LMFDB - Embedded newform 931.2.p.e.734.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [931,2,Mod(293,931)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(931, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("931.293"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,3,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			734.1
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	931.734
Dual form			931.2.p.e.293.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.395644 + 0.228425i) q^{2} +(0.895644 + 1.55130i) q^{3} +(-0.895644 + 1.55130i) q^{4} +(1.10436 - 0.637600i) q^{5} +(-0.708712 - 0.409175i) q^{6} -1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +(-0.291288 + 0.504525i) q^{10} -3.00000 q^{11} -3.20871 q^{12} +(-1.89564 + 3.28335i) q^{13} +(1.97822 + 1.14213i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(-3.79129 + 2.18890i) q^{17} -0.0953502i q^{18} +(-3.50000 - 2.59808i) q^{19} +2.28425i q^{20} +(1.18693 - 0.685275i) q^{22} +(-3.79129 + 6.56670i) q^{23} +(2.68693 - 1.55130i) q^{24} +(-1.68693 + 2.92185i) q^{25} -1.73205i q^{26} +5.00000 q^{27} +(-3.08258 - 1.77973i) q^{29} -1.04356 q^{30} +(4.10436 + 2.36965i) q^{32} +(-2.68693 - 4.65390i) q^{33} +(1.00000 - 1.73205i) q^{34} +(-0.186932 - 0.323775i) q^{36} +10.0308i q^{37} +(1.97822 + 0.228425i) q^{38} -6.79129 q^{39} +(-1.10436 - 1.91280i) q^{40} +(-2.68693 - 4.65390i) q^{41} +(3.39564 + 5.88143i) q^{43} +(2.68693 - 4.65390i) q^{44} +0.266150i q^{45} -3.46410i q^{46} +(5.29129 + 3.05493i) q^{47} +(2.50000 - 4.33013i) q^{48} -1.54135i q^{50} +(-6.79129 - 3.92095i) q^{51} +(-3.39564 - 5.88143i) q^{52} +(-1.10436 - 0.637600i) q^{53} +(-1.97822 + 1.14213i) q^{54} +(-3.31307 + 1.91280i) q^{55} +(0.895644 - 7.75650i) q^{57} +1.62614 q^{58} +(-4.89564 - 8.47950i) q^{59} +(-3.54356 + 2.04588i) q^{60} +(1.18693 + 0.685275i) q^{61} +3.41742 q^{64} +4.83465i q^{65} +(2.12614 + 1.22753i) q^{66} +(3.00000 + 1.73205i) q^{67} -7.84190i q^{68} -13.5826 q^{69} +(-3.08258 + 1.77973i) q^{71} +(0.313068 + 0.180750i) q^{72} +(5.37386 - 3.10260i) q^{73} +(-2.29129 - 3.96863i) q^{74} -6.04356 q^{75} +(7.16515 - 3.10260i) q^{76} +(2.68693 - 1.55130i) q^{78} +(6.00000 - 3.46410i) q^{79} +(-3.08258 - 1.77973i) q^{80} +(4.79129 + 8.29875i) q^{81} +(2.12614 + 1.22753i) q^{82} -13.5903i q^{83} +(-2.79129 + 4.83465i) q^{85} +(-2.68693 - 1.55130i) q^{86} -6.37600i q^{87} +5.19615i q^{88} +(-1.18693 + 2.05583i) q^{89} +(-0.0607953 - 0.105301i) q^{90} +(-6.79129 - 11.7629i) q^{92} -2.79129 q^{94} +(-5.52178 - 0.637600i) q^{95} +8.48945i q^{96} +(-1.00000 - 1.73205i) q^{97} +(0.313068 - 0.542250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{5} - 12 q^{6} - 5 q^{9} + 8 q^{10} - 12 q^{11} - 22 q^{12} - 3 q^{13} - 15 q^{15} - q^{16} - 6 q^{17} - 14 q^{19} - 9 q^{22} - 6 q^{23} - 3 q^{24} + 7 q^{25} + 20 q^{27}+ \cdots + 15 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^5 - 12 * q^6 - 5 * q^9 + 8 * q^10 - 12 * q^11 - 22 * q^12 - 3 * q^13 - 15 * q^15 - q^16 - 6 * q^17 - 14 * q^19 - 9 * q^22 - 6 * q^23 - 3 * q^24 + 7 * q^25 + 20 * q^27 + 6 * q^29 - 50 * q^30 + 21 * q^32 + 3 * q^33 + 4 * q^34 + 13 * q^36 - 15 * q^38 - 18 * q^39 - 9 * q^40 + 3 * q^41 + 9 * q^43 - 3 * q^44 + 12 * q^47 + 10 * q^48 - 18 * q^51 - 9 * q^52 - 9 * q^53 + 15 * q^54 - 27 * q^55 - q^57 + 34 * q^58 - 15 * q^59 - 60 * q^60 - 9 * q^61 + 32 * q^64 + 36 * q^66 + 12 * q^67 - 36 * q^69 + 6 * q^71 + 15 * q^72 - 6 * q^73 - 70 * q^75 - 8 * q^76 - 3 * q^78 + 24 * q^79 + 6 * q^80 + 10 * q^81 + 36 * q^82 - 2 * q^85 + 3 * q^86 + 9 * q^89 + 41 * q^90 - 18 * q^92 - 2 * q^94 - 45 * q^95 - 4 * q^97 + 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.395644	+	0.228425i	−0.279763	+	0.161521i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	−0.395644	+	0.228425i	−0.279763	+	0.161521i	0.353553	+	0.935414i	$0.384973\pi$
$3$	0.895644	+	1.55130i	0.517100	+	0.895644i	0.999803	+	0.0198595i	$0.00632191\pi$
$3$	0.895644	+	1.55130i	0.517100	+	0.895644i	−0.482703	+	0.875784i	$0.660345\pi$
$4$	−0.895644	+	1.55130i	−0.447822	+	0.775650i
$5$	1.10436	−	0.637600i	0.493883	−	0.285144i	−0.232301	−	0.972644i	$-0.574625\pi$
$5$	1.10436	−	0.637600i	0.493883	−	0.285144i	0.726184	+	0.687500i	$0.241292\pi$
$6$	−0.708712	−	0.409175i	−0.289331	−	0.167045i
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	−0.104356	+	0.180750i	−0.0347854	+	0.0602500i
$10$	−0.291288	+	0.504525i	−0.0921133	+	0.159545i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−3.20871			−0.926275
$13$	−1.89564	+	3.28335i	−0.525757	+	0.910638i	0.473793	+	0.880636i	$0.342885\pi$
$13$	−1.89564	+	3.28335i	−0.525757	+	0.910638i	−0.999550	+	0.0300015i	$0.990449\pi$
$14$		0			0
$15$	1.97822	+	1.14213i	0.510774	+	0.294896i
$16$	−1.39564	−	2.41733i	−0.348911	−	0.604332i
$17$	−3.79129	+	2.18890i	−0.919522	+	0.530886i	−0.883483	−	0.468464i	$-0.844808\pi$
$17$	−3.79129	+	2.18890i	−0.919522	+	0.530886i	−0.0360397	+	0.999350i	$0.511474\pi$
$18$		−	0.0953502i		−	0.0224743i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$			2.28425i			0.510774i
$21$		0			0
$22$	1.18693	−	0.685275i	0.253055	−	0.146101i
$23$	−3.79129	+	6.56670i	−0.790538	+	1.36925i	0.135096	+	0.990833i	$0.456866\pi$
$23$	−3.79129	+	6.56670i	−0.790538	+	1.36925i	−0.925634	+	0.378420i	$0.876468\pi$
$24$	2.68693	−	1.55130i	0.548468	−	0.316658i
$25$	−1.68693	+	2.92185i	−0.337386	+	0.584370i
$26$		−	1.73205i		−	0.339683i
$27$	5.00000			0.962250
$28$		0			0
$29$	−3.08258	−	1.77973i	−0.572420	−	0.330487i	0.185695	−	0.982607i	$-0.440546\pi$
$29$	−3.08258	−	1.77973i	−0.572420	−	0.330487i	−0.758115	+	0.652121i	$0.773880\pi$
$30$	−1.04356			−0.190527
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	4.10436	+	2.36965i	0.725555	+	0.418899i
$33$	−2.68693	−	4.65390i	−0.467735	−	0.810140i
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$		0			0
$36$	−0.186932	−	0.323775i	−0.0311553	−	0.0539626i
$37$			10.0308i			1.64905i	0.565823	+	0.824527i	$0.308559\pi$
$37$			10.0308i			1.64905i	−0.565823	+	0.824527i	$0.691441\pi$
$38$	1.97822	+	0.228425i	0.320910	+	0.0370554i
$39$	−6.79129			−1.08748
$40$	−1.10436	−	1.91280i	−0.174614	−	0.302440i
$41$	−2.68693	−	4.65390i	−0.419628	−	0.726817i	0.576274	−	0.817257i	$-0.304506\pi$
$41$	−2.68693	−	4.65390i	−0.419628	−	0.726817i	−0.995902	+	0.0904393i	$0.971173\pi$
$42$		0			0
$43$	3.39564	+	5.88143i	0.517831	+	0.896909i	0.999785	+	0.0207131i	$0.00659367\pi$
$43$	3.39564	+	5.88143i	0.517831	+	0.896909i	−0.481955	+	0.876196i	$0.660073\pi$
$44$	2.68693	−	4.65390i	0.405070	−	0.701602i
$45$			0.266150i			0.0396753i
$46$		−	3.46410i		−	0.510754i
$47$	5.29129	+	3.05493i	0.771814	+	0.445607i	0.833521	−	0.552487i	$-0.186321\pi$
$47$	5.29129	+	3.05493i	0.771814	+	0.445607i	−0.0617076	+	0.998094i	$0.519655\pi$
$48$	2.50000	−	4.33013i	0.360844	−	0.625000i
$49$		0			0
$50$		−	1.54135i		−	0.217980i
$51$	−6.79129	−	3.92095i	−0.950971	−	0.549043i
$52$	−3.39564	−	5.88143i	−0.470891	−	0.815607i
$53$	−1.10436	−	0.637600i	−0.151695	−	0.0875811i	0.422231	−	0.906488i	$-0.361247\pi$
$53$	−1.10436	−	0.637600i	−0.151695	−	0.0875811i	−0.573926	+	0.818907i	$0.694580\pi$
$54$	−1.97822	+	1.14213i	−0.269202	+	0.155424i
$55$	−3.31307	+	1.91280i	−0.446734	+	0.257922i
$56$		0			0
$57$	0.895644	−	7.75650i	0.118631	−	1.02737i
$58$	1.62614			0.213522
$59$	−4.89564	−	8.47950i	−0.637359	−	1.10394i	−0.986010	−	0.166685i	$-0.946694\pi$
$59$	−4.89564	−	8.47950i	−0.637359	−	1.10394i	0.348652	−	0.937252i	$-0.386640\pi$
$60$	−3.54356	+	2.04588i	−0.457472	+	0.264121i
$61$	1.18693	+	0.685275i	0.151971	+	0.0877405i	0.574057	−	0.818815i	$-0.305369\pi$
$61$	1.18693	+	0.685275i	0.151971	+	0.0877405i	−0.422086	+	0.906556i	$0.638702\pi$
$62$		0			0
$63$		0			0
$64$	3.41742			0.427178
$65$			4.83465i			0.599665i
$66$	2.12614	+	1.22753i	0.261709	+	0.151098i
$67$	3.00000	+	1.73205i	0.366508	+	0.211604i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	3.00000	+	1.73205i	0.366508	+	0.211604i	−0.305424	+	0.952217i	$0.598798\pi$
$68$		−	7.84190i		−	0.950971i
$69$	−13.5826			−1.63515
$70$		0			0
$71$	−3.08258	+	1.77973i	−0.365834	+	0.211215i	−0.671637	−	0.740880i	$-0.734409\pi$
$71$	−3.08258	+	1.77973i	−0.365834	+	0.211215i	0.305803	+	0.952095i	$0.401075\pi$
$72$	0.313068	+	0.180750i	0.0368954	+	0.0213016i
$73$	5.37386	−	3.10260i	0.628963	−	0.363132i	−0.151387	−	0.988475i	$-0.548374\pi$
$73$	5.37386	−	3.10260i	0.628963	−	0.363132i	0.780350	+	0.625342i	$0.215041\pi$
$74$	−2.29129	−	3.96863i	−0.266357	−	0.461344i
$75$	−6.04356			−0.697850
$76$	7.16515	−	3.10260i	0.821899	−	0.355893i
$77$		0			0
$78$	2.68693	−	1.55130i	0.304235	−	0.175650i
$79$	6.00000	−	3.46410i	0.675053	−	0.389742i	−0.122936	−	0.992415i	$-0.539231\pi$
$79$	6.00000	−	3.46410i	0.675053	−	0.389742i	0.797988	+	0.602673i	$0.205898\pi$
$80$	−3.08258	−	1.77973i	−0.344642	−	0.198979i
$81$	4.79129	+	8.29875i	0.532365	+	0.922084i
$82$	2.12614	+	1.22753i	0.234792	+	0.135558i
$83$		−	13.5903i		−	1.49172i	−0.666100	−	0.745862i	$-0.732038\pi$
$83$		−	13.5903i		−	1.49172i	0.666100	−	0.745862i	$-0.267962\pi$
$84$		0			0
$85$	−2.79129	+	4.83465i	−0.302758	+	0.524392i
$86$	−2.68693	−	1.55130i	−0.289739	−	0.167281i
$87$		−	6.37600i		−	0.683579i
$88$			5.19615i			0.553912i
$89$	−1.18693	+	2.05583i	−0.125815	+	0.217917i	−0.922051	−	0.387068i	$-0.873488\pi$
$89$	−1.18693	+	2.05583i	−0.125815	+	0.217917i	0.796237	+	0.604985i	$0.206821\pi$
$90$	−0.0607953	−	0.105301i	−0.00640839	−	0.0110997i
$91$		0			0
$92$	−6.79129	−	11.7629i	−0.708041	−	1.22636i
$93$		0			0
$94$	−2.79129			−0.287899
$95$	−5.52178	−	0.637600i	−0.566523	−	0.0654164i
$96$			8.48945i			0.866451i
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$	0.313068	−	0.542250i	0.0314645	−	0.0544982i
$100$	−3.02178	−	5.23388i	−0.302178	−	0.523388i
$101$	7.41742	+	4.28245i	0.738061	+	0.426120i	0.821364	−	0.570404i	$-0.193214\pi$
$101$	7.41742	+	4.28245i	0.738061	+	0.426120i	−0.0833027	+	0.996524i	$0.526547\pi$
$102$	3.58258			0.354728
$103$	−3.37386			−0.332437			−0.166218	−	0.986089i	$-0.553156\pi$
$103$	−3.37386			−0.332437			−0.166218	+	0.986089i	$0.553156\pi$
$104$	5.68693	+	3.28335i	0.557650	+	0.321959i
$105$		0			0
$106$	0.582576			0.0565848
$107$			9.47860i			0.916331i	0.888867	+	0.458166i	$0.151493\pi$
$107$			9.47860i			0.916331i	−0.888867	+	0.458166i	$0.848507\pi$
$108$	−4.47822	+	7.75650i	−0.430917	+	0.746370i
$109$	11.6869	−	6.74745i	1.11941	−	0.646289i	0.178156	−	0.984002i	$-0.442987\pi$
$109$	11.6869	−	6.74745i	1.11941	−	0.646289i	0.941249	+	0.337713i	$0.109653\pi$
$110$	0.873864	−	1.51358i	0.0833196	−	0.144314i
$111$	−15.5608	+	8.98403i	−1.47697	+	0.852726i
$112$		0			0
$113$			13.2288i			1.24446i	0.782836	+	0.622228i	$0.213772\pi$
$113$			13.2288i			1.24446i	−0.782836	+	0.622228i	$0.786228\pi$
$114$	1.41742	+	3.27340i	0.132754	+	0.306582i
$115$			9.66930i			0.901667i
$116$	5.52178	−	3.18800i	0.512684	−	0.295998i
$117$	−0.395644	−	0.685275i	−0.0365773	−	0.0633537i
$118$	3.87386	+	2.23658i	0.356618	+	0.205894i
$119$		0			0
$120$	1.97822	−	3.42638i	0.180586	−	0.312784i
$121$	−2.00000			−0.181818
$122$	−0.626136			−0.0566877
$123$	4.81307	−	8.33648i	0.433980	−	0.751675i
$124$		0			0
$125$			10.6784i			0.955101i
$126$		0			0
$127$	10.1869	+	5.88143i	0.903944	+	0.521892i	0.878478	−	0.477783i	$-0.158560\pi$
$127$	10.1869	+	5.88143i	0.903944	+	0.521892i	0.0254663	+	0.999676i	$0.491893\pi$
$128$	−9.56080	+	5.51993i	−0.845063	+	0.487897i
$129$	−6.08258	+	10.5353i	−0.535541	+	0.927584i
$130$	−1.10436	−	1.91280i	−0.0968584	−	0.167764i
$131$	6.16515	−	3.55945i	0.538652	−	0.310991i	−0.205881	−	0.978577i	$-0.566006\pi$
$131$	6.16515	−	3.55945i	0.538652	−	0.310991i	0.744532	+	0.667586i	$0.232673\pi$
$132$	9.62614			0.837848
$133$		0			0
$134$	−1.58258			−0.136714
$135$	5.52178	−	3.18800i	0.475239	−	0.274379i
$136$	3.79129	+	6.56670i	0.325100	+	0.563090i
$137$	4.97822	−	8.62253i	0.425318	−	0.736672i	−0.571132	−	0.820858i	$-0.693496\pi$
$137$	4.97822	−	8.62253i	0.425318	−	0.736672i	0.996450	+	0.0841858i	$0.0268289\pi$
$138$	5.37386	−	3.10260i	0.457454	−	0.264111i
$139$	9.24773	+	5.33918i	0.784382	+	0.452863i	0.837981	−	0.545699i	$-0.183736\pi$
$139$	9.24773	+	5.33918i	0.784382	+	0.452863i	−0.0535990	+	0.998563i	$0.517069\pi$
$140$		0			0
$141$			10.9445i			0.921694i
$142$	0.813068	−	1.40828i	0.0682312	−	0.118180i
$143$	5.68693	−	9.85005i	0.475565	−	0.823703i
$144$	0.582576			0.0485480
$145$	−4.53901			−0.376945
$146$	−1.41742	+	2.45505i	−0.117307	+	0.203181i
$147$		0			0
$148$	−15.5608	−	8.98403i	−1.27909	−	0.738483i
$149$	−5.60436	−	9.70703i	−0.459127	−	0.795231i	0.539788	−	0.841801i	$-0.318504\pi$
$149$	−5.60436	−	9.70703i	−0.459127	−	0.795231i	−0.998915	+	0.0465700i	$0.985171\pi$
$150$	2.39110	−	1.38050i	0.195232	−	0.112717i
$151$			17.9681i			1.46222i	0.682260	+	0.731110i	$0.260997\pi$
$151$			17.9681i			1.46222i	−0.682260	+	0.731110i	$0.739003\pi$
$152$	−4.50000	+	6.06218i	−0.364998	+	0.491708i
$153$		−	0.913701i		−	0.0738683i
$154$		0			0
$155$		0			0
$156$	6.08258	−	10.5353i	0.486996	−	0.843501i
$157$	−10.1869	+	5.88143i	−0.813006	+	0.469389i	−0.847999	−	0.529999i	$-0.822192\pi$
$157$	−10.1869	+	5.88143i	−0.813006	+	0.469389i	0.0349929	+	0.999388i	$0.488859\pi$
$158$	−1.58258	+	2.74110i	−0.125903	+	0.218070i
$159$		−	2.28425i		−	0.181153i
$160$	6.04356			0.477785
$161$		0			0
$162$	−3.79129	−	2.18890i	−0.297872	−	0.171976i
$163$	−6.00000			−0.469956			−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000			−0.469956			−0.234978	+	0.972001i	$0.575502\pi$
$164$	9.62614			0.751675
$165$	−5.93466	−	3.42638i	−0.462013	−	0.266743i
$166$	3.10436	+	5.37690i	0.240945	+	0.417329i
$167$	9.56080	−	16.5598i	0.739837	−	1.28143i	−0.212732	−	0.977111i	$-0.568236\pi$
$167$	9.56080	−	16.5598i	0.739837	−	1.28143i	0.952569	−	0.304324i	$-0.0984305\pi$
$168$		0			0
$169$	−0.686932	−	1.18980i	−0.0528409	−	0.0915231i
$170$		−	2.55040i		−	0.195607i
$171$	0.834849	−	0.361500i	0.0638425	−	0.0276446i
$172$	−12.1652			−0.927584
$173$	9.87386	+	17.1020i	0.750696	+	1.30024i	0.947486	+	0.319798i	$0.103615\pi$
$173$	9.87386	+	17.1020i	0.750696	+	1.30024i	−0.196790	+	0.980446i	$0.563052\pi$
$174$	1.45644	+	2.52263i	0.110412	+	0.191240i
$175$		0			0
$176$	4.18693	+	7.25198i	0.315602	+	0.546638i
$177$	8.76951	−	15.1892i	0.659157	−	1.14169i
$178$		−	1.08450i		−	0.0812867i
$179$		−	14.7701i		−	1.10397i	−0.833854	−	0.551985i	$-0.813871\pi$
$179$		−	14.7701i		−	1.10397i	0.833854	−	0.551985i	$-0.186129\pi$
$180$	−0.412878	−	0.238375i	−0.0307741	−	0.0177675i
$181$	−5.87386	+	10.1738i	−0.436601	+	0.756215i	−0.997425	−	0.0717202i	$-0.977151\pi$
$181$	−5.87386	+	10.1738i	−0.436601	+	0.756215i	0.560824	+	0.827935i	$0.310484\pi$
$182$		0			0
$183$			2.45505i			0.181483i
$184$	11.3739	+	6.56670i	0.838492	+	0.484104i
$185$	6.39564	+	11.0776i	0.470217	+	0.814440i
$186$		0			0
$187$	11.3739	−	6.56670i	0.831739	−	0.480205i
$188$	−9.47822	+	5.47225i	−0.691270	+	0.399105i
$189$		0			0
$190$	2.33030	−	1.00905i	0.169058	−	0.0732042i
$191$	20.5390			1.48615			0.743075	−	0.669208i	$-0.233366\pi$
$191$	20.5390			1.48615			0.743075	+	0.669208i	$0.233366\pi$
$192$	3.06080	+	5.30145i	0.220894	+	0.382599i
$193$	−21.2477	+	12.2674i	−1.52944	+	0.883025i	−0.530060	+	0.847960i	$0.677831\pi$
$193$	−21.2477	+	12.2674i	−1.52944	+	0.883025i	−0.999385	+	0.0350652i	$0.988836\pi$
$194$	0.791288	+	0.456850i	0.0568112	+	0.0327999i
$195$	−7.50000	+	4.33013i	−0.537086	+	0.310087i
$196$		0			0
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$			0.286051i			0.0203287i
$199$	−19.1216	−	11.0399i	−1.35549	−	0.782595i	−0.366481	−	0.930426i	$-0.619438\pi$
$199$	−19.1216	−	11.0399i	−1.35549	−	0.782595i	−0.989013	+	0.147831i	$0.952771\pi$
$200$	5.06080	+	2.92185i	0.357852	+	0.206606i
$201$			6.20520i			0.437681i
$202$	−3.91288			−0.275309
$203$		0			0
$204$	12.1652	−	7.02355i	0.851731	−	0.491747i
$205$	−5.93466	−	3.42638i	−0.414495	−	0.239309i
$206$	1.33485	−	0.770675i	0.0930033	−	0.0536955i
$207$	−0.791288	−	1.37055i	−0.0549983	−	0.0952599i
$208$	10.5826			0.733770
$209$	10.5000	+	7.79423i	0.726300	+	0.539138i
$210$		0			0
$211$	−12.2477	+	7.07123i	−0.843168	+	0.486803i	−0.858340	−	0.513081i	$-0.828504\pi$
$211$	−12.2477	+	7.07123i	−0.843168	+	0.486803i	0.0151716	+	0.999885i	$0.495171\pi$
$212$	1.97822	−	1.14213i	0.135865	−	0.0784415i
$213$	−5.52178	−	3.18800i	−0.378346	−	0.218438i
$214$	−2.16515	−	3.75015i	−0.148007	−	0.256355i
$215$	7.50000	+	4.33013i	0.511496	+	0.295312i
$216$		−	8.66025i		−	0.589256i
$217$		0			0
$218$	−3.08258	+	5.33918i	−0.208778	+	0.361615i
$219$	9.62614	+	5.55765i	0.650474	+	0.375551i
$220$		−	6.85275i		−	0.462013i
$221$		−	16.5975i		−	1.11647i
$222$	4.10436	−	7.10895i	0.275466	−	0.477122i
$223$	−6.79129	−	11.7629i	−0.454778	−	0.787699i	0.543897	−	0.839152i	$-0.316948\pi$
$223$	−6.79129	−	11.7629i	−0.454778	−	0.787699i	−0.998675	+	0.0514528i	$0.983615\pi$
$224$		0			0
$225$	−0.352083	−	0.609826i	−0.0234722	−	0.0406551i
$226$	−3.02178	−	5.23388i	−0.201006	−	0.348152i
$227$	26.5390			1.76146			0.880728	−	0.473622i	$-0.157054\pi$
$227$	26.5390			1.76146			0.880728	+	0.473622i	$0.157054\pi$
$228$	11.2305	+	8.33648i	0.743758	+	0.552097i
$229$			6.92820i			0.457829i	0.973447	+	0.228914i	$0.0735176\pi$
$229$			6.92820i			0.457829i	−0.973447	+	0.228914i	$0.926482\pi$
$230$	−2.20871	−	3.82560i	−0.145638	−	0.252253i
$231$		0			0
$232$	−3.08258	+	5.33918i	−0.202381	+	0.350534i
$233$	6.70871	+	11.6198i	0.439502	+	0.761240i	0.997651	−	0.0685005i	$-0.0218215\pi$
$233$	6.70871	+	11.6198i	0.439502	+	0.761240i	−0.558149	+	0.829741i	$0.688488\pi$
$234$	0.313068	+	0.180750i	0.0204659	+	0.0118160i
$235$	7.79129			0.508248
$236$	17.5390			1.14169
$237$	10.7477	+	6.20520i	0.698140	+	0.403071i
$238$		0			0
$239$	14.5390			0.940451			0.470225	−	0.882546i	$-0.344173\pi$
$239$	14.5390			0.940451			0.470225	+	0.882546i	$0.344173\pi$
$240$		−	6.37600i		−	0.411569i
$241$	3.68693	−	6.38595i	0.237496	−	0.411355i	−0.722499	−	0.691372i	$-0.757007\pi$
$241$	3.68693	−	6.38595i	0.237496	−	0.411355i	0.959995	+	0.280017i	$0.0903400\pi$
$242$	0.791288	−	0.456850i	0.0508659	−	0.0293674i
$243$	−1.08258	+	1.87508i	−0.0694473	+	0.120286i
$244$	−2.12614	+	1.22753i	−0.136112	+	0.0785843i
$245$		0			0
$246$			4.39770i			0.280387i
$247$	15.1652	−	6.56670i	0.964935	−	0.417829i
$248$		0			0
$249$	21.0826	−	12.1720i	1.33605	−	0.771371i
$250$	−2.43920	−	4.22483i	−0.154269	−	0.267201i
$251$	8.29129	+	4.78698i	0.523341	+	0.302151i	0.738301	−	0.674472i	$-0.235629\pi$
$251$	8.29129	+	4.78698i	0.523341	+	0.302151i	−0.214959	+	0.976623i	$0.568962\pi$
$252$		0			0
$253$	11.3739	−	19.7001i	0.715069	−	1.23854i
$254$	−5.37386			−0.337186
$255$	−10.0000			−0.626224
$256$	−0.895644	+	1.55130i	−0.0559777	+	0.0969563i
$257$	−9.87386	+	17.1020i	−0.615915	+	1.06680i	0.374309	+	0.927304i	$0.377880\pi$
$257$	−9.87386	+	17.1020i	−0.615915	+	1.06680i	−0.990223	+	0.139491i	$0.955453\pi$
$258$		−	5.55765i		−	0.346004i
$259$		0			0
$260$	−7.50000	−	4.33013i	−0.465130	−	0.268543i
$261$	0.643371	−	0.371450i	0.0398237	−	0.0229922i
$262$	−1.62614	+	2.81655i	−0.100463	+	0.174007i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$	−8.06080	+	4.65390i	−0.496108	+	0.286428i
$265$	−1.62614			−0.0998928
$266$		0			0
$267$	−4.25227			−0.260235
$268$	−5.37386	+	3.10260i	−0.328261	+	0.189522i
$269$	3.79129	+	6.56670i	0.231159	+	0.400379i	0.958149	−	0.286269i	$-0.0924149\pi$
$269$	3.79129	+	6.56670i	0.231159	+	0.400379i	−0.726991	+	0.686647i	$0.759082\pi$
$270$	−1.45644	+	2.52263i	−0.0886361	+	0.153522i
$271$	−11.6869	+	6.74745i	−0.709931	+	0.409879i	−0.811035	−	0.584997i	$-0.801096\pi$
$271$	−11.6869	+	6.74745i	−0.709931	+	0.409879i	0.101105	+	0.994876i	$0.467762\pi$
$272$	10.5826	+	6.10985i	0.641663	+	0.370464i
$273$		0			0
$274$			4.54860i			0.274791i
$275$	5.06080	−	8.76555i	0.305177	−	0.528583i
$276$	12.1652	−	21.0707i	0.732256	−	1.26830i
$277$	23.5390			1.41432			0.707161	−	0.707052i	$-0.249976\pi$
$277$	23.5390			1.41432			0.707161	+	0.707052i	$0.249976\pi$
$278$	−4.87841			−0.292588
$279$		0			0
$280$		0			0
$281$	1.02178	+	0.589925i	0.0609543	+	0.0351920i	0.530167	−	0.847893i	$-0.322129\pi$
$281$	1.02178	+	0.589925i	0.0609543	+	0.0351920i	−0.469213	+	0.883085i	$0.655462\pi$
$282$	−2.50000	−	4.33013i	−0.148873	−	0.257855i
$283$	−8.37386	+	4.83465i	−0.497775	+	0.287390i	−0.727794	−	0.685796i	$-0.759454\pi$
$283$	−8.37386	+	4.83465i	−0.497775	+	0.287390i	0.230020	+	0.973186i	$0.426121\pi$
$284$		−	6.37600i		−	0.378346i
$285$	−3.95644	−	9.13701i	−0.234359	−	0.541229i
$286$			5.19615i			0.307255i
$287$		0			0
$288$	−0.856629	+	0.494575i	−0.0504773	+	0.0291431i
$289$	1.08258	−	1.87508i	0.0636809	−	0.110299i
$290$	1.79583	−	1.03683i	0.105455	−	0.0608845i
$291$	1.79129	−	3.10260i	0.105007	−	0.181878i
$292$			11.1153i			0.650474i
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$		0			0
$295$	−10.8131	−	6.24293i	−0.629561	−	0.363477i
$296$	17.3739			1.00984
$297$	−15.0000			−0.870388
$298$	4.43466	+	2.56035i	0.256893	+	0.148317i
$299$	−14.3739	−	24.8963i	−0.831262	−	1.43979i
$300$	5.41288	−	9.37538i	0.312513	−	0.541288i
$301$		0			0
$302$	−4.10436	−	7.10895i	−0.236179	−	0.409074i
$303$			15.3422i			0.881387i
$304$	−1.39564	+	12.0866i	−0.0800457	+	0.693216i
$305$	1.74773			0.100075
$306$	0.208712	+	0.361500i	0.0119313	+	0.0206656i
$307$	10.1044	+	17.5013i	0.576686	+	0.998850i	0.995856	+	0.0909419i	$0.0289877\pi$
$307$	10.1044	+	17.5013i	0.576686	+	0.998850i	−0.419170	+	0.907908i	$0.637679\pi$
$308$		0			0
$309$	−3.02178	−	5.23388i	−0.171903	−	0.297745i
$310$		0			0
$311$		−	23.9826i		−	1.35993i	−0.733246	−	0.679963i	$-0.761996\pi$
$311$		−	23.9826i		−	1.35993i	0.733246	−	0.679963i	$-0.238004\pi$
$312$			11.7629i			0.665941i
$313$	−7.50000	−	4.33013i	−0.423925	−	0.244753i	0.272830	−	0.962062i	$-0.412040\pi$
$313$	−7.50000	−	4.33013i	−0.423925	−	0.244753i	−0.696755	+	0.717309i	$0.745374\pi$
$314$	2.68693	−	4.65390i	0.151632	−	0.262635i
$315$		0			0
$316$			12.4104i			0.698140i
$317$	−12.7087	−	7.33738i	−0.713792	−	0.412108i	0.0986713	−	0.995120i	$-0.468541\pi$
$317$	−12.7087	−	7.33738i	−0.713792	−	0.412108i	−0.812464	+	0.583012i	$0.801874\pi$
$318$	0.521780	+	0.903750i	0.0292600	+	0.0506798i
$319$	9.24773	+	5.33918i	0.517773	+	0.298937i
$320$	3.77405	−	2.17895i	0.210976	−	0.121807i
$321$	−14.7042	+	8.48945i	−0.820707	+	0.473835i
$322$		0			0
$323$	18.9564	+	2.18890i	1.05476	+	0.121794i
$324$	−17.1652			−0.953620
$325$	−6.39564	−	11.0776i	−0.354766	−	0.614474i
$326$	2.37386	−	1.37055i	0.131476	−	0.0759078i
$327$	20.9347	+	12.0866i	1.15769	+	0.668392i
$328$	−8.06080	+	4.65390i	−0.445083	+	0.256969i
$329$		0			0
$330$	3.13068			0.172338
$331$		−	2.09355i		−	0.115072i	−0.998343	−	0.0575360i	$-0.981676\pi$
$331$		−	2.09355i		−	0.115072i	0.998343	−	0.0575360i	$-0.0183244\pi$
$332$	21.0826	+	12.1720i	1.15706	+	0.668027i
$333$	−1.81307	−	1.04678i	−0.0993555	−	0.0573629i
$334$			8.73570i			0.477996i
$335$	4.41742			0.241350
$336$		0			0
$337$	−2.12614	+	1.22753i	−0.115818	+	0.0668676i	−0.556790	−	0.830653i	$-0.687967\pi$
$337$	−2.12614	+	1.22753i	−0.115818	+	0.0668676i	0.440972	+	0.897521i	$0.354634\pi$
$338$	0.543561	+	0.313825i	0.0295658	+	0.0170698i
$339$	−20.5218	+	11.8483i	−1.11459	+	0.643509i
$340$	−5.00000	−	8.66025i	−0.271163	−	0.469668i
$341$		0			0
$342$	−0.247727	+	0.333726i	−0.0133955	+	0.0180458i
$343$		0			0
$344$	10.1869	−	5.88143i	0.549243	−	0.317105i
$345$	−15.0000	+	8.66025i	−0.807573	+	0.466252i
$346$	−7.81307	−	4.51088i	−0.420033	−	0.242506i
$347$	−15.6434	−	27.0951i	−0.839780	−	1.45454i	−0.890078	−	0.455808i	$-0.849350\pi$
$347$	−15.6434	−	27.0951i	−0.839780	−	1.45454i	0.0502981	−	0.998734i	$-0.483983\pi$
$348$	9.89110	+	5.71063i	0.530219	+	0.306122i
$349$		−	32.1105i		−	1.71884i	−0.511273	−	0.859418i	$-0.670826\pi$
$349$		−	32.1105i		−	1.71884i	0.511273	−	0.859418i	$-0.329174\pi$
$350$		0			0
$351$	−9.47822	+	16.4168i	−0.505910	+	0.876262i
$352$	−12.3131	−	7.10895i	−0.656289	−	0.378908i
$353$			0.266150i			0.0141657i	0.999975	+	0.00708286i	$0.00225456\pi$
$353$			0.266150i			0.0141657i	−0.999975	+	0.00708286i	$0.997745\pi$
$354$			8.01270i			0.425870i
$355$	−2.26951	+	3.93090i	−0.120453	+	0.208631i
$356$	−2.12614	−	3.68258i	−0.112685	−	0.195176i
$357$		0			0
$358$	3.37386	+	5.84370i	0.178314	+	0.308849i
$359$	0.313068	+	0.542250i	0.0165231	+	0.0286189i	0.874169	−	0.485622i	$-0.161407\pi$
$359$	0.313068	+	0.542250i	0.0165231	+	0.0286189i	−0.857646	+	0.514241i	$0.828074\pi$
$360$	0.460985			0.0242960
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$		−	5.36695i		−	0.282081i
$363$	−1.79129	−	3.10260i	−0.0940182	−	0.162844i
$364$		0			0
$365$	3.95644	−	6.85275i	0.207089	−	0.358690i
$366$	−0.560795	−	0.971326i	−0.0293132	−	0.0507720i
$367$	8.37386	+	4.83465i	0.437112	+	0.252367i	0.702372	−	0.711810i	$-0.252124\pi$
$367$	8.37386	+	4.83465i	0.437112	+	0.252367i	−0.265260	+	0.964177i	$0.585458\pi$
$368$	21.1652			1.10331
$369$	1.12159			0.0583877
$370$	−5.06080	−	2.92185i	−0.263098	−	0.151900i
$371$		0			0
$372$		0			0
$373$			21.7182i			1.12453i	0.826958	+	0.562263i	$0.190069\pi$
$373$			21.7182i			1.12453i	−0.826958	+	0.562263i	$0.809931\pi$
$374$	−3.00000	+	5.19615i	−0.155126	+	0.268687i
$375$	−16.5653	+	9.56400i	−0.855431	+	0.493883i
$376$	5.29129	−	9.16478i	0.272877	−	0.472637i
$377$	11.6869	−	6.74745i	0.601908	−	0.347512i
$378$		0			0
$379$			26.3423i			1.35311i	0.736392	+	0.676556i	$0.236528\pi$
$379$			26.3423i			1.35311i	−0.736392	+	0.676556i	$0.763472\pi$
$380$	5.93466	−	7.99488i	0.304442	−	0.410129i
$381$			21.0707i			1.07948i
$382$	−8.12614	+	4.69163i	−0.415769	+	0.240045i
$383$	−8.45644	−	14.6470i	−0.432104	−	0.748426i	0.564950	−	0.825125i	$-0.308895\pi$
$383$	−8.45644	−	14.6470i	−0.432104	−	0.748426i	−0.997054	+	0.0766990i	$0.975562\pi$
$384$	−17.1261	−	9.88778i	−0.873964	−	0.504584i
$385$		0			0
$386$	5.60436	−	9.70703i	0.285254	−	0.494075i
$387$	−1.41742			−0.0720517
$388$	3.58258			0.181878
$389$	−16.9782	+	29.4071i	−0.860830	+	1.49100i	0.0102991	+	0.999947i	$0.496722\pi$
$389$	−16.9782	+	29.4071i	−0.860830	+	1.49100i	−0.871129	+	0.491054i	$0.836612\pi$
$390$	1.97822	−	3.42638i	0.100171	−	0.173501i
$391$		−	33.1950i		−	1.67874i
$392$		0			0
$393$	11.0436	+	6.37600i	0.557074	+	0.321627i
$394$	4.74773	−	2.74110i	0.239187	−	0.138095i
$395$	4.41742	−	7.65120i	0.222265	−	0.384974i
$396$	0.560795	+	0.971326i	0.0281810	+	0.0488110i
$397$	3.87386	−	2.23658i	0.194424	−	0.112251i	−0.399628	−	0.916677i	$-0.630861\pi$
$397$	3.87386	−	2.23658i	0.194424	−	0.112251i	0.594052	+	0.804427i	$0.297527\pi$
$398$	10.0871			0.505622
$399$		0			0
$400$	9.41742			0.470871
$401$	−3.64337	+	2.10350i	−0.181941	+	0.105044i	−0.588204	−	0.808712i	$-0.700165\pi$
$401$	−3.64337	+	2.10350i	−0.181941	+	0.105044i	0.406263	+	0.913756i	$0.366832\pi$
$402$	−1.41742	−	2.45505i	−0.0706947	−	0.122447i
$403$		0			0
$404$	−13.2867	+	7.67110i	−0.661040	+	0.381652i
$405$	10.5826	+	6.10985i	0.525852	+	0.303601i
$406$		0			0
$407$		−	30.0924i		−	1.49163i
$408$	−6.79129	+	11.7629i	−0.336219	+	0.582348i
$409$	−7.41742	+	12.8474i	−0.366768	+	0.635261i	−0.989058	−	0.147526i	$-0.952869\pi$
$409$	−7.41742	+	12.8474i	−0.366768	+	0.635261i	0.622290	+	0.782787i	$0.286202\pi$
$410$	3.13068			0.154613
$411$	17.8348			0.879728
$412$	3.02178	−	5.23388i	0.148872	−	0.257855i
$413$		0			0
$414$	0.626136	+	0.361500i	0.0307729	+	0.0177668i
$415$	−8.66515	−	15.0085i	−0.425356	−	0.736737i
$416$	−15.5608	+	8.98403i	−0.762931	+	0.440478i
$417$			19.1280i			0.936703i
$418$	−5.93466	−	0.685275i	−0.290274	−	0.0335179i
$419$			38.7726i			1.89416i	0.320992	+	0.947082i	$0.395984\pi$
$419$			38.7726i			1.89416i	−0.320992	+	0.947082i	$0.604016\pi$
$420$		0			0
$421$	13.8131	−	7.97498i	0.673208	−	0.388677i	−0.124083	−	0.992272i	$-0.539599\pi$
$421$	13.8131	−	7.97498i	0.673208	−	0.388677i	0.797291	+	0.603595i	$0.206266\pi$
$422$	3.23049	−	5.59538i	0.157258	−	0.272379i
$423$	−1.10436	+	0.637600i	−0.0536956	+	0.0310012i
$424$	−1.10436	+	1.91280i	−0.0536323	+	0.0928938i
$425$		−	14.7701i		−	0.716455i
$426$	2.91288			0.141129
$427$		0			0
$428$	−14.7042	−	8.48945i	−0.710753	−	0.410353i
$429$	20.3739			0.983659
$430$	−3.95644			−0.190796
$431$	−15.7087	−	9.06943i	−0.756662	−	0.436859i	0.0714340	−	0.997445i	$-0.477242\pi$
$431$	−15.7087	−	9.06943i	−0.756662	−	0.436859i	−0.828096	+	0.560586i	$0.810576\pi$
$432$	−6.97822	−	12.0866i	−0.335740	−	0.581518i
$433$	−18.1869	+	31.5007i	−0.874008	+	1.51383i	−0.0161926	+	0.999869i	$0.505154\pi$
$433$	−18.1869	+	31.5007i	−0.874008	+	1.51383i	−0.857816	+	0.513958i	$0.828179\pi$
$434$		0			0
$435$	−4.06534	−	7.04138i	−0.194918	−	0.337608i
$436$			24.1733i			1.15769i
$437$	30.3303	−	13.1334i	1.45090	−	0.628256i
$438$	−5.07803			−0.242638
$439$	−1.58258	−	2.74110i	−0.0755322	−	0.130826i	0.825785	−	0.563984i	$-0.190732\pi$
$439$	−1.58258	−	2.74110i	−0.0755322	−	0.130826i	−0.901318	+	0.433159i	$0.857399\pi$
$440$	3.31307	+	5.73840i	0.157944	+	0.273568i
$441$		0			0
$442$	3.79129	+	6.56670i	0.180333	+	0.312346i
$443$	−10.6652	+	18.4726i	−0.506717	+	0.877659i	0.493253	+	0.869886i	$0.335808\pi$
$443$	−10.6652	+	18.4726i	−0.506717	+	0.877659i	−0.999970	+	0.00777314i	$0.997526\pi$
$444$		−	32.1860i		−	1.52748i
$445$			3.02715i			0.143501i
$446$	5.37386	+	3.10260i	0.254460	+	0.146912i
$447$	10.0390	−	17.3881i	0.474829	−	0.822428i
$448$		0			0
$449$			12.6766i			0.598244i	0.954215	+	0.299122i	$0.0966937\pi$
$449$			12.6766i			0.598244i	−0.954215	+	0.299122i	$0.903306\pi$
$450$	0.278599	+	0.160849i	0.0131333	+	0.00758251i
$451$	8.06080	+	13.9617i	0.379568	+	0.657431i
$452$	−20.5218	−	11.8483i	−0.965263	−	0.557295i
$453$	−27.8739	+	16.0930i	−1.30963	+	0.756114i
$454$	−10.5000	+	6.06218i	−0.492789	+	0.284512i
$455$		0			0
$456$	−13.4347	−	1.55130i	−0.629136	−	0.0726463i
$457$	−38.0780			−1.78122			−0.890608	−	0.454773i	$-0.849721\pi$
$457$	−38.0780			−1.78122			−0.890608	+	0.454773i	$0.849721\pi$
$458$	−1.58258	−	2.74110i	−0.0739489	−	0.128083i
$459$	−18.9564	+	10.9445i	−0.884811	+	0.510846i
$460$	−15.0000	−	8.66025i	−0.699379	−	0.403786i
$461$	−4.66515	+	2.69343i	−0.217278	+	0.125445i	−0.604689	−	0.796462i	$-0.706703\pi$
$461$	−4.66515	+	2.69343i	−0.217278	+	0.125445i	0.387411	+	0.921907i	$0.373369\pi$
$462$		0			0
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$			9.93545i			0.461242i
$465$		0			0
$466$	−5.30852	−	3.06488i	−0.245913	−	0.141978i
$467$		−	20.5185i		−	0.949481i	−0.880126	−	0.474741i	$-0.842542\pi$
$467$		−	20.5185i		−	0.949481i	0.880126	−	0.474741i	$-0.157458\pi$
$468$	1.41742			0.0655205
$469$		0			0
$470$	−3.08258	+	1.77973i	−0.142189	+	0.0820926i
$471$	−18.2477	−	10.5353i	−0.840811	−	0.485442i
$472$	−14.6869	+	8.47950i	−0.676021	+	0.390301i
$473$	−10.1869	−	17.6443i	−0.468396	−	0.811285i
$474$	−5.66970			−0.260418
$475$	13.4955	−	5.84370i	0.619214	−	0.268127i
$476$		0			0
$477$	0.230493	−	0.133075i	0.0105535	−	0.00609308i
$478$	−5.75227	+	3.32108i	−0.263103	+	0.151902i
$479$	0.165151	+	0.0953502i	0.00754596	+	0.00435666i	0.503768	−	0.863839i	$-0.331947\pi$
$479$	0.165151	+	0.0953502i	0.00754596	+	0.00435666i	−0.496222	+	0.868196i	$0.665280\pi$
$480$	5.41288	+	9.37538i	0.247063	+	0.427926i
$481$	−32.9347	−	19.0148i	−1.50169	−	0.867002i
$482$			3.36875i			0.153442i
$483$		0			0
$484$	1.79129	−	3.10260i	0.0814222	−	0.141027i
$485$	−2.20871	−	1.27520i	−0.100292	−	0.0579039i
$486$		−	0.989150i		−	0.0448688i
$487$			10.0308i			0.454539i	0.973832	+	0.227270i	$0.0729799\pi$
$487$			10.0308i			0.454539i	−0.973832	+	0.227270i	$0.927020\pi$
$488$	1.18693	−	2.05583i	0.0537299	−	0.0930629i
$489$	−5.37386	−	9.30780i	−0.243015	−	0.420913i
$490$		0			0
$491$	−19.0390	−	32.9765i	−0.859219	−	1.48821i	−0.872675	−	0.488301i	$-0.837617\pi$
$491$	−19.0390	−	32.9765i	−0.859219	−	1.48821i	0.0134566	−	0.999909i	$-0.495717\pi$
$492$	8.62159	+	14.9330i	0.388691	+	0.673233i
$493$	15.5826			0.701804
$494$	−4.50000	+	6.06218i	−0.202465	+	0.272750i
$495$		−	0.798450i		−	0.0358876i
$496$		0			0
$497$		0			0
$498$	−5.56080	+	9.63158i	−0.249185	+	0.431601i
$499$	8.87386	+	15.3700i	0.397249	+	0.688055i	0.993385	−	0.114828i	$-0.0366317\pi$
$499$	8.87386	+	15.3700i	0.397249	+	0.688055i	−0.596137	+	0.802883i	$0.703298\pi$
$500$	−16.5653	−	9.56400i	−0.740825	−	0.427715i
$501$	34.2523			1.53028
$502$	−4.37386			−0.195215
$503$	−10.4174	−	6.01450i	−0.464490	−	0.268173i	0.249440	−	0.968390i	$-0.419753\pi$
$503$	−10.4174	−	6.01450i	−0.464490	−	0.268173i	−0.713930	+	0.700217i	$0.753087\pi$
$504$		0			0
$505$	10.9220			0.486021
$506$			10.3923i			0.461994i
$507$	1.23049	−	2.13128i	0.0546481	−	0.0946533i
$508$	−18.2477	+	10.5353i	−0.809612	+	0.467430i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$	3.95644	−	2.28425i	0.175194	−	0.101148i
$511$		0			0
$512$		−	22.8981i		−	1.01196i
$513$	−17.5000	−	12.9904i	−0.772644	−	0.573539i
$514$		−	9.02175i		−	0.397933i
$515$	−3.72595	+	2.15118i	−0.164185	+	0.0947922i
$516$	−10.8956	−	18.8718i	−0.479654	−	0.830785i
$517$	−15.8739	−	9.16478i	−0.698132	−	0.403067i
$518$		0			0
$519$	−17.6869	+	30.6347i	−0.776370	+	1.34471i
$520$	8.37386			0.367218
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$	−0.169697	+	0.293924i	−0.00742745	+	0.0128647i
$523$	10.7477	−	18.6156i	0.469965	−	0.814004i	−0.529445	−	0.848344i	$-0.677600\pi$
$523$	10.7477	−	18.6156i	0.469965	−	0.814004i	0.999410	+	0.0343406i	$0.0109331\pi$
$524$			12.7520i			0.557074i
$525$		0			0
$526$	4.74773	+	2.74110i	0.207011	+	0.119518i
$527$		0			0
$528$	−7.50000	+	12.9904i	−0.326396	+	0.565334i
$529$	−17.2477	−	29.8739i	−0.749901	−	1.29887i
$530$	0.643371	−	0.371450i	0.0279463	−	0.0161348i
$531$	2.04356			0.0886830
$532$		0			0
$533$	20.3739			0.882490
$534$	1.68239	−	0.971326i	0.0728040	−	0.0420334i
$535$	6.04356	+	10.4678i	0.261286	+	0.452560i
$536$	3.00000	−	5.19615i	0.129580	−	0.224440i
$537$	22.9129	−	13.2288i	0.988764	−	0.570863i
$538$	−3.00000	−	1.73205i	−0.129339	−	0.0746740i
$539$		0			0
$540$			11.4213i			0.491493i
$541$	1.87386	−	3.24563i	0.0805637	−	0.139540i	−0.822929	−	0.568145i	$-0.807661\pi$
$541$	1.87386	−	3.24563i	0.0805637	−	0.139540i	0.903492	+	0.428605i	$0.140995\pi$
$542$	3.08258	−	5.33918i	0.132408	−	0.229337i
$543$	−21.0436			−0.903066
$544$	−20.7477			−0.889551
$545$	8.60436	−	14.9032i	0.368570	−	0.638382i
$546$		0			0
$547$	−10.4347	−	6.02445i	−0.446154	−	0.257587i	0.260051	−	0.965595i	$-0.416261\pi$
$547$	−10.4347	−	6.02445i	−0.446154	−	0.257587i	−0.706204	+	0.708008i	$0.749594\pi$
$548$	8.91742	+	15.4454i	0.380933	+	0.659796i
$549$	−0.247727	+	0.143025i	−0.0105727	+	0.00610417i
$550$			4.62405i			0.197170i
$551$	6.16515	+	14.2378i	0.262644	+	0.606551i
$552$			23.5257i			1.00132i
$553$		0			0
$554$	−9.31307	+	5.37690i	−0.395674	+	0.228443i
$555$	−11.4564	+	19.8431i	−0.486299	+	0.842294i
$556$	−16.5653	+	9.56400i	−0.702527	+	0.405604i
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	−0.964686	−	0.263404i	$-0.915155\pi$
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	0.710457	+	0.703740i	$0.248488\pi$
$558$		0			0
$559$	−25.7477			−1.08901
$560$		0			0
$561$	20.3739	+	11.7629i	0.860185	+	0.496628i
$562$	−0.539015			−0.0227370
$563$	35.7042			1.50475			0.752376	−	0.658734i	$-0.228908\pi$
$563$	35.7042			1.50475			0.752376	+	0.658734i	$0.228908\pi$
$564$	−16.9782	−	9.80238i	−0.714912	−	0.412755i
$565$	8.43466	+	14.6093i	0.354849	+	0.614616i
$566$	2.20871	−	3.82560i	0.0928391	−	0.160802i
$567$		0			0
$568$	3.08258	+	5.33918i	0.129342	+	0.224027i
$569$		−	3.19795i		−	0.134065i	−0.997751	−	0.0670326i	$-0.978647\pi$
$569$		−	3.19795i		−	0.134065i	0.997751	−	0.0670326i	$-0.0213531\pi$
$570$	3.65246	+	2.71125i	0.152985	+	0.113562i
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$	10.1869	+	17.6443i	0.425937	+	0.737745i
$573$	18.3956	+	31.8622i	0.768489	+	1.33106i
$574$		0			0
$575$	−12.7913	−	22.1552i	−0.533434	−	0.923934i
$576$	−0.356629	+	0.617700i	−0.0148595	+	0.0257375i
$577$		−	30.3785i		−	1.26467i	−0.774694	−	0.632336i	$-0.782096\pi$
$577$		−	30.3785i		−	1.26467i	0.774694	−	0.632336i	$-0.217904\pi$
$578$			0.989150i			0.0411432i
$579$	−38.0608	−	21.9744i	−1.58175	−	0.913225i
$580$	4.06534	−	7.04138i	0.168804	−	0.292377i
$581$		0			0
$582$			1.63670i			0.0678434i
$583$	3.31307	+	1.91280i	0.137213	+	0.0792201i
$584$	−5.37386	−	9.30780i	−0.222372	−	0.385160i
$585$	−0.873864	−	0.504525i	−0.0361298	−	0.0208596i
$586$	8.30852	−	4.79693i	0.343222	−	0.198159i
$587$	7.26951	−	4.19705i	0.300045	−	0.173231i	−0.342418	−	0.939548i	$-0.611246\pi$
$587$	7.26951	−	4.19705i	0.300045	−	0.173231i	0.642463	+	0.766317i	$0.277913\pi$
$588$		0			0
$589$		0			0
$590$	5.70417			0.234837
$591$	−10.7477	−	18.6156i	−0.442102	−	0.765744i
$592$	24.2477	−	13.9994i	0.996575	−	0.575373i
$593$	14.8348	+	8.56490i	0.609194	+	0.351718i	0.772650	−	0.634832i	$-0.218931\pi$
$593$	14.8348	+	8.56490i	0.609194	+	0.351718i	−0.163456	+	0.986551i	$0.552264\pi$
$594$	5.93466	−	3.42638i	0.243502	−	0.140586i
$595$		0			0
$596$	20.0780			0.822428
$597$		−	39.5511i		−	1.61872i
$598$	11.3739	+	6.56670i	0.465112	+	0.268532i
$599$	31.3521	+	18.1011i	1.28101	+	0.739592i	0.977033	−	0.213087i	$-0.0683517\pi$
$599$	31.3521	+	18.1011i	1.28101	+	0.739592i	0.303978	+	0.952679i	$0.401685\pi$
$600$			10.4678i			0.427344i
$601$	20.4955			0.836027			0.418014	−	0.908441i	$-0.362726\pi$
$601$	20.4955			0.836027			0.418014	+	0.908441i	$0.362726\pi$
$602$		0			0
$603$	−0.626136	+	0.361500i	−0.0254982	+	0.0147214i
$604$	−27.8739	−	16.0930i	−1.13417	−	0.654814i
$605$	−2.20871	+	1.27520i	−0.0897969	+	0.0518443i
$606$	−3.50455	−	6.07005i	−0.142362	−	0.246579i
$607$	−14.0000			−0.568242			−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000			−0.568242			−0.284121	+	0.958788i	$0.591702\pi$
$608$	−8.20871	−	18.9572i	−0.332907	−	0.768816i
$609$		0			0
$610$	−0.691478	+	0.399225i	−0.0279971	+	0.0161641i
$611$	−20.0608	+	11.5821i	−0.811573	+	0.468562i
$612$	1.41742	+	0.818350i	0.0572960	+	0.0330799i
$613$	2.68693	+	4.65390i	0.108524	+	0.187969i	0.915173	−	0.403062i	$-0.132054\pi$
$613$	2.68693	+	4.65390i	0.108524	+	0.187969i	−0.806648	+	0.591032i	$0.798721\pi$
$614$	−7.99545	−	4.61618i	−0.322670	−	0.186294i
$615$		−	12.2753i		−	0.494986i
$616$		0			0
$617$	22.5826	−	39.1142i	0.909140	−	1.57468i	0.0938792	−	0.995584i	$-0.470073\pi$
$617$	22.5826	−	39.1142i	0.909140	−	1.57468i	0.815261	−	0.579094i	$-0.196593\pi$
$618$	2.39110	+	1.38050i	0.0961841	+	0.0555319i
$619$		−	8.66025i		−	0.348085i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$		−	8.66025i		−	0.348085i	0.984738	−	0.174042i	$-0.0556830\pi$
$620$		0			0
$621$	−18.9564	+	32.8335i	−0.760696	+	1.31756i
$622$	5.47822	+	9.48855i	0.219657	+	0.380456i
$623$		0			0
$624$	9.47822	+	16.4168i	0.379432	+	0.657196i
$625$	−1.62614	−	2.81655i	−0.0650455	−	0.112662i
$626$	3.95644			0.158131
$627$	−2.68693	+	23.2695i	−0.107306	+	0.929295i
$628$		−	21.0707i		−	0.840811i
$629$	−21.9564	−	38.0297i	−0.875461	−	1.51634i
$630$		0			0
$631$	17.1434	−	29.6932i	0.682467	−	1.18207i	−0.291759	−	0.956492i	$-0.594240\pi$
$631$	17.1434	−	29.6932i	0.682467	−	1.18207i	0.974226	−	0.225575i	$-0.0724262\pi$
$632$	−6.00000	−	10.3923i	−0.238667	−	0.413384i
$633$	−21.9392	−	12.6666i	−0.872005	−	0.503452i
$634$	6.70417			0.266256
$635$	15.0000			0.595257
$636$	3.54356	+	2.04588i	0.140511	+	0.0811243i
$637$		0			0
$638$	−4.87841			−0.193138
$639$		−	0.742901i		−	0.0293887i
$640$	−7.03901	+	12.1919i	−0.278241	+	0.481928i
$641$	−6.16515	+	3.55945i	−0.243509	+	0.140590i	−0.616788	−	0.787129i	$-0.711567\pi$
$641$	−6.16515	+	3.55945i	−0.243509	+	0.140590i	0.373280	+	0.927719i	$0.378233\pi$
$642$	3.87841	−	6.71760i	0.153069	−	0.265123i
$643$	−9.24773	+	5.33918i	−0.364695	+	0.210557i	−0.671138	−	0.741332i	$-0.734194\pi$
$643$	−9.24773	+	5.33918i	−0.364695	+	0.210557i	0.306443	+	0.951889i	$0.400861\pi$
$644$		0			0
$645$			15.5130i			0.610824i
$646$	−8.00000	+	3.46410i	−0.314756	+	0.136293i
$647$			6.66205i			0.261912i	0.991388	+	0.130956i	$0.0418047\pi$
$647$			6.66205i			0.261912i	−0.991388	+	0.130956i	$0.958195\pi$
$648$	14.3739	−	8.29875i	0.564659	−	0.326006i
$649$	14.6869	+	25.4385i	0.576513	+	0.998549i
$650$	5.06080	+	2.92185i	0.198501	+	0.114604i
$651$		0			0
$652$	5.37386	−	9.30780i	0.210457	−	0.364522i
$653$	15.0000			0.586995			0.293498	−	0.955960i	$-0.405181\pi$
$653$	15.0000			0.586995			0.293498	+	0.955960i	$0.405181\pi$
$654$	−11.0436			−0.431837
$655$	4.53901	−	7.86180i	0.177354	−	0.307186i
$656$	−7.50000	+	12.9904i	−0.292826	+	0.507189i
$657$			1.29510i			0.0505267i
$658$		0			0
$659$	−25.4174	−	14.6748i	−0.990122	−	0.571647i	−0.0848114	−	0.996397i	$-0.527029\pi$
$659$	−25.4174	−	14.6748i	−0.990122	−	0.571647i	−0.905311	+	0.424750i	$0.860362\pi$
$660$	10.6307	−	6.13763i	0.413799	−	0.238907i
$661$	−15.2477	+	26.4098i	−0.593068	+	1.02722i	0.400749	+	0.916188i	$0.368750\pi$
$661$	−15.2477	+	26.4098i	−0.593068	+	1.02722i	−0.993816	+	0.111036i	$0.964583\pi$
$662$	0.478220	+	0.828301i	0.0185865	+	0.0321928i
$663$	25.7477	−	14.8655i	0.999959	−	0.577327i
$664$	−23.5390			−0.913491
$665$		0			0
$666$	0.956439			0.0370613
$667$	23.3739	−	13.4949i	0.905040	−	0.522525i
$668$	17.1261	+	29.6633i	0.662630	+	1.14771i
$669$	12.1652	−	21.0707i	0.470332	−	0.814639i
$670$	−1.74773	+	1.00905i	−0.0675206	+	0.0389830i
$671$	−3.56080	−	2.05583i	−0.137463	−	0.0793643i
$672$		0			0
$673$			11.6874i			0.450516i	0.974299	+	0.225258i	$0.0723226\pi$
$673$			11.6874i			0.450516i	−0.974299	+	0.225258i	$0.927677\pi$
$674$	0.560795	−	0.971326i	0.0216010	−	0.0374141i
$675$	−8.43466	+	14.6093i	−0.324650	+	0.562311i
$676$	2.46099			0.0946533
$677$	−2.66970			−0.102605			−0.0513024	−	0.998683i	$-0.516337\pi$
$677$	−2.66970			−0.102605			−0.0513024	+	0.998683i	$0.516337\pi$
$678$	5.41288	−	9.37538i	0.207880	−	0.360059i
$679$		0			0
$680$	8.37386	+	4.83465i	0.321123	+	0.185400i
$681$	23.7695	+	41.1700i	0.910850	+	1.57764i
$682$		0			0
$683$			34.9470i			1.33721i	0.743618	+	0.668604i	$0.233108\pi$
$683$			34.9470i			1.33721i	−0.743618	+	0.668604i	$0.766892\pi$
$684$	−0.186932	+	1.61888i	−0.00714751	+	0.0618993i
$685$		−	12.6965i		−	0.485107i
$686$		0			0
$687$	−10.7477	+	6.20520i	−0.410051	+	0.236743i
$688$	9.47822	−	16.4168i	0.361354	−	0.625883i
$689$	4.18693	−	2.41733i	0.159509	−	0.0920928i
$690$	3.95644	−	6.85275i	0.150619	−	0.260880i
$691$			43.3013i			1.64726i	0.567129	+	0.823629i	$0.308054\pi$
$691$			43.3013i			1.64726i	−0.567129	+	0.823629i	$0.691946\pi$
$692$	−35.3739			−1.34471
$693$		0			0
$694$	12.3784	+	7.14668i	0.469878	+	0.271284i
$695$	13.6170			0.516524
$696$	−11.0436			−0.418605
$697$	20.3739	+	11.7629i	0.771715	+	0.445550i
$698$	7.33485	+	12.7043i	0.277628	+	0.480866i
$699$	−12.0172	+	20.8145i	−0.454534	+	0.787275i
$700$		0			0
$701$	10.7477	+	18.6156i	0.405936	+	0.703102i	0.994430	−	0.105400i	$-0.0336122\pi$
$701$	10.7477	+	18.6156i	0.405936	+	0.703102i	−0.588494	+	0.808502i	$0.700279\pi$
$702$		−	8.66025i		−	0.326860i
$703$	26.0608	−	35.1078i	0.982902	−	1.32412i
$704$	−10.2523			−0.386397
$705$	6.97822	+	12.0866i	0.262815	+	0.455209i
$706$	−0.0607953	−	0.105301i	−0.00228806	−	0.00396304i
$707$		0			0
$708$	15.7087	+	27.2083i	0.590370	+	1.02255i
$709$	6.70871	−	11.6198i	0.251951	−	0.436392i	−0.712112	−	0.702066i	$-0.752261\pi$
$709$	6.70871	−	11.6198i	0.251951	−	0.436392i	0.964063	+	0.265674i	$0.0855945\pi$
$710$		−	2.07365i		−	0.0778227i
$711$			1.44600i			0.0542292i
$712$	3.56080	+	2.05583i	0.133446	+	0.0770453i
$713$		0			0
$714$		0			0
$715$		−	14.5040i		−	0.542417i
$716$	22.9129	+	13.2288i	0.856294	+	0.494382i
$717$	13.0218	+	22.5544i	0.486307	+	0.842309i
$718$	−0.247727	−	0.143025i	−0.00924509	−	0.00533766i
$719$	27.1652	−	15.6838i	1.01309	−	0.584907i	0.100995	−	0.994887i	$-0.467798\pi$
$719$	27.1652	−	15.6838i	1.01309	−	0.584907i	0.912095	+	0.409980i	$0.134464\pi$
$720$	0.643371	−	0.371450i	0.0239770	−	0.0138431i
$721$		0			0
$722$	−6.33030	−	5.93905i	−0.235589	−	0.221029i
$723$	13.2087			0.491237
$724$	−10.5218	−	18.2243i	−0.391039	−	0.677299i
$725$	10.4002	−	6.00455i	0.386253	−	0.223003i
$726$	1.41742	+	0.818350i	0.0526055	+	0.0303718i
$727$	39.2477	−	22.6597i	1.45562	−	0.840401i	0.456826	−	0.889556i	$-0.348986\pi$
$727$	39.2477	−	22.6597i	1.45562	−	0.840401i	0.998791	+	0.0491546i	$0.0156527\pi$
$728$		0			0
$729$	24.8693			0.921086
$730$			3.61500i			0.133797i
$731$	−25.7477	−	14.8655i	−0.952314	−	0.549819i
$732$	−3.80852	−	2.19885i	−0.140767	−	0.0812719i
$733$			28.6464i			1.05808i	0.848597	+	0.529040i	$0.177448\pi$
$733$			28.6464i			1.05808i	−0.848597	+	0.529040i	$0.822552\pi$
$734$	−4.41742			−0.163050
$735$		0			0
$736$	−31.1216	+	17.9681i	−1.14716	+	0.662311i
$737$	−9.00000	−	5.19615i	−0.331519	−	0.191403i
$738$	−0.443751	+	0.256199i	−0.0163347	+	0.00943083i
$739$	−12.8739	−	22.2982i	−0.473573	−	0.820252i	0.525970	−	0.850503i	$-0.323703\pi$
$739$	−12.8739	−	22.2982i	−0.473573	−	0.820252i	−0.999542	+	0.0302513i	$0.990369\pi$
$740$	−22.9129			−0.842294
$741$	23.7695	+	17.6443i	0.873195	+	0.648179i
$742$		0			0
$743$	28.8956	−	16.6829i	1.06008	−	0.612037i	0.134624	−	0.990897i	$-0.457017\pi$
$743$	28.8956	−	16.6829i	1.06008	−	0.612037i	0.925454	+	0.378860i	$0.123684\pi$
$744$		0			0
$745$	−12.3784	−	7.14668i	−0.453510	−	0.261834i
$746$	−4.96099	−	8.59268i	−0.181635	−	0.314600i
$747$	2.45644	+	1.41823i	0.0898764	+	0.0518902i
$748$			23.5257i			0.860185i
$749$		0			0
$750$	4.36932	−	7.56788i	0.159545	−	0.276340i
$751$	7.81307	+	4.51088i	0.285103	+	0.164604i	0.635731	−	0.771910i	$-0.280699\pi$
$751$	7.81307	+	4.51088i	0.285103	+	0.164604i	−0.350628	+	0.936515i	$0.614032\pi$
$752$		−	17.0544i		−	0.621908i
$753$			17.1497i			0.624970i
$754$	−3.08258	+	5.33918i	−0.112261	+	0.194441i
$755$	11.4564	+	19.8431i	0.416943	+	0.722166i
$756$		0			0
$757$	14.1216	+	24.4593i	0.513258	+	0.888989i	0.999882	+	0.0153772i	$0.00489491\pi$
$757$	14.1216	+	24.4593i	0.513258	+	0.888989i	−0.486624	+	0.873612i	$0.661772\pi$
$758$	−6.01723	−	10.4222i	−0.218556	−	0.378550i
$759$	40.7477			1.47905
$760$	−1.10436	+	9.56400i	−0.0400592	+	0.346923i
$761$		−	20.5185i		−	0.743794i	−0.928274	−	0.371897i	$-0.878708\pi$
$761$		−	20.5185i		−	0.743794i	0.928274	−	0.371897i	$-0.121292\pi$
$762$	−4.81307	−	8.33648i	−0.174359	−	0.301999i
$763$		0			0
$764$	−18.3956	+	31.8622i	−0.665531	+	1.15273i
$765$	−0.582576	−	1.00905i	−0.0210631	−	0.0364823i
$766$	6.69148	+	3.86333i	0.241773	+	0.139588i
$767$	37.1216			1.34038
$768$	−3.20871			−0.115784
$769$	25.1869	+	14.5417i	0.908264	+	0.524386i	0.879872	−	0.475210i	$-0.157628\pi$
$769$	25.1869	+	14.5417i	0.908264	+	0.524386i	0.0283918	+	0.999597i	$0.490961\pi$
$770$		0			0
$771$	−35.3739			−1.27396
$772$		−	43.9488i		−	1.58175i
$773$	−19.8303	+	34.3471i	−0.713246	+	1.23538i	0.250386	+	0.968146i	$0.419443\pi$
$773$	−19.8303	+	34.3471i	−0.713246	+	1.23538i	−0.963632	+	0.267233i	$0.913891\pi$
$774$	0.560795	−	0.323775i	0.0201574	−	0.0116379i
$775$		0			0
$776$	−3.00000	+	1.73205i	−0.107694	+	0.0621770i
$777$		0			0
$778$		−	15.5130i		−	0.556168i
$779$	−2.68693	+	23.2695i	−0.0962693	+	0.833717i
$780$		−	15.5130i		−	0.555455i
$781$	9.24773	−	5.33918i	0.330910	−	0.191051i
$782$	7.58258	+	13.1334i	0.271152	+	0.469650i
$783$	−15.4129	−	8.89863i	−0.550811	−	0.318011i
$784$		0			0
$785$	−7.50000	+	12.9904i	−0.267686	+	0.463647i
$786$	−5.82576			−0.207798
$787$	25.5826			0.911920			0.455960	−	0.890000i	$-0.349296\pi$
$787$	25.5826			0.911920			0.455960	+	0.890000i	$0.349296\pi$
$788$	10.7477	−	18.6156i	0.382872	−	0.663154i
$789$	10.7477	−	18.6156i	0.382629	−	0.662733i
$790$			4.03620i			0.143602i
$791$		0			0
$792$	−0.939205	−	0.542250i	−0.0333732	−	0.0192680i
$793$	−4.50000	+	2.59808i	−0.159800	+	0.0922604i
$794$	−1.02178	+	1.76978i	−0.0362616	+	0.0628070i
$795$	−1.45644	−	2.52263i	−0.0516546	−	0.0894684i
$796$	34.2523	−	19.7756i	1.21404	−	0.700926i
$797$	48.4955			1.71780			0.858899	−	0.512146i	$-0.171149\pi$
$797$	48.4955			1.71780			0.858899	+	0.512146i	$0.171149\pi$
$798$		0			0
$799$	−26.7477			−0.946267
$800$	−13.8475	+	7.99488i	−0.489584	+	0.282662i
$801$	−0.247727	−	0.429076i	−0.00875301	−	0.0151607i
$802$	0.960985	−	1.66447i	0.0339336	−	0.0587747i
$803$	−16.1216	+	9.30780i	−0.568919	+	0.328465i
$804$	−9.62614	−	5.55765i	−0.339488	−	0.196003i
$805$		0			0
$806$		0			0
$807$	−6.79129	+	11.7629i	−0.239065	+	0.414072i
$808$	7.41742	−	12.8474i	0.260944	−	0.451968i
$809$	50.0780			1.76065			0.880325	−	0.474371i	$-0.157325\pi$
$809$	50.0780			1.76065			0.880325	+	0.474371i	$0.157325\pi$
$810$	−5.58258			−0.196152
$811$	−7.56080	+	13.0957i	−0.265495	+	0.459852i	−0.967693	−	0.252130i	$-0.918869\pi$
$811$	−7.56080	+	13.0957i	−0.265495	+	0.459852i	0.702198	+	0.711982i	$0.252202\pi$
$812$		0			0
$813$	−20.9347	−	12.0866i	−0.734211	−	0.423897i
$814$	6.87386	+	11.9059i	0.240929	+	0.417301i
$815$	−6.62614	+	3.82560i	−0.232103	+	0.134005i
$816$			21.8890i			0.766269i
$817$	3.39564	−	29.4071i	0.118799	−	1.02883i
$818$		−	6.77730i		−	0.236963i
$819$		0			0
$820$	10.6307	−	6.13763i	0.371240	−	0.214335i
$821$	8.52178	−	14.7602i	0.297412	−	0.515133i	−0.678131	−	0.734941i	$-0.737210\pi$
$821$	8.52178	−	14.7602i	0.297412	−	0.515133i	0.975543	+	0.219808i	$0.0705431\pi$
$822$	−7.05625	+	4.07393i	−0.246115	+	0.142095i
$823$	12.7087	−	22.0121i	0.442998	−	0.767295i	−0.554912	−	0.831909i	$-0.687248\pi$
$823$	12.7087	−	22.0121i	0.442998	−	0.767295i	0.997910	+	0.0646139i	$0.0205816\pi$
$824$			5.84370i			0.203575i
$825$	18.1307			0.631229
$826$		0			0
$827$	26.7042	+	15.4177i	0.928595	+	0.536124i	0.886367	−	0.462984i	$-0.153221\pi$
$827$	26.7042	+	15.4177i	0.928595	+	0.536124i	0.0422280	+	0.999108i	$0.486554\pi$
$828$	2.83485			0.0985178
$829$	−14.2523			−0.495002			−0.247501	−	0.968888i	$-0.579609\pi$
$829$	−14.2523			−0.495002			−0.247501	+	0.968888i	$0.579609\pi$
$830$	6.85663	+	3.95868i	0.237997	+	0.137408i
$831$	21.0826	+	36.5161i	0.731346	+	1.26673i
$832$	−6.47822	+	11.2206i	−0.224592	+	0.389005i
$833$		0			0
$834$	−4.36932	−	7.56788i	−0.151297	−	0.262054i
$835$		−	24.3839i		−	0.843838i
$836$	−21.4955	+	9.30780i	−0.743436	+	0.321917i
$837$		0			0
$838$	−8.85663	−	15.3401i	−0.305947	−	0.529916i
$839$	11.9174	+	20.6416i	0.411435	+	0.712627i	0.995047	−	0.0994062i	$-0.0316943\pi$
$839$	11.9174	+	20.6416i	0.411435	+	0.712627i	−0.583612	+	0.812033i	$0.698361\pi$
$840$		0			0
$841$	−8.16515	−	14.1425i	−0.281557	−	0.487671i
$842$	−3.64337	+	6.31050i	−0.125559	+	0.217474i
$843$			2.11345i			0.0727911i
$844$		−	25.3332i		−	0.872005i
$845$	−1.51723	−	0.875976i	−0.0521945	−	0.0301345i
$846$	0.291288	−	0.504525i	0.0100147	−	0.0173459i
$847$		0			0
$848$			3.55945i			0.122232i
$849$	−15.0000	−	8.66025i	−0.514799	−	0.297219i
$850$	3.37386	+	5.84370i	0.115723	+	0.200437i
$851$	−65.8693	−	38.0297i	−2.25797	−	1.30364i
$852$	9.89110	−	5.71063i	0.338863	−	0.195643i
$853$	0.873864	−	0.504525i	0.0299205	−	0.0172746i	−0.484965	−	0.874533i	$-0.661168\pi$
$853$	0.873864	−	0.504525i	0.0299205	−	0.0172746i	0.514886	+	0.857259i	$0.327834\pi$
$854$		0			0
$855$	0.691478	−	0.931524i	0.0236480	−	0.0318575i
$856$	16.4174			0.561136
$857$	6.56080	+	11.3636i	0.224112	+	0.388174i	0.956053	−	0.293195i	$-0.0947184\pi$
$857$	6.56080	+	11.3636i	0.224112	+	0.388174i	−0.731940	+	0.681369i	$0.761385\pi$
$858$	−8.06080	+	4.65390i	−0.275191	+	0.158882i
$859$	−5.68693	−	3.28335i	−0.194036	−	0.112027i	0.399835	−	0.916587i	$-0.369067\pi$
$859$	−5.68693	−	3.28335i	−0.194036	−	0.112027i	−0.593870	+	0.804561i	$0.702401\pi$
$860$	−13.4347	+	7.75650i	−0.458118	+	0.264495i
$861$		0			0
$862$	8.28674			0.282248
$863$		−	18.5203i		−	0.630437i	−0.949019	−	0.315218i	$-0.897922\pi$
$863$		−	18.5203i		−	0.630437i	0.949019	−	0.315218i	$-0.102078\pi$
$864$	20.5218	+	11.8483i	0.698165	+	0.403086i
$865$	21.8085	+	12.5912i	0.741512	+	0.428112i
$866$		−	16.6174i		−	0.564683i
$867$	3.87841			0.131718
$868$		0			0
$869$	−18.0000	+	10.3923i	−0.610608	+	0.352535i
$870$	3.21686	+	1.85725i	0.109062	+	0.0629667i
$871$	−11.3739	+	6.56670i	−0.385389	+	0.222504i
$872$	−11.6869	−	20.2424i	−0.395769	−	0.685493i
$873$	0.417424			0.0141277
$874$	−9.00000	+	12.1244i	−0.304430	+	0.410112i
$875$		0			0
$876$	−17.2432	+	9.95536i	−0.582593	+	0.336360i
$877$	37.1216	−	21.4322i	1.25351	−	0.723713i	0.281703	−	0.959502i	$-0.409101\pi$
$877$	37.1216	−	21.4322i	1.25351	−	0.723713i	0.971804	+	0.235789i	$0.0757674\pi$
$878$	1.25227	+	0.723000i	0.0422622	+	0.0244001i
$879$	−18.8085	−	32.5773i	−0.634396	−	1.09881i
$880$	9.24773	+	5.33918i	0.311741	+	0.179984i
$881$		−	13.5903i		−	0.457867i	−0.973442	−	0.228934i	$-0.926476\pi$
$881$		−	13.5903i		−	0.457867i	0.973442	−	0.228934i	$-0.0735239\pi$
$882$		0			0
$883$	−20.5000	+	35.5070i	−0.689880	+	1.19491i	0.281996	+	0.959415i	$0.409003\pi$
$883$	−20.5000	+	35.5070i	−0.689880	+	1.19491i	−0.971876	+	0.235492i	$0.924330\pi$
$884$	25.7477	+	14.8655i	0.865990	+	0.499979i
$885$		−	22.3658i		−	0.751817i
$886$		−	9.74475i		−	0.327381i
$887$	−0.708712	+	1.22753i	−0.0237962	+	0.0412163i	−0.877678	−	0.479250i	$-0.840909\pi$
$887$	−0.708712	+	1.22753i	−0.0237962	+	0.0412163i	0.853882	+	0.520467i	$0.174242\pi$
$888$	15.5608	+	26.9521i	0.522186	+	0.904453i
$889$		0			0
$890$	−0.691478	−	1.19767i	−0.0231784	−	0.0401461i
$891$	−14.3739	−	24.8963i	−0.481543	−	0.834056i
$892$	24.3303			0.814639
$893$	−10.5826	−	24.4394i	−0.354132	−	0.817834i
$894$			9.17265i			0.306779i
$895$	−9.41742	−	16.3115i	−0.314790	−	0.545232i
$896$		0			0
$897$	25.7477	−	44.5964i	0.859692	−	1.48903i
$898$	−2.89564	−	5.01540i	−0.0966289	−	0.167366i
$899$		0			0
$900$	1.26136			0.0420455
$901$	5.58258			0.185983
$902$	−6.37841	−	3.68258i	−0.212378	−	0.122616i
$903$		0			0
$904$	22.9129			0.762071
$905$			14.9807i			0.497976i
$906$	7.35208	−	12.7342i	0.244257	−	0.423065i
$907$	−34.9955	+	20.2046i	−1.16200	+	0.670884i	−0.951784	−	0.306770i	$-0.900752\pi$
$907$	−34.9955	+	20.2046i	−1.16200	+	0.670884i	−0.210221	+	0.977654i	$0.567418\pi$
$908$	−23.7695	+	41.1700i	−0.788819	+	1.36627i
$909$	−1.54811	+	0.893800i	−0.0513475	+	0.0296455i
$910$		0			0
$911$		−	7.38505i		−	0.244678i	−0.992488	−	0.122339i	$-0.960961\pi$
$911$		−	7.38505i		−	0.244678i	0.992488	−	0.122339i	$-0.0390395\pi$
$912$	−20.0000	+	8.66025i	−0.662266	+	0.286770i
$913$			40.7708i			1.34932i
$914$	15.0653	−	8.69798i	0.498317	−	0.287704i
$915$	1.56534	+	2.71125i	0.0517486	+	0.0896312i
$916$	−10.7477	−	6.20520i	−0.355115	−	0.205026i
$917$		0			0
$918$	5.00000	−	8.66025i	0.165025	−	0.285831i
$919$	22.0000			0.725713			0.362857	−	0.931845i	$-0.381802\pi$
$919$	22.0000			0.725713			0.362857	+	0.931845i	$0.381802\pi$
$920$	16.7477			0.552156
$921$	−18.0998	+	31.3498i	−0.596409	+	1.03301i
$922$	1.23049	−	2.13128i	0.0405241	−	0.0701898i
$923$		−	13.4949i		−	0.444190i
$924$		0			0
$925$	−29.3085	−	16.9213i	−0.963658	−	0.556368i
$926$	7.51723	−	4.34008i	0.247032	−	0.142624i
$927$	0.352083	−	0.609826i	0.0115639	−	0.0200293i
$928$	−8.43466	−	14.6093i	−0.276881	−	0.479572i
$929$	−3.47822	+	2.00815i	−0.114117	+	0.0658853i	−0.555972	−	0.831201i	$-0.687654\pi$
$929$	−3.47822	+	2.00815i	−0.114117	+	0.0658853i	0.441855	+	0.897086i	$0.354320\pi$
$930$		0			0
$931$		0			0
$932$	−24.0345			−0.787275
$933$	37.2042	−	21.4798i	1.21801	−	0.703218i
$934$	4.68693	+	8.11800i	0.153361	+	0.265629i
$935$	8.37386	−	14.5040i	0.273855	−	0.474330i
$936$	−1.18693	+	0.685275i	−0.0387961	+	0.0223989i
$937$	−9.93920	−	5.73840i	−0.324700	−	0.187465i	0.328786	−	0.944405i	$-0.393361\pi$
$937$	−9.93920	−	5.73840i	−0.324700	−	0.187465i	−0.653485	+	0.756939i	$0.726694\pi$
$938$		0			0
$939$		−	15.5130i		−	0.506248i
$940$	−6.97822	+	12.0866i	−0.227604	+	0.394222i
$941$	2.60436	−	4.51088i	0.0848996	−	0.147050i	−0.820449	−	0.571720i	$-0.806276\pi$
$941$	2.60436	−	4.51088i	0.0848996	−	0.147050i	0.905348	+	0.424670i	$0.139610\pi$
$942$	9.62614			0.313636
$943$	40.7477			1.32693
$944$	−13.6652	+	23.6687i	−0.444763	+	0.770352i
$945$		0			0
$946$	8.06080	+	4.65390i	0.262079	+	0.151311i
$947$	−17.9174	−	31.0339i	−0.582238	−	1.00847i	−0.995214	−	0.0977238i	$-0.968844\pi$
$947$	−17.9174	−	31.0339i	−0.582238	−	1.00847i	0.412976	−	0.910742i	$-0.364490\pi$
$948$	−19.2523	+	11.1153i	−0.625285	+	0.361008i
$949$			23.5257i			0.763677i
$950$	−4.00455	+	5.39473i	−0.129925	+	0.175028i
$951$		−	26.2867i		−	0.852405i
$952$		0			0
$953$	−42.8911	+	24.7632i	−1.38938	+	0.802158i	−0.993245	−	0.116035i	$-0.962982\pi$
$953$	−42.8911	+	24.7632i	−1.38938	+	0.802158i	−0.396134	+	0.918193i	$0.629648\pi$
$954$	−0.0607953	+	0.105301i	−0.00196832	+	0.00340923i
$955$	22.6824	−	13.0957i	0.733985	−	0.423766i
$956$	−13.0218	+	22.5544i	−0.421154	+	0.729461i
$957$			19.1280i			0.618321i
$958$	−0.0871215			−0.00281477
$959$		0			0
$960$	6.76042	+	3.90313i	0.218191	+	0.125973i
$961$	−31.0000			−1.00000
$962$	17.3739			0.560156
$963$	−1.71326	−	0.989150i	−0.0552090	−	0.0318749i
$964$	6.60436	+	11.4391i	0.212712	+	0.368428i
$965$	−15.6434	+	27.0951i	−0.503578	+	0.872223i
$966$		0			0
$967$	−11.2087	−	19.4141i	−0.360448	−	0.624314i	0.627587	−	0.778547i	$-0.284043\pi$
$967$	−11.2087	−	19.4141i	−0.360448	−	0.624314i	−0.988035	+	0.154233i	$0.950709\pi$
$968$			3.46410i			0.111340i
$969$	13.5826	+	31.3676i	0.436335	+	1.00767i
$970$	1.16515			0.0374108
$971$	−21.7259	−	37.6304i	−0.697219	−	1.20762i	−0.969427	−	0.245380i	$-0.921087\pi$
$971$	−21.7259	−	37.6304i	−0.697219	−	1.20762i	0.272208	−	0.962238i	$-0.412246\pi$
$972$	−1.93920	−	3.35880i	−0.0622000	−	0.107734i
$973$		0			0
$974$	−2.29129	−	3.96863i	−0.0734176	−	0.127163i
$975$	11.4564	−	19.8431i	0.366900	−	0.635489i
$976$		−	3.82560i		−	0.122455i
$977$			18.9572i			0.606495i	0.952912	+	0.303247i	$0.0980709\pi$
$977$			18.9572i			0.606495i	−0.952912	+	0.303247i	$0.901929\pi$
$978$	4.25227	+	2.45505i	0.135973	+	0.0785039i
$979$	3.56080	−	6.16748i	0.113804	−	0.197113i
$980$		0			0
$981$			2.81655i			0.0899256i
$982$	15.0653	+	8.69798i	0.480754	+	0.277564i
$983$	−29.1434	−	50.4778i	−0.929529	−	1.60999i	−0.784110	−	0.620622i	$-0.786880\pi$
$983$	−29.1434	−	50.4778i	−0.929529	−	1.60999i	−0.145419	−	0.989370i	$-0.546453\pi$
$984$	−14.4392	−	8.33648i	−0.460305	−	0.265757i
$985$	−13.2523	+	7.65120i	−0.422253	+	0.243788i
$986$	−6.16515	+	3.55945i	−0.196338	+	0.113356i
$987$		0			0
$988$	−3.39564	+	29.4071i	−0.108030	+	0.935566i
$989$	−51.4955			−1.63746
$990$	0.182386	+	0.315902i	0.00579661	+	0.0100400i
$991$	−30.3131	+	17.5013i	−0.962926	+	0.555946i	−0.897072	−	0.441883i	$-0.854310\pi$
$991$	−30.3131	+	17.5013i	−0.962926	+	0.555946i	−0.0658539	+	0.997829i	$0.520977\pi$
$992$		0			0
$993$	3.24773	−	1.87508i	0.103064	−	0.0595037i
$994$		0			0
$995$	−28.1561			−0.892607
$996$			43.6072i			1.38175i
$997$	4.74773	+	2.74110i	0.150362	+	0.0868116i	0.573293	−	0.819350i	$-0.305666\pi$
$997$	4.74773	+	2.74110i	0.150362	+	0.0868116i	−0.422931	+	0.906162i	$0.638999\pi$
$998$	−7.02178	−	4.05403i	−0.222271	−	0.128328i
$999$			50.1540i			1.58680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.p.e.734.1		4
7.2	even	3		133.2.s.c.31.2	yes	4
7.3	odd	6		133.2.i.c.12.1	✓	4
7.4	even	3		931.2.i.d.411.1		4
7.5	odd	6		931.2.s.c.31.2		4
7.6	odd	2		931.2.p.f.734.1		4
19.8	odd	6		931.2.p.f.293.1		4
133.27	even	6	inner	931.2.p.e.293.1		4
133.46	odd	6		931.2.s.c.901.2		4
133.65	odd	6		133.2.i.c.122.2	yes	4
133.103	even	6		931.2.i.d.521.2		4
133.122	even	6		133.2.s.c.103.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.i.c.12.1	✓	4	7.3	odd	6
133.2.i.c.122.2	yes	4	133.65	odd	6
133.2.s.c.31.2	yes	4	7.2	even	3
133.2.s.c.103.2	yes	4	133.122	even	6
931.2.i.d.411.1		4	7.4	even	3
931.2.i.d.521.2		4	133.103	even	6
931.2.p.e.293.1		4	133.27	even	6	inner
931.2.p.e.734.1		4	1.1	even	1	trivial
931.2.p.f.293.1		4	19.8	odd	6
931.2.p.f.734.1		4	7.6	odd	2
931.2.s.c.31.2		4	7.5	odd	6
931.2.s.c.901.2		4	133.46	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.395644 + 0.228425i) q^{2} +(0.895644 + 1.55130i) q^{3} +(-0.895644 + 1.55130i) q^{4} +(1.10436 - 0.637600i) q^{5} +(-0.708712 - 0.409175i) q^{6} -1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +(-0.291288 + 0.504525i) q^{10} -3.00000 q^{11} -3.20871 q^{12} +(-1.89564 + 3.28335i) q^{13} +(1.97822 + 1.14213i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(-3.79129 + 2.18890i) q^{17} -0.0953502i q^{18} +(-3.50000 - 2.59808i) q^{19} +2.28425i q^{20} +(1.18693 - 0.685275i) q^{22} +(-3.79129 + 6.56670i) q^{23} +(2.68693 - 1.55130i) q^{24} +(-1.68693 + 2.92185i) q^{25} -1.73205i q^{26} +5.00000 q^{27} +(-3.08258 - 1.77973i) q^{29} -1.04356 q^{30} +(4.10436 + 2.36965i) q^{32} +(-2.68693 - 4.65390i) q^{33} +(1.00000 - 1.73205i) q^{34} +(-0.186932 - 0.323775i) q^{36} +10.0308i q^{37} +(1.97822 + 0.228425i) q^{38} -6.79129 q^{39} +(-1.10436 - 1.91280i) q^{40} +(-2.68693 - 4.65390i) q^{41} +(3.39564 + 5.88143i) q^{43} +(2.68693 - 4.65390i) q^{44} +0.266150i q^{45} -3.46410i q^{46} +(5.29129 + 3.05493i) q^{47} +(2.50000 - 4.33013i) q^{48} -1.54135i q^{50} +(-6.79129 - 3.92095i) q^{51} +(-3.39564 - 5.88143i) q^{52} +(-1.10436 - 0.637600i) q^{53} +(-1.97822 + 1.14213i) q^{54} +(-3.31307 + 1.91280i) q^{55} +(0.895644 - 7.75650i) q^{57} +1.62614 q^{58} +(-4.89564 - 8.47950i) q^{59} +(-3.54356 + 2.04588i) q^{60} +(1.18693 + 0.685275i) q^{61} +3.41742 q^{64} +4.83465i q^{65} +(2.12614 + 1.22753i) q^{66} +(3.00000 + 1.73205i) q^{67} -7.84190i q^{68} -13.5826 q^{69} +(-3.08258 + 1.77973i) q^{71} +(0.313068 + 0.180750i) q^{72} +(5.37386 - 3.10260i) q^{73} +(-2.29129 - 3.96863i) q^{74} -6.04356 q^{75} +(7.16515 - 3.10260i) q^{76} +(2.68693 - 1.55130i) q^{78} +(6.00000 - 3.46410i) q^{79} +(-3.08258 - 1.77973i) q^{80} +(4.79129 + 8.29875i) q^{81} +(2.12614 + 1.22753i) q^{82} -13.5903i q^{83} +(-2.79129 + 4.83465i) q^{85} +(-2.68693 - 1.55130i) q^{86} -6.37600i q^{87} +5.19615i q^{88} +(-1.18693 + 2.05583i) q^{89} +(-0.0607953 - 0.105301i) q^{90} +(-6.79129 - 11.7629i) q^{92} -2.79129 q^{94} +(-5.52178 - 0.637600i) q^{95} +8.48945i q^{96} +(-1.00000 - 1.73205i) q^{97} +(0.313068 - 0.542250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{5} - 12 q^{6} - 5 q^{9} + 8 q^{10} - 12 q^{11} - 22 q^{12} - 3 q^{13} - 15 q^{15} - q^{16} - 6 q^{17} - 14 q^{19} - 9 q^{22} - 6 q^{23} - 3 q^{24} + 7 q^{25} + 20 q^{27}+ \cdots + 15 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^5 - 12 * q^6 - 5 * q^9 + 8 * q^10 - 12 * q^11 - 22 * q^12 - 3 * q^13 - 15 * q^15 - q^16 - 6 * q^17 - 14 * q^19 - 9 * q^22 - 6 * q^23 - 3 * q^24 + 7 * q^25 + 20 * q^27 + 6 * q^29 - 50 * q^30 + 21 * q^32 + 3 * q^33 + 4 * q^34 + 13 * q^36 - 15 * q^38 - 18 * q^39 - 9 * q^40 + 3 * q^41 + 9 * q^43 - 3 * q^44 + 12 * q^47 + 10 * q^48 - 18 * q^51 - 9 * q^52 - 9 * q^53 + 15 * q^54 - 27 * q^55 - q^57 + 34 * q^58 - 15 * q^59 - 60 * q^60 - 9 * q^61 + 32 * q^64 + 36 * q^66 + 12 * q^67 - 36 * q^69 + 6 * q^71 + 15 * q^72 - 6 * q^73 - 70 * q^75 - 8 * q^76 - 3 * q^78 + 24 * q^79 + 6 * q^80 + 10 * q^81 + 36 * q^82 - 2 * q^85 + 3 * q^86 + 9 * q^89 + 41 * q^90 - 18 * q^92 - 2 * q^94 - 45 * q^95 - 4 * q^97 + 15 * q^99

Introduction

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