LMFDB - Embedded newform 189.2.g.b.172.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			172.1
Root			$1.19343 - 2.06709i$ of defining polynomial
Character	$\chi$	$=$	189.172
Dual form			189.2.g.b.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19343 + 2.06709i) q^{2} +(-1.84857 - 3.20182i) q^{4} +2.92087 q^{5} +(2.35742 + 1.20106i) q^{7} +4.05086 q^{8} +O(q^{10})$	\(q+(-1.19343 + 2.06709i) q^{2} +(-1.84857 - 3.20182i) q^{4} +2.92087 q^{5} +(2.35742 + 1.20106i) q^{7} +4.05086 q^{8} +(-3.48586 + 6.03769i) q^{10} +1.35371 q^{11} +(-0.733001 + 1.26960i) q^{13} +(-5.29614 + 3.43961i) q^{14} +(-1.13729 + 1.96984i) q^{16} +(-1.65514 + 2.86678i) q^{17} +(-1.10329 - 1.91096i) q^{19} +(-5.39943 - 9.35209i) q^{20} +(-1.61557 + 2.79825i) q^{22} -2.62830 q^{23} +3.53146 q^{25} +(-1.74958 - 3.03036i) q^{26} +(-0.512277 - 9.76830i) q^{28} +(-0.521720 - 0.903646i) q^{29} +(-1.63729 - 2.83587i) q^{31} +(1.33629 + 2.31453i) q^{32} +(-3.95060 - 6.84263i) q^{34} +(6.88572 + 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +5.26683 q^{38} +11.8320 q^{40} +(0.904289 - 1.56627i) q^{41} +(-2.17129 - 3.76078i) q^{43} +(-2.50244 - 4.33435i) q^{44} +(3.13670 - 5.43292i) q^{46} +(1.98957 - 3.44604i) q^{47} +(4.11489 + 5.66283i) q^{49} +(-4.21456 + 7.29984i) q^{50} +5.42002 q^{52} +(3.22743 - 5.59008i) q^{53} +3.95402 q^{55} +(9.54959 + 4.86534i) q^{56} +2.49056 q^{58} +(-6.10700 - 10.5776i) q^{59} +(-0.279867 + 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(-2.14100 + 3.70832i) q^{65} +(-6.40588 - 11.0953i) q^{67} +12.2386 q^{68} +(-15.4693 + 10.0467i) q^{70} -12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} -25.9583 q^{74} +(-4.07903 + 7.06509i) q^{76} +(3.19128 + 1.62590i) q^{77} +(-0.383838 + 0.664827i) q^{79} +(-3.32187 + 5.75365i) q^{80} +(2.15842 + 3.73849i) q^{82} +(0.983707 + 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +10.3652 q^{86} +5.48371 q^{88} +(-3.20356 - 5.54872i) q^{89} +(-3.25286 + 2.11259i) q^{91} +(4.85859 + 8.41533i) q^{92} +(4.74884 + 8.22524i) q^{94} +(-3.22257 - 5.58166i) q^{95} +(-4.14143 - 7.17316i) q^{97} +(-16.6164 + 1.74763i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8} - 7 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 5 q^{35} + 40 q^{38} + 6 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} + 25 q^{49} - 19 q^{50} + 20 q^{52} + 21 q^{53} + 4 q^{55} + 45 q^{56} + 20 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} + 54 q^{68} - 29 q^{70} + 6 q^{71} + 15 q^{73} - 72 q^{74} + 5 q^{76} + 31 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8 - 7 * q^10 + 8 * q^11 - 8 * q^13 - 16 * q^14 + 2 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 5 * q^35 + 40 * q^38 + 6 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 + 25 * q^49 - 19 * q^50 + 20 * q^52 + 21 * q^53 + 4 * q^55 + 45 * q^56 + 20 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 54 * q^68 - 29 * q^70 + 6 * q^71 + 15 * q^73 - 72 * q^74 + 5 * q^76 + 31 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.19343	+	2.06709i	−0.843886	+	1.46165i	0.0426999	+	0.999088i	$0.486404\pi$
$2$	−1.19343	+	2.06709i	−0.843886	+	1.46165i	−0.886585	+	0.462565i	$0.846929\pi$
$3$		0			0
$3$		0			0
$4$	−1.84857	−	3.20182i	−0.924286	−	1.60091i
$5$	2.92087			1.30625			0.653125	−	0.757250i	$-0.273457\pi$
$5$	2.92087			1.30625			0.653125	+	0.757250i	$0.273457\pi$
$6$		0			0
$7$	2.35742	+	1.20106i	0.891022	+	0.453959i
$7$	2.35742	+	1.20106i	0.891022	+	0.453959i
$8$	4.05086			1.43219
$9$		0			0
$10$	−3.48586	+	6.03769i	−1.10233	+	1.90929i
$11$	1.35371			0.408160			0.204080	−	0.978954i	$-0.434580\pi$
$11$	1.35371			0.408160			0.204080	+	0.978954i	$0.434580\pi$
$12$		0			0
$13$	−0.733001	+	1.26960i	−0.203298	+	0.352123i	−0.949589	−	0.313497i	$-0.898499\pi$
$13$	−0.733001	+	1.26960i	−0.203298	+	0.352123i	0.746291	+	0.665620i	$0.231833\pi$
$14$	−5.29614	+	3.43961i	−1.41545	+	0.919275i
$15$		0			0
$16$	−1.13729	+	1.96984i	−0.284323	+	0.492461i
$17$	−1.65514	+	2.86678i	−0.401430	+	0.695297i	−0.993899	−	0.110297i	$-0.964820\pi$
$17$	−1.65514	+	2.86678i	−0.401430	+	0.695297i	0.592469	+	0.805593i	$0.298153\pi$
$18$		0			0
$19$	−1.10329	−	1.91096i	−0.253113	−	0.438404i	0.711268	−	0.702921i	$-0.248121\pi$
$19$	−1.10329	−	1.91096i	−0.253113	−	0.438404i	−0.964381	+	0.264516i	$0.914788\pi$
$20$	−5.39943	−	9.35209i	−1.20735	−	2.09119i
$21$		0			0
$22$	−1.61557	+	2.79825i	−0.344441	+	0.596589i
$23$	−2.62830			−0.548038			−0.274019	−	0.961724i	$-0.588353\pi$
$23$	−2.62830			−0.548038			−0.274019	+	0.961724i	$0.588353\pi$
$24$		0			0
$25$	3.53146			0.706292
$26$	−1.74958	−	3.03036i	−0.343121	−	0.594302i
$27$		0			0
$28$	−0.512277	−	9.76830i	−0.0968112	−	1.84603i
$29$	−0.521720	−	0.903646i	−0.0968810	−	0.167803i	0.813511	−	0.581549i	$-0.197553\pi$
$29$	−0.521720	−	0.903646i	−0.0968810	−	0.167803i	−0.910392	+	0.413747i	$0.864220\pi$
$30$		0			0
$31$	−1.63729	−	2.83587i	−0.294066	−	0.509337i	0.680701	−	0.732561i	$-0.261675\pi$
$31$	−1.63729	−	2.83587i	−0.294066	−	0.509337i	−0.974767	+	0.223224i	$0.928342\pi$
$32$	1.33629	+	2.31453i	0.236226	+	0.409155i
$33$		0			0
$34$	−3.95060	−	6.84263i	−0.677521	−	1.17350i
$35$	6.88572	+	3.50815i	1.16390	+	0.592985i
$36$		0			0
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.835090	+	0.550113i	$0.185415\pi$
$37$	5.43773	+	9.41842i	0.893957	+	1.54838i	0.0588664	+	0.998266i	$0.481251\pi$
$38$	5.26683			0.854393
$39$		0			0
$40$	11.8320			1.87081
$41$	0.904289	−	1.56627i	0.141226	−	0.244611i	−0.786732	−	0.617294i	$-0.788229\pi$
$41$	0.904289	−	1.56627i	0.141226	−	0.244611i	0.927959	+	0.372683i	$0.121562\pi$
$42$		0			0
$43$	−2.17129	−	3.76078i	−0.331118	−	0.573514i	0.651613	−	0.758551i	$-0.274093\pi$
$43$	−2.17129	−	3.76078i	−0.331118	−	0.573514i	−0.982731	+	0.185038i	$0.940759\pi$
$44$	−2.50244	−	4.33435i	−0.377257	−	0.653428i
$45$		0			0
$46$	3.13670	−	5.43292i	0.462481	−	0.801041i
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	−0.683650	−	0.729810i	$-0.739609\pi$
$47$	1.98957	−	3.44604i	0.290209	−	0.502656i	0.973859	+	0.227154i	$0.0729419\pi$
$48$		0			0
$49$	4.11489	+	5.66283i	0.587842	+	0.808976i
$50$	−4.21456	+	7.29984i	−0.596029	+	1.03235i
$51$		0			0
$52$	5.42002			0.751622
$53$	3.22743	−	5.59008i	0.443322	−	0.767856i	−0.554612	−	0.832109i	$-0.687133\pi$
$53$	3.22743	−	5.59008i	0.443322	−	0.767856i	0.997934	+	0.0642533i	$0.0204666\pi$
$54$		0			0
$55$	3.95402			0.533160
$56$	9.54959	+	4.86534i	1.27612	+	0.650158i
$57$		0			0
$58$	2.49056			0.327026
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	−0.922799	−	0.385283i	$-0.874104\pi$
$59$	−6.10700	−	10.5776i	−0.795064	−	1.37709i	0.127735	−	0.991808i	$-0.459229\pi$
$60$		0			0
$61$	−0.279867	+	0.484744i	−0.0358333	+	0.0620651i	−0.883386	−	0.468646i	$-0.844742\pi$
$61$	−0.279867	+	0.484744i	−0.0358333	+	0.0620651i	0.847553	+	0.530711i	$0.178075\pi$
$62$	7.81600			0.992632
$63$		0			0
$64$	−10.9283			−1.36604
$65$	−2.14100	+	3.70832i	−0.265558	+	0.459960i
$66$		0			0
$67$	−6.40588	−	11.0953i	−0.782603	−	1.35551i	−0.930420	−	0.366494i	$-0.880558\pi$
$67$	−6.40588	−	11.0953i	−0.782603	−	1.35551i	0.147817	−	0.989015i	$-0.452775\pi$
$68$	12.2386			1.48414
$69$		0			0
$70$	−15.4693	+	10.0467i	−1.84894	+	1.20080i
$71$	−12.9177			−1.53305			−0.766525	−	0.642214i	$-0.778016\pi$
$71$	−12.9177			−1.53305			−0.766525	+	0.642214i	$0.778016\pi$
$72$		0			0
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	−0.379069	−	0.925368i	$-0.623756\pi$
$73$	5.22772	−	9.05467i	0.611858	−	1.05977i	0.990927	−	0.134401i	$-0.0429109\pi$
$74$	−25.9583			−3.01759
$75$		0			0
$76$	−4.07903	+	7.06509i	−0.467897	+	0.810422i
$77$	3.19128	+	1.62590i	0.363680	+	0.185288i
$78$		0			0
$79$	−0.383838	+	0.664827i	−0.0431852	+	0.0747989i	−0.886810	−	0.462134i	$-0.847084\pi$
$79$	−0.383838	+	0.664827i	−0.0431852	+	0.0747989i	0.843625	+	0.536933i	$0.180417\pi$
$80$	−3.32187	+	5.75365i	−0.371397	+	0.643278i
$81$		0			0
$82$	2.15842	+	3.73849i	0.238358	+	0.412847i
$83$	0.983707	+	1.70383i	0.107976	+	0.187020i	0.914950	−	0.403567i	$-0.132230\pi$
$83$	0.983707	+	1.70383i	0.107976	+	0.187020i	−0.806974	+	0.590587i	$0.798896\pi$
$84$		0			0
$85$	−4.83443	+	8.37348i	−0.524368	+	0.908232i
$86$	10.3652			1.11770
$87$		0			0
$88$	5.48371			0.584565
$89$	−3.20356	−	5.54872i	−0.339576	−	0.588163i	0.644777	−	0.764371i	$-0.276950\pi$
$89$	−3.20356	−	5.54872i	−0.339576	−	0.588163i	−0.984353	+	0.176208i	$0.943617\pi$
$90$		0			0
$91$	−3.25286	+	2.11259i	−0.340992	+	0.221460i
$92$	4.85859	+	8.41533i	0.506543	+	0.877359i
$93$		0			0
$94$	4.74884	+	8.22524i	0.489806	+	0.848369i
$95$	−3.22257	−	5.58166i	−0.330629	−	0.572666i
$96$		0			0
$97$	−4.14143	−	7.17316i	−0.420498	−	0.728324i	0.575490	−	0.817809i	$-0.304811\pi$
$97$	−4.14143	−	7.17316i	−0.420498	−	0.728324i	−0.995988	+	0.0894847i	$0.971478\pi$
$98$	−16.6164	+	1.74763i	−1.67851	+	0.176537i
$99$		0			0
$100$	−6.52815	−	11.3071i	−0.652815	−	1.13071i
$101$	16.2266			1.61461			0.807305	−	0.590134i	$-0.200925\pi$
$101$	16.2266			1.61461			0.807305	+	0.590134i	$0.200925\pi$
$102$		0			0
$103$	−2.22683			−0.219416			−0.109708	−	0.993964i	$-0.534992\pi$
$103$	−2.22683			−0.219416			−0.109708	+	0.993964i	$0.534992\pi$
$104$	−2.96929	+	5.14295i	−0.291162	+	0.504308i
$105$		0			0
$106$	7.70346	+	13.3428i	0.748226	+	1.29597i
$107$	8.75403	+	15.1624i	0.846284	+	1.46581i	0.884501	+	0.466537i	$0.154499\pi$
$107$	8.75403	+	15.1624i	0.846284	+	1.46581i	−0.0382175	+	0.999269i	$0.512168\pi$
$108$		0			0
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	0.202218	+	0.979341i	$0.435185\pi$
$109$	−7.79917	+	13.5086i	−0.747025	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$110$	−4.71886	+	8.17331i	−0.449926	+	0.779295i
$111$		0			0
$112$	−5.04698	+	3.27780i	−0.476895	+	0.309723i
$113$	0.844555	−	1.46281i	0.0794491	−	0.137610i	−0.823563	−	0.567224i	$-0.808017\pi$
$113$	0.844555	−	1.46281i	0.0794491	−	0.137610i	0.903012	+	0.429615i	$0.141351\pi$
$114$		0			0
$115$	−7.67690			−0.715875
$116$	−1.92887	+	3.34091i	−0.179092	+	0.310196i
$117$		0			0
$118$	29.1532			2.68377
$119$	−7.34505	+	4.77029i	−0.673319	+	0.437292i
$120$		0			0
$121$	−9.16746			−0.833405
$122$	−0.668005	−	1.15702i	−0.0604784	−	0.104752i
$123$		0			0
$124$	−6.05330	+	10.4846i	−0.543602	+	0.941546i
$125$	−4.28942			−0.383657
$126$		0			0
$127$	−3.96918			−0.352208			−0.176104	−	0.984372i	$-0.556350\pi$
$127$	−3.96918			−0.352208			−0.176104	+	0.984372i	$0.556350\pi$
$128$	10.3696	−	17.9607i	0.916552	−	1.58751i
$129$		0			0
$130$	−5.11028	−	8.85127i	−0.448202	−	0.776308i
$131$	−5.32863			−0.465565			−0.232782	−	0.972529i	$-0.574783\pi$
$131$	−5.32863			−0.465565			−0.232782	+	0.972529i	$0.574783\pi$
$132$		0			0
$133$	−0.305745	−	5.83007i	−0.0265115	−	0.505531i
$134$	30.5800			2.64171
$135$		0			0
$136$	−6.70473	+	11.6129i	−0.574925	+	0.995800i
$137$	7.49543			0.640378			0.320189	−	0.947354i	$-0.396254\pi$
$137$	7.49543			0.640378			0.320189	+	0.947354i	$0.396254\pi$
$138$		0			0
$139$	7.03285	−	12.1812i	0.596518	−	1.03320i	−0.396812	−	0.917900i	$-0.629884\pi$
$139$	7.03285	−	12.1812i	0.596518	−	1.03320i	0.993331	−	0.115300i	$-0.0367830\pi$
$140$	−1.49629	−	28.5319i	−0.126460	−	2.41138i
$141$		0			0
$142$	15.4164	−	26.7021i	1.29372	−	2.24079i
$143$	−0.992275	+	1.71867i	−0.0829782	+	0.143722i
$144$		0			0
$145$	−1.52388	−	2.63943i	−0.126551	−	0.219193i
$146$	12.4779	+	21.6123i	1.03268	+	1.78865i
$147$		0			0
$148$	20.1041	−	34.8212i	1.65254	−	2.86229i
$149$	−2.17971			−0.178569			−0.0892846	−	0.996006i	$-0.528458\pi$
$149$	−2.17971			−0.178569			−0.0892846	+	0.996006i	$0.528458\pi$
$150$		0			0
$151$	14.0277			1.14156			0.570781	−	0.821102i	$-0.306641\pi$
$151$	14.0277			1.14156			0.570781	+	0.821102i	$0.306641\pi$
$152$	−4.46929	−	7.74103i	−0.362507	−	0.627880i
$153$		0			0
$154$	−7.16946	+	4.65626i	−0.577731	+	0.375212i
$155$	−4.78231	−	8.28320i	−0.384124	−	0.665322i
$156$		0			0
$157$	−1.48312	−	2.56883i	−0.118365	−	0.205015i	0.800755	−	0.598993i	$-0.204432\pi$
$157$	−1.48312	−	2.56883i	−0.118365	−	0.205015i	−0.919120	+	0.393978i	$0.871099\pi$
$158$	−0.916172	−	1.58686i	−0.0728867	−	0.126243i
$159$		0			0
$160$	3.90314	+	6.76043i	0.308570	+	0.534459i
$161$	−6.19601	−	3.15675i	−0.488314	−	0.248787i
$162$		0			0
$163$	−0.194278	−	0.336499i	−0.0152170	−	0.0263566i	0.858317	−	0.513120i	$-0.171511\pi$
$163$	−0.194278	−	0.336499i	−0.0152170	−	0.0263566i	−0.873534	+	0.486764i	$0.838177\pi$
$164$	−6.68657			−0.522133
$165$		0			0
$166$	−4.69596			−0.364477
$167$	−3.64889	+	6.32006i	−0.282360	+	0.489061i	−0.971965	−	0.235124i	$-0.924450\pi$
$167$	−3.64889	+	6.32006i	−0.282360	+	0.489061i	0.689606	+	0.724185i	$0.257784\pi$
$168$		0			0
$169$	5.42542	+	9.39710i	0.417340	+	0.722854i
$170$	−11.5392	−	19.9864i	−0.885013	−	1.53289i
$171$		0			0
$172$	−8.02756	+	13.9041i	−0.612096	+	1.06018i
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	−0.932750	−	0.360525i	$-0.882598\pi$
$173$	−2.02754	+	3.51181i	−0.154151	+	0.266998i	0.778598	+	0.627522i	$0.215931\pi$
$174$		0			0
$175$	8.32514	+	4.24151i	0.629322	+	0.320628i
$176$	−1.53957	+	2.66661i	−0.116049	+	0.201003i
$177$		0			0
$178$	15.2929			1.14625
$179$	−5.29243	+	9.16675i	−0.395575	+	0.685155i	−0.993174	−	0.116639i	$-0.962788\pi$
$179$	−5.29243	+	9.16675i	−0.395575	+	0.685155i	0.597600	+	0.801795i	$0.296121\pi$
$180$		0			0
$181$	−19.6312			−1.45917			−0.729586	−	0.683889i	$-0.760287\pi$
$181$	−19.6312			−1.45917			−0.729586	+	0.683889i	$0.760287\pi$
$182$	−0.484844	−	9.24519i	−0.0359390	−	0.685299i
$183$		0			0
$184$	−10.6469			−0.784896
$185$	15.8829	+	27.5099i	1.16773	+	2.02257i
$186$		0			0
$187$	−2.24058	+	3.88081i	−0.163848	+	0.283793i
$188$	−14.7115			−1.07294
$189$		0			0
$190$	15.3837			1.11605
$191$	4.14357	−	7.17688i	0.299818	−	0.519301i	−0.676276	−	0.736648i	$-0.736407\pi$
$191$	4.14357	−	7.17688i	0.299818	−	0.519301i	0.976094	+	0.217348i	$0.0697406\pi$
$192$		0			0
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	0.976152	+	0.217090i	$0.0696566\pi$
$193$	9.39242	+	16.2682i	0.676082	+	1.17101i	−0.300070	+	0.953917i	$0.597010\pi$
$194$	19.7701			1.41941
$195$		0			0
$196$	10.5247	−	23.6433i	0.751764	−	1.68881i
$197$	−5.99634			−0.427222			−0.213611	−	0.976919i	$-0.568522\pi$
$197$	−5.99634			−0.427222			−0.213611	+	0.976919i	$0.568522\pi$
$198$		0			0
$199$	7.20434	−	12.4783i	0.510702	−	0.884562i	−0.489221	−	0.872160i	$-0.662719\pi$
$199$	7.20434	−	12.4783i	0.510702	−	0.884562i	0.999923	−	0.0124022i	$-0.00394785\pi$
$200$	14.3054			1.01155
$201$		0			0
$202$	−19.3654	+	33.5419i	−1.36255	+	2.36000i
$203$	−0.144579	−	2.75690i	−0.0101475	−	0.193496i
$204$		0			0
$205$	2.64131	−	4.57488i	0.184477	−	0.319523i
$206$	2.65758	−	4.60306i	0.185162	−	0.320710i
$207$		0			0
$208$	−1.66727	−	2.88780i	−0.115604	−	0.200233i
$209$	−1.49354	−	2.58690i	−0.103311	−	0.178939i
$210$		0			0
$211$	−6.92418	+	11.9930i	−0.476680	+	0.825634i	−0.999643	−	0.0267212i	$-0.991493\pi$
$211$	−6.92418	+	11.9930i	−0.476680	+	0.825634i	0.522963	+	0.852356i	$0.324827\pi$
$212$	−23.8646			−1.63902
$213$		0			0
$214$	−41.7894			−2.85667
$215$	−6.34204	−	10.9847i	−0.432523	−	0.749153i
$216$		0			0
$217$	−0.453726	−	8.65184i	−0.0308010	−	0.587325i
$218$	−18.6156	−	32.2431i	−1.26081	−	2.18378i
$219$		0			0
$220$	−7.30929	−	12.6601i	−0.492792	−	0.853541i
$221$	−2.42644	−	4.20271i	−0.163220	−	0.282705i
$222$		0			0
$223$	2.33756	+	4.04878i	0.156535	+	0.271126i	0.933617	−	0.358273i	$-0.116634\pi$
$223$	2.33756	+	4.04878i	0.156535	+	0.271126i	−0.777082	+	0.629399i	$0.783301\pi$
$224$	0.370314	+	7.06130i	0.0247427	+	0.471803i
$225$		0			0
$226$	2.01584	+	3.49154i	0.134092	+	0.232254i
$227$	−19.7126			−1.30837			−0.654187	−	0.756333i	$-0.726989\pi$
$227$	−19.7126			−1.30837			−0.654187	+	0.756333i	$0.726989\pi$
$228$		0			0
$229$	28.0728			1.85510			0.927552	−	0.373694i	$-0.121909\pi$
$229$	28.0728			1.85510			0.927552	+	0.373694i	$0.121909\pi$
$230$	9.16188	−	15.8688i	0.604116	−	1.04636i
$231$		0			0
$232$	−2.11342	−	3.66054i	−0.138753	−	0.240326i
$233$	6.90113	+	11.9531i	0.452108	+	0.783074i	0.998517	−	0.0544448i	$-0.0173389\pi$
$233$	6.90113	+	11.9531i	0.452108	+	0.783074i	−0.546409	+	0.837518i	$0.684006\pi$
$234$		0			0
$235$	5.81127	−	10.0654i	0.379085	−	0.656595i
$236$	−22.5785	+	39.1070i	−1.46973	+	2.54565i
$237$		0			0
$238$	−1.09479	−	20.8759i	−0.0709647	−	1.35318i
$239$	−5.53069	+	9.57944i	−0.357751	+	0.619642i	−0.987585	−	0.157087i	$-0.949790\pi$
$239$	−5.53069	+	9.57944i	−0.357751	+	0.619642i	0.629834	+	0.776730i	$0.283123\pi$
$240$		0			0
$241$	−23.1697			−1.49249			−0.746247	−	0.665669i	$-0.768146\pi$
$241$	−23.1697			−1.49249			−0.746247	+	0.665669i	$0.768146\pi$
$242$	10.9408	−	18.9499i	0.703299	−	1.21815i
$243$		0			0
$244$	2.06942			0.132481
$245$	12.0190	+	16.5404i	0.767869	+	1.05673i
$246$		0			0
$247$	3.23486			0.205829
$248$	−6.63243	−	11.4877i	−0.421160	−	0.729470i
$249$		0			0
$250$	5.11914	−	8.86660i	0.323763	−	0.560773i
$251$	7.78402			0.491323			0.245662	−	0.969356i	$-0.420995\pi$
$251$	7.78402			0.491323			0.245662	+	0.969356i	$0.420995\pi$
$252$		0			0
$253$	−3.55796			−0.223687
$254$	4.73696	−	8.20466i	0.297223	−	0.514806i
$255$		0			0
$256$	13.8226	+	23.9414i	0.863912	+	1.49634i
$257$	−10.3760			−0.647235			−0.323618	−	0.946188i	$-0.604899\pi$
$257$	−10.3760			−0.647235			−0.323618	+	0.946188i	$0.604899\pi$
$258$		0			0
$259$	1.50690	+	28.7343i	0.0936345	+	1.78546i
$260$	15.8312			0.981807
$261$		0			0
$262$	6.35937	−	11.0148i	0.392883	−	0.680494i
$263$	19.1331			1.17980			0.589898	−	0.807478i	$-0.299168\pi$
$263$	19.1331			1.17980			0.589898	+	0.807478i	$0.299168\pi$
$264$		0			0
$265$	9.42689	−	16.3279i	0.579090	−	1.00301i
$266$	12.4162	+	6.32580i	0.761283	+	0.387860i
$267$		0			0
$268$	−23.6835	+	41.0210i	−1.44670	+	2.50576i
$269$	4.41840	−	7.65290i	0.269395	−	0.466605i	−0.699311	−	0.714818i	$-0.746510\pi$
$269$	4.41840	−	7.65290i	0.269395	−	0.466605i	0.968706	+	0.248212i	$0.0798430\pi$
$270$		0			0
$271$	−9.16955	−	15.8821i	−0.557010	−	0.964770i	−0.997744	−	0.0671321i	$-0.978615\pi$
$271$	−9.16955	−	15.8821i	−0.557010	−	0.964770i	0.440734	−	0.897638i	$-0.354718\pi$
$272$	−3.76474	−	6.52073i	−0.228271	−	0.395377i
$273$		0			0
$274$	−8.94531	+	15.4937i	−0.540406	+	0.936010i
$275$	4.78059			0.288280
$276$		0			0
$277$	5.10482			0.306719			0.153360	−	0.988170i	$-0.450991\pi$
$277$	5.10482			0.306719			0.153360	+	0.988170i	$0.450991\pi$
$278$	16.7865	+	29.0750i	1.00679	+	1.74381i
$279$		0			0
$280$	27.8931	+	14.2110i	1.66693	+	0.849270i
$281$	0.853180	+	1.47775i	0.0508964	+	0.0881552i	0.890351	−	0.455274i	$-0.150459\pi$
$281$	0.853180	+	1.47775i	0.0508964	+	0.0881552i	−0.839455	+	0.543430i	$0.817125\pi$
$282$		0			0
$283$	6.24415	+	10.8152i	0.371176	+	0.642896i	0.989747	−	0.142833i	$-0.0456213\pi$
$283$	6.24415	+	10.8152i	0.371176	+	0.642896i	−0.618571	+	0.785729i	$0.712288\pi$
$284$	23.8793	+	41.3602i	1.41698	+	2.45428i
$285$		0			0
$286$	−2.36843	−	4.10224i	−0.140048	−	0.242571i
$287$	4.01299	−	2.60626i	0.236879	−	0.153843i
$288$		0			0
$289$	3.02104	+	5.23260i	0.177708	+	0.307800i
$290$	7.27458			0.427178
$291$		0			0
$292$	−38.6552			−2.26213
$293$	2.60202	−	4.50684i	0.152012	−	0.263292i	−0.779955	−	0.625835i	$-0.784758\pi$
$293$	2.60202	−	4.50684i	0.152012	−	0.263292i	0.931967	+	0.362543i	$0.118091\pi$
$294$		0			0
$295$	−17.8377	−	30.8959i	−1.03855	−	1.79883i
$296$	22.0275	+	38.1527i	1.28032	+	2.21758i
$297$		0			0
$298$	2.60135	−	4.50566i	0.150692	−	0.261006i
$299$	1.92654	−	3.33687i	0.111415	−	0.192976i
$300$		0			0
$301$	−0.601708	−	11.4736i	−0.0346819	−	0.661328i
$302$	−16.7412	+	28.9966i	−0.963347	+	1.66857i
$303$		0			0
$304$	5.01906			0.287863
$305$	−0.817453	+	1.41587i	−0.0468072	+	0.0810725i
$306$		0			0
$307$	5.00136			0.285442			0.142721	−	0.989763i	$-0.454415\pi$
$307$	5.00136			0.285442			0.142721	+	0.989763i	$0.454415\pi$
$308$	−0.693477	−	13.2235i	−0.0395145	−	0.753478i
$309$		0			0
$310$	22.8295			1.29663
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.801652	−	0.597791i	$-0.796045\pi$
$311$	−16.1984	−	28.0565i	−0.918528	−	1.59094i	−0.116876	−	0.993146i	$-0.537288\pi$
$312$		0			0
$313$	−0.759535	+	1.31555i	−0.0429315	+	0.0743595i	−0.886693	−	0.462359i	$-0.847003\pi$
$313$	−0.759535	+	1.31555i	−0.0429315	+	0.0743595i	0.843761	+	0.536719i	$0.180336\pi$
$314$	7.08000			0.399548
$315$		0			0
$316$	2.83821			0.159662
$317$	−10.7544	+	18.6272i	−0.604029	+	1.04621i	0.388175	+	0.921586i	$0.373106\pi$
$317$	−10.7544	+	18.6272i	−0.604029	+	1.04621i	−0.992204	+	0.124623i	$0.960228\pi$
$318$		0			0
$319$	−0.706261	−	1.22328i	−0.0395430	−	0.0684905i
$320$	−31.9200			−1.78439
$321$		0			0
$322$	13.9198	−	9.04032i	0.775721	−	0.503797i
$323$	7.30441			0.406428
$324$		0			0
$325$	−2.58856	+	4.48352i	−0.143588	+	0.248701i
$326$	0.927430			0.0513656
$327$		0			0
$328$	3.66315	−	6.34476i	0.202263	−	0.350330i
$329$	8.82917	−	5.73417i	0.486768	−	0.316135i
$330$		0			0
$331$	−9.73902	+	16.8685i	−0.535305	+	0.927175i	0.463844	+	0.885917i	$0.346470\pi$
$331$	−9.73902	+	16.8685i	−0.535305	+	0.927175i	−0.999149	+	0.0412580i	$0.986863\pi$
$332$	3.63691	−	6.29931i	0.199601	−	0.345719i
$333$		0			0
$334$	−8.70942	−	15.0852i	−0.476558	−	0.825423i
$335$	−18.7107	−	32.4079i	−1.02228	−	1.77063i
$336$		0			0
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	−0.703260	−	0.710933i	$-0.748273\pi$
$337$	4.84742	−	8.39598i	0.264056	−	0.457358i	0.967316	+	0.253575i	$0.0816063\pi$
$338$	−25.8995			−1.40875
$339$		0			0
$340$	35.7472			1.93866
$341$	−2.21642	−	3.83896i	−0.120026	−	0.207891i
$342$		0			0
$343$	2.89912	+	18.2919i	0.156538	+	0.987672i
$344$	−8.79558	−	15.2344i	−0.474226	−	0.821383i
$345$		0			0
$346$	−4.83948	−	8.38222i	−0.260172	−	0.450631i
$347$	1.01302	+	1.75460i	0.0543817	+	0.0941919i	0.891935	−	0.452164i	$-0.149348\pi$
$347$	1.01302	+	1.75460i	0.0543817	+	0.0941919i	−0.837553	+	0.546356i	$0.816015\pi$
$348$		0			0
$349$	8.14577	+	14.1089i	0.436033	+	0.755231i	0.997379	−	0.0723497i	$-0.0230498\pi$
$349$	8.14577	+	14.1089i	0.436033	+	0.755231i	−0.561346	+	0.827581i	$0.689716\pi$
$350$	−18.7031	+	12.1469i	−0.999722	+	0.649276i
$351$		0			0
$352$	1.80896	+	3.13321i	0.0964180	+	0.167001i
$353$	−17.0614			−0.908089			−0.454045	−	0.890979i	$-0.650019\pi$
$353$	−17.0614			−0.908089			−0.454045	+	0.890979i	$0.650019\pi$
$354$		0			0
$355$	−37.7309			−2.00255
$356$	−11.8440	+	20.5144i	−0.627731	+	1.08726i
$357$		0			0
$358$	−12.6323	−	21.8798i	−0.667639	−	1.15639i
$359$	−1.48363	−	2.56972i	−0.0783030	−	0.135625i	0.824215	−	0.566277i	$-0.191617\pi$
$359$	−1.48363	−	2.56972i	−0.0783030	−	0.135625i	−0.902518	+	0.430652i	$0.858283\pi$
$360$		0			0
$361$	7.06549	−	12.2378i	0.371868	−	0.644094i
$362$	23.4285	−	40.5794i	1.23137	−	2.13280i
$363$		0			0
$364$	12.7773	+	6.50979i	0.669712	+	0.341206i
$365$	15.2695	−	26.4475i	0.799240	−	1.38432i
$366$		0			0
$367$	−10.1575			−0.530216			−0.265108	−	0.964219i	$-0.585408\pi$
$367$	−10.1575			−0.530216			−0.265108	+	0.964219i	$0.585408\pi$
$368$	2.98914	−	5.17733i	0.155819	−	0.269887i
$369$		0			0
$370$	−75.8207			−3.94173
$371$	14.3225	−	9.30182i	0.743585	−	0.482927i
$372$		0			0
$373$	−25.4846			−1.31954			−0.659771	−	0.751467i	$-0.729347\pi$
$373$	−25.4846			−1.31954			−0.659771	+	0.751467i	$0.729347\pi$
$374$	−5.34798	−	9.26297i	−0.276537	−	0.478977i
$375$		0			0
$376$	8.05947	−	13.9594i	0.415635	−	0.719902i
$377$	1.52969			0.0787829
$378$		0			0
$379$	9.85497			0.506216			0.253108	−	0.967438i	$-0.418547\pi$
$379$	9.85497			0.506216			0.253108	+	0.967438i	$0.418547\pi$
$380$	−11.9143	+	20.6362i	−0.611191	+	1.05861i
$381$		0			0
$382$	9.89016	+	17.1303i	0.506025	+	0.876460i
$383$	27.3127			1.39561			0.697806	−	0.716286i	$-0.254160\pi$
$383$	27.3127			1.39561			0.697806	+	0.716286i	$0.254160\pi$
$384$		0			0
$385$	9.32130	+	4.74903i	0.475057	+	0.242033i
$386$	−44.8370			−2.28214
$387$		0			0
$388$	−15.3114	+	26.5202i	−0.777321	+	1.34636i
$389$	−4.18446			−0.212161			−0.106080	−	0.994358i	$-0.533830\pi$
$389$	−4.18446			−0.212161			−0.106080	+	0.994358i	$0.533830\pi$
$390$		0			0
$391$	4.35019	−	7.53475i	0.219999	−	0.381049i
$392$	16.6688	+	22.9393i	0.841904	+	1.15861i
$393$		0			0
$394$	7.15624	−	12.3950i	0.360526	−	0.624450i
$395$	−1.12114	+	1.94187i	−0.0564107	+	0.0977062i
$396$		0			0
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	0.937745	+	0.347323i	$0.112909\pi$
$397$	15.3354	+	26.5618i	0.769664	+	1.33310i	−0.168082	+	0.985773i	$0.553757\pi$
$398$	17.1958	+	29.7840i	0.861948	+	1.49294i
$399$		0			0
$400$	−4.01629	+	6.95642i	−0.200815	+	0.347821i
$401$	6.84803			0.341974			0.170987	−	0.985273i	$-0.445304\pi$
$401$	6.84803			0.341974			0.170987	+	0.985273i	$0.445304\pi$
$402$		0			0
$403$	4.80055			0.239132
$404$	−29.9961	−	51.9547i	−1.49236	−	2.58485i
$405$		0			0
$406$	5.87130	+	2.99132i	0.291388	+	0.148457i
$407$	7.36113	+	12.7499i	0.364878	+	0.631987i
$408$		0			0
$409$	9.13490	+	15.8221i	0.451692	+	0.782353i	0.998491	−	0.0549104i	$-0.0174873\pi$
$409$	9.13490	+	15.8221i	0.451692	+	0.782353i	−0.546799	+	0.837264i	$0.684154\pi$
$410$	6.30445	+	10.9196i	0.311355	+	0.539282i
$411$		0			0
$412$	4.11646	+	7.12991i	0.202803	+	0.351265i
$413$	−1.69237	−	32.2709i	−0.0832763	−	1.58795i
$414$		0			0
$415$	2.87328	+	4.97666i	0.141044	+	0.244295i
$416$	−3.91802			−0.192097
$417$		0			0
$418$	7.12979			0.348729
$419$	−11.2310	+	19.4526i	−0.548669	+	0.950322i	0.449698	+	0.893181i	$0.351532\pi$
$419$	−11.2310	+	19.4526i	−0.548669	+	0.950322i	−0.998366	+	0.0571410i	$0.981802\pi$
$420$		0			0
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	0.999960	+	0.00894684i	$0.00284791\pi$
$421$	10.4177	+	18.0440i	0.507728	+	0.879411i	−0.492232	+	0.870464i	$0.663819\pi$
$422$	−16.5271	−	28.6258i	−0.804527	−	1.39348i
$423$		0			0
$424$	13.0739	−	22.6446i	0.634923	−	1.09972i
$425$	−5.84505	+	10.1239i	−0.283526	+	0.491082i
$426$		0			0
$427$	−1.24197	+	0.806608i	−0.0601033	+	0.0390345i
$428$	32.3649	−	56.0577i	1.56442	−	2.70965i
$429$		0			0
$430$	30.2752			1.46000
$431$	10.1213	−	17.5307i	0.487527	−	0.844422i	−0.512370	−	0.858765i	$-0.671232\pi$
$431$	10.1213	−	17.5307i	0.487527	−	0.844422i	0.999897	+	0.0143427i	$0.00456557\pi$
$432$		0			0
$433$	−21.6764			−1.04170			−0.520851	−	0.853648i	$-0.674385\pi$
$433$	−21.6764			−1.04170			−0.520851	+	0.853648i	$0.674385\pi$
$434$	18.4256	+	9.38751i	0.884458	+	0.450615i
$435$		0			0
$436$	57.6693			2.76186
$437$	2.89978	+	5.02257i	0.138715	+	0.240262i
$438$		0			0
$439$	17.7390	−	30.7249i	0.846639	−	1.46642i	−0.0375520	−	0.999295i	$-0.511956\pi$
$439$	17.7390	−	30.7249i	0.846639	−	1.46642i	0.884191	−	0.467126i	$-0.154711\pi$
$440$	16.0172			0.763589
$441$		0			0
$442$	11.5832			0.550955
$443$	−9.60313	+	16.6331i	−0.456258	+	0.790263i	−0.998760	−	0.0497923i	$-0.984144\pi$
$443$	−9.60313	+	16.6331i	−0.456258	+	0.790263i	0.542501	+	0.840055i	$0.317477\pi$
$444$		0			0
$445$	−9.35716	−	16.2071i	−0.443572	−	0.768289i
$446$	−11.1589			−0.528390
$447$		0			0
$448$	−25.7626	−	13.1256i	−1.21717	−	0.620125i
$449$	29.6082			1.39730			0.698648	−	0.715465i	$-0.253785\pi$
$449$	29.6082			1.39730			0.698648	+	0.715465i	$0.253785\pi$
$450$		0			0
$451$	1.22415	−	2.12029i	0.0576429	−	0.0998405i
$452$	−6.24488			−0.293735
$453$		0			0
$454$	23.5257	−	40.7478i	1.10412	−	1.91239i
$455$	−9.50117	+	6.17060i	−0.445422	+	0.289282i
$456$		0			0
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	−0.732267	−	0.681017i	$-0.761538\pi$
$457$	4.78098	−	8.28090i	0.223645	−	0.387364i	0.955912	+	0.293653i	$0.0948711\pi$
$458$	−33.5031	+	58.0290i	−1.56550	+	2.71152i
$459$		0			0
$460$	14.1913	+	24.5800i	0.661673	+	1.14605i
$461$	−10.9187	−	18.9118i	−0.508536	−	0.880809i	−0.999951	−	0.00988416i	$-0.996854\pi$
$461$	−10.9187	−	18.9118i	−0.508536	−	0.880809i	0.491416	−	0.870925i	$-0.336480\pi$
$462$		0			0
$463$	13.0744	−	22.6456i	0.607621	−	1.05243i	−0.384010	−	0.923329i	$-0.625457\pi$
$463$	13.0744	−	22.6456i	0.607621	−	1.05243i	0.991631	−	0.129102i	$-0.0412094\pi$
$464$	2.37339			0.110182
$465$		0			0
$466$	−32.9442			−1.52611
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	0.913758	+	0.406258i	$0.133167\pi$
$467$	17.4764	+	30.2699i	0.808709	+	1.40073i	−0.105049	+	0.994467i	$0.533500\pi$
$468$		0			0
$469$	−1.77520	−	33.8502i	−0.0819711	−	1.56306i
$470$	13.8707	+	24.0248i	0.639809	+	1.10818i
$471$		0			0
$472$	−24.7386	−	42.8485i	−1.13869	−	1.97226i
$473$	−2.93930	−	5.09102i	−0.135149	−	0.234086i
$474$		0			0
$475$	−3.89623	−	6.74848i	−0.178771	−	0.309641i
$476$	28.8515	+	14.6993i	1.32240	+	0.673741i
$477$		0			0
$478$	−13.2010	−	22.8649i	−0.603801	−	1.04581i
$479$	29.8109			1.36209			0.681047	−	0.732240i	$-0.261525\pi$
$479$	29.8109			1.36209			0.681047	+	0.732240i	$0.261525\pi$
$480$		0			0
$481$	−15.9434			−0.726959
$482$	27.6516	−	47.8939i	1.25949	−	2.18151i
$483$		0			0
$484$	16.9467	+	29.3525i	0.770304	+	1.33421i
$485$	−12.0965	−	20.9518i	−0.549276	−	0.951374i
$486$		0			0
$487$	−11.2253	+	19.4428i	−0.508667	+	0.881037i	0.491283	+	0.871000i	$0.336528\pi$
$487$	−11.2253	+	19.4428i	−0.508667	+	0.881037i	−0.999950	+	0.0100365i	$0.996805\pi$
$488$	−1.13370	+	1.96363i	−0.0513202	+	0.0888892i
$489$		0			0
$490$	−48.5344	+	5.10459i	−2.19256	+	0.230602i
$491$	−17.5222	+	30.3494i	−0.790767	+	1.36965i	0.134726	+	0.990883i	$0.456984\pi$
$491$	−17.5222	+	30.3494i	−0.790767	+	1.36965i	−0.925493	+	0.378765i	$0.876349\pi$
$492$		0			0
$493$	3.45407			0.155564
$494$	−3.86060	+	6.68675i	−0.173696	+	0.300851i
$495$		0			0
$496$	7.44830			0.334438
$497$	−30.4525	−	15.5150i	−1.36598	−	0.695943i
$498$		0			0
$499$	−8.93520			−0.399994			−0.199997	−	0.979796i	$-0.564093\pi$
$499$	−8.93520			−0.399994			−0.199997	+	0.979796i	$0.564093\pi$
$500$	7.92929	+	13.7339i	0.354609	+	0.614200i
$501$		0			0
$502$	−9.28972	+	16.0903i	−0.414621	+	0.718144i
$503$	12.6403			0.563603			0.281802	−	0.959473i	$-0.409068\pi$
$503$	12.6403			0.563603			0.281802	+	0.959473i	$0.409068\pi$
$504$		0			0
$505$	47.3958			2.10909
$506$	4.24620	−	7.35463i	0.188766	−	0.326953i
$507$		0			0
$508$	7.33732	+	12.7086i	0.325541	+	0.563854i
$509$	28.1110			1.24600			0.623000	−	0.782222i	$-0.285914\pi$
$509$	28.1110			1.24600			0.623000	+	0.782222i	$0.285914\pi$
$510$		0			0
$511$	23.1992	−	15.0669i	1.02627	−	0.666519i
$512$	−24.5070			−1.08307
$513$		0			0
$514$	12.3830	−	21.4480i	0.546192	−	0.946033i
$515$	−6.50427			−0.286613
$516$		0			0
$517$	2.69331	−	4.66495i	0.118452	−	0.205164i
$518$	−61.1947	−	31.1776i	−2.68874	−	1.36986i
$519$		0			0
$520$	−8.67288	+	15.0219i	−0.380331	+	0.658753i
$521$	−4.23768	+	7.33988i	−0.185656	+	0.321566i	−0.943797	−	0.330524i	$-0.892774\pi$
$521$	−4.23768	+	7.33988i	−0.185656	+	0.321566i	0.758141	+	0.652090i	$0.226108\pi$
$522$		0			0
$523$	16.7236	+	28.9662i	0.731273	+	1.26660i	0.956339	+	0.292259i	$0.0944069\pi$
$523$	16.7236	+	28.9662i	0.731273	+	1.26660i	−0.225066	+	0.974344i	$0.572260\pi$
$524$	9.85035	+	17.0613i	0.430315	+	0.745327i
$525$		0			0
$526$	−22.8341	+	39.5498i	−0.995613	+	1.72445i
$527$	10.8398			0.472187
$528$		0			0
$529$	−16.0921			−0.699655
$530$	22.5008	+	38.9725i	0.977371	+	1.69286i
$531$		0			0
$532$	−18.1016	+	11.7562i	−0.784806	+	0.509698i
$533$	1.32569	+	2.29616i	0.0574220	+	0.0994579i
$534$		0			0
$535$	25.5693	+	44.2874i	1.10546	+	1.91471i
$536$	−25.9493	−	44.9456i	−1.12084	−	1.94135i
$537$		0			0
$538$	10.5461	+	18.2665i	0.454677	+	0.787523i
$539$	5.57039	+	7.66586i	0.239934	+	0.330192i
$540$		0			0
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	0.600280	−	0.799790i	$-0.295056\pi$
$541$	−9.12929	−	15.8124i	−0.392499	−	0.679828i	−0.992778	+	0.119962i	$0.961723\pi$
$542$	43.7730			1.88021
$543$		0			0
$544$	−8.84701			−0.379312
$545$	−22.7803	+	39.4567i	−0.975802	+	1.69014i
$546$		0			0
$547$	−2.88599	−	4.99869i	−0.123396	−	0.213728i	0.797709	−	0.603043i	$-0.206045\pi$
$547$	−2.88599	−	4.99869i	−0.123396	−	0.213728i	−0.921105	+	0.389315i	$0.872712\pi$
$548$	−13.8558	−	23.9990i	−0.591892	−	1.02519i
$549$		0			0
$550$	−5.70532	+	9.88190i	−0.243276	+	0.421366i
$551$	−1.15122	+	1.99397i	−0.0490437	+	0.0849461i
$552$		0			0
$553$	−1.70337	+	1.10627i	−0.0724346	+	0.0470432i
$554$	−6.09227	+	10.5521i	−0.258836	+	0.448317i
$555$		0			0
$556$	−52.0029			−2.20541
$557$	−16.6911	+	28.9098i	−0.707223	+	1.22495i	0.258661	+	0.965968i	$0.416719\pi$
$557$	−16.6911	+	28.9098i	−0.707223	+	1.22495i	−0.965883	+	0.258977i	$0.916614\pi$
$558$		0			0
$559$	6.36623			0.269263
$560$	−14.7416	+	9.57402i	−0.622945	+	0.404576i
$561$		0			0
$562$	−4.07286			−0.171803
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	0.888190	−	0.459477i	$-0.151963\pi$
$563$	1.09566	+	1.89773i	0.0461764	+	0.0799799i	−0.842013	+	0.539457i	$0.818630\pi$
$564$		0			0
$565$	2.46683	−	4.27268i	0.103780	−	0.179753i
$566$	−29.8079			−1.25292
$567$		0			0
$568$	−52.3278			−2.19563
$569$	9.49302	−	16.4424i	0.397968	−	0.689301i	−0.595507	−	0.803350i	$-0.703049\pi$
$569$	9.49302	−	16.4424i	0.397968	−	0.689301i	0.993475	+	0.114049i	$0.0363822\pi$
$570$		0			0
$571$	10.8690	+	18.8257i	0.454854	+	0.787831i	0.998680	−	0.0513674i	$-0.0163580\pi$
$571$	10.8690	+	18.8257i	0.454854	+	0.787831i	−0.543825	+	0.839198i	$0.683025\pi$
$572$	7.33717			0.306782
$573$		0			0
$574$	0.598142	+	11.4056i	0.0249660	+	0.476061i
$575$	−9.28172			−0.387074
$576$		0			0
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	0.341443	+	0.939903i	$0.389084\pi$
$577$	−15.4516	+	26.7629i	−0.643258	+	1.11416i	−0.984701	+	0.174253i	$0.944249\pi$
$578$	−14.4217			−0.599862
$579$		0			0
$580$	−5.63398	+	9.75835i	−0.233938	+	0.405193i
$581$	0.272605	+	5.19815i	0.0113096	+	0.215655i
$582$		0			0
$583$	4.36902	−	7.56737i	0.180946	−	0.313408i
$584$	21.1767	−	36.6792i	0.876299	−	1.51780i
$585$		0			0
$586$	6.21069	+	10.7572i	0.256561	+	0.444377i
$587$	9.18332	+	15.9060i	0.379036	+	0.656510i	0.990922	−	0.134436i	$-0.0429222\pi$
$587$	9.18332	+	15.9060i	0.379036	+	0.656510i	−0.611886	+	0.790946i	$0.709589\pi$
$588$		0			0
$589$	−3.61282	+	6.25759i	−0.148864	+	0.257840i
$590$	85.1527			3.50568
$591$		0			0
$592$	−24.7371			−1.01669
$593$	−13.8775	−	24.0365i	−0.569880	−	0.987061i	−0.996577	−	0.0826662i	$-0.973656\pi$
$593$	−13.8775	−	24.0365i	−0.569880	−	0.987061i	0.426698	−	0.904394i	$-0.359677\pi$
$594$		0			0
$595$	−21.4539	+	13.9334i	−0.879524	+	0.571213i
$596$	4.02936	+	6.97905i	0.165049	+	0.285873i
$597$		0			0
$598$	4.59841	+	7.96468i	0.188043	+	0.325700i
$599$	0.201412	+	0.348855i	0.00822945	+	0.0142538i	0.870111	−	0.492856i	$-0.164047\pi$
$599$	0.201412	+	0.348855i	0.00822945	+	0.0142538i	−0.861881	+	0.507110i	$0.830714\pi$
$600$		0			0
$601$	12.3733	+	21.4312i	0.504717	+	0.874196i	0.999985	+	0.00545577i	$0.00173663\pi$
$601$	12.3733	+	21.4312i	0.504717	+	0.874196i	−0.495268	+	0.868740i	$0.664930\pi$
$602$	24.4351	+	12.4492i	0.995899	+	0.507392i
$603$		0			0
$604$	−25.9313	−	44.9143i	−1.05513	−	1.82754i
$605$	−26.7769			−1.08864
$606$		0			0
$607$	24.0697			0.976957			0.488479	−	0.872576i	$-0.337552\pi$
$607$	24.0697			0.976957			0.488479	+	0.872576i	$0.337552\pi$
$608$	2.94865	−	5.10721i	0.119584	−	0.207125i
$609$		0			0
$610$	−1.95115	−	3.37950i	−0.0789999	−	0.136832i
$611$	2.91672	+	5.05190i	0.117998	+	0.204378i
$612$		0			0
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	−0.583465	−	0.812138i	$-0.698303\pi$
$613$	10.1907	−	17.6509i	0.411600	−	0.712912i	0.995065	+	0.0992261i	$0.0316367\pi$
$614$	−5.96879	+	10.3382i	−0.240881	+	0.417218i
$615$		0			0
$616$	12.9274	+	6.58628i	0.520861	+	0.265369i
$617$	20.9315	−	36.2544i	0.842669	−	1.45955i	−0.0449604	−	0.998989i	$-0.514316\pi$
$617$	20.9315	−	36.2544i	0.842669	−	1.45955i	0.887630	−	0.460558i	$-0.152350\pi$
$618$		0			0
$619$	14.8219			0.595743			0.297871	−	0.954606i	$-0.403723\pi$
$619$	14.8219			0.595743			0.297871	+	0.954606i	$0.403723\pi$
$620$	−17.6809	+	30.6242i	−0.710081	+	1.22990i
$621$		0			0
$622$	77.3270			3.10053
$623$	−0.887770	−	16.9284i	−0.0355678	−	0.678221i
$624$		0			0
$625$	−30.1861			−1.20744
$626$	−1.81291	−	3.14005i	−0.0724585	−	0.125502i
$627$		0			0
$628$	−5.48329	+	9.49734i	−0.218807	+	0.378985i
$629$	−36.0007			−1.43544
$630$		0			0
$631$	−21.0294			−0.837169			−0.418585	−	0.908178i	$-0.637474\pi$
$631$	−21.0294			−0.837169			−0.418585	+	0.908178i	$0.637474\pi$
$632$	−1.55487	+	2.69312i	−0.0618496	+	0.107127i
$633$		0			0
$634$	−25.6694	−	44.4607i	−1.01946	−	1.76576i
$635$	−11.5935			−0.460072
$636$		0			0
$637$	−10.2057	+	1.07339i	−0.404366	+	0.0425291i
$638$	3.37150			0.133479
$639$		0			0
$640$	30.2882	−	52.4607i	1.19725	−	2.07369i
$641$	−11.9318			−0.471279			−0.235640	−	0.971840i	$-0.575719\pi$
$641$	−11.9318			−0.471279			−0.235640	+	0.971840i	$0.575719\pi$
$642$		0			0
$643$	−19.9678	+	34.5852i	−0.787452	+	1.36391i	0.140072	+	0.990141i	$0.455267\pi$
$643$	−19.9678	+	34.5852i	−0.787452	+	1.36391i	−0.927524	+	0.373765i	$0.878067\pi$
$644$	1.34641	+	25.6740i	0.0530562	+	1.01170i
$645$		0			0
$646$	−8.71733	+	15.0989i	−0.342979	+	0.594057i
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	−0.875582	−	0.483070i	$-0.839522\pi$
$647$	−0.494477	+	0.856459i	−0.0194399	+	0.0336709i	0.856142	+	0.516741i	$0.172855\pi$
$648$		0			0
$649$	−8.26714	−	14.3191i	−0.324514	−	0.562074i
$650$	−6.17856	−	10.7016i	−0.242343	−	0.419751i
$651$		0			0
$652$	−0.718272	+	1.24408i	−0.0281297	+	0.0487221i
$653$	−22.7147			−0.888894			−0.444447	−	0.895805i	$-0.646600\pi$
$653$	−22.7147			−0.888894			−0.444447	+	0.895805i	$0.646600\pi$
$654$		0			0
$655$	−15.5642			−0.608144
$656$	2.05688	+	3.56262i	0.0803076	+	0.139097i
$657$		0			0
$658$	1.31600	+	25.0940i	0.0513031	+	0.978267i
$659$	19.1943	+	33.2454i	0.747702	+	1.29506i	0.948922	+	0.315512i	$0.102176\pi$
$659$	19.1943	+	33.2454i	0.747702	+	1.29506i	−0.201220	+	0.979546i	$0.564491\pi$
$660$		0			0
$661$	−16.9629	−	29.3806i	−0.659780	−	1.14277i	−0.980672	−	0.195657i	$-0.937316\pi$
$661$	−16.9629	−	29.3806i	−0.659780	−	1.14277i	0.320892	−	0.947116i	$-0.396017\pi$
$662$	−23.2458	−	40.2628i	−0.903472	−	1.56486i
$663$		0			0
$664$	3.98486	+	6.90198i	0.154642	+	0.267849i
$665$	−0.893040	−	17.0288i	−0.0346306	−	0.660350i
$666$		0			0
$667$	1.37124	+	2.37505i	0.0530944	+	0.0919623i
$668$	26.9809			1.04392
$669$		0			0
$670$	89.3201			3.45074
$671$	−0.378860	+	0.656205i	−0.0146257	+	0.0253325i
$672$		0			0
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	−0.989351	−	0.145549i	$-0.953505\pi$
$673$	−16.1030	−	27.8912i	−0.620725	−	1.07513i	0.368626	−	0.929578i	$-0.379828\pi$
$674$	11.5702	+	20.0401i	0.445666	+	0.771916i
$675$		0			0
$676$	20.0585	−	34.7424i	0.771483	−	1.33625i
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	0.227421	+	0.973797i	$0.426971\pi$
$677$	−18.9842	+	32.8816i	−0.729622	+	1.26374i	−0.957043	+	0.289946i	$0.906363\pi$
$678$		0			0
$679$	−1.14767	−	21.8843i	−0.0440436	−	0.839842i
$680$	−19.5836	+	33.9198i	−0.750997	+	1.30076i
$681$		0			0
$682$	10.5806			0.405153
$683$	−7.59357	+	13.1525i	−0.290560	+	0.503265i	−0.973942	−	0.226796i	$-0.927175\pi$
$683$	−7.59357	+	13.1525i	−0.290560	+	0.503265i	0.683382	+	0.730061i	$0.260508\pi$
$684$		0			0
$685$	21.8932			0.836495
$686$	−41.2710	−	15.8375i	−1.57573	−	0.604678i
$687$		0			0
$688$	9.87754			0.376578
$689$	4.73142	+	8.19507i	0.180253	+	0.312207i
$690$		0			0
$691$	−1.34574	+	2.33089i	−0.0511943	+	0.0886711i	−0.890487	−	0.455009i	$-0.849636\pi$
$691$	−1.34574	+	2.33089i	−0.0511943	+	0.0886711i	0.839293	+	0.543680i	$0.182969\pi$
$692$	14.9922			0.569919
$693$		0			0
$694$	−4.83589			−0.183568
$695$	20.5420	−	35.5798i	0.779203	−	1.34962i
$696$		0			0
$697$	2.99344	+	5.18480i	0.113385	+	0.196388i
$698$	−38.8858			−1.47185
$699$		0			0
$700$	−1.80908	−	34.4963i	−0.0683769	−	1.30384i
$701$	11.8515			0.447625			0.223813	−	0.974632i	$-0.428150\pi$
$701$	11.8515			0.447625			0.223813	+	0.974632i	$0.428150\pi$
$702$		0			0
$703$	11.9988	−	20.7826i	0.452544	−	0.783829i
$704$	−14.7938			−0.557562
$705$		0			0
$706$	20.3617	−	35.2675i	0.766323	−	1.32731i
$707$	38.2530	+	19.4892i	1.43865	+	0.732967i
$708$		0			0
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	−0.166759	−	0.985998i	$-0.553330\pi$
$709$	20.5167	−	35.5359i	0.770520	−	1.33458i	0.937278	−	0.348582i	$-0.113337\pi$
$710$	45.0294	−	77.9931i	1.68992	−	2.92703i
$711$		0			0
$712$	−12.9772	−	22.4771i	−0.486339	−	0.842364i
$713$	4.30328	+	7.45351i	0.161159	+	0.279136i
$714$		0			0
$715$	−2.89830	+	5.02001i	−0.108390	+	0.187738i
$716$	39.1337			1.46250
$717$		0			0
$718$	7.08246			0.264315
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	0.602516	−	0.798107i	$-0.294165\pi$
$719$	−10.4555	−	18.1094i	−0.389923	−	0.675366i	−0.992439	+	0.122741i	$0.960832\pi$
$720$		0			0
$721$	−5.24958	−	2.67457i	−0.195505	−	0.0996060i
$722$	16.8644	+	29.2100i	0.627628	+	1.08708i
$723$		0			0
$724$	36.2896	+	62.8554i	1.34869	+	2.33600i
$725$	−1.84243	−	3.19119i	−0.0684263	−	0.118518i
$726$		0			0
$727$	1.32165	+	2.28917i	0.0490173	+	0.0849005i	0.889493	−	0.456949i	$-0.151058\pi$
$727$	1.32165	+	2.28917i	0.0490173	+	0.0849005i	−0.840476	+	0.541849i	$0.817724\pi$
$728$	−13.1769	+	8.55782i	−0.488368	+	0.317174i
$729$		0			0
$730$	36.4462	+	63.1267i	1.34893	+	2.33642i
$731$	14.3751			0.531683
$732$		0			0
$733$	14.1489			0.522602			0.261301	−	0.965257i	$-0.415848\pi$
$733$	14.1489			0.522602			0.261301	+	0.965257i	$0.415848\pi$
$734$	12.1223	−	20.9964i	0.447442	−	0.774992i
$735$		0			0
$736$	−3.51218	−	6.08327i	−0.129461	−	0.224232i
$737$	−8.67174	−	15.0199i	−0.319428	−	0.553265i
$738$		0			0
$739$	−7.85905	+	13.6123i	−0.289100	+	0.500736i	−0.973595	−	0.228282i	$-0.926689\pi$
$739$	−7.85905	+	13.6123i	−0.289100	+	0.500736i	0.684495	+	0.729017i	$0.260023\pi$
$740$	58.7212	−	101.708i	2.15864	−	3.73887i
$741$		0			0
$742$	2.13478	+	40.7069i	0.0783704	+	1.49440i
$743$	−10.5496	+	18.2724i	−0.387026	+	0.670348i	−0.992048	−	0.125861i	$-0.959831\pi$
$743$	−10.5496	+	18.2724i	−0.387026	+	0.670348i	0.605022	+	0.796208i	$0.293164\pi$
$744$		0			0
$745$	−6.36665			−0.233256
$746$	30.4142	−	52.6789i	1.11354	−	1.92871i
$747$		0			0
$748$	16.5675			0.605768
$749$	2.42592	+	46.2584i	0.0886412	+	1.69025i
$750$		0			0
$751$	13.0370			0.475725			0.237863	−	0.971299i	$-0.423553\pi$
$751$	13.0370			0.475725			0.237863	+	0.971299i	$0.423553\pi$
$752$	4.52544	+	7.83829i	0.165026	+	0.285833i
$753$		0			0
$754$	−1.82558	+	3.16200i	−0.0664838	+	0.115153i
$755$	40.9732			1.49117
$756$		0			0
$757$	−12.6856			−0.461065			−0.230532	−	0.973065i	$-0.574047\pi$
$757$	−12.6856			−0.461065			−0.230532	+	0.973065i	$0.574047\pi$
$758$	−11.7613	+	20.3711i	−0.427188	+	0.739912i
$759$		0			0
$760$	−13.0542	−	22.6105i	−0.473525	−	0.820169i
$761$	6.04077			0.218978			0.109489	−	0.993988i	$-0.465079\pi$
$761$	6.04077			0.218978			0.109489	+	0.993988i	$0.465079\pi$
$762$		0			0
$763$	−34.6106	+	22.4781i	−1.25299	+	0.813761i
$764$	−30.6388			−1.10847
$765$		0			0
$766$	−32.5959	+	56.4577i	−1.17774	+	2.03990i
$767$	17.9058			0.646540
$768$		0			0
$769$	0.108129	−	0.187285i	0.00389924	−	0.00675368i	−0.864069	−	0.503373i	$-0.832092\pi$
$769$	0.108129	−	0.187285i	0.00389924	−	0.00675368i	0.867968	+	0.496619i	$0.165425\pi$
$770$	−20.9410	+	13.6003i	−0.754662	+	0.490121i
$771$		0			0
$772$	34.7251	−	60.1457i	1.24979	−	2.16469i
$773$	−18.8132	+	32.5854i	−0.676663	+	1.17202i	0.299316	+	0.954154i	$0.403241\pi$
$773$	−18.8132	+	32.5854i	−0.676663	+	1.17202i	−0.975980	+	0.217861i	$0.930092\pi$
$774$		0			0
$775$	−5.78202	−	10.0148i	−0.207696	−	0.359741i
$776$	−16.7763	−	29.0575i	−0.602235	−	1.04310i
$777$		0			0
$778$	4.99388	−	8.64965i	0.179039	−	0.310105i
$779$	−3.99078			−0.142985
$780$		0			0
$781$	−17.4869			−0.625730
$782$	10.3833	+	17.9845i	0.371307	+	0.643123i
$783$		0			0
$784$	−15.8347	+	1.66541i	−0.565526	+	0.0594791i
$785$	−4.33198	−	7.50321i	−0.154615	−	0.267801i
$786$		0			0
$787$	−15.4067	−	26.6853i	−0.549191	−	0.951226i	−0.998330	−	0.0577648i	$-0.981603\pi$
$787$	−15.4067	−	26.6853i	−0.549191	−	0.951226i	0.449139	−	0.893462i	$-0.351731\pi$
$788$	11.0847	+	19.1992i	0.394875	+	0.683943i
$789$		0			0
$790$	−2.67601	−	4.63499i	−0.0952083	−	0.164906i
$791$	3.74791	−	2.43410i	0.133260	−	0.0865468i
$792$		0			0
$793$	−0.410286	−	0.710636i	−0.0145697	−	0.0252354i
$794$	−73.2074			−2.59803
$795$		0			0
$796$	−53.2710			−1.88814
$797$	17.9792	−	31.1408i	0.636855	−	1.10306i	−0.349264	−	0.937024i	$-0.613569\pi$
$797$	17.9792	−	31.1408i	0.636855	−	1.10306i	0.986119	−	0.166040i	$-0.0530981\pi$
$798$		0			0
$799$	6.58602	+	11.4073i	0.232997	+	0.403562i
$800$	4.71907	+	8.17367i	0.166844	+	0.288983i
$801$		0			0
$802$	−8.17268	+	14.1555i	−0.288587	+	0.499848i
$803$	7.07684	−	12.2574i	0.249736	−	0.432556i
$804$		0			0
$805$	−18.0977	−	9.22045i	−0.637860	−	0.324978i
$806$	−5.72914	+	9.92315i	−0.201800	+	0.349528i
$807$		0			0
$808$	65.7318			2.31244
$809$	19.4818	−	33.7435i	0.684943	−	1.18636i	−0.288511	−	0.957477i	$-0.593160\pi$
$809$	19.4818	−	33.7435i	0.684943	−	1.18636i	0.973455	−	0.228880i	$-0.0735065\pi$
$810$		0			0
$811$	−28.2811			−0.993082			−0.496541	−	0.868013i	$-0.665397\pi$
$811$	−28.2811			−0.993082			−0.496541	+	0.868013i	$0.665397\pi$
$812$	−8.55982	+	5.55924i	−0.300391	+	0.195091i
$813$		0			0
$814$	−35.1401			−1.23166
$815$	−0.567459	−	0.982867i	−0.0198772	−	0.0344283i
$816$		0			0
$817$	−4.79113	+	8.29849i	−0.167621	+	0.290327i
$818$	−43.6076			−1.52471
$819$		0			0
$820$	−19.5306			−0.682037
$821$	20.7917	−	36.0123i	0.725635	−	1.25684i	−0.233077	−	0.972458i	$-0.574879\pi$
$821$	20.7917	−	36.0123i	0.725635	−	1.25684i	0.958712	−	0.284378i	$-0.0917872\pi$
$822$		0			0
$823$	−4.22999	−	7.32656i	−0.147448	−	0.255388i	0.782835	−	0.622229i	$-0.213773\pi$
$823$	−4.22999	−	7.32656i	−0.147448	−	0.255388i	−0.930284	+	0.366841i	$0.880439\pi$
$824$	−9.02057			−0.314247
$825$		0			0
$826$	68.7265	+	35.0149i	2.39130	+	1.21832i
$827$	−44.2823			−1.53985			−0.769923	−	0.638137i	$-0.779706\pi$
$827$	−44.2823			−1.53985			−0.769923	+	0.638137i	$0.779706\pi$
$828$		0			0
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	−0.973533	−	0.228547i	$-0.926603\pi$
$829$	−8.31637	+	14.4044i	−0.288839	+	0.500284i	0.684694	+	0.728831i	$0.259936\pi$
$830$	−13.7163			−0.476099
$831$		0			0
$832$	8.01045	−	13.8745i	0.277712	−	0.481012i
$833$	−23.0448	+	2.42373i	−0.798455	+	0.0839774i
$834$		0			0
$835$	−10.6579	+	18.4601i	−0.368832	+	0.638836i
$836$	−5.52185	+	9.56412i	−0.190977	+	0.330782i
$837$		0			0
$838$	−26.8068	−	46.4308i	−0.926027	−	1.60393i
$839$	−14.8006	−	25.6354i	−0.510974	−	0.885033i	−0.999919	−	0.0127182i	$-0.995952\pi$
$839$	−14.8006	−	25.6354i	−0.510974	−	0.885033i	0.488945	−	0.872314i	$-0.337382\pi$
$840$		0			0
$841$	13.9556	−	24.1718i	0.481228	−	0.833512i
$842$	−49.7314			−1.71386
$843$		0			0
$844$	51.1994			1.76236
$845$	15.8469	+	27.4477i	0.545151	+	0.944228i
$846$		0			0
$847$	−21.6116	−	11.0107i	−0.742583	−	0.378332i
$848$	7.34105	+	12.7151i	0.252093	+	0.436638i
$849$		0			0
$850$	−13.9514	−	24.1645i	−0.478528	−	0.828834i
$851$	−14.2920	−	24.7544i	−0.489922	−	0.848570i
$852$		0			0
$853$	−15.0619	−	26.0880i	−0.515710	−	0.893236i	−0.999834	−	0.0182366i	$-0.994195\pi$
$853$	−15.0619	−	26.0880i	−0.515710	−	0.893236i	0.484124	−	0.875000i	$-0.339139\pi$
$854$	−0.185118	−	3.52990i	−0.00633460	−	0.120791i
$855$		0			0
$856$	35.4613	+	61.4208i	1.21204	+	2.09932i
$857$	−37.0894			−1.26695			−0.633475	−	0.773763i	$-0.718372\pi$
$857$	−37.0894			−1.26695			−0.633475	+	0.773763i	$0.718372\pi$
$858$		0			0
$859$	−3.78333			−0.129085			−0.0645427	−	0.997915i	$-0.520559\pi$
$859$	−3.78333			−0.129085			−0.0645427	+	0.997915i	$0.520559\pi$
$860$	−23.4474	+	40.6121i	−0.799551	+	1.38486i
$861$		0			0
$862$	24.1583	+	41.8434i	0.822835	+	1.42519i
$863$	−0.213559	−	0.369895i	−0.00726963	−	0.0125914i	0.862368	−	0.506282i	$-0.168981\pi$
$863$	−0.213559	−	0.369895i	−0.00726963	−	0.0125914i	−0.869637	+	0.493691i	$0.835647\pi$
$864$		0			0
$865$	−5.92218	+	10.2575i	−0.201360	+	0.348766i
$866$	25.8694	−	44.8071i	0.879077	−	1.52261i
$867$		0			0
$868$	−26.8629	+	17.4463i	−0.911786	+	0.592166i
$869$	−0.519608	+	0.899987i	−0.0176265	+	0.0305300i
$870$		0			0
$871$	18.7821			0.636407
$872$	−31.5933	+	54.7212i	−1.06988	+	1.85309i
$873$		0			0
$874$	−13.8428			−0.468240
$875$	−10.1120	−	5.15186i	−0.341847	−	0.174165i
$876$		0			0
$877$	11.2608			0.380249			0.190124	−	0.981760i	$-0.439111\pi$
$877$	11.2608			0.380249			0.190124	+	0.981760i	$0.439111\pi$
$878$	42.3408	+	73.3364i	1.42893	+	2.47498i
$879$		0			0
$880$	−4.49687	+	7.78881i	−0.151589	+	0.262561i
$881$	35.4810			1.19538			0.597692	−	0.801726i	$-0.296084\pi$
$881$	35.4810			1.19538			0.597692	+	0.801726i	$0.296084\pi$
$882$		0			0
$883$	−5.30092			−0.178390			−0.0891952	−	0.996014i	$-0.528429\pi$
$883$	−5.30092			−0.178390			−0.0891952	+	0.996014i	$0.528429\pi$
$884$	−8.97088	+	15.5380i	−0.301723	+	0.522600i
$885$		0			0
$886$	−22.9214	−	39.7010i	−0.770060	−	1.33378i
$887$	−57.5664			−1.93289			−0.966446	−	0.256870i	$-0.917309\pi$
$887$	−57.5664			−1.93289			−0.966446	+	0.256870i	$0.917309\pi$
$888$		0			0
$889$	−9.35705	−	4.76724i	−0.313825	−	0.159888i
$890$	44.6686			1.49730
$891$		0			0
$892$	8.64231	−	14.9689i	0.289366	−	0.501197i
$893$	−8.78032			−0.293822
$894$		0			0
$895$	−15.4585	+	26.7749i	−0.516720	+	0.894985i
$896$	46.0175	−	29.8864i	1.53734	−	0.998433i
$897$		0			0
$898$	−35.3354	+	61.2027i	−1.17916	+	2.04236i
$899$	−1.70842	+	2.95906i	−0.0569788	+	0.0986903i
$900$		0			0
$901$	10.6837	+	18.5047i	0.355925	+	0.616480i
$902$	2.92188	+	5.06085i	0.0972881	+	0.168508i
$903$		0			0
$904$	3.42117	−	5.92565i	0.113787	−	0.197084i
$905$	−57.3400			−1.90605
$906$		0			0
$907$	20.8972			0.693879			0.346939	−	0.937888i	$-0.387221\pi$
$907$	20.8972			0.693879			0.346939	+	0.937888i	$0.387221\pi$
$908$	36.4402	+	63.1163i	1.20931	+	2.09459i
$909$		0			0
$910$	−1.41616	−	27.0040i	−0.0469454	−	0.895173i
$911$	−11.3819	−	19.7141i	−0.377101	−	0.653157i	0.613539	−	0.789665i	$-0.289746\pi$
$911$	−11.3819	−	19.7141i	−0.377101	−	0.653157i	−0.990639	+	0.136508i	$0.956412\pi$
$912$		0			0
$913$	1.33166	+	2.30650i	0.0440715	+	0.0763340i
$914$	11.4116	+	19.7654i	0.377461	+	0.653782i
$915$		0			0
$916$	−51.8946	−	89.8841i	−1.71465	−	2.96986i
$917$	−12.5618	−	6.40002i	−0.414828	−	0.211347i
$918$		0			0
$919$	18.6515	+	32.3054i	0.615257	+	1.06566i	0.990339	+	0.138664i	$0.0442809\pi$
$919$	18.6515	+	32.3054i	0.615257	+	1.06566i	−0.375083	+	0.926991i	$0.622386\pi$
$920$	−31.0980			−1.02527
$921$		0			0
$922$	52.1231			1.71658
$923$	9.46870	−	16.4003i	0.311666	−	0.539822i
$924$		0			0
$925$	19.2031	+	33.2607i	0.631394	+	1.09361i
$926$	31.2070	+	54.0521i	1.02553	+	1.77626i
$927$		0			0
$928$	1.39434	−	2.41508i	0.0457716	−	0.0792787i
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	−0.815791	−	0.578347i	$-0.803698\pi$
$929$	2.83363	−	4.90799i	0.0929683	−	0.161026i	0.908759	+	0.417322i	$0.137031\pi$
$930$		0			0
$931$	6.28151	−	14.1112i	0.205868	−	0.462475i
$932$	25.5145	−	44.1923i	0.835754	−	1.44757i
$933$		0			0
$934$	−83.4275			−2.72983
$935$	−6.54444	+	11.3353i	−0.214026	+	0.370704i
$936$		0			0
$937$	−7.64754			−0.249834			−0.124917	−	0.992167i	$-0.539866\pi$
$937$	−7.64754			−0.249834			−0.124917	+	0.992167i	$0.539866\pi$
$938$	72.0900	+	36.7285i	2.35382	+	1.19923i
$939$		0			0
$940$	−42.9702			−1.40153
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	0.983178	−	0.182650i	$-0.0584674\pi$
$941$	10.2276	+	17.7147i	0.333410	+	0.577483i	−0.649768	+	0.760132i	$0.725134\pi$
$942$		0			0
$943$	−2.37674	+	4.11663i	−0.0773973	+	0.134056i
$944$	27.7817			0.904219
$945$		0			0
$946$	14.0315			0.456202
$947$	−2.38343	+	4.12823i	−0.0774512	+	0.134149i	−0.902150	−	0.431423i	$-0.858012\pi$
$947$	−2.38343	+	4.12823i	−0.0774512	+	0.134149i	0.824698	+	0.565573i	$0.191345\pi$
$948$		0			0
$949$	7.66385	+	13.2742i	0.248779	+	0.430898i
$950$	18.5996			0.603451
$951$		0			0
$952$	−29.7537	+	19.3238i	−0.964324	+	0.626287i
$953$	48.9412			1.58536			0.792680	−	0.609638i	$-0.208685\pi$
$953$	48.9412			1.58536			0.792680	+	0.609638i	$0.208685\pi$
$954$		0			0
$955$	12.1028	−	20.9627i	0.391638	−	0.678337i
$956$	40.8955			1.32266
$957$		0			0
$958$	−35.5773	+	61.6217i	−1.14945	+	1.99091i
$959$	17.6699	+	9.00249i	0.570591	+	0.290706i
$960$		0			0
$961$	10.1386	−	17.5605i	0.327050	−	0.566468i
$962$	19.0275	−	32.9565i	0.613470	−	1.06256i
$963$		0			0
$964$	42.8309	+	74.1854i	1.37949	+	2.38935i
$965$	27.4340	+	47.5171i	0.883132	+	1.52963i
$966$		0			0
$967$	−2.95856	+	5.12438i	−0.0951409	+	0.164789i	−0.909667	−	0.415337i	$-0.863664\pi$
$967$	−2.95856	+	5.12438i	−0.0951409	+	0.164789i	0.814526	+	0.580126i	$0.196997\pi$
$968$	−37.1361			−1.19360
$969$		0			0
$970$	57.7458			1.85410
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	0.534234	−	0.845337i	$-0.320600\pi$
$971$	−14.4888	−	25.0953i	−0.464966	−	0.805345i	−0.999200	+	0.0399914i	$0.987267\pi$
$972$		0			0
$973$	31.2099	−	20.2695i	1.00054	−	0.649809i
$974$	−26.7933	−	46.4074i	−0.858513	−	1.48699i
$975$		0			0
$976$	−0.636580	−	1.10259i	−0.0203764	−	0.0352930i
$977$	11.4228	+	19.7848i	0.365447	+	0.632972i	0.988848	−	0.148930i	$-0.0475830\pi$
$977$	11.4228	+	19.7848i	0.365447	+	0.632972i	−0.623401	+	0.781902i	$0.714250\pi$
$978$		0			0
$979$	−4.33670	−	7.51139i	−0.138602	−	0.240065i
$980$	30.7412	−	69.0589i	0.981992	−	2.20601i
$981$		0			0
$982$	−41.8232	−	72.4400i	−1.33463	−	2.31165i
$983$	31.2703			0.997367			0.498684	−	0.866784i	$-0.333817\pi$
$983$	31.2703			0.997367			0.498684	+	0.866784i	$0.333817\pi$
$984$		0			0
$985$	−17.5145			−0.558059
$986$	−4.12221	+	7.13988i	−0.131278	+	0.227380i
$987$		0			0
$988$	−5.97988	−	10.3574i	−0.190245	−	0.329514i
$989$	5.70679	+	9.88444i	0.181465	+	0.314307i
$990$		0			0
$991$	3.50732	−	6.07485i	0.111414	−	0.192974i	−0.804927	−	0.593374i	$-0.797796\pi$
$991$	3.50732	−	6.07485i	0.111414	−	0.192974i	0.916340	+	0.400400i	$0.131129\pi$
$992$	4.37581	−	7.57912i	0.138932	−	0.240637i
$993$		0			0
$994$	68.4140	−	44.4319i	2.16996	−	1.40930i
$995$	21.0429	−	36.4474i	0.667105	−	1.15546i
$996$		0			0
$997$	−21.2878			−0.674191			−0.337095	−	0.941470i	$-0.609445\pi$
$997$	−21.2878			−0.674191			−0.337095	+	0.941470i	$0.609445\pi$
$998$	10.6636	−	18.4698i	0.337549	−	0.584653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.g.b.172.1		10
3.2	odd	2		63.2.g.b.4.5	✓	10
4.3	odd	2		3024.2.t.i.1873.4		10
7.2	even	3		189.2.h.b.37.5		10
7.3	odd	6		1323.2.f.f.442.1		10
7.4	even	3		1323.2.f.e.442.1		10
7.5	odd	6		1323.2.h.f.226.5		10
7.6	odd	2		1323.2.g.f.361.1		10
9.2	odd	6		63.2.h.b.25.1	yes	10
9.4	even	3		567.2.e.e.487.1		10
9.5	odd	6		567.2.e.f.487.5		10
9.7	even	3		189.2.h.b.46.5		10
12.11	even	2		1008.2.t.i.193.3		10
21.2	odd	6		63.2.h.b.58.1	yes	10
21.5	even	6		441.2.h.f.373.1		10
21.11	odd	6		441.2.f.e.148.5		10
21.17	even	6		441.2.f.f.148.5		10
21.20	even	2		441.2.g.f.67.5		10
28.23	odd	6		3024.2.q.i.2305.2		10
36.7	odd	6		3024.2.q.i.2881.2		10
36.11	even	6		1008.2.q.i.529.4		10
63.2	odd	6		63.2.g.b.16.5	yes	10
63.4	even	3		3969.2.a.bc.1.5		5
63.11	odd	6		441.2.f.e.295.5		10
63.16	even	3	inner	189.2.g.b.100.1		10
63.20	even	6		441.2.h.f.214.1		10
63.23	odd	6		567.2.e.f.163.5		10
63.25	even	3		1323.2.f.e.883.1		10
63.31	odd	6		3969.2.a.bb.1.5		5
63.32	odd	6		3969.2.a.z.1.1		5
63.34	odd	6		1323.2.h.f.802.5		10
63.38	even	6		441.2.f.f.295.5		10
63.47	even	6		441.2.g.f.79.5		10
63.52	odd	6		1323.2.f.f.883.1		10
63.58	even	3		567.2.e.e.163.1		10
63.59	even	6		3969.2.a.ba.1.1		5
63.61	odd	6		1323.2.g.f.667.1		10
84.23	even	6		1008.2.q.i.625.4		10
252.79	odd	6		3024.2.t.i.289.4		10
252.191	even	6		1008.2.t.i.961.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.5	✓	10	3.2	odd	2
63.2.g.b.16.5	yes	10	63.2	odd	6
63.2.h.b.25.1	yes	10	9.2	odd	6
63.2.h.b.58.1	yes	10	21.2	odd	6
189.2.g.b.100.1		10	63.16	even	3	inner
189.2.g.b.172.1		10	1.1	even	1	trivial
189.2.h.b.37.5		10	7.2	even	3
189.2.h.b.46.5		10	9.7	even	3
441.2.f.e.148.5		10	21.11	odd	6
441.2.f.e.295.5		10	63.11	odd	6
441.2.f.f.148.5		10	21.17	even	6
441.2.f.f.295.5		10	63.38	even	6
441.2.g.f.67.5		10	21.20	even	2
441.2.g.f.79.5		10	63.47	even	6
441.2.h.f.214.1		10	63.20	even	6
441.2.h.f.373.1		10	21.5	even	6
567.2.e.e.163.1		10	63.58	even	3
567.2.e.e.487.1		10	9.4	even	3
567.2.e.f.163.5		10	63.23	odd	6
567.2.e.f.487.5		10	9.5	odd	6
1008.2.q.i.529.4		10	36.11	even	6
1008.2.q.i.625.4		10	84.23	even	6
1008.2.t.i.193.3		10	12.11	even	2
1008.2.t.i.961.3		10	252.191	even	6
1323.2.f.e.442.1		10	7.4	even	3
1323.2.f.e.883.1		10	63.25	even	3
1323.2.f.f.442.1		10	7.3	odd	6
1323.2.f.f.883.1		10	63.52	odd	6
1323.2.g.f.361.1		10	7.6	odd	2
1323.2.g.f.667.1		10	63.61	odd	6
1323.2.h.f.226.5		10	7.5	odd	6
1323.2.h.f.802.5		10	63.34	odd	6
3024.2.q.i.2305.2		10	28.23	odd	6
3024.2.q.i.2881.2		10	36.7	odd	6
3024.2.t.i.289.4		10	252.79	odd	6
3024.2.t.i.1873.4		10	4.3	odd	2
3969.2.a.z.1.1		5	63.32	odd	6
3969.2.a.ba.1.1		5	63.59	even	6
3969.2.a.bb.1.5		5	63.31	odd	6
3969.2.a.bc.1.5		5	63.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.19343 + 2.06709i) q^{2} +(-1.84857 - 3.20182i) q^{4} +2.92087 q^{5} +(2.35742 + 1.20106i) q^{7} +4.05086 q^{8} +O(q^{10})\)	\(q+(-1.19343 + 2.06709i) q^{2} +(-1.84857 - 3.20182i) q^{4} +2.92087 q^{5} +(2.35742 + 1.20106i) q^{7} +4.05086 q^{8} +(-3.48586 + 6.03769i) q^{10} +1.35371 q^{11} +(-0.733001 + 1.26960i) q^{13} +(-5.29614 + 3.43961i) q^{14} +(-1.13729 + 1.96984i) q^{16} +(-1.65514 + 2.86678i) q^{17} +(-1.10329 - 1.91096i) q^{19} +(-5.39943 - 9.35209i) q^{20} +(-1.61557 + 2.79825i) q^{22} -2.62830 q^{23} +3.53146 q^{25} +(-1.74958 - 3.03036i) q^{26} +(-0.512277 - 9.76830i) q^{28} +(-0.521720 - 0.903646i) q^{29} +(-1.63729 - 2.83587i) q^{31} +(1.33629 + 2.31453i) q^{32} +(-3.95060 - 6.84263i) q^{34} +(6.88572 + 3.50815i) q^{35} +(5.43773 + 9.41842i) q^{37} +5.26683 q^{38} +11.8320 q^{40} +(0.904289 - 1.56627i) q^{41} +(-2.17129 - 3.76078i) q^{43} +(-2.50244 - 4.33435i) q^{44} +(3.13670 - 5.43292i) q^{46} +(1.98957 - 3.44604i) q^{47} +(4.11489 + 5.66283i) q^{49} +(-4.21456 + 7.29984i) q^{50} +5.42002 q^{52} +(3.22743 - 5.59008i) q^{53} +3.95402 q^{55} +(9.54959 + 4.86534i) q^{56} +2.49056 q^{58} +(-6.10700 - 10.5776i) q^{59} +(-0.279867 + 0.484744i) q^{61} +7.81600 q^{62} -10.9283 q^{64} +(-2.14100 + 3.70832i) q^{65} +(-6.40588 - 11.0953i) q^{67} +12.2386 q^{68} +(-15.4693 + 10.0467i) q^{70} -12.9177 q^{71} +(5.22772 - 9.05467i) q^{73} -25.9583 q^{74} +(-4.07903 + 7.06509i) q^{76} +(3.19128 + 1.62590i) q^{77} +(-0.383838 + 0.664827i) q^{79} +(-3.32187 + 5.75365i) q^{80} +(2.15842 + 3.73849i) q^{82} +(0.983707 + 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +10.3652 q^{86} +5.48371 q^{88} +(-3.20356 - 5.54872i) q^{89} +(-3.25286 + 2.11259i) q^{91} +(4.85859 + 8.41533i) q^{92} +(4.74884 + 8.22524i) q^{94} +(-3.22257 - 5.58166i) q^{95} +(-4.14143 - 7.17316i) q^{97} +(-16.6164 + 1.74763i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} + 8 q^{5} - q^{7} + 6 q^{8} - 7 q^{10} + 8 q^{11} - 8 q^{13} - 16 q^{14} + 2 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} + 6 q^{23} + 2 q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 5 q^{35} + 40 q^{38} + 6 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 27 q^{47} + 25 q^{49} - 19 q^{50} + 20 q^{52} + 21 q^{53} + 4 q^{55} + 45 q^{56} + 20 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} + 54 q^{68} - 29 q^{70} + 6 q^{71} + 15 q^{73} - 72 q^{74} + 5 q^{76} + 31 q^{77} - 4 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} - 16 q^{86} + 36 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 - q^7 + 6 * q^8 - 7 * q^10 + 8 * q^11 - 8 * q^13 - 16 * q^14 + 2 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 + 6 * q^23 + 2 * q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 5 * q^35 + 40 * q^38 + 6 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 - 27 * q^47 + 25 * q^49 - 19 * q^50 + 20 * q^52 + 21 * q^53 + 4 * q^55 + 45 * q^56 + 20 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 + 54 * q^68 - 29 * q^70 + 6 * q^71 + 15 * q^73 - 72 * q^74 + 5 * q^76 + 31 * q^77 - 4 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 - 16 * q^86 + 36 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97 - 59 * q^98

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