LMFDB - Embedded newform 162.5.f.a.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,5,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, 5, names="a")

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
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:	$16.7459340196$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.3
Character	$\chi$	$=$	162.35
Dual form			162.5.f.a.125.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-6.13288 + 16.8500i) q^{5} +(8.35982 - 47.4109i) q^{7} +(19.5959 + 11.3137i) q^{8} +O(q^{10})$	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-6.13288 + 16.8500i) q^{5} +(8.35982 - 47.4109i) q^{7} +(19.5959 + 11.3137i) q^{8} +(-25.3588 - 43.9227i) q^{10} +(40.7635 + 111.997i) q^{11} +(76.8147 - 64.4552i) q^{13} +(87.5264 + 104.310i) q^{14} +(-60.1403 + 21.8893i) q^{16} +(4.38346 - 2.53079i) q^{17} +(-159.777 + 276.742i) q^{19} +(141.271 + 24.9100i) q^{20} +(-316.775 - 115.297i) q^{22} +(223.676 - 39.4401i) q^{23} +(232.469 + 195.065i) q^{25} +283.619i q^{26} -385.138 q^{28} +(-922.944 + 1099.92i) q^{29} +(80.6757 + 457.534i) q^{31} +(61.9123 - 170.103i) q^{32} +(-2.48600 + 14.0988i) q^{34} +(747.602 + 431.628i) q^{35} +(457.456 + 792.338i) q^{37} +(-309.130 - 849.327i) q^{38} +(-310.815 + 260.805i) q^{40} +(835.336 + 995.515i) q^{41} +(-3323.67 + 1209.72i) q^{43} +(825.735 - 476.738i) q^{44} +(-321.206 + 556.344i) q^{46} +(-3592.02 - 633.370i) q^{47} +(78.2948 + 28.4970i) q^{49} +(-845.294 + 149.048i) q^{50} +(-614.517 - 515.641i) q^{52} +3907.25i q^{53} -2137.14 q^{55} +(700.212 - 834.480i) q^{56} +(-705.217 - 3999.49i) q^{58} +(-627.970 + 1725.33i) q^{59} +(-592.438 + 3359.88i) q^{61} +(-1138.01 - 657.033i) q^{62} +(256.000 + 443.405i) q^{64} +(614.971 + 1689.62i) q^{65} +(6449.53 - 5411.80i) q^{67} +(-26.0282 - 31.0192i) q^{68} +(-2294.41 + 835.096i) q^{70} +(4819.88 - 2782.76i) q^{71} +(1970.23 - 3412.54i) q^{73} +(-2548.45 - 449.360i) q^{74} +(2402.26 + 874.351i) q^{76} +(5650.65 - 996.362i) q^{77} +(8379.78 + 7031.47i) q^{79} -1147.61i q^{80} -3675.69 q^{82} +(1263.92 - 1506.28i) q^{83} +(15.7605 + 89.3822i) q^{85} +(3421.60 - 9400.76i) q^{86} +(-468.301 + 2655.87i) q^{88} +(1148.77 + 663.242i) q^{89} +(-2413.72 - 4180.69i) q^{91} +(-621.455 - 1707.43i) q^{92} +(7902.89 - 6631.31i) q^{94} +(-3683.19 - 4389.46i) q^{95} +(11763.6 - 4281.60i) q^{97} +(-204.090 + 117.832i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{5}+O(q^{10}) $ 72 * q + 18 * q^5	$ 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) $ 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.81808	+	2.16670i	−0.454519	+	0.541675i
$2$	−1.81808	+	2.16670i	−0.454519	+	0.541675i
$3$		0			0
$3$		0			0
$4$	−1.38919	−	7.87846i	−0.0868241	−	0.492404i
$5$	−6.13288	+	16.8500i	−0.245315	+	0.673998i	0.754528	+	0.656268i	$0.227866\pi$
$5$	−6.13288	+	16.8500i	−0.245315	+	0.673998i	−0.999843	+	0.0177298i	$0.994356\pi$
$6$		0			0
$7$	8.35982	−	47.4109i	0.170609	−	0.967569i	−0.772483	−	0.635036i	$-0.780985\pi$
$7$	8.35982	−	47.4109i	0.170609	−	0.967569i	0.943091	−	0.332534i	$-0.107904\pi$
$8$	19.5959	+	11.3137i	0.306186	+	0.176777i
$9$		0			0
$10$	−25.3588	−	43.9227i	−0.253588	−	0.439227i
$11$	40.7635	+	111.997i	0.336889	+	0.925594i	0.986271	+	0.165132i	$0.0528051\pi$
$11$	40.7635	+	111.997i	0.336889	+	0.925594i	−0.649383	+	0.760462i	$0.724973\pi$
$12$		0			0
$13$	76.8147	−	64.4552i	0.454525	−	0.381391i	−0.386587	−	0.922253i	$-0.626346\pi$
$13$	76.8147	−	64.4552i	0.454525	−	0.381391i	0.841112	+	0.540861i	$0.181902\pi$
$14$	87.5264	+	104.310i	0.446563	+	0.532194i
$15$		0			0
$16$	−60.1403	+	21.8893i	−0.234923	+	0.0855050i
$17$	4.38346	−	2.53079i	0.0151677	−	0.00875707i	−0.492397	−	0.870371i	$-0.663879\pi$
$17$	4.38346	−	2.53079i	0.0151677	−	0.00875707i	0.507565	+	0.861614i	$0.330546\pi$
$18$		0			0
$19$	−159.777	+	276.742i	−0.442595	+	0.766597i	−0.997881	−	0.0650620i	$-0.979275\pi$
$19$	−159.777	+	276.742i	−0.442595	+	0.766597i	0.555286	+	0.831659i	$0.312609\pi$
$20$	141.271	+	24.9100i	0.353179	+	0.0622749i
$21$		0			0
$22$	−316.775	−	115.297i	−0.654494	−	0.238216i
$23$	223.676	−	39.4401i	0.422828	−	0.0745560i	0.0418144	−	0.999125i	$-0.486686\pi$
$23$	223.676	−	39.4401i	0.422828	−	0.0745560i	0.381014	+	0.924569i	$0.375575\pi$
$24$		0			0
$25$	232.469	+	195.065i	0.371950	+	0.312103i
$26$			283.619i			0.419555i
$27$		0			0
$28$	−385.138			−0.491248
$29$	−922.944	+	1099.92i	−1.09744	+	1.30787i	−0.149731	+	0.988727i	$0.547841\pi$
$29$	−922.944	+	1099.92i	−1.09744	+	1.30787i	−0.947705	+	0.319146i	$0.896604\pi$
$30$		0			0
$31$	80.6757	+	457.534i	0.0839497	+	0.476102i	0.997578	+	0.0695525i	$0.0221571\pi$
$31$	80.6757	+	457.534i	0.0839497	+	0.476102i	−0.913629	+	0.406550i	$0.866732\pi$
$32$	61.9123	−	170.103i	0.0604612	−	0.166116i
$33$		0			0
$34$	−2.48600	+	14.0988i	−0.00215052	+	0.0121962i
$35$	747.602	+	431.628i	0.610287	+	0.352349i
$36$		0			0
$37$	457.456	+	792.338i	0.334154	+	0.578771i	0.983322	−	0.181874i	$-0.0582162\pi$
$37$	457.456	+	792.338i	0.334154	+	0.578771i	−0.649168	+	0.760645i	$0.724883\pi$
$38$	−309.130	−	849.327i	−0.214079	−	0.588176i
$39$		0			0
$40$	−310.815	+	260.805i	−0.194259	+	0.163003i
$41$	835.336	+	995.515i	0.496928	+	0.592216i	0.954965	−	0.296717i	$-0.0958919\pi$
$41$	835.336	+	995.515i	0.496928	+	0.592216i	−0.458037	+	0.888933i	$0.651447\pi$
$42$		0			0
$43$	−3323.67	+	1209.72i	−1.79755	+	0.654255i	−0.798949	+	0.601399i	$0.794610\pi$
$43$	−3323.67	+	1209.72i	−1.79755	+	0.654255i	−0.998602	+	0.0528558i	$0.983168\pi$
$44$	825.735	−	476.738i	0.426516	−	0.246249i
$45$		0			0
$46$	−321.206	+	556.344i	−0.151798	+	0.262923i
$47$	−3592.02	−	633.370i	−1.62608	−	0.286722i	−0.715056	−	0.699067i	$-0.753599\pi$
$47$	−3592.02	−	633.370i	−1.62608	−	0.286722i	−0.911028	+	0.412345i	$0.864710\pi$
$48$		0			0
$49$	78.2948	+	28.4970i	0.0326092	+	0.0118688i
$50$	−845.294	+	149.048i	−0.338117	+	0.0596192i
$51$		0			0
$52$	−614.517	−	515.641i	−0.227262	−	0.190696i
$53$			3907.25i			1.39097i	0.718538	+	0.695487i	$0.244812\pi$
$53$			3907.25i			1.39097i	−0.718538	+	0.695487i	$0.755188\pi$
$54$		0			0
$55$	−2137.14			−0.706493
$56$	700.212	−	834.480i	0.223282	−	0.266097i
$57$		0			0
$58$	−705.217	−	3999.49i	−0.209637	−	1.18891i
$59$	−627.970	+	1725.33i	−0.180399	+	0.495643i	−0.996625	−	0.0820903i	$-0.973840\pi$
$59$	−627.970	+	1725.33i	−0.180399	+	0.495643i	0.816226	+	0.577733i	$0.196063\pi$
$60$		0			0
$61$	−592.438	+	3359.88i	−0.159215	+	0.902951i	0.795616	+	0.605801i	$0.207147\pi$
$61$	−592.438	+	3359.88i	−0.159215	+	0.902951i	−0.954831	+	0.297150i	$0.903964\pi$
$62$	−1138.01	−	657.033i	−0.296050	−	0.170924i
$63$		0			0
$64$	256.000	+	443.405i	0.0625000	+	0.108253i
$65$	614.971	+	1689.62i	0.145555	+	0.399910i
$66$		0			0
$67$	6449.53	−	5411.80i	1.43674	−	1.20557i	0.495150	−	0.868807i	$-0.335113\pi$
$67$	6449.53	−	5411.80i	1.43674	−	1.20557i	0.941590	−	0.336761i	$-0.109331\pi$
$68$	−26.0282	−	31.0192i	−0.00562894	−	0.00670831i
$69$		0			0
$70$	−2294.41	+	835.096i	−0.468246	+	0.170428i
$71$	4819.88	−	2782.76i	0.956136	−	0.552025i	0.0611540	−	0.998128i	$-0.480522\pi$
$71$	4819.88	−	2782.76i	0.956136	−	0.552025i	0.894982	+	0.446103i	$0.147189\pi$
$72$		0			0
$73$	1970.23	−	3412.54i	0.369719	−	0.640371i	−0.619803	−	0.784758i	$-0.712787\pi$
$73$	1970.23	−	3412.54i	0.369719	−	0.640371i	0.989521	+	0.144386i	$0.0461208\pi$
$74$	−2548.45	−	449.360i	−0.465385	−	0.0820600i
$75$		0			0
$76$	2402.26	+	874.351i	0.415903	+	0.151376i
$77$	5650.65	−	996.362i	0.953052	−	0.168049i
$78$		0			0
$79$	8379.78	+	7031.47i	1.34270	+	1.12666i	0.980924	+	0.194393i	$0.0622736\pi$
$79$	8379.78	+	7031.47i	1.34270	+	1.12666i	0.361775	+	0.932265i	$0.382171\pi$
$80$		−	1147.61i		−	0.179313i
$81$		0			0
$82$	−3675.69			−0.546652
$83$	1263.92	−	1506.28i	0.183470	−	0.218651i	−0.666468	−	0.745533i	$-0.732195\pi$
$83$	1263.92	−	1506.28i	0.183470	−	0.218651i	0.849938	+	0.526883i	$0.176639\pi$
$84$		0			0
$85$	15.7605	+	89.3822i	0.00218138	+	0.0123712i
$86$	3421.60	−	9400.76i	0.462628	−	1.27106i
$87$		0			0
$88$	−468.301	+	2655.87i	−0.0604728	+	0.342958i
$89$	1148.77	+	663.242i	0.145028	+	0.0837321i	0.570758	−	0.821118i	$-0.306649\pi$
$89$	1148.77	+	663.242i	0.145028	+	0.0837321i	−0.425730	+	0.904850i	$0.639983\pi$
$90$		0			0
$91$	−2413.72	−	4180.69i	−0.291477	−	0.504853i
$92$	−621.455	−	1707.43i	−0.0734233	−	0.201729i
$93$		0			0
$94$	7902.89	−	6631.31i	0.894397	−	0.750488i
$95$	−3683.19	−	4389.46i	−0.408110	−	0.486366i
$96$		0			0
$97$	11763.6	−	4281.60i	1.25025	−	0.455054i	0.369764	−	0.929126i	$-0.379439\pi$
$97$	11763.6	−	4281.60i	1.25025	−	0.455054i	0.880486	+	0.474072i	$0.157216\pi$
$98$	−204.090	+	117.832i	−0.0212506	+	0.0122690i
$99$		0			0
$100$	1213.87	−	2102.48i	0.121387	−	0.210248i
$101$	−18547.9	−	3270.50i	−1.81825	−	0.320606i	−0.842365	−	0.538907i	$-0.818837\pi$
$101$	−18547.9	−	3270.50i	−1.81825	−	0.320606i	−0.975882	+	0.218301i	$0.929949\pi$
$102$		0			0
$103$	7951.03	+	2893.94i	0.749461	+	0.272782i	0.688379	−	0.725351i	$-0.258323\pi$
$103$	7951.03	+	2893.94i	0.749461	+	0.272782i	0.0610821	+	0.998133i	$0.480545\pi$
$104$	2234.48	−	393.999i	0.206590	−	0.0364274i
$105$		0			0
$106$	−8465.84	−	7103.68i	−0.753457	−	0.632225i
$107$			2539.91i			0.221846i	0.993829	+	0.110923i	$0.0353806\pi$
$107$			2539.91i			0.221846i	−0.993829	+	0.110923i	$0.964619\pi$
$108$		0			0
$109$	−9372.61			−0.788874			−0.394437	−	0.918923i	$-0.629060\pi$
$109$	−9372.61			−0.788874			−0.394437	+	0.918923i	$0.629060\pi$
$110$	3885.49	−	4630.54i	0.321115	−	0.382690i
$111$		0			0
$112$	535.029	+	3034.30i	0.0426522	+	0.241892i
$113$	4435.56	−	12186.6i	0.347370	−	0.954390i	−0.635826	−	0.771833i	$-0.719340\pi$
$113$	4435.56	−	12186.6i	0.347370	−	0.954390i	0.983195	−	0.182557i	$-0.0584375\pi$
$114$		0			0
$115$	−707.215	+	4010.81i	−0.0534756	+	0.303275i
$116$	9947.83	+	5743.38i	0.739286	+	0.426827i
$117$		0			0
$118$	−2596.58	−	4497.41i	−0.186483	−	0.322997i
$119$	−83.3422	−	228.981i	−0.00588534	−	0.0161698i
$120$		0			0
$121$	334.025	−	280.280i	0.0228144	−	0.0191435i
$122$	−6202.76	−	7392.16i	−0.416740	−	0.496651i
$123$		0			0
$124$	3492.59	−	1271.20i	0.227146	−	0.0826743i
$125$	−14418.2	+	8324.33i	−0.922762	+	0.532757i
$126$		0			0
$127$	1239.33	−	2146.58i	0.0768387	−	0.133089i	−0.825046	−	0.565066i	$-0.808851\pi$
$127$	1239.33	−	2146.58i	0.0768387	−	0.133089i	0.901884	+	0.431978i	$0.142184\pi$
$128$	−1426.15	−	251.469i	−0.0870455	−	0.0153485i
$129$		0			0
$130$	−4778.97	−	1739.40i	−0.282779	−	0.102923i
$131$	24228.0	−	4272.06i	1.41181	−	0.248940i	0.584822	−	0.811162i	$-0.301164\pi$
$131$	24228.0	−	4272.06i	1.41181	−	0.248940i	0.826987	+	0.562222i	$0.190053\pi$
$132$		0			0
$133$	11784.9	+	9888.68i	0.666226	+	0.559030i
$134$			23813.3i			1.32620i
$135$		0			0
$136$	114.531			0.00619218
$137$	−11015.0	+	13127.2i	−0.586874	+	0.699409i	−0.975002	−	0.222196i	$-0.928677\pi$
$137$	−11015.0	+	13127.2i	−0.586874	+	0.699409i	0.388128	+	0.921606i	$0.373122\pi$
$138$		0			0
$139$	1803.11	+	10225.9i	0.0933239	+	0.529266i	0.995248	+	0.0973716i	$0.0310435\pi$
$139$	1803.11	+	10225.9i	0.0933239	+	0.529266i	−0.901924	+	0.431894i	$0.857845\pi$
$140$	2362.01	−	6489.56i	0.120511	−	0.331100i
$141$		0			0
$142$	−2733.51	+	15502.5i	−0.135564	+	0.768821i
$143$	10350.0	+	5975.58i	0.506138	+	0.292219i
$144$		0			0
$145$	−12873.3	−	22297.2i	−0.612286	−	1.06051i
$146$	3811.92	+	10473.2i	0.178829	+	0.491329i
$147$		0			0
$148$	5606.91	−	4704.76i	0.255977	−	0.214790i
$149$	−3216.02	−	3832.71i	−0.144859	−	0.172637i	0.688736	−	0.725012i	$-0.258166\pi$
$149$	−3216.02	−	3832.71i	−0.144859	−	0.172637i	−0.833595	+	0.552375i	$0.813721\pi$
$150$		0			0
$151$	−3141.10	+	1143.27i	−0.137761	+	0.0501410i	−0.409981	−	0.912094i	$-0.634465\pi$
$151$	−3141.10	+	1143.27i	−0.137761	+	0.0501410i	0.272219	+	0.962235i	$0.412242\pi$
$152$	−6261.95	+	3615.34i	−0.271033	+	0.156481i
$153$		0			0
$154$	−8114.50	+	14054.7i	−0.342153	+	0.592626i
$155$	−8204.21	−	1446.62i	−0.341486	−	0.0602132i
$156$		0			0
$157$	−38619.8	−	14056.5i	−1.56679	−	0.570265i	−0.594510	−	0.804088i	$-0.702654\pi$
$157$	−38619.8	−	14056.5i	−1.56679	−	0.570265i	−0.972279	+	0.233824i	$0.924876\pi$
$158$	−30470.2	+	5372.72i	−1.22057	+	0.215219i
$159$		0			0
$160$	2486.52	+	2086.44i	0.0971297	+	0.0815015i
$161$		−	10934.4i		−	0.421835i
$162$		0			0
$163$	−29411.6			−1.10699			−0.553494	−	0.832853i	$-0.686706\pi$
$163$	−29411.6			−1.10699			−0.553494	+	0.832853i	$0.686706\pi$
$164$	6682.69	−	7964.12i	0.248464	−	0.296108i
$165$		0			0
$166$	965.758	+	5477.08i	0.0350471	+	0.198762i
$167$	999.227	−	2745.35i	0.0358287	−	0.0984386i	−0.920488	−	0.390770i	$-0.872209\pi$
$167$	999.227	−	2745.35i	0.0358287	−	0.0984386i	0.956317	+	0.292331i	$0.0944310\pi$
$168$		0			0
$169$	−3213.54	+	18224.9i	−0.112515	+	0.638104i
$170$	−222.318	−	128.356i	−0.00769268	−	0.00444137i
$171$		0			0
$172$	14147.9	+	24504.9i	0.478228	+	0.828316i
$173$	6565.10	+	18037.5i	0.219356	+	0.602675i	0.999744	−	0.0226199i	$-0.00720074\pi$
$173$	6565.10	+	18037.5i	0.219356	+	0.602675i	−0.780388	+	0.625295i	$0.784979\pi$
$174$		0			0
$175$	11191.6	−	9390.86i	0.365440	−	0.306640i
$176$	−4903.06	−	5843.24i	−0.158286	−	0.188638i
$177$		0			0
$178$	−3525.60	+	1283.21i	−0.111274	+	0.0405004i
$179$	5005.86	−	2890.14i	0.156233	−	0.0902012i	−0.419845	−	0.907596i	$-0.637916\pi$
$179$	5005.86	−	2890.14i	0.156233	−	0.0902012i	0.576078	+	0.817394i	$0.304582\pi$
$180$		0			0
$181$	−4506.72	+	7805.86i	−0.137563	+	0.238267i	−0.926574	−	0.376113i	$-0.877260\pi$
$181$	−4506.72	+	7805.86i	−0.137563	+	0.238267i	0.789010	+	0.614380i	$0.210594\pi$
$182$	13446.6	+	2371.00i	0.405948	+	0.0715796i
$183$		0			0
$184$	4829.35	+	1757.74i	0.142644	+	0.0519181i
$185$	−16156.4	+	2848.81i	−0.472064	+	0.0832376i
$186$		0			0
$187$	462.126	+	387.770i	0.0132153	+	0.0110890i
$188$			29179.5i			0.825584i
$189$		0			0
$190$	16207.0			0.448947
$191$	22292.4	−	26567.0i	0.611069	−	0.728243i	−0.368438	−	0.929652i	$-0.620107\pi$
$191$	22292.4	−	26567.0i	0.611069	−	0.728243i	0.979507	+	0.201409i	$0.0645519\pi$
$192$		0			0
$193$	9146.20	+	51870.7i	0.245542	+	1.39254i	0.819230	+	0.573465i	$0.194401\pi$
$193$	9146.20	+	51870.7i	0.245542	+	1.39254i	−0.573688	+	0.819074i	$0.694488\pi$
$194$	−12110.2	+	33272.5i	−0.321772	+	0.884060i
$195$		0			0
$196$	115.746	−	656.430i	0.00301297	−	0.0170874i
$197$	17219.5	+	9941.67i	0.443698	+	0.256169i	0.705165	−	0.709043i	$-0.250873\pi$
$197$	17219.5	+	9941.67i	0.443698	+	0.256169i	−0.261467	+	0.965212i	$0.584206\pi$
$198$		0			0
$199$	−22343.2	−	38699.6i	−0.564209	−	0.977239i	−0.997123	−	0.0758033i	$-0.975848\pi$
$199$	−22343.2	−	38699.6i	−0.564209	−	0.977239i	0.432914	−	0.901435i	$-0.357485\pi$
$200$	2348.54	+	6452.56i	0.0587135	+	0.161314i
$201$		0			0
$202$	40807.8	−	34241.8i	1.00009	−	0.839178i
$203$	44432.6	+	52952.7i	1.07823	+	1.28498i
$204$		0			0
$205$	−21897.4	+	7970.00i	−0.521056	+	0.189649i
$206$	−20725.9	+	11966.1i	−0.488404	+	0.281980i
$207$		0			0
$208$	−3208.78	+	5557.77i	−0.0741675	+	0.128462i
$209$	−37507.3	−	6613.54i	−0.858663	−	0.151405i
$210$		0			0
$211$	−38649.8	−	14067.4i	−0.868126	−	0.315972i	−0.130718	−	0.991420i	$-0.541728\pi$
$211$	−38649.8	−	14067.4i	−0.868126	−	0.315972i	−0.737408	+	0.675448i	$0.763950\pi$
$212$	30783.1	−	5427.89i	0.684921	−	0.120770i
$213$		0			0
$214$	−5503.23	−	4617.75i	−0.120168	−	0.100833i
$215$		−	63422.8i		−	1.37204i
$216$		0			0
$217$	22366.6			0.474985
$218$	17040.1	−	20307.6i	0.358558	−	0.427313i
$219$		0			0
$220$	2968.88	+	16837.4i	0.0613406	+	0.347880i
$221$	173.592	−	476.939i	0.00355422	−	0.00976513i
$222$		0			0
$223$	14652.4	−	83097.6i	0.294644	−	1.67101i	−0.374002	−	0.927428i	$-0.622015\pi$
$223$	14652.4	−	83097.6i	0.294644	−	1.67101i	0.668646	−	0.743581i	$-0.266874\pi$
$224$	−7547.14	−	4357.34i	−0.150413	−	0.0868412i
$225$		0			0
$226$	18340.5	+	31766.7i	0.359083	+	0.621950i
$227$	22727.1	+	62442.1i	0.441054	+	1.21179i	0.938800	+	0.344463i	$0.111939\pi$
$227$	22727.1	+	62442.1i	0.441054	+	1.21179i	−0.497746	+	0.867323i	$0.665839\pi$
$228$		0			0
$229$	−34661.7	+	29084.6i	−0.660965	+	0.554615i	−0.910376	−	0.413782i	$-0.864207\pi$
$229$	−34661.7	+	29084.6i	−0.660965	+	0.554615i	0.249411	+	0.968398i	$0.419763\pi$
$230$	−7404.46	−	8824.29i	−0.139971	−	0.166811i
$231$		0			0
$232$	−30530.1	+	11112.1i	−0.567221	+	0.206452i
$233$	11296.3	−	6521.93i	0.208077	−	0.120134i	−0.392340	−	0.919820i	$-0.628334\pi$
$233$	11296.3	−	6521.93i	0.208077	−	0.120134i	0.600418	+	0.799687i	$0.295001\pi$
$234$		0			0
$235$	32701.7	−	56641.0i	0.592154	−	1.02564i
$236$	14465.3	+	2550.63i	0.259720	+	0.0457956i
$237$		0			0
$238$	647.656	+	235.727i	0.0114338	+	0.00416156i
$239$	2968.46	−	523.420i	0.0519679	−	0.00916335i	−0.147604	−	0.989047i	$-0.547156\pi$
$239$	2968.46	−	523.420i	0.0519679	−	0.00916335i	0.199572	+	0.979883i	$0.436045\pi$
$240$		0			0
$241$	10487.4	+	8799.95i	0.180565	+	0.151512i	0.728590	−	0.684950i	$-0.240176\pi$
$241$	10487.4	+	8799.95i	0.180565	+	0.151512i	−0.548026	+	0.836462i	$0.684620\pi$
$242$			1233.30i			0.0210591i
$243$		0			0
$244$	27293.7			0.458440
$245$	−960.345	+	1144.49i	−0.0159991	+	0.0190670i
$246$		0			0
$247$	5564.22	+	31556.3i	0.0912033	+	0.517239i
$248$	−3595.50	+	9878.55i	−0.0584596	+	0.160616i
$249$		0			0
$250$	8177.01	−	46374.1i	0.130832	−	0.741986i
$251$	−65914.7	−	38055.9i	−1.04625	−	0.604052i	−0.124651	−	0.992201i	$-0.539781\pi$
$251$	−65914.7	−	38055.9i	−1.04625	−	0.604052i	−0.921597	+	0.388149i	$0.873115\pi$
$252$		0			0
$253$	13535.0	+	23443.3i	0.211455	+	0.366250i
$254$	2397.81	+	6587.92i	0.0371661	+	0.102113i
$255$		0			0
$256$	3137.72	−	2632.86i	0.0478778	−	0.0401742i
$257$	−10506.8	−	12521.5i	−0.159075	−	0.189578i	0.680620	−	0.732637i	$-0.261711\pi$
$257$	−10506.8	−	12521.5i	−0.159075	−	0.189578i	−0.839695	+	0.543059i	$0.817266\pi$
$258$		0			0
$259$	41389.7	−	15064.6i	0.617011	−	0.224574i
$260$	12457.3	−	7192.22i	0.184279	−	0.106394i
$261$		0			0
$262$	−34792.2	+	60261.9i	−0.506850	+	0.877890i
$263$	−40970.4	−	7224.19i	−0.592323	−	0.104443i	−0.130552	−	0.991441i	$-0.541675\pi$
$263$	−40970.4	−	7224.19i	−0.592323	−	0.104443i	−0.461772	+	0.886999i	$0.652786\pi$
$264$		0			0
$265$	−65837.0	−	23962.7i	−0.937515	−	0.341227i
$266$	−42851.6	+	7555.90i	−0.605625	+	0.106788i
$267$		0			0
$268$	−51596.2	−	43294.4i	−0.718370	−	0.602784i
$269$		−	131319.i		−	1.81477i	−0.420297	−	0.907386i	$-0.638074\pi$
$269$		−	131319.i		−	1.81477i	0.420297	−	0.907386i	$-0.361926\pi$
$270$		0			0
$271$	126745.			1.72581			0.862905	−	0.505367i	$-0.168643\pi$
$271$	126745.			1.72581			0.862905	+	0.505367i	$0.168643\pi$
$272$	−208.226	+	248.154i	−0.00281447	+	0.00335415i
$273$		0			0
$274$	−8416.54	−	47732.6i	−0.112107	−	0.635790i
$275$	−12370.4	+	33987.3i	−0.163575	+	0.449419i
$276$		0			0
$277$	−3533.58	+	20039.9i	−0.0460527	+	0.261178i	−0.999137	−	0.0415259i	$-0.986778\pi$
$277$	−3533.58	+	20039.9i	−0.0460527	+	0.261178i	0.953085	+	0.302704i	$0.0978892\pi$
$278$	−25434.8	−	14684.8i	−0.329108	−	0.190010i
$279$		0			0
$280$	9766.63	+	16916.3i	0.124574	+	0.215769i
$281$	−49771.3	−	136745.i	−0.630327	−	1.73181i	−0.680171	−	0.733053i	$-0.738095\pi$
$281$	−49771.3	−	136745.i	−0.630327	−	1.73181i	0.0498439	−	0.998757i	$-0.484128\pi$
$282$		0			0
$283$	95833.6	−	80413.9i	1.19659	−	1.00406i	0.196867	−	0.980430i	$-0.436923\pi$
$283$	95833.6	−	80413.9i	1.19659	−	1.00406i	0.999721	−	0.0236266i	$-0.00752129\pi$
$284$	−28619.6	−	34107.5i	−0.354835	−	0.422876i
$285$		0			0
$286$	−31764.4	+	11561.3i	−0.388337	+	0.141343i
$287$	54181.5	−	31281.7i	0.657790	−	0.379775i
$288$		0			0
$289$	−41747.7	+	72309.1i	−0.499847	+	0.865760i
$290$	71716.2	+	12645.5i	0.852749	+	0.150363i
$291$		0			0
$292$	−29622.6	−	10781.7i	−0.347422	−	0.126451i
$293$	−62578.1	+	11034.2i	−0.728933	+	0.128530i	−0.525785	−	0.850618i	$-0.676228\pi$
$293$	−62578.1	+	11034.2i	−0.728933	+	0.128530i	−0.203148	+	0.979148i	$0.565117\pi$
$294$		0			0
$295$	−25220.5	−	21162.5i	−0.289808	−	0.243178i
$296$			20702.1i			0.236282i
$297$		0			0
$298$	14151.3			0.159354
$299$	14639.5	−	17446.7i	0.163751	−	0.195151i
$300$		0			0
$301$	29568.5	+	167691.i	0.326360	+	1.85088i
$302$	3233.64	−	8884.36i	0.0354551	−	0.0974120i
$303$		0			0
$304$	3551.36	−	20140.7i	0.0384279	−	0.217936i
$305$	−52980.5	−	30588.3i	−0.569530	−	0.328818i
$306$		0			0
$307$	53425.8	+	92536.3i	0.566858	+	0.981828i	0.996874	+	0.0790062i	$0.0251747\pi$
$307$	53425.8	+	92536.3i	0.566858	+	0.981828i	−0.430016	+	0.902821i	$0.641492\pi$
$308$	−15699.6	−	43134.3i	−0.165496	−	0.454696i
$309$		0			0
$310$	18050.3	−	15146.0i	0.187828	−	0.157607i
$311$	54517.1	+	64971.0i	0.563653	+	0.671736i	0.970315	−	0.241843i	$-0.0777518\pi$
$311$	54517.1	+	64971.0i	0.563653	+	0.671736i	−0.406662	+	0.913579i	$0.633307\pi$
$312$		0			0
$313$	106916.	−	38914.4i	1.09133	−	0.397211i	0.267216	−	0.963637i	$-0.413896\pi$
$313$	106916.	−	38914.4i	1.09133	−	0.397211i	0.824113	+	0.566426i	$0.191674\pi$
$314$	100670.	−	58121.8i	1.02103	−	0.589494i
$315$		0			0
$316$	43756.1	−	75787.8i	0.438192	−	0.758971i
$317$	132229.	+	23315.6i	1.31586	+	0.232021i	0.787139	−	0.616776i	$-0.211562\pi$
$317$	132229.	+	23315.6i	1.31586	+	0.232021i	0.528719	+	0.848797i	$0.322673\pi$
$318$		0			0
$319$	−160810.	−	58530.1i	−1.58027	−	0.575172i
$320$	−9041.37	+	1594.24i	−0.0882947	+	0.0155687i
$321$		0			0
$322$	23691.6	+	19879.6i	0.228498	+	0.191732i
$323$			1617.45i			0.0155034i
$324$		0			0
$325$	30429.9			0.288094
$326$	53472.5	−	63726.0i	0.503147	−	0.599628i
$327$		0			0
$328$	5106.21	+	28958.8i	0.0474626	+	0.269174i
$329$	−60057.3	+	165006.i	−0.554848	+	1.52443i
$330$		0			0
$331$	6323.04	−	35859.8i	0.0577125	−	0.327304i	−0.942259	−	0.334886i	$-0.891302\pi$
$331$	6323.04	−	35859.8i	0.0577125	−	0.327304i	0.999971	+	0.00758172i	$0.00241336\pi$
$332$	−13623.0	−	7865.26i	−0.123594	−	0.0713570i
$333$		0			0
$334$	4131.69	+	7156.29i	0.0370369	+	0.0641498i
$335$	51634.3	+	141864.i	0.460097	+	1.26410i
$336$		0			0
$337$	31391.9	−	26340.9i	0.276413	−	0.231938i	−0.494033	−	0.869443i	$-0.664478\pi$
$337$	31391.9	−	26340.9i	0.276413	−	0.231938i	0.770446	+	0.637505i	$0.220034\pi$
$338$	−33645.4	−	40097.1i	−0.294505	−	0.350977i
$339$		0			0
$340$	682.300	−	248.337i	0.00590225	−	0.00214824i
$341$	−47953.8	+	27686.1i	−0.412396	+	0.238097i
$342$		0			0
$343$	59800.4	−	103577.i	0.508295	−	0.880393i
$344$	−78816.8	−	13897.5i	−0.666042	−	0.117441i
$345$		0			0
$346$	−51017.7	−	18568.9i	−0.426156	−	0.155108i
$347$	71783.9	−	12657.4i	0.596167	−	0.105120i	0.132581	−	0.991172i	$-0.457673\pi$
$347$	71783.9	−	12657.4i	0.596167	−	0.105120i	0.463586	+	0.886052i	$0.346562\pi$
$348$		0			0
$349$	−95066.4	−	79770.2i	−0.780506	−	0.654923i	0.162870	−	0.986648i	$-0.447925\pi$
$349$	−95066.4	−	79770.2i	−0.780506	−	0.654923i	−0.943376	+	0.331725i	$0.892369\pi$
$350$			41322.1i			0.337324i
$351$		0			0
$352$	21574.7			0.174124
$353$	−91391.7	+	108916.i	−0.733428	+	0.874065i	−0.995861	−	0.0908851i	$-0.971030\pi$
$353$	−91391.7	+	108916.i	−0.733428	+	0.874065i	0.262434	+	0.964950i	$0.415475\pi$
$354$		0			0
$355$	17329.6	+	98281.1i	0.137509	+	0.779854i
$356$	3629.47	−	9971.90i	0.0286381	−	0.0786825i
$357$		0			0
$358$	−2838.99	+	16100.7i	−0.0221512	+	0.125626i
$359$	71878.9	+	41499.3i	0.557715	+	0.321997i	0.752228	−	0.658903i	$-0.228979\pi$
$359$	71878.9	+	41499.3i	0.557715	+	0.321997i	−0.194513	+	0.980900i	$0.562313\pi$
$360$		0			0
$361$	14103.2	+	24427.5i	0.108219	+	0.187441i
$362$	−8719.40	−	23956.4i	−0.0665380	−	0.182812i
$363$		0			0
$364$	−29584.3	+	24824.2i	−0.223284	+	0.187358i
$365$	45417.9	+	54127.0i	0.340912	+	0.406283i
$366$		0			0
$367$	26265.6	−	9559.91i	0.195009	−	0.0709776i	−0.242669	−	0.970109i	$-0.578023\pi$
$367$	26265.6	−	9559.91i	0.195009	−	0.0709776i	0.437679	+	0.899131i	$0.355801\pi$
$368$	−12588.6	+	7268.05i	−0.0929572	+	0.0536689i
$369$		0			0
$370$	23201.0	−	40185.4i	0.169474	−	0.293538i
$371$	185246.	+	32663.9i	1.34586	+	0.237312i
$372$		0			0
$373$	−127864.	−	46538.8i	−0.919033	−	0.334501i	−0.161180	−	0.986925i	$-0.551530\pi$
$373$	−127864.	−	46538.8i	−0.919033	−	0.334501i	−0.757854	+	0.652424i	$0.773752\pi$
$374$	−1680.36	+	296.293i	−0.0120132	+	0.00211826i
$375$		0			0
$376$	−63223.1	−	53050.5i	−0.447199	−	0.375244i
$377$			143979.i			1.01301i
$378$		0			0
$379$	−179302.			−1.24826			−0.624131	−	0.781319i	$-0.714547\pi$
$379$	−179302.			−1.24826			−0.624131	+	0.781319i	$0.714547\pi$
$380$	−29465.5	+	35115.7i	−0.204055	+	0.243183i
$381$		0			0
$382$	17033.5	+	96601.9i	0.116729	+	0.662002i
$383$	32955.8	−	90545.4i	0.224665	−	0.617261i	−0.775232	−	0.631677i	$-0.782367\pi$
$383$	32955.8	−	90545.4i	0.224665	−	0.617261i	0.999896	+	0.0144164i	$0.00458904\pi$
$384$		0			0
$385$	−17866.1	+	101324.i	−0.120534	+	0.683581i
$386$	−129017.	−	74487.8i	−0.865907	−	0.499932i
$387$		0			0
$388$	−50074.3	−	86731.2i	−0.332622	−	0.576118i
$389$	−15385.5	−	42271.2i	−0.101674	−	0.279348i	0.878417	−	0.477895i	$-0.158600\pi$
$389$	−15385.5	−	42271.2i	−0.101674	−	0.279348i	−0.980091	+	0.198547i	$0.936378\pi$
$390$		0			0
$391$	880.661	−	738.962i	0.00576043	−	0.00483358i
$392$	1211.85	+	1444.23i	0.00788637	+	0.00939861i
$393$		0			0
$394$	−52847.0	+	19234.7i	−0.340430	+	0.123906i
$395$	−169872.	+	98075.8i	−1.08875	+	0.628590i
$396$		0			0
$397$	−13231.1	+	22916.9i	−0.0839488	+	0.145404i	−0.904943	−	0.425533i	$-0.860087\pi$
$397$	−13231.1	+	22916.9i	−0.0839488	+	0.145404i	0.820994	+	0.570937i	$0.193420\pi$
$398$	124472.	+	21947.8i	0.785790	+	0.138556i
$399$		0			0
$400$	−18250.6	−	6642.67i	−0.114066	−	0.0415167i
$401$	−94944.9	+	16741.3i	−0.590450	+	0.104112i	−0.460887	−	0.887459i	$-0.652469\pi$
$401$	−94944.9	+	16741.3i	−0.590450	+	0.104112i	−0.129563	+	0.991571i	$0.541357\pi$
$402$		0			0
$403$	35687.5	+	29945.4i	0.219739	+	0.184383i
$404$			150673.i			0.923148i
$405$		0			0
$406$	−195515.			−1.18612
$407$	−70091.8	+	83532.1i	−0.423134	+	0.504272i
$408$		0			0
$409$	30160.7	+	171050.i	0.180300	+	1.02253i	0.931847	+	0.362851i	$0.118197\pi$
$409$	30160.7	+	171050.i	0.180300	+	1.02253i	−0.751548	+	0.659679i	$0.770692\pi$
$410$	22542.6	−	61935.2i	0.134102	−	0.368442i
$411$		0			0
$412$	11754.3	−	66662.1i	0.0692474	−	0.392722i
$413$	76549.9	+	44196.1i	0.448791	+	0.259110i
$414$		0			0
$415$	17629.3	+	30534.9i	0.102362	+	0.177297i
$416$	−6208.22	−	17056.9i	−0.0358740	−	0.0985631i
$417$		0			0
$418$	82520.7	−	69243.1i	0.472292	−	0.396300i
$419$	−76012.3	−	90587.9i	−0.432968	−	0.515991i	0.504808	−	0.863232i	$-0.331563\pi$
$419$	−76012.3	−	90587.9i	−0.432968	−	0.515991i	−0.937776	+	0.347240i	$0.887119\pi$
$420$		0			0
$421$	−25403.8	+	9246.21i	−0.143329	+	0.0521675i	−0.412689	−	0.910872i	$-0.635410\pi$
$421$	−25403.8	+	9246.21i	−0.143329	+	0.0521675i	0.269360	+	0.963040i	$0.413188\pi$
$422$	100748.	−	58167.0i	0.565734	−	0.326627i
$423$		0			0
$424$	−44205.5	+	76566.1i	−0.245892	+	0.425897i
$425$	1512.69	+	266.728i	0.00837474	+	0.00147669i
$426$		0			0
$427$	154342.	+	56176.0i	0.846505	+	0.308102i
$428$	20010.6	−	3528.41i	0.109238	−	0.0192615i
$429$		0			0
$430$	137418.	+	115308.i	0.743203	+	0.623621i
$431$		−	241929.i		−	1.30236i	−0.758921	−	0.651182i	$-0.774273\pi$
$431$		−	241929.i		−	1.30236i	0.758921	−	0.651182i	$-0.225727\pi$
$432$		0			0
$433$	−61264.5			−0.326763			−0.163382	−	0.986563i	$-0.552240\pi$
$433$	−61264.5			−0.326763			−0.163382	+	0.986563i	$0.552240\pi$
$434$	−40664.1	+	48461.6i	−0.215890	+	0.257287i
$435$		0			0
$436$	13020.3	+	73841.7i	0.0684932	+	0.388445i
$437$	−24823.5	+	68202.1i	−0.129987	+	0.357137i
$438$		0			0
$439$	−24908.6	+	141264.i	−0.129247	+	0.732996i	0.849447	+	0.527673i	$0.176936\pi$
$439$	−24908.6	+	141264.i	−0.129247	+	0.732996i	−0.978694	+	0.205323i	$0.934176\pi$
$440$	−41879.2	−	24179.0i	−0.216318	−	0.124891i
$441$		0			0
$442$	717.781	+	1243.23i	0.00367407	+	0.00636367i
$443$	−8346.13	−	22930.8i	−0.0425283	−	0.116845i	0.916611	−	0.399781i	$-0.130914\pi$
$443$	−8346.13	−	22930.8i	−0.0425283	−	0.116845i	−0.959139	+	0.282936i	$0.908692\pi$
$444$		0			0
$445$	−18220.9	+	15289.1i	−0.0920130	+	0.0772080i
$446$	153409.	+	182825.i	0.771223	+	0.919108i
$447$		0			0
$448$	23162.3	−	8430.40i	0.115406	−	0.0420042i
$449$	−253305.	+	146246.i	−1.25647	+	0.725422i	−0.972386	−	0.233379i	$-0.925022\pi$
$449$	−253305.	+	146246.i	−1.25647	+	0.725422i	−0.284081	+	0.958800i	$0.591688\pi$
$450$		0			0
$451$	−77443.3	+	134136.i	−0.380742	+	0.659464i
$452$	−102174.	−	18016.0i	−0.500105	−	0.0881821i
$453$		0			0
$454$	−176613.	−	64281.9i	−0.856862	−	0.311872i
$455$	85247.4	−	15031.4i	0.411774	−	0.0726068i
$456$		0			0
$457$	184493.	+	154808.i	0.883382	+	0.741246i	0.966872	−	0.255263i	$-0.0821620\pi$
$457$	184493.	+	154808.i	0.883382	+	0.741246i	−0.0834895	+	0.996509i	$0.526606\pi$
$458$		−	127979.i		−	0.610112i
$459$		0			0
$460$	32581.5			0.153977
$461$	115718.	−	137907.i	0.544501	−	0.648911i	−0.421690	−	0.906740i	$-0.638563\pi$
$461$	115718.	−	137907.i	0.544501	−	0.648911i	0.966190	+	0.257829i	$0.0830073\pi$
$462$		0			0
$463$	−8931.84	−	50655.0i	−0.0416657	−	0.236298i	0.956862	−	0.290543i	$-0.0938360\pi$
$463$	−8931.84	−	50655.0i	−0.0416657	−	0.236298i	−0.998528	+	0.0542449i	$0.982725\pi$
$464$	31429.6	−	86352.2i	0.145983	−	0.401086i
$465$		0			0
$466$	−6406.51	+	36333.1i	−0.0295019	+	0.167313i
$467$	235524.	+	135980.i	1.07994	+	0.623506i	0.930881	−	0.365322i	$-0.119041\pi$
$467$	235524.	+	135980.i	1.07994	+	0.623506i	0.149063	+	0.988828i	$0.452374\pi$
$468$		0			0
$469$	−202661.	−	351020.i	−0.921351	−	1.59583i
$470$	63269.8	+	173832.i	0.286418	+	0.786928i
$471$		0			0
$472$	−31825.6	+	26704.8i	−0.142854	+	0.119869i
$473$	−270969.	−	322928.i	−1.21115	−	1.44339i
$474$		0			0
$475$	−91125.7	+	33167.0i	−0.403881	+	0.147001i
$476$	−1688.24	+	974.706i	−0.00745110	+	0.00430189i
$477$		0			0
$478$	−4262.80	+	7383.38i	−0.0186569	+	0.0323147i
$479$	−190297.	−	33554.6i	−0.829395	−	0.146245i	−0.257196	−	0.966359i	$-0.582799\pi$
$479$	−190297.	−	33554.6i	−0.829395	−	0.146245i	−0.572199	+	0.820114i	$0.693910\pi$
$480$		0			0
$481$	86209.6	+	31377.7i	0.372619	+	0.135622i
$482$	−38133.7	+	6724.01i	−0.164140	+	0.0289424i
$483$		0			0
$484$	−2672.20	−	2242.24i	−0.0114072	−	0.00957177i
$485$			224475.i			0.954298i
$486$		0			0
$487$	−104769.			−0.441747			−0.220874	−	0.975302i	$-0.570891\pi$
$487$	−104769.			−0.441747			−0.220874	+	0.975302i	$0.570891\pi$
$488$	−49622.1	+	59137.3i	−0.208370	+	0.248326i
$489$		0			0
$490$	−733.796	−	4161.56i	−0.00305621	−	0.0173326i
$491$	137970.	−	379070.i	0.572299	−	1.57238i	−0.228564	−	0.973529i	$-0.573403\pi$
$491$	137970.	−	379070.i	0.572299	−	1.57238i	0.800862	−	0.598848i	$-0.204375\pi$
$492$		0			0
$493$	−1262.02	+	7157.24i	−0.00519243	+	0.0294477i
$494$	−78489.2	−	45315.7i	−0.321629	−	0.185693i
$495$		0			0
$496$	−14867.0	−	25750.3i	−0.0604309	−	0.104669i
$497$	−91639.8	−	251778.i	−0.370998	−	1.01931i
$498$		0			0
$499$	345446.	−	289864.i	1.38733	−	1.16411i	0.420920	−	0.907098i	$-0.361707\pi$
$499$	345446.	−	289864.i	1.38733	−	1.16411i	0.966409	−	0.257009i	$-0.0827371\pi$
$500$	85612.4	+	102029.i	0.342450	+	0.408116i
$501$		0			0
$502$	202294.	−	73628.9i	0.802740	−	0.292173i
$503$	20579.8	−	11881.7i	0.0813401	−	0.0469617i	−0.458778	−	0.888551i	$-0.651713\pi$
$503$	20579.8	−	11881.7i	0.0813401	−	0.0469617i	0.540118	+	0.841589i	$0.318379\pi$
$504$		0			0
$505$	168860.	−	292474.i	0.662132	−	1.14685i
$506$	−75402.3	−	13295.5i	−0.294499	−	0.0519281i
$507$		0			0
$508$	−18633.4	−	6782.02i	−0.0722048	−	0.0262804i
$509$	29985.0	−	5287.17i	0.115736	−	0.0204074i	−0.115480	−	0.993310i	$-0.536841\pi$
$509$	29985.0	−	5287.17i	0.115736	−	0.0204074i	0.231216	+	0.972902i	$0.425730\pi$
$510$		0			0
$511$	−145321.	−	121939.i	−0.556527	−	0.466981i
$512$			11585.2i			0.0441942i
$513$		0			0
$514$	46232.4			0.174993
$515$	−97525.5	+	116226.i	−0.367709	+	0.438218i
$516$		0			0
$517$	−75487.9	−	428113.i	−0.282421	−	1.60169i
$518$	−42609.2	+	117068.i	−0.158797	+	0.436292i
$519$		0			0
$520$	−7064.94	+	40067.2i	−0.0261277	+	0.148178i
$521$	442592.	+	255530.i	1.63053	+	0.941385i	0.983930	+	0.178552i	$0.0571413\pi$
$521$	442592.	+	255530.i	1.63053	+	0.941385i	0.646596	+	0.762833i	$0.276192\pi$
$522$		0			0
$523$	171072.	+	296305.i	0.625426	+	1.08327i	0.988458	+	0.151493i	$0.0484079\pi$
$523$	171072.	+	296305.i	0.625426	+	1.08327i	−0.363033	+	0.931776i	$0.618259\pi$
$524$	−67314.5	−	184945.i	−0.245158	−	0.673566i
$525$		0			0
$526$	90140.1	−	75636.5i	0.325797	−	0.273376i
$527$	1511.56	+	1801.41i	0.00544259	+	0.00648622i
$528$		0			0
$529$	−214489.	+	78067.6i	−0.766468	+	0.278971i
$530$	171617.	−	99083.0i	0.610953	−	0.352734i
$531$		0			0
$532$	61536.2	−	106584.i	0.217424	−	0.376589i
$533$	128332.	+	22628.4i	0.451732	+	0.0796525i
$534$		0			0
$535$	−42797.4	−	15577.0i	−0.149524	−	0.0544221i
$536$	187612.	−	33081.0i	0.653027	−	0.115146i
$537$		0			0
$538$	284529.	+	238748.i	0.983017	+	0.824850i
$539$			9930.41i			0.0341814i
$540$		0			0
$541$	190830.			0.652007			0.326003	−	0.945369i	$-0.394298\pi$
$541$	190830.			0.652007			0.326003	+	0.945369i	$0.394298\pi$
$542$	−230433.	+	274619.i	−0.784414	+	0.934828i
$543$		0			0
$544$	−159.104	−	902.325i	−0.000537631	−	0.00304906i
$545$	57481.1	−	157928.i	0.193523	−	0.531700i
$546$		0			0
$547$	68995.4	−	391292.i	0.230593	−	1.30776i	−0.621107	−	0.783726i	$-0.713317\pi$
$547$	68995.4	−	391292.i	0.230593	−	1.30776i	0.851700	−	0.524030i	$-0.175572\pi$
$548$	118724.	+	68545.4i	0.395347	+	0.228253i
$549$		0			0
$550$	−51150.1	−	88594.5i	−0.169091	−	0.292874i
$551$	−156929.	−	431159.i	−0.516892	−	1.42015i
$552$		0			0
$553$	403422.	−	338511.i	1.31920	−	1.10694i
$554$	−36996.2	−	44090.3i	−0.120542	−	0.143656i
$555$		0			0
$556$	78059.9	−	28411.5i	0.252510	−	0.0919061i
$557$	172091.	−	99356.6i	0.554686	−	0.320248i	−0.196324	−	0.980539i	$-0.562900\pi$
$557$	172091.	−	99356.6i	0.554686	−	0.320248i	0.751010	+	0.660291i	$0.229567\pi$
$558$		0			0
$559$	−177334.	+	307152.i	−0.567504	+	0.982945i
$560$	−54409.1	−	9593.78i	−0.173498	−	0.0305924i
$561$		0			0
$562$	386775.	+	140774.i	1.22457	+	0.445709i
$563$	273565.	−	48236.8i	0.863064	−	0.152182i	0.275443	−	0.961317i	$-0.411176\pi$
$563$	273565.	−	48236.8i	0.863064	−	0.152182i	0.587622	+	0.809136i	$0.300064\pi$
$564$		0			0
$565$	178141.	+	149478.i	0.558042	+	0.468253i
$566$			353841.i			1.10453i
$567$		0			0
$568$	125933.			0.390341
$569$	2882.95	−	3435.77i	0.00890457	−	0.0106120i	−0.761574	−	0.648078i	$-0.775573\pi$
$569$	2882.95	−	3435.77i	0.00890457	−	0.0106120i	0.770478	+	0.637466i	$0.220017\pi$
$570$		0			0
$571$	−13365.1	−	75797.2i	−0.0409921	−	0.232478i	0.957428	−	0.288673i	$-0.0932141\pi$
$571$	−13365.1	−	75797.2i	−0.0409921	−	0.232478i	−0.998420	+	0.0561956i	$0.982103\pi$
$572$	32700.3	−	89843.4i	0.0999447	−	0.274596i
$573$		0			0
$574$	−30728.1	+	174268.i	−0.0932635	+	0.528924i
$575$	59691.1	+	34462.7i	0.180540	+	0.104235i
$576$		0			0
$577$	−86539.0	−	149890.i	−0.259932	−	0.450216i	0.706291	−	0.707921i	$-0.250367\pi$
$577$	−86539.0	−	149890.i	−0.259932	−	0.450216i	−0.966224	+	0.257705i	$0.917034\pi$
$578$	−80771.7	−	221918.i	−0.241771	−	0.664259i
$579$		0			0
$580$	−157785.	+	132397.i	−0.469039	+	0.393570i
$581$	−60848.1	−	72516.0i	−0.180258	−	0.214823i
$582$		0			0
$583$	−437600.	+	159273.i	−1.28748	+	0.468604i
$584$	77216.9	−	44581.2i	0.226405	−	0.130715i
$585$		0			0
$586$	89864.1	−	155649.i	0.261692	−	0.453264i
$587$	−308437.	−	54385.7i	−0.895137	−	0.157837i	−0.292890	−	0.956146i	$-0.594617\pi$
$587$	−308437.	−	54385.7i	−0.895137	−	0.157837i	−0.602248	+	0.798309i	$0.705728\pi$
$588$		0			0
$589$	−139509.	−	50777.1i	−0.402135	−	0.146365i
$590$	91705.8	−	16170.2i	0.263447	−	0.0464527i
$591$		0			0
$592$	−44855.3	−	37638.1i	−0.127988	−	0.107395i
$593$		−	410290.i		−	1.16676i	−0.812199	−	0.583380i	$-0.801730\pi$
$593$		−	410290.i		−	1.16676i	0.812199	−	0.583380i	$-0.198270\pi$
$594$		0			0
$595$	4369.45			0.0123422
$596$	−25728.2	+	30661.7i	−0.0724297	+	0.0863184i
$597$		0			0
$598$	11186.0	+	63438.8i	0.0312803	+	0.177399i
$599$	26474.4	−	72737.9i	0.0737858	−	0.202725i	−0.897317	−	0.441387i	$-0.854487\pi$
$599$	26474.4	−	72737.9i	0.0737858	−	0.202725i	0.971103	+	0.238662i	$0.0767088\pi$
$600$		0			0
$601$	−46628.7	+	264444.i	−0.129093	+	0.732125i	0.849699	+	0.527269i	$0.176784\pi$
$601$	−46628.7	+	264444.i	−0.129093	+	0.732125i	−0.978792	+	0.204856i	$0.934327\pi$
$602$	−417095.	−	240810.i	−1.15091	−	0.664479i
$603$		0			0
$604$	13370.7	+	23158.8i	0.0366506	+	0.0634808i
$605$	2674.18	+	7347.24i	0.00730599	+	0.0200730i
$606$		0			0
$607$	136211.	−	114295.i	0.369687	−	0.310205i	−0.438950	−	0.898511i	$-0.644650\pi$
$607$	136211.	−	114295.i	0.369687	−	0.310205i	0.808638	+	0.588307i	$0.200205\pi$
$608$	37182.3	+	44312.2i	0.100584	+	0.119871i
$609$		0			0
$610$	162598.	−	59181.0i	0.436975	−	0.159046i
$611$	−316744.	+	182872.i	−0.848448	+	0.489852i
$612$		0			0
$613$	−177502.	+	307442.i	−0.472370	+	0.818168i	−0.999500	−	0.0316162i	$-0.989935\pi$
$613$	−177502.	+	307442.i	−0.472370	+	0.818168i	0.527130	+	0.849784i	$0.323268\pi$
$614$	−297631.	−	52480.3i	−0.789480	−	0.139207i
$615$		0			0
$616$	122002.	+	44405.2i	0.321519	+	0.117023i
$617$	−62952.0	+	11100.1i	−0.165363	+	0.0291580i	−0.255717	−	0.966752i	$-0.582311\pi$
$617$	−62952.0	+	11100.1i	−0.165363	+	0.0291580i	0.0903534	+	0.995910i	$0.471200\pi$
$618$		0			0
$619$	−417402.	−	350242.i	−1.08937	−	0.914086i	−0.0927009	−	0.995694i	$-0.529550\pi$
$619$	−417402.	−	350242.i	−1.08937	−	0.914086i	−0.996665	+	0.0816079i	$0.973994\pi$
$620$			66646.2i			0.173377i
$621$		0			0
$622$	−239889.			−0.620054
$623$	41048.4	−	48919.6i	0.105760	−	0.126040i
$624$		0			0
$625$	−18904.4	−	107212.i	−0.0483953	−	0.274464i
$626$	−110066.	+	302405.i	−0.280871	+	0.771686i
$627$		0			0
$628$	−57093.2	+	323792.i	−0.144765	+	0.821006i
$629$	4010.49	+	2315.46i	0.0101367	+	0.00585241i
$630$		0			0
$631$	139247.	+	241183.i	0.349726	+	0.605743i	0.986201	−	0.165554i	$-0.0529414\pi$
$631$	139247.	+	241183.i	0.349726	+	0.605743i	−0.636475	+	0.771298i	$0.719608\pi$
$632$	84657.5	+	232595.i	0.211949	+	0.582325i
$633$		0			0
$634$	−290921.	+	244112.i	−0.723763	+	0.607309i
$635$	28569.2	+	34047.4i	0.0708517	+	0.0844378i
$636$		0			0
$637$	7850.96	−	2857.52i	0.0193484	−	0.00704223i
$638$	419183.	−	242015.i	1.02982	−	0.594568i
$639$		0			0
$640$	12983.7	−	22488.4i	0.0316984	−	0.0549033i
$641$	270808.	+	47750.7i	0.659090	+	0.116215i	0.493182	−	0.869926i	$-0.335833\pi$
$641$	270808.	+	47750.7i	0.659090	+	0.116215i	0.165908	+	0.986141i	$0.446945\pi$
$642$		0			0
$643$	493747.	+	179709.i	1.19421	+	0.434659i	0.861202	−	0.508264i	$-0.169712\pi$
$643$	493747.	+	179709.i	1.19421	+	0.434659i	0.333013	+	0.942922i	$0.391935\pi$
$644$	−86146.2	+	15189.9i	−0.207713	+	0.0366255i
$645$		0			0
$646$	−3504.53	−	2940.65i	−0.00839778	−	0.00704658i
$647$		−	180771.i		−	0.431838i	−0.976411	−	0.215919i	$-0.930725\pi$
$647$		−	180771.i		−	0.431838i	0.976411	−	0.215919i	$-0.0692748\pi$
$648$		0			0
$649$	−218830.			−0.519539
$650$	−55324.0	+	65932.6i	−0.130944	+	0.156053i
$651$		0			0
$652$	40858.1	+	231718.i	0.0961132	+	0.545085i
$653$	−12896.6	+	35433.2i	−0.0302448	+	0.0830968i	−0.953896	−	0.300137i	$-0.902968\pi$
$653$	−12896.6	+	35433.2i	−0.0302448	+	0.0830968i	0.923651	+	0.383234i	$0.125190\pi$
$654$		0			0
$655$	−76603.8	+	434442.i	−0.178553	+	1.01263i
$656$	−72028.5	−	41585.7i	−0.167377	−	0.0966353i
$657$		0			0
$658$	−248330.	−	430120.i	−0.573558	−	0.993431i
$659$	264024.	+	725399.i	0.607956	+	1.67034i	0.734686	+	0.678407i	$0.237329\pi$
$659$	264024.	+	725399.i	0.607956	+	1.67034i	−0.126731	+	0.991937i	$0.540448\pi$
$660$		0			0
$661$	−441083.	+	370113.i	−1.00953	+	0.847094i	−0.988276	−	0.152681i	$-0.951209\pi$
$661$	−441083.	+	370113.i	−1.00953	+	0.847094i	−0.0212513	+	0.999774i	$0.506765\pi$
$662$	66201.6	+	78896.0i	0.151061	+	0.180028i
$663$		0			0
$664$	41809.4	−	15217.4i	0.0948282	−	0.0345146i
$665$	−238899.	+	137928.i	−0.540220	+	0.311896i
$666$		0			0
$667$	−163059.	+	282427.i	−0.366517	+	0.634826i
$668$	−23017.3	−	4058.57i	−0.0515823	−	0.00909535i
$669$		0			0
$670$	−401252.	−	146044.i	−0.893857	−	0.325337i
$671$	−400446.	+	70609.4i	−0.889404	+	0.156826i
$672$		0			0
$673$	190283.	+	159667.i	0.420117	+	0.352520i	0.828208	−	0.560421i	$-0.189361\pi$
$673$	190283.	+	159667.i	0.420117	+	0.352520i	−0.408091	+	0.912941i	$0.633805\pi$
$674$			115907.i			0.255146i
$675$		0			0
$676$	148048.			0.323974
$677$	323473.	−	385501.i	0.705767	−	0.841100i	−0.287399	−	0.957811i	$-0.592791\pi$
$677$	323473.	−	385501.i	0.705767	−	0.841100i	0.993166	+	0.116711i	$0.0372351\pi$
$678$		0			0
$679$	−104653.	−	593516.i	−0.226993	−	1.28734i
$680$	−702.403	+	1929.84i	−0.00151904	+	0.00417352i
$681$		0			0
$682$	27196.2	−	154237.i	0.0584708	−	0.331604i
$683$	−217929.	−	125822.i	−0.467169	−	0.269720i	0.247885	−	0.968790i	$-0.420265\pi$
$683$	−217929.	−	125822.i	−0.467169	−	0.269720i	−0.715054	+	0.699069i	$0.753598\pi$
$684$		0			0
$685$	−153639.	−	266111.i	−0.327431	−	0.567128i
$686$	115699.	+	317881.i	0.245857	+	0.675487i
$687$		0			0
$688$	173407.	−	145506.i	0.366344	−	0.307399i
$689$	251842.	+	300134.i	0.530506	+	0.632232i
$690$		0			0
$691$	226988.	−	82616.7i	0.475385	−	0.173026i	−0.0932049	−	0.995647i	$-0.529711\pi$
$691$	226988.	−	82616.7i	0.475385	−	0.173026i	0.568590	+	0.822621i	$0.307489\pi$
$692$	132987.	−	76780.3i	0.277714	−	0.160338i
$693$		0			0
$694$	−103084.	+	178547.i	−0.214029	+	0.370708i
$695$	−183365.	−	32332.2i	−0.379618	−	0.0669369i
$696$		0			0
$697$	6181.11	+	2249.74i	0.0127233	+	0.00463091i
$698$	345676.	−	60952.1i	0.709511	−	0.125106i
$699$		0			0
$700$	−89532.7	−	75126.9i	−0.182720	−	0.153320i
$701$			491195.i			0.999580i	0.866146	+	0.499790i	$0.166590\pi$
$701$			491195.i			0.999580i	−0.866146	+	0.499790i	$0.833410\pi$
$702$		0			0
$703$	−292364.			−0.591579
$704$	−39224.5	+	46745.9i	−0.0791429	+	0.0943189i
$705$		0			0
$706$	−69832.0	−	396037.i	−0.140102	−	0.794559i
$707$	−310115.	+	852034.i	−0.620417	+	1.70458i
$708$		0			0
$709$	83224.2	−	471988.i	0.165561	−	0.938942i	−0.782924	−	0.622118i	$-0.786272\pi$
$709$	83224.2	−	471988.i	0.165561	−	0.938942i	0.948484	−	0.316824i	$-0.102616\pi$
$710$	−244452.	−	141135.i	−0.484928	−	0.279973i
$711$		0			0
$712$	15007.5	+	25993.7i	0.0296038	+	0.0512752i
$713$	36090.4	+	99157.6i	0.0709926	+	0.195051i
$714$		0			0
$715$	−164164.	+	137750.i	−0.321118	+	0.269450i
$716$	−29723.9	−	35423.6i	−0.0579802	−	0.0690981i
$717$		0			0
$718$	−220598.	+	80291.1i	−0.427910	+	0.155747i
$719$	−585223.	+	337879.i	−1.13205	+	0.653587i	−0.944448	−	0.328660i	$-0.893403\pi$
$719$	−585223.	+	337879.i	−1.13205	+	0.653587i	−0.187597	+	0.982246i	$0.560070\pi$
$720$		0			0
$721$	203673.	−	352773.i	0.391800	−	0.678617i
$722$	−78567.7	−	13853.6i	−0.150720	−	0.0265759i
$723$		0			0
$724$	67758.8	+	24662.2i	0.129267	+	0.0470495i
$725$	−429112.	+	75664.0i	−0.816384	+	0.143950i
$726$		0			0
$727$	−477875.	−	400985.i	−0.904161	−	0.758681i	0.0668385	−	0.997764i	$-0.478709\pi$
$727$	−477875.	−	400985.i	−0.904161	−	0.758681i	−0.970999	+	0.239083i	$0.923153\pi$
$728$		−	109233.i		−	0.206105i
$729$		0			0
$730$	−199850.			−0.375024
$731$	−11507.6	+	13714.3i	−0.0215353	+	0.0256648i
$732$		0			0
$733$	112805.	+	639748.i	0.209952	+	1.19070i	0.889455	+	0.457024i	$0.151085\pi$
$733$	112805.	+	639748.i	0.209952	+	1.19070i	−0.679503	+	0.733673i	$0.737804\pi$
$734$	−27039.5	+	74290.4i	−0.0501888	+	0.137893i
$735$		0			0
$736$	7139.43	−	40489.7i	0.0131798	−	0.0747462i
$737$	869010.	+	501723.i	1.59989	+	0.923696i
$738$		0			0
$739$	253872.	+	439719.i	0.464864	+	0.805168i	0.999195	−	0.0401070i	$-0.0127699\pi$
$739$	253872.	+	439719.i	0.464864	+	0.805168i	−0.534331	+	0.845275i	$0.679437\pi$
$740$	44888.4	+	123330.i	0.0819730	+	0.225219i
$741$		0			0
$742$	−407565.	+	341988.i	−0.740268	+	0.621159i
$743$	143429.	+	170932.i	0.259813	+	0.309633i	0.880144	−	0.474708i	$-0.157446\pi$
$743$	143429.	+	170932.i	0.259813	+	0.309633i	−0.620331	+	0.784340i	$0.713002\pi$
$744$		0			0
$745$	84304.5	−	30684.3i	0.151893	−	0.0552846i
$746$	333303.	−	192432.i	0.598909	−	0.345780i
$747$		0			0
$748$	2413.05	−	4179.53i	0.00431284	−	0.00747006i
$749$	120419.	+	21233.2i	0.214651	+	0.0378488i
$750$		0			0
$751$	175471.	+	63866.3i	0.311119	+	0.113238i	0.492861	−	0.870108i	$-0.335951\pi$
$751$	175471.	+	63866.3i	0.311119	+	0.113238i	−0.181742	+	0.983346i	$0.558174\pi$
$752$	229889.	−	40535.7i	0.406521	−	0.0716806i
$753$		0			0
$754$	−311958.	−	261764.i	−0.548724	−	0.460434i
$755$		−	59938.8i		−	0.105151i
$756$		0			0
$757$	1.07794e6			1.88105			0.940526	−	0.339721i	$-0.110332\pi$
$757$	1.07794e6			1.88105			0.940526	+	0.339721i	$0.110332\pi$
$758$	325985.	−	388493.i	0.567360	−	0.676153i
$759$		0			0
$760$	−22514.5	−	127686.i	−0.0389794	−	0.221063i
$761$	169945.	−	466920.i	0.293453	−	0.806256i	−0.702102	−	0.712076i	$-0.747755\pi$
$761$	169945.	−	466920.i	0.293453	−	0.806256i	0.995555	−	0.0941798i	$-0.0300228\pi$
$762$		0			0
$763$	−78353.3	+	444364.i	−0.134589	+	0.763290i
$764$	−240276.	−	138723.i	−0.411645	−	0.237664i
$765$		0			0
$766$	136268.	+	236024.i	0.232240	+	0.402252i
$767$	62969.3	+	173007.i	0.107038	+	0.294085i
$768$		0			0
$769$	−849149.	+	712520.i	−1.43592	+	1.20488i	−0.493817	+	0.869566i	$0.664399\pi$
$769$	−849149.	+	712520.i	−1.43592	+	1.20488i	−0.942106	+	0.335316i	$0.891157\pi$
$770$	−187056.	−	222925.i	−0.315494	−	0.375991i
$771$		0			0
$772$	395955.	−	144116.i	0.664372	−	0.241812i
$773$	355140.	−	205040.i	0.594348	−	0.343147i	−0.172467	−	0.985015i	$-0.555174\pi$
$773$	355140.	−	205040.i	0.594348	−	0.343147i	0.766815	+	0.641869i	$0.221841\pi$
$774$		0			0
$775$	−70494.2	+	122100.i	−0.117368	+	0.203287i
$776$	278959.	+	49188.1i	0.463252	+	0.0816839i
$777$		0			0
$778$	119561.	+	43516.7i	0.197529	+	0.0718946i
$779$	−408968.	+	72112.0i	−0.673929	+	0.118832i
$780$		0			0
$781$	508135.	+	426376.i	0.833062	+	0.699022i
$782$			3251.62i			0.00531724i
$783$		0			0
$784$	−5332.45			−0.00867551
$785$	473701.	−	564535.i	0.768715	−	0.916118i
$786$		0			0
$787$	33938.8	+	192476.i	0.0547957	+	0.310762i	0.999871	−	0.0160921i	$-0.00512251\pi$
$787$	33938.8	+	192476.i	0.0547957	+	0.310762i	−0.945075	+	0.326854i	$0.894011\pi$
$788$	54404.0	−	149474.i	0.0876150	−	0.240720i
$789$		0			0
$790$	96340.1	−	546372.i	0.154366	−	0.875455i
$791$	−540698.	−	312172.i	−0.864174	−	0.498931i
$792$		0			0
$793$	171054.	+	296274.i	0.272011	+	0.471137i
$794$	−25598.9	−	70332.5i	−0.0406051	−	0.111562i
$795$		0			0
$796$	−273855.	+	229791.i	−0.432209	+	0.362667i
$797$	−342316.	−	407956.i	−0.538902	−	0.642239i	0.426039	−	0.904705i	$-0.359909\pi$
$797$	−342316.	−	407956.i	−0.538902	−	0.642239i	−0.964941	+	0.262466i	$0.915464\pi$
$798$		0			0
$799$	−17348.4	+	6314.30i	−0.0271748	+	0.00989081i
$800$	47573.7	−	27466.7i	0.0743339	−	0.0429167i
$801$		0			0
$802$	136344.	−	236154.i	0.211976	−	0.367153i
$803$	462507.	+	81552.5i	0.717278	+	0.126475i
$804$		0			0
$805$	184244.	+	67059.4i	0.284316	+	0.103483i
$806$	−129765.	+	22881.1i	−0.199751	+	0.0352215i
$807$		0			0
$808$	−326462.	−	273934.i	−0.500046	−	0.419589i
$809$			222506.i			0.339973i	0.985446	+	0.169986i	$0.0543724\pi$
$809$			222506.i			0.339973i	−0.985446	+	0.169986i	$0.945628\pi$
$810$		0			0
$811$	794343.			1.20772			0.603860	−	0.797090i	$-0.293628\pi$
$811$	794343.			1.20772			0.603860	+	0.797090i	$0.293628\pi$
$812$	355461.	−	423622.i	0.539113	−	0.642490i
$813$		0			0
$814$	−53556.8	−	303736.i	−0.0808288	−	0.458403i
$815$	180378.	−	495583.i	0.271561	−	0.746108i
$816$		0			0
$817$	196267.	−	1.11308e6i	0.294037	−	1.66757i
$818$	−425448.	−	245633.i	−0.635829	−	0.367096i
$819$		0			0
$820$	93210.9	+	161446.i	0.138624	+	0.240104i
$821$	120811.	+	331924.i	0.179233	+	0.492439i	0.996478	−	0.0838510i	$-0.0267220\pi$
$821$	120811.	+	331924.i	0.179233	+	0.492439i	−0.817245	+	0.576290i	$0.804500\pi$
$822$		0			0
$823$	−622240.	+	522121.i	−0.918667	+	0.770853i	−0.973748	−	0.227629i	$-0.926903\pi$
$823$	−622240.	+	522121.i	−0.918667	+	0.770853i	0.0550813	+	0.998482i	$0.482458\pi$
$824$	123067.	+	146665.i	0.181253	+	0.216009i
$825$		0			0
$826$	−234933.	+	85508.8i	−0.344338	+	0.125329i
$827$	−1639.65	+	946.652i	−0.00239740	+	0.00138414i	−0.501198	−	0.865333i	$-0.667107\pi$
$827$	−1639.65	+	946.652i	−0.00239740	+	0.00138414i	0.498801	+	0.866717i	$0.333774\pi$
$828$		0			0
$829$	375740.	−	650801.i	0.546737	−	0.946976i	−0.451758	−	0.892140i	$-0.649203\pi$
$829$	375740.	−	650801.i	0.546737	−	0.946976i	0.998495	−	0.0548361i	$-0.0174636\pi$
$830$	−98211.5	−	17317.3i	−0.142563	−	0.0251377i
$831$		0			0
$832$	48244.3	+	17559.5i	0.0696946	+	0.0253668i
$833$	415.322	−	73.2325i	0.000598543	−	0.000105539i
$834$		0			0
$835$	40130.9	+	33673.9i	0.0575581	+	0.0482970i
$836$			304687.i			0.435955i
$837$		0			0
$838$	334473.			0.476292
$839$	−332577.	+	396349.i	−0.472463	+	0.563059i	−0.948668	−	0.316275i	$-0.897568\pi$
$839$	−332577.	+	396349.i	−0.472463	+	0.563059i	0.476205	+	0.879335i	$0.342012\pi$
$840$		0			0
$841$	−235184.	−	1.33380e6i	−0.332519	−	1.88581i
$842$	26152.2	−	71852.7i	0.0368880	−	0.101349i
$843$		0			0
$844$	−57137.6	+	324043.i	−0.0802116	+	0.454903i
$845$	−287380.	−	165919.i	−0.402479	−	0.232372i
$846$		0			0
$847$	−10496.0	−	18179.5i	−0.0146304	−	0.0253405i
$848$	−85526.9	−	234983.i	−0.118935	−	0.326772i
$849$		0			0
$850$	−3328.10	+	2792.61i	−0.00460637	+	0.00386520i
$851$	133572.	+	159185.i	0.184440	+	0.219808i
$852$		0			0
$853$	1.04281e6	−	379551.i	1.43320	−	0.521641i	0.495351	−	0.868693i	$-0.335039\pi$
$853$	1.04281e6	−	379551.i	1.43320	−	0.521641i	0.937846	+	0.347051i	$0.112817\pi$
$854$	−402323.	+	232281.i	−0.551644	+	0.318492i
$855$		0			0
$856$	−28735.8	+	49771.9i	−0.0392171	+	0.0679261i
$857$	9302.46	+	1640.27i	0.0126659	+	0.00223334i	0.179978	−	0.983671i	$-0.442397\pi$
$857$	9302.46	+	1640.27i	0.0126659	+	0.00223334i	−0.167312	+	0.985904i	$0.553509\pi$
$858$		0			0
$859$	966828.	+	351897.i	1.31028	+	0.476902i	0.900330	−	0.435208i	$-0.143325\pi$
$859$	966828.	+	351897.i	1.31028	+	0.476902i	0.409946	+	0.912110i	$0.365547\pi$
$860$	−499674.	+	88106.0i	−0.675600	+	0.119127i
$861$		0			0
$862$	524187.	+	439845.i	0.705459	+	0.591950i
$863$		−	1.42253e6i		−	1.91002i	−0.296570	−	0.955011i	$-0.595843\pi$
$863$		−	1.42253e6i		−	1.91002i	0.296570	−	0.955011i	$-0.404157\pi$
$864$		0			0
$865$	−344194.			−0.460014
$866$	111384.	−	132742.i	0.148520	−	0.177000i
$867$		0			0
$868$	−31071.3	−	176214.i	−0.0412401	−	0.233884i
$869$	−445913.	+	1.22514e6i	−0.590488	+	1.62235i
$870$		0			0
$871$	146600.	−	831411.i	0.193240	−	1.09592i
$872$	−183665.	−	106039.i	−0.241542	−	0.139454i
$873$		0			0
$874$	−102642.	−	177782.i	−0.134371	−	0.232737i
$875$	274131.	+	753168.i	0.358048	+	0.983730i
$876$		0			0
$877$	−861044.	+	722502.i	−1.11951	+	0.939377i	−0.998579	−	0.0532848i	$-0.983031\pi$
$877$	−861044.	+	722502.i	−1.11951	+	0.939377i	−0.120926	+	0.992661i	$0.538586\pi$
$878$	−260791.	−	310798.i	−0.338301	−	0.403171i
$879$		0			0
$880$	128528.	−	46780.5i	0.165971	−	0.0604087i
$881$	−264055.	+	152452.i	−0.340206	+	0.196418i	−0.660363	−	0.750946i	$-0.729598\pi$
$881$	−264055.	+	152452.i	−0.340206	+	0.196418i	0.320157	+	0.947365i	$0.396264\pi$
$882$		0			0
$883$	202244.	−	350298.i	0.259391	−	0.449279i	−0.706688	−	0.707525i	$-0.749811\pi$
$883$	202244.	−	350298.i	0.259391	−	0.449279i	0.966079	+	0.258247i	$0.0831448\pi$
$884$	−3998.70	−	705.078i	−0.00511698	−	0.000902262i
$885$		0			0
$886$	64858.1	+	23606.4i	0.0826222	+	0.0300720i
$887$	386018.	−	68065.3i	0.490636	−	0.0865124i	0.0771439	−	0.997020i	$-0.475420\pi$
$887$	386018.	−	68065.3i	0.490636	−	0.0865124i	0.413493	+	0.910508i	$0.364309\pi$
$888$		0			0
$889$	−91410.9	−	76702.9i	−0.115663	−	0.0970528i
$890$		−	67276.0i		−	0.0849337i
$891$		0			0
$892$	−675036.			−0.848394
$893$	749201.	−	892863.i	0.939498	−	1.11965i
$894$		0			0
$895$	17998.3	+	102073.i	0.0224691	+	0.127429i
$896$	−23844.8	+	65513.0i	−0.0297014	+	0.0816040i
$897$		0			0
$898$	143658.	−	814722.i	0.178146	−	1.01032i
$899$	−577711.	−	333542.i	−0.714811	−	0.412696i
$900$		0			0
$901$	9888.44	+	17127.3i	0.0121809	+	0.0210979i
$902$	−149834.	−	411666.i	−0.184161	−	0.505978i
$903$		0			0
$904$	224795.	−	188625.i	0.275074	−	0.230814i
$905$	−103889.	−	123810.i	−0.126845	−	0.151168i
$906$		0			0
$907$	−616086.	+	224237.i	−0.748904	+	0.272579i	−0.688145	−	0.725573i	$-0.741575\pi$
$907$	−616086.	+	224237.i	−0.748904	+	0.272579i	−0.0607598	+	0.998152i	$0.519352\pi$
$908$	460376.	−	265798.i	0.558394	−	0.322389i
$909$		0			0
$910$	−122418.	+	212034.i	−0.147830	+	0.256049i
$911$	159621.	+	28145.5i	0.192333	+	0.0339135i	0.268985	−	0.963144i	$-0.413312\pi$
$911$	159621.	+	28145.5i	0.192333	+	0.0339135i	−0.0766518	+	0.997058i	$0.524423\pi$
$912$		0			0
$913$	220221.	+	80153.9i	0.264190	+	0.0961575i
$914$	−670847.	+	118288.i	−0.803029	+	0.141596i
$915$		0			0
$916$	277293.	+	232677.i	0.330482	+	0.277308i
$917$		−	1.18439e6i		−	1.40849i
$918$		0			0
$919$	−1.56762e6			−1.85614			−0.928068	−	0.372410i	$-0.878532\pi$
$919$	−1.56762e6			−1.85614			−0.928068	+	0.372410i	$0.878532\pi$
$920$	−59235.7	+	70594.4i	−0.0699855	+	0.0834054i
$921$		0			0
$922$	88419.5	+	501452.i	0.104013	+	0.589885i
$923$	190874.	−	524423.i	0.224049	−	0.615571i
$924$		0			0
$925$	−48212.6	+	273428.i	−0.0563479	+	0.319565i
$926$	125993.	+	72742.1i	0.146935	+	0.0848328i
$927$		0			0
$928$	129958.	+	225094.i	0.150906	+	0.261377i
$929$	−123118.	−	338263.i	−0.142656	−	0.391943i	0.847703	−	0.530472i	$-0.177985\pi$
$929$	−123118.	−	338263.i	−0.142656	−	0.391943i	−0.990359	+	0.138528i	$0.955763\pi$
$930$		0			0
$931$	−20396.0	+	17114.3i	−0.0235313	+	0.0197451i
$932$	−67075.5	−	79937.4i	−0.0772204	−	0.0920276i
$933$		0			0
$934$	−722828.	+	263088.i	−0.828593	+	0.301583i
$935$	−9368.07	+	5408.66i	−0.0107159	+	0.00618681i
$936$		0			0
$937$	23264.3	−	40295.0i	0.0264979	−	0.0458957i	−0.852472	−	0.522772i	$-0.824898\pi$
$937$	23264.3	−	40295.0i	0.0264979	−	0.0458957i	0.878970	+	0.476877i	$0.158231\pi$
$938$	1.12901e6	+	199075.i	1.28319	+	0.226261i
$939$		0			0
$940$	−491672.	−	178954.i	−0.556442	−	0.202528i
$941$	117882.	−	20785.8i	0.133128	−	0.0234740i	−0.106687	−	0.994293i	$-0.534024\pi$
$941$	117882.	−	20785.8i	0.133128	−	0.0234740i	0.239815	+	0.970819i	$0.422913\pi$
$942$		0			0
$943$	226108.	+	189727.i	0.254268	+	0.213356i
$944$		−	117508.i		−	0.131863i
$945$		0			0
$946$	1.19233e6			1.33234
$947$	−1.09092e6	+	1.30011e6i	−1.21645	+	1.44971i	−0.360415	+	0.932792i	$0.617365\pi$
$947$	−1.09092e6	+	1.30011e6i	−1.21645	+	1.44971i	−0.856035	+	0.516917i	$0.827080\pi$
$948$		0			0
$949$	−68613.1	−	389124.i	−0.0761860	−	0.432072i
$950$	93810.6	−	257742.i	0.103945	−	0.285587i
$951$		0			0
$952$	957.456	−	5430.00i	0.00105644	−	0.00599137i
$953$	1.47148e6	+	849557.i	1.62019	+	0.935420i	0.986867	+	0.161536i	$0.0516447\pi$
$953$	1.47148e6	+	849557.i	1.62019	+	0.935420i	0.633327	+	0.773884i	$0.281689\pi$
$954$		0			0
$955$	310937.	+	538559.i	0.340930	+	0.590509i
$956$	−8247.48	−	22659.8i	−0.00902414	−	0.0247936i
$957$		0			0
$958$	418678.	−	351313.i	0.456194	−	0.382792i
$959$	530289.	+	631974.i	0.576601	+	0.687167i
$960$		0			0
$961$	664997.	−	242039.i	0.720067	−	0.262083i
$962$	−224722.	+	129743.i	−0.242826	+	0.140196i
$963$		0			0
$964$	54761.2	−	94849.2i	0.0589276	−	0.102066i
$965$	−930111.	−	164004.i	−0.998804	−	0.176116i
$966$		0			0
$967$	555901.	+	202331.i	0.594490	+	0.216377i	0.621703	−	0.783253i	$-0.286441\pi$
$967$	555901.	+	202331.i	0.594490	+	0.216377i	−0.0272134	+	0.999630i	$0.508663\pi$
$968$	9716.54	−	1713.29i	0.0103696	−	0.00182844i
$969$		0			0
$970$	−486370.	−	408113.i	−0.516920	−	0.433747i
$971$		−	1.16818e6i		−	1.23900i	−0.784997	−	0.619500i	$-0.787335\pi$
$971$		−	1.16818e6i		−	1.23900i	0.784997	−	0.619500i	$-0.212665\pi$
$972$		0			0
$973$	499895.			0.528023
$974$	190478.	−	227002.i	0.200783	−	0.239283i
$975$		0			0
$976$	−37916.0	−	215032.i	−0.0398037	−	0.225738i
$977$	−389301.	+	1.06960e6i	−0.407846	+	1.12055i	0.550475	+	0.834852i	$0.314447\pi$
$977$	−389301.	+	1.06960e6i	−0.407846	+	1.12055i	−0.958320	+	0.285696i	$0.907775\pi$
$978$		0			0
$979$	−27453.2	+	155695.i	−0.0286436	+	0.162446i
$980$	10351.0	+	5976.13i	0.0107778	+	0.00622254i
$981$		0			0
$982$	570491.	+	988120.i	0.591597	+	1.02468i
$983$	−196845.	−	540827.i	−0.203712	−	0.559695i	0.795199	−	0.606349i	$-0.207366\pi$
$983$	−196845.	−	540827.i	−0.203712	−	0.559695i	−0.998911	+	0.0466541i	$0.985144\pi$
$984$		0			0
$985$	−273122.	+	229176.i	−0.281503	+	0.236209i
$986$	−13213.2	−	15746.8i	−0.0135911	−	0.0161972i
$987$		0			0
$988$	240885.	−	87675.0i	0.246772	−	0.0898177i
$989$	−695714.	+	401671.i	−0.711276	+	0.410656i
$990$		0			0
$991$	−25198.9	+	43645.7i	−0.0256586	+	0.0444421i	−0.878570	−	0.477614i	$-0.841502\pi$
$991$	−25198.9	+	43645.7i	−0.0256586	+	0.0444421i	0.852911	+	0.522056i	$0.174835\pi$
$992$	82822.6	+	14603.9i	0.0841638	+	0.0148403i
$993$		0			0
$994$	712136.	+	259196.i	0.720759	+	0.262335i
$995$	789115.	−	139142.i	0.797066	−	0.140544i
$996$		0			0
$997$	−869808.	−	729855.i	−0.875050	−	0.734254i	0.0901049	−	0.995932i	$-0.471280\pi$
$997$	−869808.	−	729855.i	−0.875050	−	0.734254i	−0.965155	+	0.261678i	$0.915724\pi$
$998$			1.27547e6i			1.28059i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.35.3		72
3.2	odd	2		54.5.f.a.11.8	yes	72
27.5	odd	18	inner	162.5.f.a.125.3		72
27.22	even	9		54.5.f.a.5.8	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.5.8	✓	72	27.22	even	9
54.5.f.a.11.8	yes	72	3.2	odd	2
162.5.f.a.35.3		72	1.1	even	1	trivial
162.5.f.a.125.3		72	27.5	odd	18	inner

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-6.13288 + 16.8500i) q^{5} +(8.35982 - 47.4109i) q^{7} +(19.5959 + 11.3137i) q^{8} +O(q^{10})\)	\(q+(-1.81808 + 2.16670i) q^{2} +(-1.38919 - 7.87846i) q^{4} +(-6.13288 + 16.8500i) q^{5} +(8.35982 - 47.4109i) q^{7} +(19.5959 + 11.3137i) q^{8} +(-25.3588 - 43.9227i) q^{10} +(40.7635 + 111.997i) q^{11} +(76.8147 - 64.4552i) q^{13} +(87.5264 + 104.310i) q^{14} +(-60.1403 + 21.8893i) q^{16} +(4.38346 - 2.53079i) q^{17} +(-159.777 + 276.742i) q^{19} +(141.271 + 24.9100i) q^{20} +(-316.775 - 115.297i) q^{22} +(223.676 - 39.4401i) q^{23} +(232.469 + 195.065i) q^{25} +283.619i q^{26} -385.138 q^{28} +(-922.944 + 1099.92i) q^{29} +(80.6757 + 457.534i) q^{31} +(61.9123 - 170.103i) q^{32} +(-2.48600 + 14.0988i) q^{34} +(747.602 + 431.628i) q^{35} +(457.456 + 792.338i) q^{37} +(-309.130 - 849.327i) q^{38} +(-310.815 + 260.805i) q^{40} +(835.336 + 995.515i) q^{41} +(-3323.67 + 1209.72i) q^{43} +(825.735 - 476.738i) q^{44} +(-321.206 + 556.344i) q^{46} +(-3592.02 - 633.370i) q^{47} +(78.2948 + 28.4970i) q^{49} +(-845.294 + 149.048i) q^{50} +(-614.517 - 515.641i) q^{52} +3907.25i q^{53} -2137.14 q^{55} +(700.212 - 834.480i) q^{56} +(-705.217 - 3999.49i) q^{58} +(-627.970 + 1725.33i) q^{59} +(-592.438 + 3359.88i) q^{61} +(-1138.01 - 657.033i) q^{62} +(256.000 + 443.405i) q^{64} +(614.971 + 1689.62i) q^{65} +(6449.53 - 5411.80i) q^{67} +(-26.0282 - 31.0192i) q^{68} +(-2294.41 + 835.096i) q^{70} +(4819.88 - 2782.76i) q^{71} +(1970.23 - 3412.54i) q^{73} +(-2548.45 - 449.360i) q^{74} +(2402.26 + 874.351i) q^{76} +(5650.65 - 996.362i) q^{77} +(8379.78 + 7031.47i) q^{79} -1147.61i q^{80} -3675.69 q^{82} +(1263.92 - 1506.28i) q^{83} +(15.7605 + 89.3822i) q^{85} +(3421.60 - 9400.76i) q^{86} +(-468.301 + 2655.87i) q^{88} +(1148.77 + 663.242i) q^{89} +(-2413.72 - 4180.69i) q^{91} +(-621.455 - 1707.43i) q^{92} +(7902.89 - 6631.31i) q^{94} +(-3683.19 - 4389.46i) q^{95} +(11763.6 - 4281.60i) q^{97} +(-204.090 + 117.832i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 72 * q + 18 * q^5	\( 72 q + 18 q^{5} - 720 q^{11} + 288 q^{14} - 288 q^{20} - 1008 q^{22} - 4716 q^{23} - 882 q^{25} + 6084 q^{29} + 3330 q^{31} + 288 q^{34} - 5346 q^{35} - 576 q^{38} + 13356 q^{41} + 1260 q^{43} - 16578 q^{47} - 5904 q^{49} - 15552 q^{50} + 2304 q^{56} + 40104 q^{59} + 8352 q^{61} + 18432 q^{64} + 19674 q^{65} - 24192 q^{67} - 10224 q^{68} + 14400 q^{70} - 39528 q^{71} - 12222 q^{73} - 33120 q^{74} + 9792 q^{76} - 28206 q^{77} + 11304 q^{79} + 30078 q^{83} - 52200 q^{85} + 46224 q^{86} - 16128 q^{88} + 102222 q^{89} + 12078 q^{91} + 27504 q^{92} + 4032 q^{94} - 46728 q^{95} + 49680 q^{97} - 82944 q^{98}+O(q^{100}) \) 72 * q + 18 * q^5 - 720 * q^11 + 288 * q^14 - 288 * q^20 - 1008 * q^22 - 4716 * q^23 - 882 * q^25 + 6084 * q^29 + 3330 * q^31 + 288 * q^34 - 5346 * q^35 - 576 * q^38 + 13356 * q^41 + 1260 * q^43 - 16578 * q^47 - 5904 * q^49 - 15552 * q^50 + 2304 * q^56 + 40104 * q^59 + 8352 * q^61 + 18432 * q^64 + 19674 * q^65 - 24192 * q^67 - 10224 * q^68 + 14400 * q^70 - 39528 * q^71 - 12222 * q^73 - 33120 * q^74 + 9792 * q^76 - 28206 * q^77 + 11304 * q^79 + 30078 * q^83 - 52200 * q^85 + 46224 * q^86 - 16128 * q^88 + 102222 * q^89 + 12078 * q^91 + 27504 * q^92 + 4032 * q^94 - 46728 * q^95 + 49680 * q^97 - 82944 * q^98

Introduction

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