LMFDB - Embedded newform 189.2.h.b.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(37,189)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.2
Root			$-0.335166 - 0.580525i$ of defining polynomial
Character	$\chi$	$=$	189.46
Dual form			189.2.h.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.670333 q^{2} -1.55065 q^{4} +(0.712469 - 1.23403i) q^{5} +(-2.36039 - 1.19522i) q^{7} +2.38012 q^{8} +O(q^{10})$	\(q-0.670333 q^{2} -1.55065 q^{4} +(0.712469 - 1.23403i) q^{5} +(-2.36039 - 1.19522i) q^{7} +2.38012 q^{8} +(-0.477591 + 0.827212i) q^{10} +(-2.46539 - 4.27018i) q^{11} +(-1.37730 - 2.38556i) q^{13} +(1.58225 + 0.801194i) q^{14} +1.50584 q^{16} +(-0.559839 + 0.969670i) q^{17} +(-2.00752 - 3.47713i) q^{19} +(-1.10479 + 1.91356i) q^{20} +(1.65263 + 2.86244i) q^{22} +(2.71830 - 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(0.923251 + 1.59912i) q^{26} +(3.66015 + 1.85337i) q^{28} +(-3.40555 + 5.89858i) q^{29} +2.50584 q^{31} -5.76965 q^{32} +(0.375279 - 0.650002i) q^{34} +(-3.15664 + 2.06124i) q^{35} +(0.709787 + 1.22939i) q^{37} +(1.34571 + 2.33083i) q^{38} +(1.69576 - 2.93714i) q^{40} +(-0.124384 - 0.215440i) q^{41} +(-0.498313 + 0.863104i) q^{43} +(3.82296 + 6.62156i) q^{44} +(-1.82217 + 3.15609i) q^{46} +9.47579 q^{47} +(4.14291 + 5.64237i) q^{49} +(-0.995294 - 1.72390i) q^{50} +(2.13572 + 3.69917i) q^{52} +(0.410229 - 0.710537i) q^{53} -7.02604 q^{55} +(-5.61802 - 2.84476i) q^{56} +(2.28285 - 3.95401i) q^{58} +6.58407 q^{59} +0.0752645 q^{61} -1.67974 q^{62} +0.855913 q^{64} -3.92514 q^{65} -12.5877 q^{67} +(0.868117 - 1.50362i) q^{68} +(2.11600 - 1.38172i) q^{70} -0.0804951 q^{71} +(5.34551 - 9.25869i) q^{73} +(-0.475793 - 0.824098i) q^{74} +(3.11297 + 5.39183i) q^{76} +(0.715488 + 13.0260i) q^{77} -1.84491 q^{79} +(1.07286 - 1.85825i) q^{80} +(0.0833788 + 0.144416i) q^{82} +(7.23583 - 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(0.334036 - 0.578567i) q^{86} +(-5.86792 - 10.1635i) q^{88} +(-6.76292 - 11.7137i) q^{89} +(0.399711 + 7.27703i) q^{91} +(-4.21515 + 7.30085i) q^{92} -6.35193 q^{94} -5.72119 q^{95} +(2.70160 - 4.67930i) q^{97} +(-2.77712 - 3.78226i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.670333			−0.473997			−0.236998	−	0.971510i	$-0.576164\pi$
$2$	−0.670333			−0.473997			−0.236998	+	0.971510i	$0.576164\pi$
$3$		0			0
$3$		0			0
$4$	−1.55065			−0.775327
$5$	0.712469	−	1.23403i	0.318626	−	0.551876i	−0.661576	−	0.749878i	$-0.730112\pi$
$5$	0.712469	−	1.23403i	0.318626	−	0.551876i	0.980202	+	0.198002i	$0.0634454\pi$
$6$		0			0
$7$	−2.36039	−	1.19522i	−0.892144	−	0.451750i
$7$	−2.36039	−	1.19522i	−0.892144	−	0.451750i
$8$	2.38012			0.841499
$9$		0			0
$10$	−0.477591	+	0.827212i	−0.151028	+	0.261587i
$11$	−2.46539	−	4.27018i	−0.743342	−	1.28751i	−0.950965	−	0.309297i	$-0.899906\pi$
$11$	−2.46539	−	4.27018i	−0.743342	−	1.28751i	0.207623	−	0.978209i	$-0.433427\pi$
$12$		0			0
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	0.609352	−	0.792900i	$-0.291429\pi$
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	−0.991347	+	0.131265i	$0.958096\pi$
$14$	1.58225	+	0.801194i	0.422874	+	0.214128i
$15$		0			0
$16$	1.50584			0.376459
$17$	−0.559839	+	0.969670i	−0.135781	+	0.235180i	−0.925896	−	0.377780i	$-0.876688\pi$
$17$	−0.559839	+	0.969670i	−0.135781	+	0.235180i	0.790115	+	0.612959i	$0.210021\pi$
$18$		0			0
$19$	−2.00752	−	3.47713i	−0.460557	−	0.797709i	0.538431	−	0.842669i	$-0.319017\pi$
$19$	−2.00752	−	3.47713i	−0.460557	−	0.797709i	−0.998989	+	0.0449606i	$0.985684\pi$
$20$	−1.10479	+	1.91356i	−0.247039	+	0.427884i
$21$		0			0
$22$	1.65263	+	2.86244i	0.352342	+	0.610274i
$23$	2.71830	−	4.70824i	0.566806	−	0.981736i	−0.430073	−	0.902794i	$-0.641512\pi$
$23$	2.71830	−	4.70824i	0.566806	−	0.981736i	0.996879	−	0.0789424i	$-0.0251543\pi$
$24$		0			0
$25$	1.48478	+	2.57171i	0.296955	+	0.514342i
$26$	0.923251	+	1.59912i	0.181064	+	0.313613i
$27$		0			0
$28$	3.66015	+	1.85337i	0.691704	+	0.350254i
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	0.354667	+	0.934993i	$0.384594\pi$
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	−0.987061	+	0.160346i	$0.948739\pi$
$30$		0			0
$31$	2.50584			0.450061			0.225031	−	0.974352i	$-0.427752\pi$
$31$	2.50584			0.450061			0.225031	+	0.974352i	$0.427752\pi$
$32$	−5.76965			−1.01994
$33$		0			0
$34$	0.375279	−	0.650002i	0.0643597	−	0.111474i
$35$	−3.15664	+	2.06124i	−0.533570	+	0.348414i
$36$		0			0
$37$	0.709787	+	1.22939i	0.116688	+	0.202110i	0.918453	−	0.395529i	$-0.129439\pi$
$37$	0.709787	+	1.22939i	0.116688	+	0.202110i	−0.801765	+	0.597639i	$0.796106\pi$
$38$	1.34571	+	2.33083i	0.218303	+	0.378111i
$39$		0			0
$40$	1.69576	−	2.93714i	0.268123	−	0.464403i
$41$	−0.124384	−	0.215440i	−0.0194256	−	0.0336460i	0.856149	−	0.516729i	$-0.172850\pi$
$41$	−0.124384	−	0.215440i	−0.0194256	−	0.0336460i	−0.875575	+	0.483083i	$0.839517\pi$
$42$		0			0
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	−0.901517	−	0.432743i	$-0.857546\pi$
$43$	−0.498313	+	0.863104i	−0.0759921	+	0.131622i	0.825525	+	0.564365i	$0.190879\pi$
$44$	3.82296	+	6.62156i	0.576333	+	0.998238i
$45$		0			0
$46$	−1.82217	+	3.15609i	−0.268664	+	0.465340i
$47$	9.47579			1.38219			0.691093	−	0.722766i	$-0.257129\pi$
$47$	9.47579			1.38219			0.691093	+	0.722766i	$0.257129\pi$
$48$		0			0
$49$	4.14291	+	5.64237i	0.591844	+	0.806053i
$50$	−0.995294	−	1.72390i	−0.140756	−	0.243796i
$51$		0			0
$52$	2.13572	+	3.69917i	0.296171	+	0.512983i
$53$	0.410229	−	0.710537i	0.0563493	−	0.0975998i	−0.836475	−	0.548005i	$-0.815387\pi$
$53$	0.410229	−	0.710537i	0.0563493	−	0.0975998i	0.892824	+	0.450406i	$0.148721\pi$
$54$		0			0
$55$	−7.02604			−0.947392
$56$	−5.61802	−	2.84476i	−0.750739	−	0.380147i
$57$		0			0
$58$	2.28285	−	3.95401i	0.299753	−	0.519187i
$59$	6.58407			0.857173			0.428586	−	0.903501i	$-0.359012\pi$
$59$	6.58407			0.857173			0.428586	+	0.903501i	$0.359012\pi$
$60$		0			0
$61$	0.0752645			0.00963663			0.00481831	−	0.999988i	$-0.498466\pi$
$61$	0.0752645			0.00963663			0.00481831	+	0.999988i	$0.498466\pi$
$62$	−1.67974			−0.213328
$63$		0			0
$64$	0.855913			0.106989
$65$	−3.92514			−0.486854
$66$		0			0
$67$	−12.5877			−1.53783			−0.768916	−	0.639350i	$-0.779204\pi$
$67$	−12.5877			−1.53783			−0.768916	+	0.639350i	$0.779204\pi$
$68$	0.868117	−	1.50362i	0.105275	−	0.182341i
$69$		0			0
$70$	2.11600	−	1.38172i	0.252911	−	0.165147i
$71$	−0.0804951			−0.00955301			−0.00477651	−	0.999989i	$-0.501520\pi$
$71$	−0.0804951			−0.00955301			−0.00477651	+	0.999989i	$0.501520\pi$
$72$		0			0
$73$	5.34551	−	9.25869i	0.625644	−	1.08365i	−0.362772	−	0.931878i	$-0.618170\pi$
$73$	5.34551	−	9.25869i	0.625644	−	1.08365i	0.988416	−	0.151769i	$-0.0484971\pi$
$74$	−0.475793	−	0.824098i	−0.0553098	−	0.0957995i
$75$		0			0
$76$	3.11297	+	5.39183i	0.357083	+	0.618485i
$77$	0.715488	+	13.0260i	0.0815374	+	1.48445i
$78$		0			0
$79$	−1.84491			−0.207569			−0.103785	−	0.994600i	$-0.533095\pi$
$79$	−1.84491			−0.207569			−0.103785	+	0.994600i	$0.533095\pi$
$80$	1.07286	−	1.85825i	0.119950	−	0.207759i
$81$		0			0
$82$	0.0833788	+	0.144416i	0.00920765	+	0.0159481i
$83$	7.23583	−	12.5328i	0.794236	−	1.37566i	−0.129088	−	0.991633i	$-0.541205\pi$
$83$	7.23583	−	12.5328i	0.794236	−	1.37566i	0.923323	−	0.384023i	$-0.125462\pi$
$84$		0			0
$85$	0.797736	+	1.38172i	0.0865266	+	0.149868i
$86$	0.334036	−	0.578567i	0.0360200	−	0.0623885i
$87$		0			0
$88$	−5.86792	−	10.1635i	−0.625522	−	1.08344i
$89$	−6.76292	−	11.7137i	−0.716868	−	1.24165i	−0.962235	−	0.272222i	$-0.912242\pi$
$89$	−6.76292	−	11.7137i	−0.716868	−	1.24165i	0.245366	−	0.969430i	$-0.421092\pi$
$90$		0			0
$91$	0.399711	+	7.27703i	0.0419011	+	0.762840i
$92$	−4.21515	+	7.30085i	−0.439460	+	0.761167i
$93$		0			0
$94$	−6.35193			−0.655152
$95$	−5.72119			−0.586982
$96$		0			0
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	−0.695654	−	0.718377i	$-0.744885\pi$
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	0.969960	+	0.243266i	$0.0782187\pi$
$98$	−2.77712	−	3.78226i	−0.280532	−	0.382066i
$99$		0			0
$100$	−2.30238	−	3.98783i	−0.230238	−	0.398783i
$101$	−2.56770	−	4.44739i	−0.255496	−	0.442531i	0.709534	−	0.704671i	$-0.248905\pi$
$101$	−2.56770	−	4.44739i	−0.255496	−	0.442531i	−0.965030	+	0.262139i	$0.915572\pi$
$102$		0			0
$103$	7.10561	−	12.3073i	0.700137	−	1.21267i	−0.268282	−	0.963341i	$-0.586456\pi$
$103$	7.10561	−	12.3073i	0.700137	−	1.21267i	0.968418	−	0.249332i	$-0.0802109\pi$
$104$	−3.27814	−	5.67791i	−0.321448	−	0.556765i
$105$		0			0
$106$	−0.274990	+	0.476296i	−0.0267094	+	0.0462620i
$107$	−3.83015	−	6.63401i	−0.370274	−	0.641334i	0.619333	−	0.785128i	$-0.287403\pi$
$107$	−3.83015	−	6.63401i	−0.370274	−	0.641334i	−0.989608	+	0.143794i	$0.954070\pi$
$108$		0			0
$109$	−0.849394	+	1.47119i	−0.0813572	+	0.140915i	−0.903833	−	0.427885i	$-0.859259\pi$
$109$	−0.849394	+	1.47119i	−0.0813572	+	0.140915i	0.822476	+	0.568800i	$0.192592\pi$
$110$	4.70979			0.449061
$111$		0			0
$112$	−3.55436	−	1.79980i	−0.335856	−	0.170065i
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	0.879807	−	0.475331i	$-0.157672\pi$
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	−0.851552	+	0.524270i	$0.824338\pi$
$114$		0			0
$115$	−3.87341	−	6.70895i	−0.361198	−	0.625613i
$116$	5.28083	−	9.14666i	0.490312	−	0.849246i
$117$		0			0
$118$	−4.41352			−0.406297
$119$	2.48041	−	1.61967i	0.227379	−	0.148475i
$120$		0			0
$121$	−6.65626	+	11.5290i	−0.605115	+	1.04809i
$122$	−0.0504522			−0.00456773
$123$		0			0
$124$	−3.88569			−0.348945
$125$	11.3561			1.01572
$126$		0			0
$127$	7.25977			0.644200			0.322100	−	0.946706i	$-0.395611\pi$
$127$	7.25977			0.644200			0.322100	+	0.946706i	$0.395611\pi$
$128$	10.9656			0.969227
$129$		0			0
$130$	2.63115			0.230767
$131$	−10.2265	+	17.7128i	−0.893492	+	1.54757i	−0.0578326	+	0.998326i	$0.518419\pi$
$131$	−10.2265	+	17.7128i	−0.893492	+	1.54757i	−0.835660	+	0.549248i	$0.814914\pi$
$132$		0			0
$133$	0.582610	+	10.6068i	0.0505187	+	0.919728i
$134$	8.43794			0.728927
$135$		0			0
$136$	−1.33248	+	2.30793i	−0.114260	+	0.197903i
$137$	6.10581	+	10.5756i	0.521655	+	0.903532i	0.999683	+	0.0251879i	$0.00801840\pi$
$137$	6.10581	+	10.5756i	0.521655	+	0.903532i	−0.478028	+	0.878345i	$0.658648\pi$
$138$		0			0
$139$	−1.24092	−	2.14933i	−0.105253	−	0.182304i	0.808588	−	0.588375i	$-0.200232\pi$
$139$	−1.24092	−	2.14933i	−0.105253	−	0.182304i	−0.913842	+	0.406071i	$0.866899\pi$
$140$	4.89486	−	3.19628i	0.413691	−	0.270135i
$141$		0			0
$142$	0.0539585			0.00452810
$143$	−6.79117	+	11.7626i	−0.567906	+	0.983642i
$144$		0			0
$145$	4.85269	+	8.40511i	0.402994	+	0.698006i
$146$	−3.58327	+	6.20640i	−0.296553	+	0.513645i
$147$		0			0
$148$	−1.10063	−	1.90635i	−0.0904715	−	0.156701i
$149$	−4.27797	+	7.40966i	−0.350465	+	0.607023i	−0.986331	−	0.164777i	$-0.947310\pi$
$149$	−4.27797	+	7.40966i	−0.350465	+	0.607023i	0.635866	+	0.771799i	$0.280643\pi$
$150$		0			0
$151$	8.82962	+	15.2933i	0.718544	+	1.24455i	0.961577	+	0.274537i	$0.0885244\pi$
$151$	8.82962	+	15.2933i	0.718544	+	1.24455i	−0.243033	+	0.970018i	$0.578142\pi$
$152$	−4.77814	−	8.27599i	−0.387559	−	0.671271i
$153$		0			0
$154$	−0.479615	−	8.73173i	−0.0386485	−	0.703623i
$155$	1.78533	−	3.09228i	0.143401	−	0.248378i
$156$		0			0
$157$	6.32149			0.504510			0.252255	−	0.967661i	$-0.418828\pi$
$157$	6.32149			0.504510			0.252255	+	0.967661i	$0.418828\pi$
$158$	1.23671			0.0983871
$159$		0			0
$160$	−4.11070	+	7.11993i	−0.324979	+	0.562880i
$161$	−12.0436	+	7.86433i	−0.949172	+	0.619796i
$162$		0			0
$163$	−4.01134	−	6.94784i	−0.314192	−	0.544197i	0.665073	−	0.746778i	$-0.268400\pi$
$163$	−4.01134	−	6.94784i	−0.314192	−	0.544197i	−0.979265	+	0.202581i	$0.935067\pi$
$164$	0.192877	+	0.334073i	0.0150612	+	0.0260867i
$165$		0			0
$166$	−4.85041	+	8.40116i	−0.376465	+	0.652057i
$167$	−1.06038	−	1.83663i	−0.0820545	−	0.142123i	0.822078	−	0.569375i	$-0.192815\pi$
$167$	−1.06038	−	1.83663i	−0.0820545	−	0.142123i	−0.904132	+	0.427253i	$0.859482\pi$
$168$		0			0
$169$	2.70608	−	4.68706i	0.208160	−	0.360543i
$170$	−0.534749	−	0.926212i	−0.0410133	−	0.0710372i
$171$		0			0
$172$	0.772712	−	1.33838i	0.0589187	−	0.102050i
$173$	18.2881			1.39042			0.695208	−	0.718808i	$-0.255312\pi$
$173$	18.2881			1.39042			0.695208	+	0.718808i	$0.255312\pi$
$174$		0			0
$175$	−0.430902	−	7.84487i	−0.0325731	−	0.593017i
$176$	−3.71247	−	6.43018i	−0.279838	−	0.484693i
$177$		0			0
$178$	4.53341	+	7.85209i	0.339793	+	0.588539i
$179$	−3.81276	+	6.60389i	−0.284979	+	0.493598i	−0.972604	−	0.232468i	$-0.925320\pi$
$179$	−3.81276	+	6.60389i	−0.284979	+	0.493598i	0.687625	+	0.726066i	$0.258653\pi$
$180$		0			0
$181$	15.5305			1.15438			0.577188	−	0.816611i	$-0.304150\pi$
$181$	15.5305			1.15438			0.577188	+	0.816611i	$0.304150\pi$
$182$	−0.267940	−	4.87803i	−0.0198610	−	0.361584i
$183$		0			0
$184$	6.46989	−	11.2062i	0.476967	−	0.826130i
$185$	2.02280			0.148719
$186$		0			0
$187$	5.52088			0.403727
$188$	−14.6937			−1.07165
$189$		0			0
$190$	3.83510			0.278227
$191$	−14.8325			−1.07324			−0.536620	−	0.843824i	$-0.680299\pi$
$191$	−14.8325			−1.07324			−0.536620	+	0.843824i	$0.680299\pi$
$192$		0			0
$193$	16.5677			1.19257			0.596286	−	0.802772i	$-0.296642\pi$
$193$	16.5677			1.19257			0.596286	+	0.802772i	$0.296642\pi$
$194$	−1.81097	+	3.13669i	−0.130020	+	0.225201i
$195$		0			0
$196$	−6.42421	−	8.74936i	−0.458872	−	0.624955i
$197$	4.03740			0.287653			0.143826	−	0.989603i	$-0.454059\pi$
$197$	4.03740			0.287653			0.143826	+	0.989603i	$0.454059\pi$
$198$		0			0
$199$	−12.6407	+	21.8943i	−0.896076	+	1.55205i	−0.0636081	+	0.997975i	$0.520261\pi$
$199$	−12.6407	+	21.8943i	−0.896076	+	1.55205i	−0.832468	+	0.554074i	$0.813073\pi$
$200$	3.53395	+	6.12097i	0.249888	+	0.432818i
$201$		0			0
$202$	1.72121	+	2.98123i	0.121104	+	0.209758i
$203$	15.0885	−	9.85259i	1.05901	−	0.691516i
$204$		0			0
$205$	−0.354480			−0.0247579
$206$	−4.76312	+	8.24997i	−0.331862	+	0.574803i
$207$		0			0
$208$	−2.07399	−	3.59226i	−0.143805	−	0.249078i
$209$	−9.89864	+	17.1449i	−0.684703	+	1.18594i
$210$		0			0
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	0.706961	−	0.707253i	$-0.250066\pi$
$211$	−3.76246	−	6.51678i	−0.259019	−	0.448634i	−0.965979	+	0.258619i	$0.916732\pi$
$212$	−0.636123	+	1.10180i	−0.0436891	+	0.0756718i
$213$		0			0
$214$	2.56747	+	4.44699i	0.175509	+	0.303990i
$215$	0.710065	+	1.22987i	0.0484261	+	0.0838764i
$216$		0			0
$217$	−5.91476	−	2.99502i	−0.401520	−	0.203315i
$218$	0.569377	−	0.986190i	0.0385631	−	0.0667932i
$219$		0			0
$220$	10.8950			0.734538
$221$	3.08427			0.207471
$222$		0			0
$223$	6.49230	−	11.2450i	0.434757	−	0.753020i	−0.562519	−	0.826784i	$-0.690168\pi$
$223$	6.49230	−	11.2450i	0.434757	−	0.753020i	0.997276	+	0.0737638i	$0.0235011\pi$
$224$	13.6186	+	6.89599i	0.909934	+	0.460758i
$225$		0			0
$226$	−0.201335	−	0.348723i	−0.0133926	−	0.0231967i
$227$	−14.4832	−	25.0857i	−0.961286	−	1.66500i	−0.719277	−	0.694723i	$-0.755527\pi$
$227$	−14.4832	−	25.0857i	−0.961286	−	1.66500i	−0.242009	−	0.970274i	$-0.577806\pi$
$228$		0			0
$229$	−7.71790	+	13.3678i	−0.510013	+	0.883369i	0.489919	+	0.871768i	$0.337026\pi$
$229$	−7.71790	+	13.3678i	−0.510013	+	0.883369i	−0.999933	+	0.0116012i	$0.996307\pi$
$230$	2.59648	+	4.49723i	0.171207	+	0.296538i
$231$		0			0
$232$	−8.10561	+	14.0393i	−0.532159	+	0.921727i
$233$	2.47324	+	4.28378i	0.162027	+	0.280640i	0.935596	−	0.353073i	$-0.114863\pi$
$233$	2.47324	+	4.28378i	0.162027	+	0.280640i	−0.773568	+	0.633713i	$0.781530\pi$
$234$		0			0
$235$	6.75121	−	11.6934i	0.440400	−	0.762795i
$236$	−10.2096			−0.664589
$237$		0			0
$238$	−1.66270	+	1.08572i	−0.107777	+	0.0703767i
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	0.574523	−	0.818489i	$-0.305188\pi$
$239$	−6.51732	−	11.2883i	−0.421571	−	0.730182i	−0.996093	+	0.0883069i	$0.971854\pi$
$240$		0			0
$241$	−7.29123	−	12.6288i	−0.469670	−	0.813492i	0.529729	−	0.848167i	$-0.322294\pi$
$241$	−7.29123	−	12.6288i	−0.469670	−	0.813492i	−0.999399	+	0.0346754i	$0.988960\pi$
$242$	4.46191	−	7.72826i	0.286823	−	0.496791i
$243$		0			0
$244$	−0.116709			−0.00747154
$245$	9.91456	−	1.09247i	0.633418	−	0.0697951i
$246$		0			0
$247$	−5.52993	+	9.57812i	−0.351861	+	0.609441i
$248$	5.96419			0.378726
$249$		0			0
$250$	−7.61238			−0.481449
$251$	14.0715			0.888187			0.444094	−	0.895980i	$-0.353526\pi$
$251$	14.0715			0.888187			0.444094	+	0.895980i	$0.353526\pi$
$252$		0			0
$253$	−26.8067			−1.68532
$254$	−4.86646			−0.305349
$255$		0			0
$256$	−9.06240			−0.566400
$257$	−4.18108	+	7.24184i	−0.260808	+	0.451733i	−0.966457	−	0.256829i	$-0.917322\pi$
$257$	−4.18108	+	7.24184i	−0.260808	+	0.451733i	0.705649	+	0.708562i	$0.250656\pi$
$258$		0			0
$259$	−0.205989	−	3.75019i	−0.0127996	−	0.233025i
$260$	6.08653			0.377471
$261$		0			0
$262$	6.85515	−	11.8735i	0.423512	−	0.733545i
$263$	1.63533	+	2.83247i	0.100839	+	0.174658i	0.912030	−	0.410122i	$-0.134514\pi$
$263$	1.63533	+	2.83247i	0.100839	+	0.174658i	−0.811192	+	0.584780i	$0.801181\pi$
$264$		0			0
$265$	−0.584551	−	1.01247i	−0.0359087	−	0.0621956i
$266$	−0.390542	−	7.11010i	−0.0239457	−	0.435948i
$267$		0			0
$268$	19.5192			1.19232
$269$	7.69349	−	13.3255i	0.469081	−	0.812471i	−0.530295	−	0.847813i	$-0.677919\pi$
$269$	7.69349	−	13.3255i	0.469081	−	0.812471i	0.999375	+	0.0353420i	$0.0112521\pi$
$270$		0			0
$271$	4.06308	+	7.03747i	0.246815	+	0.427496i	0.962640	−	0.270783i	$-0.0872827\pi$
$271$	4.06308	+	7.03747i	0.246815	+	0.427496i	−0.715825	+	0.698279i	$0.753949\pi$
$272$	−0.843026	+	1.46016i	−0.0511160	+	0.0885355i
$273$		0			0
$274$	−4.09293	−	7.08915i	−0.247263	−	0.428271i
$275$	7.32110	−	12.6805i	0.441479	−	0.764664i
$276$		0			0
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	0.605982	−	0.795478i	$-0.292780\pi$
$277$	−6.42287	−	11.1247i	−0.385913	−	0.668421i	−0.991895	+	0.127057i	$0.959447\pi$
$278$	0.831826	+	1.44077i	0.0498896	+	0.0864114i
$279$		0			0
$280$	−7.51319	+	4.90601i	−0.448999	+	0.293190i
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	−0.843620	−	0.536941i	$-0.819580\pi$
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	0.886815	+	0.462125i	$0.152913\pi$
$282$		0			0
$283$	−17.4385			−1.03661			−0.518306	−	0.855195i	$-0.673437\pi$
$283$	−17.4385			−1.03661			−0.518306	+	0.855195i	$0.673437\pi$
$284$	0.124820			0.00740671
$285$		0			0
$286$	4.55234	−	7.88489i	0.269186	−	0.466243i
$287$	0.0360979	+	0.657189i	0.00213079	+	0.0387926i
$288$		0			0
$289$	7.87316	+	13.6367i	0.463127	+	0.802160i
$290$	−3.25292	−	5.63422i	−0.191018	−	0.330853i
$291$		0			0
$292$	−8.28903	+	14.3570i	−0.485079	+	0.840181i
$293$	0.900048	+	1.55893i	0.0525814	+	0.0910736i	0.891118	−	0.453772i	$-0.149922\pi$
$293$	0.900048	+	1.55893i	0.0525814	+	0.0910736i	−0.838537	+	0.544845i	$0.816588\pi$
$294$		0			0
$295$	4.69094	−	8.12495i	0.273117	−	0.473053i
$296$	1.68938	+	2.92609i	0.0981931	+	0.170075i
$297$		0			0
$298$	2.86766	−	4.96693i	0.166119	−	0.287727i
$299$	−14.9757			−0.866068
$300$		0			0
$301$	2.20781	−	1.44167i	0.127256	−	0.0830965i
$302$	−5.91878	−	10.2516i	−0.340588	−	0.589915i
$303$		0			0
$304$	−3.02300	−	5.23599i	−0.173381	−	0.300305i
$305$	0.0536236	−	0.0928787i	0.00307048	−	0.00531822i
$306$		0			0
$307$	1.06478			0.0607699			0.0303850	−	0.999538i	$-0.490327\pi$
$307$	1.06478			0.0607699			0.0303850	+	0.999538i	$0.490327\pi$
$308$	−1.10947	−	20.1988i	−0.0632181	−	1.15093i
$309$		0			0
$310$	−1.19676	+	2.07286i	−0.0679717	+	0.117730i
$311$	16.9293			0.959970			0.479985	−	0.877277i	$-0.340642\pi$
$311$	16.9293			0.959970			0.479985	+	0.877277i	$0.340642\pi$
$312$		0			0
$313$	−8.27856			−0.467932			−0.233966	−	0.972245i	$-0.575170\pi$
$313$	−8.27856			−0.467932			−0.233966	+	0.972245i	$0.575170\pi$
$314$	−4.23750			−0.239136
$315$		0			0
$316$	2.86082			0.160934
$317$	−6.54741			−0.367739			−0.183870	−	0.982951i	$-0.558862\pi$
$317$	−6.54741			−0.367739			−0.183870	+	0.982951i	$0.558862\pi$
$318$		0			0
$319$	33.5840			1.88034
$320$	0.609811	−	1.05622i	0.0340895	−	0.0590447i
$321$		0			0
$322$	8.07325	−	5.27172i	0.449905	−	0.293781i
$323$	4.49556			0.250140
$324$		0			0
$325$	4.08997	−	7.08404i	0.226871	−	0.392952i
$326$	2.68893	+	4.65736i	0.148926	+	0.257947i
$327$		0			0
$328$	−0.296049	−	0.512773i	−0.0163466	−	0.0283131i
$329$	−22.3666	−	11.3256i	−1.23311	−	0.624403i
$330$		0			0
$331$	−26.7258			−1.46899			−0.734493	−	0.678617i	$-0.762580\pi$
$331$	−26.7258			−1.46899			−0.734493	+	0.678617i	$0.762580\pi$
$332$	−11.2203	+	19.4341i	−0.615792	+	1.06658i
$333$		0			0
$334$	0.710806	+	1.23115i	0.0388936	+	0.0673657i
$335$	−8.96834	+	15.5336i	−0.489993	+	0.848692i
$336$		0			0
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	0.706694	−	0.707520i	$-0.250186\pi$
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	−0.966077	+	0.258255i	$0.916853\pi$
$338$	−1.81397	+	3.14189i	−0.0986670	+	0.170896i
$339$		0			0
$340$	−1.23701	−	2.14257i	−0.0670864	−	0.116197i
$341$	−6.17786	−	10.7004i	−0.334550	−	0.579457i
$342$		0			0
$343$	−3.03502	−	18.2699i	−0.163876	−	0.986481i
$344$	−1.18605	+	2.05429i	−0.0639473	+	0.110760i
$345$		0			0
$346$	−12.2591			−0.659053
$347$	18.7031			1.00404			0.502018	−	0.864857i	$-0.332591\pi$
$347$	18.7031			1.00404			0.502018	+	0.864857i	$0.332591\pi$
$348$		0			0
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	0.109893	+	0.993943i	$0.464949\pi$
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	−0.915727	+	0.401801i	$0.868384\pi$
$350$	0.288848	+	5.25868i	0.0154396	+	0.281088i
$351$		0			0
$352$	14.2244	+	24.6374i	0.758164	+	1.31318i
$353$	3.12966	+	5.42074i	0.166575	+	0.288517i	0.937214	−	0.348756i	$-0.113396\pi$
$353$	3.12966	+	5.42074i	0.166575	+	0.288517i	−0.770638	+	0.637273i	$0.780062\pi$
$354$		0			0
$355$	−0.0573502	+	0.0993335i	−0.00304383	+	0.00527208i
$356$	10.4870	+	18.1639i	0.555807	+	0.962686i
$357$		0			0
$358$	2.55582	−	4.42680i	0.135079	−	0.233964i
$359$	5.09755	+	8.82921i	0.269038	+	0.465988i	0.968614	−	0.248571i	$-0.0799608\pi$
$359$	5.09755	+	8.82921i	0.269038	+	0.465988i	−0.699575	+	0.714559i	$0.746628\pi$
$360$		0			0
$361$	1.43970	−	2.49364i	0.0757739	−	0.131244i
$362$	−10.4106			−0.547171
$363$		0			0
$364$	−0.619814	−	11.2842i	−0.0324871	−	0.591450i
$365$	−7.61701	−	13.1931i	−0.398693	−	0.690556i
$366$		0			0
$367$	14.3278	+	24.8165i	0.747906	+	1.29541i	0.948824	+	0.315804i	$0.102274\pi$
$367$	14.3278	+	24.8165i	0.747906	+	1.29541i	−0.200918	+	0.979608i	$0.564392\pi$
$368$	4.09332	−	7.08984i	0.213379	−	0.369584i
$369$		0			0
$370$	−1.35595			−0.0704926
$371$	−1.81755	+	1.18683i	−0.0943624	+	0.0616173i
$372$		0			0
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	−0.579421	−	0.815028i	$-0.696721\pi$
$373$	8.03670	−	13.9200i	0.416124	−	0.720749i	0.995546	+	0.0942796i	$0.0300548\pi$
$374$	−3.70083			−0.191365
$375$		0			0
$376$	22.5535			1.16311
$377$	18.7619			0.966286
$378$		0			0
$379$	−1.01893			−0.0523388			−0.0261694	−	0.999658i	$-0.508331\pi$
$379$	−1.01893			−0.0523388			−0.0261694	+	0.999658i	$0.508331\pi$
$380$	8.87158			0.455103
$381$		0			0
$382$	9.94270			0.508713
$383$	−5.79327	+	10.0342i	−0.296022	+	0.512725i	−0.975222	−	0.221228i	$-0.928994\pi$
$383$	−5.79327	+	10.0342i	−0.296022	+	0.512725i	0.679200	+	0.733953i	$0.262327\pi$
$384$		0			0
$385$	16.5842	+	8.39766i	0.845210	+	0.427984i
$386$	−11.1059			−0.565275
$387$		0			0
$388$	−4.18924	+	7.25598i	−0.212677	+	0.368367i
$389$	8.90675	+	15.4270i	0.451590	+	0.782178i	0.998485	−	0.0550239i	$-0.0175235\pi$
$389$	8.90675	+	15.4270i	0.451590	+	0.782178i	−0.546895	+	0.837201i	$0.684190\pi$
$390$		0			0
$391$	3.04363	+	5.27172i	0.153923	+	0.266602i
$392$	9.86061	+	13.4295i	0.498036	+	0.678293i
$393$		0			0
$394$	−2.70640			−0.136346
$395$	−1.31444	+	2.27668i	−0.0661369	+	0.114552i
$396$		0			0
$397$	−6.54229	−	11.3316i	−0.328348	−	0.568715i	0.653836	−	0.756636i	$-0.273159\pi$
$397$	−6.54229	−	11.3316i	−0.328348	−	0.568715i	−0.982184	+	0.187921i	$0.939825\pi$
$398$	8.47348	−	14.6765i	0.424737	−	0.735666i
$399$		0			0
$400$	2.23583	+	3.87257i	0.111792	+	0.193629i
$401$	7.05165	−	12.2138i	0.352143	−	0.609929i	−0.634482	−	0.772938i	$-0.718787\pi$
$401$	7.05165	−	12.2138i	0.352143	−	0.609929i	0.986625	+	0.163009i	$0.0521199\pi$
$402$		0			0
$403$	−3.45129	−	5.97782i	−0.171921	−	0.297776i
$404$	3.98161	+	6.89636i	0.198093	+	0.343107i
$405$		0			0
$406$	−10.1143	+	6.60452i	−0.501966	+	0.327777i
$407$	3.49980	−	6.06183i	0.173479	−	0.300474i
$408$		0			0
$409$	−2.64599			−0.130836			−0.0654179	−	0.997858i	$-0.520838\pi$
$409$	−2.64599			−0.130836			−0.0654179	+	0.997858i	$0.520838\pi$
$410$	0.237619			0.0117352
$411$		0			0
$412$	−11.0183	+	19.0843i	−0.542835	+	0.940217i
$413$	−15.5410	−	7.86940i	−0.764722	−	0.387228i
$414$		0			0
$415$	−10.3106	−	17.8585i	−0.506128	−	0.876639i
$416$	7.94655	+	13.7638i	0.389612	+	0.674827i
$417$		0			0
$418$	6.63538	−	11.4928i	0.324547	−	0.562132i
$419$	−16.7567	−	29.0235i	−0.818619	−	1.41789i	−0.906700	−	0.421776i	$-0.861407\pi$
$419$	−16.7567	−	29.0235i	−0.818619	−	1.41789i	0.0880816	−	0.996113i	$-0.471926\pi$
$420$		0			0
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	−0.918943	−	0.394390i	$-0.870956\pi$
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	0.801024	+	0.598633i	$0.204289\pi$
$422$	2.52210	+	4.36841i	0.122774	+	0.212651i
$423$		0			0
$424$	0.976394	−	1.69116i	0.0474179	−	0.0821302i
$425$	−3.32495			−0.161284
$426$		0			0
$427$	−0.177654	−	0.0899575i	−0.00859726	−	0.00435335i
$428$	5.93923	+	10.2871i	0.287084	+	0.497244i
$429$		0			0
$430$	−0.475980	−	0.824422i	−0.0229538	−	0.0397571i
$431$	−17.6643	+	30.5954i	−0.850858	+	1.47373i	0.0295774	+	0.999562i	$0.490584\pi$
$431$	−17.6643	+	30.5954i	−0.850858	+	1.47373i	−0.880435	+	0.474166i	$0.842749\pi$
$432$		0			0
$433$	5.47404			0.263066			0.131533	−	0.991312i	$-0.458010\pi$
$433$	5.47404			0.263066			0.131533	+	0.991312i	$0.458010\pi$
$434$	3.96485	+	2.00766i	0.190319	+	0.0963708i
$435$		0			0
$436$	1.31712	−	2.28131i	0.0630785	−	0.109255i
$437$	−21.8282			−1.04419
$438$		0			0
$439$	6.39812			0.305365			0.152683	−	0.988275i	$-0.451209\pi$
$439$	6.39812			0.305365			0.152683	+	0.988275i	$0.451209\pi$
$440$	−16.7228			−0.797229
$441$		0			0
$442$	−2.06749			−0.0983404
$443$	6.38682			0.303447			0.151723	−	0.988423i	$-0.451518\pi$
$443$	6.38682			0.303447			0.151723	+	0.988423i	$0.451518\pi$
$444$		0			0
$445$	−19.2735			−0.913650
$446$	−4.35200	+	7.53789i	−0.206073	+	0.356929i
$447$		0			0
$448$	−2.02029	−	1.02300i	−0.0954497	−	0.0483323i
$449$	11.7460			0.554327			0.277163	−	0.960823i	$-0.410606\pi$
$449$	11.7460			0.554327			0.277163	+	0.960823i	$0.410606\pi$
$450$		0			0
$451$	−0.613311	+	1.06229i	−0.0288797	+	0.0500210i
$452$	−0.465741	−	0.806687i	−0.0219066	−	0.0379434i
$453$		0			0
$454$	9.70859	+	16.8158i	0.455647	+	0.789203i
$455$	9.26487	+	4.69140i	0.434344	+	0.219936i
$456$		0			0
$457$	10.5224			0.492217			0.246108	−	0.969242i	$-0.420848\pi$
$457$	10.5224			0.492217			0.246108	+	0.969242i	$0.420848\pi$
$458$	5.17356	−	8.96087i	0.241745	−	0.418714i
$459$		0			0
$460$	6.00633	+	10.4033i	0.280046	+	0.485055i
$461$	3.54278	−	6.13627i	0.165004	−	0.285794i	−0.771653	−	0.636044i	$-0.780570\pi$
$461$	3.54278	−	6.13627i	0.165004	−	0.285794i	0.936657	+	0.350249i	$0.113903\pi$
$462$		0			0
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	0.942305	+	0.334755i	$0.108654\pi$
$463$	16.3760	+	28.3641i	0.761059	+	1.31819i	−0.181246	+	0.983438i	$0.558013\pi$
$464$	−5.12820	+	8.88230i	−0.238071	+	0.412350i
$465$		0			0
$466$	−1.65789	−	2.87156i	−0.0768004	−	0.133022i
$467$	−1.96216	−	3.39856i	−0.0907978	−	0.157266i	0.817049	−	0.576568i	$-0.195608\pi$
$467$	−1.96216	−	3.39856i	−0.0907978	−	0.157266i	−0.907847	+	0.419301i	$0.862275\pi$
$468$		0			0
$469$	29.7119	+	15.0450i	1.37197	+	0.694716i
$470$	−4.52555	+	7.83849i	−0.208748	+	0.361563i
$471$		0			0
$472$	15.6709			0.721310
$473$	4.91414			0.225952
$474$		0			0
$475$	5.96145	−	10.3255i	0.273530	−	0.473768i
$476$	−3.84626	+	2.51155i	−0.176293	+	0.115117i
$477$		0			0
$478$	4.36878	+	7.56694i	0.199823	+	0.346104i
$479$	8.04324	+	13.9313i	0.367505	+	0.636537i	0.989175	−	0.146742i	$-0.0468787\pi$
$479$	8.04324	+	13.9313i	0.367505	+	0.636537i	−0.621670	+	0.783279i	$0.713545\pi$
$480$		0			0
$481$	1.95518	−	3.38647i	0.0891486	−	0.154410i
$482$	4.88755	+	8.46549i	0.222622	+	0.385592i
$483$		0			0
$484$	10.3216	−	17.8775i	0.469162	−	0.812612i
$485$	−3.84961	−	6.66771i	−0.174802	−	0.302765i
$486$		0			0
$487$	−1.75172	+	3.03407i	−0.0793781	+	0.137487i	−0.902982	−	0.429679i	$-0.858627\pi$
$487$	−1.75172	+	3.03407i	−0.0793781	+	0.137487i	0.823604	+	0.567166i	$0.191960\pi$
$488$	0.179138			0.00810921
$489$		0			0
$490$	−6.64605	+	0.732315i	−0.300238	+	0.0330826i
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.787296	+	0.616575i	$0.211480\pi$
$491$	20.5546	+	35.6017i	0.927618	+	1.60668i	0.140321	+	0.990106i	$0.455186\pi$
$492$		0			0
$493$	−3.81312	−	6.60452i	−0.171734	−	0.297452i
$494$	3.70689	−	6.42053i	0.166781	−	0.288873i
$495$		0			0
$496$	3.77338			0.169430
$497$	0.190000	+	0.0962092i	0.00852267	+	0.00431557i
$498$		0			0
$499$	−5.91486	+	10.2448i	−0.264785	+	0.458622i	−0.967507	−	0.252843i	$-0.918634\pi$
$499$	−5.91486	+	10.2448i	−0.264785	+	0.458622i	0.702722	+	0.711465i	$0.251968\pi$
$500$	−17.6094			−0.787517
$501$		0			0
$502$	−9.43261			−0.420998
$503$	−21.8595			−0.974665			−0.487332	−	0.873217i	$-0.662030\pi$
$503$	−21.8595			−0.974665			−0.487332	+	0.873217i	$0.662030\pi$
$504$		0			0
$505$	−7.31762			−0.325630
$506$	17.9694			0.798837
$507$		0			0
$508$	−11.2574			−0.499466
$509$	8.44831	−	14.6329i	0.374465	−	0.648592i	−0.615782	−	0.787917i	$-0.711160\pi$
$509$	8.44831	−	14.6329i	0.374465	−	0.648592i	0.990247	+	0.139324i	$0.0444931\pi$
$510$		0			0
$511$	−23.6836	+	15.4651i	−1.04770	+	0.684135i
$512$	−15.8563			−0.700756
$513$		0			0
$514$	2.80271	−	4.85444i	0.123622	−	0.214120i
$515$	−10.1250	−	17.5371i	−0.446163	−	0.772777i
$516$		0			0
$517$	−23.3615	−	40.4633i	−1.02744	−	1.77957i
$518$	0.138081	+	2.51387i	0.00606695	+	0.110453i
$519$		0			0
$520$	−9.34230			−0.409687
$521$	17.2466	−	29.8720i	0.755587	−	1.30872i	−0.189495	−	0.981882i	$-0.560685\pi$
$521$	17.2466	−	29.8720i	0.755587	−	1.30872i	0.945082	−	0.326834i	$-0.105982\pi$
$522$		0			0
$523$	0.995615	+	1.72445i	0.0435352	+	0.0754051i	0.886972	−	0.461823i	$-0.152805\pi$
$523$	0.995615	+	1.72445i	0.0435352	+	0.0754051i	−0.843437	+	0.537229i	$0.819471\pi$
$524$	15.8577	−	27.4664i	0.692749	−	1.19988i
$525$		0			0
$526$	−1.09622	−	1.89870i	−0.0477972	−	0.0827873i
$527$	−1.40287	+	2.42983i	−0.0611098	+	0.105845i
$528$		0			0
$529$	−3.27836	−	5.67829i	−0.142538	−	0.246882i
$530$	0.391843	+	0.678693i	0.0170206	+	0.0294805i
$531$		0			0
$532$	−0.903426	−	16.4475i	−0.0391685	−	0.713090i
$533$	−0.342629	+	0.593452i	−0.0148409	+	0.0257052i
$534$		0			0
$535$	−10.9154			−0.471916
$536$	−29.9602			−1.29408
$537$		0			0
$538$	−5.15720	+	8.93253i	−0.222343	+	0.385109i
$539$	13.8800	−	31.6016i	0.597856	−	1.36118i
$540$		0			0
$541$	−15.0681	−	26.0988i	−0.647830	−	1.12207i	−0.983640	−	0.180145i	$-0.942343\pi$
$541$	−15.0681	−	26.0988i	−0.647830	−	1.12207i	0.335810	−	0.941930i	$-0.390990\pi$
$542$	−2.72362	−	4.71745i	−0.116989	−	0.202632i
$543$		0			0
$544$	3.23008	−	5.59466i	0.138488	−	0.239869i
$545$	1.21033	+	2.09636i	0.0518450	+	0.0897982i
$546$		0			0
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	−0.653792	−	0.756674i	$-0.726823\pi$
$547$	7.68070	−	13.3034i	0.328403	−	0.568810i	0.982195	+	0.187864i	$0.0601563\pi$
$548$	−9.46800	−	16.3991i	−0.404453	−	0.700533i
$549$		0			0
$550$	−4.90757	+	8.50016i	−0.209260	+	0.362448i
$551$	27.3469			1.16502
$552$		0			0
$553$	4.35472	+	2.20508i	0.185182	+	0.0937694i
$554$	4.30546	+	7.45728i	0.182921	+	0.316829i
$555$		0			0
$556$	1.92423	+	3.33287i	0.0816056	+	0.141345i
$557$	11.6412	−	20.1631i	0.493252	−	0.854338i	−0.506718	−	0.862112i	$-0.669141\pi$
$557$	11.6412	−	20.1631i	0.493252	−	0.854338i	0.999970	+	0.00777438i	$0.00247469\pi$
$558$		0			0
$559$	2.74531			0.116114
$560$	−4.75339	+	3.10390i	−0.200867	+	0.131164i
$561$		0			0
$562$	−0.485375	+	0.840695i	−0.0204743	+	0.0354626i
$563$	−4.55885			−0.192133			−0.0960663	−	0.995375i	$-0.530626\pi$
$563$	−4.55885			−0.192133			−0.0960663	+	0.995375i	$0.530626\pi$
$564$		0			0
$565$	0.855964			0.0360107
$566$	11.6896			0.491351
$567$		0			0
$568$	−0.191588			−0.00803885
$569$	−18.1995			−0.762963			−0.381482	−	0.924376i	$-0.624586\pi$
$569$	−18.1995			−0.762963			−0.381482	+	0.924376i	$0.624586\pi$
$570$		0			0
$571$	−17.0455			−0.713332			−0.356666	−	0.934232i	$-0.616087\pi$
$571$	−17.0455			−0.713332			−0.356666	+	0.934232i	$0.616087\pi$
$572$	10.5307	−	18.2398i	0.440313	−	0.762644i
$573$		0			0
$574$	−0.0241976	−	0.440535i	−0.00100999	−	0.0183876i
$575$	16.1443			0.673264
$576$		0			0
$577$	−5.70473	+	9.88088i	−0.237491	+	0.411346i	−0.959994	−	0.280022i	$-0.909658\pi$
$577$	−5.70473	+	9.88088i	−0.237491	+	0.411346i	0.722503	+	0.691368i	$0.242992\pi$
$578$	−5.27764	−	9.14113i	−0.219521	−	0.380221i
$579$		0			0
$580$	−7.52485	−	13.0334i	−0.312452	−	0.541183i
$581$	−32.0589	+	20.9340i	−1.33003	+	0.868488i
$582$		0			0
$583$	−4.04549			−0.167547
$584$	12.7229	−	22.0368i	0.526479	−	0.911889i
$585$		0			0
$586$	−0.603332	−	1.04500i	−0.0249234	−	0.0431686i
$587$	−2.52544	+	4.37420i	−0.104236	+	0.180543i	−0.913426	−	0.407005i	$-0.866573\pi$
$587$	−2.52544	+	4.37420i	−0.104236	+	0.180543i	0.809190	+	0.587548i	$0.199906\pi$
$588$		0			0
$589$	−5.03052	−	8.71312i	−0.207279	−	0.359018i
$590$	−3.14449	+	5.44642i	−0.129457	+	0.224226i
$591$		0			0
$592$	1.06882	+	1.85126i	0.0439283	+	0.0760861i
$593$	9.98892	+	17.3013i	0.410196	+	0.710480i	0.994911	−	0.100759i	$-0.0321271\pi$
$593$	9.98892	+	17.3013i	0.410196	+	0.710480i	−0.584715	+	0.811239i	$0.698794\pi$
$594$		0			0
$595$	−0.231513	−	4.21487i	−0.00949113	−	0.172793i
$596$	6.63365	−	11.4898i	0.271725	−	0.470641i
$597$		0			0
$598$	10.0387			0.410513
$599$	−4.39321			−0.179502			−0.0897508	−	0.995964i	$-0.528607\pi$
$599$	−4.39321			−0.179502			−0.0897508	+	0.995964i	$0.528607\pi$
$600$		0			0
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	−0.503250	−	0.864141i	$-0.667862\pi$
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	0.999993	+	0.00375637i	$0.00119569\pi$
$602$	−1.47997	+	0.966399i	−0.0603191	+	0.0393875i
$603$		0			0
$604$	−13.6917	−	23.7147i	−0.557107	−	0.964937i
$605$	9.48476	+	16.4281i	0.385610	+	0.667897i
$606$		0			0
$607$	−6.56281	+	11.3671i	−0.266376	+	0.461377i	−0.967923	−	0.251246i	$-0.919160\pi$
$607$	−6.56281	+	11.3671i	−0.266376	+	0.461377i	0.701547	+	0.712623i	$0.252493\pi$
$608$	11.5827	+	20.0618i	0.469741	+	0.813615i
$609$		0			0
$610$	−0.0359456	+	0.0622597i	−0.00145540	+	0.00252082i
$611$	−13.0510	−	22.6051i	−0.527988	−	0.914502i
$612$		0			0
$613$	−23.2403	+	40.2534i	−0.938667	+	1.62582i	−0.170707	+	0.985322i	$0.554605\pi$
$613$	−23.2403	+	40.2534i	−0.938667	+	1.62582i	−0.767960	+	0.640497i	$0.778728\pi$
$614$	−0.713754			−0.0288048
$615$		0			0
$616$	1.70295	+	31.0034i	0.0686137	+	1.24916i
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	−0.996416	−	0.0845873i	$-0.973043\pi$
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	0.424953	−	0.905215i	$-0.360291\pi$
$618$		0			0
$619$	−15.9606	−	27.6446i	−0.641511	−	1.11113i	−0.985096	−	0.172008i	$-0.944975\pi$
$619$	−15.9606	−	27.6446i	−0.641511	−	1.11113i	0.343585	−	0.939122i	$-0.388359\pi$
$620$	−2.76843	+	4.79506i	−0.111183	+	0.192574i
$621$		0			0
$622$	−11.3482			−0.455023
$623$	1.96269	+	35.7322i	0.0786335	+	1.43158i
$624$		0			0
$625$	0.666993	−	1.15527i	0.0266797	−	0.0462106i
$626$	5.54939			0.221798
$627$		0			0
$628$	−9.80244			−0.391160
$629$	−1.58947			−0.0633762
$630$		0			0
$631$	38.7184			1.54135			0.770677	−	0.637226i	$-0.219918\pi$
$631$	38.7184			1.54135			0.770677	+	0.637226i	$0.219918\pi$
$632$	−4.39112			−0.174669
$633$		0			0
$634$	4.38895			0.174307
$635$	5.17236	−	8.95878i	0.205259	−	0.355519i
$636$		0			0
$637$	7.75417	−	17.6544i	0.307231	−	0.699492i
$638$	−22.5124			−0.891276
$639$		0			0
$640$	7.81261	−	13.5318i	0.308821	−	0.534893i
$641$	−20.2001	−	34.9875i	−0.797854	−	1.38192i	−0.921011	−	0.389537i	$-0.872635\pi$
$641$	−20.2001	−	34.9875i	−0.797854	−	1.38192i	0.123157	−	0.992387i	$-0.460698\pi$
$642$		0			0
$643$	6.27355	+	10.8661i	0.247405	+	0.428517i	0.962805	−	0.270198i	$-0.0870890\pi$
$643$	6.27355	+	10.8661i	0.247405	+	0.428517i	−0.715400	+	0.698715i	$0.753756\pi$
$644$	18.6755	−	12.1949i	0.735919	−	0.480545i
$645$		0			0
$646$	−3.01352			−0.118565
$647$	−17.2774	+	29.9253i	−0.679245	+	1.17649i	0.295964	+	0.955199i	$0.404359\pi$
$647$	−17.2774	+	29.9253i	−0.679245	+	1.17649i	−0.975209	+	0.221287i	$0.928974\pi$
$648$		0			0
$649$	−16.2323	−	28.1151i	−0.637173	−	1.10362i
$650$	−2.74164	+	4.74866i	−0.107536	+	0.186258i
$651$		0			0
$652$	6.22019	+	10.7737i	0.243602	+	0.421930i
$653$	−11.1472	+	19.3075i	−0.436223	+	0.755560i	−0.997395	−	0.0721392i	$-0.977017\pi$
$653$	−11.1472	+	19.3075i	−0.436223	+	0.755560i	0.561172	+	0.827699i	$0.310351\pi$
$654$		0			0
$655$	14.5721	+	25.2396i	0.569379	+	0.986194i
$656$	−0.187302	−	0.324417i	−0.00731293	−	0.0126664i
$657$		0			0
$658$	14.9931	+	7.59195i	0.584490	+	0.295965i
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	−0.927217	−	0.374526i	$-0.877806\pi$
$659$	−3.57493	+	6.19196i	−0.139259	+	0.241204i	0.787957	+	0.615730i	$0.211139\pi$
$660$		0			0
$661$	42.9060			1.66885			0.834425	−	0.551122i	$-0.185800\pi$
$661$	42.9060			1.66885			0.834425	+	0.551122i	$0.185800\pi$
$662$	17.9152			0.696294
$663$		0			0
$664$	17.2221	−	29.8296i	0.668349	−	1.15761i
$665$	13.5043	+	6.83807i	0.523672	+	0.265169i
$666$		0			0
$667$	18.5146	+	32.0683i	0.716889	+	1.24169i
$668$	1.64428	+	2.84798i	0.0636191	+	0.110192i
$669$		0			0
$670$	6.01177	−	10.4127i	0.232255	−	0.402277i
$671$	−0.185556	−	0.321392i	−0.00716331	−	0.0124072i
$672$		0			0
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	0.232944	+	0.972490i	$0.425164\pi$
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	−0.958673	+	0.284510i	$0.908169\pi$
$674$	3.19188	+	5.52850i	0.122947	+	0.212950i
$675$		0			0
$676$	−4.19619	+	7.26801i	−0.161392	+	0.279539i
$677$	26.3616			1.01316			0.506580	−	0.862193i	$-0.330910\pi$
$677$	26.3616			1.01316			0.506580	+	0.862193i	$0.330910\pi$
$678$		0			0
$679$	−11.9696	+	7.81599i	−0.459352	+	0.299950i
$680$	1.89871	+	3.28866i	0.0728121	+	0.126114i
$681$		0			0
$682$	4.14122	+	7.17280i	0.158575	+	0.274661i
$683$	−1.96588	+	3.40500i	−0.0752222	+	0.130289i	−0.901183	−	0.433439i	$-0.857300\pi$
$683$	−1.96588	+	3.40500i	−0.0752222	+	0.130289i	0.825961	+	0.563728i	$0.190633\pi$
$684$		0			0
$685$	17.4008			0.664850
$686$	2.03447	+	12.2469i	0.0776765	+	0.467589i
$687$		0			0
$688$	−0.750378	+	1.29969i	−0.0286079	+	0.0495503i
$689$	−2.26004			−0.0861006
$690$		0			0
$691$	19.9010			0.757072			0.378536	−	0.925587i	$-0.376428\pi$
$691$	19.9010			0.757072			0.378536	+	0.925587i	$0.376428\pi$
$692$	−28.3585			−1.07803
$693$		0			0
$694$	−12.5373			−0.475910
$695$	−3.53645			−0.134145
$696$		0			0
$697$	0.278541			0.0105505
$698$	10.0913	−	17.4787i	0.381963	−	0.661579i
$699$		0			0
$700$	0.668180	+	12.1647i	0.0252548	+	0.459782i
$701$	−43.7908			−1.65396			−0.826979	−	0.562234i	$-0.809942\pi$
$701$	−43.7908			−1.65396			−0.826979	+	0.562234i	$0.809942\pi$
$702$		0			0
$703$	2.84983	−	4.93604i	0.107483	−	0.186166i
$704$	−2.11016	−	3.65490i	−0.0795295	−	0.137749i
$705$		0			0
$706$	−2.09792	−	3.63370i	−0.0789561	−	0.136756i
$707$	0.745180	+	13.5665i	0.0280254	+	0.510222i
$708$		0			0
$709$	44.6344			1.67628			0.838139	−	0.545457i	$-0.183644\pi$
$709$	44.6344			1.67628			0.838139	+	0.545457i	$0.183644\pi$
$710$	0.0384437	−	0.0665865i	0.00144277	−	0.00249895i
$711$		0			0
$712$	−16.0966	−	27.8801i	−0.603244	−	1.04485i
$713$	6.81163	−	11.7981i	0.255097	−	0.441842i
$714$		0			0
$715$	9.67699	+	16.7610i	0.361899	+	0.626827i
$716$	5.91227	−	10.2403i	0.220952	−	0.382700i
$717$		0			0
$718$	−3.41705	−	5.91851i	−0.127523	−	0.220877i
$719$	19.5096	+	33.7917i	0.727586	+	1.26022i	0.957901	+	0.287100i	$0.0926912\pi$
$719$	19.5096	+	33.7917i	0.727586	+	1.26022i	−0.230315	+	0.973116i	$0.573976\pi$
$720$		0			0
$721$	−31.4819	+	20.5572i	−1.17245	+	0.765592i
$722$	−0.965081	+	1.67157i	−0.0359166	+	0.0622094i
$723$		0			0
$724$	−24.0825			−0.895019
$725$	−20.2259			−0.751171
$726$		0			0
$727$	−11.2554	+	19.4949i	−0.417439	+	0.723025i	−0.995681	−	0.0928402i	$-0.970405\pi$
$727$	−11.2554	+	19.4949i	−0.417439	+	0.723025i	0.578242	+	0.815865i	$0.303739\pi$
$728$	0.951361	+	17.3202i	0.0352598	+	0.641929i
$729$		0			0
$730$	5.10593	+	8.84373i	0.188979	+	0.327321i
$731$	−0.557951	−	0.966399i	−0.0206366	−	0.0357436i
$732$		0			0
$733$	0.448519	−	0.776858i	0.0165664	−	0.0286939i	−0.857623	−	0.514278i	$-0.828060\pi$
$733$	0.448519	−	0.776858i	0.0165664	−	0.0286939i	0.874190	+	0.485584i	$0.161393\pi$
$734$	−9.60441	−	16.6353i	−0.354505	−	0.614021i
$735$		0			0
$736$	−15.6837	+	27.1649i	−0.578108	+	1.00131i
$737$	31.0335	+	53.7517i	1.14314	+	1.97997i
$738$		0			0
$739$	1.79032	−	3.10092i	0.0658578	−	0.114069i	−0.831216	−	0.555949i	$-0.812355\pi$
$739$	1.79032	−	3.10092i	0.0658578	−	0.114069i	0.897074	+	0.441880i	$0.145688\pi$
$740$	−3.13667			−0.115306
$741$		0			0
$742$	1.21836	−	0.795574i	0.0447275	−	0.0292064i
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.814493	+	0.580173i	$0.197015\pi$
$743$	24.7964	+	42.9486i	0.909691	+	1.57563i	0.0951977	+	0.995458i	$0.469652\pi$
$744$		0			0
$745$	6.09583	+	10.5583i	0.223334	+	0.386826i
$746$	−5.38726	+	9.33101i	−0.197242	+	0.341633i
$747$		0			0
$748$	−8.56098			−0.313020
$749$	1.11156	+	20.2367i	0.0406155	+	0.739434i
$750$		0			0
$751$	21.4515	−	37.1551i	0.782776	−	1.35581i	−0.147543	−	0.989056i	$-0.547136\pi$
$751$	21.4515	−	37.1551i	0.782776	−	1.35581i	0.930319	−	0.366752i	$-0.119530\pi$
$752$	14.2690			0.520337
$753$		0			0
$754$	−12.5767			−0.458016
$755$	25.1633			0.915786
$756$		0			0
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$	0.683021			0.0248084
$759$		0			0
$760$	−13.6171			−0.493945
$761$	20.3599	−	35.2643i	0.738044	−	1.27833i	−0.215330	−	0.976541i	$-0.569083\pi$
$761$	20.3599	−	35.2643i	0.738044	−	1.27833i	0.953375	−	0.301789i	$-0.0975839\pi$
$762$		0			0
$763$	3.76330	−	2.45738i	0.136241	−	0.0889633i
$764$	23.0001			0.832113
$765$		0			0
$766$	3.88342	−	6.72627i	0.140313	−	0.243030i
$767$	−9.06826	−	15.7067i	−0.327436	−	0.567135i
$768$		0			0
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	0.948850	−	0.315728i	$-0.102249\pi$
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	−0.747853	+	0.663864i	$0.768915\pi$
$770$	−11.1169	−	5.62922i	−0.400627	−	0.202863i
$771$		0			0
$772$	−25.6908			−0.924633
$773$	0.462831	−	0.801647i	0.0166469	−	0.0288332i	−0.857582	−	0.514347i	$-0.828034\pi$
$773$	0.462831	−	0.801647i	0.0166469	−	0.0288332i	0.874229	+	0.485514i	$0.161368\pi$
$774$		0			0
$775$	3.72061	+	6.44428i	0.133648	+	0.231485i
$776$	6.43012	−	11.1373i	0.230828	−	0.399806i
$777$		0			0
$778$	−5.97049	−	10.3412i	−0.214052	−	0.370750i
$779$	−0.499408	+	0.865001i	−0.0178932	+	0.0309919i
$780$		0			0
$781$	0.198452	+	0.343728i	0.00710116	+	0.0122996i
$782$	−2.04024	−	3.53381i	−0.0729590	−	0.126369i
$783$		0			0
$784$	6.23854	+	8.49648i	0.222805	+	0.303446i
$785$	4.50386	−	7.80092i	0.160750	−	0.278427i
$786$		0			0
$787$	23.0240			0.820716			0.410358	−	0.911925i	$-0.365404\pi$
$787$	23.0240			0.820716			0.410358	+	0.911925i	$0.365404\pi$
$788$	−6.26061			−0.223025
$789$		0			0
$790$	0.881115	−	1.52614i	0.0313487	−	0.0542975i
$791$	−0.0871659	−	1.58692i	−0.00309926	−	0.0564243i
$792$		0			0
$793$	−0.103662	−	0.179548i	−0.00368114	−	0.00637593i
$794$	4.38551	+	7.59592i	0.155636	+	0.269569i
$795$		0			0
$796$	19.6014	−	33.9505i	0.694752	−	1.20335i
$797$	−11.3925	−	19.7325i	−0.403544	−	0.698960i	0.590606	−	0.806960i	$-0.298889\pi$
$797$	−11.3925	−	19.7325i	−0.403544	−	0.698960i	−0.994151	+	0.108000i	$0.965555\pi$
$798$		0			0
$799$	−5.30492	+	9.18839i	−0.187675	+	0.325062i
$800$	−8.56664	−	14.8379i	−0.302877	−	0.524598i
$801$		0			0
$802$	−4.72695	+	8.18732i	−0.166914	+	0.289104i
$803$	−52.7150			−1.86027
$804$		0			0
$805$	1.12412	+	20.4653i	0.0396199	+	0.721308i
$806$	2.31352	+	4.00713i	0.0814901	+	0.141145i
$807$		0			0
$808$	−6.11143	−	10.5853i	−0.214999	−	0.372390i
$809$	−6.73753	+	11.6697i	−0.236879	+	0.410286i	−0.959817	−	0.280627i	$-0.909458\pi$
$809$	−6.73753	+	11.6697i	−0.236879	+	0.410286i	0.722938	+	0.690913i	$0.242791\pi$
$810$		0			0
$811$	−30.7348			−1.07924			−0.539622	−	0.841907i	$-0.681433\pi$
$811$	−30.7348			−1.07924			−0.539622	+	0.841907i	$0.681433\pi$
$812$	−23.3971	+	15.2780i	−0.821077	+	0.536151i
$813$		0			0
$814$	−2.34603	+	4.06344i	−0.0822283	+	0.142424i
$815$	−11.4318			−0.400439
$816$		0			0
$817$	4.00150			0.139995
$818$	1.77369			0.0620158
$819$		0			0
$820$	0.549675			0.0191955
$821$	16.9864			0.592829			0.296414	−	0.955059i	$-0.404209\pi$
$821$	16.9864			0.592829			0.296414	+	0.955059i	$0.404209\pi$
$822$		0			0
$823$	−18.5831			−0.647768			−0.323884	−	0.946097i	$-0.604989\pi$
$823$	−18.5831			−0.647768			−0.323884	+	0.946097i	$0.604989\pi$
$824$	16.9122	−	29.2928i	0.589164	−	1.02046i
$825$		0			0
$826$	10.4176	+	5.27512i	0.362476	+	0.183545i
$827$	−14.5419			−0.505670			−0.252835	−	0.967509i	$-0.581363\pi$
$827$	−14.5419			−0.505670			−0.252835	+	0.967509i	$0.581363\pi$
$828$		0			0
$829$	4.78717	−	8.29161i	0.166265	−	0.287980i	−0.770839	−	0.637030i	$-0.780163\pi$
$829$	4.78717	−	8.29161i	0.166265	−	0.287980i	0.937104	+	0.349051i	$0.113496\pi$
$830$	6.91154	+	11.9711i	0.239903	+	0.415524i
$831$		0			0
$832$	−1.17885	−	2.04183i	−0.0408693	−	0.0707877i
$833$	−7.79060	+	0.858431i	−0.269928	+	0.0297429i
$834$		0			0
$835$	−3.02195			−0.104579
$836$	15.3494	−	26.5859i	0.530869	−	0.919492i
$837$		0			0
$838$	11.2326	+	19.4554i	0.388023	+	0.672075i
$839$	−21.2303	+	36.7720i	−0.732952	+	1.26951i	0.222664	+	0.974895i	$0.428525\pi$
$839$	−21.2303	+	36.7720i	−0.732952	+	1.26951i	−0.955616	+	0.294615i	$0.904809\pi$
$840$		0			0
$841$	−8.69551	−	15.0611i	−0.299845	−	0.519347i
$842$	1.62187	−	2.80917i	0.0558934	−	0.0968103i
$843$		0			0
$844$	5.83428	+	10.1053i	0.200824	+	0.347838i
$845$	−3.85599	−	6.67877i	−0.132650	−	0.229757i
$846$		0			0
$847$	29.4911	−	19.2572i	1.01332	−	0.661687i
$848$	0.617738	−	1.06995i	0.0212132	−	0.0367423i
$849$		0			0
$850$	2.22882			0.0764479
$851$	7.71767			0.264558
$852$		0			0
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	−0.717504	−	0.696555i	$-0.754715\pi$
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	0.961986	+	0.273099i	$0.0880486\pi$
$854$	0.119087	+	0.0603014i	0.00407507	+	0.00206347i
$855$		0			0
$856$	−9.11621	−	15.7897i	−0.311586	−	0.539682i
$857$	17.3895	+	30.1195i	0.594013	+	1.02886i	0.993685	+	0.112203i	$0.0357907\pi$
$857$	17.3895	+	30.1195i	0.594013	+	1.02886i	−0.399672	+	0.916658i	$0.630876\pi$
$858$		0			0
$859$	6.32429	−	10.9540i	0.215782	−	0.373745i	−0.737732	−	0.675093i	$-0.764103\pi$
$859$	6.32429	−	10.9540i	0.215782	−	0.373745i	0.953514	+	0.301348i	$0.0974366\pi$
$860$	−1.10107	−	1.90710i	−0.0375460	−	0.0650316i
$861$		0			0
$862$	11.8409	−	20.5091i	0.403304	−	0.698543i
$863$	−13.2398	−	22.9321i	−0.450690	−	0.780617i	0.547739	−	0.836649i	$-0.315489\pi$
$863$	−13.2398	−	22.9321i	−0.450690	−	0.780617i	−0.998429	+	0.0560318i	$0.982155\pi$
$864$		0			0
$865$	13.0297	−	22.5681i	0.443022	−	0.767337i
$866$	−3.66943			−0.124692
$867$		0			0
$868$	9.17174	+	4.64424i	0.311309	+	0.157636i
$869$	4.54843	+	7.87811i	0.154295	+	0.267247i
$870$		0			0
$871$	17.3371	+	30.0287i	0.587444	+	1.01748i
$872$	−2.02166	+	3.50162i	−0.0684621	+	0.118580i
$873$		0			0
$874$	14.6322			0.494941
$875$	−26.8049	−	13.5730i	−0.906171	−	0.458852i
$876$		0			0
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	−0.999747	−	0.0224835i	$-0.992843\pi$
$877$	−14.2267	+	24.6414i	−0.480402	+	0.832081i	0.519345	+	0.854565i	$0.326176\pi$
$878$	−4.28887			−0.144742
$879$		0			0
$880$	−10.5801			−0.356654
$881$	20.3637			0.686071			0.343036	−	0.939322i	$-0.388545\pi$
$881$	20.3637			0.686071			0.343036	+	0.939322i	$0.388545\pi$
$882$		0			0
$883$	49.1950			1.65554			0.827772	−	0.561065i	$-0.189608\pi$
$883$	49.1950			1.65554			0.827772	+	0.561065i	$0.189608\pi$
$884$	−4.78264			−0.160858
$885$		0			0
$886$	−4.28129			−0.143833
$887$	−2.10846	+	3.65196i	−0.0707952	+	0.122621i	−0.899250	−	0.437435i	$-0.855887\pi$
$887$	−2.10846	+	3.65196i	−0.0707952	+	0.122621i	0.828455	+	0.560056i	$0.189220\pi$
$888$		0			0
$889$	−17.1359	−	8.67701i	−0.574720	−	0.291018i
$890$	12.9196			0.433067
$891$		0			0
$892$	−10.0673	+	17.4371i	−0.337078	+	0.583837i
$893$	−19.0229	−	32.9486i	−0.636576	−	1.10258i
$894$		0			0
$895$	5.43294	+	9.41013i	0.181603	+	0.314546i
$896$	−25.8830	−	13.1062i	−0.864691	−	0.437849i
$897$		0			0
$898$	−7.87371			−0.262749
$899$	−8.53374	+	14.7809i	−0.284616	+	0.492970i
$900$		0			0
$901$	0.459325	+	0.795574i	0.0153023	+	0.0265044i
$902$	0.411122	−	0.712084i	0.0136889	−	0.0237098i
$903$		0			0
$904$	0.714872	+	1.23819i	0.0237763	+	0.0411817i
$905$	11.0650	−	19.1652i	0.367814	−	0.637072i
$906$		0			0
$907$	−23.9925	−	41.5563i	−0.796659	−	1.37985i	−0.921780	−	0.387713i	$-0.873265\pi$
$907$	−23.9925	−	41.5563i	−0.796659	−	1.37985i	0.125121	−	0.992142i	$-0.460068\pi$
$908$	22.4585	+	38.8993i	0.745311	+	1.29092i
$909$		0			0
$910$	−6.21054	−	3.14480i	−0.205878	−	0.104249i
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	−0.570247	−	0.821474i	$-0.693152\pi$
$911$	12.8667	−	22.2858i	0.426294	−	0.738362i	0.996540	+	0.0831113i	$0.0264857\pi$
$912$		0			0
$913$	−71.3565			−2.36155
$914$	−7.05351			−0.233309
$915$		0			0
$916$	11.9678	−	20.7288i	0.395427	−	0.684900i
$917$	45.3092	−	29.5863i	1.49624	−	0.977024i
$918$		0			0
$919$	1.13478	+	1.96550i	0.0374330	+	0.0648359i	0.884135	−	0.467232i	$-0.154749\pi$
$919$	1.13478	+	1.96550i	0.0374330	+	0.0648359i	−0.846702	+	0.532068i	$0.821415\pi$
$920$	−9.21919	−	15.9681i	−0.303948	−	0.526453i
$921$		0			0
$922$	−2.37484	+	4.11334i	−0.0782111	+	0.135466i
$923$	0.110866	+	0.192026i	0.00364920	+	0.00632060i
$924$		0			0
$925$	−2.10775	+	3.65073i	−0.0693024	+	0.120035i
$926$	−10.9774	−	19.0134i	−0.360740	−	0.624819i
$927$		0			0
$928$	19.6488	−	34.0328i	0.645004	−	1.11718i
$929$	−45.8496			−1.50428			−0.752138	−	0.659006i	$-0.770977\pi$
$929$	−45.8496			−1.50428			−0.752138	+	0.659006i	$0.770977\pi$
$930$		0			0
$931$	11.3023	−	25.7326i	0.370417	−	0.843352i
$932$	−3.83514	−	6.64266i	−0.125624	−	0.217587i
$933$		0			0
$934$	1.31530	+	2.27816i	0.0430379	+	0.0745438i
$935$	3.93346	−	6.81294i	0.128638	−	0.222807i
$936$		0			0
$937$	−56.2075			−1.83622			−0.918110	−	0.396325i	$-0.870285\pi$
$937$	−56.2075			−1.83622			−0.918110	+	0.396325i	$0.870285\pi$
$938$	−19.9169	−	10.0852i	−0.650309	−	0.329293i
$939$		0			0
$940$	−10.4688	+	18.1325i	−0.341454	+	0.591416i
$941$	35.2803			1.15011			0.575053	−	0.818116i	$-0.304982\pi$
$941$	35.2803			1.15011			0.575053	+	0.818116i	$0.304982\pi$
$942$		0			0
$943$	−1.35246			−0.0440421
$944$	9.91453			0.322691
$945$		0			0
$946$	−3.29411			−0.107101
$947$	50.7130			1.64795			0.823976	−	0.566625i	$-0.191751\pi$
$947$	50.7130			1.64795			0.823976	+	0.566625i	$0.191751\pi$
$948$		0			0
$949$	−29.4495			−0.955972
$950$	−3.99615	+	6.92154i	−0.129652	+	0.224564i
$951$		0			0
$952$	5.90367	−	3.85501i	0.191339	−	0.124942i
$953$	−25.9988			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$953$	−25.9988			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$954$		0			0
$955$	−10.5677	+	18.3038i	−0.341962	+	0.592296i
$956$	10.1061	+	17.5043i	0.326855	+	0.566130i
$957$		0			0
$958$	−5.39165	−	9.33861i	−0.174196	−	0.301717i
$959$	−1.77199	−	32.2603i	−0.0572204	−	1.04174i
$960$		0			0
$961$	−24.7208			−0.797445
$962$	−1.31062	+	2.27006i	−0.0422562	+	0.0731898i
$963$		0			0
$964$	11.3062	+	19.5829i	0.364148	+	0.630722i
$965$	11.8040	−	20.4451i	0.379984	−	0.658152i
$966$		0			0
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	0.578239	−	0.815867i	$-0.303740\pi$
$967$	−12.9810	−	22.4838i	−0.417442	−	0.723031i	−0.995681	+	0.0928360i	$0.970407\pi$
$968$	−15.8427	+	27.4404i	−0.509204	+	0.881967i
$969$		0			0
$970$	2.58052	+	4.46959i	0.0828554	+	0.143510i
$971$	3.97206	+	6.87981i	0.127469	+	0.220783i	0.922696	−	0.385530i	$-0.125981\pi$
$971$	3.97206	+	6.87981i	0.127469	+	0.220783i	−0.795226	+	0.606313i	$0.792648\pi$
$972$		0			0
$973$	0.360130	+	6.55643i	0.0115452	+	0.210189i
$974$	1.17424	−	2.03384i	0.0376249	−	0.0651683i
$975$		0			0
$976$	0.113336			0.00362779
$977$	52.2548			1.67178			0.835889	−	0.548898i	$-0.184952\pi$
$977$	52.2548			1.67178			0.835889	+	0.548898i	$0.184952\pi$
$978$		0			0
$979$	−33.3464	+	57.7577i	−1.06576	+	1.84594i
$980$	−15.3740	+	1.69404i	−0.491106	+	0.0541140i
$981$		0			0
$982$	−13.7784	−	23.8650i	−0.439688	−	0.761562i
$983$	−19.4190	−	33.6346i	−0.619369	−	1.07278i	−0.989601	−	0.143839i	$-0.954055\pi$
$983$	−19.4190	−	33.6346i	−0.619369	−	1.07278i	0.370232	−	0.928939i	$-0.379278\pi$
$984$		0			0
$985$	2.87652	−	4.98228i	0.0916535	−	0.158749i
$986$	2.55606	+	4.42722i	0.0814015	+	0.140991i
$987$		0			0
$988$	8.57501	−	14.8524i	0.272807	−	0.472516i
$989$	2.70914	+	4.69236i	0.0861455	+	0.149208i
$990$		0			0
$991$	−15.4689	+	26.7929i	−0.491385	+	0.851104i	−0.999951	−	0.00991892i	$-0.996843\pi$
$991$	−15.4689	+	26.7929i	−0.491385	+	0.851104i	0.508565	+	0.861023i	$0.330176\pi$
$992$	−14.4578			−0.459036
$993$		0			0
$994$	−0.127363	−	0.0644922i	−0.00403972	−	0.00204557i
$995$	18.0122	+	31.1981i	0.571025	+	0.989045i
$996$		0			0
$997$	−23.5335	−	40.7612i	−0.745313	−	1.29092i	−0.950048	−	0.312103i	$-0.898967\pi$
$997$	−23.5335	−	40.7612i	−0.745313	−	1.29092i	0.204735	−	0.978817i	$-0.434367\pi$
$998$	3.96492	−	6.86745i	0.125507	−	0.217385i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.h.b.46.2		10
3.2	odd	2		63.2.h.b.25.4	yes	10
4.3	odd	2		3024.2.q.i.2881.5		10
7.2	even	3		189.2.g.b.100.4		10
7.3	odd	6		1323.2.f.f.883.4		10
7.4	even	3		1323.2.f.e.883.4		10
7.5	odd	6		1323.2.g.f.667.4		10
7.6	odd	2		1323.2.h.f.802.2		10
9.2	odd	6		567.2.e.f.487.2		10
9.4	even	3		189.2.g.b.172.4		10
9.5	odd	6		63.2.g.b.4.2	✓	10
9.7	even	3		567.2.e.e.487.4		10
12.11	even	2		1008.2.q.i.529.1		10
21.2	odd	6		63.2.g.b.16.2	yes	10
21.5	even	6		441.2.g.f.79.2		10
21.11	odd	6		441.2.f.e.295.2		10
21.17	even	6		441.2.f.f.295.2		10
21.20	even	2		441.2.h.f.214.4		10
28.23	odd	6		3024.2.t.i.289.1		10
36.23	even	6		1008.2.t.i.193.4		10
36.31	odd	6		3024.2.t.i.1873.1		10
63.2	odd	6		567.2.e.f.163.2		10
63.4	even	3		1323.2.f.e.442.4		10
63.5	even	6		441.2.h.f.373.4		10
63.11	odd	6		3969.2.a.z.1.4		5
63.13	odd	6		1323.2.g.f.361.4		10
63.16	even	3		567.2.e.e.163.4		10
63.23	odd	6		63.2.h.b.58.4	yes	10
63.25	even	3		3969.2.a.bc.1.2		5
63.31	odd	6		1323.2.f.f.442.4		10
63.32	odd	6		441.2.f.e.148.2		10
63.38	even	6		3969.2.a.ba.1.4		5
63.40	odd	6		1323.2.h.f.226.2		10
63.41	even	6		441.2.g.f.67.2		10
63.52	odd	6		3969.2.a.bb.1.2		5
63.58	even	3	inner	189.2.h.b.37.2		10
63.59	even	6		441.2.f.f.148.2		10
84.23	even	6		1008.2.t.i.961.4		10
252.23	even	6		1008.2.q.i.625.1		10
252.247	odd	6		3024.2.q.i.2305.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	9.5	odd	6
63.2.g.b.16.2	yes	10	21.2	odd	6
63.2.h.b.25.4	yes	10	3.2	odd	2
63.2.h.b.58.4	yes	10	63.23	odd	6
189.2.g.b.100.4		10	7.2	even	3
189.2.g.b.172.4		10	9.4	even	3
189.2.h.b.37.2		10	63.58	even	3	inner
189.2.h.b.46.2		10	1.1	even	1	trivial
441.2.f.e.148.2		10	63.32	odd	6
441.2.f.e.295.2		10	21.11	odd	6
441.2.f.f.148.2		10	63.59	even	6
441.2.f.f.295.2		10	21.17	even	6
441.2.g.f.67.2		10	63.41	even	6
441.2.g.f.79.2		10	21.5	even	6
441.2.h.f.214.4		10	21.20	even	2
441.2.h.f.373.4		10	63.5	even	6
567.2.e.e.163.4		10	63.16	even	3
567.2.e.e.487.4		10	9.7	even	3
567.2.e.f.163.2		10	63.2	odd	6
567.2.e.f.487.2		10	9.2	odd	6
1008.2.q.i.529.1		10	12.11	even	2
1008.2.q.i.625.1		10	252.23	even	6
1008.2.t.i.193.4		10	36.23	even	6
1008.2.t.i.961.4		10	84.23	even	6
1323.2.f.e.442.4		10	63.4	even	3
1323.2.f.e.883.4		10	7.4	even	3
1323.2.f.f.442.4		10	63.31	odd	6
1323.2.f.f.883.4		10	7.3	odd	6
1323.2.g.f.361.4		10	63.13	odd	6
1323.2.g.f.667.4		10	7.5	odd	6
1323.2.h.f.226.2		10	63.40	odd	6
1323.2.h.f.802.2		10	7.6	odd	2
3024.2.q.i.2305.5		10	252.247	odd	6
3024.2.q.i.2881.5		10	4.3	odd	2
3024.2.t.i.289.1		10	28.23	odd	6
3024.2.t.i.1873.1		10	36.31	odd	6
3969.2.a.z.1.4		5	63.11	odd	6
3969.2.a.ba.1.4		5	63.38	even	6
3969.2.a.bb.1.2		5	63.52	odd	6
3969.2.a.bc.1.2		5	63.25	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.670333 q^{2} -1.55065 q^{4} +(0.712469 - 1.23403i) q^{5} +(-2.36039 - 1.19522i) q^{7} +2.38012 q^{8} +O(q^{10})\)	\(q-0.670333 q^{2} -1.55065 q^{4} +(0.712469 - 1.23403i) q^{5} +(-2.36039 - 1.19522i) q^{7} +2.38012 q^{8} +(-0.477591 + 0.827212i) q^{10} +(-2.46539 - 4.27018i) q^{11} +(-1.37730 - 2.38556i) q^{13} +(1.58225 + 0.801194i) q^{14} +1.50584 q^{16} +(-0.559839 + 0.969670i) q^{17} +(-2.00752 - 3.47713i) q^{19} +(-1.10479 + 1.91356i) q^{20} +(1.65263 + 2.86244i) q^{22} +(2.71830 - 4.70824i) q^{23} +(1.48478 + 2.57171i) q^{25} +(0.923251 + 1.59912i) q^{26} +(3.66015 + 1.85337i) q^{28} +(-3.40555 + 5.89858i) q^{29} +2.50584 q^{31} -5.76965 q^{32} +(0.375279 - 0.650002i) q^{34} +(-3.15664 + 2.06124i) q^{35} +(0.709787 + 1.22939i) q^{37} +(1.34571 + 2.33083i) q^{38} +(1.69576 - 2.93714i) q^{40} +(-0.124384 - 0.215440i) q^{41} +(-0.498313 + 0.863104i) q^{43} +(3.82296 + 6.62156i) q^{44} +(-1.82217 + 3.15609i) q^{46} +9.47579 q^{47} +(4.14291 + 5.64237i) q^{49} +(-0.995294 - 1.72390i) q^{50} +(2.13572 + 3.69917i) q^{52} +(0.410229 - 0.710537i) q^{53} -7.02604 q^{55} +(-5.61802 - 2.84476i) q^{56} +(2.28285 - 3.95401i) q^{58} +6.58407 q^{59} +0.0752645 q^{61} -1.67974 q^{62} +0.855913 q^{64} -3.92514 q^{65} -12.5877 q^{67} +(0.868117 - 1.50362i) q^{68} +(2.11600 - 1.38172i) q^{70} -0.0804951 q^{71} +(5.34551 - 9.25869i) q^{73} +(-0.475793 - 0.824098i) q^{74} +(3.11297 + 5.39183i) q^{76} +(0.715488 + 13.0260i) q^{77} -1.84491 q^{79} +(1.07286 - 1.85825i) q^{80} +(0.0833788 + 0.144416i) q^{82} +(7.23583 - 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(0.334036 - 0.578567i) q^{86} +(-5.86792 - 10.1635i) q^{88} +(-6.76292 - 11.7137i) q^{89} +(0.399711 + 7.27703i) q^{91} +(-4.21515 + 7.30085i) q^{92} -6.35193 q^{94} -5.72119 q^{95} +(2.70160 - 4.67930i) q^{97} +(-2.77712 - 3.78226i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

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