LMFDB - Embedded newform 189.2.s.b.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(17,189)]

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([5, 1]))

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

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

chi := DirichletCharacter("189.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.s (of order $6$, 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 $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$-1.04536 + 1.81062i$ of defining polynomial
Character	$\chi$	$=$	189.17
Dual form			189.2.s.b.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30778 - 0.755047i) q^{2} +(0.140193 + 0.242822i) q^{4} +0.775876 q^{5} +(2.05881 - 1.66171i) q^{7} +2.59678i q^{8} +O(q^{10})$	\(q+(-1.30778 - 0.755047i) q^{2} +(0.140193 + 0.242822i) q^{4} +0.775876 q^{5} +(2.05881 - 1.66171i) q^{7} +2.59678i q^{8} +(-1.01468 - 0.585823i) q^{10} -3.84319i q^{11} +(-2.54198 - 1.46761i) q^{13} +(-3.94715 + 0.618650i) q^{14} +(2.24108 - 3.88166i) q^{16} +(2.69901 - 4.67482i) q^{17} +(-0.376551 + 0.217402i) q^{19} +(0.108773 + 0.188400i) q^{20} +(-2.90179 + 5.02605i) q^{22} +0.0557186i q^{23} -4.39802 q^{25} +(2.21624 + 3.83863i) q^{26} +(0.692131 + 0.266964i) q^{28} +(0.187994 - 0.108538i) q^{29} +(5.67806 - 3.27823i) q^{31} +(-1.36392 + 0.787461i) q^{32} +(-7.05942 + 4.07576i) q^{34} +(1.59739 - 1.28928i) q^{35} +(3.14698 + 5.45073i) q^{37} +0.656595 q^{38} +2.01478i q^{40} +(-3.78757 + 6.56026i) q^{41} +(6.42703 + 11.1319i) q^{43} +(0.933209 - 0.538789i) q^{44} +(0.0420702 - 0.0728677i) q^{46} +(-0.482772 + 0.836186i) q^{47} +(1.47744 - 6.84231i) q^{49} +(5.75164 + 3.32071i) q^{50} -0.822998i q^{52} +(6.46438 + 3.73221i) q^{53} -2.98184i q^{55} +(4.31510 + 5.34629i) q^{56} -0.327806 q^{58} +(1.56219 + 2.70580i) q^{59} +(-3.01744 - 1.74212i) q^{61} -9.90087 q^{62} -6.58603 q^{64} +(-1.97226 - 1.13869i) q^{65} +(2.10088 + 3.63884i) q^{67} +1.51353 q^{68} +(-3.06250 + 0.479996i) q^{70} +3.50812i q^{71} +(-7.05942 - 4.07576i) q^{73} -9.50448i q^{74} +(-0.105580 - 0.0609566i) q^{76} +(-6.38626 - 7.91241i) q^{77} +(2.48110 - 4.29739i) q^{79} +(1.73880 - 3.01169i) q^{80} +(9.90662 - 5.71959i) q^{82} +(4.31033 + 7.46571i) q^{83} +(2.09410 - 3.62708i) q^{85} -19.4108i q^{86} +9.97991 q^{88} +(-7.82041 - 13.5453i) q^{89} +(-7.67222 + 1.20249i) q^{91} +(-0.0135297 + 0.00781136i) q^{92} +(1.26272 - 0.729031i) q^{94} +(-0.292157 + 0.168677i) q^{95} +(1.24162 - 0.716849i) q^{97} +(-7.09843 + 7.83270i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) $ 10 * q + 4 * q^4 + 3 * q^7	$ 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} + 6 q^{13} + 6 q^{14} - 6 q^{16} + 12 q^{17} + 3 q^{19} + 3 q^{20} + 5 q^{22} - 14 q^{25} - 3 q^{26} + 2 q^{28} + 15 q^{29} - 9 q^{31} - 48 q^{32} + 3 q^{34} + 15 q^{35} + 6 q^{37} - 36 q^{38} + 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} - 15 q^{47} - 23 q^{49} - 3 q^{50} + 9 q^{53} + 51 q^{56} - 16 q^{58} + 18 q^{59} + 12 q^{61} - 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 54 q^{68} + 9 q^{70} + 3 q^{73} + 9 q^{76} - 45 q^{77} + 20 q^{79} + 30 q^{80} + 9 q^{82} + 15 q^{83} + 18 q^{85} + 16 q^{88} - 24 q^{89} - 24 q^{91} - 39 q^{92} - 3 q^{94} + 6 q^{97} - 45 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 + 6 * q^13 + 6 * q^14 - 6 * q^16 + 12 * q^17 + 3 * q^19 + 3 * q^20 + 5 * q^22 - 14 * q^25 - 3 * q^26 + 2 * q^28 + 15 * q^29 - 9 * q^31 - 48 * q^32 + 3 * q^34 + 15 * q^35 + 6 * q^37 - 36 * q^38 + 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 - 15 * q^47 - 23 * q^49 - 3 * q^50 + 9 * q^53 + 51 * q^56 - 16 * q^58 + 18 * q^59 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 54 * q^68 + 9 * q^70 + 3 * q^73 + 9 * q^76 - 45 * q^77 + 20 * q^79 + 30 * q^80 + 9 * q^82 + 15 * q^83 + 18 * q^85 + 16 * q^88 - 24 * q^89 - 24 * q^91 - 39 * q^92 - 3 * q^94 + 6 * q^97 - 45 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.30778	−	0.755047i	−0.924740	−	0.533899i	−0.0395961	−	0.999216i	$-0.512607\pi$
$2$	−1.30778	−	0.755047i	−0.924740	−	0.533899i	−0.885144	+	0.465317i	$0.845940\pi$
$3$		0			0
$3$		0			0
$4$	0.140193	+	0.242822i	0.0700966	+	0.121411i
$5$	0.775876			0.346982			0.173491	−	0.984835i	$-0.444495\pi$
$5$	0.775876			0.346982			0.173491	+	0.984835i	$0.444495\pi$
$6$		0			0
$7$	2.05881	−	1.66171i	0.778159	−	0.628068i
$7$	2.05881	−	1.66171i	0.778159	−	0.628068i
$8$			2.59678i			0.918100i
$9$		0			0
$10$	−1.01468	−	0.585823i	−0.320869	−	0.185254i
$11$		−	3.84319i		−	1.15876i	−0.815056	−	0.579382i	$-0.803294\pi$
$11$		−	3.84319i		−	1.15876i	0.815056	−	0.579382i	$-0.196706\pi$
$12$		0			0
$13$	−2.54198	−	1.46761i	−0.705019	−	0.407043i	0.104195	−	0.994557i	$-0.466773\pi$
$13$	−2.54198	−	1.46761i	−0.705019	−	0.407043i	−0.809214	+	0.587514i	$0.800107\pi$
$14$	−3.94715	+	0.618650i	−1.05492	+	0.165341i
$15$		0			0
$16$	2.24108	−	3.88166i	0.560270	−	0.970415i
$17$	2.69901	−	4.67482i	0.654606	−	1.13381i	−0.327387	−	0.944890i	$-0.606168\pi$
$17$	2.69901	−	4.67482i	0.654606	−	1.13381i	0.981993	−	0.188920i	$-0.0604986\pi$
$18$		0			0
$19$	−0.376551	+	0.217402i	−0.0863868	+	0.0498755i	−0.542571	−	0.840010i	$-0.682549\pi$
$19$	−0.376551	+	0.217402i	−0.0863868	+	0.0498755i	0.456184	+	0.889885i	$0.349216\pi$
$20$	0.108773	+	0.188400i	0.0243223	+	0.0421274i
$21$		0			0
$22$	−2.90179	+	5.02605i	−0.618663	+	1.07156i
$23$			0.0557186i			0.0116181i	0.999983	+	0.00580906i	$0.00184909\pi$
$23$			0.0557186i			0.0116181i	−0.999983	+	0.00580906i	$0.998151\pi$
$24$		0			0
$25$	−4.39802			−0.879603
$26$	2.21624	+	3.83863i	0.434640	+	0.752818i
$27$		0			0
$28$	0.692131	+	0.266964i	0.130800	+	0.0504515i
$29$	0.187994	−	0.108538i	0.0349096	−	0.0201551i	−0.482444	−	0.875927i	$-0.660251\pi$
$29$	0.187994	−	0.108538i	0.0349096	−	0.0201551i	0.517353	+	0.855772i	$0.326917\pi$
$30$		0			0
$31$	5.67806	−	3.27823i	1.01981	−	0.588787i	0.105761	−	0.994392i	$-0.466272\pi$
$31$	5.67806	−	3.27823i	1.01981	−	0.588787i	0.914049	+	0.405604i	$0.132939\pi$
$32$	−1.36392	+	0.787461i	−0.241110	+	0.139205i
$33$		0			0
$34$	−7.05942	+	4.07576i	−1.21068	+	0.698987i
$35$	1.59739	−	1.28928i	0.270007	−	0.217928i
$36$		0			0
$37$	3.14698	+	5.45073i	0.517361	+	0.896095i	0.999797	+	0.0201636i	$0.00641872\pi$
$37$	3.14698	+	5.45073i	0.517361	+	0.896095i	−0.482436	+	0.875931i	$0.660248\pi$
$38$	0.656595			0.106514
$39$		0			0
$40$			2.01478i			0.318565i
$41$	−3.78757	+	6.56026i	−0.591519	+	1.02454i	0.402509	+	0.915416i	$0.368138\pi$
$41$	−3.78757	+	6.56026i	−0.591519	+	1.02454i	−0.994028	+	0.109125i	$0.965195\pi$
$42$		0			0
$43$	6.42703	+	11.1319i	0.980112	+	1.69760i	0.661914	+	0.749580i	$0.269745\pi$
$43$	6.42703	+	11.1319i	0.980112	+	1.69760i	0.318198	+	0.948024i	$0.396922\pi$
$44$	0.933209	−	0.538789i	0.140687	−	0.0812254i
$45$		0			0
$46$	0.0420702	−	0.0728677i	0.00620291	−	0.0107437i
$47$	−0.482772	+	0.836186i	−0.0704195	+	0.121970i	−0.899085	−	0.437774i	$-0.855767\pi$
$47$	−0.482772	+	0.836186i	−0.0704195	+	0.121970i	0.828666	+	0.559744i	$0.189100\pi$
$48$		0			0
$49$	1.47744	−	6.84231i	0.211062	−	0.977473i
$50$	5.75164	+	3.32071i	0.813405	+	0.469619i
$51$		0			0
$52$		−	0.822998i		−	0.114129i
$53$	6.46438	+	3.73221i	0.887950	+	0.512658i	0.873272	−	0.487234i	$-0.161994\pi$
$53$	6.46438	+	3.73221i	0.887950	+	0.512658i	0.0146788	+	0.999892i	$0.495327\pi$
$54$		0			0
$55$		−	2.98184i		−	0.402071i
$56$	4.31510	+	5.34629i	0.576629	+	0.714428i
$57$		0			0
$58$	−0.327806			−0.0430431
$59$	1.56219	+	2.70580i	0.203380	+	0.352265i	0.949615	−	0.313418i	$-0.101474\pi$
$59$	1.56219	+	2.70580i	0.203380	+	0.352265i	−0.746235	+	0.665682i	$0.768141\pi$
$60$		0			0
$61$	−3.01744	−	1.74212i	−0.386343	−	0.223055i	0.294231	−	0.955734i	$-0.404936\pi$
$61$	−3.01744	−	1.74212i	−0.386343	−	0.223055i	−0.680575	+	0.732679i	$0.738270\pi$
$62$	−9.90087			−1.25741
$63$		0			0
$64$	−6.58603			−0.823254
$65$	−1.97226	−	1.13869i	−0.244629	−	0.141237i
$66$		0			0
$67$	2.10088	+	3.63884i	0.256664	+	0.444555i	0.965346	−	0.260973i	$-0.0840433\pi$
$67$	2.10088	+	3.63884i	0.256664	+	0.444555i	−0.708682	+	0.705528i	$0.750710\pi$
$68$	1.51353			0.183542
$69$		0			0
$70$	−3.06250	+	0.479996i	−0.366039	+	0.0573705i
$71$			3.50812i			0.416337i	0.978093	+	0.208169i	$0.0667503\pi$
$71$			3.50812i			0.416337i	−0.978093	+	0.208169i	$0.933250\pi$
$72$		0			0
$73$	−7.05942	−	4.07576i	−0.826243	−	0.477031i	0.0263219	−	0.999654i	$-0.491621\pi$
$73$	−7.05942	−	4.07576i	−0.826243	−	0.477031i	−0.852564	+	0.522622i	$0.824954\pi$
$74$		−	9.50448i		−	1.10487i
$75$		0			0
$76$	−0.105580	−	0.0609566i	−0.0121108	−	0.00699220i
$77$	−6.38626	−	7.91241i	−0.727782	−	0.901703i
$78$		0			0
$79$	2.48110	−	4.29739i	0.279145	−	0.483494i	−0.692027	−	0.721871i	$-0.743282\pi$
$79$	2.48110	−	4.29739i	0.279145	−	0.483494i	0.971173	+	0.238377i	$0.0766155\pi$
$80$	1.73880	−	3.01169i	0.194404	−	0.336717i
$81$		0			0
$82$	9.90662	−	5.71959i	1.09400	−	0.631623i
$83$	4.31033	+	7.46571i	0.473120	+	0.819469i	0.999527	−	0.0307645i	$-0.00979420\pi$
$83$	4.31033	+	7.46571i	0.473120	+	0.819469i	−0.526406	+	0.850233i	$0.676461\pi$
$84$		0			0
$85$	2.09410	−	3.62708i	0.227137	−	0.393412i
$86$		−	19.4108i		−	2.09312i
$87$		0			0
$88$	9.97991			1.06386
$89$	−7.82041	−	13.5453i	−0.828962	−	1.43580i	−0.898853	−	0.438249i	$-0.855599\pi$
$89$	−7.82041	−	13.5453i	−0.828962	−	1.43580i	0.0698916	−	0.997555i	$-0.477735\pi$
$90$		0			0
$91$	−7.67222	+	1.20249i	−0.804267	+	0.126055i
$92$	−0.0135297	+	0.00781136i	−0.00141057	+	0.000814391i
$93$		0			0
$94$	1.26272	−	0.729031i	0.130240	−	0.0751938i
$95$	−0.292157	+	0.168677i	−0.0299747	+	0.0173059i
$96$		0			0
$97$	1.24162	−	0.716849i	0.126067	−	0.0727850i	−0.435640	−	0.900121i	$-0.643478\pi$
$97$	1.24162	−	0.716849i	0.126067	−	0.0727850i	0.561708	+	0.827336i	$0.310145\pi$
$98$	−7.09843	+	7.83270i	−0.717050	+	0.791222i
$99$		0			0
$100$	−0.616572	−	1.06793i	−0.0616572	−	0.106793i
$101$	−16.0219			−1.59424			−0.797120	−	0.603821i	$-0.793644\pi$
$101$	−16.0219			−1.59424			−0.797120	+	0.603821i	$0.793644\pi$
$102$		0			0
$103$			16.8660i			1.66186i	0.556381	+	0.830928i	$0.312190\pi$
$103$			16.8660i			1.66186i	−0.556381	+	0.830928i	$0.687810\pi$
$104$	3.81107	−	6.60097i	0.373706	−	0.647278i
$105$		0			0
$106$	−5.63599	−	9.76182i	−0.547416	−	0.948152i
$107$	3.36444	−	1.94246i	0.325253	−	0.187785i	−0.328479	−	0.944511i	$-0.606536\pi$
$107$	3.36444	−	1.94246i	0.325253	−	0.187785i	0.653731	+	0.756727i	$0.273203\pi$
$108$		0			0
$109$	1.28254	−	2.22143i	0.122845	−	0.212774i	−0.798043	−	0.602600i	$-0.794131\pi$
$109$	1.28254	−	2.22143i	0.122845	−	0.212774i	0.920889	+	0.389826i	$0.127465\pi$
$110$	−2.25143	+	3.89959i	−0.214665	+	0.371811i
$111$		0			0
$112$	−1.83623	−	11.7156i	−0.173508	−	1.10702i
$113$	9.79043	+	5.65251i	0.921006	+	0.531743i	0.883956	−	0.467570i	$-0.154871\pi$
$113$	9.79043	+	5.65251i	0.921006	+	0.531743i	0.0370501	+	0.999313i	$0.488204\pi$
$114$		0			0
$115$			0.0432307i			0.00403129i
$116$	0.0527109	+	0.0304327i	0.00489408	+	0.00282560i
$117$		0			0
$118$		−	4.71812i		−	0.434338i
$119$	−2.21144	−	14.1096i	−0.202722	−	1.29342i
$120$		0			0
$121$	−3.77009			−0.342735
$122$	2.63076	+	4.55662i	0.238178	+	0.412537i
$123$		0			0
$124$	1.59205	+	0.919171i	0.142970	+	0.0825440i
$125$	−7.29170			−0.652189
$126$		0			0
$127$	2.65660			0.235735			0.117867	−	0.993029i	$-0.462394\pi$
$127$	2.65660			0.235735			0.117867	+	0.993029i	$0.462394\pi$
$128$	11.3409	+	6.54769i	1.00241	+	0.578739i
$129$		0			0
$130$	1.71953	+	2.97830i	0.150812	+	0.261215i
$131$	8.23623			0.719602			0.359801	−	0.933029i	$-0.382845\pi$
$131$	8.23623			0.719602			0.359801	+	0.933029i	$0.382845\pi$
$132$		0			0
$133$	−0.413990	+	1.07331i	−0.0358975	+	0.0930678i
$134$		−	6.34507i		−	0.548131i
$135$		0			0
$136$	12.1395	+	7.00873i	1.04095	+	0.600994i
$137$			17.3272i			1.48036i	0.672408	+	0.740180i	$0.265260\pi$
$137$			17.3272i			1.48036i	−0.672408	+	0.740180i	$0.734740\pi$
$138$		0			0
$139$	−5.47677	−	3.16201i	−0.464533	−	0.268198i	0.249415	−	0.968397i	$-0.419762\pi$
$139$	−5.47677	−	3.16201i	−0.464533	−	0.268198i	−0.713949	+	0.700198i	$0.753095\pi$
$140$	0.537008	+	0.207131i	0.0453855	+	0.0175058i
$141$		0			0
$142$	2.64880	−	4.58785i	0.222282	−	0.385004i
$143$	−5.64031	+	9.76931i	−0.471667	+	0.816951i
$144$		0			0
$145$	0.145860	−	0.0842123i	0.0121130	−	0.00699345i
$146$	6.15478	+	10.6604i	0.509373	+	0.882260i
$147$		0			0
$148$	−0.882370	+	1.52831i	−0.0725304	+	0.125626i
$149$			12.8242i			1.05060i	0.850917	+	0.525300i	$0.176047\pi$
$149$			12.8242i			1.05060i	−0.850917	+	0.525300i	$0.823953\pi$
$150$		0			0
$151$	5.25517			0.427660			0.213830	−	0.976871i	$-0.431406\pi$
$151$	5.25517			0.427660			0.213830	+	0.976871i	$0.431406\pi$
$152$	−0.564545	−	0.977821i	−0.0457907	−	0.0793118i
$153$		0			0
$154$	2.37759	+	15.1696i	0.191591	+	1.22240i
$155$	4.40547	−	2.54350i	0.353856	−	0.204299i
$156$		0			0
$157$	−6.91794	+	3.99407i	−0.552111	+	0.318762i	−0.749973	−	0.661468i	$-0.769934\pi$
$157$	−6.91794	+	3.99407i	−0.552111	+	0.318762i	0.197862	+	0.980230i	$0.436600\pi$
$158$	−6.48946	+	3.74669i	−0.516274	+	0.298071i
$159$		0			0
$160$	−1.05823	+	0.610972i	−0.0836608	+	0.0483016i
$161$	0.0925881	+	0.114714i	0.00729697	+	0.00904075i
$162$		0			0
$163$	5.75231	+	9.96329i	0.450556	+	0.780385i	0.998421	−	0.0561817i	$-0.0178926\pi$
$163$	5.75231	+	9.96329i	0.450556	+	0.780385i	−0.547865	+	0.836567i	$0.684559\pi$
$164$	−2.12397			−0.165854
$165$		0			0
$166$		−	13.0180i		−	1.01039i
$167$	8.38240	−	14.5187i	0.648650	−	1.12349i	−0.334796	−	0.942291i	$-0.608667\pi$
$167$	8.38240	−	14.5187i	0.648650	−	1.12349i	0.983446	−	0.181204i	$-0.0579994\pi$
$168$		0			0
$169$	−2.19222	−	3.79704i	−0.168632	−	0.292080i
$170$	−5.47724	+	3.16228i	−0.420085	+	0.242536i
$171$		0			0
$172$	−1.80205	+	3.12124i	−0.137405	+	0.237992i
$173$	−0.856396	+	1.48332i	−0.0651106	+	0.112775i	−0.896743	−	0.442552i	$-0.854073\pi$
$173$	−0.856396	+	1.48332i	−0.0651106	+	0.112775i	0.831632	+	0.555326i	$0.187407\pi$
$174$		0			0
$175$	−9.05470	+	7.30823i	−0.684471	+	0.552450i
$176$	−14.9180	−	8.61288i	−1.12448	−	0.649220i
$177$		0			0
$178$			23.6191i			1.77033i
$179$	12.4141	+	7.16731i	0.927877	+	0.535710i	0.886139	−	0.463419i	$-0.153377\pi$
$179$	12.4141	+	7.16731i	0.927877	+	0.535710i	0.0417372	+	0.999129i	$0.486711\pi$
$180$		0			0
$181$			4.83147i			0.359121i	0.983747	+	0.179560i	$0.0574675\pi$
$181$			4.83147i			0.359121i	−0.983747	+	0.179560i	$0.942532\pi$
$182$	10.9415	+	4.22029i	0.811039	+	0.312829i
$183$		0			0
$184$	−0.144689			−0.0106666
$185$	2.44167	+	4.22909i	0.179515	+	0.310929i
$186$		0			0
$187$	−17.9662	−	10.3728i	−1.31382	−	0.758534i
$188$	−0.270725			−0.0197447
$189$		0			0
$190$	0.509437			0.0369584
$191$	2.72114	+	1.57105i	0.196895	+	0.113677i	0.595206	−	0.803573i	$-0.297070\pi$
$191$	2.72114	+	1.57105i	0.196895	+	0.113677i	−0.398311	+	0.917250i	$0.630404\pi$
$192$		0			0
$193$	−3.00508	−	5.20496i	−0.216311	−	0.374661i	0.737367	−	0.675493i	$-0.236069\pi$
$193$	−3.00508	−	5.20496i	−0.216311	−	0.374661i	−0.953677	+	0.300832i	$0.902736\pi$
$194$	−2.16502			−0.155439
$195$		0			0
$196$	1.86859	−	0.600491i	0.133471	−	0.0428922i
$197$		−	14.0902i		−	1.00388i	−0.864901	−	0.501942i	$-0.832619\pi$
$197$		−	14.0902i		−	1.00388i	0.864901	−	0.501942i	$-0.167381\pi$
$198$		0			0
$199$	−6.84234	−	3.95043i	−0.485041	−	0.280038i	0.237474	−	0.971394i	$-0.423681\pi$
$199$	−6.84234	−	3.95043i	−0.485041	−	0.280038i	−0.722515	+	0.691355i	$0.757014\pi$
$200$		−	11.4207i		−	0.807564i
$201$		0			0
$202$	20.9531	+	12.0973i	1.47426	+	0.851163i
$203$	0.206685	−	0.535852i	0.0145065	−	0.0376094i
$204$		0			0
$205$	−2.93869	+	5.08995i	−0.205247	+	0.355498i
$206$	12.7346	−	22.0570i	0.887263	−	1.53678i
$207$		0			0
$208$	−11.3936	+	6.57807i	−0.790001	+	0.456107i
$209$	0.835517	+	1.44716i	0.0577939	+	0.100102i
$210$		0			0
$211$	2.57821	−	4.46559i	0.177491	−	0.307424i	−0.763529	−	0.645773i	$-0.776535\pi$
$211$	2.57821	−	4.46559i	0.177491	−	0.307424i	0.941021	+	0.338349i	$0.109868\pi$
$212$			2.09292i			0.143742i
$213$		0			0
$214$	−5.86660			−0.401032
$215$	4.98658	+	8.63701i	0.340082	+	0.589039i
$216$		0			0
$217$	6.24261	−	16.1846i	0.423776	−	1.09868i
$218$	−3.35457	+	1.93676i	−0.227200	+	0.131174i
$219$		0			0
$220$	0.724055	−	0.418033i	0.0488158	−	0.0281838i
$221$	−13.7217	+	7.92220i	−0.923019	+	0.532905i
$222$		0			0
$223$	3.79823	−	2.19291i	0.254348	−	0.146848i	−0.367405	−	0.930061i	$-0.619754\pi$
$223$	3.79823	−	2.19291i	0.254348	−	0.146848i	0.621754	+	0.783213i	$0.286420\pi$
$224$	−1.49953	+	3.88768i	−0.100192	+	0.259756i
$225$		0			0
$226$	−8.53582	−	14.7845i	−0.567794	−	0.983449i
$227$	−9.67394			−0.642082			−0.321041	−	0.947065i	$-0.604033\pi$
$227$	−9.67394			−0.642082			−0.321041	+	0.947065i	$0.604033\pi$
$228$		0			0
$229$		−	8.85314i		−	0.585032i	−0.956261	−	0.292516i	$-0.905508\pi$
$229$		−	8.85314i		−	0.585032i	0.956261	−	0.292516i	$-0.0944925\pi$
$230$	0.0326412	−	0.0565363i	0.00215230	−	0.00372789i
$231$		0			0
$232$	0.281850	+	0.488179i	0.0185044	+	0.0320505i
$233$	−11.1612	+	6.44391i	−0.731194	+	0.422155i	−0.818859	−	0.573995i	$-0.805393\pi$
$233$	−11.1612	+	6.44391i	−0.731194	+	0.422155i	0.0876651	+	0.996150i	$0.472059\pi$
$234$		0			0
$235$	−0.374571	+	0.648777i	−0.0244343	+	0.0423215i
$236$	−0.438017	+	0.758668i	−0.0285125	+	0.0493851i
$237$		0			0
$238$	−7.76131	+	20.1219i	−0.503091	+	1.30431i
$239$	−4.18421	−	2.41575i	−0.270654	−	0.156262i	0.358531	−	0.933518i	$-0.383278\pi$
$239$	−4.18421	−	2.41575i	−0.270654	−	0.156262i	−0.629185	+	0.777256i	$0.716611\pi$
$240$		0			0
$241$		−	10.0336i		−	0.646323i	−0.946344	−	0.323161i	$-0.895254\pi$
$241$		−	10.0336i		−	0.646323i	0.946344	−	0.323161i	$-0.104746\pi$
$242$	4.93045	+	2.84659i	0.316941	+	0.182986i
$243$		0			0
$244$		−	0.976932i		−	0.0625417i
$245$	1.14631	−	5.30879i	0.0732349	−	0.339166i
$246$		0			0
$247$	1.27625			0.0812058
$248$	8.51284	+	14.7447i	0.540566	+	0.936288i
$249$		0			0
$250$	9.53594	+	5.50558i	0.603106	+	0.348203i
$251$	7.98203			0.503821			0.251911	−	0.967751i	$-0.418941\pi$
$251$	7.98203			0.503821			0.251911	+	0.967751i	$0.418941\pi$
$252$		0			0
$253$	0.214137			0.0134627
$254$	−3.47424	−	2.00586i	−0.217993	−	0.125859i
$255$		0			0
$256$	−3.30160	−	5.71853i	−0.206350	−	0.357408i
$257$	2.68230			0.167317			0.0836585	−	0.996494i	$-0.473340\pi$
$257$	2.68230			0.167317			0.0836585	+	0.996494i	$0.473340\pi$
$258$		0			0
$259$	15.5366	+	5.99267i	0.965397	+	0.372367i
$260$		−	0.638544i		−	0.0396008i
$261$		0			0
$262$	−10.7712	−	6.21874i	−0.665445	−	0.384195i
$263$		−	23.4359i		−	1.44512i	−0.691309	−	0.722560i	$-0.742966\pi$
$263$		−	23.4359i		−	1.44512i	0.691309	−	0.722560i	$-0.257034\pi$
$264$		0			0
$265$	5.01556	+	2.89573i	0.308103	+	0.177883i
$266$	1.35181	−	1.09107i	0.0828847	−	0.0668979i
$267$		0			0
$268$	−0.589059	+	1.02028i	−0.0359825	+	0.0623236i
$269$	1.98955	−	3.44600i	0.121305	−	0.210106i	−0.798978	−	0.601361i	$-0.794625\pi$
$269$	1.98955	−	3.44600i	0.121305	−	0.210106i	0.920283	+	0.391254i	$0.127959\pi$
$270$		0			0
$271$	10.8303	−	6.25288i	0.657895	−	0.379836i	−0.133580	−	0.991038i	$-0.542647\pi$
$271$	10.8303	−	6.25288i	0.657895	−	0.379836i	0.791474	+	0.611202i	$0.209314\pi$
$272$	−12.0974	−	20.9533i	−0.733511	−	1.27048i
$273$		0			0
$274$	13.0828	−	22.6601i	0.790363	−	1.36895i
$275$			16.9024i			1.01925i
$276$		0			0
$277$	−19.6909			−1.18311			−0.591557	−	0.806263i	$-0.701487\pi$
$277$	−19.6909			−1.18311			−0.591557	+	0.806263i	$0.701487\pi$
$278$	4.77494	+	8.27044i	0.286382	+	0.496028i
$279$		0			0
$280$	3.34798	+	4.14806i	0.200080	+	0.247894i
$281$	−7.03456	+	4.06141i	−0.419647	+	0.242283i	−0.694926	−	0.719081i	$-0.744563\pi$
$281$	−7.03456	+	4.06141i	−0.419647	+	0.242283i	0.275279	+	0.961364i	$0.411230\pi$
$282$		0			0
$283$	1.16390	−	0.671978i	0.0691867	−	0.0399450i	−0.465008	−	0.885307i	$-0.653948\pi$
$283$	1.16390	−	0.671978i	0.0691867	−	0.0399450i	0.534194	+	0.845362i	$0.320615\pi$
$284$	−0.851847	+	0.491814i	−0.0505478	+	0.0291838i
$285$		0			0
$286$	14.7526	−	8.51741i	0.872339	−	0.503645i
$287$	3.10335	+	19.8002i	0.183185	+	1.16877i
$288$		0			0
$289$	−6.06929	−	10.5123i	−0.357017	−	0.618371i
$290$	−0.254337			−0.0149352
$291$		0			0
$292$		−	2.28557i		−	0.133753i
$293$	10.6300	−	18.4117i	0.621012	−	1.07562i	−0.368285	−	0.929713i	$-0.620055\pi$
$293$	10.6300	−	18.4117i	0.621012	−	1.07562i	0.989298	−	0.145912i	$-0.0466116\pi$
$294$		0			0
$295$	1.21207	+	2.09936i	0.0705693	+	0.122230i
$296$	−14.1543	+	8.17202i	−0.822705	+	0.474989i
$297$		0			0
$298$	9.68289	−	16.7713i	0.560915	−	0.971533i
$299$	0.0817733	−	0.141636i	0.00472907	−	0.00819100i
$300$		0			0
$301$	31.7301	+	12.2387i	1.82889	+	0.705429i
$302$	−6.87261	−	3.96790i	−0.395474	−	0.228327i
$303$		0			0
$304$			1.94886i			0.111775i
$305$	−2.34116	−	1.35167i	−0.134054	−	0.0773963i
$306$		0			0
$307$			13.2098i			0.753925i	0.926229	+	0.376962i	$0.123031\pi$
$307$			13.2098i			0.753925i	−0.926229	+	0.376962i	$0.876969\pi$
$308$	1.02599	−	2.65999i	0.0584614	−	0.151567i
$309$		0			0
$310$	−7.68185			−0.436300
$311$	−10.2687	−	17.7859i	−0.582283	−	1.00854i	−0.995208	−	0.0977785i	$-0.968826\pi$
$311$	−10.2687	−	17.7859i	−0.582283	−	1.00854i	0.412925	−	0.910765i	$-0.364507\pi$
$312$		0			0
$313$	14.2976	+	8.25471i	0.808147	+	0.466584i	0.846312	−	0.532688i	$-0.178818\pi$
$313$	14.2976	+	8.25471i	0.808147	+	0.466584i	−0.0381649	+	0.999271i	$0.512151\pi$
$314$	12.0629			0.680746
$315$		0			0
$316$	1.39133			0.0782685
$317$	−8.11112	−	4.68296i	−0.455566	−	0.263021i	0.254612	−	0.967043i	$-0.418052\pi$
$317$	−8.11112	−	4.68296i	−0.455566	−	0.263021i	−0.710178	+	0.704022i	$0.751386\pi$
$318$		0			0
$319$	−0.417133	−	0.722496i	−0.0233550	−	0.0404520i
$320$	−5.10995			−0.285655
$321$		0			0
$322$	−0.0344703	−	0.219929i	−0.00192095	−	0.0122562i
$323$			2.34708i			0.130595i
$324$		0			0
$325$	11.1797	+	6.45459i	0.620137	+	0.358036i
$326$		−	17.3731i		−	0.962205i
$327$		0			0
$328$	−17.0356	−	9.83548i	−0.940631	−	0.543074i
$329$	0.395560	+	2.52378i	0.0218079	+	0.139140i
$330$		0			0
$331$	−14.4220	+	24.9796i	−0.792702	+	1.37300i	0.131586	+	0.991305i	$0.457993\pi$
$331$	−14.4220	+	24.9796i	−0.792702	+	1.37300i	−0.924288	+	0.381696i	$0.875340\pi$
$332$	−1.20856	+	2.09328i	−0.0663282	+	0.114884i
$333$		0			0
$334$	−21.9247	+	12.6582i	−1.19967	+	0.692627i
$335$	1.63003	+	2.82329i	0.0890579	+	0.154253i
$336$		0			0
$337$	−6.26205	+	10.8462i	−0.341116	+	0.590829i	−0.984640	−	0.174596i	$-0.944138\pi$
$337$	−6.26205	+	10.8462i	−0.341116	+	0.590829i	0.643525	+	0.765425i	$0.277471\pi$
$338$			6.62092i			0.360130i
$339$		0			0
$340$	1.17431			0.0636860
$341$	−12.5988	−	21.8218i	−0.682266	−	1.18172i
$342$		0			0
$343$	−8.32817	−	16.5421i	−0.449679	−	0.893190i
$344$	−28.9072	+	16.6896i	−1.55857	+	0.899841i
$345$		0			0
$346$	2.23996	−	1.29324i	0.120421	−	0.0695250i
$347$	−24.8740	+	14.3610i	−1.33531	+	0.770939i	−0.986107	−	0.166109i	$-0.946880\pi$
$347$	−24.8740	+	14.3610i	−1.33531	+	0.770939i	−0.349199	+	0.937049i	$0.613546\pi$
$348$		0			0
$349$	11.0854	−	6.40017i	0.593389	−	0.342593i	−0.173048	−	0.984913i	$-0.555361\pi$
$349$	11.0854	−	6.40017i	0.593389	−	0.342593i	0.766436	+	0.642320i	$0.222028\pi$
$350$	17.3596	−	2.72083i	0.927911	−	0.145435i
$351$		0			0
$352$	3.02636	+	5.24181i	0.161305	+	0.279389i
$353$	26.9982			1.43697			0.718485	−	0.695542i	$-0.244836\pi$
$353$	26.9982			1.43697			0.718485	+	0.695542i	$0.244836\pi$
$354$		0			0
$355$			2.72187i			0.144462i
$356$	2.19274	−	3.79793i	0.116215	−	0.201290i
$357$		0			0
$358$	−10.8233	−	18.7465i	−0.572030	−	0.990785i
$359$	24.2669	−	14.0105i	1.28076	−	0.739445i	0.303770	−	0.952745i	$-0.401755\pi$
$359$	24.2669	−	14.0105i	1.28076	−	0.739445i	0.976987	+	0.213300i	$0.0684212\pi$
$360$		0			0
$361$	−9.40547	+	16.2908i	−0.495025	+	0.857408i
$362$	3.64799	−	6.31851i	0.191734	−	0.332093i
$363$		0			0
$364$	−1.36758	−	1.69440i	−0.0716809	−	0.0888107i
$365$	−5.47724	−	3.16228i	−0.286692	−	0.165522i
$366$		0			0
$367$		−	33.4382i		−	1.74546i	−0.488202	−	0.872731i	$-0.662347\pi$
$367$		−	33.4382i		−	1.74546i	0.488202	−	0.872731i	$-0.337653\pi$
$368$	0.216281	+	0.124870i	0.0112744	+	0.00650928i
$369$		0			0
$370$		−	7.37430i		−	0.383372i
$371$	19.5108	−	3.05799i	1.01295	−	0.158763i
$372$		0			0
$373$	−7.96805			−0.412570			−0.206285	−	0.978492i	$-0.566137\pi$
$373$	−7.96805			−0.412570			−0.206285	+	0.978492i	$0.566137\pi$
$374$	15.6639	+	27.1307i	0.809961	+	1.40289i
$375$		0			0
$376$	−2.17139	−	1.25365i	−0.111981	−	0.0646522i
$377$	−0.637169			−0.0328159
$378$		0			0
$379$	3.88714			0.199669			0.0998345	−	0.995004i	$-0.468169\pi$
$379$	3.88714			0.199669			0.0998345	+	0.995004i	$0.468169\pi$
$380$	−0.0819169	−	0.0472948i	−0.00420225	−	0.00242617i
$381$		0			0
$382$	−2.37244	−	4.10918i	−0.121384	−	0.210244i
$383$	−12.6830			−0.648071			−0.324036	−	0.946045i	$-0.605040\pi$
$383$	−12.6830			−0.648071			−0.324036	+	0.946045i	$0.605040\pi$
$384$		0			0
$385$	−4.95495	−	6.13905i	−0.252528	−	0.312875i
$386$			9.07592i			0.461952i
$387$		0			0
$388$	0.348133	+	0.200995i	0.0176738	+	0.0102040i
$389$			20.5614i			1.04250i	0.853403	+	0.521252i	$0.174535\pi$
$389$			20.5614i			1.04250i	−0.853403	+	0.521252i	$0.825465\pi$
$390$		0			0
$391$	0.260474	+	0.150385i	0.0131727	+	0.00760529i
$392$	17.7680	+	3.83658i	0.897418	+	0.193776i
$393$		0			0
$394$	−10.6388	+	18.4269i	−0.535973	+	0.928332i
$395$	1.92503	−	3.33424i	0.0968586	−	0.167764i
$396$		0			0
$397$	12.9646	−	7.48513i	0.650676	−	0.375668i	−0.138039	−	0.990427i	$-0.544080\pi$
$397$	12.9646	−	7.48513i	0.650676	−	0.375668i	0.788715	+	0.614759i	$0.210747\pi$
$398$	5.96552	+	10.3326i	0.299025	+	0.517926i
$399$		0			0
$400$	−9.85630	+	17.0716i	−0.492815	+	0.853580i
$401$		−	10.3164i		−	0.515178i	−0.966255	−	0.257589i	$-0.917072\pi$
$401$		−	10.3164i		−	0.515178i	0.966255	−	0.257589i	$-0.0829280\pi$
$402$		0			0
$403$	−19.2447			−0.958647
$404$	−2.24616	−	3.89047i	−0.111751	−	0.193558i
$405$		0			0
$406$	−0.674892	+	0.544719i	−0.0334943	+	0.0270340i
$407$	20.9482	−	12.0944i	1.03836	−	0.599499i
$408$		0			0
$409$	−16.0387	+	9.25995i	−0.793063	+	0.457875i	−0.841040	−	0.540973i	$-0.818056\pi$
$409$	−16.0387	+	9.25995i	−0.793063	+	0.457875i	0.0479769	+	0.998848i	$0.484723\pi$
$410$	7.68631	−	4.43769i	0.379600	−	0.219162i
$411$		0			0
$412$	−4.09543	+	2.36450i	−0.201767	+	0.116490i
$413$	7.71252	+	2.97482i	0.379508	+	0.146381i
$414$		0			0
$415$	3.34429	+	5.79247i	0.164165	+	0.284341i
$416$	4.62275			0.226649
$417$		0			0
$418$		−	2.52342i		−	0.123424i
$419$	−6.37677	+	11.0449i	−0.311526	+	0.539578i	−0.978693	−	0.205330i	$-0.934173\pi$
$419$	−6.37677	+	11.0449i	−0.311526	+	0.539578i	0.667167	+	0.744908i	$0.267507\pi$
$420$		0			0
$421$	6.78793	+	11.7570i	0.330824	+	0.573003i	0.982674	−	0.185345i	$-0.0593402\pi$
$421$	6.78793	+	11.7570i	0.330824	+	0.573003i	−0.651850	+	0.758348i	$0.726007\pi$
$422$	−6.74347	+	3.89334i	−0.328267	+	0.189525i
$423$		0			0
$424$	−9.69173	+	16.7866i	−0.470672	+	0.815227i
$425$	−11.8703	+	20.5599i	−0.575793	+	0.997303i
$426$		0			0
$427$	−9.10724	+	1.42741i	−0.440730	+	0.0690772i
$428$	0.943342	+	0.544639i	0.0455982	+	0.0263261i
$429$		0			0
$430$		−	15.0604i		−	0.726277i
$431$	−31.3069	−	18.0750i	−1.50800	−	0.870643i	−0.999957	−	0.00931038i	$-0.997036\pi$
$431$	−31.3069	−	18.0750i	−1.50800	−	0.870643i	−0.508041	−	0.861333i	$-0.669630\pi$
$432$		0			0
$433$			33.0085i			1.58629i	0.609034	+	0.793144i	$0.291557\pi$
$433$			33.0085i			1.58629i	−0.609034	+	0.793144i	$0.708443\pi$
$434$	−20.3841	+	16.4524i	−0.978466	+	0.789740i
$435$		0			0
$436$	0.719215			0.0344442
$437$	−0.0121133	−	0.0209809i	−0.000579459	−	0.00100365i
$438$		0			0
$439$	26.4673	+	15.2809i	1.26321	+	0.729317i	0.973695	−	0.227856i	$-0.0731714\pi$
$439$	26.4673	+	15.2809i	1.26321	+	0.729317i	0.289519	+	0.957172i	$0.406505\pi$
$440$	7.74318			0.369141
$441$		0			0
$442$	23.9266			1.13807
$443$	17.9290	+	10.3513i	0.851833	+	0.491806i	0.861269	−	0.508150i	$-0.169670\pi$
$443$	17.9290	+	10.3513i	0.851833	+	0.491806i	−0.00943615	+	0.999955i	$0.503004\pi$
$444$		0			0
$445$	−6.06767	−	10.5095i	−0.287635	−	0.498199i
$446$	−6.62300			−0.313608
$447$		0			0
$448$	−13.5594	+	10.9441i	−0.640622	+	0.517059i
$449$			6.40243i			0.302150i	0.988522	+	0.151075i	$0.0482734\pi$
$449$			6.40243i			0.302150i	−0.988522	+	0.151075i	$0.951727\pi$
$450$		0			0
$451$	25.2123	+	14.5563i	1.18720	+	0.685431i
$452$			3.16977i			0.149093i
$453$		0			0
$454$	12.6514	+	7.30428i	0.593759	+	0.342807i
$455$	−5.95269	+	0.932986i	−0.279067	+	0.0437390i
$456$		0			0
$457$	1.57340	−	2.72521i	0.0736007	−	0.127480i	−0.826876	−	0.562384i	$-0.809884\pi$
$457$	1.57340	−	2.72521i	0.0736007	−	0.127480i	0.900477	+	0.434904i	$0.143218\pi$
$458$	−6.68454	+	11.5780i	−0.312348	+	0.541003i
$459$		0			0
$460$	−0.0104974	+	0.00606065i	−0.000489442	+	0.000282579i
$461$	−7.44225	−	12.8904i	−0.346620	−	0.600364i	0.639026	−	0.769185i	$-0.279337\pi$
$461$	−7.44225	−	12.8904i	−0.346620	−	0.600364i	−0.985647	+	0.168821i	$0.946004\pi$
$462$		0			0
$463$	13.3616	−	23.1429i	0.620964	−	1.07554i	−0.368342	−	0.929690i	$-0.620075\pi$
$463$	13.3616	−	23.1429i	0.620964	−	1.07554i	0.989307	−	0.145851i	$-0.0465921\pi$
$464$		−	0.972971i		−	0.0451691i
$465$		0			0
$466$	19.4618			0.901552
$467$	12.3967	+	21.4717i	0.573650	+	0.993591i	0.996187	+	0.0872454i	$0.0278064\pi$
$467$	12.3967	+	21.4717i	0.573650	+	0.993591i	−0.422537	+	0.906346i	$0.638860\pi$
$468$		0			0
$469$	10.3720	+	4.00063i	0.478936	+	0.184732i
$470$	0.979714	−	0.565638i	0.0451908	−	0.0260909i
$471$		0			0
$472$	−7.02636	+	4.05667i	−0.323414	+	0.186723i
$473$	42.7821	−	24.7003i	1.96712	−	1.13572i
$474$		0			0
$475$	1.65608	−	0.956138i	0.0759861	−	0.0438706i
$476$	3.11608	−	2.51505i	0.142825	−	0.115277i
$477$		0			0
$478$	3.64801	+	6.31855i	0.166856	+	0.289004i
$479$	−12.5271			−0.572377			−0.286189	−	0.958173i	$-0.592388\pi$
$479$	−12.5271			−0.572377			−0.286189	+	0.958173i	$0.592388\pi$
$480$		0			0
$481$		−	18.4742i		−	0.842352i
$482$	−7.57587	+	13.1218i	−0.345071	+	0.597681i
$483$		0			0
$484$	−0.528540	−	0.915459i	−0.0240246	−	0.0416118i
$485$	0.963343	−	0.556187i	0.0437432	−	0.0252551i
$486$		0			0
$487$	1.69748	−	2.94012i	0.0769202	−	0.133230i	−0.824999	−	0.565133i	$-0.808825\pi$
$487$	1.69748	−	2.94012i	0.0769202	−	0.133230i	0.901920	+	0.431904i	$0.142158\pi$
$488$	4.52390	−	7.83562i	0.204787	−	0.354702i
$489$		0			0
$490$	−5.50750	+	6.07721i	−0.248804	+	0.274540i
$491$	−0.780171	−	0.450432i	−0.0352086	−	0.0203277i	0.482292	−	0.876010i	$-0.339804\pi$
$491$	−0.780171	−	0.450432i	−0.0352086	−	0.0203277i	−0.517501	+	0.855683i	$0.673138\pi$
$492$		0			0
$493$		−	1.17178i		−	0.0527745i
$494$	−1.66905	−	0.963629i	−0.0750943	−	0.0433557i
$495$		0			0
$496$		−	29.3871i		−	1.31952i
$497$	5.82948	+	7.22257i	0.261488	+	0.323976i
$498$		0			0
$499$	21.8688			0.978984			0.489492	−	0.872008i	$-0.337182\pi$
$499$	21.8688			0.978984			0.489492	+	0.872008i	$0.337182\pi$
$500$	−1.02225	−	1.77058i	−0.0457162	−	0.0791829i
$501$		0			0
$502$	−10.4387	−	6.02681i	−0.465904	−	0.268990i
$503$	−42.9876			−1.91672			−0.958362	−	0.285557i	$-0.907821\pi$
$503$	−42.9876			−1.91672			−0.958362	+	0.285557i	$0.907821\pi$
$504$		0			0
$505$	−12.4310			−0.553173
$506$	−0.280044	−	0.161684i	−0.0124495	−	0.00718771i
$507$		0			0
$508$	0.372436	+	0.645079i	0.0165242	+	0.0286207i
$509$	30.0832			1.33342			0.666708	−	0.745319i	$-0.267703\pi$
$509$	30.0832			1.33342			0.666708	+	0.745319i	$0.267703\pi$
$510$		0			0
$511$	−21.3068	+	3.33948i	−0.942556	+	0.147730i
$512$		−	16.2193i		−	0.716799i
$513$		0			0
$514$	−3.50785	−	2.02526i	−0.154725	−	0.0893304i
$515$			13.0859i			0.576635i
$516$		0			0
$517$	3.21362	+	1.85538i	0.141335	+	0.0815997i
$518$	−15.7937	−	19.5680i	−0.693935	−	0.859767i
$519$		0			0
$520$	2.95692	−	5.12153i	0.129669	−	0.224594i
$521$	−6.00837	+	10.4068i	−0.263231	+	0.455930i	−0.967099	−	0.254401i	$-0.918122\pi$
$521$	−6.00837	+	10.4068i	−0.263231	+	0.455930i	0.703867	+	0.710331i	$0.251455\pi$
$522$		0			0
$523$	−16.1185	+	9.30602i	−0.704813	+	0.406924i	−0.809137	−	0.587620i	$-0.800065\pi$
$523$	−16.1185	+	9.30602i	−0.704813	+	0.406924i	0.104325	+	0.994543i	$0.466732\pi$
$524$	1.15466	+	1.99993i	0.0504417	+	0.0873675i
$525$		0			0
$526$	−17.6952	+	30.6490i	−0.771548	+	1.33636i
$527$		−	35.3919i		−	1.54169i
$528$		0			0
$529$	22.9969			0.999865
$530$	−4.37283	−	7.57397i	−0.189944	−	0.328992i
$531$		0			0
$532$	−0.318662	+	0.0499449i	−0.0138157	+	0.00216539i
$533$	19.2559	−	11.1174i	0.834064	−	0.481547i
$534$		0			0
$535$	2.61039	−	1.50711i	0.112857	−	0.0651580i
$536$	−9.44926	+	5.45554i	−0.408146	+	0.235643i
$537$		0			0
$538$	−5.20379	+	3.00441i	−0.224351	+	0.129529i
$539$	−26.2963	−	5.67806i	−1.13266	−	0.244572i
$540$		0			0
$541$	−21.1242	−	36.5882i	−0.908201	−	1.57305i	−0.816562	−	0.577258i	$-0.804123\pi$
$541$	−21.1242	−	36.5882i	−0.908201	−	1.57305i	−0.0916391	−	0.995792i	$-0.529211\pi$
$542$	−18.8849			−0.811176
$543$		0			0
$544$			8.50145i			0.364497i
$545$	0.995095	−	1.72356i	0.0426252	−	0.0738290i
$546$		0			0
$547$	−6.92349	−	11.9918i	−0.296027	−	0.512734i	0.679196	−	0.733957i	$-0.262329\pi$
$547$	−6.92349	−	11.9918i	−0.296027	−	0.512734i	−0.975223	+	0.221223i	$0.928995\pi$
$548$	−4.20741	+	2.42915i	−0.179732	+	0.103768i
$549$		0			0
$550$	12.7621	−	22.1046i	0.544178	−	0.942544i
$551$	−0.0471929	+	0.0817405i	−0.00201049	+	0.00348226i
$552$		0			0
$553$	−2.03289	−	12.9704i	−0.0864474	−	0.551557i
$554$	25.7514	+	14.8676i	1.09407	+	0.631664i
$555$		0			0
$556$		−	1.77317i		−	0.0751992i
$557$	27.2305	+	15.7215i	1.15379	+	0.666143i	0.949809	−	0.312831i	$-0.101277\pi$
$557$	27.2305	+	15.7215i	1.15379	+	0.666143i	0.203985	+	0.978974i	$0.434611\pi$
$558$		0			0
$559$		−	37.7296i		−	1.59579i
$560$	−1.42469	−	9.08989i	−0.0602041	−	0.384118i
$561$		0			0
$562$	12.2662			0.517419
$563$	−17.0829	−	29.5884i	−0.719956	−	1.24700i	−0.961017	−	0.276491i	$-0.910828\pi$
$563$	−17.0829	−	29.5884i	−0.719956	−	1.24700i	0.241060	−	0.970510i	$-0.422505\pi$
$564$		0			0
$565$	7.59616	+	4.38565i	0.319573	+	0.184506i
$566$	−2.02950			−0.0853063
$567$		0			0
$568$	−9.10981			−0.382239
$569$	−19.6652	−	11.3537i	−0.824407	−	0.475972i	0.0275266	−	0.999621i	$-0.491237\pi$
$569$	−19.6652	−	11.3537i	−0.824407	−	0.475972i	−0.851934	+	0.523649i	$0.824570\pi$
$570$		0			0
$571$	5.29931	+	9.17867i	0.221769	+	0.384116i	0.955345	−	0.295492i	$-0.0954835\pi$
$571$	5.29931	+	9.17867i	0.221769	+	0.384116i	−0.733576	+	0.679607i	$0.762150\pi$
$572$	−3.16293			−0.132249
$573$		0			0
$574$	10.8916	−	28.2375i	0.454606	−	1.17861i
$575$		−	0.245051i		−	0.0102193i
$576$		0			0
$577$	−12.6222	−	7.28745i	−0.525471	−	0.303381i	0.213699	−	0.976899i	$-0.431449\pi$
$577$	−12.6222	−	7.28745i	−0.525471	−	0.303381i	−0.739170	+	0.673519i	$0.764782\pi$
$578$			18.3304i			0.762444i
$579$		0			0
$580$	0.0408971	+	0.0236120i	0.00169816	+	0.000980434i
$581$	21.2800	+	8.20800i	0.882845	+	0.340525i
$582$		0			0
$583$	14.3436	−	24.8438i	0.594050	−	1.02893i
$584$	10.5838	−	18.3318i	0.437963	−	0.758574i
$585$		0			0
$586$	−27.8035	+	16.0523i	−1.14855	+	0.663116i
$587$	15.0927	+	26.1414i	0.622944	+	1.07897i	0.988935	+	0.148352i	$0.0473969\pi$
$587$	15.0927	+	26.1414i	0.622944	+	1.07897i	−0.365991	+	0.930619i	$0.619270\pi$
$588$		0			0
$589$	−1.42539	+	2.46884i	−0.0587321	+	0.101727i
$590$		−	3.66068i		−	0.150708i
$591$		0			0
$592$	28.2105			1.15945
$593$	−15.2911	−	26.4850i	−0.627930	−	1.08761i	−0.987966	−	0.154669i	$-0.950569\pi$
$593$	−15.2911	−	26.4850i	−0.627930	−	1.08761i	0.360036	−	0.932938i	$-0.382764\pi$
$594$		0			0
$595$	−1.71580	−	10.9473i	−0.0703411	−	0.448794i
$596$	−3.11400	+	1.79787i	−0.127554	+	0.0736435i
$597$		0			0
$598$	−0.213883	+	0.123485i	−0.00874633	+	0.00504970i
$599$	−2.33872	+	1.35026i	−0.0955573	+	0.0551701i	−0.547017	−	0.837121i	$-0.684237\pi$
$599$	−2.33872	+	1.35026i	−0.0955573	+	0.0551701i	0.451460	+	0.892291i	$0.350903\pi$
$600$		0			0
$601$	−21.0197	+	12.1357i	−0.857411	+	0.495026i	−0.863144	−	0.504957i	$-0.831508\pi$
$601$	−21.0197	+	12.1357i	−0.857411	+	0.495026i	0.00573343	+	0.999984i	$0.498175\pi$
$602$	−32.2552	−	39.9633i	−1.31462	−	1.62878i
$603$		0			0
$604$	0.736739	+	1.27607i	0.0299775	+	0.0519225i
$605$	−2.92512			−0.118923
$606$		0			0
$607$		−	21.4181i		−	0.869334i	−0.900591	−	0.434667i	$-0.856866\pi$
$607$		−	21.4181i		−	0.869334i	0.900591	−	0.434667i	$-0.143134\pi$
$608$	0.342391	−	0.593039i	0.0138858	−	0.0240509i
$609$		0			0
$610$	2.04115	+	3.53537i	0.0826437	+	0.143143i
$611$	2.45439	−	1.41705i	0.0992942	−	0.0573275i
$612$		0			0
$613$	−2.95306	+	5.11485i	−0.119273	+	0.206587i	−0.919480	−	0.393137i	$-0.871390\pi$
$613$	−2.95306	+	5.11485i	−0.119273	+	0.206587i	0.800207	+	0.599724i	$0.204723\pi$
$614$	9.97404	−	17.2756i	0.402520	−	0.697185i
$615$		0			0
$616$	20.5468	−	16.5837i	0.827854	−	0.668177i
$617$	1.19246	+	0.688465i	0.0480065	+	0.0277166i	0.523811	−	0.851834i	$-0.324510\pi$
$617$	1.19246	+	0.688465i	0.0480065	+	0.0277166i	−0.475805	+	0.879551i	$0.657843\pi$
$618$		0			0
$619$			33.8233i			1.35947i	0.733457	+	0.679736i	$0.237906\pi$
$619$			33.8233i			1.35947i	−0.733457	+	0.679736i	$0.762094\pi$
$620$	1.23523	+	0.713163i	0.0496082	+	0.0286413i
$621$		0			0
$622$			31.0133i			1.24352i
$623$	−38.6092	−	14.8921i	−1.54685	−	0.596640i
$624$		0			0
$625$	16.3326			0.653305
$626$	−12.4654	−	21.5907i	−0.498218	−	0.862938i
$627$		0			0
$628$	−1.93969	−	1.11988i	−0.0774022	−	0.0446882i
$629$	33.9749			1.35467
$630$		0			0
$631$	−25.0205			−0.996049			−0.498024	−	0.867163i	$-0.665941\pi$
$631$	−25.0205			−0.996049			−0.498024	+	0.867163i	$0.665941\pi$
$632$	11.1594	+	6.44287i	0.443896	+	0.256283i
$633$		0			0
$634$	7.07171	+	12.2486i	0.280853	+	0.486452i
$635$	2.06119			0.0817958
$636$		0			0
$637$	−13.7975	+	15.2247i	−0.546676	+	0.603225i
$638$			1.25982i			0.0498768i
$639$		0			0
$640$	8.79916	+	5.08020i	0.347817	+	0.200812i
$641$			10.6830i			0.421952i	0.977491	+	0.210976i	$0.0676642\pi$
$641$			10.6830i			0.421952i	−0.977491	+	0.210976i	$0.932336\pi$
$642$		0			0
$643$	−38.1128	−	22.0044i	−1.50302	−	0.867771i	−0.999994	−	0.00350106i	$-0.998886\pi$
$643$	−38.1128	−	22.0044i	−1.50302	−	0.867771i	−0.503029	−	0.864270i	$-0.667781\pi$
$644$	−0.0148749	+	0.0385646i	−0.000586152	+	0.00151966i
$645$		0			0
$646$	1.77216	−	3.06946i	0.0697246	−	0.120766i
$647$	−23.5043	+	40.7107i	−0.924050	+	1.60050i	−0.130968	+	0.991387i	$0.541808\pi$
$647$	−23.5043	+	40.7107i	−0.924050	+	1.60050i	−0.793082	+	0.609115i	$0.791525\pi$
$648$		0			0
$649$	10.3989	−	6.00380i	0.408192	−	0.235670i
$650$	−9.74704	−	16.8824i	−0.382310	−	0.662181i
$651$		0			0
$652$	−1.61287	+	2.79357i	−0.0631648	+	0.109405i
$653$			33.9388i			1.32813i	0.747677	+	0.664063i	$0.231169\pi$
$653$			33.9388i			1.32813i	−0.747677	+	0.664063i	$0.768831\pi$
$654$		0			0
$655$	6.39029			0.249689
$656$	16.9765	+	29.4041i	0.662820	+	1.14804i
$657$		0			0
$658$	1.38827	−	3.59921i	0.0541203	−	0.140312i
$659$	1.36652	−	0.788962i	0.0532322	−	0.0307336i	−0.473148	−	0.880983i	$-0.656882\pi$
$659$	1.36652	−	0.788962i	0.0532322	−	0.0307336i	0.526380	+	0.850249i	$0.323549\pi$
$660$		0			0
$661$	2.08470	−	1.20360i	0.0810854	−	0.0468147i	−0.458909	−	0.888483i	$-0.651760\pi$
$661$	2.08470	−	1.20360i	0.0810854	−	0.0468147i	0.539994	+	0.841669i	$0.318426\pi$
$662$	37.7215	−	21.7785i	1.46609	−	0.846446i
$663$		0			0
$664$	−19.3868	+	11.1930i	−0.752354	+	0.434372i
$665$	−0.321205	+	0.832756i	−0.0124558	+	0.0322929i
$666$		0			0
$667$	0.00604760	+	0.0104747i	0.000234164	+	0.000405584i
$668$	4.70062			0.181873
$669$		0			0
$670$		−	4.92299i		−	0.190192i
$671$	−6.69529	+	11.5966i	−0.258469	+	0.447681i
$672$		0			0
$673$	12.1767	+	21.0906i	0.469377	+	0.812984i	0.999387	−	0.0350069i	$-0.0111453\pi$
$673$	12.1767	+	21.0906i	0.469377	+	0.812984i	−0.530010	+	0.847991i	$0.677812\pi$
$674$	16.3788	−	9.45629i	0.630887	−	0.364243i
$675$		0			0
$676$	0.614668	−	1.06464i	0.0236411	−	0.0409476i
$677$	4.83847	−	8.38048i	0.185958	−	0.322088i	−0.757941	−	0.652323i	$-0.773795\pi$
$677$	4.83847	−	8.38048i	0.185958	−	0.322088i	0.943899	+	0.330235i	$0.107128\pi$
$678$		0			0
$679$	1.36507	−	3.53907i	0.0523865	−	0.135817i
$680$	9.41873	+	5.43791i	0.361192	+	0.208534i
$681$		0			0
$682$			38.0509i			1.45704i
$683$	−18.6341	−	10.7584i	−0.713012	−	0.411658i	0.0991632	−	0.995071i	$-0.468383\pi$
$683$	−18.6341	−	10.7584i	−0.713012	−	0.411658i	−0.812175	+	0.583413i	$0.801717\pi$
$684$		0			0
$685$			13.4437i			0.513659i
$686$	−1.59867	+	27.9216i	−0.0610374	+	1.06605i
$687$		0			0
$688$	57.6139			2.19651
$689$	−10.9549	−	18.9744i	−0.417348	−	0.722868i
$690$		0			0
$691$	−25.4980	−	14.7213i	−0.969989	−	0.560023i	−0.0707559	−	0.997494i	$-0.522541\pi$
$691$	−25.4980	−	14.7213i	−0.969989	−	0.560023i	−0.899233	+	0.437470i	$0.855874\pi$
$692$	−0.480244			−0.0182561
$693$		0			0
$694$	43.3730			1.64642
$695$	−4.24929	−	2.45333i	−0.161185	−	0.0930602i
$696$		0			0
$697$	20.4454	+	35.4124i	0.774423	+	1.34134i
$698$	−19.3297			−0.731641
$699$		0			0
$700$	−3.04400	−	1.17411i	−0.115053	−	0.0443773i
$701$			40.4325i			1.52712i	0.645740	+	0.763558i	$0.276549\pi$
$701$			40.4325i			1.52712i	−0.645740	+	0.763558i	$0.723451\pi$
$702$		0			0
$703$	−2.37000	−	1.36832i	−0.0893863	−	0.0516072i
$704$			25.3114i			0.953958i
$705$		0			0
$706$	−35.3077	−	20.3849i	−1.32882	−	0.767197i
$707$	−32.9861	+	26.6238i	−1.24057	+	1.00129i
$708$		0			0
$709$	7.95114	−	13.7718i	0.298611	−	0.517210i	−0.677207	−	0.735792i	$-0.736810\pi$
$709$	7.95114	−	13.7718i	0.298611	−	0.517210i	0.975818	+	0.218582i	$0.0701433\pi$
$710$	2.05514	−	3.55960i	0.0771280	−	0.133590i
$711$		0			0
$712$	35.1743	−	20.3079i	1.31821	−	0.761070i
$713$	0.182658	+	0.316373i	0.00684061	+	0.0118483i
$714$		0			0
$715$	−4.37619	+	7.57978i	−0.163660	+	0.283468i
$716$			4.01923i			0.150206i
$717$		0			0
$718$	−42.3143			−1.57916
$719$	13.0488	+	22.6012i	0.486638	+	0.842883i	0.999882	−	0.0153605i	$-0.00488959\pi$
$719$	13.0488	+	22.6012i	0.486638	+	0.842883i	−0.513244	+	0.858243i	$0.671556\pi$
$720$		0			0
$721$	28.0264	+	34.7239i	1.04376	+	1.29319i
$722$	24.6006	−	14.2032i	0.915539	−	0.528587i
$723$		0			0
$724$	−1.17319	+	0.677340i	−0.0436011	+	0.0251731i
$725$	−0.826800	+	0.477353i	−0.0307066	+	0.0177285i
$726$		0			0
$727$	3.74533	−	2.16237i	0.138907	−	0.0801977i	−0.428936	−	0.903335i	$-0.641111\pi$
$727$	3.74533	−	2.16237i	0.138907	−	0.0801977i	0.567843	+	0.823137i	$0.307778\pi$
$728$	−3.12261	−	19.9231i	−0.115732	−	0.738398i
$729$		0			0
$730$	4.77535	+	8.27115i	0.176744	+	0.306129i
$731$	69.3864			2.56635
$732$		0			0
$733$			42.3174i			1.56303i	0.623886	+	0.781515i	$0.285553\pi$
$733$			42.3174i			1.56303i	−0.623886	+	0.781515i	$0.714447\pi$
$734$	−25.2475	+	43.7299i	−0.931901	+	1.61410i
$735$		0			0
$736$	−0.0438762	−	0.0759958i	−0.00161730	−	0.00280124i
$737$	13.9847	−	8.07409i	0.515135	−	0.297413i
$738$		0			0
$739$	1.62120	−	2.80801i	0.0596369	−	0.103294i	−0.834666	−	0.550757i	$-0.814339\pi$
$739$	1.62120	−	2.80801i	0.0596369	−	0.103294i	0.894302	+	0.447463i	$0.147672\pi$
$740$	−0.684610	+	1.18578i	−0.0251668	+	0.0435901i
$741$		0			0
$742$	−27.8248	−	10.7324i	−1.02148	−	0.393999i
$743$	−5.41770	−	3.12791i	−0.198756	−	0.114752i	0.397319	−	0.917681i	$-0.369941\pi$
$743$	−5.41770	−	3.12791i	−0.198756	−	0.114752i	−0.596075	+	0.802929i	$0.703274\pi$
$744$		0			0
$745$			9.95001i			0.364540i
$746$	10.4205	+	6.01626i	0.381520	+	0.220271i
$747$		0			0
$748$		−	5.81678i		−	0.212682i
$749$	3.69895	−	9.58989i	0.135157	−	0.350407i
$750$		0			0
$751$	−18.9063			−0.689900			−0.344950	−	0.938621i	$-0.612104\pi$
$751$	−18.9063			−0.689900			−0.344950	+	0.938621i	$0.612104\pi$
$752$	2.16386	+	3.74791i	0.0789078	+	0.136672i
$753$		0			0
$754$	0.833277	+	0.481093i	0.0303462	+	0.0175204i
$755$	4.07736			0.148390
$756$		0			0
$757$	−40.7873			−1.48244			−0.741220	−	0.671262i	$-0.765752\pi$
$757$	−40.7873			−1.48244			−0.741220	+	0.671262i	$0.765752\pi$
$758$	−5.08353	−	2.93498i	−0.184642	−	0.106603i
$759$		0			0
$760$	−0.438017	−	0.758668i	−0.0158886	−	0.0275198i
$761$	42.6212			1.54502			0.772508	−	0.635005i	$-0.219002\pi$
$761$	42.6212			1.54502			0.772508	+	0.635005i	$0.219002\pi$
$762$		0			0
$763$	−1.05085	−	6.70473i	−0.0380435	−	0.242728i
$764$			0.881003i			0.0318736i
$765$		0			0
$766$	16.5866	+	9.57627i	0.599298	+	0.346005i
$767$		−	9.17078i		−	0.331138i
$768$		0			0
$769$	−0.932209	−	0.538211i	−0.0336163	−	0.0194084i	0.483098	−	0.875566i	$-0.339512\pi$
$769$	−0.932209	−	0.538211i	−0.0336163	−	0.0194084i	−0.516714	+	0.856158i	$0.672845\pi$
$770$	1.84471	+	11.7698i	0.0664789	+	0.424153i
$771$		0			0
$772$	0.842584	−	1.45940i	0.0303253	−	0.0525249i
$773$	−2.96855	+	5.14169i	−0.106771	+	0.184934i	−0.914461	−	0.404675i	$-0.867385\pi$
$773$	−2.96855	+	5.14169i	−0.106771	+	0.184934i	0.807689	+	0.589609i	$0.200718\pi$
$774$		0			0
$775$	−24.9722	+	14.4177i	−0.897028	+	0.517899i
$776$	1.86150	+	3.22421i	0.0668240	+	0.115742i
$777$		0			0
$778$	15.5248	−	26.8898i	0.556592	−	0.964046i
$779$		−	3.29370i		−	0.118009i
$780$		0			0
$781$	13.4824			0.482437
$782$	−0.227095	−	0.393341i	−0.00812091	−	0.0140658i
$783$		0			0
$784$	−23.2485	−	21.0691i	−0.830303	−	0.752466i
$785$	−5.36746	+	3.09891i	−0.191573	+	0.110605i
$786$		0			0
$787$	−7.65434	+	4.41923i	−0.272848	+	0.157529i	−0.630181	−	0.776448i	$-0.717019\pi$
$787$	−7.65434	+	4.41923i	−0.272848	+	0.157529i	0.357333	+	0.933977i	$0.383686\pi$
$788$	3.42140	−	1.97535i	0.121882	−	0.0703688i
$789$		0			0
$790$	−5.03502	+	2.90697i	−0.179138	+	0.103425i
$791$	29.5495	−	4.63139i	1.05066	−	0.164673i
$792$		0			0
$793$	5.11351	+	8.85687i	0.181586	+	0.314517i
$794$	−22.6065			−0.802275
$795$		0			0
$796$		−	2.21529i		−	0.0785190i
$797$	−19.0123	+	32.9303i	−0.673450	+	1.16645i	0.303469	+	0.952841i	$0.401855\pi$
$797$	−19.0123	+	32.9303i	−0.673450	+	1.16645i	−0.976919	+	0.213609i	$0.931478\pi$
$798$		0			0
$799$	2.60601	+	4.51374i	0.0921940	+	0.159685i
$800$	5.99855	−	3.46326i	0.212081	−	0.122445i
$801$		0			0
$802$	−7.78939	+	13.4916i	−0.275053	+	0.476406i
$803$	−15.6639	+	27.1307i	−0.552767	+	0.957421i
$804$		0			0
$805$	0.0718369	+	0.0890041i	0.00253192	+	0.00313698i
$806$	25.1678	+	14.5307i	0.886499	+	0.511821i
$807$		0			0
$808$		−	41.6054i		−	1.46367i
$809$	−14.6570	−	8.46222i	−0.515312	−	0.297516i	0.219702	−	0.975567i	$-0.429491\pi$
$809$	−14.6570	−	8.46222i	−0.515312	−	0.297516i	−0.735015	+	0.678051i	$0.762825\pi$
$810$		0			0
$811$			26.9840i			0.947536i	0.880650	+	0.473768i	$0.157106\pi$
$811$			26.9840i			0.947536i	−0.880650	+	0.473768i	$0.842894\pi$
$812$	0.159092	−	0.0249351i	0.00558304	−	0.000875049i
$813$		0			0
$814$	−36.5275			−1.28029
$815$	4.46308	+	7.73028i	0.156335	+	0.270780i
$816$		0			0
$817$	−4.84021	−	2.79450i	−0.169338	−	0.0977671i
$818$	27.9668			0.977836
$819$		0			0
$820$	−1.64793			−0.0575484
$821$	−27.7572	−	16.0256i	−0.968732	−	0.559297i	−0.0698823	−	0.997555i	$-0.522262\pi$
$821$	−27.7572	−	16.0256i	−0.968732	−	0.559297i	−0.898849	+	0.438258i	$0.855596\pi$
$822$		0			0
$823$	−10.3974	−	18.0089i	−0.362431	−	0.627749i	0.625929	−	0.779880i	$-0.284720\pi$
$823$	−10.3974	−	18.0089i	−0.362431	−	0.627749i	−0.988360	+	0.152131i	$0.951387\pi$
$824$	−43.7973			−1.52575
$825$		0			0
$826$	−7.84015	−	9.71373i	−0.272794	−	0.337984i
$827$		−	34.0792i		−	1.18505i	−0.805552	−	0.592525i	$-0.798131\pi$
$827$		−	34.0792i		−	1.18505i	0.805552	−	0.592525i	$-0.201869\pi$
$828$		0			0
$829$	−29.3229	−	16.9296i	−1.01843	−	0.587988i	−0.104778	−	0.994496i	$-0.533413\pi$
$829$	−29.3229	−	16.9296i	−1.01843	−	0.587988i	−0.913648	+	0.406507i	$0.866747\pi$
$830$		−	10.1004i		−	0.350589i
$831$		0			0
$832$	16.7416	+	9.66575i	0.580410	+	0.335100i
$833$	−27.9989	−	25.3742i	−0.970106	−	0.879164i
$834$		0			0
$835$	6.50371	−	11.2648i	0.225070	−	0.389833i
$836$	−0.234267	+	0.405763i	−0.00810231	+	0.0140336i
$837$		0			0
$838$	16.6788	−	9.62953i	0.576161	−	0.332647i
$839$	−11.7633	−	20.3747i	−0.406115	−	0.703412i	0.588335	−	0.808617i	$-0.299784\pi$
$839$	−11.7633	−	20.3747i	−0.406115	−	0.703412i	−0.994451	+	0.105205i	$0.966450\pi$
$840$		0			0
$841$	−14.4764	+	25.0739i	−0.499188	+	0.864618i
$842$		−	20.5008i		−	0.706506i
$843$		0			0
$844$	1.44579			0.0497661
$845$	−1.70089	−	2.94603i	−0.0585124	−	0.101347i
$846$		0			0
$847$	−7.76191	+	6.26479i	−0.266702	+	0.215261i
$848$	28.9743	−	16.7283i	0.994983	−	0.574454i
$849$		0			0
$850$	31.0474	−	17.9252i	1.06492	−	0.614831i
$851$	−0.303707	+	0.175345i	−0.0104109	+	0.00601076i
$852$		0			0
$853$	39.7270	−	22.9364i	1.36023	−	0.785328i	0.370574	−	0.928803i	$-0.379161\pi$
$853$	39.7270	−	22.9364i	1.36023	−	0.785328i	0.989654	+	0.143475i	$0.0458277\pi$
$854$	12.9880	+	5.00966i	0.444441	+	0.171427i
$855$		0			0
$856$	5.04414	+	8.73670i	0.172405	+	0.298614i
$857$	−18.2455			−0.623253			−0.311627	−	0.950205i	$-0.600874\pi$
$857$	−18.2455			−0.623253			−0.311627	+	0.950205i	$0.600874\pi$
$858$		0			0
$859$			5.81666i			0.198462i	0.995064	+	0.0992309i	$0.0316382\pi$
$859$			5.81666i			0.198462i	−0.995064	+	0.0992309i	$0.968362\pi$
$860$	−1.39817	+	2.42170i	−0.0476771	+	0.0825792i
$861$		0			0
$862$	27.2950	+	47.2763i	0.929671	+	1.61024i
$863$	27.7060	−	15.9961i	0.943123	−	0.544513i	0.0521854	−	0.998637i	$-0.483381\pi$
$863$	27.7060	−	15.9961i	0.943123	−	0.544513i	0.890938	+	0.454125i	$0.150048\pi$
$864$		0			0
$865$	−0.664458	+	1.15087i	−0.0225922	+	0.0391309i
$866$	24.9230	−	43.1679i	0.846918	−	1.46690i
$867$		0			0
$868$	4.80513	−	0.753125i	0.163097	−	0.0255627i
$869$	−16.5157	−	9.53533i	−0.560256	−	0.323464i
$870$		0			0
$871$		−	12.3332i		−	0.417893i
$872$	5.76857	+	3.33048i	0.195348	+	0.112784i
$873$		0			0
$874$			0.0365846i			0.00123749i
$875$	−15.0123	+	12.1167i	−0.507507	+	0.409619i
$876$		0			0
$877$	−48.3898			−1.63401			−0.817004	−	0.576632i	$-0.804367\pi$
$877$	−48.3898			−1.63401			−0.817004	+	0.576632i	$0.804367\pi$
$878$	−23.0756	−	39.9681i	−0.778763	−	1.34886i
$879$		0			0
$880$	−11.5745	−	6.68253i	−0.390176	−	0.225268i
$881$	−26.6822			−0.898946			−0.449473	−	0.893294i	$-0.648388\pi$
$881$	−26.6822			−0.898946			−0.449473	+	0.893294i	$0.648388\pi$
$882$		0			0
$883$	35.0484			1.17947			0.589737	−	0.807595i	$-0.299231\pi$
$883$	35.0484			1.17947			0.589737	+	0.807595i	$0.299231\pi$
$884$	−3.84736	−	2.22128i	−0.129401	−	0.0747096i
$885$		0			0
$886$	−15.6315	−	27.0745i	−0.525149	−	0.909585i
$887$	−12.9676			−0.435410			−0.217705	−	0.976015i	$-0.569857\pi$
$887$	−12.9676			−0.435410			−0.217705	+	0.976015i	$0.569857\pi$
$888$		0			0
$889$	5.46944	−	4.41449i	0.183439	−	0.148057i
$890$			18.3255i			0.614273i
$891$		0			0
$892$	1.06497	+	0.614862i	0.0356579	+	0.0205871i
$893$		−	0.419822i		−	0.0140488i
$894$		0			0
$895$	9.63184	+	5.56095i	0.321957	+	0.185882i
$896$	34.2292	−	5.36486i	1.14352	−	0.179227i
$897$		0			0
$898$	4.83414	−	8.37298i	0.161317	−	0.279410i
$899$	0.711627	−	1.23257i	0.0237341	−	0.0411086i
$900$		0			0
$901$	34.8948	−	20.1465i	1.16251	−	0.671178i
$902$	−21.9815	−	38.0730i	−0.731902	−	1.26769i
$903$		0			0
$904$	−14.6783	+	25.4236i	−0.488193	+	0.845576i
$905$			3.74863i			0.124609i
$906$		0			0
$907$	−9.12613			−0.303028			−0.151514	−	0.988455i	$-0.548415\pi$
$907$	−9.12613			−0.303028			−0.151514	+	0.988455i	$0.548415\pi$
$908$	−1.35622	−	2.34904i	−0.0450077	−	0.0779557i
$909$		0			0
$910$	8.48926	+	3.27443i	0.281416	+	0.108546i
$911$	−41.5720	+	24.0016i	−1.37734	+	0.795209i	−0.991839	−	0.127498i	$-0.959305\pi$
$911$	−41.5720	+	24.0016i	−1.37734	+	0.795209i	−0.385503	+	0.922707i	$0.625972\pi$
$912$		0			0
$913$	28.6921	−	16.5654i	0.949571	−	0.548235i
$914$	−4.11533	+	2.37599i	−0.136123	+	0.0785906i
$915$		0			0
$916$	2.14973	−	1.24115i	0.0710292	−	0.0410087i
$917$	16.9569	−	13.6862i	0.559965	−	0.451959i
$918$		0			0
$919$	19.8096	+	34.3113i	0.653459	+	1.13182i	0.982278	+	0.187432i	$0.0600163\pi$
$919$	19.8096	+	34.3113i	0.653459	+	1.13182i	−0.328818	+	0.944393i	$0.606650\pi$
$920$	−0.112261			−0.00370112
$921$		0			0
$922$			22.4770i			0.740241i
$923$	5.14856	−	8.91757i	0.169467	−	0.293526i
$924$		0			0
$925$	−13.8405	−	23.9724i	−0.455072	−	0.788208i
$926$	−34.9480	+	20.1772i	−1.14846	+	0.663065i
$927$		0			0
$928$	−0.170939	+	0.296076i	−0.00561136	+	0.00971915i
$929$	11.7897	−	20.4204i	0.386809	−	0.669973i	−0.605209	−	0.796066i	$-0.706911\pi$
$929$	11.7897	−	20.4204i	0.386809	−	0.669973i	0.992018	+	0.126093i	$0.0402439\pi$
$930$		0			0
$931$	0.931201	+	2.89768i	0.0305189	+	0.0949676i
$932$	−3.12944	−	1.80679i	−0.102508	−	0.0591832i
$933$		0			0
$934$		−	37.4403i		−	1.22509i
$935$	−13.9396	−	8.04801i	−0.455872	−	0.263198i
$936$		0			0
$937$		−	52.5144i		−	1.71557i	−0.514007	−	0.857786i	$-0.671840\pi$
$937$		−	52.5144i		−	1.71557i	0.514007	−	0.857786i	$-0.328160\pi$
$938$	−10.5437	−	13.0633i	−0.344263	−	0.426533i
$939$		0			0
$940$	−0.210049			−0.00685105
$941$	24.5713	+	42.5587i	0.801000	+	1.38737i	0.918958	+	0.394354i	$0.129032\pi$
$941$	24.5713	+	42.5587i	0.801000	+	1.38737i	−0.117958	+	0.993019i	$0.537635\pi$
$942$		0			0
$943$	−0.365528	−	0.211038i	−0.0119032	−	0.00687234i
$944$	14.0040			0.455791
$945$		0			0
$946$	−74.5995			−2.42544
$947$	−8.04907	−	4.64713i	−0.261560	−	0.151012i	0.363486	−	0.931600i	$-0.381586\pi$
$947$	−8.04907	−	4.64713i	−0.261560	−	0.151012i	−0.625046	+	0.780588i	$0.714920\pi$
$948$		0			0
$949$	11.9633	+	20.7210i	0.388344	+	0.672632i
$950$	−2.88772			−0.0936899
$951$		0			0
$952$	36.6394	−	5.74262i	1.18749	−	0.186119i
$953$			40.3761i			1.30791i	0.756534	+	0.653955i	$0.226891\pi$
$953$			40.3761i			1.30791i	−0.756534	+	0.653955i	$0.773109\pi$
$954$		0			0
$955$	2.11127	+	1.21894i	0.0683191	+	0.0394440i
$956$		−	1.35469i		−	0.0438137i
$957$		0			0
$958$	16.3827	+	9.45854i	0.529300	+	0.305592i
$959$	28.7928	+	35.6734i	0.929766	+	1.15196i
$960$		0			0
$961$	5.99358	−	10.3812i	0.193341	−	0.334877i
$962$	−13.9489	+	24.1602i	−0.449731	+	0.778957i
$963$		0			0
$964$	2.43638	−	1.40665i	0.0784706	−	0.0453050i
$965$	−2.33157	−	4.03840i	−0.0750560	−	0.130001i
$966$		0			0
$967$	8.78620	−	15.2181i	0.282545	−	0.489383i	−0.689466	−	0.724318i	$-0.742155\pi$
$967$	8.78620	−	15.2181i	0.282545	−	0.489383i	0.972011	+	0.234936i	$0.0754879\pi$
$968$		−	9.79009i		−	0.314665i
$969$		0			0
$970$	−1.67979			−0.0539348
$971$	20.1321	+	34.8697i	0.646068	+	1.11902i	0.984054	+	0.177872i	$0.0569212\pi$
$971$	20.1321	+	34.8697i	0.646068	+	1.11902i	−0.337985	+	0.941151i	$0.609745\pi$
$972$		0			0
$973$	−16.5300	+	2.59080i	−0.529928	+	0.0830573i
$974$	−4.43986	+	2.56336i	−0.142262	+	0.0821353i
$975$		0			0
$976$	−13.5246	+	7.80845i	−0.432913	+	0.249942i
$977$	22.9591	−	13.2555i	0.734527	−	0.424080i	−0.0855487	−	0.996334i	$-0.527264\pi$
$977$	22.9591	−	13.2555i	0.734527	−	0.424080i	0.820076	+	0.572254i	$0.193931\pi$
$978$		0			0
$979$	−52.0573	+	30.0553i	−1.66376	+	0.960572i
$980$	1.44979	−	0.465907i	0.0463119	−	0.0148829i
$981$		0			0
$982$	0.680195	+	1.17813i	0.0217059	+	0.0375957i
$983$	38.2714			1.22067			0.610334	−	0.792144i	$-0.291035\pi$
$983$	38.2714			1.22067			0.610334	+	0.792144i	$0.291035\pi$
$984$		0			0
$985$		−	10.9322i		−	0.348330i
$986$	−0.884752	+	1.53243i	−0.0281762	+	0.0488027i
$987$		0			0
$988$	0.178921	+	0.309901i	0.00569225	+	0.00985926i
$989$	−0.620255	+	0.358105i	−0.0197230	+	0.0113871i
$990$		0			0
$991$	30.4509	−	52.7425i	0.967305	−	1.67542i	0.264016	−	0.964518i	$-0.414953\pi$
$991$	30.4509	−	52.7425i	0.967305	−	1.67542i	0.703289	−	0.710904i	$-0.251714\pi$
$992$	−5.16295	+	8.94250i	−0.163924	+	0.283925i
$993$		0			0
$994$	−2.17030	−	13.8471i	−0.0688377	−	0.439202i
$995$	−5.30881	−	3.06504i	−0.168301	−	0.0971684i
$996$		0			0
$997$			14.4115i			0.456415i	0.973612	+	0.228208i	$0.0732865\pi$
$997$			14.4115i			0.456415i	−0.973612	+	0.228208i	$0.926713\pi$
$998$	−28.5996	−	16.5120i	−0.905306	−	0.522679i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.s.b.17.2		10
3.2	odd	2		63.2.s.b.59.4	yes	10
4.3	odd	2		3024.2.df.b.17.3		10
7.2	even	3		1323.2.i.b.1097.4		10
7.3	odd	6		1323.2.o.c.881.4		10
7.4	even	3		1323.2.o.d.881.4		10
7.5	odd	6		189.2.i.b.152.4		10
7.6	odd	2		1323.2.s.b.962.2		10
9.2	odd	6		189.2.i.b.143.2		10
9.4	even	3		567.2.p.d.80.4		10
9.5	odd	6		567.2.p.c.80.2		10
9.7	even	3		63.2.i.b.38.4	yes	10
12.11	even	2		1008.2.df.b.689.4		10
21.2	odd	6		441.2.i.b.68.2		10
21.5	even	6		63.2.i.b.5.2	✓	10
21.11	odd	6		441.2.o.c.293.2		10
21.17	even	6		441.2.o.d.293.2		10
21.20	even	2		441.2.s.b.374.4		10
28.19	even	6		3024.2.ca.b.2609.3		10
36.7	odd	6		1008.2.ca.b.353.2		10
36.11	even	6		3024.2.ca.b.2033.3		10
63.2	odd	6		1323.2.s.b.656.2		10
63.5	even	6		567.2.p.d.404.4		10
63.11	odd	6		1323.2.o.c.440.4		10
63.16	even	3		441.2.s.b.362.4		10
63.20	even	6		1323.2.i.b.521.2		10
63.25	even	3		441.2.o.d.146.2		10
63.34	odd	6		441.2.i.b.227.4		10
63.38	even	6		1323.2.o.d.440.4		10
63.40	odd	6		567.2.p.c.404.2		10
63.47	even	6	inner	189.2.s.b.89.2		10
63.52	odd	6		441.2.o.c.146.2		10
63.61	odd	6		63.2.s.b.47.4	yes	10
84.47	odd	6		1008.2.ca.b.257.2		10
252.47	odd	6		3024.2.df.b.1601.3		10
252.187	even	6		1008.2.df.b.929.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.2	✓	10	21.5	even	6
63.2.i.b.38.4	yes	10	9.7	even	3
63.2.s.b.47.4	yes	10	63.61	odd	6
63.2.s.b.59.4	yes	10	3.2	odd	2
189.2.i.b.143.2		10	9.2	odd	6
189.2.i.b.152.4		10	7.5	odd	6
189.2.s.b.17.2		10	1.1	even	1	trivial
189.2.s.b.89.2		10	63.47	even	6	inner
441.2.i.b.68.2		10	21.2	odd	6
441.2.i.b.227.4		10	63.34	odd	6
441.2.o.c.146.2		10	63.52	odd	6
441.2.o.c.293.2		10	21.11	odd	6
441.2.o.d.146.2		10	63.25	even	3
441.2.o.d.293.2		10	21.17	even	6
441.2.s.b.362.4		10	63.16	even	3
441.2.s.b.374.4		10	21.20	even	2
567.2.p.c.80.2		10	9.5	odd	6
567.2.p.c.404.2		10	63.40	odd	6
567.2.p.d.80.4		10	9.4	even	3
567.2.p.d.404.4		10	63.5	even	6
1008.2.ca.b.257.2		10	84.47	odd	6
1008.2.ca.b.353.2		10	36.7	odd	6
1008.2.df.b.689.4		10	12.11	even	2
1008.2.df.b.929.4		10	252.187	even	6
1323.2.i.b.521.2		10	63.20	even	6
1323.2.i.b.1097.4		10	7.2	even	3
1323.2.o.c.440.4		10	63.11	odd	6
1323.2.o.c.881.4		10	7.3	odd	6
1323.2.o.d.440.4		10	63.38	even	6
1323.2.o.d.881.4		10	7.4	even	3
1323.2.s.b.656.2		10	63.2	odd	6
1323.2.s.b.962.2		10	7.6	odd	2
3024.2.ca.b.2033.3		10	36.11	even	6
3024.2.ca.b.2609.3		10	28.19	even	6
3024.2.df.b.17.3		10	4.3	odd	2
3024.2.df.b.1601.3		10	252.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30778 - 0.755047i) q^{2} +(0.140193 + 0.242822i) q^{4} +0.775876 q^{5} +(2.05881 - 1.66171i) q^{7} +2.59678i q^{8} +O(q^{10})\)	\(q+(-1.30778 - 0.755047i) q^{2} +(0.140193 + 0.242822i) q^{4} +0.775876 q^{5} +(2.05881 - 1.66171i) q^{7} +2.59678i q^{8} +(-1.01468 - 0.585823i) q^{10} -3.84319i q^{11} +(-2.54198 - 1.46761i) q^{13} +(-3.94715 + 0.618650i) q^{14} +(2.24108 - 3.88166i) q^{16} +(2.69901 - 4.67482i) q^{17} +(-0.376551 + 0.217402i) q^{19} +(0.108773 + 0.188400i) q^{20} +(-2.90179 + 5.02605i) q^{22} +0.0557186i q^{23} -4.39802 q^{25} +(2.21624 + 3.83863i) q^{26} +(0.692131 + 0.266964i) q^{28} +(0.187994 - 0.108538i) q^{29} +(5.67806 - 3.27823i) q^{31} +(-1.36392 + 0.787461i) q^{32} +(-7.05942 + 4.07576i) q^{34} +(1.59739 - 1.28928i) q^{35} +(3.14698 + 5.45073i) q^{37} +0.656595 q^{38} +2.01478i q^{40} +(-3.78757 + 6.56026i) q^{41} +(6.42703 + 11.1319i) q^{43} +(0.933209 - 0.538789i) q^{44} +(0.0420702 - 0.0728677i) q^{46} +(-0.482772 + 0.836186i) q^{47} +(1.47744 - 6.84231i) q^{49} +(5.75164 + 3.32071i) q^{50} -0.822998i q^{52} +(6.46438 + 3.73221i) q^{53} -2.98184i q^{55} +(4.31510 + 5.34629i) q^{56} -0.327806 q^{58} +(1.56219 + 2.70580i) q^{59} +(-3.01744 - 1.74212i) q^{61} -9.90087 q^{62} -6.58603 q^{64} +(-1.97226 - 1.13869i) q^{65} +(2.10088 + 3.63884i) q^{67} +1.51353 q^{68} +(-3.06250 + 0.479996i) q^{70} +3.50812i q^{71} +(-7.05942 - 4.07576i) q^{73} -9.50448i q^{74} +(-0.105580 - 0.0609566i) q^{76} +(-6.38626 - 7.91241i) q^{77} +(2.48110 - 4.29739i) q^{79} +(1.73880 - 3.01169i) q^{80} +(9.90662 - 5.71959i) q^{82} +(4.31033 + 7.46571i) q^{83} +(2.09410 - 3.62708i) q^{85} -19.4108i q^{86} +9.97991 q^{88} +(-7.82041 - 13.5453i) q^{89} +(-7.67222 + 1.20249i) q^{91} +(-0.0135297 + 0.00781136i) q^{92} +(1.26272 - 0.729031i) q^{94} +(-0.292157 + 0.168677i) q^{95} +(1.24162 - 0.716849i) q^{97} +(-7.09843 + 7.83270i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) \) 10 * q + 4 * q^4 + 3 * q^7	\( 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} + 6 q^{13} + 6 q^{14} - 6 q^{16} + 12 q^{17} + 3 q^{19} + 3 q^{20} + 5 q^{22} - 14 q^{25} - 3 q^{26} + 2 q^{28} + 15 q^{29} - 9 q^{31} - 48 q^{32} + 3 q^{34} + 15 q^{35} + 6 q^{37} - 36 q^{38} + 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} - 15 q^{47} - 23 q^{49} - 3 q^{50} + 9 q^{53} + 51 q^{56} - 16 q^{58} + 18 q^{59} + 12 q^{61} - 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 54 q^{68} + 9 q^{70} + 3 q^{73} + 9 q^{76} - 45 q^{77} + 20 q^{79} + 30 q^{80} + 9 q^{82} + 15 q^{83} + 18 q^{85} + 16 q^{88} - 24 q^{89} - 24 q^{91} - 39 q^{92} - 3 q^{94} + 6 q^{97} - 45 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 + 3 * q^7 - 15 * q^10 + 6 * q^13 + 6 * q^14 - 6 * q^16 + 12 * q^17 + 3 * q^19 + 3 * q^20 + 5 * q^22 - 14 * q^25 - 3 * q^26 + 2 * q^28 + 15 * q^29 - 9 * q^31 - 48 * q^32 + 3 * q^34 + 15 * q^35 + 6 * q^37 - 36 * q^38 + 9 * q^41 + 3 * q^43 - 24 * q^44 - 13 * q^46 - 15 * q^47 - 23 * q^49 - 3 * q^50 + 9 * q^53 + 51 * q^56 - 16 * q^58 + 18 * q^59 + 12 * q^61 - 12 * q^62 + 6 * q^64 + 3 * q^65 - 10 * q^67 + 54 * q^68 + 9 * q^70 + 3 * q^73 + 9 * q^76 - 45 * q^77 + 20 * q^79 + 30 * q^80 + 9 * q^82 + 15 * q^83 + 18 * q^85 + 16 * q^88 - 24 * q^89 - 24 * q^91 - 39 * q^92 - 3 * q^94 + 6 * q^97 - 45 * q^98

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