LMFDB - Embedded newform 198.2.l.b.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(17,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("198.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.l (of order $10$, degree $4$, 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:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			35.1
Root			$0.831254 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	198.35
Dual form			198.2.l.b.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-3.29428 + 1.07038i) q^{5} +(-0.740706 + 1.01949i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-3.29428 + 1.07038i) q^{5} +(-0.740706 + 1.01949i) q^{7} +(0.809017 - 0.587785i) q^{8} -3.46382i q^{10} +(-3.28054 + 0.487899i) q^{11} +(-4.41232 - 1.43365i) q^{13} +(-0.740706 - 1.01949i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.51374 + 4.65882i) q^{17} +(1.72232 + 2.37058i) q^{19} +(3.29428 + 1.07038i) q^{20} +(0.549723 - 3.27075i) q^{22} -4.74115i q^{23} +(5.66152 - 4.11333i) q^{25} +(2.72696 - 3.75334i) q^{26} +(1.19849 - 0.389412i) q^{28} +(0.654014 + 0.475169i) q^{29} +(-3.17100 + 9.75934i) q^{31} -1.00000 q^{32} -4.89858 q^{34} +(1.34885 - 4.15134i) q^{35} +(-0.513743 - 0.373256i) q^{37} +(-2.78678 + 0.905480i) q^{38} +(-2.03598 + 2.80229i) q^{40} +(8.87375 - 6.44716i) q^{41} +2.78676i q^{43} +(2.94079 + 1.53354i) q^{44} +(4.50910 + 1.46510i) q^{46} +(2.19910 + 3.02680i) q^{47} +(1.67240 + 5.14710i) q^{49} +(2.16251 + 6.65551i) q^{50} +(2.72696 + 3.75334i) q^{52} +(-5.62328 - 1.82712i) q^{53} +(10.2848 - 5.11870i) q^{55} +1.26016i q^{56} +(-0.654014 + 0.475169i) q^{58} +(-5.43357 + 7.47866i) q^{59} +(10.5409 - 3.42494i) q^{61} +(-8.30179 - 6.03160i) q^{62} +(0.309017 - 0.951057i) q^{64} +16.0700 q^{65} -12.4414 q^{67} +(1.51374 - 4.65882i) q^{68} +(3.53134 + 2.56567i) q^{70} +(-5.59641 + 1.81838i) q^{71} +(-1.65701 + 2.28068i) q^{73} +(0.513743 - 0.373256i) q^{74} -2.93019i q^{76} +(1.93251 - 3.70588i) q^{77} +(-15.7537 - 5.11870i) q^{79} +(-2.03598 - 2.80229i) q^{80} +(3.38947 + 10.4317i) q^{82} +(-0.480018 - 1.47734i) q^{83} +(-9.97340 - 13.7272i) q^{85} +(-2.65036 - 0.861156i) q^{86} +(-2.36723 + 2.32297i) q^{88} +11.4127i q^{89} +(4.72983 - 3.43642i) q^{91} +(-2.78678 + 3.83567i) q^{92} +(-3.55822 + 1.15613i) q^{94} +(-8.21124 - 5.96582i) q^{95} +(4.63464 - 14.2640i) q^{97} -5.41199 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^8	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{8} - 4 q^{11} - 2 q^{16} + 8 q^{17} - 6 q^{22} + 6 q^{25} + 20 q^{26} - 10 q^{28} - 10 q^{29} - 14 q^{31} - 8 q^{32} - 8 q^{34} - 10 q^{35} - 20 q^{38} - 10 q^{40} + 8 q^{41} + 6 q^{44} + 20 q^{46} - 20 q^{47} + 6 q^{49} + 4 q^{50} + 20 q^{52} - 30 q^{53} + 28 q^{55} + 10 q^{58} + 20 q^{59} + 20 q^{61} - 16 q^{62} - 2 q^{64} + 64 q^{65} - 56 q^{67} + 8 q^{68} + 10 q^{70} - 20 q^{71} - 10 q^{73} - 20 q^{79} - 10 q^{80} + 12 q^{82} + 12 q^{83} - 20 q^{86} - 6 q^{88} - 20 q^{92} - 20 q^{94} - 16 q^{95} - 12 q^{97} + 44 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 - 4 * q^11 - 2 * q^16 + 8 * q^17 - 6 * q^22 + 6 * q^25 + 20 * q^26 - 10 * q^28 - 10 * q^29 - 14 * q^31 - 8 * q^32 - 8 * q^34 - 10 * q^35 - 20 * q^38 - 10 * q^40 + 8 * q^41 + 6 * q^44 + 20 * q^46 - 20 * q^47 + 6 * q^49 + 4 * q^50 + 20 * q^52 - 30 * q^53 + 28 * q^55 + 10 * q^58 + 20 * q^59 + 20 * q^61 - 16 * q^62 - 2 * q^64 + 64 * q^65 - 56 * q^67 + 8 * q^68 + 10 * q^70 - 20 * q^71 - 10 * q^73 - 20 * q^79 - 10 * q^80 + 12 * q^82 + 12 * q^83 - 20 * q^86 - 6 * q^88 - 20 * q^92 - 20 * q^94 - 16 * q^95 - 12 * q^97 + 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−3.29428	+	1.07038i	−1.47325	+	0.478688i	−0.932088	−	0.362232i	$-0.882015\pi$
$5$	−3.29428	+	1.07038i	−1.47325	+	0.478688i	−0.541161	+	0.840919i	$0.682015\pi$
$6$		0			0
$7$	−0.740706	+	1.01949i	−0.279961	+	0.385333i	−0.925721	−	0.378208i	$-0.876541\pi$
$7$	−0.740706	+	1.01949i	−0.279961	+	0.385333i	0.645760	+	0.763540i	$0.276541\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$		−	3.46382i		−	1.09535i
$11$	−3.28054	+	0.487899i	−0.989121	+	0.147107i
$11$	−3.28054	+	0.487899i	−0.989121	+	0.147107i
$12$		0			0
$13$	−4.41232	−	1.43365i	−1.22376	−	0.397623i	−0.375308	−	0.926900i	$-0.622463\pi$
$13$	−4.41232	−	1.43365i	−1.22376	−	0.397623i	−0.848449	+	0.529277i	$0.822463\pi$
$14$	−0.740706	−	1.01949i	−0.197962	−	0.272471i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.51374	+	4.65882i	0.367137	+	1.12993i	0.948632	+	0.316381i	$0.102468\pi$
$17$	1.51374	+	4.65882i	0.367137	+	1.12993i	−0.581496	+	0.813550i	$0.697532\pi$
$18$		0			0
$19$	1.72232	+	2.37058i	0.395128	+	0.543848i	0.959513	−	0.281664i	$-0.0908865\pi$
$19$	1.72232	+	2.37058i	0.395128	+	0.543848i	−0.564385	+	0.825512i	$0.690886\pi$
$20$	3.29428	+	1.07038i	0.736624	+	0.239344i
$21$		0			0
$22$	0.549723	−	3.27075i	0.117201	−	0.697326i
$23$		−	4.74115i		−	0.988599i	−0.869292	−	0.494299i	$-0.835425\pi$
$23$		−	4.74115i		−	0.988599i	0.869292	−	0.494299i	$-0.164575\pi$
$24$		0			0
$25$	5.66152	−	4.11333i	1.13230	−	0.822667i
$26$	2.72696	−	3.75334i	0.534801	−	0.736091i
$27$		0			0
$28$	1.19849	−	0.389412i	0.226493	−	0.0735920i
$29$	0.654014	+	0.475169i	0.121447	+	0.0882367i	0.646851	−	0.762617i	$-0.276086\pi$
$29$	0.654014	+	0.475169i	0.121447	+	0.0882367i	−0.525404	+	0.850853i	$0.676086\pi$
$30$		0			0
$31$	−3.17100	+	9.75934i	−0.569529	+	1.75283i	0.0845676	+	0.996418i	$0.473049\pi$
$31$	−3.17100	+	9.75934i	−0.569529	+	1.75283i	−0.654096	+	0.756411i	$0.726951\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−4.89858			−0.840099
$35$	1.34885	−	4.15134i	0.227998	−	0.701705i
$36$		0			0
$37$	−0.513743	−	0.373256i	−0.0844589	−	0.0613629i	0.544755	−	0.838596i	$-0.316623\pi$
$37$	−0.513743	−	0.373256i	−0.0844589	−	0.0613629i	−0.629213	+	0.777233i	$0.716623\pi$
$38$	−2.78678	+	0.905480i	−0.452075	+	0.146888i
$39$		0			0
$40$	−2.03598	+	2.80229i	−0.321917	+	0.443080i
$41$	8.87375	−	6.44716i	1.38585	−	1.00688i	0.389540	−	0.921009i	$-0.372634\pi$
$41$	8.87375	−	6.44716i	1.38585	−	1.00688i	0.996307	−	0.0858673i	$-0.0273661\pi$
$42$		0			0
$43$			2.78676i			0.424977i	0.977164	+	0.212488i	$0.0681568\pi$
$43$			2.78676i			0.424977i	−0.977164	+	0.212488i	$0.931843\pi$
$44$	2.94079	+	1.53354i	0.443341	+	0.231189i
$45$		0			0
$46$	4.50910	+	1.46510i	0.664831	+	0.216017i
$47$	2.19910	+	3.02680i	0.320772	+	0.441504i	0.938703	−	0.344728i	$-0.112029\pi$
$47$	2.19910	+	3.02680i	0.320772	+	0.441504i	−0.617931	+	0.786232i	$0.712029\pi$
$48$		0			0
$49$	1.67240	+	5.14710i	0.238914	+	0.735301i
$50$	2.16251	+	6.65551i	0.305825	+	0.941232i
$51$		0			0
$52$	2.72696	+	3.75334i	0.378162	+	0.520495i
$53$	−5.62328	−	1.82712i	−0.772417	−	0.250974i	−0.103818	−	0.994596i	$-0.533106\pi$
$53$	−5.62328	−	1.82712i	−0.772417	−	0.250974i	−0.668599	+	0.743623i	$0.733106\pi$
$54$		0			0
$55$	10.2848	−	5.11870i	1.38680	−	0.690205i
$56$			1.26016i			0.168397i
$57$		0			0
$58$	−0.654014	+	0.475169i	−0.0858762	+	0.0623927i
$59$	−5.43357	+	7.47866i	−0.707390	+	0.973639i	0.292459	+	0.956278i	$0.405526\pi$
$59$	−5.43357	+	7.47866i	−0.707390	+	0.973639i	−0.999849	+	0.0173610i	$0.994474\pi$
$60$		0			0
$61$	10.5409	−	3.42494i	1.34962	−	0.438519i	0.457058	−	0.889437i	$-0.348903\pi$
$61$	10.5409	−	3.42494i	1.34962	−	0.438519i	0.892566	+	0.450918i	$0.148903\pi$
$62$	−8.30179	−	6.03160i	−1.05433	−	0.766014i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	16.0700			1.99324
$66$		0			0
$67$	−12.4414			−1.51996			−0.759982	−	0.649944i	$-0.774793\pi$
$67$	−12.4414			−1.51996			−0.759982	+	0.649944i	$0.774793\pi$
$68$	1.51374	−	4.65882i	0.183568	−	0.564965i
$69$		0			0
$70$	3.53134	+	2.56567i	0.422076	+	0.306656i
$71$	−5.59641	+	1.81838i	−0.664171	+	0.215802i	−0.621652	−	0.783293i	$-0.713538\pi$
$71$	−5.59641	+	1.81838i	−0.664171	+	0.215802i	−0.0425191	+	0.999096i	$0.513538\pi$
$72$		0			0
$73$	−1.65701	+	2.28068i	−0.193938	+	0.266933i	−0.894901	−	0.446265i	$-0.852754\pi$
$73$	−1.65701	+	2.28068i	−0.193938	+	0.266933i	0.700963	+	0.713198i	$0.252754\pi$
$74$	0.513743	−	0.373256i	0.0597214	−	0.0433902i
$75$		0			0
$76$		−	2.93019i		−	0.336116i
$77$	1.93251	−	3.70588i	0.220230	−	0.422325i
$78$		0			0
$79$	−15.7537	−	5.11870i	−1.77243	−	0.575899i	−0.774071	−	0.633099i	$-0.781783\pi$
$79$	−15.7537	−	5.11870i	−1.77243	−	0.575899i	−0.998363	+	0.0571998i	$0.981783\pi$
$80$	−2.03598	−	2.80229i	−0.227629	−	0.313305i
$81$		0			0
$82$	3.38947	+	10.4317i	0.374304	+	1.15199i
$83$	−0.480018	−	1.47734i	−0.0526889	−	0.162160i	0.921250	−	0.388972i	$-0.127170\pi$
$83$	−0.480018	−	1.47734i	−0.0526889	−	0.162160i	−0.973939	+	0.226812i	$0.927170\pi$
$84$		0			0
$85$	−9.97340	−	13.7272i	−1.08177	−	1.48893i
$86$	−2.65036	−	0.861156i	−0.285796	−	0.0928608i
$87$		0			0
$88$	−2.36723	+	2.32297i	−0.252348	+	0.247630i
$89$			11.4127i			1.20974i	0.796324	+	0.604871i	$0.206775\pi$
$89$			11.4127i			1.20974i	−0.796324	+	0.604871i	$0.793225\pi$
$90$		0			0
$91$	4.72983	−	3.43642i	0.495821	−	0.360235i
$92$	−2.78678	+	3.83567i	−0.290542	+	0.399897i
$93$		0			0
$94$	−3.55822	+	1.15613i	−0.367002	+	0.119246i
$95$	−8.21124	−	5.96582i	−0.842456	−	0.612080i
$96$		0			0
$97$	4.63464	−	14.2640i	0.470577	−	1.44829i	−0.381255	−	0.924470i	$-0.624508\pi$
$97$	4.63464	−	14.2640i	0.470577	−	1.44829i	0.851831	−	0.523816i	$-0.175492\pi$
$98$	−5.41199			−0.546693
$99$		0			0
$100$	−6.99802			−0.699802
$101$	2.13215	−	6.56210i	0.212157	−	0.652953i	−0.787186	−	0.616716i	$-0.788463\pi$
$101$	2.13215	−	6.56210i	0.212157	−	0.652953i	0.999343	−	0.0362373i	$-0.0115372\pi$
$102$		0			0
$103$	−7.14088	−	5.18815i	−0.703612	−	0.511204i	0.177495	−	0.984122i	$-0.443201\pi$
$103$	−7.14088	−	5.18815i	−0.703612	−	0.511204i	−0.881107	+	0.472918i	$0.843201\pi$
$104$	−4.41232	+	1.43365i	−0.432663	+	0.140581i
$105$		0			0
$106$	3.47538	−	4.78345i	0.337559	−	0.464610i
$107$	−3.96143	+	2.87815i	−0.382966	+	0.278241i	−0.762567	−	0.646909i	$-0.776061\pi$
$107$	−3.96143	+	2.87815i	−0.382966	+	0.278241i	0.379601	+	0.925150i	$0.376061\pi$
$108$		0			0
$109$		−	3.32974i		−	0.318931i	−0.987204	−	0.159465i	$-0.949023\pi$
$109$		−	3.32974i		−	0.318931i	0.987204	−	0.159465i	$-0.0509771\pi$
$110$	1.68999	+	11.3632i	0.161135	+	1.08344i
$111$		0			0
$112$	−1.19849	−	0.389412i	−0.113246	−	0.0367960i
$113$	2.40781	+	3.31406i	0.226508	+	0.311761i	0.907111	−	0.420891i	$-0.138282\pi$
$113$	2.40781	+	3.31406i	0.226508	+	0.311761i	−0.680604	+	0.732652i	$0.738282\pi$
$114$		0			0
$115$	5.07483	+	15.6187i	0.473230	+	1.45645i
$116$	−0.249811	−	0.768840i	−0.0231944	−	0.0713850i
$117$		0			0
$118$	−5.43357	−	7.47866i	−0.500200	−	0.688467i
$119$	−5.87088	−	1.90757i	−0.538183	−	0.174866i
$120$		0			0
$121$	10.5239	−	3.20115i	0.956719	−	0.291014i
$122$			11.0834i			1.00344i
$123$		0			0
$124$	8.30179	−	6.03160i	0.745523	−	0.541654i
$125$	−4.06793	+	5.59903i	−0.363847	+	0.500792i
$126$		0			0
$127$	0.635021	−	0.206331i	0.0563490	−	0.0183089i	−0.280707	−	0.959794i	$-0.590569\pi$
$127$	0.635021	−	0.206331i	0.0563490	−	0.0183089i	0.337056	+	0.941485i	$0.390569\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−4.96590	+	15.2835i	−0.435538	+	1.34045i
$131$	8.60236			0.751591			0.375796	−	0.926703i	$-0.377369\pi$
$131$	8.60236			0.751591			0.375796	+	0.926703i	$0.377369\pi$
$132$		0			0
$133$	−3.69253			−0.320183
$134$	3.84462	−	11.8325i	0.332125	−	1.02217i
$135$		0			0
$136$	3.96303	+	2.87931i	0.339827	+	0.246899i
$137$	−17.8368	+	5.79552i	−1.52390	+	0.495145i	−0.946880	−	0.321586i	$-0.895784\pi$
$137$	−17.8368	+	5.79552i	−1.52390	+	0.495145i	−0.577019	+	0.816731i	$0.695784\pi$
$138$		0			0
$139$	2.31001	−	3.17945i	0.195932	−	0.269677i	−0.699735	−	0.714402i	$-0.746699\pi$
$139$	2.31001	−	3.17945i	0.195932	−	0.269677i	0.895667	+	0.444725i	$0.146699\pi$
$140$	−3.53134	+	2.56567i	−0.298453	+	0.216839i
$141$		0			0
$142$		−	5.88441i		−	0.493809i
$143$	15.1743	+	2.55038i	1.26894	+	0.213273i
$144$		0			0
$145$	−2.66312	−	0.865300i	−0.221160	−	0.0718592i
$146$	−1.65701	−	2.28068i	−0.137135	−	0.188750i
$147$		0			0
$148$	0.196232	+	0.603941i	0.0161302	+	0.0496437i
$149$	0.0222369	+	0.0684381i	0.00182172	+	0.00560667i	0.951963	−	0.306212i	$-0.0990617\pi$
$149$	0.0222369	+	0.0684381i	0.00182172	+	0.00560667i	−0.950142	+	0.311819i	$0.899062\pi$
$150$		0			0
$151$	12.0920	+	16.6433i	0.984037	+	1.35441i	0.934626	+	0.355632i	$0.115734\pi$
$151$	12.0920	+	16.6433i	0.984037	+	1.35441i	0.0494108	+	0.998779i	$0.484266\pi$
$152$	2.78678	+	0.905480i	0.226038	+	0.0734441i
$153$		0			0
$154$	2.92733	+	2.98310i	0.235891	+	0.240385i
$155$		−	35.5442i		−	2.85498i
$156$		0			0
$157$	−14.8891	+	10.8176i	−1.18828	+	0.863335i	−0.993081	−	0.117429i	$-0.962535\pi$
$157$	−14.8891	+	10.8176i	−1.18828	+	0.863335i	−0.195198	+	0.980764i	$0.562535\pi$
$158$	9.73635	−	13.4009i	0.774582	−	1.06612i
$159$		0			0
$160$	3.29428	−	1.07038i	0.260436	−	0.0846208i
$161$	4.83358	+	3.51180i	0.380940	+	0.276769i
$162$		0			0
$163$	−1.59805	+	4.91830i	−0.125169	+	0.385231i	−0.993932	−	0.109998i	$-0.964916\pi$
$163$	−1.59805	+	4.91830i	−0.125169	+	0.385231i	0.868763	+	0.495229i	$0.164916\pi$
$164$	−10.9686			−0.856500
$165$		0			0
$166$	1.55337			0.120565
$167$	−5.02449	+	15.4638i	−0.388807	+	1.19662i	0.544874	+	0.838518i	$0.316578\pi$
$167$	−5.02449	+	15.4638i	−0.388807	+	1.19662i	−0.933681	+	0.358107i	$0.883422\pi$
$168$		0			0
$169$	6.89599	+	5.01023i	0.530461	+	0.385402i
$170$	16.1373	−	5.24333i	1.23767	−	0.402145i
$171$		0			0
$172$	1.63802	−	2.25453i	0.124898	−	0.171907i
$173$	−3.51017	+	2.55028i	−0.266873	+	0.193895i	−0.713172	−	0.700990i	$-0.752742\pi$
$173$	−3.51017	+	2.55028i	−0.266873	+	0.193895i	0.446299	+	0.894884i	$0.352742\pi$
$174$		0			0
$175$			8.81866i			0.666628i
$176$	−1.47776	−	2.96921i	−0.111391	−	0.223813i
$177$		0			0
$178$	−10.8541	−	3.52671i	−0.813549	−	0.264338i
$179$	9.74507	+	13.4129i	0.728381	+	1.00253i	0.999204	+	0.0399011i	$0.0127043\pi$
$179$	9.74507	+	13.4129i	0.728381	+	1.00253i	−0.270823	+	0.962629i	$0.587296\pi$
$180$		0			0
$181$	2.30052	+	7.08028i	0.170997	+	0.526273i	0.999428	−	0.0338172i	$-0.0107664\pi$
$181$	2.30052	+	7.08028i	0.170997	+	0.526273i	−0.828431	+	0.560090i	$0.810766\pi$
$182$	1.80663	+	5.56025i	0.133917	+	0.412153i
$183$		0			0
$184$	−2.78678	−	3.83567i	−0.205444	−	0.282770i
$185$	2.09194	+	0.679713i	0.153803	+	0.0499735i
$186$		0			0
$187$	−7.23893	−	14.5449i	−0.529363	−	1.06363i
$188$		−	3.74133i		−	0.272865i
$189$		0			0
$190$	8.21124	−	5.96582i	0.595706	−	0.432806i
$191$	3.37446	−	4.64455i	0.244167	−	0.336068i	−0.669290	−	0.743001i	$-0.733402\pi$
$191$	3.37446	−	4.64455i	0.244167	−	0.336068i	0.913458	+	0.406933i	$0.133402\pi$
$192$		0			0
$193$	18.2699	−	5.93625i	1.31510	−	0.427301i	0.434288	−	0.900774i	$-0.357000\pi$
$193$	18.2699	−	5.93625i	1.31510	−	0.427301i	0.880808	+	0.473473i	$0.157000\pi$
$194$	12.1337	+	8.81562i	0.871146	+	0.632924i
$195$		0			0
$196$	1.67240	−	5.14710i	0.119457	−	0.367650i
$197$	8.31376			0.592331			0.296165	−	0.955137i	$-0.404292\pi$
$197$	8.31376			0.592331			0.296165	+	0.955137i	$0.404292\pi$
$198$		0			0
$199$	20.1602			1.42912			0.714558	−	0.699577i	$-0.246628\pi$
$199$	20.1602			1.42912			0.714558	+	0.699577i	$0.246628\pi$
$200$	2.16251	−	6.65551i	0.152912	−	0.470616i
$201$		0			0
$202$	5.58205	+	4.05560i	0.392752	+	0.285351i
$203$	−0.968864	+	0.314803i	−0.0680010	+	0.0220948i
$204$		0			0
$205$	−22.3318	+	30.7370i	−1.55972	+	2.14677i
$206$	7.14088	−	5.18815i	0.497529	−	0.361476i
$207$		0			0
$208$		−	4.63939i		−	0.321684i
$209$	−6.80676	−	6.93645i	−0.470834	−	0.479805i
$210$		0			0
$211$	12.1023	+	3.93228i	0.833158	+	0.270709i	0.694375	−	0.719614i	$-0.255681\pi$
$211$	12.1023	+	3.93228i	0.833158	+	0.270709i	0.138783	+	0.990323i	$0.455681\pi$
$212$	3.47538	+	4.78345i	0.238690	+	0.328529i
$213$		0			0
$214$	−1.51313	−	4.65694i	−0.103436	−	0.318342i
$215$	−2.98289	−	9.18038i	−0.203431	−	0.626096i
$216$		0			0
$217$	−7.60081	−	10.4616i	−0.515977	−	0.710181i
$218$	3.16677	+	1.02895i	0.214481	+	0.0696890i
$219$		0			0
$220$	−11.3293	−	1.90414i	−0.763820	−	0.128377i
$221$		−	22.7264i		−	1.52874i
$222$		0			0
$223$	−6.19545	+	4.50126i	−0.414878	+	0.301427i	−0.775574	−	0.631257i	$-0.782539\pi$
$223$	−6.19545	+	4.50126i	−0.414878	+	0.301427i	0.360696	+	0.932684i	$0.382539\pi$
$224$	0.740706	−	1.01949i	0.0494905	−	0.0681178i
$225$		0			0
$226$	−3.89592	+	1.26586i	−0.259152	+	0.0842037i
$227$	15.2304	+	11.0656i	1.01088	+	0.734447i	0.964393	−	0.264472i	$-0.0851976\pi$
$227$	15.2304	+	11.0656i	1.01088	+	0.734447i	0.0464864	+	0.998919i	$0.485198\pi$
$228$		0			0
$229$	−3.50426	+	10.7850i	−0.231568	+	0.712693i	0.765990	+	0.642852i	$0.222249\pi$
$229$	−3.50426	+	10.7850i	−0.231568	+	0.712693i	−0.997558	+	0.0698408i	$0.977751\pi$
$230$	−16.4225			−1.08287
$231$		0			0
$232$	0.808406			0.0530744
$233$	−2.81890	+	8.67570i	−0.184673	+	0.568364i	−0.999943	−	0.0107173i	$-0.996589\pi$
$233$	−2.81890	+	8.67570i	−0.184673	+	0.568364i	0.815270	+	0.579081i	$0.196589\pi$
$234$		0			0
$235$	−10.4843	−	7.61727i	−0.683919	−	0.496896i
$236$	8.79170	−	2.85660i	0.572291	−	0.185949i
$237$		0			0
$238$	3.62841	−	4.99407i	0.235195	−	0.323718i
$239$	4.94305	−	3.59134i	0.319739	−	0.232304i	−0.416325	−	0.909216i	$-0.636682\pi$
$239$	4.94305	−	3.59134i	0.319739	−	0.232304i	0.736064	+	0.676912i	$0.236682\pi$
$240$		0			0
$241$		−	9.09790i		−	0.586047i	−0.956105	−	0.293024i	$-0.905339\pi$
$241$		−	9.09790i		−	0.586047i	0.956105	−	0.293024i	$-0.0946615\pi$
$242$	−0.207593	+	10.9980i	−0.0133446	+	0.706981i
$243$		0			0
$244$	−10.5409	−	3.42494i	−0.674812	−	0.219260i
$245$	−11.0187	−	15.1659i	−0.703959	−	0.968916i
$246$		0			0
$247$	−4.20087	−	12.9290i	−0.267295	−	0.822649i
$248$	3.17100	+	9.75934i	0.201359	+	0.619719i
$249$		0			0
$250$	−4.06793	−	5.59903i	−0.257279	−	0.354114i
$251$	−10.2602	−	3.33374i	−0.647617	−	0.210424i	−0.0332539	−	0.999447i	$-0.510587\pi$
$251$	−10.2602	−	3.33374i	−0.647617	−	0.210424i	−0.614363	+	0.789023i	$0.710587\pi$
$252$		0			0
$253$	2.31321	+	15.5536i	0.145430	+	0.977843i
$254$			0.667701i			0.0418953i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	2.71120	−	3.73164i	0.169120	−	0.232774i	−0.716041	−	0.698058i	$-0.754048\pi$
$257$	2.71120	−	3.73164i	0.169120	−	0.232774i	0.885161	+	0.465284i	$0.154048\pi$
$258$		0			0
$259$	0.761065	−	0.247285i	0.0472903	−	0.0153656i
$260$	−13.0009	−	9.44570i	−0.806281	−	0.585797i
$261$		0			0
$262$	−2.65827	+	8.18133i	−0.164229	+	0.505444i
$263$	−16.3335			−1.00717			−0.503585	−	0.863946i	$-0.667986\pi$
$263$	−16.3335			−1.00717			−0.503585	+	0.863946i	$0.667986\pi$
$264$		0			0
$265$	20.4804			1.25810
$266$	1.14105	−	3.51180i	0.0699625	−	0.215322i
$267$		0			0
$268$	10.0653	+	7.31290i	0.614839	+	0.446706i
$269$	−3.63107	+	1.17980i	−0.221390	+	0.0719340i	−0.417612	−	0.908626i	$-0.637133\pi$
$269$	−3.63107	+	1.17980i	−0.221390	+	0.0719340i	0.196222	+	0.980560i	$0.437133\pi$
$270$		0			0
$271$	−0.152854	+	0.210385i	−0.00928519	+	0.0127800i	−0.813634	−	0.581377i	$-0.802514\pi$
$271$	−0.152854	+	0.210385i	−0.00928519	+	0.0127800i	0.804349	+	0.594157i	$0.202514\pi$
$272$	−3.96303	+	2.87931i	−0.240294	+	0.174584i
$273$		0			0
$274$		−	18.7547i		−	1.13301i
$275$	−16.5660	+	16.2562i	−0.998965	+	0.980287i
$276$		0			0
$277$	4.25141	+	1.38137i	0.255443	+	0.0829983i	0.433939	−	0.900942i	$-0.357123\pi$
$277$	4.25141	+	1.38137i	0.255443	+	0.0829983i	−0.178496	+	0.983941i	$0.557123\pi$
$278$	2.31001	+	3.17945i	0.138545	+	0.190691i
$279$		0			0
$280$	−1.34885	−	4.15134i	−0.0806094	−	0.248090i
$281$	2.61340	+	8.04321i	0.155902	+	0.479817i	0.998251	−	0.0591149i	$-0.0188278\pi$
$281$	2.61340	+	8.04321i	0.155902	+	0.479817i	−0.842349	+	0.538932i	$0.818828\pi$
$282$		0			0
$283$	−2.81836	−	3.87913i	−0.167534	−	0.230591i	0.716992	−	0.697081i	$-0.245518\pi$
$283$	−2.81836	−	3.87913i	−0.167534	−	0.230591i	−0.884526	+	0.466490i	$0.845518\pi$
$284$	5.59641	+	1.81838i	0.332086	+	0.107901i
$285$		0			0
$286$	−7.11466	+	13.6435i	−0.420699	+	0.806756i
$287$			13.8222i			0.815898i
$288$		0			0
$289$	−5.65992	+	4.11217i	−0.332936	+	0.241892i
$290$	1.64590	−	2.26538i	0.0966505	−	0.133028i
$291$		0			0
$292$	2.68110	−	0.871141i	0.156899	−	0.0509797i
$293$	5.15036	+	3.74196i	0.300888	+	0.218608i	0.727977	−	0.685602i	$-0.240461\pi$
$293$	5.15036	+	3.74196i	0.300888	+	0.218608i	−0.427089	+	0.904210i	$0.640461\pi$
$294$		0			0
$295$	9.89472	−	30.4528i	0.576093	−	1.77303i
$296$	−0.635021			−0.0369099
$297$		0			0
$298$	−0.0719601			−0.00416853
$299$	−6.79715	+	20.9195i	−0.393089	+	1.20980i
$300$		0			0
$301$	−2.84109	−	2.06417i	−0.163757	−	0.118977i
$302$	−19.5653	+	6.35717i	−1.12586	+	0.365814i
$303$		0			0
$304$	−1.72232	+	2.37058i	−0.0987821	+	0.135962i
$305$	−31.0587	+	22.5655i	−1.77842	+	1.29210i
$306$		0			0
$307$		−	4.58681i		−	0.261783i	−0.991397	−	0.130892i	$-0.958216\pi$
$307$		−	4.58681i		−	0.261783i	0.991397	−	0.130892i	$-0.0417840\pi$
$308$	−3.74170	+	1.86222i	−0.213203	+	0.106110i
$309$		0			0
$310$	33.8046	+	10.9838i	1.91997	+	0.623836i
$311$	13.4923	+	18.5706i	0.765080	+	1.05304i	0.996774	+	0.0802537i	$0.0255730\pi$
$311$	13.4923	+	18.5706i	0.765080	+	1.05304i	−0.231694	+	0.972789i	$0.574427\pi$
$312$		0			0
$313$	−4.14552	−	12.7586i	−0.234319	−	0.721159i	−0.997211	−	0.0746332i	$-0.976221\pi$
$313$	−4.14552	−	12.7586i	−0.234319	−	0.721159i	0.762892	−	0.646525i	$-0.223779\pi$
$314$	−5.68713	−	17.5032i	−0.320943	−	0.987762i
$315$		0			0
$316$	9.73635	+	13.4009i	0.547712	+	0.753861i
$317$	2.54927	+	0.828309i	0.143182	+	0.0465225i	0.379731	−	0.925097i	$-0.376017\pi$
$317$	2.54927	+	0.828309i	0.143182	+	0.0465225i	−0.236550	+	0.971619i	$0.576017\pi$
$318$		0			0
$319$	−2.37735	−	1.23972i	−0.133106	−	0.0694109i
$320$			3.46382i			0.193633i
$321$		0			0
$322$	−4.83358	+	3.51180i	−0.269365	+	0.195705i
$323$	−8.43694	+	11.6124i	−0.469444	+	0.646134i
$324$		0			0
$325$	−30.8775	+	10.0327i	−1.71278	+	0.556515i
$326$	−4.18376	−	3.03968i	−0.231717	−	0.168352i
$327$		0			0
$328$	3.38947	−	10.4317i	0.187152	−	0.575995i
$329$	−4.71469			−0.259929
$330$		0			0
$331$	−8.09494			−0.444938			−0.222469	−	0.974940i	$-0.571412\pi$
$331$	−8.09494			−0.444938			−0.222469	+	0.974940i	$0.571412\pi$
$332$	−0.480018	+	1.47734i	−0.0263444	+	0.0810798i
$333$		0			0
$334$	−13.1543	−	9.55715i	−0.719771	−	0.522944i
$335$	40.9857	−	13.3171i	2.23929	−	0.727588i
$336$		0			0
$337$	5.97906	−	8.22947i	0.325700	−	0.448288i	−0.614497	−	0.788919i	$-0.710641\pi$
$337$	5.97906	−	8.22947i	0.325700	−	0.448288i	0.940197	+	0.340632i	$0.110641\pi$
$338$	−6.89599	+	5.01023i	−0.375092	+	0.272520i
$339$		0			0
$340$			16.9678i			0.920206i
$341$	5.64103	−	33.5630i	0.305479	−	1.81754i
$342$		0			0
$343$	−14.8756	−	4.83338i	−0.803208	−	0.260978i
$344$	1.63802	+	2.25453i	0.0883159	+	0.121556i
$345$		0			0
$346$	−1.34076	−	4.12645i	−0.0720799	−	0.221839i
$347$	−11.3822	−	35.0309i	−0.611031	−	1.88056i	−0.448282	−	0.893892i	$-0.647964\pi$
$347$	−11.3822	−	35.0309i	−0.611031	−	1.88056i	−0.162748	−	0.986668i	$-0.552036\pi$
$348$		0			0
$349$	2.35836	+	3.24601i	0.126240	+	0.173755i	0.867459	−	0.497509i	$-0.165752\pi$
$349$	2.35836	+	3.24601i	0.126240	+	0.173755i	−0.741219	+	0.671264i	$0.765752\pi$
$350$	−8.38704	−	2.72512i	−0.448306	−	0.145664i
$351$		0			0
$352$	3.28054	−	0.487899i	0.174853	−	0.0260051i
$353$			6.97103i			0.371030i	0.982641	+	0.185515i	$0.0593954\pi$
$353$			6.97103i			0.371030i	−0.982641	+	0.185515i	$0.940605\pi$
$354$		0			0
$355$	16.4898	−	11.9805i	0.875188	−	0.635861i
$356$	6.70820	−	9.23305i	0.355534	−	0.489351i
$357$		0			0
$358$	−15.7679	+	5.12329i	−0.833357	+	0.270774i
$359$	−17.2644	−	12.5434i	−0.911182	−	0.662013i	0.0301312	−	0.999546i	$-0.490407\pi$
$359$	−17.2644	−	12.5434i	−0.911182	−	0.662013i	−0.941314	+	0.337533i	$0.890407\pi$
$360$		0			0
$361$	3.21809	−	9.90427i	0.169373	−	0.521277i
$362$	−7.44465			−0.391282
$363$		0			0
$364$	−5.84639			−0.306434
$365$	3.01747	−	9.28682i	0.157942	−	0.486094i
$366$		0			0
$367$	−13.8135	−	10.0361i	−0.721058	−	0.523879i	0.165664	−	0.986182i	$-0.447023\pi$
$367$	−13.8135	−	10.0361i	−0.721058	−	0.523879i	−0.886722	+	0.462303i	$0.847023\pi$
$368$	4.50910	−	1.46510i	0.235053	−	0.0763735i
$369$		0			0
$370$	−1.29289	+	1.77951i	−0.0672142	+	0.0925124i
$371$	6.02794	−	4.37955i	0.312955	−	0.227375i
$372$		0			0
$373$			35.5505i			1.84073i	0.391056	+	0.920367i	$0.372110\pi$
$373$			35.5505i			1.84073i	−0.391056	+	0.920367i	$0.627890\pi$
$374$	16.0700	−	2.39001i	0.830959	−	0.123585i
$375$		0			0
$376$	3.55822	+	1.15613i	0.183501	+	0.0596231i
$377$	−2.20449	−	3.03422i	−0.113537	−	0.156270i
$378$		0			0
$379$	−4.39984	−	13.5413i	−0.226005	−	0.695571i	−0.998188	−	0.0601712i	$-0.980835\pi$
$379$	−4.39984	−	13.5413i	−0.226005	−	0.695571i	0.772183	−	0.635400i	$-0.219165\pi$
$380$	3.13642	+	9.65289i	0.160895	+	0.495183i
$381$		0			0
$382$	3.37446	+	4.64455i	0.172652	+	0.237636i
$383$	14.9979	+	4.87311i	0.766357	+	0.249004i	0.666005	−	0.745948i	$-0.268003\pi$
$383$	14.9979	+	4.87311i	0.766357	+	0.249004i	0.100352	+	0.994952i	$0.468003\pi$
$384$		0			0
$385$	−2.39953	+	14.2768i	−0.122291	+	0.727611i
$386$			19.2101i			0.977769i
$387$		0			0
$388$	−12.1337	+	8.81562i	−0.615993	+	0.447545i
$389$	2.72321	−	3.74818i	0.138072	−	0.190040i	−0.734381	−	0.678737i	$-0.762528\pi$
$389$	2.72321	−	3.74818i	0.138072	−	0.190040i	0.872454	+	0.488697i	$0.162528\pi$
$390$		0			0
$391$	22.0882	−	7.17689i	1.11705	−	0.362951i
$392$	4.37839	+	3.18109i	0.221142	+	0.160669i
$393$		0			0
$394$	−2.56909	+	7.90686i	−0.129429	+	0.398342i
$395$	57.3762			2.88691
$396$		0			0
$397$	−3.98145			−0.199823			−0.0999116	−	0.994996i	$-0.531856\pi$
$397$	−3.98145			−0.199823			−0.0999116	+	0.994996i	$0.531856\pi$
$398$	−6.22983	+	19.1734i	−0.312273	+	0.961078i
$399$		0			0
$400$	5.66152	+	4.11333i	0.283076	+	0.205667i
$401$	18.1207	−	5.88778i	0.904906	−	0.294022i	0.180646	−	0.983548i	$-0.442181\pi$
$401$	18.1207	−	5.88778i	0.904906	−	0.294022i	0.724260	+	0.689526i	$0.242181\pi$
$402$		0			0
$403$	27.9829	−	38.5152i	1.39393	−	1.91858i
$404$	−5.58205	+	4.05560i	−0.277718	+	0.201774i
$405$		0			0
$406$		−	1.01872i		−	0.0505584i
$407$	1.86747	+	0.973828i	0.0925669	+	0.0482708i
$408$		0			0
$409$	14.4229	+	4.68627i	0.713165	+	0.231721i	0.643057	−	0.765818i	$-0.277666\pi$
$409$	14.4229	+	4.68627i	0.713165	+	0.231721i	0.0701075	+	0.997539i	$0.477666\pi$
$410$	−22.3318	−	30.7370i	−1.10289	−	1.51799i
$411$		0			0
$412$	2.72757	+	8.39461i	0.134378	+	0.413573i
$413$	−3.59978	−	11.0790i	−0.177134	−	0.545161i
$414$		0			0
$415$	3.16264	+	4.35299i	0.155248	+	0.213680i
$416$	4.41232	+	1.43365i	0.216332	+	0.0702904i
$417$		0			0
$418$	8.70037	−	4.33013i	0.425549	−	0.211794i
$419$			17.9724i			0.878010i	0.898485	+	0.439005i	$0.144669\pi$
$419$			17.9724i			0.878010i	−0.898485	+	0.439005i	$0.855331\pi$
$420$		0			0
$421$	−1.56770	+	1.13900i	−0.0764050	+	0.0555115i	−0.625332	−	0.780359i	$-0.715036\pi$
$421$	−1.56770	+	1.13900i	−0.0764050	+	0.0555115i	0.548927	+	0.835870i	$0.315036\pi$
$422$	−7.47964	+	10.2948i	−0.364103	+	0.501145i
$423$		0			0
$424$	−5.62328	+	1.82712i	−0.273091	+	0.0887326i
$425$	27.7334	+	20.1495i	1.34527	+	0.977393i
$426$		0			0
$427$	−4.31599	+	13.2833i	−0.208866	+	0.642822i
$428$	4.89660			0.236686
$429$		0			0
$430$	9.65282			0.465500
$431$	5.98403	−	18.4169i	0.288241	−	0.887113i	−0.697168	−	0.716908i	$-0.745557\pi$
$431$	5.98403	−	18.4169i	0.288241	−	0.887113i	0.985409	−	0.170205i	$-0.0544431\pi$
$432$		0			0
$433$	7.99444	+	5.80830i	0.384188	+	0.279129i	0.763070	−	0.646316i	$-0.223691\pi$
$433$	7.99444	+	5.80830i	0.384188	+	0.279129i	−0.378881	+	0.925445i	$0.623691\pi$
$434$	12.2984	−	3.99598i	0.590341	−	0.191813i
$435$		0			0
$436$	−1.95717	+	2.69381i	−0.0937315	+	0.129010i
$437$	11.2393	−	8.16581i	0.537647	−	0.390623i
$438$		0			0
$439$			21.4319i			1.02289i	0.859317	+	0.511444i	$0.170889\pi$
$439$			21.4319i			1.02289i	−0.859317	+	0.511444i	$0.829111\pi$
$440$	5.31188	−	10.1864i	0.253234	−	0.485616i
$441$		0			0
$442$	21.6141	+	7.02284i	1.02808	+	0.334042i
$443$	−9.59692	−	13.2090i	−0.455963	−	0.627580i	0.517702	−	0.855561i	$-0.326788\pi$
$443$	−9.59692	−	13.2090i	−0.455963	−	0.627580i	−0.973666	+	0.227981i	$0.926788\pi$
$444$		0			0
$445$	−12.2159	−	37.5966i	−0.579088	−	1.78225i
$446$	−2.36645	−	7.28319i	−0.112055	−	0.344869i
$447$		0			0
$448$	0.740706	+	1.01949i	0.0349951	+	0.0481666i
$449$	−29.0258	−	9.43107i	−1.36981	−	0.445080i	−0.470507	−	0.882396i	$-0.655929\pi$
$449$	−29.0258	−	9.43107i	−1.36981	−	0.445080i	−0.899308	+	0.437317i	$0.855929\pi$
$450$		0			0
$451$	−25.9651	+	25.4797i	−1.22265	+	1.19979i
$452$		−	4.09641i		−	0.192679i
$453$		0			0
$454$	−15.2304	+	11.0656i	−0.714800	+	0.519333i
$455$	−11.9031	+	16.3833i	−0.558028	+	0.768059i
$456$		0			0
$457$	−29.0891	+	9.45163i	−1.36073	+	0.442129i	−0.896287	−	0.443474i	$-0.853746\pi$
$457$	−29.0891	+	9.45163i	−1.36073	+	0.442129i	−0.464444	+	0.885602i	$0.653746\pi$
$458$	−9.17427	−	6.66550i	−0.428686	−	0.311458i
$459$		0			0
$460$	5.07483	−	15.6187i	0.236615	−	0.728226i
$461$	−25.5643			−1.19065			−0.595324	−	0.803486i	$-0.702976\pi$
$461$	−25.5643			−1.19065			−0.595324	+	0.803486i	$0.702976\pi$
$462$		0			0
$463$	19.3537			0.899444			0.449722	−	0.893169i	$-0.351523\pi$
$463$	19.3537			0.899444			0.449722	+	0.893169i	$0.351523\pi$
$464$	−0.249811	+	0.768840i	−0.0115972	+	0.0356925i
$465$		0			0
$466$	−7.37999	−	5.36188i	−0.341871	−	0.248384i
$467$	20.8870	−	6.78661i	0.966537	−	0.314047i	0.217120	−	0.976145i	$-0.430334\pi$
$467$	20.8870	−	6.78661i	0.966537	−	0.314047i	0.749417	+	0.662098i	$0.230334\pi$
$468$		0			0
$469$	9.21546	−	12.6840i	0.425530	−	0.585692i
$470$	10.4843	−	7.61727i	0.483604	−	0.351359i
$471$		0			0
$472$			9.24414i			0.425496i
$473$	−1.35966	−	9.14208i	−0.0625171	−	0.420353i
$474$		0			0
$475$	19.5019	+	6.33657i	0.894811	+	0.290742i
$476$	3.62841	+	4.99407i	0.166308	+	0.228903i
$477$		0			0
$478$	1.88808	+	5.81090i	0.0863586	+	0.265785i
$479$	7.22925	+	22.2493i	0.330313	+	1.01660i	0.968985	+	0.247119i	$0.0794839\pi$
$479$	7.22925	+	22.2493i	0.330313	+	1.01660i	−0.638672	+	0.769479i	$0.720516\pi$
$480$		0			0
$481$	1.73168	+	2.38345i	0.0789578	+	0.108676i
$482$	8.65262	+	2.81141i	0.394116	+	0.128056i
$483$		0			0
$484$	−10.3956	−	3.59601i	−0.472528	−	0.163455i
$485$			51.9504i			2.35895i
$486$		0			0
$487$	−25.3573	+	18.4232i	−1.14905	+	0.834833i	−0.988354	−	0.152171i	$-0.951374\pi$
$487$	−25.3573	+	18.4232i	−1.14905	+	0.834833i	−0.160695	+	0.987004i	$0.551374\pi$
$488$	6.51463	−	8.96662i	0.294904	−	0.405900i
$489$		0			0
$490$	17.8286	−	5.79287i	0.805415	−	0.261695i
$491$	−19.0482	−	13.8393i	−0.859635	−	0.624561i	0.0681510	−	0.997675i	$-0.478290\pi$
$491$	−19.0482	−	13.8393i	−0.859635	−	0.624561i	−0.927786	+	0.373114i	$0.878290\pi$
$492$		0			0
$493$	−1.22372	+	3.76622i	−0.0551135	+	0.169622i
$494$	13.5943			0.611637
$495$		0			0
$496$	−10.2616			−0.460758
$497$	2.29146	−	7.05240i	0.102786	−	0.316343i
$498$		0			0
$499$	32.1503	+	23.3586i	1.43925	+	1.04567i	0.988199	+	0.153174i	$0.0489495\pi$
$499$	32.1503	+	23.3586i	1.43925	+	1.04567i	0.451047	+	0.892500i	$0.351051\pi$
$500$	6.58205	−	2.13864i	0.294358	−	0.0956428i
$501$		0			0
$502$	6.34114	−	8.72783i	0.283019	−	0.389542i
$503$	20.3387	−	14.7770i	0.906859	−	0.658872i	−0.0333594	−	0.999443i	$-0.510621\pi$
$503$	20.3387	−	14.7770i	0.906859	−	0.658872i	0.940219	+	0.340572i	$0.110621\pi$
$504$		0			0
$505$			23.8996i			1.06352i
$506$	−15.5071	−	2.60632i	−0.689376	−	0.115865i
$507$		0			0
$508$	−0.635021	−	0.206331i	−0.0281745	−	0.00915446i
$509$	−6.20336	−	8.53819i	−0.274959	−	0.378449i	0.649097	−	0.760706i	$-0.275147\pi$
$509$	−6.20336	−	8.53819i	−0.274959	−	0.378449i	−0.924056	+	0.382257i	$0.875147\pi$
$510$		0			0
$511$	−1.09778	−	3.37862i	−0.0485630	−	0.149461i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	2.71120	+	3.73164i	0.119586	+	0.164596i
$515$	29.0774	+	9.44782i	1.28130	+	0.416320i
$516$		0			0
$517$	−8.69101	−	8.85660i	−0.382230	−	0.389513i
$518$			0.800232i			0.0351602i
$519$		0			0
$520$	13.0009	−	9.44570i	0.570127	−	0.414221i
$521$	5.32228	−	7.32549i	0.233173	−	0.320935i	−0.676356	−	0.736574i	$-0.736442\pi$
$521$	5.32228	−	7.32549i	0.233173	−	0.320935i	0.909530	+	0.415639i	$0.136442\pi$
$522$		0			0
$523$	−15.1739	+	4.93031i	−0.663510	+	0.215587i	−0.621362	−	0.783524i	$-0.713420\pi$
$523$	−15.1739	+	4.93031i	−0.663510	+	0.215587i	−0.0421484	+	0.999111i	$0.513420\pi$
$524$	−6.95945	−	5.05634i	−0.304025	−	0.220887i
$525$		0			0
$526$	5.04734	−	15.5341i	0.220074	−	0.677320i
$527$	−50.2671			−2.18967
$528$		0			0
$529$	0.521463			0.0226723
$530$	−6.32879	+	19.4780i	−0.274905	+	0.846071i
$531$		0			0
$532$	2.98732	+	2.17041i	0.129517	+	0.0940993i
$533$	−48.3968	+	15.7251i	−2.09630	+	0.681128i
$534$		0			0
$535$	9.96938	−	13.7217i	0.431014	−	0.593239i
$536$	−10.0653	+	7.31290i	−0.434757	+	0.315869i
$537$		0			0
$538$		−	3.81793i		−	0.164603i
$539$	−7.99763	−	16.0693i	−0.344482	−	0.692155i
$540$		0			0
$541$	11.6255	+	3.77737i	0.499821	+	0.162402i	0.548068	−	0.836434i	$-0.315363\pi$
$541$	11.6255	+	3.77737i	0.499821	+	0.162402i	−0.0482471	+	0.998835i	$0.515363\pi$
$542$	−0.152854	−	0.210385i	−0.00656562	−	0.00903681i
$543$		0			0
$544$	−1.51374	−	4.65882i	−0.0649012	−	0.199745i
$545$	3.56408	+	10.9691i	0.152668	+	0.469865i
$546$		0			0
$547$	−1.22536	−	1.68657i	−0.0523927	−	0.0721124i	0.782017	−	0.623257i	$-0.214191\pi$
$547$	−1.22536	−	1.68657i	−0.0523927	−	0.0721124i	−0.834409	+	0.551145i	$0.814191\pi$
$548$	17.8368	+	5.79552i	0.761950	+	0.247572i
$549$		0			0
$550$	−10.3414	−	20.7786i	−0.440960	−	0.886003i
$551$			2.36879i			0.100914i
$552$		0			0
$553$	16.8874	−	12.2694i	0.718124	−	0.521748i
$554$	−2.62752	+	3.61647i	−0.111632	+	0.153649i
$555$		0			0
$556$	−3.73767	+	1.21444i	−0.158512	+	0.0515038i
$557$	16.7018	+	12.1345i	0.707676	+	0.514157i	0.882423	−	0.470456i	$-0.155911\pi$
$557$	16.7018	+	12.1345i	0.707676	+	0.514157i	−0.174747	+	0.984613i	$0.555911\pi$
$558$		0			0
$559$	3.99523	−	12.2961i	0.168980	−	0.520068i
$560$	4.36498			0.184454
$561$		0			0
$562$	−8.45713			−0.356742
$563$	−11.1784	+	34.4035i	−0.471112	+	1.44993i	0.380019	+	0.924979i	$0.375918\pi$
$563$	−11.1784	+	34.4035i	−0.471112	+	1.44993i	−0.851130	+	0.524954i	$0.824082\pi$
$564$		0			0
$565$	−11.4793	−	8.34020i	−0.482938	−	0.350875i
$566$	4.56019	−	1.48170i	0.191679	−	0.0622804i
$567$		0			0
$568$	−3.45877	+	4.76059i	−0.145127	+	0.199750i
$569$	3.09965	−	2.25203i	0.129944	−	0.0944100i	−0.520915	−	0.853609i	$-0.674409\pi$
$569$	3.09965	−	2.25203i	0.129944	−	0.0944100i	0.650859	+	0.759199i	$0.274409\pi$
$570$		0			0
$571$		−	20.3742i		−	0.852633i	−0.904574	−	0.426316i	$-0.859811\pi$
$571$		−	20.3742i		−	0.852633i	0.904574	−	0.426316i	$-0.140189\pi$
$572$	−10.7772	−	10.9825i	−0.450616	−	0.459202i
$573$		0			0
$574$	−13.1457	−	4.27129i	−0.548690	−	0.178280i
$575$	−19.5019	−	26.8421i	−0.813287	−	1.11939i
$576$		0			0
$577$	−8.18252	−	25.1832i	−0.340643	−	1.04839i	−0.963875	−	0.266354i	$-0.914181\pi$
$577$	−8.18252	−	25.1832i	−0.340643	−	1.04839i	0.623233	−	0.782036i	$-0.285819\pi$
$578$	−2.16190	−	6.65363i	−0.0899230	−	0.276755i
$579$		0			0
$580$	1.64590	+	2.26538i	0.0683422	+	0.0940650i
$581$	1.86170	+	0.604902i	0.0772362	+	0.0250956i
$582$		0			0
$583$	19.3389	+	3.25033i	0.800934	+	0.134615i
$584$			2.81907i			0.116654i
$585$		0			0
$586$	−5.15036	+	3.74196i	−0.212760	+	0.154579i
$587$	−12.8336	+	17.6639i	−0.529697	+	0.729066i	−0.987084	−	0.160202i	$-0.948785\pi$
$587$	−12.8336	+	17.6639i	−0.529697	+	0.729066i	0.457387	+	0.889268i	$0.348785\pi$
$588$		0			0
$589$	−28.5968	+	9.29165i	−1.17831	+	0.382856i
$590$	25.9047	+	18.8209i	1.06648	+	0.774843i
$591$		0			0
$592$	0.196232	−	0.603941i	0.00806510	−	0.0248218i
$593$	−10.4112			−0.427536			−0.213768	−	0.976884i	$-0.568574\pi$
$593$	−10.4112			−0.427536			−0.213768	+	0.976884i	$0.568574\pi$
$594$		0			0
$595$	21.3822			0.876584
$596$	0.0222369	−	0.0684381i	0.000910858	−	0.00280333i
$597$		0			0
$598$	−17.7952	−	12.9290i	−0.727699	−	0.528704i
$599$	10.1245	−	3.28965i	0.413676	−	0.134411i	−0.0947827	−	0.995498i	$-0.530216\pi$
$599$	10.1245	−	3.28965i	0.413676	−	0.134411i	0.508458	+	0.861087i	$0.330216\pi$
$600$		0			0
$601$	−14.2697	+	19.6405i	−0.582072	+	0.801153i	−0.993921	−	0.110099i	$-0.964883\pi$
$601$	−14.2697	+	19.6405i	−0.582072	+	0.801153i	0.411849	+	0.911252i	$0.364883\pi$
$602$	2.84109	−	2.06417i	0.115794	−	0.0841293i
$603$		0			0
$604$		−	20.5722i		−	0.837072i
$605$	−31.2423	+	21.8101i	−1.27018	+	0.886705i
$606$		0			0
$607$	−23.8300	−	7.74282i	−0.967228	−	0.314271i	−0.217532	−	0.976053i	$-0.569801\pi$
$607$	−23.8300	−	7.74282i	−0.967228	−	0.314271i	−0.749697	+	0.661782i	$0.769801\pi$
$608$	−1.72232	−	2.37058i	−0.0698495	−	0.0961396i
$609$		0			0
$610$	−11.8634	−	36.5117i	−0.480334	−	1.47832i
$611$	−5.36376	−	16.5079i	−0.216994	−	0.667840i
$612$		0			0
$613$	25.8318	+	35.5544i	1.04334	+	1.43603i	0.894446	+	0.447177i	$0.147570\pi$
$613$	25.8318	+	35.5544i	1.04334	+	1.43603i	0.148891	+	0.988854i	$0.452430\pi$
$614$	4.36232	+	1.41740i	0.176049	+	0.0572017i
$615$		0			0
$616$	−0.614834	−	4.13402i	−0.0247724	−	0.166565i
$617$		−	28.7914i		−	1.15910i	−0.814938	−	0.579549i	$-0.803229\pi$
$617$		−	28.7914i		−	1.15910i	0.814938	−	0.579549i	$-0.196771\pi$
$618$		0			0
$619$	−31.8707	+	23.1554i	−1.28099	+	0.930694i	−0.999582	−	0.0288937i	$-0.990802\pi$
$619$	−31.8707	+	23.1554i	−1.28099	+	0.930694i	−0.281408	+	0.959588i	$0.590802\pi$
$620$	−20.8924	+	28.7559i	−0.839058	+	1.15486i
$621$		0			0
$622$	−21.8311	+	7.09334i	−0.875345	+	0.284417i
$623$	−11.6352	−	8.45344i	−0.466153	−	0.338680i
$624$		0			0
$625$	−3.40469	+	10.4785i	−0.136187	+	0.419142i
$626$	13.4152			0.536179
$627$		0			0
$628$	18.4039			0.734397
$629$	0.961259	−	2.95845i	0.0383279	−	0.117961i
$630$		0			0
$631$	−29.0392	−	21.0982i	−1.15603	−	0.839906i	−0.166761	−	0.985997i	$-0.553331\pi$
$631$	−29.0392	−	21.0982i	−1.15603	−	0.839906i	−0.989271	+	0.146091i	$0.953331\pi$
$632$	−15.7537	+	5.11870i	−0.626650	+	0.203611i
$633$		0			0
$634$	−1.57554	+	2.16854i	−0.0625726	+	0.0861238i
$635$	−1.87109	+	1.35943i	−0.0742519	+	0.0539472i
$636$		0			0
$637$		−	25.1083i		−	0.994827i
$638$	1.91369	−	1.87790i	0.0757635	−	0.0743470i
$639$		0			0
$640$	−3.29428	−	1.07038i	−0.130218	−	0.0423104i
$641$	10.8759	+	14.9694i	0.429574	+	0.591257i	0.967855	−	0.251508i	$-0.0809264\pi$
$641$	10.8759	+	14.9694i	0.429574	+	0.591257i	−0.538282	+	0.842765i	$0.680926\pi$
$642$		0			0
$643$	0.123389	+	0.379753i	0.00486600	+	0.0149760i	0.953460	−	0.301519i	$-0.0974938\pi$
$643$	0.123389	+	0.379753i	0.00486600	+	0.0149760i	−0.948594	+	0.316495i	$0.897494\pi$
$644$	−1.84626	−	5.68221i	−0.0727530	−	0.223911i
$645$		0			0
$646$	−8.43694	−	11.6124i	−0.331947	−	0.456886i
$647$	4.58230	+	1.48888i	0.180149	+	0.0585339i	0.397702	−	0.917515i	$-0.369808\pi$
$647$	4.58230	+	1.48888i	0.180149	+	0.0585339i	−0.217554	+	0.976048i	$0.569808\pi$
$648$		0			0
$649$	14.1762	−	27.1851i	0.556465	−	1.06711i
$650$		−	32.4665i		−	1.27344i
$651$		0			0
$652$	4.18376	−	3.03968i	0.163849	−	0.119043i
$653$	23.5227	−	32.3762i	0.920515	−	1.26698i	−0.0429313	−	0.999078i	$-0.513670\pi$
$653$	23.5227	−	32.3762i	0.920515	−	1.26698i	0.963446	−	0.267902i	$-0.0863304\pi$
$654$		0			0
$655$	−28.3386	+	9.20777i	−1.10728	+	0.359778i
$656$	8.87375	+	6.44716i	0.346462	+	0.251719i
$657$		0			0
$658$	1.45692	−	4.48394i	0.0567967	−	0.174802i
$659$	−16.1758			−0.630121			−0.315060	−	0.949072i	$-0.602025\pi$
$659$	−16.1758			−0.630121			−0.315060	+	0.949072i	$0.602025\pi$
$660$		0			0
$661$	−26.5942			−1.03440			−0.517198	−	0.855866i	$-0.673025\pi$
$661$	−26.5942			−1.03440			−0.517198	+	0.855866i	$0.673025\pi$
$662$	2.50147	−	7.69874i	0.0972225	−	0.299220i
$663$		0			0
$664$	−1.25670	−	0.913049i	−0.0487696	−	0.0354332i
$665$	12.1642	−	3.95240i	0.471709	−	0.153267i
$666$		0			0
$667$	2.25285	−	3.10078i	0.0872307	−	0.120063i
$668$	13.1543	−	9.55715i	0.508955	−	0.369777i
$669$		0			0
$670$			43.0949i			1.66490i
$671$	−32.9088	+	16.3786i	−1.27043	+	0.632288i
$672$		0			0
$673$	35.5495	+	11.5507i	1.37033	+	0.445247i	0.899479	−	0.436965i	$-0.143947\pi$
$673$	35.5495	+	11.5507i	1.37033	+	0.445247i	0.470852	+	0.882212i	$0.343947\pi$
$674$	5.97906	+	8.22947i	0.230305	+	0.316987i
$675$		0			0
$676$	−2.63403	−	8.10672i	−0.101309	−	0.311797i
$677$	−5.69647	−	17.5319i	−0.218933	−	0.673806i	−0.998851	−	0.0479247i	$-0.984739\pi$
$677$	−5.69647	−	17.5319i	−0.218933	−	0.673806i	0.779918	−	0.625882i	$-0.215261\pi$
$678$		0			0
$679$	11.1091	+	15.2904i	0.426329	+	0.586792i
$680$	−16.1373	−	5.24333i	−0.618837	−	0.201072i
$681$		0			0
$682$	30.1772	+	15.7365i	1.15554	+	0.602581i
$683$			15.1092i			0.578136i	0.957308	+	0.289068i	$0.0933455\pi$
$683$			15.1092i			0.578136i	−0.957308	+	0.289068i	$0.906655\pi$
$684$		0			0
$685$	52.5560	−	38.1842i	2.00806	−	1.45894i
$686$	9.19363	−	12.6540i	0.351015	−	0.483130i
$687$		0			0
$688$	−2.65036	+	0.861156i	−0.101044	+	0.0328313i
$689$	22.1923	+	16.1236i	0.845458	+	0.614261i
$690$		0			0
$691$	−12.4595	+	38.3463i	−0.473980	+	1.45876i	0.373349	+	0.927691i	$0.378210\pi$
$691$	−12.4595	+	38.3463i	−0.473980	+	1.45876i	−0.847329	+	0.531069i	$0.821790\pi$
$692$	4.33880			0.164937
$693$		0			0
$694$	36.8337			1.39819
$695$	−4.20660	+	12.9466i	−0.159566	+	0.491092i
$696$		0			0
$697$	43.4687	+	31.5819i	1.64650	+	1.19625i
$698$	−3.81591	+	1.23986i	−0.144434	+	0.0469296i
$699$		0			0
$700$	5.18348	−	7.13445i	0.195917	−	0.269657i
$701$	−15.9091	+	11.5586i	−0.600877	+	0.436563i	−0.846190	−	0.532881i	$-0.821109\pi$
$701$	−15.9091	+	11.5586i	−0.600877	+	0.436563i	0.245313	+	0.969444i	$0.421109\pi$
$702$		0			0
$703$		−	1.86074i		−	0.0701790i
$704$	−0.549723	+	3.27075i	−0.0207185	+	0.123271i
$705$		0			0
$706$	−6.62984	−	2.15417i	−0.249517	−	0.0810731i
$707$	5.11072	+	7.03431i	0.192209	+	0.264552i
$708$		0			0
$709$	−2.44567	−	7.52699i	−0.0918489	−	0.282682i	0.894571	−	0.446926i	$-0.147481\pi$
$709$	−2.44567	−	7.52699i	−0.0918489	−	0.282682i	−0.986420	+	0.164244i	$0.947481\pi$
$710$	6.29855	+	19.3849i	0.236380	+	0.727503i
$711$		0			0
$712$	6.70820	+	9.23305i	0.251401	+	0.346023i
$713$	46.2705	+	15.0342i	1.73284	+	0.563035i
$714$		0			0
$715$	−52.7182	+	7.84054i	−1.97155	+	0.293219i
$716$		−	16.5793i		−	0.619598i
$717$		0			0
$718$	17.2644	−	12.5434i	0.644303	−	0.468114i
$719$	−0.448532	+	0.617352i	−0.0167274	+	0.0230233i	−0.817299	−	0.576214i	$-0.804529\pi$
$719$	−0.448532	+	0.617352i	−0.0167274	+	0.0230233i	0.800571	+	0.599237i	$0.204529\pi$
$720$		0			0
$721$	10.5786	−	3.43719i	0.393967	−	0.128008i
$722$	8.42507	+	6.12117i	0.313549	+	0.227807i
$723$		0			0
$724$	2.30052	−	7.08028i	0.0854983	−	0.263137i
$725$	5.65724			0.210105
$726$		0			0
$727$	27.0317			1.00255			0.501275	−	0.865288i	$-0.332864\pi$
$727$	27.0317			1.00255			0.501275	+	0.865288i	$0.332864\pi$
$728$	1.80663	−	5.56025i	0.0669583	−	0.206077i
$729$		0			0
$730$	7.89984	+	5.73957i	0.292386	+	0.212431i
$731$	−12.9830	+	4.21844i	−0.480194	+	0.156025i
$732$		0			0
$733$	−13.6757	+	18.8230i	−0.505125	+	0.695245i	−0.983088	−	0.183135i	$-0.941375\pi$
$733$	−13.6757	+	18.8230i	−0.505125	+	0.695245i	0.477963	+	0.878380i	$0.341375\pi$
$734$	13.8135	−	10.0361i	0.509865	−	0.370439i
$735$		0			0
$736$			4.74115i			0.174761i
$737$	40.8147	−	6.07018i	1.50343	−	0.223598i
$738$		0			0
$739$	9.87067	+	3.20717i	0.363098	+	0.117978i	0.484884	−	0.874579i	$-0.338862\pi$
$739$	9.87067	+	3.20717i	0.363098	+	0.117978i	−0.121785	+	0.992556i	$0.538862\pi$
$740$	−1.29289	−	1.77951i	−0.0475276	−	0.0654162i
$741$		0			0
$742$	2.30247	+	7.08626i	0.0845262	+	0.260145i
$743$	14.7220	+	45.3096i	0.540097	+	1.66225i	0.732369	+	0.680907i	$0.238414\pi$
$743$	14.7220	+	45.3096i	0.540097	+	1.66225i	−0.192272	+	0.981342i	$0.561586\pi$
$744$		0			0
$745$	−0.146509	−	0.201653i	−0.00536768	−	0.00738798i
$746$	−33.8105	−	10.9857i	−1.23789	−	0.402215i
$747$		0			0
$748$	−2.69286	+	16.0220i	−0.0984607	+	0.585823i
$749$		−	6.17052i		−	0.225466i
$750$		0			0
$751$	−15.7434	+	11.4383i	−0.574485	+	0.417388i	−0.836732	−	0.547613i	$-0.815537\pi$
$751$	−15.7434	+	11.4383i	−0.574485	+	0.417388i	0.262247	+	0.965001i	$0.415537\pi$
$752$	−2.19910	+	3.02680i	−0.0801929	+	0.110376i
$753$		0			0
$754$	3.56694	−	1.15897i	0.129900	−	0.0422072i
$755$	−57.6492	−	41.8846i	−2.09807	−	1.52434i
$756$		0			0
$757$	10.5732	−	32.5410i	0.384290	−	1.18272i	−0.552703	−	0.833378i	$-0.686404\pi$
$757$	10.5732	−	32.5410i	0.384290	−	1.18272i	0.936994	−	0.349346i	$-0.113596\pi$
$758$	14.2382			0.517154
$759$		0			0
$760$	−10.1497			−0.368167
$761$	−4.53086	+	13.9445i	−0.164243	+	0.505489i	−0.998980	−	0.0451605i	$-0.985620\pi$
$761$	−4.53086	+	13.9445i	−0.164243	+	0.505489i	0.834736	+	0.550650i	$0.185620\pi$
$762$		0			0
$763$	3.39465	+	2.46636i	0.122895	+	0.0892881i
$764$	−5.45999	+	1.77406i	−0.197536	+	0.0641832i
$765$		0			0
$766$	−9.26921	+	12.7580i	−0.334910	+	0.460964i
$767$	34.6964	−	25.2084i	1.25281	−	0.910223i
$768$		0			0
$769$		−	8.52397i		−	0.307382i	−0.988119	−	0.153691i	$-0.950884\pi$
$769$		−	8.52397i		−	0.307382i	0.988119	−	0.153691i	$-0.0491161\pi$
$770$	−12.8365	−	6.69385i	−0.462595	−	0.241230i
$771$		0			0
$772$	−18.2699	−	5.93625i	−0.657548	−	0.213650i
$773$	−17.8117	−	24.5157i	−0.640643	−	0.881770i	0.358007	−	0.933719i	$-0.383457\pi$
$773$	−17.8117	−	24.5157i	−0.640643	−	0.881770i	−0.998650	+	0.0519495i	$0.983457\pi$
$774$		0			0
$775$	22.1907	+	68.2961i	0.797115	+	2.45327i
$776$	−4.63464	−	14.2640i	−0.166374	−	0.512047i
$777$		0			0
$778$	2.72321	+	3.74818i	0.0976319	+	0.134379i
$779$	30.5670	+	9.93181i	1.09517	+	0.355844i
$780$		0			0
$781$	17.4721	−	8.69577i	0.625200	−	0.311159i
$782$			23.2249i			0.830521i
$783$		0			0
$784$	−4.37839	+	3.18109i	−0.156371	+	0.113610i
$785$	37.4700	−	51.5731i	1.33736	−	1.84072i
$786$		0			0
$787$	39.2742	−	12.7610i	1.39997	−	0.454879i	0.490791	−	0.871277i	$-0.336708\pi$
$787$	39.2742	−	12.7610i	1.39997	−	0.454879i	0.909182	+	0.416398i	$0.136708\pi$
$788$	−6.72597	−	4.88671i	−0.239603	−	0.174082i
$789$		0			0
$790$	−17.7302	+	54.5681i	−0.630813	+	1.94144i
$791$	−5.16215			−0.183545
$792$		0			0
$793$	−51.4200			−1.82598
$794$	1.23033	−	3.78658i	0.0436629	−	0.134381i
$795$		0			0
$796$	−16.3099	−	11.8498i	−0.578089	−	0.420006i
$797$	27.4728	−	8.92644i	0.973135	−	0.316191i	0.221054	−	0.975262i	$-0.429050\pi$
$797$	27.4728	−	8.92644i	0.973135	−	0.316191i	0.752081	+	0.659071i	$0.229050\pi$
$798$		0			0
$799$	−10.7725	+	14.8270i	−0.381102	+	0.524542i
$800$	−5.66152	+	4.11333i	−0.200165	+	0.145428i
$801$		0			0
$802$			19.0533i			0.672794i
$803$	4.32314	−	8.29031i	0.152560	−	0.292559i
$804$		0			0
$805$	−19.6821	−	6.39512i	−0.693705	−	0.225398i
$806$	27.9829	+	38.5152i	0.985657	+	1.35664i
$807$		0			0
$808$	−2.13215	−	6.56210i	−0.0750089	−	0.230854i
$809$	4.77506	+	14.6961i	0.167882	+	0.516688i	0.999237	−	0.0390537i	$-0.0124343\pi$
$809$	4.77506	+	14.6961i	0.167882	+	0.516688i	−0.831355	+	0.555742i	$0.812434\pi$
$810$		0			0
$811$	−12.5801	−	17.3150i	−0.441747	−	0.608013i	0.528852	−	0.848714i	$-0.322623\pi$
$811$	−12.5801	−	17.3150i	−0.441747	−	0.608013i	−0.970599	+	0.240701i	$0.922623\pi$
$812$	0.968864	+	0.314803i	0.0340005	+	0.0110474i
$813$		0			0
$814$	−1.50324	+	1.47514i	−0.0526887	+	0.0517035i
$815$		−	17.9128i		−	0.627458i
$816$		0			0
$817$	−6.60622	+	4.79970i	−0.231123	+	0.167920i
$818$	−8.91382	+	12.2688i	−0.311664	+	0.428969i
$819$		0			0
$820$	36.1336	−	11.7405i	1.26184	−	0.409996i
$821$	29.5839	+	21.4940i	1.03249	+	0.750144i	0.968805	−	0.247826i	$-0.0797161\pi$
$821$	29.5839	+	21.4940i	1.03249	+	0.750144i	0.0636807	+	0.997970i	$0.479716\pi$
$822$		0			0
$823$	4.36726	−	13.4410i	0.152233	−	0.468525i	−0.845637	−	0.533759i	$-0.820779\pi$
$823$	4.36726	−	13.4410i	0.152233	−	0.468525i	0.997870	+	0.0652331i	$0.0207791\pi$
$824$	−8.82662			−0.307490
$825$		0			0
$826$	11.6491			0.405325
$827$	17.3875	−	53.5131i	0.604622	−	1.86083i	0.105252	−	0.994446i	$-0.466435\pi$
$827$	17.3875	−	53.5131i	0.604622	−	1.86083i	0.499370	−	0.866389i	$-0.333565\pi$
$828$		0			0
$829$	13.6804	+	9.93938i	0.475139	+	0.345209i	0.799441	−	0.600745i	$-0.205129\pi$
$829$	13.6804	+	9.93938i	0.475139	+	0.345209i	−0.324301	+	0.945954i	$0.605129\pi$
$830$	−5.11725	+	1.66270i	−0.177622	+	0.0577130i
$831$		0			0
$832$	−2.72696	+	3.75334i	−0.0945404	+	0.130124i
$833$	−21.4479	+	15.5828i	−0.743124	+	0.539912i
$834$		0			0
$835$		−	56.3203i		−	1.94904i
$836$	1.42964	+	9.61262i	0.0494451	+	0.332460i
$837$		0			0
$838$	−17.0928	−	5.55378i	−0.590461	−	0.191852i
$839$	−7.83615	−	10.7855i	−0.270534	−	0.372358i	0.652036	−	0.758188i	$-0.273915\pi$
$839$	−7.83615	−	10.7855i	−0.270534	−	0.372358i	−0.922570	+	0.385830i	$0.873915\pi$
$840$		0			0
$841$	−8.75954	−	26.9591i	−0.302053	−	0.929624i
$842$	−0.598808	−	1.84294i	−0.0206363	−	0.0635120i
$843$		0			0
$844$	−7.47964	−	10.2948i	−0.257460	−	0.354363i
$845$	−28.0802	−	9.12380i	−0.965988	−	0.313868i
$846$		0			0
$847$	−4.53157	+	13.1002i	−0.155707	+	0.450127i
$848$		−	5.91267i		−	0.203042i
$849$		0			0
$850$	−27.7334	+	20.1495i	−0.951247	+	0.691121i
$851$	−1.76967	+	2.43574i	−0.0606633	+	0.0834959i
$852$		0			0
$853$	32.4166	−	10.5328i	1.10992	−	0.360636i	0.304010	−	0.952669i	$-0.401674\pi$
$853$	32.4166	−	10.5328i	1.10992	−	0.360636i	0.805914	+	0.592033i	$0.201674\pi$
$854$	−11.2994	−	8.20951i	−0.386658	−	0.280924i
$855$		0			0
$856$	−1.51313	+	4.65694i	−0.0517178	+	0.159171i
$857$	−1.41245			−0.0482484			−0.0241242	−	0.999709i	$-0.507680\pi$
$857$	−1.41245			−0.0482484			−0.0241242	+	0.999709i	$0.507680\pi$
$858$		0			0
$859$	−34.7597			−1.18599			−0.592993	−	0.805207i	$-0.702054\pi$
$859$	−34.7597			−1.18599			−0.592993	+	0.805207i	$0.702054\pi$
$860$	−2.98289	+	9.18038i	−0.101716	+	0.313048i
$861$		0			0
$862$	15.6664	+	11.3823i	0.533599	+	0.387683i
$863$	31.8077	−	10.3349i	1.08275	−	0.351805i	0.287306	−	0.957839i	$-0.407240\pi$
$863$	31.8077	−	10.3349i	1.08275	−	0.351805i	0.795439	+	0.606034i	$0.207240\pi$
$864$		0			0
$865$	8.83372	−	12.1586i	0.300355	−	0.413404i
$866$	−7.99444	+	5.80830i	−0.271662	+	0.197374i
$867$		0			0
$868$			12.9313i			0.438916i
$869$	54.1782	+	9.10587i	1.83787	+	0.308895i
$870$		0			0
$871$	54.8956	+	17.8367i	1.86007	+	0.604373i
$872$	−1.95717	−	2.69381i	−0.0662782	−	0.0912241i
$873$		0			0
$874$	4.29302	+	13.2126i	0.145214	+	0.446921i
$875$	−2.69504	−	8.29447i	−0.0911089	−	0.280404i
$876$		0			0
$877$	−18.5024	−	25.4663i	−0.624780	−	0.859936i	0.372910	−	0.927868i	$-0.378360\pi$
$877$	−18.5024	−	25.4663i	−0.624780	−	0.859936i	−0.997690	+	0.0679313i	$0.978360\pi$
$878$	−20.3829	−	6.62281i	−0.687890	−	0.223509i
$879$		0			0
$880$	8.04635	+	8.19966i	0.271242	+	0.276411i
$881$			48.4042i			1.63078i	0.578913	+	0.815389i	$0.303477\pi$
$881$			48.4042i			1.63078i	−0.578913	+	0.815389i	$0.696523\pi$
$882$		0			0
$883$	1.42413	−	1.03469i	0.0479257	−	0.0348201i	−0.563564	−	0.826072i	$-0.690570\pi$
$883$	1.42413	−	1.03469i	0.0479257	−	0.0348201i	0.611490	+	0.791252i	$0.290570\pi$
$884$	−13.3582	+	18.3860i	−0.449286	+	0.618389i
$885$		0			0
$886$	15.5281	−	5.04540i	0.521678	−	0.169503i
$887$	−12.0530	−	8.75701i	−0.404700	−	0.294032i	0.366753	−	0.930318i	$-0.380470\pi$
$887$	−12.0530	−	8.75701i	−0.404700	−	0.294032i	−0.771453	+	0.636287i	$0.780470\pi$
$888$		0			0
$889$	−0.260011	+	0.800232i	−0.00872049	+	0.0268389i
$890$	39.5314			1.32510
$891$		0			0
$892$	7.65800			0.256409
$893$	−3.38770	+	10.4263i	−0.113365	+	0.348902i
$894$		0			0
$895$	−46.4600	−	33.7551i	−1.55299	−	1.12831i
$896$	−1.19849	+	0.389412i	−0.0400387	+	0.0130094i
$897$		0			0
$898$	17.9390	−	24.6909i	0.598631	−	0.823945i
$899$	−6.71121	+	4.87598i	−0.223832	+	0.162623i
$900$		0			0
$901$		−	28.9637i		−	0.964919i
$902$	−16.2089	−	32.5680i	−0.539698	−	1.08439i
$903$		0			0
$904$	3.89592	+	1.26586i	0.129576	+	0.0421019i
$905$	−15.1572	−	20.8620i	−0.503841	−	0.693478i
$906$		0			0
$907$	15.9847	+	49.1957i	0.530762	+	1.63352i	0.752633	+	0.658441i	$0.228784\pi$
$907$	15.9847	+	49.1957i	0.530762	+	1.63352i	−0.221871	+	0.975076i	$0.571216\pi$
$908$	−5.81751	−	17.9045i	−0.193061	−	0.594180i
$909$		0			0
$910$	−11.9031	−	16.3833i	−0.394585	−	0.543100i
$911$	−34.7390	−	11.2874i	−1.15095	−	0.373968i	−0.329452	−	0.944172i	$-0.606864\pi$
$911$	−34.7390	−	11.2874i	−1.15095	−	0.373968i	−0.821503	+	0.570205i	$0.806864\pi$
$912$		0			0
$913$	2.29552	+	4.61229i	0.0759705	+	0.152645i
$914$		−	30.5861i		−	1.01170i
$915$		0			0
$916$	9.17427	−	6.66550i	0.303127	−	0.220234i
$917$	−6.37182	+	8.77006i	−0.210416	+	0.289613i
$918$		0			0
$919$	26.2611	−	8.53274i	0.866273	−	0.281469i	0.158027	−	0.987435i	$-0.449487\pi$
$919$	26.2611	−	8.53274i	0.866273	−	0.281469i	0.708246	+	0.705966i	$0.249487\pi$
$920$	13.2861	+	9.65289i	0.438029	+	0.318246i
$921$		0			0
$922$	7.89980	−	24.3131i	0.260166	−	0.800709i
$923$	27.3001			0.898592
$924$		0			0
$925$	−4.44389			−0.146114
$926$	−5.98063	+	18.4065i	−0.196536	+	0.604875i
$927$		0			0
$928$	−0.654014	−	0.475169i	−0.0214691	−	0.0155982i
$929$	−34.2301	+	11.1220i	−1.12305	+	0.364902i	−0.810933	−	0.585140i	$-0.801040\pi$
$929$	−34.2301	+	11.1220i	−1.12305	+	0.364902i	−0.312122	+	0.950042i	$0.601040\pi$
$930$		0			0
$931$	−9.32120	+	12.8295i	−0.305490	+	0.420471i
$932$	7.37999	−	5.36188i	0.241740	−	0.175634i
$933$		0			0
$934$			21.9619i			0.718617i
$935$	39.4157	+	40.1667i	1.28903	+	1.31359i
$936$		0			0
$937$	−22.6358	−	7.35481i	−0.739479	−	0.240271i	−0.0850307	−	0.996378i	$-0.527099\pi$
$937$	−22.6358	−	7.35481i	−0.739479	−	0.240271i	−0.654448	+	0.756107i	$0.727099\pi$
$938$	9.21546	+	12.6840i	0.300895	+	0.414147i
$939$		0			0
$940$	4.00464	+	12.3250i	0.130617	+	0.401997i
$941$	13.7709	+	42.3824i	0.448918	+	1.38163i	0.878129	+	0.478424i	$0.158792\pi$
$941$	13.7709	+	42.3824i	0.448918	+	1.38163i	−0.429211	+	0.903204i	$0.641208\pi$
$942$		0			0
$943$	−30.5670	−	42.0718i	−0.995397	−	1.37005i
$944$	−8.79170	−	2.85660i	−0.286145	−	0.0929743i
$945$		0			0
$946$	9.11479	+	1.53195i	0.296347	+	0.0498079i
$947$		−	11.6080i		−	0.377210i	−0.982053	−	0.188605i	$-0.939603\pi$
$947$		−	11.6080i		−	0.377210i	0.982053	−	0.188605i	$-0.0603967\pi$
$948$		0			0
$949$	10.5809	−	7.68750i	0.343472	−	0.249547i
$950$	−12.0529	+	16.5893i	−0.391047	+	0.538230i
$951$		0			0
$952$	−5.87088	+	1.90757i	−0.190276	+	0.0618246i
$953$	−37.3702	−	27.1510i	−1.21054	−	0.879508i	−0.215259	−	0.976557i	$-0.569059\pi$
$953$	−37.3702	−	27.1510i	−1.21054	−	0.879508i	−0.995280	+	0.0970495i	$0.969059\pi$
$954$		0			0
$955$	−6.14502	+	18.9124i	−0.198848	+	0.611991i
$956$	−6.10995			−0.197610
$957$		0			0
$958$	−23.3943			−0.755836
$959$	7.30331	−	22.4773i	0.235836	−	0.725829i
$960$		0			0
$961$	−60.1099	−	43.6724i	−1.93903	−	1.40879i
$962$	−2.80192	+	0.910398i	−0.0903374	+	0.0293524i
$963$		0			0
$964$	−5.34761	+	7.36036i	−0.172235	+	0.237061i
$965$	−53.8322	+	39.1114i	−1.73292	+	1.25904i
$966$		0			0
$967$			38.9085i			1.25121i	0.780139	+	0.625606i	$0.215148\pi$
$967$			38.9085i			1.25121i	−0.780139	+	0.625606i	$0.784852\pi$
$968$	6.63243	−	8.77558i	0.213174	−	0.282058i
$969$		0			0
$970$	−49.4078	−	16.0536i	−1.58639	−	0.515449i
$971$	35.6987	+	49.1351i	1.14563	+	1.57682i	0.754247	+	0.656590i	$0.228002\pi$
$971$	35.6987	+	49.1351i	1.14563	+	1.57682i	0.391379	+	0.920229i	$0.371998\pi$
$972$		0			0
$973$	1.53040	+	4.71008i	0.0490623	+	0.150998i
$974$	−9.68563	−	29.8093i	−0.310348	−	0.955152i
$975$		0			0
$976$	6.51463	+	8.96662i	0.208528	+	0.287015i
$977$	−44.1302	−	14.3388i	−1.41185	−	0.458738i	−0.498847	−	0.866690i	$-0.666243\pi$
$977$	−44.1302	−	14.3388i	−1.41185	−	0.458738i	−0.913004	+	0.407952i	$0.866243\pi$
$978$		0			0
$979$	−5.56824	−	37.4398i	−0.177962	−	1.19658i
$980$			18.7461i			0.598823i
$981$		0			0
$982$	19.0482	−	13.8393i	0.607853	−	0.441631i
$983$	−1.54701	+	2.12928i	−0.0493420	+	0.0679134i	−0.832975	−	0.553311i	$-0.813364\pi$
$983$	−1.54701	+	2.12928i	−0.0493420	+	0.0679134i	0.783633	+	0.621224i	$0.213364\pi$
$984$		0			0
$985$	−27.3879	+	8.89887i	−0.872651	+	0.283541i
$986$	−3.20374	−	2.32765i	−0.102028	−	0.0741275i
$987$		0			0
$988$	−4.20087	+	12.9290i	−0.133647	+	0.411325i
$989$	13.2124			0.420131
$990$		0			0
$991$	−2.52152			−0.0800987			−0.0400493	−	0.999198i	$-0.512752\pi$
$991$	−2.52152			−0.0800987			−0.0400493	+	0.999198i	$0.512752\pi$
$992$	3.17100	−	9.75934i	0.100679	−	0.309859i
$993$		0			0
$994$	5.99913	+	4.35862i	0.190281	+	0.138247i
$995$	−66.4133	+	21.5790i	−2.10544	+	0.684100i
$996$		0			0
$997$	21.9452	−	30.2050i	0.695013	−	0.956603i	−0.304978	−	0.952359i	$-0.598649\pi$
$997$	21.9452	−	30.2050i	0.695013	−	0.956603i	0.999991	−	0.00424392i	$-0.00135089\pi$
$998$	−32.1503	+	23.3586i	−1.01770	+	0.739403i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.l.b.35.1	yes	8
3.2	odd	2		198.2.l.a.35.2	yes	8
4.3	odd	2		1584.2.cd.b.1025.1		8
11.4	even	5		2178.2.b.i.2177.8		8
11.6	odd	10		198.2.l.a.17.2	✓	8
11.7	odd	10		2178.2.b.j.2177.8		8
12.11	even	2		1584.2.cd.a.1025.2		8
33.17	even	10	inner	198.2.l.b.17.1	yes	8
33.26	odd	10		2178.2.b.j.2177.1		8
33.29	even	10		2178.2.b.i.2177.1		8
44.39	even	10		1584.2.cd.a.17.2		8
132.83	odd	10		1584.2.cd.b.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.l.a.17.2	✓	8	11.6	odd	10
198.2.l.a.35.2	yes	8	3.2	odd	2
198.2.l.b.17.1	yes	8	33.17	even	10	inner
198.2.l.b.35.1	yes	8	1.1	even	1	trivial
1584.2.cd.a.17.2		8	44.39	even	10
1584.2.cd.a.1025.2		8	12.11	even	2
1584.2.cd.b.17.1		8	132.83	odd	10
1584.2.cd.b.1025.1		8	4.3	odd	2
2178.2.b.i.2177.1		8	33.29	even	10
2178.2.b.i.2177.8		8	11.4	even	5
2178.2.b.j.2177.1		8	33.26	odd	10
2178.2.b.j.2177.8		8	11.7	odd	10

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-3.29428 + 1.07038i) q^{5} +(-0.740706 + 1.01949i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-3.29428 + 1.07038i) q^{5} +(-0.740706 + 1.01949i) q^{7} +(0.809017 - 0.587785i) q^{8} -3.46382i q^{10} +(-3.28054 + 0.487899i) q^{11} +(-4.41232 - 1.43365i) q^{13} +(-0.740706 - 1.01949i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.51374 + 4.65882i) q^{17} +(1.72232 + 2.37058i) q^{19} +(3.29428 + 1.07038i) q^{20} +(0.549723 - 3.27075i) q^{22} -4.74115i q^{23} +(5.66152 - 4.11333i) q^{25} +(2.72696 - 3.75334i) q^{26} +(1.19849 - 0.389412i) q^{28} +(0.654014 + 0.475169i) q^{29} +(-3.17100 + 9.75934i) q^{31} -1.00000 q^{32} -4.89858 q^{34} +(1.34885 - 4.15134i) q^{35} +(-0.513743 - 0.373256i) q^{37} +(-2.78678 + 0.905480i) q^{38} +(-2.03598 + 2.80229i) q^{40} +(8.87375 - 6.44716i) q^{41} +2.78676i q^{43} +(2.94079 + 1.53354i) q^{44} +(4.50910 + 1.46510i) q^{46} +(2.19910 + 3.02680i) q^{47} +(1.67240 + 5.14710i) q^{49} +(2.16251 + 6.65551i) q^{50} +(2.72696 + 3.75334i) q^{52} +(-5.62328 - 1.82712i) q^{53} +(10.2848 - 5.11870i) q^{55} +1.26016i q^{56} +(-0.654014 + 0.475169i) q^{58} +(-5.43357 + 7.47866i) q^{59} +(10.5409 - 3.42494i) q^{61} +(-8.30179 - 6.03160i) q^{62} +(0.309017 - 0.951057i) q^{64} +16.0700 q^{65} -12.4414 q^{67} +(1.51374 - 4.65882i) q^{68} +(3.53134 + 2.56567i) q^{70} +(-5.59641 + 1.81838i) q^{71} +(-1.65701 + 2.28068i) q^{73} +(0.513743 - 0.373256i) q^{74} -2.93019i q^{76} +(1.93251 - 3.70588i) q^{77} +(-15.7537 - 5.11870i) q^{79} +(-2.03598 - 2.80229i) q^{80} +(3.38947 + 10.4317i) q^{82} +(-0.480018 - 1.47734i) q^{83} +(-9.97340 - 13.7272i) q^{85} +(-2.65036 - 0.861156i) q^{86} +(-2.36723 + 2.32297i) q^{88} +11.4127i q^{89} +(4.72983 - 3.43642i) q^{91} +(-2.78678 + 3.83567i) q^{92} +(-3.55822 + 1.15613i) q^{94} +(-8.21124 - 5.96582i) q^{95} +(4.63464 - 14.2640i) q^{97} -5.41199 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^8	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{8} - 4 q^{11} - 2 q^{16} + 8 q^{17} - 6 q^{22} + 6 q^{25} + 20 q^{26} - 10 q^{28} - 10 q^{29} - 14 q^{31} - 8 q^{32} - 8 q^{34} - 10 q^{35} - 20 q^{38} - 10 q^{40} + 8 q^{41} + 6 q^{44} + 20 q^{46} - 20 q^{47} + 6 q^{49} + 4 q^{50} + 20 q^{52} - 30 q^{53} + 28 q^{55} + 10 q^{58} + 20 q^{59} + 20 q^{61} - 16 q^{62} - 2 q^{64} + 64 q^{65} - 56 q^{67} + 8 q^{68} + 10 q^{70} - 20 q^{71} - 10 q^{73} - 20 q^{79} - 10 q^{80} + 12 q^{82} + 12 q^{83} - 20 q^{86} - 6 q^{88} - 20 q^{92} - 20 q^{94} - 16 q^{95} - 12 q^{97} + 44 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 - 4 * q^11 - 2 * q^16 + 8 * q^17 - 6 * q^22 + 6 * q^25 + 20 * q^26 - 10 * q^28 - 10 * q^29 - 14 * q^31 - 8 * q^32 - 8 * q^34 - 10 * q^35 - 20 * q^38 - 10 * q^40 + 8 * q^41 + 6 * q^44 + 20 * q^46 - 20 * q^47 + 6 * q^49 + 4 * q^50 + 20 * q^52 - 30 * q^53 + 28 * q^55 + 10 * q^58 + 20 * q^59 + 20 * q^61 - 16 * q^62 - 2 * q^64 + 64 * q^65 - 56 * q^67 + 8 * q^68 + 10 * q^70 - 20 * q^71 - 10 * q^73 - 20 * q^79 - 10 * q^80 + 12 * q^82 + 12 * q^83 - 20 * q^86 - 6 * q^88 - 20 * q^92 - 20 * q^94 - 16 * q^95 - 12 * q^97 + 44 * q^98

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