LMFDB - Embedded newform 162.3.f.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, 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:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	162.17
Dual form			162.3.f.a.143.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483690 - 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(7.71206 + 1.35984i) q^{5} +(-0.690206 + 0.579152i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(0.483690 - 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(7.71206 + 1.35984i) q^{5} +(-0.690206 + 0.579152i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.53738 - 9.59102i) q^{10} +(15.2420 - 2.68757i) q^{11} +(-0.854187 + 0.310899i) q^{13} +(0.435804 + 1.19736i) q^{14} +(0.694593 + 3.93923i) q^{16} +(-10.6672 - 6.15869i) q^{17} +(-5.40619 - 9.36379i) q^{19} +(-10.0674 - 11.9978i) q^{20} +(3.80080 - 21.5554i) q^{22} +(21.0966 - 25.1419i) q^{23} +(34.1344 + 12.4239i) q^{25} +1.28553i q^{26} +1.80200 q^{28} +(-19.3495 + 53.1622i) q^{29} +(-37.9518 - 31.8453i) q^{31} +(5.57091 + 0.982302i) q^{32} +(-13.3440 + 11.1970i) q^{34} +(-6.11047 + 3.52788i) q^{35} +(-17.4417 + 30.2099i) q^{37} +(-15.0587 + 2.65526i) q^{38} +(-20.8137 + 7.57558i) q^{40} +(12.2490 + 33.6538i) q^{41} +(7.20864 + 40.8822i) q^{43} +(-26.8072 - 15.4771i) q^{44} +(-23.2075 - 40.1966i) q^{46} +(15.9152 + 18.9670i) q^{47} +(-8.36779 + 47.4561i) q^{49} +(33.0209 - 39.3528i) q^{50} +(1.70837 + 0.621797i) q^{52} -50.3340i q^{53} +121.202 q^{55} +(0.871609 - 2.39472i) q^{56} +(61.2895 + 51.4280i) q^{58} +(-65.7126 - 11.5869i) q^{59} +(-18.7893 + 15.7661i) q^{61} +(-60.6770 + 35.0319i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-7.01032 + 1.23611i) q^{65} +(-61.2882 + 22.3071i) q^{67} +(8.42558 + 23.1491i) q^{68} +(1.73272 + 9.82676i) q^{70} +(-24.4496 - 14.1160i) q^{71} +(-10.7760 - 18.6646i) q^{73} +(31.7104 + 37.7910i) q^{74} +(-3.75510 + 21.2962i) q^{76} +(-8.96360 + 10.6824i) q^{77} +(-27.2240 - 9.90872i) q^{79} +31.3241i q^{80} +50.6481 q^{82} +(0.0509121 - 0.139880i) q^{83} +(-73.8910 - 62.0019i) q^{85} +(57.8162 + 10.1946i) q^{86} +(-33.5343 + 28.1386i) q^{88} +(79.3008 - 45.7843i) q^{89} +(0.409508 - 0.709288i) q^{91} +(-64.6436 + 11.3984i) q^{92} +(32.9038 - 11.9760i) q^{94} +(-28.9595 - 79.5657i) q^{95} +(-17.4501 - 98.9646i) q^{97} +(59.0182 + 34.0742i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{5}+O(q^{10}) $ 36 * q - 18 * q^5	$ 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) $ 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	0.483690	−	1.32893i	0.241845	−	0.664463i
$2$	0.483690	−	1.32893i	0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	7.71206	+	1.35984i	1.54241	+	0.271969i	0.879197	−	0.476459i	$-0.158080\pi$
$5$	7.71206	+	1.35984i	1.54241	+	0.271969i	0.663216	+	0.748428i	$0.269191\pi$
$6$		0			0
$7$	−0.690206	+	0.579152i	−0.0986009	+	0.0827360i	−0.690756	−	0.723088i	$-0.742722\pi$
$7$	−0.690206	+	0.579152i	−0.0986009	+	0.0827360i	0.592155	+	0.805824i	$0.298277\pi$
$8$	−2.44949	+	1.41421i	−0.306186	+	0.176777i
$9$		0			0
$10$	5.53738	−	9.59102i	0.553738	−	0.959102i
$11$	15.2420	−	2.68757i	1.38564	−	0.244325i	0.569408	−	0.822055i	$-0.307173\pi$
$11$	15.2420	−	2.68757i	1.38564	−	0.244325i	0.816228	+	0.577730i	$0.196062\pi$
$12$		0			0
$13$	−0.854187	+	0.310899i	−0.0657067	+	0.0239153i	−0.374664	−	0.927160i	$-0.622242\pi$
$13$	−0.854187	+	0.310899i	−0.0657067	+	0.0239153i	0.308958	+	0.951076i	$0.400020\pi$
$14$	0.435804	+	1.19736i	0.0311289	+	0.0855259i
$15$		0			0
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	−10.6672	−	6.15869i	−0.627480	−	0.362276i	0.152295	−	0.988335i	$-0.451334\pi$
$17$	−10.6672	−	6.15869i	−0.627480	−	0.362276i	−0.779776	+	0.626059i	$0.784667\pi$
$18$		0			0
$19$	−5.40619	−	9.36379i	−0.284536	−	0.492831i	0.687960	−	0.725748i	$-0.258506\pi$
$19$	−5.40619	−	9.36379i	−0.284536	−	0.492831i	−0.972497	+	0.232917i	$0.925173\pi$
$20$	−10.0674	−	11.9978i	−0.503369	−	0.599892i
$21$		0			0
$22$	3.80080	−	21.5554i	0.172764	−	0.979792i
$23$	21.0966	−	25.1419i	0.917241	−	1.09313i	−0.0781224	−	0.996944i	$-0.524892\pi$
$23$	21.0966	−	25.1419i	0.917241	−	1.09313i	0.995364	−	0.0961819i	$-0.0306631\pi$
$24$		0			0
$25$	34.1344	+	12.4239i	1.36538	+	0.496956i
$26$			1.28553i			0.0494435i
$27$		0			0
$28$	1.80200			0.0643571
$29$	−19.3495	+	53.1622i	−0.667222	+	1.83318i	−0.126521	+	0.991964i	$0.540381\pi$
$29$	−19.3495	+	53.1622i	−0.667222	+	1.83318i	−0.540701	+	0.841215i	$0.681841\pi$
$30$		0			0
$31$	−37.9518	−	31.8453i	−1.22425	−	1.02727i	−0.998591	−	0.0530624i	$-0.983102\pi$
$31$	−37.9518	−	31.8453i	−1.22425	−	1.02727i	−0.225660	−	0.974206i	$-0.572454\pi$
$32$	5.57091	+	0.982302i	0.174091	+	0.0306970i
$33$		0			0
$34$	−13.3440	+	11.1970i	−0.392472	+	0.329323i
$35$	−6.11047	+	3.52788i	−0.174585	+	0.100797i
$36$		0			0
$37$	−17.4417	+	30.2099i	−0.471398	+	0.816485i	−0.999465	−	0.0327181i	$-0.989584\pi$
$37$	−17.4417	+	30.2099i	−0.471398	+	0.816485i	0.528067	+	0.849203i	$0.322917\pi$
$38$	−15.0587	+	2.65526i	−0.396282	+	0.0698751i
$39$		0			0
$40$	−20.8137	+	7.57558i	−0.520343	+	0.189389i
$41$	12.2490	+	33.6538i	0.298756	+	0.820824i	0.994709	+	0.102737i	$0.0327600\pi$
$41$	12.2490	+	33.6538i	0.298756	+	0.820824i	−0.695953	+	0.718087i	$0.745018\pi$
$42$		0			0
$43$	7.20864	+	40.8822i	0.167643	+	0.950750i	0.946298	+	0.323297i	$0.104791\pi$
$43$	7.20864	+	40.8822i	0.167643	+	0.950750i	−0.778655	+	0.627453i	$0.784098\pi$
$44$	−26.8072	−	15.4771i	−0.609254	−	0.351753i
$45$		0			0
$46$	−23.2075	−	40.1966i	−0.504512	−	0.873840i
$47$	15.9152	+	18.9670i	0.338622	+	0.403554i	0.908304	−	0.418311i	$-0.137378\pi$
$47$	15.9152	+	18.9670i	0.338622	+	0.403554i	−0.569682	+	0.821865i	$0.692933\pi$
$48$		0			0
$49$	−8.36779	+	47.4561i	−0.170771	+	0.968492i
$50$	33.0209	−	39.3528i	0.660418	−	0.787056i
$51$		0			0
$52$	1.70837	+	0.621797i	0.0328533	+	0.0119576i
$53$		−	50.3340i		−	0.949699i	−0.880067	−	0.474850i	$-0.842502\pi$
$53$		−	50.3340i		−	0.949699i	0.880067	−	0.474850i	$-0.157498\pi$
$54$		0			0
$55$	121.202			2.20367
$56$	0.871609	−	2.39472i	0.0155644	−	0.0427629i
$57$		0			0
$58$	61.2895	+	51.4280i	1.05672	+	0.886689i
$59$	−65.7126	−	11.5869i	−1.11377	−	0.196388i	−0.413667	−	0.910428i	$-0.635752\pi$
$59$	−65.7126	−	11.5869i	−1.11377	−	0.196388i	−0.700105	+	0.714040i	$0.746863\pi$
$60$		0			0
$61$	−18.7893	+	15.7661i	−0.308021	+	0.258460i	−0.783673	−	0.621173i	$-0.786656\pi$
$61$	−18.7893	+	15.7661i	−0.308021	+	0.258460i	0.475653	+	0.879633i	$0.342212\pi$
$62$	−60.6770	+	35.0319i	−0.978661	+	0.565030i
$63$		0			0
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	−7.01032	+	1.23611i	−0.107851	+	0.0190170i
$66$		0			0
$67$	−61.2882	+	22.3071i	−0.914750	+	0.332942i	−0.756148	−	0.654401i	$-0.772921\pi$
$67$	−61.2882	+	22.3071i	−0.914750	+	0.332942i	−0.158602	+	0.987343i	$0.550699\pi$
$68$	8.42558	+	23.1491i	0.123906	+	0.340428i
$69$		0			0
$70$	1.73272	+	9.82676i	0.0247532	+	0.140382i
$71$	−24.4496	−	14.1160i	−0.344361	−	0.198817i	0.317838	−	0.948145i	$-0.397043\pi$
$71$	−24.4496	−	14.1160i	−0.344361	−	0.198817i	−0.662199	+	0.749328i	$0.730377\pi$
$72$		0			0
$73$	−10.7760	−	18.6646i	−0.147617	−	0.255680i	0.782729	−	0.622362i	$-0.213827\pi$
$73$	−10.7760	−	18.6646i	−0.147617	−	0.255680i	−0.930346	+	0.366682i	$0.880494\pi$
$74$	31.7104	+	37.7910i	0.428519	+	0.510689i
$75$		0			0
$76$	−3.75510	+	21.2962i	−0.0494092	+	0.280213i
$77$	−8.96360	+	10.6824i	−0.116410	+	0.138732i
$78$		0			0
$79$	−27.2240	−	9.90872i	−0.344608	−	0.125427i	0.163918	−	0.986474i	$-0.447587\pi$
$79$	−27.2240	−	9.90872i	−0.344608	−	0.125427i	−0.508525	+	0.861047i	$0.669809\pi$
$80$			31.3241i			0.391552i
$81$		0			0
$82$	50.6481			0.617660
$83$	0.0509121	−	0.139880i	0.000613399	−	0.00168530i	−0.939386	−	0.342863i	$-0.888603\pi$
$83$	0.0509121	−	0.139880i	0.000613399	−	0.00168530i	0.939999	+	0.341177i	$0.110826\pi$
$84$		0			0
$85$	−73.8910	−	62.0019i	−0.869306	−	0.729434i
$86$	57.8162	+	10.1946i	0.672282	+	0.118541i
$87$		0			0
$88$	−33.5343	+	28.1386i	−0.381071	+	0.319757i
$89$	79.3008	−	45.7843i	0.891020	−	0.514431i	0.0167439	−	0.999860i	$-0.494670\pi$
$89$	79.3008	−	45.7843i	0.891020	−	0.514431i	0.874276	+	0.485429i	$0.161337\pi$
$90$		0			0
$91$	0.409508	−	0.709288i	0.00450008	−	0.00779437i
$92$	−64.6436	+	11.3984i	−0.702648	+	0.123896i
$93$		0			0
$94$	32.9038	−	11.9760i	0.350041	−	0.127404i
$95$	−28.9595	−	79.5657i	−0.304837	−	0.837534i
$96$		0			0
$97$	−17.4501	−	98.9646i	−0.179898	−	1.02025i	−0.932337	−	0.361591i	$-0.882234\pi$
$97$	−17.4501	−	98.9646i	−0.179898	−	1.02025i	0.752439	−	0.658662i	$-0.228877\pi$
$98$	59.0182	+	34.0742i	0.602227	+	0.347696i
$99$		0			0
$100$	−36.3251	−	62.9169i	−0.363251	−	0.629169i
$101$	67.8785	+	80.8944i	0.672064	+	0.800935i	0.989063	−	0.147491i	$-0.0471198\pi$
$101$	67.8785	+	80.8944i	0.672064	+	0.800935i	−0.316999	+	0.948426i	$0.602675\pi$
$102$		0			0
$103$	15.1042	−	85.6604i	0.146643	−	0.831654i	−0.819390	−	0.573236i	$-0.805688\pi$
$103$	15.1042	−	85.6604i	0.146643	−	0.831654i	0.966033	−	0.258418i	$-0.0832011\pi$
$104$	1.65265	−	1.96955i	0.0158908	−	0.0189379i
$105$		0			0
$106$	−66.8902	−	24.3461i	−0.631040	−	0.229680i
$107$		−	24.5062i		−	0.229030i	−0.993422	−	0.114515i	$-0.963469\pi$
$107$		−	24.5062i		−	0.229030i	0.993422	−	0.114515i	$-0.0365313\pi$
$108$		0			0
$109$	−33.5716			−0.307996			−0.153998	−	0.988071i	$-0.549215\pi$
$109$	−33.5716			−0.307996			−0.153998	+	0.988071i	$0.549215\pi$
$110$	58.6241	−	161.068i	0.532946	−	1.46426i
$111$		0			0
$112$	−2.76082	−	2.31661i	−0.0246502	−	0.0206840i
$113$	−120.158	−	21.1870i	−1.06334	−	0.187496i	−0.385503	−	0.922707i	$-0.625972\pi$
$113$	−120.158	−	21.1870i	−1.06334	−	0.187496i	−0.677839	+	0.735211i	$0.737083\pi$
$114$		0			0
$115$	196.887	−	165.208i	1.71206	−	1.43659i
$116$	97.9891	−	56.5740i	0.844733	−	0.487707i
$117$		0			0
$118$	−47.1826	+	81.7227i	−0.399853	+	0.692565i
$119$	10.9294	−	1.92714i	0.0918433	−	0.0161945i
$120$		0			0
$121$	111.392	−	40.5435i	0.920598	−	0.335070i
$122$	11.8638	+	32.5954i	0.0972440	+	0.267176i
$123$		0			0
$124$	17.2059	+	97.5797i	0.138758	+	0.786933i
$125$	76.8053	+	44.3435i	0.614442	+	0.354748i
$126$		0			0
$127$	−52.2314	−	90.4674i	−0.411271	−	0.712342i	0.583758	−	0.811927i	$-0.301582\pi$
$127$	−52.2314	−	90.4674i	−0.411271	−	0.712342i	−0.995029	+	0.0995859i	$0.968248\pi$
$128$	−7.27231	−	8.66680i	−0.0568149	−	0.0677094i
$129$		0			0
$130$	−1.74812	+	9.91409i	−0.0134471	+	0.0762622i
$131$	0.587532	−	0.700193i	0.00448497	−	0.00534498i	−0.763797	−	0.645456i	$-0.776667\pi$
$131$	0.587532	−	0.700193i	0.00448497	−	0.00534498i	0.768282	+	0.640111i	$0.221112\pi$
$132$		0			0
$133$	9.15444	+	3.33194i	0.0688304	+	0.0250522i
$134$			92.2372i			0.688337i
$135$		0			0
$136$	34.8388			0.256168
$137$	−4.80632	+	13.2053i	−0.0350826	+	0.0963887i	−0.955997	−	0.293376i	$-0.905221\pi$
$137$	−4.80632	+	13.2053i	−0.0350826	+	0.0963887i	0.920915	+	0.389764i	$0.127444\pi$
$138$		0			0
$139$	142.580	+	119.639i	1.02576	+	0.860714i	0.990340	−	0.138659i	$-0.0442792\pi$
$139$	142.580	+	119.639i	1.02576	+	0.860714i	0.0354184	+	0.999373i	$0.488724\pi$
$140$	13.8971	+	2.45044i	0.0992653	+	0.0175031i
$141$		0			0
$142$	−30.5851	+	25.6640i	−0.215388	+	0.180732i
$143$	−12.1839	+	7.03440i	−0.0852024	+	0.0491916i
$144$		0			0
$145$	−221.516	+	383.678i	−1.52770	+	2.64605i
$146$	−30.0162	+	5.29267i	−0.205590	+	0.0362511i
$147$		0			0
$148$	65.5594	−	23.8617i	0.442969	−	0.161227i
$149$	43.3633	+	119.140i	0.291029	+	0.799595i	0.995917	+	0.0902764i	$0.0287750\pi$
$149$	43.3633	+	119.140i	0.291029	+	0.799595i	−0.704888	+	0.709319i	$0.749003\pi$
$150$		0			0
$151$	−23.8651	−	135.346i	−0.158047	−	0.896331i	−0.955947	−	0.293540i	$-0.905167\pi$
$151$	−23.8651	−	135.346i	−0.158047	−	0.896331i	0.797899	−	0.602791i	$-0.205945\pi$
$152$	26.4848	+	15.2910i	0.174242	+	0.100599i
$153$		0			0
$154$	9.86052	+	17.0789i	0.0640294	+	0.110902i
$155$	−249.382	−	297.202i	−1.60891	−	1.91743i
$156$		0			0
$157$	4.03656	−	22.8925i	0.0257106	−	0.145812i	−0.969250	−	0.246078i	$-0.920858\pi$
$157$	4.03656	−	22.8925i	0.0257106	−	0.145812i	0.994961	+	0.100266i	$0.0319693\pi$
$158$	−26.3359	+	31.3859i	−0.166683	+	0.198645i
$159$		0			0
$160$	41.6275	+	15.1512i	0.260172	+	0.0946947i
$161$			29.5712i			0.183672i
$162$		0			0
$163$	157.977			0.969187			0.484593	−	0.874740i	$-0.338968\pi$
$163$	157.977			0.969187			0.484593	+	0.874740i	$0.338968\pi$
$164$	24.4980	−	67.3076i	0.149378	−	0.410412i
$165$		0			0
$166$	−0.161264	−	0.135317i	−0.000971472	−	0.000815162i
$167$	93.0755	+	16.4117i	0.557338	+	0.0982737i	0.445220	−	0.895421i	$-0.353125\pi$
$167$	93.0755	+	16.4117i	0.557338	+	0.0982737i	0.112118	+	0.993695i	$0.464237\pi$
$168$		0			0
$169$	−128.829	+	108.100i	−0.762299	+	0.639645i
$170$	−118.136	+	68.2060i	−0.694919	+	0.401212i
$171$		0			0
$172$	41.5129	−	71.9025i	0.241354	−	0.418038i
$173$	286.053	−	50.4388i	1.65348	−	0.291554i	0.732388	−	0.680888i	$-0.238406\pi$
$173$	286.053	−	50.4388i	1.65348	−	0.291554i	0.921097	+	0.389334i	$0.127295\pi$
$174$		0			0
$175$	−30.7551	+	11.1939i	−0.175743	+	0.0639654i
$176$	21.1739	+	58.1749i	0.120307	+	0.330539i
$177$		0			0
$178$	−22.4870	−	127.530i	−0.126332	−	0.716462i
$179$	−9.64834	−	5.57047i	−0.0539013	−	0.0311200i	0.472807	−	0.881166i	$-0.343241\pi$
$179$	−9.64834	−	5.57047i	−0.0539013	−	0.0311200i	−0.526709	+	0.850046i	$0.676574\pi$
$180$		0			0
$181$	−95.2763	−	165.023i	−0.526389	−	0.911732i	−0.999527	−	0.0307438i	$-0.990212\pi$
$181$	−95.2763	−	165.023i	−0.526389	−	0.911732i	0.473139	−	0.880988i	$-0.343121\pi$
$182$	−0.744517	−	0.887281i	−0.00409075	−	0.00487517i
$183$		0			0
$184$	−16.1198	+	91.4198i	−0.0876075	+	0.496847i
$185$	−175.592	+	209.263i	−0.949148	+	1.13115i
$186$		0			0
$187$	−179.141	−	65.2019i	−0.957972	−	0.348673i
$188$		−	49.5194i		−	0.263401i
$189$		0			0
$190$	−119.744			−0.630233
$191$	−5.86380	+	16.1107i	−0.0307005	+	0.0843490i	−0.954096	−	0.299501i	$-0.903180\pi$
$191$	−5.86380	+	16.1107i	−0.0307005	+	0.0843490i	0.923395	+	0.383850i	$0.125402\pi$
$192$		0			0
$193$	118.098	+	99.0962i	0.611908	+	0.513452i	0.895248	−	0.445568i	$-0.146998\pi$
$193$	118.098	+	99.0962i	0.611908	+	0.513452i	−0.283340	+	0.959019i	$0.591443\pi$
$194$	−139.957	−	24.6782i	−0.721428	−	0.127207i
$195$		0			0
$196$	73.8286	−	61.9496i	0.376677	−	0.316069i
$197$	−107.213	+	61.8996i	−0.544230	+	0.314211i	−0.746792	−	0.665058i	$-0.768407\pi$
$197$	−107.213	+	61.8996i	−0.544230	+	0.314211i	0.202561	+	0.979270i	$0.435073\pi$
$198$		0			0
$199$	−117.239	+	203.063i	−0.589139	+	1.02042i	0.405207	+	0.914225i	$0.367200\pi$
$199$	−117.239	+	203.063i	−0.589139	+	1.02042i	−0.994345	+	0.106193i	$0.966134\pi$
$200$	−101.182	+	17.8411i	−0.505910	+	0.0892055i
$201$		0			0
$202$	140.335	−	51.0777i	0.694727	−	0.252860i
$203$	−17.4339	−	47.8991i	−0.0858811	−	0.235956i
$204$		0			0
$205$	48.7010	+	276.197i	0.237566	+	1.34730i
$206$	−106.531	−	61.5054i	−0.517139	−	0.298570i
$207$		0			0
$208$	−1.81801	−	3.14889i	−0.00874045	−	0.0151389i
$209$	−107.567	−	128.193i	−0.514674	−	0.613365i
$210$		0			0
$211$	−9.24958	+	52.4570i	−0.0438369	+	0.248611i	−0.998850	−	0.0479537i	$-0.984730\pi$
$211$	−9.24958	+	52.4570i	−0.0438369	+	0.248611i	0.955013	+	0.296565i	$0.0958411\pi$
$212$	−64.7082	+	77.1162i	−0.305227	+	0.363756i
$213$		0			0
$214$	−32.5669	−	11.8534i	−0.152182	−	0.0553896i
$215$			325.089i			1.51204i
$216$		0			0
$217$	44.6378			0.205704
$218$	−16.2382	+	44.6142i	−0.0744873	+	0.204652i
$219$		0			0
$220$	−185.692	−	155.814i	−0.844054	−	0.708246i
$221$	11.0265	+	1.94427i	0.0498936	+	0.00879759i
$222$		0			0
$223$	−45.9011	+	38.5156i	−0.205835	+	0.172716i	−0.739878	−	0.672742i	$-0.765117\pi$
$223$	−45.9011	+	38.5156i	−0.205835	+	0.172716i	0.534043	+	0.845457i	$0.320672\pi$
$224$	−4.41398	+	2.54841i	−0.0197053	+	0.0113768i
$225$		0			0
$226$	−86.2750	+	149.433i	−0.381748	+	0.661206i
$227$	62.7048	−	11.0565i	0.276232	−	0.0487072i	−0.0338157	−	0.999428i	$-0.510766\pi$
$227$	62.7048	−	11.0565i	0.276232	−	0.0487072i	0.310048	+	0.950721i	$0.399655\pi$
$228$		0			0
$229$	−201.212	+	73.2350i	−0.878653	+	0.319804i	−0.741666	−	0.670769i	$-0.765964\pi$
$229$	−201.212	+	73.2350i	−0.878653	+	0.319804i	−0.136987	+	0.990573i	$0.543742\pi$
$230$	−124.317	−	341.558i	−0.540508	−	1.48503i
$231$		0			0
$232$	−27.7864	−	157.584i	−0.119769	−	0.679243i
$233$	186.691	+	107.786i	0.801248	+	0.462601i	0.843907	−	0.536489i	$-0.180250\pi$
$233$	186.691	+	107.786i	0.801248	+	0.462601i	−0.0426593	+	0.999090i	$0.513583\pi$
$234$		0			0
$235$	96.9470	+	167.917i	0.412541	+	0.714541i
$236$	85.7817	+	102.231i	0.363482	+	0.433180i
$237$		0			0
$238$	2.72539	−	15.4564i	0.0114512	−	0.0649431i
$239$	−26.8944	+	32.0515i	−0.112529	+	0.134107i	−0.819369	−	0.573267i	$-0.805676\pi$
$239$	−26.8944	+	32.0515i	−0.112529	+	0.134107i	0.706840	+	0.707374i	$0.250120\pi$
$240$		0			0
$241$	421.281	+	153.334i	1.74805	+	0.636240i	0.999636	−	0.0269874i	$-0.00859139\pi$
$241$	421.281	+	153.334i	1.74805	+	0.636240i	0.748418	+	0.663227i	$0.230814\pi$
$242$		−	167.643i		−	0.692738i
$243$		0			0
$244$	49.0553			0.201046
$245$	−129.066	+	354.606i	−0.526800	+	1.44737i
$246$		0			0
$247$	7.52908	+	6.31765i	0.0304821	+	0.0255775i
$248$	137.999	+	24.3329i	0.556446	+	0.0981164i
$249$		0			0
$250$	96.0792	−	80.6200i	0.384317	−	0.322480i
$251$	222.273	−	128.329i	0.885549	−	0.511272i	0.0130650	−	0.999915i	$-0.495841\pi$
$251$	222.273	−	128.329i	0.885549	−	0.511272i	0.872484	+	0.488643i	$0.162508\pi$
$252$		0			0
$253$	253.983	−	439.911i	1.00388	−	1.73878i
$254$	−145.488	+	25.6535i	−0.572788	+	0.100998i
$255$		0			0
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	−134.312	−	369.019i	−0.522614	−	1.43587i	−0.867600	−	0.497262i	$-0.834339\pi$
$257$	−134.312	−	369.019i	−0.522614	−	1.43587i	0.344986	−	0.938608i	$-0.387884\pi$
$258$		0			0
$259$	−5.45776	−	30.9525i	−0.0210724	−	0.119508i
$260$	12.3295	+	7.11846i	0.0474213	+	0.0273787i
$261$		0			0
$262$	−0.646322	−	1.11946i	−0.00246688	−	0.00427276i
$263$	−78.9273	−	94.0619i	−0.300104	−	0.357650i	0.594828	−	0.803853i	$-0.297220\pi$
$263$	−78.9273	−	94.0619i	−0.300104	−	0.357650i	−0.894932	+	0.446203i	$0.852776\pi$
$264$		0			0
$265$	68.4465	−	388.179i	0.258289	−	1.46483i
$266$	8.85581	−	10.5539i	0.0332925	−	0.0396765i
$267$		0			0
$268$	122.576	+	44.6142i	0.457375	+	0.166471i
$269$		−	392.295i		−	1.45835i	−0.684329	−	0.729173i	$-0.739905\pi$
$269$		−	392.295i		−	1.45835i	0.684329	−	0.729173i	$-0.260095\pi$
$270$		0			0
$271$	−43.9569			−0.162203			−0.0811013	−	0.996706i	$-0.525844\pi$
$271$	−43.9569			−0.162203			−0.0811013	+	0.996706i	$0.525844\pi$
$272$	16.8512	−	46.2982i	0.0619528	−	0.170214i
$273$		0			0
$274$	15.2240	+	12.7745i	0.0555622	+	0.0466222i
$275$	553.666	+	97.6263i	2.01333	+	0.355005i
$276$		0			0
$277$	−253.346	+	212.582i	−0.914606	+	0.767446i	−0.972990	−	0.230849i	$-0.925850\pi$
$277$	−253.346	+	212.582i	−0.914606	+	0.767446i	0.0583836	+	0.998294i	$0.481405\pi$
$278$	227.956	−	131.611i	0.819987	−	0.473420i
$279$		0			0
$280$	9.97835	−	17.2830i	0.0356370	−	0.0617251i
$281$	252.252	−	44.4788i	0.897692	−	0.158287i	0.294282	−	0.955719i	$-0.404919\pi$
$281$	252.252	−	44.4788i	0.897692	−	0.158287i	0.603410	+	0.797431i	$0.293808\pi$
$282$		0			0
$283$	146.361	−	53.2711i	0.517177	−	0.188237i	−0.0702267	−	0.997531i	$-0.522372\pi$
$283$	146.361	−	53.2711i	0.517177	−	0.188237i	0.587404	+	0.809294i	$0.300150\pi$
$284$	19.3118	+	53.0588i	0.0679993	+	0.186827i
$285$		0			0
$286$	3.45496	+	19.5940i	0.0120803	+	0.0685106i
$287$	−27.9450	−	16.1340i	−0.0973693	−	0.0562162i
$288$		0			0
$289$	−68.6411	−	118.890i	−0.237512	−	0.411383i
$290$	402.734	+	479.960i	1.38874	+	1.65503i
$291$		0			0
$292$	−7.48496	+	42.4493i	−0.0256334	+	0.145374i
$293$	131.430	−	156.632i	0.448566	−	0.534580i	−0.493617	−	0.869679i	$-0.664326\pi$
$293$	131.430	−	156.632i	0.448566	−	0.534580i	0.942183	+	0.335100i	$0.108770\pi$
$294$		0			0
$295$	−491.023	−	178.718i	−1.66448	−	0.605823i
$296$		−	98.6652i		−	0.333328i
$297$		0			0
$298$	179.302			0.601685
$299$	−10.2038	+	28.0348i	−0.0341265	+	0.0937618i
$300$		0			0
$301$	−28.6525	−	24.0423i	−0.0951909	−	0.0798747i
$302$	−191.408	−	33.7504i	−0.633801	−	0.111756i
$303$		0			0
$304$	33.1310	−	27.8002i	0.108984	−	0.0914482i
$305$	−166.343	+	96.0384i	−0.545388	+	0.314880i
$306$		0			0
$307$	284.956	−	493.559i	0.928196	−	1.60768i	0.141857	−	0.989887i	$-0.454693\pi$
$307$	284.956	−	493.559i	0.928196	−	1.60768i	0.786339	−	0.617796i	$-0.211974\pi$
$308$	27.4661	−	4.84301i	0.0891755	−	0.0157241i
$309$		0			0
$310$	−515.582	+	187.657i	−1.66317	+	0.605344i
$311$	152.905	+	420.102i	0.491654	+	1.35081i	0.899165	+	0.437609i	$0.144175\pi$
$311$	152.905	+	420.102i	0.491654	+	1.35081i	−0.407511	+	0.913200i	$0.633603\pi$
$312$		0			0
$313$	−50.5690	−	286.791i	−0.161562	−	0.916265i	−0.952538	−	0.304418i	$-0.901538\pi$
$313$	−50.5690	−	286.791i	−0.161562	−	0.916265i	0.790976	−	0.611847i	$-0.209573\pi$
$314$	−28.4700	−	16.4371i	−0.0906686	−	0.0523476i
$315$		0			0
$316$	28.9712	+	50.1795i	0.0916809	+	0.158796i
$317$	216.870	+	258.455i	0.684131	+	0.815316i	0.990633	−	0.136554i	$-0.0436028\pi$
$317$	216.870	+	258.455i	0.684131	+	0.815316i	−0.306501	+	0.951870i	$0.599158\pi$
$318$		0			0
$319$	−152.047	+	862.300i	−0.476636	+	2.70314i
$320$	40.2695	−	47.9914i	0.125842	−	0.149973i
$321$		0			0
$322$	39.2979	+	14.3033i	0.122043	+	0.0444201i
$323$			133.180i			0.412322i
$324$		0			0
$325$	−33.0197			−0.101599
$326$	76.4120	−	209.940i	0.234393	−	0.643989i
$327$		0			0
$328$	−77.5974	−	65.1120i	−0.236577	−	0.198512i
$329$	−21.9696	−	3.87383i	−0.0667768	−	0.0117746i
$330$		0			0
$331$	116.755	−	97.9694i	0.352735	−	0.295980i	−0.449152	−	0.893455i	$-0.648274\pi$
$331$	116.755	−	97.9694i	0.352735	−	0.295980i	0.801887	+	0.597475i	$0.203829\pi$
$332$	−0.257828	+	0.148857i	−0.000776590	+	0.000448365i
$333$		0			0
$334$	66.8296	−	115.752i	0.200089	−	0.346564i
$335$	−502.993	+	88.6912i	−1.50147	+	0.264750i
$336$		0			0
$337$	219.421	−	79.8628i	0.651102	−	0.236982i	0.00471178	−	0.999989i	$-0.498500\pi$
$337$	219.421	−	79.8628i	0.651102	−	0.236982i	0.646390	+	0.763007i	$0.276278\pi$
$338$	81.3439	+	223.490i	0.240662	+	0.661214i
$339$		0			0
$340$	33.4994	+	189.985i	0.0985278	+	0.558779i
$341$	−664.047	−	383.388i	−1.94735	−	1.12430i
$342$		0			0
$343$	−43.7833	−	75.8349i	−0.127648	−	0.221093i
$344$	−75.4737	−	89.9461i	−0.219400	−	0.261471i
$345$		0			0
$346$	71.3313	−	404.540i	0.206160	−	1.16919i
$347$	409.259	−	487.736i	1.17942	−	1.40558i	0.284899	−	0.958558i	$-0.408040\pi$
$347$	409.259	−	487.736i	1.17942	−	1.40558i	0.894523	−	0.447022i	$-0.147516\pi$
$348$		0			0
$349$	268.471	+	97.7153i	0.769257	+	0.279987i	0.696686	−	0.717377i	$-0.254657\pi$
$349$	268.471	+	97.7153i	0.769257	+	0.279987i	0.0725714	+	0.997363i	$0.476879\pi$
$350$			46.2857i			0.132245i
$351$		0			0
$352$	87.5518			0.248727
$353$	112.137	−	308.094i	0.317669	−	0.872788i	−0.673381	−	0.739296i	$-0.735159\pi$
$353$	112.137	−	308.094i	0.317669	−	0.872788i	0.991050	−	0.133492i	$-0.0426191\pi$
$354$		0			0
$355$	−169.361	−	142.111i	−0.477074	−	0.400313i
$356$	−180.355	−	31.8015i	−0.506615	−	0.0893299i
$357$		0			0
$358$	−12.0695	+	10.1276i	−0.0337138	+	0.0282893i
$359$	−484.455	+	279.700i	−1.34946	+	0.779109i	−0.988172	−	0.153347i	$-0.950995\pi$
$359$	−484.455	+	279.700i	−1.34946	+	0.779109i	−0.361284	+	0.932456i	$0.617661\pi$
$360$		0			0
$361$	122.046	−	211.390i	0.338078	−	0.585569i
$362$	−265.388	+	46.7951i	−0.733116	+	0.129268i
$363$		0			0
$364$	−1.53925	+	0.560239i	−0.00422870	+	0.00153912i
$365$	−57.7245	−	158.597i	−0.158149	−	0.434511i
$366$		0			0
$367$	83.2991	+	472.413i	0.226973	+	1.28723i	0.858877	+	0.512182i	$0.171163\pi$
$367$	83.2991	+	472.413i	0.226973	+	1.28723i	−0.631904	+	0.775047i	$0.717726\pi$
$368$	113.693	+	65.6408i	0.308949	+	0.178372i
$369$		0			0
$370$	193.163	+	334.568i	0.522061	+	0.904237i
$371$	29.1510	+	34.7409i	0.0785743	+	0.0936411i
$372$		0			0
$373$	59.7262	−	338.724i	0.160124	−	0.908107i	−0.793827	−	0.608144i	$-0.791914\pi$
$373$	59.7262	−	338.724i	0.160124	−	0.908107i	0.953951	−	0.299964i	$-0.0969745\pi$
$374$	−173.297	+	206.527i	−0.463361	+	0.552212i
$375$		0			0
$376$	−65.8076	−	23.9520i	−0.175020	−	0.0637022i
$377$		−	51.4262i		−	0.136409i
$378$		0			0
$379$	−104.156			−0.274817			−0.137408	−	0.990514i	$-0.543877\pi$
$379$	−104.156			−0.274817			−0.137408	+	0.990514i	$0.543877\pi$
$380$	−57.9191	+	159.131i	−0.152419	+	0.418767i
$381$		0			0
$382$	18.5736	+	15.5851i	0.0486220	+	0.0407987i
$383$	63.8855	+	11.2647i	0.166803	+	0.0294118i	0.256426	−	0.966564i	$-0.417455\pi$
$383$	63.8855	+	11.2647i	0.166803	+	0.0294118i	−0.0896229	+	0.995976i	$0.528566\pi$
$384$		0			0
$385$	−83.6542	+	70.1942i	−0.217284	+	0.182323i
$386$	188.814	−	109.012i	0.489156	−	0.282415i
$387$		0			0
$388$	−100.491	+	174.056i	−0.258998	+	0.448598i
$389$	−232.365	+	40.9722i	−0.597339	+	0.105327i	−0.464139	−	0.885762i	$-0.653636\pi$
$389$	−232.365	+	40.9722i	−0.597339	+	0.105327i	−0.133200	+	0.991089i	$0.542525\pi$
$390$		0			0
$391$	−379.882	+	138.266i	−0.971564	+	0.353620i
$392$	−46.6163	−	128.077i	−0.118919	−	0.326727i
$393$		0			0
$394$	30.4021	+	172.419i	0.0771627	+	0.437611i
$395$	−196.479	−	113.437i	−0.497415	−	0.287183i
$396$		0			0
$397$	−2.59349	−	4.49206i	−0.00653272	−	0.0113150i	0.862741	−	0.505647i	$-0.168746\pi$
$397$	−2.59349	−	4.49206i	−0.00653272	−	0.0113150i	−0.869273	+	0.494332i	$0.835413\pi$
$398$	213.149	+	254.021i	0.535550	+	0.638244i
$399$		0			0
$400$	−25.2311	+	143.093i	−0.0630778	+	0.357732i
$401$	−103.381	+	123.205i	−0.257808	+	0.307244i	−0.879387	−	0.476108i	$-0.842047\pi$
$401$	−103.381	+	123.205i	−0.257808	+	0.307244i	0.621579	+	0.783352i	$0.286492\pi$
$402$		0			0
$403$	42.3186	+	15.4027i	0.105009	+	0.0382201i
$404$		−	211.200i		−	0.522773i
$405$		0			0
$406$	−72.0870			−0.177554
$407$	−184.655	+	507.335i	−0.453698	+	1.24652i
$408$		0			0
$409$	−132.217	−	110.943i	−0.323269	−	0.271255i	0.466682	−	0.884425i	$-0.345449\pi$
$409$	−132.217	−	110.943i	−0.323269	−	0.271255i	−0.789950	+	0.613171i	$0.789894\pi$
$410$	390.601	+	68.8736i	0.952686	+	0.167984i
$411$		0			0
$412$	−133.264	+	111.822i	−0.323456	+	0.271412i
$413$	52.0658	−	30.0602i	0.126067	−	0.0727850i
$414$		0			0
$415$	0.582852	−	1.00953i	0.00140446	−	0.00243260i
$416$	−5.06400	+	0.892920i	−0.0121731	+	0.00214644i
$417$		0			0
$418$	−222.388	+	80.9427i	−0.532029	+	0.193643i
$419$	−97.9330	−	269.069i	−0.233730	−	0.642169i	0.766270	−	0.642519i	$-0.222111\pi$
$419$	−97.9330	−	269.069i	−0.233730	−	0.642169i	−1.00000		0.000350278i	$0.999889\pi$
$420$		0			0
$421$	117.029	+	663.704i	0.277979	+	1.57649i	0.729339	+	0.684153i	$0.239828\pi$
$421$	117.029	+	663.704i	0.277979	+	1.57649i	−0.451360	+	0.892342i	$0.649061\pi$
$422$	65.2375	+	37.6649i	0.154591	+	0.0892533i
$423$		0			0
$424$	71.1831	+	123.293i	0.167885	+	0.290785i
$425$	−287.602	−	342.751i	−0.676711	−	0.806473i
$426$		0			0
$427$	3.83752	−	21.7637i	0.00898717	−	0.0509688i
$428$	−31.5045	+	37.5456i	−0.0736087	+	0.0877234i
$429$		0			0
$430$	432.019	+	157.242i	1.00470	+	0.365679i
$431$			539.138i			1.25090i	0.780264	+	0.625450i	$0.215085\pi$
$431$			539.138i			1.25090i	−0.780264	+	0.625450i	$0.784915\pi$
$432$		0			0
$433$	−802.991			−1.85448			−0.927241	−	0.374466i	$-0.877826\pi$
$433$	−802.991			−1.85448			−0.927241	+	0.374466i	$0.877826\pi$
$434$	21.5908	−	59.3204i	0.0497485	−	0.136683i
$435$		0			0
$436$	51.4347	+	43.1588i	0.117969	+	0.0989881i
$437$	−349.475	−	61.6219i	−0.799715	−	0.141011i
$438$		0			0
$439$	−59.9232	+	50.2816i	−0.136499	+	0.114537i	−0.708481	−	0.705730i	$-0.750619\pi$
$439$	−59.9232	+	50.2816i	−0.136499	+	0.114537i	0.571982	+	0.820266i	$0.306175\pi$
$440$	−296.883	+	171.405i	−0.674733	+	0.389557i
$441$		0			0
$442$	7.91718	−	13.7130i	0.0179122	−	0.0310248i
$443$	537.994	−	94.8628i	1.21443	−	0.214137i	0.470505	−	0.882397i	$-0.344072\pi$
$443$	537.994	−	94.8628i	1.21443	−	0.214137i	0.743928	+	0.668260i	$0.232961\pi$
$444$		0			0
$445$	673.832	−	245.255i	1.51423	−	0.551134i
$446$	28.9825	+	79.6288i	0.0649832	+	0.178540i
$447$		0			0
$448$	1.25166	+	7.09849i	0.00279388	+	0.0158449i
$449$	592.342	+	341.989i	1.31925	+	0.761667i	0.983607	−	0.180323i	$-0.0577144\pi$
$449$	592.342	+	341.989i	1.31925	+	0.761667i	0.335639	+	0.941991i	$0.391048\pi$
$450$		0			0
$451$	277.146	+	480.031i	0.614514	+	1.06437i
$452$	156.855	+	186.932i	0.347024	+	0.413567i
$453$		0			0
$454$	15.6363	−	88.6779i	0.0344412	−	0.195326i
$455$	4.12267	−	4.91321i	0.00906081	−	0.0107983i
$456$		0			0
$457$	−80.6475	−	29.3533i	−0.176472	−	0.0642304i	0.252273	−	0.967656i	$-0.418822\pi$
$457$	−80.6475	−	29.3533i	−0.176472	−	0.0642304i	−0.428745	+	0.903426i	$0.641044\pi$
$458$			302.818i			0.661175i
$459$		0			0
$460$	−514.035			−1.11747
$461$	−1.94941	+	5.35597i	−0.00422866	+	0.0116181i	−0.941789	−	0.336205i	$-0.890857\pi$
$461$	−1.94941	+	5.35597i	−0.00422866	+	0.0116181i	0.937560	+	0.347823i	$0.113079\pi$
$462$		0			0
$463$	−247.066	−	207.313i	−0.533620	−	0.447760i	0.335729	−	0.941959i	$-0.391017\pi$
$463$	−247.066	−	207.313i	−0.533620	−	0.447760i	−0.869349	+	0.494198i	$0.835462\pi$
$464$	−222.858	−	39.2959i	−0.480298	−	0.0846894i
$465$		0			0
$466$	233.540	−	195.963i	0.501159	−	0.420522i
$467$	−32.7859	+	18.9290i	−0.0702054	+	0.0405331i	−0.534692	−	0.845047i	$-0.679572\pi$
$467$	−32.7859	+	18.9290i	−0.0702054	+	0.0405331i	0.464486	+	0.885580i	$0.346239\pi$
$468$		0			0
$469$	29.3823	−	50.8917i	0.0626489	−	0.108511i
$470$	270.042	−	47.6157i	0.574557	−	0.101310i
$471$		0			0
$472$	177.349	−	64.5496i	0.375739	−	0.136758i
$473$	219.748	+	603.753i	0.464584	+	1.27643i
$474$		0			0
$475$	−68.2021	−	386.793i	−0.143583	−	0.814302i
$476$	−19.2222	−	11.0980i	−0.0403828	−	0.0233150i
$477$		0			0
$478$	29.5855	+	51.2436i	0.0618944	+	0.107204i
$479$	−461.346	−	549.811i	−0.963145	−	1.14783i	−0.988963	−	0.148164i	$-0.952664\pi$
$479$	−461.346	−	549.811i	−0.963145	−	1.14783i	0.0258182	−	0.999667i	$-0.491781\pi$
$480$		0			0
$481$	5.50626	−	31.2275i	0.0114475	−	0.0649221i
$482$	407.538	−	485.685i	0.845515	−	1.00765i
$483$		0			0
$484$	−222.785	−	81.0870i	−0.460299	−	0.167535i
$485$		−	786.950i		−	1.62258i
$486$		0			0
$487$	52.1558			0.107096			0.0535480	−	0.998565i	$-0.482947\pi$
$487$	52.1558			0.107096			0.0535480	+	0.998565i	$0.482947\pi$
$488$	23.7275	−	65.1909i	0.0486220	−	0.133588i
$489$		0			0
$490$	408.817	+	343.038i	0.834320	+	0.700078i
$491$	−77.8114	−	13.7202i	−0.158475	−	0.0279435i	0.0938475	−	0.995587i	$-0.470083\pi$
$491$	−77.8114	−	13.7202i	−0.158475	−	0.0279435i	−0.252323	+	0.967643i	$0.581194\pi$
$492$		0			0
$493$	533.813	−	447.922i	1.08279	−	0.908565i
$494$	12.0374	−	6.94981i	0.0243673	−	0.0140685i
$495$		0			0
$496$	99.0851	−	171.620i	0.199768	−	0.346009i
$497$	25.0506	−	4.41709i	0.0504036	−	0.00888751i
$498$		0			0
$499$	27.9915	−	10.1881i	0.0560952	−	0.0204170i	−0.313820	−	0.949482i	$-0.601609\pi$
$499$	27.9915	−	10.1881i	0.0560952	−	0.0204170i	0.369915	+	0.929065i	$0.379387\pi$
$500$	−60.6655	−	166.677i	−0.121331	−	0.333354i
$501$		0			0
$502$	−63.0291	−	357.456i	−0.125556	−	0.712063i
$503$	146.080	+	84.3394i	0.290418	+	0.167673i	0.638130	−	0.769928i	$-0.279708\pi$
$503$	146.080	+	84.3394i	0.290418	+	0.167673i	−0.347713	+	0.937601i	$0.613041\pi$
$504$		0			0
$505$	413.479	+	716.167i	0.818771	+	1.41815i
$506$	−461.760	−	550.305i	−0.912570	−	1.08756i
$507$		0			0
$508$	−36.2795	+	205.751i	−0.0714164	+	0.405022i
$509$	−223.993	+	266.945i	−0.440066	+	0.524450i	−0.939798	−	0.341730i	$-0.888987\pi$
$509$	−223.993	+	266.945i	−0.440066	+	0.524450i	0.499733	+	0.866180i	$0.333432\pi$
$510$		0			0
$511$	18.2474	+	6.64149i	0.0357091	+	0.0129971i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−555.364			−1.08047
$515$	232.970	−	640.079i	0.452368	−	1.24287i
$516$		0			0
$517$	293.555	+	246.322i	0.567805	+	0.476445i
$518$	−43.7734	−	7.71843i	−0.0845047	−	0.0149005i
$519$		0			0
$520$	15.4236	−	12.9419i	0.0296607	−	0.0248883i
$521$	95.9710	−	55.4089i	0.184205	−	0.106351i	−0.405062	−	0.914289i	$-0.632750\pi$
$521$	95.9710	−	55.4089i	0.184205	−	0.106351i	0.589267	+	0.807938i	$0.299417\pi$
$522$		0			0
$523$	280.197	−	485.316i	0.535750	−	0.927946i	−0.463377	−	0.886161i	$-0.653362\pi$
$523$	280.197	−	485.316i	0.535750	−	0.927946i	0.999127	−	0.0417848i	$-0.0133044\pi$
$524$	−1.80030	+	0.317442i	−0.00343569	+	0.000605805i
$525$		0			0
$526$	−163.178	+	59.3918i	−0.310224	+	0.112912i
$527$	208.712	+	573.433i	0.396039	+	1.08811i
$528$		0			0
$529$	−95.1903	−	539.851i	−0.179944	−	1.02051i
$530$	−482.755	−	278.719i	−0.910858	−	0.525884i
$531$		0			0
$532$	−9.74195	−	16.8736i	−0.0183119	−	0.0317172i
$533$	−20.9258	−	24.9384i	−0.0392605	−	0.0467888i
$534$		0			0
$535$	33.3246	−	188.993i	0.0622889	−	0.353258i
$536$	118.578	−	141.316i	0.221227	−	0.263649i
$537$		0			0
$538$	−521.331	−	189.749i	−0.969018	−	0.352694i
$539$			745.814i			1.38370i
$540$		0			0
$541$	−313.055			−0.578660			−0.289330	−	0.957229i	$-0.593433\pi$
$541$	−313.055			−0.578660			−0.289330	+	0.957229i	$0.593433\pi$
$542$	−21.2615	+	58.4155i	−0.0392279	+	0.107778i
$543$		0			0
$544$	−53.3762	−	44.7879i	−0.0981179	−	0.0823307i
$545$	−258.906	−	45.6522i	−0.475057	−	0.0837654i
$546$		0			0
$547$	−564.255	+	473.466i	−1.03155	+	0.865569i	−0.991034	−	0.133610i	$-0.957343\pi$
$547$	−564.255	+	473.466i	−1.03155	+	0.865569i	−0.0405113	+	0.999179i	$0.512899\pi$
$548$	24.3401	−	14.0527i	0.0444162	−	0.0256437i
$549$		0			0
$550$	397.541	−	688.561i	0.722801	−	1.25193i
$551$	602.406	−	106.220i	1.09330	−	0.192778i
$552$		0			0
$553$	24.5288	−	8.92776i	0.0443559	−	0.0161442i
$554$	159.966	+	439.502i	0.288747	+	0.793325i
$555$		0			0
$556$	−64.6407	−	366.596i	−0.116260	−	0.659345i
$557$	552.604	+	319.046i	0.992108	+	0.572794i	0.905904	−	0.423483i	$-0.139193\pi$
$557$	552.604	+	319.046i	0.992108	+	0.572794i	0.0862045	+	0.996277i	$0.472526\pi$
$558$		0			0
$559$	−18.8678	−	32.6799i	−0.0337527	−	0.0584614i
$560$	−18.1414	−	21.6201i	−0.0323954	−	0.0386073i
$561$		0			0
$562$	62.9025	−	356.738i	0.111926	−	0.634764i
$563$	−224.179	+	267.166i	−0.398187	+	0.474541i	−0.927466	−	0.373907i	$-0.878018\pi$
$563$	−224.179	+	267.166i	−0.398187	+	0.474541i	0.529279	+	0.848448i	$0.322462\pi$
$564$		0			0
$565$	−897.852	−	326.791i	−1.58912	−	0.578392i
$566$		−	220.270i		−	0.389169i
$567$		0			0
$568$	79.8521			0.140585
$569$	−187.157	+	514.209i	−0.328922	+	0.903707i	0.659463	+	0.751737i	$0.270784\pi$
$569$	−187.157	+	514.209i	−0.328922	+	0.903707i	−0.988385	+	0.151970i	$0.951438\pi$
$570$		0			0
$571$	534.384	+	448.402i	0.935874	+	0.785292i	0.976863	−	0.213868i	$-0.0686062\pi$
$571$	534.384	+	448.402i	0.935874	+	0.785292i	−0.0409882	+	0.999160i	$0.513051\pi$
$572$	27.7101	+	4.88605i	0.0484443	+	0.00854204i
$573$		0			0
$574$	−34.9576	+	29.3329i	−0.0609018	+	0.0511027i
$575$	1032.48	−	596.102i	1.79562	−	1.03670i
$576$		0			0
$577$	−193.884	+	335.816i	−0.336020	+	0.582004i	−0.983680	−	0.179925i	$-0.942414\pi$
$577$	−193.884	+	335.816i	−0.336020	+	0.582004i	0.647660	+	0.761929i	$0.275748\pi$
$578$	−191.197	+	33.7131i	−0.330790	+	0.0583272i
$579$		0			0
$580$	832.630	−	303.052i	1.43557	−	0.522504i
$581$	0.0458718	+	0.126032i	7.89532e−5	+	0.000216922i
$582$		0			0
$583$	−135.276	−	767.191i	−0.232035	−	1.31594i
$584$	52.7916	+	30.4792i	0.0903966	+	0.0521905i
$585$		0			0
$586$	−144.581	−	250.422i	−0.246725	−	0.427341i
$587$	229.618	+	273.648i	0.391173	+	0.466181i	0.925307	−	0.379218i	$-0.123807\pi$
$587$	229.618	+	273.648i	0.391173	+	0.466181i	−0.534135	+	0.845399i	$0.679363\pi$
$588$		0			0
$589$	−93.0185	+	527.534i	−0.157926	+	0.895644i
$590$	−475.005	+	566.089i	−0.805094	+	0.959473i
$591$		0			0
$592$	−131.119	−	47.7233i	−0.221484	−	0.0806137i
$593$		−	828.411i		−	1.39698i	−0.715618	−	0.698492i	$-0.753855\pi$
$593$		−	828.411i		−	1.39698i	0.715618	−	0.698492i	$-0.246145\pi$
$594$		0			0
$595$	86.9085			0.146065
$596$	86.7266	−	238.279i	0.145514	−	0.399798i
$597$		0			0
$598$	32.3207	+	27.1202i	0.0540479	+	0.0453516i
$599$	−863.376	−	152.237i	−1.44136	−	0.254151i	−0.602337	−	0.798242i	$-0.705763\pi$
$599$	−863.376	−	152.237i	−1.44136	−	0.254151i	−0.839026	+	0.544091i	$0.816875\pi$
$600$		0			0
$601$	627.682	−	526.688i	1.04440	−	0.876353i	0.0519035	−	0.998652i	$-0.483471\pi$
$601$	627.682	−	526.688i	1.04440	−	0.876353i	0.992493	+	0.122299i	$0.0390267\pi$
$602$	−45.8093	+	26.4480i	−0.0760952	+	0.0439336i
$603$		0			0
$604$	−137.434	+	238.042i	−0.227540	+	0.394110i
$605$	914.197	−	161.198i	1.51107	−	0.266442i
$606$		0			0
$607$	−544.372	+	198.135i	−0.896823	+	0.326417i	−0.748979	−	0.662594i	$-0.769456\pi$
$607$	−544.372	+	198.135i	−0.896823	+	0.326417i	−0.147844	+	0.989011i	$0.547233\pi$
$608$	−20.9193	−	57.4754i	−0.0344068	−	0.0945319i
$609$		0			0
$610$	47.1694	+	267.511i	0.0773268	+	0.438542i
$611$	−19.4914	−	11.2534i	−0.0319008	−	0.0184180i
$612$		0			0
$613$	−163.781	−	283.677i	−0.267179	−	0.462768i	0.700953	−	0.713207i	$-0.252758\pi$
$613$	−163.781	−	283.677i	−0.267179	−	0.462768i	−0.968132	+	0.250439i	$0.919425\pi$
$614$	−518.073	−	617.415i	−0.843766	−	1.00556i
$615$		0			0
$616$	6.84905	−	38.8429i	0.0111186	−	0.0630566i
$617$	685.484	−	816.928i	1.11099	−	1.32403i	0.170064	−	0.985433i	$-0.445603\pi$
$617$	685.484	−	816.928i	1.11099	−	1.32403i	0.940931	−	0.338599i	$-0.109953\pi$
$618$		0			0
$619$	835.904	+	304.244i	1.35041	+	0.491509i	0.913076	−	0.407789i	$-0.133700\pi$
$619$	835.904	+	304.244i	1.35041	+	0.491509i	0.437335	+	0.899299i	$0.355922\pi$
$620$			775.938i			1.25151i
$621$		0			0
$622$	632.242			1.01647
$623$	−28.2178	+	77.5278i	−0.0452934	+	0.124443i
$624$		0			0
$625$	−163.639	−	137.309i	−0.261822	−	0.219695i
$626$	−405.584	−	71.5153i	−0.647897	−	0.114242i
$627$		0			0
$628$	−35.6144	+	29.8840i	−0.0567108	+	0.0475860i
$629$	372.107	−	214.836i	0.591585	−	0.341552i
$630$		0			0
$631$	−477.341	+	826.778i	−0.756483	+	1.31027i	0.188151	+	0.982140i	$0.439750\pi$
$631$	−477.341	+	826.778i	−0.756483	+	1.31027i	−0.944634	+	0.328126i	$0.893583\pi$
$632$	80.6979	−	14.2292i	0.127687	−	0.0225146i
$633$		0			0
$634$	448.365	−	163.192i	0.707201	−	0.257400i
$635$	−279.790	−	768.717i	−0.440614	−	1.21058i
$636$		0			0
$637$	−7.60638	−	43.1379i	−0.0119409	−	0.0677205i
$638$	1072.39	+	619.145i	1.68086	+	0.970446i
$639$		0			0
$640$	−44.2990	−	76.7281i	−0.0692172	−	0.119888i
$641$	456.345	+	543.850i	0.711926	+	0.848440i	0.993820	−	0.111005i	$-0.0354070\pi$
$641$	456.345	+	543.850i	0.711926	+	0.848440i	−0.281894	+	0.959446i	$0.590963\pi$
$642$		0			0
$643$	8.61807	−	48.8755i	0.0134029	−	0.0760116i	−0.977373	−	0.211525i	$-0.932157\pi$
$643$	8.61807	−	48.8755i	0.0134029	−	0.0760116i	0.990776	+	0.135513i	$0.0432683\pi$
$644$	38.0160	−	45.3057i	0.0590310	−	0.0703505i
$645$		0			0
$646$	176.987	+	64.4178i	0.273973	+	0.0997180i
$647$			918.622i			1.41982i	0.704294	+	0.709909i	$0.251264\pi$
$647$			918.622i			1.41982i	−0.704294	+	0.709909i	$0.748736\pi$
$648$		0			0
$649$	−1032.73			−1.59126
$650$	−15.9713	+	43.8808i	−0.0245712	+	0.0675089i
$651$		0			0
$652$	−242.035	−	203.092i	−0.371220	−	0.311491i
$653$	−342.395	−	60.3734i	−0.524341	−	0.0924555i	−0.0947886	−	0.995497i	$-0.530218\pi$
$653$	−342.395	−	60.3734i	−0.524341	−	0.0924555i	−0.429552	+	0.903042i	$0.641329\pi$
$654$		0			0
$655$	5.48323	−	4.60098i	0.00837135	−	0.00702440i
$656$	−124.062	+	71.6272i	−0.189119	+	0.109188i
$657$		0			0
$658$	−15.7745	+	27.3222i	−0.0239734	+	0.0415231i
$659$	−1263.48	+	222.786i	−1.91728	+	0.338068i	−0.998403	−	0.0564864i	$-0.982010\pi$
$659$	−1263.48	+	222.786i	−1.91728	+	0.338068i	−0.918873	+	0.394554i	$0.870899\pi$
$660$		0			0
$661$	−126.358	+	45.9904i	−0.191161	+	0.0695770i	−0.435827	−	0.900030i	$-0.643544\pi$
$661$	−126.358	+	45.9904i	−0.191161	+	0.0695770i	0.244666	+	0.969608i	$0.421322\pi$
$662$	−73.7207	−	202.546i	−0.111361	−	0.305961i
$663$		0			0
$664$	0.0731113	+	0.414635i	0.000110107	+	0.000624450i
$665$	66.0687	+	38.1448i	0.0993514	+	0.0573605i
$666$		0			0
$667$	928.391	+	1608.02i	1.39189	+	2.41083i
$668$	−121.501	−	144.800i	−0.181888	−	0.216766i
$669$		0			0
$670$	−125.428	+	711.339i	−0.187206	+	1.06170i
$671$	−244.013	+	290.804i	−0.363656	+	0.433389i
$672$		0			0
$673$	522.659	+	190.232i	0.776610	+	0.282663i	0.699758	−	0.714380i	$-0.253291\pi$
$673$	522.659	+	190.232i	0.776610	+	0.282663i	0.0768517	+	0.997043i	$0.475513\pi$
$674$		−	330.223i		−	0.489946i
$675$		0			0
$676$	336.347			0.497555
$677$	116.809	−	320.931i	0.172540	−	0.474049i	−0.823039	−	0.567985i	$-0.807723\pi$
$677$	116.809	−	320.931i	0.172540	−	0.474049i	0.995578	+	0.0939369i	$0.0299452\pi$
$678$		0			0
$679$	69.3597	+	58.1997i	0.102150	+	0.0857138i
$680$	268.679	+	47.3754i	0.395116	+	0.0696697i
$681$		0			0
$682$	−830.687	+	697.029i	−1.21802	+	1.02204i
$683$	−181.638	+	104.869i	−0.265942	+	0.153542i	−0.627042	−	0.778985i	$-0.715735\pi$
$683$	−181.638	+	104.869i	−0.265942	+	0.153542i	0.361100	+	0.932527i	$0.382401\pi$
$684$		0			0
$685$	−55.0237	+	95.3039i	−0.0803266	+	0.139130i
$686$	−121.956	+	21.5042i	−0.177779	+	0.0313473i
$687$		0			0
$688$	−156.038	+	56.7930i	−0.226799	+	0.0825480i
$689$	15.6488	+	42.9947i	0.0227123	+	0.0624016i
$690$		0			0
$691$	−50.5894	−	286.907i	−0.0732119	−	0.415205i	−0.999283	−	0.0378567i	$-0.987947\pi$
$691$	−50.5894	−	286.907i	−0.0732119	−	0.415205i	0.926071	−	0.377349i	$-0.123164\pi$
$692$	−503.101	−	290.466i	−0.727025	−	0.419748i
$693$		0			0
$694$	−450.211	−	779.788i	−0.648719	−	1.12361i
$695$	936.899	+	1116.55i	1.34806	+	1.60655i
$696$		0			0
$697$	76.6014	−	434.428i	0.109902	−	0.623283i
$698$	259.713	−	309.514i	0.372082	−	0.443430i
$699$		0			0
$700$	61.5102	+	22.3879i	0.0878717	+	0.0319827i
$701$		−	445.528i		−	0.635560i	−0.948164	−	0.317780i	$-0.897063\pi$
$701$		−	445.528i		−	0.635560i	0.948164	−	0.317780i	$-0.102937\pi$
$702$		0			0
$703$	377.173			0.536519
$704$	42.3479	−	116.350i	0.0601533	−	0.165270i
$705$		0			0
$706$	−355.195	−	298.044i	−0.503109	−	0.422158i
$707$	−93.7003	−	16.5219i	−0.132532	−	0.0233690i
$708$		0			0
$709$	−112.307	+	94.2371i	−0.158402	+	0.132915i	−0.718544	−	0.695481i	$-0.755191\pi$
$709$	−112.307	+	94.2371i	−0.158402	+	0.132915i	0.560142	+	0.828397i	$0.310747\pi$
$710$	−270.773	+	156.331i	−0.381371	+	0.220185i
$711$		0			0
$712$	−129.498	+	224.296i	−0.181879	+	0.315023i
$713$	−1601.30	+	282.353i	−2.24587	+	0.396007i
$714$		0			0
$715$	−103.529	+	37.6815i	−0.144796	+	0.0527014i
$716$	7.62086	+	20.9381i	0.0106437	+	0.0292432i
$717$		0			0
$718$	137.375	+	779.092i	0.191330	+	1.08509i
$719$	−442.793	−	255.647i	−0.615845	−	0.355559i	0.159404	−	0.987213i	$-0.449043\pi$
$719$	−442.793	−	255.647i	−0.615845	−	0.355559i	−0.775250	+	0.631655i	$0.782376\pi$
$720$		0			0
$721$	39.1853	+	67.8710i	0.0543486	+	0.0941345i
$722$	−221.890	−	264.438i	−0.307326	−	0.366257i
$723$		0			0
$724$	−66.1782	+	375.315i	−0.0914064	+	0.518392i
$725$	−1320.96	+	1574.26i	−1.82202	+	2.17140i
$726$		0			0
$727$	−233.836	−	85.1092i	−0.321644	−	0.117069i	0.176152	−	0.984363i	$-0.443635\pi$
$727$	−233.836	−	85.1092i	−0.321644	−	0.117069i	−0.497796	+	0.867294i	$0.665857\pi$
$728$			2.31653i			0.00318204i
$729$		0			0
$730$	−238.684			−0.326964
$731$	174.885	−	480.493i	0.239241	−	0.657310i
$732$		0			0
$733$	645.868	+	541.947i	0.881129	+	0.739355i	0.966411	−	0.257002i	$-0.0827346\pi$
$733$	645.868	+	541.947i	0.881129	+	0.739355i	−0.0852818	+	0.996357i	$0.527179\pi$
$734$	668.092	+	117.803i	0.910208	+	0.160494i
$735$		0			0
$736$	142.224	−	119.340i	0.193239	−	0.162147i
$737$	−874.202	+	504.721i	−1.18616	+	0.684832i
$738$		0			0
$739$	339.638	−	588.271i	0.459592	−	0.796036i	−0.539347	−	0.842083i	$-0.681329\pi$
$739$	339.638	−	588.271i	0.459592	−	0.796036i	0.998939	+	0.0460469i	$0.0146624\pi$
$740$	538.046	−	94.8721i	0.727090	−	0.128206i
$741$		0			0
$742$	60.2681	−	21.9358i	0.0812239	−	0.0295631i
$743$	−215.273	−	591.458i	−0.289735	−	0.796040i	−0.996103	−	0.0881957i	$-0.971890\pi$
$743$	−215.273	−	591.458i	−0.289735	−	0.796040i	0.706368	−	0.707845i	$-0.250332\pi$
$744$		0			0
$745$	172.409	+	977.780i	0.231421	+	1.31246i
$746$	−421.250	−	243.209i	−0.564679	−	0.326017i
$747$		0			0
$748$	190.638	+	330.194i	0.254863	+	0.441436i
$749$	14.1928	+	16.9143i	0.0189490	+	0.0225825i
$750$		0			0
$751$	123.896	−	702.649i	0.164975	−	0.935618i	−0.784116	−	0.620615i	$-0.786883\pi$
$751$	123.896	−	702.649i	0.164975	−	0.935618i	0.949090	−	0.315004i	$-0.102006\pi$
$752$	−63.6609	+	75.8681i	−0.0846555	+	0.100888i
$753$		0			0
$754$	−68.3416	−	24.8743i	−0.0906387	−	0.0329898i
$755$		−	1076.25i		−	1.42550i
$756$		0			0
$757$	1327.86			1.75411			0.877055	−	0.480390i	$-0.159505\pi$
$757$	1327.86			1.75411			0.877055	+	0.480390i	$0.159505\pi$
$758$	−50.3790	+	138.415i	−0.0664631	+	0.182606i
$759$		0			0
$760$	183.459	+	153.940i	0.241393	+	0.202553i
$761$	928.015	+	163.634i	1.21947	+	0.215025i	0.746096	−	0.665838i	$-0.231926\pi$
$761$	928.015	+	163.634i	1.21947	+	0.215025i	0.473371	+	0.880863i	$0.343037\pi$
$762$		0			0
$763$	23.1713	−	19.4430i	0.0303687	−	0.0254824i
$764$	29.6953	−	17.1446i	0.0388682	−	0.0224406i
$765$		0			0
$766$	45.8707	−	79.4505i	0.0598835	−	0.103721i
$767$	59.7332	−	10.5326i	0.0778790	−	0.0137322i
$768$		0			0
$769$	−999.812	+	363.902i	−1.30015	+	0.473214i	−0.897044	−	0.441941i	$-0.854290\pi$
$769$	−999.812	+	363.902i	−1.30015	+	0.473214i	−0.403102	+	0.915155i	$0.632068\pi$
$770$	52.8203	+	145.123i	0.0685978	+	0.188471i
$771$		0			0
$772$	−53.5414	−	303.648i	−0.0693541	−	0.393327i
$773$	−250.289	−	144.504i	−0.323789	−	0.186939i	0.329291	−	0.944228i	$-0.393190\pi$
$773$	−250.289	−	144.504i	−0.323789	−	0.186939i	−0.653080	+	0.757289i	$0.726523\pi$
$774$		0			0
$775$	−899.818	−	1558.53i	−1.16106	−	2.01101i
$776$	182.701	+	217.734i	0.235439	+	0.280586i
$777$		0			0
$778$	−57.9434	+	328.613i	−0.0744774	+	0.422382i
$779$	248.907	−	296.636i	0.319521	−	0.380790i
$780$		0			0
$781$	−410.598	−	149.446i	−0.525734	−	0.191352i
$782$			571.712i			0.731090i
$783$		0			0
$784$	−192.753			−0.245858
$785$	62.2604	−	171.059i	0.0793126	−	0.217910i
$786$		0			0
$787$	−513.070	−	430.517i	−0.651931	−	0.547035i	0.255725	−	0.966750i	$-0.417686\pi$
$787$	−513.070	−	430.517i	−0.651931	−	0.547035i	−0.907656	+	0.419714i	$0.862130\pi$
$788$	243.837	+	42.9950i	0.309438	+	0.0545622i
$789$		0			0
$790$	−245.784	+	206.237i	−0.311119	+	0.261060i
$791$	95.2040	−	54.9661i	0.120359	−	0.0694893i
$792$		0			0
$793$	11.1479	−	19.3087i	0.0140579	−	0.0243490i
$794$	−7.22406	+	1.27380i	−0.00909831	+	0.00160428i
$795$		0			0
$796$	440.673	−	160.392i	0.553609	−	0.201497i
$797$	−96.3773	−	264.795i	−0.120925	−	0.332239i	0.864430	−	0.502753i	$-0.167679\pi$
$797$	−96.3773	−	264.795i	−0.120925	−	0.332239i	−0.985355	+	0.170514i	$0.945457\pi$
$798$		0			0
$799$	−52.9583	−	300.342i	−0.0662807	−	0.375897i
$800$	177.956	+	102.743i	0.222445	+	0.128429i
$801$		0			0
$802$	113.726	+	196.979i	0.141803	+	0.245610i
$803$	−214.411	−	255.525i	−0.267012	−	0.318213i
$804$		0			0
$805$	−40.2122	+	228.055i	−0.0499531	+	0.283298i
$806$	40.9381	−	48.7881i	0.0507917	−	0.0605312i
$807$		0			0
$808$	−280.670	−	102.155i	−0.347363	−	0.126430i
$809$			747.542i			0.924032i	0.886872	+	0.462016i	$0.152874\pi$
$809$			747.542i			0.924032i	−0.886872	+	0.462016i	$0.847126\pi$
$810$		0			0
$811$	−1416.36			−1.74644			−0.873218	−	0.487330i	$-0.837971\pi$
$811$	−1416.36			−1.74644			−0.873218	+	0.487330i	$0.837971\pi$
$812$	−34.8677	+	95.7983i	−0.0429405	+	0.117978i
$813$		0			0
$814$	584.895	+	490.786i	0.718545	+	0.602931i
$815$	1218.33	+	214.825i	1.49489	+	0.263589i
$816$		0			0
$817$	343.841	−	288.517i	0.420859	−	0.353142i
$818$	−211.387	+	122.044i	−0.258420	+	0.149199i
$819$		0			0
$820$	280.458	−	485.767i	0.342022	−	0.592399i
$821$	−91.5752	+	16.1472i	−0.111541	+	0.0196677i	−0.229140	−	0.973393i	$-0.573591\pi$
$821$	−91.5752	+	16.1472i	−0.111541	+	0.0196677i	0.117599	+	0.993061i	$0.462480\pi$
$822$		0			0
$823$	35.2640	−	12.8350i	0.0428481	−	0.0155954i	−0.320507	−	0.947246i	$-0.603853\pi$
$823$	35.2640	−	12.8350i	0.0428481	−	0.0155954i	0.363355	+	0.931651i	$0.381631\pi$
$824$	84.1444	+	231.185i	0.102117	+	0.280564i
$825$		0			0
$826$	−14.7641	−	83.7314i	−0.0178742	−	0.101370i
$827$	−1138.29	−	657.194i	−1.37641	−	0.794673i	−0.384688	−	0.923047i	$-0.625691\pi$
$827$	−1138.29	−	657.194i	−1.37641	−	0.794673i	−0.991726	+	0.128374i	$0.959024\pi$
$828$		0			0
$829$	−27.7172	−	48.0077i	−0.0334346	−	0.0579103i	0.848824	−	0.528676i	$-0.177311\pi$
$829$	−27.7172	−	48.0077i	−0.0334346	−	0.0579103i	−0.882258	+	0.470765i	$0.843978\pi$
$830$	−1.05967	−	1.26287i	−0.00127671	−	0.00152153i
$831$		0			0
$832$	−1.26278	+	7.16158i	−0.00151776	+	0.00860766i
$833$	381.528	−	454.688i	0.458017	−	0.545843i
$834$		0			0
$835$	695.486	+	253.136i	0.832918	+	0.303157i
$836$			334.689i			0.400345i
$837$		0			0
$838$	−404.942			−0.483224
$839$	192.782	−	529.664i	0.229776	−	0.631305i	−0.770203	−	0.637799i	$-0.779845\pi$
$839$	192.782	−	529.664i	0.229776	−	0.631305i	0.999979	+	0.00649448i	$0.00206727\pi$
$840$		0			0
$841$	−1807.57	−	1516.73i	−2.14931	−	1.80349i
$842$	938.620	+	165.504i	1.11475	+	0.196561i
$843$		0			0
$844$	81.6085	−	68.4777i	0.0966926	−	0.0811347i
$845$	−1140.53	+	658.487i	−1.34974	+	0.779274i
$846$		0			0
$847$	−53.4028	+	92.4964i	−0.0630494	+	0.109205i
$848$	198.277	−	34.9617i	0.233818	−	0.0412284i
$849$		0			0
$850$	−594.601	+	216.417i	−0.699531	+	0.254608i
$851$	391.575	+	1075.84i	0.460135	+	1.26421i
$852$		0			0
$853$	82.4484	+	467.588i	0.0966570	+	0.548169i	0.994227	+	0.107297i	$0.0342196\pi$
$853$	82.4484	+	467.588i	0.0966570	+	0.548169i	−0.897570	+	0.440872i	$0.854669\pi$
$854$	−27.0661	−	15.6266i	−0.0316934	−	0.0182982i
$855$		0			0
$856$	34.6569	+	60.0276i	0.0404871	+	0.0701257i
$857$	478.426	+	570.166i	0.558257	+	0.665305i	0.969177	−	0.246367i	$-0.0792368\pi$
$857$	478.426	+	570.166i	0.558257	+	0.665305i	−0.410920	+	0.911672i	$0.634792\pi$
$858$		0			0
$859$	72.5615	−	411.517i	0.0844721	−	0.479065i	−0.912997	−	0.407966i	$-0.866238\pi$
$859$	72.5615	−	411.517i	0.0844721	−	0.479065i	0.997469	−	0.0710990i	$-0.0226506\pi$
$860$	417.926	−	498.065i	0.485961	−	0.579146i
$861$		0			0
$862$	716.475	+	260.776i	0.831177	+	0.302524i
$863$		−	816.761i		−	0.946420i	−0.880950	−	0.473210i	$-0.843095\pi$
$863$		−	816.761i		−	0.946420i	0.880950	−	0.473210i	$-0.156905\pi$
$864$		0			0
$865$	2274.65			2.62965
$866$	−388.398	+	1067.12i	−0.448497	+	1.23223i
$867$		0			0
$868$	−68.3891	−	57.3853i	−0.0787893	−	0.0661121i
$869$	−441.578	−	77.8621i	−0.508145	−	0.0895997i
$870$		0			0
$871$	45.4164	−	38.1089i	0.0521428	−	0.0437530i
$872$	82.2333	−	47.4774i	0.0943042	−	0.0544466i
$873$		0			0
$874$	−250.929	+	434.621i	−0.287104	+	0.497278i
$875$	−78.6931	+	13.8757i	−0.0899350	+	0.0158580i
$876$		0			0
$877$	518.635	−	188.768i	0.591374	−	0.215242i	−0.0289599	−	0.999581i	$-0.509220\pi$
$877$	518.635	−	188.768i	0.591374	−	0.215242i	0.620333	+	0.784338i	$0.286997\pi$
$878$	37.8362	+	103.954i	0.0430937	+	0.118399i
$879$		0			0
$880$	84.1859	+	477.442i	0.0956658	+	0.542548i
$881$	1220.85	+	704.859i	1.38576	+	0.800067i	0.992834	−	0.119504i	$-0.0381304\pi$
$881$	1220.85	+	704.859i	1.38576	+	0.800067i	0.392923	+	0.919571i	$0.371464\pi$
$882$		0			0
$883$	−804.703	−	1393.79i	−0.911328	−	1.57847i	−0.812190	−	0.583393i	$-0.801725\pi$
$883$	−804.703	−	1393.79i	−0.911328	−	1.57847i	−0.0991386	−	0.995074i	$-0.531609\pi$
$884$	−14.3941	−	17.1542i	−0.0162829	−	0.0194052i
$885$		0			0
$886$	134.156	−	760.838i	0.151418	−	0.858734i
$887$	761.451	−	907.462i	0.858457	−	1.02307i	−0.140996	−	0.990010i	$-0.545031\pi$
$887$	761.451	−	907.462i	0.858457	−	1.02307i	0.999453	−	0.0330591i	$-0.0105250\pi$
$888$		0			0
$889$	88.4447	+	32.1913i	0.0994879	+	0.0362106i
$890$		−	1014.10i		−	1.13944i
$891$		0			0
$892$	119.839			0.134349
$893$	91.5626	−	251.566i	0.102534	−	0.281709i
$894$		0			0
$895$	−66.8336	−	56.0801i	−0.0746745	−	0.0626593i
$896$	10.0388	+	1.77011i	0.0112040	+	0.00197557i
$897$		0			0
$898$	740.987	−	621.762i	0.825153	−	0.692385i
$899$	2427.31	−	1401.41i	2.70001	−	1.55885i
$900$		0			0
$901$	−309.992	+	536.922i	−0.344053	+	0.595917i
$902$	771.978	−	136.121i	0.855851	−	0.150910i
$903$		0			0
$904$	324.288	−	118.031i	0.358726	−	0.130565i
$905$	−510.371	−	1402.23i	−0.563946	−	1.54943i
$906$		0			0
$907$	69.1106	+	391.946i	0.0761969	+	0.432134i	0.998911	+	0.0466499i	$0.0148545\pi$
$907$	69.1106	+	391.946i	0.0761969	+	0.432134i	−0.922714	+	0.385484i	$0.874034\pi$
$908$	−110.283	−	63.6721i	−0.121457	−	0.0701235i
$909$		0			0
$910$	−4.53520	−	7.85519i	−0.00498373	−	0.00863208i
$911$	−521.570	−	621.583i	−0.572524	−	0.682308i	0.399623	−	0.916680i	$-0.369141\pi$
$911$	−521.570	−	621.583i	−0.572524	−	0.682308i	−0.972147	+	0.234372i	$0.924697\pi$
$912$		0			0
$913$	0.400064	−	2.26888i	0.000438186	−	0.00248508i
$914$	−78.0167	+	92.9767i	−0.0853574	+	0.101725i
$915$		0			0
$916$	402.423	+	146.470i	0.439327	+	0.159902i
$917$			0.823547i			0.000898089i
$918$		0			0
$919$	1571.44			1.70994			0.854972	−	0.518674i	$-0.173574\pi$
$919$	1571.44			1.70994			0.854972	+	0.518674i	$0.173574\pi$
$920$	−248.634	+	683.115i	−0.270254	+	0.742516i
$921$		0			0
$922$	6.17477	+	5.18125i	0.00669715	+	0.00561958i
$923$	25.2732	+	4.45635i	0.0273816	+	0.00482811i
$924$		0			0
$925$	−970.688	+	814.504i	−1.04939	+	0.880545i
$926$	−395.007	+	228.057i	−0.426574	+	0.246282i
$927$		0			0
$928$	−160.015	+	277.155i	−0.172430	+	0.298658i
$929$	509.792	−	89.8902i	0.548754	−	0.0967601i	0.107605	−	0.994194i	$-0.465682\pi$
$929$	509.792	−	89.8902i	0.548754	−	0.0967601i	0.441149	+	0.897434i	$0.354571\pi$
$930$		0			0
$931$	489.607	−	178.202i	0.525894	−	0.191410i
$932$	−147.460	−	405.143i	−0.158219	−	0.434703i
$933$		0			0
$934$	9.29698	+	52.7258i	0.00995394	+	0.0564516i
$935$	−1292.88	−	746.445i	−1.38276	−	0.798336i
$936$		0			0
$937$	−171.737	−	297.457i	−0.183284	−	0.317457i	0.759713	−	0.650259i	$-0.225339\pi$
$937$	−171.737	−	297.457i	−0.183284	−	0.317457i	−0.942997	+	0.332801i	$0.892006\pi$
$938$	−53.4193	−	63.6627i	−0.0569503	−	0.0678707i
$939$		0			0
$940$	67.3387	−	381.897i	0.0716369	−	0.406273i
$941$	538.505	−	641.766i	0.572269	−	0.682004i	−0.399826	−	0.916591i	$-0.630929\pi$
$941$	538.505	−	641.766i	0.572269	−	0.682004i	0.972095	+	0.234587i	$0.0753739\pi$
$942$		0			0
$943$	1104.53	+	402.017i	1.17130	+	0.426317i
$944$		−	266.905i		−	0.282738i
$945$		0			0
$946$	908.633			0.960500
$947$	−493.939	+	1357.09i	−0.521583	+	1.43304i	0.347174	+	0.937801i	$0.387141\pi$
$947$	−493.939	+	1357.09i	−0.521583	+	1.43304i	−0.868757	+	0.495238i	$0.835081\pi$
$948$		0			0
$949$	15.0076	+	12.5928i	0.0158141	+	0.0132696i
$950$	−547.008	−	96.4524i	−0.575798	−	0.101529i
$951$		0			0
$952$	−24.0460	+	20.1770i	−0.0252584	+	0.0211943i
$953$	−1132.07	+	653.600i	−1.18790	+	0.685835i	−0.957829	−	0.287339i	$-0.907229\pi$
$953$	−1132.07	+	653.600i	−1.18790	+	0.685835i	−0.230072	+	0.973174i	$0.573896\pi$
$954$		0			0
$955$	−67.1300	+	116.273i	−0.0702932	+	0.121751i
$956$	82.4092	−	14.5310i	0.0862021	−	0.0151998i
$957$		0			0
$958$	−953.807	+	347.157i	−0.995623	+	0.362377i
$959$	−4.33049	−	11.8979i	−0.00451564	−	0.0124066i
$960$		0			0
$961$	259.337	+	1470.77i	0.269862	+	1.53046i
$962$	−38.8358	−	22.4218i	−0.0403698	−	0.0233075i
$963$		0			0
$964$	−448.318	−	776.509i	−0.465060	−	0.805508i
$965$	776.025	+	924.831i	0.804171	+	0.958374i
$966$		0			0
$967$	117.727	−	667.665i	0.121745	−	0.690450i	−0.861443	−	0.507854i	$-0.830439\pi$
$967$	117.727	−	667.665i	0.121745	−	0.690450i	0.983188	−	0.182596i	$-0.0584499\pi$
$968$	−215.517	+	256.843i	−0.222642	+	0.265334i
$969$		0			0
$970$	−1045.80	−	380.640i	−1.07814	−	0.392412i
$971$			172.492i			0.177644i	0.996048	+	0.0888219i	$0.0283102\pi$
$971$			172.492i			0.177644i	−0.996048	+	0.0888219i	$0.971690\pi$
$972$		0			0
$973$	−167.699			−0.172353
$974$	25.2272	−	69.3112i	0.0259006	−	0.0711614i
$975$		0			0
$976$	−75.1571	−	63.0643i	−0.0770052	−	0.0646150i
$977$	1622.94	+	286.168i	1.66115	+	0.292905i	0.923876	−	0.382692i	$-0.125003\pi$
$977$	1622.94	+	286.168i	1.66115	+	0.292905i	0.737271	+	0.675597i	$0.236114\pi$
$978$		0			0
$979$	1085.65	−	910.971i	1.10894	−	0.930511i
$980$	653.613	−	377.363i	0.666952	−	0.385065i
$981$		0			0
$982$	−55.8698	+	96.7693i	−0.0568938	+	0.0985430i
$983$	−764.198	+	134.749i	−0.777414	+	0.137079i	−0.548256	−	0.836310i	$-0.684708\pi$
$983$	−764.198	+	134.749i	−0.777414	+	0.137079i	−0.229157	+	0.973389i	$0.573597\pi$
$984$		0			0
$985$	−911.010	+	331.580i	−0.924883	+	0.336630i
$986$	−337.056	−	926.054i	−0.341842	−	0.939202i
$987$		0			0
$988$	−3.41341	−	19.3584i	−0.00345487	−	0.0195935i
$989$	1179.93	+	681.235i	1.19306	+	0.688812i
$990$		0			0
$991$	−191.688	−	332.014i	−0.193429	−	0.335029i	0.752955	−	0.658072i	$-0.228628\pi$
$991$	−191.688	−	332.014i	−0.193429	−	0.335029i	−0.946384	+	0.323043i	$0.895294\pi$
$992$	−180.144	−	214.688i	−0.181597	−	0.216419i
$993$		0			0
$994$	6.24671	−	35.4269i	0.00628442	−	0.0356407i
$995$	−1180.29	+	1406.61i	−1.18622	+	1.41368i
$996$		0			0
$997$	−1455.50	−	529.759i	−1.45988	−	0.531353i	−0.514549	−	0.857461i	$-0.672041\pi$
$997$	−1455.50	−	529.759i	−1.45988	−	0.531353i	−0.945333	+	0.326108i	$0.894263\pi$
$998$		−	42.1265i		−	0.0422109i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.17.6		36
3.2	odd	2		54.3.f.a.23.1	✓	36
12.11	even	2		432.3.bc.c.401.6		36
27.7	even	9		54.3.f.a.47.1	yes	36
27.13	even	9		1458.3.b.c.1457.34		36
27.14	odd	18		1458.3.b.c.1457.3		36
27.20	odd	18	inner	162.3.f.a.143.6		36
108.7	odd	18		432.3.bc.c.209.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.23.1	✓	36	3.2	odd	2
54.3.f.a.47.1	yes	36	27.7	even	9
162.3.f.a.17.6		36	1.1	even	1	trivial
162.3.f.a.143.6		36	27.20	odd	18	inner
432.3.bc.c.209.6		36	108.7	odd	18
432.3.bc.c.401.6		36	12.11	even	2
1458.3.b.c.1457.3		36	27.14	odd	18
1458.3.b.c.1457.34		36	27.13	even	9

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.483690 - 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(7.71206 + 1.35984i) q^{5} +(-0.690206 + 0.579152i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(0.483690 - 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(7.71206 + 1.35984i) q^{5} +(-0.690206 + 0.579152i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(5.53738 - 9.59102i) q^{10} +(15.2420 - 2.68757i) q^{11} +(-0.854187 + 0.310899i) q^{13} +(0.435804 + 1.19736i) q^{14} +(0.694593 + 3.93923i) q^{16} +(-10.6672 - 6.15869i) q^{17} +(-5.40619 - 9.36379i) q^{19} +(-10.0674 - 11.9978i) q^{20} +(3.80080 - 21.5554i) q^{22} +(21.0966 - 25.1419i) q^{23} +(34.1344 + 12.4239i) q^{25} +1.28553i q^{26} +1.80200 q^{28} +(-19.3495 + 53.1622i) q^{29} +(-37.9518 - 31.8453i) q^{31} +(5.57091 + 0.982302i) q^{32} +(-13.3440 + 11.1970i) q^{34} +(-6.11047 + 3.52788i) q^{35} +(-17.4417 + 30.2099i) q^{37} +(-15.0587 + 2.65526i) q^{38} +(-20.8137 + 7.57558i) q^{40} +(12.2490 + 33.6538i) q^{41} +(7.20864 + 40.8822i) q^{43} +(-26.8072 - 15.4771i) q^{44} +(-23.2075 - 40.1966i) q^{46} +(15.9152 + 18.9670i) q^{47} +(-8.36779 + 47.4561i) q^{49} +(33.0209 - 39.3528i) q^{50} +(1.70837 + 0.621797i) q^{52} -50.3340i q^{53} +121.202 q^{55} +(0.871609 - 2.39472i) q^{56} +(61.2895 + 51.4280i) q^{58} +(-65.7126 - 11.5869i) q^{59} +(-18.7893 + 15.7661i) q^{61} +(-60.6770 + 35.0319i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-7.01032 + 1.23611i) q^{65} +(-61.2882 + 22.3071i) q^{67} +(8.42558 + 23.1491i) q^{68} +(1.73272 + 9.82676i) q^{70} +(-24.4496 - 14.1160i) q^{71} +(-10.7760 - 18.6646i) q^{73} +(31.7104 + 37.7910i) q^{74} +(-3.75510 + 21.2962i) q^{76} +(-8.96360 + 10.6824i) q^{77} +(-27.2240 - 9.90872i) q^{79} +31.3241i q^{80} +50.6481 q^{82} +(0.0509121 - 0.139880i) q^{83} +(-73.8910 - 62.0019i) q^{85} +(57.8162 + 10.1946i) q^{86} +(-33.5343 + 28.1386i) q^{88} +(79.3008 - 45.7843i) q^{89} +(0.409508 - 0.709288i) q^{91} +(-64.6436 + 11.3984i) q^{92} +(32.9038 - 11.9760i) q^{94} +(-28.9595 - 79.5657i) q^{95} +(-17.4501 - 98.9646i) q^{97} +(59.0182 + 34.0742i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 36 * q - 18 * q^5	\( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

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