LMFDB - Embedded newform 567.2.e.e.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, 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:	$4.52751779461$
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:	$\Z[a_1, \ldots, a_{4}]$
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			163.3
Root			$0.247934 - 0.429435i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.e.487.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} +(1.68284 + 2.04158i) q^{7} -1.86155 q^{8} +O(q^{10})$	\(q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} +(1.68284 + 2.04158i) q^{7} -1.86155 q^{8} +(-0.915516 - 1.58572i) q^{10} +(-0.446284 - 0.772987i) q^{11} -1.19671 q^{13} +(-1.29396 + 0.216492i) q^{14} +(-1.29257 + 2.23880i) q^{16} +(0.124991 + 0.216492i) q^{17} +(1.40414 - 2.43204i) q^{19} -6.47721 q^{20} +0.442596 q^{22} +(1.23886 - 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.62544 + 4.34700i) q^{28} +4.14255 q^{29} +(-1.79257 - 3.10483i) q^{31} +(-2.50249 - 4.33444i) q^{32} -0.123959 q^{34} +(-9.63571 + 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(0.696267 + 1.20597i) q^{38} +(3.43695 - 5.95298i) q^{40} -4.78186 q^{41} +9.97857 q^{43} +(0.782834 - 1.35591i) q^{44} +(0.614310 + 1.06402i) q^{46} +(-5.08653 + 8.81013i) q^{47} +(-1.33611 + 6.87130i) q^{49} +4.28189 q^{50} +(-1.04958 - 1.81793i) q^{52} +(4.94465 + 8.56438i) q^{53} +3.29588 q^{55} +(-3.13268 - 3.80050i) q^{56} +(-1.02708 + 1.77895i) q^{58} +(0.906186 + 1.56956i) q^{59} +(-5.40205 + 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(2.20948 - 3.82692i) q^{65} +(-0.514685 - 0.891460i) q^{67} +(-0.219249 + 0.379751i) q^{68} +(1.69671 - 4.53761i) q^{70} +4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(-1.17306 - 2.03181i) q^{74} +4.92604 q^{76} +(0.827091 - 2.21194i) q^{77} +(0.899562 - 1.55809i) q^{79} +(-4.77293 - 8.26696i) q^{80} +(1.18559 - 2.05350i) q^{82} +12.3231 q^{83} -0.923082 q^{85} +(-2.47403 + 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} +(1.20370 - 2.08488i) q^{89} +(-2.01387 - 2.44318i) q^{91} +4.34620 q^{92} +(-2.52225 - 4.36867i) q^{94} +(5.18489 + 8.98049i) q^{95} -11.0442 q^{97} +(-2.61951 - 2.27740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} + 16 q^{13} - 4 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} + 10 q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} + 14 q^{29} - 3 q^{31} + 2 q^{32} - 6 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} + 10 q^{41} + 14 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} - 17 q^{49} + 38 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 27 q^{56} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} - 11 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} - 10 q^{76} - 20 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} + 18 q^{83} + 12 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} + 54 q^{92} - 3 q^{94} + 14 q^{95} + 24 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 + 16 * q^13 - 4 * q^14 + 2 * q^16 - 12 * q^17 + q^19 + 10 * q^20 + 2 * q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 + 14 * q^29 - 3 * q^31 + 2 * q^32 - 6 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 + 10 * q^41 + 14 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 - 17 * q^49 + 38 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 27 * q^56 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 - 11 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 - 10 * q^76 - 20 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 + 18 * q^83 + 12 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 + 54 * q^92 - 3 * q^94 + 14 * q^95 + 24 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.247934	+	0.429435i	−0.175316	+	0.303656i	−0.940271	−	0.340428i	$-0.889428\pi$
$2$	−0.247934	+	0.429435i	−0.175316	+	0.303656i	0.764955	+	0.644084i	$0.222761\pi$
$3$		0			0
$3$		0			0
$4$	0.877057	+	1.51911i	0.438529	+	0.759554i
$5$	−1.84629	+	3.19787i	−0.825686	+	1.43013i	0.0757082	+	0.997130i	$0.475878\pi$
$5$	−1.84629	+	3.19787i	−0.825686	+	1.43013i	−0.901394	+	0.433000i	$0.857455\pi$
$6$		0			0
$7$	1.68284	+	2.04158i	0.636053	+	0.771645i
$7$	1.68284	+	2.04158i	0.636053	+	0.771645i
$8$	−1.86155			−0.658156
$9$		0			0
$10$	−0.915516	−	1.58572i	−0.289512	−	0.501449i
$11$	−0.446284	−	0.772987i	−0.134560	−	0.233064i	0.790869	−	0.611985i	$-0.209629\pi$
$11$	−0.446284	−	0.772987i	−0.134560	−	0.233064i	−0.925429	+	0.378921i	$0.876295\pi$
$12$		0			0
$13$	−1.19671			−0.331908			−0.165954	−	0.986134i	$-0.553070\pi$
$13$	−1.19671			−0.331908			−0.165954	+	0.986134i	$0.553070\pi$
$14$	−1.29396	+	0.216492i	−0.345825	+	0.0578598i
$15$		0			0
$16$	−1.29257	+	2.23880i	−0.323143	+	0.559701i
$17$	0.124991	+	0.216492i	0.0303149	+	0.0525069i	0.880785	−	0.473517i	$-0.157016\pi$
$17$	0.124991	+	0.216492i	0.0303149	+	0.0525069i	−0.850470	+	0.526024i	$0.823682\pi$
$18$		0			0
$19$	1.40414	−	2.43204i	0.322131	−	0.557948i	−0.658796	−	0.752321i	$-0.728934\pi$
$19$	1.40414	−	2.43204i	0.322131	−	0.557948i	0.980928	+	0.194374i	$0.0622675\pi$
$20$	−6.47721			−1.44835
$21$		0			0
$22$	0.442596			0.0943618
$23$	1.23886	−	2.14576i	0.258320	−	0.447423i	−0.707472	−	0.706741i	$-0.750165\pi$
$23$	1.23886	−	2.14576i	0.258320	−	0.447423i	0.965792	+	0.259318i	$0.0834979\pi$
$24$		0			0
$25$	−4.31757	−	7.47825i	−0.863514	−	1.49565i
$26$	0.296705	−	0.513909i	0.0581887	−	0.100786i
$27$		0			0
$28$	−1.62544	+	4.34700i	−0.307178	+	0.821505i
$29$	4.14255			0.769252			0.384626	−	0.923072i	$-0.374330\pi$
$29$	4.14255			0.769252			0.384626	+	0.923072i	$0.374330\pi$
$30$		0			0
$31$	−1.79257	−	3.10483i	−0.321956	−	0.557644i	0.658936	−	0.752199i	$-0.271007\pi$
$31$	−1.79257	−	3.10483i	−0.321956	−	0.557644i	−0.980892	+	0.194555i	$0.937674\pi$
$32$	−2.50249	−	4.33444i	−0.442382	−	0.766229i
$33$		0			0
$34$	−0.123959			−0.0212587
$35$	−9.63571	+	1.61215i	−1.62873	+	0.272502i
$36$		0			0
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	−0.992304	−	0.123826i	$-0.960483\pi$
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	0.603389	+	0.797447i	$0.293817\pi$
$38$	0.696267	+	1.20597i	0.112949	+	0.195634i
$39$		0			0
$40$	3.43695	−	5.95298i	0.543430	−	0.941249i
$41$	−4.78186			−0.746801			−0.373400	−	0.927670i	$-0.621808\pi$
$41$	−4.78186			−0.746801			−0.373400	+	0.927670i	$0.621808\pi$
$42$		0			0
$43$	9.97857			1.52172			0.760859	−	0.648917i	$-0.224778\pi$
$43$	9.97857			1.52172			0.760859	+	0.648917i	$0.224778\pi$
$44$	0.782834	−	1.35591i	0.118017	−	0.204411i
$45$		0			0
$46$	0.614310	+	1.06402i	0.0905751	+	0.156881i
$47$	−5.08653	+	8.81013i	−0.741947	+	1.28509i	0.209661	+	0.977774i	$0.432764\pi$
$47$	−5.08653	+	8.81013i	−0.741947	+	1.28509i	−0.951608	+	0.307316i	$0.900569\pi$
$48$		0			0
$49$	−1.33611	+	6.87130i	−0.190872	+	0.981615i
$50$	4.28189			0.605551
$51$		0			0
$52$	−1.04958	−	1.81793i	−0.145551	−	0.252102i
$53$	4.94465	+	8.56438i	0.679199	+	1.17641i	0.975222	+	0.221227i	$0.0710061\pi$
$53$	4.94465	+	8.56438i	0.679199	+	1.17641i	−0.296023	+	0.955181i	$0.595661\pi$
$54$		0			0
$55$	3.29588			0.444416
$56$	−3.13268	−	3.80050i	−0.418622	−	0.507863i
$57$		0			0
$58$	−1.02708	+	1.77895i	−0.134862	+	0.233588i
$59$	0.906186	+	1.56956i	0.117975	+	0.204339i	0.918965	−	0.394339i	$-0.129026\pi$
$59$	0.906186	+	1.56956i	0.117975	+	0.204339i	−0.800990	+	0.598678i	$0.795693\pi$
$60$		0			0
$61$	−5.40205	+	9.35663i	−0.691662	+	1.19799i	0.279631	+	0.960108i	$0.409788\pi$
$61$	−5.40205	+	9.35663i	−0.691662	+	1.19799i	−0.971293	+	0.237886i	$0.923545\pi$
$62$	1.77776			0.225776
$63$		0			0
$64$	−2.68848			−0.336060
$65$	2.20948	−	3.82692i	0.274052	−	0.474671i
$66$		0			0
$67$	−0.514685	−	0.891460i	−0.0628787	−	0.108909i	0.832872	−	0.553465i	$-0.186695\pi$
$67$	−0.514685	−	0.891460i	−0.0628787	−	0.108909i	−0.895751	+	0.444556i	$0.853361\pi$
$68$	−0.219249	+	0.379751i	−0.0265879	+	0.0460516i
$69$		0			0
$70$	1.69671	−	4.53761i	0.202796	−	0.542349i
$71$	4.94533			0.586903			0.293451	−	0.955974i	$-0.405196\pi$
$71$	4.94533			0.586903			0.293451	+	0.955974i	$0.405196\pi$
$72$		0			0
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	0.807480	−	0.589894i	$-0.200831\pi$
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	−0.914604	+	0.404351i	$0.867497\pi$
$74$	−1.17306	−	2.03181i	−0.136366	−	0.236193i
$75$		0			0
$76$	4.92604			0.565055
$77$	0.827091	−	2.21194i	0.0942557	−	0.252074i
$78$		0			0
$79$	0.899562	−	1.55809i	0.101209	−	0.175298i	−0.810974	−	0.585082i	$-0.801062\pi$
$79$	0.899562	−	1.55809i	0.101209	−	0.175298i	0.912183	+	0.409783i	$0.134396\pi$
$80$	−4.77293	−	8.26696i	−0.533630	−	0.924274i
$81$		0			0
$82$	1.18559	−	2.05350i	0.130926	−	0.226771i
$83$	12.3231			1.35264			0.676319	−	0.736609i	$-0.263574\pi$
$83$	12.3231			1.35264			0.676319	+	0.736609i	$0.263574\pi$
$84$		0			0
$85$	−0.923082			−0.100122
$86$	−2.47403	+	4.28514i	−0.266781	+	0.462079i
$87$		0			0
$88$	0.830779	+	1.43895i	0.0885613	+	0.153393i
$89$	1.20370	−	2.08488i	0.127592	−	0.220997i	−0.795151	−	0.606412i	$-0.792608\pi$
$89$	1.20370	−	2.08488i	0.127592	−	0.220997i	0.922743	+	0.385415i	$0.125942\pi$
$90$		0			0
$91$	−2.01387	−	2.44318i	−0.211111	−	0.256115i
$92$	4.34620			0.453122
$93$		0			0
$94$	−2.52225	−	4.36867i	−0.260150	−	0.450593i
$95$	5.18489	+	8.98049i	0.531958	+	0.921379i
$96$		0			0
$97$	−11.0442			−1.12137			−0.560684	−	0.828030i	$-0.689462\pi$
$97$	−11.0442			−1.12137			−0.560684	+	0.828030i	$0.689462\pi$
$98$	−2.61951	−	2.27740i	−0.264610	−	0.230052i
$99$		0			0
$100$	7.57351	−	13.1177i	0.757351	−	1.31177i
$101$	−1.29982	−	2.25136i	−0.129337	−	0.224018i	0.794083	−	0.607810i	$-0.207952\pi$
$101$	−1.29982	−	2.25136i	−0.129337	−	0.224018i	−0.923420	+	0.383791i	$0.874618\pi$
$102$		0			0
$103$	−4.85578	+	8.41045i	−0.478454	+	0.828706i	−0.999695	−	0.0247032i	$-0.992136\pi$
$103$	−4.85578	+	8.41045i	−0.478454	+	0.828706i	0.521241	+	0.853409i	$0.325469\pi$
$104$	2.22773			0.218447
$105$		0			0
$106$	−4.90379			−0.476298
$107$	5.45025	−	9.44012i	0.526896	−	0.912610i	−0.472613	−	0.881270i	$-0.656689\pi$
$107$	5.45025	−	9.44012i	0.526896	−	0.912610i	0.999509	−	0.0313403i	$-0.00997757\pi$
$108$		0			0
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	0.810731	−	0.585419i	$-0.199070\pi$
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	−0.912353	+	0.409404i	$0.865737\pi$
$110$	−0.817161	+	1.41536i	−0.0779132	+	0.134950i
$111$		0			0
$112$	−6.74589	+	1.12865i	−0.637427	+	0.106648i
$113$	15.8264			1.48882			0.744409	−	0.667724i	$-0.232731\pi$
$113$	15.8264			1.48882			0.744409	+	0.667724i	$0.232731\pi$
$114$		0			0
$115$	4.57458	+	7.92341i	0.426582	+	0.738861i
$116$	3.63325	+	6.29298i	0.337339	+	0.584289i
$117$		0			0
$118$	−0.898698			−0.0827318
$119$	−0.231645	+	0.619501i	−0.0212348	+	0.0567895i
$120$		0			0
$121$	5.10166	−	8.83634i	0.463787	−	0.803303i
$122$	−2.67871	−	4.63966i	−0.242519	−	0.420055i
$123$		0			0
$124$	3.14438	−	5.44623i	0.282374	−	0.489086i
$125$	13.4230			1.20059
$126$		0			0
$127$	−1.26946			−0.112647			−0.0563233	−	0.998413i	$-0.517938\pi$
$127$	−1.26946			−0.112647			−0.0563233	+	0.998413i	$0.517938\pi$
$128$	5.67155	−	9.82342i	0.501299	−	0.868275i
$129$		0			0
$130$	1.09561	+	1.89765i	0.0960912	+	0.166435i
$131$	−7.51444	+	13.0154i	−0.656540	+	1.13716i	0.324965	+	0.945726i	$0.394647\pi$
$131$	−7.51444	+	13.0154i	−0.656540	+	1.13716i	−0.981505	+	0.191435i	$0.938686\pi$
$132$		0			0
$133$	7.32814	−	1.22607i	0.635430	−	0.106313i
$134$	0.510432			0.0440946
$135$		0			0
$136$	−0.232677	−	0.403009i	−0.0199519	−	0.0345577i
$137$	−0.244246	−	0.423047i	−0.0208674	−	0.0361433i	0.855403	−	0.517963i	$-0.173309\pi$
$137$	−0.244246	−	0.423047i	−0.0208674	−	0.0361433i	−0.876271	+	0.481819i	$0.839976\pi$
$138$		0			0
$139$	9.86974			0.837141			0.418570	−	0.908184i	$-0.362531\pi$
$139$	9.86974			0.837141			0.418570	+	0.908184i	$0.362531\pi$
$140$	−10.9001	−	13.2237i	−0.921226	−	1.11761i
$141$		0			0
$142$	−1.22612	+	2.12370i	−0.102893	+	0.178217i
$143$	0.534073	+	0.925042i	0.0446614	+	0.0773559i
$144$		0			0
$145$	−7.64835	+	13.2473i	−0.635161	+	1.10013i
$146$	0.907699			0.0751217
$147$		0			0
$148$	−8.29934			−0.682202
$149$	10.5120	−	18.2073i	0.861175	−	1.49160i	−0.00962096	−	0.999954i	$-0.503062\pi$
$149$	10.5120	−	18.2073i	0.861175	−	1.49160i	0.870796	−	0.491645i	$-0.163604\pi$
$150$		0			0
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	0.833930	−	0.551870i	$-0.186086\pi$
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	−0.894898	+	0.446270i	$0.852752\pi$
$152$	−2.61387	+	4.52735i	−0.212013	+	0.367217i
$153$		0			0
$154$	0.744818	+	0.903596i	0.0600192	+	0.0728139i
$155$	13.2384			1.06334
$156$		0			0
$157$	8.33982	+	14.4450i	0.665590	+	1.15284i	0.979125	+	0.203259i	$0.0651534\pi$
$157$	8.33982	+	14.4450i	0.665590	+	1.15284i	−0.313535	+	0.949577i	$0.601513\pi$
$158$	0.446064	+	0.772606i	0.0354870	+	0.0614652i
$159$		0			0
$160$	18.4813			1.46108
$161$	6.46555	−	1.08175i	0.509557	−	0.0852537i
$162$		0			0
$163$	−3.34135	+	5.78738i	−0.261714	+	0.453303i	−0.966698	−	0.255921i	$-0.917621\pi$
$163$	−3.34135	+	5.78738i	−0.261714	+	0.453303i	0.704983	+	0.709224i	$0.250954\pi$
$164$	−4.19396	−	7.26416i	−0.327494	−	0.567236i
$165$		0			0
$166$	−3.05532	+	5.29197i	−0.237139	+	0.410737i
$167$	17.6310			1.36433			0.682163	−	0.731200i	$-0.261039\pi$
$167$	17.6310			1.36433			0.682163	+	0.731200i	$0.261039\pi$
$168$		0			0
$169$	−11.5679			−0.889837
$170$	0.228863	−	0.396403i	0.0175530	−	0.0304027i
$171$		0			0
$172$	8.75178	+	15.1585i	0.667317	+	1.15583i
$173$	−1.94342	+	3.36611i	−0.147756	+	0.255920i	−0.930398	−	0.366552i	$-0.880538\pi$
$173$	−1.94342	+	3.36611i	−0.147756	+	0.255920i	0.782642	+	0.622472i	$0.213872\pi$
$174$		0			0
$175$	8.00168	−	21.3994i	0.604870	−	1.61764i
$176$	2.30742			0.173928
$177$		0			0
$178$	0.596879	+	1.03382i	0.0447380	+	0.0774884i
$179$	−3.66758	−	6.35244i	−0.274128	−	0.474804i	0.695787	−	0.718248i	$-0.255056\pi$
$179$	−3.66758	−	6.35244i	−0.274128	−	0.474804i	−0.969915	+	0.243445i	$0.921723\pi$
$180$		0			0
$181$	11.2566			0.836693			0.418346	−	0.908288i	$-0.362610\pi$
$181$	11.2566			0.836693			0.418346	+	0.908288i	$0.362610\pi$
$182$	1.54849	−	0.259078i	0.114782	−	0.0192041i
$183$		0			0
$184$	−2.30619	+	3.99444i	−0.170015	+	0.294474i
$185$	−8.73545	−	15.1302i	−0.642243	−	1.11240i
$186$		0			0
$187$	0.111563	−	0.193234i	0.00815833	−	0.0141306i
$188$	−17.8447			−1.30146
$189$		0			0
$190$	−5.14204			−0.373043
$191$	−11.9230	+	20.6512i	−0.862715	+	1.49427i	0.00658302	+	0.999978i	$0.497905\pi$
$191$	−11.9230	+	20.6512i	−0.862715	+	1.49427i	−0.869298	+	0.494288i	$0.835429\pi$
$192$		0			0
$193$	−2.96728	−	5.13948i	−0.213589	−	0.369948i	0.739246	−	0.673436i	$-0.235182\pi$
$193$	−2.96728	−	5.13948i	−0.213589	−	0.369948i	−0.952835	+	0.303488i	$0.901849\pi$
$194$	2.73823	−	4.74276i	0.196594	−	0.340510i
$195$		0			0
$196$	−11.6101	+	3.99684i	−0.829292	+	0.285489i
$197$	15.4682			1.10206			0.551032	−	0.834484i	$-0.314234\pi$
$197$	15.4682			1.10206			0.551032	+	0.834484i	$0.314234\pi$
$198$		0			0
$199$	7.74818	+	13.4202i	0.549254	+	0.951336i	0.998326	+	0.0578402i	$0.0184214\pi$
$199$	7.74818	+	13.4202i	0.549254	+	0.951336i	−0.449072	+	0.893496i	$0.648245\pi$
$200$	8.03736	+	13.9211i	0.568327	+	0.984371i
$201$		0			0
$202$	1.28908			0.0906994
$203$	6.97125	+	8.45735i	0.489286	+	0.593590i
$204$		0			0
$205$	8.82870	−	15.2917i	0.616623	−	1.06802i
$206$	−2.40783	−	4.17048i	−0.167761	−	0.290571i
$207$		0			0
$208$	1.54684	−	2.67920i	0.107254	−	0.185769i
$209$	−2.50658			−0.173384
$210$		0			0
$211$	−1.54380			−0.106279			−0.0531397	−	0.998587i	$-0.516923\pi$
$211$	−1.54380			−0.106279			−0.0531397	+	0.998587i	$0.516923\pi$
$212$	−8.67347	+	15.0229i	−0.595697	+	1.03178i
$213$		0			0
$214$	2.70261	+	4.68105i	0.184746	+	0.319990i
$215$	−18.4233	+	31.9101i	−1.25646	+	2.17625i
$216$		0			0
$217$	3.32215	−	8.88461i	0.225522	−	0.603127i
$218$	1.05220			0.0712637
$219$		0			0
$220$	2.89068	+	5.00680i	0.194889	+	0.337558i
$221$	−0.149579	−	0.259078i	−0.0100617	−	0.0174275i
$222$		0			0
$223$	5.44342			0.364518			0.182259	−	0.983251i	$-0.441659\pi$
$223$	5.44342			0.364518			0.182259	+	0.983251i	$0.441659\pi$
$224$	4.63783	−	12.4032i	0.309878	−	0.828725i
$225$		0			0
$226$	−3.92389	+	6.79638i	−0.261014	+	0.452089i
$227$	−8.03818	−	13.9225i	−0.533513	−	0.924072i	−0.999234	−	0.0391399i	$-0.987538\pi$
$227$	−8.03818	−	13.9225i	−0.533513	−	0.924072i	0.465721	−	0.884932i	$-0.345795\pi$
$228$		0			0
$229$	4.98420	−	8.63289i	0.329365	−	0.570477i	−0.653021	−	0.757340i	$-0.726499\pi$
$229$	4.98420	−	8.63289i	0.329365	−	0.570477i	0.982386	+	0.186863i	$0.0598319\pi$
$230$	−4.53678			−0.299146
$231$		0			0
$232$	−7.71155			−0.506288
$233$	−8.27045	+	14.3248i	−0.541815	+	0.938451i	0.456985	+	0.889474i	$0.348929\pi$
$233$	−8.27045	+	14.3248i	−0.541815	+	0.938451i	−0.998800	+	0.0489765i	$0.984404\pi$
$234$		0			0
$235$	−18.7824	−	32.5321i	−1.22523	−	2.12216i
$236$	−1.58955	+	2.75319i	−0.103471	+	0.179217i
$237$		0			0
$238$	−0.208602	−	0.253072i	−0.0135217	−	0.0164042i
$239$	−22.0239			−1.42461			−0.712303	−	0.701872i	$-0.752348\pi$
$239$	−22.0239			−1.42461			−0.712303	+	0.701872i	$0.752348\pi$
$240$		0			0
$241$	−8.36004	−	14.4800i	−0.538517	−	0.932739i	−0.998984	−	0.0450623i	$-0.985651\pi$
$241$	−8.36004	−	14.4800i	−0.538517	−	0.932739i	0.460467	−	0.887677i	$-0.347682\pi$
$242$	2.52975	+	4.38166i	0.162619	+	0.281664i
$243$		0			0
$244$	−18.9516			−1.21325
$245$	−19.5067	−	16.9591i	−1.24624	−	1.08348i
$246$		0			0
$247$	−1.68035	+	2.91045i	−0.106918	+	0.185187i
$248$	3.33696	+	5.77978i	0.211897	+	0.367017i
$249$		0			0
$250$	−3.32803	+	5.76432i	−0.210483	+	0.364568i
$251$	8.53099			0.538471			0.269236	−	0.963074i	$-0.413229\pi$
$251$	8.53099			0.538471			0.269236	+	0.963074i	$0.413229\pi$
$252$		0			0
$253$	−2.21153			−0.139038
$254$	0.314743	−	0.545151i	0.0197488	−	0.0342058i
$255$		0			0
$256$	0.123861	+	0.214533i	0.00774131	+	0.0134083i
$257$	−8.55986	+	14.8261i	−0.533950	+	0.924828i	0.465264	+	0.885172i	$0.345959\pi$
$257$	−8.55986	+	14.8261i	−0.533950	+	0.924828i	−0.999213	+	0.0396557i	$0.987374\pi$
$258$		0			0
$259$	−12.3464	+	2.06567i	−0.767167	+	0.128354i
$260$	7.75135			0.480718
$261$		0			0
$262$	−3.72617	−	6.45392i	−0.230204	−	0.398725i
$263$	10.2763	+	17.7991i	0.633666	+	1.09754i	0.986796	+	0.161967i	$0.0517838\pi$
$263$	10.2763	+	17.7991i	0.633666	+	1.09754i	−0.353130	+	0.935574i	$0.614883\pi$
$264$		0			0
$265$	−36.5170			−2.24322
$266$	−1.29038	+	3.45094i	−0.0791183	+	0.211591i
$267$		0			0
$268$	0.902816	−	1.56372i	0.0551483	−	0.0955196i
$269$	−9.92267	−	17.1866i	−0.604996	−	1.04788i	−0.992052	−	0.125827i	$-0.959842\pi$
$269$	−9.92267	−	17.1866i	−0.604996	−	1.04788i	0.387057	−	0.922056i	$-0.373492\pi$
$270$		0			0
$271$	5.32056	−	9.21548i	0.323201	−	0.559801i	−0.657946	−	0.753065i	$-0.728574\pi$
$271$	5.32056	−	9.21548i	0.323201	−	0.559801i	0.981147	+	0.193265i	$0.0619077\pi$
$272$	−0.646243			−0.0391842
$273$		0			0
$274$	0.242228			0.0146335
$275$	−3.85373	+	6.67485i	−0.232388	+	0.402509i
$276$		0			0
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	0.949024	+	0.315205i	$0.102073\pi$
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	−0.201536	+	0.979481i	$0.564593\pi$
$278$	−2.44705	+	4.23841i	−0.146764	+	0.254203i
$279$		0			0
$280$	17.9373	−	3.00109i	1.07196	−	0.179349i
$281$	−13.6747			−0.815762			−0.407881	−	0.913035i	$-0.633732\pi$
$281$	−13.6747			−0.815762			−0.407881	+	0.913035i	$0.633732\pi$
$282$		0			0
$283$	−3.16089	−	5.47483i	−0.187896	−	0.325445i	0.756653	−	0.653817i	$-0.226833\pi$
$283$	−3.16089	−	5.47483i	−0.187896	−	0.325445i	−0.944548	+	0.328372i	$0.893500\pi$
$284$	4.33734	+	7.51249i	0.257374	+	0.445784i
$285$		0			0
$286$	−0.529660			−0.0313194
$287$	−8.04710	−	9.76255i	−0.475005	−	0.576265i
$288$		0			0
$289$	8.46875	−	14.6683i	0.498162	−	0.862842i
$290$	−3.79257	−	6.56893i	−0.222708	−	0.385741i
$291$		0			0
$292$	1.60547	−	2.78076i	0.0939533	−	0.162732i
$293$	−2.63016			−0.153655			−0.0768277	−	0.997044i	$-0.524479\pi$
$293$	−2.63016			−0.153655			−0.0768277	+	0.997044i	$0.524479\pi$
$294$		0			0
$295$	−6.69233			−0.389642
$296$	4.40382	−	7.62764i	0.255967	−	0.443348i
$297$		0			0
$298$	5.21256	+	9.02841i	0.301955	+	0.523002i
$299$	−1.48255	+	2.56786i	−0.0857384	+	0.148503i
$300$		0			0
$301$	16.7923	+	20.3721i	0.967894	+	1.17423i
$302$	0.743000			0.0427548
$303$		0			0
$304$	3.62990	+	6.28717i	0.208189	+	0.360594i
$305$	−19.9475	−	34.5501i	−1.14219	−	1.97833i
$306$		0			0
$307$	−2.79496			−0.159517			−0.0797583	−	0.996814i	$-0.525415\pi$
$307$	−2.79496			−0.159517			−0.0797583	+	0.996814i	$0.525415\pi$
$308$	4.08558	−	0.683556i	0.232797	−	0.0389492i
$309$		0			0
$310$	−3.28226	+	5.68504i	−0.186420	+	0.322889i
$311$	−7.55013	−	13.0772i	−0.428129	−	0.741541i	0.568578	−	0.822629i	$-0.307494\pi$
$311$	−7.55013	−	13.0772i	−0.428129	−	0.741541i	−0.996707	+	0.0810885i	$0.974160\pi$
$312$		0			0
$313$	12.7392	−	22.0650i	0.720064	−	1.24719i	−0.240910	−	0.970548i	$-0.577446\pi$
$313$	12.7392	−	22.0650i	0.720064	−	1.24719i	0.960974	−	0.276640i	$-0.0892209\pi$
$314$	−8.27090			−0.466754
$315$		0			0
$316$	3.15587			0.177531
$317$	16.2605	−	28.1639i	0.913278	−	1.58184i	0.103875	−	0.994590i	$-0.466876\pi$
$317$	16.2605	−	28.1639i	0.913278	−	1.58184i	0.809403	−	0.587253i	$-0.199791\pi$
$318$		0			0
$319$	−1.84875	−	3.20214i	−0.103510	−	0.179285i
$320$	4.96372	−	8.59741i	0.277480	−	0.480610i
$321$		0			0
$322$	−1.13849	+	3.04473i	−0.0634456	+	0.169676i
$323$	0.702021			0.0390615
$324$		0			0
$325$	5.16688	+	8.94931i	0.286607	+	0.496418i
$326$	−1.65687	−	2.86978i	−0.0917654	−	0.158942i
$327$		0			0
$328$	8.90165			0.491511
$329$	−26.5464	+	4.44147i	−1.46355	+	0.244866i
$330$		0			0
$331$	−9.04741	+	15.6706i	−0.497291	+	0.861333i	−0.999995	−	0.00312545i	$-0.999005\pi$
$331$	−9.04741	+	15.6706i	−0.497291	+	0.861333i	0.502704	+	0.864458i	$0.332338\pi$
$332$	10.8081	+	18.7201i	0.593170	+	1.02740i
$333$		0			0
$334$	−4.37132	+	7.57135i	−0.239188	+	0.414286i
$335$	3.80103			0.207672
$336$		0			0
$337$	25.0173			1.36278			0.681389	−	0.731921i	$-0.261376\pi$
$337$	25.0173			1.36278			0.681389	+	0.731921i	$0.261376\pi$
$338$	2.86807	−	4.96765i	0.156003	−	0.270204i
$339$		0			0
$340$	−0.809596	−	1.40226i	−0.0439065	−	0.0760483i
$341$	−1.59999	+	2.77127i	−0.0866446	+	0.150073i
$342$		0			0
$343$	−16.2768	+	8.83553i	−0.878863	+	0.477074i
$344$	−18.5756			−1.00153
$345$		0			0
$346$	−0.963682	−	1.66915i	−0.0518078	−	0.0897338i
$347$	5.37444	+	9.30881i	0.288515	+	0.499723i	0.973456	−	0.228876i	$-0.0735051\pi$
$347$	5.37444	+	9.30881i	0.288515	+	0.499723i	−0.684940	+	0.728599i	$0.740172\pi$
$348$		0			0
$349$	3.28602			0.175896			0.0879482	−	0.996125i	$-0.471969\pi$
$349$	3.28602			0.175896			0.0879482	+	0.996125i	$0.471969\pi$
$350$	7.20574	+	8.74183i	0.385163	+	0.467270i
$351$		0			0
$352$	−2.23365	+	3.86879i	−0.119054	+	0.206207i
$353$	8.40960	+	14.5658i	0.447598	+	0.775262i	0.998229	−	0.0594866i	$-0.0189463\pi$
$353$	8.40960	+	14.5658i	0.447598	+	0.775262i	−0.550631	+	0.834748i	$0.685613\pi$
$354$		0			0
$355$	−9.13051	+	15.8145i	−0.484597	+	0.839347i
$356$	4.22287			0.223812
$357$		0			0
$358$	3.63728			0.192236
$359$	−11.8921	+	20.5978i	−0.627642	+	1.08711i	0.360382	+	0.932805i	$0.382646\pi$
$359$	−11.8921	+	20.5978i	−0.627642	+	1.08711i	−0.988024	+	0.154303i	$0.950687\pi$
$360$		0			0
$361$	5.55680	+	9.62466i	0.292463	+	0.506561i
$362$	−2.79088	+	4.83395i	−0.146686	+	0.254067i
$363$		0			0
$364$	1.94518	−	5.20210i	0.101955	−	0.272664i
$365$	6.75936			0.353801
$366$		0			0
$367$	0.344992	+	0.597544i	0.0180084	+	0.0311915i	0.874889	−	0.484323i	$-0.160934\pi$
$367$	0.344992	+	0.597544i	0.0180084	+	0.0311915i	−0.856881	+	0.515515i	$0.827601\pi$
$368$	3.20263	+	5.54712i	0.166949	+	0.289164i
$369$		0			0
$370$	8.66327			0.450382
$371$	−9.16383	+	24.5074i	−0.475762	+	1.27236i
$372$		0			0
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	−0.813239	−	0.581929i	$-0.802298\pi$
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	0.910585	+	0.413321i	$0.135631\pi$
$374$	0.0553208	+	0.0958184i	0.00286057	+	0.00495465i
$375$		0			0
$376$	9.46882	−	16.4005i	0.488317	−	0.845790i
$377$	−4.95744			−0.255321
$378$		0			0
$379$	32.8735			1.68860			0.844300	−	0.535872i	$-0.180017\pi$
$379$	32.8735			1.68860			0.844300	+	0.535872i	$0.180017\pi$
$380$	−9.09489	+	15.7528i	−0.466558	+	0.808102i
$381$		0			0
$382$	−5.91222	−	10.2403i	−0.302495	−	0.523937i
$383$	−0.536335	+	0.928960i	−0.0274055	+	0.0474676i	−0.879403	−	0.476078i	$-0.842058\pi$
$383$	−0.536335	+	0.928960i	−0.0274055	+	0.0474676i	0.851997	+	0.523546i	$0.175391\pi$
$384$		0			0
$385$	5.54643	+	6.72880i	0.282672	+	0.342932i
$386$	2.94276			0.149782
$387$		0			0
$388$	−9.68640	−	16.7773i	−0.491752	−	0.851740i
$389$	−11.8718	−	20.5626i	−0.601925	−	1.04256i	−0.992529	−	0.122006i	$-0.961067\pi$
$389$	−11.8718	−	20.5626i	−0.601925	−	1.04256i	0.390605	−	0.920559i	$-0.372266\pi$
$390$		0			0
$391$	0.619387			0.0313237
$392$	2.48722	−	12.7913i	0.125624	−	0.646056i
$393$		0			0
$394$	−3.83510	+	6.64258i	−0.193209	+	0.334648i
$395$	3.32170	+	5.75336i	0.167133	+	0.289483i
$396$		0			0
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	−0.866428	−	0.499302i	$-0.833590\pi$
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	0.865622	+	0.500697i	$0.166923\pi$
$398$	−7.68415			−0.385172
$399$		0			0
$400$	22.3231			1.11616
$401$	12.2628	−	21.2398i	0.612374	−	1.06066i	−0.378465	−	0.925616i	$-0.623548\pi$
$401$	12.2628	−	21.2398i	0.612374	−	1.06066i	0.990839	−	0.135048i	$-0.0431188\pi$
$402$		0			0
$403$	2.14519	+	3.71558i	0.106860	+	0.185086i
$404$	2.28004	−	3.94914i	0.113436	−	0.196477i
$405$		0			0
$406$	−5.36029	+	0.896827i	−0.266027	+	0.0445088i
$407$	4.22306			0.209329
$408$		0			0
$409$	−13.3948	−	23.2006i	−0.662333	−	1.14719i	−0.980001	−	0.198992i	$-0.936233\pi$
$409$	−13.3948	−	23.2006i	−0.662333	−	1.14719i	0.317669	−	0.948202i	$-0.397100\pi$
$410$	4.37787	+	7.58269i	0.216208	+	0.374483i
$411$		0			0
$412$	−17.0352			−0.839263
$413$	−1.67942	+	4.49137i	−0.0826388	+	0.221006i
$414$		0			0
$415$	−22.7520	+	39.4077i	−1.11685	+	1.93445i
$416$	2.99476	+	5.18708i	0.146830	+	0.254317i
$417$		0			0
$418$	0.621466	−	1.07641i	0.0303969	−	0.0526490i
$419$	−21.0525			−1.02848			−0.514240	−	0.857646i	$-0.671926\pi$
$419$	−21.0525			−1.02848			−0.514240	+	0.857646i	$0.671926\pi$
$420$		0			0
$421$	14.8907			0.725727			0.362863	−	0.931842i	$-0.381799\pi$
$421$	14.8907			0.725727			0.362863	+	0.931842i	$0.381799\pi$
$422$	0.382760	−	0.662959i	0.0186325	−	0.0322724i
$423$		0			0
$424$	−9.20469	−	15.9430i	−0.447019	−	0.774260i
$425$	1.07932	−	1.86944i	0.0523547	−	0.0906809i
$426$		0			0
$427$	−28.1931	+	4.71698i	−1.36436	+	0.228270i
$428$	19.1207			0.924236
$429$		0			0
$430$	−9.13554	−	15.8232i	−0.440555	−	0.763064i
$431$	7.95192	+	13.7731i	0.383031	+	0.663428i	0.991494	−	0.130154i	$-0.0415471\pi$
$431$	7.95192	+	13.7731i	0.383031	+	0.663428i	−0.608463	+	0.793582i	$0.708214\pi$
$432$		0			0
$433$	−16.3658			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$433$	−16.3658			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$434$	2.99169	+	3.62944i	0.143605	+	0.174219i
$435$		0			0
$436$	1.86105	−	3.22344i	0.0891282	−	0.154375i
$437$	−3.47905	−	6.02590i	−0.166426	−	0.288258i
$438$		0			0
$439$	7.77236	−	13.4621i	0.370954	−	0.642512i	−0.618758	−	0.785582i	$-0.712364\pi$
$439$	7.77236	−	13.4621i	0.370954	−	0.642512i	0.989713	+	0.143070i	$0.0456973\pi$
$440$	−6.13543			−0.292495
$441$		0			0
$442$	0.148343			0.00705594
$443$	0.895027	−	1.55023i	0.0425240	−	0.0736537i	−0.843980	−	0.536375i	$-0.819793\pi$
$443$	0.895027	−	1.55023i	0.0425240	−	0.0736537i	0.886504	+	0.462721i	$0.153127\pi$
$444$		0			0
$445$	4.44477	+	7.69857i	0.210702	+	0.364947i
$446$	−1.34961	+	2.33759i	−0.0639058	+	0.110688i
$447$		0			0
$448$	−4.52428	−	5.48875i	−0.213752	−	0.259319i
$449$	−13.5666			−0.640250			−0.320125	−	0.947375i	$-0.603725\pi$
$449$	−13.5666			−0.640250			−0.320125	+	0.947375i	$0.603725\pi$
$450$		0			0
$451$	2.13407	+	3.69631i	0.100489	+	0.174053i
$452$	13.8806	+	24.0419i	0.652890	+	1.13084i
$453$		0			0
$454$	7.97176			0.374133
$455$	11.5312	−	1.92927i	0.540589	−	0.0904457i
$456$		0			0
$457$	−1.28459	+	2.22497i	−0.0600905	+	0.104080i	−0.894506	−	0.447057i	$-0.852472\pi$
$457$	−1.28459	+	2.22497i	−0.0600905	+	0.104080i	0.834415	+	0.551136i	$0.185806\pi$
$458$	2.47151	+	4.28078i	0.115486	+	0.200028i
$459$		0			0
$460$	−8.02434	+	13.8986i	−0.374137	+	0.648024i
$461$	36.1869			1.68539			0.842695	−	0.538391i	$-0.180967\pi$
$461$	36.1869			1.68539			0.842695	+	0.538391i	$0.180967\pi$
$462$		0			0
$463$	−16.3845			−0.761451			−0.380726	−	0.924688i	$-0.624326\pi$
$463$	−16.3845			−0.761451			−0.380726	+	0.924688i	$0.624326\pi$
$464$	−5.35455	+	9.27436i	−0.248579	+	0.430551i
$465$		0			0
$466$	−4.10105	−	7.10323i	−0.189978	−	0.329051i
$467$	4.35022	−	7.53480i	0.201304	−	0.348669i	−0.747645	−	0.664099i	$-0.768815\pi$
$467$	4.35022	−	7.53480i	0.201304	−	0.348669i	0.948949	+	0.315430i	$0.102149\pi$
$468$		0			0
$469$	0.953856	−	2.55095i	0.0440450	−	0.117792i
$470$	18.6272			0.859209
$471$		0			0
$472$	−1.68691	−	2.92181i	−0.0776462	−	0.134487i
$473$	−4.45328	−	7.71330i	−0.204762	−	0.354658i
$474$		0			0
$475$	−24.2498			−1.11266
$476$	−1.14425	+	0.191445i	−0.0524468	+	0.00877485i
$477$		0			0
$478$	5.46047	−	9.45782i	0.249756	−	0.432591i
$479$	−8.88370	−	15.3870i	−0.405907	−	0.703051i	0.588520	−	0.808483i	$-0.299711\pi$
$479$	−8.88370	−	15.3870i	−0.405907	−	0.703051i	−0.994427	+	0.105432i	$0.966378\pi$
$480$		0			0
$481$	2.83103	−	4.90349i	0.129084	−	0.223580i
$482$	8.29095			0.377643
$483$		0			0
$484$	17.8978			0.813536
$485$	20.3908	−	35.3179i	0.925898	−	1.60370i
$486$		0			0
$487$	8.32763	+	14.4239i	0.377361	+	0.653608i	0.990677	−	0.136229i	$-0.0434983\pi$
$487$	8.32763	+	14.4239i	0.377361	+	0.653608i	−0.613316	+	0.789837i	$0.710165\pi$
$488$	10.0562	−	17.4178i	0.455222	−	0.788467i
$489$		0			0
$490$	12.1192	−	4.17210i	0.547490	−	0.188476i
$491$	−6.42042			−0.289749			−0.144875	−	0.989450i	$-0.546278\pi$
$491$	−6.42042			−0.289749			−0.144875	+	0.989450i	$0.546278\pi$
$492$		0			0
$493$	0.517784	+	0.896827i	0.0233198	+	0.0403911i
$494$	−0.833230	−	1.44320i	−0.0374888	−	0.0649325i
$495$		0			0
$496$	9.26814			0.416152
$497$	8.32220	+	10.0963i	0.373302	+	0.452881i
$498$		0			0
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	−0.963382	−	0.268134i	$-0.913593\pi$
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	0.713902	+	0.700246i	$0.246926\pi$
$500$	11.7728	+	20.3911i	0.526495	+	0.911916i
$501$		0			0
$502$	−2.11512	+	3.66350i	−0.0944026	+	0.163510i
$503$	17.7223			0.790200			0.395100	−	0.918638i	$-0.370710\pi$
$503$	17.7223			0.790200			0.395100	+	0.918638i	$0.370710\pi$
$504$		0			0
$505$	9.59939			0.427167
$506$	0.548314	−	0.949708i	0.0243755	−	0.0422197i
$507$		0			0
$508$	−1.11339	−	1.92845i	−0.0493988	−	0.0855612i
$509$	15.5411	−	26.9180i	0.688848	−	1.19312i	−0.283362	−	0.959013i	$-0.591450\pi$
$509$	15.5411	−	26.9180i	0.688848	−	1.19312i	0.972211	−	0.234107i	$-0.0752167\pi$
$510$		0			0
$511$	1.69624	−	4.53635i	0.0750372	−	0.200676i
$512$	22.5634			0.997169
$513$		0			0
$514$	−4.24456	−	7.35180i	−0.187220	−	0.324274i
$515$	−17.9303	−	31.0563i	−0.790105	−	1.36850i
$516$		0			0
$517$	9.08016			0.399345
$518$	2.17402	−	5.81411i	0.0955210	−	0.255457i
$519$		0			0
$520$	−4.11304	+	7.12399i	−0.180369	+	0.312408i
$521$	2.37986	+	4.12203i	0.104263	+	0.180590i	0.913437	−	0.406980i	$-0.133418\pi$
$521$	2.37986	+	4.12203i	0.104263	+	0.180590i	−0.809174	+	0.587570i	$0.800085\pi$
$522$		0			0
$523$	20.1258	−	34.8588i	0.880038	−	1.52427i	0.0287402	−	0.999587i	$-0.490850\pi$
$523$	20.1258	−	34.8588i	0.880038	−	1.52427i	0.851298	−	0.524683i	$-0.175816\pi$
$524$	−26.3624			−1.15165
$525$		0			0
$526$	−10.1914			−0.444367
$527$	0.448113	−	0.776154i	0.0195201	−	0.0338098i
$528$		0			0
$529$	8.43046	+	14.6020i	0.366542	+	0.634869i
$530$	9.05381	−	15.6817i	0.393272	−	0.681168i
$531$		0			0
$532$	8.28972	+	10.0569i	0.359405	+	0.436022i
$533$	5.72250			0.247869
$534$		0			0
$535$	20.1255	+	34.8584i	0.870101	+	1.50706i
$536$	0.958109	+	1.65949i	0.0413840	+	0.0716792i
$537$		0			0
$538$	9.84067			0.424261
$539$	5.90771	−	2.03376i	0.254463	−	0.0876003i
$540$		0			0
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	−0.481502	−	0.876445i	$-0.659908\pi$
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	0.999775	−	0.0212301i	$-0.00675826\pi$
$542$	2.63830	+	4.56966i	0.113325	+	0.196284i
$543$		0			0
$544$	0.625580	−	1.08354i	0.0268215	−	0.0464563i
$545$	7.83538			0.335631
$546$		0			0
$547$	12.3550			0.528263			0.264131	−	0.964487i	$-0.414915\pi$
$547$	12.3550			0.528263			0.264131	+	0.964487i	$0.414915\pi$
$548$	0.428436	−	0.742073i	0.0183019	−	0.0316998i
$549$		0			0
$550$	−1.91094	−	3.30985i	−0.0814828	−	0.141132i
$551$	5.81671	−	10.0748i	0.247800	−	0.429203i
$552$		0			0
$553$	4.69478	−	0.785481i	0.199642	−	0.0334020i
$554$	−12.3379			−0.524186
$555$		0			0
$556$	8.65633	+	14.9932i	0.367110	+	0.635853i
$557$	−4.03845	−	6.99479i	−0.171114	−	0.296379i	0.767695	−	0.640815i	$-0.221403\pi$
$557$	−4.03845	−	6.99479i	−0.171114	−	0.296379i	−0.938810	+	0.344436i	$0.888070\pi$
$558$		0			0
$559$	−11.9415			−0.505070
$560$	8.84559	−	23.6563i	0.373794	−	0.999661i
$561$		0			0
$562$	3.39041	−	5.87237i	0.143016	−	0.247711i
$563$	22.6064	+	39.1554i	0.952744	+	1.65020i	0.739448	+	0.673214i	$0.235087\pi$
$563$	22.6064	+	39.1554i	0.952744	+	1.65020i	0.213296	+	0.976988i	$0.431580\pi$
$564$		0			0
$565$	−29.2200	+	50.6106i	−1.22930	+	2.12920i
$566$	3.13477			0.131764
$567$		0			0
$568$	−9.20596			−0.386274
$569$	11.2149	−	19.4248i	0.470155	−	0.814332i	−0.529263	−	0.848458i	$-0.677532\pi$
$569$	11.2149	−	19.4248i	0.470155	−	0.814332i	0.999418	+	0.0341263i	$0.0108648\pi$
$570$		0			0
$571$	10.9134	+	18.9026i	0.456713	+	0.791050i	0.998785	−	0.0492820i	$-0.0156933\pi$
$571$	10.9134	+	18.9026i	0.456713	+	0.791050i	−0.542072	+	0.840332i	$0.682360\pi$
$572$	−0.936826	+	1.62263i	−0.0391706	+	0.0678455i
$573$		0			0
$574$	6.18753	−	1.03523i	0.258262	−	0.0432098i
$575$	−21.3954			−0.892251
$576$		0			0
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	−0.977807	−	0.209508i	$-0.932814\pi$
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	0.307465	−	0.951559i	$-0.400519\pi$
$578$	4.19939	+	7.27355i	0.174671	+	0.302540i
$579$		0			0
$580$	−26.8322			−1.11414
$581$	20.7378	+	25.1586i	0.860350	+	1.04376i
$582$		0			0
$583$	4.41343	−	7.64429i	0.182786	−	0.316594i
$584$	1.70380	+	2.95107i	0.0705039	+	0.122116i
$585$		0			0
$586$	0.652105	−	1.12948i	0.0269382	−	0.0466584i
$587$	−19.4461			−0.802625			−0.401313	−	0.915941i	$-0.631446\pi$
$587$	−19.4461			−0.802625			−0.401313	+	0.915941i	$0.631446\pi$
$588$		0			0
$589$	−10.0681			−0.414848
$590$	1.65926	−	2.87392i	0.0683105	−	0.118317i
$591$		0			0
$592$	−6.11563	−	10.5926i	−0.251351	−	0.435352i
$593$	14.4202	−	24.9766i	0.592168	−	1.02566i	−0.401772	−	0.915740i	$-0.631606\pi$
$593$	14.4202	−	24.9766i	0.592168	−	1.02566i	0.993940	−	0.109925i	$-0.0350611\pi$
$594$		0			0
$595$	−1.55340	−	1.88455i	−0.0636831	−	0.0772589i
$596$	36.8784			1.51060
$597$		0			0
$598$	−0.735152	−	1.27332i	−0.0300626	−	0.0520699i
$599$	−23.4994	−	40.7022i	−0.960161	−	1.66305i	−0.722089	−	0.691800i	$-0.756818\pi$
$599$	−23.4994	−	40.7022i	−0.960161	−	1.66305i	−0.238072	−	0.971247i	$-0.576516\pi$
$600$		0			0
$601$	15.6169			0.637025			0.318512	−	0.947919i	$-0.396817\pi$
$601$	15.6169			0.637025			0.318512	+	0.947919i	$0.396817\pi$
$602$	−12.9119	+	2.16028i	−0.526248	+	0.0880463i
$603$		0			0
$604$	1.31417	−	2.27620i	0.0534727	−	0.0926174i
$605$	18.8383	+	32.6289i	0.765885	+	1.32655i
$606$		0			0
$607$	14.3266	−	24.8144i	0.581500	−	1.00719i	−0.413802	−	0.910367i	$-0.635800\pi$
$607$	14.3266	−	24.8144i	0.581500	−	1.00719i	0.995302	−	0.0968200i	$-0.0308671\pi$
$608$	−14.0554			−0.570021
$609$		0			0
$610$	19.7827			0.800977
$611$	6.08711	−	10.5432i	0.246258	−	0.426531i
$612$		0			0
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	0.993873	+	0.110524i	$0.0352529\pi$
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	−0.401220	+	0.915982i	$0.631414\pi$
$614$	0.692965	−	1.20025i	0.0279658	−	0.0484382i
$615$		0			0
$616$	−1.53967	+	4.11762i	−0.0620350	+	0.165904i
$617$	4.12801			0.166188			0.0830938	−	0.996542i	$-0.473520\pi$
$617$	4.12801			0.166188			0.0830938	+	0.996542i	$0.473520\pi$
$618$		0			0
$619$	−11.3565	−	19.6700i	−0.456456	−	0.790605i	0.542315	−	0.840175i	$-0.317548\pi$
$619$	−11.3565	−	19.6700i	−0.456456	−	0.790605i	−0.998771	+	0.0495708i	$0.984215\pi$
$620$	11.6109	+	20.1106i	0.466304	+	0.807662i
$621$		0			0
$622$	7.48774			0.300231
$623$	6.28209	−	1.05105i	0.251686	−	0.0421095i
$624$		0			0
$625$	−3.19498	+	5.53387i	−0.127799	+	0.221355i
$626$	6.31698	+	10.9413i	0.252477	+	0.437304i
$627$		0			0
$628$	−14.6290	+	25.3382i	−0.583761	+	1.01110i
$629$	−1.18276			−0.0471597
$630$		0			0
$631$	−38.6411			−1.53828			−0.769138	−	0.639082i	$-0.779314\pi$
$631$	−38.6411			−1.53828			−0.769138	+	0.639082i	$0.779314\pi$
$632$	−1.67458	+	2.90045i	−0.0666110	+	0.115374i
$633$		0			0
$634$	8.06304	+	13.9656i	0.320224	+	0.554645i
$635$	2.34380	−	4.05958i	0.0930107	−	0.161099i
$636$		0			0
$637$	1.59893	−	8.22297i	0.0633520	−	0.325806i
$638$	1.83348			0.0725881
$639$		0			0
$640$	20.9427	+	36.2737i	0.827831	+	1.43385i
$641$	−14.2363	−	24.6580i	−0.562301	−	0.973933i	−0.997295	−	0.0735002i	$-0.976583\pi$
$641$	−14.2363	−	24.6580i	−0.562301	−	0.973933i	0.434995	−	0.900433i	$-0.356750\pi$
$642$		0			0
$643$	17.0425			0.672091			0.336045	−	0.941846i	$-0.390910\pi$
$643$	17.0425			0.672091			0.336045	+	0.941846i	$0.390910\pi$
$644$	7.31395	+	8.87311i	0.288210	+	0.349650i
$645$		0			0
$646$	−0.174055	+	0.301472i	−0.00684810	+	0.0118613i
$647$	−1.68809	−	2.92386i	−0.0663657	−	0.114949i	0.830933	−	0.556372i	$-0.187807\pi$
$647$	−1.68809	−	2.92386i	−0.0663657	−	0.114949i	−0.897299	+	0.441423i	$0.854474\pi$
$648$		0			0
$649$	0.808833	−	1.40094i	0.0317495	−	0.0549917i
$650$	−5.12419			−0.200987
$651$		0			0
$652$	−11.7222			−0.459077
$653$	−9.17255	+	15.8873i	−0.358950	+	0.621719i	−0.987786	−	0.155819i	$-0.950198\pi$
$653$	−9.17255	+	15.8873i	−0.358950	+	0.621719i	0.628836	+	0.777538i	$0.283532\pi$
$654$		0			0
$655$	−27.7477	−	48.0604i	−1.08419	−	1.87787i
$656$	6.18090	−	10.7056i	0.241324	−	0.417985i
$657$		0			0
$658$	4.67444	−	12.5011i	0.182229	−	0.487345i
$659$	−27.8495			−1.08486			−0.542432	−	0.840100i	$-0.682496\pi$
$659$	−27.8495			−1.08486			−0.542432	+	0.840100i	$0.682496\pi$
$660$		0			0
$661$	−19.5071	−	33.7872i	−0.758737	−	1.31417i	−0.943495	−	0.331387i	$-0.892484\pi$
$661$	−19.5071	−	33.7872i	−0.758737	−	1.31417i	0.184758	−	0.982784i	$-0.440850\pi$
$662$	−4.48633	−	7.77054i	−0.174366	−	0.302011i
$663$		0			0
$664$	−22.9400			−0.890247
$665$	−9.60906	+	25.6981i	−0.372624	+	0.996529i
$666$		0			0
$667$	5.13203	−	8.88894i	0.198713	−	0.344181i
$668$	15.4634	+	26.7834i	0.598296	+	1.03628i
$669$		0			0
$670$	−0.942405	+	1.63229i	−0.0364083	+	0.0630610i
$671$	9.64340			0.372280
$672$		0			0
$673$	−49.2309			−1.89771			−0.948856	−	0.315711i	$-0.897757\pi$
$673$	−49.2309			−1.89771			−0.948856	+	0.315711i	$0.897757\pi$
$674$	−6.20264	+	10.7433i	−0.238917	+	0.413816i
$675$		0			0
$676$	−10.1457	−	17.5729i	−0.390219	−	0.675879i
$677$	−11.6958	+	20.2577i	−0.449505	+	0.778565i	−0.998354	−	0.0573564i	$-0.981733\pi$
$677$	−11.6958	+	20.2577i	−0.449505	+	0.778565i	0.548849	+	0.835922i	$0.315066\pi$
$678$		0			0
$679$	−18.5856	−	22.5476i	−0.713250	−	0.865299i
$680$	1.71836			0.0658961
$681$		0			0
$682$	−0.793387	−	1.37419i	−0.0303803	−	0.0526203i
$683$	15.1632	+	26.2634i	0.580204	+	1.00494i	0.995455	+	0.0952356i	$0.0303604\pi$
$683$	15.1632	+	26.2634i	0.580204	+	1.00494i	−0.415251	+	0.909707i	$0.636306\pi$
$684$		0			0
$685$	1.80380			0.0689196
$686$	0.241286	−	9.18044i	0.00921233	−	0.350511i
$687$		0			0
$688$	−12.8980	+	22.3401i	−0.491733	+	0.851707i
$689$	−5.91731	−	10.2491i	−0.225432	−	0.390459i
$690$		0			0
$691$	2.05665	−	3.56223i	0.0782387	−	0.135513i	−0.824251	−	0.566224i	$-0.808404\pi$
$691$	2.05665	−	3.56223i	0.0782387	−	0.135513i	0.902490	+	0.430711i	$0.141737\pi$
$692$	−6.81797			−0.259180
$693$		0			0
$694$	−5.33003			−0.202325
$695$	−18.2224	+	31.5621i	−0.691215	+	1.19722i
$696$		0			0
$697$	−0.597691	−	1.03523i	−0.0226392	−	0.0392122i
$698$	−0.814716	+	1.41113i	−0.0308375	+	0.0534120i
$699$		0			0
$700$	39.5259	−	6.61305i	1.49394	−	0.249950i
$701$	−29.1835			−1.10225			−0.551123	−	0.834424i	$-0.685800\pi$
$701$	−29.1835			−1.10225			−0.551123	+	0.834424i	$0.685800\pi$
$702$		0			0
$703$	6.64347	+	11.5068i	0.250563	+	0.433988i
$704$	1.19983	+	2.07816i	0.0452202	+	0.0783236i
$705$		0			0
$706$	−8.34010			−0.313884
$707$	2.40894	−	6.44236i	0.0905974	−	0.242290i
$708$		0			0
$709$	21.2309	−	36.7729i	0.797342	−	1.38104i	−0.123999	−	0.992282i	$-0.539572\pi$
$709$	21.2309	−	36.7729i	0.797342	−	1.38104i	0.921341	−	0.388755i	$-0.127095\pi$
$710$	−4.52753	−	7.84192i	−0.169915	−	0.294302i
$711$		0			0
$712$	−2.24075	+	3.88109i	−0.0839757	+	0.145450i
$713$	−8.88298			−0.332670
$714$		0			0
$715$	−3.94421			−0.147505
$716$	6.43336	−	11.1429i	0.240426	−	0.416430i
$717$		0			0
$718$	−5.89692	−	10.2138i	−0.220071	−	0.381175i
$719$	5.57126	−	9.64970i	0.207773	−	0.359873i	−0.743240	−	0.669025i	$-0.766712\pi$
$719$	5.57126	−	9.64970i	0.207773	−	0.359873i	0.951013	+	0.309152i	$0.100045\pi$
$720$		0			0
$721$	−25.3421	+	4.23997i	−0.943789	+	0.157905i
$722$	−5.51088			−0.205094
$723$		0			0
$724$	9.87264	+	17.0999i	0.366914	+	0.635513i
$725$	−17.8858	−	30.9790i	−0.664260	−	1.15053i
$726$		0			0
$727$	28.6820			1.06376			0.531878	−	0.846821i	$-0.321487\pi$
$727$	28.6820			1.06376			0.531878	+	0.846821i	$0.321487\pi$
$728$	3.74892	+	4.54810i	0.138944	+	0.168564i
$729$		0			0
$730$	−1.67588	+	2.90270i	−0.0620269	+	0.107434i
$731$	1.24724	+	2.16028i	0.0461307	+	0.0799007i
$732$		0			0
$733$	12.5264	−	21.6964i	0.462674	−	0.801375i	−0.536419	−	0.843952i	$-0.680223\pi$
$733$	12.5264	−	21.6964i	0.462674	−	0.801375i	0.999093	+	0.0425768i	$0.0135567\pi$
$734$	−0.342141			−0.0126287
$735$		0			0
$736$	−12.4009			−0.457104
$737$	−0.459391	+	0.795689i	−0.0169219	+	0.0293096i
$738$		0			0
$739$	13.7608	+	23.8344i	0.506198	+	0.876761i	0.999974	+	0.00717223i	$0.00228301\pi$
$739$	13.7608	+	23.8344i	0.506198	+	0.876761i	−0.493776	+	0.869589i	$0.664384\pi$
$740$	15.3230	−	26.5402i	0.563284	−	0.975637i
$741$		0			0
$742$	−8.25228	−	10.0115i	−0.302951	−	0.367533i
$743$	−14.0122			−0.514057			−0.257028	−	0.966404i	$-0.582743\pi$
$743$	−14.0122			−0.514057			−0.257028	+	0.966404i	$0.582743\pi$
$744$		0			0
$745$	38.8163	+	67.2318i	1.42212	+	2.46318i
$746$	0.932261	+	1.61472i	0.0341325	+	0.0591192i
$747$		0			0
$748$	0.391390			0.0143106
$749$	28.4447	−	4.75906i	1.03935	−	0.173892i
$750$		0			0
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.215692	−	0.976461i	$-0.430799\pi$
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.737795	−	0.675025i	$-0.235867\pi$
$752$	−13.1494	−	22.7755i	−0.479511	−	0.830537i
$753$		0			0
$754$	1.22912	−	2.12889i	0.0447618	−	0.0775298i
$755$	5.53289			0.201363
$756$		0			0
$757$	−43.3447			−1.57539			−0.787694	−	0.616066i	$-0.788725\pi$
$757$	−43.3447			−1.57539			−0.787694	+	0.616066i	$0.788725\pi$
$758$	−8.15047	+	14.1170i	−0.296038	+	0.512753i
$759$		0			0
$760$	−9.65191	−	16.7176i	−0.350112	−	0.606411i
$761$	−8.62550	+	14.9398i	−0.312674	+	0.541568i	−0.978940	−	0.204146i	$-0.934558\pi$
$761$	−8.62550	+	14.9398i	−0.312674	+	0.541568i	0.666266	+	0.745714i	$0.267891\pi$
$762$		0			0
$763$	1.96627	−	5.25850i	0.0711836	−	0.190370i
$764$	−41.8285			−1.51330
$765$		0			0
$766$	−0.265952	−	0.460642i	−0.00960922	−	0.0166437i
$767$	−1.08444	−	1.87831i	−0.0391570	−	0.0678218i
$768$		0			0
$769$	21.3454			0.769734			0.384867	−	0.922972i	$-0.374247\pi$
$769$	21.3454			0.769734			0.384867	+	0.922972i	$0.374247\pi$
$770$	−4.26473	+	0.713530i	−0.153690	+	0.0257138i
$771$		0			0
$772$	5.20495	−	9.01523i	0.187330	−	0.324465i
$773$	6.57357	+	11.3858i	0.236435	+	0.409517i	0.959689	−	0.281065i	$-0.0906877\pi$
$773$	6.57357	+	11.3858i	0.236435	+	0.409517i	−0.723254	+	0.690582i	$0.757354\pi$
$774$		0			0
$775$	−15.4791	+	26.8106i	−0.556027	+	0.963066i
$776$	20.5593			0.738036
$777$		0			0
$778$	11.7737			0.422108
$779$	−6.71439	+	11.6297i	−0.240568	+	0.416676i
$780$		0			0
$781$	−2.20702	−	3.82268i	−0.0789735	−	0.136786i
$782$	−0.153567	+	0.265986i	−0.00549155	+	0.00951164i
$783$		0			0
$784$	−13.6565	−	11.8729i	−0.487732	−	0.424034i
$785$	−61.5909			−2.19827
$786$		0			0
$787$	14.0650	+	24.3614i	0.501364	+	0.868389i	0.999999	+	0.00157623i	$0.000501728\pi$
$787$	14.0650	+	24.3614i	0.501364	+	0.868389i	−0.498634	+	0.866812i	$0.666165\pi$
$788$	13.5665	+	23.4979i	0.483287	+	0.837077i
$789$		0			0
$790$	−3.29425			−0.117204
$791$	26.6332	+	32.3108i	0.946968	+	1.14884i
$792$		0			0
$793$	6.46470	−	11.1972i	0.229568	−	0.397624i
$794$	−0.00795814	−	0.0137839i	−0.000282424	−	0.000489172i
$795$		0			0
$796$	−13.5912	+	23.5406i	−0.481727	+	0.834376i
$797$	25.7365			0.911635			0.455817	−	0.890073i	$-0.349347\pi$
$797$	25.7365			0.911635			0.455817	+	0.890073i	$0.349347\pi$
$798$		0			0
$799$	−2.54309			−0.0899681
$800$	−21.6094	+	37.4285i	−0.764007	+	1.32330i
$801$		0			0
$802$	6.08073	+	10.5321i	0.214718	+	0.371902i
$803$	−0.816934	+	1.41497i	−0.0288290	+	0.0499333i
$804$		0			0
$805$	−8.47799	+	22.6732i	−0.298810	+	0.799125i
$806$	−2.12747			−0.0749368
$807$		0			0
$808$	2.41968	+	4.19100i	0.0851240	+	0.147439i
$809$	−15.9353	−	27.6007i	−0.560254	−	0.970388i	−0.997474	−	0.0710338i	$-0.977370\pi$
$809$	−15.9353	−	27.6007i	−0.560254	−	0.970388i	0.437220	−	0.899355i	$-0.355963\pi$
$810$		0			0
$811$	43.3860			1.52349			0.761744	−	0.647878i	$-0.224343\pi$
$811$	43.3860			1.52349			0.761744	+	0.647878i	$0.224343\pi$
$812$	−6.73345	+	18.0077i	−0.236298	+	0.631945i
$813$		0			0
$814$	−1.04704	+	1.81353i	−0.0366987	+	0.0635641i
$815$	−12.3382	−	21.3704i	−0.432188	−	0.748571i
$816$		0			0
$817$	14.0113	−	24.2682i	0.490193	−	0.849039i
$818$	13.2842			0.464470
$819$		0			0
$820$	30.9731			1.08163
$821$	−8.19677	+	14.1972i	−0.286069	+	0.495487i	−0.972868	−	0.231361i	$-0.925682\pi$
$821$	−8.19677	+	14.1972i	−0.286069	+	0.495487i	0.686799	+	0.726848i	$0.259015\pi$
$822$		0			0
$823$	13.1890	+	22.8440i	0.459739	+	0.796292i	0.998947	−	0.0458812i	$-0.0146096\pi$
$823$	13.1890	+	22.8440i	0.459739	+	0.796292i	−0.539208	+	0.842173i	$0.681276\pi$
$824$	9.03925	−	15.6564i	0.314897	−	0.545418i
$825$		0			0
$826$	−1.51236	−	1.83476i	−0.0526219	−	0.0638396i
$827$	−36.7225			−1.27697			−0.638484	−	0.769635i	$-0.720438\pi$
$827$	−36.7225			−1.27697			−0.638484	+	0.769635i	$0.720438\pi$
$828$		0			0
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	0.996160	−	0.0875485i	$-0.0279033\pi$
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	−0.573899	+	0.818926i	$0.694570\pi$
$830$	−11.2820	−	19.5410i	−0.391604	−	0.678279i
$831$		0			0
$832$	3.21734			0.111541
$833$	−1.65458	+	0.569599i	−0.0573278	+	0.0197354i
$834$		0			0
$835$	−32.5519	+	56.3815i	−1.12650	+	1.95116i
$836$	−2.19841	−	3.80776i	−0.0760337	−	0.131694i
$837$		0			0
$838$	5.21962	−	9.04065i	0.180309	−	0.312304i
$839$	−25.6810			−0.886606			−0.443303	−	0.896372i	$-0.646193\pi$
$839$	−25.6810			−0.886606			−0.443303	+	0.896372i	$0.646193\pi$
$840$		0			0
$841$	−11.8393			−0.408251
$842$	−3.69190	+	6.39456i	−0.127231	+	0.220371i
$843$		0			0
$844$	−1.35400	−	2.34519i	−0.0466065	−	0.0807249i
$845$	21.3577	−	36.9926i	0.734726	−	1.27258i
$846$		0			0
$847$	26.6254	−	4.45468i	0.914859	−	0.153065i
$848$	−25.5653			−0.877915
$849$		0			0
$850$	0.535200	+	0.926994i	0.0183572	+	0.0317956i
$851$	5.86148	+	10.1524i	0.200929	+	0.348019i
$852$		0			0
$853$	−28.9743			−0.992061			−0.496031	−	0.868305i	$-0.665210\pi$
$853$	−28.9743			−0.992061			−0.496031	+	0.868305i	$0.665210\pi$
$854$	4.96440	−	13.2766i	0.169878	−	0.454316i
$855$		0			0
$856$	−10.1459	+	17.5732i	−0.346780	+	0.600640i
$857$	−12.6934	−	21.9856i	−0.433598	−	0.751015i	0.563582	−	0.826060i	$-0.309423\pi$
$857$	−12.6934	−	21.9856i	−0.433598	−	0.751015i	−0.997180	+	0.0750458i	$0.976090\pi$
$858$		0			0
$859$	2.97891	−	5.15963i	0.101639	−	0.176044i	−0.810721	−	0.585433i	$-0.800925\pi$
$859$	2.97891	−	5.15963i	0.101639	−	0.176044i	0.912360	+	0.409388i	$0.134258\pi$
$860$	−64.6333			−2.20398
$861$		0			0
$862$	−7.88621			−0.268605
$863$	−8.19545	+	14.1949i	−0.278977	+	0.483201i	−0.971131	−	0.238548i	$-0.923328\pi$
$863$	−8.19545	+	14.1949i	−0.278977	+	0.483201i	0.692154	+	0.721750i	$0.256662\pi$
$864$		0			0
$865$	−7.17624	−	12.4296i	−0.244000	−	0.422620i
$866$	4.05764	−	7.02804i	0.137884	−	0.238822i
$867$		0			0
$868$	16.4104	−	2.74562i	0.557005	−	0.0931923i
$869$	−1.60584			−0.0544744
$870$		0			0
$871$	0.615929	+	1.06682i	0.0208700	+	0.0361478i
$872$	1.97503	+	3.42086i	0.0668830	+	0.115845i
$873$		0			0
$874$	3.45030			0.116708
$875$	22.5888	+	27.4042i	0.763642	+	0.926432i
$876$		0			0
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	0.398295	+	0.917257i	$0.369602\pi$
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	−0.993516	+	0.113695i	$0.963731\pi$
$878$	3.85407	+	6.67544i	0.130068	+	0.225285i
$879$		0			0
$880$	−4.26017	+	7.37883i	−0.143610	+	0.248740i
$881$	−26.2582			−0.884661			−0.442331	−	0.896852i	$-0.645848\pi$
$881$	−26.2582			−0.884661			−0.442331	+	0.896852i	$0.645848\pi$
$882$		0			0
$883$	10.0087			0.336821			0.168410	−	0.985717i	$-0.446137\pi$
$883$	10.0087			0.336821			0.168410	+	0.985717i	$0.446137\pi$
$884$	0.262378	−	0.454452i	0.00882473	−	0.0152849i
$885$		0			0
$886$	0.443815	+	0.768711i	0.0149103	+	0.0258253i
$887$	−7.95282	+	13.7747i	−0.267030	+	0.462509i	−0.968093	−	0.250590i	$-0.919376\pi$
$887$	−7.95282	+	13.7747i	−0.267030	+	0.462509i	0.701064	+	0.713099i	$0.252709\pi$
$888$		0			0
$889$	−2.13630	−	2.59171i	−0.0716493	−	0.0869232i
$890$	−4.40804			−0.147758
$891$		0			0
$892$	4.77419	+	8.26914i	0.159852	+	0.276871i
$893$	14.2844	+	24.7413i	0.478009	+	0.827935i
$894$		0			0
$895$	27.0857			0.905374
$896$	29.5996	−	4.95230i	0.988853	−	0.165445i
$897$		0			0
$898$	3.36364	−	5.82599i	0.112246	−	0.194416i
$899$	−7.42583	−	12.8619i	−0.247665	−	0.428969i
$900$		0			0
$901$	−1.23608	+	2.14095i	−0.0411797	+	0.0713253i
$902$	−2.11643			−0.0704695
$903$		0			0
$904$	−29.4615			−0.979875
$905$	−20.7829	+	35.9970i	−0.690846	+	1.19658i
$906$		0			0
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	0.972311	−	0.233691i	$-0.0750804\pi$
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	−0.688538	+	0.725201i	$0.741747\pi$
$908$	14.0999	−	24.4217i	0.467922	−	0.810464i
$909$		0			0
$910$	−2.03047	+	5.43021i	−0.0673095	+	0.180010i
$911$	29.8869			0.990199			0.495099	−	0.868836i	$-0.335132\pi$
$911$	29.8869			0.990199			0.495099	+	0.868836i	$0.335132\pi$
$912$		0			0
$913$	−5.49961	−	9.52561i	−0.182011	−	0.315252i
$914$	−0.636986	−	1.10329i	−0.0210696	−	0.0364937i
$915$		0			0
$916$	17.4857			0.577744
$917$	−39.2176	+	6.56148i	−1.29508	+	0.216679i
$918$		0			0
$919$	11.8283	−	20.4873i	0.390181	−	0.675813i	−0.602292	−	0.798276i	$-0.705746\pi$
$919$	11.8283	−	20.4873i	0.390181	−	0.675813i	0.992473	+	0.122462i	$0.0390791\pi$
$920$	−8.51579	−	14.7498i	−0.280757	−	0.486286i
$921$		0			0
$922$	−8.97196	+	15.5399i	−0.295476	+	0.511779i
$923$	−5.91813			−0.194798
$924$		0			0
$925$	40.8559			1.34333
$926$	4.06227	−	7.03606i	0.133495	−	0.231219i
$927$		0			0
$928$	−10.3667	−	17.9557i	−0.340304	−	0.589423i
$929$	6.30880	−	10.9272i	0.206985	−	0.358509i	−0.743778	−	0.668426i	$-0.766968\pi$
$929$	6.30880	−	10.9272i	0.206985	−	0.358509i	0.950763	+	0.309918i	$0.100302\pi$
$930$		0			0
$931$	14.8352	+	12.8977i	0.486204	+	0.422705i
$932$	−29.0146			−0.950405
$933$		0			0
$934$	2.15714	+	3.73627i	0.0705836	+	0.122254i
$935$	0.411957	+	0.713530i	0.0134724	+	0.0233349i
$936$		0			0
$937$	−26.3440			−0.860622			−0.430311	−	0.902681i	$-0.641596\pi$
$937$	−26.3440			−0.860622			−0.430311	+	0.902681i	$0.641596\pi$
$938$	0.858974	+	1.04209i	0.0280465	+	0.0340254i
$939$		0			0
$940$	32.9465	−	57.0651i	1.07460	−	1.86126i
$941$	25.4699	+	44.1151i	0.830294	+	1.43811i	0.897805	+	0.440392i	$0.145161\pi$
$941$	25.4699	+	44.1151i	0.830294	+	1.43811i	−0.0675118	+	0.997718i	$0.521506\pi$
$942$		0			0
$943$	−5.92404	+	10.2607i	−0.192913	+	0.334136i
$944$	−4.68525			−0.152492
$945$		0			0
$946$	4.41648			0.143592
$947$	13.8399	−	23.9714i	0.449737	−	0.778967i	−0.548632	−	0.836064i	$-0.684851\pi$
$947$	13.8399	−	23.9714i	0.449737	−	0.778967i	0.998369	+	0.0570968i	$0.0181844\pi$
$948$		0			0
$949$	1.09530	+	1.89712i	0.0355551	+	0.0615832i
$950$	6.01236	−	10.4137i	0.195067	−	0.337866i
$951$		0			0
$952$	0.431217	−	1.15323i	0.0139758	−	0.0373764i
$953$	27.4017			0.887628			0.443814	−	0.896119i	$-0.353625\pi$
$953$	27.4017			0.887628			0.443814	+	0.896119i	$0.353625\pi$
$954$		0			0
$955$	−44.0265	−	76.2561i	−1.42466	−	2.46759i
$956$	−19.3162	−	33.4567i	−0.624731	−	1.08207i
$957$		0			0
$958$	8.81029			0.284648
$959$	0.452657	−	1.21057i	0.0146171	−	0.0390913i
$960$		0			0
$961$	9.07336	−	15.7155i	0.292689	−	0.506952i
$962$	1.40382	+	2.43149i	0.0452610	+	0.0783943i
$963$		0			0
$964$	14.6645	−	25.3996i	0.472310	−	0.818066i
$965$	21.9138			0.705431
$966$		0			0
$967$	−18.1814			−0.584674			−0.292337	−	0.956315i	$-0.594433\pi$
$967$	−18.1814			−0.584674			−0.292337	+	0.956315i	$0.594433\pi$
$968$	−9.49698	+	16.4492i	−0.305244	+	0.528699i
$969$		0			0
$970$	10.1111	+	17.5130i	0.324649	+	0.562309i
$971$	−19.7416	+	34.1935i	−0.633538	+	1.09732i	0.353285	+	0.935516i	$0.385065\pi$
$971$	−19.7416	+	34.1935i	−0.633538	+	1.09732i	−0.986823	+	0.161804i	$0.948269\pi$
$972$		0			0
$973$	16.6092	+	20.1499i	0.532466	+	0.645975i
$974$	−8.25881			−0.264629
$975$		0			0
$976$	−13.9651	−	24.1883i	−0.447012	−	0.774248i
$977$	5.95782	+	10.3193i	0.190608	+	0.330142i	0.945452	−	0.325762i	$-0.105621\pi$
$977$	5.95782	+	10.3193i	0.190608	+	0.330142i	−0.754844	+	0.655904i	$0.772288\pi$
$978$		0			0
$979$	−2.14878			−0.0686752
$980$	8.65423	−	44.5069i	0.276449	−	1.42172i
$981$		0			0
$982$	1.59184	−	2.75715i	0.0507977	−	0.0879842i
$983$	−9.23896	−	16.0024i	−0.294677	−	0.510396i	0.680233	−	0.732996i	$-0.261879\pi$
$983$	−9.23896	−	16.0024i	−0.294677	−	0.510396i	−0.974910	+	0.222601i	$0.928545\pi$
$984$		0			0
$985$	−28.5588	+	49.4653i	−0.909959	+	1.57609i
$986$	−0.513505			−0.0163533
$987$		0			0
$988$	−5.89504			−0.187546
$989$	12.3620	−	21.4117i	0.393090	−	0.680851i
$990$		0			0
$991$	−6.34850	−	10.9959i	−0.201667	−	0.349297i	0.747399	−	0.664376i	$-0.231302\pi$
$991$	−6.34850	−	10.9959i	−0.201667	−	0.349297i	−0.949066	+	0.315079i	$0.897969\pi$
$992$	−8.97181	+	15.5396i	−0.284855	+	0.493384i
$993$		0			0
$994$	−6.39905	+	1.07062i	−0.202966	+	0.0339581i
$995$	−57.2215			−1.81405
$996$		0			0
$997$	−20.9767	−	36.3327i	−0.664338	−	1.15067i	−0.979464	−	0.201617i	$-0.935380\pi$
$997$	−20.9767	−	36.3327i	−0.664338	−	1.15067i	0.315127	−	0.949050i	$-0.397953\pi$
$998$	−2.76345	−	4.78644i	−0.0874755	−	0.151512i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.e.163.3		10
3.2	odd	2		567.2.e.f.163.3		10
7.2	even	3		3969.2.a.bc.1.3		5
7.4	even	3	inner	567.2.e.e.487.3		10
7.5	odd	6		3969.2.a.bb.1.3		5
9.2	odd	6		63.2.h.b.58.3	yes	10
9.4	even	3		189.2.g.b.100.3		10
9.5	odd	6		63.2.g.b.16.3	yes	10
9.7	even	3		189.2.h.b.37.3		10
21.2	odd	6		3969.2.a.z.1.3		5
21.5	even	6		3969.2.a.ba.1.3		5
21.11	odd	6		567.2.e.f.487.3		10
36.7	odd	6		3024.2.q.i.2305.1		10
36.11	even	6		1008.2.q.i.625.3		10
36.23	even	6		1008.2.t.i.961.1		10
36.31	odd	6		3024.2.t.i.289.5		10
63.2	odd	6		441.2.f.e.148.3		10
63.4	even	3		189.2.h.b.46.3		10
63.5	even	6		441.2.f.f.295.3		10
63.11	odd	6		63.2.g.b.4.3	✓	10
63.13	odd	6		1323.2.g.f.667.3		10
63.16	even	3		1323.2.f.e.442.3		10
63.20	even	6		441.2.h.f.373.3		10
63.23	odd	6		441.2.f.e.295.3		10
63.25	even	3		189.2.g.b.172.3		10
63.31	odd	6		1323.2.h.f.802.3		10
63.32	odd	6		63.2.h.b.25.3	yes	10
63.34	odd	6		1323.2.h.f.226.3		10
63.38	even	6		441.2.g.f.67.3		10
63.40	odd	6		1323.2.f.f.883.3		10
63.41	even	6		441.2.g.f.79.3		10
63.47	even	6		441.2.f.f.148.3		10
63.52	odd	6		1323.2.g.f.361.3		10
63.58	even	3		1323.2.f.e.883.3		10
63.59	even	6		441.2.h.f.214.3		10
63.61	odd	6		1323.2.f.f.442.3		10
252.11	even	6		1008.2.t.i.193.1		10
252.67	odd	6		3024.2.q.i.2881.1		10
252.95	even	6		1008.2.q.i.529.3		10
252.151	odd	6		3024.2.t.i.1873.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	63.11	odd	6
63.2.g.b.16.3	yes	10	9.5	odd	6
63.2.h.b.25.3	yes	10	63.32	odd	6
63.2.h.b.58.3	yes	10	9.2	odd	6
189.2.g.b.100.3		10	9.4	even	3
189.2.g.b.172.3		10	63.25	even	3
189.2.h.b.37.3		10	9.7	even	3
189.2.h.b.46.3		10	63.4	even	3
441.2.f.e.148.3		10	63.2	odd	6
441.2.f.e.295.3		10	63.23	odd	6
441.2.f.f.148.3		10	63.47	even	6
441.2.f.f.295.3		10	63.5	even	6
441.2.g.f.67.3		10	63.38	even	6
441.2.g.f.79.3		10	63.41	even	6
441.2.h.f.214.3		10	63.59	even	6
441.2.h.f.373.3		10	63.20	even	6
567.2.e.e.163.3		10	1.1	even	1	trivial
567.2.e.e.487.3		10	7.4	even	3	inner
567.2.e.f.163.3		10	3.2	odd	2
567.2.e.f.487.3		10	21.11	odd	6
1008.2.q.i.529.3		10	252.95	even	6
1008.2.q.i.625.3		10	36.11	even	6
1008.2.t.i.193.1		10	252.11	even	6
1008.2.t.i.961.1		10	36.23	even	6
1323.2.f.e.442.3		10	63.16	even	3
1323.2.f.e.883.3		10	63.58	even	3
1323.2.f.f.442.3		10	63.61	odd	6
1323.2.f.f.883.3		10	63.40	odd	6
1323.2.g.f.361.3		10	63.52	odd	6
1323.2.g.f.667.3		10	63.13	odd	6
1323.2.h.f.226.3		10	63.34	odd	6
1323.2.h.f.802.3		10	63.31	odd	6
3024.2.q.i.2305.1		10	36.7	odd	6
3024.2.q.i.2881.1		10	252.67	odd	6
3024.2.t.i.289.5		10	36.31	odd	6
3024.2.t.i.1873.5		10	252.151	odd	6
3969.2.a.z.1.3		5	21.2	odd	6
3969.2.a.ba.1.3		5	21.5	even	6
3969.2.a.bb.1.3		5	7.5	odd	6
3969.2.a.bc.1.3		5	7.2	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} +(1.68284 + 2.04158i) q^{7} -1.86155 q^{8} +O(q^{10})\)	\(q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} +(1.68284 + 2.04158i) q^{7} -1.86155 q^{8} +(-0.915516 - 1.58572i) q^{10} +(-0.446284 - 0.772987i) q^{11} -1.19671 q^{13} +(-1.29396 + 0.216492i) q^{14} +(-1.29257 + 2.23880i) q^{16} +(0.124991 + 0.216492i) q^{17} +(1.40414 - 2.43204i) q^{19} -6.47721 q^{20} +0.442596 q^{22} +(1.23886 - 2.14576i) q^{23} +(-4.31757 - 7.47825i) q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.62544 + 4.34700i) q^{28} +4.14255 q^{29} +(-1.79257 - 3.10483i) q^{31} +(-2.50249 - 4.33444i) q^{32} -0.123959 q^{34} +(-9.63571 + 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(0.696267 + 1.20597i) q^{38} +(3.43695 - 5.95298i) q^{40} -4.78186 q^{41} +9.97857 q^{43} +(0.782834 - 1.35591i) q^{44} +(0.614310 + 1.06402i) q^{46} +(-5.08653 + 8.81013i) q^{47} +(-1.33611 + 6.87130i) q^{49} +4.28189 q^{50} +(-1.04958 - 1.81793i) q^{52} +(4.94465 + 8.56438i) q^{53} +3.29588 q^{55} +(-3.13268 - 3.80050i) q^{56} +(-1.02708 + 1.77895i) q^{58} +(0.906186 + 1.56956i) q^{59} +(-5.40205 + 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(2.20948 - 3.82692i) q^{65} +(-0.514685 - 0.891460i) q^{67} +(-0.219249 + 0.379751i) q^{68} +(1.69671 - 4.53761i) q^{70} +4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(-1.17306 - 2.03181i) q^{74} +4.92604 q^{76} +(0.827091 - 2.21194i) q^{77} +(0.899562 - 1.55809i) q^{79} +(-4.77293 - 8.26696i) q^{80} +(1.18559 - 2.05350i) q^{82} +12.3231 q^{83} -0.923082 q^{85} +(-2.47403 + 4.28514i) q^{86} +(0.830779 + 1.43895i) q^{88} +(1.20370 - 2.08488i) q^{89} +(-2.01387 - 2.44318i) q^{91} +4.34620 q^{92} +(-2.52225 - 4.36867i) q^{94} +(5.18489 + 8.98049i) q^{95} -11.0442 q^{97} +(-2.61951 - 2.27740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} + 16 q^{13} - 4 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} + 10 q^{20} + 2 q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} + 14 q^{29} - 3 q^{31} + 2 q^{32} - 6 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} + 10 q^{41} + 14 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} - 17 q^{49} + 38 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 27 q^{56} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} - 11 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} - 10 q^{76} - 20 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} + 18 q^{83} + 12 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} + 54 q^{92} - 3 q^{94} + 14 q^{95} + 24 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 5 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 + 16 * q^13 - 4 * q^14 + 2 * q^16 - 12 * q^17 + q^19 + 10 * q^20 + 2 * q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 + 14 * q^29 - 3 * q^31 + 2 * q^32 - 6 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 + 10 * q^41 + 14 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 - 17 * q^49 + 38 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 27 * q^56 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 - 11 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 - 10 * q^76 - 20 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 + 18 * q^83 + 12 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 + 54 * q^92 - 3 * q^94 + 14 * q^95 + 24 * q^97 - 59 * q^98

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