LMFDB - Embedded newform 27.11.d.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,11,Mod(8,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.8"); S:= CuspForms(chi, 11); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 11, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$17.1546458222$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 2219 x^{16} + 4286 x^{15} + 3372866 x^{14} + 7237076 x^{13} + 2694115412 x^{12} + \cdots + 64\!\cdots\!96 $ x^18 - x^17 + 2219x^16 + 4286x^15 + 3372866x^14 + 7237076x^13 + 2694115412x^12 + 6418314128x^11 + 1552978472768x^10 + 3181293598208x^9 + 476242689880064x^8 + 876490866851840x^7 + 103146891634589696x^6 + 253732818059067392x^5 + 8170091944772108288x^4 + 46925087214531510272x^3 + 516504122125249937408x^2 + 1745010292035556474880x + 6469041255171695312896
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{52} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$-15.7177 + 27.2239i$ of defining polynomial
Character	$\chi$	$=$	27.17
Dual form			27.11.d.a.8.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-47.1532 + 27.2239i) q^{2} +(970.286 - 1680.58i) q^{4} +(-3579.43 - 2066.59i) q^{5} +(-11845.8 - 20517.5i) q^{7} +49905.4i q^{8} +225043. q^{10} +(83013.5 - 47927.9i) q^{11} +(63316.4 - 109667. i) q^{13} +(1.11713e6 + 644977. i) q^{14} +(-365049. - 632283. i) q^{16} -630218. i q^{17} -3.67135e6 q^{19} +(-6.94615e6 + 4.01036e6i) q^{20} +(-2.60957e6 + 4.51991e6i) q^{22} +(-1.42416e6 - 822238. i) q^{23} +(3.65876e6 + 6.33715e6i) q^{25} +6.89489e6i q^{26} -4.59751e7 q^{28} +(-1.02842e7 + 5.93756e6i) q^{29} +(1.52371e7 - 2.63915e7i) q^{31} +(-9.83013e6 - 5.67543e6i) q^{32} +(1.71570e7 + 2.97168e7i) q^{34} +9.79213e7i q^{35} -9.14191e6 q^{37} +(1.73116e8 - 9.99487e7i) q^{38} +(1.03134e8 - 1.78633e8i) q^{40} +(-3.57733e6 - 2.06537e6i) q^{41} +(9.99200e7 + 1.73066e8i) q^{43} -1.86015e8i q^{44} +8.95383e7 q^{46} +(-3.12963e8 + 1.80689e8i) q^{47} +(-1.39407e8 + 2.41460e8i) q^{49} +(-3.45044e8 - 1.99211e8i) q^{50} +(-1.22870e8 - 2.12817e8i) q^{52} -4.00628e8i q^{53} -3.96188e8 q^{55} +(1.02393e9 - 5.91168e8i) q^{56} +(3.23288e8 - 5.59951e8i) q^{58} +(4.53388e8 + 2.61764e8i) q^{59} +(6.50111e8 + 1.12602e9i) q^{61} +1.65926e9i q^{62} +1.36565e9 q^{64} +(-4.53274e8 + 2.61698e8i) q^{65} +(-1.08644e8 + 1.88178e8i) q^{67} +(-1.05914e9 - 6.11492e8i) q^{68} +(-2.66580e9 - 4.61731e9i) q^{70} +2.30689e9i q^{71} -2.32280e8 q^{73} +(4.31071e8 - 2.48879e8i) q^{74} +(-3.56226e9 + 6.17002e9i) q^{76} +(-1.96672e9 - 1.13548e9i) q^{77} +(-1.60607e8 - 2.78180e8i) q^{79} +3.01762e9i q^{80} +2.24910e8 q^{82} +(5.60771e9 - 3.23761e9i) q^{83} +(-1.30240e9 + 2.25583e9i) q^{85} +(-9.42310e9 - 5.44043e9i) q^{86} +(2.39186e9 + 4.14282e9i) q^{88} +2.86904e9i q^{89} -3.00013e9 q^{91} +(-2.76368e9 + 1.59561e9i) q^{92} +(9.83813e9 - 1.70401e10i) q^{94} +(1.31414e10 + 7.58717e9i) q^{95} +(-3.81258e8 - 6.60359e8i) q^{97} -1.51808e10i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 4095 q^{4} - 4956 q^{5} - 6120 q^{7} - 2052 q^{10} - 969 q^{11} + 140274 q^{13} + 2134578 q^{14} - 1571841 q^{16} + 2771370 q^{19} - 14542734 q^{20} - 3475521 q^{22} + 9944382 q^{23} + 14726277 q^{25}+ \cdots - 14510723337 q^{97}+O(q^{100}) $ 18 * q + 3 * q^2 + 4095 * q^4 - 4956 * q^5 - 6120 * q^7 - 2052 * q^10 - 969 * q^11 + 140274 * q^13 + 2134578 * q^14 - 1571841 * q^16 + 2771370 * q^19 - 14542734 * q^20 - 3475521 * q^22 + 9944382 * q^23 + 14726277 * q^25 - 22968324 * q^28 + 41383956 * q^29 + 28428390 * q^31 - 165205143 * q^32 - 66263103 * q^34 + 63695196 * q^37 + 621662181 * q^38 - 75566250 * q^40 - 452543883 * q^41 + 102086037 * q^43 + 44251488 * q^46 + 289445970 * q^47 + 6735231 * q^49 - 1915252779 * q^50 + 19035576 * q^52 - 289455552 * q^55 + 4272894318 * q^56 - 83900178 * q^58 - 3065773551 * q^59 + 141349086 * q^61 - 28980486 * q^64 + 11094862926 * q^65 + 954074115 * q^67 - 21469701105 * q^68 - 1440686628 * q^70 + 772009902 * q^73 + 30101814978 * q^74 - 40906287 * q^76 - 25001072268 * q^77 + 2079634212 * q^79 - 1423292742 * q^82 + 23396438442 * q^83 - 5975304714 * q^85 - 39111097821 * q^86 + 2974531059 * q^88 + 2180413260 * q^91 + 40885098684 * q^92 + 6395997924 * q^94 - 22335455946 * q^95 - 14510723337 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−47.1532	+	27.2239i	−1.47354	+	0.850748i	−0.999556	−	0.0297860i	$-0.990517\pi$
$2$	−47.1532	+	27.2239i	−1.47354	+	0.850748i	−0.473983	+	0.880534i	$0.657184\pi$
$3$		0			0
$3$		0			0
$4$	970.286	−	1680.58i	0.947545	−	1.64120i
$5$	−3579.43	−	2066.59i	−1.14542	−	0.661308i	−0.197652	−	0.980272i	$-0.563332\pi$
$5$	−3579.43	−	2066.59i	−1.14542	−	0.661308i	−0.947767	+	0.318964i	$0.896665\pi$
$6$		0			0
$7$	−11845.8	−	20517.5i	−0.704812	−	1.22077i	−0.966759	−	0.255688i	$-0.917698\pi$
$7$	−11845.8	−	20517.5i	−0.704812	−	1.22077i	0.261948	−	0.965082i	$-0.415635\pi$
$8$			49905.4i			1.52299i
$9$		0			0
$10$	225043.			2.25043
$11$	83013.5	−	47927.9i	0.515448	−	0.297594i	−0.219622	−	0.975585i	$-0.570482\pi$
$11$	83013.5	−	47927.9i	0.515448	−	0.297594i	0.735070	+	0.677991i	$0.237149\pi$
$12$		0			0
$13$	63316.4	−	109667.i	0.170529	−	0.295366i	−0.768076	−	0.640359i	$-0.778786\pi$
$13$	63316.4	−	109667.i	0.170529	−	0.295366i	0.938605	+	0.344993i	$0.112119\pi$
$14$	1.11713e6	+	644977.i	2.07714	+	1.19923i
$15$		0			0
$16$	−365049.	−	632283.i	−0.348138	−	0.602992i
$17$		−	630218.i		−	0.443860i	−0.975063	−	0.221930i	$-0.928764\pi$
$17$		−	630218.i		−	0.443860i	0.975063	−	0.221930i	$-0.0712357\pi$
$18$		0			0
$19$	−3.67135e6			−1.48272			−0.741358	−	0.671110i	$-0.765818\pi$
$19$	−3.67135e6			−1.48272			−0.741358	+	0.671110i	$0.765818\pi$
$20$	−6.94615e6	+	4.01036e6i	−2.17067	+	1.25324i
$21$		0			0
$22$	−2.60957e6	+	4.51991e6i	−0.506356	+	0.877034i
$23$	−1.42416e6	−	822238.i	−0.221268	−	0.127749i	0.385269	−	0.922804i	$-0.374109\pi$
$23$	−1.42416e6	−	822238.i	−0.221268	−	0.127749i	−0.606537	+	0.795055i	$0.707442\pi$
$24$		0			0
$25$	3.65876e6	+	6.33715e6i	0.374657	+	0.648924i
$26$			6.89489e6i			0.580310i
$27$		0			0
$28$	−4.59751e7			−2.67136
$29$	−1.02842e7	+	5.93756e6i	−0.501393	+	0.289480i	−0.729289	−	0.684206i	$-0.760149\pi$
$29$	−1.02842e7	+	5.93756e6i	−0.501393	+	0.289480i	0.227895	+	0.973686i	$0.426816\pi$
$30$		0			0
$31$	1.52371e7	−	2.63915e7i	0.532225	−	0.921840i	−0.467067	−	0.884222i	$-0.654689\pi$
$31$	1.52371e7	−	2.63915e7i	0.532225	−	0.921840i	0.999292	−	0.0376187i	$-0.0119772\pi$
$32$	−9.83013e6	−	5.67543e6i	−0.292961	−	0.169141i
$33$		0			0
$34$	1.71570e7	+	2.97168e7i	0.377613	+	0.654046i
$35$			9.79213e7i			1.86439i
$36$		0			0
$37$	−9.14191e6			−0.131834			−0.0659172	−	0.997825i	$-0.520997\pi$
$37$	−9.14191e6			−0.131834			−0.0659172	+	0.997825i	$0.520997\pi$
$38$	1.73116e8	−	9.99487e7i	2.18484	−	1.26142i
$39$		0			0
$40$	1.03134e8	−	1.78633e8i	1.00717	−	1.74446i
$41$	−3.57733e6	−	2.06537e6i	−0.0308773	−	0.0178270i	0.484482	−	0.874801i	$-0.339008\pi$
$41$	−3.57733e6	−	2.06537e6i	−0.0308773	−	0.0178270i	−0.515359	+	0.856974i	$0.672341\pi$
$42$		0			0
$43$	9.99200e7	+	1.73066e8i	0.679689	+	1.17726i	0.975075	+	0.221877i	$0.0712184\pi$
$43$	9.99200e7	+	1.73066e8i	0.679689	+	1.17726i	−0.295386	+	0.955378i	$0.595448\pi$
$44$		−	1.86015e8i		−	1.12794i
$45$		0			0
$46$	8.95383e7			0.434730
$47$	−3.12963e8	+	1.80689e8i	−1.36459	+	0.787848i	−0.990231	−	0.139435i	$-0.955471\pi$
$47$	−3.12963e8	+	1.80689e8i	−1.36459	+	0.787848i	−0.374362	+	0.927283i	$0.622138\pi$
$48$		0			0
$49$	−1.39407e8	+	2.41460e8i	−0.493519	+	0.854800i
$50$	−3.45044e8	−	1.99211e8i	−1.10414	−	0.637477i
$51$		0			0
$52$	−1.22870e8	−	2.12817e8i	−0.323169	−	0.559744i
$53$		−	4.00628e8i		−	0.957993i	−0.877817	−	0.478997i	$-0.841001\pi$
$53$		−	4.00628e8i		−	0.957993i	0.877817	−	0.478997i	$-0.158999\pi$
$54$		0			0
$55$	−3.96188e8			−0.787206
$56$	1.02393e9	−	5.91168e8i	1.85922	−	1.07342i
$57$		0			0
$58$	3.23288e8	−	5.59951e8i	0.492549	−	0.853119i
$59$	4.53388e8	+	2.61764e8i	0.634176	+	0.366142i	0.782368	−	0.622817i	$-0.214012\pi$
$59$	4.53388e8	+	2.61764e8i	0.634176	+	0.366142i	−0.148192	+	0.988959i	$0.547345\pi$
$60$		0			0
$61$	6.50111e8	+	1.12602e9i	0.769730	+	1.33321i	0.937709	+	0.347420i	$0.112942\pi$
$61$	6.50111e8	+	1.12602e9i	0.769730	+	1.33321i	−0.167980	+	0.985790i	$0.553724\pi$
$62$			1.65926e9i			1.81116i
$63$		0			0
$64$	1.36565e9			1.27186
$65$	−4.53274e8	+	2.61698e8i	−0.390655	+	0.225545i
$66$		0			0
$67$	−1.08644e8	+	1.88178e8i	−0.0804698	+	0.139378i	−0.903452	−	0.428690i	$-0.858975\pi$
$67$	−1.08644e8	+	1.88178e8i	−0.0804698	+	0.139378i	0.822982	+	0.568067i	$0.192309\pi$
$68$	−1.05914e9	−	6.11492e8i	−0.728462	−	0.420578i
$69$		0			0
$70$	−2.66580e9	−	4.61731e9i	−1.58613	−	2.74725i
$71$			2.30689e9i			1.27860i	0.768956	+	0.639301i	$0.220776\pi$
$71$			2.30689e9i			1.27860i	−0.768956	+	0.639301i	$0.779224\pi$
$72$		0			0
$73$	−2.32280e8			−0.112046			−0.0560231	−	0.998429i	$-0.517842\pi$
$73$	−2.32280e8			−0.112046			−0.0560231	+	0.998429i	$0.517842\pi$
$74$	4.31071e8	−	2.48879e8i	0.194263	−	0.112158i
$75$		0			0
$76$	−3.56226e9	+	6.17002e9i	−1.40494	+	2.43343i
$77$	−1.96672e9	−	1.13548e9i	−0.726588	−	0.419496i
$78$		0			0
$79$	−1.60607e8	−	2.78180e8i	−0.0521951	−	0.0904045i	0.838747	−	0.544521i	$-0.183288\pi$
$79$	−1.60607e8	−	2.78180e8i	−0.0521951	−	0.0904045i	−0.890942	+	0.454116i	$0.849955\pi$
$80$			3.01762e9i			0.920905i
$81$		0			0
$82$	2.24910e8			0.0606653
$83$	5.60771e9	−	3.23761e9i	1.42362	−	0.821930i	0.427017	−	0.904243i	$-0.359564\pi$
$83$	5.60771e9	−	3.23761e9i	1.42362	−	0.821930i	0.996606	+	0.0823139i	$0.0262310\pi$
$84$		0			0
$85$	−1.30240e9	+	2.25583e9i	−0.293528	+	0.508406i
$86$	−9.42310e9	−	5.44043e9i	−2.00310	−	1.15649i
$87$		0			0
$88$	2.39186e9	+	4.14282e9i	0.453234	+	0.785024i
$89$			2.86904e9i			0.513792i	0.966439	+	0.256896i	$0.0826997\pi$
$89$			2.86904e9i			0.513792i	−0.966439	+	0.256896i	$0.917300\pi$
$90$		0			0
$91$	−3.00013e9			−0.480765
$92$	−2.76368e9	+	1.59561e9i	−0.419323	+	0.242096i
$93$		0			0
$94$	9.83813e9	−	1.70401e10i	1.34052	−	2.32185i
$95$	1.31414e10	+	7.58717e9i	1.69833	+	0.980532i
$96$		0			0
$97$	−3.81258e8	−	6.60359e8i	−0.0443977	−	0.0768991i	0.842973	−	0.537957i	$-0.180804\pi$
$97$	−3.81258e8	−	6.60359e8i	−0.0443977	−	0.0768991i	−0.887370	+	0.461057i	$0.847470\pi$
$98$		−	1.51808e10i		−	1.67944i
$99$		0			0
$100$	1.42002e10			1.42002
$101$	8.80726e8	−	5.08488e8i	0.0837981	−	0.0483809i	−0.457515	−	0.889202i	$-0.651261\pi$
$101$	8.80726e8	−	5.08488e8i	0.0837981	−	0.0483809i	0.541314	+	0.840821i	$0.317927\pi$
$102$		0			0
$103$	7.75977e9	−	1.34403e10i	0.669364	−	1.15937i	−0.308718	−	0.951154i	$-0.599900\pi$
$103$	7.75977e9	−	1.34403e10i	0.669364	−	1.15937i	0.978082	−	0.208219i	$-0.0667668\pi$
$104$	5.47299e9	+	3.15983e9i	0.449840	+	0.259715i
$105$		0			0
$106$	1.09067e10	+	1.88909e10i	0.815011	+	1.41164i
$107$		−	3.98588e9i		−	0.284188i	−0.989853	−	0.142094i	$-0.954617\pi$
$107$		−	3.98588e9i		−	0.284188i	0.989853	−	0.142094i	$-0.0453835\pi$
$108$		0			0
$109$	−1.40479e10			−0.913020			−0.456510	−	0.889718i	$-0.650901\pi$
$109$	−1.40479e10			−0.913020			−0.456510	+	0.889718i	$0.650901\pi$
$110$	1.86816e10	−	1.07858e10i	1.15998	−	0.669714i
$111$		0			0
$112$	−8.64857e9	+	1.49798e10i	−0.490743	+	0.849992i
$113$	−3.35190e9	−	1.93522e9i	−0.181928	−	0.105036i	0.406270	−	0.913753i	$-0.366829\pi$
$113$	−3.35190e9	−	1.93522e9i	−0.181928	−	0.105036i	−0.588198	+	0.808717i	$0.700162\pi$
$114$		0			0
$115$	3.39845e9	+	5.88630e9i	0.168963	+	0.292653i
$116$			2.30445e10i			1.09718i
$117$		0			0
$118$	−2.85049e10			−1.24598
$119$	−1.29305e10	+	7.46542e9i	−0.541851	+	0.312838i
$120$		0			0
$121$	−8.37455e9	+	1.45052e10i	−0.322875	+	0.559236i
$122$	−6.13097e10	−	3.53972e10i	−2.26845	−	1.30969i
$123$		0			0
$124$	−2.95688e10	−	5.12146e10i	−1.00861	−	1.74697i
$125$			1.01185e10i			0.331563i
$126$		0			0
$127$	−1.87211e10			−0.566647			−0.283324	−	0.959024i	$-0.591437\pi$
$127$	−1.87211e10			−0.566647			−0.283324	+	0.959024i	$0.591437\pi$
$128$	−5.43288e10	+	3.13667e10i	−1.58118	+	0.912892i
$129$		0			0
$130$	1.42489e10	−	2.46798e10i	0.383764	−	0.664699i
$131$	4.13770e10	+	2.38890e10i	1.07251	+	0.619215i	0.928867	−	0.370414i	$-0.120784\pi$
$131$	4.13770e10	+	2.38890e10i	1.07251	+	0.619215i	0.143645	+	0.989629i	$0.454118\pi$
$132$		0			0
$133$	4.34900e10	+	7.53269e10i	1.04504	+	1.81005i
$134$		−	1.18309e10i		−	0.273838i
$135$		0			0
$136$	3.14513e10			0.675996
$137$	5.58077e9	−	3.22206e9i	0.115636	−	0.0667622i	−0.441067	−	0.897474i	$-0.645400\pi$
$137$	5.58077e9	−	3.22206e9i	0.115636	−	0.0667622i	0.556702	+	0.830712i	$0.312066\pi$
$138$		0			0
$139$	−3.41907e10	+	5.92201e10i	−0.658923	+	1.14129i	0.321972	+	0.946749i	$0.395654\pi$
$139$	−3.41907e10	+	5.92201e10i	−0.658923	+	1.14129i	−0.980895	+	0.194539i	$0.937679\pi$
$140$	1.64565e11	+	9.50116e10i	3.05983	+	1.76659i
$141$		0			0
$142$	−6.28027e10	−	1.08777e11i	−1.08777	−	1.88407i
$143$		−	1.21385e10i		−	0.202994i
$144$		0			0
$145$	4.90820e10			0.765741
$146$	1.09528e10	−	6.32358e9i	0.165105	−	0.0953232i
$147$		0			0
$148$	−8.87027e9	+	1.53638e10i	−0.124919	+	0.216366i
$149$	−5.74744e10	−	3.31828e10i	−0.782606	−	0.451838i	0.0547473	−	0.998500i	$-0.482565\pi$
$149$	−5.74744e10	−	3.31828e10i	−0.782606	−	0.451838i	−0.837353	+	0.546663i	$0.815898\pi$
$150$		0			0
$151$	−1.52809e10	−	2.64672e10i	−0.194654	−	0.337151i	0.752133	−	0.659011i	$-0.229025\pi$
$151$	−1.52809e10	−	2.64672e10i	−0.194654	−	0.337151i	−0.946787	+	0.321861i	$0.895692\pi$
$152$		−	1.83220e11i		−	2.25816i
$153$		0			0
$154$	1.23649e11			1.42754
$155$	−1.09081e11	+	6.29778e10i	−1.21924	+	0.703929i
$156$		0			0
$157$	8.41303e10	−	1.45718e11i	0.881971	−	1.52762i	0.0328251	−	0.999461i	$-0.489550\pi$
$157$	8.41303e10	−	1.45718e11i	0.881971	−	1.52762i	0.849146	−	0.528158i	$-0.177117\pi$
$158$	1.51463e10	+	8.74472e9i	0.153823	+	0.0888097i
$159$		0			0
$160$	2.34575e10	+	4.06296e10i	0.223709	+	0.387475i
$161$			3.89602e10i			0.360157i
$162$		0			0
$163$	−2.06594e11			−1.79548			−0.897739	−	0.440529i	$-0.854791\pi$
$163$	−2.06594e11			−1.79548			−0.897739	+	0.440529i	$0.854791\pi$
$164$	−6.94207e9	+	4.00801e9i	−0.0585153	+	0.0337838i
$165$		0			0
$166$	−1.76281e11	+	3.05328e11i	−1.39851	+	2.42229i
$167$	−7.47591e10	−	4.31622e10i	−0.575548	−	0.332293i	0.183814	−	0.982961i	$-0.441156\pi$
$167$	−7.47591e10	−	4.31622e10i	−0.575548	−	0.332293i	−0.759362	+	0.650668i	$0.774489\pi$
$168$		0			0
$169$	6.09113e10	+	1.05501e11i	0.441839	+	0.765288i
$170$		−	1.41826e11i		−	0.998875i
$171$		0			0
$172$	3.87804e11			2.57614
$173$	1.22557e11	−	7.07580e10i	0.790872	−	0.456610i	−0.0493978	−	0.998779i	$-0.515730\pi$
$173$	1.22557e11	−	7.07580e10i	0.790872	−	0.456610i	0.840269	+	0.542169i	$0.182397\pi$
$174$		0			0
$175$	8.66815e10	−	1.50137e11i	0.528125	−	0.914739i
$176$	−6.06079e10	−	3.49920e10i	−0.358894	−	0.207208i
$177$		0			0
$178$	−7.81067e10	−	1.35285e11i	−0.437107	−	0.757092i
$179$			1.42065e10i			0.0773073i	0.999253	+	0.0386537i	$0.0123069\pi$
$179$			1.42065e10i			0.0773073i	−0.999253	+	0.0386537i	$0.987693\pi$
$180$		0			0
$181$	−4.39401e10			−0.226187			−0.113094	−	0.993584i	$-0.536076\pi$
$181$	−4.39401e10			−0.226187			−0.113094	+	0.993584i	$0.536076\pi$
$182$	1.41466e11	−	8.16752e10i	0.708425	−	0.409010i
$183$		0			0
$184$	4.10341e10	−	7.10732e10i	0.194561	−	0.336990i
$185$	3.27229e10	+	1.88926e10i	0.151006	+	0.0871831i
$186$		0			0
$187$	−3.02050e10	−	5.23166e10i	−0.132090	−	0.228787i
$188$			7.01280e11i			2.98609i
$189$		0			0
$190$	−8.26211e11			−3.33674
$191$	1.07489e11	−	6.20589e10i	0.422861	−	0.244139i	−0.273439	−	0.961889i	$-0.588161\pi$
$191$	1.07489e11	−	6.20589e10i	0.422861	−	0.244139i	0.696301	+	0.717750i	$0.254828\pi$
$192$		0			0
$193$	2.19924e11	−	3.80919e11i	0.821270	−	1.42248i	−0.0834668	−	0.996511i	$-0.526599\pi$
$193$	2.19924e11	−	3.80919e11i	0.821270	−	1.42248i	0.904737	−	0.425971i	$-0.140067\pi$
$194$	3.59551e10	+	2.07587e10i	0.130844	+	0.0755426i
$195$		0			0
$196$	2.70529e11	+	4.68570e11i	0.935263	+	1.61992i
$197$		−	4.41873e11i		−	1.48925i	−0.667485	−	0.744624i	$-0.732629\pi$
$197$		−	4.41873e11i		−	1.48925i	0.667485	−	0.744624i	$-0.267371\pi$
$198$		0			0
$199$	2.28125e11			0.730984			0.365492	−	0.930814i	$-0.380901\pi$
$199$	2.28125e11			0.730984			0.365492	+	0.930814i	$0.380901\pi$
$200$	−3.16258e11	+	1.82592e11i	−0.988306	+	0.570599i
$201$		0			0
$202$	−2.76861e10	+	4.79537e10i	−0.0823198	+	0.142582i
$203$	2.43648e11	+	1.40670e11i	0.706776	+	0.408057i
$204$		0			0
$205$	8.53655e9	+	1.47857e10i	0.0235783	+	0.0408389i
$206$			8.45006e11i			2.27784i
$207$		0			0
$208$	−9.24543e10			−0.237471
$209$	−3.04772e11	+	1.75960e11i	−0.764264	+	0.441248i
$210$		0			0
$211$	4.34706e10	−	7.52933e10i	0.103940	−	0.180030i	−0.809365	−	0.587307i	$-0.800188\pi$
$211$	4.34706e10	−	7.52933e10i	0.103940	−	0.180030i	0.913305	+	0.407277i	$0.133522\pi$
$212$	−6.73290e11	−	3.88724e11i	−1.57225	−	0.907742i
$213$		0			0
$214$	1.08511e11	+	1.87947e11i	0.241772	+	0.418762i
$215$		−	8.25973e11i		−	1.79793i
$216$		0			0
$217$	−7.21983e11			−1.50047
$218$	6.62406e11	−	3.82440e11i	1.34537	−	0.776750i
$219$		0			0
$220$	−3.84416e11	+	6.65828e11i	−0.745913	+	1.29196i
$221$	−6.91143e10	−	3.99032e10i	−0.131101	−	0.0756913i
$222$		0			0
$223$	−3.77470e11	−	6.53797e11i	−0.684476	−	1.18555i	−0.973601	−	0.228255i	$-0.926698\pi$
$223$	−3.77470e11	−	6.53797e11i	−0.684476	−	1.18555i	0.289126	−	0.957291i	$-0.406635\pi$
$224$			2.68919e11i			0.476850i
$225$		0			0
$226$	2.10738e11			0.357437
$227$	−4.05103e11	+	2.33886e11i	−0.672103	+	0.388039i	−0.796873	−	0.604147i	$-0.793514\pi$
$227$	−4.05103e11	+	2.33886e11i	−0.672103	+	0.388039i	0.124770	+	0.992186i	$0.460181\pi$
$228$		0			0
$229$	−3.05467e11	+	5.29084e11i	−0.485050	+	0.840131i	−0.999852	−	0.0171777i	$-0.994532\pi$
$229$	−3.05467e11	+	5.29084e11i	−0.485050	+	0.840131i	0.514803	+	0.857309i	$0.327865\pi$
$230$	−3.20496e11	−	1.85039e11i	−0.497948	−	0.287490i
$231$		0			0
$232$	−2.96316e11	−	5.13235e11i	−0.440875	−	0.763618i
$233$			5.80815e11i			0.845782i	0.906181	+	0.422891i	$0.138985\pi$
$233$			5.80815e11i			0.845782i	−0.906181	+	0.422891i	$0.861015\pi$
$234$		0			0
$235$	1.49364e12			2.08404
$236$	8.79832e11	−	5.07971e11i	1.20182	−	0.693871i
$237$		0			0
$238$	4.06476e11	−	7.04038e11i	0.532293	−	0.921958i
$239$	−3.13716e11	−	1.81124e11i	−0.402298	−	0.232267i	0.285177	−	0.958475i	$-0.407948\pi$
$239$	−3.13716e11	−	1.81124e11i	−0.402298	−	0.232267i	−0.687475	+	0.726208i	$0.741281\pi$
$240$		0			0
$241$	2.55995e11	+	4.43397e11i	0.314881	+	0.545390i	0.979412	−	0.201870i	$-0.0647019\pi$
$241$	2.55995e11	+	4.43397e11i	0.314881	+	0.545390i	−0.664531	+	0.747261i	$0.731369\pi$
$242$		−	9.11953e11i		−	1.09874i
$243$		0			0
$244$	2.52317e12			2.91741
$245$	9.97996e11	−	5.76193e11i	1.13057	−	0.652736i
$246$		0			0
$247$	−2.32457e11	+	4.02627e11i	−0.252847	+	0.437943i
$248$	1.31708e12	+	7.60416e11i	1.40396	+	0.810574i
$249$		0			0
$250$	−2.75465e11	−	4.77120e11i	−0.282076	−	0.488570i
$251$			1.92469e11i			0.193193i	0.995324	+	0.0965967i	$0.0307957\pi$
$251$			1.92469e11i			0.193193i	−0.995324	+	0.0965967i	$0.969204\pi$
$252$		0			0
$253$	−1.57632e11			−0.152070
$254$	8.82761e11	−	5.09662e11i	0.834977	−	0.482074i
$255$		0			0
$256$	1.00864e12	−	1.74702e12i	0.917352	−	1.58890i
$257$	7.33365e11	+	4.23408e11i	0.654116	+	0.377654i	0.790031	−	0.613067i	$-0.210064\pi$
$257$	7.33365e11	+	4.23408e11i	0.654116	+	0.377654i	−0.135916	+	0.990720i	$0.543398\pi$
$258$		0			0
$259$	1.08293e11	+	1.87569e11i	0.0929184	+	0.160939i
$260$			1.01569e12i			0.854856i
$261$		0			0
$262$	−2.60141e12			−2.10718
$263$	−1.86744e12	+	1.07817e12i	−1.48412	+	0.856855i	−0.999837	−	0.0180587i	$-0.994251\pi$
$263$	−1.86744e12	+	1.07817e12i	−1.48412	+	0.856855i	−0.484279	+	0.874914i	$0.660918\pi$
$264$		0			0
$265$	−8.27934e11	+	1.43402e12i	−0.633529	+	1.09730i
$266$	−4.10139e12	−	2.36794e12i	−3.07980	−	1.77812i
$267$		0			0
$268$	2.10832e11	+	3.65172e11i	0.152498	+	0.264134i
$269$			1.26825e12i			0.900414i	0.892924	+	0.450207i	$0.148650\pi$
$269$			1.26825e12i			0.900414i	−0.892924	+	0.450207i	$0.851350\pi$
$270$		0			0
$271$	4.98119e11			0.340790			0.170395	−	0.985376i	$-0.445496\pi$
$271$	4.98119e11			0.340790			0.170395	+	0.985376i	$0.445496\pi$
$272$	−3.98476e11	+	2.30060e11i	−0.267644	+	0.154525i
$273$		0			0
$274$	−1.75434e11	+	3.03861e11i	−0.113596	+	0.196753i
$275$	6.07452e11	+	3.50713e11i	0.386232	+	0.222991i
$276$		0			0
$277$	−2.40303e11	−	4.16217e11i	−0.147353	−	0.255223i	0.782895	−	0.622154i	$-0.213742\pi$
$277$	−2.40303e11	−	4.16217e11i	−0.147353	−	0.255223i	−0.930248	+	0.366930i	$0.880409\pi$
$278$		−	3.72323e12i		−	2.24231i
$279$		0			0
$280$	−4.88680e12			−2.83945
$281$	−1.86716e12	+	1.07800e12i	−1.06574	+	0.615303i	−0.927013	−	0.375028i	$-0.877633\pi$
$281$	−1.86716e12	+	1.07800e12i	−1.06574	+	0.615303i	−0.138722	+	0.990331i	$0.544300\pi$
$282$		0			0
$283$	−1.49624e12	+	2.59157e12i	−0.824270	+	1.42768i	0.0782053	+	0.996937i	$0.475081\pi$
$283$	−1.49624e12	+	2.59157e12i	−0.824270	+	1.42768i	−0.902476	+	0.430741i	$0.858252\pi$
$284$	3.87693e12	+	2.23834e12i	2.09844	+	1.21153i
$285$		0			0
$286$	3.30457e11	+	5.72369e11i	0.172697	+	0.299120i
$287$			9.78638e10i			0.0502588i
$288$		0			0
$289$	1.61882e12			0.802988
$290$	−2.31437e12	+	1.33620e12i	−1.12835	+	0.651453i
$291$		0			0
$292$	−2.25378e11	+	3.90366e11i	−0.106169	+	0.183890i
$293$	3.17381e12	+	1.83240e12i	1.46975	+	0.848559i	0.999424	−	0.0339356i	$-0.0108041\pi$
$293$	3.17381e12	+	1.83240e12i	1.46975	+	0.848559i	0.470323	+	0.882494i	$0.344137\pi$
$294$		0			0
$295$	−1.08191e12	−	1.87393e12i	−0.484265	−	0.838771i
$296$		−	4.56231e11i		−	0.200783i
$297$		0			0
$298$	3.61347e12			1.53760
$299$	−1.80345e11	+	1.04122e11i	−0.0754655	+	0.0435700i
$300$		0			0
$301$	2.36726e12	−	4.10021e12i	0.958105	−	1.65949i
$302$	1.44109e12	+	8.32011e11i	0.573661	+	0.331203i
$303$		0			0
$304$	1.34022e12	+	2.32133e12i	0.516189	+	0.894066i
$305$		−	5.37404e12i		−	2.03611i
$306$		0			0
$307$	−4.35003e12			−1.59515			−0.797573	−	0.603222i	$-0.793883\pi$
$307$	−4.35003e12			−1.59515			−0.797573	+	0.603222i	$0.793883\pi$
$308$	−3.81656e12	+	2.20349e12i	−1.37695	+	0.794982i
$309$		0			0
$310$	3.42901e12	−	5.93921e12i	1.19773	−	2.07453i
$311$	−2.62884e12	−	1.51776e12i	−0.903571	−	0.521677i	−0.0252139	−	0.999682i	$-0.508027\pi$
$311$	−2.62884e12	−	1.51776e12i	−0.903571	−	0.521677i	−0.878357	+	0.478005i	$0.841360\pi$
$312$		0			0
$313$	2.57463e12	+	4.45939e12i	0.857024	+	1.48441i	0.874755	+	0.484566i	$0.161022\pi$
$313$	2.57463e12	+	4.45939e12i	0.857024	+	1.48441i	−0.0177310	+	0.999843i	$0.505644\pi$
$314$			9.16144e12i			3.00134i
$315$		0			0
$316$	−6.23339e11			−0.197829
$317$	4.56688e12	−	2.63669e12i	1.42667	−	0.823688i	0.429814	−	0.902918i	$-0.358579\pi$
$317$	4.56688e12	−	2.63669e12i	1.42667	−	0.823688i	0.996856	+	0.0792293i	$0.0252459\pi$
$318$		0			0
$319$	−5.69149e11	+	9.85795e11i	−0.172295	+	0.298424i
$320$	−4.88826e12	−	2.82224e12i	−1.45681	−	0.841092i
$321$		0			0
$322$	−1.06065e12	−	1.83710e12i	−0.306403	−	0.530705i
$323$			2.31375e12i			0.658119i
$324$		0			0
$325$	9.26637e11			0.255560
$326$	9.74158e12	−	5.62431e12i	2.64571	−	1.52750i
$327$		0			0
$328$	1.03073e11	−	1.78528e11i	0.0271504	−	0.0470259i
$329$	7.41457e12	+	4.28080e12i	1.92356	+	1.11057i
$330$		0			0
$331$	−1.49992e12	−	2.59793e12i	−0.377509	−	0.653865i	0.613190	−	0.789935i	$-0.289886\pi$
$331$	−1.49992e12	−	2.59793e12i	−0.377509	−	0.653865i	−0.990699	+	0.136070i	$0.956553\pi$
$332$		−	1.25656e13i		−	3.11526i
$333$		0			0
$334$	4.70018e12			1.13079
$335$	7.77771e11	−	4.49046e11i	0.184343	−	0.106431i
$336$		0			0
$337$	−3.27911e12	+	5.67958e12i	−0.754408	+	1.30667i	0.191260	+	0.981539i	$0.438743\pi$
$337$	−3.27911e12	+	5.67958e12i	−0.754408	+	1.30667i	−0.945668	+	0.325134i	$0.894591\pi$
$338$	−5.74433e12	−	3.31649e12i	−1.30214	−	0.751788i
$339$		0			0
$340$	2.52740e12	+	4.37759e12i	0.556263	+	0.963475i
$341$		−	2.92113e12i		−	0.633548i
$342$		0			0
$343$	−8.67447e10			−0.0182714
$344$	−8.63695e12	+	4.98655e12i	−1.79295	+	1.03516i
$345$		0			0
$346$	−3.85263e12	+	6.67294e12i	−0.776920	+	1.34566i
$347$	−5.76565e12	−	3.32880e12i	−1.14604	−	0.661668i	−0.198123	−	0.980177i	$-0.563485\pi$
$347$	−5.76565e12	−	3.32880e12i	−1.14604	−	0.661668i	−0.947920	+	0.318509i	$0.896818\pi$
$348$		0			0
$349$	−1.83864e12	−	3.18462e12i	−0.355116	−	0.615079i	0.632022	−	0.774951i	$-0.282225\pi$
$349$	−1.83864e12	−	3.18462e12i	−0.355116	−	0.615079i	−0.987138	+	0.159871i	$0.948892\pi$
$350$			9.43925e12i			1.79720i
$351$		0			0
$352$	−1.08804e12			−0.201341
$353$	−5.13357e12	+	2.96387e12i	−0.936583	+	0.540737i	−0.888888	−	0.458125i	$-0.848521\pi$
$353$	−5.13357e12	+	2.96387e12i	−0.936583	+	0.540737i	−0.0476956	+	0.998862i	$0.515188\pi$
$354$		0			0
$355$	4.76739e12	−	8.25737e12i	0.845550	−	1.46454i
$356$	4.82167e12	+	2.78379e12i	0.843233	+	0.486841i
$357$		0			0
$358$	−3.86756e11	−	6.69881e11i	−0.0657691	−	0.113915i
$359$		−	3.82402e12i		−	0.641281i	−0.947201	−	0.320641i	$-0.896102\pi$
$359$		−	3.82402e12i		−	0.641281i	0.947201	−	0.320641i	$-0.103898\pi$
$360$		0			0
$361$	7.34776e12			1.19845
$362$	2.07192e12	−	1.19622e12i	0.333296	−	0.192428i
$363$		0			0
$364$	−2.91098e12	+	5.04196e12i	−0.455546	+	0.789029i
$365$	8.31431e11	+	4.80027e11i	0.128340	+	0.0740971i
$366$		0			0
$367$	−4.12826e12	−	7.15036e12i	−0.620065	−	1.07398i	−0.989473	−	0.144717i	$-0.953773\pi$
$367$	−4.12826e12	−	7.15036e12i	−0.620065	−	1.07398i	0.369408	−	0.929267i	$-0.379560\pi$
$368$			1.20063e12i			0.177897i
$369$		0			0
$370$	−2.05732e12			−0.296683
$371$	−8.21988e12	+	4.74575e12i	−1.16949	+	0.675205i
$372$		0			0
$373$	−4.03408e11	+	6.98723e11i	−0.0558728	+	0.0967745i	−0.892609	−	0.450832i	$-0.851127\pi$
$373$	−4.03408e11	+	6.98723e11i	−0.0558728	+	0.0967745i	0.836736	+	0.547606i	$0.184461\pi$
$374$	2.84853e12	+	1.64460e12i	0.389280	+	0.224751i
$375$		0			0
$376$	−9.01736e12	−	1.56185e13i	−1.19989	−	2.07826i
$377$			1.50378e12i			0.197459i
$378$		0			0
$379$	3.78438e12			0.483948			0.241974	−	0.970283i	$-0.422205\pi$
$379$	3.78438e12			0.483948			0.241974	+	0.970283i	$0.422205\pi$
$380$	2.55018e13	−	1.47234e13i	3.21849	−	1.85820i
$381$		0			0
$382$	−3.37898e12	+	5.85256e12i	−0.415402	+	0.719497i
$383$	1.03290e13	+	5.96345e12i	1.25333	+	0.723609i	0.971769	−	0.235935i	$-0.0758152\pi$
$383$	1.03290e13	+	5.96345e12i	1.25333	+	0.723609i	0.281559	+	0.959544i	$0.409149\pi$
$384$		0			0
$385$	4.69316e12	+	8.12879e12i	0.554832	+	0.960997i
$386$			2.39488e13i			2.79478i
$387$		0			0
$388$	−1.47972e12			−0.168275
$389$	−1.93383e10	+	1.11650e10i	−0.00217106	+	0.00125346i	−0.501085	−	0.865398i	$-0.667066\pi$
$389$	−1.93383e10	+	1.11650e10i	−0.00217106	+	0.00125346i	0.498914	+	0.866651i	$0.333732\pi$
$390$		0			0
$391$	−5.18190e11	+	8.97531e11i	−0.0567029	+	0.0982122i
$392$	−1.20502e13	−	6.95716e12i	−1.30185	−	0.751626i
$393$		0			0
$394$	1.20295e13	+	2.08358e13i	1.26697	+	2.19446i
$395$			1.32763e12i			0.138068i
$396$		0			0
$397$	−1.18603e12			−0.120266			−0.0601329	−	0.998190i	$-0.519152\pi$
$397$	−1.18603e12			−0.120266			−0.0601329	+	0.998190i	$0.519152\pi$
$398$	−1.07568e13	+	6.21047e12i	−1.07713	+	0.621884i
$399$		0			0
$400$	2.67125e12	−	4.62674e12i	0.260864	−	0.451830i
$401$	−1.39390e13	−	8.04771e12i	−1.34435	−	0.776159i	−0.356904	−	0.934141i	$-0.616168\pi$
$401$	−1.39390e13	−	8.04771e12i	−1.34435	−	0.776159i	−0.987442	+	0.157983i	$0.949501\pi$
$402$		0			0
$403$	−1.92952e12	−	3.34203e12i	−0.181520	−	0.314402i
$404$		−	1.97351e12i		−	0.183372i
$405$		0			0
$406$	−1.53184e13			−1.38862
$407$	−7.58902e11	+	4.38152e11i	−0.0679538	+	0.0392331i
$408$		0			0
$409$	−3.93802e12	+	6.82086e12i	−0.344082	+	0.595967i	−0.985187	−	0.171486i	$-0.945143\pi$
$409$	−3.93802e12	+	6.82086e12i	−0.344082	+	0.595967i	0.641105	+	0.767453i	$0.278476\pi$
$410$	−8.05052e11	−	4.64797e11i	−0.0694872	−	0.0401184i
$411$		0			0
$412$	−1.50584e13	−	2.60819e13i	−1.26851	−	2.19712i
$413$		−	1.24032e13i		−	1.03224i
$414$		0			0
$415$	−2.67633e13			−2.17419
$416$	−1.24482e12	+	7.18695e11i	−0.0999169	+	0.0576870i
$417$		0			0
$418$	9.58065e12	−	1.65942e13i	0.750782	−	1.30039i
$419$	−1.53912e13	−	8.88611e12i	−1.19180	−	0.688085i	−0.233083	−	0.972457i	$-0.574882\pi$
$419$	−1.53912e13	−	8.88611e12i	−1.19180	−	0.688085i	−0.958714	+	0.284372i	$0.908215\pi$
$420$		0			0
$421$	1.10659e13	+	1.91668e13i	0.836715	+	1.44923i	0.892626	+	0.450798i	$0.148860\pi$
$421$	1.10659e13	+	1.91668e13i	0.836715	+	1.44923i	−0.0559110	+	0.998436i	$0.517806\pi$
$422$			4.73377e12i			0.353708i
$423$		0			0
$424$	1.99935e13			1.45902
$425$	3.99379e12	−	2.30581e12i	0.288032	−	0.166295i
$426$		0			0
$427$	1.54021e13	−	2.66773e13i	1.08503	−	1.87933i
$428$	−6.69861e12	−	3.86744e12i	−0.466408	−	0.269281i
$429$		0			0
$430$	2.24863e13	+	3.89473e13i	1.52959	+	2.64933i
$431$			9.55686e12i			0.642582i	0.946980	+	0.321291i	$0.104117\pi$
$431$			9.55686e12i			0.642582i	−0.946980	+	0.321291i	$0.895883\pi$
$432$		0			0
$433$	9.29619e12			0.610753			0.305376	−	0.952232i	$-0.401218\pi$
$433$	9.29619e12			0.610753			0.305376	+	0.952232i	$0.401218\pi$
$434$	3.40438e13	−	1.96552e13i	2.21101	−	1.27652i
$435$		0			0
$436$	−1.36305e13	+	2.36088e13i	−0.865127	+	1.49844i
$437$	5.22859e12	+	3.01873e12i	0.328078	+	0.189416i
$438$		0			0
$439$	5.58491e12	+	9.67335e12i	0.342526	+	0.593273i	0.984901	−	0.173118i	$-0.0553842\pi$
$439$	5.58491e12	+	9.67335e12i	0.342526	+	0.593273i	−0.642375	+	0.766390i	$0.722051\pi$
$440$		−	1.97719e13i		−	1.19891i
$441$		0			0
$442$	4.34528e12			0.257577
$443$	−1.02124e13	+	5.89614e12i	−0.598563	+	0.345580i	−0.768476	−	0.639879i	$-0.778985\pi$
$443$	−1.02124e13	+	5.89614e12i	−0.598563	+	0.345580i	0.169913	+	0.985459i	$0.445651\pi$
$444$		0			0
$445$	5.92913e12	−	1.02696e13i	0.339774	−	0.588507i
$446$	3.55979e13	+	2.05524e13i	2.01720	+	1.16463i
$447$		0			0
$448$	−1.61772e13	−	2.80197e13i	−0.896422	−	1.55265i
$449$			4.65881e12i			0.255295i	0.991820	+	0.127648i	$0.0407427\pi$
$449$			4.65881e12i			0.255295i	−0.991820	+	0.127648i	$0.959257\pi$
$450$		0			0
$451$	−3.95956e11			−0.0212209
$452$	−6.50461e12	+	3.75544e12i	−0.344770	+	0.199053i
$453$		0			0
$454$	1.27346e13	−	2.20570e13i	0.660247	−	1.14358i
$455$	1.07388e13	+	6.20002e12i	0.550677	+	0.317933i
$456$		0			0
$457$	−7.12120e11	−	1.23343e12i	−0.0357250	−	0.0618775i	0.847610	−	0.530620i	$-0.178041\pi$
$457$	−7.12120e11	−	1.23343e12i	−0.0357250	−	0.0618775i	−0.883335	+	0.468742i	$0.844707\pi$
$458$		−	3.32640e13i		−	1.65062i
$459$		0			0
$460$	1.31899e13			0.640401
$461$	2.14243e13	−	1.23693e13i	1.02897	−	0.594075i	0.112279	−	0.993677i	$-0.464185\pi$
$461$	2.14243e13	−	1.23693e13i	1.02897	−	0.594075i	0.916689	+	0.399602i	$0.130852\pi$
$462$		0			0
$463$	−6.25322e12	+	1.08309e13i	−0.293899	+	0.509049i	−0.974728	−	0.223394i	$-0.928286\pi$
$463$	−6.25322e12	+	1.08309e13i	−0.293899	+	0.509049i	0.680829	+	0.732443i	$0.261620\pi$
$464$	7.50844e12	+	4.33500e12i	0.349108	+	0.201558i
$465$		0			0
$466$	−1.58121e13	−	2.73873e13i	−0.719547	−	1.24629i
$467$		−	1.09634e13i		−	0.493585i	−0.969068	−	0.246792i	$-0.920623\pi$
$467$		−	1.09634e13i		−	0.493585i	0.969068	−	0.246792i	$-0.0793766\pi$
$468$		0			0
$469$	5.14790e12			0.226864
$470$	−7.04299e13	+	4.06627e13i	−3.07092	+	1.77299i
$471$		0			0
$472$	−1.30634e13	+	2.26265e13i	−0.557631	+	0.965845i
$473$	1.65894e13	+	9.57790e12i	0.700689	+	0.404543i
$474$		0			0
$475$	−1.34326e13	−	2.32659e13i	−0.555509	−	0.962170i
$476$			2.89744e13i			1.18571i
$477$		0			0
$478$	1.97237e13			0.790402
$479$	−1.92106e11	+	1.10912e11i	−0.00761837	+	0.00439847i	−0.503804	−	0.863818i	$-0.668067\pi$
$479$	−1.92106e11	+	1.10912e11i	−0.00761837	+	0.00439847i	0.496186	+	0.868216i	$0.334733\pi$
$480$		0			0
$481$	−5.78833e11	+	1.00257e12i	−0.0224816	+	0.0389393i
$482$	−2.41420e13	−	1.39384e13i	−0.927980	−	0.535769i
$483$		0			0
$484$	1.62514e13	+	2.81483e13i	0.611878	+	1.05980i
$485$			3.15162e12i			0.117442i
$486$		0			0
$487$	−3.58355e13			−1.30818			−0.654091	−	0.756416i	$-0.726949\pi$
$487$	−3.58355e13			−1.30818			−0.654091	+	0.756416i	$0.726949\pi$
$488$	−5.61947e13	+	3.24440e13i	−2.03047	+	1.17229i
$489$		0			0
$490$	−3.13725e13	+	5.43388e13i	−1.11063	+	1.92366i
$491$	−2.41929e13	−	1.39678e13i	−0.847776	−	0.489464i	0.0121238	−	0.999927i	$-0.496141\pi$
$491$	−2.41929e13	−	1.39678e13i	−0.847776	−	0.489464i	−0.859900	+	0.510463i	$0.829474\pi$
$492$		0			0
$493$	3.74196e12	+	6.48126e12i	0.128489	+	0.222549i
$494$		−	2.53136e13i		−	0.860436i
$495$		0			0
$496$	−2.22492e13			−0.741150
$497$	4.73316e13	−	2.73269e13i	1.56088	−	0.901174i
$498$		0			0
$499$	1.14646e13	−	1.98572e13i	0.370558	−	0.641825i	−0.619094	−	0.785317i	$-0.712500\pi$
$499$	1.14646e13	−	1.98572e13i	0.370558	−	0.641825i	0.989651	+	0.143493i	$0.0458333\pi$
$500$	1.70050e13	+	9.81783e12i	0.544159	+	0.314170i
$501$		0			0
$502$	−5.23976e12	−	9.07554e12i	−0.164359	−	0.284678i
$503$		−	8.51470e12i		−	0.264441i	−0.991220	−	0.132221i	$-0.957789\pi$
$503$		−	8.51470e12i		−	0.264441i	0.991220	−	0.132221i	$-0.0422108\pi$
$504$		0			0
$505$	−4.20334e12			−0.127979
$506$	7.43288e12	−	4.29138e12i	0.224081	−	0.129373i
$507$		0			0
$508$	−1.81648e13	+	3.14624e13i	−0.536924	+	0.929979i
$509$	3.04001e13	+	1.75515e13i	0.889786	+	0.513718i	0.873873	−	0.486155i	$-0.161601\pi$
$509$	3.04001e13	+	1.75515e13i	0.889786	+	0.513718i	0.0159136	+	0.999873i	$0.494934\pi$
$510$		0			0
$511$	2.75153e12	+	4.76580e12i	0.0789715	+	0.136783i
$512$			4.55975e13i			1.29596i
$513$		0			0
$514$	−4.61074e13			−1.28515
$515$	−5.55512e13	+	3.20725e13i	−1.53341	+	0.885312i
$516$		0			0
$517$	−1.73201e13	+	2.99992e13i	−0.468918	+	0.812190i
$518$	−1.02127e13	−	5.89632e12i	−0.273838	−	0.158100i
$519$		0			0
$520$	−1.30601e13	−	2.26208e13i	−0.343503	−	0.594965i
$521$			3.27964e13i			0.854353i	0.904168	+	0.427176i	$0.140492\pi$
$521$			3.27964e13i			0.854353i	−0.904168	+	0.427176i	$0.859508\pi$
$522$		0			0
$523$	4.33302e12			0.110734			0.0553672	−	0.998466i	$-0.482367\pi$
$523$	4.33302e12			0.110734			0.0553672	+	0.998466i	$0.482367\pi$
$524$	8.02950e13	−	4.63583e13i	2.03251	−	1.17347i
$525$		0			0
$526$	5.87039e13	−	1.01678e14i	1.45794	−	2.52522i
$527$	−1.66324e13	−	9.60273e12i	−0.409169	−	0.236234i
$528$		0			0
$529$	−1.93611e13	−	3.35344e13i	−0.467360	−	0.809492i
$530$		−	9.01585e13i		−	2.15589i
$531$		0			0
$532$	1.68791e14			3.96087
$533$	−4.53007e11	+	2.61544e11i	−0.0105310	+	0.00608007i
$534$		0			0
$535$	−8.23717e12	+	1.42672e13i	−0.187936	+	0.325514i
$536$	−9.39107e12	−	5.42194e12i	−0.212271	−	0.122555i
$537$		0			0
$538$	−3.45267e13	−	5.98019e13i	−0.766026	−	1.32680i
$539$			2.67259e13i			0.587474i
$540$		0			0
$541$	3.20898e13			0.692437			0.346218	−	0.938154i	$-0.387466\pi$
$541$	3.20898e13			0.692437			0.346218	+	0.938154i	$0.387466\pi$
$542$	−2.34879e13	+	1.35608e13i	−0.502167	+	0.289926i
$543$		0			0
$544$	−3.57676e12	+	6.19513e12i	−0.0750750	+	0.130034i
$545$	5.02837e13	+	2.90313e13i	1.04579	+	0.603787i
$546$		0			0
$547$	4.47678e13	+	7.75400e13i	0.914174	+	1.58340i	0.808107	+	0.589036i	$0.200493\pi$
$547$	4.47678e13	+	7.75400e13i	0.914174	+	1.58340i	0.106067	+	0.994359i	$0.466174\pi$
$548$		−	1.25053e13i		−	0.253041i
$549$		0			0
$550$	−3.81911e13			−0.758838
$551$	3.77568e13	−	2.17989e13i	0.743424	−	0.429216i
$552$		0			0
$553$	−3.80503e12	+	6.59051e12i	−0.0735754	+	0.127436i
$554$	2.26621e13	+	1.30840e13i	0.434262	+	0.250721i
$555$		0			0
$556$	6.63496e13	+	1.14921e14i	1.24872	+	2.16284i
$557$			9.22814e13i			1.72123i	0.509259	+	0.860613i	$0.329920\pi$
$557$			9.22814e13i			1.72123i	−0.509259	+	0.860613i	$0.670080\pi$
$558$		0			0
$559$	2.53063e13			0.463628
$560$	6.19140e13	−	3.57460e13i	1.12421	−	0.649065i
$561$		0			0
$562$	5.86951e13	−	1.01663e14i	1.04694	−	1.81335i
$563$	−2.60722e13	−	1.50528e13i	−0.460931	−	0.266119i	0.251505	−	0.967856i	$-0.419075\pi$
$563$	−2.60722e13	−	1.50528e13i	−0.460931	−	0.266119i	−0.712436	+	0.701737i	$0.752408\pi$
$564$		0			0
$565$	7.99861e12	+	1.38540e13i	0.138922	+	0.240621i
$566$		−	1.62934e14i		−	2.80499i
$567$		0			0
$568$	−1.15126e14			−1.94730
$569$	−3.50726e13	+	2.02491e13i	−0.588039	+	0.339504i	−0.764322	−	0.644835i	$-0.776926\pi$
$569$	−3.50726e13	+	2.02491e13i	−0.588039	+	0.339504i	0.176283	+	0.984340i	$0.443593\pi$
$570$		0			0
$571$	−2.43613e13	+	4.21950e13i	−0.401346	+	0.695152i	−0.993889	−	0.110387i	$-0.964791\pi$
$571$	−2.43613e13	+	4.21950e13i	−0.401346	+	0.695152i	0.592542	+	0.805539i	$0.298124\pi$
$572$	−2.03997e13	−	1.17778e13i	−0.333153	−	0.192346i
$573$		0			0
$574$	−2.66424e12	−	4.61459e12i	−0.0427576	−	0.0740583i
$575$		−	1.20335e13i		−	0.191448i
$576$		0			0
$577$	−7.65234e12			−0.119651			−0.0598253	−	0.998209i	$-0.519054\pi$
$577$	−7.65234e12			−0.119651			−0.0598253	+	0.998209i	$0.519054\pi$
$578$	−7.63326e13	+	4.40706e13i	−1.18323	+	0.683140i
$579$		0			0
$580$	4.76235e13	−	8.24864e13i	0.725574	−	1.25673i
$581$	−1.32855e14	−	7.67041e13i	−2.00677	−	1.15861i
$582$		0			0
$583$	−1.92013e13	−	3.32576e13i	−0.285093	−	0.493796i
$584$		−	1.15920e13i		−	0.170646i
$585$		0			0
$586$	−1.99540e14			−2.88764
$587$	3.75502e13	−	2.16796e13i	0.538792	−	0.311072i	−0.205797	−	0.978595i	$-0.565979\pi$
$587$	3.75502e13	−	2.16796e13i	0.538792	−	0.311072i	0.744589	+	0.667523i	$0.232645\pi$
$588$		0			0
$589$	−5.59409e13	+	9.68925e13i	−0.789138	+	1.36683i
$590$	1.02032e14	+	5.89080e13i	1.42717	+	0.823975i
$591$		0			0
$592$	3.33724e12	+	5.78028e12i	0.0458965	+	0.0794951i
$593$		−	5.18573e13i		−	0.707190i	−0.935399	−	0.353595i	$-0.884959\pi$
$593$		−	5.18573e13i		−	0.707190i	0.935399	−	0.353595i	$-0.115041\pi$
$594$		0			0
$595$	6.17118e13			0.827529
$596$	−1.11533e14	+	6.43937e13i	−1.48311	+	0.856273i
$597$		0			0
$598$	5.66924e12	−	9.81941e12i	0.0741342	−	0.128404i
$599$	−7.14641e13	−	4.12598e13i	−0.926731	−	0.535048i	−0.0409548	−	0.999161i	$-0.513040\pi$
$599$	−7.14641e13	−	4.12598e13i	−0.926731	−	0.535048i	−0.885776	+	0.464113i	$0.846373\pi$
$600$		0			0
$601$	−3.53774e13	−	6.12755e13i	−0.451184	−	0.781474i	0.547276	−	0.836952i	$-0.315665\pi$
$601$	−3.53774e13	−	6.12755e13i	−0.451184	−	0.781474i	−0.998460	+	0.0554786i	$0.982332\pi$
$602$			2.57784e14i			3.26042i
$603$		0			0
$604$	−5.93073e13			−0.737774
$605$	5.99523e13	−	3.46135e13i	0.739655	−	0.427040i
$606$		0			0
$607$	−3.34887e13	+	5.80042e13i	−0.406401	+	0.703908i	−0.994483	−	0.104893i	$-0.966550\pi$
$607$	−3.34887e13	+	5.80042e13i	−0.406401	+	0.703908i	0.588082	+	0.808801i	$0.299883\pi$
$608$	3.60899e13	+	2.08365e13i	0.434378	+	0.250788i
$609$		0			0
$610$	1.46303e14	+	2.53404e14i	1.73222	+	3.00029i
$611$			4.57623e13i			0.537405i
$612$		0			0
$613$	−7.18483e12			−0.0830069			−0.0415035	−	0.999138i	$-0.513215\pi$
$613$	−7.18483e12			−0.0830069			−0.0415035	+	0.999138i	$0.513215\pi$
$614$	2.05118e14	−	1.18425e14i	2.35051	−	1.35707i
$615$		0			0
$616$	5.66668e13	−	9.81498e13i	0.638889	−	1.10659i
$617$	4.77180e13	+	2.75500e13i	0.533650	+	0.308103i	0.742501	−	0.669844i	$-0.233639\pi$
$617$	4.77180e13	+	2.75500e13i	0.533650	+	0.308103i	−0.208852	+	0.977947i	$0.566973\pi$
$618$		0			0
$619$	−4.51475e13	−	7.81978e13i	−0.496799	−	0.860481i	0.503194	−	0.864173i	$-0.332158\pi$
$619$	−4.51475e13	−	7.81978e13i	−0.496799	−	0.860481i	−0.999993	+	0.00369262i	$0.998825\pi$
$620$			2.44426e14i			2.66802i
$621$		0			0
$622$	1.65278e14			1.77526
$623$	5.88655e13	−	3.39860e13i	0.627221	−	0.362126i
$624$		0			0
$625$	5.66408e13	−	9.81047e13i	0.593922	−	1.02870i
$626$	−2.42804e14	−	1.40183e14i	−2.52572	−	1.45822i
$627$		0			0
$628$	−1.63261e14	−	2.82776e14i	−1.67141	−	2.89498i
$629$			5.76140e12i			0.0585160i
$630$		0			0
$631$	3.60070e13			0.359948			0.179974	−	0.983671i	$-0.442399\pi$
$631$	3.60070e13			0.359948			0.179974	+	0.983671i	$0.442399\pi$
$632$	1.38827e13	−	8.01516e12i	0.137685	−	0.0794927i
$633$		0			0
$634$	−1.43562e14	+	2.48657e14i	−1.40150	+	2.42747i
$635$	6.70110e13	+	3.86888e13i	0.649049	+	0.374728i
$636$		0			0
$637$	1.76535e13	+	3.05767e13i	0.168319	+	0.291537i
$638$		−	6.19779e13i		−	0.586319i
$639$		0			0
$640$	2.59288e14			2.41481
$641$	−8.30937e13	+	4.79742e13i	−0.767853	+	0.443320i	−0.832108	−	0.554614i	$-0.812866\pi$
$641$	−8.30937e13	+	4.79742e13i	−0.767853	+	0.443320i	0.0642554	+	0.997933i	$0.479533\pi$
$642$		0			0
$643$	7.22501e13	−	1.25141e14i	0.657331	−	1.13853i	−0.323974	−	0.946066i	$-0.605019\pi$
$643$	7.22501e13	−	1.25141e14i	0.657331	−	1.13853i	0.981304	−	0.192464i	$-0.0616478\pi$
$644$	6.54759e13	+	3.78025e13i	0.591088	+	0.341265i
$645$		0			0
$646$	−6.29895e13	−	1.09101e14i	−0.559894	−	0.969764i
$647$			4.20740e13i			0.371101i	0.982635	+	0.185551i	$0.0594069\pi$
$647$			4.20740e13i			0.371101i	−0.982635	+	0.185551i	$0.940593\pi$
$648$		0			0
$649$	5.01831e13			0.435847
$650$	−4.36939e13	+	2.52267e13i	−0.376577	+	0.217417i
$651$		0			0
$652$	−2.00455e14	+	3.47199e14i	−1.70130	+	2.94673i
$653$	−8.00162e13	−	4.61973e13i	−0.673925	−	0.389091i	0.123637	−	0.992328i	$-0.460544\pi$
$653$	−8.00162e13	−	4.61973e13i	−0.673925	−	0.389091i	−0.797562	+	0.603237i	$0.793877\pi$
$654$		0			0
$655$	−9.87374e13	−	1.71018e14i	−0.818984	−	1.41852i
$656$			3.01585e12i			0.0248251i
$657$		0			0
$658$	−4.66161e14			−3.77926
$659$	1.80488e13	−	1.04205e13i	0.145218	−	0.0838418i	−0.425630	−	0.904897i	$-0.639948\pi$
$659$	1.80488e13	−	1.04205e13i	0.145218	−	0.0838418i	0.570849	+	0.821055i	$0.306614\pi$
$660$		0			0
$661$	7.32811e13	−	1.26927e14i	0.580744	−	1.00588i	−0.414647	−	0.909982i	$-0.636095\pi$
$661$	7.32811e13	−	1.26927e14i	0.580744	−	1.00588i	0.995391	−	0.0958959i	$-0.0305716\pi$
$662$	1.41452e14	+	8.16673e13i	1.11255	+	0.642330i
$663$		0			0
$664$	1.61574e14	+	2.79855e14i	1.25179	+	2.16817i
$665$		−	3.59503e14i		−	2.76436i
$666$		0			0
$667$	1.95284e13			0.147923
$668$	−1.45075e14	+	8.37593e13i	−1.09072	+	0.629725i
$669$		0			0
$670$	−2.44496e13	+	4.23480e13i	−0.181091	+	0.313660i
$671$	1.07936e14	+	6.23168e13i	0.793512	+	0.458134i
$672$		0			0
$673$	4.77127e11	+	8.26408e11i	0.00345588	+	0.00598576i	0.867748	−	0.497004i	$-0.165567\pi$
$673$	4.77127e11	+	8.26408e11i	0.00345588	+	0.00598576i	−0.864292	+	0.502990i	$0.832233\pi$
$674$		−	3.57081e14i		−	2.56725i
$675$		0			0
$676$	2.36406e14			1.67465
$677$	−1.52267e14	+	8.79112e13i	−1.07068	+	0.618160i	−0.928368	−	0.371662i	$-0.878788\pi$
$677$	−1.52267e14	+	8.79112e13i	−1.07068	+	0.618160i	−0.142316	+	0.989821i	$0.545455\pi$
$678$		0			0
$679$	−9.03260e12	+	1.56449e13i	−0.0625841	+	0.108399i
$680$	−1.12578e14	−	6.49969e13i	−0.774299	−	0.447041i
$681$		0			0
$682$	7.95248e13	+	1.37741e14i	0.538990	+	0.933558i
$683$			1.76129e14i			1.18503i	0.805560	+	0.592514i	$0.201864\pi$
$683$			1.76129e14i			1.18503i	−0.805560	+	0.592514i	$0.798136\pi$
$684$		0			0
$685$	−2.66347e13			−0.176601
$686$	4.09029e12	−	2.36153e12i	0.0269236	−	0.0155444i
$687$		0			0
$688$	7.29513e13	−	1.26355e14i	0.473250	−	0.819694i
$689$	−4.39358e13	−	2.53663e13i	−0.282958	−	0.163366i
$690$		0			0
$691$	7.21593e13	+	1.24984e14i	0.458039	+	0.793346i	0.998857	−	0.0477930i	$-0.0152188\pi$
$691$	7.21593e13	+	1.24984e14i	0.458039	+	0.793346i	−0.540819	+	0.841139i	$0.681885\pi$
$692$		−	2.74622e14i		−	1.73063i
$693$		0			0
$694$	3.62492e14			2.25165
$695$	2.44767e14	−	1.41316e14i	1.50949	−	0.871502i
$696$		0			0
$697$	−1.30164e12	+	2.25450e12i	−0.00791272	+	0.0137052i
$698$	1.73396e14	+	1.00110e14i	1.04656	+	0.604229i
$699$		0			0
$700$	−1.68212e14	−	2.91351e14i	−1.00084	−	1.73351i
$701$			3.35226e13i			0.198038i	0.995086	+	0.0990189i	$0.0315704\pi$
$701$			3.35226e13i			0.198038i	−0.995086	+	0.0990189i	$0.968430\pi$
$702$		0			0
$703$	3.35632e13			0.195473
$704$	1.13367e14	−	6.54527e13i	0.655579	−	0.378498i
$705$		0			0
$706$	1.61376e14	−	2.79512e14i	0.920061	−	1.59359i
$707$	−2.08658e13	−	1.20469e13i	−0.118124	−	0.0681988i
$708$		0			0
$709$	−3.23633e13	−	5.60549e13i	−0.180643	−	0.312883i	0.761457	−	0.648216i	$-0.224485\pi$
$709$	−3.23633e13	−	5.60549e13i	−0.180643	−	0.312883i	−0.942100	+	0.335333i	$0.891151\pi$
$710$			5.19149e14i			2.87740i
$711$		0			0
$712$	−1.43181e14			−0.782500
$713$	−4.34002e13	+	2.50571e13i	−0.235529	+	0.135983i
$714$		0			0
$715$	−2.50852e13	+	4.34489e13i	−0.134242	+	0.232514i
$716$	2.38752e13	+	1.37843e13i	0.126876	+	0.0732522i
$717$		0			0
$718$	1.04105e14	+	1.80315e14i	0.545569	+	0.944953i
$719$		−	1.06995e14i		−	0.556823i	−0.960462	−	0.278411i	$-0.910192\pi$
$719$		−	1.06995e14i		−	0.556823i	0.960462	−	0.278411i	$-0.0898079\pi$
$720$		0			0
$721$	−3.67682e14			−1.88710
$722$	−3.46471e14	+	2.00035e14i	−1.76596	+	1.01958i
$723$		0			0
$724$	−4.26345e13	+	7.38451e13i	−0.214323	+	0.371218i
$725$	−7.52544e13	−	4.34482e13i	−0.375701	−	0.216911i
$726$		0			0
$727$	2.72924e13	+	4.72719e13i	0.134391	+	0.232772i	0.925365	−	0.379078i	$-0.123759\pi$
$727$	2.72924e13	+	4.72719e13i	0.134391	+	0.232772i	−0.790974	+	0.611850i	$0.790426\pi$
$728$		−	1.49722e14i		−	0.732201i
$729$		0			0
$730$	−5.22729e13			−0.252152
$731$	1.09070e14	−	6.29714e13i	0.522537	−	0.301687i
$732$		0			0
$733$	9.81100e13	−	1.69931e14i	0.463653	−	0.803071i	−0.535486	−	0.844544i	$-0.679872\pi$
$733$	9.81100e13	−	1.69931e14i	0.463653	−	0.803071i	0.999140	+	0.0414728i	$0.0132050\pi$
$734$	3.89322e14	+	2.24775e14i	1.82738	+	1.05504i
$735$		0			0
$736$	9.33311e12	+	1.61654e13i	0.0432153	+	0.0748510i
$737$			2.08284e13i			0.0957894i
$738$		0			0
$739$	7.34223e13			0.333124			0.166562	−	0.986031i	$-0.446733\pi$
$739$	7.34223e13			0.333124			0.166562	+	0.986031i	$0.446733\pi$
$740$	6.35011e13	−	3.66624e13i	0.286169	−	0.165220i
$741$		0			0
$742$	2.58396e14	−	4.47555e14i	1.14886	−	1.98988i
$743$	−2.26877e14	−	1.30988e14i	−1.00195	−	0.578477i	−0.0931261	−	0.995654i	$-0.529686\pi$
$743$	−2.26877e14	−	1.30988e14i	−1.00195	−	0.578477i	−0.908825	+	0.417178i	$0.863019\pi$
$744$		0			0
$745$	1.37151e14	+	2.37552e14i	0.597608	+	1.03509i
$746$		−	4.39294e13i		−	0.190135i
$747$		0			0
$748$	−1.17230e14			−0.500646
$749$	−8.17802e13	+	4.72158e13i	−0.346928	+	0.200299i
$750$		0			0
$751$	−1.58058e14	+	2.73764e14i	−0.661631	+	1.14598i	0.318556	+	0.947904i	$0.396802\pi$
$751$	−1.58058e14	+	2.73764e14i	−0.661631	+	1.14598i	−0.980187	+	0.198075i	$0.936531\pi$
$752$	2.28493e14	+	1.31921e14i	0.950132	+	0.548559i
$753$		0			0
$754$	−4.09388e13	−	7.09081e13i	−0.167988	−	0.290964i
$755$			1.26317e14i			0.514905i
$756$		0			0
$757$	−2.05979e14			−0.828597			−0.414299	−	0.910141i	$-0.635973\pi$
$757$	−2.05979e14			−0.828597			−0.414299	+	0.910141i	$0.635973\pi$
$758$	−1.78446e14	+	1.03026e14i	−0.713116	+	0.411718i
$759$		0			0
$760$	−3.78641e14	+	6.55825e14i	−1.49334	+	2.58654i
$761$	1.93859e14	+	1.11924e14i	0.759560	+	0.438532i	0.829138	−	0.559044i	$-0.188832\pi$
$761$	1.93859e14	+	1.11924e14i	0.759560	+	0.438532i	−0.0695775	+	0.997577i	$0.522165\pi$
$762$		0			0
$763$	1.66409e14	+	2.88228e14i	0.643507	+	1.11459i
$764$		−	2.40860e14i		−	0.925331i
$765$		0			0
$766$	−6.49395e14			−2.46244
$767$	5.74138e13	−	3.31478e13i	0.216291	−	0.124876i
$768$		0			0
$769$	2.42658e13	−	4.20295e13i	0.0902323	−	0.156287i	−0.817377	−	0.576104i	$-0.804572\pi$
$769$	2.42658e13	−	4.20295e13i	0.0902323	−	0.156287i	0.907609	+	0.419817i	$0.137906\pi$
$770$	−4.42595e14	−	2.55532e14i	−1.63513	−	0.944044i
$771$		0			0
$772$	−4.26778e14	−	7.39202e14i	−1.55638	−	2.69573i
$773$			3.77649e14i			1.36833i	0.729327	+	0.684165i	$0.239833\pi$
$773$			3.77649e14i			1.36833i	−0.729327	+	0.684165i	$0.760167\pi$
$774$		0			0
$775$	2.22996e14			0.797606
$776$	3.29555e13	−	1.90269e13i	0.117117	−	0.0676174i
$777$		0			0
$778$	6.07911e11	−	1.05293e12i	0.00213276	−	0.00369405i
$779$	1.31336e13	+	7.58271e12i	0.0457823	+	0.0264324i
$780$		0			0
$781$	1.10564e14	+	1.91503e14i	0.380505	+	0.659053i
$782$		−	5.64287e13i		−	0.192959i
$783$		0			0
$784$	2.03561e14			0.687250
$785$	−6.02278e14	+	3.47725e14i	−2.02045	+	1.16651i
$786$		0			0
$787$	−1.04370e14	+	1.80774e14i	−0.345701	+	0.598772i	−0.985481	−	0.169787i	$-0.945692\pi$
$787$	−1.04370e14	+	1.80774e14i	−0.345701	+	0.598772i	0.639780	+	0.768558i	$0.279025\pi$
$788$	−7.42606e14	−	4.28744e14i	−2.44415	−	1.41113i
$789$		0			0
$790$	−3.61435e13	−	6.26023e13i	−0.117461	−	0.203449i
$791$			9.16968e13i			0.296123i
$792$		0			0
$793$	1.64651e14			0.525046
$794$	5.59250e13	−	3.22883e13i	0.177216	−	0.102316i
$795$		0			0
$796$	2.21347e14	−	3.83384e14i	0.692640	−	1.19969i
$797$	1.01491e14	+	5.85958e13i	0.315599	+	0.182211i	0.649429	−	0.760422i	$-0.275008\pi$
$797$	1.01491e14	+	5.85958e13i	0.315599	+	0.182211i	−0.333830	+	0.942633i	$0.608341\pi$
$798$		0			0
$799$	1.13874e14	+	1.97235e14i	0.349695	+	0.605689i
$800$		−	8.30600e13i		−	0.253479i
$801$		0			0
$802$	8.76361e14			2.64126
$803$	−1.92824e13	+	1.11327e13i	−0.0577541	+	0.0333443i
$804$		0			0
$805$	8.05146e13	−	1.39455e14i	0.238175	−	0.412530i
$806$	1.81966e14	+	1.05058e14i	0.534954	+	0.308856i
$807$		0			0
$808$	2.53763e13	+	4.39530e13i	0.0736836	+	0.127624i
$809$		−	2.02903e13i		−	0.0585526i	−0.999571	−	0.0292763i	$-0.990680\pi$
$809$		−	2.02903e13i		−	0.0585526i	0.999571	−	0.0292763i	$-0.00932027\pi$
$810$		0			0
$811$	−6.69394e14			−1.90800			−0.953999	−	0.299810i	$-0.903077\pi$
$811$	−6.69394e14			−1.90800			−0.953999	+	0.299810i	$0.903077\pi$
$812$	4.72816e14	−	2.72980e14i	1.33940	−	0.773305i
$813$		0			0
$814$	2.38565e13	−	4.13206e13i	0.0667550	−	0.115623i
$815$	7.39490e14	+	4.26945e14i	2.05657	+	1.18736i
$816$		0			0
$817$	−3.66841e14	−	6.35388e14i	−1.00779	−	1.74554i
$818$		−	4.28834e14i		−	1.17091i
$819$		0			0
$820$	3.31316e13			0.0893661
$821$	1.74892e14	−	1.00974e14i	0.468872	−	0.270703i	−0.246896	−	0.969042i	$-0.579410\pi$
$821$	1.74892e14	−	1.00974e14i	0.468872	−	0.270703i	0.715767	+	0.698339i	$0.246077\pi$
$822$		0			0
$823$	2.29140e13	−	3.96883e13i	0.0606879	−	0.105115i	−0.834085	−	0.551636i	$-0.814004\pi$
$823$	2.29140e13	−	3.96883e13i	0.0606879	−	0.105115i	0.894773	+	0.446521i	$0.147337\pi$
$824$	6.70744e14	+	3.87254e14i	1.76572	+	1.01944i
$825$		0			0
$826$	3.37663e14	+	5.84850e14i	0.878179	+	1.52105i
$827$		−	6.19611e14i		−	1.60174i	−0.598840	−	0.800869i	$-0.704371\pi$
$827$		−	6.19611e14i		−	1.60174i	0.598840	−	0.800869i	$-0.295629\pi$
$828$		0			0
$829$	2.59623e14			0.663088			0.331544	−	0.943440i	$-0.392430\pi$
$829$	2.59623e14			0.663088			0.331544	+	0.943440i	$0.392430\pi$
$830$	1.26197e15	−	7.28601e14i	3.20376	−	1.84969i
$831$		0			0
$832$	8.64680e13	−	1.49767e14i	0.216890	−	0.375664i
$833$	1.52172e14	+	8.78568e13i	0.379412	+	0.219054i
$834$		0			0
$835$	1.78397e14	+	3.08992e14i	0.439496	+	0.761229i
$836$			6.82926e14i			1.67241i
$837$		0			0
$838$	9.67660e14			2.34155
$839$	−9.22315e13	+	5.32499e13i	−0.221855	+	0.128088i	−0.606809	−	0.794848i	$-0.707551\pi$
$839$	−9.22315e13	+	5.32499e13i	−0.221855	+	0.128088i	0.384954	+	0.922936i	$0.374217\pi$
$840$		0			0
$841$	−1.39844e14	+	2.42218e14i	−0.332403	+	0.575739i
$842$	−1.04359e15	−	6.02517e14i	−2.46587	−	1.42367i
$843$		0			0
$844$	−8.43578e13	−	1.46112e14i	−0.196976	−	0.341172i
$845$		−	5.03514e14i		−	1.16877i
$846$		0			0
$847$	3.96812e14			0.910265
$848$	−2.53311e14	+	1.46249e14i	−0.577662	+	0.333514i
$849$		0			0
$850$	−1.25547e14	+	2.17453e14i	−0.282951	+	0.490085i
$851$	1.30195e13	+	7.51683e12i	0.0291707	+	0.0168417i
$852$		0			0
$853$	−4.28236e14	−	7.41727e14i	−0.948284	−	1.64248i	−0.749038	−	0.662527i	$-0.769484\pi$
$853$	−4.28236e14	−	7.41727e14i	−0.948284	−	1.64248i	−0.199246	−	0.979950i	$-0.563849\pi$
$854$			1.67723e15i			3.69235i
$855$		0			0
$856$	1.98917e14			0.432815
$857$	−2.60383e14	+	1.50332e14i	−0.563260	+	0.325198i	−0.754453	−	0.656354i	$-0.772098\pi$
$857$	−2.60383e14	+	1.50332e14i	−0.563260	+	0.325198i	0.191193	+	0.981552i	$0.438764\pi$
$858$		0			0
$859$	2.28946e14	−	3.96546e14i	0.489517	−	0.847868i	−0.510411	−	0.859931i	$-0.670507\pi$
$859$	2.28946e14	−	3.96546e14i	0.489517	−	0.847868i	0.999927	+	0.0120631i	$0.00383990\pi$
$860$	−1.38812e15	−	8.01430e14i	−2.95076	−	1.70362i
$861$		0			0
$862$	−2.60175e14	−	4.50637e14i	−0.546676	−	0.946870i
$863$			1.19624e14i			0.249899i	0.992163	+	0.124949i	$0.0398768\pi$
$863$			1.19624e14i			0.249899i	−0.992163	+	0.124949i	$0.960123\pi$
$864$		0			0
$865$	−5.84911e14			−1.20784
$866$	−4.38345e14	+	2.53079e14i	−0.899968	+	0.519597i
$867$		0			0
$868$	−7.00530e14	+	1.21335e15i	−1.42177	+	2.46257i
$869$	−2.66651e13	−	1.53951e13i	−0.0538077	−	0.0310659i
$870$		0			0
$871$	1.37579e13	+	2.38294e13i	0.0274450	+	0.0475360i
$872$		−	7.01068e14i		−	1.39052i
$873$		0			0
$874$	−3.28726e14			−0.644581
$875$	2.07606e14	−	1.19861e14i	0.404762	−	0.233689i
$876$		0			0
$877$	−1.77392e14	+	3.07252e14i	−0.341929	+	0.592239i	−0.984791	−	0.173743i	$-0.944414\pi$
$877$	−1.77392e14	+	3.07252e14i	−0.341929	+	0.592239i	0.642862	+	0.765982i	$0.277747\pi$
$878$	−5.26693e14	−	3.04087e14i	−1.00945	−	0.582807i
$879$		0			0
$880$	1.44628e14	+	2.50503e14i	0.274056	+	0.474679i
$881$			1.31615e14i			0.247985i	0.992283	+	0.123992i	$0.0395698\pi$
$881$			1.31615e14i			0.247985i	−0.992283	+	0.123992i	$0.960430\pi$
$882$		0			0
$883$	2.50669e14			0.466978			0.233489	−	0.972359i	$-0.424986\pi$
$883$	2.50669e14			0.466978			0.233489	+	0.972359i	$0.424986\pi$
$884$	−1.34121e14	+	7.74349e13i	−0.248448	+	0.143442i
$885$		0			0
$886$	3.21032e14	−	5.56044e14i	0.588004	−	1.01845i
$887$	−4.59076e14	−	2.65047e14i	−0.836115	−	0.482731i	0.0198267	−	0.999803i	$-0.493689\pi$
$887$	−4.59076e14	−	2.65047e14i	−0.836115	−	0.482731i	−0.855942	+	0.517072i	$0.827022\pi$
$888$		0			0
$889$	2.21766e14	+	3.84110e14i	0.399380	+	0.691746i
$890$			6.45657e14i			1.15625i
$891$		0			0
$892$	−1.46501e15			−2.59429
$893$	1.14900e15	−	6.63373e14i	2.02330	−	1.16816i
$894$		0			0
$895$	2.93589e13	−	5.08511e13i	0.0511240	−	0.0885493i
$896$	1.28713e15	+	7.43126e14i	2.22886	+	1.28683i
$897$		0			0
$898$	−1.26831e14	−	2.19678e14i	−0.217192	−	0.376188i
$899$			3.61886e14i			0.616273i
$900$		0			0
$901$	−2.52483e14			−0.425215
$902$	1.86706e13	−	1.07795e13i	0.0312698	−	0.0180536i
$903$		0			0
$904$	9.65781e13	−	1.67278e14i	0.159969	−	0.277075i
$905$	1.57281e14	+	9.08061e13i	0.259079	+	0.149579i
$906$		0			0
$907$	8.14287e13	+	1.41039e14i	0.132660	+	0.229775i	0.924701	−	0.380694i	$-0.124315\pi$
$907$	8.14287e13	+	1.41039e14i	0.132660	+	0.229775i	−0.792041	+	0.610468i	$0.790981\pi$
$908$			9.07746e14i			1.47074i
$909$		0			0
$910$	−6.75156e14			−1.08193
$911$	−5.43664e14	+	3.13884e14i	−0.866440	+	0.500239i	−0.866164	−	0.499761i	$-0.833421\pi$
$911$	−5.43664e14	+	3.13884e14i	−0.866440	+	0.500239i	−0.000276280		1.00000i	$0.500088\pi$
$912$		0			0
$913$	3.10344e14	−	5.37531e14i	0.489203	−	0.847325i
$914$	6.71576e13	+	3.87734e13i	0.105284	+	0.0607860i
$915$		0			0
$916$	5.92780e14	+	1.02673e15i	0.919213	+	1.59212i
$917$		−	1.13193e15i		−	1.74572i
$918$		0			0
$919$	4.50497e14			0.687249			0.343625	−	0.939107i	$-0.388345\pi$
$919$	4.50497e14			0.687249			0.343625	+	0.939107i	$0.388345\pi$
$920$	−2.93758e14	+	1.69601e14i	−0.445708	+	0.257330i
$921$		0			0
$922$	−6.73484e14	+	1.16651e15i	−1.01082	+	1.75079i
$923$	2.52990e14	+	1.46064e14i	0.377655	+	0.218039i
$924$		0			0
$925$	−3.34480e13	−	5.79337e13i	−0.0493926	−	0.0855505i
$926$		−	6.80949e14i		−	1.00014i
$927$		0			0
$928$	1.34793e14			0.195851
$929$	−1.03635e15	+	5.98335e14i	−1.49771	+	0.864701i	−0.999997	−	0.00264344i	$-0.999159\pi$
$929$	−1.03635e15	+	5.98335e14i	−1.49771	+	0.864701i	−0.497709	+	0.867344i	$0.665825\pi$
$930$		0			0
$931$	5.11812e14	−	8.86484e14i	0.731749	−	1.26743i
$932$	9.76109e14	+	5.63557e14i	1.38809	+	0.801416i
$933$		0			0
$934$	2.98468e14	+	5.16961e14i	0.419917	+	0.727317i
$935$			2.49685e14i			0.349410i
$936$		0			0
$937$	−2.50981e14			−0.347491			−0.173746	−	0.984791i	$-0.555587\pi$
$937$	−2.50981e14			−0.347491			−0.173746	+	0.984791i	$0.555587\pi$
$938$	−2.42740e14	+	1.40146e14i	−0.334293	+	0.193004i
$939$		0			0
$940$	1.44926e15	−	2.51019e15i	1.97472	−	3.42032i
$941$	−4.10529e14	−	2.37019e14i	−0.556410	−	0.321244i	0.195293	−	0.980745i	$-0.437434\pi$
$941$	−4.10529e14	−	2.37019e14i	−0.556410	−	0.321244i	−0.751703	+	0.659501i	$0.770768\pi$
$942$		0			0
$943$	3.39646e12	+	5.88284e12i	0.00455478	+	0.00788912i
$944$		−	3.82226e14i		−	0.509871i
$945$		0			0
$946$	−1.04299e15			−1.37666
$947$	9.99584e14	−	5.77110e14i	1.31241	−	0.757720i	0.329915	−	0.944011i	$-0.392980\pi$
$947$	9.99584e14	−	5.77110e14i	1.31241	−	0.757720i	0.982495	+	0.186290i	$0.0596465\pi$
$948$		0			0
$949$	−1.47071e13	+	2.54735e13i	−0.0191072	+	0.0330946i
$950$	1.26678e15	+	7.31375e14i	1.63713	+	0.945197i
$951$		0			0
$952$	−3.72565e14	−	6.45301e14i	−0.476450	−	0.825235i
$953$			6.84549e14i			0.870844i	0.900227	+	0.435422i	$0.143401\pi$
$953$			6.84549e14i			0.870844i	−0.900227	+	0.435422i	$0.856599\pi$
$954$		0			0
$955$	−5.13001e14			−0.645805
$956$	−6.08789e14	+	3.51485e14i	−0.762390	+	0.440166i
$957$		0			0
$958$	6.03893e12	−	1.04597e13i	0.00748398	−	0.0129626i
$959$	−1.32217e14	−	7.63355e13i	−0.163003	−	0.0941096i
$960$		0			0
$961$	−5.45271e13	−	9.44437e13i	−0.0665266	−	0.115227i
$962$		−	6.30325e13i		−	0.0765048i
$963$		0			0
$964$	9.93555e14			1.19346
$965$	−1.57441e15	+	9.08984e14i	−1.88140	+	1.08622i
$966$		0			0
$967$	−6.95779e14	+	1.20512e15i	−0.822884	+	1.42528i	0.0806413	+	0.996743i	$0.474303\pi$
$967$	−6.95779e14	+	1.20512e15i	−0.822884	+	1.42528i	−0.903526	+	0.428534i	$0.859030\pi$
$968$	−7.23885e14	−	4.17935e14i	−0.851713	−	0.491736i
$969$		0			0
$970$	−8.57994e13	−	1.48609e14i	−0.0999138	−	0.173056i
$971$		−	1.59646e15i		−	1.84953i	−0.380540	−	0.924765i	$-0.624262\pi$
$971$		−	1.59646e15i		−	1.84953i	0.380540	−	0.924765i	$-0.375738\pi$
$972$		0			0
$973$	1.62006e15			1.85767
$974$	1.68976e15	−	9.75583e14i	1.92766	−	1.11293i
$975$		0			0
$976$	4.74644e14	−	8.22108e14i	0.535944	−	0.928282i
$977$	1.74684e13	+	1.00854e13i	0.0196237	+	0.0113298i	0.509780	−	0.860305i	$-0.329727\pi$
$977$	1.74684e13	+	1.00854e13i	0.0196237	+	0.0113298i	−0.490156	+	0.871635i	$0.663060\pi$
$978$		0			0
$979$	1.37507e14	+	2.38169e14i	0.152901	+	0.264833i
$980$		−	2.23629e15i		−	2.47399i
$981$		0			0
$982$	1.52103e15			1.66564
$983$	3.93894e14	−	2.27415e14i	0.429152	−	0.247771i	−0.269833	−	0.962907i	$-0.586969\pi$
$983$	3.93894e14	−	2.27415e14i	0.429152	−	0.247771i	0.698985	+	0.715136i	$0.253635\pi$
$984$		0			0
$985$	−9.13170e14	+	1.58166e15i	−0.984851	+	1.70581i
$986$	−3.52891e14	−	2.03742e14i	−0.378666	−	0.218623i
$987$		0			0
$988$	4.51099e14	+	7.81326e14i	0.479167	+	0.829942i
$989$		−	3.28632e14i		−	0.347319i
$990$		0			0
$991$	2.07903e14			0.217517			0.108758	−	0.994068i	$-0.465313\pi$
$991$	2.07903e14			0.217517			0.108758	+	0.994068i	$0.465313\pi$
$992$	−2.99566e14	+	1.72955e14i	−0.311842	+	0.180042i
$993$		0			0
$994$	−1.48789e15	+	2.57711e15i	−1.53334	+	2.65583i
$995$	−8.16560e14	−	4.71441e14i	−0.837283	−	0.483406i
$996$		0			0
$997$	−6.59438e14	−	1.14218e15i	−0.669419	−	1.15947i	−0.978067	−	0.208291i	$-0.933210\pi$
$997$	−6.59438e14	−	1.14218e15i	−0.669419	−	1.15947i	0.308648	−	0.951176i	$-0.400124\pi$
$998$			1.24844e15i			1.26100i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.d.a.17.1		18
3.2	odd	2		9.11.d.a.5.9	yes	18
9.2	odd	6	inner	27.11.d.a.8.1		18
9.4	even	3		81.11.b.a.80.2		18
9.5	odd	6		81.11.b.a.80.17		18
9.7	even	3		9.11.d.a.2.9	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.11.d.a.2.9	✓	18	9.7	even	3
9.11.d.a.5.9	yes	18	3.2	odd	2
27.11.d.a.8.1		18	9.2	odd	6	inner
27.11.d.a.17.1		18	1.1	even	1	trivial
81.11.b.a.80.2		18	9.4	even	3
81.11.b.a.80.17		18	9.5	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-47.1532 + 27.2239i) q^{2} +(970.286 - 1680.58i) q^{4} +(-3579.43 - 2066.59i) q^{5} +(-11845.8 - 20517.5i) q^{7} +49905.4i q^{8} +225043. q^{10} +(83013.5 - 47927.9i) q^{11} +(63316.4 - 109667. i) q^{13} +(1.11713e6 + 644977. i) q^{14} +(-365049. - 632283. i) q^{16} -630218. i q^{17} -3.67135e6 q^{19} +(-6.94615e6 + 4.01036e6i) q^{20} +(-2.60957e6 + 4.51991e6i) q^{22} +(-1.42416e6 - 822238. i) q^{23} +(3.65876e6 + 6.33715e6i) q^{25} +6.89489e6i q^{26} -4.59751e7 q^{28} +(-1.02842e7 + 5.93756e6i) q^{29} +(1.52371e7 - 2.63915e7i) q^{31} +(-9.83013e6 - 5.67543e6i) q^{32} +(1.71570e7 + 2.97168e7i) q^{34} +9.79213e7i q^{35} -9.14191e6 q^{37} +(1.73116e8 - 9.99487e7i) q^{38} +(1.03134e8 - 1.78633e8i) q^{40} +(-3.57733e6 - 2.06537e6i) q^{41} +(9.99200e7 + 1.73066e8i) q^{43} -1.86015e8i q^{44} +8.95383e7 q^{46} +(-3.12963e8 + 1.80689e8i) q^{47} +(-1.39407e8 + 2.41460e8i) q^{49} +(-3.45044e8 - 1.99211e8i) q^{50} +(-1.22870e8 - 2.12817e8i) q^{52} -4.00628e8i q^{53} -3.96188e8 q^{55} +(1.02393e9 - 5.91168e8i) q^{56} +(3.23288e8 - 5.59951e8i) q^{58} +(4.53388e8 + 2.61764e8i) q^{59} +(6.50111e8 + 1.12602e9i) q^{61} +1.65926e9i q^{62} +1.36565e9 q^{64} +(-4.53274e8 + 2.61698e8i) q^{65} +(-1.08644e8 + 1.88178e8i) q^{67} +(-1.05914e9 - 6.11492e8i) q^{68} +(-2.66580e9 - 4.61731e9i) q^{70} +2.30689e9i q^{71} -2.32280e8 q^{73} +(4.31071e8 - 2.48879e8i) q^{74} +(-3.56226e9 + 6.17002e9i) q^{76} +(-1.96672e9 - 1.13548e9i) q^{77} +(-1.60607e8 - 2.78180e8i) q^{79} +3.01762e9i q^{80} +2.24910e8 q^{82} +(5.60771e9 - 3.23761e9i) q^{83} +(-1.30240e9 + 2.25583e9i) q^{85} +(-9.42310e9 - 5.44043e9i) q^{86} +(2.39186e9 + 4.14282e9i) q^{88} +2.86904e9i q^{89} -3.00013e9 q^{91} +(-2.76368e9 + 1.59561e9i) q^{92} +(9.83813e9 - 1.70401e10i) q^{94} +(1.31414e10 + 7.58717e9i) q^{95} +(-3.81258e8 - 6.60359e8i) q^{97} -1.51808e10i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 4095 q^{4} - 4956 q^{5} - 6120 q^{7} - 2052 q^{10} - 969 q^{11} + 140274 q^{13} + 2134578 q^{14} - 1571841 q^{16} + 2771370 q^{19} - 14542734 q^{20} - 3475521 q^{22} + 9944382 q^{23} + 14726277 q^{25}+ \cdots - 14510723337 q^{97}+O(q^{100}) \) 18 * q + 3 * q^2 + 4095 * q^4 - 4956 * q^5 - 6120 * q^7 - 2052 * q^10 - 969 * q^11 + 140274 * q^13 + 2134578 * q^14 - 1571841 * q^16 + 2771370 * q^19 - 14542734 * q^20 - 3475521 * q^22 + 9944382 * q^23 + 14726277 * q^25 - 22968324 * q^28 + 41383956 * q^29 + 28428390 * q^31 - 165205143 * q^32 - 66263103 * q^34 + 63695196 * q^37 + 621662181 * q^38 - 75566250 * q^40 - 452543883 * q^41 + 102086037 * q^43 + 44251488 * q^46 + 289445970 * q^47 + 6735231 * q^49 - 1915252779 * q^50 + 19035576 * q^52 - 289455552 * q^55 + 4272894318 * q^56 - 83900178 * q^58 - 3065773551 * q^59 + 141349086 * q^61 - 28980486 * q^64 + 11094862926 * q^65 + 954074115 * q^67 - 21469701105 * q^68 - 1440686628 * q^70 + 772009902 * q^73 + 30101814978 * q^74 - 40906287 * q^76 - 25001072268 * q^77 + 2079634212 * q^79 - 1423292742 * q^82 + 23396438442 * q^83 - 5975304714 * q^85 - 39111097821 * q^86 + 2974531059 * q^88 + 2180413260 * q^91 + 40885098684 * q^92 + 6395997924 * q^94 - 22335455946 * q^95 - 14510723337 * q^97

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