LMFDB - Embedded newform 27.11.d.a.8.3

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			8.3
Root			$-9.48684 - 16.4317i$ of defining polynomial
Character	$\chi$	$=$	27.8
Dual form			27.11.d.a.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-28.4605 - 16.4317i) q^{2} +(28.0010 + 48.4991i) q^{4} +(4600.38 - 2656.03i) q^{5} +(-1786.25 + 3093.87i) q^{7} +31811.7i q^{8} -174572. q^{10} +(169079. + 97617.9i) q^{11} +(220523. + 381956. i) q^{13} +(101675. - 58702.1i) q^{14} +(551393. - 955040. i) q^{16} -265563. i q^{17} -811519. q^{19} +(257630. + 148743. i) q^{20} +(-3.20805e6 - 5.55651e6i) q^{22} +(9.14778e6 - 5.28147e6i) q^{23} +(9.22616e6 - 1.59802e7i) q^{25} -1.44942e7i q^{26} -200066. q^{28} +(1.13762e7 + 6.56804e6i) q^{29} +(-4.61108e6 - 7.98662e6i) q^{31} +(-3.17493e6 + 1.83305e6i) q^{32} +(-4.36365e6 + 7.55807e6i) q^{34} +1.89773e7i q^{35} -4.13264e7 q^{37} +(2.30963e7 + 1.33346e7i) q^{38} +(8.44928e7 + 1.46346e8i) q^{40} +(-2.10108e7 + 1.21306e7i) q^{41} +(5.44344e7 - 9.42832e7i) q^{43} +1.09336e7i q^{44} -3.47134e8 q^{46} +(-5.13663e7 - 2.96563e7i) q^{47} +(1.34856e8 + 2.33578e8i) q^{49} +(-5.25163e8 + 3.03203e8i) q^{50} +(-1.23497e7 + 2.13903e7i) q^{52} -4.16883e8i q^{53} +1.03710e9 q^{55} +(-9.84212e7 - 5.68235e7i) q^{56} +(-2.15848e8 - 3.73859e8i) q^{58} +(5.12892e7 - 2.96118e7i) q^{59} +(-5.98641e8 + 1.03688e9i) q^{61} +3.03071e8i q^{62} -1.00877e9 q^{64} +(2.02897e9 + 1.17143e9i) q^{65} +(-8.05765e8 - 1.39563e9i) q^{67} +(1.28796e7 - 7.43602e6i) q^{68} +(3.11829e8 - 5.40103e8i) q^{70} -2.21707e9i q^{71} +1.54099e9 q^{73} +(1.17617e9 + 6.79063e8i) q^{74} +(-2.27233e7 - 3.93579e7i) q^{76} +(-6.04034e8 + 3.48739e8i) q^{77} +(2.40338e9 - 4.16277e9i) q^{79} -5.85806e9i q^{80} +7.97306e8 q^{82} +(-3.47374e8 - 2.00556e8i) q^{83} +(-7.05343e8 - 1.22169e9i) q^{85} +(-3.09847e9 + 1.78890e9i) q^{86} +(-3.10539e9 + 5.37870e9i) q^{88} +6.44300e9i q^{89} -1.57563e9 q^{91} +(5.12293e8 + 2.95773e8i) q^{92} +(9.74608e8 + 1.68807e9i) q^{94} +(-3.73329e9 + 2.15542e9i) q^{95} +(-2.76286e9 + 4.78541e9i) q^{97} -8.86367e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−28.4605	−	16.4317i	−0.889391	−	0.513490i	−0.0156480	−	0.999878i	$-0.504981\pi$
$2$	−28.4605	−	16.4317i	−0.889391	−	0.513490i	−0.873743	+	0.486387i	$0.838314\pi$
$3$		0			0
$3$		0			0
$4$	28.0010	+	48.4991i	0.0273447	+	0.0473624i
$5$	4600.38	−	2656.03i	1.47212	−	0.849929i	0.472612	−	0.881271i	$-0.343311\pi$
$5$	4600.38	−	2656.03i	1.47212	−	0.849929i	0.999509	+	0.0313416i	$0.00997798\pi$
$6$		0			0
$7$	−1786.25	+	3093.87i	−0.106280	+	0.184082i	−0.914260	−	0.405127i	$-0.867227\pi$
$7$	−1786.25	+	3093.87i	−0.106280	+	0.184082i	0.807981	+	0.589209i	$0.200561\pi$
$8$			31811.7i			0.970816i
$9$		0			0
$10$	−174572.			−1.74572
$11$	169079.	+	97617.9i	1.04985	+	0.606130i	0.922607	−	0.385741i	$-0.126054\pi$
$11$	169079.	+	97617.9i	1.04985	+	0.606130i	0.127242	+	0.991872i	$0.459388\pi$
$12$		0			0
$13$	220523.	+	381956.i	0.593931	+	1.02872i	0.993697	+	0.112102i	$0.0357583\pi$
$13$	220523.	+	381956.i	0.593931	+	1.02872i	−0.399765	+	0.916618i	$0.630908\pi$
$14$	101675.	−	58702.1i	0.189049	−	0.109147i
$15$		0			0
$16$	551393.	−	955040.i	0.525849	−	0.910798i
$17$		−	265563.i		−	0.187035i	−0.995618	−	0.0935176i	$-0.970189\pi$
$17$		−	265563.i		−	0.187035i	0.995618	−	0.0935176i	$-0.0298111\pi$
$18$		0			0
$19$	−811519.			−0.327741			−0.163871	−	0.986482i	$-0.552398\pi$
$19$	−811519.			−0.327741			−0.163871	+	0.986482i	$0.552398\pi$
$20$	257630.	+	148743.i	0.0805093	+	0.0464821i
$21$		0			0
$22$	−3.20805e6	−	5.55651e6i	−0.622484	−	1.07817i
$23$	9.14778e6	−	5.28147e6i	1.42127	−	0.820570i	0.424862	−	0.905258i	$-0.360323\pi$
$23$	9.14778e6	−	5.28147e6i	1.42127	−	0.820570i	0.996408	+	0.0846876i	$0.0269892\pi$
$24$		0			0
$25$	9.22616e6	−	1.59802e7i	0.944759	−	1.63637i
$26$		−	1.44942e7i		−	1.21991i
$27$		0			0
$28$	−200066.			−0.0116248
$29$	1.13762e7	+	6.56804e6i	0.554634	+	0.320218i	0.750989	−	0.660315i	$-0.229577\pi$
$29$	1.13762e7	+	6.56804e6i	0.554634	+	0.320218i	−0.196355	+	0.980533i	$0.562911\pi$
$30$		0			0
$31$	−4.61108e6	−	7.98662e6i	−0.161062	−	0.278968i	0.774188	−	0.632956i	$-0.218159\pi$
$31$	−4.61108e6	−	7.98662e6i	−0.161062	−	0.278968i	−0.935250	+	0.353988i	$0.884825\pi$
$32$	−3.17493e6	+	1.83305e6i	−0.0946204	+	0.0546291i
$33$		0			0
$34$	−4.36365e6	+	7.55807e6i	−0.0960408	+	0.166347i
$35$			1.89773e7i			0.361322i
$36$		0			0
$37$	−4.13264e7			−0.595963			−0.297981	−	0.954572i	$-0.596313\pi$
$37$	−4.13264e7			−0.595963			−0.297981	+	0.954572i	$0.596313\pi$
$38$	2.30963e7	+	1.33346e7i	0.291490	+	0.168292i
$39$		0			0
$40$	8.44928e7	+	1.46346e8i	0.825125	+	1.42916i
$41$	−2.10108e7	+	1.21306e7i	−0.181353	+	0.104704i	−0.587928	−	0.808913i	$-0.700056\pi$
$41$	−2.10108e7	+	1.21306e7i	−0.181353	+	0.104704i	0.406575	+	0.913617i	$0.366723\pi$
$42$		0			0
$43$	5.44344e7	−	9.42832e7i	0.370281	−	0.641346i	−0.619328	−	0.785133i	$-0.712595\pi$
$43$	5.44344e7	−	9.42832e7i	0.370281	−	0.641346i	0.989609	+	0.143787i	$0.0459280\pi$
$44$			1.09336e7i			0.0662978i
$45$		0			0
$46$	−3.47134e8			−1.68542
$47$	−5.13663e7	−	2.96563e7i	−0.223970	−	0.129309i	0.383817	−	0.923409i	$-0.374609\pi$
$47$	−5.13663e7	−	2.96563e7i	−0.223970	−	0.129309i	−0.607787	+	0.794100i	$0.707943\pi$
$48$		0			0
$49$	1.34856e8	+	2.33578e8i	0.477409	+	0.826897i
$50$	−5.25163e8	+	3.03203e8i	−1.68052	+	0.970249i
$51$		0			0
$52$	−1.23497e7	+	2.13903e7i	−0.0324817	+	0.0562600i
$53$		−	4.16883e8i		−	0.996860i	−0.866930	−	0.498430i	$-0.833910\pi$
$53$		−	4.16883e8i		−	0.996860i	0.866930	−	0.498430i	$-0.166090\pi$
$54$		0			0
$55$	1.03710e9			2.06067
$56$	−9.84212e7	−	5.68235e7i	−0.178710	−	0.103178i
$57$		0			0
$58$	−2.15848e8	−	3.73859e8i	−0.328858	−	0.569598i
$59$	5.12892e7	−	2.96118e7i	0.0717407	−	0.0414195i	−0.463701	−	0.885992i	$-0.653479\pi$
$59$	5.12892e7	−	2.96118e7i	0.0717407	−	0.0414195i	0.535441	+	0.844572i	$0.320145\pi$
$60$		0			0
$61$	−5.98641e8	+	1.03688e9i	−0.708790	+	1.22766i	0.256517	+	0.966540i	$0.417425\pi$
$61$	−5.98641e8	+	1.03688e9i	−0.708790	+	1.22766i	−0.965306	+	0.261120i	$0.915908\pi$
$62$			3.03071e8i			0.330816i
$63$		0			0
$64$	−1.00877e9			−0.939492
$65$	2.02897e9	+	1.17143e9i	1.74868	+	1.00960i
$66$		0			0
$67$	−8.05765e8	−	1.39563e9i	−0.596807	−	1.03370i	−0.993289	−	0.115658i	$-0.963102\pi$
$67$	−8.05765e8	−	1.39563e9i	−0.596807	−	1.03370i	0.396482	−	0.918043i	$-0.370231\pi$
$68$	1.28796e7	−	7.43602e6i	0.00885843	−	0.00511442i
$69$		0			0
$70$	3.11829e8	−	5.40103e8i	0.185535	−	0.321356i
$71$		−	2.21707e9i		−	1.22882i	−0.788988	−	0.614408i	$-0.789395\pi$
$71$		−	2.21707e9i		−	1.22882i	0.788988	−	0.614408i	$-0.210605\pi$
$72$		0			0
$73$	1.54099e9			0.743338			0.371669	−	0.928365i	$-0.378786\pi$
$73$	1.54099e9			0.743338			0.371669	+	0.928365i	$0.378786\pi$
$74$	1.17617e9	+	6.79063e8i	0.530044	+	0.306021i
$75$		0			0
$76$	−2.27233e7	−	3.93579e7i	−0.00896197	−	0.0155226i
$77$	−6.04034e8	+	3.48739e8i	−0.223156	+	0.128839i
$78$		0			0
$79$	2.40338e9	−	4.16277e9i	0.781064	−	1.35284i	−0.150258	−	0.988647i	$-0.548010\pi$
$79$	2.40338e9	−	4.16277e9i	0.781064	−	1.35284i	0.931322	−	0.364196i	$-0.118656\pi$
$80$		−	5.85806e9i		−	1.78774i
$81$		0			0
$82$	7.97306e8			0.215058
$83$	−3.47374e8	−	2.00556e8i	−0.0881875	−	0.0509151i	0.455258	−	0.890360i	$-0.349547\pi$
$83$	−3.47374e8	−	2.00556e8i	−0.0881875	−	0.0509151i	−0.543445	+	0.839445i	$0.682880\pi$
$84$		0			0
$85$	−7.05343e8	−	1.22169e9i	−0.158967	−	0.275338i
$86$	−3.09847e9	+	1.78890e9i	−0.658650	+	0.380272i
$87$		0			0
$88$	−3.10539e9	+	5.37870e9i	−0.588441	+	1.01921i
$89$			6.44300e9i			1.15382i	0.816808	+	0.576910i	$0.195742\pi$
$89$			6.44300e9i			1.15382i	−0.816808	+	0.576910i	$0.804258\pi$
$90$		0			0
$91$	−1.57563e9			−0.252492
$92$	5.12293e8	+	2.95773e8i	0.0777283	+	0.0448765i
$93$		0			0
$94$	9.74608e8	+	1.68807e9i	0.132798	+	0.230012i
$95$	−3.73329e9	+	2.15542e9i	−0.482474	+	0.278557i
$96$		0			0
$97$	−2.76286e9	+	4.78541e9i	−0.321736	+	0.557263i	−0.980846	−	0.194783i	$-0.937600\pi$
$97$	−2.76286e9	+	4.78541e9i	−0.321736	+	0.557263i	0.659110	+	0.752046i	$0.270933\pi$
$98$		−	8.86367e9i		−	0.980580i
$99$		0			0
$100$	1.03337e9			0.103337
$101$	1.51991e10	+	8.77521e9i	1.44614	+	0.834931i	0.998249	−	0.0591555i	$-0.0188408\pi$
$101$	1.51991e10	+	8.77521e9i	1.44614	+	0.834931i	0.447894	+	0.894087i	$0.352174\pi$
$102$		0			0
$103$	7.24041e9	+	1.25408e10i	0.624564	+	1.08178i	0.988625	+	0.150402i	$0.0480567\pi$
$103$	7.24041e9	+	1.25408e10i	0.624564	+	1.08178i	−0.364061	+	0.931375i	$0.618610\pi$
$104$	−1.21507e10	+	7.01520e9i	−0.998697	+	0.576598i
$105$		0			0
$106$	−6.85008e9	+	1.18647e10i	−0.511878	+	0.886599i
$107$			1.55323e10i			1.10743i	0.832705	+	0.553717i	$0.186791\pi$
$107$			1.55323e10i			1.10743i	−0.832705	+	0.553717i	$0.813209\pi$
$108$		0			0
$109$	−1.19798e10			−0.778607			−0.389303	−	0.921110i	$-0.627284\pi$
$109$	−1.19798e10			−0.778607			−0.389303	+	0.921110i	$0.627284\pi$
$110$	−2.95165e10	−	1.70414e10i	−1.83274	−	1.05814i
$111$		0			0
$112$	1.96985e9	+	3.41187e9i	0.111774	+	0.193599i
$113$	5.23508e9	−	3.02248e9i	0.284139	−	0.164048i	−0.351157	−	0.936317i	$-0.614212\pi$
$113$	5.23508e9	−	3.02248e9i	0.284139	−	0.164048i	0.635296	+	0.772269i	$0.280878\pi$
$114$		0			0
$115$	2.80555e10	−	4.85935e10i	1.39485	−	2.41596i
$116$			7.35645e8i			0.0350250i
$117$		0			0
$118$	−1.94629e9			−0.0850741
$119$	8.21618e8	+	4.74361e8i	0.0344298	+	0.0198781i
$120$		0			0
$121$	6.08980e9	+	1.05478e10i	0.234788	+	0.406665i
$122$	3.40753e10	−	1.96734e10i	1.26078	−	0.727913i
$123$		0			0
$124$	2.58229e8	−	4.47266e8i	0.00880839	−	0.0152566i
$125$		−	4.61443e10i		−	1.51205i
$126$		0			0
$127$	−6.98534e9			−0.211431			−0.105716	−	0.994396i	$-0.533713\pi$
$127$	−6.98534e9			−0.211431			−0.105716	+	0.994396i	$0.533713\pi$
$128$	3.19613e10	+	1.84529e10i	0.930197	+	0.537049i
$129$		0			0
$130$	−3.84971e10	−	6.66789e10i	−1.03684	−	1.79586i
$131$	1.99015e10	−	1.14901e10i	0.515858	−	0.297831i	−0.219381	−	0.975639i	$-0.570404\pi$
$131$	1.99015e10	−	1.14901e10i	0.515858	−	0.297831i	0.735238	+	0.677809i	$0.237070\pi$
$132$		0			0
$133$	1.44957e9	−	2.51073e9i	0.0348323	−	0.0603313i
$134$			5.29603e10i			1.22582i
$135$		0			0
$136$	8.44802e9			0.181577
$137$	−3.22308e10	−	1.86085e10i	−0.667834	−	0.385574i	0.127422	−	0.991849i	$-0.459330\pi$
$137$	−3.22308e10	−	1.86085e10i	−0.667834	−	0.385574i	−0.795255	+	0.606275i	$0.792663\pi$
$138$		0			0
$139$	7.67071e9	+	1.32861e10i	0.147830	+	0.256048i	0.930425	−	0.366482i	$-0.119438\pi$
$139$	7.67071e9	+	1.32861e10i	0.147830	+	0.256048i	−0.782595	+	0.622531i	$0.786105\pi$
$140$	−9.20381e8	+	5.31382e8i	−0.0171130	+	0.00988022i
$141$		0			0
$142$	−3.64302e10	+	6.30989e10i	−0.630986	+	1.09290i
$143$			8.61078e10i			1.44000i
$144$		0			0
$145$	6.97796e10			1.08865
$146$	−4.38575e10	−	2.53211e10i	−0.661118	−	0.381697i
$147$		0			0
$148$	−1.15718e9	−	2.00429e9i	−0.0162964	−	0.0282262i
$149$	1.08699e11	−	6.27575e10i	1.48011	−	0.854543i	0.480366	−	0.877068i	$-0.340504\pi$
$149$	1.08699e11	−	6.27575e10i	1.48011	−	0.854543i	0.999746	+	0.0225252i	$0.00717061\pi$
$150$		0			0
$151$	−1.84674e10	+	3.19865e10i	−0.235246	+	0.407458i	−0.959344	−	0.282239i	$-0.908923\pi$
$151$	−1.84674e10	+	3.19865e10i	−0.235246	+	0.407458i	0.724098	+	0.689697i	$0.242256\pi$
$152$		−	2.58158e10i		−	0.318176i
$153$		0			0
$154$	2.29215e10			0.264630
$155$	−4.24254e10	−	2.44943e10i	−0.474206	−	0.273783i
$156$		0			0
$157$	−3.91244e9	−	6.77655e9i	−0.0410156	−	0.0710412i	0.844789	−	0.535100i	$-0.179726\pi$
$157$	−3.91244e9	−	6.77655e9i	−0.0410156	−	0.0710412i	−0.885804	+	0.464059i	$0.846393\pi$
$158$	−1.36803e11	+	7.89832e10i	−1.38934	+	0.802138i
$159$		0			0
$160$	−9.73726e9	+	1.68654e10i	−0.0928617	+	0.160841i
$161$			3.77360e10i			0.348841i
$162$		0			0
$163$	−5.11323e10			−0.444383			−0.222192	−	0.975003i	$-0.571321\pi$
$163$	−5.11323e10			−0.444383			−0.222192	+	0.975003i	$0.571321\pi$
$164$	−1.17665e9	−	6.79337e8i	−0.00991806	−	0.00572619i
$165$		0			0
$166$	6.59096e9	+	1.14159e10i	0.0522888	+	0.0905668i
$167$	−6.69019e10	+	3.86258e10i	−0.515058	+	0.297369i	−0.734910	−	0.678164i	$-0.762776\pi$
$167$	−6.69019e10	+	3.86258e10i	−0.515058	+	0.297369i	0.219852	+	0.975533i	$0.429442\pi$
$168$		0			0
$169$	−2.83312e10	+	4.90710e10i	−0.205509	+	0.355952i
$170$			4.63599e10i			0.326511i
$171$		0			0
$172$	6.09687e9			0.0405009
$173$	−1.09000e11	−	6.29310e10i	−0.703387	−	0.406101i	0.105220	−	0.994449i	$-0.466445\pi$
$173$	−1.09000e11	−	6.29310e10i	−0.703387	−	0.406101i	−0.808608	+	0.588348i	$0.799779\pi$
$174$		0			0
$175$	3.29604e10	+	5.70891e10i	0.200818	+	0.347827i
$176$	1.86458e11	−	1.07652e11i	1.10412	−	0.637466i
$177$		0			0
$178$	1.05869e11	−	1.83371e11i	0.592475	−	1.02620i
$179$		−	6.27752e10i		−	0.341604i	−0.985305	−	0.170802i	$-0.945364\pi$
$179$		−	6.27752e10i		−	0.341604i	0.985305	−	0.170802i	$-0.0546358\pi$
$180$		0			0
$181$	−1.47944e11			−0.761559			−0.380779	−	0.924666i	$-0.624344\pi$
$181$	−1.47944e11			−0.761559			−0.380779	+	0.924666i	$0.624344\pi$
$182$	4.48433e10	+	2.58903e10i	0.224564	+	0.129652i
$183$		0			0
$184$	1.68013e11	+	2.91006e11i	0.796623	+	1.37979i
$185$	−1.90117e11	+	1.09764e11i	−0.877329	+	0.506526i
$186$		0			0
$187$	2.59237e10	−	4.49012e10i	0.113368	−	0.196359i
$188$		−	3.32162e9i		−	0.0141436i
$189$		0			0
$190$	1.41669e11			0.572145
$191$	1.17276e11	+	6.77092e10i	0.461362	+	0.266367i	0.712617	−	0.701554i	$-0.247510\pi$
$191$	1.17276e11	+	6.77092e10i	0.461362	+	0.266367i	−0.251255	+	0.967921i	$0.580843\pi$
$192$		0			0
$193$	−1.10408e11	−	1.91233e11i	−0.412302	−	0.714127i	0.582839	−	0.812587i	$-0.301942\pi$
$193$	−1.10408e11	−	1.91233e11i	−0.412302	−	0.714127i	−0.995141	+	0.0984601i	$0.968608\pi$
$194$	1.57265e11	−	9.07969e10i	0.572299	−	0.330417i
$195$		0			0
$196$	−7.55221e9	+	1.30808e10i	−0.0261092	+	0.0452225i
$197$			4.46791e10i			0.150582i	0.997162	+	0.0752911i	$0.0239886\pi$
$197$			4.46791e10i			0.150582i	−0.997162	+	0.0752911i	$0.976011\pi$
$198$		0			0
$199$	−4.46907e11			−1.43203			−0.716014	−	0.698086i	$-0.754035\pi$
$199$	−4.46907e11			−1.43203			−0.716014	+	0.698086i	$0.754035\pi$
$200$	5.08357e11	+	2.93500e11i	1.58861	+	0.917187i
$201$		0			0
$202$	−2.88383e11	−	4.99494e11i	−0.857458	−	1.48516i
$203$	−4.06413e10	+	2.34643e10i	−0.117893	+	0.0680654i
$204$		0			0
$205$	−6.44385e10	+	1.11611e11i	−0.177982	+	0.308274i
$206$		−	4.75889e11i		−	1.28283i
$207$		0			0
$208$	4.86378e11			1.24927
$209$	−1.37211e11	−	7.92188e10i	−0.344079	−	0.198654i
$210$		0			0
$211$	6.42362e10	+	1.11260e11i	0.153592	+	0.266028i	0.932545	−	0.361053i	$-0.117583\pi$
$211$	6.42362e10	+	1.11260e11i	0.153592	+	0.266028i	−0.778954	+	0.627081i	$0.784249\pi$
$212$	2.02184e10	−	1.16731e10i	0.0472137	−	0.0272588i
$213$		0			0
$214$	2.55223e11	−	4.42059e11i	0.568657	−	0.984943i
$215$		−	5.78318e11i		−	1.25885i
$216$		0			0
$217$	3.29461e10			0.0684707
$218$	3.40952e11	+	1.96849e11i	0.692486	+	0.399807i
$219$		0			0
$220$	2.90399e10	+	5.02986e10i	0.0563484	+	0.0975983i
$221$	1.01434e11	−	5.85627e10i	0.192407	−	0.111086i
$222$		0			0
$223$	2.10363e11	−	3.64359e11i	0.381456	−	0.660702i	−0.609814	−	0.792544i	$-0.708756\pi$
$223$	2.10363e11	−	3.64359e11i	0.381456	−	0.660702i	0.991271	+	0.131843i	$0.0420893\pi$
$224$		−	1.30971e10i		−	0.0232239i
$225$		0			0
$226$	−1.98658e11			−0.336948
$227$	−7.33509e11	−	4.23491e11i	−1.21696	−	0.702612i	−0.252693	−	0.967547i	$-0.581316\pi$
$227$	−7.33509e11	−	4.23491e11i	−1.21696	−	0.702612i	−0.964266	+	0.264935i	$0.914649\pi$
$228$		0			0
$229$	4.59850e11	+	7.96484e11i	0.730195	+	1.26474i	0.956799	+	0.290749i	$0.0939044\pi$
$229$	4.59850e11	+	7.96484e11i	0.730195	+	1.26474i	−0.226604	+	0.973987i	$0.572762\pi$
$230$	−1.59695e12	+	9.21998e11i	−2.48114	+	1.43249i
$231$		0			0
$232$	−2.08940e11	+	3.61895e11i	−0.310872	+	0.538447i
$233$			8.27043e11i			1.20434i	0.798368	+	0.602169i	$0.205697\pi$
$233$			8.27043e11i			1.20434i	−0.798368	+	0.602169i	$0.794303\pi$
$234$		0			0
$235$	−3.15072e11			−0.439614
$236$	2.87229e9	+	1.65832e9i	0.00392345	+	0.00226521i
$237$		0			0
$238$	−1.55891e10	−	2.70011e10i	−0.0204144	−	0.0353588i
$239$	4.09810e11	−	2.36604e11i	0.525524	−	0.303412i	−0.213668	−	0.976906i	$-0.568541\pi$
$239$	4.09810e11	−	2.36604e11i	0.525524	−	0.303412i	0.739192	+	0.673495i	$0.235208\pi$
$240$		0			0
$241$	−6.09297e11	+	1.05533e12i	−0.749452	+	1.29809i	0.198633	+	0.980074i	$0.436350\pi$
$241$	−6.09297e11	+	1.05533e12i	−0.749452	+	1.29809i	−0.948086	+	0.318015i	$0.896984\pi$
$242$		−	4.00263e11i		−	0.482246i
$243$		0			0
$244$	−6.70501e10			−0.0775265
$245$	1.24078e12	+	7.16364e11i	1.40561	+	0.811528i
$246$		0			0
$247$	−1.78958e11	−	3.09965e11i	−0.194656	−	0.337154i
$248$	2.54068e11	−	1.46686e11i	0.270827	−	0.156362i
$249$		0			0
$250$	−7.58228e11	+	1.31329e12i	−0.776426	+	1.34481i
$251$			2.44960e11i			0.245882i	0.992414	+	0.122941i	$0.0392326\pi$
$251$			2.44960e11i			0.245882i	−0.992414	+	0.122941i	$0.960767\pi$
$252$		0			0
$253$	2.06227e12			1.98949
$254$	1.98806e11	+	1.14781e11i	0.188045	+	0.108568i
$255$		0			0
$256$	−8.99325e10	−	1.55768e11i	−0.0817932	−	0.141670i
$257$	−7.78492e11	+	4.49463e11i	−0.694366	+	0.400892i	−0.805246	−	0.592941i	$-0.797967\pi$
$257$	−7.78492e11	+	4.49463e11i	−0.694366	+	0.400892i	0.110880	+	0.993834i	$0.464633\pi$
$258$		0			0
$259$	7.38192e10	−	1.27859e11i	0.0633389	−	0.109706i
$260$			1.31204e11i			0.110429i
$261$		0			0
$262$	−7.55210e11			−0.611732
$263$	−1.39389e12	−	8.04761e11i	−1.10777	−	0.639570i	−0.169518	−	0.985527i	$-0.554221\pi$
$263$	−1.39389e12	−	8.04761e11i	−1.10777	−	0.639570i	−0.938250	+	0.345957i	$0.887554\pi$
$264$		0			0
$265$	−1.10725e12	−	1.91782e12i	−0.847261	−	1.46750i
$266$	−8.25112e10	+	4.76379e10i	−0.0619591	+	0.0357721i
$267$		0			0
$268$	4.51243e10	−	7.81577e10i	0.0326390	−	0.0565324i
$269$			2.61272e11i			0.185495i	0.995690	+	0.0927474i	$0.0295649\pi$
$269$			2.61272e11i			0.185495i	−0.995690	+	0.0927474i	$0.970435\pi$
$270$		0			0
$271$	5.12325e10			0.0350509			0.0175254	−	0.999846i	$-0.494421\pi$
$271$	5.12325e10			0.0350509			0.0175254	+	0.999846i	$0.494421\pi$
$272$	−2.53624e11	−	1.46430e11i	−0.170351	−	0.0983523i
$273$		0			0
$274$	6.11537e11	+	1.05921e12i	0.395977	+	0.685852i
$275$	3.11990e12	−	1.80128e12i	1.98371	−	1.14529i
$276$		0			0
$277$	1.38895e12	−	2.40574e12i	0.851705	−	1.47520i	−0.0279632	−	0.999609i	$-0.508902\pi$
$277$	1.38895e12	−	2.40574e12i	0.851705	−	1.47520i	0.879668	−	0.475588i	$-0.157765\pi$
$278$		−	5.04171e11i		−	0.303636i
$279$		0			0
$280$	−6.03699e11			−0.350777
$281$	−5.73785e11	−	3.31275e11i	−0.327505	−	0.189085i	0.327228	−	0.944945i	$-0.393885\pi$
$281$	−5.73785e11	−	3.31275e11i	−0.327505	−	0.189085i	−0.654733	+	0.755860i	$0.727219\pi$
$282$		0			0
$283$	1.28301e11	+	2.22224e11i	0.0706803	+	0.122422i	0.899200	−	0.437539i	$-0.144150\pi$
$283$	1.28301e11	+	2.22224e11i	0.0706803	+	0.122422i	−0.828519	+	0.559960i	$0.810816\pi$
$284$	1.07526e11	−	6.20800e10i	0.0581997	−	0.0336016i
$285$		0			0
$286$	1.41490e12	−	2.45067e12i	0.739426	−	1.28072i
$287$		−	8.66730e10i		−	0.0445117i
$288$		0			0
$289$	1.94547e12			0.965018
$290$	−1.98596e12	−	1.14660e12i	−0.968236	−	0.559011i
$291$		0			0
$292$	4.31493e10	+	7.47367e10i	0.0203263	+	0.0352062i
$293$	8.98407e11	−	5.18696e11i	0.416040	−	0.240201i	−0.277342	−	0.960771i	$-0.589453\pi$
$293$	8.98407e11	−	5.18696e11i	0.416040	−	0.240201i	0.693382	+	0.720571i	$0.256120\pi$
$294$		0			0
$295$	1.57300e11	−	2.72451e11i	0.0704073	−	0.121949i
$296$		−	1.31466e12i		−	0.578570i
$297$		0			0
$298$	−4.12484e12			−1.75520
$299$	4.03458e12	+	2.32937e12i	1.68827	+	0.974725i
$300$		0			0
$301$	1.94467e11	+	3.36826e11i	0.0787069	+	0.136324i
$302$	1.05119e12	−	6.06903e11i	0.418451	−	0.241593i
$303$		0			0
$304$	−4.47466e11	+	7.75034e11i	−0.172342	+	0.298506i
$305$			6.36003e12i			2.40968i
$306$		0			0
$307$	−4.44346e12			−1.62941			−0.814703	−	0.579878i	$-0.803100\pi$
$307$	−4.44346e12			−1.62941			−0.814703	+	0.579878i	$0.803100\pi$
$308$	−3.38271e10	−	1.95301e10i	−0.0122042	−	0.00704612i
$309$		0			0
$310$	8.04965e11	+	1.39424e12i	0.281170	+	0.487001i
$311$	1.87220e12	−	1.08091e12i	0.643501	−	0.371525i	−0.142461	−	0.989800i	$-0.545502\pi$
$311$	1.87220e12	−	1.08091e12i	0.643501	−	0.371525i	0.785962	+	0.618275i	$0.212168\pi$
$312$		0			0
$313$	−1.68206e12	+	2.91341e12i	−0.559912	+	0.969796i	0.437591	+	0.899174i	$0.355832\pi$
$313$	−1.68206e12	+	2.91341e12i	−0.559912	+	0.969796i	−0.997503	+	0.0706222i	$0.977502\pi$
$314$			2.57152e11i			0.0842446i
$315$		0			0
$316$	2.69188e11			0.0854318
$317$	−4.82315e12	−	2.78465e12i	−1.50673	−	0.869909i	−0.999969	−	0.00782054i	$-0.997511\pi$
$317$	−4.82315e12	−	2.78465e12i	−1.50673	−	0.869909i	−0.506757	−	0.862089i	$-0.669156\pi$
$318$		0			0
$319$	1.28232e12	+	2.22104e12i	0.388188	+	0.672361i
$320$	−4.64073e12	+	2.67933e12i	−1.38305	+	0.798502i
$321$		0			0
$322$	6.20067e11	−	1.07399e12i	0.179126	−	0.310256i
$323$			2.15510e11i			0.0612991i
$324$		0			0
$325$	8.13831e12			2.24449
$326$	1.45525e12	+	8.40191e11i	0.395230	+	0.228186i
$327$		0			0
$328$	−3.85895e11	−	6.68390e11i	−0.101648	−	0.176060i
$329$	1.83506e11	−	1.05947e11i	0.0476069	−	0.0274859i
$330$		0			0
$331$	−1.43482e12	+	2.48518e12i	−0.361125	+	0.625487i	−0.988146	−	0.153515i	$-0.950941\pi$
$331$	−1.43482e12	+	2.48518e12i	−0.361125	+	0.625487i	0.627021	+	0.779002i	$0.284274\pi$
$332$		−	2.24631e10i		−	0.00556902i
$333$		0			0
$334$	2.53875e12			0.610784
$335$	−7.41364e12	−	4.28027e12i	−1.75714	−	1.01449i
$336$		0			0
$337$	−1.02801e12	−	1.78057e12i	−0.236510	−	0.409647i	0.723201	−	0.690638i	$-0.242670\pi$
$337$	−1.02801e12	−	1.78057e12i	−0.236510	−	0.409647i	−0.959710	+	0.280991i	$0.909337\pi$
$338$	1.61264e12	−	9.31057e11i	0.365556	−	0.211054i
$339$		0			0
$340$	3.95006e10	−	6.84170e10i	0.00869378	−	0.0150581i
$341$		−	1.80049e12i		−	0.390499i
$342$		0			0
$343$	−1.97269e12			−0.415516
$344$	2.99931e12	+	1.73165e12i	0.622629	+	0.359475i
$345$		0			0
$346$	2.06812e12	+	3.58210e12i	0.417058	+	0.722365i
$347$	−6.95132e12	+	4.01335e12i	−1.38172	+	0.797736i	−0.992363	−	0.123351i	$-0.960636\pi$
$347$	−6.95132e12	+	4.01335e12i	−1.38172	+	0.797736i	−0.389356	+	0.921087i	$0.627302\pi$
$348$		0			0
$349$	−1.34088e12	+	2.32247e12i	−0.258978	+	0.448562i	−0.965968	−	0.258661i	$-0.916719\pi$
$349$	−1.34088e12	+	2.32247e12i	−0.258978	+	0.448562i	0.706991	+	0.707223i	$0.250052\pi$
$350$		−	2.16638e12i		−	0.412472i
$351$		0			0
$352$	−7.15754e11			−0.132449
$353$	4.48889e12	+	2.59166e12i	0.818965	+	0.472830i	0.850060	−	0.526687i	$-0.176566\pi$
$353$	4.48889e12	+	2.59166e12i	0.818965	+	0.472830i	−0.0310943	+	0.999516i	$0.509899\pi$
$354$		0			0
$355$	−5.88859e12	−	1.01993e13i	−1.04441	−	1.80897i
$356$	−3.12479e11	+	1.80410e11i	−0.0546476	+	0.0315508i
$357$		0			0
$358$	−1.03150e12	+	1.78661e12i	−0.175410	+	0.303820i
$359$			3.36392e12i			0.564122i	0.959396	+	0.282061i	$0.0910181\pi$
$359$			3.36392e12i			0.564122i	−0.959396	+	0.282061i	$0.908982\pi$
$360$		0			0
$361$	−5.47250e12			−0.892586
$362$	4.21055e12	+	2.43096e12i	0.677324	+	0.391053i
$363$		0			0
$364$	−4.41191e10	−	7.64166e10i	−0.00690431	−	0.0119586i
$365$	7.08915e12	−	4.09292e12i	1.09428	−	0.631784i
$366$		0			0
$367$	3.32859e12	−	5.76529e12i	0.499954	−	0.865946i	−0.500046	−	0.865999i	$-0.666684\pi$
$367$	3.32859e12	−	5.76529e12i	0.499954	−	0.865946i	1.00000		5.29711e-5i	$1.68612e-5\pi$
$368$		−	1.16487e13i		−	1.72599i
$369$		0			0
$370$	7.21444e12			1.04039
$371$	1.28978e12	+	7.44655e11i	0.183504	+	0.105946i
$372$		0			0
$373$	4.76065e12	+	8.24569e12i	0.659360	+	1.14204i	0.980782	+	0.195108i	$0.0625059\pi$
$373$	4.76065e12	+	8.24569e12i	0.659360	+	1.14204i	−0.321422	+	0.946936i	$0.604161\pi$
$374$	−1.47561e12	+	8.51941e11i	−0.201657	+	0.116426i
$375$		0			0
$376$	9.43418e11	−	1.63405e12i	0.125535	−	0.217433i
$377$			5.79360e12i			0.760750i
$378$		0			0
$379$	−8.87221e10			−0.0113458			−0.00567291	−	0.999984i	$-0.501806\pi$
$379$	−8.87221e10			−0.0113458			−0.00567291	+	0.999984i	$0.501806\pi$
$380$	−2.09072e11	−	1.20708e11i	−0.0263862	−	0.0152341i
$381$		0			0
$382$	−2.22515e12	−	3.85408e12i	−0.273554	−	0.473809i
$383$	5.86193e12	−	3.38439e12i	0.711290	−	0.410663i	−0.100249	−	0.994962i	$-0.531964\pi$
$383$	5.86193e12	−	3.38439e12i	0.711290	−	0.410663i	0.811538	+	0.584299i	$0.198630\pi$
$384$		0			0
$385$	−1.85252e12	+	3.20866e12i	−0.219008	+	0.379333i
$386$			7.25678e12i			0.846851i
$387$		0			0
$388$	−3.09451e11			−0.0351911
$389$	4.58918e12	+	2.64956e12i	0.515213	+	0.297458i	0.734974	−	0.678095i	$-0.237194\pi$
$389$	4.58918e12	+	2.64956e12i	0.515213	+	0.297458i	−0.219761	+	0.975554i	$0.570528\pi$
$390$		0			0
$391$	−1.40256e12	−	2.42931e12i	−0.153476	−	0.265827i
$392$	−7.43051e12	+	4.29001e12i	−0.802765	+	0.463476i
$393$		0			0
$394$	7.34154e11	−	1.27159e12i	0.0773225	−	0.133926i
$395$		−	2.55338e13i		−	2.65540i
$396$		0			0
$397$	−3.13721e12			−0.318120			−0.159060	−	0.987269i	$-0.550846\pi$
$397$	−3.13721e12			−0.318120			−0.159060	+	0.987269i	$0.550846\pi$
$398$	1.27192e13	+	7.34344e12i	1.27363	+	0.735333i
$399$		0			0
$400$	−1.01745e13	−	1.76227e13i	−0.993602	−	1.72097i
$401$	−1.27712e13	+	7.37343e12i	−1.23171	+	0.711128i	−0.967386	−	0.253306i	$-0.918482\pi$
$401$	−1.27712e13	+	7.37343e12i	−1.23171	+	0.711128i	−0.264324	+	0.964434i	$0.585149\pi$
$402$		0			0
$403$	2.03369e12	−	3.52246e12i	0.191320	−	0.331376i
$404$			9.82857e11i			0.0913237i
$405$		0			0
$406$	1.54223e12			0.139804
$407$	−6.98744e12	−	4.03420e12i	−0.625671	−	0.361231i
$408$		0			0
$409$	1.09536e13	+	1.89723e13i	0.957066	+	1.65769i	0.729568	+	0.683908i	$0.239721\pi$
$409$	1.09536e13	+	1.89723e13i	0.957066	+	1.65769i	0.227498	+	0.973779i	$0.426946\pi$
$410$	3.66791e12	−	2.11767e12i	0.316591	−	0.182784i
$411$		0			0
$412$	−4.05477e11	+	7.02307e11i	−0.0341570	+	0.0591617i
$413$			2.11576e11i			0.0176082i
$414$		0			0
$415$	−2.13074e12			−0.173097
$416$	−1.40029e12	−	8.08457e11i	−0.112396	−	0.0648919i
$417$		0			0
$418$	2.60340e12	+	4.50922e12i	0.204014	+	0.353362i
$419$	3.49651e12	−	2.01871e12i	0.270747	−	0.156316i	−0.358480	−	0.933537i	$-0.616705\pi$
$419$	3.49651e12	−	2.01871e12i	0.270747	−	0.156316i	0.629227	+	0.777221i	$0.283372\pi$
$420$		0			0
$421$	8.17356e12	−	1.41570e13i	0.618017	−	1.07044i	−0.371830	−	0.928301i	$-0.621270\pi$
$421$	8.17356e12	−	1.41570e13i	0.618017	−	1.07044i	0.989847	−	0.142136i	$-0.0453971\pi$
$422$		−	4.22204e12i		−	0.315471i
$423$		0			0
$424$	1.32617e13			0.967768
$425$	−4.24375e12	−	2.45013e12i	−0.306059	−	0.176703i
$426$		0			0
$427$	−2.13864e12	−	3.70423e12i	−0.150660	−	0.260951i
$428$	−7.53304e11	+	4.34921e11i	−0.0524507	+	0.0302825i
$429$		0			0
$430$	−9.50274e12	+	1.64592e13i	−0.646408	+	1.11961i
$431$		−	2.50079e12i		−	0.168148i	−0.996460	−	0.0840739i	$-0.973207\pi$
$431$		−	2.50079e12i		−	0.168148i	0.996460	−	0.0840739i	$-0.0267932\pi$
$432$		0			0
$433$	−2.23242e13			−1.46668			−0.733341	−	0.679861i	$-0.762040\pi$
$433$	−2.23242e13			−1.46668			−0.733341	+	0.679861i	$0.762040\pi$
$434$	−9.37662e11	−	5.41360e11i	−0.0608973	−	0.0351591i
$435$		0			0
$436$	−3.35447e11	−	5.81011e11i	−0.0212908	−	0.0368767i
$437$	−7.42360e12	+	4.28602e12i	−0.465808	+	0.268935i
$438$		0			0
$439$	−6.20881e12	+	1.07540e13i	−0.380790	+	0.659548i	−0.991175	−	0.132557i	$-0.957681\pi$
$439$	−6.20881e12	+	1.07540e13i	−0.380790	+	0.659548i	0.610385	+	0.792105i	$0.291015\pi$
$440$			3.29920e13i			2.00053i
$441$		0			0
$442$	−3.84914e12			−0.228166
$443$	−1.60103e13	−	9.24354e12i	−0.938383	−	0.541776i	−0.0489299	−	0.998802i	$-0.515581\pi$
$443$	−1.60103e13	−	9.24354e12i	−0.938383	−	0.541776i	−0.889453	+	0.457027i	$0.848914\pi$
$444$		0			0
$445$	1.71128e13	+	2.96402e13i	0.980665	+	1.69856i
$446$	−1.19741e13	+	6.91324e12i	−0.678528	+	0.391748i
$447$		0			0
$448$	1.80192e12	−	3.12101e12i	0.0998491	−	0.172944i
$449$			2.39447e13i			1.31213i	0.754704	+	0.656065i	$0.227780\pi$
$449$			2.39447e13i			1.31213i	−0.754704	+	0.656065i	$0.772220\pi$
$450$		0			0
$451$	−4.73666e12			−0.253857
$452$	2.93175e11	+	1.69264e11i	0.0155394	+	0.00897167i
$453$		0			0
$454$	1.39174e13	+	2.41056e13i	0.721568	+	1.24979i
$455$	−7.24849e12	+	4.18492e12i	−0.371698	+	0.214600i
$456$		0			0
$457$	−7.61659e10	+	1.31923e11i	−0.00382102	+	0.00661821i	−0.867930	−	0.496687i	$-0.834550\pi$
$457$	−7.61659e10	+	1.31923e11i	−0.00382102	+	0.00661821i	0.864109	+	0.503305i	$0.167883\pi$
$458$		−	3.02245e13i		−	1.49979i
$459$		0			0
$460$	3.14232e12			0.152567
$461$	1.58511e13	+	9.15163e12i	0.761298	+	0.439535i	0.829761	−	0.558118i	$-0.188476\pi$
$461$	1.58511e13	+	9.15163e12i	0.761298	+	0.439535i	−0.0684638	+	0.997654i	$0.521810\pi$
$462$		0			0
$463$	−1.66199e13	−	2.87865e13i	−0.781130	−	1.35296i	−0.931284	−	0.364294i	$-0.881310\pi$
$463$	−1.66199e13	−	2.87865e13i	−0.781130	−	1.35296i	0.150154	−	0.988663i	$-0.452023\pi$
$464$	1.25455e13	−	7.24314e12i	0.583307	−	0.336773i
$465$		0			0
$466$	1.35897e13	−	2.35381e13i	0.618416	−	1.07113i
$467$		−	7.43166e12i		−	0.334581i	−0.985908	−	0.167291i	$-0.946498\pi$
$467$		−	7.43166e12i		−	0.334581i	0.985908	−	0.167291i	$-0.0535018\pi$
$468$		0			0
$469$	5.75718e12			0.253714
$470$	8.96713e12	+	5.17717e12i	0.390988	+	0.225737i
$471$		0			0
$472$	9.42002e11	+	1.63160e12i	0.0402107	+	0.0696470i
$473$	1.84075e13	−	1.06276e13i	0.777478	−	0.448877i
$474$		0			0
$475$	−7.48721e12	+	1.29682e13i	−0.309636	+	0.536306i
$476$			5.31303e10i			0.00217424i
$477$		0			0
$478$	−1.55512e13			−0.623196
$479$	−1.02071e13	−	5.89306e12i	−0.404785	−	0.233703i	0.283762	−	0.958895i	$-0.408418\pi$
$479$	−1.02071e13	−	5.89306e12i	−0.404785	−	0.233703i	−0.688546	+	0.725192i	$0.741751\pi$
$480$		0			0
$481$	−9.11341e12	−	1.57849e13i	−0.353961	−	0.613079i
$482$	3.46818e13	−	2.00236e13i	1.33311	−	0.769673i
$483$		0			0
$484$	−3.41041e11	+	5.90700e11i	−0.0128404	+	0.0222403i
$485$			2.93529e13i			1.09381i
$486$		0			0
$487$	2.09936e13			0.766375			0.383187	−	0.923671i	$-0.374826\pi$
$487$	2.09936e13			0.766375			0.383187	+	0.923671i	$0.374826\pi$
$488$	−3.29848e13	−	1.90438e13i	−1.19183	−	0.688104i
$489$		0			0
$490$	−2.35422e13	−	4.07762e13i	−0.833424	−	1.44353i
$491$	3.28779e13	−	1.89821e13i	1.15212	−	0.665176i	0.202716	−	0.979238i	$-0.435023\pi$
$491$	3.28779e13	−	1.89821e13i	1.15212	−	0.665176i	0.949403	+	0.314062i	$0.101690\pi$
$492$		0			0
$493$	1.74423e12	−	3.02109e12i	0.0598920	−	0.103736i
$494$			1.17624e13i			0.399815i
$495$		0			0
$496$	−1.01701e13			−0.338778
$497$	6.85932e12	+	3.96023e12i	0.226203	+	0.130599i
$498$		0			0
$499$	−2.27482e13	−	3.94011e13i	−0.735267	−	1.27352i	−0.954606	−	0.297871i	$-0.903724\pi$
$499$	−2.27482e13	−	3.94011e13i	−0.735267	−	1.27352i	0.219339	−	0.975649i	$-0.429610\pi$
$500$	2.23795e12	−	1.29208e12i	0.0716145	−	0.0413467i
$501$		0			0
$502$	4.02511e12	−	6.97169e12i	0.126258	−	0.218685i
$503$			2.11543e12i			0.0656990i	0.999460	+	0.0328495i	$0.0104582\pi$
$503$			2.11543e12i			0.0656990i	−0.999460	+	0.0328495i	$0.989542\pi$
$504$		0			0
$505$	9.32288e13			2.83853
$506$	−5.86932e13	−	3.38865e13i	−1.76944	−	1.02158i
$507$		0			0
$508$	−1.95596e11	−	3.38782e11i	−0.00578152	−	0.0100139i
$509$	−2.50999e13	+	1.44914e13i	−0.734653	+	0.424152i	−0.820122	−	0.572189i	$-0.806095\pi$
$509$	−2.50999e13	+	1.44914e13i	−0.734653	+	0.424152i	0.0854689	+	0.996341i	$0.472761\pi$
$510$		0			0
$511$	−2.75259e12	+	4.76763e12i	−0.0790019	+	0.136835i
$512$		−	3.18805e13i		−	0.906099i
$513$		0			0
$514$	2.95417e13			0.823418
$515$	6.66172e13	+	3.84615e13i	1.83887	+	1.06167i
$516$		0			0
$517$	−5.78998e12	−	1.00285e13i	−0.156756	−	0.271510i
$518$	−4.20186e12	+	2.42595e12i	−0.112666	+	0.0650478i
$519$		0			0
$520$	−3.72651e13	+	6.45451e13i	−0.980135	+	1.69764i
$521$		−	4.68220e13i		−	1.21972i	−0.792508	−	0.609861i	$-0.791225\pi$
$521$		−	4.68220e13i		−	1.21972i	0.792508	−	0.609861i	$-0.208775\pi$
$522$		0			0
$523$	−7.10610e13			−1.81603			−0.908014	−	0.418939i	$-0.862402\pi$
$523$	−7.10610e13			−1.81603			−0.908014	+	0.418939i	$0.862402\pi$
$524$	1.11452e12	+	6.43470e11i	0.0282119	+	0.0162882i
$525$		0			0
$526$	2.64472e13	+	4.58079e13i	0.656827	+	1.13766i
$527$	−2.12095e12	+	1.22453e12i	−0.0521768	+	0.0301243i
$528$		0			0
$529$	3.50747e13	−	6.07511e13i	0.846672	−	1.46648i
$530$			7.27761e13i			1.74024i
$531$		0			0
$532$	1.62358e11			0.00380991
$533$	−9.26672e12	−	5.35014e12i	−0.215422	−	0.124374i
$534$		0			0
$535$	4.12544e13	+	7.14546e13i	0.941241	+	1.63028i
$536$	4.43972e13	−	2.56327e13i	1.00353	−	0.579390i
$537$		0			0
$538$	4.29314e12	−	7.43594e12i	0.0952498	−	0.164977i
$539$			5.26576e13i			1.15749i
$540$		0			0
$541$	−5.91756e13			−1.27690			−0.638449	−	0.769664i	$-0.720424\pi$
$541$	−5.91756e13			−1.27690			−0.638449	+	0.769664i	$0.720424\pi$
$542$	−1.45810e12	−	8.41836e11i	−0.0311739	−	0.0179983i
$543$		0			0
$544$	4.86790e11	+	8.43146e11i	0.0102176	+	0.0176973i
$545$	−5.51117e13	+	3.18188e13i	−1.14620	+	0.661760i
$546$		0			0
$547$	−2.68575e13	+	4.65185e13i	−0.548439	+	0.949924i	0.449943	+	0.893057i	$0.351444\pi$
$547$	−2.68575e13	+	4.65185e13i	−0.548439	+	0.949924i	−0.998382	+	0.0568668i	$0.981889\pi$
$548$		−	2.08422e12i		−	0.0421736i
$549$		0			0
$550$	−1.18392e14			−2.35239
$551$	−9.23198e12	−	5.33009e12i	−0.181776	−	0.104949i
$552$		0			0
$553$	8.58605e12	+	1.48715e13i	0.166023	+	0.287560i
$554$	−7.90608e13	+	4.56458e13i	−1.51500	+	0.874685i
$555$		0			0
$556$	−4.29574e11	+	7.44045e11i	−0.00808471	+	0.0140031i
$557$			2.77658e13i			0.517887i	0.965893	+	0.258943i	$0.0833743\pi$
$557$			2.77658e13i			0.517887i	−0.965893	+	0.258943i	$0.916626\pi$
$558$		0			0
$559$	4.80161e13			0.879686
$560$	1.81241e13	+	1.04639e13i	0.329091	+	0.190001i
$561$		0			0
$562$	1.08868e13	+	1.88565e13i	0.194187	+	0.336341i
$563$	3.27738e13	−	1.89219e13i	0.579408	−	0.334521i	−0.181490	−	0.983393i	$-0.558092\pi$
$563$	3.27738e13	−	1.89219e13i	0.579408	−	0.334521i	0.760898	+	0.648872i	$0.224759\pi$
$564$		0			0
$565$	1.60556e13	−	2.78091e13i	0.278858	−	0.482997i
$566$		−	8.43282e12i		−	0.145175i
$567$		0			0
$568$	7.05287e13			1.19295
$569$	1.27885e12	+	7.38342e11i	0.0214416	+	0.0123793i	0.510682	−	0.859769i	$-0.329393\pi$
$569$	1.27885e12	+	7.38342e11i	0.0214416	+	0.0123793i	−0.489241	+	0.872149i	$0.662726\pi$
$570$		0			0
$571$	−3.60446e12	−	6.24311e12i	−0.0593827	−	0.102854i	0.834806	−	0.550545i	$-0.185580\pi$
$571$	−3.60446e12	−	6.24311e12i	−0.0593827	−	0.102854i	−0.894188	+	0.447691i	$0.852247\pi$
$572$	−4.17615e12	+	2.41110e12i	−0.0682018	+	0.0393763i
$573$		0			0
$574$	−1.42418e12	+	2.46676e12i	−0.0228563	+	0.0395883i
$575$		−	1.94911e14i		−	3.10097i
$576$		0			0
$577$	7.54481e13			1.17969			0.589847	−	0.807515i	$-0.299188\pi$
$577$	7.54481e13			1.17969			0.589847	+	0.807515i	$0.299188\pi$
$578$	−5.53691e13	−	3.19674e13i	−0.858279	−	0.495527i
$579$		0			0
$580$	1.95389e12	+	3.38424e12i	0.0297688	+	0.0515610i
$581$	1.24099e12	−	7.16486e11i	0.0187451	−	0.0108225i
$582$		0			0
$583$	4.06952e13	−	7.04862e13i	0.604227	−	1.04655i
$584$			4.90216e13i			0.721644i
$585$		0			0
$586$	−3.40922e13			−0.493363
$587$	3.98143e13	+	2.29868e13i	0.571279	+	0.329828i	0.757660	−	0.652650i	$-0.226343\pi$
$587$	3.98143e13	+	2.29868e13i	0.571279	+	0.329828i	−0.186381	+	0.982478i	$0.559676\pi$
$588$		0			0
$589$	3.74198e12	+	6.48129e12i	0.0527867	+	0.0914293i
$590$	−8.95366e12	+	5.16940e12i	−0.125239	+	0.0723069i
$591$		0			0
$592$	−2.27871e13	+	3.94684e13i	−0.313387	+	0.542802i
$593$		−	2.34722e13i		−	0.320096i	−0.987109	−	0.160048i	$-0.948835\pi$
$593$		−	2.34722e13i		−	0.320096i	0.987109	−	0.160048i	$-0.0511649\pi$
$594$		0			0
$595$	5.03967e12			0.0675798
$596$	6.08736e12	+	3.51454e12i	0.0809464	+	0.0467344i
$597$		0			0
$598$	−7.65509e13	−	1.32590e14i	−1.00102	−	1.73382i
$599$	−1.12967e14	+	6.52215e13i	−1.46493	+	0.845779i	−0.999233	−	0.0391640i	$-0.987531\pi$
$599$	−1.12967e14	+	6.52215e13i	−1.46493	+	0.845779i	−0.465699	+	0.884943i	$0.654197\pi$
$600$		0			0
$601$	−4.46521e13	+	7.73397e13i	−0.569468	+	0.986348i	0.427150	+	0.904181i	$0.359518\pi$
$601$	−4.46521e13	+	7.73397e13i	−0.569468	+	0.986348i	−0.996619	+	0.0821673i	$0.973816\pi$
$602$		−	1.27817e13i		−	0.161661i
$603$		0			0
$604$	−2.06842e12			−0.0257309
$605$	5.60308e13	+	3.23494e13i	0.691273	+	0.399107i
$606$		0			0
$607$	3.08075e13	+	5.33601e13i	0.373863	+	0.647550i	0.990156	−	0.139967i	$-0.0446997\pi$
$607$	3.08075e13	+	5.33601e13i	0.373863	+	0.647550i	−0.616293	+	0.787517i	$0.711366\pi$
$608$	2.57652e12	−	1.48755e12i	0.0310110	−	0.0179042i
$609$		0			0
$610$	1.04506e14	−	1.81010e14i	1.23735	−	2.14315i
$611$		−	2.61596e13i		−	0.307202i
$612$		0			0
$613$	−5.04824e13			−0.583227			−0.291613	−	0.956536i	$-0.594192\pi$
$613$	−5.04824e13			−0.583227			−0.291613	+	0.956536i	$0.594192\pi$
$614$	1.26463e14	+	7.30136e13i	1.44918	+	0.836685i
$615$		0			0
$616$	−1.10940e13	−	1.92153e13i	−0.125079	−	0.216643i
$617$	1.27328e14	−	7.35127e13i	1.42396	−	0.822123i	0.427324	−	0.904099i	$-0.359456\pi$
$617$	1.27328e14	−	7.35127e13i	1.42396	−	0.822123i	0.996634	+	0.0819758i	$0.0261230\pi$
$618$		0			0
$619$	−2.95318e13	+	5.11506e13i	−0.324965	+	0.562856i	−0.981505	−	0.191435i	$-0.938686\pi$
$619$	−2.95318e13	+	5.11506e13i	−0.324965	+	0.562856i	0.656540	+	0.754291i	$0.272019\pi$
$620$		−	2.74345e12i		−	0.0299460i
$621$		0			0
$622$	−7.10449e13			−0.763099
$623$	−1.99338e13	−	1.15088e13i	−0.212398	−	0.122628i
$624$		0			0
$625$	−3.24612e13	−	5.62245e13i	−0.340380	−	0.589556i
$626$	9.57446e13	−	5.52782e13i	0.995962	−	0.575019i
$627$		0			0
$628$	2.19104e11	−	3.79500e11i	0.00224312	−	0.00388520i
$629$			1.09748e13i			0.111466i
$630$		0			0
$631$	−7.75492e13			−0.775230			−0.387615	−	0.921821i	$-0.626701\pi$
$631$	−7.75492e13			−0.775230			−0.387615	+	0.921821i	$0.626701\pi$
$632$	1.32425e14	+	7.64556e13i	1.31336	+	0.758270i
$633$		0			0
$634$	9.15129e13	+	1.58505e14i	0.893380	+	1.54738i
$635$	−3.21352e13	+	1.85533e13i	−0.311252	+	0.179701i
$636$		0			0
$637$	−5.94777e13	+	1.03018e14i	−0.567097	+	0.982240i
$638$		−	8.42825e13i		−	0.797322i
$639$		0			0
$640$	1.96045e14			1.82582
$641$	1.39437e13	+	8.05042e12i	0.128851	+	0.0743924i	0.563040	−	0.826429i	$-0.309632\pi$
$641$	1.39437e13	+	8.05042e12i	0.128851	+	0.0743924i	−0.434189	+	0.900822i	$0.642965\pi$
$642$		0			0
$643$	−9.17679e13	−	1.58947e14i	−0.834903	−	1.44609i	−0.894110	−	0.447848i	$-0.852190\pi$
$643$	−9.17679e13	−	1.58947e14i	−0.834903	−	1.44609i	0.0592068	−	0.998246i	$-0.481143\pi$
$644$	−1.83016e12	+	1.05665e12i	−0.0165219	+	0.00953893i
$645$		0			0
$646$	3.54119e12	−	6.13352e12i	0.0314765	−	0.0545189i
$647$			5.13585e13i			0.452992i	0.974012	+	0.226496i	$0.0727271\pi$
$647$			5.13585e13i			0.452992i	−0.974012	+	0.226496i	$0.927273\pi$
$648$		0			0
$649$	1.15626e13			0.100423
$650$	−2.31621e14	−	1.33726e14i	−1.99623	−	1.15252i
$651$		0			0
$652$	−1.43175e12	−	2.47987e12i	−0.0121515	−	0.0210470i
$653$	−1.74591e14	+	1.00800e14i	−1.47047	+	0.848975i	−0.999450	−	0.0331487i	$-0.989447\pi$
$653$	−1.74591e14	+	1.00800e14i	−1.47047	+	0.848975i	−0.471018	+	0.882124i	$0.656113\pi$
$654$		0			0
$655$	6.10363e13	−	1.05718e14i	0.506270	−	0.876885i
$656$			2.67549e13i			0.220234i
$657$		0			0
$658$	−6.96356e12			−0.0564549
$659$	4.33193e11	+	2.50104e11i	0.00348542	+	0.00201231i	0.501742	−	0.865017i	$-0.332693\pi$
$659$	4.33193e11	+	2.50104e11i	0.00348542	+	0.00201231i	−0.498256	+	0.867030i	$0.666026\pi$
$660$		0			0
$661$	−5.50932e13	−	9.54243e13i	−0.436607	−	0.756226i	0.560818	−	0.827939i	$-0.310487\pi$
$661$	−5.50932e13	−	9.54243e13i	−0.436607	−	0.756226i	−0.997425	+	0.0717132i	$0.977153\pi$
$662$	8.16715e13	−	4.71531e13i	0.642363	−	0.370869i
$663$		0			0
$664$	6.38004e12	−	1.10506e13i	0.0494291	−	0.0856138i
$665$		−	1.54004e13i		−	0.118420i
$666$		0			0
$667$	1.38756e14			1.05105
$668$	−3.74664e12	−	2.16312e12i	−0.0281682	−	0.0162629i
$669$		0			0
$670$	1.40664e14	+	2.43637e14i	1.04186	+	1.80455i
$671$	−2.02435e14	+	1.16876e14i	−1.48824	+	0.859238i
$672$		0			0
$673$	−1.17227e14	+	2.03042e14i	−0.849085	+	1.47066i	0.0329417	+	0.999457i	$0.489512\pi$
$673$	−1.17227e14	+	2.03042e14i	−0.849085	+	1.47066i	−0.882026	+	0.471200i	$0.843821\pi$
$674$			6.75679e13i			0.485782i
$675$		0			0
$676$	−3.17320e12			−0.0224783
$677$	−1.69905e14	−	9.80947e13i	−1.19471	−	0.689767i	−0.235340	−	0.971913i	$-0.575620\pi$
$677$	−1.69905e14	−	9.80947e13i	−1.19471	−	0.689767i	−0.959371	+	0.282146i	$0.908954\pi$
$678$		0			0
$679$	−9.87029e12	−	1.70958e13i	−0.0683882	−	0.118452i
$680$	3.88640e13	−	2.24382e13i	0.267303	−	0.154327i
$681$		0			0
$682$	−2.95852e13	+	5.12430e13i	−0.200517	+	0.347306i
$683$		−	1.69532e13i		−	0.114064i	−0.998372	−	0.0570319i	$-0.981836\pi$
$683$		−	1.69532e13i		−	0.114064i	0.998372	−	0.0570319i	$-0.0181637\pi$
$684$		0			0
$685$	−1.97698e14			−1.31084
$686$	5.61437e13	+	3.24146e13i	0.369556	+	0.213363i
$687$		0			0
$688$	−6.00295e13	−	1.03974e14i	−0.389424	−	0.674502i
$689$	1.59231e14	−	9.19320e13i	1.02549	−	0.592067i
$690$		0			0
$691$	3.84322e13	−	6.65665e13i	0.243952	−	0.422538i	−0.717884	−	0.696162i	$-0.754889\pi$
$691$	3.84322e13	−	6.65665e13i	0.243952	−	0.422538i	0.961837	+	0.273625i	$0.0882227\pi$
$692$		−	7.04851e12i		−	0.0444188i
$693$		0			0
$694$	2.63784e14			1.63852
$695$	7.05763e13	+	4.07472e13i	0.435246	+	0.251289i
$696$		0			0
$697$	3.22144e12	+	5.57970e12i	0.0195833	+	0.0339193i
$698$	7.63242e13	−	4.40658e13i	0.460665	−	0.265965i
$699$		0			0
$700$	−1.84585e12	+	3.19710e12i	−0.0109826	+	0.0190224i
$701$		−	4.90611e13i		−	0.289833i	−0.989444	−	0.144916i	$-0.953709\pi$
$701$		−	4.90611e13i		−	0.289833i	0.989444	−	0.144916i	$-0.0462913\pi$
$702$		0			0
$703$	3.35372e13			0.195322
$704$	−1.70562e14	−	9.84742e13i	−0.986325	−	0.569455i
$705$		0			0
$706$	−8.51708e13	−	1.47520e14i	−0.485587	−	0.841062i
$707$	−5.42987e13	+	3.13494e13i	−0.307392	+	0.177473i
$708$		0			0
$709$	−1.44379e14	+	2.50072e14i	−0.805884	+	1.39583i	0.109808	+	0.993953i	$0.464976\pi$
$709$	−1.44379e14	+	2.50072e14i	−0.805884	+	1.39583i	−0.915692	+	0.401880i	$0.868357\pi$
$710$			3.87038e14i			2.14517i
$711$		0			0
$712$	−2.04963e14			−1.12015
$713$	−8.43622e13	−	4.87065e13i	−0.457826	−	0.264326i
$714$		0			0
$715$	2.28705e14	+	3.96128e14i	1.22390	+	2.11985i
$716$	3.04454e12	−	1.75776e12i	0.0161792	−	0.00934105i
$717$		0			0
$718$	5.52749e13	−	9.57389e13i	0.289671	−	0.501726i
$719$			3.60117e14i			1.87413i	0.349159	+	0.937063i	$0.386467\pi$
$719$			3.60117e14i			1.87413i	−0.349159	+	0.937063i	$0.613533\pi$
$720$		0			0
$721$	−5.17326e13			−0.265514
$722$	1.55750e14	+	8.99225e13i	0.793858	+	0.458334i
$723$		0			0
$724$	−4.14256e12	−	7.17513e12i	−0.0208246	−	0.0360692i
$725$	2.09917e14	−	1.21196e14i	1.04799	−	0.605057i
$726$		0			0
$727$	2.06898e13	−	3.58358e13i	0.101879	−	0.176460i	−0.810580	−	0.585628i	$-0.800848\pi$
$727$	2.06898e13	−	3.58358e13i	0.101879	−	0.176460i	0.912459	+	0.409169i	$0.134181\pi$
$728$		−	5.01235e13i		−	0.245123i
$729$		0			0
$730$	−2.69014e14			−1.29766
$731$	−2.50382e13	−	1.44558e13i	−0.119954	−	0.0692556i
$732$		0			0
$733$	−1.06927e14	−	1.85203e14i	−0.505323	−	0.875244i	−0.999981	−	0.00615689i	$-0.998040\pi$
$733$	−1.06927e14	−	1.85203e14i	−0.505323	−	0.875244i	0.494659	−	0.869087i	$-0.335293\pi$
$734$	−1.89467e14	+	1.09389e14i	−0.889310	+	0.513443i
$735$		0			0
$736$	−1.93624e13	+	3.35366e13i	−0.0896541	+	0.155285i
$737$		−	3.14628e14i		−	1.44697i
$738$		0			0
$739$	3.13831e13			0.142388			0.0711941	−	0.997462i	$-0.477319\pi$
$739$	3.13831e13			0.142388			0.0711941	+	0.997462i	$0.477319\pi$
$740$	−1.06469e13	−	6.14700e12i	−0.0479806	−	0.0277016i
$741$		0			0
$742$	−2.44719e13	−	4.23865e13i	−0.108805	−	0.188455i
$743$	2.67909e14	−	1.54677e14i	1.18316	−	0.683096i	0.226414	−	0.974031i	$-0.427300\pi$
$743$	2.67909e14	−	1.54677e14i	1.18316	−	0.683096i	0.956743	+	0.290935i	$0.0939663\pi$
$744$		0			0
$745$	3.33371e14	−	5.77416e14i	1.45260	−	2.51598i
$746$		−	3.12902e14i		−	1.35430i
$747$		0			0
$748$	2.90356e12			0.0124000
$749$	−4.80550e13	−	2.77446e13i	−0.203859	−	0.117698i
$750$		0			0
$751$	2.27578e14	+	3.94177e14i	0.952645	+	1.65003i	0.739669	+	0.672971i	$0.234982\pi$
$751$	2.27578e14	+	3.94177e14i	0.952645	+	1.65003i	0.212976	+	0.977057i	$0.431684\pi$
$752$	−5.66460e13	+	3.27046e13i	−0.235548	+	0.135994i
$753$		0			0
$754$	9.51986e13	−	1.64889e14i	0.390638	−	0.676604i
$755$			1.96200e14i			0.799769i
$756$		0			0
$757$	2.72559e14			1.09643			0.548214	−	0.836338i	$-0.315308\pi$
$757$	2.72559e14			1.09643			0.548214	+	0.836338i	$0.315308\pi$
$758$	2.52508e12	+	1.45785e12i	0.0100909	+	0.00582596i
$759$		0			0
$760$	−6.85675e13	−	1.18762e14i	−0.270427	−	0.468394i
$761$	2.81791e14	−	1.62692e14i	1.10409	−	0.637446i	0.166797	−	0.985991i	$-0.446658\pi$
$761$	2.81791e14	−	1.62692e14i	1.10409	−	0.637446i	0.937292	+	0.348546i	$0.113324\pi$
$762$		0			0
$763$	2.13989e13	−	3.70640e13i	0.0827502	−	0.143328i
$764$			7.58369e12i			0.0291349i
$765$		0			0
$766$	−2.22445e14			−0.843487
$767$	2.26208e13	+	1.30601e13i	0.0852181	+	0.0492007i
$768$		0			0
$769$	−3.42300e13	−	5.92881e13i	−0.127284	−	0.220463i	0.795339	−	0.606165i	$-0.207293\pi$
$769$	−3.42300e13	−	5.92881e13i	−0.127284	−	0.220463i	−0.922624	+	0.385702i	$0.873959\pi$
$770$	1.05448e14	−	6.08802e13i	0.389568	−	0.224917i
$771$		0			0
$772$	6.18307e12	−	1.07094e13i	0.0225485	−	0.0390552i
$773$		−	1.34878e14i		−	0.488702i	−0.969687	−	0.244351i	$-0.921425\pi$
$773$		−	1.34878e14i		−	0.488702i	0.969687	−	0.244351i	$-0.0785749\pi$
$774$		0			0
$775$	−1.70170e14			−0.608660
$776$	−1.52232e14	−	8.78912e13i	−0.541000	−	0.312347i
$777$		0			0
$778$	−8.70736e13	−	1.50816e14i	−0.305484	−	0.529114i
$779$	1.70507e13	−	9.84422e12i	0.0594367	−	0.0343158i
$780$		0			0
$781$	2.16425e14	−	3.74860e14i	0.744823	−	1.29007i
$782$			9.21861e13i			0.315233i
$783$		0			0
$784$	2.97435e14			1.00418
$785$	−3.59974e13	−	2.07831e13i	−0.120760	−	0.0697208i
$786$		0			0
$787$	−2.68184e14	−	4.64509e14i	−0.888300	−	1.53858i	−0.841883	−	0.539659i	$-0.818553\pi$
$787$	−2.68184e14	−	4.64509e14i	−0.888300	−	1.53858i	−0.0464171	−	0.998922i	$-0.514780\pi$
$788$	−2.16690e12	+	1.25106e12i	−0.00713193	+	0.00411762i
$789$		0			0
$790$	−4.19563e14	+	7.26705e14i	−1.36352	+	2.36169i
$791$			2.15955e13i			0.0697400i
$792$		0			0
$793$	−5.28055e14			−1.68389
$794$	8.92866e13	+	5.15496e13i	0.282933	+	0.163351i
$795$		0			0
$796$	−1.25138e13	−	2.16746e13i	−0.0391584	−	0.0678243i
$797$	−2.51255e14	+	1.45062e14i	−0.781311	+	0.451090i	−0.836895	−	0.547364i	$-0.815631\pi$
$797$	−2.51255e14	+	1.45062e14i	−0.781311	+	0.451090i	0.0555838	+	0.998454i	$0.482298\pi$
$798$		0			0
$799$	−7.87563e12	+	1.36410e13i	−0.0241853	+	0.0418902i
$800$			6.76480e13i			0.206445i
$801$		0			0
$802$	4.84632e14			1.46063
$803$	2.60550e14	+	1.50428e14i	0.780392	+	0.450560i
$804$		0			0
$805$	1.00228e14	+	1.73600e14i	0.296490	+	0.513535i
$806$	−1.15760e14	+	6.68340e13i	−0.340316	+	0.196482i
$807$		0			0
$808$	−2.79154e14	+	4.83509e14i	−0.810564	+	1.40394i
$809$			2.94489e14i			0.849820i	0.905236	+	0.424910i	$0.139694\pi$
$809$			2.94489e14i			0.849820i	−0.905236	+	0.424910i	$0.860306\pi$
$810$		0			0
$811$	3.53231e14			1.00682			0.503412	−	0.864046i	$-0.332078\pi$
$811$	3.53231e14			1.00682			0.503412	+	0.864046i	$0.332078\pi$
$812$	−2.27599e12	−	1.31404e12i	−0.00644748	−	0.00372245i
$813$		0			0
$814$	1.32577e14	+	2.29631e14i	0.370978	+	0.642552i
$815$	−2.35228e14	+	1.35809e14i	−0.654185	+	0.377694i
$816$		0			0
$817$	−4.41746e13	+	7.65127e13i	−0.121356	+	0.210195i
$818$		−	7.19947e14i		−	1.96578i
$819$		0			0
$820$	−7.21736e12			−0.0194674
$821$	−1.25805e14	−	7.26336e13i	−0.337274	−	0.194725i	0.321792	−	0.946810i	$-0.395715\pi$
$821$	−1.25805e14	−	7.26336e13i	−0.337274	−	0.194725i	−0.659066	+	0.752085i	$0.729048\pi$
$822$		0			0
$823$	3.25505e14	+	5.63791e14i	0.862101	+	1.49320i	0.869898	+	0.493233i	$0.164185\pi$
$823$	3.25505e14	+	5.63791e14i	0.862101	+	1.49320i	−0.00779686	+	0.999970i	$0.502482\pi$
$824$	−3.98943e14	+	2.30330e14i	−1.05021	+	0.606337i
$825$		0			0
$826$	3.47655e12	−	6.02156e12i	0.00904166	−	0.0156606i
$827$			1.30511e14i			0.337381i	0.985669	+	0.168691i	$0.0539539\pi$
$827$			1.30511e14i			0.337381i	−0.985669	+	0.168691i	$0.946046\pi$
$828$		0			0
$829$	5.27820e14			1.34807			0.674036	−	0.738699i	$-0.264559\pi$
$829$	5.27820e14			1.34807			0.674036	+	0.738699i	$0.264559\pi$
$830$	6.06418e13	+	3.50116e13i	0.153951	+	0.0888835i
$831$		0			0
$832$	−2.22457e14	−	3.85307e14i	−0.557994	−	0.966474i
$833$	6.20297e13	−	3.58129e13i	0.154659	−	0.0892923i
$834$		0			0
$835$	−2.05183e14	+	3.55387e14i	−0.505485	+	0.875526i
$836$		−	8.87281e12i		−	0.0217285i
$837$		0			0
$838$	−1.32683e14			−0.321067
$839$	6.49308e14	+	3.74878e14i	1.56186	+	0.901738i	0.997070	+	0.0765009i	$0.0243748\pi$
$839$	6.49308e14	+	3.74878e14i	1.56186	+	0.901738i	0.564786	+	0.825237i	$0.308959\pi$
$840$		0			0
$841$	−1.24075e14	−	2.14905e14i	−0.294921	−	0.510818i
$842$	−4.65247e14	+	2.68611e14i	−1.09932	+	0.634692i
$843$		0			0
$844$	−3.59735e12	+	6.23079e12i	−0.00839983	+	0.0145489i
$845$			3.00993e14i			0.698672i
$846$		0			0
$847$	−4.35115e13			−0.0998131
$848$	−3.98140e14	−	2.29866e14i	−0.907938	−	0.524198i
$849$		0			0
$850$	8.05195e13	+	1.39464e14i	0.181471	+	0.314317i
$851$	−3.78045e14	+	2.18264e14i	−0.847024	+	0.489030i
$852$		0			0
$853$	−1.56448e14	+	2.70976e14i	−0.346437	+	0.600047i	−0.985614	−	0.169013i	$-0.945942\pi$
$853$	−1.56448e14	+	2.70976e14i	−0.346437	+	0.600047i	0.639176	+	0.769060i	$0.279275\pi$
$854$			1.40566e14i			0.309450i
$855$		0			0
$856$	−4.94110e14			−1.07512
$857$	−4.91736e14	−	2.83904e14i	−1.06372	−	0.614140i	−0.137263	−	0.990535i	$-0.543830\pi$
$857$	−4.91736e14	−	2.83904e14i	−1.06372	−	0.614140i	−0.926460	+	0.376394i	$0.877164\pi$
$858$		0			0
$859$	−8.21583e12	−	1.42302e13i	−0.0175665	−	0.0304261i	0.857109	−	0.515136i	$-0.172259\pi$
$859$	−8.21583e12	−	1.42302e13i	−0.0175665	−	0.0304261i	−0.874675	+	0.484710i	$0.838925\pi$
$860$	2.80479e13	−	1.61935e13i	0.0596222	−	0.0344229i
$861$		0			0
$862$	−4.10922e13	+	7.11739e13i	−0.0863423	+	0.149549i
$863$		−	4.20844e14i		−	0.879158i	−0.898204	−	0.439579i	$-0.855128\pi$
$863$		−	4.20844e14i		−	0.879158i	0.898204	−	0.439579i	$-0.144872\pi$
$864$		0			0
$865$	−6.68586e14			−1.38063
$866$	6.35358e14	+	3.66824e14i	1.30445	+	0.753127i
$867$		0			0
$868$	9.22521e11	+	1.59785e12i	0.00187231	+	0.00324294i
$869$	8.12723e14	−	4.69226e14i	1.64000	−	0.946854i
$870$		0			0
$871$	3.55379e14	−	6.15534e14i	0.708925	−	1.22789i
$872$		−	3.81099e14i		−	0.755884i
$873$		0			0
$874$	2.81706e14			0.552381
$875$	1.42764e14	+	8.24250e13i	0.278342	+	0.160701i
$876$		0			0
$877$	−2.05307e14	−	3.55602e14i	−0.395736	−	0.685436i	0.597458	−	0.801900i	$-0.296177\pi$
$877$	−2.05307e14	−	3.55602e14i	−0.395736	−	0.685436i	−0.993195	+	0.116464i	$0.962844\pi$
$878$	3.53412e14	−	2.04042e14i	0.677343	−	0.391064i
$879$		0			0
$880$	5.71852e14	−	9.90476e14i	1.08360	−	1.87685i
$881$			2.02510e14i			0.381563i	0.981633	+	0.190782i	$0.0611022\pi$
$881$			2.02510e14i			0.381563i	−0.981633	+	0.190782i	$0.938898\pi$
$882$		0			0
$883$	4.02569e14			0.749957			0.374979	−	0.927033i	$-0.377650\pi$
$883$	4.02569e14			0.749957			0.374979	+	0.927033i	$0.377650\pi$
$884$	5.68047e12	+	3.27962e12i	0.0105226	+	0.00607523i
$885$		0			0
$886$	3.03774e14	+	5.26152e14i	0.556393	+	0.963701i
$887$	−1.43038e14	+	8.25833e13i	−0.260516	+	0.150409i	−0.624570	−	0.780969i	$-0.714726\pi$
$887$	−1.43038e14	+	8.25833e13i	−0.260516	+	0.150409i	0.364054	+	0.931378i	$0.381392\pi$
$888$		0			0
$889$	1.24775e13	−	2.16117e13i	0.0224709	−	0.0389207i
$890$		−	1.12477e15i		−	2.01425i
$891$		0			0
$892$	2.35614e13			0.0417232
$893$	4.16847e13	+	2.40667e13i	0.0734040	+	0.0423798i
$894$		0			0
$895$	−1.66733e14	−	2.88789e14i	−0.290339	−	0.502882i
$896$	−1.14182e14	+	6.59228e13i	−0.197722	+	0.114155i
$897$		0			0
$898$	3.93451e14	−	6.81477e14i	0.673766	−	1.16700i
$899$		−	1.21143e14i		−	0.206300i
$900$		0			0
$901$	−1.10709e14			−0.186448
$902$	1.34808e14	+	7.78313e13i	0.225778	+	0.130353i
$903$		0			0
$904$	9.61501e13	+	1.66537e14i	0.159260	+	0.275847i
$905$	−6.80597e14	+	3.92943e14i	−1.12111	+	0.647271i
$906$		0			0
$907$	−2.08486e14	+	3.61109e14i	−0.339658	+	0.588304i	−0.984368	−	0.176122i	$-0.943645\pi$
$907$	−2.08486e14	+	3.61109e14i	−0.339658	+	0.588304i	0.644711	+	0.764427i	$0.276978\pi$
$908$		−	4.74326e13i		−	0.0768508i
$909$		0			0
$910$	2.75061e14			0.440780
$911$	−8.19359e14	−	4.73057e14i	−1.30582	−	0.753914i	−0.324422	−	0.945913i	$-0.605170\pi$
$911$	−8.19359e14	−	4.73057e14i	−1.30582	−	0.753914i	−0.981395	+	0.191999i	$0.938503\pi$
$912$		0			0
$913$	−3.91558e13	−	6.78199e13i	−0.0617223	−	0.106906i
$914$	4.33544e12	−	2.50307e12i	0.00679677	−	0.00392412i
$915$		0			0
$916$	−2.57525e13	+	4.46046e13i	−0.0399339	+	0.0691676i
$917$			8.20969e13i			0.126614i
$918$		0			0
$919$	−4.56833e14			−0.696914			−0.348457	−	0.937325i	$-0.613294\pi$
$919$	−4.56833e14			−0.696914			−0.348457	+	0.937325i	$0.613294\pi$
$920$	1.54584e15	+	8.92492e14i	2.34545	+	1.35415i
$921$		0			0
$922$	−3.00754e14	−	5.20920e14i	−0.451394	−	0.781838i
$923$	8.46823e14	−	4.88913e14i	1.26411	−	0.729833i
$924$		0			0
$925$	−3.81284e14	+	6.60404e14i	−0.563041	+	0.975216i
$926$			1.09237e15i			1.60441i
$927$		0			0
$928$	−4.81581e13			−0.0699729
$929$	1.05626e14	+	6.09831e13i	0.152648	+	0.0881314i	0.574378	−	0.818590i	$-0.305244\pi$
$929$	1.05626e14	+	6.09831e13i	0.152648	+	0.0881314i	−0.421730	+	0.906721i	$0.638577\pi$
$930$		0			0
$931$	−1.09438e14	−	1.89553e14i	−0.156467	−	0.271008i
$932$	−4.01108e13	+	2.31580e13i	−0.0570403	+	0.0329323i
$933$		0			0
$934$	−1.22115e14	+	2.11509e14i	−0.171804	+	0.297574i
$935$		−	2.75417e14i		−	0.385418i
$936$		0			0
$937$	1.70076e14			0.235475			0.117737	−	0.993045i	$-0.462436\pi$
$937$	1.70076e14			0.235475			0.117737	+	0.993045i	$0.462436\pi$
$938$	−1.63852e14	−	9.46001e13i	−0.225651	−	0.130280i
$939$		0			0
$940$	−8.82233e12	−	1.52807e13i	−0.0120211	−	0.0208211i
$941$	3.49074e14	−	2.01538e14i	0.473118	−	0.273155i	−0.244426	−	0.969668i	$-0.578600\pi$
$941$	3.49074e14	−	2.01538e14i	0.473118	−	0.273155i	0.717544	+	0.696513i	$0.245266\pi$
$942$		0			0
$943$	−1.28135e14	+	2.21936e14i	−0.171834	+	0.297625i
$944$		−	6.53110e13i		−	0.0871217i
$945$		0			0
$946$	−6.98515e14			−0.921977
$947$	−9.23539e14	−	5.33205e14i	−1.21257	−	0.700075i	−0.249248	−	0.968440i	$-0.580184\pi$
$947$	−9.23539e14	−	5.33205e14i	−1.21257	−	0.700075i	−0.963317	+	0.268365i	$0.913517\pi$
$948$		0			0
$949$	3.39824e14	+	5.88592e14i	0.441492	+	0.764686i
$950$	4.26180e14	−	2.46055e14i	0.550776	−	0.317991i
$951$		0			0
$952$	−1.50902e13	+	2.61371e13i	−0.0192980	+	0.0334250i
$953$			1.49756e15i			1.90511i	0.304374	+	0.952553i	$0.401553\pi$
$953$			1.49756e15i			1.90511i	−0.304374	+	0.952553i	$0.598447\pi$
$954$		0			0
$955$	7.19350e14			0.905573
$956$	2.29501e13	+	1.32503e13i	0.0287406	+	0.0165934i
$957$		0			0
$958$	1.93666e14	+	3.35439e14i	0.240008	+	0.415706i
$959$	1.15144e14	−	6.64786e13i	0.141955	−	0.0819575i
$960$		0			0
$961$	3.67290e14	−	6.36165e14i	0.448118	−	0.776163i
$962$			5.98995e14i			0.727022i
$963$		0			0
$964$	−6.82436e13			−0.0819741
$965$	−1.01584e15	−	5.86495e14i	−1.21392	−	0.700854i
$966$		0			0
$967$	−1.35995e14	−	2.35550e14i	−0.160839	−	0.278581i	0.774331	−	0.632781i	$-0.218087\pi$
$967$	−1.35995e14	−	2.35550e14i	−0.160839	−	0.278581i	−0.935170	+	0.354200i	$0.884753\pi$
$968$	−3.35545e14	+	1.93727e14i	−0.394797	+	0.227936i
$969$		0			0
$970$	4.82318e14	−	8.35400e14i	0.561662	−	0.972827i
$971$		−	8.53100e14i		−	0.988334i	−0.869367	−	0.494167i	$-0.835473\pi$
$971$		−	8.53100e14i		−	0.988334i	0.869367	−	0.494167i	$-0.164527\pi$
$972$		0			0
$973$	−5.48071e13			−0.0628453
$974$	−5.97488e14	−	3.44960e14i	−0.681607	−	0.393526i
$975$		0			0
$976$	6.60173e14	+	1.14345e15i	0.745433	+	1.29113i
$977$	5.42026e14	−	3.12939e14i	0.608902	−	0.351550i	−0.163634	−	0.986521i	$-0.552321\pi$
$977$	5.42026e14	−	3.12939e14i	0.608902	−	0.351550i	0.772536	+	0.634971i	$0.218988\pi$
$978$		0			0
$979$	−6.28952e14	+	1.08938e15i	−0.699365	+	1.21134i
$980$			8.02355e13i			0.0887639i
$981$		0			0
$982$	−1.24763e15			−1.36625
$983$	1.01027e15	+	5.83278e14i	1.10070	+	0.635489i	0.936405	−	0.350922i	$-0.114132\pi$
$983$	1.01027e15	+	5.83278e14i	1.10070	+	0.635489i	0.164295	+	0.986411i	$0.447465\pi$
$984$		0			0
$985$	1.18669e14	+	2.05541e14i	0.127984	+	0.221675i
$986$	−9.92833e13	+	5.73212e13i	−0.106535	+	0.0615079i
$987$		0			0
$988$	1.00220e13	−	1.73586e13i	0.0106456	−	0.0184387i
$989$		−	1.14998e15i		−	1.21537i
$990$		0			0
$991$	−7.46502e14			−0.781021			−0.390511	−	0.920598i	$-0.627702\pi$
$991$	−7.46502e14			−0.781021			−0.390511	+	0.920598i	$0.627702\pi$
$992$	2.92797e13	+	1.69047e13i	0.0304795	+	0.0175974i
$993$		0			0
$994$	−1.30146e14	−	2.25420e14i	−0.134122	−	0.232306i
$995$	−2.05594e15	+	1.18700e15i	−2.10812	+	1.21712i
$996$		0			0
$997$	2.31616e14	−	4.01170e14i	0.235122	−	0.407242i	−0.724186	−	0.689604i	$-0.757785\pi$
$997$	2.31616e14	−	4.01170e14i	0.235122	−	0.407242i	0.959308	+	0.282362i	$0.0911178\pi$
$998$			1.49517e15i			1.51021i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.11.d.a.8.3		18
3.2	odd	2		9.11.d.a.2.7	✓	18
9.2	odd	6		81.11.b.a.80.5		18
9.4	even	3		9.11.d.a.5.7	yes	18
9.5	odd	6	inner	27.11.d.a.17.3		18
9.7	even	3		81.11.b.a.80.14		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.11.d.a.2.7	✓	18	3.2	odd	2
9.11.d.a.5.7	yes	18	9.4	even	3
27.11.d.a.8.3		18	1.1	even	1	trivial
27.11.d.a.17.3		18	9.5	odd	6	inner
81.11.b.a.80.5		18	9.2	odd	6
81.11.b.a.80.14		18	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(-28.4605 - 16.4317i) q^{2} +(28.0010 + 48.4991i) q^{4} +(4600.38 - 2656.03i) q^{5} +(-1786.25 + 3093.87i) q^{7} +31811.7i q^{8} -174572. q^{10} +(169079. + 97617.9i) q^{11} +(220523. + 381956. i) q^{13} +(101675. - 58702.1i) q^{14} +(551393. - 955040. i) q^{16} -265563. i q^{17} -811519. q^{19} +(257630. + 148743. i) q^{20} +(-3.20805e6 - 5.55651e6i) q^{22} +(9.14778e6 - 5.28147e6i) q^{23} +(9.22616e6 - 1.59802e7i) q^{25} -1.44942e7i q^{26} -200066. q^{28} +(1.13762e7 + 6.56804e6i) q^{29} +(-4.61108e6 - 7.98662e6i) q^{31} +(-3.17493e6 + 1.83305e6i) q^{32} +(-4.36365e6 + 7.55807e6i) q^{34} +1.89773e7i q^{35} -4.13264e7 q^{37} +(2.30963e7 + 1.33346e7i) q^{38} +(8.44928e7 + 1.46346e8i) q^{40} +(-2.10108e7 + 1.21306e7i) q^{41} +(5.44344e7 - 9.42832e7i) q^{43} +1.09336e7i q^{44} -3.47134e8 q^{46} +(-5.13663e7 - 2.96563e7i) q^{47} +(1.34856e8 + 2.33578e8i) q^{49} +(-5.25163e8 + 3.03203e8i) q^{50} +(-1.23497e7 + 2.13903e7i) q^{52} -4.16883e8i q^{53} +1.03710e9 q^{55} +(-9.84212e7 - 5.68235e7i) q^{56} +(-2.15848e8 - 3.73859e8i) q^{58} +(5.12892e7 - 2.96118e7i) q^{59} +(-5.98641e8 + 1.03688e9i) q^{61} +3.03071e8i q^{62} -1.00877e9 q^{64} +(2.02897e9 + 1.17143e9i) q^{65} +(-8.05765e8 - 1.39563e9i) q^{67} +(1.28796e7 - 7.43602e6i) q^{68} +(3.11829e8 - 5.40103e8i) q^{70} -2.21707e9i q^{71} +1.54099e9 q^{73} +(1.17617e9 + 6.79063e8i) q^{74} +(-2.27233e7 - 3.93579e7i) q^{76} +(-6.04034e8 + 3.48739e8i) q^{77} +(2.40338e9 - 4.16277e9i) q^{79} -5.85806e9i q^{80} +7.97306e8 q^{82} +(-3.47374e8 - 2.00556e8i) q^{83} +(-7.05343e8 - 1.22169e9i) q^{85} +(-3.09847e9 + 1.78890e9i) q^{86} +(-3.10539e9 + 5.37870e9i) q^{88} +6.44300e9i q^{89} -1.57563e9 q^{91} +(5.12293e8 + 2.95773e8i) q^{92} +(9.74608e8 + 1.68807e9i) q^{94} +(-3.73329e9 + 2.15542e9i) q^{95} +(-2.76286e9 + 4.78541e9i) q^{97} -8.86367e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 4095 q^{4} - 4956 q^{5} - 6120 q^{7} - 2052 q^{10} - 969 q^{11} + 140274 q^{13} + 2134578 q^{14} - 1571841 q^{16} + 2771370 q^{19} - 14542734 q^{20} - 3475521 q^{22} + 9944382 q^{23} + 14726277 q^{25}+ \cdots - 14510723337 q^{97}+O(q^{100}) \) 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

Introduction

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