LMFDB - Embedded newform 162.5.f.a.17.10

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			17.10
Character	$\chi$	$=$	162.17
Dual form			162.5.f.a.143.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-6.60957 - 1.16545i) q^{5} +(-57.7034 + 48.4189i) q^{7} +(-19.5959 + 11.3137i) q^{8} +O(q^{10})$	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-6.60957 - 1.16545i) q^{5} +(-57.7034 + 48.4189i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(-9.49154 + 16.4398i) q^{10} +(188.923 - 33.3122i) q^{11} +(123.156 - 44.8251i) q^{13} +(72.8692 + 200.206i) q^{14} +(11.1135 + 63.0277i) q^{16} +(324.835 + 187.544i) q^{17} +(86.3550 + 149.571i) q^{19} +(34.5127 + 41.1307i) q^{20} +(94.2211 - 534.354i) q^{22} +(214.782 - 255.967i) q^{23} +(-544.980 - 198.356i) q^{25} -370.693i q^{26} +602.611 q^{28} +(-218.431 + 600.135i) q^{29} +(1227.17 + 1029.72i) q^{31} +(178.269 + 31.4337i) q^{32} +(812.701 - 681.937i) q^{34} +(437.824 - 252.778i) q^{35} +(713.966 - 1236.63i) q^{37} +(481.077 - 84.8268i) q^{38} +(142.706 - 51.9408i) q^{40} +(828.426 + 2276.08i) q^{41} +(25.5842 + 145.095i) q^{43} +(-1329.09 - 767.349i) q^{44} +(-472.547 - 818.475i) q^{46} +(597.596 + 712.188i) q^{47} +(568.361 - 3223.34i) q^{49} +(-1054.40 + 1256.59i) q^{50} +(-985.247 - 358.601i) q^{52} -2438.32i q^{53} -1287.52 q^{55} +(582.953 - 1601.65i) q^{56} +(1383.76 + 1161.12i) q^{58} +(1219.47 + 215.026i) q^{59} +(-3503.38 + 2939.68i) q^{61} +(3923.98 - 2265.51i) q^{62} +(256.000 - 443.405i) q^{64} +(-866.249 + 152.743i) q^{65} +(638.032 - 232.225i) q^{67} +(-1026.30 - 2819.73i) q^{68} +(-248.304 - 1408.20i) q^{70} +(5251.07 + 3031.71i) q^{71} +(3339.15 + 5783.58i) q^{73} +(-2596.09 - 3093.90i) q^{74} +(239.926 - 1360.69i) q^{76} +(-9288.54 + 11069.6i) q^{77} +(-7904.74 - 2877.09i) q^{79} -429.538i q^{80} +6850.89 q^{82} +(122.643 - 336.960i) q^{83} +(-1928.45 - 1618.16i) q^{85} +(410.391 + 72.3629i) q^{86} +(-3325.23 + 2790.20i) q^{88} +(-625.806 + 361.309i) q^{89} +(-4936.13 + 8549.62i) q^{91} +(-2632.52 + 464.184i) q^{92} +(2470.99 - 899.367i) q^{94} +(-396.453 - 1089.24i) q^{95} +(2237.22 + 12687.9i) q^{97} +(-8017.33 - 4628.81i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$2$	0.967379	−	2.65785i	0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−6.12836	−	5.14230i	−0.383022	−	0.321394i
$5$	−6.60957	−	1.16545i	−0.264383	−	0.0466178i	0.0398852	−	0.999204i	$-0.487301\pi$
$5$	−6.60957	−	1.16545i	−0.264383	−	0.0466178i	−0.304268	+	0.952586i	$0.598412\pi$
$6$		0			0
$7$	−57.7034	+	48.4189i	−1.17762	+	0.988140i	−0.177628	+	0.984098i	$0.556842\pi$
$7$	−57.7034	+	48.4189i	−1.17762	+	0.988140i	−0.999992	+	0.00404221i	$0.998713\pi$
$8$	−19.5959	+	11.3137i	−0.306186	+	0.176777i
$9$		0			0
$10$	−9.49154	+	16.4398i	−0.0949154	+	0.164398i
$11$	188.923	−	33.3122i	1.56134	−	0.275307i	0.674818	−	0.737984i	$-0.264222\pi$
$11$	188.923	−	33.3122i	1.56134	−	0.275307i	0.886527	+	0.462677i	$0.153111\pi$
$12$		0			0
$13$	123.156	−	44.8251i	0.728733	−	0.265237i	0.0491046	−	0.998794i	$-0.484363\pi$
$13$	123.156	−	44.8251i	0.728733	−	0.265237i	0.679628	+	0.733557i	$0.262141\pi$
$14$	72.8692	+	200.206i	0.371781	+	1.02146i
$15$		0			0
$16$	11.1135	+	63.0277i	0.0434120	+	0.246202i
$17$	324.835	+	187.544i	1.12400	+	0.648939i	0.942418	−	0.334437i	$-0.108546\pi$
$17$	324.835	+	187.544i	1.12400	+	0.648939i	0.181578	+	0.983377i	$0.441879\pi$
$18$		0			0
$19$	86.3550	+	149.571i	0.239211	+	0.414325i	0.960488	−	0.278321i	$-0.0897780\pi$
$19$	86.3550	+	149.571i	0.239211	+	0.414325i	−0.721277	+	0.692646i	$0.756445\pi$
$20$	34.5127	+	41.1307i	0.0862818	+	0.102827i
$21$		0			0
$22$	94.2211	−	534.354i	0.194672	−	1.10404i
$23$	214.782	−	255.967i	0.406015	−	0.483870i	−0.523829	−	0.851823i	$-0.675497\pi$
$23$	214.782	−	255.967i	0.406015	−	0.483870i	0.929844	+	0.367954i	$0.119941\pi$
$24$		0			0
$25$	−544.980	−	198.356i	−0.871968	−	0.317370i
$26$		−	370.693i		−	0.548362i
$27$		0			0
$28$	602.611			0.768636
$29$	−218.431	+	600.135i	−0.259728	+	0.713596i	0.739456	+	0.673205i	$0.235083\pi$
$29$	−218.431	+	600.135i	−0.259728	+	0.713596i	−0.999184	+	0.0403916i	$0.987139\pi$
$30$		0			0
$31$	1227.17	+	1029.72i	1.27697	+	1.07151i	0.993654	+	0.112480i	$0.0358795\pi$
$31$	1227.17	+	1029.72i	1.27697	+	1.07151i	0.283318	+	0.959026i	$0.408565\pi$
$32$	178.269	+	31.4337i	0.174091	+	0.0306970i
$33$		0			0
$34$	812.701	−	681.937i	0.703029	−	0.589911i
$35$	437.824	−	252.778i	0.357407	−	0.206349i
$36$		0			0
$37$	713.966	−	1236.63i	0.521524	−	0.903306i	−0.478163	−	0.878271i	$-0.658697\pi$
$37$	713.966	−	1236.63i	0.521524	−	0.903306i	0.999687	−	0.0250344i	$-0.00796952\pi$
$38$	481.077	−	84.8268i	0.333155	−	0.0587443i
$39$		0			0
$40$	142.706	−	51.9408i	0.0891913	−	0.0324630i
$41$	828.426	+	2276.08i	0.492817	+	1.35400i	0.898091	+	0.439809i	$0.144954\pi$
$41$	828.426	+	2276.08i	0.492817	+	1.35400i	−0.405274	+	0.914195i	$0.632824\pi$
$42$		0			0
$43$	25.5842	+	145.095i	0.0138368	+	0.0784722i	0.990944	−	0.134274i	$-0.0428703\pi$
$43$	25.5842	+	145.095i	0.0138368	+	0.0784722i	−0.977107	+	0.212746i	$0.931759\pi$
$44$	−1329.09	−	767.349i	−0.686512	−	0.396358i
$45$		0			0
$46$	−472.547	−	818.475i	−0.223321	−	0.386803i
$47$	597.596	+	712.188i	0.270528	+	0.322403i	0.884155	−	0.467193i	$-0.154735\pi$
$47$	597.596	+	712.188i	0.270528	+	0.322403i	−0.613627	+	0.789596i	$0.710290\pi$
$48$		0			0
$49$	568.361	−	3223.34i	0.236719	−	1.34250i
$50$	−1054.40	+	1256.59i	−0.421762	+	0.502636i
$51$		0			0
$52$	−985.247	−	358.601i	−0.364367	−	0.132619i
$53$		−	2438.32i		−	0.868038i	−0.900904	−	0.434019i	$-0.857095\pi$
$53$		−	2438.32i		−	0.868038i	0.900904	−	0.434019i	$-0.142905\pi$
$54$		0			0
$55$	−1287.52			−0.425627
$56$	582.953	−	1601.65i	0.185891	−	0.510731i
$57$		0			0
$58$	1383.76	+	1161.12i	0.411345	+	0.345159i
$59$	1219.47	+	215.026i	0.350322	+	0.0617712i	0.346040	−	0.938220i	$-0.387526\pi$
$59$	1219.47	+	215.026i	0.350322	+	0.0617712i	0.00428158	+	0.999991i	$0.498637\pi$
$60$		0			0
$61$	−3503.38	+	2939.68i	−0.941515	+	0.790025i	−0.977848	−	0.209315i	$-0.932877\pi$
$61$	−3503.38	+	2939.68i	−0.941515	+	0.790025i	0.0363333	+	0.999340i	$0.488432\pi$
$62$	3923.98	−	2265.51i	1.02081	−	0.589362i
$63$		0			0
$64$	256.000	−	443.405i	0.0625000	−	0.108253i
$65$	−866.249	+	152.743i	−0.205029	+	0.0361522i
$66$		0			0
$67$	638.032	−	232.225i	0.142132	−	0.0517320i	−0.269974	−	0.962867i	$-0.587015\pi$
$67$	638.032	−	232.225i	0.142132	−	0.0517320i	0.412107	+	0.911136i	$0.364793\pi$
$68$	−1026.30	−	2819.73i	−0.221950	−	0.609804i
$69$		0			0
$70$	−248.304	−	1408.20i	−0.0506743	−	0.287388i
$71$	5251.07	+	3031.71i	1.04167	+	0.601410i	0.920307	−	0.391197i	$-0.127939\pi$
$71$	5251.07	+	3031.71i	1.04167	+	0.601410i	0.121366	+	0.992608i	$0.461272\pi$
$72$		0			0
$73$	3339.15	+	5783.58i	0.626600	+	1.08530i	0.988229	+	0.152980i	$0.0488871\pi$
$73$	3339.15	+	5783.58i	0.626600	+	1.08530i	−0.361630	+	0.932322i	$0.617780\pi$
$74$	−2596.09	−	3093.90i	−0.474085	−	0.564993i
$75$		0			0
$76$	239.926	−	1360.69i	0.0415385	−	0.235577i
$77$	−9288.54	+	11069.6i	−1.56663	+	1.86703i
$78$		0			0
$79$	−7904.74	−	2877.09i	−1.26658	−	0.460998i	−0.380609	−	0.924736i	$-0.624286\pi$
$79$	−7904.74	−	2877.09i	−1.26658	−	0.460998i	−0.885972	+	0.463738i	$0.846508\pi$
$80$		−	429.538i		−	0.0671154i
$81$		0			0
$82$	6850.89			1.01887
$83$	122.643	−	336.960i	0.0178028	−	0.0489127i	−0.930473	−	0.366361i	$-0.880604\pi$
$83$	122.643	−	336.960i	0.0178028	−	0.0489127i	0.948276	+	0.317448i	$0.102826\pi$
$84$		0			0
$85$	−1928.45	−	1618.16i	−0.266913	−	0.223967i
$86$	410.391	+	72.3629i	0.0554882	+	0.00978407i
$87$		0			0
$88$	−3325.23	+	2790.20i	−0.429394	+	0.360305i
$89$	−625.806	+	361.309i	−0.0790060	+	0.0456141i	−0.538983	−	0.842317i	$-0.681191\pi$
$89$	−625.806	+	361.309i	−0.0790060	+	0.0456141i	0.459977	+	0.887931i	$0.347858\pi$
$90$		0			0
$91$	−4936.13	+	8549.62i	−0.596079	+	1.03244i
$92$	−2632.52	+	464.184i	−0.311025	+	0.0548422i
$93$		0			0
$94$	2470.99	−	899.367i	0.279650	−	0.101784i
$95$	−396.453	−	1089.24i	−0.0439283	−	0.120692i
$96$		0			0
$97$	2237.22	+	12687.9i	0.237774	+	1.34849i	0.836692	+	0.547674i	$0.184487\pi$
$97$	2237.22	+	12687.9i	0.237774	+	1.34849i	−0.598917	+	0.800811i	$0.704402\pi$
$98$	−8017.33	−	4628.81i	−0.834791	−	0.481967i
$99$		0			0
$100$	2319.82	+	4018.05i	0.231982	+	0.401805i
$101$	−10496.5	−	12509.2i	−1.02897	−	1.22627i	−0.973708	−	0.227802i	$-0.926846\pi$
$101$	−10496.5	−	12509.2i	−1.02897	−	1.22627i	−0.0552582	−	0.998472i	$-0.517598\pi$
$102$		0			0
$103$	−606.832	+	3441.51i	−0.0571997	+	0.324396i	−0.999959	−	0.00907891i	$-0.997110\pi$
$103$	−606.832	+	3441.51i	−0.0571997	+	0.324396i	0.942759	+	0.333475i	$0.108221\pi$
$104$	−1906.21	+	2271.74i	−0.176240	+	0.210035i
$105$		0			0
$106$	−6480.69	−	2358.78i	−0.576779	−	0.209930i
$107$		−	8234.07i		−	0.719195i	−0.933107	−	0.359598i	$-0.882914\pi$
$107$		−	8234.07i		−	0.719195i	0.933107	−	0.359598i	$-0.117086\pi$
$108$		0			0
$109$	−13578.3			−1.14286			−0.571431	−	0.820650i	$-0.693611\pi$
$109$	−13578.3			−1.14286			−0.571431	+	0.820650i	$0.693611\pi$
$110$	−1245.52	+	3422.04i	−0.102936	+	0.282813i
$111$		0			0
$112$	−3693.01	−	3098.81i	−0.294405	−	0.247035i
$113$	17967.8	+	3168.21i	1.40714	+	0.248117i	0.825075	−	0.565024i	$-0.191133\pi$
$113$	17967.8	+	3168.21i	1.40714	+	0.248117i	0.582067	+	0.813141i	$0.302244\pi$
$114$		0			0
$115$	−1717.93	+	1441.52i	−0.129900	+	0.108999i
$116$	4424.70	−	2554.60i	0.328827	−	0.189848i
$117$		0			0
$118$	1751.20	−	3033.16i	0.125768	−	0.217837i
$119$	−27824.7	+	4906.25i	−1.96488	+	0.346462i
$120$		0			0
$121$	20824.1	−	7579.34i	1.42231	−	0.517679i
$122$	4424.15	+	12155.2i	0.297242	+	0.816665i
$123$		0			0
$124$	−2225.41	−	12621.0i	−0.144733	−	0.820822i
$125$	7003.63	+	4043.55i	0.448233	+	0.258787i
$126$		0			0
$127$	8973.35	+	15542.3i	0.556349	+	0.963625i	0.997797	+	0.0663381i	$0.0211316\pi$
$127$	8973.35	+	15542.3i	0.556349	+	0.963625i	−0.441448	+	0.897287i	$0.645535\pi$
$128$	−930.856	−	1109.35i	−0.0568149	−	0.0677094i
$129$		0			0
$130$	−432.023	+	2450.12i	−0.0255635	+	0.144978i
$131$	10046.4	−	11972.8i	0.585419	−	0.697675i	−0.389300	−	0.921111i	$-0.627283\pi$
$131$	10046.4	−	11972.8i	0.585419	−	0.697675i	0.974719	+	0.223436i	$0.0717275\pi$
$132$		0			0
$133$	−12225.0	−	4449.55i	−0.691110	−	0.251544i
$134$		−	1920.45i		−	0.106953i
$135$		0			0
$136$	−8487.25			−0.458870
$137$	−3853.13	+	10586.4i	−0.205292	+	0.564036i	−0.999021	−	0.0442359i	$-0.985915\pi$
$137$	−3853.13	+	10586.4i	−0.205292	+	0.564036i	0.793729	+	0.608272i	$0.208137\pi$
$138$		0			0
$139$	−22488.5	−	18870.1i	−1.16394	−	0.976661i	−0.163987	−	0.986462i	$-0.552436\pi$
$139$	−22488.5	−	18870.1i	−1.16394	−	0.976661i	−0.999952	+	0.00980150i	$0.996880\pi$
$140$	−3983.00	−	702.310i	−0.203214	−	0.0358322i
$141$		0			0
$142$	13137.6	−	11023.8i	0.651538	−	0.546705i
$143$	21773.7	−	12571.1i	1.06478	−	0.614752i
$144$		0			0
$145$	2143.16	−	3712.06i	0.101934	−	0.176555i
$146$	18602.1	−	3280.05i	0.872683	−	0.153878i
$147$		0			0
$148$	−10734.5	+	3907.05i	−0.490072	+	0.178372i
$149$	−4202.96	−	11547.5i	−0.189314	−	0.520136i	0.808331	−	0.588728i	$-0.200371\pi$
$149$	−4202.96	−	11547.5i	−0.189314	−	0.520136i	−0.997645	+	0.0685929i	$0.978149\pi$
$150$		0			0
$151$	−2270.45	−	12876.3i	−0.0995766	−	0.564727i	−0.993249	−	0.116006i	$-0.962991\pi$
$151$	−2270.45	−	12876.3i	−0.0995766	−	0.564727i	0.893672	−	0.448721i	$-0.148120\pi$
$152$	−3384.41	−	1953.99i	−0.146486	−	0.0845737i
$153$		0			0
$154$	20436.0	+	35396.1i	0.861695	+	1.49250i
$155$	−6910.99	−	8236.19i	−0.287658	−	0.342818i
$156$		0			0
$157$	6475.04	−	36721.8i	0.262690	−	1.48979i	−0.512844	−	0.858482i	$-0.671408\pi$
$157$	6475.04	−	36721.8i	0.262690	−	1.48979i	0.775534	−	0.631306i	$-0.217481\pi$
$158$	−15293.8	+	18226.4i	−0.612632	+	0.730107i
$159$		0			0
$160$	−1141.65	−	415.526i	−0.0445957	−	0.0162315i
$161$			25169.6i			0.971014i
$162$		0			0
$163$	23579.0			0.887461			0.443731	−	0.896160i	$-0.353655\pi$
$163$	23579.0			0.887461			0.443731	+	0.896160i	$0.353655\pi$
$164$	6627.41	−	18208.6i	0.246409	−	0.677002i
$165$		0			0
$166$	−776.946	−	651.935i	−0.0281952	−	0.0236586i
$167$	7645.97	+	1348.19i	0.274157	+	0.0483413i	0.309036	−	0.951050i	$-0.399994\pi$
$167$	7645.97	+	1348.19i	0.274157	+	0.0483413i	−0.0348792	+	0.999392i	$0.511105\pi$
$168$		0			0
$169$	−8720.91	+	7317.71i	−0.305343	+	0.256213i
$170$	−6166.37	+	3560.15i	−0.213369	+	0.123189i
$171$		0			0
$172$	589.333	−	1020.76i	0.0199207	−	0.0345036i
$173$	−26463.9	+	4666.31i	−0.884224	+	0.155913i	−0.597278	−	0.802034i	$-0.703751\pi$
$173$	−26463.9	+	4666.31i	−0.884224	+	0.155913i	−0.286946	+	0.957947i	$0.592640\pi$
$174$		0			0
$175$	41051.3	−	14941.5i	1.34045	−	0.487885i
$176$	4199.18	+	11537.2i	0.135562	+	0.372455i
$177$		0			0
$178$	354.915	+	2012.82i	0.0112017	+	0.0635281i
$179$	40093.9	+	23148.2i	1.25133	+	0.722456i	0.971374	−	0.237557i	$-0.0763466\pi$
$179$	40093.9	+	23148.2i	1.25133	+	0.722456i	0.279957	+	0.960013i	$0.409680\pi$
$180$		0			0
$181$	−1866.28	−	3232.50i	−0.0569667	−	0.0986691i	0.836136	−	0.548523i	$-0.184810\pi$
$181$	−1866.28	−	3232.50i	−0.0569667	−	0.0986691i	−0.893102	+	0.449853i	$0.851476\pi$
$182$	17948.5	+	21390.2i	0.541859	+	0.645762i
$183$		0			0
$184$	−1312.91	+	7445.89i	−0.0387793	+	0.219928i
$185$	−6160.23	+	7341.48i	−0.179992	+	0.214506i
$186$		0			0
$187$	67616.2	+	24610.3i	1.93360	+	0.703774i
$188$		−	7437.56i		−	0.210433i
$189$		0			0
$190$	−3278.57			−0.0908191
$191$	12449.7	−	34205.4i	0.341266	−	0.937621i	−0.643762	−	0.765226i	$-0.722627\pi$
$191$	12449.7	−	34205.4i	0.341266	−	0.937621i	0.985028	−	0.172395i	$-0.0551506\pi$
$192$		0			0
$193$	38605.0	+	32393.4i	1.03640	+	0.869646i	0.991599	−	0.129350i	$-0.0412891\pi$
$193$	38605.0	+	32393.4i	1.03640	+	0.869646i	0.0448045	+	0.998996i	$0.485734\pi$
$194$	35886.8	+	6327.81i	0.953523	+	0.168132i
$195$		0			0
$196$	−20058.5	+	16831.1i	−0.522139	+	0.438127i
$197$	−13635.0	+	7872.15i	−0.351335	+	0.202844i	−0.665273	−	0.746600i	$-0.731685\pi$
$197$	−13635.0	+	7872.15i	−0.351335	+	0.202844i	0.313938	+	0.949444i	$0.398352\pi$
$198$		0			0
$199$	25992.2	−	45019.7i	0.656351	−	1.13683i	−0.325202	−	0.945645i	$-0.605432\pi$
$199$	25992.2	−	45019.7i	0.656351	−	1.13683i	0.981553	−	0.191189i	$-0.0612344\pi$
$200$	12923.5	−	2278.77i	0.323088	−	0.0569691i
$201$		0			0
$202$	−43401.7	+	15796.9i	−1.06366	+	0.387142i
$203$	−16453.6	−	45206.0i	−0.399273	−	1.09699i
$204$		0			0
$205$	−2822.89	−	16009.4i	−0.0671717	−	0.380950i
$206$	8560.00	+	4942.12i	0.201716	+	0.116461i
$207$		0			0
$208$	4193.91	+	7264.07i	0.0969377	+	0.167901i
$209$	21297.0	+	25380.8i	0.487557	+	0.581048i
$210$		0			0
$211$	3795.00	−	21522.5i	0.0852408	−	0.483424i	−0.912064	−	0.410049i	$-0.865512\pi$
$211$	3795.00	−	21522.5i	0.0852408	−	0.483424i	0.997304	−	0.0733757i	$-0.0233772\pi$
$212$	−12538.6	+	14942.9i	−0.278982	+	0.332478i
$213$		0			0
$214$	−21884.9	−	7965.46i	−0.477879	−	0.173934i
$215$		−	988.833i		−	0.0213917i
$216$		0			0
$217$	−120670.			−2.56258
$218$	−13135.4	+	36089.2i	−0.276395	+	0.759389i
$219$		0			0
$220$	7890.39	+	6620.83i	0.163025	+	0.136794i
$221$	48412.0	+	8536.34i	0.991216	+	0.174778i
$222$		0			0
$223$	30304.5	−	25428.5i	0.609393	−	0.511342i	−0.285056	−	0.958511i	$-0.592012\pi$
$223$	30304.5	−	25428.5i	0.609393	−	0.511342i	0.894449	+	0.447169i	$0.147568\pi$
$224$	−11808.7	+	6817.77i	−0.235346	+	0.135877i
$225$		0			0
$226$	25802.3	−	44690.9i	0.505175	−	0.874988i
$227$	38739.5	−	6830.81i	0.751799	−	0.132562i	0.215399	−	0.976526i	$-0.430895\pi$
$227$	38739.5	−	6830.81i	0.751799	−	0.132562i	0.536400	+	0.843964i	$0.319784\pi$
$228$		0			0
$229$	−91465.9	+	33290.9i	−1.74417	+	0.634825i	−0.999469	−	0.0325752i	$-0.989629\pi$
$229$	−91465.9	+	33290.9i	−1.74417	+	0.634825i	−0.744699	+	0.667401i	$0.767407\pi$
$230$	2169.44	+	5960.50i	0.0410103	+	0.112675i
$231$		0			0
$232$	−2509.39	−	14231.5i	−0.0466221	−	0.264407i
$233$	−49708.6	−	28699.3i	−0.915630	−	0.528639i	−0.0333917	−	0.999442i	$-0.510631\pi$
$233$	−49708.6	−	28699.3i	−0.915630	−	0.528639i	−0.882238	+	0.470803i	$0.843964\pi$
$234$		0			0
$235$	−3119.84	−	5403.72i	−0.0564933	−	0.0978492i
$236$	−6367.62	−	7588.64i	−0.114328	−	0.136251i
$237$		0			0
$238$	−13877.0	+	78700.1i	−0.244986	+	1.38938i
$239$	1108.55	−	1321.12i	0.0194071	−	0.0231284i	−0.756254	−	0.654279i	$-0.772972\pi$
$239$	1108.55	−	1321.12i	0.0194071	−	0.0231284i	0.775661	+	0.631150i	$0.217417\pi$
$240$		0			0
$241$	15251.5	+	5551.09i	0.262590	+	0.0955750i	0.469960	−	0.882688i	$-0.344268\pi$
$241$	15251.5	+	5551.09i	0.262590	+	0.0955750i	−0.207370	+	0.978263i	$0.566490\pi$
$242$		−	62679.4i		−	1.07027i
$243$		0			0
$244$	36586.7			0.614530
$245$	−7513.25	+	20642.5i	−0.125169	+	0.343898i
$246$		0			0
$247$	17339.7	+	14549.7i	0.284215	+	0.238485i
$248$	−35697.4	−	6294.42i	−0.580408	−	0.102342i
$249$		0			0
$250$	17522.3	−	14703.0i	0.280357	−	0.235248i
$251$	−18775.2	+	10839.9i	−0.298014	+	0.172059i	−0.641550	−	0.767081i	$-0.721708\pi$
$251$	−18775.2	+	10839.9i	−0.298014	+	0.172059i	0.343536	+	0.939139i	$0.388375\pi$
$252$		0			0
$253$	32050.4	−	55512.8i	0.500716	−	0.867266i
$254$	49989.8	−	8814.55i	0.774843	−	0.136626i
$255$		0			0
$256$	−3848.98	+	1400.91i	−0.0587308	+	0.0213763i
$257$	−37907.0	−	104148.i	−0.573922	−	1.57684i	−0.798252	−	0.602324i	$-0.794242\pi$
$257$	−37907.0	−	104148.i	−0.573922	−	1.57684i	0.224330	−	0.974513i	$-0.427981\pi$
$258$		0			0
$259$	18677.8	+	105927.i	0.278436	+	1.57909i
$260$	6094.13	+	3518.45i	0.0901499	+	0.0520481i
$261$		0			0
$262$	−22103.3	−	38284.0i	−0.321999	−	0.557718i
$263$	−5315.13	−	6334.32i	−0.0768426	−	0.0915775i	0.726253	−	0.687427i	$-0.241260\pi$
$263$	−5315.13	−	6334.32i	−0.0768426	−	0.0915775i	−0.803096	+	0.595850i	$0.796815\pi$
$264$		0			0
$265$	−2841.73	+	16116.2i	−0.0404661	+	0.229494i
$266$	−23652.5	+	28188.0i	−0.334283	+	0.398383i
$267$		0			0
$268$	−5104.26	−	1857.80i	−0.0710662	−	0.0258660i
$269$			70465.7i			0.973808i	0.873455	+	0.486904i	$0.161874\pi$
$269$			70465.7i			0.973808i	−0.873455	+	0.486904i	$0.838126\pi$
$270$		0			0
$271$	−137984.			−1.87885			−0.939424	−	0.342757i	$-0.888639\pi$
$271$	−137984.			−1.87885			−0.939424	+	0.342757i	$0.888639\pi$
$272$	−8210.39	+	22557.9i	−0.110975	+	0.304902i
$273$		0			0
$274$	24409.6	+	20482.1i	0.325132	+	0.272818i
$275$	−109567.	−	19319.6i	−1.44882	−	0.255465i
$276$		0			0
$277$	−77113.5	+	64705.9i	−1.00501	+	0.843305i	−0.987671	−	0.156545i	$-0.949964\pi$
$277$	−77113.5	+	64705.9i	−1.00501	+	0.843305i	−0.0173408	+	0.999850i	$0.505520\pi$
$278$	−71908.7	+	41516.5i	−0.930448	+	0.537194i
$279$		0			0
$280$	−5719.71	+	9906.83i	−0.0729555	+	0.126363i
$281$	−35465.1	+	6253.45i	−0.449147	+	0.0791967i	−0.393646	−	0.919262i	$-0.628787\pi$
$281$	−35465.1	+	6253.45i	−0.449147	+	0.0791967i	−0.0555005	+	0.998459i	$0.517675\pi$
$282$		0			0
$283$	69243.7	−	25202.6i	0.864585	−	0.314683i	0.128612	−	0.991695i	$-0.458948\pi$
$283$	69243.7	−	25202.6i	0.864585	−	0.314683i	0.735972	+	0.677012i	$0.236725\pi$
$284$	−16590.5	−	45582.0i	−0.205694	−	0.565141i
$285$		0			0
$286$	−12348.6	−	70032.3i	−0.150968	−	0.856183i
$287$	−158008.	−	91226.1i	−1.91830	−	1.10753i
$288$		0			0
$289$	28584.6	+	49510.0i	0.342245	+	0.592786i
$290$	−7792.87	−	9287.18i	−0.0926619	−	0.110430i
$291$		0			0
$292$	9277.39	−	52614.7i	0.108808	−	0.617080i
$293$	38777.7	−	46213.4i	0.451696	−	0.538311i	−0.491354	−	0.870960i	$-0.663498\pi$
$293$	38777.7	−	46213.4i	0.451696	−	0.538311i	0.943051	+	0.332649i	$0.107942\pi$
$294$		0			0
$295$	−7809.58	−	2842.45i	−0.0897395	−	0.0326625i
$296$			32310.4i			0.368773i
$297$		0			0
$298$	−34757.5			−0.391395
$299$	14977.9	−	41151.5i	0.167536	−	0.460302i
$300$		0			0
$301$	−8501.63	−	7133.71i	−0.0938359	−	0.0787377i
$302$	−36419.8	−	6421.79i	−0.399322	−	0.0704113i
$303$		0			0
$304$	−8467.43	+	7105.02i	−0.0916230	+	0.0768808i
$305$	26581.9	−	15347.0i	0.285750	−	0.164978i
$306$		0			0
$307$	65546.4	−	113530.i	0.695460	−	1.20457i	−0.274565	−	0.961568i	$-0.588534\pi$
$307$	65546.4	−	113530.i	0.695460	−	1.20457i	0.970025	−	0.243004i	$-0.0781327\pi$
$308$	113847.	−	20074.3i	1.20011	−	0.211611i
$309$		0			0
$310$	−28576.1	+	10400.9i	−0.297358	+	0.108230i
$311$	40598.9	+	111545.i	0.419753	+	1.15326i	0.951846	+	0.306575i	$0.0991831\pi$
$311$	40598.9	+	111545.i	0.419753	+	1.15326i	−0.532094	+	0.846685i	$0.678595\pi$
$312$		0			0
$313$	3449.99	+	19565.9i	0.0352151	+	0.199715i	0.997340	−	0.0728958i	$-0.0232241\pi$
$313$	3449.99	+	19565.9i	0.0352151	+	0.199715i	−0.962124	+	0.272611i	$0.912113\pi$
$314$	−91337.3	−	52733.6i	−0.926379	−	0.534845i
$315$		0			0
$316$	33648.2	+	58280.4i	0.336967	+	0.583644i
$317$	78273.6	+	93282.8i	0.778927	+	0.928289i	0.998884	−	0.0472205i	$-0.0150363\pi$
$317$	78273.6	+	93282.8i	0.778927	+	0.928289i	−0.219958	+	0.975509i	$0.570592\pi$
$318$		0			0
$319$	−21274.8	+	120655.i	−0.209067	+	1.18568i
$320$	−2208.81	+	2632.36i	−0.0215705	+	0.0257067i
$321$		0			0
$322$	66897.2	+	24348.6i	0.645203	+	0.234835i
$323$			64781.3i			0.620933i
$324$		0			0
$325$	−76008.8			−0.719610
$326$	22809.8	−	62669.4i	0.214628	−	0.589685i
$327$		0			0
$328$	−41984.7	−	35229.3i	−0.390250	−	0.327459i
$329$	−68966.6	−	12160.7i	−0.637158	−	0.112348i
$330$		0			0
$331$	72437.4	−	60782.2i	0.661160	−	0.554779i	−0.249274	−	0.968433i	$-0.580192\pi$
$331$	72437.4	−	60782.2i	0.661160	−	0.554779i	0.910434	+	0.413654i	$0.135748\pi$
$332$	−2484.35	+	1434.34i	−0.0225391	+	0.0130130i
$333$		0			0
$334$	10979.8	−	19017.6i	0.0984244	−	0.170476i
$335$	−4487.77	+	791.314i	−0.0399890	+	0.00705114i
$336$		0			0
$337$	−104522.	+	38043.1i	−0.920343	+	0.334978i	−0.758375	−	0.651818i	$-0.774006\pi$
$337$	−104522.	+	38043.1i	−0.920343	+	0.334978i	−0.161968	+	0.986796i	$0.551784\pi$
$338$	11013.0	+	30257.9i	0.0963987	+	0.264853i
$339$		0			0
$340$	3497.15	+	19833.3i	0.0302522	+	0.171568i
$341$	266142.	+	153657.i	2.28879	+	1.32143i
$342$		0			0
$343$	32844.7	+	56888.6i	0.279175	+	0.483545i
$344$	−2142.91	−	2553.82i	−0.0181087	−	0.0215811i
$345$		0			0
$346$	−13198.3	+	74851.3i	−0.110247	+	0.625241i
$347$	149116.	−	177710.i	1.23841	−	1.47589i	0.413623	−	0.910448i	$-0.364263\pi$
$347$	149116.	−	177710.i	1.23841	−	1.47589i	0.824792	−	0.565437i	$-0.191292\pi$
$348$		0			0
$349$	−11632.4	−	4233.84i	−0.0955033	−	0.0347603i	0.293827	−	0.955859i	$-0.405071\pi$
$349$	−11632.4	−	4233.84i	−0.0955033	−	0.0347603i	−0.389330	+	0.921098i	$0.627293\pi$
$350$		−	123562.i		−	1.00867i
$351$		0			0
$352$	34726.2			0.280267
$353$	−53613.1	+	147301.i	−0.430251	+	1.18210i	0.515409	+	0.856944i	$0.327640\pi$
$353$	−53613.1	+	147301.i	−0.430251	+	1.18210i	−0.945659	+	0.325159i	$0.894582\pi$
$354$		0			0
$355$	−31174.1	−	26158.1i	−0.247364	−	0.207563i
$356$	5693.13	+	1003.85i	0.0449211	+	0.00792081i
$357$		0			0
$358$	100310.	−	84170.5i	0.782673	−	0.656740i
$359$	−93373.7	+	53909.3i	−0.724496	+	0.418288i	−0.816405	−	0.577480i	$-0.804036\pi$
$359$	−93373.7	+	53909.3i	−0.724496	+	0.418288i	0.0919095	+	0.995767i	$0.470703\pi$
$360$		0			0
$361$	50246.1	−	87028.8i	0.385557	−	0.667803i
$362$	−10396.9	+	1833.26i	−0.0793391	+	0.0139896i
$363$		0			0
$364$	74215.1	−	27012.1i	0.560131	−	0.203871i
$365$	−15329.9	−	42118.6i	−0.115068	−	0.316146i
$366$		0			0
$367$	4768.86	+	27045.5i	0.0354064	+	0.200800i	0.997380	−	0.0723435i	$-0.0230478\pi$
$367$	4768.86	+	27045.5i	0.0354064	+	0.200800i	−0.961973	+	0.273143i	$0.911937\pi$
$368$	18520.0	+	10692.5i	0.136756	+	0.0789559i
$369$		0			0
$370$	13553.3	+	23475.0i	0.0990013	+	0.171475i
$371$	118061.	+	140699.i	0.857743	+	1.02222i
$372$		0			0
$373$	−29019.3	+	164577.i	−0.208579	+	1.18291i	0.683130	+	0.730297i	$0.260618\pi$
$373$	−29019.3	+	164577.i	−0.208579	+	1.18291i	−0.891708	+	0.452611i	$0.850493\pi$
$374$	130821.	−	155906.i	0.935264	−	1.11460i
$375$		0			0
$376$	−19767.9	−	7194.94i	−0.139825	−	0.0508922i
$377$			83701.3i			0.588911i
$378$		0			0
$379$	−195471.			−1.36083			−0.680416	−	0.732826i	$-0.738201\pi$
$379$	−195471.			−1.36083			−0.680416	+	0.732826i	$0.738201\pi$
$380$	−3171.62	+	8713.96i	−0.0219641	+	0.0603460i
$381$		0			0
$382$	−78869.2	−	66179.1i	−0.540481	−	0.453518i
$383$	166604.	+	29376.8i	1.13576	+	0.200266i	0.709752	−	0.704452i	$-0.248807\pi$
$383$	166604.	+	29376.8i	1.13576	+	0.200266i	0.426012	+	0.904717i	$0.359918\pi$
$384$		0			0
$385$	74294.3	−	62340.3i	0.501227	−	0.420579i
$386$	123443.	−	71269.6i	0.828496	−	0.478333i
$387$		0			0
$388$	51534.5	−	89260.4i	0.342322	−	0.592919i
$389$	−87202.6	+	15376.2i	−0.576275	+	0.101613i	−0.454187	−	0.890906i	$-0.650070\pi$
$389$	−87202.6	+	15376.2i	−0.576275	+	0.101613i	−0.122088	+	0.992519i	$0.538959\pi$
$390$		0			0
$391$	117774.	−	42866.1i	0.770361	−	0.280389i
$392$	25330.3	+	69594.5i	0.164842	+	0.452901i
$393$		0			0
$394$	7732.84	+	43855.1i	0.0498134	+	0.282506i
$395$	48893.8	+	28228.9i	0.313372	+	0.180925i
$396$		0			0
$397$	−12881.4	−	22311.2i	−0.0817301	−	0.141561i	0.822263	−	0.569108i	$-0.192711\pi$
$397$	−12881.4	−	22311.2i	−0.0817301	−	0.141561i	−0.903993	+	0.427547i	$0.859378\pi$
$398$	−94511.6	−	112634.i	−0.596649	−	0.711058i
$399$		0			0
$400$	6445.32	−	36553.2i	0.0402833	−	0.228458i
$401$	−164197.	+	195682.i	−1.02112	+	1.21692i	−0.0451551	+	0.998980i	$0.514378\pi$
$401$	−164197.	+	195682.i	−1.02112	+	1.21692i	−0.975962	+	0.217940i	$0.930066\pi$
$402$		0			0
$403$	197290.	+	71807.8i	1.21477	+	0.442142i
$404$			130637.i			0.800393i
$405$		0			0
$406$	−136068.			−0.825473
$407$	93689.7	−	257410.i	0.565592	−	1.55395i
$408$		0			0
$409$	−52194.9	−	43796.7i	−0.312019	−	0.261815i	0.473307	−	0.880898i	$-0.343060\pi$
$409$	−52194.9	−	43796.7i	−0.312019	−	0.261815i	−0.785326	+	0.619082i	$0.787505\pi$
$410$	−45281.4	−	7984.34i	−0.269372	−	0.0474976i
$411$		0			0
$412$	21416.2	−	17970.3i	0.126168	−	0.105867i
$413$	−80778.8	+	46637.7i	−0.473585	+	0.273424i
$414$		0			0
$415$	−1203.33	+	2084.22i	−0.00698695	+	0.0121018i
$416$	23363.9	−	4119.69i	0.135008	−	0.0238055i
$417$		0			0
$418$	88060.5	−	32051.4i	0.503998	−	0.183440i
$419$	50821.2	+	139630.i	0.289479	+	0.795337i	0.996140	+	0.0877840i	$0.0279785\pi$
$419$	50821.2	+	139630.i	0.289479	+	0.795337i	−0.706661	+	0.707553i	$0.749799\pi$
$420$		0			0
$421$	−22332.6	−	126654.i	−0.126001	−	0.714589i	−0.980708	−	0.195478i	$-0.937374\pi$
$421$	−22332.6	−	126654.i	−0.126001	−	0.714589i	0.854707	−	0.519111i	$-0.173737\pi$
$422$	−53532.5	−	30907.0i	−0.300603	−	0.173553i
$423$		0			0
$424$	27586.4	+	47781.1i	0.153449	+	0.265781i
$425$	−139828.	−	166640.i	−0.774134	−	0.922577i
$426$		0			0
$427$	59820.5	−	339259.i	0.328091	−	1.86070i
$428$	−42342.0	+	50461.3i	−0.231145	+	0.275468i
$429$		0			0
$430$	−2628.17	−	956.576i	−0.0142140	−	0.00517348i
$431$		−	225052.i		−	1.21151i	−0.795650	−	0.605757i	$-0.792870\pi$
$431$		−	225052.i		−	1.21151i	0.795650	−	0.605757i	$-0.207130\pi$
$432$		0			0
$433$	194814.			1.03907			0.519534	−	0.854450i	$-0.326105\pi$
$433$	194814.			1.03907			0.519534	+	0.854450i	$0.326105\pi$
$434$	−116733.	+	320722.i	−0.619748	+	1.70274i
$435$		0			0
$436$	83212.9	+	69823.9i	0.437741	+	0.367309i
$437$	56832.8	+	10021.2i	0.297602	+	0.0524753i
$438$		0			0
$439$	37204.7	−	31218.4i	0.193049	−	0.161988i	−0.541140	−	0.840933i	$-0.682007\pi$
$439$	37204.7	−	31218.4i	0.193049	−	0.161988i	0.734189	+	0.678945i	$0.237563\pi$
$440$	25230.2	−	14566.6i	0.130321	−	0.0752410i
$441$		0			0
$442$	69521.1	−	120414.i	0.355854	−	0.616357i
$443$	82742.0	−	14589.7i	0.421618	−	0.0743426i	0.0411857	−	0.999152i	$-0.486886\pi$
$443$	82742.0	−	14589.7i	0.421618	−	0.0743426i	0.380432	+	0.924809i	$0.375775\pi$
$444$		0			0
$445$	4557.40	−	1658.76i	0.0230143	−	0.00837651i
$446$	−38269.3	−	105144.i	−0.192389	−	0.528585i
$447$		0			0
$448$	6697.11	+	37981.2i	0.0333681	+	0.189240i
$449$	−13962.5	−	8061.26i	−0.0692582	−	0.0399862i	0.464971	−	0.885326i	$-0.346065\pi$
$449$	−13962.5	−	8061.26i	−0.0692582	−	0.0399862i	−0.534229	+	0.845340i	$0.679398\pi$
$450$		0			0
$451$	232330.	+	402407.i	1.14222	+	1.97839i
$452$	−93821.2	−	111812.i	−0.459223	−	0.547281i
$453$		0			0
$454$	19320.5	−	109572.i	0.0937358	−	0.531602i
$455$	42589.8	−	50756.6i	0.205723	−	0.245171i
$456$		0			0
$457$	−207003.	−	75342.9i	−0.991160	−	0.360753i	−0.204991	−	0.978764i	$-0.565716\pi$
$457$	−207003.	−	75342.9i	−0.991160	−	0.360753i	−0.786169	+	0.618011i	$0.787939\pi$
$458$			275308.i			1.31246i
$459$		0			0
$460$	17940.8			0.0847864
$461$	54210.9	−	148943.i	0.255085	−	0.700840i	−0.744368	−	0.667770i	$-0.767249\pi$
$461$	54210.9	−	148943.i	0.255085	−	0.700840i	0.999453	−	0.0330708i	$-0.0105287\pi$
$462$		0			0
$463$	−14464.1	−	12136.8i	−0.0674727	−	0.0566163i	0.608428	−	0.793609i	$-0.291801\pi$
$463$	−14464.1	−	12136.8i	−0.0674727	−	0.0566163i	−0.675900	+	0.736993i	$0.736245\pi$
$464$	−40252.6	−	7097.63i	−0.186964	−	0.0329668i
$465$		0			0
$466$	−124366.	+	104355.i	−0.572702	+	0.480554i
$467$	165513.	−	95558.9i	0.758923	−	0.438165i	−0.0699858	−	0.997548i	$-0.522295\pi$
$467$	165513.	−	95558.9i	0.758923	−	0.438165i	0.828909	+	0.559383i	$0.188962\pi$
$468$		0			0
$469$	−25572.5	+	44293.0i	−0.116259	+	0.201367i
$470$	−17380.4	+	3064.63i	−0.0786798	+	0.0138734i
$471$		0			0
$472$	−26329.4	+	9583.11i	−0.118183	+	0.0430153i
$473$	9666.86	+	26559.5i	0.0432079	+	0.118713i
$474$		0			0
$475$	−17393.3	−	98642.4i	−0.0770895	−	0.437196i
$476$	195749.	+	113016.i	0.863944	+	0.498799i
$477$		0			0
$478$	−2438.95	−	4224.38i	−0.0106745	−	0.0184888i
$479$	25205.6	+	30038.9i	0.109857	+	0.130922i	0.818171	−	0.574975i	$-0.194988\pi$
$479$	25205.6	+	30038.9i	0.109857	+	0.130922i	−0.708314	+	0.705897i	$0.750544\pi$
$480$		0			0
$481$	32497.3	−	184301.i	0.140461	−	0.796596i
$482$	29508.0	−	35166.2i	0.127012	−	0.151367i
$483$		0			0
$484$	−166592.	−	60634.7i	−0.711156	−	0.258840i
$485$		−	86468.9i		−	0.367601i
$486$		0			0
$487$	152661.			0.643679			0.321839	−	0.946794i	$-0.395699\pi$
$487$	152661.			0.643679			0.321839	+	0.946794i	$0.395699\pi$
$488$	35393.2	−	97242.0i	0.148621	−	0.408333i
$489$		0			0
$490$	47596.5	+	39938.2i	0.198236	+	0.166340i
$491$	−414139.	−	73023.8i	−1.71784	−	0.302902i	−0.773971	−	0.633221i	$-0.781732\pi$
$491$	−414139.	−	73023.8i	−1.71784	−	0.302902i	−0.943869	+	0.330319i	$0.892844\pi$
$492$		0			0
$493$	−183505.	+	153979.i	−0.755014	+	0.633532i
$494$	55445.0	−	32011.2i	0.227200	−	0.131174i
$495$		0			0
$496$	−51262.6	+	88789.4i	−0.208371	+	0.360909i
$497$	−449796.	+	79311.3i	−1.82097	+	0.321087i
$498$		0			0
$499$	−456720.	+	166232.i	−1.83421	+	0.667597i	−0.842563	+	0.538598i	$0.818954\pi$
$499$	−456720.	+	166232.i	−1.83421	+	0.667597i	−0.991645	+	0.128999i	$0.958823\pi$
$500$	−22127.6	−	60795.1i	−0.0885104	−	0.243180i
$501$		0			0
$502$	10648.0	+	60387.9i	0.0422534	+	0.239631i
$503$	−74223.5	−	42852.9i	−0.293363	−	0.169373i	0.346094	−	0.938200i	$-0.387508\pi$
$503$	−74223.5	−	42852.9i	−0.293363	−	0.169373i	−0.639457	+	0.768826i	$0.720841\pi$
$504$		0			0
$505$	54798.4	+	94913.7i	0.214875	+	0.372174i
$506$	−116540.	−	138887.i	−0.455171	−	0.542451i
$507$		0			0
$508$	24931.3	−	141392.i	0.0966090	−	0.547897i
$509$	30075.9	−	35843.0i	0.116087	−	0.138347i	−0.704872	−	0.709335i	$-0.748995\pi$
$509$	30075.9	−	35843.0i	0.116087	−	0.138347i	0.820958	+	0.570988i	$0.193440\pi$
$510$		0			0
$511$	−472714.	−	172054.i	−1.81033	−	0.658905i
$512$			11585.2i			0.0441942i
$513$		0			0
$514$	−313482.			−1.18655
$515$	8021.80	−	22039.7i	0.0302453	−	0.0830982i
$516$		0			0
$517$	136624.	+	114641.i	0.511147	+	0.428904i
$518$	299606.	+	52828.7i	1.11658	+	0.196884i
$519$		0			0
$520$	15246.9	−	12793.6i	0.0563863	−	0.0473137i
$521$	86297.8	−	49824.1i	0.317925	−	0.183554i	−0.332542	−	0.943088i	$-0.607906\pi$
$521$	86297.8	−	49824.1i	0.317925	−	0.183554i	0.650467	+	0.759534i	$0.274573\pi$
$522$		0			0
$523$	−190520.	+	329991.i	−0.696526	+	1.20642i	0.273137	+	0.961975i	$0.411939\pi$
$523$	−190520.	+	329991.i	−0.696526	+	1.20642i	−0.969663	+	0.244444i	$0.921395\pi$
$524$	−123135.	+	21712.1i	−0.448457	+	0.0790750i
$525$		0			0
$526$	−21977.4	+	7999.13i	−0.0794339	+	0.0289116i
$527$	205511.	+	564636.i	0.739968	+	2.03305i
$528$		0			0
$529$	29206.0	+	165635.i	0.104366	+	0.591891i
$530$	40085.6	+	23143.4i	0.142704	+	0.0823902i
$531$		0			0
$532$	52038.5	+	90133.3i	0.183866	+	0.318465i
$533$	204051.	+	243179.i	0.718264	+	0.855994i
$534$		0			0
$535$	−9596.36	+	54423.7i	−0.0335273	+	0.190143i
$536$	−9875.51	+	11769.2i	−0.0343740	+	0.0409653i
$537$		0			0
$538$	187287.	+	68167.1i	0.647059	+	0.235510i
$539$		−	627895.i		−	2.16127i
$540$		0			0
$541$	16116.5			0.0550651			0.0275326	−	0.999621i	$-0.491235\pi$
$541$	16116.5			0.0550651			0.0275326	+	0.999621i	$0.491235\pi$
$542$	−133483.	+	366742.i	−0.454390	+	1.24842i
$543$		0			0
$544$	52012.9	+	43644.0i	0.175757	+	0.147478i
$545$	89747.0	+	15824.8i	0.302153	+	0.0532777i
$546$		0			0
$547$	27346.3	−	22946.3i	0.0913954	−	0.0766898i	−0.595945	−	0.803025i	$-0.703222\pi$
$547$	27346.3	−	22946.3i	0.0913954	−	0.0766898i	0.687341	+	0.726335i	$0.258778\pi$
$548$	78051.7	−	45063.2i	0.259909	−	0.150059i
$549$		0			0
$550$	−157341.	+	272523.i	−0.520136	+	0.900902i
$551$	−108626.	+	19153.6i	−0.357791	+	0.0630881i
$552$		0			0
$553$	595435.	−	216721.i	1.94708	−	0.708680i
$554$	97380.8	+	267552.i	0.317288	+	0.871742i
$555$		0			0
$556$	40781.8	+	231285.i	0.131922	+	0.748166i
$557$	−350870.	−	202575.i	−1.13093	−	0.652943i	−0.186762	−	0.982405i	$-0.559799\pi$
$557$	−350870.	−	202575.i	−1.13093	−	0.652943i	−0.944169	+	0.329462i	$0.893133\pi$
$558$		0			0
$559$	9654.74	+	16722.5i	0.0308970	+	0.0535152i
$560$	20797.8	+	24785.8i	0.0663194	+	0.0790363i
$561$		0			0
$562$	−17687.4	+	100310.i	−0.0560005	+	0.317595i
$563$	−171162.	+	203982.i	−0.539995	+	0.643540i	−0.965186	−	0.261563i	$-0.915762\pi$
$563$	−171162.	+	203982.i	−0.539995	+	0.643540i	0.425192	+	0.905103i	$0.360207\pi$
$564$		0			0
$565$	−115067.	−	41881.0i	−0.360458	−	0.131196i
$566$		−	208420.i		−	0.650589i
$567$		0			0
$568$	−137200.			−0.425261
$569$	161529.	−	443797.i	0.498914	−	1.37075i	−0.393412	−	0.919362i	$-0.628705\pi$
$569$	161529.	−	443797.i	0.498914	−	1.37075i	0.892326	−	0.451392i	$-0.149072\pi$
$570$		0			0
$571$	55958.0	+	46954.4i	0.171629	+	0.144014i	0.724556	−	0.689216i	$-0.242045\pi$
$571$	55958.0	+	46954.4i	0.171629	+	0.144014i	−0.552927	+	0.833230i	$0.686489\pi$
$572$	−198081.	−	34927.1i	−0.605413	−	0.106751i
$573$		0			0
$574$	−395319.	+	331712.i	−1.19984	+	1.00679i
$575$	−167824.	+	96893.5i	−0.507598	+	0.293062i
$576$		0			0
$577$	272353.	−	471729.i	0.818050	−	1.41690i	−0.0890664	−	0.996026i	$-0.528388\pi$
$577$	272353.	−	471729.i	0.818050	−	1.41690i	0.907117	−	0.420879i	$-0.138278\pi$
$578$	159243.	−	28078.8i	0.476654	−	0.0840470i
$579$		0			0
$580$	−32222.6	+	11728.1i	−0.0957866	+	0.0348635i
$581$	9238.27	+	25381.9i	0.0273677	+	0.0751922i
$582$		0			0
$583$	−81225.7	−	460654.i	−0.238977	−	1.35531i
$584$	−130867.	−	75556.3i	−0.383712	−	0.221536i
$585$		0			0
$586$	−85315.7	−	147771.i	−0.248447	−	0.430323i
$587$	−103637.	−	123509.i	−0.300772	−	0.358446i	0.594398	−	0.804171i	$-0.297390\pi$
$587$	−103637.	−	123509.i	−0.300772	−	0.358446i	−0.895170	+	0.445725i	$0.852946\pi$
$588$		0			0
$589$	−48043.9	+	272471.i	−0.138487	+	0.785397i
$590$	−15109.6	+	18007.0i	−0.0434060	+	0.0517293i
$591$		0			0
$592$	85876.3	+	31256.4i	0.245036	+	0.0891858i
$593$		−	117759.i		−	0.334876i	−0.985883	−	0.167438i	$-0.946451\pi$
$593$		−	117759.i		−	0.334876i	0.985883	−	0.167438i	$-0.0535495\pi$
$594$		0			0
$595$	189627.			0.535633
$596$	−33623.7	+	92380.2i	−0.0946569	+	0.260068i
$597$		0			0
$598$	−94885.2	−	79618.1i	−0.265336	−	0.222643i
$599$	−404884.	−	71392.0i	−1.12844	−	0.198974i	−0.421895	−	0.906645i	$-0.638635\pi$
$599$	−404884.	−	71392.0i	−1.12844	−	0.198974i	−0.706542	+	0.707671i	$0.749746\pi$
$600$		0			0
$601$	−175595.	+	147341.i	−0.486141	+	0.407921i	−0.852641	−	0.522497i	$-0.825001\pi$
$601$	−175595.	+	147341.i	−0.486141	+	0.407921i	0.366500	+	0.930418i	$0.380556\pi$
$602$	−27184.6	+	15695.1i	−0.0750120	+	0.0433082i
$603$		0			0
$604$	−52299.9	+	90586.1i	−0.143360	+	0.248306i
$605$	−146471.	+	25826.9i	−0.400168	+	0.0705604i
$606$		0			0
$607$	−169334.	+	61632.7i	−0.459587	+	0.167276i	−0.561429	−	0.827525i	$-0.689748\pi$
$607$	−169334.	+	61632.7i	−0.459587	+	0.167276i	0.101843	+	0.994801i	$0.467526\pi$
$608$	10692.9	+	29378.4i	0.0289259	+	0.0794733i
$609$		0			0
$610$	−15075.4	−	85497.1i	−0.0405145	−	0.229769i
$611$	105521.	+	60922.8i	0.282656	+	0.163191i
$612$		0			0
$613$	−106139.	−	183838.i	−0.282458	−	0.489232i	0.689532	−	0.724256i	$-0.257816\pi$
$613$	−106139.	−	183838.i	−0.282458	−	0.489232i	−0.971990	+	0.235024i	$0.924483\pi$
$614$	−238337.	−	284039.i	−0.632200	−	0.753427i
$615$		0			0
$616$	56778.6	−	322008.i	0.149632	−	0.848604i
$617$	14096.6	−	16799.7i	0.0370292	−	0.0441297i	−0.747212	−	0.664586i	$-0.768608\pi$
$617$	14096.6	−	16799.7i	0.0370292	−	0.0441297i	0.784241	+	0.620456i	$0.213052\pi$
$618$		0			0
$619$	341346.	+	124240.i	0.890867	+	0.324249i	0.746587	−	0.665288i	$-0.231691\pi$
$619$	341346.	+	124240.i	0.890867	+	0.324249i	0.144280	+	0.989537i	$0.453913\pi$
$620$			86012.7i			0.223758i
$621$		0			0
$622$	335743.			0.867814
$623$	18616.9	−	51149.6i	0.0479658	−	0.131785i
$624$		0			0
$625$	236091.	+	198104.i	0.604394	+	0.507146i
$626$	55340.6	+	9758.04i	0.141220	+	0.0249008i
$627$		0			0
$628$	−228516.	+	191748.i	−0.579425	+	0.486195i
$629$	463842.	−	267799.i	1.17238	−	0.676875i
$630$		0			0
$631$	140816.	−	243901.i	0.353667	−	0.612569i	−0.633222	−	0.773970i	$-0.718268\pi$
$631$	140816.	−	243901.i	0.353667	−	0.612569i	0.986889	+	0.161401i	$0.0516012\pi$
$632$	187451.	−	33052.7i	0.469304	−	0.0827509i
$633$		0			0
$634$	323652.	−	117800.i	0.805193	−	0.293066i
$635$	−41196.3	−	113186.i	−0.102167	−	0.280702i
$636$		0			0
$637$	−74489.3	−	422450.i	−0.183576	−	1.04111i
$638$	300104.	+	173265.i	0.737276	+	0.425666i
$639$		0			0
$640$	4859.67	+	8417.20i	0.0118644	+	0.0205498i
$641$	155029.	+	184756.i	0.377308	+	0.449658i	0.920963	−	0.389651i	$-0.127404\pi$
$641$	155029.	+	184756.i	0.377308	+	0.449658i	−0.543655	+	0.839309i	$0.682960\pi$
$642$		0			0
$643$	54772.6	−	310631.i	0.132477	−	0.751317i	−0.844106	−	0.536177i	$-0.819868\pi$
$643$	54772.6	−	310631.i	0.132477	−	0.751317i	0.976583	−	0.215140i	$-0.0690208\pi$
$644$	129430.	−	154249.i	0.312078	−	0.371920i
$645$		0			0
$646$	172179.	+	62668.1i	0.412587	+	0.150169i
$647$			593721.i			1.41832i	0.705049	+	0.709159i	$0.250925\pi$
$647$			593721.i			1.41832i	−0.705049	+	0.709159i	$0.749075\pi$
$648$		0			0
$649$	237549.			0.563979
$650$	−73529.3	+	202020.i	−0.174034	+	0.478154i
$651$		0			0
$652$	−144500.	−	121250.i	−0.339917	−	0.285224i
$653$	37915.0	+	6685.44i	0.0889170	+	0.0156785i	0.217930	−	0.975964i	$-0.430070\pi$
$653$	37915.0	+	6685.44i	0.0889170	+	0.0156785i	−0.129013	+	0.991643i	$0.541181\pi$
$654$		0			0
$655$	−80355.8	+	67426.6i	−0.187299	+	0.157162i
$656$	−134249.	+	77509.0i	−0.311964	+	0.180113i
$657$		0			0
$658$	−99038.1	+	171539.i	−0.228745	+	0.396197i
$659$	189781.	−	33463.6i	0.437001	−	0.0770551i	0.0491804	−	0.998790i	$-0.484339\pi$
$659$	189781.	−	33463.6i	0.437001	−	0.0770551i	0.387821	+	0.921735i	$0.373228\pi$
$660$		0			0
$661$	346403.	−	126080.i	0.792828	−	0.288566i	0.0863167	−	0.996268i	$-0.472490\pi$
$661$	346403.	−	126080.i	0.792828	−	0.288566i	0.706511	+	0.707702i	$0.250268\pi$
$662$	−91475.7	−	251327.i	−0.208732	−	0.573487i
$663$		0			0
$664$	1408.96	+	7990.58i	0.00319566	+	0.0181235i
$665$	75616.6	+	43657.3i	0.170991	+	0.0987219i
$666$		0			0
$667$	106700.	+	184809.i	0.239834	+	0.415405i
$668$	−39924.4	−	47580.0i	−0.0894717	−	0.106628i
$669$		0			0
$670$	−2238.18	+	12693.3i	−0.00498591	+	0.0282765i
$671$	−563940.	+	672078.i	−1.25253	+	1.49271i
$672$		0			0
$673$	−257581.	−	93752.0i	−0.568702	−	0.206990i	0.0416347	−	0.999133i	$-0.486743\pi$
$673$	−257581.	−	93752.0i	−0.568702	−	0.206990i	−0.610336	+	0.792142i	$0.708966\pi$
$674$			314607.i			0.692547i
$675$		0			0
$676$	91074.7			0.199299
$677$	76527.9	−	210259.i	0.166972	−	0.458751i	−0.827782	−	0.561050i	$-0.810398\pi$
$677$	76527.9	−	210259.i	0.166972	−	0.458751i	0.994754	+	0.102299i	$0.0326199\pi$
$678$		0			0
$679$	−743429.	−	623811.i	−1.61250	−	1.35305i
$680$	56097.1	+	9891.43i	0.121317	+	0.0213915i
$681$		0			0
$682$	665859.	−	558722.i	1.43157	−	1.20123i
$683$	138463.	−	79941.7i	0.296820	−	0.171369i	−0.344194	−	0.938899i	$-0.611848\pi$
$683$	138463.	−	79941.7i	0.296820	−	0.171369i	0.641013	+	0.767530i	$0.278514\pi$
$684$		0			0
$685$	37805.4	−	65480.9i	0.0805699	−	0.139551i
$686$	182975.	−	32263.4i	0.388815	−	0.0685586i
$687$		0			0
$688$	−8860.68	+	3225.02i	−0.0187193	+	0.00681327i
$689$	−109298.	−	300293.i	−0.230236	−	0.632568i
$690$		0			0
$691$	57644.0	+	326916.i	0.120725	+	0.684667i	0.983755	+	0.179515i	$0.0574527\pi$
$691$	57644.0	+	326916.i	0.120725	+	0.684667i	−0.863030	+	0.505153i	$0.831436\pi$
$692$	186176.	+	107489.i	0.388787	+	0.224466i
$693$		0			0
$694$	−328075.	−	568242.i	−0.681167	−	1.17982i
$695$	126647.	+	150932.i	0.262196	+	0.312473i
$696$		0			0
$697$	−157763.	+	894716.i	−0.324742	+	1.84170i
$698$	−22505.9	+	26821.4i	−0.0461939	+	0.0550518i
$699$		0			0
$700$	−328411.	−	119532.i	−0.670226	−	0.243942i
$701$			51630.6i			0.105068i	0.998619	+	0.0525341i	$0.0167298\pi$
$701$			51630.6i			0.105068i	−0.998619	+	0.0525341i	$0.983270\pi$
$702$		0			0
$703$	246618.			0.499016
$704$	33593.4	−	92297.2i	0.0677812	−	0.186227i
$705$		0			0
$706$	339639.	+	284991.i	0.681410	+	0.571771i
$707$	1.21136e6	+	213596.i	2.42346	+	0.427321i
$708$		0			0
$709$	59265.0	−	49729.2i	0.117898	−	0.0989280i	−0.581933	−	0.813237i	$-0.697703\pi$
$709$	59265.0	−	49729.2i	0.117898	−	0.0989280i	0.699830	+	0.714309i	$0.253259\pi$
$710$	−99681.6	+	57551.2i	−0.197742	+	0.114166i
$711$		0			0
$712$	8175.50	−	14160.4i	0.0161270	−	0.0279328i
$713$	527147.	−	92950.3i	1.03694	−	0.182840i
$714$		0			0
$715$	−158566.	+	57713.3i	−0.310169	+	0.112892i
$716$	−126674.	−	348035.i	−0.247094	−	0.678886i
$717$		0			0
$718$	52955.3	+	300324.i	0.102721	+	0.582561i
$719$	−590408.	−	340872.i	−1.14207	−	0.659377i	−0.195130	−	0.980777i	$-0.562513\pi$
$719$	−590408.	−	340872.i	−1.14207	−	0.659377i	−0.946943	+	0.321401i	$0.895846\pi$
$720$		0			0
$721$	−131618.	−	227969.i	−0.253189	−	0.438536i
$722$	−182703.	−	217737.i	−0.350486	−	0.417693i
$723$		0			0
$724$	−5185.23	+	29406.9i	−0.00989216	+	0.0561012i
$725$	238081.	−	283734.i	0.452949	−	0.539803i
$726$		0			0
$727$	209520.	+	76259.1i	0.396421	+	0.144286i	0.532536	−	0.846408i	$-0.321239\pi$
$727$	209520.	+	76259.1i	0.396421	+	0.144286i	−0.136114	+	0.990693i	$0.543461\pi$
$728$		−	223384.i		−	0.421491i
$729$		0			0
$730$	−126775.			−0.237896
$731$	−18901.0	+	51930.1i	−0.0353712	+	0.0971816i
$732$		0			0
$733$	−114579.	−	96143.0i	−0.213254	−	0.178941i	0.529904	−	0.848058i	$-0.322228\pi$
$733$	−114579.	−	96143.0i	−0.213254	−	0.178941i	−0.743157	+	0.669117i	$0.766673\pi$
$734$	76496.3	+	13488.4i	0.141987	+	0.0250361i
$735$		0			0
$736$	46335.0	−	38879.7i	0.0855369	−	0.0717740i
$737$	112803.	−	65126.8i	0.207676	−	0.119902i
$738$		0			0
$739$	−495510.	+	858248.i	−0.907326	+	1.57153i	−0.0895612	+	0.995981i	$0.528546\pi$
$739$	−495510.	+	858248.i	−0.907326	+	1.57153i	−0.817765	+	0.575553i	$0.804787\pi$
$740$	75504.1	−	13313.4i	0.137882	−	0.0243123i
$741$		0			0
$742$	488167.	−	177678.i	0.886667	−	0.322720i
$743$	25089.7	+	68933.5i	0.0454484	+	0.124868i	0.960340	−	0.278830i	$-0.0899467\pi$
$743$	25089.7	+	68933.5i	0.0454484	+	0.124868i	−0.914892	+	0.403699i	$0.867724\pi$
$744$		0			0
$745$	14321.7	+	81222.5i	0.0258037	+	0.146340i
$746$	409348.	+	236337.i	0.735555	+	0.424673i
$747$		0			0
$748$	−287823.	−	498523.i	−0.514424	−	0.891009i
$749$	398684.	+	475133.i	0.710666	+	0.846938i
$750$		0			0
$751$	−33994.7	+	192794.i	−0.0602743	+	0.341832i	−1.00000		9.68045e-5i	$-0.999969\pi$
$751$	−33994.7	+	192794.i	−0.0602743	+	0.341832i	0.939726	+	0.341929i	$0.111080\pi$
$752$	−38246.2	+	45580.0i	−0.0676320	+	0.0806007i
$753$		0			0
$754$	222466.	+	80970.9i	0.391309	+	0.142425i
$755$			87753.2i			0.153946i
$756$		0			0
$757$	306196.			0.534328			0.267164	−	0.963651i	$-0.413914\pi$
$757$	306196.			0.534328			0.267164	+	0.963651i	$0.413914\pi$
$758$	−189095.	+	519534.i	−0.329110	+	0.904223i
$759$		0			0
$760$	20092.2	+	16859.4i	0.0347857	+	0.0291887i
$761$	445266.	+	78512.4i	0.768866	+	0.135572i	0.544304	−	0.838888i	$-0.316794\pi$
$761$	445266.	+	78512.4i	0.768866	+	0.135572i	0.224562	+	0.974460i	$0.427905\pi$
$762$		0			0
$763$	783515.	−	657447.i	1.34586	−	1.12931i
$764$	−252191.	+	145602.i	−0.432058	+	0.249449i
$765$		0			0
$766$	239249.	−	414391.i	0.407748	−	0.706240i
$767$	159824.	−	28181.2i	0.271675	−	0.0479037i
$768$		0			0
$769$	−392895.	+	143002.i	−0.664391	+	0.241819i	−0.652131	−	0.758106i	$-0.726125\pi$
$769$	−392895.	+	143002.i	−0.664391	+	0.241819i	−0.0122600	+	0.999925i	$0.503903\pi$
$770$	−93820.6	−	257770.i	−0.158240	−	0.434762i
$771$		0			0
$772$	−70008.3	−	397037.i	−0.117467	−	0.666187i
$773$	176927.	+	102149.i	0.296098	+	0.170952i	0.640689	−	0.767801i	$-0.278649\pi$
$773$	176927.	+	102149.i	0.296098	+	0.170952i	−0.344591	+	0.938753i	$0.611982\pi$
$774$		0			0
$775$	−464532.	−	804592.i	−0.773414	−	1.33959i
$776$	−187388.	−	223320.i	−0.311184	−	0.370855i
$777$		0			0
$778$	−43490.4	+	246646.i	−0.0718512	+	0.407488i
$779$	−268898.	+	320460.i	−0.443111	+	0.528079i
$780$		0			0
$781$	1.09304e6	+	397834.i	1.79198	+	0.652229i
$782$		−	354492.i		−	0.579687i
$783$		0			0
$784$	209476.			0.340802
$785$	−85594.5	+	235169.i	−0.138901	+	0.381628i
$786$		0			0
$787$	326192.	+	273707.i	0.526652	+	0.441913i	0.866943	−	0.498407i	$-0.166081\pi$
$787$	326192.	+	273707.i	0.526652	+	0.441913i	−0.340292	+	0.940320i	$0.610526\pi$
$788$	124041.	+	21871.8i	0.199762	+	0.0352234i
$789$		0			0
$790$	122327.	−	102645.i	0.196005	−	0.164468i
$791$	−1.19020e6	+	687164.i	−1.90225	+	1.09827i
$792$		0			0
$793$	−299690.	+	519078.i	−0.476569	+	0.825442i
$794$	−71761.2	+	12653.4i	−0.113828	+	0.0200709i
$795$		0			0
$796$	−390794.	+	142237.i	−0.616768	+	0.224485i
$797$	−344427.	−	946306.i	−0.542227	−	1.48976i	−0.843983	−	0.536371i	$-0.819795\pi$
$797$	−344427.	−	946306.i	−0.542227	−	1.48976i	0.301756	−	0.953385i	$-0.402427\pi$
$798$		0			0
$799$	60554.0	+	343419.i	0.0948526	+	0.537936i
$800$	−90918.1	−	52491.6i	−0.142059	−	0.0820181i
$801$		0			0
$802$	361253.	+	625709.i	0.561647	+	0.972800i
$803$	823505.	+	981415.i	1.27713	+	1.52202i
$804$		0			0
$805$	29333.9	−	166361.i	0.0452666	−	0.256719i
$806$	381709.	−	454903.i	0.587574	−	0.700243i
$807$		0			0
$808$	347214.	+	126375.i	0.531832	+	0.193571i
$809$			611532.i			0.934377i	0.884158	+	0.467189i	$0.154733\pi$
$809$			611532.i			0.934377i	−0.884158	+	0.467189i	$0.845267\pi$
$810$		0			0
$811$	−42731.4			−0.0649689			−0.0324844	−	0.999472i	$-0.510342\pi$
$811$	−42731.4			−0.0649689			−0.0324844	+	0.999472i	$0.510342\pi$
$812$	−131629.	+	361648.i	−0.199636	+	0.548496i
$813$		0			0
$814$	−593525.	−	498027.i	−0.895757	−	0.751630i
$815$	−155847.	−	27480.0i	−0.234630	−	0.0413715i
$816$		0			0
$817$	−19492.7	+	16356.3i	−0.0292031	+	0.0245043i
$818$	−166898.	+	96358.3i	−0.249427	+	0.144007i
$819$		0			0
$820$	−65025.5	+	112627.i	−0.0967066	+	0.167501i
$821$	−1.04025e6	+	183425.i	−1.54331	+	0.272127i	−0.879545	−	0.475815i	$-0.842153\pi$
$821$	−1.04025e6	+	183425.i	−1.54331	+	0.272127i	−0.663764	+	0.747942i	$0.731042\pi$
$822$		0			0
$823$	−930715.	+	338753.i	−1.37410	+	0.500130i	−0.920383	−	0.391017i	$-0.872123\pi$
$823$	−930715.	+	338753.i	−1.37410	+	0.500130i	−0.453713	+	0.891148i	$0.649901\pi$
$824$	−27044.9	−	74305.2i	−0.0398318	−	0.109437i
$825$		0			0
$826$	45812.3	+	259815.i	0.0671463	+	0.380806i
$827$	−84013.5	−	48505.2i	−0.122840	−	0.0709214i	0.437321	−	0.899305i	$-0.355927\pi$
$827$	−84013.5	−	48505.2i	−0.122840	−	0.0709214i	−0.560161	+	0.828384i	$0.689261\pi$
$828$		0			0
$829$	−237186.	−	410819.i	−0.345128	−	0.597780i	0.640249	−	0.768168i	$-0.278831\pi$
$829$	−237186.	−	410819.i	−0.345128	−	0.597780i	−0.985377	+	0.170388i	$0.945498\pi$
$830$	4375.49	+	5214.50i	0.00635141	+	0.00756932i
$831$		0			0
$832$	11652.2	−	66083.2i	0.0168331	−	0.0954650i
$833$	789140.	−	940460.i	1.13727	−	1.35535i
$834$		0			0
$835$	−48965.3	−	17821.9i	−0.0702289	−	0.0255612i
$836$		−	265058.i		−	0.379252i
$837$		0			0
$838$	420279.			0.598481
$839$	208187.	−	571988.i	0.295753	−	0.812574i	−0.699445	−	0.714687i	$-0.746569\pi$
$839$	208187.	−	571988.i	0.295753	−	0.812574i	0.995197	−	0.0978875i	$-0.0312085\pi$
$840$		0			0
$841$	229359.	+	192455.i	0.324283	+	0.272106i
$842$	−358233.	−	63166.1i	−0.505291	−	0.0890964i
$843$		0			0
$844$	−133933.	+	112383.i	−0.188019	+	0.157766i
$845$	66169.9	−	38203.2i	0.0926717	−	0.0535040i
$846$		0			0
$847$	−834635.	+	1.44563e6i	−1.16340	+	2.01507i
$848$	153682.	−	27098.2i	0.213713	−	0.0376833i
$849$		0			0
$850$	−578172.	+	210438.i	−0.800239	+	0.291263i
$851$	−163188.	−	448356.i	−0.225336	−	0.619105i
$852$		0			0
$853$	−41685.0	−	236408.i	−0.0572904	−	0.324910i	0.942671	−	0.333724i	$-0.108305\pi$
$853$	−41685.0	−	236408.i	−0.0572904	−	0.324910i	−0.999961	+	0.00881416i	$0.997194\pi$
$854$	−843831.	−	487186.i	−1.15702	−	0.668004i
$855$		0			0
$856$	93157.8	+	161354.i	0.127137	+	0.220208i
$857$	−757698.	−	902989.i	−1.03166	−	1.22948i	−0.972905	−	0.231206i	$-0.925733\pi$
$857$	−757698.	−	902989.i	−1.03166	−	1.22948i	−0.0587504	−	0.998273i	$-0.518712\pi$
$858$		0			0
$859$	−30380.9	+	172299.i	−0.0411732	+	0.233505i	−0.998449	−	0.0556710i	$-0.982270\pi$
$859$	−30380.9	+	172299.i	−0.0411732	+	0.233505i	0.957276	+	0.289176i	$0.0933813\pi$
$860$	−5084.88	+	6059.92i	−0.00687517	+	0.00819351i
$861$		0			0
$862$	−598155.	−	217711.i	−0.805007	−	0.292998i
$863$			299746.i			0.402469i	0.979543	+	0.201234i	$0.0644953\pi$
$863$			299746.i			0.402469i	−0.979543	+	0.201234i	$0.935505\pi$
$864$		0			0
$865$	180354.			0.241042
$866$	188459.	−	517787.i	0.251293	−	0.690423i
$867$		0			0
$868$	739506.	+	620519.i	0.981527	+	0.823599i
$869$	−1.58923e6	−	280223.i	−2.10449	−	0.371078i
$870$		0			0
$871$	68168.0	−	57199.7i	0.0898554	−	0.0753976i
$872$	266080.	−	153621.i	0.349928	−	0.202031i
$873$		0			0
$874$	81613.6	−	141359.i	0.106841	−	0.185055i
$875$	−599917.	+	105782.i	−0.783565	+	0.138164i
$876$		0			0
$877$	−458173.	+	166761.i	−0.595703	+	0.216818i	−0.622236	−	0.782830i	$-0.713776\pi$
$877$	−458173.	+	166761.i	−0.595703	+	0.216818i	0.0265328	+	0.999648i	$0.491553\pi$
$878$	−46983.0	−	129085.i	−0.0609469	−	0.167450i
$879$		0			0
$880$	−14308.9	−	81149.5i	−0.0184773	−	0.104790i
$881$	824821.	+	476211.i	1.06269	+	0.613546i	0.926176	−	0.377091i	$-0.123076\pi$
$881$	824821.	+	476211.i	1.06269	+	0.613546i	0.136517	+	0.990638i	$0.456409\pi$
$882$		0			0
$883$	−554106.	−	959740.i	−0.710676	−	1.23093i	−0.964604	−	0.263704i	$-0.915056\pi$
$883$	−554106.	−	959740.i	−0.710676	−	1.23093i	0.253928	−	0.967223i	$-0.418278\pi$
$884$	−252789.	−	301263.i	−0.323485	−	0.385515i
$885$		0			0
$886$	41265.8	−	234030.i	0.0525681	−	0.298129i
$887$	−355134.	+	423232.i	−0.451383	+	0.537937i	−0.942964	−	0.332895i	$-0.891975\pi$
$887$	−355134.	+	423232.i	−0.451383	+	0.537937i	0.491581	+	0.870832i	$0.336419\pi$
$888$		0			0
$889$	−1.27033e6	−	462363.i	−1.60736	−	0.585033i
$890$		−	13717.5i		−	0.0173179i
$891$		0			0
$892$	−316478.			−0.397753
$893$	−54917.4	+	150884.i	−0.0688663	+	0.189209i
$894$		0			0
$895$	−238025.	−	199727.i	−0.297151	−	0.249339i
$896$	107427.	+	18942.3i	0.133813	+	0.0235948i
$897$		0			0
$898$	−34932.7	+	29312.0i	−0.0433191	+	0.0363490i
$899$	−886021.	+	511545.i	−1.09629	+	0.632942i
$900$		0			0
$901$	457291.	−	792051.i	0.563304	−	0.975672i
$902$	1.29429e6	−	228218.i	1.59081	−	0.280503i
$903$		0			0
$904$	−387940.	+	141198.i	−0.474709	+	0.172780i
$905$	8568.04	+	23540.5i	0.0104613	+	0.0287421i
$906$		0			0
$907$	38192.6	+	216601.i	0.0464263	+	0.263297i	0.999182	−	0.0404413i	$-0.0128764\pi$
$907$	38192.6	+	216601.i	0.0464263	+	0.263297i	−0.952756	+	0.303738i	$0.901765\pi$
$908$	−272535.	−	157348.i	−0.330561	−	0.190849i
$909$		0			0
$910$	−93703.0	−	162298.i	−0.113154	−	0.195989i
$911$	648254.	+	772559.i	0.781104	+	0.930883i	0.998983	−	0.0450927i	$-0.0143583\pi$
$911$	648254.	+	772559.i	0.781104	+	0.930883i	−0.217879	+	0.975976i	$0.569914\pi$
$912$		0			0
$913$	11945.2	−	67744.8i	0.0143302	−	0.0812708i
$914$	−400500.	+	477298.i	−0.479414	+	0.571343i
$915$		0			0
$916$	731727.	+	266327.i	0.872084	+	0.317413i
$917$			1.17730e6i			1.40007i
$918$		0			0
$919$	−451648.			−0.534773			−0.267387	−	0.963589i	$-0.586160\pi$
$919$	−451648.			−0.534773			−0.267387	+	0.963589i	$0.586160\pi$
$920$	17355.6	−	47684.0i	0.0205051	−	0.0563374i
$921$		0			0
$922$	−343427.	−	288169.i	−0.403992	−	0.338989i
$923$	782597.	+	137993.i	0.918618	+	0.161977i
$924$		0			0
$925$	−634389.	+	532316.i	−0.741434	+	0.622137i
$926$	−46250.0	+	26702.4i	−0.0539374	+	0.0311407i
$927$		0			0
$928$	−57804.0	+	100119.i	−0.0671215	+	0.116258i
$929$	−20761.6	+	3660.82i	−0.0240563	+	0.00424177i	−0.185663	−	0.982613i	$-0.559443\pi$
$929$	−20761.6	+	3660.82i	−0.0240563	+	0.00424177i	0.161607	+	0.986855i	$0.448332\pi$
$930$		0			0
$931$	531200.	−	193341.i	0.612856	−	0.223061i
$932$	157052.	+	431496.i	0.180805	+	0.496758i
$933$		0			0
$934$	−93867.7	−	532350.i	−0.107603	−	0.610244i
$935$	−418232.	−	241466.i	−0.478403	−	0.276206i
$936$		0			0
$937$	−356646.	−	617729.i	−0.406217	−	0.703588i	0.588245	−	0.808682i	$-0.299819\pi$
$937$	−356646.	−	617729.i	−0.406217	−	0.703588i	−0.994462	+	0.105094i	$0.966486\pi$
$938$	92985.8	+	110816.i	0.105684	+	0.125950i
$939$		0			0
$940$	−8668.07	+	49159.1i	−0.00980995	+	0.0556350i
$941$	574948.	−	685196.i	0.649306	−	0.773812i	−0.336504	−	0.941682i	$-0.609244\pi$
$941$	574948.	−	685196.i	0.649306	−	0.773812i	0.985809	+	0.167870i	$0.0536889\pi$
$942$		0			0
$943$	760532.	+	276811.i	0.855253	+	0.311286i
$944$			79250.1i			0.0889316i
$945$		0			0
$946$	79942.7			0.0893298
$947$	412156.	−	1.13239e6i	0.459580	−	1.26269i	−0.466218	−	0.884670i	$-0.654384\pi$
$947$	412156.	−	1.13239e6i	0.459580	−	1.26269i	0.925799	−	0.378017i	$-0.123394\pi$
$948$		0			0
$949$	670485.	+	562604.i	0.744486	+	0.624698i
$950$	−279003.	−	49195.7i	−0.309144	−	0.0545105i
$951$		0			0
$952$	489743.	−	410943.i	0.540374	−	0.453427i
$953$	470114.	−	271420.i	0.517627	−	0.298852i	−0.218336	−	0.975874i	$-0.570063\pi$
$953$	470114.	−	271420.i	0.517627	−	0.298852i	0.735963	+	0.677021i	$0.236730\pi$
$954$		0			0
$955$	−122152.	+	211573.i	−0.133935	+	0.231982i
$956$	−13587.2	+	2395.79i	−0.0148667	+	0.00262139i
$957$		0			0
$958$	104222.	−	37933.8i	0.113561	−	0.0413328i
$959$	−290242.	−	797434.i	−0.315590	−	0.867077i
$960$		0			0
$961$	285259.	+	1.61779e6i	0.308882	+	1.75176i
$962$	−458408.	−	264662.i	−0.495339	−	0.285984i
$963$		0			0
$964$	−64921.2	−	112447.i	−0.0698607	−	0.121002i
$965$	−217410.	−	259099.i	−0.233466	−	0.278234i
$966$		0			0
$967$	195026.	−	1.10604e6i	0.208564	−	1.18282i	−0.683169	−	0.730260i	$-0.739399\pi$
$967$	195026.	−	1.10604e6i	0.208564	−	1.18282i	0.891733	−	0.452563i	$-0.149490\pi$
$968$	−322316.	+	384121.i	−0.343979	+	0.409938i
$969$		0			0
$970$	−229822.	−	83648.2i	−0.244257	−	0.0889024i
$971$		−	1.44475e6i		−	1.53234i	−0.642639	−	0.766169i	$-0.722160\pi$
$971$		−	1.44475e6i		−	1.53234i	0.642639	−	0.766169i	$-0.277840\pi$
$972$		0			0
$973$	2.21133e6			2.33576
$974$	147681.	−	405749.i	0.155670	−	0.427701i
$975$		0			0
$976$	−224216.	−	188140.i	−0.235379	−	0.197506i
$977$	62359.1	+	10995.6i	0.0653297	+	0.0115194i	0.206217	−	0.978506i	$-0.433885\pi$
$977$	62359.1	+	10995.6i	0.0653297	+	0.0115194i	−0.140888	+	0.990026i	$0.544996\pi$
$978$		0			0
$979$	−106193.	+	89106.5i	−0.110798	+	0.0929703i
$980$	152194.	−	87869.1i	0.158469	−	0.0914922i
$981$		0			0
$982$	−594716.	+	1.03008e6i	−0.616718	+	1.06819i
$983$	651230.	−	114829.i	0.673950	−	0.118835i	0.173809	−	0.984779i	$-0.444393\pi$
$983$	651230.	−	114829.i	0.673950	−	0.118835i	0.500141	+	0.865944i	$0.333281\pi$
$984$		0			0
$985$	99295.9	−	36140.8i	0.102343	−	0.0372499i
$986$	231735.	+	636687.i	0.238362	+	0.654895i
$987$		0			0
$988$	−31444.7	−	178332.i	−0.0322132	−	0.182690i
$989$	42634.6	+	24615.1i	0.0435882	+	0.0251657i
$990$		0			0
$991$	−682628.	−	1.18235e6i	−0.695083	−	1.20392i	−0.970153	−	0.242495i	$-0.922034\pi$
$991$	−682628.	−	1.18235e6i	−0.695083	−	1.20392i	0.275070	−	0.961424i	$-0.411299\pi$
$992$	186399.	+	222141.i	0.189417	+	0.225739i
$993$		0			0
$994$	−224326.	+	1.27222e6i	−0.227042	+	1.28762i
$995$	−224265.	+	267269.i	−0.226525	+	0.269962i
$996$		0			0
$997$	−181417.	−	66030.5i	−0.182511	−	0.0664285i	0.249148	−	0.968465i	$-0.419849\pi$
$997$	−181417.	−	66030.5i	−0.182511	−	0.0664285i	−0.431659	+	0.902037i	$0.642072\pi$
$998$			1.37470e6i			1.38022i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.5.f.a.17.10		72
3.2	odd	2		54.5.f.a.23.3	✓	72
27.7	even	9		54.5.f.a.47.3	yes	72
27.20	odd	18	inner	162.5.f.a.143.10		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.5.f.a.23.3	✓	72	3.2	odd	2
54.5.f.a.47.3	yes	72	27.7	even	9
162.5.f.a.17.10		72	1.1	even	1	trivial
162.5.f.a.143.10		72	27.20	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)

\(f(q)\)	\(=\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-6.60957 - 1.16545i) q^{5} +(-57.7034 + 48.4189i) q^{7} +(-19.5959 + 11.3137i) q^{8} +O(q^{10})\)	\(q+(0.967379 - 2.65785i) q^{2} +(-6.12836 - 5.14230i) q^{4} +(-6.60957 - 1.16545i) q^{5} +(-57.7034 + 48.4189i) q^{7} +(-19.5959 + 11.3137i) q^{8} +(-9.49154 + 16.4398i) q^{10} +(188.923 - 33.3122i) q^{11} +(123.156 - 44.8251i) q^{13} +(72.8692 + 200.206i) q^{14} +(11.1135 + 63.0277i) q^{16} +(324.835 + 187.544i) q^{17} +(86.3550 + 149.571i) q^{19} +(34.5127 + 41.1307i) q^{20} +(94.2211 - 534.354i) q^{22} +(214.782 - 255.967i) q^{23} +(-544.980 - 198.356i) q^{25} -370.693i q^{26} +602.611 q^{28} +(-218.431 + 600.135i) q^{29} +(1227.17 + 1029.72i) q^{31} +(178.269 + 31.4337i) q^{32} +(812.701 - 681.937i) q^{34} +(437.824 - 252.778i) q^{35} +(713.966 - 1236.63i) q^{37} +(481.077 - 84.8268i) q^{38} +(142.706 - 51.9408i) q^{40} +(828.426 + 2276.08i) q^{41} +(25.5842 + 145.095i) q^{43} +(-1329.09 - 767.349i) q^{44} +(-472.547 - 818.475i) q^{46} +(597.596 + 712.188i) q^{47} +(568.361 - 3223.34i) q^{49} +(-1054.40 + 1256.59i) q^{50} +(-985.247 - 358.601i) q^{52} -2438.32i q^{53} -1287.52 q^{55} +(582.953 - 1601.65i) q^{56} +(1383.76 + 1161.12i) q^{58} +(1219.47 + 215.026i) q^{59} +(-3503.38 + 2939.68i) q^{61} +(3923.98 - 2265.51i) q^{62} +(256.000 - 443.405i) q^{64} +(-866.249 + 152.743i) q^{65} +(638.032 - 232.225i) q^{67} +(-1026.30 - 2819.73i) q^{68} +(-248.304 - 1408.20i) q^{70} +(5251.07 + 3031.71i) q^{71} +(3339.15 + 5783.58i) q^{73} +(-2596.09 - 3093.90i) q^{74} +(239.926 - 1360.69i) q^{76} +(-9288.54 + 11069.6i) q^{77} +(-7904.74 - 2877.09i) q^{79} -429.538i q^{80} +6850.89 q^{82} +(122.643 - 336.960i) q^{83} +(-1928.45 - 1618.16i) q^{85} +(410.391 + 72.3629i) q^{86} +(-3325.23 + 2790.20i) q^{88} +(-625.806 + 361.309i) q^{89} +(-4936.13 + 8549.62i) q^{91} +(-2632.52 + 464.184i) q^{92} +(2470.99 - 899.367i) q^{94} +(-396.453 - 1089.24i) q^{95} +(2237.22 + 12687.9i) q^{97} +(-8017.33 - 4628.81i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{5}+O(q^{10}) \) 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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