LMFDB - Embedded newform 189.2.g.b.172.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(100,189)]

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([4, 2]))

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

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.g (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:	$\Z[a_1, \ldots, a_{4}]$
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			172.3
Root			$0.247934 - 0.429435i$ of defining polynomial
Character	$\chi$	$=$	189.172
Dual form			189.2.g.b.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +3.69258 q^{5} +(-2.60948 - 0.436591i) q^{7} -1.86155 q^{8} +O(q^{10})$	\(q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +3.69258 q^{5} +(-2.60948 - 0.436591i) q^{7} -1.86155 q^{8} +(-0.915516 + 1.58572i) q^{10} +0.892568 q^{11} +(0.598355 - 1.03638i) q^{13} +(0.834466 - 1.01236i) q^{14} +(-1.29257 + 2.23880i) q^{16} +(0.124991 - 0.216492i) q^{17} +(1.40414 + 2.43204i) q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} -2.47772 q^{23} +8.63514 q^{25} +(0.296705 + 0.513909i) q^{26} +(-1.62544 - 4.34700i) q^{28} +(-2.07128 - 3.58755i) q^{29} +(-1.79257 - 3.10483i) q^{31} +(-2.50249 - 4.33444i) q^{32} +(0.0619793 + 0.107351i) q^{34} +(-9.63571 - 1.61215i) q^{35} +(-2.36568 - 4.09747i) q^{37} -1.39253 q^{38} -6.87391 q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(0.782834 + 1.35591i) q^{44} +(0.614310 - 1.06402i) q^{46} +(-5.08653 + 8.81013i) q^{47} +(6.61878 + 2.27855i) q^{49} +(-2.14095 + 3.70823i) q^{50} +2.09917 q^{52} +(4.94465 - 8.56438i) q^{53} +3.29588 q^{55} +(4.85767 + 0.812734i) q^{56} +2.05416 q^{58} +(0.906186 + 1.56956i) q^{59} +(-5.40205 + 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(2.20948 - 3.82692i) q^{65} +(-0.514685 - 0.891460i) q^{67} +0.438499 q^{68} +(3.08133 - 3.73820i) q^{70} +4.94533 q^{71} +(-0.915262 + 1.58528i) q^{73} +2.34613 q^{74} +(-2.46302 + 4.26607i) q^{76} +(-2.32914 - 0.389687i) q^{77} +(0.899562 - 1.55809i) q^{79} +(-4.77293 + 8.26696i) q^{80} +(1.18559 + 2.05350i) q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +4.94806 q^{86} -1.66156 q^{88} +(1.20370 + 2.08488i) q^{89} +(-2.01387 + 2.44318i) q^{91} +(-2.17310 - 3.76392i) q^{92} +(-2.52225 - 4.36867i) q^{94} +(5.18489 + 8.98049i) q^{95} +(5.52210 + 9.56456i) q^{97} +(-2.61951 + 2.27740i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8} - 7 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 5 q^{35} + 40 q^{38} + 6 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} + 25 q^{49} - 19 q^{50} + 20 q^{52} + 21 q^{53} + 4 q^{55} + 45 q^{56} + 20 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} + 54 q^{68} - 29 q^{70} + 6 q^{71} + 15 q^{73} - 72 q^{74} + 5 q^{76} + 31 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8 - 7 * q^10 + 8 * q^11 - 8 * q^13 - 16 * q^14 + 2 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 5 * q^35 + 40 * q^38 + 6 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 + 25 * q^49 - 19 * q^50 + 20 * q^52 + 21 * q^53 + 4 * q^55 + 45 * q^56 + 20 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 54 * q^68 - 29 * q^70 + 6 * q^71 + 15 * q^73 - 72 * q^74 + 5 * q^76 + 31 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.247934	+	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
$5$	3.69258			1.65137			0.825686	−	0.564130i	$-0.190788\pi$
$5$	3.69258			1.65137			0.825686	+	0.564130i	$0.190788\pi$
$6$		0			0
$7$	−2.60948	−	0.436591i	−0.986291	−	0.165016i
$7$	−2.60948	−	0.436591i	−0.986291	−	0.165016i
$8$	−1.86155			−0.658156
$9$		0			0
$10$	−0.915516	+	1.58572i	−0.289512	+	0.501449i
$11$	0.892568			0.269119			0.134560	−	0.990905i	$-0.457038\pi$
$11$	0.892568			0.269119			0.134560	+	0.990905i	$0.457038\pi$
$12$		0			0
$13$	0.598355	−	1.03638i	0.165954	−	0.287441i	−0.771040	−	0.636787i	$-0.780263\pi$
$13$	0.598355	−	1.03638i	0.165954	−	0.287441i	0.936994	+	0.349346i	$0.113596\pi$
$14$	0.834466	−	1.01236i	0.223021	−	0.270563i
$15$		0			0
$16$	−1.29257	+	2.23880i	−0.323143	+	0.559701i
$17$	0.124991	−	0.216492i	0.0303149	−	0.0525069i	−0.850470	−	0.526024i	$-0.823682\pi$
$17$	0.124991	−	0.216492i	0.0303149	−	0.0525069i	0.880785	+	0.473517i	$0.157016\pi$
$18$		0			0
$19$	1.40414	+	2.43204i	0.322131	+	0.557948i	0.980928	−	0.194374i	$-0.0622675\pi$
$19$	1.40414	+	2.43204i	0.322131	+	0.557948i	−0.658796	+	0.752321i	$0.728934\pi$
$20$	3.23860	+	5.60943i	0.724174	+	1.25431i
$21$		0			0
$22$	−0.221298	+	0.383300i	−0.0471809	+	0.0817198i
$23$	−2.47772			−0.516639			−0.258320	−	0.966059i	$-0.583169\pi$
$23$	−2.47772			−0.516639			−0.258320	+	0.966059i	$0.583169\pi$
$24$		0			0
$25$	8.63514			1.72703
$26$	0.296705	+	0.513909i	0.0581887	+	0.100786i
$27$		0			0
$28$	−1.62544	−	4.34700i	−0.307178	−	0.821505i
$29$	−2.07128	−	3.58755i	−0.384626	−	0.666192i	0.607091	−	0.794632i	$-0.292336\pi$
$29$	−2.07128	−	3.58755i	−0.384626	−	0.666192i	−0.991717	+	0.128440i	$0.959003\pi$
$30$		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
$34$	0.0619793	+	0.107351i	0.0106294	+	0.0184106i
$35$	−9.63571	−	1.61215i	−1.62873	−	0.272502i
$36$		0			0
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	0.603389	−	0.797447i	$-0.293817\pi$
$37$	−2.36568	−	4.09747i	−0.388915	−	0.673621i	−0.992304	+	0.123826i	$0.960483\pi$
$38$	−1.39253			−0.225899
$39$		0			0
$40$	−6.87391			−1.08686
$41$	2.39093	−	4.14121i	0.373400	−	0.646748i	−0.616686	−	0.787209i	$-0.711525\pi$
$41$	2.39093	−	4.14121i	0.373400	−	0.646748i	0.990086	+	0.140461i	$0.0448584\pi$
$42$		0			0
$43$	−4.98928	−	8.64169i	−0.760859	−	1.31785i	−0.942408	−	0.334464i	$-0.891445\pi$
$43$	−4.98928	−	8.64169i	−0.760859	−	1.31785i	0.181550	−	0.983382i	$-0.441889\pi$
$44$	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
$49$	6.61878	+	2.27855i	0.945540	+	0.325507i
$50$	−2.14095	+	3.70823i	−0.302776	+	0.524423i
$51$		0			0
$52$	2.09917			0.291102
$53$	4.94465	−	8.56438i	0.679199	−	1.17641i	−0.296023	−	0.955181i	$-0.595661\pi$
$53$	4.94465	−	8.56438i	0.679199	−	1.17641i	0.975222	−	0.221227i	$-0.0710061\pi$
$54$		0			0
$55$	3.29588			0.444416
$56$	4.85767	+	0.812734i	0.649133	+	0.108606i
$57$		0			0
$58$	2.05416			0.269724
$59$	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	$0.853361\pi$
$68$	0.438499			0.0531758
$69$		0			0
$70$	3.08133	−	3.73820i	0.368290	−	0.446801i
$71$	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	−0.914604	−	0.404351i	$-0.867497\pi$
$73$	−0.915262	+	1.58528i	−0.107123	+	0.185543i	0.807480	+	0.589894i	$0.200831\pi$
$74$	2.34613			0.272732
$75$		0			0
$76$	−2.46302	+	4.26607i	−0.282527	+	0.489352i
$77$	−2.32914	−	0.389687i	−0.265430	−	0.0444090i
$78$		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
$83$	−6.16156	−	10.6721i	−0.676319	−	1.17142i	−0.976082	−	0.217405i	$-0.930241\pi$
$83$	−6.16156	−	10.6721i	−0.676319	−	1.17142i	0.299763	−	0.954014i	$-0.403092\pi$
$84$		0			0
$85$	0.461541	−	0.799412i	0.0500611	−	0.0867084i
$86$	4.94806			0.533563
$87$		0			0
$88$	−1.66156			−0.177123
$89$	1.20370	+	2.08488i	0.127592	+	0.220997i	0.922743	−	0.385415i	$-0.125942\pi$
$89$	1.20370	+	2.08488i	0.127592	+	0.220997i	−0.795151	+	0.606412i	$0.792608\pi$
$90$		0			0
$91$	−2.01387	+	2.44318i	−0.211111	+	0.256115i
$92$	−2.17310	−	3.76392i	−0.226561	−	0.392416i
$93$		0			0
$94$	−2.52225	−	4.36867i	−0.260150	−	0.450593i
$95$	5.18489	+	8.98049i	0.531958	+	0.921379i
$96$		0			0
$97$	5.52210	+	9.56456i	0.560684	+	0.971134i	0.997437	+	0.0715522i	$0.0227952\pi$
$97$	5.52210	+	9.56456i	0.560684	+	0.971134i	−0.436752	+	0.899582i	$0.643871\pi$
$98$	−2.61951	+	2.27740i	−0.264610	+	0.230052i
$99$		0			0
$100$	7.57351	+	13.1177i	0.757351	+	1.31177i
$101$	2.59964			0.258674			0.129337	−	0.991601i	$-0.458715\pi$
$101$	2.59964			0.258674			0.129337	+	0.991601i	$0.458715\pi$
$102$		0			0
$103$	9.71155			0.956908			0.478454	−	0.878113i	$-0.341197\pi$
$103$	9.71155			0.956908			0.478454	+	0.878113i	$0.341197\pi$
$104$	−1.11387	+	1.92927i	−0.109224	+	0.189181i
$105$		0			0
$106$	2.45189	+	4.24680i	0.238149	+	0.412486i
$107$	5.45025	+	9.44012i	0.526896	+	0.912610i	0.999509	+	0.0313403i	$0.00997757\pi$
$107$	5.45025	+	9.44012i	0.526896	+	0.912610i	−0.472613	+	0.881270i	$0.656689\pi$
$108$		0			0
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	−0.912353	−	0.409404i	$-0.865737\pi$
$109$	−1.06096	+	1.83764i	−0.101622	+	0.176014i	0.810731	+	0.585419i	$0.199070\pi$
$110$	−0.817161	+	1.41536i	−0.0779132	+	0.134950i
$111$		0			0
$112$	4.35039	−	5.27779i	0.411073	−	0.498704i
$113$	−7.91318	+	13.7060i	−0.744409	+	1.28935i	0.206061	+	0.978539i	$0.433935\pi$
$113$	−7.91318	+	13.7060i	−0.744409	+	1.28935i	−0.950470	+	0.310816i	$0.899398\pi$
$114$		0			0
$115$	−9.14916			−0.853164
$116$	3.63325	−	6.29298i	0.337339	−	0.584289i
$117$		0			0
$118$	−0.898698			−0.0827318
$119$	−0.420681	+	0.510360i	−0.0385638	+	0.0467847i
$120$		0			0
$121$	−10.2033			−0.927575
$122$	−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
$131$	15.0289			1.31308			0.656540	−	0.754291i	$-0.272019\pi$
$131$	15.0289			1.31308			0.656540	+	0.754291i	$0.272019\pi$
$132$		0			0
$133$	−2.60226	−	6.95939i	−0.225645	−	0.603455i
$134$	0.510432			0.0440946
$135$		0			0
$136$	−0.232677	+	0.403009i	−0.0199519	+	0.0345577i
$137$	0.488493			0.0417347			0.0208674	−	0.999782i	$-0.493357\pi$
$137$	0.488493			0.0417347			0.0208674	+	0.999782i	$0.493357\pi$
$138$		0			0
$139$	−4.93487	+	8.54745i	−0.418570	+	0.724985i	−0.995796	−	0.0915997i	$-0.970802\pi$
$139$	−4.93487	+	8.54745i	−0.418570	+	0.724985i	0.577226	+	0.816585i	$0.304135\pi$
$140$	−6.00205	−	16.0516i	−0.507266	−	1.35661i
$141$		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
$146$	−0.453849	−	0.786090i	−0.0375609	−	0.0650573i
$147$		0			0
$148$	4.14967	−	7.18744i	0.341101	−	0.590804i
$149$	−21.0240			−1.72235			−0.861175	−	0.508309i	$-0.830271\pi$
$149$	−21.0240			−1.72235			−0.861175	+	0.508309i	$0.830271\pi$
$150$		0			0
$151$	1.49838			0.121937			0.0609683	−	0.998140i	$-0.480581\pi$
$151$	1.49838			0.121937			0.0609683	+	0.998140i	$0.480581\pi$
$152$	−2.61387	−	4.52735i	−0.212013	−	0.367217i
$153$		0			0
$154$	0.744818	−	0.903596i	0.0600192	−	0.0728139i
$155$	−6.61922	−	11.4648i	−0.531669	−	0.920877i
$156$		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
$160$	−9.24065	−	16.0053i	−0.730538	−	1.26533i
$161$	6.46555	+	1.08175i	0.509557	+	0.0852537i
$162$		0			0
$163$	−3.34135	−	5.78738i	−0.261714	−	0.453303i	0.704983	−	0.709224i	$-0.250954\pi$
$163$	−3.34135	−	5.78738i	−0.261714	−	0.453303i	−0.966698	+	0.255921i	$0.917621\pi$
$164$	8.38793			0.654987
$165$		0			0
$166$	6.11064			0.474278
$167$	−8.81549	+	15.2689i	−0.682163	+	1.18154i	0.292156	+	0.956371i	$0.405627\pi$
$167$	−8.81549	+	15.2689i	−0.682163	+	1.18154i	−0.974319	+	0.225170i	$0.927706\pi$
$168$		0			0
$169$	5.78394	+	10.0181i	0.444919	+	0.770622i
$170$	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
$175$	−22.5332	−	3.77002i	−1.70335	−	0.284987i
$176$	−1.15371	+	1.99829i	−0.0869642	+	0.150626i
$177$		0			0
$178$	−1.19376			−0.0894759
$179$	−3.66758	+	6.35244i	−0.274128	+	0.474804i	−0.969915	−	0.243445i	$-0.921723\pi$
$179$	−3.66758	+	6.35244i	−0.274128	+	0.474804i	0.695787	+	0.718248i	$0.255056\pi$
$180$		0			0
$181$	11.2566			0.836693			0.418346	−	0.908288i	$-0.362610\pi$
$181$	11.2566			0.836693			0.418346	+	0.908288i	$0.362610\pi$
$182$	−0.549879	−	1.47057i	−0.0407598	−	0.109006i
$183$		0			0
$184$	4.61238			0.340029
$185$	−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	$0.901849\pi$
$194$	−5.47647			−0.393188
$195$		0			0
$196$	2.34368	+	12.0531i	0.167406	+	0.860933i
$197$	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	−0.449072	−	0.893496i	$-0.648245\pi$
$199$	7.74818	−	13.4202i	0.549254	−	0.951336i	0.998326	−	0.0578402i	$-0.0184214\pi$
$200$	−16.0747			−1.13665
$201$		0			0
$202$	−0.644540	+	1.11638i	−0.0453497	+	0.0785480i
$203$	3.83866	+	10.2660i	0.269421	+	0.720529i
$204$		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
$209$	1.25329	+	2.17076i	0.0866918	+	0.150155i
$210$		0			0
$211$	0.771898	−	1.33697i	0.0531397	−	0.0920406i	−0.838232	−	0.545314i	$-0.816410\pi$
$211$	0.771898	−	1.33697i	0.0531397	−	0.0920406i	0.891372	+	0.453273i	$0.149744\pi$
$212$	17.3469			1.19139
$213$		0			0
$214$	−5.40522			−0.369493
$215$	−18.4233	−	31.9101i	−1.25646	−	2.17625i
$216$		0			0
$217$	3.32215	+	8.88461i	0.225522	+	0.603127i
$218$	−0.526098	−	0.911229i	−0.0356319	−	0.0617162i
$219$		0			0
$220$	2.89068	+	5.00680i	0.194889	+	0.337558i
$221$	−0.149579	−	0.259078i	−0.0100617	−	0.0174275i
$222$		0			0
$223$	−2.72171	−	4.71414i	−0.182259	−	0.315682i	0.760390	−	0.649466i	$-0.225008\pi$
$223$	−2.72171	−	4.71414i	−0.182259	−	0.315682i	−0.942649	+	0.333784i	$0.891674\pi$
$224$	4.63783	+	12.4032i	0.309878	+	0.828725i
$225$		0			0
$226$	−3.92389	−	6.79638i	−0.261014	−	0.452089i
$227$	16.0764			1.06703			0.533513	−	0.845792i	$-0.320872\pi$
$227$	16.0764			1.06703			0.533513	+	0.845792i	$0.320872\pi$
$228$		0			0
$229$	−9.96840			−0.658730			−0.329365	−	0.944203i	$-0.606835\pi$
$229$	−9.96840			−0.658730			−0.329365	+	0.944203i	$0.606835\pi$
$230$	2.26839	−	3.92897i	0.149573	−	0.259068i
$231$		0			0
$232$	3.85578	+	6.67840i	0.253144	+	0.438458i
$233$	−8.27045	−	14.3248i	−0.541815	−	0.938451i	−0.998800	−	0.0489765i	$-0.984404\pi$
$233$	−8.27045	−	14.3248i	−0.541815	−	0.938451i	0.456985	−	0.889474i	$-0.348929\pi$
$234$		0			0
$235$	−18.7824	+	32.5321i	−1.22523	+	2.12216i
$236$	−1.58955	+	2.75319i	−0.103471	+	0.179217i
$237$		0			0
$238$	−0.114865	−	0.307191i	−0.00744560	−	0.0199122i
$239$	11.0119	−	19.0732i	0.712303	−	1.23375i	−0.251687	−	0.967809i	$-0.580985\pi$
$239$	11.0119	−	19.0732i	0.712303	−	1.23375i	0.963990	−	0.265937i	$-0.0856813\pi$
$240$		0			0
$241$	16.7201			1.07703			0.538517	−	0.842615i	$-0.318985\pi$
$241$	16.7201			1.07703			0.538517	+	0.842615i	$0.318985\pi$
$242$	2.52975	−	4.38166i	0.162619	−	0.281664i
$243$		0			0
$244$	−18.9516			−1.21325
$245$	24.4404	+	8.41373i	1.56144	+	0.537533i
$246$		0			0
$247$	3.36069			0.213836
$248$	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
$257$	17.1197			1.06790			0.533950	−	0.845516i	$-0.320707\pi$
$257$	17.1197			1.06790			0.533950	+	0.845516i	$0.320707\pi$
$258$		0			0
$259$	4.38427	+	11.7251i	0.272425	+	0.728563i
$260$	7.75135			0.480718
$261$		0			0
$262$	−3.72617	+	6.45392i	−0.230204	+	0.398725i
$263$	−20.5527			−1.26733			−0.633666	−	0.773607i	$-0.718451\pi$
$263$	−20.5527			−1.26733			−0.633666	+	0.773607i	$0.718451\pi$
$264$		0			0
$265$	18.2585	−	31.6246i	1.12161	−	1.94269i
$266$	3.63379	+	0.607968i	0.222802	+	0.0372769i
$267$		0			0
$268$	0.902816	−	1.56372i	0.0551483	−	0.0955196i
$269$	−9.92267	+	17.1866i	−0.604996	+	1.04788i	0.387057	+	0.922056i	$0.373492\pi$
$269$	−9.92267	+	17.1866i	−0.604996	+	1.04788i	−0.992052	+	0.125827i	$0.959842\pi$
$270$		0			0
$271$	5.32056	+	9.21548i	0.323201	+	0.559801i	0.981147	−	0.193265i	$-0.0619077\pi$
$271$	5.32056	+	9.21548i	0.323201	+	0.559801i	−0.657946	+	0.753065i	$0.728574\pi$
$272$	0.323121	+	0.559663i	0.0195921	+	0.0339345i
$273$		0			0
$274$	−0.121114	+	0.209776i	−0.00731676	+	0.0126730i
$275$	7.70745			0.464777
$276$		0			0
$277$	−24.8813			−1.49497			−0.747487	−	0.664276i	$-0.768740\pi$
$277$	−24.8813			−1.49497			−0.747487	+	0.664276i	$0.768740\pi$
$278$	−2.44705	−	4.23841i	−0.146764	−	0.254203i
$279$		0			0
$280$	17.9373	+	3.00109i	1.07196	+	0.179349i
$281$	6.83733	+	11.8426i	0.407881	+	0.706470i	0.994652	−	0.103282i	$-0.0329346\pi$
$281$	6.83733	+	11.8426i	0.407881	+	0.706470i	−0.586771	+	0.809753i	$0.699601\pi$
$282$		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
$286$	0.264830	+	0.458699i	0.0156597	+	0.0271234i
$287$	−8.04710	+	9.76255i	−0.475005	+	0.576265i
$288$		0			0
$289$	8.46875	+	14.6683i	0.498162	+	0.862842i
$290$	7.58515			0.445415
$291$		0			0
$292$	−3.21095			−0.187907
$293$	1.31508	−	2.27778i	0.0768277	−	0.133069i	−0.825052	−	0.565057i	$-0.808854\pi$
$293$	1.31508	−	2.27778i	0.0768277	−	0.133069i	0.901880	+	0.431987i	$0.142188\pi$
$294$		0			0
$295$	3.34616	+	5.79573i	0.194821	+	0.337440i
$296$	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
$301$	9.24656	+	24.7286i	0.532963	+	1.42533i
$302$	−0.371500	+	0.643457i	−0.0213774	+	0.0370268i
$303$		0			0
$304$	−7.25980			−0.416378
$305$	−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	$0.525415\pi$
$308$	−1.45081	−	3.87999i	−0.0826677	−	0.221083i
$309$		0			0
$310$	6.56452			0.372840
$311$	−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
$320$	−9.92743			−0.554960
$321$		0			0
$322$	−2.06757	+	2.50833i	−0.115221	+	0.139784i
$323$	0.702021			0.0390615
$324$		0			0
$325$	5.16688	−	8.94931i	0.286607	−	0.496418i
$326$	3.31373			0.183531
$327$		0			0
$328$	−4.45083	+	7.70906i	−0.245756	+	0.425661i
$329$	17.1196	−	20.7691i	0.943836	−	1.14504i
$330$		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
$335$	−1.90051	−	3.29179i	−0.103836	−	0.179850i
$336$		0			0
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	0.293168	+	0.956061i	$0.405290\pi$
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	−0.974557	+	0.224139i	$0.928043\pi$
$338$	−5.73615			−0.312005
$339$		0			0
$340$	1.61919			0.0878130
$341$	−1.59999	−	2.77127i	−0.0866446	−	0.150073i
$342$		0			0
$343$	−16.2768	−	8.83553i	−0.878863	−	0.477074i
$344$	9.28778	+	16.0869i	0.500764	+	0.867348i
$345$		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
$349$	−1.64301	−	2.84577i	−0.0879482	−	0.152331i	0.818695	−	0.574228i	$-0.194698\pi$
$349$	−1.64301	−	2.84577i	−0.0879482	−	0.152331i	−0.906644	+	0.421897i	$0.861364\pi$
$350$	7.20574	−	8.74183i	0.385163	−	0.467270i
$351$		0			0
$352$	−2.23365	−	3.86879i	−0.119054	−	0.206207i
$353$	−16.8192			−0.895195			−0.447598	−	0.894235i	$-0.647720\pi$
$353$	−16.8192			−0.895195			−0.447598	+	0.894235i	$0.647720\pi$
$354$		0			0
$355$	18.2610			0.969195
$356$	−2.11144	+	3.65711i	−0.111906	+	0.193827i
$357$		0			0
$358$	−1.81864	−	3.14997i	−0.0961180	−	0.166481i
$359$	−11.8921	−	20.5978i	−0.627642	−	1.08711i	−0.988024	−	0.154303i	$-0.950687\pi$
$359$	−11.8921	−	20.5978i	−0.627642	−	1.08711i	0.360382	−	0.932805i	$-0.382646\pi$
$360$		0			0
$361$	5.55680	−	9.62466i	0.292463	−	0.506561i
$362$	−2.79088	+	4.83395i	−0.146686	+	0.254067i
$363$		0			0
$364$	−5.47774	−	0.916478i	−0.287112	−	0.0480365i
$365$	−3.37968	+	5.85377i	−0.176900	+	0.306401i
$366$		0			0
$367$	−0.689984			−0.0360169			−0.0180084	−	0.999838i	$-0.505733\pi$
$367$	−0.689984			−0.0360169			−0.0180084	+	0.999838i	$0.505733\pi$
$368$	3.20263	−	5.54712i	0.166949	−	0.289164i
$369$		0			0
$370$	8.66327			0.450382
$371$	−16.6421	+	20.1898i	−0.864014	+	1.04820i
$372$		0			0
$373$	−3.76012			−0.194691			−0.0973457	−	0.995251i	$-0.531035\pi$
$373$	−3.76012			−0.194691			−0.0973457	+	0.995251i	$0.531035\pi$
$374$	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
$383$	1.07267			0.0548109			0.0274055	−	0.999624i	$-0.491275\pi$
$383$	1.07267			0.0548109			0.0274055	+	0.999624i	$0.491275\pi$
$384$		0			0
$385$	−8.60053	−	1.43895i	−0.438324	−	0.0733357i
$386$	2.94276			0.149782
$387$		0			0
$388$	−9.68640	+	16.7773i	−0.491752	+	0.851740i
$389$	23.7436			1.20385			0.601925	−	0.798553i	$-0.294401\pi$
$389$	23.7436			1.20385			0.601925	+	0.798553i	$0.294401\pi$
$390$		0			0
$391$	−0.309693	+	0.536405i	−0.0156619	+	0.0271271i
$392$	−12.3212	−	4.24163i	−0.622313	−	0.214235i
$393$		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	0.865622	−	0.500697i	$-0.166923\pi$
$397$	−0.0160489	−	0.0277975i	−0.000805471	−	0.00139512i	−0.866428	+	0.499302i	$0.833590\pi$
$398$	3.84208	+	6.65467i	0.192586	+	0.333569i
$399$		0			0
$400$	−11.1616	+	19.3324i	−0.558078	+	0.966619i
$401$	−24.5256			−1.22475			−0.612374	−	0.790568i	$-0.709785\pi$
$401$	−24.5256			−1.22475			−0.612374	+	0.790568i	$0.709785\pi$
$402$		0			0
$403$	−4.29039			−0.213719
$404$	2.28004	+	3.94914i	0.113436	+	0.196477i
$405$		0			0
$406$	−5.36029	−	0.896827i	−0.266027	−	0.0445088i
$407$	−2.11153	−	3.65728i	−0.104665	−	0.181284i
$408$		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
$412$	8.51759	+	14.7529i	0.419631	+	0.726823i
$413$	−1.67942	−	4.49137i	−0.0826388	−	0.221006i
$414$		0			0
$415$	−22.7520	−	39.4077i	−1.11685	−	1.93445i
$416$	−5.98952			−0.293660
$417$		0			0
$418$	−1.24293			−0.0607938
$419$	10.5262	−	18.2320i	0.514240	−	0.890689i	−0.485624	−	0.874168i	$-0.661407\pi$
$419$	10.5262	−	18.2320i	0.514240	−	0.890689i	0.999864	−	0.0165215i	$-0.00525920\pi$
$420$		0			0
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	0.625568	−	0.780170i	$-0.284867\pi$
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	−0.988431	+	0.151672i	$0.951534\pi$
$422$	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
$427$	18.1816	−	22.0575i	0.879868	−	1.06744i
$428$	−9.56037	+	16.5590i	−0.462118	+	0.800412i
$429$		0			0
$430$	18.2711			0.881110
$431$	7.95192	−	13.7731i	0.383031	−	0.663428i	−0.608463	−	0.793582i	$-0.708214\pi$
$431$	7.95192	−	13.7731i	0.383031	−	0.663428i	0.991494	+	0.130154i	$0.0415471\pi$
$432$		0			0
$433$	−16.3658			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$433$	−16.3658			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$434$	−4.63903	−	0.776154i	−0.222681	−	0.0372566i
$435$		0			0
$436$	−3.72210			−0.178256
$437$	−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
$446$	2.69922			0.127812
$447$		0			0
$448$	7.01554	+	1.17377i	0.331453	+	0.0554553i
$449$	−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
$452$	−27.7612			−1.30578
$453$		0			0
$454$	−3.98588	+	6.90375i	−0.187067	+	0.324009i
$455$	−7.43638	+	9.02164i	−0.348623	+	0.422941i
$456$		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
$461$	−18.0934	−	31.3388i	−0.842695	−	1.45959i	−0.887608	−	0.460600i	$-0.847634\pi$
$461$	−18.0934	−	31.3388i	−0.842695	−	1.45959i	0.0449122	−	0.998991i	$-0.485699\pi$
$462$		0			0
$463$	8.19224	−	14.1894i	0.380726	−	0.659436i	−0.610440	−	0.792062i	$-0.709008\pi$
$463$	8.19224	−	14.1894i	0.380726	−	0.659436i	0.991166	+	0.132626i	$0.0423409\pi$
$464$	10.7091			0.497158
$465$		0			0
$466$	8.20210			0.379955
$467$	4.35022	+	7.53480i	0.201304	+	0.348669i	0.948949	−	0.315430i	$-0.102149\pi$
$467$	4.35022	+	7.53480i	0.201304	+	0.348669i	−0.747645	+	0.664099i	$0.768815\pi$
$468$		0			0
$469$	0.953856	+	2.55095i	0.0440450	+	0.117792i
$470$	−9.31361	−	16.1316i	−0.429605	−	0.744097i
$471$		0			0
$472$	−1.68691	−	2.92181i	−0.0776462	−	0.134487i
$473$	−4.45328	−	7.71330i	−0.204762	−	0.354658i
$474$		0			0
$475$	12.1249	+	21.0010i	0.556330	+	0.963591i
$476$	−1.14425	−	0.191445i	−0.0524468	−	0.00877485i
$477$		0			0
$478$	5.46047	+	9.45782i	0.249756	+	0.432591i
$479$	17.7674			0.811813			0.405907	−	0.913915i	$-0.366956\pi$
$479$	17.7674			0.811813			0.405907	+	0.913915i	$0.366956\pi$
$480$		0			0
$481$	−5.66207			−0.258168
$482$	−4.14548	+	7.18018i	−0.188821	+	0.327048i
$483$		0			0
$484$	−8.94890	−	15.4999i	−0.406768	−	0.704543i
$485$	20.3908	+	35.3179i	0.925898	+	1.60370i
$486$		0			0
$487$	8.32763	−	14.4239i	0.377361	−	0.653608i	−0.613316	−	0.789837i	$-0.710165\pi$
$487$	8.32763	−	14.4239i	0.377361	−	0.653608i	0.990677	+	0.136229i	$0.0434983\pi$
$488$	10.0562	−	17.4178i	0.455222	−	0.788467i
$489$		0			0
$490$	−9.67274	+	8.40948i	−0.436970	+	0.379902i
$491$	3.21021	−	5.56025i	0.144875	−	0.250930i	−0.784451	−	0.620190i	$-0.787055\pi$
$491$	3.21021	−	5.56025i	0.144875	−	0.250930i	0.929326	+	0.369260i	$0.120389\pi$
$492$		0			0
$493$	−1.03557			−0.0466396
$494$	−0.833230	+	1.44320i	−0.0374888	+	0.0649325i
$495$		0			0
$496$	9.26814			0.416152
$497$	−12.9047	−	2.15909i	−0.578857	−	0.0968483i
$498$		0			0
$499$	11.1459			0.498960			0.249480	−	0.968380i	$-0.419740\pi$
$499$	11.1459			0.498960			0.249480	+	0.968380i	$0.419740\pi$
$500$	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
$509$	−31.0823			−1.37770			−0.688848	−	0.724906i	$-0.741883\pi$
$509$	−31.0823			−1.37770			−0.688848	+	0.724906i	$0.741883\pi$
$510$		0			0
$511$	3.08048	−	3.73716i	0.136272	−	0.165322i
$512$	22.5634			0.997169
$513$		0			0
$514$	−4.24456	+	7.35180i	−0.187220	+	0.324274i
$515$	35.8607			1.58021
$516$		0			0
$517$	−4.54008	+	7.86365i	−0.199672	+	0.345843i
$518$	−6.12218	−	1.02430i	−0.268993	−	0.0450051i
$519$		0			0
$520$	−4.11304	+	7.12399i	−0.180369	+	0.312408i
$521$	2.37986	−	4.12203i	0.104263	−	0.180590i	−0.809174	−	0.587570i	$-0.800085\pi$
$521$	2.37986	−	4.12203i	0.104263	−	0.180590i	0.913437	+	0.406980i	$0.133418\pi$
$522$		0			0
$523$	20.1258	+	34.8588i	0.880038	+	1.52427i	0.851298	+	0.524683i	$0.175816\pi$
$523$	20.1258	+	34.8588i	0.880038	+	1.52427i	0.0287402	+	0.999587i	$0.490850\pi$
$524$	13.1812	+	22.8305i	0.575823	+	0.997355i
$525$		0			0
$526$	5.09571	−	8.82602i	0.222183	−	0.384833i
$527$	−0.896226			−0.0390402
$528$		0			0
$529$	−16.8609			−0.733084
$530$	9.05381	+	15.6817i	0.393272	+	0.681168i
$531$		0			0
$532$	8.28972	−	10.0569i	0.359405	−	0.436022i
$533$	−2.86125	−	4.95583i	−0.123935	−	0.214661i
$534$		0			0
$535$	20.1255	+	34.8584i	0.870101	+	1.50706i
$536$	0.958109	+	1.65949i	0.0413840	+	0.0716792i
$537$		0			0
$538$	−4.92033	−	8.52227i	−0.212131	−	0.367421i
$539$	5.90771	+	2.03376i	0.254463	+	0.0876003i
$540$		0			0
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	0.999775	+	0.0212301i	$0.00675826\pi$
$541$	12.0547	+	20.8794i	0.518273	+	0.897675i	−0.481502	+	0.876445i	$0.659908\pi$
$542$	−5.27659			−0.226649
$543$		0			0
$544$	−1.25116			−0.0536431
$545$	−3.91769	+	6.78564i	−0.167815	+	0.290665i
$546$		0			0
$547$	−6.17751	−	10.6998i	−0.264131	−	0.457489i	0.703204	−	0.710988i	$-0.251752\pi$
$547$	−6.17751	−	10.6998i	−0.264131	−	0.457489i	−0.967336	+	0.253499i	$0.918419\pi$
$548$	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
$553$	−3.02763	+	3.67306i	−0.128748	+	0.156194i
$554$	6.16893	−	10.6849i	0.262093	−	0.453958i
$555$		0			0
$556$	−17.3127			−0.734220
$557$	−4.03845	+	6.99479i	−0.171114	+	0.296379i	−0.938810	−	0.344436i	$-0.888070\pi$
$557$	−4.03845	+	6.99479i	−0.171114	+	0.296379i	0.767695	+	0.640815i	$0.221403\pi$
$558$		0			0
$559$	−11.9415			−0.505070
$560$	16.0641	−	19.4887i	0.678834	−	0.823546i
$561$		0			0
$562$	−6.78083			−0.286032
$563$	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	$0.682360\pi$
$572$	1.87365			0.0783413
$573$		0			0
$574$	−2.19723	−	5.87617i	−0.0917104	−	0.245267i
$575$	−21.3954			−0.892251
$576$		0			0
$577$	−16.1022	+	27.8898i	−0.670342	+	1.16107i	0.307465	+	0.951559i	$0.400519\pi$
$577$	−16.1022	+	27.8898i	−0.670342	+	1.16107i	−0.977807	+	0.209508i	$0.932814\pi$
$578$	−8.39877			−0.349343
$579$		0			0
$580$	13.4161	−	23.2373i	0.557072	−	0.964878i
$581$	11.4191	+	30.5388i	0.473744	+	1.26696i
$582$		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
$587$	9.72304	+	16.8408i	0.401313	+	0.695094i	0.993885	−	0.110424i	$-0.0352208\pi$
$587$	9.72304	+	16.8408i	0.401313	+	0.695094i	−0.592572	+	0.805518i	$0.701887\pi$
$588$		0			0
$589$	5.03404	−	8.71921i	0.207424	−	0.359269i
$590$	−3.31851			−0.136621
$591$		0			0
$592$	12.2313			0.502701
$593$	14.4202	+	24.9766i	0.592168	+	1.02566i	0.993940	+	0.109925i	$0.0350611\pi$
$593$	14.4202	+	24.9766i	0.592168	+	1.02566i	−0.401772	+	0.915740i	$0.631606\pi$
$594$		0			0
$595$	−1.55340	+	1.88455i	−0.0636831	+	0.0772589i
$596$	−18.4392	−	31.9377i	−0.755300	−	1.30822i
$597$		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
$601$	−7.80843	−	13.5246i	−0.318512	−	0.551680i	0.661665	−	0.749799i	$-0.269850\pi$
$601$	−7.80843	−	13.5246i	−0.318512	−	0.551680i	−0.980178	+	0.198119i	$0.936517\pi$
$602$	−12.9119	−	2.16028i	−0.526248	−	0.0880463i
$603$		0			0
$604$	1.31417	+	2.27620i	0.0534727	+	0.0926174i
$605$	−37.6766			−1.53177
$606$		0			0
$607$	−28.6532			−1.16300			−0.581500	−	0.813547i	$-0.697534\pi$
$607$	−28.6532			−1.16300			−0.581500	+	0.813547i	$0.697534\pi$
$608$	7.02769	−	12.1723i	0.285010	−	0.493652i
$609$		0			0
$610$	−9.89134	−	17.1323i	−0.400489	−	0.693667i
$611$	6.08711	+	10.5432i	0.246258	+	0.426531i
$612$		0			0
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	−0.401220	−	0.915982i	$-0.631414\pi$
$613$	14.6734	−	25.4151i	0.592653	−	1.02651i	0.993873	−	0.110524i	$-0.0352529\pi$
$614$	0.692965	−	1.20025i	0.0279658	−	0.0484382i
$615$		0			0
$616$	4.33580	+	0.725421i	0.174694	+	0.0292280i
$617$	−2.06401	+	3.57497i	−0.0830938	+	0.143923i	−0.904577	−	0.426310i	$-0.859813\pi$
$617$	−2.06401	+	3.57497i	−0.0830938	+	0.143923i	0.821484	+	0.570232i	$0.193147\pi$
$618$		0			0
$619$	22.7130			0.912912			0.456456	−	0.889746i	$-0.349119\pi$
$619$	22.7130			0.912912			0.456456	+	0.889746i	$0.349119\pi$
$620$	11.6109	−	20.1106i	0.466304	−	0.807662i
$621$		0			0
$622$	7.48774			0.300231
$623$	−2.23080	−	5.96597i	−0.0893753	−	0.239022i
$624$		0			0
$625$	6.38996			0.255598
$626$	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
$635$	−4.68759			−0.186021
$636$		0			0
$637$	6.32183	−	5.49620i	0.250480	−	0.217767i
$638$	1.83348			0.0725881
$639$		0			0
$640$	20.9427	−	36.2737i	0.827831	−	1.43385i
$641$	28.4726			1.12460			0.562301	−	0.826933i	$-0.309916\pi$
$641$	28.4726			1.12460			0.562301	+	0.826933i	$0.309916\pi$
$642$		0			0
$643$	−8.52125	+	14.7592i	−0.336045	+	0.582048i	−0.983685	−	0.179899i	$-0.942423\pi$
$643$	−8.52125	+	14.7592i	−0.336045	+	0.582048i	0.647640	+	0.761947i	$0.275756\pi$
$644$	4.02737	+	10.7706i	0.158700	+	0.424422i
$645$		0			0
$646$	−0.174055	+	0.301472i	−0.00684810	+	0.0118613i
$647$	−1.68809	+	2.92386i	−0.0663657	+	0.114949i	−0.897299	−	0.441423i	$-0.854474\pi$
$647$	−1.68809	+	2.92386i	−0.0663657	+	0.114949i	0.830933	+	0.556372i	$0.187807\pi$
$648$		0			0
$649$	0.808833	+	1.40094i	0.0317495	+	0.0549917i
$650$	2.56209	+	4.43768i	0.100494	+	0.174060i
$651$		0			0
$652$	5.86110	−	10.1517i	0.229538	−	0.397572i
$653$	18.3451			0.717899			0.358950	−	0.933357i	$-0.383135\pi$
$653$	18.3451			0.717899			0.358950	+	0.933357i	$0.383135\pi$
$654$		0			0
$655$	55.4954			2.16838
$656$	6.18090	+	10.7056i	0.241324	+	0.417985i
$657$		0			0
$658$	4.67444	+	12.5011i	0.182229	+	0.487345i
$659$	13.9248	+	24.1184i	0.542432	+	0.939519i	0.998764	+	0.0497098i	$0.0158297\pi$
$659$	13.9248	+	24.1184i	0.542432	+	0.939519i	−0.456332	+	0.889810i	$0.650837\pi$
$660$		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
$664$	11.4700	+	19.8667i	0.445123	+	0.770976i
$665$	−9.60906	−	25.6981i	−0.372624	−	0.996529i
$666$		0			0
$667$	5.13203	+	8.88894i	0.198713	+	0.344181i
$668$	−30.9268			−1.19659
$669$		0			0
$670$	1.88481			0.0728165
$671$	−4.82170	+	8.35143i	−0.186140	+	0.322404i
$672$		0			0
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.747841	+	0.663878i	$0.231090\pi$
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.201014	+	0.979588i	$0.435576\pi$
$674$	−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
$679$	−10.2340	−	27.3694i	−0.392745	−	1.05034i
$680$	−0.859180	+	1.48814i	−0.0329480	+	0.0570677i
$681$		0			0
$682$	1.58677			0.0607607
$683$	15.1632	−	26.2634i	0.580204	−	1.00494i	−0.415251	−	0.909707i	$-0.636306\pi$
$683$	15.1632	−	26.2634i	0.580204	−	1.00494i	0.995455	−	0.0952356i	$-0.0303604\pi$
$684$		0			0
$685$	1.80380			0.0689196
$686$	7.82985	−	4.79918i	0.298945	−	0.183234i
$687$		0			0
$688$	25.7961			0.983466
$689$	−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
$698$	1.62943			0.0616749
$699$		0			0
$700$	−14.0359	−	37.5369i	−0.530506	−	1.41876i
$701$	−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
$704$	−2.39965			−0.0904403
$705$		0			0
$706$	4.17005	−	7.22274i	0.156942	−	0.271831i
$707$	−6.78372	−	1.13498i	−0.255128	−	0.0426853i
$708$		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
$713$	4.44149	+	7.69288i	0.166335	+	0.288101i
$714$		0			0
$715$	1.97211	−	3.41579i	0.0737526	−	0.127743i
$716$	−12.8667			−0.480852
$717$		0			0
$718$	11.7938			0.440142
$719$	5.57126	+	9.64970i	0.207773	+	0.359873i	0.951013	−	0.309152i	$-0.100045\pi$
$719$	5.57126	+	9.64970i	0.207773	+	0.359873i	−0.743240	+	0.669025i	$0.766712\pi$
$720$		0			0
$721$	−25.3421	−	4.23997i	−0.943789	−	0.157905i
$722$	2.75544	+	4.77256i	0.102547	+	0.177616i
$723$		0			0
$724$	9.87264	+	17.0999i	0.366914	+	0.635513i
$725$	−17.8858	−	30.9790i	−0.664260	−	1.15053i
$726$		0			0
$727$	−14.3410	−	24.8393i	−0.531878	−	0.921239i	−0.999308	−	0.0372089i	$-0.988153\pi$
$727$	−14.3410	−	24.8393i	−0.531878	−	0.921239i	0.467430	−	0.884030i	$-0.345180\pi$
$728$	3.74892	−	4.54810i	0.138944	−	0.168564i
$729$		0			0
$730$	−1.67588	−	2.90270i	−0.0620269	−	0.107434i
$731$	−2.49447			−0.0922614
$732$		0			0
$733$	−25.0528			−0.925348			−0.462674	−	0.886529i	$-0.653110\pi$
$733$	−25.0528			−0.925348			−0.462674	+	0.886529i	$0.653110\pi$
$734$	0.171071	−	0.296303i	0.00631433	−	0.0109367i
$735$		0			0
$736$	6.20047	+	10.7395i	0.228552	+	0.395864i
$737$	−0.459391	−	0.795689i	−0.0169219	−	0.0293096i
$738$		0			0
$739$	13.7608	−	23.8344i	0.506198	−	0.876761i	−0.493776	−	0.869589i	$-0.664384\pi$
$739$	13.7608	−	23.8344i	0.506198	−	0.876761i	0.999974	−	0.00717223i	$-0.00228301\pi$
$740$	15.3230	−	26.5402i	0.563284	−	0.975637i
$741$		0			0
$742$	−4.54405	−	12.1524i	−0.166817	−	0.446129i
$743$	7.00608	−	12.1349i	0.257028	−	0.445186i	−0.708416	−	0.705795i	$-0.750590\pi$
$743$	7.00608	−	12.1349i	0.257028	−	0.445186i	0.965444	+	0.260609i	$0.0839233\pi$
$744$		0			0
$745$	−77.6326			−2.84424
$746$	0.932261	−	1.61472i	0.0341325	−	0.0591192i
$747$		0			0
$748$	0.391390			0.0143106
$749$	−10.1009	−	27.0133i	−0.369077	−	0.987046i
$750$		0			0
$751$	−52.2594			−1.90697			−0.953486	−	0.301436i	$-0.902534\pi$
$751$	−52.2594			−1.90697			−0.953486	+	0.301436i	$0.902534\pi$
$752$	−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
$761$	17.2510			0.625348			0.312674	−	0.949860i	$-0.398775\pi$
$761$	17.2510			0.625348			0.312674	+	0.949860i	$0.398775\pi$
$762$		0			0
$763$	3.57086	−	4.33209i	0.129274	−	0.156832i
$764$	−41.8285			−1.51330
$765$		0			0
$766$	−0.265952	+	0.460642i	−0.00960922	+	0.0166437i
$767$	2.16889			0.0783139
$768$		0			0
$769$	−10.6727	+	18.4856i	−0.384867	+	0.666609i	−0.991751	−	0.128182i	$-0.959086\pi$
$769$	−10.6727	+	18.4856i	−0.384867	+	0.666609i	0.606884	+	0.794790i	$0.292419\pi$
$770$	2.75030	−	3.33660i	0.0991140	−	0.120243i
$771$		0			0
$772$	5.20495	−	9.01523i	0.187330	−	0.324465i
$773$	6.57357	−	11.3858i	0.236435	−	0.409517i	−0.723254	−	0.690582i	$-0.757354\pi$
$773$	6.57357	−	11.3858i	0.236435	−	0.409517i	0.959689	+	0.281065i	$0.0906877\pi$
$774$		0			0
$775$	−15.4791	−	26.8106i	−0.556027	−	0.963066i
$776$	−10.2796	−	17.8049i	−0.369018	−	0.639158i
$777$		0			0
$778$	−5.88685	+	10.1963i	−0.211054	+	0.365556i
$779$	13.4288			0.481136
$780$		0			0
$781$	4.41405			0.157947
$782$	−0.153567	−	0.265986i	−0.00549155	−	0.00951164i
$783$		0			0
$784$	−13.6565	+	11.8729i	−0.487732	+	0.424034i
$785$	30.7954	+	53.3393i	1.09914	+	1.90376i
$786$		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
$790$	1.64713	+	2.85291i	0.0586021	+	0.101502i
$791$	26.6332	−	32.3108i	0.946968	−	1.14884i
$792$		0			0
$793$	6.46470	+	11.1972i	0.229568	+	0.397624i
$794$	0.0159163			0.000564847
$795$		0			0
$796$	27.1824			0.963455
$797$	−12.8683	+	22.2885i	−0.455817	+	0.789499i	−0.998735	−	0.0502873i	$-0.983986\pi$
$797$	−12.8683	+	22.2885i	−0.455817	+	0.789499i	0.542917	+	0.839786i	$0.317320\pi$
$798$		0			0
$799$	1.27155	+	2.20238i	0.0449841	+	0.0779147i
$800$	−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
$805$	23.8746	+	3.99444i	0.841468	+	0.140786i
$806$	1.06373	−	1.84244i	0.0374684	−	0.0648972i
$807$		0			0
$808$	−4.83936			−0.170248
$809$	−15.9353	+	27.6007i	−0.560254	+	0.970388i	0.437220	+	0.899355i	$0.355963\pi$
$809$	−15.9353	+	27.6007i	−0.560254	+	0.970388i	−0.997474	+	0.0710338i	$0.977370\pi$
$810$		0			0
$811$	43.3860			1.52349			0.761744	−	0.647878i	$-0.224343\pi$
$811$	43.3860			1.52349			0.761744	+	0.647878i	$0.224343\pi$
$812$	−12.2284	+	14.8352i	−0.429132	+	0.520612i
$813$		0			0
$814$	2.09408			0.0733975
$815$	−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	$0.681276\pi$
$824$	−18.0785			−0.629794
$825$		0			0
$826$	2.34513	+	0.392363i	0.0815977	+	0.0136521i
$827$	−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	−0.573899	−	0.818926i	$-0.694570\pi$
$829$	12.1579	−	21.0581i	0.422261	−	0.731377i	0.996160	+	0.0875485i	$0.0279033\pi$
$830$	22.5640			0.783209
$831$		0			0
$832$	−1.60867	+	2.78629i	−0.0557705	+	0.0965974i
$833$	1.32058	−	1.14811i	0.0457553	−	0.0397797i
$834$		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
$839$	12.8405	+	22.2404i	0.443303	+	0.767824i	0.997932	−	0.0642741i	$-0.0204732\pi$
$839$	12.8405	+	22.2404i	0.443303	+	0.767824i	−0.554629	+	0.832098i	$0.687140\pi$
$840$		0			0
$841$	5.91963	−	10.2531i	0.204125	−	0.353555i
$842$	7.38381			0.254463
$843$		0			0
$844$	2.70800			0.0932131
$845$	21.3577	+	36.9926i	0.734726	+	1.27258i
$846$		0			0
$847$	26.6254	+	4.45468i	0.914859	+	0.153065i
$848$	12.7826	+	22.1402i	0.438958	+	0.760297i
$849$		0			0
$850$	0.535200	+	0.926994i	0.0183572	+	0.0317956i
$851$	5.86148	+	10.1524i	0.200929	+	0.348019i
$852$		0			0
$853$	14.4872	+	25.0925i	0.496031	+	0.859150i	0.999990	−	0.00457743i	$-0.00145705\pi$
$853$	14.4872	+	25.0925i	0.496031	+	0.859150i	−0.503959	+	0.863728i	$0.668124\pi$
$854$	4.96440	+	13.2766i	0.169878	+	0.454316i
$855$		0			0
$856$	−10.1459	−	17.5732i	−0.346780	−	0.600640i
$857$	25.3868			0.867197			0.433598	−	0.901106i	$-0.357244\pi$
$857$	25.3868			0.867197			0.433598	+	0.901106i	$0.357244\pi$
$858$		0			0
$859$	−5.95783			−0.203279			−0.101639	−	0.994821i	$-0.532409\pi$
$859$	−5.95783			−0.203279			−0.101639	+	0.994821i	$0.532409\pi$
$860$	32.3166	−	55.9740i	1.10199	−	1.90870i
$861$		0			0
$862$	3.94310	+	6.82966i	0.134303	+	0.232619i
$863$	−8.19545	−	14.1949i	−0.278977	−	0.483201i	0.692154	−	0.721750i	$-0.256662\pi$
$863$	−8.19545	−	14.1949i	−0.278977	−	0.483201i	−0.971131	+	0.238548i	$0.923328\pi$
$864$		0			0
$865$	−7.17624	+	12.4296i	−0.244000	+	0.422620i
$866$	4.05764	−	7.02804i	0.137884	−	0.238822i
$867$		0			0
$868$	−10.5830	+	12.8390i	−0.359209	+	0.435784i
$869$	0.802920	−	1.39070i	0.0272372	−	0.0471762i
$870$		0			0
$871$	−1.23186			−0.0417399
$872$	1.97503	−	3.42086i	0.0668830	−	0.115845i
$873$		0			0
$874$	3.45030			0.116708
$875$	−35.0272	−	5.86038i	−1.18413	−	0.198117i
$876$		0			0
$877$	35.2539			1.19044			0.595220	−	0.803563i	$-0.297065\pi$
$877$	35.2539			1.19044			0.595220	+	0.803563i	$0.297065\pi$
$878$	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
$887$	15.9056			0.534059			0.267030	−	0.963688i	$-0.413958\pi$
$887$	15.9056			0.534059			0.267030	+	0.963688i	$0.413958\pi$
$888$		0			0
$889$	3.31264	+	0.554236i	0.111102	+	0.0185885i
$890$	−4.40804			−0.147758
$891$		0			0
$892$	4.77419	−	8.26914i	0.159852	−	0.276871i
$893$	−28.5688			−0.956017
$894$		0			0
$895$	−13.5428	+	23.4569i	−0.452687	+	0.784077i
$896$	−19.0886	+	23.1579i	−0.637706	+	0.773650i
$897$		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
$902$	1.05822	+	1.83288i	0.0352348	+	0.0610284i
$903$		0			0
$904$	14.7307	−	25.5144i	0.489937	−	0.848597i
$905$	41.5657			1.38169
$906$		0			0
$907$	−17.0925			−0.567547			−0.283773	−	0.958891i	$-0.591586\pi$
$907$	−17.0925			−0.567547			−0.283773	+	0.958891i	$0.591586\pi$
$908$	14.0999	+	24.4217i	0.467922	+	0.810464i
$909$		0			0
$910$	−2.03047	−	5.43021i	−0.0673095	−	0.180010i
$911$	−14.9435	−	25.8829i	−0.495099	−	0.857537i	0.504885	−	0.863187i	$-0.331535\pi$
$911$	−14.9435	−	25.8829i	−0.495099	−	0.857537i	−0.999984	+	0.00564955i	$0.998202\pi$
$912$		0			0
$913$	−5.49961	−	9.52561i	−0.182011	−	0.315252i
$914$	−0.636986	−	1.10329i	−0.0210696	−	0.0364937i
$915$		0			0
$916$	−8.74286	−	15.1431i	−0.288872	−	0.500341i
$917$	−39.2176	−	6.56148i	−1.29508	−	0.216679i
$918$		0			0
$919$	11.8283	+	20.4873i	0.390181	+	0.675813i	0.992473	−	0.122462i	$-0.0390791\pi$
$919$	11.8283	+	20.4873i	0.390181	+	0.675813i	−0.602292	+	0.798276i	$0.705746\pi$
$920$	17.0316			0.561515
$921$		0			0
$922$	17.9439			0.590952
$923$	2.95907	−	5.12525i	0.0973989	−	0.168700i
$924$		0			0
$925$	−20.4280	−	35.3823i	−0.671667	−	1.16336i
$926$	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
$931$	3.75215	+	19.2965i	0.122972	+	0.632417i
$932$	14.5073	−	25.1274i	0.475203	−	0.823075i
$933$		0			0
$934$	−4.31427			−0.141167
$935$	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	$0.641596\pi$
$938$	−1.33196	−	0.222850i	−0.0434901	−	0.00727630i
$939$		0			0
$940$	−65.8930			−2.14919
$941$	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
$950$	−12.0247			−0.390134
$951$		0			0
$952$	0.783117	−	0.950060i	0.0253810	−	0.0307916i
$953$	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
$956$	38.6324			1.24946
$957$		0			0
$958$	−4.40515	+	7.62994i	−0.142324	+	0.246512i
$959$	−1.27471	−	0.213271i	−0.0411626	−	0.00688689i
$960$		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
$965$	−10.9569	−	18.9779i	−0.352715	−	0.610921i
$966$		0			0
$967$	9.09069	−	15.7455i	0.292337	−	0.506342i	−0.682025	−	0.731329i	$-0.738900\pi$
$967$	9.09069	−	15.7455i	0.292337	−	0.506342i	0.974362	+	0.224986i	$0.0722338\pi$
$968$	18.9940			0.610489
$969$		0			0
$970$	−20.2223			−0.649299
$971$	−19.7416	−	34.1935i	−0.633538	−	1.09732i	−0.986823	−	0.161804i	$-0.948269\pi$
$971$	−19.7416	−	34.1935i	−0.633538	−	1.09732i	0.353285	−	0.935516i	$-0.385065\pi$
$972$		0			0
$973$	16.6092	−	20.1499i	0.532466	−	0.645975i
$974$	4.12941	+	7.15234i	0.132315	+	0.229176i
$975$		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
$979$	1.07439	+	1.86090i	0.0343376	+	0.0594745i
$980$	8.65423	+	44.5069i	0.276449	+	1.42172i
$981$		0			0
$982$	1.59184	+	2.75715i	0.0507977	+	0.0879842i
$983$	18.4779			0.589354			0.294677	−	0.955597i	$-0.404788\pi$
$983$	18.4779			0.589354			0.294677	+	0.955597i	$0.404788\pi$
$984$		0			0
$985$	57.1176			1.81992
$986$	0.256752	−	0.444708i	0.00817666	−	0.0141624i
$987$		0			0
$988$	2.94752	+	5.10525i	0.0937731	+	0.162420i
$989$	12.3620	+	21.4117i	0.393090	+	0.680851i
$990$		0			0
$991$	−6.34850	+	10.9959i	−0.201667	+	0.349297i	−0.949066	−	0.315079i	$-0.897969\pi$
$991$	−6.34850	+	10.9959i	−0.201667	+	0.349297i	0.747399	+	0.664376i	$0.231302\pi$
$992$	−8.97181	+	15.5396i	−0.284855	+	0.493384i
$993$		0			0
$994$	4.12671	−	5.00643i	0.130891	−	0.158794i
$995$	28.6108	−	49.5553i	0.907023	−	1.57101i
$996$		0			0
$997$	41.9533			1.32868			0.664338	−	0.747432i	$-0.268714\pi$
$997$	41.9533			1.32868			0.664338	+	0.747432i	$0.268714\pi$
$998$	−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	189.2.g.b.172.3		10
3.2	odd	2		63.2.g.b.4.3	✓	10
4.3	odd	2		3024.2.t.i.1873.5		10
7.2	even	3		189.2.h.b.37.3		10
7.3	odd	6		1323.2.f.f.442.3		10
7.4	even	3		1323.2.f.e.442.3		10
7.5	odd	6		1323.2.h.f.226.3		10
7.6	odd	2		1323.2.g.f.361.3		10
9.2	odd	6		63.2.h.b.25.3	yes	10
9.4	even	3		567.2.e.e.487.3		10
9.5	odd	6		567.2.e.f.487.3		10
9.7	even	3		189.2.h.b.46.3		10
12.11	even	2		1008.2.t.i.193.1		10
21.2	odd	6		63.2.h.b.58.3	yes	10
21.5	even	6		441.2.h.f.373.3		10
21.11	odd	6		441.2.f.e.148.3		10
21.17	even	6		441.2.f.f.148.3		10
21.20	even	2		441.2.g.f.67.3		10
28.23	odd	6		3024.2.q.i.2305.1		10
36.7	odd	6		3024.2.q.i.2881.1		10
36.11	even	6		1008.2.q.i.529.3		10
63.2	odd	6		63.2.g.b.16.3	yes	10
63.4	even	3		3969.2.a.bc.1.3		5
63.11	odd	6		441.2.f.e.295.3		10
63.16	even	3	inner	189.2.g.b.100.3		10
63.20	even	6		441.2.h.f.214.3		10
63.23	odd	6		567.2.e.f.163.3		10
63.25	even	3		1323.2.f.e.883.3		10
63.31	odd	6		3969.2.a.bb.1.3		5
63.32	odd	6		3969.2.a.z.1.3		5
63.34	odd	6		1323.2.h.f.802.3		10
63.38	even	6		441.2.f.f.295.3		10
63.47	even	6		441.2.g.f.79.3		10
63.52	odd	6		1323.2.f.f.883.3		10
63.58	even	3		567.2.e.e.163.3		10
63.59	even	6		3969.2.a.ba.1.3		5
63.61	odd	6		1323.2.g.f.667.3		10
84.23	even	6		1008.2.q.i.625.3		10
252.79	odd	6		3024.2.t.i.289.5		10
252.191	even	6		1008.2.t.i.961.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	3.2	odd	2
63.2.g.b.16.3	yes	10	63.2	odd	6
63.2.h.b.25.3	yes	10	9.2	odd	6
63.2.h.b.58.3	yes	10	21.2	odd	6
189.2.g.b.100.3		10	63.16	even	3	inner
189.2.g.b.172.3		10	1.1	even	1	trivial
189.2.h.b.37.3		10	7.2	even	3
189.2.h.b.46.3		10	9.7	even	3
441.2.f.e.148.3		10	21.11	odd	6
441.2.f.e.295.3		10	63.11	odd	6
441.2.f.f.148.3		10	21.17	even	6
441.2.f.f.295.3		10	63.38	even	6
441.2.g.f.67.3		10	21.20	even	2
441.2.g.f.79.3		10	63.47	even	6
441.2.h.f.214.3		10	63.20	even	6
441.2.h.f.373.3		10	21.5	even	6
567.2.e.e.163.3		10	63.58	even	3
567.2.e.e.487.3		10	9.4	even	3
567.2.e.f.163.3		10	63.23	odd	6
567.2.e.f.487.3		10	9.5	odd	6
1008.2.q.i.529.3		10	36.11	even	6
1008.2.q.i.625.3		10	84.23	even	6
1008.2.t.i.193.1		10	12.11	even	2
1008.2.t.i.961.1		10	252.191	even	6
1323.2.f.e.442.3		10	7.4	even	3
1323.2.f.e.883.3		10	63.25	even	3
1323.2.f.f.442.3		10	7.3	odd	6
1323.2.f.f.883.3		10	63.52	odd	6
1323.2.g.f.361.3		10	7.6	odd	2
1323.2.g.f.667.3		10	63.61	odd	6
1323.2.h.f.226.3		10	7.5	odd	6
1323.2.h.f.802.3		10	63.34	odd	6
3024.2.q.i.2305.1		10	28.23	odd	6
3024.2.q.i.2881.1		10	36.7	odd	6
3024.2.t.i.289.5		10	252.79	odd	6
3024.2.t.i.1873.5		10	4.3	odd	2
3969.2.a.z.1.3		5	63.32	odd	6
3969.2.a.ba.1.3		5	63.59	even	6
3969.2.a.bb.1.3		5	63.31	odd	6
3969.2.a.bc.1.3		5	63.4	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +3.69258 q^{5} +(-2.60948 - 0.436591i) q^{7} -1.86155 q^{8} +O(q^{10})\)	\(q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} +3.69258 q^{5} +(-2.60948 - 0.436591i) q^{7} -1.86155 q^{8} +(-0.915516 + 1.58572i) q^{10} +0.892568 q^{11} +(0.598355 - 1.03638i) q^{13} +(0.834466 - 1.01236i) q^{14} +(-1.29257 + 2.23880i) q^{16} +(0.124991 - 0.216492i) q^{17} +(1.40414 + 2.43204i) q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} -2.47772 q^{23} +8.63514 q^{25} +(0.296705 + 0.513909i) q^{26} +(-1.62544 - 4.34700i) q^{28} +(-2.07128 - 3.58755i) q^{29} +(-1.79257 - 3.10483i) q^{31} +(-2.50249 - 4.33444i) q^{32} +(0.0619793 + 0.107351i) q^{34} +(-9.63571 - 1.61215i) q^{35} +(-2.36568 - 4.09747i) q^{37} -1.39253 q^{38} -6.87391 q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(0.782834 + 1.35591i) q^{44} +(0.614310 - 1.06402i) q^{46} +(-5.08653 + 8.81013i) q^{47} +(6.61878 + 2.27855i) q^{49} +(-2.14095 + 3.70823i) q^{50} +2.09917 q^{52} +(4.94465 - 8.56438i) q^{53} +3.29588 q^{55} +(4.85767 + 0.812734i) q^{56} +2.05416 q^{58} +(0.906186 + 1.56956i) q^{59} +(-5.40205 + 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(2.20948 - 3.82692i) q^{65} +(-0.514685 - 0.891460i) q^{67} +0.438499 q^{68} +(3.08133 - 3.73820i) q^{70} +4.94533 q^{71} +(-0.915262 + 1.58528i) q^{73} +2.34613 q^{74} +(-2.46302 + 4.26607i) q^{76} +(-2.32914 - 0.389687i) q^{77} +(0.899562 - 1.55809i) q^{79} +(-4.77293 + 8.26696i) q^{80} +(1.18559 + 2.05350i) q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +4.94806 q^{86} -1.66156 q^{88} +(1.20370 + 2.08488i) q^{89} +(-2.01387 + 2.44318i) q^{91} +(-2.17310 - 3.76392i) q^{92} +(-2.52225 - 4.36867i) q^{94} +(5.18489 + 8.98049i) q^{95} +(5.52210 + 9.56456i) q^{97} +(-2.61951 + 2.27740i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8} - 7 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 5 q^{35} + 40 q^{38} + 6 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} + 25 q^{49} - 19 q^{50} + 20 q^{52} + 21 q^{53} + 4 q^{55} + 45 q^{56} + 20 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} + 54 q^{68} - 29 q^{70} + 6 q^{71} + 15 q^{73} - 72 q^{74} + 5 q^{76} + 31 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8 - 7 * q^10 + 8 * q^11 - 8 * q^13 - 16 * q^14 + 2 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 5 * q^35 + 40 * q^38 + 6 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 + 25 * q^49 - 19 * q^50 + 20 * q^52 + 21 * q^53 + 4 * q^55 + 45 * q^56 + 20 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 54 * q^68 - 29 * q^70 + 6 * q^71 + 15 * q^73 - 72 * q^74 + 5 * q^76 + 31 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97 - 59 * q^98

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