LMFDB - Embedded newform 931.2.s.c.31.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [931,2,Mod(31,931)] 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([1, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("931.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-3,-2] 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			31.2
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	931.31
Dual form			931.2.s.c.901.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395644 + 0.228425i) q^{2} +1.79129 q^{3} +(-0.895644 - 1.55130i) q^{4} +(1.10436 + 0.637600i) q^{5} +(0.708712 + 0.409175i) q^{6} -1.73205i q^{8} +0.208712 q^{9} +(0.291288 + 0.504525i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-1.60436 - 2.77883i) q^{12} +(1.89564 - 3.28335i) q^{13} +(1.97822 + 1.14213i) q^{15} +(-1.39564 + 2.41733i) q^{16} +4.37780i q^{17} +(0.0825757 + 0.0476751i) q^{18} +(0.500000 - 4.33013i) q^{19} -2.28425i q^{20} +(1.18693 - 0.685275i) q^{22} +7.58258 q^{23} -3.10260i q^{24} +(-1.68693 - 2.92185i) q^{25} +(1.50000 - 0.866025i) q^{26} -5.00000 q^{27} +(-3.08258 - 1.77973i) q^{29} +(0.521780 + 0.903750i) 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} +(8.68693 - 5.01540i) q^{37} +(1.18693 - 1.59898i) q^{38} +(3.39564 - 5.88143i) q^{39} +(1.10436 - 1.91280i) q^{40} +(2.68693 + 4.65390i) q^{41} +(3.39564 + 5.88143i) q^{43} -5.37386 q^{44} +(0.230493 + 0.133075i) q^{45} +(3.00000 + 1.73205i) q^{46} +6.10985i q^{47} +(-2.50000 + 4.33013i) q^{48} -1.54135i q^{50} +7.84190i q^{51} -6.79129 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} +(-0.813068 - 1.40828i) q^{58} -9.79129 q^{59} -4.09175i q^{60} +1.37055i q^{61} +3.41742 q^{64} +(4.18693 - 2.41733i) q^{65} +(2.12614 - 1.22753i) q^{66} +(-3.00000 + 1.73205i) q^{67} +(6.79129 - 3.92095i) q^{68} +13.5826 q^{69} +(-3.08258 + 1.77973i) q^{71} -0.361500i q^{72} -6.20520i q^{73} +4.58258 q^{74} +(-3.02178 - 5.23388i) 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} -9.58258 q^{81} +2.45505i q^{82} +13.5903i q^{83} +(-2.79129 + 4.83465i) q^{85} +3.10260i q^{86} +(-5.52178 - 3.18800i) q^{87} +(-4.50000 - 2.59808i) q^{88} -2.37386 q^{89} +(0.0607953 + 0.105301i) q^{90} +(-6.79129 - 11.7629i) q^{92} +(-1.39564 + 2.41733i) q^{94} +(3.31307 - 4.46320i) q^{95} +(-7.35208 + 4.24473i) 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} - 2 q^{3} + q^{4} + 9 q^{5} + 12 q^{6} + 10 q^{9} - 8 q^{10} + 6 q^{11} - 11 q^{12} + 3 q^{13} - 15 q^{15} - q^{16} - 18 q^{18} + 2 q^{19} - 9 q^{22} + 12 q^{23} + 7 q^{25} + 6 q^{26} - 20 q^{27}+ \cdots + 15 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 2 * q^3 + q^4 + 9 * q^5 + 12 * q^6 + 10 * q^9 - 8 * q^10 + 6 * q^11 - 11 * q^12 + 3 * q^13 - 15 * q^15 - q^16 - 18 * q^18 + 2 * q^19 - 9 * q^22 + 12 * q^23 + 7 * q^25 + 6 * q^26 - 20 * q^27 + 6 * q^29 + 25 * q^30 - 21 * q^32 - 3 * q^33 - 4 * q^34 + 13 * q^36 + 21 * q^37 - 9 * q^38 + 9 * q^39 + 9 * q^40 - 3 * q^41 + 9 * q^43 + 6 * q^44 + 33 * q^45 + 12 * q^46 - 10 * q^48 - 18 * q^52 + 9 * q^53 + 15 * q^54 + 27 * q^55 - q^57 - 17 * q^58 - 30 * q^59 + 32 * q^64 + 3 * q^65 + 36 * q^66 - 12 * q^67 + 18 * q^68 + 36 * q^69 + 6 * q^71 - 35 * q^75 + 8 * q^76 - 3 * q^78 - 24 * q^79 + 6 * q^80 - 20 * q^81 - 2 * q^85 - 45 * q^87 - 18 * q^88 + 18 * q^89 - 41 * q^90 - 18 * q^92 - q^94 + 27 * q^95 + 21 * q^96 + 4 * q^97 + 15 * q^99

Character values

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

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

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	$-0.281693\pi$
$2$	0.395644	+	0.228425i	0.279763	+	0.161521i	−0.353553	+	0.935414i	$0.615027\pi$
$3$	1.79129			1.03420			0.517100	−	0.855925i	$-0.327011\pi$
$3$	1.79129			1.03420			0.517100	+	0.855925i	$0.327011\pi$
$4$	−0.895644	−	1.55130i	−0.447822	−	0.775650i
$5$	1.10436	+	0.637600i	0.493883	+	0.285144i	0.726184	−	0.687500i	$-0.241292\pi$
$5$	1.10436	+	0.637600i	0.493883	+	0.285144i	−0.232301	+	0.972644i	$0.574625\pi$
$6$	0.708712	+	0.409175i	0.289331	+	0.167045i
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	0.208712			0.0695707
$10$	0.291288	+	0.504525i	0.0921133	+	0.159545i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−1.60436	−	2.77883i	−0.463138	−	0.802178i
$13$	1.89564	−	3.28335i	0.525757	−	0.910638i	−0.473793	−	0.880636i	$-0.657115\pi$
$13$	1.89564	−	3.28335i	0.525757	−	0.910638i	0.999550	−	0.0300015i	$-0.00955122\pi$
$14$		0			0
$15$	1.97822	+	1.14213i	0.510774	+	0.294896i
$16$	−1.39564	+	2.41733i	−0.348911	+	0.604332i
$17$			4.37780i			1.06177i	0.847443	+	0.530886i	$0.178141\pi$
$17$			4.37780i			1.06177i	−0.847443	+	0.530886i	$0.821859\pi$
$18$	0.0825757	+	0.0476751i	0.0194633	+	0.0112371i
$19$	0.500000	−	4.33013i	0.114708	−	0.993399i
$19$	0.500000	−	4.33013i	0.114708	−	0.993399i
$20$		−	2.28425i		−	0.510774i
$21$		0			0
$22$	1.18693	−	0.685275i	0.253055	−	0.146101i
$23$	7.58258			1.58108			0.790538	−	0.612413i	$-0.209801\pi$
$23$	7.58258			1.58108			0.790538	+	0.612413i	$0.209801\pi$
$24$		−	3.10260i		−	0.633316i
$25$	−1.68693	−	2.92185i	−0.337386	−	0.584370i
$26$	1.50000	−	0.866025i	0.294174	−	0.169842i
$27$	−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	$0.773880\pi$
$30$	0.521780	+	0.903750i	0.0952636	+	0.165001i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−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
$37$	8.68693	−	5.01540i	1.42812	−	0.824527i	0.431150	−	0.902280i	$-0.358108\pi$
$37$	8.68693	−	5.01540i	1.42812	−	0.824527i	0.996973	+	0.0777531i	$0.0247746\pi$
$38$	1.18693	−	1.59898i	0.192546	−	0.259388i
$39$	3.39564	−	5.88143i	0.543738	−	0.941782i
$40$	1.10436	−	1.91280i	0.174614	−	0.302440i
$41$	2.68693	+	4.65390i	0.419628	+	0.726817i	0.995902	−	0.0904393i	$-0.0288271\pi$
$41$	2.68693	+	4.65390i	0.419628	+	0.726817i	−0.576274	+	0.817257i	$0.695494\pi$
$42$		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	$0.660073\pi$
$44$	−5.37386			−0.810140
$45$	0.230493	+	0.133075i	0.0343598	+	0.0198376i
$46$	3.00000	+	1.73205i	0.442326	+	0.255377i
$47$			6.10985i			0.891214i	0.895229	+	0.445607i	$0.147012\pi$
$47$			6.10985i			0.891214i	−0.895229	+	0.445607i	$0.852988\pi$
$48$	−2.50000	+	4.33013i	−0.360844	+	0.625000i
$49$		0			0
$50$		−	1.54135i		−	0.217980i
$51$			7.84190i			1.09809i
$52$	−6.79129			−0.941782
$53$	1.10436	−	0.637600i	0.151695	−	0.0875811i	−0.422231	−	0.906488i	$-0.638753\pi$
$53$	1.10436	−	0.637600i	0.151695	−	0.0875811i	0.573926	+	0.818907i	$0.305420\pi$
$54$	−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
$58$	−0.813068	−	1.40828i	−0.106761	−	0.184916i
$59$	−9.79129			−1.27472			−0.637359	−	0.770567i	$-0.719973\pi$
$59$	−9.79129			−1.27472			−0.637359	+	0.770567i	$0.719973\pi$
$60$		−	4.09175i		−	0.528243i
$61$			1.37055i			0.175481i	0.996143	+	0.0877405i	$0.0279646\pi$
$61$			1.37055i			0.175481i	−0.996143	+	0.0877405i	$0.972035\pi$
$62$		0			0
$63$		0			0
$64$	3.41742			0.427178
$65$	4.18693	−	2.41733i	0.519325	−	0.299832i
$66$	2.12614	−	1.22753i	0.261709	−	0.151098i
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	0.305424	+	0.952217i	$0.401202\pi$
$68$	6.79129	−	3.92095i	0.823565	−	0.475485i
$69$	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	$0.401075\pi$
$72$		−	0.361500i		−	0.0426032i
$73$		−	6.20520i		−	0.726264i	−0.931738	−	0.363132i	$-0.881707\pi$
$73$		−	6.20520i		−	0.726264i	0.931738	−	0.363132i	$-0.118293\pi$
$74$	4.58258			0.532714
$75$	−3.02178	−	5.23388i	−0.348925	−	0.604356i
$76$	−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	$-0.460769\pi$
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	−0.797988	+	0.602673i	$0.794102\pi$
$80$	−3.08258	+	1.77973i	−0.344642	+	0.198979i
$81$	−9.58258			−1.06473
$82$			2.45505i			0.271115i
$83$			13.5903i			1.49172i	0.666100	+	0.745862i	$0.267962\pi$
$83$			13.5903i			1.49172i	−0.666100	+	0.745862i	$0.732038\pi$
$84$		0			0
$85$	−2.79129	+	4.83465i	−0.302758	+	0.524392i
$86$			3.10260i			0.334562i
$87$	−5.52178	−	3.18800i	−0.591997	−	0.341790i
$88$	−4.50000	−	2.59808i	−0.479702	−	0.276956i
$89$	−2.37386			−0.251629			−0.125815	−	0.992054i	$-0.540154\pi$
$89$	−2.37386			−0.251629			−0.125815	+	0.992054i	$0.540154\pi$
$90$	0.0607953	+	0.105301i	0.00640839	+	0.0110997i
$91$		0			0
$92$	−6.79129	−	11.7629i	−0.708041	−	1.22636i
$93$		0			0
$94$	−1.39564	+	2.41733i	−0.143950	+	0.249328i
$95$	3.31307	−	4.46320i	0.339914	−	0.457915i
$96$	−7.35208	+	4.24473i	−0.750369	+	0.433226i
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$		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	−0.0833027	−	0.996524i	$-0.526547\pi$
$101$	7.41742	−	4.28245i	0.738061	−	0.426120i	0.821364	+	0.570404i	$0.193214\pi$
$102$	−1.79129	+	3.10260i	−0.177364	+	0.307203i
$103$	−1.68693	−	2.92185i	−0.166218	−	0.287899i	0.770869	−	0.636994i	$-0.219822\pi$
$103$	−1.68693	−	2.92185i	−0.166218	−	0.287899i	−0.937087	+	0.349095i	$0.886489\pi$
$104$	−5.68693	−	3.28335i	−0.557650	−	0.321959i
$105$		0			0
$106$	0.582576			0.0565848
$107$	8.20871	−	4.73930i	0.793566	−	0.458166i	−0.0476503	−	0.998864i	$-0.515173\pi$
$107$	8.20871	−	4.73930i	0.793566	−	0.458166i	0.841216	+	0.540698i	$0.181840\pi$
$108$	4.47822	+	7.75650i	0.430917	+	0.746370i
$109$			13.4949i			1.29258i	0.763093	+	0.646289i	$0.223680\pi$
$109$			13.4949i			1.29258i	−0.763093	+	0.646289i	$0.776320\pi$
$110$	1.74773			0.166639
$111$	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	$0.786228\pi$
$114$	2.12614	−	2.86423i	0.199131	−	0.268259i
$115$	8.37386	+	4.83465i	0.780867	+	0.450834i
$116$			6.37600i			0.591997i
$117$	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
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−0.313068	+	0.542250i	−0.0283439	+	0.0490930i
$123$	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
$130$	2.20871			0.193717
$131$	6.16515	+	3.55945i	0.538652	+	0.310991i	0.744532	−	0.667586i	$-0.232673\pi$
$131$	6.16515	+	3.55945i	0.538652	+	0.310991i	−0.205881	+	0.978577i	$0.566006\pi$
$132$	−9.62614			−0.837848
$133$		0			0
$134$	−1.58258			−0.136714
$135$	−5.52178	−	3.18800i	−0.475239	−	0.274379i
$136$	7.58258			0.650201
$137$	4.97822	+	8.62253i	0.425318	+	0.736672i	0.996450	−	0.0841858i	$-0.0268289\pi$
$137$	4.97822	+	8.62253i	0.425318	+	0.736672i	−0.571132	+	0.820858i	$0.693496\pi$
$138$	5.37386	+	3.10260i	0.457454	+	0.264111i
$139$	−9.24773	−	5.33918i	−0.784382	−	0.452863i	0.0535990	−	0.998563i	$-0.482931\pi$
$139$	−9.24773	−	5.33918i	−0.784382	−	0.452863i	−0.837981	+	0.545699i	$0.816264\pi$
$140$		0			0
$141$			10.9445i			0.921694i
$142$	−1.62614			−0.136462
$143$	−5.68693	−	9.85005i	−0.475565	−	0.823703i
$144$	−0.291288	+	0.504525i	−0.0242740	+	0.0420438i
$145$	−2.26951	−	3.93090i	−0.188472	−	0.326444i
$146$	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	−0.998915	−	0.0465700i	$-0.985171\pi$
$149$	−5.60436	+	9.70703i	−0.459127	+	0.795231i	0.539788	+	0.841801i	$0.318504\pi$
$150$		−	2.76100i		−	0.225435i
$151$	−15.5608	−	8.98403i	−1.26632	−	0.731110i	−0.292030	−	0.956409i	$-0.594331\pi$
$151$	−15.5608	−	8.98403i	−1.26632	−	0.731110i	−0.974290	+	0.225299i	$0.927664\pi$
$152$	−7.50000	−	0.866025i	−0.608330	−	0.0702439i
$153$			0.913701i			0.0738683i
$154$		0			0
$155$		0			0
$156$	−12.1652			−0.973992
$157$			11.7629i			0.938778i	0.882991	+	0.469389i	$0.155526\pi$
$157$			11.7629i			0.938778i	−0.882991	+	0.469389i	$0.844474\pi$
$158$	−1.58258	−	2.74110i	−0.125903	−	0.218070i
$159$	1.97822	−	1.14213i	0.156883	−	0.0905765i
$160$	−6.04356			−0.477785
$161$		0			0
$162$	−3.79129	−	2.18890i	−0.297872	−	0.171976i
$163$	3.00000	+	5.19615i	0.234978	+	0.406994i	0.959266	−	0.282503i	$-0.0911648\pi$
$163$	3.00000	+	5.19615i	0.234978	+	0.406994i	−0.724288	+	0.689497i	$0.757831\pi$
$164$	4.81307	−	8.33648i	0.375837	−	0.650970i
$165$	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	$0.431764\pi$
$167$	−9.56080	+	16.5598i	−0.739837	+	1.28143i	−0.952569	+	0.304324i	$0.901569\pi$
$168$		0			0
$169$	−0.686932	−	1.18980i	−0.0528409	−	0.0915231i
$170$	−2.20871	+	1.27520i	−0.169400	+	0.0978034i
$171$	0.104356	−	0.903750i	0.00798031	−	0.0691115i
$172$	6.08258	−	10.5353i	0.463792	−	0.803311i
$173$	−9.87386	+	17.1020i	−0.750696	+	1.30024i	0.196790	+	0.980446i	$0.436948\pi$
$173$	−9.87386	+	17.1020i	−0.750696	+	1.30024i	−0.947486	+	0.319798i	$0.896385\pi$
$174$	−1.45644	−	2.52263i	−0.110412	−	0.191240i
$175$		0			0
$176$	4.18693	+	7.25198i	0.315602	+	0.546638i
$177$	−17.5390			−1.31831
$178$	−0.939205	−	0.542250i	−0.0703964	−	0.0406434i
$179$	12.7913	+	7.38505i	0.956066	+	0.551985i	0.894960	−	0.446146i	$-0.147204\pi$
$179$	12.7913	+	7.38505i	0.956066	+	0.551985i	0.0611058	+	0.998131i	$0.480537\pi$
$180$		−	0.476751i		−	0.0355349i
$181$	5.87386	−	10.1738i	0.436601	−	0.756215i	−0.560824	−	0.827935i	$-0.689516\pi$
$181$	5.87386	−	10.1738i	0.436601	−	0.756215i	0.997425	+	0.0717202i	$0.0228489\pi$
$182$		0			0
$183$			2.45505i			0.181483i
$184$		−	13.1334i		−	0.968208i
$185$	12.7913			0.940434
$186$		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
$191$	−10.2695	−	17.7873i	−0.743075	−	1.28704i	−0.951089	−	0.308918i	$-0.900033\pi$
$191$	−10.2695	−	17.7873i	−0.743075	−	1.28704i	0.208013	−	0.978126i	$-0.433300\pi$
$192$	6.12159			0.441788
$193$		−	24.5348i		−	1.76605i	−0.469325	−	0.883025i	$-0.655503\pi$
$193$		−	24.5348i		−	1.76605i	0.469325	−	0.883025i	$-0.344497\pi$
$194$			0.913701i			0.0655999i
$195$	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	$0.640599\pi$
$198$	0.247727	−	0.143025i	0.0176052	−	0.0101644i
$199$	−19.1216	+	11.0399i	−1.35549	+	0.782595i	−0.989013	−	0.147831i	$-0.952771\pi$
$199$	−19.1216	+	11.0399i	−1.35549	+	0.782595i	−0.366481	+	0.930426i	$0.619438\pi$
$200$	−5.06080	+	2.92185i	−0.357852	+	0.206606i
$201$	−5.37386	+	3.10260i	−0.379043	+	0.218841i
$202$	3.91288			0.275309
$203$		0			0
$204$	12.1652	−	7.02355i	0.851731	−	0.491747i
$205$			6.85275i			0.478617i
$206$		−	1.54135i		−	0.107391i
$207$	1.58258			0.109997
$208$	5.29129	+	9.16478i	0.366885	+	0.635463i
$209$	−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
$214$	4.33030			0.296013
$215$			8.66025i			0.590624i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−3.08258	+	5.33918i	−0.208778	+	0.361615i
$219$		−	11.1153i		−	0.751103i
$220$	−5.93466	−	3.42638i	−0.400115	−	0.231006i
$221$	14.3739	+	8.29875i	0.966891	+	0.558235i
$222$	8.20871			0.550933
$223$	6.79129	+	11.7629i	0.454778	+	0.787699i	0.998675	−	0.0514528i	$-0.0163852\pi$
$223$	6.79129	+	11.7629i	0.454778	+	0.787699i	−0.543897	+	0.839152i	$0.683052\pi$
$224$		0			0
$225$	−0.352083	−	0.609826i	−0.0234722	−	0.0406551i
$226$	−3.02178	+	5.23388i	−0.201006	+	0.348152i
$227$	13.2695	−	22.9835i	0.880728	−	1.52547i	0.0301953	−	0.999544i	$-0.490387\pi$
$227$	13.2695	−	22.9835i	0.880728	−	1.52547i	0.850533	−	0.525922i	$-0.176280\pi$
$228$	−12.8348	+	5.55765i	−0.850009	+	0.368065i
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	−0.684969	−	0.728572i	$-0.740184\pi$
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	0.288478	+	0.957487i	$0.406851\pi$
$230$	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	−0.558149	−	0.829741i	$-0.688488\pi$
$233$	6.70871	−	11.6198i	0.439502	−	0.761240i	0.997651	+	0.0685005i	$0.0218215\pi$
$234$	0.313068	−	0.180750i	0.0204659	−	0.0118160i
$235$	−3.89564	+	6.74745i	−0.254124	+	0.440155i
$236$	8.76951	+	15.1892i	0.570846	+	0.988735i
$237$	−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	$0.344173\pi$
$240$	−5.52178	+	3.18800i	−0.356429	+	0.205785i
$241$	−3.68693	−	6.38595i	−0.237496	−	0.411355i	0.722499	−	0.691372i	$-0.242993\pi$
$241$	−3.68693	−	6.38595i	−0.237496	−	0.411355i	−0.959995	+	0.280017i	$0.909660\pi$
$242$			0.913701i			0.0587349i
$243$	−2.16515			−0.138895
$244$	2.12614	−	1.22753i	0.136112	−	0.0785843i
$245$		0			0
$246$			4.39770i			0.280387i
$247$	−13.2695	−	9.85005i	−0.844319	−	0.626744i
$248$		0			0
$249$			24.3441i			1.54274i
$250$	2.43920	−	4.22483i	0.154269	−	0.267201i
$251$	−8.29129	−	4.78698i	−0.523341	−	0.302151i	0.214959	−	0.976623i	$-0.431038\pi$
$251$	−8.29129	−	4.78698i	−0.523341	−	0.302151i	−0.738301	+	0.674472i	$0.764371\pi$
$252$		0			0
$253$	11.3739	−	19.7001i	0.715069	−	1.23854i
$254$	2.68693	+	4.65390i	0.168593	+	0.292012i
$255$	−5.00000	+	8.66025i	−0.313112	+	0.542326i
$256$	−0.895644	−	1.55130i	−0.0559777	−	0.0969563i
$257$	−19.7477			−1.23183			−0.615915	−	0.787813i	$-0.711213\pi$
$257$	−19.7477			−1.23183			−0.615915	+	0.787813i	$0.711213\pi$
$258$			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
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$	−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
$269$	7.58258			0.462318			0.231159	−	0.972916i	$-0.425748\pi$
$269$	7.58258			0.462318			0.231159	+	0.972916i	$0.425748\pi$
$270$	−1.45644	−	2.52263i	−0.0886361	−	0.153522i
$271$	−11.6869	−	6.74745i	−0.709931	−	0.409879i	0.101105	−	0.994876i	$-0.467762\pi$
$271$	−11.6869	−	6.74745i	−0.709931	−	0.409879i	−0.811035	+	0.584997i	$0.801096\pi$
$272$	−10.5826	−	6.10985i	−0.641663	−	0.370464i
$273$		0			0
$274$			4.54860i			0.274791i
$275$	−10.1216			−0.610355
$276$	−12.1652	−	21.0707i	−0.732256	−	1.26830i
$277$	−11.7695	+	20.3854i	−0.707161	+	1.22484i	0.258745	+	0.965946i	$0.416691\pi$
$277$	−11.7695	+	20.3854i	−0.707161	+	1.22484i	−0.965906	+	0.258893i	$0.916642\pi$
$278$	−2.43920	−	4.22483i	−0.146294	−	0.253388i
$279$		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
$283$			9.66930i			0.574781i	0.957814	+	0.287390i	$0.0927877\pi$
$283$			9.66930i			0.574781i	−0.957814	+	0.287390i	$0.907212\pi$
$284$	5.52178	+	3.18800i	0.327657	+	0.189173i
$285$	5.93466	−	7.99488i	0.351539	−	0.473576i
$286$		−	5.19615i		−	0.307255i
$287$		0			0
$288$	−0.856629	+	0.494575i	−0.0504773	+	0.0291431i
$289$	−2.16515			−0.127362
$290$		−	2.07365i		−	0.121769i
$291$	1.79129	+	3.10260i	0.105007	+	0.181878i
$292$	−9.62614	+	5.55765i	−0.563327	+	0.325237i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$	−10.8131	−	6.24293i	−0.629561	−	0.363477i
$296$	−8.68693	−	15.0462i	−0.504918	−	0.874543i
$297$	−7.50000	+	12.9904i	−0.435194	+	0.753778i
$298$	−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
$303$	13.2867	−	7.67110i	0.763303	−	0.440693i
$304$	9.76951	+	7.25198i	0.560320	+	0.415929i
$305$	−0.873864	+	1.51358i	−0.0500373	+	0.0866671i
$306$	−0.208712	+	0.361500i	−0.0119313	+	0.0206656i
$307$	−10.1044	−	17.5013i	−0.576686	−	0.998850i	−0.995856	−	0.0909419i	$-0.971012\pi$
$307$	−10.1044	−	17.5013i	−0.576686	−	0.998850i	0.419170	−	0.907908i	$-0.362321\pi$
$308$		0			0
$309$	−3.02178	−	5.23388i	−0.171903	−	0.297745i
$310$		0			0
$311$	−20.7695	−	11.9913i	−1.17773	−	0.679963i	−0.222242	−	0.974991i	$-0.571338\pi$
$311$	−20.7695	−	11.9913i	−1.17773	−	0.679963i	−0.955489	+	0.295028i	$0.904671\pi$
$312$	−10.1869	−	5.88143i	−0.576721	−	0.332970i
$313$		−	8.66025i		−	0.489506i	−0.969585	−	0.244753i	$-0.921293\pi$
$313$		−	8.66025i		−	0.489506i	0.969585	−	0.244753i	$-0.0787070\pi$
$314$	−2.68693	+	4.65390i	−0.151632	+	0.262635i
$315$		0			0
$316$			12.4104i			0.698140i
$317$			14.6748i			0.824216i	0.911135	+	0.412108i	$0.135207\pi$
$317$			14.6748i			0.824216i	−0.911135	+	0.412108i	$0.864793\pi$
$318$	1.04356			0.0585200
$319$	−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
$324$	8.58258	+	14.8655i	0.476810	+	0.825859i
$325$	−12.7913			−0.709533
$326$			2.74110i			0.151816i
$327$			24.1733i			1.33678i
$328$	8.06080	−	4.65390i	0.445083	−	0.256969i
$329$		0			0
$330$	3.13068			0.172338
$331$	−1.81307	+	1.04678i	−0.0996552	+	0.0575360i	−0.548999	−	0.835823i	$-0.684991\pi$
$331$	−1.81307	+	1.04678i	−0.0996552	+	0.0575360i	0.449344	+	0.893359i	$0.351658\pi$
$332$	21.0826	−	12.1720i	1.15706	−	0.668027i
$333$	1.81307	−	1.04678i	0.0993555	−	0.0573629i
$334$	−7.56534	+	4.36785i	−0.413957	+	0.238998i
$335$	−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	$0.354634\pi$
$338$		−	0.627650i		−	0.0341397i
$339$			23.6965i			1.28702i
$340$	10.0000			0.542326
$341$		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
$347$	31.2867			1.67956			0.839780	−	0.542927i	$-0.182684\pi$
$347$	31.2867			1.67956			0.839780	+	0.542927i	$0.182684\pi$
$348$			11.4213i			0.612244i
$349$			32.1105i			1.71884i	0.511273	+	0.859418i	$0.329174\pi$
$349$			32.1105i			1.71884i	−0.511273	+	0.859418i	$0.670826\pi$
$350$		0			0
$351$	−9.47822	+	16.4168i	−0.505910	+	0.876262i
$352$			14.2179i			0.757817i
$353$	0.230493	+	0.133075i	0.0122679	+	0.00708286i	0.506121	−	0.862462i	$-0.331079\pi$
$353$	0.230493	+	0.133075i	0.0122679	+	0.00708286i	−0.493854	+	0.869545i	$0.664412\pi$
$354$	−6.93920	−	4.00635i	−0.368815	−	0.212935i
$355$	−4.53901			−0.240906
$356$	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	−0.857646	−	0.514241i	$-0.828074\pi$
$359$	0.313068	−	0.542250i	0.0165231	−	0.0286189i	0.874169	+	0.485622i	$0.161407\pi$
$360$	0.230493	−	0.399225i	0.0121480	−	0.0210410i
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	4.64792	−	2.68348i	0.244289	−	0.141040i
$363$	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	−0.265260	−	0.964177i	$-0.585458\pi$
$367$	8.37386	−	4.83465i	0.437112	−	0.252367i	0.702372	+	0.711810i	$0.252124\pi$
$368$	−10.5826	+	18.3296i	−0.551655	+	0.955494i
$369$	0.560795	+	0.971326i	0.0291938	+	0.0505652i
$370$	5.06080	+	2.92185i	0.263098	+	0.151900i
$371$		0			0
$372$		0			0
$373$	18.8085	−	10.8591i	0.973868	−	0.562263i	0.0734550	−	0.997299i	$-0.476597\pi$
$373$	18.8085	−	10.8591i	0.973868	−	0.562263i	0.900413	+	0.435035i	$0.143264\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$		−	19.1280i		−	0.987766i
$376$	10.5826			0.545755
$377$	−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	$0.763472\pi$
$380$	−9.89110	−	1.14213i	−0.507403	−	0.0585898i
$381$	18.2477	+	10.5353i	0.934859	+	0.539741i
$382$		−	9.38325i		−	0.480089i
$383$	8.45644	−	14.6470i	0.432104	−	0.748426i	−0.564950	−	0.825125i	$-0.691105\pi$
$383$	8.45644	−	14.6470i	0.432104	−	0.748426i	0.997054	+	0.0766990i	$0.0244381\pi$
$384$	17.1261	+	9.88778i	0.873964	+	0.504584i
$385$		0			0
$386$	5.60436	−	9.70703i	0.285254	−	0.494075i
$387$	0.708712	+	1.22753i	0.0360259	+	0.0623986i
$388$	1.79129	−	3.10260i	0.0909389	−	0.157511i
$389$	−16.9782	−	29.4071i	−0.860830	−	1.49100i	−0.871129	−	0.491054i	$-0.836612\pi$
$389$	−16.9782	−	29.4071i	−0.860830	−	1.49100i	0.0102991	−	0.999947i	$-0.496722\pi$
$390$	3.95644			0.200342
$391$			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
$396$	−1.12159			−0.0563620
$397$	3.87386	+	2.23658i	0.194424	+	0.112251i	0.594052	−	0.804427i	$-0.297527\pi$
$397$	3.87386	+	2.23658i	0.194424	+	0.112251i	−0.399628	+	0.916677i	$0.630861\pi$
$398$	−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	$-0.299835\pi$
$401$	3.64337	+	2.10350i	0.181941	+	0.105044i	−0.406263	+	0.913756i	$0.633168\pi$
$402$	−2.83485			−0.141389
$403$		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
$408$	13.5826			0.672438
$409$	7.41742	+	12.8474i	0.366768	+	0.635261i	0.989058	−	0.147526i	$-0.0471309\pi$
$409$	7.41742	+	12.8474i	0.366768	+	0.635261i	−0.622290	+	0.782787i	$0.713798\pi$
$410$	−1.56534	+	2.71125i	−0.0773067	+	0.133899i
$411$	8.91742	+	15.4454i	0.439864	+	0.761867i
$412$	−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
$416$			17.9681i			0.880957i
$417$	−16.5653	−	9.56400i	−0.811208	−	0.468351i
$418$	−2.37386	−	5.48220i	−0.116109	−	0.268143i
$419$		−	38.7726i		−	1.89416i	−0.320992	−	0.947082i	$-0.604016\pi$
$419$		−	38.7726i		−	1.89416i	0.320992	−	0.947082i	$-0.395984\pi$
$420$		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	$0.206266\pi$
$422$	−6.46099			−0.314516
$423$			1.27520i			0.0620024i
$424$	−1.10436	−	1.91280i	−0.0536323	−	0.0928938i
$425$	12.7913	−	7.38505i	0.620469	−	0.358228i
$426$	−2.91288			−0.141129
$427$		0			0
$428$	−14.7042	−	8.48945i	−0.710753	−	0.410353i
$429$	−10.1869	−	17.6443i	−0.491830	−	0.851874i
$430$	−1.97822	+	3.42638i	−0.0953982	+	0.165235i
$431$	15.7087	−	9.06943i	0.756662	−	0.436859i	−0.0714340	−	0.997445i	$-0.522758\pi$
$431$	15.7087	−	9.06943i	0.756662	−	0.436859i	0.828096	+	0.560586i	$0.189424\pi$
$432$	6.97822	−	12.0866i	0.335740	−	0.581518i
$433$	18.1869	−	31.5007i	0.874008	−	1.51383i	0.0161926	−	0.999869i	$-0.494846\pi$
$433$	18.1869	−	31.5007i	0.874008	−	1.51383i	0.857816	−	0.513958i	$-0.171821\pi$
$434$		0			0
$435$	−4.06534	−	7.04138i	−0.194918	−	0.337608i
$436$	20.9347	−	12.0866i	1.00259	−	0.578845i
$437$	3.79129	−	32.8335i	0.181362	−	1.57064i
$438$	2.53901	−	4.39770i	0.121319	−	0.210130i
$439$	1.58258	−	2.74110i	0.0755322	−	0.130826i	−0.825785	−	0.563984i	$-0.809268\pi$
$439$	1.58258	−	2.74110i	0.0755322	−	0.130826i	0.901318	+	0.433159i	$0.142601\pi$
$440$	−3.31307	−	5.73840i	−0.157944	−	0.273568i
$441$		0			0
$442$	3.79129	+	6.56670i	0.180333	+	0.312346i
$443$	21.3303			1.01343			0.506717	−	0.862113i	$-0.330859\pi$
$443$	21.3303			1.01343			0.506717	+	0.862113i	$0.330859\pi$
$444$	−27.8739	−	16.0930i	−1.32284	−	0.763739i
$445$	−2.62159	−	1.51358i	−0.124275	−	0.0717504i
$446$			6.20520i			0.293825i
$447$	−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	$0.903306\pi$
$450$		−	0.321699i		−	0.0151650i
$451$	16.1216			0.759136
$452$	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
$457$	19.0390	+	32.9765i	0.890608	+	1.54258i	0.839148	+	0.543902i	$0.183054\pi$
$457$	19.0390	+	32.9765i	0.890608	+	1.54258i	0.0514591	+	0.998675i	$0.483613\pi$
$458$	−3.16515			−0.147898
$459$		−	21.8890i		−	1.02169i
$460$		−	17.3205i		−	0.807573i
$461$	4.66515	−	2.69343i	0.217278	−	0.125445i	−0.387411	−	0.921907i	$-0.626631\pi$
$461$	4.66515	−	2.69343i	0.217278	−	0.125445i	0.604689	+	0.796462i	$0.293297\pi$
$462$		0			0
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	8.60436	−	4.96773i	0.399447	−	0.230621i
$465$		0			0
$466$	5.30852	−	3.06488i	0.245913	−	0.141978i
$467$	17.7695	−	10.2592i	0.822275	−	0.474741i	−0.0289255	−	0.999582i	$-0.509209\pi$
$467$	17.7695	−	10.2592i	0.822275	−	0.474741i	0.851200	+	0.524841i	$0.175875\pi$
$468$	−1.41742			−0.0655205
$469$		0			0
$470$	−3.08258	+	1.77973i	−0.142189	+	0.0820926i
$471$			21.0707i			0.970885i
$472$			16.9590i			0.780602i
$473$	20.3739			0.936791
$474$	−2.83485	−	4.91010i	−0.130209	−	0.225528i
$475$	−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	−0.496222	−	0.868196i	$-0.665280\pi$
$479$	0.165151	−	0.0953502i	0.00754596	−	0.00435666i	0.503768	+	0.863839i	$0.331947\pi$
$480$	−10.8258			−0.494126
$481$		−	38.0297i		−	1.73400i
$482$		−	3.36875i		−	0.153442i
$483$		0			0
$484$	1.79129	−	3.10260i	0.0814222	−	0.141027i
$485$			2.55040i			0.115808i
$486$	−0.856629	−	0.494575i	−0.0388575	−	0.0224344i
$487$	−8.68693	−	5.01540i	−0.393642	−	0.227270i	0.290095	−	0.956998i	$-0.406313\pi$
$487$	−8.68693	−	5.01540i	−0.393642	−	0.227270i	−0.683737	+	0.729728i	$0.739647\pi$
$488$	2.37386			0.107460
$489$	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
$493$	7.79129	−	13.4949i	0.350902	−	0.607780i
$494$	−3.00000	−	6.92820i	−0.134976	−	0.311715i
$495$	0.691478	−	0.399225i	0.0310796	−	0.0179438i
$496$		0			0
$497$		0			0
$498$	−5.56080	+	9.63158i	−0.249185	+	0.431601i
$499$	8.87386	−	15.3700i	0.397249	−	0.688055i	−0.596137	−	0.802883i	$-0.703298\pi$
$499$	8.87386	−	15.3700i	0.397249	−	0.688055i	0.993385	+	0.114828i	$0.0366317\pi$
$500$	−16.5653	+	9.56400i	−0.740825	+	0.427715i
$501$	−17.1261	+	29.6633i	−0.765139	+	1.32526i
$502$	−2.18693	−	3.78788i	−0.0976075	−	0.169061i
$503$	10.4174	+	6.01450i	0.464490	+	0.268173i	0.713930	−	0.700217i	$-0.246913\pi$
$503$	10.4174	+	6.01450i	0.464490	+	0.268173i	−0.249440	+	0.968390i	$0.580247\pi$
$504$		0			0
$505$	10.9220			0.486021
$506$	9.00000	−	5.19615i	0.400099	−	0.230997i
$507$	−1.23049	−	2.13128i	−0.0546481	−	0.0946533i
$508$		−	21.0707i		−	0.934859i
$509$	15.0000			0.664863			0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000			0.664863			0.332432	+	0.943127i	$0.392131\pi$
$510$	−3.95644	+	2.28425i	−0.175194	+	0.101148i
$511$		0			0
$512$		−	22.8981i		−	1.01196i
$513$	−2.50000	+	21.6506i	−0.110378	+	0.955899i
$514$	−7.81307	−	4.51088i	−0.344620	−	0.198966i
$515$		−	4.30235i		−	0.189584i
$516$	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
$520$	−4.18693	−	7.25198i	−0.183609	−	0.318020i
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$	−0.169697	−	0.293924i	−0.00742745	−	0.0128647i
$523$	21.4955			0.939931			0.469965	−	0.882685i	$-0.344266\pi$
$523$	21.4955			0.939931			0.469965	+	0.882685i	$0.344266\pi$
$524$		−	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
$529$	34.4955			1.49980
$530$	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
$535$	12.0871			0.522572
$536$	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
$541$	−3.74773			−0.161127			−0.0805637	−	0.996749i	$-0.525672\pi$
$541$	−3.74773			−0.161127			−0.0805637	+	0.996749i	$0.525672\pi$
$542$	−3.08258	−	5.33918i	−0.132408	−	0.229337i
$543$	10.5218	−	18.2243i	0.451533	−	0.782078i
$544$	−10.3739	−	17.9681i	−0.444776	−	0.770374i
$545$	−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
$549$			0.286051i			0.0122083i
$550$	−4.00455	−	2.31203i	−0.170754	−	0.0985851i
$551$	−9.24773	+	12.4581i	−0.393966	+	0.530732i
$552$		−	23.5257i		−	1.00132i
$553$		0			0
$554$	−9.31307	+	5.37690i	−0.395674	+	0.228443i
$555$	22.9129			0.972598
$556$			19.1280i			0.811208i
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	0.710457	−	0.703740i	$-0.248488\pi$
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	−0.964686	+	0.263404i	$0.915155\pi$
$558$		0			0
$559$	25.7477			1.08901
$560$		0			0
$561$	20.3739	+	11.7629i	0.860185	+	0.496628i
$562$	0.269507	+	0.466801i	0.0113685	+	0.0196908i
$563$	17.8521	−	30.9207i	0.752376	−	1.30315i	−0.194293	−	0.980944i	$-0.562241\pi$
$563$	17.8521	−	30.9207i	0.752376	−	1.30315i	0.946668	−	0.322209i	$-0.104425\pi$
$564$	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
$569$	−2.76951	+	1.59898i	−0.116104	+	0.0670326i	−0.556927	−	0.830561i	$-0.688020\pi$
$569$	−2.76951	+	1.59898i	−0.116104	+	0.0670326i	0.440823	+	0.897594i	$0.354686\pi$
$570$	4.17424	−	1.80750i	0.174840	−	0.0757079i
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	−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
$576$	0.713258			0.0297191
$577$	−26.3085	−	15.1892i	−1.09524	−	0.632336i	−0.160272	−	0.987073i	$-0.551237\pi$
$577$	−26.3085	−	15.1892i	−1.09524	−	0.632336i	−0.934966	+	0.354737i	$0.884570\pi$
$578$	−0.856629	−	0.494575i	−0.0356311	−	0.0205716i
$579$		−	43.9488i		−	1.82645i
$580$	−4.06534	+	7.04138i	−0.168804	+	0.292377i
$581$		0			0
$582$			1.63670i			0.0678434i
$583$		−	3.82560i		−	0.158440i
$584$	−10.7477			−0.444744
$585$	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	−0.642463	−	0.766317i	$-0.722087\pi$
$587$	−7.26951	+	4.19705i	−0.300045	+	0.173231i	0.342418	+	0.939548i	$0.388754\pi$
$588$		0			0
$589$		0			0
$590$	−2.85208	−	4.93995i	−0.117418	−	0.203375i
$591$	−21.4955			−0.884205
$592$			27.9989i			1.15075i
$593$			17.1298i			0.703437i	0.936106	+	0.351718i	$0.114403\pi$
$593$			17.1298i			0.703437i	−0.936106	+	0.351718i	$0.885597\pi$
$594$	−5.93466	+	3.42638i	−0.243502	+	0.140586i
$595$		0			0
$596$	20.0780			0.822428
$597$	−34.2523	+	19.7756i	−1.40185	+	0.809360i
$598$	11.3739	−	6.56670i	0.465112	−	0.268532i
$599$	−31.3521	+	18.1011i	−1.28101	+	0.739592i	−0.977033	−	0.213087i	$-0.931648\pi$
$599$	−31.3521	+	18.1011i	−1.28101	+	0.739592i	−0.303978	+	0.952679i	$0.598315\pi$
$600$	−9.06534	+	5.23388i	−0.370091	+	0.213672i
$601$	−20.4955			−0.836027			−0.418014	−	0.908441i	$-0.637274\pi$
$601$	−20.4955			−0.836027			−0.418014	+	0.908441i	$0.637274\pi$
$602$		0			0
$603$	−0.626136	+	0.361500i	−0.0254982	+	0.0147214i
$604$			32.1860i			1.30963i
$605$			2.55040i			0.103689i
$606$	7.00909			0.284725
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$	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
$613$	−5.37386			−0.217048			−0.108524	−	0.994094i	$-0.534612\pi$
$613$	−5.37386			−0.217048			−0.108524	+	0.994094i	$0.534612\pi$
$614$		−	9.23236i		−	0.372588i
$615$			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	$-0.196593\pi$
$618$		−	2.76100i		−	0.111064i
$619$	−7.50000	−	4.33013i	−0.301450	−	0.174042i	0.341644	−	0.939829i	$-0.389016\pi$
$619$	−7.50000	−	4.33013i	−0.301450	−	0.174042i	−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$	−37.9129			−1.52139
$622$	−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
$626$	1.97822	−	3.42638i	0.0790656	−	0.136946i
$627$	−18.8085	−	13.9617i	−0.751140	−	0.557577i
$628$	18.2477	−	10.5353i	0.728164	−	0.420405i
$629$	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
$634$	−3.35208	+	5.80598i	−0.133128	+	0.230585i
$635$	7.50000	+	12.9904i	0.297628	+	0.515508i
$636$	−3.54356	−	2.04588i	−0.140511	−	0.0811243i
$637$		0			0
$638$	−4.87841			−0.193138
$639$	−0.643371	+	0.371450i	−0.0254514	+	0.0146944i
$640$	7.03901	+	12.1919i	0.278241	+	0.481928i
$641$		−	7.11890i		−	0.281180i	−0.990068	−	0.140590i	$-0.955100\pi$
$641$		−	7.11890i		−	0.281180i	0.990068	−	0.140590i	$-0.0448999\pi$
$642$	7.75682			0.306137
$643$	9.24773	−	5.33918i	0.364695	−	0.210557i	−0.306443	−	0.951889i	$-0.599139\pi$
$643$	9.24773	−	5.33918i	0.364695	−	0.210557i	0.671138	+	0.741332i	$0.265806\pi$
$644$		0			0
$645$			15.5130i			0.610824i
$646$	7.00000	+	5.19615i	0.275411	+	0.204440i
$647$	5.76951	+	3.33103i	0.226823	+	0.130956i	0.609105	−	0.793089i	$-0.291529\pi$
$647$	5.76951	+	3.33103i	0.226823	+	0.130956i	−0.382283	+	0.924045i	$0.624862\pi$
$648$			16.5975i			0.652012i
$649$	−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
$653$	−7.50000	−	12.9904i	−0.293498	−	0.508353i	0.681137	−	0.732156i	$-0.261486\pi$
$653$	−7.50000	−	12.9904i	−0.293498	−	0.508353i	−0.974634	+	0.223803i	$0.928153\pi$
$654$	−5.52178	+	9.56400i	−0.215919	+	0.373982i
$655$	4.53901	+	7.86180i	0.177354	+	0.307186i
$656$	−15.0000			−0.585652
$657$		−	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	0.993816	+	0.111036i	$0.0354168\pi$
$661$	15.2477	+	26.4098i	0.593068	+	1.02722i	−0.400749	+	0.916188i	$0.631250\pi$
$662$	−0.956439			−0.0371731
$663$	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
$668$	34.2523			1.32526
$669$	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	$0.927677\pi$
$674$	−1.12159			−0.0432021
$675$	8.43466	+	14.6093i	0.324650	+	0.562311i
$676$	−1.23049	+	2.13128i	−0.0473266	+	0.0819721i
$677$	−1.33485	−	2.31203i	−0.0513024	−	0.0888584i	0.839234	−	0.543771i	$-0.183004\pi$
$677$	−1.33485	−	2.31203i	−0.0513024	−	0.0888584i	−0.890536	+	0.454912i	$0.849671\pi$
$678$	−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
$683$	−30.2650	−	17.4735i	−1.15806	−	0.668604i	−0.207219	−	0.978295i	$-0.566441\pi$
$683$	−30.2650	−	17.4735i	−1.15806	−	0.668604i	−0.950837	+	0.309690i	$0.899775\pi$
$684$	−1.49545	+	0.647551i	−0.0571801	+	0.0247597i
$685$			12.6965i			0.485107i
$686$		0			0
$687$	−10.7477	+	6.20520i	−0.410051	+	0.236743i
$688$	−18.9564			−0.722707
$689$		−	4.83465i		−	0.184186i
$690$	3.95644	+	6.85275i	0.150619	+	0.260880i
$691$	−37.5000	+	21.6506i	−1.42657	+	0.823629i	−0.996848	−	0.0793336i	$-0.974721\pi$
$691$	−37.5000	+	21.6506i	−1.42657	+	0.823629i	−0.429719	+	0.902963i	$0.641387\pi$
$692$	35.3739			1.34471
$693$		0			0
$694$	12.3784	+	7.14668i	0.469878	+	0.271284i
$695$	−6.80852	−	11.7927i	−0.258262	−	0.447323i
$696$	−5.52178	+	9.56400i	−0.209303	+	0.362523i
$697$	−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	$0.700279\pi$
$702$	−7.50000	+	4.33013i	−0.283069	+	0.163430i
$703$	−17.3739	−	40.1232i	−0.655268	−	1.51328i
$704$	5.12614	−	8.87873i	0.193199	−	0.334630i
$705$	−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
$709$	−13.4174			−0.503902			−0.251951	−	0.967740i	$-0.581072\pi$
$709$	−13.4174			−0.503902			−0.251951	+	0.967740i	$0.581072\pi$
$710$	−1.79583	−	1.03683i	−0.0673964	−	0.0389114i
$711$	−1.25227	−	0.723000i	−0.0469639	−	0.0271146i
$712$			4.11165i			0.154091i
$713$		0			0
$714$		0			0
$715$		−	14.5040i		−	0.542417i
$716$		−	26.4575i		−	0.988764i
$717$	26.0436			0.972615
$718$	0.247727	−	0.143025i	0.00924509	−	0.00533766i
$719$	27.1652	+	15.6838i	1.01309	+	0.584907i	0.912095	−	0.409980i	$-0.134464\pi$
$719$	27.1652	+	15.6838i	1.01309	+	0.584907i	0.100995	+	0.994887i	$0.467798\pi$
$720$	−0.643371	+	0.371450i	−0.0239770	+	0.0138431i
$721$		0			0
$722$	−6.33030	−	5.93905i	−0.235589	−	0.221029i
$723$	−6.60436	−	11.4391i	−0.245619	−	0.425424i
$724$	−21.0436			−0.782078
$725$			12.0091i			0.446007i
$726$			1.63670i			0.0607437i
$727$	−39.2477	+	22.6597i	−1.45562	+	0.840401i	−0.998791	−	0.0491546i	$-0.984347\pi$
$727$	−39.2477	+	22.6597i	−1.45562	+	0.840401i	−0.456826	+	0.889556i	$0.651014\pi$
$728$		0			0
$729$	24.8693			0.921086
$730$	3.13068	−	1.80750i	0.115872	−	0.0668986i
$731$	−25.7477	+	14.8655i	−0.952314	+	0.549819i
$732$	3.80852	−	2.19885i	0.140767	−	0.0812719i
$733$	−24.8085	+	14.3232i	−0.916324	+	0.529040i	−0.882460	−	0.470387i	$-0.844114\pi$
$733$	−24.8085	+	14.3232i	−0.916324	+	0.529040i	−0.0338633	+	0.999426i	$0.510781\pi$
$734$	4.41742			0.163050
$735$		0			0
$736$	−31.1216	+	17.9681i	−1.14716	+	0.662311i
$737$			10.3923i			0.382805i
$738$			0.512399i			0.0188617i
$739$	25.7477			0.947145			0.473573	−	0.880755i	$-0.342964\pi$
$739$	25.7477			0.947145			0.473573	+	0.880755i	$0.342964\pi$
$740$	−11.4564	−	19.8431i	−0.421147	−	0.729448i
$741$	−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
$746$	9.92197			0.363269
$747$			2.83645i			0.103780i
$748$		−	23.5257i		−	0.860185i
$749$		0			0
$750$	4.36932	−	7.56788i	0.159545	−	0.276340i
$751$		−	9.02175i		−	0.329208i	−0.986360	−	0.164604i	$-0.947365\pi$
$751$		−	9.02175i		−	0.329208i	0.986360	−	0.164604i	$-0.0526347\pi$
$752$	−14.7695	−	8.52718i	−0.538589	−	0.310954i
$753$	−14.8521	−	8.57485i	−0.541240	−	0.312485i
$754$	−6.16515			−0.224522
$755$	−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
$759$	20.3739	−	35.2886i	0.739524	−	1.28089i
$760$	−7.73049	−	5.73840i	−0.280414	−	0.208154i
$761$	17.7695	−	10.2592i	0.644144	−	0.371897i	−0.142065	−	0.989857i	$-0.545374\pi$
$761$	17.7695	−	10.2592i	0.644144	−	0.371897i	0.786209	+	0.617961i	$0.212041\pi$
$762$	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
$767$	−18.5608	+	32.1482i	−0.670191	+	1.16081i
$768$	−1.60436	−	2.77883i	−0.0578922	−	0.100272i
$769$	−25.1869	−	14.5417i	−0.908264	−	0.524386i	−0.0283918	−	0.999597i	$-0.509039\pi$
$769$	−25.1869	−	14.5417i	−0.908264	−	0.524386i	−0.879872	+	0.475210i	$0.842372\pi$
$770$		0			0
$771$	−35.3739			−1.27396
$772$	−38.0608	+	21.9744i	−1.36984	+	0.790876i
$773$	19.8303	+	34.3471i	0.713246	+	1.23538i	0.963632	+	0.267233i	$0.0861093\pi$
$773$	19.8303	+	34.3471i	0.713246	+	1.23538i	−0.250386	+	0.968146i	$0.580557\pi$
$774$			0.647551i			0.0232757i
$775$		0			0
$776$	3.00000	−	1.73205i	0.107694	−	0.0621770i
$777$		0			0
$778$		−	15.5130i		−	0.556168i
$779$	21.4955	−	9.30780i	0.770155	−	0.333487i
$780$	−13.4347	−	7.75650i	−0.481038	−	0.277727i
$781$			10.6784i			0.382102i
$782$	−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
$786$	2.91288	+	5.04525i	0.103899	+	0.179958i
$787$	12.7913	−	22.1552i	0.455960	−	0.789746i	−0.542783	−	0.839873i	$-0.682629\pi$
$787$	12.7913	−	22.1552i	0.455960	−	0.789746i	0.998743	+	0.0501270i	$0.0159626\pi$
$788$	10.7477	+	18.6156i	0.382872	+	0.663154i
$789$	21.4955			0.765258
$790$		−	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
$795$	2.91288			0.103309
$796$	34.2523	+	19.7756i	1.21404	+	0.700926i
$797$	−48.4955			−1.71780			−0.858899	−	0.512146i	$-0.828851\pi$
$797$	−48.4955			−1.71780			−0.858899	+	0.512146i	$0.828851\pi$
$798$		0			0
$799$	−26.7477			−0.946267
$800$	13.8475	+	7.99488i	0.489584	+	0.282662i
$801$	−0.495454			−0.0175060
$802$	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
$807$	13.5826			0.478129
$808$	−7.41742	−	12.8474i	−0.260944	−	0.451968i
$809$	−25.0390	+	43.3688i	−0.880325	+	1.52477i	−0.0293449	+	0.999569i	$0.509342\pi$
$809$	−25.0390	+	43.3688i	−0.880325	+	1.52477i	−0.850980	+	0.525198i	$0.823991\pi$
$810$	−2.79129	−	4.83465i	−0.0980759	−	0.169872i
$811$	7.56080	−	13.0957i	0.265495	−	0.459852i	−0.702198	−	0.711982i	$-0.747798\pi$
$811$	7.56080	−	13.0957i	0.265495	−	0.459852i	0.967693	+	0.252130i	$0.0811311\pi$
$812$		0			0
$813$	−20.9347	−	12.0866i	−0.734211	−	0.423897i
$814$	6.87386	−	11.9059i	0.240929	−	0.417301i
$815$			7.65120i			0.268010i
$816$	−18.9564	−	10.9445i	−0.663608	−	0.383134i
$817$	27.1652	−	11.7629i	0.950388	−	0.411530i
$818$			6.77730i			0.236963i
$819$		0			0
$820$	10.6307	−	6.13763i	0.371240	−	0.214335i
$821$	−17.0436			−0.594824			−0.297412	−	0.954749i	$-0.596124\pi$
$821$	−17.0436			−0.594824			−0.297412	+	0.954749i	$0.596124\pi$
$822$			8.14786i			0.284189i
$823$	12.7087	+	22.0121i	0.442998	+	0.767295i	0.997910	−	0.0646139i	$-0.0205816\pi$
$823$	12.7087	+	22.0121i	0.442998	+	0.767295i	−0.554912	+	0.831909i	$0.687248\pi$
$824$	−5.06080	+	2.92185i	−0.176301	+	0.101788i
$825$	−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	$0.486554\pi$
$828$	−1.41742	−	2.45505i	−0.0492589	−	0.0853189i
$829$	−7.12614	+	12.3428i	−0.247501	+	0.428684i	−0.962832	−	0.270102i	$-0.912943\pi$
$829$	−7.12614	+	12.3428i	−0.247501	+	0.428684i	0.715331	+	0.698786i	$0.246276\pi$
$830$	−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
$835$	−21.1170	+	12.1919i	−0.730785	+	0.421919i
$836$	−2.68693	+	23.2695i	−0.0929295	+	0.804793i
$837$		0			0
$838$	8.85663	−	15.3401i	0.305947	−	0.529916i
$839$	−11.9174	−	20.6416i	−0.411435	−	0.712627i	0.583612	−	0.812033i	$-0.301639\pi$
$839$	−11.9174	−	20.6416i	−0.411435	−	0.712627i	−0.995047	+	0.0994062i	$0.968306\pi$
$840$		0			0
$841$	−8.16515	−	14.1425i	−0.281557	−	0.487671i
$842$	7.28674			0.251118
$843$	1.83030	+	1.05673i	0.0630390	+	0.0363956i
$844$	21.9392	+	12.6666i	0.755179	+	0.436003i
$845$		−	1.75195i		−	0.0602690i
$846$	−0.291288	+	0.504525i	−0.0100147	+	0.0173459i
$847$		0			0
$848$			3.55945i			0.122232i
$849$			17.3205i			0.594438i
$850$	6.74773			0.231445
$851$	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	−0.514886	−	0.857259i	$-0.672166\pi$
$853$	−0.873864	+	0.504525i	−0.0299205	+	0.0172746i	0.484965	+	0.874533i	$0.338832\pi$
$854$		0			0
$855$	0.691478	−	0.931524i	0.0236480	−	0.0318575i
$856$	−8.20871	−	14.2179i	−0.280568	−	0.485958i
$857$	13.1216			0.448225			0.224112	−	0.974563i	$-0.428052\pi$
$857$	13.1216			0.448225			0.224112	+	0.974563i	$0.428052\pi$
$858$		−	9.30780i		−	0.317763i
$859$		−	6.56670i		−	0.224053i	−0.993705	−	0.112027i	$-0.964266\pi$
$859$		−	6.56670i		−	0.224053i	0.993705	−	0.112027i	$-0.0357342\pi$
$860$	13.4347	−	7.75650i	0.458118	−	0.264495i
$861$		0			0
$862$	8.28674			0.282248
$863$	−16.0390	+	9.26013i	−0.545974	+	0.315218i	−0.747497	−	0.664265i	$-0.768744\pi$
$863$	−16.0390	+	9.26013i	−0.545974	+	0.315218i	0.201522	+	0.979484i	$0.435411\pi$
$864$	20.5218	−	11.8483i	0.698165	−	0.403086i
$865$	−21.8085	+	12.5912i	−0.741512	+	0.428112i
$866$	14.3911	−	8.30870i	0.489029	−	0.282341i
$867$	−3.87841			−0.131718
$868$		0			0
$869$	−18.0000	+	10.3923i	−0.610608	+	0.352535i
$870$		−	3.71450i		−	0.125933i
$871$			13.1334i			0.445008i
$872$	23.3739			0.791539
$873$	0.208712	+	0.361500i	0.00706384	+	0.0122349i
$874$	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	$-0.590899\pi$
$877$	−37.1216	−	21.4322i	−1.25351	−	0.723713i	−0.971804	+	0.235789i	$0.924233\pi$
$878$	1.25227	−	0.723000i	0.0422622	−	0.0244001i
$879$	37.6170			1.26879
$880$			10.6784i			0.359967i
$881$			13.5903i			0.457867i	0.973442	+	0.228934i	$0.0735239\pi$
$881$			13.5903i			0.457867i	−0.973442	+	0.228934i	$0.926476\pi$
$882$		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	$0.924330\pi$
$884$		−	29.7309i		−	0.999959i
$885$	−19.3693	−	11.1829i	−0.651092	−	0.375908i
$886$	8.43920	+	4.87238i	0.283521	+	0.163691i
$887$	−1.41742			−0.0475925			−0.0237962	−	0.999717i	$-0.507575\pi$
$887$	−1.41742			−0.0475925			−0.0237962	+	0.999717i	$0.507575\pi$
$888$	−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
$892$	12.1652	−	21.0707i	0.407319	−	0.705498i
$893$	26.4564	+	3.05493i	0.885331	+	0.102229i
$894$	−7.94375	+	4.58633i	−0.265679	+	0.153390i
$895$	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
$900$	−0.630682	+	1.09237i	−0.0210227	+	0.0364125i
$901$	2.79129	+	4.83465i	0.0929913	+	0.161066i
$902$	6.37841	+	3.68258i	0.212378	+	0.122616i
$903$		0			0
$904$	22.9129			0.762071
$905$	12.9737	−	7.49035i	0.431260	−	0.248988i
$906$	−7.35208	−	12.7342i	−0.244257	−	0.423065i
$907$		−	40.4093i		−	1.34177i	−0.741562	−	0.670884i	$-0.765915\pi$
$907$		−	40.4093i		−	1.34177i	0.741562	−	0.670884i	$-0.234085\pi$
$908$	−47.5390			−1.57764
$909$	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	$-0.0390395\pi$
$912$	17.5000	+	12.9904i	0.579483	+	0.430155i
$913$	35.3085	+	20.3854i	1.16854	+	0.674658i
$914$			17.3960i			0.575407i
$915$	−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
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	0.625573	−	0.780165i	$-0.284865\pi$
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	−0.988430	+	0.151680i	$0.951532\pi$
$920$	8.37386	−	14.5040i	0.276078	−	0.478181i
$921$	−18.0998	−	31.3498i	−0.596409	−	1.03301i
$922$	2.46099			0.0810482
$923$			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
$928$	16.8693			0.553762
$929$	−3.47822	−	2.00815i	−0.114117	−	0.0658853i	0.441855	−	0.897086i	$-0.354320\pi$
$929$	−3.47822	−	2.00815i	−0.114117	−	0.0658853i	−0.555972	+	0.831201i	$0.687654\pi$
$930$		0			0
$931$		0			0
$932$	−24.0345			−0.787275
$933$	−37.2042	−	21.4798i	−1.21801	−	0.703218i
$934$	9.37386			0.306722
$935$	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	0.653485	−	0.756939i	$-0.273306\pi$
$937$	9.93920	+	5.73840i	0.324700	+	0.187465i	−0.328786	+	0.944405i	$0.606639\pi$
$938$		0			0
$939$		−	15.5130i		−	0.506248i
$940$	13.9564			0.455209
$941$	−2.60436	−	4.51088i	−0.0848996	−	0.147050i	0.820449	−	0.571720i	$-0.193724\pi$
$941$	−2.60436	−	4.51088i	−0.0848996	−	0.147050i	−0.905348	+	0.424670i	$0.860390\pi$
$942$	−4.81307	+	8.33648i	−0.156818	+	0.271617i
$943$	20.3739	+	35.2886i	0.663464	+	1.14915i
$944$	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	0.412976	+	0.910742i	$0.364490\pi$
$947$	−17.9174	+	31.0339i	−0.582238	+	1.00847i	−0.995214	+	0.0977238i	$0.968844\pi$
$948$			22.2306i			0.722017i
$949$	−20.3739	−	11.7629i	−0.661364	−	0.381838i
$950$	−6.67424	−	0.770675i	−0.216541	−	0.0250040i
$951$			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	$0.629648\pi$
$954$	0.121591			0.00393664
$955$		−	26.1914i		−	0.847533i
$956$	−13.0218	−	22.5544i	−0.421154	−	0.729461i
$957$	−16.5653	+	9.56400i	−0.535481	+	0.309160i
$958$	0.0871215			0.00281477
$959$		0			0
$960$	6.76042	+	3.90313i	0.218191	+	0.125973i
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	8.68693	−	15.0462i	0.280078	−	0.485109i
$963$	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	$0.950709\pi$
$968$	3.00000	−	1.73205i	0.0964237	−	0.0556702i
$969$	33.9564	+	3.92095i	1.09084	+	0.125959i
$970$	−0.582576	+	1.00905i	−0.0187054	+	0.0323987i
$971$	21.7259	−	37.6304i	0.697219	−	1.20762i	−0.272208	−	0.962238i	$-0.587754\pi$
$971$	21.7259	−	37.6304i	0.697219	−	1.20762i	0.969427	−	0.245380i	$-0.0789127\pi$
$972$	1.93920	+	3.35880i	0.0622000	+	0.107734i
$973$		0			0
$974$	−2.29129	−	3.96863i	−0.0734176	−	0.127163i
$975$	−22.9129			−0.733799
$976$	−3.31307	−	1.91280i	−0.106049	−	0.0612273i
$977$	−16.4174	−	9.47860i	−0.525240	−	0.303247i	0.213836	−	0.976870i	$-0.431404\pi$
$977$	−16.4174	−	9.47860i	−0.525240	−	0.303247i	−0.739076	+	0.673622i	$0.764738\pi$
$978$			4.91010i			0.157008i
$979$	−3.56080	+	6.16748i	−0.113804	+	0.197113i
$980$		0			0
$981$			2.81655i			0.0899256i
$982$		−	17.3960i		−	0.555127i
$983$	−58.2867			−1.85906			−0.929529	−	0.368749i	$-0.879786\pi$
$983$	−58.2867			−1.85906			−0.929529	+	0.368749i	$0.879786\pi$
$984$	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
$989$	25.7477	+	44.5964i	0.818730	+	1.41808i
$990$	0.364772			0.0115932
$991$		−	35.0025i		−	1.11189i	−0.831219	−	0.555946i	$-0.812356\pi$
$991$		−	35.0025i		−	1.11189i	0.831219	−	0.555946i	$-0.187644\pi$
$992$		0			0
$993$	−3.24773	+	1.87508i	−0.103064	+	0.0595037i
$994$		0			0
$995$	−28.1561			−0.892607
$996$	37.7650	−	21.8036i	1.19663	−	0.690874i
$997$	4.74773	−	2.74110i	0.150362	−	0.0868116i	−0.422931	−	0.906162i	$-0.638999\pi$
$997$	4.74773	−	2.74110i	0.150362	−	0.0868116i	0.573293	+	0.819350i	$0.305666\pi$
$998$	7.02178	−	4.05403i	0.222271	−	0.128328i
$999$	−43.4347	+	25.0770i	−1.37421	+	0.793402i

Twists

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

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

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.395644 + 0.228425i) q^{2} +1.79129 q^{3} +(-0.895644 - 1.55130i) q^{4} +(1.10436 + 0.637600i) q^{5} +(0.708712 + 0.409175i) q^{6} -1.73205i q^{8} +0.208712 q^{9} +(0.291288 + 0.504525i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-1.60436 - 2.77883i) q^{12} +(1.89564 - 3.28335i) q^{13} +(1.97822 + 1.14213i) q^{15} +(-1.39564 + 2.41733i) q^{16} +4.37780i q^{17} +(0.0825757 + 0.0476751i) q^{18} +(0.500000 - 4.33013i) q^{19} -2.28425i q^{20} +(1.18693 - 0.685275i) q^{22} +7.58258 q^{23} -3.10260i q^{24} +(-1.68693 - 2.92185i) q^{25} +(1.50000 - 0.866025i) q^{26} -5.00000 q^{27} +(-3.08258 - 1.77973i) q^{29} +(0.521780 + 0.903750i) 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} +(8.68693 - 5.01540i) q^{37} +(1.18693 - 1.59898i) q^{38} +(3.39564 - 5.88143i) q^{39} +(1.10436 - 1.91280i) q^{40} +(2.68693 + 4.65390i) q^{41} +(3.39564 + 5.88143i) q^{43} -5.37386 q^{44} +(0.230493 + 0.133075i) q^{45} +(3.00000 + 1.73205i) q^{46} +6.10985i q^{47} +(-2.50000 + 4.33013i) q^{48} -1.54135i q^{50} +7.84190i q^{51} -6.79129 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} +(-0.813068 - 1.40828i) q^{58} -9.79129 q^{59} -4.09175i q^{60} +1.37055i q^{61} +3.41742 q^{64} +(4.18693 - 2.41733i) q^{65} +(2.12614 - 1.22753i) q^{66} +(-3.00000 + 1.73205i) q^{67} +(6.79129 - 3.92095i) q^{68} +13.5826 q^{69} +(-3.08258 + 1.77973i) q^{71} -0.361500i q^{72} -6.20520i q^{73} +4.58258 q^{74} +(-3.02178 - 5.23388i) 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} -9.58258 q^{81} +2.45505i q^{82} +13.5903i q^{83} +(-2.79129 + 4.83465i) q^{85} +3.10260i q^{86} +(-5.52178 - 3.18800i) q^{87} +(-4.50000 - 2.59808i) q^{88} -2.37386 q^{89} +(0.0607953 + 0.105301i) q^{90} +(-6.79129 - 11.7629i) q^{92} +(-1.39564 + 2.41733i) q^{94} +(3.31307 - 4.46320i) q^{95} +(-7.35208 + 4.24473i) q^{96} +(1.00000 + 1.73205i) q^{97} +(0.313068 - 0.542250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 2 q^{3} + q^{4} + 9 q^{5} + 12 q^{6} + 10 q^{9} - 8 q^{10} + 6 q^{11} - 11 q^{12} + 3 q^{13} - 15 q^{15} - q^{16} - 18 q^{18} + 2 q^{19} - 9 q^{22} + 12 q^{23} + 7 q^{25} + 6 q^{26} - 20 q^{27}+ \cdots + 15 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 2 * q^3 + q^4 + 9 * q^5 + 12 * q^6 + 10 * q^9 - 8 * q^10 + 6 * q^11 - 11 * q^12 + 3 * q^13 - 15 * q^15 - q^16 - 18 * q^18 + 2 * q^19 - 9 * q^22 + 12 * q^23 + 7 * q^25 + 6 * q^26 - 20 * q^27 + 6 * q^29 + 25 * q^30 - 21 * q^32 - 3 * q^33 - 4 * q^34 + 13 * q^36 + 21 * q^37 - 9 * q^38 + 9 * q^39 + 9 * q^40 - 3 * q^41 + 9 * q^43 + 6 * q^44 + 33 * q^45 + 12 * q^46 - 10 * q^48 - 18 * q^52 + 9 * q^53 + 15 * q^54 + 27 * q^55 - q^57 - 17 * q^58 - 30 * q^59 + 32 * q^64 + 3 * q^65 + 36 * q^66 - 12 * q^67 + 18 * q^68 + 36 * q^69 + 6 * q^71 - 35 * q^75 + 8 * q^76 - 3 * q^78 - 24 * q^79 + 6 * q^80 - 20 * q^81 - 2 * q^85 - 45 * q^87 - 18 * q^88 + 18 * q^89 - 41 * q^90 - 18 * q^92 - q^94 + 27 * q^95 + 21 * q^96 + 4 * q^97 + 15 * q^99

Introduction

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