	0.940388	+	1.62880i
$467$	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
$469$	2.56155			0.118282
$470$	22.9309	+	39.7174i	1.05772	+	1.83203i
$471$		0			0
$472$	3.50758	−	6.07530i	0.161449	−	0.279638i
$473$	9.12311			0.419481
$474$		0			0
$475$	−27.3693	+	47.4050i	−1.25579	+	2.17509i
$476$	0.384472			0.0176222
$477$		0			0
$478$	−19.8078	−	34.3081i	−0.905986	−	1.56921i
$479$	5.12311	+	8.87348i	0.234081	+	0.405440i	0.959005	−	0.283389i	$-0.0914587\pi$
$479$	5.12311	+	8.87348i	0.234081	+	0.405440i	−0.724924	+	0.688828i	$0.758125\pi$
$480$		0			0
$481$	−25.2732	+	10.2258i	−1.15236	+	0.466257i
$482$	−27.8078			−1.26661
$483$		0			0
$484$	1.53457	+	2.65794i	0.0697530	+	0.120816i
$485$	15.2462	−	26.4072i	0.692295	−	1.19909i
$486$		0			0
$487$	−3.56155	+	6.16879i	−0.161389	+	0.279535i	−0.935367	−	0.353678i	$-0.884931\pi$
$487$	−3.56155	+	6.16879i	−0.161389	+	0.279535i	0.773978	+	0.633213i	$0.218264\pi$
$488$	4.72680	−	8.18706i	0.213972	−	0.370611i
$489$		0			0
$490$	18.5885	−	32.1963i	0.839745	−	1.45448i
$491$	−18.1231	−	31.3901i	−0.817884	−	1.41662i	−0.907238	−	0.420617i	$-0.861814\pi$
$491$	−18.1231	−	31.3901i	−0.817884	−	1.41662i	0.0893539	−	0.996000i	$-0.471520\pi$
$492$		0			0
$493$	−10.4384			−0.470124
$494$	5.56155	−	39.7174i	0.250226	−	1.78697i
$495$		0			0
$496$	6.00000	+	10.3923i	0.269408	+	0.466628i
$497$	3.93087	+	6.80847i	0.176324	+	0.305401i
$498$		0			0
$499$	4.49242			0.201108			0.100554	−	0.994932i	$-0.467938\pi$
$499$	4.49242			0.201108			0.100554	+	0.994932i	$0.467938\pi$
$500$	−2.09612	+	3.63058i	−0.0937412	+	0.162365i
$501$		0			0
$502$	−29.2614			−1.30600
$503$	−14.1231	+	24.4619i	−0.629718	+	1.09070i	0.357890	+	0.933764i	$0.383496\pi$
$503$	−14.1231	+	24.4619i	−0.629718	+	1.09070i	−0.987608	+	0.156940i	$0.949837\pi$
$504$		0			0
$505$	−13.4654	−	23.3228i	−0.599204	−	1.03785i
$506$	−6.24621			−0.277678
$507$		0			0
$508$	2.38447			0.105794
$509$	−6.90388	−	11.9579i	−0.306009	−	0.530023i	0.671476	−	0.741026i	$-0.265660\pi$
$509$	−6.90388	−	11.9579i	−0.306009	−	0.530023i	−0.977486	+	0.211003i	$0.932327\pi$
$510$		0			0
$511$	2.84233	−	4.92306i	0.125737	−	0.217783i
$512$	−11.4233			−0.504843
$513$		0			0
$514$	22.7808	−	39.4575i	1.00482	−	1.74039i
$515$	−12.2462			−0.539633
$516$		0			0
$517$	8.24621	+	14.2829i	0.362668	+	0.628159i
$518$	−3.31534	−	5.74234i	−0.145668	−	0.252304i
$519$		0			0
$520$	−4.34233	+	31.0104i	−0.190424	+	1.35990i
$521$	9.06913			0.397326			0.198663	−	0.980068i	$-0.436340\pi$
$521$	9.06913			0.397326			0.198663	+	0.980068i	$0.436340\pi$
$522$		0			0
$523$	−16.9309	−	29.3251i	−0.740335	−	1.28230i	−0.952343	−	0.305030i	$-0.901333\pi$
$523$	−16.9309	−	29.3251i	−0.740335	−	1.28230i	0.212007	−	0.977268i	$-0.432000\pi$
$524$	1.61553	−	2.79818i	0.0705747	−	0.122239i
$525$		0			0
$526$	7.31534	−	12.6705i	0.318964	−	0.552462i
$527$	−2.00000	+	3.46410i	−0.0871214	+	0.150899i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	−1.90388	−	3.29762i	−0.0826994	−	0.143239i
$531$		0			0
$532$	1.75379			0.0760364
$533$	−5.21922	+	2.11176i	−0.226070	+	0.0914704i
$534$		0			0
$535$	−14.6847	−	25.4346i	−0.634873	−	1.09963i
$536$	5.56155	+	9.63289i	0.240222	+	0.416078i
$537$		0			0
$538$	33.3693			1.43865
$539$	6.68466	−	11.5782i	0.287929	−	0.498707i
$540$		0			0
$541$	19.7386			0.848630			0.424315	−	0.905515i	$-0.360515\pi$
$541$	19.7386			0.848630			0.424315	+	0.905515i	$0.360515\pi$
$542$	23.3693	−	40.4768i	1.00380	−	1.73863i
$543$		0			0
$544$	1.90388	+	3.29762i	0.0816283	+	0.141384i
$545$	−10.0000			−0.428353
$546$		0			0
$547$	3.93087			0.168072			0.0840359	−	0.996463i	$-0.473219\pi$
$547$	3.93087			0.168072			0.0840359	+	0.996463i	$0.473219\pi$
$548$	−1.21922	−	2.11176i	−0.0520827	−	0.0902098i
$549$		0			0
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$	−47.6155			−2.02849
$552$		0			0
$553$	−1.52699	+	2.64482i	−0.0649341	+	0.112469i
$554$	8.30019			0.352641
$555$		0			0
$556$	3.93087	+	6.80847i	0.166706	+	0.288743i
$557$	−21.4654	−	37.1792i	−0.909520	−	1.57533i	−0.814733	−	0.579837i	$-0.803116\pi$
$557$	−21.4654	−	37.1792i	−0.909520	−	1.57533i	−0.0947869	−	0.995498i	$-0.530217\pi$
$558$		0			0
$559$	12.9654	+	10.1192i	0.548379	+	0.427997i
$560$	−9.36932			−0.395926
$561$		0			0
$562$	13.9039	+	24.0822i	0.586500	+	1.01585i
$563$	−11.6847	+	20.2384i	−0.492450	+	0.852948i	−0.999962	−	0.00869657i	$-0.997232\pi$
$563$	−11.6847	+	20.2384i	−0.492450	+	0.852948i	0.507513	+	0.861644i	$0.330565\pi$
$564$		0			0
$565$	10.3423	−	17.9134i	0.435105	−	0.753624i
$566$	10.6847	−	18.5064i	0.449110	−	0.777881i
$567$		0			0
$568$	−17.0691	+	29.5646i	−0.716205	+	1.24050i
$569$	−4.36932	−	7.56788i	−0.183171	−	0.317262i	0.759787	−	0.650171i	$-0.225303\pi$
$569$	−4.36932	−	7.56788i	−0.183171	−	0.317262i	−0.942959	+	0.332910i	$0.891970\pi$
$570$		0			0
$571$	−5.36932			−0.224699			−0.112349	−	0.993669i	$-0.535838\pi$
$571$	−5.36932			−0.224699			−0.112349	+	0.993669i	$0.535838\pi$
$572$	0.438447	−	3.13114i	0.0183324	−	0.130920i
$573$		0			0
$574$	−0.684658	−	1.18586i	−0.0285771	−	0.0494970i
$575$	7.68466	+	13.3102i	0.320472	+	0.555074i
$576$		0			0
$577$	−17.3153			−0.720847			−0.360424	−	0.932789i	$-0.617368\pi$
$577$	−17.3153			−0.720847			−0.360424	+	0.932789i	$0.617368\pi$
$578$	11.3693	−	19.6922i	0.472901	−	0.819089i
$579$		0			0
$580$	−10.4384			−0.433433
$581$	−0.246211	+	0.426450i	−0.0102146	+	0.0176921i
$582$		0			0
$583$	−0.684658	−	1.18586i	−0.0283557	−	0.0491134i
$584$	24.6847			1.02146
$585$		0			0
$586$	−31.9157			−1.31843
$587$	19.6847	+	34.0948i	0.812473	+	1.40724i	0.911128	+	0.412123i	$0.135212\pi$
$587$	19.6847	+	34.0948i	0.812473	+	1.40724i	−0.0986556	+	0.995122i	$0.531454\pi$
$588$		0			0
$589$	−9.12311	+	15.8017i	−0.375911	+	0.651097i
$590$	16.0000			0.658710
$591$		0			0
$592$	17.7116	−	30.6775i	0.727944	−	1.26084i
$593$	17.4233			0.715489			0.357744	−	0.933820i	$-0.383546\pi$
$593$	17.4233			0.715489			0.357744	+	0.933820i	$0.383546\pi$
$594$		0			0
$595$	−1.56155	−	2.70469i	−0.0640174	−	0.110881i
$596$	−0.534565	−	0.925894i	−0.0218966	−	0.0379261i
$597$		0			0
$598$	−8.87689	−	6.92820i	−0.363003	−	0.283315i
$599$	41.6155			1.70036			0.850182	−	0.526489i	$-0.176492\pi$
$599$	41.6155			1.70036			0.850182	+	0.526489i	$0.176492\pi$
$600$		0			0
$601$	3.53457	+	6.12205i	0.144178	+	0.249723i	0.929066	−	0.369914i	$-0.120613\pi$
$601$	3.53457	+	6.12205i	0.144178	+	0.249723i	−0.784888	+	0.619638i	$0.787280\pi$
$602$	−2.00000	+	3.46410i	−0.0815139	+	0.141186i
$603$		0			0
$604$	2.05398	−	3.55759i	0.0835751	−	0.144756i
$605$	12.4654	−	21.5908i	0.506792	−	0.877789i
$606$		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	$0.0614000\pi$
$608$	8.68466	+	15.0423i	0.352209	+	0.610045i
$609$		0			0
$610$	21.5616			0.873002
$611$	−4.12311	+	29.4449i	−0.166803	+	1.19121i
$612$		0			0
$613$	17.4309	+	30.1912i	0.704026	+	1.21941i	0.967042	+	0.254618i	$0.0819496\pi$
$613$	17.4309	+	30.1912i	0.704026	+	1.21941i	−0.263016	+	0.964792i	$0.584717\pi$
$614$	−24.0540	−	41.6627i	−0.970739	−	1.68137i
$615$		0			0
$616$	−2.73863			−0.110343
$617$	4.90388	−	8.49377i	0.197423	−	0.341946i	−0.750269	−	0.661132i	$-0.770076\pi$
$617$	4.90388	−	8.49377i	0.197423	−	0.341946i	0.947692	+	0.319186i	$0.103409\pi$
$618$		0			0
$619$	29.3002			1.17767			0.588837	−	0.808252i	$-0.299586\pi$
$619$	29.3002			1.17767			0.588837	+	0.808252i	$0.299586\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$		0			0
$622$	−14.9309	−	25.8610i	−0.598673	−	1.03693i
$623$	−2.73863			−0.109721
$624$		0			0
$625$	−4.36932			−0.174773
$626$	10.6847	+	18.5064i	0.427045	+	0.739663i
$627$		0			0
$628$	−4.46543	+	7.73436i	−0.178190	+	0.308635i
$629$	11.8078			0.470806
$630$		0			0
$631$	9.28078	−	16.0748i	0.369462	−	0.639927i	−0.620020	−	0.784586i	$-0.712875\pi$
$631$	9.28078	−	16.0748i	0.369462	−	0.639927i	0.989481	+	0.144660i	$0.0462087\pi$
$632$	−13.2614			−0.527509
$633$		0			0
$634$	10.9730	+	19.0058i	0.435794	+	0.754817i
$635$	−9.68466	−	16.7743i	−0.384324	−	0.665669i
$636$		0			0
$637$	22.3423	−	9.03996i	0.885235	−	0.358176i
$638$	−20.8769			−0.826524
$639$		0			0
$640$	−24.1501	−	41.8292i	−0.954616	−	1.65344i
$641$	−9.58854	+	16.6078i	−0.378725	+	0.655970i	−0.990877	−	0.134770i	$-0.956971\pi$
$641$	−9.58854	+	16.6078i	−0.378725	+	0.655970i	0.612152	+	0.790740i	$0.290304\pi$
$642$		0			0
$643$	15.7732	−	27.3200i	0.622034	−	1.07739i	−0.367072	−	0.930192i	$-0.619640\pi$
$643$	15.7732	−	27.3200i	0.622034	−	1.07739i	0.989106	−	0.147202i	$-0.0470269\pi$
$644$	0.246211	−	0.426450i	0.00970208	−	0.0168045i
$645$		0			0
$646$	−8.68466	+	15.0423i	−0.341693	+	0.591830i
$647$	−3.19224	−	5.52911i	−0.125500	−	0.217372i	0.796428	−	0.604733i	$-0.206720\pi$
$647$	−3.19224	−	5.52911i	−0.125500	−	0.217372i	−0.921928	+	0.387361i	$0.873387\pi$
$648$		0			0
$649$	5.75379			0.225856
$650$	−40.1080	+	16.2281i	−1.57316	+	0.636520i
$651$		0			0
$652$	1.05398	+	1.82554i	0.0412769	+	0.0714936i
$653$	11.5616	+	20.0252i	0.452439	+	0.783647i	0.998537	−	0.0540745i	$-0.0172209\pi$
$653$	11.5616	+	20.0252i	0.452439	+	0.783647i	−0.546098	+	0.837721i	$0.683888\pi$
$654$		0			0
$655$	−26.2462			−1.02552
$656$	3.65767	−	6.33527i	0.142808	−	0.247351i
$657$		0			0
$658$	−7.23106			−0.281896
$659$	−1.12311	+	1.94528i	−0.0437500	+	0.0757772i	−0.887071	−	0.461633i	$-0.847264\pi$
$659$	−1.12311	+	1.94528i	−0.0437500	+	0.0757772i	0.843321	+	0.537410i	$0.180597\pi$
$660$		0			0
$661$	−2.81534	−	4.87631i	−0.109504	−	0.189667i	0.806065	−	0.591827i	$-0.201593\pi$
$661$	−2.81534	−	4.87631i	−0.109504	−	0.189667i	−0.915569	+	0.402160i	$0.868260\pi$
$662$	−4.98485			−0.193742
$663$		0			0
$664$	−2.13826			−0.0829806
$665$	−7.12311	−	12.3376i	−0.276222	−	0.478431i
$666$		0			0
$667$	−6.68466	+	11.5782i	−0.258831	+	0.448308i
$668$	−4.49242			−0.173817
$669$		0			0
$670$	−12.6847	+	21.9705i	−0.490051	+	0.848793i
$671$	7.75379			0.299332
$672$		0			0
$673$	11.6231	+	20.1318i	0.448038	+	0.776024i	0.998258	−	0.0589952i	$-0.0187897\pi$
$673$	11.6231	+	20.1318i	0.448038	+	0.776024i	−0.550220	+	0.835019i	$0.685456\pi$
$674$	4.78078	+	8.28055i	0.184149	+	0.318955i
$675$		0			0
$676$	4.09612	−	3.96355i	0.157543	−	0.152444i
$677$	15.6155			0.600153			0.300077	−	0.953915i	$-0.402988\pi$
$677$	15.6155			0.600153			0.300077	+	0.953915i	$0.402988\pi$
$678$		0			0
$679$	2.40388	+	4.16365i	0.0922525	+	0.159786i
$680$	6.78078	−	11.7446i	0.260031	−	0.450387i
$681$		0			0
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	−19.0540	+	33.0025i	−0.729080	+	1.26280i	0.228192	+	0.973616i	$0.426719\pi$
$683$	−19.0540	+	33.0025i	−0.729080	+	1.26280i	−0.957272	+	0.289188i	$0.906615\pi$
$684$		0			0
$685$	−9.90388	+	17.1540i	−0.378408	+	0.655422i
$686$	6.00000	+	10.3923i	0.229081	+	0.396780i
$687$		0			0
$688$	−21.3693			−0.814698
$689$	0.342329	−	2.44472i	0.0130417	−	0.0931364i
$690$		0			0
$691$	25.6501	+	44.4273i	0.975776	+	1.69009i	0.677352	+	0.735659i	$0.263128\pi$
$691$	25.6501	+	44.4273i	0.975776	+	1.69009i	0.298424	+	0.954433i	$0.403539\pi$
$692$	4.43845	+	7.68762i	0.168724	+	0.292239i
$693$		0			0
$694$	−43.1231			−1.63693
$695$	31.9309	−	55.3059i	1.21121	−	2.09787i
$696$		0			0
$697$	2.43845			0.0923628
$698$	−5.31534	+	9.20644i	−0.201189	+	0.348469i
$699$		0			0
$700$	−0.946025	−	1.63856i	−0.0357564	−	0.0619319i
$701$	5.36932			0.202796			0.101398	−	0.994846i	$-0.467668\pi$
$701$	5.36932			0.202796			0.101398	+	0.994846i	$0.467668\pi$
$702$		0			0
$703$	53.8617			2.03143
$704$	−5.56155	−	9.63289i	−0.209609	−	0.363053i
$705$		0			0
$706$	4.15009	−	7.18817i	0.156191	−	0.270530i
$707$	4.24621			0.159695
$708$		0			0
$709$	3.74621	−	6.48863i	0.140692	−	0.243686i	−0.787065	−	0.616869i	$-0.788401\pi$
$709$	3.74621	−	6.48863i	0.140692	−	0.243686i	0.927757	+	0.373184i	$0.121734\pi$
$710$	−77.8617			−2.92210
$711$		0			0
$712$	−5.94602	−	10.2988i	−0.222837	−	0.385964i
$713$	2.56155	+	4.43674i	0.0959309	+	0.166157i
$714$		0			0
$715$	−23.8078	+	9.63289i	−0.890360	+	0.360250i
$716$	2.13826			0.0799106
$717$		0			0
$718$	−7.31534	−	12.6705i	−0.273006	−	0.472860i
$719$	−11.6847	+	20.2384i	−0.435764	+	0.754766i	−0.997358	−	0.0726475i	$-0.976855\pi$
$719$	−11.6847	+	20.2384i	−0.435764	+	0.754766i	0.561593	+	0.827413i	$0.310189\pi$
$720$		0			0
$721$	0.965435	−	1.67218i	0.0359547	−	0.0622753i
$722$	−24.7808	+	42.9216i	−0.922245	+	1.59738i
$723$		0			0
$724$	0.588540	−	1.01938i	0.0218729	−	0.0378850i
$725$	25.6847	+	44.4871i	0.953904	+	1.65221i
$726$		0			0
$727$	−38.6695			−1.43417			−0.717086	−	0.696984i	$-0.754525\pi$
$727$	−38.6695			−1.43417			−0.717086	+	0.696984i	$0.754525\pi$
$728$	−3.89205	−	3.03765i	−0.144249	−	0.112583i
$729$		0			0
$730$	28.1501	+	48.7574i	1.04188	+	1.80459i
$731$	−3.56155	−	6.16879i	−0.131729	−	0.228161i
$732$		0			0
$733$	20.5076			0.757465			0.378732	−	0.925506i	$-0.376360\pi$
$733$	20.5076			0.757465			0.378732	+	0.925506i	$0.376360\pi$
$734$	13.3153	−	23.0628i	0.491478	−	0.851265i
$735$		0			0
$736$	4.87689			0.179765
$737$	−4.56155	+	7.90084i	−0.168027	+	0.291031i
$738$		0			0
$739$	−5.12311	−	8.87348i	−0.188456	−	0.326416i	0.756279	−	0.654249i	$-0.227015\pi$
$739$	−5.12311	−	8.87348i	−0.188456	−	0.326416i	−0.944736	+	0.327833i	$0.893682\pi$
$740$	11.8078			0.434062
$741$		0			0
$742$	0.600373			0.0220404
$743$	−6.31534	−	10.9385i	−0.231687	−	0.401294i	0.726617	−	0.687042i	$-0.241091\pi$
$743$	−6.31534	−	10.9385i	−0.231687	−	0.401294i	−0.958305	+	0.285748i	$0.907758\pi$
$744$		0			0
$745$	−4.34233	+	7.52113i	−0.159091	+	0.275553i
$746$	44.3002			1.62195
$747$		0			0
$748$	−0.684658	+	1.18586i	−0.0250336	+	0.0433595i
$749$	4.63068			0.169201
$750$		0			0
$751$	−22.0540	−	38.1986i	−0.804761	−	1.39389i	−0.916452	−	0.400144i	$-0.868960\pi$
$751$	−22.0540	−	38.1986i	−0.804761	−	1.39389i	0.111691	−	0.993743i	$-0.464373\pi$
$752$	−19.3153	−	33.4552i	−0.704358	−	1.21998i
$753$		0			0
$754$	−29.6695	−	23.1563i	−1.08050	−	0.843304i
$755$	−33.3693			−1.21443
$756$		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	$-0.350207\pi$
$758$	−18.4924	+	32.0298i	−0.671675	+	1.16338i
$759$		0			0
$760$	30.9309	−	53.5738i	1.12198	−	1.94333i
$761$	4.68466	−	8.11407i	0.169819	−	0.294135i	−0.768537	−	0.639805i	$-0.779015\pi$
$761$	4.68466	−	8.11407i	0.169819	−	0.294135i	0.938356	+	0.345670i	$0.112348\pi$
$762$		0			0
$763$	0.788354	−	1.36547i	0.0285403	−	0.0494333i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$		0			0
$766$	35.5076			1.28294
$767$	8.17708	+	6.38202i	0.295257	+	0.230441i
$768$		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	$0.728121\pi$
$770$	−3.12311	−	5.40938i	−0.112549	−	0.194940i
$771$		0			0
$772$	−5.91571			−0.212911
$773$	−12.1231	+	20.9978i	−0.436038	+	0.755240i	−0.997380	−	0.0723444i	$-0.976952\pi$
$773$	−12.1231	+	20.9978i	−0.436038	+	0.755240i	0.561342	+	0.827584i	$0.310285\pi$
$774$		0			0
$775$	19.6847			0.707094
$776$	−10.4384	+	18.0799i	−0.374718	+	0.649031i
$777$		0			0
$778$	26.5885	+	46.0527i	0.953245	+	1.65107i
$779$	11.1231			0.398527
$780$		0			0
$781$	−28.0000			−1.00192
$782$	2.43845	+	4.22351i	0.0871987	+	0.151033i
$783$		0			0
$784$	−15.6577	+	27.1199i	−0.559203	+	0.968567i
$785$	72.5464			2.58929
$786$		0			0
$787$	−22.0885	+	38.2585i	−0.787371	+	1.36377i	0.140201	+	0.990123i	$0.455225\pi$
$787$	−22.0885	+	38.2585i	−0.787371	+	1.36377i	−0.927572	+	0.373644i	$0.878108\pi$
$788$	−5.86174			−0.208816
$789$		0			0
$790$	−15.1231	−	26.1940i	−0.538056	−	0.931940i
$791$	1.63068	+	2.82443i	0.0579804	+	0.100425i
$792$		0			0
$793$	11.0194	+	8.60039i	0.391311	+	0.305409i
$794$	39.1231			1.38843
$795$		0			0
$796$	−4.86174	−	8.42078i	−0.172320	−	0.298467i
$797$	−0.192236	+	0.332962i	−0.00680935	+	0.0117941i	−0.869410	−	0.494091i	$-0.835501\pi$
$797$	−0.192236	+	0.332962i	−0.00680935	+	0.0117941i	0.862601	+	0.505885i	$0.168834\pi$
$798$		0			0
$799$	6.43845	−	11.1517i	0.227776	−	0.394519i
$800$	9.36932	−	16.2281i	0.331255	−	0.573751i
$801$		0			0
$802$	11.2732	−	19.5258i	0.398070	−	0.689478i
$803$	10.1231	+	17.5337i	0.357237	+	0.618752i
$804$		0			0
$805$	−4.00000			−0.140981
$806$	−13.3693	+	5.40938i	−0.470914	+	0.190537i
$807$		0			0
$808$	9.21922	+	15.9682i	0.324331	+	0.561758i
$809$	−8.15009	−	14.1164i	−0.286542	−	0.496305i	0.686440	−	0.727187i	$-0.259172\pi$
$809$	−8.15009	−	14.1164i	−0.286542	−	0.496305i	−0.972982	+	0.230881i	$0.925839\pi$
$810$		0			0
$811$	2.56155			0.0899483			0.0449741	−	0.998988i	$-0.485679\pi$
$811$	2.56155			0.0899483			0.0449741	+	0.998988i	$0.485679\pi$
$812$	0.822919	−	1.42534i	0.0288788	−	0.0500195i
$813$		0			0
$814$	23.6155			0.827724
$815$	8.56155	−	14.8290i	0.299898	−	0.519439i
$816$		0			0
$817$	−16.2462	−	28.1393i	−0.568383	−	0.984468i
$818$	9.94602			0.347755
$819$		0			0
$820$	2.43845			0.0851543
$821$	3.24621	+	5.62260i	0.113294	+	0.196230i	0.917096	−	0.398666i	$-0.130527\pi$
$821$	3.24621	+	5.62260i	0.113294	+	0.196230i	−0.803803	+	0.594896i	$0.797193\pi$
$822$		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	$0.211194\pi$
$824$	8.38447			0.292087
$825$		0			0
$826$	−1.26137	+	2.18475i	−0.0438885	+	0.0760172i
$827$	14.7386			0.512513			0.256256	−	0.966609i	$-0.417511\pi$
$827$	14.7386			0.512513			0.256256	+	0.966609i	$0.417511\pi$
$828$		0			0
$829$	−6.74621	−	11.6848i	−0.234306	−	0.405829i	0.724765	−	0.688996i	$-0.241948\pi$
$829$	−6.74621	−	11.6848i	−0.234306	−	0.405829i	−0.959071	+	0.283167i	$0.908615\pi$
$830$	−2.43845	−	4.22351i	−0.0846397	−	0.146600i
$831$		0			0
$832$	2.78078	−	19.8587i	0.0964061	−	0.688477i
$833$	−10.4384			−0.361671
$834$		0			0
$835$	18.2462	+	31.6034i	0.631436	+	1.09368i
$836$	−3.12311	+	5.40938i	−0.108015	+	0.187087i
$837$		0			0
$838$	−26.7386	+	46.3127i	−0.923671	+	1.59984i
$839$	10.8078	−	18.7196i	0.373125	−	0.646272i	−0.616919	−	0.787027i	$-0.711619\pi$
$839$	10.8078	−	18.7196i	0.373125	−	0.646272i	0.990045	+	0.140754i	$0.0449528\pi$
$840$		0			0
$841$	−7.84233	+	13.5833i	−0.270425	+	0.468390i
$842$	−24.3963	−	42.2556i	−0.840752	−	1.45623i
$843$		0			0
$844$	8.63068			0.297080
$845$	−44.5194	−	12.7173i	−1.53151	−	0.437488i
$846$		0			0
$847$	1.96543	+	3.40423i	0.0675331	+	0.116971i
$848$	1.60370	+	2.77768i	0.0550711	+	0.0953860i
$849$		0			0
$850$	18.7386			0.642730
$851$	7.56155	−	13.0970i	0.259207	−	0.448959i
$852$		0			0
$853$	2.12311			0.0726938			0.0363469	−	0.999339i	$-0.488428\pi$
$853$	2.12311			0.0726938			0.0363469	+	0.999339i	$0.488428\pi$
$854$	−1.69981	+	2.94416i	−0.0581664	+	0.100747i
$855$		0			0
$856$	10.0540	+	17.4140i	0.343638	+	0.595198i
$857$	−35.5616			−1.21476			−0.607380	−	0.794412i	$-0.707779\pi$
$857$	−35.5616			−1.21476			−0.607380	+	0.794412i	$0.707779\pi$
$858$		0			0
$859$	24.5616			0.838029			0.419015	−	0.907979i	$-0.362376\pi$
$859$	24.5616			0.838029			0.419015	+	0.907979i	$0.362376\pi$
$860$	−3.56155	−	6.16879i	−0.121448	−	0.210354i
$861$		0			0
$862$	−8.68466	+	15.0423i	−0.295801	+	0.512342i
$863$	−30.4924			−1.03797			−0.518987	−	0.854782i	$-0.673691\pi$
$863$	−30.4924			−1.03797			−0.518987	+	0.854782i	$0.673691\pi$
$864$		0			0
$865$	36.0540	−	62.4473i	1.22587	−	2.12327i
$866$	13.6695			0.464509
$867$		0			0
$868$	−0.315342	−	0.546188i	−0.0107034	−	0.0185388i
$869$	−5.43845	−	9.41967i	−0.184487	−	0.319540i
$870$		0			0
$871$	−15.2462	+	6.16879i	−0.516598	+	0.209021i
$872$	6.84658			0.231855
$873$		0			0
$874$	11.1231	+	19.2658i	0.376245	+	0.651675i
$875$	−2.68466	+	4.64996i	−0.0907580	+	0.157198i
$876$		0			0
$877$	−11.7808	+	20.4049i	−0.397809	+	0.689025i	−0.993455	−	0.114222i	$-0.963563\pi$
$877$	−11.7808	+	20.4049i	−0.397809	+	0.689025i	0.595647	+	0.803247i	$0.296896\pi$
$878$	10.6847	−	18.5064i	0.360590	−	0.624560i
$879$		0			0
$880$	16.6847	−	28.8987i	0.562440	−	0.974174i
$881$	−4.53457	−	7.85410i	−0.152773	−	0.264611i	0.779473	−	0.626436i	$-0.215487\pi$
$881$	−4.53457	−	7.85410i	−0.152773	−	0.264611i	−0.932246	+	0.361825i	$0.882154\pi$
$882$		0			0
$883$	8.80776			0.296405			0.148202	−	0.988957i	$-0.452651\pi$
$883$	8.80776			0.296405			0.148202	+	0.988957i	$0.452651\pi$
$884$	−2.28835	+	0.925894i	−0.0769657	+	0.0311412i
$885$		0			0
$886$	−27.1231	−	46.9786i	−0.911219	−	1.57828i
$887$	12.3153	+	21.3308i	0.413509	+	0.716218i	0.995271	−	0.0971410i	$-0.0309698\pi$
$887$	12.3153	+	21.3308i	0.413509	+	0.716218i	−0.581762	+	0.813359i	$0.697636\pi$
$888$		0			0
$889$	3.05398			0.102427
$890$	13.5616	−	23.4893i	0.454584	−	0.787363i
$891$		0			0
$892$	3.50758			0.117442
$893$	29.3693	−	50.8691i	0.982807	−	1.70227i
$894$		0			0
$895$	−8.68466	−	15.0423i	−0.290296	−	0.502808i
$896$	7.61553			0.254417
$897$		0			0
$898$	12.8769			0.429708
$899$	8.56155	+	14.8290i	0.285544	+	0.494576i
$900$		0			0
$901$	−0.534565	+	0.925894i	−0.0178089	+	0.0308460i
$902$	4.87689			0.162383
$903$		0			0
$904$	−7.08096	+	12.2646i	−0.235509	+	0.407914i
$905$	−9.56155			−0.317837
$906$		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	$0.987230\pi$
$908$	1.56155	+	2.70469i	0.0518220	+	0.0897583i
$909$		0			0
$910$	1.56155	−	11.1517i	0.0517650	−	0.369676i
$911$	−38.7386			−1.28347			−0.641734	−	0.766927i	$-0.721785\pi$
$911$	−38.7386			−1.28347			−0.641734	+	0.766927i	$0.721785\pi$
$912$		0			0
$913$	−0.876894	−	1.51883i	−0.0290210	−	0.0502658i
$914$	−9.84991	+	17.0605i	−0.325806	+	0.564312i
$915$		0			0
$916$	3.56155	−	6.16879i	0.117677	−	0.203823i
$917$	2.06913	−	3.58384i	0.0683287	−	0.118349i
$918$		0			0
$919$	−5.75379	+	9.96585i	−0.189800	+	0.328743i	−0.945183	−	0.326540i	$-0.894117\pi$
$919$	−5.75379	+	9.96585i	−0.189800	+	0.328743i	0.755383	+	0.655283i	$0.227451\pi$
$920$	−8.68466	−	15.0423i	−0.286325	−	0.495929i
$921$		0			0
$922$	25.2850			0.832718
$923$	−39.7926	−	31.0572i	−1.30979	−	1.02226i
$924$		0			0
$925$	−29.0540	−	50.3230i	−0.955289	−	1.65461i
$926$	11.1771	+	19.3593i	0.367302	+	0.636185i
$927$		0			0
$928$	16.3002			0.535080
$929$	−3.90388	+	6.76172i	−0.128082	+	0.221845i	−0.922934	−	0.384959i	$-0.874215\pi$
$929$	−3.90388	+	6.76172i	−0.128082	+	0.221845i	0.794851	+	0.606804i	$0.207549\pi$
$930$		0			0
$931$	−47.6155			−1.56054
$932$	5.69981	−	9.87237i	0.186704	−	0.323380i
$933$		0			0
$934$	−20.3002	−	35.1610i	−0.664242	−	1.15050i
$935$	11.1231			0.363764
$936$		0			0
$937$	−7.56155			−0.247025			−0.123513	−	0.992343i	$-0.539416\pi$
$937$	−7.56155			−0.247025			−0.123513	+	0.992343i	$0.539416\pi$
$938$	−2.00000	−	3.46410i	−0.0653023	−	0.113107i
$939$		0			0
$940$	6.43845	−	11.1517i	0.209999	−	0.363729i
$941$	−30.4924			−0.994025			−0.497012	−	0.867744i	$-0.665570\pi$
$941$	−30.4924			−0.994025			−0.497012	+	0.867744i	$0.665570\pi$
$942$		0			0
$943$	1.56155	−	2.70469i	0.0508512	−	0.0880768i
$944$	−13.4773			−0.438648
$945$		0			0
$946$	−7.12311	−	12.3376i	−0.231592	−	0.401129i
$947$	−19.3693	−	33.5486i	−0.629418	−	1.09018i	−0.987669	−	0.156559i	$-0.949960\pi$
$947$	−19.3693	−	33.5486i	−0.629418	−	1.09018i	0.358250	−	0.933626i	$-0.383373\pi$
$948$		0			0
$949$	−5.06155	+	36.1467i	−0.164305	+	1.17337i
$950$	85.4773			2.77325
$951$		0			0
$952$	1.06913	+	1.85179i	0.0346507	+	0.0600168i
$953$	15.4924	−	26.8337i	0.501849	−	0.869228i	−0.498149	−	0.867091i	$-0.665987\pi$
$953$	15.4924	−	26.8337i	0.501849	−	0.869228i	0.999998	−	0.00213612i	$-0.000679948\pi$
$954$		0			0
$955$	−16.2462	+	28.1393i	−0.525715	+	0.910565i
$956$	−5.56155	+	9.63289i	−0.179873	+	0.311550i
$957$		0			0
$958$	8.00000	−	13.8564i	0.258468	−	0.447680i
$959$	−1.56155	−	2.70469i	−0.0504252	−	0.0873390i
$960$		0			0
$961$	−24.4384			−0.788337
$962$	33.5616	+	26.1940i	1.08207	+	0.844528i
$963$		0			0
$964$	3.90388	+	6.76172i	0.125736	+	0.217780i
$965$	24.0270	+	41.6160i	0.773456	+	1.33967i
$966$		0			0
$967$	−0.876894			−0.0281990			−0.0140995	−	0.999901i	$-0.504488\pi$
$967$	−0.876894			−0.0281990			−0.0140995	+	0.999901i	$0.504488\pi$
$968$	−8.53457	+	14.7823i	−0.274311	+	0.475121i
$969$		0			0
$970$	−47.6155			−1.52884
$971$	−6.49242	+	11.2452i	−0.208352	+	0.360876i	−0.951195	−	0.308589i	$-0.900143\pi$
$971$	−6.49242	+	11.2452i	−0.208352	+	0.360876i	0.742844	+	0.669465i	$0.233477\pi$
$972$		0			0
$973$	5.03457	+	8.72012i	0.161401	+	0.279554i
$974$	11.1231			0.356407
$975$		0			0
$976$	−18.1619			−0.581349
$977$	30.5885	+	52.9809i	0.978614	+	1.69501i	0.667453	+	0.744652i	$0.267385\pi$
$977$	30.5885	+	52.9809i	0.978614	+	1.69501i	0.311162	+	0.950357i	$0.399282\pi$
$978$		0			0
$979$	4.87689	−	8.44703i	0.155866	−	0.269968i
$980$	−10.4384			−0.333444
$981$		0			0
$982$	−28.3002	+	49.0174i	−0.903095	+	1.56421i
$983$	−13.6155			−0.434268			−0.217134	−	0.976142i	$-0.569671\pi$
$983$	−13.6155			−0.434268			−0.217134	+	0.976142i	$0.569671\pi$
$984$		0			0
$985$	23.8078	+	41.2363i	0.758578	+	1.31390i
$986$	8.15009	+	14.1164i	0.259552	+	0.449557i
$987$		0			0
$988$	−10.4384	+	4.22351i	−0.332091	+	0.134368i
$989$	−9.12311			−0.290098
$990$		0			0
$991$	25.1771	+	43.6080i	0.799776	+	1.38525i	0.919762	+	0.392478i	$0.128382\pi$
$991$	25.1771	+	43.6080i	0.799776	+	1.38525i	−0.119985	+	0.992776i	$0.538285\pi$
$992$	3.12311	−	5.40938i	0.0991587	−	0.171748i
$993$		0			0
$994$	6.13826	−	10.6318i	0.194694	−	0.337220i
$995$	−39.4924	+	68.4029i	−1.25199	+	2.16852i
$996$		0			0
$997$	10.3078	−	17.8536i	0.326450	−	0.565428i	−0.655355	−	0.755321i	$-0.727481\pi$
$997$	10.3078	−	17.8536i	0.326450	−	0.565428i	0.981805	+	0.189893i	$0.0608141\pi$
$998$	−3.50758	−	6.07530i	−0.111030	−	0.192310i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.g.c.55.1		4
3.2	odd	2		39.2.e.b.16.2	✓	4
4.3	odd	2		1872.2.t.r.289.2		4
12.11	even	2		624.2.q.h.289.1		4
13.2	odd	12		1521.2.b.h.1351.2		4
13.3	even	3		1521.2.a.g.1.2		2
13.9	even	3	inner	117.2.g.c.100.1		4
13.10	even	6		1521.2.a.m.1.1		2
13.11	odd	12		1521.2.b.h.1351.3		4
15.2	even	4		975.2.bb.i.874.2		8
15.8	even	4		975.2.bb.i.874.3		8
15.14	odd	2		975.2.i.k.601.1		4
39.2	even	12		507.2.b.d.337.3		4
39.5	even	4		507.2.j.g.361.3		8
39.8	even	4		507.2.j.g.361.2		8
39.11	even	12		507.2.b.d.337.2		4
39.17	odd	6		507.2.e.g.22.1		4
39.20	even	12		507.2.j.g.316.3		8
39.23	odd	6		507.2.a.d.1.2		2
39.29	odd	6		507.2.a.g.1.1		2
39.32	even	12		507.2.j.g.316.2		8
39.35	odd	6		39.2.e.b.22.2	yes	4
39.38	odd	2		507.2.e.g.484.1		4
52.35	odd	6		1872.2.t.r.1153.2		4
156.23	even	6		8112.2.a.bo.1.2		2
156.35	even	6		624.2.q.h.529.1		4
156.107	even	6		8112.2.a.bk.1.1		2
195.74	odd	6		975.2.i.k.451.1		4
195.113	even	12		975.2.bb.i.724.2		8
195.152	even	12		975.2.bb.i.724.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.b.16.2	✓	4	3.2	odd	2
39.2.e.b.22.2	yes	4	39.35	odd	6
117.2.g.c.55.1		4	1.1	even	1	trivial
117.2.g.c.100.1		4	13.9	even	3	inner
507.2.a.d.1.2		2	39.23	odd	6
507.2.a.g.1.1		2	39.29	odd	6
507.2.b.d.337.2		4	39.11	even	12
507.2.b.d.337.3		4	39.2	even	12
507.2.e.g.22.1		4	39.17	odd	6
507.2.e.g.484.1		4	39.38	odd	2
507.2.j.g.316.2		8	39.32	even	12
507.2.j.g.316.3		8	39.20	even	12
507.2.j.g.361.2		8	39.8	even	4
507.2.j.g.361.3		8	39.5	even	4
624.2.q.h.289.1		4	12.11	even	2
624.2.q.h.529.1		4	156.35	even	6
975.2.i.k.451.1		4	195.74	odd	6
975.2.i.k.601.1		4	15.14	odd	2
975.2.bb.i.724.2		8	195.113	even	12
975.2.bb.i.724.3		8	195.152	even	12
975.2.bb.i.874.2		8	15.2	even	4
975.2.bb.i.874.3		8	15.8	even	4
1521.2.a.g.1.2		2	13.3	even	3
1521.2.a.m.1.1		2	13.10	even	6
1521.2.b.h.1351.2		4	13.2	odd	12
1521.2.b.h.1351.3		4	13.11	odd	12
1872.2.t.r.289.2		4	4.3	odd	2
1872.2.t.r.1153.2		4	52.35	odd	6
8112.2.a.bk.1.1		2	156.107	even	6
8112.2.a.bo.1.2		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 - 1.35234i) q^{2} +(-0.219224 + 0.379706i) q^{4} +3.56155 q^{5} +(-0.280776 + 0.486319i) q^{7} -2.43845 q^{8} +(-2.78078 - 4.81645i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 3.57071i) q^{13} +0.876894 q^{14} +(2.34233 + 4.05703i) q^{16} +(-0.780776 + 1.35234i) q^{17} +(-3.56155 + 6.16879i) q^{19} +(-0.780776 + 1.35234i) q^{20} +(-1.56155 + 2.70469i) q^{22} +(1.00000 + 1.73205i) q^{23} +7.68466 q^{25} +(-5.21922 + 2.11176i) q^{26} +(-0.123106 - 0.213225i) q^{28} +(3.34233 + 5.78908i) q^{29} +2.56155 q^{31} +(1.21922 - 2.11176i) q^{32} +2.43845 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-3.78078 - 6.54850i) q^{37} +11.1231 q^{38} -8.68466 q^{40} +(-0.780776 - 1.35234i) q^{41} +(-2.28078 + 3.95042i) q^{43} +0.876894 q^{44} +(1.56155 - 2.70469i) q^{46} -8.24621 q^{47} +(3.34233 + 5.78908i) q^{49} +(-6.00000 - 10.3923i) q^{50} +(1.24621 + 0.972638i) q^{52} +0.684658 q^{53} +(-3.56155 - 6.16879i) q^{55} +(0.684658 - 1.18586i) q^{56} +(5.21922 - 9.03996i) q^{58} +(-1.43845 + 2.49146i) q^{59} +(-1.93845 + 3.35749i) q^{61} +(-2.00000 - 3.46410i) q^{62} +5.56155 q^{64} +(1.78078 - 12.7173i) q^{65} +(-2.28078 - 3.95042i) q^{67} +(-0.342329 - 0.592932i) q^{68} +3.12311 q^{70} +(7.00000 - 12.1244i) q^{71} -10.1231 q^{73} +(-5.90388 + 10.2258i) q^{74} +(-1.56155 - 2.70469i) q^{76} +1.12311 q^{77} +5.43845 q^{79} +(8.34233 + 14.4493i) q^{80} +(-1.21922 + 2.11176i) q^{82} +0.876894 q^{83} +(-2.78078 + 4.81645i) q^{85} +7.12311 q^{86} +(2.43845 + 4.22351i) q^{88} +(2.43845 + 4.22351i) q^{89} +(1.59612 + 1.24573i) q^{91} -0.876894 q^{92} +(6.43845 + 11.1517i) q^{94} +(-12.6847 + 21.9705i) q^{95} +(4.28078 - 7.41452i) q^{97} +(5.21922 - 9.03996i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 5 q^{4} + 6 q^{5} + 3 q^{7} - 18 q^{8} - 7 q^{10} - 4 q^{11} + 2 q^{13} + 20 q^{14} - 3 q^{16} + q^{17} - 6 q^{19} + q^{20} + 2 q^{22} + 4 q^{23} + 6 q^{25} - 25 q^{26} + 16 q^{28} + q^{29}+ \cdots + 25 q^{98}+O(q^{100}) \) 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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