LMFDB - Embedded newform 252.5.z.f.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,5,Mod(73,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.73"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	252.z (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,27,0,66] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$26.0492306971$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.11337408.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 12 $ x^6 + 18x^4 + 81x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.1
Root			$-0.391571i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.5.z.f.145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-38.3327 + 22.1314i) q^{5} +(42.3967 + 24.5667i) q^{7} +(11.7557 - 20.3615i) q^{11} +136.269i q^{13} +(227.333 + 131.251i) q^{17} +(-387.162 + 223.528i) q^{19} +(-374.585 - 648.800i) q^{23} +(667.098 - 1155.45i) q^{25} -406.524 q^{29} +(-584.199 - 337.287i) q^{31} +(-2168.87 - 3.40909i) q^{35} +(-372.666 - 645.476i) q^{37} -2476.20i q^{41} -2636.68 q^{43} +(579.099 - 334.343i) q^{47} +(1193.96 + 2083.09i) q^{49} +(-1014.61 + 1757.36i) q^{53} +1040.68i q^{55} +(1014.22 + 585.561i) q^{59} +(-2022.05 + 1167.43i) q^{61} +(-3015.83 - 5223.58i) q^{65} +(3779.79 - 6546.78i) q^{67} -7575.36 q^{71} +(3284.18 + 1896.12i) q^{73} +(998.615 - 574.460i) q^{77} +(-3897.33 - 6750.37i) q^{79} -2181.41i q^{83} -11619.0 q^{85} +(-8050.38 + 4647.89i) q^{89} +(-3347.69 + 5777.37i) q^{91} +(9893.98 - 17136.9i) q^{95} -9981.90i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 27 q^{5} + 66 q^{7} - 135 q^{11} + 1107 q^{17} - 747 q^{19} - 243 q^{23} + 1878 q^{25} + 540 q^{29} - 5355 q^{31} - 6021 q^{35} + 2355 q^{37} - 948 q^{43} + 9747 q^{47} + 8430 q^{49} - 6291 q^{53}+ \cdots + 20655 q^{95}+O(q^{100}) $ 6 * q + 27 * q^5 + 66 * q^7 - 135 * q^11 + 1107 * q^17 - 747 * q^19 - 243 * q^23 + 1878 * q^25 + 540 * q^29 - 5355 * q^31 - 6021 * q^35 + 2355 * q^37 - 948 * q^43 + 9747 * q^47 + 8430 * q^49 - 6291 * q^53 + 2943 * q^59 + 4041 * q^61 - 7668 * q^65 + 1659 * q^67 - 2268 * q^71 - 8703 * q^73 + 10665 * q^77 - 7773 * q^79 - 702 * q^85 - 14985 * q^89 - 20952 * q^91 + 20655 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−38.3327	+	22.1314i	−1.53331	+	0.885256i	−0.534102	+	0.845420i	$0.679350\pi$
$5$	−38.3327	+	22.1314i	−1.53331	+	0.885256i	−0.999206	+	0.0398360i	$0.987316\pi$
$6$		0			0
$7$	42.3967	+	24.5667i	0.865238	+	0.501361i
$7$	42.3967	+	24.5667i	0.865238	+	0.501361i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	11.7557	−	20.3615i	0.0971545	−	0.168276i	−0.813351	−	0.581773i	$-0.802359\pi$
$11$	11.7557	−	20.3615i	0.0971545	−	0.168276i	0.910506	+	0.413496i	$0.135693\pi$
$12$		0			0
$13$			136.269i			0.806328i	0.915128	+	0.403164i	$0.132090\pi$
$13$			136.269i			0.806328i	−0.915128	+	0.403164i	$0.867910\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	227.333	+	131.251i	0.786618	+	0.454154i	0.838771	−	0.544485i	$-0.183275\pi$
$17$	227.333	+	131.251i	0.786618	+	0.454154i	−0.0521523	+	0.998639i	$0.516608\pi$
$18$		0			0
$19$	−387.162	+	223.528i	−1.07247	+	0.619191i	−0.928855	−	0.370442i	$-0.879206\pi$
$19$	−387.162	+	223.528i	−1.07247	+	0.619191i	−0.143615	+	0.989634i	$0.545873\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−374.585	−	648.800i	−0.708100	−	1.22646i	−0.965561	−	0.260176i	$-0.916219\pi$
$23$	−374.585	−	648.800i	−0.708100	−	1.22646i	0.257462	−	0.966288i	$-0.417114\pi$
$24$		0			0
$25$	667.098	−	1155.45i	1.06736	−	1.84872i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−406.524			−0.483382			−0.241691	−	0.970353i	$-0.577702\pi$
$29$	−406.524			−0.483382			−0.241691	+	0.970353i	$0.577702\pi$
$30$		0			0
$31$	−584.199	−	337.287i	−0.607907	−	0.350975i	0.164239	−	0.986421i	$-0.447483\pi$
$31$	−584.199	−	337.287i	−0.607907	−	0.350975i	−0.772146	+	0.635445i	$0.780817\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2168.87	−	3.40909i	−1.77051	−	0.00278293i
$36$		0			0
$37$	−372.666	−	645.476i	−0.272218	−	0.471495i	0.697212	−	0.716865i	$-0.254424\pi$
$37$	−372.666	−	645.476i	−0.272218	−	0.471495i	−0.969429	+	0.245370i	$0.921090\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	2476.20i		−	1.47305i	−0.676410	−	0.736526i	$-0.736465\pi$
$41$		−	2476.20i		−	1.47305i	0.676410	−	0.736526i	$-0.263535\pi$
$42$		0			0
$43$	−2636.68			−1.42601			−0.713003	−	0.701161i	$-0.752665\pi$
$43$	−2636.68			−1.42601			−0.713003	+	0.701161i	$0.752665\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	579.099	−	334.343i	0.262154	−	0.151355i	−0.363163	−	0.931726i	$-0.618303\pi$
$47$	579.099	−	334.343i	0.262154	−	0.151355i	0.625317	+	0.780371i	$0.284970\pi$
$48$		0			0
$49$	1193.96	+	2083.09i	0.497275	+	0.867593i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1014.61	+	1757.36i	−0.361200	+	0.625617i	−0.988159	−	0.153436i	$-0.950966\pi$
$53$	−1014.61	+	1757.36i	−0.361200	+	0.625617i	0.626959	+	0.779053i	$0.284300\pi$
$54$		0			0
$55$			1040.68i			0.344026i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1014.22	+	585.561i	0.291359	+	0.168216i	0.638555	−	0.769576i	$-0.279533\pi$
$59$	1014.22	+	585.561i	0.291359	+	0.168216i	−0.347195	+	0.937793i	$0.612866\pi$
$60$		0			0
$61$	−2022.05	+	1167.43i	−0.543416	+	0.313741i	−0.746462	−	0.665428i	$-0.768249\pi$
$61$	−2022.05	+	1167.43i	−0.543416	+	0.313741i	0.203047	+	0.979169i	$0.434916\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3015.83	−	5223.58i	−0.713807	−	1.23635i
$66$		0			0
$67$	3779.79	−	6546.78i	0.842011	−	1.45841i	−0.0461815	−	0.998933i	$-0.514705\pi$
$67$	3779.79	−	6546.78i	0.842011	−	1.45841i	0.888192	−	0.459472i	$-0.151961\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7575.36			−1.50275			−0.751375	−	0.659876i	$-0.770609\pi$
$71$	−7575.36			−1.50275			−0.751375	+	0.659876i	$0.770609\pi$
$72$		0			0
$73$	3284.18	+	1896.12i	0.616284	+	0.355812i	0.775421	−	0.631445i	$-0.217538\pi$
$73$	3284.18	+	1896.12i	0.616284	+	0.355812i	−0.159137	+	0.987257i	$0.550871\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	998.615	−	574.460i	0.168429	−	0.0968898i
$78$		0			0
$79$	−3897.33	−	6750.37i	−0.624472	−	1.08162i	−0.988643	−	0.150285i	$-0.951981\pi$
$79$	−3897.33	−	6750.37i	−0.624472	−	1.08162i	0.364171	−	0.931332i	$-0.381353\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	2181.41i		−	0.316651i	−0.987387	−	0.158326i	$-0.949390\pi$
$83$		−	2181.41i		−	0.316651i	0.987387	−	0.158326i	$-0.0506096\pi$
$84$		0			0
$85$	−11619.0			−1.60817
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8050.38	+	4647.89i	−1.01633	+	0.586781i	−0.913040	−	0.407870i	$-0.866272\pi$
$89$	−8050.38	+	4647.89i	−1.01633	+	0.586781i	−0.103294	+	0.994651i	$0.532938\pi$
$90$		0			0
$91$	−3347.69	+	5777.37i	−0.404261	+	0.697666i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	9893.98	−	17136.9i	1.09629	−	1.89882i
$96$		0			0
$97$		−	9981.90i		−	1.06089i	−0.847720	−	0.530444i	$-0.822025\pi$
$97$		−	9981.90i		−	1.06089i	0.847720	−	0.530444i	$-0.177975\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	675.552	+	390.030i	0.0662241	+	0.0382345i	0.532746	−	0.846275i	$-0.321160\pi$
$101$	675.552	+	390.030i	0.0662241	+	0.0382345i	−0.466522	+	0.884509i	$0.654493\pi$
$102$		0			0
$103$	2383.90	−	1376.35i	0.224706	−	0.129734i	−0.383422	−	0.923573i	$-0.625254\pi$
$103$	2383.90	−	1376.35i	0.224706	−	0.129734i	0.608127	+	0.793840i	$0.291921\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7429.46	+	12868.2i	0.648917	+	1.12396i	0.983382	+	0.181550i	$0.0581113\pi$
$107$	7429.46	+	12868.2i	0.648917	+	1.12396i	−0.334464	+	0.942408i	$0.608555\pi$
$108$		0			0
$109$	−1378.33	+	2387.33i	−0.116011	+	0.200937i	−0.918183	−	0.396155i	$-0.870344\pi$
$109$	−1378.33	+	2387.33i	−0.116011	+	0.200937i	0.802172	+	0.597092i	$0.203677\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6264.79			−0.490625			−0.245312	−	0.969444i	$-0.578891\pi$
$113$	−6264.79			−0.490625			−0.245312	+	0.969444i	$0.578891\pi$
$114$		0			0
$115$	28717.7	+	16580.2i	2.17147	+	1.25370i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6413.76	+	11149.4i	0.452917	+	0.787331i
$120$		0			0
$121$	7044.11	+	12200.8i	0.481122	+	0.833328i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			31391.0i			2.00902i
$126$		0			0
$127$	12855.0			0.797010			0.398505	−	0.917166i	$-0.369529\pi$
$127$	12855.0			0.797010			0.398505	+	0.917166i	$0.369529\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	21412.5	−	12362.5i	1.24774	−	0.720383i	0.277082	−	0.960846i	$-0.410633\pi$
$131$	21412.5	−	12362.5i	1.24774	−	0.720383i	0.970658	+	0.240464i	$0.0772995\pi$
$132$		0			0
$133$	−21905.7	−	34.4320i	−1.23838	−	0.00194652i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	661.078	−	1145.02i	0.0352218	−	0.0610059i	−0.847877	−	0.530193i	$-0.822120\pi$
$137$	661.078	−	1145.02i	0.0352218	−	0.0610059i	0.883099	+	0.469187i	$0.155453\pi$
$138$		0			0
$139$			5119.78i			0.264985i	0.991184	+	0.132493i	$0.0422981\pi$
$139$			5119.78i			0.264985i	−0.991184	+	0.132493i	$0.957702\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2774.64	+	1601.94i	0.135686	+	0.0783384i
$144$		0			0
$145$	15583.2	−	8996.95i	0.741173	−	0.427917i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5104.93	+	8842.00i	0.229942	+	0.398270i	0.957791	−	0.287467i	$-0.0928132\pi$
$149$	5104.93	+	8842.00i	0.229942	+	0.398270i	−0.727849	+	0.685737i	$0.759480\pi$
$150$		0			0
$151$	−14672.1	+	25412.8i	−0.643483	+	1.11455i	0.341166	+	0.940003i	$0.389178\pi$
$151$	−14672.1	+	25412.8i	−0.643483	+	1.11455i	−0.984650	+	0.174543i	$0.944155\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	29858.6			1.24281
$156$		0			0
$157$	−26033.1	−	15030.2i	−1.05615	−	0.609770i	−0.131787	−	0.991278i	$-0.542072\pi$
$157$	−26033.1	−	15030.2i	−1.05615	−	0.609770i	−0.924366	+	0.381508i	$0.875405\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	57.7005	−	36709.3i	0.00222602	−	1.41620i
$162$		0			0
$163$	−15439.7	−	26742.3i	−0.581115	−	1.00652i	−0.995348	−	0.0963500i	$-0.969283\pi$
$163$	−15439.7	−	26742.3i	−0.581115	−	1.00652i	0.414232	−	0.910171i	$-0.364050\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			12858.8i			0.461070i	0.973064	+	0.230535i	$0.0740477\pi$
$167$			12858.8i			0.461070i	−0.973064	+	0.230535i	$0.925952\pi$
$168$		0			0
$169$	9991.63			0.349835
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−13588.8	+	7845.51i	−0.454035	+	0.262137i	−0.709533	−	0.704672i	$-0.751094\pi$
$173$	−13588.8	+	7845.51i	−0.454035	+	0.262137i	0.255498	+	0.966810i	$0.417761\pi$
$174$		0			0
$175$	56668.2	−	32598.8i	1.85039	−	1.06445i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−15993.2	+	27701.0i	−0.499148	+	0.864550i	−1.00000		0.000983488i	$-0.999687\pi$
$179$	−15993.2	+	27701.0i	−0.499148	+	0.864550i	0.500851	+	0.865533i	$0.333020\pi$
$180$		0			0
$181$			47967.6i			1.46417i	0.681215	+	0.732083i	$0.261452\pi$
$181$			47967.6i			1.46417i	−0.681215	+	0.732083i	$0.738548\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	28570.6	+	16495.2i	0.834787	+	0.481965i
$186$		0			0
$187$	5344.91	−	3085.88i	0.152847	−	0.0882462i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2227.93	+	3858.88i	0.0610709	+	0.105778i	0.894944	−	0.446178i	$-0.147215\pi$
$191$	2227.93	+	3858.88i	0.0610709	+	0.105778i	−0.833873	+	0.551956i	$0.813882\pi$
$192$		0			0
$193$	14699.9	−	25460.9i	0.394638	−	0.683533i	−0.598417	−	0.801185i	$-0.704203\pi$
$193$	14699.9	−	25460.9i	0.394638	−	0.683533i	0.993055	+	0.117652i	$0.0375366\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−23816.0			−0.613671			−0.306836	−	0.951763i	$-0.599270\pi$
$197$	−23816.0			−0.613671			−0.306836	+	0.951763i	$0.599270\pi$
$198$		0			0
$199$	−42280.9	−	24410.9i	−1.06767	−	0.616421i	−0.140128	−	0.990133i	$-0.544751\pi$
$199$	−42280.9	−	24410.9i	−1.06767	−	0.616421i	−0.927545	+	0.373713i	$0.878085\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−17235.3	−	9986.94i	−0.418241	−	0.242349i
$204$		0			0
$205$	54801.8	+	94919.4i	1.30403	+	2.25864i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			10510.9i			0.240629i
$210$		0			0
$211$	−9582.07			−0.215226			−0.107613	−	0.994193i	$-0.534321\pi$
$211$	−9582.07			−0.215226			−0.107613	+	0.994193i	$0.534321\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	101071.	−	58353.5i	2.18651	−	1.26238i
$216$		0			0
$217$	−16482.1	−	28651.7i	−0.350019	−	0.608458i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−17885.5	+	30978.5i	−0.366197	+	0.634273i
$222$		0			0
$223$			54978.9i			1.10557i	0.833324	+	0.552785i	$0.186435\pi$
$223$			54978.9i			1.10557i	−0.833324	+	0.552785i	$0.813565\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7518.24	+	4340.66i	0.145903	+	0.0842372i	0.571174	−	0.820829i	$-0.306488\pi$
$227$	7518.24	+	4340.66i	0.145903	+	0.0842372i	−0.425271	+	0.905066i	$0.639821\pi$
$228$		0			0
$229$	−6262.86	+	3615.86i	−0.119427	+	0.0689511i	−0.558523	−	0.829489i	$-0.688632\pi$
$229$	−6262.86	+	3615.86i	−0.119427	+	0.0689511i	0.439097	+	0.898440i	$0.355299\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4422.96	+	7660.79i	0.0814707	+	0.141111i	0.903882	−	0.427782i	$-0.140705\pi$
$233$	4422.96	+	7660.79i	0.0814707	+	0.141111i	−0.822411	+	0.568894i	$0.807372\pi$
$234$		0			0
$235$	−14799.0	+	25632.5i	−0.267976	+	0.464147i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−88491.7			−1.54920			−0.774599	−	0.632453i	$-0.782048\pi$
$239$	−88491.7			−1.54920			−0.774599	+	0.632453i	$0.782048\pi$
$240$		0			0
$241$	−53365.8	−	30810.7i	−0.918816	−	0.530479i	−0.0355589	−	0.999368i	$-0.511321\pi$
$241$	−53365.8	−	30810.7i	−0.918816	−	0.530479i	−0.883257	+	0.468889i	$0.844654\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−91869.3	−	53426.6i	−1.53052	−	0.890072i
$246$		0			0
$247$	−30460.0	−	52758.4i	−0.499271	−	0.864763i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	57796.3i		−	0.917386i	−0.888595	−	0.458693i	$-0.848318\pi$
$251$		−	57796.3i		−	0.917386i	0.888595	−	0.458693i	$-0.151682\pi$
$252$		0			0
$253$	−17614.0			−0.275180
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−60734.3	+	35065.0i	−0.919534	+	0.530893i	−0.883486	−	0.468457i	$-0.844810\pi$
$257$	−60734.3	+	35065.0i	−0.919534	+	0.530893i	−0.0360479	+	0.999350i	$0.511477\pi$
$258$		0			0
$259$	57.4050	−	36521.2i	0.000855756	−	0.544435i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	11120.9	−	19262.0i	0.160779	−	0.278477i	−0.774369	−	0.632734i	$-0.781933\pi$
$263$	11120.9	−	19262.0i	0.160779	−	0.278477i	0.935148	+	0.354257i	$0.115266\pi$
$264$		0			0
$265$		−	89819.0i		−	1.27902i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−40332.3	−	23285.9i	−0.557376	−	0.321801i	0.194715	−	0.980860i	$-0.437622\pi$
$269$	−40332.3	−	23285.9i	−0.557376	−	0.321801i	−0.752092	+	0.659058i	$0.770955\pi$
$270$		0			0
$271$	71958.3	−	41545.1i	0.979811	−	0.565694i	0.0775980	−	0.996985i	$-0.475275\pi$
$271$	71958.3	−	41545.1i	0.979811	−	0.565694i	0.902213	+	0.431291i	$0.141942\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−15684.4	−	27166.2i	−0.207397	−	0.359222i
$276$		0			0
$277$	4514.06	−	7818.59i	0.0588313	−	0.101899i	−0.835110	−	0.550083i	$-0.814596\pi$
$277$	4514.06	−	7818.59i	0.0588313	−	0.101899i	0.893941	+	0.448185i	$0.147929\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−64188.4			−0.812912			−0.406456	−	0.913670i	$-0.633236\pi$
$281$	−64188.4			−0.812912			−0.406456	+	0.913670i	$0.633236\pi$
$282$		0			0
$283$	19563.7	+	11295.1i	0.244274	+	0.141032i	0.617140	−	0.786854i	$-0.288291\pi$
$283$	19563.7	+	11295.1i	0.244274	+	0.141032i	−0.372865	+	0.927885i	$0.621625\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	60832.0	−	104983.i	0.738530	−	1.27454i
$288$		0			0
$289$	−7307.06	−	12656.2i	−0.0874877	−	0.151533i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			130473.i			1.51980i	0.650040	+	0.759900i	$0.274752\pi$
$293$			130473.i			1.51980i	−0.650040	+	0.759900i	$0.725248\pi$
$294$		0			0
$295$	−51837.2			−0.595658
$296$		0			0
$297$		0			0
$298$		0			0
$299$	88411.6	−	51044.5i	0.988933	−	0.570961i
$300$		0			0
$301$	−111787.	−	64774.5i	−1.23383	−	0.714943i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	51673.7	−	89501.6i	0.555482	−	0.962124i
$306$		0			0
$307$			56173.9i			0.596015i	0.954563	+	0.298008i	$0.0963221\pi$
$307$			56173.9i			0.596015i	−0.954563	+	0.298008i	$0.903678\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−40087.2	−	23144.4i	−0.414462	−	0.239290i	0.278243	−	0.960511i	$-0.410248\pi$
$311$	−40087.2	−	23144.4i	−0.414462	−	0.239290i	−0.692705	+	0.721221i	$0.743581\pi$
$312$		0			0
$313$	−119814.	+	69174.4i	−1.22298	+	0.706085i	−0.965551	−	0.260213i	$-0.916207\pi$
$313$	−119814.	+	69174.4i	−1.22298	+	0.706085i	−0.257424	+	0.966299i	$0.582874\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−29152.7	−	50493.9i	−0.290108	−	0.502482i	0.683727	−	0.729738i	$-0.260358\pi$
$317$	−29152.7	−	50493.9i	−0.290108	−	0.502482i	−0.973835	+	0.227256i	$0.927025\pi$
$318$		0			0
$319$	−4778.97	+	8277.42i	−0.0469627	+	0.0813418i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−117353.			−1.12483
$324$		0			0
$325$	157452.	+	90905.1i	1.49067	+	0.860640i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	32765.6	+	51.5018i	0.302709	+	0.000475806i
$330$		0			0
$331$	−494.602	−	856.675i	−0.00451440	−	0.00781916i	0.863759	−	0.503904i	$-0.168104\pi$
$331$	−494.602	−	856.675i	−0.00451440	−	0.00781916i	−0.868274	+	0.496085i	$0.834770\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			334608.i			2.98158i
$336$		0			0
$337$	−55958.7			−0.492728			−0.246364	−	0.969177i	$-0.579236\pi$
$337$	−55958.7			−0.492728			−0.246364	+	0.969177i	$0.579236\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−13735.3	+	7930.09i	−0.118122	+	0.0681976i
$342$		0			0
$343$	−554.769	+	117648.i	−0.00471546	+	0.999989i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	65322.2	−	113141.i	0.542502	−	0.939641i	−0.456257	−	0.889848i	$-0.650810\pi$
$347$	65322.2	−	113141.i	0.542502	−	0.939641i	0.998760	−	0.0497936i	$-0.0158563\pi$
$348$		0			0
$349$			110948.i			0.910899i	0.890262	+	0.455450i	$0.150522\pi$
$349$			110948.i			0.910899i	−0.890262	+	0.455450i	$0.849478\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14727.9	−	8503.18i	−0.118193	−	0.0682389i	0.439738	−	0.898126i	$-0.355071\pi$
$353$	−14727.9	−	8503.18i	−0.118193	−	0.0682389i	−0.557931	+	0.829887i	$0.688405\pi$
$354$		0			0
$355$	290384.	−	167653.i	2.30418	−	1.33032i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	35732.4	+	61890.3i	0.277251	+	0.480212i	0.970701	−	0.240293i	$-0.0772434\pi$
$359$	35732.4	+	61890.3i	0.277251	+	0.480212i	−0.693450	+	0.720505i	$0.743910\pi$
$360$		0			0
$361$	34769.0	−	60221.8i	0.266795	−	0.462103i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−167855.			−1.25994
$366$		0			0
$367$	147543.	+	85183.8i	1.09543	+	0.632448i	0.935017	−	0.354602i	$-0.115383\pi$
$367$	147543.	+	85183.8i	1.09543	+	0.632448i	0.160415	+	0.987050i	$0.448717\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−86188.6	+	49580.5i	−0.626184	+	0.360216i
$372$		0			0
$373$	−75346.0	−	130503.i	−0.541555	−	0.938001i	−0.998815	−	0.0486680i	$-0.984502\pi$
$373$	−75346.0	−	130503.i	−0.541555	−	0.938001i	0.457260	−	0.889333i	$-0.348831\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	55396.8i		−	0.389764i
$378$		0			0
$379$	−211477.			−1.47226			−0.736129	−	0.676841i	$-0.763348\pi$
$379$	−211477.			−1.47226			−0.736129	+	0.676841i	$0.763348\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	102769.	−	59333.6i	0.700590	−	0.404486i	−0.106977	−	0.994261i	$-0.534117\pi$
$383$	102769.	−	59333.6i	0.700590	−	0.404486i	0.807567	+	0.589776i	$0.200784\pi$
$384$		0			0
$385$	−25566.0	+	44121.4i	−0.172481	+	0.297665i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	107858.	−	186816.i	0.712778	−	1.23457i	−0.251033	−	0.967979i	$-0.580770\pi$
$389$	107858.	−	186816.i	0.712778	−	1.23457i	0.963810	−	0.266588i	$-0.0858964\pi$
$390$		0			0
$391$		−	196658.i		−	1.28635i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	298790.	+	172507.i	1.91502	+	1.10564i
$396$		0			0
$397$	−134011.	+	77371.1i	−0.850273	+	0.490905i	−0.860743	−	0.509040i	$-0.830001\pi$
$397$	−134011.	+	77371.1i	−0.850273	+	0.490905i	0.0104699	+	0.999945i	$0.496667\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	100029.	+	173255.i	0.622067	+	1.07745i	0.989100	+	0.147244i	$0.0470403\pi$
$401$	100029.	+	173255.i	0.622067	+	1.07745i	−0.367033	+	0.930208i	$0.619626\pi$
$402$		0			0
$403$	45962.0	−	79608.5i	0.283001	−	0.490173i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17523.8			−0.105789
$408$		0			0
$409$	190382.	+	109917.i	1.13810	+	0.657080i	0.945958	−	0.324288i	$-0.105125\pi$
$409$	190382.	+	109917.i	1.13810	+	0.657080i	0.192137	+	0.981368i	$0.438458\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	28614.4	+	49741.9i	0.167758	+	0.291623i
$414$		0			0
$415$	48277.7	+	83619.4i	0.280318	+	0.485524i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	31359.8i		−	0.178626i	−0.996004	−	0.0893132i	$-0.971533\pi$
$419$		−	31359.8i		−	0.178626i	0.996004	−	0.0893132i	$-0.0284672\pi$
$420$		0			0
$421$	−73690.7			−0.415766			−0.207883	−	0.978154i	$-0.566657\pi$
$421$	−73690.7			−0.415766			−0.207883	+	0.978154i	$0.566657\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	303306.	−	175114.i	1.67920	−	0.969489i
$426$		0			0
$427$	−114408.	−	179.830i	−0.627481	−	0.000986291i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−132586.	+	229646.i	−0.713746	+	1.23624i	0.249695	+	0.968325i	$0.419670\pi$
$431$	−132586.	+	229646.i	−0.713746	+	1.23624i	−0.963441	+	0.267920i	$0.913664\pi$
$432$		0			0
$433$			124873.i			0.666027i	0.942922	+	0.333014i	$0.108066\pi$
$433$			124873.i			0.666027i	−0.942922	+	0.333014i	$0.891934\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	290050.	+	167460.i	1.51883	+	0.876898i
$438$		0			0
$439$	−120989.	+	69852.8i	−0.627792	+	0.362456i	−0.779896	−	0.625909i	$-0.784728\pi$
$439$	−120989.	+	69852.8i	−0.627792	+	0.362456i	0.152105	+	0.988364i	$0.451395\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−110595.	−	191556.i	−0.563544	−	0.976087i	−0.997183	−	0.0750005i	$-0.976104\pi$
$443$	−110595.	−	191556.i	−0.563544	−	0.976087i	0.433639	−	0.901087i	$-0.357229\pi$
$444$		0			0
$445$	205729.	−	356332.i	1.03890	−	1.79943i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−255878.			−1.26923			−0.634615	−	0.772828i	$-0.718841\pi$
$449$	−255878.			−1.26923			−0.634615	+	0.772828i	$0.718841\pi$
$450$		0			0
$451$	−50419.0	−	29109.4i	−0.247880	−	0.143114i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	464.555	−	295551.i	0.00224396	−	1.42761i
$456$		0			0
$457$	159964.	+	277065.i	0.765929	+	1.32663i	0.939754	+	0.341852i	$0.111054\pi$
$457$	159964.	+	277065.i	0.765929	+	1.32663i	−0.173825	+	0.984777i	$0.555613\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			369557.i			1.73892i	0.494002	+	0.869461i	$0.335534\pi$
$461$			369557.i			1.73892i	−0.494002	+	0.869461i	$0.664466\pi$
$462$		0			0
$463$	32715.0			0.152611			0.0763053	−	0.997084i	$-0.475688\pi$
$463$	32715.0			0.152611			0.0763053	+	0.997084i	$0.475688\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−265325.	+	153186.i	−1.21659	+	0.702400i	−0.964187	−	0.265222i	$-0.914555\pi$
$467$	−265325.	+	153186.i	−1.21659	+	0.702400i	−0.252405	+	0.967622i	$0.581221\pi$
$468$		0			0
$469$	321083.	−	184705.i	1.45973	−	0.839717i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−30996.0	+	53686.7i	−0.138543	+	0.239963i
$474$		0			0
$475$			596460.i			2.64359i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	226801.	+	130944.i	0.988493	+	0.570707i	0.904824	−	0.425787i	$-0.140003\pi$
$479$	226801.	+	130944.i	0.988493	+	0.570707i	0.0836697	+	0.996494i	$0.473336\pi$
$480$		0			0
$481$	87958.7	−	50783.0i	0.380180	−	0.219497i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	220913.	+	382633.i	0.939158	+	1.62667i
$486$		0			0
$487$	−41127.7	+	71235.3i	−0.173411	+	0.300357i	−0.939610	−	0.342246i	$-0.888812\pi$
$487$	−41127.7	+	71235.3i	−0.173411	+	0.300357i	0.766199	+	0.642603i	$0.222146\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	102923.			0.426924			0.213462	−	0.976951i	$-0.431526\pi$
$491$	102923.			0.426924			0.213462	+	0.976951i	$0.431526\pi$
$492$		0			0
$493$	−92416.2	−	53356.5i	−0.380237	−	0.219530i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−321170.	−	186101.i	−1.30024	−	0.753420i
$498$		0			0
$499$	−75028.2	−	129953.i	−0.301317	−	0.521896i	0.675118	−	0.737710i	$-0.264093\pi$
$499$	−75028.2	−	129953.i	−0.301317	−	0.521896i	−0.976434	+	0.215814i	$0.930759\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	91806.6i		−	0.362859i	−0.983404	−	0.181430i	$-0.941928\pi$
$503$		−	91806.6i		−	0.362859i	0.983404	−	0.181430i	$-0.0580725\pi$
$504$		0			0
$505$	−34527.6			−0.135389
$506$		0			0
$507$		0			0
$508$		0			0
$509$	412600.	−	238215.i	1.59255	−	0.919460i	0.599684	−	0.800237i	$-0.295293\pi$
$509$	412600.	−	238215.i	1.59255	−	0.919460i	0.992867	−	0.119224i	$-0.0380405\pi$
$510$		0			0
$511$	92656.9	+	161071.i	0.354843	+	0.616843i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−60921.0	+	105518.i	−0.229696	+	0.397844i
$516$		0			0
$517$		−	15721.7i		−	0.0588192i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−147768.	−	85314.0i	−0.544384	−	0.314300i	0.202470	−	0.979289i	$-0.435103\pi$
$521$	−147768.	−	85314.0i	−0.544384	−	0.314300i	−0.746854	+	0.664988i	$0.768437\pi$
$522$		0			0
$523$	85040.5	−	49098.2i	0.310901	−	0.179499i	−0.336428	−	0.941709i	$-0.609219\pi$
$523$	85040.5	−	49098.2i	0.310901	−	0.179499i	0.647330	+	0.762210i	$0.275886\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−88538.3	−	153353.i	−0.318794	−	0.552167i
$528$		0			0
$529$	−140707.	+	243711.i	−0.502810	+	0.870892i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	337430.			1.18776
$534$		0			0
$535$	−569582.	−	328849.i	−1.98998	−	1.14892i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	56450.5	+	177.461i	0.194308	+	0.000610838i
$540$		0			0
$541$	52833.7	+	91510.6i	0.180516	+	0.312663i	0.942056	−	0.335454i	$-0.108890\pi$
$541$	52833.7	+	91510.6i	0.180516	+	0.312663i	−0.761540	+	0.648118i	$0.775557\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	122017.i		−	0.410798i
$546$		0			0
$547$	−127121.			−0.424855			−0.212428	−	0.977177i	$-0.568137\pi$
$547$	−127121.			−0.424855			−0.212428	+	0.977177i	$0.568137\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	157391.	−	90869.5i	0.518413	−	0.299306i
$552$		0			0
$553$	600.340	−	381938.i	0.00196312	−	1.24894i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15246.5	−	26407.6i	0.0491427	−	0.0851176i	−0.840408	−	0.541955i	$-0.817684\pi$
$557$	15246.5	−	26407.6i	0.0491427	−	0.0851176i	0.889550	+	0.456837i	$0.151018\pi$
$558$		0			0
$559$		−	359300.i		−	1.14983i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−459404.	−	265237.i	−1.44936	−	0.836791i	−0.450921	−	0.892564i	$-0.648905\pi$
$563$	−459404.	−	265237.i	−1.44936	−	0.836791i	−0.998444	+	0.0557725i	$0.982238\pi$
$564$		0			0
$565$	240146.	−	138649.i	0.752279	−	0.434329i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−169366.	−	293351.i	−0.523121	−	0.906072i	−0.999638	−	0.0269067i	$-0.991434\pi$
$569$	−169366.	−	293351.i	−0.523121	−	0.906072i	0.476517	−	0.879165i	$-0.341899\pi$
$570$		0			0
$571$	53455.6	−	92587.8i	0.163954	−	0.283976i	−0.772330	−	0.635222i	$-0.780909\pi$
$571$	53455.6	−	92587.8i	0.163954	−	0.283976i	0.936283	+	0.351246i	$0.114242\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−999538.			−3.02318
$576$		0			0
$577$	−104337.	−	60238.8i	−0.313390	−	0.180936i	0.335052	−	0.942200i	$-0.391246\pi$
$577$	−104337.	−	60238.8i	−0.313390	−	0.180936i	−0.648443	+	0.761264i	$0.724579\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	53590.0	−	92484.6i	0.158757	−	0.273979i
$582$		0			0
$583$	23854.9	+	41317.9i	0.0701844	+	0.121563i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			525818.i			1.52602i	0.646389	+	0.763008i	$0.276278\pi$
$587$			525818.i			1.52602i	−0.646389	+	0.763008i	$0.723722\pi$
$588$		0			0
$589$	301573.			0.869283
$590$		0			0
$591$		0			0
$592$		0			0
$593$	64283.0	−	37113.8i	0.182804	−	0.105542i	−0.405805	−	0.913960i	$-0.633009\pi$
$593$	64283.0	−	37113.8i	0.182804	−	0.105542i	0.588610	+	0.808417i	$0.299676\pi$
$594$		0			0
$595$	−492609.	−	285441.i	−1.39145	−	0.806274i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10990.7	−	19036.5i	0.0306318	−	0.0530558i	−0.850303	−	0.526293i	$-0.823581\pi$
$599$	10990.7	−	19036.5i	0.0306318	−	0.0530558i	0.880935	+	0.473237i	$0.156915\pi$
$600$		0			0
$601$			77418.2i			0.214336i	0.994241	+	0.107168i	$0.0341782\pi$
$601$			77418.2i			0.214336i	−0.994241	+	0.107168i	$0.965822\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−540039.	−	311792.i	−1.47542	−	0.851832i
$606$		0			0
$607$	155765.	−	89931.2i	0.422760	−	0.244081i	−0.273498	−	0.961873i	$-0.588181\pi$
$607$	155765.	−	89931.2i	0.422760	−	0.244081i	0.696257	+	0.717792i	$0.254847\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	45560.7	+	78913.5i	0.122042	+	0.211382i
$612$		0			0
$613$	−314637.	+	544968.i	−0.837316	+	1.45027i	0.0548147	+	0.998497i	$0.482543\pi$
$613$	−314637.	+	544968.i	−0.837316	+	1.45027i	−0.892131	+	0.451777i	$0.850790\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	52877.1			0.138899			0.0694493	−	0.997585i	$-0.477876\pi$
$617$	52877.1			0.138899			0.0694493	+	0.997585i	$0.477876\pi$
$618$		0			0
$619$	447040.	+	258099.i	1.16672	+	0.673603i	0.952904	−	0.303271i	$-0.0980789\pi$
$619$	447040.	+	258099.i	1.16672	+	0.673603i	0.213811	+	0.976875i	$0.431412\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−455493.	−	715.955i	−1.17356	−	0.00184463i
$624$		0			0
$625$	−277790.	−	481147.i	−0.711143	−	1.23174i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	195651.i		−	0.494515i
$630$		0			0
$631$	193439.			0.485831			0.242915	−	0.970047i	$-0.421896\pi$
$631$	193439.			0.485831			0.242915	+	0.970047i	$0.421896\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−492766.	+	284499.i	−1.22206	+	0.705558i
$636$		0			0
$637$	−283862.	+	162700.i	−0.699565	+	0.400967i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	376563.	−	652226.i	0.916477	−	1.58738i	0.111751	−	0.993736i	$-0.464354\pi$
$641$	376563.	−	652226.i	0.916477	−	1.58738i	0.804725	−	0.593648i	$-0.202313\pi$
$642$		0			0
$643$		−	7110.23i		−	0.0171974i	−0.999963	−	0.00859868i	$-0.997263\pi$
$643$		−	7110.23i		−	0.0171974i	0.999963	−	0.00859868i	$-0.00273708\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	341808.	+	197343.i	0.816534	+	0.471426i	0.849220	−	0.528040i	$-0.177073\pi$
$647$	341808.	+	197343.i	0.816534	+	0.471426i	−0.0326859	+	0.999466i	$0.510406\pi$
$648$		0			0
$649$	23845.8	−	13767.4i	0.0566137	−	0.0326860i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	115578.	+	200186.i	0.271049	+	0.469470i	0.969131	−	0.246548i	$-0.0792963\pi$
$653$	115578.	+	200186.i	0.271049	+	0.469470i	−0.698082	+	0.716018i	$0.745963\pi$
$654$		0			0
$655$	−547198.	+	947775.i	−1.27545	+	2.20914i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	772498.			1.77880			0.889399	−	0.457131i	$-0.151123\pi$
$659$	772498.			1.77880			0.889399	+	0.457131i	$0.151123\pi$
$660$		0			0
$661$	−195287.	−	112749.i	−0.446962	−	0.258053i	0.259584	−	0.965720i	$-0.416414\pi$
$661$	−195287.	−	112749.i	−0.446962	−	0.258053i	−0.706546	+	0.707667i	$0.749748\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	840468.	−	483484.i	1.90054	−	1.09330i
$666$		0			0
$667$	152278.	+	263753.i	0.342282	+	0.592851i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			54895.8i			0.121925i
$672$		0			0
$673$	59564.6			0.131510			0.0657549	−	0.997836i	$-0.479054\pi$
$673$	59564.6			0.131510			0.0657549	+	0.997836i	$0.479054\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−687131.	+	396715.i	−1.49921	+	0.865569i	−1.00000		0.000912440i	$-0.999710\pi$
$677$	−687131.	+	396715.i	−1.49921	+	0.865569i	−0.499210	+	0.866481i	$0.666376\pi$
$678$		0			0
$679$	245222.	−	423199.i	0.531888	−	0.917921i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−46304.3	+	80201.3i	−0.0992612	+	0.171925i	−0.911379	−	0.411568i	$-0.864981\pi$
$683$	−46304.3	+	80201.3i	−0.0992612	+	0.171925i	0.812118	+	0.583493i	$0.198315\pi$
$684$		0			0
$685$			58522.3i			0.124721i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−239474.	−	138261.i	−0.504453	−	0.291246i
$690$		0			0
$691$	−162273.	+	93688.2i	−0.339852	+	0.196213i	−0.660206	−	0.751084i	$-0.729531\pi$
$691$	−162273.	+	93688.2i	−0.339852	+	0.196213i	0.320355	+	0.947298i	$0.396198\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−113308.	−	196255.i	−0.234580	−	0.406304i
$696$		0			0
$697$	325003.	−	562921.i	0.668993	−	1.15873i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−326056.			−0.663522			−0.331761	−	0.943363i	$-0.607643\pi$
$701$	−326056.			−0.663522			−0.331761	+	0.943363i	$0.607643\pi$
$702$		0			0
$703$	288564.	+	166603.i	0.583891	+	0.337110i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	19059.4	+	33132.0i	0.0381303	+	0.0662841i
$708$		0			0
$709$	−32372.6	−	56070.9i	−0.0643998	−	0.111544i	0.832028	−	0.554734i	$-0.187180\pi$
$709$	−32372.6	−	56070.9i	−0.0643998	−	0.111544i	−0.896428	+	0.443190i	$0.853847\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			505371.i			0.994102i
$714$		0			0
$715$	−141813.			−0.277398
$716$		0			0
$717$		0			0
$718$		0			0
$719$	616355.	−	355853.i	1.19227	−	0.688355i	0.233446	−	0.972370i	$-0.425000\pi$
$719$	616355.	−	355853.i	1.19227	−	0.688355i	0.958820	+	0.284014i	$0.0916664\pi$
$720$		0			0
$721$	134882.	+	212.011i	0.259468	+	0.000407838i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−271191.	+	469717.i	−0.515941	+	0.893635i
$726$		0			0
$727$		−	763134.i		−	1.44388i	−0.691954	−	0.721941i	$-0.743250\pi$
$727$		−	763134.i		−	1.44388i	0.691954	−	0.721941i	$-0.256750\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−599404.	−	346066.i	−1.12172	−	0.647626i
$732$		0			0
$733$	−17848.0	+	10304.6i	−0.0332187	+	0.0191788i	−0.516517	−	0.856277i	$-0.672772\pi$
$733$	−17848.0	+	10304.6i	−0.0332187	+	0.0191788i	0.483299	+	0.875456i	$0.339439\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−88868.0	−	153924.i	−0.163610	−	0.283381i
$738$		0			0
$739$	393194.	−	681032.i	0.719976	−	1.24703i	−0.241033	−	0.970517i	$-0.577486\pi$
$739$	393194.	−	681032.i	0.719976	−	1.24703i	0.961009	−	0.276518i	$-0.0891805\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−740479.			−1.34133			−0.670664	−	0.741761i	$-0.733991\pi$
$743$	−740479.			−1.34133			−0.670664	+	0.741761i	$0.733991\pi$
$744$		0			0
$745$	−391372.	−	225959.i	−0.705143	−	0.407114i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1144.42	+	728086.i	−0.00203997	+	1.29783i
$750$		0			0
$751$	247292.	+	428322.i	0.438460	+	0.759436i	0.997571	−	0.0696574i	$-0.0221906\pi$
$751$	247292.	+	428322.i	0.438460	+	0.759436i	−0.559111	+	0.829093i	$0.688857\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	1.29885e6i		−	2.27859i
$756$		0			0
$757$	−139399.			−0.243258			−0.121629	−	0.992576i	$-0.538812\pi$
$757$	−139399.			−0.243258			−0.121629	+	0.992576i	$0.538812\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	207340.	−	119708.i	0.358025	−	0.206706i	−0.310189	−	0.950675i	$-0.600392\pi$
$761$	207340.	−	119708.i	0.358025	−	0.206706i	0.668214	+	0.743969i	$0.267059\pi$
$762$		0			0
$763$	−117085.	+	67354.1i	−0.201119	+	0.115695i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−79794.1	+	138208.i	−0.135638	+	0.234931i
$768$		0			0
$769$		−	98701.5i		−	0.166906i	−0.996512	−	0.0834528i	$-0.973405\pi$
$769$		−	98701.5i		−	0.166906i	0.996512	−	0.0834528i	$-0.0265948\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	507921.	+	293248.i	0.850036	+	0.490769i	0.860663	−	0.509175i	$-0.170049\pi$
$773$	507921.	+	293248.i	0.850036	+	0.490769i	−0.0106268	+	0.999944i	$0.503383\pi$
$774$		0			0
$775$	−779435.	+	450007.i	−1.29771	+	0.749232i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	553500.	+	958690.i	0.912100	+	1.57980i
$780$		0			0
$781$	−89053.6	+	154245.i	−0.145999	+	0.252877i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.33056e6			2.15921
$786$		0			0
$787$	−129536.	−	74787.4i	−0.209141	−	0.120748i	0.391771	−	0.920063i	$-0.371863\pi$
$787$	−129536.	−	74787.4i	−0.209141	−	0.120748i	−0.600912	+	0.799315i	$0.705196\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−265606.	−	153905.i	−0.424507	−	0.245980i
$792$		0			0
$793$	−159085.	−	275544.i	−0.252978	−	0.438171i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			241092.i			0.379547i	0.981828	+	0.189774i	$0.0607754\pi$
$797$			241092.i			0.379547i	−0.981828	+	0.189774i	$0.939225\pi$
$798$		0			0
$799$	175531.			0.274954
$800$		0			0
$801$		0			0
$802$		0			0
$803$	77215.6	−	44580.4i	0.119750	−	0.0691374i
$804$		0			0
$805$	810215.	+	1.40844e6i	1.25028	+	2.17344i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	100933.	−	174820.i	0.154218	−	0.267113i	−0.778556	−	0.627575i	$-0.784048\pi$
$809$	100933.	−	174820.i	0.154218	−	0.267113i	0.932774	+	0.360462i	$0.117381\pi$
$810$		0			0
$811$			1.16747e6i			1.77503i	0.460779	+	0.887515i	$0.347570\pi$
$811$			1.16747e6i			1.77503i	−0.460779	+	0.887515i	$0.652430\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.18369e6	+	683402.i	1.78206	+	1.02887i
$816$		0			0
$817$	1.02082e6	−	589373.i	1.52935	−	0.882970i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−324585.	−	562198.i	−0.481551	−	0.834071i	0.518225	−	0.855245i	$-0.326593\pi$
$821$	−324585.	−	562198.i	−0.481551	−	0.834071i	−0.999776	+	0.0211734i	$0.993260\pi$
$822$		0			0
$823$	245486.	−	425193.i	0.362432	−	0.627750i	−0.625929	−	0.779880i	$-0.715280\pi$
$823$	245486.	−	425193.i	0.362432	−	0.627750i	0.988360	+	0.152130i	$0.0486133\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	709017.			1.03668			0.518341	−	0.855174i	$-0.326550\pi$
$827$	709017.			1.03668			0.518341	+	0.855174i	$0.326550\pi$
$828$		0			0
$829$	534645.	+	308677.i	0.777958	+	0.449154i	0.835706	−	0.549177i	$-0.185059\pi$
$829$	534645.	+	308677.i	0.777958	+	0.449154i	−0.0577480	+	0.998331i	$0.518392\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1981.33	+	630262.i	−0.00285540	+	0.908304i
$834$		0			0
$835$	−284583.	−	492912.i	−0.408165	−	0.706963i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	493961.i		−	0.701728i	−0.936426	−	0.350864i	$-0.885888\pi$
$839$		−	493961.i		−	0.701728i	0.936426	−	0.350864i	$-0.114112\pi$
$840$		0			0
$841$	−542019.			−0.766342
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−383006.	+	221129.i	−0.536404	+	0.309693i
$846$		0			0
$847$	−1085.07	+	690322.i	−0.00151248	+	0.962243i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−279190.	+	483571.i	−0.385514	+	0.667730i
$852$		0			0
$853$			505142.i			0.694249i	0.937819	+	0.347124i	$0.112842\pi$
$853$			505142.i			0.694249i	−0.937819	+	0.347124i	$0.887158\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	969980.	+	560018.i	1.32069	+	0.762501i	0.983839	−	0.179056i	$-0.0573043\pi$
$857$	969980.	+	560018.i	1.32069	+	0.762501i	0.336852	+	0.941557i	$0.390638\pi$
$858$		0			0
$859$	−605141.	+	349379.i	−0.820107	+	0.473489i	−0.850453	−	0.526050i	$-0.823672\pi$
$859$	−605141.	+	349379.i	−0.820107	+	0.473489i	0.0303463	+	0.999539i	$0.490339\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	479533.	+	830576.i	0.643868	+	1.11521i	0.984562	+	0.175038i	$0.0560049\pi$
$863$	479533.	+	830576.i	0.643868	+	1.11521i	−0.340693	+	0.940175i	$0.610662\pi$
$864$		0			0
$865$	347264.	−	601479.i	0.464117	−	0.803875i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−183263.			−0.242681
$870$		0			0
$871$	892127.	+	515069.i	1.17595	+	0.678937i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−771172.	+	1.33087e6i	−1.00724	+	1.73828i
$876$		0			0
$877$	498442.	+	863326.i	0.648060	+	1.12247i	0.983586	+	0.180442i	$0.0577527\pi$
$877$	498442.	+	863326.i	0.648060	+	1.12247i	−0.335526	+	0.942031i	$0.608914\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	494568.i		−	0.637198i	−0.947890	−	0.318599i	$-0.896788\pi$
$881$		−	494568.i		−	0.637198i	0.947890	−	0.318599i	$-0.103212\pi$
$882$		0			0
$883$	887278.			1.13799			0.568995	−	0.822341i	$-0.307333\pi$
$883$	887278.			1.13799			0.568995	+	0.822341i	$0.307333\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−542062.	+	312960.i	−0.688973	+	0.397779i	−0.803227	−	0.595673i	$-0.796885\pi$
$887$	−542062.	+	312960.i	−0.688973	+	0.397779i	0.114254	+	0.993452i	$0.463552\pi$
$888$		0			0
$889$	545008.	+	315804.i	0.689604	+	0.399589i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−149470.	+	258890.i	−0.187435	+	0.324647i
$894$		0			0
$895$		−	1.41581e6i		−	1.76750i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	237491.	+	137115.i	0.293851	+	0.169655i
$900$		0			0
$901$	−461309.	+	266337.i	−0.568253	+	0.328081i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.06159e6	−	1.83873e6i	−1.29616	−	2.24502i
$906$		0			0
$907$	634131.	−	1.09835e6i	0.770840	−	1.33513i	−0.166263	−	0.986081i	$-0.553170\pi$
$907$	634131.	−	1.09835e6i	0.770840	−	1.33513i	0.937103	−	0.349052i	$-0.113496\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.09985e6			1.32525			0.662625	−	0.748951i	$-0.269442\pi$
$911$	1.09985e6			1.32525			0.662625	+	0.748951i	$0.269442\pi$
$912$		0			0
$913$	−44416.7	−	25644.0i	−0.0532850	−	0.0307641i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.21152e6	+	1904.30i	1.44076	+	0.00226463i
$918$		0			0
$919$	−430660.	−	745925.i	−0.509922	−	0.883211i	−0.999934	−	0.0114950i	$-0.996341\pi$
$919$	−430660.	−	745925.i	−0.509922	−	0.883211i	0.490012	−	0.871716i	$-0.336992\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	1.03229e6i		−	1.21171i
$924$		0			0
$925$	−994418.			−1.16221
$926$		0			0
$927$		0			0
$928$		0			0
$929$	326247.	−	188359.i	0.378021	−	0.218250i	−0.298936	−	0.954273i	$-0.596632\pi$
$929$	326247.	−	188359.i	0.378021	−	0.218250i	0.676957	+	0.736023i	$0.263298\pi$
$930$		0			0
$931$	−927884.	−	539610.i	−1.07052	−	0.622560i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−136590.	+	236580.i	−0.156241	+	0.270617i
$936$		0			0
$937$		−	417813.i		−	0.475885i	−0.971279	−	0.237943i	$-0.923527\pi$
$937$		−	417813.i		−	0.475885i	0.971279	−	0.237943i	$-0.0764731\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−213031.	−	122994.i	−0.240582	−	0.138900i	0.374862	−	0.927081i	$-0.377690\pi$
$941$	−213031.	−	122994.i	−0.240582	−	0.138900i	−0.615444	+	0.788180i	$0.711023\pi$
$942$		0			0
$943$	−1.60656e6	+	927546.i	−1.80665	+	1.04307i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−722964.	−	1.25221e6i	−0.806152	−	1.39630i	−0.915511	−	0.402294i	$-0.868213\pi$
$947$	−722964.	−	1.25221e6i	−0.806152	−	1.39630i	0.109359	−	0.994002i	$-0.465120\pi$
$948$		0			0
$949$	−258384.	+	447533.i	−0.286901	+	0.496928i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−907377.			−0.999084			−0.499542	−	0.866290i	$-0.666498\pi$
$953$	−907377.			−0.999084			−0.499542	+	0.866290i	$0.666498\pi$
$954$		0			0
$955$	−170805.	−	98614.2i	−0.187281	−	0.108127i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	56156.9	−	32304.6i	0.0610612	−	0.0351259i
$960$		0			0
$961$	−234235.	−	405707.i	−0.253633	−	0.439305i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			1.30132e6i			1.39742i
$966$		0			0
$967$	−50286.2			−0.0537770			−0.0268885	−	0.999638i	$-0.508560\pi$
$967$	−50286.2			−0.0537770			−0.0268885	+	0.999638i	$0.508560\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−677500.	+	391155.i	−0.718573	+	0.414868i	−0.814227	−	0.580546i	$-0.802839\pi$
$971$	−677500.	+	391155.i	−0.718573	+	0.414868i	0.0956544	+	0.995415i	$0.469506\pi$
$972$		0			0
$973$	−125776.	+	217062.i	−0.132853	+	0.229275i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	638714.	−	1.10629e6i	0.669141	−	1.15899i	−0.309004	−	0.951061i	$-0.599996\pi$
$977$	638714.	−	1.10629e6i	0.669141	−	1.15899i	0.978145	−	0.207925i	$-0.0666711\pi$
$978$		0			0
$979$			218557.i			0.228033i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.36250e6	−	786638.i	−1.41003	−	0.814081i	−0.414639	−	0.909986i	$-0.636092\pi$
$983$	−1.36250e6	−	786638.i	−1.41003	−	0.814081i	−0.995391	+	0.0959049i	$0.969426\pi$
$984$		0			0
$985$	912930.	−	527080.i	0.940947	−	0.543256i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	987661.	+	1.71068e6i	1.00975	+	1.74894i
$990$		0			0
$991$	−162173.	+	280892.i	−0.165132	+	0.286017i	−0.936702	−	0.350127i	$-0.886138\pi$
$991$	−162173.	+	280892.i	−0.165132	+	0.286017i	0.771570	+	0.636144i	$0.219472\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.16099e6			2.18276
$996$		0			0
$997$	−1.57129e6	−	907185.i	−1.58076	−	0.912652i	−0.994748	−	0.102350i	$-0.967364\pi$
$997$	−1.57129e6	−	907185.i	−1.58076	−	0.912652i	−0.586012	−	0.810303i	$-0.699303\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.5.z.f.73.1		6
3.2	odd	2		28.5.h.a.17.2	yes	6
7.5	odd	6	inner	252.5.z.f.145.1		6
12.11	even	2		112.5.s.c.17.2		6
15.2	even	4		700.5.o.a.549.3		12
15.8	even	4		700.5.o.a.549.4		12
15.14	odd	2		700.5.s.a.101.2		6
21.2	odd	6		196.5.h.c.117.2		6
21.5	even	6		28.5.h.a.5.2	✓	6
21.11	odd	6		196.5.b.a.97.4		6
21.17	even	6		196.5.b.a.97.3		6
21.20	even	2		196.5.h.c.129.2		6
84.11	even	6		784.5.c.e.97.3		6
84.47	odd	6		112.5.s.c.33.2		6
84.59	odd	6		784.5.c.e.97.4		6
105.47	odd	12		700.5.o.a.649.4		12
105.68	odd	12		700.5.o.a.649.3		12
105.89	even	6		700.5.s.a.201.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.5.h.a.5.2	✓	6	21.5	even	6
28.5.h.a.17.2	yes	6	3.2	odd	2
112.5.s.c.17.2		6	12.11	even	2
112.5.s.c.33.2		6	84.47	odd	6
196.5.b.a.97.3		6	21.17	even	6
196.5.b.a.97.4		6	21.11	odd	6
196.5.h.c.117.2		6	21.2	odd	6
196.5.h.c.129.2		6	21.20	even	2
252.5.z.f.73.1		6	1.1	even	1	trivial
252.5.z.f.145.1		6	7.5	odd	6	inner
700.5.o.a.549.3		12	15.2	even	4
700.5.o.a.549.4		12	15.8	even	4
700.5.o.a.649.3		12	105.68	odd	12
700.5.o.a.649.4		12	105.47	odd	12
700.5.s.a.101.2		6	15.14	odd	2
700.5.s.a.201.2		6	105.89	even	6
784.5.c.e.97.3		6	84.11	even	6
784.5.c.e.97.4		6	84.59	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-38.3327 + 22.1314i) q^{5} +(42.3967 + 24.5667i) q^{7} +(11.7557 - 20.3615i) q^{11} +136.269i q^{13} +(227.333 + 131.251i) q^{17} +(-387.162 + 223.528i) q^{19} +(-374.585 - 648.800i) q^{23} +(667.098 - 1155.45i) q^{25} -406.524 q^{29} +(-584.199 - 337.287i) q^{31} +(-2168.87 - 3.40909i) q^{35} +(-372.666 - 645.476i) q^{37} -2476.20i q^{41} -2636.68 q^{43} +(579.099 - 334.343i) q^{47} +(1193.96 + 2083.09i) q^{49} +(-1014.61 + 1757.36i) q^{53} +1040.68i q^{55} +(1014.22 + 585.561i) q^{59} +(-2022.05 + 1167.43i) q^{61} +(-3015.83 - 5223.58i) q^{65} +(3779.79 - 6546.78i) q^{67} -7575.36 q^{71} +(3284.18 + 1896.12i) q^{73} +(998.615 - 574.460i) q^{77} +(-3897.33 - 6750.37i) q^{79} -2181.41i q^{83} -11619.0 q^{85} +(-8050.38 + 4647.89i) q^{89} +(-3347.69 + 5777.37i) q^{91} +(9893.98 - 17136.9i) q^{95} -9981.90i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 27 q^{5} + 66 q^{7} - 135 q^{11} + 1107 q^{17} - 747 q^{19} - 243 q^{23} + 1878 q^{25} + 540 q^{29} - 5355 q^{31} - 6021 q^{35} + 2355 q^{37} - 948 q^{43} + 9747 q^{47} + 8430 q^{49} - 6291 q^{53}+ \cdots + 20655 q^{95}+O(q^{100}) \) 6 * q + 27 * q^5 + 66 * q^7 - 135 * q^11 + 1107 * q^17 - 747 * q^19 - 243 * q^23 + 1878 * q^25 + 540 * q^29 - 5355 * q^31 - 6021 * q^35 + 2355 * q^37 - 948 * q^43 + 9747 * q^47 + 8430 * q^49 - 6291 * q^53 + 2943 * q^59 + 4041 * q^61 - 7668 * q^65 + 1659 * q^67 - 2268 * q^71 - 8703 * q^73 + 10665 * q^77 - 7773 * q^79 - 702 * q^85 - 14985 * q^89 - 20952 * q^91 + 20655 * q^95

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